LMFDB - Embedded newform 735.2.v.a.178.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(178,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("735.178");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.v (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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			178.2
Character	$\chi$	$=$	735.178
Dual form			735.2.v.a.607.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03317 - 0.544785i) q^{2} +(0.258819 + 0.965926i) q^{3} +(2.10492 + 1.21528i) q^{4} +(2.22675 + 0.203934i) q^{5} -2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-2.03317 - 0.544785i) q^{2} +(0.258819 + 0.965926i) q^{3} +(2.10492 + 1.21528i) q^{4} +(2.22675 + 0.203934i) q^{5} -2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-4.41625 - 1.62773i) q^{10} +(1.33594 - 2.31391i) q^{11} +(-0.629073 + 2.34773i) q^{12} +(1.22714 - 1.22714i) q^{13} +(0.379340 + 2.20366i) q^{15} +(-1.47676 - 2.55782i) q^{16} +(6.48349 - 1.73725i) q^{17} +(2.03317 - 0.544785i) q^{18} +(-3.00865 - 5.21113i) q^{19} +(4.43929 + 3.13538i) q^{20} +(-3.97676 + 3.97676i) q^{22} +(-0.0643048 + 0.239989i) q^{23} +(0.453132 - 0.784847i) q^{24} +(4.91682 + 0.908218i) q^{25} +(-3.16351 + 1.82645i) q^{26} +(-0.707107 - 0.707107i) q^{27} +0.304889i q^{29} +(0.429257 - 4.68706i) q^{30} +(-6.28197 - 3.62690i) q^{31} +(2.07815 + 7.75576i) q^{32} +(2.58083 + 0.691531i) q^{33} -14.1284 q^{34} -2.43055 q^{36} +(1.00463 + 0.269190i) q^{37} +(3.27813 + 12.2341i) q^{38} +(1.50294 + 0.867721i) q^{39} +(-1.29627 - 1.55764i) q^{40} +7.05736i q^{41} +(0.304889 + 0.304889i) q^{43} +(5.62407 - 3.24706i) q^{44} +(-2.03039 + 0.936763i) q^{45} +(0.261485 - 0.452905i) q^{46} +(0.203827 - 0.760694i) q^{47} +(2.08845 - 2.08845i) q^{48} +(-9.50193 - 4.52517i) q^{50} +(3.35610 + 5.81294i) q^{51} +(4.07435 - 1.09172i) q^{52} +(6.81689 - 1.82658i) q^{53} +(1.05244 + 1.82289i) q^{54} +(3.44668 - 4.88005i) q^{55} +(4.25487 - 4.25487i) q^{57} +(0.166099 - 0.619890i) q^{58} +(3.99419 - 6.91813i) q^{59} +(-1.87957 + 5.09952i) q^{60} +(-4.79266 + 2.76704i) q^{61} +(10.7964 + 10.7964i) q^{62} -10.9939i q^{64} +(2.98279 - 2.48228i) q^{65} +(-4.87052 - 2.81199i) q^{66} +(-1.25567 - 4.68622i) q^{67} +(15.7585 + 4.22247i) q^{68} -0.248455 q^{69} +15.3087 q^{71} +(0.875383 + 0.234558i) q^{72} +(3.66788 + 13.6887i) q^{73} +(-1.89593 - 1.09462i) q^{74} +(0.395296 + 4.98435i) q^{75} -14.6253i q^{76} +(-2.58300 - 2.58300i) q^{78} +(9.78372 - 5.64863i) q^{79} +(-2.76675 - 5.99679i) q^{80} +(0.500000 - 0.866025i) q^{81} +(3.84475 - 14.3488i) q^{82} +(-4.88941 + 4.88941i) q^{83} +(14.7914 - 2.54621i) q^{85} +(-0.453791 - 0.785990i) q^{86} +(-0.294500 + 0.0789112i) q^{87} +(-2.33891 + 0.626709i) q^{88} +(-3.45626 - 5.98641i) q^{89} +(4.63845 - 0.798469i) q^{90} +(-0.427009 + 0.427009i) q^{92} +(1.87742 - 7.00662i) q^{93} +(-0.828829 + 1.43557i) q^{94} +(-5.63678 - 12.2174i) q^{95} +(-6.95363 + 4.01468i) q^{96} +(-8.84137 - 8.84137i) q^{97} +2.67187i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 48 q^{8}+O(q^{10}) $ 32 * q + 48 * q^8	$ 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) $ 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.03317	−	0.544785i	−1.43766	−	0.385221i	−0.545950	−	0.837818i	$-0.683831\pi$
$2$	−2.03317	−	0.544785i	−1.43766	−	0.385221i	−0.891715	+	0.452597i	$0.850498\pi$
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	2.10492	+	1.21528i	1.05246	+	0.607638i
$5$	2.22675	+	0.203934i	0.995832	+	0.0912019i
$5$	2.22675	+	0.203934i	0.995832	+	0.0912019i
$6$		−	2.10489i		−	0.859317i
$7$		0			0
$7$		0			0
$8$	−0.640825	−	0.640825i	−0.226566	−	0.226566i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	−4.41625	−	1.62773i	−1.39654	−	0.514733i
$11$	1.33594	−	2.31391i	0.402800	−	0.697670i	−0.591263	−	0.806479i	$-0.701370\pi$
$11$	1.33594	−	2.31391i	0.402800	−	0.697670i	0.994063	+	0.108809i	$0.0347038\pi$
$12$	−0.629073	+	2.34773i	−0.181598	+	0.677732i
$13$	1.22714	−	1.22714i	0.340348	−	0.340348i	−0.516150	−	0.856498i	$-0.672635\pi$
$13$	1.22714	−	1.22714i	0.340348	−	0.340348i	0.856498	+	0.516150i	$0.172635\pi$
$14$		0			0
$15$	0.379340	+	2.20366i	0.0979452	+	0.568982i
$16$	−1.47676	−	2.55782i	−0.369190	−	0.639456i
$17$	6.48349	−	1.73725i	1.57248	−	0.421344i	0.635890	−	0.771780i	$-0.280633\pi$
$17$	6.48349	−	1.73725i	1.57248	−	0.421344i	0.936587	+	0.350436i	$0.113966\pi$
$18$	2.03317	−	0.544785i	0.479222	−	0.128407i
$19$	−3.00865	−	5.21113i	−0.690231	−	1.19551i	−0.971762	−	0.235963i	$-0.924176\pi$
$19$	−3.00865	−	5.21113i	−0.690231	−	1.19551i	0.281531	−	0.959552i	$-0.409158\pi$
$20$	4.43929	+	3.13538i	0.992656	+	0.701092i
$21$		0			0
$22$	−3.97676	+	3.97676i	−0.847848	+	0.847848i
$23$	−0.0643048	+	0.239989i	−0.0134085	+	0.0500411i	−0.972306	−	0.233712i	$-0.924913\pi$
$23$	−0.0643048	+	0.239989i	−0.0134085	+	0.0500411i	0.958897	+	0.283753i	$0.0915795\pi$
$24$	0.453132	−	0.784847i	0.0924951	−	0.160206i
$25$	4.91682	+	0.908218i	0.983364	+	0.181644i
$26$	−3.16351	+	1.82645i	−0.620416	+	0.358197i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$		0			0
$29$			0.304889i			0.0566165i	0.999599	+	0.0283083i	$0.00901200\pi$
$29$			0.304889i			0.0566165i	−0.999599	+	0.0283083i	$0.990988\pi$
$30$	0.429257	−	4.68706i	0.0783713	−	0.855736i
$31$	−6.28197	−	3.62690i	−1.12827	−	0.651410i	−0.184774	−	0.982781i	$-0.559155\pi$
$31$	−6.28197	−	3.62690i	−1.12827	−	0.651410i	−0.943500	+	0.331371i	$0.892489\pi$
$32$	2.07815	+	7.75576i	0.367369	+	1.37104i
$33$	2.58083	+	0.691531i	0.449265	+	0.120380i
$34$	−14.1284			−2.42301
$35$		0			0
$36$	−2.43055			−0.405092
$37$	1.00463	+	0.269190i	0.165160	+	0.0442546i	0.340452	−	0.940262i	$-0.389420\pi$
$37$	1.00463	+	0.269190i	0.165160	+	0.0442546i	−0.175291	+	0.984517i	$0.556087\pi$
$38$	3.27813	+	12.2341i	0.531783	+	1.98464i
$39$	1.50294	+	0.867721i	0.240662	+	0.138947i
$40$	−1.29627	−	1.55764i	−0.204958	−	0.246285i
$41$			7.05736i			1.10217i	0.834447	+	0.551087i	$0.185787\pi$
$41$			7.05736i			1.10217i	−0.834447	+	0.551087i	$0.814213\pi$
$42$		0			0
$43$	0.304889	+	0.304889i	0.0464952	+	0.0464952i	0.729972	−	0.683477i	$-0.239533\pi$
$43$	0.304889	+	0.304889i	0.0464952	+	0.0464952i	−0.683477	+	0.729972i	$0.739533\pi$
$44$	5.62407	−	3.24706i	0.847861	−	0.489513i
$45$	−2.03039	+	0.936763i	−0.302672	+	0.139644i
$46$	0.261485	−	0.452905i	0.0385538	−	0.0667772i
$47$	0.203827	−	0.760694i	0.0297313	−	0.110959i	−0.949466	−	0.313871i	$-0.898374\pi$
$47$	0.203827	−	0.760694i	0.0297313	−	0.110959i	0.979197	+	0.202912i	$0.0650407\pi$
$48$	2.08845	−	2.08845i	0.301442	−	0.301442i
$49$		0			0
$50$	−9.50193	−	4.52517i	−1.34378	−	0.639955i
$51$	3.35610	+	5.81294i	0.469948	+	0.813974i
$52$	4.07435	−	1.09172i	0.565011	−	0.151394i
$53$	6.81689	−	1.82658i	0.936372	−	0.250900i	0.241802	−	0.970326i	$-0.422262\pi$
$53$	6.81689	−	1.82658i	0.936372	−	0.250900i	0.694570	+	0.719426i	$0.255595\pi$
$54$	1.05244	+	1.82289i	0.143219	+	0.248063i
$55$	3.44668	−	4.88005i	0.464750	−	0.658026i
$56$		0			0
$57$	4.25487	−	4.25487i	0.563571	−	0.563571i
$58$	0.166099	−	0.619890i	0.0218099	−	0.0813956i
$59$	3.99419	−	6.91813i	0.519999	−	0.900664i	−0.479731	−	0.877416i	$-0.659266\pi$
$59$	3.99419	−	6.91813i	0.519999	−	0.900664i	0.999730	−	0.0232486i	$-0.00740092\pi$
$60$	−1.87957	+	5.09952i	−0.242651	+	0.658346i
$61$	−4.79266	+	2.76704i	−0.613637	+	0.354284i	−0.774388	−	0.632711i	$-0.781942\pi$
$61$	−4.79266	+	2.76704i	−0.613637	+	0.354284i	0.160750	+	0.986995i	$0.448609\pi$
$62$	10.7964	+	10.7964i	1.37114	+	1.37114i
$63$		0			0
$64$		−	10.9939i		−	1.37423i
$65$	2.98279	−	2.48228i	0.369970	−	0.307889i
$66$	−4.87052	−	2.81199i	−0.599519	−	0.346133i
$67$	−1.25567	−	4.68622i	−0.153404	−	0.572513i	−0.999237	−	0.0390641i	$-0.987562\pi$
$67$	−1.25567	−	4.68622i	−0.153404	−	0.572513i	0.845832	−	0.533449i	$-0.179104\pi$
$68$	15.7585	+	4.22247i	1.91099	+	0.512049i
$69$	−0.248455			−0.0299104
$70$		0			0
$71$	15.3087			1.81681			0.908407	−	0.418087i	$-0.137299\pi$
$71$	15.3087			1.81681			0.908407	+	0.418087i	$0.137299\pi$
$72$	0.875383	+	0.234558i	0.103165	+	0.0276430i
$73$	3.66788	+	13.6887i	0.429293	+	1.60214i	0.754366	+	0.656454i	$0.227944\pi$
$73$	3.66788	+	13.6887i	0.429293	+	1.60214i	−0.325073	+	0.945689i	$0.605389\pi$
$74$	−1.89593	−	1.09462i	−0.220397	−	0.127247i
$75$	0.395296	+	4.98435i	0.0456449	+	0.575543i
$76$		−	14.6253i		−	1.67764i
$77$		0			0
$78$	−2.58300	−	2.58300i	−0.292467	−	0.292467i
$79$	9.78372	−	5.64863i	1.10075	−	0.635521i	0.164335	−	0.986405i	$-0.447452\pi$
$79$	9.78372	−	5.64863i	1.10075	−	0.635521i	0.936419	+	0.350884i	$0.114119\pi$
