LMFDB - Embedded newform 735.2.v.a.313.8

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			313.8
Character	$\chi$	$=$	735.313
Dual form			735.2.v.a.472.8

$q$-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 $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	0.544785	+	2.03317i	0.385221	+	1.43766i	0.837818	+	0.545950i	$0.183831\pi$
$2$	0.544785	+	2.03317i	0.385221	+	1.43766i	−0.452597	+	0.891715i	$0.649502\pi$
$3$	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	0.994063	−	0.108809i	$-0.0347038\pi$
$11$	1.33594	+	2.31391i	0.402800	+	0.697670i	−0.591263	+	0.806479i	$0.701370\pi$
$12$	−2.34773	+	0.629073i	−0.677732	+	0.181598i
$13$	−1.22714	+	1.22714i	−0.340348	+	0.340348i	−0.856498	−	0.516150i	$-0.827365\pi$
$13$	−1.22714	+	1.22714i	−0.340348	+	0.340348i	0.516150	+	0.856498i	$0.327365\pi$
$14$		0			0
$15$	0.379340	+	2.20366i	0.0979452	+	0.568982i
$16$	−1.47676	+	2.55782i	−0.369190	+	0.639456i
$17$	1.73725	−	6.48349i	0.421344	−	1.57248i	−0.350436	−	0.936587i	$-0.613966\pi$
$17$	1.73725	−	6.48349i	0.421344	−	1.57248i	0.771780	−	0.635890i	$-0.219367\pi$
$18$	−0.544785	+	2.03317i	−0.128407	+	0.479222i
$19$	3.00865	−	5.21113i	0.690231	−	1.19551i	−0.281531	−	0.959552i	$-0.590842\pi$
$19$	3.00865	−	5.21113i	0.690231	−	1.19551i	0.971762	−	0.235963i	$-0.0758243\pi$
$20$	−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	−0.233712	−	0.972306i	$-0.575087\pi$
$23$	0.239989	−	0.0643048i	0.0500411	−	0.0134085i	0.283753	+	0.958897i	$0.408421\pi$
$24$	−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	$0.00901200\pi$
$29$			0.304889i			0.0566165i	−0.999599	+	0.0283083i	$0.990988\pi$
$30$	−4.27374	+	1.97178i	−0.780274	+	0.359996i
$31$	−6.28197	+	3.62690i	−1.12827	+	0.651410i	−0.943500	−	0.331371i	$-0.892489\pi$
$31$	−6.28197	+	3.62690i	−1.12827	+	0.651410i	−0.184774	+	0.982781i	$0.559155\pi$
$32$	−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	0.940262	−	0.340452i	$-0.110580\pi$
$37$	−0.269190	−	1.00463i	−0.0442546	−	0.165160i	−0.984517	+	0.175291i	$0.943913\pi$
$38$	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	0.729972	−	0.683477i	$-0.239533\pi$
$43$	0.304889	+	0.304889i	0.0464952	+	0.0464952i	−0.683477	+	0.729972i	$0.739533\pi$
$44$	−5.62407	−	3.24706i	−0.847861	−	0.489513i
$45$	−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	$-0.565041\pi$
$47$	0.760694	−	0.203827i	0.110959	−	0.0297313i	0.313871	+	0.949466i	$0.398374\pi$
$48$	−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	0.719426	+	0.694570i	$0.244405\pi$
$53$	−1.82658	+	6.81689i	−0.250900	+	0.936372i	−0.970326	+	0.241802i	$0.922262\pi$
$54$	−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	−0.999730	−	0.0232486i	$-0.992599\pi$
$59$	−3.99419	−	6.91813i	−0.519999	−	0.900664i	0.479731	−	0.877416i	$-0.340734\pi$
$60$	−3.47653	−	4.17752i	−0.448818	−	0.539315i
$61$	−4.79266	−	2.76704i	−0.613637	−	0.354284i	0.160750	−	0.986995i	$-0.448609\pi$
$61$	−4.79266	−	2.76704i	−0.613637	−	0.354284i	−0.774388	+	0.632711i	$0.781942\pi$
$62$	−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	0.533449	−	0.845832i	$-0.320896\pi$
$67$	4.68622	+	1.25567i	0.572513	+	0.153404i	0.0390641	+	0.999237i	$0.487562\pi$
$68$	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	$-0.105389\pi$
$73$	13.6887	+	3.66788i	1.60214	+	0.429293i	0.656454	+	0.754366i	$0.272056\pi$
$74$	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	−0.164335	−	0.986405i	$-0.552548\pi$
$79$	−9.78372	−	5.64863i	−1.10075	−	0.635521i	−0.936419	+	0.350884i	$0.885881\pi$
$80$	−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	$-0.626099\pi$
$83$	4.88941	−	4.88941i	0.536682	−	0.536682i	0.922553	+	0.385871i	$0.126099\pi$
$84$		0			0
$85$	14.7914	−	2.54621i	1.60435	−	0.276175i
$86$	−0.453791	+	0.785990i	−0.0489336	+	0.0847554i
$87$	−0.0789112	+	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	$-0.713936\pi$
