LMFDB - Embedded newform 735.2.v.a.472.8

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			472.8
Character	$\chi$	$=$	735.472
Dual form			735.2.v.a.313.8

$q$-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	0.516150	−	0.856498i	$-0.327365\pi$
$13$	−1.22714	−	1.22714i	−0.340348	−	0.340348i	−0.856498	+	0.516150i	$0.827365\pi$
$14$		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	$0.219367\pi$
$17$	1.73725	+	6.48349i	0.421344	+	1.57248i	−0.350436	+	0.936587i	$0.613966\pi$
$18$	−0.544785	−	2.03317i	−0.128407	−	0.479222i
$19$	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
$23$	0.239989	+	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	−0.184774	−	0.982781i	$-0.559155\pi$
$31$	−6.28197	−	3.62690i	−1.12827	−	0.651410i	−0.943500	+	0.331371i	$0.892489\pi$
$32$	−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	$0.185787\pi$
$41$			7.05736i			1.10217i	−0.834447	+	0.551087i	$0.814213\pi$
$42$		0			0
$43$	0.304889	−	0.304889i	0.0464952	−	0.0464952i	−0.683477	−	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	0.313871	−	0.949466i	$-0.398374\pi$
$47$	0.760694	+	0.203827i	0.110959	+	0.0297313i	−0.202912	+	0.979197i	$0.565041\pi$
$48$	−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	$0.340734\pi$
$59$	−3.99419	+	6.91813i	−0.519999	+	0.900664i	−0.999730	+	0.0232486i	$0.992599\pi$
$60$	−3.47653	+	4.17752i	−0.448818	+	0.539315i
$61$	−4.79266	+	2.76704i	−0.613637	+	0.354284i	−0.774388	−	0.632711i	$-0.781942\pi$
$61$	−4.79266	+	2.76704i	−0.613637	+	0.354284i	0.160750	+	0.986995i	$0.448609\pi$
$62$	−10.7964	+	10.7964i	−1.37114	+	1.37114i
$63$		0			0
$64$			10.9939i			1.37423i
$65$	−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	0.656454	−	0.754366i	$-0.272056\pi$
$73$	13.6887	−	3.66788i	1.60214	−	0.429293i	0.945689	+	0.325073i	$0.105389\pi$
$74$	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	0.922553	−	0.385871i	$-0.126099\pi$
$83$	4.88941	+	4.88941i	0.536682	+	0.536682i	−0.385871	+	0.922553i	$0.626099\pi$
$84$		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	0.988994	−	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
$93$	−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	−0.0975276	−	0.995233i	$-0.531093\pi$
$97$	8.84137	−	8.84137i	0.897705	−	0.897705i	0.995233	+	0.0975276i	$0.0310934\pi$
$98$		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	0.155038	−	0.987908i	$-0.450450\pi$
$101$	−6.26104	−	3.61481i	−0.622996	−	0.359687i	−0.778035	+	0.628221i	$0.783783\pi$
$102$	13.6470	−	3.65671i	1.35126	−	0.362068i
$103$	2.54219	−	9.48757i	0.250489	−	0.934838i	−0.720056	−	0.693916i	$-0.755884\pi$
$103$	2.54219	−	9.48757i	0.250489	−	0.934838i	0.970545	−	0.240921i	$-0.0774496\pi$
$104$	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	−0.810056	−	0.586352i	$-0.800564\pi$
$131$	−8.09529	+	4.67382i	−0.707289	+	0.408353i	0.102767	+	0.994705i	$0.467230\pi$
$132$	−4.59204	+	4.59204i	−0.399686	+	0.399686i
$133$		0			0
$134$		−	10.2119i		−	0.882177i
$135$	−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	$-0.607159\pi$
$139$	−7.78902			−0.660656			−0.330328	+	0.943866i	$0.607159\pi$
$140$		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	0.926805	−	0.375544i	$-0.122544\pi$
$157$	−0.796951	−	2.97426i	−0.0636036	−	0.237372i	−0.990408	+	0.138172i	$0.955877\pi$
