LMFDB - Embedded newform 490.2.l.a.423.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(117,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("490.117");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.l (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{48})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{8} + 1 $ x^16 - x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			423.3
Root			$0.608761 - 0.793353i$ of defining polynomial
Character	$\chi$	$=$	490.423
Dual form			490.2.l.a.117.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.965926 + 0.258819i) q^{2} +(-0.478235 - 1.78480i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.01088 - 0.977945i) q^{5} -1.84776i q^{6} +(0.707107 + 0.707107i) q^{8} +(-0.358719 + 0.207107i) q^{9} +(2.19547 - 0.424170i) q^{10} +(-1.41421 + 2.44949i) q^{11} +(0.478235 - 1.78480i) q^{12} +(4.23671 - 4.23671i) q^{13} +(-2.70711 - 3.12132i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-5.04817 + 1.35265i) q^{17} +(-0.400100 + 0.107206i) q^{18} +(0.699709 + 1.21193i) q^{19} +(2.23044 + 0.158513i) q^{20} +(-2.00000 + 2.00000i) q^{22} +(0.151613 - 0.565826i) q^{23} +(0.923880 - 1.60021i) q^{24} +(3.08725 - 3.93305i) q^{25} +(5.18889 - 2.99581i) q^{26} +(-3.37849 - 3.37849i) q^{27} +0.828427i q^{29} +(-1.80701 - 3.71561i) q^{30} +(-1.32565 - 0.765367i) q^{31} +(0.258819 + 0.965926i) q^{32} +(5.04817 + 1.35265i) q^{33} -5.22625 q^{34} -0.414214 q^{36} +(-3.53225 - 0.946464i) q^{37} +(0.362196 + 1.35173i) q^{38} +(-9.58783 - 5.53553i) q^{39} +(2.11342 + 0.730392i) q^{40} +3.69552i q^{41} +(4.00000 + 4.00000i) q^{43} +(-2.44949 + 1.41421i) q^{44} +(-0.518801 + 0.767274i) q^{45} +(0.292893 - 0.507306i) q^{46} +(-0.396183 + 1.47858i) q^{47} +(1.30656 - 1.30656i) q^{48} +(4.00000 - 3.00000i) q^{50} +(4.82843 + 8.36308i) q^{51} +(5.78746 - 1.55075i) q^{52} +(11.2597 - 3.01702i) q^{53} +(-2.38896 - 4.13779i) q^{54} +(-0.448342 + 6.30864i) q^{55} +(1.82843 - 1.82843i) q^{57} +(-0.214413 + 0.800199i) q^{58} +(-4.61940 + 8.00103i) q^{59} +(-0.783763 - 4.05670i) q^{60} +(-5.57717 + 3.21998i) q^{61} +(-1.08239 - 1.08239i) q^{62} +1.00000i q^{64} +(4.37623 - 12.6628i) q^{65} +(4.52607 + 2.61313i) q^{66} +(3.83788 + 14.3232i) q^{67} +(-5.04817 - 1.35265i) q^{68} -1.08239 q^{69} -0.585786 q^{71} +(-0.400100 - 0.107206i) q^{72} +(-1.51676 - 5.66062i) q^{73} +(-3.16693 - 1.82843i) q^{74} +(-8.49614 - 3.62919i) q^{75} +1.39942i q^{76} +(-7.82843 - 7.82843i) q^{78} +(-4.39167 + 2.53553i) q^{79} +(1.85236 + 1.25250i) q^{80} +(-5.03553 + 8.72180i) q^{81} +(-0.956470 + 3.56960i) q^{82} +(-5.31911 + 5.31911i) q^{83} +(-8.82843 + 7.65685i) q^{85} +(2.82843 + 4.89898i) q^{86} +(1.47858 - 0.396183i) q^{87} +(-2.73205 + 0.732051i) q^{88} +(5.67459 + 9.82868i) q^{89} +(-0.699709 + 0.606854i) q^{90} +(0.414214 - 0.414214i) q^{92} +(-0.732051 + 2.73205i) q^{93} +(-0.765367 + 1.32565i) q^{94} +(2.59223 + 1.75277i) q^{95} +(1.60021 - 0.923880i) q^{96} +(4.59220 + 4.59220i) q^{97} -1.17157i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{15} + 8 q^{16} - 8 q^{18} - 32 q^{22} + 8 q^{23} - 16 q^{30} + 16 q^{36} - 32 q^{37} + 64 q^{43} + 16 q^{46} + 64 q^{50} + 32 q^{51} + 32 q^{53} - 16 q^{57} + 16 q^{58} + 8 q^{60} - 8 q^{65}+ \cdots - 64 q^{95}+O(q^{100}) $ 16 * q - 32 * q^15 + 8 * q^16 - 8 * q^18 - 32 * q^22 + 8 * q^23 - 16 * q^30 + 16 * q^36 - 32 * q^37 + 64 * q^43 + 16 * q^46 + 64 * q^50 + 32 * q^51 + 32 * q^53 - 16 * q^57 + 16 * q^58 + 8 * q^60 - 8 * q^65 - 16 * q^67 - 32 * q^71 - 8 * q^72 - 80 * q^78 - 24 * q^81 - 96 * q^85 - 16 * q^88 - 16 * q^92 + 16 * q^93 - 64 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−0.478235	−	1.78480i	−0.276109	−	1.03045i	−0.955094	−	0.296302i	$-0.904247\pi$
$3$	−0.478235	−	1.78480i	−0.276109	−	1.03045i	0.678985	−	0.734152i	$-0.262420\pi$
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	2.01088	−	0.977945i	0.899291	−	0.437350i
$5$	2.01088	−	0.977945i	0.899291	−	0.437350i
$6$		−	1.84776i		−	0.754344i
$7$		0			0
$7$		0			0
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.358719	+	0.207107i	−0.119573	+	0.0690356i
$10$	2.19547	−	0.424170i	0.694268	−	0.134134i
$11$	−1.41421	+	2.44949i	−0.426401	+	0.738549i	−0.996550	−	0.0829925i	$-0.973552\pi$
$11$	−1.41421	+	2.44949i	−0.426401	+	0.738549i	0.570149	+	0.821541i	$0.306886\pi$
$12$	0.478235	−	1.78480i	0.138055	−	0.515227i
$13$	4.23671	−	4.23671i	1.17505	−	1.17505i	0.194064	−	0.980989i	$-0.437833\pi$
$13$	4.23671	−	4.23671i	1.17505	−	1.17505i	0.980989	−	0.194064i	$-0.0621670\pi$
$14$		0			0
$15$	−2.70711	−	3.12132i	−0.698972	−	0.805921i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−5.04817	+	1.35265i	−1.22436	+	0.328067i	−0.812382	−	0.583126i	$-0.801829\pi$
$17$	−5.04817	+	1.35265i	−1.22436	+	0.328067i	−0.411980	+	0.911193i	$0.635163\pi$
$18$	−0.400100	+	0.107206i	−0.0943044	+	0.0252688i
$19$	0.699709	+	1.21193i	0.160524	+	0.278036i	0.935057	−	0.354498i	$-0.115348\pi$
$19$	0.699709	+	1.21193i	0.160524	+	0.278036i	−0.774533	+	0.632534i	$0.782015\pi$
$20$	2.23044	+	0.158513i	0.498742	+	0.0354445i
$21$		0			0
$22$	−2.00000	+	2.00000i	−0.426401	+	0.426401i
$23$	0.151613	−	0.565826i	0.0316134	−	0.117983i	−0.948316	−	0.317327i	$-0.897215\pi$
$23$	0.151613	−	0.565826i	0.0316134	−	0.117983i	0.979929	+	0.199344i	$0.0638813\pi$
$24$	0.923880	−	1.60021i	0.188586	−	0.326641i
$25$	3.08725	−	3.93305i	0.617449	−	0.786611i
$26$	5.18889	−	2.99581i	1.01763	−	0.587527i
$27$	−3.37849	−	3.37849i	−0.650191	−	0.650191i
$28$		0			0
$29$			0.828427i			0.153835i	0.997037	+	0.0769175i	$0.0245078\pi$
$29$			0.828427i			0.153835i	−0.997037	+	0.0769175i	$0.975492\pi$
$30$	−1.80701	−	3.71561i	−0.329913	−	0.678375i
$31$	−1.32565	−	0.765367i	−0.238095	−	0.137464i	0.376206	−	0.926536i	$-0.377228\pi$
$31$	−1.32565	−	0.765367i	−0.238095	−	0.137464i	−0.614301	+	0.789072i	$0.710562\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	5.04817	+	1.35265i	0.878774	+	0.235467i
$34$	−5.22625			−0.896295
$35$		0			0
$36$	−0.414214			−0.0690356
$37$	−3.53225	−	0.946464i	−0.580698	−	0.155598i	−0.0434997	−	0.999053i	$-0.513851\pi$
$37$	−3.53225	−	0.946464i	−0.580698	−	0.155598i	−0.537199	+	0.843456i	$0.680517\pi$
$38$	0.362196	+	1.35173i	0.0587559	+	0.219280i
$39$	−9.58783	−	5.53553i	−1.53528	−	0.886395i
$40$	2.11342	+	0.730392i	0.334160	+	0.115485i
$41$			3.69552i			0.577143i	0.957458	+	0.288571i	$0.0931803\pi$
$41$			3.69552i			0.577143i	−0.957458	+	0.288571i	$0.906820\pi$
$42$		0			0
$43$	4.00000	+	4.00000i	0.609994	+	0.609994i	0.942944	−	0.332950i	$-0.108044\pi$
$43$	4.00000	+	4.00000i	0.609994	+	0.609994i	−0.332950	+	0.942944i	$0.608044\pi$
$44$	−2.44949	+	1.41421i	−0.369274	+	0.213201i
$45$	−0.518801	+	0.767274i	−0.0773383	+	0.114378i
$46$	0.292893	−	0.507306i	0.0431847	−	0.0747982i
$47$	−0.396183	+	1.47858i	−0.0577892	+	0.215672i	−0.988782	−	0.149365i	$-0.952277\pi$
$47$	−0.396183	+	1.47858i	−0.0577892	+	0.215672i	0.930993	+	0.365037i	$0.118944\pi$
$48$	1.30656	−	1.30656i	0.188586	−	0.188586i
$49$		0			0
$50$	4.00000	−	3.00000i	0.565685	−	0.424264i
$51$	4.82843	+	8.36308i	0.676115	+	1.17107i
$52$	5.78746	−	1.55075i	0.802576	−	0.215050i
$53$	11.2597	−	3.01702i	1.54663	−	0.414419i	0.618231	−	0.785997i	$-0.287850\pi$
$53$	11.2597	−	3.01702i	1.54663	−	0.414419i	0.928402	+	0.371578i	$0.121183\pi$
$54$	−2.38896	−	4.13779i	−0.325096	−	0.563082i
$55$	−0.448342	+	6.30864i	−0.0604544	+	0.850657i
$56$		0			0
$57$	1.82843	−	1.82843i	0.242181	−	0.242181i
$58$	−0.214413	+	0.800199i	−0.0281538	+	0.105071i
$59$	−4.61940	+	8.00103i	−0.601394	+	1.04165i	0.391216	+	0.920299i	$0.372055\pi$
$59$	−4.61940	+	8.00103i	−0.601394	+	1.04165i	−0.992610	+	0.121347i	$0.961279\pi$
$60$	−0.783763	−	4.05670i	−0.101183	−	0.523717i
$61$	−5.57717	+	3.21998i	−0.714083	+	0.412276i	−0.812571	−	0.582862i	$-0.801933\pi$
$61$	−5.57717	+	3.21998i	−0.714083	+	0.412276i	0.0984878	+	0.995138i	$0.468599\pi$
$62$	−1.08239	−	1.08239i	−0.137464	−	0.137464i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	4.37623	−	12.6628i	0.542805	−	1.57062i
$66$	4.52607	+	2.61313i	0.557120	+	0.321654i
$67$	3.83788	+	14.3232i	0.468872	+	1.74985i	0.643724	+	0.765258i	$0.277389\pi$
$67$	3.83788	+	14.3232i	0.468872	+	1.74985i	−0.174852	+	0.984595i	$0.555945\pi$
$68$	−5.04817	−	1.35265i	−0.612181	−	0.164033i
$69$	−1.08239			−0.130305
$70$		0			0
$71$	−0.585786			−0.0695201			−0.0347600	−	0.999396i	$-0.511067\pi$
$71$	−0.585786			−0.0695201			−0.0347600	+	0.999396i	$0.511067\pi$
$72$	−0.400100	−	0.107206i	−0.0471522	−	0.0126344i
$73$	−1.51676	−	5.66062i	−0.177523	−	0.662525i	−0.996108	−	0.0881398i	$-0.971908\pi$
