LMFDB - Embedded newform 490.2.l.c.117.2

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:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			117.2
Root			$-1.01089 - 0.750919i$ of defining polynomial
Character	$\chi$	$=$	490.117
Dual form			490.2.l.c.423.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(0.0749894 - 0.279864i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.20382 + 0.378409i) q^{5} +0.289737i q^{6} +(-0.707107 + 0.707107i) q^{8} +(2.52538 + 1.45803i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(0.0749894 - 0.279864i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.20382 + 0.378409i) q^{5} +0.289737i q^{6} +(-0.707107 + 0.707107i) q^{8} +(2.52538 + 1.45803i) q^{9} +(2.03078 - 0.935904i) q^{10} +(-2.81288 - 4.87205i) q^{11} +(-0.0749894 - 0.279864i) q^{12} +(1.42962 + 1.42962i) q^{13} +(-0.0593598 + 0.645146i) q^{15} +(0.500000 - 0.866025i) q^{16} +(5.12784 + 1.37400i) q^{17} +(-2.81669 - 0.754730i) q^{18} +(1.94590 - 3.37040i) q^{19} +(-1.71936 + 1.42962i) q^{20} +(3.97801 + 3.97801i) q^{22} +(-0.290892 - 1.08562i) q^{23} +(0.144868 + 0.250919i) q^{24} +(4.71361 - 1.66789i) q^{25} +(-1.75092 - 1.01089i) q^{26} +(1.21205 - 1.21205i) q^{27} -3.15502i q^{29} +(-0.109639 - 0.638527i) q^{30} +(3.33287 - 1.92423i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.57445 + 0.421872i) q^{33} -5.30873 q^{34} +2.91605 q^{36} +(4.86824 - 1.30444i) q^{37} +(-1.00727 + 3.75919i) q^{38} +(0.507306 - 0.292893i) q^{39} +(1.29076 - 1.82591i) q^{40} -7.21050i q^{41} +(1.85669 - 1.85669i) q^{43} +(-4.87205 - 2.81288i) q^{44} +(-6.11719 - 2.25760i) q^{45} +(0.561961 + 0.973344i) q^{46} +(1.52590 + 5.69475i) q^{47} +(-0.204875 - 0.204875i) q^{48} +(-4.12132 + 2.83103i) q^{50} +(0.769067 - 1.33206i) q^{51} +(1.95290 + 0.523277i) q^{52} +(1.33599 + 0.357978i) q^{53} +(-0.857049 + 1.48445i) q^{54} +(8.04270 + 9.67269i) q^{55} +(-0.797333 - 0.797333i) q^{57} +(0.816578 + 3.04751i) q^{58} +(-2.73923 - 4.74448i) q^{59} +(0.271166 + 0.588393i) q^{60} +(3.99172 + 2.30462i) q^{61} +(-2.72127 + 2.72127i) q^{62} -1.00000i q^{64} +(-3.69160 - 2.60964i) q^{65} +(1.41161 - 0.814995i) q^{66} +(0.218698 - 0.816193i) q^{67} +(5.12784 - 1.37400i) q^{68} -0.325641 q^{69} +4.77710 q^{71} +(-2.81669 + 0.754730i) q^{72} +(-1.45256 + 5.42104i) q^{73} +(-4.36475 + 2.51999i) q^{74} +(-0.113311 - 1.44425i) q^{75} -3.89180i q^{76} +(-0.414214 + 0.414214i) q^{78} +(5.41079 + 3.12392i) q^{79} +(-0.774197 + 2.09777i) q^{80} +(4.12576 + 7.14603i) q^{81} +(1.86622 + 6.96481i) q^{82} +(-5.67281 - 5.67281i) q^{83} +(-11.8207 - 1.08763i) q^{85} +(-1.31288 + 2.27397i) q^{86} +(-0.882976 - 0.236593i) q^{87} +(5.43407 + 1.45605i) q^{88} +(5.96090 - 10.3246i) q^{89} +(6.49307 + 0.597426i) q^{90} +(-0.794732 - 0.794732i) q^{92} +(-0.288594 - 1.07705i) q^{93} +(-2.94782 - 5.10577i) q^{94} +(-3.01302 + 8.16409i) q^{95} +(0.250919 + 0.144868i) q^{96} +(6.63103 - 6.63103i) q^{97} -16.4050i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5}+O(q^{10}) $ 16 * q + 12 * q^5	$ 16 q + 12 q^{5} + 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} + 36 q^{17} - 8 q^{18} - 8 q^{22} - 4 q^{23} + 12 q^{25} - 12 q^{26} + 20 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} - 8 q^{46} - 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} + 8 q^{57} - 32 q^{58} + 8 q^{60} + 12 q^{61} - 8 q^{65} + 32 q^{67} + 36 q^{68} + 16 q^{71} - 8 q^{72} + 12 q^{73} + 48 q^{75} + 16 q^{78} + 12 q^{80} + 48 q^{82} + 24 q^{85} + 12 q^{86} + 24 q^{87} - 4 q^{88} + 8 q^{92} + 28 q^{93} + 20 q^{95} - 12 q^{96}+O(q^{100}) $ 16 * q + 12 * q^5 + 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 + 36 * q^17 - 8 * q^18 - 8 * q^22 - 4 * q^23 + 12 * q^25 - 12 * q^26 + 20 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^36 + 4 * q^37 - 24 * q^38 - 8 * q^43 + 12 * q^45 - 8 * q^46 - 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 + 8 * q^57 - 32 * q^58 + 8 * q^60 + 12 * q^61 - 8 * q^65 + 32 * q^67 + 36 * q^68 + 16 * q^71 - 8 * q^72 + 12 * q^73 + 48 * q^75 + 16 * q^78 + 12 * q^80 + 48 * q^82 + 24 * q^85 + 12 * q^86 + 24 * q^87 - 4 * q^88 + 8 * q^92 + 28 * q^93 + 20 * q^95 - 12 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	0.0749894	−	0.279864i	0.0432952	−	0.161580i	−0.940894	−	0.338702i	$-0.890012\pi$
$3$	0.0749894	−	0.279864i	0.0432952	−	0.161580i	0.984189	+	0.177122i	$0.0566788\pi$
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.20382	+	0.378409i	−0.985577	+	0.169230i
$5$	−2.20382	+	0.378409i	−0.985577	+	0.169230i
$6$			0.289737i			0.118285i
$7$		0			0
$7$		0			0
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.52538	+	1.45803i	0.841792	+	0.486009i
$10$	2.03078	−	0.935904i	0.642190	−	0.295959i
$11$	−2.81288	−	4.87205i	−0.848115	−	1.46898i	−0.882888	−	0.469583i	$-0.844404\pi$
$11$	−2.81288	−	4.87205i	−0.848115	−	1.46898i	0.0347729	−	0.999395i	$-0.488929\pi$
$12$	−0.0749894	−	0.279864i	−0.0216476	−	0.0807899i
$13$	1.42962	+	1.42962i	0.396505	+	0.396505i	0.876998	−	0.480493i	$-0.159542\pi$
$13$	1.42962	+	1.42962i	0.396505	+	0.396505i	−0.480493	+	0.876998i	$0.659542\pi$
$14$		0			0
$15$	−0.0593598	+	0.645146i	−0.0153266	+	0.166576i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	5.12784	+	1.37400i	1.24368	+	0.333244i	0.819893	−	0.572516i	$-0.194033\pi$
$17$	5.12784	+	1.37400i	1.24368	+	0.333244i	0.423790	+	0.905760i	$0.360699\pi$
$18$	−2.81669	−	0.754730i	−0.663900	−	0.177892i
$19$	1.94590	−	3.37040i	0.446420	−	0.773223i	−0.551729	−	0.834023i	$-0.686032\pi$
$19$	1.94590	−	3.37040i	0.446420	−	0.773223i	0.998150	+	0.0608002i	$0.0193652\pi$
$20$	−1.71936	+	1.42962i	−0.384460	+	0.319673i
$21$		0			0
$22$	3.97801	+	3.97801i	0.848115	+	0.848115i
$23$	−0.290892	−	1.08562i	−0.0606552	−	0.226368i	0.928944	−	0.370220i	$-0.120718\pi$
$23$	−0.290892	−	1.08562i	−0.0606552	−	0.226368i	−0.989599	+	0.143852i	$0.954051\pi$
$24$	0.144868	+	0.250919i	0.0295711	+	0.0512187i
$25$	4.71361	−	1.66789i	0.942723	−	0.333577i
$26$	−1.75092	−	1.01089i	−0.343384	−	0.198253i
$27$	1.21205	−	1.21205i	0.233259	−	0.233259i
$28$		0			0
$29$		−	3.15502i		−	0.585872i	−0.956132	−	0.292936i	$-0.905368\pi$
$29$		−	3.15502i		−	0.585872i	0.956132	−	0.292936i	$-0.0946322\pi$
$30$	−0.109639	−	0.638527i	−0.0200172	−	0.116579i
$31$	3.33287	−	1.92423i	0.598601	−	0.345602i	−0.169890	−	0.985463i	$-0.554341\pi$
$31$	3.33287	−	1.92423i	0.598601	−	0.345602i	0.768491	+	0.639861i	$0.221008\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−1.57445	+	0.421872i	−0.274076	+	0.0734386i
$34$	−5.30873			−0.910440
$35$		0			0
$36$	2.91605			0.486009
$37$	4.86824	−	1.30444i	0.800334	−	0.214449i	0.164603	−	0.986360i	$-0.447366\pi$
$37$	4.86824	−	1.30444i	0.800334	−	0.214449i	0.635731	+	0.771911i	$0.280699\pi$
$38$	−1.00727	+	3.75919i	−0.163401	+	0.609822i
$39$	0.507306	−	0.292893i	0.0812340	−	0.0469005i
$40$	1.29076	−	1.82591i	0.204087	−	0.288702i
$41$		−	7.21050i		−	1.12609i	−0.826426	−	0.563046i	$-0.809629\pi$
$41$		−	7.21050i		−	1.12609i	0.826426	−	0.563046i	$-0.190371\pi$
$42$		0			0
$43$	1.85669	−	1.85669i	0.283143	−	0.283143i	−0.551218	−	0.834361i	$-0.685837\pi$
$43$	1.85669	−	1.85669i	0.283143	−	0.283143i	0.834361	+	0.551218i	$0.185837\pi$
$44$	−4.87205	−	2.81288i	−0.734489	−	0.424058i
$45$	−6.11719	−	2.25760i	−0.911897	−	0.336543i
$46$	0.561961	+	0.973344i	0.0828566	+	0.143512i
$47$	1.52590	+	5.69475i	0.222576	+	0.830665i	0.983361	+	0.181661i	$0.0581474\pi$
$47$	1.52590	+	5.69475i	0.222576	+	0.830665i	−0.760785	+	0.649004i	$0.775186\pi$
$48$	−0.204875	−	0.204875i	−0.0295711	−	0.0295711i
$49$		0			0
$50$	−4.12132	+	2.83103i	−0.582843	+	0.400368i
$51$	0.769067	−	1.33206i	0.107691	−	0.186526i
$52$	1.95290	+	0.523277i	0.270818	+	0.0725655i
$53$	1.33599	+	0.357978i	0.183512	+	0.0491720i	0.349405	−	0.936972i	$-0.386384\pi$
$53$	1.33599	+	0.357978i	0.183512	+	0.0491720i	−0.165892	+	0.986144i	$0.553050\pi$
$54$	−0.857049	+	1.48445i	−0.116630	+	0.202008i
$55$	8.04270	+	9.67269i	1.08448	+	1.30426i
$56$		0			0
$57$	−0.797333	−	0.797333i	−0.105609	−	0.105609i
$58$	0.816578	+	3.04751i	0.107222	+	0.400158i
$59$	−2.73923	−	4.74448i	−0.356617	−	0.617679i	0.630776	−	0.775965i	$-0.282737\pi$
$59$	−2.73923	−	4.74448i	−0.356617	−	0.617679i	−0.987393	+	0.158286i	$0.949403\pi$
$60$	0.271166	+	0.588393i	0.0350074	+	0.0759612i
$61$	3.99172	+	2.30462i	0.511088	+	0.295077i	0.733281	−	0.679926i	$-0.237988\pi$
$61$	3.99172	+	2.30462i	0.511088	+	0.295077i	−0.222193	+	0.975003i	$0.571322\pi$
$62$	−2.72127	+	2.72127i	−0.345602	+	0.345602i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−3.69160	−	2.60964i	−0.457887	−	0.323686i
$66$	1.41161	−	0.814995i	0.173758	−	0.100319i
$67$	0.218698	−	0.816193i	0.0267182	−	0.0997138i	−0.951279	−	0.308331i	$-0.900230\pi$
$67$	0.218698	−	0.816193i	0.0267182	−	0.0997138i	0.977997	+	0.208617i	$0.0668963\pi$
