LMFDB - Embedded newform 100.9.d.c.99.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [100,9,Mod(99,100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(100, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("100.99"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	100.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,104] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$40.7378610061$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			99.15
Character	$\chi$	$=$	100.99
Dual form			100.9.d.c.99.16

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.49522 - 15.3556i) q^{2} -98.1237 q^{3} +(-215.586 + 138.053i) q^{4} +(441.088 + 1506.74i) q^{6} +820.952 q^{7} +(3088.99 + 2689.86i) q^{8} +3067.27 q^{9} -21147.7i q^{11} +(21154.1 - 13546.3i) q^{12} +36649.1i q^{13} +(-3690.36 - 12606.2i) q^{14} +(27418.7 - 59524.7i) q^{16} -110563. i q^{17} +(-13788.0 - 47099.6i) q^{18} -184840. i q^{19} -80554.9 q^{21} +(-324735. + 95063.7i) q^{22} -181906. q^{23} +(-303103. - 263939. i) q^{24} +(562767. - 164746. i) q^{26} +342818. q^{27} +(-176986. + 113335. i) q^{28} +229647. q^{29} -388118. i q^{31} +(-1.03729e6 - 153452. i) q^{32} +2.07510e6i q^{33} +(-1.69776e6 + 497005. i) q^{34} +(-661260. + 423446. i) q^{36} +1.32611e6i q^{37} +(-2.83831e6 + 830894. i) q^{38} -3.59615e6i q^{39} -303036. q^{41} +(362112. + 1.23696e6i) q^{42} -962361. q^{43} +(2.91951e6 + 4.55916e6i) q^{44} +(817709. + 2.79327e6i) q^{46} +8.76124e6 q^{47} +(-2.69042e6 + 5.84078e6i) q^{48} -5.09084e6 q^{49} +1.08489e7i q^{51} +(-5.05952e6 - 7.90103e6i) q^{52} +577555. i q^{53} +(-1.54104e6 - 5.26416e6i) q^{54} +(2.53591e6 + 2.20825e6i) q^{56} +1.81371e7i q^{57} +(-1.03231e6 - 3.52636e6i) q^{58} -4.11725e6i q^{59} +2.10168e7 q^{61} +(-5.95976e6 + 1.74467e6i) q^{62} +2.51808e6 q^{63} +(2.30649e6 + 1.66179e7i) q^{64} +(3.18642e7 - 9.32801e6i) q^{66} -3.85926e7 q^{67} +(1.52636e7 + 2.38359e7i) q^{68} +1.78493e7 q^{69} -2.07744e7i q^{71} +(9.47475e6 + 8.25053e6i) q^{72} +2.70559e7i q^{73} +(2.03632e7 - 5.96116e6i) q^{74} +(2.55177e7 + 3.98488e7i) q^{76} -1.73613e7i q^{77} +(-5.52208e7 + 1.61655e7i) q^{78} +5.62358e7i q^{79} -5.37629e7 q^{81} +(1.36221e6 + 4.65328e6i) q^{82} -6.22189e7 q^{83} +(1.73665e7 - 1.11209e7i) q^{84} +(4.32602e6 + 1.47776e7i) q^{86} -2.25338e7 q^{87} +(5.68845e7 - 6.53251e7i) q^{88} -6.04409e7 q^{89} +3.00871e7i q^{91} +(3.92165e7 - 2.51127e7i) q^{92} +3.80836e7i q^{93} +(-3.93837e7 - 1.34534e8i) q^{94} +(1.01782e8 + 1.50573e7i) q^{96} +1.31334e8i q^{97} +(2.28844e7 + 7.81727e7i) q^{98} -6.48658e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) $ 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−4.49522	−	15.3556i	−0.280951	−	0.959722i
$2$	−4.49522	−	15.3556i	−0.280951	−	0.959722i
$3$	−98.1237			−1.21140			−0.605702	−	0.795692i	$-0.707108\pi$
$3$	−98.1237			−1.21140			−0.605702	+	0.795692i	$0.707108\pi$
$4$	−215.586	+	138.053i	−0.842133	+	0.539270i
$5$		0			0
$5$		0			0
$6$	441.088	+	1506.74i	0.340345	+	1.16261i
$7$	820.952			0.341921			0.170960	−	0.985278i	$-0.445313\pi$
$7$	820.952			0.341921			0.170960	+	0.985278i	$0.445313\pi$
$8$	3088.99	+	2689.86i	0.754148	+	0.656705i
$9$	3067.27			0.467500
$10$		0			0
$11$		−	21147.7i		−	1.44442i	−0.691674	−	0.722210i	$-0.743127\pi$
$11$		−	21147.7i		−	1.44442i	0.691674	−	0.722210i	$-0.256873\pi$
$12$	21154.1	−	13546.3i	1.02016	−	0.653274i
$13$			36649.1i			1.28319i	0.767045	+	0.641593i	$0.221726\pi$
$13$			36649.1i			1.28319i	−0.767045	+	0.641593i	$0.778274\pi$
$14$	−3690.36	−	12606.2i	−0.0960630	−	0.328149i
$15$		0			0
$16$	27418.7	−	59524.7i	0.418376	−	0.908274i
$17$		−	110563.i		−	1.32378i	−0.749603	−	0.661888i	$-0.769755\pi$
$17$		−	110563.i		−	1.32378i	0.749603	−	0.661888i	$-0.230245\pi$
$18$	−13788.0	−	47099.6i	−0.131345	−	0.448670i
$19$		−	184840.i		−	1.41834i	−0.705037	−	0.709170i	$-0.749070\pi$
$19$		−	184840.i		−	1.41834i	0.705037	−	0.709170i	$-0.250930\pi$
$20$		0			0
$21$	−80554.9			−0.414204
$22$	−324735.	+	95063.7i	−1.38624	+	0.405811i
$23$	−181906.			−0.650035			−0.325017	−	0.945708i	$-0.605370\pi$
$23$	−181906.			−0.650035			−0.325017	+	0.945708i	$0.605370\pi$
$24$	−303103.	−	263939.i	−0.913577	−	0.795535i
$25$		0			0
$26$	562767.	−	164746.i	1.23150	−	0.360513i
$27$	342818.			0.645073
$28$	−176986.	+	113335.i	−0.287943	+	0.184388i
$29$	229647.			0.324690			0.162345	−	0.986734i	$-0.448094\pi$
$29$	229647.			0.324690			0.162345	+	0.986734i	$0.448094\pi$
$30$		0			0
$31$		−	388118.i		−	0.420259i	−0.977674	−	0.210129i	$-0.932611\pi$
$31$		−	388118.i		−	0.420259i	0.977674	−	0.210129i	$-0.0673885\pi$
$32$	−1.03729e6	−	153452.i	−0.989234	−	0.146344i
$33$			2.07510e6i			1.74978i
$34$	−1.69776e6	+	497005.i	−1.27046	+	0.371916i
$35$		0			0
$36$	−661260.	+	423446.i	−0.393697	+	0.252109i
$37$			1.32611e6i			0.707576i	0.935326	+	0.353788i	$0.115107\pi$
$37$			1.32611e6i			0.707576i	−0.935326	+	0.353788i	$0.884893\pi$
$38$	−2.83831e6	+	830894.i	−1.36121	+	0.398484i
$39$		−	3.59615e6i		−	1.55446i
$40$		0			0
$41$	−303036.			−0.107240			−0.0536202	−	0.998561i	$-0.517076\pi$
$41$	−303036.			−0.107240			−0.0536202	+	0.998561i	$0.517076\pi$
$42$	362112.	+	1.23696e6i	0.116371	+	0.397521i
$43$	−962361.			−0.281491			−0.140745	−	0.990046i	$-0.544950\pi$
$43$	−962361.			−0.281491			−0.140745	+	0.990046i	$0.544950\pi$
$44$	2.91951e6	+	4.55916e6i	0.778932	+	1.21639i
$45$		0			0
$46$	817709.	+	2.79327e6i	0.182628	+	0.623853i
$47$	8.76124e6			1.79545			0.897727	−	0.440552i	$-0.145217\pi$
$47$	8.76124e6			1.79545			0.897727	+	0.440552i	$0.145217\pi$
$48$	−2.69042e6	+	5.84078e6i	−0.506822	+	1.10029i
$49$	−5.09084e6			−0.883090
$50$		0			0
$51$			1.08489e7i			1.60363i
$52$	−5.05952e6	−	7.90103e6i	−0.691984	−	1.08061i
$53$			577555.i			0.0731965i	0.999330	+	0.0365982i	$0.0116522\pi$
$53$			577555.i			0.0731965i	−0.999330	+	0.0365982i	$0.988348\pi$
$54$	−1.54104e6	−	5.26416e6i	−0.181234	−	0.619091i
$55$		0			0
$56$	2.53591e6	+	2.20825e6i	0.257859	+	0.224541i
$57$			1.81371e7i			1.71818i
$58$	−1.03231e6	−	3.52636e6i	−0.0912220	−	0.311612i
$59$		−	4.11725e6i		−	0.339781i	−0.985463	−	0.169891i	$-0.945659\pi$
$59$		−	4.11725e6i		−	0.339781i	0.985463	−	0.169891i	$-0.0543414\pi$
$60$		0			0
$61$	2.10168e7			1.51791			0.758956	−	0.651142i	$-0.225710\pi$
$61$	2.10168e7			1.51791			0.758956	+	0.651142i	$0.225710\pi$
$62$	−5.95976e6	+	1.74467e6i	−0.403332	+	0.118072i
$63$	2.51808e6			0.159848
$64$	2.30649e6	+	1.66179e7i	0.137477	+	0.990505i
$65$		0			0
$66$	3.18642e7	−	9.32801e6i	1.67930	−	0.491601i
$67$	−3.85926e7			−1.91516			−0.957580	−	0.288168i	$-0.906954\pi$
$67$	−3.85926e7			−1.91516			−0.957580	+	0.288168i	$0.906954\pi$
$68$	1.52636e7	+	2.38359e7i	0.713873	+	1.11480i
$69$	1.78493e7			0.787455
$70$		0			0
$71$		−	2.07744e7i		−	0.817515i	−0.912643	−	0.408758i	$-0.865962\pi$
$71$		−	2.07744e7i		−	0.817515i	0.912643	−	0.408758i	$-0.134038\pi$
$72$	9.47475e6	+	8.25053e6i	0.352564	+	0.307009i
$73$			2.70559e7i			0.952732i	0.879247	+	0.476366i	$0.158046\pi$
$73$			2.70559e7i			0.952732i	−0.879247	+	0.476366i	$0.841954\pi$
$74$	2.03632e7	−	5.96116e6i	0.679077	−	0.198794i
$75$		0			0
$76$	2.55177e7	+	3.98488e7i	0.764869	+	1.19443i
$77$		−	1.73613e7i		−	0.493877i
$78$	−5.52208e7	+	1.61655e7i	−1.49185	+	0.436727i
$79$			5.62358e7i			1.44379i	0.692002	+	0.721896i	$0.256729\pi$
$79$			5.62358e7i			1.44379i	−0.692002	+	0.721896i	$0.743271\pi$
$80$		0			0
$81$	−5.37629e7			−1.24894
$82$	1.36221e6	+	4.65328e6i	0.0301293	+	0.102921i
