LMFDB - Embedded newform 630.2.bw.a.607.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(103,630)]

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, 10]))

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

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

chi := DirichletCharacter("630.103");

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.bw (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			607.12
Character	$\chi$	$=$	630.607
Dual form			630.2.bw.a.493.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.266905 - 1.71136i) q^{3} +1.00000i q^{4} +(-0.634884 + 2.14404i) q^{5} +(-1.02139 + 1.39885i) q^{6} +(-1.85766 - 1.88390i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.85752 + 0.913543i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.266905 - 1.71136i) q^{3} +1.00000i q^{4} +(-0.634884 + 2.14404i) q^{5} +(-1.02139 + 1.39885i) q^{6} +(-1.85766 - 1.88390i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.85752 + 0.913543i) q^{9} +(1.96500 - 1.06714i) q^{10} +(3.22528 - 5.58636i) q^{11} +(1.71136 - 0.266905i) q^{12} +(0.264005 - 0.0707399i) q^{13} +(-0.0185518 + 2.64569i) q^{14} +(3.83869 + 0.514260i) q^{15} -1.00000 q^{16} +(-1.85204 - 0.496253i) q^{17} +(2.66655 + 1.37460i) q^{18} +(-3.64418 + 6.31190i) q^{19} +(-2.14404 - 0.634884i) q^{20} +(-2.72822 + 3.68196i) q^{21} +(-6.23077 + 1.66953i) q^{22} +(-4.00290 - 1.07257i) q^{23} +(-1.39885 - 1.02139i) q^{24} +(-4.19384 - 2.72244i) q^{25} +(-0.236700 - 0.136659i) q^{26} +(2.32609 + 4.64643i) q^{27} +(1.88390 - 1.85766i) q^{28} +(-6.46173 + 3.73068i) q^{29} +(-2.35073 - 3.07800i) q^{30} +8.30069i q^{31} +(0.707107 + 0.707107i) q^{32} +(-10.4211 - 4.02860i) q^{33} +(0.958686 + 1.66049i) q^{34} +(5.21857 - 2.78686i) q^{35} +(-0.913543 - 2.85752i) q^{36} +(-3.11198 + 0.833854i) q^{37} +(7.04001 - 1.88637i) q^{38} +(-0.191526 - 0.432928i) q^{39} +(1.06714 + 1.96500i) q^{40} +(-4.07142 - 2.35064i) q^{41} +(4.53268 - 0.674398i) q^{42} +(0.146117 + 0.0391519i) q^{43} +(5.58636 + 3.22528i) q^{44} +(-0.144480 - 6.70665i) q^{45} +(2.07205 + 3.58890i) q^{46} +(8.09709 - 8.09709i) q^{47} +(0.266905 + 1.71136i) q^{48} +(-0.0981647 + 6.99931i) q^{49} +(1.04044 + 4.89055i) q^{50} +(-0.354949 + 3.30196i) q^{51} +(0.0707399 + 0.264005i) q^{52} +(-7.07759 - 1.89643i) q^{53} +(1.64073 - 4.93032i) q^{54} +(9.92971 + 10.4618i) q^{55} +(-2.64569 - 0.0185518i) q^{56} +(11.7746 + 4.55183i) q^{57} +(7.20712 + 1.93114i) q^{58} -6.27798 q^{59} +(-0.514260 + 3.83869i) q^{60} +4.09079i q^{61} +(5.86947 - 5.86947i) q^{62} +(7.02934 + 3.68623i) q^{63} -1.00000i q^{64} +(-0.0159431 + 0.610950i) q^{65} +(4.52020 + 10.2175i) q^{66} +(-4.73557 - 4.73557i) q^{67} +(0.496253 - 1.85204i) q^{68} +(-0.767168 + 7.13669i) q^{69} +(-5.66069 - 1.71948i) q^{70} -3.51520 q^{71} +(-1.37460 + 2.66655i) q^{72} +(0.669977 - 2.50039i) q^{73} +(2.79013 + 1.61088i) q^{74} +(-3.53972 + 7.90382i) q^{75} +(-6.31190 - 3.64418i) q^{76} +(-16.5156 + 4.30146i) q^{77} +(-0.170697 + 0.441555i) q^{78} +3.29520i q^{79} +(0.634884 - 2.14404i) q^{80} +(7.33088 - 5.22094i) q^{81} +(1.21678 + 4.54108i) q^{82} +(2.02567 - 7.55991i) q^{83} +(-3.68196 - 2.72822i) q^{84} +(2.23982 - 3.65579i) q^{85} +(-0.0756356 - 0.131005i) q^{86} +(8.10922 + 10.0626i) q^{87} +(-1.66953 - 6.23077i) q^{88} +(8.10279 - 14.0344i) q^{89} +(-4.64015 + 4.84448i) q^{90} +(-0.623700 - 0.365948i) q^{91} +(1.07257 - 4.00290i) q^{92} +(14.2055 - 2.21550i) q^{93} -11.4510 q^{94} +(-11.2194 - 11.8206i) q^{95} +(1.02139 - 1.39885i) q^{96} +(-3.68177 - 0.986528i) q^{97} +(5.01867 - 4.87985i) q^{98} +(-4.11295 + 18.9096i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q+O(q^{10}) $ 192 * q	$ 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) $ 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$2$	−0.707107	−	0.707107i	−0.500000	−	0.500000i
$3$	−0.266905	−	1.71136i	−0.154098	−	0.988056i
$3$	−0.266905	−	1.71136i	−0.154098	−	0.988056i
$4$			1.00000i			0.500000i
$5$	−0.634884	+	2.14404i	−0.283929	+	0.958845i
$5$	−0.634884	+	2.14404i	−0.283929	+	0.958845i
$6$	−1.02139	+	1.39885i	−0.416979	+	0.571077i
$7$	−1.85766	−	1.88390i	−0.702131	−	0.712048i
$7$	−1.85766	−	1.88390i	−0.702131	−	0.712048i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.85752	+	0.913543i	−0.952508	+	0.304514i
$10$	1.96500	−	1.06714i	0.621387	−	0.337458i
$11$	3.22528	−	5.58636i	0.972460	−	1.68435i	0.284385	−	0.958710i	$-0.408211\pi$
$11$	3.22528	−	5.58636i	0.972460	−	1.68435i	0.688075	−	0.725640i	$-0.258456\pi$
$12$	1.71136	−	0.266905i	0.494028	−	0.0770489i
$13$	0.264005	−	0.0707399i	0.0732218	−	0.0196197i	−0.222022	−	0.975042i	$-0.571266\pi$
$13$	0.264005	−	0.0707399i	0.0732218	−	0.0196197i	0.295244	+	0.955422i	$0.404599\pi$
$14$	−0.0185518	+	2.64569i	−0.00495819	+	0.707089i
$15$	3.83869	+	0.514260i	0.991145	+	0.132781i
$16$	−1.00000			−0.250000
$17$	−1.85204	−	0.496253i	−0.449186	−	0.120359i	0.0271327	−	0.999632i	$-0.491362\pi$
$17$	−1.85204	−	0.496253i	−0.449186	−	0.120359i	−0.476318	+	0.879273i	$0.658029\pi$
$18$	2.66655	+	1.37460i	0.628511	+	0.323997i
$19$	−3.64418	+	6.31190i	−0.836032	+	1.44805i	0.0571560	+	0.998365i	$0.481797\pi$
$19$	−3.64418	+	6.31190i	−0.836032	+	1.44805i	−0.893188	+	0.449684i	$0.851537\pi$
$20$	−2.14404	−	0.634884i	−0.479423	−	0.141964i
$21$	−2.72822	+	3.68196i	−0.595346	+	0.803470i
$22$	−6.23077	+	1.66953i	−1.32840	+	0.355945i
$23$	−4.00290	−	1.07257i	−0.834663	−	0.223647i	−0.183916	−	0.982942i	$-0.558877\pi$
$23$	−4.00290	−	1.07257i	−0.834663	−	0.223647i	−0.650747	+	0.759295i	$0.725544\pi$
$24$	−1.39885	−	1.02139i	−0.285538	−	0.208489i
$25$	−4.19384	−	2.72244i	−0.838769	−	0.544488i
$26$	−0.236700	−	0.136659i	−0.0464208	−	0.0268011i
$27$	2.32609	+	4.64643i	0.447656	+	0.894206i
$28$	1.88390	−	1.85766i	0.356024	−	0.351066i
$29$	−6.46173	+	3.73068i	−1.19991	+	0.692770i	−0.960536	−	0.278156i	$-0.910277\pi$
$29$	−6.46173	+	3.73068i	−1.19991	+	0.692770i	−0.239377	+	0.970927i	$0.576943\pi$
$30$	−2.35073	−	3.07800i	−0.429182	−	0.561963i
$31$			8.30069i			1.49085i	0.666591	+	0.745424i	$0.267753\pi$
$31$			8.30069i			1.49085i	−0.666591	+	0.745424i	$0.732247\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	−10.4211	−	4.02860i	−1.81409	−	0.701290i
$34$	0.958686	+	1.66049i	0.164413	+	0.284772i
$35$	5.21857	−	2.78686i	0.882099	−	0.471064i
$36$	−0.913543	−	2.85752i	−0.152257	−	0.476254i
$37$	−3.11198	+	0.833854i	−0.511607	+	0.137085i	−0.505382	−	0.862896i	$-0.668648\pi$
$37$	−3.11198	+	0.833854i	−0.511607	+	0.137085i	−0.00622538	+	0.999981i	$0.501982\pi$
$38$	7.04001	−	1.88637i	1.14204	−	0.306009i
$39$	−0.191526	−	0.432928i	−0.0306687	−	0.0693239i
$40$	1.06714	+	1.96500i	0.168729	+	0.310694i
$41$	−4.07142	−	2.35064i	−0.635849	−	0.367108i	0.147164	−	0.989112i	$-0.452985\pi$
$41$	−4.07142	−	2.35064i	−0.635849	−	0.367108i	−0.783014	+	0.622004i	$0.786319\pi$
$42$	4.53268	−	0.674398i	0.699408	−	0.104062i
$43$	0.146117	+	0.0391519i	0.0222826	+	0.00597060i	0.269943	−	0.962876i	$-0.412995\pi$
$43$	0.146117	+	0.0391519i	0.0222826	+	0.00597060i	−0.247661	+	0.968847i	$0.579662\pi$
$44$	5.58636	+	3.22528i	0.842175	+	0.486230i
$45$	−0.144480	−	6.70665i	−0.0215378	−	0.999768i
$46$	2.07205	+	3.58890i	0.305508	+	0.529155i
$47$	8.09709	−	8.09709i	1.18108	−	1.18108i	0.201619	−	0.979464i	$-0.435380\pi$
$47$	8.09709	−	8.09709i	1.18108	−	1.18108i	0.979464	−	0.201619i	$-0.0646201\pi$
$48$	0.266905	+	1.71136i	0.0385244	+	0.247014i
$49$	−0.0981647	+	6.99931i	−0.0140235	+	0.999902i
$50$	1.04044	+	4.89055i	0.147141	+	0.691628i
$51$	−0.354949	+	3.30196i	−0.0497028	+	0.462367i
$52$	0.0707399	+	0.264005i	0.00980987	+	0.0366109i
$53$	−7.07759	−	1.89643i	−0.972182	−	0.260495i	−0.262433	−	0.964950i	$-0.584525\pi$
$53$	−7.07759	−	1.89643i	−0.972182	−	0.260495i	−0.709749	+	0.704455i	$0.751192\pi$
$54$	1.64073	−	4.93032i	0.223275	−	0.670931i
$55$	9.92971	+	10.4618i	1.33892	+	1.41067i
$56$	−2.64569	−	0.0185518i	−0.353545	−	0.00247909i
$57$	11.7746	+	4.55183i	1.55958	+	0.602905i
$58$	7.20712	+	1.93114i	0.946342	+	0.253571i
$59$	−6.27798			−0.817324			−0.408662	−	0.912686i	$-0.634004\pi$
$59$	−6.27798			−0.817324			−0.408662	+	0.912686i	$0.634004\pi$
$60$	−0.514260	+	3.83869i	−0.0663907	+	0.495573i
$61$			4.09079i			0.523772i	0.965099	+	0.261886i	$0.0843444\pi$
$61$			4.09079i			0.523772i	−0.965099	+	0.261886i	$0.915656\pi$
$62$	5.86947	−	5.86947i	0.745424	−	0.745424i
$63$	7.02934	+	3.68623i	0.885614	+	0.464422i
$64$		−	1.00000i		−	0.125000i
$65$	−0.0159431	+	0.610950i	−0.00197750	+	0.0757790i
$66$	4.52020	+	10.2175i	0.556398	+	1.25769i
$67$	−4.73557	−	4.73557i	−0.578541	−	0.578541i	0.355960	−	0.934501i	$-0.384154\pi$
$67$	−4.73557	−	4.73557i	−0.578541	−	0.578541i	−0.934501	+	0.355960i	$0.884154\pi$
$68$	0.496253	−	1.85204i	0.0601795	−	0.224593i
$69$	−0.767168	+	7.13669i	−0.0923562	+	0.859157i
$70$	−5.66069	−	1.71948i	−0.676582	−	0.205517i
$71$	−3.51520			−0.417178			−0.208589	−	0.978003i	$-0.566887\pi$
$71$	−3.51520			−0.417178			−0.208589	+	0.978003i	$0.566887\pi$
$72$	−1.37460	+	2.66655i	−0.161998	+	0.314256i
$73$	0.669977	−	2.50039i	0.0784148	−	0.292648i	−0.915571	−	0.402156i	$-0.868261\pi$
$73$	0.669977	−	2.50039i	0.0784148	−	0.292648i	0.993986	+	0.109508i	$0.0349275\pi$
$74$	2.79013	+	1.61088i	0.324346	+	0.187261i
$75$	−3.53972	+	7.90382i	−0.408732	+	0.912655i
$76$	−6.31190	−	3.64418i	−0.724025	−	0.418016i