$68$	5.12784	−	1.37400i	0.621842	−	0.166622i
$69$	−0.325641			−0.0392026
$70$		0			0
$71$	4.77710			0.566937			0.283469	−	0.958982i	$-0.408515\pi$
$71$	4.77710			0.566937			0.283469	+	0.958982i	$0.408515\pi$
$72$	−2.81669	+	0.754730i	−0.331950	+	0.0889458i
$73$	−1.45256	+	5.42104i	−0.170010	+	0.634485i	0.827338	+	0.561704i	$0.189854\pi$
$73$	−1.45256	+	5.42104i	−0.170010	+	0.634485i	−0.997348	+	0.0727807i	$0.976813\pi$
$74$	−4.36475	+	2.51999i	−0.507391	+	0.292943i
$75$	−0.113311	−	1.44425i	−0.0130840	−	0.166767i
$76$		−	3.89180i		−	0.446420i
$77$		0			0
$78$	−0.414214	+	0.414214i	−0.0469005	+	0.0469005i
$79$	5.41079	+	3.12392i	0.608761	+	0.351469i	0.772481	−	0.635038i	$-0.219016\pi$
$79$	5.41079	+	3.12392i	0.608761	+	0.351469i	−0.163719	+	0.986507i	$0.552349\pi$
$80$	−0.774197	+	2.09777i	−0.0865578	+	0.234537i
$81$	4.12576	+	7.14603i	0.458418	+	0.794003i
$82$	1.86622	+	6.96481i	0.206089	+	0.769135i
$83$	−5.67281	−	5.67281i	−0.622672	−	0.622672i	0.323542	−	0.946214i	$-0.395126\pi$
$83$	−5.67281	−	5.67281i	−0.622672	−	0.622672i	−0.946214	+	0.323542i	$0.895126\pi$
$84$		0			0
$85$	−11.8207	−	1.08763i	−1.28214	−	0.117970i
$86$	−1.31288	+	2.27397i	−0.141571	+	0.245209i
$87$	−0.882976	−	0.236593i	−0.0946650	−	0.0253654i
$88$	5.43407	+	1.45605i	0.579273	+	0.155216i
$89$	5.96090	−	10.3246i	0.631855	−	1.09440i	−0.355318	−	0.934746i	$-0.615627\pi$
$89$	5.96090	−	10.3246i	0.631855	−	1.09440i	0.987172	−	0.159659i	$-0.0510393\pi$
$90$	6.49307	+	0.597426i	0.684429	+	0.0629742i
$91$		0			0
$92$	−0.794732	−	0.794732i	−0.0828566	−	0.0828566i
$93$	−0.288594	−	1.07705i	−0.0299258	−	0.111685i
$94$	−2.94782	−	5.10577i	−0.304044	−	0.526620i
$95$	−3.01302	+	8.16409i	−0.309129	+	0.837618i
$96$	0.250919	+	0.144868i	0.0256094	+	0.0147856i
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	−0.285191	−	0.958471i	$-0.592057\pi$
$97$	6.63103	−	6.63103i	0.673279	−	0.673279i	0.958471	+	0.285191i	$0.0920572\pi$
$98$		0			0
$99$		−	16.4050i		−	1.64877i
$100$	3.24817	−	3.80124i	0.324817	−	0.380124i
$101$	−13.9423	+	8.04960i	−1.38731	+	0.800965i	−0.993012	−	0.118016i	$-0.962347\pi$
$101$	−13.9423	+	8.04960i	−1.38731	+	0.800965i	−0.394301	+	0.918981i	$0.629013\pi$
$102$	−0.398099	+	1.48572i	−0.0394176	+	0.147109i
$103$	−18.9993	+	5.09084i	−1.87206	+	0.501616i	−0.872132	+	0.489271i	$0.837263\pi$
$103$	−18.9993	+	5.09084i	−1.87206	+	0.501616i	−0.999924	+	0.0123445i	$0.996071\pi$
$104$	−2.02179			−0.198253
$105$		0			0
$106$	−1.38312			−0.134340
$107$	−2.70557	+	0.724955i	−0.261557	+	0.0700840i	−0.387214	−	0.921990i	$-0.626563\pi$
$107$	−2.70557	+	0.724955i	−0.261557	+	0.0700840i	0.125657	+	0.992074i	$0.459896\pi$
$108$	0.443641	−	1.65569i	0.0426894	−	0.159319i
$109$	−5.11895	+	2.95543i	−0.490306	+	0.283078i	−0.724701	−	0.689063i	$-0.758022\pi$
$109$	−5.11895	+	2.95543i	−0.490306	+	0.283078i	0.234395	+	0.972141i	$0.424689\pi$
$110$	−10.2721	−	7.26150i	−0.979409	−	0.692356i
$111$		−	1.46027i		−	0.138602i
$112$		0			0
$113$	−13.5818	+	13.5818i	−1.27767	+	1.27767i	−0.335697	+	0.941970i	$0.608972\pi$
$113$	−13.5818	+	13.5818i	−1.27767	+	1.27767i	−0.941970	+	0.335697i	$0.891028\pi$
$114$	0.976529	+	0.563800i	0.0914604	+	0.0528047i
$115$	1.05188	+	2.28244i	0.0980886	+	0.212839i
$116$	−1.57751	−	2.73232i	−0.146468	−	0.253690i
$117$	1.52590	+	5.69475i	0.141070	+	0.526480i
$118$	3.87385	+	3.87385i	0.356617	+	0.356617i
$119$		0			0
$120$	−0.414214	−	0.498161i	−0.0378124	−	0.0454757i
$121$	−10.3246	+	17.8827i	−0.938599	+	1.62570i
$122$	−4.45219	−	1.19296i	−0.403082	−	0.108006i
$123$	−2.01796	−	0.540712i	−0.181954	−	0.0487543i
$124$	1.92423	−	3.33287i	0.172801	−	0.299300i
$125$	−9.75680	+	5.45939i	−0.872674	+	0.488303i
$126$		0			0
$127$	4.63487	+	4.63487i	0.411278	+	0.411278i	0.882184	−	0.470906i	$-0.156073\pi$
$127$	4.63487	+	4.63487i	0.411278	+	0.411278i	−0.470906	+	0.882184i	$0.656073\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−0.380390	−	0.658854i	−0.0334915	−	0.0580089i
$130$	4.24124	+	1.56526i	0.371981	+	0.137282i
$131$	6.66437	+	3.84768i	0.582269	+	0.336173i	0.762035	−	0.647536i	$-0.224201\pi$
$131$	6.66437	+	3.84768i	0.582269	+	0.336173i	−0.179766	+	0.983709i	$0.557534\pi$
$132$	−1.15258	+	1.15258i	−0.100319	+	0.100319i
$133$		0			0
$134$			0.844985i			0.0729956i
$135$	−2.21249	+	3.12979i	−0.190421	+	0.269369i
$136$	−4.59749	+	2.65436i	−0.394232	+	0.227610i
$137$	−2.28687	+	8.53471i	−0.195380	+	0.729170i	0.796788	+	0.604259i	$0.206531\pi$
$137$	−2.28687	+	8.53471i	−0.195380	+	0.729170i	−0.992168	+	0.124910i	$0.960136\pi$
$138$	0.314545	−	0.0842822i	0.0267759	−	0.00717458i
$139$	−11.0631			−0.938361			−0.469180	−	0.883102i	$-0.655451\pi$
$139$	−11.0631			−0.938361			−0.469180	+	0.883102i	$0.655451\pi$
$140$		0			0
$141$	1.70818			0.143855
$142$	−4.61432	+	1.23640i	−0.387225	+	0.103757i
$143$	2.94383	−	10.9865i	0.246176	−	0.918740i
$144$	2.52538	−	1.45803i	0.210448	−	0.121502i
$145$	1.19389	+	6.95307i	0.0991468	+	0.577421i
$146$		−	5.61227i		−	0.464475i
$147$		0			0
$148$	3.56380	−	3.56380i	0.292943	−	0.292943i
$149$	−4.37243	−	2.52443i	−0.358204	−	0.206809i	0.310089	−	0.950708i	$-0.399641\pi$
$149$	−4.37243	−	2.52443i	−0.358204	−	0.206809i	−0.668293	+	0.743899i	$0.732975\pi$
$150$	0.483248	+	1.36571i	0.0394571	+	0.111510i
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	−0.998479	−	0.0551270i	$-0.982444\pi$
$151$	−6.72142	−	11.6418i	−0.546981	−	0.947399i	0.451498	−	0.892272i	$-0.350890\pi$
$152$	1.00727	+	3.75919i	0.0817006	+	0.304911i
$153$	10.9464	+	10.9464i	0.884963	+	0.884963i
$154$		0			0
$155$	−6.61688	+	5.50184i	−0.531481	+	0.441918i
$156$	0.292893	−	0.507306i	0.0234502	−	0.0406170i
$157$	1.06529	+	0.285443i	0.0850191	+	0.0227808i	0.301078	−	0.953600i	$-0.402654\pi$
$157$	1.06529	+	0.285443i	0.0850191	+	0.0227808i	−0.216059	+	0.976380i	$0.569320\pi$
$158$	−6.03495	−	1.61706i	−0.480115	−	0.128646i
$159$	0.200370	−	0.347052i	0.0158904	−	0.0275230i
$160$	0.204875	−	2.22666i	0.0161968	−	0.176033i
$161$		0			0
$162$	−5.83471	−	5.83471i	−0.458418	−	0.458418i
$163$	−3.42705	−	12.7899i	−0.268428	−	1.00179i	−0.960119	−	0.279592i	$-0.909801\pi$
$163$	−3.42705	−	12.7899i	−0.268428	−	1.00179i	0.691691	−	0.722193i	$-0.256866\pi$
$164$	−3.60525	−	6.24448i	−0.281523	−	0.487612i
$165$	3.31016	−	1.52551i	0.257695	−	0.118761i
$166$	6.94775	+	4.01128i	0.539250	+	0.311336i
$167$	4.70680	−	4.70680i	0.364223	−	0.364223i	−0.501142	−	0.865365i	$-0.667087\pi$
$167$	4.70680	−	4.70680i	0.364223	−	0.364223i	0.865365	+	0.501142i	$0.167087\pi$
$168$		0			0
$169$		−	8.91237i		−	0.685567i
$170$	11.6995	−	2.00887i	0.897308	−	0.154073i
$171$	9.82827	−	5.67435i	0.751586	−	0.433929i
$172$	0.679597	−	2.53629i	0.0518188	−	0.193390i
$173$	6.81421	−	1.82586i	0.518075	−	0.138818i	0.00969875	−	0.999953i	$-0.496913\pi$
$173$	6.81421	−	1.82586i	0.518075	−	0.138818i	0.508376	+	0.861135i	$0.330246\pi$
$174$	0.914124			0.0692996
$175$		0			0
$176$	−5.62576			−0.424058
$177$	−1.53322	+	0.410826i	−0.115244	+	0.0308796i
$178$	−3.08559	+	11.5156i	−0.231275	+	0.863129i
$179$	1.91075	−	1.10317i	0.142816	−	0.0824550i	−0.426889	−	0.904304i	$-0.640391\pi$
$179$	1.91075	−	1.10317i	0.142816	−	0.0824550i	0.569706	+	0.821849i	$0.307057\pi$
$180$	−6.42644	+	1.10346i	−0.478999	+	0.0822470i
$181$			4.11867i			0.306139i	0.988215	+	0.153069i	$0.0489158\pi$
$181$			4.11867i			0.306139i	−0.988215	+	0.153069i	$0.951084\pi$
$182$		0			0
$183$	0.944318	−	0.944318i	0.0698060	−	0.0698060i
$184$	0.973344	+	0.561961i	0.0717559	+	0.0414283i
$185$	−10.2351	+	4.71693i	−0.752499	+	0.346796i
$186$	0.557521	+	0.965654i	0.0408794	+	0.0708052i
$187$	−7.72980	−	28.8480i	−0.565259	−	2.10957i
$188$	4.16885	+	4.16885i	0.304044	+	0.304044i
$189$		0			0
$190$	0.797333	−	8.66573i	0.0578446	−	0.628678i
$191$	8.60117	−	14.8977i	0.622359	−	1.07796i	−0.366686	−	0.930345i	$-0.619508\pi$
$191$	8.60117	−	14.8977i	0.622359	−	1.07796i	0.989045	−	0.147613i	$-0.0471589\pi$
$192$	−0.279864	−	0.0749894i	−0.0201975	−	0.00541190i
$193$	11.6562	+	3.12327i	0.839032	+	0.224818i	0.652650	−	0.757659i	$-0.273657\pi$
$193$	11.6562	+	3.12327i	0.839032	+	0.224818i	0.186382	+	0.982477i	$0.440324\pi$
$194$	−4.68885	+	8.12132i	−0.336640	+	0.583077i
$195$	−1.00718	+	0.837452i	−0.0721254	+	0.0599712i
$196$		0			0
$197$	14.3135	+	14.3135i	1.01979	+	1.01979i	0.999800	+	0.0199932i	$0.00636444\pi$
$197$	14.3135	+	14.3135i	1.01979	+	1.01979i	0.0199932	+	0.999800i	$0.493636\pi$
$198$	4.24593	+	15.8460i	0.301745	+	1.12613i
$199$	3.76653	+	6.52383i	0.267002	+	0.462462i	0.968086	−	0.250617i	$-0.0806335\pi$
$199$	3.76653	+	6.52383i	0.267002	+	0.462462i	−0.701084	+	0.713079i	$0.747300\pi$
$200$	−2.15365	+	4.51240i	−0.152286	+	0.319075i
$201$	−0.212023	−	0.122412i	−0.0149550	−	0.00863425i
$202$	11.3839	−	11.3839i	0.800965	−	0.800965i
$203$		0			0
