LMFDB - Embedded newform 25.8.d.a.16.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,8,Mod(6,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25.6"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	25.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.80962563710$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.11
Character	$\chi$	$=$	25.16
Dual form			25.8.d.a.11.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(6.07706 + 4.41524i) q^{2} +(2.68014 + 8.24862i) q^{3} +(-22.1179 - 68.0718i) q^{4} +(2.44590 - 279.498i) q^{5} +(-20.1323 + 61.9609i) q^{6} -1153.54 q^{7} +(463.260 - 1425.77i) q^{8} +(1708.46 - 1241.27i) q^{9} +(1248.91 - 1687.73i) q^{10} +(348.723 + 253.362i) q^{11} +(502.220 - 364.884i) q^{12} +(226.996 - 164.922i) q^{13} +(-7010.13 - 5093.16i) q^{14} +(2312.03 - 728.918i) q^{15} +(1698.48 - 1234.02i) q^{16} +(10128.2 - 31171.5i) q^{17} +15863.0 q^{18} +(-9489.41 + 29205.4i) q^{19} +(-19080.0 + 6015.40i) q^{20} +(-3091.65 - 9515.11i) q^{21} +(1000.56 + 3079.39i) q^{22} +(3591.97 + 2609.72i) q^{23} +13002.2 q^{24} +(-78113.0 - 1367.25i) q^{25} +2107.64 q^{26} +(30163.2 + 21914.9i) q^{27} +(25513.8 + 78523.5i) q^{28} +(34370.4 + 105781. i) q^{29} +(17268.7 + 5778.49i) q^{30} +(-44813.9 + 137923. i) q^{31} -176120. q^{32} +(-1155.26 + 3555.53i) q^{33} +(199180. - 144713. i) q^{34} +(-2821.44 + 322412. i) q^{35} +(-122283. - 88843.9i) q^{36} +(391685. - 284576. i) q^{37} +(-186617. + 135585. i) q^{38} +(1968.76 + 1430.39i) q^{39} +(-397365. - 132967. i) q^{40} +(419919. - 305089. i) q^{41} +(23223.4 - 71474.3i) q^{42} +146858. q^{43} +(9533.80 - 29342.0i) q^{44} +(-342754. - 480548. i) q^{45} +(10306.1 + 31718.9i) q^{46} +(-361137. - 1.11147e6i) q^{47} +(14731.1 + 10702.8i) q^{48} +507109. q^{49} +(-468661. - 353197. i) q^{50} +284267. q^{51} +(-16247.2 - 11804.3i) q^{52} +(276465. + 850871. i) q^{53} +(86544.3 + 266356. i) q^{54} +(71667.1 - 96847.6i) q^{55} +(-534388. + 1.64468e6i) q^{56} -266337. q^{57} +(-258179. + 794593. i) q^{58} +(2.09776e6 - 1.52412e6i) q^{59} +(-100756. - 141262. i) q^{60} +(2.34954e6 + 1.70704e6i) q^{61} +(-881302. + 640303. i) q^{62} +(-1.97078e6 + 1.43185e6i) q^{63} +(-1.28770e6 - 935565. i) q^{64} +(-45540.1 - 63848.2i) q^{65} +(-22719.1 + 16506.4i) q^{66} +(195149. - 600608. i) q^{67} -2.34592e6 q^{68} +(-11899.6 + 36623.3i) q^{69} +(-1.44067e6 + 1.94686e6i) q^{70} +(1.22575e6 + 3.77247e6i) q^{71} +(-978301. - 3.01090e6i) q^{72} +(-130322. - 94684.3i) q^{73} +3.63676e6 q^{74} +(-198076. - 647990. i) q^{75} +2.19795e6 q^{76} +(-402265. - 292263. i) q^{77} +(5648.77 + 17385.1i) q^{78} +(-1.13946e6 - 3.50690e6i) q^{79} +(-340751. - 477740. i) q^{80} +(1.32726e6 - 4.08487e6i) q^{81} +3.89892e6 q^{82} +(-985421. + 3.03281e6i) q^{83} +(-579330. + 420908. i) q^{84} +(-8.68760e6 - 2.90706e6i) q^{85} +(892465. + 648414. i) q^{86} +(-780432. + 567017. i) q^{87} +(522784. - 379825. i) q^{88} +(5.36779e6 + 3.89993e6i) q^{89} +(38799.2 - 4.43366e6i) q^{90} +(-261848. + 190244. i) q^{91} +(98201.7 - 302234. i) q^{92} -1.25778e6 q^{93} +(2.71274e6 - 8.34895e6i) q^{94} +(8.13963e6 + 2.72370e6i) q^{95} +(-472025. - 1.45274e6i) q^{96} +(-2.38159e6 - 7.32979e6i) q^{97} +(3.08173e6 + 2.23901e6i) q^{98} +910271. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16}+ \cdots + 71266232 q^{99}+O(q^{100}) $ 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	6.07706	+	4.41524i	0.537142	+	0.390256i	0.823022	−	0.568009i	$-0.192286\pi$
$2$	6.07706	+	4.41524i	0.537142	+	0.390256i	−0.285881	+	0.958265i	$0.592286\pi$
$3$	2.68014	+	8.24862i	0.0573104	+	0.176383i	0.975614	−	0.219494i	$-0.0704406\pi$
$3$	2.68014	+	8.24862i	0.0573104	+	0.176383i	−0.918303	+	0.395877i	$0.870441\pi$
$4$	−22.1179	−	68.0718i	−0.172796	−	0.531811i
$5$	2.44590	−	279.498i	0.00875071	−	0.999962i
$5$	2.44590	−	279.498i	0.00875071	−	0.999962i
$6$	−20.1323	+	61.9609i	−0.0380508	+	0.117108i
$7$	−1153.54			−1.27113			−0.635564	−	0.772048i	$-0.719232\pi$
$7$	−1153.54			−1.27113			−0.635564	+	0.772048i	$0.719232\pi$
$8$	463.260	−	1425.77i	0.319896	−	0.984540i
$9$	1708.46	−	1241.27i	0.781190	−	0.567568i
$10$	1248.91	−	1687.73i	0.394942	−	0.533706i
$11$	348.723	+	253.362i	0.0789962	+	0.0573941i	0.626582	−	0.779355i	$-0.284453\pi$
$11$	348.723	+	253.362i	0.0789962	+	0.0573941i	−0.547586	+	0.836749i	$0.684453\pi$
$12$	502.220	−	364.884i	0.0838995	−	0.0609566i
$13$	226.996	−	164.922i	0.0286560	−	0.0208198i	−0.573365	−	0.819300i	$-0.694362\pi$
$13$	226.996	−	164.922i	0.0286560	−	0.0208198i	0.602021	+	0.798480i	$0.294362\pi$
$14$	−7010.13	−	5093.16i	−0.682775	−	0.496065i
$15$	2312.03	−	728.918i	0.176878	−	0.0557647i
$16$	1698.48	−	1234.02i	0.103667	−	0.0753186i
$17$	10128.2	−	31171.5i	0.499992	−	1.53882i	−0.309038	−	0.951050i	$-0.600007\pi$
$17$	10128.2	−	31171.5i	0.499992	−	1.53882i	0.809030	−	0.587767i	$-0.199993\pi$
$18$	15863.0			0.641107
$19$	−9489.41	+	29205.4i	−0.317396	+	0.976845i	0.657361	+	0.753576i	$0.271673\pi$
$19$	−9489.41	+	29205.4i	−0.317396	+	0.976845i	−0.974757	+	0.223269i	$0.928327\pi$
$20$	−19080.0	+	6015.40i	−0.533303	+	0.168136i
$21$	−3091.65	−	9515.11i	−0.0728488	−	0.224205i
$22$	1000.56	+	3079.39i	0.0200337	+	0.0616575i
$23$	3591.97	+	2609.72i	0.0615582	+	0.0447246i	0.618139	−	0.786069i	$-0.287887\pi$
$23$	3591.97	+	2609.72i	0.0615582	+	0.0447246i	−0.556581	+	0.830794i	$0.687887\pi$
$24$	13002.2			0.191990
$25$	−78113.0	−	1367.25i	−0.999847	−	0.0175008i
$26$	2107.64			0.0235174
$27$	30163.2	+	21914.9i	0.294920	+	0.214272i
$28$	25513.8	+	78523.5i	0.219646	+	0.675999i
$29$	34370.4	+	105781.i	0.261693	+	0.805407i	0.992437	+	0.122756i	$0.0391732\pi$
$29$	34370.4	+	105781.i	0.261693	+	0.805407i	−0.730744	+	0.682651i	$0.760827\pi$
$30$	17268.7	+	5778.49i	0.116771	+	0.0390742i
$31$	−44813.9	+	137923.i	−0.270176	+	0.831517i	0.720279	+	0.693684i	$0.244014\pi$
$31$	−44813.9	+	137923.i	−0.270176	+	0.831517i	−0.990456	+	0.137833i	$0.955986\pi$
$32$	−176120.			−0.950129
$33$	−1155.26	+	3555.53i	−0.00559605	+	0.0172229i
$34$	199180.	−	144713.i	0.869099	−	0.631437i
$35$	−2821.44	+	322412.i	−0.0111233	+	1.27108i
$36$	−122283.	−	88843.9i	−0.436825	−	0.317372i
$37$	391685.	−	284576.i	1.27125	−	0.923617i	0.271998	−	0.962298i	$-0.412316\pi$
$37$	391685.	−	284576.i	1.27125	−	0.923617i	0.999252	+	0.0386812i	$0.0123157\pi$
$38$	−186617.	+	135585.i	−0.551706	+	0.400838i
$39$	1968.76	+	1430.39i	0.00531455	+	0.00386125i
$40$	−397365.	−	132967.i	−0.981703	−	0.328500i
$41$	419919.	−	305089.i	0.951529	−	0.691326i	0.000360909	−	1.00000i	$-0.499885\pi$
$41$	419919.	−	305089.i	0.951529	−	0.691326i	0.951168	+	0.308674i	$0.0998851\pi$
$42$	23223.4	−	71474.3i	0.0483675	−	0.148860i
$43$	146858.			0.281681			0.140841	−	0.990032i	$-0.455020\pi$
$43$	146858.			0.281681			0.140841	+	0.990032i	$0.455020\pi$
$44$	9533.80	−	29342.0i	0.0168726	−	0.0519285i
$45$	−342754.	−	480548.i	−0.560710	−	0.786127i
$46$	10306.1	+	31718.9i	0.0156114	+	0.0480469i
$47$	−361137.	−	1.11147e6i	−0.507376	−	1.56154i	−0.796740	−	0.604322i	$-0.793444\pi$
$47$	−361137.	−	1.11147e6i	−0.507376	−	1.56154i	0.289364	−	0.957219i	$-0.406556\pi$
$48$	14731.1	+	10702.8i	0.0192261	+	0.0139686i
$49$	507109.			0.615765
$50$	−468661.	−	353197.i	−0.530229	−	0.399597i
$51$	284267.			0.300076
$52$	−16247.2	−	11804.3i	−0.0160238	−	0.0116420i
$53$	276465.	+	850871.i	0.255079	+	0.785052i	0.993814	+	0.111056i	$0.0354234\pi$
$53$	276465.	+	850871.i	0.255079	+	0.785052i	−0.738735	+	0.673996i	$0.764577\pi$
$54$	86544.3	+	266356.i	0.0747929	+	0.230189i
$55$	71667.1	−	96847.6i	0.0580831	−	0.0784909i
$56$	−534388.	+	1.64468e6i	−0.406629	+	1.25148i
$57$	−266337.			−0.190489
$58$	−258179.	+	794593.i	−0.173749	+	0.534745i
$59$	2.09776e6	−	1.52412e6i	1.32976	−	0.966130i	0.330010	−	0.943978i	$-0.392948\pi$
$59$	2.09776e6	−	1.52412e6i	1.32976	−	0.966130i	0.999755	−	0.0221528i	$-0.00705203\pi$
$60$	−100756.	−	141262.i	−0.0602200	−	0.0844297i
$61$	2.34954e6	+	1.70704e6i	1.32534	+	0.962919i	0.999849	+	0.0173751i	$0.00553095\pi$
$61$	2.34954e6	+	1.70704e6i	1.32534	+	0.962919i	0.325495	+	0.945544i	$0.394469\pi$
$62$	−881302.	+	640303.i	−0.469628	+	0.341204i
$63$	−1.97078e6	+	1.43185e6i	−0.992993	+	0.721451i
$64$	−1.28770e6	−	935565.i	−0.614021	−	0.446112i
$65$	−45540.1	−	63848.2i	−0.0205683	−	0.0288371i
$66$	−22719.1	+	16506.4i	−0.00972720	+	0.00706723i
$67$	195149.	−	600608.i	0.0792693	−	0.243966i	−0.903567	−	0.428448i	$-0.859061\pi$
$67$	195149.	−	600608.i	0.0792693	−	0.243966i	0.982836	+	0.184482i	$0.0590607\pi$
$68$	−2.34592e6			−0.904756
$69$	−11899.6	+	36623.3i	−0.00436075	+	0.0134210i
$70$	−1.44067e6	+	1.94686e6i	−0.502021	+	0.678408i
$71$	1.22575e6	+	3.77247e6i	0.406441	+	1.25090i	0.919686	+	0.392655i	$0.128443\pi$
$71$	1.22575e6	+	3.77247e6i	0.406441	+	1.25090i	−0.513245	+	0.858242i	$0.671557\pi$
$72$	−978301.	−	3.01090e6i	−0.308893	−	0.950676i
$73$	−130322.	−	94684.3i	−0.0392091	−	0.0284871i	0.568008	−	0.823023i	$-0.307714\pi$
$73$	−130322.	−	94684.3i	−0.0392091	−	0.0284871i	−0.607217	+	0.794536i	$0.707714\pi$
$74$	3.63676e6			1.04329
$75$	−198076.	−	647990.i	−0.0542148	−	0.177359i
$76$	2.19795e6			0.574341
$77$	−402265.	−	292263.i	−0.100414	−	0.0729552i
$78$	5648.77	+	17385.1i	0.00134779	+	0.00414807i
$79$	−1.13946e6	−	3.50690e6i	−0.260019	−	0.800256i	−0.992799	−	0.119790i	$-0.961778\pi$
$79$	−1.13946e6	−	3.50690e6i	−0.260019	−	0.800256i	0.732780	−	0.680465i	$-0.238222\pi$
$80$	−340751.	−	477740.i	−0.0744085	−	0.104322i
$81$	1.32726e6	−	4.08487e6i	0.277496	−	0.854045i
$82$	3.89892e6			0.780900
$83$	−985421.	+	3.03281e6i	−0.189168	+	0.582200i	−0.999995	−	0.00308584i	$-0.999018\pi$
