LMFDB - Embedded newform 35.2.k.b.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,2,Mod(3,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("35.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	35.k (of order $12$, degree $4$, 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:	$0.279476407074$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			3.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	35.3
Dual form			35.2.k.b.12.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.133975i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} -0.267949i q^{6} +(-2.50000 + 0.866025i) q^{7} +(-1.36603 - 1.36603i) q^{8} +(2.36603 - 1.36603i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.133975i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} -0.267949i q^{6} +(-2.50000 + 0.866025i) q^{7} +(-1.36603 - 1.36603i) q^{8} +(2.36603 - 1.36603i) q^{9} +(-0.232051 + 1.13397i) q^{10} +(1.36603 - 2.36603i) q^{11} +(-0.232051 + 0.866025i) q^{12} +(-2.00000 + 2.00000i) q^{13} +(-1.36603 + 0.0980762i) q^{14} +(1.09808 - 0.366025i) q^{15} +(1.23205 + 2.13397i) q^{16} +(3.73205 - 1.00000i) q^{17} +(1.36603 - 0.366025i) q^{18} +(0.366025 + 0.633975i) q^{19} +(1.73205 - 3.46410i) q^{20} +(0.767949 + 1.13397i) q^{21} +(1.00000 - 1.00000i) q^{22} +(0.0358984 - 0.133975i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(-1.26795 + 0.732051i) q^{26} +(-2.09808 - 2.09808i) q^{27} +(4.50000 + 0.866025i) q^{28} +3.00000i q^{29} +(0.598076 - 0.0358984i) q^{30} +(-6.46410 - 3.73205i) q^{31} +(1.33013 + 4.96410i) q^{32} +(-1.36603 - 0.366025i) q^{33} +2.00000 q^{34} +(-2.26795 - 5.46410i) q^{35} -4.73205 q^{36} +(-4.73205 - 1.26795i) q^{37} +(0.0980762 + 0.366025i) q^{38} +(1.26795 + 0.732051i) q^{39} +(2.86603 - 3.23205i) q^{40} +6.46410i q^{41} +(0.232051 + 0.669873i) q^{42} +(2.83013 + 2.83013i) q^{43} +(-4.09808 + 2.36603i) q^{44} +(3.36603 + 5.09808i) q^{45} +(0.0358984 - 0.0621778i) q^{46} +(2.36603 - 8.83013i) q^{47} +(0.901924 - 0.901924i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-2.56218 - 0.366025i) q^{50} +(-1.00000 - 1.73205i) q^{51} +(4.73205 - 1.26795i) q^{52} +(6.83013 - 1.83013i) q^{53} +(-0.767949 - 1.33013i) q^{54} +(5.46410 + 2.73205i) q^{55} +(4.59808 + 2.23205i) q^{56} +(0.267949 - 0.267949i) q^{57} +(-0.401924 + 1.50000i) q^{58} +(-4.09808 + 7.09808i) q^{59} +(-1.96410 - 0.401924i) q^{60} +(1.33013 - 0.767949i) q^{61} +(-2.73205 - 2.73205i) q^{62} +(-4.73205 + 5.46410i) q^{63} -2.26795i q^{64} +(-4.73205 - 4.19615i) q^{65} +(-0.633975 - 0.366025i) q^{66} +(2.86603 + 10.6962i) q^{67} +(-6.46410 - 1.73205i) q^{68} -0.0717968 q^{69} +(-0.401924 - 3.03590i) q^{70} +1.26795 q^{71} +(-5.09808 - 1.36603i) q^{72} +(-3.46410 - 12.9282i) q^{73} +(-2.19615 - 1.26795i) q^{74} +(0.964102 + 2.40192i) q^{75} -1.26795i q^{76} +(-1.36603 + 7.09808i) q^{77} +(0.535898 + 0.535898i) q^{78} +(2.83013 - 1.63397i) q^{79} +(-4.59808 + 3.03590i) q^{80} +(3.33013 - 5.76795i) q^{81} +(-0.866025 + 3.23205i) q^{82} +(-2.09808 + 2.09808i) q^{83} +(-0.169873 - 2.36603i) q^{84} +(2.73205 + 8.19615i) q^{85} +(1.03590 + 1.79423i) q^{86} +(1.50000 - 0.401924i) q^{87} +(-5.09808 + 1.36603i) q^{88} +(-0.330127 - 0.571797i) q^{89} +(1.00000 + 3.00000i) q^{90} +(3.26795 - 6.73205i) q^{91} +(-0.169873 + 0.169873i) q^{92} +(-1.00000 + 3.73205i) q^{93} +(2.36603 - 4.09808i) q^{94} +(-1.36603 + 0.901924i) q^{95} +(2.30385 - 1.33013i) q^{96} +(-5.92820 - 5.92820i) q^{97} +(3.33013 - 1.42820i) q^{98} -7.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{3} - 6 q^{4} + 4 q^{5} - 10 q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 + 4 * q^5 - 10 * q^7 - 2 * q^8 + 6 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} - 6 q^{4} + 4 q^{5} - 10 q^{7} - 2 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 6 q^{12} - 8 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} + 10 q^{21} + 4 q^{22} + 14 q^{23} - 2 q^{24} - 6 q^{25} - 12 q^{26} + 2 q^{27} + 18 q^{28} - 8 q^{30} - 12 q^{31} - 12 q^{32} - 2 q^{33} + 8 q^{34} - 16 q^{35} - 12 q^{36} - 12 q^{37} - 10 q^{38} + 12 q^{39} + 8 q^{40} - 6 q^{42} - 6 q^{43} - 6 q^{44} + 10 q^{45} + 14 q^{46} + 6 q^{47} + 14 q^{48} + 22 q^{49} + 14 q^{50} - 4 q^{51} + 12 q^{52} + 10 q^{53} - 10 q^{54} + 8 q^{55} + 8 q^{56} + 8 q^{57} - 12 q^{58} - 6 q^{59} + 6 q^{60} - 12 q^{61} - 4 q^{62} - 12 q^{63} - 12 q^{65} - 6 q^{66} + 8 q^{67} - 12 q^{68} - 28 q^{69} - 12 q^{70} + 12 q^{71} - 10 q^{72} + 12 q^{74} - 10 q^{75} - 2 q^{77} + 16 q^{78} - 6 q^{79} - 8 q^{80} - 4 q^{81} + 2 q^{83} - 18 q^{84} + 4 q^{85} + 18 q^{86} + 6 q^{87} - 10 q^{88} + 16 q^{89} + 4 q^{90} + 20 q^{91} - 18 q^{92} - 4 q^{93} + 6 q^{94} - 2 q^{95} + 30 q^{96} + 4 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 + 4 * q^5 - 10 * q^7 - 2 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 6 * q^12 - 8 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 + 10 * q^21 + 4 * q^22 + 14 * q^23 - 2 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 18 * q^28 - 8 * q^30 - 12 * q^31 - 12 * q^32 - 2 * q^33 + 8 * q^34 - 16 * q^35 - 12 * q^36 - 12 * q^37 - 10 * q^38 + 12 * q^39 + 8 * q^40 - 6 * q^42 - 6 * q^43 - 6 * q^44 + 10 * q^45 + 14 * q^46 + 6 * q^47 + 14 * q^48 + 22 * q^49 + 14 * q^50 - 4 * q^51 + 12 * q^52 + 10 * q^53 - 10 * q^54 + 8 * q^55 + 8 * q^56 + 8 * q^57 - 12 * q^58 - 6 * q^59 + 6 * q^60 - 12 * q^61 - 4 * q^62 - 12 * q^63 - 12 * q^65 - 6 * q^66 + 8 * q^67 - 12 * q^68 - 28 * q^69 - 12 * q^70 + 12 * q^71 - 10 * q^72 + 12 * q^74 - 10 * q^75 - 2 * q^77 + 16 * q^78 - 6 * q^79 - 8 * q^80 - 4 * q^81 + 2 * q^83 - 18 * q^84 + 4 * q^85 + 18 * q^86 + 6 * q^87 - 10 * q^88 + 16 * q^89 + 4 * q^90 + 20 * q^91 - 18 * q^92 - 4 * q^93 + 6 * q^94 - 2 * q^95 + 30 * q^96 + 4 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.133975i	0.353553	+	0.0947343i	0.431224	−	0.902245i	$-0.358082\pi$
$2$	0.500000	+	0.133975i	0.353553	+	0.0947343i	−0.0776710	+	0.996979i	$0.524748\pi$
$3$	−0.133975	−	0.500000i	−0.0773503	−	0.288675i	0.916406	−	0.400251i	$-0.131077\pi$
$3$	−0.133975	−	0.500000i	−0.0773503	−	0.288675i	−0.993756	+	0.111576i	$0.964410\pi$
$4$	−1.50000	−	0.866025i	−0.750000	−	0.433013i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$5$	0.133975	+	2.23205i	0.0599153	+	0.998203i
$6$		−	0.267949i		−	0.109390i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−1.36603	−	1.36603i	−0.482963	−	0.482963i
$9$	2.36603	−	1.36603i	0.788675	−	0.455342i
$10$	−0.232051	+	1.13397i	−0.0733809	+	0.358594i
$11$	1.36603	−	2.36603i	0.411872	−	0.713384i	−0.583222	−	0.812313i	$-0.698208\pi$
$11$	1.36603	−	2.36603i	0.411872	−	0.713384i	0.995094	+	0.0989291i	$0.0315417\pi$
$12$	−0.232051	+	0.866025i	−0.0669873	+	0.250000i
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	−0.927794	−	0.373094i	$-0.878297\pi$
$13$	−2.00000	+	2.00000i	−0.554700	+	0.554700i	0.373094	+	0.927794i	$0.378297\pi$
$14$	−1.36603	+	0.0980762i	−0.365086	+	0.0262120i
$15$	1.09808	−	0.366025i	0.283522	−	0.0945074i
$16$	1.23205	+	2.13397i	0.308013	+	0.533494i
$17$	3.73205	−	1.00000i	0.905155	−	0.242536i	0.223926	−	0.974606i	$-0.428112\pi$
$17$	3.73205	−	1.00000i	0.905155	−	0.242536i	0.681229	+	0.732070i	$0.261446\pi$
$18$	1.36603	−	0.366025i	0.321975	−	0.0862730i
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	0.904953	−	0.425512i	$-0.139906\pi$
$19$	0.366025	+	0.633975i	0.0839720	+	0.145444i	−0.820981	+	0.570956i	$0.806573\pi$
$20$	1.73205	−	3.46410i	0.387298	−	0.774597i
$21$	0.767949	+	1.13397i	0.167580	+	0.247454i
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	0.0358984	−	0.133975i	0.00748533	−	0.0279356i	−0.962082	−	0.272760i	$-0.912064\pi$
$23$	0.0358984	−	0.133975i	0.00748533	−	0.0279356i	0.969567	+	0.244824i	$0.0787302\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−4.96410	+	0.598076i	−0.992820	+	0.119615i
$26$	−1.26795	+	0.732051i	−0.248665	+	0.143567i
$27$	−2.09808	−	2.09808i	−0.403775	−	0.403775i
$28$	4.50000	+	0.866025i	0.850420	+	0.163663i
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$	0.598076	−	0.0358984i	0.109193	−	0.00655412i
$31$	−6.46410	−	3.73205i	−1.16099	−	0.670296i	−0.209447	−	0.977820i	$-0.567166\pi$
$31$	−6.46410	−	3.73205i	−1.16099	−	0.670296i	−0.951540	+	0.307524i	$0.900500\pi$
$32$	1.33013	+	4.96410i	0.235135	+	0.877537i
$33$	−1.36603	−	0.366025i	−0.237795	−	0.0637168i
$34$	2.00000			0.342997
$35$	−2.26795	−	5.46410i	−0.383353	−	0.923602i
$36$	−4.73205			−0.788675
$37$	−4.73205	−	1.26795i	−0.777944	−	0.208450i	−0.152066	−	0.988370i	$-0.548593\pi$
$37$	−4.73205	−	1.26795i	−0.777944	−	0.208450i	−0.625878	+	0.779921i	$0.715259\pi$
$38$	0.0980762	+	0.366025i	0.0159101	+	0.0593772i
$39$	1.26795	+	0.732051i	0.203034	+	0.117222i
$40$	2.86603	−	3.23205i	0.453158	−	0.511032i
$41$			6.46410i			1.00952i	0.863259	+	0.504762i	$0.168420\pi$
$41$			6.46410i			1.00952i	−0.863259	+	0.504762i	$0.831580\pi$
$42$	0.232051	+	0.669873i	0.0358062	+	0.103364i
$43$	2.83013	+	2.83013i	0.431590	+	0.431590i	0.889169	−	0.457579i	$-0.151283\pi$
$43$	2.83013	+	2.83013i	0.431590	+	0.431590i	−0.457579	+	0.889169i	$0.651283\pi$
$44$	−4.09808	+	2.36603i	−0.617808	+	0.356692i
$45$	3.36603	+	5.09808i	0.501777	+	0.759976i
$46$	0.0358984	−	0.0621778i	0.00529293	−	0.00916762i
$47$	2.36603	−	8.83013i	0.345120	−	1.28801i	−0.547351	−	0.836903i	$-0.684364\pi$
$47$	2.36603	−	8.83013i	0.345120	−	1.28801i	0.892472	−	0.451103i	$-0.148969\pi$
$48$	0.901924	−	0.901924i	0.130181	−	0.130181i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	−2.56218	−	0.366025i	−0.362347	−	0.0517638i
$51$	−1.00000	−	1.73205i	−0.140028	−	0.242536i
$52$	4.73205	−	1.26795i	0.656217	−	0.175833i
$53$	6.83013	−	1.83013i	0.938190	−	0.251387i	0.242846	−	0.970065i	$-0.421919\pi$
$53$	6.83013	−	1.83013i	0.938190	−	0.251387i	0.695344	+	0.718677i	$0.255252\pi$
$54$	−0.767949	−	1.33013i	−0.104505	−	0.181007i