$73$	−1.51676	−	5.66062i	−0.177523	−	0.662525i	0.818585	−	0.574385i	$-0.194759\pi$
$74$	−3.16693	−	1.82843i	−0.368148	−	0.212550i
$75$	−8.49614	−	3.62919i	−0.981049	−	0.419062i
$76$			1.39942i			0.160524i
$77$		0			0
$78$	−7.82843	−	7.82843i	−0.886395	−	0.886395i
$79$	−4.39167	+	2.53553i	−0.494102	+	0.285270i	−0.726275	−	0.687405i	$-0.758750\pi$
$79$	−4.39167	+	2.53553i	−0.494102	+	0.285270i	0.232173	+	0.972675i	$0.425417\pi$
$80$	1.85236	+	1.25250i	0.207101	+	0.140033i
$81$	−5.03553	+	8.72180i	−0.559504	+	0.969089i
$82$	−0.956470	+	3.56960i	−0.105624	+	0.394196i
$83$	−5.31911	+	5.31911i	−0.583848	+	0.583848i	−0.935958	−	0.352111i	$-0.885464\pi$
$83$	−5.31911	+	5.31911i	−0.583848	+	0.583848i	0.352111	+	0.935958i	$0.385464\pi$
$84$		0			0
$85$	−8.82843	+	7.65685i	−0.957577	+	0.830502i
$86$	2.82843	+	4.89898i	0.304997	+	0.528271i
$87$	1.47858	−	0.396183i	0.158520	−	0.0424753i
$88$	−2.73205	+	0.732051i	−0.291238	+	0.0780369i
$89$	5.67459	+	9.82868i	0.601506	+	1.04184i	0.992593	+	0.121485i	$0.0387656\pi$
$89$	5.67459	+	9.82868i	0.601506	+	1.04184i	−0.391088	+	0.920353i	$0.627901\pi$
$90$	−0.699709	+	0.606854i	−0.0737558	+	0.0639680i
$91$		0			0
$92$	0.414214	−	0.414214i	0.0431847	−	0.0431847i
$93$	−0.732051	+	2.73205i	−0.0759101	+	0.283300i
$94$	−0.765367	+	1.32565i	−0.0789416	+	0.136731i
$95$	2.59223	+	1.75277i	0.265957	+	0.179830i
$96$	1.60021	−	0.923880i	0.163320	−	0.0942931i
$97$	4.59220	+	4.59220i	0.466267	+	0.466267i	0.900703	−	0.434436i	$-0.143052\pi$
$97$	4.59220	+	4.59220i	0.466267	+	0.466267i	−0.434436	+	0.900703i	$0.643052\pi$
$98$		0			0
$99$		−	1.17157i		−	0.117748i
$100$	4.64016	−	1.86250i	0.464016	−	0.186250i
$101$	2.37676	+	1.37222i	0.236496	+	0.136541i	0.613565	−	0.789644i	$-0.289735\pi$
$101$	2.37676	+	1.37222i	0.236496	+	0.136541i	−0.377069	+	0.926185i	$0.623068\pi$
$102$	2.49938	+	9.32780i	0.247475	+	0.923590i
$103$	−13.6659	−	3.66178i	−1.34655	−	0.360806i	−0.487687	−	0.873019i	$-0.662159\pi$
$103$	−13.6659	−	3.66178i	−1.34655	−	0.360806i	−0.858858	+	0.512213i	$0.828826\pi$
$104$	5.99162			0.587527
$105$		0			0
$106$	11.6569			1.13221
$107$	4.99536	+	1.33850i	0.482919	+	0.129398i	0.492062	−	0.870560i	$-0.336243\pi$
$107$	4.99536	+	1.33850i	0.482919	+	0.129398i	−0.00914234	+	0.999958i	$0.502910\pi$
$108$	−1.23661	−	4.61511i	−0.118993	−	0.444089i
$109$	−10.5154	−	6.07107i	−1.00719	−	0.581503i	−0.0968240	−	0.995302i	$-0.530868\pi$
$109$	−10.5154	−	6.07107i	−1.00719	−	0.581503i	−0.910368	+	0.413799i	$0.864202\pi$
$110$	−2.06586	+	5.97764i	−0.196972	+	0.569946i
$111$			6.75699i			0.641345i
$112$		0			0
$113$	1.17157	+	1.17157i	0.110212	+	0.110212i	0.760062	−	0.649850i	$-0.225168\pi$
$113$	1.17157	+	1.17157i	0.110212	+	0.110212i	−0.649850	+	0.760062i	$0.725168\pi$
$114$	2.23936	−	1.29289i	0.209735	−	0.121091i
$115$	−0.248473	−	1.28608i	−0.0231702	−	0.119927i
$116$	−0.414214	+	0.717439i	−0.0384588	+	0.0666125i
$117$	−0.642340	+	2.39724i	−0.0593843	+	0.221625i
$118$	−6.53281	+	6.53281i	−0.601394	+	0.601394i
$119$		0			0
$120$	0.292893	−	4.12132i	0.0267374	−	0.376223i
$121$	1.50000	+	2.59808i	0.136364	+	0.236189i
$122$	−6.22052	+	1.66678i	−0.563180	+	0.150904i
$123$	6.59575	−	1.76733i	0.594719	−	0.159355i
$124$	−0.765367	−	1.32565i	−0.0687320	−	0.119047i
$125$	2.36176	−	10.9280i	0.211242	−	0.977434i
$126$		0			0
$127$	3.58579	−	3.58579i	0.318187	−	0.318187i	−0.529883	−	0.848071i	$-0.677764\pi$
$127$	3.58579	−	3.58579i	0.318187	−	0.318187i	0.848071	+	0.529883i	$0.177764\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	5.22625	−	9.05213i	0.460146	−	0.796996i
$130$	7.50449	−	11.0987i	0.658187	−	0.973417i
$131$	−12.6879	+	7.32538i	−1.10855	+	0.640021i	−0.938453	−	0.345406i	$-0.887741\pi$
$131$	−12.6879	+	7.32538i	−1.10855	+	0.640021i	−0.170096	+	0.985427i	$0.554408\pi$
$132$	3.69552	+	3.69552i	0.321654	+	0.321654i
$133$		0			0
$134$			14.8284i			1.28098i
$135$	−10.0977	−	3.48975i	−0.869073	−	0.300350i
$136$	−4.52607	−	2.61313i	−0.388107	−	0.224074i
$137$	−2.99100	−	11.1626i	−0.255539	−	0.953683i	−0.967790	−	0.251759i	$-0.918991\pi$
$137$	−2.99100	−	11.1626i	−0.255539	−	0.953683i	0.712251	−	0.701924i	$-0.247676\pi$
$138$	−1.04551	−	0.280144i	−0.0889998	−	0.0238474i
$139$	8.60474			0.729845			0.364922	−	0.931038i	$-0.381095\pi$
$139$	8.60474			0.729845			0.364922	+	0.931038i	$0.381095\pi$
$140$		0			0
$141$	2.82843			0.238197
$142$	−0.565826	−	0.151613i	−0.0474831	−	0.0127231i
$143$	4.38617	+	16.3694i	0.366790	+	1.36888i
$144$	−0.358719	−	0.207107i	−0.0298933	−	0.0172589i
$145$	0.810156	+	1.66586i	0.0672798	+	0.138343i
$146$		−	5.86030i		−	0.485002i
$147$		0			0
$148$	−2.58579	−	2.58579i	−0.212550	−	0.212550i
$149$	−14.9941	+	8.65685i	−1.22837	+	0.709197i	−0.966688	−	0.255958i	$-0.917609\pi$
$149$	−14.9941	+	8.65685i	−1.22837	+	0.709197i	−0.261678	+	0.965155i	$0.584276\pi$
$150$	−7.26734	−	5.70449i	−0.593375	−	0.465769i
$151$	4.41421	−	7.64564i	0.359224	−	0.622194i	−0.628608	−	0.777723i	$-0.716375\pi$
$151$	4.41421	−	7.64564i	0.359224	−	0.622194i	0.987831	+	0.155529i	$0.0497082\pi$
$152$	−0.362196	+	1.35173i	−0.0293780	+	0.109640i
$153$	1.53073	−	1.53073i	0.123752	−	0.123752i
$154$		0			0
$155$	−3.41421	−	0.242641i	−0.274236	−	0.0194894i
$156$	−5.53553	−	9.58783i	−0.443197	−	0.767640i
$157$	13.9722	−	3.74383i	1.11510	−	0.298790i	0.346201	−	0.938160i	$-0.387472\pi$
$157$	13.9722	−	3.74383i	1.11510	−	0.298790i	0.768899	+	0.639370i	$0.220805\pi$
$158$	−4.89828	+	1.31249i	−0.389686	+	0.104416i
$159$	−10.7695	−	18.6534i	−0.854079	−	1.47931i
$160$	1.46508	+	1.68925i	0.115824	+	0.133547i
$161$		0			0
$162$	−7.12132	+	7.12132i	−0.559504	+	0.559504i
$163$	4.99876	−	18.6556i	0.391533	−	1.46122i	−0.436073	−	0.899911i	$-0.643631\pi$
$163$	4.99876	−	18.6556i	0.391533	−	1.46122i	0.827606	−	0.561309i	$-0.189702\pi$
$164$	−1.84776	+	3.20041i	−0.144286	+	0.249910i
$165$	11.4741	−	2.21682i	0.893255	−	0.172579i
$166$	−6.51455	+	3.76118i	−0.505627	+	0.291924i
$167$	1.71644	+	1.71644i	0.132822	+	0.132822i	0.770392	−	0.637570i	$-0.220060\pi$
$167$	1.71644	+	1.71644i	0.132822	+	0.132822i	−0.637570	+	0.770392i	$0.720060\pi$
$168$		0			0
$169$		−	22.8995i		−	1.76150i
$170$	−10.5093	+	5.11099i	−0.806030	+	0.391995i
$171$	−0.501998	−	0.289829i	−0.0383888	−	0.0221638i
$172$	1.46410	+	5.46410i	0.111637	+	0.416634i
$173$	18.1542	+	4.86440i	1.38024	+	0.369834i	0.871208	−	0.490914i	$-0.163337\pi$
$173$	18.1542	+	4.86440i	1.38024	+	0.369834i	0.509031	+	0.860748i	$0.330004\pi$
$174$	1.53073			0.116045
$175$		0			0
$176$	−2.82843			−0.213201
$177$	16.4894	+	4.41832i	1.23942	+	0.332101i
$178$	2.93739	+	10.9625i	0.220166	+	0.821672i
$179$	−11.8272	−	6.82843i	−0.884005	−	0.510381i	−0.0120283	−	0.999928i	$-0.503829\pi$
$179$	−11.8272	−	6.82843i	−0.884005	−	0.510381i	−0.871977	+	0.489547i	$0.837162\pi$
$180$	−0.832932	+	0.405078i	−0.0620831	+	0.0301927i
$181$		−	8.79045i		−	0.653389i	−0.945130	−	0.326695i	$-0.894065\pi$
$181$		−	8.79045i		−	0.653389i	0.945130	−	0.326695i	$-0.105935\pi$
$182$		0			0
$183$	8.41421	+	8.41421i	0.621997	+	0.621997i
$184$	0.507306	−	0.292893i	0.0373991	−	0.0215924i
$185$	−8.02851	+	1.55113i	−0.590268	+	0.114041i
$186$	−1.41421	+	2.44949i	−0.103695	+	0.179605i
$187$	3.82588	−	14.2784i	0.279776	−	1.04414i
$188$	−1.08239	+	1.08239i	−0.0789416	+	0.0789416i
$189$		0			0
$190$	2.05025	+	2.36396i	0.148741	+	0.171500i
$191$	−0.878680	−	1.52192i	−0.0635790	−	0.110122i	0.832484	−	0.554049i	$-0.186918\pi$
$191$	−0.878680	−	1.52192i	−0.0635790	−	0.110122i	−0.896063	+	0.443927i	$0.853585\pi$
$192$	1.78480	−	0.478235i	0.128807	−	0.0345137i
$193$	−11.2597	+	3.01702i	−0.810488	+	0.217170i	−0.640184	−	0.768222i	$-0.721142\pi$
$193$	−11.2597	+	3.01702i	−0.810488	+	0.217170i	−0.170304	+	0.985392i	$0.554475\pi$
$194$	3.24718	+	5.62427i	0.233134	+	0.403799i
$195$	−24.6934	−	1.75490i	−1.76833	−	0.125671i
$196$		0			0
$197$	0.585786	−	0.585786i	0.0417356	−	0.0417356i	−0.685931	−	0.727667i	$-0.740605\pi$
$197$	0.585786	−	0.585786i	0.0417356	−	0.0417356i	0.727667	+	0.685931i	$0.240605\pi$
$198$	0.303225	−	1.13165i	0.0215493	−	0.0804230i
$199$	14.0167	−	24.2776i	0.993618	−	1.72100i	0.399123	−	0.916897i	$-0.369315\pi$
$199$	14.0167	−	24.2776i	0.993618	−	1.72100i	0.594495	−	0.804099i	$-0.297352\pi$
$200$	4.96410	−	0.598076i	0.351015	−	0.0422904i
$201$	23.7285	−	13.6997i	1.67368	−	0.966301i
$202$	1.94061	+	1.94061i	0.136541	+	0.136541i
$203$		0			0
$204$			9.65685i			0.676115i
$205$	3.61401	+	7.43123i	0.252414	+	0.519020i
$206$	−12.2525	−	7.07401i	−0.853675	−	0.492870i
$207$	0.0628000	+	0.234373i	0.00436490	+	0.0162900i
$208$	5.78746	+	1.55075i	0.401288	+	0.107525i
$209$	−3.95815			−0.273791
$210$		0			0
