LMFDB - Embedded newform 630.2.cd.a.23.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(23,630)]

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([10, 9, 4]))

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

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

chi := DirichletCharacter("630.23");

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.cd (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			23.10
Character	$\chi$	$=$	630.23
Dual form			630.2.cd.a.137.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.717442 + 1.57648i) q^{3} +1.00000i q^{4} +(2.15148 - 0.609219i) q^{5} +(1.62204 - 0.607429i) q^{6} +(-0.673710 - 2.55854i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.97055 - 2.26206i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.717442 + 1.57648i) q^{3} +1.00000i q^{4} +(2.15148 - 0.609219i) q^{5} +(1.62204 - 0.607429i) q^{6} +(-0.673710 - 2.55854i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.97055 - 2.26206i) q^{9} +(-1.95211 - 1.09054i) q^{10} +(-4.13272 - 2.38603i) q^{11} +(-1.57648 - 0.717442i) q^{12} +(-1.30169 + 0.348786i) q^{13} +(-1.33277 + 2.28554i) q^{14} +(-0.583140 + 3.82883i) q^{15} -1.00000 q^{16} +(-1.32567 + 4.94748i) q^{17} +(-0.206125 + 2.99291i) q^{18} +(-1.62774 - 0.939777i) q^{19} +(0.609219 + 2.15148i) q^{20} +(4.51682 + 0.773514i) q^{21} +(1.23510 + 4.60945i) q^{22} +(-4.99991 - 1.33972i) q^{23} +(0.607429 + 1.62204i) q^{24} +(4.25770 - 2.62144i) q^{25} +(1.16706 + 0.673803i) q^{26} +(4.97984 - 1.48364i) q^{27} +(2.55854 - 0.673710i) q^{28} +(-4.90075 - 8.48834i) q^{29} +(3.11973 - 2.29505i) q^{30} -2.30702 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.72650 - 4.80330i) q^{33} +(4.43579 - 2.56100i) q^{34} +(-3.00818 - 5.09420i) q^{35} +(2.26206 - 1.97055i) q^{36} +(0.910632 + 3.39853i) q^{37} +(0.486464 + 1.81551i) q^{38} +(0.384032 - 2.30231i) q^{39} +(1.09054 - 1.95211i) q^{40} +(-4.61203 - 2.66276i) q^{41} +(-2.64692 - 3.74083i) q^{42} +(-0.100575 + 0.375353i) q^{43} +(2.38603 - 4.13272i) q^{44} +(-5.61769 - 3.66627i) q^{45} +(2.58814 + 4.48280i) q^{46} +(-1.56599 - 1.56599i) q^{47} +(0.717442 - 1.57648i) q^{48} +(-6.09223 + 3.44742i) q^{49} +(-4.86429 - 1.15701i) q^{50} +(-6.84849 - 5.63942i) q^{51} +(-0.348786 - 1.30169i) q^{52} +(-0.0971817 - 0.0260397i) q^{53} +(-4.57037 - 2.47219i) q^{54} +(-10.3451 - 2.61575i) q^{55} +(-2.28554 - 1.33277i) q^{56} +(2.64935 - 1.89186i) q^{57} +(-2.53681 + 9.46751i) q^{58} +1.49375 q^{59} +(-3.82883 - 0.583140i) q^{60} +13.4441 q^{61} +(1.63131 + 1.63131i) q^{62} +(-4.45998 + 6.56571i) q^{63} -1.00000i q^{64} +(-2.58806 + 1.54342i) q^{65} +(-8.15280 - 1.35991i) q^{66} +(2.59071 - 2.59071i) q^{67} +(-4.94748 - 1.32567i) q^{68} +(5.69918 - 6.92106i) q^{69} +(-1.47504 + 5.72925i) q^{70} -14.1744i q^{71} +(-2.99291 - 0.206125i) q^{72} +(-1.48882 + 5.55636i) q^{73} +(1.75921 - 3.04704i) q^{74} +(1.07798 + 8.59290i) q^{75} +(0.939777 - 1.62774i) q^{76} +(-3.32048 + 12.1812i) q^{77} +(-1.89953 + 1.35643i) q^{78} -3.85958i q^{79} +(-2.15148 + 0.609219i) q^{80} +(-1.23383 + 8.91502i) q^{81} +(1.37835 + 5.14406i) q^{82} +(-4.36758 - 1.17029i) q^{83} +(-0.773514 + 4.51682i) q^{84} +(0.161943 + 11.4520i) q^{85} +(0.336532 - 0.194297i) q^{86} +(16.8977 - 1.63602i) q^{87} +(-4.60945 + 1.23510i) q^{88} +(7.07233 - 12.2496i) q^{89} +(1.37986 + 6.56475i) q^{90} +(1.76934 + 3.09544i) q^{91} +(1.33972 - 4.99991i) q^{92} +(1.65515 - 3.63697i) q^{93} +2.21464i q^{94} +(-4.07458 - 1.03026i) q^{95} +(-1.62204 + 0.607429i) q^{96} +(10.9879 + 2.94420i) q^{97} +(6.74555 + 1.87016i) q^{98} +(2.74641 + 14.0502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{6}+O(q^{10}) $ 192 * q + 8 * q^6	$ 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−0.717442	+	1.57648i	−0.414215	+	0.910179i
$3$	−0.717442	+	1.57648i	−0.414215	+	0.910179i
$4$			1.00000i			0.500000i
$5$	2.15148	−	0.609219i	0.962170	−	0.272451i
$5$	2.15148	−	0.609219i	0.962170	−	0.272451i
$6$	1.62204	−	0.607429i	0.662197	−	0.247982i
$7$	−0.673710	−	2.55854i	−0.254638	−	0.967036i
$7$	−0.673710	−	2.55854i	−0.254638	−	0.967036i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−1.97055	−	2.26206i	−0.656852	−	0.754020i
$10$	−1.95211	−	1.09054i	−0.617310	−	0.344859i
$11$	−4.13272	−	2.38603i	−1.24606	−	0.719414i	−0.275740	−	0.961232i	$-0.588923\pi$
$11$	−4.13272	−	2.38603i	−1.24606	−	0.719414i	−0.970322	+	0.241818i	$0.922256\pi$