$55$	5.46410	+	2.73205i	0.736779	+	0.368390i
$56$	4.59808	+	2.23205i	0.614444	+	0.298270i
$57$	0.267949	−	0.267949i	0.0354907	−	0.0354907i
$58$	−0.401924	+	1.50000i	−0.0527752	+	0.196960i
$59$	−4.09808	+	7.09808i	−0.533524	+	0.924091i	0.465709	+	0.884938i	$0.345799\pi$
$59$	−4.09808	+	7.09808i	−0.533524	+	0.924091i	−0.999233	+	0.0391530i	$0.987534\pi$
$60$	−1.96410	−	0.401924i	−0.253564	−	0.0518881i
$61$	1.33013	−	0.767949i	0.170305	−	0.0983258i	−0.412424	−	0.910992i	$-0.635318\pi$
$61$	1.33013	−	0.767949i	0.170305	−	0.0983258i	0.582730	+	0.812666i	$0.301985\pi$
$62$	−2.73205	−	2.73205i	−0.346971	−	0.346971i
$63$	−4.73205	+	5.46410i	−0.596182	+	0.688412i
$64$		−	2.26795i		−	0.283494i
$65$	−4.73205	−	4.19615i	−0.586939	−	0.520469i
$66$	−0.633975	−	0.366025i	−0.0780369	−	0.0450546i
$67$	2.86603	+	10.6962i	0.350141	+	1.30674i	0.886490	+	0.462747i	$0.153136\pi$
$67$	2.86603	+	10.6962i	0.350141	+	1.30674i	−0.536350	+	0.843996i	$0.680197\pi$
$68$	−6.46410	−	1.73205i	−0.783887	−	0.210042i
$69$	−0.0717968			−0.00864332
$70$	−0.401924	−	3.03590i	−0.0480391	−	0.362859i
$71$	1.26795			0.150478			0.0752389	−	0.997166i	$-0.476028\pi$
$71$	1.26795			0.150478			0.0752389	+	0.997166i	$0.476028\pi$
$72$	−5.09808	−	1.36603i	−0.600814	−	0.160988i
$73$	−3.46410	−	12.9282i	−0.405442	−	1.51313i	−0.803238	−	0.595658i	$-0.796891\pi$
$73$	−3.46410	−	12.9282i	−0.405442	−	1.51313i	0.397796	−	0.917474i	$-0.369775\pi$
$74$	−2.19615	−	1.26795i	−0.255298	−	0.147396i
$75$	0.964102	+	2.40192i	0.111325	+	0.277350i
$76$		−	1.26795i		−	0.145444i
$77$	−1.36603	+	7.09808i	−0.155673	+	0.808901i
$78$	0.535898	+	0.535898i	0.0606785	+	0.0606785i
$79$	2.83013	−	1.63397i	0.318414	−	0.183837i	−0.332271	−	0.943184i	$-0.607815\pi$
$79$	2.83013	−	1.63397i	0.318414	−	0.183837i	0.650686	+	0.759347i	$0.274482\pi$
$80$	−4.59808	+	3.03590i	−0.514081	+	0.339424i
$81$	3.33013	−	5.76795i	0.370014	−	0.640883i
$82$	−0.866025	+	3.23205i	−0.0956365	+	0.356920i
$83$	−2.09808	+	2.09808i	−0.230294	+	0.230294i	−0.812815	−	0.582522i	$-0.802066\pi$
$83$	−2.09808	+	2.09808i	−0.230294	+	0.230294i	0.582522	+	0.812815i	$0.302066\pi$
$84$	−0.169873	−	2.36603i	−0.0185347	−	0.258155i
$85$	2.73205	+	8.19615i	0.296333	+	0.888998i
$86$	1.03590	+	1.79423i	0.111704	+	0.193477i
$87$	1.50000	−	0.401924i	0.160817	−	0.0430908i
$88$	−5.09808	+	1.36603i	−0.543457	+	0.145619i
$89$	−0.330127	−	0.571797i	−0.0349934	−	0.0606103i	0.847998	−	0.529999i	$-0.177808\pi$
$89$	−0.330127	−	0.571797i	−0.0349934	−	0.0606103i	−0.882992	+	0.469389i	$0.844474\pi$
$90$	1.00000	+	3.00000i	0.105409	+	0.316228i
$91$	3.26795	−	6.73205i	0.342574	−	0.705711i
$92$	−0.169873	+	0.169873i	−0.0177105	+	0.0177105i
$93$	−1.00000	+	3.73205i	−0.103695	+	0.386996i
$94$	2.36603	−	4.09808i	0.244037	−	0.422684i
$95$	−1.36603	+	0.901924i	−0.140151	+	0.0925354i
$96$	2.30385	−	1.33013i	0.235135	−	0.135756i
$97$	−5.92820	−	5.92820i	−0.601918	−	0.601918i	0.338903	−	0.940821i	$-0.389944\pi$
$97$	−5.92820	−	5.92820i	−0.601918	−	0.601918i	−0.940821	+	0.338903i	$0.889944\pi$
$98$	3.33013	−	1.42820i	0.336394	−	0.144270i
$99$		−	7.46410i		−	0.750170i
$100$	7.96410	+	3.40192i	0.796410	+	0.340192i
$101$	7.16025	+	4.13397i	0.712472	+	0.411346i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	7.16025	+	4.13397i	0.712472	+	0.411346i	−0.0995037	+	0.995037i	$0.531726\pi$
$102$	−0.267949	−	1.00000i	−0.0265309	−	0.0990148i
$103$	4.59808	+	1.23205i	0.453062	+	0.121398i	0.478132	−	0.878288i	$-0.341314\pi$
$103$	4.59808	+	1.23205i	0.453062	+	0.121398i	−0.0250698	+	0.999686i	$0.507981\pi$
$104$	5.46410			0.535799
$105$	−2.42820	+	1.86603i	−0.236968	+	0.182105i
$106$	3.66025			0.355515
$107$	12.6962	+	3.40192i	1.22738	+	0.328876i	0.813560	−	0.581481i	$-0.197526\pi$
$107$	12.6962	+	3.40192i	1.22738	+	0.328876i	0.413823	+	0.910357i	$0.364193\pi$
$108$	1.33013	+	4.96410i	0.127992	+	0.477671i
$109$	−8.76795	−	5.06218i	−0.839817	−	0.484869i	0.0173849	−	0.999849i	$-0.494466\pi$
$109$	−8.76795	−	5.06218i	−0.839817	−	0.484869i	−0.857202	+	0.514980i	$0.827799\pi$
$110$	2.36603	+	2.09808i	0.225592	+	0.200044i
$111$			2.53590i			0.240697i
$112$	−4.92820	−	4.26795i	−0.465671	−	0.403283i
$113$	−7.73205	−	7.73205i	−0.727370	−	0.727370i	0.242725	−	0.970095i	$-0.421959\pi$
$113$	−7.73205	−	7.73205i	−0.727370	−	0.727370i	−0.970095	+	0.242725i	$0.921959\pi$
$114$	0.169873	−	0.0980762i	0.0159101	−	0.00918568i
$115$	0.303848	+	0.0621778i	0.0283339	+	0.00579811i
$116$	2.59808	−	4.50000i	0.241225	−	0.417815i
$117$	−2.00000	+	7.46410i	−0.184900	+	0.690056i
$118$	−3.00000	+	3.00000i	−0.276172	+	0.276172i
$119$	−8.46410	+	5.73205i	−0.775903	+	0.525456i
$120$	−2.00000	−	1.00000i	−0.182574	−	0.0912871i
$121$	1.76795	+	3.06218i	0.160723	+	0.278380i
$122$	0.767949	−	0.205771i	0.0695269	−	0.0186297i
$123$	3.23205	−	0.866025i	0.291424	−	0.0780869i
$124$	6.46410	+	11.1962i	0.580493	+	1.00544i
$125$	−2.00000	−	11.0000i	−0.178885	−	0.983870i
$126$	−3.09808	+	2.09808i	−0.275999	+	0.186911i
$127$	0.464102	−	0.464102i	0.0411824	−	0.0411824i	−0.686216	−	0.727398i	$-0.740729\pi$
$127$	0.464102	−	0.464102i	0.0411824	−	0.0411824i	0.727398	+	0.686216i	$0.240729\pi$
$128$	2.96410	−	11.0622i	0.261992	−	0.977768i
$129$	1.03590	−	1.79423i	0.0912058	−	0.157973i
$130$	−1.80385	−	2.73205i	−0.158208	−	0.239617i
$131$	−13.3923	+	7.73205i	−1.17009	+	0.675552i	−0.953702	−	0.300755i	$-0.902761\pi$
$131$	−13.3923	+	7.73205i	−1.17009	+	0.675552i	−0.216390	+	0.976307i	$0.569428\pi$
$132$	1.73205	+	1.73205i	0.150756	+	0.150756i
$133$	−1.46410	−	1.26795i	−0.126954	−	0.109945i
$134$			5.73205i			0.495174i
$135$	4.40192	−	4.96410i	0.378857	−	0.427242i
$136$	−6.46410	−	3.73205i	−0.554292	−	0.320021i
$137$	−3.53590	−	13.1962i	−0.302092	−	1.12742i	−0.935420	−	0.353539i	$-0.884978\pi$
$137$	−3.53590	−	13.1962i	−0.302092	−	1.12742i	0.633327	−	0.773884i	$-0.281689\pi$
$138$	−0.0358984	−	0.00961894i	−0.00305587	−	0.000818819i
$139$	−5.66025			−0.480096			−0.240048	−	0.970761i	$-0.577163\pi$
$139$	−5.66025			−0.480096			−0.240048	+	0.970761i	$0.577163\pi$
$140$	−1.33013	+	10.1603i	−0.112416	+	0.858698i
$141$	−4.73205			−0.398511
$142$	0.633975	+	0.169873i	0.0532020	+	0.0142554i
$143$	2.00000	+	7.46410i	0.167248	+	0.624180i
$144$	5.83013	+	3.36603i	0.485844	+	0.280502i
$145$	−6.69615	+	0.401924i	−0.556085	+	0.0333780i
$146$		−	6.92820i		−	0.573382i
$147$	−2.90192	−	2.16987i	−0.239347	−	0.178968i
$148$	6.00000	+	6.00000i	0.493197	+	0.493197i
$149$	0.696152	−	0.401924i	0.0570310	−	0.0329269i	−0.471213	−	0.882019i	$-0.656184\pi$
$149$	0.696152	−	0.401924i	0.0570310	−	0.0329269i	0.528244	+	0.849092i	$0.322850\pi$
$150$	0.160254	+	1.33013i	0.0130847	+	0.108604i
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	0.433350	+	0.901226i	$0.357331\pi$
$151$	−6.92820	+	12.0000i	−0.563809	+	0.976546i	−0.997159	+	0.0753205i	$0.976002\pi$
$152$	0.366025	−	1.36603i	0.0296886	−	0.110799i
$153$	7.46410	−	7.46410i	0.603437	−	0.603437i
$154$	−1.63397	+	3.36603i	−0.131669	+	0.271242i
$155$	7.46410	−	14.9282i	0.599531	−	1.19906i
$156$	−1.26795	−	2.19615i	−0.101517	−	0.175833i
$157$	−4.63397	+	1.24167i	−0.369831	+	0.0990960i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−4.63397	+	1.24167i	−0.369831	+	0.0990960i	0.0691164	+	0.997609i	$0.477982\pi$
$158$	1.63397	−	0.437822i	0.129992	−	0.0348313i
$159$	−1.83013	−	3.16987i	−0.145139	−	0.251387i
$160$	−10.9019	+	3.63397i	−0.861873	+	0.287291i
$161$	0.0262794	+	0.366025i	0.00207111	+	0.0288468i
$162$	2.43782	−	2.43782i	0.191533	−	0.191533i
$163$	−3.63397	+	13.5622i	−0.284635	+	1.06227i	0.664471	+	0.747314i	$0.268657\pi$
$163$	−3.63397	+	13.5622i	−0.284635	+	1.06227i	−0.949106	+	0.314958i	$0.898010\pi$
$164$	5.59808	−	9.69615i	0.437136	−	0.757142i
$165$	0.633975	−	3.09808i	0.0493549	−	0.241185i
$166$	−1.33013	+	0.767949i	−0.103238	+	0.0596044i
$167$	11.7583	+	11.7583i	0.909887	+	0.909887i	0.996263	−	0.0863757i	$-0.0275285\pi$
$167$	11.7583	+	11.7583i	0.909887	+	0.909887i	−0.0863757	+	0.996263i	$0.527529\pi$
$168$	0.500000	−	2.59808i	0.0385758	−	0.200446i
$169$			5.00000i			0.384615i
$170$	0.267949	+	4.46410i	0.0205508	+	0.342381i
$171$	1.73205	+	1.00000i	0.132453	+	0.0764719i
$172$	−1.79423	−	6.69615i	−0.136809	−	0.510577i
$173$	19.9282	+	5.33975i	1.51511	+	0.405973i	0.918130	−	0.396280i	$-0.129699\pi$
$173$	19.9282	+	5.33975i	1.51511	+	0.405973i	0.596984	+	0.802253i	$0.296366\pi$
$174$	0.803848			0.0609395
$175$	11.8923	−	5.79423i	0.898974	−	0.438003i
$176$	6.73205			0.507447
$177$	4.09808	+	1.09808i	0.308030	+	0.0825365i
$178$	−0.0884573	−	0.330127i	−0.00663015	−	0.0247441i
$179$	6.80385	+	3.92820i	0.508543	+	0.293608i	0.732235	−	0.681052i	$-0.238477\pi$
$179$	6.80385	+	3.92820i	0.508543	+	0.293608i	−0.223691	+	0.974660i	$0.571811\pi$
$180$	−0.633975	−	10.5622i	−0.0472537	−	0.787258i
$181$			1.19615i			0.0889093i	0.999011	+	0.0444547i	$0.0141550\pi$
$181$			1.19615i			0.0889093i	−0.999011	+	0.0444547i	$0.985845\pi$
$182$	2.53590	−	2.92820i	0.187973	−	0.217053i
$183$	−0.562178	−	0.562178i	−0.0415574	−	0.0415574i
$184$	−0.232051	+	0.133975i	−0.0171070	+	0.00987674i
$185$	2.19615	−	10.7321i	0.161464	−	0.789036i
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	2.73205	−	10.1962i	0.199787	−	0.745617i
$188$	−11.1962	+	11.1962i	−0.816563	+	0.816563i
$189$	7.06218	+	3.42820i	0.513698	+	0.249365i
$190$	−0.803848	+	0.267949i	−0.0583172	+	0.0194391i
$191$	−6.63397	−	11.4904i	−0.480018	−	0.831415i	0.519720	−	0.854337i	$-0.326036\pi$
$191$	−6.63397	−	11.4904i	−0.480018	−	0.831415i	−0.999737	+	0.0229220i	$0.992703\pi$
$192$	−1.13397	+	0.303848i	−0.0818376	+	0.0219283i
$193$	−7.83013	+	2.09808i	−0.563625	+	0.151023i	−0.529371	−	0.848390i	$-0.677572\pi$
$193$	−7.83013	+	2.09808i	−0.563625	+	0.151023i	−0.0342537	+	0.999413i	$0.510905\pi$
$194$	−2.16987	−	3.75833i	−0.155788	−	0.269832i
$195$	−1.46410	+	2.92820i	−0.104846	+	0.209693i