$204$		−	1.53813i		−	0.107691i
$205$	2.72852	+	15.8906i	0.190568	+	1.10985i
$206$	17.0343	−	9.83476i	1.18684	−	0.685220i
$207$	0.848257	−	3.16574i	0.0589579	−	0.220034i
$208$	1.95290	−	0.523277i	0.135409	−	0.0362827i
$209$	−21.8944			−1.51446
$210$		0			0
$211$	19.5766			1.34771			0.673854	−	0.738865i	$-0.264638\pi$
$211$	19.5766			1.34771			0.673854	+	0.738865i	$0.264638\pi$
$212$	1.33599	−	0.357978i	0.0917562	−	0.0245860i
$213$	0.358232	−	1.33694i	0.0245456	−	0.0916056i
$214$	2.42575	−	1.40051i	0.165821	−	0.0957366i
$215$	−3.38922	+	4.79440i	−0.231143	+	0.326975i
$216$			1.71410i			0.116630i
$217$		0			0
$218$	4.17960	−	4.17960i	0.283078	−	0.283078i
$219$	1.40823	+	0.813041i	0.0951593	+	0.0549402i
$220$	11.8015	+	4.35544i	0.795659	+	0.293644i
$221$	5.36656	+	9.29516i	0.360994	+	0.625260i
$222$	0.377945	+	1.41051i	0.0253660	+	0.0946672i
$223$	−1.46027	−	1.46027i	−0.0977867	−	0.0977867i	0.656521	−	0.754308i	$-0.272027\pi$
$223$	−1.46027	−	1.46027i	−0.0977867	−	0.0977867i	−0.754308	+	0.656521i	$0.772027\pi$
$224$		0			0
$225$	14.3355	+	2.66053i	0.955698	+	0.177369i
$226$	9.60377	−	16.6342i	0.638833	−	1.10649i
$227$	18.0081	+	4.82525i	1.19524	+	0.320263i	0.800954	−	0.598726i	$-0.204326\pi$
$227$	18.0081	+	4.82525i	1.19524	+	0.320263i	0.394283	+	0.918989i	$0.370993\pi$
$228$	−1.08918	−	0.291844i	−0.0721325	−	0.0193278i
$229$	2.00384	−	3.47074i	0.132417	−	0.229353i	−0.792191	−	0.610274i	$-0.791059\pi$
$229$	2.00384	−	3.47074i	0.132417	−	0.229353i	0.924608	+	0.380920i	$0.124393\pi$
$230$	−1.60678	−	1.93242i	−0.105948	−	0.127420i
$231$		0			0
$232$	2.23093	+	2.23093i	0.146468	+	0.146468i
$233$	−3.55400	−	13.2637i	−0.232830	−	0.868934i	−0.979115	−	0.203307i	$-0.934831\pi$
$233$	−3.55400	−	13.2637i	−0.232830	−	0.868934i	0.746285	−	0.665627i	$-0.231836\pi$
$234$	−2.94782	−	5.10577i	−0.192705	−	0.333775i
$235$	−5.51775	−	11.9728i	−0.359939	−	0.781017i
$236$	−4.74448	−	2.73923i	−0.308839	−	0.178308i
$237$	1.28003	−	1.28003i	0.0831466	−	0.0831466i
$238$		0			0
$239$			19.6621i			1.27183i	0.771758	+	0.635916i	$0.219378\pi$
$239$			19.6621i			1.27183i	−0.771758	+	0.635916i	$0.780622\pi$
$240$	0.529033	+	0.373980i	0.0341489	+	0.0241403i
$241$	5.09667	−	2.94256i	0.328305	−	0.189547i	−0.326783	−	0.945099i	$-0.605965\pi$
$241$	5.09667	−	2.94256i	0.328305	−	0.189547i	0.655088	+	0.755552i	$0.272631\pi$
$242$	5.34440	−	19.9456i	0.343551	−	1.28215i
$243$	7.27638	−	1.94970i	0.466780	−	0.125073i
$244$	4.60924			0.295077
$245$		0			0
$246$	2.08915			0.133199
$247$	7.60029	−	2.03649i	0.483595	−	0.129579i
$248$	−0.996056	+	3.71733i	−0.0632496	+	0.236051i
$249$	−2.01302	+	1.16222i	−0.127570	+	0.0736525i
$250$	8.01135	−	7.79861i	0.506682	−	0.493227i
$251$			7.09950i			0.448116i	0.974576	+	0.224058i	$0.0719306\pi$
$251$			7.09950i			0.448116i	−0.974576	+	0.224058i	$0.928069\pi$
$252$		0			0
$253$	−4.47097	+	4.47097i	−0.281088	+	0.281088i
$254$	−5.67653	−	3.27735i	−0.356177	−	0.205639i
$255$	−1.19082	+	3.22665i	−0.0745720	+	0.202060i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	2.55891	+	9.54998i	0.159620	+	0.595711i	0.998665	+	0.0516491i	$0.0164478\pi$
$257$	2.55891	+	9.54998i	0.159620	+	0.595711i	−0.839045	+	0.544062i	$0.816886\pi$
$258$	0.537952	+	0.537952i	0.0334915	+	0.0334915i
$259$		0			0
$260$	−4.50184	−	0.414214i	−0.279192	−	0.0256884i
$261$	4.60010	−	7.96760i	0.284739	−	0.493182i
$262$	−7.43314	−	1.99170i	−0.459221	−	0.123048i
$263$	−13.2797	−	3.55829i	−0.818861	−	0.219413i	−0.175013	−	0.984566i	$-0.555997\pi$
$263$	−13.2797	−	3.55829i	−0.818861	−	0.219413i	−0.643849	+	0.765153i	$0.722663\pi$
$264$	0.814995	−	1.41161i	0.0501595	−	0.0868788i
$265$	−3.07974	−	0.283366i	−0.189187	−	0.0174071i
$266$		0			0
$267$	−2.44248	−	2.44248i	−0.149477	−	0.149477i
$268$	−0.218698	−	0.816193i	−0.0133591	−	0.0498569i
$269$	13.2510	+	22.9514i	0.807928	+	1.39937i	0.914296	+	0.405046i	$0.132745\pi$
$269$	13.2510	+	22.9514i	0.807928	+	1.39937i	−0.106368	+	0.994327i	$0.533922\pi$
$270$	1.32705	−	3.59578i	0.0807617	−	0.218832i
$271$	11.0824	+	6.39844i	0.673209	+	0.388678i	0.797292	−	0.603594i	$-0.206265\pi$
$271$	11.0824	+	6.39844i	0.673209	+	0.388678i	−0.124082	+	0.992272i	$0.539599\pi$
$272$	3.75384	−	3.75384i	0.227610	−	0.227610i
$273$		0			0
$274$		−	8.83578i		−	0.533789i
$275$	−21.3849	−	18.2734i	−1.28956	−	1.10193i
$276$	−0.282014	+	0.162821i	−0.0169752	+	0.00980065i
$277$	5.20313	−	19.4184i	0.312626	−	1.16674i	−0.613554	−	0.789653i	$-0.710261\pi$
$277$	5.20313	−	19.4184i	0.312626	−	1.16674i	0.926180	−	0.377083i	$-0.123073\pi$
$278$	10.6861	−	2.86334i	0.640912	−	0.171732i
$279$	11.2223			0.671863
$280$		0			0
$281$	−14.1498			−0.844107			−0.422054	−	0.906571i	$-0.638691\pi$
$281$	−14.1498			−0.844107			−0.422054	+	0.906571i	$0.638691\pi$
$282$	−1.64998	+	0.442111i	−0.0982548	+	0.0263273i
$283$	7.00563	−	26.1454i	0.416442	−	1.55418i	−0.365489	−	0.930816i	$-0.619098\pi$
$283$	7.00563	−	26.1454i	0.416442	−	1.55418i	0.781930	−	0.623366i	$-0.214235\pi$
$284$	4.13709	−	2.38855i	0.245491	−	0.141734i
$285$	2.05889	+	1.45546i	0.121958	+	0.0862139i
$286$			11.3741i			0.672564i
$287$		0			0
$288$	−2.06196	+	2.06196i	−0.121502	+	0.121502i
$289$	9.68442	+	5.59130i	0.569672	+	0.328900i
$290$	−2.95279	−	6.40715i	−0.173394	−	0.376241i
$291$	−1.35853	−	2.35305i	−0.0796385	−	0.137938i
$292$	1.45256	+	5.42104i	0.0850048	+	0.317242i
$293$	−17.1191	−	17.1191i	−1.00011	−	1.00011i	−1.00000		0.000106876i	$-0.999966\pi$
$293$	−17.1191	−	17.1191i	−1.00011	−	1.00011i	−0.000106876	−	1.00000i	$-0.500034\pi$
$294$		0			0
$295$	7.83211	+	9.41941i	0.456003	+	0.548420i
$296$	−2.51999	+	4.36475i	−0.146471	+	0.253696i
$297$	−9.31453	−	2.49582i	−0.540484	−	0.144822i
$298$	4.87682	+	1.30674i	0.282506	+	0.0756974i
$299$	1.13616	−	1.96790i	0.0657061	−	0.113806i
$300$	−0.820253	−	1.19410i	−0.0473573	−	0.0689413i
$301$		0			0
$302$	9.50552	+	9.50552i	0.546981	+	0.546981i
$303$	1.20727	+	4.50559i	0.0693558	+	0.258840i
$304$	−1.94590	−	3.37040i	−0.111605	−	0.193306i
$305$	−9.66911	−	3.56846i	−0.553652	−	0.204329i
$306$	−13.4065	−	7.74027i	−0.766401	−	0.442482i
$307$	−17.2974	+	17.2974i	−0.987217	+	0.987217i	−0.999919	−	0.0127019i	$-0.995957\pi$
$307$	−17.2974	+	17.2974i	−0.987217	+	0.987217i	0.0127019	+	0.999919i	$0.495957\pi$
$308$		0			0
$309$			5.69898i			0.324204i
$310$	4.96744	−	7.02694i	0.282131	−	0.399104i
$311$	9.51095	−	5.49115i	0.539316	−	0.311374i	−0.205486	−	0.978660i	$-0.565877\pi$
$311$	9.51095	−	5.49115i	0.539316	−	0.311374i	0.744802	+	0.667286i	$0.232544\pi$
$312$	−0.151613	+	0.565826i	−0.00858338	+	0.0320336i
$313$	−28.4088	+	7.61212i	−1.60576	+	0.430262i	−0.946776	−	0.321893i	$-0.895681\pi$
$313$	−28.4088	+	7.61212i	−1.60576	+	0.430262i	−0.658985	+	0.752156i	$0.729014\pi$
$314$	−1.10287			−0.0622383
$315$		0			0
$316$	6.24784			0.351469
$317$	−4.14766	+	1.11136i	−0.232956	+	0.0624203i	−0.373408	−	0.927667i	$-0.621811\pi$
$317$	−4.14766	+	1.11136i	−0.232956	+	0.0624203i	0.140453	+	0.990087i	$0.455144\pi$
$318$	−0.103719	+	0.387086i	−0.00581629	+	0.0217067i
$319$	−15.3714	+	8.87468i	−0.860633	+	0.496887i
$320$	0.378409	+	2.20382i	0.0211537	+	0.123197i
$321$			0.811556i			0.0452966i
$322$		0			0
$323$	14.6092	−	14.6092i	0.812878	−	0.812878i
$324$	7.14603	+	4.12576i	0.397001	+	0.229209i
$325$	9.12312	+	4.35423i	0.506060	+	0.241529i
$326$	6.62056	+	11.4671i	0.366679	+	0.635106i
$327$	0.443251	+	1.65424i	0.0245119	+	0.0914795i
$328$	5.09860	+	5.09860i	0.281523	+	0.281523i
$329$		0			0
$330$	−2.80253	+	2.33027i	−0.154274	+	0.128277i
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.291863	+	0.956460i	$0.594275\pi$
$331$	−17.7249	+	30.7005i	−0.974250	+	1.68745i	−0.682387	+	0.730991i	$0.739058\pi$
$332$	−7.74921	−	2.07639i	−0.425293	−	0.113957i
$333$	14.1960	+	3.80382i	0.777939	+	0.208448i
$334$	−3.32821	+	5.76463i	−0.182112	+	0.315426i
$335$	−0.173116	+	1.88150i	−0.00945835	+	0.102797i
$336$		0			0
$337$	−12.1473	−	12.1473i	−0.661708	−	0.661708i	0.294075	−	0.955782i	$-0.404989\pi$
$337$	−12.1473	−	12.1473i	−0.661708	−	0.661708i	−0.955782	+	0.294075i	$0.904989\pi$
$338$	2.30669	+	8.60869i	0.125468	+	0.468251i
$339$	2.78257	+	4.81955i	0.151128	+	0.261762i
$340$	−10.7809	+	4.96846i	−0.584675	+	0.269453i
$341$	−18.7499	−	10.8253i	−1.01536	−	0.586221i
$342$	−8.02475	+	8.02475i	−0.433929	+	0.433929i
$343$		0			0
$344$			2.62576i			0.141571i
$345$	0.717654	−	0.123226i	0.0386372	−	0.00663424i
$346$	−6.10945	+	3.52729i	−0.328446	+	0.189628i
$347$	2.32323	−	8.67040i	0.124717	−	0.465452i	−0.875112	−	0.483920i	$-0.839212\pi$
$347$	2.32323	−	8.67040i	0.124717	−	0.465452i	0.999829	+	0.0184687i	$0.00587911\pi$
$348$	−0.882976	+	0.236593i	−0.0473325	+	0.0126827i
$349$	26.0251			1.39309			0.696546	−	0.717512i	$-0.254719\pi$
$349$	26.0251			1.39309			0.696546	+	0.717512i	$0.254719\pi$
$350$		0			0
$351$	3.46554			0.184977
