LMFDB - Embedded newform 38.8.e.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,8,Mod(5,38)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, 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:	$11.8706309684$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	38.17
Dual form			38.8.e.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38919 - 7.87846i) q^{2} +(-46.9776 - 39.4189i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-248.833 + 90.5677i) q^{5} +(-375.821 + 315.351i) q^{6} +(81.2847 + 140.789i) q^{7} +(-256.000 + 443.405i) q^{8} +(273.278 + 1549.84i) q^{9} +O(q^{10})$	\(q+(1.38919 - 7.87846i) q^{2} +(-46.9776 - 39.4189i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-248.833 + 90.5677i) q^{5} +(-375.821 + 315.351i) q^{6} +(81.2847 + 140.789i) q^{7} +(-256.000 + 443.405i) q^{8} +(273.278 + 1549.84i) q^{9} +(367.859 + 2086.23i) q^{10} +(926.087 - 1604.03i) q^{11} +(1962.40 + 3398.97i) q^{12} +(3434.27 - 2881.70i) q^{13} +(1222.12 - 444.816i) q^{14} +(15259.6 + 5554.06i) q^{15} +(3137.72 + 2632.86i) q^{16} +(2.63223 - 14.9281i) q^{17} +12590.0 q^{18} +(2655.91 + 29779.5i) q^{19} +16947.3 q^{20} +(1731.19 - 9818.09i) q^{21} +(-11350.8 - 9524.43i) q^{22} +(18055.4 + 6571.63i) q^{23} +(29504.8 - 10738.9i) q^{24} +(-6132.03 + 5145.38i) q^{25} +(-17932.5 - 31060.0i) q^{26} +(-18803.9 + 32569.3i) q^{27} +(-1806.71 - 10246.4i) q^{28} +(22722.9 + 128868. i) q^{29} +(64955.9 - 112507. i) q^{30} +(74880.8 + 129697. i) q^{31} +(25101.7 - 21062.9i) q^{32} +(-106734. + 38848.2i) q^{33} +(-113.954 - 41.4758i) q^{34} +(-32977.2 - 27671.2i) q^{35} +(17489.8 - 99189.6i) q^{36} -167136. q^{37} +(238306. + 20444.7i) q^{38} -274927. q^{39} +(23543.0 - 133519. i) q^{40} +(-321108. - 269442. i) q^{41} +(-74946.5 - 27278.3i) q^{42} +(-732234. + 266511. i) q^{43} +(-90806.2 + 76195.5i) q^{44} +(-208366. - 360900. i) q^{45} +(76856.7 - 133120. i) q^{46} +(-8858.33 - 50238.1i) q^{47} +(-43618.1 - 247371. i) q^{48} +(398557. - 690321. i) q^{49} +(32019.2 + 55458.8i) q^{50} +(-712.106 + 597.528i) q^{51} +(-269617. + 98132.4i) q^{52} +(-289536. - 105382. i) q^{53} +(230474. + 193390. i) q^{54} +(-85167.4 + 483009. i) q^{55} -83235.5 q^{56} +(1.04911e6 - 1.50366e6i) q^{57} +1.04685e6 q^{58} +(-328833. + 1.86490e6i) q^{59} +(-796146. - 668046. i) q^{60} +(2.83965e6 + 1.03355e6i) q^{61} +(1.12584e6 - 409772. i) q^{62} +(-195987. + 164453. i) q^{63} +(-131072. - 227023. i) q^{64} +(-593571. + 1.02809e6i) q^{65} +(157790. + 894870. i) q^{66} +(554285. + 3.14351e6i) q^{67} +(-485.069 + 840.164i) q^{68} +(-589154. - 1.02044e6i) q^{69} +(-263818. + 221369. i) q^{70} +(-1.33278e6 + 485092. i) q^{71} +(-757165. - 275585. i) q^{72} +(1.59779e6 + 1.34071e6i) q^{73} +(-232182. + 1.31677e6i) q^{74} +490893. q^{75} +(492125. - 1.84908e6i) q^{76} +301107. q^{77} +(-381925. + 2.16600e6i) q^{78} +(-598479. - 502183. i) q^{79} +(-1.01922e6 - 370965. i) q^{80} +(5.40142e6 - 1.96596e6i) q^{81} +(-2.56887e6 + 2.15554e6i) q^{82} +(-2.74441e6 - 4.75346e6i) q^{83} +(-319026. + 552569. i) q^{84} +(697.020 + 3953.00i) q^{85} +(1.08249e6 + 6.13911e6i) q^{86} +(4.01236e6 - 6.94961e6i) q^{87} +(474156. + 821263. i) q^{88} +(4.58045e6 - 3.84345e6i) q^{89} +(-3.13280e6 + 1.14024e6i) q^{90} +(684866. + 249271. i) q^{91} +(-942010. - 790440. i) q^{92} +(1.59481e6 - 9.04459e6i) q^{93} -408105. q^{94} +(-3.35794e6 - 7.16957e6i) q^{95} -2.00950e6 q^{96} +(305598. - 1.73313e6i) q^{97} +(-4.88500e6 - 4.09900e6i) q^{98} +(2.73906e6 + 996938. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) $ 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	1.38919	−	7.87846i	0.122788	−	0.696364i
$2$	1.38919	−	7.87846i	0.122788	−	0.696364i
$3$	−46.9776	−	39.4189i	−1.00454	−	0.842908i	−0.0169317	−	0.999857i	$-0.505390\pi$
$3$	−46.9776	−	39.4189i	−1.00454	−	0.842908i	−0.987607	+	0.156949i	$0.949834\pi$
$4$	−60.1403	−	21.8893i	−0.469846	−	0.171010i
$5$	−248.833	+	90.5677i	−0.890251	+	0.324025i	−0.746339	−	0.665566i	$-0.768190\pi$
$5$	−248.833	+	90.5677i	−0.890251	+	0.324025i	−0.143912	+	0.989591i	$0.545968\pi$
$6$	−375.821	+	315.351i	−0.710316	+	0.596026i
$7$	81.2847	+	140.789i	0.0895706	+	0.155141i	0.907330	−	0.420420i	$-0.138117\pi$
$7$	81.2847	+	140.789i	0.0895706	+	0.155141i	−0.817759	+	0.575561i	$0.804784\pi$
$8$	−256.000	+	443.405i	−0.176777	+	0.306186i
$9$	273.278	+	1549.84i	0.124956	+	0.708659i
$10$	367.859	+	2086.23i	0.116327	+	0.659725i
$11$	926.087	−	1604.03i	0.209786	−	0.363361i	−0.741861	−	0.670554i	$-0.766056\pi$
$11$	926.087	−	1604.03i	0.209786	−	0.363361i	0.951647	+	0.307193i	$0.0993898\pi$
$12$	1962.40	+	3398.97i	0.327833	+	0.567823i
$13$	3434.27	−	2881.70i	0.433544	−	0.363787i	−0.399743	−	0.916627i	$-0.630901\pi$
$13$	3434.27	−	2881.70i	0.433544	−	0.363787i	0.833287	+	0.552841i	$0.186456\pi$
$14$	1222.12	−	444.816i	0.119033	−	0.0433244i
$15$	15259.6	+	5554.06i	1.16741	+	0.424904i
$16$	3137.72	+	2632.86i	0.191511	+	0.160697i
$17$	2.63223	−	14.9281i	0.000129943	−	0.000736943i	−0.984743	−	0.174017i	$-0.944325\pi$
$17$	2.63223	−	14.9281i	0.000129943	−	0.000736943i	0.984873	+	0.173280i	$0.0554365\pi$
$18$	12590.0			0.508828
$19$	2655.91	+	29779.5i	0.0888333	+	0.996047i
$19$	2655.91	+	29779.5i	0.0888333	+	0.996047i
$20$	16947.3			0.473693
$21$	1731.19	−	9818.09i	0.0407923	−	0.231345i
$22$	−11350.8	−	9524.43i	−0.227272	−	0.190704i
$23$	18055.4	+	6571.63i	0.309428	+	0.112623i	0.492067	−	0.870557i	$-0.336242\pi$
$23$	18055.4	+	6571.63i	0.309428	+	0.112623i	−0.182638	+	0.983180i	$0.558464\pi$
$24$	29504.8	−	10738.9i	0.435666	−	0.158569i
$25$	−6132.03	+	5145.38i	−0.0784899	+	0.0658609i
$26$	−17932.5	−	31060.0i	−0.200094	−	0.346573i
$27$	−18803.9	+	32569.3i	−0.183854	+	0.318445i
$28$	−1806.71	−	10246.4i	−0.0155538	−	0.0882098i
$29$	22722.9	+	128868.i	0.173010	+	0.981186i	0.940416	+	0.340025i	$0.110436\pi$
$29$	22722.9	+	128868.i	0.173010	+	0.981186i	−0.767407	+	0.641161i	$0.778453\pi$
$30$	64955.9	−	112507.i	0.439232	−	0.760773i
$31$	74880.8	+	129697.i	0.451445	+	0.781925i	0.998476	−	0.0551868i	$-0.0175754\pi$
$31$	74880.8	+	129697.i	0.451445	+	0.781925i	−0.547031	+	0.837112i	$0.684242\pi$
$32$	25101.7	−	21062.9i	0.135419	−	0.113630i
$33$	−106734.	+	38848.2i	−0.517018	+	0.188179i
$34$	−113.954	−	41.4758i	−0.000497225	−	0.000180975i
$35$	−32977.2	−	27671.2i	−0.130010	−	0.109091i
$36$	17489.8	−	99189.6i	0.0624779	−	0.354330i
$37$	−167136.			−0.542454			−0.271227	−	0.962515i	$-0.587429\pi$
$37$	−167136.			−0.542454			−0.271227	+	0.962515i	$0.587429\pi$
$38$	238306.	+	20444.7i	0.704519	+	0.0604421i
$39$	−274927.			−0.742150
$40$	23543.0	−	133519.i	0.0581637	−	0.329863i
$41$	−321108.	−	269442.i	−0.727626	−	0.610551i	0.201857	−	0.979415i	$-0.435302\pi$
$41$	−321108.	−	269442.i	−0.727626	−	0.610551i	−0.929483	+	0.368864i	$0.879747\pi$
$42$	−74946.5	−	27278.3i	−0.156091	−	0.0568126i
$43$	−732234.	+	266511.i	−1.40446	+	0.511183i	−0.929500	−	0.368823i	$-0.879761\pi$
$43$	−732234.	+	266511.i	−1.40446	+	0.511183i	−0.474963	+	0.880006i	$0.657539\pi$
$44$	−90806.2	+	76195.5i	−0.160706	+	0.134848i
$45$	−208366.	−	360900.i	−0.340865	−	0.590396i
$46$	76856.7	−	133120.i	0.116420	−	0.201646i
$47$	−8858.33	−	50238.1i	−0.0124454	−	0.0705815i	0.977953	−	0.208827i	$-0.0669647\pi$
$47$	−8858.33	−	50238.1i	−0.0124454	−	0.0705815i	−0.990398	+	0.138246i	$0.955854\pi$
$48$	−43618.1	−	247371.i	−0.0569276	−	0.322852i
$49$	398557.	−	690321.i	0.483954	−	0.838233i
$50$	32019.2	+	55458.8i	0.0362256	+	0.0627445i
$51$	−712.106	+	597.528i	−0.000751707	+	0.000630757i
$52$	−269617.	+	98132.4i	−0.265910	+	0.0967834i
$53$	−289536.	−	105382.i	−0.267139	−	0.0972305i	0.204978	−	0.978767i	$-0.434288\pi$
$53$	−289536.	−	105382.i	−0.267139	−	0.0972305i	−0.472117	+	0.881536i	$0.656510\pi$
$54$	230474.	+	193390.i	0.199179	+	0.167131i
$55$	−85167.4	+	483009.i	−0.0690246	+	0.391458i
$56$	−83235.5			−0.0633360
$57$	1.04911e6	−	1.50366e6i	0.750339	−	1.07545i
$58$	1.04685e6			0.704506
$59$	−328833.	+	1.86490e6i	−0.208446	+	1.18215i	0.683479	+	0.729970i	$0.260466\pi$
$59$	−328833.	+	1.86490e6i	−0.208446	+	1.18215i	−0.891925	+	0.452184i	$0.850645\pi$
$60$	−796146.	−	668046.i	−0.475842	−	0.399279i
$61$	2.83965e6	+	1.03355e6i	1.60181	+	0.583010i	0.979796	−	0.199999i	$-0.0640939\pi$
$61$	2.83965e6	+	1.03355e6i	1.60181	+	0.583010i	0.622010	+	0.783009i	$0.286316\pi$
$62$	1.12584e6	−	409772.i	0.599937	−	0.218359i
$63$	−195987.	+	164453.i	−0.0987496	+	0.0828607i
$64$	−131072.	−	227023.i	−0.0625000	−	0.108253i
$65$	−593571.	+	1.02809e6i	−0.268087	+	0.464340i
$66$	157790.	+	894870.i	0.0675577	+	0.383139i
$67$	554285.	+	3.14351e6i	0.225150	+	1.27689i	0.862399	+	0.506229i	$0.168961\pi$
$67$	554285.	+	3.14351e6i	0.225150	+	1.27689i	−0.637249	+	0.770658i	$0.719928\pi$
$68$	−485.069	+	840.164i	−0.000187078	+	0.000324028i
$69$	−589154.	−	1.02044e6i	−0.215902	−	0.373953i
$70$	−263818.	+	221369.i	−0.0919308	+	0.0771391i
$71$	−1.33278e6	+	485092.i	−0.441931	+	0.160850i	−0.553395	−	0.832919i	$-0.686668\pi$
$71$	−1.33278e6	+	485092.i	−0.441931	+	0.160850i	0.111465	+	0.993768i	$0.464446\pi$
$72$	−757165.	−	275585.i	−0.239071	−	0.0870147i
$73$	1.59779e6	+	1.34071e6i	0.480718	+	0.403370i	0.850686	−	0.525674i	$-0.176187\pi$
$73$	1.59779e6	+	1.34071e6i	0.480718	+	0.403370i	−0.369968	+	0.929044i	$0.620631\pi$
$74$	−232182.	+	1.31677e6i	−0.0666068	+	0.377746i
$75$	490893.			0.134361
$76$	492125.	−	1.84908e6i	0.128596	−	0.483180i
$77$	301107.			0.0751628
$78$	−381925.	+	2.16600e6i	−0.0911270	+	0.516807i
$79$	−598479.	−	502183.i	−0.136570	−	0.114595i	0.571944	−	0.820293i	$-0.306189\pi$
$79$	−598479.	−	502183.i	−0.136570	−	0.114595i	−0.708514	+	0.705697i	$0.750634\pi$
$80$	−1.01922e6	−	370965.i	−0.222563	−	0.0810062i
$81$	5.40142e6	−	1.96596e6i	1.12930	−	0.411033i
$82$	−2.56887e6	+	2.15554e6i	−0.514509	+	0.431724i
$83$	−2.74441e6	−	4.75346e6i	−0.526837	−	0.912508i	−0.999511	−	0.0312710i	$-0.990045\pi$
$83$	−2.74441e6	−	4.75346e6i	−0.526837	−	0.912508i	0.472674	−	0.881237i	$-0.343289\pi$