$158$	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	−0.423555	−	0.905870i	$-0.639218\pi$
$167$	6.23288	−	6.23288i	0.482315	−	0.482315i	0.905870	+	0.423555i	$0.139218\pi$
$168$		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	$0.201896\pi$
$173$	−2.47775	+	9.24710i	−0.188380	+	0.703044i	−0.993882	+	0.110450i	$0.964771\pi$
$174$	−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	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$		0			0
$183$	−3.91319	+	3.91319i	−0.289271	+	0.289271i
$184$	−0.194999	+	0.112583i	−0.0143755	+	0.00829971i
$185$	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	−0.917922	−	0.396761i	$-0.870134\pi$
$199$	−1.62730	+	2.81856i	−0.115356	+	0.199803i	0.802566	+	0.596563i	$0.203468\pi$
$200$	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	0.843730	−	0.536768i	$-0.180355\pi$
$223$	4.58392	+	4.58392i	0.306962	+	0.306962i	−0.536768	+	0.843730i	$0.680355\pi$
$224$		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	$-0.851926\pi$
$227$	−5.18339	−	19.3447i	−0.344034	−	1.28395i	0.549703	−	0.835360i	$-0.314741\pi$
$228$	−3.78532	−	14.1270i	−0.250689	−	0.935583i
$229$	−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
$233$	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	0.148101	−	0.988972i	$-0.452684\pi$
$241$	−9.84735	−	5.68537i	−0.634324	−	0.366227i	−0.782425	+	0.622745i	$0.786017\pi$
$242$	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	$-0.929606\pi$
$251$		−	6.95039i		−	0.438705i	0.975646	−	0.219352i	$-0.0703944\pi$
$252$		0			0
$253$	0.469405	−	0.469405i	0.0295112	−	0.0295112i
$254$	7.37578	−	4.25841i	0.462798	−	0.267196i
$255$	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	0.661620	−	0.749840i	$-0.269869\pi$
$257$	13.7817	+	3.69280i	0.859679	+	0.230350i	0.198060	+	0.980190i	$0.436536\pi$
$258$	−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	−0.999518	−	0.0310287i	$-0.990122\pi$
$269$	−7.75593	+	13.4337i	−0.472888	+	0.819065i	0.526631	+	0.850094i	$0.323455\pi$
$270$	−4.68706	+	0.429257i	−0.285245	+	0.0261238i
$271$	−11.5544	+	6.67091i	−0.701877	+	0.405229i	−0.808046	−	0.589119i	$-0.799475\pi$
$271$	−11.5544	+	6.67091i	−0.701877	+	0.405229i	0.106169	+	0.994348i	$0.466142\pi$
$272$	14.0181	−	14.0181i	0.849974	−	0.849974i
$273$		0			0
$274$			22.3835i			1.35224i
$275$	−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	−0.848630	−	0.528987i	$-0.822572\pi$
$283$	−22.1902	+	5.94585i	−1.31907	+	0.353444i	−0.470441	+	0.882431i	$0.655905\pi$
$284$	−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	0.774192	−	0.632951i	$-0.218157\pi$
$293$	2.41765	+	2.41765i	0.141240	+	0.141240i	−0.632951	+	0.774192i	$0.718157\pi$
$294$		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	−0.882319	−	0.470652i	$-0.844019\pi$
$307$	−7.21300	+	7.21300i	−0.411667	+	0.411667i	0.470652	+	0.882319i	$0.344019\pi$
$308$		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	0.730182	−	0.683253i	$-0.239435\pi$
$311$	8.88036	+	5.12708i	0.503559	+	0.290730i	−0.226623	+	0.973983i	$0.572769\pi$
$312$	1.51918	−	0.407062i	0.0860064	−	0.0230453i
$313$	−8.08564	+	30.1760i	−0.457027	+	1.70565i	0.225031	+	0.974352i	$0.427752\pi$
$313$	−8.08564	+	30.1760i	−0.457027	+	1.70565i	−0.682059	+	0.731298i	$0.738915\pi$