$83$	−985421.	+	3.03281e6i	−0.189168	+	0.582200i	0.810827	+	0.585286i	$0.199018\pi$
$84$	−579330.	+	420908.i	−0.106647	+	0.0774835i
$85$	−8.68760e6	−	2.90706e6i	−1.53438	−	0.513438i
$86$	892465.	+	648414.i	0.151303	+	0.109928i
$87$	−780432.	+	567017.i	−0.127063	+	0.0923164i
$88$	522784.	−	379825.i	0.0817774	−	0.0594147i
$89$	5.36779e6	+	3.89993e6i	0.807106	+	0.586397i	0.912990	−	0.407981i	$-0.133767\pi$
$89$	5.36779e6	+	3.89993e6i	0.807106	+	0.586397i	−0.105884	+	0.994378i	$0.533767\pi$
$90$	38799.2	−	4.43366e6i	0.00561014	−	0.641082i
$91$	−261848.	+	190244.i	−0.0364254	+	0.0264646i
$92$	98201.7	−	302234.i	0.0131481	−	0.0404655i
$93$	−1.25778e6			−0.162150
$94$	2.71274e6	−	8.34895e6i	0.336869	−	1.03678i
$95$	8.13963e6	+	2.72370e6i	0.974030	+	0.325932i
$96$	−472025.	−	1.45274e6i	−0.0544523	−	0.167587i
$97$	−2.38159e6	−	7.32979e6i	−0.264952	−	0.815437i	−0.991705	−	0.128538i	$-0.958971\pi$
$97$	−2.38159e6	−	7.32979e6i	−0.264952	−	0.815437i	0.726753	−	0.686899i	$-0.241029\pi$
$98$	3.08173e6	+	2.23901e6i	0.330753	+	0.240306i
$99$	910271.			0.0942861
$100$	1.63462e6	+	5.34754e6i	0.163462	+	0.534754i
$101$	−8.72630e6			−0.842762			−0.421381	−	0.906884i	$-0.638455\pi$
$101$	−8.72630e6			−0.842762			−0.421381	+	0.906884i	$0.638455\pi$
$102$	1.72751e6	+	1.25511e6i	0.161183	+	0.117107i
$103$	−1.14557e6	−	3.52569e6i	−0.103298	−	0.317917i	0.886030	−	0.463629i	$-0.153453\pi$
$103$	−1.14557e6	−	3.52569e6i	−0.103298	−	0.317917i	−0.989327	+	0.145712i	$0.953453\pi$
$104$	−129982.	−	400044.i	−0.0113310	−	0.0348732i
$105$	−2.66701e6	+	840835.i	−0.224834	+	0.0708840i
$106$	−2.07671e6	+	6.39146e6i	−0.169358	+	0.521230i
$107$	−3.47058e6			−0.273879			−0.136940	−	0.990579i	$-0.543727\pi$
$107$	−3.47058e6			−0.273879			−0.136940	+	0.990579i	$0.543727\pi$
$108$	824638.	−	2.53798e6i	0.0629913	−	0.193867i
$109$	−1.52440e7	+	1.10754e7i	−1.12747	+	0.819158i	−0.985325	−	0.170687i	$-0.945401\pi$
$109$	−1.52440e7	+	1.10754e7i	−1.12747	+	0.819158i	−0.142149	+	0.989845i	$0.545401\pi$
$110$	863131.	−	272121.i	0.0618304	−	0.0194934i
$111$	3.39713e6	+	2.46816e6i	0.235766	+	0.171294i
$112$	−1.95926e6	+	1.42349e6i	−0.131774	+	0.0957395i
$113$	1.05729e6	−	768163.i	0.0689315	−	0.0500817i	−0.552786	−	0.833323i	$-0.686435\pi$
$113$	1.05729e6	−	768163.i	0.0689315	−	0.0500817i	0.621717	+	0.783242i	$0.286435\pi$
$114$	−1.61855e6	−	1.17594e6i	−0.102320	−	0.0743395i
$115$	738197.	−	997566.i	0.0452616	−	0.0611645i
$116$	6.44052e6	−	4.67931e6i	0.383105	−	0.278342i
$117$	183101.	−	563526.i	0.0105691	−	0.0325285i
$118$	1.94776e7			1.09131
$119$	−1.16833e7	+	3.59576e7i	−0.635553	+	1.95603i
$120$	31802.1	−	3.63409e6i	0.00168005	−	0.191982i
$121$	−5.96445e6	−	1.83567e7i	−0.306071	−	0.941989i
$122$	6.74130e6	+	2.07476e7i	0.336112	+	1.03445i
$123$	3.64201e6	+	2.64607e6i	0.176471	+	0.128214i
$124$	1.03799e7			0.488895
$125$	−573199.	+	2.18291e7i	−0.0262495	+	0.999655i
$126$	−1.82985e7			−0.814928
$127$	6.04010e6	+	4.38839e6i	0.261656	+	0.190104i	0.710877	−	0.703316i	$-0.248298\pi$
$127$	6.04010e6	+	4.38839e6i	0.261656	+	0.190104i	−0.449221	+	0.893421i	$0.648298\pi$
$128$	3.27161e6	+	1.00690e7i	0.137888	+	0.424376i
$129$	393600.	+	1.21138e6i	0.0161432	+	0.0496838i
$130$	5155.07	−	589080.i	0.000205794	−	0.0235165i
$131$	1.07990e6	−	3.32359e6i	0.0419695	−	0.129169i	−0.927876	−	0.372888i	$-0.878368\pi$
$131$	1.07990e6	−	3.32359e6i	0.0419695	−	0.129169i	0.969846	+	0.243719i	$0.0783675\pi$
$132$	267583.			0.0101263
$133$	1.09464e7	−	3.36896e7i	0.403451	−	1.24169i
$134$	3.83776e6	−	2.78830e6i	0.137788	−	0.100109i
$135$	6.19893e6	−	8.37695e6i	0.216845	−	0.293034i
$136$	−3.97513e7	−	2.88810e7i	−1.35508	−	0.984524i
$137$	1.28545e7	−	9.33937e6i	0.427105	−	0.310310i	−0.353385	−	0.935478i	$-0.614970\pi$
$137$	1.28545e7	−	9.33937e6i	0.427105	−	0.310310i	0.780490	+	0.625168i	$0.214970\pi$
$138$	−234015.	+	170022.i	−0.00757997	+	0.00550717i
$139$	−4.76527e7	−	3.46217e7i	−1.50500	−	1.09345i	−0.968337	−	0.249648i	$-0.919685\pi$
$139$	−4.76527e7	−	3.46217e7i	−1.50500	−	1.09345i	−0.536662	−	0.843797i	$-0.680315\pi$
$140$	2.20095e7	−	6.93900e6i	0.677896	−	0.213722i
$141$	8.20016e6	−	5.95777e6i	0.246352	−	0.178985i
$142$	−9.20742e6	+	2.83375e7i	−0.269854	+	0.830525i
$143$	120944.			0.00345865
$144$	1.37004e6	−	4.21655e6i	0.0382353	−	0.117676i
$145$	2.96497e7	−	9.34772e6i	0.807666	−	0.254635i
$146$	−373919.	−	1.15081e6i	−0.00994358	−	0.0306032i
$147$	1.35912e6	+	4.18295e6i	0.0352897	+	0.108611i
$148$	−2.80348e7	−	2.03685e7i	−0.710856	−	0.516467i
$149$	1.42458e7			0.352804			0.176402	−	0.984318i	$-0.443554\pi$
$149$	1.42458e7			0.352804			0.176402	+	0.984318i	$0.443554\pi$
$150$	1.65731e6	−	4.81243e6i	0.0400945	−	0.116425i
$151$	3.54311e7			0.837463			0.418731	−	0.908110i	$-0.362475\pi$
$151$	3.54311e7			0.837463			0.418731	+	0.908110i	$0.362475\pi$
$152$	3.72440e7	+	2.70594e7i	0.860209	+	0.624978i
$153$	−2.13886e7	−	6.58273e7i	−0.482794	−	1.48589i
$154$	−1.15418e6	−	3.55220e6i	−0.0254654	−	0.0783745i
$155$	3.84396e7	+	1.28627e7i	0.829121	+	0.277442i
$156$	53824.3	−	165654.i	0.00113512	−	0.00349354i
$157$	−6.89639e7			−1.42224			−0.711120	−	0.703071i	$-0.751812\pi$
$157$	−6.89639e7			−1.42224			−0.711120	+	0.703071i	$0.751812\pi$
$158$	8.55925e6	−	2.63427e7i	0.172638	−	0.531324i
$159$	−6.27755e6	+	4.56091e6i	−0.123851	+	0.0899832i
$160$	−430771.	+	4.92250e7i	−0.00831431	+	0.950093i
$161$	−4.14348e6	−	3.01042e6i	−0.0782483	−	0.0568507i
$162$	2.61015e7	−	1.89639e7i	0.482351	−	0.350449i
$163$	−1.54094e7	+	1.11956e7i	−0.278694	+	0.202483i	−0.718348	−	0.695684i	$-0.755101\pi$
$163$	−1.54094e7	+	1.11956e7i	−0.278694	+	0.202483i	0.439653	+	0.898168i	$0.355101\pi$
$164$	−3.00557e7	−	2.18367e7i	−0.532075	−	0.386575i
$165$	990937.	+	331590.i	0.0171732	+	0.00574655i
$166$	−1.93791e7	+	1.40797e7i	−0.328817	+	0.238900i
$167$	−2.59574e7	+	7.98888e7i	−0.431275	+	1.32733i	0.465581	+	0.885005i	$0.345845\pi$
$167$	−2.59574e7	+	7.98888e7i	−0.431275	+	1.32733i	−0.896856	+	0.442322i	$0.854155\pi$
$168$	−1.49986e7			−0.244043
$169$	−1.93660e7	+	5.96025e7i	−0.308629	+	0.949863i
$170$	−3.99597e7	−	5.60243e7i	−0.623808	−	0.874591i
$171$	2.00395e7	+	6.16753e7i	0.306479	+	0.943245i
$172$	−3.24818e6	−	9.99688e6i	−0.0486733	−	0.149801i
$173$	8.59231e7	+	6.24268e7i	1.26168	+	0.916663i	0.998839	−	0.0481767i	$-0.0153411\pi$
$173$	8.59231e7	+	6.24268e7i	1.26168	+	0.916663i	0.262839	+	0.964840i	$0.415341\pi$
$174$	−7.24625e6			−0.104278
$175$	9.01064e7	+	1.57717e6i	1.27093	+	0.0222457i
$176$	904953.			0.0125121
$177$	1.81942e7	+	1.32188e7i	0.246618	+	0.179179i
$178$	1.54013e7	+	4.74002e7i	0.204685	+	0.629956i
$179$	8.15099e6	+	2.50862e7i	0.106224	+	0.326925i	0.990016	−	0.140956i	$-0.0450175\pi$
$179$	8.15099e6	+	2.50862e7i	0.106224	+	0.326925i	−0.883791	+	0.467881i	$0.845018\pi$
$180$	−2.51308e7	+	3.39606e7i	−0.321183	+	0.434031i
$181$	1.18993e7	−	3.66221e7i	0.149157	−	0.459059i	−0.848365	−	0.529412i	$-0.822413\pi$
$181$	1.18993e7	−	3.66221e7i	0.149157	−	0.459059i	0.997522	+	0.0703530i	$0.0224126\pi$
$182$	−2.43124e6			−0.0298936
$183$	−7.78364e6	+	2.39556e7i	−0.0938867	+	0.288954i
$184$	5.38487e6	−	3.91234e6i	0.0637254	−	0.0462992i
$185$	−7.85803e7	−	1.10171e8i	−0.912457	−	1.27928i
$186$	−7.64363e6	−	5.55342e6i	−0.0870972	−	0.0632799i
$187$	1.14296e7	−	8.30411e6i	0.127816	−	0.0928640i
$188$	−6.76719e7	+	4.91665e7i	−0.742772	+	0.539656i
$189$	−3.47944e7	−	2.52796e7i	−0.374881	−	0.272367i
$190$	3.74392e7	+	5.24906e7i	0.395995	+	0.555193i
$191$	−5.89855e7	+	4.28555e7i	−0.612531	+	0.445030i	−0.850305	−	0.526290i	$-0.823582\pi$
$191$	−5.89855e7	+	4.28555e7i	−0.612531	+	0.445030i	0.237773	+	0.971321i	$0.423582\pi$
$192$	4.26592e6	−	1.31292e7i	0.0434969	−	0.133870i
$193$	2.71019e7			0.271362			0.135681	−	0.990753i	$-0.456678\pi$
$193$	2.71019e7			0.271362			0.135681	+	0.990753i	$0.456678\pi$
$194$	1.78897e7	−	5.50589e7i	0.175913	−	0.541404i
$195$	404606.	−	546765.i	0.00390761	−	0.00528056i
$196$	−1.12162e7	−	3.45198e7i	−0.106402	−	0.327470i
$197$	−3.40314e7	−	1.04738e8i	−0.317138	−	0.976051i	−0.974865	−	0.222795i	$-0.928482\pi$
$197$	−3.40314e7	−	1.04738e8i	−0.317138	−	0.976051i	0.657727	−	0.753256i	$-0.271518\pi$
$198$	5.53177e6	+	4.01907e6i	0.0506450	+	0.0367957i
$199$	1.86918e8			1.68138			0.840689	−	0.541518i	$-0.182150\pi$
$199$	1.86918e8			1.68138			0.840689	+	0.541518i	$0.182150\pi$
$200$	−3.81360e7	+	1.10738e8i	−0.337078	+	0.978791i
$201$	5.47721e6			0.0475744
$202$	−5.30302e7	−	3.85287e7i	−0.452683	−	0.328893i
$203$	−3.96476e7	−	1.22023e8i	−0.332645	−	1.02378i
$204$	−6.28739e6	−	1.93506e7i	−0.0518519	−	0.159584i
$205$	−8.42446e7	−	1.18113e8i	−0.682973	−	0.957542i
$206$	8.60511e6	−	2.64838e7i	0.0685837	−	0.211079i
$207$	9.37613e6			0.0734729
$208$	182031.	−	560234.i	0.00140257	−	0.00431666i
$209$	−1.07087e7	+	7.78033e6i	−0.0811382	+	0.0589503i
$210$	−1.99201e7	−	6.66571e6i	−0.148431	−	0.0496682i
$211$	1.99531e8	+	1.44968e8i	1.46225	+	1.06239i	0.982770	+	0.184832i	$0.0591742\pi$
$211$	1.99531e8	+	1.44968e8i	1.46225	+	1.06239i	0.479479	+	0.877554i	$0.340826\pi$
$212$	5.18055e7	−	3.76389e7i	0.373423	−	0.271307i
$213$	−2.78325e7	+	2.02215e7i	−0.197344	+	0.143379i
$214$	−2.10909e7	−	1.53235e7i	−0.147112	−	0.106883i
$215$	359200.	−	4.10465e7i	0.00246491	−	0.281670i
$216$	4.52189e7	−	3.28534e7i	0.305303	−	0.221816i
$217$	5.16946e7	−	1.59100e8i	0.343428	−	1.05696i
$218$	−1.41540e8			−0.925295
$219$	431735.	−	1.32874e6i	0.00277755	−	0.00854843i
$220$	−8.17771e6	−	2.73644e6i	−0.0517788	−	0.0173264i
$221$	−2.84180e6	−	8.74617e6i	−0.0177101	−	0.0545061i
$222$	9.74704e6	+	2.99983e7i	0.0597912	+	0.184018i
$223$	1.96479e8	+	1.42750e8i	1.18645	+	0.862005i	0.992884	−	0.119083i	$-0.0379954\pi$