$352$	5.43407	−	1.45605i	0.289637	−	0.0776079i
$353$	−2.57944	+	9.62659i	−0.137290	+	0.512372i	0.862688	+	0.505736i	$0.168779\pi$
$353$	−2.57944	+	9.62659i	−0.137290	+	0.512372i	−0.999978	+	0.00663577i	$0.997888\pi$
$354$	1.37465	−	0.793655i	0.0730619	−	0.0421823i
$355$	−10.5278	+	1.80770i	−0.558760	+	0.0959425i
$356$		−	11.9218i		−	0.631855i
$357$		0			0
$358$	−1.56012	+	1.56012i	−0.0824550	+	0.0824550i
$359$	10.0235	+	5.78705i	0.529019	+	0.305429i	0.740617	−	0.671928i	$-0.234533\pi$
$359$	10.0235	+	5.78705i	0.529019	+	0.305429i	−0.211598	+	0.977357i	$0.567867\pi$
$360$	5.92187	−	2.72915i	0.312110	−	0.143839i
$361$	1.92693	+	3.33754i	0.101417	+	0.175660i
$362$	−1.06599	−	3.97833i	−0.0560273	−	0.209097i
$363$	4.23050	+	4.23050i	0.222044	+	0.222044i
$364$		0			0
$365$	1.14981	−	12.4966i	0.0601840	−	0.654104i
$366$	−0.667734	+	1.15655i	−0.0349030	+	0.0604538i
$367$	−16.1256	−	4.32083i	−0.841747	−	0.225545i	−0.187915	−	0.982185i	$-0.560173\pi$
$367$	−16.1256	−	4.32083i	−0.841747	−	0.225545i	−0.653832	+	0.756640i	$0.726840\pi$
$368$	−1.08562	−	0.290892i	−0.0565921	−	0.0151638i
$369$	10.5131	−	18.2092i	0.547290	−	0.947935i
$370$	8.66551	−	7.20525i	0.450499	−	0.374583i
$371$		0			0
$372$	−0.788454	−	0.788454i	−0.0408794	−	0.0408794i
$373$	0.822767	+	3.07061i	0.0426013	+	0.158990i	0.983950	−	0.178446i	$-0.0571070\pi$
$373$	0.822767	+	3.07061i	0.0426013	+	0.158990i	−0.941348	+	0.337436i	$0.890440\pi$
$374$	14.9328	+	25.8644i	0.772158	+	1.33742i
$375$	0.796232	+	3.13998i	0.0411172	+	0.162148i
$376$	−5.10577	−	2.94782i	−0.263310	−	0.152022i
$377$	4.51047	−	4.51047i	0.232301	−	0.232301i
$378$		0			0
$379$			7.15349i			0.367450i	0.982978	+	0.183725i	$0.0588156\pi$
$379$			7.15349i			0.367450i	−0.982978	+	0.183725i	$0.941184\pi$
$380$	1.47269	+	8.57682i	0.0755475	+	0.439982i
$381$	1.64470	−	0.949568i	0.0842605	−	0.0486478i
$382$	−4.45229	+	16.6162i	−0.227799	+	0.850158i
$383$	14.0961	−	3.77704i	0.720278	−	0.192998i	0.119982	−	0.992776i	$-0.461716\pi$
$383$	14.0961	−	3.77704i	0.720278	−	0.192998i	0.600296	+	0.799778i	$0.295050\pi$
$384$	0.289737			0.0147856
$385$		0			0
$386$	−12.0674			−0.614214
$387$	7.39595	−	1.98174i	0.375957	−	0.100737i
$388$	2.42713	−	9.05816i	0.123219	−	0.459858i
$389$	5.36634	−	3.09826i	0.272084	−	0.157088i	−0.357750	−	0.933817i	$-0.616456\pi$
$389$	5.36634	−	3.09826i	0.272084	−	0.157088i	0.629834	+	0.776729i	$0.283123\pi$
$390$	0.756109	−	1.06959i	0.0382870	−	0.0541609i
$391$		−	5.96659i		−	0.301744i
$392$		0			0
$393$	1.57658	−	1.57658i	0.0795282	−	0.0795282i
$394$	−17.5304	−	10.1212i	−0.883167	−	0.509897i
$395$	−13.1065	−	4.83706i	−0.659460	−	0.243379i
$396$	−8.20251	−	14.2072i	−0.412191	−	0.713937i
$397$	−0.754685	−	2.81652i	−0.0378766	−	0.141357i	0.944398	−	0.328804i	$-0.106646\pi$
$397$	−0.754685	−	2.81652i	−0.0378766	−	0.141357i	−0.982275	+	0.187447i	$0.939979\pi$
$398$	−5.32668	−	5.32668i	−0.267002	−	0.267002i
$399$		0			0
$400$	0.912375	−	4.91605i	0.0456187	−	0.245803i
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	−0.501358	−	0.865240i	$-0.667166\pi$
$401$	9.98528	−	17.2950i	0.498641	−	0.863672i	0.999999	+	0.00156835i	$0.000499221\pi$
$402$	0.236481	+	0.0633649i	0.0117946	+	0.00316035i
$403$	7.51565	+	2.01381i	0.374381	+	0.100315i
$404$	−8.04960	+	13.9423i	−0.400483	+	0.693656i
$405$	−11.7965	−	14.1873i	−0.586175	−	0.704973i
$406$		0			0
$407$	−20.0491	−	20.0491i	−0.993796	−	0.993796i
$408$	0.398099	+	1.48572i	0.0197088	+	0.0735543i
$409$	−17.1791	−	29.7550i	−0.849451	−	1.47129i	−0.881699	−	0.471812i	$-0.843600\pi$
$409$	−17.1791	−	29.7550i	−0.849451	−	1.47129i	0.0322484	−	0.999480i	$-0.489733\pi$
$410$	−6.74834	−	14.6430i	−0.333277	−	0.723165i
$411$	2.21707	+	1.28003i	0.109360	+	0.0631390i
$412$	−13.9084	+	13.9084i	−0.685220	+	0.685220i
$413$		0			0
$414$			3.27741i			0.161076i
$415$	14.6485	+	10.3552i	0.719065	+	0.508317i
$416$	−1.75092	+	1.01089i	−0.0858459	+	0.0495631i
$417$	−0.829616	+	3.09617i	−0.0406265	+	0.151620i
$418$	21.1483	−	5.66668i	1.03440	−	0.277166i
$419$	31.1360			1.52109			0.760547	−	0.649283i	$-0.224931\pi$
$419$	31.1360			1.52109			0.760547	+	0.649283i	$0.224931\pi$
$420$		0			0
$421$	−33.6728			−1.64111			−0.820555	−	0.571567i	$-0.806336\pi$
$421$	−33.6728			−1.64111			−0.820555	+	0.571567i	$0.806336\pi$
$422$	−18.9095	+	5.06679i	−0.920501	+	0.246648i
$423$	−4.44962	+	16.6062i	−0.216348	+	0.807421i
$424$	−1.19782	+	0.691560i	−0.0581711	+	0.0335851i
$425$	26.4623	−	2.07615i	1.28361	−	0.100708i
$426$			1.38410i			0.0670599i
$427$		0			0
$428$	−1.98061	+	1.98061i	−0.0957366	+	0.0957366i
$429$	−2.85398	−	1.64775i	−0.137792	−	0.0795540i
$430$	2.03285	−	5.50823i	0.0980330	−	0.265630i
$431$	7.37284	+	12.7701i	0.355137	+	0.615116i	0.987141	−	0.159849i	$-0.0511008\pi$
$431$	7.37284	+	12.7701i	0.355137	+	0.615116i	−0.632004	+	0.774965i	$0.717767\pi$
$432$	−0.443641	−	1.65569i	−0.0213447	−	0.0796595i
$433$	9.98256	+	9.98256i	0.479731	+	0.479731i	0.905046	−	0.425315i	$-0.139837\pi$
$433$	9.98256	+	9.98256i	0.479731	+	0.479731i	−0.425315	+	0.905046i	$0.639837\pi$
$434$		0			0
$435$	2.03545	+	0.187281i	0.0975922	+	0.00897944i
$436$	−2.95543	+	5.11895i	−0.141539	+	0.245153i
$437$	−4.22504	−	1.13210i	−0.202111	−	0.0541555i
$438$	−1.57067	−	0.420861i	−0.0750498	−	0.0201095i
$439$	−19.2142	+	33.2800i	−0.917046	+	1.58837i	−0.113167	+	0.993576i	$0.536100\pi$
$439$	−19.2142	+	33.2800i	−0.917046	+	1.58837i	−0.803878	+	0.594794i	$0.797234\pi$
$440$	−12.5267	−	1.15258i	−0.597186	−	0.0549470i
$441$		0			0
$442$	−7.58946	−	7.58946i	−0.360994	−	0.360994i
$443$	1.48448	+	5.54016i	0.0705299	+	0.263221i	0.992183	−	0.124795i	$-0.0398272\pi$
$443$	1.48448	+	5.54016i	0.0705299	+	0.263221i	−0.921653	+	0.388016i	$0.873161\pi$
$444$	−0.730133	−	1.26463i	−0.0346506	−	0.0600166i
$445$	−9.22982	+	25.0092i	−0.437536	+	1.18555i
$446$	1.78845	+	1.03256i	0.0846857	+	0.0488933i
$447$	−1.03438	+	1.03438i	−0.0489247	+	0.0489247i
$448$		0			0
$449$			7.30267i			0.344635i	0.985042	+	0.172317i	$0.0551254\pi$
$449$			7.30267i			0.344635i	−0.985042	+	0.172317i	$0.944875\pi$
$450$	−14.5356	+	1.14042i	−0.685215	+	0.0537597i
$451$	−35.1299	+	20.2823i	−1.65420	+	0.955055i
$452$	−4.97128	+	18.5531i	−0.233829	+	0.872663i
$453$	−3.76217	+	1.00807i	−0.176762	+	0.0473633i
$454$	−18.6433			−0.874974
$455$		0			0
$456$	1.12760			0.0528047
$457$	−4.97047	+	1.33183i	−0.232509	+	0.0623006i	−0.373192	−	0.927754i	$-0.621737\pi$
$457$	−4.97047	+	1.33183i	−0.232509	+	0.0623006i	0.140683	+	0.990055i	$0.455070\pi$
$458$	−1.03726	+	3.87111i	−0.0484680	+	0.180885i
$459$	7.88056	−	4.54984i	0.367833	−	0.212368i
$460$	2.05218	+	1.45071i	0.0956833	+	0.0676397i
$461$			29.4110i			1.36981i	0.728634	+	0.684903i	$0.240155\pi$
$461$			29.4110i			1.36981i	−0.728634	+	0.684903i	$0.759845\pi$
$462$		0			0
$463$	−4.04625	+	4.04625i	−0.188045	+	0.188045i	−0.794851	−	0.606805i	$-0.792451\pi$
$463$	−4.04625	+	4.04625i	−0.188045	+	0.188045i	0.606805	+	0.794851i	$0.292451\pi$
$464$	−2.73232	−	1.57751i	−0.126845	−	0.0732340i
$465$	1.04357	+	2.26441i	0.0483945	+	0.105009i
$466$	6.86580	+	11.8919i	0.318052	+	0.550882i
$467$	−4.30747	−	16.0757i	−0.199326	−	0.743894i	−0.991105	−	0.133086i	$-0.957511\pi$
$467$	−4.30747	−	16.0757i	−0.199326	−	0.743894i	0.791779	−	0.610808i	$-0.209155\pi$
$468$	4.16885	+	4.16885i	0.192705	+	0.192705i
$469$		0			0
$470$	8.42852	+	10.1367i	0.388779	+	0.467571i
$471$	0.159770	−	0.276731i	0.00736184	−	0.0127511i
$472$	5.29178	+	1.41793i	0.243574	+	0.0652654i
$473$	−14.2686	−	3.82325i	−0.656069	−	0.175793i
$474$	−0.905115	+	1.56771i	−0.0415733	+	0.0720071i
$475$	3.55078	−	19.1323i	0.162921	−	0.877851i
$476$		0			0
$477$	2.85194	+	2.85194i	0.130581	+	0.130581i
$478$	−5.08891	−	18.9921i	−0.232762	−	0.868678i
$479$	−7.69460	−	13.3274i	−0.351575	−	0.608946i	0.634950	−	0.772553i	$-0.281021\pi$
$479$	−7.69460	−	13.3274i	−0.351575	−	0.608946i	−0.986526	+	0.163607i	$0.947687\pi$
$480$	−0.607800	−	0.224313i	−0.0277421	−	0.0102385i
$481$	8.82459	+	5.09488i	0.402367	+	0.232306i
$482$	−4.16141	+	4.16141i	−0.189547	+	0.189547i
$483$		0			0
$484$			20.6492i			0.938599i
$485$	−12.1043	+	17.1228i	−0.549629	+	0.777507i
$486$	−6.52383	+	3.76653i	−0.295927	+	0.170853i
$487$	−9.31541	+	34.7656i	−0.422122	+	1.57538i	0.348007	+	0.937492i	$0.386858\pi$
$487$	−9.31541	+	34.7656i	−0.422122	+	1.57538i	−0.770129	+	0.637888i	$0.779808\pi$
$488$	−4.45219	+	1.19296i	−0.201541	+	0.0540028i
$489$	−3.83644			−0.173490
$490$		0			0
$491$	−15.2823			−0.689680			−0.344840	−	0.938661i	$-0.612067\pi$
$491$	−15.2823			−0.689680			−0.344840	+	0.938661i	$0.612067\pi$
$492$	−2.01796	+	0.540712i	−0.0909768	+	0.0243772i
$493$	4.33499	−	16.1784i	0.195238	−	0.728639i
$494$	−6.81423	+	3.93420i	−0.306587	+	0.177008i
$495$	6.20780	+	36.1536i	0.279020	+	1.62499i
$496$		−	3.84846i		−	0.172801i
