LMFDB - Embedded newform 735.2.v.a.472.7

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			472.7
Character	$\chi$	$=$	735.472
Dual form			735.2.v.a.313.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.544785 - 2.03317i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-2.10492 - 1.21528i) q^{4} +(-0.936763 + 2.03039i) q^{5} +2.10489i q^{6} +(-0.640825 + 0.640825i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(0.544785 - 2.03317i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-2.10492 - 1.21528i) q^{4} +(-0.936763 + 2.03039i) q^{5} +2.10489i q^{6} +(-0.640825 + 0.640825i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.61778 + 3.01072i) q^{10} +(1.33594 - 2.31391i) q^{11} +(2.34773 + 0.629073i) q^{12} +(1.22714 + 1.22714i) q^{13} +(0.379340 - 2.20366i) q^{15} +(-1.47676 - 2.55782i) q^{16} +(-1.73725 - 6.48349i) q^{17} +(-0.544785 - 2.03317i) q^{18} +(-3.00865 - 5.21113i) q^{19} +(4.43929 - 3.13538i) q^{20} +(-3.97676 - 3.97676i) q^{22} +(0.239989 + 0.0643048i) q^{23} +(0.453132 - 0.784847i) q^{24} +(-3.24495 - 3.80398i) q^{25} +(3.16351 - 1.82645i) q^{26} +(-0.707107 + 0.707107i) q^{27} -0.304889i q^{29} +(-4.27374 - 1.97178i) q^{30} +(6.28197 + 3.62690i) q^{31} +(-7.75576 + 2.07815i) q^{32} +(-0.691531 + 2.58083i) q^{33} -14.1284 q^{34} -2.43055 q^{36} +(-0.269190 + 1.00463i) q^{37} +(-12.2341 + 3.27813i) q^{38} +(-1.50294 - 0.867721i) q^{39} +(-0.700822 - 1.90142i) q^{40} -7.05736i q^{41} +(0.304889 - 0.304889i) q^{43} +(-5.62407 + 3.24706i) q^{44} +(0.203934 + 2.22675i) q^{45} +(0.261485 - 0.452905i) q^{46} +(-0.760694 - 0.203827i) q^{47} +(2.08845 + 2.08845i) q^{48} +(-9.50193 + 4.52517i) q^{50} +(3.35610 + 5.81294i) q^{51} +(-1.09172 - 4.07435i) q^{52} +(-1.82658 - 6.81689i) q^{53} +(1.05244 + 1.82289i) q^{54} +(3.44668 + 4.88005i) q^{55} +(4.25487 + 4.25487i) q^{57} +(-0.619890 - 0.166099i) q^{58} +(3.99419 - 6.91813i) q^{59} +(-3.47653 + 4.17752i) q^{60} +(4.79266 - 2.76704i) q^{61} +(10.7964 - 10.7964i) q^{62} +10.9939i q^{64} +(-3.64112 + 1.34203i) q^{65} +(4.87052 + 2.81199i) q^{66} +(4.68622 - 1.25567i) q^{67} +(-4.22247 + 15.7585i) q^{68} -0.248455 q^{69} +15.3087 q^{71} +(-0.234558 + 0.875383i) q^{72} +(-13.6887 + 3.66788i) q^{73} +(1.89593 + 1.09462i) q^{74} +(4.11893 + 2.83451i) q^{75} +14.6253i q^{76} +(-2.58300 + 2.58300i) q^{78} +(-9.78372 + 5.64863i) q^{79} +(6.57675 - 0.602322i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-14.3488 - 3.84475i) q^{82} +(-4.88941 - 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} +(-0.453791 - 0.785990i) q^{86} +(0.0789112 + 0.294500i) q^{87} +(0.626709 + 2.33891i) q^{88} +(-3.45626 - 5.98641i) q^{89} +(4.63845 + 0.798469i) q^{90} +(-0.427009 - 0.427009i) q^{92} +(-7.00662 - 1.87742i) q^{93} +(-0.828829 + 1.43557i) q^{94} +(13.3990 - 1.22713i) 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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.544785	−	2.03317i	0.385221	−	1.43766i	−0.452597	−	0.891715i	$-0.649502\pi$
$2$	0.544785	−	2.03317i	0.385221	−	1.43766i	0.837818	−	0.545950i	$-0.183831\pi$
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	−2.10492	−	1.21528i	−1.05246	−	0.607638i
$5$	−0.936763	+	2.03039i	−0.418933	+	0.908017i
$5$	−0.936763	+	2.03039i	−0.418933	+	0.908017i
$6$			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
$10$	3.61778	+	3.01072i	1.14404	+	0.952073i
$11$	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	$0.0347038\pi$
$12$	2.34773	+	0.629073i	0.677732	+	0.181598i
$13$	1.22714	+	1.22714i	0.340348	+	0.340348i	0.856498	−	0.516150i	$-0.172635\pi$
$13$	1.22714	+	1.22714i	0.340348	+	0.340348i	−0.516150	+	0.856498i	$0.672635\pi$
$14$		0			0
$15$	0.379340	−	2.20366i	0.0979452	−	0.568982i
$16$	−1.47676	−	2.55782i	−0.369190	−	0.639456i
$17$	−1.73725	−	6.48349i	−0.421344	−	1.57248i	−0.771780	−	0.635890i	$-0.780633\pi$
$17$	−1.73725	−	6.48349i	−0.421344	−	1.57248i	0.350436	−	0.936587i	$-0.386034\pi$
$18$	−0.544785	−	2.03317i	−0.128407	−	0.479222i
$19$	−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
$23$	0.239989	+	0.0643048i	0.0500411	+	0.0134085i	0.283753	−	0.958897i	$-0.408421\pi$
$23$	0.239989	+	0.0643048i	0.0500411	+	0.0134085i	−0.233712	+	0.972306i	$0.575087\pi$
$24$	0.453132	−	0.784847i	0.0924951	−	0.160206i
$25$	−3.24495	−	3.80398i	−0.648990	−	0.760797i
$26$	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	$-0.990988\pi$
$29$		−	0.304889i		−	0.0566165i	0.999599	−	0.0283083i	$-0.00901200\pi$
$30$	−4.27374	−	1.97178i	−0.780274	−	0.359996i
$31$	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	$0.440845\pi$
$32$	−7.75576	+	2.07815i	−1.37104	+	0.367369i
$33$	−0.691531	+	2.58083i	−0.120380	+	0.449265i
$34$	−14.1284			−2.42301
$35$		0			0
$36$	−2.43055			−0.405092
$37$	−0.269190	+	1.00463i	−0.0442546	+	0.165160i	−0.984517	−	0.175291i	$-0.943913\pi$
$37$	−0.269190	+	1.00463i	−0.0442546	+	0.165160i	0.940262	+	0.340452i	$0.110580\pi$
$38$	−12.2341	+	3.27813i	−1.98464	+	0.531783i
$39$	−1.50294	−	0.867721i	−0.240662	−	0.138947i
$40$	−0.700822	−	1.90142i	−0.110810	−	0.300642i
$41$		−	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	−0.683477	−	0.729972i	$-0.739533\pi$
$43$	0.304889	−	0.304889i	0.0464952	−	0.0464952i	0.729972	+	0.683477i	$0.239533\pi$
$44$	−5.62407	+	3.24706i	−0.847861	+	0.489513i
$45$	0.203934	+	2.22675i	0.0304006	+	0.331944i
$46$	0.261485	−	0.452905i	0.0385538	−	0.0667772i
$47$	−0.760694	−	0.203827i	−0.110959	−	0.0297313i	0.202912	−	0.979197i	$-0.434959\pi$
$47$	−0.760694	−	0.203827i	−0.110959	−	0.0297313i	−0.313871	+	0.949466i	$0.601626\pi$
$48$	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
$52$	−1.09172	−	4.07435i	−0.151394	−	0.565011i
$53$	−1.82658	−	6.81689i	−0.250900	−	0.936372i	−0.970326	−	0.241802i	$-0.922262\pi$
$53$	−1.82658	−	6.81689i	−0.250900	−	0.936372i	0.719426	−	0.694570i	$-0.244405\pi$
$54$	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
$58$	−0.619890	−	0.166099i	−0.0813956	−	0.0218099i
$59$	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	$-0.00740092\pi$
$60$	−3.47653	+	4.17752i	−0.448818	+	0.539315i
$61$	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
$65$	−3.64112	+	1.34203i	−0.451625	+	0.166459i
$66$	4.87052	+	2.81199i	0.599519	+	0.346133i
$67$	4.68622	−	1.25567i	0.572513	−	0.153404i	0.0390641	−	0.999237i	$-0.487562\pi$
$67$	4.68622	−	1.25567i	0.572513	−	0.153404i	0.533449	+	0.845832i	$0.320896\pi$
$68$	−4.22247	+	15.7585i	−0.512049	+	1.91099i
$69$	−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	$0.137299\pi$
$72$	−0.234558	+	0.875383i	−0.0276430	+	0.103165i
$73$	−13.6887	+	3.66788i	−1.60214	+	0.429293i	−0.945689	−	0.325073i	$-0.894611\pi$