$314$	−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	$-0.476368\pi$
$349$	2.77139			0.148349			0.0741746	+	0.997245i	$0.476368\pi$
$350$		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	−0.293929	−	0.955827i	$-0.594963\pi$
$353$	−1.32582	+	0.355252i	−0.0705663	+	0.0189082i	0.223363	+	0.974735i	$0.428296\pi$
$354$	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	$-0.923982\pi$
$367$	−4.75960	−	17.7631i	−0.248449	−	0.927225i	0.723169	−	0.690671i	$-0.242685\pi$
$368$	−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	−0.962179	−	0.272418i	$-0.912177\pi$
$383$	0.142890	−	0.533272i	0.00730133	−	0.0272489i	0.969480	+	0.245169i	$0.0788434\pi$
$384$	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	−0.383072	−	0.923718i	$-0.625134\pi$
$397$	−23.4452	−	6.28213i	−1.17668	−	0.315291i	−0.793609	+	0.608427i	$0.791801\pi$
$398$	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	−0.896844	−	0.442347i	$-0.854146\pi$
$409$	−1.32139	+	2.28872i	−0.0653386	+	0.113170i	0.831506	+	0.555516i	$0.187479\pi$
$410$	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	$-0.578789\pi$
$419$	−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	$0.724927\pi$
$422$	−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	0.304935	−	0.952373i	$-0.401365\pi$
$433$	−13.4723	−	13.4723i	−0.647438	−	0.647438i	−0.952373	+	0.304935i	$0.901365\pi$
$434$		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	$0.0432883\pi$
$439$	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
$443$	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	$0.246041\pi$
$461$			29.9845i			1.39652i	−0.715846	+	0.698259i	$0.753959\pi$
$462$		0			0
$463$	7.70220	−	7.70220i	0.357951	−	0.357951i	−0.505106	−	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	0.315559	−	0.948906i	$-0.397808\pi$
$467$	2.47197	+	0.662362i	0.114389	+	0.0306504i	−0.201170	+	0.979556i	$0.564475\pi$
$468$	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	−0.815457	−	0.578818i	$-0.803514\pi$
$479$	2.04728	−	3.54599i	0.0935425	−	0.162020i	0.908999	+	0.416798i	$0.136848\pi$
$480$	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	0.983153	−	0.182786i	$-0.0585115\pi$
$503$	17.9504	+	17.9504i	0.800367	+	0.800367i	−0.182786	+	0.983153i	$0.558511\pi$
$504$		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	0.990250	−	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
$513$	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	0.342907	−	0.939370i	$-0.388589\pi$
$521$	−6.82841	−	3.94238i	−0.299158	−	0.172719i	−0.642065	+	0.766651i	$0.721922\pi$
$522$	−0.619890	+	0.166099i	−0.0271319	+	0.00726996i
$523$	0.450757	−	1.68225i	0.0197102	−	0.0735595i	−0.955370	−	0.295411i	$-0.904543\pi$
$523$	0.450757	−	1.68225i	0.0197102	−	0.0735595i	0.975080	+	0.221852i	$0.0712101\pi$
$524$	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	0.500892	−	0.865510i	$-0.333005\pi$
$563$	32.4459	−	8.69386i	1.36743	−	0.366402i	0.866540	+	0.499107i	$0.166339\pi$
$564$	−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	$-0.746764\pi$
$577$	−10.8309	−	40.4214i	−0.450896	−	1.68277i	0.248986	−	0.968507i	$-0.419903\pi$
$578$	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	$0.533604\pi$
$587$	−26.6462	+	26.6462i	−1.09981	+	1.09981i	−0.994433	+	0.105375i	$0.966396\pi$
