LMFDB - Embedded newform 570.2.bc.b.169.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.10
Character	$\chi$	$=$	570.169
Dual form			570.2.bc.b.199.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.15457 + 0.598186i) q^{5} +(0.766044 - 0.642788i) q^{6} +(2.40081 - 1.38611i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})$	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.15457 + 0.598186i) q^{5} +(0.766044 - 0.642788i) q^{6} +(2.40081 - 1.38611i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(2.01796 + 0.963235i) q^{10} +(-1.10454 + 1.91312i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-0.659181 - 0.785581i) q^{13} +(2.60503 - 0.948155i) q^{14} +(1.84317 - 1.26599i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-8.11995 - 1.43177i) q^{17} -1.00000i q^{18} +(-1.67623 + 4.02371i) q^{19} +(1.82004 + 1.29902i) q^{20} +(0.481391 - 2.73010i) q^{21} +(-1.41997 + 1.69226i) q^{22} +(0.822825 - 2.26069i) q^{23} +(0.939693 - 0.342020i) q^{24} +(4.28435 + 2.57767i) q^{25} +(-0.512752 - 0.888112i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(2.73010 - 0.481391i) q^{28} +(-0.0148958 - 0.0844781i) q^{29} +(2.03500 - 0.926694i) q^{30} +(-0.201850 - 0.349614i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.755552 + 2.07586i) q^{33} +(-7.74796 - 2.82003i) q^{34} +(6.00187 - 1.55034i) q^{35} +(0.173648 - 0.984808i) q^{36} -4.33025i q^{37} +(-2.34948 + 3.67151i) q^{38} -1.02550 q^{39} +(1.56682 + 1.59533i) q^{40} +(8.79291 + 7.37813i) q^{41} +(0.948155 - 2.60503i) q^{42} +(-1.50315 - 4.12987i) q^{43} +(-1.69226 + 1.41997i) q^{44} +(0.214961 - 2.22571i) q^{45} +(1.20289 - 2.08347i) q^{46} +(-10.4322 + 1.83947i) q^{47} +(0.984808 - 0.173648i) q^{48} +(0.342598 - 0.593398i) q^{49} +(3.77165 + 3.28248i) q^{50} +(-6.31620 + 5.29992i) q^{51} +(-0.350743 - 0.963658i) q^{52} +(2.71590 - 7.46188i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(-3.52422 + 3.46124i) q^{55} +2.77222 q^{56} +(2.00488 + 3.87046i) q^{57} -0.0857813i q^{58} +(-0.545658 + 3.09458i) q^{59} +(2.16501 - 0.559241i) q^{60} +(5.31303 + 1.93378i) q^{61} +(-0.138073 - 0.379353i) q^{62} +(-1.78195 - 2.12364i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.950328 - 2.08690i) q^{65} +(0.383604 + 2.17553i) q^{66} +(3.21125 - 0.566229i) q^{67} +(-7.14056 - 4.12260i) q^{68} +(-1.20289 - 2.08347i) q^{69} +(6.17990 - 0.484572i) q^{70} +(-5.99681 + 2.18266i) q^{71} +(0.342020 - 0.939693i) q^{72} +(5.49130 - 6.54427i) q^{73} +(0.751940 - 4.26447i) q^{74} +(4.72853 - 1.62511i) q^{75} +(-2.95133 + 3.20774i) q^{76} +6.12407i q^{77} +(-1.00992 - 0.178077i) q^{78} +(-9.58185 - 8.04013i) q^{79} +(1.26599 + 1.84317i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(7.37813 + 8.79291i) q^{82} +(-10.0943 + 5.82793i) q^{83} +(1.38611 - 2.40081i) q^{84} +(-16.6385 - 7.94208i) q^{85} +(-0.763168 - 4.32814i) q^{86} +(-0.0742888 - 0.0428906i) q^{87} +(-1.91312 + 1.10454i) q^{88} +(-8.44569 + 7.08677i) q^{89} +(0.598186 - 2.15457i) q^{90} +(-2.67147 - 0.972336i) q^{91} +(1.54640 - 1.84293i) q^{92} +(-0.397566 - 0.0701016i) q^{93} -10.5931 q^{94} +(-6.01849 + 7.66667i) q^{95} +1.00000 q^{96} +(0.603596 + 0.106430i) q^{97} +(0.440436 - 0.524891i) q^{98} +(2.07586 + 0.755552i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 6 q^{5}+O(q^{10}) $ 60 * q + 6 * q^5	$ 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$-1$

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 $

$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$2$	0.984808	+	0.173648i	0.696364	+	0.122788i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$3$	0.642788	−	0.766044i	0.371114	−	0.442276i
$4$	0.939693	+	0.342020i	0.469846	+	0.171010i
$5$	2.15457	+	0.598186i	0.963553	+	0.267517i
$5$	2.15457	+	0.598186i	0.963553	+	0.267517i
$6$	0.766044	−	0.642788i	0.312736	−	0.262417i
$7$	2.40081	−	1.38611i	0.907422	−	0.523900i	0.0278209	−	0.999613i	$-0.491143\pi$
$7$	2.40081	−	1.38611i	0.907422	−	0.523900i	0.879601	+	0.475713i	$0.157810\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	−0.173648	−	0.984808i	−0.0578827	−	0.328269i
$10$	2.01796	+	0.963235i	0.638136	+	0.304602i
$11$	−1.10454	+	1.91312i	−0.333032	+	0.576829i	−0.983105	−	0.183043i	$-0.941405\pi$
$11$	−1.10454	+	1.91312i	−0.333032	+	0.576829i	0.650073	+	0.759872i	$0.274738\pi$
$12$	0.866025	−	0.500000i	0.250000	−	0.144338i
$13$	−0.659181	−	0.785581i	−0.182824	−	0.217881i	0.666847	−	0.745195i	$-0.267644\pi$
$13$	−0.659181	−	0.785581i	−0.182824	−	0.217881i	−0.849671	+	0.527314i	$0.823199\pi$
$14$	2.60503	−	0.948155i	0.696224	−	0.253405i
$15$	1.84317	−	1.26599i	0.475904	−	0.326877i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−8.11995	−	1.43177i	−1.96938	−	0.347254i	−0.987395	−	0.158273i	$-0.949407\pi$
$17$	−8.11995	−	1.43177i	−1.96938	−	0.347254i	−0.981981	−	0.188981i	$-0.939481\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−1.67623	+	4.02371i	−0.384554	+	0.923102i
$19$	−1.67623	+	4.02371i	−0.384554	+	0.923102i
$20$	1.82004	+	1.29902i	0.406974	+	0.290469i
$21$	0.481391	−	2.73010i	0.105048	−	0.595757i
$22$	−1.41997	+	1.69226i	−0.302739	+	0.360791i
$23$	0.822825	−	2.26069i	0.171571	−	0.471387i	−0.823869	−	0.566781i	$-0.808189\pi$
$23$	0.822825	−	2.26069i	0.171571	−	0.471387i	0.995440	+	0.0953936i	$0.0304110\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	4.28435	+	2.57767i	0.856869	+	0.515533i
$26$	−0.512752	−	0.888112i	−0.100559	−	0.174173i
$27$	−0.866025	−	0.500000i	−0.166667	−	0.0962250i
$28$	2.73010	−	0.481391i	0.515941	−	0.0909743i
$29$	−0.0148958	−	0.0844781i	−0.00276607	−	0.0156872i	0.983393	−	0.181486i	$-0.0580908\pi$
$29$	−0.0148958	−	0.0844781i	−0.00276607	−	0.0156872i	−0.986160	+	0.165799i	$0.946980\pi$
$30$	2.03500	−	0.926694i	0.371539	−	0.169190i
$31$	−0.201850	−	0.349614i	−0.0362532	−	0.0627925i	0.847329	−	0.531068i	$-0.178209\pi$
$31$	−0.201850	−	0.349614i	−0.0362532	−	0.0627925i	−0.883583	+	0.468275i	$0.844876\pi$
$32$	0.642788	+	0.766044i	0.113630	+	0.135419i
$33$	0.755552	+	2.07586i	0.131525	+	0.361361i
$34$	−7.74796	−	2.82003i	−1.32876	−	0.483631i
$35$	6.00187	−	1.55034i	1.01450	−	0.262055i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$		−	4.33025i		−	0.711889i	−0.934507	−	0.355945i	$-0.884159\pi$
$37$		−	4.33025i		−	0.711889i	0.934507	−	0.355945i	$-0.115841\pi$
$38$	−2.34948	+	3.67151i	−0.381136	+	0.595597i
$39$	−1.02550			−0.164212
$40$	1.56682	+	1.59533i	0.247736	+	0.252244i
$41$	8.79291	+	7.37813i	1.37322	+	1.15227i	0.971645	+	0.236445i	$0.0759823\pi$
$41$	8.79291	+	7.37813i	1.37322	+	1.15227i	0.401577	+	0.915825i	$0.368462\pi$
$42$	0.948155	−	2.60503i	0.146303	−	0.401965i
$43$	−1.50315	−	4.12987i	−0.229228	−	0.629799i	0.770745	−	0.637144i	$-0.219884\pi$
$43$	−1.50315	−	4.12987i	−0.229228	−	0.629799i	−0.999973	+	0.00734509i	$0.997662\pi$
$44$	−1.69226	+	1.41997i	−0.255118	+	0.214069i
$45$	0.214961	−	2.22571i	0.0320445	−	0.331789i
$46$	1.20289	−	2.08347i	0.177356	−	0.307190i
$47$	−10.4322	+	1.83947i	−1.52169	+	0.268315i	−0.871097	−	0.491112i	$-0.836591\pi$
$47$	−10.4322	+	1.83947i	−1.52169	+	0.268315i	−0.650593	+	0.759427i	$0.725480\pi$
$48$	0.984808	−	0.173648i	0.142145	−	0.0250640i
$49$	0.342598	−	0.593398i	0.0489426	−	0.0847711i
$50$	3.77165	+	3.28248i	0.533392	+	0.464212i
$51$	−6.31620	+	5.29992i	−0.884444	+	0.742137i
$52$	−0.350743	−	0.963658i	−0.0486393	−	0.133635i
$53$	2.71590	−	7.46188i	0.373058	−	1.02497i	−0.601115	−	0.799163i	$-0.705277\pi$
$53$	2.71590	−	7.46188i	0.373058	−	1.02497i	0.974172	−	0.225805i	$-0.0725013\pi$
$54$	−0.766044	−	0.642788i	−0.104245	−	0.0874723i
$55$	−3.52422	+	3.46124i	−0.475206	+	0.466714i
$56$	2.77222			0.370453
$57$	2.00488	+	3.87046i	0.265553	+	0.512655i
$58$		−	0.0857813i		−	0.0112636i
$59$	−0.545658	+	3.09458i	−0.0710387	+	0.402880i	0.928466	+	0.371417i	$0.121128\pi$
$59$	−0.545658	+	3.09458i	−0.0710387	+	0.402880i	−0.999505	+	0.0314634i	$0.989983\pi$
$60$	2.16501	−	0.559241i	0.279501	−	0.0721977i
$61$	5.31303	+	1.93378i	0.680264	+	0.247596i	0.658961	−	0.752177i	$-0.270996\pi$
$61$	5.31303	+	1.93378i	0.680264	+	0.247596i	0.0213029	+	0.999773i	$0.493219\pi$
$62$	−0.138073	−	0.379353i	−0.0175353	−	0.0481779i
$63$	−1.78195	−	2.12364i	−0.224504	−	0.267554i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−0.950328	−	2.08690i	−0.117874	−	0.258849i
$66$	0.383604	+	2.17553i	0.0472184	+	0.267789i
$67$	3.21125	−	0.566229i	0.392316	−	0.0691759i	0.0259894	−	0.999662i	$-0.491726\pi$
$67$	3.21125	−	0.566229i	0.392316	−	0.0691759i	0.366327	+	0.930486i	$0.380615\pi$
$68$	−7.14056	−	4.12260i	−0.865920	−	0.499939i
$69$	−1.20289	−	2.08347i	−0.144811	−	0.250820i
$70$	6.17990	−	0.484572i	0.738639	−	0.0579174i
$71$	−5.99681	+	2.18266i	−0.711690	+	0.259034i	−0.672394	−	0.740194i	$-0.734734\pi$
$71$	−5.99681	+	2.18266i	−0.711690	+	0.259034i	−0.0392962	+	0.999228i	$0.512512\pi$
$72$	0.342020	−	0.939693i	0.0403075	−	0.110744i
$73$	5.49130	−	6.54427i	0.642708	−	0.765949i	−0.342088	−	0.939668i	$-0.611134\pi$
$73$	5.49130	−	6.54427i	0.642708	−	0.765949i	0.984795	+	0.173719i	$0.0555784\pi$
$74$	0.751940	−	4.26447i	0.0874113	−	0.495734i
$75$	4.72853	−	1.62511i	0.546004	−	0.187651i
$76$	−2.95133	+	3.20774i	−0.338541	+	0.367954i
$77$			6.12407i			0.697903i
$78$	−1.00992	−	0.178077i	−0.114351	−	0.0201632i
$79$	−9.58185	−	8.04013i	−1.07804	−	0.904585i	−0.0822860	−	0.996609i	$-0.526222\pi$
