LMFDB - Embedded newform 37.8.c.a.26.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,8,Mod(10,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("37.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	37.c (of order $3$, degree $2$, 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:	$11.5582459429$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.20
Character	$\chi$	$=$	37.26
Dual form			37.8.c.a.10.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.53293 + 16.5115i) q^{2} +(19.4337 - 33.6601i) q^{3} +(-117.754 + 203.955i) q^{4} +(-179.660 + 311.180i) q^{5} +741.040 q^{6} +(35.6214 - 61.6981i) q^{7} -2049.72 q^{8} +(338.163 + 585.716i) q^{9} +O(q^{10})$	\(q+(9.53293 + 16.5115i) q^{2} +(19.4337 - 33.6601i) q^{3} +(-117.754 + 203.955i) q^{4} +(-179.660 + 311.180i) q^{5} +741.040 q^{6} +(35.6214 - 61.6981i) q^{7} -2049.72 q^{8} +(338.163 + 585.716i) q^{9} -6850.74 q^{10} -5482.90 q^{11} +(4576.77 + 7927.21i) q^{12} +(-2016.85 + 3493.28i) q^{13} +1358.31 q^{14} +(6982.91 + 12094.7i) q^{15} +(-4467.35 - 7737.68i) q^{16} +(1912.35 + 3312.28i) q^{17} +(-6447.37 + 11167.2i) q^{18} +(4629.97 - 8019.35i) q^{19} +(-42311.2 - 73285.1i) q^{20} +(-1384.51 - 2398.04i) q^{21} +(-52268.1 - 90531.0i) q^{22} -5222.95 q^{23} +(-39833.6 + 68993.8i) q^{24} +(-25492.8 - 44154.8i) q^{25} -76905.9 q^{26} +111290. q^{27} +(8389.10 + 14530.3i) q^{28} +208260. q^{29} +(-133135. + 230597. i) q^{30} +167954. q^{31} +(-46007.9 + 79688.1i) q^{32} +(-106553. + 184555. i) q^{33} +(-36460.6 + 63151.6i) q^{34} +(12799.5 + 22169.3i) q^{35} -159280. q^{36} +(-141831. + 273525. i) q^{37} +176549. q^{38} +(78389.6 + 135775. i) q^{39} +(368252. - 637831. i) q^{40} +(109331. - 189366. i) q^{41} +(26396.9 - 45720.8i) q^{42} +796029. q^{43} +(645631. - 1.11827e6i) q^{44} -243017. q^{45} +(-49790.1 - 86238.9i) q^{46} -962035. q^{47} -347269. q^{48} +(409234. + 708814. i) q^{49} +(486042. - 841849. i) q^{50} +148656. q^{51} +(-474982. - 822693. i) q^{52} +(46775.7 + 81018.0i) q^{53} +(1.06092e6 + 1.83757e6i) q^{54} +(985056. - 1.70617e6i) q^{55} +(-73013.8 + 126464. i) q^{56} +(-179955. - 311691. i) q^{57} +(1.98533e6 + 3.43869e6i) q^{58} +(-1.07471e6 - 1.86146e6i) q^{59} -3.28905e6 q^{60} +(-1.37678e6 + 2.38466e6i) q^{61} +(1.60110e6 + 2.77318e6i) q^{62} +48183.4 q^{63} -2.89800e6 q^{64} +(-724693. - 1.25521e6i) q^{65} -4.06305e6 q^{66} +(1.76557e6 - 3.05805e6i) q^{67} -900743. q^{68} +(-101501. + 175805. i) q^{69} +(-244033. + 422677. i) q^{70} +(-1.10506e6 + 1.91401e6i) q^{71} +(-693139. - 1.20055e6i) q^{72} +3.10635e6 q^{73} +(-5.86838e6 + 265659. i) q^{74} -1.98168e6 q^{75} +(1.09039e6 + 1.88861e6i) q^{76} +(-195308. + 338284. i) q^{77} +(-1.49457e6 + 2.58866e6i) q^{78} +(3.52554e6 - 6.10641e6i) q^{79} +3.21042e6 q^{80} +(1.42321e6 - 2.46508e6i) q^{81} +4.16897e6 q^{82} +(-1.54212e6 - 2.67104e6i) q^{83} +652125. q^{84} -1.37429e6 q^{85} +(7.58849e6 + 1.31436e7i) q^{86} +(4.04726e6 - 7.01007e6i) q^{87} +1.12384e7 q^{88} +(-556313. - 963563. i) q^{89} +(-2.31667e6 - 4.01258e6i) q^{90} +(143686. + 248871. i) q^{91} +(615021. - 1.06525e6i) q^{92} +(3.26397e6 - 5.65336e6i) q^{93} +(-9.17102e6 - 1.58847e7i) q^{94} +(1.66364e6 + 2.88151e6i) q^{95} +(1.78821e6 + 3.09727e6i) q^{96} -3.88297e6 q^{97} +(-7.80239e6 + 1.35141e7i) q^{98} +(-1.85411e6 - 3.21142e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9}+O(q^{10}) $ 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9} + 10028 q^{10} + 14876 q^{11} - 4836 q^{12} - 5922 q^{13} + 20176 q^{14} - 8460 q^{15} - 36726 q^{16} - 19095 q^{17} - 7338 q^{18} - 34334 q^{19} - 75668 q^{20} - 32764 q^{21} + 18526 q^{22} - 99896 q^{23} - 203760 q^{24} - 322660 q^{25} + 101516 q^{26} + 846616 q^{27} - 73490 q^{28} + 168186 q^{29} - 88790 q^{30} - 38052 q^{31} - 172292 q^{32} - 54536 q^{33} + 90724 q^{34} - 247046 q^{35} + 352004 q^{36} + 740185 q^{37} + 1994976 q^{38} - 591380 q^{39} - 38962 q^{40} - 292827 q^{41} - 1499386 q^{42} + 630980 q^{43} - 1727390 q^{44} - 994286 q^{45} + 576988 q^{46} + 3394668 q^{47} - 79840 q^{48} + 728851 q^{49} - 69656 q^{50} - 3970200 q^{51} - 2043140 q^{52} + 584438 q^{53} - 2160774 q^{54} + 2019874 q^{55} - 658986 q^{56} + 4295748 q^{57} - 5684872 q^{58} - 1773152 q^{59} + 20208544 q^{60} - 3596569 q^{61} - 1538738 q^{62} + 11795092 q^{63} - 9622852 q^{64} - 5027290 q^{65} - 17464952 q^{66} - 3249754 q^{67} + 5608668 q^{68} + 9599384 q^{69} - 5102080 q^{70} - 1162530 q^{71} - 4730172 q^{72} - 5266532 q^{73} + 4052290 q^{74} + 35543072 q^{75} - 13781226 q^{76} + 121180 q^{77} - 7012890 q^{78} - 13545718 q^{79} - 17840888 q^{80} - 16689077 q^{81} - 43173544 q^{82} + 7359048 q^{83} + 41186680 q^{84} + 21047382 q^{85} + 6732838 q^{86} + 7672800 q^{87} + 42023140 q^{88} + 2955725 q^{89} - 14596808 q^{90} - 19887752 q^{91} + 13352900 q^{92} + 9156784 q^{93} + 690474 q^{94} - 5667270 q^{95} + 29986904 q^{96} + 52065982 q^{97} - 53664462 q^{98} - 35534038 q^{99}+O(q^{100}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9 + 10028 * q^10 + 14876 * q^11 - 4836 * q^12 - 5922 * q^13 + 20176 * q^14 - 8460 * q^15 - 36726 * q^16 - 19095 * q^17 - 7338 * q^18 - 34334 * q^19 - 75668 * q^20 - 32764 * q^21 + 18526 * q^22 - 99896 * q^23 - 203760 * q^24 - 322660 * q^25 + 101516 * q^26 + 846616 * q^27 - 73490 * q^28 + 168186 * q^29 - 88790 * q^30 - 38052 * q^31 - 172292 * q^32 - 54536 * q^33 + 90724 * q^34 - 247046 * q^35 + 352004 * q^36 + 740185 * q^37 + 1994976 * q^38 - 591380 * q^39 - 38962 * q^40 - 292827 * q^41 - 1499386 * q^42 + 630980 * q^43 - 1727390 * q^44 - 994286 * q^45 + 576988 * q^46 + 3394668 * q^47 - 79840 * q^48 + 728851 * q^49 - 69656 * q^50 - 3970200 * q^51 - 2043140 * q^52 + 584438 * q^53 - 2160774 * q^54 + 2019874 * q^55 - 658986 * q^56 + 4295748 * q^57 - 5684872 * q^58 - 1773152 * q^59 + 20208544 * q^60 - 3596569 * q^61 - 1538738 * q^62 + 11795092 * q^63 - 9622852 * q^64 - 5027290 * q^65 - 17464952 * q^66 - 3249754 * q^67 + 5608668 * q^68 + 9599384 * q^69 - 5102080 * q^70 - 1162530 * q^71 - 4730172 * q^72 - 5266532 * q^73 + 4052290 * q^74 + 35543072 * q^75 - 13781226 * q^76 + 121180 * q^77 - 7012890 * q^78 - 13545718 * q^79 - 17840888 * q^80 - 16689077 * q^81 - 43173544 * q^82 + 7359048 * q^83 + 41186680 * q^84 + 21047382 * q^85 + 6732838 * q^86 + 7672800 * q^87 + 42023140 * q^88 + 2955725 * q^89 - 14596808 * q^90 - 19887752 * q^91 + 13352900 * q^92 + 9156784 * q^93 + 690474 * q^94 - 5667270 * q^95 + 29986904 * q^96 + 52065982 * q^97 - 53664462 * q^98 - 35534038 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	9.53293	+	16.5115i	0.842600	+	1.45943i	0.887689	+	0.460443i	$0.152310\pi$
$2$	9.53293	+	16.5115i	0.842600	+	1.45943i	−0.0450891	+	0.998983i	$0.514357\pi$
$3$	19.4337	−	33.6601i	0.415557	−	0.719766i	−0.579929	−	0.814667i	$-0.696920\pi$
$3$	19.4337	−	33.6601i	0.415557	−	0.719766i	0.995487	+	0.0949003i	$0.0302532\pi$
$4$	−117.754	+	203.955i	−0.919950	+	1.59340i
$5$	−179.660	+	311.180i	−0.642770	+	1.11331i	0.342041	+	0.939685i	$0.388882\pi$
$5$	−179.660	+	311.180i	−0.642770	+	1.11331i	−0.984812	+	0.173626i	$0.944452\pi$
$6$	741.040			1.40059
$7$	35.6214	−	61.6981i	0.0392526	−	0.0679874i	−0.845732	−	0.533608i	$-0.820836\pi$
$7$	35.6214	−	61.6981i	0.0392526	−	0.0679874i	0.884984	+	0.465621i	$0.154169\pi$
$8$	−2049.72			−1.41540
$9$	338.163	+	585.716i	0.154624	+	0.267817i
$10$	−6850.74			−2.16639
$11$	−5482.90			−1.24204			−0.621020	−	0.783795i	$-0.713281\pi$
$11$	−5482.90			−1.24204			−0.621020	+	0.783795i	$0.713281\pi$
$12$	4576.77	+	7927.21i	0.764584	+	1.32430i
$13$	−2016.85	+	3493.28i	−0.254608	+	0.440993i	−0.964789	−	0.263025i	$-0.915280\pi$
$13$	−2016.85	+	3493.28i	−0.254608	+	0.440993i	0.710181	+	0.704019i	$0.248613\pi$
$14$	1358.31			0.132297
$15$	6982.91	+	12094.7i	0.534216	+	0.925289i
$16$	−4467.35	−	7737.68i	−0.272666	−	0.472271i
$17$	1912.35	+	3312.28i	0.0944052	+	0.163515i	0.909360	−	0.416010i	$-0.136572\pi$
$17$	1912.35	+	3312.28i	0.0944052	+	0.163515i	−0.814955	+	0.579524i	$0.803238\pi$
$18$	−6447.37	+	11167.2i	−0.260573	+	0.451325i
$19$	4629.97	−	8019.35i	0.154861	−	0.268226i	−0.778148	−	0.628081i	$-0.783840\pi$
$19$	4629.97	−	8019.35i	0.154861	−	0.268226i	0.933008	+	0.359855i	$0.117174\pi$
$20$	−42311.2	−	73285.1i	−1.18263	−	2.04838i
$21$	−1384.51	−	2398.04i	−0.0326234	−	0.0565053i
$22$	−52268.1	−	90531.0i	−1.04654	−	1.81267i
$23$	−5222.95			−0.0895094			−0.0447547	−	0.998998i	$-0.514251\pi$
$23$	−5222.95			−0.0895094			−0.0447547	+	0.998998i	$0.514251\pi$
$24$	−39833.6	+	68993.8i	−0.588180	+	1.01876i
$25$	−25492.8	−	44154.8i	−0.326308	−	0.565181i
$26$	−76905.9			−0.858130
$27$	111290.			1.08814
$28$	8389.10	+	14530.3i	0.0722208	+	0.125090i
$29$	208260.			1.58567			0.792836	−	0.609436i	$-0.208604\pi$
$29$	208260.			1.58567			0.792836	+	0.609436i	$0.208604\pi$
$30$	−133135.	+	230597.i	−0.900261	+	1.55930i
$31$	167954.			1.01257			0.506285	−	0.862366i	$-0.331018\pi$
$31$	167954.			1.01257			0.506285	+	0.862366i	$0.331018\pi$
$32$	−46007.9	+	79688.1i	−0.248203	+	0.429901i
$33$	−106553.	+	184555.i	−0.516139	+	0.893979i
$34$	−36460.6	+	63151.6i	−0.159092	+	0.275555i
$35$	12799.5	+	22169.3i	0.0504608	+	0.0874006i
$36$	−159280.			−0.568986
$37$	−141831.	+	273525.i	−0.460324	+	0.887751i
$37$	−141831.	+	273525.i	−0.460324	+	0.887751i
$38$	176549.			0.521942
$39$	78389.6	+	135775.i	0.211608	+	0.366516i
$40$	368252.	−	637831.i	0.909777	−	1.57578i
$41$	109331.	−	189366.i	0.247741	−	0.429101i	−0.715157	−	0.698963i	$-0.753645\pi$
$41$	109331.	−	189366.i	0.247741	−	0.429101i	0.962899	+	0.269863i	$0.0869784\pi$
$42$	26396.9	−	45720.8i	0.0549769	−	0.0952228i