$223$	1.96479e8	+	1.42750e8i	1.18645	+	0.862005i	0.193564	+	0.981088i	$0.437995\pi$
$224$	2.03161e8			1.20774
$225$	−1.35150e8	+	9.46236e7i	−0.791004	+	0.553810i
$226$	9.81682e6			0.0565706
$227$	−1.49494e8	−	1.08614e8i	−0.848269	−	0.616304i	0.0763991	−	0.997077i	$-0.475658\pi$
$227$	−1.49494e8	−	1.08614e8i	−0.848269	−	0.616304i	−0.924668	+	0.380774i	$0.875658\pi$
$228$	5.89081e6	+	1.81301e7i	0.0329157	+	0.101304i
$229$	5.15559e6	+	1.58673e7i	0.0283697	+	0.0873129i	0.964239	−	0.265035i	$-0.0853835\pi$
$229$	5.15559e6	+	1.58673e7i	0.0283697	+	0.0873129i	−0.935869	+	0.352348i	$0.885383\pi$
$230$	8.89057e6	−	2.80295e6i	0.0481817	−	0.0151903i
$231$	1.33264e6	−	4.10144e6i	0.00711329	−	0.0218925i
$232$	1.66742e8			0.876670
$233$	−8.21515e6	+	2.52836e7i	−0.0425471	+	0.130946i	−0.970074	−	0.242811i	$-0.921931\pi$
$233$	−8.21515e6	+	2.52836e7i	−0.0425471	+	0.130946i	0.927527	+	0.373757i	$0.121931\pi$
$234$	3.60082e6	−	2.61615e6i	0.0183716	−	0.0133477i
$235$	−3.11535e8	+	9.82185e7i	−1.56592	+	0.493692i
$236$	−1.50147e8	−	1.09088e8i	−0.743576	−	0.540240i
$237$	2.58732e7	−	1.87980e7i	0.126250	−	0.0917259i
$238$	−2.29762e8	+	1.66932e8i	−1.10474	+	0.802637i
$239$	1.20055e8	+	8.72248e7i	0.568835	+	0.413283i	0.834682	−	0.550732i	$-0.185652\pi$
$239$	1.20055e8	+	8.72248e7i	0.568835	+	0.413283i	−0.265847	+	0.964015i	$0.585652\pi$
$240$	3.02744e6	−	4.09114e6i	0.0141363	−	0.0191032i
$241$	−6.23207e7	+	4.52786e7i	−0.286796	+	0.208369i	−0.721876	−	0.692022i	$-0.756720\pi$
$241$	−6.23207e7	+	4.52786e7i	−0.286796	+	0.208369i	0.435080	+	0.900392i	$0.356720\pi$
$242$	4.48029e7	−	1.37889e8i	0.203214	−	0.625427i
$243$	1.18791e8			0.531084
$244$	6.42346e7	−	1.97694e8i	0.283077	−	0.871221i
$245$	1.24034e6	−	1.41736e8i	0.00538838	−	0.615741i
$246$	1.04496e7	+	3.21607e7i	0.0447537	+	0.137738i
$247$	2.66256e6	+	8.19451e6i	0.0112424	+	0.0346006i
$248$	1.75886e8	+	1.27788e8i	0.732234	+	0.531999i
$249$	−2.76576e7			−0.113532
$250$	−9.98641e7	+	1.30126e8i	−0.404221	+	0.526712i
$251$	9.68092e7			0.386419			0.193210	−	0.981157i	$-0.438110\pi$
$251$	9.68092e7			0.386419			0.193210	+	0.981157i	$0.438110\pi$
$252$	1.41058e8	+	1.02485e8i	0.555261	+	0.403420i
$253$	591399.	+	1.82014e6i	0.00229593	+	0.00706615i
$254$	1.73302e7	+	5.33370e7i	0.0663570	+	0.204226i
$255$	695289.	−	7.94521e7i	0.00262588	−	0.300065i
$256$	−8.75328e7	+	2.69398e8i	−0.326085	+	1.00359i
$257$	−3.81802e8			−1.40305			−0.701524	−	0.712646i	$-0.747497\pi$
$257$	−3.81802e8			−1.40305			−0.701524	+	0.712646i	$0.747497\pi$
$258$	−2.95659e6	+	9.09945e6i	−0.0107182	+	0.0329872i
$259$	−4.51824e8	+	3.28269e8i	−1.61592	+	1.17403i
$260$	−3.33901e6	+	4.51218e6i	−0.0117818	+	0.0159214i
$261$	1.90024e8	+	1.38060e8i	0.661555	+	0.480648i
$262$	2.12371e7	−	1.54296e7i	0.0729525	−	0.0530031i
$263$	−2.12641e8	+	1.54493e8i	−0.720780	+	0.523677i	−0.886633	−	0.462473i	$-0.846962\pi$
$263$	−2.12641e8	+	1.54493e8i	−0.720780	+	0.523677i	0.165853	+	0.986150i	$0.446962\pi$
$264$	4.53417e6	+	3.29427e6i	0.0151664	+	0.0110191i
$265$	2.38493e8	−	7.51902e7i	0.787254	−	0.248199i
$266$	2.15270e8	−	1.56402e8i	0.701289	−	0.509516i
$267$	−1.77826e7	+	5.47293e7i	−0.0571750	+	0.175967i
$268$	−4.52007e7			−0.143441
$269$	1.40223e8	−	4.31562e8i	0.439224	−	1.35179i	−0.449472	−	0.893295i	$-0.648388\pi$
$269$	1.40223e8	−	4.31562e8i	0.439224	−	1.35179i	0.888696	−	0.458498i	$-0.151612\pi$
$270$	7.46576e7	−	2.35375e7i	0.230835	−	0.0727757i
$271$	7.32939e7	+	2.25575e8i	0.223705	+	0.688492i	0.998421	+	0.0561826i	$0.0178929\pi$
$271$	7.32939e7	+	2.25575e8i	0.223705	+	0.688492i	−0.774716	+	0.632310i	$0.782107\pi$
$272$	−2.12636e7	−	6.54427e7i	−0.0640688	−	0.197183i
$273$	−2.27104e6	−	1.65001e6i	−0.00675547	−	0.00490814i
$274$	1.19353e8			0.350516
$275$	−2.68934e7	−	2.02677e7i	−0.0779796	−	0.0587678i
$276$	2.75621e6			0.00789096
$277$	1.92203e7	+	1.39644e7i	0.0543353	+	0.0394769i	0.614621	−	0.788822i	$-0.289309\pi$
$277$	1.92203e7	+	1.39644e7i	0.0543353	+	0.0394769i	−0.560286	+	0.828299i	$0.689309\pi$
$278$	−1.36725e8	−	4.20797e8i	−0.381673	−	1.17467i
$279$	9.46371e7	+	2.91263e8i	0.260883	+	0.802917i
$280$	4.58376e8	+	1.53383e8i	1.24787	+	0.417565i
$281$	−8.00123e7	+	2.46253e8i	−0.215122	+	0.662077i	0.784023	+	0.620732i	$0.213164\pi$
$281$	−8.00123e7	+	2.46253e8i	−0.215122	+	0.662077i	−0.999145	+	0.0413456i	$0.986836\pi$
$282$	7.61379e7			0.202176
$283$	2.03594e8	−	6.26599e8i	0.533966	−	1.64338i	−0.211908	−	0.977290i	$-0.567968\pi$
$283$	2.03594e8	−	6.26599e8i	0.533966	−	1.64338i	0.745873	−	0.666088i	$-0.232032\pi$
$284$	2.29688e8	−	1.66878e8i	0.595009	−	0.432300i
$285$	−651434.	+	7.44407e7i	−0.00166691	+	0.190482i
$286$	734981.	+	533995.i	0.00185778	+	0.00134976i
$287$	−4.84393e8	+	3.51932e8i	−1.20951	+	0.878764i
$288$	−3.00894e8	+	2.18612e8i	−0.742232	+	0.539263i
$289$	−5.37112e8	−	3.90235e8i	−1.30895	−	0.951006i
$290$	2.21455e8	+	7.41039e7i	0.533204	+	0.178422i
$291$	5.40777e7	−	3.92897e7i	0.128645	−	0.0934660i
$292$	−3.56289e6	+	1.09655e7i	−0.00837457	+	0.0257743i
$293$	1.72715e8			0.401138			0.200569	−	0.979680i	$-0.435721\pi$
$293$	1.72715e8			0.401138			0.200569	+	0.979680i	$0.435721\pi$
$294$	−1.02093e7	+	3.14209e7i	−0.0234304	+	0.0721112i
$295$	−4.20856e8	−	5.90048e8i	−0.954457	−	1.33817i
$296$	−2.24287e8	−	6.90284e8i	−0.502670	−	1.54706i
$297$	4.96621e6	+	1.52844e7i	0.0109996	+	0.0338533i
$298$	8.65725e7	+	6.28986e7i	0.189506	+	0.137684i
$299$	1.24576e6			0.00269517
$300$	−3.97288e7	+	2.78155e7i	−0.0849534	+	0.0594789i
$301$	−1.69406e8			−0.358053
$302$	2.15317e8	+	1.56437e8i	0.449836	+	0.326825i
$303$	−2.33877e7	−	7.19799e7i	−0.0482990	−	0.148649i
$304$	1.99224e7	+	6.13149e7i	0.0406710	+	0.125172i
$305$	4.82861e8	−	6.52516e8i	0.974480	−	1.31687i
$306$	1.60664e8	−	4.94473e8i	0.320548	−	0.986546i
$307$	7.32875e8			1.44559			0.722796	−	0.691062i	$-0.242857\pi$
$307$	7.32875e8			1.44559			0.722796	+	0.691062i	$0.242857\pi$
$308$	−1.09976e7	+	3.38472e7i	−0.0214472	+	0.0660077i
$309$	2.60118e7	−	1.88987e7i	0.0501552	−	0.0364399i
$310$	1.76808e8	+	2.47888e8i	0.337082	+	0.472595i
$311$	−4.98698e8	−	3.62325e8i	−0.940105	−	0.683026i	0.00834120	−	0.999965i	$-0.497345\pi$
$311$	−4.98698e8	−	3.62325e8i	−0.940105	−	0.683026i	−0.948446	+	0.316939i	$0.897345\pi$
$312$	2.95145e6	−	2.14435e6i	0.00550166	−	0.00399719i
$313$	−1.03028e8	+	7.48544e7i	−0.189911	+	0.137979i	−0.678678	−	0.734436i	$-0.737447\pi$
$313$	−1.03028e8	+	7.48544e7i	−0.189911	+	0.137979i	0.488767	+	0.872414i	$0.337447\pi$
$314$	−4.19098e8	−	3.04492e8i	−0.763944	−	0.555038i
$315$	3.95380e8	+	5.54331e8i	0.712734	+	0.999268i
$316$	−2.13519e8	+	1.55130e8i	−0.380655	+	0.276562i
$317$	−2.55733e8	+	7.87066e8i	−0.450899	+	1.38773i	0.424983	+	0.905201i	$0.360280\pi$
$317$	−2.55733e8	+	7.87066e8i	−0.450899	+	1.38773i	−0.875882	+	0.482525i	$0.839720\pi$
$318$	−5.82866e7			−0.101642
$319$	−1.48152e7	+	4.55965e7i	−0.0255529	+	0.0786437i
$320$	−2.64638e8	+	3.57620e8i	−0.451468	+	0.610094i
$321$	−9.30164e6	−	2.86275e7i	−0.0156961	−	0.0483077i
$322$	−1.18885e7	−	3.65890e7i	−0.0198441	−	0.0610738i
$323$	8.14266e8	+	5.91599e8i	1.34449	+	0.976829i
$324$	−3.07421e8			−0.502141
$325$	−1.79568e7	+	1.25722e7i	−0.0290160	+	0.0203151i
$326$	−1.43075e8			−0.228719
$327$	−1.32213e8	−	9.60585e7i	−0.209102	−	0.151921i
$328$	−2.40454e8	−	7.40042e8i	−0.376248	−	1.15797i
$329$	4.16586e8	+	1.28212e9i	0.644939	+	1.98492i
$330$	4.55794e6	+	6.39032e6i	0.00698183	+	0.00978867i
$331$	2.03249e7	−	6.25536e7i	0.0308056	−	0.0948100i	−0.934472	−	0.356038i	$-0.884127\pi$
$331$	2.03249e7	−	6.25536e7i	0.0308056	−	0.0948100i	0.965277	+	0.261228i	$0.0841274\pi$
$332$	2.28244e8			0.342308
$333$	3.15944e8	−	9.72374e8i	0.468872	−	1.44304i
$334$	−5.10473e8	+	3.70881e8i	−0.749653	+	0.544655i
$335$	−1.67391e8	−	5.60128e7i	−0.243263	−	0.0814011i
$336$	−1.69929e7	−	1.23461e7i	−0.0244389	−	0.0177559i
$337$	−1.69813e8	+	1.23376e8i	−0.241694	+	0.175601i	−0.702038	−	0.712140i	$-0.747726\pi$
$337$	−1.69813e8	+	1.23376e8i	−0.241694	+	0.175601i	0.460344	+	0.887741i	$0.347726\pi$
$338$	−3.80848e8	+	2.76702e8i	−0.536468	+	0.389767i
$339$	9.16996e6	+	6.66237e6i	0.0127841	+	0.00928816i
$340$	−5.73788e6	+	6.55679e8i	−0.00791726	+	0.904721i
$341$	−5.05721e7	+	3.67428e7i	−0.0690670	+	0.0501801i
$342$	−1.50530e8	+	4.63284e8i	−0.203485	+	0.626262i
$343$	3.65019e8			0.488412
$344$	6.80333e7	−	2.09385e8i	0.0901088	−	0.277326i
$345$	1.02070e7	+	3.41549e6i	0.0133823	+	0.00447803i
$346$	2.46531e8	+	7.58743e8i	0.319966	+	0.984755i
$347$	1.91725e8	+	5.90067e8i	0.246334	+	0.758138i	0.995414	+	0.0956590i	$0.0304958\pi$
$347$	1.91725e8	+	5.90067e8i	0.246334	+	0.758138i	−0.749080	+	0.662479i	$0.769504\pi$
$348$	5.58594e7	+	4.05842e7i	0.0710507	+	0.0516214i
$349$	−3.39227e8			−0.427171			−0.213585	−	0.976924i	$-0.568514\pi$
$349$	−3.39227e8			−0.427171			−0.213585	+	0.976924i	$0.568514\pi$
$350$	5.40619e8	+	4.07426e8i	0.673989	+	0.507938i
$351$	1.04612e7			0.0129123
$352$	−6.14169e7	−	4.46220e7i	−0.0750566	−	0.0545318i
$353$	−1.78751e8	−	5.50138e8i	−0.216290	−	0.665671i	−0.999060	−	0.0433599i	$-0.986194\pi$
$353$	−1.78751e8	−	5.50138e8i	−0.216290	−	0.665671i	0.782770	−	0.622311i	$-0.213806\pi$
$354$	5.22027e7	+	1.60663e8i	0.0625434	+	0.192489i
$355$	1.05739e9	−	3.33367e8i	1.25441	−	0.395479i
$356$	1.46751e8	−	4.51653e8i	0.172388	−	0.530555i
$357$	−3.27913e8			−0.381435
$358$	−6.12275e7	+	1.88439e8i	−0.0705270	+	0.217060i
$359$	−9.17705e8	+	6.66752e8i	−1.04682	+	0.760561i	−0.971606	−	0.236607i	$-0.923965\pi$
$359$	−9.17705e8	+	6.66752e8i	−1.04682	+	0.760561i	−0.0752162	+	0.997167i	$0.523965\pi$
$360$	−8.43933e8	+	2.66069e8i	−0.953343	+	0.300563i