$12$	−1.57648	−	0.717442i	−0.455089	−	0.207108i
$13$	−1.30169	+	0.348786i	−0.361023	+	0.0967359i	−0.434771	−	0.900541i	$-0.643171\pi$
$13$	−1.30169	+	0.348786i	−0.361023	+	0.0967359i	0.0737478	+	0.997277i	$0.476504\pi$
$14$	−1.33277	+	2.28554i	−0.356199	+	0.610837i
$15$	−0.583140	+	3.82883i	−0.150566	+	0.988600i
$16$	−1.00000			−0.250000
$17$	−1.32567	+	4.94748i	−0.321523	+	1.19994i	0.596238	+	0.802808i	$0.296661\pi$
$17$	−1.32567	+	4.94748i	−0.321523	+	1.19994i	−0.917761	+	0.397133i	$0.870005\pi$
$18$	−0.206125	+	2.99291i	−0.0485841	+	0.705436i
$19$	−1.62774	−	0.939777i	−0.373429	−	0.215600i	0.301526	−	0.953458i	$-0.402504\pi$
$19$	−1.62774	−	0.939777i	−0.373429	−	0.215600i	−0.674956	+	0.737858i	$0.735837\pi$
$20$	0.609219	+	2.15148i	0.136225	+	0.481085i
$21$	4.51682	+	0.773514i	0.985651	+	0.168795i
$22$	1.23510	+	4.60945i	0.263324	+	0.982738i
$23$	−4.99991	−	1.33972i	−1.04255	−	0.279351i	−0.303382	−	0.952869i	$-0.598116\pi$
$23$	−4.99991	−	1.33972i	−1.04255	−	0.279351i	−0.739171	+	0.673518i	$0.764782\pi$
$24$	0.607429	+	1.62204i	0.123991	+	0.331099i
$25$	4.25770	−	2.62144i	0.851541	−	0.524288i
$26$	1.16706	+	0.673803i	0.228880	+	0.132144i
$27$	4.97984	−	1.48364i	0.958371	−	0.285526i
$28$	2.55854	−	0.673710i	0.483518	−	0.127319i
$29$	−4.90075	−	8.48834i	−0.910046	−	1.57625i	−0.813997	−	0.580869i	$-0.802713\pi$
$29$	−4.90075	−	8.48834i	−0.910046	−	1.57625i	−0.0960483	−	0.995377i	$-0.530620\pi$
$30$	3.11973	−	2.29505i	0.569583	−	0.419017i
$31$	−2.30702			−0.414354			−0.207177	−	0.978304i	$-0.566428\pi$
$31$	−2.30702			−0.414354			−0.207177	+	0.978304i	$0.566428\pi$
$32$	0.707107	+	0.707107i	0.125000	+	0.125000i
$33$	6.72650	−	4.80330i	1.17093	−	0.836147i
$34$	4.43579	−	2.56100i	0.760732	−	0.439209i
$35$	−3.00818	−	5.09420i	−0.508475	−	0.861077i
$36$	2.26206	−	1.97055i	0.377010	−	0.328426i
$37$	0.910632	+	3.39853i	0.149707	+	0.558714i	0.999501	+	0.0315987i	$0.0100598\pi$
$37$	0.910632	+	3.39853i	0.149707	+	0.558714i	−0.849794	+	0.527116i	$0.823273\pi$
$38$	0.486464	+	1.81551i	0.0789149	+	0.294514i
$39$	0.384032	−	2.30231i	0.0614943	−	0.368665i
$40$	1.09054	−	1.95211i	0.172430	−	0.308655i
$41$	−4.61203	−	2.66276i	−0.720279	−	0.415853i	0.0945765	−	0.995518i	$-0.469850\pi$
$41$	−4.61203	−	2.66276i	−0.720279	−	0.415853i	−0.814855	+	0.579664i	$0.803184\pi$
$42$	−2.64692	−	3.74083i	−0.408428	−	0.577223i
$43$	−0.100575	+	0.375353i	−0.0153376	+	0.0572408i	−0.973171	−	0.230085i	$-0.926100\pi$
$43$	−0.100575	+	0.375353i	−0.0153376	+	0.0572408i	0.957833	+	0.287326i	$0.0927662\pi$
$44$	2.38603	−	4.13272i	0.359707	−	0.623031i
$45$	−5.61769	−	3.66627i	−0.837436	−	0.546535i
$46$	2.58814	+	4.48280i	0.381601	+	0.660952i
$47$	−1.56599	−	1.56599i	−0.228423	−	0.228423i	0.583611	−	0.812033i	$-0.301639\pi$
$47$	−1.56599	−	1.56599i	−0.228423	−	0.228423i	−0.812033	+	0.583611i	$0.801639\pi$
$48$	0.717442	−	1.57648i	0.103554	−	0.227545i
$49$	−6.09223	+	3.44742i	−0.870319	+	0.492489i
$50$	−4.86429	−	1.15701i	−0.687915	−	0.163626i
$51$	−6.84849	−	5.63942i	−0.958981	−	0.789677i
$52$	−0.348786	−	1.30169i	−0.0483679	−	0.180512i
$53$	−0.0971817	−	0.0260397i	−0.0133489	−	0.00357683i	0.252138	−	0.967691i	$-0.418866\pi$
$53$	−0.0971817	−	0.0260397i	−0.0133489	−	0.00357683i	−0.265487	+	0.964114i	$0.585533\pi$
$54$	−4.57037	−	2.47219i	−0.621949	−	0.336422i
$55$	−10.3451	−	2.61575i	−1.39493	−	0.352708i
$56$	−2.28554	−	1.33277i	−0.305419	−	0.178099i
$57$	2.64935	−	1.89186i	0.350914	−	0.250583i
$58$	−2.53681	+	9.46751i	−0.333100	+	1.24315i
$59$	1.49375			0.194469			0.0972347	−	0.995261i	$-0.469000\pi$
$59$	1.49375			0.194469			0.0972347	+	0.995261i	$0.469000\pi$
$60$	−3.82883	−	0.583140i	−0.494300	−	0.0752831i
$61$	13.4441			1.72134			0.860668	−	0.509167i	$-0.170046\pi$
$61$	13.4441			1.72134			0.860668	+	0.509167i	$0.170046\pi$
$62$	1.63131	+	1.63131i	0.207177	+	0.207177i
$63$	−4.45998	+	6.56571i	−0.561905	+	0.827202i
$64$		−	1.00000i		−	0.125000i
$65$	−2.58806	+	1.54342i	−0.321010	+	0.191437i
$66$	−8.15280	−	1.35991i	−1.00354	−	0.167393i
$67$	2.59071	−	2.59071i	0.316506	−	0.316506i	−0.530917	−	0.847424i	$-0.678153\pi$
$67$	2.59071	−	2.59071i	0.316506	−	0.316506i	0.847424	+	0.530917i	$0.178153\pi$
$68$	−4.94748	−	1.32567i	−0.599970	−	0.160762i
$69$	5.69918	−	6.92106i	0.686101	−	0.833198i
$70$	−1.47504	+	5.72925i	−0.176301	+	0.684776i
$71$		−	14.1744i		−	1.68220i	−0.540882	−	0.841099i	$-0.681909\pi$
$71$		−	14.1744i		−	1.68220i	0.540882	−	0.841099i	$-0.318091\pi$
