LMFDB - Embedded newform 630.2.cg.a.157.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(157,630)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([4, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("630.157"); 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.cg (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			157.5
Character	$\chi$	$=$	630.157
Dual form			630.2.cg.a.313.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.26782 + 1.18010i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.44041 + 1.71033i) q^{5} +(0.919188 - 1.46802i) q^{6} +(2.43402 - 1.03708i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.214733 - 2.99231i) q^{9} +(0.948666 - 2.02485i) q^{10} -1.00712 q^{11} +(-0.507915 + 1.65591i) q^{12} +(6.24485 - 1.67330i) q^{13} +(-2.08267 + 1.63172i) q^{14} +(-0.192172 - 3.86821i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.660546 + 2.46519i) q^{17} +(0.567049 + 2.94592i) q^{18} +(0.970602 + 1.68113i) q^{19} +(-0.392270 + 2.20139i) q^{20} +(-1.86204 + 4.18722i) q^{21} +(0.972806 - 0.260663i) q^{22} +(6.15284 - 6.15284i) q^{23} +(0.0620279 - 1.73094i) q^{24} +(-0.850430 - 4.92715i) q^{25} +(-5.59898 + 3.23257i) q^{26} +(3.25897 + 4.04711i) q^{27} +(1.58938 - 2.11515i) q^{28} +(-0.891458 + 0.514684i) q^{29} +(1.18679 + 3.68667i) q^{30} +(-8.57421 + 4.95032i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(1.27685 - 1.18851i) q^{33} +(-1.27608 - 2.21023i) q^{34} +(-1.73224 + 5.65680i) q^{35} +(-1.31019 - 2.69878i) q^{36} +(-2.50491 + 9.34846i) q^{37} +(-1.37264 - 1.37264i) q^{38} +(-5.94268 + 9.49098i) q^{39} +(-0.190859 - 2.22791i) q^{40} +(3.07498 + 1.77534i) q^{41} +(0.714857 - 4.52648i) q^{42} +(5.62656 + 1.50763i) q^{43} +(-0.872194 + 0.503562i) q^{44} +(4.80851 + 4.67741i) q^{45} +(-4.35072 + 7.53566i) q^{46} +(-0.303337 - 1.13207i) q^{47} +(0.388086 + 1.68801i) q^{48} +(4.84891 - 5.04857i) q^{49} +(2.09669 + 4.53915i) q^{50} +(-3.74662 - 2.34591i) q^{51} +(4.57154 - 4.57154i) q^{52} +(1.68862 + 6.30201i) q^{53} +(-4.19540 - 3.06572i) q^{54} +(1.45067 - 1.72251i) q^{55} +(-0.987783 + 2.45444i) q^{56} +(-3.21445 - 0.985965i) q^{57} +(0.727873 - 0.727873i) q^{58} +(2.19946 + 3.80957i) q^{59} +(-2.10053 - 3.25388i) q^{60} +(6.29136 + 3.63232i) q^{61} +(7.00081 - 7.00081i) q^{62} +(-2.58061 - 7.50603i) q^{63} -1.00000i q^{64} +(-6.13326 + 13.0910i) q^{65} +(-0.925735 + 1.47848i) q^{66} +(-0.510289 + 1.90442i) q^{67} +(1.80465 + 1.80465i) q^{68} +(-0.539731 + 15.0617i) q^{69} +(0.209127 - 5.91238i) q^{70} -0.160752 q^{71} +(1.96404 + 2.26772i) q^{72} +(-1.29040 + 0.345761i) q^{73} -9.67824i q^{74} +(6.89271 + 5.24314i) q^{75} +(1.68113 + 0.970602i) q^{76} +(-2.45136 + 1.04447i) q^{77} +(3.28374 - 10.7057i) q^{78} +(-7.71704 - 4.45544i) q^{79} +(0.760980 + 2.10260i) q^{80} +(-8.90778 - 1.28509i) q^{81} +(-3.42970 - 0.918985i) q^{82} +(0.351284 - 1.31101i) q^{83} +(0.481039 + 4.55726i) q^{84} +(-5.16774 - 2.42114i) q^{85} -5.82504 q^{86} +(0.522831 - 1.70454i) q^{87} +(0.712144 - 0.712144i) q^{88} +(8.81248 + 15.2637i) q^{89} +(-5.85527 - 3.27350i) q^{90} +(13.4647 - 10.5493i) q^{91} +(2.25210 - 8.40494i) q^{92} +(5.02868 - 16.3945i) q^{93} +(0.586003 + 1.01499i) q^{94} +(-4.27335 - 0.761475i) q^{95} +(-0.811752 - 1.53005i) q^{96} +(15.3828 + 4.12181i) q^{97} +(-3.37702 + 6.13153i) q^{98} +(-0.216263 + 3.01362i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{11} - 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 12 q^{30} - 60 q^{33} + 48 q^{35} - 16 q^{36} + 12 q^{41} + 4 q^{42} - 36 q^{45} + 12 q^{46} - 16 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) $ 192 * q - 16 * q^11 - 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 + 12 * q^21 - 16 * q^23 - 36 * q^27 + 12 * q^30 - 60 * q^33 + 48 * q^35 - 16 * q^36 + 12 * q^41 + 4 * q^42 - 36 * q^45 + 12 * q^46 - 16 * q^50 + 24 * q^51 - 40 * q^53 + 8 * q^56 - 32 * q^57 + 24 * q^58 + 8 * q^60 + 36 * q^61 - 108 * q^63 - 8 * q^65 + 16 * q^71 - 8 * q^72 + 80 * q^77 - 16 * q^78 + 4 * q^81 - 168 * q^83 - 16 * q^86 + 36 * q^90 + 8 * q^92 - 60 * q^93 + 64 * q^95 - 12 * q^96 - 48 * q^98

Character values

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

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

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−1.26782	+	1.18010i	−0.731976	+	0.681330i
$3$	−1.26782	+	1.18010i	−0.731976	+	0.681330i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−1.44041	+	1.71033i	−0.644172	+	0.764881i
$5$	−1.44041	+	1.71033i	−0.644172	+	0.764881i
$6$	0.919188	−	1.46802i	0.375257	−	0.599318i
$7$	2.43402	−	1.03708i	0.919973	−	0.391981i
$7$	2.43402	−	1.03708i	0.919973	−	0.391981i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.214733	−	2.99231i	0.0715777	−	0.997435i
$10$	0.948666	−	2.02485i	0.299994	−	0.640315i
$11$	−1.00712			−0.303659			−0.151830	−	0.988407i	$-0.548516\pi$
$11$	−1.00712			−0.303659			−0.151830	+	0.988407i	$0.548516\pi$
$12$	−0.507915	+	1.65591i	−0.146622	+	0.478019i
$13$	6.24485	−	1.67330i	1.73201	−	0.464090i	0.751364	−	0.659888i	$-0.229396\pi$
$13$	6.24485	−	1.67330i	1.73201	−	0.464090i	0.980644	+	0.195797i	$0.0627294\pi$
$14$	−2.08267	+	1.63172i	−0.556616	+	0.436095i
$15$	−0.192172	−	3.86821i	−0.0496187	−	0.998768i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	0.660546	+	2.46519i	0.160206	+	0.597897i	0.998603	+	0.0528371i	$0.0168264\pi$
$17$	0.660546	+	2.46519i	0.160206	+	0.597897i	−0.838397	+	0.545060i	$0.816507\pi$
$18$	0.567049	+	2.94592i	0.133655	+	0.694360i
$19$	0.970602	+	1.68113i	0.222671	+	0.385678i	0.955618	−	0.294608i	$-0.0951890\pi$
$19$	0.970602	+	1.68113i	0.222671	+	0.385678i	−0.732947	+	0.680286i	$0.761856\pi$
$20$	−0.392270	+	2.20139i	−0.0877142	+	0.492246i
$21$	−1.86204	+	4.18722i	−0.406330	+	0.913726i
$22$	0.972806	−	0.260663i	0.207403	−	0.0555735i
$23$	6.15284	−	6.15284i	1.28296	−	1.28296i	0.343979	−	0.938977i	$-0.388225\pi$
$23$	6.15284	−	6.15284i	1.28296	−	1.28296i	0.938977	−	0.343979i	$-0.111775\pi$
$24$	0.0620279	−	1.73094i	0.0126614	−	0.353327i
$25$	−0.850430	−	4.92715i	−0.170086	−	0.985429i
$26$	−5.59898	+	3.23257i	−1.09805	+	0.633959i
$27$	3.25897	+	4.04711i	0.627190	+	0.778867i
$28$	1.58938	−	2.11515i	0.300365	−	0.399726i
$29$	−0.891458	+	0.514684i	−0.165540	+	0.0955744i	−0.580481	−	0.814274i	$-0.697135\pi$
$29$	−0.891458	+	0.514684i	−0.165540	+	0.0955744i	0.414941	+	0.909848i	$0.363802\pi$
$30$	1.18679	+	3.68667i	0.216677	+	0.673091i
$31$	−8.57421	+	4.95032i	−1.53997	+	0.889104i	−0.541135	+	0.840936i	$0.682005\pi$
$31$	−8.57421	+	4.95032i	−1.53997	+	0.889104i	−0.998839	+	0.0481684i	$0.984662\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	1.27685	−	1.18851i	0.222271	−	0.206892i
$34$	−1.27608	−	2.21023i	−0.218845	−	0.379051i
$35$	−1.73224	+	5.65680i	−0.292802	+	0.956173i
$36$	−1.31019	−	2.69878i	−0.218365	−	0.449796i
$37$	−2.50491	+	9.34846i	−0.411805	+	1.53688i	0.379345	+	0.925255i	$0.376149\pi$
$37$	−2.50491	+	9.34846i	−0.411805	+	1.53688i	−0.791150	+	0.611622i	$0.790517\pi$
$38$	−1.37264	−	1.37264i	−0.222671	−	0.222671i
$39$	−5.94268	+	9.49098i	−0.951590	+	1.51977i
$40$	−0.190859	−	2.22791i	−0.0301774	−	0.352263i
$41$	3.07498	+	1.77534i	0.480232	+	0.277262i	0.720513	−	0.693441i	$-0.243906\pi$
$41$	3.07498	+	1.77534i	0.480232	+	0.277262i	−0.240281	+	0.970703i	$0.577240\pi$
$42$	0.714857	−	4.52648i	0.110305	−	0.698450i
$43$	5.62656	+	1.50763i	0.858042	+	0.229912i	0.660910	−	0.750465i	$-0.270170\pi$
$43$	5.62656	+	1.50763i	0.858042	+	0.229912i	0.197132	+	0.980377i	$0.436837\pi$
$44$	−0.872194	+	0.503562i	−0.131488	+	0.0759148i
$45$	4.80851	+	4.67741i	0.716811	+	0.697268i
$46$	−4.35072	+	7.53566i	−0.641478	+	1.11107i
$47$	−0.303337	−	1.13207i	−0.0442463	−	0.165130i	0.940267	−	0.340437i	$-0.110575\pi$
$47$	−0.303337	−	1.13207i	−0.0442463	−	0.165130i	−0.984514	+	0.175307i	$0.943908\pi$
$48$	0.388086	+	1.68801i	0.0560154	+	0.243644i
$49$	4.84891	−	5.04857i	0.692702	−	0.721224i
$50$	2.09669	+	4.53915i	0.296517	+	0.641933i
$51$	−3.74662	−	2.34591i	−0.524632	−	0.328493i
$52$	4.57154	−	4.57154i	0.633959	−	0.633959i
$53$	1.68862	+	6.30201i	0.231950	+	0.865648i	0.979500	+	0.201443i	$0.0645631\pi$
$53$	1.68862	+	6.30201i	0.231950	+	0.865648i	−0.747551	+	0.664205i	$0.768770\pi$
$54$	−4.19540	−	3.06572i	−0.570921	−	0.417192i
$55$	1.45067	−	1.72251i	0.195609	−	0.232263i
$56$	−0.987783	+	2.45444i	−0.131998	+	0.327989i
$57$	−3.21445	−	0.985965i	−0.425764	−	0.130594i
$58$	0.727873	−	0.727873i	0.0955744	−	0.0955744i
$59$	2.19946	+	3.80957i	0.286345	+	0.495964i	0.972934	−	0.231081i	$-0.0742263\pi$
$59$	2.19946	+	3.80957i	0.286345	+	0.495964i	−0.686589	+	0.727045i	$0.740893\pi$
$60$	−2.10053	−	3.25388i	−0.271178	−	0.420075i
$61$	6.29136	+	3.63232i	0.805526	+	0.465070i	0.845400	−	0.534134i	$-0.179362\pi$
$61$	6.29136	+	3.63232i	0.805526	+	0.465070i	−0.0398740	+	0.999205i	$0.512696\pi$
$62$	7.00081	−	7.00081i	0.889104	−	0.889104i
$63$	−2.58061	−	7.50603i	−0.325126	−	0.945671i
$64$		−	1.00000i		−	0.125000i
$65$	−6.13326	+	13.0910i	−0.760737	+	1.62373i
$66$	−0.925735	+	1.47848i	−0.113950	+	0.181988i
$67$	−0.510289	+	1.90442i	−0.0623417	+	0.232662i	−0.990066	−	0.140604i	$-0.955096\pi$
$67$	−0.510289	+	1.90442i	−0.0623417	+	0.232662i	0.927724	+	0.373266i	$0.121762\pi$
$68$	1.80465	+	1.80465i	0.218845	+	0.218845i
$69$	−0.539731	+	15.0617i	−0.0649760	+	1.81321i
$70$	0.209127	−	5.91238i	0.0249955	−	0.706665i