$196$	−12.0000	+	1.73205i	−0.857143	+	0.123718i
$197$	−10.1244	+	10.1244i	−0.721330	+	0.721330i	−0.968876	−	0.247546i	$-0.920376\pi$
$197$	−10.1244	+	10.1244i	−0.721330	+	0.721330i	0.247546	+	0.968876i	$0.420376\pi$
$198$	1.00000	−	3.73205i	0.0710669	−	0.265225i
$199$	−5.53590	+	9.58846i	−0.392429	+	0.679708i	−0.992769	−	0.120037i	$-0.961699\pi$
$199$	−5.53590	+	9.58846i	−0.392429	+	0.679708i	0.600340	+	0.799745i	$0.295032\pi$
$200$	7.59808	+	5.96410i	0.537265	+	0.421726i
$201$	4.96410	−	2.86603i	0.350141	−	0.202154i
$202$	3.02628	+	3.02628i	0.212928	+	0.212928i
$203$	−2.59808	−	7.50000i	−0.182349	−	0.526397i
$204$			3.46410i			0.242536i
$205$	−14.4282	+	0.866025i	−1.00771	+	0.0604858i
$206$	2.13397	+	1.23205i	0.148681	+	0.0858410i
$207$	−0.0980762	−	0.366025i	−0.00681677	−	0.0254405i
$208$	−6.73205	−	1.80385i	−0.466784	−	0.125074i
$209$	2.00000			0.138343
$210$	−1.46410	+	0.607695i	−0.101033	+	0.0419349i
$211$	−0.196152			−0.0135037			−0.00675184	−	0.999977i	$-0.502149\pi$
$211$	−0.196152			−0.0135037			−0.00675184	+	0.999977i	$0.502149\pi$
$212$	−11.8301	−	3.16987i	−0.812496	−	0.217708i
$213$	−0.169873	−	0.633975i	−0.0116395	−	0.0434392i
$214$	5.89230	+	3.40192i	0.402790	+	0.232551i
$215$	−5.93782	+	6.69615i	−0.404956	+	0.456674i
$216$			5.73205i			0.390017i
$217$	19.3923	+	3.73205i	1.31644	+	0.253348i
$218$	−3.70577	−	3.70577i	−0.250987	−	0.250987i
$219$	−6.00000	+	3.46410i	−0.405442	+	0.234082i
$220$	−5.83013	−	8.83013i	−0.393067	−	0.595327i
$221$	−5.46410	+	9.46410i	−0.367555	+	0.636624i
$222$	−0.339746	+	1.26795i	−0.0228023	+	0.0850992i
$223$	18.1244	−	18.1244i	1.21370	−	1.21370i	0.243895	−	0.969802i	$-0.421575\pi$
$223$	18.1244	−	18.1244i	1.21370	−	1.21370i	0.969802	−	0.243895i	$-0.0784252\pi$
$224$	−7.62436	−	11.2583i	−0.509424	−	0.752229i
$225$	−10.9282	+	8.19615i	−0.728547	+	0.546410i
$226$	−2.83013	−	4.90192i	−0.188257	−	0.326071i
$227$	−19.0263	+	5.09808i	−1.26282	+	0.338371i	−0.827275	−	0.561797i	$-0.810110\pi$
$227$	−19.0263	+	5.09808i	−1.26282	+	0.338371i	−0.435543	+	0.900168i	$0.643444\pi$
$228$	−0.633975	+	0.169873i	−0.0419860	+	0.0112501i
$229$	−9.19615	−	15.9282i	−0.607699	−	1.05257i	−0.991619	−	0.129199i	$-0.958759\pi$
$229$	−9.19615	−	15.9282i	−0.607699	−	1.05257i	0.383920	−	0.923366i	$-0.374574\pi$
$230$	0.143594	+	0.0717968i	0.00946828	+	0.00473414i
$231$	3.73205	−	0.267949i	0.245551	−	0.0176298i
$232$	4.09808	−	4.09808i	0.269052	−	0.269052i
$233$	−1.73205	+	6.46410i	−0.113470	+	0.423477i	−0.999168	−	0.0407854i	$-0.987014\pi$
$233$	−1.73205	+	6.46410i	−0.113470	+	0.423477i	0.885698	+	0.464263i	$0.153681\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$	20.0263	+	4.09808i	1.30637	+	0.267329i
$236$	12.2942	−	7.09808i	0.800286	−	0.462045i
$237$	−1.19615	−	1.19615i	−0.0776984	−	0.0776984i
$238$	−5.00000	+	1.73205i	−0.324102	+	0.112272i
$239$		−	2.39230i		−	0.154745i	−0.997002	−	0.0773727i	$-0.975347\pi$
$239$		−	2.39230i		−	0.154745i	0.997002	−	0.0773727i	$-0.0246531\pi$
$240$	2.13397	+	1.89230i	0.137747	+	0.122148i
$241$	21.4641	+	12.3923i	1.38262	+	0.798259i	0.992470	−	0.122491i	$-0.0390882\pi$
$241$	21.4641	+	12.3923i	1.38262	+	0.798259i	0.390155	+	0.920749i	$0.372422\pi$
$242$	0.473721	+	1.76795i	0.0304519	+	0.113648i
$243$	−11.9282	−	3.19615i	−0.765195	−	0.205033i
$244$	−2.66025			−0.170305
$245$	10.4019	+	11.6962i	0.664555	+	0.747240i
$246$	1.73205			0.110432
$247$	−2.00000	−	0.535898i	−0.127257	−	0.0340984i
$248$	3.73205	+	13.9282i	0.236985	+	0.884442i
$249$	1.33013	+	0.767949i	0.0842934	+	0.0486668i
$250$	0.473721	−	5.76795i	0.0299607	−	0.364797i
$251$		−	21.8564i		−	1.37956i	−0.724017	−	0.689782i	$-0.757706\pi$
$251$		−	21.8564i		−	1.37956i	0.724017	−	0.689782i	$-0.242294\pi$
$252$	11.8301	−	4.09808i	0.745228	−	0.258155i
$253$	−0.267949	−	0.267949i	−0.0168458	−	0.0168458i
$254$	0.294229	−	0.169873i	0.0184615	−	0.0106588i
$255$	3.73205	−	2.46410i	0.233710	−	0.154308i
$256$	0.696152	−	1.20577i	0.0435095	−	0.0753607i
$257$	−0.732051	+	2.73205i	−0.0456641	+	0.170421i	−0.984992	−	0.172600i	$-0.944783\pi$
$257$	−0.732051	+	2.73205i	−0.0456641	+	0.170421i	0.939328	+	0.343020i	$0.111450\pi$
$258$	0.758330	−	0.758330i	0.0472116	−	0.0472116i
$259$	12.9282	−	0.928203i	0.803319	−	0.0576757i
$260$	3.46410	+	10.3923i	0.214834	+	0.644503i
$261$	4.09808	+	7.09808i	0.253665	+	0.439360i
$262$	−7.73205	+	2.07180i	−0.477688	+	0.127996i
$263$	−15.1603	+	4.06218i	−0.934821	+	0.250485i	−0.693909	−	0.720062i	$-0.744113\pi$
$263$	−15.1603	+	4.06218i	−0.934821	+	0.250485i	−0.240912	+	0.970547i	$0.577447\pi$
$264$	1.36603	+	2.36603i	0.0840731	+	0.145619i
$265$	5.00000	+	15.0000i	0.307148	+	0.921443i
$266$	−0.562178	−	0.830127i	−0.0344693	−	0.0508984i
$267$	−0.241670	+	0.241670i	−0.0147899	+	0.0147899i
$268$	4.96410	−	18.5263i	0.303231	−	1.13167i
$269$	11.4282	−	19.7942i	0.696790	−	1.20688i	−0.272784	−	0.962075i	$-0.587944\pi$
$269$	11.4282	−	19.7942i	0.696790	−	1.20688i	0.969574	−	0.244800i	$-0.0787223\pi$
$270$	2.86603	−	1.89230i	0.174421	−	0.115162i
$271$	18.4186	−	10.6340i	1.11885	−	0.645968i	0.177742	−	0.984077i	$-0.443121\pi$
$271$	18.4186	−	10.6340i	1.11885	−	0.645968i	0.941107	+	0.338109i	$0.109787\pi$
$272$	6.73205	+	6.73205i	0.408191	+	0.408191i
$273$	−3.80385	−	0.732051i	−0.230219	−	0.0443057i
$274$		−	7.07180i		−	0.427223i
$275$	−5.36603	+	12.5622i	−0.323584	+	0.757528i
$276$	0.107695	+	0.0621778i	0.00648249	+	0.00374267i
$277$	−1.39230	−	5.19615i	−0.0836555	−	0.312207i	0.911401	−	0.411520i	$-0.135002\pi$
$277$	−1.39230	−	5.19615i	−0.0836555	−	0.312207i	−0.995056	+	0.0993135i	$0.968335\pi$
$278$	−2.83013	−	0.758330i	−0.169740	−	0.0454816i
$279$	−20.3923			−1.22086
$280$	−4.36603	+	10.5622i	−0.260920	+	0.631211i
$281$	−0.928203			−0.0553720			−0.0276860	−	0.999617i	$-0.508814\pi$
$281$	−0.928203			−0.0553720			−0.0276860	+	0.999617i	$0.508814\pi$
$282$	−2.36603	−	0.633975i	−0.140895	−	0.0377526i
$283$	−0.509619	−	1.90192i	−0.0302937	−	0.113058i	0.949123	−	0.314904i	$-0.101972\pi$
$283$	−0.509619	−	1.90192i	−0.0302937	−	0.113058i	−0.979417	+	0.201847i	$0.935306\pi$
$284$	−1.90192	−	1.09808i	−0.112858	−	0.0651588i
$285$	0.633975	+	0.562178i	0.0375534	+	0.0333005i
$286$			4.00000i			0.236525i
$287$	−5.59808	−	16.1603i	−0.330444	−	0.953910i
$288$	9.92820	+	9.92820i	0.585025	+	0.585025i
$289$	−1.79423	+	1.03590i	−0.105543	+	0.0609352i
$290$	−3.40192	−	0.696152i	−0.199768	−	0.0408795i
$291$	−2.16987	+	3.75833i	−0.127200	+	0.220317i
$292$	−6.00000	+	22.3923i	−0.351123	+	1.31041i
$293$	−2.39230	+	2.39230i	−0.139760	+	0.139760i	−0.773525	−	0.633765i	$-0.781508\pi$
$293$	−2.39230	+	2.39230i	−0.139760	+	0.139760i	0.633765	+	0.773525i	$0.281508\pi$
$294$	−1.16025	−	1.47372i	−0.0676674	−	0.0859491i
$295$	−16.3923	−	8.19615i	−0.954397	−	0.477198i
$296$	4.73205	+	8.19615i	0.275045	+	0.476392i
$297$	−7.83013	+	2.09808i	−0.454350	+	0.121743i
$298$	0.401924	−	0.107695i	0.0232828	−	0.00623861i
$299$	0.196152	+	0.339746i	0.0113438	+	0.0196480i
$300$	0.633975	−	4.43782i	0.0366025	−	0.256218i
$301$	−9.52628	−	4.62436i	−0.549086	−	0.266543i
$302$	−5.07180	+	5.07180i	−0.291849	+	0.291849i
$303$	1.10770	−	4.13397i	0.0636354	−	0.237491i
$304$	−0.901924	+	1.56218i	−0.0517289	+	0.0895970i
$305$	1.89230	+	2.86603i	0.108353	+	0.164108i
$306$	4.73205	−	2.73205i	0.270513	−	0.156181i
$307$	6.29423	+	6.29423i	0.359231	+	0.359231i	0.863529	−	0.504299i	$-0.168249\pi$
$307$	6.29423	+	6.29423i	0.359231	+	0.359231i	−0.504299	+	0.863529i	$0.668249\pi$
$308$	8.19615	−	9.46410i	0.467019	−	0.539267i
$309$		−	2.46410i		−	0.140178i
$310$	5.73205	−	6.46410i	0.325559	−	0.367136i
$311$	−13.2224	−	7.63397i	−0.749775	−	0.432883i	0.0758374	−	0.997120i	$-0.475837\pi$
$311$	−13.2224	−	7.63397i	−0.749775	−	0.432883i	−0.825613	+	0.564237i	$0.809170\pi$
$312$	−0.732051	−	2.73205i	−0.0414442	−	0.154672i
$313$	−5.19615	−	1.39230i	−0.293704	−	0.0786977i	0.108958	−	0.994046i	$-0.465248\pi$
$313$	−5.19615	−	1.39230i	−0.293704	−	0.0786977i	−0.402662	+	0.915349i	$0.631915\pi$
$314$	−2.48334			−0.140143
$315$	−12.8301	−	9.83013i	−0.722896	−	0.553865i
$316$	−5.66025			−0.318414
$317$	9.19615	+	2.46410i	0.516507	+	0.138398i	0.507651	−	0.861563i	$-0.330514\pi$
$317$	9.19615	+	2.46410i	0.516507	+	0.138398i	0.00885679	+	0.999961i	$0.497181\pi$
$318$	−0.490381	−	1.83013i	−0.0274992	−	0.102628i
$319$	7.09808	+	4.09808i	0.397416	+	0.229448i
$320$	5.06218	−	0.303848i	0.282984	−	0.0169856i
$321$		−	6.80385i		−	0.379754i
$322$	−0.0358984	+	0.186533i	−0.00200054	+	0.0103951i
$323$	2.00000	+	2.00000i	0.111283	+	0.111283i
$324$	−9.99038	+	5.76795i	−0.555021	+	0.320442i
$325$	8.73205	−	11.1244i	0.484367	−	0.617068i
$326$	−3.63397	+	6.29423i	−0.201267	+	0.348605i
$327$	−1.35641	+	5.06218i	−0.0750094	+	0.279939i
$328$	8.83013	−	8.83013i	0.487562	−	0.487562i
$329$	1.73205	+	24.1244i	0.0954911	+	1.33002i
$330$	0.732051	−	1.46410i	0.0402981	−	0.0805961i
$331$	0.928203	+	1.60770i	0.0510187	+	0.0883669i	0.890407	−	0.455165i	$-0.150420\pi$
$331$	0.928203	+	1.60770i	0.0510187	+	0.0883669i	−0.839388	+	0.543532i	$0.817087\pi$
$332$	4.96410	−	1.33013i	0.272440	−	0.0730002i
$333$	−12.9282	+	3.46410i	−0.708461	+	0.189832i
$334$	4.30385	+	7.45448i	0.235496	+	0.407891i
$335$	−23.4904	+	7.83013i	−1.28342	+	0.427806i
$336$	−1.47372	+	3.03590i	−0.0803980	+	0.165622i
$337$	9.53590	−	9.53590i	0.519453	−	0.519453i	−0.397953	−	0.917406i	$-0.630279\pi$
$337$	9.53590	−	9.53590i	0.519453	−	0.519453i	0.917406	+	0.397953i	$0.130279\pi$
$338$	−0.669873	+	2.50000i	−0.0364363	+	0.135982i
$339$	−2.83013	+	4.90192i	−0.153711	+	0.266236i
$340$	3.00000	−	14.6603i	0.162698	−	0.795064i
$341$	−17.6603	+	10.1962i	−0.956356	+	0.552153i
$342$	0.732051	+	0.732051i	0.0395848	+	0.0395848i
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		−	7.73205i		−	0.416884i
$345$	−0.00961894	−	0.160254i	−0.000517866	−	0.00862779i