$80$	−2.76675	−	5.99679i	−0.309332	−	0.670462i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	3.84475	−	14.3488i	0.424581	−	1.58456i
$83$	−4.88941	+	4.88941i	−0.536682	+	0.536682i	−0.922553	−	0.385871i	$-0.873901\pi$
$83$	−4.88941	+	4.88941i	−0.536682	+	0.536682i	0.385871	+	0.922553i	$0.373901\pi$
$84$		0			0
$85$	14.7914	−	2.54621i	1.60435	−	0.276175i
$86$	−0.453791	−	0.785990i	−0.0489336	−	0.0847554i
$87$	−0.294500	+	0.0789112i	−0.0315738	+	0.00846017i
$88$	−2.33891	+	0.626709i	−0.249329	+	0.0668074i
$89$	−3.45626	−	5.98641i	−0.366363	−	0.634559i	0.622631	−	0.782515i	$-0.286064\pi$
$89$	−3.45626	−	5.98641i	−0.366363	−	0.634559i	−0.988994	+	0.147957i	$0.952730\pi$
$90$	4.63845	−	0.798469i	0.488935	−	0.0841660i
$91$		0			0
$92$	−0.427009	+	0.427009i	−0.0445188	+	0.0445188i
$93$	1.87742	−	7.00662i	0.194679	−	0.726553i
$94$	−0.828829	+	1.43557i	−0.0854872	+	0.148068i
$95$	−5.63678	−	12.2174i	−0.578321	−	1.25348i
$96$	−6.95363	+	4.01468i	−0.709702	+	0.409746i
$97$	−8.84137	−	8.84137i	−0.897705	−	0.897705i	0.0975276	−	0.995233i	$-0.468907\pi$
$97$	−8.84137	−	8.84137i	−0.897705	−	0.897705i	−0.995233	+	0.0975276i	$0.968907\pi$
$98$		0			0
$99$			2.67187i			0.268533i
$100$	9.24578	+	7.88702i	0.924578	+	0.788702i
$101$	−6.26104	−	3.61481i	−0.622996	−	0.359687i	0.155038	−	0.987908i	$-0.450450\pi$
$101$	−6.26104	−	3.61481i	−0.622996	−	0.359687i	−0.778035	+	0.628221i	$0.783783\pi$
$102$	−3.65671	−	13.6470i	−0.362068	−	1.35126i
$103$	9.48757	+	2.54219i	0.934838	+	0.250489i	0.693916	−	0.720056i	$-0.255884\pi$
$103$	9.48757	+	2.54219i	0.934838	+	0.250489i	0.240921	+	0.970545i	$0.422550\pi$
$104$	−1.57277			−0.154222
$105$		0			0
$106$	−14.8550			−1.44284
$107$	10.2082	+	2.73529i	0.986867	+	0.264430i	0.715934	−	0.698168i	$-0.246001\pi$
$107$	10.2082	+	2.73529i	0.986867	+	0.264430i	0.270933	+	0.962598i	$0.412668\pi$
$108$	−0.629073	−	2.34773i	−0.0605326	−	0.225911i
$109$	−5.15590	−	2.97676i	−0.493846	−	0.285122i	0.232323	−	0.972639i	$-0.425367\pi$
$109$	−5.15590	−	2.97676i	−0.493846	−	0.285122i	−0.726168	+	0.687517i	$0.758701\pi$
$110$	−9.66624	+	8.04425i	−0.921640	+	0.766989i
$111$			1.04007i			0.0987192i
$112$		0			0
$113$	6.99031	+	6.99031i	0.657593	+	0.657593i	0.954810	−	0.297217i	$-0.0960585\pi$
$113$	6.99031	+	6.99031i	0.657593	+	0.657593i	−0.297217	+	0.954810i	$0.596058\pi$
$114$	−10.9688	+	6.33286i	−1.02733	+	0.593127i
$115$	−0.192132	+	0.521281i	−0.0179164	+	0.0486097i
$116$	−0.370525	+	0.641768i	−0.0344024	+	0.0595866i
$117$	−0.449165	+	1.67631i	−0.0415253	+	0.154975i
$118$	−11.8897	+	11.8897i	−1.09454	+	1.09454i
$119$		0			0
$120$	1.16907	−	1.65525i	0.106721	−	0.151103i
$121$	1.93055	+	3.34381i	0.175505	+	0.303983i
$122$	11.2517	−	3.01489i	1.01868	−	0.272955i
$123$	−6.81689	+	1.82658i	−0.614658	+	0.164697i
$124$	−8.81536	−	15.2686i	−0.791643	−	1.37117i
$125$	10.7633	+	3.02508i	0.962700	+	0.270571i
$126$		0			0
$127$	2.86110	−	2.86110i	0.253882	−	0.253882i	−0.568678	−	0.822560i	$-0.692545\pi$
$127$	2.86110	−	2.86110i	0.253882	−	0.253882i	0.822560	+	0.568678i	$0.192545\pi$
$128$	−1.83298	+	6.84079i	−0.162014	+	0.604646i
$129$	−0.215589	+	0.373412i	−0.0189816	+	0.0328771i
$130$	−7.41682	+	3.42191i	−0.650498	+	0.300121i
$131$	−8.09529	+	4.67382i	−0.707289	+	0.408353i	−0.810056	−	0.586352i	$-0.800564\pi$
$131$	−8.09529	+	4.67382i	−0.707289	+	0.408353i	0.102767	+	0.994705i	$0.467230\pi$
$132$	4.59204	+	4.59204i	0.399686	+	0.399686i
$133$		0			0
$134$			10.2119i			0.882177i
$135$	−1.43035	−	1.71875i	−0.123105	−	0.147927i
$136$	−5.26805	−	3.04151i	−0.451732	−	0.260807i
$137$	2.75230	+	10.2717i	0.235145	+	0.877573i	0.978083	+	0.208213i	$0.0667648\pi$
$137$	2.75230	+	10.2717i	0.235145	+	0.877573i	−0.742938	+	0.669360i	$0.766569\pi$
$138$	0.505150	+	0.135354i	0.0430012	+	0.0115221i
$139$	7.78902			0.660656			0.330328	−	0.943866i	$-0.392841\pi$
$139$	7.78902			0.660656			0.330328	+	0.943866i	$0.392841\pi$
$140$		0			0
$141$	0.787528			0.0663218
$142$	−31.1252	−	8.33998i	−2.61197	−	0.699875i
$143$	−1.20011	−	4.47888i	−0.100358	−	0.374543i
$144$	2.55782	+	1.47676i	0.213152	+	0.123063i
$145$	−0.0621772	+	0.678912i	−0.00516353	+	0.0563806i
$146$		−	29.8296i		−	2.46872i
$147$		0			0
$148$	1.78753	+	1.78753i	0.146934	+	0.146934i
$149$	−12.3716	+	7.14275i	−1.01352	+	0.585157i	−0.912221	−	0.409699i	$-0.865634\pi$
$149$	−12.3716	+	7.14275i	−1.01352	+	0.585157i	−0.101301	+	0.994856i	$0.532301\pi$
$150$	1.91170	−	10.3494i	0.156089	−	0.845022i
$151$	−4.88995	+	8.46964i	−0.397939	+	0.689250i	−0.993471	−	0.114081i	$-0.963608\pi$
$151$	−4.88995	+	8.46964i	−0.397939	+	0.689250i	0.595533	+	0.803331i	$0.296941\pi$
$152$	−1.41141	+	5.26744i	−0.114480	+	0.427245i
$153$	−4.74624	+	4.74624i	−0.383711	+	0.383711i
$154$		0			0
$155$	−13.2487	−	9.35729i	−1.06416	−	0.751596i
$156$	2.10904	+	3.65296i	0.168858	+	0.292471i
$157$	−2.97426	+	0.796951i	−0.237372	+	0.0636036i	−0.375544	−	0.926805i	$-0.622544\pi$
$157$	−2.97426	+	0.796951i	−0.237372	+	0.0636036i	0.138172	+	0.990408i	$0.455877\pi$
$158$	−22.9692	+	6.15458i	−1.82733	+	0.489632i
$159$	3.52868	+	6.11186i	0.279843	+	0.484702i
$160$	3.04586	+	17.6939i	0.240796	+	1.39883i
$161$		0			0
$162$	−1.48838	+	1.48838i	−0.116938	+	0.116938i
$163$	−5.00566	+	18.6814i	−0.392074	+	1.46324i	0.434633	+	0.900607i	$0.356878\pi$
$163$	−5.00566	+	18.6814i	−0.392074	+	1.46324i	−0.826707	+	0.562632i	$0.809789\pi$
$164$	−8.57664	+	14.8552i	−0.669723	+	1.15999i
$165$	5.60583	+	2.06618i	0.436414	+	0.160852i
$166$	12.6047	−	7.27730i	0.978311	−	0.564828i
$167$	−6.23288	−	6.23288i	−0.482315	−	0.482315i	0.423555	−	0.905870i	$-0.360782\pi$
$167$	−6.23288	−	6.23288i	−0.482315	−	0.482315i	−0.905870	+	0.423555i	$0.860782\pi$
$168$		0			0
$169$			9.98824i			0.768326i
$170$	−31.4605	−	2.88126i	−2.41291	−	0.220983i
$171$	5.21113	+	3.00865i	0.398505	+	0.230077i
$172$	0.271243	+	1.01229i	0.0206821	+	0.0771866i
$173$	−9.24710	−	2.47775i	−0.703044	−	0.188380i	−0.110450	−	0.993882i	$-0.535229\pi$
$173$	−9.24710	−	2.47775i	−0.703044	−	0.188380i	−0.592594	+	0.805501i	$0.701896\pi$
$174$	0.641758			0.0486515
$175$		0			0
$176$	−7.89143			−0.594839
$177$	7.71617	+	2.06754i	0.579983	+	0.155406i
$178$	3.76583	+	14.0543i	0.282261	+	1.05341i
$179$	1.12673	+	0.650516i	0.0842155	+	0.0486218i	0.541516	−	0.840690i	$-0.317850\pi$
$179$	1.12673	+	0.650516i	0.0842155	+	0.0486218i	−0.457301	+	0.889312i	$0.651184\pi$
$180$	−5.41223	−	0.495671i	−0.403404	−	0.0369452i
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$		0			0
$183$	−3.91319	−	3.91319i	−0.289271	−	0.289271i
$184$	0.194999	−	0.112583i	0.0143755	−	0.00829971i
$185$	2.18217	+	0.804297i	0.160436	+	0.0591331i
$186$	−7.63421	+	13.2228i	−0.559767	+	0.969545i
$187$	4.64170	−	17.3230i	0.339434	−	1.26679i
$188$	1.35349	−	1.35349i	0.0987136	−	0.0987136i
$189$		0			0
$190$	4.80462	+	27.9109i	0.348564	+	2.02487i
$191$	−0.968954	−	1.67828i	−0.0701110	−	0.121436i	0.828839	−	0.559488i	$-0.189002\pi$
$191$	−0.968954	−	1.67828i	−0.0701110	−	0.121436i	−0.898950	+	0.438052i	$0.855669\pi$
$192$	10.6192	−	2.84542i	0.766378	−	0.205350i
$193$	10.6931	−	2.86520i	0.769703	−	0.206241i	0.147463	−	0.989068i	$-0.452889\pi$
$193$	10.6931	−	2.86520i	0.769703	−	0.206241i	0.622240	+	0.782826i	$0.286223\pi$
$194$	13.1593	+	22.7926i	0.944784	+	1.63641i
$195$	3.16970	+	2.23870i	0.226987	+	0.160316i
$196$		0			0
$197$	−8.50767	+	8.50767i	−0.606146	+	0.606146i	−0.941937	−	0.335790i	$-0.890997\pi$
$197$	−8.50767	+	8.50767i	−0.606146	+	0.606146i	0.335790	+	0.941937i	$0.390997\pi$
$198$	1.45560	−	5.43236i	0.103445	−	0.386061i
$199$	1.62730	−	2.81856i	0.115356	−	0.199803i	−0.802566	−	0.596563i	$-0.796532\pi$
$199$	1.62730	−	2.81856i	0.115356	−	0.199803i	0.917922	+	0.396761i	$0.129866\pi$
$200$	−2.56881	−	3.73283i	−0.181643	−	0.263951i
$201$	4.20155	−	2.42577i	0.296355	−	0.171100i
$202$	10.7604	+	10.7604i	0.757101	+	0.757101i
$203$		0			0
$204$			16.3144i			1.14223i
$205$	−1.43923	+	15.7150i	−0.100520	+	1.09758i
$206$	−17.9048	−	10.3374i	−1.24749	−	0.720238i
$207$	−0.0643048	−	0.239989i	−0.00446949	−	0.0166804i
$208$	−4.95101	−	1.32662i	−0.343291	−	0.0919845i
$209$	−16.0774			−1.11210
$210$		0			0
$211$	−17.2508			−1.18759			−0.593797	−	0.804615i	$-0.702372\pi$
$211$	−17.2508			−1.18759			−0.593797	+	0.804615i	$0.702372\pi$
$212$	16.5688	+	4.43960i	1.13795	+	0.304913i
$213$	3.96220	+	14.7871i	0.271485	+	1.01320i
$214$	−19.2649	−	11.1226i	−1.31692	−	0.760324i
$215$	0.616735	+	0.741089i	0.0420610	+	0.0505419i
$216$			0.906263i			0.0616634i
$217$		0			0
$218$	8.86110	+	8.86110i	0.600150	+	0.600150i
$219$	−12.2730	+	7.08580i	−0.829330	+	0.478814i