$89$	3.45626	−	5.98641i	0.366363	−	0.634559i	0.988994	+	0.147957i	$0.0472697\pi$
$90$	−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	$-0.0310934\pi$
$97$	8.84137	+	8.84137i	0.897705	+	0.897705i	−0.0975276	+	0.995233i	$0.531093\pi$
$98$		0			0
$99$			2.67187i			0.268533i
$100$	2.20747	−	11.9506i	0.220747	−	1.19506i
$101$	−6.26104	+	3.61481i	−0.622996	+	0.359687i	−0.778035	−	0.628221i	$-0.783783\pi$
$101$	−6.26104	+	3.61481i	−0.622996	+	0.359687i	0.155038	+	0.987908i	$0.450450\pi$
$102$	13.6470	+	3.65671i	1.35126	+	0.362068i
$103$	2.54219	+	9.48757i	0.250489	+	0.934838i	0.970545	+	0.240921i	$0.0774496\pi$
$103$	2.54219	+	9.48757i	0.250489	+	0.934838i	−0.720056	+	0.693916i	$0.755884\pi$
$104$	1.57277			0.154222
$105$		0			0
$106$	−14.8550			−1.44284
$107$	−2.73529	−	10.2082i	−0.264430	−	0.986867i	−0.962598	−	0.270933i	$-0.912668\pi$
$107$	−2.73529	−	10.2082i	−0.264430	−	0.986867i	0.698168	−	0.715934i	$-0.253999\pi$
$108$	−2.34773	−	0.629073i	−0.225911	−	0.0605326i
$109$	5.15590	−	2.97676i	0.493846	−	0.285122i	−0.232323	−	0.972639i	$-0.574633\pi$
$109$	5.15590	−	2.97676i	0.493846	−	0.285122i	0.726168	+	0.687517i	$0.241299\pi$
$110$	−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	0.954810	−	0.297217i	$-0.0960585\pi$
$113$	6.99031	+	6.99031i	0.657593	+	0.657593i	−0.297217	+	0.954810i	$0.596058\pi$
$114$	10.9688	+	6.33286i	1.02733	+	0.593127i
$115$	0.355376	+	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	−0.568678	−	0.822560i	$-0.692545\pi$
$127$	2.86110	−	2.86110i	0.253882	−	0.253882i	0.822560	+	0.568678i	$0.192545\pi$
$128$	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	$-0.467230\pi$
$131$	−8.09529	−	4.67382i	−0.707289	−	0.408353i	−0.810056	+	0.586352i	$0.800564\pi$
$132$	−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	−0.208213	−	0.978083i	$-0.566765\pi$
$137$	−10.2717	−	2.75230i	−0.877573	−	0.235145i	−0.669360	+	0.742938i	$0.733431\pi$
$138$	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	0.912221	−	0.409699i	$-0.134366\pi$
$149$	12.3716	+	7.14275i	1.01352	+	0.585157i	0.101301	+	0.994856i	$0.467699\pi$
$150$	−8.00696	−	6.83026i	−0.653765	−	0.557688i
$151$	−4.88995	−	8.46964i	−0.397939	−	0.689250i	0.595533	−	0.803331i	$-0.296941\pi$
$151$	−4.88995	−	8.46964i	−0.397939	−	0.689250i	−0.993471	+	0.114081i	$0.963608\pi$
$152$	−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	$-0.955877\pi$
$157$	−0.796951	+	2.97426i	−0.0636036	+	0.237372i	0.926805	+	0.375544i	$0.122544\pi$
$158$	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	0.562632	−	0.826707i	$-0.309789\pi$
$163$	18.6814	−	5.00566i	1.46324	−	0.392074i	0.900607	+	0.434633i	$0.143122\pi$
$164$	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	$-0.139218\pi$
$167$	6.23288	+	6.23288i	0.482315	+	0.482315i	−0.423555	+	0.905870i	$0.639218\pi$
$168$		0			0
$169$			9.98824i			0.768326i
$170$	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	−0.993882	−	0.110450i	$-0.964771\pi$
$173$	−2.47775	−	9.24710i	−0.188380	−	0.703044i	0.805501	−	0.592594i	$-0.201896\pi$
$174$	−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	−0.541516	−	0.840690i	$-0.682150\pi$
$179$	−1.12673	+	0.650516i	−0.0842155	+	0.0486218i	0.457301	+	0.889312i	$0.348816\pi$
$180$	−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	−0.898950	−	0.438052i	$-0.855669\pi$
$191$	−0.968954	+	1.67828i	−0.0701110	+	0.121436i	0.828839	+	0.559488i	$0.189002\pi$
$192$	2.84542	−	10.6192i	0.205350	−	0.766378i
$193$	−2.86520	+	10.6931i	−0.206241	+	0.769703i	0.782826	+	0.622240i	$0.213777\pi$
$193$	−2.86520	+	10.6931i	−0.206241	+	0.769703i	−0.989068	+	0.147463i	$0.952889\pi$
$194$	−13.1593	+	22.7926i	−0.944784	+	1.63641i
$195$	−3.16970	−	2.23870i	−0.226987	−	0.160316i
$196$		0			0
$197$	−8.50767	+	8.50767i	−0.606146	+	0.606146i	−0.941937	−	0.335790i	$-0.890997\pi$
