LMFDB - Embedded newform 175.2.o.a.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(68,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("175.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.o (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:	$1.39738203537$
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:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			82.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	175.82
Dual form			175.2.o.a.143.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.133975i) q^{2} +(0.133975 - 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +0.267949i q^{6} +(2.50000 + 0.866025i) q^{7} +(1.36603 - 1.36603i) q^{8} +(2.36603 + 1.36603i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.133975i) q^{2} +(0.133975 - 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +0.267949i q^{6} +(2.50000 + 0.866025i) q^{7} +(1.36603 - 1.36603i) q^{8} +(2.36603 + 1.36603i) q^{9} +(1.36603 + 2.36603i) q^{11} +(0.232051 + 0.866025i) q^{12} +(2.00000 + 2.00000i) q^{13} +(-1.36603 - 0.0980762i) q^{14} +(1.23205 - 2.13397i) q^{16} +(-3.73205 - 1.00000i) q^{17} +(-1.36603 - 0.366025i) q^{18} +(0.366025 - 0.633975i) q^{19} +(0.767949 - 1.13397i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-0.0358984 - 0.133975i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-1.26795 - 0.732051i) q^{26} +(2.09808 - 2.09808i) q^{27} +(-4.50000 + 0.866025i) q^{28} -3.00000i q^{29} +(-6.46410 + 3.73205i) q^{31} +(-1.33013 + 4.96410i) q^{32} +(1.36603 - 0.366025i) q^{33} +2.00000 q^{34} -4.73205 q^{36} +(4.73205 - 1.26795i) q^{37} +(-0.0980762 + 0.366025i) q^{38} +(1.26795 - 0.732051i) q^{39} -6.46410i q^{41} +(-0.232051 + 0.669873i) q^{42} +(-2.83013 + 2.83013i) q^{43} +(-4.09808 - 2.36603i) q^{44} +(0.0358984 + 0.0621778i) q^{46} +(-2.36603 - 8.83013i) q^{47} +(-0.901924 - 0.901924i) q^{48} +(5.50000 + 4.33013i) q^{49} +(-1.00000 + 1.73205i) q^{51} +(-4.73205 - 1.26795i) q^{52} +(-6.83013 - 1.83013i) q^{53} +(-0.767949 + 1.33013i) q^{54} +(4.59808 - 2.23205i) q^{56} +(-0.267949 - 0.267949i) q^{57} +(0.401924 + 1.50000i) q^{58} +(-4.09808 - 7.09808i) q^{59} +(1.33013 + 0.767949i) q^{61} +(2.73205 - 2.73205i) q^{62} +(4.73205 + 5.46410i) q^{63} +2.26795i q^{64} +(-0.633975 + 0.366025i) q^{66} +(-2.86603 + 10.6962i) q^{67} +(6.46410 - 1.73205i) q^{68} -0.0717968 q^{69} +1.26795 q^{71} +(5.09808 - 1.36603i) q^{72} +(3.46410 - 12.9282i) q^{73} +(-2.19615 + 1.26795i) q^{74} +1.26795i q^{76} +(1.36603 + 7.09808i) q^{77} +(-0.535898 + 0.535898i) q^{78} +(2.83013 + 1.63397i) q^{79} +(3.33013 + 5.76795i) q^{81} +(0.866025 + 3.23205i) q^{82} +(2.09808 + 2.09808i) q^{83} +(-0.169873 + 2.36603i) q^{84} +(1.03590 - 1.79423i) q^{86} +(-1.50000 - 0.401924i) q^{87} +(5.09808 + 1.36603i) q^{88} +(-0.330127 + 0.571797i) q^{89} +(3.26795 + 6.73205i) q^{91} +(0.169873 + 0.169873i) q^{92} +(1.00000 + 3.73205i) q^{93} +(2.36603 + 4.09808i) q^{94} +(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} + 10 q^{7} + 2 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 4 * q^3 - 6 * q^4 + 10 * q^7 + 2 * q^8 + 6 * q^9	$ 4 q - 2 q^{2} + 4 q^{3} - 6 q^{4} + 10 q^{7} + 2 q^{8} + 6 q^{9} + 2 q^{11} - 6 q^{12} + 8 q^{13} - 2 q^{14} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} + 10 q^{21} - 4 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{26} - 2 q^{27} - 18 q^{28} - 12 q^{31} + 12 q^{32} + 2 q^{33} + 8 q^{34} - 12 q^{36} + 12 q^{37} + 10 q^{38} + 12 q^{39} + 6 q^{42} + 6 q^{43} - 6 q^{44} + 14 q^{46} - 6 q^{47} - 14 q^{48} + 22 q^{49} - 4 q^{51} - 12 q^{52} - 10 q^{53} - 10 q^{54} + 8 q^{56} - 8 q^{57} + 12 q^{58} - 6 q^{59} - 12 q^{61} + 4 q^{62} + 12 q^{63} - 6 q^{66} - 8 q^{67} + 12 q^{68} - 28 q^{69} + 12 q^{71} + 10 q^{72} + 12 q^{74} + 2 q^{77} - 16 q^{78} - 6 q^{79} - 4 q^{81} - 2 q^{83} - 18 q^{84} + 18 q^{86} - 6 q^{87} + 10 q^{88} + 16 q^{89} + 20 q^{91} + 18 q^{92} + 4 q^{93} + 6 q^{94} + 30 q^{96} - 4 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 - 6 * q^4 + 10 * q^7 + 2 * q^8 + 6 * q^9 + 2 * q^11 - 6 * q^12 + 8 * q^13 - 2 * q^14 - 2 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 + 10 * q^21 - 4 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^26 - 2 * q^27 - 18 * q^28 - 12 * q^31 + 12 * q^32 + 2 * q^33 + 8 * q^34 - 12 * q^36 + 12 * q^37 + 10 * q^38 + 12 * q^39 + 6 * q^42 + 6 * q^43 - 6 * q^44 + 14 * q^46 - 6 * q^47 - 14 * q^48 + 22 * q^49 - 4 * q^51 - 12 * q^52 - 10 * q^53 - 10 * q^54 + 8 * q^56 - 8 * q^57 + 12 * q^58 - 6 * q^59 - 12 * q^61 + 4 * q^62 + 12 * q^63 - 6 * q^66 - 8 * q^67 + 12 * q^68 - 28 * q^69 + 12 * q^71 + 10 * q^72 + 12 * q^74 + 2 * q^77 - 16 * q^78 - 6 * q^79 - 4 * q^81 - 2 * q^83 - 18 * q^84 + 18 * q^86 - 6 * q^87 + 10 * q^88 + 16 * q^89 + 20 * q^91 + 18 * q^92 + 4 * q^93 + 6 * q^94 + 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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	$-0.641918\pi$
$2$	−0.500000	+	0.133975i	−0.353553	+	0.0947343i	0.0776710	+	0.996979i	$0.475252\pi$
$3$	0.133975	−	0.500000i	0.0773503	−	0.288675i	−0.916406	−	0.400251i	$-0.868923\pi$
$3$	0.133975	−	0.500000i	0.0773503	−	0.288675i	0.993756	+	0.111576i	$0.0355897\pi$
$4$	−1.50000	+	0.866025i	−0.750000	+	0.433013i
$5$		0			0
$5$		0			0
$6$			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			0
$11$	1.36603	+	2.36603i	0.411872	+	0.713384i	0.995094	−	0.0989291i	$-0.0315417\pi$
$11$	1.36603	+	2.36603i	0.411872	+	0.713384i	−0.583222	+	0.812313i	$0.698208\pi$
$12$	0.232051	+	0.866025i	0.0669873	+	0.250000i
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	0.927794	−	0.373094i	$-0.121703\pi$
$13$	2.00000	+	2.00000i	0.554700	+	0.554700i	−0.373094	+	0.927794i	$0.621703\pi$
$14$	−1.36603	−	0.0980762i	−0.365086	−	0.0262120i
$15$		0			0
$16$	1.23205	−	2.13397i	0.308013	−	0.533494i
$17$	−3.73205	−	1.00000i	−0.905155	−	0.242536i	−0.223926	−	0.974606i	$-0.571888\pi$
$17$	−3.73205	−	1.00000i	−0.905155	−	0.242536i	−0.681229	+	0.732070i	$0.738554\pi$
$18$	−1.36603	−	0.366025i	−0.321975	−	0.0862730i
$19$	0.366025	−	0.633975i	0.0839720	−	0.145444i	−0.820981	−	0.570956i	$-0.806573\pi$
