LMFDB - Embedded newform 429.2.bi.a.5.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.16
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.655660 + 1.28681i) q^{2} +(-0.748233 + 1.56210i) q^{3} +(-0.0504074 - 0.0693798i) q^{4} +(-2.04378 + 1.04136i) q^{5} +(-1.51953 - 1.98704i) q^{6} +(-1.36274 - 0.215838i) q^{7} +(-2.73054 + 0.432475i) q^{8} +(-1.88029 - 2.33763i) q^{9} +O(q^{10})$	\(q+(-0.655660 + 1.28681i) q^{2} +(-0.748233 + 1.56210i) q^{3} +(-0.0504074 - 0.0693798i) q^{4} +(-2.04378 + 1.04136i) q^{5} +(-1.51953 - 1.98704i) q^{6} +(-1.36274 - 0.215838i) q^{7} +(-2.73054 + 0.432475i) q^{8} +(-1.88029 - 2.33763i) q^{9} -3.31273i q^{10} +(2.79966 - 1.77818i) q^{11} +(0.146095 - 0.0268289i) q^{12} +(-0.483797 + 3.57295i) q^{13} +(1.17124 - 1.61207i) q^{14} +(-0.0974779 - 3.97177i) q^{15} +(1.28680 - 3.96035i) q^{16} +(1.09871 - 3.38148i) q^{17} +(4.24090 - 0.886884i) q^{18} +(-1.67554 + 0.265379i) q^{19} +(0.175271 + 0.0893052i) q^{20} +(1.35681 - 1.96724i) q^{21} +(0.452552 + 4.76849i) q^{22} -5.26387 q^{23} +(1.36751 - 4.58896i) q^{24} +(0.153697 - 0.211546i) q^{25} +(-4.28048 - 2.96519i) q^{26} +(5.05850 - 1.18811i) q^{27} +(0.0537176 + 0.105427i) q^{28} +(5.74667 + 7.90962i) q^{29} +(5.17481 + 2.47870i) q^{30} +(4.69354 + 2.39148i) q^{31} +(0.342800 + 0.342800i) q^{32} +(0.682897 + 5.70383i) q^{33} +(3.63093 + 3.63093i) q^{34} +(3.00992 - 0.977983i) q^{35} +(-0.0674034 + 0.248288i) q^{36} +(-11.4419 - 1.81222i) q^{37} +(0.757092 - 2.33009i) q^{38} +(-5.21929 - 3.42913i) q^{39} +(5.13027 - 3.72736i) q^{40} +(-1.68364 - 10.6301i) q^{41} +(1.64185 + 3.03579i) q^{42} -1.17448i q^{43} +(-0.264493 - 0.104606i) q^{44} +(6.27723 + 2.81954i) q^{45} +(3.45131 - 6.77358i) q^{46} +(-4.49337 + 0.711680i) q^{47} +(5.22363 + 4.97337i) q^{48} +(-4.84691 - 1.57486i) q^{49} +(0.171445 + 0.336480i) q^{50} +(4.46011 + 4.24643i) q^{51} +(0.272277 - 0.146537i) q^{52} +(3.23142 - 1.04995i) q^{53} +(-1.78779 + 7.28830i) q^{54} +(-3.87016 + 6.54967i) q^{55} +3.81437 q^{56} +(0.839145 - 2.81592i) q^{57} +(-13.9460 + 2.20883i) q^{58} +(0.675878 - 4.26733i) q^{59} +(-0.270647 + 0.206970i) q^{60} +(1.78987 - 5.50865i) q^{61} +(-6.15473 + 4.47167i) q^{62} +(2.05781 + 3.59143i) q^{63} +(7.25483 - 2.35724i) q^{64} +(-2.73195 - 7.80614i) q^{65} +(-7.78746 - 2.86102i) q^{66} +(-1.80650 + 1.80650i) q^{67} +(-0.289990 + 0.0942233i) q^{68} +(3.93860 - 8.22268i) q^{69} +(-0.715012 + 4.51441i) q^{70} +(-14.2934 + 7.28286i) q^{71} +(6.14518 + 5.56980i) q^{72} +(1.53400 + 0.242962i) q^{73} +(9.83396 - 13.5353i) q^{74} +(0.215454 + 0.398375i) q^{75} +(0.102871 + 0.102871i) q^{76} +(-4.19901 + 1.81894i) q^{77} +(7.83471 - 4.46787i) q^{78} +(2.72905 + 8.39915i) q^{79} +(1.49422 + 9.43413i) q^{80} +(-1.92899 + 8.79085i) q^{81} +(14.7828 + 4.80321i) q^{82} +(-5.12809 + 2.61289i) q^{83} +(-0.204880 + 0.00502831i) q^{84} +(1.27581 + 8.05517i) q^{85} +(1.51133 + 0.770062i) q^{86} +(-16.6554 + 3.05862i) q^{87} +(-6.87555 + 6.06618i) q^{88} +(-9.80067 + 9.80067i) q^{89} +(-7.74393 + 6.22891i) q^{90} +(1.43047 - 4.76459i) q^{91} +(0.265338 + 0.365206i) q^{92} +(-7.24758 + 5.54238i) q^{93} +(2.03033 - 6.24871i) q^{94} +(3.14808 - 2.28721i) q^{95} +(-0.791980 + 0.278992i) q^{96} +(-6.96600 - 3.54935i) q^{97} +(5.20446 - 5.20446i) q^{98} +(-9.42090 - 3.20104i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−0.655660	+	1.28681i	−0.463622	+	0.909909i	0.534289	+	0.845302i	$0.320579\pi$
$2$	−0.655660	+	1.28681i	−0.463622	+	0.909909i	−0.997911	+	0.0646070i	$0.979421\pi$
$3$	−0.748233	+	1.56210i	−0.431993	+	0.901877i
$3$	−0.748233	+	1.56210i	−0.431993	+	0.901877i
$4$	−0.0504074	−	0.0693798i	−0.0252037	−	0.0346899i
$5$	−2.04378	+	1.04136i	−0.914008	+	0.465710i	−0.846729	−	0.532024i	$-0.821432\pi$
$5$	−2.04378	+	1.04136i	−0.914008	+	0.465710i	−0.0672787	+	0.997734i	$0.521432\pi$
$6$	−1.51953	−	1.98704i	−0.620345	−	0.811204i
$7$	−1.36274	−	0.215838i	−0.515069	−	0.0815789i	−0.106512	−	0.994311i	$-0.533968\pi$
$7$	−1.36274	−	0.215838i	−0.515069	−	0.0815789i	−0.408558	+	0.912733i	$0.633968\pi$
$8$	−2.73054	+	0.432475i	−0.965392	+	0.152903i
$9$	−1.88029	−	2.33763i	−0.626765	−	0.779209i
$10$		−	3.31273i		−	1.04758i
$11$	2.79966	−	1.77818i	0.844128	−	0.536142i
$11$	2.79966	−	1.77818i	0.844128	−	0.536142i
$12$	0.146095	−	0.0268289i	0.0421739	−	0.00774485i
$13$	−0.483797	+	3.57295i	−0.134181	+	0.990957i
$13$	−0.483797	+	3.57295i	−0.134181	+	0.990957i
$14$	1.17124	−	1.61207i	0.313027	−	0.430844i
$15$	−0.0974779	−	3.97177i	−0.0251687	−	1.02551i
$16$	1.28680	−	3.96035i	0.321699	−	0.990088i
$17$	1.09871	−	3.38148i	0.266476	−	0.820130i	−0.724873	−	0.688882i	$-0.758102\pi$
$17$	1.09871	−	3.38148i	0.266476	−	0.820130i	0.991350	−	0.131247i	$-0.0418982\pi$
$18$	4.24090	−	0.886884i	0.999590	−	0.209041i
$19$	−1.67554	+	0.265379i	−0.384395	+	0.0608821i	−0.345641	−	0.938367i	$-0.612339\pi$
$19$	−1.67554	+	0.265379i	−0.384395	+	0.0608821i	−0.0387532	+	0.999249i	$0.512339\pi$
$20$	0.175271	+	0.0893052i	0.0391918	+	0.0199692i
$21$	1.35681	−	1.96724i	0.296080	−	0.429288i
$22$	0.452552	+	4.76849i	0.0964844	+	1.01665i
$23$	−5.26387			−1.09759			−0.548796	−	0.835956i	$-0.684914\pi$
$23$	−5.26387			−1.09759			−0.548796	+	0.835956i	$0.684914\pi$
$24$	1.36751	−	4.58896i	0.279143	−	0.936718i
$25$	0.153697	−	0.211546i	0.0307394	−	0.0423091i
$26$	−4.28048	−	2.96519i	−0.839471	−	0.581522i
$27$	5.05850	−	1.18811i	0.973508	−	0.228652i
$28$	0.0537176	+	0.105427i	0.0101517	+	0.0199238i
$29$	5.74667	+	7.90962i	1.06713	+	1.46878i	0.872948	+	0.487813i	$0.162205\pi$
$29$	5.74667	+	7.90962i	1.06713	+	1.46878i	0.194182	+	0.980965i	$0.437795\pi$
$30$	5.17481	+	2.47870i	0.944786	+	0.452546i
$31$	4.69354	+	2.39148i	0.842984	+	0.429522i	0.821473	−	0.570247i	$-0.193152\pi$
$31$	4.69354	+	2.39148i	0.842984	+	0.429522i	0.0215105	+	0.999769i	$0.493152\pi$
$32$	0.342800	+	0.342800i	0.0605990	+	0.0605990i
$33$	0.682897	+	5.70383i	0.118877	+	0.992909i
$34$	3.63093	+	3.63093i	0.622699	+	0.622699i
$35$	3.00992	−	0.977983i	0.508770	−	0.165309i
$36$	−0.0674034	+	0.248288i	−0.0112339	+	0.0413814i
$37$	−11.4419	−	1.81222i	−1.88104	−	0.297927i	−0.892751	−	0.450550i	$-0.851228\pi$
$37$	−11.4419	−	1.81222i	−1.88104	−	0.297927i	−0.988284	+	0.152623i	$0.951228\pi$
$38$	0.757092	−	2.33009i	0.122816	−	0.377990i
$39$	−5.21929	−	3.42913i	−0.835756	−	0.549101i
$40$	5.13027	−	3.72736i	0.811168	−	0.589348i
$41$	−1.68364	−	10.6301i	−0.262941	−	1.66014i	−0.666736	−	0.745294i	$-0.732309\pi$
$41$	−1.68364	−	10.6301i	−0.262941	−	1.66014i	0.403795	−	0.914849i	$-0.367691\pi$
$42$	1.64185	+	3.03579i	0.253343	+	0.468433i
$43$		−	1.17448i		−	0.179107i	−0.995982	−	0.0895535i	$-0.971456\pi$
$43$		−	1.17448i		−	0.179107i	0.995982	−	0.0895535i	$-0.0285440\pi$
$44$	−0.264493	−	0.104606i	−0.0398739	−	0.0157700i
$45$	6.27723	+	2.81954i	0.935753	+	0.420312i
$46$	3.45131	−	6.77358i	0.508868	−	0.998709i
$47$	−4.49337	+	0.711680i	−0.655425	+	0.103809i	−0.475285	−	0.879832i	$-0.657655\pi$
$47$	−4.49337	+	0.711680i	−0.655425	+	0.103809i	−0.180140	+	0.983641i	$0.557655\pi$
$48$	5.22363	+	4.97337i	0.753966	+	0.717844i
$49$	−4.84691	−	1.57486i	−0.692415	−	0.224979i
$50$	0.171445	+	0.336480i	0.0242460	+	0.0475855i
$51$	4.46011	+	4.24643i	0.624540	+	0.594619i
$52$	0.272277	−	0.146537i	0.0377581	−	0.0203210i
$53$	3.23142	−	1.04995i	0.443869	−	0.144222i	−0.0785510	−	0.996910i	$-0.525029\pi$
$53$	3.23142	−	1.04995i	0.443869	−	0.144222i	0.522420	+	0.852688i	$0.325029\pi$
$54$	−1.78779	+	7.28830i	−0.243287	+	0.991812i
$55$	−3.87016	+	6.54967i	−0.521853	+	0.883157i
$56$	3.81437			0.509717
$57$	0.839145	−	2.81592i	0.111147	−	0.372977i
$58$	−13.9460	+	2.20883i	−1.83120	+	0.290034i
$59$	0.675878	−	4.26733i	0.0879918	−	0.555558i	−0.903826	−	0.427900i	$-0.859254\pi$
$59$	0.675878	−	4.26733i	0.0879918	−	0.555558i	0.991818	−	0.127659i	$-0.0407463\pi$
$60$	−0.270647	+	0.206970i	−0.0349404	+	0.0267197i
$61$	1.78987	−	5.50865i	0.229169	−	0.705310i	−0.768672	−	0.639643i	$-0.779082\pi$
$61$	1.78987	−	5.50865i	0.229169	−	0.705310i	0.997842	−	0.0656674i	$-0.0209176\pi$
$62$	−6.15473	+	4.47167i	−0.781651	+	0.567903i
$63$	2.05781	+	3.59143i	0.259260	+	0.452477i
$64$	7.25483	−	2.35724i	0.906854	−	0.294655i
$65$	−2.73195	−	7.80614i	−0.338856	−	0.968232i
$66$	−7.78746	−	2.86102i	−0.958571	−	0.352167i
$67$	−1.80650	+	1.80650i	−0.220699	+	0.220699i	−0.808793	−	0.588094i	$-0.799879\pi$
$67$	−1.80650	+	1.80650i	−0.220699	+	0.220699i	0.588094	+	0.808793i	$0.299879\pi$
$68$	−0.289990	+	0.0942233i	−0.0351664	+	0.0114263i
$69$	3.93860	−	8.22268i	0.474152	−	0.989894i
$70$	−0.715012	+	4.51441i	−0.0854603	+	0.539575i
$71$	−14.2934	+	7.28286i	−1.69632	+	0.864316i	−0.709066	+	0.705142i	$0.750883\pi$
$71$	−14.2934	+	7.28286i	−1.69632	+	0.864316i	−0.987251	+	0.159174i	$0.949117\pi$
$72$	6.14518	+	5.56980i	0.724217	+	0.656408i
$73$	1.53400	+	0.242962i	0.179542	+	0.0284366i	0.245558	−	0.969382i	$-0.421029\pi$
$73$	1.53400	+	0.242962i	0.179542	+	0.0284366i	−0.0660162	+	0.997819i	$0.521029\pi$
$74$	9.83396	−	13.5353i	1.14318	−	1.57345i
$75$	0.215454	+	0.398375i	0.0248785	+	0.0460004i
$76$	0.102871	+	0.102871i	0.0118002	+	0.0118002i
$77$	−4.19901	+	1.81894i	−0.478522	+	0.207287i
$78$	7.83471	−	4.46787i	0.887106	−	0.505887i
$79$	2.72905	+	8.39915i	0.307042	+	0.944979i	0.978907	+	0.204305i	$0.0654935\pi$