$361$	−3.97487e7	−	2.88791e7i	−0.0444680	−	0.0323079i
$362$	2.34008e8	−	1.70017e8i	0.259269	−	0.188370i
$363$	1.35432e8	−	9.83970e7i	0.148610	−	0.107971i
$364$	1.87418e7	+	1.36167e7i	0.0203683	+	0.0147985i
$365$	−2.67828e7	+	3.61931e7i	−0.0288291	+	0.0389583i
$366$	−1.53072e8	+	1.11213e8i	−0.163196	+	0.118569i
$367$	5.50117e8	−	1.69309e9i	0.580930	−	1.78792i	−0.0341029	−	0.999418i	$-0.510857\pi$
$367$	5.50117e8	−	1.69309e9i	0.580930	−	1.78792i	0.615033	−	0.788501i	$-0.289143\pi$
$368$	9.32135e6			0.00975015
$369$	3.38718e8	−	1.04247e9i	0.350951	−	1.08011i
$370$	8.89516e6	−	1.01647e9i	0.00912951	−	1.04325i
$371$	−3.18913e8	−	9.81513e8i	−0.324238	−	0.997901i
$372$	2.78195e7	+	8.56196e7i	0.0280188	+	0.0862329i
$373$	1.15718e9	+	8.40738e8i	1.15457	+	0.838841i	0.989081	−	0.147371i	$-0.0470812\pi$
$373$	1.15718e9	+	8.40738e8i	1.15457	+	0.838841i	0.165484	+	0.986212i	$0.447081\pi$
$374$	1.06123e8			0.104896
$375$	−1.81596e8	+	5.37769e7i	−0.177827	+	0.0526607i
$376$	−1.75199e9			−1.69971
$377$	2.52476e7	+	1.83434e7i	0.0242675	+	0.0176314i
$378$	−9.98322e7	−	3.07252e8i	−0.0950713	−	0.292599i
$379$	−4.59287e7	−	1.41354e8i	−0.0433358	−	0.133374i	0.927048	−	0.374943i	$-0.122338\pi$
$379$	−4.59287e7	−	1.41354e8i	−0.0433358	−	0.133374i	−0.970384	+	0.241570i	$0.922338\pi$
$380$	5.37596e6	−	6.14322e8i	0.00502590	−	0.574319i
$381$	−2.00099e7	+	6.15840e7i	−0.0185356	+	0.0570467i
$382$	−5.47676e8			−0.502692
$383$	2.15896e8	−	6.64459e8i	0.196358	−	0.604328i	−0.803600	−	0.595170i	$-0.797085\pi$
$383$	2.15896e8	−	6.64459e8i	0.196358	−	0.604328i	0.999958	−	0.00915816i	$-0.00291517\pi$
$384$	−7.42869e7	+	5.39726e7i	−0.0669503	+	0.0486423i
$385$	−8.26707e7	+	1.11717e8i	−0.0738311	+	0.0997719i
$386$	1.64700e8	+	1.19661e8i	0.145760	+	0.105901i
$387$	2.50901e8	−	1.82291e8i	0.220047	−	0.159873i
$388$	−4.46276e8	+	3.24239e8i	−0.387876	+	0.281808i
$389$	8.07583e8	+	5.86744e8i	0.695607	+	0.505388i	0.878498	−	0.477745i	$-0.158546\pi$
$389$	8.07583e8	+	5.86744e8i	0.695607	+	0.505388i	−0.182892	+	0.983133i	$0.558546\pi$
$390$	4.87292e6	−	1.53630e6i	0.00415971	−	0.00131144i
$391$	1.17729e8	−	8.55354e7i	0.0996016	−	0.0723648i
$392$	2.34923e8	−	7.23018e8i	0.196981	−	0.606245i
$393$	3.03093e7			0.0251885
$394$	2.55633e8	−	7.86756e8i	0.210562	−	0.648043i
$395$	−9.82958e8	+	3.09899e8i	−0.802500	+	0.253006i
$396$	−2.01333e7	−	6.19638e7i	−0.0162922	−	0.0501424i
$397$	1.21921e8	+	3.75233e8i	0.0977936	+	0.300978i	0.987972	−	0.154635i	$-0.0494202\pi$
$397$	1.21921e8	+	3.75233e8i	0.0977936	+	0.300978i	−0.890178	+	0.455613i	$0.849420\pi$
$398$	1.13591e9	+	8.25289e8i	0.903138	+	0.656168i
$399$	3.07230e8			0.242136
$400$	−1.34361e8	+	9.40708e7i	−0.104969	+	0.0734928i
$401$	2.55787e9			1.98095			0.990475	−	0.137695i	$-0.0439694\pi$
$401$	2.55787e9			1.98095			0.990475	+	0.137695i	$0.0439694\pi$
$402$	3.32854e7	+	2.41832e7i	0.0255542	+	0.0185662i
$403$	1.25740e7	+	3.86988e7i	0.00956986	+	0.0294530i
$404$	1.93007e8	+	5.94015e8i	0.145626	+	0.448190i
$405$	−1.13847e9	−	3.80956e8i	−0.851584	−	0.284959i
$406$	2.97819e8	−	9.16593e8i	0.220857	−	0.679729i
$407$	2.08690e8			0.153434
$408$	1.31690e8	−	4.05299e8i	0.0959933	−	0.295437i
$409$	−7.49116e8	+	5.44264e8i	−0.541399	+	0.393349i	−0.824604	−	0.565710i	$-0.808602\pi$
$409$	−7.49116e8	+	5.44264e8i	−0.541399	+	0.393349i	0.283205	+	0.959059i	$0.408602\pi$
$410$	9.53635e6	−	1.08974e9i	0.00683343	−	0.780870i
$411$	1.11489e8	+	8.10014e7i	0.0792110	+	0.0575501i
$412$	−2.14663e8	+	1.55961e8i	−0.151222	+	0.109869i
$413$	−2.41985e9	+	1.75813e9i	−1.69030	+	1.22807i
$414$	5.69793e7	+	4.13979e7i	0.0394654	+	0.0286733i
$415$	8.45254e8	+	2.82841e8i	0.580522	+	0.194256i
$416$	−3.99784e7	+	2.90460e7i	−0.0272269	+	0.0197815i
$417$	1.57866e8	−	4.85861e8i	0.106613	−	0.328122i
$418$	−9.94296e7			−0.0665884
$419$	5.31379e8	−	1.63542e9i	0.352903	−	1.08612i	−0.604313	−	0.796747i	$-0.706552\pi$
$419$	5.31379e8	−	1.63542e9i	0.352903	−	1.08612i	0.957215	−	0.289376i	$-0.0934479\pi$
$420$	1.16226e8	+	1.62951e8i	0.0765473	+	0.107321i
$421$	5.17805e8	+	1.59364e9i	0.338204	+	1.04089i	0.965122	+	0.261800i	$0.0843162\pi$
$421$	5.17805e8	+	1.59364e9i	0.338204	+	1.04089i	−0.626918	+	0.779085i	$0.715684\pi$
$422$	5.72494e8	+	1.76195e9i	0.370832	+	1.14130i
$423$	−1.99662e9	−	1.45063e9i	−1.28264	−	0.931891i
$424$	1.34122e9			0.854514
$425$	−8.33767e8	+	2.42106e9i	−0.526846	+	1.52983i
$426$	−2.58423e8			−0.161956
$427$	−2.71029e9	−	1.96914e9i	−1.68468	−	1.22399i
$428$	7.67618e7	+	2.36249e8i	0.0473252	+	0.145652i
$429$	324146.	+	997618.i	0.000198216	+	0.000610048i
$430$	1.83413e8	−	2.47856e8i	0.111248	−	0.150335i
$431$	−8.53070e8	+	2.62548e9i	−0.513232	+	1.57957i	0.273243	+	0.961945i	$0.411904\pi$
$431$	−8.53070e8	+	2.62548e9i	−0.513232	+	1.57957i	−0.786475	+	0.617622i	$0.788096\pi$
$432$	7.82751e7			0.0467122
$433$	−3.67991e8	+	1.13256e9i	−0.217836	+	0.670431i	0.781104	+	0.624401i	$0.214657\pi$
$433$	−3.67991e8	+	1.13256e9i	−0.217836	+	0.670431i	−0.998940	+	0.0460296i	$0.985343\pi$
$434$	1.01662e9	−	7.38614e8i	0.596956	−	0.433714i
$435$	1.56571e8	+	2.19516e8i	0.0912009	+	0.127866i
$436$	1.09109e9	+	7.92723e8i	0.630460	+	0.458056i
$437$	−1.10304e8	+	8.01403e7i	−0.0632273	+	0.0459374i
$438$	8.49040e6	−	6.16864e6i	0.00482802	−	0.00350776i
$439$	−8.24993e8	−	5.99392e8i	−0.465398	−	0.338131i	0.330247	−	0.943894i	$-0.392868\pi$
$439$	−8.24993e8	−	5.99392e8i	−0.465398	−	0.338131i	−0.795645	+	0.605763i	$0.792868\pi$
$440$	−1.04882e8	−	1.47046e8i	−0.0586968	−	0.0822941i
$441$	8.66377e8	−	6.29459e8i	0.481029	−	0.349488i
$442$	2.13467e7	−	6.56983e7i	0.0117585	−	0.0361890i
$443$	−1.28840e9			−0.704107			−0.352054	−	0.935980i	$-0.614517\pi$
$443$	−1.28840e9			−0.704107			−0.352054	+	0.935980i	$0.614517\pi$
$444$	9.28747e7	−	2.85839e8i	0.0503567	−	0.154982i
$445$	1.10315e9	−	1.49075e9i	0.593437	−	0.801944i
$446$	5.63737e8	+	1.73500e9i	0.300888	+	0.926037i
$447$	3.81807e7	+	1.17508e8i	0.0202194	+	0.0622288i
$448$	1.48541e9	+	1.07921e9i	0.780499	+	0.567066i
$449$	1.62106e9			0.845158			0.422579	−	0.906326i	$-0.361125\pi$
$449$	1.62106e9			0.845158			0.422579	+	0.906326i	$0.361125\pi$
$450$	−1.23910e9	−	2.16886e7i	−0.641009	−	0.0112199i
$451$	2.23733e8			0.114845
$452$	−7.56751e7	−	5.49812e7i	−0.0385451	−	0.0280046i
$453$	9.49604e7	+	2.92258e8i	0.0479953	+	0.147714i
$454$	−4.28929e8	−	1.32011e9i	−0.215124	−	0.662085i
$455$	5.25323e7	+	7.36513e7i	0.0261449	+	0.0366556i
$456$	−1.23383e8	+	3.79735e8i	−0.0609368	+	0.187544i
$457$	7.13086e8			0.349490			0.174745	−	0.984614i	$-0.444090\pi$
$457$	7.13086e8			0.349490			0.174745	+	0.984614i	$0.444090\pi$
$458$	−3.87271e7	+	1.19190e8i	−0.0188359	+	0.0579708i
$459$	9.88620e8	−	7.18275e8i	0.477183	−	0.346694i
$460$	−8.42334e7	−	2.81864e7i	−0.0403489	−	0.0135017i
$461$	−1.36239e9	−	9.89832e8i	−0.647660	−	0.470553i	0.214813	−	0.976655i	$-0.431086\pi$
$461$	−1.36239e9	−	9.89832e8i	−0.647660	−	0.470553i	−0.862473	+	0.506103i	$0.831086\pi$
$462$	2.62074e7	−	1.90408e7i	0.0123645	−	0.00898334i
$463$	−2.89278e9	+	2.10172e9i	−1.35451	+	0.984107i	−0.355734	+	0.934587i	$0.615769\pi$
$463$	−2.89278e9	+	2.10172e9i	−1.35451	+	0.984107i	−0.998773	+	0.0495196i	$0.984231\pi$
$464$	1.88914e8	+	1.37254e8i	0.0877910	+	0.0637839i
$465$	−3.07641e6	+	3.51548e8i	−0.00141892	+	0.162143i
$466$	−1.61557e8	+	1.17378e8i	−0.0739564	+	0.0537325i
$467$	−5.90230e8	+	1.81654e9i	−0.268171	+	0.825347i	0.722774	+	0.691084i	$0.242867\pi$
$467$	−5.90230e8	+	1.81654e9i	−0.268171	+	0.825347i	−0.990946	+	0.134263i	$0.957133\pi$
$468$	−4.24101e7			−0.0191253
$469$	−2.25112e8	+	6.92824e8i	−0.100761	+	0.310112i
$470$	−2.32688e9	−	7.78625e8i	−1.03379	−	0.345928i
$471$	−1.84833e8	−	5.68857e8i	−0.0815091	−	0.250859i
$472$	−1.20122e9	−	3.69698e9i	−0.525807	−	1.61827i
$473$	5.12127e7	+	3.72082e7i	0.0222517	+	0.0161668i
$474$	2.40231e8			0.103611
$475$	7.81177e8	−	2.26835e9i	0.334443	−	0.971140i
$476$	2.70611e9			1.15006
$477$	1.52849e9	+	1.11051e9i	0.644835	+	0.468500i
$478$	3.44461e8	+	1.06014e9i	0.144259	+	0.443983i
$479$	4.34376e7	+	1.33687e8i	0.0180589	+	0.0555795i	0.959680	−	0.281095i	$-0.0906977\pi$
$479$	4.34376e7	+	1.33687e8i	0.0180589	+	0.0555795i	−0.941621	+	0.336675i	$0.890698\pi$
$480$	−4.07193e8	+	1.28377e8i	−0.168057	+	0.0529837i
$481$	4.19780e7	−	1.29195e8i	0.0171994	−	0.0529344i
$482$	−5.78643e8			−0.235367
$483$	1.37267e7	−	4.22464e7i	0.00554307	−	0.0170598i
$484$	−1.11765e9	+	8.12022e8i	−0.448072	+	0.325543i
$485$	−2.05449e9	+	6.47722e8i	−0.817724	+	0.257806i
$486$	7.21903e8	+	5.24493e8i	0.285267	+	0.207259i
$487$	1.94486e9	−	1.41302e9i	0.763022	−	0.554368i	−0.136814	−	0.990597i	$-0.543686\pi$
$487$	1.94486e9	−	1.41302e9i	0.763022	−	0.554368i	0.899836	+	0.436229i	$0.143686\pi$
$488$	3.52229e9	−	2.55909e9i	1.37201	−	0.996820i
$489$	−1.33647e8	−	9.71004e7i	−0.0516867	−	0.0375526i
$490$	6.33336e8	−	8.55861e8i	0.243191	−	0.328637i
$491$	6.40741e7	−	4.65526e7i	0.0244285	−	0.0177484i	−0.575504	−	0.817799i	$-0.695194\pi$
$491$	6.40741e7	−	4.65526e7i	0.0244285	−	0.0177484i	0.599933	+	0.800051i	$0.295194\pi$
$492$	9.95695e7	−	3.06443e8i	0.0376919	−	0.116004i
$493$	3.64547e9			1.37022
$494$	−2.00002e7	+	6.15544e7i	−0.00746433	+	0.0229728i
$495$	2.22643e6	−	2.54419e8i	0.000825070	−	0.0942825i
$496$	9.40841e7	+	2.89561e8i	0.0346203	+	0.106550i
$497$	−1.41395e9	−	4.35169e9i	−0.516638	−	1.59005i
$498$	−1.68077e8	−	1.22115e8i	−0.0609825	−	0.0443064i
$499$	−1.86707e9			−0.672681			−0.336341	−	0.941740i	$-0.609189\pi$
$499$	−1.86707e9			−0.672681			−0.336341	+	0.941740i	$0.609189\pi$
$500$	1.49862e9	−	4.43794e8i	0.536163	−	0.158777i
$501$	−7.28542e8			−0.258835
$502$	5.88316e8	+	4.27436e8i	0.207562	+	0.150803i