$77$	−16.5156	+	4.30146i	−1.88213	+	0.490197i
$78$	−0.170697	+	0.441555i	−0.0193276	+	0.0499963i
$79$			3.29520i			0.370739i	0.982669	+	0.185369i	$0.0593481\pi$
$79$			3.29520i			0.370739i	−0.982669	+	0.185369i	$0.940652\pi$
$80$	0.634884	−	2.14404i	0.0709822	−	0.239711i
$81$	7.33088	−	5.22094i	0.814542	−	0.580105i
$82$	1.21678	+	4.54108i	0.134371	+	0.501479i
$83$	2.02567	−	7.55991i	0.222346	−	0.829808i	−0.761104	−	0.648630i	$-0.775342\pi$
$83$	2.02567	−	7.55991i	0.222346	−	0.829808i	0.983450	−	0.181178i	$-0.0579911\pi$
$84$	−3.68196	−	2.72822i	−0.401735	−	0.297673i
$85$	2.23982	−	3.65579i	0.242942	−	0.396526i
$86$	−0.0756356	−	0.131005i	−0.00815600	−	0.0141266i
$87$	8.10922	+	10.0626i	0.869399	+	1.07883i
$88$	−1.66953	−	6.23077i	−0.177973	−	0.664202i
$89$	8.10279	−	14.0344i	0.858894	−	1.48765i	−0.0140916	−	0.999901i	$-0.504486\pi$
$89$	8.10279	−	14.0344i	0.858894	−	1.48765i	0.872985	−	0.487747i	$-0.162181\pi$
$90$	−4.64015	+	4.84448i	−0.489115	+	0.510653i
$91$	−0.623700	−	0.365948i	−0.0653815	−	0.0383618i
$92$	1.07257	−	4.00290i	0.111824	−	0.417331i
$93$	14.2055	−	2.21550i	1.47304	−	0.229736i
$94$	−11.4510			−1.18108
$95$	−11.2194	−	11.8206i	−1.15108	−	1.21277i
$96$	1.02139	−	1.39885i	0.104245	−	0.142769i
$97$	−3.68177	−	0.986528i	−0.373827	−	0.100167i	0.0670134	−	0.997752i	$-0.478653\pi$
$97$	−3.68177	−	0.986528i	−0.373827	−	0.100167i	−0.440841	+	0.897585i	$0.645320\pi$
$98$	5.01867	−	4.87985i	0.506963	−	0.492939i
$99$	−4.11295	+	18.9096i	−0.413367	+	1.90048i
$100$	2.72244	−	4.19384i	0.272244	−	0.419384i
$101$	2.44844	+	1.41361i	0.243629	+	0.140659i	0.616844	−	0.787086i	$-0.288411\pi$
$101$	2.44844	+	1.41361i	0.243629	+	0.140659i	−0.373214	+	0.927745i	$0.621744\pi$
$102$	2.58583	−	2.08385i	0.256035	−	0.206332i
$103$	0.255681	−	0.954215i	0.0251930	−	0.0940216i	−0.952185	−	0.305523i	$-0.901169\pi$
$103$	0.255681	−	0.954215i	0.0251930	−	0.0940216i	0.977378	+	0.211502i	$0.0678353\pi$
$104$	0.136659	−	0.236700i	0.0134005	−	0.0232104i
$105$	−6.16218	−	8.18703i	−0.601367	−	0.798973i
$106$	3.66363	+	6.34559i	0.355843	+	0.616338i
$107$	−4.33591	+	1.16180i	−0.419168	+	0.112316i	−0.462237	−	0.886756i	$-0.652953\pi$
$107$	−4.33591	+	1.16180i	−0.419168	+	0.112316i	0.0430691	+	0.999072i	$0.486286\pi$
$108$	−4.64643	+	2.32609i	−0.447103	+	0.223828i
$109$	−2.53384	+	1.46292i	−0.242698	+	0.140122i	−0.616416	−	0.787421i	$-0.711416\pi$
$109$	−2.53384	+	1.46292i	−0.242698	+	0.140122i	0.373718	+	0.927542i	$0.378083\pi$
$110$	0.376272	−	14.4190i	0.0358761	−	1.37480i
$111$	2.25763	+	5.10317i	0.214285	+	0.484372i
$112$	1.85766	+	1.88390i	0.175533	+	0.178012i
$113$	3.14933	+	11.7534i	0.296264	+	1.10567i	0.940209	+	0.340599i	$0.110630\pi$
$113$	3.14933	+	11.7534i	0.296264	+	1.10567i	−0.643945	+	0.765072i	$0.722703\pi$
$114$	−5.10727	−	11.5445i	−0.478340	−	1.08124i
$115$	4.84102	−	7.90143i	0.451428	−	0.736813i
$116$	−3.73068	−	6.46173i	−0.346385	−	0.599957i
$117$	−0.689777	+	0.443321i	−0.0637699	+	0.0409850i
$118$	4.43920	+	4.43920i	0.408662	+	0.408662i
$119$	2.50558	+	4.41093i	0.229686	+	0.404349i
$120$	3.07800	−	2.35073i	0.280982	−	0.214591i
$121$	−15.3049	−	26.5089i	−1.39136	−	2.40990i
$122$	2.89262	−	2.89262i	0.261886	−	0.261886i
$123$	−2.93611	+	7.59508i	−0.264740	+	0.684825i
$124$	−8.30069			−0.745424
$125$	8.49963	−	7.26335i	0.760230	−	0.649654i
$126$	−2.36394	−	7.57706i	−0.210596	−	0.675018i
$127$	−3.94446	−	3.94446i	−0.350015	−	0.350015i	0.510100	−	0.860115i	$-0.329608\pi$
$127$	−3.94446	−	3.94446i	−0.350015	−	0.350015i	−0.860115	+	0.510100i	$0.829608\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	0.0280037	−	0.260509i	0.00246559	−	0.0229365i
$130$	0.443280	−	0.420733i	0.0388783	−	0.0369008i
$131$	3.08423	−	1.78068i	0.269470	−	0.155579i	−0.359177	−	0.933270i	$-0.616942\pi$
$131$	3.08423	−	1.78068i	0.269470	−	0.155579i	0.628647	+	0.777691i	$0.283609\pi$
$132$	4.02860	−	10.4211i	0.350645	−	0.907043i
$133$	18.6607	−	4.86013i	1.61808	−	0.421426i
$134$			6.69710i			0.578541i
$135$	−11.4389	+	2.03730i	−0.984507	+	0.175343i
$136$	−1.66049	+	0.958686i	−0.142386	+	0.0822067i
$137$	−11.1787	+	2.99533i	−0.955061	+	0.255908i	−0.702509	−	0.711675i	$-0.747937\pi$
$137$	−11.1787	+	2.99533i	−0.955061	+	0.255908i	−0.252553	+	0.967583i	$0.581270\pi$
$138$	5.58887	−	4.50393i	0.475756	−	0.383400i
$139$	5.33889	−	9.24722i	0.452838	−	0.784339i	−0.545723	−	0.837966i	$-0.683745\pi$
$139$	5.33889	−	9.24722i	0.452838	−	0.784339i	0.998561	+	0.0536268i	$0.0170781\pi$
$140$	2.78686	+	5.21857i	0.235532	+	0.441049i
$141$	−16.0182	−	11.6959i	−1.34898	−	0.984973i
$142$	2.48562	+	2.48562i	0.208589	+	0.208589i
$143$	0.456313	−	1.70298i	0.0381588	−	0.142411i
$144$	2.85752	−	0.913543i	0.238127	−	0.0761286i
$145$	−3.89629	−	16.2228i	−0.323570	−	1.34723i
$146$	−2.24179	+	1.29430i	−0.185531	+	0.107117i
$147$	12.0046	−	1.70016i	0.990119	−	0.140227i
$148$	−0.833854	−	3.11198i	−0.0685423	−	0.255804i
$149$	19.3909	−	11.1954i	1.58857	−	0.917159i	0.595023	−	0.803709i	$-0.297143\pi$
$149$	19.3909	−	11.1954i	1.58857	−	0.917159i	0.993544	−	0.113451i	$-0.0361904\pi$
$150$	8.09180	−	3.08589i	0.660693	−	0.251962i
$151$	−1.93066	+	3.34400i	−0.157115	+	0.272131i	−0.933827	−	0.357725i	$-0.883553\pi$
$151$	−1.93066	+	3.34400i	−0.157115	+	0.272131i	0.776712	+	0.629856i	$0.216886\pi$
$152$	1.88637	+	7.04001i	0.153004	+	0.571020i
$153$	5.74560	−	0.273865i	0.464504	−	0.0221407i
$154$	14.7199	+	8.63673i	1.18616	+	0.695967i
$155$	−17.7970	−	5.26997i	−1.42949	−	0.423295i
$156$	0.432928	−	0.191526i	0.0346619	−	0.0153344i
$157$	−2.69416	+	2.69416i	−0.215018	+	0.215018i	−0.806395	−	0.591377i	$-0.798584\pi$
$157$	−2.69416	+	2.69416i	−0.215018	+	0.215018i	0.591377	+	0.806395i	$0.298584\pi$
$158$	2.33006	−	2.33006i	0.185369	−	0.185369i
$159$	−1.35644	+	12.6185i	−0.107573	+	1.00071i
$160$	−1.96500	+	1.06714i	−0.155347	+	0.0843646i
$161$	5.41542	+	9.53355i	0.426795	+	0.751349i
$162$	−8.87548	−	1.49195i	−0.697323	−	0.117219i
$163$	−0.726086	−	2.70979i	−0.0568715	−	0.212247i	0.931643	−	0.363376i	$-0.118376\pi$
$163$	−0.726086	−	2.70979i	−0.0568715	−	0.212247i	−0.988514	+	0.151129i	$0.951709\pi$
$164$	2.35064	−	4.07142i	0.183554	−	0.317925i
$165$	15.2537	−	19.7857i	1.18750	−	1.54031i
$166$	−6.77803	+	3.91330i	−0.526077	+	0.303731i
$167$	3.93690	+	14.6927i	0.304647	+	1.13696i	0.933249	+	0.359230i	$0.116961\pi$
$167$	3.93690	+	14.6927i	0.304647	+	1.13696i	−0.628603	+	0.777727i	$0.716373\pi$
$168$	0.674398	+	4.53268i	0.0520310	+	0.349704i
$169$	−11.1936	+	6.46265i	−0.861049	+	0.497127i
$170$	−4.16882	+	1.00124i	−0.319734	+	0.0767919i
$171$	4.64713	−	21.3655i	0.355375	−	1.63386i
$172$	−0.0391519	+	0.146117i	−0.00298530	+	0.0111413i
$173$	0.598873	+	0.598873i	0.0455315	+	0.0455315i	0.729506	−	0.683974i	$-0.239750\pi$
$173$	0.598873	+	0.598873i	0.0455315	+	0.0455315i	−0.683974	+	0.729506i	$0.739750\pi$
$174$	1.38127	−	12.8494i	0.104714	−	0.974113i
$175$	2.66195	+	12.9582i	0.201225	+	0.979545i
$176$	−3.22528	+	5.58636i	−0.243115	+	0.421087i
$177$	1.67563	+	10.7439i	0.125948	+	0.807561i
$178$	−15.6534	+	4.19431i	−1.17327	+	0.314377i
$179$	5.94666	−	3.43331i	0.444474	−	0.256617i	−0.261019	−	0.965334i	$-0.584059\pi$
$179$	5.94666	−	3.43331i	0.444474	−	0.256617i	0.705494	+	0.708716i	$0.250725\pi$
$180$	6.70665	−	0.144480i	0.499884	−	0.0107689i
$181$			2.85030i			0.211861i	0.994374	+	0.105930i	$0.0337821\pi$
$181$			2.85030i			0.211861i	−0.994374	+	0.105930i	$0.966218\pi$
$182$	0.182258	+	0.699787i	0.0135099	+	0.0518717i
$183$	7.00082	−	1.09185i	0.517515	−	0.0807120i
$184$	−3.58890	+	2.07205i	−0.264577	+	0.152754i
$185$	0.187931	−	7.20163i	0.0138169	−	0.529474i
$186$	−11.6114	−	8.47820i	−0.851388	−	0.621652i
$187$	−8.74560	+	8.74560i	−0.639542	+	0.639542i
$188$	8.09709	+	8.09709i	0.590541	+	0.590541i
$189$	4.43231	−	13.0136i	0.322403	−	0.946602i
$190$	−0.425141	+	16.2917i	−0.0308430	+	1.18192i
$191$	−0.571610			−0.0413602			−0.0206801	−	0.999786i	$-0.506583\pi$
$191$	−0.571610			−0.0413602			−0.0206801	+	0.999786i	$0.506583\pi$
$192$	−1.71136	+	0.266905i	−0.123507	+	0.0192622i
$193$	0.477642	−	0.477642i	0.0343814	−	0.0343814i	−0.689707	−	0.724088i	$-0.742261\pi$
$193$	0.477642	−	0.477642i	0.0343814	−	0.0343814i	0.724088	+	0.689707i	$0.242261\pi$
$194$	1.90583	+	3.30099i	0.136830	+	0.236997i
$195$	1.04981	−	0.135781i	0.0751786	−	0.00972350i
$196$	−6.99931	−	0.0981647i	−0.499951	−	0.00701176i
$197$	−0.477841	−	0.477841i	−0.0340448	−	0.0340448i	0.689879	−	0.723924i	$-0.257664\pi$
$197$	−0.477841	−	0.477841i	−0.0340448	−	0.0340448i	−0.723924	+	0.689879i	$0.757664\pi$
$198$	16.2794	−	10.4628i	1.15693	−	0.743559i
$199$	−11.9897	−	20.7667i	−0.849924	−	1.47211i	−0.881275	−	0.472604i	$-0.843314\pi$
$199$	−11.9897	−	20.7667i	−0.849924	−	1.47211i	0.0313506	−	0.999508i	$-0.490019\pi$
$200$	−4.89055	+	1.04044i	−0.345814	+	0.0735703i
$201$	−6.84032	+	9.36822i	−0.482479	+	0.660783i
$202$	−0.731738	−	2.73088i	−0.0514849	−	0.192144i
$203$	19.0320	+	5.24290i	1.33578	+	0.367980i
$204$	−3.30196	−	0.354949i	−0.231184	−	0.0248514i
$205$	7.62475	−	7.23693i	0.532536	−	0.505449i
$206$	−0.855526	+	0.493938i	−0.0596073	+	0.0344143i
$207$	12.4182	−	0.591917i	0.863126	−	0.0411411i
$208$	−0.264005	+	0.0707399i	−0.0183055	+	0.00490493i
$209$	23.5070	+	40.7153i	1.62601	+	2.81634i
$210$	−1.43179	+	10.1464i	−0.0988026	+	0.700170i
$211$	12.3211	−	21.3408i	0.848219	−	1.46916i	−0.0345765	−	0.999402i	$-0.511008\pi$