$79$	−9.58185	−	8.04013i	−1.07804	−	0.904585i	−0.995757	+	0.0920234i	$0.970667\pi$
$80$	1.26599	+	1.84317i	0.141542	+	0.206072i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	7.37813	+	8.79291i	0.814778	+	0.971015i
$83$	−10.0943	+	5.82793i	−1.10799	+	0.639698i	−0.938308	−	0.345800i	$-0.887607\pi$
$83$	−10.0943	+	5.82793i	−1.10799	+	0.639698i	−0.169682	+	0.985499i	$0.554274\pi$
$84$	1.38611	−	2.40081i	0.151237	−	0.261950i
$85$	−16.6385	−	7.94208i	−1.80470	−	0.861439i
$86$	−0.763168	−	4.32814i	−0.0822945	−	0.466716i
$87$	−0.0742888	−	0.0428906i	−0.00796459	−	0.00459836i
$88$	−1.91312	+	1.10454i	−0.203940	+	0.117745i
$89$	−8.44569	+	7.08677i	−0.895241	+	0.751196i	−0.969254	−	0.246061i	$-0.920864\pi$
$89$	−8.44569	+	7.08677i	−0.895241	+	0.751196i	0.0740135	+	0.997257i	$0.476419\pi$
$90$	0.598186	−	2.15457i	0.0630543	−	0.227112i
$91$	−2.67147	−	0.972336i	−0.280046	−	0.101929i
$92$	1.54640	−	1.84293i	0.161224	−	0.192139i
$93$	−0.397566	−	0.0701016i	−0.0412257	−	0.00726920i
$94$	−10.5931			−1.09260
$95$	−6.01849	+	7.66667i	−0.617484	+	0.786583i
$96$	1.00000			0.102062
$97$	0.603596	+	0.106430i	0.0612859	+	0.0108063i	0.204207	−	0.978928i	$-0.434538\pi$
$97$	0.603596	+	0.106430i	0.0612859	+	0.0108063i	−0.142921	+	0.989734i	$0.545650\pi$
$98$	0.440436	−	0.524891i	0.0444908	−	0.0530220i
$99$	2.07586	+	0.755552i	0.208632	+	0.0759358i
$100$	3.14436	+	3.88755i	0.314436	+	0.388755i
$101$	6.94672	−	5.82899i	0.691224	−	0.580006i	−0.228038	−	0.973652i	$-0.573231\pi$
$101$	6.94672	−	5.82899i	0.691224	−	0.580006i	0.919262	+	0.393646i	$0.128787\pi$
$102$	−7.14056	+	4.12260i	−0.707021	+	0.408199i
$103$	9.20468	+	5.31432i	0.906964	+	0.523636i	0.879453	−	0.475986i	$-0.157909\pi$
$103$	9.20468	+	5.31432i	0.906964	+	0.523636i	0.0275108	+	0.999622i	$0.491242\pi$
$104$	−0.178077	−	1.00992i	−0.0174619	−	0.0990312i
$105$	2.67030	−	5.59424i	0.260595	−	0.545942i
$106$	3.97038	−	6.87691i	0.385638	−	0.667944i
$107$	−6.80853	+	3.93091i	−0.658206	+	0.380015i	−0.791593	−	0.611049i	$-0.790748\pi$
$107$	−6.80853	+	3.93091i	−0.658206	+	0.380015i	0.133387	+	0.991064i	$0.457415\pi$
$108$	−0.642788	−	0.766044i	−0.0618523	−	0.0737127i
$109$	1.89856	−	0.691020i	0.181849	−	0.0661877i	−0.249491	−	0.968377i	$-0.580263\pi$
$109$	1.89856	−	0.691020i	0.181849	−	0.0661877i	0.431340	+	0.902189i	$0.358041\pi$
$110$	−4.07172	+	2.79668i	−0.388223	+	0.266653i
$111$	−3.31717	−	2.78343i	−0.314851	−	0.264192i
$112$	2.73010	+	0.481391i	0.257970	+	0.0454871i
$113$			20.3838i			1.91754i	0.284177	+	0.958772i	$0.408280\pi$
$113$			20.3838i			1.91754i	−0.284177	+	0.958772i	$0.591720\pi$
$114$	1.30232	+	4.15980i	0.121974	+	0.389601i
$115$	3.12515	−	4.37862i	0.291422	−	0.408308i
$116$	0.0148958	−	0.0844781i	0.00138304	−	0.00784359i
$117$	−0.659181	+	0.785581i	−0.0609413	+	0.0726270i
$118$	−1.07474	+	2.95282i	−0.0989376	+	0.271829i
$119$	−21.4790	+	7.81773i	−1.96898	+	0.716650i
$120$	2.22923	−	0.174796i	0.203500	−	0.0159566i
$121$	3.05997	+	5.30002i	0.278179	+	0.481820i
$122$	4.89651	+	2.82700i	0.443310	+	0.255945i
$123$	11.3039	−	1.99319i	1.01924	−	0.179720i
$124$	−0.0701016	−	0.397566i	−0.00629531	−	0.0357025i
$125$	7.68900	+	8.11660i	0.687725	+	0.725971i
$126$	−1.38611	−	2.40081i	−0.123484	−	0.213881i
$127$	−3.32845	−	3.96669i	−0.295352	−	0.351987i	0.597878	−	0.801587i	$-0.296011\pi$
$127$	−3.32845	−	3.96669i	−0.295352	−	0.351987i	−0.893230	+	0.449601i	$0.851566\pi$
$128$	0.342020	+	0.939693i	0.0302306	+	0.0830579i
$129$	−4.12987	−	1.50315i	−0.363614	−	0.132345i
$130$	−0.573504	−	2.22022i	−0.0502996	−	0.194726i
$131$	3.15063	−	17.8681i	0.275272	−	1.56115i	−0.462824	−	0.886450i	$-0.653164\pi$
$131$	3.15063	−	17.8681i	0.275272	−	1.56115i	0.738096	−	0.674695i	$-0.235725\pi$
$132$			2.20909i			0.192276i
$133$	1.55298	+	11.9836i	0.134660	+	1.03911i
$134$	3.26078			0.281689
$135$	−1.56682	−	1.59533i	−0.134850	−	0.137304i
$136$	−6.31620	−	5.29992i	−0.541609	−	0.454464i
$137$	−0.401229	+	1.10237i	−0.0342793	+	0.0941816i	−0.955652	−	0.294500i	$-0.904847\pi$
$137$	−0.401229	+	1.10237i	−0.0342793	+	0.0941816i	0.921372	+	0.388681i	$0.127069\pi$
$138$	−0.822825	−	2.26069i	−0.0700435	−	0.192443i
$139$	2.11224	−	1.77238i	0.179158	−	0.150332i	−0.548799	−	0.835955i	$-0.684915\pi$
$139$	2.11224	−	1.77238i	0.179158	−	0.150332i	0.727957	+	0.685623i	$0.240470\pi$
$140$	6.17016	+	0.595919i	0.521474	+	0.0503643i
$141$	−5.29656	+	9.17390i	−0.446050	+	0.772582i
$142$	−6.28472	+	1.10816i	−0.527402	+	0.0929951i
$143$	2.23101	−	0.393387i	0.186566	−	0.0328967i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$	0.0184396	−	0.190924i	0.00153133	−	0.0158554i
$146$	6.54427	−	5.49130i	0.541608	−	0.454463i
$147$	−0.234351	−	0.643874i	−0.0193290	−	0.0531059i
$148$	1.48103	−	4.06911i	0.121740	−	0.334478i
$149$	−16.3974	−	13.7590i	−1.34333	−	1.12719i	−0.980758	−	0.195228i	$-0.937455\pi$
$149$	−16.3974	−	13.7590i	−1.34333	−	1.12719i	−0.362569	−	0.931957i	$-0.618100\pi$
$150$	4.93889	−	0.779318i	0.403259	−	0.0636310i
$151$	6.67936			0.543558			0.271779	−	0.962360i	$-0.412388\pi$
$151$	6.67936			0.543558			0.271779	+	0.962360i	$0.412388\pi$
$152$	−3.46352	+	2.64652i	−0.280928	+	0.214661i
$153$			8.24521i			0.666586i
$154$	−1.06343	+	6.03103i	−0.0856939	+	0.485994i
$155$	−0.225765	−	0.874011i	−0.0181339	−	0.0702022i
$156$	−0.963658	−	0.350743i	−0.0771544	−	0.0280819i
$157$	−5.13098	−	14.0973i	−0.409497	−	1.12508i	−0.957456	−	0.288579i	$-0.906817\pi$
$157$	−5.13098	−	14.0973i	−0.409497	−	1.12508i	0.547959	−	0.836505i	$-0.315405\pi$
$158$	−8.04013	−	9.58185i	−0.639638	−	0.762291i
$159$	−3.97038	−	6.87691i	−0.314872	−	0.545374i
$160$	0.926694	+	2.03500i	0.0732616	+	0.160881i
$161$	−1.15812	−	6.56802i	−0.0912726	−	0.517633i
$162$	−0.984808	+	0.173648i	−0.0773738	+	0.0136431i
$163$	−11.2373	−	6.48785i	−0.880172	−	0.508167i	−0.00945660	−	0.999955i	$-0.503010\pi$
$163$	−11.2373	−	6.48785i	−0.880172	−	0.508167i	−0.870715	+	0.491788i	$0.836344\pi$
$164$	5.73917	+	9.94053i	0.448154	+	0.776225i
$165$	0.386139	+	4.92455i	0.0300608	+	0.383376i
$166$	−10.9529	+	3.98654i	−0.850112	+	0.309415i
$167$	−4.11761	+	11.3130i	−0.318630	+	0.875428i	0.672207	+	0.740363i	$0.265347\pi$
$167$	−4.11761	+	11.3130i	−0.318630	+	0.875428i	−0.990837	+	0.135065i	$0.956876\pi$
$168$	1.78195	−	2.12364i	0.137480	−	0.163843i
$169$	2.07481	−	11.7668i	0.159601	−	0.905140i
$170$	−15.0066	−	10.7107i	−1.15096	−	0.821471i
$171$	4.25366	+	0.952058i	0.325285	+	0.0728057i
$172$		−	4.39491i		−	0.335109i
$173$	23.1331	+	4.07900i	1.75878	+	0.310120i	0.957557	−	0.288245i	$-0.0930718\pi$
$173$	23.1331	+	4.07900i	1.75878	+	0.310120i	0.801223	+	0.598365i	$0.204183\pi$
$174$	−0.0657123	−	0.0551392i	−0.00498164	−	0.00418009i
$175$	13.8588	+	0.249920i	1.04763	+	0.0188922i
$176$	−2.07586	+	0.755552i	−0.156474	+	0.0569519i
$177$	2.01984	+	2.40716i	0.151821	+	0.180933i
$178$	−9.54798	+	5.51253i	−0.715651	+	0.413182i
$179$	−9.34740	+	16.1902i	−0.698657	+	1.21011i	0.270275	+	0.962783i	$0.412885\pi$
$179$	−9.34740	+	16.1902i	−0.698657	+	1.21011i	−0.968932	+	0.247327i	$0.920448\pi$
$180$	0.963235	−	2.01796i	0.0717953	−	0.150410i
$181$	1.23439	+	7.00057i	0.0917515	+	0.520348i	0.995694	+	0.0926956i	$0.0295483\pi$
$181$	1.23439	+	7.00057i	0.0917515	+	0.520348i	−0.903943	+	0.427653i	$0.859341\pi$
$182$	−2.46204	−	1.42146i	−0.182499	−	0.105366i
$183$	4.89651	−	2.82700i	0.361961	−	0.208978i
$184$	1.84293	−	1.54640i	0.135863	−	0.114002i
$185$	2.59030	−	9.32983i	0.190442	−	0.685943i
$186$	−0.379353	−	0.138073i	−0.0278155	−	0.0101240i
$187$	11.7080	−	13.9530i	0.856172	−	1.02035i
$188$	−10.4322	−	1.83947i	−0.760845	−	0.134157i
$189$	−2.77222			−0.201649
$190$	−7.25836	+	6.50509i	−0.526577	+	0.471929i
$191$	14.9834			1.08416			0.542080	−	0.840327i	$-0.317637\pi$
$191$	14.9834			1.08416			0.542080	+	0.840327i	$0.317637\pi$
$192$	0.984808	+	0.173648i	0.0710724	+	0.0125320i
$193$	9.68697	−	11.5445i	0.697283	−	0.830990i	−0.294933	−	0.955518i	$-0.595297\pi$
$193$	9.68697	−	11.5445i	0.697283	−	0.830990i	0.992216	+	0.124528i	$0.0397417\pi$
$194$	0.575944	+	0.209627i	0.0413504	+	0.0150503i
$195$	−2.20952	−	0.613442i	−0.158227	−	0.0439295i
$196$	0.524891	−	0.440436i	0.0374922	−	0.0314597i
$197$	3.10916	−	1.79507i	0.221518	−	0.127894i	−0.385135	−	0.922860i	$-0.625845\pi$
$197$	3.10916	−	1.79507i	0.221518	−	0.127894i	0.606653	+	0.794967i	$0.292512\pi$
$198$	1.91312	+	1.10454i	0.135960	+	0.0784965i
$199$	−1.38562	−	7.85824i	−0.0982239	−	0.557056i	−0.993712	−	0.111969i	$-0.964284\pi$
$199$	−1.38562	−	7.85824i	−0.0982239	−	0.557056i	0.895488	−	0.445086i	$-0.146827\pi$
$200$	2.42152	+	4.37450i	0.171227	+	0.309324i
$201$	1.63039	−	2.82392i	0.114999	−	0.199184i
$202$	7.85337	−	4.53415i	0.552561	−	0.319021i
$203$	−0.152858	−	0.182169i	−0.0107285	−	0.0127857i
$204$	−7.74796	+	2.82003i	−0.542466	+	0.197441i
$205$	14.5315	+	21.1565i	1.01492	+	1.47763i
$206$	8.14202	+	6.83196i	0.567281	+	0.476005i
$207$	−2.36923	−	0.417759i	−0.164673	−	0.0290363i
$208$		−	1.02550i		−	0.0711059i
$209$	−5.84639	−	7.65121i	−0.404403	−	0.529245i
$210$	3.60116	−	5.04556i	0.248504	−	0.348176i
$211$	0.0125256	−	0.0710364i	0.000862300	−	0.00489035i	−0.984374	−	0.176093i	$-0.943654\pi$
$211$	0.0125256	−	0.0710364i	0.000862300	−	0.00489035i	0.985236	+	0.171202i	$0.0547652\pi$
$212$	5.10423	−	6.08298i	0.350560	−	0.417781i
$213$	−2.18266	+	5.99681i	−0.149553	+	0.410894i