$19$	0.366025	−	0.633975i	0.0839720	−	0.145444i	0.904953	+	0.425512i	$0.139906\pi$
$20$		0			0
$21$	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	$-0.0879364\pi$
$23$	−0.0358984	−	0.133975i	−0.00748533	−	0.0279356i	−0.969567	+	0.244824i	$0.921270\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	−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	$-0.910149\pi$
$29$		−	3.00000i		−	0.557086i	0.960424	−	0.278543i	$-0.0898515\pi$
$30$		0			0
$31$	−6.46410	+	3.73205i	−1.16099	+	0.670296i	−0.951540	−	0.307524i	$-0.900500\pi$
$31$	−6.46410	+	3.73205i	−1.16099	+	0.670296i	−0.209447	+	0.977820i	$0.567166\pi$
$32$	−1.33013	+	4.96410i	−0.235135	+	0.877537i
$33$	1.36603	−	0.366025i	0.237795	−	0.0637168i
$34$	2.00000			0.342997
$35$		0			0
$36$	−4.73205			−0.788675
$37$	4.73205	−	1.26795i	0.777944	−	0.208450i	0.152066	−	0.988370i	$-0.451407\pi$
$37$	4.73205	−	1.26795i	0.777944	−	0.208450i	0.625878	+	0.779921i	$0.284741\pi$
$38$	−0.0980762	+	0.366025i	−0.0159101	+	0.0593772i
$39$	1.26795	−	0.732051i	0.203034	−	0.117222i
$40$		0			0
$41$		−	6.46410i		−	1.00952i	−0.863259	−	0.504762i	$-0.831580\pi$
$41$		−	6.46410i		−	1.00952i	0.863259	−	0.504762i	$-0.168420\pi$
$42$	−0.232051	+	0.669873i	−0.0358062	+	0.103364i
$43$	−2.83013	+	2.83013i	−0.431590	+	0.431590i	−0.889169	−	0.457579i	$-0.848717\pi$
$43$	−2.83013	+	2.83013i	−0.431590	+	0.431590i	0.457579	+	0.889169i	$0.348717\pi$
$44$	−4.09808	−	2.36603i	−0.617808	−	0.356692i
$45$		0			0
$46$	0.0358984	+	0.0621778i	0.00529293	+	0.00916762i
$47$	−2.36603	−	8.83013i	−0.345120	−	1.28801i	−0.892472	−	0.451103i	$-0.851031\pi$
$47$	−2.36603	−	8.83013i	−0.345120	−	1.28801i	0.547351	−	0.836903i	$-0.315636\pi$
$48$	−0.901924	−	0.901924i	−0.130181	−	0.130181i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$	−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	$-0.578081\pi$
$53$	−6.83013	−	1.83013i	−0.938190	−	0.251387i	−0.695344	+	0.718677i	$0.744748\pi$
$54$	−0.767949	+	1.33013i	−0.104505	+	0.181007i
$55$		0			0
$56$	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	−0.999233	−	0.0391530i	$-0.987534\pi$
$59$	−4.09808	−	7.09808i	−0.533524	−	0.924091i	0.465709	−	0.884938i	$-0.345799\pi$
$60$		0			0
$61$	1.33013	+	0.767949i	0.170305	+	0.0983258i	0.582730	−	0.812666i	$-0.301985\pi$
$61$	1.33013	+	0.767949i	0.170305	+	0.0983258i	−0.412424	+	0.910992i	$0.635318\pi$
$62$	2.73205	−	2.73205i	0.346971	−	0.346971i
$63$	4.73205	+	5.46410i	0.596182	+	0.688412i
$64$			2.26795i			0.283494i
$65$		0			0
$66$	−0.633975	+	0.366025i	−0.0780369	+	0.0450546i
$67$	−2.86603	+	10.6962i	−0.350141	+	1.30674i	0.536350	+	0.843996i	$0.319803\pi$
$67$	−2.86603	+	10.6962i	−0.350141	+	1.30674i	−0.886490	+	0.462747i	$0.846864\pi$
$68$	6.46410	−	1.73205i	0.783887	−	0.210042i
$69$	−0.0717968			−0.00864332
$70$		0			0
$71$	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	−0.397796	−	0.917474i	$-0.630225\pi$
$73$	3.46410	−	12.9282i	0.405442	−	1.51313i	0.803238	−	0.595658i	$-0.203109\pi$
$74$	−2.19615	+	1.26795i	−0.255298	+	0.147396i
$75$		0			0
$76$			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	0.650686	−	0.759347i	$-0.274482\pi$
$79$	2.83013	+	1.63397i	0.318414	+	0.183837i	−0.332271	+	0.943184i	$0.607815\pi$
$80$		0			0
$81$	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	$-0.197934\pi$
$83$	2.09808	+	2.09808i	0.230294	+	0.230294i	−0.582522	+	0.812815i	$0.697934\pi$
$84$	−0.169873	+	2.36603i	−0.0185347	+	0.258155i
$85$		0			0
$86$	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	−0.882992	−	0.469389i	$-0.844474\pi$
$89$	−0.330127	+	0.571797i	−0.0349934	+	0.0606103i	0.847998	+	0.529999i	$0.177808\pi$
$90$		0			0
$91$	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
$95$		0			0
$96$	2.30385	+	1.33013i	0.235135	+	0.135756i
$97$	5.92820	−	5.92820i	0.601918	−	0.601918i	−0.338903	−	0.940821i	$-0.610056\pi$
$97$	5.92820	−	5.92820i	0.601918	−	0.601918i	0.940821	+	0.338903i	$0.110056\pi$
$98$	−3.33013	−	1.42820i	−0.336394	−	0.144270i
$99$			7.46410i			0.750170i
$100$		0			0
$101$	7.16025	−	4.13397i	0.712472	−	0.411346i	−0.0995037	−	0.995037i	$-0.531726\pi$
$101$	7.16025	−	4.13397i	0.712472	−	0.411346i	0.811976	+	0.583691i	$0.198392\pi$
$102$	0.267949	−	1.00000i	0.0265309	−	0.0990148i
$103$	−4.59808	+	1.23205i	−0.453062	+	0.121398i	−0.478132	−	0.878288i	$-0.658686\pi$
$103$	−4.59808	+	1.23205i	−0.453062	+	0.121398i	0.0250698	+	0.999686i	$0.492019\pi$
$104$	5.46410			0.535799
$105$		0			0
$106$	3.66025			0.355515
$107$	−12.6962	+	3.40192i	−1.22738	+	0.328876i	−0.813560	−	0.581481i	$-0.802474\pi$
$107$	−12.6962	+	3.40192i	−1.22738	+	0.328876i	−0.413823	+	0.910357i	$0.635807\pi$
$108$	−1.33013	+	4.96410i	−0.127992	+	0.477671i
$109$	−8.76795	+	5.06218i	−0.839817	+	0.484869i	−0.857202	−	0.514980i	$-0.827799\pi$
$109$	−8.76795	+	5.06218i	−0.839817	+	0.484869i	0.0173849	+	0.999849i	$0.494466\pi$
$110$		0			0
$111$		−	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	$-0.578041\pi$
$113$	7.73205	−	7.73205i	0.727370	−	0.727370i	0.970095	+	0.242725i	$0.0780413\pi$
$114$	0.169873	+	0.0980762i	0.0159101	+	0.00918568i
$115$		0			0
$116$	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
$120$		0			0
$121$	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
$125$		0			0
$126$	−3.09808	−	2.09808i	−0.275999	−	0.186911i
$127$	−0.464102	−	0.464102i	−0.0411824	−	0.0411824i	0.686216	−	0.727398i	$-0.259271\pi$
$127$	−0.464102	−	0.464102i	−0.0411824	−	0.0411824i	−0.727398	+	0.686216i	$0.759271\pi$
$128$	−2.96410	−	11.0622i	−0.261992	−	0.977768i
$129$	1.03590	+	1.79423i	0.0912058	+	0.157973i
$130$		0			0
$131$	−13.3923	−	7.73205i	−1.17009	−	0.675552i	−0.216390	−	0.976307i	$-0.569428\pi$
$131$	−13.3923	−	7.73205i	−1.17009	−	0.675552i	−0.953702	+	0.300755i	$0.902761\pi$
$132$	−1.73205	+	1.73205i	−0.150756	+	0.150756i
$133$	1.46410	−	1.26795i	0.126954	−	0.109945i
$134$		−	5.73205i		−	0.495174i
$135$		0			0
$136$	−6.46410	+	3.73205i	−0.554292	+	0.320021i
$137$	3.53590	−	13.1962i	0.302092	−	1.12742i	−0.633327	−	0.773884i	$-0.718311\pi$
$137$	3.53590	−	13.1962i	0.302092	−	1.12742i	0.935420	−	0.353539i	$-0.115022\pi$
$138$	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	$0.577163\pi$