$79$	2.72905	+	8.39915i	0.307042	+	0.944979i	−0.671865	+	0.740674i	$0.734507\pi$
$80$	1.49422	+	9.43413i	0.167059	+	1.05477i
$81$	−1.92899	+	8.79085i	−0.214332	+	0.976761i
$82$	14.7828	+	4.80321i	1.63248	+	0.530426i
$83$	−5.12809	+	2.61289i	−0.562881	+	0.286802i	−0.712188	−	0.701989i	$-0.752296\pi$
$83$	−5.12809	+	2.61289i	−0.562881	+	0.286802i	0.149307	+	0.988791i	$0.452296\pi$
$84$	−0.204880	+	0.00502831i	−0.0223543	+	0.000548634i
$85$	1.27581	+	8.05517i	0.138381	+	0.873706i
$86$	1.51133	+	0.770062i	0.162971	+	0.0830379i
$87$	−16.6554	+	3.05862i	−1.78565	+	0.327919i
$88$	−6.87555	+	6.06618i	−0.732936	+	0.646657i
$89$	−9.80067	+	9.80067i	−1.03887	+	1.03887i	−0.0396553	+	0.999213i	$0.512626\pi$
$89$	−9.80067	+	9.80067i	−1.03887	+	1.03887i	−0.999213	+	0.0396553i	$0.987374\pi$
$90$	−7.74393	+	6.22891i	−0.816281	+	0.656584i
$91$	1.43047	−	4.76459i	0.149954	−	0.499465i
$92$	0.265338	+	0.365206i	0.0276634	+	0.0380754i
$93$	−7.24758	+	5.54238i	−0.751539	+	0.574718i
$94$	2.03033	−	6.24871i	0.209412	−	0.644505i
$95$	3.14808	−	2.28721i	0.322986	−	0.234663i
$96$	−0.791980	+	0.278992i	−0.0808311	+	0.0284745i
$97$	−6.96600	−	3.54935i	−0.707290	−	0.360382i	0.0630548	−	0.998010i	$-0.479916\pi$
$97$	−6.96600	−	3.54935i	−0.707290	−	0.360382i	−0.770344	+	0.637628i	$0.779916\pi$
$98$	5.20446	−	5.20446i	0.525730	−	0.525730i
$99$	−9.42090	−	3.20104i	−0.946836	−	0.321717i
$100$	−0.0224245			−0.00224245
$101$	−2.02536	−	6.23342i	−0.201531	−	0.620249i	−0.999838	−	0.0179980i	$-0.994271\pi$
$101$	−2.02536	−	6.23342i	−0.201531	−	0.620249i	0.798307	−	0.602251i	$-0.205729\pi$
$102$	−8.38864	+	2.95508i	−0.830599	+	0.292596i
$103$	0.380680	+	0.523960i	0.0375095	+	0.0516274i	0.827360	−	0.561672i	$-0.189842\pi$
$103$	0.380680	+	0.523960i	0.0375095	+	0.0516274i	−0.789850	+	0.613300i	$0.789842\pi$
$104$	−0.224183	−	9.96530i	−0.0219830	−	0.977179i
$105$	−0.724420	+	5.43355i	−0.0706961	+	0.530260i
$106$	−0.767628	+	4.84661i	−0.0745586	+	0.470745i
$107$	−5.65347	+	7.78134i	−0.546542	+	0.752250i	−0.989538	−	0.144273i	$-0.953916\pi$
$107$	−5.65347	+	7.78134i	−0.546542	+	0.752250i	0.442996	+	0.896524i	$0.353916\pi$
$108$	−0.337417	−	0.291068i	−0.0324679	−	0.0280080i
$109$	−12.4252	+	12.4252i	−1.19012	+	1.19012i	−0.213085	+	0.977034i	$0.568351\pi$
$109$	−12.4252	+	12.4252i	−1.19012	+	1.19012i	−0.977034	+	0.213085i	$0.931649\pi$
$110$	−5.89064	−	9.27450i	−0.561650	−	0.884289i
$111$	11.3921	−	16.5174i	1.08129	−	1.56776i
$112$	−2.60837	+	5.11921i	−0.246468	+	0.483720i
$113$	−4.59961	+	6.33083i	−0.432695	+	0.595554i	−0.968569	−	0.248744i	$-0.919982\pi$
$113$	−4.59961	+	6.33083i	−0.432695	+	0.595554i	0.535874	+	0.844298i	$0.319982\pi$
$114$	3.07334	+	2.92610i	0.287845	+	0.274054i
$115$	10.7582	−	5.48158i	1.00321	−	0.511160i
$116$	0.259093	−	0.797406i	0.0240562	−	0.0740373i
$117$	9.26189	−	5.58725i	0.856262	−	0.516542i
$118$	5.04807	+	3.66764i	0.464713	+	0.337633i
$119$	−2.22711	+	4.37095i	−0.204159	+	0.400685i
$120$	1.98386	+	10.8029i	0.181101	+	0.986167i
$121$	4.67614	−	9.95659i	0.425103	−	0.905145i
$122$	5.91501	+	5.91501i	0.535520	+	0.535520i
$123$	17.8650	+	5.32378i	1.61083	+	0.480029i
$124$	−0.0706687	−	0.446185i	−0.00634624	−	0.0400686i
$125$	1.70031	−	10.7354i	0.152081	−	0.960199i
$126$	−5.97069	+	0.293250i	−0.531912	+	0.0261248i
$127$	−1.46932	−	0.477411i	−0.130381	−	0.0423634i	0.243100	−	0.970001i	$-0.421836\pi$
$127$	−1.46932	−	0.477411i	−0.130381	−	0.0423634i	−0.373481	+	0.927638i	$0.621836\pi$
$128$	−1.87507	+	11.8387i	−0.165735	+	1.04641i
$129$	1.83466	+	0.878787i	0.161532	+	0.0773729i
$130$	11.8362	+	1.60269i	1.03810	+	0.140565i
$131$			10.9791i			0.959244i	0.877475	+	0.479622i	$0.159226\pi$
$131$			10.9791i			0.959244i	−0.877475	+	0.479622i	$0.840774\pi$
$132$	0.361308	−	0.334894i	0.0314478	−	0.0291488i
$133$	2.34061			0.202956
$134$	−1.14017	−	3.50907i	−0.0984953	−	0.303137i
$135$	−9.10122	+	7.69596i	−0.783309	+	0.662363i
$136$	−1.53767	+	9.70844i	−0.131854	+	0.832492i
$137$	−4.98987	−	9.79317i	−0.426313	−	0.836687i	−0.999847	−	0.0175050i	$-0.994428\pi$
$137$	−4.98987	−	9.79317i	−0.426313	−	0.836687i	0.573533	−	0.819182i	$-0.305572\pi$
$138$	7.99860	+	10.4595i	0.680886	+	0.890371i
$139$	7.59472	−	5.51789i	0.644176	−	0.468021i	−0.217107	−	0.976148i	$-0.569662\pi$
$139$	7.59472	−	5.51789i	0.644176	−	0.468021i	0.861282	+	0.508127i	$0.169662\pi$
$140$	−0.219575	−	0.159530i	−0.0185574	−	0.0134828i
$141$	2.25038	−	7.55158i	0.189516	−	0.635958i
$142$		−	23.1679i		−	1.94421i
$143$	4.99888	+	10.8633i	0.418028	+	0.908434i
$144$	−11.6774	+	4.43858i	−0.973115	+	0.369882i
$145$	−19.9817	−	10.1812i	−1.65939	−	0.845502i
$146$	−1.31843	+	1.81466i	−0.109114	+	0.150183i
$147$	6.08670	−	6.39298i	0.502022	−	0.527284i
$148$	0.451025	+	0.885186i	0.0370740	+	0.0727618i
$149$	11.9747	−	6.10143i	0.981008	−	0.499849i	0.111498	−	0.993765i	$-0.464435\pi$
$149$	11.9747	−	6.10143i	0.981008	−	0.499849i	0.869510	+	0.493916i	$0.164435\pi$
$150$	−0.653896	+	0.0160484i	−0.0533904	+	0.00131034i
$151$	2.72098	+	17.1796i	0.221430	+	1.39806i	0.808489	+	0.588512i	$0.200286\pi$
$151$	2.72098	+	17.1796i	0.221430	+	1.39806i	−0.587058	+	0.809545i	$0.699714\pi$
$152$	4.46035	−	1.44926i	0.361782	−	0.117550i
$153$	−9.97053	+	3.78980i	−0.806070	+	0.306388i
$154$	0.412507	−	6.59592i	0.0332408	−	0.531514i
$155$	−12.0830			−0.970527
$156$	0.0251783	+	0.534968i	0.00201588	+	0.0428317i
$157$	5.35632	+	3.89159i	0.427481	+	0.310583i	0.780641	−	0.624980i	$-0.214893\pi$
$157$	5.35632	+	3.89159i	0.427481	+	0.310583i	−0.353160	+	0.935563i	$0.614893\pi$
$158$	−12.5974	−	1.99523i	−1.00220	−	0.158732i
$159$	−0.777728	+	5.83339i	−0.0616779	+	0.462618i
$160$	−1.05759	−	0.343631i	−0.0836095	−	0.0271664i
$161$	7.17331	+	1.13614i	0.565336	+	0.0895405i
$162$	−10.0473	−	8.24604i	−0.789394	−	0.647870i
$163$	−2.26810	+	4.45140i	−0.177652	+	0.348661i	−0.962612	−	0.270886i	$-0.912683\pi$
$163$	−2.26810	+	4.45140i	−0.177652	+	0.348661i	0.784960	+	0.619546i	$0.212683\pi$
$164$	−0.652647	+	0.652647i	−0.0509631	+	0.0509631i
$165$	−7.33543	−	10.9463i	−0.571063	−	0.852165i
$166$		−	8.31202i		−	0.645138i
$167$	21.1930	+	10.7984i	1.63996	+	0.835602i	0.997603	+	0.0691978i	$0.0220439\pi$
$167$	21.1930	+	10.7984i	1.63996	+	0.835602i	0.642358	+	0.766404i	$0.277956\pi$
$168$	−2.85404	+	5.95842i	−0.220194	+	0.459702i
$169$	−12.5319	−	3.45716i	−0.963991	−	0.265935i
$170$	−11.2019	−	3.63973i	−0.859149	−	0.279154i
$171$	3.77086	+	3.41779i	0.288365	+	0.261365i
$172$	−0.0814854	+	0.0592026i	−0.00621321	+	0.00451416i
$173$	2.73959	+	1.99043i	0.208287	+	0.151329i	0.687038	−	0.726621i	$-0.258910\pi$
$173$	2.73959	+	1.99043i	0.208287	+	0.151329i	−0.478751	+	0.877951i	$0.658910\pi$
$174$	6.98446	−	23.4377i	0.529490	−	1.77681i
$175$	−0.255109	+	0.255109i	−0.0192844	+	0.0192844i
$176$	−3.43964	−	13.3758i	−0.259273	−	1.00824i
$177$	6.16026	+	4.24874i	0.463034	+	0.319355i
$178$	−6.18565	−	19.0375i	−0.463634	−	1.42692i
$179$	10.1368	+	7.36484i	0.757662	+	0.550474i	0.898192	−	0.439602i	$-0.144881\pi$
$179$	10.1368	+	7.36484i	0.757662	+	0.550474i	−0.140530	+	0.990076i	$0.544881\pi$
$180$	−0.120799	−	0.577639i	−0.00900385	−	0.0430546i
$181$	−16.4153	−	5.33367i	−1.22014	−	0.396448i	−0.373008	−	0.927828i	$-0.621674\pi$
$181$	−16.4153	−	5.33367i	−1.22014	−	0.396448i	−0.847134	+	0.531380i	$0.821674\pi$
$182$	5.19320	+	4.96469i	0.384946	+	0.368007i
$183$	7.26580	+	6.91770i	0.537104	+	0.511371i
$184$	14.3732	−	2.27649i	1.05961	−	0.167825i
$185$	25.2719	−	8.21135i	1.85803	−	0.603710i
$186$	−2.38001	−	12.9601i	−0.174511	−	0.950283i
$187$	−2.93688	−	11.4207i	−0.214766	−	0.835163i
$188$	0.275875	+	0.275875i	0.0201203	+	0.0201203i
$189$	−7.14988	+	0.527279i	−0.520077	+	0.0383539i
$190$	0.879129	+	5.55060i	0.0637787	+	0.402683i
$191$	1.63499	+	2.25037i	0.118304	+	0.162831i	0.864062	−	0.503386i	$-0.167912\pi$
$191$	1.63499	+	2.25037i	0.118304	+	0.162831i	−0.745758	+	0.666217i	$0.767912\pi$
$192$	−1.74607	+	13.0965i	−0.126012	+	0.945159i
$193$	3.00970	−	1.53352i	0.216643	−	0.110385i	−0.342302	−	0.939590i	$-0.611206\pi$
$193$	3.00970	−	1.53352i	0.216643	−	0.110385i	0.558945	+	0.829205i	$0.311206\pi$
$194$	9.13465	−	6.63671i	0.655830	−	0.476488i
$195$	14.2381	+	1.57325i	1.01961	+	0.112663i
$196$	0.135057	+	0.415662i	0.00964691	+	0.0296901i
$197$	−4.45604	−	4.45604i	−0.317480	−	0.317480i	0.530319	−	0.847798i	$-0.322072\pi$
$197$	−4.45604	−	4.45604i	−0.317480	−	0.317480i	−0.847798	+	0.530319i	$0.822072\pi$
$198$	10.2960	−	10.0241i	0.731707	−	0.712379i
$199$		−	13.1030i		−	0.928845i	−0.885614	−	0.464422i	$-0.846262\pi$
$199$		−	13.1030i		−	0.928845i	0.885614	−	0.464422i	$-0.153738\pi$
$200$	−0.328188	+	0.644104i	−0.0232064	+	0.0455451i
$201$	−1.47025	−	4.17362i	−0.103703	−	0.294384i
$202$	9.34915	+	1.48076i	0.657804	+	0.104186i
$203$	−6.12406	−	12.0191i	−0.429824	−	0.843578i
$204$	0.0697939	−	0.523493i	0.00488655	−	0.0366518i
$205$	14.5108	+	19.9724i	1.01348	+	1.39493i
$206$	−0.923831	+	0.146321i	−0.0643664	+	0.0101946i
$207$	9.89762	+	12.3050i	0.687932	+	0.855254i
$208$	13.5276	+	6.51366i	0.937969	+	0.451641i
$209$	−4.21903	+	3.72238i	−0.291837	+	0.257482i
$210$	−6.51695	−	4.49475i	−0.449712	−	0.310167i
$211$	1.19544	+	3.67918i	0.0822973	+	0.253285i	0.983736	−	0.179623i	$-0.0574876\pi$
$211$	1.19544	+	3.67918i	0.0822973	+	0.253285i	−0.901438	+	0.432908i	$0.857488\pi$