$73$	−13.6887	+	3.66788i	−1.60214	+	0.429293i	−0.656454	+	0.754366i	$0.727944\pi$
$74$	1.89593	+	1.09462i	0.220397	+	0.127247i
$75$	4.11893	+	2.83451i	0.475613	+	0.327301i
$76$			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	−0.936419	−	0.350884i	$-0.885881\pi$
$79$	−9.78372	+	5.64863i	−1.10075	+	0.635521i	−0.164335	+	0.986405i	$0.552548\pi$
$80$	6.57675	−	0.602322i	0.735303	−	0.0673417i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−14.3488	−	3.84475i	−1.58456	−	0.424581i
$83$	−4.88941	−	4.88941i	−0.536682	−	0.536682i	0.385871	−	0.922553i	$-0.373901\pi$
$83$	−4.88941	−	4.88941i	−0.536682	−	0.536682i	−0.922553	+	0.385871i	$0.873901\pi$
$84$		0			0
$85$	14.7914	+	2.54621i	1.60435	+	0.276175i
$86$	−0.453791	−	0.785990i	−0.0489336	−	0.0847554i
$87$	0.0789112	+	0.294500i	0.00846017	+	0.0315738i
$88$	0.626709	+	2.33891i	0.0668074	+	0.249329i
$89$	−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
$93$	−7.00662	−	1.87742i	−0.726553	−	0.194679i
$94$	−0.828829	+	1.43557i	−0.0854872	+	0.148068i
$95$	13.3990	−	1.22713i	1.37471	−	0.125901i
$96$	6.95363	−	4.01468i	0.709702	−	0.409746i
$97$	−8.84137	+	8.84137i	−0.897705	+	0.897705i	−0.995233	−	0.0975276i	$-0.968907\pi$
$97$	−8.84137	+	8.84137i	−0.897705	+	0.897705i	0.0975276	+	0.995233i	$0.468907\pi$
$98$		0			0
$99$		−	2.67187i		−	0.268533i
$100$	2.20747	+	11.9506i	0.220747	+	1.19506i
$101$	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	$0.549550\pi$
$102$	13.6470	−	3.65671i	1.35126	−	0.362068i
$103$	−2.54219	+	9.48757i	−0.250489	+	0.934838i	0.720056	+	0.693916i	$0.244116\pi$
$103$	−2.54219	+	9.48757i	−0.250489	+	0.934838i	−0.970545	+	0.240921i	$0.922550\pi$
$104$	−1.57277			−0.154222
$105$		0			0
$106$	−14.8550			−1.44284
$107$	−2.73529	+	10.2082i	−0.264430	+	0.986867i	0.698168	+	0.715934i	$0.253999\pi$
$107$	−2.73529	+	10.2082i	−0.264430	+	0.986867i	−0.962598	+	0.270933i	$0.912668\pi$
$108$	2.34773	−	0.629073i	0.225911	−	0.0605326i
$109$	5.15590	+	2.97676i	0.493846	+	0.285122i	0.726168	−	0.687517i	$-0.241299\pi$
$109$	5.15590	+	2.97676i	0.493846	+	0.285122i	−0.232323	+	0.972639i	$0.574633\pi$
$110$	11.7996	−	4.34909i	1.12505	−	0.414669i
$111$		−	1.04007i		−	0.0987192i
$112$		0			0
$113$	6.99031	−	6.99031i	0.657593	−	0.657593i	−0.297217	−	0.954810i	$-0.596058\pi$
$113$	6.99031	−	6.99031i	0.657593	−	0.657593i	0.954810	+	0.297217i	$0.0960585\pi$
$114$	10.9688	−	6.33286i	1.02733	−	0.593127i
$115$	−0.355376	+	0.427032i	−0.0331390	+	0.0398210i
$116$	−0.370525	+	0.641768i	−0.0344024	+	0.0595866i
$117$	1.67631	+	0.449165i	0.154975	+	0.0415253i
$118$	−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
$122$	−3.01489	−	11.2517i	−0.272955	−	1.01868i
$123$	1.82658	+	6.81689i	0.164697	+	0.614658i
$124$	−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	0.822560	−	0.568678i	$-0.192545\pi$
$127$	2.86110	+	2.86110i	0.253882	+	0.253882i	−0.568678	+	0.822560i	$0.692545\pi$
$128$	6.84079	+	1.83298i	0.604646	+	0.162014i
$129$	−0.215589	+	0.373412i	−0.0189816	+	0.0328771i
$130$	0.744951	+	8.13411i	0.0653365	+	0.713409i
$131$	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
$135$	−0.773310	−	2.09809i	−0.0665559	−	0.180575i
$136$	5.26805	+	3.04151i	0.451732	+	0.260807i
$137$	−10.2717	+	2.75230i	−0.877573	+	0.235145i	−0.669360	−	0.742938i	$-0.733431\pi$
$137$	−10.2717	+	2.75230i	−0.877573	+	0.235145i	−0.208213	+	0.978083i	$0.566765\pi$
$138$	−0.135354	+	0.505150i	−0.0115221	+	0.0430012i
$139$	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
$142$	8.33998	−	31.1252i	0.699875	−	2.61197i
$143$	4.47888	−	1.20011i	0.374543	−	0.100358i
$144$	−2.55782	−	1.47676i	−0.213152	−	0.123063i
$145$	0.619044	+	0.285609i	0.0514088	+	0.0237185i
$146$			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	0.101301	−	0.994856i	$-0.467699\pi$
$149$	12.3716	−	7.14275i	1.01352	−	0.585157i	0.912221	+	0.409699i	$0.134366\pi$
$150$	8.00696	−	6.83026i	0.653765	−	0.557688i
$151$	−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	$0.296941\pi$
$152$	5.26744	+	1.41141i	0.427245	+	0.114480i
$153$	−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
$157$	0.796951	+	2.97426i	0.0636036	+	0.237372i	0.990408	−	0.138172i	$-0.0441226\pi$
$157$	0.796951	+	2.97426i	0.0636036	+	0.237372i	−0.926805	+	0.375544i	$0.877456\pi$
$158$	6.15458	+	22.9692i	0.489632	+	1.82733i
$159$	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
$163$	18.6814	+	5.00566i	1.46324	+	0.392074i	0.900607	−	0.434633i	$-0.143122\pi$
$163$	18.6814	+	5.00566i	1.46324	+	0.392074i	0.562632	+	0.826707i	$0.309789\pi$
$164$	−8.57664	+	14.8552i	−0.669723	+	1.15999i
$165$	−4.59228	−	3.82170i	−0.357509	−	0.297519i
$166$	−12.6047	+	7.27730i	−0.978311	+	0.564828i
$167$	−6.23288	+	6.23288i	−0.482315	+	0.482315i	−0.905870	−	0.423555i	$-0.860782\pi$
$167$	−6.23288	+	6.23288i	−0.482315	+	0.482315i	0.423555	+	0.905870i	$0.360782\pi$
$168$		0			0
$169$		−	9.98824i		−	0.768326i
$170$	13.2350	−	28.6862i	1.01508	−	2.20013i
$171$	−5.21113	−	3.00865i	−0.398505	−	0.230077i
$172$	−1.01229	+	0.271243i	−0.0771866	+	0.0206821i
$173$	2.47775	−	9.24710i	0.188380	−	0.703044i	−0.805501	−	0.592594i	$-0.798104\pi$
$173$	2.47775	−	9.24710i	0.188380	−	0.703044i	0.993882	−	0.110450i	$-0.0352294\pi$
$174$	0.641758			0.0486515
$175$		0			0
$176$	−7.89143			−0.594839
$177$	−2.06754	+	7.71617i	−0.155406	+	0.579983i
$178$	−14.0543	+	3.76583i	−1.05341	+	0.282261i
$179$	−1.12673	−	0.650516i	−0.0842155	−	0.0486218i	0.457301	−	0.889312i	$-0.348816\pi$
$179$	−1.12673	−	0.650516i	−0.0842155	−	0.0486218i	−0.541516	+	0.840690i	$0.682150\pi$
$180$	2.27685	−	4.93496i	0.169706	−	0.367830i
$181$			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
$185$	−1.78762	−	1.48766i	−0.131429	−	0.109375i
$186$	−7.63421	+	13.2228i	−0.559767	+	0.969545i
$187$	−17.3230	−	4.64170i	−1.26679	−	0.339434i
$188$	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	$0.855669\pi$
$192$	−2.84542	−	10.6192i	−0.205350	−	0.766378i
$193$	−2.86520	−	10.6931i	−0.206241	−	0.769703i	−0.989068	−	0.147463i	$-0.952889\pi$
$193$	−2.86520	−	10.6931i	−0.206241	−	0.769703i	0.782826	−	0.622240i	$-0.213777\pi$
$194$	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	0.335790	−	0.941937i	$-0.390997\pi$
$197$	−8.50767	−	8.50767i	−0.606146	−	0.606146i	−0.941937	+	0.335790i	$0.890997\pi$
$198$	−5.43236	−	1.45560i	−0.386061	−	0.103445i
$199$	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	$0.129866\pi$
$200$	4.51713	+	0.358242i	0.319410	+	0.0253316i
$201$	−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
$205$	14.3292	+	6.61108i	1.00079	+	0.461738i
$206$	17.9048	+	10.3374i	1.24749	+	0.720238i
$207$	0.239989	−	0.0643048i	0.0166804	−	0.00446949i