$140$		0			0
$141$	−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
$145$		0			0
$146$			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	0.528244	−	0.849092i	$-0.322850\pi$
$149$	0.696152	+	0.401924i	0.0570310	+	0.0329269i	−0.471213	+	0.882019i	$0.656184\pi$
$150$		0			0
$151$	−6.92820	−	12.0000i	−0.563809	−	0.976546i	−0.997159	−	0.0753205i	$-0.976002\pi$
$151$	−6.92820	−	12.0000i	−0.563809	−	0.976546i	0.433350	−	0.901226i	$-0.357331\pi$
$152$	−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
$155$		0			0
$156$	−1.26795	+	2.19615i	−0.101517	+	0.175833i
$157$	4.63397	+	1.24167i	0.369831	+	0.0990960i	0.438948	−	0.898513i	$-0.355351\pi$
$157$	4.63397	+	1.24167i	0.369831	+	0.0990960i	−0.0691164	+	0.997609i	$0.522018\pi$
$158$	−1.63397	−	0.437822i	−0.129992	−	0.0348313i
$159$	−1.83013	+	3.16987i	−0.145139	+	0.251387i
$160$		0			0
$161$	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	0.949106	+	0.314958i	$0.101990\pi$
$163$	3.63397	+	13.5622i	0.284635	+	1.06227i	−0.664471	+	0.747314i	$0.731343\pi$
$164$	5.59808	+	9.69615i	0.437136	+	0.757142i
$165$		0			0
$166$	−1.33013	−	0.767949i	−0.103238	−	0.0596044i
$167$	−11.7583	+	11.7583i	−0.909887	+	0.909887i	−0.996263	−	0.0863757i	$-0.972471\pi$
$167$	−11.7583	+	11.7583i	−0.909887	+	0.909887i	0.0863757	+	0.996263i	$0.472471\pi$
$168$	−0.500000	−	2.59808i	−0.0385758	−	0.200446i
$169$		−	5.00000i		−	0.384615i
$170$		0			0
$171$	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	$-0.870301\pi$
$173$	−19.9282	+	5.33975i	−1.51511	+	0.405973i	−0.596984	+	0.802253i	$0.703634\pi$
$174$	0.803848			0.0609395
$175$		0			0
$176$	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	−0.223691	−	0.974660i	$-0.571811\pi$
$179$	6.80385	−	3.92820i	0.508543	−	0.293608i	0.732235	+	0.681052i	$0.238477\pi$
$180$		0			0
$181$		−	1.19615i		−	0.0889093i	−0.999011	−	0.0444547i	$-0.985845\pi$
$181$		−	1.19615i		−	0.0889093i	0.999011	−	0.0444547i	$-0.0141550\pi$
$182$	−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
$185$		0			0
$186$	−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			0
$191$	−6.63397	+	11.4904i	−0.480018	+	0.831415i	−0.999737	−	0.0229220i	$-0.992703\pi$
$191$	−6.63397	+	11.4904i	−0.480018	+	0.831415i	0.519720	+	0.854337i	$0.326036\pi$
$192$	1.13397	+	0.303848i	0.0818376	+	0.0219283i
$193$	7.83013	+	2.09808i	0.563625	+	0.151023i	0.529371	−	0.848390i	$-0.322428\pi$
$193$	7.83013	+	2.09808i	0.563625	+	0.151023i	0.0342537	+	0.999413i	$0.489095\pi$
$194$	−2.16987	+	3.75833i	−0.155788	+	0.269832i
$195$		0			0
$196$	−12.0000	−	1.73205i	−0.857143	−	0.123718i
$197$	10.1244	+	10.1244i	0.721330	+	0.721330i	0.968876	−	0.247546i	$-0.0796240\pi$
$197$	10.1244	+	10.1244i	0.721330	+	0.721330i	−0.247546	+	0.968876i	$0.579624\pi$
$198$	−1.00000	−	3.73205i	−0.0710669	−	0.265225i
$199$	−5.53590	−	9.58846i	−0.392429	−	0.679708i	0.600340	−	0.799745i	$-0.295032\pi$
$199$	−5.53590	−	9.58846i	−0.392429	−	0.679708i	−0.992769	+	0.120037i	$0.961699\pi$
$200$		0			0
$201$	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
$205$		0			0
$206$	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
$210$		0			0
$211$	−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
$215$		0			0
$216$		−	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
$220$		0			0
$221$	−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	−0.969802	−	0.243895i	$-0.921575\pi$
$223$	−18.1244	−	18.1244i	−1.21370	−	1.21370i	−0.243895	−	0.969802i	$-0.578425\pi$
$224$	−7.62436	+	11.2583i	−0.509424	+	0.752229i
$225$		0			0
$226$	−2.83013	+	4.90192i	−0.188257	+	0.326071i
$227$	19.0263	+	5.09808i	1.26282	+	0.338371i	0.827275	−	0.561797i	$-0.189890\pi$
$227$	19.0263	+	5.09808i	1.26282	+	0.338371i	0.435543	+	0.900168i	$0.356556\pi$
$228$	0.633975	+	0.169873i	0.0419860	+	0.0112501i
$229$	−9.19615	+	15.9282i	−0.607699	+	1.05257i	0.383920	+	0.923366i	$0.374574\pi$
$229$	−9.19615	+	15.9282i	−0.607699	+	1.05257i	−0.991619	+	0.129199i	$0.958759\pi$
$230$		0			0
$231$	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	$-0.0129860\pi$
$233$	1.73205	+	6.46410i	0.113470	+	0.423477i	−0.885698	+	0.464263i	$0.846319\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$		0			0
$236$	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	$0.0246531\pi$
$239$			2.39230i			0.154745i	−0.997002	+	0.0773727i	$0.975347\pi$
$240$		0			0
$241$	21.4641	−	12.3923i	1.38262	−	0.798259i	0.390155	−	0.920749i	$-0.372422\pi$
$241$	21.4641	−	12.3923i	1.38262	−	0.798259i	0.992470	+	0.122491i	$0.0390882\pi$
$242$	−0.473721	+	1.76795i	−0.0304519	+	0.113648i
$243$	11.9282	−	3.19615i	0.765195	−	0.205033i
$244$	−2.66025			−0.170305
$245$		0			0
$246$	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			0
$251$			21.8564i			1.37956i	0.724017	+	0.689782i	$0.242294\pi$
$251$			21.8564i			1.37956i	−0.724017	+	0.689782i	$0.757706\pi$
$252$	−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
$255$		0			0
$256$	0.696152	+	1.20577i	0.0435095	+	0.0753607i
$257$	0.732051	+	2.73205i	0.0456641	+	0.170421i	0.984992	−	0.172600i	$-0.0552167\pi$
$257$	0.732051	+	2.73205i	0.0456641	+	0.170421i	−0.939328	+	0.343020i	$0.888550\pi$
$258$	−0.758330	−	0.758330i	−0.0472116	−	0.0472116i
$259$	12.9282	+	0.928203i	0.803319	+	0.0576757i
$260$		0			0
$261$	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	$-0.255887\pi$
$263$	15.1603	+	4.06218i	0.934821	+	0.250485i	0.240912	+	0.970547i	$0.422553\pi$
$264$	1.36603	−	2.36603i	0.0840731	−	0.145619i
$265$		0			0
$266$	−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	0.969574	+	0.244800i	$0.0787223\pi$
$269$	11.4282	+	19.7942i	0.696790	+	1.20688i	−0.272784	+	0.962075i	$0.587944\pi$
$270$		0			0
$271$	18.4186	+	10.6340i	1.11885	+	0.645968i	0.941107	−	0.338109i	$-0.109787\pi$
$271$	18.4186	+	10.6340i	1.11885	+	0.645968i	0.177742	+	0.984077i	$0.443121\pi$
$272$	−6.73205	+	6.73205i	−0.408191	+	0.408191i
$273$	3.80385	−	0.732051i	0.230219	−	0.0443057i
$274$			7.07180i			0.427223i
$275$		0			0
$276$	0.107695	−	0.0621778i	0.00648249	−	0.00374267i
$277$	1.39230	−	5.19615i	0.0836555	−	0.312207i	−0.911401	−	0.411520i	$-0.864998\pi$