$212$	−0.235733	−	0.171270i	−0.0161902	−	0.0117629i
$213$	−0.681722	−	27.7770i	−0.0467108	−	1.90325i
$214$	−6.30631	−	12.3768i	−0.431091	−	0.846063i
$215$	1.22306	+	2.40039i	0.0834120	+	0.163705i
$216$	−13.2986	+	5.43186i	−0.904855	+	0.369591i
$217$	−5.87992	−	4.27201i	−0.399155	−	0.290003i
$218$	−7.84211	−	24.1355i	−0.531135	−	1.63466i
$219$	−1.52732	+	2.21447i	−0.103207	+	0.149640i
$220$	0.649500	−	0.0616405i	0.0437893	−	0.00415580i
$221$	11.5503	+	5.56158i	0.776957	+	0.374112i
$222$	13.7853	+	25.4892i	0.925211	+	1.71072i
$223$	14.4653	−	2.29108i	0.968670	−	0.153422i	0.348000	−	0.937495i	$-0.386861\pi$
$223$	14.4653	−	2.29108i	0.968670	−	0.153422i	0.620669	+	0.784072i	$0.286861\pi$
$224$	−0.393159	−	0.541137i	−0.0262691	−	0.0361563i
$225$	−0.783510	+	0.0384821i	−0.0522340	+	0.00256547i
$226$	−5.13076	−	10.0697i	−0.341293	−	0.669825i
$227$	19.8953	+	3.15110i	1.32049	+	0.209146i	0.776593	−	0.630003i	$-0.216946\pi$
$227$	19.8953	+	3.15110i	1.32049	+	0.209146i	0.543902	+	0.839149i	$0.316946\pi$
$228$	−0.237667	+	0.0837233i	−0.0157399	+	0.00554471i
$229$	−0.744658	+	1.46147i	−0.0492084	+	0.0965769i	−0.914301	−	0.405035i	$-0.867259\pi$
$229$	−0.744658	+	1.46147i	−0.0492084	+	0.0965769i	0.865093	+	0.501612i	$0.167259\pi$
$230$			17.4378i			1.14981i
$231$	0.300485	−	7.92026i	0.0197705	−	0.521115i
$232$	−19.1122	−	19.1122i	−1.25478	−	1.25478i
$233$	3.56766	+	10.9801i	0.233725	+	0.719332i	0.997288	+	0.0735984i	$0.0234483\pi$
$233$	3.56766	+	10.9801i	0.233725	+	0.719332i	−0.763563	+	0.645733i	$0.776552\pi$
$234$	1.11705	+	15.5816i	0.0730240	+	1.01860i
$235$	8.44236	−	6.13373i	0.550719	−	0.400121i
$236$	−0.330136	+	0.168212i	−0.0214900	+	0.0109497i
$237$	−15.1623	−	2.02149i	−0.984895	−	0.131310i
$238$	−4.16434	−	5.73172i	−0.269934	−	0.371532i
$239$	−0.147243	−	0.929655i	−0.00952435	−	0.0601344i	0.982468	−	0.186429i	$-0.0596915\pi$
$239$	−0.147243	−	0.929655i	−0.00952435	−	0.0601344i	−0.991993	+	0.126295i	$0.959691\pi$
$240$	−15.8550	−	4.72481i	−1.02344	−	0.304985i
$241$	−1.14445	−	1.14445i	−0.0737205	−	0.0737205i	0.669285	−	0.743006i	$-0.266600\pi$
$241$	−1.14445	−	1.14445i	−0.0737205	−	0.0737205i	−0.743006	+	0.669285i	$0.766600\pi$
$242$	9.74624	+	12.5454i	0.626512	+	0.806450i
$243$	−12.2888	−	9.59088i	−0.788328	−	0.615255i
$244$	−0.472412	+	0.153496i	−0.0302431	+	0.00982656i
$245$	11.5460	−	1.82871i	0.737649	−	0.116832i
$246$	−18.5640	+	19.4982i	−1.18360	+	1.24316i
$247$	−0.137565	−	6.11499i	−0.00875306	−	0.389088i
$248$	−13.8501	−	4.50018i	−0.879485	−	0.285762i
$249$	−0.244583	−	9.96562i	−0.0154998	−	0.631546i
$250$	12.6995	+	9.22671i	0.803186	+	0.583549i
$251$	6.96868	+	21.4474i	0.439859	+	1.35375i	0.888024	+	0.459797i	$0.152078\pi$
$251$	6.96868	+	21.4474i	0.439859	+	1.35375i	−0.448165	+	0.893951i	$0.647922\pi$
$252$	0.145444	−	0.323805i	0.00916208	−	0.0203978i
$253$	−14.7370	+	9.36012i	−0.926509	+	0.588466i
$254$	1.57771	−	1.57771i	0.0989943	−	0.0989943i
$255$	−13.5376	−	4.03420i	−0.847755	−	0.252632i
$256$	−1.66210	−	1.20759i	−0.103881	−	0.0754741i
$257$	−5.72575	+	4.16000i	−0.357163	+	0.259494i	−0.751868	−	0.659314i	$-0.770847\pi$
$257$	−5.72575	+	4.16000i	−0.357163	+	0.259494i	0.394705	+	0.918808i	$0.370847\pi$
$258$	−2.33374	+	1.78466i	−0.145292	+	0.111108i
$259$	15.2012	+	4.93918i	0.944559	+	0.306906i
$260$	−0.403878	+	0.583029i	−0.0250475	+	0.0361579i
$261$	7.68429	−	28.3060i	0.475646	−	1.75210i
$262$	−14.1279	−	7.19853i	−0.872825	−	0.444726i
$263$			17.1310i			1.05634i	0.849137	+	0.528172i	$0.177122\pi$
$263$			17.1310i			1.05634i	−0.849137	+	0.528172i	$0.822878\pi$
$264$	−4.33144	−	15.2792i	−0.266582	−	0.940370i
$265$	−5.51094	+	5.51094i	−0.338534	+	0.338534i
$266$	−1.53464	+	3.01191i	−0.0940950	+	0.184672i
$267$	−7.97641	−	22.6428i	−0.488148	−	1.38572i
$268$	0.216396	+	0.0342737i	0.0132185	+	0.00209360i
$269$	−13.7006	−	4.45160i	−0.835342	−	0.271419i	−0.140048	−	0.990145i	$-0.544726\pi$
$269$	−13.7006	−	4.45160i	−0.835342	−	0.271419i	−0.695294	+	0.718726i	$0.744726\pi$
$270$	−3.93589	−	16.7574i	−0.239531	−	1.01983i
$271$	−13.3989	−	2.12217i	−0.813924	−	0.128913i	−0.264424	−	0.964407i	$-0.585182\pi$
$271$	−13.3989	−	2.12217i	−0.813924	−	0.128913i	−0.549500	+	0.835494i	$0.685182\pi$
$272$	−11.9780	−	8.70256i	−0.726275	−	0.527670i
$273$	6.37243	+	5.79956i	0.385677	+	0.351005i
$274$	15.8736			0.958957
$275$	0.0541317	−	0.865556i	0.00326426	−	0.0521950i
$276$	−0.769023	+	0.141224i	−0.0462897	+	0.00850069i
$277$	6.18946	−	2.01108i	0.371888	−	0.120834i	−0.117109	−	0.993119i	$-0.537363\pi$
$277$	6.18946	−	2.01108i	0.371888	−	0.120834i	0.488997	+	0.872285i	$0.337363\pi$
$278$	2.12089	+	13.3908i	0.127203	+	0.803126i
$279$	−3.23485	−	15.4684i	−0.193665	−	0.926069i
$280$	−7.79576	+	3.97214i	−0.465886	+	0.237381i
$281$	−0.853285	−	1.67467i	−0.0509027	−	0.0999022i	0.864154	−	0.503228i	$-0.167854\pi$
$281$	−0.853285	−	1.67467i	−0.0509027	−	0.0999022i	−0.915057	+	0.403325i	$0.867854\pi$
$282$	8.24193	+	7.84706i	0.490800	+	0.467286i
$283$	0.705253	−	0.970698i	0.0419230	−	0.0577020i	−0.787541	−	0.616262i	$-0.788646\pi$
$283$	0.705253	−	0.970698i	0.0419230	−	0.0577020i	0.829464	+	0.558560i	$0.188646\pi$
$284$	1.22578	+	0.624565i	0.0727365	+	0.0370611i
$285$	1.21735	+	6.62898i	0.0721097	+	0.392667i
$286$	−17.2565	−	0.690039i	−1.02040	−	0.0408028i
$287$			14.8495i			0.876539i
$288$	0.156773	−	1.44590i	0.00923795	−	0.0852005i
$289$	3.52604	+	2.56182i	0.207414	+	0.150695i
$290$	26.2024	−	19.0372i	1.53866	−	1.11790i
$291$	10.7566	−	8.22582i	0.630564	−	0.482206i
$292$	−0.0604684	−	0.118676i	−0.00353865	−	0.00694499i
$293$	−3.85797	+	24.3583i	−0.225385	+	1.42302i	0.572347	+	0.820012i	$0.306033\pi$
$293$	−3.85797	+	24.3583i	−0.225385	+	1.42302i	−0.797732	+	0.603013i	$0.793967\pi$
$294$	4.23572	+	12.0240i	0.247032	+	0.701255i
$295$	3.06247	+	9.42532i	0.178304	+	0.548764i
$296$	32.0263			1.86149
$297$	12.0494	−	12.3212i	0.699175	−	0.714950i
$298$			19.4096i			1.12437i
$299$	2.54664	−	18.8075i	0.147276	−	1.08767i
$300$	0.0167787	−	0.0350292i	0.000968721	−	0.00202241i
$301$	−0.253498	+	1.60052i	−0.0146114	+	0.0922525i
$302$	−23.8908	−	7.76261i	−1.37476	−	0.446688i
$303$	11.2527	+	1.50024i	0.646448	+	0.0861867i
$304$	−1.10508	+	6.97721i	−0.0633807	+	0.400170i
$305$	2.07838	+	13.1224i	0.119008	+	0.751386i
$306$	1.66054	−	15.3150i	0.0949268	−	0.875498i
$307$	−6.41862	−	6.41862i	−0.366330	−	0.366330i	0.499807	−	0.866137i	$-0.333404\pi$
$307$	−6.41862	−	6.41862i	−0.366330	−	0.366330i	−0.866137	+	0.499807i	$0.833404\pi$
$308$	0.337859	+	0.199639i	0.0192513	+	0.0113755i
$309$	−1.10331	+	0.202614i	−0.0627653	+	0.0115263i
$310$	7.92232	−	15.5484i	0.449957	−	0.883091i
$311$	−15.6417	−	11.3644i	−0.886962	−	0.644416i	0.0481222	−	0.998841i	$-0.484676\pi$
$311$	−15.6417	−	11.3644i	−0.886962	−	0.644416i	−0.935084	+	0.354426i	$0.884676\pi$
$312$	15.7345	+	7.10618i	0.890791	+	0.402308i
$313$	1.88025	−	5.78681i	0.106278	−	0.327090i	−0.883750	−	0.467959i	$-0.844990\pi$
$313$	1.88025	−	5.78681i	0.106278	−	0.327090i	0.990028	+	0.140869i	$0.0449896\pi$
$314$	−8.51965	+	4.34098i	−0.480792	+	0.244976i
$315$	−7.94569	−	5.19717i	−0.447689	−	0.292828i
$316$	0.445168	−	0.612721i	0.0250426	−	0.0344682i
$317$	−2.96800	+	5.82502i	−0.166699	+	0.327166i	−0.959211	−	0.282691i	$-0.908773\pi$
$317$	−2.96800	+	5.82502i	−0.166699	+	0.327166i	0.792512	+	0.609857i	$0.208773\pi$
$318$	−6.99651	−	4.82551i	−0.392345	−	0.270601i
$319$	30.1534	+	11.9256i	1.68827	+	0.667704i
$320$	−12.3726	+	12.3726i	−0.691648	+	0.691648i
$321$	−7.92509	−	14.6535i	−0.442335	−	0.817880i
$322$	−6.16525	+	8.48573i	−0.343576	+	0.472891i
$323$	−0.943555	+	5.95737i	−0.0525008	+	0.331477i
$324$	0.707143	−	0.309291i	0.0392857	−	0.0171828i
$325$	0.681483	+	0.651496i	0.0378019	+	0.0361385i
$326$	−4.24098	−	5.83721i	−0.234886	−	0.323293i
$327$	−10.1124	−	28.7063i	−0.559218	−	1.58746i
$328$	9.19451	+	28.2978i	0.507682	+	1.56248i
$329$	6.27692			0.346058
$330$	18.8952	−	2.26226i	1.04015	−	0.124533i
$331$	−14.4533	+	14.4533i	−0.794426	+	0.794426i	−0.982210	−	0.187784i	$-0.939869\pi$
$331$	−14.4533	+	14.4533i	−0.794426	+	0.794426i	0.187784	+	0.982210i	$0.439869\pi$
$332$	0.439775	+	0.224077i	0.0241358	+	0.0122978i
$333$	17.2778	+	30.1544i	0.946819	+	1.65245i
$334$	−27.7908	+	20.1912i	−1.52064	+	1.10481i
$335$	1.81088	−	5.57332i	0.0989390	−	0.304503i
$336$	−6.04504	−	7.90489i	−0.329784	−	0.431247i
$337$	−17.0832	−	23.5131i	−0.930584	−	1.28084i	−0.959632	−	0.281260i	$-0.909248\pi$
$337$	−17.0832	−	23.5131i	−0.930584	−	1.28084i	0.0290480	−	0.999578i	$-0.490752\pi$
$338$	12.6653	−	13.8594i	0.688904	−	0.753850i
$339$	−6.44778	−	11.9220i	−0.350195	−	0.647513i
$340$	0.494556	−	0.494556i	0.0268211	−	0.0268211i
$341$	17.3928	−	1.65065i	0.941871	−	0.0893879i
$342$	−6.87043	+	2.61145i	−0.371510	+	0.141211i
$343$	14.8706	+	7.57697i	0.802939	+	0.409118i
$344$	0.507935	+	3.20697i	0.0273860	+	0.172908i
$345$	0.513111	+	20.9069i	0.0276250	+	1.12559i
$346$	−4.35753	+	2.22027i	−0.234262	+	0.119363i
$347$	−7.34217	−	2.38561i	−0.394148	−	0.128067i	0.105236	−	0.994447i	$-0.466440\pi$
$347$	−7.34217	−	2.38561i	−0.394148	−	0.128067i	−0.499384	+	0.866381i	$0.666440\pi$
$348$	1.05176	+	1.00137i	0.0563805	+	0.0536793i
$349$	−0.972677	−	6.14124i	−0.0520662	−	0.328733i	−0.999949	−	0.0101134i	$-0.996781\pi$