$43$	796029.			1.52682			0.763412	−	0.645912i	$-0.223523\pi$
$43$	796029.			1.52682			0.763412	+	0.645912i	$0.223523\pi$
$44$	645631.	−	1.11827e6i	1.14261	−	1.97907i
$45$	−243017.			−0.397551
$46$	−49790.1	−	86238.9i	−0.0754206	−	0.130632i
$47$	−962035.			−1.35160			−0.675801	−	0.737085i	$-0.736202\pi$
$47$	−962035.			−1.35160			−0.675801	+	0.737085i	$0.736202\pi$
$48$	−347269.			−0.453233
$49$	409234.	+	708814.i	0.496918	+	0.860688i
$50$	486042.	−	841849.i	0.549894	−	0.952444i
$51$	148656.			0.156923
$52$	−474982.	−	822693.i	−0.468453	−	0.811384i
$53$	46775.7	+	81018.0i	0.0431574	+	0.0747508i	0.886797	−	0.462159i	$-0.152925\pi$
$53$	46775.7	+	81018.0i	0.0431574	+	0.0747508i	−0.843640	+	0.536910i	$0.819592\pi$
$54$	1.06092e6	+	1.83757e6i	0.916863	+	1.58805i
$55$	985056.	−	1.70617e6i	0.798347	−	1.38278i
$56$	−73013.8	+	126464.i	−0.0555580	+	0.0962293i
$57$	−179955.	−	311691.i	−0.128707	−	0.222927i
$58$	1.98533e6	+	3.43869e6i	1.33609	+	2.31417i
$59$	−1.07471e6	−	1.86146e6i	−0.681256	−	1.17997i	−0.974598	−	0.223962i	$-0.928101\pi$
$59$	−1.07471e6	−	1.86146e6i	−0.681256	−	1.17997i	0.293342	−	0.956007i	$-0.405232\pi$
$60$	−3.28905e6			−1.96581
$61$	−1.37678e6	+	2.38466e6i	−0.776625	+	1.34515i	0.157251	+	0.987559i	$0.449737\pi$
$61$	−1.37678e6	+	2.38466e6i	−0.776625	+	1.34515i	−0.933876	+	0.357596i	$0.883597\pi$
$62$	1.60110e6	+	2.77318e6i	0.853192	+	1.47777i
$63$	48183.4			0.0242776
$64$	−2.89800e6			−1.38188
$65$	−724693.	−	1.25521e6i	−0.327309	−	0.566915i
$66$	−4.06305e6			−1.73959
$67$	1.76557e6	−	3.05805e6i	0.717170	−	1.24217i	−0.244947	−	0.969537i	$-0.578770\pi$
$67$	1.76557e6	−	3.05805e6i	0.717170	−	1.24217i	0.962117	−	0.272638i	$-0.0878962\pi$
$68$	−900743.			−0.347392
$69$	−101501.	+	175805.i	−0.0371963	+	0.0644259i
$70$	−244033.	+	422677.i	−0.0850365	+	0.147288i
$71$	−1.10506e6	+	1.91401e6i	−0.366421	+	0.634659i	−0.989003	−	0.147895i	$-0.952750\pi$
$71$	−1.10506e6	+	1.91401e6i	−0.366421	+	0.634659i	0.622582	+	0.782554i	$0.286084\pi$
$72$	−693139.	−	1.20055e6i	−0.218855	−	0.379068i
$73$	3.10635e6			0.934589			0.467295	−	0.884102i	$-0.345229\pi$
$73$	3.10635e6			0.934589			0.467295	+	0.884102i	$0.345229\pi$
$74$	−5.86838e6	+	265659.i	−1.68348	+	0.0762102i
$75$	−1.98168e6			−0.542398
$76$	1.09039e6	+	1.88861e6i	0.284928	+	0.493510i
$77$	−195308.	+	338284.i	−0.0487532	+	0.0844431i
$78$	−1.49457e6	+	2.58866e6i	−0.356602	+	0.617653i
$79$	3.52554e6	−	6.10641e6i	0.804509	−	1.39345i	−0.112113	−	0.993695i	$-0.535762\pi$
$79$	3.52554e6	−	6.10641e6i	0.804509	−	1.39345i	0.916622	−	0.399755i	$-0.130905\pi$
$80$	3.21042e6			0.701046
$81$	1.42321e6	−	2.46508e6i	0.297559	−	0.515386i
$82$	4.16897e6			0.834988
$83$	−1.54212e6	−	2.67104e6i	−0.296037	−	0.512751i	0.679188	−	0.733964i	$-0.262332\pi$
$83$	−1.54212e6	−	2.67104e6i	−0.296037	−	0.512751i	−0.975226	+	0.221213i	$0.928999\pi$
$84$	652125.			0.120047
$85$	−1.37429e6			−0.242723
$86$	7.58849e6	+	1.31436e7i	1.28650	+	2.22829i
$87$	4.04726e6	−	7.01007e6i	0.658937	−	1.14131i
$88$	1.12384e7			1.75798
$89$	−556313.	−	963563.i	−0.0836477	−	0.144882i	0.821166	−	0.570689i	$-0.193324\pi$
$89$	−556313.	−	963563.i	−0.0836477	−	0.144882i	−0.904814	+	0.425807i	$0.859990\pi$
$90$	−2.31667e6	−	4.01258e6i	−0.334977	−	0.580197i
$91$	143686.	+	248871.i	0.0199880	+	0.0346202i
$92$	615021.	−	1.06525e6i	0.0823442	−	0.142624i
$93$	3.26397e6	−	5.65336e6i	0.420781	−	0.728814i
$94$	−9.17102e6	−	1.58847e7i	−1.13886	−	1.97256i
$95$	1.66364e6	+	2.88151e6i	0.199080	+	0.344816i
$96$	1.78821e6	+	3.09727e6i	0.206285	+	0.357297i
$97$	−3.88297e6			−0.431979			−0.215990	−	0.976396i	$-0.569298\pi$
$97$	−3.88297e6			−0.431979			−0.215990	+	0.976396i	$0.569298\pi$
$98$	−7.80239e6	+	1.35141e7i	−0.837407	+	1.45043i
$99$	−1.85411e6	−	3.21142e6i	−0.192049	−	0.332639i
$100$	1.20075e7			1.20075
$101$	−1.99299e7			−1.92478			−0.962389	−	0.271674i	$-0.912423\pi$
$101$	−1.99299e7			−1.92478			−0.962389	+	0.271674i	$0.912423\pi$
$102$	1.41713e6	+	2.45454e6i	0.132223	+	0.229018i
$103$	9.40716e6			0.848258			0.424129	−	0.905602i	$-0.360580\pi$
$103$	9.40716e6			0.848258			0.424129	+	0.905602i	$0.360580\pi$
$104$	4.13397e6	−	7.16024e6i	0.360372	−	0.624182i
$105$	994964.			0.0838774
$106$	−891820.	+	1.54468e6i	−0.0727288	+	0.125970i
$107$	−3.06755e6	+	5.31314e6i	−0.242074	+	0.419284i	−0.961305	−	0.275487i	$-0.911161\pi$
$107$	−3.06755e6	+	5.31314e6i	−0.242074	+	0.419284i	0.719231	+	0.694771i	$0.244494\pi$
$108$	−1.31048e7	+	2.26982e7i	−1.00103	+	1.73384i
$109$	5.65133e6	+	9.78838e6i	0.417982	+	0.723966i	0.995736	−	0.0922446i	$-0.0294042\pi$
$109$	5.65133e6	+	9.78838e6i	0.417982	+	0.723966i	−0.577754	+	0.816211i	$0.696071\pi$
$110$	3.75619e7			2.69075
$111$	6.45060e6	+	1.00896e7i	0.447682	+	0.700237i
$112$	−636534.			−0.0428113
$113$	−2.03064e6	−	3.51717e6i	−0.132391	−	0.229308i	0.792207	−	0.610253i	$-0.208932\pi$
$113$	−2.03064e6	−	3.51717e6i	−0.132391	−	0.229308i	−0.924598	+	0.380945i	$0.875599\pi$
$114$	3.43100e6	−	5.94266e6i	0.216897	−	0.375677i
$115$	938355.	−	1.62528e6i	0.0575340	−	0.0996518i
$116$	−2.45234e7	+	4.24757e7i	−1.45874	+	2.52661i
$117$	−2.72810e6			−0.157474
$118$	2.04903e7	−	3.54903e7i	1.14805	−	1.98848i
$119$	272482.			0.0148226
$120$	−1.43130e7	−	2.47908e7i	−0.756129	−	1.30965i
$121$	1.05750e7			0.542663
$122$	−5.24992e7			−2.61754
$123$	−4.24940e6	−	7.36017e6i	−0.205901	−	0.356632i
$124$	−1.97772e7	+	3.42551e7i	−0.931514	+	1.61343i
$125$	−9.75173e6			−0.446577
$126$	459329.	+	795581.i	0.0204563	+	0.0354313i
$127$	−995719.	−	1.72464e6i	−0.0431344	−	0.0747110i	0.843652	−	0.536890i	$-0.180401\pi$
$127$	−995719.	−	1.72464e6i	−0.0431344	−	0.0747110i	−0.886787	+	0.462179i	$0.847068\pi$
$128$	−2.17375e7	−	3.76504e7i	−0.916166	−	1.58685i
$129$	1.54698e7	−	2.67944e7i	0.634483	−	1.09896i
$130$	1.38169e7	−	2.39316e7i	0.551581	−	0.955365i
$131$	4.76042e6	+	8.24529e6i	0.185010	+	0.320447i	0.943580	−	0.331145i	$-0.107435\pi$
$131$	4.76042e6	+	8.24529e6i	0.185010	+	0.320447i	−0.758570	+	0.651592i	$0.774101\pi$
$132$	−2.50940e7	−	4.34640e7i	−0.949644	−	1.64483i
$133$	−329852.	−	571321.i	−0.0121573	−	0.0210571i
$134$	6.73241e7			2.41715
$135$	−1.99943e7	+	3.46312e7i	−0.699421	+	1.21143i
$136$	−3.91977e6	−	6.78925e6i	−0.133621	−	0.231438i
$137$	5.46353e7			1.81531			0.907656	−	0.419715i	$-0.137870\pi$
$137$	5.46353e7			1.81531			0.907656	+	0.419715i	$0.137870\pi$
$138$	−3.87042e6			−0.125366
$139$	145647.	+	252268.i	0.00459991	+	0.00796728i	0.868316	−	0.496011i	$-0.165202\pi$
$139$	145647.	+	252268.i	0.00459991	+	0.00796728i	−0.863716	+	0.503978i	$0.831869\pi$
$140$	−6.02873e6			−0.185685
$141$	−1.86959e7	+	3.23822e7i	−0.561668	+	0.972837i
$142$	−4.21377e7			−1.23498
$143$	1.10582e7	−	1.91533e7i	0.316233	−	0.547732i
$144$	3.02139e6	−	5.23320e6i	0.0843214	−	0.146049i
$145$	−3.74160e7	+	6.48064e7i	−1.01922	+	1.76535i
$146$	2.96126e7	+	5.12906e7i	0.787485	+	1.36396i
$147$	3.18117e7			0.825992
$148$	−3.90858e7	−	6.11356e7i	−0.991067	−	1.55017i
$149$	1.84995e7			0.458150			0.229075	−	0.973409i	$-0.426430\pi$
$149$	1.84995e7			0.458150			0.229075	+	0.973409i	$0.426430\pi$
$150$	−1.88912e7	−	3.27205e7i	−0.457025	−	0.791590i
$151$	−3.87968e7	+	6.71980e7i	−0.917015	+	1.58832i	−0.113091	+	0.993585i	$0.536075\pi$
$151$	−3.87968e7	+	6.71980e7i	−0.917015	+	1.58832i	−0.803924	+	0.594732i	$0.797258\pi$
$152$	−9.49014e6	+	1.64374e7i	−0.219190	+	0.379647i
$153$	−1.29337e6	+	2.24018e6i	−0.0291946	+	0.0505666i
$154$	−7.44745e6			−0.164318
$155$	−3.01746e7	+	5.22640e7i	−0.650850	+	1.12731i
$156$	−3.69226e7			−0.778676
$157$	−1.43325e7	−	2.48246e7i	−0.295579	−	0.511958i	0.679540	−	0.733638i	$-0.262179\pi$
$157$	−1.43325e7	−	2.48246e7i	−0.295579	−	0.511958i	−0.975119	+	0.221680i	$0.928846\pi$
$158$	1.34435e8			2.71152
$159$	3.63610e6			0.0717375
$160$	−1.65315e7	−	2.86335e7i	−0.319076	−	0.552655i
$161$	−186049.	+	322246.i	−0.00351347	+	0.00608551i
$162$	5.42696e7			1.00289
$163$	−1.22706e7	−	2.12532e7i	−0.221926	−	0.384387i	0.733467	−	0.679725i	$-0.237901\pi$
$163$	−1.22706e7	−	2.12532e7i	−0.221926	−	0.384387i	−0.955393	+	0.295338i	$0.904568\pi$
$164$	2.57482e7	+	4.45971e7i	0.455819	+	0.789502i
$165$	−3.82865e7	−	6.63142e7i	−0.663518	−	1.14925i
$166$	2.94019e7	−	5.09257e7i	0.498882	−	0.864089i
$167$	2.87077e7	−	4.97232e7i	0.476970	−	0.826136i	−0.522682	−	0.852528i	$-0.675068\pi$
$167$	2.87077e7	−	4.97232e7i	0.476970	−	0.826136i	0.999652	+	0.0263916i	$0.00840169\pi$
$168$	2.83786e6	+	4.91531e6i	0.0461751	+	0.0799776i
$169$	2.32389e7	+	4.02510e7i	0.370350	+	0.641465i
$170$	−1.31010e7	−	2.26916e7i	−0.204519	−	0.354237i
$171$	6.26275e6			0.0957808
$172$	−9.37352e7	+	1.62354e8i	−1.40460	+	2.43284i
$173$	2.25457e7	+	3.90502e7i	0.331056	+	0.573406i	0.982719	−	0.185103i	$-0.0592618\pi$
$173$	2.25457e7	+	3.90502e7i	0.331056	+	0.573406i	−0.651663	+	0.758508i	$0.725928\pi$
$174$	1.54329e8			2.22088
$175$	−3.63236e6			−0.0512336
$176$	2.44940e7	+	4.24249e7i	0.338662	+	0.586579i
$177$	−8.35425e7			−1.13240
$178$	1.06066e7	−	1.83712e7i	0.140963	−	0.244155i
$179$	3.94575e7			0.514214			0.257107	−	0.966383i	$-0.417231\pi$
$179$	3.94575e7			0.514214			0.257107	+	0.966383i	$0.417231\pi$
$180$	2.86162e7	−	4.95646e7i	0.365727	−	0.633458i
$181$	6.91716e7	−	1.19809e8i	0.867067	−	1.50180i	0.00208665	−	0.999998i	$-0.499336\pi$
$181$	6.91716e7	−	1.19809e8i	0.867067	−	1.50180i	0.864980	−	0.501806i	$-0.167331\pi$
$182$	−2.73950e6	+	4.74495e6i	−0.0336838	+	0.0583420i
$183$	5.35120e7	+	9.26855e7i	0.645465	+	1.11798i
$184$	1.07056e7			0.126692
$185$	−5.96343e7	−	9.32763e7i	−0.692460	−	1.08310i
$186$	1.24461e8			1.41820
$187$	−1.04852e7	−	1.81609e7i	−0.117255	−	0.203092i