$220$	13.1856	−	6.08345i	0.888972	−	0.410146i
$221$	5.82432	−	10.0880i	0.391786	−	0.678593i
$222$	0.566615	−	2.11464i	0.0380287	−	0.141925i
$223$	−4.58392	+	4.58392i	−0.306962	+	0.306962i	−0.843730	−	0.536768i	$-0.819645\pi$
$223$	−4.58392	+	4.58392i	−0.306962	+	0.306962i	0.536768	+	0.843730i	$0.319645\pi$
$224$		0			0
$225$	−4.71220	+	1.67187i	−0.314147	+	0.111458i
$226$	−10.4042	−	18.0207i	−0.692080	−	1.19872i
$227$	−19.3447	+	5.18339i	−1.28395	+	0.344034i	−0.835360	−	0.549703i	$-0.814741\pi$
$227$	−19.3447	+	5.18339i	−1.28395	+	0.344034i	−0.448592	+	0.893737i	$0.648074\pi$
$228$	14.1270	−	3.78532i	0.935583	−	0.250689i
$229$	14.4654	+	25.0547i	0.955898	+	1.65566i	0.732300	+	0.680982i	$0.238447\pi$
$229$	14.4654	+	25.0547i	0.955898	+	1.65566i	0.223598	+	0.974681i	$0.428220\pi$
$230$	0.674623	−	0.955180i	0.0444833	−	0.0629827i
$231$		0			0
$232$	0.195381	−	0.195381i	0.0128274	−	0.0128274i
$233$	−1.75160	+	6.53706i	−0.114751	+	0.428257i	−0.999268	−	0.0382507i	$-0.987821\pi$
$233$	−1.75160	+	6.53706i	−0.114751	+	0.428257i	0.884517	+	0.466508i	$0.154488\pi$
$234$	1.82645	−	3.16351i	0.119399	−	0.206805i
$235$	0.609003	−	1.65231i	0.0397270	−	0.107785i
$236$	16.8149	−	9.70808i	1.09456	−	0.631942i
$237$	7.98837	+	7.98837i	0.518901	+	0.518901i
$238$		0			0
$239$		−	16.1769i		−	1.04640i	−0.852210	−	0.523200i	$-0.824738\pi$
$239$		−	16.1769i		−	1.04640i	0.852210	−	0.523200i	$-0.175262\pi$
$240$	5.07637	−	4.22456i	0.327678	−	0.272694i
$241$	−9.84735	−	5.68537i	−0.634324	−	0.366227i	0.148101	−	0.988972i	$-0.452684\pi$
$241$	−9.84735	−	5.68537i	−0.634324	−	0.366227i	−0.782425	+	0.622745i	$0.786017\pi$
$242$	−2.10347	−	7.85026i	−0.135216	−	0.504634i
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	−13.4509			−0.861105
$245$		0			0
$246$	14.8550			0.947117
$247$	−10.0868	−	2.70276i	−0.641810	−	0.171972i
$248$	1.70144	+	6.34985i	0.108041	+	0.403216i
$249$	−5.98828	−	3.45733i	−0.379492	−	0.219100i
$250$	−20.2356	−	12.0142i	−1.27981	−	0.759843i
$251$		−	6.95039i		−	0.438705i	−0.975646	−	0.219352i	$-0.929606\pi$
$251$		−	6.95039i		−	0.438705i	0.975646	−	0.219352i	$-0.0703944\pi$
$252$		0			0
$253$	0.469405	+	0.469405i	0.0295112	+	0.0295112i
$254$	−7.37578	+	4.25841i	−0.462798	+	0.267196i
$255$	6.28774	+	13.6284i	0.393754	+	0.853442i
$256$	−3.54033	+	6.13203i	−0.221271	+	0.383252i
$257$	3.69280	−	13.7817i	0.230350	−	0.859679i	−0.749840	−	0.661620i	$-0.769869\pi$
$257$	3.69280	−	13.7817i	0.230350	−	0.859679i	0.980190	−	0.198060i	$-0.0634640\pi$
$258$	0.641758	−	0.641758i	0.0399541	−	0.0399541i
$259$		0			0
$260$	9.29520	−	1.60009i	0.576464	−	0.0992332i
$261$	−0.152445	−	0.264042i	−0.00943609	−	0.0163438i
$262$	19.0053	−	5.09245i	1.17415	−	0.314613i
$263$	−24.8595	+	6.66107i	−1.53290	+	0.410739i	−0.923964	−	0.382480i	$-0.875070\pi$
$263$	−24.8595	+	6.66107i	−1.53290	+	0.410739i	−0.608936	+	0.793219i	$0.708403\pi$
$264$	−1.21071	−	2.09701i	−0.0745140	−	0.129062i
$265$	15.5520	−	2.67714i	0.955352	−	0.164456i
$266$		0			0
$267$	4.88789	−	4.88789i	0.299134	−	0.299134i
$268$	3.05197	−	11.3901i	0.186429	−	0.695761i
$269$	7.75593	−	13.4337i	0.472888	−	0.819065i	−0.526631	−	0.850094i	$-0.676545\pi$
$269$	7.75593	−	13.4337i	0.472888	−	0.819065i	0.999518	+	0.0310287i	$0.00987831\pi$
$270$	1.97178	+	4.27374i	0.119999	+	0.260091i
$271$	−11.5544	+	6.67091i	−0.701877	+	0.405229i	−0.808046	−	0.589119i	$-0.799475\pi$
$271$	−11.5544	+	6.67091i	−0.701877	+	0.405229i	0.106169	+	0.994348i	$0.466142\pi$
$272$	−14.0181	−	14.0181i	−0.849974	−	0.849974i
$273$		0			0
$274$		−	22.3835i		−	1.35224i
$275$	8.67009	−	10.1638i	0.522826	−	0.612898i
$276$	−0.522977	−	0.301941i	−0.0314795	−	0.0181747i
$277$	−0.734104	−	2.73971i	−0.0441080	−	0.164613i	0.940359	−	0.340184i	$-0.110489\pi$
$277$	−0.734104	−	2.73971i	−0.0441080	−	0.164613i	−0.984467	+	0.175571i	$0.943823\pi$
$278$	−15.8364	−	4.24334i	−0.949802	−	0.254499i
$279$	7.25379			0.434273
$280$		0			0
$281$	13.5557			0.808664			0.404332	−	0.914612i	$-0.367504\pi$
$281$	13.5557			0.808664			0.404332	+	0.914612i	$0.367504\pi$
$282$	−1.60117	−	0.429034i	−0.0953486	−	0.0255486i
$283$	−5.94585	−	22.1902i	−0.353444	−	1.31907i	−0.882431	−	0.470441i	$-0.844095\pi$
$283$	−5.94585	−	22.1902i	−0.353444	−	1.31907i	0.528987	−	0.848630i	$-0.322572\pi$
$284$	32.2237	+	18.6044i	1.91212	+	1.10397i
$285$	10.3422	−	8.60681i	0.612621	−	0.509824i
$286$			9.76010i			0.577127i
$287$		0			0
$288$	−5.67761	−	5.67761i	−0.334557	−	0.334557i
$289$	24.2952	−	14.0268i	1.42913	−	0.825107i
$290$	0.496278	−	1.34647i	0.0291424	−	0.0790673i
$291$	6.25179	−	10.8284i	0.366487	−	0.634773i
$292$	−8.91497	+	33.2711i	−0.521709	+	1.94705i
$293$	−2.41765	+	2.41765i	−0.141240	+	0.141240i	−0.774192	−	0.632951i	$-0.781843\pi$
$293$	−2.41765	+	2.41765i	−0.141240	+	0.141240i	0.632951	+	0.774192i	$0.281843\pi$
$294$		0			0
$295$	10.3049	−	14.5904i	0.599974	−	0.849486i
$296$	−0.471289	−	0.816297i	−0.0273931	−	0.0474463i
$297$	−2.58083	+	0.691531i	−0.149755	+	0.0401267i
$298$	29.0448	−	7.78253i	1.68252	−	0.450830i
$299$	0.215589	+	0.373412i	0.0124679	+	0.0215950i
$300$	−5.22529	+	10.9720i	−0.301682	+	0.633472i
$301$		0			0
$302$	14.5562	−	14.5562i	0.837616	−	0.837616i
$303$	1.87116	−	6.98328i	0.107496	−	0.401179i
$304$	−8.88610	+	15.3912i	−0.509653	+	0.882744i
$305$	−11.2363	+	5.18413i	−0.643391	+	0.296842i
$306$	12.2356	−	7.06422i	0.699462	−	0.403834i
$307$	7.21300	+	7.21300i	0.411667	+	0.411667i	0.882319	−	0.470652i	$-0.155981\pi$
$307$	7.21300	+	7.21300i	0.411667	+	0.411667i	−0.470652	+	0.882319i	$0.655981\pi$
$308$		0			0
$309$			9.82225i			0.558768i
$310$	21.8391	+	26.2426i	1.24038	+	1.49048i
$311$	8.88036	+	5.12708i	0.503559	+	0.290730i	0.730182	−	0.683253i	$-0.239435\pi$
$311$	8.88036	+	5.12708i	0.503559	+	0.290730i	−0.226623	+	0.973983i	$0.572769\pi$
$312$	−0.407062	−	1.51918i	−0.0230453	−	0.0860064i
$313$	−30.1760	−	8.08564i	−1.70565	−	0.457027i	−0.731298	−	0.682059i	$-0.761085\pi$
$313$	−30.1760	−	8.08564i	−1.70565	−	0.457027i	−0.974352	+	0.225031i	$0.927752\pi$
$314$	6.48134			0.365763
$315$		0			0
$316$	27.4586			1.54467
$317$	16.7425	+	4.48613i	0.940351	+	0.251966i	0.696263	−	0.717787i	$-0.254845\pi$
$317$	16.7425	+	4.48613i	0.940351	+	0.251966i	0.244088	+	0.969753i	$0.421511\pi$
$318$	−3.84475	−	14.3488i	−0.215603	−	0.804640i
$319$	0.705486	+	0.407313i	0.0394996	+	0.0228051i
$320$	2.24202	−	24.4805i	0.125332	−	1.36850i
$321$			10.5683i			0.589867i
$322$		0			0
$323$	−28.5595	−	28.5595i	−1.58909	−	1.58909i
$324$	2.10492	−	1.21528i	0.116940	−	0.0675153i
$325$	7.14815	−	4.91913i	0.396508	−	0.272864i
$326$	20.3547	−	35.2553i	1.12734	−	1.95261i
$327$	1.54088	−	5.75066i	0.0852111	−	0.318012i
$328$	4.52253	−	4.52253i	0.249715	−	0.249715i
$329$		0			0
$330$	−10.2720	−	7.25487i	−0.565453	−	0.399367i
$331$	−0.631541	−	1.09386i	−0.0347126	−	0.0601240i	0.848147	−	0.529761i	$-0.177718\pi$
$331$	−0.631541	−	1.09386i	−0.0347126	−	0.0601240i	−0.882860	+	0.469637i	$0.844385\pi$
$332$	−16.2338	+	4.34983i	−0.890945	+	0.238728i
$333$	−1.00463	+	0.269190i	−0.0550535	+	0.0147515i
$334$	9.27690	+	16.0681i	0.507609	+	0.879205i
$335$	−1.84038	−	10.6911i	−0.100551	−	0.584118i
$336$		0			0
$337$	−9.55621	+	9.55621i	−0.520560	+	0.520560i	−0.917741	−	0.397180i	$-0.869989\pi$
$337$	−9.55621	+	9.55621i	−0.520560	+	0.520560i	0.397180	+	0.917741i	$0.369989\pi$
$338$	5.44145	−	20.3078i	0.295976	−	1.10460i
$339$	−4.94289	+	8.56135i	−0.268461	+	0.464988i
$340$	34.2290	+	12.6161i	1.85633	+	0.684201i
$341$	−16.7846	+	9.69060i	−0.908938	+	0.524775i
$342$	−8.95602	−	8.95602i	−0.484286	−	0.484286i
$343$		0			0
$344$		−	0.390761i		−	0.0210684i
$345$	−0.553246	−	0.0506683i	−0.0297858	−	0.00272789i
$346$	17.4510	+	10.0754i	0.938174	+	0.541655i
$347$	2.39738	+	8.94713i	0.128698	+	0.480307i	0.999944	−	0.0105386i	$-0.00335460\pi$
$347$	2.39738	+	8.94713i	0.128698	+	0.480307i	−0.871247	+	0.490846i	$0.836688\pi$
$348$	−0.715799	−	0.191798i	−0.0383708	−	0.0102814i
$349$	−2.77139			−0.148349			−0.0741746	−	0.997245i	$-0.523632\pi$
$349$	−2.77139			−0.148349			−0.0741746	+	0.997245i	$0.523632\pi$
$350$		0			0
$351$	−1.73544			−0.0926310
$352$	20.7224	+	5.55255i	1.10451	+	0.295952i
$353$	−0.355252	−	1.32582i	−0.0189082	−	0.0705663i	0.955827	−	0.293929i	$-0.0949631\pi$
$353$	−0.355252	−	1.32582i	−0.0189082	−	0.0705663i	−0.974735	+	0.223363i	$0.928296\pi$
$354$	−14.5619	−	8.40731i	−0.773956	−	0.446844i
$355$	34.0887	+	3.12197i	1.80924	+	0.165697i
$356$		−	16.8012i		−	0.890463i
$357$		0			0
$358$	−1.93643	−	1.93643i	−0.102344	−	0.102344i
$359$	8.07840	−	4.66406i	0.426361	−	0.246160i	−0.271434	−	0.962457i	$-0.587498\pi$