$72$	−2.99291	−	0.206125i	−0.352718	−	0.0242921i
$73$	−1.48882	+	5.55636i	−0.174254	+	0.650323i	0.822424	+	0.568875i	$0.192621\pi$
$73$	−1.48882	+	5.55636i	−0.174254	+	0.650323i	−0.996678	+	0.0814481i	$0.974046\pi$
$74$	1.75921	−	3.04704i	0.204504	−	0.354211i
$75$	1.07798	+	8.59290i	0.124475	+	0.992223i
$76$	0.939777	−	1.62774i	0.107800	−	0.186715i
$77$	−3.32048	+	12.1812i	−0.378404	+	1.38818i
$78$	−1.89953	+	1.35643i	−0.215080	+	0.153585i
$79$		−	3.85958i		−	0.434237i	−0.976145	−	0.217118i	$-0.930334\pi$
$79$		−	3.85958i		−	0.434237i	0.976145	−	0.217118i	$-0.0696658\pi$
$80$	−2.15148	+	0.609219i	−0.240542	+	0.0681127i
$81$	−1.23383	+	8.91502i	−0.137092	+	0.990558i
$82$	1.37835	+	5.14406i	0.152213	+	0.568066i
$83$	−4.36758	−	1.17029i	−0.479404	−	0.128456i	0.0110209	−	0.999939i	$-0.496492\pi$
$83$	−4.36758	−	1.17029i	−0.479404	−	0.128456i	−0.490425	+	0.871483i	$0.663159\pi$
$84$	−0.773514	+	4.51682i	−0.0843973	+	0.492826i
$85$	0.161943	+	11.4520i	0.0175652	+	1.24215i
$86$	0.336532	−	0.194297i	0.0362892	−	0.0209516i
$87$	16.8977	−	1.63602i	1.81162	−	0.175400i
$88$	−4.60945	+	1.23510i	−0.491369	+	0.131662i
$89$	7.07233	−	12.2496i	0.749665	−	1.29846i	−0.198318	−	0.980138i	$-0.563548\pi$
$89$	7.07233	−	12.2496i	0.749665	−	1.29846i	0.947983	−	0.318321i	$-0.103119\pi$
$90$	1.37986	+	6.56475i	0.145450	+	0.691986i
$91$	1.76934	+	3.09544i	0.185478	+	0.324490i
$92$	1.33972	−	4.99991i	0.139676	−	0.521276i
$93$	1.65515	−	3.63697i	0.171632	−	0.377136i
$94$			2.21464i			0.228423i
$95$	−4.07458	−	1.03026i	−0.418043	−	0.105702i
$96$	−1.62204	+	0.607429i	−0.165549	+	0.0619955i
$97$	10.9879	+	2.94420i	1.11565	+	0.298938i	0.769122	−	0.639102i	$-0.220694\pi$
$97$	10.9879	+	2.94420i	1.11565	+	0.298938i	0.346529	+	0.938039i	$0.387360\pi$
$98$	6.74555	+	1.87016i	0.681404	+	0.188915i
$99$	2.74641	+	14.0502i	0.276025	+	1.41210i
$100$	2.62144	+	4.25770i	0.262144	+	0.425770i
$101$	−7.94244	−	4.58557i	−0.790302	−	0.456281i	0.0497666	−	0.998761i	$-0.484152\pi$
$101$	−7.94244	−	4.58557i	−0.790302	−	0.456281i	−0.840069	+	0.542480i	$0.817486\pi$
$102$	0.854942	+	8.83029i	0.0846519	+	0.874329i
$103$	2.51252	−	9.37684i	0.247566	−	0.923927i	−0.724511	−	0.689263i	$-0.757934\pi$
$103$	2.51252	−	9.37684i	0.247566	−	0.923927i	0.972077	−	0.234664i	$-0.0753990\pi$
$104$	−0.673803	+	1.16706i	−0.0660718	+	0.114440i
$105$	10.1891	−	1.08754i	0.994352	−	0.106133i
$106$	0.0503049	+	0.0871307i	0.00488605	+	0.00846288i
$107$	−15.6669	+	4.19794i	−1.51458	+	0.405831i	−0.917953	−	0.396688i	$-0.870159\pi$
$107$	−15.6669	+	4.19794i	−1.51458	+	0.405831i	−0.596627	+	0.802519i	$0.703493\pi$
$108$	1.48364	+	4.97984i	0.142763	+	0.479185i
$109$	6.33702	−	3.65868i	0.606977	−	0.350438i	−0.164805	−	0.986326i	$-0.552699\pi$
$109$	6.33702	−	3.65868i	0.606977	−	0.350438i	0.771781	+	0.635888i	$0.219366\pi$
$110$	5.46545	+	9.16468i	0.521110	+	0.873817i
$111$	−6.01102	−	1.00265i	−0.570541	−	0.0951677i
$112$	0.673710	+	2.55854i	0.0636596	+	0.241759i
$113$	4.07785	+	15.2187i	0.383612	+	1.43166i	0.840344	+	0.542054i	$0.182353\pi$
$113$	4.07785	+	15.2187i	0.383612	+	1.43166i	−0.456732	+	0.889604i	$0.650980\pi$
$114$	−3.21112	−	0.535623i	−0.300749	−	0.0501657i
$115$	−11.5734	+	0.163659i	−1.07922	+	0.0152613i
$116$	8.48834	−	4.90075i	0.788123	−	0.455023i
$117$	3.35402	+	2.25719i	0.310079	+	0.208678i
$118$	−1.05624	−	1.05624i	−0.0972347	−	0.0972347i
$119$	13.5514	+	0.0586192i	1.24226	+	0.00537361i
$120$	2.29505	+	3.11973i	0.209508	+	0.284792i
$121$	5.88624	+	10.1953i	0.535113	+	0.926842i
$122$	−9.50639	−	9.50639i	−0.860668	−	0.860668i
$123$	7.50664	−	5.36039i	0.676851	−	0.483330i
$124$		−	2.30702i		−	0.207177i
$125$	7.56332	−	8.23384i	0.676484	−	0.736457i
$126$	7.79634	−	1.48897i	0.694553	−	0.132648i
$127$	−8.38188	+	8.38188i	−0.743772	+	0.743772i	−0.973302	−	0.229530i	$-0.926281\pi$
$127$	−8.38188	+	8.38188i	−0.743772	+	0.743772i	0.229530	+	0.973302i	$0.426281\pi$
$128$	−0.707107	+	0.707107i	−0.0625000	+	0.0625000i
$129$	−0.519578	−	0.427849i	−0.0457463	−	0.0376700i
$130$	2.92140	+	0.738676i	0.256224	+	0.0647862i
$131$	−16.3307	+	9.42856i	−1.42682	+	0.823777i	−0.996869	−	0.0790734i	$-0.974804\pi$
$131$	−16.3307	+	9.42856i	−1.42682	+	0.823777i	−0.429955	+	0.902850i	$0.641471\pi$
$132$	4.80330	+	6.72650i	0.418073	+	0.585466i
$133$	−1.30783	+	4.79777i	−0.113403	+	0.416020i
$134$	−3.66382			−0.316506
$135$	9.81015	−	6.22582i	0.844324	−	0.535834i
$136$	2.56100	+	4.43579i	0.219604	+	0.380366i