$188$	1.13283e8	−	1.96212e8i	1.24341	−	2.15364i
$189$	3.96431e6	−	6.86638e6i	0.0427121	−	0.0739795i
$190$	−3.17187e7	+	5.49385e7i	−0.335489	+	0.581084i
$191$	−1.43576e7			−0.149096			−0.0745481	−	0.997217i	$-0.523751\pi$
$191$	−1.43576e7			−0.149096			−0.0745481	+	0.997217i	$0.523751\pi$
$192$	−5.63189e7	+	9.75472e7i	−0.574249	+	0.994628i
$193$	−1.46784e8			−1.46969			−0.734847	−	0.678233i	$-0.762746\pi$
$193$	−1.46784e8			−1.46969			−0.734847	+	0.678233i	$0.762746\pi$
$194$	−3.70161e7	−	6.41137e7i	−0.363986	−	0.630442i
$195$	−5.63339e7			−0.544062
$196$	−1.92755e8			−1.82856
$197$	1.66292e7	+	2.88026e7i	0.154967	+	0.268411i	0.933047	−	0.359754i	$-0.117139\pi$
$197$	1.66292e7	+	2.88026e7i	0.154967	+	0.268411i	−0.778080	+	0.628165i	$0.783806\pi$
$198$	3.53503e7	−	6.12285e7i	0.323642	−	0.560564i
$199$	1.60626e8			1.44487			0.722437	−	0.691436i	$-0.243022\pi$
$199$	1.60626e8			1.44487			0.722437	+	0.691436i	$0.243022\pi$
$200$	5.22530e7	+	9.05048e7i	0.461856	+	0.799957i
$201$	−6.86229e7	−	1.18858e8i	−0.596050	−	1.03239i
$202$	−1.89991e8	−	3.29073e8i	−1.62182	−	2.80907i
$203$	7.41852e6	−	1.28493e7i	0.0622416	−	0.107806i
$204$	−1.75048e7	+	3.03192e7i	−0.144361	+	0.250041i
$205$	3.92846e7	+	6.80430e7i	0.318482	+	0.551626i
$206$	8.96778e7	+	1.55326e8i	0.714742	+	1.23797i
$207$	−1.76621e6	−	3.05917e6i	−0.0138403	−	0.0239721i
$208$	3.60399e7			0.277691
$209$	−2.53857e7	+	4.39693e7i	−0.192343	+	0.333148i
$210$	9.48492e6	+	1.64284e7i	0.0706751	+	0.122413i
$211$	−2.26788e8			−1.66200			−0.831002	−	0.556270i	$-0.812232\pi$
$211$	−2.26788e8			−1.66200			−0.831002	+	0.556270i	$0.812232\pi$
$212$	−2.20320e7			−0.158811
$213$	4.29506e7	+	7.43927e7i	0.304538	+	0.527475i
$214$	−1.16971e8			−0.815886
$215$	−1.43014e8	+	2.47708e8i	−0.981397	+	1.69983i
$216$	−2.28113e8			−1.54015
$217$	5.98277e6	−	1.03625e7i	0.0397460	−	0.0688420i
$218$	−1.07747e8	+	1.86624e8i	−0.704383	+	1.22003i
$219$	6.03679e7	−	1.04560e8i	0.388375	−	0.672686i
$220$	2.31988e8	+	4.01815e8i	1.46888	+	2.54417i
$221$	−1.54277e7			−0.0961451
$222$	−1.05102e8	+	2.02693e8i	−0.644727	+	1.24338i
$223$	2.29749e8			1.38735			0.693675	−	0.720288i	$-0.255991\pi$
$223$	2.29749e8			1.38735			0.693675	+	0.720288i	$0.255991\pi$
$224$	3.27773e6	+	5.67720e6i	0.0194852	+	0.0337494i
$225$	1.72414e7	−	2.98630e7i	0.100910	−	0.174781i
$226$	3.87159e7	−	6.70579e7i	0.223105	−	0.386430i
$227$	−1.04940e8	+	1.81761e8i	−0.595456	+	1.03136i	0.398026	+	0.917374i	$0.369695\pi$
$227$	−1.04940e8	+	1.81761e8i	−0.595456	+	1.03136i	−0.993482	+	0.113986i	$0.963638\pi$
$228$	8.47614e7			0.473616
$229$	4.12248e7	−	7.14034e7i	0.226848	−	0.392912i	−0.730025	−	0.683421i	$-0.760491\pi$
$229$	4.12248e7	−	7.14034e7i	0.226848	−	0.392912i	0.956872	+	0.290509i	$0.0938247\pi$
$230$	3.57811e7			0.193913
$231$	7.59113e6	+	1.31482e7i	0.0405195	+	0.0701819i
$232$	−4.26874e8			−2.24436
$233$	2.25257e7			0.116663			0.0583315	−	0.998297i	$-0.481422\pi$
$233$	2.25257e7			0.116663			0.0583315	+	0.998297i	$0.481422\pi$
$234$	−2.60067e7	−	4.50450e7i	−0.132688	−	0.229822i
$235$	1.72839e8	−	2.99366e8i	0.868769	−	1.50475i
$236$	5.06205e8			2.50688
$237$	−1.37029e8	−	2.37340e8i	−0.668639	−	1.15812i
$238$	2.59755e6	+	4.49910e6i	0.0124895	+	0.0216325i
$239$	2.52213e7	+	4.36846e7i	0.119502	+	0.206984i	0.919570	−	0.392925i	$-0.128537\pi$
$239$	2.52213e7	+	4.36846e7i	0.119502	+	0.206984i	−0.800068	+	0.599909i	$0.795204\pi$
$240$	6.23902e7	−	1.08063e8i	0.291325	−	0.504589i
$241$	2.00413e8	−	3.47126e8i	0.922288	−	1.59745i	0.126423	−	0.991976i	$-0.459650\pi$
$241$	2.00413e8	−	3.47126e8i	0.922288	−	1.59745i	0.795865	−	0.605474i	$-0.207016\pi$
$242$	1.00811e8	+	1.74609e8i	0.457248	+	0.791977i
$243$	6.63790e7	+	1.14972e8i	0.296763	+	0.514008i
$244$	−3.24243e8	−	5.61605e8i	−1.42891	−	2.47495i
$245$	−2.94091e8			−1.27762
$246$	8.10184e7	−	1.40328e8i	0.346985	−	0.600996i
$247$	1.86759e7	+	3.23476e7i	0.0788574	+	0.136585i
$248$	−3.44259e8			−1.43319
$249$	−1.19877e8			−0.492082
$250$	−9.29626e7	−	1.61016e8i	−0.376286	−	0.651747i
$251$	1.67065e7			0.0666847			0.0333423	−	0.999444i	$-0.489385\pi$
$251$	1.67065e7			0.0666847			0.0333423	+	0.999444i	$0.489385\pi$
$252$	−5.67377e6	+	9.82725e6i	−0.0223342	+	0.0386839i
$253$	2.86369e7			0.111174
$254$	1.89842e7	−	3.28817e7i	0.0726901	−	0.125903i
$255$	−2.67075e7	+	4.62587e7i	−0.100865	+	0.174704i
$256$	2.28971e8	−	3.96590e8i	0.852984	−	1.47741i
$257$	1.31111e8	+	2.27091e8i	0.481807	+	0.834513i	0.999782	−	0.0208821i	$-0.00664748\pi$
$257$	1.31111e8	+	2.27091e8i	0.481807	+	0.834513i	−0.517975	+	0.855395i	$0.673314\pi$
$258$	5.89889e8			2.13846
$259$	1.18238e7	+	1.84940e7i	0.0422870	+	0.0661427i
$260$	3.41341e8			1.20443
$261$	7.04259e7	+	1.21981e8i	0.245183	+	0.424670i
$262$	−9.07616e7	+	1.57204e8i	−0.311779	+	0.540018i
$263$	1.15889e8	−	2.00726e8i	0.392824	−	0.680391i	−0.599997	−	0.800002i	$-0.704832\pi$
$263$	1.15889e8	−	2.00726e8i	0.392824	−	0.680391i	0.992821	+	0.119611i	$0.0381649\pi$
$264$	2.18403e8	−	3.78286e8i	0.730543	−	1.26534i
$265$	−3.36149e7			−0.110961
$266$	6.28892e6	−	1.08927e7i	0.0204876	−	0.0354855i
$267$	−4.32449e7			−0.139042
$268$	4.15803e8	+	7.20193e8i	1.31952	+	2.28548i
$269$	3.89447e8			1.21987			0.609937	−	0.792450i	$-0.291195\pi$
$269$	3.89447e8			1.21987			0.609937	+	0.792450i	$0.291195\pi$
$270$	−7.62419e8			−2.35733
$271$	1.38181e8	+	2.39337e8i	0.421751	+	0.730494i	0.996111	−	0.0881086i	$-0.0280822\pi$
$271$	1.38181e8	+	2.39337e8i	0.421751	+	0.730494i	−0.574360	+	0.818603i	$0.694749\pi$
$272$	1.70863e7	−	2.95943e7i	0.0514821	−	0.0891696i
$273$	1.11694e7			0.0332247
$274$	5.20834e8	+	9.02112e8i	1.52958	+	2.64931i
$275$	1.39774e8	+	2.42096e8i	0.405287	+	0.701978i
$276$	−2.39043e7	−	4.14034e7i	−0.0684374	−	0.118537i
$277$	−1.56663e8	+	2.71348e8i	−0.442881	+	0.767092i	−0.997902	−	0.0647441i	$-0.979377\pi$
$277$	−1.56663e8	+	2.71348e8i	−0.442881	+	0.767092i	0.555021	+	0.831836i	$0.312710\pi$
$278$	−2.77688e6	+	4.80971e6i	−0.00775177	+	0.0134265i
$279$	5.67959e7	+	9.83735e7i	0.156568	+	0.271183i
$280$	−2.62353e7	−	4.54409e7i	−0.0714221	−	0.123707i
$281$	−1.74158e8	−	3.01650e8i	−0.468243	−	0.811021i	0.531098	−	0.847310i	$-0.321779\pi$
$281$	−1.74158e8	−	3.01650e8i	−0.468243	−	0.811021i	−0.999341	+	0.0362895i	$0.988446\pi$
$282$	−7.12907e8			−1.89305
$283$	−2.04138e7	+	3.53578e7i	−0.0535393	+	0.0927327i	−0.891553	−	0.452917i	$-0.850384\pi$
$283$	−2.04138e7	+	3.53578e7i	−0.0535393	+	0.0927327i	0.838014	+	0.545649i	$0.183717\pi$
$284$	−2.60249e8	−	4.50764e8i	−0.674177	−	1.16771i
$285$	1.29323e8			0.330916
$286$	4.21667e8			1.06583
$287$	−7.78902e6	−	1.34910e7i	−0.0194490	−	0.0336866i
$288$	−6.22327e7			−0.153513
$289$	1.97855e8	−	3.42695e8i	0.482175	−	0.835152i
$290$	−1.42674e9			−3.43519
$291$	−7.54604e7	+	1.30701e8i	−0.179512	+	0.310924i
$292$	−3.65784e8	+	6.33557e8i	−0.859775	+	1.48917i
$293$	2.47149e8	−	4.28074e8i	0.574013	−	0.994219i	−0.422136	−	0.906533i	$-0.638719\pi$
$293$	2.47149e8	−	4.28074e8i	0.574013	−	0.994219i	0.996148	−	0.0876862i	$-0.0279473\pi$
$294$	3.03259e8	+	5.25259e8i	0.695981	+	1.20548i
$295$	7.72330e8			1.75156
$296$	2.90712e8	−	5.60649e8i	0.651542	−	1.25652i
$297$	−6.10192e8			−1.35151
$298$	1.76354e8	+	3.05455e8i	0.386037	+	0.668636i
$299$	1.05339e7	−	1.82453e7i	0.0227898	−	0.0394731i
$300$	2.33349e8	−	4.04173e8i	0.498979	−	0.864257i
$301$	2.83557e7	−	4.91134e7i	0.0599318	−	0.103805i
$302$	−1.47939e9			−3.09071
$303$	−3.87312e8	+	6.70844e8i	−0.799856	+	1.38539i
$304$	−8.27349e7			−0.168901
$305$	−4.94706e8	−	8.56855e8i	−0.998384	−	1.72925i
$306$	−4.93185e7			−0.0983976
$307$	8.80242e8			1.73627			0.868136	−	0.496327i	$-0.165318\pi$
$307$	8.80242e8			1.73627			0.868136	+	0.496327i	$0.165318\pi$
$308$	−4.59965e7	−	7.96684e7i	−0.0897011	−	0.155367i
$309$	1.82816e8	−	3.16646e8i	0.352500	−	0.610548i
$310$	−1.15061e9			−2.19363
$311$	2.41091e8	+	4.17581e8i	0.454484	+	0.787190i	0.998658	−	0.0517823i	$-0.0164902\pi$
$311$	2.41091e8	+	4.17581e8i	0.454484	+	0.787190i	−0.544174	+	0.838972i	$0.683157\pi$
$312$	−1.60677e8	−	2.78300e8i	−0.299510	−	0.518767i
$313$	−4.15968e8	−	7.20477e8i	−0.766751	−	1.32805i	−0.939316	−	0.343054i	$-0.888539\pi$
$313$	−4.15968e8	−	7.20477e8i	−0.766751	−	1.32805i	0.172564	−	0.984998i	$-0.444795\pi$
$314$	2.73262e8	−	4.73303e8i	0.498110	−	0.862752i
$315$	−8.65662e6	+	1.49937e7i	−0.0156049	+	0.0270285i
$316$	8.30290e8	+	1.43810e9i	1.48022	+	2.56381i
$317$	2.00791e8	+	3.47780e8i	0.354027	+	0.613194i	0.986951	−	0.161021i	$-0.0514786\pi$
$317$	2.00791e8	+	3.47780e8i	0.354027	+	0.613194i	−0.632924	+	0.774214i	$0.718145\pi$
$318$	3.46627e7	+	6.00376e7i	0.0604460	+	0.104696i
$319$	−1.14187e9			−1.96947
$320$	5.20655e8	−	9.01801e8i	0.888229	−	1.53846i
$321$	1.19227e8	+	2.06508e8i	0.201191	+	0.348473i
$322$	−7.09437e6			−0.0118418
$323$	3.54165e7			0.0584786
$324$	3.35177e8	+	5.80543e8i	0.547478	+	0.948259i
$325$	2.05660e8			0.332322
$326$	2.33949e8	−	4.05211e8i	0.373989	−	0.647769i
$327$	4.39305e8			0.694782
$328$	−2.24097e8	+	3.88147e8i	−0.350653	+	0.607349i
$329$	−3.42691e7	+	5.93557e7i	−0.0530538	+	0.0918919i
$330$	7.29966e8	−	1.26434e9i	1.11816	−	1.93671i
$331$	−6.52340e8	−	1.12989e9i	−0.988727	−	1.71252i	−0.624036	−	0.781396i	$-0.714508\pi$
$331$	−6.52340e8	−	1.12989e9i	−0.988727	−	1.71252i	−0.364691	−	0.931129i	$-0.618825\pi$
$332$	7.26363e8			1.08936
$333$	−2.08170e8	+	9.42375e6i	−0.308932	+	0.0139852i
$334$	1.09468e9			1.60758
$335$	6.34402e8	+	1.09882e9i	0.921951	+	1.59687i
$336$	−1.23702e7	+	2.14258e7i	−0.0177905	+	0.0308141i
$337$	1.42735e8	−	2.47225e8i	0.203155	−	0.351874i	−0.746389	−	0.665510i	$-0.768214\pi$