$71$	−0.160752			−0.0190777			−0.00953885	−	0.999955i	$-0.503036\pi$
$71$	−0.160752			−0.0190777			−0.00953885	+	0.999955i	$0.503036\pi$
$72$	1.96404	+	2.26772i	0.231464	+	0.267253i
$73$	−1.29040	+	0.345761i	−0.151029	+	0.0404682i	−0.333542	−	0.942735i	$-0.608244\pi$
$73$	−1.29040	+	0.345761i	−0.151029	+	0.0404682i	0.182512	+	0.983204i	$0.441577\pi$
$74$		−	9.67824i		−	1.12507i
$75$	6.89271	+	5.24314i	0.795902	+	0.605426i
$76$	1.68113	+	0.970602i	0.192839	+	0.111336i
$77$	−2.45136	+	1.04447i	−0.279358	+	0.119029i
$78$	3.28374	−	10.7057i	0.371810	−	1.21218i
$79$	−7.71704	−	4.45544i	−0.868235	−	0.501276i	−0.00147384	−	0.999999i	$-0.500469\pi$
$79$	−7.71704	−	4.45544i	−0.868235	−	0.501276i	−0.866761	+	0.498723i	$0.833802\pi$
$80$	0.760980	+	2.10260i	0.0850802	+	0.235077i
$81$	−8.90778	−	1.28509i	−0.989753	−	0.142788i
$82$	−3.42970	−	0.918985i	−0.378747	−	0.101485i
$83$	0.351284	−	1.31101i	0.0385584	−	0.143902i	−0.943963	−	0.330051i	$-0.892934\pi$
$83$	0.351284	−	1.31101i	0.0385584	−	0.143902i	0.982522	+	0.186149i	$0.0596007\pi$
$84$	0.481039	+	4.55726i	0.0524857	+	0.497238i
$85$	−5.16774	−	2.42114i	−0.560520	−	0.262610i
$86$	−5.82504			−0.628131
$87$	0.522831	−	1.70454i	0.0560533	−	0.182745i
$88$	0.712144	−	0.712144i	0.0759148	−	0.0759148i
$89$	8.81248	+	15.2637i	0.934121	+	1.61794i	0.776194	+	0.630494i	$0.217147\pi$
$89$	8.81248	+	15.2637i	0.934121	+	1.61794i	0.157926	+	0.987451i	$0.449519\pi$
$90$	−5.85527	−	3.27350i	−0.617200	−	0.345057i
$91$	13.4647	−	10.5493i	1.41149	−	1.10587i
$92$	2.25210	−	8.40494i	0.234797	−	0.876275i
$93$	5.02868	−	16.3945i	0.521450	−	1.70003i
$94$	0.586003	+	1.01499i	0.0604416	+	0.104688i
$95$	−4.27335	−	0.761475i	−0.438436	−	0.0781257i
$96$	−0.811752	−	1.53005i	−0.0828491	−	0.156160i
$97$	15.3828	+	4.12181i	1.56189	+	0.418507i	0.933261	−	0.359200i	$-0.116950\pi$
$97$	15.3828	+	4.12181i	1.56189	+	0.418507i	0.628627	+	0.777707i	$0.283617\pi$
$98$	−3.37702	+	6.13153i	−0.341131	+	0.619378i
$99$	−0.216263	+	3.01362i	−0.0217352	+	0.302880i
$100$	−3.20007	−	3.84182i	−0.320007	−	0.384182i
$101$		−	18.7048i		−	1.86120i	−0.366040	−	0.930599i	$-0.619287\pi$
$101$		−	18.7048i		−	1.86120i	0.366040	−	0.930599i	$-0.380713\pi$
$102$	4.22613	+	1.29628i	0.418449	+	0.128350i
$103$	2.07248	+	2.07248i	0.204208	+	0.204208i	0.801800	−	0.597592i	$-0.203876\pi$
$103$	2.07248	+	2.07248i	0.204208	+	0.204208i	−0.597592	+	0.801800i	$0.703876\pi$
$104$	−3.23257	+	5.59898i	−0.316980	+	0.549025i
$105$	−4.47941	−	9.21601i	−0.437146	−	0.899391i
$106$	−3.26216	−	5.65023i	−0.316849	−	0.548799i
$107$	−1.06183	+	3.96280i	−0.102651	+	0.383099i	−0.998068	−	0.0621295i	$-0.980211\pi$
$107$	−1.06183	+	3.96280i	−0.102651	+	0.383099i	0.895417	+	0.445228i	$0.146877\pi$
$108$	4.84591	+	1.87541i	0.466298	+	0.180462i
$109$	−0.761082	−	0.439411i	−0.0728984	−	0.0420879i	0.463108	−	0.886302i	$-0.346734\pi$
$109$	−0.761082	−	0.439411i	−0.0728984	−	0.0420879i	−0.536006	+	0.844214i	$0.680068\pi$
$110$	−0.955423	+	2.03928i	−0.0910960	+	0.194438i
$111$	−7.85633	−	14.8082i	−0.745690	−	1.40553i
$112$	0.318869	−	2.62647i	0.0301303	−	0.248178i
$113$	−1.76771	−	6.59718i	−0.166292	−	0.620611i	−0.997872	−	0.0652054i	$-0.979230\pi$
$113$	−1.76771	−	6.59718i	−0.166292	−	0.620611i	0.831580	−	0.555405i	$-0.187437\pi$
$114$	3.36011	+	0.120409i	0.314703	+	0.0112773i
$115$	1.66074	+	19.3860i	0.154865	+	1.80775i
$116$	−0.514684	+	0.891458i	−0.0477872	+	0.0827698i
$117$	−3.66605	−	19.0458i	−0.338927	−	1.76078i
$118$	−3.11050	−	3.11050i	−0.286345	−	0.286345i
$119$	4.16440	+	5.31529i	0.381749	+	0.487252i
$120$	2.87113	+	2.59935i	0.262097	+	0.237287i
$121$	−9.98570			−0.907791
$122$	−7.01710	−	1.88023i	−0.635298	−	0.170228i
$123$	−5.99361	+	1.37797i	−0.540425	+	0.124247i
$124$	−4.95032	+	8.57421i	−0.444552	+	0.769987i
$125$	9.65200	+	5.64260i	0.863301	+	0.504690i
$126$	4.43538	+	6.58236i	0.395135	+	0.586403i
$127$	−9.72634	−	9.72634i	−0.863073	−	0.863073i	0.128621	−	0.991694i	$-0.458945\pi$
$127$	−9.72634	−	9.72634i	−0.863073	−	0.863073i	−0.991694	+	0.128621i	$0.958945\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−8.91262	+	4.72849i	−0.784712	+	0.416321i
$130$	2.53608	−	14.2323i	0.222429	−	1.24826i
$131$		−	15.5635i		−	1.35979i	−0.733311	−	0.679894i	$-0.762026\pi$
$131$		−	15.5635i		−	1.35979i	0.733311	−	0.679894i	$-0.237974\pi$
$132$	0.511533	−	1.66770i	0.0445232	−	0.145155i
$133$	4.10594	+	3.08531i	0.356030	+	0.267531i
$134$		−	1.97160i		−	0.170321i
$135$	−11.6161	−	0.255595i	−0.999758	−	0.0219981i
$136$	−2.21023	−	1.27608i	−0.189526	−	0.109423i
$137$	11.0705	+	11.0705i	0.945818	+	0.945818i	0.998606	−	0.0527878i	$-0.0168107\pi$
$137$	11.0705	+	11.0705i	0.945818	+	0.945818i	−0.0527878	+	0.998606i	$0.516811\pi$
$138$	−3.37690	−	14.6881i	−0.287461	−	1.25034i
$139$	3.24421	−	5.61914i	0.275171	−	0.476609i	−0.695008	−	0.719002i	$-0.744599\pi$
$139$	3.24421	−	5.61914i	0.275171	−	0.476609i	0.970178	+	0.242393i	$0.0779323\pi$
$140$	1.32824	+	5.76505i	0.112256	+	0.487236i
$141$	1.72053	+	1.07729i	0.144895	+	0.0907245i
$142$	0.155274	−	0.0416055i	0.0130303	−	0.00349146i
$143$	−6.28933	+	1.68522i	−0.525940	+	0.140925i
$144$	−2.48405	−	1.68212i	−0.207004	−	0.140176i
$145$	0.403790	−	2.26604i	0.0335329	−	0.188184i
$146$	1.15694	−	0.667958i	0.0957489	−	0.0552806i
$147$	−0.189736	+	12.1229i	−0.0156492	+	0.999878i
$148$	2.50491	+	9.34846i	0.205903	+	0.768439i
$149$			4.62497i			0.378893i	0.981891	+	0.189446i	$0.0606693\pi$
$149$			4.62497i			0.378893i	−0.981891	+	0.189446i	$0.939331\pi$
$150$	−8.01487	−	3.28052i	−0.654412	−	0.267853i
$151$	8.83337			0.718850			0.359425	−	0.933174i	$-0.382973\pi$
$151$	8.83337			0.718850			0.359425	+	0.933174i	$0.382973\pi$
$152$	−1.87506	−	0.502420i	−0.152087	−	0.0407517i
$153$	7.51845	−	1.44720i	0.607831	−	0.116999i
$154$	2.09750	−	1.64334i	0.169022	−	0.132424i
$155$	3.88372	−	21.7952i	0.311948	−	1.75063i
$156$	−0.401019	+	11.1908i	−0.0321072	+	0.895979i
$157$	8.39117	+	2.24841i	0.669689	+	0.179442i	0.577615	−	0.816310i	$-0.303984\pi$
$157$	8.39117	+	2.24841i	0.669689	+	0.179442i	0.0920740	+	0.995752i	$0.470650\pi$
$158$	8.60724	+	2.30630i	0.684756	+	0.183480i
$159$	−9.57786	−	5.99708i	−0.759574	−	0.475599i
$160$	−1.27924	−	1.83400i	−0.101133	−	0.144990i
$161$	8.59513	−	21.3572i	0.677391	−	1.68318i
$162$	8.93686	−	1.06420i	0.702146	−	0.0836113i
$163$	−12.4411	−	3.33358i	−0.974461	−	0.261106i	−0.263751	−	0.964591i	$-0.584960\pi$
$163$	−12.4411	−	3.33358i	−0.974461	−	0.261106i	−0.710710	+	0.703485i	$0.751626\pi$
$164$	3.55069			0.277262
$165$	0.193541	+	3.89577i	0.0150672	+	0.303285i
$166$			1.35726i			0.105344i
$167$	−2.51776	−	9.39639i	−0.194830	−	0.727115i	−0.992311	−	0.123771i	$-0.960501\pi$
$167$	−2.51776	−	9.39639i	−0.194830	−	0.727115i	0.797481	−	0.603344i	$-0.206165\pi$
$168$	−1.64415	−	4.27747i	−0.126849	−	0.330014i
$169$	24.9398	−	14.3990i	1.91845	−	1.10762i
$170$	5.61829	+	1.00113i	0.430903	+	0.0767834i
$171$	5.23888	−	2.54334i	0.400627	−	0.194494i
$172$	5.62656	−	1.50763i	0.429021	−	0.114956i
$173$	3.25853	−	0.873121i	0.247742	−	0.0663821i	−0.132811	−	0.991141i	$-0.542400\pi$
$173$	3.25853	−	0.873121i	0.247742	−	0.0663821i	0.380553	+	0.924759i	$0.375734\pi$
$174$	−0.0638495	+	1.78177i	−0.00484042	+	0.135076i
$175$	−7.17983	−	11.1108i	−0.542744	−	0.839898i
$176$	−0.503562	+	0.872194i	−0.0379574	+	0.0657441i
$177$	−7.28419	−	2.23427i	−0.547513	−	0.167938i
$178$	−12.4627	−	12.4627i	−0.934121	−	0.934121i
$179$	−14.7822	−	8.53453i	−1.10488	−	0.637901i	−0.167379	−	0.985893i	$-0.553530\pi$
$179$	−14.7822	−	8.53453i	−1.10488	−	0.637901i	−0.937498	+	0.347992i	$0.886864\pi$
$180$	6.50300	+	1.64650i	0.484705	+	0.122723i
$181$			14.0499i			1.04432i	0.852846	+	0.522162i	$0.174874\pi$
$181$			14.0499i			1.04432i	−0.852846	+	0.522162i	$0.825126\pi$
$182$	−10.2756	+	13.6748i	−0.761676	+	1.01364i
$183$	−12.2628	+	2.81930i	−0.906492	+	0.208409i
$184$			8.70143i			0.641478i
$185$	−12.3808	−	17.7498i	−0.910255	−	1.30499i
$186$	−0.614116	+	17.1374i	−0.0450292	+	1.25658i
$187$	−0.665252	−	2.48275i	−0.0486480	−	0.181557i
$188$	−0.828733	−	0.828733i	−0.0604416	−	0.0604416i
$189$	12.1296	+	6.47092i	0.882299	+	0.470690i
$190$	4.32482	−	0.370495i	0.313756	−	0.0268786i
$191$	−6.87365	+	11.9055i	−0.497360	+	0.861452i	−0.999995	−	0.00304629i	$-0.999030\pi$
$191$	−6.87365	+	11.9055i	−0.497360	+	0.861452i	0.502636	+	0.864498i	$0.332364\pi$
$192$	1.18010	+	1.26782i	0.0851663	+	0.0914970i
$193$	−4.99207	−	1.33762i	−0.359337	−	0.0962841i	0.0746336	−	0.997211i	$-0.476221\pi$
$193$	−4.99207	−	1.33762i	−0.359337	−	0.0962841i	−0.433971	+	0.900927i	$0.642888\pi$
$194$	−15.9255			−1.14338
$195$	−7.67277	−	23.8348i	−0.549459	−	1.70685i
$196$	1.67500	−	6.79665i	0.119643	−	0.485475i
$197$	7.13746	+	7.13746i	0.508523	+	0.508523i	0.914073	−	0.405550i	$-0.132920\pi$
$197$	7.13746	+	7.13746i	0.508523	+	0.508523i	−0.405550	+	0.914073i	$0.632920\pi$
$198$	−0.571089	−	2.96691i	−0.0405855	−	0.210849i
$199$	−0.0161375	+	0.0279509i	−0.00114396	+	0.00198139i	−0.866597	−	0.499009i	$-0.833697\pi$
$199$	−0.0161375	+	0.0279509i	−0.00114396	+	0.00198139i	0.865453	+	0.500990i	$0.167031\pi$
$200$	4.08536	+	2.88267i	0.288879	+	0.203836i
$201$	−1.60045	−	3.01666i	−0.112887	−	0.212779i
$202$	4.84116	+	18.0675i	0.340623	+	1.27122i
$203$	−1.63606	+	2.17727i	−0.114829	+	0.152814i
$204$	−4.41763	−	0.158305i	−0.309296	−	0.0110835i
