LMFDB - Embedded newform 735.2.v.a.178.1

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			178.1
Character	$\chi$	$=$	735.178
Dual form			735.2.v.a.607.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.03317 - 0.544785i) q^{2} +(-0.258819 - 0.965926i) q^{3} +(2.10492 + 1.21528i) q^{4} +(-2.22675 - 0.203934i) q^{5} +2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(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	−0.856498	−	0.516150i	$-0.827365\pi$
$13$	−1.22714	+	1.22714i	−0.340348	+	0.340348i	0.516150	+	0.856498i	$0.327365\pi$
$14$		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	−0.936587	−	0.350436i	$-0.886034\pi$
$17$	−6.48349	+	1.73725i	−1.57248	+	0.421344i	−0.635890	+	0.771780i	$0.719367\pi$
$18$	2.03317	−	0.544785i	0.479222	−	0.128407i
$19$	3.00865	+	5.21113i	0.690231	+	1.19551i	0.971762	+	0.235963i	$0.0758243\pi$
$19$	3.00865	+	5.21113i	0.690231	+	1.19551i	−0.281531	+	0.959552i	$0.590842\pi$
$20$	−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	0.943500	−	0.331371i	$-0.107511\pi$
$31$	6.28197	+	3.62690i	1.12827	+	0.651410i	0.184774	+	0.982781i	$0.440845\pi$
$32$	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	$-0.814213\pi$
$41$		−	7.05736i		−	1.10217i	0.834447	−	0.551087i	$-0.185787\pi$
$42$		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	−0.979197	−	0.202912i	$-0.934959\pi$
$47$	−0.203827	+	0.760694i	−0.0297313	+	0.110959i	0.949466	+	0.313871i	$0.101626\pi$
$48$	−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	$0.340734\pi$
$59$	−3.99419	+	6.91813i	−0.519999	+	0.900664i	−0.999730	+	0.0232486i	$0.992599\pi$
$60$	−1.87957	+	5.09952i	−0.242651	+	0.658346i
$61$	4.79266	−	2.76704i	0.613637	−	0.354284i	−0.160750	−	0.986995i	$-0.551391\pi$
$61$	4.79266	−	2.76704i	0.613637	−	0.354284i	0.774388	+	0.632711i	$0.218058\pi$
$62$	−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	$-0.772056\pi$
$73$	−3.66788	−	13.6887i	−0.429293	−	1.60214i	0.325073	−	0.945689i	$-0.394611\pi$
$74$	−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	−0.385871	−	0.922553i	$-0.626099\pi$
$83$	4.88941	−	4.88941i	0.536682	−	0.536682i	0.922553	+	0.385871i	$0.126099\pi$
$84$		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	0.988994	−	0.147957i	$-0.0472697\pi$
$89$	3.45626	+	5.98641i	0.366363	+	0.634559i	−0.622631	+	0.782515i	$0.713936\pi$
$90$	−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	0.995233	−	0.0975276i	$-0.0310934\pi$
$97$	8.84137	+	8.84137i	0.897705	+	0.897705i	−0.0975276	+	0.995233i	$0.531093\pi$
$98$		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	0.778035	−	0.628221i	$-0.216217\pi$
$101$	6.26104	+	3.61481i	0.622996	+	0.359687i	−0.155038	+	0.987908i	$0.549550\pi$
$102$	−3.65671	−	13.6470i	−0.362068	−	1.35126i
$103$	−9.48757	−	2.54219i	−0.934838	−	0.250489i	−0.240921	−	0.970545i	$-0.577450\pi$
$103$	−9.48757	−	2.54219i	−0.934838	−	0.250489i	−0.693916	+	0.720056i	$0.744116\pi$
$104$	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	−0.102767	−	0.994705i	$-0.532770\pi$
$131$	8.09529	−	4.67382i	0.707289	−	0.408353i	0.810056	+	0.586352i	$0.199436\pi$
$132$	−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	$-0.607159\pi$
$139$	−7.78902			−0.660656			−0.330328	+	0.943866i	$0.607159\pi$
$140$		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	−0.138172	−	0.990408i	$-0.544123\pi$
$157$	2.97426	−	0.796951i	0.237372	−	0.0636036i	0.375544	+	0.926805i	$0.377456\pi$
