LMFDB - Embedded newform 630.2.bz.a.223.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(13,630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(630, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9, 6]))

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

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

chi := DirichletCharacter("630.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.bz (of order $12$, degree $4$, 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:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			223.27
Character	$\chi$	$=$	630.223
Dual form			630.2.bz.a.517.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(-1.68882 - 0.384583i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.94548 - 1.10233i) q^{5} +(-0.0656192 - 1.73081i) q^{6} +(-2.64469 + 0.0747801i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.70419 + 1.29898i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(-1.68882 - 0.384583i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.94548 - 1.10233i) q^{5} +(-0.0656192 - 1.73081i) q^{6} +(-2.64469 + 0.0747801i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.70419 + 1.29898i) q^{9} +(0.561239 - 2.16449i) q^{10} +(0.535848 - 0.928117i) q^{11} +(1.65485 - 0.511349i) q^{12} +(-1.78804 - 0.479104i) q^{13} +(-0.756729 - 2.53522i) q^{14} +(2.86161 + 2.60982i) q^{15} +(0.500000 - 0.866025i) q^{16} +(5.63237 + 5.63237i) q^{17} +(-0.554820 + 2.94825i) q^{18} +4.65324 q^{19} +(2.23599 - 0.0180954i) q^{20} +(4.49516 + 0.890814i) q^{21} +(1.03518 + 0.277376i) q^{22} +(1.07581 - 4.01496i) q^{23} +(0.922232 + 1.46611i) q^{24} +(2.56975 + 4.28910i) q^{25} -1.85112i q^{26} +(-4.06732 - 3.23372i) q^{27} +(2.25298 - 1.38711i) q^{28} +(0.832365 + 0.480566i) q^{29} +(-1.78025 + 3.43958i) q^{30} +(4.15818 - 2.40073i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.26189 + 1.36134i) q^{33} +(-3.98269 + 6.89822i) q^{34} +(5.22762 + 2.76983i) q^{35} +(-2.99139 + 0.227148i) q^{36} +(-5.99141 + 5.99141i) q^{37} +(1.20435 + 4.49469i) q^{38} +(2.83542 + 1.49677i) q^{39} +(0.596197 + 2.15512i) q^{40} +(4.30034 - 2.48280i) q^{41} +(0.302973 + 4.57255i) q^{42} +(-1.88694 + 0.505604i) q^{43} +1.07170i q^{44} +(-3.82904 - 5.50803i) q^{45} +4.15660 q^{46} +(11.8221 - 3.16773i) q^{47} +(-1.17747 + 1.27027i) q^{48} +(6.98882 - 0.395541i) q^{49} +(-3.47785 + 3.59229i) q^{50} +(-7.34592 - 11.6781i) q^{51} +(1.78804 - 0.479104i) q^{52} +(2.68452 + 2.68452i) q^{53} +(2.07083 - 4.76567i) q^{54} +(-2.06557 + 1.21495i) q^{55} +(1.92296 + 1.81720i) q^{56} +(-7.85847 - 1.78956i) q^{57} +(-0.248759 + 0.928383i) q^{58} +(4.14219 + 7.17448i) q^{59} +(-3.78314 - 0.829365i) q^{60} +(-10.3754 - 5.99025i) q^{61} +(3.39514 + 3.39514i) q^{62} +(-7.24890 - 3.23318i) q^{63} +1.00000i q^{64} +(2.95046 + 2.90309i) q^{65} +(-1.64155 - 0.866548i) q^{66} +(1.81119 + 0.485306i) q^{67} +(-7.69396 - 2.06159i) q^{68} +(-3.36092 + 6.36679i) q^{69} +(-1.32245 + 5.76638i) q^{70} +0.780557 q^{71} +(-0.993637 - 2.83067i) q^{72} +(-1.59208 + 1.59208i) q^{73} +(-7.33795 - 4.23657i) q^{74} +(-2.69033 - 8.23178i) q^{75} +(-4.02983 + 2.32662i) q^{76} +(-1.34775 + 2.49466i) q^{77} +(-0.711908 + 3.12619i) q^{78} +(-4.01966 - 2.32075i) q^{79} +(-1.92738 + 1.13367i) q^{80} +(5.62531 + 7.02537i) q^{81} +(3.51121 + 3.51121i) q^{82} +(-1.32374 - 4.94028i) q^{83} +(-4.33833 + 1.47611i) q^{84} +(-4.74893 - 17.1664i) q^{85} +(-0.976751 - 1.69178i) q^{86} +(-1.22089 - 1.13170i) q^{87} +(-1.03518 + 0.277376i) q^{88} +11.1343 q^{89} +(4.32932 - 5.12416i) q^{90} +(4.76465 + 1.13337i) q^{91} +(1.07581 + 4.01496i) q^{92} +(-7.94567 + 2.45522i) q^{93} +(6.11958 + 10.5994i) q^{94} +(-9.05278 - 5.12939i) q^{95} +(-1.53173 - 0.808576i) q^{96} +(1.36089 - 0.364649i) q^{97} +(2.19090 + 6.64830i) q^{98} +(2.65464 - 1.81375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	−1.68882	−	0.384583i	−0.975038	−	0.222039i
$3$	−1.68882	−	0.384583i	−0.975038	−	0.222039i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−1.94548	−	1.10233i	−0.870043	−	0.492975i
$5$	−1.94548	−	1.10233i	−0.870043	−	0.492975i
$6$	−0.0656192	−	1.73081i	−0.0267889	−	0.706599i
$7$	−2.64469	+	0.0747801i	−0.999600	+	0.0282642i
$7$	−2.64469	+	0.0747801i	−0.999600	+	0.0282642i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	2.70419	+	1.29898i	0.901397	+	0.432993i
$10$	0.561239	−	2.16449i	0.177479	−	0.684471i
$11$	0.535848	−	0.928117i	0.161564	−	0.279838i	−0.773866	−	0.633350i	$-0.781679\pi$
$11$	0.535848	−	0.928117i	0.161564	−	0.279838i	0.935430	+	0.353512i	$0.115013\pi$
$12$	1.65485	−	0.511349i	0.477713	−	0.147614i
$13$	−1.78804	−	0.479104i	−0.495914	−	0.132880i	0.00218924	−	0.999998i	$-0.499303\pi$
$13$	−1.78804	−	0.479104i	−0.495914	−	0.132880i	−0.498103	+	0.867118i	$0.665970\pi$
$14$	−0.756729	−	2.53522i	−0.202244	−	0.677567i
$15$	2.86161	+	2.60982i	0.738865	+	0.673853i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	5.63237	+	5.63237i	1.36605	+	1.36605i	0.865991	+	0.500060i	$0.166689\pi$
$17$	5.63237	+	5.63237i	1.36605	+	1.36605i	0.500060	+	0.865991i	$0.333311\pi$
$18$	−0.554820	+	2.94825i	−0.130772	+	0.694909i
$19$	4.65324			1.06753			0.533764	−	0.845634i	$-0.320777\pi$
$19$	4.65324			1.06753			0.533764	+	0.845634i	$0.320777\pi$
$20$	2.23599	−	0.0180954i	0.499984	−	0.00404624i
$21$	4.49516	+	0.890814i	0.980924	+	0.194392i
$22$	1.03518	+	0.277376i	0.220701	+	0.0591367i
$23$	1.07581	−	4.01496i	0.224321	−	0.837178i	−0.758354	−	0.651843i	$-0.773996\pi$
$23$	1.07581	−	4.01496i	0.224321	−	0.837178i	0.982675	−	0.185335i	$-0.0593370\pi$
$24$	0.922232	+	1.46611i	0.188250	+	0.299269i
$25$	2.56975	+	4.28910i	0.513951	+	0.857820i
$26$		−	1.85112i		−	0.363034i
$27$	−4.06732	−	3.23372i	−0.782755	−	0.622329i
$28$	2.25298	−	1.38711i	0.425774	−	0.262139i
$29$	0.832365	+	0.480566i	0.154566	+	0.0892389i	0.575288	−	0.817951i	$-0.304890\pi$
$29$	0.832365	+	0.480566i	0.154566	+	0.0892389i	−0.420722	+	0.907190i	$0.638223\pi$
$30$	−1.78025	+	3.43958i	−0.325028	+	0.627978i
$31$	4.15818	−	2.40073i	0.746831	−	0.431183i	−0.0777168	−	0.996975i	$-0.524763\pi$
$31$	4.15818	−	2.40073i	0.746831	−	0.431183i	0.824548	+	0.565792i	$0.191430\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−1.26189	+	1.36134i	−0.219666	+	0.236979i
$34$	−3.98269	+	6.89822i	−0.683025	+	1.18303i
$35$	5.22762	+	2.76983i	0.883629	+	0.468187i
$36$	−2.99139	+	0.227148i	−0.498565	+	0.0378581i
$37$	−5.99141	+	5.99141i	−0.984982	+	0.984982i	−0.999889	−	0.0149065i	$-0.995255\pi$
$37$	−5.99141	+	5.99141i	−0.984982	+	0.984982i	0.0149065	+	0.999889i	$0.495255\pi$
$38$	1.20435	+	4.49469i	0.195371	+	0.729135i
$39$	2.83542	+	1.49677i	0.454030	+	0.239675i
$40$	0.596197	+	2.15512i	0.0942670	+	0.340755i
$41$	4.30034	−	2.48280i	0.671600	−	0.387749i	−0.125082	−	0.992146i	$-0.539920\pi$
$41$	4.30034	−	2.48280i	0.671600	−	0.387749i	0.796683	+	0.604398i	$0.206586\pi$
$42$	0.302973	+	4.57255i	0.0467497	+	0.705560i
$43$	−1.88694	+	0.505604i	−0.287755	+	0.0771039i	−0.399809	−	0.916598i	$-0.630924\pi$
$43$	−1.88694	+	0.505604i	−0.287755	+	0.0771039i	0.112054	+	0.993702i	$0.464257\pi$
$44$			1.07170i			0.161564i
$45$	−3.82904	−	5.50803i	−0.570800	−	0.821089i
$46$	4.15660			0.612857
$47$	11.8221	−	3.16773i	1.72443	−	0.462061i	0.745546	−	0.666455i	$-0.232189\pi$
$47$	11.8221	−	3.16773i	1.72443	−	0.462061i	0.978889	+	0.204394i	$0.0655223\pi$
$48$	−1.17747	+	1.27027i	−0.169953	+	0.183347i
$49$	6.98882	−	0.395541i	0.998402	−	0.0565058i
$50$	−3.47785	+	3.59229i	−0.491842	+	0.508027i
$51$	−7.34592	−	11.6781i	−1.02863	−	1.63527i
$52$	1.78804	−	0.479104i	0.247957	−	0.0664398i
$53$	2.68452	+	2.68452i	0.368748	+	0.368748i	0.867020	−	0.498273i	$-0.166032\pi$
$53$	2.68452	+	2.68452i	0.368748	+	0.368748i	−0.498273	+	0.867020i	$0.666032\pi$
$54$	2.07083	−	4.76567i	0.281805	−	0.648526i
$55$	−2.06557	+	1.21495i	−0.278521	+	0.163824i
$56$	1.92296	+	1.81720i	0.256966	+	0.242834i
$57$	−7.85847	−	1.78956i	−1.04088	−	0.237033i
$58$	−0.248759	+	0.928383i	−0.0326637	+	0.121903i
$59$	4.14219	+	7.17448i	0.539267	+	0.934037i	0.998944	+	0.0459510i	$0.0146318\pi$
$59$	4.14219	+	7.17448i	0.539267	+	0.934037i	−0.459677	+	0.888086i	$0.652035\pi$
$60$	−3.78314	−	0.829365i	−0.488401	−	0.107071i
$61$	−10.3754	−	5.99025i	−1.32844	−	0.766973i	−0.343378	−	0.939197i	$-0.611571\pi$
$61$	−10.3754	−	5.99025i	−1.32844	−	0.766973i	−0.985058	+	0.172224i	$0.944905\pi$
$62$	3.39514	+	3.39514i	0.431183	+	0.431183i
$63$	−7.24890	−	3.23318i	−0.913276	−	0.407342i
$64$			1.00000i			0.125000i
$65$	2.95046	+	2.90309i	0.365960	+	0.360084i
$66$	−1.64155	−	0.866548i	−0.202061	−	0.106665i
$67$	1.81119	+	0.485306i	0.221272	+	0.0592896i	0.367752	−	0.929924i	$-0.380128\pi$
$67$	1.81119	+	0.485306i	0.221272	+	0.0592896i	−0.146480	+	0.989214i	$0.546794\pi$
$68$	−7.69396	−	2.06159i	−0.933030	−	0.250005i
$69$	−3.36092	+	6.36679i	−0.404608	+	0.766472i
$70$	−1.32245	+	5.76638i	−0.158062	+	0.689214i
$71$	0.780557			0.0926351			0.0463175	−	0.998927i	$-0.485251\pi$
$71$	0.780557			0.0926351			0.0463175	+	0.998927i	$0.485251\pi$
$72$	−0.993637	−	2.83067i	−0.117101	−	0.333598i
$73$	−1.59208	+	1.59208i	−0.186339	+	0.186339i	−0.794111	−	0.607772i	$-0.792063\pi$
$73$	−1.59208	+	1.59208i	−0.186339	+	0.186339i	0.607772	+	0.794111i	$0.292063\pi$
$74$	−7.33795	−	4.23657i	−0.853020	−	0.492491i
$75$	−2.69033	−	8.23178i	−0.310652	−	0.950524i