$337$	1.42735e8	−	2.47225e8i	0.203155	−	0.351874i	0.949543	+	0.313636i	$0.101547\pi$
$338$	−4.43070e8	+	7.67419e8i	−0.624114	+	1.08100i
$339$	−1.57851e8			−0.220064
$340$	1.61827e8	−	2.80293e8i	0.223293	−	0.386755i
$341$	−9.20876e8			−1.25765
$342$	5.97023e7	+	1.03407e8i	0.0807049	+	0.139785i
$343$	1.16981e8			0.156526
$344$	−1.63163e9			−2.16107
$345$	−3.64714e7	−	6.31703e7i	−0.0478173	−	0.0828221i
$346$	−4.29852e8	+	7.44526e8i	−0.557896	+	0.966304i
$347$	−1.32741e9			−1.70550			−0.852750	−	0.522319i	$-0.825067\pi$
$347$	−1.32741e9			−1.70550			−0.852750	+	0.522319i	$0.825067\pi$
$348$	9.53160e8	+	1.65092e9i	1.21238	+	2.09990i
$349$	−5.65755e8	−	9.79916e8i	−0.712425	−	1.23396i	−0.963944	−	0.266104i	$-0.914263\pi$
$349$	−5.65755e8	−	9.79916e8i	−0.712425	−	1.23396i	0.251519	−	0.967852i	$-0.419070\pi$
$350$	−3.46270e7	−	5.99757e7i	−0.0431695	−	0.0747717i
$351$	−2.24455e8	+	3.88768e8i	−0.277048	+	0.479861i
$352$	2.52257e8	−	4.36921e8i	0.308279	−	0.533954i
$353$	−1.89388e8	−	3.28030e8i	−0.229162	−	0.396919i	0.728398	−	0.685154i	$-0.240265\pi$
$353$	−1.89388e8	−	3.28030e8i	−0.229162	−	0.396919i	−0.957560	+	0.288235i	$0.906932\pi$
$354$	−7.96405e8	−	1.37941e9i	−0.954163	−	1.65266i
$355$	−3.97068e8	−	6.87742e8i	−0.471049	−	0.815880i
$356$	2.62031e8			0.307807
$357$	5.29533e6	−	9.17179e6i	0.00615963	−	0.0106688i
$358$	3.76146e8	+	6.51503e8i	0.433277	+	0.750457i
$359$	5.40983e8			0.617096			0.308548	−	0.951209i	$-0.400157\pi$
$359$	5.40983e8			0.617096			0.308548	+	0.951209i	$0.400157\pi$
$360$	4.98117e8			0.562694
$361$	4.04063e8	+	6.99857e8i	0.452036	+	0.782950i
$362$	2.63763e9			2.92236
$363$	2.05511e8	−	3.55955e8i	0.225508	−	0.390591i
$364$	−6.76782e7			−0.0735519
$365$	−5.58087e8	+	9.66635e8i	−0.600726	+	1.04049i
$366$	−1.02025e9	+	1.76713e9i	−1.08774	+	1.88402i
$367$	4.80281e8	−	8.31871e8i	0.507182	−	0.878465i	−0.492783	−	0.870152i	$-0.664020\pi$
$367$	4.80281e8	−	8.31871e8i	0.507182	−	0.878465i	0.999965	−	0.00831320i	$-0.00264620\pi$
$368$	2.33328e7	+	4.04136e7i	0.0244061	+	0.0422727i
$369$	1.47886e8			0.153227
$370$	9.71644e8	−	1.87385e9i	0.997243	−	1.92322i
$371$	6.66487e6			0.00677615
$372$	7.68689e8	+	1.33141e9i	0.774195	+	1.34094i
$373$	−4.00653e8	+	6.93951e8i	−0.399749	+	0.692386i	−0.993695	−	0.112120i	$-0.964236\pi$
$373$	−4.00653e8	+	6.93951e8i	−0.399749	+	0.692386i	0.593946	+	0.804505i	$0.297569\pi$
$374$	1.99910e8	−	3.46253e8i	0.197598	−	0.342250i
$375$	−1.89512e8	+	3.28245e8i	−0.185578	+	0.321431i
$376$	1.97190e9			1.91306
$377$	−4.20029e8	+	7.27512e8i	−0.403724	+	0.699271i
$378$	1.51166e8			0.143957
$379$	5.18526e8	+	8.98113e8i	0.489253	+	0.847410i	0.999924	−	0.0123659i	$-0.00393629\pi$
$379$	5.18526e8	+	8.98113e8i	0.489253	+	0.847410i	−0.510671	+	0.859776i	$0.670603\pi$
$380$	−7.83598e8			−0.732573
$381$	−7.74020e7			−0.0716992
$382$	−1.36870e8	−	2.37067e8i	−0.125628	−	0.217595i
$383$	9.89102e7	−	1.71318e8i	0.0899592	−	0.155814i	−0.817534	−	0.575880i	$-0.804660\pi$
$383$	9.89102e7	−	1.71318e8i	0.0899592	−	0.155814i	0.907494	+	0.420066i	$0.137993\pi$
$384$	−1.68976e9			−1.52288
$385$	−7.01782e7	−	1.21552e8i	−0.0626743	−	0.108555i
$386$	−1.39928e9	−	2.42362e9i	−1.23836	−	2.14491i
$387$	2.69187e8	+	4.66246e8i	0.236084	+	0.408909i
$388$	4.57233e8	−	7.91952e8i	0.397399	−	0.688316i
$389$	−5.03503e8	+	8.72093e8i	−0.433689	+	0.751172i	−0.997188	−	0.0749454i	$-0.976122\pi$
$389$	−5.03503e8	+	8.72093e8i	−0.433689	+	0.751172i	0.563498	+	0.826117i	$0.309455\pi$
$390$	−5.37027e8	−	9.30158e8i	−0.458427	−	0.794018i
$391$	−9.98810e6	−	1.72999e7i	−0.00845015	−	0.0146361i
$392$	−8.38813e8	−	1.45287e9i	−0.703338	−	1.21822i
$393$	3.70050e8			0.307530
$394$	−3.17050e8	+	5.49147e8i	−0.261151	+	0.452326i
$395$	1.26680e9	+	2.19415e9i	1.03423	+	1.79134i
$396$	8.73314e8			0.706703
$397$	4.56779e8			0.366386			0.183193	−	0.983077i	$-0.441357\pi$
$397$	4.56779e8			0.366386			0.183193	+	0.983077i	$0.441357\pi$
$398$	1.53124e9	+	2.65218e9i	1.21745	+	2.10869i
$399$	−2.56410e7			−0.0202083
$400$	−2.27771e8	+	3.94510e8i	−0.177946	+	0.308211i
$401$	−1.51616e9			−1.17419			−0.587095	−	0.809518i	$-0.699728\pi$
$401$	−1.51616e9			−1.17419			−0.587095	+	0.809518i	$0.699728\pi$
$402$	1.30836e9	−	2.26614e9i	1.00446	−	1.73978i
$403$	−3.38738e8	+	5.86712e8i	−0.257808	+	0.446537i
$404$	2.34682e9	−	4.06481e9i	1.77070	−	3.06694i
$405$	5.11388e8	+	8.85751e8i	0.382524	+	0.662550i
$406$	2.82881e8			0.209779
$407$	7.77642e8	−	1.49971e9i	0.571741	−	1.10262i
$408$	−3.04703e8			−0.222109
$409$	4.85646e7	+	8.41163e7i	0.0350984	+	0.0607923i	0.883041	−	0.469296i	$-0.155492\pi$
$409$	4.85646e7	+	8.41163e7i	0.0350984	+	0.0607923i	−0.847943	+	0.530088i	$0.822159\pi$
$410$	−7.48996e8	+	1.29730e9i	−0.536705	+	0.929601i
$411$	1.06177e9	−	1.83903e9i	0.754366	−	1.30660i
$412$	−1.10773e9	+	1.91864e9i	−0.780355	+	1.35161i
$413$	−1.53131e8			−0.106964
$414$	3.36743e7	−	5.83256e7i	0.0233237	−	0.0403978i
$415$	1.10823e9			0.761136
$416$	−1.85582e8	−	3.21438e8i	−0.126389	−	0.218912i
$417$	1.13218e7			0.00764611
$418$	−9.67999e8			−0.648273
$419$	−8.13130e7	−	1.40838e8i	−0.0540021	−	0.0935344i	0.837761	−	0.546038i	$-0.183864\pi$
$419$	−8.13130e7	−	1.40838e8i	−0.0540021	−	0.0935344i	−0.891763	+	0.452503i	$0.850531\pi$
$420$	−1.17161e8	+	2.02928e8i	−0.0771630	+	0.133650i
$421$	4.36060e8			0.284812			0.142406	−	0.989808i	$-0.454516\pi$
$421$	4.36060e8			0.284812			0.142406	+	0.989808i	$0.454516\pi$
$422$	−2.16196e9	−	3.74462e9i	−1.40040	−	2.42557i
$423$	−3.25325e8	−	5.63479e8i	−0.208990	−	0.361982i
$424$	−9.58770e7	−	1.66064e8i	−0.0610849	−	0.105802i
$425$	9.75022e7	−	1.68879e8i	0.0616102	−	0.106712i
$426$	−8.18891e8	+	1.41836e9i	−0.513207	+	0.888900i
$427$	9.80860e7	+	1.69890e8i	0.0609691	+	0.105602i
$428$	−7.22429e8	−	1.25128e9i	−0.445391	−	0.771441i
$429$	−4.29802e8	−	7.44439e8i	−0.262826	−	0.455228i
$430$	−5.45338e9			−3.30770
$431$	−3.41972e8	+	5.92313e8i	−0.205741	+	0.356354i	−0.950369	−	0.311126i	$-0.899294\pi$
$431$	−3.41972e8	+	5.92313e8i	−0.205741	+	0.356354i	0.744628	+	0.667480i	$0.232627\pi$
$432$	−4.97172e8	−	8.61127e8i	−0.296697	−	0.513895i
$433$	1.12971e8			0.0668745			0.0334372	−	0.999441i	$-0.489355\pi$
$433$	1.12971e8			0.0668745			0.0334372	+	0.999441i	$0.489355\pi$
$434$	2.28133e8			0.133960
$435$	1.45426e9	+	2.51885e9i	0.847091	+	1.46720i
$436$	−2.66186e9			−1.53809
$437$	−2.41821e7	+	4.18847e7i	−0.0138615	+	0.0240088i
$438$	2.30193e9			1.30898
$439$	2.13391e8	−	3.69604e8i	0.120379	−	0.208502i	−0.799538	−	0.600615i	$-0.794922\pi$
$439$	2.13391e8	−	3.69604e8i	0.120379	−	0.208502i	0.919917	+	0.392113i	$0.128256\pi$
$440$	−2.01909e9	+	3.49716e9i	−1.12998	+	1.95718i
$441$	−2.76776e8	+	4.79389e8i	−0.153671	+	0.266166i
$442$	−1.47071e8	−	2.54734e8i	−0.0810119	−	0.140317i
$443$	−3.65711e8			−0.199860			−0.0999298	−	0.994994i	$-0.531862\pi$
$443$	−3.65711e8			−0.199860			−0.0999298	+	0.994994i	$0.531862\pi$
$444$	−2.81742e9	+	1.27543e8i	−1.52760	+	0.0691539i
$445$	3.99788e8			0.215065
$446$	2.19018e9	+	3.79350e9i	1.16898	+	2.02473i
$447$	3.59513e8	−	6.22695e8i	0.190388	−	0.329761i
$448$	−1.03231e8	+	1.78801e8i	−0.0542422	+	0.0939502i
$449$	3.77887e8	−	6.54519e8i	0.197015	−	0.341240i	−0.750544	−	0.660820i	$-0.770209\pi$
$449$	3.77887e8	−	6.54519e8i	0.197015	−	0.341240i	0.947559	+	0.319580i	$0.103542\pi$
$450$	6.57446e8			0.340107
$451$	−5.99449e8	+	1.03828e9i	−0.307705	+	0.532960i
$452$	9.56461e8			0.487172
$453$	1.50793e9	+	2.61181e9i	0.762145	+	1.32007i
$454$	−4.00154e9			−2.00693
$455$	−1.03258e8			−0.0513908
$456$	3.68857e8	+	6.38879e8i	0.182172	+	0.315531i
$457$	1.39549e9	−	2.41706e9i	0.683942	−	1.18462i	−0.289826	−	0.957079i	$-0.593597\pi$
$457$	1.39549e9	−	2.41706e9i	0.683942	−	1.18462i	0.973768	−	0.227543i	$-0.0730693\pi$
$458$	1.57197e9			0.764567
$459$	2.12825e8	+	3.68624e8i	0.102726	+	0.177926i
$460$	2.20989e8	+	3.82765e8i	0.105857	+	0.183349i
$461$	−3.07043e8	−	5.31813e8i	−0.145964	−	0.252817i	0.783768	−	0.621053i	$-0.213295\pi$
$461$	−3.07043e8	−	5.31813e8i	−0.145964	−	0.252817i	−0.929732	+	0.368237i	$0.879962\pi$
$462$	−1.44731e8	+	2.50682e8i	−0.0682835	+	0.118271i
$463$	−1.41716e9	+	2.45460e9i	−0.663569	+	1.14934i	0.316102	+	0.948725i	$0.397626\pi$
$463$	−1.41716e9	+	2.45460e9i	−0.663569	+	1.14934i	−0.979671	+	0.200610i	$0.935708\pi$
$464$	−9.30372e8	−	1.61145e9i	−0.432358	−	0.748866i
$465$	1.17281e9	+	2.03136e9i	0.540931	+	0.936920i
$466$	2.14736e8	+	3.71934e8i	0.0983003	+	0.170261i
$467$	−1.70194e9			−0.773279			−0.386639	−	0.922231i	$-0.626364\pi$
$467$	−1.70194e9			−0.773279			−0.386639	+	0.922231i	$0.626364\pi$
$468$	3.21243e8	−	5.56409e8i	0.144868	−	0.250919i
$469$	−1.25784e8	−	2.17864e8i	−0.0563015	−	0.0975171i
$470$	6.59065e9			2.92810
$471$	−1.11413e9			−0.491320
$472$	2.20286e9	+	3.81546e9i	0.964249	+	1.67013i
$473$	−4.36454e9			−1.89638
$474$	2.61257e9	−	4.52510e9i	1.12679	−	1.95166i
$475$	−4.72124e8			−0.202129
$476$	−3.20858e7	+	5.55741e7i	−0.0136360	+	0.0236183i
$477$	−3.16357e7	+	5.47946e7i	−0.0133464	+	0.0231166i
$478$	−4.80866e8	+	8.32885e8i	−0.201385	+	0.348809i
$479$	−1.93545e9	−	3.35230e9i	−0.804653	−	1.39370i	−0.916525	−	0.399977i	$-0.869018\pi$
$479$	−1.93545e9	−	3.35230e9i	−0.804653	−	1.39370i	0.111873	−	0.993723i	$-0.464315\pi$
$480$	−1.28508e9			−0.530377
$481$	−6.69450e8	−	1.04711e9i	−0.274290	−	0.429028i
$482$	7.64210e9			3.10848
$483$	7.23124e6	+	1.25249e7i	0.00292010	+	0.00505776i
$484$	−1.24524e9	+	2.15682e9i	−0.499223	+	0.864680i
$485$	6.97613e8	−	1.20830e9i	0.277663	−	0.480927i
$486$	−1.26557e9	+	2.19204e9i	−0.500104	+	0.866206i
$487$	−1.02006e9			−0.400197			−0.200098	−	0.979776i	$-0.564126\pi$