$211$	−10.3431			−0.712052			−0.356026	−	0.934476i	$-0.615868\pi$
$211$	−10.3431			−0.712052			−0.356026	+	0.934476i	$0.615868\pi$
$212$	11.2597	+	3.01702i	0.773316	+	0.207210i
$213$	0.280144	+	1.04551i	0.0191951	+	0.0716372i
$214$	4.47871	+	2.58579i	0.306159	+	0.176761i
$215$	11.9553	+	4.13172i	0.815344	+	0.281781i
$216$		−	4.77791i		−	0.325096i
$217$		0			0
$218$	−8.58579	−	8.58579i	−0.581503	−	0.581503i
$219$	−9.37769	+	5.41421i	−0.633686	+	0.365859i
$220$	−3.54260	+	5.23928i	−0.238842	+	0.353232i
$221$	−15.6569	+	27.1185i	−1.05319	+	1.82419i
$222$	−1.74884	+	6.52675i	−0.117374	+	0.438047i
$223$	−6.75699	+	6.75699i	−0.452481	+	0.452481i	−0.896177	−	0.443696i	$-0.853667\pi$
$223$	−6.75699	+	6.75699i	−0.452481	+	0.452481i	0.443696	+	0.896177i	$0.353667\pi$
$224$		0			0
$225$	−0.292893	+	2.05025i	−0.0195262	+	0.136684i
$226$	0.828427	+	1.43488i	0.0551062	+	0.0954467i
$227$	−11.4481	+	3.06750i	−0.759836	+	0.203597i	−0.617876	−	0.786275i	$-0.712007\pi$
$227$	−11.4481	+	3.06750i	−0.759836	+	0.203597i	−0.141959	+	0.989873i	$0.545340\pi$
$228$	2.49768	−	0.669251i	0.165413	−	0.0443222i
$229$	3.85403	+	6.67538i	0.254682	+	0.441121i	0.964809	−	0.262952i	$-0.0846960\pi$
$229$	3.85403	+	6.67538i	0.254682	+	0.441121i	−0.710127	+	0.704073i	$0.751363\pi$
$230$	0.0928546	−	1.30656i	0.00612265	−	0.0861522i
$231$		0			0
$232$	−0.585786	+	0.585786i	−0.0384588	+	0.0384588i
$233$	1.09808	−	4.09808i	0.0719374	−	0.268474i	−0.920584	−	0.390544i	$-0.872287\pi$
$233$	1.09808	−	4.09808i	0.0719374	−	0.268474i	0.992521	+	0.122071i	$0.0389534\pi$
$234$	−1.24090	+	2.14931i	−0.0811205	+	0.140505i
$235$	0.649291	+	3.36068i	0.0423550	+	0.219226i
$236$	−8.00103	+	4.61940i	−0.520823	+	0.300697i
$237$	6.62567	+	6.62567i	0.430383	+	0.430383i
$238$		0			0
$239$			6.48528i			0.419498i	0.977755	+	0.209749i	$0.0672647\pi$
$239$			6.48528i			0.419498i	−0.977755	+	0.209749i	$0.932735\pi$
$240$	1.34959	−	3.90508i	0.0871156	−	0.252072i
$241$	5.85172	+	3.37849i	0.376942	+	0.217628i	0.676487	−	0.736454i	$-0.263501\pi$
$241$	5.85172	+	3.37849i	0.376942	+	0.217628i	−0.299545	+	0.954082i	$0.596835\pi$
$242$	0.776457	+	2.89778i	0.0499126	+	0.186276i
$243$	4.12950	+	1.10650i	0.264908	+	0.0709818i
$244$	−6.43996			−0.412276
$245$		0			0
$246$	6.82843			0.435365
$247$	8.09907	+	2.17014i	0.515332	+	0.138083i
$248$	−0.396183	−	1.47858i	−0.0251576	−	0.0938896i
$249$	12.0373	+	6.94975i	0.762834	+	0.440422i
$250$	5.10967	−	9.94441i	0.323164	−	0.628940i
$251$		−	14.0936i		−	0.889582i	−0.895634	−	0.444791i	$-0.853278\pi$
$251$		−	14.0936i		−	0.889582i	0.895634	−	0.444791i	$-0.146722\pi$
$252$		0			0
$253$	1.17157	+	1.17157i	0.0736562	+	0.0736562i
$254$	4.39167	−	2.53553i	0.275558	−	0.159094i
$255$	17.8880	+	12.0952i	1.12019	+	0.757430i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	2.86941	−	10.7088i	0.178989	−	0.667996i	−0.816849	−	0.576852i	$-0.804281\pi$
$257$	2.86941	−	10.7088i	0.178989	−	0.667996i	0.995838	−	0.0911440i	$-0.0290524\pi$
$258$	7.39104	−	7.39104i	0.460146	−	0.460146i
$259$		0			0
$260$	10.1213	−	8.77817i	0.627698	−	0.544399i
$261$	−0.171573	−	0.297173i	−0.0106201	−	0.0183945i
$262$	−14.1515	+	3.79189i	−0.874285	+	0.234264i
$263$	26.5203	−	7.10610i	1.63531	−	0.438181i	0.679864	−	0.733338i	$-0.262039\pi$
$263$	26.5203	−	7.10610i	1.63531	−	0.438181i	0.955449	+	0.295158i	$0.0953722\pi$
$264$	2.61313	+	4.52607i	0.160827	+	0.278560i
$265$	19.6913	−	17.0782i	1.20963	−	1.04910i
$266$		0			0
$267$	14.8284	−	14.8284i	0.907485	−	0.907485i
$268$	−3.83788	+	14.3232i	−0.234436	+	0.874926i
$269$	−13.4483	+	23.2932i	−0.819958	+	1.42021i	0.0857542	+	0.996316i	$0.472670\pi$
$269$	−13.4483	+	23.2932i	−0.819958	+	1.42021i	−0.905712	+	0.423893i	$0.860663\pi$
$270$	−8.85043	−	5.98432i	−0.538620	−	0.364194i
$271$	16.2295	−	9.37011i	0.985872	−	0.569194i	0.0818345	−	0.996646i	$-0.473922\pi$
$271$	16.2295	−	9.37011i	0.985872	−	0.569194i	0.904038	+	0.427452i	$0.140589\pi$
$272$	−3.69552	−	3.69552i	−0.224074	−	0.224074i
$273$		0			0
$274$		−	11.5563i		−	0.698145i
$275$	5.26795	+	13.1244i	0.317669	+	0.791428i
$276$	−0.937379	−	0.541196i	−0.0564236	−	0.0325762i
$277$	−0.643238	−	2.40060i	−0.0386484	−	0.144238i	0.943906	−	0.330216i	$-0.107121\pi$
$277$	−0.643238	−	2.40060i	−0.0386484	−	0.144238i	−0.982554	+	0.185978i	$0.940455\pi$
$278$	8.31155	+	2.22707i	0.498493	+	0.133571i
$279$	0.634051			0.0379596
$280$		0			0
$281$	−5.65685			−0.337460			−0.168730	−	0.985662i	$-0.553967\pi$
$281$	−5.65685			−0.337460			−0.168730	+	0.985662i	$0.553967\pi$
$282$	2.73205	+	0.732051i	0.162691	+	0.0435930i
$283$	−1.15456	−	4.30888i	−0.0686316	−	0.256137i	0.923082	−	0.384602i	$-0.125661\pi$
$283$	−1.15456	−	4.30888i	−0.0686316	−	0.256137i	−0.991714	+	0.128466i	$0.958995\pi$
$284$	−0.507306	−	0.292893i	−0.0301031	−	0.0173800i
$285$	1.88864	−	5.46484i	0.111873	−	0.323709i
$286$			16.9469i			1.00209i
$287$		0			0
$288$	−0.292893	−	0.292893i	−0.0172589	−	0.0172589i
$289$	8.93193	−	5.15685i	0.525408	−	0.303344i
$290$	0.351394	+	1.81879i	0.0206345	+	0.106803i
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$	1.51676	−	5.66062i	0.0887615	−	0.331263i
$293$	2.38896	−	2.38896i	0.139564	−	0.139564i	−0.633873	−	0.773437i	$-0.718536\pi$
$293$	2.38896	−	2.38896i	0.139564	−	0.139564i	0.773437	+	0.633873i	$0.218536\pi$
$294$		0			0
$295$	−1.46447	+	20.6066i	−0.0852645	+	1.19976i
$296$	−1.82843	−	3.16693i	−0.106275	−	0.184074i
$297$	13.0535	−	3.49767i	0.757441	−	0.202956i
$298$	−16.7238	+	4.48112i	−0.968781	+	0.259584i
$299$	−1.75490	−	3.03958i	−0.101489	−	0.175784i
$300$	−5.54328	−	7.39104i	−0.320041	−	0.426722i
$301$		0			0
$302$	6.24264	−	6.24264i	0.359224	−	0.359224i
$303$	1.31249	−	4.89828i	0.0754005	−	0.281399i
$304$	−0.699709	+	1.21193i	−0.0401311	+	0.0695090i
$305$	−8.06603	+	11.9291i	−0.461860	+	0.683061i
$306$	1.87476	−	1.08239i	0.107173	−	0.0618762i
$307$	−23.1626	−	23.1626i	−1.32196	−	1.32196i	−0.912186	−	0.409776i	$-0.865607\pi$
$307$	−23.1626	−	23.1626i	−1.32196	−	1.32196i	−0.409776	−	0.912186i	$-0.634393\pi$
$308$		0			0
$309$			26.1421i			1.48717i
$310$	−3.23508	−	1.11804i	−0.183740	−	0.0635002i
$311$	−2.97297	−	1.71644i	−0.168581	−	0.0973305i	0.413335	−	0.910579i	$-0.364364\pi$
$311$	−2.97297	−	1.71644i	−0.168581	−	0.0973305i	−0.581917	+	0.813248i	$0.697697\pi$
$312$	−2.86540	−	10.6938i	−0.162222	−	0.605419i
$313$	−9.23021	−	2.47323i	−0.521723	−	0.139795i	−0.0116593	−	0.999932i	$-0.503711\pi$
$313$	−9.23021	−	2.47323i	−0.521723	−	0.139795i	−0.510063	+	0.860137i	$0.670378\pi$
$314$	14.4650			0.816310
$315$		0			0
$316$	−5.07107			−0.285270
$317$	−29.9153	−	8.01577i	−1.68021	−	0.450211i	−0.712375	−	0.701799i	$-0.752380\pi$
$317$	−29.9153	−	8.01577i	−1.68021	−	0.450211i	−0.967834	+	0.251589i	$0.919047\pi$
$318$	−5.57472	−	20.8051i	−0.312615	−	1.16669i
$319$	−2.02922	−	1.17157i	−0.113615	−	0.0655955i
$320$	0.977945	+	2.01088i	0.0546688	+	0.112411i
$321$		−	9.55582i		−	0.533354i
$322$		0			0
$323$	−5.17157	−	5.17157i	−0.287754	−	0.287754i
$324$	−8.72180	+	5.03553i	−0.484544	+	0.279752i
$325$	−3.58344	−	29.7430i	−0.198774	−	1.64985i
$326$	9.65685	−	16.7262i	0.534844	−	0.926376i
$327$	−5.80680	+	21.6713i	−0.321117	+	1.19842i
$328$	−2.61313	+	2.61313i	−0.144286	+	0.144286i
$329$		0			0
$330$	11.6569	+	0.828427i	0.641689	+	0.0456034i
$331$	−11.6569	−	20.1903i	−0.640719	−	1.10976i	−0.985273	−	0.170991i	$-0.945303\pi$
$331$	−11.6569	−	20.1903i	−0.640719	−	1.10976i	0.344554	−	0.938767i	$-0.388030\pi$
$332$	−7.26603	+	1.94693i	−0.398775	+	0.106852i
$333$	1.46311	−	0.392038i	0.0801777	−	0.0214836i
$334$	1.21371	+	2.10220i	0.0664112	+	0.115028i
$335$	21.7248	+	25.0489i	1.18695	+	1.36857i
$336$		0			0
$337$	3.75736	−	3.75736i	0.204676	−	0.204676i	−0.597324	−	0.802000i	$-0.703769\pi$
$337$	3.75736	−	3.75736i	0.204676	−	0.204676i	0.802000	+	0.597324i	$0.203769\pi$
$338$	5.92683	−	22.1192i	0.322377	−	1.20313i
$339$	1.53073	−	2.65131i	0.0831380	−	0.143999i
$340$	−11.4741	+	2.21682i	−0.622269	+	0.120224i
$341$	3.74952	−	2.16478i	0.203048	−	0.117230i
$342$	−0.409880	−	0.409880i	−0.0221638	−	0.0221638i
$343$		0			0
$344$			5.65685i			0.304997i
$345$	−2.17656	+	1.05852i	−0.117182	+	0.0569888i
$346$	16.2766	+	9.39731i	0.875036	+	0.505202i
$347$	−1.94495	−	7.25866i	−0.104411	−	0.389665i	0.893867	−	0.448332i	$-0.147982\pi$
$347$	−1.94495	−	7.25866i	−0.104411	−	0.389665i	−0.998278	+	0.0586667i	$0.981315\pi$
$348$	1.47858	+	0.396183i	0.0792600	+	0.0212376i
$349$	−2.66752			−0.142789			−0.0713945	−	0.997448i	$-0.522745\pi$
$349$	−2.66752			−0.142789			−0.0713945	+	0.997448i	$0.522745\pi$
$350$		0			0
$351$	−28.6274			−1.52802
$352$	−2.73205	−	0.732051i	−0.145619	−	0.0390184i