$359$	8.07840	−	4.66406i	0.426361	−	0.246160i	0.697795	+	0.716297i	$0.254164\pi$
$360$	1.90142	+	0.700822i	0.100214	+	0.0369366i
$361$	−8.60390	+	14.9024i	−0.452837	+	0.784336i
$362$	−4.62265	+	17.2520i	−0.242961	+	0.906744i
$363$	−2.73021	+	2.73021i	−0.143299	+	0.143299i
$364$		0			0
$365$	5.37586	+	31.2293i	0.281385	+	1.63462i
$366$	5.82432	+	10.0880i	0.304442	+	0.527309i
$367$	−17.7631	+	4.75960i	−0.927225	+	0.248449i	−0.690671	−	0.723169i	$-0.742685\pi$
$367$	−17.7631	+	4.75960i	−0.927225	+	0.248449i	−0.236554	+	0.971618i	$0.576018\pi$
$368$	0.708812	−	0.189926i	0.0369494	−	0.00990056i
$369$	−3.52868	−	6.11186i	−0.183696	−	0.318170i
$370$	−3.99853	−	2.82408i	−0.207874	−	0.146817i
$371$		0			0
$372$	12.4668	−	12.4668i	0.646373	−	0.646373i
$373$	7.56784	−	28.2436i	0.391848	−	1.46240i	−0.435235	−	0.900317i	$-0.643335\pi$
$373$	7.56784	−	28.2436i	0.391848	−	1.46240i	0.827083	−	0.562080i	$-0.189999\pi$
$374$	−18.8747	+	32.6919i	−0.975986	+	1.69046i
$375$	−0.136251	+	11.1795i	−0.00703599	+	0.577307i
$376$	−0.618089	+	0.356854i	−0.0318755	+	0.0184033i
$377$	0.374143	+	0.374143i	0.0192693	+	0.0192693i
$378$		0			0
$379$		−	22.0077i		−	1.13046i	−0.824933	−	0.565230i	$-0.808787\pi$
$379$		−	22.0077i		−	1.13046i	0.824933	−	0.565230i	$-0.191213\pi$
$380$	2.98260	−	32.5670i	0.153004	−	1.67065i
$381$	3.50412	+	2.02311i	0.179522	+	0.103647i
$382$	1.05574	+	3.94009i	0.0540165	+	0.201592i
$383$	0.533272	+	0.142890i	0.0272489	+	0.00730133i	0.272418	−	0.962179i	$-0.412177\pi$
$383$	0.533272	+	0.142890i	0.0272489	+	0.00730133i	−0.245169	+	0.969480i	$0.578843\pi$
$384$	−7.08211			−0.361407
$385$		0			0
$386$	−23.3017			−1.18602
$387$	−0.416487	−	0.111597i	−0.0211712	−	0.00567281i
$388$	−7.86567	−	29.3551i	−0.399319	−	1.49028i
$389$	22.4560	+	12.9650i	1.13857	+	0.657352i	0.946075	−	0.323947i	$-0.105010\pi$
$389$	22.4560	+	12.9650i	1.13857	+	0.657352i	0.192491	+	0.981299i	$0.438343\pi$
$390$	−5.22493	−	6.27844i	−0.264574	−	0.317921i
$391$			1.66768i			0.0843381i
$392$		0			0
$393$	−6.60978	−	6.60978i	−0.333419	−	0.333419i
$394$	21.9324	−	12.6626i	1.10494	−	0.637935i
$395$	22.9378	−	10.5829i	1.15413	−	0.532481i
$396$	−3.24706	+	5.62407i	−0.163171	+	0.282620i
$397$	−6.28213	+	23.4452i	−0.315291	+	1.17668i	0.608427	+	0.793609i	$0.291801\pi$
$397$	−6.28213	+	23.4452i	−0.315291	+	1.17668i	−0.923718	+	0.383072i	$0.874866\pi$
$398$	−4.84408	+	4.84408i	−0.242812	+	0.242812i
$399$		0			0
$400$	−4.93791	−	13.9176i	−0.246895	−	0.695879i
$401$	6.47088	+	11.2079i	0.323140	+	0.559696i	0.981134	−	0.193328i	$-0.0619280\pi$
$401$	6.47088	+	11.2079i	0.323140	+	0.559696i	−0.657994	+	0.753023i	$0.728595\pi$
$402$	−9.86397	+	2.64304i	−0.491970	+	0.131823i
$403$	−12.1596	+	3.25815i	−0.605712	+	0.162300i
$404$	−8.78598	−	15.2178i	−0.437119	−	0.757112i
$405$	1.28999	−	1.82645i	0.0640999	−	0.0907572i
$406$		0			0
$407$	1.96500	−	1.96500i	0.0974016	−	0.0974016i
$408$	1.57440	−	5.87575i	0.0779445	−	0.290893i
$409$	1.32139	−	2.28872i	0.0653386	−	0.113170i	−0.831506	−	0.555516i	$-0.812521\pi$
$409$	1.32139	−	2.28872i	0.0653386	−	0.113170i	0.896844	+	0.442347i	$0.145854\pi$
$410$	11.4875	−	31.1671i	0.567326	−	1.53923i
$411$	−9.20938	+	5.31704i	−0.454265	+	0.262270i
$412$	16.8811	+	16.8811i	0.831672	+	0.831672i
$413$		0			0
$414$			0.522969i			0.0257025i
$415$	−11.8846	+	9.89037i	−0.583392	+	0.485499i
$416$	12.0676	+	6.96724i	0.591663	+	0.341597i
$417$	2.01595	+	7.52362i	0.0987214	+	0.368433i
$418$	32.6881	+	8.75874i	1.59883	+	0.428404i
$419$	10.0302			0.490007			0.245003	−	0.969522i	$-0.421211\pi$
$419$	10.0302			0.490007			0.245003	+	0.969522i	$0.421211\pi$
$420$		0			0
$421$	−26.6440			−1.29855			−0.649274	−	0.760555i	$-0.724927\pi$
$421$	−26.6440			−1.29855			−0.649274	+	0.760555i	$0.724927\pi$
$422$	35.0737	+	9.39797i	1.70736	+	0.457486i
$423$	0.203827	+	0.760694i	0.00991042	+	0.0369862i
$424$	−5.53895	−	3.19791i	−0.268995	−	0.155304i
$425$	33.4560	−	2.65331i	1.62285	−	0.128704i
$426$		−	32.2232i		−	1.56122i
$427$		0			0
$428$	18.1634	+	18.1634i	0.877960	+	0.877960i
$429$	4.01565	−	2.31844i	0.193878	−	0.111935i
$430$	−0.850190	−	1.84274i	−0.0409998	−	0.0888650i
$431$	−11.1873	+	19.3771i	−0.538876	+	0.933360i	0.460089	+	0.887873i	$0.347817\pi$
$431$	−11.1873	+	19.3771i	−0.538876	+	0.933360i	−0.998965	+	0.0454873i	$0.985516\pi$
$432$	−0.764428	+	2.85288i	−0.0367785	+	0.137259i
$433$	13.4723	−	13.4723i	0.647438	−	0.647438i	−0.304935	−	0.952373i	$-0.598635\pi$
$433$	13.4723	−	13.4723i	0.647438	−	0.647438i	0.952373	+	0.304935i	$0.0986349\pi$
$434$		0			0
$435$	−0.671871	+	0.115657i	−0.0322138	+	0.00554532i
$436$	−7.23517	−	12.5317i	−0.346502	−	0.600159i
$437$	1.44408	−	0.386941i	0.0690799	−	0.0185099i
$438$	28.8132	−	7.72048i	1.37675	−	0.368899i
$439$	−12.8395	−	22.2386i	−0.612795	−	1.06139i	−0.990767	−	0.135576i	$-0.956712\pi$
$439$	−12.8395	−	22.2386i	−0.612795	−	1.06139i	0.377972	−	0.925817i	$-0.376622\pi$
$440$	−5.33598	+	0.918542i	−0.254383	+	0.0437898i
$441$		0			0
$442$	−17.3376	+	17.3376i	−0.824665	+	0.824665i
$443$	−5.72284	+	21.3579i	−0.271900	+	1.01475i	0.685990	+	0.727611i	$0.259369\pi$
$443$	−5.72284	+	21.3579i	−0.271900	+	1.01475i	−0.957890	+	0.287135i	$0.907297\pi$
$444$	−1.26397	+	2.18927i	−0.0599855	+	0.103898i
$445$	−6.47539	−	14.0351i	−0.306963	−	0.665327i
$446$	11.8171	−	6.82261i	0.559556	−	0.323060i
$447$	−10.1014	−	10.1014i	−0.477779	−	0.477779i
$448$		0			0
$449$			7.01947i			0.331269i	0.986187	+	0.165635i	$0.0529673\pi$
$449$			7.01947i			0.331269i	−0.986187	+	0.165635i	$0.947033\pi$
$450$	10.4915	−	0.832054i	0.494574	−	0.0392234i
$451$	16.3301	+	9.42818i	0.768954	+	0.443956i
$452$	6.21888	+	23.2092i	0.292512	+	1.09167i
$453$	−9.44666	−	2.53123i	−0.443843	−	0.118927i
$454$	42.1548			1.97842
$455$		0			0
$456$	−5.45325			−0.255372
$457$	−15.3158	−	4.10385i	−0.716442	−	0.191970i	−0.117858	−	0.993030i	$-0.537603\pi$
$457$	−15.3158	−	4.10385i	−0.716442	−	0.191970i	−0.598584	+	0.801060i	$0.704270\pi$
$458$	−15.7610	−	58.8209i	−0.736464	−	2.74852i
$459$	−5.81294	−	3.35610i	−0.271325	−	0.156649i
$460$	−1.03792	+	0.863761i	−0.0483934	+	0.0402731i
$461$			29.9845i			1.39652i	0.715846	+	0.698259i	$0.246041\pi$
$461$			29.9845i			1.39652i	−0.715846	+	0.698259i	$0.753959\pi$
$462$		0			0
$463$	7.70220	+	7.70220i	0.357951	+	0.357951i	0.863057	−	0.505106i	$-0.168547\pi$
$463$	7.70220	+	7.70220i	0.357951	+	0.357951i	−0.505106	+	0.863057i	$0.668547\pi$
$464$	0.779853	−	0.450249i	0.0362038	−	0.0209023i
$465$	5.60943	−	15.2191i	0.260131	−	0.705770i
$466$	7.12259	−	12.3367i	0.329948	−	0.571486i
$467$	0.662362	−	2.47197i	0.0306504	−	0.114389i	−0.948906	−	0.315559i	$-0.897808\pi$
$467$	0.662362	−	2.47197i	0.0306504	−	0.114389i	0.979556	+	0.201170i	$0.0644745\pi$
$468$	−2.98263	+	2.98263i	−0.137872	+	0.137872i
$469$		0			0
$470$	−2.13836	+	3.02764i	−0.0986350	+	0.139654i
$471$	−1.53959	−	2.66665i	−0.0709407	−	0.122873i
$472$	−6.99289	+	1.87374i	−0.321874	+	0.0862458i
$473$	1.11280	−	0.298173i	0.0511665	−	0.0137100i
$474$	−11.8897	−	20.5936i	−0.546114	−	0.945897i
$475$	−10.0601	−	28.3547i	−0.461591	−	1.30100i
$476$		0			0
$477$	−4.99031	+	4.99031i	−0.228491	+	0.228491i
$478$	−8.81295	+	32.8904i	−0.403095	+	1.50437i
$479$	−2.04728	+	3.54599i	−0.0935425	+	0.162020i	−0.908999	−	0.416798i	$-0.863152\pi$
$479$	−2.04728	+	3.54599i	−0.0935425	+	0.162020i	0.815457	+	0.578818i	$0.196486\pi$
$480$	−16.3027	+	7.52160i	−0.744114	+	0.343313i
$481$	1.56316	−	0.902491i	0.0712740	−	0.0411500i
$482$	16.9240	+	16.9240i	0.770867	+	0.770867i
$483$		0			0
$484$			9.38461i			0.426573i
$485$	−17.8845	−	21.4906i	−0.812092	−	0.975836i
$486$	−1.82289	−	1.05244i	−0.0826878	−	0.0477398i
$487$	−3.77185	−	14.0767i	−0.170919	−	0.637878i	−0.997211	−	0.0746360i	$-0.976221\pi$
$487$	−3.77185	−	14.0767i	−0.170919	−	0.637878i	0.826292	−	0.563242i	$-0.190446\pi$
$488$	4.84445	+	1.29807i	0.219298	+	0.0587607i
$489$	−19.3404			−0.874603
$490$		0			0
$491$	−8.55953			−0.386286			−0.193143	−	0.981171i	$-0.561868\pi$
$491$	−8.55953			−0.386286			−0.193143	+	0.981171i	$0.561868\pi$
$492$	−16.5688	−	4.43960i	−0.746979	−	0.200153i
$493$	0.529668	+	1.97675i	0.0238550	+	0.0890282i
$494$	19.0358	+	10.9903i	0.856460	+	0.494477i
$495$	−0.544884	+	5.94959i	−0.0244907	+	0.267414i
$496$			21.4242i			0.961976i
$497$		0			0
$498$	10.2917	+	10.2917i	0.461180	+	0.461180i
$499$	−20.5736	+	11.8782i	−0.921002	+	0.531741i	−0.883955	−	0.467572i	$-0.845129\pi$
$499$	−20.5736	+	11.8782i	−0.921002	+	0.531741i	−0.0370477	+	0.999313i	$0.511795\pi$
$500$	18.9796	+	19.4479i	0.848794	+	0.869738i
$501$	4.40731	−	7.63369i	0.196904	−	0.341048i