$497$		0			0
$498$	1.64362	−	1.64362i	0.0736525	−	0.0736525i
$499$	−27.3534	−	15.7925i	−1.22451	−	0.706969i	−0.258630	−	0.965976i	$-0.583271\pi$
$499$	−27.3534	−	15.7925i	−1.22451	−	0.706969i	−0.965875	+	0.259008i	$0.916604\pi$
$500$	−5.71994	+	9.60637i	−0.255803	+	0.429610i
$501$	−0.964305	−	1.67023i	−0.0430820	−	0.0746202i
$502$	−1.83749	−	6.85759i	−0.0820110	−	0.306069i
$503$	−16.9777	−	16.9777i	−0.756997	−	0.756997i	0.218778	−	0.975775i	$-0.429793\pi$
$503$	−16.9777	−	16.9777i	−0.756997	−	0.756997i	−0.975775	+	0.218778i	$0.929793\pi$
$504$		0			0
$505$	27.6803	−	23.0157i	1.23176	−	1.02419i
$506$	3.16146	−	5.47580i	0.140544	−	0.243429i
$507$	−2.49426	−	0.668334i	−0.110774	−	0.0296817i
$508$	6.33135	+	1.69648i	0.280908	+	0.0752691i
$509$	−10.7571	+	18.6318i	−0.476799	+	0.825840i	−0.999647	−	0.0265865i	$-0.991536\pi$
$509$	−10.7571	+	18.6318i	−0.476799	+	0.825840i	0.522848	+	0.852426i	$0.324870\pi$
$510$	0.315125	−	3.42491i	0.0139540	−	0.151657i
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.72657	−	6.44363i	−0.0762297	−	0.284493i
$514$	−4.94343	−	8.56228i	−0.218045	−	0.377666i
$515$	39.9445	−	18.4088i	1.76017	−	0.811188i
$516$	−0.658854	−	0.380390i	−0.0290044	−	0.0167457i
$517$	23.4529	−	23.4529i	1.03146	−	1.03146i
$518$		0			0
$519$		−	2.04397i		−	0.0897205i
$520$	4.45565	−	0.765062i	0.195393	−	0.0335502i
$521$	−11.4657	+	6.61973i	−0.502322	+	0.290016i	−0.729672	−	0.683798i	$-0.760327\pi$
$521$	−11.4657	+	6.61973i	−0.502322	+	0.290016i	0.227350	+	0.973813i	$0.426994\pi$
$522$	−2.38118	+	8.88670i	−0.104222	+	0.388960i
$523$	26.0126	−	6.97006i	1.13745	−	0.304779i	0.359526	−	0.933135i	$-0.382938\pi$
$523$	26.0126	−	6.97006i	1.13745	−	0.304779i	0.777926	+	0.628356i	$0.216272\pi$
$524$	7.69535			0.336173
$525$		0			0
$526$	13.7482			0.599448
$527$	19.7343	−	5.28779i	0.859640	−	0.230340i
$528$	−0.421872	+	1.57445i	−0.0183596	+	0.0685191i
$529$	18.8246	−	10.8684i	0.818462	−	0.472539i
$530$	3.04814	−	0.523384i	0.132403	−	0.0227344i
$531$		−	15.9755i		−	0.693276i
$532$		0			0
$533$	10.3083	−	10.3083i	0.446501	−	0.446501i
$534$	2.99141	+	1.72709i	0.129451	+	0.0747386i
$535$	5.68825	−	2.62148i	0.245924	−	0.113336i
$536$	0.422492	+	0.731778i	0.0182489	+	0.0316080i
$537$	−0.165453	−	0.617477i	−0.00713980	−	0.0266461i
$538$	−18.7398	−	18.7398i	−0.807928	−	0.807928i
$539$		0			0
$540$	−0.351176	+	3.81672i	−0.0151122	+	0.164245i
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	−0.718171	−	0.695867i	$-0.755020\pi$
$541$	5.66491	−	9.81190i	0.243553	−	0.421847i	0.961724	+	0.274020i	$0.0883536\pi$
$542$	−12.3608	−	3.31208i	−0.530943	−	0.142266i
$543$	1.15267	+	0.308857i	0.0494658	+	0.0132543i
$544$	−2.65436	+	4.59749i	−0.113805	+	0.197116i
$545$	10.1629	−	8.45027i	0.435329	−	0.361970i
$546$		0			0
$547$	−30.9149	−	30.9149i	−1.32182	−	1.32182i	−0.912298	−	0.409527i	$-0.865694\pi$
$547$	−30.9149	−	30.9149i	−1.32182	−	1.32182i	−0.409527	−	0.912298i	$-0.634306\pi$
$548$	2.28687	+	8.53471i	0.0976902	+	0.364585i
$549$	6.72040	+	11.6401i	0.286820	+	0.496786i
$550$	25.3857	+	12.1159i	1.08245	+	0.516625i
$551$	−10.6337	−	6.13935i	−0.453009	−	0.261545i
$552$	0.230263	−	0.230263i	0.00980065	−	0.00980065i
$553$		0			0
$554$			20.1034i			0.854110i
$555$	0.552577	+	3.21816i	0.0234556	+	0.136603i
$556$	−9.58094	+	5.53156i	−0.406322	+	0.234590i
$557$	−6.83277	+	25.5003i	−0.289514	+	1.08048i	0.655963	+	0.754793i	$0.272263\pi$
$557$	−6.83277	+	25.5003i	−0.289514	+	1.08048i	−0.945477	+	0.325688i	$0.894404\pi$
$558$	−10.8399	+	2.90455i	−0.458891	+	0.122959i
$559$	5.30873			0.224535
$560$		0			0
$561$	−8.65318			−0.365337
$562$	13.6677	−	3.66224i	0.576536	−	0.154482i
$563$	−5.22648	+	19.5055i	−0.220270	+	0.822058i	0.763975	+	0.645246i	$0.223245\pi$
$563$	−5.22648	+	19.5055i	−0.220270	+	0.822058i	−0.984245	+	0.176812i	$0.943422\pi$
$564$	1.47933	−	0.854092i	0.0622911	−	0.0359638i
$565$	24.7923	−	35.0712i	1.04302	−	1.47546i
$566$			27.0677i			1.13774i
$567$		0			0
$568$	−3.37792	+	3.37792i	−0.141734	+	0.141734i
$569$	21.4890	+	12.4067i	0.900867	+	0.520116i	0.877481	−	0.479611i	$-0.159222\pi$
$569$	21.4890	+	12.4067i	0.900867	+	0.520116i	0.0233856	+	0.999727i	$0.492555\pi$
$570$	−2.36544	−	0.872983i	−0.0990773	−	0.0365653i
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	0.814116	−	0.580703i	$-0.197222\pi$
$571$	−2.29029	−	3.96690i	−0.0958458	−	0.166010i	−0.909961	+	0.414693i	$0.863889\pi$
$572$	−2.94383	−	10.9865i	−0.123088	−	0.459370i
$573$	−3.52433	−	3.52433i	−0.147231	−	0.147231i
$574$		0			0
$575$	−3.18185	−	4.63204i	−0.132692	−	0.193169i
$576$	1.45803	−	2.52538i	0.0607511	−	0.105224i
$577$	19.1065	+	5.11957i	0.795414	+	0.213131i	0.633570	−	0.773686i	$-0.281589\pi$
$577$	19.1065	+	5.11957i	0.795414	+	0.213131i	0.161845	+	0.986816i	$0.448256\pi$
$578$	−10.8016	−	2.89427i	−0.449286	−	0.120386i
$579$	1.74818	−	3.02794i	0.0726520	−	0.125837i
$580$	4.51047	+	5.42460i	0.187287	+	0.225244i
$581$		0			0
$582$	1.92125	+	1.92125i	0.0796385	+	0.0796385i
$583$	−2.01390	−	7.51596i	−0.0834071	−	0.311279i
$584$	−2.80614	−	4.86037i	−0.116119	−	0.201124i
$585$	−5.51775	−	11.9728i	−0.228131	−	0.495013i
$586$	20.9665	+	12.1050i	0.866118	+	0.500053i
$587$	−19.3782	+	19.3782i	−0.799824	+	0.799824i	−0.983068	−	0.183244i	$-0.941340\pi$
$587$	−19.3782	+	19.3782i	−0.799824	+	0.799824i	0.183244	+	0.983068i	$0.441340\pi$
$588$		0			0
$589$		−	14.9775i		−	0.617136i
$590$	−10.0032	−	7.07136i	−0.411823	−	0.291123i
$591$	5.07919	−	2.93247i	0.208930	−	0.120626i
$592$	1.30444	−	4.86824i	0.0536122	−	0.200083i
$593$	−3.12741	+	0.837988i	−0.128428	+	0.0344121i	−0.322460	−	0.946583i	$-0.604510\pi$
$593$	−3.12741	+	0.837988i	−0.128428	+	0.0344121i	0.194033	+	0.980995i	$0.437843\pi$
$594$	9.64311			0.395661
$595$		0			0
$596$	−5.04885			−0.206809
$597$	2.10824	−	0.564900i	0.0862844	−	0.0231198i
$598$	−0.588122	+	2.19490i	−0.0240501	+	0.0897562i
$599$	6.75802	−	3.90174i	0.276125	−	0.159421i	−0.355543	−	0.934660i	$-0.615704\pi$
$599$	6.75802	−	3.90174i	0.276125	−	0.159421i	0.631668	+	0.775239i	$0.282371\pi$
$600$	1.10136	+	0.941113i	0.0449628	+	0.0384208i
$601$			31.7170i			1.29377i	0.762590	+	0.646883i	$0.223928\pi$
$601$			31.7170i			1.29377i	−0.762590	+	0.646883i	$0.776072\pi$
$602$		0			0
$603$	1.74233	−	1.74233i	0.0709530	−	0.0709530i
$604$	−11.6418	−	6.72142i	−0.473699	−	0.273491i
$605$	15.9865	−	43.3171i	0.649945	−	1.76109i
$606$	−2.33227	−	4.03960i	−0.0947418	−	0.164098i
$607$	−0.199219	−	0.743495i	−0.00808604	−	0.0301775i	0.961765	−	0.273876i	$-0.0883059\pi$
$607$	−0.199219	−	0.743495i	−0.00808604	−	0.0301775i	−0.969851	+	0.243699i	$0.921639\pi$
$608$	2.75192	+	2.75192i	0.111605	+	0.111605i
$609$		0			0
$610$	10.2632	+	0.944318i	0.415546	+	0.0382343i
$611$	−5.95987	+	10.3228i	−0.241110	+	0.417615i
$612$	14.9530	+	4.00666i	0.604441	+	0.161960i
$613$	−33.8086	−	9.05898i	−1.36552	−	0.365889i	−0.499676	−	0.866212i	$-0.666548\pi$
$613$	−33.8086	−	9.05898i	−1.36552	−	0.365889i	−0.865839	+	0.500323i	$0.833214\pi$
$614$	12.2311	−	21.1850i	0.493609	−	0.854955i
$615$	4.65183	+	0.428014i	0.187580	+	0.0172592i
$616$		0			0
$617$	21.5403	+	21.5403i	0.867179	+	0.867179i	0.992159	−	0.124980i	$-0.0398866\pi$
$617$	21.5403	+	21.5403i	0.867179	+	0.867179i	−0.124980	+	0.992159i	$0.539887\pi$
$618$	−1.47501	−	5.50479i	−0.0593334	−	0.221435i
$619$	21.6707	+	37.5348i	0.871021	+	1.50865i	0.860942	+	0.508703i	$0.169875\pi$
$619$	21.6707	+	37.5348i	0.871021	+	1.50865i	0.0100783	+	0.999949i	$0.496792\pi$
$620$	−2.97947	+	8.07317i	−0.119658	+	0.324226i
$621$	−1.66841	−	0.963256i	−0.0669509	−	0.0386541i
$622$	−7.76566	+	7.76566i	−0.311374	+	0.311374i
$623$		0			0
$624$		−	0.585786i		−	0.0234502i
$625$	19.4363	−	15.7235i	0.777452	−	0.628942i
$626$	25.4707	−	14.7055i	1.01801	−	0.587749i
$627$	−1.64184	+	6.12745i	−0.0655690	+	0.244707i
$628$	1.06529	−	0.285443i	0.0425096	−	0.0113904i
$629$	26.7559			1.06683
$630$		0			0
$631$	7.53463			0.299949			0.149974	−	0.988690i	$-0.452081\pi$
$631$	7.53463			0.299949			0.149974	+	0.988690i	$0.452081\pi$
$632$	−6.03495	+	1.61706i	−0.240058	+	0.0643232i
$633$	1.46804	−	5.47879i	0.0583492	−	0.217762i
$634$	3.71869	−	2.14699i	0.147688	−	0.0852677i
$635$	−11.9683	−	8.46052i	−0.474946	−	0.335746i
$636$		−	0.400741i		−	0.0158904i
$637$		0			0
$638$	12.5507	−	12.5507i	0.496887	−	0.496887i
$639$	12.0640	+	6.96513i	0.477243	+	0.275536i
$640$	−0.935904	−	2.03078i	−0.0369949	−	0.0802738i
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	0.519233	−	0.854633i	$-0.326218\pi$
$641$	−12.1657	−	21.0717i	−0.480518	−	0.832281i	−0.999750	+	0.0223521i	$0.992885\pi$
$642$	−0.210046	−	0.783903i	−0.00828986	−	0.0309382i
$643$	6.21713	+	6.21713i	0.245180	+	0.245180i	0.818989	−	0.573809i	$-0.194535\pi$
$643$	6.21713	+	6.21713i	0.245180	+	0.245180i	−0.573809	+	0.818989i	$0.694535\pi$
$644$		0			0