$205$	−7.46566	+	2.70200i	−0.521424	+	0.188716i
$206$	−2.53826	−	1.46547i	−0.176849	−	0.102104i
$207$	−17.0900	−	19.7324i	−1.18783	−	1.37150i
$208$	1.67330	−	6.24485i	0.116023	−	0.433002i
$209$	−0.977516	−	1.69311i	−0.0676162	−	0.117115i
$210$	6.71206	+	7.74263i	0.463176	+	0.534292i
$211$	5.38928	−	9.33451i	0.371013	−	0.642614i	−0.618708	−	0.785621i	$-0.712344\pi$
$211$	5.38928	−	9.33451i	0.371013	−	0.642614i	0.989722	+	0.143007i	$0.0456771\pi$
$212$	4.61339	+	4.61339i	0.316849	+	0.316849i
$213$	0.203804	−	0.189703i	0.0139644	−	0.0129982i
$214$		−	4.10260i		−	0.280448i
$215$	−10.6831	+	7.45164i	−0.728582	+	0.508198i
$216$	−5.16618	−	0.557296i	−0.351514	−	0.0379192i
$217$	−15.7359	+	20.9414i	−1.06822	+	1.42159i
$218$	0.848876	+	0.227456i	0.0574932	+	0.0154052i
$219$	1.22796	−	1.96116i	0.0829777	−	0.132523i
$220$	0.395064	−	2.21707i	0.0266352	−	0.149475i
$221$	8.25002	+	14.2895i	0.554956	+	0.961213i
$222$	11.4213	+	12.2703i	0.766546	+	0.823526i
$223$	1.99521	−	7.44621i	0.133609	−	0.498635i	−0.866391	−	0.499367i	$-0.833566\pi$
$223$	1.99521	−	7.44621i	0.133609	−	0.498635i	1.00000		0.000731290i	$0.000232777\pi$
$224$	0.371776	+	2.61950i	0.0248403	+	0.175023i
$225$	−14.9261	+	1.48673i	−0.995076	+	0.0991151i
$226$	3.41495	+	5.91487i	0.227159	+	0.393451i
$227$	−0.503456	+	0.503456i	−0.0334155	+	0.0334155i	−0.723617	−	0.690202i	$-0.757522\pi$
$227$	−0.503456	+	0.503456i	−0.0334155	+	0.0334155i	0.690202	+	0.723617i	$0.257522\pi$
$228$	−3.27678	+	0.753354i	−0.217010	+	0.0498921i
$229$	16.9498			1.12007			0.560036	−	0.828468i	$-0.310787\pi$
$229$	16.9498			1.12007			0.560036	+	0.828468i	$0.310787\pi$
$230$	−6.62162	−	18.2956i	−0.436617	−	1.20638i
$231$	1.87530	−	4.21705i	0.123386	−	0.277461i
$232$	0.266420	−	0.994293i	0.0174913	−	0.0652785i
$233$	26.3528	+	7.06121i	1.72643	+	0.462595i	0.979355	−	0.202147i	$-0.0647919\pi$
$233$	26.3528	+	7.06121i	1.72643	+	0.462595i	0.747073	+	0.664742i	$0.231459\pi$
$234$	8.47055	+	17.4480i	0.553737	+	1.14061i
$235$	2.37314	+	1.11184i	0.154807	+	0.0725286i
$236$	3.80957	+	2.19946i	0.247982	+	0.143173i
$237$	15.0417	−	3.45818i	0.977062	−	0.224633i
$238$	−5.39819	−	4.05635i	−0.349913	−	0.262934i
$239$	−11.6795	−	6.74318i	−0.755486	−	0.436180i	0.0721870	−	0.997391i	$-0.477002\pi$
$239$	−11.6795	−	6.74318i	−0.755486	−	0.436180i	−0.827673	+	0.561211i	$0.810335\pi$
$240$	−3.44606	−	1.76768i	−0.222442	−	0.114103i
$241$			17.4148i			1.12179i	0.827888	+	0.560894i	$0.189543\pi$
$241$			17.4148i			1.12179i	−0.827888	+	0.560894i	$0.810457\pi$
$242$	9.64545	−	2.58449i	0.620033	−	0.166137i
$243$	12.8100	−	8.88279i	0.821762	−	0.569832i
$244$	7.26463			0.465070
$245$	1.65027	+	15.5652i	0.105432	+	0.994427i
$246$	5.43273	−	2.88228i	0.346378	−	0.183767i
$247$	8.87430	+	8.87430i	0.564658	+	0.564658i
$248$	2.56248	−	9.56329i	0.162717	−	0.607270i
$249$	1.10176	+	2.07667i	0.0698210	+	0.131604i
$250$	−10.7835	−	2.95222i	−0.682010	−	0.186715i
$251$		−	0.469533i		−	0.0296367i	−0.999890	−	0.0148183i	$-0.995283\pi$
$251$		−	0.469533i		−	0.0296367i	0.999890	−	0.0148183i	$-0.00471700\pi$
$252$	−5.98789	−	5.21011i	−0.377201	−	0.328206i
$253$	−6.19667	+	6.19667i	−0.389581	+	0.389581i
$254$	11.9123	+	6.87756i	0.747443	+	0.431537i
$255$	9.40895	−	3.02888i	0.589211	−	0.189676i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.29313	+	5.29313i	−0.330176	+	0.330176i	−0.852653	−	0.522477i	$-0.825008\pi$
$257$	−5.29313	+	5.29313i	−0.330176	+	0.330176i	0.522477	+	0.852653i	$0.325008\pi$
$258$	7.38511	−	6.87413i	0.459777	−	0.427965i
$259$	3.59813	+	25.3522i	0.223577	+	1.57531i
$260$	1.23393	+	14.4037i	0.0765249	+	0.893282i
$261$	1.34867	+	2.77803i	0.0834803	+	0.171956i
$262$	4.02813	+	15.0332i	0.248858	+	0.928752i
$263$	13.7908	−	13.7908i	0.850379	−	0.850379i	−0.139801	−	0.990180i	$-0.544646\pi$
$263$	13.7908	−	13.7908i	0.850379	−	0.850379i	0.990180	+	0.139801i	$0.0446462\pi$
$264$	−0.0624697	+	1.74327i	−0.00384475	+	0.107291i
$265$	−13.2108	−	6.18940i	−0.811533	−	0.380212i
$266$	−4.76457	−	1.91749i	−0.292135	−	0.117569i
$267$	−29.1853	−	8.95197i	−1.78611	−	0.547852i
$268$	0.510289	+	1.90442i	0.0311709	+	0.116331i
$269$	−4.98051	+	8.62650i	−0.303667	+	0.525967i	−0.976964	−	0.213406i	$-0.931544\pi$
$269$	−4.98051	+	8.62650i	−0.303667	+	0.525967i	0.673297	+	0.739373i	$0.264878\pi$
$270$	11.2865	−	2.75959i	0.686873	−	0.167943i
$271$	−21.1335	+	12.2014i	−1.28377	+	0.741185i	−0.977535	−	0.210771i	$-0.932403\pi$
$271$	−21.1335	+	12.2014i	−1.28377	+	0.741185i	−0.306235	+	0.951956i	$0.599069\pi$
$272$	2.46519	+	0.660546i	0.149474	+	0.0400515i
$273$	−4.62165	+	29.2643i	−0.279715	+	1.77116i
$274$	−13.5586	−	7.82804i	−0.819102	−	0.472909i
$275$	0.856488	+	4.96224i	0.0516482	+	0.299235i
$276$	7.06341	+	13.3136i	0.425167	+	0.801387i
$277$	3.72475	+	3.72475i	0.223799	+	0.223799i	0.810096	−	0.586297i	$-0.199415\pi$
$277$	3.72475	+	3.72475i	0.223799	+	0.223799i	−0.586297	+	0.810096i	$0.699415\pi$
$278$	−1.67933	+	6.26734i	−0.100719	+	0.375890i
$279$	12.9717	+	26.7197i	0.776596	+	1.59966i
$280$	−2.77508	−	5.22484i	−0.165843	−	0.312244i
$281$	−6.02787	−	10.4406i	−0.359593	−	0.622833i	0.628300	−	0.777971i	$-0.283751\pi$
$281$	−6.02787	−	10.4406i	−0.359593	−	0.622833i	−0.987893	+	0.155138i	$0.950418\pi$
$282$	−1.94073	−	0.595279i	−0.115569	−	0.0354483i
$283$	−6.24112	+	23.2922i	−0.370996	+	1.38458i	0.488111	+	0.872782i	$0.337686\pi$
$283$	−6.24112	+	23.2922i	−0.370996	+	1.38458i	−0.859107	+	0.511796i	$0.828981\pi$
$284$	−0.139215	+	0.0803758i	−0.00826088	+	0.00476942i
$285$	6.31645	−	4.07756i	0.374154	−	0.241534i
$286$	5.63886	−	3.25560i	0.333433	−	0.192507i
$287$	9.32576	+	1.13220i	0.550482	+	0.0668319i
$288$	2.83477	+	0.981882i	0.167040	+	0.0578579i
$289$	9.08158	−	5.24325i	0.534211	−	0.308427i
$290$	0.196464	+	2.29334i	0.0115367	+	0.134669i
$291$	−24.3668	+	12.9275i	−1.42841	+	0.757825i
$292$	−0.944636	+	0.944636i	−0.0552806	+	0.0552806i
$293$	−3.00845	+	0.806113i	−0.175756	+	0.0470936i	−0.345624	−	0.938373i	$-0.612333\pi$
$293$	−3.00845	+	0.806113i	−0.175756	+	0.0470936i	0.169868	+	0.985467i	$0.445666\pi$
$294$	−2.95436	−	11.7589i	−0.172302	−	0.685793i
$295$	−9.68374	−	1.72556i	−0.563809	−	0.100466i
$296$	−4.83912	−	8.38160i	−0.281268	−	0.487171i
$297$	−3.28219	−	4.07594i	−0.190452	−	0.236510i
$298$	−1.19703	−	4.46738i	−0.0693422	−	0.258788i
$299$	28.1280	−	48.7191i	1.62668	−	2.81750i
$300$	8.59083	+	1.09434i	0.495992	+	0.0631815i
$301$	15.2587	−	2.16561i	0.879497	−	0.124824i
$302$	−8.53238	+	2.28625i	−0.490984	+	0.131559i
$303$	22.0735	+	23.7143i	1.26809	+	1.36235i
$304$	1.94120			0.111336
$305$	−15.2746	+	5.52824i	−0.874620	+	0.316546i
$306$	−6.88770	+	3.34380i	−0.393744	+	0.191153i
$307$	0.932254	−	0.932254i	0.0532065	−	0.0532065i	−0.680003	−	0.733209i	$-0.738021\pi$
$307$	0.932254	−	0.932254i	0.0532065	−	0.0532065i	0.733209	+	0.680003i	$0.238021\pi$
$308$	−1.60070	+	2.13022i	−0.0912085	+	0.121380i
$309$	−5.07327	−	0.181800i	−0.288608	−	0.0103422i
$310$	1.88962	+	22.0577i	0.107323	+	1.25279i
$311$	11.2845	−	6.51510i	0.639884	−	0.369437i	−0.144686	−	0.989478i	$-0.546217\pi$
$311$	11.2845	−	6.51510i	0.639884	−	0.369437i	0.784570	+	0.620040i	$0.212884\pi$
$312$	−2.50903	−	10.9132i	−0.142046	−	0.617841i
$313$	−27.5450	+	7.38067i	−1.55694	+	0.417180i	−0.931693	−	0.363248i	$-0.881668\pi$
$313$	−27.5450	+	7.38067i	−1.55694	+	0.417180i	−0.625246	+	0.780428i	$0.715001\pi$
$314$	−8.68718			−0.490246
$315$	16.5549	+	6.39809i	0.932763	+	0.360491i
$316$	−8.91087			−0.501276
$317$	11.8629	−	3.17866i	0.666288	−	0.178531i	0.0902057	−	0.995923i	$-0.471248\pi$
$317$	11.8629	−	3.17866i	0.666288	−	0.178531i	0.576082	+	0.817392i	$0.304581\pi$
$318$	10.8037	+	3.31380i	0.605839	+	0.185829i
$319$	0.897809	−	0.518350i	0.0502676	−	0.0290220i
$320$	1.71033	+	1.44041i	0.0956101	+	0.0805214i
$321$	−3.33029	−	6.27719i	−0.185879	−	0.350358i
$322$	−2.77462	+	22.8540i	−0.154623	+	1.27360i
$323$	−3.50319	+	3.50319i	−0.194922	+	0.194922i
$324$	−8.35691	+	3.34097i	−0.464273	+	0.185609i
$325$	−13.5554	−	29.3462i	−0.751919	−	1.62784i
$326$	12.8800			0.713355
$327$	1.48346	−	0.341058i	0.0820357	−	0.0188606i
$328$	−3.42970	+	0.918985i	−0.189373	+	0.0507425i
$329$	−1.91238	−	2.44090i	−0.105433	−	0.134571i
$330$	−1.19525	−	3.71293i	−0.0657961	−	0.204390i
$331$	−1.49142	+	2.58322i	−0.0819760	+	0.141987i	−0.904099	−	0.427324i	$-0.859456\pi$
$331$	−1.49142	+	2.58322i	−0.0819760	+	0.141987i	0.822123	+	0.569310i	$0.192790\pi$
$332$	−0.351284	−	1.31101i	−0.0192792	−	0.0719510i
$333$	27.4356	+	9.50289i	1.50346	+	0.520755i
$334$	4.86393	+	8.42458i	0.266142	+	0.460972i
$335$	−2.52216	−	3.61591i	−0.137800	−	0.197559i
$336$	2.69522	+	3.70618i	0.147036	+	0.202189i
$337$	−15.1177	+	4.05078i	−0.823515	+	0.220660i	−0.645882	−	0.763437i	$-0.723510\pi$
$337$	−15.1177	+	4.05078i	−0.823515	+	0.220660i	−0.177632	+	0.984097i	$0.556844\pi$
$338$	−20.3633	+	20.3633i	−1.10762	+	1.10762i
$339$	10.0265	+	6.27797i	0.544563	+	0.340972i
$340$	−5.68597	+	0.487101i	−0.308365	+	0.0264167i
$341$	8.63529	−	4.98559i	0.467627	−	0.269985i
$342$	−4.40210	+	3.81260i	−0.238038	+	0.206162i
$343$	6.56656	−	17.3171i	0.354561	−	0.935033i
$344$	−5.04464	+	2.91252i	−0.271989	+	0.157033i
$345$	−24.9829	−	22.6181i	−1.34503	−	1.21772i
$346$	−2.92152	+	1.68674i	−0.157062	+	0.0906797i
$347$	1.08173	−	4.03705i	0.0580701	−	0.216720i	−0.930793	−	0.365545i	$-0.880882\pi$