$503$	−8.23964e8	−	2.53590e9i	−0.288682	−	0.888473i	−0.985271	−	0.171002i	$-0.945300\pi$
$503$	−8.23964e8	−	2.53590e9i	−0.288682	−	0.888473i	0.696588	−	0.717471i	$-0.254700\pi$
$504$	1.12851e9	+	3.47319e9i	0.392643	+	1.20843i
$505$	−2.13436e7	+	2.43898e9i	−0.00737477	+	0.842730i
$506$	−4.44239e6	+	1.36723e7i	−0.00152437	+	0.00469152i
$507$	−5.43542e8			−0.185228
$508$	1.65131e8	−	5.08222e8i	0.0558865	−	0.172001i
$509$	1.68717e9	−	1.22580e9i	0.567082	−	0.412009i	−0.266962	−	0.963707i	$-0.586020\pi$
$509$	1.68717e9	−	1.22580e9i	0.567082	−	0.412009i	0.834044	+	0.551698i	$0.186020\pi$
$510$	3.55026e8	−	4.79766e8i	0.118513	−	0.160152i
$511$	1.50331e8	+	1.09222e8i	0.0498398	+	0.0362107i
$512$	−6.25057e8	+	4.54131e8i	−0.205814	+	0.149533i
$513$	−9.26263e8	+	6.72970e8i	−0.302917	+	0.220082i
$514$	−2.32024e9	−	1.68575e9i	−0.753635	−	0.547548i
$515$	−9.88225e8	+	3.11560e8i	−0.318809	+	0.100512i
$516$	7.37549e7	−	5.35861e7i	0.0236329	−	0.0171703i
$517$	1.55666e8	−	4.79092e8i	0.0495425	−	0.152476i
$518$	−4.19515e9			−1.32615
$519$	−2.84649e8	+	8.76060e8i	−0.0893767	+	0.275073i
$520$	−1.12129e8	+	3.53513e7i	−0.0349710	+	0.0110254i
$521$	−8.87235e8	−	2.73063e9i	−0.274857	−	0.845922i	−0.989257	−	0.146185i	$-0.953300\pi$
$521$	−8.87235e8	−	2.73063e9i	−0.274857	−	0.845922i	0.714400	−	0.699737i	$-0.246700\pi$
$522$	5.45216e8	+	1.67800e9i	0.167773	+	0.516352i
$523$	2.44029e8	+	1.77297e8i	0.0745908	+	0.0541934i	0.624456	−	0.781060i	$-0.285321\pi$
$523$	2.44029e8	+	1.77297e8i	0.0745908	+	0.0541934i	−0.549865	+	0.835254i	$0.685321\pi$
$524$	−2.50128e8			−0.0759455
$525$	2.28488e8	+	7.47481e8i	0.0689139	+	0.225446i
$526$	−1.97436e9			−0.591529
$527$	3.84539e9	+	2.79384e9i	1.14447	+	0.831504i
$528$	2.42540e6	+	7.46462e6i	0.000717075	+	0.00220693i
$529$	−1.04606e9	−	3.21943e9i	−0.307228	−	0.945550i
$530$	1.78132e9	+	5.96069e8i	0.519728	+	0.173913i
$531$	1.69211e9	−	5.20779e9i	0.490454	−	1.50946i
$532$	−2.53542e9			−0.730061
$533$	4.50039e7	−	1.38508e8i	0.0128737	−	0.0396213i
$534$	−3.49709e8	+	2.54079e8i	−0.0993831	+	0.0722061i
$535$	−8.48869e6	+	9.70020e8i	−0.00239664	+	0.273869i
$536$	−7.65921e8	−	5.56474e8i	−0.214836	−	0.156088i
$537$	−1.85081e8	+	1.34469e8i	−0.0515764	+	0.0374724i
$538$	2.75759e9	−	2.00351e9i	0.763471	−	0.554694i
$539$	1.76840e8	+	1.28482e8i	0.0486430	+	0.0353412i
$540$	−7.07342e8	−	2.36692e8i	−0.193309	−	0.0646853i
$541$	−4.98970e9	+	3.62523e9i	−1.35483	+	0.984340i	−0.356073	+	0.934458i	$0.615884\pi$
$541$	−4.98970e9	+	3.62523e9i	−1.35483	+	0.984340i	−0.998755	+	0.0498818i	$0.984116\pi$
$542$	−5.50559e8	+	1.69445e9i	−0.148527	+	0.457120i
$543$	3.33974e8			0.0895186
$544$	−1.78378e9	+	5.48992e9i	−0.475057	+	1.46207i
$545$	3.05827e9	+	4.28776e9i	0.809261	+	1.13460i
$546$	−6.51607e6	−	2.00544e7i	−0.00171321	−	0.00527273i
$547$	8.57137e8	+	2.63800e9i	0.223921	+	0.689157i	0.998399	+	0.0565572i	$0.0180123\pi$
$547$	8.57137e8	+	2.63800e9i	0.223921	+	0.689157i	−0.774479	+	0.632600i	$0.781988\pi$
$548$	−9.20063e8	−	6.68465e8i	−0.238828	−	0.173519i
$549$	6.13301e9			1.58187
$550$	−7.39461e7	−	2.41909e8i	−0.0189516	−	0.0619986i
$551$	−3.41554e9			−0.869818
$552$	4.67036e7	+	3.39322e7i	0.0118185	+	0.00858667i
$553$	1.31441e9	+	4.04535e9i	0.330517	+	1.01723i
$554$	5.51470e7	+	1.69725e8i	0.0137796	+	0.0424094i
$555$	6.98154e8	−	9.43453e8i	0.173351	−	0.234258i
$556$	−1.30279e9	+	4.00957e9i	−0.321449	+	0.989318i
$557$	2.17301e9			0.532805			0.266402	−	0.963862i	$-0.414165\pi$
$557$	2.17301e9			0.532805			0.266402	+	0.963862i	$0.414165\pi$
$558$	−7.10882e8	+	2.18787e9i	−0.173212	+	0.533091i
$559$	3.33361e7	−	2.42201e7i	0.00807186	−	0.00586455i
$560$	3.93070e8	+	5.51092e8i	0.0945827	+	0.132607i
$561$	9.91305e7	+	7.20225e7i	0.0237049	+	0.0172226i
$562$	−1.57351e9	+	1.14322e9i	−0.373931	+	0.271677i
$563$	3.82534e9	−	2.77927e9i	0.903422	−	0.656375i	−0.0359206	−	0.999355i	$-0.511436\pi$
$563$	3.82534e9	−	2.77927e9i	0.903422	−	0.656375i	0.939343	+	0.342980i	$0.111436\pi$
$564$	−5.86926e8	−	4.26427e8i	−0.137755	−	0.100085i
$565$	−2.12114e8	−	2.97388e8i	−0.0494765	−	0.0693671i
$566$	4.00384e9	−	2.90896e9i	0.928153	−	0.674343i
$567$	−1.53104e9	+	4.71206e9i	−0.352733	+	1.08560i
$568$	5.94650e9			1.36158
$569$	−2.57296e9	+	7.91877e9i	−0.585519	+	1.80204i	0.0116584	+	0.999932i	$0.496289\pi$
$569$	−2.57296e9	+	7.91877e9i	−0.585519	+	1.80204i	−0.597177	+	0.802109i	$0.703711\pi$
$570$	−3.32633e8	+	4.49504e8i	−0.0752320	+	0.101665i
$571$	−1.91951e9	−	5.90765e9i	−0.431484	−	1.32797i	−0.896647	−	0.442746i	$-0.854004\pi$
$571$	−1.91951e9	−	5.90765e9i	−0.431484	−	1.32797i	0.465163	−	0.885225i	$-0.345996\pi$
$572$	−2.67501e6	−	8.23284e6i	−0.000597640	−	0.00183935i
$573$	−5.11588e8	−	3.71691e8i	−0.113600	−	0.0825354i
$574$	−4.49755e9			−0.992623
$575$	−2.77012e8	−	2.08764e8i	−0.0607660	−	0.0457951i
$576$	−3.36127e9			−0.732866
$577$	8.33941e8	+	6.05894e8i	0.180726	+	0.131305i	0.674470	−	0.738302i	$-0.264372\pi$
$577$	8.33941e8	+	6.05894e8i	0.180726	+	0.131305i	−0.493744	+	0.869607i	$0.664372\pi$
$578$	−1.54108e9	−	4.74296e9i	−0.331954	−	1.02165i
$579$	7.26368e7	+	2.23553e8i	0.0155518	+	0.0478637i
$580$	−1.29210e9	−	1.81156e9i	−0.274979	−	0.385526i
$581$	1.13672e9	−	3.49847e9i	0.240457	−	0.740050i
$582$	5.02107e8			0.105576
$583$	−1.19169e8	+	3.66764e8i	−0.0249071	+	0.0766561i
$584$	−1.95371e8	+	1.41945e8i	−0.0405895	+	0.0294900i
$585$	−1.57057e8	−	5.25546e7i	−0.0324347	−	0.0108534i
$586$	1.04960e9	+	7.62580e8i	0.215468	+	0.156547i
$587$	2.84974e9	−	2.07046e9i	0.581530	−	0.422506i	−0.257745	−	0.966213i	$-0.582980\pi$
$587$	2.84974e9	−	2.07046e9i	0.581530	−	0.422506i	0.839275	+	0.543707i	$0.182980\pi$
$588$	2.54680e8	−	1.85036e8i	0.0516623	−	0.0375349i
$589$	−3.60284e9	−	2.61762e9i	−0.726510	−	0.527840i
$590$	4.76402e7	−	5.44394e9i	0.00954974	−	1.09127i
$591$	7.72735e8	−	5.61425e8i	0.153984	−	0.111876i
$592$	3.14098e8	−	9.66693e8i	0.0622213	−	0.191497i
$593$	−6.88056e9			−1.35498			−0.677490	−	0.735532i	$-0.736932\pi$
$593$	−6.88056e9			−1.35498			−0.677490	+	0.735532i	$0.736932\pi$
$594$	−3.73045e7	+	1.14811e8i	−0.00730313	+	0.0224767i
$595$	1.00215e10	+	3.35341e9i	1.95040	+	0.652646i
$596$	−3.15086e8	−	9.69736e8i	−0.0609632	−	0.187625i
$597$	5.00967e8	+	1.54182e9i	0.0963604	+	0.296567i
$598$	7.57058e6	+	5.50035e6i	0.00144769	+	0.00105181i
$599$	−5.51933e9			−1.04928			−0.524641	−	0.851324i	$-0.675800\pi$
$599$	−5.51933e9			−1.04928			−0.524641	+	0.851324i	$0.675800\pi$
$600$	−1.01564e9	−	1.77772e7i	−0.191960	−	0.00335996i
$601$	3.02510e9			0.568433			0.284217	−	0.958760i	$-0.408267\pi$
$601$	3.02510e9			0.568433			0.284217	+	0.958760i	$0.408267\pi$
$602$	−1.02949e9	−	7.47970e8i	−0.192325	−	0.139732i
$603$	−4.12112e8	−	1.26835e9i	−0.0765428	−	0.235574i
$604$	−7.83661e8	−	2.41186e9i	−0.144710	−	0.445372i
$605$	−5.14524e9	+	1.62215e9i	−0.944631	+	0.297816i
$606$	1.75681e8	−	5.40689e8i	0.0320678	−	0.0986946i
$607$	1.47941e9			0.268489			0.134245	−	0.990948i	$-0.457139\pi$
$607$	1.47941e9			0.268489			0.134245	+	0.990948i	$0.457139\pi$
$608$	1.67127e9	−	5.14364e9i	0.301567	−	0.928129i
$609$	9.00259e8	−	6.54076e8i	0.161513	−	0.117346i
$610$	5.81540e9	−	1.83343e9i	1.03735	−	0.327047i
$611$	−2.65282e8	−	1.92738e8i	−0.0470504	−	0.0341841i
$612$	−4.00791e9	+	2.91192e9i	−0.706787	+	0.513511i
$613$	6.67925e9	−	4.85276e9i	1.17116	−	0.850897i	0.180012	−	0.983664i	$-0.442386\pi$
$613$	6.67925e9	−	4.85276e9i	1.17116	−	0.850897i	0.991147	+	0.132767i	$0.0423863\pi$
$614$	4.45373e9	+	3.23582e9i	0.776487	+	0.564151i
$615$	7.48479e8	−	1.01146e9i	0.129753	−	0.175342i
$616$	−6.03052e8	+	4.38143e8i	−0.103949	+	0.0755237i
$617$	−9.92394e7	+	3.05427e8i	−0.0170093	+	0.0523492i	−0.959201	−	0.282725i	$-0.908762\pi$
$617$	−9.92394e7	+	3.05427e8i	−0.0170093	+	0.0523492i	0.942192	+	0.335075i	$0.108762\pi$
$618$	2.41518e8			0.0411613
$619$	1.79131e9	−	5.51309e9i	0.303567	−	0.934282i	−0.676641	−	0.736313i	$-0.736565\pi$
$619$	1.79131e9	−	5.51309e9i	0.303567	−	0.934282i	0.980208	−	0.197970i	$-0.0634347\pi$
$620$	2.53881e7	−	2.90115e9i	0.00427818	−	0.488877i
$621$	5.11538e7	+	1.57435e8i	0.00857151	+	0.0263804i
$622$	−1.43086e9	−	4.40375e9i	−0.238414	−	0.733763i
$623$	−6.19196e9	−	4.49872e9i	−1.02593	−	0.745385i
$624$	5.10903e6			0.000841768
$625$	6.09978e9	+	2.13600e8i	0.999387	+	0.0349961i
$626$	−9.56609e8			−0.155856
$627$	−9.28779e7	−	6.74797e7i	−0.0150479	−	0.0109329i
$628$	1.52533e9	+	4.69450e9i	0.245757	+	0.756363i
$629$	−4.90358e9	−	1.50917e10i	−0.785663	−	2.41802i
$630$	−4.47564e7	+	5.11440e9i	−0.00713120	+	0.814897i
$631$	−3.11456e9	+	9.58564e9i	−0.493508	+	1.51886i	0.325760	+	0.945453i	$0.394380\pi$
$631$	−3.11456e9	+	9.58564e9i	−0.493508	+	1.51886i	−0.819268	+	0.573410i	$0.805620\pi$
$632$	−5.52789e9			−0.871063
$633$	−6.61013e8	+	2.03439e9i	−0.103585	+	0.318802i
$634$	−5.02920e9	+	3.65392e9i	−0.783765	+	0.569439i
$635$	1.24132e9	−	1.67746e9i	0.192387	−	0.259983i
$636$	4.49315e8	+	3.26447e8i	0.0692550	+	0.0503167i
$637$	1.15111e8	−	8.36334e7i	0.0176454	−	0.0128201i
$638$	−2.91352e8	+	2.11680e8i	−0.0444167	+	0.0322706i
$639$	6.77681e9	+	4.92364e9i	1.02748	+	0.746506i
$640$	2.82226e9	−	8.89780e8i	0.425566	−	0.134169i
$641$	1.03441e9	−	7.51545e8i	0.155128	−	0.112707i	−0.507513	−	0.861644i	$-0.669435\pi$
$641$	1.03441e9	−	7.51545e8i	0.155128	−	0.112707i	0.662642	+	0.748937i	$0.269435\pi$
$642$	6.98708e7	−	2.15040e8i	0.0104213	−	0.0320736i
$643$	−6.82194e8			−0.101197			−0.0505987	−	0.998719i	$-0.516113\pi$
$643$	−6.82194e8			−0.101197			−0.0505987	+	0.998719i	$0.516113\pi$
$644$	−1.13279e8	+	3.48638e8i	−0.0167128	+	0.0514369i
$645$	3.39540e8	−	1.07047e8i	0.0498232	−	0.0157079i