$83$	−6.22189e7			−1.31102			−0.655511	−	0.755186i	$-0.727547\pi$
$83$	−6.22189e7			−1.31102			−0.655511	+	0.755186i	$0.727547\pi$
$84$	1.73665e7	−	1.11209e7i	0.348815	−	0.223368i
$85$		0			0
$86$	4.32602e6	+	1.47776e7i	0.0790852	+	0.270153i
$87$	−2.25338e7			−0.393331
$88$	5.68845e7	−	6.53251e7i	0.948557	−	1.08931i
$89$	−6.04409e7			−0.963321			−0.481661	−	0.876358i	$-0.659966\pi$
$89$	−6.04409e7			−0.963321			−0.481661	+	0.876358i	$0.659966\pi$
$90$		0			0
$91$			3.00871e7i			0.438748i
$92$	3.92165e7	−	2.51127e7i	0.547416	−	0.350544i
$93$			3.80836e7i			0.509103i
$94$	−3.93837e7	−	1.34534e8i	−0.504435	−	1.72314i
$95$		0			0
$96$	1.01782e8	+	1.50573e7i	1.19836	+	0.177281i
$97$			1.31334e8i			1.48351i	0.670671	+	0.741755i	$0.266006\pi$
$97$			1.31334e8i			1.48351i	−0.670671	+	0.741755i	$0.733994\pi$
$98$	2.28844e7	+	7.81727e7i	0.248105	+	0.847521i
$99$		−	6.48658e7i		−	0.675266i
$100$		0			0
$101$	−1.55397e8			−1.49333			−0.746665	−	0.665200i	$-0.768346\pi$
$101$	−1.55397e8			−1.49333			−0.746665	+	0.665200i	$0.768346\pi$
$102$	1.66590e8	−	4.87680e7i	1.53904	−	0.450541i
$103$	3.83213e7			0.340480			0.170240	−	0.985403i	$-0.445546\pi$
$103$	3.83213e7			0.340480			0.170240	+	0.985403i	$0.445546\pi$
$104$	−9.85810e7	+	1.13209e8i	−0.842675	+	0.967712i
$105$		0			0
$106$	8.86868e6	−	2.59624e6i	0.0702483	−	0.0205646i
$107$	−3.36904e7			−0.257022			−0.128511	−	0.991708i	$-0.541020\pi$
$107$	−3.36904e7			−0.257022			−0.128511	+	0.991708i	$0.541020\pi$
$108$	−7.39068e7	+	4.73271e7i	−0.543237	+	0.347869i
$109$	−1.87899e8			−1.33112			−0.665562	−	0.746343i	$-0.731808\pi$
$109$	−1.87899e8			−1.33112			−0.665562	+	0.746343i	$0.731808\pi$
$110$		0			0
$111$		−	1.30123e8i		−	0.857161i
$112$	2.25094e7	−	4.88669e7i	0.143051	−	0.310558i
$113$		−	2.44191e8i		−	1.49767i	−0.662757	−	0.748835i	$-0.730614\pi$
$113$		−	2.44191e8i		−	1.49767i	0.662757	−	0.748835i	$-0.269386\pi$
$114$	2.78506e8	−	8.15304e7i	1.64898	−	0.482726i
$115$		0			0
$116$	−4.95087e7	+	3.17035e7i	−0.273432	+	0.175096i
$117$			1.12413e8i			0.599889i
$118$	−6.32226e7	+	1.85079e7i	−0.326095	+	0.0954619i
$119$		−	9.07670e7i		−	0.452627i
$120$		0			0
$121$	−2.32868e8			−1.08635
$122$	−9.44749e7	−	3.22724e8i	−0.426459	−	1.45677i
$123$	2.97350e7			0.129911
$124$	5.35809e7	+	8.36728e7i	0.226633	+	0.353914i
$125$		0			0
$126$	−1.13193e7	−	3.86665e7i	−0.0449095	−	0.153410i
$127$	−4.32402e7			−0.166216			−0.0831080	−	0.996541i	$-0.526485\pi$
$127$	−4.32402e7			−0.166216			−0.0831080	+	0.996541i	$0.526485\pi$
$128$	2.44809e8	−	1.10119e8i	0.911985	−	0.410223i
$129$	9.44304e7			0.340999
$130$		0			0
$131$		−	3.46986e8i		−	1.17822i	−0.808052	−	0.589111i	$-0.799478\pi$
$131$		−	3.46986e8i		−	1.17822i	0.808052	−	0.589111i	$-0.200522\pi$
$132$	−2.86473e8	−	4.47362e8i	−0.943602	−	1.47354i
$133$		−	1.51744e8i		−	0.484960i
$134$	1.73482e8	+	5.92611e8i	0.538066	+	1.83802i
$135$		0			0
$136$	2.97400e8	−	3.41528e8i	0.869330	−	0.998323i
$137$			4.54595e8i			1.29045i	0.763991	+	0.645227i	$0.223237\pi$
$137$			4.54595e8i			1.29045i	−0.763991	+	0.645227i	$0.776763\pi$
$138$	−8.02366e7	−	2.74086e8i	−0.221236	−	0.755738i
$139$		−	1.24500e8i		−	0.333511i	−0.985998	−	0.166755i	$-0.946671\pi$
$139$		−	1.24500e8i		−	0.333511i	0.985998	−	0.166755i	$-0.0533290\pi$
$140$		0			0
$141$	−8.59686e8			−2.17502
$142$	−3.19003e8	+	9.33856e7i	−0.784587	+	0.229682i
$143$	7.75046e8			1.85346
$144$	8.41003e7	−	1.82578e8i	0.195590	−	0.424618i
$145$		0			0
$146$	4.15459e8	−	1.21622e8i	0.914358	−	0.267671i
$147$	4.99532e8			1.06978
$148$	−1.83074e8	−	2.85891e8i	−0.381575	−	0.595873i
$149$	2.17967e8			0.442228			0.221114	−	0.975248i	$-0.429031\pi$
$149$	2.17967e8			0.442228			0.221114	+	0.975248i	$0.429031\pi$
$150$		0			0
$151$			2.00315e8i			0.385306i	0.981267	+	0.192653i	$0.0617091\pi$
$151$			2.00315e8i			0.385306i	−0.981267	+	0.192653i	$0.938291\pi$
$152$	4.97193e8	−	5.70967e8i	0.931431	−	1.06964i
$153$		−	3.39126e8i		−	0.618865i
$154$	−2.66592e8	+	7.80427e7i	−0.473985	+	0.138755i
$155$		0			0
$156$	4.96459e8	+	7.75279e8i	0.838272	+	1.30906i
$157$		−	2.01644e7i		−	0.0331885i	−0.999862	−	0.0165942i	$-0.994718\pi$
$157$		−	2.01644e7i		−	0.0331885i	0.999862	−	0.0165942i	$-0.00528235\pi$
$158$	8.63532e8	−	2.52792e8i	1.38564	−	0.405635i
$159$		−	5.66719e7i		−	0.0886705i
$160$		0			0
$161$	−1.49336e8			−0.222260
$162$	2.41676e8	+	8.25560e8i	0.350892	+	1.19864i
$163$	−1.92932e7			−0.0273309			−0.0136654	−	0.999907i	$-0.504350\pi$
$163$	−1.92932e7			−0.0273309			−0.0136654	+	0.999907i	$0.504350\pi$
$164$	6.53303e7	−	4.18350e7i	0.0903107	−	0.0578315i
$165$		0			0
$166$	2.79687e8	+	9.55405e8i	0.368333	+	1.25822i
$167$	2.03394e8			0.261500			0.130750	−	0.991415i	$-0.458261\pi$
$167$	2.03394e8			0.261500			0.130750	+	0.991415i	$0.458261\pi$
$168$	−2.48833e8	−	2.16682e8i	−0.312371	−	0.272010i
$169$	−5.27425e8			−0.646567
$170$		0			0
$171$		−	5.66952e8i		−	0.663074i
$172$	2.07472e8	−	1.32857e8i	0.237053	−	0.151800i
$173$			4.16190e8i			0.464630i	0.972641	+	0.232315i	$0.0746301\pi$
$173$			4.16190e8i			0.464630i	−0.972641	+	0.232315i	$0.925370\pi$
$174$	1.01294e8	+	3.46019e8i	0.110507	+	0.377488i
$175$		0			0
$176$	−1.25881e9	−	5.79843e8i	−1.31193	−	0.604310i
$177$			4.04000e8i			0.411612i
$178$	2.71695e8	+	9.28104e8i	0.270646	+	0.924521i
$179$			5.41911e8i			0.527856i	0.964542	+	0.263928i	$0.0850182\pi$
$179$			5.41911e8i			0.527856i	−0.964542	+	0.263928i	$0.914982\pi$
$180$		0			0
$181$	−1.43210e9			−1.33432			−0.667159	−	0.744915i	$-0.732490\pi$
$181$	−1.43210e9			−1.33432			−0.667159	+	0.744915i	$0.732490\pi$
$182$	4.62005e8	−	1.35248e8i	0.421076	−	0.123267i
$183$	−2.06224e9			−1.83880
$184$	−5.61907e8	−	4.89303e8i	−0.490222	−	0.426881i
$185$		0			0
$186$	5.84794e8	−	1.71194e8i	0.488598	−	0.143033i
$187$	−2.33816e9			−1.91209
$188$	−1.88880e9	+	1.20952e9i	−1.51201	+	0.968235i
$189$	2.81437e8			0.220564
$190$		0			0
$191$			1.75647e9i			1.31980i	0.751355	+	0.659898i	$0.229400\pi$
$191$			1.75647e9i			1.31980i	−0.751355	+	0.659898i	$0.770600\pi$
$192$	−2.26321e8	−	1.63061e9i	−0.166540	−	1.19990i
$193$			6.79519e8i			0.489748i	0.969555	+	0.244874i	$0.0787466\pi$
$193$			6.79519e8i			0.489748i	−0.969555	+	0.244874i	$0.921253\pi$
$194$	2.01671e9	−	5.90376e8i	1.42376	−	0.416794i
$195$		0			0
$196$	1.09751e9	−	7.02806e8i	0.743679	−	0.476224i
$197$			4.80726e8i			0.319178i	0.987184	+	0.159589i	$0.0510168\pi$
$197$			4.80726e8i			0.319178i	−0.987184	+	0.159589i	$0.948983\pi$
$198$	−9.96050e8	+	2.91586e8i	−0.648067	+	0.189717i
$199$			6.20901e8i			0.395922i	0.980210	+	0.197961i	$0.0634320\pi$
$199$			6.20901e8i			0.395922i	−0.980210	+	0.197961i	$0.936568\pi$
$200$		0			0
$201$	3.78685e9			2.32003
$202$	6.98541e8	+	2.38620e9i	0.419553	+	1.43318i
$203$	1.88529e8			0.111018
$204$	−1.49772e9	−	2.33886e9i	−0.864788	−	1.35047i
$205$		0			0
$206$	−1.72263e8	−	5.88445e8i	−0.0956582	−	0.326766i
$207$	−5.57955e8			−0.303891
$208$	2.18152e9	+	1.00487e9i	1.16549	+	0.536854i
$209$	−3.90894e9			−2.04868
$210$		0			0
$211$		−	2.32298e9i		−	1.17197i	−0.810322	−	0.585984i	$-0.800708\pi$
$211$		−	2.32298e9i		−	1.17197i	0.810322	−	0.585984i	$-0.199292\pi$
$212$	−7.97333e7	−	1.24513e8i	−0.0394727	−	0.0616411i
$213$			2.03846e9i			0.990341i
$214$	1.51446e8	+	5.17334e8i	0.0722107	+	0.246670i
$215$		0			0
$216$	1.05896e9	+	9.22134e8i	0.486480	+	0.423623i
$217$		−	3.18626e8i		−	0.143695i
$218$	8.44647e8	+	2.88529e9i	0.373981	+	1.27751i
$219$		−	2.65483e9i		−	1.15414i
$220$		0			0
$221$	4.05204e9			1.69865