$76$	−4.02983	+	2.32662i	−0.462253	+	0.266882i
$77$	−1.34775	+	2.49466i	−0.153590	+	0.284292i
$78$	−0.711908	+	3.12619i	−0.0806077	+	0.353972i
$79$	−4.01966	−	2.32075i	−0.452247	−	0.261105i	0.256532	−	0.966536i	$-0.417420\pi$
$79$	−4.01966	−	2.32075i	−0.452247	−	0.261105i	−0.708779	+	0.705431i	$0.750753\pi$
$80$	−1.92738	+	1.13367i	−0.215488	+	0.126748i
$81$	5.62531	+	7.02537i	0.625035	+	0.780597i
$82$	3.51121	+	3.51121i	0.387749	+	0.387749i
$83$	−1.32374	−	4.94028i	−0.145300	−	0.542266i	−0.999742	−	0.0227197i	$-0.992767\pi$
$83$	−1.32374	−	4.94028i	−0.145300	−	0.542266i	0.854442	−	0.519547i	$-0.173899\pi$
$84$	−4.33833	+	1.47611i	−0.473350	+	0.161057i
$85$	−4.74893	−	17.1664i	−0.515094	−	1.86195i
$86$	−0.976751	−	1.69178i	−0.105326	−	0.182430i
$87$	−1.22089	−	1.13170i	−0.130894	−	0.121331i
$88$	−1.03518	+	0.277376i	−0.110351	+	0.0295683i
$89$	11.1343			1.18024			0.590119	−	0.807317i	$-0.299081\pi$
$89$	11.1343			1.18024			0.590119	+	0.807317i	$0.299081\pi$
$90$	4.32932	−	5.12416i	0.456351	−	0.540133i
$91$	4.76465	+	1.13337i	0.499471	+	0.118810i
$92$	1.07581	+	4.01496i	0.112161	+	0.418589i
$93$	−7.94567	+	2.45522i	−0.823928	+	0.254594i
$94$	6.11958	+	10.5994i	0.631187	+	1.09325i
$95$	−9.05278	−	5.12939i	−0.928795	−	0.526265i
$96$	−1.53173	−	0.808576i	−0.156332	−	0.0825249i
$97$	1.36089	−	0.364649i	0.138177	−	0.0370245i	−0.189067	−	0.981964i	$-0.560546\pi$
$97$	1.36089	−	0.364649i	0.138177	−	0.0370245i	0.327245	+	0.944940i	$0.393880\pi$
$98$	2.19090	+	6.64830i	0.221315	+	0.671580i
$99$	2.65464	−	1.81375i	0.266801	−	0.182289i
$100$	−4.37002	−	2.42959i	−0.437002	−	0.242959i
$101$	15.6965	+	9.06240i	1.56186	+	0.901743i	0.997069	+	0.0765120i	$0.0243783\pi$
$101$	15.6965	+	9.06240i	1.56186	+	0.901743i	0.564796	+	0.825231i	$0.308955\pi$
$102$	9.37896	−	10.1181i	0.928655	−	1.00185i
$103$	−14.5803	−	3.90677i	−1.43664	−	0.384946i	−0.545283	−	0.838252i	$-0.683578\pi$
$103$	−14.5803	−	3.90677i	−1.43664	−	0.384946i	−0.891355	+	0.453306i	$0.850244\pi$
$104$	0.925559	+	1.60311i	0.0907585	+	0.157198i
$105$	−7.76326	−	6.68819i	−0.757616	−	0.652700i
$106$	−1.89825	+	3.28786i	−0.184374	+	0.319345i
$107$	4.87915	−	4.87915i	0.471685	−	0.471685i	−0.430774	−	0.902460i	$-0.641760\pi$
$107$	4.87915	−	4.87915i	0.471685	−	0.471685i	0.902460	+	0.430774i	$0.141760\pi$
$108$	5.13926	+	0.766824i	0.494525	+	0.0737877i
$109$			4.45261i			0.426483i	0.977000	+	0.213241i	$0.0684021\pi$
$109$			4.45261i			0.426483i	−0.977000	+	0.213241i	$0.931598\pi$
$110$	−1.70816	−	1.68073i	−0.162867	−	0.160252i
$111$	12.4226	−	7.81420i	1.17910	−	0.741691i
$112$	−1.25759	+	2.32776i	−0.118831	+	0.219953i
$113$	2.09360	−	7.81341i	0.196949	−	0.735023i	−0.794805	−	0.606865i	$-0.792427\pi$
$113$	2.09360	−	7.81341i	0.196949	−	0.735023i	0.991754	−	0.128158i	$-0.0409066\pi$
$114$	−0.305342	−	8.05387i	−0.0285979	−	0.754314i
$115$	−6.51875	+	6.62512i	−0.607877	+	0.617796i
$116$	−0.961133			−0.0892389
$117$	−4.21286	−	3.61822i	−0.389479	−	0.334504i
$118$	−5.85793	+	5.85793i	−0.539267	+	0.539267i
$119$	−15.3171	−	14.4747i	−1.40412	−	1.32689i
$120$	−0.178044	−	3.86889i	−0.0162531	−	0.353180i
$121$	4.92573	+	8.53162i	0.447794	+	0.775602i
$122$	3.10078	−	11.5723i	0.280732	−	1.04770i
$123$	−8.21732	+	2.53916i	−0.740931	+	0.228948i
$124$	−2.40073	+	4.15818i	−0.215592	+	0.373415i
$125$	−0.271407	−	11.1770i	−0.0242753	−	0.999705i
$126$	1.24686	−	7.83871i	0.111079	−	0.698328i
$127$	14.6310	−	14.6310i	1.29829	−	1.29829i	0.368771	−	0.929520i	$-0.379779\pi$
$127$	14.6310	−	14.6310i	1.29829	−	1.29829i	0.929520	−	0.368771i	$-0.120221\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	3.38114	−	0.128187i	0.297693	−	0.0112863i
$130$	−2.04054	+	3.60130i	−0.178967	+	0.315855i
$131$	−7.31548	+	4.22360i	−0.639157	+	0.369017i	−0.784290	−	0.620395i	$-0.786972\pi$
$131$	−7.31548	+	4.22360i	−0.639157	+	0.369017i	0.145133	+	0.989412i	$0.453639\pi$
$132$	0.412156	−	1.80990i	0.0358736	−	0.157531i
$133$	−12.3064	+	0.347970i	−1.06710	+	0.0301728i
$134$			1.87508i			0.161982i
$135$	4.34825	+	10.7746i	0.374238	+	0.927333i
$136$		−	7.96538i		−	0.683025i
$137$	3.47707	+	12.9766i	0.297066	+	1.10867i	0.939563	+	0.342377i	$0.111232\pi$
$137$	3.47707	+	12.9766i	0.297066	+	1.10867i	−0.642496	+	0.766289i	$0.722101\pi$
$138$	−7.01972	−	1.59855i	−0.597558	−	0.136078i
$139$	0.148558	+	0.257310i	0.0126005	+	0.0218247i	0.872257	−	0.489048i	$-0.162656\pi$
$139$	0.148558	+	0.257310i	0.0126005	+	0.0218247i	−0.859656	+	0.510873i	$0.829322\pi$
$140$	−5.91217	+	0.215065i	−0.499670	+	0.0181763i
$141$	−21.1836	+	0.803124i	−1.78398	+	0.0676353i
$142$	0.202023	+	0.753960i	0.0169534	+	0.0632709i
$143$	−1.40278	+	1.40278i	−0.117307	+	0.117307i
$144$	2.47704	−	1.69241i	0.206420	−	0.141034i
$145$	−1.08961	−	1.85247i	−0.0904868	−	0.153839i
$146$	−1.94990	−	1.12577i	−0.161375	−	0.0931696i
$147$	−11.9549	−	2.01978i	−0.986026	−	0.166589i
$148$	2.19301	−	8.18442i	0.180264	−	0.672756i
$149$	12.1510	−	7.01536i	0.995446	−	0.574721i	0.0885481	−	0.996072i	$-0.471777\pi$
$149$	12.1510	−	7.01536i	0.995446	−	0.574721i	0.906898	+	0.421351i	$0.138444\pi$
$150$	7.25498	−	4.72920i	0.592367	−	0.386137i
$151$	7.23079	−	12.5241i	0.588433	−	1.01920i	−0.406005	−	0.913871i	$-0.633078\pi$
$151$	7.23079	−	12.5241i	0.588433	−	1.01920i	0.994438	−	0.105325i	$-0.0335884\pi$
$152$	−3.29034	−	3.29034i	−0.266882	−	0.266882i
$153$	7.91469	+	22.5473i	0.639865	+	1.82284i
$154$	−2.75848	−	0.656163i	−0.222284	−	0.0528751i
$155$	−10.7360	+	0.0868840i	−0.862338	+	0.00697869i
$156$	−3.20393	+	0.121469i	−0.256519	+	0.00972529i
$157$	−3.65782	+	13.6512i	−0.291926	+	1.08948i	0.651703	+	0.758475i	$0.274055\pi$
$157$	−3.65782	+	13.6512i	−0.291926	+	1.08948i	−0.943628	+	0.331007i	$0.892612\pi$
$158$	1.20131	−	4.48335i	0.0955710	−	0.356676i
$159$	−3.50124	−	5.56609i	−0.277667	−	0.441419i
$160$	−1.59388	−	1.56829i	−0.126007	−	0.123984i
$161$	−2.54494	+	10.6988i	−0.200569	+	0.843183i
$162$	−5.33005	+	7.25194i	−0.418768	+	0.569766i
$163$	10.0304	+	10.0304i	0.785638	+	0.785638i	0.980776	−	0.195138i	$-0.0625154\pi$
$163$	10.0304	+	10.0304i	0.785638	+	0.785638i	−0.195138	+	0.980776i	$0.562515\pi$
$164$	−2.48280	+	4.30034i	−0.193874	+	0.335800i
$165$	3.95561	−	1.25744i	0.307944	−	0.0978917i
$166$	4.42934	−	2.55728i	0.343783	−	0.198483i
$167$	−4.11852	+	15.3705i	−0.318701	+	1.18941i	0.601793	+	0.798652i	$0.294453\pi$
$167$	−4.11852	+	15.3705i	−0.318701	+	1.18941i	−0.920494	+	0.390756i	$0.872213\pi$
$168$	−2.54866	−	3.80846i	−0.196633	−	0.293829i
$169$	−8.29078	−	4.78668i	−0.637752	−	0.368206i
$170$	15.3523	−	9.03009i	1.17747	−	0.692577i
$171$	12.5833	+	6.04446i	0.962267	+	0.462232i
$172$	1.38134	−	1.38134i	0.105326	−	0.105326i
$173$	−3.06488	−	11.4383i	−0.233019	−	0.869637i	−0.979032	−	0.203706i	$-0.934701\pi$
$173$	−3.06488	−	11.4383i	−0.233019	−	0.869637i	0.746013	−	0.665931i	$-0.231965\pi$
$174$	0.777149	−	1.47220i	0.0589155	−	0.111607i
$175$	−7.11695	−	11.1512i	−0.537991	−	0.842951i
$176$	−0.535848	−	0.928117i	−0.0403911	−	0.0699594i
$177$	−4.23621	−	13.7094i	−0.318413	−	1.03046i
$178$	2.88178	+	10.7549i	0.215998	+	0.806117i
$179$		−	20.1929i		−	1.50929i	−0.656133	−	0.754646i	$-0.727809\pi$
$179$		−	20.1929i		−	1.50929i	0.656133	−	0.754646i	$-0.272191\pi$
$180$	6.07007	+	2.85557i	0.452436	+	0.212842i
$181$		−	0.0470166i		−	0.00349472i	−0.999998	−	0.00174736i	$-0.999444\pi$
$181$		−	0.0470166i		−	0.00349472i	0.999998	−	0.00174736i	$-0.000556202\pi$
$182$	0.138427	+	4.89564i	0.0102609	+	0.362889i
$183$	15.2184	+	14.1066i	1.12498	+	1.04279i
$184$	−3.59972	+	2.07830i	−0.265375	+	0.153214i
$185$	18.2606	−	5.05166i	1.34255	−	0.371405i
$186$	−4.42805	−	7.03947i	−0.324680	−	0.516159i
$187$	8.24559	−	2.20940i	0.602978	−	0.161567i
$188$	−8.65440	+	8.65440i	−0.631187	+	0.631187i
$189$	10.9986	+	8.24804i	0.800032	+	0.599957i
$190$	2.61158	−	10.0719i	0.189464	−	0.730692i
$191$	−7.71765	+	13.3674i	−0.558430	+	0.967229i	0.439198	+	0.898390i	$0.355263\pi$
$191$	−7.71765	+	13.3674i	−0.558430	+	0.967229i	−0.997628	+	0.0688384i	$0.978071\pi$
$192$	0.384583	−	1.68882i	0.0277549	−	0.121880i
$193$	−2.33225	+	8.70407i	−0.167879	+	0.626532i	0.829777	+	0.558096i	$0.188468\pi$
$193$	−2.33225	+	8.70407i	−0.167879	+	0.626532i	−0.997655	+	0.0684367i	$0.978199\pi$
$194$	0.704448	+	1.22014i	0.0505764	+	0.0876009i
$195$	−3.86631	−	6.03748i	−0.276872	−	0.432353i
$196$	−5.85472	+	3.83696i	−0.418194	+	0.274068i
$197$	8.06515	−	8.06515i	0.574618	−	0.574618i	−0.358798	−	0.933415i	$-0.616813\pi$
$197$	8.06515	−	8.06515i	0.574618	−	0.574618i	0.933415	+	0.358798i	$0.116813\pi$
$198$	2.43902	+	2.09475i	0.173334	+	0.148868i
$199$	11.2548			0.797833			0.398916	−	0.916987i	$-0.369386\pi$
$199$	11.2548			0.797833			0.398916	+	0.916987i	$0.369386\pi$
$200$	1.21576	−	4.84994i	0.0859673	−	0.342943i
$201$	−2.87212	−	1.51614i	−0.202584	−	0.106941i
$202$	−4.69104	+	17.5072i	−0.330061	+	1.23180i
$203$	−2.23729	−	1.20871i	−0.157027	−	0.0848346i
$204$	12.2008	+	6.44061i	0.854229	+	0.450933i
$205$	−11.1031	+	0.0898544i	−0.775472	+	0.00627570i
$206$		−	15.0946i		−	1.05169i
$207$	8.12453	−	9.45978i	0.564694	−	0.657500i
$208$	−1.30894	+	1.30894i	−0.0907585	+	0.0907585i
$209$	2.49343	−	4.31875i	0.172474	−	0.298734i
$210$	4.45102	−	9.22976i	0.307149	−	0.636914i
$211$	7.87579	+	13.6413i	0.542192	+	0.939104i	0.998778	+	0.0494248i	$0.0157388\pi$