$277$	1.39230	−	5.19615i	0.0836555	−	0.312207i	0.995056	+	0.0993135i	$0.0316647\pi$
$278$	2.83013	−	0.758330i	0.169740	−	0.0454816i
$279$	−20.3923			−1.22086
$280$		0			0
$281$	−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	$-0.898028\pi$
$283$	0.509619	−	1.90192i	0.0302937	−	0.113058i	0.979417	+	0.201847i	$0.0646943\pi$
$284$	−1.90192	+	1.09808i	−0.112858	+	0.0651588i
$285$		0			0
$286$		−	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
$290$		0			0
$291$	−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	$-0.218492\pi$
$293$	2.39230	+	2.39230i	0.139760	+	0.139760i	−0.633765	+	0.773525i	$0.718492\pi$
$294$	−1.16025	+	1.47372i	−0.0676674	+	0.0859491i
$295$		0			0
$296$	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			0
$301$	−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
$305$		0			0
$306$	4.73205	+	2.73205i	0.270513	+	0.156181i
$307$	−6.29423	+	6.29423i	−0.359231	+	0.359231i	−0.863529	−	0.504299i	$-0.831751\pi$
$307$	−6.29423	+	6.29423i	−0.359231	+	0.359231i	0.504299	+	0.863529i	$0.331751\pi$
$308$	−8.19615	−	9.46410i	−0.467019	−	0.539267i
$309$			2.46410i			0.140178i
$310$		0			0
$311$	−13.2224	+	7.63397i	−0.749775	+	0.432883i	−0.825613	−	0.564237i	$-0.809170\pi$
$311$	−13.2224	+	7.63397i	−0.749775	+	0.432883i	0.0758374	+	0.997120i	$0.475837\pi$
$312$	0.732051	−	2.73205i	0.0414442	−	0.154672i
$313$	5.19615	−	1.39230i	0.293704	−	0.0786977i	−0.108958	−	0.994046i	$-0.534752\pi$
$313$	5.19615	−	1.39230i	0.293704	−	0.0786977i	0.402662	+	0.915349i	$0.368085\pi$
$314$	−2.48334			−0.140143
$315$		0			0
$316$	−5.66025			−0.318414
$317$	−9.19615	+	2.46410i	−0.516507	+	0.138398i	−0.507651	−	0.861563i	$-0.669486\pi$
$317$	−9.19615	+	2.46410i	−0.516507	+	0.138398i	−0.00885679	+	0.999961i	$0.502819\pi$
$318$	0.490381	−	1.83013i	0.0274992	−	0.102628i
$319$	7.09808	−	4.09808i	0.397416	−	0.229448i
$320$		0			0
$321$			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
$325$		0			0
$326$	−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			0
$331$	0.928203	−	1.60770i	0.0510187	−	0.0883669i	−0.839388	−	0.543532i	$-0.817087\pi$
$331$	0.928203	−	1.60770i	0.0510187	−	0.0883669i	0.890407	+	0.455165i	$0.150420\pi$
$332$	−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
$335$		0			0
$336$	−1.47372	−	3.03590i	−0.0803980	−	0.165622i
$337$	−9.53590	−	9.53590i	−0.519453	−	0.519453i	0.397953	−	0.917406i	$-0.369721\pi$
$337$	−9.53590	−	9.53590i	−0.519453	−	0.519453i	−0.917406	+	0.397953i	$0.869721\pi$
$338$	0.669873	+	2.50000i	0.0364363	+	0.135982i
$339$	−2.83013	−	4.90192i	−0.153711	−	0.266236i
$340$		0			0
$341$	−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			0
$346$	9.24871	−	5.33975i	0.497214	−	0.287067i
$347$	7.79423	−	29.0885i	0.418416	−	1.56155i	−0.359477	−	0.933154i	$-0.617045\pi$
$347$	7.79423	−	29.0885i	0.418416	−	1.56155i	0.777893	−	0.628396i	$-0.216288\pi$
$348$	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	$0.446347\pi$
$350$		0			0
$351$	8.39230			0.447948
$352$	−13.5622	+	3.63397i	−0.722867	+	0.193691i
$353$	−3.63397	+	13.5622i	−0.193417	+	0.721842i	0.799254	+	0.600993i	$0.205228\pi$
$353$	−3.63397	+	13.5622i	−0.193417	+	0.721842i	−0.992671	+	0.120849i	$0.961438\pi$
$354$	1.90192	−	1.09808i	0.101086	−	0.0583621i
$355$		0			0
$356$		−	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	0.996693	+	0.0812542i	$0.0258926\pi$
$359$	29.6603	+	17.1244i	1.56541	+	0.903789i	0.568715	+	0.822535i	$0.307441\pi$
$360$		0			0
$361$	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
$365$		0			0
$366$	−0.205771	+	0.356406i	−0.0107558	+	0.0186297i
$367$	−0.500000	−	0.133975i	−0.0260998	−	0.00699342i	0.245746	−	0.969334i	$-0.420967\pi$
$367$	−0.500000	−	0.133975i	−0.0260998	−	0.00699342i	−0.271845	+	0.962341i	$0.587634\pi$
$368$	−0.330127	−	0.0884573i	−0.0172091	−	0.00461115i
$369$	8.83013	−	15.2942i	0.459678	−	0.796186i
$370$		0			0
$371$	−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	$-0.149780\pi$
$373$	−2.07180	−	7.73205i	−0.107274	−	0.400350i	−0.998593	+	0.0530251i	$0.983114\pi$
$374$	2.73205	+	4.73205i	0.141271	+	0.244689i
$375$		0			0
$376$	−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	$0.0191395\pi$
$379$			2.33975i			0.120185i	−0.998193	+	0.0600923i	$0.980860\pi$
$380$		0			0
$381$	−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	$-0.882847\pi$
$383$	−30.5526	+	8.18653i	−1.56116	+	0.418312i	−0.628131	+	0.778107i	$0.716180\pi$
$384$	−5.92820			−0.302522
$385$		0			0
$386$	−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	−0.604279	−	0.796773i	$-0.706539\pi$
$389$	−4.26795	+	2.46410i	−0.216394	+	0.124935i	0.387886	+	0.921707i	$0.373206\pi$
$390$		0			0
$391$			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
$395$		0			0
$396$	−6.46410	−	11.1962i	−0.324833	−	0.562628i
$397$	0.973721	+	3.63397i	0.0488696	+	0.182384i	0.986046	−	0.166471i	$-0.0532372\pi$
$397$	0.973721	+	3.63397i	0.0488696	+	0.182384i	−0.937177	+	0.348855i	$0.886571\pi$
$398$	4.05256	+	4.05256i	0.203136	+	0.203136i
$399$	−0.437822	−	0.901924i	−0.0219185	−	0.0451527i
$400$		0			0
$401$	−5.50000	+	9.52628i	−0.274657	+	0.475720i	−0.970049	−	0.242911i	$-0.921898\pi$
$401$	−5.50000	+	9.52628i	−0.274657	+	0.475720i	0.695392	+	0.718631i	$0.255231\pi$
$402$	−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
$405$		0			0
$406$	−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	−0.999835	−	0.0181564i	$-0.994220\pi$
$409$	−10.4282	−	18.0622i	−0.515641	−	0.893117i	0.484194	−	0.874961i	$-0.339113\pi$
$410$		0			0
$411$	−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
$415$		0			0
$416$	−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	$0.301984\pi$
$420$		0			0
$421$	−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
$425$		0			0
$426$			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
$430$		0			0
$431$	−3.09808	−	5.36603i	−0.149229	−	0.258472i	0.781714	−	0.623637i	$-0.214346\pi$
$431$	−3.09808	−	5.36603i	−0.149229	−	0.258472i	−0.930943	+	0.365165i	$0.881013\pi$
$432$	−1.89230	−	7.06218i	−0.0910436	−	0.339779i
$433$	17.5359	+	17.5359i	0.842721	+	0.842721i	0.989212	−	0.146491i	$-0.0467978\pi$
