LMFDB - Embedded newform 19.9.f.a.3.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,9,Mod(2,19)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("19.2");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.74019359116$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$12$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.5
Character	$\chi$	$=$	19.3
Dual form			19.9.f.a.13.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.34622 + 7.56314i) q^{2} +(-20.1988 - 55.4957i) q^{3} +(27.5275 + 156.116i) q^{4} +(-27.4521 + 155.689i) q^{5} +(547.908 + 199.422i) q^{6} +(-956.918 - 1657.43i) q^{7} +(-3544.29 - 2046.29i) q^{8} +(2354.23 - 1975.44i) q^{9} +O(q^{10})$	\(q+(-6.34622 + 7.56314i) q^{2} +(-20.1988 - 55.4957i) q^{3} +(27.5275 + 156.116i) q^{4} +(-27.4521 + 155.689i) q^{5} +(547.908 + 199.422i) q^{6} +(-956.918 - 1657.43i) q^{7} +(-3544.29 - 2046.29i) q^{8} +(2354.23 - 1975.44i) q^{9} +(-1003.28 - 1195.66i) q^{10} +(7676.75 - 13296.5i) q^{11} +(8107.75 - 4681.01i) q^{12} +(11119.9 - 30551.8i) q^{13} +(18608.2 + 3281.13i) q^{14} +(9194.57 - 1621.25i) q^{15} +(-165.617 + 60.2797i) q^{16} +(-36193.6 - 30370.1i) q^{17} +30341.9i q^{18} +(-104295. - 78141.5i) q^{19} -25061.2 q^{20} +(-72651.7 + 86583.0i) q^{21} +(51845.0 + 142443. i) q^{22} +(21242.3 + 120471. i) q^{23} +(-41970.3 + 238025. i) q^{24} +(343582. + 125054. i) q^{25} +(160497. + 277990. i) q^{26} +(-492744. - 284486. i) q^{27} +(232410. - 195015. i) q^{28} +(236390. + 281719. i) q^{29} +(-46089.0 + 79828.6i) q^{30} +(-774065. + 446906. i) q^{31} +(358931. - 986153. i) q^{32} +(-892961. - 157453. i) q^{33} +(459386. - 81002.1i) q^{34} +(284313. - 103481. i) q^{35} +(373203. + 313155. i) q^{36} -914089. i q^{37} +(1.25287e6 - 292895. i) q^{38} -1.92010e6 q^{39} +(415883. - 495631. i) q^{40} +(144754. + 397708. i) q^{41} +(-193775. - 1.09895e6i) q^{42} +(697460. - 3.95549e6i) q^{43} +(2.28712e6 + 832445. i) q^{44} +(242925. + 420758. i) q^{45} +(-1.04595e6 - 603878. i) q^{46} +(-1.56894e6 + 1.31649e6i) q^{47} +(6690.53 + 7973.46i) q^{48} +(1.05102e6 - 1.82041e6i) q^{49} +(-3.12625e6 + 1.80494e6i) q^{50} +(-954341. + 2.62203e6i) q^{51} +(5.07572e6 + 894987. i) q^{52} +(-3.38886e6 + 597548. i) q^{53} +(5.27867e6 - 1.92128e6i) q^{54} +(1.85938e6 + 1.56020e6i) q^{55} +7.83255e6i q^{56} +(-2.22988e6 + 7.36630e6i) q^{57} -3.63086e6 q^{58} +(-1.21638e7 + 1.44962e7i) q^{59} +(506206. + 1.39079e6i) q^{60} +(-253099. - 1.43539e6i) q^{61} +(1.53237e6 - 8.69052e6i) q^{62} +(-5.52696e6 - 2.01165e6i) q^{63} +(5.15800e6 + 8.93392e6i) q^{64} +(4.45130e6 + 2.56996e6i) q^{65} +(6.85777e6 - 5.75435e6i) q^{66} +(-2.16200e7 - 2.57657e7i) q^{67} +(3.74494e6 - 6.48642e6i) q^{68} +(6.25657e6 - 3.61223e6i) q^{69} +(-1.02167e6 + 2.80701e6i) q^{70} +(2.50327e7 + 4.41394e6i) q^{71} +(-1.23864e7 + 2.18406e6i) q^{72} +(2.31159e7 - 8.41349e6i) q^{73} +(6.91338e6 + 5.80101e6i) q^{74} -2.15933e7i q^{75} +(9.32816e6 - 1.84332e7i) q^{76} -2.93841e7 q^{77} +(1.21854e7 - 1.45220e7i) q^{78} +(-1.42027e7 - 3.90216e7i) q^{79} +(-4838.33 - 27439.5i) q^{80} +(-2.33357e6 + 1.32343e7i) q^{81} +(-3.92656e6 - 1.42915e6i) q^{82} +(3.14243e7 + 5.44284e7i) q^{83} +(-1.55169e7 - 8.95870e6i) q^{84} +(5.72187e6 - 4.80122e6i) q^{85} +(2.54897e7 + 3.03774e7i) q^{86} +(1.08594e7 - 1.88090e7i) q^{87} +(-5.44172e7 + 3.14178e7i) q^{88} +(-5.94786e6 + 1.63416e7i) q^{89} +(-4.72390e6 - 832952. i) q^{90} +(-6.12783e7 + 1.08050e7i) q^{91} +(-1.82227e7 + 6.63253e6i) q^{92} +(4.04366e7 + 3.39303e7i) q^{93} -2.02208e7i q^{94} +(1.50289e7 - 1.40924e7i) q^{95} -6.19773e7 q^{96} +(-3.00164e7 + 3.57722e7i) q^{97} +(7.09804e6 + 1.95017e7i) q^{98} +(-8.19357e6 - 4.64681e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 6 q^{2} + 162 q^{3} - 720 q^{4} - 6 q^{5} - 720 q^{6} + 3282 q^{7} - 9 q^{8} + 8562 q^{9}+O(q^{10}) $ 72 * q - 6 * q^2 + 162 * q^3 - 720 * q^4 - 6 * q^5 - 720 * q^6 + 3282 * q^7 - 9 * q^8 + 8562 * q^9	\( 72 q - 6 q^{2} + 162 q^{3} - 720 q^{4} - 6 q^{5} - 720 q^{6} + 3282 q^{7} - 9 q^{8} + 8562 q^{9} - 2793 q^{10} + 10482 q^{11} - 124425 q^{12} + 108465 q^{13} + 91905 q^{14} - 236277 q^{15} - 207120 q^{16} + 40269 q^{17} + 188304 q^{19} + 1700646 q^{20} + 386850 q^{21} - 1237254 q^{22} - 1339566 q^{23} - 1289928 q^{24} + 59748 q^{25} - 842907 q^{26} + 4849875 q^{27} - 2065044 q^{28} - 1312269 q^{29} + 299940 q^{30} + 3498759 q^{31} + 9109881 q^{32} - 1670298 q^{33} - 12448236 q^{34} - 5923416 q^{35} - 6763797 q^{36} + 5067372 q^{38} + 18303516 q^{39} + 15014562 q^{40} - 11716206 q^{41} - 9228981 q^{42} + 12974721 q^{43} - 2631387 q^{44} - 31264995 q^{45} - 30318354 q^{46} + 1571889 q^{47} + 55683057 q^{48} + 1898838 q^{49} + 30782124 q^{50} + 12474372 q^{51} - 839439 q^{52} - 49160157 q^{53} - 65504571 q^{54} - 27903114 q^{55} + 18105312 q^{57} + 85061964 q^{58} + 51376881 q^{59} + 61200294 q^{60} - 51972462 q^{61} - 85396644 q^{62} + 41912118 q^{63} - 35891445 q^{64} + 2267586 q^{65} + 53209500 q^{66} + 35494521 q^{67} + 13755102 q^{68} + 54287784 q^{69} + 98126001 q^{70} - 5729388 q^{71} - 580668798 q^{72} - 255453906 q^{73} + 159588693 q^{74} + 128877954 q^{76} + 345629838 q^{77} + 120889431 q^{78} + 73477881 q^{79} - 93973551 q^{80} + 114909627 q^{81} + 67089591 q^{82} + 55994352 q^{83} + 143496459 q^{84} - 29709876 q^{85} - 592637892 q^{86} - 151341879 q^{87} - 412023537 q^{88} - 7283562 q^{89} + 350808846 q^{90} + 81065763 q^{91} + 496900692 q^{92} - 609570561 q^{93} - 222935505 q^{95} + 89754174 q^{96} - 180436449 q^{97} + 472058181 q^{98} + 865983036 q^{99}+O(q^{100}) \) 72 * q - 6 * q^2 + 162 * q^3 - 720 * q^4 - 6 * q^5 - 720 * q^6 + 3282 * q^7 - 9 * q^8 + 8562 * q^9 - 2793 * q^10 + 10482 * q^11 - 124425 * q^12 + 108465 * q^13 + 91905 * q^14 - 236277 * q^15 - 207120 * q^16 + 40269 * q^17 + 188304 * q^19 + 1700646 * q^20 + 386850 * q^21 - 1237254 * q^22 - 1339566 * q^23 - 1289928 * q^24 + 59748 * q^25 - 842907 * q^26 + 4849875 * q^27 - 2065044 * q^28 - 1312269 * q^29 + 299940 * q^30 + 3498759 * q^31 + 9109881 * q^32 - 1670298 * q^33 - 12448236 * q^34 - 5923416 * q^35 - 6763797 * q^36 + 5067372 * q^38 + 18303516 * q^39 + 15014562 * q^40 - 11716206 * q^41 - 9228981 * q^42 + 12974721 * q^43 - 2631387 * q^44 - 31264995 * q^45 - 30318354 * q^46 + 1571889 * q^47 + 55683057 * q^48 + 1898838 * q^49 + 30782124 * q^50 + 12474372 * q^51 - 839439 * q^52 - 49160157 * q^53 - 65504571 * q^54 - 27903114 * q^55 + 18105312 * q^57 + 85061964 * q^58 + 51376881 * q^59 + 61200294 * q^60 - 51972462 * q^61 - 85396644 * q^62 + 41912118 * q^63 - 35891445 * q^64 + 2267586 * q^65 + 53209500 * q^66 + 35494521 * q^67 + 13755102 * q^68 + 54287784 * q^69 + 98126001 * q^70 - 5729388 * q^71 - 580668798 * q^72 - 255453906 * q^73 + 159588693 * q^74 + 128877954 * q^76 + 345629838 * q^77 + 120889431 * q^78 + 73477881 * q^79 - 93973551 * q^80 + 114909627 * q^81 + 67089591 * q^82 + 55994352 * q^83 + 143496459 * q^84 - 29709876 * q^85 - 592637892 * q^86 - 151341879 * q^87 - 412023537 * q^88 - 7283562 * q^89 + 350808846 * q^90 + 81065763 * q^91 + 496900692 * q^92 - 609570561 * q^93 - 222935505 * q^95 + 89754174 * q^96 - 180436449 * q^97 + 472058181 * q^98 + 865983036 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−6.34622	+	7.56314i	−0.396639	+	0.472696i	−0.926992	−	0.375081i	$-0.877615\pi$
$2$	−6.34622	+	7.56314i	−0.396639	+	0.472696i	0.530353	+	0.847777i	$0.322059\pi$
$3$	−20.1988	−	55.4957i	−0.249368	−	0.685132i	−0.999710	−	0.0240828i	$-0.992333\pi$
$3$	−20.1988	−	55.4957i	−0.249368	−	0.685132i	0.750342	−	0.661050i	$-0.229889\pi$
$4$	27.5275	+	156.116i	0.107529	+	0.609828i
$5$	−27.4521	+	155.689i	−0.0439234	+	0.249102i	−0.998862	−	0.0477027i	$-0.984810\pi$
$5$	−27.4521	+	155.689i	−0.0439234	+	0.249102i	0.954938	+	0.296805i	$0.0959211\pi$
$6$	547.908	+	199.422i	0.422768	+	0.153875i
$7$	−956.918	−	1657.43i	−0.398550	−	0.690309i	0.594997	−	0.803728i	$-0.297153\pi$
$7$	−956.918	−	1657.43i	−0.398550	−	0.690309i	−0.993547	+	0.113419i	$0.963820\pi$
$8$	−3544.29	−	2046.29i	−0.865304	−	0.499583i
$9$	2354.23	−	1975.44i	0.358822	−	0.301088i
$10$	−1003.28	−	1195.66i	−0.100328	−	0.119566i
$11$	7676.75	−	13296.5i	0.524332	−	0.908170i	−0.475266	−	0.879842i	$-0.657648\pi$
$11$	7676.75	−	13296.5i	0.524332	−	0.908170i	0.999599	−	0.0283284i	$-0.00901842\pi$
$12$	8107.75	−	4681.01i	0.390999	−	0.225743i
$13$	11119.9	−	30551.8i	0.389340	−	1.06970i	−0.577960	−	0.816065i	$-0.696151\pi$
$13$	11119.9	−	30551.8i	0.389340	−	1.06970i	0.967300	−	0.253637i	$-0.0816267\pi$
$14$	18608.2	+	3281.13i	0.484387	+	0.0854104i
$15$	9194.57	−	1621.25i	0.181621	−	0.0320247i
$16$	−165.617	+	60.2797i	−0.00252712	+	0.000919795i
$17$	−36193.6	−	30370.1i	−0.433348	−	0.363622i	0.399865	−	0.916574i	$-0.369057\pi$
$17$	−36193.6	−	30370.1i	−0.433348	−	0.363622i	−0.833213	+	0.552952i	$0.813501\pi$
$18$			30341.9i			0.289037i
$19$	−104295.	−	78141.5i	−0.800294	−	0.599608i
$19$	−104295.	−	78141.5i	−0.800294	−	0.599608i
$20$	−25061.2			−0.156633
$21$	−72651.7	+	86583.0i	−0.373567	+	0.445200i
$22$	51845.0	+	142443.i	0.221318	+	0.608066i
$23$	21242.3	+	120471.i	0.0759085	+	0.430499i	0.998951	+	0.0457997i	$0.0145836\pi$
$23$	21242.3	+	120471.i	0.0759085	+	0.430499i	−0.923042	+	0.384699i	$0.874305\pi$
$24$	−41970.3	+	238025.i	−0.126502	+	0.717428i
$25$	343582.	+	125054.i	0.879570	+	0.320137i
$26$	160497.	+	277990.i	0.351216	+	0.608325i
$27$	−492744.	−	284486.i	−0.927185	−	0.535311i
$28$	232410.	−	195015.i	0.378114	−	0.317275i
$29$	236390.	+	281719.i	0.334224	+	0.398312i	0.906815	−	0.421529i	$-0.138506\pi$
$29$	236390.	+	281719.i	0.334224	+	0.398312i	−0.572591	+	0.819841i	$0.694062\pi$
$30$	−46089.0	+	79828.6i	−0.0569001	+	0.0985538i
$31$	−774065.	+	446906.i	−0.838167	+	0.483916i	−0.856641	−	0.515914i	$-0.827453\pi$
$31$	−774065.	+	446906.i	−0.838167	+	0.483916i	0.0184740	+	0.999829i	$0.494119\pi$
$32$	358931.	−	986153.i	0.342303	−	0.940469i
$33$	−892961.	−	157453.i	−0.752969	−	0.132769i
$34$	459386.	−	81002.1i	0.343765	−	0.0606151i
$35$	284313.	−	103481.i	0.189463	−	0.0689589i
$36$	373203.	+	313155.i	0.222196	+	0.186444i
$37$		−	914089.i		−	0.487732i	−0.969809	−	0.243866i	$-0.921584\pi$
$37$		−	914089.i		−	0.487732i	0.969809	−	0.243866i	$-0.0784157\pi$
$38$	1.25287e6	−	292895.i	0.600860	−	0.140468i
$39$	−1.92010e6			−0.829976
$40$	415883.	−	495631.i	0.162454	−	0.193606i
$41$	144754.	+	397708.i	0.0512265	+	0.140744i	0.962667	−	0.270688i	$-0.0872511\pi$
$41$	144754.	+	397708.i	0.0512265	+	0.140744i	−0.911441	+	0.411432i	$0.865029\pi$
$42$	−193775.	−	1.09895e6i	−0.0622730	−	0.353168i
$43$	697460.	−	3.95549e6i	0.204007	−	1.15698i	−0.694987	−	0.719022i	$-0.744590\pi$
$43$	697460.	−	3.95549e6i	0.204007	−	1.15698i	0.898994	−	0.437960i	$-0.144299\pi$