$211$	7.87579	+	13.6413i	0.542192	+	0.939104i	−0.456586	+	0.889679i	$0.650928\pi$
$212$	−3.66713	−	0.982604i	−0.251859	−	0.0674855i
$213$	−1.31822	−	0.300189i	−0.0903227	−	0.0205686i
$214$	5.97571	+	3.45008i	0.408491	+	0.235843i
$215$	4.22833	+	1.09638i	0.288370	+	0.0747727i
$216$	0.589442	+	5.16261i	0.0401065	+	0.351271i
$217$	−10.8176	+	6.66013i	−0.734345	+	0.452119i
$218$	−4.30089	+	1.15242i	−0.291293	+	0.0780518i
$219$	3.30102	−	2.07645i	0.223062	−	0.140313i
$220$	1.18136	−	2.08496i	0.0796472	−	0.140568i
$221$	−7.37242	−	12.7694i	−0.495923	−	0.858963i
$222$	10.7631	+	9.97683i	0.722374	+	0.669601i
$223$	3.21692	+	12.0057i	0.215421	+	0.803961i	0.986018	+	0.166639i	$0.0532914\pi$
$223$	3.21692	+	12.0057i	0.215421	+	0.803961i	−0.770597	+	0.637322i	$0.780042\pi$
$224$	−2.57393	−	0.612265i	−0.171978	−	0.0409087i
$225$	1.37766	+	14.9366i	0.0918442	+	0.995773i
$226$	8.08903			0.538075
$227$	−15.8853	+	4.25644i	−1.05434	+	0.282510i	−0.744045	−	0.668130i	$-0.767095\pi$
$227$	−15.8853	+	4.25644i	−1.05434	+	0.282510i	−0.310297	+	0.950640i	$0.600428\pi$
$228$	7.70041	−	2.37943i	0.509972	−	0.157582i
$229$	−1.71609	−	2.97235i	−0.113402	−	0.196418i	0.803738	−	0.594984i	$-0.202842\pi$
$229$	−1.71609	−	2.97235i	−0.113402	−	0.196418i	−0.917140	+	0.398565i	$0.869508\pi$
$230$	−8.08656	−	4.58192i	−0.533212	−	0.302123i
$231$	3.23550	−	3.69469i	0.212880	−	0.243093i
$232$	−0.248759	−	0.928383i	−0.0163319	−	0.0609513i
$233$	6.92139	+	6.92139i	0.453435	+	0.453435i	0.896493	−	0.443058i	$-0.146106\pi$
$233$	6.92139	+	6.92139i	0.453435	+	0.453435i	−0.443058	+	0.896493i	$0.646106\pi$
$234$	2.40456	−	5.00578i	0.157191	−	0.327238i
$235$	−26.4915	−	6.86910i	−1.72812	−	0.448091i
$236$	−7.17448	−	4.14219i	−0.467019	−	0.269633i
$237$	5.89594	+	5.46521i	0.382982	+	0.355003i
$238$	10.0171	−	18.5415i	0.649315	−	1.20187i
$239$	−11.9152	+	6.87924i	−0.770730	+	0.444981i	−0.833135	−	0.553070i	$-0.813456\pi$
$239$	−11.9152	+	6.87924i	−0.770730	+	0.444981i	0.0624049	+	0.998051i	$0.480123\pi$
$240$	3.69098	−	1.17332i	0.238252	−	0.0757374i
$241$	11.8609	+	6.84791i	0.764030	+	0.441113i	0.830741	−	0.556660i	$-0.187917\pi$
$241$	11.8609	+	6.84791i	0.764030	+	0.441113i	−0.0667111	+	0.997772i	$0.521251\pi$
$242$	−6.96604	+	6.96604i	−0.447794	+	0.447794i
$243$	−6.79828	−	14.0280i	−0.436110	−	0.899894i
$244$	11.9805			0.766973
$245$	−14.0326	−	6.93444i	−0.896509	−	0.443025i
$246$	−4.57944	−	7.28014i	−0.291974	−	0.464165i
$247$	−8.32020	−	2.22939i	−0.529401	−	0.141853i
$248$	−4.63785	−	1.24271i	−0.294503	−	0.0789120i
$249$	0.335613	+	8.85231i	0.0212686	+	0.560993i
$250$	10.7260	−	3.15499i	0.678369	−	0.199539i
$251$		−	19.6030i		−	1.23733i	−0.785655	−	0.618665i	$-0.787674\pi$
$251$		−	19.6030i		−	1.23733i	0.785655	−	0.618665i	$-0.212326\pi$
$252$	7.89432	−	0.824434i	0.497295	−	0.0519345i
$253$	−3.14988	−	3.14988i	−0.198032	−	0.198032i
$254$	17.9192	+	10.3457i	1.12435	+	0.649146i
$255$	1.41819	+	30.8172i	0.0888102	+	1.92984i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.442111	−	1.64998i	0.0275781	−	0.102923i	−0.950765	−	0.309913i	$-0.899700\pi$
$257$	0.442111	−	1.64998i	0.0275781	−	0.102923i	0.978343	+	0.206990i	$0.0663668\pi$
$258$	0.998922	+	3.23275i	0.0621902	+	0.201262i
$259$	15.3974	−	16.2935i	0.956749	−	1.01243i
$260$	−4.00672	−	1.03892i	−0.248486	−	0.0644311i
$261$	1.62663	+	2.38077i	0.100686	+	0.147366i
$262$	−5.97307	−	5.97307i	−0.369017	−	0.369017i
$263$	14.7720	−	3.95814i	0.910879	−	0.244069i	0.227196	−	0.973849i	$-0.427044\pi$
$263$	14.7720	−	3.95814i	0.910879	−	0.244069i	0.683682	+	0.729780i	$0.260377\pi$
$264$	1.85490	−	0.0703239i	0.114161	−	0.00432813i
$265$	−2.26346	−	8.18190i	−0.139043	−	0.502610i
$266$	−3.52125	−	11.7970i	−0.215901	−	0.723322i
$267$	−18.8038	−	4.28207i	−1.15078	−	0.262059i
$268$	−1.81119	+	0.485306i	−0.110636	+	0.0296448i
$269$	−0.819688			−0.0499772			−0.0249886	−	0.999688i	$-0.507955\pi$
$269$	−0.819688			−0.0499772			−0.0249886	+	0.999688i	$0.507955\pi$
$270$	−9.28208	+	6.98877i	−0.564890	+	0.425323i
$271$			22.4996i			1.36675i	0.730066	+	0.683376i	$0.239489\pi$
$271$			22.4996i			1.36675i	−0.730066	+	0.683376i	$0.760511\pi$
$272$	7.69396	−	2.06159i	0.466515	−	0.125002i
$273$	−7.61074	−	3.74646i	−0.460623	−	0.226746i
$274$	−11.6345	+	6.71718i	−0.702866	+	0.405800i
$275$	5.35778	−	0.0867241i	0.323086	−	0.00522966i
$276$	−0.272752	−	7.19427i	−0.0164178	−	0.433044i
$277$	2.91936	+	10.8952i	0.175407	+	0.654629i	0.996482	+	0.0838079i	$0.0267082\pi$
$277$	2.91936	+	10.8952i	0.175407	+	0.654629i	−0.821075	+	0.570821i	$0.806625\pi$
$278$	−0.210093	+	0.210093i	−0.0126005	+	0.0126005i
$279$	14.3630	−	1.09064i	0.859891	−	0.0652950i
$280$	−1.73792	−	5.65505i	−0.103860	−	0.337954i
$281$	−12.2190	+	21.1640i	−0.728925	+	1.26254i	0.228412	+	0.973564i	$0.426647\pi$
$281$	−12.2190	+	21.1640i	−0.728925	+	1.26254i	−0.957338	+	0.288971i	$0.906687\pi$
$282$	−6.25849	−	20.2540i	−0.372688	−	1.20611i
$283$	10.3533	+	2.77416i	0.615441	+	0.164907i	0.553054	−	0.833145i	$-0.313462\pi$
$283$	10.3533	+	2.77416i	0.615441	+	0.164907i	0.0623864	+	0.998052i	$0.480129\pi$
$284$	−0.675982	+	0.390279i	−0.0401122	+	0.0231588i
$285$	13.3158	+	12.1441i	0.788759	+	0.719357i
$286$	−1.71805	−	0.991918i	−0.101591	−	0.0586533i
$287$	−11.1874	+	6.88783i	−0.660373	+	0.406576i
$288$	2.27585	+	1.95461i	0.134106	+	0.115177i
$289$			46.4472i			2.73219i
$290$	1.50734	−	1.53193i	0.0885138	−	0.0899582i
$291$	−2.43853	+	0.0924506i	−0.142949	+	0.00541955i
$292$	0.582743	−	2.17483i	0.0341025	−	0.127272i
$293$	13.0794	+	3.50461i	0.764105	+	0.204741i	0.619766	−	0.784787i	$-0.287228\pi$
$293$	13.0794	+	3.50461i	0.764105	+	0.204741i	0.144340	+	0.989528i	$0.453894\pi$
$294$	−1.14321	−	12.0703i	−0.0666731	−	0.703956i
$295$	−0.149909	−	18.5238i	−0.00872802	−	1.07850i
$296$	8.47314			0.492491
$297$	−5.18073	+	2.04216i	−0.300617	+	0.118498i
$298$	9.92122	+	9.92122i	0.574721	+	0.574721i
$299$	−3.84717	+	6.66350i	−0.222488	+	0.385360i
$300$	6.44578	+	5.78377i	0.372147	+	0.333926i
$301$	4.95257	−	1.47827i	0.285461	−	0.0852062i
$302$	13.9688	+	3.74293i	0.803815	+	0.215382i
$303$	−23.0233	−	21.3413i	−1.32265	−	1.22603i
$304$	2.32662	−	4.02983i	0.133441	−	0.231126i
$305$	13.5819	+	23.0910i	0.777698	+	1.32219i
$306$	−19.7306	+	13.4807i	−1.12792	+	0.770639i
$307$	−12.7556	−	12.7556i	−0.727998	−	0.727998i	0.242223	−	0.970221i	$-0.422124\pi$
$307$	−12.7556	−	12.7556i	−0.727998	−	0.727998i	−0.970221	+	0.242223i	$0.922124\pi$
$308$	−0.0801416	−	2.83431i	−0.00456649	−	0.161500i
$309$	23.1209	+	12.2051i	1.31530	+	0.694326i
$310$	−2.86261	−	10.3477i	−0.162585	−	0.587710i
$311$	−20.2415	+	11.6864i	−1.14779	+	0.662675i	−0.948347	−	0.317235i	$-0.897246\pi$
$311$	−20.2415	+	11.6864i	−1.14779	+	0.662675i	−0.199440	+	0.979910i	$0.563912\pi$
$312$	−0.946567	−	3.06332i	−0.0535888	−	0.173426i
$313$	−6.16212	−	22.9973i	−0.348303	−	1.29989i	−0.888705	−	0.458479i	$-0.848394\pi$
$313$	−6.16212	−	22.9973i	−0.348303	−	1.29989i	0.540402	−	0.841407i	$-0.318272\pi$
$314$	−14.1327			−0.797556
$315$	10.5385	+	14.2807i	0.593780	+	0.804628i
$316$	4.64150			0.261105
$317$	8.77494	+	32.7485i	0.492850	+	1.83934i	0.541755	+	0.840537i	$0.317760\pi$
$317$	8.77494	+	32.7485i	0.492850	+	1.83934i	−0.0489049	+	0.998803i	$0.515573\pi$
$318$	4.47024	−	4.82255i	0.250679	−	0.270435i
$319$	0.892043	−	0.515021i	0.0499448	−	0.0288357i
$320$	1.10233	−	1.94548i	0.0616219	−	0.108755i
$321$	−10.1164	+	6.36354i	−0.564643	+	0.355178i
$322$	−10.9929	+	0.310831i	−0.612612	+	0.0173219i
$323$	26.2088	+	26.2088i	1.45830	+	1.45830i
$324$	−8.38435	−	3.27149i	−0.465797	−	0.181750i
$325$	−2.53990	−	8.90027i	−0.140888	−	0.493698i
$326$	−7.09253	+	12.2846i	−0.392819	+	0.680382i
$327$	1.71240	−	7.51964i	0.0946958	−	0.415837i
$328$	−4.79641	−	1.28519i	−0.264837	−	0.0709629i
$329$	−31.0290	+	9.26174i	−1.71069	+	0.510616i
$330$	2.23838	+	3.49538i	0.123219	+	0.192414i
$331$	2.55408	−	4.42380i	0.140385	−	0.243154i	−0.787257	−	0.616625i	$-0.788499\pi$
$331$	2.55408	−	4.42380i	0.140385	−	0.243154i	0.927642	+	0.373472i	$0.121833\pi$
$332$	3.61654	+	3.61654i	0.198483	+	0.198483i
$333$	−23.9847	+	8.41922i	−1.31435	+	0.461371i
$334$	−15.9128			−0.870707
$335$	−2.98866	−	2.94067i	−0.163288	−	0.160666i
$336$	3.01905	−	3.44751i	0.164702	−	0.188077i
$337$	23.5002	+	6.29687i	1.28014	+	0.343012i	0.833907	−	0.551905i	$-0.186099\pi$
$337$	23.5002	+	6.29687i	1.28014	+	0.343012i	0.446232	+	0.894917i	$0.352765\pi$
$338$	2.47777	−	9.24716i	0.134773	−	0.502979i
$339$	−6.54060	+	12.3902i	−0.355236	+	0.672945i
$340$	12.6959	+	12.4920i	0.688530	+	0.677476i
$341$		−	5.14570i		−	0.278655i
$342$	−2.58171	+	13.7189i	−0.139603	+	0.741835i
$343$	−18.4537	+	1.56871i	−0.996406	+	0.0847023i
$344$	1.69178	+	0.976751i	0.0912148	+	0.0526629i
$345$	13.5569	−	8.68161i	0.729878	−	0.467402i
$346$	10.2553	−	5.92090i	0.551328	−	0.318309i
$347$	−8.25134	−	2.21094i	−0.442955	−	0.118689i	0.0304461	−	0.999536i	$-0.490307\pi$
$347$	−8.25134	−	2.21094i	−0.442955	−	0.118689i	−0.473401	+	0.880847i	$0.656974\pi$
$348$	1.62318	+	0.369635i	0.0870113	+	0.0198145i
$349$	10.7398	−	18.6018i	0.574887	−	0.995733i	−0.421167	−	0.906983i	$-0.638379\pi$
$349$	10.7398	−	18.6018i	0.574887	−	0.995733i	0.996054	−	0.0887502i	$-0.0282873\pi$
$350$	8.92922	−	9.76059i	0.477287	−	0.521725i
$351$	5.72324	+	7.73069i	0.305484	+	0.412634i
$352$	0.757804	−	0.757804i	0.0403911	−	0.0403911i