$433$	17.5359	+	17.5359i	0.842721	+	0.842721i	−0.146491	+	0.989212i	$0.546798\pi$
$434$	9.19615	−	4.46410i	0.441429	−	0.214284i
$435$		0			0
$436$	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	−0.823682	−	0.567051i	$-0.808084\pi$
$439$	1.66025	−	2.87564i	0.0792396	−	0.137247i	0.902922	+	0.429804i	$0.141417\pi$
$440$		0			0
$441$	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	0.997872	+	0.0652010i	$0.0207689\pi$
$443$	3.50000	+	13.0622i	0.166290	+	0.620603i	−0.831582	+	0.555402i	$0.812564\pi$
$444$	2.19615	+	3.80385i	0.104225	+	0.180523i
$445$		0			0
$446$	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	$-0.715258\pi$
$449$		−	33.0526i		−	1.55985i	0.625875	−	0.779923i	$-0.284742\pi$
$450$		0			0
$451$	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
$455$		0			0
$456$	−0.732051			−0.0342814
$457$	11.7321	−	3.14359i	0.548802	−	0.147051i	0.0262453	−	0.999656i	$-0.491645\pi$
$457$	11.7321	−	3.14359i	0.548802	−	0.147051i	0.522557	+	0.852604i	$0.324978\pi$
$458$	2.46410	−	9.19615i	0.115140	−	0.429708i
$459$	−9.92820	+	5.73205i	−0.463409	+	0.267549i
$460$		0			0
$461$		−	5.60770i		−	0.261176i	−0.991437	−	0.130588i	$-0.958313\pi$
$461$		−	5.60770i		−	0.261176i	0.991437	−	0.130588i	$-0.0416866\pi$
$462$	−1.90192	+	0.366025i	−0.0884855	+	0.0170290i
$463$	4.75833	−	4.75833i	0.221138	−	0.221138i	−0.587839	−	0.808978i	$-0.700021\pi$
$463$	4.75833	−	4.75833i	0.221138	−	0.221138i	0.808978	+	0.587839i	$0.200021\pi$
$464$	−6.40192	−	3.69615i	−0.297202	−	0.171590i
$465$		0			0
$466$	−1.73205	−	3.00000i	−0.0802357	−	0.138972i
$467$	−3.64359	−	13.5981i	−0.168605	−	0.629244i	−0.997553	−	0.0699173i	$-0.977726\pi$
$467$	−3.64359	−	13.5981i	−0.168605	−	0.629244i	0.828947	−	0.559327i	$-0.188940\pi$
$468$	−9.46410	−	9.46410i	−0.437478	−	0.437478i
$469$	−16.4282	+	24.2583i	−0.758584	+	1.12015i
$470$		0			0
$471$	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
$475$		0			0
$476$	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	0.975823	−	0.218560i	$-0.0701361\pi$
$479$	6.53590	+	11.3205i	0.298633	+	0.517247i	−0.677191	+	0.735808i	$0.736803\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	−5.53590	+	3.19615i	−0.251113	+	0.144980i
$487$	−7.29423	+	27.2224i	−0.330533	+	1.23357i	0.578098	+	0.815967i	$0.303795\pi$
$487$	−7.29423	+	27.2224i	−0.330533	+	1.23357i	−0.908631	+	0.417599i	$0.862872\pi$
$488$	2.86603	−	0.767949i	0.129739	−	0.0347634i
$489$	7.26795			0.328668
$490$		0			0
$491$	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
$495$		0			0
$496$			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	0.259860	−	0.965646i	$-0.416324\pi$
$499$	−9.97372	−	5.75833i	−0.446485	−	0.257778i	−0.706345	+	0.707868i	$0.749657\pi$
$500$		0			0
$501$	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	$-0.0623470\pi$
$503$	17.6340	+	17.6340i	0.786260	+	0.786260i	−0.194619	+	0.980879i	$0.562347\pi$
$504$	13.9282	+	1.00000i	0.620411	+	0.0445435i
$505$		0			0
$506$	−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	0.00739389	+	0.999973i	$0.497646\pi$
$509$	−19.4545	+	33.6962i	−0.862305	+	1.49356i	−0.869699	+	0.493583i	$0.835687\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	−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			0
$521$	−20.6603	+	11.9282i	−0.905142	+	0.522584i	−0.878865	−	0.477071i	$-0.841699\pi$
$521$	−20.6603	+	11.9282i	−0.905142	+	0.522584i	−0.0262772	+	0.999655i	$0.508365\pi$
$522$	−1.09808	+	4.09808i	−0.0480615	+	0.179368i
$523$	42.8827	−	11.4904i	1.87513	−	0.502439i	0.875307	−	0.483568i	$-0.160659\pi$
$523$	42.8827	−	11.4904i	1.87513	−	0.502439i	0.999822	−	0.0188717i	$-0.00600740\pi$
$524$	26.7846			1.17009
$525$		0			0
$526$	−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			0
$531$		−	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
$535$		0			0
$536$	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
$540$		0			0
$541$	−18.3564	+	31.7942i	−0.789204	+	1.36694i	0.137252	+	0.990536i	$0.456173\pi$
$541$	−18.3564	+	31.7942i	−0.789204	+	1.36694i	−0.926455	+	0.376404i	$0.877160\pi$
$542$	−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
$545$		0			0
$546$	−1.80385	+	0.875644i	−0.0771975	+	0.0374741i
$547$	16.7583	+	16.7583i	0.716534	+	0.716534i	0.967894	−	0.251359i	$-0.0808776\pi$
$547$	16.7583	+	16.7583i	0.716534	+	0.716534i	−0.251359	+	0.967894i	$0.580878\pi$
$548$	6.12436	+	22.8564i	0.261620	+	0.976377i
$549$	2.09808	+	3.63397i	0.0895437	+	0.155094i
$550$		0			0
$551$	−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
$555$		0			0
$556$	8.49038	−	4.90192i	0.360072	−	0.207888i
$557$	−8.36603	+	31.2224i	−0.354480	+	1.32294i	0.526658	+	0.850077i	$0.323445\pi$
$557$	−8.36603	+	31.2224i	−0.354480	+	1.32294i	−0.881138	+	0.472860i	$0.843222\pi$
$558$	10.1962	−	2.73205i	0.431638	−	0.115657i
$559$	−11.3205			−0.478806
$560$		0			0
$561$	−5.46410			−0.230695
$562$	0.464102	−	0.124356i	0.0195769	−	0.00524563i
$563$	6.35641	−	23.7224i	0.267891	−	0.999781i	−0.692567	−	0.721354i	$-0.743520\pi$
$563$	6.35641	−	23.7224i	0.267891	−	0.999781i	0.960457	−	0.278427i	$-0.0898132\pi$
$564$	7.09808	−	4.09808i	0.298883	−	0.172560i
$565$		0			0
$566$			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	−0.127536	−	0.991834i	$-0.540707\pi$
$569$	−25.0526	−	14.4641i	−1.05026	−	0.606367i	−0.922722	+	0.385467i	$0.874040\pi$
$570$		0			0
$571$	9.02628	+	15.6340i	0.377738	+	0.654261i	0.990733	−	0.135826i	$-0.0433687\pi$
$571$	9.02628	+	15.6340i	0.377738	+	0.654261i	−0.612995	+	0.790087i	$0.710035\pi$
$572$	−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			0
$576$	−3.09808	+	5.36603i	−0.129087	+	0.223584i
$577$	−5.63397	−	1.50962i	−0.234545	−	0.0628463i	0.139632	−	0.990204i	$-0.455408\pi$
$577$	−5.63397	−	1.50962i	−0.234545	−	0.0628463i	−0.374177	+	0.927357i	$0.622075\pi$
$578$	1.03590	+	0.277568i	0.0430877	+	0.0115453i
$579$	2.09808	−	3.63397i	0.0871931	−	0.151023i
$580$		0			0
$581$	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
$585$		0			0
$586$	−1.51666	−	0.875644i	−0.0626527	−	0.0361725i
$587$	−15.7846	+	15.7846i	−0.651501	+	0.651501i	−0.953354	−	0.301854i	$-0.902395\pi$
$587$	−15.7846	+	15.7846i	−0.651501	+	0.651501i	0.301854	+	0.953354i	$0.402395\pi$