$214$	−7.38769	+	2.68890i	−0.505012	+	0.183809i
$215$	−0.768211	−	9.79725i	−0.0523916	−	0.668167i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	−0.969205	−	0.559571i	−0.0657940	−	0.0379862i
$218$	1.98971	−	0.350840i	0.134760	−	0.0237619i
$219$	−1.48347	−	8.41316i	−0.100243	−	0.568508i
$220$	−4.49550	+	2.04715i	−0.303086	+	0.138019i
$221$	4.22775	+	7.32267i	0.284389	+	0.492576i
$222$	−2.78343	−	3.31717i	−0.186812	−	0.222634i
$223$	5.19677	+	14.2780i	0.348002	+	0.956127i	0.982999	+	0.183612i	$0.0587791\pi$
$223$	5.19677	+	14.2780i	0.348002	+	0.956127i	−0.634997	+	0.772515i	$0.718999\pi$
$224$	2.60503	+	0.948155i	0.174056	+	0.0633512i
$225$	1.79454	−	4.66687i	0.119636	−	0.311124i
$226$	−3.53960	+	20.0741i	−0.235451	+	1.33531i
$227$		−	6.94543i		−	0.460984i	−0.973074	−	0.230492i	$-0.925966\pi$
$227$		−	6.94543i		−	0.460984i	0.973074	−	0.230492i	$-0.0740336\pi$
$228$	0.560194	+	4.32275i	0.0370997	+	0.286281i
$229$	−12.7080			−0.839770			−0.419885	−	0.907577i	$-0.637930\pi$
$229$	−12.7080			−0.839770			−0.419885	+	0.907577i	$0.637930\pi$
$230$	3.83801	−	3.76942i	0.253071	−	0.248548i
$231$	4.69131	+	3.93648i	0.308666	+	0.259001i
$232$	0.0293389	−	0.0806080i	0.00192620	−	0.00529218i
$233$	1.99216	+	5.47342i	0.130511	+	0.358576i	0.987686	−	0.156449i	$-0.0500048\pi$
$233$	1.99216	+	5.47342i	0.130511	+	0.358576i	−0.857175	+	0.515025i	$0.827783\pi$
$234$	−0.785581	+	0.659181i	−0.0513551	+	0.0430920i
$235$	−23.5772	−	2.27710i	−1.53801	−	0.148542i
$236$	−1.57116	+	2.72133i	−0.102274	+	0.177143i
$237$	−12.3182	+	2.17203i	−0.800153	+	0.141089i
$238$	−22.5103	+	3.96917i	−1.45912	+	0.257283i
$239$	11.3367	−	19.6357i	0.733308	−	1.27013i	−0.222154	−	0.975011i	$-0.571309\pi$
$239$	11.3367	−	19.6357i	0.733308	−	1.27013i	0.955462	−	0.295114i	$-0.0953578\pi$
$240$	2.22571	+	0.214961i	0.143669	+	0.0138757i
$241$	18.4842	−	15.5101i	1.19067	−	0.999092i	0.190824	−	0.981624i	$-0.438884\pi$
$241$	18.4842	−	15.5101i	1.19067	−	0.999092i	0.999847	−	0.0174674i	$-0.00556031\pi$
$242$	2.09314	+	5.75086i	0.134552	+	0.369679i
$243$	−0.342020	+	0.939693i	−0.0219406	+	0.0602813i
$244$	4.33122	+	3.63433i	0.277278	+	0.232664i
$245$	1.09311	−	1.07358i	0.0698365	−	0.0685885i
$246$	11.4783			0.731832
$247$	4.26589	−	1.33554i	0.271432	−	0.0849781i
$248$		−	0.403699i		−	0.0256349i
$249$	−2.02402	+	11.4788i	−0.128267	+	0.727438i
$250$	6.16276	+	9.32847i	0.389767	+	0.589984i
$251$	6.10922	+	2.22357i	0.385610	+	0.140351i	0.527549	−	0.849525i	$-0.323111\pi$
$251$	6.10922	+	2.22357i	0.385610	+	0.140351i	−0.141938	+	0.989876i	$0.545333\pi$
$252$	−0.948155	−	2.60503i	−0.0597281	−	0.164102i
$253$	3.41614	+	4.07120i	0.214771	+	0.255954i
$254$	−2.58907	−	4.48440i	−0.162453	−	0.281376i
$255$	−16.7790	+	7.64079i	−1.05074	+	0.478485i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−4.99515	+	0.880780i	−0.311589	+	0.0549416i	−0.327256	−	0.944936i	$-0.606124\pi$
$257$	−4.99515	+	0.880780i	−0.311589	+	0.0549416i	0.0156669	+	0.999877i	$0.495013\pi$
$258$	−3.80610	−	2.19746i	−0.236958	−	0.136808i
$259$	−6.00220	−	10.3961i	−0.372959	−	0.645984i
$260$	−0.179254	−	2.28608i	−0.0111168	−	0.141777i
$261$	−0.0806080	+	0.0293389i	−0.00498951	+	0.00181603i
$262$	6.20553	−	17.0496i	0.383379	−	1.05333i
$263$	1.78586	−	2.12830i	0.110121	−	0.131237i	−0.708168	−	0.706043i	$-0.750478\pi$
$263$	1.78586	−	2.12830i	0.110121	−	0.131237i	0.818289	+	0.574807i	$0.194923\pi$
$264$	−0.383604	+	2.17553i	−0.0236092	+	0.133894i
$265$	10.3152	−	14.4525i	0.633657	−	0.887812i
$266$	−0.551546	+	12.0712i	−0.0338175	+	0.740134i
$267$			11.0251i			0.674723i
$268$	3.21125	+	0.566229i	0.196158	+	0.0345880i
$269$	22.0141	+	18.4720i	1.34222	+	1.12626i	0.981050	+	0.193757i	$0.0620674\pi$
$269$	22.0141	+	18.4720i	1.34222	+	1.12626i	0.361171	+	0.932500i	$0.382377\pi$
$270$	−1.26599	−	1.84317i	−0.0770457	−	0.112172i
$271$	−4.29777	+	1.56426i	−0.261071	+	0.0950221i	−0.469240	−	0.883071i	$-0.655472\pi$
$271$	−4.29777	+	1.56426i	−0.261071	+	0.0950221i	0.208169	+	0.978093i	$0.433250\pi$
$272$	−5.29992	−	6.31620i	−0.321355	−	0.382976i
$273$	−2.46204	+	1.42146i	−0.149010	+	0.0860307i
$274$	−0.586557	+	1.01595i	−0.0354352	+	0.0613756i
$275$	−9.66365	+	5.34935i	−0.582740	+	0.322578i
$276$	−0.417759	−	2.36923i	−0.0251461	−	0.142611i
$277$	20.1635	+	11.6414i	1.21151	+	0.699464i	0.963088	−	0.269188i	$-0.0867553\pi$
$277$	20.1635	+	11.6414i	1.21151	+	0.699464i	0.248420	+	0.968652i	$0.420089\pi$
$278$	2.38792	−	1.37867i	0.143218	−	0.0826871i
$279$	−0.309251	+	0.259493i	−0.0185144	+	0.0155354i
$280$	5.97294	+	1.65830i	0.356951	+	0.0991025i
$281$	−18.9722	−	6.90532i	−1.13179	−	0.411937i	−0.292847	−	0.956159i	$-0.594603\pi$
$281$	−18.9722	−	6.90532i	−1.13179	−	0.411937i	−0.838941	+	0.544222i	$0.816825\pi$
$282$	−6.80912	+	8.11479i	−0.405477	+	0.483229i
$283$	−26.0354	−	4.59074i	−1.54764	−	0.272891i	−0.666415	−	0.745581i	$-0.732172\pi$
$283$	−26.0354	−	4.59074i	−1.54764	−	0.272891i	−0.881229	+	0.472690i	$0.843283\pi$
$284$	−6.38167			−0.378682
$285$	2.00440	+	9.53847i	0.118730	+	0.565010i
$286$	2.26543			0.133957
$287$	31.3370	+	5.52556i	1.84977	+	0.326164i
$288$	0.642788	−	0.766044i	0.0378766	−	0.0451396i
$289$	47.9088	+	17.4374i	2.81816	+	1.02573i
$290$	0.0513132	−	0.184822i	0.00301321	−	0.0108531i
$291$	0.469514	−	0.393969i	0.0275234	−	0.0230949i
$292$	7.39841	−	4.27147i	0.432959	−	0.249969i
$293$	10.7234	+	6.19118i	0.626470	+	0.361693i	0.779384	−	0.626547i	$-0.215532\pi$
$293$	10.7234	+	6.19118i	0.626470	+	0.361693i	−0.152914	+	0.988240i	$0.548866\pi$
$294$	−0.118983	−	0.674787i	−0.00693924	−	0.0393544i
$295$	−3.02679	+	6.34109i	−0.176227	+	0.369192i
$296$	2.16513	−	3.75011i	0.125845	−	0.217971i
$297$	1.91312	−	1.10454i	0.111011	−	0.0640921i
$298$	−13.7590	−	16.3974i	−0.797040	−	0.949876i
$299$	−2.31835	+	0.843810i	−0.134074	+	0.0487988i
$300$	4.99919	+	0.0901517i	0.288628	+	0.00520491i
$301$	−9.33322	−	7.83150i	−0.537958	−	0.451400i
$302$	6.57788	+	1.15986i	0.378515	+	0.0667423i
$303$		−	9.06829i		−	0.520960i
$304$	−3.87046	+	2.00488i	−0.221986	+	0.114988i
$305$	10.2905	+	7.34465i	0.589234	+	0.420554i
$306$	−1.43177	+	8.11995i	−0.0818486	+	0.464186i
$307$	6.72733	−	8.01732i	0.383949	−	0.457573i	−0.539108	−	0.842237i	$-0.681238\pi$
$307$	6.72733	−	8.01732i	0.383949	−	0.457573i	0.923056	+	0.384664i	$0.125683\pi$
$308$	−2.09456	+	5.75474i	−0.119348	+	0.327907i
$309$	9.98766	−	3.63521i	0.568178	−	0.206800i
$310$	−0.0705648	−	0.899936i	−0.00400781	−	0.0511129i
$311$	7.43388	+	12.8759i	0.421537	+	0.730123i	0.996090	−	0.0883443i	$-0.0281576\pi$
$311$	7.43388	+	12.8759i	0.421537	+	0.730123i	−0.574553	+	0.818467i	$0.694824\pi$
$312$	−0.888112	−	0.512752i	−0.0502795	−	0.0290289i
$313$	21.9983	−	3.87890i	1.24342	−	0.219248i	0.487038	−	0.873381i	$-0.338077\pi$
$313$	21.9983	−	3.87890i	1.24342	−	0.219248i	0.756380	+	0.654133i	$0.226966\pi$
$314$	−2.60507	−	14.7741i	−0.147013	−	0.833749i
$315$	−2.56900	−	5.64147i	−0.144747	−	0.317861i
$316$	−6.25411	−	10.8324i	−0.351821	−	0.609372i
$317$	−7.69034	−	9.16499i	−0.431932	−	0.514757i	0.505546	−	0.862799i	$-0.331291\pi$
$317$	−7.69034	−	9.16499i	−0.431932	−	0.514757i	−0.937479	+	0.348042i	$0.886846\pi$
$318$	−2.71590	−	7.46188i	−0.152300	−	0.418441i
$319$	0.178070	+	0.0648122i	0.00997001	+	0.00362879i
$320$	0.559241	+	2.16501i	0.0312625	+	0.121027i
$321$	−1.36519	+	7.74238i	−0.0761975	+	0.432137i
$322$		−	6.66934i		−	0.371668i
$323$	19.3719	−	30.2723i	1.07788	−	1.68440i
$324$	−1.00000			−0.0555556
$325$	−0.799193	−	5.06485i	−0.0443313	−	0.280948i
$326$	−9.93996	−	8.34061i	−0.550523	−	0.461944i
$327$	0.691020	−	1.89856i	0.0382135	−	0.104991i
$328$	3.92582	+	10.7861i	0.216767	+	0.595563i
$329$	−22.4960	+	18.8764i	−1.24024	+	1.04069i
$330$	−0.474867	+	4.91679i	−0.0261406	+	0.270660i
$331$	−15.1922	+	26.3137i	−0.835040	+	1.44633i	0.0589582	+	0.998260i	$0.481222\pi$
$331$	−15.1922	+	26.3137i	−0.835040	+	1.44633i	−0.893998	+	0.448071i	$0.852111\pi$
$332$	−11.4788	+	2.02402i	−0.629980	+	0.111082i
$333$	−4.26447	+	0.751940i	−0.233691	+	0.0412061i
$334$	−6.01954	+	10.4261i	−0.329374	+	0.570493i
$335$	7.25756	+	0.700941i	0.396523	+	0.0382965i
$336$	2.12364	−	1.78195i	0.115854	−	0.0972132i
$337$	−3.71982	−	10.2201i	−0.202631	−	0.556725i	0.796201	−	0.605032i	$-0.206840\pi$
$337$	−3.71982	−	10.2201i	−0.202631	−	0.556725i	−0.998833	+	0.0483067i	$0.984618\pi$
$338$	4.08657	−	11.2278i	0.222280	−	0.610710i
$339$	15.6149	+	13.1024i	0.848084	+	0.711627i
$340$	−12.9188	−	13.1538i	−0.700618	−	0.713366i
$341$	0.891806			0.0482940
$342$	4.02371	+	1.67623i	0.217577	+	0.0906403i
$343$			17.5060i			0.945236i
$344$	0.763168	−	4.32814i	0.0411473	−	0.233358i
$345$	−1.34541	−	5.20852i	−0.0724344	−	0.280418i
$346$	22.0734	+	8.03406i	1.18667	+	0.431913i
$347$	−3.73835	−	10.2710i	−0.200685	−	0.551379i	0.797999	−	0.602659i	$-0.205892\pi$
$347$	−3.73835	−	10.2710i	−0.200685	−	0.551379i	−0.998684	+	0.0512803i	$0.983670\pi$
$348$	−0.0551392	−	0.0657123i	−0.00295577	−	0.00352255i
$349$	1.38778	+	2.40370i	0.0742861	+	0.128667i	0.900776	−	0.434285i	$-0.142999\pi$
$349$	1.38778	+	2.40370i	0.0742861	+	0.128667i	−0.826490	+	0.562952i	$0.809666\pi$
$350$	13.6049	+	2.65269i	0.727212	+	0.141792i
$351$	0.178077	+	1.00992i	0.00950504	+	0.0539058i
$352$	−2.17553	+	0.383604i	−0.115956	+	0.0204462i
$353$	1.10585	+	0.638465i	0.0588587	+	0.0339821i	0.529141	−	0.848534i	$-0.322514\pi$