$353$	−3.10149	−	11.5749i	−0.165076	−	0.616071i	−0.998031	−	0.0627298i	$-0.980019\pi$
$353$	−3.10149	−	11.5749i	−0.165076	−	0.616071i	0.832955	−	0.553341i	$-0.186647\pi$
$354$	14.7840	+	8.53553i	0.785760	+	0.453659i
$355$	−1.17794	+	0.572867i	−0.0625188	+	0.0304046i
$356$			11.3492i			0.601506i
$357$		0			0
$358$	−9.65685	−	9.65685i	−0.510381	−	0.510381i
$359$	14.6969	−	8.48528i	0.775675	−	0.447836i	−0.0592205	−	0.998245i	$-0.518862\pi$
$359$	14.6969	−	8.48528i	0.775675	−	0.447836i	0.834895	+	0.550409i	$0.185528\pi$
$360$	−0.909393	+	0.175697i	−0.0479292	+	0.00926003i
$361$	8.52082	−	14.7585i	0.448464	−	0.776762i
$362$	2.27514	−	8.49093i	0.119579	−	0.446273i
$363$	3.91969	−	3.91969i	0.205730	−	0.205730i
$364$		0			0
$365$	−8.58579	−	9.89949i	−0.449401	−	0.518163i
$366$	5.94975	+	10.3053i	0.310998	+	0.538665i
$367$	4.18204	−	1.12057i	0.218301	−	0.0584935i	−0.148011	−	0.988986i	$-0.547287\pi$
$367$	4.18204	−	1.12057i	0.218301	−	0.0584935i	0.366312	+	0.930492i	$0.380620\pi$
$368$	0.565826	−	0.151613i	0.0294957	−	0.00790336i
$369$	−0.765367	−	1.32565i	−0.0398434	−	0.0690108i
$370$	−8.15640	−	0.579658i	−0.424031	−	0.0301350i
$371$		0			0
$372$	−2.00000	+	2.00000i	−0.103695	+	0.103695i
$373$	−5.51639	+	20.5875i	−0.285628	+	1.06598i	0.662751	+	0.748840i	$0.269389\pi$
$373$	−5.51639	+	20.5875i	−0.285628	+	1.06598i	−0.948379	+	0.317139i	$0.897278\pi$
$374$	7.39104	−	12.8017i	0.382181	−	0.661958i
$375$	−20.6338	+	1.01091i	−1.06553	+	0.0522033i
$376$	−1.32565	+	0.765367i	−0.0683654	+	0.0394708i
$377$	3.50981	+	3.50981i	0.180764	+	0.180764i
$378$		0			0
$379$		−	6.14214i		−	0.315500i	−0.987479	−	0.157750i	$-0.949576\pi$
$379$		−	6.14214i		−	0.315500i	0.987479	−	0.157750i	$-0.0504241\pi$
$380$	1.36855	+	2.81406i	0.0702053	+	0.144358i
$381$	−8.11475	−	4.68506i	−0.415731	−	0.240023i
$382$	−0.454838	−	1.69748i	−0.0232715	−	0.0868506i
$383$	−14.5321	−	3.89386i	−0.742554	−	0.198967i	−0.132341	−	0.991204i	$-0.542249\pi$
$383$	−14.5321	−	3.89386i	−0.742554	−	0.198967i	−0.610213	+	0.792237i	$0.708916\pi$
$384$	1.84776			0.0942931
$385$		0			0
$386$	−11.6569			−0.593318
$387$	−2.26330	−	0.606451i	−0.115050	−	0.0308276i
$388$	1.68086	+	6.27306i	0.0853329	+	0.318467i
$389$	0.123093	+	0.0710678i	0.00624107	+	0.00360328i	0.503117	−	0.864218i	$-0.332186\pi$
$389$	0.123093	+	0.0710678i	0.00624107	+	0.00360328i	−0.496876	+	0.867821i	$0.665520\pi$
$390$	−23.3978	−	8.08622i	−1.18479	−	0.409462i
$391$			3.06147i			0.154825i
$392$		0			0
$393$	19.1421	+	19.1421i	0.965593	+	0.965593i
$394$	0.717439	−	0.414214i	0.0361441	−	0.0208678i
$395$	−6.35150	+	9.39346i	−0.319579	+	0.472636i
$396$	0.585786	−	1.01461i	0.0294369	−	0.0509862i
$397$	−0.410261	+	1.53111i	−0.0205904	+	0.0768444i	−0.975457	−	0.220192i	$-0.929332\pi$
$397$	−0.410261	+	1.53111i	−0.0205904	+	0.0768444i	0.954866	+	0.297036i	$0.0959983\pi$
$398$	19.8226	−	19.8226i	0.993618	−	0.993618i
$399$		0			0
$400$	4.94975	+	0.707107i	0.247487	+	0.0353553i
$401$	9.87868	+	17.1104i	0.493318	+	0.854451i	0.999970	−	0.00769892i	$-0.00245067\pi$
$401$	9.87868	+	17.1104i	0.493318	+	0.854451i	−0.506653	+	0.862150i	$0.669117\pi$
$402$	26.4658	−	7.09148i	1.31999	−	0.353691i
$403$	−8.85906	+	2.37378i	−0.441301	+	0.118246i
$404$	1.37222	+	2.37676i	0.0682705	+	0.118248i
$405$	−1.59639	+	22.4629i	−0.0793253	+	1.11619i
$406$		0			0
$407$	7.31371	−	7.31371i	0.362527	−	0.362527i
$408$	−2.49938	+	9.32780i	−0.123738	+	0.461795i
$409$	−12.4860	+	21.6263i	−0.617392	+	1.06935i	0.372568	+	0.928005i	$0.378477\pi$
$409$	−12.4860	+	21.6263i	−0.617392	+	1.06935i	−0.989960	+	0.141349i	$0.954856\pi$
$410$	1.56753	+	8.11339i	0.0774146	+	0.400692i
$411$	−18.4925	+	10.6767i	−0.912170	+	0.526642i
$412$	−10.0042	−	10.0042i	−0.492870	−	0.492870i
$413$		0			0
$414$			0.242641i			0.0119251i
$415$	−5.49427	+	15.8979i	−0.269703	+	0.780395i
$416$	5.18889	+	2.99581i	0.254406	+	0.146882i
$417$	−4.11509	−	15.3577i	−0.201517	−	0.752071i
$418$	−3.82328	−	1.02444i	−0.187003	−	0.0501072i
$419$	−11.5893			−0.566174			−0.283087	−	0.959094i	$-0.591358\pi$
$419$	−11.5893			−0.566174			−0.283087	+	0.959094i	$0.591358\pi$
$420$		0			0
$421$	17.7990			0.867470			0.433735	−	0.901041i	$-0.357195\pi$
$421$	17.7990			0.867470			0.433735	+	0.901041i	$0.357195\pi$
$422$	−9.99071	−	2.67700i	−0.486340	−	0.130314i
$423$	−0.164104	−	0.612446i	−0.00797903	−	0.0297781i
$424$	10.0951	+	5.82843i	0.490263	+	0.283053i
$425$	−10.2649	+	24.0307i	−0.497920	+	1.16566i
$426$			1.08239i			0.0524421i
$427$		0			0
$428$	3.65685	+	3.65685i	0.176761	+	0.176761i
$429$	27.1185	−	15.6569i	1.30929	−	0.755920i
$430$	10.4786	+	7.08519i	0.505321	+	0.341678i
$431$	−2.82843	+	4.89898i	−0.136241	+	0.235976i	−0.926071	−	0.377350i	$-0.876835\pi$
$431$	−2.82843	+	4.89898i	−0.136241	+	0.235976i	0.789830	+	0.613326i	$0.210169\pi$
$432$	1.23661	−	4.61511i	0.0594966	−	0.222044i
$433$	10.4525	−	10.4525i	0.502315	−	0.502315i	−0.409841	−	0.912157i	$-0.634416\pi$
$433$	10.4525	−	10.4525i	0.502315	−	0.502315i	0.912157	+	0.409841i	$0.134416\pi$
$434$		0			0
$435$	2.58579	−	2.24264i	0.123979	−	0.107526i
$436$	−6.07107	−	10.5154i	−0.290751	−	0.503596i
$437$	0.791827	−	0.212169i	0.0378782	−	0.0101494i
$438$	−10.4595	+	2.80260i	−0.499772	+	0.133914i
$439$	−6.94269	−	12.0251i	−0.331357	−	0.573927i	0.651421	−	0.758716i	$-0.274173\pi$
$439$	−6.94269	−	12.0251i	−0.331357	−	0.573927i	−0.982778	+	0.184789i	$0.940840\pi$
$440$	−4.77791	+	4.14386i	−0.227778	+	0.197551i
$441$		0			0
$442$	−22.1421	+	22.1421i	−1.05319	+	1.05319i
$443$	−1.51613	+	5.65826i	−0.0720334	+	0.268832i	−0.992544	−	0.121885i	$-0.961106\pi$
$443$	−1.51613	+	5.65826i	−0.0720334	+	0.268832i	0.920511	+	0.390717i	$0.127773\pi$
$444$	−3.37849	+	5.85172i	−0.160336	+	0.277710i
$445$	21.0228	+	14.2148i	0.996577	+	0.673847i
$446$	−8.27558	+	4.77791i	−0.391860	+	0.226241i
$447$	22.6215	+	22.6215i	1.06996	+	1.06996i
$448$		0			0
$449$		−	25.6569i		−	1.21082i	−0.795913	−	0.605411i	$-0.793009\pi$
$449$		−	25.6569i		−	1.21082i	0.795913	−	0.605411i	$-0.206991\pi$
$450$	−0.813558	+	1.90459i	−0.0383515	+	0.0897830i
$451$	−9.05213	−	5.22625i	−0.426248	−	0.246095i
$452$	0.428825	+	1.60040i	0.0201703	+	0.0752764i
$453$	−15.7570	−	4.22206i	−0.740327	−	0.198370i
$454$	−11.8519			−0.556238
$455$		0			0
$456$	2.58579			0.121091
$457$	2.26330	+	0.606451i	0.105873	+	0.0283686i	0.311367	−	0.950290i	$-0.399213\pi$
$457$	2.26330	+	0.606451i	0.105873	+	0.0283686i	−0.205494	+	0.978658i	$0.565880\pi$
$458$	1.99499	+	7.44542i	0.0932199	+	0.347901i
$459$	21.6251	+	12.4853i	1.00938	+	0.582763i
$460$	0.427854	−	1.23801i	0.0199488	−	0.0577225i
$461$			34.0250i			1.58470i	0.610064	+	0.792352i	$0.291144\pi$
$461$			34.0250i			1.58470i	−0.610064	+	0.792352i	$0.708856\pi$
$462$		0			0
$463$	−12.9706	−	12.9706i	−0.602793	−	0.602793i	0.338260	−	0.941053i	$-0.390162\pi$
$463$	−12.9706	−	12.9706i	−0.602793	−	0.602793i	−0.941053	+	0.338260i	$0.890162\pi$
$464$	−0.717439	+	0.414214i	−0.0333063	+	0.0192294i
$465$	1.19973	+	6.20972i	0.0556363	+	0.287969i
$466$	2.12132	−	3.67423i	0.0982683	−	0.170206i
$467$	−6.38116	+	23.8148i	−0.295285	+	1.10202i	0.645706	+	0.763586i	$0.276563\pi$
$467$	−6.38116	+	23.8148i	−0.295285	+	1.10202i	−0.940991	+	0.338432i	$0.890103\pi$
$468$	−1.75490	+	1.75490i	−0.0811205	+	0.0811205i
$469$		0			0
$470$	−0.242641	+	3.41421i	−0.0111922	+	0.157486i
$471$	−13.3640	−	23.1471i	−0.615779	−	1.06656i
$472$	−8.92399	+	2.39118i	−0.410760	+	0.110063i
$473$	−15.4548	+	4.14110i	−0.710613	+	0.190408i
$474$	4.68506	+	8.11475i	0.215192	+	0.372723i
$475$	6.92676	+	0.989538i	0.317822	+	0.0454031i
$476$		0			0
$477$	−3.41421	+	3.41421i	−0.156326	+	0.156326i
$478$	−1.67851	+	6.26430i	−0.0767735	+	0.286522i
$479$	−5.54328	+	9.60124i	−0.253279	+	0.438692i	−0.964427	−	0.264351i	$-0.914842\pi$
$479$	−5.54328	+	9.60124i	−0.253279	+	0.438692i	0.711148	+	0.703043i	$0.248176\pi$
$480$	2.31431	−	3.42272i	0.105633	−	0.156225i
$481$	−18.9750	+	10.9552i	−0.865187	+	0.499516i
$482$	4.77791	+	4.77791i	0.217628	+	0.217628i
$483$		0			0
$484$			3.00000i			0.136364i
$485$	13.7253	+	4.74343i	0.623232	+	0.215388i
$486$	3.70241	+	2.13759i	0.167945	+	0.0969630i
$487$	0.402813	+	1.50332i	0.0182532	+	0.0681218i	0.974452	−	0.224597i	$-0.0721066\pi$
$487$	0.402813	+	1.50332i	0.0182532	+	0.0681218i	−0.956199	+	0.292719i	$0.905440\pi$
$488$	−6.22052	−	1.66678i	−0.281590	−	0.0754518i
$489$	−35.6871			−1.61383
$490$		0			0
$491$	25.1716			1.13598			0.567989	−	0.823036i	$-0.307722\pi$
$491$	25.1716			1.13598			0.567989	+	0.823036i	$0.307722\pi$
$492$	6.59575	+	1.76733i	0.297360	+	0.0796773i
$493$	−1.12057	−	4.18204i	−0.0504682	−	0.188350i