$646$	2.33629e9	+	7.19036e9i	0.340968	+	1.04939i
$647$	3.02720e9	+	9.31678e9i	0.439417	+	1.35239i	0.888492	+	0.458892i	$0.151754\pi$
$647$	3.02720e9	+	9.31678e9i	0.439417	+	1.35239i	−0.449075	+	0.893494i	$0.648246\pi$
$648$	−5.20921e9	−	3.78471e9i	−0.752072	−	0.546412i
$649$	1.11769e9			0.160496
$650$	−1.64634e8	−	2.88166e6i	−0.0235138	−	0.000411572i
$651$	1.45090e9			0.206113
$652$	1.10292e9	+	8.01322e8i	0.155840	+	0.113224i
$653$	2.52149e9	+	7.76034e9i	0.354373	+	1.09065i	0.956372	+	0.292152i	$0.0943712\pi$
$653$	2.52149e9	+	7.76034e9i	0.354373	+	1.09065i	−0.601999	+	0.798497i	$0.705629\pi$
$654$	−3.79346e8	−	1.16751e9i	−0.0530290	−	0.163206i
$655$	−9.26294e8	−	3.09959e8i	−0.128797	−	0.0430982i
$656$	3.36739e8	−	1.03638e9i	0.0465726	−	0.143336i
$657$	−3.40179e8			−0.0467981
$658$	−3.12925e9	+	9.63084e9i	−0.428203	+	1.31787i
$659$	2.04127e9	−	1.48307e9i	0.277845	−	0.201866i	−0.440132	−	0.897933i	$-0.645068\pi$
$659$	2.04127e9	−	1.48307e9i	0.277845	−	0.201866i	0.717977	+	0.696067i	$0.245068\pi$
$660$	654481.	−	7.47889e7i	8.86122e−5	−	0.0101259i
$661$	−3.34393e9	−	2.42950e9i	−0.450351	−	0.327199i	0.339383	−	0.940648i	$-0.389782\pi$
$661$	−3.34393e9	−	2.42950e9i	−0.450351	−	0.327199i	−0.789734	+	0.613449i	$0.789782\pi$
$662$	3.99705e8	−	2.90403e8i	0.0535472	−	0.0389043i
$663$	6.45275e7	−	4.68819e7i	0.00859899	−	0.00624753i
$664$	3.86758e9	+	2.80996e9i	0.512685	+	0.372488i
$665$	−9.38938e9	−	3.14190e9i	−1.23812	−	0.414301i
$666$	6.21328e9	−	4.51421e9i	0.815007	−	0.592137i
$667$	−1.52602e8	+	4.69661e8i	−0.0199122	+	0.0612835i
$668$	6.01230e9			0.780410
$669$	−6.50902e8	+	2.00327e9i	−0.0840474	+	0.258671i
$670$	−7.69936e8	−	1.07947e9i	−0.0988993	−	0.138659i
$671$	3.86839e8	+	1.19057e9i	0.0494313	+	0.152134i
$672$	5.44499e8	+	1.67580e9i	0.0692158	+	0.213024i
$673$	−6.10786e9	−	4.43762e9i	−0.772389	−	0.561173i	0.130296	−	0.991475i	$-0.458407\pi$
$673$	−6.10786e9	−	4.43762e9i	−0.772389	−	0.561173i	−0.902685	+	0.430302i	$0.858407\pi$
$674$	−1.57670e9			−0.198353
$675$	−2.32618e9	−	1.75308e9i	−0.291125	−	0.219401i
$676$	4.48559e9			0.558478
$677$	−1.52451e8	−	1.10762e8i	−0.0188830	−	0.0137193i	0.578304	−	0.815822i	$-0.303715\pi$
$677$	−1.52451e8	−	1.10762e8i	−0.0188830	−	0.0137193i	−0.597187	+	0.802102i	$0.703715\pi$
$678$	2.63105e7	+	8.09752e7i	0.00324208	+	0.00997811i
$679$	2.74726e9	+	8.45520e9i	0.336787	+	1.03652i
$680$	−8.16941e9	+	1.10398e10i	−0.996344	+	1.34641i
$681$	4.95250e8	−	1.52422e9i	0.0600910	−	0.184941i
$682$	−4.69558e8			−0.0566819
$683$	−4.26302e8	+	1.31202e9i	−0.0511970	+	0.157568i	−0.973386	−	0.229171i	$-0.926399\pi$
$683$	−4.26302e8	+	1.31202e9i	−0.0511970	+	0.157568i	0.922189	+	0.386739i	$0.126399\pi$
$684$	3.75512e9	−	2.72825e9i	0.448670	−	0.325978i
$685$	−2.57889e9	−	3.61566e9i	−0.306560	−	0.429804i
$686$	2.21825e9	+	1.61165e9i	0.262346	+	0.190606i
$687$	−1.17066e8	+	8.50531e7i	−0.0137746	+	0.0100079i
$688$	2.49435e8	−	1.81225e8i	0.0292011	−	0.0212158i
$689$	2.03084e8	+	1.47549e8i	0.0236542	+	0.0171858i
$690$	4.69484e7	+	6.58227e7i	0.00544063	+	0.00762788i
$691$	−1.13734e10	+	8.26326e9i	−1.31135	+	0.952749i	−0.311349	+	0.950296i	$0.600781\pi$
$691$	−1.13734e10	+	8.26326e9i	−1.31135	+	0.952749i	−0.999997	+	0.00245318i	$0.999219\pi$
$692$	2.34907e9	−	7.22969e9i	0.269479	−	0.829370i
$693$	−1.05003e9			−0.119850
$694$	−1.44017e9	+	4.43239e9i	−0.163552	+	0.503361i
$695$	−9.79326e9	+	1.32342e10i	−1.10657	+	1.49537i
$696$	4.46891e8	+	1.37539e9i	0.0502423	+	0.154630i
$697$	−5.25705e9	−	1.61795e10i	−0.588068	−	1.80989i
$698$	−2.06150e9	−	1.49777e9i	−0.229451	−	0.166706i
$699$	−2.30573e8			−0.0255351
$700$	−1.88560e9	−	6.16859e9i	−0.207781	−	0.679740i
$701$	9.62820e9			1.05568			0.527840	−	0.849344i	$-0.323002\pi$
$701$	9.62820e9			1.05568			0.527840	+	0.849344i	$0.323002\pi$
$702$	6.35732e7	+	4.61886e7i	0.00693576	+	0.00503912i
$703$	4.59429e9	+	1.41398e10i	0.498740	+	1.53497i
$704$	−2.12012e8	−	6.52506e8i	−0.0229011	−	0.0704823i
$705$	−1.64513e9	−	2.30650e9i	−0.176822	−	0.247909i
$706$	1.34271e9	−	4.13245e9i	0.143604	−	0.441968i
$707$	1.00661e10			1.07126
$708$	4.97414e8	−	1.53088e9i	0.0526746	−	0.162116i
$709$	1.24327e10	−	9.03289e9i	1.31010	−	0.951842i	0.310099	−	0.950704i	$-0.399638\pi$
$709$	1.24327e10	−	9.03289e9i	1.31010	−	0.951842i	0.999999	−	0.00113834i	$-0.000362345\pi$
$710$	7.89775e9	+	2.64276e9i	0.828132	+	0.277111i
$711$	−6.29974e9	−	4.57703e9i	−0.657324	−	0.477574i
$712$	8.04707e9	−	5.84654e9i	0.835522	−	0.607042i
$713$	−5.20912e8	+	3.78464e8i	−0.0538209	+	0.0391031i
$714$	−1.99275e9	−	1.44782e9i	−0.204885	−	0.148857i
$715$	295816.	−	3.38034e7i	3.02656e−5	−	0.00345852i
$716$	1.52738e9	−	1.10970e9i	0.155507	−	0.112983i
$717$	−3.97721e8	+	1.22406e9i	−0.0402960	+	0.124018i
$718$	−8.52083e9			−0.859105
$719$	−9.09679e8	+	2.79970e9i	−0.0912719	+	0.280906i	−0.986264	−	0.165176i	$-0.947181\pi$
$719$	−9.09679e8	+	2.79970e9i	−0.0912719	+	0.280906i	0.894992	+	0.446082i	$0.147181\pi$
$720$	−1.17517e9	−	3.93237e8i	−0.117337	−	0.0392636i
$721$	1.32145e9	+	4.06702e9i	0.131304	+	0.404113i
$722$	−1.14047e8	−	3.51001e8i	−0.0112773	−	0.0347078i
$723$	−5.40515e8	−	3.92707e8i	−0.0531892	−	0.0386442i
$724$	−2.75612e9			−0.269906
$725$	−2.54015e9	−	8.30988e9i	−0.247557	−	0.809864i
$726$	1.25748e9			0.121961
$727$	−1.41648e10	−	1.02913e10i	−1.36723	−	0.993349i	−0.997948	−	0.0640301i	$-0.979605\pi$
$727$	−1.41648e10	−	1.02913e10i	−1.36723	−	0.993349i	−0.369279	−	0.929319i	$-0.620395\pi$
$728$	1.49940e8	+	4.61467e8i	0.0144031	+	0.0443283i
$729$	−2.58433e9	−	7.95375e9i	−0.247060	−	0.760371i
$730$	−3.22562e8	+	1.01695e8i	−0.0306890	+	0.00967540i
$731$	1.48741e9	−	4.57779e9i	0.140838	−	0.433456i
$732$	1.80286e9			0.169892
$733$	−5.38484e9	+	1.65728e10i	−0.505021	+	1.55429i	0.295715	+	0.955276i	$0.404442\pi$
$733$	−5.38484e9	+	1.65728e10i	−0.505021	+	1.55429i	−0.800736	+	0.599018i	$0.795558\pi$
$734$	1.08185e10	−	7.86009e9i	1.00979	−	0.733654i
$735$	1.17245e9	−	3.69641e8i	0.108915	−	0.0343379i
$736$	−6.32617e8	−	4.59623e8i	−0.0584882	−	0.0424942i
$737$	2.20224e8	−	1.60002e8i	0.0202642	−	0.0147228i
$738$	6.66116e9	−	4.83961e9i	0.610032	−	0.443214i
$739$	5.36678e9	+	3.89919e9i	0.489168	+	0.355401i	0.804864	−	0.593459i	$-0.202238\pi$
$739$	5.36678e9	+	3.89919e9i	0.489168	+	0.355401i	−0.315696	+	0.948860i	$0.602238\pi$
$740$	−5.76152e9	+	7.78585e9i	−0.522668	+	0.706309i
$741$	−6.04574e7	+	4.39249e7i	−0.00545866	+	0.00396595i
$742$	2.39557e9	−	7.37279e9i	0.215275	−	0.662550i
$743$	6.11265e9			0.546725			0.273362	−	0.961911i	$-0.411864\pi$
$743$	6.11265e9			0.546725			0.273362	+	0.961911i	$0.411864\pi$
$744$	−5.82680e8	+	1.79331e9i	−0.0518711	+	0.159643i
$745$	3.48437e7	−	3.98166e9i	0.00308729	−	0.352791i
$746$	3.32017e9	+	1.02184e10i	0.292802	+	0.901153i
$747$	2.08099e9	+	6.40462e9i	0.182662	+	0.562175i
$748$	−8.18075e8	−	5.94366e8i	−0.0714723	−	0.0519276i
$749$	4.00345e9			0.348135
$750$	−1.34101e9	−	4.74986e8i	−0.116069	−	0.0411118i
$751$	−6.47738e9			−0.558033			−0.279016	−	0.960286i	$-0.590008\pi$
$751$	−6.47738e9			−0.558033			−0.279016	+	0.960286i	$0.590008\pi$
$752$	−1.98495e9	−	1.44215e9i	−0.170211	−	0.123666i
$753$	2.59462e8	+	7.98543e8i	0.0221458	+	0.0681579i
$754$	7.24403e7	+	2.22948e8i	0.00615433	+	0.0189411i
$755$	8.66609e7	−	9.90292e9i	0.00732840	−	0.837431i
$756$	−9.51252e8	+	2.92765e9i	−0.0800699	+	0.246430i
$757$	−1.56639e10			−1.31239			−0.656195	−	0.754591i	$-0.727835\pi$
$757$	−1.56639e10			−1.31239			−0.656195	+	0.754591i	$0.727835\pi$
$758$	3.45001e8	−	1.06180e9i	0.0287725	−	0.0885526i
$759$	−1.34286e7	+	9.75646e6i	−0.00111477	+	0.000809927i
$760$	7.65413e9	−	1.03434e10i	0.632482	−	0.854707i
$761$	1.08751e10	+	7.90122e9i	0.894514	+	0.649902i	0.937051	−	0.349193i	$-0.113544\pi$
$761$	1.08751e10	+	7.90122e9i	0.894514	+	0.649902i	−0.0425371	+	0.999095i	$0.513544\pi$
$762$	−3.93510e8	+	2.85901e8i	−0.0322191	+	0.0234085i
$763$	1.75846e10	−	1.27759e10i	1.43316	−	1.04125i
$764$	4.22188e9	+	3.06738e9i	0.342515	+	0.248852i
$765$	−1.84509e10	+	5.81706e9i	−1.49006	+	0.469773i
$766$	4.24576e9	−	3.08473e9i	0.341315	−	0.247980i
$767$	2.24823e8	−	6.91935e8i	0.0179911	−	0.0553709i
$768$	−2.45676e9			−0.195704
$769$	2.21066e9	−	6.80370e9i	0.175299	−	0.539514i	−0.824348	−	0.566083i	$-0.808458\pi$
$769$	2.21066e9	−	6.80370e9i	0.175299	−	0.539514i	0.999647	+	0.0265687i	$0.00845808\pi$
$770$	−9.95655e8	+	3.13902e8i	−0.0785943	+	0.0247786i
$771$	−1.02328e9	−	3.14934e9i	−0.0804092	−	0.247474i
$772$	−5.99436e8	−	1.84487e9i	−0.0468902	−	0.144313i
$773$	−6.02978e9	−	4.38089e9i	−0.469541	−	0.341141i	0.327721	−	0.944774i	$-0.393719\pi$
$773$	−6.02978e9	−	4.38089e9i	−0.469541	−	0.341141i	−0.797262	+	0.603633i	$0.793719\pi$
$774$	2.32960e9			0.180588
$775$	3.68913e9	−	1.07123e10i	0.284687	−	0.826662i
$776$	−1.15539e10			−0.887588
$777$	−3.91872e9	−	2.84712e9i	−0.299689	−	0.217737i
$778$	2.31712e9	+	7.13136e9i	0.176409	+	0.542930i
$779$	4.92546e9	+	1.51590e10i	0.373307	+	1.14892i
$780$	−4.61683e7	−	1.54489e7i	−0.00348348	−	0.00116565i
$781$	−5.28353e8	+	1.62610e9i	−0.0396868	+	0.122143i
$782$	1.09311e9			0.0817410
$783$	−1.28146e9	+	3.94393e9i	−0.0953978	+	0.293604i
$784$	8.61315e8	−	6.25782e8i	0.0638345	−	0.0463785i
$785$	−1.68679e8	+	1.92753e10i	−0.0124456	+	1.42219i
$786$	1.84192e8	+	1.33823e8i	0.0135298	+	0.00982996i
$787$	9.56237e9	−	6.94747e9i	0.699285	−	0.508060i	−0.180415	−	0.983591i	$-0.557744\pi$
$787$	9.56237e9	−	6.94747e9i	0.699285	−	0.508060i	0.879699	+	0.475531i	$0.157744\pi$
$788$	−6.37700e9	+	4.63316e9i	−0.464274	+	0.337315i
$789$	−1.84426e9	−	1.33994e9i	−0.133676	−	0.0971213i
$790$	−7.34178e9	−	2.45672e9i	−0.529793	−	0.177281i