$353$	−0.946206	−	3.53129i	−0.0503615	−	0.187951i	0.936163	−	0.351567i	$-0.114351\pi$
$353$	−0.946206	−	3.53129i	−0.0503615	−	0.187951i	−0.986524	+	0.163615i	$0.947684\pi$
$354$	12.1458	−	7.64011i	0.645543	−	0.406067i
$355$	−1.51856	−	0.860429i	−0.0805965	−	0.0456668i
$356$	−9.64262	+	5.56717i	−0.511058	+	0.295059i
$357$	20.3010	+	30.3358i	1.07444	+	1.60554i
$358$	19.5049	−	5.22632i	1.03087	−	0.276219i
$359$		−	17.8932i		−	0.944366i	−0.881501	−	0.472183i	$-0.843466\pi$
$359$		−	17.8932i		−	0.944366i	0.881501	−	0.472183i	$-0.156534\pi$
$360$	−1.18722	+	6.60231i	−0.0625722	+	0.347972i
$361$	2.65269			0.139615
$362$	0.0454146	−	0.0121688i	0.00238694	−	0.000639578i
$363$	−5.03754	−	16.3027i	−0.264402	−	0.855669i
$364$	−4.69300	+	1.40079i	−0.245980	+	0.0734216i
$365$	4.85236	−	1.34236i	0.253984	−	0.0702626i
$366$	−9.68714	+	18.3509i	−0.506355	+	0.959218i
$367$	27.4980	−	7.36807i	1.43538	−	0.384610i	0.544470	−	0.838780i	$-0.316731\pi$
$367$	27.4980	−	7.36807i	1.43538	−	0.384610i	0.890915	+	0.454170i	$0.150064\pi$
$368$	−2.93916	−	2.93916i	−0.153214	−	0.153214i
$369$	14.8541	−	1.12793i	0.773271	−	0.0587176i
$370$	9.60573	+	16.3310i	0.499378	+	0.849006i
$371$	−7.30050	−	6.89900i	−0.379023	−	0.358178i
$372$	5.65354	−	6.09912i	0.293123	−	0.316224i
$373$	1.79414	−	6.69581i	0.0928969	−	0.346696i	−0.903795	−	0.427965i	$-0.859231\pi$
$373$	1.79414	−	6.69581i	0.0928969	−	0.346696i	0.996692	+	0.0812691i	$0.0258973\pi$
$374$	4.26823	+	7.39280i	0.220705	+	0.382272i
$375$	−3.84014	+	18.9803i	−0.198304	+	0.980141i
$376$	−10.5994	−	6.11958i	−0.546624	−	0.315593i
$377$	−1.25806	−	1.25806i	−0.0647935	−	0.0647935i
$378$	−5.12034	+	12.7586i	−0.263362	+	0.656232i
$379$		−	8.70596i		−	0.447195i	−0.974682	−	0.223598i	$-0.928220\pi$
$379$		−	8.70596i		−	0.447195i	0.974682	−	0.223598i	$-0.0717802\pi$
$380$	10.4046	−	0.0842021i	0.533746	−	0.00431948i
$381$	−30.3359	+	19.0822i	−1.55415	+	0.977612i
$382$	−14.9094	−	3.99495i	−0.762829	−	0.204399i
$383$	2.26544	+	0.607023i	0.115759	+	0.0310174i	0.316233	−	0.948681i	$-0.397582\pi$
$383$	2.26544	+	0.607023i	0.115759	+	0.0310174i	−0.200475	+	0.979699i	$0.564248\pi$
$384$	1.73081	−	0.0656192i	0.0883249	−	0.00334862i
$385$	5.37194	−	3.36763i	0.273779	−	0.171630i
$386$	−9.01111			−0.458654
$387$	−5.75941	−	1.08384i	−0.292767	−	0.0550948i
$388$	−0.996240	+	0.996240i	−0.0505764	+	0.0505764i
$389$	−19.2408	−	11.1087i	−0.975547	−	0.563232i	−0.0746244	−	0.997212i	$-0.523776\pi$
$389$	−19.2408	−	11.1087i	−0.975547	−	0.563232i	−0.900923	+	0.433979i	$0.857109\pi$
$390$	4.83109	−	5.29718i	0.244632	−	0.268233i
$391$	28.6731	−	16.5544i	1.45006	−	0.837193i
$392$	−5.22153	−	4.66215i	−0.263727	−	0.235474i
$393$	13.9788	−	4.31946i	0.705138	−	0.217888i
$394$	9.87775	+	5.70292i	0.497634	+	0.287309i
$395$	5.26192	+	8.94594i	0.264756	+	0.450119i
$396$	−1.39211	+	2.89807i	−0.0699562	+	0.145634i
$397$	−10.0485	−	10.0485i	−0.504320	−	0.504320i	0.408457	−	0.912778i	$-0.366067\pi$
$397$	−10.0485	−	10.0485i	−0.504320	−	0.504320i	−0.912778	+	0.408457i	$0.866067\pi$
$398$	2.91296	+	10.8713i	0.146014	+	0.544930i
$399$	20.9171	+	4.14517i	1.04716	+	0.207518i
$400$	4.99935	−	0.0809222i	0.249967	−	0.00404611i
$401$	−7.63139	−	13.2180i	−0.381094	−	0.660074i	0.610125	−	0.792305i	$-0.291119\pi$
$401$	−7.63139	−	13.2180i	−0.381094	−	0.660074i	−0.991219	+	0.132231i	$0.957786\pi$
$402$	0.721123	−	3.16666i	0.0359663	−	0.157939i
$403$	−8.58520	+	2.30040i	−0.427659	+	0.114591i
$404$	−18.1248			−0.901743
$405$	−3.19966	−	19.8686i	−0.158992	−	0.987280i
$406$	0.588468	−	2.47389i	0.0292052	−	0.122777i
$407$	2.35024	+	8.77122i	0.116497	+	0.434773i
$408$	−3.06335	+	13.4520i	−0.151658	+	0.665976i
$409$	−15.9234	−	27.5802i	−0.787364	−	1.36375i	−0.927577	−	0.373632i	$-0.878112\pi$
$409$	−15.9234	−	27.5802i	−0.787364	−	1.36375i	0.140213	−	0.990121i	$-0.455221\pi$
$410$	−2.96048	−	10.7015i	−0.146208	−	0.528509i
$411$	−0.881552	−	23.2523i	−0.0434838	−	1.14695i
$412$	14.5803	−	3.90677i	0.718319	−	0.192473i
$413$	−11.4913	−	18.6645i	−0.565451	−	0.918422i
$414$	11.2402	+	5.39933i	0.552427	+	0.265362i
$415$	−2.87049	+	11.0704i	−0.140907	+	0.543425i
$416$	−1.60311	−	0.925559i	−0.0785992	−	0.0453792i
$417$	−0.151930	−	0.491682i	−0.00744004	−	0.0240778i
$418$	4.81694	+	1.29070i	0.235604	+	0.0631300i
$419$	5.05516	+	8.75579i	0.246960	+	0.427748i	0.962681	−	0.270639i	$-0.0872349\pi$
$419$	5.05516	+	8.75579i	0.246960	+	0.427748i	−0.715720	+	0.698387i	$0.753902\pi$
$420$	10.0673	+	1.91051i	0.491233	+	0.0932235i
$421$	2.79138	−	4.83482i	0.136044	−	0.235635i	−0.789952	−	0.613169i	$-0.789895\pi$
$421$	2.79138	−	4.83482i	0.136044	−	0.235635i	0.925996	+	0.377534i	$0.123228\pi$
$422$	−11.1381	+	11.1381i	−0.542192	+	0.542192i
$423$	36.0841	+	6.79053i	1.75447	+	0.330167i
$424$		−	3.79649i		−	0.184374i
$425$	−9.68399	+	38.6316i	−0.469743	+	1.87391i
$426$	−0.0512195	−	1.35099i	−0.00248159	−	0.0654559i
$427$	27.8878	+	15.0665i	1.34958	+	0.729119i
$428$	−1.78589	+	6.66504i	−0.0863244	+	0.322167i
$429$	2.90853	−	1.82956i	0.140425	−	0.0883318i
$430$	0.0353493	+	4.36802i	0.00170470	+	0.210645i
$431$	0.851647			0.0410224			0.0205112	−	0.999790i	$-0.493471\pi$
$431$	0.851647			0.0410224			0.0205112	+	0.999790i	$0.493471\pi$
$432$	−4.83414	+	1.90554i	−0.232583	+	0.0916803i
$433$	19.6583	−	19.6583i	0.944717	−	0.944717i	−0.0538332	−	0.998550i	$-0.517144\pi$
$433$	19.6583	−	19.6583i	0.944717	−	0.944717i	0.998550	+	0.0538332i	$0.0171439\pi$
$434$	−9.23299	−	8.72521i	−0.443198	−	0.418824i
$435$	1.12772	+	3.54752i	0.0540698	+	0.170091i
$436$	−2.22631	−	3.85608i	−0.106621	−	0.184673i
$437$	5.00599	−	18.6826i	0.239469	−	0.893710i
$438$	2.86006	+	2.65112i	0.136659	+	0.126675i
$439$	−17.1705	+	29.7401i	−0.819501	+	1.41942i	0.0865496	+	0.996248i	$0.472416\pi$
$439$	−17.1705	+	29.7401i	−0.819501	+	1.41942i	−0.906050	+	0.423170i	$0.860917\pi$
$440$	2.31968	+	0.601478i	0.110586	+	0.0286744i
$441$	19.4129	+	8.00870i	0.924424	+	0.381367i
$442$	10.4262	−	10.4262i	0.495923	−	0.495923i
$443$	33.6177	−	9.00783i	1.59722	−	0.427975i	0.653021	−	0.757340i	$-0.273501\pi$
$443$	33.6177	−	9.00783i	1.59722	−	0.427975i	0.944203	+	0.329365i	$0.106835\pi$
$444$	−6.85118	+	12.9786i	−0.325142	+	0.615936i
$445$	−21.6616	−	12.2737i	−1.02686	−	0.581828i
$446$	−10.7640	+	6.21461i	−0.509691	+	0.294270i
$447$	−23.2187	+	7.17460i	−1.09821	+	0.339347i
$448$	−0.0747801	−	2.64469i	−0.00353303	−	0.124950i
$449$		−	12.0818i		−	0.570176i	−0.958501	−	0.285088i	$-0.907977\pi$
$449$		−	12.0818i		−	0.570176i	0.958501	−	0.285088i	$-0.0920228\pi$
$450$	−14.0711	+	5.19660i	−0.663317	+	0.244970i
$451$		−	5.32162i		−	0.250585i
$452$	2.09360	+	7.81341i	0.0984745	+	0.367512i
$453$	−17.0280	+	18.3700i	−0.800046	+	0.863100i
$454$	−8.22282	−	14.2423i	−0.385916	−	0.668426i
$455$	−8.02017	−	7.45715i	−0.375991	−	0.349597i
$456$	4.29137	+	6.82219i	0.200962	+	0.319478i
$457$	−1.08318	−	4.04247i	−0.0506688	−	0.189099i	0.935953	−	0.352125i	$-0.114541\pi$
$457$	−1.08318	−	4.04247i	−0.0506688	−	0.189099i	−0.986622	+	0.163027i	$0.947874\pi$
$458$	2.42691	−	2.42691i	0.113402	−	0.113402i
$459$	−4.69513	−	41.1221i	−0.219150	−	1.91942i
$460$	2.33284	−	8.99690i	0.108769	−	0.419483i
$461$	31.9737	+	18.4600i	1.48916	+	0.859770i	0.999923	−	0.0123788i	$-0.00394040\pi$
$461$	31.9737	+	18.4600i	1.48916	+	0.859770i	0.489241	+	0.872148i	$0.337274\pi$
$462$	4.40621	+	2.16900i	0.204995	+	0.100911i
$463$	−0.435959	+	1.62702i	−0.0202607	+	0.0756141i	−0.975316	−	0.220814i	$-0.929129\pi$
$463$	−0.435959	+	1.62702i	−0.0202607	+	0.0756141i	0.955055	+	0.296428i	$0.0957954\pi$
$464$	0.832365	−	0.480566i	0.0386416	−	0.0223097i
$465$	18.1646	+	3.98216i	0.842361	+	0.184668i
$466$	−4.89416	+	8.47693i	−0.226718	+	0.392686i
$467$	−25.7944	−	25.7944i	−1.19362	−	1.19362i	−0.976043	−	0.217577i	$-0.930185\pi$
$467$	−25.7944	−	25.7944i	−1.19362	−	1.19362i	−0.217577	−	0.976043i	$-0.569815\pi$
$468$	5.45756	+	1.02704i	0.252276	+	0.0474748i
$469$	−4.82633	−	1.14805i	−0.222859	−	0.0530118i
$470$	−0.221472	−	27.3667i	−0.0102157	−	1.26233i
$471$	11.4274	−	21.6476i	0.526546	−	0.997467i
$472$	2.14415	−	8.00209i	0.0986926	−	0.368326i
$473$	−0.541854	+	2.02223i	−0.0249145	+	0.0929821i
$474$	−3.75301	+	7.10954i	−0.172381	+	0.326552i
$475$	11.9577	+	19.9582i	0.548656	+	0.915746i
$476$	20.5023	+	4.87692i	0.939723	+	0.223533i
$477$	3.77233	+	10.7466i	0.172723	+	0.492053i
$478$	−9.72872	−	9.72872i	−0.444981	−	0.444981i
$479$	−13.9501	+	24.1623i	−0.637397	+	1.10400i	0.348604	+	0.937270i	$0.386656\pi$
$479$	−13.9501	+	24.1623i	−0.637397	+	1.10400i	−0.986002	+	0.166735i	$0.946678\pi$
$480$	2.08863	+	3.26153i	0.0953327	+	0.148868i
$481$	13.5834	−	7.84239i	0.619350	−	0.357582i
$482$	−3.54474	+	13.2291i	−0.161458	+	0.602571i
$483$	8.41250	−	17.0896i	0.382782	−	0.777602i
$484$	−8.53162	−	4.92573i	−0.387801	−	0.223897i
$485$	−3.04954	−	0.790727i	−0.138472	−	0.0359051i
$486$	11.7904	−	10.1973i	0.534825	−	0.462560i
$487$	−5.13613	+	5.13613i	−0.232740	+	0.232740i	−0.813836	−	0.581095i	$-0.802624\pi$
$487$	−5.13613	+	5.13613i	−0.232740	+	0.232740i	0.581095	+	0.813836i	$0.302624\pi$
$488$	3.10078	+	11.5723i	0.140366	+	0.523852i
$489$	−13.0819	−	20.7969i	−0.591585	−	0.940469i
$490$	3.06625	−	15.3492i	0.138519	−	0.693406i
$491$	3.91686	+	6.78419i	0.176765	+	0.306166i	0.940771	−	0.339043i	$-0.110103\pi$