$197$	−8.50767	+	8.50767i	−0.606146	+	0.606146i	0.335790	+	0.941937i	$0.390997\pi$
$198$	−5.43236	+	1.45560i	−0.386061	+	0.103445i
$199$	−1.62730	−	2.81856i	−0.115356	−	0.199803i	0.802566	−	0.596563i	$-0.203468\pi$
$199$	−1.62730	−	2.81856i	−0.115356	−	0.199803i	−0.917922	+	0.396761i	$0.870134\pi$
$200$	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	$-0.680355\pi$
$223$	4.58392	−	4.58392i	0.306962	−	0.306962i	0.843730	+	0.536768i	$0.180355\pi$
$224$		0			0
$225$	−4.71220	+	1.67187i	−0.314147	+	0.111458i
$226$	−10.4042	+	18.0207i	−0.692080	+	1.19872i
$227$	−5.18339	+	19.3447i	−0.344034	+	1.28395i	0.549703	+	0.835360i	$0.314741\pi$
$227$	−5.18339	+	19.3447i	−0.344034	+	1.28395i	−0.893737	+	0.448592i	$0.851926\pi$
$228$	−3.78532	+	14.1270i	−0.250689	+	0.935583i
$229$	−14.4654	+	25.0547i	−0.955898	+	1.65566i	−0.223598	+	0.974681i	$0.571780\pi$
$229$	−14.4654	+	25.0547i	−0.955898	+	1.65566i	−0.732300	+	0.680982i	$0.761553\pi$
$230$	−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	−0.0382507	−	0.999268i	$-0.512179\pi$
$233$	6.53706	−	1.75160i	0.428257	−	0.114751i	0.466508	+	0.884517i	$0.345512\pi$
$234$	−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	$-0.824738\pi$
$239$		−	16.1769i		−	1.04640i	0.852210	−	0.523200i	$-0.175262\pi$
$240$	−6.19676	−	2.28399i	−0.399999	−	0.147431i
$241$	−9.84735	+	5.68537i	−0.634324	+	0.366227i	−0.782425	−	0.622745i	$-0.786017\pi$
$241$	−9.84735	+	5.68537i	−0.634324	+	0.366227i	0.148101	+	0.988972i	$0.452684\pi$
$242$	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	$-0.436536\pi$
$257$	13.7817	−	3.69280i	0.859679	−	0.230350i	0.661620	+	0.749840i	$0.269869\pi$
$258$	−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	−0.382480	−	0.923964i	$-0.624930\pi$
$263$	6.66107	−	24.8595i	0.410739	−	1.53290i	0.793219	−	0.608936i	$-0.208403\pi$
$264$	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	$-0.323455\pi$
$269$	−7.75593	−	13.4337i	−0.472888	−	0.819065i	−0.999518	+	0.0310287i	$0.990122\pi$
$270$	−4.68706	−	0.429257i	−0.285245	−	0.0261238i
$271$	−11.5544	−	6.67091i	−0.701877	−	0.405229i	0.106169	−	0.994348i	$-0.466142\pi$
$271$	−11.5544	−	6.67091i	−0.701877	−	0.405229i	−0.808046	+	0.589119i	$0.799475\pi$
$272$	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	0.340184	−	0.940359i	$-0.389511\pi$
$277$	2.73971	+	0.734104i	0.164613	+	0.0441080i	−0.175571	+	0.984467i	$0.556177\pi$
$278$	−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	$-0.655905\pi$
$283$	−22.1902	−	5.94585i	−1.31907	−	0.353444i	−0.848630	+	0.528987i	$0.822572\pi$
$284$	−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	$-0.718157\pi$
$293$	2.41765	−	2.41765i	0.141240	−	0.141240i	0.774192	+	0.632951i	$0.218157\pi$
$294$		0			0
$295$	10.3049	−	14.5904i	0.599974	−	0.849486i
$296$	−0.471289	+	0.816297i	−0.0273931	+	0.0474463i
$297$	−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	$-0.344019\pi$
$307$	−7.21300	−	7.21300i	−0.411667	−	0.411667i	−0.882319	+	0.470652i	$0.844019\pi$
$308$		0			0
$309$			9.82225i			0.558768i
$310$	11.8072	−	32.0345i	0.670605	−	1.81944i
$311$	8.88036	−	5.12708i	0.503559	−	0.290730i	−0.226623	−	0.973983i	$-0.572769\pi$
$311$	8.88036	−	5.12708i	0.503559	−	0.290730i	0.730182	+	0.683253i	$0.239435\pi$
$312$	1.51918	+	0.407062i	0.0860064	+	0.0230453i
$313$	−8.08564	−	30.1760i	−0.457027	−	1.70565i	−0.682059	−	0.731298i	$-0.738915\pi$
$313$	−8.08564	−	30.1760i	−0.457027	−	1.70565i	0.225031	−	0.974352i	$-0.427752\pi$
$314$	−6.48134			−0.365763
$315$		0			0
$316$	27.4586			1.54467
$317$	−4.48613	−	16.7425i	−0.251966	−	0.940351i	−0.969753	−	0.244088i	$-0.921511\pi$
$317$	−4.48613	−	16.7425i	−0.251966	−	0.940351i	0.717787	−	0.696263i	$-0.245155\pi$
$318$	−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	−0.882860	−	0.469637i	$-0.844385\pi$