$44$	2.28712e6	+	832445.i	0.610209	+	0.222098i
$45$	242925.	+	420758.i	0.0592409	+	0.102608i
$46$	−1.04595e6	−	603878.i	−0.233603	−	0.134871i
$47$	−1.56894e6	+	1.31649e6i	−0.321524	+	0.269791i	−0.789236	−	0.614090i	$-0.789523\pi$
$47$	−1.56894e6	+	1.31649e6i	−0.321524	+	0.269791i	0.467711	+	0.883881i	$0.345079\pi$
$48$	6690.53	+	7973.46i	0.00126036	+	0.00150204i
$49$	1.05102e6	−	1.82041e6i	0.182316	−	0.315780i
$50$	−3.12625e6	+	1.80494e6i	−0.500199	+	0.288790i
$51$	−954341.	+	2.62203e6i	−0.141066	+	0.387576i
$52$	5.07572e6	+	894987.i	0.694200	+	0.122406i
$53$	−3.38886e6	+	597548.i	−0.429487	+	0.0757302i	−0.384213	−	0.923244i	$-0.625527\pi$
$53$	−3.38886e6	+	597548.i	−0.429487	+	0.0757302i	−0.0452741	+	0.998975i	$0.514416\pi$
$54$	5.27867e6	−	1.92128e6i	0.620797	−	0.225952i
$55$	1.85938e6	+	1.56020e6i	0.203197	+	0.170502i
$56$			7.83255e6i			0.796436i
$57$	−2.22988e6	+	7.36630e6i	−0.211243	+	0.697830i
$58$	−3.63086e6			−0.320847
$59$	−1.21638e7	+	1.44962e7i	−1.00383	+	1.19632i	−0.0233471	+	0.999727i	$0.507432\pi$
$59$	−1.21638e7	+	1.44962e7i	−1.00383	+	1.19632i	−0.980485	+	0.196593i	$0.937012\pi$
$60$	506206.	+	1.39079e6i	0.0390591	+	0.107314i
$61$	−253099.	−	1.43539e6i	−0.0182798	−	0.103670i	0.974303	−	0.225242i	$-0.0723174\pi$
$61$	−253099.	−	1.43539e6i	−0.0182798	−	0.103670i	−0.992583	+	0.121573i	$0.961206\pi$
$62$	1.53237e6	−	8.69052e6i	0.103705	−	0.588138i
$63$	−5.52696e6	−	2.01165e6i	−0.350852	−	0.127700i
$64$	5.15800e6	+	8.93392e6i	0.307441	+	0.532503i
$65$	4.45130e6	+	2.56996e6i	0.249364	+	0.143970i
$66$	6.85777e6	−	5.75435e6i	0.361416	−	0.303264i
$67$	−2.16200e7	−	2.57657e7i	−1.07289	−	1.27863i	−0.958470	−	0.285194i	$-0.907942\pi$
$67$	−2.16200e7	−	2.57657e7i	−1.07289	−	1.27863i	−0.114425	−	0.993432i	$-0.536503\pi$
$68$	3.74494e6	−	6.48642e6i	0.175149	−	0.303368i
$69$	6.25657e6	−	3.61223e6i	0.276019	−	0.159360i
$70$	−1.02167e6	+	2.80701e6i	−0.0425518	+	0.116910i
$71$	2.50327e7	+	4.41394e6i	0.985085	+	0.173697i	0.642912	−	0.765940i	$-0.277726\pi$
$71$	2.50327e7	+	4.41394e6i	0.985085	+	0.173697i	0.342173	+	0.939637i	$0.388837\pi$
$72$	−1.23864e7	+	2.18406e6i	−0.460909	+	0.0812707i
$73$	2.31159e7	−	8.41349e6i	0.813990	−	0.296268i	0.0987188	−	0.995115i	$-0.468526\pi$
$73$	2.31159e7	−	8.41349e6i	0.813990	−	0.296268i	0.715271	+	0.698847i	$0.246303\pi$
$74$	6.91338e6	+	5.80101e6i	0.230549	+	0.193454i
$75$		−	2.15933e7i		−	0.682454i
$76$	9.32816e6	−	1.84332e7i	0.279603	−	0.552517i
$77$	−2.93841e7			−0.835891
$78$	1.21854e7	−	1.45220e7i	0.329201	−	0.392326i
$79$	−1.42027e7	−	3.90216e7i	−0.364639	−	1.00184i	−0.977368	−	0.211544i	$-0.932151\pi$
$79$	−1.42027e7	−	3.90216e7i	−0.364639	−	1.00184i	0.612730	−	0.790293i	$-0.290072\pi$
$80$	−4838.33	−	27439.5i	−0.000118123	−	0.000669911i
$81$	−2.33357e6	+	1.32343e7i	−0.0542101	+	0.307441i
$82$	−3.92656e6	−	1.42915e6i	−0.0868474	−	0.0316099i
$83$	3.14243e7	+	5.44284e7i	0.662145	+	1.14687i	0.980051	+	0.198746i	$0.0636869\pi$
$83$	3.14243e7	+	5.44284e7i	0.662145	+	1.14687i	−0.317907	+	0.948122i	$0.602980\pi$
$84$	−1.55169e7	−	8.95870e6i	−0.311665	−	0.179940i
$85$	5.72187e6	−	4.80122e6i	0.109613	−	0.0919763i
$86$	2.54897e7	+	3.03774e7i	0.465984	+	0.555338i
$87$	1.08594e7	−	1.88090e7i	0.189552	−	0.328314i
$88$	−5.44172e7	+	3.14178e7i	−0.907414	+	0.523896i
$89$	−5.94786e6	+	1.63416e7i	−0.0947984	+	0.260456i	−0.978024	−	0.208492i	$-0.933145\pi$
$89$	−5.94786e6	+	1.63416e7i	−0.0947984	+	0.260456i	0.883226	+	0.468948i	$0.155367\pi$
$90$	−4.72390e6	−	832952.i	−0.0719997	−	0.0126955i
$91$	−6.12783e7	+	1.08050e7i	−0.893596	+	0.157565i
$92$	−1.82227e7	+	6.63253e6i	−0.254368	+	0.0925823i
$93$	4.04366e7	+	3.39303e7i	0.540558	+	0.453582i
$94$		−	2.02208e7i		−	0.258993i
$95$	1.50289e7	−	1.40924e7i	0.184515	−	0.173018i
$96$	−6.19773e7			−0.729705
$97$	−3.00164e7	+	3.57722e7i	−0.339057	+	0.404072i	−0.908450	−	0.417993i	$-0.862734\pi$
$97$	−3.00164e7	+	3.57722e7i	−0.339057	+	0.404072i	0.569394	+	0.822065i	$0.307178\pi$
$98$	7.09804e6	+	1.95017e7i	0.0769545	+	0.211431i
$99$	−8.19357e6	−	4.64681e7i	−0.0852967	−	0.483742i
$100$	−1.00649e7	+	5.70811e7i	−0.100649	+	0.570811i
$101$	1.81812e8	+	6.61741e7i	1.74718	+	0.635920i	0.999601	−	0.0282573i	$-0.00899577\pi$
$101$	1.81812e8	+	6.61741e7i	1.74718	+	0.635920i	0.747575	+	0.664177i	$0.231218\pi$
$102$	−1.37743e7	−	2.38578e7i	−0.127253	−	0.220409i
$103$	6.73456e7	+	3.88820e7i	0.598357	+	0.345462i	0.768395	−	0.639976i	$-0.221056\pi$
$103$	6.73456e7	+	3.88820e7i	0.598357	+	0.345462i	−0.170038	+	0.985438i	$0.554389\pi$
$104$	−1.01930e8	+	8.55295e7i	−0.871302	+	0.731110i
$105$	−1.14856e7	−	1.36880e7i	−0.0944920	−	0.112611i
$106$	1.69871e7	−	2.94226e7i	0.134554	−	0.233054i
$107$	8.01567e7	−	4.62785e7i	0.611512	−	0.353057i	−0.162045	−	0.986783i	$-0.551809\pi$
$107$	8.01567e7	−	4.62785e7i	0.611512	−	0.353057i	0.773557	+	0.633727i	$0.218476\pi$
$108$	3.08488e7	−	8.47565e7i	0.226748	−	0.622985i
$109$	4.14684e7	+	7.31200e6i	0.293773	+	0.0518000i	0.318592	−	0.947892i	$-0.396790\pi$
$109$	4.14684e7	+	7.31200e6i	0.293773	+	0.0518000i	−0.0248195	+	0.999692i	$0.507901\pi$
$110$	−2.36000e7	+	4.16133e6i	−0.161192	+	0.0284224i
$111$	−5.07280e7	+	1.84635e7i	−0.334161	+	0.121625i
$112$	258392.	+	216816.i	0.00164212	+	0.00137791i
$113$		−	1.02097e8i		−	0.626179i	−0.949724	−	0.313089i	$-0.898636\pi$
$113$		−	1.02097e8i		−	0.626179i	0.949724	−	0.313089i	$-0.101364\pi$
$114$	−4.15610e7	−	6.36131e7i	−0.246074	−	0.376640i
$115$	−1.93392e7			−0.110572
$116$	−3.74736e7	+	4.46593e7i	−0.206963	+	0.246649i
$117$	−3.41741e7	−	9.38927e7i	−0.182370	−	0.501058i
$118$	−3.24429e7	−	1.83993e8i	−0.167337	−	0.949015i
$119$	−1.57019e7	+	8.90501e7i	−0.0783007	+	0.444065i
$120$	−3.59057e7	−	1.30686e7i	−0.173156	−	0.0630238i
$121$	−1.06856e7	−	1.85080e7i	−0.0498490	−	0.0863411i
$122$	1.24623e7	+	7.19511e6i	0.0562547	+	0.0324787i
$123$	1.91472e7	−	1.60664e7i	0.0836538	−	0.0701939i
$124$	−9.10773e7	−	1.08542e8i	−0.385233	−	0.459103i
$125$	−5.97786e7	+	1.03540e8i	−0.244853	+	0.424098i
$126$	5.02897e7	−	2.90348e7i	0.199525	−	0.115196i
$127$	1.34859e8	−	3.70521e8i	0.518399	−	1.42429i	−0.353884	−	0.935289i	$-0.615139\pi$
$127$	1.34859e8	−	3.70521e8i	0.518399	−	1.42429i	0.872283	−	0.489001i	$-0.162638\pi$
$128$	1.64274e8	+	2.89659e7i	0.611967	+	0.107906i
$129$	−2.33601e8	+	4.11901e7i	−0.843559	+	0.148742i
$130$	−4.76859e7	+	1.73563e7i	−0.166962	+	0.0607691i
$131$	3.33296e8	+	2.79668e8i	1.13174	+	0.949639i	0.999137	−	0.0415314i	$-0.0132237\pi$
$131$	3.33296e8	+	2.79668e8i	1.13174	+	0.949639i	0.132598	+	0.991170i	$0.457668\pi$
$132$		−	1.43740e8i		−	0.473458i
$133$	−2.97122e7	+	2.47637e8i	−0.0949572	+	0.791424i
$134$	3.32075e8			1.02995
$135$	5.78182e7	−	6.89050e7i	0.174072	−	0.207451i
$136$	6.61345e7	+	1.81703e8i	0.193318	+	0.531137i
$137$	1.87754e7	+	1.06481e8i	0.0532976	+	0.302266i	0.999791	−	0.0204584i	$-0.00651256\pi$
$137$	1.87754e7	+	1.06481e8i	0.0532976	+	0.302266i	−0.946493	+	0.322724i	$0.895401\pi$
$138$	−1.23858e7	+	7.02433e7i	−0.0341513	+	0.193682i
$139$	−2.01994e8	−	7.35196e7i	−0.541101	−	0.196945i	0.0569872	−	0.998375i	$-0.481851\pi$
$139$	−2.01994e8	−	7.35196e7i	−0.541101	−	0.196945i	−0.598088	+	0.801430i	$0.704073\pi$
$140$	2.39815e7	+	4.15373e7i	0.0624259	+	0.108125i
$141$	1.04750e8	+	6.04777e7i	0.265020	+	0.153010i
$142$	−1.92246e8	+	1.61314e8i	−0.472829	+	0.396751i
$143$	−3.20867e8	−	3.82395e8i	−0.767328	−	0.914466i
$144$	−270823.	+	469079.i	−0.000629847	+	0.00109093i
$145$	−5.03499e7	+	2.90695e7i	−0.113901	+	0.0657606i
$146$	−8.30662e7	+	2.28222e8i	−0.182815	+	0.502281i
$147$	−1.22254e8	−	2.15567e7i	−0.261815	−	0.0461651i
$148$	1.42704e8	−	2.51626e7i	0.297433	−	0.0524455i
$149$	−7.73876e8	+	2.81668e8i	−1.57010	+	0.571469i	−0.973021	−	0.230716i	$-0.925893\pi$
$149$	−7.73876e8	+	2.81668e8i	−1.57010	+	0.571469i	−0.597076	+	0.802185i	$0.703671\pi$
$150$	1.63313e8	+	1.37036e8i	0.322593	+	0.270688i
$151$			1.72505e6i			0.00331813i	0.999999	+	0.00165907i	$0.000528097\pi$
$151$			1.72505e6i			0.00331813i	−0.999999	+	0.00165907i	$0.999472\pi$
$152$	2.09751e8	+	4.90374e8i	0.392944	+	0.918657i
$153$	−1.45202e8			−0.264977
$154$	1.86478e8	−	2.22236e8i	0.331547	−	0.395122i
$155$	−4.83286e7	−	1.32782e8i	−0.0837293	−	0.230044i
$156$	−5.28555e7	−	2.99759e8i	−0.0892467	−	0.506143i
$157$	−1.57588e8	+	8.93725e8i	−0.259373	+	1.47097i	0.525222	+	0.850965i	$0.323982\pi$
$157$	−1.57588e8	+	8.93725e8i	−0.259373	+	1.47097i	−0.784594	+	0.620009i	$0.787129\pi$
$158$	3.85260e8	+	1.40223e8i	0.618194	+	0.225004i
$159$	1.01612e8	+	1.75998e8i	0.158985	+	0.275371i
$160$	1.43680e8	+	8.29535e7i	0.219238	+	0.126577i
$161$	1.79345e8	−	1.50489e8i	0.266924	−	0.223975i
$162$	−8.52836e7	−	1.01637e8i	−0.123824	−	0.147568i
$163$	6.42194e8	−	1.11231e9i	0.909736	−	1.57571i	0.0953063	−	0.995448i	$-0.469617\pi$
$163$	6.42194e8	−	1.11231e9i	0.909736	−	1.57571i	0.814430	−	0.580262i	$-0.197050\pi$
$164$	−5.81039e7	+	3.35463e7i	−0.0803212	+	0.0463734i
$165$	4.90274e7	−	1.34702e8i	0.0661459	−	0.181734i
$166$	−6.11075e8	−	1.07749e8i	−0.804752	−	0.141900i
$167$	−7.46752e8	+	1.31673e8i	−0.960087	+	0.169289i	−0.631665	−	0.775242i	$-0.717628\pi$
$167$	−7.46752e8	+	1.31673e8i	−0.960087	+	0.169289i	−0.328422	+	0.944531i	$0.606517\pi$
$168$	4.34673e8	−	1.58208e8i	0.545664	−	0.198605i
$169$	−1.84871e8	−	1.55125e8i	−0.226632	−	0.190167i
$170$			7.37449e7i			0.0882951i
$171$	−3.99899e8	+	2.20651e7i	−0.467698	+	0.0258061i
$172$	6.36715e8			0.727497
$173$	9.06151e8	−	1.07991e9i	1.01162	−	1.20560i	0.0330956	−	0.999452i	$-0.489463\pi$
$173$	9.06151e8	−	1.07991e9i	1.01162	−	1.20560i	0.978521	−	0.206146i	$-0.0660921\pi$
$174$	7.33390e7	+	2.01497e8i	0.0800089	+	0.219823i
$175$	−1.21512e8	−	6.89130e8i	−0.129559	−	0.734766i
$176$	−469891.	+	2.66488e6i	−0.000489718	+	0.00277733i
$177$	1.05017e9	+	3.82232e8i	1.06996	+	0.389434i
$178$	−8.58474e7	−	1.48692e8i	−0.0855159	−	0.148118i
$179$	−5.56974e8	−	3.21569e8i	−0.542529	−	0.313229i	0.203574	−	0.979060i	$-0.434744\pi$
$179$	−5.56974e8	−	3.21569e8i	−0.542529	−	0.313229i	−0.746103	+	0.665830i	$0.768078\pi$
$180$	−5.90000e7	+	4.95069e7i	−0.0562033	+	0.0471602i
$181$	−6.72580e8	−	8.01549e8i	−0.626656	−	0.746820i	0.355543	−	0.934660i	$-0.384296\pi$
$181$	−6.72580e8	−	8.01549e8i	−0.626656	−	0.746820i	−0.982200	+	0.187840i	$0.939851\pi$
$182$	3.07166e8	−	5.32027e8i	0.279955	−	0.484895i
$183$	−7.45459e7	+	4.30391e7i	−0.0664691	+	0.0383759i
$184$	1.71231e8	−	4.70452e8i	0.149386	−	0.410435i
$185$	1.42313e8	+	2.50937e7i	0.121495	+	0.0214229i
$186$	−5.13239e8	+	9.04979e7i	−0.428813	+	0.0756113i
$187$	−6.81666e8	+	2.48106e8i	−0.557449	+	0.202895i
$188$	−2.48715e8	−	2.08696e8i	−0.199100	−	0.167064i