$487$	−1.02006e9			−0.400197			−0.200098	+	0.979776i	$0.564126\pi$
$488$	2.82202e9	−	4.88788e9i	1.09923	−	1.90393i
$489$	−9.53849e8			−0.368892
$490$	−2.80355e9	−	4.85590e9i	−1.07652	−	1.86459i
$491$	2.67211e9			1.01875			0.509377	−	0.860544i	$-0.329876\pi$
$491$	2.67211e9			1.01875			0.509377	+	0.860544i	$0.329876\pi$
$492$	2.00153e9			0.757676
$493$	3.98266e8	+	6.89817e8i	0.149696	+	0.259280i
$494$	−3.56072e8	+	6.16736e8i	−0.132891	+	0.230173i
$495$	1.33244e9			0.493775
$496$	−7.50311e8	−	1.29958e9i	−0.276093	−	0.478207i
$497$	7.87273e7	+	1.36360e8i	0.0287659	+	0.0498240i
$498$	−1.14278e9	−	1.97935e9i	−0.414628	−	0.718157i
$499$	−1.29993e9	+	2.25154e9i	−0.468347	+	0.811201i	−0.999346	−	0.0361716i	$-0.988484\pi$
$499$	−1.29993e9	+	2.25154e9i	−0.468347	+	0.811201i	0.530998	+	0.847373i	$0.321817\pi$
$500$	1.14830e9	−	1.98892e9i	0.410829	−	0.711576i
$501$	−1.11579e9	−	1.93261e9i	−0.396417	−	0.686614i
$502$	1.59261e8	+	2.75849e8i	0.0561885	+	0.0973214i
$503$	−5.66366e8	−	9.80975e8i	−0.198431	−	0.343692i	0.749589	−	0.661904i	$-0.230251\pi$
$503$	−5.66366e8	−	9.80975e8i	−0.198431	−	0.343692i	−0.948020	+	0.318211i	$0.896918\pi$
$504$	−9.87623e7			−0.0343625
$505$	3.58061e9	−	6.20179e9i	1.23719	−	2.14288i
$506$	2.72994e8	+	4.72839e8i	0.0936754	+	0.162251i
$507$	1.80647e9			0.615606
$508$	4.68998e8			0.158726
$509$	−1.39754e9	−	2.42062e9i	−0.469735	−	0.813605i	0.529666	−	0.848206i	$-0.322317\pi$
$509$	−1.39754e9	−	2.42062e9i	−0.469735	−	0.813605i	−0.999401	+	0.0346012i	$0.988984\pi$
$510$	−1.01840e9			−0.339957
$511$	1.10653e8	−	1.91656e8i	0.0366850	−	0.0635403i
$512$	3.16628e9			1.04257
$513$	5.15270e8	−	8.92474e8i	0.168509	−	0.291867i
$514$	−2.49974e9	+	4.32968e9i	−0.811940	+	1.40632i
$515$	−1.69009e9	+	2.92732e9i	−0.545235	+	0.944375i
$516$	3.64324e9	+	6.31028e9i	1.16739	+	2.02197i
$517$	5.27474e9			1.67874
$518$	−1.92649e8	+	3.71531e8i	−0.0608994	+	0.117447i
$519$	1.75258e9			0.550291
$520$	1.48542e9	+	2.57282e9i	0.463272	+	0.802411i
$521$	−7.27488e7	+	1.26005e8i	−0.0225369	+	0.0390350i	−0.877074	−	0.480355i	$-0.840508\pi$
$521$	−7.27488e7	+	1.26005e8i	−0.0225369	+	0.0390350i	0.854537	+	0.519391i	$0.173841\pi$
$522$	−1.34273e9	+	2.32568e9i	−0.413183	+	0.715653i
$523$	1.94345e9	−	3.36615e9i	0.594042	−	1.02891i	−0.399640	−	0.916672i	$-0.630865\pi$
$523$	1.94345e9	−	3.36615e9i	0.594042	−	1.02891i	0.993681	−	0.112238i	$-0.0358019\pi$
$524$	−2.24223e9			−0.680801
$525$	−7.05901e7	+	1.22266e8i	−0.0212905	+	0.0368763i
$526$	4.41906e9			1.32397
$527$	3.21187e8	+	5.56312e8i	0.0955919	+	0.165570i
$528$	1.90404e9			0.562933
$529$	−3.37755e9			−0.991988
$530$	−3.20448e8	−	5.55033e8i	−0.0934959	−	0.161940i
$531$	7.26856e8	−	1.25895e9i	0.210677	−	0.364904i
$532$	1.55365e8			0.0447366
$533$	4.41007e8	+	7.63846e8i	0.126154	+	0.218505i
$534$	−4.12250e8	−	7.14039e8i	−0.117157	−	0.202921i
$535$	−1.10223e9	−	1.90912e9i	−0.311196	−	0.539007i
$536$	−3.61891e9	+	6.26814e9i	−1.01508	+	1.75817i
$537$	7.66805e8	−	1.32815e9i	0.213685	−	0.370114i
$538$	3.71257e9	+	6.43036e9i	1.02787	+	1.78032i
$539$	−2.24379e9	−	3.88635e9i	−0.617193	−	1.06901i
$540$	−4.70881e9	−	8.15590e9i	−1.28687	−	2.22892i
$541$	3.88979e9			1.05618			0.528088	−	0.849190i	$-0.322909\pi$
$541$	3.88979e9			1.05618			0.528088	+	0.849190i	$0.322909\pi$
$542$	−2.63454e9	+	4.56316e9i	−0.710735	+	1.23103i
$543$	−2.68852e9	−	4.65665e9i	−0.720632	−	1.24817i
$544$	−3.51933e8			−0.0937267
$545$	−4.06126e9			−1.07467
$546$	1.06477e8	+	1.84424e8i	0.0279951	+	0.0484889i
$547$	−1.06477e9			−0.278165			−0.139082	−	0.990281i	$-0.544415\pi$
$547$	−1.06477e9			−0.278165			−0.139082	+	0.990281i	$0.544415\pi$
$548$	−6.43350e9	+	1.11432e10i	−1.67000	+	2.89252i
$549$	−1.86231e9			−0.480340
$550$	−2.66492e9	+	4.61577e9i	−0.682990	+	1.18297i
$551$	9.64239e8	−	1.67011e9i	0.245558	−	0.425319i
$552$	2.08049e8	−	3.60351e8i	0.0526476	−	0.0911883i
$553$	−2.51169e8	−	4.35038e8i	−0.0631581	−	0.109393i
$554$	−5.97383e9			−1.49269
$555$	−4.29861e9	+	1.94596e8i	−1.06734	+	0.0483179i
$556$	−6.86018e7			−0.0169268
$557$	2.58899e9	+	4.48427e9i	0.634801	+	1.09951i	0.986557	+	0.163416i	$0.0522512\pi$
$557$	2.58899e9	+	4.48427e9i	0.634801	+	1.09951i	−0.351756	+	0.936092i	$0.614415\pi$
$558$	−1.08286e9	+	1.87557e9i	−0.263848	+	0.456998i
$559$	−1.60547e9	+	2.78075e9i	−0.388741	+	0.673320i
$560$	1.14360e8	−	1.98077e8i	0.0275178	−	0.0476623i
$561$	−8.15065e8			−0.194905
$562$	3.32047e9	−	5.75123e9i	0.789083	−	1.36673i
$563$	1.10692e9			0.261420			0.130710	−	0.991421i	$-0.458274\pi$
$563$	1.10692e9			0.261420			0.130710	+	0.991421i	$0.458274\pi$
$564$	−4.40302e9	−	7.62625e9i	−1.03341	−	1.78992i
$565$	1.45930e9			0.340388
$566$	−7.78415e8			−0.180449
$567$	−1.01394e8	−	1.75619e8i	−0.0233599	−	0.0404605i
$568$	2.26505e9	−	3.92318e9i	0.518632	−	0.898296i
$569$	5.42996e9			1.23567			0.617836	−	0.786307i	$-0.288010\pi$
$569$	5.42996e9			1.23567			0.617836	+	0.786307i	$0.288010\pi$
$570$	1.23282e9	+	2.13531e9i	0.278830	+	0.482947i
$571$	3.01043e8	+	5.21423e8i	0.0676710	+	0.117210i	0.897876	−	0.440249i	$-0.145110\pi$
$571$	3.01043e8	+	5.21423e8i	0.0676710	+	0.117210i	−0.830205	+	0.557459i	$0.811776\pi$
$572$	2.60428e9	+	4.51074e9i	0.581837	+	1.00777i
$573$	−2.79022e8	+	4.83280e8i	−0.0619580	+	0.107314i
$574$	1.48504e8	−	2.57217e8i	0.0327754	−	0.0567687i
$575$	1.33148e8	+	2.30618e8i	0.0292076	+	0.0505890i
$576$	−9.79998e8	−	1.69741e9i	−0.213671	−	0.370090i
$577$	1.92636e9	+	3.33655e9i	0.417467	+	0.723073i	0.995684	−	0.0928094i	$-0.0295847\pi$
$577$	1.92636e9	+	3.33655e9i	0.417467	+	0.723073i	−0.578217	+	0.815883i	$0.696251\pi$
$578$	7.54456e9			1.62512
$579$	−2.85255e9	+	4.94076e9i	−0.610742	+	1.05784i
$580$	−8.81173e9	−	1.52624e10i	−1.87527	−	3.24806i
$581$	−2.19731e8			−0.0464809
$582$	−2.87744e9			−0.605028
$583$	−2.56466e8	−	4.44213e8i	−0.0536032	−	0.0928435i
$584$	−6.36714e9			−1.32282
$585$	4.90129e8	−	8.48928e8i	0.101220	−	0.175318i
$586$	9.42420e9			1.93465
$587$	−2.61686e9	+	4.53254e9i	−0.534008	+	0.924929i	0.465203	+	0.885204i	$0.345981\pi$
$587$	−2.61686e9	+	4.53254e9i	−0.534008	+	0.924929i	−0.999211	+	0.0397248i	$0.987352\pi$
$588$	−3.74594e9	+	6.48816e9i	−0.759872	+	1.31614i
$589$	7.77624e8	−	1.34688e9i	0.156807	−	0.271598i
$590$	7.36257e9	+	1.27523e10i	1.47587	+	2.55628i
$591$	1.29267e9			0.257591
$592$	2.75006e9	−	1.24494e8i	0.544773	−	0.0246616i
$593$	−7.36318e8			−0.145002			−0.0725010	−	0.997368i	$-0.523098\pi$
$593$	−7.36318e8			−0.145002			−0.0725010	+	0.997368i	$0.523098\pi$
$594$	−5.81691e9	−	1.00752e10i	−1.13878	−	1.97243i
$595$	−4.89541e7	+	8.47910e7i	−0.00952751	+	0.0165021i
$596$	−2.17838e9	+	3.77307e9i	−0.421475	+	0.730016i
$597$	3.12156e9	−	5.40670e9i	0.600428	−	1.03997i
$598$	4.01676e8			0.0768107
$599$	2.26385e9	−	3.92111e9i	0.430382	−	0.745443i	−0.566524	−	0.824045i	$-0.691712\pi$
$599$	2.26385e9	−	3.92111e9i	0.430382	−	0.745443i	0.996906	+	0.0786018i	$0.0250456\pi$
$600$	4.06187e9			0.767710
$601$	2.98510e8	+	5.17035e8i	0.0560917	+	0.0971537i	0.892708	−	0.450636i	$-0.148803\pi$
$601$	2.98510e8	+	5.17035e8i	0.0560917	+	0.0971537i	−0.836616	+	0.547790i	$0.815469\pi$
$602$	1.08125e9			0.201994
$603$	2.38820e9			0.443567
$604$	−9.13692e9	−	1.58256e10i	−1.68722	−	2.92234i
$605$	−1.89990e9	+	3.29072e9i	−0.348808	+	0.604153i
$606$	−1.47689e10			−2.69583
$607$	2.56052e9	+	4.43496e9i	0.464695	+	0.804876i	0.999188	−	0.0402973i	$-0.0128305\pi$
$607$	2.56052e9	+	4.43496e9i	0.464695	+	0.804876i	−0.534492	+	0.845173i	$0.679497\pi$
$608$	4.26031e8	+	7.37907e8i	0.0768739	+	0.133149i
$609$	−2.88338e8	−	4.99417e8i	−0.0517299	−	0.0895989i
$610$	9.43199e9	−	1.63367e10i	1.68248	−	2.91413i
$611$	1.94028e9	−	3.36066e9i	0.344128	−	0.596047i
$612$	−3.04598e8	−	5.27580e8i	−0.0537152	−	0.0930375i
$613$	2.60949e9	+	4.51978e9i	0.457556	+	0.792511i	0.998831	−	0.0483348i	$-0.0153914\pi$
$613$	2.60949e9	+	4.51978e9i	0.457556	+	0.792511i	−0.541275	+	0.840846i	$0.682058\pi$
$614$	8.39129e9	+	1.45341e10i	1.46298	+	2.53396i
$615$	3.05378e9			0.529389
$616$	4.00327e8	−	6.93387e8i	0.0690053	−	0.119521i
$617$	−3.17497e9	−	5.49921e9i	−0.544179	−	0.942545i	−0.998658	−	0.0517877i	$-0.983508\pi$
$617$	−3.17497e9	−	5.49921e9i	−0.544179	−	0.942545i	0.454480	−	0.890757i	$-0.349825\pi$
$618$	6.97108e9			1.18807
$619$	−7.43850e9			−1.26057			−0.630287	−	0.776362i	$-0.717063\pi$
$619$	−7.43850e9			−1.26057			−0.630287	+	0.776362i	$0.717063\pi$
$620$	−7.10634e9	−	1.23085e10i	−1.19750	−	2.07413i
$621$	−5.81262e8			−0.0973984
$622$	−4.59660e9	+	7.96155e9i	−0.765897	+	1.32657i
$623$	−7.92666e7			−0.0131336
$624$	7.00388e8	−	1.21311e9i	0.115397	−	0.199873i
$625$	3.74362e9	−	6.48414e9i	0.613354	−	1.06236i
$626$	7.93078e9	−	1.37365e10i	1.29213	−	2.23803i
$627$	9.86674e8	+	1.70897e9i	0.159859	+	0.276884i
$628$	6.75082e9			1.08767
$629$	−1.17722e9	+	5.32923e7i	−0.188617	+	0.00853861i
$630$	−3.30092e8			−0.0525948
$631$	−3.26490e9	−	5.65497e9i	−0.517329	−	0.896040i	−0.999797	−	0.0201267i	$-0.993593\pi$
$631$	−3.26490e9	−	5.65497e9i	−0.517329	−	0.896040i	0.482468	−	0.875913i	$-0.339740\pi$
$632$	−7.22636e9	+	1.25164e10i	−1.13870	+	1.97229i
$633$	−4.40733e9	+	7.63373e9i	−0.690658	+	1.19625i
$634$	−3.82825e9	+	6.63073e9i	−0.596607	+	1.03335i
$635$	7.15562e8			0.110902
$636$	−4.28164e8	+	7.41602e8i	−0.0659949	+	0.114306i
$637$	−3.30145e9			−0.506077
$638$	−1.08854e10	−	1.88540e10i	−1.65947	−	2.87429i
$639$	−1.49476e9			−0.226630
$640$	1.56214e10			2.35554
$641$	5.93365e9	+	1.02774e10i	0.889854	+	1.54127i	0.840047	+	0.542514i	$0.182528\pi$
$641$	5.93365e9	+	1.02774e10i	0.889854	+	1.54127i	0.0498079	+	0.998759i	$0.484139\pi$
$642$	−2.27317e9	+	3.93725e9i	−0.339047	+	0.587247i