$491$	3.91686	+	6.78419i	0.176765	+	0.306166i	−0.764006	+	0.645210i	$0.776770\pi$
$492$	5.84683	−	6.30764i	0.263595	−	0.284370i
$493$	1.98146	+	7.39492i	0.0892406	+	0.333050i
$494$		−	8.61370i		−	0.387549i
$495$	−7.16388	+	0.602329i	−0.321993	+	0.0270727i
$496$		−	4.80145i		−	0.215592i
$497$	−2.06434	+	0.0583701i	−0.0925981	+	0.00261826i
$498$	−8.46381	+	2.61532i	−0.379273	+	0.117195i
$499$	−32.5560	+	18.7962i	−1.45741	+	0.841434i	−0.998883	−	0.0472480i	$-0.984955\pi$
$499$	−32.5560	+	18.7962i	−1.45741	+	0.841434i	−0.458524	+	0.888682i	$0.651622\pi$
$500$	5.82357	+	9.54390i	0.260438	+	0.426816i
$501$	12.8667	−	24.3741i	0.574840	−	1.08895i
$502$	18.9350	−	5.07363i	0.845112	−	0.226447i
$503$	11.4740	−	11.4740i	0.511602	−	0.511602i	−0.403415	−	0.915017i	$-0.632177\pi$
$503$	11.4740	−	11.4740i	0.511602	−	0.511602i	0.915017	+	0.403415i	$0.132177\pi$
$504$	2.83954	+	7.41195i	0.126483	+	0.330154i
$505$	−20.5475	−	34.9334i	−0.914353	−	1.55452i
$506$	2.22730	−	3.85780i	0.0990158	−	0.171500i
$507$	12.1607	+	11.2723i	0.540076	+	0.500621i
$508$	−5.35532	+	19.9863i	−0.237604	+	0.886749i
$509$	−2.65031	−	4.59048i	−0.117473	−	0.203469i	0.801293	−	0.598273i	$-0.204146\pi$
$509$	−2.65031	−	4.59048i	−0.117473	−	0.203469i	−0.918766	+	0.394803i	$0.870813\pi$
$510$	−29.4000	+	9.34593i	−1.30186	+	0.413845i
$511$	4.09152	−	4.32963i	0.180998	−	0.191532i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−18.9262	−	15.0473i	−0.835613	−	0.664354i
$514$	1.70818			0.0753448
$515$	24.0590	+	23.6728i	1.06017	+	1.04315i
$516$	−2.86406	+	1.80158i	−0.126083	+	0.0793102i
$517$	3.39484	−	12.6697i	0.149305	−	0.557214i
$518$	19.7235	+	10.6557i	0.866599	+	0.468185i
$519$	0.777049	+	20.4959i	0.0341087	+	0.899668i
$520$	−0.0334966	−	4.13909i	−0.00146892	−	0.181511i
$521$		−	2.99957i		−	0.131414i	−0.997839	−	0.0657068i	$-0.979070\pi$
$521$		−	2.99957i		−	0.131414i	0.997839	−	0.0657068i	$-0.0209302\pi$
$522$	−1.87864	+	2.18739i	−0.0822259	+	0.0957396i
$523$	9.86039	−	9.86039i	0.431165	−	0.431165i	−0.457860	−	0.889024i	$-0.651384\pi$
$523$	9.86039	−	9.86039i	0.431165	−	0.431165i	0.889024	+	0.457860i	$0.151384\pi$
$524$	4.22360	−	7.31548i	0.184509	−	0.319578i
$525$	7.73066	+	21.5694i	0.337394	+	0.941364i
$526$	7.64653	+	13.2442i	0.333405	+	0.577474i
$527$	36.9422	+	9.89863i	1.60923	+	0.431191i
$528$	0.548011	+	1.77350i	0.0238491	+	0.0771815i
$529$	4.95602	+	2.86136i	0.215479	+	0.124407i
$530$	7.31728	−	4.30396i	0.317842	−	0.186952i
$531$	1.88178	+	24.7818i	0.0816623	+	1.07544i
$532$	10.4837	−	6.45456i	0.454525	−	0.279840i
$533$	−8.87871	+	2.37904i	−0.384580	+	0.103048i
$534$	−0.730626	−	19.2714i	−0.0316173	−	0.833955i
$535$	−14.8707	+	4.11385i	−0.642916	+	0.177857i
$536$	−0.937540	−	1.62387i	−0.0404955	−	0.0701403i
$537$	−7.76585	+	34.1021i	−0.335121	+	1.47162i
$538$	−0.212151	−	0.791758i	−0.00914647	−	0.0341351i
$539$	3.37784	−	6.69839i	0.145494	−	0.288520i
$540$	−9.15301	−	7.15698i	−0.393883	−	0.307987i
$541$	25.7394			1.10663			0.553313	−	0.832974i	$-0.313363\pi$
$541$	25.7394			1.10663			0.553313	+	0.832974i	$0.313363\pi$
$542$	−21.7329	+	5.82332i	−0.933509	+	0.250133i
$543$	−0.0180818	+	0.0794024i	−0.000775964	+	0.00340748i
$544$	3.98269	+	6.89822i	0.170756	+	0.295759i
$545$	4.90823	−	8.66245i	0.210246	−	0.371059i
$546$	1.64900	−	8.32107i	0.0705707	−	0.356109i
$547$	−10.6357	−	39.6931i	−0.454751	−	1.69715i	−0.688819	−	0.724933i	$-0.741871\pi$
$547$	−10.6357	−	39.6931i	−0.454751	−	1.69715i	0.234068	−	0.972220i	$-0.424796\pi$
$548$	−9.49953	−	9.49953i	−0.405800	−	0.405800i
$549$	−20.2759	−	29.6762i	−0.865355	−	1.26655i
$550$	1.47046	+	5.15277i	0.0627008	+	0.219715i
$551$	3.87320	+	2.23619i	0.165004	+	0.0952650i
$552$	6.87853	−	2.12547i	0.292770	−	0.0904661i
$553$	10.8043	+	5.83709i	0.459446	+	0.248218i
$554$	−9.76836	+	5.63977i	−0.415018	+	0.239611i
$555$	−32.7816	+	1.50859i	−1.39150	+	0.0640360i
$556$	−0.257310	−	0.148558i	−0.0109124	−	0.00630026i
$557$	8.56185	−	8.56185i	0.362777	−	0.362777i	−0.502057	−	0.864834i	$-0.667423\pi$
$557$	8.56185	−	8.56185i	0.362777	−	0.362777i	0.864834	+	0.502057i	$0.167423\pi$
$558$	4.77090	+	13.5913i	0.201968	+	0.575366i
$559$	3.61616			0.152947
$560$	5.01256	−	3.14234i	0.211819	−	0.132788i
$561$	−14.7750	+	0.560156i	−0.623800	+	0.0236498i
$562$	−23.6053	−	6.32503i	−0.995731	−	0.266805i
$563$	−15.4563	−	4.14150i	−0.651404	−	0.174543i	−0.0820407	−	0.996629i	$-0.526144\pi$
$563$	−15.4563	−	4.14150i	−0.651404	−	0.174543i	−0.569364	+	0.822086i	$0.692810\pi$
$564$	17.9440	−	11.2873i	0.755579	−	0.475283i
$565$	−12.6860	+	12.8930i	−0.533703	+	0.542411i
$566$			10.7185i			0.450534i
$567$	−15.4026	−	18.1593i	−0.646848	−	0.762619i
$568$	−0.551937	−	0.551937i	−0.0231588	−	0.0231588i
$569$	−20.8223	−	12.0218i	−0.872918	−	0.503980i	−0.00460135	−	0.999989i	$-0.501465\pi$
$569$	−20.8223	−	12.0218i	−0.872918	−	0.503980i	−0.868317	+	0.496010i	$0.834798\pi$
$570$	−8.28396	+	16.0052i	−0.346977	+	0.670384i
$571$	−1.38426	−	2.39760i	−0.0579293	−	0.100336i	0.835606	−	0.549329i	$-0.185116\pi$
$571$	−1.38426	−	2.39760i	−0.0579293	−	0.100336i	−0.893536	+	0.448992i	$0.851783\pi$
$572$	0.513455	−	1.91624i	0.0214686	−	0.0801220i
$573$	18.1745	−	19.6069i	0.759253	−	0.819091i
$574$	−9.54865	−	9.02352i	−0.398553	−	0.376634i
$575$	19.9851	−	5.70323i	0.833437	−	0.237841i
$576$	−1.29898	+	2.70419i	−0.0541241	+	0.112675i
$577$	−2.32700	−	2.32700i	−0.0968743	−	0.0968743i	0.657009	−	0.753883i	$-0.271821\pi$
$577$	−2.32700	−	2.32700i	−0.0968743	−	0.0968743i	−0.753883	+	0.657009i	$0.771821\pi$
$578$	−44.8646	+	12.0214i	−1.86612	+	0.500025i
$579$	7.28617	−	13.8026i	0.302803	−	0.573617i
$580$	1.86986	+	1.05948i	0.0776417	+	0.0439926i
$581$	3.87034	+	12.9665i	0.160569	+	0.537943i
$582$	−0.720438	−	2.33151i	−0.0298631	−	0.0966441i
$583$	3.93005	−	1.05305i	0.162766	−	0.0436130i
$584$	2.25155			0.0931696
$585$	4.20757	+	11.6831i	0.173962	+	0.483037i
$586$			13.5408i			0.559364i
$587$	−5.04220	+	1.35105i	−0.208114	+	0.0557640i	−0.361370	−	0.932423i	$-0.617691\pi$
$587$	−5.04220	+	1.35105i	−0.208114	+	0.0557640i	0.153256	+	0.988187i	$0.451024\pi$
$588$	11.3632	−	4.22829i	0.468609	−	0.174372i
$589$	19.3490	−	11.1712i	0.797263	−	0.460300i
$590$	17.8538	−	4.93912i	0.735030	−	0.203340i
$591$	−16.7223	+	10.5188i	−0.687862	+	0.432687i
$592$	2.19301	+	8.18442i	0.0901321	+	0.336378i
$593$	−12.5324	+	12.5324i	−0.514643	+	0.514643i	−0.915946	−	0.401302i	$-0.868558\pi$
$593$	−12.5324	+	12.5324i	−0.514643	+	0.514643i	0.401302	+	0.915946i	$0.368558\pi$
$594$	−3.31345	−	4.47565i	−0.135952	−	0.183638i
$595$	13.8432	+	45.0446i	0.567515	+	1.84665i
$596$	−7.01536	+	12.1510i	−0.287360	+	0.497723i
$597$	−19.0073	−	4.32841i	−0.777917	−	0.177150i
$598$	−7.43217	−	1.99144i	−0.303924	−	0.0814362i
$599$	20.4655	−	11.8157i	0.836196	−	0.482778i	−0.0197735	−	0.999804i	$-0.506294\pi$
$599$	20.4655	−	11.8157i	0.836196	−	0.482778i	0.855969	+	0.517027i	$0.172961\pi$
$600$	−3.91840	+	7.72309i	−0.159968	+	0.315294i
$601$	−33.5837	−	19.3896i	−1.36991	−	0.790917i	−0.378992	−	0.925400i	$-0.623729\pi$
$601$	−33.5837	−	19.3896i	−1.36991	−	0.790917i	−0.990916	+	0.134483i	$0.957063\pi$
$602$	2.70972	+	4.40121i	0.110440	+	0.179380i
$603$	4.26740	+	3.66505i	0.173782	+	0.149253i
$604$			14.4616i			0.588433i
$605$	−0.178266	−	22.0278i	−0.00724753	−	0.895559i
$606$	14.6553	−	27.7624i	0.595330	−	1.12777i
$607$	9.20337	−	34.3475i	0.373553	−	1.39412i	−0.481893	−	0.876230i	$-0.660051\pi$
$607$	9.20337	−	34.3475i	0.373553	−	1.39412i	0.855447	−	0.517891i	$-0.173283\pi$
$608$	4.49469	+	1.20435i	0.182284	+	0.0488428i
$609$	3.31352	+	2.90170i	0.134271	+	0.117583i
$610$	−18.7889	+	19.0955i	−0.760741	+	0.773154i
$611$	−22.6561			−0.916569
$612$	−18.1280	−	15.5692i	−0.732781	−	0.629349i
$613$	−22.3917	−	22.3917i	−0.904391	−	0.904391i	0.0914208	−	0.995812i	$-0.470859\pi$
$613$	−22.3917	−	22.3917i	−0.904391	−	0.904391i	−0.995812	+	0.0914208i	$0.970859\pi$
$614$	9.01954	−	15.6223i	0.363999	−	0.630465i
$615$	18.7856	+	4.11830i	0.757508	+	0.166066i
$616$	2.71699	−	0.810984i	0.109471	−	0.0326755i
$617$	−30.6823	−	8.22130i	−1.23522	−	0.330977i	−0.418612	−	0.908165i	$-0.637483\pi$
$617$	−30.6823	−	8.22130i	−1.23522	−	0.330977i	−0.816611	+	0.577188i	$0.804150\pi$
$618$	−5.80513	+	25.4920i	−0.233516	+	1.02544i
$619$	−5.27437	+	9.13547i	−0.211995	+	0.367186i	−0.952339	−	0.305043i	$-0.901329\pi$
$619$	−5.27437	+	9.13547i	−0.211995	+	0.367186i	0.740344	+	0.672228i	$0.234663\pi$
$620$	9.25422	−	5.44325i	0.371659	−	0.218606i
$621$	−17.3589	+	12.8513i	−0.696589	+	0.515704i
$622$	−16.5271	−	16.5271i	−0.662675	−	0.662675i
$623$	−29.4469	+	0.832626i	−1.17977	+	0.0333585i
$624$	2.71395	−	1.70716i	0.108645	−	0.0683410i
$625$	−11.7927	+	22.0439i	−0.471709	+	0.881754i
$626$	20.6188	−	11.9043i	0.824095	−	0.475791i
$627$	−5.87187	+	6.33464i	−0.234500	+	0.252981i
$628$	−3.65782	−	13.6512i	−0.145963	−	0.544741i
$629$	−67.4917			−2.69107
$630$	−11.0665	+	13.8756i	−0.440902	+	0.552816i
$631$	−36.3250			−1.44607			−0.723037	−	0.690809i	$-0.757254\pi$
$631$	−36.3250			−1.44607			−0.723037	+	0.690809i	$0.757254\pi$
$632$	1.20131	+	4.48335i	0.0477855	+	0.178338i
$633$	−8.05456	−	26.0665i	−0.320140	−	1.03605i
$634$	−29.3615	+	16.9519i	−1.16609	+	0.673245i
$635$	−44.5924	+	12.3361i	−1.76959	+	0.489544i
$636$	5.81521	+	3.06975i	0.230588	+	0.121724i
$637$	−12.6858	−	2.64113i	−0.502630	−	0.104645i