$189$			1.08892e9i			0.853392i
$190$	1.12064e7	+	2.03099e8i	0.00859905	+	0.155845i
$191$	1.20096e7			0.00902391			0.00451196	−	0.999990i	$-0.498564\pi$
$191$	1.20096e7			0.00902391			0.00451196	+	0.999990i	$0.498564\pi$
$192$	3.91609e8	−	4.66701e8i	0.288169	−	0.343427i
$193$	9.26808e8	+	2.54638e9i	0.667976	+	1.83525i	0.536445	+	0.843936i	$0.319767\pi$
$193$	9.26808e8	+	2.54638e9i	0.667976	+	1.83525i	0.131531	+	0.991312i	$0.458011\pi$
$194$	−8.00589e7	−	4.54037e8i	−0.0565201	−	0.320541i
$195$	5.27109e7	−	2.98938e8i	0.0364554	−	0.206749i
$196$	3.13127e8	+	1.13969e8i	0.212176	+	0.0772258i
$197$	1.14747e9	+	1.98748e9i	0.761865	+	1.31959i	0.941888	+	0.335927i	$0.109049\pi$
$197$	1.14747e9	+	1.98748e9i	0.761865	+	1.31959i	−0.180023	+	0.983662i	$0.557617\pi$
$198$	4.03442e8	+	2.32928e8i	0.262495	+	0.151551i
$199$	−3.01150e8	+	2.52695e8i	−0.192031	+	0.161133i	−0.733734	−	0.679437i	$-0.762224\pi$
$199$	−3.01150e8	+	2.52695e8i	−0.192031	+	0.161133i	0.541703	+	0.840570i	$0.317780\pi$
$200$	−9.61856e8	−	1.14630e9i	−0.601160	−	0.716435i
$201$	−9.93190e8	+	1.72026e9i	−0.608483	+	1.05392i
$202$	−1.65430e9	+	9.55112e8i	−0.993595	+	0.573652i
$203$	2.40723e8	−	6.61382e8i	0.141754	−	0.389465i
$204$	−4.35612e8	−	7.68101e7i	−0.251524	−	0.0443504i
$205$	−6.58925e7	+	1.16186e7i	−0.0373096	+	0.00657869i
$206$	−7.21460e8	+	2.62590e8i	−0.400630	+	0.145817i
$207$	2.87992e8	+	2.41654e8i	0.156856	+	0.131617i
$208$			5.73020e6i			0.00306137i
$209$	−1.83966e9	+	7.86890e8i	−0.964166	+	0.412410i
$210$	1.76414e8			0.0907100
$211$	2.12122e9	−	2.52797e9i	1.07018	−	1.27539i	0.110623	−	0.993862i	$-0.464715\pi$
$211$	2.12122e9	−	2.52797e9i	1.07018	−	1.27539i	0.959554	−	0.281524i	$-0.0908401\pi$
$212$	−1.86574e8	−	5.12607e8i	−0.0923648	−	0.253770i
$213$	−2.60675e8	−	1.47836e9i	−0.126643	−	0.718228i
$214$	−1.58682e8	+	8.99930e8i	−0.0756611	+	0.429095i
$215$	5.96679e8	+	2.17173e8i	0.279246	+	0.101637i
$216$	1.16428e9	+	2.01660e9i	0.534865	+	0.926413i
$217$	1.48143e9	+	8.55306e8i	0.668103	+	0.385729i
$218$	−3.18469e8	+	2.67228e8i	−0.141007	+	0.118319i
$219$	−9.33825e8	−	1.11289e9i	−0.405966	−	0.483811i
$220$	−1.92389e8	+	3.33227e8i	−0.0821276	+	0.142249i
$221$	−1.33033e9	+	7.68066e8i	−0.557686	+	0.321980i
$222$	1.82289e8	−	5.00836e8i	0.0750498	−	0.206198i
$223$	1.91136e9	+	3.37024e8i	0.772898	+	0.136283i	0.546169	−	0.837675i	$-0.316086\pi$
$223$	1.91136e9	+	3.37024e8i	0.772898	+	0.136283i	0.226729	+	0.973958i	$0.427197\pi$
$224$	−1.97795e9	+	3.48766e8i	−0.785639	+	0.138529i
$225$	1.05591e9	−	3.84319e8i	0.411999	−	0.149955i
$226$	7.72172e8	+	6.47929e8i	0.295992	+	0.248367i
$227$		−	3.44989e9i		−	1.29928i	−0.760243	−	0.649638i	$-0.774920\pi$
$227$		−	3.44989e9i		−	1.29928i	0.760243	−	0.649638i	$-0.225080\pi$
$228$	−1.21138e9	−	1.45345e8i	−0.448272	−	0.0537849i
$229$	4.29229e9			1.56080			0.780399	−	0.625282i	$-0.215016\pi$
$229$	4.29229e9			1.56080			0.780399	+	0.625282i	$0.215016\pi$
$230$	1.22731e8	−	1.46265e8i	0.0438573	−	0.0522671i
$231$	5.93523e8	+	1.63069e9i	0.208444	+	0.572696i
$232$	−2.61355e8	−	1.48222e9i	−0.0902149	−	0.511634i
$233$	9.64621e8	−	5.47064e9i	0.327290	−	1.85616i	−0.165775	−	0.986164i	$-0.553013\pi$
$233$	9.64621e8	−	5.47064e9i	0.327290	−	1.85616i	0.493066	−	0.869992i	$-0.335876\pi$
$234$	9.27000e8	+	3.37400e8i	0.309183	+	0.112534i
$235$	−1.61893e8	−	2.80407e8i	−0.0530831	−	0.0919426i
$236$	−2.59794e9	−	1.49992e9i	−0.837492	−	0.483526i
$237$	−1.87866e9	+	1.57638e9i	−0.595462	+	0.499652i
$238$	−5.73850e8	−	6.83888e8i	−0.178851	−	0.213146i
$239$	1.09529e9	−	1.89709e9i	0.335688	−	0.581429i	−0.647929	−	0.761701i	$-0.724364\pi$
$239$	1.09529e9	−	1.89709e9i	0.335688	−	0.581429i	0.983617	+	0.180272i	$0.0576978\pi$
$240$	−1.42505e6	+	822752.i	−0.000429521	+	0.000247984i
$241$	−1.42005e9	+	3.90154e9i	−0.420953	+	1.15656i	0.530209	+	0.847867i	$0.322114\pi$
$241$	−1.42005e9	+	3.90154e9i	−0.420953	+	1.15656i	−0.951162	+	0.308693i	$0.900109\pi$
$242$	2.07791e8	+	3.66392e7i	0.0605851	+	0.0106828i
$243$	−2.89473e9	+	5.10419e8i	−0.830200	+	0.146387i
$244$	2.17121e8	−	7.90255e7i	0.0612551	−	0.0222950i
$245$	2.54565e8	+	2.13606e8i	0.0706537	+	0.0592855i
$246$			2.46774e8i			0.0673845i
$247$	−3.54711e9	+	2.31747e9i	−0.952987	+	0.622625i
$248$	3.65801e9			0.967025
$249$	2.38581e9	−	2.84330e9i	0.620639	−	0.739649i
$250$	−4.03715e8	−	1.10920e9i	−0.103351	−	0.283955i
$251$	−1.10960e9	−	6.29286e9i	−0.279558	−	1.58545i	−0.724100	−	0.689694i	$-0.757745\pi$
$251$	−1.10960e9	−	6.29286e9i	−0.279558	−	1.58545i	0.444542	−	0.895758i	$-0.353366\pi$
$252$	1.61907e8	−	9.18223e8i	0.0401481	−	0.227691i
$253$	1.76492e9	+	6.42378e8i	0.430767	+	0.156787i
$254$	1.94646e9	+	3.37137e9i	0.467639	+	0.809974i
$255$	−3.82022e8	−	2.20561e8i	−0.0903500	−	0.0521636i
$256$	−3.28463e9	+	2.75613e9i	−0.764763	+	0.641713i
$257$	6.12396e8	+	7.29826e8i	0.140378	+	0.167296i	0.831653	−	0.555296i	$-0.187395\pi$
$257$	6.12396e8	+	7.29826e8i	0.140378	+	0.167296i	−0.691275	+	0.722592i	$0.742950\pi$
$258$	1.17096e9	−	2.02816e9i	0.264278	−	0.457744i
$259$	−1.51504e9	+	8.74708e8i	−0.336686	+	0.194386i
$260$	−2.78679e8	+	7.65664e8i	−0.0609833	+	0.167550i
$261$	1.11303e9	+	1.96258e8i	0.239854	+	0.0422927i
$262$	−4.23034e9	+	7.45923e8i	−0.897781	+	0.158303i
$263$	−2.90657e8	+	1.05791e8i	−0.0607517	+	0.0221118i	−0.372217	−	0.928146i	$-0.621402\pi$
$263$	−2.90657e8	+	1.05791e8i	−0.0607517	+	0.0221118i	0.311466	+	0.950257i	$0.399180\pi$
$264$	2.84271e9	+	2.38532e9i	0.585218	+	0.491056i
$265$		−	5.44012e8i		−	0.110313i
$266$	−1.68435e9	−	1.79628e9i	−0.336439	−	0.358795i
$267$	1.02703e9			0.202087
$268$	3.42730e9	−	4.08450e9i	0.664375	−	0.791771i
$269$	1.97009e9	+	5.41278e9i	0.376251	+	1.03374i	0.972898	+	0.231237i	$0.0742772\pi$
$269$	1.97009e9	+	5.41278e9i	0.376251	+	1.03374i	−0.596647	+	0.802504i	$0.703501\pi$
$270$	1.54211e8	+	8.74573e8i	0.0290175	+	0.164566i
$271$	−1.57448e9	+	8.92933e9i	−0.291918	+	1.65555i	0.387554	+	0.921847i	$0.373320\pi$
$271$	−1.57448e9	+	8.92933e9i	−0.291918	+	1.65555i	−0.679472	+	0.733702i	$0.737791\pi$
$272$	7.82498e6	+	2.84806e6i	0.00142958	+	0.000520324i
$273$	1.83738e9	+	3.18243e9i	0.330787	+	0.572940i
$274$	−9.24481e8	−	5.33749e8i	−0.164020	−	0.0946968i
$275$	4.30037e9	−	3.60844e9i	0.751926	−	0.630941i
$276$	7.36155e8	+	8.77315e8i	0.126862	+	0.151189i
$277$	−6.02061e8	+	1.04280e9i	−0.102264	+	0.177126i	−0.912617	−	0.408816i	$-0.865942\pi$
$277$	−6.02061e8	+	1.04280e9i	−0.102264	+	0.177126i	0.810353	+	0.585942i	$0.199275\pi$
$278$	1.83794e9	−	1.06113e9i	0.307717	−	0.177660i
$279$	−9.39493e8	+	2.58124e9i	−0.155052	+	0.426001i
$280$	−1.21944e9	−	2.15020e8i	−0.198394	−	0.0349822i
$281$	−1.11507e10	+	1.96617e9i	−1.78845	+	0.315353i	−0.966972	−	0.254883i	$-0.917963\pi$
$281$	−1.11507e10	+	1.96617e9i	−1.78845	+	0.315353i	−0.821481	+	0.570235i	$0.806852\pi$
$282$	−1.12217e9	+	4.08437e8i	−0.177444	+	0.0645845i
$283$	−6.49321e8	−	5.44845e8i	−0.101231	−	0.0849430i	0.590767	−	0.806842i	$-0.298825\pi$
$283$	−6.49321e8	−	5.44845e8i	−0.101231	−	0.0849430i	−0.691999	+	0.721899i	$0.743270\pi$
$284$			4.02951e9i			0.619411i
$285$	−1.08564e9	−	5.49388e8i	−0.164553	−	0.0832722i
$286$	4.92840e9			0.736617
$287$	5.20656e8	−	6.20494e8i	0.0767403	−	0.0914555i
$288$	−1.10308e9	−	3.03068e9i	−0.160338	−	0.440525i
$289$	−8.23689e8	−	4.67137e9i	−0.118079	−	0.669658i
$290$	9.96749e7	−	5.65285e8i	0.0140927	−	0.0799236i
$291$	2.59150e9	+	9.43229e8i	0.361392	+	0.131536i
$292$	1.94980e9	+	3.37716e9i	0.268200	+	0.464537i
$293$	−2.23323e9	−	1.28935e9i	−0.303014	−	0.174945i	0.340782	−	0.940142i	$-0.389308\pi$
$293$	−2.23323e9	−	1.28935e9i	−0.303014	−	0.174945i	−0.643796	+	0.765197i	$0.722641\pi$
$294$	9.38890e8	−	7.87822e8i	0.125668	−	0.105448i
$295$	−1.92298e9	−	2.29172e9i	−0.253914	−	0.302603i
$296$	−1.87049e9	+	3.23979e9i	−0.243663	+	0.422037i
$297$	−7.56535e9	+	4.36786e9i	−0.972306	+	0.561361i
$298$	2.78090e9	−	7.64046e9i	0.352631	−	0.968845i
$299$	3.91682e9	+	6.90641e8i	0.490059	+	0.0864107i
$300$	3.37106e9	−	5.94408e8i	0.416180	−	0.0733837i
$301$	−7.22337e9	+	2.62909e9i	−0.879982	+	0.320287i
$302$	−1.30468e7	−	1.09475e7i	−0.00156847	−	0.00131610i
$303$		−	1.14264e10i		−	1.35562i
$304$	2.19834e7	+	6.65469e6i	0.00257395	+	0.000779172i
$305$	2.30423e8			0.0266273
$306$	9.21487e8	−	1.09819e9i	0.105100	−	0.125254i
$307$	−7.18808e7	−	1.97491e8i	−0.00809206	−	0.0222328i	0.935581	−	0.353113i	$-0.114877\pi$
$307$	−7.18808e7	−	1.97491e8i	−0.00809206	−	0.0222328i	−0.943673	+	0.330880i	$0.892655\pi$
$308$	−8.08870e8	−	4.58733e9i	−0.0898827	−	0.509750i
$309$	7.97485e8	−	4.52276e9i	0.0874760	−	0.496101i
$310$	1.31095e9	+	4.77147e8i	0.141951	+	0.0516661i
$311$	2.58268e9	+	4.47334e9i	0.276077	+	0.478179i	0.970406	−	0.241479i	$-0.0776323\pi$
$311$	2.58268e9	+	4.47334e9i	0.276077	+	0.478179i	−0.694330	+	0.719657i	$0.744299\pi$
$312$	6.80538e9	+	3.92909e9i	0.718182	+	0.414642i
$313$	2.64330e9	−	2.21799e9i	0.275403	−	0.231091i	−0.494616	−	0.869112i	$-0.664691\pi$
$313$	2.64330e9	−	2.21799e9i	0.275403	−	0.231091i	0.770019	+	0.638021i	$0.220247\pi$
$314$	−5.75927e9	−	6.86364e9i	−0.592447	−	0.706050i
$315$	4.64918e8	−	8.05262e8i	0.0472209	−	0.0817890i
$316$	5.70094e9	−	3.29144e9i	0.571739	−	0.330094i
$317$	2.00176e9	−	5.49979e9i	0.198232	−	0.544639i	−0.800253	−	0.599663i	$-0.795301\pi$
$317$	2.00176e9	−	5.49979e9i	0.198232	−	0.544639i	0.998485	+	0.0550240i	$0.0175235\pi$
$318$	−1.97595e9	−	3.48413e8i	−0.193227	−	0.0340711i
$319$	5.56059e9	−	9.80482e8i	0.536980	−	0.0946840i
$320$	−1.53251e9	+	5.57788e8i	−0.146151	+	0.0531948i
$321$	−4.18733e9	−	3.51359e9i	−0.394382	−	0.330926i
$322$			2.31145e9i			0.215011i
$323$	1.40166e9	+	5.99567e9i	0.128775	+	0.550843i
$324$	−2.13033e9			−0.193315
$325$	7.64121e9	−	9.10645e9i	0.684903	−	0.816235i
$326$	4.33706e9	+	1.19160e10i	0.383995	+	1.05502i
$327$	−4.31827e8	−	2.44901e9i	−0.0377675	−	0.214190i
$328$	3.00779e8	−	1.70580e9i	0.0259867	−	0.147378i
$329$	3.68334e9	+	1.34063e9i	0.314383	+	0.114426i
$330$	7.07628e8	+	1.22565e9i	0.0596691	+	0.103350i
$331$	1.21740e9	+	7.02864e8i	0.101419	+	0.0585544i	0.549852	−	0.835262i	$-0.314684\pi$
$331$	1.21740e9	+	7.02864e8i	0.101419	+	0.0585544i	−0.448433	+	0.893817i	$0.648018\pi$
$332$	−7.63212e9	+	6.40411e9i	−0.628193	+	0.527116i
$333$	−1.80572e9	−	2.15198e9i	−0.146850	−	0.175009i
$334$	3.74320e9	−	6.48341e9i	0.300786	−	0.520976i
$335$	4.60496e9	−	2.65867e9i	0.365634	−	0.211099i
$336$	6.81318e6	−	1.87190e7i	0.000534555	−	0.00146868i
$337$	−7.71739e9	−	1.36078e9i	−0.598344	−	0.105504i	−0.133731	−	0.991018i	$-0.542696\pi$
$337$	−7.71739e9	−	1.36078e9i	−0.598344	−	0.105504i	−0.464614	+	0.885514i	$0.653807\pi$
$338$	2.34646e9	−	4.13744e8i	0.179782	−	0.0317004i
$339$	−5.66594e9	+	2.06223e9i	−0.429015	+	0.156149i