$643$	8.31581e9			1.23358			0.616788	−	0.787129i	$-0.288433\pi$
$643$	8.31581e9			1.23358			0.616788	+	0.787129i	$0.288433\pi$
$644$	−4.38159e7	−	7.58913e7i	−0.00646444	−	0.0111967i
$645$	5.55859e9	+	9.62777e9i	0.815654	+	1.41275i
$646$	3.37623e8	+	5.84780e8i	0.0492740	+	0.0853451i
$647$	−3.38181e9	+	5.85747e9i	−0.490890	+	0.850247i	−0.999945	−	0.0104872i	$-0.996662\pi$
$647$	−3.38181e9	+	5.85747e9i	−0.490890	+	0.850247i	0.509055	+	0.860734i	$0.329995\pi$
$648$	−2.91718e9	+	5.05271e9i	−0.421164	+	0.729478i
$649$	5.89253e9	+	1.02062e10i	0.846147	+	1.46557i
$650$	1.96055e9	+	3.39577e9i	0.280014	+	0.484999i
$651$	−2.32535e8	−	4.02762e8i	−0.0330335	−	0.0572156i
$652$	5.77961e9			0.816643
$653$	−5.91332e9	+	1.02422e10i	−0.831066	+	1.43945i	0.0661281	+	0.997811i	$0.478935\pi$
$653$	−5.91332e9	+	1.02422e10i	−0.831066	+	1.43945i	−0.897194	+	0.441637i	$0.854398\pi$
$654$	4.18786e9	+	7.25359e9i	0.585423	+	1.01398i
$655$	−3.42103e9			−0.475677
$656$	−1.95368e9			−0.270202
$657$	1.05045e9	+	1.81944e9i	0.144510	+	0.250299i
$658$	−1.30674e9			−0.178813
$659$	−5.04881e8	+	8.74480e8i	−0.0687211	+	0.119028i	−0.898339	−	0.439304i	$-0.855225\pi$
$659$	−5.04881e8	+	8.74480e8i	−0.0687211	+	0.119028i	0.829617	+	0.558332i	$0.188559\pi$
$660$	1.80335e10			2.44161
$661$	2.26311e9	−	3.91983e9i	0.304790	−	0.527913i	−0.672424	−	0.740166i	$-0.734747\pi$
$661$	2.26311e9	−	3.91983e9i	0.304790	−	0.527913i	0.977215	+	0.212253i	$0.0680802\pi$
$662$	1.24374e10	−	2.15423e10i	1.66620	−	2.88595i
$663$	−2.99817e8	+	5.19297e8i	−0.0399538	+	0.0692020i
$664$	3.16092e9	+	5.47487e9i	0.419011	+	0.725748i
$665$	2.37045e8			0.0312575
$666$	−2.14007e9	−	3.34736e9i	−0.280717	−	0.439080i
$667$	−1.08773e9			−0.141932
$668$	6.76087e9	+	1.17102e10i	0.877577	+	1.52001i
$669$	4.46486e9	−	7.73337e9i	0.576523	−	0.998568i
$670$	−1.20954e10	+	2.09499e10i	−1.55367	+	2.69104i
$671$	7.54877e9	−	1.30748e10i	0.964600	−	1.67074i
$672$	2.54794e8			0.0323889
$673$	−6.24890e9	+	1.08234e10i	−0.790225	+	1.36871i	0.135602	+	0.990763i	$0.456703\pi$
$673$	−6.24890e9	+	1.08234e10i	−0.790225	+	1.36871i	−0.925827	+	0.377947i	$0.876630\pi$
$674$	5.44274e9			0.684712
$675$	−2.83709e9	−	4.91399e9i	−0.355067	−	0.614994i
$676$	−1.09459e10			−1.36281
$677$	−3.12125e9			−0.386606			−0.193303	−	0.981139i	$-0.561920\pi$
$677$	−3.12125e9			−0.386606			−0.193303	+	0.981139i	$0.561920\pi$
$678$	−1.50479e9	−	2.60637e9i	−0.185426	−	0.321168i
$679$	−1.38317e8	+	2.39572e8i	−0.0169563	+	0.0293692i
$680$	2.81690e9			0.343550
$681$	4.07874e9	+	7.06458e9i	0.494892	+	0.857179i
$682$	−8.77865e9	−	1.52051e10i	−1.05970	−	1.83545i
$683$	−3.34521e9	−	5.79407e9i	−0.401745	−	0.695843i	0.592192	−	0.805797i	$-0.298263\pi$
$683$	−3.34521e9	−	5.79407e9i	−0.401745	−	0.695843i	−0.993937	+	0.109954i	$0.964929\pi$
$684$	−7.37461e8	+	1.27732e9i	−0.0881135	+	0.152617i
$685$	−9.81576e9	+	1.70014e10i	−1.16683	+	2.02101i
$686$	1.11518e9	+	1.93154e9i	0.131889	+	0.228439i
$687$	−1.60230e9	−	2.77527e9i	−0.188536	−	0.326555i
$688$	−3.55614e9	−	6.15942e9i	−0.416313	−	0.721074i
$689$	−3.77358e8			−0.0439528
$690$	6.95359e8	−	1.20440e9i	0.0805818	−	0.139572i
$691$	−7.01143e9	−	1.21442e10i	−0.808414	−	1.40021i	−0.913962	−	0.405799i	$-0.866993\pi$
$691$	−7.01143e9	−	1.21442e10i	−0.808414	−	1.40021i	0.105549	−	0.994414i	$-0.466340\pi$
$692$	−1.06193e10			−1.21822
$693$	−2.64184e8			−0.0301537
$694$	−1.26541e10	−	2.19175e10i	−1.43705	−	2.48905i
$695$	−1.04668e8			−0.0118267
$696$	−8.29574e9	+	1.43687e10i	−0.932659	+	1.61541i
$697$	8.36313e8			0.0935522
$698$	1.07866e10	−	1.86829e10i	1.20058	−	2.07946i
$699$	4.37758e8	−	7.58220e8i	0.0484802	−	0.0839702i
$700$	4.27723e8	−	7.40838e8i	0.0471324	−	0.0816357i
$701$	−4.30586e9	−	7.45796e9i	−0.472114	−	0.817725i	0.527377	−	0.849631i	$-0.323175\pi$
$701$	−4.30586e9	−	7.45796e9i	−0.472114	−	0.817725i	−0.999491	+	0.0319064i	$0.989842\pi$
$702$	−8.55886e9			−0.933762
$703$	1.53682e9	+	2.40380e9i	0.166832	+	0.260949i
$704$	1.58895e10			1.71635
$705$	−6.71780e9	−	1.16356e10i	−0.722047	−	1.25062i
$706$	3.61085e9	−	6.25418e9i	0.386183	−	0.668889i
$707$	−7.09932e8	+	1.22964e9i	−0.0755525	+	0.130861i
$708$	9.83743e9	−	1.70389e10i	1.04175	−	1.80437i
$709$	2.40175e9			0.253085			0.126542	−	0.991961i	$-0.459612\pi$
$709$	2.40175e9			0.253085			0.126542	+	0.991961i	$0.459612\pi$
$710$	7.57045e9	−	1.31124e10i	0.793812	−	1.37492i
$711$	4.76883e9			0.497586
$712$	1.14028e9	+	1.97503e9i	0.118395	+	0.205066i
$713$	−8.77217e8			−0.0906345
$714$	2.01920e8			0.0207604
$715$	3.97342e9	+	6.88216e9i	0.406530	+	0.704131i
$716$	−4.64626e9	+	8.04756e9i	−0.473051	+	0.819349i
$717$	1.96057e9			0.198640
$718$	5.15715e9	+	8.93245e9i	0.519965	+	0.900606i
$719$	−6.15645e8	−	1.06633e9i	−0.0617703	−	0.106989i	0.833487	−	0.552540i	$-0.186341\pi$
$719$	−6.15645e8	−	1.06633e9i	−0.0617703	−	0.106989i	−0.895257	+	0.445551i	$0.853008\pi$
$720$	1.08564e9	+	1.88039e9i	0.108399	+	0.187752i
$721$	3.35096e8	−	5.80404e8i	0.0332963	−	0.0576709i
$722$	−7.70380e9	+	1.33434e10i	−0.761772	+	1.31943i
$723$	−7.78954e9	−	1.34919e10i	−0.766527	−	1.32766i
$724$	1.62904e10	+	2.82158e10i	1.59532	+	2.76317i
$725$	−5.30913e9	−	9.19568e9i	−0.517417	−	0.896192i
$726$	7.83648e9			0.760051
$727$	8.71014e9	−	1.50864e10i	0.840727	−	1.45618i	−0.0485545	−	0.998821i	$-0.515461\pi$
$727$	8.71014e9	−	1.50864e10i	0.840727	−	1.45618i	0.889281	−	0.457361i	$-0.151205\pi$
$728$	−2.94516e8	−	5.10116e8i	−0.0282910	−	0.0490015i
$729$	1.13851e10			1.08840
$730$	−2.12808e10			−2.02469
$731$	1.52228e9	+	2.63667e9i	0.144140	+	0.249658i
$732$	−2.52049e10			−2.37518
$733$	−4.22680e9	+	7.32104e9i	−0.396413	+	0.686608i	−0.993280	−	0.115732i	$-0.963079\pi$
$733$	−4.22680e9	+	7.32104e9i	−0.396413	+	0.686608i	0.596867	+	0.802340i	$0.296412\pi$
$734$	1.83139e10			1.70941
$735$	−5.71528e9	+	9.89916e9i	−0.530924	+	0.919587i
$736$	2.40297e8	−	4.16207e8i	0.0222165	−	0.0384802i
$737$	−9.68041e9	+	1.67670e10i	−0.890754	+	1.54283i
$738$	1.40979e9	+	2.44183e9i	0.129109	+	0.223624i
$739$	−8.99239e9			−0.819633			−0.409817	−	0.912168i	$-0.634407\pi$
$739$	−8.99239e9			−0.819633			−0.409817	+	0.912168i	$0.634407\pi$
$740$	2.60463e10	−	1.17910e9i	2.36285	−	0.106965i
$741$	1.45177e9			0.131079
$742$	6.35358e7	+	1.10047e8i	0.00570958	+	0.00988929i
$743$	−6.45765e9	+	1.11850e10i	−0.577582	+	1.00040i	0.418174	+	0.908367i	$0.362670\pi$
$743$	−6.45765e9	+	1.11850e10i	−0.577582	+	1.00040i	−0.995756	+	0.0920341i	$0.970663\pi$
$744$	−6.69022e9	+	1.15878e10i	−0.595573	+	1.03156i
$745$	−3.32361e9	+	5.75667e9i	−0.294485	+	0.510064i
$746$	−1.52776e10			−1.34731
$747$	1.04298e9	−	1.80649e9i	0.0915490	−	0.158568i
$748$	4.93868e9			0.431475
$749$	2.18541e8	+	3.78523e8i	0.0190040	+	0.0329159i
$750$	−7.22643e9			−0.625474
$751$	−5.99083e9			−0.516116			−0.258058	−	0.966129i	$-0.583083\pi$
$751$	−5.99083e9			−0.516116			−0.258058	+	0.966129i	$0.583083\pi$
$752$	4.29775e9	+	7.44393e9i	0.368535	+	0.638322i
$753$	3.24668e8	−	5.62342e8i	0.0277113	−	0.0479974i
$754$	−1.60164e10			−1.36071
$755$	−1.39404e10	−	2.41456e10i	−1.17886	−	2.04185i
$756$	9.33623e8	+	1.61708e9i	0.0785860	+	0.136115i
$757$	1.05026e10	+	1.81911e10i	0.879958	+	1.52413i	0.851386	+	0.524540i	$0.175763\pi$
$757$	1.05026e10	+	1.81911e10i	0.879958	+	1.52413i	0.0285721	+	0.999592i	$0.490904\pi$
$758$	−9.88614e9	+	1.71233e10i	−0.824489	+	1.42806i
$759$	5.56521e8	−	9.63922e8i	0.0461993	−	0.0800195i
$760$	−3.40999e9	−	5.90628e9i	−0.281777	−	0.488052i
$761$	7.39655e9	+	1.28112e10i	0.608391	+	1.05376i	0.991506	+	0.130063i	$0.0415181\pi$
$761$	7.39655e9	+	1.28112e10i	0.608391	+	1.05376i	−0.383115	+	0.923701i	$0.625149\pi$
$762$	−7.37868e8	−	1.27802e9i	−0.0604138	−	0.104640i
$763$	8.05233e8			0.0656275
$764$	1.69066e9	−	2.92832e9i	0.137161	−	0.237570i
$765$	−4.64734e8	−	8.04942e8i	−0.0375309	−	0.0650054i
$766$	3.77162e9			0.303198
$767$	8.67013e9			0.693812
$768$	−8.89951e9	−	1.54144e10i	−0.708928	−	1.22790i
$769$	−3.32869e8			−0.0263956			−0.0131978	−	0.999913i	$-0.504201\pi$
$769$	−3.32869e8			−0.0263956			−0.0131978	+	0.999913i	$0.504201\pi$
$770$	1.33801e9	−	2.31750e9i	0.105619	−	0.182937i
$771$	1.01919e10			0.800873
$772$	1.72843e10	−	2.99373e10i	1.35205	−	2.34181i
$773$	−5.18209e8	+	8.97565e8i	−0.0403531	+	0.0698936i	−0.885497	−	0.464646i	$-0.846182\pi$
$773$	−5.18209e8	+	8.97565e8i	−0.0403531	+	0.0698936i	0.845143	+	0.534540i	$0.179515\pi$
$774$	−5.13229e9	+	8.88939e9i	−0.397849	+	0.689094i
$775$	−4.28162e9	−	7.41599e9i	−0.330409	−	0.572286i
$776$	7.95899e9			0.611423
$777$	8.52291e8	−	3.85828e7i	0.0651800	−	0.00295067i
$778$	−1.91994e10			−1.46171
$779$	−1.01240e9	−	1.75352e9i	−0.0767307	−	0.132902i
$780$	6.63351e9	−	1.14896e10i	0.500510	−	0.866908i
$781$	6.05891e9	−	1.04943e10i	0.455109	−	0.788272i
$782$	1.90432e8	−	3.29838e8i	0.0142402	−	0.0246647i
$783$	2.31773e10			1.72543
$784$	3.65638e9	−	6.33304e9i	0.270985	−	0.469360i
$785$	1.02999e10			0.759958
$786$	3.52767e9	+	6.11010e9i	0.259124	+	0.448817i
$787$	−1.57296e10			−1.15029			−0.575144	−	0.818052i	$-0.695054\pi$
$787$	−1.57296e10			−1.15029			−0.575144	+	0.818052i	$0.695054\pi$
$788$	−7.83259e9			−0.570248
$789$	−4.50431e9	−	7.80170e9i	−0.326482	−	0.565483i
$790$	−2.41526e10	+	4.18335e10i	−1.74288	+	3.01876i
$791$	−2.89337e8			−0.0207867
$792$	3.80041e9	+	6.58250e9i	0.271827	+	0.470818i
$793$	−5.55353e9	−	9.61900e9i	−0.395470	−	0.684973i
$794$	4.35444e9	+	7.54212e9i	0.308717	+	0.534714i
$795$	−6.53261e8	+	1.13148e9i	−0.0461107	+	0.0798661i
$796$	−1.89143e10	+	3.27605e10i	−1.32921	+	2.30226i
$797$	−9.92532e9	−	1.71912e10i	−0.694449	−	1.20282i	−0.970366	−	0.241640i	$-0.922315\pi$