$331$	−0.631541	+	1.09386i	−0.0347126	+	0.0601240i	0.848147	+	0.529761i	$0.177718\pi$
$332$	−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	−0.917741	−	0.397180i	$-0.869989\pi$
$337$	−9.55621	+	9.55621i	−0.520560	+	0.520560i	0.397180	+	0.917741i	$0.369989\pi$
$338$	−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	0.0105386	−	0.999944i	$-0.496645\pi$
$347$	−8.94713	−	2.39738i	−0.480307	−	0.128698i	−0.490846	+	0.871247i	$0.663312\pi$
$348$	−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	0.223363	−	0.974735i	$-0.428296\pi$
$353$	−1.32582	−	0.355252i	−0.0705663	−	0.0189082i	−0.293929	+	0.955827i	$0.594963\pi$
$354$	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	0.271434	−	0.962457i	$-0.412502\pi$
$359$	−8.07840	−	4.66406i	−0.426361	−	0.246160i	−0.697795	+	0.716297i	$0.745836\pi$
$360$	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	0.723169	+	0.690671i	$0.242685\pi$
$367$	−4.75960	+	17.7631i	−0.248449	+	0.927225i	−0.971618	+	0.236554i	$0.923982\pi$
$368$	−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	−0.900317	−	0.435235i	$-0.856665\pi$
$373$	−28.2436	+	7.56784i	−1.46240	+	0.391848i	−0.562080	+	0.827083i	$0.689999\pi$
$374$	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	$-0.808787\pi$
$379$		−	22.0077i		−	1.13046i	0.824933	−	0.565230i	$-0.191213\pi$
$380$	−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	$-0.0788434\pi$
$383$	0.142890	+	0.533272i	0.00730133	+	0.0272489i	−0.962179	+	0.272418i	$0.912177\pi$
$384$	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	−0.946075	−	0.323947i	$-0.894990\pi$
$389$	−22.4560	+	12.9650i	−1.13857	+	0.657352i	−0.192491	+	0.981299i	$0.561657\pi$
$390$	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	$-0.791801\pi$
$397$	−23.4452	+	6.28213i	−1.17668	+	0.315291i	−0.383072	+	0.923718i	$0.625134\pi$
$398$	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	−0.657994	−	0.753023i	$-0.728595\pi$
$401$	6.47088	−	11.2079i	0.323140	−	0.559696i	0.981134	+	0.193328i	$0.0619280\pi$
$402$	−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	$-0.187479\pi$
$409$	−1.32139	−	2.28872i	−0.0653386	−	0.113170i	−0.896844	+	0.442347i	$0.854146\pi$
$410$	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	−0.998965	−	0.0454873i	$-0.985516\pi$
$431$	−11.1873	−	19.3771i	−0.538876	−	0.933360i	0.460089	−	0.887873i	$-0.347817\pi$
$432$	−2.85288	+	0.764428i	−0.137259	+	0.0367785i
$433$	−13.4723	+	13.4723i	−0.647438	+	0.647438i	−0.952373	−	0.304935i	$-0.901365\pi$
$433$	−13.4723	+	13.4723i	−0.647438	+	0.647438i	0.304935	+	0.952373i	$0.401365\pi$
$434$		0			0
$435$	−0.671871	+	0.115657i	−0.0322138	+	0.00554532i
$436$	−7.23517	+	12.5317i	−0.346502	+	0.600159i
$437$	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	−0.377972	−	0.925817i	$-0.623378\pi$
$439$	12.8395	−	22.2386i	0.612795	−	1.06139i	0.990767	−	0.135576i	$-0.0432883\pi$
$440$	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	0.287135	−	0.957890i	$-0.407297\pi$
$443$	21.3579	−	5.72284i	1.01475	−	0.271900i	0.727611	+	0.685990i	$0.240631\pi$
$444$	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	$0.0529673\pi$
$449$			7.01947i			0.331269i	−0.986187	+	0.165635i	$0.947033\pi$
$450$	−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	0.993030	+	0.117858i	$0.0376029\pi$
$457$	4.10385	+	15.3158i	0.191970	+	0.716442i	−0.801060	+	0.598584i	$0.795730\pi$
$458$	−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	0.863057	−	0.505106i	$-0.168547\pi$
$463$	7.70220	+	7.70220i	0.357951	+	0.357951i	−0.505106	+	0.863057i	$0.668547\pi$
$464$	−0.779853	−	0.450249i	−0.0362038	−	0.0209023i
$465$	−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	$-0.564475\pi$
$467$	2.47197	−	0.662362i	0.114389	−	0.0306504i	0.315559	+	0.948906i	$0.397808\pi$
$468$	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	$-0.136848\pi$