$340$	9.07057e8	+	7.61111e8i	0.0678764	+	0.0569551i
$341$			1.37232e10i			1.01493i
$342$	2.37096e9	−	3.16452e9i	0.173309	−	0.231315i
$343$	−1.50558e10			−1.08775
$344$	−1.05661e10	+	1.25922e10i	−0.754537	+	0.899223i
$345$	3.90628e8	+	1.07324e9i	0.0275732	+	0.0757567i
$346$	2.41686e9	+	1.37067e10i	0.168635	+	0.956374i
$347$	−3.04023e9	+	1.72420e10i	−0.209695	+	1.18924i	0.680183	+	0.733042i	$0.261900\pi$
$347$	−3.04023e9	+	1.72420e10i	−0.209695	+	1.18924i	−0.889878	+	0.456198i	$0.849211\pi$
$348$	3.23532e9	+	1.17756e9i	0.220597	+	0.0802909i
$349$	−1.25823e10	−	2.17932e10i	−0.848123	−	1.46899i	−0.882881	−	0.469597i	$-0.844399\pi$
$349$	−1.25823e10	−	2.17932e10i	−0.848123	−	1.46899i	0.0347575	−	0.999396i	$-0.488934\pi$
$350$	5.98312e9	+	3.45436e9i	0.398709	+	0.230195i
$351$	−1.41708e10	+	1.18907e10i	−0.933612	+	0.783394i
$352$	−1.03570e10	−	1.23430e10i	−0.674626	−	0.803988i
$353$	5.59113e9	−	9.68412e9i	0.360082	−	0.623679i	−0.627892	−	0.778300i	$-0.716082\pi$
$353$	5.59113e9	−	9.68412e9i	0.360082	−	0.623679i	0.987974	+	0.154621i	$0.0494155\pi$
$354$	−9.55551e9	+	5.51688e9i	−0.608472	+	0.351302i
$355$	−1.37440e9	+	3.77614e9i	−0.0865367	+	0.237758i
$356$	−2.71492e9	−	4.78713e8i	−0.169027	−	0.0298041i
$357$	5.25906e9	−	9.27315e8i	0.323769	−	0.0570892i
$358$	5.96676e9	−	2.17172e9i	0.363251	−	0.132212i
$359$	2.01223e10	+	1.68846e10i	1.21144	+	1.01652i	0.999228	+	0.0392907i	$0.0125098\pi$
$359$	2.01223e10	+	1.68846e10i	1.21144	+	1.01652i	0.212208	+	0.977225i	$0.431935\pi$
$360$		−	1.98838e9i		−	0.118383i
$361$	4.77138e9	+	1.62995e10i	0.280941	+	0.959725i
$362$	1.03306e10			0.601575
$363$	−8.11277e8	+	9.66843e8i	−0.0467243	+	0.0556839i
$364$	−3.37367e9	−	9.26909e9i	−0.192175	−	0.527997i
$365$	6.75306e8	+	3.82985e9i	0.0380478	+	0.215780i
$366$	1.47575e8	−	8.36937e8i	0.00822408	−	0.0466411i
$367$	3.63871e9	+	1.32438e9i	0.200578	+	0.0730045i	0.440356	−	0.897823i	$-0.354852\pi$
$367$	3.63871e9	+	1.32438e9i	0.200578	+	0.0730045i	−0.239778	+	0.970828i	$0.577075\pi$
$368$	−1.07801e7	−	1.86716e7i	−0.000587800	−	0.00101810i
$369$	1.12643e9	+	6.50345e8i	0.0607574	+	0.0350783i
$370$	−1.09294e9	+	9.17085e8i	−0.0583162	+	0.0489331i
$371$	4.23326e9	+	5.04500e9i	0.223449	+	0.266296i
$372$	−4.18395e9	+	7.24681e9i	−0.218481	+	0.378421i
$373$	1.23184e10	−	7.11205e9i	0.636386	−	0.367417i	−0.146835	−	0.989161i	$-0.546909\pi$
$373$	1.23184e10	−	7.11205e9i	0.636386	−	0.367417i	0.783221	+	0.621744i	$0.213575\pi$
$374$	2.44954e9	−	6.73007e9i	0.125198	−	0.343980i
$375$	6.95346e9	+	1.22608e9i	0.351622	+	0.0620004i
$376$	8.25469e9	−	1.45553e9i	0.413000	−	0.0728230i
$377$	1.12356e10	−	4.08944e9i	0.556202	−	0.202441i
$378$	−8.23564e9	−	6.91053e9i	−0.403395	−	0.338489i
$379$		−	5.42970e9i		−	0.263159i	−0.991306	−	0.131580i	$-0.957995\pi$
$379$		−	5.42970e9i		−	0.263159i	0.991306	−	0.131580i	$-0.0420049\pi$
$380$	2.61376e9	+	1.95832e9i	0.125352	+	0.0939181i
$381$	−2.32863e10			−1.10510
$382$	−7.62156e7	+	9.08302e7i	−0.00357924	+	0.00426557i
$383$	−2.86103e9	−	7.86062e9i	−0.132962	−	0.365310i	0.855289	−	0.518152i	$-0.173380\pi$
$383$	−2.86103e9	−	7.86062e9i	−0.132962	−	0.365310i	−0.988251	+	0.152842i	$0.951158\pi$
$384$	−1.71065e9	−	9.70156e9i	−0.0786747	−	0.446187i
$385$	8.06657e8	−	4.57478e9i	0.0367152	−	0.208222i
$386$	−2.51404e10	−	9.15035e9i	−1.13246	−	0.412181i
$387$	−6.17184e9	−	1.06899e10i	−0.275151	−	0.476575i
$388$	−6.41089e9	−	3.70133e9i	−0.282873	−	0.163317i
$389$	3.32031e10	−	2.78607e10i	1.45004	−	1.21673i	0.517488	−	0.855691i	$-0.326867\pi$
$389$	3.32031e10	−	2.78607e10i	1.45004	−	1.21673i	0.932551	−	0.361037i	$-0.117577\pi$
$390$	1.92640e9	+	2.29579e9i	0.0832697	+	0.0992370i
$391$	2.88988e9	−	5.00542e9i	0.123644	−	0.214158i
$392$	−7.45019e9	+	4.30137e9i	−0.315517	+	0.182164i
$393$	8.78823e9	−	2.41455e10i	0.368410	−	1.01220i
$394$	−2.23137e10	−	3.93451e9i	−0.925950	−	0.163270i
$395$	6.46513e9	−	1.13998e9i	0.265576	−	0.0468282i
$396$	7.02886e9	−	2.55830e9i	0.285828	−	0.104033i
$397$	4.18159e9	+	3.50877e9i	0.168337	+	0.141251i	0.723064	−	0.690781i	$-0.242733\pi$
$397$	4.18159e9	+	3.50877e9i	0.168337	+	0.141251i	−0.554727	+	0.832032i	$0.687177\pi$
$398$		−	3.88129e9i		−	0.154684i
$399$	1.43429e10	−	3.35307e9i	0.565909	−	0.132297i
$400$	−6.44413e7			−0.00251724
$401$	−1.22345e10	+	1.45806e10i	−0.473162	+	0.563893i	−0.948852	−	0.315720i	$-0.897754\pi$
$401$	−1.22345e10	+	1.45806e10i	−0.473162	+	0.563893i	0.475690	+	0.879613i	$0.342198\pi$
$402$	−6.70752e9	−	1.84288e10i	−0.256837	−	0.705654i
$403$	5.04623e9	+	2.86186e10i	0.191314	+	1.08500i
$404$	−5.32602e9	+	3.02054e10i	−0.199930	+	1.13386i
$405$	−1.99637e9	−	7.26621e8i	−0.0742030	−	0.0270077i
$406$	3.47444e9	+	6.01790e9i	0.127873	+	0.221483i
$407$	−1.21542e10	−	7.01723e9i	−0.442944	−	0.255734i
$408$	8.74790e9	−	7.34036e9i	0.315692	−	0.264897i
$409$	8.57889e9	+	1.02239e10i	0.306576	+	0.365363i	0.897231	−	0.441561i	$-0.145575\pi$
$409$	8.57889e9	+	1.02239e10i	0.306576	+	0.365363i	−0.590655	+	0.806924i	$0.701131\pi$
$410$	3.30295e8	−	5.72088e8i	0.0116887	−	0.0202455i
$411$	5.52998e9	−	3.19274e9i	0.193801	−	0.111891i
$412$	−4.21625e9	+	1.15841e10i	−0.146331	+	0.402042i
$413$	3.56663e10	+	6.28893e9i	1.22591	+	0.216161i
$414$	−3.65533e9	+	6.44533e8i	−0.124430	+	0.0219404i
$415$	−9.33656e9	+	3.39823e9i	−0.314771	+	0.114567i
$416$	−2.61374e10	−	2.19319e10i	−0.872750	−	0.732324i
$417$			1.26948e10i			0.419838i
$418$	5.72352e9	−	1.89074e10i	0.187481	−	0.619335i
$419$	−6.66640e9			−0.216290			−0.108145	−	0.994135i	$-0.534491\pi$
$419$	−6.66640e9			−0.216290			−0.108145	+	0.994135i	$0.534491\pi$
$420$	1.82074e9	−	2.16988e9i	0.0585128	−	0.0697329i
$421$	−8.49495e9	−	2.33397e10i	−0.270416	−	0.742962i	−0.998356	−	0.0573207i	$-0.981744\pi$
$421$	−8.49495e9	−	2.33397e10i	−0.270416	−	0.742962i	0.727940	−	0.685641i	$-0.240478\pi$
$422$	5.65765e9	+	3.20861e10i	0.178396	+	1.01174i
$423$	−1.09299e9	+	6.19867e9i	−0.0341394	+	0.193614i
$424$	1.32338e10	+	4.81673e9i	0.409471	+	0.149035i
$425$	−8.63760e9	−	1.49608e10i	−0.264751	−	0.458562i
$426$	1.28354e10	+	7.41050e9i	0.389735	+	0.225014i
$427$	−2.13687e9	+	1.79305e9i	−0.0642787	+	0.0539362i
$428$	9.43133e9	+	1.12398e10i	0.281059	+	0.334953i
$429$	−1.47401e10	+	2.55307e10i	−0.435183	+	0.753760i
$430$	−5.42917e9	+	3.13453e9i	−0.158803	+	0.0916852i
$431$	−2.47738e9	+	6.80655e9i	−0.0717933	+	0.197251i	−0.970399	−	0.241506i	$-0.922359\pi$
$431$	−2.47738e9	+	6.80655e9i	−0.0717933	+	0.197251i	0.898606	+	0.438756i	$0.144581\pi$
$432$	9.87556e7	+	1.74133e7i	0.00283548	+	0.000499972i
$433$	−8.85628e9	+	1.56160e9i	−0.251942	+	0.0444241i	−0.298193	−	0.954506i	$-0.596384\pi$
$433$	−8.85628e9	+	1.56160e9i	−0.251942	+	0.0444241i	0.0462509	+	0.998930i	$0.485273\pi$
$434$	−1.58703e10	+	5.77632e9i	−0.447328	+	0.162814i
$435$	2.63024e9	+	2.20703e9i	0.0734579	+	0.0616385i
$436$			6.67517e9i			0.184721i
$437$	7.19832e9	−	1.42245e10i	0.197381	−	0.390041i
$438$	1.43432e10			0.389717
$439$	−4.37901e10	+	5.21870e10i	−1.17901	+	1.40509i	−0.284130	+	0.958786i	$0.591705\pi$
$439$	−4.37901e10	+	5.21870e10i	−1.17901	+	1.40509i	−0.894881	+	0.446304i	$0.852740\pi$
$440$	−3.39753e9	−	9.33464e9i	−0.0906468	−	0.249050i
$441$	−1.12177e9	−	6.36189e9i	−0.0296586	−	0.168202i
$442$	2.63358e9	−	1.49358e10i	0.0690014	−	0.391326i
$443$	−1.43389e10	−	5.21895e9i	−0.372308	−	0.135509i	0.149088	−	0.988824i	$-0.452366\pi$
$443$	−1.43389e10	−	5.21895e9i	−0.372308	−	0.135509i	−0.521396	+	0.853315i	$0.674588\pi$
$444$	−4.27886e9	−	7.41120e9i	−0.110102	−	0.190703i
$445$	−2.38093e9	−	1.37463e9i	−0.0607164	−	0.0350546i
$446$	−1.46789e10	+	1.23170e10i	−0.370982	+	0.311291i
$447$	3.12627e10	+	3.72575e10i	0.783063	+	0.933219i
$448$	9.87157e9	−	1.70981e10i	0.245061	−	0.424458i
$449$	4.06876e10	−	2.34910e10i	1.00110	−	0.577984i	0.0925250	−	0.995710i	$-0.470506\pi$
$449$	4.06876e10	−	2.34910e10i	1.00110	−	0.577984i	0.908573	+	0.417726i	$0.137173\pi$
$450$	−3.79437e9	+	1.04249e10i	−0.0925315	+	0.254228i
$451$	6.39937e9	+	1.12838e9i	0.154679	+	0.0272741i
$452$	1.59390e10	−	2.81047e9i	0.381862	−	0.0673325i
$453$	9.57328e7	−	3.48439e7i	0.00227336	−	0.000827435i
$454$	2.60920e10	+	2.18938e10i	0.614163	+	0.515344i
$455$		−	9.83697e9i		−	0.229517i
$456$	2.29769e10	−	2.15453e10i	0.531414	−	0.498302i
$457$	−5.93483e10			−1.36064			−0.680321	−	0.732915i	$-0.738159\pi$
$457$	−5.93483e10			−1.36064			−0.680321	+	0.732915i	$0.738159\pi$
$458$	−2.72398e10	+	3.24631e10i	−0.619073	+	0.737783i
$459$	9.19435e9	+	2.52613e10i	0.207143	+	0.569121i
$460$	−5.32358e8	−	3.01915e9i	−0.0118898	−	0.0674301i
$461$	1.33730e10	−	7.58422e10i	0.296092	−	1.67922i	−0.366641	−	0.930362i	$-0.619492\pi$
$461$	1.33730e10	−	7.58422e10i	0.296092	−	1.67922i	0.662733	−	0.748856i	$-0.269397\pi$
$462$	−1.60998e10	−	5.85984e9i	−0.353388	−	0.128623i
$463$	−2.64452e9	−	4.58045e9i	−0.0575471	−	0.0996745i	0.835817	−	0.549009i	$-0.184995\pi$
$463$	−2.64452e9	−	4.58045e9i	−0.0575471	−	0.0996745i	−0.893364	+	0.449334i	$0.851661\pi$
$464$	−5.61322e7	−	3.24079e7i	−0.00121099	−	0.000699164i
$465$	−6.39264e9	+	5.36406e9i	−0.136731	+	0.114731i
$466$	3.52535e10	+	4.20135e10i	0.747581	+	0.890933i
$467$	−2.86234e10	+	4.95772e10i	−0.601802	+	1.04235i	0.390746	+	0.920499i	$0.372217\pi$
$467$	−2.86234e10	+	4.95772e10i	−0.601802	+	1.04235i	−0.992548	+	0.121854i	$0.961116\pi$
$468$	1.37174e10	−	7.91976e9i	0.285949	−	0.165093i
$469$	−2.20164e10	+	6.04894e10i	−0.455045	+	1.25022i
$470$	3.14816e9	+	5.55106e8i	0.0645157	+	0.0113759i
$471$	5.27810e10	−	9.30671e9i	1.07249	−	0.189109i
$472$	7.27756e10	−	2.64881e10i	1.46628	−	0.533683i
$473$	−4.72401e10	−	3.96391e10i	−0.943769	−	0.791917i
$474$		−	2.42126e10i		−	0.479654i
$475$	−2.60621e10	−	3.98905e10i	−0.511958	−	0.783601i
$476$	−1.43344e10			−0.279223
$477$	−6.79775e9	+	8.10124e9i	−0.131308	+	0.156487i
$478$	7.39703e9	+	2.03232e10i	0.141692	+	0.389296i
$479$	−3.78960e9	−	2.14919e10i	−0.0719866	−	0.408256i	−0.999413	−	0.0342513i	$-0.989095\pi$
$479$	−3.78960e9	−	2.14919e10i	−0.0719866	−	0.408256i	0.927427	−	0.374005i	$-0.122016\pi$
$480$	1.70141e9	−	9.64917e9i	0.0320512	−	0.181771i
$481$	−2.79270e10	−	1.01646e10i	−0.521728	−	0.189893i
$482$	−2.04960e10	−	3.55001e10i	−0.379735	−	0.657720i
$483$	−1.19740e10	−	6.91322e9i	−0.220015	−	0.127026i
$484$	2.59524e9	−	2.17767e9i	0.0472930	−	0.0396835i
$485$	−4.74532e9	−	5.65525e9i	−0.0857626	−	0.102208i
$486$	1.45102e10	−	2.51325e10i	0.260093	−	0.450495i
$487$	3.17425e10	−	1.83265e10i	0.564319	−	0.325810i	−0.190558	−	0.981676i	$-0.561030\pi$
$487$	3.17425e10	−	1.83265e10i	0.564319	−	0.325810i	0.754877	+	0.655866i	$0.227696\pi$
$488$	−2.04018e9	+	5.60536e9i	−0.0359741	+	0.0988381i
$489$	−7.47001e10	−	1.31716e10i	−1.30643	−	0.230359i