$502$	−3.78647	+	14.1313i	−0.168998	+	0.630710i
$503$	−17.9504	+	17.9504i	−0.800367	+	0.800367i	−0.983153	−	0.182786i	$-0.941489\pi$
$503$	−17.9504	+	17.9504i	−0.800367	+	0.800367i	0.182786	+	0.983153i	$0.441489\pi$
$504$		0			0
$505$	−13.2046	−	9.32611i	−0.587596	−	0.415007i
$506$	−0.698653	−	1.21010i	−0.0310589	−	0.0537956i
$507$	−9.64790	+	2.58515i	−0.428478	+	0.114810i
$508$	9.49942	−	2.54536i	0.421469	−	0.112932i
$509$	−8.44887	−	14.6339i	−0.374489	−	0.648635i	0.615761	−	0.787933i	$-0.288849\pi$
$509$	−8.44887	−	14.6339i	−0.374489	−	0.648635i	−0.990250	+	0.139298i	$0.955515\pi$
$510$	−5.35948	−	31.1342i	−0.237322	−	1.37865i
$511$		0			0
$512$	20.5543	−	20.5543i	0.908382	−	0.908382i
$513$	−1.55739	+	5.81226i	−0.0687604	+	0.256617i
$514$	−15.0161	+	26.0087i	−0.662333	+	1.14720i
$515$	20.6080	+	7.59564i	0.908097	+	0.334704i
$516$	−0.907596	+	0.524001i	−0.0399547	+	0.0230679i
$517$	−1.48788	−	1.48788i	−0.0654367	−	0.0654367i
$518$		0			0
$519$		−	9.57331i		−	0.420221i
$520$	−3.50216	−	0.320740i	−0.153580	−	0.0140654i
$521$	−6.82841	−	3.94238i	−0.299158	−	0.172719i	0.342907	−	0.939370i	$-0.388589\pi$
$521$	−6.82841	−	3.94238i	−0.299158	−	0.172719i	−0.642065	+	0.766651i	$0.721922\pi$
$522$	0.166099	+	0.619890i	0.00726996	+	0.0271319i
$523$	1.68225	+	0.450757i	0.0735595	+	0.0197102i	0.295411	−	0.955370i	$-0.404543\pi$
$523$	1.68225	+	0.450757i	0.0735595	+	0.0197102i	−0.221852	+	0.975080i	$0.571210\pi$
$524$	−22.7199			−0.992524
$525$		0			0
$526$	54.1722			2.36202
$527$	−47.0299	−	12.6016i	−2.04865	−	0.548935i
$528$	−2.04245	−	7.62253i	−0.0888863	−	0.331728i
$529$	19.8651	+	11.4691i	0.863701	+	0.498658i
$530$	−33.0783	−	3.02942i	−1.43683	−	0.131590i
$531$			7.98837i			0.346666i
$532$		0			0
$533$	8.66039	+	8.66039i	0.375123	+	0.375123i
$534$	−12.6007	+	7.27503i	−0.545287	+	0.314821i
$535$	22.1734	+	8.17260i	0.958638	+	0.353332i
$536$	−2.19838	+	3.80771i	−0.0949557	+	0.164468i
$537$	−0.336732	+	1.25670i	−0.0145310	+	0.0542306i
$538$	−23.0876	+	23.0876i	−0.995375	+	0.995375i
$539$		0			0
$540$	−0.922006	−	5.35610i	−0.0396768	−	0.230490i
$541$	−17.4747	−	30.2671i	−0.751298	−	1.30129i	−0.947194	−	0.320661i	$-0.896095\pi$
$541$	−17.4747	−	30.2671i	−0.751298	−	1.30129i	0.195896	−	0.980625i	$-0.437238\pi$
$542$	27.1261	−	7.26843i	1.16517	−	0.312206i
$543$	8.19615	−	2.19615i	0.351731	−	0.0942459i
$544$	26.9473	+	46.6741i	1.15536	+	2.00114i
$545$	−10.8738	−	7.67996i	−0.465784	−	0.328973i
$546$		0			0
$547$	3.83548	−	3.83548i	0.163993	−	0.163993i	−0.620340	−	0.784333i	$-0.713005\pi$
$547$	3.83548	−	3.83548i	0.163993	−	0.163993i	0.784333	+	0.620340i	$0.213005\pi$
$548$	−6.68961	+	24.9660i	−0.285766	+	1.06649i
$549$	2.76704	−	4.79266i	0.118095	−	0.204546i
$550$	−23.1648	+	15.9413i	−0.987750	+	0.679738i
$551$	1.58882	−	0.917304i	0.0676859	−	0.0390785i
$552$	0.159216	+	0.159216i	0.00677668	+	0.00677668i
$553$		0			0
$554$			5.97022i			0.253650i
$555$	−0.212105	+	2.31598i	−0.00900337	+	0.0983077i
$556$	16.3953	+	9.46581i	0.695314	+	0.401440i
$557$	−5.97158	−	22.2863i	−0.253024	−	0.944299i	−0.969179	−	0.246358i	$-0.920766\pi$
$557$	−5.97158	−	22.2863i	−0.253024	−	0.944299i	0.716155	−	0.697941i	$-0.245900\pi$
$558$	−14.7482	−	3.95176i	−0.624339	−	0.167291i
$559$	0.748285			0.0316491
$560$		0			0
$561$	17.9341			0.757180
$562$	−27.5609	−	7.38493i	−1.16259	−	0.311514i
$563$	8.69386	+	32.4459i	0.366402	+	1.36743i	0.865510	+	0.500892i	$0.166995\pi$
$563$	8.69386	+	32.4459i	0.366402	+	1.36743i	−0.499107	+	0.866540i	$0.666339\pi$
$564$	1.65768	+	0.957064i	0.0698011	+	0.0402997i
$565$	14.1401	+	16.9912i	0.594879	+	0.714826i
$566$			48.3556i			2.03254i
$567$		0			0
$568$	−9.81023	−	9.81023i	−0.411628	−	0.411628i
$569$	0.240575	−	0.138896i	0.0100854	−	0.00582283i	−0.494949	−	0.868922i	$-0.664813\pi$
$569$	0.240575	−	0.138896i	0.0100854	−	0.00582283i	0.505034	+	0.863099i	$0.331480\pi$
$570$	−25.7163	+	11.8648i	−1.07714	+	0.496961i
$571$	1.55769	−	2.69800i	0.0651874	−	0.112908i	−0.831590	−	0.555390i	$-0.812569\pi$
$571$	1.55769	−	2.69800i	0.0651874	−	0.112908i	0.896777	+	0.442483i	$0.145902\pi$
$572$	2.91693	−	10.8861i	0.121963	−	0.455173i
$573$	1.37031	−	1.37031i	0.0572454	−	0.0572454i
$574$		0			0
$575$	−0.534138	+	1.12158i	−0.0222751	+	0.0467731i
$576$	5.49693	+	9.52095i	0.229039	+	0.396706i
$577$	−40.4214	+	10.8309i	−1.68277	+	0.450896i	−0.968507	−	0.248986i	$-0.919903\pi$
$577$	−40.4214	+	10.8309i	−1.68277	+	0.450896i	−0.714259	+	0.699882i	$0.753236\pi$
$578$	−57.0377	+	15.2832i	−2.37246	+	0.635698i
$579$	5.53513	+	9.58713i	0.230032	+	0.398428i
$580$	−0.955943	+	1.35349i	−0.0396934	+	0.0562007i
$581$		0			0
$582$	−18.6101	+	18.6101i	−0.771413	+	0.771413i
$583$	4.88039	−	18.2139i	0.202125	−	0.754341i
$584$	6.42160	−	11.1225i	0.265728	−	0.460254i
$585$	−1.34203	+	3.64112i	−0.0554863	+	0.150542i
$586$	6.23257	−	3.59838i	0.257465	−	0.148648i
$587$	26.6462	+	26.6462i	1.09981	+	1.09981i	0.994433	+	0.105375i	$0.0336041\pi$
$587$	26.6462	+	26.6462i	1.09981	+	1.09981i	0.105375	+	0.994433i	$0.466396\pi$
$588$		0			0
$589$			43.6482i			1.79849i
$590$	−28.9002	+	24.0507i	−1.18980	+	0.990153i
$591$	−10.4197	−	6.01583i	−0.428610	−	0.247458i
$592$	−0.795059	−	2.96720i	−0.0326767	−	0.121951i
$593$	−20.7484	−	5.55952i	−0.852036	−	0.228302i	−0.193732	−	0.981055i	$-0.562059\pi$
$593$	−20.7484	−	5.55952i	−0.852036	−	0.228302i	−0.658304	+	0.752752i	$0.728726\pi$
$594$	5.62399			0.230755
$595$		0			0
$596$	−34.7217			−1.42225
$597$	3.14370	+	0.842351i	0.128663	+	0.0344751i
$598$	−0.234900	−	0.876657i	−0.00960576	−	0.0358492i
$599$	−19.2930	−	11.1388i	−0.788290	−	0.455119i	0.0510705	−	0.998695i	$-0.483737\pi$
$599$	−19.2930	−	11.1388i	−0.788290	−	0.455119i	−0.839360	+	0.543576i	$0.817070\pi$
$600$	2.94078	−	3.44741i	0.120057	−	0.140740i
$601$		−	22.3458i		−	0.911503i	−0.890107	−	0.455752i	$-0.849371\pi$
$601$		−	22.3458i		−	0.911503i	0.890107	−	0.455752i	$-0.150629\pi$
$602$		0			0
$603$	3.43055	+	3.43055i	0.139703	+	0.139703i
$604$	−20.5859	+	11.8853i	−0.837629	+	0.483605i
$605$	3.61694	+	7.83954i	0.147049	+	0.318723i
$606$	−7.60877	+	13.1788i	−0.309085	+	0.535351i
$607$	−0.210840	+	0.786867i	−0.00855775	+	0.0319380i	−0.970073	−	0.242815i	$-0.921929\pi$
$607$	−0.210840	+	0.786867i	−0.00855775	+	0.0319380i	0.961515	+	0.274753i	$0.0885960\pi$
$608$	34.1639	−	34.1639i	1.38553	−	1.38553i
$609$		0			0
$610$	25.6696	−	4.41880i	1.03933	−	0.178912i
$611$	−0.683354	−	1.18360i	−0.0276456	−	0.0478835i
$612$	−15.7585	+	4.22247i	−0.636998	+	0.170683i
$613$	22.4996	−	6.02876i	0.908752	−	0.243499i	0.225981	−	0.974132i	$-0.427441\pi$
$613$	22.4996	−	6.02876i	0.908752	−	0.243499i	0.682771	+	0.730632i	$0.260775\pi$
$614$	−10.7357	−	18.5947i	−0.433257	−	0.750423i
$615$	−15.5520	+	2.67714i	−0.627117	+	0.107953i
$616$		0			0
$617$	−3.70013	+	3.70013i	−0.148962	+	0.148962i	−0.777654	−	0.628692i	$-0.783590\pi$
$617$	−3.70013	+	3.70013i	−0.148962	+	0.148962i	0.628692	+	0.777654i	$0.283590\pi$
$618$	5.35101	−	19.9703i	0.215249	−	0.803322i
$619$	19.9420	−	34.5405i	0.801536	−	1.38830i	−0.117068	−	0.993124i	$-0.537350\pi$
$619$	19.9420	−	34.5405i	0.801536	−	1.38830i	0.918605	−	0.395178i	$-0.129317\pi$
$620$	−16.5158	−	35.7972i	−0.663290	−	1.43765i
$621$	0.215168	−	0.124227i	0.00863440	−	0.00498507i
$622$	−15.2621	−	15.2621i	−0.611954	−	0.611954i
$623$		0			0
$624$		−	5.12566i		−	0.205191i
$625$	23.3503	+	8.93109i	0.934011	+	0.357244i
$626$	56.9479	+	32.8789i	2.27610	+	1.31410i
$627$	−4.16114	−	15.5296i	−0.166180	−	0.620193i
$628$	−7.22910	−	1.93703i	−0.288473	−	0.0772960i
$629$	6.98117			0.278357
$630$		0			0
$631$	−33.9725			−1.35242			−0.676211	−	0.736708i	$-0.736379\pi$
$631$	−33.9725			−1.35242			−0.676211	+	0.736708i	$0.736379\pi$
$632$	−9.88943	−	2.64987i	−0.393381	−	0.105406i
$633$	−4.46483	−	16.6630i	−0.177461	−	0.662294i
$634$	−31.5962	−	18.2421i	−1.25485	−	0.724486i
$635$	6.95444	−	5.78748i	0.275978	−	0.229669i
$636$			17.1533i			0.680172i
$637$		0			0
$638$	−1.21247	−	1.21247i	−0.0480022	−	0.0480022i
$639$	−13.2578	+	7.65437i	−0.524469	+	0.302802i
$640$	−5.47666	+	14.8589i	−0.216484	+	0.587350i
$641$	9.05563	−	15.6848i	0.357676	−	0.619513i	−0.629896	−	0.776679i	$-0.716903\pi$
$641$	9.05563	−	15.6848i	0.357676	−	0.619513i	0.987572	+	0.157167i	$0.0502359\pi$
$642$	5.75748	−	21.4872i	0.227229	−	0.848032i
$643$	32.1062	−	32.1062i	1.26614	−	1.26614i	0.318082	−	0.948063i	$-0.396961\pi$
$643$	32.1062	−	32.1062i	1.26614	−	1.26614i	0.948063	−	0.318082i	$-0.103039\pi$
$644$		0			0
$645$	−0.556214	+	0.787528i	−0.0219009	+	0.0310089i
$646$	42.5074	+	73.6251i	1.67243	+	2.89674i
$647$	−17.6596	+	4.73187i	−0.694270	+	0.186029i	−0.588663	−	0.808379i	$-0.700345\pi$