$208$	1.32662	−	4.95101i	0.0919845	−	0.343291i
$209$	−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	$0.702372\pi$
$212$	−4.43960	+	16.5688i	−0.304913	+	1.13795i
$213$	−14.7871	+	3.96220i	−1.01320	+	0.271485i
$214$	19.2649	+	11.1226i	1.31692	+	0.760324i
$215$	0.333435	+	0.904653i	0.0227401	+	0.0616968i
$216$		−	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
$220$	−1.32437	−	14.4608i	−0.0892890	−	0.974946i
$221$	5.82432	−	10.0880i	0.391786	−	0.678593i
$222$	−2.11464	−	0.566615i	−0.141925	−	0.0380287i
$223$	−4.58392	−	4.58392i	−0.306962	−	0.306962i	0.536768	−	0.843730i	$-0.319645\pi$
$223$	−4.58392	−	4.58392i	−0.306962	−	0.306962i	−0.843730	+	0.536768i	$0.819645\pi$
$224$		0			0
$225$	−4.71220	−	1.67187i	−0.314147	−	0.111458i
$226$	−10.4042	−	18.0207i	−0.692080	−	1.19872i
$227$	5.18339	+	19.3447i	0.344034	+	1.28395i	0.893737	+	0.448592i	$0.148074\pi$
$227$	5.18339	+	19.3447i	0.344034	+	1.28395i	−0.549703	+	0.835360i	$0.685259\pi$
$228$	−3.78532	−	14.1270i	−0.250689	−	0.935583i
$229$	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
$233$	6.53706	+	1.75160i	0.428257	+	0.114751i	0.466508	−	0.884517i	$-0.345512\pi$
$233$	6.53706	+	1.75160i	0.428257	+	0.114751i	−0.0382507	+	0.999268i	$0.512179\pi$
$234$	1.82645	−	3.16351i	0.119399	−	0.206805i
$235$	1.12644	−	1.35357i	0.0734807	−	0.0882969i
$236$	−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	$0.175262\pi$
$239$			16.1769i			1.04640i	−0.852210	+	0.523200i	$0.824738\pi$
$240$	−6.19676	+	2.28399i	−0.399999	+	0.147431i
$241$	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	$0.547316\pi$
$242$	7.85026	−	2.10347i	0.504634	−	0.135216i
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−13.4509			−0.861105
$245$		0			0
$246$	14.8550			0.947117
$247$	2.70276	−	10.0868i	0.171972	−	0.641810i
$248$	−6.34985	+	1.70144i	−0.403216	+	0.108041i
$249$	5.98828	+	3.45733i	0.379492	+	0.219100i
$250$	−0.286794	−	23.5316i	−0.0181384	−	1.48827i
$251$			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
$255$	−14.9464	+	1.36884i	−0.935979	+	0.0857203i
$256$	−3.54033	+	6.13203i	−0.221271	+	0.383252i
$257$	−13.7817	−	3.69280i	−0.859679	−	0.230350i	−0.198060	−	0.980190i	$-0.563464\pi$
$257$	−13.7817	−	3.69280i	−0.859679	−	0.230350i	−0.661620	+	0.749840i	$0.730131\pi$
$258$	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
$262$	−5.09245	−	19.0053i	−0.314613	−	1.17415i
$263$	6.66107	+	24.8595i	0.410739	+	1.53290i	0.793219	+	0.608936i	$0.208403\pi$
$263$	6.66107	+	24.8595i	0.410739	+	1.53290i	−0.382480	+	0.923964i	$0.624930\pi$
$264$	−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
$268$	−11.3901	−	3.05197i	−0.695761	−	0.186429i
$269$	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	$0.00987831\pi$
$270$	−4.68706	+	0.429257i	−0.285245	+	0.0261238i
$271$	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
$275$	−13.1371	+	2.42664i	−0.792198	+	0.146332i
$276$	0.522977	+	0.301941i	0.0314795	+	0.0181747i
$277$	2.73971	−	0.734104i	0.164613	−	0.0441080i	−0.175571	−	0.984467i	$-0.556177\pi$
$277$	2.73971	−	0.734104i	0.164613	−	0.0441080i	0.340184	+	0.940359i	$0.389511\pi$
$278$	4.24334	−	15.8364i	0.254499	−	0.949802i
$279$	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	$0.367504\pi$
$282$	0.429034	−	1.60117i	0.0255486	−	0.0953486i
$283$	22.1902	−	5.94585i	1.31907	−	0.353444i	0.470441	−	0.882431i	$-0.344095\pi$
$283$	22.1902	−	5.94585i	1.31907	−	0.353444i	0.848630	+	0.528987i	$0.177428\pi$
$284$	−32.2237	−	18.6044i	−1.91212	−	1.10397i
$285$	−12.6248	+	4.65323i	−0.747831	+	0.275634i
$286$		−	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
$290$	0.917936	−	1.10302i	0.0539031	−	0.0647717i
$291$	6.25179	−	10.8284i	0.366487	−	0.634773i
$292$	33.2711	+	8.91497i	1.94705	+	0.521709i
$293$	−2.41765	−	2.41765i	−0.141240	−	0.141240i	0.632951	−	0.774192i	$-0.281843\pi$
$293$	−2.41765	−	2.41765i	−0.141240	−	0.141240i	−0.774192	+	0.632951i	$0.781843\pi$
$294$		0			0
$295$	10.3049	+	14.5904i	0.599974	+	0.849486i
$296$	−0.471289	−	0.816297i	−0.0273931	−	0.0474463i
$297$	0.691531	+	2.58083i	0.0401267	+	0.149755i
$298$	−7.78253	−	29.0448i	−0.450830	−	1.68252i
$299$	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
$303$	−6.98328	−	1.87116i	−0.401179	−	0.107496i
$304$	−8.88610	+	15.3912i	−0.509653	+	0.882744i
$305$	1.12859	+	12.3230i	0.0646227	+	0.705614i
$306$	−12.2356	+	7.06422i	−0.699462	+	0.403834i
$307$	7.21300	−	7.21300i	0.411667	−	0.411667i	−0.470652	−	0.882319i	$-0.655981\pi$
$307$	7.21300	−	7.21300i	0.411667	−	0.411667i	0.882319	+	0.470652i	$0.155981\pi$
$308$		0			0
$309$		−	9.82225i		−	0.558768i
$310$	11.8072	+	32.0345i	0.670605	+	1.81944i
$311$	−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	$0.760565\pi$
$312$	1.51918	−	0.407062i	0.0860064	−	0.0230453i
$313$	8.08564	−	30.1760i	0.457027	−	1.70565i	−0.225031	−	0.974352i	$-0.572248\pi$
$313$	8.08564	−	30.1760i	0.457027	−	1.70565i	0.682059	−	0.731298i	$-0.261085\pi$
$314$	6.48134			0.365763
$315$		0			0
$316$	27.4586			1.54467
$317$	−4.48613	+	16.7425i	−0.251966	+	0.940351i	0.717787	+	0.696263i	$0.245155\pi$
$317$	−4.48613	+	16.7425i	−0.251966	+	0.940351i	−0.969753	+	0.244088i	$0.921511\pi$
$318$	14.3488	−	3.84475i	0.804640	−	0.215603i
$319$	−0.705486	−	0.407313i	−0.0394996	−	0.0228051i
$320$	−22.3218	−	10.2986i	−1.24783	−	0.575711i
$321$		−	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
$325$	0.686013	−	8.65005i	0.0380532	−	0.479818i
$326$	20.3547	−	35.2553i	1.12734	−	1.95261i
$327$	−5.75066	−	1.54088i	−0.318012	−	0.0852111i
$328$	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	$0.844385\pi$
$332$	4.34983	+	16.2338i	0.238728	+	0.890945i
$333$	0.269190	+	1.00463i	0.0147515	+	0.0550535i
$334$	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	0.397180	−	0.917741i	$-0.369989\pi$
$337$	−9.55621	−	9.55621i	−0.520560	−	0.520560i	−0.917741	+	0.397180i	$0.869989\pi$
$338$	−20.3078	−	5.44145i	−1.10460	−	0.295976i
$339$	−4.94289	+	8.56135i	−0.268461	+	0.464988i
$340$	−28.0403	−	23.3352i	−1.52070	−	1.26553i
$341$	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
$345$	0.232743	−	0.504460i	0.0125305	−	0.0271592i
$346$	−17.4510	−	10.0754i	−0.938174	−	0.541655i
$347$	−8.94713	+	2.39738i	−0.480307	+	0.128698i	−0.490846	−	0.871247i	$-0.663312\pi$
$347$	−8.94713	+	2.39738i	−0.480307	+	0.128698i	0.0105386	+	0.999944i	$0.496645\pi$
$348$	0.191798	−	0.715799i	0.0102814	−	0.0383708i
$349$	−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
$352$	−5.55255	+	20.7224i	−0.295952	+	1.10451i
$353$	1.32582	−	0.355252i	0.0705663	−	0.0189082i	−0.223363	−	0.974735i	$-0.571704\pi$
$353$	1.32582	−	0.355252i	0.0705663	−	0.0189082i	0.293929	+	0.955827i	$0.405037\pi$