$84$	−319026.	+	552569.i	−0.0587284	+	0.101721i
$85$	697.020	+	3953.00i	0.000123106	+	0.000698168i
$86$	1.08249e6	+	6.13911e6i	0.183518	+	1.04078i
$87$	4.01236e6	−	6.94961e6i	0.653254	−	1.13147i
$88$	474156.	+	821263.i	0.0741707	+	0.128467i
$89$	4.58045e6	−	3.84345e6i	0.688720	−	0.577905i	−0.229820	−	0.973233i	$-0.573814\pi$
$89$	4.58045e6	−	3.84345e6i	0.688720	−	0.577905i	0.918540	+	0.395329i	$0.129369\pi$
$90$	−3.13280e6	+	1.14024e6i	−0.452984	+	0.164873i
$91$	684866.	+	249271.i	0.0952709	+	0.0346758i
$92$	−942010.	−	790440.i	−0.126124	−	0.105831i
$93$	1.59481e6	−	9.04459e6i	0.205597	−	1.16600i
$94$	−408105.			−0.0506786
$95$	−3.35794e6	−	7.16957e6i	−0.401828	−	0.857947i
$96$	−2.00950e6			−0.231813
$97$	305598.	−	1.73313e6i	0.0339977	−	0.192811i	−0.963079	−	0.269220i	$-0.913234\pi$
$97$	305598.	−	1.73313e6i	0.0339977	−	0.192811i	0.997077	+	0.0764088i	$0.0243454\pi$
$98$	−4.88500e6	−	4.09900e6i	−0.524292	−	0.439933i
$99$	2.73906e6	+	996938.i	0.283713	+	0.103263i
$100$	481411.	−	175219.i	0.0481411	−	0.0175219i
$101$	−1.01928e7	+	8.55274e6i	−0.984389	+	0.826000i	−0.984746	−	0.173999i	$-0.944331\pi$
$101$	−1.01928e7	+	8.55274e6i	−0.984389	+	0.826000i	0.000356752		1.00000i	$0.499886\pi$
$102$	3718.35	+	6440.37i	0.000346936	+	0.000600911i
$103$	−7.15918e6	+	1.24001e7i	−0.645555	+	1.11813i	0.338618	+	0.940924i	$0.390040\pi$
$103$	−7.15918e6	+	1.24001e7i	−0.645555	+	1.11813i	−0.984173	+	0.177210i	$0.943293\pi$
$104$	398585.	+	2.26049e6i	0.0347460	+	0.197054i
$105$	458424.	+	2.59985e6i	0.0386460	+	0.219173i
$106$	−1.23247e6	+	2.13470e6i	−0.100509	+	0.174087i
$107$	−8.03557e6	−	1.39180e7i	−0.634123	−	1.09833i	−0.986700	−	0.162550i	$-0.948028\pi$
$107$	−8.03557e6	−	1.39180e7i	−0.634123	−	1.09833i	0.352578	−	0.935783i	$-0.385305\pi$
$108$	1.84379e6	−	1.54712e6i	0.140841	−	0.118179i
$109$	−1.58139e7	+	5.75578e6i	−1.16962	+	0.425708i	−0.852526	−	0.522685i	$-0.824930\pi$
$109$	−1.58139e7	+	5.75578e6i	−1.16962	+	0.425708i	−0.317097	+	0.948393i	$0.602708\pi$
$110$	3.68705e6	+	1.34198e6i	0.264122	+	0.0961326i
$111$	7.85164e6	+	6.58831e6i	0.544916	+	0.457239i
$112$	−115630.	+	655768.i	−0.00777688	+	0.0441049i
$113$	−1.70933e7			−1.11443			−0.557214	−	0.830369i	$-0.688130\pi$
$113$	−1.70933e7			−1.11443			−0.557214	+	0.830369i	$0.688130\pi$
$114$	−1.03891e7	−	1.03542e7i	−0.656769	−	0.654561i
$115$	−5.08796e6			−0.311961
$116$	1.45426e6	−	8.24754e6i	0.0865048	−	0.490593i
$117$	5.40467e6	+	4.53506e6i	0.311974	+	0.261778i
$118$	1.42358e7	+	5.18139e6i	0.797616	+	0.290308i
$119$	2315.68	−	842.837i	0.000125969	−	4.58489e-5i
$120$	−6.36917e6	+	5.34436e6i	−0.336471	+	0.282333i
$121$	8.02831e6	+	1.39054e7i	0.411979	+	0.713569i
$122$	1.20876e7	−	2.09363e7i	0.602670	−	1.04385i
$123$	4.46380e6	+	2.53155e7i	0.216290	+	1.22664i
$124$	−1.66437e6	−	9.43913e6i	−0.0783926	−	0.444586i
$125$	1.14037e7	−	1.97518e7i	0.522228	−	0.904525i
$126$	1.02337e6	+	1.77253e6i	0.0455760	+	0.0789400i
$127$	1.54236e7	−	1.29419e7i	0.668147	−	0.560642i	−0.244369	−	0.969682i	$-0.578581\pi$
$127$	1.54236e7	−	1.29419e7i	0.668147	−	0.560642i	0.912516	+	0.409041i	$0.134137\pi$
$128$	−1.97068e6	+	717268.i	−0.0830579	+	0.0302306i
$129$	4.49042e7	+	1.63438e7i	1.84172	+	0.670330i
$130$	7.27523e6	+	6.10464e6i	0.290432	+	0.243702i
$131$	29648.1	−	168142.i	0.00115225	−	0.00653473i	−0.984226	−	0.176915i	$-0.943388\pi$
$131$	29648.1	−	168142.i	0.00115225	−	0.00653473i	0.985378	+	0.170380i	$0.0544995\pi$
$132$	7.26940e6			0.275100
$133$	−3.97674e6	+	2.79454e6i	−0.146571	+	0.102998i
$134$	2.55360e7			0.916824
$135$	1.72930e6	−	9.80732e6i	0.0604924	−	0.343070i
$136$	5945.35	+	4988.74i	0.000202671	+	0.000170061i
$137$	3.97044e7	+	1.44512e7i	1.31922	+	0.480157i	0.903208	−	0.429203i	$-0.141205\pi$
$137$	3.97044e7	+	1.44512e7i	1.31922	+	0.480157i	0.416012	+	0.909359i	$0.363428\pi$
$138$	−8.85798e6	+	3.22404e6i	−0.286918	+	0.104430i
$139$	−3.40826e7	+	2.85987e7i	−1.07642	+	0.903221i	−0.995618	−	0.0935096i	$-0.970191\pi$
$139$	−3.40826e7	+	2.85987e7i	−1.07642	+	0.903221i	−0.0807983	+	0.996730i	$0.525747\pi$
$140$	1.37756e6	+	2.38600e6i	0.0424289	+	0.0734891i
$141$	−1.56419e6	+	2.70925e6i	−0.0469918	+	0.0813922i
$142$	1.97030e6	+	1.11741e7i	0.0577462	+	0.327495i
$143$	−1.44189e6	−	8.17738e6i	−0.0412341	−	0.233850i
$144$	−3.22303e6	+	5.58245e6i	−0.0899489	+	0.155796i
$145$	−1.73254e7	−	3.00085e7i	−0.471950	−	0.817442i
$146$	1.27823e7	−	1.07256e7i	0.339919	−	0.285226i
$147$	−4.59350e7	+	1.67190e7i	−1.19270	+	0.434109i
$148$	1.00516e7	+	3.65848e6i	0.254870	+	0.0927652i
$149$	−1.20261e7	−	1.00911e7i	−0.297832	−	0.249911i	0.481609	−	0.876386i	$-0.340052\pi$
$149$	−1.20261e7	−	1.00911e7i	−0.297832	−	0.249911i	−0.779441	+	0.626475i	$0.784497\pi$
$150$	681942.	−	3.86748e6i	0.0164979	−	0.0935641i
$151$	−4.55787e7			−1.07732			−0.538658	−	0.842525i	$-0.681068\pi$
$151$	−4.55787e7			−1.07732			−0.538658	+	0.842525i	$0.681068\pi$
$152$	−1.38843e7	−	6.44591e6i	−0.320679	−	0.148878i
$153$	23855.5			0.000538478
$154$	418293.	−	2.37226e6i	0.00922907	−	0.0523407i
$155$	−3.03792e7	−	2.54912e7i	−0.655262	−	0.549830i
$156$	1.65342e7	+	6.01796e6i	0.348697	+	0.126915i
$157$	3.80814e7	−	1.38605e7i	0.785351	−	0.285844i	0.0819486	−	0.996637i	$-0.473886\pi$
$157$	3.80814e7	−	1.38605e7i	0.785351	−	0.285844i	0.703402	+	0.710792i	$0.251663\pi$
$158$	−4.78783e6	+	4.01747e6i	−0.0965693	+	0.0810312i
$159$	9.44764e6	+	1.63638e7i	0.186395	+	0.322845i
$160$	−4.33852e6	+	7.51454e6i	−0.0837378	+	0.145038i
$161$	542413.	+	3.07618e6i	0.0102433	+	0.0580926i
$162$	−7.98514e6	−	4.52860e7i	−0.147564	−	0.836876i
$163$	−3.90382e7	+	6.76162e7i	−0.706047	+	1.22291i	0.260266	+	0.965537i	$0.416190\pi$
$163$	−3.90382e7	+	6.76162e7i	−0.706047	+	1.22291i	−0.966312	+	0.257372i	$0.917144\pi$
$164$	1.34137e7	+	2.32332e7i	0.237462	+	0.411296i
$165$	2.30406e7	−	1.93334e7i	0.399301	−	0.335053i
$166$	−4.12625e7	+	1.50183e7i	−0.700127	+	0.254826i
$167$	6.99429e7	+	2.54572e7i	1.16208	+	0.422963i	0.849840	−	0.527040i	$-0.176698\pi$
$167$	6.99429e7	+	2.54572e7i	1.16208	+	0.422963i	0.312240	+	0.950003i	$0.398921\pi$
$168$	3.91020e6	+	3.28105e6i	0.0636234	+	0.0533864i
$169$	−7.40611e6	+	4.20021e7i	−0.118028	+	0.669373i
$170$	32111.8			0.000501295
$171$	−4.54276e7	+	1.22543e7i	−0.694757	+	0.187414i
$172$	4.98705e7			0.747299
$173$	1.20446e7	−	6.83084e7i	0.176861	−	1.00303i	−0.759113	−	0.650958i	$-0.774367\pi$
$173$	1.20446e7	−	6.83084e7i	0.176861	−	1.00303i	0.935974	−	0.352069i	$-0.114522\pi$
$174$	−4.91783e7	−	4.12655e7i	−0.707704	−	0.593834i
$175$	−1.22285e6	−	445082.i	−0.0172481	−	0.00627780i
$176$	7.12898e6	−	2.59474e6i	0.0985674	−	0.0358756i
$177$	8.89602e7	−	7.46465e7i	1.20584	−	1.01182i
$178$	−2.39174e7	−	4.14261e7i	−0.317866	−	0.550560i
$179$	−4.61819e7	+	7.99895e7i	−0.601848	+	1.04243i	0.390694	+	0.920521i	$0.372235\pi$
$179$	−4.61819e7	+	7.99895e7i	−0.601848	+	1.04243i	−0.992541	+	0.121910i	$0.961098\pi$
$180$	4.63134e6	+	2.62656e7i	0.0591906	+	0.335687i
$181$	−2.69211e6	−	1.52677e7i	−0.0337456	−	0.191381i	0.963275	−	0.268517i	$-0.0865335\pi$
$181$	−2.69211e6	−	1.52677e7i	−0.0337456	−	0.191381i	−0.997021	+	0.0771360i	$0.975422\pi$
$182$	2.91528e6	−	5.04940e6i	0.0358451	−	0.0620855i
$183$	−9.26586e7	−	1.60489e8i	−1.11765	−	1.93583i
$184$	−7.53608e6	+	6.32352e6i	−0.0891832	+	0.0748336i
$185$	4.15888e7	−	1.51371e7i	0.482920	−	0.175769i
$186$	−6.90420e7	−	2.51292e7i	−0.786716	−	0.286341i
$187$	−21507.5	−	18046.9i	−0.000240516	−	0.000201817i
$188$	−566933.	+	3.21524e6i	−0.00622271	+	0.0352907i
$189$	−6.11387e6			−0.0658718
$190$	−6.11500e7	+	1.64955e7i	−0.646783	+	0.174473i
$191$	−8.21025e7			−0.852589			−0.426294	−	0.904585i	$-0.640181\pi$
$191$	−8.21025e7			−0.852589			−0.426294	+	0.904585i	$0.640181\pi$
$192$	−2.79156e6	+	1.58317e7i	−0.0284638	+	0.161426i
$193$	−5.97156e7	−	5.01073e7i	−0.597912	−	0.501708i	0.292862	−	0.956155i	$-0.405392\pi$
$193$	−5.97156e7	−	5.01073e7i	−0.597912	−	0.501708i	−0.890774	+	0.454447i	$0.849837\pi$
$194$	−1.32299e7	−	4.81529e6i	−0.130092	−	0.0473496i
$195$	6.84109e7	−	2.48995e7i	0.660700	−	0.240475i
$196$	−3.90800e7	+	3.27920e7i	−0.370730	+	0.311080i
$197$	−2.66947e7	−	4.62366e7i	−0.248767	−	0.430877i	0.714417	−	0.699720i	$-0.246692\pi$
$197$	−2.66947e7	−	4.62366e7i	−0.248767	−	0.430877i	−0.963184	+	0.268843i	$0.913359\pi$
$198$	1.16594e7	−	2.01947e7i	0.106745	−	0.184888i
$199$	2.86516e7	+	1.62491e8i	0.257729	+	1.46165i	0.788970	+	0.614432i	$0.210615\pi$
$199$	2.86516e7	+	1.62491e8i	0.257729	+	1.46165i	−0.531241	+	0.847221i	$0.678274\pi$
$200$	−711689.	−	4.03619e6i	−0.00629050	−	0.0356752i
$201$	9.78746e7	−	1.69524e8i	0.850127	−	1.47246i
$202$	5.32228e7	+	9.21846e7i	0.454326	+	0.786916i
$203$	−1.62962e7	+	1.36741e7i	−0.136725	+	0.114726i
$204$	55905.7	−	20348.0i	0.000461053	−	0.000167809i
$205$	1.04305e8	+	3.79639e7i	0.845603	+	0.307774i
$206$	8.77480e7	+	7.36293e7i	0.699362	+	0.586834i
$207$	−5.25081e6	+	2.97788e7i	−0.0411463	+	0.233352i
$208$	1.83629e7			0.141488
$209$	5.02268e7	+	2.33182e7i	0.380560	+	0.176678i
$210$	2.11197e7			0.157369
$211$	−4.64968e7	+	2.63696e8i	−0.340749	+	1.93248i	0.0199497	+	0.999801i	$0.493649\pi$
$211$	−4.64968e7	+	2.63696e8i	−0.340749	+	1.93248i	−0.360699	+	0.932682i	$0.617462\pi$
$212$	1.51060e7	+	1.26755e7i	0.108887	+	0.0913668i
$213$	8.17326e7	+	2.97482e7i	0.579518	+	0.210927i
$214$	−1.20815e8	+	4.39732e7i	−0.842702	+	0.306719i
$215$	1.58066e8	−	1.32633e8i	1.08469	−	0.910162i
$216$	−9.62759e6	−	1.66755e7i	−0.0650024	−	0.112587i
$217$	−1.21733e7	+	2.10848e7i	−0.0808724	+	0.140075i
$218$	2.33783e7	+	1.32585e8i	0.152832	+	0.866755i
$219$	−2.22113e7	−	1.25966e8i	−0.142896	−	0.810401i
$220$	1.56947e7	−	2.71840e7i	0.0993743	−	0.172121i
$221$	−33978.5	−	58852.5i	−0.000211754	−	0.000366769i
$222$	6.28131e7	−	5.27064e7i	0.385314	−	0.323317i
$223$	1.41257e8	−	5.14134e7i	0.852988	−	0.310462i	0.121730	−	0.992563i	$-0.461156\pi$
$223$	1.41257e8	−	5.14134e7i	0.852988	−	0.310462i	0.731258	+	0.682101i	$0.238933\pi$
$224$	5.00581e6	+	1.82197e6i	0.0297582	+	0.0108311i
$225$	−9.65025e6	−	8.09752e6i	−0.0564807	−	0.0473929i