$346$	9.24871	+	5.33975i	0.497214	+	0.287067i
$347$	−7.79423	−	29.0885i	−0.418416	−	1.56155i	−0.777893	−	0.628396i	$-0.783712\pi$
$347$	−7.79423	−	29.0885i	−0.418416	−	1.56155i	0.359477	−	0.933154i	$-0.382955\pi$
$348$	−2.59808	−	0.696152i	−0.139272	−	0.0373177i
$349$	6.26795			0.335516			0.167758	−	0.985828i	$-0.446347\pi$
$349$	6.26795			0.335516			0.167758	+	0.985828i	$0.446347\pi$
$350$	6.72243	−	1.30385i	0.359329	−	0.0696936i
$351$	8.39230			0.447948
$352$	13.5622	+	3.63397i	0.722867	+	0.193691i
$353$	3.63397	+	13.5622i	0.193417	+	0.721842i	0.992671	+	0.120849i	$0.0385615\pi$
$353$	3.63397	+	13.5622i	0.193417	+	0.721842i	−0.799254	+	0.600993i	$0.794772\pi$
$354$	1.90192	+	1.09808i	0.101086	+	0.0583621i
$355$	0.169873	+	2.83013i	0.00901592	+	0.150208i
$356$			1.14359i			0.0606103i
$357$	4.00000	+	3.46410i	0.211702	+	0.183340i
$358$	2.87564	+	2.87564i	0.151983	+	0.151983i
$359$	29.6603	−	17.1244i	1.56541	−	0.903789i	0.568715	−	0.822535i	$-0.307441\pi$
$359$	29.6603	−	17.1244i	1.56541	−	0.903789i	0.996693	−	0.0812542i	$-0.0258926\pi$
$360$	2.36603	−	11.5622i	0.124700	−	0.609380i
$361$	9.23205	−	15.9904i	0.485897	−	0.841599i
$362$	−0.160254	+	0.598076i	−0.00842277	+	0.0314342i
$363$	1.29423	−	1.29423i	0.0679294	−	0.0679294i
$364$	−10.7321	+	7.26795i	−0.562512	+	0.380944i
$365$	28.3923	−	9.46410i	1.48612	−	0.495374i
$366$	−0.205771	−	0.356406i	−0.0107558	−	0.0186297i
$367$	0.500000	−	0.133975i	0.0260998	−	0.00699342i	−0.245746	−	0.969334i	$-0.579033\pi$
$367$	0.500000	−	0.133975i	0.0260998	−	0.00699342i	0.271845	+	0.962341i	$0.412366\pi$
$368$	0.330127	−	0.0884573i	0.0172091	−	0.00461115i
$369$	8.83013	+	15.2942i	0.459678	+	0.796186i
$370$	2.53590	−	5.07180i	0.131835	−	0.263670i
$371$	−15.4904	+	10.4904i	−0.804221	+	0.544633i
$372$	4.73205	−	4.73205i	0.245345	−	0.245345i
$373$	2.07180	−	7.73205i	0.107274	−	0.400350i	−0.891320	−	0.453376i	$-0.850220\pi$
$373$	2.07180	−	7.73205i	0.107274	−	0.400350i	0.998593	+	0.0530251i	$0.0168863\pi$
$374$	2.73205	−	4.73205i	0.141271	−	0.244689i
$375$	−5.23205	+	2.47372i	−0.270182	+	0.127742i
$376$	−15.2942	+	8.83013i	−0.788740	+	0.455379i
$377$	−6.00000	−	6.00000i	−0.309016	−	0.309016i
$378$	3.07180	+	2.66025i	0.157996	+	0.136829i
$379$		−	2.33975i		−	0.120185i	−0.998193	−	0.0600923i	$-0.980860\pi$
$379$		−	2.33975i		−	0.120185i	0.998193	−	0.0600923i	$-0.0191395\pi$
$380$	2.83013	−	0.169873i	0.145182	−	0.00871430i
$381$	−0.294229	−	0.169873i	−0.0150738	−	0.00870286i
$382$	−1.77757	−	6.63397i	−0.0909483	−	0.339424i
$383$	30.5526	+	8.18653i	1.56116	+	0.418312i	0.933031	−	0.359795i	$-0.117153\pi$
$383$	30.5526	+	8.18653i	1.56116	+	0.418312i	0.628131	+	0.778107i	$0.283820\pi$
$384$	−5.92820			−0.302522
$385$	−16.0263	−	2.09808i	−0.816775	−	0.106928i
$386$	−4.19615			−0.213579
$387$	10.5622	+	2.83013i	0.536906	+	0.143863i
$388$	3.75833	+	14.0263i	0.190800	+	0.712076i
$389$	−4.26795	−	2.46410i	−0.216394	−	0.124935i	0.387886	−	0.921707i	$-0.373206\pi$
$389$	−4.26795	−	2.46410i	−0.216394	−	0.124935i	−0.604279	+	0.796773i	$0.706539\pi$
$390$	−1.12436	+	1.26795i	−0.0569340	+	0.0642051i
$391$		−	0.535898i		−	0.0271015i
$392$	−13.4282	−	1.59808i	−0.678227	−	0.0807150i
$393$	5.66025	+	5.66025i	0.285522	+	0.285522i
$394$	−6.41858	+	3.70577i	−0.323364	+	0.186694i
$395$	4.02628	+	6.09808i	0.202584	+	0.306828i
$396$	−6.46410	+	11.1962i	−0.324833	+	0.562628i
$397$	−0.973721	+	3.63397i	−0.0488696	+	0.182384i	−0.986046	−	0.166471i	$-0.946763\pi$
$397$	−0.973721	+	3.63397i	−0.0488696	+	0.182384i	0.937177	+	0.348855i	$0.113429\pi$
$398$	−4.05256	+	4.05256i	−0.203136	+	0.203136i
$399$	−0.437822	+	0.901924i	−0.0219185	+	0.0451527i
$400$	−7.39230	−	9.85641i	−0.369615	−	0.492820i
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	0.695392	−	0.718631i	$-0.255231\pi$
$401$	−5.50000	−	9.52628i	−0.274657	−	0.475720i	−0.970049	+	0.242911i	$0.921898\pi$
$402$	2.86603	−	0.767949i	0.142944	−	0.0383018i
$403$	20.3923	−	5.46410i	1.01581	−	0.272186i
$404$	−7.16025	−	12.4019i	−0.356236	−	0.617019i
$405$	13.3205	+	6.66025i	0.661901	+	0.330951i
$406$	−0.294229	−	4.09808i	−0.0146023	−	0.203384i
$407$	−9.46410	+	9.46410i	−0.469118	+	0.469118i
$408$	−1.00000	+	3.73205i	−0.0495074	+	0.184764i
$409$	−10.4282	+	18.0622i	−0.515641	+	0.893117i	0.484194	+	0.874961i	$0.339113\pi$
$409$	−10.4282	+	18.0622i	−0.515641	+	0.893117i	−0.999835	+	0.0181564i	$0.994220\pi$
$410$	−7.33013	−	1.50000i	−0.362009	−	0.0740797i
$411$	−6.12436	+	3.53590i	−0.302092	+	0.174413i
$412$	−5.83013	−	5.83013i	−0.287230	−	0.287230i
$413$	4.09808	−	21.2942i	0.201653	−	1.04782i
$414$		−	0.196152i		−	0.00964037i
$415$	−4.96410	−	4.40192i	−0.243678	−	0.216082i
$416$	−12.5885	−	7.26795i	−0.617200	−	0.356341i
$417$	0.758330	+	2.83013i	0.0371356	+	0.138592i
$418$	1.00000	+	0.267949i	0.0489116	+	0.0131058i
$419$	23.8564			1.16546			0.582731	−	0.812665i	$-0.301984\pi$
$419$	23.8564			1.16546			0.582731	+	0.812665i	$0.301984\pi$
$420$	5.25833	−	0.696152i	0.256580	−	0.0339688i
$421$	−17.3397			−0.845088			−0.422544	−	0.906343i	$-0.638863\pi$
$421$	−17.3397			−0.845088			−0.422544	+	0.906343i	$0.638863\pi$
$422$	−0.0980762	−	0.0262794i	−0.00477428	−	0.00127926i
$423$	−6.46410	−	24.1244i	−0.314295	−	1.17297i
$424$	−11.8301	−	6.83013i	−0.574522	−	0.331700i
$425$	−17.9282	+	7.19615i	−0.869646	+	0.349065i
$426$		−	0.339746i		−	0.0164607i
$427$	−2.66025	+	3.07180i	−0.128739	+	0.148655i
$428$	−16.0981	−	16.0981i	−0.778130	−	0.778130i
$429$	3.46410	−	2.00000i	0.167248	−	0.0965609i
$430$	−3.86603	+	2.55256i	−0.186436	+	0.123095i
$431$	−3.09808	+	5.36603i	−0.149229	+	0.258472i	−0.930943	−	0.365165i	$-0.881013\pi$
$431$	−3.09808	+	5.36603i	−0.149229	+	0.258472i	0.781714	+	0.623637i	$0.214346\pi$
$432$	1.89230	−	7.06218i	0.0910436	−	0.339779i
$433$	−17.5359	+	17.5359i	−0.842721	+	0.842721i	−0.989212	−	0.146491i	$-0.953202\pi$
$433$	−17.5359	+	17.5359i	−0.842721	+	0.842721i	0.146491	+	0.989212i	$0.453202\pi$
$434$	9.19615	+	4.46410i	0.441429	+	0.214284i
$435$	1.09808	+	3.29423i	0.0526487	+	0.157946i
$436$	8.76795	+	15.1865i	0.419909	+	0.727303i
$437$	0.0980762	−	0.0262794i	0.00469162	−	0.00125712i
$438$	−3.46410	+	0.928203i	−0.165521	+	0.0443513i
$439$	1.66025	+	2.87564i	0.0792396	+	0.137247i	0.902922	−	0.429804i	$-0.141417\pi$
$439$	1.66025	+	2.87564i	0.0792396	+	0.137247i	−0.823682	+	0.567051i	$0.808084\pi$
$440$	−3.73205	−	11.1962i	−0.177919	−	0.533756i
$441$	7.09808	−	17.7583i	0.338004	−	0.845635i
$442$	−4.00000	+	4.00000i	−0.190261	+	0.190261i
$443$	−3.50000	+	13.0622i	−0.166290	+	0.620603i	0.831582	+	0.555402i	$0.187436\pi$
$443$	−3.50000	+	13.0622i	−0.166290	+	0.620603i	−0.997872	+	0.0652010i	$0.979231\pi$
$444$	2.19615	−	3.80385i	0.104225	−	0.180523i
$445$	1.23205	−	0.813467i	0.0584048	−	0.0385620i
$446$	11.4904	−	6.63397i	0.544085	−	0.314128i
$447$	−0.294229	−	0.294229i	−0.0139165	−	0.0139165i
$448$	1.96410	+	5.66987i	0.0927951	+	0.267876i
$449$			33.0526i			1.55985i	0.625875	+	0.779923i	$0.284742\pi$
$449$			33.0526i			1.55985i	−0.625875	+	0.779923i	$0.715258\pi$
$450$	−6.56218	+	2.63397i	−0.309344	+	0.124167i
$451$	15.2942	+	8.83013i	0.720177	+	0.415794i
$452$	4.90192	+	18.2942i	0.230567	+	0.860488i
$453$	6.92820	+	1.85641i	0.325515	+	0.0872216i
$454$	−10.1962			−0.478529
$455$	15.4641	+	6.39230i	0.724968	+	0.299676i
$456$	−0.732051			−0.0342814
$457$	−11.7321	−	3.14359i	−0.548802	−	0.147051i	−0.0262453	−	0.999656i	$-0.508355\pi$
$457$	−11.7321	−	3.14359i	−0.548802	−	0.147051i	−0.522557	+	0.852604i	$0.675022\pi$
$458$	−2.46410	−	9.19615i	−0.115140	−	0.429708i
$459$	−9.92820	−	5.73205i	−0.463409	−	0.267549i
$460$	−0.401924	−	0.356406i	−0.0187398	−	0.0166175i
$461$			5.60770i			0.261176i	0.991437	+	0.130588i	$0.0416866\pi$
$461$			5.60770i			0.261176i	−0.991437	+	0.130588i	$0.958313\pi$
$462$	1.90192	+	0.366025i	0.0884855	+	0.0170290i
$463$	−4.75833	−	4.75833i	−0.221138	−	0.221138i	0.587839	−	0.808978i	$-0.299979\pi$
$463$	−4.75833	−	4.75833i	−0.221138	−	0.221138i	−0.808978	+	0.587839i	$0.799979\pi$
$464$	−6.40192	+	3.69615i	−0.297202	+	0.171590i
$465$	−8.46410	−	1.73205i	−0.392513	−	0.0803219i
$466$	−1.73205	+	3.00000i	−0.0802357	+	0.138972i
$467$	3.64359	−	13.5981i	0.168605	−	0.629244i	−0.828947	−	0.559327i	$-0.811060\pi$
$467$	3.64359	−	13.5981i	0.168605	−	0.629244i	0.997553	−	0.0699173i	$-0.0222736\pi$
$468$	9.46410	−	9.46410i	0.437478	−	0.437478i
$469$	−16.4282	−	24.2583i	−0.758584	−	1.12015i
$470$	9.46410	+	4.73205i	0.436546	+	0.218273i
$471$	1.24167	+	2.15064i	0.0572131	+	0.0990960i
$472$	15.2942	−	4.09808i	0.703974	−	0.188629i
$473$	10.5622	−	2.83013i	0.485649	−	0.130129i
$474$	−0.437822	−	0.758330i	−0.0201098	−	0.0348313i
$475$	−2.19615	−	2.92820i	−0.100766	−	0.134355i
$476$	17.6603	−	1.26795i	0.809456	−	0.0581164i
$477$	13.6603	−	13.6603i	0.625460	−	0.625460i
$478$	0.320508	−	1.19615i	0.0146597	−	0.0547107i
$479$	6.53590	−	11.3205i	0.298633	−	0.517247i	−0.677191	−	0.735808i	$-0.736803\pi$
$479$	6.53590	−	11.3205i	0.298633	−	0.517247i	0.975823	+	0.218560i	$0.0701361\pi$
$480$	3.27757	+	4.96410i	0.149600	+	0.226579i
$481$	12.0000	−	6.92820i	0.547153	−	0.315899i
$482$	9.07180	+	9.07180i	0.413209	+	0.413209i
$483$	0.179492	−	0.0621778i	0.00816717	−	0.00282919i
$484$		−	6.12436i		−	0.278380i
$485$	12.4378	−	14.0263i	0.564772	−	0.636901i
$486$	−5.53590	−	3.19615i	−0.251113	−	0.144980i
$487$	7.29423	+	27.2224i	0.330533	+	1.23357i	0.908631	+	0.417599i	$0.137128\pi$
$487$	7.29423	+	27.2224i	0.330533	+	1.23357i	−0.578098	+	0.815967i	$0.696205\pi$
$488$	−2.86603	−	0.767949i	−0.129739	−	0.0347634i
$489$	7.26795			0.328668
$490$	3.63397	+	7.24167i	0.164166	+	0.327145i
$491$	37.7128			1.70196			0.850978	−	0.525202i	$-0.176010\pi$
$491$	37.7128			1.70196			0.850978	+	0.525202i	$0.176010\pi$
$492$	−5.59808	−	1.50000i	−0.252381	−	0.0676252i
$493$	3.00000	+	11.1962i	0.135113	+	0.504249i