$791$	−1.21962e9	+	8.86106e8i	−0.0876207	+	0.0636602i
$792$	4.21692e8	−	1.29783e9i	0.0301618	−	0.0928284i
$793$	8.14864e8			0.0580269
$794$	−9.15827e8	+	2.81862e9i	−0.0649294	+	0.199832i
$795$	1.25941e9	+	1.76572e9i	0.0888960	+	0.124634i
$796$	−4.13423e9	−	1.27238e10i	−0.290535	−	0.894176i
$797$	−8.00746e8	−	2.46444e9i	−0.0560262	−	0.172431i	0.919128	−	0.393960i	$-0.128895\pi$
$797$	−8.00746e8	−	2.46444e9i	−0.0560262	−	0.172431i	−0.975154	+	0.221529i	$0.928895\pi$
$798$	1.86706e9	+	1.35650e9i	0.130061	+	0.0944950i
$799$	−3.83038e10			−2.65661
$800$	1.37572e10	+	2.40799e8i	0.949984	+	0.0166280i
$801$	1.40115e10			0.963324
$802$	1.55443e10	+	1.12936e10i	1.06405	+	0.773078i
$803$	−2.14568e7	−	6.60372e7i	−0.00146238	−	0.00450074i
$804$	−1.21144e8	−	3.72844e8i	−0.00822066	−	0.0253006i
$805$	−8.51539e8	+	1.15073e9i	−0.0575333	+	0.0777478i
$806$	−9.44516e7	+	2.90692e8i	−0.00635384	+	0.0195551i
$807$	3.93561e9			0.263605
$808$	−4.04254e9	+	1.24417e10i	−0.269597	+	0.829733i
$809$	−3.75379e9	+	2.72729e9i	−0.249258	+	0.181097i	−0.705398	−	0.708811i	$-0.749232\pi$
$809$	−3.75379e9	+	2.72729e9i	−0.249258	+	0.181097i	0.456140	+	0.889908i	$0.349232\pi$
$810$	−5.23652e9	−	7.34170e9i	−0.346214	−	0.485399i
$811$	9.11462e9	+	6.62216e9i	0.600020	+	0.435940i	0.845886	−	0.533364i	$-0.179072\pi$
$811$	9.11462e9	+	6.62216e9i	0.600020	+	0.435940i	−0.245866	+	0.969304i	$0.579072\pi$
$812$	−7.42939e9	+	5.39777e9i	−0.486975	+	0.353808i
$813$	−1.66425e9	+	1.20915e9i	−0.108618	+	0.0789155i
$814$	1.26822e9	+	9.21418e8i	0.0824157	+	0.0598785i
$815$	3.09145e9	+	4.33427e9i	0.200037	+	0.280456i
$816$	4.82823e8	−	3.50791e8i	0.0311080	−	0.0226013i
$817$	−1.39359e9	+	4.28904e9i	−0.0894045	+	0.275159i
$818$	−6.95548e9			−0.444315
$819$	−2.11214e8	+	6.50050e8i	−0.0134347	+	0.0413478i
$820$	−6.17683e9	+	8.34708e9i	−0.391216	+	0.528672i
$821$	3.54660e9	+	1.09153e10i	0.223672	+	0.688391i	0.998424	+	0.0561257i	$0.0178748\pi$
$821$	3.54660e9	+	1.09153e10i	0.223672	+	0.688391i	−0.774752	+	0.632265i	$0.782125\pi$
$822$	3.19884e8	+	9.84502e8i	0.0200882	+	0.0618251i
$823$	−1.04214e10	−	7.57162e9i	−0.651671	−	0.473467i	0.212169	−	0.977233i	$-0.431947\pi$
$823$	−1.04214e10	−	7.57162e9i	−0.651671	−	0.473467i	−0.863840	+	0.503766i	$0.831947\pi$
$824$	−5.55750e9			−0.346047
$825$	9.51023e7	−	2.76154e8i	0.00589661	−	0.0171223i
$826$	−2.24682e10			−1.38719
$827$	7.98438e9	+	5.80099e9i	0.490876	+	0.356643i	0.805521	−	0.592567i	$-0.201885\pi$
$827$	7.98438e9	+	5.80099e9i	0.490876	+	0.356643i	−0.314645	+	0.949209i	$0.601885\pi$
$828$	−2.07380e8	−	6.38250e8i	−0.0126958	−	0.0390737i
$829$	1.49518e8	+	4.60169e8i	0.00911492	+	0.0280528i	0.955511	−	0.294957i	$-0.0953053\pi$
$829$	1.49518e8	+	4.60169e8i	0.00911492	+	0.0280528i	−0.946396	+	0.323010i	$0.895305\pi$
$830$	3.88785e9	+	5.45085e9i	0.236013	+	0.330895i
$831$	−6.36739e7	+	1.95968e8i	−0.00384909	+	0.0118463i
$832$	−4.46597e8			−0.0268834
$833$	5.13612e9	−	1.58074e10i	0.307877	−	0.947549i
$834$	3.10455e9	−	2.25559e9i	0.185318	−	0.134642i
$835$	2.22652e10	+	7.45045e9i	1.32350	+	0.442873i
$836$	7.66475e8	+	5.56877e8i	0.0453708	+	0.0329638i
$837$	−4.37430e9	+	3.17812e9i	−0.257851	+	0.187340i
$838$	1.04500e10	−	7.59236e9i	0.613425	−	0.445680i
$839$	1.77044e10	+	1.28630e10i	1.03494	+	0.751928i	0.969291	−	0.245915i	$-0.0790884\pi$
$839$	1.77044e10	+	1.28630e10i	1.03494	+	0.751928i	0.0656484	+	0.997843i	$0.479088\pi$
$840$	−3.66849e7	+	4.19206e9i	−0.00213555	+	0.244034i
$841$	3.94710e9	−	2.86774e9i	0.228819	−	0.166247i
$842$	−3.88958e9	+	1.19709e10i	−0.224548	+	0.691089i
$843$	−2.24569e9			−0.129108
$844$	5.45501e9	−	1.67888e10i	0.312318	−	0.961216i
$845$	1.66114e10	+	5.55854e9i	0.947126	+	0.316929i
$846$	−5.72870e9	−	1.76311e10i	−0.325282	−	1.00111i
$847$	6.88023e9	+	2.11752e10i	0.389055	+	1.19739i
$848$	1.51956e9	+	1.10403e9i	0.0855723	+	0.0621719i
$849$	5.71424e9			0.320466
$850$	−1.57564e10	+	1.10316e10i	−0.880017	+	0.616131i
$851$	2.14959e9			0.119564
$852$	1.99211e9	+	1.44735e9i	0.110351	+	0.0801744i
$853$	−3.01939e9	−	9.29271e9i	−0.166570	−	0.512650i	0.832579	−	0.553907i	$-0.186864\pi$
$853$	−3.01939e9	−	9.29271e9i	−0.166570	−	0.512650i	−0.999149	+	0.0412571i	$0.986864\pi$
$854$	−7.77635e9	−	2.39332e10i	−0.427242	−	1.31491i
$855$	1.72871e10	−	5.45015e9i	0.945891	−	0.298213i
$856$	−1.60778e9	+	4.94824e9i	−0.0876130	+	0.269645i
$857$	−1.82327e9			−0.0989505			−0.0494752	−	0.998775i	$-0.515755\pi$
$857$	−1.82327e9			−0.0989505			−0.0494752	+	0.998775i	$0.515755\pi$
$858$	−2.43487e6	+	7.49377e6i	−0.000131605	+	0.000405037i
$859$	−1.25951e10	+	9.15090e9i	−0.677995	+	0.492592i	−0.872692	−	0.488271i	$-0.837628\pi$
$859$	−1.25951e10	+	9.15090e9i	−0.677995	+	0.492592i	0.194697	+	0.980863i	$0.437628\pi$
$860$	−2.80205e9	+	8.83409e8i	−0.150221	+	0.0473606i
$861$	−4.20120e9	−	3.05235e9i	−0.224317	−	0.162976i
$862$	−1.67763e10	+	1.21887e10i	−0.892114	+	0.648159i
$863$	−6.79906e8	+	4.93980e8i	−0.0360090	+	0.0261621i	−0.605644	−	0.795736i	$-0.707085\pi$
$863$	−6.79906e8	+	4.93980e8i	−0.0360090	+	0.0261621i	0.569635	+	0.821898i	$0.307085\pi$
$864$	−5.31233e9	−	3.85964e9i	−0.280212	−	0.203586i
$865$	1.76583e10	−	2.38626e10i	0.927668	−	1.25361i
$866$	−7.23684e9	+	5.25787e9i	−0.378648	+	0.275104i
$867$	1.77936e9	−	5.47632e9i	0.0927252	−	0.285379i
$868$	−1.19736e10			−0.621448
$869$	4.91159e8	−	1.51163e9i	0.0253894	−	0.0781407i
$870$	−1.77236e7	+	2.02531e9i	−0.000912503	+	0.104274i
$871$	−5.47554e7	−	1.68520e8i	−0.00280778	−	0.00864146i
$872$	8.72904e9	+	2.68652e10i	0.445819	+	1.37209i
$873$	−1.31671e10	−	9.56648e9i	−0.669794	−	0.486634i
$874$	−1.02416e9			−0.0518894
$875$	6.61207e8	−	2.51807e10i	0.0333664	−	1.27069i
$876$	−9.99990e7			−0.00502610
$877$	−2.42556e10	−	1.76227e10i	−1.21427	−	0.882215i	−0.218654	−	0.975802i	$-0.570167\pi$
$877$	−2.42556e10	−	1.76227e10i	−1.21427	−	0.882215i	−0.995611	+	0.0935869i	$0.970167\pi$
$878$	−2.36707e9	−	7.28509e9i	−0.118027	−	0.363249i
$879$	4.62901e8	+	1.42466e9i	0.0229894	+	0.0707540i
$880$	2.21342e6	−	2.52932e8i	0.000109490	−	0.0125117i
$881$	4.62293e9	−	1.42279e10i	0.227773	−	0.701012i	−0.770226	−	0.637771i	$-0.779856\pi$
$881$	4.62293e9	−	1.42279e10i	0.227773	−	0.701012i	0.997998	−	0.0632405i	$-0.0201435\pi$
$882$	8.04424e9			0.394771
$883$	9.63492e9	−	2.96532e10i	0.470962	−	1.44947i	−0.380365	−	0.924836i	$-0.624202\pi$
$883$	9.63492e9	−	2.96532e10i	0.470962	−	1.44947i	0.851327	−	0.524636i	$-0.175798\pi$
$884$	−5.32513e8	+	3.86893e8i	−0.0259267	+	0.0188369i
$885$	3.73913e9	−	5.05289e9i	0.181330	−	0.245041i
$886$	−7.82971e9	−	5.68862e9i	−0.378205	−	0.274782i
$887$	−2.07270e10	+	1.50591e10i	−0.997251	+	0.724545i	−0.961497	−	0.274816i	$-0.911383\pi$
$887$	−2.07270e10	+	1.50591e10i	−0.997251	+	0.724545i	−0.0357537	+	0.999361i	$0.511383\pi$
$888$	5.09277e9	−	3.70011e9i	0.244067	−	0.177325i
$889$	−6.96749e9	−	5.06218e9i	−0.332598	−	0.241647i
$890$	1.32859e10	−	4.18868e9i	0.631723	−	0.199165i
$891$	1.49780e9	−	1.08821e9i	0.0709383	−	0.0515397i
$892$	5.37157e9	−	1.65320e10i	0.253410	−	0.779917i
$893$	3.58878e10			1.68642
$894$	−2.86800e8	+	8.82681e8i	−0.0134245	+	0.0413164i
$895$	7.03146e9	−	2.21682e9i	0.327842	−	0.103360i
$896$	−3.77393e9	−	1.16150e10i	−0.175273	−	0.539436i
$897$	3.33882e6	+	1.02758e7i	0.000154461	+	0.000475383i
$898$	9.85131e9	+	7.15739e9i	0.453970	+	0.329828i
$899$	−1.61299e10			−0.740413
$900$	9.43044e9	+	7.10706e9i	0.431204	+	0.324968i
$901$	2.93231e10			1.33559
$902$	1.35964e9	+	9.87837e8i	0.0616881	+	0.0448190i
$903$	−4.54033e8	−	1.39737e9i	−0.0205201	−	0.0631544i
$904$	−6.05423e8	−	1.86330e9i	−0.0272565	−	0.0838868i
$905$	−1.02067e10	−	3.41539e9i	−0.457736	−	0.153169i
$906$	−7.13310e8	+	2.19534e9i	−0.0318662	+	0.0980740i
$907$	3.72736e10			1.65873			0.829364	−	0.558708i	$-0.188703\pi$
$907$	3.72736e10			1.65873			0.829364	+	0.558708i	$0.188703\pi$
$908$	−4.08705e9	+	1.25786e10i	−0.181180	+	0.557614i
$909$	−1.49086e10	+	1.08317e10i	−0.658358	+	0.478325i
$910$	−5.94657e6	+	6.79527e8i	−0.000261590	+	0.0298925i
$911$	−3.40826e10	−	2.47625e10i	−1.49355	−	1.08512i	−0.972865	−	0.231372i	$-0.925678\pi$
$911$	−3.40826e10	−	2.47625e10i	−1.49355	−	1.08512i	−0.520680	−	0.853752i	$-0.674322\pi$
$912$	−4.52369e8	+	3.28665e8i	−0.0197474	+	0.0143474i
$913$	−1.11204e9	+	8.07943e8i	−0.0483584	+	0.0351344i
$914$	4.33347e9	+	3.14845e9i	0.187726	+	0.136391i
$915$	6.67650e9	+	2.23410e9i	0.288121	+	0.0964117i
$916$	9.66084e8	−	7.01901e8i	0.0415318	−	0.0301746i
$917$	−1.24571e9	+	3.83389e9i	−0.0533486	+	0.164190i
$918$	9.17927e9			0.391614
$919$	−6.31382e9	+	1.94319e10i	−0.268342	+	0.825871i	0.722563	+	0.691305i	$0.242964\pi$
$919$	−6.31382e9	+	1.94319e10i	−0.268342	+	0.825871i	−0.990905	+	0.134566i	$0.957036\pi$
$920$	−1.08032e9	−	1.51463e9i	−0.0457398	−	0.0641282i
$921$	1.96421e9	+	6.04521e9i	0.0828474	+	0.254978i
$922$	−3.90896e9	−	1.20305e10i	−0.164249	−	0.505507i
$923$	9.00403e8	+	6.54181e8i	0.0376904	+	0.0273837i
$924$	−3.08668e8			−0.0128718
$925$	−3.09848e10	+	2.16935e10i	−1.28722	+	0.901227i
$926$	−2.68592e10			−1.11162
$927$	−6.33350e9	−	4.60155e9i	−0.261135	−	0.189725i
$928$	−6.05330e9	−	1.86301e10i	−0.248642	−	0.765241i
$929$	5.51071e9	+	1.69602e10i	0.225503	+	0.694027i	0.998240	+	0.0593008i	$0.0188871\pi$
$929$	5.51071e9	+	1.69602e10i	0.225503	+	0.694027i	−0.772737	+	0.634726i	$0.781113\pi$
$930$	−1.57087e9	+	2.12280e9i	−0.0640396	+	0.0865402i
$931$	−4.81216e9	+	1.48103e10i	−0.195441	+	0.601506i
$932$	1.90280e9			0.0769907
$933$	1.65210e9	−	5.08465e9i	0.0665966	−	0.204963i
$934$	−1.16073e10	+	8.43323e9i	−0.466143	+	0.338672i
$935$	−2.29303e9	−	3.21487e9i	−0.0917420	−	0.128624i
$936$	−7.18634e8	−	5.22118e8i	−0.0286446	−	0.0208115i