$347$	1.08173	−	4.03705i	0.0580701	−	0.216720i	0.988864	+	0.148825i	$0.0475491\pi$
$348$	−0.399483	−	1.73759i	−0.0214145	−	0.0931444i
$349$	2.66539	+	4.61659i	0.142675	+	0.247120i	0.928503	−	0.371325i	$-0.121096\pi$
$349$	2.66539	+	4.61659i	0.142675	+	0.247120i	−0.785828	+	0.618445i	$0.787763\pi$
$350$	9.81087	+	8.87394i	0.524413	+	0.474332i
$351$	27.1238	+	19.8203i	1.44776	+	1.05793i
$352$	0.260663	−	0.972806i	0.0138934	−	0.0518508i
$353$	−21.5184	−	21.5184i	−1.14531	−	1.14531i	−0.987464	−	0.157845i	$-0.949545\pi$
$353$	−21.5184	−	21.5184i	−1.14531	−	1.14531i	−0.157845	−	0.987464i	$-0.550455\pi$
$354$	7.61426	+	0.272855i	0.404693	+	0.0145021i
$355$	0.231548	−	0.274937i	0.0122893	−	0.0145922i
$356$	15.2637	+	8.81248i	0.808972	+	0.467060i
$357$	−11.5523	−	1.82443i	−0.611411	−	0.0965589i
$358$	16.4874	+	4.41780i	0.871389	+	0.233488i
$359$	0.962109	−	0.555474i	0.0507782	−	0.0293168i	−0.474396	−	0.880312i	$-0.657334\pi$
$359$	0.962109	−	0.555474i	0.0507782	−	0.0293168i	0.525174	+	0.850995i	$0.324000\pi$
$360$	−6.70756	+	0.0927016i	−0.353520	+	0.00488580i
$361$	7.61586	−	13.1911i	0.400835	−	0.694267i
$362$	−3.63639	−	13.5712i	−0.191124	−	0.713286i
$363$	12.6601	−	11.7841i	0.664481	−	0.618506i
$364$	6.38616	−	15.8683i	0.334726	−	0.831726i
$365$	1.26734	−	2.70504i	0.0663355	−	0.141588i
$366$	11.1153	−	5.89708i	0.581004	−	0.308245i
$367$	−17.2202	+	17.2202i	−0.898888	+	0.898888i	−0.995338	−	0.0964498i	$-0.969251\pi$
$367$	−17.2202	+	17.2202i	−0.898888	+	0.898888i	0.0964498	+	0.995338i	$0.469251\pi$
$368$	−2.25210	−	8.40494i	−0.117399	−	0.438138i
$369$	5.97267	−	8.82007i	0.310925	−	0.459154i
$370$	16.5529	+	13.9406i	0.860547	+	0.724740i
$371$	10.6459	+	13.5880i	0.552705	+	0.705453i
$372$	−3.84230	−	16.7124i	−0.199214	−	0.866499i
$373$	18.2463	−	18.2463i	0.944759	−	0.944759i	−0.0537929	−	0.998552i	$-0.517131\pi$
$373$	18.2463	−	18.2463i	0.944759	−	0.944759i	0.998552	+	0.0537929i	$0.0171311\pi$
$374$	1.28517	+	2.22598i	0.0664544	+	0.115102i
$375$	−18.8958	+	4.23651i	−0.975776	+	0.218772i
$376$	1.01499	+	0.586003i	0.0523440	+	0.0302208i
$377$	−4.70580	+	4.70580i	−0.242361	+	0.242361i
$378$	−13.3911	−	3.11105i	−0.688763	−	0.160015i
$379$			35.3475i			1.81568i	0.419317	+	0.907840i	$0.362269\pi$
$379$			35.3475i			1.81568i	−0.419317	+	0.907840i	$0.637731\pi$
$380$	−4.08157	+	1.47722i	−0.209380	+	0.0757797i
$381$	23.8093	+	0.853201i	1.21979	+	0.0437108i
$382$	3.55806	−	13.2789i	0.182046	−	0.679406i
$383$	−6.90072	−	6.90072i	−0.352610	−	0.352610i	0.508470	−	0.861080i	$-0.330211\pi$
$383$	−6.90072	−	6.90072i	−0.352610	−	0.352610i	−0.861080	+	0.508470i	$0.830211\pi$
$384$	−1.46802	−	0.919188i	−0.0749148	−	0.0469071i
$385$	1.74458	−	5.69709i	0.0889119	−	0.290351i
$386$	5.16817			0.263053
$387$	5.71950	−	16.5126i	0.290739	−	0.839385i
$388$	15.3828	−	4.12181i	0.780944	−	0.209253i
$389$			0.933400i			0.0473253i	0.999720	+	0.0236626i	$0.00753276\pi$
$389$			0.933400i			0.0473253i	−0.999720	+	0.0236626i	$0.992467\pi$
$390$	13.5802	+	21.0368i	0.687662	+	1.06524i
$391$	19.2322	+	11.1037i	0.972613	+	0.561538i
$392$	0.141178	+	6.99858i	0.00713057	+	0.353481i
$393$	18.3664	+	19.7317i	0.926465	+	0.995332i
$394$	−8.74156	−	5.04694i	−0.440394	−	0.254261i
$395$	18.7360	−	6.78100i	0.942709	−	0.341189i
$396$	1.31952	+	2.71800i	0.0663084	+	0.136585i
$397$	−6.71304	−	1.79875i	−0.336918	−	0.0902769i	0.0863936	−	0.996261i	$-0.472466\pi$
$397$	−6.71304	−	1.79875i	−0.336918	−	0.0902769i	−0.423311	+	0.905984i	$0.639132\pi$
$398$	0.00835337	−	0.0311752i	0.000418717	−	0.00156267i
$399$	−8.84657	+	0.933795i	−0.442882	+	0.0467482i
$400$	−4.69225	−	1.72708i	−0.234612	−	0.0863539i
$401$	−18.5534			−0.926514			−0.463257	−	0.886224i	$-0.653319\pi$
$401$	−18.5534			−0.926514			−0.463257	+	0.886224i	$0.653319\pi$
$402$	2.32669	+	2.49964i	0.116045	+	0.124671i
$403$	−45.2613	+	45.2613i	−2.25462	+	2.25462i
$404$	−9.35241	−	16.1988i	−0.465300	−	0.805922i
$405$	15.0288	−	13.3841i	0.746787	−	0.665063i
$406$	1.01679	−	2.52652i	0.0504625	−	0.125389i
$407$	2.52276	−	9.41505i	0.125048	−	0.466687i
$408$	4.30807	−	0.990455i	0.213281	−	0.0490348i
$409$	−15.3558	−	26.5971i	−0.759297	−	1.31514i	−0.943209	−	0.332199i	$-0.892210\pi$
$409$	−15.3558	−	26.5971i	−0.759297	−	1.31514i	0.183912	−	0.982943i	$-0.441124\pi$
$410$	6.51194	−	4.54219i	0.321602	−	0.224323i
$411$	−27.0997	−	0.971113i	−1.33673	−	0.0479015i
$412$	2.83106	+	0.758581i	0.139477	+	0.0373726i
$413$	9.30438	+	6.99156i	0.457838	+	0.344032i
$414$	21.6148	+	14.6368i	1.06231	+	0.719361i
$415$	1.73626	+	2.48920i	0.0852297	+	0.122190i
$416$			6.46514i			0.316980i
$417$	2.51807	+	10.9526i	0.123310	+	0.536349i
$418$	1.38242	+	1.38242i	0.0676162	+	0.0676162i
$419$	−14.9327	+	25.8642i	−0.729511	+	1.26355i	0.227579	+	0.973760i	$0.426919\pi$
$419$	−14.9327	+	25.8642i	−0.729511	+	1.26355i	−0.957090	+	0.289791i	$0.906414\pi$
$420$	−8.48729	−	5.74159i	−0.414137	−	0.280161i
$421$	−12.0478	−	20.8674i	−0.587175	−	1.01702i	−0.994600	−	0.103779i	$-0.966907\pi$
$421$	−12.0478	−	20.8674i	−0.587175	−	1.01702i	0.407425	−	0.913239i	$-0.366427\pi$
$422$	−2.78970	+	10.4113i	−0.135800	+	0.506814i
$423$	−3.45264	+	0.664585i	−0.167873	+	0.0323132i
$424$	−5.65023	−	3.26216i	−0.274399	−	0.158425i
$425$	11.5846	−	5.35108i	0.561936	−	0.259566i
$426$	−0.147761	+	0.235987i	−0.00715903	+	0.0114336i
$427$	19.0803	+	2.31647i	0.923361	+	0.112102i
$428$	1.06183	+	3.96280i	0.0513255	+	0.191549i
$429$	5.98501	−	9.55859i	0.288959	−	0.461493i
$430$	8.39046	−	9.96273i	0.404624	−	0.480445i
$431$	16.1888	−	28.0399i	0.779789	−	1.35063i	−0.152275	−	0.988338i	$-0.548660\pi$
$431$	16.1888	−	28.0399i	0.779789	−	1.35063i	0.932063	−	0.362295i	$-0.118007\pi$
$432$	5.13439	−	0.798799i	0.247028	−	0.0384322i
$433$	−2.67065	−	2.67065i	−0.128343	−	0.128343i	0.640017	−	0.768361i	$-0.278927\pi$
$433$	−2.67065	−	2.67065i	−0.128343	−	0.128343i	−0.768361	+	0.640017i	$0.778927\pi$
$434$	9.77969	−	24.3006i	0.469440	−	1.16646i
$435$	2.16222	+	3.34944i	0.103670	+	0.160593i
$436$	−0.878821			−0.0420879
$437$	16.3157	+	4.37178i	0.780486	+	0.209131i
$438$	−0.678531	+	2.21215i	−0.0324215	+	0.105701i
$439$	5.36032	−	9.28434i	0.255834	−	0.443118i	−0.709288	−	0.704919i	$-0.750983\pi$
$439$	5.36032	−	9.28434i	0.255834	−	0.443118i	0.965122	+	0.261802i	$0.0843166\pi$
$440$	0.192218	+	2.24378i	0.00916364	+	0.106968i
$441$	−14.0656	−	15.5935i	−0.669792	−	0.742549i
$442$	−11.6673	−	11.6673i	−0.554956	−	0.554956i
$443$	−3.37859	−	12.6091i	−0.160522	−	0.599075i	−0.998569	−	0.0534774i	$-0.982969\pi$
$443$	−3.37859	−	12.6091i	−0.160522	−	0.599075i	0.838047	−	0.545597i	$-0.183697\pi$
$444$	−14.2079	−	8.89612i	−0.674276	−	0.422191i
$445$	−38.7994	−	6.91374i	−1.83927	−	0.327743i
$446$			7.70889i			0.365026i
$447$	−5.45793	−	5.86363i	−0.258151	−	0.277340i
$448$	−1.03708	−	2.43402i	−0.0489976	−	0.114997i
$449$		−	12.5739i		−	0.593398i	−0.954971	−	0.296699i	$-0.904114\pi$
$449$		−	12.5739i		−	0.593398i	0.954971	−	0.296699i	$-0.0958859\pi$
$450$	14.0328	−	5.29924i	0.661510	−	0.249808i
$451$	−3.09689	−	1.78799i	−0.145827	−	0.0841931i
$452$	−4.82947	−	4.82947i	−0.227159	−	0.227159i
$453$	−11.1991	+	10.4243i	−0.526181	+	0.489774i
$454$	0.355997	−	0.616605i	0.0167078	−	0.0289387i
$455$	−1.35204	+	38.2244i	−0.0633845	+	1.79199i
$456$	2.97014	−	1.57578i	0.139090	−	0.0737925i
$457$	−0.327337	+	0.0877098i	−0.0153122	+	0.00410289i	−0.266467	−	0.963844i	$-0.585856\pi$
$457$	−0.327337	+	0.0877098i	−0.0153122	+	0.00410289i	0.251155	+	0.967947i	$0.419190\pi$
$458$	−16.3722	+	4.38692i	−0.765024	+	0.204988i
$459$	−7.82420	+	10.7073i	−0.365202	+	0.499774i
$460$	11.1312	+	15.9584i	0.518997	+	0.744064i
$461$	−15.0694	+	8.70031i	−0.701851	+	0.405214i	−0.808036	−	0.589133i	$-0.799470\pi$
$461$	−15.0694	+	8.70031i	−0.701851	+	0.405214i	0.106186	+	0.994346i	$0.466136\pi$
$462$	−0.719949	+	4.55872i	−0.0334951	+	0.212091i
$463$	−3.10958	−	11.6051i	−0.144515	−	0.539335i	−0.999777	−	0.0211397i	$-0.993271\pi$
$463$	−3.10958	−	11.6051i	−0.144515	−	0.539335i	0.855262	−	0.518196i	$-0.173396\pi$
$464$			1.02937i			0.0477872i
$465$	20.7966	+	32.2156i	0.964421	+	1.49396i
$466$	−27.2824			−1.26383
$467$	22.0222	+	5.90084i	1.01907	+	0.273058i	0.729413	−	0.684073i	$-0.239793\pi$
$467$	22.0222	+	5.90084i	1.01907	+	0.273058i	0.289654	+	0.957132i	$0.406460\pi$
$468$	−12.6978	−	14.6611i	−0.586956	−	0.677710i
$469$	0.732994	+	5.16462i	0.0338465	+	0.238480i
$470$	−2.58004	−	0.459743i	−0.119009	−	0.0212063i
$471$	−13.2918	+	7.05184i	−0.612456	+	0.324932i
$472$	−4.24903	−	1.13852i	−0.195577	−	0.0524048i
$473$	−5.66664	−	1.51837i	−0.260552	−	0.0698148i
$474$	−13.6341	+	7.23342i	−0.626235	+	0.332242i
$475$	7.45775	−	6.21198i	0.342185	−	0.285025i
$476$	6.26412	+	2.52098i	0.287115	+	0.115549i
$477$	19.2201	−	3.69961i	0.880030	−	0.169394i
$478$	13.0268	+	3.49052i	0.595833	+	0.159653i
$479$	−25.8385			−1.18059			−0.590295	−	0.807188i	$-0.700988\pi$
$479$	−25.8385			−1.18059			−0.590295	+	0.807188i	$0.700988\pi$
$480$	3.78614	+	0.815543i	0.172813	+	0.0372243i
$481$			62.5712i			2.85300i
$482$	−4.50729	−	16.8214i	−0.205302	−	0.766196i
$483$	14.3065	+	37.2201i	0.650968	+	1.69357i
$484$	−8.64787	+	4.99285i	−0.393085	+	0.226948i
$485$	−29.2072	+	20.3725i	−1.32623	+	0.925068i
$486$	−10.0745	+	11.8956i	−0.456987	+	0.539595i
$487$	8.38252	−	2.24609i	0.379848	−	0.101780i	−0.0638424	−	0.997960i	$-0.520336\pi$