$158$	−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	0.905870	−	0.423555i	$-0.139218\pi$
$167$	6.23288	+	6.23288i	0.482315	+	0.482315i	−0.423555	+	0.905870i	$0.639218\pi$
$168$		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	0.592594	−	0.805501i	$-0.298104\pi$
$173$	9.24710	+	2.47775i	0.703044	+	0.188380i	0.110450	+	0.993882i	$0.464771\pi$
$174$	−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	$0.102123\pi$
$181$			8.48528i			0.630706i	−0.948974	+	0.315353i	$0.897877\pi$
$182$		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	−0.917922	−	0.396761i	$-0.870134\pi$
$199$	−1.62730	+	2.81856i	−0.115356	+	0.199803i	0.802566	+	0.596563i	$0.203468\pi$
$200$	−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	−0.536768	−	0.843730i	$-0.680355\pi$
$223$	4.58392	−	4.58392i	0.306962	−	0.306962i	0.843730	+	0.536768i	$0.180355\pi$
$224$		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	0.448592	−	0.893737i	$-0.351926\pi$
$227$	19.3447	−	5.18339i	1.28395	−	0.344034i	0.835360	+	0.549703i	$0.185259\pi$
$228$	14.1270	−	3.78532i	0.935583	−	0.250689i
$229$	−14.4654	−	25.0547i	−0.955898	−	1.65566i	−0.732300	−	0.680982i	$-0.761553\pi$
$229$	−14.4654	−	25.0547i	−0.955898	−	1.65566i	−0.223598	−	0.974681i	$-0.571780\pi$
$230$	−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	0.782425	−	0.622745i	$-0.213983\pi$
$241$	9.84735	+	5.68537i	0.634324	+	0.366227i	−0.148101	+	0.988972i	$0.547316\pi$
$242$	−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	$0.0703944\pi$
$251$			6.95039i			0.438705i	−0.975646	+	0.219352i	$0.929606\pi$
$252$		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	$0.230131\pi$
$257$	−3.69280	+	13.7817i	−0.230350	+	0.859679i	−0.980190	+	0.198060i	$0.936536\pi$
$258$	−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	−0.999518	−	0.0310287i	$-0.990122\pi$
$269$	−7.75593	+	13.4337i	−0.472888	+	0.819065i	0.526631	+	0.850094i	$0.323455\pi$
$270$	1.97178	+	4.27374i	0.119999	+	0.260091i
$271$	11.5544	−	6.67091i	0.701877	−	0.405229i	−0.106169	−	0.994348i	$-0.533858\pi$
$271$	11.5544	−	6.67091i	0.701877	−	0.405229i	0.808046	+	0.589119i	$0.200525\pi$
$272$	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	$0.155905\pi$
$283$	5.94585	+	22.1902i	0.353444	+	1.31907i	−0.528987	+	0.848630i	$0.677428\pi$
$284$	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	−0.632951	−	0.774192i	$-0.718157\pi$
$293$	2.41765	−	2.41765i	0.141240	−	0.141240i	0.774192	+	0.632951i	$0.218157\pi$
$294$		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	0.470652	−	0.882319i	$-0.344019\pi$
$307$	−7.21300	−	7.21300i	−0.411667	−	0.411667i	−0.882319	+	0.470652i	$0.844019\pi$
$308$		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	0.226623	−	0.973983i	$-0.427231\pi$
$311$	−8.88036	−	5.12708i	−0.503559	−	0.290730i	−0.730182	+	0.683253i	$0.760565\pi$
$312$	−0.407062	−	1.51918i	−0.0230453	−	0.0860064i
$313$	30.1760	+	8.08564i	1.70565	+	0.457027i	0.974352	−	0.225031i	$-0.0722485\pi$
$313$	30.1760	+	8.08564i	1.70565	+	0.457027i	0.731298	+	0.682059i	$0.238915\pi$
$314$	−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	$-0.476368\pi$
$349$	2.77139			0.148349			0.0741746	+	0.997245i	$0.476368\pi$
$350$		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	0.974735	−	0.223363i	$-0.0717036\pi$
$353$	0.355252	+	1.32582i	0.0189082	+	0.0705663i	−0.955827	+	0.293929i	$0.905037\pi$