$353$	1.10585	+	0.638465i	0.0588587	+	0.0339821i	−0.470282	+	0.882516i	$0.655848\pi$
$354$	1.57116	+	2.72133i	0.0835062	+	0.144637i
$355$	−14.2262	+	1.11549i	−0.755047	+	0.0592039i
$356$	−10.3602	+	3.77079i	−0.549088	+	0.199852i
$357$	−7.81773	+	21.4790i	−0.413758	+	1.13679i
$358$	−12.0168	+	14.3210i	−0.635107	+	0.756891i
$359$	−1.65861	+	9.40646i	−0.0875382	+	0.496454i	0.909242	+	0.416268i	$0.136662\pi$
$359$	−1.65861	+	9.40646i	−0.0875382	+	0.496454i	−0.996780	+	0.0801854i	$0.974449\pi$
$360$	1.29902	−	1.82004i	0.0684642	−	0.0959247i
$361$	−13.3805	−	13.4894i	−0.704236	−	0.709966i
$362$			7.10857i			0.373618i
$363$	6.02696	+	1.06272i	0.316333	+	0.0557781i
$364$	−2.17780	−	1.82739i	−0.114148	−	0.0957815i
$365$	15.7461	−	10.8153i	0.824187	−	0.566098i
$366$	5.31303	−	1.93378i	0.277716	−	0.101081i
$367$	2.33576	+	2.78365i	0.121925	+	0.145305i	0.823554	−	0.567238i	$-0.191988\pi$
$367$	2.33576	+	2.78365i	0.121925	+	0.145305i	−0.701629	+	0.712543i	$0.747543\pi$
$368$	2.08347	−	1.20289i	0.108608	−	0.0627049i
$369$	5.73917	−	9.94053i	0.298769	−	0.517483i
$370$	4.17105	−	8.73829i	0.216843	−	0.454282i
$371$	−3.82261	−	21.6791i	−0.198460	−	1.12552i
$372$	−0.349614	−	0.201850i	−0.0181266	−	0.0104654i
$373$	−2.95351	+	1.70521i	−0.152927	+	0.0882925i	−0.574511	−	0.818497i	$-0.694808\pi$
$373$	−2.95351	+	1.70521i	−0.152927	+	0.0882925i	0.421584	+	0.906789i	$0.361474\pi$
$374$	13.9530	−	11.7080i	0.721494	−	0.605405i
$375$	11.1601	−	0.672867i	0.576304	−	0.0347467i
$376$	−9.95427	−	3.62306i	−0.513352	−	0.186845i
$377$	−0.0565454	+	0.0673882i	−0.00291224	+	0.00347067i
$378$	−2.73010	−	0.481391i	−0.140421	−	0.0247601i
$379$	18.2545			0.937670			0.468835	−	0.883286i	$-0.344674\pi$
$379$	18.2545			0.937670			0.468835	+	0.883286i	$0.344674\pi$
$380$	−8.27769	+	5.14587i	−0.424636	+	0.263977i
$381$	−5.17814			−0.265284
$382$	14.7558	+	2.60184i	0.754970	+	0.133122i
$383$	24.0997	−	28.7209i	1.23144	−	1.46757i	0.395752	−	0.918357i	$-0.370484\pi$
$383$	24.0997	−	28.7209i	1.23144	−	1.46757i	0.835684	−	0.549211i	$-0.185072\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$	−3.66333	+	13.1947i	−0.186701	+	0.672466i
$386$	11.5445	−	9.68697i	0.587599	−	0.493054i
$387$	−3.80610	+	2.19746i	−0.193475	+	0.111703i
$388$	0.530793	+	0.306454i	0.0269469	+	0.0155578i
$389$	−4.58983	−	26.0302i	−0.232714	−	1.31978i	−0.847376	−	0.530994i	$-0.821819\pi$
$389$	−4.58983	−	26.0302i	−0.232714	−	1.31978i	0.614662	−	0.788791i	$-0.289292\pi$
$390$	−2.06943	−	0.987801i	−0.104790	−	0.0500193i
$391$	−9.91807	+	17.1786i	−0.501579	+	0.868759i
$392$	0.593398	−	0.342598i	0.0299711	−	0.0173038i
$393$	−11.6626	−	13.8989i	−0.588300	−	0.701108i
$394$	3.37363	−	1.22790i	0.169961	−	0.0618608i
$395$	−15.8353	−	23.0548i	−0.796760	−	1.16001i
$396$	1.69226	+	1.41997i	0.0850392	+	0.0713563i
$397$	13.5970	+	2.39752i	0.682413	+	0.120328i	0.504099	−	0.863646i	$-0.331825\pi$
$397$	13.5970	+	2.39752i	0.682413	+	0.120328i	0.178314	+	0.983974i	$0.442936\pi$
$398$		−	7.97946i		−	0.399974i
$399$	10.1782	+	6.51327i	0.509548	+	0.326071i
$400$	1.62511	+	4.72853i	0.0812554	+	0.236427i
$401$	6.12226	−	34.7210i	0.305731	−	1.73389i	−0.314314	−	0.949319i	$-0.601774\pi$
$401$	6.12226	−	34.7210i	0.305731	−	1.73389i	0.620045	−	0.784567i	$-0.287114\pi$
$402$	2.09599	−	2.49791i	0.104539	−	0.124584i
$403$	−0.141595	+	0.389028i	−0.00705333	+	0.0193789i
$404$	8.52141	−	3.10154i	0.423956	−	0.154307i
$405$	−2.22923	+	0.174796i	−0.110771	+	0.00868566i
$406$	−0.118902	−	0.205945i	−0.00590102	−	0.0102209i
$407$	8.28431	+	4.78295i	0.410638	+	0.237082i
$408$	−8.11995	+	1.43177i	−0.401997	+	0.0708830i
$409$	2.57866	+	14.6243i	0.127507	+	0.723126i	0.979787	+	0.200041i	$0.0641076\pi$
$409$	2.57866	+	14.6243i	0.127507	+	0.723126i	−0.852281	+	0.523084i	$0.824781\pi$
$410$	10.6369	+	23.3584i	0.525319	+	1.15359i
$411$	0.586557	+	1.01595i	0.0289327	+	0.0501130i
$412$	6.83196	+	8.14202i	0.336587	+	0.401128i
$413$	2.97941	+	8.18585i	0.146607	+	0.402799i
$414$	−2.26069	−	0.822825i	−0.111107	−	0.0404396i
$415$	−25.2350	+	6.51844i	−1.23874	+	0.319977i
$416$	0.178077	−	1.00992i	0.00873094	−	0.0495156i
$417$		−	2.75734i		−	0.135027i
$418$	−4.42895	−	8.55018i	−0.216627	−	0.418203i
$419$	19.2011			0.938038			0.469019	−	0.883188i	$-0.344608\pi$
$419$	19.2011			0.938038			0.469019	+	0.883188i	$0.344608\pi$
$420$	4.42260	−	4.34357i	0.215801	−	0.211944i
$421$	16.9562	+	14.2280i	0.826397	+	0.693429i	0.954461	−	0.298337i	$-0.0964319\pi$
$421$	16.9562	+	14.2280i	0.826397	+	0.693429i	−0.128064	+	0.991766i	$0.540876\pi$
$422$	0.0246707	−	0.0677822i	0.00120095	−	0.00329958i
$423$	3.62306	+	9.95427i	0.176159	+	0.483993i
$424$	6.08298	−	5.10423i	0.295416	−	0.247883i
$425$	−31.0981	−	27.0647i	−1.50848	−	1.31283i
$426$	−3.19083	+	5.52669i	−0.154596	+	0.267769i
$427$	15.4360	−	2.72179i	0.747001	−	0.131716i
$428$	−7.74238	+	1.36519i	−0.374242	+	0.0659890i
$429$	1.13271	−	1.96192i	0.0546879	−	0.0947222i
$430$	0.944734	−	9.78180i	0.0455591	−	0.471720i
$431$	20.4202	−	17.1346i	0.983605	−	0.825343i	−0.00102429	−	0.999999i	$-0.500326\pi$
$431$	20.4202	−	17.1346i	0.983605	−	0.825343i	0.984629	+	0.174657i	$0.0558816\pi$
$432$	−0.342020	−	0.939693i	−0.0164555	−	0.0452110i
$433$	−10.4062	+	28.5909i	−0.500091	+	1.37399i	0.391094	+	0.920351i	$0.372097\pi$
$433$	−10.4062	+	28.5909i	−0.500091	+	1.37399i	−0.891186	+	0.453639i	$0.850126\pi$
$434$	−0.857313	−	0.719371i	−0.0411523	−	0.0345309i
$435$	−0.134404	−	0.136849i	−0.00644417	−	0.00656143i
$436$	2.02041			0.0967600
$437$	7.71712	+	7.10026i	0.369160	+	0.339651i
$438$		−	8.54294i		−	0.408198i
$439$	1.37242	−	7.78337i	0.0655019	−	0.371480i	−0.934382	−	0.356272i	$-0.884048\pi$
$439$	1.37242	−	7.78337i	0.0655019	−	0.371480i	0.999884	−	0.0152082i	$-0.00484112\pi$
$440$	−4.78268	+	1.23541i	−0.228006	+	0.0588959i
$441$	−0.643874	−	0.234351i	−0.0306607	−	0.0111596i
$442$	2.89195	+	7.94556i	0.137556	+	0.377932i
$443$	−4.73213	−	5.63953i	−0.224830	−	0.267942i	0.641823	−	0.766852i	$-0.278178\pi$
$443$	−4.73213	−	5.63953i	−0.224830	−	0.267942i	−0.866654	+	0.498910i	$0.833734\pi$
$444$	−2.16513	−	3.75011i	−0.102752	−	0.177972i
$445$	−22.4360	+	10.2169i	−1.06357	+	0.484326i
$446$	2.63847	+	14.9635i	0.124935	+	0.708543i
$447$	−21.0801	+	3.71699i	−0.997054	+	0.175807i
$448$	2.40081	+	1.38611i	0.113428	+	0.0654875i
$449$	11.1568	+	19.3241i	0.526520	+	0.911959i	0.999523	+	0.0308980i	$0.00983671\pi$
$449$	11.1568	+	19.3241i	0.526520	+	0.911959i	−0.473003	+	0.881061i	$0.656830\pi$
$450$	2.57767	−	4.28435i	0.121512	−	0.201966i
$451$	−23.8274	+	8.67248i	−1.12199	+	0.408371i
$452$	−6.97166	+	19.1545i	−0.327919	+	0.900951i
$453$	4.29341	−	5.11668i	0.201722	−	0.240403i
$454$	1.20606	−	6.83991i	0.0566032	−	0.321013i
$455$	−5.17424	−	3.69300i	−0.242572	−	0.173131i
$456$	−0.198955	+	4.35436i	−0.00931691	+	0.203911i
$457$		−	20.3524i		−	0.952045i	−0.879433	−	0.476022i	$-0.842078\pi$
$457$		−	20.3524i		−	0.952045i	0.879433	−	0.476022i	$-0.157922\pi$
$458$	−12.5150	−	2.20673i	−0.584786	−	0.103114i
$459$	6.31620	+	5.29992i	0.294815	+	0.247379i
$460$	4.43425	−	3.04569i	0.206748	−	0.142006i
$461$	−22.8048	+	8.30028i	−1.06213	+	0.386583i	−0.813227	−	0.581946i	$-0.802291\pi$
$461$	−22.8048	+	8.30028i	−1.06213	+	0.386583i	−0.248900	+	0.968529i	$0.580069\pi$
$462$	3.93648	+	4.69131i	0.183141	+	0.218260i
$463$	−29.0482	+	16.7710i	−1.34999	+	0.779415i	−0.988247	−	0.152864i	$-0.951150\pi$
$463$	−29.0482	+	16.7710i	−1.34999	+	0.779415i	−0.361739	+	0.932279i	$0.617817\pi$
$464$	0.0428906	−	0.0742888i	0.00199115	−	0.00344877i
$465$	−0.814650	−	0.388857i	−0.0377785	−	0.0180328i
$466$	1.01145	+	5.73620i	0.0468544	+	0.265724i
$467$	19.5763	+	11.3024i	0.905884	+	0.523012i	0.879105	−	0.476629i	$-0.158142\pi$
$467$	19.5763	+	11.3024i	0.905884	+	0.523012i	0.0267794	+	0.999641i	$0.491475\pi$
$468$	−0.888112	+	0.512752i	−0.0410530	+	0.0237020i
$469$	6.92474	−	5.81055i	0.319755	−	0.268306i
$470$	−22.8236	−	6.33665i	−1.05277	−	0.292288i
$471$	−14.0973	−	5.13098i	−0.649567	−	0.236423i
$472$	−2.01984	+	2.40716i	−0.0929709	+	0.110798i
$473$	9.56124	+	1.68590i	0.439626	+	0.0775180i
$474$	−12.5082			−0.574522
$475$	−17.5534	+	12.9182i	−0.805403	+	0.592728i
$476$	−22.8575			−1.04767
$477$	−7.82013	−	1.37890i	−0.358059	−	0.0631355i
$478$	14.5741	−	17.3688i	0.666605	−	0.794429i
$479$	−13.2217	−	4.81229i	−0.604113	−	0.219879i	0.0218124	−	0.999762i	$-0.493056\pi$
$479$	−13.2217	−	4.81229i	−0.604113	−	0.219879i	−0.625925	+	0.779883i	$0.715279\pi$
$480$	2.15457	+	0.598186i	0.0983422	+	0.0273033i
$481$	−3.40177	+	2.85442i	−0.155107	+	0.130150i
$482$	20.8967	−	12.0647i	0.951817	−	0.549532i
$483$	−5.77582	−	3.33467i	−0.262809	−	0.151733i
$484$	1.06272	+	6.02696i	0.0483053	+	0.273953i
$485$	1.23682	+	0.590374i	0.0561613	+	0.0268075i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−3.58998	+	2.07267i	−0.162677	+	0.0939219i	−0.579129	−	0.815236i	$-0.696607\pi$
$487$	−3.58998	+	2.07267i	−0.162677	+	0.0939219i	0.416451	+	0.909158i	$0.363274\pi$
$488$	3.63433	+	4.33122i	0.164518	+	0.196065i
$489$	−12.1932	+	4.43795i	−0.551394	+	0.200691i
$490$	1.26293	−	0.867453i	0.0570535	−	0.0391875i
$491$	−9.69762	−	8.13727i	−0.437647	−	0.367230i	0.397181	−	0.917740i	$-0.369989\pi$
$491$	−9.69762	−	8.13727i	−0.437647	−	0.367230i	−0.834828	+	0.550511i	$0.814433\pi$
$492$	11.3039	+	1.99319i	0.509621	+	0.0898600i