$647$	−17.6596	+	4.73187i	−0.694270	+	0.186029i	−0.105607	+	0.994408i	$0.533679\pi$
$648$	−0.875383	+	0.234558i	−0.0343883	+	0.00921432i
$649$	−10.6720	−	18.4844i	−0.418911	−	0.725575i
$650$	−17.2132	+	6.10719i	−0.675159	+	0.239544i
$651$		0			0
$652$	−33.2396	+	33.2396i	−1.30176	+	1.30176i
$653$	−3.44041	+	12.8398i	−0.134634	+	0.502459i	0.865366	+	0.501141i	$0.167086\pi$
$653$	−3.44041	+	12.8398i	−0.134634	+	0.502459i	−0.999999	+	0.00131826i	$0.999580\pi$
$654$	−6.26575	+	10.8526i	−0.245010	+	0.424370i
$655$	−18.9793	+	8.75652i	−0.741584	+	0.342146i
$656$	18.0515	−	10.4220i	0.704792	−	0.406912i
$657$	−10.0208	−	10.0208i	−0.390950	−	0.390950i
$658$		0			0
$659$			9.13808i			0.355969i	0.984033	+	0.177985i	$0.0569577\pi$
$659$			9.13808i			0.355969i	−0.984033	+	0.177985i	$0.943042\pi$
$660$	9.28884	+	11.1618i	0.361568	+	0.434472i
$661$	−24.6676	−	14.2418i	−0.959458	−	0.553943i	−0.0634519	−	0.997985i	$-0.520211\pi$
$661$	−24.6676	−	14.2418i	−0.959458	−	0.553943i	−0.896006	+	0.444042i	$0.853544\pi$
$662$	0.688108	+	2.56805i	0.0267441	+	0.0998102i
$663$	11.2517	+	3.01489i	0.436980	+	0.117089i
$664$	6.26651			0.243188
$665$		0			0
$666$	2.18923			0.0848310
$667$	−0.0731700	−	0.0196059i	−0.00283316	−	0.000759142i
$668$	−5.54504	−	20.6944i	−0.214544	−	0.800690i
$669$	−5.61413	−	3.24132i	−0.217055	−	0.125317i
$670$	−2.08256	+	22.7394i	−0.0804562	+	0.878500i
$671$			14.7864i			0.570821i
$672$		0			0
$673$	26.8815	+	26.8815i	1.03621	+	1.03621i	0.999319	+	0.0368867i	$0.0117441\pi$
$673$	26.8815	+	26.8815i	1.03621	+	1.03621i	0.0368867	+	0.999319i	$0.488256\pi$
$674$	24.6354	−	14.2233i	0.948922	−	0.547860i
$675$	−2.83451	−	4.11893i	−0.109100	−	0.158538i
$676$	−12.1385	+	21.0245i	−0.466864	+	0.808633i
$677$	−0.438111	+	1.63505i	−0.0168380	+	0.0628402i	−0.973834	−	0.227262i	$-0.927023\pi$
$677$	−0.438111	+	1.63505i	−0.0168380	+	0.0628402i	0.956996	+	0.290102i	$0.0936893\pi$
$678$	14.7138	−	14.7138i	0.565081	−	0.565081i
$679$		0			0
$680$	−11.1104	−	7.84702i	−0.426063	−	0.300919i
$681$	−10.0135	−	17.3440i	−0.383720	−	0.664623i
$682$	39.4052	−	10.5586i	1.50890	−	0.404309i
$683$	−3.29967	+	0.884144i	−0.126258	+	0.0338308i	−0.321395	−	0.946945i	$-0.604152\pi$
$683$	−3.29967	+	0.884144i	−0.126258	+	0.0338308i	0.195137	+	0.980776i	$0.437485\pi$
$684$	7.31267	+	12.6659i	0.279607	+	0.484293i
$685$	4.03393	+	23.4338i	0.154129	+	0.895361i
$686$		0			0
$687$	−20.4571	+	20.4571i	−0.780487	+	0.780487i
$688$	0.329605	−	1.23010i	0.0125661	−	0.0468972i
$689$	6.12382	−	10.6068i	0.233299	−	0.404086i
$690$	1.09724	+	0.404417i	0.0417711	+	0.0153959i
$691$	−36.0875	+	20.8351i	−1.37283	+	0.792606i	−0.991284	−	0.131743i	$-0.957943\pi$
$691$	−36.0875	+	20.8351i	−1.37283	+	0.792606i	−0.381549	+	0.924348i	$0.624609\pi$
$692$	−16.4533	−	16.4533i	−0.625459	−	0.625459i
$693$		0			0
$694$		−	19.4970i		−	0.740098i
$695$	17.3442	+	1.58844i	0.657903	+	0.0602531i
$696$	0.239292	+	0.138155i	0.00907032	+	0.00523675i
$697$	12.2604	+	45.7563i	0.464395	+	1.73314i
$698$	5.63470	+	1.50981i	0.213276	+	0.0571472i
$699$	−6.76767			−0.255977
$700$		0			0
$701$	13.7870			0.520727			0.260364	−	0.965511i	$-0.416158\pi$
$701$	13.7870			0.520727			0.260364	+	0.965511i	$0.416158\pi$
$702$	3.52844	+	0.945442i	0.133172	+	0.0356834i
$703$	−1.61980	−	6.04516i	−0.0610918	−	0.227998i
$704$	−25.4388	−	14.6871i	−0.958760	−	0.553540i
$705$	1.75363	+	0.160603i	0.0660454	+	0.00604868i
$706$			2.88915i			0.108735i
$707$		0			0
$708$	13.7293	+	13.7293i	0.515978	+	0.515978i
$709$	−21.3668	+	12.3361i	−0.802446	+	0.463293i	−0.844326	−	0.535830i	$-0.819999\pi$
$709$	−21.3668	+	12.3361i	−0.802446	+	0.463293i	0.0418795	+	0.999123i	$0.486665\pi$
$710$	−67.6072	−	24.9185i	−2.53725	−	0.935175i
$711$	−5.64863	+	9.78372i	−0.211840	+	0.366918i
$712$	−1.62139	+	6.05110i	−0.0607641	+	0.226775i
$713$	1.27438	−	1.27438i	0.0477257	−	0.0477257i
$714$		0			0
$715$	−1.75895	−	10.2181i	−0.0657811	−	0.382135i
$716$	1.58111	+	2.73857i	0.0590890	+	0.102345i
$717$	15.6257	−	4.18690i	0.583553	−	0.156363i
$718$	−18.9656	+	5.08182i	−0.707791	+	0.189652i
$719$	14.9558	+	25.9043i	0.557758	+	0.966066i	0.997683	+	0.0680313i	$0.0216718\pi$
$719$	14.9558	+	25.9043i	0.557758	+	0.966066i	−0.439925	+	0.898035i	$0.644995\pi$
$720$	5.39447	+	3.81000i	0.201040	+	0.141990i
$721$		0			0
$722$	25.6118	−	25.6118i	0.953171	−	0.953171i
$723$	2.94297	−	10.9833i	0.109450	−	0.408473i
$724$	10.3120	−	17.8608i	0.383241	−	0.663793i
$725$	−0.276906	+	1.49909i	−0.0102840	+	0.0556747i
$726$	7.03835	−	4.06359i	0.261218	−	0.150814i
$727$	−29.8488	−	29.8488i	−1.10703	−	1.10703i	−0.993539	−	0.113491i	$-0.963797\pi$
$727$	−29.8488	−	29.8488i	−1.10703	−	1.10703i	−0.113491	−	0.993539i	$-0.536203\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	6.08326	−	66.4231i	0.225152	−	2.45843i
$731$	2.50641	+	1.44708i	0.0927031	+	0.0535222i
$732$	−3.48135	−	12.9926i	−0.128674	−	0.480219i
$733$	5.28252	+	1.41545i	0.195114	+	0.0522807i	0.355053	−	0.934846i	$-0.384463\pi$
$733$	5.28252	+	1.41545i	0.195114	+	0.0522807i	−0.159938	+	0.987127i	$0.551130\pi$
$734$	38.7082			1.42875
$735$		0			0
$736$	−1.99493			−0.0735342
$737$	−12.5210	−	3.35499i	−0.461216	−	0.123583i
$738$	3.84475	+	14.3488i	0.141527	+	0.528186i
$739$	−10.3694	−	5.98677i	−0.381444	−	0.220227i	0.297002	−	0.954877i	$-0.404013\pi$
$739$	−10.3694	−	5.98677i	−0.381444	−	0.220227i	−0.678446	+	0.734650i	$0.737346\pi$
$740$	3.61584	+	4.34491i	0.132921	+	0.159722i
$741$		−	10.4427i		−	0.383621i
$742$		0			0
$743$	−12.0406	−	12.0406i	−0.441728	−	0.441728i	0.450864	−	0.892593i	$-0.351116\pi$
$743$	−12.0406	−	12.0406i	−0.441728	−	0.441728i	−0.892593	+	0.450864i	$0.851116\pi$
$744$	−5.69312	+	3.28692i	−0.208720	+	0.120504i
$745$	−29.0051	+	13.3821i	−1.06267	+	0.490283i
$746$	−30.7733	+	53.3010i	−1.12669	+	1.95149i
$747$	1.78965	−	6.67906i	0.0654798	−	0.244374i
$748$	30.8227	−	30.8227i	1.12699	−	1.12699i
$749$		0			0
$750$	6.36745	−	22.6556i	0.232506	−	0.827264i
$751$	12.0559	+	20.8815i	0.439928	+	0.761977i	0.997683	−	0.0680281i	$-0.0216707\pi$
$751$	12.0559	+	20.8815i	0.439928	+	0.761977i	−0.557756	+	0.830005i	$0.688337\pi$
$752$	−2.24673	+	0.602008i	−0.0819296	+	0.0219530i
$753$	6.71356	−	1.79889i	0.244656	−	0.0655553i
$754$	−0.556866	−	0.964521i	−0.0202799	−	0.0351258i
$755$	−12.6159	+	17.8625i	−0.459141	+	0.650085i
$756$		0			0
$757$	29.2896	−	29.2896i	1.06455	−	1.06455i	0.0667825	−	0.997768i	$-0.478727\pi$
$757$	29.2896	−	29.2896i	1.06455	−	1.06455i	0.997768	−	0.0667825i	$-0.0212733\pi$
$758$	−11.9895	+	44.7453i	−0.435477	+	1.62522i
$759$	−0.331920	+	0.574902i	−0.0120479	+	0.0208676i
$760$	−4.21705	+	11.4414i	−0.152969	+	0.415024i
$761$	27.9728	−	16.1501i	1.01401	−	0.585440i	0.101648	−	0.994820i	$-0.467589\pi$
$761$	27.9728	−	16.1501i	1.01401	−	0.585440i	0.912364	+	0.409381i	$0.134255\pi$
$762$	−6.02230	−	6.02230i	−0.218165	−	0.218165i
$763$		0			0
$764$		−	4.71018i		−	0.170408i
$765$	−11.5366	+	9.60077i	−0.417107	+	0.347117i
$766$	−1.00639	−	0.581037i	−0.0363622	−	0.0209937i
$767$	−3.58810	−	13.3910i	−0.129559	−	0.483520i
$768$	−6.83939	−	1.83261i	−0.246795	−	0.0661286i
$769$	18.4310			0.664640			0.332320	−	0.943167i	$-0.392169\pi$
$769$	18.4310			0.664640			0.332320	+	0.943167i	$0.392169\pi$
$770$		0			0
$771$	14.2679			0.513845
$772$	25.9900	+	6.96401i	0.935401	+	0.250640i
$773$	6.51389	+	24.3102i	0.234288	+	0.874376i	0.978468	+	0.206397i	$0.0661738\pi$
$773$	6.51389	+	24.3102i	0.234288	+	0.874376i	−0.744180	+	0.667979i	$0.767160\pi$
$774$	0.785990	+	0.453791i	0.0282518	+	0.0163112i
$775$	−27.5933	−	23.5382i	−0.991181	−	0.845517i
$776$			11.3315i			0.406779i
$777$		0			0
$778$	−38.5937	−	38.5937i	−1.38365	−	1.38365i
$779$	36.7768	−	21.2331i	1.31767	−	0.760755i
$780$	3.95134	+	8.56434i	0.141481	+	0.306653i
$781$	20.4515	−	35.4230i	0.731812	−	1.26754i
$782$	0.908526	−	3.39067i	0.0324888	−	0.121250i
$783$	0.215589	−	0.215589i	0.00770453	−	0.00770453i
$784$		0			0
$785$	−6.78546	+	1.16806i	−0.242184	+	0.0416898i
$786$	9.83786	+	17.0397i	0.350905	+	0.607785i
$787$	21.9481	−	5.88096i	0.782364	−	0.209634i	0.154537	−	0.987987i	$-0.450611\pi$
$787$	21.9481	−	5.88096i	0.782364	−	0.209634i	0.627827	+	0.778353i	$0.283945\pi$
$788$	−28.2471	+	7.56880i	−1.00626	+	0.269627i
$789$	−12.8682	−	22.2884i	−0.458120	−	0.793487i
$790$	−52.4018	+	9.02051i	−1.86437	+	0.320935i
$791$		0			0
$792$	1.71220	−	1.71220i	0.0608404	−	0.0608404i
$793$	−2.48572	+	9.27683i	−0.0882705	+	0.329430i
$794$	25.5452	−	44.2456i	0.906565	−	1.57022i
$795$	6.61108	+	14.3292i	0.234471	+	0.508204i
$796$	6.85066	−	3.95523i	0.242815	−	0.140189i