$494$	7.26143	+	4.19239i	0.326707	+	0.188624i
$495$	−1.14573	−	2.35589i	−0.0514969	−	0.105889i
$496$		−	1.53073i		−	0.0687320i
$497$		0			0
$498$	9.82843	+	9.82843i	0.440422	+	0.440422i
$499$	−6.50794	+	3.75736i	−0.291335	+	0.168203i	−0.638544	−	0.769585i	$-0.720463\pi$
$499$	−6.50794	+	3.75736i	−0.291335	+	0.168203i	0.347209	+	0.937788i	$0.387130\pi$
$500$	7.50936	−	8.28308i	0.335829	−	0.370431i
$501$	2.24264	−	3.88437i	0.100194	−	0.173541i
$502$	3.64770	−	13.6134i	0.162805	−	0.607596i
$503$	−18.1062	+	18.1062i	−0.807314	+	0.807314i	−0.984227	−	0.176912i	$-0.943389\pi$
$503$	−18.1062	+	18.1062i	−0.807314	+	0.807314i	0.176912	+	0.984227i	$0.443389\pi$
$504$		0			0
$505$	6.12132	+	0.435029i	0.272395	+	0.0193585i
$506$	0.828427	+	1.43488i	0.0368281	+	0.0637881i
$507$	−40.8710	+	10.9513i	−1.81514	+	0.486366i
$508$	4.89828	−	1.31249i	0.217326	−	0.0582323i
$509$	7.23252	+	12.5271i	0.320576	+	0.555254i	0.980607	−	0.195984i	$-0.0627902\pi$
$509$	7.23252	+	12.5271i	0.320576	+	0.555254i	−0.660031	+	0.751238i	$0.729457\pi$
$510$	14.1480	+	16.3128i	0.626485	+	0.722343i
$511$		0			0
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	1.73054	−	6.45846i	0.0764052	−	0.285148i
$514$	5.54328	−	9.60124i	0.244503	−	0.423492i
$515$	−31.0615	+	6.00116i	−1.36873	+	0.264443i
$516$	9.05213	−	5.22625i	0.398498	−	0.230073i
$517$	−3.06147	−	3.06147i	−0.134643	−	0.134643i
$518$		0			0
$519$		−	34.7279i		−	1.52439i
$520$	12.0484	−	5.85948i	0.528357	−	0.256955i
$521$	31.7767	+	18.3463i	1.39216	+	0.803765i	0.993554	−	0.113357i	$-0.0361603\pi$
$521$	31.7767	+	18.3463i	1.39216	+	0.803765i	0.398607	+	0.917122i	$0.369494\pi$
$522$	−0.0888127	−	0.331453i	−0.00388722	−	0.0145073i
$523$	2.39724	+	0.642340i	0.104824	+	0.0280876i	0.310850	−	0.950459i	$-0.399386\pi$
$523$	2.39724	+	0.642340i	0.104824	+	0.0280876i	−0.206026	+	0.978547i	$0.566053\pi$
$524$	−14.6508			−0.640021
$525$		0			0
$526$	27.4558			1.19713
$527$	7.72741	+	2.07055i	0.336611	+	0.0901947i
$528$	1.35265	+	5.04817i	0.0588667	+	0.219693i
$529$	19.6214	+	11.3284i	0.853105	+	0.492540i
$530$	23.4405	−	11.3998i	1.01819	−	0.495174i
$531$		−	3.82683i		−	0.166070i
$532$		0			0
$533$	15.6569	+	15.6569i	0.678174	+	0.678174i
$534$	18.1610	−	10.4853i	0.785905	−	0.453743i
$535$	11.3540	−	2.19362i	0.490877	−	0.0948386i
$536$	−7.41421	+	12.8418i	−0.320245	+	0.554681i
$537$	−6.53119	+	24.3747i	−0.281842	+	1.05185i
$538$	−19.0188	+	19.0188i	−0.819958	+	0.819958i
$539$		0			0
$540$	−7.00000	−	8.07107i	−0.301232	−	0.347323i
$541$	−5.48528	−	9.50079i	−0.235831	−	0.408471i	0.723683	−	0.690132i	$-0.242448\pi$
$541$	−5.48528	−	9.50079i	−0.235831	−	0.408471i	−0.959514	+	0.281662i	$0.909114\pi$
$542$	18.1017	−	4.85033i	0.777533	−	0.208339i
$543$	−15.6892	+	4.20390i	−0.673287	+	0.180407i
$544$	−2.61313	−	4.52607i	−0.112037	−	0.194054i
$545$	−27.0823	−	1.92468i	−1.16008	−	0.0824443i
$546$		0			0
$547$	−30.6274	+	30.6274i	−1.30953	+	1.30953i	−0.387783	+	0.921751i	$0.626759\pi$
$547$	−30.6274	+	30.6274i	−1.30953	+	1.30953i	−0.921751	+	0.387783i	$0.873241\pi$
$548$	2.99100	−	11.1626i	0.127769	−	0.476842i
$549$	1.33376	−	2.31014i	0.0569235	−	0.0985943i
$550$	1.69161	+	14.0406i	0.0721307	+	0.598693i
$551$	−1.00400	+	0.579658i	−0.0427717	+	0.0246942i
$552$	−0.765367	−	0.765367i	−0.0325762	−	0.0325762i
$553$		0			0
$554$		−	2.48528i		−	0.105589i
$555$	6.60796	+	13.5875i	0.280492	+	0.576756i
$556$	7.45193	+	4.30237i	0.316032	+	0.182461i
$557$	−9.78310	−	36.5110i	−0.414523	−	1.54702i	−0.785789	−	0.618495i	$-0.787743\pi$
$557$	−9.78310	−	36.5110i	−0.414523	−	1.54702i	0.371266	−	0.928527i	$-0.378924\pi$
$558$	0.612446	+	0.164104i	0.0259269	+	0.00694709i
$559$	33.8937			1.43355
$560$		0			0
$561$	−27.3137			−1.15319
$562$	−5.46410	−	1.46410i	−0.230489	−	0.0617594i
$563$	−1.29876	−	4.84703i	−0.0547361	−	0.204278i	0.933142	−	0.359507i	$-0.117055\pi$
$563$	−1.29876	−	4.84703i	−0.0547361	−	0.204278i	−0.987879	+	0.155229i	$0.950388\pi$
$564$	2.44949	+	1.41421i	0.103142	+	0.0595491i
$565$	3.50162	+	1.21015i	0.147314	+	0.0509116i
$566$		−	4.46088i		−	0.187505i
$567$		0			0
$568$	−0.414214	−	0.414214i	−0.0173800	−	0.0173800i
$569$	−1.22474	+	0.707107i	−0.0513440	+	0.0296435i	−0.525452	−	0.850823i	$-0.676104\pi$
$569$	−1.22474	+	0.707107i	−0.0513440	+	0.0296435i	0.474108	+	0.880467i	$0.342771\pi$
$570$	3.23869	−	4.78982i	0.135654	−	0.200623i
$571$	12.7279	−	22.0454i	0.532647	−	0.922572i	−0.466626	−	0.884455i	$-0.654531\pi$
$571$	12.7279	−	22.0454i	0.532647	−	0.922572i	0.999273	−	0.0381170i	$-0.0121360\pi$
$572$	−4.38617	+	16.3694i	−0.183395	+	0.684439i
$573$	−2.29610	+	2.29610i	−0.0959210	+	0.0959210i
$574$		0			0
$575$	−1.75736	−	2.34315i	−0.0732869	−	0.0977159i
$576$	−0.207107	−	0.358719i	−0.00862945	−	0.0149466i
$577$	−35.9496	+	9.63268i	−1.49660	+	0.401014i	−0.911961	−	0.410277i	$-0.865432\pi$
$577$	−35.9496	+	9.63268i	−1.49660	+	0.401014i	−0.584643	+	0.811291i	$0.698765\pi$
$578$	9.96228	−	2.66938i	0.414376	−	0.111032i
$579$	10.7695	+	18.6534i	0.447566	+	0.775208i
$580$	−0.131316	+	1.84776i	−0.00545261	+	0.0767240i
$581$		0			0
$582$	8.48528	−	8.48528i	0.351726	−	0.351726i
$583$	−8.53341	+	31.8471i	−0.353418	+	1.31897i
$584$	2.93015	−	5.07517i	0.121251	−	0.210012i
$585$	1.05271	+	5.44873i	0.0435241	+	0.225277i
$586$	2.92586	−	1.68925i	0.120866	−	0.0697821i
$587$	−16.0886	−	16.0886i	−0.664049	−	0.664049i	0.292283	−	0.956332i	$-0.405585\pi$
$587$	−16.0886	−	16.0886i	−0.664049	−	0.664049i	−0.956332	+	0.292283i	$0.905585\pi$
$588$		0			0
$589$		−	2.14214i		−	0.0882652i
$590$	−6.74795	+	19.5254i	−0.277809	+	0.803849i
$591$	−1.32565	−	0.765367i	−0.0545301	−	0.0314830i
$592$	−0.946464	−	3.53225i	−0.0388994	−	0.145175i
$593$	−31.2602	−	8.37616i	−1.28370	−	0.343967i	−0.448438	−	0.893814i	$-0.648020\pi$
$593$	−31.2602	−	8.37616i	−1.28370	−	0.343967i	−0.835266	+	0.549846i	$0.814686\pi$
$594$	13.5140			0.554485
$595$		0			0
$596$	−17.3137			−0.709197
$597$	−50.0340	−	13.4066i	−2.04775	−	0.548694i
$598$	−0.908405	−	3.39022i	−0.0371475	−	0.138636i
$599$	16.0448	+	9.26346i	0.655572	+	0.378495i	0.790588	−	0.612349i	$-0.209775\pi$
$599$	16.0448	+	9.26346i	0.655572	+	0.378495i	−0.135016	+	0.990843i	$0.543109\pi$
$600$	−3.44145	−	8.57390i	−0.140497	−	0.350028i
$601$			16.5754i			0.676126i	0.941123	+	0.338063i	$0.109772\pi$
$601$			16.5754i			0.676126i	−0.941123	+	0.338063i	$0.890228\pi$
$602$		0			0
$603$	−4.34315	−	4.34315i	−0.176867	−	0.176867i
$604$	7.64564	−	4.41421i	0.311097	−	0.179612i
$605$	5.55709	+	3.75749i	0.225928	+	0.152764i
$606$	2.53553	−	4.39167i	0.102999	−	0.178400i
$607$	7.88384	−	29.4229i	0.319995	−	1.19424i	−0.599253	−	0.800560i	$-0.704536\pi$
$607$	7.88384	−	29.4229i	0.319995	−	1.19424i	0.919248	−	0.393679i	$-0.128798\pi$
$608$	−0.989538	+	0.989538i	−0.0401311	+	0.0401311i
$609$		0			0
$610$	−10.8787	+	9.43503i	−0.440465	+	0.382013i
$611$	4.58579	+	7.94282i	0.185521	+	0.321332i
$612$	2.09102	−	0.560287i	0.0845245	−	0.0226483i
$613$	−27.1832	+	7.28372i	−1.09792	+	0.294187i	−0.761917	−	0.647674i	$-0.775742\pi$
$613$	−27.1832	+	7.28372i	−1.09792	+	0.294187i	−0.336002	+	0.941861i	$0.609075\pi$
$614$	−16.3785	−	28.3683i	−0.660981	−	1.14485i
$615$	11.5349	−	10.0042i	0.465132	−	0.403407i
$616$		0			0
$617$	−28.4853	+	28.4853i	−1.14677	+	1.14677i	−0.159591	+	0.987183i	$0.551018\pi$
$617$	−28.4853	+	28.4853i	−1.14677	+	1.14677i	−0.987183	+	0.159591i	$0.948982\pi$
$618$	−6.76608	+	25.2514i	−0.272172	+	1.01576i
$619$	−0.344222	+	0.596210i	−0.0138354	+	0.0239637i	−0.872860	−	0.487970i	$-0.837737\pi$
$619$	−0.344222	+	0.596210i	−0.0138354	+	0.0239637i	0.859025	+	0.511934i	$0.171071\pi$
$620$	−2.83548	−	1.91724i	−0.113875	−	0.0769982i
$621$	−2.42386	+	1.39942i	−0.0972662	+	0.0561567i
$622$	−2.42742	−	2.42742i	−0.0973305	−	0.0973305i
$623$		0			0
$624$		−	11.0711i		−	0.443197i
$625$	−5.93782	−	24.2846i	−0.237513	−	0.971384i
$626$	−8.27558	−	4.77791i	−0.330759	−	0.190964i
$627$	1.89293	+	7.06450i	0.0755962	+	0.282129i
$628$	13.9722	+	3.74383i	0.557550	+	0.149395i
$629$	19.1116			0.762031
$630$		0			0
$631$	41.3553			1.64633			0.823165	−	0.567802i	$-0.192206\pi$
$631$	41.3553			1.64633			0.823165	+	0.567802i	$0.192206\pi$
$632$	−4.89828	−	1.31249i	−0.194843	−	0.0522080i
$633$	4.94646	+	18.4604i	0.196604	+	0.733736i
$634$	−26.8213	−	15.4853i	−1.06521	−	0.614999i
$635$	3.70387	−	10.7173i	0.146984	−	0.425302i
$636$		−	21.5391i		−	0.854079i
$637$		0			0
$638$	−1.65685	−	1.65685i	−0.0655955	−	0.0655955i
$639$	0.210133	−	0.121320i	0.00831273	−	0.00479936i
$640$	0.424170	+	2.19547i	0.0167668	+	0.0867835i
$641$	18.6066	−	32.2276i	0.734917	−	1.27291i	−0.219843	−	0.975535i	$-0.570555\pi$