$479$	2.04728	+	3.54599i	0.0935425	+	0.162020i	−0.815457	+	0.578818i	$0.803514\pi$
$480$	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	0.563242	−	0.826292i	$-0.309554\pi$
$487$	14.0767	+	3.77185i	0.637878	+	0.170919i	0.0746360	+	0.997211i	$0.476221\pi$
$488$	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	0.883955	−	0.467572i	$-0.154871\pi$
$499$	20.5736	+	11.8782i	0.921002	+	0.531741i	0.0370477	+	0.999313i	$0.488205\pi$
$500$	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	$-0.558511\pi$
$503$	17.9504	−	17.9504i	0.800367	−	0.800367i	0.983153	+	0.182786i	$0.0585115\pi$
$504$		0			0
$505$	−13.2046	−	9.32611i	−0.587596	−	0.415007i
$506$	−0.698653	+	1.21010i	−0.0310589	+	0.0537956i
$507$	−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	$-0.711151\pi$
$509$	8.44887	−	14.6339i	0.374489	−	0.648635i	0.990250	+	0.139298i	$0.0444847\pi$
$510$	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	$-0.721922\pi$
$521$	−6.82841	+	3.94238i	−0.299158	+	0.172719i	0.342907	+	0.939370i	$0.388589\pi$
$522$	−0.619890	−	0.166099i	−0.0271319	−	0.00726996i
$523$	0.450757	+	1.68225i	0.0197102	+	0.0735595i	0.975080	−	0.221852i	$-0.0712101\pi$
$523$	0.450757	+	1.68225i	0.0197102	+	0.0735595i	−0.955370	+	0.295411i	$0.904543\pi$
$524$	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	0.195896	+	0.980625i	$0.437238\pi$
$541$	−17.4747	+	30.2671i	−0.751298	+	1.30129i	−0.947194	+	0.320661i	$0.896095\pi$
$542$	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	−0.620340	−	0.784333i	$-0.713005\pi$
$547$	3.83548	−	3.83548i	0.163993	−	0.163993i	0.784333	+	0.620340i	$0.213005\pi$
$548$	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	0.697941	−	0.716155i	$-0.254100\pi$
$557$	22.2863	+	5.97158i	0.944299	+	0.253024i	0.246358	+	0.969179i	$0.420766\pi$
$558$	−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	$-0.166339\pi$
$563$	32.4459	+	8.69386i	1.36743	+	0.366402i	0.500892	+	0.865510i	$0.333005\pi$
$564$	−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	0.494949	−	0.868922i	$-0.335187\pi$
$569$	−0.240575	−	0.138896i	−0.0100854	−	0.00582283i	−0.505034	+	0.863099i	$0.668520\pi$
$570$	−2.58297	+	28.2034i	−0.108189	+	1.18131i
$571$	1.55769	+	2.69800i	0.0651874	+	0.112908i	0.896777	−	0.442483i	$-0.145902\pi$
$571$	1.55769	+	2.69800i	0.0651874	+	0.112908i	−0.831590	+	0.555390i	$0.812569\pi$
$572$	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	0.248986	+	0.968507i	$0.419903\pi$
$577$	−10.8309	+	40.4214i	−0.450896	+	1.68277i	−0.699882	+	0.714259i	$0.746764\pi$
$578$	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	−0.994433	−	0.105375i	$-0.966396\pi$
$587$	−26.6462	−	26.6462i	−1.09981	−	1.09981i	−0.105375	−	0.994433i	$-0.533604\pi$
$588$		0			0
$589$			43.6482i			1.79849i
$590$	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	−0.981055	−	0.193732i	$-0.937941\pi$
$593$	−5.55952	−	20.7484i	−0.228302	−	0.852036i	0.752752	−	0.658304i	$-0.228726\pi$
$594$	−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	−0.0510705	−	0.998695i	$-0.516263\pi$
$599$	19.2930	−	11.1388i	0.788290	−	0.455119i	0.839360	+	0.543576i	$0.182930\pi$
$600$	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	$-0.588596\pi$
$607$	−0.786867	+	0.210840i	−0.0319380	+	0.00855775i	0.242815	+	0.970073i	$0.421929\pi$
$608$	−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	0.730632	+	0.682771i	$0.239225\pi$
$613$	−6.02876	+	22.4996i	−0.243499	+	0.908752i	−0.974132	+	0.225981i	$0.927441\pi$
$614$	10.7357	−	18.5947i	0.433257	−	0.750423i
$615$	15.5520	−	2.67714i	0.627117	−	0.107953i
$616$		0			0
$617$	−3.70013	+	3.70013i	−0.148962	+	0.148962i	−0.777654	−	0.628692i	$-0.783590\pi$
$617$	−3.70013	+	3.70013i	−0.148962	+	0.148962i	0.628692	+	0.777654i	$0.283590\pi$
$618$	−19.9703	+	5.35101i	−0.803322	+	0.215249i