$797$	−9.92532e9	−	1.71912e10i	−0.694449	−	1.20282i	0.275917	−	0.961182i	$-0.411019\pi$
$798$	−2.44434e8	−	4.23372e8i	−0.0170275	−	0.0294925i
$799$	−1.83975e9	−	3.18653e9i	−0.127598	−	0.221006i
$800$	4.69148e9			0.323963
$801$	3.76249e8	−	6.51683e8i	0.0258679	−	0.0448046i
$802$	−1.44534e10	−	2.50340e10i	−0.989372	−	1.71364i
$803$	−1.70318e10			−1.16080
$804$	3.23224e10			2.19335
$805$	−6.68510e7	−	1.15789e8i	−0.00451671	−	0.00782318i
$806$	−1.29167e10			−0.868917
$807$	7.56839e9	−	1.31088e10i	0.506928	−	0.878025i
$808$	4.08507e10			2.72433
$809$	1.14795e10	−	1.98830e10i	0.762257	−	1.32027i	−0.179428	−	0.983771i	$-0.557425\pi$
$809$	1.14795e10	−	1.98830e10i	0.762257	−	1.32027i	0.941685	−	0.336497i	$-0.109242\pi$
$810$	−9.75006e9	+	1.68876e10i	−0.644629	+	1.11653i
$811$	−5.35207e9	+	9.27006e9i	−0.352329	+	0.610253i	−0.986657	−	0.162812i	$-0.947944\pi$
$811$	−5.35207e9	+	9.27006e9i	−0.352329	+	0.610253i	0.634328	+	0.773064i	$0.281277\pi$
$812$	1.74711e9	+	3.02609e9i	0.114518	+	0.198352i
$813$	1.07415e10			0.701047
$814$	3.21757e10	−	1.45658e9i	2.09094	−	0.0946561i
$815$	8.81811e9			0.570589
$816$	−6.64099e8	−	1.15025e9i	−0.0427875	−	0.0741102i
$817$	3.68559e9	−	6.38363e9i	0.236445	−	0.409535i
$818$	−9.25925e8	+	1.60375e9i	−0.0591479	+	0.102447i
$819$	−9.71786e7	+	1.68318e8i	−0.00618126	+	0.0107063i
$820$	−1.85036e10			−1.17195
$821$	9.17746e9	−	1.58958e10i	0.578791	−	1.00249i	−0.416828	−	0.908986i	$-0.636858\pi$
$821$	9.17746e9	−	1.58958e10i	0.578791	−	1.00249i	0.995618	−	0.0935094i	$-0.0298085\pi$
$822$	4.04870e10			2.54252
$823$	1.21398e10	+	2.10267e10i	0.759122	+	1.31484i	0.943299	+	0.331944i	$0.107705\pi$
$823$	1.21398e10	+	2.10267e10i	0.759122	+	1.31484i	−0.184177	+	0.982893i	$0.558962\pi$
$824$	−1.92820e10			−1.20062
$825$	1.08653e10			0.673680
$826$	−1.45979e9	−	2.52843e9i	−0.0901280	−	0.156106i
$827$	−5.12935e9	+	8.88430e9i	−0.315350	+	0.546203i	−0.979512	−	0.201386i	$-0.935455\pi$
$827$	−5.12935e9	+	8.88430e9i	−0.315350	+	0.546203i	0.664162	+	0.747589i	$0.268789\pi$
$828$	8.31910e8			0.0509296
$829$	−8.84871e9	−	1.53264e10i	−0.539435	−	0.934329i	−0.998934	−	0.0461506i	$-0.985305\pi$
$829$	−8.84871e9	−	1.53264e10i	−0.539435	−	0.934329i	0.459500	−	0.888178i	$-0.348029\pi$
$830$	1.05647e10	+	1.82986e10i	0.641333	+	1.11082i
$831$	6.08908e9	+	1.05466e10i	0.368085	+	0.637542i
$832$	5.84484e9	−	1.01236e10i	0.351836	−	0.609398i
$833$	−1.56519e9	+	2.71100e9i	−0.0938233	+	0.162507i
$834$	1.07930e8	+	1.86941e8i	0.00644261	+	0.0111589i
$835$	1.03152e10	+	1.78665e10i	0.613164	+	1.06203i
$836$	−5.97851e9	−	1.03551e10i	−0.353892	−	0.612959i
$837$	1.86916e10			1.10181
$838$	1.55030e9	−	2.68520e9i	0.0910044	−	0.157624i
$839$	5.28085e9	+	9.14671e9i	0.308700	+	0.534685i	0.978078	−	0.208237i	$-0.0667726\pi$
$839$	5.28085e9	+	9.14671e9i	0.308700	+	0.534685i	−0.669378	+	0.742922i	$0.733439\pi$
$840$	−2.03939e9			−0.118720
$841$	2.61224e10			1.51435
$842$	4.15693e9	+	7.20001e9i	0.239983	+	0.415663i
$843$	−1.35381e10			−0.778327
$844$	2.67051e10	−	4.62546e10i	1.52896	−	2.64824i
$845$	−1.67004e10			−0.952200
$846$	6.20260e9	−	1.07432e10i	0.352190	−	0.610012i
$847$	3.76696e8	−	6.52456e8i	0.0213009	−	0.0368943i
$848$	4.17928e8	−	7.23872e8i	0.0235351	−	0.0407639i
$849$	7.93433e8	+	1.37427e9i	0.0444973	+	0.0770715i
$850$	3.71793e9			0.207651
$851$	7.40774e8	−	1.42861e9i	0.0412033	−	0.0794621i
$852$	−2.02304e10			−1.12064
$853$	−3.72891e9	−	6.45867e9i	−0.205713	−	0.356305i	0.744647	−	0.667459i	$-0.232618\pi$
$853$	−3.72891e9	−	6.45867e9i	−0.205713	−	0.356305i	−0.950360	+	0.311154i	$0.899285\pi$
$854$	−1.87009e9	+	3.23910e9i	−0.102745	+	0.177960i
$855$	−1.12516e9	+	1.94884e9i	−0.0615651	+	0.106634i
$856$	6.28760e9	−	1.08904e10i	0.342631	−	0.593454i
$857$	−2.14810e10			−1.16580			−0.582898	−	0.812546i	$-0.698081\pi$
$857$	−2.14810e10			−1.16580			−0.582898	+	0.812546i	$0.698081\pi$
$858$	8.19455e9	−	1.41934e10i	0.442914	−	0.767150i
$859$	9.03456e9			0.486330			0.243165	−	0.969985i	$-0.421814\pi$
$859$	9.03456e9			0.486330			0.243165	+	0.969985i	$0.421814\pi$
$860$	−3.36809e10	−	5.83370e10i	−1.80567	−	3.12752i
$861$	−6.05478e8			−0.0323286
$862$	−1.30400e10			−0.693429
$863$	5.32139e9	+	9.21692e9i	0.281830	+	0.488144i	0.971836	−	0.235660i	$-0.0757252\pi$
$863$	5.32139e9	+	9.21692e9i	0.281830	+	0.488144i	−0.690005	+	0.723804i	$0.742392\pi$
$864$	−5.12022e9	+	8.86849e9i	−0.270079	+	0.467790i
$865$	−1.62022e10			−0.851172
$866$	1.07695e9	+	1.86533e9i	0.0563484	+	0.0975983i
$867$	−7.69011e9	−	1.33197e10i	−0.400743	−	0.694107i
$868$	1.40898e9	+	2.44043e9i	0.0731286	+	0.126662i
$869$	−1.93302e10	+	3.34808e10i	−0.999232	+	1.73072i
$870$	−2.77267e10	+	4.80241e10i	−1.42752	+	2.47253i
$871$	7.12176e9	+	1.23352e10i	0.365194	+	0.632535i
$872$	−1.15836e10	−	2.00634e10i	−0.591611	−	1.02470i
$873$	−1.31308e9	−	2.27432e9i	−0.0667944	−	0.115691i
$874$	−9.22107e8			−0.0467187
$875$	−3.47370e8	+	6.01663e8i	−0.0175293	+	0.0303616i
$876$	1.42171e10	+	2.46247e10i	0.714572	+	1.23767i
$877$	−2.52162e10			−1.26236			−0.631178	−	0.775638i	$-0.717428\pi$
$877$	−2.52162e10			−1.26236			−0.631178	+	0.775638i	$0.717428\pi$
$878$	8.13696e9			0.405725
$879$	−9.60602e9	−	1.66381e10i	−0.477070	−	0.826310i
$880$	−1.76024e10			−0.870727
$881$	3.09450e9	−	5.35983e9i	0.152467	−	0.264080i	−0.779667	−	0.626194i	$-0.784612\pi$
$881$	3.09450e9	−	5.35983e9i	0.152467	−	0.264080i	0.932134	+	0.362114i	$0.117945\pi$
$882$	−1.05539e10			−0.517934
$883$	−7.99753e9	+	1.38521e10i	−0.390925	+	0.677102i	−0.992572	−	0.121660i	$-0.961178\pi$
$883$	−7.99753e9	+	1.38521e10i	−0.390925	+	0.677102i	0.601647	+	0.798762i	$0.294511\pi$
$884$	1.81666e9	−	3.14655e9i	0.0884487	−	0.153198i
$885$	1.50092e10	−	2.59967e10i	0.727875	−	1.26072i
$886$	−3.48630e9	−	6.03845e9i	−0.168402	−	0.291680i
$887$	−6.25595e9			−0.300996			−0.150498	−	0.988610i	$-0.548088\pi$
$887$	−6.25595e9			−0.300996			−0.150498	+	0.988610i	$0.548088\pi$
$888$	−1.32219e10	−	2.06809e10i	−0.633649	−	0.991115i
$889$	−1.41876e8			−0.00677254
$890$	3.81116e9	+	6.60111e9i	0.181214	+	0.313872i
$891$	−7.80333e9	+	1.35158e10i	−0.369580	+	0.640131i
$892$	−2.70537e10	+	4.68584e10i	−1.27629	+	2.21060i
$893$	−4.45420e9	+	7.71490e9i	−0.209310	+	0.362535i
$894$	1.37089e10			0.641683
$895$	−7.08893e9	+	1.22784e10i	−0.330522	+	0.572480i
$896$	−3.09728e9			−0.143847
$897$	−4.09425e8	−	7.09145e8i	−0.0189409	−	0.0328066i
$898$	1.44095e10			0.664019
$899$	3.49782e10			1.60560
$900$	4.06048e9	+	7.03296e9i	0.185664	+	0.321580i
$901$	−1.78903e8	+	3.09869e8i	−0.00814856	+	0.0141137i
$902$	−2.28580e10			−1.03709
$903$	−1.10211e9	−	1.90891e9i	−0.0498102	−	0.0862737i
$904$	4.16224e9	+	7.20921e9i	0.187386	+	0.324562i
$905$	2.48547e10	+	4.30496e10i	1.11465	+	1.93063i
$906$	−2.87500e10	+	4.97964e10i	−1.28437	+	2.22459i
$907$	1.22082e9	−	2.11451e9i	0.0543281	−	0.0940990i	−0.837582	−	0.546311i	$-0.816032\pi$
$907$	1.22082e9	−	2.11451e9i	0.0543281	−	0.0940990i	0.891910	+	0.452212i	$0.149365\pi$
$908$	−2.47141e10	−	4.28060e10i	−1.09558	−	1.89760i
$909$	−6.73957e9	−	1.16733e10i	−0.297617	−	0.515488i
$910$	−9.84355e8	−	1.70495e9i	−0.0433019	−	0.0750011i
$911$	−4.34191e9			−0.190268			−0.0951342	−	0.995464i	$-0.530328\pi$
$911$	−4.34191e9			−0.190268			−0.0951342	+	0.995464i	$0.530328\pi$
$912$	−1.60785e9	+	2.78487e9i	−0.0701879	+	0.121569i
$913$	8.45531e9	+	1.46450e10i	0.367690	+	0.636858i
$914$	5.32124e10			2.30516
$915$	−3.84558e10			−1.65954
$916$	9.70873e9	+	1.68160e10i	0.417377	+	0.722918i
$917$	6.78292e8			0.0290485
$918$	−4.05770e9	+	7.02814e9i	−0.173113	+	0.299841i
$919$	3.61112e10			1.53475			0.767376	−	0.641197i	$-0.221562\pi$
$919$	3.61112e10			1.53475			0.767376	+	0.641197i	$0.221562\pi$
$920$	−1.92336e9	+	3.33136e9i	−0.0814336	+	0.141047i
$921$	1.71064e10	−	2.96291e10i	0.721520	−	1.24971i
$922$	5.85403e9	−	1.01395e10i	0.245978	−	0.426047i
$923$	−4.45746e9	−	7.72055e9i	−0.186587	−	0.323178i
$924$	−3.57553e9			−0.149104
$925$	1.56931e10	−	7.10419e8i	0.651948	−	0.0295134i
$926$	−5.40388e10			−2.23649
$927$	3.18115e9	+	5.50992e9i	0.131161	+	0.227178i
$928$	−9.58162e9	+	1.65958e10i	−0.393569	+	0.681681i
$929$	1.95813e10	−	3.39158e10i	0.801285	−	1.38787i	−0.117486	−	0.993075i	$-0.537483\pi$
$929$	1.95813e10	−	3.39158e10i	0.801285	−	1.38787i	0.918771	−	0.394792i	$-0.129183\pi$
$930$	−2.23606e10	+	3.87297e10i	−0.911577	+	1.57890i
$931$	7.57897e9			0.307812
$932$	−2.65249e9	+	4.59424e9i	−0.107324	+	0.185891i
$933$	1.87411e10			0.755457
$934$	−1.62245e10	−	2.81017e10i	−0.651565	−	1.12854i
$935$	7.53508e9			0.301472
$936$	5.59182e9			0.222889
$937$	−2.09003e9	−	3.62004e9i	−0.0829973	−	0.143756i	0.821539	−	0.570153i	$-0.193116\pi$
$937$	−2.09003e9	−	3.62004e9i	−0.0829973	−	0.143756i	−0.904536	+	0.426397i	$0.859783\pi$
$938$	2.39818e9	−	4.15377e9i	0.0948793	−	0.164336i
$939$	−3.23352e10			−1.27452
$940$	4.07048e10	+	7.05029e10i	1.59845	+	2.76859i
$941$	−1.96940e10	−	3.41111e10i	−0.770497	−	1.33454i	−0.937291	−	0.348549i	$-0.886675\pi$
$941$	−1.96940e10	−	3.41111e10i	−0.770497	−	1.33454i	0.166794	−	0.985992i	$-0.446659\pi$
$942$	−1.06210e10	−	1.83961e10i	−0.413986	−	0.717045i
$943$	−5.71029e8	+	9.89051e8i	−0.0221752	+	0.0384085i
$944$	−9.60224e9	+	1.66316e10i	−0.371510	+	0.643474i
$945$	1.42445e9	+	2.46723e9i	0.0549082	+	0.0951037i
$946$	−4.16069e10	−	7.20652e10i	−1.59789	−	2.76762i
$947$	−7.86254e9	−	1.36183e10i	−0.300842	−	0.521073i	0.675485	−	0.737374i	$-0.263934\pi$
$947$	−7.86254e9	−	1.36183e10i	−0.300842	−	0.521073i	−0.976327	+	0.216301i	$0.930601\pi$
$948$	6.45424e10			2.46046
$949$	−6.26504e9	+	1.08514e10i	−0.237954	+	0.412148i
$950$	−4.50072e9	−	7.79548e9i	−0.170314	−	0.294992i