$226$	−2.37458e7	+	1.34669e8i	−0.136838	+	0.776048i
$227$	1.46678e8			0.832290			0.416145	−	0.909298i	$-0.363381\pi$
$227$	1.46678e8			0.832290			0.416145	+	0.909298i	$0.363381\pi$
$228$	−9.60077e7	+	6.74666e7i	−0.536456	+	0.376978i
$229$	−6.37901e7			−0.351017			−0.175509	−	0.984478i	$-0.556157\pi$
$229$	−6.37901e7			−0.351017			−0.175509	+	0.984478i	$0.556157\pi$
$230$	−7.06811e6	+	4.00853e7i	−0.0383051	+	0.217239i
$231$	−1.41453e7	−	1.18693e7i	−0.0755039	−	0.0633553i
$232$	−6.29577e7	−	2.29147e7i	−0.331010	−	0.120478i
$233$	8.99813e7	−	3.27505e7i	0.466022	−	0.169618i	−0.0983275	−	0.995154i	$-0.531349\pi$
$233$	8.99813e7	−	3.27505e7i	0.466022	−	0.169618i	0.564349	+	0.825536i	$0.309127\pi$
$234$	4.32374e7	−	3.62805e7i	0.220599	−	0.185105i
$235$	6.75419e6	+	1.16986e7i	0.0339497	+	0.0588026i
$236$	6.05975e7	−	1.04958e8i	0.300098	−	0.519785i
$237$	8.31959e6	+	4.71828e7i	0.0405960	+	0.230231i
$238$	−3423.36	−	19414.8i	−1.64601e−5	−	9.33499e-5i
$239$	5.43671e7	−	9.41667e7i	0.257599	−	0.446174i	−0.707999	−	0.706213i	$-0.750402\pi$
$239$	5.43671e7	−	9.41667e7i	0.257599	−	0.446174i	0.965598	+	0.260039i	$0.0837354\pi$
$240$	3.32574e7	+	5.76035e7i	0.155292	+	0.268974i
$241$	−2.97636e8	+	2.49746e8i	−1.36970	+	1.14932i	−0.396851	+	0.917883i	$0.629897\pi$
$241$	−2.97636e8	+	2.49746e8i	−1.36970	+	1.14932i	−0.972851	+	0.231433i	$0.925658\pi$
$242$	1.20706e8	−	4.39335e7i	0.547490	−	0.199270i
$243$	−2.53954e8	−	9.24317e7i	−1.13536	−	0.413237i
$244$	−1.48154e8	−	1.24316e8i	−0.652902	−	0.547850i
$245$	−3.66532e7	+	2.07871e8i	−0.159232	+	0.903051i
$246$	2.05648e8			0.880748
$247$	9.49366e7	+	9.46174e7i	0.400862	+	0.399514i
$248$	−7.66780e7			−0.319220
$249$	−5.84503e7	+	3.31488e8i	−0.239932	+	1.36072i
$250$	−1.39772e8	−	1.17282e8i	−0.565756	−	0.474725i
$251$	1.43072e7	+	5.20741e6i	0.0571081	+	0.0207856i	0.370416	−	0.928866i	$-0.379215\pi$
$251$	1.43072e7	+	5.20741e6i	0.0571081	+	0.0207856i	−0.313308	+	0.949652i	$0.601437\pi$
$252$	1.53865e7	−	5.60022e6i	0.0605671	−	0.0220446i
$253$	2.72620e7	−	2.28755e7i	0.105837	−	0.0888074i
$254$	−8.05362e7	−	1.39493e8i	−0.308371	−	0.534113i
$255$	123078.	−	213178.i	0.000464827	−	0.000805104i
$256$	2.91333e6	+	1.65223e7i	0.0108530	+	0.0615505i
$257$	−5.61101e7	−	3.18216e8i	−0.206193	−	1.16938i	−0.895551	−	0.444960i	$-0.853218\pi$
$257$	−5.61101e7	−	3.18216e8i	−0.206193	−	1.16938i	0.689357	−	0.724422i	$-0.257893\pi$
$258$	1.91144e8	−	3.31071e8i	0.692934	−	1.20020i
$259$	−1.35856e7	−	2.35309e7i	−0.0485880	−	0.0841568i
$260$	5.82018e7	−	4.88371e7i	0.205367	−	0.172323i
$261$	−1.93514e8	+	7.04335e7i	−0.673708	+	0.245210i
$262$	−1.28352e6	−	467162.i	−0.00440907	−	0.00160477i
$263$	−3.77257e8	−	3.16556e8i	−1.27877	−	1.07301i	−0.993413	−	0.114593i	$-0.963444\pi$
$263$	−3.77257e8	−	3.16556e8i	−1.27877	−	1.07301i	−0.285357	−	0.958421i	$-0.592112\pi$
$264$	1.00985e7	−	5.72717e7i	0.0337789	−	0.191570i
$265$	8.15902e7			0.269326
$266$	1.64922e7	+	3.52128e7i	0.0537271	+	0.114713i
$267$	−3.66683e8			−1.17897
$268$	3.54742e7	−	2.01184e8i	0.112575	−	0.638444i
$269$	−1.08610e8	−	9.11345e7i	−0.340202	−	0.285463i	0.456640	−	0.889652i	$-0.349053\pi$
$269$	−1.08610e8	−	9.11345e7i	−0.340202	−	0.285463i	−0.796841	+	0.604189i	$0.793497\pi$
$270$	−7.48643e7	−	2.72484e7i	−0.231474	−	0.0842495i
$271$	4.56258e8	−	1.66064e8i	1.39257	−	0.506855i	0.466608	−	0.884464i	$-0.345476\pi$
$271$	4.56258e8	−	1.66064e8i	1.39257	−	0.506855i	0.925965	+	0.377609i	$0.123254\pi$
$272$	47562.8	−	39909.9i	0.000143310	−	0.000120251i
$273$	−2.23474e7	−	3.87068e7i	−0.0664748	−	0.115138i
$274$	1.69010e8	−	2.92735e8i	0.496348	−	0.859700i
$275$	2.57455e6	+	1.46010e7i	0.00746513	+	0.0423369i
$276$	1.30951e7	+	7.42660e7i	0.0374910	+	0.212622i
$277$	−7.95990e6	+	1.37870e7i	−0.0225024	+	0.0389753i	−0.877057	−	0.480386i	$-0.840497\pi$
$277$	−7.95990e6	+	1.37870e7i	−0.0225024	+	0.0389753i	0.854555	+	0.519361i	$0.173830\pi$
$278$	1.77967e8	+	3.08247e8i	0.496800	+	0.860483i
$279$	−1.80547e8	+	1.51497e8i	−0.497708	+	0.417627i
$280$	2.07117e7	−	7.53845e6i	0.0563849	−	0.0205224i
$281$	−2.22734e8	−	8.10685e7i	−0.598845	−	0.217962i	0.0247704	−	0.999693i	$-0.492115\pi$
$281$	−2.22734e8	−	8.10685e7i	−0.598845	−	0.217962i	−0.623615	+	0.781731i	$0.714337\pi$
$282$	1.91718e7	+	1.60870e7i	0.0509086	+	0.0427174i
$283$	−4.29356e7	+	2.43500e8i	−0.112607	+	0.638625i	0.875300	+	0.483580i	$0.160664\pi$
$283$	−4.29356e7	+	2.43500e8i	−0.112607	+	0.638625i	−0.987907	+	0.155046i	$0.950447\pi$
$284$	9.07721e7			0.235146
$285$	−1.24869e8	+	4.69175e8i	−0.319519	+	1.20054i
$286$	−6.64282e7			−0.167908
$287$	1.18333e7	−	6.71101e7i	0.0295474	−	0.167572i
$288$	3.95038e7	+	3.31476e7i	0.0974462	+	0.0817671i
$289$	3.85592e8	+	1.40344e8i	0.939692	+	0.342020i
$290$	−2.60489e8	+	9.48104e7i	−0.627187	+	0.228277i
$291$	−8.26746e7	+	6.93722e7i	−0.196674	+	0.165029i
$292$	−6.67446e7	−	1.15605e8i	−0.156883	−	0.271729i
$293$	−3.30563e7	+	5.72551e7i	−0.0767745	+	0.132977i	−0.901857	−	0.432036i	$-0.857795\pi$
$293$	−3.30563e7	+	5.72551e7i	−0.0767745	+	0.132977i	0.825082	+	0.565013i	$0.191129\pi$
$294$	6.79075e7	+	3.85123e8i	0.155848	+	0.883860i
$295$	−8.70756e7	−	4.93831e8i	−0.197478	−	1.11996i
$296$	4.27867e7	−	7.41088e7i	0.0958933	−	0.166092i
$297$	3.48280e7	+	6.03239e7i	0.0771403	+	0.133611i
$298$	−9.62085e7	+	8.07285e7i	−0.210599	+	0.176714i
$299$	8.09447e7	−	2.94615e7i	0.175121	−	0.0637390i
$300$	−2.95225e7	−	1.07453e7i	−0.0631289	−	0.0229771i
$301$	−9.70413e7	−	8.14273e7i	−0.205104	−	0.172103i
$302$	−6.33173e7	+	3.59090e8i	−0.132281	+	0.750204i
$303$	8.15971e8			1.68510
$304$	−7.00717e7	+	1.00432e8i	−0.143049	+	0.205029i
$305$	−8.00203e8			−1.61492
$306$	33139.7	−	187944.i	6.61185e−5	−	0.000374977i
$307$	1.21660e8	+	1.02085e8i	0.239974	+	0.201362i	0.754841	−	0.655908i	$-0.227714\pi$
$307$	1.21660e8	+	1.02085e8i	0.239974	+	0.201362i	−0.514867	+	0.857270i	$0.672159\pi$
$308$	−1.81087e7	−	6.59101e6i	−0.0353149	−	0.0128536i
$309$	8.25118e8	−	3.00318e8i	1.59097	−	0.579065i
$310$	−2.43034e8	+	2.03929e8i	−0.463340	+	0.388789i
$311$	1.90556e7	+	3.30052e7i	0.0359220	+	0.0622188i	0.883427	−	0.468568i	$-0.155230\pi$
$311$	1.90556e7	+	3.30052e7i	0.0359220	+	0.0622188i	−0.847505	+	0.530787i	$0.821897\pi$
$312$	7.03814e7	−	1.21904e8i	0.131195	−	0.227236i
$313$	−1.37489e8	−	7.79737e8i	−0.253432	−	1.43729i	−0.800065	−	0.599913i	$-0.795202\pi$
$313$	−1.37489e8	−	7.79737e8i	−0.253432	−	1.43729i	0.546633	−	0.837372i	$-0.315909\pi$
$314$	−5.62972e7	−	3.19277e8i	−0.102620	−	0.581988i
$315$	3.38739e7	−	5.86713e7i	0.0610630	−	0.105764i
$316$	2.50003e7	+	4.33017e7i	0.0445697	+	0.0771970i
$317$	−7.72363e8	+	6.48089e8i	−1.36180	+	1.14269i	−0.386381	+	0.922339i	$0.626275\pi$
$317$	−7.72363e8	+	6.48089e8i	−1.36180	+	1.14269i	−0.975421	+	0.220348i	$0.929281\pi$
$318$	1.42046e8	−	5.17006e7i	0.247705	−	0.0901572i
$319$	2.27751e8	+	8.28946e7i	0.392819	+	0.142975i
$320$	5.31760e7	+	4.46199e7i	0.0907174	+	0.0761209i
$321$	−1.71141e8	+	9.70588e8i	−0.288793	+	1.63782i
$322$	2.49891e7			0.0417114
$323$	451542.	+	38738.7i	0.000745572	+	6.39641e-5i
$324$	−3.67877e8			−0.600890
$325$	−6.23162e6	+	3.53413e7i	−0.0100695	+	0.0571072i
$326$	4.78480e8	+	4.01493e8i	0.764896	+	0.641824i
$327$	9.69785e8	+	3.52973e8i	1.53376	+	0.558244i
$328$	2.01676e8	−	7.34039e7i	0.315569	−	0.114858i
$329$	6.35293e6	−	5.33075e6i	0.00983533	−	0.00825282i
$330$	−1.20310e8	−	2.08382e8i	−0.184290	−	0.319199i
$331$	1.95954e8	−	3.39402e8i	0.296999	−	0.514418i	−0.678449	−	0.734648i	$-0.737347\pi$
$331$	1.95954e8	−	3.39402e8i	0.296999	−	0.514418i	0.975448	+	0.220230i	$0.0706808\pi$
$332$	6.10000e7	+	3.45948e8i	0.0914843	+	0.518833i
$333$	−4.56745e7	−	2.59033e8i	−0.0677828	−	0.384415i
$334$	2.97727e8	−	5.15678e8i	0.437225	−	0.757297i
$335$	−4.22624e8	−	7.32007e8i	−0.614183	−	1.06380i
$336$	3.12816e7	−	2.62484e7i	0.0449886	−	0.0377499i
$337$	1.00548e9	−	3.65965e8i	1.43110	−	0.520877i	0.493852	−	0.869546i	$-0.335588\pi$
$337$	1.00548e9	−	3.65965e8i	1.43110	−	0.520877i	0.937246	+	0.348669i	$0.113366\pi$
$338$	3.20624e8	+	1.16698e8i	0.451635	+	0.164382i
$339$	8.03003e8	+	6.73800e8i	1.11949	+	0.939360i
$340$	44609.3	−	252992.i	6.15530e−5	−	0.000349084i
$341$	2.77385e8			0.378828
$342$	3.34378e7	+	3.74923e8i	0.0452008	+	0.506816i
$343$	2.63469e8			0.352533
$344$	6.92794e7	−	3.92903e8i	0.0917592	−	0.520392i
$345$	2.39020e8	+	2.00562e8i	0.313377	+	0.262955i
$346$	−5.21433e8	−	1.89786e8i	−0.676756	−	0.246319i
$347$	7.02175e7	−	2.55571e7i	0.0902177	−	0.0328366i	−0.296517	−	0.955028i	$-0.595825\pi$
$347$	7.02175e7	−	2.55571e7i	0.0902177	−	0.0328366i	0.386735	+	0.922191i	$0.373603\pi$
$348$	−3.93427e8	+	3.30124e8i	−0.500422	+	0.419904i
$349$	−2.42874e8	−	4.20669e8i	−0.305838	−	0.529727i	0.671610	−	0.740905i	$-0.265603\pi$
$349$	−2.42874e8	−	4.20669e8i	−0.305838	−	0.529727i	−0.977448	+	0.211178i	$0.932270\pi$
$350$	−5.20533e6	+	9.01590e6i	−0.00648949	+	0.0112401i
$351$	2.92771e7	+	1.66039e8i	0.0361371	+	0.204944i
$352$	−1.05391e7	−	5.97700e7i	−0.0128796	−	0.0730439i
$353$	−8.28156e7	+	1.43441e8i	−0.100208	+	0.173565i	−0.911770	−	0.410701i	$-0.865284\pi$
$353$	−8.28156e7	+	1.43441e8i	−0.100208	+	0.173565i	0.811563	+	0.584266i	$0.198617\pi$
$354$	−4.64517e8	−	8.04568e8i	−0.556532	−	0.963942i
$355$	2.87705e8	−	2.41414e8i	0.341310	−	0.286393i
$356$	−3.59600e8	+	1.30884e8i	−0.422420	+	0.153748i
$357$	−142009.	−	51686.9i	−0.000165187	−	6.01232e-5i
$358$	5.66039e8	+	4.74963e8i	0.652012	+	0.547103i
$359$	−1.45599e8	+	8.25732e8i	−0.166084	+	0.941908i	0.781856	+	0.623459i	$0.214273\pi$
$359$	−1.45599e8	+	8.25732e8i	−0.166084	+	0.941908i	−0.947940	+	0.318449i	$0.896838\pi$
$360$	2.13366e8			0.241028
$361$	−8.79764e8	+	1.58183e8i	−0.984217	+	0.176964i
$362$	−1.24026e8			−0.137414
$363$	1.70986e8	−	9.69712e8i	0.187624	−	1.06407i
$364$	−3.57317e7	−	2.99824e7i	−0.0388328	−	0.0325846i
$365$	−5.19007e8	−	1.88903e8i	−0.558661	−	0.203336i
$366$	−1.39313e9	+	5.07058e8i	−1.48528	+	0.540597i
$367$	−5.92990e8	+	4.97577e8i	−0.626204	+	0.525448i	−0.899747	−	0.436412i	$-0.856249\pi$