$354$	14.5619	+	8.40731i	0.773956	+	0.446844i
$355$	−14.3407	+	31.0827i	−0.761123	+	1.64970i
$356$			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	−0.697795	−	0.716297i	$-0.745836\pi$
$359$	−8.07840	+	4.66406i	−0.426361	+	0.246160i	0.271434	+	0.962457i	$0.412502\pi$
$360$	−1.55764	−	1.29627i	−0.0820949	−	0.0683195i
$361$	−8.60390	+	14.9024i	−0.452837	+	0.784336i
$362$	17.2520	+	4.62265i	0.906744	+	0.242961i
$363$	−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
$367$	4.75960	+	17.7631i	0.248449	+	0.927225i	0.971618	+	0.236554i	$0.0760180\pi$
$367$	4.75960	+	17.7631i	0.248449	+	0.927225i	−0.723169	+	0.690671i	$0.757315\pi$
$368$	−0.189926	−	0.708812i	−0.00990056	−	0.0369494i
$369$	−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
$373$	−28.2436	−	7.56784i	−1.46240	−	0.391848i	−0.562080	−	0.827083i	$-0.689999\pi$
$373$	−28.2436	−	7.56784i	−1.46240	−	0.391848i	−0.900317	+	0.435235i	$0.856665\pi$
$374$	−18.8747	+	32.6919i	−0.975986	+	1.69046i
$375$	−9.61361	+	5.70775i	−0.496445	+	0.294747i
$376$	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	$0.191213\pi$
$379$			22.0077i			1.13046i	−0.824933	+	0.565230i	$0.808787\pi$
$380$	−29.6951	−	13.7005i	−1.52333	−	0.702820i
$381$	−3.50412	−	2.02311i	−0.179522	−	0.103647i
$382$	−3.94009	+	1.05574i	−0.201592	+	0.0540165i
$383$	−0.142890	+	0.533272i	−0.00730133	+	0.0272489i	−0.969480	−	0.245169i	$-0.921157\pi$
$383$	−0.142890	+	0.533272i	−0.00730133	+	0.0272489i	0.962179	+	0.272418i	$0.0878233\pi$
$384$	−7.08211			−0.361407
$385$		0			0
$386$	−23.3017			−1.18602
$387$	0.111597	−	0.416487i	0.00567281	−	0.0211712i
$388$	29.3551	−	7.86567i	1.49028	−	0.399319i
$389$	−22.4560	−	12.9650i	−1.13857	−	0.657352i	−0.192491	−	0.981299i	$-0.561657\pi$
$389$	−22.4560	−	12.9650i	−1.13857	−	0.657352i	−0.946075	+	0.323947i	$0.894990\pi$
$390$	−2.82483	−	7.66414i	−0.143041	−	0.388089i
$391$		−	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
$395$	−2.30389	−	25.1562i	−0.115921	−	1.26574i
$396$	−3.24706	+	5.62407i	−0.163171	+	0.282620i
$397$	23.4452	+	6.28213i	1.17668	+	0.315291i	0.793609	−	0.608427i	$-0.208199\pi$
$397$	23.4452	+	6.28213i	1.17668	+	0.315291i	0.383072	+	0.923718i	$0.374866\pi$
$398$	−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	$0.728595\pi$
$402$	2.64304	+	9.86397i	0.131823	+	0.491970i
$403$	3.25815	+	12.1596i	0.162300	+	0.605712i
$404$	−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
$408$	−5.87575	−	1.57440i	−0.290893	−	0.0779445i
$409$	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	$0.145854\pi$
$410$	21.2477	−	25.5320i	1.04935	−	1.26093i
$411$	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
$415$	14.5076	−	5.34718i	0.712151	−	0.262483i
$416$	−12.0676	−	6.96724i	−0.591663	−	0.341597i
$417$	−7.52362	+	2.01595i	−0.368433	+	0.0987214i
$418$	−8.75874	+	32.6881i	−0.428404	+	1.59883i
$419$	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	$0.724927\pi$
$422$	−9.39797	+	35.0737i	−0.457486	+	1.70736i
$423$	−0.760694	+	0.203827i	−0.0369862	+	0.00991042i
$424$	5.53895	+	3.19791i	0.268995	+	0.155304i
$425$	−19.0258	+	27.6471i	−0.922887	+	1.34108i
$426$			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
$430$	2.02096	−	0.185087i	0.0974593	−	0.00892567i
$431$	−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	$0.985516\pi$
$432$	2.85288	+	0.764428i	0.137259	+	0.0367785i
$433$	13.4723	+	13.4723i	0.647438	+	0.647438i	0.952373	−	0.304935i	$-0.0986349\pi$
$433$	13.4723	+	13.4723i	0.647438	+	0.647438i	−0.304935	+	0.952373i	$0.598635\pi$
$434$		0			0
$435$	−0.671871	−	0.115657i	−0.0322138	−	0.00554532i
$436$	−7.23517	−	12.5317i	−0.346502	−	0.600159i
$437$	−0.386941	−	1.44408i	−0.0185099	−	0.0690799i
$438$	−7.72048	−	28.8132i	−0.368899	−	1.37675i
$439$	−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
$443$	21.3579	+	5.72284i	1.01475	+	0.271900i	0.727611	−	0.685990i	$-0.240631\pi$
$443$	21.3579	+	5.72284i	1.01475	+	0.271900i	0.287135	+	0.957890i	$0.407297\pi$
$444$	−1.26397	+	2.18927i	−0.0599855	+	0.103898i
$445$	15.3924	−	1.40969i	0.729671	−	0.0668259i
$446$	−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	$-0.947033\pi$
$449$		−	7.01947i		−	0.331269i	0.986187	−	0.165635i	$-0.0529673\pi$
$450$	−5.96633	+	8.66987i	−0.281255	+	0.408702i
$451$	−16.3301	−	9.42818i	−0.768954	−	0.443956i
$452$	−23.2092	+	6.21888i	−1.09167	+	0.292512i
$453$	2.53123	−	9.44666i	0.118927	−	0.443843i
$454$	42.1548			1.97842
$455$		0			0
$456$	−5.45325			−0.255372
$457$	4.10385	−	15.3158i	0.191970	−	0.716442i	−0.801060	−	0.598584i	$-0.795730\pi$
$457$	4.10385	−	15.3158i	0.191970	−	0.716442i	0.993030	−	0.117858i	$-0.0376029\pi$
$458$	58.8209	−	15.7610i	2.74852	−	0.736464i
$459$	5.81294	+	3.35610i	0.271325	+	0.156649i
$460$	1.26700	−	0.466988i	0.0590742	−	0.0217734i
$461$		−	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	−0.505106	−	0.863057i	$-0.668547\pi$
$463$	7.70220	−	7.70220i	0.357951	−	0.357951i	0.863057	+	0.505106i	$0.168547\pi$
$464$	−0.779853	+	0.450249i	−0.0362038	+	0.0209023i
$465$	10.3754	−	12.4675i	0.481149	−	0.578165i
$466$	7.12259	−	12.3367i	0.329948	−	0.571486i
$467$	−2.47197	−	0.662362i	−0.114389	−	0.0306504i	0.201170	−	0.979556i	$-0.435525\pi$
$467$	−2.47197	−	0.662362i	−0.114389	−	0.0306504i	−0.315559	+	0.948906i	$0.602192\pi$
$468$	−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
$472$	1.87374	+	6.99289i	0.0862458	+	0.321874i
$473$	−0.298173	−	1.11280i	−0.0137100	−	0.0511665i
$474$	−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
$478$	32.8904	+	8.81295i	1.50437	+	0.403095i
$479$	−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	$0.196486\pi$
$480$	1.63746	+	17.8794i	0.0747393	+	0.816078i
$481$	−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
$485$	−9.66915	−	26.2337i	−0.439053	−	1.19121i
$486$	1.82289	+	1.05244i	0.0826878	+	0.0477398i
$487$	14.0767	−	3.77185i	0.637878	−	0.170919i	0.0746360	−	0.997211i	$-0.476221\pi$
$487$	14.0767	−	3.77185i	0.637878	−	0.170919i	0.563242	+	0.826292i	$0.309554\pi$
$488$	−1.29807	+	4.84445i	−0.0587607	+	0.219298i
$489$	−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	$0.561868\pi$
$492$	4.43960	−	16.5688i	0.200153	−	0.746979i
$493$	−1.97675	+	0.529668i	−0.0890282	+	0.0238550i
$494$	−19.0358	−	10.9903i	−0.856460	−	0.494477i
$495$	5.42494	+	2.50291i	0.243833	+	0.112497i
$496$		−	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	0.0370477	−	0.999313i	$-0.488205\pi$
$499$	20.5736	−	11.8782i	0.921002	−	0.531741i	0.883955	+	0.467572i	$0.154871\pi$
$500$	−26.3322	−	6.71285i	−1.17761	−	0.300208i
$501$	4.40731	−	7.63369i	0.196904	−	0.341048i
$502$	14.1313	+	3.78647i	0.630710	+	0.168998i