$137$	7.85469	−	2.10466i	0.671071	−	0.179813i	0.0928338	−	0.995682i	$-0.470407\pi$
$137$	7.85469	−	2.10466i	0.671071	−	0.179813i	0.578237	+	0.815869i	$0.303741\pi$
$138$	−8.92386	+	0.864002i	−0.759650	+	0.0735487i
$139$	−1.01702	−	0.587175i	−0.0862623	−	0.0498036i	0.456248	−	0.889852i	$-0.349193\pi$
$139$	−1.01702	−	0.587175i	−0.0862623	−	0.0498036i	−0.542511	+	0.840049i	$0.682526\pi$
$140$	5.09420	−	3.00818i	0.430538	−	0.254238i
$141$	3.59224	−	1.34524i	0.302521	−	0.113289i
$142$	−10.0228	+	10.0228i	−0.841099	+	0.841099i
$143$	6.21172	+	1.66443i	0.519450	+	0.139186i
$144$	1.97055	+	2.26206i	0.164213	+	0.188505i
$145$	−15.7151	−	15.2768i	−1.30507	−	1.26867i
$146$	4.98170	−	2.87618i	0.412288	−	0.238035i
$147$	−1.06396	−	12.0776i	−0.0877541	−	0.996142i
$148$	−3.39853	+	0.910632i	−0.279357	+	0.0748535i
$149$	6.68740	+	11.5829i	0.547853	+	0.948910i	0.998421	+	0.0561675i	$0.0178881\pi$
$149$	6.68740	+	11.5829i	0.547853	+	0.948910i	−0.450568	+	0.892742i	$0.648779\pi$
$150$	5.31385	−	6.83835i	0.433874	−	0.558349i
$151$	−1.38052	+	2.39113i	−0.112345	+	0.194587i	−0.916715	−	0.399541i	$-0.869170\pi$
$151$	−1.38052	+	2.39113i	−0.112345	+	0.194587i	0.804370	+	0.594128i	$0.202503\pi$
$152$	−1.81551	+	0.486464i	−0.147257	+	0.0394575i
$153$	13.8038	−	6.75053i	1.11597	−	0.545748i
$154$	10.9613	−	6.26547i	0.883291	−	0.504886i
$155$	−4.96351	+	1.40548i	−0.398678	+	0.112891i
$156$	2.30231	+	0.384032i	0.184333	+	0.0307472i
$157$	6.56772	−	6.56772i	0.524161	−	0.524161i	−0.394664	−	0.918825i	$-0.629139\pi$
$157$	6.56772	−	6.56772i	0.524161	−	0.524161i	0.918825	+	0.394664i	$0.129139\pi$
$158$	−2.72914	+	2.72914i	−0.217118	+	0.217118i
$159$	0.110773	−	0.134523i	0.00878489	−	0.0106683i
$160$	1.95211	+	1.09054i	0.154328	+	0.0862148i
$161$	−0.0592403	+	13.6950i	−0.00466879	+	1.07932i
$162$	7.17632	−	5.43143i	0.563825	−	0.426733i
$163$	7.45837	−	1.99846i	0.584184	−	0.156532i	0.0453904	−	0.998969i	$-0.485547\pi$
$163$	7.45837	−	1.99846i	0.584184	−	0.156532i	0.538794	+	0.842438i	$0.318880\pi$
$164$	2.66276	−	4.61203i	0.207927	−	0.360139i
$165$	11.5456	−	14.4321i	0.898827	−	1.12354i
$166$	2.26083	+	3.91587i	0.175474	+	0.303930i
$167$	21.4839	−	5.75659i	1.66247	−	0.445458i	0.699407	−	0.714723i	$-0.253447\pi$
$167$	21.4839	−	5.75659i	1.66247	−	0.445458i	0.963066	+	0.269265i	$0.0867807\pi$
$168$	3.74083	−	2.64692i	0.288611	−	0.204214i
$169$	−9.68559	+	5.59198i	−0.745045	+	0.430152i
$170$	7.98329	−	8.21231i	0.612290	−	0.629855i
$171$	1.08172	+	5.53393i	0.0827213	+	0.423190i
$172$	−0.375353	−	0.100575i	−0.0286204	−	0.00766881i
$173$	0.383597	−	0.383597i	0.0291643	−	0.0291643i	−0.692374	−	0.721539i	$-0.743435\pi$
$173$	0.383597	−	0.383597i	0.0291643	−	0.0291643i	0.721539	+	0.692374i	$0.243435\pi$
$174$	−13.1053	−	10.7916i	−0.993510	−	0.818110i
$175$	−9.57551	−	9.12741i	−0.723841	−	0.689967i
$176$	4.13272	+	2.38603i	0.311515	+	0.179853i
$177$	−1.07168	+	2.35486i	−0.0805522	+	0.177002i
$178$	−13.6627	+	3.66091i	−1.02406	+	0.274397i
$179$	12.8143	+	22.1951i	0.957789	+	1.65894i	0.727853	+	0.685734i	$0.240518\pi$
$179$	12.8143	+	22.1951i	0.957789	+	1.65894i	0.229936	+	0.973206i	$0.426148\pi$
$180$	3.66627	−	5.61769i	0.273268	−	0.418718i
$181$	−18.7914			−1.39676			−0.698378	−	0.715729i	$-0.746095\pi$
$181$	−18.7914			−1.39676			−0.698378	+	0.715729i	$0.746095\pi$
$182$	0.937690	−	3.43992i	0.0695062	−	0.254984i
$183$	−9.64533	+	21.1942i	−0.713003	+	1.56672i
$184$	−4.48280	+	2.58814i	−0.330476	+	0.190800i
$185$	4.02965	+	6.75708i	0.296266	+	0.496790i
$186$	−3.74210	+	1.40135i	−0.274384	+	0.102752i
$187$	17.2835	−	17.2835i	1.26389	−	1.26389i
$188$	1.56599	−	1.56599i	0.114211	−	0.114211i
$189$	−7.15091	−	11.7416i	−0.520152	−	0.854074i
$190$	2.15266	+	3.60966i	0.156170	+	0.261872i
$191$			0.184891i			0.0133783i	0.999978	+	0.00668913i	$0.00212923\pi$
$191$			0.184891i			0.0133783i	−0.999978	+	0.00668913i	$0.997871\pi$
$192$	1.57648	+	0.717442i	0.113772	+	0.0517769i
$193$	4.80188	+	4.80188i	0.345647	+	0.345647i	0.858485	−	0.512839i	$-0.171406\pi$
$193$	4.80188	+	4.80188i	0.345647	+	0.345647i	−0.512839	+	0.858485i	$0.671406\pi$
$194$	−5.68775	−	9.85147i	−0.408357	−	0.707294i
$195$	−0.576377	−	5.18733i	−0.0412752	−	0.371473i
$196$	−3.44742	−	6.09223i	−0.246245	−	0.435159i
$197$	−13.9180	−	13.9180i	−0.991613	−	0.991613i	0.00835192	−	0.999965i	$-0.497341\pi$
$197$	−13.9180	−	13.9180i	−0.991613	−	0.991613i	−0.999965	+	0.00835192i	$0.997341\pi$