$487$	8.38252	−	2.24609i	0.379848	−	0.101780i	0.443691	+	0.896180i	$0.353669\pi$
$488$	−7.01710	+	1.88023i	−0.317649	+	0.0851138i
$489$	19.7070	−	10.4553i	0.891182	−	0.472807i
$490$	−5.62262	−	14.6077i	−0.254004	−	0.659911i
$491$	−2.38788	+	4.13592i	−0.107763	+	0.186652i	−0.914864	−	0.403762i	$-0.867702\pi$
$491$	−2.38788	+	4.13592i	−0.107763	+	0.186652i	0.807100	+	0.590414i	$0.201036\pi$
$492$	−4.50163	+	4.19016i	−0.202949	+	0.188907i
$493$	−1.85764	−	1.85764i	−0.0836641	−	0.0836641i
$494$	−10.8688	−	6.27508i	−0.489008	−	0.282329i
$495$	−4.84277	−	4.71073i	−0.217666	−	0.211732i
$496$			9.90065i			0.444552i
$497$	−0.391272	+	0.166713i	−0.0175510	+	0.00747809i
$498$	−1.60170	−	1.72076i	−0.0717738	−	0.0771090i
$499$		−	22.0160i		−	0.985573i	−0.870150	−	0.492786i	$-0.835978\pi$
$499$		−	22.0160i		−	0.985573i	0.870150	−	0.492786i	$-0.164022\pi$
$500$	11.1802	+	0.0606400i	0.499993	+	0.00271190i
$501$	14.2807	+	8.94173i	0.638016	+	0.399487i
$502$	0.121524	+	0.453534i	0.00542389	+	0.0202422i
$503$	−5.47098	−	5.47098i	−0.243939	−	0.243939i	0.574538	−	0.818478i	$-0.305182\pi$
$503$	−5.47098	−	5.47098i	−0.243939	−	0.243939i	−0.818478	+	0.574538i	$0.805182\pi$
$504$	7.13233	+	3.48280i	0.317699	+	0.155136i
$505$	31.9913	+	26.9426i	1.42360	+	1.19893i
$506$	4.38171	−	7.58934i	0.194791	−	0.337387i
$507$	−14.6269	+	47.6868i	−0.649605	+	2.11785i
$508$	−13.2864	−	3.56009i	−0.589490	−	0.157953i
$509$	−28.8062			−1.27681			−0.638407	−	0.769699i	$-0.720406\pi$
$509$	−28.8062			−1.27681			−0.638407	+	0.769699i	$0.720406\pi$
$510$	−8.30442	+	5.36088i	−0.367726	+	0.237384i
$511$	−2.78227	+	2.17984i	−0.123080	+	0.0964304i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−3.64056	+	9.40689i	−0.160735	+	0.415325i
$514$	3.74281	−	6.48273i	0.165088	−	0.285941i
$515$	−6.52985	+	0.559394i	−0.287740	+	0.0246498i
$516$	−5.35431	+	8.55130i	−0.235710	+	0.376450i
$517$	0.305498	+	1.14014i	0.0134358	+	0.0501431i
$518$	−10.0371	−	23.5570i	−0.441007	−	1.03504i
$519$	−3.10086	+	4.95235i	−0.136113	+	0.217384i
$520$	−4.91984	−	13.5936i	−0.215749	−	0.596118i
$521$	−19.6108	−	11.3223i	−0.859163	−	0.496038i	0.00456915	−	0.999990i	$-0.498546\pi$
$521$	−19.6108	−	11.3223i	−0.859163	−	0.496038i	−0.863732	+	0.503952i	$0.831879\pi$
$522$	−2.02172	−	2.33432i	−0.0884882	−	0.102170i
$523$	−0.698514	+	2.60689i	−0.0305439	+	0.113991i	−0.979515	−	0.201372i	$-0.935460\pi$
$523$	−0.698514	+	2.60689i	−0.0305439	+	0.113991i	0.948971	+	0.315364i	$0.102127\pi$
$524$	−7.78174	−	13.4784i	−0.339947	−	0.588805i
$525$	22.2146	+	5.61359i	0.969524	+	0.244997i
$526$	−9.75159	+	16.8902i	−0.425189	+	0.736450i
$527$	−17.8672	−	17.8672i	−0.778306	−	0.778306i
$528$	−0.390850	−	1.70004i	−0.0170096	−	0.0739846i
$529$		−	52.7149i		−	2.29195i
$530$	14.3626	+	2.55930i	0.623871	+	0.111169i
$531$	11.8717	−	5.76341i	0.515188	−	0.250111i
$532$	5.09850	+	0.618990i	0.221048	+	0.0268366i
$533$	22.1735	+	5.94137i	0.960441	+	0.257349i
$534$	30.5077	+	1.09324i	1.32020	+	0.0473091i
$535$	−5.24822	−	7.52415i	−0.226900	−	0.325297i
$536$	−0.985802	−	1.70746i	−0.0425802	−	0.0737510i
$537$	28.8128	−	6.62426i	1.24336	−	0.285858i
$538$	2.57810	−	9.62161i	0.111150	−	0.414817i
$539$	−4.88345	+	5.08453i	−0.210345	+	0.219006i
$540$	−10.1877	+	5.58672i	−0.438407	+	0.240414i
$541$	−17.3131	−	29.9872i	−0.744350	−	1.28925i	−0.950498	−	0.310731i	$-0.899426\pi$
$541$	−17.3131	−	29.9872i	−0.744350	−	1.28925i	0.206148	−	0.978521i	$-0.433907\pi$
$542$	17.2554	−	17.2554i	0.741185	−	0.741185i
$543$	−16.5803	−	17.8128i	−0.711529	−	0.764420i
$544$	−2.55215			−0.109423
$545$	1.84781	−	0.668766i	0.0791513	−	0.0286468i
$546$	−3.10998	−	29.4633i	−0.133095	−	1.26091i
$547$	−0.452339	+	1.68815i	−0.0193406	+	0.0721801i	−0.974922	−	0.222548i	$-0.928563\pi$
$547$	−0.452339	+	1.68815i	−0.0193406	+	0.0721801i	0.955581	+	0.294728i	$0.0952292\pi$
$548$	15.1226	+	4.05209i	0.646006	+	0.173097i
$549$	12.2200	−	18.0457i	0.521535	−	0.770171i
$550$	−2.11163	−	4.57148i	−0.0900401	−	0.194929i
$551$	−1.73050	−	0.999106i	−0.0737219	−	0.0425633i
$552$	−10.2686	−	11.0318i	−0.437059	−	0.469547i
$553$	−23.4041	−	2.84140i	−0.995244	−	0.120829i
$554$	−4.56187	−	2.63380i	−0.193815	−	0.111899i
$555$	36.6432	+	7.89302i	1.55542	+	0.335040i
$556$		−	6.48843i		−	0.275171i
$557$	28.3975	−	7.60909i	1.20324	−	0.322407i	0.399134	−	0.916893i	$-0.369311\pi$
$557$	28.3975	−	7.60909i	1.20324	−	0.322407i	0.804107	+	0.594485i	$0.202644\pi$
$558$	−19.4453	−	22.4519i	−0.823184	−	0.950464i
$559$	37.6597			1.59284
$560$	4.03281	+	4.32856i	0.170417	+	0.182915i
$561$	3.77331	+	2.36262i	0.159309	+	0.0997499i
$562$	8.52470	+	8.52470i	0.359593	+	0.359593i
$563$	5.71729	−	21.3372i	0.240955	−	0.899257i	−0.734418	−	0.678697i	$-0.762545\pi$
$563$	5.71729	−	21.3372i	0.240955	−	0.899257i	0.975373	−	0.220560i	$-0.0707885\pi$
$564$	2.02867	+	0.0726971i	0.0854225	+	0.00306110i
$565$	13.8296	+	6.47930i	0.581814	+	0.272586i
$566$		−	24.1139i		−	1.01358i
$567$	−23.0145	+	6.11017i	−0.966517	+	0.256603i
$568$	0.113668	−	0.113668i	0.00476942	−	0.00476942i
$569$	−32.4544	−	18.7375i	−1.36056	−	0.785518i	−0.370859	−	0.928689i	$-0.620937\pi$
$569$	−32.4544	−	18.7375i	−1.36056	−	0.785518i	−0.989698	+	0.143171i	$0.954270\pi$
$570$	−5.04587	+	5.57344i	−0.211348	+	0.233446i
$571$	−14.1602	−	24.5261i	−0.592585	−	1.02639i	−0.993883	−	0.110439i	$-0.964774\pi$
$571$	−14.1602	−	24.5261i	−0.592585	−	1.02639i	0.401298	−	0.915948i	$-0.368559\pi$
$572$	−4.60411	+	4.60411i	−0.192507	+	0.192507i
$573$	−5.33513	−	23.2056i	−0.222878	−	0.969428i
$574$	−9.30102	+	1.32006i	−0.388217	+	0.0550982i
$575$	−35.5485	−	25.0834i	−1.48248	−	1.04605i
$576$	−2.99231	−	0.214733i	−0.124679	−	0.00894721i
$577$	−4.39511	−	16.4028i	−0.182971	−	0.682857i	−0.995056	−	0.0993173i	$-0.968334\pi$
$577$	−4.39511	−	16.4028i	−0.182971	−	0.682857i	0.812085	−	0.583539i	$-0.198333\pi$
$578$	−7.41508	+	7.41508i	−0.308427	+	0.308427i
$579$	7.90757	−	4.19528i	0.328628	−	0.174350i
$580$	−0.783328	−	2.16434i	−0.0325259	−	0.0898695i
$581$	−0.504595	−	3.55534i	−0.0209341	−	0.147500i
$582$	20.1906	−	18.7936i	0.836928	−	0.779020i
$583$	−1.70065	−	6.34690i	−0.0704336	−	0.262862i
$584$	0.667958	−	1.15694i	0.0276403	−	0.0478744i
$585$	37.8552	+	21.1636i	1.56512	+	0.875009i
$586$	2.69731	−	1.55729i	0.111425	−	0.0643311i
$587$	−16.9070	−	4.53022i	−0.697826	−	0.186982i	−0.107570	−	0.994198i	$-0.534307\pi$
$587$	−16.9070	−	4.53022i	−0.697826	−	0.186982i	−0.590257	+	0.807216i	$0.700974\pi$
$588$	5.89712	+	10.5936i	0.243193	+	0.436872i
$589$	−16.6443	−	9.60959i	−0.685816	−	0.395956i
$590$	9.80038	−	0.839571i	0.403475	−	0.0345646i
$591$	−17.4719	−	0.626102i	−0.718698	−	0.0257544i
$592$	6.84355	+	6.84355i	0.281268	+	0.281268i
$593$	7.56384	−	28.2286i	0.310610	−	1.15921i	−0.617399	−	0.786650i	$-0.711813\pi$
$593$	7.56384	−	28.2286i	0.310610	−	1.15921i	0.928008	−	0.372560i	$-0.121520\pi$
$594$	4.22528	+	3.08756i	0.173365	+	0.126684i
$595$	−15.0893	−	0.533725i	−0.618602	−	0.0218806i
$596$	2.31249	+	4.00534i	0.0947231	+	0.164065i
$597$	−0.0125255	−	0.0544806i	−0.000512633	−	0.00222974i
$598$	−14.5601	+	54.3391i	−0.595408	+	2.22209i
$599$	20.3483	−	11.7481i	0.831410	−	0.480015i	−0.0229249	−	0.999737i	$-0.507298\pi$
$599$	20.3483	−	11.7481i	0.831410	−	0.480015i	0.854335	+	0.519722i	$0.173965\pi$
$600$	−8.58134	+	1.16642i	−0.350332	+	0.0476190i
$601$	−37.8743	+	21.8667i	−1.54492	+	0.891962i	−0.546407	+	0.837520i	$0.684005\pi$
$601$	−37.8743	+	21.8667i	−1.54492	+	0.891962i	−0.998517	+	0.0544424i	$0.982662\pi$
$602$	−14.1783	+	6.04106i	−0.577863	+	0.246215i
$603$	5.58904	+	1.93588i	0.227603	+	0.0788352i
$604$	7.64993	−	4.41669i	0.311271	−	0.179712i
$605$	14.3835	−	17.0788i	0.584773	−	0.694352i
$606$	−27.4591	−	17.1932i	−1.11545	−	0.698427i
$607$	14.8374	−	14.8374i	0.602232	−	0.602232i	−0.338672	−	0.940904i	$-0.609978\pi$
$607$	14.8374	−	14.8374i	0.602232	−	0.602232i	0.940904	+	0.338672i	$0.109978\pi$
$608$	−1.87506	+	0.502420i	−0.0760437	+	0.0203758i
$609$	−0.495166	−	4.69109i	−0.0200651	−	0.190093i
$610$	13.3233	−	9.29323i	0.539445	−	0.376272i
$611$	−3.78859	−	6.56203i	−0.153270	−	0.265471i
$612$	5.78757	−	5.01253i	0.233949	−	0.202620i
$613$	−6.51129	−	24.3004i	−0.262988	−	0.981486i	−0.963470	−	0.267816i	$-0.913698\pi$
$613$	−6.51129	−	24.3004i	−0.262988	−	0.981486i	0.700482	−	0.713670i	$-0.252968\pi$
$614$	−0.659203	+	1.14177i	−0.0266033	+	0.0460782i
$615$	6.27648	−	12.2359i	0.253092	−	0.493398i
$616$	0.994820	−	2.47193i	0.0400824	−	0.0995967i
$617$	−22.8238	+	6.11563i	−0.918853	+	0.246206i	−0.687095	−	0.726567i	$-0.741114\pi$
$617$	−22.8238	+	6.11563i	−0.918853	+	0.246206i	−0.231758	+	0.972773i	$0.574448\pi$
$618$	4.94745	−	1.13745i	0.199016	−	0.0457551i
$619$	35.7380			1.43643			0.718217	−	0.695820i	$-0.244959\pi$
$619$	35.7380			1.43643			0.718217	+	0.695820i	$0.244959\pi$
$620$	−7.53420	−	20.8171i	−0.302581	−	0.836033i
$621$	44.9532	+	4.84928i	1.80391	+	0.194595i
$622$	−9.21374	+	9.21374i	−0.369437	+	0.369437i
$623$	37.2794	+	28.0128i	1.49357	+	1.12231i
$624$	5.24809	+	9.89200i	0.210092	+	0.395997i
$625$	−23.5535	+	8.38039i	−0.942141	+	0.335216i
$626$	24.6962	−	14.2584i	0.987059	−	0.569879i
$627$	3.23735	+	0.992989i	0.129287	+	0.0396562i
$628$	8.39117	−	2.24841i	0.334844	−	0.0897212i
$629$	−24.7004			−0.984868
$630$	−17.6467	−	1.89536i	−0.703063	−	0.0755128i
$631$	28.6356			1.13996			0.569982	−	0.821657i	$-0.306950\pi$
$631$	28.6356			1.13996			0.569982	+	0.821657i	$0.306950\pi$