$349$	−0.972677	−	6.14124i	−0.0520662	−	0.328733i	0.947883	−	0.318620i	$-0.103219\pi$
$350$	−0.161011	−	0.495541i	−0.00860640	−	0.0264878i
$351$	1.79777	+	18.6485i	0.0959580	+	0.995385i
$352$	1.56928	+	0.350161i	0.0836429	+	0.0186636i
$353$	3.91329	+	3.91329i	0.208283	+	0.208283i	0.803537	−	0.595254i	$-0.202949\pi$
$353$	3.91329	+	3.91329i	0.208283	+	0.208283i	−0.595254	+	0.803537i	$0.702949\pi$
$354$	−9.50634	+	5.14133i	−0.505256	+	0.273258i
$355$	21.6286	−	29.7692i	1.14793	−	1.57998i
$356$	1.17399	+	0.185943i	0.0622216	+	0.00985493i
$357$	−5.16145	−	6.74946i	−0.273173	−	0.357219i
$358$	−16.1234	+	8.21530i	−0.852150	+	0.434192i
$359$	2.19004	−	13.8274i	0.115586	−	0.729782i	−0.860021	−	0.510258i	$-0.829550\pi$
$359$	2.19004	−	13.8274i	0.115586	−	0.729782i	0.975607	−	0.219523i	$-0.0704502\pi$
$360$	−18.3596	−	4.98413i	−0.967636	−	0.262687i
$361$	−15.3331	+	4.98202i	−0.807004	+	0.262211i
$362$	17.6263	−	17.6263i	0.926416	−	0.926416i
$363$	12.0543	+	14.7544i	0.632688	+	0.774407i
$364$	−0.402673	+	0.140925i	−0.0211058	+	0.00738648i
$365$	−3.38818	+	1.10089i	−0.177346	+	0.0576231i
$366$	−13.6656	+	4.81401i	−0.714314	+	0.251633i
$367$	−7.11965	+	5.17273i	−0.371642	+	0.270014i	−0.757892	−	0.652380i	$-0.773770\pi$
$367$	−7.11965	+	5.17273i	−0.371642	+	0.270014i	0.386249	+	0.922394i	$0.373770\pi$
$368$	−6.77353	+	20.8468i	−0.353095	+	1.08671i
$369$	−21.6835	+	23.9234i	−1.12880	+	1.24540i
$370$	−6.00339	+	37.9039i	−0.312101	+	1.97053i
$371$	−4.63021	+	0.733354i	−0.240389	+	0.0380738i
$372$	0.749861	+	0.223459i	0.0388785	+	0.0115858i
$373$	34.3337			1.77773			0.888866	−	0.458166i	$-0.151494\pi$
$373$	34.3337			1.77773			0.888866	+	0.458166i	$0.151494\pi$
$374$	16.6218	+	3.70889i	0.859492	+	0.191782i
$375$	15.4974	+	10.6886i	0.800284	+	0.551957i
$376$	11.9615	−	3.88654i	0.616869	−	0.200433i
$377$	−31.0409	+	16.7059i	−1.59869	+	0.860398i
$378$	4.00939	−	9.54622i	0.206221	−	0.491005i
$379$	10.8646	+	21.3229i	0.558076	+	1.09529i	0.981875	+	0.189530i	$0.0606963\pi$
$379$	10.8646	+	21.3229i	0.558076	+	1.09529i	−0.423799	+	0.905756i	$0.639304\pi$
$380$	−0.317373	−	0.103121i	−0.0162809	−	0.00528998i
$381$	1.84516	−	1.93801i	0.0945302	−	0.0992870i
$382$	−3.96779	+	0.628437i	−0.203010	+	0.0321536i
$383$	4.50285	−	8.83735i	0.230085	−	0.451567i	−0.746882	−	0.664956i	$-0.768450\pi$
$383$	4.50285	−	8.83735i	0.230085	−	0.451567i	0.976967	+	0.213389i	$0.0684501\pi$
$384$	−17.0903	−	11.7872i	−0.872135	−	0.601513i
$385$	6.68771	−	8.09020i	0.340837	−	0.412315i
$386$			4.87837i			0.248302i
$387$	−2.74550	+	2.20837i	−0.139562	+	0.112258i
$388$	0.104884	+	0.662213i	0.00532469	+	0.0336188i
$389$	19.0500	−	13.8406i	0.965872	−	0.701747i	0.0113647	−	0.999935i	$-0.496382\pi$
$389$	19.0500	−	13.8406i	0.965872	−	0.701747i	0.954507	+	0.298189i	$0.0963824\pi$
$390$	−11.3598	+	17.2901i	−0.575226	+	0.875519i
$391$	−5.78347	+	17.7997i	−0.292482	+	0.900168i
$392$	13.9158	+	2.20404i	0.702852	+	0.111321i
$393$	−17.1503	−	8.21489i	−0.865120	−	0.414387i
$394$	8.65570	−	2.81241i	0.436068	−	0.141687i
$395$	−14.3241	−	14.3241i	−0.720725	−	0.720725i
$396$	0.252795	+	0.814977i	0.0127034	+	0.0409541i
$397$	−3.68774	−	3.68774i	−0.185082	−	0.185082i	0.608484	−	0.793566i	$-0.291778\pi$
$397$	−3.68774	−	3.68774i	−0.185082	−	0.185082i	−0.793566	+	0.608484i	$0.791778\pi$
$398$	16.8610	+	8.59109i	0.845164	+	0.430633i
$399$	−1.75132	+	3.65626i	−0.0876757	+	0.183042i
$400$	−0.640019	−	0.880911i	−0.0320009	−	0.0440455i
$401$	3.21389	+	6.30762i	0.160494	+	0.314988i	0.957224	−	0.289348i	$-0.0934386\pi$
$401$	3.21389	+	6.30762i	0.160494	+	0.314988i	−0.796730	+	0.604336i	$0.793439\pi$
$402$	6.33461	+	0.844553i	0.315942	+	0.0421225i
$403$	−10.8153	+	15.6128i	−0.538750	+	0.777727i
$404$	−0.330381	+	0.454730i	−0.0164371	+	0.0226237i
$405$	−5.21200	−	19.9754i	−0.258986	−	0.992584i
$406$	19.4816			0.966855
$407$	−35.2558	+	15.2722i	−1.74757	+	0.757014i
$408$	−14.0150	−	9.66616i	−0.693845	−	0.478546i
$409$	−11.2684	−	5.74153i	−0.557186	−	0.283901i	0.152635	−	0.988283i	$-0.451224\pi$
$409$	−11.2684	−	5.74153i	−0.557186	−	0.283901i	−0.709821	+	0.704382i	$0.751224\pi$
$410$	−35.2147	+	5.57745i	−1.73913	+	0.275451i
$411$	19.0315	−	0.467084i	0.938753	−	0.0230395i
$412$	0.0171632	−	0.0528230i	0.000845571	−	0.00260240i
$413$	−1.84210	+	5.66940i	−0.0906437	+	0.278973i
$414$	−22.3236	+	4.66844i	−1.09714	+	0.229441i
$415$	7.75974	−	10.6804i	0.380911	−	0.524279i
$416$	−1.39065	+	1.05896i	−0.0681822	+	0.0519197i
$417$	2.93685	+	15.9924i	0.143818	+	0.783149i
$418$	−2.02373	−	7.86969i	−0.0989837	−	0.384919i
$419$		−	35.1974i		−	1.71950i	−0.510712	−	0.859752i	$-0.670618\pi$
$419$		−	35.1974i		−	1.71950i	0.510712	−	0.859752i	$-0.329382\pi$
$420$	0.413495	−	0.223631i	0.0201765	−	0.0109121i
$421$	−26.7571	+	4.23791i	−1.30406	+	0.206543i	−0.769533	−	0.638607i	$-0.779511\pi$
$421$	−26.7571	+	4.23791i	−1.30406	+	0.206543i	−0.534529	+	0.845150i	$0.679511\pi$
$422$	−5.51819	−	0.873995i	−0.268621	−	0.0425454i
$423$	10.1125	+	9.16565i	0.491686	+	0.445649i
$424$	−8.36943	+	4.26444i	−0.406456	+	0.207099i
$425$	−0.546469	−	0.752151i	−0.0265077	−	0.0364847i
$426$	36.1905	+	17.3350i	1.75344	+	0.839884i
$427$	−3.62811	+	7.12056i	−0.175576	+	0.344588i
$428$	0.824845			0.0398704
$429$	−20.7099	−	0.319539i	−0.999881	−	0.0154275i
$430$	−3.89075			−0.187628
$431$	−1.31201	+	2.57496i	−0.0631971	+	0.124031i	−0.920444	−	0.390874i	$-0.872173\pi$
$431$	−1.31201	+	2.57496i	−0.0631971	+	0.124031i	0.857247	+	0.514905i	$0.172173\pi$
$432$	1.80392	−	21.5623i	0.0867910	−	1.03742i
$433$	15.4271	+	21.2336i	0.741379	+	1.02042i	0.998538	+	0.0540515i	$0.0172135\pi$
$433$	15.4271	+	21.2336i	0.741379	+	1.02042i	−0.257159	+	0.966369i	$0.582786\pi$
$434$	9.35248	−	4.76533i	0.448933	−	0.228743i
$435$	30.8550	−	23.5955i	1.47938	−	1.13132i
$436$	1.48838	+	0.235736i	0.0712805	+	0.0112897i
$437$	8.81981	−	1.39692i	0.421909	−	0.0668238i
$438$	−1.84819	−	3.41731i	−0.0883098	−	0.163285i
$439$			38.4814i			1.83662i	0.395867	+	0.918308i	$0.370444\pi$
$439$			38.4814i			1.83662i	−0.395867	+	0.918308i	$0.629556\pi$
$440$	7.73507	−	19.5579i	0.368755	−	0.932386i
$441$	5.43219	+	14.2915i	0.258676	+	0.680545i
$442$	−14.7297	+	11.2165i	−0.700622	+	0.533513i
$443$	−5.34737	+	7.36003i	−0.254061	+	0.349685i	−0.916928	−	0.399052i	$-0.869339\pi$
$443$	−5.34737	+	7.36003i	−0.254061	+	0.349685i	0.662867	+	0.748737i	$0.269339\pi$
$444$	−1.72022	+	0.0422188i	−0.0816379	+	0.00200361i
$445$	9.82443	−	30.2365i	0.465722	−	1.43335i
$446$	−6.53616	+	20.1162i	−0.309496	+	0.952531i
$447$	0.571133	+	23.2710i	0.0270136	+	1.10068i
$448$	−10.3953	+	1.64645i	−0.491130	+	0.0777874i
$449$	−12.3010	−	6.26766i	−0.580519	−	0.295789i	0.138966	−	0.990297i	$-0.455622\pi$
$449$	−12.3010	−	6.26766i	−0.580519	−	0.295789i	−0.719485	+	0.694508i	$0.755622\pi$
$450$	0.464197	−	1.03346i	0.0218825	−	0.0487176i
$451$	−23.6159	−	26.7668i	−1.11203	−	1.26040i
$452$	0.671086			0.0315652
$453$	−28.8721	−	8.60391i	−1.35653	−	0.404247i
$454$	−17.0994	+	23.5353i	−0.802514	+	1.10457i
$455$	2.03809	+	11.2274i	0.0955471	+	0.526350i
$456$	−1.07351	+	8.05188i	−0.0502715	+	0.377064i
$457$	6.25082	+	12.2679i	0.292401	+	0.573869i	0.989741	−	0.142871i	$-0.0456334\pi$
$457$	6.25082	+	12.2679i	0.292401	+	0.573869i	−0.697340	+	0.716740i	$0.745633\pi$
$458$	−1.39239	−	1.91646i	−0.0650621	−	0.0895503i
$459$	1.54024	−	18.4106i	0.0718924	−	0.859333i
$460$	−0.922605	−	0.470091i	−0.0430167	−	0.0219181i
$461$	−14.5011	−	14.5011i	−0.675383	−	0.675383i	0.283569	−	0.958952i	$-0.408482\pi$
$461$	−14.5011	−	14.5011i	−0.675383	−	0.675383i	−0.958952	+	0.283569i	$0.908482\pi$
$462$	9.99481	+	5.57966i	0.465001	+	0.259589i
$463$	25.7022	+	25.7022i	1.19448	+	1.19448i	0.975795	+	0.218688i	$0.0701778\pi$
$463$	25.7022	+	25.7022i	1.19448	+	1.19448i	0.218688	+	0.975795i	$0.429822\pi$
$464$	38.7197	−	12.5808i	1.79752	−	0.584048i
$465$	9.04087	−	18.8748i	0.419261	−	0.875296i
$466$	−16.4685	−	2.60835i	−0.762886	−	0.120829i
$467$	−1.02818	+	3.16440i	−0.0475783	+	0.146431i	−0.972023	−	0.234884i	$-0.924529\pi$
$467$	−1.02818	+	3.16440i	−0.0475783	+	0.146431i	0.924445	+	0.381315i	$0.124529\pi$
$468$	−0.854510	−	0.360950i	−0.0394998	−	0.0166849i
$469$	2.85171	−	2.07189i	0.131680	−	0.0956710i
$470$	2.35760	+	14.8853i	0.108748	+	0.686609i
$471$	−10.0868	+	5.45527i	−0.464776	+	0.251366i
$472$			11.9444i			0.549786i
$473$	−2.08844	−	3.28815i	−0.0960268	−	0.151189i
$474$	12.5425	−	18.1855i	0.576098	−	0.835286i
$475$	−0.201385	+	0.395241i	−0.00924018	+	0.0181349i
$476$	0.415519	−	0.0658117i	0.0190453	−	0.00301648i
$477$	−8.53040	−	5.57962i	−0.390580	−	0.255473i
$478$	1.29283	+	0.420065i	0.0591325	+	0.0192133i
$479$	2.49716	+	4.90096i	0.114098	+	0.223930i	0.940993	−	0.338427i	$-0.109895\pi$
$479$	2.49716	+	4.90096i	0.114098	+	0.223930i	−0.826895	+	0.562357i	$0.809895\pi$
$480$	1.32811	−	1.39494i	0.0606194	−	0.0636698i
$481$	12.0105	−	40.0045i	0.547632	−	1.82405i
$482$	2.22305	−	0.722314i	0.101257	−	0.0329005i
$483$	−7.14207	+	10.3553i	−0.324976	+	0.471183i
$484$	−0.926499	+	0.177456i	−0.0421136	+	0.00806619i
$485$	17.9331			0.814302
$486$	20.3989	−	9.52497i	0.925312	−	0.432061i
$487$	38.9239	−	6.16495i	1.76381	−	0.279360i	0.811470	−	0.584394i	$-0.198668\pi$
$487$	38.9239	−	6.16495i	1.76381	−	0.279360i	0.952342	+	0.305033i	$0.0986676\pi$
$488$	−2.50495	+	15.8157i	−0.113394	+	0.715941i