$222$	−1.99811e9	+	5.84932e8i	−0.822636	+	0.240820i
$223$	−1.52445e9			−0.616446			−0.308223	−	0.951314i	$-0.599734\pi$
$223$	−1.52445e9			−0.616446			−0.308223	+	0.951314i	$0.599734\pi$
$224$	−8.51563e8	−	1.25977e8i	−0.338240	−	0.0500379i
$225$		0			0
$226$	−3.74969e9	+	1.09769e9i	−1.43735	+	0.420772i
$227$	−7.14722e8			−0.269174			−0.134587	−	0.990902i	$-0.542971\pi$
$227$	−7.14722e8			−0.269174			−0.134587	+	0.990902i	$0.542971\pi$
$228$	−2.50389e9	−	3.91012e9i	−0.926565	−	1.44694i
$229$	4.05044e9			1.47286			0.736428	−	0.676516i	$-0.236511\pi$
$229$	4.05044e9			1.47286			0.736428	+	0.676516i	$0.236511\pi$
$230$		0			0
$231$			1.70355e9i			0.598285i
$232$	7.09377e8	+	6.17719e8i	0.244864	+	0.213226i
$233$		−	1.91668e9i		−	0.650318i	−0.945659	−	0.325159i	$-0.894582\pi$
$233$		−	1.91668e9i		−	0.650318i	0.945659	−	0.325159i	$-0.105418\pi$
$234$	1.72616e9	−	5.05319e8i	0.575727	−	0.168540i
$235$		0			0
$236$	5.68399e8	+	8.87622e8i	0.183234	+	0.286141i
$237$		−	5.51807e9i		−	1.74901i
$238$	−1.39378e9	+	4.08017e8i	−0.434396	+	0.127166i
$239$			3.09701e9i			0.949186i	0.880205	+	0.474593i	$0.157405\pi$
$239$			3.09701e9i			0.949186i	−0.880205	+	0.474593i	$0.842595\pi$
$240$		0			0
$241$	−1.93463e9			−0.573496			−0.286748	−	0.958006i	$-0.592574\pi$
$241$	−1.93463e9			−0.573496			−0.286748	+	0.958006i	$0.592574\pi$
$242$	1.04679e9	+	3.57582e9i	0.305211	+	1.04259i
$243$	3.02619e9			0.867903
$244$	−4.53092e9	+	2.90143e9i	−1.27828	+	0.818564i
$245$		0			0
$246$	−1.33665e8	−	4.56597e8i	−0.0364988	−	0.124679i
$247$	6.77420e9			1.82000
$248$	1.04398e9	−	1.19889e9i	0.275986	−	0.316937i
$249$	6.10515e9			1.58818
$250$		0			0
$251$			5.70277e9i			1.43678i	0.695639	+	0.718391i	$0.255121\pi$
$251$			5.70277e9i			1.43678i	−0.695639	+	0.718391i	$0.744879\pi$
$252$	−5.42862e8	+	3.47629e8i	−0.134613	+	0.0862012i
$253$			3.84691e9i			0.938923i
$254$	1.94374e8	+	6.63977e8i	0.0466986	+	0.159521i
$255$		0			0
$256$	−2.79140e9	−	3.26417e9i	−0.649924	−	0.759999i
$257$			1.76094e9i			0.403656i	0.979421	+	0.201828i	$0.0646882\pi$
$257$			1.76094e9i			0.403656i	−0.979421	+	0.201828i	$0.935312\pi$
$258$	−4.24485e8	−	1.45003e9i	−0.0958041	−	0.327264i
$259$			1.08867e9i			0.241935i
$260$		0			0
$261$	7.04389e8			0.151793
$262$	−5.32816e9	+	1.55978e9i	−1.13076	+	0.331023i
$263$	2.58682e8			0.0540683			0.0270342	−	0.999635i	$-0.491394\pi$
$263$	2.58682e8			0.0540683			0.0270342	+	0.999635i	$0.491394\pi$
$264$	−5.58172e9	+	6.40995e9i	−1.14909	+	1.31959i
$265$		0			0
$266$	−2.33012e9	+	6.82124e8i	−0.465427	+	0.136250i
$267$	5.93069e9			1.16697
$268$	8.32003e9	−	5.32783e9i	1.61282	−	1.03279i
$269$	3.03788e9			0.580178			0.290089	−	0.957000i	$-0.406315\pi$
$269$	3.03788e9			0.580178			0.290089	+	0.957000i	$0.406315\pi$
$270$		0			0
$271$			1.65010e9i			0.305937i	0.988231	+	0.152968i	$0.0488833\pi$
$271$			1.65010e9i			0.305937i	−0.988231	+	0.152968i	$0.951117\pi$
$272$	−6.58123e9	−	3.03149e9i	−1.20235	−	0.553836i
$273$		−	2.95226e9i		−	0.531501i
$274$	6.98056e9	−	2.04350e9i	1.23848	−	0.362554i
$275$		0			0
$276$	−3.84807e9	+	2.46416e9i	−0.663141	+	0.424651i
$277$		−	5.17850e9i		−	0.879599i	−0.898096	−	0.439800i	$-0.855049\pi$
$277$		−	5.17850e9i		−	0.879599i	0.898096	−	0.439800i	$-0.144951\pi$
$278$	−1.91176e9	+	5.59654e8i	−0.320078	+	0.0937002i
$279$		−	1.19046e9i		−	0.196471i
$280$		0			0
$281$	8.47832e9			1.35983			0.679915	−	0.733291i	$-0.262017\pi$
$281$	8.47832e9			1.35983			0.679915	+	0.733291i	$0.262017\pi$
$282$	3.86448e9	+	1.32010e10i	0.611075	+	2.08742i
$283$	3.20005e8			0.0498898			0.0249449	−	0.999689i	$-0.492059\pi$
$283$	3.20005e8			0.0498898			0.0249449	+	0.999689i	$0.492059\pi$
$284$	2.86798e9	+	4.47868e9i	0.440861	+	0.688456i
$285$		0			0
$286$	−3.48400e9	−	1.19013e10i	−0.520732	−	1.77881i
$287$	−2.48778e8			−0.0366677
$288$	−3.18163e9	−	4.70679e8i	−0.462467	−	0.0684156i
$289$	−5.24844e9			−0.752383
$290$		0			0
$291$		−	1.28870e10i		−	1.79713i
$292$	−3.73516e9	−	5.83288e9i	−0.513780	−	0.802327i
$293$		−	7.87248e9i		−	1.06817i	−0.845430	−	0.534086i	$-0.820656\pi$
$293$		−	7.87248e9i		−	1.06817i	0.845430	−	0.534086i	$-0.179344\pi$
$294$	−2.24551e9	−	7.67059e9i	−0.300556	−	1.02669i
$295$		0			0
$296$	−3.56706e9	+	4.09634e9i	−0.464669	+	0.533617i
$297$		−	7.24983e9i		−	0.931756i
$298$	−9.79811e8	−	3.34701e9i	−0.124245	−	0.424416i
$299$		−	6.66670e9i		−	0.834116i
$300$		0			0
$301$	−7.90052e8			−0.0962475
$302$	3.07595e9	−	9.00459e8i	0.369786	−	0.108252i
$303$	1.52481e10			1.80903
$304$	−1.10025e10	−	5.06805e9i	−1.28824	−	0.593399i
$305$		0			0
$306$	−5.20747e9	+	1.52445e9i	−0.593938	+	0.173871i
$307$	−1.47434e10			−1.65976			−0.829881	−	0.557941i	$-0.811592\pi$
$307$	−1.47434e10			−1.65976			−0.829881	+	0.557941i	$0.811592\pi$
$308$	2.39678e9	+	3.74285e9i	0.266333	+	0.415910i
$309$	−3.76023e9			−0.412459
$310$		0			0
$311$			6.36308e9i			0.680184i	0.940392	+	0.340092i	$0.110458\pi$
$311$			6.36308e9i			0.680184i	−0.940392	+	0.340092i	$0.889542\pi$
$312$	9.67314e9	−	1.11085e10i	1.02082	−	1.17229i
$313$		−	4.35717e9i		−	0.453970i	−0.973898	−	0.226985i	$-0.927113\pi$
$313$		−	4.35717e9i		−	0.453970i	0.973898	−	0.226985i	$-0.0728869\pi$
$314$	−3.09636e8	+	9.06435e7i	−0.0318517	+	0.00932434i
$315$		0			0
$316$	−7.76353e9	−	1.21237e10i	−0.778594	−	1.21586i
$317$		−	1.02074e9i		−	0.101083i	−0.998722	−	0.0505413i	$-0.983905\pi$
$317$		−	1.02074e9i		−	0.101083i	0.998722	−	0.0505413i	$-0.0160947\pi$
$318$	−8.70228e8	+	2.54752e8i	−0.0850990	+	0.0249121i
$319$		−	4.85652e9i		−	0.468989i
$320$		0			0
$321$	3.30583e9			0.311358
$322$	6.71299e8	+	2.29314e9i	0.0624443	+	0.213308i
$323$	−2.04364e10			−1.87757
$324$	1.15905e10	−	7.42214e9i	1.05178	−	0.673518i
$325$		0			0
$326$	8.67271e7	+	2.96258e8i	0.00767865	+	0.0262301i
$327$	1.84373e10			1.61253
$328$	−9.36074e8	−	8.15125e8i	−0.0808751	−	0.0704253i
$329$	7.19256e9			0.613903
$330$		0			0
$331$		−	1.01219e10i		−	0.843235i	−0.906774	−	0.421617i	$-0.861463\pi$
$331$		−	1.01219e10i		−	0.843235i	0.906774	−	0.421617i	$-0.138537\pi$
$332$	1.34135e10	−	8.58951e9i	1.10405	−	0.706995i
$333$			4.06754e9i			0.330792i
$334$	−9.14299e8	−	3.12322e9i	−0.0734687	−	0.250967i
$335$		0			0
$336$	−2.20871e9	+	4.79500e9i	−0.173293	+	0.376211i
$337$		−	1.94388e9i		−	0.150713i	−0.997157	−	0.0753563i	$-0.975991\pi$
$337$		−	1.94388e9i		−	0.150713i	0.997157	−	0.0753563i	$-0.0240094\pi$
$338$	2.37089e9	+	8.09890e9i	0.181654	+	0.620525i
$339$			2.39609e10i			1.81428i
$340$		0			0
$341$	−8.20782e9			−0.607030
$342$	−8.70586e9	+	2.54857e9i	−0.636367	+	0.186291i
$343$	−8.91196e9			−0.643868
$344$	−2.97272e9	−	2.58862e9i	−0.212286	−	0.184856i
$345$		0			0
$346$	6.39083e9	−	1.87087e9i	0.445916	−	0.130538i
$347$	−2.15696e10			−1.48773			−0.743865	−	0.668330i	$-0.767009\pi$
$347$	−2.15696e10			−1.48773			−0.743865	+	0.668330i	$0.767009\pi$
$348$	4.85798e9	−	3.11087e9i	0.331237	−	0.212112i
$349$	−1.37934e10			−0.929760			−0.464880	−	0.885374i	$-0.653903\pi$
$349$	−1.37934e10			−0.929760			−0.464880	+	0.885374i	$0.653903\pi$
$350$		0			0
$351$			1.25640e10i			0.827749i
$352$	−3.24517e9	+	2.19363e10i	−0.211382	+	1.42887i
$353$			1.69884e10i			1.09409i	0.837102	+	0.547047i	$0.184248\pi$
$353$			1.69884e10i			1.09409i	−0.837102	+	0.547047i	$0.815752\pi$
$354$	6.20364e9	−	1.81607e9i	0.395033	−	0.115643i
$355$		0			0
$356$	1.30302e10	−	8.34406e9i	0.811244	−	0.519490i
$357$			8.90639e9i			0.548314i
$358$	8.32134e9	−	2.43601e9i	0.506595	−	0.148302i
$359$			1.35600e10i			0.816358i	0.912902	+	0.408179i	$0.133836\pi$