$951$	1.56084e10			0.588475
$952$	−5.58511e8			−0.0209799
$953$	5.66393e9	+	9.81021e9i	0.211979	+	0.367158i	0.952334	−	0.305058i	$-0.0986759\pi$
$953$	5.66393e9	+	9.81021e9i	0.211979	+	0.367158i	−0.740355	+	0.672216i	$0.765343\pi$
$954$	−1.20632e9			−0.0449825
$955$	2.57949e9	−	4.46781e9i	0.0958346	−	0.165990i
$956$	−1.18796e10			−0.439743
$957$	−2.21907e10	+	3.84355e10i	−0.818426	+	1.41756i
$958$	3.69011e10	−	6.39146e10i	1.35600	−	2.34866i
$959$	1.94619e9	−	3.37089e9i	0.0712556	−	0.123418i
$960$	−2.02365e10	−	3.50506e10i	−0.738220	−	1.27863i
$961$	6.96022e8			0.0252983
$962$	1.09076e10	−	2.10357e10i	0.395018	−	0.761806i
$963$	−4.14932e9			−0.149722
$964$	4.71988e10	+	8.17506e10i	1.69692	+	2.93915i
$965$	2.63711e10	−	4.56761e10i	0.944676	−	1.63623i
$966$	−1.37870e8	+	2.38797e8i	−0.00492095	+	0.00852334i
$967$	2.28698e10	−	3.96116e10i	0.813334	−	1.40874i	−0.0971844	−	0.995266i	$-0.530984\pi$
$967$	2.28698e10	−	3.96116e10i	0.813334	−	1.40874i	0.910518	−	0.413469i	$-0.135683\pi$
$968$	−2.16757e10			−0.768085
$969$	6.88273e8	−	1.19212e9i	0.0243012	−	0.0420909i
$970$	2.66012e10			0.935837
$971$	−2.32070e10	−	4.01956e10i	−0.813488	−	1.40900i	−0.910409	−	0.413710i	$-0.864233\pi$
$971$	−2.32070e10	−	4.01956e10i	−0.813488	−	1.40900i	0.0969209	−	0.995292i	$-0.469101\pi$
$972$	−3.12655e10			−1.09203
$973$	2.07526e7			0.000722233
$974$	−9.72415e9	−	1.68427e10i	−0.337206	−	0.584058i
$975$	3.99674e9	−	6.92256e9i	0.138099	−	0.239194i
$976$	2.46023e10			0.847036
$977$	−1.52970e10	−	2.64951e10i	−0.524776	−	0.908939i	−0.999584	−	0.0288493i	$-0.990816\pi$
$977$	−1.52970e10	−	2.64951e10i	−0.524776	−	0.908939i	0.474808	−	0.880090i	$-0.342518\pi$
$978$	−9.09298e9	−	1.57495e10i	−0.310828	−	0.538370i
$979$	3.05021e9	+	5.28311e9i	0.103894	+	0.179949i
$980$	3.46303e10	−	5.99815e10i	1.17534	−	2.03576i
$981$	−3.82214e9	+	6.62014e9i	−0.129260	+	0.223885i
$982$	2.54730e10	+	4.41206e10i	0.858402	+	1.48680i
$983$	2.28598e10	+	3.95944e10i	0.767601	+	1.32952i	0.938860	+	0.344298i	$0.111883\pi$
$983$	2.28598e10	+	3.95944e10i	0.767601	+	1.32952i	−0.171259	+	0.985226i	$0.554784\pi$
$984$	8.71006e9	+	1.50863e10i	0.291433	+	0.504776i
$985$	−1.19504e10			−0.398433
$986$	−7.59328e9	+	1.31520e10i	−0.252267	+	0.436939i
$987$	1.33195e9	+	2.30700e9i	0.0440938	+	0.0763727i
$988$	−8.79662e9			−0.290179
$989$	−4.15762e9			−0.136665
$990$	1.27020e10	+	2.20006e10i	0.416055	+	0.720628i
$991$	5.25800e10			1.71618			0.858091	−	0.513498i	$-0.171651\pi$
$991$	5.25800e10			1.71618			0.858091	+	0.513498i	$0.171651\pi$
$992$	−7.72723e9	+	1.33840e10i	−0.251323	+	0.435305i
$993$	−5.07095e10			−1.64349
$994$	−1.50100e9	+	2.59981e9i	−0.0484763	+	0.0839634i
$995$	−2.88580e10	+	4.99836e10i	−0.928723	+	1.60859i
$996$	1.41159e10	−	2.44495e10i	0.452690	−	0.784083i
$997$	1.92240e10	+	3.32970e10i	0.614344	+	1.06407i	0.990499	+	0.137518i	$0.0439125\pi$
$997$	1.92240e10	+	3.32970e10i	0.614344	+	1.06407i	−0.376155	+	0.926557i	$0.622754\pi$
$998$	−4.95686e10			−1.57852
$999$	−1.57843e10	+	3.04406e10i	−0.500895	+	0.965993i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.8.c.a.26.20	yes	42
37.10	even	3	inner	37.8.c.a.10.20	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.8.c.a.10.20	✓	42	37.10	even	3	inner
37.8.c.a.26.20	yes	42	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(9.53293 + 16.5115i) q^{2} +(19.4337 - 33.6601i) q^{3} +(-117.754 + 203.955i) q^{4} +(-179.660 + 311.180i) q^{5} +741.040 q^{6} +(35.6214 - 61.6981i) q^{7} -2049.72 q^{8} +(338.163 + 585.716i) q^{9} +O(q^{10})\)	\(q+(9.53293 + 16.5115i) q^{2} +(19.4337 - 33.6601i) q^{3} +(-117.754 + 203.955i) q^{4} +(-179.660 + 311.180i) q^{5} +741.040 q^{6} +(35.6214 - 61.6981i) q^{7} -2049.72 q^{8} +(338.163 + 585.716i) q^{9} -6850.74 q^{10} -5482.90 q^{11} +(4576.77 + 7927.21i) q^{12} +(-2016.85 + 3493.28i) q^{13} +1358.31 q^{14} +(6982.91 + 12094.7i) q^{15} +(-4467.35 - 7737.68i) q^{16} +(1912.35 + 3312.28i) q^{17} +(-6447.37 + 11167.2i) q^{18} +(4629.97 - 8019.35i) q^{19} +(-42311.2 - 73285.1i) q^{20} +(-1384.51 - 2398.04i) q^{21} +(-52268.1 - 90531.0i) q^{22} -5222.95 q^{23} +(-39833.6 + 68993.8i) q^{24} +(-25492.8 - 44154.8i) q^{25} -76905.9 q^{26} +111290. q^{27} +(8389.10 + 14530.3i) q^{28} +208260. q^{29} +(-133135. + 230597. i) q^{30} +167954. q^{31} +(-46007.9 + 79688.1i) q^{32} +(-106553. + 184555. i) q^{33} +(-36460.6 + 63151.6i) q^{34} +(12799.5 + 22169.3i) q^{35} -159280. q^{36} +(-141831. + 273525. i) q^{37} +176549. q^{38} +(78389.6 + 135775. i) q^{39} +(368252. - 637831. i) q^{40} +(109331. - 189366. i) q^{41} +(26396.9 - 45720.8i) q^{42} +796029. q^{43} +(645631. - 1.11827e6i) q^{44} -243017. q^{45} +(-49790.1 - 86238.9i) q^{46} -962035. q^{47} -347269. q^{48} +(409234. + 708814. i) q^{49} +(486042. - 841849. i) q^{50} +148656. q^{51} +(-474982. - 822693. i) q^{52} +(46775.7 + 81018.0i) q^{53} +(1.06092e6 + 1.83757e6i) q^{54} +(985056. - 1.70617e6i) q^{55} +(-73013.8 + 126464. i) q^{56} +(-179955. - 311691. i) q^{57} +(1.98533e6 + 3.43869e6i) q^{58} +(-1.07471e6 - 1.86146e6i) q^{59} -3.28905e6 q^{60} +(-1.37678e6 + 2.38466e6i) q^{61} +(1.60110e6 + 2.77318e6i) q^{62} +48183.4 q^{63} -2.89800e6 q^{64} +(-724693. - 1.25521e6i) q^{65} -4.06305e6 q^{66} +(1.76557e6 - 3.05805e6i) q^{67} -900743. q^{68} +(-101501. + 175805. i) q^{69} +(-244033. + 422677. i) q^{70} +(-1.10506e6 + 1.91401e6i) q^{71} +(-693139. - 1.20055e6i) q^{72} +3.10635e6 q^{73} +(-5.86838e6 + 265659. i) q^{74} -1.98168e6 q^{75} +(1.09039e6 + 1.88861e6i) q^{76} +(-195308. + 338284. i) q^{77} +(-1.49457e6 + 2.58866e6i) q^{78} +(3.52554e6 - 6.10641e6i) q^{79} +3.21042e6 q^{80} +(1.42321e6 - 2.46508e6i) q^{81} +4.16897e6 q^{82} +(-1.54212e6 - 2.67104e6i) q^{83} +652125. q^{84} -1.37429e6 q^{85} +(7.58849e6 + 1.31436e7i) q^{86} +(4.04726e6 - 7.01007e6i) q^{87} +1.12384e7 q^{88} +(-556313. - 963563. i) q^{89} +(-2.31667e6 - 4.01258e6i) q^{90} +(143686. + 248871. i) q^{91} +(615021. - 1.06525e6i) q^{92} +(3.26397e6 - 5.65336e6i) q^{93} +(-9.17102e6 - 1.58847e7i) q^{94} +(1.66364e6 + 2.88151e6i) q^{95} +(1.78821e6 + 3.09727e6i) q^{96} -3.88297e6 q^{97} +(-7.80239e6 + 1.35141e7i) q^{98} +(-1.85411e6 - 3.21142e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9}+O(q^{10}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9	\( 42 q - 16 q^{2} - 68 q^{3} - 1126 q^{4} - 337 q^{5} + 252 q^{6} - 158 q^{7} + 6264 q^{8} - 12773 q^{9} + 10028 q^{10} + 14876 q^{11} - 4836 q^{12} - 5922 q^{13} + 20176 q^{14} - 8460 q^{15} - 36726 q^{16} - 19095 q^{17} - 7338 q^{18} - 34334 q^{19} - 75668 q^{20} - 32764 q^{21} + 18526 q^{22} - 99896 q^{23} - 203760 q^{24} - 322660 q^{25} + 101516 q^{26} + 846616 q^{27} - 73490 q^{28} + 168186 q^{29} - 88790 q^{30} - 38052 q^{31} - 172292 q^{32} - 54536 q^{33} + 90724 q^{34} - 247046 q^{35} + 352004 q^{36} + 740185 q^{37} + 1994976 q^{38} - 591380 q^{39} - 38962 q^{40} - 292827 q^{41} - 1499386 q^{42} + 630980 q^{43} - 1727390 q^{44} - 994286 q^{45} + 576988 q^{46} + 3394668 q^{47} - 79840 q^{48} + 728851 q^{49} - 69656 q^{50} - 3970200 q^{51} - 2043140 q^{52} + 584438 q^{53} - 2160774 q^{54} + 2019874 q^{55} - 658986 q^{56} + 4295748 q^{57} - 5684872 q^{58} - 1773152 q^{59} + 20208544 q^{60} - 3596569 q^{61} - 1538738 q^{62} + 11795092 q^{63} - 9622852 q^{64} - 5027290 q^{65} - 17464952 q^{66} - 3249754 q^{67} + 5608668 q^{68} + 9599384 q^{69} - 5102080 q^{70} - 1162530 q^{71} - 4730172 q^{72} - 5266532 q^{73} + 4052290 q^{74} + 35543072 q^{75} - 13781226 q^{76} + 121180 q^{77} - 7012890 q^{78} - 13545718 q^{79} - 17840888 q^{80} - 16689077 q^{81} - 43173544 q^{82} + 7359048 q^{83} + 41186680 q^{84} + 21047382 q^{85} + 6732838 q^{86} + 7672800 q^{87} + 42023140 q^{88} + 2955725 q^{89} - 14596808 q^{90} - 19887752 q^{91} + 13352900 q^{92} + 9156784 q^{93} + 690474 q^{94} - 5667270 q^{95} + 29986904 q^{96} + 52065982 q^{97} - 53664462 q^{98} - 35534038 q^{99}+O(q^{100}) \) 42 * q - 16 * q^2 - 68 * q^3 - 1126 * q^4 - 337 * q^5 + 252 * q^6 - 158 * q^7 + 6264 * q^8 - 12773 * q^9 + 10028 * q^10 + 14876 * q^11 - 4836 * q^12 - 5922 * q^13 + 20176 * q^14 - 8460 * q^15 - 36726 * q^16 - 19095 * q^17 - 7338 * q^18 - 34334 * q^19 - 75668 * q^20 - 32764 * q^21 + 18526 * q^22 - 99896 * q^23 - 203760 * q^24 - 322660 * q^25 + 101516 * q^26 + 846616 * q^27 - 73490 * q^28 + 168186 * q^29 - 88790 * q^30 - 38052 * q^31 - 172292 * q^32 - 54536 * q^33 + 90724 * q^34 - 247046 * q^35 + 352004 * q^36 + 740185 * q^37 + 1994976 * q^38 - 591380 * q^39 - 38962 * q^40 - 292827 * q^41 - 1499386 * q^42 + 630980 * q^43 - 1727390 * q^44 - 994286 * q^45 + 576988 * q^46 + 3394668 * q^47 - 79840 * q^48 + 728851 * q^49 - 69656 * q^50 - 3970200 * q^51 - 2043140 * q^52 + 584438 * q^53 - 2160774 * q^54 + 2019874 * q^55 - 658986 * q^56 + 4295748 * q^57 - 5684872 * q^58 - 1773152 * q^59 + 20208544 * q^60 - 3596569 * q^61 - 1538738 * q^62 + 11795092 * q^63 - 9622852 * q^64 - 5027290 * q^65 - 17464952 * q^66 - 3249754 * q^67 + 5608668 * q^68 + 9599384 * q^69 - 5102080 * q^70 - 1162530 * q^71 - 4730172 * q^72 - 5266532 * q^73 + 4052290 * q^74 + 35543072 * q^75 - 13781226 * q^76 + 121180 * q^77 - 7012890 * q^78 - 13545718 * q^79 - 17840888 * q^80 - 16689077 * q^81 - 43173544 * q^82 + 7359048 * q^83 + 41186680 * q^84 + 21047382 * q^85 + 6732838 * q^86 + 7672800 * q^87 + 42023140 * q^88 + 2955725 * q^89 - 14596808 * q^90 - 19887752 * q^91 + 13352900 * q^92 + 9156784 * q^93 + 690474 * q^94 - 5667270 * q^95 + 29986904 * q^96 + 52065982 * q^97 - 53664462 * q^98 - 35534038 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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