$641$	18.6066	−	32.2276i	0.734917	−	1.27291i	0.954760	−	0.297378i	$-0.0961120\pi$
$642$	2.47323	−	9.23021i	0.0976105	−	0.364287i
$643$	20.9435	−	20.9435i	0.825930	−	0.825930i	−0.161021	−	0.986951i	$-0.551479\pi$
$643$	20.9435	−	20.9435i	0.825930	−	0.825930i	0.986951	+	0.161021i	$0.0514787\pi$
$644$		0			0
$645$	1.65685	−	23.3137i	0.0652386	−	0.917976i
$646$	−3.65685	−	6.33386i	−0.143877	−	0.249202i
$647$	32.6337	−	8.74418i	1.28296	−	0.343769i	0.447980	−	0.894043i	$-0.352143\pi$
$647$	32.6337	−	8.74418i	1.28296	−	0.343769i	0.834984	+	0.550274i	$0.185477\pi$
$648$	−9.72790	+	2.60658i	−0.382148	+	0.102396i
$649$	−13.0656	−	22.6303i	−0.512871	−	0.888318i
$650$	4.23671	−	29.6570i	0.166178	−	1.16324i
$651$		0			0
$652$	13.6569	−	13.6569i	0.534844	−	0.534844i
$653$	3.19464	−	11.9226i	0.125016	−	0.466566i	−0.874824	−	0.484440i	$-0.839023\pi$
$653$	3.19464	−	11.9226i	0.125016	−	0.466566i	0.999840	+	0.0178744i	$0.00568992\pi$
$654$	−11.2179	+	19.4299i	−0.438653	+	0.759770i
$655$	−18.3500	+	27.1385i	−0.716995	+	1.06039i
$656$	−3.20041	+	1.84776i	−0.124955	+	0.0721429i
$657$	1.71644	+	1.71644i	0.0669648	+	0.0669648i
$658$		0			0
$659$			29.6569i			1.15527i	0.816296	+	0.577634i	$0.196024\pi$
$659$			29.6569i			1.15527i	−0.816296	+	0.577634i	$0.803976\pi$
$660$	11.0452	+	3.81722i	0.429936	+	0.148585i
$661$	−41.1700	−	23.7695i	−1.60133	−	0.924526i	−0.991222	−	0.132205i	$-0.957794\pi$
$661$	−41.1700	−	23.7695i	−1.60133	−	0.924526i	−0.610104	−	0.792321i	$-0.708873\pi$
$662$	−6.03403	−	22.5193i	−0.234519	−	0.875238i
$663$	55.8887	+	14.9753i	2.17054	+	0.581593i
$664$	−7.52235			−0.291924
$665$		0			0
$666$	1.51472			0.0586942
$667$	0.468746	+	0.125600i	0.0181499	+	0.00486325i
$668$	0.628262	+	2.34470i	0.0243082	+	0.0907193i
$669$	15.2913	+	8.82843i	0.591195	+	0.341327i
$670$	14.5014	+	29.8181i	0.560238	+	1.15197i
$671$		−	18.2150i		−	0.703181i
$672$		0			0
$673$	−22.7990	−	22.7990i	−0.878836	−	0.878836i	0.114578	−	0.993414i	$-0.463448\pi$
$673$	−22.7990	−	22.7990i	−0.878836	−	0.878836i	−0.993414	+	0.114578i	$0.963448\pi$
$674$	4.60181	−	2.65685i	0.177255	−	0.102338i
$675$	−23.7180	+	2.85755i	−0.912907	+	0.109987i
$676$	11.4497	−	19.8315i	0.440375	−	0.762752i
$677$	8.22613	−	30.7003i	0.316156	−	1.17991i	−0.606753	−	0.794891i	$-0.707528\pi$
$677$	8.22613	−	30.7003i	0.316156	−	1.17991i	0.922909	−	0.385019i	$-0.125805\pi$
$678$	2.16478	−	2.16478i	0.0831380	−	0.0831380i
$679$		0			0
$680$	−11.6569	−	0.828427i	−0.447020	−	0.0317687i
$681$	10.9497	+	18.9655i	0.419595	+	0.726760i
$682$	4.18204	−	1.12057i	0.160139	−	0.0429090i
$683$	34.5792	−	9.26546i	1.32314	−	0.354533i	0.472984	−	0.881071i	$-0.343177\pi$
$683$	34.5792	−	9.26546i	1.32314	−	0.354533i	0.850151	+	0.526538i	$0.176510\pi$
$684$	−0.289829	−	0.501998i	−0.0110819	−	0.0191944i
$685$	−16.9309	−	19.5215i	−0.646897	−	0.745879i
$686$		0			0
$687$	10.0711	−	10.0711i	0.384235	−	0.384235i
$688$	−1.46410	+	5.46410i	−0.0558184	+	0.208317i
$689$	34.9217	−	60.4862i	1.33041	−	2.30434i
$690$	−2.37636	+	0.459118i	−0.0904664	+	0.0174783i
$691$	21.7401	−	12.5516i	0.827031	−	0.477487i	−0.0258041	−	0.999667i	$-0.508215\pi$
$691$	21.7401	−	12.5516i	0.827031	−	0.477487i	0.852835	+	0.522181i	$0.174881\pi$
$692$	13.2898	+	13.2898i	0.505202	+	0.505202i
$693$		0			0
$694$		−	7.51472i		−	0.285255i
$695$	17.3031	−	8.41497i	0.656343	−	0.319198i
$696$	1.32565	+	0.765367i	0.0502488	+	0.0290112i
$697$	−4.99876	−	18.6556i	−0.189341	−	0.706632i
$698$	−2.57663	−	0.690405i	−0.0975267	−	0.0261322i
$699$	−7.83938			−0.296512
$700$		0			0
$701$	−13.1127			−0.495260			−0.247630	−	0.968855i	$-0.579652\pi$
$701$	−13.1127			−0.495260			−0.247630	+	0.968855i	$0.579652\pi$
$702$	−27.6520	−	7.40932i	−1.04366	−	0.279647i
$703$	−1.32450	−	4.94309i	−0.0499544	−	0.186432i
$704$	−2.44949	−	1.41421i	−0.0923186	−	0.0533002i
$705$	5.68762	−	2.76605i	0.214208	−	0.104175i
$706$		−	11.9832i		−	0.450995i
$707$		0			0
$708$	12.0711	+	12.0711i	0.453659	+	0.453659i
$709$	35.7787	−	20.6569i	1.34370	−	0.775784i	0.356350	−	0.934353i	$-0.384021\pi$
$709$	35.7787	−	20.6569i	1.34370	−	0.775784i	0.987348	+	0.158568i	$0.0506877\pi$
$710$	−1.28608	+	0.248473i	−0.0482656	+	0.00932502i
$711$	1.05025	−	1.81909i	0.0393875	−	0.0682212i
$712$	−2.93739	+	10.9625i	−0.110083	+	0.410836i
$713$	−0.634051	+	0.634051i	−0.0237454	+	0.0237454i
$714$		0			0
$715$	24.8284	+	28.6274i	0.928531	+	1.07060i
$716$	−6.82843	−	11.8272i	−0.255190	−	0.442003i
$717$	11.5749	−	3.10149i	0.432273	−	0.115827i
$718$	16.3923	−	4.39230i	0.611755	−	0.163919i
$719$	21.8561	+	37.8558i	0.815094	+	1.41178i	0.909260	+	0.416228i	$0.136648\pi$
$719$	21.8561	+	37.8558i	0.815094	+	1.41178i	−0.0941658	+	0.995557i	$0.530018\pi$
$720$	−0.923880	−	0.0656581i	−0.0344310	−	0.00244693i
$721$		0			0
$722$	12.0503	−	12.0503i	0.448464	−	0.448464i
$723$	3.23143	−	12.0599i	0.120178	−	0.448511i
$724$	4.39523	−	7.61276i	0.163347	−	0.282926i
$725$	3.25825	+	2.55756i	0.121008	+	0.0949853i
$726$	4.80062	−	2.77164i	0.178168	−	0.102865i
$727$	22.8841	+	22.8841i	0.848724	+	0.848724i	0.989974	−	0.141250i	$-0.0451122\pi$
$727$	22.8841	+	22.8841i	0.848724	+	0.848724i	−0.141250	+	0.989974i	$0.545112\pi$
$728$		0			0
$729$			22.3137i			0.826434i
$730$	−5.73106	−	11.7843i	−0.212116	−	0.436158i
$731$	−25.6033	−	14.7821i	−0.946972	−	0.546735i
$732$	3.07982	+	11.4940i	0.113833	+	0.424832i
$733$	29.9828	+	8.03387i	1.10744	+	0.296738i	0.765791	−	0.643090i	$-0.222348\pi$
$733$	29.9828	+	8.03387i	1.10744	+	0.296738i	0.341649	+	0.939827i	$0.389014\pi$
$734$	4.32957			0.159807
$735$		0			0
$736$	0.585786			0.0215924
$737$	−40.5120	−	10.8552i	−1.49228	−	0.399855i
$738$	−0.396183	−	1.47858i	−0.0145837	−	0.0544271i
$739$	−8.36308	−	4.82843i	−0.307641	−	0.177617i	0.338229	−	0.941064i	$-0.390172\pi$
$739$	−8.36308	−	4.82843i	−0.307641	−	0.177617i	−0.645870	+	0.763447i	$0.723505\pi$
$740$	−7.72845	−	2.67094i	−0.284104	−	0.0981857i
$741$		−	15.4930i		−	0.569151i
$742$		0			0
$743$	27.0416	+	27.0416i	0.992061	+	0.992061i	0.999969	−	0.00790753i	$-0.00251707\pi$
$743$	27.0416	+	27.0416i	0.992061	+	0.992061i	−0.00790753	+	0.999969i	$0.502517\pi$
$744$	−2.44949	+	1.41421i	−0.0898027	+	0.0518476i
$745$	−21.6854	+	32.0713i	−0.794491	+	1.17500i
$746$	−10.6569	+	18.4582i	−0.390175	+	0.675803i
$747$	0.806444	−	3.00969i	0.0295062	−	0.110119i
$748$	10.4525	−	10.4525i	0.382181	−	0.382181i
$749$		0			0
$750$	−20.1924	−	4.36396i	−0.737322	−	0.159349i
$751$	1.24264	+	2.15232i	0.0453446	+	0.0785392i	0.887807	−	0.460216i	$-0.152228\pi$
$751$	1.24264	+	2.15232i	0.0453446	+	0.0785392i	−0.842462	+	0.538755i	$0.818895\pi$
$752$	−1.47858	+	0.396183i	−0.0539181	+	0.0144473i
$753$	−25.1543	+	6.74007i	−0.916673	+	0.245622i
$754$	2.48181	+	4.29862i	0.0903822	+	0.156547i
$755$	1.39942	−	19.6913i	0.0509300	−	0.716640i
$756$		0			0
$757$	7.89949	−	7.89949i	0.287112	−	0.287112i	−0.548825	−	0.835937i	$-0.684925\pi$
$757$	7.89949	−	7.89949i	0.287112	−	0.287112i	0.835937	+	0.548825i	$0.184925\pi$
$758$	1.58970	−	5.93285i	0.0577406	−	0.215491i
$759$	1.53073	−	2.65131i	0.0555621	−	0.0962364i
$760$	0.593590	+	3.07238i	0.0215318	+	0.111447i
$761$	22.8578	−	13.1969i	0.828594	−	0.478389i	−0.0247771	−	0.999693i	$-0.507888\pi$
$761$	22.8578	−	13.1969i	0.828594	−	0.478389i	0.853371	+	0.521304i	$0.174554\pi$
$762$	−6.62567	−	6.62567i	−0.240023	−	0.240023i
$763$		0			0
$764$		−	1.75736i		−	0.0635790i
$765$	1.58114	−	4.57509i	0.0571663	−	0.165413i
$766$	−13.0291	−	7.52235i	−0.470760	−	0.271794i
$767$	14.3270	+	53.4692i	0.517319	+	1.93066i
$768$	1.78480	+	0.478235i	0.0644034	+	0.0172568i
$769$	17.5809			0.633984			0.316992	−	0.948428i	$-0.397327\pi$
$769$	17.5809			0.633984			0.316992	+	0.948428i	$0.397327\pi$
$770$		0			0
$771$	−20.4853			−0.737759
$772$	−11.2597	−	3.01702i	−0.405244	−	0.108585i
$773$	5.37663	+	20.0658i	0.193384	+	0.721718i	0.992679	+	0.120780i	$0.0385396\pi$
$773$	5.37663	+	20.0658i	0.193384	+	0.721718i	−0.799295	+	0.600938i	$0.794794\pi$
$774$	−2.02922	−	1.17157i	−0.0729389	−	0.0421113i
$775$	−7.10285	+	2.85099i	−0.255142	+	0.102411i
$776$			6.49435i			0.233134i
$777$		0			0
$778$	0.100505	+	0.100505i	0.00360328	+	0.00360328i
$779$	−4.47871	+	2.58579i	−0.160467	+	0.0926454i
$780$	−20.5076	−	13.8665i	−0.734291	−	0.496500i
$781$	0.828427	−	1.43488i	0.0296435	−	0.0513440i
$782$	−0.792366	+	2.95715i	−0.0283350	+	0.105747i
$783$	2.79884	−	2.79884i	0.100022	−	0.100022i
$784$		0			0
$785$	24.4350	−	21.1924i	0.872124	−	0.756389i
$786$	13.5355	+	23.4442i	0.482797	+	0.836228i
$787$	33.2987	−	8.92237i	1.18697	−	0.318048i	0.389283	−	0.921118i	$-0.372723\pi$
$787$	33.2987	−	8.92237i	1.18697	−	0.318048i	0.797688	+	0.603070i	$0.206056\pi$