$645$	1.08763	+	1.30805i	0.0428252	+	0.0515045i
$646$	−10.3303	+	17.8925i	−0.406439	+	0.703973i
$647$	−19.9243	−	5.33869i	−0.783304	−	0.209886i	−0.155063	−	0.987905i	$-0.549558\pi$
$647$	−19.9243	−	5.33869i	−0.783304	−	0.209886i	−0.628241	+	0.778019i	$0.716225\pi$
$648$	−7.97036	−	2.13565i	−0.313105	−	0.0838963i
$649$	−15.4102	+	26.6913i	−0.604905	+	1.04773i
$650$	−9.93921	−	1.84463i	−0.389848	−	0.0723523i
$651$		0			0
$652$	−9.36288	−	9.36288i	−0.366679	−	0.366679i
$653$	6.76544	+	25.2490i	0.264752	+	0.988069i	0.962402	+	0.271630i	$0.0875625\pi$
$653$	6.76544	+	25.2490i	0.264752	+	0.988069i	−0.697650	+	0.716439i	$0.745771\pi$
$654$	−0.856296	−	1.48315i	−0.0334838	−	0.0579957i
$655$	−16.1430	−	5.95772i	−0.630761	−	0.232787i
$656$	−6.24448	−	3.60525i	−0.243806	−	0.140761i
$657$	−11.5723	+	11.5723i	−0.451478	+	0.451478i
$658$		0			0
$659$			24.2448i			0.944443i	0.881480	+	0.472222i	$0.156548\pi$
$659$			24.2448i			0.944443i	−0.881480	+	0.472222i	$0.843452\pi$
$660$	2.10392	−	2.97621i	0.0818951	−	0.115849i
$661$	−15.5301	+	8.96630i	−0.604050	+	0.348749i	−0.770633	−	0.637279i	$-0.780060\pi$
$661$	−15.5301	+	8.96630i	−0.604050	+	0.348749i	0.166583	+	0.986027i	$0.446727\pi$
$662$	9.17510	−	34.2419i	0.356600	−	1.33085i
$663$	3.00382	−	0.804871i	0.116659	−	0.0312586i
$664$	8.02257			0.311336
$665$		0			0
$666$	−14.6968			−0.569491
$667$	−3.42516	+	0.917769i	−0.132623	+	0.0355362i
$668$	1.72281	−	6.42961i	0.0666574	−	0.248769i
$669$	−0.518181	+	0.299172i	−0.0200340	+	0.0115667i
$670$	−0.319750	−	1.86219i	−0.0123530	−	0.0719427i
$671$		−	25.9305i		−	1.00104i
$672$		0			0
$673$	−4.85386	+	4.85386i	−0.187103	+	0.187103i	−0.794442	−	0.607340i	$-0.792237\pi$
$673$	−4.85386	+	4.85386i	−0.187103	+	0.187103i	0.607340	+	0.794442i	$0.292237\pi$
$674$	14.8774	+	8.58946i	0.573056	+	0.330854i
$675$	3.69158	−	7.73470i	0.142089	−	0.297709i
$676$	−4.45619	−	7.71834i	−0.171392	−	0.296859i
$677$	4.78306	+	17.8506i	0.183828	+	0.686055i	0.994878	+	0.101079i	$0.0322294\pi$
$677$	4.78306	+	17.8506i	0.183828	+	0.686055i	−0.811051	+	0.584976i	$0.801104\pi$
$678$	−3.93514	−	3.93514i	−0.151128	−	0.151128i
$679$		0			0
$680$	9.12760	−	7.58946i	0.350027	−	0.291043i
$681$	2.70083	−	4.67797i	0.103496	−	0.179260i
$682$	20.9128	+	5.60357i	0.800793	+	0.214572i
$683$	25.8878	+	6.93661i	0.990569	+	0.265422i	0.717489	−	0.696569i	$-0.245291\pi$
$683$	25.8878	+	6.93661i	0.990569	+	0.265422i	0.273079	+	0.961992i	$0.411958\pi$
$684$	5.67435	−	9.82827i	0.216964	−	0.375793i
$685$	1.81023	−	19.6743i	0.0691653	−	0.751717i
$686$		0			0
$687$	−0.821071	−	0.821071i	−0.0313258	−	0.0313258i
$688$	−0.679597	−	2.53629i	−0.0259094	−	0.0966951i
$689$	1.39819	+	2.42173i	0.0532667	+	0.0922606i
$690$	−0.661307	+	0.304769i	−0.0251755	+	0.0116024i
$691$	−25.1773	−	14.5361i	−0.957790	−	0.552980i	−0.0622976	−	0.998058i	$-0.519843\pi$
$691$	−25.1773	−	14.5361i	−0.957790	−	0.552980i	−0.895492	+	0.445077i	$0.853176\pi$
$692$	4.98835	−	4.98835i	0.189628	−	0.189628i
$693$		0			0
$694$			8.97626i			0.340734i
$695$	24.3811	−	4.18638i	0.924827	−	0.158798i
$696$	0.791655	−	0.457062i	0.0300076	−	0.0173249i
$697$	9.90723	−	36.9743i	0.375263	−	1.40050i
$698$	−25.1383	+	6.73580i	−0.951500	+	0.254954i
$699$	−3.97855			−0.150483
$700$		0			0
$701$	25.4462			0.961089			0.480545	−	0.876970i	$-0.340439\pi$
$701$	25.4462			0.961089			0.480545	+	0.876970i	$0.340439\pi$
$702$	−3.34746	+	0.896949i	−0.126342	+	0.0338531i
$703$	5.07663	−	18.9462i	0.191469	−	0.714571i
$704$	−4.87205	+	2.81288i	−0.183622	+	0.106014i
$705$	−3.76452	+	0.646392i	−0.141780	+	0.0243445i
$706$		−	9.96618i		−	0.375082i
$707$		0			0
$708$	−1.12240	+	1.12240i	−0.0421823	+	0.0421823i
$709$	−27.1994	−	15.7036i	−1.02150	−	0.589760i	−0.106958	−	0.994263i	$-0.534111\pi$
$709$	−27.1994	−	15.7036i	−1.02150	−	0.589760i	−0.914537	+	0.404503i	$0.867445\pi$
$710$	9.70125	−	4.47091i	0.364081	−	0.167790i
$711$	9.10952	+	15.7781i	0.341634	+	0.591727i
$712$	3.08559	+	11.5156i	0.115637	+	0.431565i
$713$	−3.05850	−	3.05850i	−0.114542	−	0.114542i
$714$		0			0
$715$	−2.33027	+	25.3263i	−0.0871470	+	0.947149i
$716$	1.10317	−	1.91075i	0.0412275	−	0.0714081i
$717$	5.50271	+	1.47445i	0.205502	+	0.0550642i
$718$	−11.1797	−	2.99560i	−0.417224	−	0.111795i
$719$	5.40214	−	9.35678i	0.201466	−	0.348949i	−0.747535	−	0.664222i	$-0.768763\pi$
$719$	5.40214	−	9.35678i	0.201466	−	0.348949i	0.949001	+	0.315273i	$0.102096\pi$
$720$	−5.01373	+	4.16885i	−0.186851	+	0.155364i
$721$		0			0
$722$	−2.72509	−	2.72509i	−0.101417	−	0.101417i
$723$	−0.441322	−	1.64704i	−0.0164129	−	0.0612539i
$724$	2.05934	+	3.56688i	0.0765347	+	0.132562i
$725$	−5.26221	−	14.8715i	−0.195433	−	0.552315i
$726$	−5.18128	−	2.99141i	−0.192295	−	0.111022i
$727$	−33.6108	+	33.6108i	−1.24656	+	1.24656i	−0.289326	+	0.957231i	$0.593431\pi$
$727$	−33.6108	+	33.6108i	−1.24656	+	1.24656i	−0.957231	+	0.289326i	$0.906569\pi$
$728$		0			0
$729$			22.5720i			0.835998i
$730$	2.12373	+	12.3684i	0.0786029	+	0.457776i
$731$	12.0719	−	6.96972i	0.446496	−	0.257785i
$732$	0.345644	−	1.28996i	0.0127754	−	0.0476784i
$733$	−24.8800	+	6.66658i	−0.918964	+	0.246236i	−0.687143	−	0.726523i	$-0.741135\pi$
$733$	−24.8800	+	6.66658i	−0.918964	+	0.246236i	−0.231822	+	0.972758i	$0.574469\pi$
$734$	16.6944			0.616202
$735$		0			0
$736$	1.12392			0.0414283
$737$	−4.59170	+	1.23034i	−0.169138	+	0.0453203i
$738$	−5.44198	+	20.3098i	−0.200322	+	0.747613i
$739$	10.4948	−	6.05920i	0.386059	−	0.222891i	−0.294392	−	0.955685i	$-0.595117\pi$
$739$	10.4948	−	6.05920i	0.386059	−	0.222891i	0.680451	+	0.732793i	$0.261784\pi$
$740$	−6.50539	+	9.20253i	−0.239143	+	0.338292i
$741$		−	2.27977i		−	0.0837493i
$742$		0			0
$743$	23.2618	−	23.2618i	0.853393	−	0.853393i	−0.137157	−	0.990549i	$-0.543796\pi$
$743$	23.2618	−	23.2618i	0.853393	−	0.853393i	0.990549	+	0.137157i	$0.0437964\pi$
$744$	0.965654	+	0.557521i	0.0354026	+	0.0204397i
$745$	10.5913	+	3.90881i	0.388036	+	0.143208i
$746$	−1.58946	−	2.75303i	−0.0581944	−	0.100796i
$747$	−6.05487	−	22.5971i	−0.221536	−	0.826784i
$748$	−21.1182	−	21.1182i	−0.772158	−	0.772158i
$749$		0			0
$750$	−1.58179	−	2.82690i	−0.0577587	−	0.103224i
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	−0.964903	−	0.262607i	$-0.915418\pi$
$751$	−6.98887	+	12.1051i	−0.255028	+	0.441721i	0.709875	+	0.704327i	$0.248751\pi$
$752$	5.69475	+	1.52590i	0.207666	+	0.0556440i
$753$	1.98690	+	0.532387i	0.0724065	+	0.0194013i
$754$	−3.18939	+	5.52418i	−0.116151	+	0.201179i
$755$	19.2181	+	23.1130i	0.699420	+	0.841169i
$756$		0			0
$757$	17.5547	+	17.5547i	0.638036	+	0.638036i	0.950071	−	0.312035i	$-0.101010\pi$
$757$	17.5547	+	17.5547i	0.638036	+	0.638036i	−0.312035	+	0.950071i	$0.601010\pi$
$758$	−1.85146	−	6.90974i	−0.0672481	−	0.250973i
$759$	0.915990	+	1.58654i	0.0332483	+	0.0575878i
$760$	−3.64236	−	7.90341i	−0.132122	−	0.286687i
$761$	−18.9372	−	10.9334i	−0.686471	−	0.396334i	0.115817	−	0.993271i	$-0.463051\pi$
$761$	−18.9372	−	10.9334i	−0.686471	−	0.396334i	−0.802289	+	0.596936i	$0.796385\pi$
$762$	−1.34289	+	1.34289i	−0.0486478	+	0.0486478i
$763$		0			0
$764$		−	17.2023i		−	0.622359i
$765$	−28.2660	−	19.9816i	−1.02196	−	0.722437i
$766$	−12.6382	+	7.29669i	−0.456638	+	0.263640i
$767$	2.86675	−	10.6989i	0.103512	−	0.386313i
$768$	−0.279864	+	0.0749894i	−0.0100987	+	0.00270595i
$769$	−31.0506			−1.11971			−0.559857	−	0.828589i	$-0.689144\pi$
$769$	−31.0506			−1.11971			−0.559857	+	0.828589i	$0.689144\pi$
$770$		0			0
$771$	2.86459			0.103166
$772$	11.6562	−	3.12327i	0.419516	−	0.112409i
$773$	1.57065	−	5.86173i	0.0564922	−	0.210832i	−0.931910	−	0.362689i	$-0.881859\pi$
$773$	1.57065	−	5.86173i	0.0564922	−	0.210832i	0.988402	+	0.151857i	$0.0485254\pi$
$774$	−6.63103	+	3.82843i	−0.238347	+	0.137610i
$775$	12.5004	−	14.6289i	0.449029	−	0.525487i
$776$			9.37769i			0.336640i
$777$		0			0
$778$	−4.38160	+	4.38160i	−0.157088	+	0.157088i
$779$	−24.3023	−	14.0309i	−0.870720	−	0.502710i
$780$	−0.453514	+	1.22884i	−0.0162384	+	0.0439996i
$781$	−13.4374	−	23.2743i	−0.480828	−	0.832819i
$782$	1.54427	+	5.76329i	0.0552229	+	0.206095i
$783$	−3.82404	−	3.82404i	−0.136660	−	0.136660i
$784$		0			0
$785$	−2.45571	−	0.225950i	−0.0876481	−	0.00806449i
$786$	−1.11481	+	1.93091i	−0.0397641	+	0.0688734i
$787$	21.5993	+	5.78752i	0.769932	+	0.206303i	0.622342	−	0.782746i	$-0.286182\pi$
$787$	21.5993	+	5.78752i	0.769932	+	0.206303i	0.147591	+	0.989049i	$0.452848\pi$
$788$	19.5526	+	5.23910i	0.696532	+	0.186635i
$789$	−1.99167	+	3.44968i	−0.0709055	+	0.122812i
$790$	13.9118	+	1.28003i	0.494961	+	0.0455413i
$791$		0			0
$792$	11.6001	+	11.6001i	0.412191	+	0.412191i
$793$	2.41191	+	9.00138i	0.0856495	+	0.319648i
$794$	1.45794	+	2.52523i	0.0517403	+	0.0896169i
$795$	−0.310252	+	0.840660i	−0.0110035	+	0.0298151i
$796$	6.52383	+	3.76653i	0.231231	+	0.133501i