$588$		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	$0.228726\pi$
$593$	−5.55952	+	20.7484i	−0.228302	+	0.852036i	−0.981055	+	0.193732i	$0.937941\pi$
$594$	−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	$-0.849371\pi$
$601$		−	22.3458i		−	0.911503i	0.890107	−	0.455752i	$-0.150629\pi$
$602$		0			0
$603$	3.43055	−	3.43055i	0.139703	−	0.139703i
$604$	20.5859	−	11.8853i	0.837629	−	0.483605i
$605$	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	0.242815	−	0.970073i	$-0.421929\pi$
$607$	−0.786867	−	0.210840i	−0.0319380	−	0.00855775i	−0.274753	+	0.961515i	$0.588596\pi$
$608$	−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	$0.462650\pi$
$619$	−19.9420	+	34.5405i	−0.801536	+	1.38830i	−0.918605	+	0.395178i	$0.870683\pi$
$620$	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	$-0.896961\pi$
$643$	−32.1062	−	32.1062i	−1.26614	−	1.26614i	−0.318082	−	0.948063i	$-0.603039\pi$
$644$		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	$-0.966321\pi$
$647$	−4.73187	−	17.6596i	−0.186029	−	0.694270i	0.808379	−	0.588663i	$-0.200345\pi$
$648$	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	−0.0634519	−	0.997985i	$-0.520211\pi$
$661$	−24.6676	−	14.2418i	−0.959458	−	0.553943i	−0.896006	+	0.444042i	$0.853544\pi$
$662$	−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	0.227262	−	0.973834i	$-0.427023\pi$
$677$	−1.63505	−	0.438111i	−0.0628402	−	0.0168380i	−0.290102	+	0.956996i	$0.593689\pi$
$678$	−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	−0.991284	−	0.131743i	$-0.957943\pi$
$691$	−36.0875	+	20.8351i	−1.37283	+	0.792606i	−0.381549	+	0.924348i	$0.624609\pi$
$692$	16.4533	−	16.4533i	0.625459	−	0.625459i
$693$		0			0
$694$			19.4970i			0.740098i
$695$	−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	$-0.978328\pi$
$719$	−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
$723$	−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	$-0.463797\pi$
$727$	29.8488	−	29.8488i	1.10703	−	1.10703i	0.993539	−	0.113491i	$-0.0362034\pi$
$728$		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	−0.934846	−	0.355053i	$-0.884463\pi$
$733$	1.41545	−	5.28252i	0.0522807	−	0.195114i	0.987127	+	0.159938i	$0.0511296\pi$
$734$	−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	0.101648	−	0.994820i	$-0.467589\pi$
$761$	27.9728	−	16.1501i	1.01401	−	0.585440i	0.912364	+	0.409381i	$0.134255\pi$
$762$	6.02230	−	6.02230i	0.218165	−	0.218165i
$763$		0			0
$764$			4.71018i			0.170408i
$765$	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	$-0.607831\pi$
$769$	−18.4310			−0.664640			−0.332320	+	0.943167i	$0.607831\pi$
$770$		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	0.206397	−	0.978468i	$-0.433826\pi$
$773$	24.3102	−	6.51389i	0.874376	−	0.234288i	0.667979	+	0.744180i	$0.267160\pi$
$774$	−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	$0.0493886\pi$
$787$	5.88096	+	21.9481i	0.209634	+	0.782364i	−0.778353	+	0.627827i	$0.783945\pi$
$788$	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	−0.0913664	−	0.995817i	$-0.529123\pi$
$797$	25.5337	−	25.5337i	0.904451	−	0.904451i	0.995817	+	0.0913664i	$0.0291235\pi$
$798$		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	$0.205398\pi$
$811$			34.2545i			1.20284i	−0.798933	+	0.601420i	$0.794602\pi$
$812$		0			0
$813$	−9.43409	+	9.43409i	−0.330868	+	0.330868i