$588$	−2.47372	+	5.76795i	−0.102015	+	0.237866i
$589$			5.46410i			0.225144i
$590$		0			0
$591$	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	$-0.728801\pi$
$593$	−20.7583	+	5.56218i	−0.852442	+	0.228411i	−0.193962	+	0.981009i	$0.562134\pi$
$594$	−4.19615			−0.172170
$595$		0			0
$596$	−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	−0.779498	−	0.626405i	$-0.784526\pi$
$599$	−15.3397	+	8.85641i	−0.626765	+	0.361863i	0.152733	+	0.988267i	$0.451193\pi$
$600$		0			0
$601$		−	41.1769i		−	1.67964i	−0.542864	−	0.839821i	$-0.682660\pi$
$601$		−	41.1769i		−	1.67964i	0.542864	−	0.839821i	$-0.317340\pi$
$602$	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
$605$		0			0
$606$	1.10770	+	1.91858i	0.0449970	+	0.0779372i
$607$	−3.40192	−	12.6962i	−0.138080	−	0.515321i	−0.999966	−	0.00821951i	$-0.997384\pi$
$607$	−3.40192	−	12.6962i	−0.138080	−	0.515321i	0.861886	−	0.507101i	$-0.169283\pi$
$608$	2.66025	+	2.66025i	0.107888	+	0.107888i
$609$	−3.40192	−	2.30385i	−0.137853	−	0.0933566i
$610$		0			0
$611$	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	$-0.587012\pi$
$613$	−24.3923	−	6.53590i	−0.985196	−	0.263982i	−0.715231	+	0.698888i	$0.753679\pi$
$614$	2.30385	−	3.99038i	0.0929757	−	0.161039i
$615$		0			0
$616$	11.5622	+	7.83013i	0.465853	+	0.315485i
$617$	−33.9090	−	33.9090i	−1.36512	−	1.36512i	−0.867249	−	0.497874i	$-0.834114\pi$
$617$	−33.9090	−	33.9090i	−1.36512	−	1.36512i	−0.497874	−	0.867249i	$-0.665886\pi$
$618$	−0.330127	−	1.23205i	−0.0132797	−	0.0495604i
$619$	5.09808	+	8.83013i	0.204909	+	0.354913i	0.950104	−	0.311934i	$-0.100977\pi$
$619$	5.09808	+	8.83013i	0.204909	+	0.354913i	−0.745195	+	0.666847i	$0.767643\pi$
$620$		0			0
$621$	−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
$625$		0			0
$626$	−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
$630$		0			0
$631$	−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
$635$		0			0
$636$		−	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
$640$		0			0
$641$	−5.33013	−	9.23205i	−0.210527	−	0.364644i	0.741352	−	0.671116i	$-0.234185\pi$
$641$	−5.33013	−	9.23205i	−0.210527	−	0.364644i	−0.951880	+	0.306472i	$0.900851\pi$
$642$	−0.911543	−	3.40192i	−0.0359757	−	0.134263i
$643$	−17.5359	−	17.5359i	−0.691548	−	0.691548i	0.271024	−	0.962573i	$-0.412638\pi$
$643$	−17.5359	−	17.5359i	−0.691548	−	0.691548i	−0.962573	+	0.271024i	$0.912638\pi$
$644$	0.277568	+	0.571797i	0.0109377	+	0.0225319i
$645$		0			0
$646$	0.732051	−	1.26795i	0.0288022	−	0.0498868i
$647$	−39.5526	−	10.5981i	−1.55497	−	0.416653i	−0.623904	−	0.781501i	$-0.714454\pi$
$647$	−39.5526	−	10.5981i	−1.55497	−	0.416653i	−0.931067	+	0.364847i	$0.881121\pi$
$648$	12.4282	+	3.33013i	0.488226	+	0.130820i
$649$	11.1962	−	19.3923i	0.439487	−	0.761215i
$650$		0			0
$651$	−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	0.989096	+	0.147274i	$0.0470500\pi$
$653$	5.26795	+	19.6603i	0.206151	+	0.769365i	−0.782945	+	0.622091i	$0.786283\pi$
$654$	−1.35641	−	2.34936i	−0.0530397	−	0.0918674i
$655$		0			0
$656$	−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	$-0.818899\pi$
$659$		−	27.6603i		−	1.07749i	0.842469	−	0.538745i	$-0.181101\pi$
$660$		0			0
$661$	−41.7224	+	24.0885i	−1.62281	+	0.936932i	−0.636652	+	0.771151i	$0.719681\pi$
$661$	−41.7224	+	24.0885i	−1.62281	+	0.936932i	−0.986163	+	0.165781i	$0.946985\pi$
$662$	−0.248711	+	0.928203i	−0.00966644	+	0.0360756i
$663$	−5.46410	+	1.46410i	−0.212208	+	0.0568610i
$664$	5.73205			0.222447
$665$		0			0
$666$	−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
$670$		0			0
$671$			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	$-0.788200\pi$
$673$	−4.39230	+	4.39230i	−0.169311	+	0.169311i	0.617366	+	0.786676i	$0.288200\pi$
$674$	6.04552	+	3.49038i	0.232865	+	0.134444i
$675$		0			0
$676$	4.33013	+	7.50000i	0.166543	+	0.288462i
$677$	6.92820	+	25.8564i	0.266272	+	0.993742i	0.961467	+	0.274921i	$0.0886516\pi$
$677$	6.92820	+	25.8564i	0.266272	+	0.993742i	−0.695194	+	0.718822i	$0.744682\pi$
$678$	2.07180	+	2.07180i	0.0795669	+	0.0795669i
$679$	19.9545	−	9.68653i	0.765783	−	0.371735i
$680$		0			0
$681$	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	$-0.526400\pi$
$683$	−17.0622	−	4.57180i	−0.652866	−	0.174935i	−0.570024	+	0.821628i	$0.693066\pi$
$684$	−1.73205	+	3.00000i	−0.0662266	+	0.114708i
$685$		0			0
$686$	−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			0
$691$	−44.0263	−	25.4186i	−1.67484	−	0.966969i	−0.964867	−	0.262738i	$-0.915375\pi$
$691$	−44.0263	−	25.4186i	−1.67484	−	0.966969i	−0.709971	−	0.704231i	$-0.751292\pi$
$692$	25.2679	−	25.2679i	0.960543	−	0.960543i
$693$	−6.46410	+	18.6603i	−0.245551	+	0.708844i
$694$			15.5885i			0.591730i
$695$		0			0
$696$	−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
$700$		0			0
$701$	−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			0
$706$		−	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	0.812244	−	0.583317i	$-0.198246\pi$
$709$	18.9904	+	10.9641i	0.713199	+	0.411765i	−0.0990456	+	0.995083i	$0.531579\pi$
$710$		0			0
$711$	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
$715$		0			0
$716$	−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	−0.241624	−	0.970370i	$-0.577680\pi$
$719$	19.2942	−	33.4186i	0.719553	−	1.24630i	0.961177	−	0.275933i	$-0.0889867\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	0.820508	+	0.473721i	0.0304519	+	0.0175814i
$727$	10.0981	−	10.0981i	0.374517	−	0.374517i	−0.494602	−	0.869119i	$-0.664686\pi$
$727$	10.0981	−	10.0981i	0.374517	−	0.374517i	0.869119	+	0.494602i	$0.164686\pi$
$728$	13.6603	+	4.73205i	0.506283	+	0.175381i
$729$			13.5885i			0.503276i
$730$		0			0
$731$	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	$-0.556731\pi$
$733$	4.36603	−	1.16987i	0.161263	−	0.0432102i	0.338547	+	0.940949i	$0.390065\pi$
$734$	0.267949			0.00989019
$735$		0			0
$736$	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	−0.814608	−	0.580012i	$-0.803048\pi$
$739$	−19.5622	+	11.2942i	−0.719606	+	0.415465i	0.0950014	+	0.995477i	$0.469714\pi$
$740$		0			0
$741$		−	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	$-0.698833\pi$