$198$	7.99302	−	11.8770i	0.568039	−	0.844064i
$199$	19.3909	−	11.1953i	1.37458	−	0.793617i	0.383083	−	0.923714i	$-0.374862\pi$
$199$	19.3909	−	11.1953i	1.37458	−	0.793617i	0.991501	+	0.130097i	$0.0415289\pi$
$200$	1.15701	−	4.86429i	0.0818132	−	0.343957i
$201$	2.22551	+	5.94289i	0.156976	+	0.419179i
$202$	2.37367	+	8.85864i	0.167011	+	0.623292i
$203$	−18.4161	+	18.2574i	−1.29255	+	1.28142i
$204$	5.63942	−	6.84849i	0.394839	−	0.479490i
$205$	−11.5449	−	2.91913i	−0.806330	−	0.203881i
$206$	−8.40704	+	4.85381i	−0.585747	+	0.338181i
$207$	6.82206	+	13.9501i	0.474166	+	0.969598i
$208$	1.30169	−	0.348786i	0.0902558	−	0.0241840i
$209$	4.48466	+	7.76766i	0.310211	+	0.537301i
$210$	−7.97377	−	6.43576i	−0.550242	−	0.444110i
$211$	−3.62926	+	6.28605i	−0.249848	+	0.432750i	−0.963484	−	0.267768i	$-0.913714\pi$
$211$	−3.62926	+	6.28605i	−0.249848	+	0.432750i	0.713635	+	0.700517i	$0.247047\pi$
$212$	0.0260397	−	0.0971817i	0.00178842	−	0.00667446i
$213$	22.3457	+	10.1693i	1.53110	+	0.696792i
$214$	14.0466	+	8.10981i	0.960206	+	0.554375i
$215$	0.0122862	+	0.868835i	0.000837911	+	0.0592541i
$216$	2.47219	−	4.57037i	0.168211	−	0.310974i
$217$	1.55426	+	5.90261i	0.105510	+	0.400695i
$218$	−7.06803	−	1.89387i	−0.478707	−	0.128269i
$219$	−7.69133	−	6.33346i	−0.519732	−	0.427976i
$220$	2.61575	−	10.3451i	0.176354	−	0.697464i
$221$		−	6.90245i		−	0.464309i
$222$	3.54145	+	4.95942i	0.237687	+	0.332854i
$223$	−3.06109	+	11.4241i	−0.204986	+	0.765016i	0.784468	+	0.620169i	$0.212936\pi$
$223$	−3.06109	+	11.4241i	−0.204986	+	0.765016i	−0.989454	+	0.144848i	$0.953731\pi$
$224$	1.33277	−	2.28554i	0.0890497	−	0.152709i
$225$	−14.3199	−	4.46549i	−0.954660	−	0.297699i
$226$	7.87780	−	13.6447i	0.524023	−	0.907635i
$227$	−16.9495	+	4.54160i	−1.12498	+	0.301437i	−0.772896	−	0.634533i	$-0.781192\pi$
$227$	−16.9495	+	4.54160i	−1.12498	+	0.301437i	−0.352081	+	0.935970i	$0.614526\pi$
$228$	1.89186	+	2.64935i	0.125291	+	0.175457i
$229$	−12.7960	+	7.38778i	−0.845585	+	0.488198i	−0.859159	−	0.511709i	$-0.829012\pi$
$229$	−12.7960	+	7.38778i	−0.845585	+	0.488198i	0.0135741	+	0.999908i	$0.495679\pi$
$230$	8.29933	+	8.06788i	0.547242	+	0.531981i
$231$	−16.8211	−	13.9740i	−1.10675	−	0.919420i
$232$	−9.46751	−	2.53681i	−0.621573	−	0.166550i
$233$	3.01913	+	11.2675i	0.197790	+	0.738161i	0.991527	+	0.129900i	$0.0414658\pi$
$233$	3.01913	+	11.2675i	0.197790	+	0.738161i	−0.793737	+	0.608261i	$0.791868\pi$
$234$	−0.775575	−	3.96773i	−0.0507010	−	0.259379i
$235$	−4.32321	−	2.41515i	−0.282015	−	0.157547i
$236$			1.49375i			0.0972347i
$237$	6.08454	+	2.76902i	0.395233	+	0.179867i
$238$	−9.54086	−	9.62376i	−0.618442	−	0.623816i
$239$	0.228112	−	0.395101i	0.0147553	−	0.0255570i	−0.858553	−	0.512724i	$-0.828636\pi$
$239$	0.228112	−	0.395101i	0.0147553	−	0.0255570i	0.873309	+	0.487167i	$0.161970\pi$
$240$	0.583140	−	3.82883i	0.0376415	−	0.247150i
$241$	8.97190	−	15.5398i	0.577931	−	1.00101i	−0.417786	−	0.908546i	$-0.637194\pi$
$241$	8.97190	−	15.5398i	0.577931	−	1.00101i	0.995716	−	0.0924598i	$-0.0294730\pi$
$242$	3.04694	−	11.3713i	0.195865	−	0.730977i
$243$	−13.1691	−	8.34111i	−0.844800	−	0.535083i
$244$			13.4441i			0.860668i
$245$	−11.0071	+	11.1286i	−0.703215	+	0.710977i
$246$	−9.09836	−	1.51763i	−0.580091	−	0.0967606i
$247$	2.44659	+	0.655562i	0.155673	+	0.0417124i
$248$	−1.63131	+	1.63131i	−0.103588	+	0.103588i
$249$	4.97842	−	6.04577i	0.315495	−	0.383135i
$250$	−11.1703	+	0.474129i	−0.706471	+	0.0299866i
$251$			2.76147i			0.174302i	0.996195	+	0.0871511i	$0.0277763\pi$
$251$			2.76147i			0.174302i	−0.996195	+	0.0871511i	$0.972224\pi$
$252$	−6.56571	−	4.45998i	−0.413601	−	0.280953i
$253$	17.4666	+	17.4666i	1.09812	+	1.09812i
$254$	11.8538			0.743772
$255$	−18.1700	−	7.96086i	−1.13785	−	0.498528i
$256$	1.00000			0.0625000
$257$	5.37417	−	20.0567i	0.335232	−	1.25110i	−0.568386	−	0.822762i	$-0.692432\pi$
$257$	5.37417	−	20.0567i	0.335232	−	1.25110i	0.903618	−	0.428339i	$-0.140901\pi$
$258$	0.0648623	+	0.669932i	0.00403815	+	0.0417081i
$259$	8.08176	−	4.61951i	0.502176	−	0.287042i
$260$	−1.54342	−	2.58806i	−0.0957187	−	0.160505i
$261$	−9.54394	+	27.8125i	−0.590755	+	1.72155i
$262$	18.2146	+	4.88058i	1.12530	+	0.301523i
$263$	0.383236	+	1.43026i	0.0236313	+	0.0881933i	0.976734	−	0.214453i	$-0.0687967\pi$
$263$	0.383236	+	1.43026i	0.0236313	+	0.0881933i	−0.953103	+	0.302646i	$0.902130\pi$
$264$	1.35991	−	8.15280i	0.0836965	−	0.501770i