$490$	−3.23106e9	+	5.69722e8i	−0.0560480	+	0.00988277i
$491$	3.62281e9	−	1.31860e9i	0.0623333	−	0.0226875i	−0.310665	−	0.950519i	$-0.600552\pi$
$491$	3.62281e9	−	1.31860e9i	0.0623333	−	0.0226875i	0.372999	+	0.927832i	$0.378330\pi$
$492$	3.03531e9	+	2.54692e9i	0.0518015	+	0.0434666i
$493$		−	1.73756e10i		−	0.294139i
$494$	4.98342e9	−	4.15345e10i	0.0836797	−	0.697431i
$495$	7.45949e9			0.124248
$496$	1.01259e8	−	1.20676e8i	0.00167304	−	0.00199385i
$497$	−1.66384e10	−	4.57137e10i	−0.272701	−	0.749240i
$498$	6.36337e9	+	3.60885e10i	0.103459	+	0.586747i
$499$	8.26292e9	−	4.68613e10i	0.133270	−	0.755810i	−0.842779	−	0.538259i	$-0.819082\pi$
$499$	8.26292e9	−	4.68613e10i	0.133270	−	0.755810i	0.976049	−	0.217551i	$-0.0698067\pi$
$500$	−1.78097e10	−	6.48222e9i	−0.284956	−	0.103715i
$501$	2.23908e10	+	3.87819e10i	0.355400	+	0.615572i
$502$	5.46355e10	+	3.15438e10i	0.860320	+	0.496706i
$503$	3.26084e10	−	2.73617e10i	0.509398	−	0.427435i	−0.351519	−	0.936181i	$-0.614335\pi$
$503$	3.26084e10	−	2.73617e10i	0.509398	−	0.427435i	0.860917	+	0.508745i	$0.169890\pi$
$504$	1.54727e10	+	1.84396e10i	0.239797	+	0.285779i
$505$	−1.52937e10	+	2.64895e10i	−0.235151	+	0.407293i
$506$	−1.60590e10	+	9.27165e9i	−0.244972	+	0.141434i
$507$	−4.87460e9	+	1.33929e10i	−0.0737747	+	0.202694i
$508$	6.15567e10	+	1.08541e10i	0.924316	+	0.162982i
$509$	8.92118e10	−	1.57305e10i	1.32908	−	0.234353i	0.536386	−	0.843973i	$-0.319789\pi$
$509$	8.92118e10	−	1.57305e10i	1.32908	−	0.234353i	0.792694	+	0.609620i	$0.208678\pi$
$510$	4.09253e9	−	1.48956e9i	0.0604938	−	0.0220180i
$511$	−3.60648e10	−	3.02619e10i	−0.528932	−	0.443827i
$512$			3.69614e8i			0.00537859i
$513$	2.91607e10	+	6.81743e10i	0.421044	+	0.984353i
$514$	−9.40618e9			−0.134760
$515$	−7.90228e9	+	9.41757e9i	−0.112337	+	0.133878i
$516$	−1.28609e10	−	3.53350e10i	−0.181414	−	0.498432i
$517$	5.46046e9	+	3.09678e10i	0.0764306	+	0.433459i
$518$	2.99924e9	−	1.70095e10i	0.0416574	−	0.236251i
$519$	−7.82335e10	−	2.84746e10i	−1.07826	−	0.392454i
$520$	−1.05178e10	−	1.82173e10i	−0.143850	−	0.249156i
$521$	−8.09224e10	−	4.67206e10i	−1.09829	−	0.634100i	−0.162521	−	0.986705i	$-0.551962\pi$
$521$	−8.09224e10	−	4.67206e10i	−1.09829	−	0.634100i	−0.935772	+	0.352606i	$0.885296\pi$
$522$	−8.54789e9	+	7.17254e9i	−0.115127	+	0.0966030i
$523$	8.44723e10	+	1.00670e11i	1.12904	+	1.34553i	0.930864	+	0.365365i	$0.119056\pi$
$523$	8.44723e10	+	1.00670e11i	1.12904	+	1.34553i	0.198171	+	0.980167i	$0.436500\pi$
$524$	−3.44860e10	+	5.97314e10i	−0.457422	+	0.792278i
$525$	−3.57894e10	+	2.06630e10i	−0.471104	+	0.271992i
$526$	1.04447e9	−	2.86965e9i	0.0136443	−	0.0374875i
$527$	4.15888e10	+	7.33323e9i	0.539180	+	0.0950720i
$528$	1.57381e8	−	2.77505e7i	0.00202496	−	0.000357055i
$529$	5.95262e10	−	2.16658e10i	0.760126	−	0.276663i
$530$	4.11443e9	+	3.45242e9i	0.0521443	+	0.0437542i
$531$			5.81564e10i			0.731508i
$532$	−3.94780e10	+	2.17827e9i	−0.492843	+	0.0271935i
$533$	1.37603e10			0.170498
$534$	−6.51776e9	+	7.76756e9i	−0.0801555	+	0.0955256i
$535$	5.00457e9	+	1.37500e10i	0.0610874	+	0.167836i
$536$	2.39033e10	+	1.35562e11i	0.289600	+	1.64240i
$537$	−6.59551e9	+	3.74050e10i	−0.0793143	+	0.449814i
$538$	−5.34403e10	−	1.94507e10i	−0.637881	−	0.232170i
$539$	−1.61368e10	−	2.79497e10i	−0.191188	−	0.331148i
$540$	1.23488e10	+	7.12957e9i	0.145227	+	0.0838471i
$541$	3.50608e10	−	2.94195e10i	0.409292	−	0.343437i	−0.414780	−	0.909922i	$-0.636142\pi$
$541$	3.50608e10	−	2.94195e10i	0.409292	−	0.343437i	0.824072	+	0.566485i	$0.191697\pi$
$542$	−5.75417e10	−	6.85756e10i	−0.666785	−	0.794644i
$543$	−3.08973e10	+	5.35156e10i	−0.355403	+	0.615575i
$544$	−4.29406e10	+	2.47917e10i	−0.490311	+	0.283081i
$545$	−2.27679e9	+	6.25544e9i	−0.0258070	+	0.0709042i
$546$	−3.57296e10	−	6.30009e9i	−0.402029	−	0.0708886i
$547$	1.23069e10	−	2.17003e9i	0.137467	−	0.0242391i	−0.104491	−	0.994526i	$-0.533321\pi$
$547$	1.23069e10	−	2.17003e9i	0.137467	−	0.0242391i	0.241958	+	0.970287i	$0.422210\pi$
$548$	−1.61065e10	+	5.86229e9i	−0.178599	+	0.0650048i
$549$	−3.43138e9	−	2.87927e9i	−0.0377729	−	0.0316952i
$550$			5.54243e10i			0.605688i
$551$	−2.64042e9	−	4.78538e10i	−0.0286462	−	0.519170i
$552$	−2.95667e10			−0.318454
$553$	−5.10848e10	+	6.08805e10i	−0.546250	+	0.650995i
$554$	−4.06603e9	−	1.11713e10i	−0.0431650	−	0.118595i
$555$	−1.48197e9	−	8.40465e9i	−0.0156195	−	0.0885824i
$556$	5.91723e9	−	3.35583e10i	0.0619183	−	0.351156i
$557$	1.07751e11	+	3.92183e10i	1.11944	+	0.407444i	0.834449	−	0.551086i	$-0.185786\pi$
$557$	1.07751e11	+	3.92183e10i	1.11944	+	0.407444i	0.284993	+	0.958529i	$0.408009\pi$
$558$	−1.35600e10	−	2.34866e10i	−0.139870	−	0.242261i
$559$	−1.13091e11	−	6.52934e10i	−1.15820	−	0.668686i
$560$	−4.08493e7	+	3.42766e7i	−0.000415367	+	0.000348534i
$561$	2.75377e10	+	3.28181e10i	0.278020	+	0.331331i
$562$	5.58945e10	−	9.68122e10i	0.560304	−	0.970476i
$563$	2.85552e10	−	1.64863e10i	0.284218	−	0.164093i	−0.351114	−	0.936333i	$-0.614197\pi$
$563$	2.85552e10	−	1.64863e10i	0.284218	−	0.164093i	0.635331	+	0.772240i	$0.280864\pi$
$564$	−6.55802e9	+	1.80180e10i	−0.0648122	+	0.178070i
$565$	1.58953e10	+	2.80278e9i	0.155982	+	0.0275039i
$566$	8.24148e9	−	1.45320e9i	0.0803044	−	0.0141598i
$567$	2.41680e10	−	8.79643e9i	0.233834	−	0.0851088i
$568$	−7.96907e10	−	6.68685e10i	−0.765622	−	0.642433i
$569$			1.26359e11i			1.20547i	0.797942	+	0.602734i	$0.205922\pi$
$569$			1.26359e11i			1.20547i	−0.797942	+	0.602734i	$0.794078\pi$
$570$	1.10448e10	−	4.72426e9i	0.104630	−	0.0447543i
$571$	1.11695e11			1.05073			0.525363	−	0.850878i	$-0.323929\pi$
$571$	1.11695e11			1.05073			0.525363	+	0.850878i	$0.323929\pi$
$572$	5.08653e10	−	6.06189e10i	0.475157	−	0.566270i
$573$	−2.42579e8	−	6.66481e8i	−0.00225027	−	0.00618257i
$574$	1.38868e9	+	7.87558e9i	0.0127925	+	0.0725496i
$575$	−7.76688e9	+	4.40482e10i	−0.0710518	+	0.402955i
$576$	2.97915e10	+	1.08432e10i	0.270647	+	0.0985073i
$577$	−2.91636e10	−	5.05128e10i	−0.263110	−	0.455720i	0.703957	−	0.710243i	$-0.251415\pi$
$577$	−2.91636e10	−	5.05128e10i	−0.263110	−	0.455720i	−0.967067	+	0.254523i	$0.918082\pi$
$578$	4.05575e10	+	2.34159e10i	0.363379	+	0.209797i
$579$	1.22593e11	−	1.02868e11i	1.09082	−	0.915303i
$580$	−5.92422e9	−	7.06022e9i	−0.0523503	−	0.0623887i
$581$	6.01409e10	−	1.04167e11i	0.527795	−	0.914168i
$582$	−2.35800e10	+	1.36139e10i	−0.205519	+	0.118656i
$583$	−1.80701e10	+	4.96473e10i	−0.156418	+	0.429755i
$584$	−9.91457e10	−	1.74821e10i	−0.852359	−	0.150294i
$585$	1.55562e10	−	2.74298e9i	0.132825	−	0.0234206i
$586$	2.39241e10	−	8.70767e9i	0.202883	−	0.0738434i
$587$	−1.07148e11	−	8.99075e10i	−0.902464	−	0.757257i	0.0682062	−	0.997671i	$-0.478272\pi$
$587$	−1.07148e11	−	8.99075e10i	−0.902464	−	0.757257i	−0.970670	+	0.240414i	$0.922717\pi$
$588$		−	1.96793e10i		−	0.164626i
$589$	1.15653e11	+	1.38764e10i	0.960939	+	0.115296i
$590$	2.95363e10			0.243752
$591$	8.71193e10	−	1.03825e11i	0.714109	−	0.851041i
$592$	5.51010e7	+	1.51389e8i	0.000448614	+	0.00123256i
$593$	1.18719e10	+	6.73289e10i	0.0960067	+	0.544481i	0.994434	+	0.105359i	$0.0335993\pi$
$593$	1.18719e10	+	6.73289e10i	0.0960067	+	0.544481i	−0.898427	+	0.439122i	$0.855290\pi$
$594$	1.49767e10	−	8.49372e10i	0.120301	−	0.682263i
$595$	−1.34331e10	−	4.88924e9i	−0.107178	−	0.0390097i
$596$	−6.52758e10	−	1.13061e11i	−0.517329	−	0.896040i
$597$	2.01063e10	+	1.16084e10i	0.158283	+	0.0913850i
$598$	−3.00804e10	+	2.52405e10i	−0.235223	+	0.197375i
$599$	−4.68384e10	−	5.58198e10i	−0.363827	−	0.433592i	0.552814	−	0.833305i	$-0.313554\pi$
$599$	−4.68384e10	−	5.58198e10i	−0.363827	−	0.433592i	−0.916640	+	0.399713i	$0.869110\pi$
$600$	−4.41862e10	+	7.65327e10i	−0.340943	+	0.590530i
$601$	7.04334e9	−	4.06647e9i	0.0539859	−	0.0311688i	−0.472764	−	0.881189i	$-0.656744\pi$
$601$	7.04334e9	−	4.06647e9i	0.0539859	−	0.0311688i	0.526750	+	0.850020i	$0.323410\pi$
$602$	2.59569e10	−	7.13161e10i	0.197637	−	0.543002i
$603$	−1.01797e11	−	1.79496e10i	−0.769957	−	0.135764i
$604$	−2.69308e8	+	4.74862e7i	−0.00202349	+	0.000356796i
$605$	3.17483e9	−	1.15554e9i	0.0236973	−	0.00862511i
$606$	8.64195e10	+	7.25146e10i	0.640798	+	0.537694i
$607$		−	6.51057e10i		−	0.479584i	−0.970824	−	0.239792i	$-0.922921\pi$
$607$		−	6.51057e10i		−	0.479584i	0.970824	−	0.239792i	$-0.0770792\pi$
$608$	−1.14494e11	+	7.48036e10i	−0.837855	+	0.547405i
$609$	−4.15662e10			−0.302184
$610$	−1.46232e9	+	1.74272e9i	−0.0105614	+	0.0125866i
$611$	2.27747e10	+	6.25731e10i	0.163414	+	0.448976i
$612$	−3.99706e9	−	2.26684e10i	−0.0284928	−	0.161590i
$613$	−8.63952e9	+	4.89971e10i	−0.0611854	+	0.347000i	0.938811	+	0.344432i	$0.111928\pi$
$613$	−8.63952e9	+	4.89971e10i	−0.0611854	+	0.347000i	−0.999997	+	0.00256767i	$0.999183\pi$
$614$	1.94982e9	+	7.09677e8i	0.0137190	+	0.00499329i
$615$	1.97573e9	+	3.42207e9i	0.0138111	+	0.0239215i
$616$	1.04146e11	+	6.01285e10i	0.723299	+	0.417597i
$617$	−1.34768e11	+	1.13084e11i	−0.929920	+	0.780295i	−0.975803	−	0.218652i	$-0.929834\pi$
$617$	−1.34768e11	+	1.13084e11i	−0.929920	+	0.780295i	0.0458833	+	0.998947i	$0.485390\pi$
$618$	2.91453e10	+	3.47340e10i	0.199808	+	0.238122i
$619$	−1.12696e10	+	1.95194e10i	−0.0767617	+	0.132955i	−0.901851	−	0.432047i	$-0.857791\pi$
$619$	−1.12696e10	+	1.95194e10i	−0.0767617	+	0.132955i	0.825089	+	0.565002i	$0.191125\pi$
$620$	1.93990e10	−	1.12000e10i	0.131284	−	0.0757970i
$621$	2.38053e10	−	6.54046e10i	0.160069	−	0.439787i
$622$	−5.02227e10	−	8.85562e9i	−0.335536	−	0.0591640i
$623$	3.27767e10	−	5.77942e9i	0.217577	−	0.0383647i
$624$	3.18002e8	−	1.15743e8i	0.00209745	−	0.000763408i
$625$	9.49315e10	+	7.96570e10i	0.622143	+	0.522040i
$626$			3.40675e10i			0.221842i
$627$	8.08279e10	+	8.61989e10i	0.522987	+	0.557740i
$628$	−1.43863e11			−0.924932
$629$	−2.77609e10	+	3.30842e10i	−0.177350	+	0.211358i
$630$	3.13983e9	+	8.62661e9i	0.0199317	+	0.0547618i
$631$	−4.59854e10	−	2.60796e11i	−0.290070	−	1.64507i	−0.686593	−	0.727042i	$-0.740895\pi$
$631$	−4.59854e10	−	2.60796e11i	−0.290070	−	1.64507i	0.396523	−	0.918025i	$-0.370217\pi$
$632$	−2.95113e10	+	1.67367e11i	−0.184978	+	1.04906i
$633$	−1.83138e11	−	6.66566e10i	−1.14068	−	0.415172i
$634$	2.88920e10	+	5.00424e10i	0.178822	+	0.309729i
$635$	5.39839e10	+	3.11676e10i	0.332024	+	0.191694i
$636$	−2.46789e10	+	2.07081e10i	−0.150833	+	0.126564i
$637$	−4.39295e10	−	5.23532e10i	−0.266808	−	0.317969i
$638$	−2.78732e10	+	4.82778e10i	−0.168230	+	0.291384i
$639$	6.76522e10	−	3.90590e10i	0.405769	−	0.234271i
$640$	−9.01932e9	+	2.47804e10i	−0.0537594	+	0.147703i
$641$	6.99752e10	+	1.23385e10i	0.414488	+	0.0730854i	0.377004	−	0.926212i	$-0.376954\pi$
$641$	6.99752e10	+	1.23385e10i	0.414488	+	0.0730854i	0.0374844	+	0.999297i	$0.488066\pi$