$619$	−19.9420	−	34.5405i	−0.801536	−	1.38830i	−0.918605	−	0.395178i	$-0.870683\pi$
$619$	−19.9420	−	34.5405i	−0.801536	−	1.38830i	0.117068	−	0.993124i	$-0.462650\pi$
$620$	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	0.987572	−	0.157167i	$-0.0502359\pi$
$641$	9.05563	+	15.6848i	0.357676	+	0.619513i	−0.629896	+	0.776679i	$0.716903\pi$
$642$	21.4872	−	5.75748i	0.848032	−	0.227229i
$643$	−32.1062	+	32.1062i	−1.26614	+	1.26614i	−0.318082	+	0.948063i	$0.603039\pi$
$643$	−32.1062	+	32.1062i	−1.26614	+	1.26614i	−0.948063	+	0.318082i	$0.896961\pi$
$644$		0			0
$645$	−0.556214	+	0.787528i	−0.0219009	+	0.0310089i
$646$	42.5074	−	73.6251i	1.67243	−	2.89674i
$647$	−4.73187	+	17.6596i	−0.186029	+	0.694270i	0.808379	+	0.588663i	$0.200345\pi$
$647$	−4.73187	+	17.6596i	−0.186029	+	0.694270i	−0.994408	+	0.105607i	$0.966321\pi$
$648$	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	0.00131826	−	0.999999i	$-0.499580\pi$
$653$	12.8398	−	3.44041i	0.502459	−	0.134634i	0.501141	+	0.865366i	$0.332914\pi$
$654$	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	$0.0569577\pi$
$659$			9.13808i			0.355969i	−0.984033	+	0.177985i	$0.943042\pi$
$660$	5.02197	−	13.6253i	0.195480	−	0.530363i
$661$	−24.6676	+	14.2418i	−0.959458	+	0.553943i	−0.896006	−	0.444042i	$-0.853544\pi$
$661$	−24.6676	+	14.2418i	−0.959458	+	0.553943i	−0.0634519	+	0.997985i	$0.520211\pi$
$662$	−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	0.999319	+	0.0368867i	$0.0117441\pi$
$673$	26.8815	+	26.8815i	1.03621	+	1.03621i	0.0368867	+	0.999319i	$0.488256\pi$
$674$	−24.6354	−	14.2233i	−0.948922	−	0.547860i
$675$	−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	$-0.593689\pi$
$677$	−1.63505	+	0.438111i	−0.0628402	+	0.0168380i	0.227262	+	0.973834i	$0.427023\pi$
$678$	−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	−0.946945	−	0.321395i	$-0.895848\pi$
$683$	0.884144	−	3.29967i	0.0338308	−	0.126258i	0.980776	+	0.195137i	$0.0625150\pi$
$684$	−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	$-0.624609\pi$
$691$	−36.0875	−	20.8351i	−1.37283	−	0.792606i	−0.991284	+	0.131743i	$0.957943\pi$
$692$	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	0.844326	−	0.535830i	$-0.180001\pi$
$709$	21.3668	+	12.3361i	0.802446	+	0.463293i	−0.0418795	+	0.999123i	$0.513335\pi$
$710$	−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	0.439925	+	0.898035i	$0.355005\pi$
$719$	−14.9558	+	25.9043i	−0.557758	+	0.966066i	−0.997683	+	0.0680313i	$0.978328\pi$
$720$	−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	0.993539	+	0.113491i	$0.0362034\pi$
$727$	29.8488	+	29.8488i	1.10703	+	1.10703i	0.113491	+	0.993539i	$0.463797\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$	−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	$-0.0511296\pi$
$733$	1.41545	+	5.28252i	0.0522807	+	0.195114i	−0.934846	+	0.355053i	$0.884463\pi$
$734$	−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	−0.297002	−	0.954877i	$-0.595987\pi$
$739$	10.3694	−	5.98677i	0.381444	−	0.220227i	0.678446	+	0.734650i	$0.262654\pi$
$740$	−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	0.450864	−	0.892593i	$-0.351116\pi$
$743$	−12.0406	−	12.0406i	−0.441728	−	0.441728i	−0.892593	+	0.450864i	$0.851116\pi$
$744$	5.69312	+	3.28692i	0.208720	+	0.120504i
$745$	−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	−0.557756	−	0.830005i	$-0.688337\pi$
$751$	12.0559	−	20.8815i	0.439928	−	0.761977i	0.997683	+	0.0680281i	$0.0216707\pi$
$752$	−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	0.0667825	−	0.997768i	$-0.478727\pi$
$757$	29.2896	−	29.2896i	1.06455	−	1.06455i	0.997768	−	0.0667825i	$-0.0212733\pi$
$758$	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	$-0.134255\pi$
$761$	27.9728	+	16.1501i	1.01401	+	0.585440i	0.101648	+	0.994820i	$0.467589\pi$