$211$	12.3211	−	21.3408i	0.848219	−	1.46916i	0.882796	−	0.469757i	$-0.155658\pi$
$212$	1.89643	−	7.07759i	0.130248	−	0.486091i
$213$	0.938226	+	6.01579i	0.0642862	+	0.412195i
$214$	3.88747	+	2.24443i	0.265742	+	0.153426i
$215$	−0.176711	+	0.288424i	−0.0120516	+	0.0196703i
$216$	4.93032	+	1.64073i	0.335466	+	0.111637i
$217$	15.6377	−	15.4199i	1.06155	−	1.04677i
$218$	2.82613	+	0.757261i	0.191410	+	0.0512882i
$219$	−4.45789	−	0.479207i	−0.301236	−	0.0323818i
$220$	−10.4618	+	9.92971i	−0.705337	+	0.669461i
$221$	−0.524053			−0.0352516
$222$	2.01210	−	5.20487i	0.135043	−	0.349328i
$223$	−0.0876914	+	0.327269i	−0.00587225	+	0.0219155i	−0.968800	−	0.247845i	$-0.920278\pi$
$223$	−0.0876914	+	0.327269i	−0.00587225	+	0.0219155i	0.962928	+	0.269760i	$0.0869444\pi$
$224$	0.0185518	−	2.64569i	0.00123955	−	0.176772i
$225$	14.4711	+	3.94817i	0.964738	+	0.263211i
$226$	6.08403	−	10.5378i	0.404704	−	0.700967i
$227$	−4.60463	−	17.1847i	−0.305620	−	1.14059i	−0.932410	−	0.361402i	$-0.882298\pi$
$227$	−4.60463	−	17.1847i	−0.305620	−	1.14059i	0.626790	−	0.779188i	$-0.284368\pi$
$228$	−4.55183	+	11.7746i	−0.301452	+	0.779792i
$229$	10.9999	+	19.0524i	0.726893	+	1.25902i	0.958190	+	0.286133i	$0.0923698\pi$
$229$	10.9999	+	19.0524i	0.726893	+	1.25902i	−0.231297	+	0.972883i	$0.574297\pi$
$230$	−9.01028	+	2.16404i	−0.594120	+	0.142692i
$231$	11.7695	+	27.1162i	0.774374	+	1.78411i
$232$	−1.93114	+	7.20712i	−0.126786	+	0.473171i
$233$	−2.98175	−	11.1280i	−0.195341	−	0.729021i	−0.992178	−	0.124828i	$-0.960162\pi$
$233$	−2.98175	−	11.1280i	−0.195341	−	0.729021i	0.796838	−	0.604193i	$-0.206505\pi$
$234$	0.801221	+	0.174270i	0.0523775	+	0.0113924i
$235$	12.2198	+	22.5012i	0.797132	+	1.46782i
$236$		−	6.27798i		−	0.408662i
$237$	5.63927	−	0.879505i	0.366310	−	0.0571300i
$238$	1.34729	−	4.89071i	0.0873317	−	0.317018i
$239$	3.03740	+	1.75365i	0.196473	+	0.113434i	0.595009	−	0.803719i	$-0.297148\pi$
$239$	3.03740	+	1.75365i	0.196473	+	0.113434i	−0.398536	+	0.917153i	$0.630482\pi$
$240$	−3.83869	−	0.514260i	−0.247786	−	0.0331954i
$241$	−17.6504	−	10.1905i	−1.13696	−	0.656425i	−0.191285	−	0.981535i	$-0.561265\pi$
$241$	−17.6504	−	10.1905i	−1.13696	−	0.656425i	−0.945676	+	0.325110i	$0.894599\pi$
$242$	−7.92241	+	29.5668i	−0.509272	+	1.90063i
$243$	−10.8916	−	11.1523i	−0.698695	−	0.715420i
$244$	−4.09079			−0.261886
$245$	−14.9445	−	4.65422i	−0.954769	−	0.297347i
$246$	7.44667	−	3.29439i	0.474783	−	0.210043i
$247$	−0.515578	+	1.92416i	−0.0328054	+	0.122432i
$248$	5.86947	+	5.86947i	0.372712	+	0.372712i
$249$	−13.4784	−	1.44888i	−0.854160	−	0.0918190i
$250$	−11.1461	−	0.874180i	−0.704942	−	0.0552880i
$251$			18.2438i			1.15154i	0.817613	+	0.575768i	$0.195297\pi$
$251$			18.2438i			1.15154i	−0.817613	+	0.575768i	$0.804703\pi$
$252$	−3.68623	+	7.02934i	−0.232211	+	0.442807i
$253$	−18.9023	+	18.9023i	−1.18838	+	1.18838i
$254$			5.57831i			0.350015i
$255$	−6.85420	−	2.85739i	−0.429227	−	0.178937i
$256$	1.00000			0.0625000
$257$	−16.1983	−	4.34031i	−1.01042	−	0.270741i	−0.284615	−	0.958642i	$-0.591866\pi$
$257$	−16.1983	−	4.34031i	−1.01042	−	0.270741i	−0.725805	+	0.687900i	$0.758533\pi$
$258$	−0.204009	+	0.164406i	−0.0127010	+	0.0102355i
$259$	7.35192	+	4.31365i	0.456826	+	0.268037i
$260$	−0.610950	−	0.0159431i	−0.0378895	−	0.000988748i
$261$	15.0564	−	16.5636i	0.931968	−	1.02526i
$262$	−3.44001	−	0.921748i	−0.212525	−	0.0569458i
$263$	−7.22622	−	26.9686i	−0.445588	−	1.66296i	−0.714380	−	0.699758i	$-0.753291\pi$
$263$	−7.22622	−	26.9686i	−0.445588	−	1.66296i	0.268792	−	0.963198i	$-0.413376\pi$
$264$	−10.2175	+	4.52020i	−0.628844	+	0.278199i
$265$	8.55949	−	13.9706i	0.525805	−	0.858210i
$266$	−16.6317	−	9.75845i	−1.01976	−	0.598329i
$267$	−26.1807	−	10.1209i	−1.60223	−	0.619391i
$268$	4.73557	−	4.73557i	0.289271	−	0.289271i
$269$	−3.86035	−	6.68633i	−0.235370	−	0.407673i	0.724010	−	0.689789i	$-0.242297\pi$
$269$	−3.86035	−	6.68633i	−0.235370	−	0.407673i	−0.959380	+	0.282117i	$0.908963\pi$
$270$	9.52914	+	6.64797i	0.579925	+	0.404582i
$271$	11.0808	+	6.39752i	0.673112	+	0.388621i	0.797255	−	0.603643i	$-0.206285\pi$
$271$	11.0808	+	6.39752i	0.673112	+	0.388621i	−0.124143	+	0.992264i	$0.539618\pi$
$272$	1.85204	+	0.496253i	0.112296	+	0.0300897i
$273$	−0.459801	+	1.16505i	−0.0278284	+	0.0705120i
$274$	10.0226	+	5.78653i	0.605485	+	0.349577i
$275$	−28.7348	+	14.6477i	−1.73278	+	0.883288i
$276$	−7.13669	−	0.767168i	−0.429578	−	0.0461781i
$277$	24.8785	−	6.66617i	1.49480	−	0.400532i	0.583448	−	0.812151i	$-0.301703\pi$
$277$	24.8785	−	6.66617i	1.49480	−	0.400532i	0.911356	+	0.411619i	$0.135037\pi$
$278$	−10.3139	+	2.76361i	−0.618589	+	0.165750i
$279$	−7.58304	−	23.7194i	−0.453984	−	1.42004i
$280$	1.71948	−	5.66069i	0.102759	−	0.338291i
$281$	−1.18537	−	2.05312i	−0.0707133	−	0.122479i	0.828501	−	0.559988i	$-0.189194\pi$
$281$	−1.18537	−	2.05312i	−0.0707133	−	0.122479i	−0.899214	+	0.437509i	$0.855861\pi$
$282$	3.05634	+	19.5968i	0.182002	+	1.16698i
$283$	−4.15658	−	4.15658i	−0.247083	−	0.247083i	0.572689	−	0.819772i	$-0.305900\pi$
$283$	−4.15658	−	4.15658i	−0.247083	−	0.247083i	−0.819772	+	0.572689i	$0.805900\pi$
$284$		−	3.51520i		−	0.208589i
$285$	−17.2348	+	22.3554i	−1.02090	+	1.32422i
$286$	−1.52685	+	0.881529i	−0.0902847	+	0.0521259i
$287$	3.13497	+	12.0369i	0.185051	+	0.710513i
$288$	−2.66655	−	1.37460i	−0.157128	−	0.0809992i
$289$	−11.5386	−	6.66184i	−0.678744	−	0.391873i
$290$	−8.71614	+	14.2263i	−0.511829	+	0.835399i
$291$	−0.705623	+	6.56416i	−0.0413643	+	0.384798i
$292$	2.50039	+	0.669977i	0.146324	+	0.0392074i
$293$	−16.1887	+	4.33776i	−0.945756	+	0.253415i	−0.698561	−	0.715551i	$-0.746176\pi$
$293$	−16.1887	+	4.33776i	−0.945756	+	0.253415i	−0.247196	+	0.968966i	$0.579509\pi$
$294$	−9.69070	−	7.28631i	−0.565173	−	0.424946i
$295$	3.98579	−	13.4603i	0.232062	−	0.783687i
$296$	−1.61088	+	2.79013i	−0.0936306	+	0.162173i
$297$	33.4589	+	1.99168i	1.94148	+	0.115569i
$298$	−21.6278	−	5.79514i	−1.25286	−	0.335704i
$299$	−1.13266			−0.0655034
$300$	−7.90382	−	3.53972i	−0.456327	−	0.204366i
$301$	−0.197678	−	0.348001i	−0.0113940	−	0.0200584i
$302$	3.72975	−	0.999383i	0.214623	−	0.0575081i
$303$	1.76570	−	4.56747i	0.101437	−	0.262395i
$304$	3.64418	−	6.31190i	0.209008	−	0.362012i
$305$	−8.77082	−	2.59717i	−0.502216	−	0.148714i
$306$	−4.25640	−	3.86910i	−0.243322	−	0.221182i
$307$	−11.2410	+	11.2410i	−0.641556	+	0.641556i	−0.950938	−	0.309382i	$-0.899878\pi$
$307$	−11.2410	+	11.2410i	−0.641556	+	0.641556i	0.309382	+	0.950938i	$0.399878\pi$
$308$	−4.30146	−	16.5156i	−0.245098	−	0.941066i
$309$	−1.70125	−	0.182878i	−0.0967808	−	0.0104036i
$310$	8.85797	+	16.3108i	0.503099	+	0.926393i
$311$			24.8967i			1.41176i	0.708330	+	0.705882i	$0.249449\pi$
$311$			24.8967i			1.41176i	−0.708330	+	0.705882i	$0.750551\pi$
$312$	−0.441555	−	0.170697i	−0.0249981	−	0.00966380i
$313$	11.7491	+	11.7491i	0.664098	+	0.664098i	0.956343	−	0.292245i	$-0.0944023\pi$
$313$	11.7491	+	11.7491i	0.664098	+	0.664098i	−0.292245	+	0.956343i	$0.594402\pi$
$314$	3.81012			0.215018
$315$	−12.3663	+	12.7309i	−0.696760	+	0.717304i
$316$	−3.29520			−0.185369
$317$	−12.2410	−	12.2410i	−0.687523	−	0.687523i	0.274161	−	0.961684i	$-0.411600\pi$
$317$	−12.2410	−	12.2410i	−0.687523	−	0.687523i	−0.961684	+	0.274161i	$0.911600\pi$
$318$	9.88177	−	7.96347i	0.554142	−	0.446569i
$319$			48.1300i			2.69476i
$320$	2.14404	+	0.634884i	0.119856	+	0.0354911i
$321$	3.14554	+	7.11022i	0.175567	+	0.396854i
$322$	2.91196	−	10.5705i	0.162277	−	0.589072i
$323$	9.88146	−	9.88146i	0.549819	−	0.549819i
$324$	5.22094	+	7.33088i	0.290052	+	0.407271i
$325$	−1.29978	−	0.422065i	−0.0720989	−	0.0234120i
$326$	−1.40269	+	2.42953i	−0.0776879	+	0.134559i
$327$	3.17987	+	3.94586i	0.175847	+	0.218207i
$328$	−4.54108	+	1.21678i	−0.250739	+	0.0671854i
$329$	−30.2958	−	0.212437i	−1.67026	−	0.0117121i
$330$	−24.7766	+	3.20457i	−1.36391	+	0.176406i
$331$	15.0516			0.827312			0.413656	−	0.910433i	$-0.364252\pi$
$331$	15.0516			0.827312			0.413656	+	0.910433i	$0.364252\pi$
$332$	7.55991	+	2.02567i	0.414904	+	0.111173i
$333$	8.13081	−	5.22569i	0.445565	−	0.286366i
$334$	7.60551	−	13.1731i	0.416155	−	0.720802i
$335$	13.1598	−	7.14672i	0.718996	−	0.390467i
$336$	2.72822	−	3.68196i	0.148836	−	0.200867i
$337$	−17.8850	+	4.79226i	−0.974257	+	0.261051i	−0.710624	−	0.703572i	$-0.751587\pi$
$337$	−17.8850	+	4.79226i	−0.974257	+	0.261051i	−0.263633	+	0.964623i	$0.584921\pi$
$338$	12.4849	+	3.34531i	0.679088	+	0.181961i
$339$	19.2738	−	8.52669i	1.04681	−	0.463106i
$340$	3.65579	+	2.23982i	0.198263	+	0.121471i
$341$	46.3706	+	26.7721i	2.51111	+	1.44979i
$342$	−18.3937	+	11.8217i	−0.994618	+	0.639244i
$343$	13.3684	−	12.8174i	0.721824	−	0.692077i
$344$	0.131005	−	0.0756356i	0.00706330	−	0.00407800i
$345$	−14.8143	−	6.17581i	−0.797576	−	0.332495i
$346$		−	0.846934i		−	0.0455315i
$347$	18.5095	+	18.5095i	0.993642	+	0.993642i	0.999980	−	0.00633800i	$-0.00201746\pi$
$347$	18.5095	+	18.5095i	0.993642	+	0.993642i	−0.00633800	+	0.999980i	$0.502017\pi$
$348$	−10.0626	+	8.10922i	−0.539413	+	0.434700i
$349$	6.70347	+	11.6108i	0.358829	+	0.621509i	0.987765	−	0.155947i	$-0.0498429\pi$
$349$	6.70347	+	11.6108i	0.358829	+	0.621509i	−0.628937	+	0.777456i	$0.716510\pi$
$350$	7.28052	−	11.0451i	0.389160	−	0.590385i
$351$	0.942788	+	1.06213i	0.0503223	+	0.0566925i
$352$	6.23077	−	1.66953i	0.332101	−	0.0889863i