$494$	−0.928203	−	0.535898i	−0.0417618	−	0.0241112i
$495$	16.6603	−	1.00000i	0.748823	−	0.0449467i
$496$		−	18.3923i		−	0.825839i
$497$	−3.16987	+	1.09808i	−0.142188	+	0.0492554i
$498$	0.562178	+	0.562178i	0.0251918	+	0.0251918i
$499$	−9.97372	+	5.75833i	−0.446485	+	0.257778i	−0.706345	−	0.707868i	$-0.749657\pi$
$499$	−9.97372	+	5.75833i	−0.446485	+	0.257778i	0.259860	+	0.965646i	$0.416324\pi$
$500$	−6.52628	+	18.2321i	−0.291864	+	0.815362i
$501$	4.30385	−	7.45448i	0.192282	−	0.333042i
$502$	2.92820	−	10.9282i	0.130692	−	0.487750i
$503$	−17.6340	+	17.6340i	−0.786260	+	0.786260i	−0.980879	−	0.194619i	$-0.937653\pi$
$503$	−17.6340	+	17.6340i	−0.786260	+	0.786260i	0.194619	+	0.980879i	$0.437653\pi$
$504$	13.9282	−	1.00000i	0.620411	−	0.0445435i
$505$	−8.26795	+	16.5359i	−0.367919	+	0.735838i
$506$	−0.0980762	−	0.169873i	−0.00436002	−	0.00755178i
$507$	2.50000	−	0.669873i	0.111029	−	0.0297501i
$508$	−1.09808	+	0.294229i	−0.0487193	+	0.0130543i
$509$	−19.4545	−	33.6962i	−0.862305	−	1.49356i	−0.869699	−	0.493583i	$-0.835687\pi$
$509$	−19.4545	−	33.6962i	−0.862305	−	1.49356i	0.00739389	−	0.999973i	$-0.497646\pi$
$510$	2.19615	−	0.732051i	0.0972473	−	0.0324158i
$511$	19.8564	+	29.3205i	0.878396	+	1.29706i
$512$	−15.6865	+	15.6865i	−0.693253	+	0.693253i
$513$	0.562178	−	2.09808i	0.0248208	−	0.0926323i
$514$	−0.732051	+	1.26795i	−0.0322894	+	0.0559268i
$515$	−2.13397	+	10.4282i	−0.0940342	+	0.459522i
$516$	−3.10770	+	1.79423i	−0.136809	+	0.0789865i
$517$	−17.6603	−	17.6603i	−0.776697	−	0.776697i
$518$	6.58846	+	1.26795i	0.289480	+	0.0557105i
$519$		−	10.6795i		−	0.468778i
$520$	0.732051	+	12.1962i	0.0321026	+	0.534837i
$521$	−20.6603	−	11.9282i	−0.905142	−	0.522584i	−0.0262772	−	0.999655i	$-0.508365\pi$
$521$	−20.6603	−	11.9282i	−0.905142	−	0.522584i	−0.878865	+	0.477071i	$0.841699\pi$
$522$	1.09808	+	4.09808i	0.0480615	+	0.179368i
$523$	−42.8827	−	11.4904i	−1.87513	−	0.502439i	−0.999822	−	0.0188717i	$-0.993993\pi$
$523$	−42.8827	−	11.4904i	−1.87513	−	0.502439i	−0.875307	−	0.483568i	$-0.839341\pi$
$524$	26.7846			1.17009
$525$	−4.49038	−	5.16987i	−0.195976	−	0.225632i
$526$	−8.12436			−0.354239
$527$	−27.8564	−	7.46410i	−1.21344	−	0.325141i
$528$	−0.901924	−	3.36603i	−0.0392512	−	0.146487i
$529$	19.9019	+	11.4904i	0.865301	+	0.499582i
$530$	0.490381	+	8.16987i	0.0213008	+	0.354877i
$531$			22.3923i			0.971743i
$532$	1.09808	+	3.16987i	0.0476076	+	0.137431i
$533$	−12.9282	−	12.9282i	−0.559983	−	0.559983i
$534$	−0.153212	+	0.0884573i	−0.00663015	+	0.00382792i
$535$	−5.89230	+	28.7942i	−0.254747	+	1.24488i
$536$	10.6962	−	18.5263i	0.462003	−	0.800213i
$537$	1.05256	−	3.92820i	0.0454213	−	0.169514i
$538$	8.36603	−	8.36603i	0.360685	−	0.360685i
$539$	−2.73205	−	18.9282i	−0.117678	−	0.815295i
$540$	−10.9019	+	3.63397i	−0.469144	+	0.156381i
$541$	−18.3564	−	31.7942i	−0.789204	−	1.36694i	−0.926455	−	0.376404i	$-0.877160\pi$
$541$	−18.3564	−	31.7942i	−0.789204	−	1.36694i	0.137252	−	0.990536i	$-0.456173\pi$
$542$	10.6340	−	2.84936i	0.456768	−	0.122391i
$543$	0.598076	−	0.160254i	0.0256659	−	0.00687716i
$544$	9.92820	+	17.1962i	0.425668	+	0.737279i
$545$	10.1244	−	20.2487i	0.433680	−	0.867359i
$546$	−1.80385	−	0.875644i	−0.0771975	−	0.0374741i
$547$	−16.7583	+	16.7583i	−0.716534	+	0.716534i	−0.967894	−	0.251359i	$-0.919122\pi$
$547$	−16.7583	+	16.7583i	−0.716534	+	0.716534i	0.251359	+	0.967894i	$0.419122\pi$
$548$	−6.12436	+	22.8564i	−0.261620	+	0.976377i
$549$	2.09808	−	3.63397i	0.0895437	−	0.155094i
$550$	−4.36603	+	5.56218i	−0.186168	+	0.237172i
$551$	−1.90192	+	1.09808i	−0.0810247	+	0.0467796i
$552$	0.0980762	+	0.0980762i	0.00417440	+	0.00417440i
$553$	−5.66025	+	6.53590i	−0.240698	+	0.277935i
$554$		−	2.78461i		−	0.118307i
$555$	−5.66025	+	0.339746i	−0.240264	+	0.0144214i
$556$	8.49038	+	4.90192i	0.360072	+	0.207888i
$557$	8.36603	+	31.2224i	0.354480	+	1.32294i	0.881138	+	0.472860i	$0.156778\pi$
$557$	8.36603	+	31.2224i	0.354480	+	1.32294i	−0.526658	+	0.850077i	$0.676555\pi$
$558$	−10.1962	−	2.73205i	−0.431638	−	0.115657i
$559$	−11.3205			−0.478806
$560$	8.86603	−	11.5718i	0.374658	−	0.488998i
$561$	−5.46410			−0.230695
$562$	−0.464102	−	0.124356i	−0.0195769	−	0.00524563i
$563$	−6.35641	−	23.7224i	−0.267891	−	0.999781i	−0.960457	−	0.278427i	$-0.910187\pi$
$563$	−6.35641	−	23.7224i	−0.267891	−	0.999781i	0.692567	−	0.721354i	$-0.256480\pi$
$564$	7.09808	+	4.09808i	0.298883	+	0.172560i
$565$	16.2224	−	18.2942i	0.682483	−	0.769644i
$566$		−	1.01924i		−	0.0428418i
$567$	−3.33013	+	17.3038i	−0.139852	+	0.726693i
$568$	−1.73205	−	1.73205i	−0.0726752	−	0.0726752i
$569$	−25.0526	+	14.4641i	−1.05026	+	0.606367i	−0.922722	−	0.385467i	$-0.874040\pi$
$569$	−25.0526	+	14.4641i	−1.05026	+	0.606367i	−0.127536	+	0.991834i	$0.540707\pi$
$570$	0.241670	+	0.366025i	0.0101224	+	0.0153311i
$571$	9.02628	−	15.6340i	0.377738	−	0.654261i	−0.612995	−	0.790087i	$-0.710035\pi$
$571$	9.02628	−	15.6340i	0.377738	−	0.654261i	0.990733	+	0.135826i	$0.0433687\pi$
$572$	3.46410	−	12.9282i	0.144841	−	0.540555i
$573$	−4.85641	+	4.85641i	−0.202879	+	0.202879i
$574$	−0.633975	−	8.83013i	−0.0264616	−	0.368562i
$575$	−0.0980762	+	0.686533i	−0.00409006	+	0.0286304i
$576$	−3.09808	−	5.36603i	−0.129087	−	0.223584i
$577$	5.63397	−	1.50962i	0.234545	−	0.0628463i	−0.139632	−	0.990204i	$-0.544592\pi$
$577$	5.63397	−	1.50962i	0.234545	−	0.0628463i	0.374177	+	0.927357i	$0.377925\pi$
$578$	−1.03590	+	0.277568i	−0.0430877	+	0.0115453i
$579$	2.09808	+	3.63397i	0.0871931	+	0.151023i
$580$	10.3923	+	5.19615i	0.431517	+	0.215758i
$581$	3.42820	−	7.06218i	0.142226	−	0.292989i
$582$	−1.58846	+	1.58846i	−0.0658437	+	0.0658437i
$583$	5.00000	−	18.6603i	0.207079	−	0.772829i
$584$	−12.9282	+	22.3923i	−0.534973	+	0.926600i
$585$	−16.9282	−	3.46410i	−0.699895	−	0.143223i
$586$	−1.51666	+	0.875644i	−0.0626527	+	0.0361725i
$587$	15.7846	+	15.7846i	0.651501	+	0.651501i	0.953354	−	0.301854i	$-0.0976054\pi$
$587$	15.7846	+	15.7846i	0.651501	+	0.651501i	−0.301854	+	0.953354i	$0.597605\pi$
$588$	2.47372	+	5.76795i	0.102015	+	0.237866i
$589$		−	5.46410i		−	0.225144i
$590$	−7.09808	−	6.29423i	−0.292223	−	0.259129i
$591$	6.41858	+	3.70577i	0.264025	+	0.152435i
$592$	−3.12436	−	11.6603i	−0.128410	−	0.479233i
$593$	20.7583	+	5.56218i	0.852442	+	0.228411i	0.658481	−	0.752598i	$-0.271199\pi$
$593$	20.7583	+	5.56218i	0.852442	+	0.228411i	0.193962	+	0.981009i	$0.437866\pi$
$594$	−4.19615			−0.172170
$595$	−13.9282	−	18.1244i	−0.571001	−	0.743026i
$596$	−1.39230			−0.0570310
$597$	5.53590	+	1.48334i	0.226569	+	0.0607090i
$598$	0.0525589	+	0.196152i	0.00214929	+	0.00802127i
$599$	−15.3397	−	8.85641i	−0.626765	−	0.361863i	0.152733	−	0.988267i	$-0.451193\pi$
$599$	−15.3397	−	8.85641i	−0.626765	−	0.361863i	−0.779498	+	0.626405i	$0.784526\pi$
$600$	1.96410	−	4.59808i	0.0801841	−	0.187716i
$601$			41.1769i			1.67964i	0.542864	+	0.839821i	$0.317340\pi$
$601$			41.1769i			1.67964i	−0.542864	+	0.839821i	$0.682660\pi$
$602$	−4.14359	−	3.58846i	−0.168880	−	0.146255i
$603$	21.3923	+	21.3923i	0.871162	+	0.871162i
$604$	20.7846	−	12.0000i	0.845714	−	0.488273i
$605$	−6.59808	+	4.35641i	−0.268250	+	0.177113i
$606$	1.10770	−	1.91858i	0.0449970	−	0.0779372i
$607$	3.40192	−	12.6962i	0.138080	−	0.515321i	−0.861886	−	0.507101i	$-0.830717\pi$
$607$	3.40192	−	12.6962i	0.138080	−	0.515321i	0.999966	−	0.00821951i	$-0.00261638\pi$
$608$	−2.66025	+	2.66025i	−0.107888	+	0.107888i
$609$	−3.40192	+	2.30385i	−0.137853	+	0.0933566i
$610$	0.562178	+	1.68653i	0.0227619	+	0.0682857i
$611$	12.9282	+	22.3923i	0.523019	+	0.905896i
$612$	−17.6603	+	4.73205i	−0.713873	+	0.191282i
$613$	24.3923	−	6.53590i	0.985196	−	0.263982i	0.269965	−	0.962870i	$-0.412988\pi$
$613$	24.3923	−	6.53590i	0.985196	−	0.263982i	0.715231	+	0.698888i	$0.246321\pi$
$614$	2.30385	+	3.99038i	0.0929757	+	0.161039i
$615$	2.36603	+	7.09808i	0.0954074	+	0.286222i
$616$	11.5622	−	7.83013i	0.465853	−	0.315485i
$617$	33.9090	−	33.9090i	1.36512	−	1.36512i	0.497874	−	0.867249i	$-0.334114\pi$
$617$	33.9090	−	33.9090i	1.36512	−	1.36512i	0.867249	−	0.497874i	$-0.165886\pi$
$618$	0.330127	−	1.23205i	0.0132797	−	0.0495604i
$619$	5.09808	−	8.83013i	0.204909	−	0.354913i	−0.745195	−	0.666847i	$-0.767643\pi$
$619$	5.09808	−	8.83013i	0.204909	−	0.354913i	0.950104	+	0.311934i	$0.100977\pi$
$620$	−24.1244	+	15.9282i	−0.968857	+	0.639692i
$621$	−0.356406	+	0.205771i	−0.0143021	+	0.00825732i
$622$	−5.58846	−	5.58846i	−0.224077	−	0.224077i
$623$	1.32051	+	1.14359i	0.0529050	+	0.0458171i
$624$			3.60770i			0.144423i
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−2.41154	−	1.39230i	−0.0963846	−	0.0556477i
$627$	−0.267949	−	1.00000i	−0.0107009	−	0.0399362i
$628$	8.02628	+	2.15064i	0.320283	+	0.0858197i
$629$	−18.9282			−0.754717
$630$	−5.09808	−	6.63397i	−0.203112	−	0.264304i
$631$	−4.58846			−0.182664			−0.0913318	−	0.995821i	$-0.529112\pi$
$631$	−4.58846			−0.182664			−0.0913318	+	0.995821i	$0.529112\pi$
$632$	−6.09808	−	1.63397i	−0.242568	−	0.0649960i
$633$	0.0262794	+	0.0980762i	0.00104451	+	0.00389818i
$634$	4.26795	+	2.46410i	0.169502	+	0.0978620i
$635$	1.09808	+	0.973721i	0.0435758	+	0.0386409i
$636$			6.33975i			0.251387i
$637$	−2.33975	+	19.6603i	−0.0927041	+	0.778968i
$638$	3.00000	+	3.00000i	0.118771	+	0.118771i
$639$	3.00000	−	1.73205i	0.118678	−	0.0685189i
$640$	25.0885	+	5.13397i	0.991708	+	0.202938i
$641$	−5.33013	+	9.23205i	−0.210527	+	0.364644i	−0.951880	−	0.306472i	$-0.900851\pi$
$641$	−5.33013	+	9.23205i	−0.210527	+	0.364644i	0.741352	+	0.671116i	$0.234185\pi$
$642$	0.911543	−	3.40192i	0.0359757	−	0.134263i
$643$	17.5359	−	17.5359i	0.691548	−	0.691548i	−0.271024	−	0.962573i	$-0.587362\pi$
$643$	17.5359	−	17.5359i	0.691548	−	0.691548i	0.962573	+	0.271024i	$0.0873623\pi$
$644$	0.277568	−	0.571797i	0.0109377	−	0.0225319i
$645$	4.14359	+	2.07180i	0.163154	+	0.0815769i
$646$	0.732051	+	1.26795i	0.0288022	+	0.0498868i