$937$	4.68103e9	−	3.40097e9i	0.185889	−	0.135056i	−0.490949	−	0.871188i	$-0.663350\pi$
$937$	4.68103e9	−	3.40097e9i	0.185889	−	0.135056i	0.676838	+	0.736132i	$0.263350\pi$
$938$	−4.42701e9	+	3.21641e9i	−0.175146	+	0.127251i
$939$	−8.93576e8	−	6.49221e8i	−0.0352210	−	0.0255896i
$940$	1.35764e10	+	1.90344e10i	0.533135	+	0.747466i
$941$	1.13071e10	−	8.21511e9i	0.442373	−	0.321403i	−0.344204	−	0.938895i	$-0.611851\pi$
$941$	1.13071e10	−	8.21511e9i	0.442373	−	0.321403i	0.786577	+	0.617492i	$0.211851\pi$
$942$	1.38840e9	−	4.27306e9i	0.0541174	−	0.166556i
$943$	2.30454e9			0.0894937
$944$	1.68223e9	−	5.17736e9i	0.0650853	−	0.200312i
$945$	−7.15071e9	+	9.66314e9i	−0.275637	+	0.372483i
$946$	1.46939e8	+	4.52233e8i	0.00564312	+	0.0173677i
$947$	−9.60406e9	−	2.95582e10i	−0.367477	−	1.13098i	−0.948416	−	0.317030i	$-0.897314\pi$
$947$	−9.60406e9	−	2.95582e10i	−0.367477	−	1.13098i	0.580939	−	0.813947i	$-0.302686\pi$
$948$	−1.85187e9	−	1.34546e9i	−0.0705963	−	0.0512912i
$949$	−4.51980e7			−0.00171667
$950$	1.47626e10	−	1.03358e10i	0.558637	−	0.391121i
$951$	−7.17761e9			−0.270613
$952$	4.58547e10	+	3.33154e10i	1.72248	+	1.25146i
$953$	1.56190e10	+	4.80702e10i	0.584557	+	1.79908i	0.601040	+	0.799219i	$0.294753\pi$
$953$	1.56190e10	+	4.80702e10i	0.584557	+	1.79908i	−0.0164830	+	0.999864i	$0.505247\pi$
$954$	4.38555e9	+	1.34973e10i	0.163533	+	0.503302i
$955$	1.18337e10	+	1.65911e10i	0.439653	+	0.616402i
$956$	3.28220e9	−	1.01016e10i	0.121496	−	0.373926i
$957$	−4.15815e8			−0.0153359
$958$	−3.26288e8	+	1.00421e9i	−0.0119901	+	0.0369017i
$959$	−1.48282e10	+	1.07733e10i	−0.542905	+	0.394443i
$960$	−3.65914e9	−	1.22443e9i	−0.133484	−	0.0446667i
$961$	5.24367e9	+	3.80975e9i	0.190591	+	0.138473i
$962$	8.25530e8	−	5.99782e8i	0.0298965	−	0.0217211i
$963$	−5.92936e9	+	4.30793e9i	−0.213952	+	0.155445i
$964$	4.46060e9	+	3.24082e9i	0.160370	+	0.116516i
$965$	6.62884e7	−	7.57492e9i	0.00237461	−	0.271351i
$966$	2.69946e8	−	1.96127e8i	0.00963511	−	0.00700032i
$967$	−1.61793e10	+	4.97949e10i	−0.575398	+	1.77089i	0.0594220	+	0.998233i	$0.481074\pi$
$967$	−1.61793e10	+	4.97949e10i	−0.575398	+	1.77089i	−0.634820	+	0.772660i	$0.718926\pi$
$968$	−2.89354e10			−1.02534
$969$	−2.69753e9	+	8.30214e9i	−0.0952430	+	0.293128i
$970$	−1.53451e10	−	5.13481e9i	−0.539844	−	0.180644i
$971$	−3.06165e9	−	9.42279e9i	−0.107322	−	0.330303i	0.882946	−	0.469474i	$-0.155556\pi$
$971$	−3.06165e9	−	9.42279e9i	−0.107322	−	0.330303i	−0.990268	+	0.139171i	$0.955556\pi$
$972$	−2.62741e9	−	8.08635e9i	−0.0917691	−	0.282436i
$973$	5.49693e10	+	3.99375e10i	1.91304	+	1.38991i
$974$	1.80579e10			0.626196
$975$	−1.51830e8	−	1.14424e8i	−0.00524616	−	0.00395367i
$976$	6.09718e9			0.209920
$977$	−2.24948e10	−	1.63434e10i	−0.771706	−	0.560677i	0.130773	−	0.991412i	$-0.458254\pi$
$977$	−2.24948e10	−	1.63434e10i	−0.771706	−	0.560677i	−0.902478	+	0.430735i	$0.858254\pi$
$978$	−3.83461e8	−	1.18017e9i	−0.0131080	−	0.0403421i
$979$	8.83778e8	+	2.71999e9i	0.0301026	+	0.0926462i
$980$	−9.67564e9	+	3.05046e9i	−0.328389	+	0.103532i
$981$	−1.22962e10	+	3.78439e10i	−0.415844	+	1.27984i
$982$	5.94923e8			0.0200480
$983$	8.55706e9	−	2.63359e10i	0.287334	−	0.884323i	−0.698355	−	0.715751i	$-0.746084\pi$
$983$	8.55706e9	−	2.63359e10i	0.287334	−	0.884323i	0.985689	−	0.168572i	$-0.0539156\pi$
$984$	5.45988e9	−	3.96683e9i	0.182684	−	0.132728i
$985$	−2.93573e10	+	9.25553e9i	−0.978789	+	0.308585i
$986$	2.21538e10	+	1.60957e10i	0.736001	+	0.534736i
$987$	−9.45921e9	+	6.87252e9i	−0.313144	+	0.227513i
$988$	4.98925e8	−	3.62490e8i	0.0164583	−	0.0119577i
$989$	5.27510e8	+	3.83258e8i	0.0173398	+	0.0125981i
$990$	1.13685e9	−	1.53629e9i	0.0372375	−	0.0503210i
$991$	−1.99847e10	+	1.45198e10i	−0.652290	+	0.473916i	−0.864051	−	0.503405i	$-0.832080\pi$
$991$	−1.99847e10	+	1.45198e10i	−0.652290	+	0.473916i	0.211760	+	0.977322i	$0.432080\pi$
$992$	7.89261e9	−	2.42910e10i	0.256702	−	0.790049i
$993$	5.70455e8			0.0184884
$994$	1.06211e10	−	3.26884e10i	0.343019	−	1.05570i
$995$	4.57183e8	−	5.22432e10i	0.0147133	−	1.68131i
$996$	6.11727e8	+	1.88270e9i	0.0196178	+	0.0603774i
$997$	−4.60042e9	−	1.41586e10i	−0.147016	−	0.452469i	0.850249	−	0.526381i	$-0.176452\pi$
$997$	−4.60042e9	−	1.41586e10i	−0.147016	−	0.452469i	−0.997265	+	0.0739123i	$0.976452\pi$
$998$	−1.13463e10	−	8.24358e9i	−0.361325	−	0.262518i
$999$	1.80509e10			0.572822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.8.d.a.16.11	yes	68
25.6	even	5		625.8.a.d.1.13		34
25.11	even	5	inner	25.8.d.a.11.11	✓	68
25.19	even	10		625.8.a.c.1.22		34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.8.d.a.11.11	✓	68	25.11	even	5	inner
25.8.d.a.16.11	yes	68	1.1	even	1	trivial
625.8.a.c.1.22		34	25.19	even	10
625.8.a.d.1.13		34	25.6	even	5

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(6.07706 + 4.41524i) q^{2} +(2.68014 + 8.24862i) q^{3} +(-22.1179 - 68.0718i) q^{4} +(2.44590 - 279.498i) q^{5} +(-20.1323 + 61.9609i) q^{6} -1153.54 q^{7} +(463.260 - 1425.77i) q^{8} +(1708.46 - 1241.27i) q^{9} +(1248.91 - 1687.73i) q^{10} +(348.723 + 253.362i) q^{11} +(502.220 - 364.884i) q^{12} +(226.996 - 164.922i) q^{13} +(-7010.13 - 5093.16i) q^{14} +(2312.03 - 728.918i) q^{15} +(1698.48 - 1234.02i) q^{16} +(10128.2 - 31171.5i) q^{17} +15863.0 q^{18} +(-9489.41 + 29205.4i) q^{19} +(-19080.0 + 6015.40i) q^{20} +(-3091.65 - 9515.11i) q^{21} +(1000.56 + 3079.39i) q^{22} +(3591.97 + 2609.72i) q^{23} +13002.2 q^{24} +(-78113.0 - 1367.25i) q^{25} +2107.64 q^{26} +(30163.2 + 21914.9i) q^{27} +(25513.8 + 78523.5i) q^{28} +(34370.4 + 105781. i) q^{29} +(17268.7 + 5778.49i) q^{30} +(-44813.9 + 137923. i) q^{31} -176120. q^{32} +(-1155.26 + 3555.53i) q^{33} +(199180. - 144713. i) q^{34} +(-2821.44 + 322412. i) q^{35} +(-122283. - 88843.9i) q^{36} +(391685. - 284576. i) q^{37} +(-186617. + 135585. i) q^{38} +(1968.76 + 1430.39i) q^{39} +(-397365. - 132967. i) q^{40} +(419919. - 305089. i) q^{41} +(23223.4 - 71474.3i) q^{42} +146858. q^{43} +(9533.80 - 29342.0i) q^{44} +(-342754. - 480548. i) q^{45} +(10306.1 + 31718.9i) q^{46} +(-361137. - 1.11147e6i) q^{47} +(14731.1 + 10702.8i) q^{48} +507109. q^{49} +(-468661. - 353197. i) q^{50} +284267. q^{51} +(-16247.2 - 11804.3i) q^{52} +(276465. + 850871. i) q^{53} +(86544.3 + 266356. i) q^{54} +(71667.1 - 96847.6i) q^{55} +(-534388. + 1.64468e6i) q^{56} -266337. q^{57} +(-258179. + 794593. i) q^{58} +(2.09776e6 - 1.52412e6i) q^{59} +(-100756. - 141262. i) q^{60} +(2.34954e6 + 1.70704e6i) q^{61} +(-881302. + 640303. i) q^{62} +(-1.97078e6 + 1.43185e6i) q^{63} +(-1.28770e6 - 935565. i) q^{64} +(-45540.1 - 63848.2i) q^{65} +(-22719.1 + 16506.4i) q^{66} +(195149. - 600608. i) q^{67} -2.34592e6 q^{68} +(-11899.6 + 36623.3i) q^{69} +(-1.44067e6 + 1.94686e6i) q^{70} +(1.22575e6 + 3.77247e6i) q^{71} +(-978301. - 3.01090e6i) q^{72} +(-130322. - 94684.3i) q^{73} +3.63676e6 q^{74} +(-198076. - 647990. i) q^{75} +2.19795e6 q^{76} +(-402265. - 292263. i) q^{77} +(5648.77 + 17385.1i) q^{78} +(-1.13946e6 - 3.50690e6i) q^{79} +(-340751. - 477740. i) q^{80} +(1.32726e6 - 4.08487e6i) q^{81} +3.89892e6 q^{82} +(-985421. + 3.03281e6i) q^{83} +(-579330. + 420908. i) q^{84} +(-8.68760e6 - 2.90706e6i) q^{85} +(892465. + 648414. i) q^{86} +(-780432. + 567017. i) q^{87} +(522784. - 379825. i) q^{88} +(5.36779e6 + 3.89993e6i) q^{89} +(38799.2 - 4.43366e6i) q^{90} +(-261848. + 190244. i) q^{91} +(98201.7 - 302234. i) q^{92} -1.25778e6 q^{93} +(2.71274e6 - 8.34895e6i) q^{94} +(8.13963e6 + 2.72370e6i) q^{95} +(-472025. - 1.45274e6i) q^{96} +(-2.38159e6 - 7.32979e6i) q^{97} +(3.08173e6 + 2.23901e6i) q^{98} +910271. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 11 q^{2} + 23 q^{3} - 1091 q^{4} + 475 q^{5} - 179 q^{6} + 1734 q^{7} + 220 q^{8} - 14554 q^{9} + 4245 q^{10} + 466 q^{11} + 9979 q^{12} - 7407 q^{13} - 20177 q^{14} - 9285 q^{15} - 68527 q^{16}+ \cdots + 71266232 q^{99}+O(q^{100}) \) 68 * q - 11 * q^2 + 23 * q^3 - 1091 * q^4 + 475 * q^5 - 179 * q^6 + 1734 * q^7 + 220 * q^8 - 14554 * q^9 + 4245 * q^10 + 466 * q^11 + 9979 * q^12 - 7407 * q^13 - 20177 * q^14 - 9285 * q^15 - 68527 * q^16 + 71504 * q^17 + 116208 * q^18 - 48685 * q^19 - 138265 * q^20 - 2274 * q^21 - 271952 * q^22 - 63227 * q^23 + 553980 * q^24 + 276615 * q^25 + 675246 * q^26 - 270235 * q^27 - 782613 * q^28 - 99655 * q^29 - 1011285 * q^30 + 39051 * q^31 + 1045974 * q^32 + 1766456 * q^33 + 605893 * q^34 - 476935 * q^35 - 2928227 * q^36 + 83909 * q^37 + 1937525 * q^38 + 1316257 * q^39 + 2903410 * q^40 - 1964944 * q^41 - 3462547 * q^42 - 3439822 * q^43 - 3557652 * q^44 - 2121790 * q^45 + 2982521 * q^46 + 1663474 * q^47 + 1678378 * q^48 + 6584354 * q^49 + 408485 * q^50 + 3922076 * q^51 - 5301176 * q^52 + 788553 * q^53 - 6946145 * q^54 - 2630560 * q^55 - 415350 * q^56 - 14598410 * q^57 + 4727030 * q^58 - 3625740 * q^59 + 29158890 * q^60 - 4161559 * q^61 + 19658928 * q^62 + 2426738 * q^63 - 4408596 * q^64 - 2030220 * q^65 - 6985528 * q^66 + 8470434 * q^67 - 29099218 * q^68 - 360673 * q^69 - 22417320 * q^70 - 4808044 * q^71 + 25676065 * q^72 + 5517633 * q^73 + 14050068 * q^74 + 257240 * q^75 + 22502000 * q^76 - 9936772 * q^77 + 14948561 * q^78 - 5343505 * q^79 - 3987180 * q^80 - 5865817 * q^81 - 76614542 * q^82 - 645927 * q^83 + 5992628 * q^84 + 48268560 * q^85 - 27540609 * q^86 + 65370380 * q^87 - 3612320 * q^88 + 11153500 * q^89 + 7267975 * q^90 - 9123484 * q^91 - 33863736 * q^92 - 118704764 * q^93 - 30761227 * q^94 - 26382485 * q^95 + 1256206 * q^96 + 55538244 * q^97 + 102201752 * q^98 + 71266232 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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