$353$	−0.990394	+	0.265375i	−0.0527133	+	0.0141245i	−0.285079	−	0.958504i	$-0.592020\pi$
$353$	−0.990394	+	0.265375i	−0.0527133	+	0.0141245i	0.232366	+	0.972628i	$0.425353\pi$
$354$	6.41224	−	8.78193i	0.340807	−	0.466754i
$355$	2.23175	−	7.53675i	0.118449	−	0.400009i
$356$	14.0344	+	8.10279i	0.743824	+	0.429447i
$357$	6.87995	−	5.46525i	0.364126	−	0.289252i
$358$	−6.63264	−	1.77721i	−0.350546	−	0.0939285i
$359$	−8.43686	−	4.87102i	−0.445280	−	0.257083i	0.260554	−	0.965459i	$-0.416095\pi$
$359$	−8.43686	−	4.87102i	−0.445280	−	0.257083i	−0.705835	+	0.708376i	$0.749428\pi$
$360$	−4.84448	−	4.64015i	−0.255326	−	0.244558i
$361$	−17.0601	−	29.5489i	−0.897898	−	1.55520i
$362$	2.01546	−	2.01546i	0.105930	−	0.105930i
$363$	−41.2814	+	33.2676i	−2.16671	+	1.74610i
$364$	0.365948	−	0.623700i	0.0191809	−	0.0326908i
$365$	4.93558	+	3.02391i	0.258340	+	0.158279i
$366$	−5.72238	−	4.17827i	−0.299114	−	0.218402i
$367$	8.56035	+	31.9477i	0.446847	+	1.66765i	0.711014	+	0.703178i	$0.248236\pi$
$367$	8.56035	+	31.9477i	0.446847	+	1.66765i	−0.264168	+	0.964477i	$0.585097\pi$
$368$	4.00290	+	1.07257i	0.208666	+	0.0559118i
$369$	13.7816	+	2.99758i	0.717441	+	0.156048i
$370$	−5.22521	+	4.95943i	−0.271646	+	0.257829i
$371$	9.57509	+	16.8564i	0.497114	+	0.875141i
$372$	2.21550	+	14.2055i	0.114868	+	0.736520i
$373$	18.9616	+	5.08074i	0.981793	+	0.263071i	0.713799	−	0.700350i	$-0.246973\pi$
$373$	18.9616	+	5.08074i	0.981793	+	0.263071i	0.267993	+	0.963421i	$0.413640\pi$
$374$	12.3681			0.639542
$375$	−14.6988	−	12.6073i	−0.759044	−	0.651039i
$376$		−	11.4510i		−	0.590541i
$377$	−1.44202	+	1.44202i	−0.0742679	+	0.0742679i
$378$	−12.3361	+	6.06791i	−0.634503	+	0.312099i
$379$		−	19.9833i		−	1.02647i	−0.858248	−	0.513236i	$-0.828447\pi$
$379$		−	19.9833i		−	1.02647i	0.858248	−	0.513236i	$-0.171553\pi$
$380$	11.8206	−	11.2194i	0.606384	−	0.575541i
$381$	−5.69761	+	7.80321i	−0.291897	+	0.399770i
$382$	0.404189	+	0.404189i	0.0206801	+	0.0206801i
$383$	−7.07868	+	26.4180i	−0.361704	+	1.34990i	0.510131	+	0.860097i	$0.329597\pi$
$383$	−7.07868	+	26.4180i	−0.361704	+	1.34990i	−0.871835	+	0.489800i	$0.837070\pi$
$384$	1.39885	+	1.02139i	0.0713846	+	0.0521224i
$385$	1.26300	−	38.1412i	0.0643683	−	1.94385i
$386$	−0.675488			−0.0343814
$387$	−0.453299	+	0.0216066i	−0.0230425	+	0.00109832i
$388$	0.986528	−	3.68177i	0.0500834	−	0.186914i
$389$	−28.2033	−	16.2832i	−1.42997	−	0.825591i	−0.432849	−	0.901466i	$-0.642492\pi$
$389$	−28.2033	−	16.2832i	−1.42997	−	0.825591i	−0.997117	+	0.0758750i	$0.975825\pi$
$390$	−0.838341	−	0.646317i	−0.0424511	−	0.0327276i
$391$	6.88127	+	3.97290i	0.348001	+	0.200918i
$392$	4.87985	+	5.01867i	0.246470	+	0.253481i
$393$	−3.87059	−	4.80296i	−0.195245	−	0.242277i
$394$			0.675769i			0.0340448i
$395$	−7.06504	−	2.09207i	−0.355481	−	0.105263i
$396$	−18.9096	−	4.11295i	−0.950242	−	0.206683i
$397$	−2.53362	−	9.45560i	−0.127159	−	0.474563i	0.872749	−	0.488170i	$-0.162335\pi$
$397$	−2.53362	−	9.45560i	−0.127159	−	0.474563i	−0.999907	+	0.0136068i	$0.995669\pi$
$398$	−6.20630	+	23.1622i	−0.311094	+	1.16102i
$399$	−13.2981	−	30.6380i	−0.665736	−	1.53382i
$400$	4.19384	+	2.72244i	0.209692	+	0.136122i
$401$	−5.00032	−	8.66080i	−0.249704	−	0.432500i	0.713740	−	0.700411i	$-0.247000\pi$
$401$	−5.00032	−	8.66080i	−0.249704	−	0.432500i	−0.963444	+	0.267911i	$0.913667\pi$
$402$	11.4612	−	1.78749i	0.571631	−	0.0891519i
$403$	0.587190	+	2.19142i	0.0292500	+	0.109163i
$404$	−1.41361	+	2.44844i	−0.0703297	+	0.121815i
$405$	6.53967	+	19.0324i	0.324959	+	0.945728i
$406$	−9.75034	−	17.1649i	−0.483901	−	0.851881i
$407$	−5.37883	+	20.0741i	−0.266619	+	0.995035i
$408$	2.08385	+	2.58583i	0.103166	+	0.128018i
$409$	−5.40467			−0.267244			−0.133622	−	0.991032i	$-0.542661\pi$
$409$	−5.40467			−0.267244			−0.133622	+	0.991032i	$0.542661\pi$
$410$	−10.5088	−	0.274233i	−0.518992	−	0.0135434i
$411$	8.10974	+	18.3314i	0.400024	+	0.904219i
$412$	0.954215	+	0.255681i	0.0470108	+	0.0125965i
$413$	11.6624	+	11.8271i	0.573868	+	0.581973i
$414$	−9.19956	−	8.36246i	−0.452134	−	0.410993i
$415$	14.9227	+	9.14280i	0.732527	+	0.448802i
$416$	0.236700	+	0.136659i	0.0116052	+	0.00670026i
$417$	−17.2503	−	6.66864i	−0.844752	−	0.326565i
$418$	12.1681	−	45.4121i	0.595163	−	2.22118i
$419$	7.09438	−	12.2878i	0.346583	−	0.600299i	−0.639057	−	0.769159i	$-0.720675\pi$
$419$	7.09438	−	12.2878i	0.346583	−	0.600299i	0.985640	+	0.168860i	$0.0540086\pi$
$420$	8.18703	−	6.16218i	0.399486	−	0.300684i
$421$	2.82850	+	4.89910i	0.137852	+	0.238768i	0.926684	−	0.375843i	$-0.122647\pi$
$421$	2.82850	+	4.89910i	0.137852	+	0.238768i	−0.788831	+	0.614610i	$0.789313\pi$
$422$	−23.8025	+	6.37787i	−1.15869	+	0.310470i
$423$	−15.7406	+	30.5347i	−0.765334	+	1.48465i
$424$	−6.34559	+	3.66363i	−0.308169	+	0.177922i
$425$	6.41615	+	7.12327i	0.311229	+	0.345529i
$426$	3.59038	−	4.91723i	0.173954	−	0.238241i
$427$	7.70664	−	7.59931i	0.372950	−	0.367756i
$428$	−1.16180	−	4.33591i	−0.0561579	−	0.209584i
$429$	−3.03621	−	0.326382i	−0.146590	−	0.0157579i
$430$	0.328900	−	0.0789932i	0.0158609	−	0.00380939i
$431$	15.7011	+	27.1950i	0.756294	+	1.30994i	0.944729	+	0.327853i	$0.106325\pi$
$431$	15.7011	+	27.1950i	0.756294	+	1.30994i	−0.188435	+	0.982086i	$0.560341\pi$
$432$	−2.32609	−	4.64643i	−0.111914	−	0.223551i
$433$	16.2616	+	16.2616i	0.781483	+	0.781483i	0.980081	−	0.198598i	$-0.0636389\pi$
$433$	16.2616	+	16.2616i	0.781483	+	0.781483i	−0.198598	+	0.980081i	$0.563639\pi$
$434$	−21.9610	−	0.153993i	−1.05416	−	0.00739190i
$435$	−26.7231	+	10.9979i	−1.28128	+	0.527310i
$436$	−1.46292	−	2.53384i	−0.0700609	−	0.121349i
$437$	21.3573	−	21.3573i	1.02166	−	1.02166i
$438$	2.81335	+	3.49105i	0.134427	+	0.166809i
$439$	1.97001			0.0940235			0.0470117	−	0.998894i	$-0.485030\pi$
$439$	1.97001			0.0940235			0.0470117	+	0.998894i	$0.485030\pi$
$440$	14.4190	+	0.376272i	0.687399	+	0.0179381i
$441$	−6.11366	−	20.0904i	−0.291127	−	0.956684i
$442$	0.370561	+	0.370561i	0.0176258	+	0.0176258i
$443$	−14.9853	+	14.9853i	−0.711971	+	0.711971i	−0.966947	−	0.254976i	$-0.917932\pi$
$443$	−14.9853	+	14.9853i	−0.711971	+	0.711971i	0.254976	+	0.966947i	$0.417932\pi$
$444$	−5.10317	+	2.25763i	−0.242186	+	0.107142i
$445$	24.9461	+	26.2830i	1.18256	+	1.24593i
$446$	0.293421	−	0.169407i	0.0138939	−	0.00802164i
$447$	−24.3349	−	30.1968i	−1.15100	−	1.42826i
$448$	−1.88390	+	1.85766i	−0.0890059	+	0.0877664i
$449$			4.94983i			0.233597i	0.993156	+	0.116798i	$0.0372631\pi$
$449$			4.94983i			0.233597i	−0.993156	+	0.116798i	$0.962737\pi$
$450$	−7.44081	−	13.0244i	−0.350763	−	0.613975i
$451$	−26.2630	+	15.1629i	−1.23668	+	0.713995i
$452$	−11.7534	+	3.14933i	−0.552835	+	0.148132i
$453$	6.23810	+	2.41153i	0.293092	+	0.113303i
$454$	−8.89547	+	15.4074i	−0.417485	+	0.723105i
$455$	1.18059	−	1.10491i	0.0553467	−	0.0517987i
$456$	11.5445	−	5.10727i	0.540622	−	0.239170i
$457$	−5.04668	−	5.04668i	−0.236074	−	0.236074i	0.579148	−	0.815222i	$-0.303385\pi$
$457$	−5.04668	−	5.04668i	−0.236074	−	0.236074i	−0.815222	+	0.579148i	$0.803385\pi$
$458$	5.69396	−	21.2502i	0.266061	−	0.992954i
$459$	−2.00221	−	9.75970i	−0.0934552	−	0.455544i
$460$	7.90143	+	4.84102i	0.368406	+	0.225714i
$461$	2.35656	−	1.36056i	0.109756	−	0.0633677i	−0.444117	−	0.895969i	$-0.646483\pi$
$461$	2.35656	−	1.36056i	0.109756	−	0.0633677i	0.553873	+	0.832601i	$0.313149\pi$
$462$	10.8518	−	27.4963i	0.504869	−	1.27924i
$463$	−4.10436	−	15.3177i	−0.190746	−	0.711874i	−0.993327	−	0.115331i	$-0.963207\pi$
$463$	−4.10436	−	15.3177i	−0.190746	−	0.711874i	0.802581	−	0.596543i	$-0.203459\pi$
$464$	6.46173	−	3.73068i	0.299978	−	0.173193i
$465$	−4.26871	+	31.8638i	−0.197957	+	1.47765i
$466$	−5.76029	+	9.97711i	−0.266840	+	0.462181i
$467$	−3.88608	−	14.5030i	−0.179826	−	0.671121i	−0.995679	−	0.0928612i	$-0.970399\pi$
$467$	−3.88608	−	14.5030i	−0.179826	−	0.671121i	0.815853	−	0.578260i	$-0.196268\pi$
$468$	−0.443321	−	0.689777i	−0.0204925	−	0.0318849i
$469$	−0.124243	+	17.7184i	−0.00573703	+	0.818161i
$470$	7.27007	−	24.5515i	0.335343	−	1.13248i
$471$	5.32977	+	3.89160i	0.245583	+	0.179316i
$472$	−4.43920	+	4.43920i	−0.204331	+	0.204331i
$473$	0.689984	−	0.689984i	0.0317255	−	0.0317255i
$474$	−4.60947	−	3.36567i	−0.211720	−	0.154590i
$475$	32.4669	−	16.5501i	1.48968	−	0.759370i
$476$	−4.41093	+	2.50558i	−0.202175	+	0.114843i
$477$	21.9568	−	1.04658i	1.00534	−	0.0479195i
$478$	−0.907754	−	3.38778i	−0.0415197	−	0.154954i
$479$	11.7682	−	20.3831i	0.537702	−	0.931327i	−0.461325	−	0.887231i	$-0.652626\pi$
$479$	11.7682	−	20.3831i	0.537702	−	0.931327i	0.999027	−	0.0440960i	$-0.0140407\pi$
$480$	2.35073	+	3.07800i	0.107295	+	0.140491i
$481$	−0.762593	+	0.440283i	−0.0347712	+	0.0200752i
$482$	5.27497	+	19.6864i	0.240268	+	0.896693i
$483$	14.8700	−	11.8123i	0.676607	−	0.537479i
$484$	26.5089	−	15.3049i	1.20495	−	0.695678i
$485$	4.45266	−	7.26755i	0.202185	−	0.330002i
$486$	−0.184358	+	15.5874i	−0.00836265	+	0.707057i
$487$	−6.08510	+	22.7099i	−0.275742	+	1.02908i	0.679600	+	0.733582i	$0.262153\pi$
$487$	−6.08510	+	22.7099i	−0.275742	+	1.02908i	−0.955342	+	0.295501i	$0.904514\pi$
$488$	2.89262	+	2.89262i	0.130943	+	0.130943i
$489$	−4.44364	+	1.96585i	−0.200948	+	0.0888990i
$490$	7.27633	+	13.8584i	0.328711	+	0.626058i
$491$	6.25109	−	10.8272i	0.282108	−	0.488625i	−0.689796	−	0.724004i	$-0.742300\pi$
$491$	6.25109	−	10.8272i	0.282108	−	0.488625i	0.971904	+	0.235379i	$0.0756331\pi$