$489$	−5.25645	−	6.87368i	−0.237705	−	0.310839i
$490$	−5.21707	+	16.0565i	−0.235683	+	0.725359i
$491$	−20.1848	+	14.6651i	−0.910927	+	0.661827i	−0.941249	−	0.337713i	$-0.890347\pi$
$491$	−20.1848	+	14.6651i	−0.910927	+	0.661827i	0.0303220	+	0.999540i	$0.490347\pi$
$492$	−0.531165	−	1.50783i	−0.0239468	−	0.0679782i
$493$	33.0601	−	10.7419i	1.48895	−	0.483790i
$494$	7.95900	+	3.83234i	0.358092	+	0.172425i
$495$	22.5877	−	3.26831i	1.01524	−	0.146900i
$496$	15.5107	−	15.5107i	0.696452	−	0.696452i
$497$	21.0502	−	6.83962i	0.944230	−	0.306799i
$498$	12.9842	+	6.21933i	0.581835	+	0.278695i
$499$	−2.85398	+	18.0193i	−0.127762	+	0.806655i	0.837704	+	0.546124i	$0.183897\pi$
$499$	−2.85398	+	18.0193i	−0.127762	+	0.806655i	−0.965466	+	0.260530i	$0.916103\pi$
$500$	−0.830525	+	0.423174i	−0.0371422	+	0.0189249i
$501$	−32.7254	+	25.0258i	−1.46206	+	1.11807i
$502$	−32.1677	−	5.09487i	−1.43572	−	0.227395i
$503$	−9.76005	+	13.4336i	−0.435179	+	0.598973i	−0.969132	−	0.246541i	$-0.920706\pi$
$503$	−9.76005	+	13.4336i	−0.435179	+	0.598973i	0.533953	+	0.845514i	$0.320706\pi$
$504$	−7.17215	−	8.91658i	−0.319473	−	0.397176i
$505$	10.6306	+	10.6306i	0.473057	+	0.473057i
$506$	−2.38218	−	25.1007i	−0.105901	−	1.11586i
$507$	14.7772	−	16.9893i	0.656278	−	0.754519i
$508$	0.0409419	+	0.126006i	0.00181650	+	0.00559062i
$509$	−0.408564	−	2.57957i	−0.0181093	−	0.114338i	0.976978	−	0.213341i	$-0.0684345\pi$
$509$	−0.408564	−	2.57957i	−0.0181093	−	0.114338i	−0.995087	+	0.0990034i	$0.968435\pi$
$510$	14.0673	−	14.7751i	0.622909	−	0.654254i
$511$	−2.03801	−	0.662191i	−0.0901565	−	0.0292936i
$512$	−18.7161	+	9.53632i	−0.827142	+	0.421450i
$513$	−8.16040	+	3.33314i	−0.360290	+	0.147162i
$514$	−1.59897	−	10.0955i	−0.0705274	−	0.445292i
$515$	−1.32366	−	0.674438i	−0.0583274	−	0.0297193i
$516$	−0.0315101	−	0.171586i	−0.00138716	−	0.00755363i
$517$	−11.3144	+	9.98248i	−0.497606	+	0.439029i
$518$	−16.3226	+	16.3226i	−0.717174	+	0.717174i
$519$	−5.15909	+	2.79020i	−0.226459	+	0.122476i
$520$	10.8357	+	20.1335i	0.475175	+	0.882911i
$521$	4.94161	+	6.80155i	0.216496	+	0.297981i	0.903427	−	0.428741i	$-0.141043\pi$
$521$	4.94161	+	6.80155i	0.216496	+	0.297981i	−0.686931	+	0.726722i	$0.741043\pi$
$522$	31.3860	+	28.4473i	1.37373	+	1.24510i
$523$	4.40014	−	13.5422i	0.192405	−	0.592161i	−0.807592	−	0.589741i	$-0.799230\pi$
$523$	4.40014	−	13.5422i	0.192405	−	0.592161i	0.999997	−	0.00241972i	$-0.000770222\pi$
$524$	0.761725	−	0.553425i	0.0332761	−	0.0241765i
$525$	−0.207624	−	0.589387i	−0.00906146	−	0.0257229i
$526$	−22.0443	−	11.2321i	−0.961177	−	0.489744i
$527$	13.2436	−	13.2436i	0.576899	−	0.576899i
$528$	23.4679	+	4.63515i	1.02131	+	0.201719i
$529$	4.70833			0.204710
$530$	−3.47820	−	10.7048i	−0.151083	−	0.464987i
$531$	−11.2463	+	6.44388i	−0.488046	+	0.279640i
$532$	−0.117984	−	0.162391i	−0.00511525	−	0.00704054i
$533$	38.7953	−	0.872754i	1.68041	−	0.0378032i
$534$	34.3667	+	4.58188i	1.48719	+	0.198277i
$535$	3.45130	−	21.7907i	0.149213	−	0.942093i
$536$	4.15146	−	5.71400i	0.179316	−	0.246807i
$537$	−19.0893	+	10.3241i	−0.823764	+	0.445518i
$538$	14.7113	−	14.7113i	0.634249	−	0.634249i
$539$	−16.3701	+	4.20963i	−0.705108	+	0.181322i
$540$	0.992713	+	0.243508i	0.0427196	+	0.0104789i
$541$	9.81008	−	19.2534i	0.421768	−	0.827767i	−0.578162	−	0.815922i	$-0.696230\pi$
$541$	9.81008	−	19.2534i	0.421768	−	0.827767i	0.999930	−	0.0118444i	$-0.00377028\pi$
$542$	11.5159	−	15.8503i	0.494652	−	0.680829i
$543$	20.6142	−	21.6515i	0.884640	−	0.929156i
$544$	1.53581	−	0.782533i	0.0658472	−	0.0335508i
$545$	12.4553	−	38.3335i	0.533527	−	1.64203i
$546$	−11.6410	+	4.39754i	−0.498191	+	0.188197i
$547$	−7.58982	−	5.51433i	−0.324517	−	0.235776i	0.413583	−	0.910466i	$-0.364277\pi$
$547$	−7.58982	−	5.51433i	−0.324517	−	0.235776i	−0.738101	+	0.674691i	$0.764277\pi$
$548$	−0.427922	+	0.839845i	−0.0182799	+	0.0358764i
$549$	−16.2426	+	6.17383i	−0.693219	+	0.263493i
$550$	1.07831	+	0.637168i	0.0459793	+	0.0271689i
$551$	−11.7278	−	11.7278i	−0.499621	−	0.499621i
$552$	−7.19841	+	24.1557i	−0.306385	+	1.02813i
$553$	−1.90615	−	12.0349i	−0.0810576	−	0.511778i
$554$	−1.47032	+	9.28321i	−0.0624677	+	0.394406i
$555$	−6.08238	+	45.6212i	−0.258183	+	1.93651i
$556$	−0.765660	−	0.248778i	−0.0324712	−	0.0105505i
$557$	5.95049	−	37.5699i	0.252130	−	1.59189i	−0.458744	−	0.888569i	$-0.651700\pi$
$557$	5.95049	−	37.5699i	0.252130	−	1.59189i	0.710874	−	0.703319i	$-0.248300\pi$
$558$	22.0258	+	5.97940i	0.932426	+	0.253128i
$559$	4.19636	+	0.568211i	0.177487	+	0.0240328i
$560$		−	13.1788i		−	0.556907i
$561$	20.0377	+	3.95765i	0.845992	+	0.167092i
$562$	2.71443			0.114502
$563$	2.50796	+	7.71871i	0.105698	+	0.325305i	0.989894	−	0.141812i	$-0.0452928\pi$
$563$	2.50796	+	7.71871i	0.105698	+	0.325305i	−0.884196	+	0.467117i	$0.845293\pi$
$564$	−0.637363	+	0.224525i	−0.0268378	+	0.00945420i
$565$	2.80795	−	17.7287i	0.118131	−	0.745852i
$566$	0.786693	+	1.54397i	0.0330672	+	0.0648980i
$567$	4.52612	−	11.5633i	0.190079	−	0.485614i
$568$	35.8791	−	26.0677i	1.50545	−	1.09378i
$569$	−8.75188	−	6.35862i	−0.366898	−	0.266567i	0.389025	−	0.921227i	$-0.372812\pi$
$569$	−8.75188	−	6.35862i	−0.366898	−	0.266567i	−0.755923	+	0.654660i	$0.772812\pi$
$570$	−9.32837	−	2.77986i	−0.390723	−	0.116436i
$571$		−	22.7880i		−	0.953646i	−0.878999	−	0.476823i	$-0.841788\pi$
$571$		−	22.7880i		−	0.953646i	0.878999	−	0.476823i	$-0.158212\pi$
$572$	0.501713	−	0.894412i	0.0209777	−	0.0373972i
$573$	−4.73866	+	0.870212i	−0.197960	+	0.0363536i
$574$	−19.1084	−	9.73623i	−0.797570	−	0.406382i
$575$	−0.809041	+	1.11355i	−0.0337393	+	0.0464382i
$576$	−19.1516	−	12.5268i	−0.797981	−	0.521949i
$577$	−12.0494	−	23.6482i	−0.501622	−	0.984489i	−0.993501	−	0.113825i	$-0.963690\pi$
$577$	−12.0494	−	23.6482i	−0.501622	−	0.984489i	0.491879	−	0.870664i	$-0.336310\pi$
$578$	−5.60845	+	2.85765i	−0.233281	+	0.118862i
$579$	0.143547	+	5.84887i	0.00596562	+	0.243071i
$580$	0.300857	+	1.89954i	0.0124924	+	0.0788739i
$581$	7.55223	−	2.45387i	0.313319	−	0.101804i
$582$	3.53234	+	19.2350i	0.146420	+	0.797317i
$583$	7.17985	−	8.68554i	0.297359	−	0.359718i
$584$	−4.29373			−0.177676
$585$	−13.1110	+	21.0641i	−0.542072	+	0.870893i
$586$	−28.8148	−	20.9352i	−1.19033	−	0.864825i
$587$	−2.13711	−	0.338485i	−0.0882080	−	0.0139708i	0.112174	−	0.993689i	$-0.464218\pi$
$587$	−2.13711	−	0.338485i	−0.0882080	−	0.0139708i	−0.200382	+	0.979718i	$0.564218\pi$
$588$	−0.750358	−	0.100040i	−0.0309443	−	0.00412560i
$589$	−8.49884	−	2.76144i	−0.350189	−	0.113783i
$590$	−14.1365	−	2.23900i	−0.581990	−	0.0921782i
$591$	10.2949	−	3.62661i	0.423476	−	0.149179i
$592$	−21.9004	+	42.9820i	−0.900102	+	1.76655i
$593$	−23.2167	+	23.2167i	−0.953394	+	0.953394i	−0.998961	−	0.0455673i	$-0.985490\pi$
$593$	−23.2167	+	23.2167i	−0.953394	+	0.953394i	0.0455673	+	0.998961i	$0.485490\pi$
$594$	7.95474	+	23.5837i	0.326387	+	0.967652i
$595$		−	11.2525i		−	0.461308i
$596$	−1.02693	−	0.523248i	−0.0420647	−	0.0214331i
$597$	20.4681	+	9.80408i	0.837704	+	0.401254i
$598$	22.5319	+	15.6084i	0.921397	+	0.638274i
$599$	−13.7803	−	4.47749i	−0.563047	−	0.182945i	0.0136445	−	0.999907i	$-0.495657\pi$
$599$	−13.7803	−	4.47749i	−0.563047	−	0.182945i	−0.576692	+	0.816962i	$0.695657\pi$
$600$	−0.760593	−	0.994601i	−0.0310511	−	0.0406044i
$601$	−5.52251	+	4.01234i	−0.225268	+	0.163667i	−0.694695	−	0.719305i	$-0.744461\pi$
$601$	−5.52251	+	4.01234i	−0.225268	+	0.163667i	0.469427	+	0.882971i	$0.344461\pi$
$602$	−1.89335	−	1.37560i	−0.0771672	−	0.0560652i
$603$	7.61968	+	0.826172i	0.310297	+	0.0336443i
$604$	1.05476	−	1.05476i	0.0429176	−	0.0429176i
$605$	0.811382	+	25.2187i	0.0329874	+	1.02528i
$606$	−9.30844	+	13.4963i	−0.378129	+	0.548251i
$607$	−7.58247	−	23.3364i	−0.307763	−	0.947197i	−0.978632	−	0.205621i	$-0.934079\pi$
$607$	−7.58247	−	23.3364i	−0.307763	−	0.947197i	0.670869	−	0.741576i	$-0.265921\pi$
$608$	−0.665345	−	0.483401i	−0.0269833	−	0.0196045i
$609$	23.3573	−	0.573251i	0.946485	−	0.0232293i
$610$	−18.2487	−	5.92935i	−0.738867	−	0.240072i
$611$	−0.368915	−	16.3989i	−0.0149247	−	0.663427i
$612$	0.765525	+	0.500720i	0.0309445	+	0.0202404i
$613$	−30.6367	+	4.85238i	−1.23741	+	0.195986i	−0.740642	−	0.671900i	$-0.765479\pi$
$613$	−30.6367	+	4.85238i	−1.23741	+	0.195986i	−0.496764	+	0.867886i	$0.665479\pi$
$614$	12.4680	−	4.05108i	0.503166	−	0.163488i
$615$	−42.0562	+	7.72324i	−1.69587	+	0.311431i
$616$	10.6789	−	6.78265i	0.430267	−	0.273281i
$617$	14.9209	+	14.9209i	0.600693	+	0.600693i	0.940497	−	0.339803i	$-0.110360\pi$
$617$	14.9209	+	14.9209i	0.600693	+	0.600693i	−0.339803	+	0.940497i	$0.610360\pi$
$618$	0.462675	−	1.55260i	0.0186115	−	0.0624546i
$619$	−5.12364	−	32.3494i	−0.205936	−	1.30023i	−0.846526	−	0.532348i	$-0.821310\pi$
$619$	−5.12364	−	32.3494i	−0.205936	−	1.30023i	0.640589	−	0.767884i	$-0.278690\pi$
$620$	0.609071	+	0.838314i	0.0244609	+	0.0336675i
$621$	−26.6273	+	6.25407i	−1.06852	+	0.250967i
$622$	24.8794	−	12.6767i	0.997574	−	0.508289i
$623$	15.4712	−	11.2405i	0.619839	−	0.450339i
$624$	−20.2968	+	16.2577i	−0.812521	+	0.650827i
$625$	8.10831	+	24.9548i	0.324332	+	0.998193i
$626$	6.21370	+	6.21370i	0.248349	+	0.248349i
$627$	−2.65790	−	9.37575i	−0.106146	−	0.374431i
$628$		−	0.567786i		−	0.0226571i
$629$	−18.6993	+	36.6994i	−0.745590	+	1.46330i
$630$	11.8974	−	6.81698i	0.474005	−	0.271595i