$503$	−17.9504	−	17.9504i	−0.800367	−	0.800367i	0.182786	−	0.983153i	$-0.441489\pi$
$503$	−17.9504	−	17.9504i	−0.800367	−	0.800367i	−0.983153	+	0.182786i	$0.941489\pi$
$504$		0			0
$505$	−13.2046	+	9.32611i	−0.587596	+	0.415007i
$506$	−0.698653	−	1.21010i	−0.0310589	−	0.0537956i
$507$	2.58515	+	9.64790i	0.114810	+	0.428478i
$508$	−2.54536	−	9.49942i	−0.112932	−	0.421469i
$509$	−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
$513$	5.81226	+	1.55739i	0.256617	+	0.0687604i
$514$	−15.0161	+	26.0087i	−0.662333	+	1.14720i
$515$	−16.8820	−	14.0492i	−0.743910	−	0.619083i
$516$	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
$520$	1.47331	−	3.19333i	0.0646089	−	0.140037i
$521$	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	$0.611411\pi$
$522$	−0.619890	+	0.166099i	−0.0271319	+	0.00726996i
$523$	−0.450757	+	1.68225i	−0.0197102	+	0.0735595i	−0.975080	−	0.221852i	$-0.928790\pi$
$523$	−0.450757	+	1.68225i	−0.0197102	+	0.0735595i	0.955370	+	0.295411i	$0.0954566\pi$
$524$	−22.7199			−0.992524
$525$		0			0
$526$	54.1722			2.36202
$527$	12.6016	−	47.0299i	0.548935	−	2.04865i
$528$	7.62253	−	2.04245i	0.331728	−	0.0888863i
$529$	−19.8651	−	11.4691i	−0.863701	−	0.498658i
$530$	13.9156	−	30.1613i	0.604454	−	1.31012i
$531$		−	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
$535$	−18.1644	−	15.1164i	−0.785314	−	0.653539i
$536$	−2.19838	+	3.80771i	−0.0949557	+	0.164468i
$537$	1.25670	+	0.336732i	0.0542306	+	0.0145310i
$538$	−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	$-0.437238\pi$
$542$	−7.26843	−	27.1261i	−0.312206	−	1.16517i
$543$	−2.19615	−	8.19615i	−0.0942459	−	0.351731i
$544$	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	0.784333	−	0.620340i	$-0.213005\pi$
$547$	3.83548	+	3.83548i	0.163993	+	0.163993i	−0.620340	+	0.784333i	$0.713005\pi$
$548$	24.9660	+	6.68961i	1.06649	+	0.285766i
$549$	2.76704	−	4.79266i	0.118095	−	0.204546i
$550$	−2.22314	+	28.0319i	−0.0947950	+	1.19529i
$551$	−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
$555$	2.11175	+	0.974300i	0.0896387	+	0.0413567i
$556$	−16.3953	−	9.46581i	−0.695314	−	0.401440i
$557$	22.2863	−	5.97158i	0.944299	−	0.253024i	0.246358	−	0.969179i	$-0.420766\pi$
$557$	22.2863	−	5.97158i	0.944299	−	0.253024i	0.697941	+	0.716155i	$0.254100\pi$
$558$	3.95176	−	14.7482i	0.167291	−	0.624339i
$559$	0.748285			0.0316491
$560$		0			0
$561$	17.9341			0.757180
$562$	7.38493	−	27.5609i	0.311514	−	1.16259i
$563$	−32.4459	+	8.69386i	−1.36743	+	0.366402i	−0.866540	−	0.499107i	$-0.833661\pi$
$563$	−32.4459	+	8.69386i	−1.36743	+	0.366402i	−0.500892	+	0.865510i	$0.666995\pi$
$564$	−1.65768	−	0.957064i	−0.0698011	−	0.0402997i
$565$	7.64478	+	20.7413i	0.321618	+	0.872593i
$566$		−	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	−0.505034	−	0.863099i	$-0.668520\pi$
$569$	−0.240575	+	0.138896i	−0.0100854	+	0.00582283i	0.494949	+	0.868922i	$0.335187\pi$
$570$	2.58297	+	28.2034i	0.108189	+	1.18131i
$571$	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	$0.145902\pi$
$572$	−10.8861	−	2.91693i	−0.455173	−	0.121963i
$573$	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
$577$	10.8309	+	40.4214i	0.450896	+	1.68277i	0.699882	+	0.714259i	$0.253236\pi$
$577$	10.8309	+	40.4214i	0.450896	+	1.68277i	−0.248986	+	0.968507i	$0.580097\pi$
$578$	15.2832	+	57.0377i	0.635698	+	2.37246i
$579$	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
$583$	−18.2139	−	4.88039i	−0.754341	−	0.202125i
$584$	6.42160	−	11.1225i	0.265728	−	0.460254i
$585$	−2.48228	+	2.98279i	−0.102630	+	0.123323i
$586$	−6.23257	+	3.59838i	−0.257465	+	0.148648i
$587$	26.6462	−	26.6462i	1.09981	−	1.09981i	0.105375	−	0.994433i	$-0.466396\pi$
$587$	26.6462	−	26.6462i	1.09981	−	1.09981i	0.994433	−	0.105375i	$-0.0336041\pi$
$588$		0			0
$589$		−	43.6482i		−	1.79849i
$590$	35.2786	−	13.0029i	1.45240	−	0.535322i
$591$	10.4197	+	6.01583i	0.428610	+	0.247458i
$592$	2.96720	−	0.795059i	0.121951	−	0.0326767i
$593$	5.55952	−	20.7484i	0.228302	−	0.852036i	−0.752752	−	0.658304i	$-0.771274\pi$
$593$	5.55952	−	20.7484i	0.228302	−	0.852036i	0.981055	−	0.193732i	$-0.0620591\pi$
$594$	5.62399			0.230755
$595$		0			0
$596$	−34.7217			−1.42225
$597$	−0.842351	+	3.14370i	−0.0344751	+	0.128663i
$598$	0.876657	−	0.234900i	0.0358492	−	0.00960576i
$599$	19.2930	+	11.1388i	0.788290	+	0.455119i	0.839360	−	0.543576i	$-0.182930\pi$
$599$	19.2930	+	11.1388i	0.788290	+	0.455119i	−0.0510705	+	0.998695i	$0.516263\pi$
$600$	−4.45594	+	0.823085i	−0.181913	+	0.0336023i
$601$			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
$605$	−8.59771	+	0.787409i	−0.349547	+	0.0320127i
$606$	−7.60877	+	13.1788i	−0.309085	+	0.535351i
$607$	0.786867	+	0.210840i	0.0319380	+	0.00855775i	0.274753	−	0.961515i	$-0.411404\pi$
$607$	0.786867	+	0.210840i	0.0319380	+	0.00855775i	−0.242815	+	0.970073i	$0.578071\pi$
$608$	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
$612$	4.22247	+	15.7585i	0.170683	+	0.636998i
$613$	−6.02876	−	22.4996i	−0.243499	−	0.908752i	−0.974132	−	0.225981i	$-0.927441\pi$
$613$	−6.02876	−	22.4996i	−0.243499	−	0.908752i	0.730632	−	0.682771i	$-0.239225\pi$
$614$	−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	0.628692	−	0.777654i	$-0.283590\pi$
$617$	−3.70013	−	3.70013i	−0.148962	−	0.148962i	−0.777654	+	0.628692i	$0.783590\pi$
$618$	−19.9703	−	5.35101i	−0.803322	−	0.215249i
$619$	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	$-0.129317\pi$
$620$	39.2592	−	3.59550i	1.57669	−	0.144399i
$621$	−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
$625$	−3.94059	+	24.6875i	−0.157624	+	0.987499i
$626$	−56.9479	−	32.8789i	−2.27610	−	1.31410i
$627$	15.5296	−	4.16114i	0.620193	−	0.166180i
$628$	1.93703	−	7.22910i	0.0772960	−	0.288473i
$629$	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	$0.736379\pi$
$632$	2.64987	−	9.88943i	0.105406	−	0.393381i
$633$	16.6630	−	4.46483i	0.662294	−	0.177461i
$634$	31.5962	+	18.2421i	1.25485	+	0.724486i
$635$	−8.48933	+	3.12898i	−0.336889	+	0.124170i
$636$		−	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
$640$	−10.1299	+	12.1724i	−0.400418	+	0.481156i
$641$	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	$0.0502359\pi$
$642$	−21.4872	−	5.75748i	−0.848032	−	0.227229i
$643$	32.1062	+	32.1062i	1.26614	+	1.26614i	0.948063	+	0.318082i	$0.103039\pi$
$643$	32.1062	+	32.1062i	1.26614	+	1.26614i	0.318082	+	0.948063i	$0.396961\pi$
$644$		0			0
$645$	−0.556214	−	0.787528i	−0.0219009	−	0.0310089i
$646$	42.5074	+	73.6251i	1.67243	+	2.89674i
$647$	4.73187	+	17.6596i	0.186029	+	0.694270i	0.994408	+	0.105607i	$0.0336787\pi$
$647$	4.73187	+	17.6596i	0.186029	+	0.694270i	−0.808379	+	0.588663i	$0.799655\pi$
$648$	0.234558	+	0.875383i	0.00921432	+	0.0343883i