$632$	8.60724	−	2.30630i	0.342378	−	0.0917398i
$633$	4.18301	+	18.1944i	0.166260	+	0.723161i
$634$	−10.6360	+	6.14070i	−0.422409	+	0.243878i
$635$	30.6451	−	2.62528i	1.21612	−	0.104181i
$636$	−11.2932	−	0.404690i	−0.447805	−	0.0160470i
$637$	21.8329	−	39.6412i	0.865052	−	1.57064i
$638$	−0.733058	+	0.733058i	−0.0290220	+	0.0290220i
$639$	−0.0345187	+	0.481018i	−0.00136554	+	0.0190288i
$640$	−2.02485	−	0.948666i	−0.0800394	−	0.0374993i
$641$	34.8940			1.37823			0.689115	−	0.724652i	$-0.258000\pi$
$641$	34.8940			1.37823			0.689115	+	0.724652i	$0.258000\pi$
$642$	4.84147	+	5.20135i	0.191078	+	0.205281i
$643$	2.55595	−	0.684864i	0.100797	−	0.0270084i	−0.208068	−	0.978114i	$-0.566718\pi$
$643$	2.55595	−	0.684864i	0.100797	−	0.0270084i	0.308865	+	0.951106i	$0.400051\pi$
$644$	−3.23498	−	22.7934i	−0.127476	−	0.898186i
$645$	4.75057	−	22.0545i	0.187054	−	0.868394i
$646$	2.47713	−	4.29051i	0.0974612	−	0.168808i
$647$	−1.21277	−	4.52613i	−0.0476790	−	0.177940i	0.937980	−	0.346689i	$-0.112694\pi$
$647$	−1.21277	−	4.52613i	−0.0476790	−	0.177940i	−0.985659	+	0.168749i	$0.946027\pi$
$648$	7.20745	−	5.39005i	0.283135	−	0.211741i
$649$	−2.21513	−	3.83671i	−0.0869513	−	0.150604i
$650$	20.6889	+	24.8379i	0.811485	+	0.974222i
$651$	−4.76260	−	45.1198i	−0.186661	−	1.76838i
$652$	−12.4411	+	3.33358i	−0.487231	+	0.130553i
$653$	−23.4420	+	23.4420i	−0.917355	+	0.917355i	−0.996836	−	0.0794809i	$-0.974674\pi$
$653$	−23.4420	+	23.4420i	−0.917355	+	0.917355i	0.0794809	+	0.996836i	$0.474674\pi$
$654$	−1.34464	+	0.713385i	−0.0525797	+	0.0278956i
$655$	26.6186	+	22.4178i	1.04008	+	0.875936i
$656$	3.07498	−	1.77534i	0.120058	−	0.0693155i
$657$	0.757531	+	3.93551i	0.0295541	+	0.153539i
$658$	2.47897	+	1.86276i	0.0966403	+	0.0726181i
$659$	−36.6245	+	21.1452i	−1.42669	+	0.823698i	−0.996858	−	0.0792121i	$-0.974760\pi$
$659$	−36.6245	+	21.1452i	−1.42669	+	0.823698i	−0.429829	+	0.902910i	$0.641426\pi$
$660$	2.11550	+	3.27706i	0.0823455	+	0.127560i
$661$	27.7107	−	15.9988i	1.07782	−	0.622280i	0.147513	−	0.989060i	$-0.452873\pi$
$661$	27.7107	−	15.9988i	1.07782	−	0.622280i	0.930308	+	0.366780i	$0.119540\pi$
$662$	0.772017	−	2.88121i	0.0300053	−	0.111981i
$663$	−27.3225	−	8.38061i	−1.06112	−	0.325476i
$664$	0.678629	+	1.17542i	0.0263359	+	0.0456151i
$665$	−11.1911	+	2.57838i	−0.433974	+	0.0999851i
$666$	−28.9602	−	2.07824i	−1.12219	−	0.0805301i
$667$	−2.31823	+	8.65177i	−0.0897624	+	0.334998i
$668$	−6.87864	−	6.87864i	−0.266142	−	0.266142i
$669$	6.25771	+	11.7950i	0.241937	+	0.456021i
$670$	3.37209	+	2.83992i	0.130275	+	0.109716i
$671$	−6.33617	−	3.65819i	−0.244605	−	0.141223i
$672$	−3.56261	−	2.88232i	−0.137431	−	0.111188i
$673$	−2.58830	−	0.693533i	−0.0997717	−	0.0267338i	0.208588	−	0.978004i	$-0.433113\pi$
$673$	−2.58830	−	0.693533i	−0.0997717	−	0.0267338i	−0.308360	+	0.951270i	$0.599780\pi$
$674$	13.5542	−	7.82551i	0.522087	−	0.301427i
$675$	17.1692	−	19.4992i	0.660842	−	0.750525i
$676$	14.3990	−	24.9398i	0.553809	−	0.959225i
$677$	4.54065	+	16.9459i	0.174511	+	0.651285i	0.996634	+	0.0819754i	$0.0261229\pi$
$677$	4.54065	+	16.9459i	0.174511	+	0.651285i	−0.822123	+	0.569310i	$0.807210\pi$
$678$	−11.3097	−	3.46901i	−0.434346	−	0.133226i
$679$	41.7167	−	5.92070i	1.60094	−	0.227215i
$680$	5.36615	−	1.94214i	0.205782	−	0.0744776i
$681$	0.0441635	−	1.23242i	0.00169235	−	0.0472264i
$682$	−7.05068	+	7.05068i	−0.269985	+	0.269985i
$683$	0.00281453	+	0.0105040i	0.000107695	+	0.000401922i	0.965980	−	0.258618i	$-0.0832671\pi$
$683$	0.00281453	+	0.0105040i	0.000107695	+	0.000401922i	−0.965872	+	0.259020i	$0.916600\pi$
$684$	3.26533	−	4.82204i	0.124853	−	0.184375i
$685$	−34.8803	+	2.98810i	−1.33271	+	0.114169i
$686$	−1.86083	+	18.4265i	−0.0710468	+	0.703528i
$687$	−21.4893	+	20.0024i	−0.819866	+	0.763140i
$688$	4.11893	−	4.11893i	0.157033	−	0.157033i
$689$	21.0903	+	36.5295i	0.803478	+	1.39166i
$690$	29.9856	+	15.3814i	1.14153	+	0.585558i
$691$	1.05289	+	0.607889i	0.0400540	+	0.0231252i	0.519893	−	0.854231i	$-0.325972\pi$
$691$	1.05289	+	0.607889i	0.0400540	+	0.0231252i	−0.479839	+	0.877356i	$0.659305\pi$
$692$	2.38541	−	2.38541i	0.0906797	−	0.0906797i
$693$	2.59899	+	7.55950i	0.0987275	+	0.287162i
$694$			4.17947i			0.158650i
$695$	4.93756	+	13.6425i	0.187292	+	0.517491i
$696$	0.835591	+	1.57499i	0.0316730	+	0.0596997i
$697$	−2.34539	+	8.75312i	−0.0888381	+	0.331548i
$698$	−3.76943	−	3.76943i	−0.142675	−	0.142675i
$699$	−41.7435	+	22.1466i	−1.57888	+	0.837660i
$700$	−11.7733	−	6.03233i	−0.444990	−	0.228000i
$701$	12.5012			0.472165			0.236082	−	0.971733i	$-0.424137\pi$
$701$	12.5012			0.472165			0.236082	+	0.971733i	$0.424137\pi$
$702$	−31.3295	−	12.1248i	−1.18245	−	0.457621i
$703$	−18.1473	+	4.86255i	−0.684437	+	0.183394i
$704$			1.00712i			0.0379574i
$705$	−4.32080	+	1.39093i	−0.162731	+	0.0523853i
$706$	26.3545	+	15.2158i	0.991866	+	0.572654i
$707$	−19.3985	−	45.5279i	−0.729554	−	1.71225i
$708$	−7.42543	+	1.70716i	−0.279065	+	0.0641589i
$709$	−22.6883	−	13.0991i	−0.852075	−	0.491946i	0.00927515	−	0.999957i	$-0.497048\pi$
$709$	−22.6883	−	13.0991i	−0.852075	−	0.491946i	−0.861351	+	0.508011i	$0.830381\pi$
$710$	−0.152499	+	0.325498i	−0.00572320	+	0.0122157i
$711$	−14.9891	+	22.1350i	−0.562136	+	0.830128i
$712$	−17.0244	−	4.56167i	−0.638016	−	0.170956i
$713$	−22.2972	+	83.2143i	−0.835037	+	3.11640i
$714$	11.6308	−	1.22769i	0.435273	−	0.0459450i
$715$	6.17695	−	13.1842i	0.231005	−	0.493062i
$716$	−17.0691			−0.637901
$717$	22.7651	−	5.23386i	0.850180	−	0.195462i
$718$	−0.785559	+	0.785559i	−0.0293168	+	0.0293168i
$719$	4.68417	+	8.11323i	0.174690	+	0.302572i	0.940054	−	0.341026i	$-0.110774\pi$
$719$	4.68417	+	8.11323i	0.174690	+	0.302572i	−0.765364	+	0.643598i	$0.777441\pi$
$720$	6.45502	−	1.82559i	0.240564	−	0.0680356i
$721$	7.19381	+	2.89513i	0.267911	+	0.107820i
$722$	−3.94226	+	14.7127i	−0.146716	+	0.547551i
$723$	−20.5512	−	22.0789i	−0.764308	−	0.821122i
$724$	7.02497	+	12.1676i	0.261081	+	0.452205i
$725$	3.29405	+	3.95464i	0.122338	+	0.146872i
$726$	−9.17873	+	14.6592i	−0.340655	+	0.544056i
$727$	18.3227	+	4.90954i	0.679550	+	0.182085i	0.582053	−	0.813151i	$-0.302250\pi$
$727$	18.3227	+	4.90954i	0.679550	+	0.182085i	0.0974969	+	0.995236i	$0.468916\pi$
$728$	−2.06153	+	16.9805i	−0.0764055	+	0.629338i
$729$	−5.75819	+	26.3788i	−0.213266	+	0.976994i
$730$	−0.524040	+	2.94088i	−0.0193956	+	0.108847i
$731$			14.8664i			0.549854i
$732$	−9.21024	+	8.57299i	−0.340420	+	0.316867i
$733$	−7.14810	−	7.14810i	−0.264021	−	0.264021i	0.562664	−	0.826685i	$-0.309776\pi$
$733$	−7.14810	−	7.14810i	−0.264021	−	0.264021i	−0.826685	+	0.562664i	$0.809776\pi$
$734$	12.1765	−	21.0904i	0.449444	−	0.778460i
$735$	−20.4608	−	17.7864i	−0.754707	−	0.656062i
$736$	4.35072	+	7.53566i	0.160370	+	0.277768i
$737$	0.513924	−	1.91799i	0.0189306	−	0.0706501i
$738$	−3.48635	+	10.0654i	−0.128334	+	0.370511i
$739$	6.62986	+	3.82775i	0.243883	+	0.140806i	0.616960	−	0.786994i	$-0.288364\pi$
$739$	6.62986	+	3.82775i	0.243883	+	0.140806i	−0.373077	+	0.927800i	$0.621697\pi$
$740$	−19.5970	−	9.18141i	−0.720401	−	0.337515i
$741$	−21.7236	−	0.778459i	−0.798035	−	0.0285974i
$742$	−13.7999	−	10.3696i	−0.506612	−	0.380681i
$743$	10.2522	+	38.2618i	0.376118	+	1.40369i	0.851705	+	0.524022i	$0.175569\pi$
$743$	10.2522	+	38.2618i	0.376118	+	1.40369i	−0.475587	+	0.879668i	$0.657764\pi$
$744$	8.03687	+	15.1485i	0.294646	+	0.555371i
$745$	−7.91021	−	6.66186i	−0.289808	−	0.244072i
$746$	−12.9021	+	22.3471i	−0.472380	+	0.818185i
$747$	−3.84751	−	1.33267i	−0.140773	−	0.0487597i
$748$	−1.81750	−	1.81750i	−0.0664544	−	0.0664544i
$749$	1.52525	+	10.7468i	0.0557313	+	0.392678i
$750$	17.1555	−	8.98275i	0.626429	−	0.328004i
$751$	43.0021			1.56917			0.784584	−	0.620023i	$-0.212877\pi$
$751$	43.0021			1.56917			0.784584	+	0.620023i	$0.212877\pi$
$752$	−1.13207	−	0.303337i	−0.0412824	−	0.0110616i
$753$	0.554096	+	0.595284i	0.0201924	+	0.0216933i
$754$	3.32750	−	5.76340i	0.121180	−	0.209891i
$755$	−12.7237	+	15.1079i	−0.463063	+	0.549835i
$756$	13.7400	−	0.460821i	0.499719	−	0.0167599i
$757$	−9.11781	−	9.11781i	−0.331393	−	0.331393i	0.521723	−	0.853115i	$-0.325290\pi$
$757$	−9.11781	−	9.11781i	−0.331393	−	0.331393i	−0.853115	+	0.521723i	$0.825290\pi$
$758$	−9.14861	−	34.1431i	−0.332292	−	1.24013i
$759$	0.543576	−	15.1689i	0.0197306	−	0.550598i
$760$	3.56016	−	2.48327i	0.129141	−	0.0900777i
$761$		−	4.77823i		−	0.173211i	−0.996243	−	0.0866054i	$-0.972398\pi$
$761$		−	4.77823i		−	0.173211i	0.996243	−	0.0866054i	$-0.0276019\pi$
$762$	−23.2188	+	5.33817i	−0.841130	+	0.193381i
$763$	−2.30819	−	0.280229i	−0.0835622	−	0.0101450i
$764$			13.7473i			0.497360i
$765$	−8.35448	+	14.9436i	−0.302057	+	0.540285i
$766$	8.45162	+	4.87954i	0.305369	+	0.176305i
$767$	20.1098	+	20.1098i	0.726124	+	0.726124i
$768$	1.65591	+	0.507915i	0.0597523	+	0.0183278i
$769$	5.16382	−	8.94400i	0.186212	−	0.322529i	−0.757772	−	0.652519i	$-0.773712\pi$
$769$	5.16382	−	8.94400i	0.186212	−	0.322529i	0.943984	+	0.329990i	$0.107046\pi$
$770$	−0.210617	+	5.95450i	−0.00759011	+	0.214585i
$771$	0.464317	−	12.9571i	0.0167220	−	0.466640i
$772$	−4.99207	+	1.33762i	−0.179669	+	0.0481421i
$773$	−10.1983	+	2.73264i	−0.366809	+	0.0982862i	−0.437515	−	0.899211i	$-0.644141\pi$
$773$	−10.1983	+	2.73264i	−0.366809	+	0.0982862i	0.0707062	+	0.997497i	$0.477475\pi$
$774$	−1.25083	+	17.4303i	−0.0449601	+	0.626520i