$359$			1.35600e10i			0.816358i	−0.912902	+	0.408179i	$0.866164\pi$
$360$		0			0
$361$	−1.71821e10			−1.01169
$362$	6.43761e9	+	2.19907e10i	0.374878	+	1.28057i
$363$	2.28499e10			1.31601
$364$	−4.15362e9	−	6.48637e9i	−0.236604	−	0.369484i
$365$		0			0
$366$	9.27023e9	+	3.16669e10i	0.516614	+	1.76474i
$367$	−9.93203e9			−0.547487			−0.273743	−	0.961803i	$-0.588262\pi$
$367$	−9.93203e9			−0.547487			−0.273743	+	0.961803i	$0.588262\pi$
$368$	−4.98763e9	+	1.08279e10i	−0.271959	+	0.590410i
$369$	−9.29491e8			−0.0501349
$370$		0			0
$371$			4.74145e8i			0.0250274i
$372$	−5.25756e9	−	8.21028e9i	−0.274544	−	0.428733i
$373$		−	2.08933e10i		−	1.07937i	−0.841867	−	0.539686i	$-0.818543\pi$
$373$		−	2.08933e10i		−	1.07937i	0.841867	−	0.539686i	$-0.181457\pi$
$374$	1.05105e10	+	3.59037e10i	0.537203	+	1.83507i
$375$		0			0
$376$	2.70634e10	+	2.35666e10i	1.35404	+	1.17908i
$377$			8.41636e9i			0.416638i
$378$	−1.26512e9	−	4.32162e9i	−0.0619677	−	0.211680i
$379$		−	2.78733e10i		−	1.35093i	−0.737394	−	0.675463i	$-0.763944\pi$
$379$		−	2.78733e10i		−	1.35093i	0.737394	−	0.675463i	$-0.236056\pi$
$380$		0			0
$381$	4.24289e9			0.201355
$382$	2.69715e10	−	7.89571e9i	1.26664	−	0.370798i
$383$	−3.14260e10			−1.46048			−0.730238	−	0.683193i	$-0.760591\pi$
$383$	−3.14260e10			−1.46048			−0.730238	+	0.683193i	$0.760591\pi$
$384$	−2.40216e10	+	1.08052e10i	−1.10478	+	0.496946i
$385$		0			0
$386$	1.04344e10	−	3.05459e9i	0.470022	−	0.137595i
$387$	−2.95182e9			−0.131597
$388$	−1.81311e10	−	2.83138e10i	−0.800013	−	1.24931i
$389$	2.45574e10			1.07247			0.536233	−	0.844070i	$-0.319847\pi$
$389$	2.45574e10			1.07247			0.536233	+	0.844070i	$0.319847\pi$
$390$		0			0
$391$			2.01121e10i			0.860500i
$392$	−1.57255e10	−	1.36937e10i	−0.665980	−	0.579930i
$393$			3.40476e10i			1.42730i
$394$	7.38181e9	−	2.16097e9i	0.306322	−	0.0896733i
$395$		0			0
$396$	8.95492e9	+	1.39842e10i	0.364151	+	0.568663i
$397$			3.64363e10i			1.46681i	0.679794	+	0.733403i	$0.262069\pi$
$397$			3.64363e10i			1.46681i	−0.679794	+	0.733403i	$0.737931\pi$
$398$	9.53428e9	−	2.79109e9i	0.379975	−	0.111235i
$399$			1.48897e10i			0.587483i
$400$		0			0
$401$	−1.07267e10			−0.414847			−0.207423	−	0.978251i	$-0.566508\pi$
$401$	−1.07267e10			−0.414847			−0.207423	+	0.978251i	$0.566508\pi$
$402$	−1.70227e10	−	5.81492e10i	−0.651816	−	2.22659i
$403$	1.42242e10			0.539270
$404$	3.35013e10	−	2.14530e10i	1.25758	−	0.805308i
$405$		0			0
$406$	−8.47480e8	−	2.89497e9i	−0.0311907	−	0.106547i
$407$	2.80443e10			1.02204
$408$	−2.91820e10	+	3.35120e10i	−1.05311	+	1.20937i
$409$	3.91731e7			0.00139989			0.000699947	−	1.00000i	$-0.499777\pi$
$409$	3.91731e7			0.00139989			0.000699947		1.00000i	$0.499777\pi$
$410$		0			0
$411$		−	4.46066e10i		−	1.56326i
$412$	−8.26154e9	+	5.29038e9i	−0.286729	+	0.183611i
$413$		−	3.38006e9i		−	0.116178i
$414$	2.50813e9	+	8.56771e9i	0.0853785	+	0.291651i
$415$		0			0
$416$	5.62389e9	−	3.80156e10i	0.187786	−	1.26937i
$417$			1.22164e10i			0.404016i
$418$	1.75715e10	+	6.00239e10i	0.575579	+	1.96616i
$419$		−	3.53613e10i		−	1.14729i	−0.819105	−	0.573644i	$-0.805529\pi$
$419$		−	3.53613e10i		−	1.14729i	0.819105	−	0.573644i	$-0.194471\pi$
$420$		0			0
$421$	9.81579e9			0.312462			0.156231	−	0.987721i	$-0.450066\pi$
$421$	9.81579e9			0.312462			0.156231	+	0.987721i	$0.450066\pi$
$422$	−3.56707e10	+	1.04423e10i	−1.12476	+	0.329266i
$423$	2.68731e10			0.839375
$424$	−1.55354e9	+	1.78406e9i	−0.0480685	+	0.0552009i
$425$		0			0
$426$	3.13018e10	−	9.16334e9i	0.950452	−	0.278237i
$427$	1.72537e10			0.519005
$428$	7.26317e9	−	4.65106e9i	0.216447	−	0.138604i
$429$	−7.60504e10			−2.24529
$430$		0			0
$431$			9.11726e9i			0.264214i	0.991235	+	0.132107i	$0.0421742\pi$
$431$			9.11726e9i			0.264214i	−0.991235	+	0.132107i	$0.957826\pi$
$432$	9.39962e9	−	2.04061e10i	0.269883	−	0.585903i
$433$		−	4.67005e9i		−	0.132852i	−0.997791	−	0.0664262i	$-0.978840\pi$
$433$		−	4.67005e9i		−	0.132852i	0.997791	−	0.0664262i	$-0.0211597\pi$
$434$	−4.89268e9	+	1.43229e9i	−0.137907	+	0.0403713i
$435$		0			0
$436$	4.05084e10	−	2.59400e10i	1.12098	−	0.717835i
$437$			3.36235e10i			0.921970i
$438$	−4.07664e10	+	1.19340e10i	−1.10766	+	0.324258i
$439$		−	3.39406e10i		−	0.913822i	−0.889512	−	0.456911i	$-0.848956\pi$
$439$		−	3.39406e10i		−	0.913822i	0.889512	−	0.456911i	$-0.151044\pi$
$440$		0			0
$441$	−1.56150e10			−0.412844
$442$	−1.82148e10	−	6.22213e10i	−0.477238	−	1.63023i
$443$	7.20845e9			0.187166			0.0935830	−	0.995611i	$-0.470168\pi$
$443$	7.20845e9			0.187166			0.0935830	+	0.995611i	$0.470168\pi$
$444$	1.79639e10	+	2.80527e10i	0.462241	+	0.721843i
$445$		0			0
$446$	6.85276e9	+	2.34088e10i	0.173191	+	0.591617i
$447$	−2.13878e10			−0.535717
$448$	1.89351e9	+	1.36425e10i	0.0470063	+	0.338674i
$449$	2.32977e10			0.573229			0.286614	−	0.958046i	$-0.407470\pi$
$449$	2.32977e10			0.573229			0.286614	+	0.958046i	$0.407470\pi$
$450$		0			0
$451$			6.40852e9i			0.154900i
$452$	3.37113e10	+	5.26442e10i	0.807648	+	1.26124i
$453$		−	1.96556e10i		−	0.466761i
$454$	3.21283e9	+	1.09749e10i	0.0756248	+	0.258333i
$455$		0			0
$456$	−4.87864e10	+	5.60254e10i	−1.12834	+	1.29576i
$457$			1.72652e10i			0.395829i	0.980219	+	0.197915i	$0.0634168\pi$
$457$			1.72652e10i			0.395829i	−0.980219	+	0.197915i	$0.936583\pi$
$458$	−1.82076e10	−	6.21967e10i	−0.413800	−	1.41353i
$459$		−	3.79030e10i		−	0.853932i
$460$		0			0
$461$	−5.65725e10			−1.25257			−0.626285	−	0.779594i	$-0.715425\pi$
$461$	−5.65725e10			−1.25257			−0.626285	+	0.779594i	$0.715425\pi$
$462$	2.61590e10	−	7.65785e9i	0.574187	−	0.168089i
$463$	−7.57511e10			−1.64841			−0.824205	−	0.566292i	$-0.808377\pi$
$463$	−7.57511e10			−1.64841			−0.824205	+	0.566292i	$0.808377\pi$
$464$	6.29662e9	−	1.36697e10i	0.135842	−	0.294908i
$465$		0			0
$466$	−2.94317e10	+	8.61589e9i	−0.624124	+	0.182708i
$467$	−5.63076e10			−1.18386			−0.591929	−	0.805990i	$-0.701633\pi$
$467$	−5.63076e10			−1.18386			−0.591929	+	0.805990i	$0.701633\pi$
$468$	−1.55189e10	−	2.42346e10i	−0.323502	−	0.505187i
$469$	−3.16827e10			−0.654833
$470$		0			0
$471$			1.97861e9i			0.0402046i
$472$	1.10748e10	−	1.27181e10i	0.223136	−	0.256245i
$473$			2.03518e10i			0.406591i
$474$	−8.47330e10	+	2.48049e10i	−1.67857	+	0.491388i
$475$		0			0
$476$	1.25307e10	+	1.95681e10i	0.244088	+	0.381172i
$477$			1.77152e9i			0.0342193i
$478$	4.75563e10	−	1.39218e10i	0.910955	−	0.266675i
$479$			8.37112e10i			1.59016i	0.606502	+	0.795082i	$0.292572\pi$
$479$			8.37112e10i			1.59016i	−0.606502	+	0.795082i	$0.707428\pi$
$480$		0			0
$481$	−4.86008e10			−0.907952
$482$	8.69659e9	+	2.97073e10i	0.161124	+	0.550397i
$483$	1.46534e10			0.269247
$484$	5.02031e10	−	3.21482e10i	0.914849	−	0.585835i
$485$		0			0
$486$	−1.36034e10	−	4.64688e10i	−0.243838	−	0.832945i
$487$	3.58034e10			0.636514			0.318257	−	0.948004i	$-0.396902\pi$
$487$	3.58034e10			0.636514			0.318257	+	0.948004i	$0.396902\pi$
$488$	6.49205e10	+	5.65322e10i	1.14473	+	0.996820i
$489$	1.89312e9			0.0331088
$490$		0			0
$491$		−	5.45993e10i		−	0.939423i	−0.882820	−	0.469712i	$-0.844358\pi$
$491$		−	5.45993e10i		−	0.939423i	0.882820	−	0.469712i	$-0.155642\pi$
$492$	−6.41045e9	+	4.10501e9i	−0.109403	+	0.0700574i
$493$		−	2.53905e10i		−	0.429817i
$494$	−3.04515e10	−	1.04022e11i	−0.511330	−	1.74669i
$495$		0			0
$496$	−2.31026e10	−	1.06417e10i	−0.381710	−	0.175826i
$497$		−	1.70548e10i		−	0.279525i
$498$	−2.74440e10	−	9.37479e10i	−0.446200	−	1.52421i
$499$			6.97805e10i			1.12547i	0.826639	+	0.562733i	$0.190250\pi$