$762$	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	0.667979	−	0.744180i	$-0.267160\pi$
$773$	24.3102	+	6.51389i	0.874376	+	0.234288i	0.206397	+	0.978468i	$0.433826\pi$
$774$	−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	−0.778353	−	0.627827i	$-0.783945\pi$
$787$	5.88096	−	21.9481i	0.209634	−	0.782364i	0.987987	−	0.154537i	$-0.0493886\pi$
$788$	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	$-0.0291235\pi$
$797$	25.5337	+	25.5337i	0.904451	+	0.904451i	−0.0913664	+	0.995817i	$0.529123\pi$
$798$		0			0
$799$		−	5.28605i		−	0.187007i
$800$	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	−0.856770	−	0.515699i	$-0.827532\pi$
$809$	−23.8507	+	13.7702i	−0.838546	+	0.484135i	0.0182236	+	0.999834i	$0.494199\pi$
$810$	−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	−0.00418940	+	0.999991i	$0.501334\pi$
$821$	−24.8741	+	43.0832i	−0.868113	+	1.50361i	−0.863923	+	0.503624i	$0.832000\pi$
$822$	5.79328	−	21.6208i	0.202064	−	0.754113i
$823$	−2.23428	+	8.33846i	−0.0778822	+	0.290660i	−0.993871	−	0.110543i	$-0.964741\pi$
$823$	−2.23428	+	8.33846i	−0.0778822	+	0.290660i	0.915989	+	0.401203i	$0.131408\pi$
$824$	4.45077	−	7.70896i	0.155050	−	0.268555i
$825$	−12.0614	−	5.74409i	−0.419925	−	0.199984i
$826$		0			0
$827$	−4.96734	+	4.96734i	−0.172731	+	0.172731i	−0.788178	−	0.615447i	$-0.788976\pi$
$827$	−4.96734	+	4.96734i	−0.172731	+	0.172731i	0.615447	+	0.788178i	$0.288976\pi$
$828$	−0.583305	+	0.156296i	−0.0202713	+	0.00543167i
$829$	−14.1750	−	24.5518i	−0.492318	−	0.852720i	0.507643	−	0.861568i	$-0.330517\pi$
$829$	−14.1750	−	24.5518i	−0.492318	−	0.852720i	−0.999961	+	0.00884765i	$0.997184\pi$
$830$	−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	−0.390184	−	0.920737i	$-0.627589\pi$
$853$	15.4954	−	15.4954i	0.530553	−	0.530553i	0.920737	+	0.390184i	$0.127589\pi$
$854$		0			0
$855$	10.9903	+	7.76222i	0.375861	+	0.265462i
$856$	−4.78885	+	8.29453i	−0.163680	+	0.283501i
$857$	6.52792	−	24.3625i	0.222989	−	0.832208i	−0.760211	−	0.649677i	$-0.774904\pi$
$857$	6.52792	−	24.3625i	0.222989	−	0.832208i	0.983200	−	0.182531i	$-0.0584291\pi$
$858$	2.52610	−	9.42753i	0.0862396	−	0.321851i
$859$	8.63556	−	14.9572i	0.294641	−	0.510334i	−0.680260	−	0.732971i	$-0.738133\pi$
$859$	8.63556	−	14.9572i	0.294641	−	0.510334i	0.974901	+	0.222637i	$0.0714665\pi$
$860$	−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	−0.326613	−	0.945158i	$-0.605907\pi$
$863$	−4.02135	+	1.07752i	−0.136888	+	0.0366791i	0.189724	+	0.981837i	$0.439241\pi$
$864$	−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	0.893323	−	0.449416i	$-0.148368\pi$
$877$	−3.11025	−	11.6076i	−0.105026	−	0.391961i	−0.998348	+	0.0574555i	$0.981701\pi$
$878$	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	0.987350	−	0.158559i	$-0.0506848\pi$
$883$	24.6278	+	24.6278i	0.828791	+	0.828791i	−0.158559	+	0.987350i	$0.550685\pi$
$884$	−24.5194	−	14.1563i	−0.824678	−	0.476128i
$885$	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	$-0.577797\pi$
$887$	1.00060	−	0.268110i	0.0335969	−	0.00900226i	0.275578	+	0.961279i	$0.411131\pi$
$888$	−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	0.737092	−	0.675792i	$-0.236198\pi$
$907$	31.2469	+	8.37259i	1.03754	+	0.278007i	0.300445	+	0.953799i	$0.402865\pi$
$908$	−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	0.693705	−	0.720260i	$-0.255977\pi$
$919$	12.6351	+	7.29488i	0.416794	+	0.240636i	−0.276911	+	0.960896i	$0.589311\pi$
$920$	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	$-0.968718\pi$
$929$	−12.5763	+	21.7828i	−0.412615	+	0.714669i	0.582560	+	0.812788i	$0.302051\pi$
$930$	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	$-0.477324\pi$
$937$	−28.3540	−	28.3540i	−0.926286	−	0.926286i	−0.997464	+	0.0711778i	$0.977324\pi$
$938$		0			0
$939$		−	31.2405i		−	1.01950i
$940$	−4.01602	−	1.48021i	−0.130988	−	0.0482793i