$788$	0.800199	−	0.214413i	0.0285059	−	0.00763814i
$789$	−25.3659	−	43.9350i	−0.903050	−	1.56413i
$790$	−8.56628	+	7.42950i	−0.304775	+	0.264330i
$791$		0			0
$792$	0.828427	−	0.828427i	0.0294369	−	0.0294369i
$793$	−9.98674	+	37.2710i	−0.354639	+	1.32353i
$794$	−0.792563	+	1.37276i	−0.0281270	+	0.0487174i
$795$	−39.8982	−	26.9776i	−1.41504	−	0.956797i
$796$	24.2776	−	14.0167i	0.860498	−	0.496809i
$797$	−16.6683	−	16.6683i	−0.590421	−	0.590421i	0.347324	−	0.937745i	$-0.387090\pi$
$797$	−16.6683	−	16.6683i	−0.590421	−	0.590421i	−0.937745	+	0.347324i	$0.887090\pi$
$798$		0			0
$799$		−	8.00000i		−	0.283020i
$800$	4.59808	+	1.96410i	0.162567	+	0.0694415i
$801$	−4.07117	−	2.35049i	−0.143848	−	0.0830506i
$802$	5.11358	+	19.0841i	0.180567	+	0.673885i
$803$	16.0106	+	4.29004i	0.565003	+	0.151392i
$804$	27.3994			0.966301
$805$		0			0
$806$	−9.17157			−0.323055
$807$	48.0051	+	12.8629i	1.68986	+	0.452796i
$808$	0.710314	+	2.65093i	0.0249888	+	0.0932593i
$809$	29.3578	+	16.9497i	1.03217	+	0.595921i	0.917604	−	0.397495i	$-0.130120\pi$
$809$	29.3578	+	16.9497i	1.03217	+	0.595921i	0.114562	+	0.993416i	$0.463454\pi$
$810$	−7.35583	+	21.2844i	−0.258458	+	0.747856i
$811$		−	50.6005i		−	1.77682i	−0.459048	−	0.888411i	$-0.651809\pi$
$811$		−	50.6005i		−	1.77682i	0.459048	−	0.888411i	$-0.348191\pi$
$812$		0			0
$813$	−24.4853	−	24.4853i	−0.858736	−	0.858736i
$814$	8.95743	−	5.17157i	0.313958	−	0.181264i
$815$	−8.19229	−	42.4026i	−0.286963	−	1.48530i
$816$	−4.82843	+	8.36308i	−0.169029	+	0.292766i
$817$	−2.04889	+	7.64656i	−0.0716816	+	0.267519i
$818$	−17.6578	+	17.6578i	−0.617392	+	0.617392i
$819$		0			0
$820$	−0.585786	+	8.24264i	−0.0204565	+	0.287845i
$821$	17.2426	+	29.8651i	0.601772	+	1.04230i	0.992553	+	0.121816i	$0.0388719\pi$
$821$	17.2426	+	29.8651i	0.601772	+	1.04230i	−0.390780	+	0.920484i	$0.627795\pi$
$822$	−20.6258	+	5.52665i	−0.719406	+	0.192764i
$823$	3.20080	−	0.857651i	0.111573	−	0.0298958i	−0.202601	−	0.979261i	$-0.564939\pi$
$823$	3.20080	−	0.857651i	0.111573	−	0.0298958i	0.314173	+	0.949366i	$0.398273\pi$
$824$	−7.07401	−	12.2525i	−0.246435	−	0.426838i
$825$	20.9050	−	15.6788i	0.727819	−	0.545864i
$826$		0			0
$827$	−7.51472	+	7.51472i	−0.261312	+	0.261312i	−0.825587	−	0.564275i	$-0.809156\pi$
$827$	−7.51472	+	7.51472i	−0.261312	+	0.261312i	0.564275	+	0.825587i	$0.309156\pi$
$828$	−0.0628000	+	0.234373i	−0.00218245	+	0.00814502i
$829$	−20.4295	+	35.3849i	−0.709545	+	1.22897i	0.255481	+	0.966814i	$0.417766\pi$
$829$	−20.4295	+	35.3849i	−0.709545	+	1.22897i	−0.965026	+	0.262154i	$0.915567\pi$
$830$	−9.42173	+	13.9341i	−0.327033	+	0.483661i
$831$	−3.97696	+	2.29610i	−0.137959	+	0.0796508i
$832$	4.23671	+	4.23671i	0.146882	+	0.146882i
$833$		0			0
$834$		−	15.8995i		−	0.550554i
$835$	5.13014	+	1.77297i	0.177536	+	0.0613561i
$836$	−3.42786	−	1.97908i	−0.118555	−	0.0684477i
$837$	1.89293	+	7.06450i	0.0654291	+	0.244185i
$838$	−11.1944	−	2.99953i	−0.386704	−	0.103617i
$839$	20.6424			0.712654			0.356327	−	0.934361i	$-0.384029\pi$
$839$	20.6424			0.712654			0.356327	+	0.934361i	$0.384029\pi$
$840$		0			0
$841$	28.3137			0.976335
$842$	17.1925	+	4.60672i	0.592493	+	0.158758i
$843$	2.70531	+	10.0963i	0.0931757	+	0.347737i
$844$	−8.95743	−	5.17157i	−0.308327	−	0.178013i
$845$	−22.3945	−	46.0480i	−0.770393	−	1.58410i
$846$		−	0.634051i		−	0.0217991i
$847$		0			0
$848$	8.24264	+	8.24264i	0.283053	+	0.283053i
$849$	−7.13834	+	4.12132i	−0.244987	+	0.141443i
$850$	−16.1347	+	20.5551i	−0.553417	+	0.705035i
$851$	−1.07107	+	1.85514i	−0.0367157	+	0.0635935i
$852$	−0.280144	+	1.04551i	−0.00959757	+	0.0358186i
$853$	−26.7268	+	26.7268i	−0.915110	+	0.915110i	−0.996669	−	0.0815587i	$-0.974010\pi$
$853$	−26.7268	+	26.7268i	−0.915110	+	0.915110i	0.0815587	+	0.996669i	$0.474010\pi$
$854$		0			0
$855$	−1.29289	−	0.0918831i	−0.0442160	−	0.00314234i
$856$	2.58579	+	4.47871i	0.0883804	+	0.153079i
$857$	15.6519	−	4.19391i	0.534658	−	0.143261i	0.0186197	−	0.999827i	$-0.494073\pi$
$857$	15.6519	−	4.19391i	0.534658	−	0.143261i	0.516038	+	0.856565i	$0.327406\pi$
$858$	30.2467	−	8.10458i	1.03261	−	0.276686i
$859$	20.3366	+	35.2241i	0.693876	+	1.20183i	0.970558	+	0.240867i	$0.0774319\pi$
$859$	20.3366	+	35.2241i	0.693876	+	1.20183i	−0.276682	+	0.960962i	$0.589235\pi$
$860$	8.28772	+	9.55582i	0.282609	+	0.325851i
$861$		0			0
$862$	−4.00000	+	4.00000i	−0.136241	+	0.136241i
$863$	−0.894438	+	3.33809i	−0.0304470	+	0.113630i	−0.979477	−	0.201556i	$-0.935400\pi$
$863$	−0.894438	+	3.33809i	−0.0304470	+	0.113630i	0.949030	+	0.315186i	$0.102067\pi$
$864$	2.38896	−	4.13779i	0.0812739	−	0.140771i
$865$	41.2630	−	7.97210i	1.40298	−	0.271060i
$866$	12.8017	−	7.39104i	0.435018	−	0.251158i
$867$	−13.4755	−	13.4755i	−0.457652	−	0.457652i
$868$		0			0
$869$		−	14.3431i		−	0.486558i
$870$	3.07812	−	1.49697i	0.104358	−	0.0507522i
$871$	76.9431	+	44.4231i	2.60712	+	1.50522i
$872$	−3.14262	−	11.7284i	−0.106422	−	0.397174i
$873$	−2.59839	−	0.696236i	−0.0879421	−	0.0235640i
$874$	0.819760			0.0277288
$875$		0			0
$876$	−10.8284			−0.365859
$877$	29.4465	+	7.89017i	0.994338	+	0.266432i	0.719072	−	0.694936i	$-0.244567\pi$
$877$	29.4465	+	7.89017i	0.994338	+	0.266432i	0.275267	+	0.961368i	$0.411234\pi$
$878$	−3.59380	−	13.4123i	−0.121285	−	0.452642i
$879$	−5.40629	−	3.12132i	−0.182349	−	0.105280i
$880$	−5.68762	+	2.76605i	−0.191730	+	0.0932434i
$881$			13.5140i			0.455297i	0.973743	+	0.227649i	$0.0731038\pi$
$881$			13.5140i			0.455297i	−0.973743	+	0.227649i	$0.926896\pi$
$882$		0			0
$883$	−28.8284	−	28.8284i	−0.970154	−	0.970154i	0.0294135	−	0.999567i	$-0.490636\pi$
$883$	−28.8284	−	28.8284i	−0.970154	−	0.970154i	−0.999567	+	0.0294135i	$0.990636\pi$
$884$	−27.1185	+	15.6569i	−0.912093	+	0.526597i
$885$	37.4790	−	7.24103i	1.25984	−	0.243404i
$886$	−2.92893	+	5.07306i	−0.0983994	+	0.170433i
$887$	11.9136	−	44.4623i	0.400021	−	1.49290i	−0.413036	−	0.910715i	$-0.635532\pi$
$887$	11.9136	−	44.4623i	0.400021	−	1.49290i	0.813057	−	0.582184i	$-0.197802\pi$
$888$	−4.77791	+	4.77791i	−0.160336	+	0.160336i
$889$		0			0
$890$	16.6274	+	19.1716i	0.557352	+	0.642633i
$891$	−14.2426	−	24.6690i	−0.477146	−	0.826442i
$892$	−9.23021	+	2.47323i	−0.309050	+	0.0828098i
$893$	−2.06914	+	0.554425i	−0.0692413	+	0.0185531i
$894$	15.9958	+	27.7055i	0.534979	+	0.926611i
$895$	−30.4608	−	2.16478i	−1.01819	−	0.0723608i
$896$		0			0
$897$	−4.58579	+	4.58579i	−0.153115	+	0.153115i
$898$	6.64048	−	24.7826i	0.221596	−	0.827007i
$899$	0.634051	−	1.09821i	0.0211468	−	0.0366273i
$900$	−1.27878	+	1.62912i	−0.0426260	+	0.0543041i
$901$	−52.7597	+	30.4608i	−1.75768	+	1.01480i
$902$	−7.39104	−	7.39104i	−0.246095	−	0.246095i
$903$		0			0
$904$			1.65685i			0.0551062i
$905$	−8.59658	−	17.6765i	−0.285760	−	0.587587i
$906$	−14.1273	−	8.15640i	−0.469348	−	0.270978i
$907$	4.08908	+	15.2607i	0.135776	+	0.506722i	0.999994	+	0.00360386i	$0.00114715\pi$
$907$	4.08908	+	15.2607i	0.135776	+	0.506722i	−0.864218	+	0.503118i	$0.832186\pi$
$908$	−11.4481	−	3.06750i	−0.379918	−	0.101799i
$909$	−1.13679			−0.0377048
$910$		0			0
$911$	−28.1421			−0.932391			−0.466195	−	0.884682i	$-0.654376\pi$
$911$	−28.1421			−0.932391			−0.466195	+	0.884682i	$0.654376\pi$
$912$	2.49768	+	0.669251i	0.0827064	+	0.0221611i
$913$	−5.50674	−	20.5514i	−0.182247	−	0.680154i
$914$	2.02922	+	1.17157i	0.0671208	+	0.0387522i
$915$	25.1486	+	8.69130i	0.831386	+	0.287326i
$916$			7.70806i			0.254682i
$917$		0			0
$918$	17.6569	+	17.6569i	0.582763	+	0.582763i
$919$	−7.26143	+	4.19239i	−0.239532	+	0.138294i	−0.614962	−	0.788557i	$-0.710829\pi$
$919$	−7.26143	+	4.19239i	−0.239532	+	0.138294i	0.375429	+	0.926851i	$0.377495\pi$
$920$	0.733696	−	1.08509i	0.0241892	−	0.0357743i
$921$	−30.2635	+	52.4178i	−0.997215	+	1.72723i
$922$	−8.80633	+	32.8657i	−0.290021	+	1.08237i
$923$	−2.48181	+	2.48181i	−0.0816898	+	0.0816898i
$924$		0			0
$925$	−14.6274	+	10.9706i	−0.480947	+	0.360710i
$926$	−9.17157	−	15.8856i	−0.301397	−	0.522034i
$927$	5.66062	−	1.51676i	0.185919	−	0.0498169i
$928$	−0.800199	+	0.214413i	−0.0262678	+	0.00703844i
$929$	−16.6298	−	28.8037i	−0.545607	−	0.945019i	−0.998568	−	0.0534890i	$-0.982966\pi$
$929$	−16.6298	−	28.8037i	−0.545607	−	0.945019i	0.452961	−	0.891530i	$-0.350368\pi$
$930$	−0.448342	+	6.30864i	−0.0147017	+	0.206869i
$931$		0			0
$932$	3.00000	−	3.00000i	0.0982683	−	0.0982683i
$933$	−1.64173	+	6.12701i	−0.0537477	+	0.200589i
$934$	−12.3275	+	21.3518i	−0.403367	+	0.698652i
$935$	−6.27010	−	32.4536i	−0.205054	−	1.06135i
$936$	−2.14931	+	1.24090i	−0.0702524	+	0.0405602i
$937$	17.7666	+	17.7666i	0.580410	+	0.580410i	0.935016	−	0.354606i	$-0.115385\pi$