$492$	−7.59508	−	2.93611i	−0.342413	−	0.132370i
$493$	13.8187	−	3.70272i	0.622365	−	0.166762i
$494$	1.72516	−	0.996020i	0.0776185	−	0.0448131i
$495$	−37.9317	−	20.8237i	−1.70490	−	0.935957i
$496$		−	8.30069i		−	0.372712i
$497$	6.53007	+	6.62230i	0.292914	+	0.297051i
$498$	8.50616	+	10.5552i	0.381170	+	0.472989i
$499$	31.1500	−	17.9845i	1.39447	−	0.805095i	0.400660	−	0.916227i	$-0.368781\pi$
$499$	31.1500	−	17.9845i	1.39447	−	0.805095i	0.993806	+	0.111132i	$0.0354477\pi$
$500$	7.26335	+	8.49963i	0.324827	+	0.380115i
$501$	24.0938	−	10.6590i	1.07643	−	0.476210i
$502$	12.9003	−	12.9003i	0.575768	−	0.575768i
$503$	−29.6651	−	29.6651i	−1.32270	−	1.32270i	−0.911581	−	0.411120i	$-0.865138\pi$
$503$	−29.6651	−	29.6651i	−1.32270	−	1.32270i	−0.411120	−	0.911581i	$-0.634862\pi$
$504$	7.57706	−	2.36394i	0.337509	−	0.105298i
$505$	−4.58532	+	4.35209i	−0.204044	+	0.193666i
$506$	26.7319			1.18838
$507$	14.0476	+	17.4315i	0.623875	+	0.774158i
$508$	3.94446	−	3.94446i	0.175007	−	0.175007i
$509$	14.6031	+	25.2933i	0.647270	+	1.12110i	0.983772	+	0.179422i	$0.0574228\pi$
$509$	14.6031	+	25.2933i	0.647270	+	1.12110i	−0.336502	+	0.941683i	$0.609244\pi$
$510$	2.82617	+	6.86713i	0.125145	+	0.304082i
$511$	−5.95507	+	3.38271i	−0.263437	+	0.149642i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−37.8045	−	2.25036i	−1.66911	−	0.0993556i
$514$	8.38484	+	14.5230i	0.369840	+	0.640581i
$515$	1.88355	+	1.15401i	0.0829992	+	0.0508517i
$516$	0.260509	+	0.0280037i	0.0114683	+	0.00123280i
$517$	−19.1178	−	71.3487i	−0.840801	−	3.13791i
$518$	−2.14838	−	8.24880i	−0.0943945	−	0.362432i
$519$	0.865046	−	1.18473i	0.0379713	−	0.0520039i
$520$	0.420733	+	0.443280i	0.0184504	+	0.0194391i
$521$	−5.65905	+	3.26726i	−0.247928	+	0.143141i	−0.618815	−	0.785537i	$-0.712387\pi$
$521$	−5.65905	+	3.26726i	−0.247928	+	0.143141i	0.370887	+	0.928678i	$0.379054\pi$
$522$	−22.3587	+	1.06573i	−0.978614	+	0.0466458i
$523$	−5.69309	+	1.52546i	−0.248941	+	0.0667036i	−0.381132	−	0.924521i	$-0.624466\pi$
$523$	−5.69309	+	1.52546i	−0.248941	+	0.0667036i	0.132191	+	0.991224i	$0.457799\pi$
$524$	1.78068	+	3.08423i	0.0777894	+	0.134735i
$525$	21.4656	−	8.01417i	0.936837	−	0.349767i
$526$	−13.9600	+	24.1794i	−0.608684	+	1.05427i
$527$	4.11924	−	15.3732i	0.179437	−	0.669667i
$528$	10.4211	+	4.02860i	0.453521	+	0.175322i
$529$	−5.04578	−	2.91318i	−0.219382	−	0.126660i
$530$	−15.9312	+	3.82627i	−0.692007	+	0.166202i
$531$	17.9395	−	5.73521i	0.778507	−	0.248887i
$532$	4.86013	+	18.6607i	0.210713	+	0.809042i
$533$	−1.24116	−	0.332568i	−0.0537606	−	0.0144051i
$534$	11.3560	+	25.6691i	0.491420	+	1.11081i
$535$	0.261843	−	10.0340i	0.0113204	−	0.433807i
$536$	−6.69710			−0.289271
$537$	−7.46283	−	9.26053i	−0.322045	−	0.399621i
$538$	−1.99827	+	7.45763i	−0.0861513	+	0.321521i
$539$	38.7840	+	23.1232i	1.67055	+	0.995985i
$540$	−2.03730	−	11.4389i	−0.0876713	−	0.492254i
$541$	11.2899	−	19.5546i	0.485389	−	0.840719i	−0.514470	−	0.857508i	$-0.672011\pi$
$541$	11.2899	−	19.5546i	0.485389	−	0.840719i	0.999859	+	0.0167899i	$0.00534463\pi$
$542$	−3.31160	−	12.3591i	−0.142245	−	0.530867i
$543$	4.87789	−	0.760759i	0.209330	−	0.0326473i
$544$	−0.958686	−	1.66049i	−0.0411033	−	0.0711931i
$545$	−1.52786	−	6.36145i	−0.0654462	−	0.272495i
$546$	1.14894	−	0.498686i	0.0491702	−	0.0213418i
$547$	5.08488	−	18.9770i	0.217414	−	0.811400i	−0.767889	−	0.640583i	$-0.778693\pi$
$547$	5.08488	−	18.9770i	0.217414	−	0.811400i	0.985303	−	0.170817i	$-0.0546406\pi$
$548$	−2.99533	−	11.1787i	−0.127954	−	0.477531i
$549$	−3.73711	−	11.6895i	−0.159496	−	0.498896i
$550$	30.6761	+	9.96114i	1.30803	+	0.424744i
$551$		−	54.3811i		−	2.31671i
$552$	4.50393	+	5.58887i	0.191700	+	0.237878i
$553$	6.20782	−	6.12137i	0.263983	−	0.260307i
$554$	−22.3055	−	12.8781i	−0.947668	−	0.547136i
$555$	−12.3748	+	1.60053i	−0.525279	+	0.0679389i
$556$	9.24722	+	5.33889i	0.392170	+	0.226419i
$557$	0.372122	−	1.38878i	0.0157673	−	0.0588445i	−0.957594	−	0.288121i	$-0.906969\pi$
$557$	0.372122	−	1.38878i	0.0157673	−	0.0588445i	0.973361	+	0.229277i	$0.0736361\pi$
$558$	−11.4101	+	22.1342i	−0.483030	+	0.937014i
$559$	0.0413452			0.00174871
$560$	−5.21857	+	2.78686i	−0.220525	+	0.117766i
$561$	17.3011	+	12.6326i	0.730455	+	0.533351i
$562$	−0.613593	+	2.28996i	−0.0258829	+	0.0965962i
$563$	−5.72608	−	5.72608i	−0.241325	−	0.241325i	0.576073	−	0.817398i	$-0.304584\pi$
$563$	−5.72608	−	5.72608i	−0.241325	−	0.241325i	−0.817398	+	0.576073i	$0.804584\pi$
$564$	11.6959	−	16.0182i	0.492487	−	0.674489i
$565$	−27.1993	−	0.709782i	−1.14429	−	0.0298608i
$566$			5.87829i			0.247083i
$567$	−23.4540	−	4.11189i	−0.984977	−	0.172683i
$568$	−2.48562	+	2.48562i	−0.104294	+	0.104294i
$569$			16.9832i			0.711974i	0.934491	+	0.355987i	$0.115855\pi$
$569$			16.9832i			0.711974i	−0.934491	+	0.355987i	$0.884145\pi$
$570$	27.9945	−	3.62077i	1.17256	−	0.151657i
$571$	27.8862			1.16700			0.583500	−	0.812113i	$-0.301683\pi$
$571$	27.8862			1.16700			0.583500	+	0.812113i	$0.301683\pi$
$572$	1.70298	+	0.456313i	0.0712053	+	0.0190794i
$573$	0.152566	+	0.978231i	0.00637352	+	0.0408662i
$574$	6.29458	−	10.7281i	0.262731	−	0.447782i
$575$	13.8675	+	15.3959i	0.578316	+	0.642052i
$576$	0.913543	+	2.85752i	0.0380643	+	0.119063i
$577$	−21.4107	−	5.73697i	−0.891337	−	0.238833i	−0.216045	−	0.976383i	$-0.569316\pi$
$577$	−21.4107	−	5.73697i	−0.891337	−	0.238833i	−0.675292	+	0.737550i	$0.735983\pi$
$578$	3.44842	+	12.8697i	0.143435	+	0.535308i
$579$	−0.944903	−	0.689933i	−0.0392688	−	0.0286726i
$580$	16.2228	−	3.89629i	0.673614	−	0.161785i
$581$	−18.0051	+	10.2276i	−0.746979	+	0.424313i
$582$	5.14051	−	4.14261i	0.213081	−	0.171717i
$583$	−33.4214	+	33.4214i	−1.38417	+	1.38417i
$584$	−1.29430	−	2.24179i	−0.0535583	−	0.0927657i
$585$	−0.512571	−	1.76037i	−0.0211922	−	0.0727823i
$586$	14.5144	+	8.37991i	0.599586	+	0.346171i
$587$	−27.8008	−	7.44919i	−1.14746	−	0.307461i	−0.365513	−	0.930806i	$-0.619106\pi$
$587$	−27.8008	−	7.44919i	−1.14746	−	0.307461i	−0.781947	+	0.623345i	$0.785773\pi$
$588$	1.70016	+	12.0046i	0.0701133	+	0.495060i
$589$	−52.3931	−	30.2492i	−2.15882	−	1.24640i
$590$	−12.3362	+	6.69946i	−0.507874	+	0.275813i
$591$	−0.690221	+	0.945298i	−0.0283919	+	0.0388843i
$592$	3.11198	−	0.833854i	0.127902	−	0.0342712i
$593$	−11.7549	+	3.14973i	−0.482718	+	0.129344i	−0.491968	−	0.870613i	$-0.663722\pi$
$593$	−11.7549	+	3.14973i	−0.482718	+	0.129344i	0.00925009	+	0.999957i	$0.497056\pi$
$594$	−22.2507	−	25.0674i	−0.912957	−	1.02853i
$595$	−11.0480	+	2.57164i	−0.452923	+	0.105427i
$596$	11.1954	+	19.3909i	0.458580	+	0.794283i
$597$	−32.3392	+	26.0614i	−1.32356	+	1.06662i
$598$	0.800912	+	0.800912i	0.0327517	+	0.0327517i
$599$		−	31.4639i		−	1.28558i	−0.766043	−	0.642789i	$-0.777777\pi$
$599$		−	31.4639i		−	1.28558i	0.766043	−	0.642789i	$-0.222223\pi$
$600$	3.08589	+	8.09180i	0.125981	+	0.330347i
$601$	11.9703	−	6.91104i	0.488278	−	0.281907i	−0.235582	−	0.971854i	$-0.575700\pi$
$601$	11.9703	−	6.91104i	0.488278	−	0.281907i	0.723860	+	0.689947i	$0.242366\pi$
$602$	−0.106294	+	0.385853i	−0.00433223	+	0.0157262i
$603$	17.8581	+	9.20585i	0.727239	+	0.374891i
$604$	−3.34400	−	1.93066i	−0.136066	−	0.0785575i
$605$	66.5531	−	15.9843i	2.70577	−	0.649856i
$606$	−4.47823	+	1.98116i	−0.181916	+	0.0804790i
$607$	−19.6269	−	5.25901i	−0.796631	−	0.213457i	−0.162527	−	0.986704i	$-0.551964\pi$
$607$	−19.6269	−	5.25901i	−0.796631	−	0.213457i	−0.634105	+	0.773247i	$0.718631\pi$
$608$	−7.04001	+	1.88637i	−0.285510	+	0.0765022i
$609$	3.89278	−	33.9699i	0.157743	−	1.37653i
$610$	4.36543	+	8.03839i	0.176751	+	0.325465i
$611$	1.56489	−	2.71046i	0.0633085	−	0.109654i
$612$	0.273865	+	5.74560i	0.0110703	+	0.232252i
$613$	−24.6487	−	6.60459i	−0.995551	−	0.266757i	−0.275970	−	0.961166i	$-0.588999\pi$
$613$	−24.6487	−	6.60459i	−0.995551	−	0.266757i	−0.719580	+	0.694409i	$0.755666\pi$
$614$	15.8971			0.641556
$615$	−14.4201	−	11.1171i	−0.581474	−	0.448286i
$616$	−8.63673	+	14.7199i	−0.347984	+	0.593082i
$617$	−8.26535	+	2.21469i	−0.332751	+	0.0891603i	−0.421326	−	0.906909i	$-0.638435\pi$
$617$	−8.26535	+	2.21469i	−0.332751	+	0.0891603i	0.0885755	+	0.996069i	$0.471769\pi$
$618$	1.07365	+	1.33228i	0.0431886	+	0.0535922i
$619$	−20.5641	+	35.6181i	−0.826541	+	1.43161i	0.0741948	+	0.997244i	$0.476361\pi$
$619$	−20.5641	+	35.6181i	−0.826541	+	1.43161i	−0.900736	+	0.434367i	$0.856972\pi$
$620$	5.26997	−	17.7970i	0.211647	−	0.714746i
$621$	−4.32747	−	21.0941i	−0.173656	−	0.846477i
$622$	17.6046	−	17.6046i	0.705882	−	0.705882i
$623$	−41.4917	+	10.8064i	−1.66233	+	0.432951i
$624$	0.191526	+	0.432928i	0.00766718	+	0.0173310i
$625$	10.1767	+	22.8350i	0.407067	+	0.913398i
$626$		−	16.6157i		−	0.664098i
$627$	63.4046	−	51.0962i	2.53213	−	2.04058i
$628$	−2.69416	−	2.69416i	−0.107509	−	0.107509i
$629$	6.17732			0.246306
$630$	17.7464	−	0.257829i	0.707032	−	0.0102721i
$631$	−13.1747			−0.524478			−0.262239	−	0.965003i	$-0.584461\pi$
$631$	−13.1747			−0.524478			−0.262239	+	0.965003i	$0.584461\pi$
$632$	2.33006	+	2.33006i	0.0926846	+	0.0926846i
$633$	−39.8104	−	15.3899i	−1.58232	−	0.611694i
$634$			17.3114i			0.687523i
$635$	10.9614	−	5.95283i	0.434989	−	0.236231i
$636$	−12.6185	−	1.35644i	−0.500356	−	0.0537864i
$637$	0.469215	+	1.85480i	0.0185910	+	0.0734898i
$638$	34.0331	−	34.0331i	1.34738	−	1.34738i
$639$	10.0448	−	3.21129i	0.397365	−	0.127037i
$640$	−1.06714	−	1.96500i	−0.0421823	−	0.0776734i