$265$	−0.224948	+	0.00318099i	−0.0138184	+	0.000195406i
$266$	4.31731	−	2.46776i	0.264711	−	0.151308i
$267$	14.2373	+	19.9378i	0.871307	+	1.22017i
$268$	2.59071	+	2.59071i	0.158253	+	0.158253i
$269$	4.20016	+	7.27489i	0.256088	+	0.443558i	0.965190	−	0.261548i	$-0.0842329\pi$
$269$	4.20016	+	7.27489i	0.256088	+	0.443558i	−0.709102	+	0.705106i	$0.750900\pi$
$270$	−11.3391	−	2.53450i	−0.690079	−	0.154245i
$271$	11.8659	−	20.5523i	0.720802	−	1.24847i	−0.239876	−	0.970803i	$-0.577107\pi$
$271$	11.8659	−	20.5523i	0.720802	−	1.24847i	0.960679	−	0.277663i	$-0.0895598\pi$
$272$	1.32567	−	4.94748i	0.0803808	−	0.299985i
$273$	−6.14928	+	0.568531i	−0.372172	+	0.0344091i
$274$	−7.04232	−	4.06588i	−0.425442	−	0.245629i
$275$	−23.8507	+	0.674680i	−1.43825	+	0.0406847i
$276$	6.92106	+	5.69918i	0.416599	+	0.343050i
$277$	−2.66071	−	9.92990i	−0.159867	−	0.596630i	−0.998639	−	0.0521485i	$-0.983393\pi$
$277$	−2.66071	−	9.92990i	−0.159867	−	0.596630i	0.838773	−	0.544482i	$-0.183274\pi$
$278$	0.303944	+	1.13434i	0.0182294	+	0.0680329i
$279$	4.54612	+	5.21862i	0.272169	+	0.312431i
$280$	−5.72925	−	1.47504i	−0.342388	−	0.0881503i
$281$	−16.1374	+	9.31691i	−0.962674	+	0.555800i	−0.896995	−	0.442041i	$-0.854255\pi$
$281$	−16.1374	+	9.31691i	−0.962674	+	0.555800i	−0.0656791	+	0.997841i	$0.520921\pi$
$282$	−3.49132	−	1.58887i	−0.207905	−	0.0946161i
$283$	2.79729	+	2.79729i	0.166282	+	0.166282i	0.785343	−	0.619061i	$-0.212487\pi$
$283$	2.79729	+	2.79729i	0.166282	+	0.166282i	−0.619061	+	0.785343i	$0.712487\pi$
$284$	14.1744			0.841099
$285$	4.54745	−	5.68432i	0.269368	−	0.336710i
$286$	−3.21542	−	5.56928i	−0.190132	−	0.329318i
$287$	−3.70560	+	13.5940i	−0.218734	+	0.802428i
$288$	0.206125	−	2.99291i	0.0121460	−	0.176359i
$289$	−7.99773	−	4.61749i	−0.470455	−	0.271617i
$290$	0.309894	+	21.9146i	0.0181976	+	1.28687i
$291$	−12.5246	+	15.2099i	−0.734206	+	0.891618i
$292$	−5.55636	−	1.48882i	−0.325161	−	0.0871268i
$293$	7.88717	+	29.4353i	0.460774	+	1.71963i	0.670535	+	0.741878i	$0.266065\pi$
$293$	7.88717	+	29.4353i	0.460774	+	1.71963i	−0.209761	+	0.977753i	$0.567269\pi$
$294$	−7.78781	+	9.29247i	−0.454194	+	0.541948i
$295$	3.21376	−	0.910020i	0.187113	−	0.0529834i
$296$	3.04704	+	1.75921i	0.177105	+	0.102252i
$297$	−24.1203	−	5.75058i	−1.39960	−	0.333682i
$298$	3.46165	−	12.9191i	0.200528	−	0.748381i
$299$	6.97560			0.403409
$300$	−8.59290	+	1.07798i	−0.496111	+	0.0622374i
$301$	1.02811	+	0.00444729i	0.0592594	+	0.000256337i
$302$	2.66696	−	0.714609i	0.153466	−	0.0411211i
$303$	12.9273	−	9.23119i	0.742653	−	0.530318i
$304$	1.62774	+	0.939777i	0.0933574	+	0.0538999i
$305$	28.9246	−	8.19038i	1.65622	−	0.468980i
$306$	−14.5341	−	4.98742i	−0.830860	−	0.285112i
$307$	−4.52891	+	4.52891i	−0.258478	+	0.258478i	−0.824435	−	0.565957i	$-0.808507\pi$
$307$	−4.52891	+	4.52891i	−0.258478	+	0.258478i	0.565957	+	0.824435i	$0.308507\pi$
$308$	−12.1812	−	3.32048i	−0.694088	−	0.189202i
$309$	12.9798	+	10.6883i	0.738394	+	0.608034i
$310$	4.50356	+	2.51590i	0.255785	+	0.142894i
$311$		−	21.7069i		−	1.23089i	−0.788181	−	0.615443i	$-0.788977\pi$
$311$		−	21.7069i		−	1.23089i	0.788181	−	0.615443i	$-0.211023\pi$
$312$	−1.35643	−	1.89953i	−0.0767927	−	0.107540i
$313$	−23.7087	−	23.7087i	−1.34010	−	1.34010i	−0.895958	−	0.444138i	$-0.853510\pi$
$313$	−23.7087	−	23.7087i	−1.34010	−	1.34010i	−0.444138	−	0.895958i	$-0.646490\pi$
$314$	−9.28816			−0.524161
$315$	−5.59559	+	16.8431i	−0.315276	+	0.949000i
$316$	3.85958			0.217118
$317$	−23.8963	−	23.8963i	−1.34215	−	1.34215i	−0.893914	−	0.448238i	$-0.852052\pi$
$317$	−23.8963	−	23.8963i	−1.34215	−	1.34215i	−0.448238	−	0.893914i	$-0.647948\pi$
$318$	−0.173450	+	0.0167933i	−0.00972661	+	0.000941723i
$319$			46.7732i			2.61880i
$320$	−0.609219	−	2.15148i	−0.0340564	−	0.120271i
$321$	4.62216	−	27.7103i	0.257984	−	1.54664i
$322$	9.72574	−	9.64196i	0.541994	−	0.537326i
$323$	6.80738	−	6.80738i	0.378773	−	0.378773i
$324$	−8.91502	−	1.23383i	−0.495279	−	0.0685460i
$325$	−4.62788	+	4.89733i	−0.256709	+	0.271655i
$326$	−6.68699	−	3.86073i	−0.370358	−	0.213826i
$327$	1.22138	+	12.6151i	0.0675425	+	0.697614i
$328$	−5.14406	+	1.37835i	−0.284033	+	0.0761064i
$329$	−2.95161	+	5.06165i	−0.162728	+	0.279058i
$330$	−18.3690	+	2.04103i	−1.01118	+	0.112355i
$331$	−10.2905			−0.565617			−0.282809	−	0.959176i	$-0.591266\pi$
$331$	−10.2905			−0.565617			−0.282809	+	0.959176i	$0.591266\pi$
$332$	1.17029	−	4.36758i	0.0642280	−	0.239702i
$333$	5.89322	−	8.75689i	0.322946	−	0.479874i