$649$	−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
$653$	12.8398	+	3.44041i	0.502459	+	0.134634i	0.501141	−	0.865366i	$-0.332914\pi$
$653$	12.8398	+	3.44041i	0.502459	+	0.134634i	0.00131826	+	0.999999i	$0.499580\pi$
$654$	−6.26575	+	10.8526i	−0.245010	+	0.424370i
$655$	1.90630	+	20.8148i	0.0744852	+	0.813303i
$656$	−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	$-0.943042\pi$
$659$		−	9.13808i		−	0.355969i	0.984033	−	0.177985i	$-0.0569577\pi$
$660$	5.02197	+	13.6253i	0.195480	+	0.530363i
$661$	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	$0.479789\pi$
$662$	−2.56805	+	0.688108i	−0.0998102	+	0.0267441i
$663$	−3.01489	+	11.2517i	−0.117089	+	0.436980i
$664$	6.26651			0.243188
$665$		0			0
$666$	2.18923			0.0848310
$667$	0.0196059	−	0.0731700i	0.000759142	−	0.00283316i
$668$	20.6944	−	5.54504i	0.800690	−	0.214544i
$669$	5.61413	+	3.24132i	0.217055	+	0.125317i
$670$	20.7342	+	9.56616i	0.801031	+	0.369573i
$671$		−	14.7864i		−	0.570821i
$672$		0			0
$673$	26.8815	−	26.8815i	1.03621	−	1.03621i	0.0368867	−	0.999319i	$-0.488256\pi$
$673$	26.8815	−	26.8815i	1.03621	−	1.03621i	0.999319	−	0.0368867i	$-0.0117441\pi$
$674$	−24.6354	+	14.2233i	−0.948922	+	0.547860i
$675$	4.98435	+	0.395296i	0.191848	+	0.0152150i
$676$	−12.1385	+	21.0245i	−0.466864	+	0.808633i
$677$	1.63505	+	0.438111i	0.0628402	+	0.0168380i	0.290102	−	0.956996i	$-0.406311\pi$
$677$	1.63505	+	0.438111i	0.0628402	+	0.0168380i	−0.227262	+	0.973834i	$0.572977\pi$
$678$	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
$682$	−10.5586	−	39.4052i	−0.404309	−	1.50890i
$683$	0.884144	+	3.29967i	0.0338308	+	0.126258i	0.980776	−	0.195137i	$-0.0625150\pi$
$683$	0.884144	+	3.29967i	0.0338308	+	0.126258i	−0.946945	+	0.321395i	$0.895848\pi$
$684$	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
$688$	−1.23010	−	0.329605i	−0.0468972	−	0.0125661i
$689$	6.12382	−	10.6068i	0.233299	−	0.404086i
$690$	−0.898855	−	0.748027i	−0.0342188	−	0.0284769i
$691$	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
$695$	−7.29647	+	15.8147i	−0.276771	+	0.599887i
$696$	−0.239292	−	0.138155i	−0.00907032	−	0.00523675i
$697$	−45.7563	+	12.2604i	−1.73314	+	0.464395i
$698$	−1.50981	+	5.63470i	−0.0571472	+	0.213276i
$699$	−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	$0.416158\pi$
$702$	−0.945442	+	3.52844i	−0.0356834	+	0.133172i
$703$	6.04516	−	1.61980i	0.227998	−	0.0610918i
$704$	25.4388	+	14.6871i	0.958760	+	0.553540i
$705$	−0.737727	+	1.59899i	−0.0277844	+	0.0602214i
$706$		−	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	−0.0418795	−	0.999123i	$-0.513335\pi$
$709$	21.3668	−	12.3361i	0.802446	−	0.463293i	0.844326	+	0.535830i	$0.180001\pi$
$710$	55.3837	+	46.0903i	2.07851	+	1.72974i
$711$	−5.64863	+	9.78372i	−0.211840	+	0.366918i
$712$	6.05110	+	1.62139i	0.226775	+	0.0607641i
$713$	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
$717$	−4.18690	−	15.6257i	−0.156363	−	0.583553i
$718$	5.08182	+	18.9656i	0.189652	+	0.707791i
$719$	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
$723$	−10.9833	−	2.94297i	−0.408473	−	0.109450i
$724$	10.3120	−	17.8608i	0.383241	−	0.663793i
$725$	−1.15979	+	0.989351i	−0.0430737	+	0.0367436i
$726$	−7.03835	+	4.06359i	−0.261218	+	0.150814i
$727$	−29.8488	+	29.8488i	−1.10703	+	1.10703i	−0.113491	+	0.993539i	$0.536203\pi$
$727$	−29.8488	+	29.8488i	−1.10703	+	1.10703i	−0.993539	+	0.113491i	$0.963797\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$	−60.5657	−	27.9433i	−2.24164	−	1.03423i
$731$	−2.50641	−	1.44708i	−0.0927031	−	0.0535222i
$732$	12.9926	−	3.48135i	0.480219	−	0.128674i
$733$	−1.41545	+	5.28252i	−0.0522807	+	0.195114i	−0.987127	−	0.159938i	$-0.948870\pi$
$733$	−1.41545	+	5.28252i	−0.0522807	+	0.195114i	0.934846	+	0.355053i	$0.115537\pi$
$734$	38.7082			1.42875
$735$		0			0
$736$	−1.99493			−0.0735342
$737$	3.35499	−	12.5210i	0.123583	−	0.461216i
$738$	−14.3488	+	3.84475i	−0.528186	+	0.141527i
$739$	10.3694	+	5.98677i	0.381444	+	0.220227i	0.678446	−	0.734650i	$-0.262654\pi$
$739$	10.3694	+	5.98677i	0.381444	+	0.220227i	−0.297002	+	0.954877i	$0.595987\pi$
$740$	1.95489	+	5.30387i	0.0718630	+	0.194974i
$741$			10.4427i			0.383621i
$742$		0			0
$743$	−12.0406	+	12.0406i	−0.441728	+	0.441728i	−0.892593	−	0.450864i	$-0.851116\pi$
$743$	−12.0406	+	12.0406i	−0.441728	+	0.441728i	0.450864	+	0.892593i	$0.351116\pi$
$744$	5.69312	−	3.28692i	0.208720	−	0.120504i
$745$	2.91330	+	31.8102i	0.106735	+	1.16544i
$746$	−30.7733	+	53.3010i	−1.12669	+	1.95149i
$747$	−6.67906	−	1.78965i	−0.244374	−	0.0654798i
$748$	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	$0.688337\pi$
$752$	0.602008	+	2.24673i	0.0219530	+	0.0819296i
$753$	−1.79889	−	6.71356i	−0.0655553	−	0.244656i
$754$	−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	0.997768	+	0.0667825i	$0.0212733\pi$
$757$	29.2896	+	29.2896i	1.06455	+	1.06455i	0.0667825	+	0.997768i	$0.478727\pi$
$758$	44.7453	+	11.9895i	1.62522	+	0.435477i
$759$	−0.331920	+	0.574902i	−0.0120479	+	0.0208676i
$760$	−7.80004	+	9.37279i	−0.282937	+	0.339987i
$761$	−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
$765$	14.0828	−	5.19061i	0.509165	−	0.187667i
$766$	1.00639	+	0.581037i	0.0363622	+	0.0209937i
$767$	13.3910	−	3.58810i	0.483520	−	0.129559i
$768$	1.83261	−	6.83939i	0.0661286	−	0.246795i
$769$	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
$772$	−6.96401	+	25.9900i	−0.250640	+	0.935401i
$773$	−24.3102	+	6.51389i	−0.874376	+	0.234288i	−0.667979	−	0.744180i	$-0.732840\pi$
$773$	−24.3102	+	6.51389i	−0.874376	+	0.234288i	−0.206397	+	0.978468i	$0.566174\pi$
$774$	−0.785990	−	0.453791i	−0.0282518	−	0.0163112i
$775$	−6.58802	−	35.6656i	−0.236649	−	1.28115i
$776$		−	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
$780$	−9.39261	+	0.860208i	−0.336309	+	0.0308004i
$781$	20.4515	−	35.4230i	0.731812	−	1.26754i
$782$	−3.39067	−	0.908526i	−0.121250	−	0.0324888i
$783$	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
$787$	−5.88096	−	21.9481i	−0.209634	−	0.782364i	−0.987987	−	0.154537i	$-0.950611\pi$
$787$	−5.88096	−	21.9481i	−0.209634	−	0.782364i	0.778353	−	0.627827i	$-0.216055\pi$
$788$	7.56880	+	28.2471i	0.269627	+	1.00626i
$789$	−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
$793$	9.27683	+	2.48572i	0.329430	+	0.0882705i
$794$	25.5452	−	44.2456i	0.906565	−	1.57022i
$795$	−15.7150	+	1.43923i	−0.557353	+	0.0510444i
$796$	−6.85066	+	3.95523i	−0.242815	+	0.140189i
$797$	−25.5337	+	25.5337i	−0.904451	+	0.904451i	−0.995817	−	0.0913664i	$-0.970877\pi$
$797$	−25.5337	+	25.5337i	−0.904451	+	0.904451i	0.0913664	+	0.995817i	$0.470877\pi$
$798$		0			0
$799$			5.28605i			0.187007i
$800$	33.0723	+	22.7593i	1.16928	+	0.804663i