$642$	5.31474e10	−	9.37133e9i	0.312854	−	0.0551647i
$643$	−3.09057e11	+	1.12488e11i	−1.80799	+	0.658053i	−0.810616	+	0.585578i	$0.800868\pi$
$643$	−3.09057e11	+	1.12488e11i	−1.80799	+	0.658053i	−0.997370	+	0.0724758i	$0.976910\pi$
$644$	2.84306e10	+	2.38561e10i	0.165289	+	0.138694i
$645$		−	3.74998e10i		−	0.216666i
$646$	−5.42413e10	−	2.74490e10i	−0.311459	−	0.157614i
$647$	8.20167e10			0.468043			0.234021	−	0.972231i	$-0.424811\pi$
$647$	8.20167e10			0.468043			0.234021	+	0.972231i	$0.424811\pi$
$648$	3.53521e10	−	4.21310e10i	0.200500	−	0.238947i
$649$	9.93713e10	+	2.73020e11i	0.560121	+	1.53892i
$650$	2.03804e10	+	1.15583e11i	0.114172	+	0.647502i
$651$	1.75427e10	−	9.94893e10i	0.0976723	−	0.553927i
$652$	1.91328e11	+	6.96376e10i	1.05874	+	0.385348i
$653$	1.51540e11	+	2.62475e11i	0.833441	+	1.44356i	0.895293	+	0.445477i	$0.146966\pi$
$653$	1.51540e11	+	2.62475e11i	0.833441	+	1.44356i	−0.0618521	+	0.998085i	$0.519701\pi$
$654$	2.12627e10	+	1.22760e10i	0.116227	+	0.0671037i
$655$	−5.26910e10	+	4.42130e10i	−0.286267	+	0.240206i
$656$	−4.79474e7	−	5.71415e7i	−0.000258911	−	0.000308558i
$657$	3.77998e10	−	6.54713e10i	0.202875	−	0.351390i
$658$	−3.35147e10	+	1.93497e10i	−0.178785	+	0.103222i
$659$	2.93452e10	−	8.06253e10i	0.155595	−	0.427493i	−0.837262	−	0.546801i	$-0.815845\pi$
$659$	2.93452e10	−	8.06253e10i	0.155595	−	0.427493i	0.992857	+	0.119308i	$0.0380675\pi$
$660$	2.23787e10	+	3.94597e9i	0.117939	+	0.0207959i
$661$	−6.76815e9	+	1.19341e9i	−0.0354539	+	0.00625148i	−0.191347	−	0.981522i	$-0.561286\pi$
$661$	−6.76815e9	+	1.19341e9i	−0.0354539	+	0.00625148i	0.155893	+	0.987774i	$0.450174\pi$
$662$	−1.30417e10	+	4.74680e9i	−0.0679052	+	0.0247155i
$663$	6.94954e10	+	5.83136e10i	0.359668	+	0.301798i
$664$		−	2.57213e11i		−	1.32319i
$665$	−3.77387e10	−	1.14240e10i	−0.192974	−	0.0584161i
$666$	2.77352e10			0.140973
$667$	−2.89175e10	+	3.44625e10i	−0.146102	+	0.174118i
$668$	−4.11124e10	−	1.12955e11i	−0.206475	−	0.567285i
$669$	−1.99037e10	−	1.12880e11i	−0.0993642	−	0.563522i
$670$	−9.11618e9	+	5.17004e10i	−0.0452391	+	0.256564i
$671$	−2.10287e10	−	7.65383e9i	−0.103734	−	0.0377562i
$672$	5.93072e10	+	1.02723e11i	0.290824	+	0.503722i
$673$	−1.39011e11	−	8.02583e10i	−0.677627	−	0.391228i	0.121334	−	0.992612i	$-0.461283\pi$
$673$	−1.39011e11	−	8.02583e10i	−0.677627	−	0.391228i	−0.798960	+	0.601384i	$0.794616\pi$
$674$	5.92681e10	−	4.97319e10i	0.287198	−	0.240988i
$675$	−1.33722e11	−	1.59364e11i	−0.644151	−	0.767670i
$676$	1.91285e10	−	3.31315e10i	0.0915996	−	0.158655i
$677$	1.23155e11	−	7.11037e10i	0.586271	−	0.338484i	−0.177351	−	0.984148i	$-0.556753\pi$
$677$	1.23155e11	−	7.11037e10i	0.586271	−	0.338484i	0.763622	+	0.645664i	$0.223419\pi$
$678$	2.03604e10	−	5.59396e10i	0.0963533	−	0.264729i
$679$	8.80132e10	+	1.55191e10i	0.414065	+	0.0730109i
$680$	−3.01047e10	+	5.30827e9i	−0.140799	+	0.0248266i
$681$	−1.91454e11	+	6.96836e10i	−0.890177	+	0.323998i
$682$	−1.03790e11	−	8.70902e10i	−0.479754	−	0.402561i
$683$			1.54330e11i			0.709197i	0.935019	+	0.354598i	$0.115382\pi$
$683$			1.54330e11i			0.709197i	−0.935019	+	0.354598i	$0.884618\pi$
$684$	−1.44529e10	−	6.18232e10i	−0.0660285	−	0.282441i
$685$	−1.70933e10			−0.0776360
$686$	9.55477e10	−	1.13869e11i	0.431443	−	0.514174i
$687$	−8.66990e10	−	2.38204e11i	−0.389213	−	1.06935i
$688$	1.22925e8	+	6.97140e8i	0.000548637	+	0.00311147i
$689$	−1.94278e10	+	1.10180e11i	−0.0862077	+	0.488908i
$690$	−1.05961e10	−	3.85666e9i	−0.0467465	−	0.0170143i
$691$	−8.60381e10	−	1.49022e11i	−0.377380	−	0.653641i	0.613300	−	0.789850i	$-0.289841\pi$
$691$	−8.60381e10	−	1.49022e11i	−0.377380	−	0.653641i	−0.990680	+	0.136209i	$0.956508\pi$
$692$	1.93535e11	+	1.11738e11i	0.843986	+	0.487276i
$693$	−6.91770e10	+	5.80464e10i	−0.299936	+	0.251676i
$694$	−1.11110e11	−	1.32415e11i	−0.478976	−	0.570821i
$695$	1.69913e10	−	2.94299e10i	0.0728264	−	0.126139i
$696$	−7.69776e10	+	4.44430e10i	−0.328040	+	0.189394i
$697$	6.83925e9	−	1.87907e10i	0.0289786	−	0.0796181i
$698$	2.44675e11	+	4.31429e10i	1.03079	+	0.181755i
$699$	−3.23081e11	+	5.69679e10i	−1.35333	+	0.238628i
$700$	1.04239e11	−	3.79400e10i	0.434150	−	0.158018i
$701$	2.11603e11	+	1.77556e11i	0.876295	+	0.735299i	0.965414	−	0.260722i	$-0.0839607\pi$
$701$	2.11603e11	+	1.77556e11i	0.876295	+	0.735299i	−0.0891190	+	0.996021i	$0.528405\pi$
$702$		−	1.82637e11i		−	0.752039i
$703$	−7.14282e10	+	9.53350e10i	−0.292448	+	0.390329i
$704$	1.58387e11			0.644805
$705$	−1.22913e10	+	1.46482e10i	−0.0497556	+	0.0592965i
$706$	3.77598e10	+	1.03744e11i	0.151988	+	0.417585i
$707$	−6.43001e10	−	3.64664e11i	−0.257356	−	1.45954i
$708$	−3.07639e10	+	1.74471e11i	−0.122436	+	0.694368i
$709$	2.75763e11	+	1.00369e11i	1.09132	+	0.397207i	0.824109	−	0.566432i	$-0.191677\pi$
$709$	2.75763e11	+	1.00369e11i	1.09132	+	0.397207i	0.267208	+	0.963639i	$0.413899\pi$
$710$	−1.98372e10	−	3.43590e10i	−0.0780632	−	0.135209i
$711$	−1.10521e11	−	6.38095e10i	−0.432481	−	0.249693i
$712$	5.45207e10	−	4.57483e10i	0.212149	−	0.178014i
$713$	−7.02822e10	−	8.37591e10i	−0.271949	−	0.324096i
$714$	−2.63618e10	+	4.56599e10i	−0.101434	+	0.175688i
$715$	6.83431e10	−	3.94579e10i	0.261499	−	0.150977i
$716$	3.48700e10	−	9.58047e10i	0.132678	−	0.364531i
$717$	−1.27404e11	−	2.24648e10i	−0.482066	−	0.0850012i
$718$	−2.55402e11	+	4.50342e10i	−0.961005	+	0.169451i
$719$	9.49951e10	−	3.45754e10i	0.355456	−	0.129375i	−0.158119	−	0.987420i	$-0.550543\pi$
$719$	9.49951e10	−	3.45754e10i	0.355456	−	0.129375i	0.513575	+	0.858045i	$0.328321\pi$
$720$	−6.55956e7	−	5.50413e7i	−0.000244087	−	0.000204813i
$721$		−	1.48828e11i		−	0.550735i
$722$	−1.53556e11	−	6.73540e10i	−0.565090	−	0.247865i
$723$	2.45202e11			0.897369
$724$	1.06620e11	−	1.27065e11i	0.388048	−	0.462458i
$725$	4.59894e10	+	1.26355e11i	0.166459	+	0.457341i
$726$	−2.16381e9	−	1.22716e10i	−0.00778885	−	0.0441728i
$727$	−3.95089e9	+	2.24066e10i	−0.0141435	+	0.0802119i	−0.991063	−	0.133398i	$-0.957411\pi$
$727$	−3.95089e9	+	2.24066e10i	−0.0141435	+	0.0802119i	0.976919	+	0.213610i	$0.0685222\pi$
$728$	2.39298e11	+	8.70973e10i	0.851949	+	0.310084i
$729$	1.30881e11	+	2.26693e11i	0.463411	+	0.802652i
$730$	−3.32513e10	−	1.91977e10i	−0.117089	−	0.0676016i
$731$	−1.45372e11	+	1.21982e11i	−0.509110	+	0.427194i
$732$	−8.77116e9	−	1.04531e10i	−0.0305501	−	0.0364082i
$733$	1.79027e11	−	3.10083e11i	0.620157	−	1.07414i	−0.369299	−	0.929311i	$-0.620402\pi$
$733$	1.79027e11	−	3.10083e11i	0.620157	−	1.07414i	0.989456	−	0.144833i	$-0.0462644\pi$
$734$	−3.31086e10	+	1.91153e10i	−0.114066	+	0.0658561i
$735$	6.71229e9	−	1.84419e10i	0.0229996	−	0.0631910i
$736$	1.26428e11	+	2.22926e10i	0.430854	+	0.0759713i
$737$	−5.08566e11	+	8.96740e10i	−1.72376	+	0.303946i
$738$	−1.20672e10	+	4.39212e9i	−0.0406801	+	0.0148064i
$739$	2.97348e11	+	2.49504e11i	0.996980	+	0.836566i	0.986563	−	0.163380i	$-0.0522396\pi$
$739$	2.97348e11	+	2.49504e11i	0.996980	+	0.836566i	0.0104171	+	0.999946i	$0.496684\pi$
$740$			2.29082e10i			0.0763948i
$741$	2.00257e11	+	1.50039e11i	0.664225	+	0.497660i
$742$	−6.50212e10			−0.214506
$743$	−1.80926e11	+	2.15619e11i	−0.593671	+	0.707509i	−0.976307	−	0.216390i	$-0.930572\pi$
$743$	−1.80926e11	+	2.15619e11i	−0.593671	+	0.707509i	0.382636	+	0.923899i	$0.375016\pi$
$744$	−7.38873e10	−	2.03004e11i	−0.241145	−	0.662540i
$745$	−2.26080e10	−	1.28216e11i	−0.0733900	−	0.416216i
$746$	−2.43861e10	+	1.38301e11i	−0.0787386	+	0.446549i
$747$	1.81500e11	+	6.60606e10i	0.582900	+	0.212158i
$748$	−5.74979e10	−	9.95893e10i	−0.183673	−	0.318131i
$749$	−1.53407e11	−	8.85695e10i	−0.487436	−	0.281421i
$750$	−5.34012e10	+	4.48090e10i	−0.168774	+	0.141618i
$751$	5.76666e10	+	6.87244e10i	0.181286	+	0.216048i	0.849033	−	0.528340i	$-0.177185\pi$
$751$	5.76666e10	+	6.87244e10i	0.181286	+	0.216048i	−0.667747	+	0.744389i	$0.732741\pi$
$752$	1.80485e8	−	3.12609e8i	0.000564377	−	0.000977530i
$753$	−3.26814e11	+	1.88686e11i	−1.01653	+	0.586895i
$754$	−4.03749e10	+	1.10929e11i	−0.124918	+	0.343210i
$755$	−2.68571e8	−	4.73563e7i	−0.000826554	−	0.000145744i
$756$	−1.69998e11	+	2.99752e10i	−0.520423	+	0.0917646i
$757$	−7.22078e10	+	2.62815e10i	−0.219888	+	0.0800325i	−0.449615	−	0.893222i	$-0.648439\pi$
$757$	−7.22078e10	+	2.62815e10i	−0.219888	+	0.0800325i	0.229727	+	0.973255i	$0.426217\pi$
$758$	4.10655e10	+	3.44581e10i	0.124394	+	0.104379i
$759$		−	1.10921e11i		−	0.334230i
$760$	−8.21039e10	+	1.91941e10i	−0.246099	+	0.0575326i
$761$	−2.71807e11			−0.810441			−0.405220	−	0.914219i	$-0.632805\pi$
$761$	−2.71807e11			−0.810441			−0.405220	+	0.914219i	$0.632805\pi$
$762$	1.47780e11	−	1.76118e11i	0.438325	−	0.522376i
$763$	−2.75627e10	−	7.57280e10i	−0.0813250	−	0.223439i
$764$	3.30594e8	+	1.87489e9i	0.000970334	+	0.00550304i
$765$	3.98612e9	−	2.26064e10i	0.0116387	−	0.0660063i
$766$	7.76077e10	+	2.82469e10i	0.225419	+	0.0820457i
$767$	3.07625e11	+	5.32823e11i	0.888875	+	1.53958i
$768$	2.19299e11	+	1.26613e11i	0.630365	+	0.363942i
$769$	9.20816e10	−	7.72656e10i	0.263310	−	0.220943i	−0.501568	−	0.865118i	$-0.667243\pi$
$769$	9.20816e10	−	7.72656e10i	0.263310	−	0.220943i	0.764878	+	0.644175i	$0.222799\pi$
$770$	2.94804e10	+	3.51334e10i	0.0838631	+	0.0999442i
$771$	2.81325e10	−	4.87270e10i	0.0796143	−	0.137896i
$772$	−3.72019e11	+	2.14785e11i	−1.04736	+	0.604693i
$773$	4.30539e10	−	1.18290e11i	0.120585	−	0.331306i	−0.864684	−	0.502317i	$-0.832481\pi$
$773$	4.30539e10	−	1.18290e11i	0.120585	−	0.331306i	0.985269	+	0.171011i	$0.0547034\pi$
$774$	1.20017e11	+	2.11623e10i	0.334411	+	0.0589656i
$775$	−3.21842e11	+	5.67494e10i	−0.892146	+	0.157309i
$776$	1.79587e11	−	6.53644e10i	0.495255	−	0.180258i
$777$	7.91445e10	+	6.64101e10i	0.217138	+	0.182201i
$778$			4.27929e11i			1.16803i
$779$	1.59804e10	−	5.27903e10i	0.0433947	−	0.143352i
$780$	4.81201e10			0.130001
$781$	2.50860e11	−	2.98963e11i	0.674259	−	0.803550i
$782$	1.95168e10	+	5.36221e10i	0.0521894	+	0.143389i
$783$	−3.63348e10	−	2.06065e11i	−0.0966665	−	0.548223i
$784$	−6.43322e7	+	3.64846e8i	−0.000170280	+	0.000965707i
$785$	−1.34817e11	−	4.90693e10i	−0.355030	−	0.129221i
$786$	1.26843e11	+	2.19699e11i	0.332336	+	0.575623i
$787$	2.91767e11	+	1.68452e11i	0.760567	+	0.439114i	0.829499	−	0.558508i	$-0.188626\pi$
$787$	2.91767e11	+	1.68452e11i	0.760567	+	0.439114i	−0.0689321	+	0.997621i	$0.521959\pi$
$788$	−2.78691e11	+	2.33850e11i	−0.722800	+	0.606501i
$789$	1.17419e10	+	1.39934e10i	0.0302990	+	0.0361090i
$790$	−3.24074e10	+	5.61312e10i	−0.0832023	+	0.144111i
$791$	−1.69218e11	+	9.76983e10i	−0.432257	+	0.249563i
$792$	−6.60469e10	+	1.81462e11i	−0.167862	+	0.461197i
$793$	−4.66682e10	−	8.22887e9i	−0.118013	−	0.0208088i
$794$	−5.30746e10	+	9.35849e9i	−0.133538	+	0.0235463i
$795$	−3.01903e10	+	1.09884e10i	−0.0755787	+	0.0275084i