$647$	39.5526	−	10.5981i	1.55497	−	0.416653i	0.623904	−	0.781501i	$-0.285546\pi$
$647$	39.5526	−	10.5981i	1.55497	−	0.416653i	0.931067	+	0.364847i	$0.118879\pi$
$648$	−12.4282	+	3.33013i	−0.488226	+	0.130820i
$649$	11.1962	+	19.3923i	0.439487	+	0.761215i
$650$	5.85641	−	4.39230i	0.229707	−	0.172280i
$651$	−0.732051	−	10.1962i	−0.0286913	−	0.399619i
$652$	17.1962	−	17.1962i	0.673453	−	0.673453i
$653$	−5.26795	+	19.6603i	−0.206151	+	0.769365i	0.782945	+	0.622091i	$0.213717\pi$
$653$	−5.26795	+	19.6603i	−0.206151	+	0.769365i	−0.989096	+	0.147274i	$0.952950\pi$
$654$	−1.35641	+	2.34936i	−0.0530397	+	0.0918674i
$655$	−19.0526	−	28.8564i	−0.744445	−	1.12751i
$656$	−13.7942	+	7.96410i	−0.538574	+	0.310946i
$657$	−25.8564	−	25.8564i	−1.00875	−	1.00875i
$658$	−2.36603	+	12.2942i	−0.0922373	+	0.479279i
$659$			27.6603i			1.07749i	0.842469	+	0.538745i	$0.181101\pi$
$659$			27.6603i			1.07749i	−0.842469	+	0.538745i	$0.818899\pi$
$660$	−3.63397	+	4.09808i	−0.141452	+	0.159517i
$661$	−41.7224	−	24.0885i	−1.62281	−	0.936932i	−0.986163	−	0.165781i	$-0.946985\pi$
$661$	−41.7224	−	24.0885i	−1.62281	−	0.936932i	−0.636652	−	0.771151i	$-0.719681\pi$
$662$	0.248711	+	0.928203i	0.00966644	+	0.0360756i
$663$	5.46410	+	1.46410i	0.212208	+	0.0568610i
$664$	5.73205			0.222447
$665$	2.63397	−	3.43782i	0.102141	−	0.133313i
$666$	−6.92820			−0.268462
$667$	0.401924	+	0.107695i	0.0155626	+	0.00416997i
$668$	−7.45448	−	27.8205i	−0.288423	−	1.07641i
$669$	−11.4904	−	6.63397i	−0.444244	−	0.256484i
$670$	−12.7942	+	0.767949i	−0.494284	+	0.0296685i
$671$		−	4.19615i		−	0.161991i
$672$	−4.60770	+	5.32051i	−0.177746	+	0.205243i
$673$	4.39230	+	4.39230i	0.169311	+	0.169311i	0.786676	−	0.617366i	$-0.211800\pi$
$673$	4.39230	+	4.39230i	0.169311	+	0.169311i	−0.617366	+	0.786676i	$0.711800\pi$
$674$	6.04552	−	3.49038i	0.232865	−	0.134444i
$675$	11.6699	+	9.16025i	0.449174	+	0.352578i
$676$	4.33013	−	7.50000i	0.166543	−	0.288462i
$677$	−6.92820	+	25.8564i	−0.266272	+	0.993742i	0.695194	+	0.718822i	$0.255318\pi$
$677$	−6.92820	+	25.8564i	−0.266272	+	0.993742i	−0.961467	+	0.274921i	$0.911348\pi$
$678$	−2.07180	+	2.07180i	−0.0795669	+	0.0795669i
$679$	19.9545	+	9.68653i	0.765783	+	0.371735i
$680$	7.46410	−	14.9282i	0.286235	−	0.572470i
$681$	5.09808	+	8.83013i	0.195359	+	0.338371i
$682$	−10.1962	+	2.73205i	−0.390431	+	0.104616i
$683$	17.0622	−	4.57180i	0.652866	−	0.174935i	0.0828417	−	0.996563i	$-0.473600\pi$
$683$	17.0622	−	4.57180i	0.652866	−	0.174935i	0.570024	+	0.821628i	$0.306934\pi$
$684$	−1.73205	−	3.00000i	−0.0662266	−	0.114708i
$685$	28.9808	−	9.66025i	1.10730	−	0.369099i
$686$	−7.08846	+	6.45448i	−0.270639	+	0.246433i
$687$	−6.73205	+	6.73205i	−0.256844	+	0.256844i
$688$	−2.55256	+	9.52628i	−0.0973154	+	0.363186i
$689$	−10.0000	+	17.3205i	−0.380970	+	0.659859i
$690$	0.0166605	−	0.0814157i	0.000634254	−	0.00309944i
$691$	−44.0263	+	25.4186i	−1.67484	+	0.966969i	−0.709971	+	0.704231i	$0.751292\pi$
$691$	−44.0263	+	25.4186i	−1.67484	+	0.966969i	−0.964867	+	0.262738i	$0.915375\pi$
$692$	−25.2679	−	25.2679i	−0.960543	−	0.960543i
$693$	6.46410	+	18.6603i	0.245551	+	0.708844i
$694$		−	15.5885i		−	0.591730i
$695$	−0.758330	−	12.6340i	−0.0287651	−	0.479234i
$696$	−2.59808	−	1.50000i	−0.0984798	−	0.0568574i
$697$	6.46410	+	24.1244i	0.244845	+	0.913775i
$698$	3.13397	+	0.839746i	0.118623	+	0.0317849i
$699$	3.46410			0.131024
$700$	−22.8564	−	1.60770i	−0.863891	−	0.0607652i
$701$	−20.2679			−0.765510			−0.382755	−	0.923850i	$-0.625025\pi$
$701$	−20.2679			−0.765510			−0.382755	+	0.923850i	$0.625025\pi$
$702$	4.19615	+	1.12436i	0.158374	+	0.0424361i
$703$	−0.928203	−	3.46410i	−0.0350078	−	0.130651i
$704$	−5.36603	−	3.09808i	−0.202240	−	0.116763i
$705$	−0.633975	−	10.5622i	−0.0238769	−	0.397795i
$706$			7.26795i			0.273533i
$707$	−21.4808	−	4.13397i	−0.807867	−	0.155474i
$708$	−5.19615	−	5.19615i	−0.195283	−	0.195283i
$709$	18.9904	−	10.9641i	0.713199	−	0.411765i	−0.0990456	−	0.995083i	$-0.531579\pi$
$709$	18.9904	−	10.9641i	0.713199	−	0.411765i	0.812244	+	0.583317i	$0.198246\pi$
$710$	−0.294229	+	1.43782i	−0.0110422	+	0.0539605i
$711$	4.46410	−	7.73205i	0.167417	−	0.289975i
$712$	−0.330127	+	1.23205i	−0.0123720	+	0.0461731i
$713$	−0.732051	+	0.732051i	−0.0274155	+	0.0274155i
$714$	1.53590	+	2.26795i	0.0574796	+	0.0848759i
$715$	−16.3923	+	5.46410i	−0.613037	+	0.204346i
$716$	−6.80385	−	11.7846i	−0.254272	−	0.440412i
$717$	−1.19615	+	0.320508i	−0.0446711	+	0.0119696i
$718$	17.1244	−	4.58846i	0.639075	−	0.171240i
$719$	19.2942	+	33.4186i	0.719553	+	1.24630i	0.961177	+	0.275933i	$0.0889867\pi$
$719$	19.2942	+	33.4186i	0.719553	+	1.24630i	−0.241624	+	0.970370i	$0.577680\pi$
$720$	−6.73205	+	13.4641i	−0.250889	+	0.501777i
$721$	−12.5622	+	0.901924i	−0.467840	+	0.0335894i
$722$	6.75833	−	6.75833i	0.251519	−	0.251519i
$723$	3.32051	−	12.3923i	0.123491	−	0.460875i
$724$	1.03590	−	1.79423i	0.0384989	−	0.0666820i
$725$	−1.79423	−	14.8923i	−0.0666360	−	0.553086i
$726$	0.820508	−	0.473721i	0.0304519	−	0.0175814i
$727$	−10.0981	−	10.0981i	−0.374517	−	0.374517i	0.494602	−	0.869119i	$-0.335314\pi$
$727$	−10.0981	−	10.0981i	−0.374517	−	0.374517i	−0.869119	+	0.494602i	$0.835314\pi$
$728$	−13.6603	+	4.73205i	−0.506283	+	0.175381i
$729$		−	13.5885i		−	0.503276i
$730$	15.4641	−	0.928203i	0.572352	−	0.0343543i
$731$	13.3923	+	7.73205i	0.495332	+	0.285980i
$732$	0.356406	+	1.33013i	0.0131732	+	0.0491629i
$733$	−4.36603	−	1.16987i	−0.161263	−	0.0432102i	0.177284	−	0.984160i	$-0.443269\pi$
$733$	−4.36603	−	1.16987i	−0.161263	−	0.0432102i	−0.338547	+	0.940949i	$0.609935\pi$
$734$	0.267949			0.00989019
$735$	4.45448	−	6.76795i	0.164306	−	0.249640i
$736$	0.712813			0.0262746
$737$	29.2224	+	7.83013i	1.07642	+	0.288426i
$738$	2.36603	+	8.83013i	0.0870946	+	0.325041i
$739$	−19.5622	−	11.2942i	−0.719606	−	0.415465i	0.0950014	−	0.995477i	$-0.469714\pi$
$739$	−19.5622	−	11.2942i	−0.719606	−	0.415465i	−0.814608	+	0.580012i	$0.803048\pi$
$740$	−12.5885	+	14.1962i	−0.462761	+	0.521861i
$741$			1.07180i			0.0393734i
$742$	−9.15064	+	3.16987i	−0.335930	+	0.116370i
$743$	−6.16987	−	6.16987i	−0.226351	−	0.226351i	0.584816	−	0.811166i	$-0.301167\pi$
$743$	−6.16987	−	6.16987i	−0.226351	−	0.226351i	−0.811166	+	0.584816i	$0.801167\pi$
$744$	6.46410	−	3.73205i	0.236985	−	0.136824i
$745$	0.990381	+	1.50000i	0.0362848	+	0.0549557i
$746$	2.07180	−	3.58846i	0.0758539	−	0.131383i
$747$	−2.09808	+	7.83013i	−0.0767646	+	0.286489i
$748$	−12.9282	+	12.9282i	−0.472702	+	0.472702i
$749$	−34.6865	+	2.49038i	−1.26742	+	0.0909965i
$750$	−2.94744	+	0.535898i	−0.107625	+	0.0195682i
$751$	3.19615	+	5.53590i	0.116629	+	0.202008i	0.918430	−	0.395584i	$-0.129458\pi$
$751$	3.19615	+	5.53590i	0.116629	+	0.202008i	−0.801801	+	0.597592i	$0.796124\pi$
$752$	21.7583	−	5.83013i	0.793445	−	0.212603i
$753$	−10.9282	+	2.92820i	−0.398246	+	0.106710i
$754$	−2.19615	−	3.80385i	−0.0799792	−	0.138528i
$755$	−27.7128	−	13.8564i	−1.00857	−	0.504286i
$756$	−7.62436	−	11.2583i	−0.277295	−	0.409462i
$757$	12.7321	−	12.7321i	0.462754	−	0.462754i	−0.436803	−	0.899557i	$-0.643889\pi$
$757$	12.7321	−	12.7321i	0.462754	−	0.462754i	0.899557	+	0.436803i	$0.143889\pi$
$758$	0.313467	−	1.16987i	0.0113856	−	0.0424917i
$759$	−0.0980762	+	0.169873i	−0.00355994	+	0.00616600i
$760$	3.09808	+	0.633975i	0.112379	+	0.0229967i
$761$	24.9282	−	14.3923i	0.903647	−	0.521721i	0.0252651	−	0.999681i	$-0.491957\pi$
$761$	24.9282	−	14.3923i	0.903647	−	0.521721i	0.878382	+	0.477960i	$0.158624\pi$
$762$	−0.124356	−	0.124356i	−0.00450493	−	0.00450493i
$763$	26.3038	+	5.06218i	0.952263	+	0.183263i
$764$			22.9808i			0.831415i
$765$	17.6603	+	15.6603i	0.638508	+	0.566198i
$766$	14.1795	+	8.18653i	0.512326	+	0.295791i
$767$	−6.00000	−	22.3923i	−0.216647	−	0.808539i
$768$	−0.696152	−	0.186533i	−0.0251202	−	0.00673095i
$769$	15.1769			0.547294			0.273647	−	0.961830i	$-0.411770\pi$
$769$	15.1769			0.547294			0.273647	+	0.961830i	$0.411770\pi$
$770$	−7.73205	−	3.19615i	−0.278644	−	0.115181i
$771$	1.46410			0.0527283
$772$	13.5622	+	3.63397i	0.488113	+	0.130790i
$773$	4.07180	+	15.1962i	0.146452	+	0.546568i	0.999686	+	0.0250395i	$0.00797116\pi$
$773$	4.07180	+	15.1962i	0.146452	+	0.546568i	−0.853234	+	0.521528i	$0.825362\pi$
$774$	4.90192	+	2.83013i	0.176196	+	0.101727i
$775$	34.3205	+	14.6603i	1.23283	+	0.526612i
$776$			16.1962i			0.581408i
$777$	−2.19615	−	6.33975i	−0.0787865	−	0.227437i
$778$	−1.80385	−	1.80385i	−0.0646711	−	0.0646711i
$779$	−4.09808	+	2.36603i	−0.146829	+	0.0847717i
$780$	4.73205	−	3.12436i	0.169435	−	0.111870i
$781$	1.73205	−	3.00000i	0.0619777	−	0.107348i
$782$	0.0717968	−	0.267949i	0.00256745	−	0.00958184i
$783$	6.29423	−	6.29423i	0.224937	−	0.224937i
$784$	16.0167	+	6.40192i	0.572024	+	0.228640i
$785$	−3.39230	−	10.1769i	−0.121077	−	0.363230i
$786$	2.07180	+	3.58846i	0.0738985	+	0.127996i
$787$	31.1865	−	8.35641i	1.11168	−	0.297874i	0.344168	−	0.938908i	$-0.388161\pi$
$787$	31.1865	−	8.35641i	1.11168	−	0.297874i	0.767512	+	0.641034i	$0.221494\pi$
$788$	23.9545	−	6.41858i	0.853343	−	0.228653i
$789$	4.06218	+	7.03590i	0.144617	+	0.250485i
$790$	1.19615	+	3.58846i	0.0425572	+	0.127672i
$791$	26.0263	+	12.6340i	0.925388	+	0.449212i
$792$	−10.1962	+	10.1962i	−0.362305	+	0.362305i
$793$	−1.12436	+	4.19615i	−0.0399270	+	0.149010i
$794$	−0.973721	+	1.68653i	−0.0345560	+	0.0598528i
$795$	6.83013	−	4.50962i	0.242240	−	0.159940i
$796$	16.6077	−	9.58846i	0.588644	−	0.339854i
$797$	22.5359	+	22.5359i	0.798262	+	0.798262i	0.982821	−	0.184559i	$-0.0590857\pi$
$797$	22.5359	+	22.5359i	0.798262	+	0.798262i	−0.184559	+	0.982821i	$0.559086\pi$
$798$	−0.339746	+	0.392305i	−0.0120269	+	0.0138874i
$799$		−	35.3205i		−	1.24955i
$800$	−9.57180	−	23.8468i	−0.338414	−	0.843111i
$801$	−1.56218	−	0.901924i	−0.0551968	−	0.0318679i
$802$	−1.47372	−	5.50000i	−0.0520389	−	0.194212i