$801$	−5.98641	−	3.45626i	−0.211520	−	0.122121i
$802$	26.3127	−	7.05048i	0.929135	−	0.248961i
$803$	−9.80010	+	36.5745i	−0.345838	+	1.29069i
$804$	11.7919			0.415868
$805$		0			0
$806$	26.4974			0.933332
$807$	−4.01477	+	14.9833i	−0.141326	+	0.527438i
$808$	−6.32869	+	1.69577i	−0.222642	+	0.0596569i
$809$	−23.8507	−	13.7702i	−0.838546	−	0.484135i	0.0182236	−	0.999834i	$-0.494199\pi$
$809$	−23.8507	−	13.7702i	−0.838546	−	0.484135i	−0.856770	+	0.515699i	$0.827532\pi$
$810$	4.41625	−	1.62773i	0.155171	−	0.0571926i
$811$		−	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
$815$	−27.6635	+	33.2414i	−0.969009	+	1.16439i
$816$	9.91232	−	17.1686i	0.347000	−	0.601022i
$817$	−2.50612	−	0.671513i	−0.0876781	−	0.0234933i
$818$	−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	$-0.501334\pi$
$822$	−5.79328	−	21.6208i	−0.202064	−	0.754113i
$823$	−2.23428	−	8.33846i	−0.0778822	−	0.290660i	0.915989	−	0.401203i	$-0.131408\pi$
$823$	−2.23428	−	8.33846i	−0.0778822	−	0.290660i	−0.993871	+	0.110543i	$0.964741\pi$
$824$	−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	0.615447	−	0.788178i	$-0.288976\pi$
$827$	−4.96734	−	4.96734i	−0.172731	−	0.172731i	−0.788178	+	0.615447i	$0.788976\pi$
$828$	−0.583305	−	0.156296i	−0.0202713	−	0.00543167i
$829$	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	$0.00281633\pi$
$830$	−2.96817	−	32.4094i	−0.103027	−	1.12495i
$831$	−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
$835$	−6.81644	−	18.4939i	−0.235892	−	0.640008i
$836$	33.8417	+	19.5385i	1.17044	+	0.675754i
$837$	−7.00662	+	1.87742i	−0.242184	+	0.0648931i
$838$	5.46430	−	20.3930i	0.188761	−	0.704466i
$839$	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
$842$	−14.5152	+	54.1716i	−0.500228	+	1.86688i
$843$	−13.0938	+	3.50847i	−0.450974	+	0.120838i
$844$	36.3115	+	20.9645i	1.24989	+	0.721627i
$845$	20.2800	+	9.35662i	0.697654	+	0.321877i
$846$			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
$850$	45.8461	+	53.7443i	1.57251	+	1.84342i
$851$	−0.129205	+	0.223790i	−0.00442910	+	0.00767143i
$852$	35.9408	+	9.63032i	1.23131	+	0.329929i
$853$	−15.4954	−	15.4954i	−0.530553	−	0.530553i	0.390184	−	0.920737i	$-0.372411\pi$
$853$	−15.4954	−	15.4954i	−0.530553	−	0.530553i	−0.920737	+	0.390184i	$0.872411\pi$
$854$		0			0
$855$	10.9903	−	7.76222i	0.375861	−	0.265462i
$856$	−4.78885	−	8.29453i	−0.163680	−	0.283501i
$857$	−6.52792	−	24.3625i	−0.222989	−	0.832208i	−0.983200	−	0.182531i	$-0.941571\pi$
$857$	−6.52792	−	24.3625i	−0.222989	−	0.832208i	0.760211	−	0.649677i	$-0.225096\pi$
$858$	2.52610	+	9.42753i	0.0862396	+	0.321851i
$859$	−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
$863$	−4.02135	−	1.07752i	−0.136888	−	0.0366791i	0.189724	−	0.981837i	$-0.439241\pi$
$863$	−4.02135	−	1.07752i	−0.136888	−	0.0366791i	−0.326613	+	0.945158i	$0.605907\pi$
$864$	4.01468	−	6.95363i	0.136582	−	0.236567i
$865$	16.4541	+	13.6931i	0.559458	+	0.465581i
$866$	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
$870$	−0.601175	+	1.30302i	−0.0203817	+	0.0441764i
$871$	7.29154	+	4.20978i	0.247065	+	0.142643i
$872$	−5.21161	+	1.39645i	−0.176487	+	0.0472897i
$873$	−3.23617	+	12.0775i	−0.109528	+	0.408763i
$874$	−3.14686			−0.106444
$875$		0			0
$876$	−34.4448			−1.16378
$877$	−3.11025	+	11.6076i	−0.105026	+	0.391961i	−0.998348	−	0.0574555i	$-0.981701\pi$
$877$	−3.11025	+	11.6076i	−0.105026	+	0.391961i	0.893323	+	0.449416i	$0.148368\pi$
$878$	−52.2096	+	13.9895i	−1.76199	+	0.472124i
$879$	2.96100	+	1.70953i	0.0998721	+	0.0576612i
$880$	7.39240	−	16.0227i	0.249198	−	0.540124i
$881$			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	−0.158559	−	0.987350i	$-0.550685\pi$
$883$	24.6278	−	24.6278i	0.828791	−	0.828791i	0.987350	+	0.158559i	$0.0506848\pi$
$884$	−24.5194	+	14.1563i	−0.824678	+	0.476128i
$885$	−13.7300	−	11.4261i	−0.461530	−	0.384085i
$886$	23.2710	−	40.3065i	0.781803	−	1.35412i
$887$	−1.00060	−	0.268110i	−0.0335969	−	0.00900226i	0.241981	−	0.970281i	$-0.422203\pi$
$887$	−1.00060	−	0.268110i	−0.0335969	−	0.00900226i	−0.275578	+	0.961279i	$0.588869\pi$
$888$	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
$892$	4.07805	+	15.2195i	0.136543	+	0.509587i
$893$	1.22649	+	4.57732i	0.0410429	+	0.153174i
$894$	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
$898$	−14.2717	−	3.82410i	−0.476254	−	0.127612i
$899$	1.10580	−	1.91530i	0.0368806	−	0.0638790i
$900$	7.88702	+	9.24578i	0.262901	+	0.308193i
$901$	−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
$905$	−17.2284	−	7.94870i	−0.572692	−	0.264224i
$906$	−17.8276	−	10.2928i	−0.592284	−	0.341955i
$907$	31.2469	−	8.37259i	1.03754	−	0.278007i	0.300445	−	0.953799i	$-0.402865\pi$
$907$	31.2469	−	8.37259i	1.03754	−	0.278007i	0.737092	+	0.675792i	$0.236198\pi$
$908$	12.5985	−	47.0183i	0.418096	−	1.56036i
$909$	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	$0.365316\pi$
$912$	4.59978	−	17.1666i	0.152314	−	0.568444i
$913$	−17.8456	+	4.78171i	−0.590602	+	0.158251i
$914$	−28.9038	−	16.6876i	−0.956053	−	0.551977i
$915$	−4.27956	−	11.6110i	−0.141478	−	0.383849i
$916$		−	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	−0.276911	−	0.960896i	$-0.589311\pi$
$919$	12.6351	−	7.29488i	0.416794	−	0.240636i	0.693705	+	0.720260i	$0.255977\pi$
$920$	−0.0459188	−	0.501387i	−0.00151390	−	0.0165302i
$921$	−5.10036	+	8.83408i	−0.168063	+	0.291093i
$922$	−60.9634	−	16.3351i	−2.00772	−	0.537968i
$923$	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
$927$	2.54219	+	9.48757i	0.0834963	+	0.311613i
$928$	0.633606	+	2.36465i	0.0207991	+	0.0776234i
$929$	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
$933$	9.90476	+	2.65397i	0.324267	+	0.0868871i
$934$	−2.69338	+	4.66507i	−0.0881301	+	0.152646i
$935$	25.6520	−	30.8243i	0.838911	−	1.00806i
$936$	−1.36206	+	0.786383i	−0.0445202	+	0.0257037i
$937$	28.3540	−	28.3540i	0.926286	−	0.926286i	−0.0711778	−	0.997464i	$-0.522676\pi$
$937$	28.3540	−	28.3540i	0.926286	−	0.926286i	0.997464	+	0.0711778i	$0.0226758\pi$
$938$		0			0
$939$			31.2405i			1.01950i
$940$	−4.01602	+	1.48021i	−0.130988	+	0.0482793i
$941$	−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	$0.667222\pi$
$942$	−6.26049	+	1.67749i	−0.203978	+	0.0546557i
$943$	0.453822	−	1.69369i	0.0147785	−	0.0551541i
$944$	−23.5938			−0.767914
$945$		0			0
$946$	−2.42494			−0.0788417
$947$	6.57640	−	24.5435i	0.213704	−	0.797556i	−0.772914	−	0.634511i	$-0.781202\pi$
$947$	6.57640	−	24.5435i	0.213704	−	0.797556i	0.986619	−	0.163045i	$-0.0521316\pi$
$948$	−26.5230	+	7.10681i	−0.861426	+	0.230818i
$949$	−21.2990	−	12.2970i	−0.691395	−	0.399177i
$950$	52.1692	+	35.9011i	1.69259	+	1.16479i
$951$		−	17.3331i		−	0.562064i
$952$		0			0