$797$	−25.5337	−	25.5337i	−0.904451	−	0.904451i	0.0913664	−	0.995817i	$-0.470877\pi$
$797$	−25.5337	−	25.5337i	−0.904451	−	0.904451i	−0.995817	+	0.0913664i	$0.970877\pi$
$798$		0			0
$799$		−	5.28605i		−	0.187007i
$800$	3.17397	+	40.0211i	0.112217	+	1.41496i
$801$	5.98641	+	3.45626i	0.211520	+	0.122121i
$802$	−7.05048	−	26.3127i	−0.248961	−	0.929135i
$803$	36.5745	+	9.80010i	1.29069	+	0.345838i
$804$	11.7919			0.415868
$805$		0			0
$806$	26.4974			0.933332
$807$	14.9833	+	4.01477i	0.527438	+	0.141326i
$808$	1.69577	+	6.32869i	0.0596569	+	0.222642i
$809$	23.8507	+	13.7702i	0.838546	+	0.484135i	0.856770	−	0.515699i	$-0.172468\pi$
$809$	23.8507	+	13.7702i	0.838546	+	0.484135i	−0.0182236	+	0.999834i	$0.505801\pi$
$810$	−3.61778	+	3.01072i	−0.127116	+	0.105786i
$811$			34.2545i			1.20284i	0.798933	+	0.601420i	$0.205398\pi$
$811$			34.2545i			1.20284i	−0.798933	+	0.601420i	$0.794602\pi$
$812$		0			0
$813$	−9.43409	−	9.43409i	−0.330868	−	0.330868i
$814$	−5.06568	+	2.92467i	−0.177552	+	0.102510i
$815$	−14.9561	+	40.5780i	−0.523890	+	1.42138i
$816$	9.91232	−	17.1686i	0.347000	−	0.601022i
$817$	0.671513	−	2.50612i	0.0234933	−	0.0876781i
$818$	−3.93347	+	3.93347i	−0.137530	+	0.137530i
$819$		0			0
$820$	−22.1275	+	31.3297i	−0.772726	+	1.09408i
$821$	−24.8741	−	43.0832i	−0.868113	−	1.50361i	−0.863923	−	0.503624i	$-0.832000\pi$
$821$	−24.8741	−	43.0832i	−0.868113	−	1.50361i	−0.00418940	−	0.999991i	$-0.501334\pi$
$822$	21.6208	−	5.79328i	0.754113	−	0.202064i
$823$	8.33846	−	2.23428i	0.290660	−	0.0778822i	−0.110543	−	0.993871i	$-0.535259\pi$
$823$	8.33846	−	2.23428i	0.290660	−	0.0778822i	0.401203	+	0.915989i	$0.368592\pi$
$824$	−4.45077	−	7.70896i	−0.155050	−	0.268555i
$825$	12.0614	+	5.74409i	0.419925	+	0.199984i
$826$		0			0
$827$	−4.96734	+	4.96734i	−0.172731	+	0.172731i	−0.788178	−	0.615447i	$-0.788976\pi$
$827$	−4.96734	+	4.96734i	−0.172731	+	0.172731i	0.615447	+	0.788178i	$0.288976\pi$
$828$	0.156296	−	0.583305i	0.00543167	−	0.0202713i
$829$	14.1750	−	24.5518i	0.492318	−	0.852720i	−0.507643	−	0.861568i	$-0.669483\pi$
$829$	14.1750	−	24.5518i	0.492318	−	0.852720i	0.999961	+	0.00884765i	$0.00281633\pi$
$830$	29.5515	−	13.6342i	1.02575	−	0.473250i
$831$	2.45636	−	1.41818i	0.0852101	−	0.0491961i
$832$	−13.4910	−	13.4910i	−0.467717	−	0.467717i
$833$		0			0
$834$		−	16.3950i		−	0.567713i
$835$	−12.6080	−	15.1502i	−0.436317	−	0.524293i
$836$	−33.8417	−	19.5385i	−1.17044	−	0.675754i
$837$	1.87742	+	7.00662i	0.0648931	+	0.242184i
$838$	−20.3930	−	5.46430i	−0.704466	−	0.188761i
$839$	32.8100			1.13273			0.566364	−	0.824156i	$-0.308350\pi$
$839$	32.8100			1.13273			0.566364	+	0.824156i	$0.308350\pi$
$840$		0			0
$841$	28.9070			0.996795
$842$	54.1716	+	14.5152i	1.86688	+	0.500228i
$843$	3.50847	+	13.0938i	0.120838	+	0.450974i
$844$	−36.3115	−	20.9645i	−1.24989	−	0.721627i
$845$	−2.03694	+	22.2413i	−0.0700728	+	0.765124i
$846$		−	1.65766i		−	0.0569915i
$847$		0			0
$848$	−14.7390	−	14.7390i	−0.506139	−	0.506139i
$849$	19.8952	−	11.4865i	0.682801	−	0.394216i
$850$	−69.4670	−	12.8317i	−2.38270	−	0.440123i
$851$	−0.129205	+	0.223790i	−0.00442910	+	0.00767143i
$852$	−9.63032	+	35.9408i	−0.329929	+	1.23131i
$853$	−15.4954	+	15.4954i	−0.530553	+	0.530553i	−0.920737	−	0.390184i	$-0.872411\pi$
$853$	−15.4954	+	15.4954i	−0.530553	+	0.530553i	0.390184	+	0.920737i	$0.372411\pi$
$854$		0			0
$855$	10.9903	+	7.76222i	0.375861	+	0.265462i
$856$	−4.78885	−	8.29453i	−0.163680	−	0.283501i
$857$	24.3625	−	6.52792i	0.832208	−	0.222989i	0.182531	−	0.983200i	$-0.441571\pi$
$857$	24.3625	−	6.52792i	0.832208	−	0.222989i	0.649677	+	0.760211i	$0.274904\pi$
$858$	−9.42753	+	2.52610i	−0.321851	+	0.0862396i
$859$	−8.63556	−	14.9572i	−0.294641	−	0.510334i	0.680260	−	0.732971i	$-0.261867\pi$
$859$	−8.63556	−	14.9572i	−0.294641	−	0.510334i	−0.974901	+	0.222637i	$0.928534\pi$
$860$	0.397549	+	2.30944i	0.0135563	+	0.0787511i
$861$		0			0
$862$	33.3021	−	33.3021i	1.13427	−	1.13427i
$863$	1.07752	−	4.02135i	0.0366791	−	0.136888i	−0.945158	−	0.326613i	$-0.894093\pi$
$863$	1.07752	−	4.02135i	0.0366791	−	0.136888i	0.981837	+	0.189724i	$0.0607594\pi$
$864$	4.01468	−	6.95363i	0.136582	−	0.236567i
$865$	−20.0857	−	7.40313i	−0.682934	−	0.251714i
$866$	−34.7309	+	20.0519i	−1.18021	+	0.681392i
$867$	19.8369	+	19.8369i	0.673697	+	0.673697i
$868$		0			0
$869$		−	30.1848i		−	1.02395i
$870$	1.42903	+	0.130876i	0.0484488	+	0.00443711i
$871$	−7.29154	−	4.20978i	−0.247065	−	0.142643i
$872$	1.39645	+	5.21161i	0.0472897	+	0.176487i
$873$	12.0775	+	3.23617i	0.408763	+	0.109528i
$874$	−3.14686			−0.106444
$875$		0			0
$876$	−34.4448			−1.16378
$877$	11.6076	+	3.11025i	0.391961	+	0.105026i	0.449416	−	0.893323i	$-0.351632\pi$
$877$	11.6076	+	3.11025i	0.391961	+	0.105026i	−0.0574555	+	0.998348i	$0.518299\pi$
$878$	13.9895	+	52.2096i	0.472124	+	1.76199i
$879$	−2.96100	−	1.70953i	−0.0998721	−	0.0576612i
$880$	−17.5722	−	1.60933i	−0.592360	−	0.0542504i
$881$		−	35.7762i		−	1.20533i	−0.797994	−	0.602665i	$-0.794106\pi$
$881$		−	35.7762i		−	1.20533i	0.797994	−	0.602665i	$-0.205894\pi$
$882$		0			0
$883$	24.6278	+	24.6278i	0.828791	+	0.828791i	0.987350	−	0.158559i	$-0.0506848\pi$
$883$	24.6278	+	24.6278i	0.828791	+	0.828791i	−0.158559	+	0.987350i	$0.550685\pi$
$884$	24.5194	−	14.1563i	0.824678	−	0.476128i
$885$	16.7603	+	6.17749i	0.563393	+	0.207654i
$886$	23.2710	−	40.3065i	0.781803	−	1.35412i
$887$	0.268110	−	1.00060i	0.00900226	−	0.0335969i	−0.961279	−	0.275578i	$-0.911131\pi$
$887$	0.268110	−	1.00060i	0.00900226	−	0.0335969i	0.970281	+	0.241981i	$0.0777973\pi$
$888$	0.666503	−	0.666503i	0.0223664	−	0.0223664i
$889$		0			0
$890$	5.51943	+	32.0633i	0.185012	+	1.07477i
$891$	−1.33594	−	2.31391i	−0.0447555	−	0.0775188i
$892$	−15.2195	+	4.07805i	−0.509587	+	0.136543i
$893$	−4.57732	+	1.22649i	−0.153174	+	0.0410429i
$894$	15.0347	+	26.0409i	0.502835	+	0.870936i
$895$	2.37628	+	1.67831i	0.0794301	+	0.0560998i
$896$		0			0
$897$	−0.304889	+	0.304889i	−0.0101800	+	0.0101800i
$898$	3.82410	−	14.2717i	0.127612	−	0.476254i
$899$	1.10580	−	1.91530i	0.0368806	−	0.0638790i
$900$	−11.9506	−	2.20747i	−0.398353	−	0.0735824i
$901$	41.0240	−	23.6852i	1.36671	−	0.789069i
$902$	−28.0654	−	28.0654i	−0.934477	−	0.934477i
$903$		0			0
$904$		−	8.95913i		−	0.297976i
$905$	1.73043	−	18.8946i	0.0575216	−	0.628077i
$906$	17.8276	+	10.2928i	0.592284	+	0.341955i
$907$	−8.37259	−	31.2469i	−0.278007	−	1.03754i	−0.953799	−	0.300445i	$-0.902865\pi$
$907$	−8.37259	−	31.2469i	−0.278007	−	1.03754i	0.675792	−	0.737092i	$-0.263802\pi$
$908$	−47.0183	−	12.5985i	−1.56036	−	0.418096i
$909$	7.22962			0.239791
$910$		0			0
$911$	24.7867			0.821220			0.410610	−	0.911811i	$-0.365316\pi$
$911$	24.7867			0.821220			0.410610	+	0.911811i	$0.365316\pi$
$912$	−17.1666	−	4.59978i	−0.568444	−	0.152314i
$913$	4.78171	+	17.8456i	0.158251	+	0.590602i
$914$	28.9038	+	16.6876i	0.956053	+	0.551977i
$915$	−7.91566	−	9.51172i	−0.261684	−	0.314448i
$916$			70.3176i			2.32336i
$917$		0			0
$918$	9.99031	+	9.99031i	0.329729	+	0.329729i
$919$	−12.6351	+	7.29488i	−0.416794	+	0.240636i	−0.693705	−	0.720260i	$-0.744023\pi$
$919$	−12.6351	+	7.29488i	−0.416794	+	0.240636i	0.276911	+	0.960896i	$0.410689\pi$
$920$	0.457173	−	0.210927i	0.0150726	−	0.00695404i
$921$	−5.10036	+	8.83408i	−0.168063	+	0.291093i
$922$	16.3351	−	60.9634i	0.537968	−	2.00772i
$923$	18.7860	−	18.7860i	0.618349	−	0.618349i
$924$		0			0
$925$	4.69511	+	2.23598i	0.154374	+	0.0735187i
$926$	−11.4638	−	19.8559i	−0.376724	−	0.652505i
$927$	−9.48757	+	2.54219i	−0.311613	+	0.0834963i
$928$	−2.36465	+	0.633606i	−0.0776234	+	0.0207991i
$929$	12.5763	+	21.7828i	0.412615	+	0.714669i	0.995175	−	0.0981182i	$-0.0312823\pi$
$929$	12.5763	+	21.7828i	0.412615	+	0.714669i	−0.582560	+	0.812788i	$0.697949\pi$
$930$	−19.6960	+	27.8871i	−0.645859	+	0.914453i
$931$		0			0
$932$	−11.6313	+	11.6313i	−0.380996	+	0.380996i
$933$	−2.65397	+	9.90476i	−0.0868871	+	0.324267i
$934$	−2.69338	+	4.66507i	−0.0881301	+	0.152646i
$935$	13.8686	−	37.6275i	0.453553	−	1.23055i
$936$	1.36206	−	0.786383i	0.0445202	−	0.0257037i
$937$	28.3540	+	28.3540i	0.926286	+	0.926286i	0.997464	−	0.0711778i	$-0.0226758\pi$
$937$	28.3540	+	28.3540i	0.926286	+	0.926286i	−0.0711778	+	0.997464i	$0.522676\pi$
$938$		0			0
$939$		−	31.2405i		−	1.01950i
$940$	3.28991	−	2.73787i	0.107305	−	0.0892993i
$941$	0.0926410	+	0.0534863i	0.00302001	+	0.00174360i	0.501509	−	0.865152i	$-0.332778\pi$
$941$	0.0926410	+	0.0534863i	0.00302001	+	0.00174360i	−0.498489	+	0.866896i	$0.666112\pi$
$942$	1.67749	+	6.26049i	0.0546557	+	0.203978i
$943$	−1.69369	−	0.453822i	−0.0551541	−	0.0147785i