$641$	−19.8658	+	34.4085i	−0.784650	+	1.35905i	0.144558	+	0.989496i	$0.453824\pi$
$641$	−19.8658	+	34.4085i	−0.784650	+	1.35905i	−0.929208	+	0.369558i	$0.879509\pi$
$642$	2.80345	−	7.25192i	0.110643	−	0.286210i
$643$	14.1800	−	3.79952i	0.559204	−	0.149838i	0.0318634	−	0.999492i	$-0.489856\pi$
$643$	14.1800	−	3.79952i	0.559204	−	0.149838i	0.527341	+	0.849654i	$0.323189\pi$
$644$	−9.53355	+	5.41542i	−0.375675	+	0.213398i
$645$	0.540763	+	0.225434i	0.0212925	+	0.00887645i
$646$	−13.9745			−0.549819
$647$	30.2403	+	8.10287i	1.18887	+	0.318557i	0.798439	−	0.602076i	$-0.205659\pi$
$647$	30.2403	+	8.10287i	1.18887	+	0.318557i	0.390431	+	0.920632i	$0.372326\pi$
$648$	1.49195	−	8.87548i	0.0586094	−	0.348662i
$649$	−20.2483	+	35.0710i	−0.794814	+	1.37666i
$650$	0.620639	+	1.21753i	0.0243435	+	0.0477554i
$651$	−30.5628	−	22.6461i	−1.19785	−	0.887570i
$652$	2.70979	−	0.726086i	0.106124	−	0.0284357i
$653$	−11.8895	−	3.18578i	−0.465271	−	0.124669i	0.0185648	−	0.999828i	$-0.494090\pi$
$653$	−11.8895	−	3.18578i	−0.465271	−	0.124669i	−0.483836	+	0.875159i	$0.660757\pi$
$654$	0.541637	−	5.03866i	0.0211797	−	0.197027i
$655$	1.85973	+	7.74325i	0.0726656	+	0.302554i
$656$	4.07142	+	2.35064i	0.158962	+	0.0917770i
$657$	0.369737	+	7.75697i	0.0144248	+	0.302628i
$658$	21.2722	+	21.5726i	0.829275	+	0.840987i
$659$	19.6309	−	11.3339i	0.764710	−	0.441505i	−0.0662746	−	0.997801i	$-0.521111\pi$
$659$	19.6309	−	11.3339i	0.764710	−	0.441505i	0.830984	+	0.556296i	$0.187778\pi$
$660$	19.7857	+	15.2537i	0.770155	+	0.593750i
$661$			37.5665i			1.46117i	0.682822	+	0.730584i	$0.260752\pi$
$661$			37.5665i			1.46117i	−0.682822	+	0.730584i	$0.739248\pi$
$662$	−10.6431	−	10.6431i	−0.413656	−	0.413656i
$663$	0.139872	+	0.896844i	0.00543219	+	0.0348305i
$664$	−3.91330	−	6.77803i	−0.151865	−	0.263039i
$665$	−1.42703	+	43.0949i	−0.0553379	+	1.67115i
$666$	−9.44447	−	2.05423i	−0.365966	−	0.0795997i
$667$	29.8671	−	8.00287i	1.15646	−	0.309872i
$668$	−14.6927	+	3.93690i	−0.568478	+	0.152323i
$669$	0.583481	+	0.0627220i	0.0225587	+	0.00242497i
$670$	−14.3589	−	4.25188i	−0.554732	−	0.164265i
$671$	22.8526	+	13.1939i	0.882214	+	0.509347i
$672$	−4.53268	+	0.674398i	−0.174852	+	0.0260155i
$673$	19.1768	+	5.13840i	0.739210	+	0.198071i	0.608727	−	0.793380i	$-0.291680\pi$
$673$	19.1768	+	5.13840i	0.739210	+	0.198071i	0.130483	+	0.991451i	$0.458347\pi$
$674$	16.0352	+	9.25794i	0.617654	+	0.356603i
$675$	2.89435	−	25.8190i	0.111404	−	0.993775i
$676$	−6.46265	−	11.1936i	−0.248563	−	0.430524i
$677$	8.40770	−	8.40770i	0.323134	−	0.323134i	−0.526834	−	0.849968i	$-0.676621\pi$
$677$	8.40770	−	8.40770i	0.323134	−	0.323134i	0.849968	+	0.526834i	$0.176621\pi$
$678$	−19.6579	−	7.59937i	−0.754958	−	0.291852i
$679$	4.98098	+	8.76873i	0.191152	+	0.336513i
$680$	−1.00124	−	4.16882i	−0.0383960	−	0.159867i
$681$	−28.1803	+	12.4669i	−1.07987	+	0.477732i
$682$	−13.8582	−	51.7197i	−0.530660	−	1.98045i
$683$	−27.7576	−	7.43761i	−1.06211	−	0.284592i	−0.314864	−	0.949137i	$-0.601959\pi$
$683$	−27.7576	−	7.43761i	−1.06211	−	0.284592i	−0.747249	+	0.664544i	$0.768626\pi$
$684$	21.3655	+	4.64713i	0.816931	+	0.177687i
$685$	0.675074	−	25.8693i	0.0257933	−	0.988416i
$686$	−18.5162	−	0.389563i	−0.706950	−	0.0148736i
$687$	29.6696	−	23.9100i	1.13196	−	0.912222i
$688$	−0.146117	−	0.0391519i	−0.00557065	−	0.00149265i
$689$	−2.00267			−0.0762958
$690$	6.10834	+	14.8423i	0.232541	+	0.565035i
$691$			14.8628i			0.565406i	0.959208	+	0.282703i	$0.0912311\pi$
$691$			14.8628i			0.565406i	−0.959208	+	0.282703i	$0.908769\pi$
$692$	−0.598873	+	0.598873i	−0.0227657	+	0.0227657i
$693$	43.2643	−	27.3793i	1.64347	−	1.04005i
$694$		−	26.1764i		−	0.993642i
$695$	16.4369	+	17.3177i	0.623486	+	0.656898i
$696$	12.8494	+	1.38127i	0.487056	+	0.0523568i
$697$	6.37393	+	6.37393i	0.241430	+	0.241430i
$698$	3.46997	−	12.9501i	0.131340	−	0.490169i
$699$	−18.2482	+	8.07297i	−0.690212	+	0.305348i
$700$	−12.9582	+	2.66195i	−0.489773	+	0.100612i
$701$	−26.5330			−1.00214			−0.501069	−	0.865407i	$-0.667060\pi$
$701$	−26.5330			−1.00214			−0.501069	+	0.865407i	$0.667060\pi$
$702$	0.0843898	−	1.41769i	0.00318509	−	0.0535074i
$703$	6.07742	−	22.6812i	0.229214	−	0.855439i
$704$	−5.58636	−	3.22528i	−0.210544	−	0.121557i
$705$	35.2462	−	26.9182i	1.32745	−	1.01380i
$706$	0.887963	+	0.512666i	0.0334189	+	0.0192944i
$707$	−1.88529	−	7.23864i	−0.0709035	−	0.272237i
$708$	−10.7439	+	1.67563i	−0.403781	+	0.0629739i
$709$		−	8.39199i		−	0.315168i	−0.987506	−	0.157584i	$-0.949630\pi$
$709$		−	8.39199i		−	0.315168i	0.987506	−	0.157584i	$-0.0503705\pi$
$710$	−6.90737	+	3.75120i	−0.259229	+	0.140780i
$711$	−3.01030	−	9.41610i	−0.112895	−	0.353131i
$712$	−4.19431	−	15.6534i	−0.157188	−	0.586635i
$713$	8.90310	−	33.2268i	0.333424	−	1.24435i
$714$	−8.72938	−	1.00034i	−0.326689	−	0.0374368i
$715$	3.36156	+	2.05955i	0.125715	+	0.0770229i
$716$	3.43331	+	5.94666i	0.128309	+	0.222237i
$717$	2.19042	−	5.66616i	0.0818029	−	0.211606i
$718$	2.52143	+	9.41009i	0.0940988	+	0.351182i
$719$	1.04035	−	1.80193i	0.0387984	−	0.0672008i	−0.845974	−	0.533224i	$-0.820980\pi$
$719$	1.04035	−	1.80193i	0.0387984	−	0.0672008i	0.884773	+	0.466023i	$0.154314\pi$
$720$	0.144480	+	6.70665i	0.00538446	+	0.249942i
$721$	−2.27262	+	1.29093i	−0.0846367	+	0.0480769i
$722$	−8.83094	+	32.9575i	−0.328653	+	1.22655i
$723$	−12.7286	+	32.9261i	−0.473381	+	1.22453i
$724$	−2.85030			−0.105930
$725$	37.2560	+	1.94576i	1.38365	+	0.0722637i
$726$	52.7141	+	5.66657i	1.95640	+	0.210306i
$727$	−12.6214	−	3.38189i	−0.468102	−	0.125427i	0.0170554	−	0.999855i	$-0.494571\pi$
$727$	−12.6214	−	3.38189i	−0.468102	−	0.125427i	−0.485157	+	0.874427i	$0.661238\pi$
$728$	−0.699787	+	0.182258i	−0.0259358	+	0.00675493i
$729$	−16.1786	+	21.6160i	−0.599207	+	0.800594i
$730$	−1.35175	−	5.62821i	−0.0500306	−	0.208309i
$731$	−0.251185	−	0.145022i	−0.00929041	−	0.00536382i
$732$	1.09185	+	7.00082i	0.0403560	+	0.258758i
$733$	−5.09160	+	19.0021i	−0.188062	+	0.701859i	0.805892	+	0.592063i	$0.201686\pi$
$733$	−5.09160	+	19.0021i	−0.188062	+	0.701859i	−0.993954	+	0.109796i	$0.964980\pi$
$734$	16.5373	−	28.6435i	0.610404	−	1.05725i
$735$	−3.97629	+	26.8177i	−0.146668	+	0.989186i
$736$	−2.07205	−	3.58890i	−0.0763769	−	0.132289i
$737$	−41.7281	+	11.1810i	−1.53707	+	0.411858i
$738$	−7.62545	−	11.8647i	−0.280697	−	0.436744i
$739$	−1.45360	+	0.839236i	−0.0534715	+	0.0308718i	−0.526497	−	0.850177i	$-0.676495\pi$
$739$	−1.45360	+	0.839236i	−0.0534715	+	0.0308718i	0.473026	+	0.881049i	$0.343162\pi$
$740$	7.20163	+	0.187931i	0.264737	+	0.00690847i
$741$	3.43055	+	0.368772i	0.126024	+	0.0135472i
$742$	5.14867	−	18.6899i	0.189014	−	0.686128i
$743$	0.712072	+	2.65749i	0.0261234	+	0.0974939i	0.977757	−	0.209742i	$-0.0672625\pi$
$743$	0.712072	+	2.65749i	0.0261234	+	0.0974939i	−0.951633	+	0.307236i	$0.900596\pi$
$744$	8.47820	−	11.6114i	0.310826	−	0.425694i
$745$	11.6923	+	48.6827i	0.428374	+	1.78360i
$746$	−9.81523	−	17.0005i	−0.359361	−	0.622432i
$747$	1.11790	+	23.4532i	0.0409018	+	0.858106i
$748$	−8.74560	−	8.74560i	−0.319771	−	0.319771i
$749$	10.2434	+	6.01018i	0.374285	+	0.219607i
$750$	1.47892	+	19.3084i	0.0540024	+	0.705042i
$751$	8.05133	+	13.9453i	0.293797	+	0.508872i	0.974704	−	0.223498i	$-0.0717476\pi$
$751$	8.05133	+	13.9453i	0.293797	+	0.508872i	−0.680907	+	0.732370i	$0.738414\pi$
$752$	−8.09709	+	8.09709i	−0.295271	+	0.295271i
$753$	31.2217	−	4.86935i	1.13778	−	0.177449i
$754$	2.03933			0.0742679
$755$	−5.94394	−	6.26247i	−0.216322	−	0.227915i
$756$	13.0136	+	4.43231i	0.473301	+	0.161202i
$757$	11.7019	+	11.7019i	0.425314	+	0.425314i	0.887029	−	0.461715i	$-0.152766\pi$
$757$	11.7019	+	11.7019i	0.425314	+	0.425314i	−0.461715	+	0.887029i	$0.652766\pi$
$758$	−14.1303	+	14.1303i	−0.513236	+	0.513236i
$759$	37.3938	+	27.3035i	1.35731	+	0.991055i
$760$	−16.2917	−	0.425141i	−0.590962	−	0.0154215i
$761$	−26.0710	+	15.0521i	−0.945074	+	0.545639i	−0.891547	−	0.452928i	$-0.850380\pi$
$761$	−26.0710	+	15.0521i	−0.945074	+	0.545639i	−0.0535268	+	0.998566i	$0.517046\pi$
$762$	9.54652	−	1.48888i	0.345834	−	0.0539365i
$763$	7.46302	+	2.05590i	0.270179	+	0.0744287i
$764$		−	0.571610i		−	0.0206801i
$765$	−3.06061	+	12.4927i	−0.110657	+	0.451674i
$766$	23.6857	−	13.6750i	0.855800	−	0.494097i
$767$	−1.65742	+	0.444104i	−0.0598459	+	0.0160357i
$768$	−0.266905	−	1.71136i	−0.00963111	−	0.0617535i
$769$	−6.20698	+	10.7508i	−0.223829	+	0.387684i	−0.955968	−	0.293472i	$-0.905189\pi$
$769$	−6.20698	+	10.7508i	−0.223829	+	0.387684i	0.732138	+	0.681156i	$0.238523\pi$
$770$	−27.8630	+	26.0768i	−1.00411	+	0.939743i
$771$	−3.10445	+	28.8796i	−0.111804	+	1.04007i
$772$	0.477642	+	0.477642i	0.0171907	+	0.0171907i
$773$	−8.22219	+	30.6856i	−0.295732	+	1.10369i	0.644903	+	0.764264i	$0.276898\pi$
$773$	−8.22219	+	30.6856i	−0.295732	+	1.10369i	−0.940635	+	0.339421i	$0.889769\pi$
$774$	0.335809	+	0.305253i	0.0120704	+	0.0109721i
$775$	22.5981	−	34.8118i	0.811748	−	1.25048i
$776$	−3.30099	+	1.90583i	−0.118498	+	0.0684151i
$777$	5.41995	−	13.7331i	0.194440	−	0.492674i
$778$	8.42881	+	31.4567i	0.302187	+	1.12778i
$779$	29.6740	−	17.1323i	1.06318	−	0.613828i
$780$	0.135781	+	1.04981i	0.00486175	+	0.0375893i
$781$	−11.3375	+	19.6372i	−0.405689	+	0.702674i
$782$	−2.05652	−	7.67505i	−0.0735412	−	0.274459i
$783$	−32.3649	−	21.3461i	−1.15663	−	0.762846i
$784$	0.0981647	−	6.99931i	0.00350588	−	0.249975i