$796$	−4.77396e10	−	4.00583e10i	−0.118912	−	0.0997792i
$797$		−	3.66333e11i		−	0.907910i	−0.891025	−	0.453955i	$-0.850013\pi$
$797$		−	3.66333e11i		−	0.907910i	0.891025	−	0.453955i	$-0.149987\pi$
$798$	−6.56638e10	+	1.29757e11i	−0.161925	+	0.319977i
$799$	9.67676e10			0.237434
$800$	2.46644e11	−	2.93939e11i	0.602159	−	0.717625i
$801$	1.82792e10	+	5.02216e10i	0.0444044	+	0.122000i
$802$	−3.26316e10	−	1.85063e11i	−0.0788753	−	0.447324i
$803$	6.55847e10	−	3.71949e11i	0.157739	−	0.894584i
$804$	−2.95900e11	−	1.07699e11i	−0.708142	−	0.257743i
$805$	1.85060e10	+	3.20533e10i	0.0440686	+	0.0763290i
$806$	−2.48471e11	−	1.43455e11i	−0.588756	−	0.339918i
$807$	2.60593e11	−	2.18663e11i	0.614424	−	0.515563i
$808$	−5.08981e11	−	6.06580e11i	−1.19414	−	1.42312i
$809$	6.95785e10	−	1.20513e11i	0.162435	−	0.281346i	−0.773306	−	0.634033i	$-0.781398\pi$
$809$	6.95785e10	−	1.20513e11i	0.162435	−	0.281346i	0.935742	+	0.352686i	$0.114732\pi$
$810$	1.81650e10	−	1.04875e10i	0.0421983	−	0.0243632i
$811$	1.28214e11	−	3.52265e11i	0.296382	−	0.814303i	−0.698715	−	0.715400i	$-0.746244\pi$
$811$	1.28214e11	−	3.52265e11i	0.296382	−	0.814303i	0.995097	−	0.0989031i	$-0.0315334\pi$
$812$	1.09879e11	+	1.93746e10i	0.252749	+	0.0445665i
$813$	5.27343e11	−	9.29847e10i	1.20706	−	0.212838i
$814$	1.30206e11	−	4.73909e10i	0.296573	−	0.107944i
$815$	1.55545e11	+	1.30518e11i	0.352554	+	0.295828i
$816$		−	4.91781e8i		−	0.00110920i
$817$	−3.81830e11	+	3.58038e11i	−0.857001	+	0.803602i
$818$	−1.31768e11			−0.294305
$819$	−1.22919e11	+	1.46489e11i	−0.273201	+	0.325589i
$820$	−3.62771e9	−	9.96705e9i	−0.00802374	−	0.0220451i
$821$	−7.20761e10	−	4.08764e11i	−0.158642	−	0.899705i	−0.955380	−	0.295380i	$-0.904554\pi$
$821$	−7.20761e10	−	4.08764e11i	−0.158642	−	0.899705i	0.796738	−	0.604325i	$-0.206557\pi$
$822$	−1.09474e10	+	6.20858e10i	−0.0239786	+	0.135989i
$823$	4.81738e11	+	1.75338e11i	1.05005	+	0.382188i	0.808683	−	0.588245i	$-0.200181\pi$
$823$	4.81738e11	+	1.75338e11i	1.05005	+	0.382188i	0.241371	+	0.970433i	$0.422403\pi$
$824$	−1.59128e11	−	2.75618e11i	−0.345174	−	0.597859i
$825$	−2.87115e11	−	1.65766e11i	−0.619784	−	0.357833i
$826$	−2.73910e11	+	2.29838e11i	−0.588421	+	0.493744i
$827$	−3.48334e11	−	4.15128e11i	−0.744686	−	0.887482i	0.252091	−	0.967704i	$-0.418882\pi$
$827$	−3.48334e11	−	4.15128e11i	−0.744686	−	0.887482i	−0.996777	+	0.0802213i	$0.974437\pi$
$828$	−2.97984e10	+	5.16124e10i	−0.0633975	+	0.109808i
$829$	4.90457e11	−	2.83165e11i	1.03844	−	0.599545i	0.119051	−	0.992888i	$-0.462015\pi$
$829$	4.90457e11	−	2.83165e11i	1.03844	−	0.599545i	0.919392	+	0.393343i	$0.128681\pi$
$830$	3.35506e10	−	9.21796e10i	0.0706950	−	0.194233i
$831$	7.00319e10	+	1.23485e10i	0.146856	+	0.0258947i
$832$	3.30303e11	−	5.82414e10i	0.689318	−	0.121545i
$833$	−9.33261e10	+	3.39679e10i	−0.193831	+	0.0705487i
$834$	−9.60124e10	−	8.05640e10i	−0.198455	−	0.166524i
$835$		−	1.19876e11i		−	0.246596i
$836$	−1.73487e11	−	2.65539e11i	−0.355175	−	0.543630i
$837$	5.08554e11			1.03618
$838$	4.23065e10	−	5.04189e10i	0.0857889	−	0.102239i
$839$	2.87341e11	+	7.89462e11i	0.579895	+	1.59325i	0.788358	+	0.615217i	$0.210932\pi$
$839$	2.87341e11	+	7.89462e11i	0.579895	+	1.59325i	−0.208463	+	0.978030i	$0.566846\pi$
$840$	1.26985e10	+	7.20169e10i	0.0255056	+	0.144650i
$841$	6.33817e10	−	3.59456e11i	0.126701	−	0.718557i
$842$	2.30432e11	+	8.38704e10i	0.458452	+	0.166863i
$843$	3.34345e11	+	5.79103e11i	0.662041	+	1.14669i
$844$	4.53048e11	+	2.61568e11i	0.892843	+	0.515483i
$845$	2.92263e10	−	2.45238e10i	0.0573254	−	0.0481017i
$846$	−3.99450e10	−	4.76046e10i	−0.0779796	−	0.0929325i
$847$	−2.04505e10	+	3.54212e10i	−0.0397347	+	0.0688224i
$848$	5.25233e8	−	3.03244e8i	0.00101571	−	0.000586419i
$849$	−1.71211e10	+	4.70398e10i	−0.0329534	+	0.0905388i
$850$	1.67966e11	+	2.96170e10i	0.321771	+	0.0567369i
$851$	1.10121e11	−	1.94174e10i	0.209968	−	0.0370230i
$852$	2.23620e11	−	8.13912e10i	0.424378	−	0.154461i
$853$	−4.27970e11	−	3.59109e11i	−0.808383	−	0.678314i	0.141838	−	0.989890i	$-0.454699\pi$
$853$	−4.27970e11	−	3.59109e11i	−0.808383	−	0.678314i	−0.950221	+	0.311576i	$0.899143\pi$
$854$		−	2.75405e10i		−	0.0517775i
$855$	7.54278e9	−	6.28655e10i	0.0141145	−	0.117638i
$856$	−3.78798e11			−0.705525
$857$	−8.55238e10	+	1.01923e11i	−0.158549	+	0.188951i	−0.839471	−	0.543405i	$-0.817135\pi$
$857$	−8.55238e10	+	1.01923e11i	−0.158549	+	0.188951i	0.680922	+	0.732356i	$0.261579\pi$
$858$	−9.95477e10	−	2.73505e11i	−0.183688	−	0.504680i
$859$	1.70672e11	+	9.67930e11i	0.313466	+	1.77775i	0.580697	+	0.814120i	$0.302780\pi$
$859$	1.70672e11	+	9.67930e11i	0.313466	+	1.77775i	−0.267231	+	0.963633i	$0.586109\pi$
$860$	−1.74792e10	+	9.91295e10i	−0.0319542	+	0.181221i
$861$	−4.49514e10	−	1.63610e10i	−0.0817957	−	0.0297712i
$862$	−3.57569e10	−	6.19327e10i	−0.0647635	−	0.112174i
$863$	−3.93319e11	−	2.27083e11i	−0.709091	−	0.409394i	0.101633	−	0.994822i	$-0.467593\pi$
$863$	−3.93319e11	−	2.27083e11i	−0.709091	−	0.409394i	−0.810724	+	0.585428i	$0.800926\pi$
$864$	−4.57408e11	+	3.83811e11i	−0.820821	+	0.688751i
$865$	1.43254e11	+	1.70723e11i	0.255883	+	0.304950i
$866$	4.43933e10	−	7.68915e10i	0.0789308	−	0.136712i
$867$	−2.42604e11	+	1.40067e11i	−0.429359	+	0.247891i
$868$	−9.27469e10	+	2.54820e11i	−0.163388	+	0.448905i
$869$	−6.27883e11	−	1.10713e11i	−1.10103	−	0.194141i
$870$	−3.33842e10	+	5.88653e9i	−0.0582725	+	0.0102750i
$871$	−1.02760e12	+	3.74017e11i	−1.78547	+	0.649858i
$872$	−1.32013e11	−	1.10772e11i	−0.228324	−	0.191587i
$873$			1.43512e11i			0.247076i
$874$	6.18993e10	+	1.44714e11i	0.106082	+	0.248007i
$875$	2.28813e11			0.390345
$876$	1.48034e11	−	1.76420e11i	0.251389	−	0.299593i
$877$	3.95682e11	+	1.08713e12i	0.668880	+	1.83773i	0.531181	+	0.847258i	$0.321748\pi$
$877$	3.95682e11	+	1.08713e12i	0.668880	+	1.83773i	0.137698	+	0.990474i	$0.456030\pi$
$878$	−1.16796e11	−	6.62381e11i	−0.196539	−	1.11463i
$879$	−2.64452e10	+	1.49978e11i	−0.0442987	+	0.251230i
$880$	−4.01993e8	−	1.46314e8i	−0.000670329	−	0.000243980i
$881$	−5.24925e10	−	9.09197e10i	−0.0871352	−	0.150923i	0.819164	−	0.573560i	$-0.194438\pi$
$881$	−5.24925e10	−	9.09197e10i	−0.0871352	−	0.150923i	−0.906299	+	0.422637i	$0.861105\pi$
$882$	5.52348e10	+	3.18898e10i	0.0912722	+	0.0526960i
$883$	8.30825e11	−	6.97145e11i	1.36668	−	1.14678i	0.392824	−	0.919614i	$-0.371498\pi$
$883$	8.30825e11	−	6.97145e11i	1.36668	−	1.14678i	0.973856	−	0.227167i	$-0.0729463\pi$
$884$	−1.56528e11	−	1.86543e11i	−0.256320	−	0.305471i
$885$	−8.83388e10	+	1.53007e11i	−0.144005	+	0.249424i
$886$	1.30470e11	−	7.53268e10i	0.211726	−	0.122240i
$887$	−1.79162e11	+	4.92244e11i	−0.289436	+	0.795218i	0.706710	+	0.707504i	$0.250179\pi$
$887$	−1.79162e11	+	4.92244e11i	−0.289436	+	0.795218i	−0.996146	+	0.0877148i	$0.972044\pi$
$888$	2.17576e11	+	3.83646e10i	0.349913	+	0.0616990i
$889$	−7.43163e11	+	1.31040e11i	−1.18981	+	0.209795i
$890$	2.55064e10	−	9.28356e9i	0.0406527	−	0.0147964i
$891$	1.58056e11	+	1.32625e11i	0.250784	+	0.210433i
$892$			3.07671e11i			0.485990i
$893$	2.66505e11	−	1.47049e10i	0.419083	−	0.0231237i
$894$	−4.80184e11			−0.751722
$895$	6.53549e10	−	7.78870e10i	0.101856	−	0.121387i
$896$	−1.09187e11	−	2.99990e11i	−0.169411	−	0.465452i
$897$	−4.07874e10	−	2.31317e11i	−0.0630023	−	0.357304i
$898$	−8.05470e10	+	4.56805e11i	−0.123864	+	0.702466i
$899$	−3.08883e11	−	1.12424e11i	−0.472885	−	0.172116i
$900$	8.90649e10	+	1.54265e11i	0.135749	+	0.235124i
$901$	1.40803e11	+	8.12925e10i	0.213654	+	0.123353i
$902$	−4.91460e10	+	4.12384e10i	−0.0742441	+	0.0622982i
$903$	2.91807e11	+	3.47762e11i	0.438878	+	0.523035i
$904$	−2.08920e11	+	3.61860e11i	−0.312829	+	0.541835i
$905$	1.43256e11	−	8.27089e10i	0.213559	−	0.123299i
$906$	−3.44013e8	+	9.45168e8i	−0.000510578	+	0.00140280i
$907$	−8.56647e11	−	1.51050e11i	−1.26582	−	0.223199i	−0.499872	−	0.866099i	$-0.666620\pi$
$907$	−8.56647e11	−	1.51050e11i	−1.26582	−	0.223199i	−0.765950	+	0.642900i	$0.777731\pi$
$908$	5.38583e11	−	9.49668e10i	0.792336	−	0.139710i
$909$	5.58750e11	−	2.03368e11i	0.818393	−	0.297871i
$910$	7.43983e10	+	6.24276e10i	0.108492	+	0.0910356i
$911$			1.02689e12i			1.49090i	0.666560	+	0.745452i	$0.267766\pi$
$911$			1.02689e12i			1.49090i	−0.666560	+	0.745452i	$0.732234\pi$
$912$	−7.47316e7	−	1.35440e9i	−0.000108025	−	0.00195780i
$913$	9.64945e11			1.38874
$914$	3.76638e11	−	4.48859e11i	0.539683	−	0.643170i
$915$	−4.65427e9	−	1.27875e10i	−0.00663998	−	0.0182432i
$916$	1.18156e11	+	6.70095e11i	0.167831	+	0.951819i
$917$	1.44594e11	−	8.20035e11i	0.204491	−	1.15972i
$918$	−2.49404e11	−	9.07755e10i	−0.351182	−	0.127820i
$919$	−5.10306e11	−	8.83877e11i	−0.715433	−	1.23917i	−0.962792	−	0.270243i	$-0.912896\pi$
$919$	−5.10306e11	−	8.83877e11i	−0.715433	−	1.23917i	0.247359	−	0.968924i	$-0.420437\pi$
$920$	6.85435e10	+	3.95736e10i	0.0956787	+	0.0552401i
$921$	−9.50799e9	+	7.97815e9i	−0.0132145	+	0.0110883i
$922$	4.88737e11	+	5.82454e11i	0.676318	+	0.806005i
$923$	4.13215e11	−	7.15709e11i	0.569337	−	0.986120i
$924$	−2.38239e11	+	1.37547e11i	−0.326832	+	0.188697i
$925$	1.14310e11	−	3.14064e11i	0.156141	−	0.428995i
$926$	5.14253e10	+	9.06767e9i	0.0699412	+	0.0123325i
$927$	2.35356e11	−	4.14997e10i	0.318718	−	0.0561986i
$928$	3.62666e11	−	1.31999e11i	0.489006	−	0.177984i
$929$	−5.56617e11	−	4.67057e11i	−0.747298	−	0.627058i	0.187489	−	0.982267i	$-0.439965\pi$
$929$	−5.56617e11	−	4.67057e11i	−0.747298	−	0.627058i	−0.934787	+	0.355209i	$0.884410\pi$
$930$		−	8.23899e10i		−	0.110139i
$931$	−2.51865e11	+	1.07732e11i	−0.335251	+	0.143399i
$932$	8.80608e11			1.16713
$933$	1.96084e11	−	2.33684e11i	0.258771	−	0.308391i
$934$	−1.93309e11	−	5.31111e11i	−0.254017	−	0.697907i
$935$	−1.99142e10	−	1.12939e11i	−0.0260565	−	0.147774i
$936$	−7.10091e10	+	4.02713e11i	−0.0925147	+	0.524677i
$937$	−7.19720e11	−	2.61957e11i	−0.933695	−	0.339837i	−0.170022	−	0.985440i	$-0.554384\pi$
$937$	−7.19720e11	−	2.61957e11i	−0.933695	−	0.339837i	−0.763673	+	0.645603i	$0.776606\pi$
$938$	−3.17769e11	−	5.50392e11i	−0.410488	−	0.710986i
$939$	−1.76481e11	−	1.01891e11i	−0.227004	−	0.131061i
$940$	3.93195e10	−	3.29930e10i	0.0503612	−	0.0422581i
$941$	6.86019e11	+	8.17566e11i	0.874939	+	1.04271i	0.998729	+	0.0504036i	$0.0160508\pi$
$941$	6.86019e11	+	8.17566e11i	0.874939	+	1.04271i	−0.123790	+	0.992308i	$0.539505\pi$
$942$	−2.64572e11	+	4.58252e11i	−0.336001	+	0.581971i
$943$	−4.48374e10	+	2.58869e10i	−0.0567014	+	0.0327366i
$944$	1.14070e9	−	3.13406e9i	0.00143643	−	0.00394656i
$945$	−1.69533e11	−	2.98932e10i	−0.212582	−	0.0374839i
$946$	5.99592e11	−	1.05724e11i	0.748672	−	0.132011i
$947$	−1.01374e12	+	3.68972e11i	−1.26045	+	0.458768i	−0.883921	−	0.467636i	$-0.845106\pi$