$334$	−19.2619	−	11.1209i	−1.05397	−	0.608507i
$335$	3.99555	−	7.15217i	0.218300	−	0.390765i
$336$	−4.51682	−	0.773514i	−0.246413	−	0.0421987i
$337$	−5.02156	−	18.7407i	−0.273542	−	1.02087i	−0.956812	−	0.290707i	$-0.906110\pi$
$337$	−5.02156	−	18.7407i	−0.273542	−	1.02087i	0.683270	−	0.730166i	$-0.260557\pi$
$338$	10.8029	+	2.89462i	0.587599	+	0.157447i
$339$	−26.9176	−	4.48992i	−1.46196	−	0.243859i
$340$	−11.4520	+	0.161943i	−0.621073	+	0.00878258i
$341$	9.53428	+	5.50462i	0.516310	+	0.298092i
$342$	3.14819	−	4.67797i	0.170234	−	0.252956i
$343$	12.9248	+	13.2646i	0.697871	+	0.716223i
$344$	0.194297	+	0.336532i	0.0104758	+	0.0181446i
$345$	8.04521	−	18.3626i	0.433140	−	0.988607i
$346$	−0.542488			−0.0291643
$347$	−8.22861	−	8.22861i	−0.441735	−	0.441735i	0.450860	−	0.892595i	$-0.351117\pi$
$347$	−8.22861	−	8.22861i	−0.441735	−	0.441735i	−0.892595	+	0.450860i	$0.851117\pi$
$348$	1.63602	+	16.8977i	0.0876999	+	0.905810i
$349$	−16.5339	+	9.54588i	−0.885042	+	0.510979i	−0.872317	−	0.488940i	$-0.837384\pi$
$349$	−16.5339	+	9.54588i	−0.885042	+	0.510979i	−0.0127243	+	0.999919i	$0.504050\pi$
$350$	0.316857	+	13.2250i	0.0169367	+	0.706904i
$351$	−5.96473	+	3.66813i	−0.318374	+	0.195790i
$352$	−1.23510	−	4.60945i	−0.0658309	−	0.245684i
$353$	−3.45648	−	12.8998i	−0.183970	−	0.686586i	−0.994849	−	0.101371i	$-0.967677\pi$
$353$	−3.45648	−	12.8998i	−0.183970	−	0.686586i	0.810879	−	0.585214i	$-0.198990\pi$
$354$	2.42293	−	0.907346i	0.128777	−	0.0482249i
$355$	−8.63534	−	30.4960i	−0.458316	−	1.61856i
$356$	12.2496	+	7.07233i	0.649229	+	0.374833i
$357$	−9.81478	+	21.3215i	−0.519453	+	1.12845i
$358$	6.63319	−	24.7554i	0.350575	−	1.30836i
$359$	4.83887	−	8.38116i	0.255386	−	0.442341i	−0.709615	−	0.704590i	$-0.751131\pi$
$359$	4.83887	−	8.38116i	0.255386	−	0.442341i	0.965000	+	0.262249i	$0.0844642\pi$
$360$	−6.56475	+	1.37986i	−0.345993	+	0.0727252i
$361$	−7.73364	−	13.3951i	−0.407034	−	0.705003i
$362$	13.2876	+	13.2876i	0.698378	+	0.698378i
$363$	−20.2956	+	1.96501i	−1.06524	+	0.103136i
$364$	−3.09544	+	1.76934i	−0.162245	+	0.0927388i
$365$	0.181873	+	12.8614i	0.00951966	+	0.673197i
$366$	21.8069	−	8.16632i	1.13986	−	0.426860i
$367$	4.73020	+	17.6534i	0.246915	+	0.921498i	0.972411	+	0.233272i	$0.0749433\pi$
$367$	4.73020	+	17.6534i	0.246915	+	0.921498i	−0.725497	+	0.688225i	$0.758390\pi$
$368$	4.99991	+	1.33972i	0.260638	+	0.0698378i
$369$	3.06495	+	15.6798i	0.159555	+	0.816258i
$370$	1.92858	−	7.62737i	0.100262	−	0.396528i
$371$	−0.00115144	+	0.266186i	−5.97796e−5	+	0.0138197i
$372$	3.63697	+	1.65515i	0.188568	+	0.0858158i
$373$	3.57769	−	13.3521i	0.185246	−	0.691347i	−0.809332	−	0.587351i	$-0.800171\pi$
$373$	3.57769	−	13.3521i	0.185246	−	0.691347i	0.994578	−	0.103995i	$-0.0331626\pi$
$374$	−24.4425			−1.26389
$375$	7.55421	+	17.8307i	0.390098	+	0.920773i
$376$	−2.21464			−0.114211
$377$	9.33986	+	9.33986i	0.481027	+	0.481027i
$378$	−3.24609	+	13.3590i	−0.166961	+	0.687113i
$379$			10.0920i			0.518391i	0.965825	+	0.259195i	$0.0834573\pi$
$379$			10.0920i			0.518391i	−0.965825	+	0.259195i	$0.916543\pi$
$380$	1.03026	−	4.07458i	0.0528511	−	0.209021i
$381$	−7.20033	−	19.2274i	−0.368884	−	0.985047i
$382$	0.130738	−	0.130738i	0.00668913	−	0.00668913i
$383$	−5.50457	−	1.47495i	−0.281270	−	0.0753662i	0.115426	−	0.993316i	$-0.463177\pi$
$383$	−5.50457	−	1.47495i	−0.281270	−	0.0753662i	−0.396696	+	0.917950i	$0.629843\pi$
$384$	−0.607429	−	1.62204i	−0.0309977	−	0.0827746i
$385$	0.277074	+	28.2305i	0.0141210	+	1.43876i
$386$		−	6.79088i		−	0.345647i
$387$	1.04726	−	0.512146i	0.0532352	−	0.0260338i
$388$	−2.94420	+	10.9879i	−0.149469	+	0.557826i
$389$	16.6562	−	28.8494i	0.844503	−	1.46272i	−0.0415495	−	0.999136i	$-0.513229\pi$
$389$	16.6562	−	28.8494i	0.844503	−	1.46272i	0.886052	−	0.463585i	$-0.153437\pi$
$390$	−3.26044	+	4.07556i	−0.165099	+	0.206374i
$391$	13.2565	−	22.9609i	0.670410	−	1.16118i
$392$	−1.87016	+	6.74555i	−0.0944574	+	0.340702i
$393$	−3.14754	−	32.5095i	−0.158773	−	1.63989i
$394$			19.6830i			0.991613i
$395$	−2.35133	−	8.30380i	−0.118308	−	0.417810i
$396$	−14.0502	+	2.74641i	−0.706052	+	0.138013i
$397$	−3.10111	−	11.5735i	−0.155640	−	0.580858i	−0.999050	−	0.0435861i	$-0.986122\pi$
$397$	−3.10111	−	11.5735i	−0.155640	−	0.580858i	0.843409	−	0.537272i	$-0.180545\pi$
$398$	−21.6277	−	5.79514i	−1.08410	−	0.290484i
$399$	−6.62529	−	5.50388i	−0.331679	−	0.275539i
$400$	−4.25770	+	2.62144i	−0.212885	+	0.131072i