$354$	−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	0.236554	−	0.971618i	$-0.423982\pi$
$367$	17.7631	−	4.75960i	0.927225	−	0.248449i	0.690671	+	0.723169i	$0.257315\pi$
$368$	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	0.245169	−	0.969480i	$-0.421157\pi$
$383$	−0.533272	−	0.142890i	−0.0272489	−	0.00730133i	−0.272418	+	0.962179i	$0.587823\pi$
$384$	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	$-0.708199\pi$
$397$	6.28213	−	23.4452i	0.315291	−	1.17668i	0.923718	−	0.383072i	$-0.125134\pi$
$398$	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	−0.896844	−	0.442347i	$-0.854146\pi$
$409$	−1.32139	+	2.28872i	−0.0653386	+	0.113170i	0.831506	+	0.555516i	$0.187479\pi$
$410$	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	$-0.578789\pi$
$419$	−10.0302			−0.490007			−0.245003	+	0.969522i	$0.578789\pi$
$420$		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	−0.952373	−	0.304935i	$-0.901365\pi$
$433$	−13.4723	+	13.4723i	−0.647438	+	0.647438i	0.304935	+	0.952373i	$0.401365\pi$
$434$		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	$0.0432883\pi$
$439$	12.8395	+	22.2386i	0.612795	+	1.06139i	−0.377972	+	0.925817i	$0.623378\pi$
$440$	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	$-0.753959\pi$
$461$		−	29.9845i		−	1.39652i	0.715846	−	0.698259i	$-0.246041\pi$
$462$		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	−0.979556	−	0.201170i	$-0.935525\pi$
$467$	−0.662362	+	2.47197i	−0.0306504	+	0.114389i	0.948906	+	0.315559i	$0.102192\pi$
$468$	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	−0.815457	−	0.578818i	$-0.803514\pi$
$479$	2.04728	−	3.54599i	0.0935425	−	0.162020i	0.908999	+	0.416798i	$0.136848\pi$
$480$	−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	−0.182786	−	0.983153i	$-0.558511\pi$
$503$	17.9504	−	17.9504i	0.800367	−	0.800367i	0.983153	+	0.182786i	$0.0585115\pi$
$504$		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	0.990250	−	0.139298i	$-0.0444847\pi$
$509$	8.44887	+	14.6339i	0.374489	+	0.648635i	−0.615761	+	0.787933i	$0.711151\pi$
$510$	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	0.642065	−	0.766651i	$-0.278078\pi$
$521$	6.82841	+	3.94238i	0.299158	+	0.172719i	−0.342907	+	0.939370i	$0.611411\pi$
$522$	0.166099	+	0.619890i	0.00726996	+	0.0271319i
$523$	−1.68225	−	0.450757i	−0.0735595	−	0.0197102i	0.221852	−	0.975080i	$-0.428790\pi$
$523$	−1.68225	−	0.450757i	−0.0735595	−	0.0197102i	−0.295411	+	0.955370i	$0.595457\pi$
$524$	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	$-0.833005\pi$
$563$	−8.69386	−	32.4459i	−0.366402	−	1.36743i	0.499107	−	0.866540i	$-0.333661\pi$
$564$	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	0.714259	−	0.699882i	$-0.246764\pi$
$577$	40.4214	−	10.8309i	1.68277	−	0.450896i	0.968507	+	0.248986i	$0.0800974\pi$
$578$	−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	$-0.966396\pi$
$587$	−26.6462	−	26.6462i	−1.09981	−	1.09981i	−0.105375	−	0.994433i	$-0.533604\pi$
$588$		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	0.658304	−	0.752752i	$-0.271274\pi$
$593$	20.7484	+	5.55952i	0.852036	+	0.228302i	0.193732	+	0.981055i	$0.437941\pi$
$594$	−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	$0.150629\pi$
$601$			22.3458i			0.911503i	−0.890107	+	0.455752i	$0.849371\pi$
$602$		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	−0.961515	−	0.274753i	$-0.911404\pi$
$607$	0.210840	−	0.786867i	0.00855775	−	0.0319380i	0.970073	+	0.242815i	$0.0780707\pi$