$493$			0.707285i			0.0318545i
$494$	4.43300	−	0.574481i	0.199450	−	0.0258471i
$495$	4.02063	+	2.86964i	0.180714	+	0.128981i
$496$	0.0701016	−	0.397566i	0.00314765	−	0.0178512i
$497$	−11.3718	+	13.5524i	−0.510095	+	0.607907i
$498$	−3.98654	+	10.9529i	−0.178641	+	0.490812i
$499$	−36.6223	+	13.3294i	−1.63944	+	0.596707i	−0.986941	−	0.161082i	$-0.948502\pi$
$499$	−36.6223	+	13.3294i	−1.63944	+	0.596707i	−0.652499	+	0.757790i	$0.726279\pi$
$500$	4.44926	+	10.2569i	0.198977	+	0.458703i
$501$	6.01954	+	10.4261i	0.268933	+	0.465806i
$502$	5.63029	+	3.25065i	0.251292	+	0.145083i
$503$	−28.3263	+	4.99470i	−1.26301	+	0.222703i	−0.764751	−	0.644326i	$-0.777138\pi$
$503$	−28.3263	+	4.99470i	−1.26301	+	0.222703i	−0.498258	+	0.867029i	$0.666027\pi$
$504$	−0.481391	−	2.73010i	−0.0214428	−	0.121608i
$505$	18.4540	−	8.40353i	0.821192	−	0.373952i
$506$	2.65729	+	4.60255i	0.118131	+	0.204609i
$507$	−7.68025	−	9.15296i	−0.341092	−	0.406497i
$508$	−1.77103	−	4.86586i	−0.0785767	−	0.215888i
$509$	−3.11129	−	1.13242i	−0.137905	−	0.0501935i	0.272145	−	0.962256i	$-0.412267\pi$
$509$	−3.11129	−	1.13242i	−0.137905	−	0.0501935i	−0.410051	+	0.912063i	$0.634489\pi$
$510$	−17.8509	+	4.61106i	−0.790452	+	0.204181i
$511$	4.11249	−	23.3231i	0.181926	−	1.03175i
$512$			1.00000i			0.0441942i
$513$	3.46352	−	2.64652i	0.152918	−	0.116847i
$514$	−5.07221			−0.223726
$515$	16.6532	+	16.9562i	0.733826	+	0.747179i
$516$	−3.36670	−	2.82499i	−0.148211	−	0.124363i
$517$	8.00365	−	21.9898i	0.352000	−	0.967112i
$518$	−4.10575	−	11.2805i	−0.180396	−	0.495635i
$519$	17.9944	−	15.0991i	0.789866	−	0.662776i
$520$	0.220443	−	2.28248i	0.00966707	−	0.100093i
$521$	7.88958	−	13.6652i	0.345649	−	0.598682i	−0.639823	−	0.768523i	$-0.720992\pi$
$521$	7.88958	−	13.6652i	0.345649	−	0.598682i	0.985471	+	0.169841i	$0.0543255\pi$
$522$	−0.0844781	+	0.0148958i	−0.00369751	+	0.000651970i
$523$	2.54917	−	0.449487i	0.111467	−	0.0196547i	−0.117636	−	0.993057i	$-0.537532\pi$
$523$	2.54917	−	0.449487i	0.111467	−	0.0196547i	0.229103	+	0.973402i	$0.426421\pi$
$524$	9.07189	−	15.7130i	0.396307	−	0.686424i
$525$	9.09974	−	10.4558i	0.397145	−	0.456330i
$526$	2.12830	−	1.78586i	0.0927985	−	0.0778672i
$527$	1.13844	+	3.12784i	0.0495913	+	0.136251i
$528$	−0.755552	+	2.07586i	−0.0328812	+	0.0903403i
$529$	13.1853	+	11.0638i	0.573275	+	0.481035i
$530$	12.6681	−	12.4417i	0.550269	−	0.540435i
$531$	3.14232			0.136365
$532$	−2.63931	+	11.7921i	−0.114429	+	0.511251i
$533$		−	11.7711i		−	0.509862i
$534$	−1.91448	+	10.8576i	−0.0828477	+	0.469853i
$535$	−17.0209	+	4.39665i	−0.735877	+	0.190084i
$536$	3.06413	+	1.11525i	0.132350	+	0.0481716i
$537$	6.39400	+	17.5674i	0.275921	+	0.758088i
$538$	18.4720	+	22.0141i	0.796384	+	0.949093i
$539$	0.756830	+	1.31087i	0.0325990	+	0.0564631i
$540$	−0.926694	−	2.03500i	−0.0398786	−	0.0875726i
$541$	−5.18954	−	29.4314i	−0.223116	−	1.26535i	−0.866254	−	0.499603i	$-0.833479\pi$
$541$	−5.18954	−	29.4314i	−0.223116	−	1.26535i	0.643138	−	0.765750i	$-0.277632\pi$
$542$	−4.50411	+	0.794197i	−0.193468	+	0.0341137i
$543$	6.15620	+	3.55428i	0.264188	+	0.152529i
$544$	−4.12260	−	7.14056i	−0.176755	−	0.306149i
$545$	4.50395	−	0.353158i	0.192928	−	0.0151276i
$546$	−2.67147	+	0.972336i	−0.114328	+	0.0416121i
$547$	−3.21974	+	8.84616i	−0.137666	+	0.378235i	−0.989299	−	0.145905i	$-0.953391\pi$
$547$	−3.21974	+	8.84616i	−0.137666	+	0.378235i	0.851632	+	0.524139i	$0.175613\pi$
$548$	−0.754063	+	0.898658i	−0.0322120	+	0.0383888i
$549$	0.981808	−	5.56811i	0.0419025	−	0.237641i
$550$	−10.4457	+	3.59000i	−0.445408	+	0.153078i
$551$	0.364884	+	0.0816688i	0.0155446	+	0.00347921i
$552$		−	2.40578i		−	0.102397i
$553$	−34.1487	−	6.02134i	−1.45215	−	0.256054i
$554$	17.8357	+	14.9659i	0.757765	+	0.635840i
$555$	−5.48206	−	7.98138i	−0.232700	−	0.338791i
$556$	2.59105	−	0.943065i	0.109885	−	0.0399949i
$557$	−19.4451	−	23.1737i	−0.823914	−	0.981903i	0.176083	−	0.984375i	$-0.443657\pi$
$557$	−19.4451	−	23.1737i	−0.823914	−	0.981903i	−0.999997	+	0.00247257i	$0.999213\pi$
$558$	−0.349614	+	0.201850i	−0.0148003	+	0.00854497i
$559$	−2.25350	+	3.90317i	−0.0953128	+	0.165087i
$560$	5.59424	+	2.67030i	0.236400	+	0.112841i
$561$	−3.16289	−	17.9377i	−0.133537	−	0.757329i
$562$	−17.4849	−	10.0949i	−0.737556	−	0.425828i
$563$	−23.9898	+	13.8505i	−1.01105	+	0.583729i	−0.911499	−	0.411303i	$-0.865074\pi$
$563$	−23.9898	+	13.8505i	−1.01105	+	0.583729i	−0.0995501	+	0.995033i	$0.531740\pi$
$564$	−8.11479	+	6.80912i	−0.341695	+	0.286716i
$565$	−12.1933	+	43.9183i	−0.512975	+	1.84766i
$566$	−24.8427	−	9.04200i	−1.04422	−	0.380064i
$567$	−1.78195	+	2.12364i	−0.0748348	+	0.0891846i
$568$	−6.28472	−	1.10816i	−0.263701	−	0.0464976i
$569$	18.9310			0.793627			0.396814	−	0.917899i	$-0.370116\pi$
$569$	18.9310			0.793627			0.396814	+	0.917899i	$0.370116\pi$
$570$	0.317607	+	9.74162i	0.0133031	+	0.408031i
$571$	−42.8998			−1.79530			−0.897649	−	0.440710i	$-0.854727\pi$
$571$	−42.8998			−1.79530			−0.897649	+	0.440710i	$0.854727\pi$
$572$	2.23101	+	0.393387i	0.0932832	+	0.0164483i
$573$	9.63113	−	11.4779i	0.402346	−	0.479498i
$574$	29.9014	+	10.8832i	1.24806	+	0.454257i
$575$	9.35258	−	7.56462i	0.390030	−	0.315467i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	−8.57223	+	4.94918i	−0.356866	+	0.206037i	−0.667705	−	0.744426i	$-0.732723\pi$
$577$	−8.57223	+	4.94918i	−0.356866	+	0.206037i	0.310839	+	0.950463i	$0.399390\pi$
$578$	44.1530	+	25.4917i	1.83652	+	1.06032i
$579$	−2.61692	−	14.8413i	−0.108756	−	0.616783i
$580$	0.0826276	−	0.173104i	0.00343092	−	0.00718773i
$581$	−16.1563	+	27.9835i	−0.670276	+	1.16095i
$582$	0.530793	−	0.306454i	0.0220021	−	0.0127029i
$583$	11.2757	+	13.4378i	0.466991	+	0.556538i
$584$	8.02774	−	2.92186i	0.332190	−	0.120907i
$585$	−1.89018	+	1.29828i	−0.0781492	+	0.0536772i
$586$	9.48544	+	7.95923i	0.391840	+	0.328793i
$587$	−24.6978	−	4.35490i	−1.01939	−	0.179746i	−0.361113	−	0.932522i	$-0.617603\pi$
$587$	−24.6978	−	4.35490i	−1.01939	−	0.179746i	−0.658276	+	0.752776i	$0.728714\pi$
$588$		−	0.685197i		−	0.0282570i
$589$	1.74509	−	0.226150i	0.0719052	−	0.00931834i
$590$	−4.08193	+	5.71916i	−0.168050	+	0.235454i
$591$	0.623422	−	3.53560i	0.0256441	−	0.145435i
$592$	2.78343	−	3.31717i	0.114398	−	0.136335i
$593$	1.81088	−	4.97535i	0.0743639	−	0.204313i	−0.896941	−	0.442150i	$-0.854216\pi$
$593$	1.81088	−	4.97535i	0.0743639	−	0.204313i	0.971305	+	0.237837i	$0.0764383\pi$
$594$	2.07586	−	0.755552i	0.0851737	−	0.0310007i
$595$	−50.9546	+	3.99539i	−2.08893	+	0.163795i
$596$	−10.7026	−	18.5375i	−0.438397	−	0.759326i
$597$	−6.91042	−	3.98973i	−0.282825	−	0.163289i
$598$	−2.42965	+	0.428413i	−0.0993559	+	0.0175191i
$599$	−5.57949	−	31.6429i	−0.227972	−	1.29289i	−0.856922	−	0.515447i	$-0.827626\pi$
$599$	−5.57949	−	31.6429i	−0.227972	−	1.29289i	0.628950	−	0.777446i	$-0.283485\pi$
$600$	4.90758	+	0.956882i	0.200351	+	0.0390645i
$601$	10.9909	+	19.0367i	0.448327	+	0.776525i	0.998277	−	0.0586725i	$-0.0186868\pi$
$601$	10.9909	+	19.0367i	0.448327	+	0.776525i	−0.549951	+	0.835197i	$0.685353\pi$
$602$	−7.83150	−	9.33322i	−0.319188	−	0.380394i
$603$	−1.11525	−	3.06413i	−0.0454166	−	0.124781i
$604$	6.27654	+	2.28447i	0.255389	+	0.0929540i
$605$	3.42252	+	13.2497i	0.139145	+	0.538677i
$606$	1.57469	−	8.93053i	0.0639675	−	0.362778i
$607$			14.4522i			0.586598i	0.956021	+	0.293299i	$0.0947532\pi$
$607$			14.4522i			0.586598i	−0.956021	+	0.293299i	$0.905247\pi$
$608$	−4.15980	+	1.30232i	−0.168702	+	0.0528161i
$609$	−0.237805			−0.00963632
$610$	8.85881	+	9.02000i	0.358683	+	0.365209i
$611$	8.32175	+	6.98278i	0.336662	+	0.282493i
$612$	−2.82003	+	7.74796i	−0.113993	+	0.313193i
$613$	−1.88674	−	5.18377i	−0.0762046	−	0.209370i	0.895741	−	0.444576i	$-0.146646\pi$
$613$	−1.88674	−	5.18377i	−0.0762046	−	0.209370i	−0.971946	+	0.235206i	$0.924424\pi$
$614$	8.01732	−	6.72733i	0.323553	−	0.271493i
$615$	25.5475	+	2.46739i	1.03017	+	0.0994949i
$616$	−3.06204	+	5.30360i	−0.123373	+	0.213688i
$617$	−20.7777	+	3.66367i	−0.836480	+	0.147494i	−0.575450	−	0.817837i	$-0.695173\pi$
$617$	−20.7777	+	3.66367i	−0.836480	+	0.147494i	−0.261029	+	0.965331i	$0.584062\pi$
$618$	10.4672	−	1.84565i	0.421051	−	0.0742427i
$619$	−6.22396	+	10.7802i	−0.250162	+	0.433294i	−0.963570	−	0.267455i	$-0.913817\pi$
$619$	−6.22396	+	10.7802i	−0.250162	+	0.433294i	0.713408	+	0.700749i	$0.247151\pi$
$620$	0.0867795	−	0.898518i	0.00348515	−	0.0360853i
$621$	−1.84293	+	1.54640i	−0.0739544	+	0.0620551i
$622$	5.08507	+	13.9711i	0.203893	+	0.560191i
$623$	−10.4535	+	28.7206i	−0.418809	+	1.15067i
$624$	−0.785581	−	0.659181i	−0.0314484	−	0.0263884i
$625$	11.7113	+	22.0872i	0.468451	+	0.883490i
$626$	22.3377			0.892793
$627$	−9.61915	−	0.439508i	−0.384152	−	0.0175523i
$628$		−	15.0020i		−	0.598645i
$629$	−6.19991	+	35.1614i	−0.247206	+	1.40198i
$630$	−1.55034	−	6.00187i	−0.0617670	−	0.239120i
$631$	5.75733	+	2.09550i	0.229196	+	0.0834205i	0.454065	−	0.890968i	$-0.349973\pi$
$631$	5.75733	+	2.09550i	0.229196	+	0.0834205i	−0.224869	+	0.974389i	$0.572196\pi$
$632$	−4.27806	−	11.7539i	−0.170172	−	0.467544i
$633$	−0.0463657	−	0.0552565i	−0.00184287	−	0.00219625i
$634$	−5.98202	−	10.3612i	−0.237576	−	0.411494i
$635$	−4.79855	−	10.5375i	−0.190425	−	0.418169i
$636$	−1.37890	−	7.82013i	−0.0546769	−	0.310088i
$637$	−0.691997	+	0.122018i	−0.0274179	+	0.00483452i
$638$	0.164110	+	0.0947491i	0.00649719	+	0.00375115i