$944$	−23.5938			−0.767914
$945$		0			0
$946$	−2.42494			−0.0788417
$947$	−24.5435	−	6.57640i	−0.797556	−	0.213704i	−0.163045	−	0.986619i	$-0.552132\pi$
$947$	−24.5435	−	6.57640i	−0.797556	−	0.213704i	−0.634511	+	0.772914i	$0.718798\pi$
$948$	7.10681	+	26.5230i	0.230818	+	0.861426i
$949$	21.2990	+	12.2970i	0.691395	+	0.399177i
$950$	5.00671	+	63.1304i	0.162439	+	2.04822i
$951$			17.3331i			0.562064i
$952$		0			0
$953$	31.8008	+	31.8008i	1.03013	+	1.03013i	0.999532	+	0.0305973i	$0.00974093\pi$
$953$	31.8008	+	31.8008i	1.03013	+	1.03013i	0.0305973	+	0.999532i	$0.490259\pi$
$954$	12.8648	−	7.42748i	0.416512	−	0.240473i
$955$	−1.81536	−	3.93470i	−0.0587437	−	0.127324i
$956$	19.6594	−	34.0512i	0.635832	−	1.10129i
$957$	−0.210840	+	0.786867i	−0.00681550	+	0.0254358i
$958$	6.09425	−	6.09425i	0.196896	−	0.196896i
$959$		0			0
$960$	24.2267	−	4.17041i	0.781912	−	0.134599i
$961$	10.8087	+	18.7213i	0.348669	+	0.603913i
$962$	−3.66983	+	0.983327i	−0.118320	+	0.0317037i
$963$	−10.2082	+	2.73529i	−0.328956	+	0.0881434i
$964$	−13.8186	−	23.9345i	−0.445067	−	0.770878i
$965$	24.3951	−	4.19940i	0.785305	−	0.135183i
$966$		0			0
$967$	0.210995	−	0.210995i	0.00678513	−	0.00678513i	−0.703706	−	0.710491i	$-0.748473\pi$
$967$	0.210995	−	0.210995i	0.00678513	−	0.00678513i	0.710491	+	0.703706i	$0.248473\pi$
$968$	0.905654	−	3.37995i	0.0291088	−	0.108636i
$969$	20.1946	−	34.9781i	0.648745	−	1.12366i
$970$	24.6543	+	53.4371i	0.791603	+	1.71576i
$971$	−46.8662	+	27.0582i	−1.50401	+	0.868340i	−0.504020	+	0.863692i	$0.668146\pi$
$971$	−46.8662	+	27.0582i	−1.50401	+	0.868340i	−0.999989	+	0.00464820i	$0.998520\pi$
$972$	1.71866	+	1.71866i	0.0551260	+	0.0551260i
$973$		0			0
$974$			30.6752i			0.982896i
$975$	6.60159	+	5.63142i	0.211420	+	0.180350i
$976$	14.1552	+	8.17252i	0.453098	+	0.261596i
$977$	9.18653	+	34.2846i	0.293903	+	1.09686i	0.942085	+	0.335375i	$0.108863\pi$
$977$	9.18653	+	34.2846i	0.293903	+	1.09686i	−0.648181	+	0.761486i	$0.724470\pi$
$978$	39.3222	+	10.5364i	1.25739	+	0.336916i
$979$	−18.4693			−0.590283
$980$		0			0
$981$	5.95352			0.190081
$982$	17.4029	+	4.66310i	0.555350	+	0.148806i
$983$	−0.451521	−	1.68510i	−0.0144013	−	0.0537463i	0.958351	−	0.285592i	$-0.0921902\pi$
$983$	−0.451521	−	1.68510i	−0.0144013	−	0.0537463i	−0.972753	+	0.231846i	$0.925524\pi$
$984$	5.53895	+	3.19791i	0.176575	+	0.101946i
$985$	−20.6794	+	17.2094i	−0.658902	+	0.548339i
$986$		−	4.30761i		−	0.137182i
$987$		0			0
$988$	−17.9474	−	17.9474i	−0.570982	−	0.570982i
$989$	−0.0927759	+	0.0535642i	−0.00295010	+	0.00170324i
$990$	4.34909	−	11.7996i	0.138223	−	0.375017i
$991$	−24.4818	+	42.4038i	−0.777691	+	1.34700i	0.155579	+	0.987823i	$0.450276\pi$
$991$	−24.4818	+	42.4038i	−0.777691	+	1.34700i	−0.933270	+	0.359177i	$0.883058\pi$
$992$	15.0745	−	56.2587i	0.478615	−	1.78622i
$993$	0.893133	−	0.893133i	0.0283427	−	0.0283427i
$994$		0			0
$995$	4.19838	−	5.94437i	0.133098	−	0.188449i
$996$	−8.40323	−	14.5548i	−0.266267	−	0.461187i
$997$	−16.3710	+	4.38661i	−0.518476	+	0.138925i	−0.508562	−	0.861026i	$-0.669823\pi$
$997$	−16.3710	+	4.38661i	−0.518476	+	0.138925i	−0.00991437	+	0.999951i	$0.503156\pi$
$998$	48.3007	−	12.9421i	1.52893	−	0.409676i
$999$	−0.520035	−	0.900728i	−0.0164532	−	0.0284978i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.v.a.178.2		32
5.2	odd	4	inner	735.2.v.a.472.8		32
7.2	even	3	inner	735.2.v.a.313.7		32
7.3	odd	6		105.2.m.a.13.7	✓	16
7.4	even	3		105.2.m.a.13.8	yes	16
7.5	odd	6	inner	735.2.v.a.313.8		32
7.6	odd	2	inner	735.2.v.a.178.1		32
21.11	odd	6		315.2.p.e.118.2		16
21.17	even	6		315.2.p.e.118.1		16
28.3	even	6		1680.2.cz.d.433.8		16
28.11	odd	6		1680.2.cz.d.433.1		16
35.2	odd	12	inner	735.2.v.a.607.1		32
35.3	even	12		525.2.m.b.307.1		16
35.4	even	6		525.2.m.b.118.1		16
35.12	even	12	inner	735.2.v.a.607.2		32
35.17	even	12		105.2.m.a.97.8	yes	16
35.18	odd	12		525.2.m.b.307.2		16
35.24	odd	6		525.2.m.b.118.2		16
35.27	even	4	inner	735.2.v.a.472.7		32
35.32	odd	12		105.2.m.a.97.7	yes	16
105.17	odd	12		315.2.p.e.307.2		16
105.32	even	12		315.2.p.e.307.1		16
140.67	even	12		1680.2.cz.d.97.8		16
140.87	odd	12		1680.2.cz.d.97.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	7.3	odd	6
105.2.m.a.13.8	yes	16	7.4	even	3
105.2.m.a.97.7	yes	16	35.32	odd	12
105.2.m.a.97.8	yes	16	35.17	even	12
315.2.p.e.118.1		16	21.17	even	6
315.2.p.e.118.2		16	21.11	odd	6
315.2.p.e.307.1		16	105.32	even	12
315.2.p.e.307.2		16	105.17	odd	12
525.2.m.b.118.1		16	35.4	even	6
525.2.m.b.118.2		16	35.24	odd	6
525.2.m.b.307.1		16	35.3	even	12
525.2.m.b.307.2		16	35.18	odd	12
735.2.v.a.178.1		32	7.6	odd	2	inner
735.2.v.a.178.2		32	1.1	even	1	trivial
735.2.v.a.313.7		32	7.2	even	3	inner
735.2.v.a.313.8		32	7.5	odd	6	inner
735.2.v.a.472.7		32	35.27	even	4	inner
735.2.v.a.472.8		32	5.2	odd	4	inner
735.2.v.a.607.1		32	35.2	odd	12	inner
735.2.v.a.607.2		32	35.12	even	12	inner
1680.2.cz.d.97.1		16	140.87	odd	12
1680.2.cz.d.97.8		16	140.67	even	12
1680.2.cz.d.433.1		16	28.11	odd	6
1680.2.cz.d.433.8		16	28.3	even	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.03317 - 0.544785i) q^{2} +(0.258819 + 0.965926i) q^{3} +(2.10492 + 1.21528i) q^{4} +(2.22675 + 0.203934i) q^{5} -2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-2.03317 - 0.544785i) q^{2} +(0.258819 + 0.965926i) q^{3} +(2.10492 + 1.21528i) q^{4} +(2.22675 + 0.203934i) q^{5} -2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-4.41625 - 1.62773i) q^{10} +(1.33594 - 2.31391i) q^{11} +(-0.629073 + 2.34773i) q^{12} +(1.22714 - 1.22714i) q^{13} +(0.379340 + 2.20366i) q^{15} +(-1.47676 - 2.55782i) q^{16} +(6.48349 - 1.73725i) q^{17} +(2.03317 - 0.544785i) q^{18} +(-3.00865 - 5.21113i) q^{19} +(4.43929 + 3.13538i) q^{20} +(-3.97676 + 3.97676i) q^{22} +(-0.0643048 + 0.239989i) q^{23} +(0.453132 - 0.784847i) q^{24} +(4.91682 + 0.908218i) q^{25} +(-3.16351 + 1.82645i) q^{26} +(-0.707107 - 0.707107i) q^{27} +0.304889i q^{29} +(0.429257 - 4.68706i) q^{30} +(-6.28197 - 3.62690i) q^{31} +(2.07815 + 7.75576i) q^{32} +(2.58083 + 0.691531i) q^{33} -14.1284 q^{34} -2.43055 q^{36} +(1.00463 + 0.269190i) q^{37} +(3.27813 + 12.2341i) q^{38} +(1.50294 + 0.867721i) q^{39} +(-1.29627 - 1.55764i) q^{40} +7.05736i q^{41} +(0.304889 + 0.304889i) q^{43} +(5.62407 - 3.24706i) q^{44} +(-2.03039 + 0.936763i) q^{45} +(0.261485 - 0.452905i) q^{46} +(0.203827 - 0.760694i) q^{47} +(2.08845 - 2.08845i) q^{48} +(-9.50193 - 4.52517i) q^{50} +(3.35610 + 5.81294i) q^{51} +(4.07435 - 1.09172i) q^{52} +(6.81689 - 1.82658i) q^{53} +(1.05244 + 1.82289i) q^{54} +(3.44668 - 4.88005i) q^{55} +(4.25487 - 4.25487i) q^{57} +(0.166099 - 0.619890i) q^{58} +(3.99419 - 6.91813i) q^{59} +(-1.87957 + 5.09952i) q^{60} +(-4.79266 + 2.76704i) q^{61} +(10.7964 + 10.7964i) q^{62} -10.9939i q^{64} +(2.98279 - 2.48228i) q^{65} +(-4.87052 - 2.81199i) q^{66} +(-1.25567 - 4.68622i) q^{67} +(15.7585 + 4.22247i) q^{68} -0.248455 q^{69} +15.3087 q^{71} +(0.875383 + 0.234558i) q^{72} +(3.66788 + 13.6887i) q^{73} +(-1.89593 - 1.09462i) q^{74} +(0.395296 + 4.98435i) q^{75} -14.6253i q^{76} +(-2.58300 - 2.58300i) q^{78} +(9.78372 - 5.64863i) q^{79} +(-2.76675 - 5.99679i) q^{80} +(0.500000 - 0.866025i) q^{81} +(3.84475 - 14.3488i) q^{82} +(-4.88941 + 4.88941i) q^{83} +(14.7914 - 2.54621i) q^{85} +(-0.453791 - 0.785990i) q^{86} +(-0.294500 + 0.0789112i) q^{87} +(-2.33891 + 0.626709i) q^{88} +(-3.45626 - 5.98641i) q^{89} +(4.63845 - 0.798469i) q^{90} +(-0.427009 + 0.427009i) q^{92} +(1.87742 - 7.00662i) q^{93} +(-0.828829 + 1.43557i) q^{94} +(-5.63678 - 12.2174i) q^{95} +(-6.95363 + 4.01468i) q^{96} +(-8.84137 - 8.84137i) q^{97} +2.67187i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 48 q^{8}+O(q^{10}) \) 32 * q + 48 * q^8	\( 32 q + 48 q^{8} + 16 q^{11} + 16 q^{15} + 48 q^{16} - 32 q^{22} + 40 q^{23} + 8 q^{30} - 48 q^{32} - 32 q^{36} - 32 q^{37} - 32 q^{43} - 64 q^{46} - 144 q^{50} + 16 q^{51} - 24 q^{53} + 16 q^{57} - 32 q^{58} - 40 q^{60} - 40 q^{65} + 32 q^{67} + 128 q^{71} - 24 q^{72} - 16 q^{78} + 16 q^{81} + 96 q^{85} - 64 q^{86} + 64 q^{88} - 80 q^{92} - 24 q^{93} + 72 q^{95}+O(q^{100}) \) 32 * q + 48 * q^8 + 16 * q^11 + 16 * q^15 + 48 * q^16 - 32 * q^22 + 40 * q^23 + 8 * q^30 - 48 * q^32 - 32 * q^36 - 32 * q^37 - 32 * q^43 - 64 * q^46 - 144 * q^50 + 16 * q^51 - 24 * q^53 + 16 * q^57 - 32 * q^58 - 40 * q^60 - 40 * q^65 + 32 * q^67 + 128 * q^71 - 24 * q^72 - 16 * q^78 + 16 * q^81 + 96 * q^85 - 64 * q^86 + 64 * q^88 - 80 * q^92 - 24 * q^93 + 72 * q^95

Introduction

L-functions

Modular forms

Varieties

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