$803$	−35.3205	−	9.46410i	−1.24643	−	0.333981i
$804$	−9.92820			−0.350141
$805$	−0.813467	+	0.107695i	−0.0286709	+	0.00379576i
$806$	10.9282			0.384930
$807$	−11.4282	−	3.06218i	−0.402292	−	0.107794i
$808$	−4.13397	−	15.4282i	−0.145433	−	0.542762i
$809$	−3.99038	−	2.30385i	−0.140294	−	0.0809990i	0.428210	−	0.903679i	$-0.359144\pi$
$809$	−3.99038	−	2.30385i	−0.140294	−	0.0809990i	−0.568504	+	0.822680i	$0.692478\pi$
$810$	5.76795	+	5.11474i	0.202665	+	0.179714i
$811$		−	42.9282i		−	1.50741i	−0.657211	−	0.753707i	$-0.728264\pi$
$811$		−	42.9282i		−	1.50741i	0.657211	−	0.753707i	$-0.271736\pi$
$812$	−2.59808	+	13.5000i	−0.0911746	+	0.473757i
$813$	−7.78461	−	7.78461i	−0.273018	−	0.273018i
$814$	−6.00000	+	3.46410i	−0.210300	+	0.121417i
$815$	−30.7583	−	6.29423i	−1.07742	−	0.220477i
$816$	2.46410	−	4.26795i	0.0862608	−	0.149408i
$817$	−0.758330	+	2.83013i	−0.0265306	+	0.0990136i
$818$	−7.63397	+	7.63397i	−0.266916	+	0.266916i
$819$	−1.46410	−	20.3923i	−0.0511599	−	0.712565i
$820$	22.3923	+	11.1962i	0.781973	+	0.390987i
$821$	24.6603	+	42.7128i	0.860649	+	1.49069i	0.871304	+	0.490744i	$0.163275\pi$
$821$	24.6603	+	42.7128i	0.860649	+	1.49069i	−0.0106549	+	0.999943i	$0.503392\pi$
$822$	−3.53590	+	0.947441i	−0.123329	+	0.0330458i
$823$	−53.3827	+	14.3038i	−1.86080	+	0.498601i	−0.999947	−	0.0102479i	$-0.996738\pi$
$823$	−53.3827	+	14.3038i	−1.86080	+	0.498601i	−0.860856	+	0.508849i	$0.830071\pi$
$824$	−4.59808	−	7.96410i	−0.160182	−	0.277443i
$825$	7.00000	+	1.00000i	0.243709	+	0.0348155i
$826$	4.90192	−	10.0981i	0.170560	−	0.351357i
$827$	−33.2224	+	33.2224i	−1.15526	+	1.15526i	−0.169774	+	0.985483i	$0.554304\pi$
$827$	−33.2224	+	33.2224i	−1.15526	+	1.15526i	−0.985483	+	0.169774i	$0.945696\pi$
$828$	−0.169873	+	0.633975i	−0.00590349	+	0.0220321i
$829$	−7.26795	+	12.5885i	−0.252426	+	0.437215i	−0.964193	−	0.265200i	$-0.914562\pi$
$829$	−7.26795	+	12.5885i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$830$	−1.89230	−	2.86603i	−0.0656829	−	0.0994812i
$831$	−2.41154	+	1.39230i	−0.0836555	+	0.0482985i
$832$	4.53590	+	4.53590i	0.157254	+	0.157254i
$833$	16.1962	−	21.6603i	0.561163	−	0.750483i
$834$			1.51666i			0.0525177i
$835$	−24.6699	+	27.8205i	−0.853736	+	0.962768i
$836$	−3.00000	−	1.73205i	−0.103757	−	0.0599042i
$837$	5.73205	+	21.3923i	0.198129	+	0.739426i
$838$	11.9282	+	3.19615i	0.412053	+	0.110409i
$839$	6.87564			0.237374			0.118687	−	0.992932i	$-0.462132\pi$
$839$	6.87564			0.237374			0.118687	+	0.992932i	$0.462132\pi$
$840$	5.86603	+	0.767949i	0.202397	+	0.0264968i
$841$	20.0000			0.689655
$842$	−8.66987	−	2.32309i	−0.298784	−	0.0800588i
$843$	0.124356	+	0.464102i	0.00428304	+	0.0159845i
$844$	0.294229	+	0.169873i	0.0101278	+	0.00584727i
$845$	−11.1603	+	0.669873i	−0.383924	+	0.0230443i
$846$		−	12.9282i		−	0.444481i
$847$	−7.07180	−	6.12436i	−0.242990	−	0.210435i
$848$	12.3205	+	12.3205i	0.423088	+	0.423088i
$849$	−0.882686	+	0.509619i	−0.0302937	+	0.0174901i
$850$	−9.92820	+	1.19615i	−0.340535	+	0.0410277i
$851$	−0.339746	+	0.588457i	−0.0116463	+	0.0201721i
$852$	−0.294229	+	1.09808i	−0.0100801	+	0.0376195i
$853$	−18.1244	+	18.1244i	−0.620566	+	0.620566i	−0.945676	−	0.325110i	$-0.894599\pi$
$853$	−18.1244	+	18.1244i	−0.620566	+	0.620566i	0.325110	+	0.945676i	$0.394599\pi$
$854$	−1.74167	+	1.17949i	−0.0595987	+	0.0403614i
$855$	−2.00000	+	4.00000i	−0.0683986	+	0.136797i
$856$	−12.6962	−	21.9904i	−0.433946	−	0.751616i
$857$	−11.0981	+	2.97372i	−0.379103	+	0.101580i	−0.443338	−	0.896354i	$-0.646206\pi$
$857$	−11.0981	+	2.97372i	−0.379103	+	0.101580i	0.0642351	+	0.997935i	$0.479539\pi$
$858$	2.00000	−	0.535898i	0.0682789	−	0.0182953i
$859$	−17.4641	−	30.2487i	−0.595867	−	1.03207i	−0.993424	−	0.114495i	$-0.963475\pi$
$859$	−17.4641	−	30.2487i	−0.595867	−	1.03207i	0.397556	−	0.917578i	$-0.369858\pi$
$860$	14.7058	−	4.90192i	0.501463	−	0.167154i
$861$	−7.33013	+	4.96410i	−0.249810	+	0.169176i
$862$	−2.26795	+	2.26795i	−0.0772467	+	0.0772467i
$863$	13.3827	−	49.9449i	0.455552	−	1.70014i	−0.230908	−	0.972976i	$-0.574170\pi$
$863$	13.3827	−	49.9449i	0.455552	−	1.70014i	0.686460	−	0.727167i	$-0.259164\pi$
$864$	7.62436	−	13.2058i	0.259386	−	0.449269i
$865$	−9.24871	+	45.1962i	−0.314466	+	1.53672i
$866$	−11.1173	+	6.41858i	−0.377782	+	0.218112i
$867$	0.758330	+	0.758330i	0.0257542	+	0.0257542i
$868$	−25.8564	−	22.3923i	−0.877624	−	0.760044i
$869$		−	8.92820i		−	0.302869i
$870$	0.107695	+	1.79423i	0.00365121	+	0.0608300i
$871$	−27.1244	−	15.6603i	−0.919074	−	0.530627i
$872$	5.06218	+	18.8923i	0.171427	+	0.639774i
$873$	−22.1244	−	5.92820i	−0.748796	−	0.200639i
$874$	0.0525589			0.00177783
$875$	14.5263	+	25.7679i	0.491078	+	0.871116i
$876$	12.0000			0.405442
$877$	−39.1506	−	10.4904i	−1.32202	−	0.354235i	−0.472288	−	0.881444i	$-0.656572\pi$
$877$	−39.1506	−	10.4904i	−1.32202	−	0.354235i	−0.849735	+	0.527209i	$0.823238\pi$
$878$	0.444864	+	1.66025i	0.0150134	+	0.0560309i
$879$	1.51666	+	0.875644i	0.0511557	+	0.0295348i
$880$	0.901924	+	15.0263i	0.0304038	+	0.506536i
$881$		−	25.1436i		−	0.847109i	−0.905871	−	0.423555i	$-0.860782\pi$
$881$		−	25.1436i		−	0.847109i	0.905871	−	0.423555i	$-0.139218\pi$
$882$	5.92820	−	7.92820i	0.199613	−	0.266956i
$883$	8.07180	+	8.07180i	0.271638	+	0.271638i	0.829759	−	0.558122i	$-0.188478\pi$
$883$	8.07180	+	8.07180i	0.271638	+	0.271638i	−0.558122	+	0.829759i	$0.688478\pi$
$884$	16.3923	−	9.46410i	0.551333	−	0.318312i
$885$	−1.90192	+	9.29423i	−0.0639325	+	0.312422i
$886$	−3.50000	+	6.06218i	−0.117585	+	0.203663i
$887$	2.91858	−	10.8923i	0.0979965	−	0.365728i	−0.899460	−	0.437003i	$-0.856040\pi$
$887$	2.91858	−	10.8923i	0.0979965	−	0.365728i	0.997457	+	0.0712748i	$0.0227067\pi$
$888$	3.46410	−	3.46410i	0.116248	−	0.116248i
$889$	−0.758330	+	1.56218i	−0.0254336	+	0.0523938i
$890$	0.725009	−	0.241670i	0.0243024	−	0.00810079i
$891$	−9.09808	−	15.7583i	−0.304797	−	0.527924i
$892$	−42.8827	+	11.4904i	−1.43582	+	0.384726i
$893$	6.46410	−	1.73205i	0.216313	−	0.0579609i
$894$	−0.107695	−	0.186533i	−0.00360186	−	0.00623861i
$895$	−7.85641	+	15.7128i	−0.262611	+	0.525221i
$896$	2.16987	+	30.2224i	0.0724904	+	1.00966i
$897$	0.143594	−	0.143594i	0.00479445	−	0.00479445i
$898$	−4.42820	+	16.5263i	−0.147771	+	0.551489i
$899$	11.1962	−	19.3923i	0.373413	−	0.646770i
$900$	23.4904	−	2.83013i	0.783013	−	0.0943376i
$901$	23.6603	−	13.6603i	0.788237	−	0.455089i
$902$	6.46410	+	6.46410i	0.215231	+	0.215231i
$903$	−1.03590	+	5.38269i	−0.0344725	+	0.179125i
$904$			21.1244i			0.702586i
$905$	−2.66987	+	0.160254i	−0.0887496	+	0.00532702i
$906$	3.21539	+	1.85641i	0.106824	+	0.0616750i
$907$	−8.69615	−	32.4545i	−0.288751	−	1.07763i	−0.946055	−	0.324007i	$-0.894970\pi$
$907$	−8.69615	−	32.4545i	−0.288751	−	1.07763i	0.657304	−	0.753626i	$-0.271697\pi$
$908$	32.9545	+	8.83013i	1.09363	+	0.293038i
$909$	22.5885			0.749212
$910$	6.87564	+	5.26795i	0.227925	+	0.174631i
$911$	−7.51666			−0.249038			−0.124519	−	0.992217i	$-0.539739\pi$
$911$	−7.51666			−0.249038			−0.124519	+	0.992217i	$0.539739\pi$
$912$	0.901924	+	0.241670i	0.0298657	+	0.00800249i
$913$	2.09808	+	7.83013i	0.0694362	+	0.259139i
$914$	−5.44486	−	3.14359i	−0.180100	−	0.103981i
$915$	1.17949	−	1.33013i	0.0389928	−	0.0439726i
$916$			31.8564i			1.05257i
$917$	26.7846	−	30.9282i	0.884506	−	1.02134i
$918$	−4.19615	−	4.19615i	−0.138494	−	0.138494i
$919$	−48.6673	+	28.0981i	−1.60539	+	0.926870i	−0.615002	+	0.788526i	$0.710845\pi$
$919$	−48.6673	+	28.0981i	−1.60539	+	0.926870i	−0.990384	+	0.138344i	$0.955822\pi$
$920$	−0.330127	−	0.500000i	−0.0108840	−	0.0164845i
$921$	2.30385	−	3.99038i	0.0759144	−	0.131488i
$922$	−0.751289	+	2.80385i	−0.0247424	+	0.0923398i
$923$	−2.53590	+	2.53590i	−0.0834701	+	0.0834701i
$924$	−5.83013	−	2.83013i	−0.191797	−	0.0931043i
$925$	24.2487	+	3.46410i	0.797293	+	0.113899i
$926$	−1.74167	−	3.01666i	−0.0572348	−	0.0991336i
$927$	12.5622	−	3.36603i	0.412596	−	0.110555i
$928$	−14.8923	+	3.99038i	−0.488864	+	0.130991i
$929$	−18.1603	−	31.4545i	−0.595819	−	1.03199i	−0.993431	−	0.114435i	$-0.963494\pi$
$929$	−18.1603	−	31.4545i	−0.595819	−	1.03199i	0.397612	−	0.917554i	$-0.369839\pi$
$930$	−4.00000	−	2.00000i	−0.131165	−	0.0655826i
$931$	4.75833	+	1.90192i	0.155948	+	0.0623330i
$932$	8.19615	−	8.19615i	0.268474	−	0.268474i
$933$	−2.04552	+	7.63397i	−0.0669672	+	0.249925i
$934$	3.64359	−	6.31089i	0.119222	−	0.206499i
$935$	23.1244	+	4.73205i	0.756247	+	0.154755i
$936$	12.9282	−	7.46410i	0.422572	−	0.243972i
$937$	17.0718	+	17.0718i	0.557711	+	0.557711i	0.928655	−	0.370944i	$-0.120966\pi$
$937$	17.0718	+	17.0718i	0.557711	+	0.557711i	−0.370944	+	0.928655i	$0.620966\pi$
$938$	−4.96410	−	14.3301i	−0.162084	−	0.467895i
$939$			2.78461i			0.0908723i
$940$	−26.4904	−	23.4904i	−0.864021	−	0.766172i
$941$	35.1962	+	20.3205i	1.14736	+	0.662430i	0.948243	−	0.317546i	$-0.102859\pi$
$941$	35.1962	+	20.3205i	1.14736	+	0.662430i	0.199119	+	0.979975i	$0.436192\pi$
$942$	0.332704	+	1.24167i	0.0108401	+	0.0404558i
$943$	0.866025	+	0.232051i	0.0282017	+	0.00755661i
$944$	−20.1962			−0.657329
$945$	−6.70577	+	16.2224i	−0.218139	+	0.527716i
$946$	5.66025			0.184031
$947$	−1.30385	−	0.349365i	−0.0423694	−	0.0113528i	0.237572	−	0.971370i	$-0.423648\pi$
$947$	−1.30385	−	0.349365i	−0.0423694	−	0.0113528i	−0.279941	+	0.960017i	$0.590315\pi$
$948$	0.758330	+	2.83013i	0.0246294	+	0.0919183i
$949$	32.7846	+	18.9282i	1.06423	+	0.614435i
$950$	−0.705771	−	1.75833i	−0.0228982	−	0.0570478i
$951$		−	4.92820i		−	0.159808i
$952$	19.3923	+	3.73205i	0.628508	+	0.120956i
$953$	−37.8564	−	37.8564i	−1.22629	−	1.22629i	−0.965357	−	0.260932i	$-0.915970\pi$
$953$	−37.8564	−	37.8564i	−1.22629	−	1.22629i	−0.260932	−	0.965357i	$-0.584030\pi$
$954$	8.66025	−	5.00000i	0.280386	−	0.161881i
$955$	24.7583	−	16.3468i	0.801161	−	0.528970i
$956$	−2.07180	+	3.58846i	−0.0670067	+	0.116059i
$957$	1.09808	−	4.09808i	0.0354958	−	0.132472i