$814$	5.06568	−	2.92467i	0.177552	−	0.102510i
$815$	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	−0.999961	−	0.00884765i	$-0.997184\pi$
$829$	−14.1750	+	24.5518i	−0.492318	+	0.852720i	0.507643	+	0.861568i	$0.330517\pi$
$830$	−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	$-0.691650\pi$
$839$	−32.8100			−1.13273			−0.566364	+	0.824156i	$0.691650\pi$
$840$		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	0.920737	−	0.390184i	$-0.127589\pi$
$853$	15.4954	+	15.4954i	0.530553	+	0.530553i	−0.390184	+	0.920737i	$0.627589\pi$
$854$		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	$0.0584291\pi$
$857$	6.52792	+	24.3625i	0.222989	+	0.832208i	−0.760211	+	0.649677i	$0.774904\pi$
$858$	2.52610	+	9.42753i	0.0862396	+	0.321851i
$859$	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
$863$	−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	$-0.794106\pi$
$881$		−	35.7762i		−	1.20533i	0.797994	−	0.602665i	$-0.205894\pi$
$882$		0			0
$883$	24.6278	−	24.6278i	0.828791	−	0.828791i	−0.158559	−	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	0.275578	−	0.961279i	$-0.411131\pi$
$887$	1.00060	+	0.268110i	0.0335969	+	0.00900226i	−0.241981	+	0.970281i	$0.577797\pi$
$888$	−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	0.582560	−	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
$933$	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	−0.997464	−	0.0711778i	$-0.977324\pi$
$937$	−28.3540	+	28.3540i	−0.926286	+	0.926286i	0.0711778	+	0.997464i	$0.477324\pi$
$938$		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	0.501509	−	0.865152i	$-0.332778\pi$
$941$	0.0926410	+	0.0534863i	0.00302001	+	0.00174360i	−0.498489	+	0.866896i	$0.666112\pi$
$942$	−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	$0.668146\pi$
$971$	−46.8662	+	27.0582i	−1.50401	+	0.868340i	−0.999989	+	0.00464820i	$0.998520\pi$
$972$	−1.71866	+	1.71866i	−0.0551260	+	0.0551260i
$973$		0			0
$974$		−	30.6752i		−	0.982896i
$975$	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	−0.285592	−	0.958351i	$-0.592190\pi$
$983$	−1.68510	+	0.451521i	−0.0537463	+	0.0144013i	0.231846	+	0.972753i	$0.425524\pi$
$984$	−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	$-0.996844\pi$
$997$	−4.38661	−	16.3710i	−0.138925	−	0.518476i	0.861026	−	0.508562i	$-0.169823\pi$
$998$	−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.472.8		32
5.3	odd	4	inner	735.2.v.a.178.2		32
7.2	even	3	inner	735.2.v.a.607.1		32
7.3	odd	6		105.2.m.a.97.8	yes	16
7.4	even	3		105.2.m.a.97.7	yes	16
7.5	odd	6	inner	735.2.v.a.607.2		32
7.6	odd	2	inner	735.2.v.a.472.7		32
21.11	odd	6		315.2.p.e.307.1		16
21.17	even	6		315.2.p.e.307.2		16
28.3	even	6		1680.2.cz.d.97.1		16
28.11	odd	6		1680.2.cz.d.97.8		16
35.3	even	12		105.2.m.a.13.7	✓	16
35.4	even	6		525.2.m.b.307.2		16
35.13	even	4	inner	735.2.v.a.178.1		32
35.17	even	12		525.2.m.b.118.2		16
35.18	odd	12		105.2.m.a.13.8	yes	16
35.23	odd	12	inner	735.2.v.a.313.7		32
35.24	odd	6		525.2.m.b.307.1		16
35.32	odd	12		525.2.m.b.118.1		16
35.33	even	12	inner	735.2.v.a.313.8		32
105.38	odd	12		315.2.p.e.118.1		16
105.53	even	12		315.2.p.e.118.2		16
140.3	odd	12		1680.2.cz.d.433.8		16
140.123	even	12		1680.2.cz.d.433.1		16

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