$638$	0.728350	+	0.728350i	0.0288357	+	0.0288357i
$639$	2.11078	+	1.01393i	0.0835010	+	0.0401103i
$640$	2.16449	+	0.561239i	0.0855589	+	0.0221849i
$641$	20.9696	−	36.3204i	0.828249	−	1.43457i	−0.0711616	−	0.997465i	$-0.522671\pi$
$641$	20.9696	−	36.3204i	0.828249	−	1.43457i	0.899411	−	0.437105i	$-0.143996\pi$
$642$	−8.76503	−	8.12470i	−0.345928	−	0.320656i
$643$	11.4168	+	3.05913i	0.450236	+	0.120640i	0.476810	−	0.879006i	$-0.341793\pi$
$643$	11.4168	+	3.05913i	0.450236	+	0.120640i	−0.0265737	+	0.999647i	$0.508460\pi$
$644$	−3.14542	−	10.5379i	−0.123947	−	0.415251i
$645$	−6.71923	−	3.47773i	−0.264569	−	0.136936i
$646$	−18.5324	+	32.0991i	−0.729148	+	1.26292i
$647$	7.25742	+	7.25742i	0.285318	+	0.285318i	0.835226	−	0.549907i	$-0.185337\pi$
$647$	7.25742	+	7.25742i	0.285318	+	0.285318i	−0.549907	+	0.835226i	$0.685337\pi$
$648$	0.989991	−	8.94539i	0.0388905	−	0.351408i
$649$	8.87833			0.348505
$650$	7.93962	−	4.75691i	0.311418	−	0.186582i
$651$	20.8303	−	7.08748i	0.816403	−	0.277780i
$652$	−13.7017	−	3.67136i	−0.536601	−	0.143782i
$653$	10.2459	−	38.2381i	0.400952	−	1.49637i	−0.410448	−	0.911884i	$-0.634628\pi$
$653$	10.2459	−	38.2381i	0.400952	−	1.49637i	0.811401	−	0.584490i	$-0.198705\pi$
$654$	7.70662	−	0.292177i	0.301352	−	0.0114250i
$655$	18.8879	−	0.152855i	0.738010	−	0.00597254i
$656$		−	4.96561i		−	0.193874i
$657$	−6.37338	+	2.23722i	−0.248649	+	0.0872822i
$658$	−16.9771	−	27.5746i	−0.661834	−	1.07497i
$659$	−23.0215	−	13.2915i	−0.896790	−	0.517762i	−0.0206326	−	0.999787i	$-0.506568\pi$
$659$	−23.0215	−	13.2915i	−0.896790	−	0.517762i	−0.876157	+	0.482025i	$0.839901\pi$
$660$	−2.79694	+	3.06678i	−0.108871	+	0.119374i
$661$	−38.2229	+	22.0680i	−1.48670	+	0.858345i	−0.999885	−	0.0151617i	$-0.995174\pi$
$661$	−38.2229	+	22.0680i	−1.48670	+	0.858345i	−0.486812	+	0.873507i	$0.661840\pi$
$662$	4.93410	+	1.32209i	0.191769	+	0.0513844i
$663$	7.53976	+	24.4005i	0.292820	+	0.947636i
$664$	−2.55728	+	4.42934i	−0.0992417	+	0.171892i
$665$	24.3254	+	12.8887i	0.943299	+	0.499803i
$666$	−14.3400	−	20.9883i	−0.555665	−	0.813282i
$667$	2.82492	−	2.82492i	0.109381	−	0.109381i
$668$	−4.11852	−	15.3705i	−0.159351	−	0.594704i
$669$	−0.815595	−	21.5126i	−0.0315327	−	0.831724i
$670$	2.06695	−	3.64792i	0.0798532	−	0.140931i
$671$	−11.1193	+	6.41973i	−0.429256	+	0.247831i
$672$	4.11143	+	2.02389i	0.158602	+	0.0780734i
$673$	−1.16524	+	0.312224i	−0.0449165	+	0.0120354i	−0.281207	−	0.959647i	$-0.590735\pi$
$673$	−1.16524	+	0.312224i	−0.0449165	+	0.0120354i	0.236291	+	0.971682i	$0.424068\pi$
$674$			24.3292i			0.937127i
$675$	3.41774	−	25.7550i	0.131549	−	0.991310i
$676$	9.57336			0.368206
$677$	27.6716	−	7.41458i	1.06351	−	0.284965i	0.315683	−	0.948865i	$-0.397766\pi$
$677$	27.6716	−	7.41458i	1.06351	−	0.284965i	0.747822	+	0.663899i	$0.231100\pi$
$678$	−13.6609	−	3.11090i	−0.524643	−	0.119473i
$679$	−3.57187	+	1.06615i	−0.137076	+	0.0409152i
$680$	−8.78044	+	15.4964i	−0.336715	+	0.594262i
$681$	28.4642	−	1.07915i	1.09075	−	0.0413531i
$682$	4.97036	−	1.33180i	0.190325	−	0.0509974i
$683$	17.4807	+	17.4807i	0.668879	+	0.668879i	0.957456	−	0.288578i	$-0.0931824\pi$
$683$	17.4807	+	17.4807i	0.668879	+	0.668879i	−0.288578	+	0.957456i	$0.593182\pi$
$684$	−13.9197	+	1.05698i	−0.532232	+	0.0404145i
$685$	7.53989	−	29.0785i	0.288085	−	1.11103i
$686$	−6.29143	−	17.4189i	−0.240208	−	0.665057i
$687$	1.75504	+	5.67972i	0.0669589	+	0.216695i
$688$	−0.505604	+	1.88694i	−0.0192760	+	0.0719389i
$689$	−3.51387	−	6.08621i	−0.133868	−	0.231866i
$690$	11.8946	+	10.8480i	0.452818	+	0.412975i
$691$	7.84506	+	4.52935i	0.298440	+	0.172305i	0.641742	−	0.766921i	$-0.278212\pi$
$691$	7.84506	+	4.52935i	0.298440	+	0.172305i	−0.343302	+	0.939225i	$0.611545\pi$
$692$	8.37341	+	8.37341i	0.318309	+	0.318309i
$693$	−6.88508	+	4.99533i	−0.261543	+	0.189757i
$694$		−	8.54241i		−	0.324266i
$695$	−0.00537642	−	0.664350i	−0.000203939	−	0.0252002i
$696$	0.0630687	+	1.66354i	0.00239061	+	0.0630561i
$697$	38.2052	+	10.2370i	1.44712	+	0.387756i
$698$	20.7477	+	5.55932i	0.785310	+	0.210423i
$699$	−9.02710	−	14.3508i	−0.341436	−	0.542797i
$700$	11.7391	+	6.09874i	0.443695	+	0.230511i
$701$	−37.4287			−1.41366			−0.706831	−	0.707382i	$-0.749876\pi$
$701$	−37.4287			−1.41366			−0.706831	+	0.707382i	$0.749876\pi$
$702$	−5.98599	+	7.52908i	−0.225927	+	0.284167i
$703$	−27.8795	+	27.8795i	−1.05150	+	1.05150i
$704$	0.928117	+	0.535848i	0.0349797	+	0.0201955i
$705$	42.0976	+	21.7888i	1.58549	+	0.820615i
$706$	3.16607	−	1.82793i	0.119156	−	0.0687950i
$707$	−42.1902	−	22.7935i	−1.58673	−	0.857238i
$708$	10.5233	+	9.75456i	0.395492	+	0.366599i
$709$	−3.92464	−	2.26589i	−0.147393	−	0.0850973i	0.424490	−	0.905433i	$-0.360453\pi$
$709$	−3.92464	−	2.26589i	−0.147393	−	0.0850973i	−0.571883	+	0.820335i	$0.693787\pi$
$710$	0.438079	−	1.68951i	0.0164408	−	0.0634061i
$711$	−7.85532	−	11.4972i	−0.294598	−	0.431179i
$712$	−7.87316	−	7.87316i	−0.295059	−	0.295059i
$713$	−5.16543	−	19.2776i	−0.193447	−	0.721954i
$714$	−24.0478	+	27.4607i	−0.899968	+	1.02769i
$715$	4.27541	−	1.18276i	0.159891	−	0.0442326i
$716$	10.0965	+	17.4876i	0.377323	+	0.653542i
$717$	22.7682	−	7.03539i	0.850294	−	0.262741i
$718$	17.2835	−	4.63109i	0.645014	−	0.172831i
$719$	22.2323			0.829126			0.414563	−	0.910021i	$-0.363934\pi$
$719$	22.2323			0.829126			0.414563	+	0.910021i	$0.363934\pi$
$720$	−6.68462	+	0.562033i	−0.249121	+	0.0209457i
$721$	38.8525	+	9.24191i	1.44694	+	0.344187i
$722$	0.686566	+	2.56230i	0.0255513	+	0.0953589i
$723$	−17.3973	−	16.1264i	−0.647014	−	0.599746i
$724$	0.0235083	+	0.0407176i	0.000873680	+	0.00151326i
$725$	0.0777770	+	4.80503i	0.00288857	+	0.178454i
$726$	14.4434	−	9.08533i	0.536044	−	0.337188i
$727$	6.81878	−	1.82709i	0.252895	−	0.0677629i	−0.130145	−	0.991495i	$-0.541544\pi$
$727$	6.81878	−	1.82709i	0.252895	−	0.0677629i	0.383039	+	0.923732i	$0.374877\pi$
$728$	−2.56770	−	4.17053i	−0.0951653	−	0.154570i
$729$	6.08613	+	26.3051i	0.225412	+	0.974264i
$730$	2.55251	+	4.33959i	0.0944725	+	0.160615i
$731$	−13.4757	−	7.78019i	−0.498416	−	0.287761i
$732$	−20.2328	−	4.60749i	−0.747828	−	0.170298i
$733$	46.5769	+	12.4802i	1.72036	+	0.460968i	0.977926	−	0.208953i	$-0.0670056\pi$
$733$	46.5769	+	12.4802i	1.72036	+	0.460968i	0.742432	+	0.669922i	$0.233672\pi$
$734$	14.2340	+	24.6540i	0.525387	+	0.909997i
$735$	21.0316	+	17.1077i	0.775762	+	0.631026i
$736$	2.07830	−	3.59972i	0.0766071	−	0.132687i
$737$	1.42094	−	1.42094i	0.0523411	−	0.0523411i
$738$	4.93401	+	14.0560i	0.181623	+	0.517408i
$739$		−	6.13110i		−	0.225536i	−0.993621	−	0.112768i	$-0.964028\pi$
$739$		−	6.13110i		−	0.225536i	0.993621	−	0.112768i	$-0.0359717\pi$
$740$	−13.2884	+	13.5052i	−0.488490	+	0.496461i
$741$	13.1939	+	6.96483i	0.484690	+	0.255859i
$742$	4.77441	−	8.83733i	0.175274	−	0.324429i
$743$	−0.407454	+	1.52064i	−0.0149481	+	0.0557869i	−0.972997	−	0.230818i	$-0.925860\pi$
$743$	−0.407454	+	1.52064i	−0.0149481	+	0.0557869i	0.958049	+	0.286605i	$0.0925266\pi$
$744$	7.35454	+	3.88234i	0.269630	+	0.142333i
$745$	−31.3726	+	0.253891i	−1.14940	+	0.00930184i
$746$	6.93201			0.253799
$747$	2.83766	−	15.0790i	0.103824	−	0.551711i
$748$	−6.03619	+	6.03619i	−0.220705	+	0.220705i
$749$	−12.5390	+	13.2687i	−0.458165	+	0.484829i
$750$	−19.3275	+	1.20318i	−0.705741	+	0.0439340i
$751$	−7.49597	−	12.9834i	−0.273532	−	0.473771i	0.696232	−	0.717817i	$-0.254859\pi$
$751$	−7.49597	−	12.9834i	−0.273532	−	0.473771i	−0.969764	+	0.244046i	$0.921525\pi$
$752$	3.16773	−	11.8221i	0.115515	−	0.431109i
$753$	−7.53897	+	33.1058i	−0.274735	+	1.20644i
$754$	0.889585	−	1.54081i	0.0323968	−	0.0561128i
$755$	−27.8730	+	16.3946i	−1.01440	+	0.596662i
$756$	−13.6491	−	1.64370i	−0.496413	−	0.0597809i
$757$	−6.12750	+	6.12750i	−0.222708	+	0.222708i	−0.809638	−	0.586930i	$-0.800336\pi$
$757$	−6.12750	+	6.12750i	−0.222708	+	0.222708i	0.586930	+	0.809638i	$0.300336\pi$
$758$	8.40932	−	2.25327i	0.305440	−	0.0818424i
$759$	4.10818	+	6.53096i	0.149118	+	0.237059i
$760$	2.77425	+	10.0283i	0.100633	+	0.363765i
$761$	25.6723	−	14.8219i	0.930620	−	0.537294i	0.0436126	−	0.999049i	$-0.486113\pi$
$761$	25.6723	−	14.8219i	0.930620	−	0.537294i	0.887008	+	0.461755i	$0.152780\pi$
$762$	−26.2835	−	24.3634i	−0.952151	−	0.882592i
$763$	−0.332967	−	11.7758i	−0.0120542	−	0.426313i
$764$		−	15.4353i		−	0.558430i
$765$	9.45669	−	52.5899i	0.341907	−	1.90139i
$766$			2.34536i			0.0847411i
$767$	−3.96908	−	14.8128i	−0.143315	−	0.534859i
$768$	0.511349	+	1.65485i	0.0184517	+	0.0597142i
$769$	16.0830	+	27.8567i	0.579970	+	1.00454i	0.995482	+	0.0949494i	$0.0302689\pi$
$769$	16.0830	+	27.8567i	0.579970	+	1.00454i	−0.415512	+	0.909587i	$0.636398\pi$
$770$	4.64324	+	4.31729i	0.167331	+	0.155584i
$771$	−1.38120	+	2.61648i	−0.0497426	+	0.0942303i
$772$	−2.33225	−	8.70407i	−0.0839394	−	0.313266i
$773$	4.04252	−	4.04252i	0.145399	−	0.145399i	−0.630660	−	0.776059i	$-0.717216\pi$
$773$	4.04252	−	4.04252i	0.145399	−	0.145399i	0.776059	+	0.630660i	$0.217216\pi$
$774$	−0.443735	−	5.84369i	−0.0159497	−	0.210047i
$775$	20.9824	+	11.6656i	0.753712	+	0.419039i
$776$	−1.22014	−	0.704448i	−0.0438004	−	0.0252882i
$777$	−32.2696	+	21.5951i	−1.15767	+	0.774721i
$778$	5.75028	−	21.4603i	0.206157	−	0.769390i
$779$	20.0105	−	11.5531i	0.716952	−	0.413932i
$780$	6.36706	+	3.29546i	0.227977	+	0.117996i
$781$	0.418260	−	0.724448i	0.0149665	−	0.0259228i