$785$	−4.06592	−	7.48688i	−0.145119	−	0.267218i
$786$	−0.659288	+	6.13312i	−0.0235160	+	0.218761i
$787$	22.5236	−	22.5236i	0.802881	−	0.802881i	−0.180664	−	0.983545i	$-0.557825\pi$
$787$	22.5236	−	22.5236i	0.802881	−	0.802881i	0.983545	+	0.180664i	$0.0578247\pi$
$788$	0.477841	−	0.477841i	0.0170224	−	0.0170224i
$789$	−44.2244	+	19.5648i	−1.57443	+	0.696524i
$790$	3.51643	+	6.47505i	0.125109	+	0.230372i
$791$	16.2919	−	27.7670i	0.579274	−	0.987280i
$792$	10.4628	+	16.2794i	0.371779	+	0.578463i
$793$	0.289382	+	1.07999i	0.0102763	+	0.0383515i
$794$	−4.89458	+	8.47766i	−0.173702	+	0.300861i
$795$	−26.1934	−	10.9195i	−0.928984	−	0.387276i
$796$	20.7667	−	11.9897i	0.736056	−	0.424962i
$797$	9.48571	+	35.4012i	0.336001	+	1.25397i	0.902780	+	0.430103i	$0.141523\pi$
$797$	9.48571	+	35.4012i	0.336001	+	1.25397i	−0.566778	+	0.823870i	$0.691810\pi$
$798$	−12.2612	+	31.0675i	−0.434040	+	1.09978i
$799$	−19.0143	+	10.9779i	−0.672679	+	0.388372i
$800$	−1.04044	−	4.89055i	−0.0367852	−	0.172907i
$801$	−10.3328	+	47.5060i	−0.365093	+	1.67854i
$802$	−2.58835	+	9.65987i	−0.0913980	+	0.341102i
$803$	−11.8072	−	11.8072i	−0.416667	−	0.416667i
$804$	−9.36822	−	6.84032i	−0.330392	−	0.241240i
$805$	−23.8785	+	5.55821i	−0.841607	+	0.195901i
$806$	1.13436	−	1.96478i	0.0399563	−	0.0692063i
$807$	−10.4124	+	8.39108i	−0.366533	+	0.295380i
$808$	2.73088	−	0.731738i	0.0960722	−	0.0257425i
$809$	20.3110	−	11.7266i	0.714097	−	0.412284i	−0.0984792	−	0.995139i	$-0.531398\pi$
$809$	20.3110	−	11.7266i	0.714097	−	0.412284i	0.812576	+	0.582855i	$0.198064\pi$
$810$	8.83371	−	18.0822i	0.310385	−	0.635343i
$811$		−	18.4752i		−	0.648753i	−0.945928	−	0.324376i	$-0.894846\pi$
$811$		−	18.4752i		−	0.648753i	0.945928	−	0.324376i	$-0.105154\pi$
$812$	−5.24290	+	19.0320i	−0.183990	+	0.667891i
$813$	7.99094	−	20.6708i	0.280254	−	0.724958i
$814$	17.9979	−	10.3911i	0.630827	−	0.364208i
$815$	6.27089	+	0.163642i	0.219660	+	0.00573214i
$816$	0.354949	−	3.30196i	0.0124257	−	0.115592i
$817$	−0.779598	+	0.779598i	−0.0272747	+	0.0272747i
$818$	3.82168	+	3.82168i	0.133622	+	0.133622i
$819$	2.11655	+	0.475929i	0.0739581	+	0.0166303i
$820$	7.23693	+	7.62475i	0.252724	+	0.266268i
$821$	−5.93556			−0.207152			−0.103576	−	0.994622i	$-0.533029\pi$
$821$	−5.93556			−0.207152			−0.103576	+	0.994622i	$0.533029\pi$
$822$	7.22777	−	18.6967i	0.252097	−	0.652122i
$823$	−17.6834	+	17.6834i	−0.616405	+	0.616405i	−0.944607	−	0.328203i	$-0.893557\pi$
$823$	−17.6834	+	17.6834i	−0.616405	+	0.616405i	0.328203	+	0.944607i	$0.393557\pi$
$824$	−0.493938	−	0.855526i	−0.0172072	−	0.0298037i
$825$	32.7370	+	45.2662i	1.13975	+	1.57597i
$826$	0.116468	−	16.6096i	0.00405244	−	0.577921i
$827$	−21.0838	−	21.0838i	−0.733157	−	0.733157i	0.238087	−	0.971244i	$-0.423480\pi$
$827$	−21.0838	−	21.0838i	−0.733157	−	0.733157i	−0.971244	+	0.238087i	$0.923480\pi$
$828$	0.591917	+	12.4182i	0.0205705	+	0.431563i
$829$	−8.45878	−	14.6510i	−0.293785	−	0.508851i	0.680916	−	0.732361i	$-0.261582\pi$
$829$	−8.45878	−	14.6510i	−0.293785	−	0.508851i	−0.974702	+	0.223510i	$0.928248\pi$
$830$	−4.08702	−	17.0169i	−0.141862	−	0.590665i
$831$	−18.0484	−	40.7969i	−0.626093	−	1.41523i
$832$	−0.0707399	−	0.264005i	−0.00245247	−	0.00915273i
$833$	3.65523	−	12.9143i	0.126646	−	0.447454i
$834$	7.48238	+	16.9133i	0.259094	+	0.585658i
$835$	−34.0013	−	0.887283i	−1.17666	−	0.0307057i
$836$	−40.7153	+	23.5070i	−1.40817	+	0.813007i
$837$	−38.5686	+	19.3082i	−1.33312	+	0.667388i
$838$	−13.7053	+	3.67232i	−0.473441	+	0.126858i
$839$	0.323295	+	0.559963i	0.0111614	+	0.0193321i	0.871552	−	0.490303i	$-0.163114\pi$
$839$	0.323295	+	0.559963i	0.0111614	+	0.0193321i	−0.860391	+	0.509635i	$0.829780\pi$
$840$	−10.1464	−	1.43179i	−0.350085	−	0.0494013i
$841$	13.3360	−	23.0986i	0.459861	−	0.796503i
$842$	1.46414	−	5.46424i	0.0504575	−	0.188310i
$843$	−3.19726	+	2.57659i	−0.110119	+	0.0887425i
$844$	21.3408	+	12.3211i	0.734579	+	0.424110i
$845$	−6.74954	−	28.1027i	−0.232191	−	0.966761i
$846$	32.7216	−	10.4610i	1.12499	−	0.359657i
$847$	−21.5087	+	78.0776i	−0.739049	+	2.68278i
$848$	7.07759	+	1.89643i	0.243045	+	0.0651238i
$849$	−6.00401	+	8.22283i	−0.206057	+	0.282207i
$850$	0.500009	−	9.57382i	0.0171502	−	0.328379i
$851$	13.3513			0.457678
$852$	−6.01579	+	0.938226i	−0.206097	+	0.0321431i
$853$	1.31065	−	4.89141i	0.0448758	−	0.167479i	−0.939851	−	0.341584i	$-0.889037\pi$
$853$	1.31065	−	4.89141i	0.0448758	−	0.167479i	0.984727	+	0.174105i	$0.0557033\pi$
$854$	−10.8229	−	0.0758916i	−0.370353	−	0.00259696i
$855$	42.8582	+	23.5283i	1.46572	+	0.804650i
$856$	−2.24443	+	3.88747i	−0.0767131	+	0.132871i
$857$	−9.30758	−	34.7364i	−0.317941	−	1.18657i	−0.921220	−	0.389042i	$-0.872806\pi$
$857$	−9.30758	−	34.7364i	−0.317941	−	1.18657i	0.603279	−	0.797530i	$-0.293860\pi$
$858$	1.91614	+	2.37771i	0.0654160	+	0.0811738i
$859$	−13.1991	−	22.8615i	−0.450348	−	0.780025i	0.548060	−	0.836439i	$-0.315367\pi$
$859$	−13.1991	−	22.8615i	−0.450348	−	0.780025i	−0.998407	+	0.0564142i	$0.982033\pi$
$860$	−0.288424	−	0.176711i	−0.00983517	−	0.00602578i
$861$	19.7627	−	8.57777i	0.673510	−	0.292330i
$862$	8.12747	−	30.3321i	0.276823	−	1.03312i
$863$	14.0970	+	52.6108i	0.479868	+	1.79089i	0.602135	+	0.798394i	$0.294317\pi$
$863$	14.0970	+	52.6108i	0.479868	+	1.79089i	−0.122267	+	0.992497i	$0.539017\pi$
$864$	−1.64073	+	4.93032i	−0.0558186	+	0.167733i
$865$	−1.66422	+	0.903795i	−0.0565853	+	0.0307299i
$866$		−	22.9974i		−	0.781483i
$867$	−8.32110	+	21.5249i	−0.282599	+	0.731024i
$868$	15.4199	+	15.6377i	0.523385	+	0.530777i
$869$	18.4081	+	10.6279i	0.624453	+	0.360528i
$870$	26.6728	+	11.1194i	0.904292	+	0.376983i
$871$	−1.58521	−	0.915220i	−0.0537127	−	0.0310110i
$872$	−0.757261	+	2.82613i	−0.0256441	+	0.0957050i
$873$	11.4220	−	0.544431i	0.386576	−	0.0184262i
$874$	−30.2037			−1.02166
$875$	−29.4729	−	2.51959i	−0.996366	−	0.0851776i
$876$	0.479207	−	4.45789i	0.0161909	−	0.150618i
$877$	9.42628	−	35.1793i	0.318303	−	1.18792i	−0.602572	−	0.798064i	$-0.705858\pi$
$877$	9.42628	−	35.1793i	0.318303	−	1.18792i	0.920875	−	0.389858i	$-0.127476\pi$
$878$	−1.39301	−	1.39301i	−0.0470117	−	0.0470117i
$879$	11.7443	+	26.5470i	0.396127	+	0.895409i
$880$	−9.92971	−	10.4618i	−0.334730	−	0.352668i
$881$		−	7.79918i		−	0.262761i	−0.991332	−	0.131381i	$-0.958059\pi$
$881$		−	7.79918i		−	0.262761i	0.991332	−	0.131381i	$-0.0419410\pi$
$882$	−9.88303	+	18.5291i	−0.332779	+	0.623906i
$883$	7.57466	−	7.57466i	0.254908	−	0.254908i	−0.568071	−	0.822979i	$-0.692310\pi$
$883$	7.57466	−	7.57466i	0.254908	−	0.254908i	0.822979	+	0.568071i	$0.192310\pi$
$884$		−	0.524053i		−	0.0176258i
$885$	−24.0992	−	3.22852i	−0.810086	−	0.108525i
$886$	21.1923			0.711971
$887$	−44.0633	−	11.8067i	−1.47950	−	0.396431i	−0.573322	−	0.819330i	$-0.694346\pi$
$887$	−44.0633	−	11.8067i	−1.47950	−	0.396431i	−0.906177	+	0.422899i	$0.861012\pi$
$888$	5.20487	+	2.01210i	0.174664	+	0.0675217i
$889$	−0.103488	+	14.7585i	−0.00347087	+	0.494983i
$890$	0.945297	−	36.2244i	0.0316864	−	1.21425i
$891$	−5.52187	−	57.7919i	−0.184990	−	1.93610i
$892$	−0.327269	−	0.0876914i	−0.0109578	−	0.00293612i
$893$	21.6008	+	80.6153i	0.722843	+	2.69769i
$894$	−4.14503	+	38.5597i	−0.138630	+	1.28963i
$895$	3.58572	+	14.9297i	0.119857	+	0.499043i
$896$	2.64569	+	0.0185518i	0.0883862	+	0.000619773i
$897$	0.302313	+	1.93839i	0.0100939	+	0.0647210i
$898$	3.50006	−	3.50006i	0.116798	−	0.116798i
$899$	−30.9672	−	53.6368i	−1.03281	−	1.78889i
$900$	−3.94817	+	14.4711i	−0.131606	+	0.482369i
$901$	12.1669	+	7.02454i	0.405337	+	0.234021i
$902$	29.2926	+	7.84892i	0.975336	+	0.261340i
$903$	−0.542794	+	0.431181i	−0.0180630	+	0.0143488i
$904$	10.5378	+	6.08403i	0.350484	+	0.202352i
$905$	−6.11116	−	1.80961i	−0.203142	−	0.0601534i
$906$	−2.70580	−	6.11621i	−0.0898941	−	0.203198i
$907$	−23.3251	+	6.24994i	−0.774497	+	0.207526i	−0.624357	−	0.781139i	$-0.714639\pi$
$907$	−23.3251	+	6.24994i	−0.774497	+	0.207526i	−0.150140	+	0.988665i	$0.547972\pi$
$908$	17.1847	−	4.60463i	0.570295	−	0.152810i
$909$	−8.28788	−	1.80266i	−0.274892	−	0.0597906i
$910$	−1.61609	−	0.0535146i	−0.0535727	−	0.00177399i
$911$	−4.81298	−	8.33632i	−0.159461	−	0.276195i	0.775213	−	0.631699i	$-0.217642\pi$
$911$	−4.81298	−	8.33632i	−0.159461	−	0.276195i	−0.934674	+	0.355505i	$0.884309\pi$
$912$	−11.7746	−	4.55183i	−0.389896	−	0.150726i
$913$	−35.6990	−	35.6990i	−1.18146	−	1.18146i
$914$			7.13709i			0.236074i
$915$	−2.10373	+	15.7033i	−0.0695471	+	0.519134i
$916$	−19.0524	+	10.9999i	−0.629508	+	0.363447i
$917$	−9.08409	−	2.50247i	−0.299983	−	0.0826390i
$918$	−5.48537	+	8.31693i	−0.181044	+	0.274499i
$919$	46.8830	+	27.0679i	1.54653	+	0.892888i	0.998403	+	0.0564915i	$0.0179914\pi$
$919$	46.8830	+	27.0679i	1.54653	+	0.892888i	0.548125	+	0.836397i	$0.315342\pi$
$920$	−2.16404	−	9.01028i	−0.0713462	−	0.297060i
$921$	22.2377	+	16.2371i	0.732756	+	0.535031i
$922$	−2.62840	−	0.704279i	−0.0865619	−	0.0231942i
$923$	−0.928032	+	0.248665i	−0.0305465	+	0.00818492i
$924$	−27.1162	+	11.7695i	−0.892056	+	0.387187i
$925$	15.3213	+	4.97513i	0.503761	+	0.163581i
$926$	−7.92902	+	13.7335i	−0.260564	+	0.451310i
$927$	0.141102	+	2.96027i	0.00463439	+	0.0972280i
$928$	−7.20712	−	1.93114i	−0.236585	−	0.0633929i
$929$	38.9978			1.27948			0.639738	−	0.768593i	$-0.279043\pi$
$929$	38.9978			1.27948			0.639738	+	0.768593i	$0.279043\pi$
$930$	25.5495	−	19.5126i	0.837802	−	0.639845i