$608$	−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	$0.462650\pi$
$619$	−19.9420	+	34.5405i	−0.801536	+	1.38830i	−0.918605	+	0.395178i	$0.870683\pi$
$620$	−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	$0.603039\pi$
$643$	−32.1062	+	32.1062i	−1.26614	+	1.26614i	−0.948063	+	0.318082i	$0.896961\pi$
$644$		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	0.105607	−	0.994408i	$-0.466321\pi$
$647$	17.6596	−	4.73187i	0.694270	−	0.186029i	0.588663	+	0.808379i	$0.299655\pi$
$648$	−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	0.896006	−	0.444042i	$-0.146456\pi$
$661$	24.6676	+	14.2418i	0.959458	+	0.553943i	0.0634519	+	0.997985i	$0.479789\pi$
$662$	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	−0.956996	−	0.290102i	$-0.906311\pi$
$677$	0.438111	−	1.63505i	0.0168380	−	0.0628402i	0.973834	+	0.227262i	$0.0729774\pi$
$678$	−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	0.381549	−	0.924348i	$-0.375391\pi$
$691$	36.0875	−	20.8351i	1.37283	−	0.792606i	0.991284	+	0.131743i	$0.0420573\pi$
$692$	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	$-0.978328\pi$
$719$	−14.9558	−	25.9043i	−0.557758	−	0.966066i	0.439925	−	0.898035i	$-0.355005\pi$
$720$	−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	$0.0362034\pi$
$727$	29.8488	+	29.8488i	1.10703	+	1.10703i	0.113491	+	0.993539i	$0.463797\pi$
$728$		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	0.159938	−	0.987127i	$-0.448870\pi$
$733$	−5.28252	−	1.41545i	−0.195114	−	0.0522807i	−0.355053	+	0.934846i	$0.615537\pi$
$734$	−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	−0.912364	−	0.409381i	$-0.865745\pi$
$761$	−27.9728	+	16.1501i	−1.01401	+	0.585440i	−0.101648	+	0.994820i	$0.532411\pi$
$762$	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	$-0.607831\pi$
$769$	−18.4310			−0.664640			−0.332320	+	0.943167i	$0.607831\pi$
$770$		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	$-0.933826\pi$
$773$	−6.51389	−	24.3102i	−0.234288	−	0.874376i	0.744180	−	0.667979i	$-0.232840\pi$
$774$	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	−0.627827	−	0.778353i	$-0.716055\pi$
$787$	−21.9481	+	5.88096i	−0.782364	+	0.209634i	−0.154537	+	0.987987i	$0.549389\pi$
$788$	−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	0.995817	−	0.0913664i	$-0.0291235\pi$
$797$	25.5337	+	25.5337i	0.904451	+	0.904451i	−0.0913664	+	0.995817i	$0.529123\pi$
$798$		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	$-0.794602\pi$
$811$		−	34.2545i		−	1.20284i	0.798933	−	0.601420i	$-0.205398\pi$
$812$		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	−0.999961	−	0.00884765i	$-0.997184\pi$
$829$	−14.1750	+	24.5518i	−0.492318	+	0.852720i	0.507643	+	0.861568i	$0.330517\pi$
$830$	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	$-0.691650\pi$
$839$	−32.8100			−1.13273			−0.566364	+	0.824156i	$0.691650\pi$
$840$		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	−0.390184	−	0.920737i	$-0.627589\pi$
$853$	15.4954	−	15.4954i	0.530553	−	0.530553i	0.920737	+	0.390184i	$0.127589\pi$
$854$		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	−0.649677	−	0.760211i	$-0.725096\pi$
$857$	−24.3625	+	6.52792i	−0.832208	+	0.222989i	−0.182531	+	0.983200i	$0.558429\pi$
$858$	−9.42753	+	2.52610i	−0.321851	+	0.0862396i
$859$	8.63556	+	14.9572i	0.294641	+	0.510334i	0.974901	−	0.222637i	$-0.0714665\pi$
$859$	8.63556	+	14.9572i	0.294641	+	0.510334i	−0.680260	+	0.732971i	$0.738133\pi$