$782$	23.4115	+	23.4115i	0.837193	+	0.837193i
$783$	−1.83148	−	4.64625i	−0.0654516	−	0.166043i
$784$	3.15186	−	6.25026i	0.112566	−	0.223224i
$785$	22.1642	−	22.5259i	0.791076	−	0.803984i
$786$	7.79027	+	12.3845i	0.277870	+	0.441742i
$787$	−11.2402	+	41.9489i	−0.400669	+	1.49532i	0.411237	+	0.911528i	$0.365097\pi$
$787$	−11.2402	+	41.9489i	−0.400669	+	1.49532i	−0.811906	+	0.583788i	$0.801570\pi$
$788$	−2.95205	+	11.0172i	−0.105162	+	0.392471i
$789$	−26.4694	+	1.00352i	−0.942334	+	0.0357262i
$790$	−7.27923	+	7.39801i	−0.258983	+	0.263209i
$791$	−4.95263	+	20.8206i	−0.176095	+	0.740296i
$792$	−3.15963	−	0.594599i	−0.112273	−	0.0211281i
$793$	15.6817	+	15.6817i	0.556874	+	0.556874i
$794$	7.10537	−	12.3069i	0.252160	−	0.436754i
$795$	0.675941	+	14.6882i	0.0239732	+	0.520937i
$796$	−9.74696	+	5.62741i	−0.345472	+	0.199458i
$797$	−3.04097	+	11.3490i	−0.107717	+	0.402004i	−0.998639	−	0.0521514i	$-0.983392\pi$
$797$	−3.04097	+	11.3490i	−0.107717	+	0.402004i	0.890923	+	0.454155i	$0.150059\pi$
$798$	1.40981	+	21.2772i	0.0499066	+	0.753204i
$799$	84.4284	+	48.7448i	2.98686	+	1.72447i
$800$	1.37209	+	4.80805i	0.0485107	+	0.169990i
$801$	30.1094	+	14.4633i	1.06386	+	0.511034i
$802$	10.7924	−	10.7924i	0.381094	−	0.381094i
$803$	0.624524	+	2.33075i	0.0220390	+	0.0822505i
$804$	3.24540	−	0.123041i	0.114456	−	0.00433933i
$805$	16.7447	−	18.0089i	0.590173	−	0.634730i
$806$	−4.44402	−	7.69728i	−0.156534	−	0.271125i
$807$	1.38430	+	0.315238i	0.0487297	+	0.0110969i
$808$	−4.69104	−	17.5072i	−0.165030	−	0.615902i
$809$			19.8697i			0.698583i	0.937014	+	0.349291i	$0.113578\pi$
$809$			19.8697i			0.698583i	−0.937014	+	0.349291i	$0.886422\pi$
$810$	18.3635	−	8.23301i	0.645227	−	0.289278i
$811$			34.3758i			1.20710i	0.797326	+	0.603549i	$0.206247\pi$
$811$			34.3758i			1.20710i	−0.797326	+	0.603549i	$0.793753\pi$
$812$	2.54190	−	0.0718736i	0.0892033	−	0.00252227i
$813$	8.65295	−	37.9976i	0.303472	−	1.33264i
$814$	−7.86406	+	4.54032i	−0.275635	+	0.159138i
$815$	−8.45709	−	30.5705i	−0.296239	−	1.07084i
$816$	−13.7865	+	0.522681i	−0.482625	+	0.0182975i
$817$	−8.78039	+	2.35270i	−0.307187	+	0.0823105i
$818$	22.5191	−	22.5191i	0.787364	−	0.787364i
$819$	11.4123	+	9.25404i	0.398778	+	0.323362i
$820$	9.57061	−	5.62935i	0.334220	−	0.196585i
$821$	−5.09842	+	8.83072i	−0.177936	+	0.308194i	−0.941173	−	0.337924i	$-0.890275\pi$
$821$	−5.09842	+	8.83072i	−0.177936	+	0.308194i	0.763237	+	0.646118i	$0.223609\pi$
$822$	22.2318	−	6.86965i	0.775424	−	0.239607i
$823$	2.65347	−	9.90288i	0.0924941	−	0.345193i	−0.904134	−	0.427250i	$-0.859482\pi$
$823$	2.65347	−	9.90288i	0.0924941	−	0.345193i	0.996628	+	0.0820574i	$0.0261491\pi$
$824$	7.54731	+	13.0723i	0.262923	+	0.455396i
$825$	−9.08165	−	1.91405i	−0.316183	−	0.0666386i
$826$	15.0544	−	15.9305i	0.523809	−	0.554293i
$827$	−33.8949	+	33.8949i	−1.17864	+	1.17864i	−0.198551	+	0.980090i	$0.563624\pi$
$827$	−33.8949	+	33.8949i	−1.17864	+	1.17864i	−0.980090	+	0.198551i	$0.936376\pi$
$828$	−2.30616	+	12.2547i	−0.0801446	+	0.425880i
$829$	−4.47218			−0.155325			−0.0776626	−	0.996980i	$-0.524746\pi$
$829$	−4.47218			−0.155325			−0.0776626	+	0.996980i	$0.524746\pi$
$830$	−11.4361	+	0.0925497i	−0.396954	+	0.00321245i
$831$	−0.740154	−	19.5227i	−0.0256756	−	0.677235i
$832$	0.479104	−	1.78804i	0.0166100	−	0.0619892i
$833$	41.5914	+	37.1358i	1.44106	+	1.28668i
$834$	0.435606	−	0.274010i	0.0150838	−	0.00948818i
$835$	24.9558	−	25.3631i	0.863633	−	0.877725i
$836$			4.98687i			0.172474i
$837$	−24.6759	−	3.68187i	−0.852924	−	0.127264i
$838$	−7.14907	+	7.14907i	−0.246960	+	0.246960i
$839$	14.3317	−	24.8232i	0.494785	−	0.856992i	−0.505197	−	0.863004i	$-0.668580\pi$
$839$	14.3317	−	24.8232i	0.494785	−	0.856992i	0.999982	+	0.00601183i	$0.00191364\pi$
$840$	0.760187	+	10.2187i	0.0262289	+	0.352579i
$841$	−14.0381	−	24.3147i	−0.484073	−	0.838439i
$842$	5.39254	+	1.44493i	0.185839	+	0.0497955i
$843$	28.7749	−	31.0428i	0.991062	−	1.06917i
$844$	−13.6413	−	7.87579i	−0.469552	−	0.271096i
$845$	10.8530	+	18.4515i	0.373355	+	0.634751i
$846$	2.78011	+	36.6121i	0.0955820	+	1.25875i
$847$	−13.6651	−	22.1952i	−0.469537	−	0.762635i
$848$	3.66713	−	0.982604i	0.125930	−	0.0337428i
$849$	−16.4179	−	8.66675i	−0.563462	−	0.297442i
$850$	−39.8217	+	0.644576i	−1.36587	+	0.0221088i
$851$	17.6097	+	30.5009i	0.603653	+	1.04556i
$852$	1.29170	−	0.399137i	0.0442530	−	0.0136742i
$853$	−3.98774	−	14.8825i	−0.136538	−	0.509565i	−0.999987	−	0.00512962i	$-0.998367\pi$
$853$	−3.98774	−	14.8825i	−0.136538	−	0.509565i	0.863449	−	0.504436i	$-0.168299\pi$
$854$	−7.33524	+	30.8370i	−0.251007	+	1.05522i
$855$	−17.8175	−	25.6302i	−0.609345	−	0.876535i
$856$	−6.90016			−0.235843
$857$	−16.8315	+	4.50997i	−0.574951	+	0.154058i	−0.534566	−	0.845126i	$-0.679525\pi$
$857$	−16.8315	+	4.50997i	−0.574951	+	0.154058i	−0.0403849	+	0.999184i	$0.512858\pi$
$858$	2.52000	+	2.33590i	0.0860313	+	0.0797463i
$859$	7.04980	+	12.2106i	0.240536	+	0.416621i	0.960867	−	0.277010i	$-0.0893434\pi$
$859$	7.04980	+	12.2106i	0.240536	+	0.416621i	−0.720331	+	0.693630i	$0.756010\pi$
$860$	−4.21004	+	1.16467i	−0.143561	+	0.0397150i
$861$	21.5424	−	7.32979i	0.734164	−	0.249799i
$862$	0.220422	+	0.822627i	0.00750762	+	0.0280188i
$863$	−11.7550	−	11.7550i	−0.400145	−	0.400145i	0.478139	−	0.878284i	$-0.341311\pi$
$863$	−11.7550	−	11.7550i	−0.400145	−	0.400145i	−0.878284	+	0.478139i	$0.841311\pi$
$864$	−3.09178	−	4.17623i	−0.105184	−	0.142078i
$865$	−6.64608	+	25.6314i	−0.225973	+	0.871495i
$866$	24.0764	+	13.9005i	0.818149	+	0.472358i
$867$	17.8628	−	78.4407i	0.606652	−	2.66399i
$868$	6.03824	−	11.1766i	0.204951	−	0.379360i
$869$	−4.30785	+	2.48714i	−0.146134	+	0.0843705i
$870$	−3.13477	+	2.00746i	−0.106279	+	0.0680591i
$871$	−3.00597	−	1.73550i	−0.101853	−	0.0588050i
$872$	3.14847	−	3.14847i	0.106621	−	0.106621i
$873$	4.15378	+	0.781683i	0.140584	+	0.0264560i
$874$	19.3417			0.654241
$875$	1.55361	+	29.5396i	0.0525215	+	0.998620i
$876$	−1.82055	+	3.44877i	−0.0615105	+	0.116523i
$877$	31.1289	+	8.34097i	1.05115	+	0.281655i	0.742727	−	0.669595i	$-0.233532\pi$
$877$	31.1289	+	8.34097i	1.05115	+	0.281655i	0.308423	+	0.951249i	$0.400199\pi$
$878$	−33.1708	−	8.88808i	−1.11946	−	0.299958i
$879$	−20.7408	−	10.9487i	−0.699571	−	0.369292i
$880$	0.0193927	+	2.39631i	0.000653729	+	0.0807795i
$881$		−	10.0495i		−	0.338575i	−0.985567	−	0.169288i	$-0.945853\pi$
$881$		−	10.0495i		−	0.338575i	0.985567	−	0.169288i	$-0.0541467\pi$
$882$	−2.71138	+	20.8242i	−0.0912969	+	0.701188i
$883$	−5.70063	−	5.70063i	−0.191842	−	0.191842i	0.604650	−	0.796491i	$-0.293313\pi$
$883$	−5.70063	−	5.70063i	−0.191842	−	0.191842i	−0.796491	+	0.604650i	$0.793313\pi$
$884$	12.7694	+	7.37242i	0.429482	+	0.247961i
$885$	−6.87077	+	31.3409i	−0.230958	+	1.05351i
$886$	17.4018	+	30.1408i	0.584625	+	1.01260i
$887$	4.03468	−	15.0576i	0.135471	−	0.505585i	−0.864524	−	0.502591i	$-0.832380\pi$
$887$	4.03468	−	15.0576i	0.135471	−	0.505585i	0.999996	−	0.00299434i	$-0.000953129\pi$
$888$	−14.3096	−	3.25862i	−0.480198	−	0.109352i
$889$	−37.6004	+	39.7886i	−1.26108	+	1.33447i
$890$	6.24903	−	24.1001i	0.209468	−	0.807839i
$891$	9.53468	−	1.45641i	0.319424	−	0.0487916i
$892$	−8.78878	−	8.78878i	−0.294270	−	0.294270i
$893$	55.0112	−	14.7402i	1.84088	−	0.493263i
$894$	−12.9396	−	20.5706i	−0.432764	−	0.687985i
$895$	−22.2592	+	39.2849i	−0.744043	+	1.31315i
$896$	2.53522	−	0.756729i	0.0846959	−	0.0252806i
$897$	9.05983	−	9.77386i	0.302499	−	0.326340i
$898$	11.6701	−	3.12700i	0.389437	−	0.104349i
$899$	4.61483			0.153913
$900$	−8.66139	−	12.2466i	−0.288713	−	0.408221i
$901$			30.2405i			1.00746i
$902$	5.14029	−	1.37734i	0.171153	−	0.0458603i
$903$	−8.93249	+	0.591858i	−0.297255	+	0.0196958i
$904$	−7.00531	+	4.04452i	−0.232993	+	0.134519i
$905$	−0.0518277	+	0.0914697i	−0.00172281	+	0.00304056i
$906$	−22.1513	−	11.6933i	−0.735927	−	0.388483i
$907$	2.19884	+	8.20620i	0.0730114	+	0.272482i	0.992775	−	0.119990i	$-0.0382864\pi$
$907$	2.19884	+	8.20620i	0.0730114	+	0.272482i	−0.919764	+	0.392473i	$0.871620\pi$
$908$	11.6288	−	11.6288i	0.385916	−	0.385916i
$909$	30.6746	+	44.8959i	1.01741	+	1.48910i
$910$	5.12729	−	9.67694i	0.169968	−	0.320787i
$911$	−20.8371	+	36.0909i	−0.690364	+	1.19575i	0.281355	+	0.959604i	$0.409216\pi$
$911$	−20.8371	+	36.0909i	−0.690364	+	1.19575i	−0.971719	+	0.236141i	$0.924117\pi$
$912$	−5.47904	+	5.91086i	−0.181429	+	0.195728i
$913$	−5.29448	−	1.41865i	−0.175222	−	0.0469506i
$914$	3.62438	−	2.09253i	0.119884	−	0.0692149i
$915$	−14.0569	−	44.2198i	−0.464708	−	1.46186i
$916$	2.97235	+	1.71609i	0.0982092	+	0.0567011i
$917$	19.0314	−	11.7172i	0.628471	−	0.386935i
$918$	38.5057	−	15.1783i	1.27088	−	0.500960i
$919$			49.5786i			1.63545i	0.575612	+	0.817723i	$0.304764\pi$
$919$			49.5786i			1.63545i	−0.575612	+	0.817723i	$0.695236\pi$
$920$	9.29413	−	0.0752151i	0.306418	−	0.00247977i
$921$	16.6362	+	26.4473i	0.548182	+	0.871470i
$922$	−9.55562	+	35.6621i	−0.314698	+	1.17447i
$923$	−1.39567	−	0.373968i	−0.0459390	−	0.0123093i
$924$	−0.954682	+	4.81745i	−0.0314067	+	0.158482i
$925$	−41.0942	−	10.3013i	−1.35117	−	0.338705i
$926$	−1.68442			−0.0553533
$927$	−34.3531	−	29.5041i	−1.12830	−	0.969043i
$928$	0.679623	+	0.679623i	0.0223097	+	0.0223097i
$929$	−0.859829	+	1.48927i	−0.0282101	+	0.0488613i	−0.879786	−	0.475370i	$-0.842314\pi$
$929$	−0.859829	+	1.48927i	−0.0282101	+	0.0488613i	0.851576	+	0.524232i	$0.175647\pi$