$367$	−5.92990e8	+	4.97577e8i	−0.626204	+	0.525448i	0.273543	+	0.961860i	$0.411805\pi$
$368$	3.93506e7	+	6.81573e7i	0.0411608	+	0.0712927i
$369$	3.29839e8	−	5.71298e8i	0.341751	−	0.591930i
$370$	−6.14824e7	−	3.48684e8i	−0.0631023	−	0.357871i
$371$	−8.69812e6	−	4.93295e7i	−0.00884335	−	0.0501531i
$372$	−2.93892e8	+	5.09036e8i	−0.295997	+	0.512682i
$373$	−7.79517e8	−	1.35016e9i	−0.777759	−	1.34712i	−0.933231	−	0.359277i	$-0.883023\pi$
$373$	−7.79517e8	−	1.35016e9i	−0.777759	−	1.34712i	0.155472	−	0.987840i	$-0.450310\pi$
$374$	−172060.	+	144375.i	−0.000170070	+	0.000142706i
$375$	−1.31431e9	+	4.78370e8i	−1.28703	+	0.468440i
$376$	2.45436e7	+	8.93313e6i	0.0238111	+	0.00866655i
$377$	4.49394e8	+	3.77087e8i	0.431949	+	0.362449i
$378$	−8.49329e6	+	4.81679e7i	−0.00808826	+	0.0458708i
$379$	1.63541e9			1.54308			0.771541	−	0.636179i	$-0.219486\pi$
$379$	1.63541e9			1.54308			0.771541	+	0.636179i	$0.219486\pi$
$380$	4.50106e7	+	5.04683e8i	0.0420797	+	0.471820i
$381$	−1.23472e9			−1.14375
$382$	−1.14056e8	+	6.46841e8i	−0.104687	+	0.593712i
$383$	−8.60239e8	−	7.21826e8i	−0.782390	−	0.656503i	0.161459	−	0.986879i	$-0.448380\pi$
$383$	−8.60239e8	−	7.21826e8i	−0.782390	−	0.656503i	−0.943849	+	0.330376i	$0.892824\pi$
$384$	1.20852e8	+	4.39864e7i	0.108916	+	0.0396423i
$385$	−7.49252e7	+	2.72705e7i	−0.0669137	+	0.0243546i
$386$	−4.77725e8	+	4.00859e8i	−0.422787	+	0.354761i
$387$	−6.13153e8	−	1.06201e9i	−0.537750	−	0.931410i
$388$	−5.63159e7	+	9.75420e7i	−0.0489463	+	0.0847775i
$389$	1.03284e7	+	5.85754e7i	0.00889633	+	0.0504536i	0.988933	−	0.148364i	$-0.0474009\pi$
$389$	1.03284e7	+	5.85754e7i	0.00889633	+	0.0504536i	−0.980036	+	0.198818i	$0.936290\pi$
$390$	−1.01135e8	−	5.73563e8i	−0.0863324	−	0.489615i
$391$	145628.	−	252235.i	0.000123204	−	0.000213396i
$392$	2.04061e8	+	3.53444e8i	0.171104	+	0.296360i
$393$	−8.02079e6	+	6.73024e6i	−0.00666566	+	0.00559315i
$394$	−4.01357e8	+	1.46082e8i	−0.330593	+	0.120326i
$395$	1.94403e8	+	7.07568e7i	0.158713	+	0.0577668i
$396$	−1.42906e8	−	1.19912e8i	−0.115642	−	0.0970355i
$397$	−3.49101e7	+	1.97985e8i	−0.0280017	+	0.158806i	−0.995602	−	0.0936800i	$-0.970137\pi$
$397$	−3.49101e7	+	1.97985e8i	−0.0280017	+	0.158806i	0.967601	+	0.252486i	$0.0812480\pi$
$398$	1.31998e9			1.04949
$399$	2.96976e8	+	2.54781e7i	0.234054	+	0.0200799i
$400$	−3.27876e7			−0.0256153
$401$	1.49512e8	−	8.47924e8i	0.115790	−	0.656677i	−0.870566	−	0.492051i	$-0.836247\pi$
$401$	1.49512e8	−	8.47924e8i	0.115790	−	0.656677i	0.986356	−	0.164626i	$-0.0526416\pi$
$402$	−1.19962e9	−	1.00660e9i	−0.920985	−	0.772798i
$403$	6.30910e8	+	2.29632e8i	0.480175	+	0.174769i
$404$	8.00209e8	−	2.91252e8i	0.603766	−	0.219753i
$405$	−1.16600e9	+	9.78389e8i	−0.872179	+	0.731845i
$406$	8.50925e7	+	1.47385e8i	0.0631030	+	0.109298i
$407$	−1.54782e8	+	2.68091e8i	−0.113800	+	0.197107i
$408$	−82647.7	−	468718.i	−6.02449e−5	−	0.000341666i
$409$	9.97495e7	+	5.65708e8i	0.0720907	+	0.408847i	0.999403	+	0.0345574i	$0.0110022\pi$
$409$	9.97495e7	+	5.65708e8i	0.0720907	+	0.408847i	−0.927312	+	0.374289i	$0.877887\pi$
$410$	4.43996e8	−	7.69024e8i	0.318153	−	0.551057i
$411$	−1.29557e9	−	2.24399e9i	−0.920479	−	1.59432i
$412$	7.01984e8	−	5.89035e8i	0.494524	−	0.414955i
$413$	−2.89287e8	+	1.05292e8i	−0.202071	+	0.0735478i
$414$	2.27317e8	+	8.27367e7i	0.157446	+	0.0573056i
$415$	1.11341e9	+	9.34262e8i	0.764692	+	0.641653i
$416$	2.55095e7	−	1.44671e8i	0.0173730	−	0.0985271i
$417$	2.72845e9			1.84263
$418$	2.53486e8	−	3.63316e8i	0.169761	−	0.243315i
$419$	2.17537e9			1.44472			0.722360	−	0.691517i	$-0.243057\pi$
$419$	2.17537e9			1.44472			0.722360	+	0.691517i	$0.243057\pi$
$420$	2.93391e7	−	1.66391e8i	0.0193230	−	0.109586i
$421$	−1.36412e9	−	1.14463e9i	−0.890974	−	0.747616i	0.0774311	−	0.996998i	$-0.475328\pi$
$421$	−1.36412e9	−	1.14463e9i	−0.890974	−	0.747616i	−0.968405	+	0.249382i	$0.919773\pi$
$422$	2.01293e9	+	7.32647e8i	1.30387	+	0.474571i
$423$	7.54401e7	−	2.74580e7i	0.0484631	−	0.0176391i
$424$	1.20848e8	−	1.01404e8i	0.0769945	−	0.0646061i
$425$	60669.9	+	105083.i	3.83365e−5	+	6.64007e-5i
$426$	3.47912e8	−	6.02601e8i	0.218040	−	0.377656i
$427$	8.53075e7	+	4.83803e8i	0.0530261	+	0.300726i
$428$	1.78606e8	+	1.01293e9i	0.110114	+	0.624489i
$429$	−2.54607e8	+	4.40992e8i	−0.155693	+	0.269668i
$430$	−8.25364e8	−	1.42957e9i	−0.500617	−	0.867095i
$431$	−1.60099e9	+	1.34339e9i	−0.963203	+	0.808223i	−0.981471	−	0.191610i	$-0.938629\pi$
$431$	−1.60099e9	+	1.34339e9i	−0.963203	+	0.808223i	0.0182686	+	0.999833i	$0.494185\pi$
$432$	−1.44752e8	+	5.26852e7i	−0.0863834	+	0.0314410i
$433$	7.61349e8	+	2.77109e8i	0.450688	+	0.164037i	0.557384	−	0.830255i	$-0.311805\pi$
$433$	7.61349e8	+	2.77109e8i	0.450688	+	0.164037i	−0.106696	+	0.994292i	$0.534027\pi$
$434$	1.49205e8	+	1.25198e8i	0.0876131	+	0.0735161i
$435$	−3.68996e8	+	2.09268e9i	−0.214936	+	1.21896i
$436$	1.07704e9			0.622343
$437$	−1.47746e8	+	5.55135e8i	−0.0846899	+	0.318210i
$438$	−1.02328e9			−0.581880
$439$	2.50127e8	−	1.41854e9i	0.141103	−	0.800232i	−0.829312	−	0.558786i	$-0.811267\pi$
$439$	2.50127e8	−	1.41854e9i	0.141103	−	0.800232i	0.970414	−	0.241446i	$-0.0776217\pi$
$440$	−1.92366e8	−	1.61414e8i	−0.107657	−	0.0903351i
$441$	1.17880e9	+	4.29049e8i	0.654494	+	0.238216i
$442$	−510870.	+	185941.i	−0.000281405	+	0.000102423i
$443$	−1.72970e9	+	1.45139e9i	−0.945274	+	0.793179i	−0.978495	−	0.206269i	$-0.933868\pi$
$443$	−1.72970e9	+	1.45139e9i	−0.945274	+	0.793179i	0.0332212	+	0.999448i	$0.489423\pi$
$444$	−3.27987e8	−	5.68090e8i	−0.177834	−	0.308018i
$445$	−7.91672e8	+	1.37122e9i	−0.425878	+	0.737642i
$446$	−2.08826e8	−	1.18431e9i	−0.111458	−	0.632112i
$447$	1.67177e8	+	9.48108e8i	0.0885320	+	0.502090i
$448$	2.13083e7	−	3.69070e7i	0.0111963	−	0.0193926i
$449$	−1.18846e8	−	2.05846e8i	−0.0619613	−	0.107320i	0.833381	−	0.552699i	$-0.186402\pi$
$449$	−1.18846e8	−	2.05846e8i	−0.0619613	−	0.107320i	−0.895342	+	0.445379i	$0.853069\pi$
$450$	−7.72020e7	+	6.47802e7i	−0.0399379	+	0.0335119i
$451$	−7.29567e8	+	2.65541e8i	−0.374496	+	0.136305i
$452$	1.02800e9	+	3.74161e8i	0.523610	+	0.190578i
$453$	2.14118e9	+	1.79666e9i	1.08221	+	0.908078i
$454$	2.03763e8	−	1.15560e9i	0.102195	−	0.579577i
$455$	−1.92993e8			−0.0960509
$456$	3.98160e8	+	8.50117e8i	0.196644	+	0.419857i
$457$	1.06548e9			0.522203			0.261102	−	0.965311i	$-0.415914\pi$
$457$	1.06548e9			0.522203			0.261102	+	0.965311i	$0.415914\pi$
$458$	−8.86162e7	+	5.02567e8i	−0.0431007	+	0.244436i
$459$	436702.	+	366436.i	0.000210785	+	0.000176870i
$460$	3.05991e8	+	1.11372e8i	0.146574	+	0.0533485i
$461$	−2.60634e9	+	9.48631e8i	−1.23902	+	0.450966i	−0.876677	−	0.481079i	$-0.840245\pi$
$461$	−2.60634e9	+	9.48631e8i	−1.23902	+	0.450966i	−0.362342	+	0.932045i	$0.618023\pi$
$462$	−1.13162e8	+	9.49543e7i	−0.0533893	+	0.0447990i
$463$	1.26569e8	+	2.19224e8i	0.0592644	+	0.102649i	0.894135	−	0.447797i	$-0.147791\pi$
$463$	1.26569e8	+	2.19224e8i	0.0592644	+	0.102649i	−0.834871	+	0.550446i	$0.814458\pi$
$464$	−2.67993e8	+	4.64177e8i	−0.124540	+	0.215710i
$465$	4.22308e8	+	2.39503e9i	0.194780	+	1.10465i
$466$	−1.33023e8	−	7.54410e8i	−0.0608942	−	0.345348i
$467$	2.06586e9	−	3.57818e9i	0.938625	−	1.62575i	0.170585	−	0.985343i	$-0.445434\pi$
$467$	2.06586e9	−	3.57818e9i	0.938625	−	1.62575i	0.768040	−	0.640402i	$-0.221232\pi$
$468$	−2.25770e8	−	3.91045e8i	−0.101813	−	0.176346i
$469$	−3.97517e8	+	3.33556e8i	−0.177931	+	0.149301i
$470$	1.01550e8	−	3.69611e7i	0.0451166	−	0.0164211i
$471$	−2.33534e9	−	8.49993e8i	−1.02986	−	0.374837i
$472$	−7.42726e8	−	6.23221e8i	−0.325111	−	0.272801i
$473$	−2.50620e8	+	1.42134e9i	−0.108894	+	0.617566i
$474$	3.83285e8			0.165309
$475$	−1.69513e8	−	1.68943e8i	−0.0725730	−	0.0723290i
$476$	−157715.			−6.70267e−5
$477$	8.42018e7	−	4.77532e8i	0.0355228	−	0.201460i
$478$	−6.66362e8	−	5.59144e8i	−0.279070	−	0.234167i
$479$	2.38544e9	+	8.68230e8i	0.991732	+	0.360961i	0.786391	−	0.617729i	$-0.211947\pi$
$479$	2.38544e9	+	8.68230e8i	0.991732	+	0.360961i	0.205341	+	0.978690i	$0.434170\pi$
$480$	5.00028e8	−	1.81995e8i	0.206372	−	0.0751131i
$481$	−5.73990e8	+	4.81635e8i	−0.235178	+	0.197338i
$482$	1.55415e9	+	2.69186e9i	0.632160	+	1.09493i
$483$	9.57783e7	−	1.65893e8i	0.0386770	−	0.0669905i
$484$	−1.78445e8	−	1.01201e9i	−0.0715395	−	0.405720i
$485$	8.09231e7	+	4.58938e8i	0.0322090	+	0.182666i
$486$	−1.08101e9	+	1.87236e9i	−0.427171	+	0.739882i
$487$	−1.70392e9	−	2.95128e9i	−0.668495	−	1.15787i	−0.978325	−	0.207075i	$-0.933606\pi$
$487$	−1.70392e9	−	2.95128e9i	−0.668495	−	1.15787i	0.309830	−	0.950792i	$-0.399728\pi$
$488$	−1.18523e9	+	9.94526e8i	−0.461672	+	0.387389i
$489$	4.49928e9	−	1.63760e9i	1.74005	−	0.633327i
$490$	1.58678e9	+	5.77542e8i	0.609301	+	0.221767i
$491$	−4.93456e8	−	4.14059e8i	−0.188132	−	0.157862i	0.543857	−	0.839178i	$-0.316963\pi$
$491$	−4.93456e8	−	4.14059e8i	−0.188132	−	0.157862i	−0.731989	+	0.681316i	$0.761408\pi$
$492$	2.85683e8	−	1.62019e9i	0.108145	−	0.613322i
$493$	1.98356e6			0.000745559
$494$	8.77324e8	−	6.16513e8i	0.327428	−	0.230090i
$495$	−7.71859e8			−0.286035
$496$	−1.06520e8	+	6.04104e8i	−0.0391963	+	0.222293i
$497$	−1.76630e8	−	1.48210e8i	−0.0645383	−	0.0541541i
$498$	2.53042e9	+	9.20997e8i	0.918099	+	0.334161i
$499$	3.82876e8	−	1.39355e8i	0.137945	−	0.0502079i	−0.272125	−	0.962262i	$-0.587726\pi$
$499$	3.82876e8	−	1.39355e8i	0.137945	−	0.0502079i	0.410070	+	0.912054i	$0.365504\pi$
$500$	−1.11817e9	+	9.38258e8i	−0.400050	+	0.335682i
$501$	−2.28226e9	−	3.95299e9i	−0.810836	−	1.40441i
$502$	6.09018e7	−	1.05485e8i	0.0214866	−	0.0372158i
$503$	2.39348e8	+	1.35741e9i	0.0838574	+	0.475579i	0.997597	+	0.0692792i	$0.0220699\pi$
$503$	2.39348e8	+	1.35741e9i	0.0838574	+	0.475579i	−0.913740	+	0.406300i	$0.866819\pi$
$504$	−2.27464e7	−	1.29001e8i	−0.00791419	−	0.0448836i
$505$	1.76169e9	−	3.05133e9i	0.608708	−	1.05431i
$506$	−1.42352e8	−	2.46561e8i	−0.0488469	−	0.0846052i
$507$	2.00360e9	−	1.68122e9i	0.682784	−	0.572924i
$508$	−1.21087e9	+	4.40720e8i	−0.409802	+	0.149156i