$775$	31.6827	+	38.0365i	1.13808	+	1.36631i
$776$	−13.7919	+	7.96273i	−0.495099	+	0.285845i
$777$	−34.4798	−	27.8958i	−1.23696	−	1.00076i
$778$	−0.241582	−	0.901596i	−0.00866113	−	0.0323238i
$779$			6.89261i			0.246953i
$780$	−18.5622	−	16.8052i	−0.664635	−	0.601722i
$781$	0.161897			0.00579312
$782$	−21.4507	−	5.74770i	−0.767076	−	0.205537i
$783$	−4.98822	−	1.93049i	−0.178264	−	0.0689900i
$784$	−1.94773	−	6.72357i	−0.0695619	−	0.240127i
$785$	−15.9323	+	11.1130i	−0.568646	+	0.396640i
$786$	−22.8476	−	14.3058i	−0.814946	−	0.510270i
$787$	−36.2132	−	9.70329i	−1.29086	−	0.345885i	−0.452873	−	0.891575i	$-0.649601\pi$
$787$	−36.2132	−	9.70329i	−1.29086	−	0.345885i	−0.837987	+	0.545690i	$0.816268\pi$
$788$	9.74995	+	2.61249i	0.347327	+	0.0930661i
$789$	−1.20974	+	33.7588i	−0.0430679	+	1.20185i
$790$	−16.3425	+	11.3992i	−0.581440	+	0.405564i
$791$	−11.1445	−	14.2244i	−0.396252	−	0.505762i
$792$	−1.97803	−	2.28387i	−0.0702863	−	0.0811539i
$793$	45.3665	+	12.1559i	1.61101	+	0.431669i
$794$	6.94985			0.246641
$795$	24.0530	−	7.74301i	0.853073	−	0.274616i
$796$			0.0322750i			0.00114396i
$797$	0.808220	+	3.01632i	0.0286286	+	0.106844i	0.978762	−	0.205001i	$-0.0657198\pi$
$797$	0.808220	+	3.01632i	0.0286286	+	0.106844i	−0.950133	+	0.311845i	$0.899053\pi$
$798$	8.30344	−	3.19164i	0.293939	−	0.112983i
$799$	2.59040	−	1.49557i	0.0916419	−	0.0529095i
$800$	4.97937	+	0.453786i	0.176047	+	0.0160438i
$801$	47.5659	−	23.0920i	1.68066	−	0.815916i
$802$	17.9212	−	4.80198i	0.632821	−	0.169564i
$803$	1.29959	−	0.348224i	0.0458615	−	0.0122885i
$804$	−2.89436	−	1.81227i	−0.102076	−	0.0639140i
$805$	24.1472	+	45.4636i	0.851077	+	1.60238i
$806$	32.0045	−	55.4335i	1.12731	−	1.95256i
$807$	−3.86573	−	16.8143i	−0.136080	−	0.591893i
$808$	13.2263	+	13.2263i	0.465300	+	0.465300i
$809$	19.6798	+	11.3621i	0.691904	+	0.399471i	0.804325	−	0.594190i	$-0.202527\pi$
$809$	19.6798	+	11.3621i	0.691904	+	0.399471i	−0.112421	+	0.993661i	$0.535860\pi$
$810$	−11.0526	+	16.8178i	−0.388350	+	0.590918i
$811$		−	13.5347i		−	0.475269i	−0.971355	−	0.237635i	$-0.923628\pi$
$811$		−	13.5347i		−	0.475269i	0.971355	−	0.237635i	$-0.0763721\pi$
$812$	−0.328233	+	2.70360i	−0.0115187	+	0.0948777i
$813$	12.3946	−	40.4089i	0.434697	−	1.41720i
$814$			9.74718i			0.341639i
$815$	23.6218	−	16.4766i	0.827435	−	0.577150i
$816$	−3.90493	+	2.07172i	−0.136700	+	0.0725246i
$817$	2.92662	+	10.9223i	0.102390	+	0.382123i
$818$	21.7164	+	21.7164i	0.759297	+	0.759297i
$819$	−28.6753	−	42.5559i	−1.00200	−	1.48702i
$820$	−5.11445	+	6.07283i	−0.178604	+	0.212072i
$821$	16.5553	−	28.6745i	0.577782	−	1.00075i	−0.417951	−	0.908470i	$-0.637252\pi$
$821$	16.5553	−	28.6745i	0.577782	−	1.00075i	0.995733	−	0.0922788i	$-0.0294151\pi$
$822$	26.4277	−	6.07590i	0.921771	−	0.211921i
$823$	2.93077	+	0.785299i	0.102160	+	0.0273738i	0.309537	−	0.950887i	$-0.399826\pi$
$823$	2.93077	+	0.785299i	0.102160	+	0.0273738i	−0.207377	+	0.978261i	$0.566493\pi$
$824$	−2.93093			−0.102104
$825$	−6.94181	−	5.28049i	−0.241683	−	0.183843i
$826$	−10.7969	−	4.34518i	−0.375672	−	0.151188i
$827$	−0.785007	−	0.785007i	−0.0272974	−	0.0272974i	0.693326	−	0.720624i	$-0.256144\pi$
$827$	−0.785007	−	0.785007i	−0.0272974	−	0.0272974i	−0.720624	+	0.693326i	$0.756144\pi$
$828$	−24.6665	−	8.54378i	−0.857222	−	0.296917i
$829$	−15.3996	+	26.6728i	−0.534849	+	0.926386i	0.464322	+	0.885667i	$0.346298\pi$
$829$	−15.3996	+	26.6728i	−0.534849	+	0.926386i	−0.999171	+	0.0407191i	$0.987035\pi$
$830$	−2.32135	−	1.95501i	−0.0805754	−	0.0678594i
$831$	−9.11788	−	0.326738i	−0.316296	−	0.0113344i
$832$	−1.67330	−	6.24485i	−0.0580113	−	0.216501i
$833$	15.6486	+	8.61869i	0.542193	+	0.298620i
$834$	−5.26699	−	9.92763i	−0.182381	−	0.343766i
$835$	19.6975	+	9.22849i	0.681660	+	0.319365i
$836$	−1.69311	−	0.977516i	−0.0585573	−	0.0338081i
$837$	−47.9776	−	18.5678i	−1.65835	−	0.641797i
$838$	7.72975	−	28.8478i	0.267020	−	0.996531i
$839$	−13.6159	−	23.5834i	−0.470071	−	0.814188i	0.529343	−	0.848408i	$-0.322439\pi$
$839$	−13.6159	−	23.5834i	−0.470071	−	0.814188i	−0.999414	+	0.0342203i	$0.989105\pi$
$840$	9.68413	+	3.34928i	0.334134	+	0.115561i
$841$	−13.9702	+	24.1971i	−0.481731	+	0.834383i
$842$	17.0382	+	17.0382i	0.587175	+	0.587175i
$843$	19.9632	+	6.12329i	0.687568	+	0.210897i
$844$		−	10.7786i		−	0.371013i
$845$	−11.2966	+	63.3958i	−0.388615	+	2.18088i
$846$	3.16298	−	1.53555i	0.108746	−	0.0527932i
$847$	−24.3054	+	10.3560i	−0.835144	+	0.355837i
$848$	6.30201	+	1.68862i	0.216412	+	0.0579874i
$849$	−19.5745	−	36.8954i	−0.671794	−	1.26625i
$850$	−9.80492	+	8.16707i	−0.336306	+	0.280128i
$851$	42.1073	+	72.9319i	1.44342	+	2.50007i
$852$	0.0816480	−	0.266189i	0.00279722	−	0.00911949i
$853$	−5.55096	+	20.7165i	−0.190061	+	0.709318i	0.803429	+	0.595401i	$0.203007\pi$
$853$	−5.55096	+	20.7165i	−0.190061	+	0.709318i	−0.993490	+	0.113918i	$0.963660\pi$
$854$	−19.0297	+	2.70081i	−0.651183	+	0.0924199i
$855$	−3.19620	+	12.6237i	−0.109308	+	0.431720i
$856$	−2.05130	−	3.55295i	−0.0701119	−	0.121437i
$857$	−1.51510	+	1.51510i	−0.0517547	+	0.0517547i	−0.732510	−	0.680756i	$-0.761652\pi$
$857$	−1.51510	+	1.51510i	−0.0517547	+	0.0517547i	0.680756	+	0.732510i	$0.261652\pi$
$858$	−3.30713	+	10.7819i	−0.112904	+	0.368089i
$859$	−36.5584			−1.24736			−0.623679	−	0.781681i	$-0.714363\pi$
$859$	−36.5584			−1.24736			−0.623679	+	0.781681i	$0.714363\pi$
$860$	−5.52602	+	11.7949i	−0.188436	+	0.402202i
$861$	−13.1595	+	9.56988i	−0.448474	+	0.326141i
$862$	−8.37996	+	31.2744i	−0.285422	+	1.06521i
$863$	21.0751	+	5.64706i	0.717405	+	0.192228i	0.599014	−	0.800739i	$-0.295560\pi$
$863$	21.0751	+	5.64706i	0.717405	+	0.192228i	0.118392	+	0.992967i	$0.462226\pi$
$864$	−4.75269	+	2.10046i	−0.161690	+	0.0714590i
$865$	−3.20030	+	6.83080i	−0.108814	+	0.232254i
$866$	3.27087	+	1.88844i	0.111149	+	0.0641717i
$867$	−5.32625	+	17.3647i	−0.180889	+	0.589735i
$868$	−3.15701	+	26.0037i	−0.107156	+	0.882623i
$869$	7.77201	+	4.48717i	0.263648	+	0.152217i
$870$	−2.95544	−	2.67569i	−0.100199	−	0.0907144i
$871$			12.7467i			0.431906i
$872$	0.848876	−	0.227456i	0.0287466	−	0.00770262i
$873$	15.6369	−	45.1450i	0.529229	−	1.52793i
$874$	−16.8913			−0.571355
$875$	29.3450	+	3.72428i	0.992042	+	0.125904i
$876$	0.0828641	−	2.31239i	0.00279972	−	0.0781285i
$877$	1.68865	+	1.68865i	0.0570215	+	0.0570215i	0.735043	−	0.678021i	$-0.237162\pi$
$877$	1.68865	+	1.68865i	0.0570215	+	0.0570215i	−0.678021	+	0.735043i	$0.737162\pi$
$878$	−2.77470	+	10.3553i	−0.0936418	+	0.349476i
$879$	2.86288	−	4.57228i	0.0965627	−	0.154219i
$880$	−0.766401	−	2.11757i	−0.0258354	−	0.0713834i
$881$			53.6206i			1.80652i	0.429091	+	0.903261i	$0.358834\pi$
$881$			53.6206i			1.80652i	−0.429091	+	0.903261i	$0.641166\pi$
$882$	17.6223	+	11.4217i	0.593372	+	0.384590i
$883$	−34.2231	+	34.2231i	−1.15170	+	1.15170i	−0.165489	+	0.986212i	$0.552920\pi$
$883$	−34.2231	+	34.2231i	−1.15170	+	1.15170i	−0.986212	+	0.165489i	$0.947080\pi$
$884$	14.2895	+	8.25002i	0.480606	+	0.277478i
$885$	14.3136	−	9.24007i	0.481145	−	0.310601i
$886$	6.52693	+	11.3050i	0.219277	+	0.379798i
$887$	32.9284	−	32.9284i	1.10563	−	1.10563i	0.111907	−	0.993719i	$-0.464304\pi$
$887$	32.9284	−	32.9284i	1.10563	−	1.10563i	0.993719	−	0.111907i	$-0.0356960\pi$
$888$	16.0263	+	4.91572i	0.537806	+	0.164961i
$889$	−33.7611	−	13.5871i	−1.13231	−	0.455696i
$890$	39.2668	−	3.36387i	1.31623	−	0.112757i
$891$	8.97123	+	1.29425i	0.300548	+	0.0433589i
$892$	−1.99521	−	7.44621i	−0.0668045	−	0.249318i
$893$	1.60874	−	1.60874i	0.0538344	−	0.0538344i
$894$	6.78957	+	4.25122i	0.227077	+	0.142182i
$895$	35.8893	−	12.9892i	1.19965	−	0.434182i
$896$	1.63172	+	2.08267i	0.0545118	+	0.0695770i
$897$	21.8322	+	94.9609i	0.728954	+	3.17065i
$898$	3.25436	+	12.1454i	0.108599	+	0.405299i
$899$	5.09570	−	8.82601i	0.169951	−	0.294364i
$900$	−12.1831	+	8.75061i	−0.406102	+	0.291687i
$901$	−14.4203	+	8.32554i	−0.480409	+	0.277364i
$902$	3.45413	+	0.925532i	0.115010	+	0.0308168i
$903$	−16.7897	+	20.7524i	−0.558725	+	0.690596i
$904$	5.91487	+	3.41495i	0.196726	+	0.113580i
$905$	−24.0300	−	20.2377i	−0.798783	−	0.672723i
$906$	8.11953	−	12.9676i	0.269753	−	0.430820i
$907$	−4.42669	−	4.42669i	−0.146986	−	0.146986i	0.629784	−	0.776770i	$-0.283143\pi$
$907$	−4.42669	−	4.42669i	−0.146986	−	0.146986i	−0.776770	+	0.629784i	$0.783143\pi$
$908$	−0.184278	+	0.687734i	−0.00611547	+	0.0228232i
$909$	−55.9705	−	4.01654i	−1.85642	−	0.133220i
$910$	−8.58723	−	37.2719i	−0.284664	−	1.23555i
$911$	−22.0050	−	38.1138i	−0.729058	−	1.26277i	−0.957282	−	0.289157i	$-0.906625\pi$
$911$	−22.0050	−	38.1138i	−0.729058	−	1.26277i	0.228223	−	0.973609i	$-0.426708\pi$
$912$	−2.46110	+	2.29081i	−0.0814950	+	0.0758564i
$913$	−0.353787	+	1.32035i	−0.0117086	+	0.0436972i
$914$	0.293483	−	0.169442i	0.00970754	−	0.00560465i
$915$	12.8415	−	25.0343i	0.424529	−	0.827610i
$916$	14.6789	−	8.47489i	0.485006	−	0.280018i
$917$	−16.1406	−	37.8818i	−0.533011	−	1.25097i
$918$	4.78634	−	12.3675i	0.157973	−	0.408189i
$919$	−0.228358	+	0.131843i	−0.00753285	+	0.00434909i	−0.503762	−	0.863843i	$-0.668051\pi$
$919$	−0.228358	+	0.131843i	−0.00753285	+	0.00434909i	0.496229	+	0.868192i	$0.334718\pi$
$920$	−14.8823	−	12.5336i	−0.490655	−	0.413222i
$921$	−0.0817780	+	2.28208i	−0.00269468	+	0.0751972i
$922$	12.3041	−	12.3041i	0.405214	−	0.405214i
$923$	−1.00387	+	0.268986i	−0.0330427	+	0.00885377i
$924$	−0.484466	−	4.58972i	−0.0159377	−	0.150991i