$930$	0.854868	+	18.5763i	0.0280322	+	0.609140i
$931$	32.5207	−	1.84055i	1.06582	−	0.0603215i
$932$	−9.45479	−	2.53340i	−0.309702	−	0.0829844i
$933$	38.6785	−	11.9517i	1.26628	−	0.391280i
$934$	18.2394	−	31.5915i	0.596810	−	1.03371i
$935$	−18.4771	−	4.79100i	−0.604265	−	0.156682i
$936$	0.420478	+	5.53741i	0.0137438	+	0.180996i
$937$	−7.48143	−	7.48143i	−0.244408	−	0.244408i	0.574263	−	0.818671i	$-0.305289\pi$
$937$	−7.48143	−	7.48143i	−0.244408	−	0.244408i	−0.818671	+	0.574263i	$0.805289\pi$
$938$	−0.140219	−	4.95901i	−0.00457830	−	0.161917i
$939$	1.56230	+	41.2081i	0.0509837	+	1.34477i
$940$	26.3769	−	7.29695i	0.860319	−	0.238000i
$941$	−5.49515	+	3.17263i	−0.179137	+	0.103425i	−0.586887	−	0.809669i	$-0.699647\pi$
$941$	−5.49515	+	3.17263i	−0.179137	+	0.103425i	0.407750	+	0.913093i	$0.366313\pi$
$942$	23.8676	+	5.43520i	0.777647	+	0.177088i
$943$	−5.34203	−	19.9367i	−0.173960	−	0.649229i
$944$	8.28437			0.269633
$945$	−12.3055	−	28.1704i	−0.400299	−	0.916385i
$946$	−2.09356			−0.0680676
$947$	−2.29447	−	8.56307i	−0.0745601	−	0.278262i	0.918573	−	0.395251i	$-0.129342\pi$
$947$	−2.29447	−	8.56307i	−0.0745601	−	0.278262i	−0.993133	+	0.116989i	$0.962676\pi$
$948$	−7.83864	−	1.78504i	−0.254587	−	0.0579754i
$949$	3.60949	−	2.08394i	0.117169	−	0.0676475i
$950$	−16.1833	+	16.7158i	−0.525055	+	0.542333i
$951$	−2.22474	−	58.6809i	−0.0721421	−	1.90286i
$952$	0.595651	+	21.0660i	0.0193052	+	0.682752i
$953$	36.8926	+	36.8926i	1.19507	+	1.19507i	0.975626	+	0.219442i	$0.0704236\pi$
$953$	36.8926	+	36.8926i	1.19507	+	1.19507i	0.219442	+	0.975626i	$0.429576\pi$
$954$	−9.40407	+	6.42522i	−0.304468	+	0.208024i
$955$	29.7497	−	17.4985i	0.962678	−	0.566239i
$956$	6.87924	−	11.9152i	0.222491	−	0.385365i
$957$	−1.70456	+	0.526711i	−0.0551007	+	0.0170262i
$958$	−26.9496	−	7.22112i	−0.870701	−	0.233304i
$959$	−10.1662	−	34.0591i	−0.328283	−	1.09983i
$960$	−2.60982	+	2.86161i	−0.0842316	+	0.0923582i
$961$	−3.97303	+	6.88150i	−0.128162	+	0.221984i
$962$	11.0908	+	11.0908i	0.357582	+	0.357582i
$963$	19.5321	−	6.85625i	0.629412	−	0.220940i
$964$	−13.6958			−0.441113
$965$	14.1321	−	14.3627i	0.454927	−	0.462350i
$966$	18.6846	+	3.70275i	0.601166	+	0.119134i
$967$	29.9967	+	8.03760i	0.964629	+	0.258472i	0.706559	−	0.707654i	$-0.250247\pi$
$967$	29.9967	+	8.03760i	0.964629	+	0.258472i	0.258071	+	0.966126i	$0.416913\pi$
$968$	2.54975	−	9.51579i	0.0819520	−	0.305849i
$969$	−34.1824	−	54.3413i	−1.09810	−	1.74569i
$970$	−0.0254945	−	3.15028i	−0.000818578	−	0.101149i
$971$		−	21.4595i		−	0.688667i	−0.938847	−	0.344333i	$-0.888105\pi$
$971$		−	21.4595i		−	0.688667i	0.938847	−	0.344333i	$-0.111895\pi$
$972$	12.9015	+	8.74942i	0.413814	+	0.280638i
$973$	−0.412132	−	0.669397i	−0.0132123	−	0.0214599i
$974$	−6.29045	−	3.63179i	−0.201559	−	0.116370i
$975$	0.866533	+	16.0077i	0.0277513	+	0.512657i
$976$	−10.3754	+	5.99025i	−0.332109	+	0.191743i
$977$	56.1992	+	15.0585i	1.79797	+	0.481765i	0.993658	−	0.112442i	$-0.0358672\pi$
$977$	56.1992	+	15.0585i	1.79797	+	0.481765i	0.804312	+	0.594207i	$0.202534\pi$
$978$	16.7024	−	18.0188i	0.534085	−	0.576178i
$979$	5.96631	−	10.3340i	0.190684	−	0.330275i
$980$	15.6198	−	1.01089i	0.498956	−	0.0322918i
$981$	−5.78385	+	12.0407i	−0.184664	+	0.384431i
$982$	−5.53927	+	5.53927i	−0.176765	+	0.176765i
$983$	−7.71120	−	28.7786i	−0.245949	−	0.917895i	−0.972904	−	0.231209i	$-0.925732\pi$
$983$	−7.71120	−	28.7786i	−0.245949	−	0.917895i	0.726955	−	0.686685i	$-0.240935\pi$
$984$	7.60598	+	4.01507i	0.242470	+	0.127996i
$985$	−24.5810	+	6.80013i	−0.783215	+	0.216670i
$986$	−6.63010	+	3.82789i	−0.211145	+	0.121905i
$987$	55.9642	−	3.70813i	1.78136	−	0.118031i
$988$	8.32020	−	2.22939i	0.264701	−	0.0709263i
$989$			8.11992i			0.258198i
$990$	−2.43595	−	6.76389i	−0.0774197	−	0.214970i
$991$	−17.3014			−0.549596			−0.274798	−	0.961502i	$-0.588611\pi$
$991$	−17.3014			−0.549596			−0.274798	+	0.961502i	$0.588611\pi$
$992$	4.63785	−	1.24271i	0.147252	−	0.0394560i
$993$	−6.01468	+	6.48872i	−0.190870	+	0.205913i
$994$	−0.590670	−	1.97889i	−0.0187349	−	0.0627665i
$995$	−21.8960	−	12.4065i	−0.694149	−	0.393312i
$996$	−4.71681	−	7.49852i	−0.149458	−	0.237600i
$997$	21.8327	−	5.85006i	0.691450	−	0.185273i	0.104052	−	0.994572i	$-0.466819\pi$
$997$	21.8327	−	5.85006i	0.691450	−	0.185273i	0.587398	+	0.809298i	$0.300152\pi$
$998$	−26.5819	−	26.5819i	−0.841434	−	0.841434i
$999$	43.7435	−	4.99443i	1.38398	−	0.158017i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bz.a.223.27	yes	192
5.2	odd	4	inner	630.2.bz.a.97.10	yes	192
7.6	odd	2	inner	630.2.bz.a.223.46	yes	192
9.4	even	3	inner	630.2.bz.a.13.15	yes	192
35.27	even	4	inner	630.2.bz.a.97.15	yes	192
45.22	odd	12	inner	630.2.bz.a.517.46	yes	192
63.13	odd	6	inner	630.2.bz.a.13.10	✓	192
315.202	even	12	inner	630.2.bz.a.517.27	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bz.a.13.10	✓	192	63.13	odd	6	inner
630.2.bz.a.13.15	yes	192	9.4	even	3	inner
630.2.bz.a.97.10	yes	192	5.2	odd	4	inner
630.2.bz.a.97.15	yes	192	35.27	even	4	inner
630.2.bz.a.223.27	yes	192	1.1	even	1	trivial
630.2.bz.a.223.46	yes	192	7.6	odd	2	inner
630.2.bz.a.517.27	yes	192	315.202	even	12	inner
630.2.bz.a.517.46	yes	192	45.22	odd	12	inner

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:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.68882 - 0.384583i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.94548 - 1.10233i) q^{5} +(-0.0656192 - 1.73081i) q^{6} +(-2.64469 + 0.0747801i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.70419 + 1.29898i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(-1.68882 - 0.384583i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.94548 - 1.10233i) q^{5} +(-0.0656192 - 1.73081i) q^{6} +(-2.64469 + 0.0747801i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.70419 + 1.29898i) q^{9} +(0.561239 - 2.16449i) q^{10} +(0.535848 - 0.928117i) q^{11} +(1.65485 - 0.511349i) q^{12} +(-1.78804 - 0.479104i) q^{13} +(-0.756729 - 2.53522i) q^{14} +(2.86161 + 2.60982i) q^{15} +(0.500000 - 0.866025i) q^{16} +(5.63237 + 5.63237i) q^{17} +(-0.554820 + 2.94825i) q^{18} +4.65324 q^{19} +(2.23599 - 0.0180954i) q^{20} +(4.49516 + 0.890814i) q^{21} +(1.03518 + 0.277376i) q^{22} +(1.07581 - 4.01496i) q^{23} +(0.922232 + 1.46611i) q^{24} +(2.56975 + 4.28910i) q^{25} -1.85112i q^{26} +(-4.06732 - 3.23372i) q^{27} +(2.25298 - 1.38711i) q^{28} +(0.832365 + 0.480566i) q^{29} +(-1.78025 + 3.43958i) q^{30} +(4.15818 - 2.40073i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.26189 + 1.36134i) q^{33} +(-3.98269 + 6.89822i) q^{34} +(5.22762 + 2.76983i) q^{35} +(-2.99139 + 0.227148i) q^{36} +(-5.99141 + 5.99141i) q^{37} +(1.20435 + 4.49469i) q^{38} +(2.83542 + 1.49677i) q^{39} +(0.596197 + 2.15512i) q^{40} +(4.30034 - 2.48280i) q^{41} +(0.302973 + 4.57255i) q^{42} +(-1.88694 + 0.505604i) q^{43} +1.07170i q^{44} +(-3.82904 - 5.50803i) q^{45} +4.15660 q^{46} +(11.8221 - 3.16773i) q^{47} +(-1.17747 + 1.27027i) q^{48} +(6.98882 - 0.395541i) q^{49} +(-3.47785 + 3.59229i) q^{50} +(-7.34592 - 11.6781i) q^{51} +(1.78804 - 0.479104i) q^{52} +(2.68452 + 2.68452i) q^{53} +(2.07083 - 4.76567i) q^{54} +(-2.06557 + 1.21495i) q^{55} +(1.92296 + 1.81720i) q^{56} +(-7.85847 - 1.78956i) q^{57} +(-0.248759 + 0.928383i) q^{58} +(4.14219 + 7.17448i) q^{59} +(-3.78314 - 0.829365i) q^{60} +(-10.3754 - 5.99025i) q^{61} +(3.39514 + 3.39514i) q^{62} +(-7.24890 - 3.23318i) q^{63} +1.00000i q^{64} +(2.95046 + 2.90309i) q^{65} +(-1.64155 - 0.866548i) q^{66} +(1.81119 + 0.485306i) q^{67} +(-7.69396 - 2.06159i) q^{68} +(-3.36092 + 6.36679i) q^{69} +(-1.32245 + 5.76638i) q^{70} +0.780557 q^{71} +(-0.993637 - 2.83067i) q^{72} +(-1.59208 + 1.59208i) q^{73} +(-7.33795 - 4.23657i) q^{74} +(-2.69033 - 8.23178i) q^{75} +(-4.02983 + 2.32662i) q^{76} +(-1.34775 + 2.49466i) q^{77} +(-0.711908 + 3.12619i) q^{78} +(-4.01966 - 2.32075i) q^{79} +(-1.92738 + 1.13367i) q^{80} +(5.62531 + 7.02537i) q^{81} +(3.51121 + 3.51121i) q^{82} +(-1.32374 - 4.94028i) q^{83} +(-4.33833 + 1.47611i) q^{84} +(-4.74893 - 17.1664i) q^{85} +(-0.976751 - 1.69178i) q^{86} +(-1.22089 - 1.13170i) q^{87} +(-1.03518 + 0.277376i) q^{88} +11.1343 q^{89} +(4.32932 - 5.12416i) q^{90} +(4.76465 + 1.13337i) q^{91} +(1.07581 + 4.01496i) q^{92} +(-7.94567 + 2.45522i) q^{93} +(6.11958 + 10.5994i) q^{94} +(-9.05278 - 5.12939i) q^{95} +(-1.53173 - 0.808576i) q^{96} +(1.36089 - 0.364649i) q^{97} +(2.19090 + 6.64830i) q^{98} +(2.65464 - 1.81375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} + 24 q^{15} + 96 q^{16} - 8 q^{18} + 8 q^{23} + 48 q^{30} - 24 q^{35} + 8 q^{36} - 44 q^{42} + 48 q^{46} + 32 q^{50} - 160 q^{53} - 4 q^{56} + 88 q^{57} + 24 q^{58} + 8 q^{60} - 48 q^{63} - 8 q^{65} + 16 q^{71} + 16 q^{72} - 16 q^{77} - 16 q^{78} - 8 q^{81} - 16 q^{86} + 8 q^{92} - 120 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 + 24 * q^15 + 96 * q^16 - 8 * q^18 + 8 * q^23 + 48 * q^30 - 24 * q^35 + 8 * q^36 - 44 * q^42 + 48 * q^46 + 32 * q^50 - 160 * q^53 - 4 * q^56 + 88 * q^57 + 24 * q^58 + 8 * q^60 - 48 * q^63 - 8 * q^65 + 16 * q^71 + 16 * q^72 - 16 * q^77 - 16 * q^78 - 8 * q^81 - 16 * q^86 + 8 * q^92 - 120 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

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Database

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