$941$	0.0926410	−	0.0534863i	0.00302001	−	0.00174360i	−0.498489	−	0.866896i	$-0.666112\pi$
$941$	0.0926410	−	0.0534863i	0.00302001	−	0.00174360i	0.501509	+	0.865152i	$0.332778\pi$
$942$	−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	0.986619	+	0.163045i	$0.0521316\pi$
$947$	6.57640	+	24.5435i	0.213704	+	0.797556i	−0.772914	+	0.634511i	$0.781202\pi$
$948$	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	0.999532	+	0.0305973i	$0.00974093\pi$
$953$	31.8008	+	31.8008i	1.03013	+	1.03013i	0.0305973	+	0.999532i	$0.490259\pi$
$954$	−12.8648	−	7.42748i	−0.416512	−	0.240473i
$955$	−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	−0.703706	−	0.710491i	$-0.748473\pi$
$967$	0.210995	−	0.210995i	0.00678513	−	0.00678513i	0.710491	+	0.703706i	$0.248473\pi$
$968$	−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	−0.999989	−	0.00464820i	$-0.998520\pi$
$971$	−46.8662	−	27.0582i	−1.50401	−	0.868340i	−0.504020	−	0.863692i	$-0.668146\pi$
$972$	−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	−0.335375	−	0.942085i	$-0.608863\pi$
$977$	−34.2846	−	9.18653i	−1.09686	−	0.293903i	−0.761486	+	0.648181i	$0.775530\pi$
$978$	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	$-0.425524\pi$
$983$	−1.68510	−	0.451521i	−0.0537463	−	0.0144013i	−0.285592	+	0.958351i	$0.592190\pi$
$984$	−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	−0.933270	−	0.359177i	$-0.883058\pi$
$991$	−24.4818	−	42.4038i	−0.777691	−	1.34700i	0.155579	−	0.987823i	$-0.450276\pi$
$992$	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	0.861026	+	0.508562i	$0.169823\pi$
$997$	−4.38661	+	16.3710i	−0.138925	+	0.518476i	−0.999951	+	0.00991437i	$0.996844\pi$
$998$	−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.313.8		32
5.2	odd	4	inner	735.2.v.a.607.2		32
7.2	even	3		105.2.m.a.13.7	✓	16
7.3	odd	6	inner	735.2.v.a.178.2		32
7.4	even	3	inner	735.2.v.a.178.1		32
7.5	odd	6		105.2.m.a.13.8	yes	16
7.6	odd	2	inner	735.2.v.a.313.7		32
21.2	odd	6		315.2.p.e.118.1		16
21.5	even	6		315.2.p.e.118.2		16
28.19	even	6		1680.2.cz.d.433.1		16
28.23	odd	6		1680.2.cz.d.433.8		16
35.2	odd	12		105.2.m.a.97.8	yes	16
35.9	even	6		525.2.m.b.118.2		16
35.12	even	12		105.2.m.a.97.7	yes	16
35.17	even	12	inner	735.2.v.a.472.8		32
35.19	odd	6		525.2.m.b.118.1		16
35.23	odd	12		525.2.m.b.307.1		16
35.27	even	4	inner	735.2.v.a.607.1		32
35.32	odd	12	inner	735.2.v.a.472.7		32
35.33	even	12		525.2.m.b.307.2		16
105.2	even	12		315.2.p.e.307.2		16
105.47	odd	12		315.2.p.e.307.1		16
140.47	odd	12		1680.2.cz.d.97.8		16
140.107	even	12		1680.2.cz.d.97.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.7	✓	16	7.2	even	3
105.2.m.a.13.8	yes	16	7.5	odd	6
105.2.m.a.97.7	yes	16	35.12	even	12
105.2.m.a.97.8	yes	16	35.2	odd	12
315.2.p.e.118.1		16	21.2	odd	6
315.2.p.e.118.2		16	21.5	even	6
315.2.p.e.307.1		16	105.47	odd	12
315.2.p.e.307.2		16	105.2	even	12
525.2.m.b.118.1		16	35.19	odd	6
525.2.m.b.118.2		16	35.9	even	6
525.2.m.b.307.1		16	35.23	odd	12
525.2.m.b.307.2		16	35.33	even	12
735.2.v.a.178.1		32	7.4	even	3	inner
735.2.v.a.178.2		32	7.3	odd	6	inner
735.2.v.a.313.7		32	7.6	odd	2	inner
735.2.v.a.313.8		32	1.1	even	1	trivial
735.2.v.a.472.7		32	35.32	odd	12	inner
735.2.v.a.472.8		32	35.17	even	12	inner
735.2.v.a.607.1		32	35.27	even	4	inner
735.2.v.a.607.2		32	5.2	odd	4	inner
1680.2.cz.d.97.1		16	140.107	even	12
1680.2.cz.d.97.8		16	140.47	odd	12
1680.2.cz.d.433.1		16	28.19	even	6
1680.2.cz.d.433.8		16	28.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.544785 + 2.03317i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-2.10492 + 1.21528i) q^{4} +(0.936763 + 2.03039i) q^{5} +2.10489i q^{6} +(-0.640825 - 0.640825i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(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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