$953$	31.8008	−	31.8008i	1.03013	−	1.03013i	0.0305973	−	0.999532i	$-0.490259\pi$
$953$	31.8008	−	31.8008i	1.03013	−	1.03013i	0.999532	−	0.0305973i	$-0.00974093\pi$
$954$	−12.8648	+	7.42748i	−0.416512	+	0.240473i
$955$	4.31523	−	0.395204i	0.139638	−	0.0127885i
$956$	19.6594	−	34.0512i	0.635832	−	1.10129i
$957$	0.786867	+	0.210840i	0.0254358	+	0.00681550i
$958$	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
$962$	0.983327	+	3.66983i	0.0317037	+	0.118320i
$963$	2.73529	+	10.2082i	0.0881434	+	0.328956i
$964$	−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	0.710491	−	0.703706i	$-0.248473\pi$
$967$	0.210995	+	0.210995i	0.00678513	+	0.00678513i	−0.703706	+	0.710491i	$0.748473\pi$
$968$	−3.37995	−	0.905654i	−0.108636	−	0.0291088i
$969$	20.1946	−	34.9781i	0.648745	−	1.12366i
$970$	−58.6050	+	5.36726i	−1.88169	+	0.172332i
$971$	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
$975$	1.57616	+	8.53286i	0.0504775	+	0.273270i
$976$	−14.1552	−	8.17252i	−0.453098	−	0.261596i
$977$	−34.2846	+	9.18653i	−1.09686	+	0.293903i	−0.761486	−	0.648181i	$-0.775530\pi$
$977$	−34.2846	+	9.18653i	−1.09686	+	0.293903i	−0.335375	+	0.942085i	$0.608863\pi$
$978$	−10.5364	+	39.3222i	−0.336916	+	1.25739i
$979$	−18.4693			−0.590283
$980$		0			0
$981$	5.95352			0.190081
$982$	−4.66310	+	17.4029i	−0.148806	+	0.555350i
$983$	1.68510	−	0.451521i	0.0537463	−	0.0144013i	−0.231846	−	0.972753i	$-0.574476\pi$
$983$	1.68510	−	0.451521i	0.0537463	−	0.0144013i	0.285592	+	0.958351i	$0.407810\pi$
$984$	−5.53895	−	3.19791i	−0.176575	−	0.101946i
$985$	25.2435	−	9.30420i	0.804326	−	0.296457i
$986$			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
$990$	8.04425	−	9.66624i	0.255663	−	0.307213i
$991$	−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	$0.883058\pi$
$992$	−56.2587	−	15.0745i	−1.78622	−	0.478615i
$993$	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
$997$	4.38661	+	16.3710i	0.138925	+	0.518476i	0.999951	+	0.00991437i	$0.00315589\pi$
$997$	4.38661	+	16.3710i	0.138925	+	0.518476i	−0.861026	+	0.508562i	$0.830177\pi$
$998$	−12.9421	−	48.3007i	−0.409676	−	1.52893i
$999$	−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.472.7		32
5.3	odd	4	inner	735.2.v.a.178.1		32
7.2	even	3	inner	735.2.v.a.607.2		32
7.3	odd	6		105.2.m.a.97.7	yes	16
7.4	even	3		105.2.m.a.97.8	yes	16
7.5	odd	6	inner	735.2.v.a.607.1		32
7.6	odd	2	inner	735.2.v.a.472.8		32
21.11	odd	6		315.2.p.e.307.2		16
21.17	even	6		315.2.p.e.307.1		16
28.3	even	6		1680.2.cz.d.97.8		16
28.11	odd	6		1680.2.cz.d.97.1		16
35.3	even	12		105.2.m.a.13.8	yes	16
35.4	even	6		525.2.m.b.307.1		16
35.13	even	4	inner	735.2.v.a.178.2		32
35.17	even	12		525.2.m.b.118.1		16
35.18	odd	12		105.2.m.a.13.7	✓	16
35.23	odd	12	inner	735.2.v.a.313.8		32
35.24	odd	6		525.2.m.b.307.2		16
35.32	odd	12		525.2.m.b.118.2		16
35.33	even	12	inner	735.2.v.a.313.7		32
105.38	odd	12		315.2.p.e.118.2		16
105.53	even	12		315.2.p.e.118.1		16
140.3	odd	12		1680.2.cz.d.433.1		16
140.123	even	12		1680.2.cz.d.433.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	35.18	odd	12
105.2.m.a.13.8	yes	16	35.3	even	12
105.2.m.a.97.7	yes	16	7.3	odd	6
105.2.m.a.97.8	yes	16	7.4	even	3
315.2.p.e.118.1		16	105.53	even	12
315.2.p.e.118.2		16	105.38	odd	12
315.2.p.e.307.1		16	21.17	even	6
315.2.p.e.307.2		16	21.11	odd	6
525.2.m.b.118.1		16	35.17	even	12
525.2.m.b.118.2		16	35.32	odd	12
525.2.m.b.307.1		16	35.4	even	6
525.2.m.b.307.2		16	35.24	odd	6
735.2.v.a.178.1		32	5.3	odd	4	inner
735.2.v.a.178.2		32	35.13	even	4	inner
735.2.v.a.313.7		32	35.33	even	12	inner
735.2.v.a.313.8		32	35.23	odd	12	inner
735.2.v.a.472.7		32	1.1	even	1	trivial
735.2.v.a.472.8		32	7.6	odd	2	inner
735.2.v.a.607.1		32	7.5	odd	6	inner
735.2.v.a.607.2		32	7.2	even	3	inner
1680.2.cz.d.97.1		16	28.11	odd	6
1680.2.cz.d.97.8		16	28.3	even	6
1680.2.cz.d.433.1		16	140.3	odd	12
1680.2.cz.d.433.8		16	140.123	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.v (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.544785 - 2.03317i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-2.10492 - 1.21528i) q^{4} +(-0.936763 + 2.03039i) q^{5} +2.10489i q^{6} +(-0.640825 + 0.640825i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.544785 - 2.03317i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(-2.10492 - 1.21528i) q^{4} +(-0.936763 + 2.03039i) q^{5} +2.10489i q^{6} +(-0.640825 + 0.640825i) q^{8} +(0.866025 - 0.500000i) q^{9} +(3.61778 + 3.01072i) q^{10} +(1.33594 - 2.31391i) q^{11} +(2.34773 + 0.629073i) q^{12} +(1.22714 + 1.22714i) q^{13} +(0.379340 - 2.20366i) q^{15} +(-1.47676 - 2.55782i) q^{16} +(-1.73725 - 6.48349i) q^{17} +(-0.544785 - 2.03317i) q^{18} +(-3.00865 - 5.21113i) q^{19} +(4.43929 - 3.13538i) q^{20} +(-3.97676 - 3.97676i) q^{22} +(0.239989 + 0.0643048i) q^{23} +(0.453132 - 0.784847i) q^{24} +(-3.24495 - 3.80398i) q^{25} +(3.16351 - 1.82645i) q^{26} +(-0.707107 + 0.707107i) q^{27} -0.304889i q^{29} +(-4.27374 - 1.97178i) q^{30} +(6.28197 + 3.62690i) q^{31} +(-7.75576 + 2.07815i) q^{32} +(-0.691531 + 2.58083i) q^{33} -14.1284 q^{34} -2.43055 q^{36} +(-0.269190 + 1.00463i) q^{37} +(-12.2341 + 3.27813i) q^{38} +(-1.50294 - 0.867721i) q^{39} +(-0.700822 - 1.90142i) q^{40} -7.05736i q^{41} +(0.304889 - 0.304889i) q^{43} +(-5.62407 + 3.24706i) q^{44} +(0.203934 + 2.22675i) q^{45} +(0.261485 - 0.452905i) q^{46} +(-0.760694 - 0.203827i) q^{47} +(2.08845 + 2.08845i) q^{48} +(-9.50193 + 4.52517i) q^{50} +(3.35610 + 5.81294i) q^{51} +(-1.09172 - 4.07435i) q^{52} +(-1.82658 - 6.81689i) q^{53} +(1.05244 + 1.82289i) q^{54} +(3.44668 + 4.88005i) q^{55} +(4.25487 + 4.25487i) q^{57} +(-0.619890 - 0.166099i) q^{58} +(3.99419 - 6.91813i) q^{59} +(-3.47653 + 4.17752i) q^{60} +(4.79266 - 2.76704i) q^{61} +(10.7964 - 10.7964i) q^{62} +10.9939i q^{64} +(-3.64112 + 1.34203i) q^{65} +(4.87052 + 2.81199i) q^{66} +(4.68622 - 1.25567i) q^{67} +(-4.22247 + 15.7585i) q^{68} -0.248455 q^{69} +15.3087 q^{71} +(-0.234558 + 0.875383i) q^{72} +(-13.6887 + 3.66788i) q^{73} +(1.89593 + 1.09462i) q^{74} +(4.11893 + 2.83451i) q^{75} +14.6253i q^{76} +(-2.58300 + 2.58300i) q^{78} +(-9.78372 + 5.64863i) q^{79} +(6.57675 - 0.602322i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-14.3488 - 3.84475i) q^{82} +(-4.88941 - 4.88941i) q^{83} +(14.7914 + 2.54621i) q^{85} +(-0.453791 - 0.785990i) q^{86} +(0.0789112 + 0.294500i) q^{87} +(0.626709 + 2.33891i) q^{88} +(-3.45626 - 5.98641i) q^{89} +(4.63845 + 0.798469i) q^{90} +(-0.427009 - 0.427009i) q^{92} +(-7.00662 - 1.87742i) q^{93} +(-0.828829 + 1.43557i) q^{94} +(13.3990 - 1.22713i) 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

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