$743$	6.16987	−	6.16987i	0.226351	−	0.226351i	0.811166	+	0.584816i	$0.198833\pi$
$744$	6.46410	+	3.73205i	0.236985	+	0.136824i
$745$		0			0
$746$	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
$750$		0			0
$751$	3.19615	−	5.53590i	0.116629	−	0.202008i	−0.801801	−	0.597592i	$-0.796124\pi$
$751$	3.19615	−	5.53590i	0.116629	−	0.202008i	0.918430	+	0.395584i	$0.129458\pi$
$752$	−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
$755$		0			0
$756$	−7.62436	+	11.2583i	−0.277295	+	0.409462i
$757$	−12.7321	−	12.7321i	−0.462754	−	0.462754i	0.436803	−	0.899557i	$-0.356111\pi$
$757$	−12.7321	−	12.7321i	−0.462754	−	0.462754i	−0.899557	+	0.436803i	$0.856111\pi$
$758$	−0.313467	−	1.16987i	−0.0113856	−	0.0424917i
$759$	−0.0980762	−	0.169873i	−0.00355994	−	0.00616600i
$760$		0			0
$761$	24.9282	+	14.3923i	0.903647	+	0.521721i	0.878382	−	0.477960i	$-0.158624\pi$
$761$	24.9282	+	14.3923i	0.903647	+	0.521721i	0.0252651	+	0.999681i	$0.491957\pi$
$762$	0.124356	−	0.124356i	0.00450493	−	0.00450493i
$763$	−26.3038	+	5.06218i	−0.952263	+	0.183263i
$764$		−	22.9808i		−	0.831415i
$765$		0			0
$766$	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	$0.411770\pi$
$770$		0			0
$771$	1.46410			0.0527283
$772$	−13.5622	+	3.63397i	−0.488113	+	0.130790i
$773$	−4.07180	+	15.1962i	−0.146452	+	0.546568i	0.853234	+	0.521528i	$0.174638\pi$
$773$	−4.07180	+	15.1962i	−0.146452	+	0.546568i	−0.999686	+	0.0250395i	$0.992029\pi$
$774$	4.90192	−	2.83013i	0.176196	−	0.101727i
$775$		0			0
$776$		−	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
$780$		0			0
$781$	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
$785$		0			0
$786$	2.07180	−	3.58846i	0.0738985	−	0.127996i
$787$	−31.1865	−	8.35641i	−1.11168	−	0.297874i	−0.344168	−	0.938908i	$-0.611839\pi$
$787$	−31.1865	−	8.35641i	−1.11168	−	0.297874i	−0.767512	+	0.641034i	$0.778506\pi$
$788$	−23.9545	−	6.41858i	−0.853343	−	0.228653i
$789$	4.06218	−	7.03590i	0.144617	−	0.250485i
$790$		0			0
$791$	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
$795$		0			0
$796$	16.6077	+	9.58846i	0.588644	+	0.339854i
$797$	−22.5359	+	22.5359i	−0.798262	+	0.798262i	−0.982821	−	0.184559i	$-0.940914\pi$
$797$	−22.5359	+	22.5359i	−0.798262	+	0.798262i	0.184559	+	0.982821i	$0.440914\pi$
$798$	0.339746	+	0.392305i	0.0120269	+	0.0138874i
$799$			35.3205i			1.24955i
$800$		0			0
$801$	−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			0
$806$	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	−0.568504	−	0.822680i	$-0.692478\pi$
$809$	−3.99038	+	2.30385i	−0.140294	+	0.0809990i	0.428210	+	0.903679i	$0.359144\pi$
$810$		0			0
$811$			42.9282i			1.50741i	0.657211	+	0.753707i	$0.271736\pi$
$811$			42.9282i			1.50741i	−0.657211	+	0.753707i	$0.728264\pi$
$812$	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
$815$		0			0
$816$	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
$820$		0			0
$821$	24.6603	−	42.7128i	0.860649	−	1.49069i	−0.0106549	−	0.999943i	$-0.503392\pi$
$821$	24.6603	−	42.7128i	0.860649	−	1.49069i	0.871304	−	0.490744i	$-0.163275\pi$
$822$	3.53590	+	0.947441i	0.123329	+	0.0330458i
$823$	53.3827	+	14.3038i	1.86080	+	0.498601i	0.999947	−	0.0102479i	$-0.00326207\pi$
$823$	53.3827	+	14.3038i	1.86080	+	0.498601i	0.860856	+	0.508849i	$0.169929\pi$
$824$	−4.59808	+	7.96410i	−0.160182	+	0.277443i
$825$		0			0
$826$	4.90192	+	10.0981i	0.170560	+	0.351357i
$827$	33.2224	+	33.2224i	1.15526	+	1.15526i	0.985483	+	0.169774i	$0.0543038\pi$
$827$	33.2224	+	33.2224i	1.15526	+	1.15526i	0.169774	+	0.985483i	$0.445696\pi$
$828$	0.169873	+	0.633975i	0.00590349	+	0.0220321i
$829$	−7.26795	−	12.5885i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$829$	−7.26795	−	12.5885i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	−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	$0.462132\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$			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
$850$		0			0
$851$	−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	$-0.105401\pi$
$853$	18.1244	+	18.1244i	0.620566	+	0.620566i	−0.325110	+	0.945676i	$0.605401\pi$
$854$	−1.74167	−	1.17949i	−0.0595987	−	0.0403614i
$855$		0			0
$856$	−12.6962	+	21.9904i	−0.433946	+	0.751616i
$857$	11.0981	+	2.97372i	0.379103	+	0.101580i	0.443338	−	0.896354i	$-0.353794\pi$
$857$	11.0981	+	2.97372i	0.379103	+	0.101580i	−0.0642351	+	0.997935i	$0.520461\pi$
$858$	−2.00000	−	0.535898i	−0.0682789	−	0.0182953i
$859$	−17.4641	+	30.2487i	−0.595867	+	1.03207i	0.397556	+	0.917578i	$0.369858\pi$
$859$	−17.4641	+	30.2487i	−0.595867	+	1.03207i	−0.993424	+	0.114495i	$0.963475\pi$
$860$		0			0
$861$	−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	−0.686460	−	0.727167i	$-0.740836\pi$
$863$	−13.3827	−	49.9449i	−0.455552	−	1.70014i	0.230908	−	0.972976i	$-0.425830\pi$
$864$	7.62436	+	13.2058i	0.259386	+	0.449269i
$865$		0			0
$866$	−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			0
$871$	−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
$875$		0			0
$876$	12.0000			0.405442
$877$	39.1506	−	10.4904i	1.32202	−	0.354235i	0.472288	−	0.881444i	$-0.343428\pi$
$877$	39.1506	−	10.4904i	1.32202	−	0.354235i	0.849735	+	0.527209i	$0.176762\pi$
$878$	−0.444864	+	1.66025i	−0.0150134	+	0.0560309i
$879$	1.51666	−	0.875644i	0.0511557	−	0.0295348i
$880$		0			0
$881$			25.1436i			0.847109i	0.905871	+	0.423555i	$0.139218\pi$
$881$			25.1436i			0.847109i	−0.905871	+	0.423555i	$0.860782\pi$
$882$	−5.92820	−	7.92820i	−0.199613	−	0.266956i
$883$	−8.07180	+	8.07180i	−0.271638	+	0.271638i	−0.829759	−	0.558122i	$-0.811522\pi$
$883$	−8.07180	+	8.07180i	−0.271638	+	0.271638i	0.558122	+	0.829759i	$0.311522\pi$
$884$	16.3923	+	9.46410i	0.551333	+	0.318312i
$885$		0			0
$886$	−3.50000	−	6.06218i	−0.117585	−	0.203663i
$887$	−2.91858	−	10.8923i	−0.0979965	−	0.365728i	0.899460	−	0.437003i	$-0.143960\pi$
$887$	−2.91858	−	10.8923i	−0.0979965	−	0.365728i	−0.997457	+	0.0712748i	$0.977293\pi$
$888$	−3.46410	−	3.46410i	−0.116248	−	0.116248i
$889$	−0.758330	−	1.56218i	−0.0254336	−	0.0523938i
$890$		0			0
$891$	−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
$895$		0			0