$631$	−2.01980	−	0.319905i	−0.0804071	−	0.0127352i	0.116101	−	0.993237i	$-0.462960\pi$
$631$	−2.01980	−	0.319905i	−0.0804071	−	0.0127352i	−0.196508	+	0.980502i	$0.562960\pi$
$632$	−11.0842	−	21.7540i	−0.440906	−	0.865327i
$633$	−6.64170	−	0.885495i	−0.263984	−	0.0351952i
$634$	−5.54967	−	7.63847i	−0.220406	−	0.303362i
$635$	3.50013	−	0.554366i	0.138898	−	0.0219993i
$636$	0.443923	−	0.240087i	0.0176027	−	0.00952009i
$637$	7.97179	−	16.5558i	0.315854	−	0.655966i
$638$	−35.1163	+	30.9825i	−1.39027	+	1.22661i
$639$	43.9004	+	19.7187i	1.73667	+	0.780061i
$640$	−8.49615	−	26.1485i	−0.335840	−	1.03361i
$641$	−6.66261	−	4.84067i	−0.263157	−	0.191195i	0.448381	−	0.893843i	$-0.352001\pi$
$641$	−6.66261	−	4.84067i	−0.263157	−	0.191195i	−0.711538	+	0.702648i	$0.752001\pi$
$642$	24.0524	−	0.590311i	0.949273	−	0.0232977i
$643$	−7.77504	−	15.2594i	−0.306618	−	0.601771i	0.685357	−	0.728207i	$-0.259646\pi$
$643$	−7.77504	−	15.2594i	−0.306618	−	0.601771i	−0.991975	+	0.126436i	$0.959646\pi$
$644$	−0.282763	−	0.554953i	−0.0111424	−	0.0218682i
$645$	−4.66478	+	0.114486i	−0.183675	+	0.00450789i
$646$	−7.04732	−	5.12018i	−0.277273	−	0.201451i
$647$	4.16319	+	12.8130i	0.163672	+	0.503730i	0.998936	−	0.0461190i	$-0.0146853\pi$
$647$	4.16319	+	12.8130i	0.163672	+	0.503730i	−0.835264	+	0.549849i	$0.814685\pi$
$648$	1.46536	−	24.8380i	0.0575650	−	0.975729i
$649$	−5.69586	−	13.1489i	−0.223582	−	0.516138i
$650$	−1.28517	+	0.449776i	−0.0504085	+	0.0176417i
$651$	11.0729	−	5.98854i	0.433979	−	0.234710i
$652$	0.423167	−	0.0670230i	0.0165725	−	0.00262482i
$653$	−21.8227	−	30.0364i	−0.853988	−	1.17541i	−0.982970	−	0.183767i	$-0.941171\pi$
$653$	−21.8227	−	30.0364i	−0.853988	−	1.17541i	0.128981	−	0.991647i	$-0.458829\pi$
$654$	43.5698	+	5.80887i	1.70371	+	0.227145i
$655$	−11.4331	−	22.4388i	−0.446730	−	0.876757i
$656$	−44.2655	−	7.01096i	−1.72828	−	0.273732i
$657$	−2.31642	−	4.04277i	−0.0903722	−	0.157723i
$658$	−4.11553	+	8.07718i	−0.160440	+	0.314881i
$659$		−	17.7337i		−	0.690808i	−0.938454	−	0.345404i	$-0.887742\pi$
$659$		−	17.7337i		−	0.690808i	0.938454	−	0.345404i	$-0.112258\pi$
$660$	−0.389689	+	1.06070i	−0.0151686	+	0.0412878i
$661$	16.5309	+	16.5309i	0.642978	+	0.642978i	0.951286	−	0.308309i	$-0.0997630\pi$
$661$	16.5309	+	16.5309i	0.642978	+	0.642978i	−0.308309	+	0.951286i	$0.599763\pi$
$662$	−9.12214	−	28.0751i	−0.354542	−	1.09117i
$663$	−17.3300	+	13.8813i	−0.673043	+	0.539106i
$664$	12.8724	−	9.35238i	0.499548	−	0.362943i
$665$	−4.78370	+	2.43742i	−0.185504	+	0.0945189i
$666$	−50.1312	+	2.46219i	−1.94254	+	0.0954080i
$667$	−30.2497	−	41.6352i	−1.17127	−	1.61212i
$668$	−0.319094	−	2.01468i	−0.0123461	−	0.0779504i
$669$	−7.24454	+	24.3105i	−0.280090	+	0.939898i
$670$	5.98446	+	5.98446i	0.231200	+	0.231200i
$671$	−4.78436	−	18.6050i	−0.184698	−	0.718239i
$672$	1.13948	−	0.209256i	0.0439565	−	0.00807222i
$673$	−8.39070	+	2.72630i	−0.323438	+	0.105091i	−0.466236	−	0.884661i	$-0.654390\pi$
$673$	−8.39070	+	2.72630i	−0.323438	+	0.105091i	0.142798	+	0.989752i	$0.454390\pi$
$674$	41.4575	−	6.56623i	1.59688	−	0.252922i
$675$	0.526136	−	1.25271i	0.0202510	−	0.0482169i
$676$	0.391842	+	1.04373i	0.0150709	+	0.0401433i
$677$	3.21870	+	1.04582i	0.123705	+	0.0401941i	0.370215	−	0.928946i	$-0.379284\pi$
$677$	3.21870	+	1.04582i	0.123705	+	0.0401941i	−0.246510	+	0.969140i	$0.579284\pi$
$678$	19.5688	−	0.480272i	0.751536	−	0.0184447i
$679$	8.72679	+	6.34038i	0.334903	+	0.243322i
$680$	−6.96732	−	21.4432i	−0.267185	−	0.822310i
$681$	−19.8086	+	28.7206i	−0.759068	+	1.10057i
$682$	−9.27967	+	23.4634i	−0.355337	+	0.898459i
$683$	−12.1229	+	12.1229i	−0.463871	+	0.463871i	−0.899922	−	0.436051i	$-0.856377\pi$
$683$	−12.1229	+	12.1229i	−0.463871	+	0.463871i	0.436051	+	0.899922i	$0.356377\pi$
$684$	0.0470464	−	0.433903i	0.00179886	−	0.0165907i
$685$	20.3964	+	14.8189i	0.779308	+	0.566200i
$686$	−19.5002	+	14.1677i	−0.744520	+	0.540925i
$687$	−1.72579	−	2.25675i	−0.0658428	−	0.0861004i
$688$	−4.65137	−	1.51132i	−0.177332	−	0.0576186i
$689$	2.18807	+	12.0536i	0.0833587	+	0.459207i
$690$	−27.2395	−	13.0475i	−1.03699	−	0.496711i
$691$	44.6910	+	22.7712i	1.70012	+	0.866257i	0.986103	+	0.166132i	$0.0531279\pi$
$691$	44.6910	+	22.7712i	1.70012	+	0.866257i	0.714021	+	0.700124i	$0.246872\pi$
$692$		−	0.290405i		−	0.0110395i
$693$	12.1474	+	6.39559i	0.461441	+	0.242948i
$694$	7.88379	−	7.88379i	0.299265	−	0.299265i
$695$	−9.77586	+	19.1862i	−0.370819	+	0.727774i
$696$	44.1556	−	15.5548i	1.67371	−	0.589601i
$697$	−37.7953	−	5.98619i	−1.43160	−	0.226743i
$698$	8.54032	+	2.77492i	0.323256	+	0.105032i
$699$	−19.8215	−	2.64267i	−0.749716	−	0.0999548i
$700$	0.0305588	+	0.00484004i	0.00115502	+	0.000182936i
$701$	−17.0244	−	12.3689i	−0.643002	−	0.467168i	0.217878	−	0.975976i	$-0.430086\pi$
$701$	−17.0244	−	12.3689i	−0.643002	−	0.467168i	−0.860880	+	0.508808i	$0.830086\pi$
$702$	−25.1758	−	9.91372i	−0.950198	−	0.374169i
$703$	19.6522			0.741198
$704$	16.1194	−	19.4999i	0.607524	−	0.734929i
$705$	3.26463	+	17.7773i	0.122953	+	0.669530i
$706$	−7.60143	+	2.46985i	−0.286083	+	0.0929541i
$707$	1.41464	+	8.93171i	0.0532032	+	0.335912i
$708$	−0.0157458	−	0.641566i	−0.000591762	−	0.0241115i
$709$	33.9083	−	17.2772i	1.27345	−	0.648857i	0.319153	−	0.947703i	$-0.396602\pi$
$709$	33.9083	−	17.2772i	1.27345	−	0.648857i	0.954301	+	0.298846i	$0.0966016\pi$
$710$	24.1262	+	47.3502i	0.905438	+	1.77702i
$711$	14.5027	−	22.1724i	0.543892	−	0.831529i
$712$	22.5226	−	30.9997i	0.844069	−	1.16176i
$713$	−24.7062	−	12.5884i	−0.925253	−	0.471440i
$714$	12.0694	−	2.21644i	0.451686	−	0.0829480i
$715$	−21.5292	−	16.9966i	−0.805148	−	0.635637i
$716$		−	1.07453i		−	0.0401572i
$717$	1.56238	+	0.465591i	0.0583483	+	0.0173878i
$718$	16.3572	+	11.8842i	0.610446	+	0.443515i
$719$	−37.8019	+	27.4647i	−1.40977	+	1.02426i	−0.416418	+	0.909173i	$0.636715\pi$
$719$	−37.8019	+	27.4647i	−1.40977	+	1.02426i	−0.993355	+	0.115087i	$0.963285\pi$
$720$	19.2439	−	21.2319i	0.717177	−	0.791264i
$721$	−0.405679	−	0.796189i	−0.0151083	−	0.0296516i
$722$	3.64240	−	22.9972i	0.135556	−	0.855867i
$723$	2.64406	−	0.931426i	0.0983336	−	0.0346401i
$724$	0.457405	+	1.40775i	0.0169993	+	0.0523186i
$725$	2.55649			0.0949457
$726$	−26.8896	+	5.83767i	−0.997968	+	0.216656i
$727$			13.2400i			0.491045i	0.969391	+	0.245522i	$0.0789595\pi$
$727$			13.2400i			0.491045i	−0.969391	+	0.245522i	$0.921041\pi$
$728$	−1.84538	+	13.6286i	−0.0683944	+	0.505108i
$729$	24.1768	−	12.0201i	0.895436	−	0.445190i
$730$	0.804869	−	5.08174i	0.0297895	−	0.188084i
$731$	−3.97149	−	1.29042i	−0.146891	−	0.0477277i
$732$	0.113699	−	0.852803i	0.00420243	−	0.0315205i
$733$	−2.82612	+	17.8434i	−0.104385	+	0.659062i	0.878902	+	0.477002i	$0.158276\pi$
$733$	−2.82612	+	17.8434i	−0.104385	+	0.659062i	−0.983287	+	0.182060i	$0.941724\pi$
$734$	−1.98822	−	12.5531i	−0.0733867	−	0.463345i
$735$	−5.78250	+	19.4043i	−0.213291	+	0.715739i
$736$	−1.80445	−	1.80445i	−0.0665130	−	0.0665130i
$737$	−1.84529	+	8.26987i	−0.0679723	+	0.304625i
$738$	−16.5678	−	43.5880i	−0.609870	−	1.60450i
$739$	−11.0778	+	21.7413i	−0.407502	+	0.799768i	−0.999983	−	0.00581665i	$-0.998148\pi$
$739$	−11.0778	+	21.7413i	−0.407502	+	0.799768i	0.592481	+	0.805584i	$0.298148\pi$
$740$	−1.84359	−	1.33945i	−0.0677719	−	0.0492392i
$741$	9.65514	+	4.36055i	0.354690	+	0.160189i
$742$	2.09216	−	6.43901i	0.0768057	−	0.236384i
$743$	24.7506	−	12.6110i	0.908010	−	0.462654i	0.0633707	−	0.997990i	$-0.479815\pi$
$743$	24.7506	−	12.6110i	0.908010	−	0.462654i	0.844639	+	0.535336i	$0.179815\pi$
$744$	17.3929	−	18.2681i	0.637653	−	0.669740i
$745$	−18.1200	+	24.9400i	−0.663865	+	0.913731i
$746$	−22.5113	+	44.1808i	−0.824196	+	1.61757i
$747$	15.7503	+	7.07455i	0.576272	+	0.258844i
$748$	−0.644325	+	0.779447i	−0.0235588	+	0.0284994i
$749$	9.38375	−	9.38375i	0.342875	−	0.342875i
$750$	−23.9152	+	12.9341i	−0.873260	+	0.472286i
$751$	−10.0792	+	13.8728i	−0.367795	+	0.506226i	−0.952300	−	0.305164i	$-0.901289\pi$
$751$	−10.0792	+	13.8728i	−0.367795	+	0.506226i	0.584505	+	0.811390i	$0.301289\pi$
$752$	−2.96355	+	18.7111i	−0.108070	+	0.682324i
$753$	−38.7171	−	5.16190i	−1.41093	−	0.188110i
$754$	−1.14500	−	50.8969i	−0.0416983	−	1.85356i
$755$	−23.4513	−	32.2779i	−0.853478	−	1.17471i
$756$	0.396989	+	0.469479i	0.0144384	+	0.0170748i
$757$	9.04490	+	27.8373i	0.328742	+	1.01177i	0.969723	+	0.244208i	$0.0785280\pi$
$757$	9.04490	+	27.8373i	0.328742	+	1.01177i	−0.640980	+	0.767557i	$0.721472\pi$
$758$	−34.5619			−1.25535
$759$	−3.59468	−	30.0242i	−0.130479	−	1.08981i
$760$	−7.60680	+	7.60680i	−0.275928	+	0.275928i
$761$	18.8437	+	9.60132i	0.683082	+	0.348048i	0.760854	−	0.648924i	$-0.224781\pi$
$761$	18.8437	+	9.60132i	0.683082	+	0.348048i	−0.0777716	+	0.996971i	$0.524781\pi$
$762$	1.28404	+	3.64503i	0.0465159	+	0.132045i
$763$	19.6142	−	14.2506i	0.710082	−	0.515905i
$764$	0.0737148	−	0.226871i	0.00266691	−	0.00820790i
$765$	16.4311	−	18.1285i	0.594067	−	0.655436i
$766$	8.41961	+	11.5886i	0.304213	+	0.418713i
$767$	14.9199	+	4.47939i	0.538728	+	0.161742i
$768$	3.13000	−	1.69280i	0.112944	−	0.0610838i
$769$	0.632092	−	0.632092i	0.0227938	−	0.0227938i	−0.695618	−	0.718412i	$-0.744869\pi$
$769$	0.632092	−	0.632092i	0.0227938	−	0.0227938i	0.718412	+	0.695618i	$0.244869\pi$
$770$	6.02565	+	13.9102i	0.217149	+	0.501289i
$771$	−2.21413	−	12.0568i	−0.0797399	−	0.434216i