$499$			6.97805e10i			1.12547i	−0.826639	+	0.562733i	$0.809750\pi$
$500$		0			0
$501$	−1.99578e10			−0.316782
$502$	8.75692e10	−	2.56352e10i	1.37891	−	0.403666i
$503$	6.40878e10			1.00116			0.500580	−	0.865691i	$-0.333120\pi$
$503$	6.40878e10			1.00116			0.500580	+	0.865691i	$0.333120\pi$
$504$	7.77831e9	+	6.77329e9i	0.120549	+	0.104973i
$505$		0			0
$506$	5.90714e10	−	1.72927e10i	0.901105	−	0.263791i
$507$	5.17529e10			0.783254
$508$	9.32198e9	−	5.96944e9i	0.139976	−	0.0896353i
$509$	1.03640e11			1.54402			0.772012	−	0.635608i	$-0.219250\pi$
$509$	1.03640e11			1.54402			0.772012	+	0.635608i	$0.219250\pi$
$510$		0			0
$511$			2.22116e10i			0.325759i
$512$	−3.75752e10	+	5.75367e10i	−0.546791	+	0.837269i
$513$		−	6.33664e10i		−	0.914933i
$514$	2.70402e10	−	7.91580e9i	0.387398	−	0.113408i
$515$		0			0
$516$	−2.03579e10	+	1.30364e10i	−0.287166	+	0.183891i
$517$		−	1.85281e11i		−	2.59339i
$518$	1.67172e10	−	4.89383e9i	0.232190	−	0.0679719i
$519$		−	4.08382e10i		−	0.562855i
$520$		0			0
$521$	−3.35410e10			−0.455225			−0.227612	−	0.973752i	$-0.573092\pi$
$521$	−3.35410e10			−0.455225			−0.227612	+	0.973752i	$0.573092\pi$
$522$	−3.16638e9	−	1.08163e10i	−0.0426463	−	0.145679i
$523$	−3.32143e10			−0.443934			−0.221967	−	0.975054i	$-0.571248\pi$
$523$	−3.32143e10			−0.443934			−0.221967	+	0.975054i	$0.571248\pi$
$524$	4.79025e10	+	7.48053e10i	0.635379	+	0.992219i
$525$		0			0
$526$	−1.16283e9	−	3.97220e9i	−0.0151906	−	0.0518906i
$527$	−4.29115e10			−0.556329
$528$	1.23519e11	+	5.68963e10i	1.58928	+	0.732063i
$529$	−4.52211e10			−0.577455
$530$		0			0
$531$		−	1.26287e10i		−	0.158848i
$532$	2.09488e10	+	3.27140e10i	0.261524	+	0.408401i
$533$		−	1.11060e10i		−	0.137609i
$534$	−2.66597e10	−	9.10690e10i	−0.327862	−	1.11997i
$535$		0			0
$536$	−1.19212e11	−	1.03809e11i	−1.44431	−	1.25769i
$537$		−	5.31743e10i		−	0.639447i
$538$	−1.36559e10	−	4.66483e10i	−0.163002	−	0.556810i
$539$			1.07660e11i			1.27555i
$540$		0			0
$541$	1.39040e11			1.62312			0.811562	−	0.584266i	$-0.198618\pi$
$541$	1.39040e11			1.62312			0.811562	+	0.584266i	$0.198618\pi$
$542$	2.53381e10	−	7.41754e9i	0.293614	−	0.0859533i
$543$	1.40523e11			1.61640
$544$	−1.69662e10	+	1.14686e11i	−0.193726	+	1.30952i
$545$		0			0
$546$	−4.53336e10	+	1.32711e10i	−0.510093	+	0.149326i
$547$	−7.05870e10			−0.788452			−0.394226	−	0.919013i	$-0.628987\pi$
$547$	−7.05870e10			−0.788452			−0.394226	+	0.919013i	$0.628987\pi$
$548$	−6.27583e10	−	9.80043e10i	−0.695903	−	1.08673i
$549$	6.44640e10			0.709623
$550$		0			0
$551$		−	4.24479e10i		−	0.460521i
$552$	5.51364e10	+	4.80123e10i	0.593857	+	0.517125i
$553$			4.61669e10i			0.493662i
$554$	−7.95187e10	+	2.32785e10i	−0.844171	+	0.247124i
$555$		0			0
$556$	1.71876e10	+	2.68404e10i	0.179852	+	0.280860i
$557$			1.36274e11i			1.41577i	0.706328	+	0.707884i	$0.250350\pi$
$557$			1.36274e11i			1.41577i	−0.706328	+	0.707884i	$0.749650\pi$
$558$	−1.82802e10	+	5.35138e9i	−0.188557	+	0.0551987i
$559$		−	3.52696e10i		−	0.361205i
$560$		0			0
$561$	2.29429e11			2.31631
$562$	−3.81119e10	−	1.30189e11i	−0.382046	−	1.30506i
$563$	−9.28198e10			−0.923862			−0.461931	−	0.886916i	$-0.652843\pi$
$563$	−9.28198e10			−0.923862			−0.461931	+	0.886916i	$0.652843\pi$
$564$	1.85336e11	−	1.18682e11i	1.83166	−	1.17292i
$565$		0			0
$566$	−1.43849e9	−	4.91386e9i	−0.0140166	−	0.0478803i
$567$	−4.41368e10			−0.427040
$568$	5.58804e10	−	6.41720e10i	0.536866	−	0.616527i
$569$	3.45537e10			0.329644			0.164822	−	0.986323i	$-0.447295\pi$
$569$	3.45537e10			0.329644			0.164822	+	0.986323i	$0.447295\pi$
$570$		0			0
$571$			9.27891e10i			0.872876i	0.899734	+	0.436438i	$0.143760\pi$
$571$			9.27891e10i			0.872876i	−0.899734	+	0.436438i	$0.856240\pi$
$572$	−1.67089e11	+	1.06997e11i	−1.56086	+	0.999515i
$573$		−	1.72351e11i		−	1.59881i
$574$	1.11831e9	+	3.82012e9i	0.0103018	+	0.0351908i
$575$		0			0
$576$	7.07460e9	+	5.09716e10i	0.0642706	+	0.463061i
$577$		−	3.75444e10i		−	0.338721i	−0.985554	−	0.169361i	$-0.945830\pi$
$577$		−	3.75444e10i		−	0.338721i	0.985554	−	0.169361i	$-0.0541702\pi$
$578$	2.35929e10	+	8.05927e10i	0.211383	+	0.722079i
$579$		−	6.66770e10i		−	0.593282i
$580$		0			0
$581$	−5.10787e10			−0.448266
$582$	−1.97887e11	+	5.79299e10i	−1.72475	+	0.504906i
$583$	1.22140e10			0.105726
$584$	−7.27767e10	+	8.35754e10i	−0.625664	+	0.718501i
$585$		0			0
$586$	−1.20886e11	+	3.53885e10i	−1.02515	+	0.300104i
$587$	2.66542e10			0.224498			0.112249	−	0.993680i	$-0.464195\pi$
$587$	2.66542e10			0.224498			0.112249	+	0.993680i	$0.464195\pi$
$588$	−1.07692e11	+	6.89620e10i	−0.900896	+	0.576900i
$589$	−7.17395e10			−0.596070
$590$		0			0
$591$		−	4.71706e10i		−	0.386653i
$592$	7.89363e10	+	3.63602e10i	0.642673	+	0.296033i
$593$			1.07542e11i			0.869681i	0.900508	+	0.434840i	$0.143195\pi$
$593$			1.07542e11i			0.869681i	−0.900508	+	0.434840i	$0.856805\pi$
$594$	−1.11325e11	+	3.25896e10i	−0.894227	+	0.261778i
$595$		0			0
$596$	−4.69907e10	+	3.00911e10i	−0.372415	+	0.238480i
$597$		−	6.09251e10i		−	0.479622i
$598$	−1.02371e11	+	2.99683e10i	−0.800519	+	0.234346i
$599$		−	5.10104e10i		−	0.396234i	−0.980178	−	0.198117i	$-0.936517\pi$
$599$		−	5.10104e10i		−	0.396234i	0.980178	−	0.198117i	$-0.0634825\pi$
$600$		0			0
$601$	1.64304e11			1.25936			0.629681	−	0.776854i	$-0.283186\pi$
$601$	1.64304e11			1.25936			0.629681	+	0.776854i	$0.283186\pi$
$602$	3.55146e9	+	1.21317e10i	0.0270409	+	0.0923709i
$603$	−1.18374e11			−0.895337
$604$	−2.76541e10	−	4.31851e10i	−0.207784	−	0.324479i
$605$		0			0
$606$	−6.85435e10	−	2.34143e11i	−0.508248	−	1.73616i
$607$	2.64985e11			1.95194			0.975969	−	0.217909i	$-0.0699235\pi$
$607$	2.64985e11			1.95194			0.975969	+	0.217909i	$0.0699235\pi$
$608$	−2.83641e10	+	1.91732e11i	−0.207565	+	1.40307i
$609$	−1.84992e10			−0.134488
$610$		0			0
$611$			3.21092e11i			2.30390i
$612$	4.68175e10	+	7.31109e10i	0.333735	+	0.521167i
$613$			2.58975e11i			1.83407i	0.398804	+	0.917036i	$0.369425\pi$
$613$			2.58975e11i			1.83407i	−0.398804	+	0.917036i	$0.630575\pi$
$614$	6.62750e10	+	2.26394e11i	0.466312	+	1.59291i
$615$		0			0
$616$	4.66995e10	−	5.36288e10i	0.324331	−	0.372456i
$617$			2.43563e10i			0.168063i	0.996463	+	0.0840313i	$0.0267796\pi$
$617$			2.43563e10i			0.168063i	−0.996463	+	0.0840313i	$0.973220\pi$
$618$	1.69031e10	+	5.77404e10i	0.115881	+	0.395846i
$619$		−	6.16901e10i		−	0.420197i	−0.977680	−	0.210098i	$-0.932622\pi$
$619$		−	6.16901e10i		−	0.420197i	0.977680	−	0.210098i	$-0.0673784\pi$
$620$		0			0
$621$	−6.23608e10			−0.419320
$622$	9.77087e10	−	2.86035e10i	0.652787	−	0.191098i
$623$	−4.96191e10			−0.329380
$624$	−2.14059e11	−	9.86015e10i	−1.41187	−	0.650347i
$625$		0			0
$626$	−6.69068e10	+	1.95864e10i	−0.435685	+	0.127543i
$627$	3.83560e11			2.48178
$628$	2.78376e9	+	4.34717e9i	0.0178975	+	0.0279491i
$629$	1.46619e11			0.936673
$630$		0			0
$631$			2.91259e10i			0.183722i	0.995772	+	0.0918611i	$0.0292816\pi$
$631$			2.91259e10i			0.183722i	−0.995772	+	0.0918611i	$0.970718\pi$
$632$	−1.51267e11	+	1.73712e11i	−0.948145	+	1.08883i
$633$			2.27940e11i			1.41973i
$634$	−1.56740e10	+	4.58844e9i	−0.0970113	+	0.0283993i
$635$		0			0
$636$	7.82373e9	+	1.22177e10i	0.0478173	+	0.0746723i
$637$		−	1.86575e11i		−	1.13317i
$638$	−7.45745e10	+	2.18311e10i	−0.450099	+	0.131763i
$639$		−	6.37207e10i		−	0.382188i
$640$		0			0
$641$	2.97316e11			1.76111			0.880555	−	0.473943i	$-0.157170\pi$
$641$	2.97316e11			1.76111			0.880555	+	0.473943i	$0.157170\pi$
$642$	−1.48604e10	−	5.07628e10i	−0.0874764	−	0.298817i