$797$	−16.5528	+	16.5528i	−0.586330	+	0.586330i	−0.936636	−	0.350305i	$-0.886078\pi$
$797$	−16.5528	+	16.5528i	−0.586330	+	0.586330i	0.350305	+	0.936636i	$0.386078\pi$
$798$		0			0
$799$			31.2984i			1.10726i
$800$	0.391082	+	4.98468i	0.0138268	+	0.176235i
$801$	30.1070	−	17.3823i	1.06378	−	0.614174i
$802$	−5.16876	+	19.2901i	−0.182515	+	0.681156i
$803$	30.4975	−	8.17177i	1.07623	−	0.288376i
$804$	−0.244823			−0.00863425
$805$		0			0
$806$	−7.78078			−0.274066
$807$	7.41697	−	1.98737i	0.261090	−	0.0699588i
$808$	4.16678	−	15.5506i	0.146587	−	0.547069i
$809$	2.84139	−	1.64048i	0.0998980	−	0.0576762i	−0.449219	−	0.893422i	$-0.648298\pi$
$809$	2.84139	−	1.64048i	0.0998980	−	0.0576762i	0.549117	+	0.835746i	$0.314964\pi$
$810$	15.0665	+	10.6507i	0.529384	+	0.374228i
$811$		−	17.8693i		−	0.627476i	−0.949510	−	0.313738i	$-0.898419\pi$
$811$		−	17.8693i		−	0.627476i	0.949510	−	0.313738i	$-0.101581\pi$
$812$		0			0
$813$	2.62176	−	2.62176i	0.0919491	−	0.0919491i
$814$	24.5550	+	14.1768i	0.860653	+	0.496898i
$815$	12.3924	+	26.8898i	0.434088	+	0.941910i
$816$	−0.769067	−	1.33206i	−0.0269227	−	0.0466316i
$817$	−2.64486	−	9.87074i	−0.0925318	−	0.345333i
$818$	24.2949	+	24.2949i	0.849451	+	0.849451i
$819$		0			0
$820$	10.3083	+	12.3974i	0.359981	+	0.432937i
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	−0.744312	−	0.667832i	$-0.767222\pi$
$821$	5.90837	−	10.2336i	0.206204	−	0.357155i	0.950516	+	0.310677i	$0.100556\pi$
$822$	−2.47282	−	0.662590i	−0.0862495	−	0.0231105i
$823$	−34.0995	−	9.13692i	−1.18863	−	0.318493i	−0.390287	−	0.920693i	$-0.627624\pi$
$823$	−34.0995	−	9.13692i	−1.18863	−	0.318493i	−0.798345	+	0.602200i	$0.794291\pi$
$824$	9.83476	−	17.0343i	0.342610	−	0.593418i
$825$	−6.71771	+	4.61455i	−0.233881	+	0.160658i
$826$		0			0
$827$	−17.2835	−	17.2835i	−0.601005	−	0.601005i	0.339574	−	0.940579i	$-0.389717\pi$
$827$	−17.2835	−	17.2835i	−0.601005	−	0.601005i	−0.940579	+	0.339574i	$0.889717\pi$
$828$	−0.848257	−	3.16574i	−0.0294790	−	0.110017i
$829$	−17.2877	−	29.9431i	−0.600426	−	1.03997i	−0.992756	−	0.120144i	$-0.961664\pi$
$829$	−17.2877	−	29.9431i	−0.600426	−	1.03997i	0.392330	−	0.919824i	$-0.371669\pi$
$830$	−16.8295	−	6.21104i	−0.584159	−	0.215589i
$831$	−5.04433	−	2.91234i	−0.174986	−	0.101028i
$832$	1.42962	−	1.42962i	0.0495631	−	0.0495631i
$833$		0			0
$834$		−	3.20539i		−	0.110994i
$835$	−8.59183	+	12.1540i	−0.297332	+	0.420607i
$836$	−18.9611	+	10.9472i	−0.655782	+	0.378616i
$837$	1.70734	−	6.37187i	0.0590142	−	0.220244i
$838$	−30.0751	+	8.05859i	−1.03893	+	0.278379i
$839$	50.1328			1.73078			0.865388	−	0.501102i	$-0.167072\pi$
$839$	50.1328			1.73078			0.865388	+	0.501102i	$0.167072\pi$
$840$		0			0
$841$	19.0459			0.656754
$842$	32.5254	−	8.71515i	1.12090	−	0.300344i
$843$	−1.06109	+	3.96003i	−0.0365458	+	0.136391i
$844$	16.9538	−	9.78829i	0.583575	−	0.336927i
$845$	3.37252	+	19.6412i	0.116018	+	0.675679i
$846$		−	17.1920i		−	0.591073i
$847$		0			0
$848$	0.978013	−	0.978013i	0.0335851	−	0.0335851i
$849$	−6.79181	−	3.92125i	−0.233094	−	0.134577i
$850$	−25.0233	+	8.85436i	−0.858292	+	0.303702i
$851$	−2.83227	−	4.90563i	−0.0970888	−	0.168163i
$852$	−0.358232	−	1.33694i	−0.0122728	−	0.0458028i
$853$	2.37500	+	2.37500i	0.0813183	+	0.0813183i	0.746596	−	0.665278i	$-0.231687\pi$
$853$	2.37500	+	2.37500i	0.0813183	+	0.0813183i	−0.665278	+	0.746596i	$0.731687\pi$
$854$		0			0
$855$	−19.5125	+	16.2243i	−0.667312	+	0.554860i
$856$	1.40051	−	2.42575i	0.0478683	−	0.0829103i
$857$	40.5097	+	10.8545i	1.38378	+	0.370784i	0.872494	−	0.488624i	$-0.162501\pi$
$857$	40.5097	+	10.8545i	1.38378	+	0.370784i	0.511290	+	0.859408i	$0.329168\pi$
$858$	3.18320	+	0.852937i	0.108673	+	0.0291188i
$859$	1.17847	−	2.04117i	0.0402090	−	0.0696440i	−0.845221	−	0.534418i	$-0.820531\pi$
$859$	1.17847	−	2.04117i	0.0402090	−	0.0696440i	0.885430	+	0.464774i	$0.153864\pi$
$860$	−0.537952	+	5.84668i	−0.0183440	+	0.199370i
$861$		0			0
$862$	−10.4268	−	10.4268i	−0.355137	−	0.355137i
$863$	12.5138	+	46.7022i	0.425975	+	1.58976i	0.761784	+	0.647831i	$0.224324\pi$
$863$	12.5138	+	46.7022i	0.425975	+	1.58976i	−0.335808	+	0.941930i	$0.609009\pi$
$864$	0.857049	+	1.48445i	0.0291574	+	0.0505021i
$865$	−14.3263	+	6.60242i	−0.487110	+	0.224489i
$866$	−12.2261	−	7.05873i	−0.415459	−	0.239865i
$867$	2.29104	−	2.29104i	0.0778076	−	0.0778076i
$868$		0			0
$869$		−	35.1489i		−	1.19234i
$870$	−2.01456	+	0.345913i	−0.0683000	+	0.0117275i
$871$	1.47950	−	0.854190i	0.0501310	−	0.0289431i
$872$	1.52984	−	5.70944i	0.0518069	−	0.193346i
$873$	26.4141	−	7.07763i	0.893980	−	0.239541i
$874$	4.37408			0.147955
$875$		0			0
$876$	1.62608			0.0549402
$877$	13.3115	−	3.56681i	0.449498	−	0.120443i	−0.0269665	−	0.999636i	$-0.508585\pi$
$877$	13.3115	−	3.56681i	0.449498	−	0.120443i	0.476465	+	0.879194i	$0.341918\pi$
$878$	9.94602	−	37.1191i	0.335662	−	1.25271i
$879$	−6.07477	+	3.50727i	−0.204897	+	0.118297i
$880$	12.3981	−	2.12884i	0.417941	−	0.0717631i
$881$		−	3.32542i		−	0.112036i	−0.998430	−	0.0560181i	$-0.982160\pi$
$881$		−	3.32542i		−	0.112036i	0.998430	−	0.0560181i	$-0.0178405\pi$
$882$		0			0
$883$	−36.8930	+	36.8930i	−1.24155	+	1.24155i	−0.282191	+	0.959358i	$0.591061\pi$
$883$	−36.8930	+	36.8930i	−1.24155	+	1.24155i	−0.959358	+	0.282191i	$0.908939\pi$
$884$	9.29516	+	5.36656i	0.312630	+	0.180497i
$885$	3.22348	−	1.48557i	0.108356	−	0.0499369i
$886$	−2.86780	−	4.96718i	−0.0963456	−	0.166876i
$887$	9.27107	+	34.6001i	0.311292	+	1.16176i	0.927392	+	0.374090i	$0.122045\pi$
$887$	9.27107	+	34.6001i	0.311292	+	1.16176i	−0.616101	+	0.787668i	$0.711289\pi$
$888$	1.03256	+	1.03256i	0.0346506	+	0.0346506i
$889$		0			0
$890$	2.44248	−	26.5458i	0.0818721	−	0.889819i
$891$	23.2105	−	40.2018i	0.777582	−	1.34681i
$892$	−1.99476	−	0.534495i	−0.0667895	−	0.0178962i
$893$	22.1628	+	5.93852i	0.741651	+	0.198725i
$894$	0.731419	−	1.26686i	0.0244623	−	0.0423700i
$895$	−3.79349	+	3.15423i	−0.126803	+	0.105434i
$896$		0			0
$897$	−0.465543	−	0.465543i	−0.0155440	−	0.0155440i
$898$	−1.89007	−	7.05384i	−0.0630725	−	0.235390i
$899$	−6.07098	−	10.5152i	−0.202479	−	0.350703i
$900$	13.7451	−	4.86365i	0.458172	−	0.162122i
$901$	6.35888	+	3.67130i	0.211845	+	0.122309i
$902$	28.6835	−	28.6835i	0.955055	−	0.955055i
$903$		0			0
$904$		−	19.2075i		−	0.638833i
$905$	−1.55854	−	9.07680i	−0.0518077	−	0.301723i
$906$	3.37307	−	1.94744i	0.112063	−	0.0646994i
$907$	−4.46661	+	16.6696i	−0.148312	+	0.553506i	0.851274	+	0.524721i	$0.175830\pi$
$907$	−4.46661	+	16.6696i	−0.148312	+	0.553506i	−0.999586	+	0.0287849i	$0.990836\pi$
$908$	18.0081	−	4.82525i	0.597618	−	0.160131i
$909$	−46.9461			−1.55710
$910$		0			0
$911$	5.56820			0.184483			0.0922414	−	0.995737i	$-0.470597\pi$
$911$	5.56820			0.184483			0.0922414	+	0.995737i	$0.470597\pi$
$912$	−1.08918	+	0.291844i	−0.0360663	+	0.00966392i
$913$	−11.6813	+	43.5952i	−0.386594	+	1.44279i
$914$	4.45641	−	2.57291i	0.147405	−	0.0851042i
$915$	−1.72377	+	2.43844i	−0.0569859	+	0.0806124i
$916$		−	4.00767i		−	0.132417i
$917$		0			0
$918$	−6.43445	+	6.43445i	−0.212368	+	0.212368i
$919$	5.37964	+	3.10593i	0.177458	+	0.102455i	0.586098	−	0.810240i	$-0.300663\pi$
$919$	5.37964	+	3.10593i	0.177458	+	0.102455i	−0.408640	+	0.912696i	$0.633997\pi$
$920$	−2.35772	−	0.870136i	−0.0777318	−	0.0286875i
$921$	3.54381	+	6.13806i	0.116773	+	0.202256i
$922$	−7.61212	−	28.4088i	−0.250692	−	0.935595i
$923$	6.82943	+	6.82943i	0.224794	+	0.224794i
$924$		0			0
$925$	20.7713	−	14.2683i	0.682958	−	0.469139i
$926$	2.86113	−	4.95563i	0.0940226	−	0.162852i
$927$	−55.4029	−	14.8452i	−1.81967	−	0.487579i
$928$	3.04751	+	0.816578i	0.100039	+	0.0268055i
$929$	−0.0947297	+	0.164077i	−0.00310798	+	0.00538318i	−0.867575	−	0.497306i	$-0.834323\pi$
$929$	−0.0947297	+	0.164077i	−0.00310798	+	0.00538318i	0.864467	+	0.502689i	$0.167656\pi$
$930$	−1.59409	−	1.91715i	−0.0522721	−	0.0628660i
$931$		0			0
$932$	−9.70971	−	9.70971i	−0.318052	−	0.318052i
$933$	−0.823556	−	3.07355i	−0.0269620	−	0.100624i
$934$	8.32139	+	14.4131i	0.272284	+	0.471610i
$935$	27.9514	+	60.6507i	0.914108	+	1.98349i
$936$	−5.10577	−	2.94782i	−0.166887	−	0.0963525i
$937$	34.2022	−	34.2022i	1.11734	−	1.11734i	0.125208	−	0.992131i	$-0.460040\pi$
$937$	34.2022	−	34.2022i	1.11734	−	1.11734i	0.992131	−	0.125208i	$-0.0399598\pi$
$938$		0			0
$939$			8.52144i			0.278087i
$940$	−10.7649	−	7.60984i	−0.351112	−	0.248206i
$941$	16.3826	−	9.45851i	0.534058	−	0.308339i	−0.208609	−	0.977999i	$-0.566894\pi$
$941$	16.3826	−	9.45851i	0.534058	−	0.308339i	0.742667	+	0.669660i	$0.233560\pi$
$942$	−0.0827033	+	0.308653i	−0.00269462	+	0.0100565i
$943$	−7.82790	+	2.09748i	−0.254911	+	0.0683033i
$944$	−5.47845			−0.178308
$945$		0			0
$946$	14.7719			0.480276
$947$	−45.5435	+	12.2033i	−1.47996	+	0.396555i	−0.906335	−	0.422560i	$-0.861131\pi$
$947$	−45.5435	+	12.2033i	−1.47996	+	0.396555i	−0.573629	+	0.819115i	$0.694465\pi$