$772$	−0.258106	−	0.131512i	−0.00928946	−	0.00473321i
$773$	−6.36044	−	40.1583i	−0.228769	−	1.44439i	−0.788151	−	0.615482i	$-0.788961\pi$
$773$	−6.36044	−	40.1583i	−0.228769	−	1.44439i	0.559382	−	0.828910i	$-0.311039\pi$
$774$	−1.04163	−	4.98087i	−0.0374406	−	0.179034i
$775$	1.22729	−	0.625335i	0.0440855	−	0.0224627i
$776$	20.5559	+	6.67903i	0.737915	+	0.239763i
$777$	−19.0896	+	20.0501i	−0.684834	+	0.719295i
$778$	5.31987	+	33.5883i	0.190727	+	1.20420i
$779$	5.64201	+	17.3643i	0.202146	+	0.622141i
$780$	−0.608553	−	1.06714i	−0.0217897	−	0.0382097i
$781$	−27.0664	+	45.8058i	−0.968511	+	1.63906i
$782$	−19.1127	−	19.1127i	−0.683470	−	0.683470i
$783$	38.4670	+	33.1831i	1.37470	+	1.18587i
$784$	−12.4740	+	17.1689i	−0.445499	+	0.613177i
$785$	−14.9997	−	2.37572i	−0.535363	−	0.0847931i
$786$	21.8158	−	16.6830i	0.778143	−	0.595062i
$787$	36.6396	−	18.6688i	1.30606	−	0.665472i	0.344172	−	0.938907i	$-0.388160\pi$
$787$	36.6396	−	18.6688i	1.30606	−	0.665472i	0.961890	+	0.273435i	$0.0881598\pi$
$788$	−0.0845419	+	0.533776i	−0.00301168	+	0.0190150i
$789$	−26.7603	−	12.8180i	−0.952693	−	0.456333i
$790$	27.8241	−	9.04061i	0.989938	−	0.321650i
$791$	7.63453	−	7.63453i	0.271453	−	0.271453i
$792$	27.1085	+	4.66627i	0.963259	+	0.165809i
$793$	18.8162	+	9.06017i	0.668182	+	0.321736i
$794$	7.16331	−	2.32750i	0.254216	−	0.0825999i
$795$	−4.48515	−	12.7321i	−0.159072	−	0.451561i
$796$	−0.909082	+	0.660487i	−0.0322216	+	0.0234103i
$797$	3.40106	−	10.4674i	0.120472	−	0.370774i	−0.872577	−	0.488476i	$-0.837553\pi$
$797$	3.40106	−	10.4674i	0.120472	−	0.370774i	0.993049	+	0.117702i	$0.0375529\pi$
$798$	−3.55662	−	4.65087i	−0.125903	−	0.164639i
$799$	−2.53038	+	15.9762i	−0.0895183	+	0.565196i
$800$	0.125205	−	0.0198305i	0.00442667	−	0.000701115i
$801$	41.3384	+	4.48216i	1.46062	+	0.158369i
$802$	−10.2239			−0.361018
$803$	4.72671	−	2.04753i	0.166802	−	0.0722556i
$804$	−0.215454	+	0.312387i	−0.00759846	+	0.0110170i
$805$	−15.8438	+	5.14797i	−0.558422	+	0.181442i
$806$	−12.9994	−	24.1539i	−0.457884	−	0.850784i
$807$	17.2051	−	18.0709i	0.605648	−	0.636125i
$808$	8.22613	+	16.1447i	0.289394	+	0.567969i
$809$	37.2434	+	12.1011i	1.30941	+	0.425453i	0.878845	−	0.477107i	$-0.158315\pi$
$809$	37.2434	+	12.1011i	1.30941	+	0.425453i	0.430564	+	0.902560i	$0.358315\pi$
$810$	29.1217	+	6.39023i	1.02323	+	0.224530i
$811$	43.5250	−	6.89369i	1.52837	−	0.242070i	0.665078	−	0.746774i	$-0.268398\pi$
$811$	43.5250	−	6.89369i	1.52837	−	0.242070i	0.863292	+	0.504704i	$0.168398\pi$
$812$	−0.525188	+	1.03074i	−0.0184305	+	0.0361719i
$813$	13.3405	−	19.3425i	0.467873	−	0.678370i
$814$	3.46350	−	55.3807i	0.121396	−	1.94109i
$815$		−	11.4596i		−	0.401413i
$816$	22.5566	−	12.1993i	0.789639	−	0.427062i
$817$	0.311683	+	1.96789i	0.0109044	+	0.0688477i
$818$	14.7765	−	10.7357i	0.516647	−	0.375366i
$819$	−13.8275	+	5.61493i	−0.483173	+	0.196202i
$820$	0.654229	−	2.01351i	0.0228467	−	0.0703148i
$821$	27.2161	+	4.31060i	0.949847	+	0.150441i	0.612086	−	0.790791i	$-0.290330\pi$
$821$	27.2161	+	4.31060i	0.949847	+	0.150441i	0.337761	+	0.941232i	$0.390330\pi$
$822$	−11.8771	+	24.7960i	−0.414263	+	0.864862i
$823$	−41.9447	+	13.6287i	−1.46210	+	0.475066i	−0.928711	−	0.370803i	$-0.879082\pi$
$823$	−41.9447	+	13.6287i	−1.46210	+	0.475066i	−0.533390	+	0.845869i	$0.679082\pi$
$824$	−1.26606	−	1.26606i	−0.0441053	−	0.0441053i
$825$	1.31158	+	0.732197i	0.0456633	+	0.0254918i
$826$	−6.08762	−	6.08762i	−0.211815	−	0.211815i
$827$	−22.4314	−	11.4294i	−0.780017	−	0.397439i	0.0181800	−	0.999835i	$-0.494213\pi$
$827$	−22.4314	−	11.4294i	−0.780017	−	0.397439i	−0.798197	+	0.602396i	$0.794213\pi$
$828$	0.354803	−	1.30696i	0.0123302	−	0.0454199i
$829$	25.4693	+	35.0555i	0.884586	+	1.21753i	0.975129	+	0.221636i	$0.0711398\pi$
$829$	25.4693	+	35.0555i	0.884586	+	1.21753i	−0.0905429	+	0.995893i	$0.528860\pi$
$830$	8.65580	+	16.9880i	0.300447	+	0.589661i
$831$	−1.48966	+	11.1733i	−0.0516758	+	0.387597i
$832$	4.91242	+	27.0615i	0.170307	+	0.938190i
$833$	−10.6507	+	14.6594i	−0.369025	+	0.507919i
$834$	−22.5046	−	6.70639i	−0.779271	−	0.232223i
$835$	−54.5588			−1.88809
$836$	0.470929	+	0.105080i	0.0162874	+	0.00363428i
$837$	26.5836	+	6.52083i	0.918863	+	0.225393i
$838$	45.2922	+	23.0775i	1.56459	+	0.797199i
$839$	11.3868	−	1.80350i	0.393117	−	0.0622637i	0.0432533	−	0.999064i	$-0.486228\pi$
$839$	11.3868	−	1.80350i	0.393117	−	0.0622637i	0.349864	+	0.936800i	$0.386228\pi$
$840$	−0.371817	−	15.1498i	−0.0128289	−	0.522718i
$841$	−20.5763	+	63.3273i	−0.709527	+	2.18370i
$842$	12.0902	−	37.2098i	0.416656	−	1.28233i
$843$	3.25445	−	0.0798729i	0.112089	−	0.00275097i
$844$	0.195002	−	0.268397i	0.00671224	−	0.00923861i
$845$	29.2126	−	5.98451i	1.00494	−	0.205873i
$846$	−18.4248	+	7.00326i	−0.633456	+	0.240777i
$847$	−8.52139	+	12.5590i	−0.292798	+	0.431533i
$848$		−	14.1486i		−	0.485866i
$849$	0.988630	+	1.82798i	0.0339297	+	0.0627362i
$850$	1.32617	−	0.210045i	0.0454872	−	0.00720447i
$851$	60.2286	+	9.53928i	2.06461	+	0.327002i
$852$	−1.89280	+	1.44746i	−0.0648462	+	0.0495893i
$853$	4.15960	−	2.11942i	0.142422	−	0.0725677i	−0.381327	−	0.924440i	$-0.624533\pi$
$853$	4.15960	−	2.11942i	0.142422	−	0.0725677i	0.523749	+	0.851872i	$0.324533\pi$
$854$	−6.78397	−	9.33733i	−0.232143	−	0.319517i
$855$	−11.2660	−	3.05840i	−0.385288	−	0.104595i
$856$	12.0718	−	23.6922i	0.412606	−	0.809784i
$857$	−43.8082			−1.49646			−0.748230	−	0.663439i	$-0.769096\pi$
$857$	−43.8082			−1.49646			−0.748230	+	0.663439i	$0.769096\pi$
$858$	13.9898	−	26.4400i	0.477604	−	0.902648i
$859$	−36.3038			−1.23867			−0.619334	−	0.785127i	$-0.712597\pi$
$859$	−36.3038			−1.23867			−0.619334	+	0.785127i	$0.712597\pi$
$860$	0.104887	−	0.205853i	0.00357663	−	0.00701953i
$861$	−23.1964	−	11.1109i	−0.790530	−	0.378658i
$862$	−2.45324	−	3.37659i	−0.0835576	−	0.115007i
$863$	23.9649	−	12.2107i	0.815775	−	0.415658i	0.00426109	−	0.999991i	$-0.498644\pi$
$863$	23.9649	−	12.2107i	0.815775	−	0.415658i	0.811514	+	0.584333i	$0.198644\pi$
$864$	2.14133	+	1.32677i	0.0728497	+	0.0451375i
$865$	−7.67188	−	1.21511i	−0.260852	−	0.0413149i
$866$	−37.4384	+	5.92966i	−1.27221	+	0.201498i
$867$	−6.64011	+	3.59118i	−0.225510	+	0.121963i
$868$			0.623289i			0.0211558i
$869$	22.5756	+	18.6620i	0.765826	+	0.633065i
$870$	10.1324	+	55.1750i	0.343520	+	1.87061i
$871$	−5.58055	−	7.32851i	−0.189090	−	0.248317i
$872$	28.5539	−	39.3011i	0.966958	−	1.33090i
$873$	4.80106	+	22.9577i	0.162491	+	0.777001i
$874$	−3.98523	+	12.2653i	−0.134802	+	0.414879i
$875$	−4.63419	+	14.2626i	−0.156664	+	0.482162i
$876$	0.230628	−	0.00566023i	0.00779219	−	0.000191241i
$877$	1.98272	−	0.314031i	0.0669516	−	0.0106041i	−0.122869	−	0.992423i	$-0.539209\pi$
$877$	1.98272	−	0.314031i	0.0669516	−	0.0106041i	0.189820	+	0.981819i	$0.439209\pi$
$878$	−49.5180	−	25.2307i	−1.67115	−	0.851495i
$879$	−35.1633	−	24.2522i	−1.18603	−	0.818006i
$880$	20.9589	+	23.7553i	0.706524	+	0.800791i
$881$	−1.01631			−0.0342403			−0.0171202	−	0.999853i	$-0.505450\pi$
$881$	−1.01631			−0.0342403			−0.0171202	+	0.999853i	$0.505450\pi$
$882$	−21.9520	−	2.38017i	−0.739162	−	0.0801444i
$883$	−18.0122	+	24.7916i	−0.606157	+	0.834304i	−0.996254	−	0.0864698i	$-0.972441\pi$
$883$	−18.0122	+	24.7916i	−0.606157	+	0.834304i	0.390097	+	0.920774i	$0.372441\pi$
$884$	−0.196359	−	1.08170i	−0.00660426	−	0.0363816i
$885$	−17.0147	−	2.26846i	−0.571943	−	0.0762535i
$886$	−5.96486	−	11.7067i	−0.200394	−	0.393294i
$887$	−15.1721	−	20.8826i	−0.509428	−	0.701168i	0.474395	−	0.880312i	$-0.342667\pi$
$887$	−15.1721	−	20.8826i	−0.509428	−	0.701168i	−0.983823	+	0.179145i	$0.942667\pi$
$888$	−23.9631	+	50.0282i	−0.804150	+	1.67884i
$889$	1.89926	+	0.967724i	0.0636993	+	0.0324564i
$890$	32.4670	+	32.4670i	1.08830	+	1.08830i
$891$	10.2312	+	28.0414i	0.342759	+	0.939423i
$892$	−0.888114	−	0.888114i	−0.0297363	−	0.0297363i
$893$	7.33994	−	2.38489i	0.245622	−	0.0798073i
$894$	−30.3197	−	14.5229i	−1.01404	−	0.485719i
$895$	−28.3869	−	4.49605i	−0.948871	−	0.150286i
$896$	5.11049	−	15.7285i	0.170730	−	0.525452i
$897$	27.4737	+	18.0505i	0.917320	+	0.602689i
$898$	16.1305	−	11.7195i	0.538282	−	0.391085i
$899$	8.05656	+	50.8671i	0.268701	+	1.69651i
$900$	0.0421646	+	0.0524200i	0.00140549	+	0.00174733i
$901$		−	12.0806i		−	0.402462i
$902$	49.9276	−	12.8391i	1.66241	−	0.427496i
$903$	−2.31049	−	1.59355i	−0.0768884	−	0.0530300i
$904$	9.82151	−	19.2758i	0.326659	−	0.641104i
$905$	39.1037	−	6.19341i	1.29985	−	0.205876i
$906$	30.0019	−	31.5116i	0.996745	−	1.04690i
$907$	13.6685	+	4.44117i	0.453856	+	0.147467i	0.527019	−	0.849853i	$-0.323309\pi$
$907$	13.6685	+	4.44117i	0.453856	+	0.147467i	−0.0731635	+	0.997320i	$0.523309\pi$
$908$	−0.784246	−	1.53917i	−0.0260261	−	0.0510791i
$909$	−10.7631	+	16.4552i	−0.356991	+	0.545785i
$910$	−15.7838	−	4.73875i	−0.523228	−	0.157088i
$911$	−6.71718	+	2.18255i	−0.222550	+	0.0723109i	−0.418170	−	0.908369i	$-0.637328\pi$
$911$	−6.71718	+	2.18255i	−0.222550	+	0.0723109i	0.195619	+	0.980680i	$0.437328\pi$
$912$	−10.0722	−	6.94682i	−0.333524	−	0.230032i
$913$	−9.71068	+	16.4339i	−0.321377	+	0.543882i
$914$	−19.8848			−0.657732
$915$	−22.0536	−	6.57197i	−0.729068	−	0.217263i
$916$	0.138933	−	0.0220048i	0.00459048	−	0.000727060i
$917$	2.36969	−	14.9616i	0.0782541	−	0.494077i
$918$	22.6810	+	14.0531i	0.748584	+	0.463821i