$643$	2.02204e11			1.18289			0.591447	−	0.806344i	$-0.298557\pi$
$643$	2.02204e11			1.18289			0.591447	+	0.806344i	$0.298557\pi$
$644$	3.21948e10	−	2.06163e10i	0.187173	−	0.119858i
$645$		0			0
$646$	9.18663e10	+	3.13813e11i	0.527504	+	1.80194i
$647$	−2.98562e11			−1.70380			−0.851898	−	0.523708i	$-0.824548\pi$
$647$	−2.98562e11			−1.70380			−0.851898	+	0.523708i	$0.824548\pi$
$648$	−1.66073e11	−	1.44615e11i	−0.941888	−	0.820188i
$649$	−8.70705e10			−0.490786
$650$		0			0
$651$			3.12648e10i			0.174073i
$652$	4.15934e9	−	2.66349e9i	0.0230162	−	0.0147387i
$653$		−	3.34280e10i		−	0.183847i	−0.995766	−	0.0919237i	$-0.970698\pi$
$653$		−	3.34280e10i		−	0.183847i	0.995766	−	0.0919237i	$-0.0293016\pi$
$654$	−8.28799e10	−	2.83116e11i	−0.453042	−	1.54758i
$655$		0			0
$656$	−8.30883e9	+	1.80381e10i	−0.0448668	+	0.0974037i
$657$			8.29877e10i			0.445402i
$658$	−3.23321e10	−	1.10446e11i	−0.172477	−	0.589176i
$659$		−	7.70116e10i		−	0.408333i	−0.978936	−	0.204166i	$-0.934552\pi$
$659$		−	7.70116e10i		−	0.408333i	0.978936	−	0.204166i	$-0.0654484\pi$
$660$		0			0
$661$	−2.47987e11			−1.29904			−0.649520	−	0.760344i	$-0.725030\pi$
$661$	−2.47987e11			−1.29904			−0.649520	+	0.760344i	$0.725030\pi$
$662$	−1.55427e11	+	4.55000e10i	−0.809271	+	0.236908i
$663$	−3.97601e11			−2.05775
$664$	−1.92193e11	−	1.67360e11i	−0.988704	−	0.860954i
$665$		0			0
$666$	6.24593e10	−	1.82845e10i	0.317468	−	0.0929363i
$667$	−4.17743e10			−0.211060
$668$	−4.38488e10	+	2.80791e10i	−0.220218	+	0.141019i
$669$	1.49585e11			0.746765
$670$		0			0
$671$		−	4.44457e11i		−	2.19250i
$672$	8.35585e10	+	1.23613e10i	0.409745	+	0.0606161i
$673$		−	1.03219e11i		−	0.503151i	−0.967838	−	0.251576i	$-0.919051\pi$
$673$		−	1.03219e11i		−	0.503151i	0.967838	−	0.251576i	$-0.0809487\pi$
$674$	−2.98493e10	+	8.73816e9i	−0.144642	+	0.0423429i
$675$		0			0
$676$	1.13705e11	−	7.28127e10i	0.544496	−	0.348674i
$677$		−	3.83549e10i		−	0.182585i	−0.995824	−	0.0912926i	$-0.970900\pi$
$677$		−	3.83549e10i		−	0.182585i	0.995824	−	0.0912926i	$-0.0290999\pi$
$678$	3.67933e11	−	1.07710e11i	1.74121	−	0.509725i
$679$			1.07819e11i			0.507243i
$680$		0			0
$681$	7.01312e10			0.326079
$682$	3.68959e10	+	1.26036e11i	0.170546	+	0.582580i
$683$	2.47284e10			0.113635			0.0568177	−	0.998385i	$-0.481905\pi$
$683$	2.47284e10			0.113635			0.0568177	+	0.998385i	$0.481905\pi$
$684$	7.82695e10	+	1.22227e11i	0.357576	+	0.558396i
$685$		0			0
$686$	4.00612e10	+	1.36848e11i	0.180895	+	0.617934i
$687$	−3.97444e11			−1.78422
$688$	−2.63866e10	+	5.72842e10i	−0.117769	+	0.255671i
$689$	−2.11669e10			−0.0939247
$690$		0			0
$691$			3.63864e10i			0.159598i	0.996811	+	0.0797988i	$0.0254278\pi$
$691$			3.63864e10i			0.159598i	−0.996811	+	0.0797988i	$0.974572\pi$
$692$	−5.74564e10	−	8.97248e10i	−0.250561	−	0.391281i
$693$		−	5.32517e10i		−	0.230887i
$694$	9.69601e10	+	3.31213e11i	0.417979	+	1.42781i
$695$		0			0
$696$	−6.96067e10	−	6.06129e10i	−0.296629	−	0.258302i
$697$			3.35046e10i			0.141962i
$698$	6.20045e10	+	2.11806e11i	0.261217	+	0.892311i
$699$			1.88072e11i			0.787797i
$700$		0			0
$701$	1.36852e11			0.566732			0.283366	−	0.959012i	$-0.408549\pi$
$701$	1.36852e11			0.566732			0.283366	+	0.959012i	$0.408549\pi$
$702$	1.92927e11	−	5.64778e10i	0.794409	−	0.232557i
$703$	2.45118e11			1.00358
$704$	3.51431e11	−	4.87770e10i	1.43070	−	0.198575i
$705$		0			0
$706$	2.60867e11	−	7.63667e10i	1.05003	−	0.307387i
$707$	−1.27573e11			−0.510601
$708$	−5.57735e10	−	8.70967e10i	−0.221970	−	0.346632i
$709$	−1.84677e11			−0.730848			−0.365424	−	0.930841i	$-0.619076\pi$
$709$	−1.84677e11			−0.730848			−0.365424	+	0.930841i	$0.619076\pi$
$710$		0			0
$711$			1.72490e11i			0.674972i
$712$	−1.86701e11	−	1.62578e11i	−0.726486	−	0.632618i
$713$			7.06011e10i			0.273183i
$714$	1.36763e11	−	4.00362e10i	0.526229	−	0.154049i
$715$		0			0
$716$	−7.48125e10	−	1.16828e11i	−0.284657	−	0.444525i
$717$		−	3.03890e11i		−	1.14985i
$718$	2.08221e11	−	6.09550e10i	0.783477	−	0.229357i
$719$			2.26289e11i			0.846735i	0.905958	+	0.423368i	$0.139152\pi$
$719$			2.26289e11i			0.846735i	−0.905958	+	0.423368i	$0.860848\pi$
$720$		0			0
$721$	3.14600e10			0.116417
$722$	7.72373e10	+	2.63841e11i	0.284235	+	0.970941i
$723$	1.89833e11			0.694735
$724$	3.08741e11	−	1.97706e11i	1.12367	−	0.719558i
$725$		0			0
$726$	−1.02715e11	−	3.50873e11i	−0.369733	−	1.26300i
$727$	6.89485e10			0.246824			0.123412	−	0.992356i	$-0.460616\pi$
$727$	6.89485e10			0.246824			0.123412	+	0.992356i	$0.460616\pi$
$728$	−8.09303e10	+	9.29388e10i	−0.288128	+	0.330881i
$729$	5.57976e10			0.197563
$730$		0			0
$731$			1.06402e11i			0.372631i
$732$	4.44591e11	−	2.84699e11i	1.54852	−	0.991612i
$733$		−	3.05441e11i		−	1.05806i	−0.848603	−	0.529031i	$-0.822556\pi$
$733$		−	3.05441e11i		−	1.05806i	0.848603	−	0.529031i	$-0.177444\pi$
$734$	4.46466e10	+	1.52512e11i	0.153817	+	0.525435i
$735$		0			0
$736$	1.88689e11	+	2.79140e10i	0.643036	+	0.0951284i
$737$			8.16147e11i			2.76629i
$738$	4.17827e9	+	1.42729e10i	0.0140854	+	0.0481155i
$739$			3.94495e11i			1.32271i	0.750074	+	0.661354i	$0.230018\pi$
$739$			3.94495e11i			1.32271i	−0.750074	+	0.661354i	$0.769982\pi$
$740$		0			0
$741$	−6.64710e11			−2.20475
$742$	7.28076e9	−	2.13139e9i	0.0240193	−	0.00703147i
$743$	−5.69341e10			−0.186817			−0.0934086	−	0.995628i	$-0.529776\pi$
$743$	−5.69341e10			−0.186817			−0.0934086	+	0.995628i	$0.529776\pi$
$744$	−1.02440e11	+	1.17640e11i	−0.334331	+	0.383939i
$745$		0			0
$746$	−3.20828e11	+	9.39198e10i	−1.03590	+	0.303251i
$747$	−1.90842e11			−0.612902
$748$	5.04075e11	−	3.22790e11i	1.61023	−	1.03113i
$749$	−2.76582e10			−0.0878813
$750$		0			0
$751$		−	2.12038e11i		−	0.666583i	−0.942824	−	0.333292i	$-0.891841\pi$
$751$		−	2.12038e11i		−	0.666583i	0.942824	−	0.333292i	$-0.108159\pi$
$752$	2.40222e11	−	5.21510e11i	0.751174	−	1.63076i
$753$		−	5.59577e11i		−	1.74052i
$754$	1.29238e11	−	3.78334e10i	0.399856	−	0.117055i
$755$		0			0
$756$	−6.06739e10	+	3.88533e10i	−0.185744	+	0.118943i
$757$		−	6.46697e10i		−	0.196933i	−0.995140	−	0.0984663i	$-0.968606\pi$
$757$		−	6.46697e10i		−	0.196933i	0.995140	−	0.0984663i	$-0.0313937\pi$
$758$	−4.28010e11	+	1.25297e11i	−1.29651	+	0.379544i
$759$		−	3.77473e11i		−	1.13741i
$760$		0			0
$761$	−2.88384e11			−0.859869			−0.429935	−	0.902860i	$-0.641463\pi$
$761$	−2.88384e11			−0.859869			−0.429935	+	0.902860i	$0.641463\pi$
$762$	−1.90727e10	−	6.51519e10i	−0.0565708	−	0.193245i
$763$	−1.54256e11			−0.455139
$764$	−2.42486e11	−	3.78670e11i	−0.711726	−	1.11144i
$765$		0			0
$766$	1.41267e11	+	4.82564e11i	0.410322	+	1.40165i
$767$	1.50893e11			0.436002
$768$	2.73903e11	+	3.20293e11i	0.787320	+	0.920666i
$769$	−3.09585e11			−0.885267			−0.442633	−	0.896703i	$-0.645956\pi$
$769$	−3.09585e11			−0.885267			−0.442633	+	0.896703i	$0.645956\pi$
$770$		0			0
$771$		−	1.72790e11i		−	0.488991i
$772$	−9.38097e10	−	1.46495e11i	−0.264106	−	0.412433i
$773$		−	5.21097e11i		−	1.45949i	−0.683721	−	0.729744i	$-0.739639\pi$
$773$		−	5.21097e11i		−	1.45949i	0.683721	−	0.729744i	$-0.260361\pi$
$774$	1.32691e10	+	4.53268e10i	0.0369723	+	0.126296i
$775$		0			0
$776$	−3.53271e11	+	4.05690e11i	−0.974229	+	1.11879i
$777$		−	1.06825e11i		−	0.293081i
$778$	−1.10391e11	−	3.77092e11i	−0.301311	−	1.02927i
$779$			5.60130e10i			0.152103i
$780$		0			0
$781$	−4.39332e11			−1.18083
$782$	3.08833e11	−	9.04084e10i	0.825841	−	0.241759i
$783$	7.87272e10			0.209449
$784$	−1.39584e11	+	3.03030e11i	−0.369463	+	0.802088i
$785$		0			0
$786$	5.22819e11	−	1.53051e11i	1.36981	−	0.401002i