$925$	48.1915	+	4.39185i	1.58453	+	0.144403i
$926$	6.00725	+	10.4049i	0.197410	+	0.341925i
$927$	6.64653	−	5.75647i	0.218301	−	0.189067i
$928$	−0.266420	−	0.994293i	−0.00874566	−	0.0326393i
$929$	−18.2146	+	31.5486i	−0.597601	+	1.03507i	0.395573	+	0.918434i	$0.370546\pi$
$929$	−18.2146	+	31.5486i	−0.597601	+	1.03507i	−0.993174	+	0.116640i	$0.962787\pi$
$930$	−28.4260	−	25.7353i	−0.932125	−	0.843893i
$931$	13.1937	+	3.25151i	0.432405	+	0.106564i
$932$	26.3528	−	7.06121i	0.863214	−	0.231298i
$933$	−6.61822	+	21.5768i	−0.216671	+	0.706392i
$934$	−22.7991			−0.746009
$935$	5.20455	+	2.43839i	0.170207	+	0.0797438i
$936$	16.0597	+	10.8751i	0.524928	+	0.355464i
$937$	−7.88964	+	7.88964i	−0.257743	+	0.257743i	−0.824136	−	0.566392i	$-0.808339\pi$
$937$	−7.88964	+	7.88964i	−0.257743	+	0.257743i	0.566392	+	0.824136i	$0.308339\pi$
$938$	−2.04472	−	4.79893i	−0.0667625	−	0.156691i
$939$	26.2122	−	41.8632i	0.855404	−	1.36616i
$940$	2.61112	−	0.223687i	0.0851654	−	0.00729588i
$941$	−11.1358	+	6.42924i	−0.363016	+	0.209587i	−0.670403	−	0.741997i	$-0.733879\pi$
$941$	−11.1358	+	6.42924i	−0.363016	+	0.209587i	0.307387	+	0.951585i	$0.400545\pi$
$942$	11.0138	−	10.2517i	0.358848	−	0.334020i
$943$	29.8433	−	7.99649i	0.971832	−	0.260402i
$944$	4.39892			0.143173
$945$	−28.5390	+	11.4248i	−0.928374	+	0.371648i
$946$	5.86654			0.190738
$947$	14.4066	−	3.86023i	0.468150	−	0.125440i	−0.0170294	−	0.999855i	$-0.505421\pi$
$947$	14.4066	−	3.86023i	0.468150	−	0.125440i	0.485180	+	0.874415i	$0.338754\pi$
$948$	11.2974	−	10.5157i	0.366922	−	0.341534i
$949$	−7.47977	+	4.31844i	−0.242803	+	0.140183i
$950$	−5.59586	+	7.93052i	−0.181554	+	0.257300i
$951$	−11.2889	+	18.0294i	−0.366068	+	0.584643i
$952$	−6.70315	−	0.813803i	−0.217250	−	0.0263755i
$953$	−4.20631	+	4.20631i	−0.136256	+	0.136256i	−0.771945	−	0.635689i	$-0.780716\pi$
$953$	−4.20631	+	4.20631i	−0.136256	+	0.136256i	0.635689	+	0.771945i	$0.280716\pi$
$954$	−17.6077	+	8.54809i	−0.570071	+	0.276755i
$955$	−10.4614	−	28.9050i	−0.338523	−	0.935344i
$956$	−13.4864			−0.436180
$957$	−0.526555	+	1.71668i	−0.0170211	+	0.0554923i
$958$	24.9580	−	6.68748i	0.806357	−	0.216063i
$959$	38.4269	+	15.4648i	1.24087	+	0.499385i
$960$	−3.86821	+	0.192172i	−0.124846	+	0.00620233i
$961$	33.5114	−	58.0435i	1.08101	−	1.87237i
$962$	−16.1946	−	60.4391i	−0.522135	−	1.94864i
$963$	11.6299	+	4.02827i	0.374769	+	0.129809i
$964$	8.70742	+	15.0817i	0.280447	+	0.485749i
$965$	9.47841	−	6.61135i	0.305121	−	0.212827i
$966$	−23.4523	−	32.2491i	−0.754565	−	1.03760i
$967$	27.6017	−	7.39587i	0.887612	−	0.237835i	0.213924	−	0.976850i	$-0.431376\pi$
$967$	27.6017	−	7.39587i	0.887612	−	0.237835i	0.673689	+	0.739015i	$0.264709\pi$
$968$	7.06096	−	7.06096i	0.226948	−	0.226948i
$969$	0.307302	−	8.57551i	0.00987195	−	0.275485i
$970$	22.9392	−	27.2377i	0.736534	−	0.874551i
$971$	−49.2925	+	28.4590i	−1.58187	+	0.913294i	−0.587285	+	0.809380i	$0.699803\pi$
$971$	−49.2925	+	28.4590i	−1.58187	+	0.913294i	−0.994586	+	0.103913i	$0.966864\pi$
$972$	6.65238	−	14.0977i	0.213375	−	0.452185i
$973$	2.06896	−	17.0416i	0.0663278	−	0.546330i
$974$	−7.51557	+	4.33911i	−0.240814	+	0.139034i
$975$	51.8173	+	21.2090i	1.65948	+	0.679232i
$976$	6.29136	−	3.63232i	0.201381	−	0.116268i
$977$	−4.68399	+	17.4809i	−0.149854	+	0.559263i	0.849637	+	0.527368i	$0.176821\pi$
$977$	−4.68399	+	17.4809i	−0.149854	+	0.559263i	−0.999491	+	0.0318954i	$0.989846\pi$
$978$	−16.3295	+	15.1996i	−0.522159	+	0.486030i
$979$	−8.87525	−	15.3724i	−0.283654	−	0.491304i
$980$	9.21179	+	12.6548i	0.294260	+	0.404241i
$981$	−1.47828	+	2.18303i	−0.0471979	+	0.0696989i
$982$	1.23606	−	4.61302i	0.0394441	−	0.147208i
$983$	−5.50977	−	5.50977i	−0.175734	−	0.175734i	0.613759	−	0.789493i	$-0.289657\pi$
$983$	−5.50977	−	5.50977i	−0.175734	−	0.175734i	−0.789493	+	0.613759i	$0.789657\pi$
$984$	3.26375	−	5.21249i	0.104044	−	0.166168i
$985$	−22.4882	+	1.92650i	−0.716535	+	0.0613835i
$986$	2.27514	+	1.31355i	0.0724552	+	0.0418320i
$987$	5.30506	+	0.837817i	0.168862	+	0.0266680i
$988$	12.1225	+	3.24822i	0.385669	+	0.103340i
$989$	43.8956	−	25.3431i	1.39580	−	0.805864i
$990$	5.89698	+	3.29682i	0.187418	+	0.104780i
$991$	−1.60809	+	2.78529i	−0.0510825	+	0.0884775i	−0.890436	−	0.455108i	$-0.849600\pi$
$991$	−1.60809	+	2.78529i	−0.0510825	+	0.0884775i	0.839353	+	0.543586i	$0.182934\pi$
$992$	−2.56248	−	9.56329i	−0.0813587	−	0.303635i
$993$	−1.15760	−	5.03508i	−0.0367353	−	0.159783i
$994$	0.334792	−	0.262301i	0.0106189	−	0.00831968i
$995$	−0.0245606	−	0.0678612i	−0.000778623	−	0.00215134i
$996$	1.99249	+	1.24757i	0.0631344	+	0.0395309i
$997$	10.8166	−	10.8166i	0.342564	−	0.342564i	−0.514766	−	0.857331i	$-0.672121\pi$
$997$	10.8166	−	10.8166i	0.342564	−	0.342564i	0.857331	+	0.514766i	$0.172121\pi$
$998$	5.69817	+	21.2659i	0.180372	+	0.673159i
$999$	−45.9977	+	20.3287i	−1.45530	+	0.643173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cg.a.157.5	yes	192
5.3	odd	4	inner	630.2.cg.a.283.32	yes	192
7.5	odd	6		630.2.bw.a.607.37	yes	192
9.7	even	3		630.2.bw.a.367.26	yes	192
35.33	even	12		630.2.bw.a.103.26	✓	192
45.43	odd	12		630.2.bw.a.493.37	yes	192
63.61	odd	6	inner	630.2.cg.a.187.32	yes	192
315.313	even	12	inner	630.2.cg.a.313.5	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bw.a.103.26	✓	192	35.33	even	12
630.2.bw.a.367.26	yes	192	9.7	even	3
630.2.bw.a.493.37	yes	192	45.43	odd	12
630.2.bw.a.607.37	yes	192	7.5	odd	6
630.2.cg.a.157.5	yes	192	1.1	even	1	trivial
630.2.cg.a.187.32	yes	192	63.61	odd	6	inner
630.2.cg.a.283.32	yes	192	5.3	odd	4	inner
630.2.cg.a.313.5	yes	192	315.313	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-1.26782 + 1.18010i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-1.44041 + 1.71033i) q^{5} +(0.919188 - 1.46802i) q^{6} +(2.43402 - 1.03708i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.214733 - 2.99231i) q^{9} +(0.948666 - 2.02485i) q^{10} -1.00712 q^{11} +(-0.507915 + 1.65591i) q^{12} +(6.24485 - 1.67330i) q^{13} +(-2.08267 + 1.63172i) q^{14} +(-0.192172 - 3.86821i) q^{15} +(0.500000 - 0.866025i) q^{16} +(0.660546 + 2.46519i) q^{17} +(0.567049 + 2.94592i) q^{18} +(0.970602 + 1.68113i) q^{19} +(-0.392270 + 2.20139i) q^{20} +(-1.86204 + 4.18722i) q^{21} +(0.972806 - 0.260663i) q^{22} +(6.15284 - 6.15284i) q^{23} +(0.0620279 - 1.73094i) q^{24} +(-0.850430 - 4.92715i) q^{25} +(-5.59898 + 3.23257i) q^{26} +(3.25897 + 4.04711i) q^{27} +(1.58938 - 2.11515i) q^{28} +(-0.891458 + 0.514684i) q^{29} +(1.18679 + 3.68667i) q^{30} +(-8.57421 + 4.95032i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(1.27685 - 1.18851i) q^{33} +(-1.27608 - 2.21023i) q^{34} +(-1.73224 + 5.65680i) q^{35} +(-1.31019 - 2.69878i) q^{36} +(-2.50491 + 9.34846i) q^{37} +(-1.37264 - 1.37264i) q^{38} +(-5.94268 + 9.49098i) q^{39} +(-0.190859 - 2.22791i) q^{40} +(3.07498 + 1.77534i) q^{41} +(0.714857 - 4.52648i) q^{42} +(5.62656 + 1.50763i) q^{43} +(-0.872194 + 0.503562i) q^{44} +(4.80851 + 4.67741i) q^{45} +(-4.35072 + 7.53566i) q^{46} +(-0.303337 - 1.13207i) q^{47} +(0.388086 + 1.68801i) q^{48} +(4.84891 - 5.04857i) q^{49} +(2.09669 + 4.53915i) q^{50} +(-3.74662 - 2.34591i) q^{51} +(4.57154 - 4.57154i) q^{52} +(1.68862 + 6.30201i) q^{53} +(-4.19540 - 3.06572i) q^{54} +(1.45067 - 1.72251i) q^{55} +(-0.987783 + 2.45444i) q^{56} +(-3.21445 - 0.985965i) q^{57} +(0.727873 - 0.727873i) q^{58} +(2.19946 + 3.80957i) q^{59} +(-2.10053 - 3.25388i) q^{60} +(6.29136 + 3.63232i) q^{61} +(7.00081 - 7.00081i) q^{62} +(-2.58061 - 7.50603i) q^{63} -1.00000i q^{64} +(-6.13326 + 13.0910i) q^{65} +(-0.925735 + 1.47848i) q^{66} +(-0.510289 + 1.90442i) q^{67} +(1.80465 + 1.80465i) q^{68} +(-0.539731 + 15.0617i) q^{69} +(0.209127 - 5.91238i) q^{70} -0.160752 q^{71} +(1.96404 + 2.26772i) q^{72} +(-1.29040 + 0.345761i) q^{73} -9.67824i q^{74} +(6.89271 + 5.24314i) q^{75} +(1.68113 + 0.970602i) q^{76} +(-2.45136 + 1.04447i) q^{77} +(3.28374 - 10.7057i) q^{78} +(-7.71704 - 4.45544i) q^{79} +(0.760980 + 2.10260i) q^{80} +(-8.90778 - 1.28509i) q^{81} +(-3.42970 - 0.918985i) q^{82} +(0.351284 - 1.31101i) q^{83} +(0.481039 + 4.55726i) q^{84} +(-5.16774 - 2.42114i) q^{85} -5.82504 q^{86} +(0.522831 - 1.70454i) q^{87} +(0.712144 - 0.712144i) q^{88} +(8.81248 + 15.2637i) q^{89} +(-5.85527 - 3.27350i) q^{90} +(13.4647 - 10.5493i) q^{91} +(2.25210 - 8.40494i) q^{92} +(5.02868 - 16.3945i) q^{93} +(0.586003 + 1.01499i) q^{94} +(-4.27335 - 0.761475i) q^{95} +(-0.811752 - 1.53005i) q^{96} +(15.3828 + 4.12181i) q^{97} +(-3.37702 + 6.13153i) q^{98} +(-0.216263 + 3.01362i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{11} - 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} + 12 q^{21} - 16 q^{23} - 36 q^{27} + 12 q^{30} - 60 q^{33} + 48 q^{35} - 16 q^{36} + 12 q^{41} + 4 q^{42} - 36 q^{45} + 12 q^{46} - 16 q^{50}+ \cdots - 48 q^{98}+O(q^{100}) \) 192 * q - 16 * q^11 - 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 + 12 * q^21 - 16 * q^23 - 36 * q^27 + 12 * q^30 - 60 * q^33 + 48 * q^35 - 16 * q^36 + 12 * q^41 + 4 * q^42 - 36 * q^45 + 12 * q^46 - 16 * q^50 + 24 * q^51 - 40 * q^53 + 8 * q^56 - 32 * q^57 + 24 * q^58 + 8 * q^60 + 36 * q^61 - 108 * q^63 - 8 * q^65 + 16 * q^71 - 8 * q^72 + 80 * q^77 - 16 * q^78 + 4 * q^81 - 168 * q^83 - 16 * q^86 + 36 * q^90 + 8 * q^92 - 60 * q^93 + 64 * q^95 - 12 * q^96 - 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more