$896$	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
$900$		0			0
$901$	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
$905$		0			0
$906$	3.21539	−	1.85641i	0.106824	−	0.0616750i
$907$	8.69615	−	32.4545i	0.288751	−	1.07763i	−0.657304	−	0.753626i	$-0.728303\pi$
$907$	8.69615	−	32.4545i	0.288751	−	1.07763i	0.946055	−	0.324007i	$-0.105030\pi$
$908$	−32.9545	+	8.83013i	−1.09363	+	0.293038i
$909$	22.5885			0.749212
$910$		0			0
$911$	−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
$915$		0			0
$916$		−	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	−0.990384	−	0.138344i	$-0.955822\pi$
$919$	−48.6673	−	28.0981i	−1.60539	−	0.926870i	−0.615002	−	0.788526i	$-0.710845\pi$
$920$		0			0
$921$	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
$925$		0			0
$926$	−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	0.397612	+	0.917554i	$0.369839\pi$
$929$	−18.1603	+	31.4545i	−0.595819	+	1.03199i	−0.993431	+	0.114435i	$0.963494\pi$
$930$		0			0
$931$	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
$935$		0			0
$936$	12.9282	+	7.46410i	0.422572	+	0.243972i
$937$	−17.0718	+	17.0718i	−0.557711	+	0.557711i	−0.928655	−	0.370944i	$-0.879034\pi$
$937$	−17.0718	+	17.0718i	−0.557711	+	0.557711i	0.370944	+	0.928655i	$0.379034\pi$
$938$	4.96410	−	14.3301i	0.162084	−	0.467895i
$939$		−	2.78461i		−	0.0908723i
$940$		0			0
$941$	35.1962	−	20.3205i	1.14736	−	0.662430i	0.199119	−	0.979975i	$-0.436192\pi$
$941$	35.1962	−	20.3205i	1.14736	−	0.662430i	0.948243	+	0.317546i	$0.102859\pi$
$942$	−0.332704	+	1.24167i	−0.0108401	+	0.0404558i
$943$	−0.866025	+	0.232051i	−0.0282017	+	0.00755661i
$944$	−20.1962			−0.657329
$945$		0			0
$946$	5.66025			0.184031
$947$	1.30385	−	0.349365i	0.0423694	−	0.0113528i	−0.237572	−	0.971370i	$-0.576352\pi$
$947$	1.30385	−	0.349365i	0.0423694	−	0.0113528i	0.279941	+	0.960017i	$0.409685\pi$
$948$	−0.758330	+	2.83013i	−0.0246294	+	0.0919183i
$949$	32.7846	−	18.9282i	1.06423	−	0.614435i
$950$		0			0
$951$			4.92820i			0.159808i
$952$	−19.3923	+	3.73205i	−0.628508	+	0.120956i
$953$	37.8564	−	37.8564i	1.22629	−	1.22629i	0.260932	−	0.965357i	$-0.415970\pi$
$953$	37.8564	−	37.8564i	1.22629	−	1.22629i	0.965357	−	0.260932i	$-0.0840299\pi$
$954$	8.66025	+	5.00000i	0.280386	+	0.161881i
$955$		0			0
$956$	−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			0
$961$	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
$965$		0			0
$966$	0.0980762	+	0.00704156i	0.00315555	+	0.000226558i
$967$	13.5622	+	13.5622i	0.436130	+	0.436130i	0.890707	−	0.454577i	$-0.150210\pi$
$967$	13.5622	+	13.5622i	0.436130	+	0.436130i	−0.454577	+	0.890707i	$0.650210\pi$
$968$	−1.76795	−	6.59808i	−0.0568240	−	0.212070i
$969$	0.732051	+	1.26795i	0.0235169	+	0.0407324i
$970$		0			0
$971$	29.0718	+	16.7846i	0.932958	+	0.538644i	0.887746	−	0.460334i	$-0.152270\pi$
$971$	29.0718	+	16.7846i	0.932958	+	0.538644i	0.0452124	+	0.998977i	$0.485604\pi$
$972$	−15.1244	+	15.1244i	−0.485114	+	0.485114i
$973$	−14.1506	−	4.90192i	−0.453649	−	0.157148i
$974$		−	14.5885i		−	0.467444i
$975$		0			0
$976$	3.27757	−	1.89230i	0.104912	−	0.0605712i
$977$	0.150635	−	0.562178i	0.00481924	−	0.0179857i	−0.963474	−	0.267801i	$-0.913703\pi$
$977$	0.150635	−	0.562178i	0.00481924	−	0.0179857i	0.968294	+	0.249815i	$0.0803698\pi$
$978$	−3.63397	+	0.973721i	−0.116202	+	0.0311362i
$979$	−1.80385			−0.0576512
$980$		0			0
$981$	−27.6603			−0.883124
$982$	−18.8564	+	5.05256i	−0.601732	+	0.161234i
$983$	−14.5000	+	54.1147i	−0.462478	+	1.72599i	0.202639	+	0.979253i	$0.435048\pi$
$983$	−14.5000	+	54.1147i	−0.462478	+	1.72599i	−0.665118	+	0.746739i	$0.731619\pi$
$984$	−5.59808	+	3.23205i	−0.178460	+	0.103034i
$985$		0			0
$986$		−	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
$990$		0			0
$991$	−15.8564	−	27.4641i	−0.503695	−	0.872426i	−0.999991	−	0.00427229i	$-0.998640\pi$
$991$	−15.8564	−	27.4641i	−0.503695	−	0.872426i	0.496296	−	0.868154i	$-0.334693\pi$
$992$	−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
$995$		0			0
$996$	−1.33013	+	2.30385i	−0.0421467	+	0.0730002i
$997$	39.8827	+	10.6865i	1.26310	+	0.338446i	0.827382	−	0.561639i	$-0.189829\pi$
$997$	39.8827	+	10.6865i	1.26310	+	0.338446i	0.435715	+	0.900085i	$0.356496\pi$
$998$	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	175.2.o.a.82.1		4
5.2	odd	4		35.2.k.a.33.1	yes	4
5.3	odd	4		175.2.o.b.68.1		4
5.4	even	2		35.2.k.b.12.1	yes	4
7.3	odd	6		175.2.o.b.157.1		4
15.2	even	4		315.2.bz.b.208.1		4
15.14	odd	2		315.2.bz.a.82.1		4
20.7	even	4		560.2.ci.a.33.1		4
20.19	odd	2		560.2.ci.b.257.1		4
35.2	odd	12		245.2.f.a.48.1		4
35.3	even	12	inner	175.2.o.a.143.1		4
35.4	even	6		245.2.l.a.227.1		4
35.9	even	6		245.2.f.b.97.1		4
35.12	even	12		245.2.f.b.48.1		4
35.17	even	12		35.2.k.b.3.1	yes	4
35.19	odd	6		245.2.f.a.97.1		4
35.24	odd	6		35.2.k.a.17.1	✓	4
35.27	even	4		245.2.l.a.68.1		4
35.32	odd	12		245.2.l.b.178.1		4
35.34	odd	2		245.2.l.b.117.1		4
105.17	odd	12		315.2.bz.a.73.1		4
105.59	even	6		315.2.bz.b.262.1		4
140.59	even	6		560.2.ci.a.17.1		4
140.87	odd	12		560.2.ci.b.353.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.k.a.17.1	✓	4	35.24	odd	6
35.2.k.a.33.1	yes	4	5.2	odd	4
35.2.k.b.3.1	yes	4	35.17	even	12
35.2.k.b.12.1	yes	4	5.4	even	2
175.2.o.a.82.1		4	1.1	even	1	trivial
175.2.o.a.143.1		4	35.3	even	12	inner
175.2.o.b.68.1		4	5.3	odd	4
175.2.o.b.157.1		4	7.3	odd	6
245.2.f.a.48.1		4	35.2	odd	12
245.2.f.a.97.1		4	35.19	odd	6
245.2.f.b.48.1		4	35.12	even	12
245.2.f.b.97.1		4	35.9	even	6
245.2.l.a.68.1		4	35.27	even	4
245.2.l.a.227.1		4	35.4	even	6
245.2.l.b.117.1		4	35.34	odd	2
245.2.l.b.178.1		4	35.32	odd	12
315.2.bz.a.73.1		4	105.17	odd	12
315.2.bz.a.82.1		4	15.14	odd	2
315.2.bz.b.208.1		4	15.2	even	4
315.2.bz.b.262.1		4	105.59	even	6
560.2.ci.a.17.1		4	140.59	even	6
560.2.ci.a.33.1		4	20.7	even	4
560.2.ci.b.257.1		4	20.19	odd	2
560.2.ci.b.353.1		4	140.87	odd	12

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.o (of order \(12\), degree \(4\), minimal)

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

Introduction

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Modular forms

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