$787$	5.00687e11			1.30517			0.652585	−	0.757715i	$-0.273684\pi$
$787$	5.00687e11			1.30517			0.652585	+	0.757715i	$0.273684\pi$
$788$	−6.63657e10	−	1.03638e11i	−0.172123	−	0.268790i
$789$	−2.53828e10			−0.0654986
$790$		0			0
$791$		−	2.00469e11i		−	0.512084i
$792$	1.74480e11	−	2.00370e11i	0.443450	−	0.509250i
$793$			7.70245e11i			1.94776i
$794$	5.59500e11	−	1.63789e11i	1.40773	−	0.412101i
$795$		0			0
$796$	−8.57173e10	−	1.33858e11i	−0.213509	−	0.333419i
$797$			4.22774e11i			1.04779i	0.851783	+	0.523896i	$0.175522\pi$
$797$			4.22774e11i			1.04779i	−0.851783	+	0.523896i	$0.824478\pi$
$798$	2.28640e11	−	6.69326e10i	0.563820	−	0.165054i
$799$		−	9.68670e11i		−	2.37678i
$800$		0			0
$801$	−1.85388e11			−0.450352
$802$	4.82187e10	+	1.64714e11i	0.116552	+	0.398137i
$803$	5.72172e11			1.37615
$804$	−8.16392e11	+	5.22787e11i	−1.95378	+	1.25112i
$805$		0			0
$806$	−6.39407e10	−	2.18420e11i	−0.151509	−	0.517550i
$807$	−2.98088e11			−0.702830
$808$	−4.80018e11	−	4.17996e11i	−1.12619	−	0.980677i
$809$	−1.06326e9			−0.00248226			−0.00124113	−	0.999999i	$-0.500395\pi$
$809$	−1.06326e9			−0.00248226			−0.00124113	+	0.999999i	$0.500395\pi$
$810$		0			0
$811$		−	2.59999e11i		−	0.601020i	−0.953779	−	0.300510i	$-0.902843\pi$
$811$		−	2.59999e11i		−	0.601020i	0.953779	−	0.300510i	$-0.0971569\pi$
$812$	−4.06443e10	+	2.60270e10i	−0.0934921	+	0.0598688i
$813$		−	1.61913e11i		−	0.370613i
$814$	−1.26065e11	−	4.30635e11i	−0.287142	−	0.980871i
$815$		0			0
$816$	6.45775e11	+	2.97461e11i	1.45653	+	0.670919i
$817$			1.77882e11i			0.399250i
$818$	−1.76092e8	−	6.01525e8i	−0.000393302	−	0.00134351i
$819$			9.22853e10i			0.205115i
$820$		0			0
$821$	−2.68005e11			−0.589889			−0.294944	−	0.955514i	$-0.595301\pi$
$821$	−2.68005e11			−0.589889			−0.294944	+	0.955514i	$0.595301\pi$
$822$	−6.84958e11	+	2.00516e11i	−1.50030	+	0.439200i
$823$	8.13596e10			0.177341			0.0886705	−	0.996061i	$-0.471738\pi$
$823$	8.13596e10			0.177341			0.0886705	+	0.996061i	$0.471738\pi$
$824$	1.18374e11	+	1.03079e11i	0.256772	+	0.223595i
$825$		0			0
$826$	−5.19027e10	+	1.51941e10i	−0.111499	+	0.0326404i
$827$	3.60895e11			0.771540			0.385770	−	0.922595i	$-0.373936\pi$
$827$	3.60895e11			0.771540			0.385770	+	0.922595i	$0.373936\pi$
$828$	1.20287e11	−	7.70275e10i	0.255917	−	0.163879i
$829$	−3.75987e11			−0.796077			−0.398038	−	0.917369i	$-0.630309\pi$
$829$	−3.75987e11			−0.796077			−0.398038	+	0.917369i	$0.630309\pi$
$830$		0			0
$831$			5.08134e11i			1.06555i
$832$	−6.09031e11	+	8.45306e10i	−1.27100	+	0.176409i
$833$			5.62859e11i			1.16901i
$834$	1.87589e11	−	5.49154e10i	0.387743	−	0.113509i
$835$		0			0
$836$	8.42713e11	−	5.39641e11i	1.72526	−	1.10479i
$837$		−	1.33054e11i		−	0.271098i
$838$	−5.42993e11	+	1.58957e11i	−1.10108	+	0.322332i
$839$			3.78533e11i			0.763935i	0.924176	+	0.381967i	$0.124753\pi$
$839$			3.78533e11i			0.763935i	−0.924176	+	0.381967i	$0.875247\pi$
$840$		0			0
$841$	−4.47509e11			−0.894576
$842$	−4.41241e10	−	1.50727e11i	−0.0877865	−	0.299876i
$843$	−8.31925e11			−1.64730
$844$	3.20695e11	+	5.00802e11i	0.632008	+	0.986953i
$845$		0			0
$846$	−1.20800e11	−	4.12651e11i	−0.235823	−	0.805566i
$847$	−1.91174e11			−0.371445
$848$	3.43788e10	+	1.58358e10i	0.0664825	+	0.0306236i
$849$	−3.14001e10			−0.0604366
$850$		0			0
$851$		−	2.41228e11i		−	0.459949i
$852$	−2.81416e11	−	4.39464e11i	−0.534061	−	0.833999i
$853$			3.42638e11i			0.647202i	0.946194	+	0.323601i	$0.104894\pi$
$853$			3.42638e11i			0.647202i	−0.946194	+	0.323601i	$0.895106\pi$
$854$	−7.75594e10	−	2.64941e11i	−0.145815	−	0.498101i
$855$		0			0
$856$	−1.04069e11	−	9.06225e10i	−0.193833	−	0.168788i
$857$		−	3.33508e11i		−	0.618277i	−0.951017	−	0.309138i	$-0.899959\pi$
$857$		−	3.33508e11i		−	0.618277i	0.951017	−	0.309138i	$-0.100041\pi$
$858$	3.41863e11	+	1.16780e12i	0.630816	+	2.15485i
$859$		−	1.00496e12i		−	1.84576i	−0.385084	−	0.922881i	$-0.625828\pi$
$859$		−	1.00496e12i		−	1.84576i	0.385084	−	0.922881i	$-0.374172\pi$
$860$		0			0
$861$	2.44110e10			0.0444194
$862$	1.40001e11	−	4.09841e10i	0.253572	−	0.0742312i
$863$	4.79204e11			0.863928			0.431964	−	0.901891i	$-0.357821\pi$
$863$	4.79204e11			0.863928			0.431964	+	0.901891i	$0.357821\pi$
$864$	−3.55601e11	−	5.26063e10i	−0.638128	−	0.0944023i
$865$		0			0
$866$	−7.17111e10	+	2.09929e10i	−0.127501	+	0.0373251i
$867$	5.14997e11			0.911440
$868$	4.39873e10	+	6.86913e10i	0.0774905	+	0.121010i
$869$	1.18926e12			2.08544
$870$		0			0
$871$		−	1.41438e12i		−	2.45751i
$872$	−5.80418e11	−	5.05422e11i	−1.00386	−	0.874155i
$873$			4.02837e11i			0.693541i
$874$	5.16307e11	−	1.51145e11i	0.884835	−	0.259029i
$875$		0			0
$876$	3.66507e11	+	5.72344e11i	0.622395	+	0.971943i
$877$			4.59890e11i			0.777420i	0.921360	+	0.388710i	$0.127079\pi$
$877$			4.59890e11i			0.777420i	−0.921360	+	0.388710i	$0.872921\pi$
$878$	−5.21177e11	+	1.52570e11i	−0.877015	+	0.256739i
$879$			7.72477e11i			1.29399i
$880$		0			0
$881$	7.20232e11			1.19555			0.597777	−	0.801663i	$-0.296051\pi$
$881$	7.20232e11			1.19555			0.597777	+	0.801663i	$0.296051\pi$
$882$	7.01927e10	+	2.39776e11i	0.115989	+	0.396216i
$883$	−8.35891e11			−1.37501			−0.687507	−	0.726178i	$-0.741295\pi$
$883$	−8.35891e11			−1.37501			−0.687507	+	0.726178i	$0.741295\pi$
$884$	−8.73563e11	+	5.59396e11i	−1.43049	+	0.916032i
$885$		0			0
$886$	−3.24036e10	−	1.10690e11i	−0.0525845	−	0.179627i
$887$	−2.07019e11			−0.334439			−0.167219	−	0.985920i	$-0.553479\pi$
$887$	−2.07019e11			−0.334439			−0.167219	+	0.985920i	$0.553479\pi$
$888$	3.50013e11	−	4.01949e11i	0.562902	−	0.646426i
$889$	−3.54981e10			−0.0568327
$890$		0			0
$891$			1.13696e12i			1.80400i
$892$	3.28651e11	−	2.10456e11i	0.519129	−	0.332431i
$893$		−	1.61942e12i		−	2.54657i
$894$	9.61427e10	+	3.28421e11i	0.150510	+	0.514140i
$895$		0			0
$896$	2.00976e11	−	9.04020e10i	0.311827	−	0.140264i
$897$			6.54162e11i			1.01045i
$898$	−1.04728e11	−	3.57749e11i	−0.161049	−	0.550140i
$899$		−	8.91301e10i		−	0.136454i
$900$		0			0
$901$	6.38563e10			0.0968957
$902$	9.84064e10	−	2.88077e10i	0.148661	−	0.0435194i
$903$	7.75228e10			0.116595
$904$	6.56841e11	−	7.54303e11i	0.983527	−	1.12946i
$905$		0			0
$906$	−3.01823e11	+	8.83564e10i	−0.447961	+	0.131137i
$907$	−1.16689e12			−1.72426			−0.862128	−	0.506690i	$-0.830869\pi$
$907$	−1.16689e12			−1.72426			−0.862128	+	0.506690i	$0.830869\pi$
$908$	1.54084e11	−	9.86696e10i	0.226681	−	0.145158i
$909$	−4.76643e11			−0.698132
$910$		0			0
$911$			1.15580e12i			1.67806i	0.544084	+	0.839031i	$0.316877\pi$
$911$			1.15580e12i			1.67806i	−0.544084	+	0.839031i	$0.683123\pi$
$912$	1.07961e12	+	4.97296e11i	1.56058	+	0.718846i
$913$			1.31579e12i			1.89366i
$914$	2.65117e11	−	7.76110e10i	0.379886	−	0.111209i
$915$		0			0
$916$	−8.73218e11	+	5.59176e11i	−1.24034	+	0.794267i
$917$		−	2.84859e11i		−	0.402858i
$918$	−5.82022e11	+	1.70382e11i	−0.819537	+	0.239913i
$919$			1.20572e11i			0.169038i	0.996422	+	0.0845192i	$0.0269354\pi$
$919$			1.20572e11i			0.169038i	−0.996422	+	0.0845192i	$0.973065\pi$
$920$		0			0
$921$	1.44668e12			2.01064
$922$	2.54306e11	+	8.68702e11i	0.351911	+	1.20212i
$923$	7.61364e11			1.04902
$924$	−2.35181e11	−	3.67262e11i	−0.322637	−	0.503835i
$925$		0			0
$926$	3.40518e11	+	1.16320e12i	0.463123	+	1.58201i
$927$	1.17542e11			0.159174
$928$	−2.38210e11	−	3.52399e10i	−0.321194	−	0.0475163i
$929$	−7.85328e11			−1.05436			−0.527179	−	0.849754i	$-0.676750\pi$
$929$	−7.85328e11			−1.05436			−0.527179	+	0.849754i	$0.676750\pi$
$930$		0			0