$948$	0.468522	−	1.74855i	0.0152169	−	0.0567902i
$949$	−9.82664	+	5.67341i	−0.318986	+	0.184167i
$950$	1.52201	+	19.3994i	0.0493806	+	0.629400i
$951$			1.24412i			0.0403434i
$952$		0			0
$953$	18.8431	−	18.8431i	0.610389	−	0.610389i	−0.332658	−	0.943047i	$-0.607946\pi$
$953$	18.8431	−	18.8431i	0.610389	−	0.610389i	0.943047	+	0.332658i	$0.107946\pi$
$954$	−3.49290	−	2.01662i	−0.113087	−	0.0652906i
$955$	−13.3180	+	36.0865i	−0.430960	+	1.16773i
$956$	9.83103	+	17.0278i	0.317958	+	0.550720i
$957$	1.33101	+	4.96741i	0.0430256	+	0.160574i
$958$	10.8818	+	10.8818i	0.351575	+	0.351575i
$959$		0			0
$960$	0.645146	+	0.0593598i	0.0208220	+	0.00191583i
$961$	−8.09467	+	14.0204i	−0.261118	+	0.452270i
$962$	−9.84255	−	2.63730i	−0.317337	−	0.0850301i
$963$	−7.88958	−	2.11401i	−0.254238	−	0.0681229i
$964$	2.94256	−	5.09667i	0.0947735	−	0.164153i
$965$	−26.8700	−	2.47231i	−0.864976	−	0.0795863i
$966$		0			0
$967$	27.3703	+	27.3703i	0.880169	+	0.880169i	0.993551	−	0.113383i	$-0.0361687\pi$
$967$	27.3703	+	27.3703i	0.880169	+	0.880169i	−0.113383	+	0.993551i	$0.536169\pi$
$968$	−5.34440	−	19.9456i	−0.171776	−	0.641075i
$969$	−2.99306	−	5.18413i	−0.0961509	−	0.166538i
$970$	7.26018	−	19.6722i	0.233110	−	0.631636i
$971$	27.8750	+	16.0936i	0.894550	+	0.516469i	0.875428	−	0.483348i	$-0.160580\pi$
$971$	27.8750	+	16.0936i	0.894550	+	0.516469i	0.0191221	+	0.999817i	$0.493913\pi$
$972$	5.32668	−	5.32668i	0.170853	−	0.170853i
$973$		0			0
$974$		−	35.9920i		−	1.15326i
$975$	1.90273	−	2.22671i	0.0609362	−	0.0713119i
$976$	3.99172	−	2.30462i	0.127772	−	0.0737691i
$977$	−6.02479	+	22.4848i	−0.192750	+	0.719353i	0.800088	+	0.599883i	$0.204786\pi$
$977$	−6.02479	+	22.4848i	−0.192750	+	0.719353i	−0.992838	+	0.119470i	$0.961881\pi$
$978$	3.70572	−	0.992944i	0.118496	−	0.0317508i
$979$	−67.0692			−2.14354
$980$		0			0
$981$	−17.2364			−0.550314
$982$	14.7616	−	3.95535i	0.471060	−	0.126220i
$983$	−14.7630	+	55.0964i	−0.470868	+	1.75730i	0.165793	+	0.986160i	$0.446981\pi$
$983$	−14.7630	+	55.0964i	−0.470868	+	1.75730i	−0.636662	+	0.771143i	$0.719685\pi$
$984$	1.80926	−	1.04457i	0.0576770	−	0.0332998i
$985$	−36.9606	−	26.1279i	−1.17766	−	0.832505i
$986$			16.7491i			0.533401i
$987$		0			0
$988$	5.56380	−	5.56380i	0.177008	−	0.177008i
$989$	−2.55577	−	1.47557i	−0.0812687	−	0.0469205i
$990$	−15.3535	−	33.3150i	−0.487967	−	1.05882i
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.808478	+	0.588526i	$0.200292\pi$
$991$	28.7703	+	49.8316i	0.913918	+	1.58295i	0.105440	+	0.994426i	$0.466375\pi$
$992$	0.996056	+	3.71733i	0.0316248	+	0.118025i
$993$	7.26279	+	7.26279i	0.230478	+	0.230478i
$994$		0			0
$995$	−10.7694	−	12.9520i	−0.341414	−	0.410607i
$996$	−1.16222	+	2.01302i	−0.0368262	+	0.0637849i
$997$	−23.4284	−	6.27762i	−0.741985	−	0.198814i	−0.132025	−	0.991246i	$-0.542148\pi$
$997$	−23.4284	−	6.27762i	−0.741985	−	0.198814i	−0.609960	+	0.792432i	$0.708815\pi$
$998$	30.5087	+	8.17479i	0.965737	+	0.258768i
$999$	4.31951	−	7.48160i	0.136663	−	0.236707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.l.c.117.2		16
5.3	odd	4	inner	490.2.l.c.313.4		16
7.2	even	3		490.2.g.c.97.7		16
7.3	odd	6	inner	490.2.l.c.227.4		16
7.4	even	3		70.2.k.a.17.3	yes	16
7.5	odd	6		490.2.g.c.97.6		16
7.6	odd	2		70.2.k.a.47.1	yes	16
21.11	odd	6		630.2.bv.c.577.1		16
21.20	even	2		630.2.bv.c.397.3		16
28.11	odd	6		560.2.ci.c.17.3		16
28.27	even	2		560.2.ci.c.257.3		16
35.3	even	12	inner	490.2.l.c.423.2		16
35.4	even	6		350.2.o.c.157.2		16
35.13	even	4		70.2.k.a.33.3	yes	16
35.18	odd	12		70.2.k.a.3.1	✓	16
35.23	odd	12		490.2.g.c.293.6		16
35.27	even	4		350.2.o.c.243.2		16
35.32	odd	12		350.2.o.c.143.4		16
35.33	even	12		490.2.g.c.293.7		16
35.34	odd	2		350.2.o.c.257.4		16
105.53	even	12		630.2.bv.c.73.3		16
105.83	odd	4		630.2.bv.c.523.1		16
140.83	odd	4		560.2.ci.c.33.3		16
140.123	even	12		560.2.ci.c.353.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.1	✓	16	35.18	odd	12
70.2.k.a.17.3	yes	16	7.4	even	3
70.2.k.a.33.3	yes	16	35.13	even	4
70.2.k.a.47.1	yes	16	7.6	odd	2
350.2.o.c.143.4		16	35.32	odd	12
350.2.o.c.157.2		16	35.4	even	6
350.2.o.c.243.2		16	35.27	even	4
350.2.o.c.257.4		16	35.34	odd	2
490.2.g.c.97.6		16	7.5	odd	6
490.2.g.c.97.7		16	7.2	even	3
490.2.g.c.293.6		16	35.23	odd	12
490.2.g.c.293.7		16	35.33	even	12
490.2.l.c.117.2		16	1.1	even	1	trivial
490.2.l.c.227.4		16	7.3	odd	6	inner
490.2.l.c.313.4		16	5.3	odd	4	inner
490.2.l.c.423.2		16	35.3	even	12	inner
560.2.ci.c.17.3		16	28.11	odd	6
560.2.ci.c.33.3		16	140.83	odd	4
560.2.ci.c.257.3		16	28.27	even	2
560.2.ci.c.353.3		16	140.123	even	12
630.2.bv.c.73.3		16	105.53	even	12
630.2.bv.c.397.3		16	21.20	even	2
630.2.bv.c.523.1		16	105.83	odd	4
630.2.bv.c.577.1		16	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)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.0749894 - 0.279864i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.20382 + 0.378409i) q^{5} +0.289737i q^{6} +(-0.707107 + 0.707107i) q^{8} +(2.52538 + 1.45803i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(0.0749894 - 0.279864i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.20382 + 0.378409i) q^{5} +0.289737i q^{6} +(-0.707107 + 0.707107i) q^{8} +(2.52538 + 1.45803i) q^{9} +(2.03078 - 0.935904i) q^{10} +(-2.81288 - 4.87205i) q^{11} +(-0.0749894 - 0.279864i) q^{12} +(1.42962 + 1.42962i) q^{13} +(-0.0593598 + 0.645146i) q^{15} +(0.500000 - 0.866025i) q^{16} +(5.12784 + 1.37400i) q^{17} +(-2.81669 - 0.754730i) q^{18} +(1.94590 - 3.37040i) q^{19} +(-1.71936 + 1.42962i) q^{20} +(3.97801 + 3.97801i) q^{22} +(-0.290892 - 1.08562i) q^{23} +(0.144868 + 0.250919i) q^{24} +(4.71361 - 1.66789i) q^{25} +(-1.75092 - 1.01089i) q^{26} +(1.21205 - 1.21205i) q^{27} -3.15502i q^{29} +(-0.109639 - 0.638527i) q^{30} +(3.33287 - 1.92423i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-1.57445 + 0.421872i) q^{33} -5.30873 q^{34} +2.91605 q^{36} +(4.86824 - 1.30444i) q^{37} +(-1.00727 + 3.75919i) q^{38} +(0.507306 - 0.292893i) q^{39} +(1.29076 - 1.82591i) q^{40} -7.21050i q^{41} +(1.85669 - 1.85669i) q^{43} +(-4.87205 - 2.81288i) q^{44} +(-6.11719 - 2.25760i) q^{45} +(0.561961 + 0.973344i) q^{46} +(1.52590 + 5.69475i) q^{47} +(-0.204875 - 0.204875i) q^{48} +(-4.12132 + 2.83103i) q^{50} +(0.769067 - 1.33206i) q^{51} +(1.95290 + 0.523277i) q^{52} +(1.33599 + 0.357978i) q^{53} +(-0.857049 + 1.48445i) q^{54} +(8.04270 + 9.67269i) q^{55} +(-0.797333 - 0.797333i) q^{57} +(0.816578 + 3.04751i) q^{58} +(-2.73923 - 4.74448i) q^{59} +(0.271166 + 0.588393i) q^{60} +(3.99172 + 2.30462i) q^{61} +(-2.72127 + 2.72127i) q^{62} -1.00000i q^{64} +(-3.69160 - 2.60964i) q^{65} +(1.41161 - 0.814995i) q^{66} +(0.218698 - 0.816193i) q^{67} +(5.12784 - 1.37400i) q^{68} -0.325641 q^{69} +4.77710 q^{71} +(-2.81669 + 0.754730i) q^{72} +(-1.45256 + 5.42104i) q^{73} +(-4.36475 + 2.51999i) q^{74} +(-0.113311 - 1.44425i) q^{75} -3.89180i q^{76} +(-0.414214 + 0.414214i) q^{78} +(5.41079 + 3.12392i) q^{79} +(-0.774197 + 2.09777i) q^{80} +(4.12576 + 7.14603i) q^{81} +(1.86622 + 6.96481i) q^{82} +(-5.67281 - 5.67281i) q^{83} +(-11.8207 - 1.08763i) q^{85} +(-1.31288 + 2.27397i) q^{86} +(-0.882976 - 0.236593i) q^{87} +(5.43407 + 1.45605i) q^{88} +(5.96090 - 10.3246i) q^{89} +(6.49307 + 0.597426i) q^{90} +(-0.794732 - 0.794732i) q^{92} +(-0.288594 - 1.07705i) q^{93} +(-2.94782 - 5.10577i) q^{94} +(-3.01302 + 8.16409i) q^{95} +(0.250919 + 0.144868i) q^{96} +(6.63103 - 6.63103i) q^{97} -16.4050i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5}+O(q^{10}) \) 16 * q + 12 * q^5	\( 16 q + 12 q^{5} + 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} + 36 q^{17} - 8 q^{18} - 8 q^{22} - 4 q^{23} + 12 q^{25} - 12 q^{26} + 20 q^{30} - 24 q^{31} - 48 q^{33} - 8 q^{36} + 4 q^{37} - 24 q^{38} - 8 q^{43} + 12 q^{45} - 8 q^{46} - 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} + 8 q^{57} - 32 q^{58} + 8 q^{60} + 12 q^{61} - 8 q^{65} + 32 q^{67} + 36 q^{68} + 16 q^{71} - 8 q^{72} + 12 q^{73} + 48 q^{75} + 16 q^{78} + 12 q^{80} + 48 q^{82} + 24 q^{85} + 12 q^{86} + 24 q^{87} - 4 q^{88} + 8 q^{92} + 28 q^{93} + 20 q^{95} - 12 q^{96}+O(q^{100}) \) 16 * q + 12 * q^5 + 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 + 36 * q^17 - 8 * q^18 - 8 * q^22 - 4 * q^23 + 12 * q^25 - 12 * q^26 + 20 * q^30 - 24 * q^31 - 48 * q^33 - 8 * q^36 + 4 * q^37 - 24 * q^38 - 8 * q^43 + 12 * q^45 - 8 * q^46 - 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 + 8 * q^57 - 32 * q^58 + 8 * q^60 + 12 * q^61 - 8 * q^65 + 32 * q^67 + 36 * q^68 + 16 * q^71 - 8 * q^72 + 12 * q^73 + 48 * q^75 + 16 * q^78 + 12 * q^80 + 48 * q^82 + 24 * q^85 + 12 * q^86 + 24 * q^87 - 4 * q^88 + 8 * q^92 + 28 * q^93 + 20 * q^95 - 12 * q^96

Introduction

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