$931$	−43.8212	−	26.1263i	−1.43618	−	0.856256i
$932$	11.1280	−	2.98175i	0.364511	−	0.0976703i
$933$	42.6073	−	6.64506i	1.39490	−	0.217550i
$934$	−7.50733	+	13.0031i	−0.245647	+	0.425474i
$935$	−13.1985	−	24.3034i	−0.431637	−	0.794806i
$936$	−0.174270	+	0.801221i	−0.00569621	+	0.0261887i
$937$	−30.6400	+	30.6400i	−1.00096	+	1.00096i	−0.000964165		1.00000i	$0.500307\pi$
$937$	−30.6400	+	30.6400i	−1.00096	+	1.00096i	−1.00000		0.000964165i	$0.999693\pi$
$938$	12.6167	−	12.4410i	0.411949	−	0.406212i
$939$	16.9711	−	23.2429i	0.553830	−	0.758502i
$940$	−22.5012	+	12.2198i	−0.733910	+	0.398566i
$941$		−	34.4828i		−	1.12411i	−0.827101	−	0.562054i	$-0.810011\pi$
$941$		−	34.4828i		−	1.12411i	0.827101	−	0.562054i	$-0.189989\pi$
$942$	−1.01694	−	6.52050i	−0.0331337	−	0.212449i
$943$	13.7763	+	13.7763i	0.448617	+	0.448617i
$944$	6.27798			0.204331
$945$	25.0878	+	17.7652i	0.816106	+	0.577903i
$946$	−0.975785			−0.0317255
$947$	34.1266	+	34.1266i	1.10897	+	1.10897i	0.993287	+	0.115679i	$0.0369045\pi$
$947$	34.1266	+	34.1266i	1.10897	+	1.10897i	0.115679	+	0.993287i	$0.463095\pi$
$948$	0.879505	+	5.63927i	0.0285650	+	0.183155i
$949$		−	0.707509i		−	0.0229667i
$950$	−34.6602	−	11.2549i	−1.12453	−	0.365156i
$951$	−17.6816	+	24.2160i	−0.573365	+	0.785256i
$952$	4.89071	+	1.34729i	0.158509	+	0.0436658i
$953$	−22.2775	+	22.2775i	−0.721638	+	0.721638i	−0.968939	−	0.247301i	$-0.920456\pi$
$953$	−22.2775	+	22.2775i	−0.721638	+	0.721638i	0.247301	+	0.968939i	$0.420456\pi$
$954$	−16.2659	−	14.7858i	−0.526627	−	0.478708i
$955$	0.362906	−	1.22556i	0.0117434	−	0.0396581i
$956$	−1.75365	+	3.03740i	−0.0567170	+	0.0982366i
$957$	82.3679	−	12.8462i	2.66258	−	0.415257i
$958$	−22.7344	+	6.09166i	−0.734514	+	0.196813i
$959$	26.4092	+	15.4953i	0.852797	+	0.500368i
$960$	0.514260	−	3.83869i	0.0165977	−	0.123893i
$961$	−37.9014			−1.22263
$962$	0.850562	+	0.227907i	0.0274232	+	0.00734803i
$963$	11.3286	−	7.28092i	0.365059	−	0.234624i
$964$	10.1905	−	17.6504i	0.328212	−	0.568481i
$965$	0.720838	+	1.32733i	0.0232046	+	0.0427283i
$966$	−18.8672	−	2.16208i	−0.607043	−	0.0695639i
$967$	−30.9125	+	8.28298i	−0.994079	+	0.266363i	−0.718963	−	0.695048i	$-0.755383\pi$
$967$	−30.9125	+	8.28298i	−0.994079	+	0.266363i	−0.275116	+	0.961411i	$0.588716\pi$
$968$	−29.5668	−	7.92241i	−0.950314	−	0.254636i
$969$	−19.5482	−	14.2733i	−0.627978	−	0.458526i
$970$	−8.28744	+	1.99043i	−0.266094	+	0.0639088i
$971$	17.4353	+	10.0663i	0.559524	+	0.323042i	0.752955	−	0.658073i	$-0.228628\pi$
$971$	17.4353	+	10.0663i	0.559524	+	0.323042i	−0.193430	+	0.981114i	$0.561961\pi$
$972$	11.1523	−	10.8916i	0.357710	−	0.349347i
$973$	−27.3387	+	7.12030i	−0.876439	+	0.228266i
$974$	20.3611	−	11.7555i	0.652413	−	0.376671i
$975$	−0.375388	+	2.33705i	−0.0120220	+	0.0748455i
$976$		−	4.09079i		−	0.130943i
$977$	11.7853	+	11.7853i	0.377046	+	0.377046i	0.870035	−	0.492989i	$-0.164096\pi$
$977$	11.7853	+	11.7853i	0.377046	+	0.377046i	−0.492989	+	0.870035i	$0.664096\pi$
$978$	4.53220	+	1.75206i	0.144924	+	0.0560246i
$979$	−52.2676	−	90.5301i	−1.67048	−	2.89335i
$980$	4.65422	−	14.9445i	0.148674	−	0.477385i
$981$	5.90408	−	6.49509i	0.188503	−	0.207372i
$982$	−12.0762	+	3.23580i	−0.385366	+	0.103259i
$983$	−7.67109	+	2.05546i	−0.244670	+	0.0655590i	−0.379070	−	0.925368i	$-0.623756\pi$
$983$	−7.67109	+	2.05546i	−0.244670	+	0.0655590i	0.134400	+	0.990927i	$0.457089\pi$
$984$	3.29439	+	7.44667i	0.105021	+	0.237391i
$985$	1.32789	−	0.721138i	0.0423100	−	0.0229774i
$986$	−12.3895	−	7.15311i	−0.394563	−	0.227801i
$987$	7.72255	+	51.9038i	0.245812	+	1.65212i
$988$	−1.92416	−	0.515578i	−0.0612158	−	0.0164027i
$989$	−0.542898	−	0.313442i	−0.0172631	−	0.00996688i
$990$	12.0972	+	41.5464i	0.384473	+	1.32043i
$991$	−17.9373	−	31.0683i	−0.569798	−	0.986918i	−0.996586	−	0.0825666i	$-0.973688\pi$
$991$	−17.9373	−	31.0683i	−0.569798	−	0.986918i	0.426788	−	0.904352i	$-0.359645\pi$
$992$	−5.86947	+	5.86947i	−0.186356	+	0.186356i
$993$	−4.01736	−	25.7588i	−0.127487	−	0.817430i
$994$	0.0652135	−	9.30013i	0.00206845	−	0.294982i
$995$	52.1367	−	12.5219i	1.65285	−	0.396971i
$996$	1.44888	−	13.4784i	0.0459095	−	0.427080i
$997$	7.23467	+	27.0001i	0.229124	+	0.855103i	0.980710	+	0.195468i	$0.0626225\pi$
$997$	7.23467	+	27.0001i	0.229124	+	0.855103i	−0.751586	+	0.659635i	$0.770711\pi$
$998$	−34.7433	−	9.30944i	−1.09978	−	0.294685i
$999$	−11.1132	−	12.5200i	−0.351606	−	0.396115i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.bw.a.607.12	yes	192
5.3	odd	4	inner	630.2.bw.a.103.23	✓	192
7.3	odd	6		630.2.cg.a.157.44	yes	192
9.7	even	3		630.2.cg.a.187.18	yes	192
35.3	even	12		630.2.cg.a.283.18	yes	192
45.43	odd	12		630.2.cg.a.313.44	yes	192
63.52	odd	6	inner	630.2.bw.a.367.23	yes	192
315.178	even	12	inner	630.2.bw.a.493.12	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.23	✓	192	5.3	odd	4	inner
630.2.bw.a.367.23	yes	192	63.52	odd	6	inner
630.2.bw.a.493.12	yes	192	315.178	even	12	inner
630.2.bw.a.607.12	yes	192	1.1	even	1	trivial
630.2.cg.a.157.44	yes	192	7.3	odd	6
630.2.cg.a.187.18	yes	192	9.7	even	3
630.2.cg.a.283.18	yes	192	35.3	even	12
630.2.cg.a.313.44	yes	192	45.43	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.266905 - 1.71136i) q^{3} +1.00000i q^{4} +(-0.634884 + 2.14404i) q^{5} +(-1.02139 + 1.39885i) q^{6} +(-1.85766 - 1.88390i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.85752 + 0.913543i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.266905 - 1.71136i) q^{3} +1.00000i q^{4} +(-0.634884 + 2.14404i) q^{5} +(-1.02139 + 1.39885i) q^{6} +(-1.85766 - 1.88390i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.85752 + 0.913543i) q^{9} +(1.96500 - 1.06714i) q^{10} +(3.22528 - 5.58636i) q^{11} +(1.71136 - 0.266905i) q^{12} +(0.264005 - 0.0707399i) q^{13} +(-0.0185518 + 2.64569i) q^{14} +(3.83869 + 0.514260i) q^{15} -1.00000 q^{16} +(-1.85204 - 0.496253i) q^{17} +(2.66655 + 1.37460i) q^{18} +(-3.64418 + 6.31190i) q^{19} +(-2.14404 - 0.634884i) q^{20} +(-2.72822 + 3.68196i) q^{21} +(-6.23077 + 1.66953i) q^{22} +(-4.00290 - 1.07257i) q^{23} +(-1.39885 - 1.02139i) q^{24} +(-4.19384 - 2.72244i) q^{25} +(-0.236700 - 0.136659i) q^{26} +(2.32609 + 4.64643i) q^{27} +(1.88390 - 1.85766i) q^{28} +(-6.46173 + 3.73068i) q^{29} +(-2.35073 - 3.07800i) q^{30} +8.30069i q^{31} +(0.707107 + 0.707107i) q^{32} +(-10.4211 - 4.02860i) q^{33} +(0.958686 + 1.66049i) q^{34} +(5.21857 - 2.78686i) q^{35} +(-0.913543 - 2.85752i) q^{36} +(-3.11198 + 0.833854i) q^{37} +(7.04001 - 1.88637i) q^{38} +(-0.191526 - 0.432928i) q^{39} +(1.06714 + 1.96500i) q^{40} +(-4.07142 - 2.35064i) q^{41} +(4.53268 - 0.674398i) q^{42} +(0.146117 + 0.0391519i) q^{43} +(5.58636 + 3.22528i) q^{44} +(-0.144480 - 6.70665i) q^{45} +(2.07205 + 3.58890i) q^{46} +(8.09709 - 8.09709i) q^{47} +(0.266905 + 1.71136i) q^{48} +(-0.0981647 + 6.99931i) q^{49} +(1.04044 + 4.89055i) q^{50} +(-0.354949 + 3.30196i) q^{51} +(0.0707399 + 0.264005i) q^{52} +(-7.07759 - 1.89643i) q^{53} +(1.64073 - 4.93032i) q^{54} +(9.92971 + 10.4618i) q^{55} +(-2.64569 - 0.0185518i) q^{56} +(11.7746 + 4.55183i) q^{57} +(7.20712 + 1.93114i) q^{58} -6.27798 q^{59} +(-0.514260 + 3.83869i) q^{60} +4.09079i q^{61} +(5.86947 - 5.86947i) q^{62} +(7.02934 + 3.68623i) q^{63} -1.00000i q^{64} +(-0.0159431 + 0.610950i) q^{65} +(4.52020 + 10.2175i) q^{66} +(-4.73557 - 4.73557i) q^{67} +(0.496253 - 1.85204i) q^{68} +(-0.767168 + 7.13669i) q^{69} +(-5.66069 - 1.71948i) q^{70} -3.51520 q^{71} +(-1.37460 + 2.66655i) q^{72} +(0.669977 - 2.50039i) q^{73} +(2.79013 + 1.61088i) q^{74} +(-3.53972 + 7.90382i) q^{75} +(-6.31190 - 3.64418i) q^{76} +(-16.5156 + 4.30146i) q^{77} +(-0.170697 + 0.441555i) q^{78} +3.29520i q^{79} +(0.634884 - 2.14404i) q^{80} +(7.33088 - 5.22094i) q^{81} +(1.21678 + 4.54108i) q^{82} +(2.02567 - 7.55991i) q^{83} +(-3.68196 - 2.72822i) q^{84} +(2.23982 - 3.65579i) q^{85} +(-0.0756356 - 0.131005i) q^{86} +(8.10922 + 10.0626i) q^{87} +(-1.66953 - 6.23077i) q^{88} +(8.10279 - 14.0344i) q^{89} +(-4.64015 + 4.84448i) q^{90} +(-0.623700 - 0.365948i) q^{91} +(1.07257 - 4.00290i) q^{92} +(14.2055 - 2.21550i) q^{93} -11.4510 q^{94} +(-11.2194 - 11.8206i) q^{95} +(1.02139 - 1.39885i) q^{96} +(-3.68177 - 0.986528i) q^{97} +(5.01867 - 4.87985i) q^{98} +(-4.11295 + 18.9096i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q+O(q^{10}) \) 192 * q	\( 192 q + 8 q^{11} - 12 q^{15} - 192 q^{16} + 36 q^{17} - 8 q^{18} + 8 q^{23} + 36 q^{27} + 12 q^{30} + 48 q^{35} - 16 q^{36} - 12 q^{41} + 4 q^{42} + 48 q^{45} + 12 q^{46} - 16 q^{50} - 24 q^{51} - 40 q^{53} - 4 q^{56} - 32 q^{57} - 12 q^{58} - 16 q^{60} - 12 q^{63} + 16 q^{65} - 36 q^{68} + 16 q^{71} - 8 q^{72} + 96 q^{75} - 64 q^{77} - 16 q^{78} + 16 q^{81} + 168 q^{83} + 8 q^{86} - 36 q^{87} - 36 q^{90} + 8 q^{92} - 48 q^{93} - 128 q^{95} - 48 q^{98}+O(q^{100}) \) 192 * q + 8 * q^11 - 12 * q^15 - 192 * q^16 + 36 * q^17 - 8 * q^18 + 8 * q^23 + 36 * q^27 + 12 * q^30 + 48 * q^35 - 16 * q^36 - 12 * q^41 + 4 * q^42 + 48 * q^45 + 12 * q^46 - 16 * q^50 - 24 * q^51 - 40 * q^53 - 4 * q^56 - 32 * q^57 - 12 * q^58 - 16 * q^60 - 12 * q^63 + 16 * q^65 - 36 * q^68 + 16 * q^71 - 8 * q^72 + 96 * q^75 - 64 * q^77 - 16 * q^78 + 16 * q^81 + 168 * q^83 + 8 * q^86 - 36 * q^87 - 36 * q^90 + 8 * q^92 - 48 * q^93 - 128 * q^95 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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