$639$	3.19083	+	5.52669i	0.126227	+	0.218632i
$640$	0.174796	+	2.22923i	0.00690940	+	0.0881179i
$641$	−14.6675	+	5.33853i	−0.579331	+	0.210859i	−0.615031	−	0.788503i	$-0.710856\pi$
$641$	−14.6675	+	5.33853i	−0.579331	+	0.210859i	0.0356994	+	0.999363i	$0.488634\pi$
$642$	−2.68890	+	7.38769i	−0.106122	+	0.291569i
$643$	20.9020	−	24.9101i	0.824295	−	0.982357i	−0.175703	−	0.984443i	$-0.556220\pi$
$643$	20.9020	−	24.9101i	0.824295	−	0.982357i	0.999998	+	0.00208656i	$0.000664174\pi$
$644$	1.15812	−	6.56802i	0.0456363	−	0.258816i
$645$	−7.99892	−	5.70907i	−0.314957	−	0.224794i
$646$	24.3344	−	26.4485i	0.957423	−	1.04060i
$647$			11.6694i			0.458772i	0.973336	+	0.229386i	$0.0736718\pi$
$647$			11.6694i			0.458772i	−0.973336	+	0.229386i	$0.926328\pi$
$648$	−0.984808	−	0.173648i	−0.0386869	−	0.00682154i
$649$	−5.31762	−	4.46201i	−0.208735	−	0.175149i
$650$	0.0924509	−	5.12669i	0.00362622	−	0.201085i
$651$	−1.05165	+	0.382769i	−0.0412174	+	0.0150019i
$652$	−8.34061	−	9.93996i	−0.326644	−	0.389279i
$653$	2.32188	−	1.34054i	0.0908621	−	0.0524593i	−0.453880	−	0.891063i	$-0.649961\pi$
$653$	2.32188	−	1.34054i	0.0908621	−	0.0524593i	0.544743	+	0.838603i	$0.316627\pi$
$654$	1.01020	−	1.74972i	0.0395021	−	0.0684197i
$655$	17.4767	−	36.6135i	0.682872	−	1.43061i
$656$	1.99319	+	11.3039i	0.0778210	+	0.441345i
$657$	−7.39841	−	4.27147i	−0.288639	−	0.166646i
$658$	−25.4321	+	14.6832i	−0.991445	+	0.572411i
$659$	18.5929	−	15.6013i	0.724276	−	0.607740i	−0.204288	−	0.978911i	$-0.565488\pi$
$659$	18.5929	−	15.6013i	0.724276	−	0.607740i	0.928565	+	0.371171i	$0.121044\pi$
$660$	−1.32144	+	4.75963i	−0.0514372	+	0.185268i
$661$	0.332603	+	0.121057i	0.0129367	+	0.00470859i	0.348480	−	0.937316i	$-0.386698\pi$
$661$	0.332603	+	0.121057i	0.0129367	+	0.00470859i	−0.335544	+	0.942025i	$0.608920\pi$
$662$	−19.5307	+	23.2758i	−0.759084	+	0.904641i
$663$	8.32703	+	1.46828i	0.323395	+	0.0570233i
$664$	−11.6559			−0.452335
$665$	−3.82242	+	26.7485i	−0.148227	+	1.03726i
$666$	−4.33025			−0.167794
$667$	−0.203236	−	0.0358359i	−0.00786931	−	0.00138757i
$668$	−7.73857	+	9.22247i	−0.299414	+	0.356828i
$669$	14.2780	+	5.19677i	0.552020	+	0.200919i
$670$	7.02559	+	1.95055i	0.271422	+	0.0753565i
$671$	−9.56804	+	8.02854i	−0.369370	+	0.309938i
$672$	2.40081	−	1.38611i	0.0926133	−	0.0534703i
$673$	4.91771	+	2.83924i	0.189564	+	0.109445i	0.591778	−	0.806101i	$-0.298426\pi$
$673$	4.91771	+	2.83924i	0.189564	+	0.109445i	−0.402215	+	0.915545i	$0.631759\pi$
$674$	−1.88860	−	10.7108i	−0.0727462	−	0.412564i
$675$	−2.42152	−	4.37450i	−0.0932043	−	0.168375i
$676$	5.97417	−	10.3476i	0.229776	−	0.397983i
$677$	−40.0081	+	23.0987i	−1.53764	+	0.887756i	−0.538661	+	0.842522i	$0.681070\pi$
$677$	−40.0081	+	23.0987i	−1.53764	+	0.887756i	−0.998976	+	0.0452331i	$0.985597\pi$
$678$	13.1024	+	15.6149i	0.503196	+	0.599686i
$679$	1.59664	−	0.581131i	0.0612736	−	0.0223018i
$680$	−10.4384	−	15.1973i	−0.400293	−	0.582790i
$681$	−5.32051	−	4.46444i	−0.203882	−	0.171078i
$682$	0.878258	+	0.154860i	0.0336302	+	0.00592991i
$683$		−	49.4702i		−	1.89292i	−0.322816	−	0.946462i	$-0.604630\pi$
$683$		−	49.4702i		−	1.89292i	0.322816	−	0.946462i	$-0.395370\pi$
$684$	3.67151	+	2.34948i	0.140384	+	0.0898345i
$685$	−1.52390	+	2.13512i	−0.0582251	+	0.0815787i
$686$	−3.03989	+	17.2401i	−0.116063	+	0.658229i
$687$	−8.16857	+	9.73492i	−0.311650	+	0.371410i
$688$	1.50315	−	4.12987i	0.0573070	−	0.157450i
$689$	−7.65219	+	2.78517i	−0.291525	+	0.106106i
$690$	−0.420520	−	5.36302i	−0.0160089	−	0.204167i
$691$	3.81625	+	6.60995i	0.145177	+	0.251454i	0.929439	−	0.368976i	$-0.120291\pi$
$691$	3.81625	+	6.60995i	0.145177	+	0.251454i	−0.784262	+	0.620430i	$0.786958\pi$
$692$	20.3429	+	11.7450i	0.773323	+	0.446478i
$693$	6.03103	−	1.06343i	0.229100	−	0.0403965i
$694$	−1.89801	−	10.7642i	−0.0720476	−	0.408602i
$695$	5.61119	−	2.55521i	0.212845	−	0.0969246i
$696$	−0.0428906	−	0.0742888i	−0.00162577	−	0.00281591i
$697$	−60.8342	−	72.4994i	−2.30426	−	2.74611i
$698$	0.949296	+	2.60817i	0.0359314	+	0.0987207i
$699$	5.47342	+	1.99216i	0.207024	+	0.0753505i
$700$	12.9376	+	4.97485i	0.488994	+	0.188032i
$701$	−4.20880	+	23.8693i	−0.158964	+	0.901531i	0.796107	+	0.605156i	$0.206889\pi$
$701$	−4.20880	+	23.8693i	−0.158964	+	0.901531i	−0.955072	+	0.296375i	$0.904222\pi$
$702$			1.02550i			0.0387051i
$703$	17.4237	+	7.25852i	0.657147	+	0.273760i
$704$	−2.20909			−0.0832581
$705$	−16.8995	+	16.5975i	−0.636472	+	0.625098i
$706$	0.978185	+	0.820795i	0.0368145	+	0.0308910i
$707$	8.59814	−	23.6232i	0.323367	−	0.888442i
$708$	1.07474	+	2.95282i	0.0403911	+	0.110974i
$709$	14.4115	−	12.0927i	0.541236	−	0.454151i	−0.330724	−	0.943727i	$-0.607293\pi$
$709$	14.4115	−	12.0927i	0.541236	−	0.454151i	0.871960	+	0.489576i	$0.162849\pi$
$710$	−14.2038	−	1.37181i	−0.533057	−	0.0514831i
$711$	−6.25411	+	10.8324i	−0.234547	+	0.406248i
$712$	−10.8576	+	1.91448i	−0.406904	+	0.0717482i
$713$	−0.956456	+	0.168649i	−0.0358195	+	0.00631595i
$714$	−11.4288	+	19.7952i	−0.427711	+	0.740817i
$715$	5.04219	+	0.486978i	0.188567	+	0.0182119i
$716$	−14.3210	+	12.0168i	−0.535203	+	0.449088i
$717$	−7.75473	−	21.3059i	−0.289606	−	0.795685i
$718$	−3.26683	+	8.97554i	−0.121917	+	0.334964i
$719$	29.6559	+	24.8843i	1.10598	+	0.928026i	0.997813	−	0.0661068i	$-0.0210578\pi$
$719$	29.6559	+	24.8843i	1.10598	+	0.928026i	0.108166	+	0.994133i	$0.465502\pi$
$720$	1.59533	−	1.56682i	0.0594544	−	0.0583919i
$721$	29.4649			1.09733
$722$	−10.8348	−	15.6079i	−0.403229	−	0.580867i
$723$		−	24.1294i		−	0.897382i
$724$	−1.23439	+	7.00057i	−0.0458757	+	0.260174i
$725$	0.153938	−	0.400330i	0.00571710	−	0.0148679i
$726$	5.75086	+	2.09314i	0.213434	+	0.0776838i
$727$	13.5312	+	37.1767i	0.501845	+	1.37881i	0.889471	+	0.456991i	$0.151073\pi$
$727$	13.5312	+	37.1767i	0.501845	+	1.37881i	−0.387626	+	0.921817i	$0.626705\pi$
$728$	−1.82739	−	2.17780i	−0.0677277	−	0.0807148i
$729$	0.500000	+	0.866025i	0.0185185	+	0.0320750i
$730$	17.3849	−	7.91670i	0.643445	−	0.293010i
$731$	6.29248	+	35.6864i	0.232736	+	1.31991i
$732$	5.56811	−	0.981808i	0.205803	−	0.0362887i
$733$	−2.72916	−	1.57568i	−0.100804	−	0.0581991i	0.448751	−	0.893657i	$-0.351869\pi$
$733$	−2.72916	−	1.57568i	−0.100804	−	0.0581991i	−0.549554	+	0.835458i	$0.685202\pi$
$734$	1.81690	+	3.14696i	0.0670628	+	0.116156i
$735$	−0.119769	−	1.52746i	−0.00441776	−	0.0563412i
$736$	2.26069	−	0.822825i	0.0833302	−	0.0303297i
$737$	−2.46369	+	6.76894i	−0.0907513	+	0.249337i
$738$	7.37813	−	8.79291i	0.271593	−	0.323672i
$739$	4.86021	−	27.5636i	0.178786	−	1.01394i	−0.754897	−	0.655843i	$-0.772313\pi$
$739$	4.86021	−	27.5636i	0.178786	−	1.01394i	0.933683	−	0.358101i	$-0.116576\pi$
$740$	5.62507	−	7.88124i	0.206782	−	0.289720i
$741$	1.71898	−	4.12633i	0.0631485	−	0.151584i
$742$		−	22.0135i		−	0.808143i
$743$	−35.5567	−	6.26960i	−1.30445	−	0.230009i	−0.522117	−	0.852874i	$-0.674858\pi$
$743$	−35.5567	−	6.26960i	−1.30445	−	0.230009i	−0.782330	+	0.622864i	$0.785969\pi$
$744$	−0.309251	−	0.259493i	−0.0113377	−	0.00951347i
$745$	−27.0989	−	39.4535i	−0.992826	−	1.44547i
$746$	−3.20475	+	1.16643i	−0.117334	+	0.0427062i
$747$	7.49224	+	8.92891i	0.274127	+	0.326692i
$748$	15.7741	−	9.10719i	0.576759	−	0.332992i
$749$	−10.8973	+	18.8747i	−0.398180	+	0.689668i
$750$	11.1074	+	1.27528i	0.405584	+	0.0465667i
$751$	−4.02853	−	22.8469i	−0.147003	−	0.833696i	−0.965737	−	0.259523i	$-0.916435\pi$
$751$	−4.02853	−	22.8469i	−0.147003	−	0.833696i	0.818734	−	0.574173i	$-0.194676\pi$
$752$	−9.17390	−	5.29656i	−0.334538	−	0.193146i
$753$	5.63029	−	3.25065i	0.205179	−	0.118460i
$754$	−0.0673882	+	0.0565454i	−0.00245413	+	0.00205926i
$755$	14.3911	+	3.99550i	0.523747	+	0.145411i
$756$	−2.60503	−	0.948155i	−0.0947442	−	0.0344841i
$757$	25.9724	−	30.9527i	0.943984	−	1.12500i	−0.0480269	−	0.998846i	$-0.515293\pi$
$757$	25.9724	−	30.9527i	0.943984	−	1.12500i	0.992011	−	0.126150i	$-0.0402622\pi$
$758$	17.9772	+	3.16986i	0.652960	+	0.115134i
$759$	5.31457			0.192907
$760$	−9.04550	+	3.63028i	−0.328115	+	0.131684i
$761$	−41.2261			−1.49445			−0.747223	−	0.664573i	$-0.768613\pi$
$761$	−41.2261			−1.49445			−0.747223	+	0.664573i	$0.768613\pi$
$762$	−5.09947	−	0.899175i	−0.184734	−	0.0325737i
$763$	3.60026	−	4.29063i	0.130338	−	0.155331i
$764$	14.0798	+	5.12462i	0.509388	+	0.185402i
$765$	−4.93217	+	17.7649i	−0.178323	+	0.642291i
$766$	28.7209	−	24.0997i	1.03773	−	0.870757i
$767$	2.79073	−	1.61123i	0.100768	−	0.0581782i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	2.21700	+	12.5732i	0.0799469	+	0.453402i	0.998333	+	0.0577162i	$0.0183818\pi$
$769$	2.21700	+	12.5732i	0.0799469	+	0.453402i	−0.918386	+	0.395685i	$0.870507\pi$
$770$	−5.89892	+	12.3582i	−0.212582	+	0.445357i
$771$	−2.53611	+	4.39266i	−0.0913356	+	0.158198i
$772$	13.0512	−	7.53512i	0.469724	−	0.271195i
$773$	13.5195	+	16.1119i	0.486261	+	0.579504i	0.952262	−	0.305281i	$-0.0987502\pi$
$773$	13.5195	+	16.1119i	0.486261	+	0.579504i	−0.466001	+	0.884784i	$0.654306\pi$
$774$	−4.12987	+	1.50315i	−0.148445	+	0.0540295i
$775$	0.0363942	−	2.01817i	0.00130732	−	0.0724947i
$776$	0.469514	+	0.393969i	0.0168546	+	0.0141427i
$777$	−11.8220	−	2.08454i	−0.424113	−	0.0747826i
$778$		−	26.4318i		−	0.947625i
$779$	−44.4264	+	23.0127i	−1.59174	+	0.824514i
$780$	−1.86646	−	1.33215i	−0.0668300	−	0.0476985i
$781$	2.44803	−	13.8835i	0.0875975	−	0.496790i
$782$	−12.7504	+	15.1954i	−0.455954	+	0.543385i