$860$	−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	$0.205894\pi$
$881$			35.7762i			1.20533i	−0.797994	+	0.602665i	$0.794106\pi$
$882$		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	−0.970281	−	0.241981i	$-0.922203\pi$
$887$	−0.268110	+	1.00060i	−0.00900226	+	0.0335969i	0.961279	+	0.275578i	$0.0888694\pi$
$888$	−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	0.582560	−	0.812788i	$-0.302051\pi$
$929$	−12.5763	−	21.7828i	−0.412615	−	0.714669i	−0.995175	+	0.0981182i	$0.968718\pi$
$930$	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	0.0711778	−	0.997464i	$-0.477324\pi$
$937$	−28.3540	−	28.3540i	−0.926286	−	0.926286i	−0.997464	+	0.0711778i	$0.977324\pi$
$938$		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	0.498489	−	0.866896i	$-0.333888\pi$
$941$	−0.0926410	−	0.0534863i	−0.00302001	−	0.00174360i	−0.501509	+	0.865152i	$0.667222\pi$
$942$	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	$-0.331854\pi$
$971$	46.8662	−	27.0582i	1.50401	−	0.868340i	0.999989	−	0.00464820i	$-0.00147957\pi$
$972$	−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	0.972753	−	0.231846i	$-0.0744764\pi$
$983$	0.451521	+	1.68510i	0.0144013	+	0.0537463i	−0.958351	+	0.285592i	$0.907810\pi$
$984$	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	0.00991437	−	0.999951i	$-0.496844\pi$
$997$	16.3710	−	4.38661i	0.518476	−	0.138925i	0.508562	+	0.861026i	$0.330177\pi$
$998$	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.178.1		32
5.2	odd	4	inner	735.2.v.a.472.7		32
7.2	even	3	inner	735.2.v.a.313.8		32
7.3	odd	6		105.2.m.a.13.8	yes	16
7.4	even	3		105.2.m.a.13.7	✓	16
7.5	odd	6	inner	735.2.v.a.313.7		32
7.6	odd	2	inner	735.2.v.a.178.2		32
21.11	odd	6		315.2.p.e.118.1		16
21.17	even	6		315.2.p.e.118.2		16
28.3	even	6		1680.2.cz.d.433.1		16
28.11	odd	6		1680.2.cz.d.433.8		16
35.2	odd	12	inner	735.2.v.a.607.2		32
35.3	even	12		525.2.m.b.307.2		16
35.4	even	6		525.2.m.b.118.2		16
35.12	even	12	inner	735.2.v.a.607.1		32
35.17	even	12		105.2.m.a.97.7	yes	16
35.18	odd	12		525.2.m.b.307.1		16
35.24	odd	6		525.2.m.b.118.1		16
35.27	even	4	inner	735.2.v.a.472.8		32
35.32	odd	12		105.2.m.a.97.8	yes	16
105.17	odd	12		315.2.p.e.307.1		16
105.32	even	12		315.2.p.e.307.2		16
140.67	even	12		1680.2.cz.d.97.1		16
140.87	odd	12		1680.2.cz.d.97.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	7.4	even	3
105.2.m.a.13.8	yes	16	7.3	odd	6
105.2.m.a.97.7	yes	16	35.17	even	12
105.2.m.a.97.8	yes	16	35.32	odd	12
315.2.p.e.118.1		16	21.11	odd	6
315.2.p.e.118.2		16	21.17	even	6
315.2.p.e.307.1		16	105.17	odd	12
315.2.p.e.307.2		16	105.32	even	12
525.2.m.b.118.1		16	35.24	odd	6
525.2.m.b.118.2		16	35.4	even	6
525.2.m.b.307.1		16	35.18	odd	12
525.2.m.b.307.2		16	35.3	even	12
735.2.v.a.178.1		32	1.1	even	1	trivial
735.2.v.a.178.2		32	7.6	odd	2	inner
735.2.v.a.313.7		32	7.5	odd	6	inner
735.2.v.a.313.8		32	7.2	even	3	inner
735.2.v.a.472.7		32	5.2	odd	4	inner
735.2.v.a.472.8		32	35.27	even	4	inner
735.2.v.a.607.1		32	35.12	even	12	inner
735.2.v.a.607.2		32	35.2	odd	12	inner
1680.2.cz.d.97.1		16	140.67	even	12
1680.2.cz.d.97.8		16	140.87	odd	12
1680.2.cz.d.433.1		16	28.3	even	6
1680.2.cz.d.433.8		16	28.11	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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
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

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