$931$			9.40988e11i			1.25252i
$932$	2.64603e11	+	4.13209e11i	0.350697	+	0.547654i
$933$		−	6.24370e11i		−	0.823977i
$934$	2.53115e11	+	8.64635e11i	0.332606	+	1.13617i
$935$		0			0
$936$	−3.02374e11	+	3.47241e11i	−0.393950	+	0.452405i
$937$		−	4.90137e11i		−	0.635856i	−0.948115	−	0.317928i	$-0.897013\pi$
$937$		−	4.90137e11i		−	0.635856i	0.948115	−	0.317928i	$-0.102987\pi$
$938$	1.42421e11	+	4.86505e11i	0.183976	+	0.628458i
$939$			4.27542e11i			0.549941i
$940$		0			0
$941$	5.66225e11			0.722155			0.361077	−	0.932536i	$-0.382409\pi$
$941$	5.66225e11			0.722155			0.361077	+	0.932536i	$0.382409\pi$
$942$	3.03826e10	−	8.89428e9i	0.0385853	−	0.0112955i
$943$	5.51241e10			0.0697100
$944$	−2.45078e11	−	1.12889e11i	−0.308614	−	0.142156i
$945$		0			0
$946$	3.12513e11	−	9.14856e10i	0.390214	−	0.114232i
$947$	−3.38620e10			−0.0421029			−0.0210515	−	0.999778i	$-0.506701\pi$
$947$	−3.38620e10			−0.0421029			−0.0210515	+	0.999778i	$0.506701\pi$
$948$	7.61786e11	+	1.18962e12i	0.943191	+	1.47290i
$949$	−9.91575e11			−1.22253
$950$		0			0
$951$			1.00159e11i			0.122452i
$952$	2.44151e11	−	2.80378e11i	0.297242	−	0.341347i
$953$			2.54903e11i			0.309032i	0.987990	+	0.154516i	$0.0493819\pi$
$953$			2.54903e11i			0.309032i	−0.987990	+	0.154516i	$0.950618\pi$
$954$	2.72026e10	−	7.96335e9i	0.0328410	−	0.00961396i
$955$		0			0
$956$	−4.27552e11	−	6.67673e11i	−0.511868	−	0.799341i
$957$			4.76540e11i			0.568135i
$958$	1.28543e12	−	3.76300e11i	1.52611	−	0.446758i
$959$			3.73201e11i			0.441233i
$960$		0			0
$961$	7.02256e11			0.823383
$962$	2.18471e11	+	7.46292e11i	0.255090	+	0.871382i
$963$	−1.03337e11			−0.120158
$964$	4.17080e11	−	2.67082e11i	0.482960	−	0.309269i
$965$		0			0
$966$	−6.58704e10	−	2.25012e11i	−0.0756453	−	0.258402i
$967$	9.19624e11			1.05173			0.525865	−	0.850568i	$-0.323742\pi$
$967$	9.19624e11			1.05173			0.525865	+	0.850568i	$0.323742\pi$
$968$	−7.19327e11	−	6.26384e11i	−0.819266	−	0.713410i
$969$	2.00530e12			2.27449
$970$		0			0
$971$		−	1.35436e12i		−	1.52355i	−0.647840	−	0.761776i	$-0.724328\pi$
$971$		−	1.35436e12i		−	1.52355i	0.647840	−	0.761776i	$-0.275672\pi$
$972$	−6.52404e11	+	4.17775e11i	−0.730889	+	0.468034i
$973$		−	1.02208e11i		−	0.114034i
$974$	−1.60944e11	−	5.49781e11i	−0.178829	−	0.610877i
$975$		0			0
$976$	5.76251e11	−	1.25102e12i	0.635057	−	1.37868i
$977$		−	1.38499e12i		−	1.52008i	−0.649874	−	0.760042i	$-0.725178\pi$
$977$		−	1.38499e12i		−	1.52008i	0.649874	−	0.760042i	$-0.274822\pi$
$978$	−8.50999e9	−	2.90699e10i	−0.00930194	−	0.0317752i
$979$			1.27819e12i			1.39144i
$980$		0			0
$981$	−5.76336e11			−0.622300
$982$	−8.38403e11	+	2.45436e11i	−0.901585	+	0.263932i
$983$	−1.57780e12			−1.68981			−0.844905	−	0.534916i	$-0.820343\pi$
$983$	−1.57780e12			−1.68981			−0.844905	+	0.534916i	$0.820343\pi$
$984$	9.18511e10	+	7.99831e10i	0.0979724	+	0.0853135i
$985$		0			0
$986$	−3.89885e11	+	1.14136e11i	−0.412505	+	0.120758i
$987$	−7.05761e11			−0.743685
$988$	−1.46042e12	+	9.35200e11i	−1.53268	+	0.981469i
$989$	1.75060e11			0.182979
$990$		0			0
$991$			1.83814e11i			0.190583i	0.995449	+	0.0952917i	$0.0303784\pi$
$991$			1.83814e11i			0.190583i	−0.995449	+	0.0952917i	$0.969622\pi$
$992$	−5.95576e10	+	4.02590e11i	−0.0615022	+	0.415734i
$993$			9.93195e11i			1.02150i
$994$	−2.61886e11	+	7.66651e10i	−0.268267	+	0.0785330i
$995$		0			0
$996$	−1.31618e12	+	8.42835e11i	−1.33746	+	0.856456i
$997$		−	2.34014e11i		−	0.236844i	−0.992963	−	0.118422i	$-0.962217\pi$
$997$		−	2.34014e11i		−	0.236844i	0.992963	−	0.118422i	$-0.0377835\pi$
$998$	1.07152e12	−	3.13679e11i	1.08013	−	0.316201i
$999$			4.54615e11i			0.456438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.9.d.c.99.15		32
4.3	odd	2	inner	100.9.d.c.99.17		32
5.2	odd	4		100.9.b.d.51.15		16
5.3	odd	4		20.9.b.a.11.2	yes	16
5.4	even	2	inner	100.9.d.c.99.18		32
15.8	even	4		180.9.c.a.91.15		16
20.3	even	4		20.9.b.a.11.1	✓	16
20.7	even	4		100.9.b.d.51.16		16
20.19	odd	2	inner	100.9.d.c.99.16		32
40.3	even	4		320.9.b.d.191.4		16
40.13	odd	4		320.9.b.d.191.13		16
60.23	odd	4		180.9.c.a.91.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.9.b.a.11.1	✓	16	20.3	even	4
20.9.b.a.11.2	yes	16	5.3	odd	4
100.9.b.d.51.15		16	5.2	odd	4
100.9.b.d.51.16		16	20.7	even	4
100.9.d.c.99.15		32	1.1	even	1	trivial
100.9.d.c.99.16		32	20.19	odd	2	inner
100.9.d.c.99.17		32	4.3	odd	2	inner
100.9.d.c.99.18		32	5.4	even	2	inner
180.9.c.a.91.15		16	15.8	even	4
180.9.c.a.91.16		16	60.23	odd	4
320.9.b.d.191.4		16	40.3	even	4
320.9.b.d.191.13		16	40.13	odd	4

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	100.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.49522 - 15.3556i) q^{2} -98.1237 q^{3} +(-215.586 + 138.053i) q^{4} +(441.088 + 1506.74i) q^{6} +820.952 q^{7} +(3088.99 + 2689.86i) q^{8} +3067.27 q^{9} -21147.7i q^{11} +(21154.1 - 13546.3i) q^{12} +36649.1i q^{13} +(-3690.36 - 12606.2i) q^{14} +(27418.7 - 59524.7i) q^{16} -110563. i q^{17} +(-13788.0 - 47099.6i) q^{18} -184840. i q^{19} -80554.9 q^{21} +(-324735. + 95063.7i) q^{22} -181906. q^{23} +(-303103. - 263939. i) q^{24} +(562767. - 164746. i) q^{26} +342818. q^{27} +(-176986. + 113335. i) q^{28} +229647. q^{29} -388118. i q^{31} +(-1.03729e6 - 153452. i) q^{32} +2.07510e6i q^{33} +(-1.69776e6 + 497005. i) q^{34} +(-661260. + 423446. i) q^{36} +1.32611e6i q^{37} +(-2.83831e6 + 830894. i) q^{38} -3.59615e6i q^{39} -303036. q^{41} +(362112. + 1.23696e6i) q^{42} -962361. q^{43} +(2.91951e6 + 4.55916e6i) q^{44} +(817709. + 2.79327e6i) q^{46} +8.76124e6 q^{47} +(-2.69042e6 + 5.84078e6i) q^{48} -5.09084e6 q^{49} +1.08489e7i q^{51} +(-5.05952e6 - 7.90103e6i) q^{52} +577555. i q^{53} +(-1.54104e6 - 5.26416e6i) q^{54} +(2.53591e6 + 2.20825e6i) q^{56} +1.81371e7i q^{57} +(-1.03231e6 - 3.52636e6i) q^{58} -4.11725e6i q^{59} +2.10168e7 q^{61} +(-5.95976e6 + 1.74467e6i) q^{62} +2.51808e6 q^{63} +(2.30649e6 + 1.66179e7i) q^{64} +(3.18642e7 - 9.32801e6i) q^{66} -3.85926e7 q^{67} +(1.52636e7 + 2.38359e7i) q^{68} +1.78493e7 q^{69} -2.07744e7i q^{71} +(9.47475e6 + 8.25053e6i) q^{72} +2.70559e7i q^{73} +(2.03632e7 - 5.96116e6i) q^{74} +(2.55177e7 + 3.98488e7i) q^{76} -1.73613e7i q^{77} +(-5.52208e7 + 1.61655e7i) q^{78} +5.62358e7i q^{79} -5.37629e7 q^{81} +(1.36221e6 + 4.65328e6i) q^{82} -6.22189e7 q^{83} +(1.73665e7 - 1.11209e7i) q^{84} +(4.32602e6 + 1.47776e7i) q^{86} -2.25338e7 q^{87} +(5.68845e7 - 6.53251e7i) q^{88} -6.04409e7 q^{89} +3.00871e7i q^{91} +(3.92165e7 - 2.51127e7i) q^{92} +3.80836e7i q^{93} +(-3.93837e7 - 1.34534e8i) q^{94} +(1.01782e8 + 1.50573e7i) q^{96} +1.31334e8i q^{97} +(2.28844e7 + 7.81727e7i) q^{98} -6.48658e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 104 q^{4} + 8736 q^{6} + 77600 q^{9} - 136944 q^{14} - 162848 q^{16} + 828992 q^{21} - 327584 q^{24} + 2074248 q^{26} - 5529792 q^{29} - 7587928 q^{34} - 10937832 q^{36} - 17152896 q^{41} - 33842400 q^{44}+ \cdots - 906779904 q^{96}+O(q^{100}) \) 32 * q + 104 * q^4 + 8736 * q^6 + 77600 * q^9 - 136944 * q^14 - 162848 * q^16 + 828992 * q^21 - 327584 * q^24 + 2074248 * q^26 - 5529792 * q^29 - 7587928 * q^34 - 10937832 * q^36 - 17152896 * q^41 - 33842400 * q^44 - 15948304 * q^46 + 65607200 * q^49 - 17797408 * q^54 + 68269536 * q^56 + 16743424 * q^61 + 95087744 * q^64 + 38716000 * q^66 - 15054528 * q^69 + 276421752 * q^74 + 5140800 * q^76 + 281173344 * q^81 - 139523648 * q^84 - 203449344 * q^86 - 213294912 * q^89 - 110529264 * q^94 - 906779904 * q^96

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