$947$	−1.01374e12	+	3.68972e11i	−1.26045	+	0.458768i	−0.376533	+	0.926403i	$0.622884\pi$
$948$	−2.97813e11	−	2.49895e11i	−0.368731	−	0.309402i
$949$		−	7.99788e11i		−	0.986075i
$950$	4.67093e11	+	5.60431e10i	0.573467	+	0.0688062i
$951$	−3.45648e11			−0.422583
$952$	2.37875e11	−	2.83488e11i	0.289602	−	0.345134i
$953$	−2.58647e11	−	7.10627e11i	−0.313571	−	0.861530i	−0.991929	−	0.126798i	$-0.959530\pi$
$953$	−2.58647e11	−	7.10627e11i	−0.313571	−	0.861530i	0.678357	−	0.734732i	$-0.262692\pi$
$954$	−1.81308e10	−	1.02825e11i	−0.0218888	−	0.124138i
$955$	−3.29689e8	+	1.86976e9i	−0.000396361	+	0.00224788i
$956$	3.26317e11	+	1.18770e11i	0.390668	+	0.142192i
$957$	−1.66730e11	−	2.88784e11i	−0.198777	−	0.344291i
$958$	1.86596e11	+	1.07731e11i	0.221534	+	0.127903i
$959$	1.58518e11	−	1.33012e11i	0.187415	−	0.157260i
$960$	6.19097e10	+	7.37811e10i	0.0728909	+	0.0868681i
$961$	−2.69949e10	+	4.67566e10i	−0.0316511	+	0.0548213i
$962$	2.54107e11	−	1.46709e11i	0.296700	−	0.171300i
$963$	9.72874e10	−	2.67295e11i	0.113123	−	0.310803i
$964$	−6.48184e11	−	1.14292e11i	−0.750568	−	0.132345i
$965$	−4.21886e11	+	7.43900e10i	−0.486504	+	0.0857838i
$966$	1.28276e11	−	4.66885e10i	0.147311	−	0.0536168i
$967$	2.20066e11	+	1.84658e11i	0.251679	+	0.211184i	0.759895	−	0.650046i	$-0.225250\pi$
$967$	2.20066e11	+	1.84658e11i	0.251679	+	0.211184i	−0.508216	+	0.861230i	$0.669695\pi$
$968$			8.74634e10i			0.0996150i
$969$	3.04422e11	−	1.98891e11i	0.345288	−	0.225591i
$970$	7.28862e10			0.0823301
$971$	−7.15324e11	+	8.52489e11i	−0.804684	+	0.958986i	−0.999762	−	0.0218022i	$-0.993060\pi$
$971$	−7.15324e11	+	8.52489e11i	−0.804684	+	0.958986i	0.195078	+	0.980788i	$0.437504\pi$
$972$	−1.59369e11	−	4.37863e11i	−0.178542	−	0.490539i
$973$	7.14376e10	+	4.05143e11i	0.0797032	+	0.452019i
$974$	−6.28388e10	+	3.56377e11i	−0.0698220	+	0.395980i
$975$	−6.59712e11	−	2.40116e11i	−0.730022	−	0.265706i
$976$	1.28443e8	+	2.22469e8i	0.000141550	+	0.000245172i
$977$	−1.05060e12	−	6.06564e11i	−1.15308	−	0.665731i	−0.203444	−	0.979087i	$-0.565213\pi$
$977$	−1.05060e12	−	6.06564e11i	−1.15308	−	0.665731i	−0.949636	+	0.313356i	$0.898547\pi$
$978$	5.73682e11	−	4.81377e11i	0.627070	−	0.526174i
$979$	1.71626e11	+	2.04536e11i	0.186833	+	0.222659i
$980$	−2.63397e10	+	4.56217e10i	−0.0285566	+	0.0494615i
$981$	1.12071e11	−	6.47040e10i	0.121009	−	0.0698643i
$982$	−1.30185e10	+	3.57679e10i	−0.0139995	+	0.0384634i
$983$	6.38807e11	+	1.12639e11i	0.684157	+	0.120635i	0.504914	−	0.863170i	$-0.331524\pi$
$983$	6.38807e11	+	1.12639e11i	0.684157	+	0.120635i	0.179243	+	0.983805i	$0.442635\pi$
$984$	−1.00740e11	+	1.77632e10i	−0.107454	+	0.0189470i
$985$	−3.40930e11	+	1.24088e11i	−0.362176	+	0.131821i
$986$	1.31414e11	+	1.10270e11i	0.139038	+	0.116667i
$987$		−	2.31489e11i		−	0.243928i
$988$	−4.59438e11	−	4.89967e11i	−0.482168	−	0.514209i
$989$	4.91338e11			0.513565
$990$	−4.73396e10	+	5.64171e10i	−0.0492815	+	0.0587314i
$991$	2.00809e11	+	5.51718e11i	0.208204	+	0.572035i	0.999209	−	0.0397748i	$-0.0126640\pi$
$991$	2.00809e11	+	5.51718e11i	0.208204	+	0.572035i	−0.791005	+	0.611810i	$0.790442\pi$
$992$	1.62883e11	+	9.23755e11i	0.168201	+	0.953916i
$993$	1.44160e10	−	8.17573e10i	0.0148268	−	0.0840872i
$994$	4.51330e11	+	1.64271e11i	0.462327	+	0.168273i
$995$	−3.10745e10	−	5.38227e10i	−0.0317039	−	0.0549127i
$996$	5.09560e11	+	2.94195e11i	0.517796	+	0.298949i
$997$	4.32330e11	−	3.62768e11i	0.437557	−	0.367154i	−0.397237	−	0.917716i	$-0.630031\pi$
$997$	4.32330e11	−	3.62768e11i	0.437557	−	0.367154i	0.834794	+	0.550562i	$0.185587\pi$
$998$	3.01980e11	+	3.59886e11i	0.304408	+	0.362780i
$999$	−2.60045e11	+	4.50412e11i	−0.261088	+	0.452218i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.9.f.a.3.5	✓	72
19.13	odd	18	inner	19.9.f.a.13.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.9.f.a.3.5	✓	72	1.1	even	1	trivial
19.9.f.a.13.5	yes	72	19.13	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.34622 + 7.56314i) q^{2} +(-20.1988 - 55.4957i) q^{3} +(27.5275 + 156.116i) q^{4} +(-27.4521 + 155.689i) q^{5} +(547.908 + 199.422i) q^{6} +(-956.918 - 1657.43i) q^{7} +(-3544.29 - 2046.29i) q^{8} +(2354.23 - 1975.44i) q^{9} +O(q^{10})\)	\(q+(-6.34622 + 7.56314i) q^{2} +(-20.1988 - 55.4957i) q^{3} +(27.5275 + 156.116i) q^{4} +(-27.4521 + 155.689i) q^{5} +(547.908 + 199.422i) q^{6} +(-956.918 - 1657.43i) q^{7} +(-3544.29 - 2046.29i) q^{8} +(2354.23 - 1975.44i) q^{9} +(-1003.28 - 1195.66i) q^{10} +(7676.75 - 13296.5i) q^{11} +(8107.75 - 4681.01i) q^{12} +(11119.9 - 30551.8i) q^{13} +(18608.2 + 3281.13i) q^{14} +(9194.57 - 1621.25i) q^{15} +(-165.617 + 60.2797i) q^{16} +(-36193.6 - 30370.1i) q^{17} +30341.9i q^{18} +(-104295. - 78141.5i) q^{19} -25061.2 q^{20} +(-72651.7 + 86583.0i) q^{21} +(51845.0 + 142443. i) q^{22} +(21242.3 + 120471. i) q^{23} +(-41970.3 + 238025. i) q^{24} +(343582. + 125054. i) q^{25} +(160497. + 277990. i) q^{26} +(-492744. - 284486. i) q^{27} +(232410. - 195015. i) q^{28} +(236390. + 281719. i) q^{29} +(-46089.0 + 79828.6i) q^{30} +(-774065. + 446906. i) q^{31} +(358931. - 986153. i) q^{32} +(-892961. - 157453. i) q^{33} +(459386. - 81002.1i) q^{34} +(284313. - 103481. i) q^{35} +(373203. + 313155. i) q^{36} -914089. i q^{37} +(1.25287e6 - 292895. i) q^{38} -1.92010e6 q^{39} +(415883. - 495631. i) q^{40} +(144754. + 397708. i) q^{41} +(-193775. - 1.09895e6i) q^{42} +(697460. - 3.95549e6i) q^{43} +(2.28712e6 + 832445. i) q^{44} +(242925. + 420758. i) q^{45} +(-1.04595e6 - 603878. i) q^{46} +(-1.56894e6 + 1.31649e6i) q^{47} +(6690.53 + 7973.46i) q^{48} +(1.05102e6 - 1.82041e6i) q^{49} +(-3.12625e6 + 1.80494e6i) q^{50} +(-954341. + 2.62203e6i) q^{51} +(5.07572e6 + 894987. i) q^{52} +(-3.38886e6 + 597548. i) q^{53} +(5.27867e6 - 1.92128e6i) q^{54} +(1.85938e6 + 1.56020e6i) q^{55} +7.83255e6i q^{56} +(-2.22988e6 + 7.36630e6i) q^{57} -3.63086e6 q^{58} +(-1.21638e7 + 1.44962e7i) q^{59} +(506206. + 1.39079e6i) q^{60} +(-253099. - 1.43539e6i) q^{61} +(1.53237e6 - 8.69052e6i) q^{62} +(-5.52696e6 - 2.01165e6i) q^{63} +(5.15800e6 + 8.93392e6i) q^{64} +(4.45130e6 + 2.56996e6i) q^{65} +(6.85777e6 - 5.75435e6i) q^{66} +(-2.16200e7 - 2.57657e7i) q^{67} +(3.74494e6 - 6.48642e6i) q^{68} +(6.25657e6 - 3.61223e6i) q^{69} +(-1.02167e6 + 2.80701e6i) q^{70} +(2.50327e7 + 4.41394e6i) q^{71} +(-1.23864e7 + 2.18406e6i) q^{72} +(2.31159e7 - 8.41349e6i) q^{73} +(6.91338e6 + 5.80101e6i) q^{74} -2.15933e7i q^{75} +(9.32816e6 - 1.84332e7i) q^{76} -2.93841e7 q^{77} +(1.21854e7 - 1.45220e7i) q^{78} +(-1.42027e7 - 3.90216e7i) q^{79} +(-4838.33 - 27439.5i) q^{80} +(-2.33357e6 + 1.32343e7i) q^{81} +(-3.92656e6 - 1.42915e6i) q^{82} +(3.14243e7 + 5.44284e7i) q^{83} +(-1.55169e7 - 8.95870e6i) q^{84} +(5.72187e6 - 4.80122e6i) q^{85} +(2.54897e7 + 3.03774e7i) q^{86} +(1.08594e7 - 1.88090e7i) q^{87} +(-5.44172e7 + 3.14178e7i) q^{88} +(-5.94786e6 + 1.63416e7i) q^{89} +(-4.72390e6 - 832952. i) q^{90} +(-6.12783e7 + 1.08050e7i) q^{91} +(-1.82227e7 + 6.63253e6i) q^{92} +(4.04366e7 + 3.39303e7i) q^{93} -2.02208e7i q^{94} +(1.50289e7 - 1.40924e7i) q^{95} -6.19773e7 q^{96} +(-3.00164e7 + 3.57722e7i) q^{97} +(7.09804e6 + 1.95017e7i) q^{98} +(-8.19357e6 - 4.64681e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 6 q^{2} + 162 q^{3} - 720 q^{4} - 6 q^{5} - 720 q^{6} + 3282 q^{7} - 9 q^{8} + 8562 q^{9}+O(q^{10}) \) 72 * q - 6 * q^2 + 162 * q^3 - 720 * q^4 - 6 * q^5 - 720 * q^6 + 3282 * q^7 - 9 * q^8 + 8562 * q^9	\( 72 q - 6 q^{2} + 162 q^{3} - 720 q^{4} - 6 q^{5} - 720 q^{6} + 3282 q^{7} - 9 q^{8} + 8562 q^{9} - 2793 q^{10} + 10482 q^{11} - 124425 q^{12} + 108465 q^{13} + 91905 q^{14} - 236277 q^{15} - 207120 q^{16} + 40269 q^{17} + 188304 q^{19} + 1700646 q^{20} + 386850 q^{21} - 1237254 q^{22} - 1339566 q^{23} - 1289928 q^{24} + 59748 q^{25} - 842907 q^{26} + 4849875 q^{27} - 2065044 q^{28} - 1312269 q^{29} + 299940 q^{30} + 3498759 q^{31} + 9109881 q^{32} - 1670298 q^{33} - 12448236 q^{34} - 5923416 q^{35} - 6763797 q^{36} + 5067372 q^{38} + 18303516 q^{39} + 15014562 q^{40} - 11716206 q^{41} - 9228981 q^{42} + 12974721 q^{43} - 2631387 q^{44} - 31264995 q^{45} - 30318354 q^{46} + 1571889 q^{47} + 55683057 q^{48} + 1898838 q^{49} + 30782124 q^{50} + 12474372 q^{51} - 839439 q^{52} - 49160157 q^{53} - 65504571 q^{54} - 27903114 q^{55} + 18105312 q^{57} + 85061964 q^{58} + 51376881 q^{59} + 61200294 q^{60} - 51972462 q^{61} - 85396644 q^{62} + 41912118 q^{63} - 35891445 q^{64} + 2267586 q^{65} + 53209500 q^{66} + 35494521 q^{67} + 13755102 q^{68} + 54287784 q^{69} + 98126001 q^{70} - 5729388 q^{71} - 580668798 q^{72} - 255453906 q^{73} + 159588693 q^{74} + 128877954 q^{76} + 345629838 q^{77} + 120889431 q^{78} + 73477881 q^{79} - 93973551 q^{80} + 114909627 q^{81} + 67089591 q^{82} + 55994352 q^{83} + 143496459 q^{84} - 29709876 q^{85} - 592637892 q^{86} - 151341879 q^{87} - 412023537 q^{88} - 7283562 q^{89} + 350808846 q^{90} + 81065763 q^{91} + 496900692 q^{92} - 609570561 q^{93} - 222935505 q^{95} + 89754174 q^{96} - 180436449 q^{97} + 472058181 q^{98} + 865983036 q^{99}+O(q^{100}) \) 72 * q - 6 * q^2 + 162 * q^3 - 720 * q^4 - 6 * q^5 - 720 * q^6 + 3282 * q^7 - 9 * q^8 + 8562 * q^9 - 2793 * q^10 + 10482 * q^11 - 124425 * q^12 + 108465 * q^13 + 91905 * q^14 - 236277 * q^15 - 207120 * q^16 + 40269 * q^17 + 188304 * q^19 + 1700646 * q^20 + 386850 * q^21 - 1237254 * q^22 - 1339566 * q^23 - 1289928 * q^24 + 59748 * q^25 - 842907 * q^26 + 4849875 * q^27 - 2065044 * q^28 - 1312269 * q^29 + 299940 * q^30 + 3498759 * q^31 + 9109881 * q^32 - 1670298 * q^33 - 12448236 * q^34 - 5923416 * q^35 - 6763797 * q^36 + 5067372 * q^38 + 18303516 * q^39 + 15014562 * q^40 - 11716206 * q^41 - 9228981 * q^42 + 12974721 * q^43 - 2631387 * q^44 - 31264995 * q^45 - 30318354 * q^46 + 1571889 * q^47 + 55683057 * q^48 + 1898838 * q^49 + 30782124 * q^50 + 12474372 * q^51 - 839439 * q^52 - 49160157 * q^53 - 65504571 * q^54 - 27903114 * q^55 + 18105312 * q^57 + 85061964 * q^58 + 51376881 * q^59 + 61200294 * q^60 - 51972462 * q^61 - 85396644 * q^62 + 41912118 * q^63 - 35891445 * q^64 + 2267586 * q^65 + 53209500 * q^66 + 35494521 * q^67 + 13755102 * q^68 + 54287784 * q^69 + 98126001 * q^70 - 5729388 * q^71 - 580668798 * q^72 - 255453906 * q^73 + 159588693 * q^74 + 128877954 * q^76 + 345629838 * q^77 + 120889431 * q^78 + 73477881 * q^79 - 93973551 * q^80 + 114909627 * q^81 + 67089591 * q^82 + 55994352 * q^83 + 143496459 * q^84 - 29709876 * q^85 - 592637892 * q^86 - 151341879 * q^87 - 412023537 * q^88 - 7283562 * q^89 + 350808846 * q^90 + 81065763 * q^91 + 496900692 * q^92 - 609570561 * q^93 - 222935505 * q^95 + 89754174 * q^96 - 180436449 * q^97 + 472058181 * q^98 + 865983036 * q^99

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