$509$	−4.66477e9	−	1.69784e9i	−1.56790	−	0.570668i	−0.595370	−	0.803452i	$-0.702994\pi$
$509$	−4.66477e9	−	1.69784e9i	−1.56790	−	0.570668i	−0.972529	+	0.232784i	$0.925217\pi$
$510$	−1.50854e6	−	1.26581e6i	−0.000503571	−	0.000422546i
$511$	−5.88810e7	+	3.33931e8i	−0.0195210	+	0.110709i
$512$	1.34218e8			0.0441942
$513$	−1.01984e9	−	4.73469e8i	−0.333519	−	0.154839i
$514$	−2.58500e9			−0.839633
$515$	6.58393e8	−	3.73393e9i	0.212403	−	1.20460i
$516$	−2.34280e9	−	1.96584e9i	−0.750691	−	0.629904i
$517$	−8.87870e7	−	3.23158e7i	−0.0282574	−	0.0102849i
$518$	−2.04260e8	+	7.43446e7i	−0.0645698	+	0.0235015i
$519$	−3.25847e9	+	2.73418e9i	−1.02312	+	0.858502i
$520$	−3.03908e8	−	5.26385e8i	−0.0947831	−	0.164169i
$521$	5.97523e8	−	1.03494e9i	0.185107	−	0.320614i	−0.758506	−	0.651666i	$-0.774070\pi$
$521$	5.97523e8	−	1.03494e9i	0.185107	−	0.320614i	0.943613	+	0.331052i	$0.107404\pi$
$522$	2.86080e8	+	1.62244e9i	0.0880321	+	0.499255i
$523$	9.30209e7	+	5.27548e8i	0.0284331	+	0.161252i	0.995718	−	0.0924391i	$-0.0294664\pi$
$523$	9.30209e7	+	5.27548e8i	0.0284331	+	0.161252i	−0.967285	+	0.253691i	$0.918355\pi$
$524$	−5.46356e6	+	9.46317e6i	−0.00165889	+	0.00287327i
$525$	3.99021e7	+	6.91125e7i	0.0120348	+	0.0208448i
$526$	−3.01806e9	+	2.53245e9i	−0.904226	+	0.758736i
$527$	2.13324e6	−	776436.i	0.000634896	−	0.000231083i
$528$	−4.37184e8	−	1.59122e8i	−0.129255	−	0.0470448i
$529$	−2.32544e9	−	1.95127e9i	−0.682982	−	0.573090i
$530$	1.13344e8	−	6.42805e8i	0.0330699	−	0.187549i
$531$	−2.98016e9			−0.863791
$532$	3.00333e8	−	8.10164e7i	0.0864794	−	0.0233282i
$533$	−1.87922e9			−0.537568
$534$	−5.09391e8	+	2.88890e9i	−0.144763	+	0.820990i
$535$	3.26003e9	+	2.73549e9i	0.920415	+	0.772320i
$536$	−1.53574e9	−	5.58965e8i	−0.430766	−	0.156786i
$537$	5.32261e9	−	1.93727e9i	1.48325	−	0.539860i
$538$	−8.68879e8	+	7.29076e8i	−0.240559	+	0.201853i
$539$	−7.38197e8	−	1.27859e9i	−0.203054	−	0.351700i
$540$	−3.18676e8	+	5.51963e8i	−0.0870905	+	0.150845i
$541$	2.89038e8	+	1.63921e9i	0.0784810	+	0.445088i	0.998574	+	0.0533874i	$0.0170018\pi$
$541$	2.89038e8	+	1.63921e9i	0.0784810	+	0.445088i	−0.920093	+	0.391700i	$0.871887\pi$
$542$	−6.74505e8	−	3.82531e9i	−0.181965	−	1.03197i
$543$	−4.75367e8	+	8.23361e8i	−0.127418	+	0.220694i
$544$	−248355.	−	430164.i	−6.61420e−5	−	0.000114561i
$545$	3.41372e9	−	2.86445e9i	0.903317	−	0.757973i
$546$	−3.35995e8	+	1.22292e8i	−0.0883401	+	0.0321532i
$547$	3.13221e8	+	1.14003e8i	0.0818267	+	0.0297825i	0.382609	−	0.923910i	$-0.375026\pi$
$547$	3.13221e8	+	1.14003e8i	0.0818267	+	0.0297825i	−0.300782	+	0.953693i	$0.597248\pi$
$548$	−2.07151e9	−	1.73820e9i	−0.537719	−	0.451200i
$549$	−8.25816e8	+	4.68344e9i	−0.213000	+	1.20799i
$550$	1.18610e8			0.0303985
$551$	−3.77727e9	+	1.01894e9i	−0.961938	+	0.259487i
$552$	6.03293e8			0.152666
$553$	2.20548e7	−	1.25079e8i	0.00554582	−	0.0314519i
$554$	9.75622e7	+	8.18644e7i	0.0243780	+	0.0204555i
$555$	−2.55043e9	−	9.28281e8i	−0.633269	−	0.230491i
$556$	2.67574e9	−	9.73890e8i	0.660210	−	0.240297i
$557$	5.09319e9	−	4.27369e9i	1.24881	−	1.04788i	0.252029	−	0.967720i	$-0.418902\pi$
$557$	5.09319e9	−	4.27369e9i	1.24881	−	1.04788i	0.996782	−	0.0801569i	$-0.0255421\pi$
$558$	9.42747e8	+	1.63289e9i	0.229708	+	0.397865i
$559$	−1.74669e9	+	3.02535e9i	−0.422935	+	0.732545i
$560$	−3.06190e7	−	1.73649e8i	−0.00736771	−	0.0417843i
$561$	298980.	+	1.69560e6i	7.14945e−5	+	0.000405465i
$562$	−9.48114e8	+	1.64218e9i	−0.225312	+	0.390251i
$563$	2.98190e9	+	5.16480e9i	0.704229	+	1.21976i	0.966969	+	0.254894i	$0.0820405\pi$
$563$	2.98190e9	+	5.16480e9i	0.704229	+	1.21976i	−0.262740	+	0.964867i	$0.584626\pi$
$564$	1.53374e8	−	1.28696e8i	0.0359978	−	0.0302057i
$565$	4.25338e9	−	1.54810e9i	0.992120	−	0.361102i
$566$	1.85876e9	+	6.76533e8i	0.430889	+	0.156831i
$567$	7.15838e8	+	6.00660e8i	0.164920	+	0.138385i
$568$	1.26099e8	−	7.15145e8i	0.0288731	−	0.163748i
$569$	4.83635e9			1.10059			0.550294	−	0.834971i	$-0.314516\pi$
$569$	4.83635e9			1.10059			0.550294	+	0.834971i	$0.314516\pi$
$570$	3.52292e9	+	1.63555e9i	0.796783	+	0.369914i
$571$	−5.47708e7			−0.0123118			−0.00615592	−	0.999981i	$-0.501960\pi$
$571$	−5.47708e7			−0.0123118			−0.00615592	+	0.999981i	$0.501960\pi$
$572$	−9.22811e7	+	5.23352e8i	−0.0206171	+	0.116925i
$573$	3.85698e9	+	3.23639e9i	0.856458	+	0.718654i
$574$	−5.12285e8	−	1.86457e8i	−0.113063	−	0.0411516i
$575$	−1.44530e8	+	5.26046e7i	−0.0317044	+	0.0115395i
$576$	3.16030e8	−	2.65181e8i	0.0689049	−	0.0578180i
$577$	5.23244e8	+	9.06286e8i	0.113394	+	0.196404i	0.917137	−	0.398573i	$-0.130494\pi$
$577$	5.23244e8	+	9.06286e8i	0.113394	+	0.196404i	−0.803743	+	0.594977i	$0.797161\pi$
$578$	1.64135e9	−	2.84291e9i	0.353553	−	0.612372i
$579$	8.30120e8	+	4.70785e9i	0.177732	+	1.00797i
$580$	3.85092e8	+	2.18397e9i	0.0819533	+	0.464780i
$581$	4.46157e8	−	7.72767e8i	0.0943782	−	0.163468i
$582$	4.31696e8	+	7.47719e8i	0.0907711	+	0.157220i
$583$	−4.37172e8	+	3.66831e8i	−0.0913718	+	0.0766701i
$584$	−1.00351e9	+	3.65248e8i	−0.208486	+	0.0758827i
$585$	−1.75559e9	−	6.38982e8i	−0.362558	−	0.131960i
$586$	4.05161e8	+	3.39971e8i	0.0831737	+	0.0697910i
$587$	2.73956e7	−	1.55368e8i	0.00559046	−	0.0317051i	−0.981885	−	0.189478i	$-0.939320\pi$
$587$	2.73956e7	−	1.55368e8i	0.00559046	−	0.0317051i	0.987475	+	0.157773i	$0.0504315\pi$
$588$	3.12851e9			0.634625
$589$	−3.66345e9	+	2.57438e9i	−0.738731	+	0.519121i
$590$	−4.01159e9			−0.804145
$591$	−5.68541e8	+	3.22436e9i	−0.113294	+	0.642521i
$592$	−5.24425e8	−	4.40045e8i	−0.103886	−	0.0871707i
$593$	5.78655e8	+	2.10613e8i	0.113954	+	0.0414757i	0.398368	−	0.917226i	$-0.369577\pi$
$593$	5.78655e8	+	2.10613e8i	0.113954	+	0.0414757i	−0.284414	+	0.958702i	$0.591799\pi$
$594$	5.23643e8	−	1.90590e8i	0.102514	−	0.0373120i
$595$	−499882.	+	419451.i	−9.72878e−5	+	8.16341e-5i
$596$	5.02365e8	+	8.70122e8i	0.0971980	+	0.168352i
$597$	5.05924e9	−	8.76287e9i	0.973140	−	1.68553i
$598$	−1.19664e8	−	6.78647e8i	−0.0228828	−	0.129775i
$599$	−4.60235e8	−	2.61012e9i	−0.0874955	−	0.496212i	−0.996790	−	0.0800587i	$-0.974489\pi$
$599$	−4.60235e8	−	2.61012e9i	−0.0874955	−	0.496212i	0.909295	−	0.416153i	$-0.136622\pi$
$600$	−1.25669e8	+	2.17665e8i	−0.0237519	+	0.0411394i
$601$	4.28758e9	+	7.42631e9i	0.805660	+	1.39544i	0.915845	+	0.401533i	$0.131522\pi$
$601$	4.28758e9	+	7.42631e9i	0.805660	+	1.39544i	−0.110185	+	0.993911i	$0.535144\pi$
$602$	−7.76330e8	+	6.51418e8i	−0.145030	+	0.121695i
$603$	−4.72045e9	+	1.71810e9i	−0.876744	+	0.319109i
$604$	2.74112e9	+	9.97686e8i	0.506173	+	0.184232i
$605$	−3.25709e9	−	2.73302e9i	−0.597979	−	0.501764i
$606$	1.13353e9	−	6.42859e9i	0.206910	−	1.17344i
$607$	−1.28182e9			−0.232631			−0.116315	−	0.993212i	$-0.537108\pi$
$607$	−1.28182e9			−0.232631			−0.116315	+	0.993212i	$0.537108\pi$
$608$	6.93909e8	+	6.91576e8i	0.125210	+	0.124789i
$609$	1.30457e9			0.234050
$610$	−1.11163e9	+	6.30437e9i	−0.198292	+	1.12457i
$611$	−1.75193e8	−	1.47004e8i	−0.0310722	−	0.0260727i
$612$	−1.43468e6	−	522179.i	−0.000253002	−	9.20852e-5i
$613$	−1.67353e9	+	6.09114e8i	−0.293441	+	0.106804i	−0.484546	−	0.874766i	$-0.661015\pi$
$613$	−1.67353e9	+	6.09114e8i	−0.293441	+	0.106804i	0.191105	+	0.981570i	$0.438793\pi$
$614$	9.73283e8	−	8.16681e8i	0.169687	−	0.142385i
$615$	−3.40350e9	−	5.89504e9i	−0.590015	−	1.02194i
$616$	−7.70833e7	+	1.33512e8i	−0.0132870	+	0.0230138i
$617$	−1.11452e9	−	6.32077e9i	−0.191025	−	1.08336i	−0.917966	−	0.396658i	$-0.870170\pi$
$617$	−1.11452e9	−	6.32077e9i	−0.191025	−	1.08336i	0.726941	−	0.686700i	$-0.240941\pi$
$618$	−1.21981e9	−	6.91786e9i	−0.207889	−	1.17900i
$619$	−1.76496e9	+	3.05699e9i	−0.299100	+	0.518057i	−0.975930	−	0.218082i	$-0.930020\pi$
$619$	−1.76496e9	+	3.05699e9i	−0.299100	+	0.518057i	0.676830	+	0.736139i	$0.263353\pi$
$620$	1.26903e9	+	2.19803e9i	0.213846	+	0.370392i
$621$	−5.53545e8	+	4.64480e8i	−0.0927540	+	0.0778298i
$622$	2.86502e8	−	1.04278e8i	0.0477377	−	0.0173751i
$623$	9.13436e8	+	3.32464e8i	0.151346	+	0.0550853i
$624$	−8.62645e8	−	7.23845e8i	−0.142130	−	0.119261i
$625$	−9.40142e8	+	5.33181e9i	−0.154033	+	0.873564i
$626$	−6.33413e9			−1.03199
$627$	−1.44036e9	−	3.07532e9i	−0.233364	−	0.498258i
$628$	−2.59362e9			−0.417876
$629$	−439939.	+	2.49502e6i	−7.04881e−5	+	0.000399758i
$630$	−4.15182e8	−	3.48379e8i	−0.0661526	−	0.0555086i
$631$	−7.48256e9	−	2.72343e9i	−1.18562	−	0.431532i	−0.327440	−	0.944872i	$-0.606186\pi$
$631$	−7.48256e9	−	2.72343e9i	−1.18562	−	0.431532i	−0.858185	+	0.513340i	$0.828408\pi$
$632$	3.75881e8	−	1.36810e8i	0.0592299	−	0.0215579i
$633$	1.25789e10	−	1.05550e10i	1.97120	−	1.65403i
$634$	4.03299e9	+	6.98535e9i	0.628514	+	1.08862i
$635$	−2.66577e9	+	4.61725e9i	−0.413156	+	0.715608i
$636$	−2.09992e8	−	1.19093e9i	−0.0323671	−	0.183563i
$637$	−6.20543e8	−	3.51927e9i	−0.0951226	−	0.539467i
$638$	9.69470e8	−	1.67917e9i	0.147796	−	0.255990i
$639$	−1.11603e9	−	1.93303e9i	−0.169209	−	0.293079i
$640$	4.25408e8	−	3.56960e8i	0.0641469	−	0.0538256i
$641$	2.41720e8	−	8.79788e7i	0.0362501	−	0.0131940i	−0.323831	−	0.946115i	$-0.604971\pi$
$641$	2.41720e8	−	8.79788e7i	0.0362501	−	0.0131940i	0.360082	+	0.932921i	$0.382749\pi$
$642$	7.40900e9	+	2.69665e9i	1.10506	+	0.402210i
$643$	5.20403e9	+	4.36670e9i	0.771972	+	0.647761i	0.941213	−	0.337814i	$-0.109687\pi$
$643$	5.20403e9	+	4.36670e9i	0.771972	+	0.647761i	−0.169241	+	0.985575i	$0.554132\pi$
$644$	3.47145e7	−	1.96876e8i	0.00512165	−	0.0290463i
$645$	−1.26538e10			−1.85679
$646$	932478.	−	3.50365e6i	0.000136090	−	0.000511336i
$647$	9.91475e9			1.43919			0.719593	−	0.694397i	$-0.244329\pi$
$647$	9.91475e9			1.43919			0.719593	+	0.694397i	$0.244329\pi$
$648$	−5.11049e8	+	2.89830e9i	−0.0737819	+	0.418438i
$649$	2.68683e9	+	2.25452e9i	0.385819	+	0.323741i
$650$	2.69778e8	+	9.81912e7i	0.0385310	+	0.0140241i
$651$	1.40301e9	−	5.10655e8i	0.199310	−	0.0725428i
$652$	3.82784e9	−	3.21194e9i	0.540863	−	0.453838i
$653$	3.03495e9	+	5.25669e9i	0.426536	+	0.738782i	0.996562	−	0.0828445i	$-0.0264005\pi$
$653$	3.03495e9	+	5.25669e9i	0.426536	+	0.738782i	−0.570027	+	0.821626i	$0.693067\pi$