$958$	4.78461	−	4.78461i	0.154584	−	0.154584i
$959$	20.2679	+	29.9282i	0.654486	+	0.966432i
$960$	−0.830127	−	2.49038i	−0.0267922	−	0.0803767i
$961$	12.3564	+	21.4019i	0.398594	+	0.690385i
$962$	6.92820	−	1.85641i	0.223374	−	0.0598529i
$963$	34.6865	−	9.29423i	1.11776	−	0.299502i
$964$	−21.4641	−	37.1769i	−0.691312	−	1.19739i
$965$	−5.73205	−	17.1962i	−0.184521	−	0.553564i
$966$	0.0980762	−	0.00704156i	0.00315555	−	0.000226558i
$967$	−13.5622	+	13.5622i	−0.436130	+	0.436130i	−0.890707	−	0.454577i	$-0.849790\pi$
$967$	−13.5622	+	13.5622i	−0.436130	+	0.436130i	0.454577	+	0.890707i	$0.349790\pi$
$968$	1.76795	−	6.59808i	0.0568240	−	0.212070i
$969$	0.732051	−	1.26795i	0.0235169	−	0.0407324i
$970$	8.09808	−	5.34679i	0.260014	−	0.171675i
$971$	29.0718	−	16.7846i	0.932958	−	0.538644i	0.0452124	−	0.998977i	$-0.485604\pi$
$971$	29.0718	−	16.7846i	0.932958	−	0.538644i	0.887746	+	0.460334i	$0.152270\pi$
$972$	15.1244	+	15.1244i	0.485114	+	0.485114i
$973$	14.1506	−	4.90192i	0.453649	−	0.157148i
$974$			14.5885i			0.467444i
$975$	−6.73205	−	2.87564i	−0.215598	−	0.0920943i
$976$	3.27757	+	1.89230i	0.104912	+	0.0605712i
$977$	−0.150635	−	0.562178i	−0.00481924	−	0.0179857i	0.963474	−	0.267801i	$-0.0862969\pi$
$977$	−0.150635	−	0.562178i	−0.00481924	−	0.0179857i	−0.968294	+	0.249815i	$0.919630\pi$
$978$	3.63397	+	0.973721i	0.116202	+	0.0311362i
$979$	−1.80385			−0.0576512
$980$	−5.47372	−	26.5526i	−0.174852	−	0.848190i
$981$	−27.6603			−0.883124
$982$	18.8564	+	5.05256i	0.601732	+	0.161234i
$983$	14.5000	+	54.1147i	0.462478	+	1.72599i	0.665118	+	0.746739i	$0.268381\pi$
$983$	14.5000	+	54.1147i	0.462478	+	1.72599i	−0.202639	+	0.979253i	$0.564952\pi$
$984$	−5.59808	−	3.23205i	−0.178460	−	0.103034i
$985$	−23.9545	−	21.2417i	−0.763253	−	0.676816i
$986$			6.00000i			0.191079i
$987$	11.8301	−	4.09808i	0.376557	−	0.130443i
$988$	2.53590	+	2.53590i	0.0806777	+	0.0806777i
$989$	0.480762	−	0.277568i	0.0152873	−	0.00882615i
$990$	8.46410	+	1.73205i	0.269007	+	0.0550482i
$991$	−15.8564	+	27.4641i	−0.503695	+	0.872426i	0.496296	+	0.868154i	$0.334693\pi$
$991$	−15.8564	+	27.4641i	−0.503695	+	0.872426i	−0.999991	+	0.00427229i	$0.998640\pi$
$992$	9.92820	−	37.0526i	0.315221	−	1.17642i
$993$	0.679492	−	0.679492i	0.0215630	−	0.0215630i
$994$	−1.73205	+	0.124356i	−0.0549373	+	0.00394432i
$995$	−22.1436	−	11.0718i	−0.701999	−	0.351000i
$996$	−1.33013	−	2.30385i	−0.0421467	−	0.0730002i
$997$	−39.8827	+	10.6865i	−1.26310	+	0.338446i	−0.827382	−	0.561639i	$-0.810171\pi$
$997$	−39.8827	+	10.6865i	−1.26310	+	0.338446i	−0.435715	+	0.900085i	$0.643504\pi$
$998$	−5.75833	+	1.54294i	−0.182277	+	0.0488409i
$999$	7.26795	+	12.5885i	0.229948	+	0.398281i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.2.k.b.3.1	yes	4
3.2	odd	2		315.2.bz.a.73.1		4
4.3	odd	2		560.2.ci.b.353.1		4
5.2	odd	4		35.2.k.a.17.1	✓	4
5.3	odd	4		175.2.o.b.157.1		4
5.4	even	2		175.2.o.a.143.1		4
7.2	even	3		245.2.l.a.68.1		4
7.3	odd	6		245.2.f.a.48.1		4
7.4	even	3		245.2.f.b.48.1		4
7.5	odd	6		35.2.k.a.33.1	yes	4
7.6	odd	2		245.2.l.b.178.1		4
15.2	even	4		315.2.bz.b.262.1		4
20.7	even	4		560.2.ci.a.17.1		4
21.5	even	6		315.2.bz.b.208.1		4
28.19	even	6		560.2.ci.a.33.1		4
35.2	odd	12		245.2.l.b.117.1		4
35.12	even	12	inner	35.2.k.b.12.1	yes	4
35.17	even	12		245.2.f.b.97.1		4
35.19	odd	6		175.2.o.b.68.1		4
35.27	even	4		245.2.l.a.227.1		4
35.32	odd	12		245.2.f.a.97.1		4
35.33	even	12		175.2.o.a.82.1		4
105.47	odd	12		315.2.bz.a.82.1		4
140.47	odd	12		560.2.ci.b.257.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.17.1	✓	4	5.2	odd	4
35.2.k.a.33.1	yes	4	7.5	odd	6
35.2.k.b.3.1	yes	4	1.1	even	1	trivial
35.2.k.b.12.1	yes	4	35.12	even	12	inner
175.2.o.a.82.1		4	35.33	even	12
175.2.o.a.143.1		4	5.4	even	2
175.2.o.b.68.1		4	35.19	odd	6
175.2.o.b.157.1		4	5.3	odd	4
245.2.f.a.48.1		4	7.3	odd	6
245.2.f.a.97.1		4	35.32	odd	12
245.2.f.b.48.1		4	7.4	even	3
245.2.f.b.97.1		4	35.17	even	12
245.2.l.a.68.1		4	7.2	even	3
245.2.l.a.227.1		4	35.27	even	4
245.2.l.b.117.1		4	35.2	odd	12
245.2.l.b.178.1		4	7.6	odd	2
315.2.bz.a.73.1		4	3.2	odd	2
315.2.bz.a.82.1		4	105.47	odd	12
315.2.bz.b.208.1		4	21.5	even	6
315.2.bz.b.262.1		4	15.2	even	4
560.2.ci.a.17.1		4	20.7	even	4
560.2.ci.a.33.1		4	28.19	even	6
560.2.ci.b.257.1		4	140.47	odd	12
560.2.ci.b.353.1		4	4.3	odd	2

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	35.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.133975i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} -0.267949i q^{6} +(-2.50000 + 0.866025i) q^{7} +(-1.36603 - 1.36603i) q^{8} +(2.36603 - 1.36603i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.133975i) q^{2} +(-0.133975 - 0.500000i) q^{3} +(-1.50000 - 0.866025i) q^{4} +(0.133975 + 2.23205i) q^{5} -0.267949i q^{6} +(-2.50000 + 0.866025i) q^{7} +(-1.36603 - 1.36603i) q^{8} +(2.36603 - 1.36603i) q^{9} +(-0.232051 + 1.13397i) q^{10} +(1.36603 - 2.36603i) q^{11} +(-0.232051 + 0.866025i) q^{12} +(-2.00000 + 2.00000i) q^{13} +(-1.36603 + 0.0980762i) q^{14} +(1.09808 - 0.366025i) q^{15} +(1.23205 + 2.13397i) q^{16} +(3.73205 - 1.00000i) q^{17} +(1.36603 - 0.366025i) q^{18} +(0.366025 + 0.633975i) q^{19} +(1.73205 - 3.46410i) q^{20} +(0.767949 + 1.13397i) q^{21} +(1.00000 - 1.00000i) q^{22} +(0.0358984 - 0.133975i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-4.96410 + 0.598076i) q^{25} +(-1.26795 + 0.732051i) q^{26} +(-2.09808 - 2.09808i) q^{27} +(4.50000 + 0.866025i) q^{28} +3.00000i q^{29} +(0.598076 - 0.0358984i) q^{30} +(-6.46410 - 3.73205i) q^{31} +(1.33013 + 4.96410i) q^{32} +(-1.36603 - 0.366025i) q^{33} +2.00000 q^{34} +(-2.26795 - 5.46410i) q^{35} -4.73205 q^{36} +(-4.73205 - 1.26795i) q^{37} +(0.0980762 + 0.366025i) q^{38} +(1.26795 + 0.732051i) q^{39} +(2.86603 - 3.23205i) q^{40} +6.46410i q^{41} +(0.232051 + 0.669873i) q^{42} +(2.83013 + 2.83013i) q^{43} +(-4.09808 + 2.36603i) q^{44} +(3.36603 + 5.09808i) q^{45} +(0.0358984 - 0.0621778i) q^{46} +(2.36603 - 8.83013i) q^{47} +(0.901924 - 0.901924i) q^{48} +(5.50000 - 4.33013i) q^{49} +(-2.56218 - 0.366025i) q^{50} +(-1.00000 - 1.73205i) q^{51} +(4.73205 - 1.26795i) q^{52} +(6.83013 - 1.83013i) q^{53} +(-0.767949 - 1.33013i) q^{54} +(5.46410 + 2.73205i) q^{55} +(4.59808 + 2.23205i) q^{56} +(0.267949 - 0.267949i) q^{57} +(-0.401924 + 1.50000i) q^{58} +(-4.09808 + 7.09808i) q^{59} +(-1.96410 - 0.401924i) q^{60} +(1.33013 - 0.767949i) q^{61} +(-2.73205 - 2.73205i) q^{62} +(-4.73205 + 5.46410i) q^{63} -2.26795i q^{64} +(-4.73205 - 4.19615i) q^{65} +(-0.633975 - 0.366025i) q^{66} +(2.86603 + 10.6962i) q^{67} +(-6.46410 - 1.73205i) q^{68} -0.0717968 q^{69} +(-0.401924 - 3.03590i) q^{70} +1.26795 q^{71} +(-5.09808 - 1.36603i) q^{72} +(-3.46410 - 12.9282i) q^{73} +(-2.19615 - 1.26795i) q^{74} +(0.964102 + 2.40192i) q^{75} -1.26795i q^{76} +(-1.36603 + 7.09808i) q^{77} +(0.535898 + 0.535898i) q^{78} +(2.83013 - 1.63397i) q^{79} +(-4.59808 + 3.03590i) q^{80} +(3.33013 - 5.76795i) q^{81} +(-0.866025 + 3.23205i) q^{82} +(-2.09808 + 2.09808i) q^{83} +(-0.169873 - 2.36603i) q^{84} +(2.73205 + 8.19615i) q^{85} +(1.03590 + 1.79423i) q^{86} +(1.50000 - 0.401924i) q^{87} +(-5.09808 + 1.36603i) q^{88} +(-0.330127 - 0.571797i) q^{89} +(1.00000 + 3.00000i) q^{90} +(3.26795 - 6.73205i) q^{91} +(-0.169873 + 0.169873i) q^{92} +(-1.00000 + 3.73205i) q^{93} +(2.36603 - 4.09808i) q^{94} +(-1.36603 + 0.901924i) q^{95} +(2.30385 - 1.33013i) q^{96} +(-5.92820 - 5.92820i) q^{97} +(3.33013 - 1.42820i) q^{98} -7.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{3} - 6 q^{4} + 4 q^{5} - 10 q^{7} - 2 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 + 4 * q^5 - 10 * q^7 - 2 * q^8 + 6 * q^9	\( 4 q + 2 q^{2} - 4 q^{3} - 6 q^{4} + 4 q^{5} - 10 q^{7} - 2 q^{8} + 6 q^{9} + 6 q^{10} + 2 q^{11} + 6 q^{12} - 8 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} + 8 q^{17} + 2 q^{18} - 2 q^{19} + 10 q^{21} + 4 q^{22} + 14 q^{23} - 2 q^{24} - 6 q^{25} - 12 q^{26} + 2 q^{27} + 18 q^{28} - 8 q^{30} - 12 q^{31} - 12 q^{32} - 2 q^{33} + 8 q^{34} - 16 q^{35} - 12 q^{36} - 12 q^{37} - 10 q^{38} + 12 q^{39} + 8 q^{40} - 6 q^{42} - 6 q^{43} - 6 q^{44} + 10 q^{45} + 14 q^{46} + 6 q^{47} + 14 q^{48} + 22 q^{49} + 14 q^{50} - 4 q^{51} + 12 q^{52} + 10 q^{53} - 10 q^{54} + 8 q^{55} + 8 q^{56} + 8 q^{57} - 12 q^{58} - 6 q^{59} + 6 q^{60} - 12 q^{61} - 4 q^{62} - 12 q^{63} - 12 q^{65} - 6 q^{66} + 8 q^{67} - 12 q^{68} - 28 q^{69} - 12 q^{70} + 12 q^{71} - 10 q^{72} + 12 q^{74} - 10 q^{75} - 2 q^{77} + 16 q^{78} - 6 q^{79} - 8 q^{80} - 4 q^{81} + 2 q^{83} - 18 q^{84} + 4 q^{85} + 18 q^{86} + 6 q^{87} - 10 q^{88} + 16 q^{89} + 4 q^{90} + 20 q^{91} - 18 q^{92} - 4 q^{93} + 6 q^{94} - 2 q^{95} + 30 q^{96} + 4 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^3 - 6 * q^4 + 4 * q^5 - 10 * q^7 - 2 * q^8 + 6 * q^9 + 6 * q^10 + 2 * q^11 + 6 * q^12 - 8 * q^13 - 2 * q^14 - 6 * q^15 - 2 * q^16 + 8 * q^17 + 2 * q^18 - 2 * q^19 + 10 * q^21 + 4 * q^22 + 14 * q^23 - 2 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 18 * q^28 - 8 * q^30 - 12 * q^31 - 12 * q^32 - 2 * q^33 + 8 * q^34 - 16 * q^35 - 12 * q^36 - 12 * q^37 - 10 * q^38 + 12 * q^39 + 8 * q^40 - 6 * q^42 - 6 * q^43 - 6 * q^44 + 10 * q^45 + 14 * q^46 + 6 * q^47 + 14 * q^48 + 22 * q^49 + 14 * q^50 - 4 * q^51 + 12 * q^52 + 10 * q^53 - 10 * q^54 + 8 * q^55 + 8 * q^56 + 8 * q^57 - 12 * q^58 - 6 * q^59 + 6 * q^60 - 12 * q^61 - 4 * q^62 - 12 * q^63 - 12 * q^65 - 6 * q^66 + 8 * q^67 - 12 * q^68 - 28 * q^69 - 12 * q^70 + 12 * q^71 - 10 * q^72 + 12 * q^74 - 10 * q^75 - 2 * q^77 + 16 * q^78 - 6 * q^79 - 8 * q^80 - 4 * q^81 + 2 * q^83 - 18 * q^84 + 4 * q^85 + 18 * q^86 + 6 * q^87 - 10 * q^88 + 16 * q^89 + 4 * q^90 + 20 * q^91 - 18 * q^92 - 4 * q^93 + 6 * q^94 - 2 * q^95 + 30 * q^96 + 4 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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