$937$	17.7666	+	17.7666i	0.580410	+	0.580410i	−0.354606	+	0.935016i	$0.615385\pi$
$938$		0			0
$939$			17.6569i			0.576210i
$940$	−1.11804	+	3.23508i	−0.0364663	+	0.105517i
$941$	20.1870	+	11.6549i	0.658076	+	0.379940i	0.791544	−	0.611113i	$-0.209278\pi$
$941$	20.1870	+	11.6549i	0.658076	+	0.379940i	−0.133467	+	0.991053i	$0.542611\pi$
$942$	−6.91770	−	25.8172i	−0.225391	−	0.841170i
$943$	2.09102	+	0.560287i	0.0680930	+	0.0182455i
$944$	−9.23880			−0.300697
$945$		0			0
$946$	−16.0000			−0.520205
$947$	−31.3784	−	8.40781i	−1.01966	−	0.273217i	−0.290000	−	0.957027i	$-0.593655\pi$
$947$	−31.3784	−	8.40781i	−1.01966	−	0.273217i	−0.729660	+	0.683810i	$0.760322\pi$
$948$	2.42516	+	9.05083i	0.0787656	+	0.293957i
$949$	−30.4085	−	17.5563i	−0.987101	−	0.569903i
$950$	6.43463	+	2.74860i	0.208767	+	0.0891763i
$951$			57.2261i			1.85568i
$952$		0			0
$953$	23.1421	+	23.1421i	0.749647	+	0.749647i	0.974413	−	0.224766i	$-0.0721616\pi$
$953$	23.1421	+	23.1421i	0.749647	+	0.749647i	−0.224766	+	0.974413i	$0.572162\pi$
$954$	−4.18154	+	2.41421i	−0.135382	+	0.0781631i
$955$	−3.25527	−	2.20109i	−0.105338	−	0.0712255i
$956$	−3.24264	+	5.61642i	−0.104874	+	0.181648i
$957$	−1.12057	+	4.18204i	−0.0362230	+	0.135186i
$958$	−7.83938	+	7.83938i	−0.253279	+	0.253279i
$959$		0			0
$960$	3.12132	−	2.70711i	0.100740	−	0.0873715i
$961$	−14.3284	−	24.8176i	−0.462207	−	0.800567i
$962$	−21.1639	+	5.67085i	−0.682351	+	0.182835i
$963$	−2.06914	+	0.554425i	−0.0666772	+	0.0178661i
$964$	3.37849	+	5.85172i	0.108814	+	0.188471i
$965$	−19.6913	+	17.0782i	−0.633885	+	0.549766i
$966$		0			0
$967$	−2.21320	+	2.21320i	−0.0711718	+	0.0711718i	−0.741797	−	0.670625i	$-0.766026\pi$
$967$	−2.21320	+	2.21320i	−0.0711718	+	0.0711718i	0.670625	+	0.741797i	$0.266026\pi$
$968$	−0.776457	+	2.89778i	−0.0249563	+	0.0931381i
$969$	−6.75699	+	11.7034i	−0.217066	+	0.375969i
$970$	12.0299	+	8.13416i	0.386257	+	0.261172i
$971$	16.0492	−	9.26599i	0.515042	−	0.297360i	−0.219862	−	0.975531i	$-0.570561\pi$
$971$	16.0492	−	9.26599i	0.515042	−	0.297360i	0.734904	+	0.678171i	$0.237227\pi$
$972$	3.02301	+	3.02301i	0.0969630	+	0.0969630i
$973$		0			0
$974$			1.55635i			0.0498686i
$975$	−51.3715	+	20.6199i	−1.64521	+	0.660365i
$976$	−5.57717	−	3.21998i	−0.178521	−	0.103069i
$977$	−9.45386	−	35.2823i	−0.302456	−	1.12878i	−0.935113	−	0.354349i	$-0.884703\pi$
$977$	−9.45386	−	35.2823i	−0.302456	−	1.12878i	0.632658	−	0.774432i	$-0.281964\pi$
$978$	−34.4711	−	9.23650i	−1.10226	−	0.295351i
$979$	−32.1003			−1.02593
$980$		0			0
$981$	5.02944			0.160578
$982$	24.3139	+	6.51488i	0.775887	+	0.207898i
$983$	−10.5212	−	39.2656i	−0.335573	−	1.25238i	−0.903246	−	0.429123i	$-0.858823\pi$
$983$	−10.5212	−	39.2656i	−0.335573	−	1.25238i	0.567673	−	0.823254i	$-0.307844\pi$
$984$	5.91359	+	3.41421i	0.188518	+	0.108841i
$985$	0.605077	−	1.75081i	0.0192794	−	0.0557855i
$986$		−	4.32957i		−	0.137882i
$987$		0			0
$988$	5.92893	+	5.92893i	0.188624	+	0.188624i
$989$	2.86976	−	1.65685i	0.0912529	−	0.0526849i
$990$	−0.496946	−	2.57215i	−0.0157940	−	0.0817483i
$991$	16.2929	−	28.2201i	0.517561	−	0.896442i	−0.482231	−	0.876044i	$-0.660173\pi$
$991$	16.2929	−	28.2201i	0.517561	−	0.896442i	0.999792	−	0.0203976i	$-0.00649321\pi$
$992$	0.396183	−	1.47858i	0.0125788	−	0.0469448i
$993$	−30.4608	+	30.4608i	−0.966645	+	0.966645i
$994$		0			0
$995$	4.44365	−	62.5269i	0.140873	−	1.98224i
$996$	6.94975	+	12.0373i	0.220211	+	0.381417i
$997$	−0.634209	+	0.169936i	−0.0200856	+	0.00538192i	−0.268848	−	0.963183i	$-0.586643\pi$
$997$	−0.634209	+	0.169936i	−0.0200856	+	0.00538192i	0.248762	+	0.968565i	$0.419976\pi$
$998$	−7.25866	+	1.94495i	−0.229769	+	0.0615664i
$999$	8.73606	+	15.1313i	0.276397	+	0.478733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.l.a.423.3		16
5.2	odd	4	inner	490.2.l.a.227.1		16
7.2	even	3	inner	490.2.l.a.313.2		16
7.3	odd	6		70.2.g.a.13.2	yes	8
7.4	even	3		70.2.g.a.13.1	✓	8
7.5	odd	6	inner	490.2.l.a.313.1		16
7.6	odd	2	inner	490.2.l.a.423.4		16
21.11	odd	6		630.2.p.a.433.4		8
21.17	even	6		630.2.p.a.433.3		8
28.3	even	6		560.2.bj.c.433.1		8
28.11	odd	6		560.2.bj.c.433.4		8
35.2	odd	12	inner	490.2.l.a.117.4		16
35.3	even	12		350.2.g.a.307.4		8
35.4	even	6		350.2.g.a.293.4		8
35.12	even	12	inner	490.2.l.a.117.3		16
35.17	even	12		70.2.g.a.27.1	yes	8
35.18	odd	12		350.2.g.a.307.3		8
35.24	odd	6		350.2.g.a.293.3		8
35.27	even	4	inner	490.2.l.a.227.2		16
35.32	odd	12		70.2.g.a.27.2	yes	8
105.17	odd	12		630.2.p.a.307.4		8
105.32	even	12		630.2.p.a.307.3		8
140.67	even	12		560.2.bj.c.97.1		8
140.87	odd	12		560.2.bj.c.97.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.g.a.13.1	✓	8	7.4	even	3
70.2.g.a.13.2	yes	8	7.3	odd	6
70.2.g.a.27.1	yes	8	35.17	even	12
70.2.g.a.27.2	yes	8	35.32	odd	12
350.2.g.a.293.3		8	35.24	odd	6
350.2.g.a.293.4		8	35.4	even	6
350.2.g.a.307.3		8	35.18	odd	12
350.2.g.a.307.4		8	35.3	even	12
490.2.l.a.117.3		16	35.12	even	12	inner
490.2.l.a.117.4		16	35.2	odd	12	inner
490.2.l.a.227.1		16	5.2	odd	4	inner
490.2.l.a.227.2		16	35.27	even	4	inner
490.2.l.a.313.1		16	7.5	odd	6	inner
490.2.l.a.313.2		16	7.2	even	3	inner
490.2.l.a.423.3		16	1.1	even	1	trivial
490.2.l.a.423.4		16	7.6	odd	2	inner
560.2.bj.c.97.1		8	140.67	even	12
560.2.bj.c.97.4		8	140.87	odd	12
560.2.bj.c.433.1		8	28.3	even	6
560.2.bj.c.433.4		8	28.11	odd	6
630.2.p.a.307.3		8	105.32	even	12
630.2.p.a.307.4		8	105.17	odd	12
630.2.p.a.433.3		8	21.17	even	6
630.2.p.a.433.4		8	21.11	odd	6

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.l (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-0.478235 - 1.78480i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.01088 - 0.977945i) q^{5} -1.84776i q^{6} +(0.707107 + 0.707107i) q^{8} +(-0.358719 + 0.207107i) q^{9} +(2.19547 - 0.424170i) q^{10} +(-1.41421 + 2.44949i) q^{11} +(0.478235 - 1.78480i) q^{12} +(4.23671 - 4.23671i) q^{13} +(-2.70711 - 3.12132i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-5.04817 + 1.35265i) q^{17} +(-0.400100 + 0.107206i) q^{18} +(0.699709 + 1.21193i) q^{19} +(2.23044 + 0.158513i) q^{20} +(-2.00000 + 2.00000i) q^{22} +(0.151613 - 0.565826i) q^{23} +(0.923880 - 1.60021i) q^{24} +(3.08725 - 3.93305i) q^{25} +(5.18889 - 2.99581i) q^{26} +(-3.37849 - 3.37849i) q^{27} +0.828427i q^{29} +(-1.80701 - 3.71561i) q^{30} +(-1.32565 - 0.765367i) q^{31} +(0.258819 + 0.965926i) q^{32} +(5.04817 + 1.35265i) q^{33} -5.22625 q^{34} -0.414214 q^{36} +(-3.53225 - 0.946464i) q^{37} +(0.362196 + 1.35173i) q^{38} +(-9.58783 - 5.53553i) q^{39} +(2.11342 + 0.730392i) q^{40} +3.69552i q^{41} +(4.00000 + 4.00000i) q^{43} +(-2.44949 + 1.41421i) q^{44} +(-0.518801 + 0.767274i) q^{45} +(0.292893 - 0.507306i) q^{46} +(-0.396183 + 1.47858i) q^{47} +(1.30656 - 1.30656i) q^{48} +(4.00000 - 3.00000i) q^{50} +(4.82843 + 8.36308i) q^{51} +(5.78746 - 1.55075i) q^{52} +(11.2597 - 3.01702i) q^{53} +(-2.38896 - 4.13779i) q^{54} +(-0.448342 + 6.30864i) q^{55} +(1.82843 - 1.82843i) q^{57} +(-0.214413 + 0.800199i) q^{58} +(-4.61940 + 8.00103i) q^{59} +(-0.783763 - 4.05670i) q^{60} +(-5.57717 + 3.21998i) q^{61} +(-1.08239 - 1.08239i) q^{62} +1.00000i q^{64} +(4.37623 - 12.6628i) q^{65} +(4.52607 + 2.61313i) q^{66} +(3.83788 + 14.3232i) q^{67} +(-5.04817 - 1.35265i) q^{68} -1.08239 q^{69} -0.585786 q^{71} +(-0.400100 - 0.107206i) q^{72} +(-1.51676 - 5.66062i) q^{73} +(-3.16693 - 1.82843i) q^{74} +(-8.49614 - 3.62919i) q^{75} +1.39942i q^{76} +(-7.82843 - 7.82843i) q^{78} +(-4.39167 + 2.53553i) q^{79} +(1.85236 + 1.25250i) q^{80} +(-5.03553 + 8.72180i) q^{81} +(-0.956470 + 3.56960i) q^{82} +(-5.31911 + 5.31911i) q^{83} +(-8.82843 + 7.65685i) q^{85} +(2.82843 + 4.89898i) q^{86} +(1.47858 - 0.396183i) q^{87} +(-2.73205 + 0.732051i) q^{88} +(5.67459 + 9.82868i) q^{89} +(-0.699709 + 0.606854i) q^{90} +(0.414214 - 0.414214i) q^{92} +(-0.732051 + 2.73205i) q^{93} +(-0.765367 + 1.32565i) q^{94} +(2.59223 + 1.75277i) q^{95} +(1.60021 - 0.923880i) q^{96} +(4.59220 + 4.59220i) q^{97} -1.17157i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{15} + 8 q^{16} - 8 q^{18} - 32 q^{22} + 8 q^{23} - 16 q^{30} + 16 q^{36} - 32 q^{37} + 64 q^{43} + 16 q^{46} + 64 q^{50} + 32 q^{51} + 32 q^{53} - 16 q^{57} + 16 q^{58} + 8 q^{60} - 8 q^{65}+ \cdots - 64 q^{95}+O(q^{100}) \) 16 * q - 32 * q^15 + 8 * q^16 - 8 * q^18 - 32 * q^22 + 8 * q^23 - 16 * q^30 + 16 * q^36 - 32 * q^37 + 64 * q^43 + 16 * q^46 + 64 * q^50 + 32 * q^51 + 32 * q^53 - 16 * q^57 + 16 * q^58 + 8 * q^60 - 8 * q^65 - 16 * q^67 - 32 * q^71 - 8 * q^72 - 80 * q^78 - 24 * q^81 - 96 * q^85 - 16 * q^88 - 16 * q^92 + 16 * q^93 - 64 * q^95

Introduction

L-functions

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