$783$	−0.0293389	+	0.0806080i	−0.00104849	+	0.00288070i
$784$	0.643874	−	0.234351i	0.0229955	−	0.00836968i
$785$	−2.62228	−	33.4428i	−0.0935933	−	1.19363i
$786$	−9.07189	−	15.7130i	−0.323583	−	0.560463i
$787$	13.2396	+	7.64388i	0.471941	+	0.272475i	0.717052	−	0.697020i	$-0.245491\pi$
$787$	13.2396	+	7.64388i	0.471941	+	0.272475i	−0.245111	+	0.969495i	$0.578824\pi$
$788$	3.53560	−	0.623422i	0.125951	−	0.0222085i
$789$	−0.482447	−	2.73609i	−0.0171756	−	0.0974076i
$790$	−11.5913	−	25.4543i	−0.412400	−	0.905622i
$791$	28.2541	+	48.9376i	1.00460	+	1.74002i
$792$	1.41997	+	1.69226i	0.0504566	+	0.0601318i
$793$	−1.98310	−	5.44853i	−0.0704221	−	0.193483i
$794$	12.9741	+	4.72218i	0.460433	+	0.167584i
$795$	−4.44080	−	17.1918i	−0.157499	−	0.609730i
$796$	1.38562	−	7.85824i	0.0491120	−	0.278528i
$797$			14.0700i			0.498386i	0.968454	+	0.249193i	$0.0801653\pi$
$797$			14.0700i			0.498386i	−0.968454	+	0.249193i	$0.919835\pi$
$798$	8.89257	+	8.18174i	0.314794	+	0.289631i
$799$	87.3424			3.08995
$800$	0.779318	+	4.93889i	0.0275530	+	0.174616i
$801$	8.44569	+	7.08677i	0.298414	+	0.250399i
$802$	12.0585	−	33.1304i	0.425800	−	1.16988i
$803$	6.45464	+	17.7340i	0.227779	+	0.625818i
$804$	2.49791	−	2.09599i	0.0880943	−	0.0739199i
$805$	1.43365	−	14.8440i	0.0505295	−	0.523184i
$806$	−0.206997	+	0.358530i	−0.00729117	+	0.0126287i
$807$	28.3007	−	4.99018i	0.996233	−	0.175663i
$808$	8.93053	−	1.57469i	0.314175	−	0.0553975i
$809$	26.7913	−	46.4039i	0.941932	−	1.63147i	0.180151	−	0.983639i	$-0.442341\pi$
$809$	26.7913	−	46.4039i	0.941932	−	1.63147i	0.761781	−	0.647835i	$-0.224325\pi$
$810$	−2.22571	−	0.214961i	−0.0782035	−	0.00755296i
$811$	30.6299	−	25.7016i	1.07556	−	0.902504i	0.0800180	−	0.996793i	$-0.474502\pi$
$811$	30.6299	−	25.7016i	1.07556	−	0.902504i	0.995545	+	0.0942890i	$0.0300578\pi$
$812$	−0.0813339	−	0.223463i	−0.00285426	−	0.00784202i
$813$	−1.56426	+	4.29777i	−0.0548611	+	0.150730i
$814$	7.32791	+	6.14884i	0.256843	+	0.215517i
$815$	−20.3306	−	20.7005i	−0.712149	−	0.725107i
$816$	−8.24521			−0.288640
$817$	19.1370	+	0.874388i	0.669519	+	0.0305910i
$818$			14.8499i			0.519215i
$819$	−0.493668	+	2.79973i	−0.0172502	+	0.0978305i
$820$	6.41915	+	24.8507i	0.224167	+	0.867822i
$821$	2.28532	+	0.831790i	0.0797584	+	0.0290297i	0.381591	−	0.924331i	$-0.375376\pi$
$821$	2.28532	+	0.831790i	0.0797584	+	0.0290297i	−0.301833	+	0.953361i	$0.597598\pi$
$822$	0.401229	+	1.10237i	0.0139945	+	0.0384495i
$823$	29.6293	+	35.3109i	1.03281	+	1.23086i	0.972554	+	0.232677i	$0.0747485\pi$
$823$	29.6293	+	35.3109i	1.03281	+	1.23086i	0.0602600	+	0.998183i	$0.480807\pi$
$824$	5.31432	+	9.20468i	0.185133	+	0.320660i
$825$	−2.11383	+	10.8413i	−0.0735943	+	0.377445i
$826$	1.51268	+	8.57886i	0.0526330	+	0.298497i
$827$	18.0814	−	3.18824i	0.628752	−	0.110866i	0.149814	−	0.988714i	$-0.452133\pi$
$827$	18.0814	−	3.18824i	0.628752	−	0.110866i	0.478939	+	0.877848i	$0.341022\pi$
$828$	−2.08347	−	1.20289i	−0.0724054	−	0.0418033i
$829$	−17.4417	−	30.2099i	−0.605774	−	1.04923i	−0.991929	−	0.126798i	$-0.959530\pi$
$829$	−17.4417	−	30.2099i	−0.605774	−	1.04923i	0.386154	−	0.922434i	$-0.373803\pi$
$830$	−25.9835	+	2.03739i	−0.901902	+	0.0707190i
$831$	21.8787	−	7.96319i	0.758963	−	0.276240i
$832$	0.350743	−	0.963658i	0.0121598	−	0.0334088i
$833$	−3.63149	+	4.32784i	−0.125824	+	0.149951i
$834$	0.478807	−	2.71545i	0.0165797	−	0.0940283i
$835$	−15.6390	+	21.9116i	−0.541209	+	0.758283i
$836$	−2.87694	−	9.18936i	−0.0995011	−	0.317821i
$837$			0.403699i			0.0139539i
$838$	18.9094	+	3.33424i	0.653216	+	0.115180i
$839$	20.4117	+	17.1274i	0.704689	+	0.591304i	0.923103	−	0.384552i	$-0.125644\pi$
$839$	20.4117	+	17.1274i	0.704689	+	0.591304i	−0.218415	+	0.975856i	$0.570089\pi$
$840$	5.10967	−	3.50960i	0.176300	−	0.121093i
$841$	27.2442	−	9.91607i	0.939454	−	0.341933i
$842$	14.2280	+	16.9562i	0.490328	+	0.584351i
$843$	−17.4849	+	10.0949i	−0.602212	+	0.347687i
$844$	0.0360661	−	0.0624684i	0.00124145	−	0.00215025i
$845$	11.5091	−	24.1113i	0.395924	−	0.829455i
$846$	1.83947	+	10.4322i	0.0632424	+	0.358666i
$847$	14.6928	+	8.48290i	0.504851	+	0.291476i
$848$	6.87691	−	3.97038i	0.236154	−	0.136344i
$849$	−20.2519	+	16.9934i	−0.695045	+	0.583212i
$850$	−25.9259	−	32.0536i	−0.889250	−	1.09943i
$851$	−9.78937	−	3.56304i	−0.335575	−	0.122139i
$852$	−4.10206	+	4.88864i	−0.140534	+	0.167482i
$853$	−46.2924	−	8.16260i	−1.58502	−	0.279482i	−0.689427	−	0.724355i	$-0.742138\pi$
$853$	−46.2924	−	8.16260i	−1.58502	−	0.279482i	−0.895594	+	0.444873i	$0.853249\pi$
$854$	15.6741			0.536358
$855$	8.59529	+	4.59575i	0.293953	+	0.157171i
$856$	−7.86182			−0.268711
$857$	38.7339	+	6.82983i	1.32312	+	0.233303i	0.790194	−	0.612856i	$-0.209980\pi$
$857$	38.7339	+	6.82983i	1.32312	+	0.233303i	0.532930	+	0.846159i	$0.321091\pi$
$858$	1.45619	−	1.73542i	0.0497134	−	0.0592462i
$859$	−29.1651	−	10.6152i	−0.995101	−	0.362187i	−0.207408	−	0.978255i	$-0.566503\pi$
$859$	−29.1651	−	10.6152i	−0.995101	−	0.362187i	−0.787693	+	0.616068i	$0.788725\pi$
$860$	2.62897	−	9.46914i	0.0896473	−	0.322895i
$861$	24.3759	−	20.4538i	0.830728	−	0.697063i
$862$	23.0853	−	13.3283i	0.786289	−	0.453964i
$863$	9.01512	+	5.20488i	0.306878	+	0.177176i	0.645529	−	0.763736i	$-0.276637\pi$
$863$	9.01512	+	5.20488i	0.306878	+	0.177176i	−0.338650	+	0.940912i	$0.609970\pi$
$864$	−0.173648	−	0.984808i	−0.00590763	−	0.0335038i
$865$	47.4020	+	22.6264i	1.61172	+	0.769321i
$866$	−15.2129	+	26.3495i	−0.516955	+	0.895392i
$867$	44.1530	−	25.4917i	1.49951	−	0.865745i
$868$	−0.719371	−	0.857313i	−0.0244170	−	0.0290991i
$869$	25.9653	−	9.45061i	0.880814	−	0.320590i
$870$	−0.108598	−	0.158109i	−0.00368183	−	0.00536041i
$871$	−2.56161	−	2.14945i	−0.0867969	−	0.0728312i
$872$	1.98971	+	0.350840i	0.0673802	+	0.0118809i
$873$		−	0.612907i		−	0.0207438i
$874$	6.36694	+	8.33245i	0.215365	+	0.281849i
$875$	29.7103	+	8.82863i	1.00439	+	0.298462i
$876$	1.48347	−	8.41316i	0.0501217	−	0.284254i
$877$	−20.6281	+	24.5836i	−0.696560	+	0.830128i	−0.992133	−	0.125192i	$-0.960045\pi$
$877$	−20.6281	+	24.5836i	−0.696560	+	0.830128i	0.295572	+	0.955320i	$0.404490\pi$
$878$	2.70314	−	7.42680i	0.0912264	−	0.250642i
$879$	11.6356	−	4.23502i	0.392459	−	0.142844i
$880$	−4.92455	+	0.386139i	−0.166007	+	0.0130167i
$881$	−8.64598	−	14.9753i	−0.291290	−	0.504530i	0.682825	−	0.730582i	$-0.260751\pi$
$881$	−8.64598	−	14.9753i	−0.291290	−	0.504530i	−0.974115	+	0.226052i	$0.927418\pi$
$882$	−0.593398	−	0.342598i	−0.0199807	−	0.0115359i
$883$	14.0110	−	2.47052i	0.471508	−	0.0831396i	0.0671550	−	0.997743i	$-0.478608\pi$
$883$	14.0110	−	2.47052i	0.471508	−	0.0831396i	0.404353	+	0.914603i	$0.367497\pi$
$884$	1.46828	+	8.32703i	0.0493836	+	0.280068i
$885$	2.91197	+	6.39463i	0.0978848	+	0.214953i
$886$	−3.68094	−	6.37558i	−0.123664	−	0.214192i
$887$	21.6269	+	25.7739i	0.726160	+	0.865404i	0.995214	−	0.0977215i	$-0.0311554\pi$
$887$	21.6269	+	25.7739i	0.726160	+	0.865404i	−0.269054	+	0.963125i	$0.586711\pi$
$888$	−1.48103	−	4.06911i	−0.0497002	−	0.136550i
$889$	−13.4892	−	4.90968i	−0.452414	−	0.164665i
$890$	−23.8693	+	6.16567i	−0.800101	+	0.206674i
$891$	0.383604	−	2.17553i	0.0128512	−	0.0728828i
$892$			15.1943i			0.508744i
$893$	10.0853	−	45.0595i	0.337490	−	1.50786i
$894$	−21.4053			−0.715900
$895$	−29.8244	+	29.2914i	−0.996918	+	0.979103i
$896$	2.12364	+	1.78195i	0.0709459	+	0.0595307i
$897$	−0.843810	+	2.31835i	−0.0281740	+	0.0774074i
$898$	7.63167	+	20.9678i	0.254672	+	0.699706i
$899$	−0.0265280	+	0.0222596i	−0.000884758	+	0.000742400i
$900$	3.28248	−	3.77165i	0.109416	−	0.125722i
$901$	−32.7366	+	56.7015i	−1.09062	+	1.88900i
$902$	−24.9714	+	4.40313i	−0.831457	+	0.146608i
$903$	−11.9986	+	2.11567i	−0.399287	+	0.0704051i
$904$	−10.1919	+	17.6529i	−0.338977	+	0.587126i
$905$	−1.52806	+	15.8216i	−0.0507946	+	0.525929i
$906$	5.11668	−	4.29341i	0.169990	−	0.142639i
$907$	13.4312	+	36.9019i	0.445975	+	1.22531i	0.935503	+	0.353319i	$0.114947\pi$
$907$	13.4312	+	36.9019i	0.445975	+	1.22531i	−0.489528	+	0.871988i	$0.662831\pi$
$908$	2.37548	−	6.52657i	0.0788329	−	0.216592i
$909$	−6.94672	−	5.82899i	−0.230408	−	0.193335i
$910$	−4.45434	−	4.53539i	−0.147660	−	0.150347i
$911$	53.6442			1.77731			0.888656	−	0.458574i	$-0.151640\pi$
$911$	53.6442			1.77731			0.888656	+	0.458574i	$0.151640\pi$
$912$	−0.952058	+	4.25366i	−0.0315258	+	0.140853i
$913$		−	25.7488i		−	0.852161i
$914$	3.53416	−	20.0432i	0.116900	−	0.662970i
$915$	12.2410	−	3.16195i	0.404674	−	0.104531i
$916$	−11.9416	−	4.34640i	−0.394563	−	0.143609i
$917$	−17.2031	−	47.2651i	−0.568096	−	1.56083i
$918$	5.29992	+	6.31620i	0.174923	+	0.208466i
$919$	22.4350	+	38.8586i	0.740064	+	1.28183i	0.952466	+	0.304645i	$0.0985379\pi$
$919$	22.4350	+	38.8586i	0.740064	+	1.28183i	−0.212402	+	0.977182i	$0.568129\pi$
$920$	4.89577	−	2.22942i	0.161409	−	0.0735018i
$921$	−1.81738	−	10.3069i	−0.0598847	−	0.339623i
$922$	−23.8997	+	4.21416i	−0.787095	+	0.138786i
$923$	5.66764	+	3.27221i	0.186553	+	0.107706i
$924$	3.06204	+	5.30360i	0.100734	+	0.174476i
$925$	11.1620	−	18.5523i	0.367003	−	0.609996i
$926$	−31.5192	+	11.4720i	−1.03578	+	0.376995i
$927$	3.63521	−	9.98766i	0.119396	−	0.328038i
$928$	0.0551392	−	0.0657123i	0.00181003	−	0.00215711i
$929$	−7.61321	+	43.1766i	−0.249781	+	1.41658i	0.559340	+	0.828938i	$0.311055\pi$
$929$	−7.61321	+	43.1766i	−0.249781	+	1.41658i	−0.809122	+	0.587641i	$0.800057\pi$