$654$	4.12809e9	−	7.15007e9i	0.577069	−	0.999512i
$655$	7.85087e6	+	4.45245e7i	0.00109162	+	0.00619091i
$656$	−2.98145e8	−	1.69087e9i	−0.0412348	−	0.233854i
$657$	−1.64123e9	+	2.84270e9i	−0.225783	+	0.391068i
$658$	−3.31727e7	−	5.74567e7i	−0.00453931	−	0.00786231i
$659$	−8.81251e9	+	7.39457e9i	−1.19950	+	1.00650i	−0.199856	+	0.979825i	$0.564048\pi$
$659$	−8.81251e9	+	7.39457e9i	−1.19950	+	1.00650i	−0.999644	+	0.0266753i	$0.991508\pi$
$660$	−1.80886e9	+	6.58373e8i	−0.244908	+	0.0891391i
$661$	−2.90634e9	−	1.05782e9i	−0.391418	−	0.142465i	0.138811	−	0.990319i	$-0.455672\pi$
$661$	−2.90634e9	−	1.05782e9i	−0.391418	−	0.142465i	−0.530229	+	0.847854i	$0.677894\pi$
$662$	−2.40175e9	−	2.01531e9i	−0.321754	−	0.269984i
$663$	−723672.	+	4.10415e6i	−9.64371e−5	+	0.000546922i
$664$	2.81028e9			0.372530
$665$	7.36449e8	−	1.05554e9i	0.0971107	−	0.139187i
$666$	−2.10423e9			−0.276016
$667$	−4.36601e8	+	2.47609e9i	−0.0569697	+	0.323091i
$668$	−3.64915e9	−	3.06200e9i	−0.473668	−	0.397455i
$669$	−8.66258e9	−	3.15292e9i	−1.11855	−	0.407119i
$670$	−6.35419e9	+	2.31274e9i	−0.816203	+	0.297074i
$671$	4.28760e9	−	3.59772e9i	0.547880	−	0.459726i
$672$	−1.63341e8	−	2.82915e8i	−0.0207636	−	0.0359636i
$673$	−6.42051e9	+	1.11207e10i	−0.811927	+	1.40630i	0.0995862	+	0.995029i	$0.468248\pi$
$673$	−6.42051e9	+	1.11207e10i	−0.811927	+	1.40630i	−0.911513	+	0.411270i	$0.865085\pi$
$674$	−1.48644e9	−	8.43004e9i	−0.186999	−	1.06052i
$675$	−5.22754e7	−	2.96469e8i	−0.00654236	−	0.0371036i
$676$	1.36480e9	−	2.36391e9i	0.169925	−	0.294318i
$677$	3.66040e9	+	6.34000e9i	0.453386	+	0.785288i	0.998594	−	0.0530128i	$-0.0168824\pi$
$677$	3.66040e9	+	6.34000e9i	0.453386	+	0.785288i	−0.545207	+	0.838301i	$0.683549\pi$
$678$	6.42403e9	−	5.39040e9i	0.791596	−	0.664228i
$679$	2.68847e8	−	9.78523e7i	0.0329580	−	0.0119957i
$680$	−1.93122e6	−	702905.i	−0.000235532	−	8.57266e-5i
$681$	−6.89058e9	−	5.78189e9i	−0.836067	−	0.701543i
$682$	3.85339e8	−	2.18536e9i	0.0465155	−	0.263802i
$683$	−1.13816e10			−1.36688			−0.683441	−	0.730005i	$-0.739518\pi$
$683$	−1.13816e10			−1.36688			−0.683441	+	0.730005i	$0.739518\pi$
$684$	3.00027e9	+	2.57399e8i	0.358479	+	0.0307546i
$685$	−1.11886e10			−1.33002
$686$	3.66007e8	−	2.07573e9i	0.0432868	−	0.245492i
$687$	2.99670e9	+	2.51453e9i	0.352611	+	0.295875i
$688$	−2.99923e9	−	1.09163e9i	−0.351116	−	0.127796i
$689$	−1.29803e9	+	4.72443e8i	−0.151188	+	0.0550278i
$690$	1.91216e9	−	1.60449e9i	0.221591	−	0.185937i
$691$	−2.57377e9	−	4.45789e9i	−0.296754	−	0.513992i	0.678638	−	0.734473i	$-0.262571\pi$
$691$	−2.57377e9	−	4.45789e9i	−0.296754	−	0.513992i	−0.975391	+	0.220481i	$0.929237\pi$
$692$	−2.21959e9	+	3.84444e9i	−0.254625	+	0.441024i
$693$	8.22859e7	+	4.66666e8i	0.00939202	+	0.0532648i
$694$	−1.03805e8	−	5.88709e8i	−0.0117886	−	0.0668563i
$695$	5.89074e9	−	1.02031e10i	0.665615	−	1.15288i
$696$	2.05433e9	+	3.55820e9i	0.230960	+	0.400035i
$697$	−4.86749e6	+	4.08431e6i	−0.000544490	+	0.000456882i
$698$	−3.65162e9	+	1.32908e9i	−0.406436	+	0.147931i
$699$	−5.51809e9	−	2.00842e9i	−0.611109	−	0.222426i
$700$	6.38003e7	+	5.35348e7i	0.00703039	+	0.00589920i
$701$	−3.13415e9	+	1.77746e10i	−0.343642	+	1.94889i	−0.0293369	+	0.999570i	$0.509340\pi$
$701$	−3.13415e9	+	1.77746e10i	−0.343642	+	1.94889i	−0.314305	+	0.949322i	$0.601772\pi$
$702$	1.34880e9			0.147153
$703$	−4.43897e8	−	4.97722e9i	−0.0481880	−	0.540310i
$704$	−4.85536e8			−0.0524466
$705$	1.43850e8	−	8.15815e8i	0.0154614	−	0.0876859i
$706$	1.01505e9	+	8.51725e8i	0.108560	+	0.0910926i
$707$	−2.03265e9	−	7.39823e8i	−0.216319	−	0.0787336i
$708$	−6.98406e9	+	2.54199e9i	−0.739590	+	0.269189i
$709$	9.52366e9	−	7.99130e9i	1.00356	−	0.842084i	0.0160839	−	0.999871i	$-0.494880\pi$
$709$	9.52366e9	−	7.99130e9i	1.00356	−	0.842084i	0.987473	+	0.157786i	$0.0504357\pi$
$710$	−1.50229e9	−	2.60204e9i	−0.157525	−	0.272842i
$711$	6.14751e8	−	1.06478e9i	0.0641440	−	0.111101i
$712$	5.31611e8	+	3.01492e9i	0.0551968	+	0.313037i
$713$	4.99681e8	+	2.83383e9i	0.0516273	+	0.292793i
$714$	−604490.	+	1.04701e6i	−6.21506e−5	+	0.000107648i
$715$	1.09940e9	+	1.90421e9i	0.112482	+	0.194825i
$716$	4.52831e9	−	3.79970e9i	0.461042	−	0.386860i
$717$	−6.26598e9	+	2.28063e9i	−0.634852	+	0.231067i
$718$	6.30323e9	+	2.29419e9i	0.635518	+	0.231310i
$719$	8.56812e9	+	7.18951e9i	0.859675	+	0.721353i	0.961898	−	0.273408i	$-0.0881511\pi$
$719$	8.56812e9	+	7.18951e9i	0.859675	+	0.721353i	−0.102223	+	0.994762i	$0.532596\pi$
$720$	2.96406e8	−	1.68100e9i	0.0295953	−	0.167843i
$721$	−2.32773e9			−0.231291
$722$	2.40853e7	+	7.15093e9i	0.00238161	+	0.707103i
$723$	2.38270e10			2.34469
$724$	−1.72295e8	+	9.77133e8i	−0.0168728	+	0.0956905i
$725$	−8.02411e8	−	6.73303e8i	−0.0782013	−	0.0656187i
$726$	−7.40231e9	−	2.69422e9i	−0.717941	−	0.261309i
$727$	1.67204e10	−	6.08572e9i	1.61390	−	0.587410i	0.631690	−	0.775221i	$-0.282361\pi$
$727$	1.67204e10	−	6.08572e9i	1.61390	−	0.587410i	0.982205	+	0.187811i	$0.0601392\pi$
$728$	−2.85853e8	+	2.39860e8i	−0.0274589	+	0.0230408i
$729$	2.00107e9	+	3.46596e9i	0.191301	+	0.331343i
$730$	−2.20926e9	+	3.82656e9i	−0.210193	+	0.364064i
$731$	2.05110e6	+	1.16324e7i	0.000194212	+	0.00110143i
$732$	2.05952e9	+	1.16801e10i	0.194078	+	1.10067i
$733$	−8.50853e9	+	1.47372e10i	−0.797978	+	1.38214i	0.122954	+	0.992412i	$0.460763\pi$
$733$	−8.50853e9	+	1.47372e10i	−0.797978	+	1.38214i	−0.920931	+	0.389725i	$0.872570\pi$
$734$	3.09637e9	+	5.36307e9i	0.289013	+	0.500585i
$735$	9.91592e9	−	8.32045e9i	0.921144	−	0.772931i
$736$	5.91640e8	−	2.15339e8i	0.0546997	−	0.0199091i
$737$	5.55559e9	+	2.02207e9i	0.511204	+	0.186063i
$738$	−4.04274e9	−	3.39226e9i	−0.370236	−	0.310665i
$739$	2.78787e9	−	1.58108e10i	0.254107	−	1.44111i	−0.544248	−	0.838924i	$-0.683185\pi$
$739$	2.78787e9	−	1.58108e10i	0.254107	−	1.44111i	0.798355	−	0.602187i	$-0.205704\pi$
$740$	−2.83251e9			−0.256957
$741$	−7.30182e8	−	8.18720e9i	−0.0659276	−	0.739216i
$742$	−4.00724e8			−0.0360107
$743$	1.52234e9	−	8.63361e9i	0.136160	−	0.772203i	−0.837884	−	0.545848i	$-0.816208\pi$
$743$	1.52234e9	−	8.63361e9i	0.136160	−	0.772203i	0.974045	−	0.226356i	$-0.0726812\pi$
$744$	3.60215e9	+	3.02256e9i	0.320668	+	0.269073i
$745$	3.90640e9	+	1.42181e9i	0.346123	+	0.125978i
$746$	−1.17201e10	+	4.26577e9i	−1.03358	+	0.376194i
$747$	6.61711e9	−	5.55241e9i	0.580826	−	0.487371i
$748$	898432.	+	1.55613e6i	7.84927e−5	+	0.000135953i
$749$	1.30634e9	−	2.26264e9i	0.113597	−	0.196757i
$750$	1.94300e9	+	1.10193e10i	0.168174	+	0.953760i
$751$	−2.41434e7	−	1.36924e8i	−0.00207997	−	0.0117961i	0.983750	−	0.179543i	$-0.0574619\pi$
$751$	−2.41434e7	−	1.36924e8i	−0.00207997	−	0.0117961i	−0.985830	+	0.167747i	$0.946351\pi$
$752$	1.04475e8	−	1.80956e8i	0.00895879	−	0.0155171i
$753$	−4.66849e8	−	8.08607e8i	−0.0398469	−	0.0690168i
$754$	3.59516e9	−	3.01669e9i	0.305434	−	0.256290i
$755$	1.13415e10	−	4.12796e9i	0.959081	−	0.349077i
$756$	3.67690e8	+	1.33828e8i	0.0309496	+	0.0112647i
$757$	−6.52045e9	−	5.47131e9i	−0.546314	−	0.458412i	0.327377	−	0.944894i	$-0.393835\pi$
$757$	−6.52045e9	−	5.47131e9i	−0.546314	−	0.458412i	−0.873691	+	0.486482i	$0.838280\pi$
$758$	2.27189e9	−	1.28845e10i	0.189472	−	1.07455i
$759$	−2.18243e9			−0.181173
$760$	4.03865e9	+	3.46484e8i	0.333725	+	0.0286310i
$761$	2.05573e10			1.69091			0.845455	−	0.534047i	$-0.179330\pi$
$761$	2.05573e10			1.69091			0.845455	+	0.534047i	$0.179330\pi$
$762$	−1.71525e9	+	9.72768e9i	−0.140438	+	0.796465i
$763$	−2.09578e9	−	1.75857e9i	−0.170808	−	0.143325i
$764$	4.93767e9	+	1.79716e9i	0.400586	+	0.145801i
$765$	−5.93602e6	+	2.16054e6i	−0.000479381	+	0.000174480i
$766$	−6.88191e9	+	5.77461e9i	−0.553233	+	0.464218i
$767$	4.24479e9	+	7.35219e9i	0.339682	+	0.588346i
$768$	5.14431e8	−	8.91020e8i	0.0409791	−	0.0709779i
$769$	−2.69370e9	−	1.52768e10i	−0.213603	−	1.21140i	−0.883314	−	0.468782i	$-0.844693\pi$
$769$	−2.69370e9	−	1.52768e10i	−0.213603	−	1.21140i	0.669711	−	0.742622i	$-0.266418\pi$
$770$	1.10765e8	+	6.28179e8i	0.00874348	+	0.0495868i
$771$	−9.90781e9	+	1.71608e10i	−0.778551	+	1.34849i
$772$	2.49450e9	+	4.32060e9i	0.195130	+	0.337974i
$773$	3.40568e8	−	2.85770e8i	0.0265201	−	0.0222530i	−0.629431	−	0.777056i	$-0.716712\pi$
$773$	3.40568e8	−	2.85770e8i	0.0265201	−	0.0222530i	0.655951	+	0.754803i	$0.272268\pi$
$774$	−9.21880e9	+	3.35537e9i	−0.714630	+	0.260104i
$775$	−1.12651e9	−	4.10018e8i	−0.0869322	−	0.0316407i
$776$	6.90247e8	+	5.79186e8i	0.0530260	+	0.0444941i
$777$	−2.89344e8	+	1.64095e9i	−0.0221280	+	0.125494i
$778$	4.75832e8			0.0362264
$779$	7.17101e9	−	1.02781e10i	0.543499	−	0.778986i
$780$	−4.65929e9			−0.351551
$781$	−4.56168e8	+	2.58706e9i	−0.0342646	+	0.194324i
$782$	−1.78492e6	−	1.49773e6i	−0.000133474	−	0.000111998i
$783$	−4.62441e9	−	1.68315e9i	−0.344263	−	0.125301i
$784$	3.06808e9	−	1.11669e9i	0.227384	−	0.0827610i
$785$	−8.22057e9	+	6.89788e9i	−0.606538	+	0.508946i
$786$	4.18816e7	+	7.25410e7i	0.00307641	+	0.00532850i
$787$	−1.11617e10	+	1.93327e10i	−0.816245	+	1.41378i	0.0921857	+	0.995742i	$0.470615\pi$
$787$	−1.11617e10	+	1.93327e10i	−0.816245	+	1.41378i	−0.908431	+	0.418036i	$0.862719\pi$
$788$	5.93342e8	+	3.36501e9i	0.0431980	+	0.244988i
$789$	5.24434e9	+	2.97421e10i	0.380120	+	2.15577i
$790$	8.27516e8	−	1.43330e9i	0.0597147	−	0.103429i
$791$	−1.38942e9	−	2.40655e9i	−0.0998200	−	0.172893i
$792$	−1.14325e9	+	9.59299e8i	−0.0817715	+	0.0686145i
$793$	1.27305e10	−	4.63352e9i	0.906545	−	0.329955i
$794$	1.51132e9	+	5.50076e8i	0.107148	+	0.0389988i
$795$	−3.83291e9	−	3.21620e9i	−0.270548	−	0.227017i
$796$	1.83370e9	−	1.03994e10i	0.128864	−	0.730826i
$797$	−2.77973e10			−1.94490			−0.972451	−	0.233107i	$-0.925111\pi$
$797$	−2.77973e10			−1.94490			−0.972451	+	0.233107i	$0.925111\pi$
$798$	6.13283e8	−	2.30432e9i	0.0427219	−	0.160521i
$799$	−773277.			−5.36317e−5
$800$	−4.55481e7	+	2.58316e8i	−0.00314525	+	0.0178376i
$801$	7.20846e9	+	6.04861e9i	0.495597	+	0.415855i
$802$	−6.47264e9	−	2.35585e9i	−0.443069	−	0.161264i
$803$	3.63023e9	−	1.32129e9i	0.247417	−	0.0900524i
$804$	−9.59696e9	+	8.05281e9i	−0.651235	+	0.546451i