$919$	−15.6005	+	48.0133i	−0.514611	+	1.58381i	0.269376	+	0.963035i	$0.413182\pi$
$919$	−15.6005	+	48.0133i	−0.514611	+	1.58381i	−0.783988	+	0.620776i	$0.786818\pi$
$920$	−27.0051	+	19.6204i	−0.890332	+	0.646864i
$921$	14.8291	−	5.22388i	0.488637	−	0.172133i
$922$	28.1679	−	9.15230i	0.927660	−	0.301415i
$923$	−19.1061	−	54.5930i	−0.628887	−	1.79695i
$924$	−0.564653	+	0.378392i	−0.0185757	+	0.0124482i
$925$	−2.14195	+	2.14195i	−0.0704269	+	0.0704269i
$926$	−49.9257	+	16.2218i	−1.64066	+	0.533082i
$927$	0.509034	−	1.87509i	0.0167189	−	0.0615859i
$928$	−0.741456	+	4.68137i	−0.0243395	+	0.153673i
$929$	5.49648	−	2.80059i	0.180334	−	0.0918845i	−0.361493	−	0.932375i	$-0.617733\pi$
$929$	5.49648	−	2.80059i	0.180334	−	0.0918845i	0.541827	+	0.840490i	$0.317733\pi$
$930$	18.3604	+	24.0093i	0.602061	+	0.787295i
$931$	8.53911	+	1.35246i	0.279858	+	0.0443251i
$932$	0.581963	−	0.801003i	0.0190628	−	0.0262377i
$933$	29.4560	−	15.9307i	0.964345	−	0.521548i
$934$	−3.39784	−	3.39784i	−0.111181	−	0.111181i
$935$	17.8954	+	20.2831i	0.585242	+	0.663327i
$936$	−22.8736	+	19.2618i	−0.747648	+	0.629590i
$937$	−5.13678	−	15.8094i	−0.167811	−	0.516470i	0.831421	−	0.555643i	$-0.187528\pi$
$937$	−5.13678	−	15.8094i	−0.167811	−	0.516470i	−0.999232	+	0.0391726i	$0.987528\pi$
$938$	0.796366	+	5.02806i	0.0260023	+	0.164172i
$939$	7.63270	+	7.26702i	0.249084	+	0.237150i
$940$	−0.851115	−	0.276544i	−0.0277603	−	0.00901987i
$941$	−7.85736	+	4.00352i	−0.256143	+	0.130511i	−0.577347	−	0.816499i	$-0.695912\pi$
$941$	−7.85736	+	4.00352i	−0.256143	+	0.130511i	0.321205	+	0.947010i	$0.395912\pi$
$942$	−0.406343	−	16.5566i	−0.0132394	−	0.539443i
$943$	8.86248	+	55.9555i	0.288602	+	1.82216i
$944$	−16.0304	−	8.16790i	−0.521745	−	0.265842i
$945$	14.0637	−	8.52324i	0.457493	−	0.277261i
$946$	5.60051	−	0.531515i	0.182088	−	0.0172810i
$947$	27.3547	−	27.3547i	0.888909	−	0.888909i	−0.105509	−	0.994418i	$-0.533647\pi$
$947$	27.3547	−	27.3547i	0.888909	−	0.888909i	0.994418	+	0.105509i	$0.0336473\pi$
$948$	0.624040	+	1.15385i	0.0202679	+	0.0374754i
$949$	−1.61024	+	5.36337i	−0.0522705	+	0.174102i
$950$	−0.376557	−	0.518287i	−0.0122171	−	0.0168154i
$951$	−6.87850	−	8.99478i	−0.223051	−	0.291676i
$952$	4.19089	−	12.8982i	0.135828	−	0.418034i
$953$	40.0420	−	29.0922i	1.29709	−	0.942389i	0.297164	−	0.954826i	$-0.403959\pi$
$953$	40.0420	−	29.0922i	1.29709	−	0.942389i	0.999923	+	0.0124375i	$0.00395908\pi$
$954$	12.7729	−	7.31863i	0.413539	−	0.236949i
$955$	−5.68502	−	2.89666i	−0.183963	−	0.0937338i
$956$	−0.0570772	+	0.0570772i	−0.00184601	+	0.00184601i
$957$	−41.1907	+	38.1795i	−1.33151	+	1.23417i
$958$	−7.94387			−0.256655
$959$	4.68619	+	14.4226i	0.151325	+	0.465730i
$960$	−10.0696	−	28.5847i	−0.324995	−	0.922568i
$961$	−1.91122	−	2.63057i	−0.0616524	−	0.0848572i
$962$	43.6032	+	41.6846i	1.40582	+	1.34396i
$963$	28.8200	−	1.41550i	0.928713	−	0.0456137i
$964$	−0.0217130	+	0.137091i	−0.000699329	+	0.00441539i
$965$	−4.55423	+	6.26836i	−0.146606	+	0.201786i
$966$	−8.64250	−	15.9800i	−0.278068	−	0.514149i
$967$	11.6950	−	11.6950i	0.376086	−	0.376086i	−0.493602	−	0.869688i	$-0.664320\pi$
$967$	11.6950	−	11.6950i	0.376086	−	0.376086i	0.869688	+	0.493602i	$0.164320\pi$
$968$	−8.46241	+	29.2092i	−0.271992	+	0.938819i
$969$	−8.59999	−	5.93143i	−0.276271	−	0.190545i
$970$	−11.7580	+	23.0765i	−0.377528	+	0.740941i
$971$	−2.61346	+	3.59711i	−0.0838698	+	0.115437i	−0.848890	−	0.528569i	$-0.822729\pi$
$971$	−2.61346	+	3.59711i	−0.0838698	+	0.115437i	0.765021	+	0.644006i	$0.222729\pi$
$972$	−0.0459658	+	1.33605i	−0.00147435	+	0.0428537i
$973$	−11.5406	+	5.88024i	−0.369976	+	0.188512i
$974$	−17.5878	+	54.1296i	−0.563549	+	1.73443i
$975$	−1.52761	+	0.577072i	−0.0489226	+	0.0184811i
$976$	−19.5130	−	14.1770i	−0.624596	−	0.453795i
$977$	−19.7026	+	38.6686i	−0.630343	+	1.23712i	0.326137	+	0.945322i	$0.394253\pi$
$977$	−19.7026	+	38.6686i	−0.630343	+	1.23712i	−0.956481	+	0.291796i	$0.905747\pi$
$978$	12.2915	−	2.25723i	0.393040	−	0.0721783i
$979$	−10.0111	+	44.8659i	−0.319957	+	1.43392i
$980$	−0.708881	−	0.708881i	−0.0226444	−	0.0226444i
$981$	52.4085	+	5.68245i	1.67327	+	0.181427i
$982$	−5.63678	−	35.5892i	−0.179877	−	1.13570i
$983$	1.63803	−	10.3421i	0.0522450	−	0.329862i	−0.947698	−	0.319169i	$-0.896596\pi$
$983$	1.63803	−	10.3421i	0.0522450	−	0.329862i	0.999943	−	0.0106929i	$-0.00340371\pi$
$984$	−51.0835	−	6.81064i	−1.62848	−	0.217115i
$985$	13.7475	+	4.46684i	0.438032	+	0.142325i
$986$	−7.85349	+	49.5850i	−0.250106	+	1.57911i
$987$	−4.69660	+	9.80516i	−0.149494	+	0.312102i
$988$	−0.417323	+	0.317785i	−0.0132768	+	0.0101101i
$989$			6.18233i			0.196587i
$990$	−10.6042	+	31.2089i	−0.337023	+	0.991884i
$991$	−59.1790			−1.87988			−0.939942	−	0.341335i	$-0.889121\pi$
$991$	−59.1790			−1.87988			−0.939942	+	0.341335i	$0.889121\pi$
$992$	0.789145	+	2.42874i	0.0250554	+	0.0771125i
$993$	−11.7630	−	33.3919i	−0.373289	−	1.05966i
$994$	−5.00051	+	31.5720i	−0.158606	+	1.00140i
$995$	13.6449	+	26.7796i	0.432573	+	0.848972i
$996$	−0.679084	+	0.519310i	−0.0215176	+	0.0164550i
$997$	35.2062	−	25.5788i	1.11499	−	0.810088i	0.131548	−	0.991310i	$-0.458005\pi$
$997$	35.2062	−	25.5788i	1.11499	−	0.810088i	0.983442	+	0.181222i	$0.0580053\pi$
$998$	−21.3161	−	15.4871i	−0.674749	−	0.490234i
$999$	−60.0319	+	4.42715i	−1.89933	+	0.140069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.16	✓	416
3.2	odd	2	inner	429.2.bi.a.5.37	yes	416
11.9	even	5	inner	429.2.bi.a.317.37	yes	416
13.8	odd	4	inner	429.2.bi.a.203.16	yes	416
33.20	odd	10	inner	429.2.bi.a.317.16	yes	416
39.8	even	4	inner	429.2.bi.a.203.37	yes	416
143.86	odd	20	inner	429.2.bi.a.86.37	yes	416
429.86	even	20	inner	429.2.bi.a.86.16	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.16	✓	416	1.1	even	1	trivial
429.2.bi.a.5.37	yes	416	3.2	odd	2	inner
429.2.bi.a.86.16	yes	416	429.86	even	20	inner
429.2.bi.a.86.37	yes	416	143.86	odd	20	inner
429.2.bi.a.203.16	yes	416	13.8	odd	4	inner
429.2.bi.a.203.37	yes	416	39.8	even	4	inner
429.2.bi.a.317.16	yes	416	33.20	odd	10	inner
429.2.bi.a.317.37	yes	416	11.9	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.655660 + 1.28681i) q^{2} +(-0.748233 + 1.56210i) q^{3} +(-0.0504074 - 0.0693798i) q^{4} +(-2.04378 + 1.04136i) q^{5} +(-1.51953 - 1.98704i) q^{6} +(-1.36274 - 0.215838i) q^{7} +(-2.73054 + 0.432475i) q^{8} +(-1.88029 - 2.33763i) q^{9} +O(q^{10})\)	\(q+(-0.655660 + 1.28681i) q^{2} +(-0.748233 + 1.56210i) q^{3} +(-0.0504074 - 0.0693798i) q^{4} +(-2.04378 + 1.04136i) q^{5} +(-1.51953 - 1.98704i) q^{6} +(-1.36274 - 0.215838i) q^{7} +(-2.73054 + 0.432475i) q^{8} +(-1.88029 - 2.33763i) q^{9} -3.31273i q^{10} +(2.79966 - 1.77818i) q^{11} +(0.146095 - 0.0268289i) q^{12} +(-0.483797 + 3.57295i) q^{13} +(1.17124 - 1.61207i) q^{14} +(-0.0974779 - 3.97177i) q^{15} +(1.28680 - 3.96035i) q^{16} +(1.09871 - 3.38148i) q^{17} +(4.24090 - 0.886884i) q^{18} +(-1.67554 + 0.265379i) q^{19} +(0.175271 + 0.0893052i) q^{20} +(1.35681 - 1.96724i) q^{21} +(0.452552 + 4.76849i) q^{22} -5.26387 q^{23} +(1.36751 - 4.58896i) q^{24} +(0.153697 - 0.211546i) q^{25} +(-4.28048 - 2.96519i) q^{26} +(5.05850 - 1.18811i) q^{27} +(0.0537176 + 0.105427i) q^{28} +(5.74667 + 7.90962i) q^{29} +(5.17481 + 2.47870i) q^{30} +(4.69354 + 2.39148i) q^{31} +(0.342800 + 0.342800i) q^{32} +(0.682897 + 5.70383i) q^{33} +(3.63093 + 3.63093i) q^{34} +(3.00992 - 0.977983i) q^{35} +(-0.0674034 + 0.248288i) q^{36} +(-11.4419 - 1.81222i) q^{37} +(0.757092 - 2.33009i) q^{38} +(-5.21929 - 3.42913i) q^{39} +(5.13027 - 3.72736i) q^{40} +(-1.68364 - 10.6301i) q^{41} +(1.64185 + 3.03579i) q^{42} -1.17448i q^{43} +(-0.264493 - 0.104606i) q^{44} +(6.27723 + 2.81954i) q^{45} +(3.45131 - 6.77358i) q^{46} +(-4.49337 + 0.711680i) q^{47} +(5.22363 + 4.97337i) q^{48} +(-4.84691 - 1.57486i) q^{49} +(0.171445 + 0.336480i) q^{50} +(4.46011 + 4.24643i) q^{51} +(0.272277 - 0.146537i) q^{52} +(3.23142 - 1.04995i) q^{53} +(-1.78779 + 7.28830i) q^{54} +(-3.87016 + 6.54967i) q^{55} +3.81437 q^{56} +(0.839145 - 2.81592i) q^{57} +(-13.9460 + 2.20883i) q^{58} +(0.675878 - 4.26733i) q^{59} +(-0.270647 + 0.206970i) q^{60} +(1.78987 - 5.50865i) q^{61} +(-6.15473 + 4.47167i) q^{62} +(2.05781 + 3.59143i) q^{63} +(7.25483 - 2.35724i) q^{64} +(-2.73195 - 7.80614i) q^{65} +(-7.78746 - 2.86102i) q^{66} +(-1.80650 + 1.80650i) q^{67} +(-0.289990 + 0.0942233i) q^{68} +(3.93860 - 8.22268i) q^{69} +(-0.715012 + 4.51441i) q^{70} +(-14.2934 + 7.28286i) q^{71} +(6.14518 + 5.56980i) q^{72} +(1.53400 + 0.242962i) q^{73} +(9.83396 - 13.5353i) q^{74} +(0.215454 + 0.398375i) q^{75} +(0.102871 + 0.102871i) q^{76} +(-4.19901 + 1.81894i) q^{77} +(7.83471 - 4.46787i) q^{78} +(2.72905 + 8.39915i) q^{79} +(1.49422 + 9.43413i) q^{80} +(-1.92899 + 8.79085i) q^{81} +(14.7828 + 4.80321i) q^{82} +(-5.12809 + 2.61289i) q^{83} +(-0.204880 + 0.00502831i) q^{84} +(1.27581 + 8.05517i) q^{85} +(1.51133 + 0.770062i) q^{86} +(-16.6554 + 3.05862i) q^{87} +(-6.87555 + 6.06618i) q^{88} +(-9.80067 + 9.80067i) q^{89} +(-7.74393 + 6.22891i) q^{90} +(1.43047 - 4.76459i) q^{91} +(0.265338 + 0.365206i) q^{92} +(-7.24758 + 5.54238i) q^{93} +(2.03033 - 6.24871i) q^{94} +(3.14808 - 2.28721i) q^{95} +(-0.791980 + 0.278992i) q^{96} +(-6.96600 - 3.54935i) q^{97} +(5.20446 - 5.20446i) q^{98} +(-9.42090 - 3.20104i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more