$930$	−0.734749	−	0.524412i	−0.0240934	−	0.0171961i
$931$	1.81339	+	2.37319i	0.0594313	+	0.0777782i
$932$			5.82469i			0.190794i
$933$	14.6419	+	2.58176i	0.479354	+	0.0845230i
$934$	17.3163	+	14.5301i	0.566606	+	0.475439i
$935$	33.5722	−	23.0592i	1.09793	−	0.754117i
$936$	−0.963658	+	0.350743i	−0.0314982	+	0.0114644i
$937$	−8.17920	−	9.74759i	−0.267203	−	0.318440i	0.615714	−	0.787970i	$-0.288868\pi$
$937$	−8.17920	−	9.74759i	−0.267203	−	0.318440i	−0.882917	+	0.469530i	$0.844423\pi$
$938$	7.82853	−	4.51980i	0.255611	−	0.147577i
$939$	11.1688	−	19.3450i	0.364481	−	0.631300i
$940$	−21.3765	−	10.2037i	−0.697225	−	0.332807i
$941$	−3.27335	−	18.5641i	−0.106708	−	0.605172i	−0.990524	−	0.137338i	$-0.956145\pi$
$941$	−3.27335	−	18.5641i	−0.106708	−	0.605172i	0.883816	−	0.467834i	$-0.154966\pi$
$942$	−12.9921	−	7.50100i	−0.423306	−	0.244396i
$943$	23.9147	−	13.8072i	0.778770	−	0.449623i
$944$	−2.40716	+	2.01984i	−0.0783463	+	0.0657403i
$945$	−5.97294	−	1.65830i	−0.194300	−	0.0539446i
$946$	9.12323	+	3.32058i	0.296622	+	0.107961i
$947$	−7.38292	+	8.79862i	−0.239913	+	0.285917i	−0.872543	−	0.488537i	$-0.837531\pi$
$947$	−7.38292	+	8.79862i	−0.239913	+	0.285917i	0.632631	+	0.774454i	$0.281975\pi$
$948$	−12.3182	−	2.17203i	−0.400076	−	0.0705443i
$949$	−8.76082			−0.284388
$950$	−19.5299	+	9.67383i	−0.633634	+	0.313861i
$951$	−11.9640			−0.387961
$952$	−22.5103	−	3.96917i	−0.729562	−	0.128641i
$953$	−18.6595	+	22.2375i	−0.604439	+	0.720342i	−0.978312	−	0.207138i	$-0.933585\pi$
$953$	−18.6595	+	22.2375i	−0.604439	+	0.720342i	0.373873	+	0.927480i	$0.378030\pi$
$954$	−7.46188	−	2.71590i	−0.241587	−	0.0879306i
$955$	32.2828	+	8.96285i	1.04465	+	0.290031i
$956$	17.3688	−	14.5741i	0.561746	−	0.471361i
$957$	0.164110	−	0.0947491i	0.00530493	−	0.00306280i
$958$	−12.1851	−	7.03510i	−0.393684	−	0.227294i
$959$	0.564726	+	3.20272i	0.0182360	+	0.103421i
$960$	2.01796	+	0.963235i	0.0651295	+	0.0310883i
$961$	15.4185	−	26.7056i	0.497371	−	0.861473i
$962$	−3.84575	+	2.22035i	−0.123992	+	0.0715868i
$963$	5.05348	+	6.02250i	0.162846	+	0.194072i
$964$	22.6742	−	8.25274i	0.730287	−	0.265803i
$965$	27.7770	−	19.0788i	0.894173	−	0.614168i
$966$	−5.10901	−	4.28697i	−0.164380	−	0.137931i
$967$	−1.55494	−	0.274178i	−0.0500035	−	0.00881697i	0.148590	−	0.988899i	$-0.452526\pi$
$967$	−1.55494	−	0.274178i	−0.0500035	−	0.00881697i	−0.198594	+	0.980082i	$0.563638\pi$
$968$			6.11994i			0.196702i
$969$	−10.7379	−	34.2984i	−0.344951	−	1.10182i
$970$	1.11552	+	0.796177i	0.0358171	+	0.0255637i
$971$	1.18329	−	6.71078i	0.0379736	−	0.215359i	−0.959916	−	0.280287i	$-0.909570\pi$
$971$	1.18329	−	6.71078i	0.0379736	−	0.215359i	0.997890	+	0.0649274i	$0.0206816\pi$
$972$	−0.642788	+	0.766044i	−0.0206174	+	0.0245709i
$973$	2.61438	−	7.18296i	0.0838133	−	0.230275i
$974$	−3.89535	+	1.41779i	−0.124815	+	0.0454290i
$975$	−4.39361	−	2.64341i	−0.140708	−	0.0846568i
$976$	2.82700	+	4.89651i	0.0904902	+	0.156734i
$977$	−30.8729	−	17.8245i	−0.987712	−	0.570256i	−0.0831225	−	0.996539i	$-0.526489\pi$
$977$	−30.8729	−	17.8245i	−0.987712	−	0.570256i	−0.904590	+	0.426283i	$0.859823\pi$
$978$	−12.7786	+	2.25321i	−0.408613	+	0.0720496i
$979$	−4.22925	−	23.9853i	−0.135168	−	0.766573i
$980$	1.39438	−	0.634968i	0.0445418	−	0.0202833i
$981$	−1.01020	−	1.74972i	−0.0322533	−	0.0558644i
$982$	−8.13727	−	9.69762i	−0.259671	−	0.309463i
$983$	18.0595	+	49.6181i	0.576009	+	1.58257i	0.794847	+	0.606810i	$0.207551\pi$
$983$	18.0595	+	49.6181i	0.576009	+	1.58257i	−0.218838	+	0.975761i	$0.570226\pi$
$984$	10.7861	+	3.92582i	0.343848	+	0.125151i
$985$	7.77268	−	2.00776i	0.247658	−	0.0639724i
$986$	−0.122819	+	0.696539i	−0.00391134	+	0.0221823i
$987$			29.3664i			0.934744i
$988$	4.46541	+	0.204029i	0.142064	+	0.00649102i
$989$	−10.5732			−0.336208
$990$	3.46124	+	3.52422i	0.110005	+	0.112007i
$991$	−17.2449	−	14.4702i	−0.547803	−	0.459661i	0.326393	−	0.945234i	$-0.394167\pi$
$991$	−17.2449	−	14.4702i	−0.547803	−	0.459661i	−0.874196	+	0.485573i	$0.838611\pi$
$992$	0.138073	−	0.379353i	0.00438383	−	0.0120445i
$993$	10.3921	+	28.5520i	0.329783	+	0.906071i
$994$	−13.5524	+	11.3718i	−0.429855	+	0.360692i
$995$	1.71527	−	17.7600i	0.0543778	−	0.563029i
$996$	−5.82793	+	10.0943i	−0.184665	+	0.319849i
$997$	−25.1388	+	4.43264i	−0.796152	+	0.140383i	−0.556906	−	0.830576i	$-0.688012\pi$
$997$	−25.1388	+	4.43264i	−0.796152	+	0.140383i	−0.239247	+	0.970959i	$0.576900\pi$
$998$	−38.3806	+	6.76753i	−1.21492	+	0.214222i
$999$	−2.16513	+	3.75011i	−0.0685016	+	0.118648i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.b.169.10	yes	60
5.4	even	2	inner	570.2.bc.b.169.3	✓	60
19.9	even	9	inner	570.2.bc.b.199.3	yes	60
95.9	even	18	inner	570.2.bc.b.199.10	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.b.169.3	✓	60	5.4	even	2	inner
570.2.bc.b.169.10	yes	60	1.1	even	1	trivial
570.2.bc.b.199.3	yes	60	19.9	even	9	inner
570.2.bc.b.199.10	yes	60	95.9	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.15457 + 0.598186i) q^{5} +(0.766044 - 0.642788i) q^{6} +(2.40081 - 1.38611i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +O(q^{10})\)	\(q+(0.984808 + 0.173648i) q^{2} +(0.642788 - 0.766044i) q^{3} +(0.939693 + 0.342020i) q^{4} +(2.15457 + 0.598186i) q^{5} +(0.766044 - 0.642788i) q^{6} +(2.40081 - 1.38611i) q^{7} +(0.866025 + 0.500000i) q^{8} +(-0.173648 - 0.984808i) q^{9} +(2.01796 + 0.963235i) q^{10} +(-1.10454 + 1.91312i) q^{11} +(0.866025 - 0.500000i) q^{12} +(-0.659181 - 0.785581i) q^{13} +(2.60503 - 0.948155i) q^{14} +(1.84317 - 1.26599i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-8.11995 - 1.43177i) q^{17} -1.00000i q^{18} +(-1.67623 + 4.02371i) q^{19} +(1.82004 + 1.29902i) q^{20} +(0.481391 - 2.73010i) q^{21} +(-1.41997 + 1.69226i) q^{22} +(0.822825 - 2.26069i) q^{23} +(0.939693 - 0.342020i) q^{24} +(4.28435 + 2.57767i) q^{25} +(-0.512752 - 0.888112i) q^{26} +(-0.866025 - 0.500000i) q^{27} +(2.73010 - 0.481391i) q^{28} +(-0.0148958 - 0.0844781i) q^{29} +(2.03500 - 0.926694i) q^{30} +(-0.201850 - 0.349614i) q^{31} +(0.642788 + 0.766044i) q^{32} +(0.755552 + 2.07586i) q^{33} +(-7.74796 - 2.82003i) q^{34} +(6.00187 - 1.55034i) q^{35} +(0.173648 - 0.984808i) q^{36} -4.33025i q^{37} +(-2.34948 + 3.67151i) q^{38} -1.02550 q^{39} +(1.56682 + 1.59533i) q^{40} +(8.79291 + 7.37813i) q^{41} +(0.948155 - 2.60503i) q^{42} +(-1.50315 - 4.12987i) q^{43} +(-1.69226 + 1.41997i) q^{44} +(0.214961 - 2.22571i) q^{45} +(1.20289 - 2.08347i) q^{46} +(-10.4322 + 1.83947i) q^{47} +(0.984808 - 0.173648i) q^{48} +(0.342598 - 0.593398i) q^{49} +(3.77165 + 3.28248i) q^{50} +(-6.31620 + 5.29992i) q^{51} +(-0.350743 - 0.963658i) q^{52} +(2.71590 - 7.46188i) q^{53} +(-0.766044 - 0.642788i) q^{54} +(-3.52422 + 3.46124i) q^{55} +2.77222 q^{56} +(2.00488 + 3.87046i) q^{57} -0.0857813i q^{58} +(-0.545658 + 3.09458i) q^{59} +(2.16501 - 0.559241i) q^{60} +(5.31303 + 1.93378i) q^{61} +(-0.138073 - 0.379353i) q^{62} +(-1.78195 - 2.12364i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-0.950328 - 2.08690i) q^{65} +(0.383604 + 2.17553i) q^{66} +(3.21125 - 0.566229i) q^{67} +(-7.14056 - 4.12260i) q^{68} +(-1.20289 - 2.08347i) q^{69} +(6.17990 - 0.484572i) q^{70} +(-5.99681 + 2.18266i) q^{71} +(0.342020 - 0.939693i) q^{72} +(5.49130 - 6.54427i) q^{73} +(0.751940 - 4.26447i) q^{74} +(4.72853 - 1.62511i) q^{75} +(-2.95133 + 3.20774i) q^{76} +6.12407i q^{77} +(-1.00992 - 0.178077i) q^{78} +(-9.58185 - 8.04013i) q^{79} +(1.26599 + 1.84317i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(7.37813 + 8.79291i) q^{82} +(-10.0943 + 5.82793i) q^{83} +(1.38611 - 2.40081i) q^{84} +(-16.6385 - 7.94208i) q^{85} +(-0.763168 - 4.32814i) q^{86} +(-0.0742888 - 0.0428906i) q^{87} +(-1.91312 + 1.10454i) q^{88} +(-8.44569 + 7.08677i) q^{89} +(0.598186 - 2.15457i) q^{90} +(-2.67147 - 0.972336i) q^{91} +(1.54640 - 1.84293i) q^{92} +(-0.397566 - 0.0701016i) q^{93} -10.5931 q^{94} +(-6.01849 + 7.66667i) q^{95} +1.00000 q^{96} +(0.603596 + 0.106430i) q^{97} +(0.440436 - 0.524891i) q^{98} +(2.07586 + 0.755552i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 6 q^{5}+O(q^{10}) \) 60 * q + 6 * q^5	\( 60 q + 6 q^{5} + 6 q^{10} - 12 q^{11} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 18 q^{21} - 6 q^{25} - 6 q^{26} + 12 q^{29} + 6 q^{30} - 36 q^{31} - 6 q^{35} - 12 q^{39} - 6 q^{40} - 30 q^{41} - 6 q^{44} - 6 q^{45} - 36 q^{46} + 18 q^{49} - 90 q^{55} + 24 q^{56} + 60 q^{59} + 6 q^{60} + 36 q^{61} + 30 q^{64} + 24 q^{65} - 12 q^{66} + 36 q^{69} - 72 q^{70} - 72 q^{71} + 6 q^{74} + 6 q^{76} + 6 q^{80} + 12 q^{84} + 18 q^{85} - 12 q^{86} + 60 q^{89} + 12 q^{90} - 48 q^{91} - 156 q^{94} - 84 q^{95} + 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q + 6 * q^5 + 6 * q^10 - 12 * q^11 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 18 * q^21 - 6 * q^25 - 6 * q^26 + 12 * q^29 + 6 * q^30 - 36 * q^31 - 6 * q^35 - 12 * q^39 - 6 * q^40 - 30 * q^41 - 6 * q^44 - 6 * q^45 - 36 * q^46 + 18 * q^49 - 90 * q^55 + 24 * q^56 + 60 * q^59 + 6 * q^60 + 36 * q^61 + 30 * q^64 + 24 * q^65 - 12 * q^66 + 36 * q^69 - 72 * q^70 - 72 * q^71 + 6 * q^74 + 6 * q^76 + 6 * q^80 + 12 * q^84 + 18 * q^85 - 12 * q^86 + 60 * q^89 + 12 * q^90 - 48 * q^91 - 156 * q^94 - 84 * q^95 + 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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