$805$	−4.13573e8	−	7.16329e8i	−0.0279426	−	0.0483979i
$806$	2.68560e9	−	4.65160e9i	0.180663	−	0.312917i
$807$	1.50981e9	+	8.56256e9i	0.101127	+	0.573517i
$808$	−1.18298e9	−	6.70902e9i	−0.0788929	−	0.447424i
$809$	−9.85686e8	+	1.70726e9i	−0.0654514	+	0.113365i	−0.896894	−	0.442245i	$-0.854182\pi$
$809$	−9.85686e8	+	1.70726e9i	−0.0654514	+	0.113365i	0.831443	+	0.555610i	$0.187515\pi$
$810$	6.08841e9	+	1.05454e10i	0.402538	+	0.697216i
$811$	6.37039e8	−	5.34539e8i	0.0419366	−	0.0351889i	−0.621578	−	0.783352i	$-0.713508\pi$
$811$	6.37039e8	−	5.34539e8i	0.0419366	−	0.0351889i	0.663515	+	0.748163i	$0.269064\pi$
$812$	1.27937e9	−	4.65654e8i	0.0838593	−	0.0305223i
$813$	−2.79800e10	−	1.01839e10i	−1.82613	−	0.664655i
$814$	1.89712e9	+	1.59187e9i	0.123285	+	0.103448i
$815$	3.59014e9	−	2.03607e10i	0.232306	−	1.31747i
$816$	−3.80759e6			−0.000245321
$817$	−9.88132e9	−	2.10977e10i	−0.633925	−	1.35350i
$818$	4.59548e9			0.293558
$819$	−1.99170e8	+	1.12955e9i	−0.0126687	+	0.0718476i
$820$	−5.44193e9	−	4.56632e9i	−0.344671	−	0.289213i
$821$	1.69423e10	+	6.16648e9i	1.06849	+	0.388899i	0.815612	−	0.578599i	$-0.196400\pi$
$821$	1.69423e10	+	6.16648e9i	1.06849	+	0.388899i	0.252879	+	0.967498i	$0.418623\pi$
$822$	−1.94790e10	+	7.08977e9i	−1.22325	+	0.445226i
$823$	−7.90816e9	+	6.63573e9i	−0.494511	+	0.414944i	−0.855640	−	0.517572i	$-0.826836\pi$
$823$	−7.90816e9	+	6.63573e9i	−0.494511	+	0.414944i	0.361129	+	0.932516i	$0.382392\pi$
$824$	−3.66550e9	−	6.34883e9i	−0.228238	−	0.395320i
$825$	4.54610e8	−	7.87407e8i	0.0281871	−	0.0488214i
$826$	4.27665e8	+	2.42541e9i	0.0264042	+	0.149746i
$827$	7.24196e8	+	4.10712e9i	0.0445233	+	0.252504i	0.998943	−	0.0459633i	$-0.0146357\pi$
$827$	7.24196e8	+	4.10712e9i	0.0445233	+	0.252504i	−0.954420	+	0.298467i	$0.903525\pi$
$828$	9.67623e8	−	1.67597e9i	0.0592380	−	0.102603i
$829$	−6.14590e9	−	1.06450e10i	−0.374666	−	0.648941i	0.615611	−	0.788050i	$-0.288909\pi$
$829$	−6.14590e9	−	1.06450e10i	−0.374666	−	0.648941i	−0.990277	+	0.139109i	$0.955576\pi$
$830$	8.90728e9	−	7.47410e9i	0.540719	−	0.453717i
$831$	9.17404e8	−	3.33908e8i	0.0554571	−	0.0201847i
$832$	−1.10435e9	−	4.01950e8i	−0.0664776	−	0.0241959i
$833$	−9.25610e6	−	7.76679e6i	−0.000554843	−	0.000465569i
$834$	3.79032e9	−	2.14960e10i	0.226253	−	1.28314i
$835$	−1.97097e10			−1.17159
$836$	−2.51024e9	−	2.50179e9i	−0.148591	−	0.148091i
$837$	−5.63220e9			−0.332001
$838$	3.02199e9	−	1.71386e10i	0.177394	−	1.00605i
$839$	1.87926e9	+	1.57688e9i	0.109855	+	0.0921791i	0.696060	−	0.717983i	$-0.254935\pi$
$839$	1.87926e9	+	1.57688e9i	0.109855	+	0.0921791i	−0.586206	+	0.810162i	$0.699379\pi$
$840$	−1.27014e9	−	4.62295e8i	−0.0739393	−	0.0269117i
$841$	1.19015e8	−	4.33178e7i	0.00689945	−	0.00251119i
$842$	−1.09130e10	+	9.15706e9i	−0.630014	+	0.528644i
$843$	7.26788e9	+	1.25883e10i	0.417841	+	0.723722i
$844$	8.56846e9	−	1.48410e10i	0.490574	−	0.849699i
$845$	−1.96115e9	−	1.11223e10i	−0.111818	−	0.634154i
$846$	−1.11526e8	−	6.32496e8i	−0.00633258	−	0.0359138i
$847$	−1.30516e9	+	2.26060e9i	−0.0738025	+	0.127830i
$848$	−6.31025e8	−	1.09297e9i	−0.0355354	−	0.0615491i
$849$	1.16155e10	−	9.74657e9i	0.651420	−	0.546607i
$850$	912177.	−	332005.i	5.09464e−5	−	1.85430e-5i
$851$	−3.01770e9	−	1.09835e9i	−0.167851	−	0.0610927i
$852$	−4.26426e9	−	3.57814e9i	−0.236214	−	0.198207i
$853$	4.65047e9	−	2.63741e10i	0.256552	−	1.45498i	−0.535505	−	0.844532i	$-0.679879\pi$
$853$	4.65047e9	−	2.63741e10i	0.256552	−	1.45498i	0.792057	−	0.610447i	$-0.209010\pi$
$854$	3.93013e9			0.215926
$855$	1.01940e10	−	7.16354e9i	0.557781	−	0.391964i
$856$	8.22842e9			0.448392
$857$	−1.76168e8	+	9.99097e8i	−0.00956079	+	0.0542219i	−0.989215	−	0.146471i	$-0.953208\pi$
$857$	−1.76168e8	+	9.99097e8i	−0.00956079	+	0.0542219i	0.979654	+	0.200693i	$0.0643195\pi$
$858$	3.12064e9	+	2.61853e9i	0.168670	+	0.141531i
$859$	1.56178e10	+	5.68441e9i	0.840705	+	0.305992i	0.726245	−	0.687436i	$-0.241264\pi$
$859$	1.56178e10	+	5.68441e9i	0.840705	+	0.305992i	0.114460	+	0.993428i	$0.463486\pi$
$860$	−1.24094e10	+	4.51666e9i	−0.665284	+	0.242143i
$861$	−3.20131e9	+	2.68621e9i	−0.170929	+	0.143427i
$862$	8.35977e9	+	1.44795e10i	0.444548	+	0.769980i
$863$	−7.81481e9	+	1.35356e10i	−0.413886	+	0.716871i	−0.995311	−	0.0967288i	$-0.969162\pi$
$863$	−7.81481e9	+	1.35356e10i	−0.413886	+	0.716871i	0.581425	+	0.813600i	$0.302495\pi$
$864$	2.13992e8	+	1.21361e9i	0.0112875	+	0.0640148i
$865$	3.18944e9	+	1.80882e10i	0.167555	+	0.950253i
$866$	3.24084e9	−	5.61331e9i	0.169569	−	0.293702i
$867$	−1.25820e10	−	2.17926e10i	−0.655666	−	1.13565i
$868$	1.19364e9	−	1.00158e9i	0.0619518	−	0.0519838i
$869$	−1.35976e9	+	4.94912e8i	−0.0702899	+	0.0255834i
$870$	1.59745e10	+	5.81424e9i	0.822451	+	0.299348i
$871$	1.09622e10	+	9.19838e9i	0.562127	+	0.471680i
$872$	1.49621e9	−	8.48543e9i	0.0764161	−	0.433377i
$873$	2.76959e9			0.140885
$874$	4.16836e9	+	1.93520e9i	0.211191	+	0.0980473i
$875$	3.70778e9			0.187105
$876$	−1.42152e9	+	8.06185e9i	−0.0714478	+	0.405201i
$877$	−7.41008e9	−	6.21780e9i	−0.370958	−	0.311270i	0.438183	−	0.898886i	$-0.355622\pi$
$877$	−7.41008e9	−	6.21780e9i	−0.370958	−	0.311270i	−0.809140	+	0.587616i	$0.800067\pi$
$878$	−1.08284e10	−	3.94123e9i	−0.539928	−	0.196518i
$879$	3.80984e9	−	1.38667e9i	0.189211	−	0.0688670i
$880$	−1.53892e9	+	1.29131e9i	−0.0761251	+	0.0638765i
$881$	1.10672e10	+	1.91690e10i	0.545284	+	0.944459i	0.998589	+	0.0531038i	$0.0169114\pi$
$881$	1.10672e10	+	1.91690e10i	0.545284	+	0.944459i	−0.453305	+	0.891355i	$0.649755\pi$
$882$	5.01782e9	−	8.69112e9i	0.246249	−	0.426516i
$883$	−2.89778e9	−	1.64341e10i	−0.141645	−	0.803311i	−0.970000	−	0.243106i	$-0.921834\pi$
$883$	−2.89778e9	−	1.64341e10i	−0.141645	−	0.803311i	0.828354	−	0.560205i	$-0.189278\pi$
$884$	755239.	+	4.28317e6i	3.67707e−5	+	0.000208537i
$885$	−1.53757e10	+	2.66314e10i	−0.745645	+	1.29149i
$886$	9.03185e9	+	1.56436e10i	0.436273	+	0.755648i
$887$	−2.30419e10	+	1.93344e10i	−1.10863	+	0.930249i	−0.997975	−	0.0636103i	$-0.979739\pi$
$887$	−2.30419e10	+	1.93344e10i	−1.10863	+	0.930249i	−0.110653	+	0.993859i	$0.535294\pi$
$888$	−4.93131e9	+	1.79485e9i	−0.236329	+	0.0860166i
$889$	3.07578e9	+	1.11949e9i	0.146825	+	0.0534398i
$890$	9.70330e9	+	8.14203e9i	0.461375	+	0.387140i
$891$	1.84873e9	−	1.04847e10i	0.0875593	−	0.496574i
$892$	−9.62065e9			−0.453866
$893$	1.47254e9	−	3.97225e8i	0.0691969	−	0.0186662i
$894$	7.70187e9			0.360508
$895$	4.24711e9	−	2.40866e10i	0.198022	−	1.12304i
$896$	−2.61169e8	−	2.19147e8i	−0.0121295	−	0.0101779i
$897$	−4.96393e9	−	1.80672e9i	−0.229642	−	0.0835830i
$898$	−1.78685e9	+	6.50361e8i	−0.0823420	+	0.0299700i
$899$	−1.50123e10	+	1.25968e10i	−0.689110	+	0.578232i
$900$	4.03120e8	+	6.98225e8i	0.0184326	+	0.0319262i
$901$	−2.33529e6	+	4.04483e6i	−0.000106366	+	0.000184231i
$902$	1.07855e9	+	6.11675e9i	0.0489347	+	0.277522i
$903$	1.34899e9	+	7.65052e9i	0.0609681	+	0.345767i
$904$	4.37589e9	−	7.57926e9i	0.197005	−	0.341222i
$905$	2.05265e9	+	3.55529e9i	0.0920543	+	0.159443i
$906$	1.71294e10	−	1.43733e10i	0.765235	−	0.642108i
$907$	−9.53899e9	+	3.47191e9i	−0.424499	+	0.154505i	−0.545431	−	0.838156i	$-0.683634\pi$
$907$	−9.53899e9	+	3.47191e9i	−0.424499	+	0.154505i	0.120932	+	0.992661i	$0.461412\pi$
$908$	−8.82126e9	−	3.21068e9i	−0.391048	−	0.142330i
$909$	−1.60408e10	−	1.34598e10i	−0.708358	−	0.594383i
$910$	−2.68103e8	+	1.52049e9i	−0.0117939	+	0.0668864i
$911$	−1.83410e10			−0.803725			−0.401863	−	0.915700i	$-0.631637\pi$
$911$	−1.83410e10			−0.803725			−0.401863	+	0.915700i	$0.631637\pi$
$912$	7.25073e9	−	1.95592e9i	0.316519	−	0.0853826i
$913$	−1.01663e10			−0.442093
$914$	1.48015e9	−	8.39436e9i	0.0641202	−	0.363644i
$915$	3.75916e10	+	3.15431e10i	1.62225	+	1.36123i
$916$	3.83635e9	+	1.39632e9i	0.164924	+	0.0600275i
$917$	2.60826e7	−	9.49328e6i	0.00111701	−	0.000406559i
$918$	3.49361e6	−	2.93149e6i	0.000149048	−	0.000125066i
$919$	1.45039e9	+	2.51216e9i	0.0616427	+	0.106768i	0.895200	−	0.445665i	$-0.147033\pi$
$919$	1.45039e9	+	2.51216e9i	0.0616427	+	0.106768i	−0.833557	+	0.552433i	$0.813699\pi$
$920$	1.30252e9	−	2.25602e9i	0.0551475	−	0.0955183i
$921$	−1.69123e9	−	9.59143e9i	−0.0713335	−	0.404552i
$922$	3.85306e9	+	2.18518e10i	0.161900	+	0.918182i
$923$	−3.17924e9	+	5.50661e9i	−0.133081	+	0.230504i
$924$	5.90891e8	+	1.02345e9i	0.0246408	+	0.0426792i
$925$	1.02488e9	−	8.59977e8i	0.0425772	−	0.0357265i
$926$	1.90298e9	−	6.92627e8i	0.0787581	−	0.0286656i
$927$	−2.11745e10	−	7.70690e9i	−0.873041	−	0.317761i
$928$	3.28471e9	+	2.75620e9i	0.134921	+	0.113212i
$929$	−1.93693e9	+	1.09849e10i	−0.0792608	+	0.449511i	0.919187	+	0.393821i	$0.128847\pi$
$929$	−1.93693e9	+	1.09849e10i	−0.0792608	+	0.449511i	−0.998448	+	0.0556899i	$0.982264\pi$
$930$	1.94558e10			0.793157
$931$	2.16159e10	+	1.00354e10i	0.877911	+	0.407578i
$932$	−6.12839e9			−0.247965
$933$	4.05844e8	−	2.30166e9i	0.0163596	−	0.0927801i
$934$	−2.53207e10	−	2.12466e10i	−1.01686	−	0.853246i
$935$	6.98622e6	+	2.54278e6i	0.000279513	+	0.000101734i
$936$	−3.39447e9	+	1.23548e9i	−0.135303	+	0.0492461i
$937$	2.12105e10	−	1.77977e10i	0.842290	−	0.706766i	−0.115787	−	0.993274i	$-0.536939\pi$
$937$	2.12105e10	−	1.77977e10i	0.842290	−	0.706766i	0.958078	+	0.286508i	$0.0924946\pi$
$938$	2.07568e9	+	3.59519e9i	0.0821205	+	0.142237i
$939$	−2.42775e10	+	4.20499e10i	−0.956917	+	1.65743i
$940$	−1.50125e8	−	8.51402e8i	−0.00589530	−	0.0334339i
$941$	8.60672e9	+	4.88112e10i	0.336724	+	1.90966i	0.409503	+	0.912309i	$0.365702\pi$
$941$	8.60672e9	+	4.88112e10i	0.336724	+	1.90966i	−0.0727788	+	0.997348i	$0.523187\pi$
$942$	−9.94085e9	+	1.72181e10i	−0.387476	+	0.671129i
$943$	−4.02707e9	−	6.97509e9i	−0.156386	−	0.270869i
$944$	−5.94181e9	+	4.98577e9i	−0.229888	+	0.192899i
$945$	1.52133e9	−	5.53719e8i	0.0586424	−	0.0213441i
$946$	1.08498e10	+	3.94900e9i	0.416680	+	0.151659i
$947$	6.32133e9	+	5.30423e9i	0.241871	+	0.202954i	0.755662	−	0.654961i	$-0.227315\pi$
$947$	6.32133e9	+	5.30423e9i	0.241871	+	0.202954i	−0.513792	+	0.857915i	$0.671760\pi$
$948$	5.32454e8	−	3.01970e9i	0.0202980	−	0.115116i
$949$	9.35076e9			0.355153
$950$	−1.56650e9	+	1.10081e9i	−0.0592784	+	0.0416561i
$951$	6.18307e10			2.33116
$952$	−219095.	+	1.24255e6i	−8.23006e−6	+	4.66750e-5i
$953$	1.64211e10	+	1.37790e10i	0.614580	+	0.515694i	0.896095	−	0.443863i	$-0.146392\pi$
$953$	1.64211e10	+	1.37790e10i	0.614580	+	0.515694i	−0.281515	+	0.959557i	$0.590837\pi$
$954$	−3.64525e9	−	1.32676e9i	−0.135928	−	0.0494736i
$955$	2.04298e10	−	7.43583e9i	0.759018	−	0.276260i
$956$	−5.33090e9	+	4.47316e9i	−0.197332	+	0.165581i
$957$	−7.43159e9	−	1.28719e10i	−0.274088	−	0.474734i
$958$	1.01541e10	−	1.75875e10i	0.373133	−	0.646285i
$959$	1.19278e9	+	6.76462e9i	0.0436714	+	0.247673i
$960$	−7.39212e8	−	4.19228e9i	−0.0269662	−	0.152933i
$961$	2.54203e9	−	4.40293e9i	0.0923951	−	0.160033i
$962$	2.99716e9	+	5.19124e9i	0.108542	+	0.188000i
$963$	1.93747e10	−	1.62573e10i	0.699106	−	0.586620i
$964$	2.33667e10	−	8.50479e9i	0.840094	−	0.305769i
$965$	1.93973e10	+	7.06004e9i	0.694857	+	0.252907i
$966$	−1.17393e9	−	9.85042e8i	−0.0419007	−	0.0351589i
$967$	−1.17434e9	+	6.66001e9i	−0.0417639	+	0.236855i	−0.998543	−	0.0539606i	$-0.982815\pi$
$967$	−1.17434e9	+	6.66001e9i	−0.0417639	+	0.236855i	0.956779	+	0.290815i	$0.0939266\pi$
$968$	−8.22099e9			−0.291313
$969$	−1.96854e7	−	1.96192e7i	−0.000695040	−	0.000692703i
$970$	3.72814e9			0.131157
$971$	9.07526e9	−	5.14684e10i	0.318121	−	1.80415i	−0.236042	−	0.971743i	$-0.575850\pi$
$971$	9.07526e9	−	5.14684e10i	0.318121	−	1.80415i	0.554162	−	0.832409i	$-0.313039\pi$
$972$	1.32496e10	+	1.11177e10i	0.462776	+	0.388315i
$973$	−6.79677e9	−	2.47382e9i	−0.236542	−	0.0860941i
$974$	−2.56186e10	+	9.32440e9i	−0.888380	+	0.323344i
$975$	1.68586e9	−	1.41461e9i	0.0582513	−	0.0488787i
$976$	6.18883e9	+	1.07194e10i	0.213076	+	0.369058i
$977$	−5.18964e9	+	8.98873e9i	−0.178036	+	0.308367i	−0.941208	−	0.337829i	$-0.890308\pi$
$977$	−5.18964e9	+	8.98873e9i	−0.178036	+	0.308367i	0.763172	+	0.646195i	$0.223641\pi$
$978$	−6.65146e9	−	3.77223e10i	−0.227369	−	1.28947i
$979$	−1.92312e9	−	1.09065e10i	−0.0655038	−	0.371490i
$980$	6.75448e9	−	1.16991e10i	0.229246	−	0.397065i
$981$	−1.32421e10	−	2.29360e10i	−0.447833	−	0.775669i
$982$	−3.94765e9	+	3.31247e9i	−0.133030	+	0.111625i
$983$	−3.17629e10	+	1.15608e10i	−1.06655	+	0.388194i	−0.814887	−	0.579620i	$-0.803201\pi$
$983$	−3.17629e10	+	1.15608e10i	−1.06655	+	0.388194i	−0.251667	+	0.967814i	$0.580979\pi$
$984$	−1.23677e10	−	4.50149e9i	−0.413816	−	0.150617i
$985$	1.08300e10	+	9.08749e9i	0.361080	+	0.302982i
$986$	2.75554e6	−	1.56274e7i	9.15455e−5	−	0.000519181i
$987$	−5.08578e8			−0.0168363
$988$	−3.63841e9	−	7.76842e9i	−0.120022	−	0.256261i
$989$	−1.49722e10			−0.492151
$990$	−1.07226e9	+	6.08106e9i	−0.0351217	+	0.199185i
$991$	1.62057e10	+	1.35982e10i	0.528945	+	0.443838i	0.867737	−	0.497024i	$-0.165574\pi$
$991$	1.62057e10	+	1.35982e10i	0.528945	+	0.443838i	−0.338792	+	0.940861i	$0.610018\pi$
$992$	4.61144e9	+	1.67843e9i	0.149984	+	0.0545898i
$993$	−2.25843e10	+	8.22001e9i	−0.731954	+	0.266410i
$994$	−1.41304e9	+	1.18568e9i	−0.0456355	+	0.0382927i
$995$	−2.18459e10	−	3.78382e10i	−0.703055	−	1.21773i
$996$	1.07713e10	−	1.86564e10i	0.345429	−	0.598301i
$997$	−9.40664e9	−	5.33477e10i	−0.300609	−	1.70484i	−0.643487	−	0.765457i	$-0.722513\pi$
$997$	−9.40664e9	−	5.33477e10i	−0.300609	−	1.70484i	0.342879	−	0.939380i	$-0.388598\pi$
$998$	−5.66021e8	−	3.21006e9i	−0.0180250	−	0.102225i
$999$	3.14280e9	−	5.44349e9i	0.0997327	−	0.172742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.8.e.a.17.1	yes	30
19.9	even	9	inner	38.8.e.a.9.1	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.8.e.a.9.1	✓	30	19.9	even	9	inner
38.8.e.a.17.1	yes	30	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:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38919 - 7.87846i) q^{2} +(-46.9776 - 39.4189i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-248.833 + 90.5677i) q^{5} +(-375.821 + 315.351i) q^{6} +(81.2847 + 140.789i) q^{7} +(-256.000 + 443.405i) q^{8} +(273.278 + 1549.84i) q^{9} +O(q^{10})\)	\(q+(1.38919 - 7.87846i) q^{2} +(-46.9776 - 39.4189i) q^{3} +(-60.1403 - 21.8893i) q^{4} +(-248.833 + 90.5677i) q^{5} +(-375.821 + 315.351i) q^{6} +(81.2847 + 140.789i) q^{7} +(-256.000 + 443.405i) q^{8} +(273.278 + 1549.84i) q^{9} +(367.859 + 2086.23i) q^{10} +(926.087 - 1604.03i) q^{11} +(1962.40 + 3398.97i) q^{12} +(3434.27 - 2881.70i) q^{13} +(1222.12 - 444.816i) q^{14} +(15259.6 + 5554.06i) q^{15} +(3137.72 + 2632.86i) q^{16} +(2.63223 - 14.9281i) q^{17} +12590.0 q^{18} +(2655.91 + 29779.5i) q^{19} +16947.3 q^{20} +(1731.19 - 9818.09i) q^{21} +(-11350.8 - 9524.43i) q^{22} +(18055.4 + 6571.63i) q^{23} +(29504.8 - 10738.9i) q^{24} +(-6132.03 + 5145.38i) q^{25} +(-17932.5 - 31060.0i) q^{26} +(-18803.9 + 32569.3i) q^{27} +(-1806.71 - 10246.4i) q^{28} +(22722.9 + 128868. i) q^{29} +(64955.9 - 112507. i) q^{30} +(74880.8 + 129697. i) q^{31} +(25101.7 - 21062.9i) q^{32} +(-106734. + 38848.2i) q^{33} +(-113.954 - 41.4758i) q^{34} +(-32977.2 - 27671.2i) q^{35} +(17489.8 - 99189.6i) q^{36} -167136. q^{37} +(238306. + 20444.7i) q^{38} -274927. q^{39} +(23543.0 - 133519. i) q^{40} +(-321108. - 269442. i) q^{41} +(-74946.5 - 27278.3i) q^{42} +(-732234. + 266511. i) q^{43} +(-90806.2 + 76195.5i) q^{44} +(-208366. - 360900. i) q^{45} +(76856.7 - 133120. i) q^{46} +(-8858.33 - 50238.1i) q^{47} +(-43618.1 - 247371. i) q^{48} +(398557. - 690321. i) q^{49} +(32019.2 + 55458.8i) q^{50} +(-712.106 + 597.528i) q^{51} +(-269617. + 98132.4i) q^{52} +(-289536. - 105382. i) q^{53} +(230474. + 193390. i) q^{54} +(-85167.4 + 483009. i) q^{55} -83235.5 q^{56} +(1.04911e6 - 1.50366e6i) q^{57} +1.04685e6 q^{58} +(-328833. + 1.86490e6i) q^{59} +(-796146. - 668046. i) q^{60} +(2.83965e6 + 1.03355e6i) q^{61} +(1.12584e6 - 409772. i) q^{62} +(-195987. + 164453. i) q^{63} +(-131072. - 227023. i) q^{64} +(-593571. + 1.02809e6i) q^{65} +(157790. + 894870. i) q^{66} +(554285. + 3.14351e6i) q^{67} +(-485.069 + 840.164i) q^{68} +(-589154. - 1.02044e6i) q^{69} +(-263818. + 221369. i) q^{70} +(-1.33278e6 + 485092. i) q^{71} +(-757165. - 275585. i) q^{72} +(1.59779e6 + 1.34071e6i) q^{73} +(-232182. + 1.31677e6i) q^{74} +490893. q^{75} +(492125. - 1.84908e6i) q^{76} +301107. q^{77} +(-381925. + 2.16600e6i) q^{78} +(-598479. - 502183. i) q^{79} +(-1.01922e6 - 370965. i) q^{80} +(5.40142e6 - 1.96596e6i) q^{81} +(-2.56887e6 + 2.15554e6i) q^{82} +(-2.74441e6 - 4.75346e6i) q^{83} +(-319026. + 552569. i) q^{84} +(697.020 + 3953.00i) q^{85} +(1.08249e6 + 6.13911e6i) q^{86} +(4.01236e6 - 6.94961e6i) q^{87} +(474156. + 821263. i) q^{88} +(4.58045e6 - 3.84345e6i) q^{89} +(-3.13280e6 + 1.14024e6i) q^{90} +(684866. + 249271. i) q^{91} +(-942010. - 790440. i) q^{92} +(1.59481e6 - 9.04459e6i) q^{93} -408105. q^{94} +(-3.35794e6 - 7.16957e6i) q^{95} -2.00950e6 q^{96} +(305598. - 1.73313e6i) q^{97} +(-4.88500e6 - 4.09900e6i) q^{98} +(2.73906e6 + 996938. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9}+O(q^{10}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9	\( 30 q + 45 q^{3} + 360 q^{6} + 1806 q^{7} - 7680 q^{8} - 3105 q^{9} + 9786 q^{11} - 11130 q^{13} + 6144 q^{14} - 1818 q^{15} - 65250 q^{17} + 29040 q^{18} + 105906 q^{19} - 47616 q^{20} + 172854 q^{21} + 102336 q^{22} + 101004 q^{23} + 23040 q^{24} - 132756 q^{25} - 92112 q^{26} + 43659 q^{27} + 96384 q^{28} - 273912 q^{29} + 58710 q^{31} - 406965 q^{33} + 84960 q^{34} + 356100 q^{35} - 198720 q^{36} - 2598852 q^{37} - 219336 q^{38} + 1769844 q^{39} + 43377 q^{41} - 79056 q^{42} + 1126698 q^{43} + 818688 q^{44} - 912546 q^{45} - 530880 q^{46} + 588306 q^{47} - 368640 q^{48} - 2778285 q^{49} + 1665288 q^{50} + 3972045 q^{51} - 430080 q^{52} + 6520866 q^{53} - 486648 q^{54} - 1666818 q^{55} - 1849344 q^{56} - 6947844 q^{57} - 4573152 q^{58} - 970467 q^{59} + 4634496 q^{60} - 4037670 q^{61} + 755952 q^{62} + 7946472 q^{63} - 3932160 q^{64} + 1497690 q^{65} + 6499272 q^{66} - 4817025 q^{67} + 1472064 q^{68} + 10299876 q^{69} + 2848800 q^{70} - 25171290 q^{71} + 3179520 q^{72} + 1347750 q^{73} - 3123936 q^{74} + 8817984 q^{75} + 1583232 q^{76} - 11476764 q^{77} - 930960 q^{78} + 10777986 q^{79} - 5365035 q^{81} + 347016 q^{82} + 9745314 q^{83} + 877056 q^{84} + 29258556 q^{85} - 9338208 q^{86} + 25598802 q^{87} + 5010432 q^{88} - 20353740 q^{89} - 30112128 q^{90} + 19748724 q^{91} - 14097792 q^{92} - 18738174 q^{93} + 12376608 q^{94} - 20427204 q^{95} - 23005029 q^{97} + 14869008 q^{98} - 45819771 q^{99}+O(q^{100}) \) 30 * q + 45 * q^3 + 360 * q^6 + 1806 * q^7 - 7680 * q^8 - 3105 * q^9 + 9786 * q^11 - 11130 * q^13 + 6144 * q^14 - 1818 * q^15 - 65250 * q^17 + 29040 * q^18 + 105906 * q^19 - 47616 * q^20 + 172854 * q^21 + 102336 * q^22 + 101004 * q^23 + 23040 * q^24 - 132756 * q^25 - 92112 * q^26 + 43659 * q^27 + 96384 * q^28 - 273912 * q^29 + 58710 * q^31 - 406965 * q^33 + 84960 * q^34 + 356100 * q^35 - 198720 * q^36 - 2598852 * q^37 - 219336 * q^38 + 1769844 * q^39 + 43377 * q^41 - 79056 * q^42 + 1126698 * q^43 + 818688 * q^44 - 912546 * q^45 - 530880 * q^46 + 588306 * q^47 - 368640 * q^48 - 2778285 * q^49 + 1665288 * q^50 + 3972045 * q^51 - 430080 * q^52 + 6520866 * q^53 - 486648 * q^54 - 1666818 * q^55 - 1849344 * q^56 - 6947844 * q^57 - 4573152 * q^58 - 970467 * q^59 + 4634496 * q^60 - 4037670 * q^61 + 755952 * q^62 + 7946472 * q^63 - 3932160 * q^64 + 1497690 * q^65 + 6499272 * q^66 - 4817025 * q^67 + 1472064 * q^68 + 10299876 * q^69 + 2848800 * q^70 - 25171290 * q^71 + 3179520 * q^72 + 1347750 * q^73 - 3123936 * q^74 + 8817984 * q^75 + 1583232 * q^76 - 11476764 * q^77 - 930960 * q^78 + 10777986 * q^79 - 5365035 * q^81 + 347016 * q^82 + 9745314 * q^83 + 877056 * q^84 + 29258556 * q^85 - 9338208 * q^86 + 25598802 * q^87 + 5010432 * q^88 - 20353740 * q^89 - 30112128 * q^90 + 19748724 * q^91 - 14097792 * q^92 - 18738174 * q^93 + 12376608 * q^94 - 20427204 * q^95 - 23005029 * q^97 + 14869008 * q^98 - 45819771 * q^99

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