$401$	33.3421	−	19.2501i	1.66502	−	0.961303i	0.694765	−	0.719237i	$-0.255508\pi$
$401$	33.3421	−	19.2501i	1.66502	−	0.961303i	0.970260	−	0.242066i	$-0.0778249\pi$
$402$	2.62858	−	5.77593i	0.131102	−	0.288077i
$403$	3.00302	−	0.804658i	0.149591	−	0.0400829i
$404$	4.58557	−	7.94244i	0.228141	−	0.395151i
$405$	2.77665	+	19.9321i	0.137973	+	0.990436i
$406$	25.9321	+	0.112174i	1.28699	+	0.00556709i
$407$	4.34558	−	16.2179i	0.215403	−	0.803894i
$408$	−8.83029	+	0.854942i	−0.437165	+	0.0423259i
$409$		−	5.48937i		−	0.271432i	−0.990748	−	0.135716i	$-0.956667\pi$
$409$		−	5.48937i		−	0.271432i	0.990748	−	0.135716i	$-0.0433334\pi$
$410$	6.09933	+	10.2276i	0.301225	+	0.505105i
$411$	−2.31734	+	13.8927i	−0.114306	+	0.685276i
$412$	9.37684	+	2.51252i	0.461964	+	0.123783i
$413$	−1.00635	−	3.82181i	−0.0495194	−	0.188059i
$414$	5.04027	−	14.6881i	0.247716	−	0.721882i
$415$	−10.1097	+	0.142961i	−0.496266	+	0.00701769i
$416$	−1.16706	−	0.673803i	−0.0572199	−	0.0330359i
$417$	1.65532	−	1.18204i	0.0810613	−	0.0578847i
$418$	2.32143	−	8.66370i	0.113545	−	0.423756i
$419$	5.20034	−	9.00726i	0.254053	−	0.440033i	−0.710585	−	0.703612i	$-0.751569\pi$
$419$	5.20034	−	9.00726i	0.254053	−	0.440033i	0.964638	+	0.263578i	$0.0849028\pi$
$420$	1.08754	+	10.1891i	0.0530663	+	0.497176i
$421$	2.65150	+	4.59253i	0.129226	+	0.223826i	0.923377	−	0.383895i	$-0.125417\pi$
$421$	2.65150	+	4.59253i	0.129226	+	0.223826i	−0.794151	+	0.607721i	$0.792084\pi$
$422$	7.01118	−	1.87864i	0.341299	−	0.0914508i
$423$	−0.456492	+	6.62821i	−0.0221954	+	0.322275i
$424$	−0.0871307	+	0.0503049i	−0.00423144	+	0.00244302i
$425$	7.32520	+	24.5401i	0.355324	+	1.19037i
$426$	−8.60997	−	22.9916i	−0.417154	−	1.11395i
$427$	−9.05740	−	34.3971i	−0.438318	−	1.66459i
$428$	−4.19794	−	15.6669i	−0.202915	−	0.757290i
$429$	−7.08048	+	8.59850i	−0.341849	+	0.415140i
$430$	0.605672	−	0.623047i	0.0292081	−	0.0300460i
$431$	−28.3027	+	16.3406i	−1.36329	+	0.787097i	−0.990061	−	0.140641i	$-0.955084\pi$
$431$	−28.3027	+	16.3406i	−1.36329	+	0.787097i	−0.373232	+	0.927738i	$0.621750\pi$
$432$	−4.97984	+	1.48364i	−0.239593	+	0.0713815i
$433$	−18.6732	−	18.6732i	−0.897375	−	0.897375i	0.0978280	−	0.995203i	$-0.468811\pi$
$433$	−18.6732	−	18.6732i	−0.897375	−	0.897375i	−0.995203	+	0.0978280i	$0.968811\pi$
$434$	3.07474	−	5.27280i	0.147592	−	0.253103i
$435$	35.3582	−	13.8142i	1.69530	−	0.662342i
$436$	3.65868	+	6.33702i	0.175219	+	0.303488i
$437$	6.87952	+	6.87952i	0.329092	+	0.329092i
$438$	0.960159	+	9.91702i	0.0458782	+	0.473854i
$439$			23.7720i			1.13458i	0.823519	+	0.567288i	$0.192007\pi$
$439$			23.7720i			1.13458i	−0.823519	+	0.567288i	$0.807993\pi$
$440$	−9.16468	+	5.46545i	−0.436909	+	0.260555i
$441$	19.8034	+	6.98765i	0.943017	+	0.332745i
$442$	−4.88077	+	4.88077i	−0.232155	+	0.232155i
$443$	−15.0067	+	15.0067i	−0.712990	+	0.712990i	−0.967160	−	0.254170i	$-0.918198\pi$
$443$	−15.0067	+	15.0067i	−0.712990	+	0.712990i	0.254170	+	0.967160i	$0.418198\pi$
$444$	1.00265	−	6.01102i	0.0475839	−	0.285270i
$445$	7.75324	−	30.6634i	0.367539	−	1.45358i
$446$	10.2426	−	5.91356i	0.485001	−	0.280015i
$447$	−23.0580	+	2.23246i	−1.09061	+	0.105592i
$448$	−2.55854	+	0.673710i	−0.120880	+	0.0318298i
$449$	−8.16454			−0.385309			−0.192654	−	0.981267i	$-0.561710\pi$
$449$	−8.16454			−0.385309			−0.192654	+	0.981267i	$0.561710\pi$
$450$	6.96812	+	13.2833i	0.328480	+	0.626180i
$451$	12.7068	+	22.0089i	0.598341	+	1.03636i
$452$	−15.2187	+	4.07785i	−0.715829	+	0.191806i
$453$	−2.77912	−	3.89185i	−0.130574	−	0.182855i
$454$	15.1965	+	8.77370i	0.713206	+	0.411770i
$455$	5.69250	+	5.58184i	0.266868	+	0.261681i
$456$	0.535623	−	3.21112i	0.0250828	−	0.150374i
$457$	23.6638	−	23.6638i	1.10694	−	1.10694i	0.113395	−	0.993550i	$-0.463827\pi$
$457$	23.6638	−	23.6638i	1.10694	−	1.10694i	0.993550	−	0.113395i	$-0.0361725\pi$
$458$	14.2721	+	3.82420i	0.666891	+	0.178693i
$459$	0.738621	+	26.6045i	0.0344759	+	1.24179i
$460$	−0.163659	−	11.5734i	−0.00763063	−	0.539611i
$461$	20.4255	−	11.7927i	0.951310	−	0.549239i	0.0578226	−	0.998327i	$-0.481584\pi$
$461$	20.4255	−	11.7927i	0.951310	−	0.549239i	0.893488	+	0.449088i	$0.148251\pi$
$462$	2.01324	+	21.7754i	0.0936646	+	1.01308i
$463$	31.4215	−	8.41936i	1.46028	−	0.391281i	0.560693	−	0.828024i	$-0.310535\pi$
$463$	31.4215	−	8.41936i	1.46028	−	0.391281i	0.899586	+	0.436743i	$0.143868\pi$
$464$	4.90075	+	8.48834i	0.227511	+	0.394061i
$465$	1.34532	−	8.83320i	0.0623876	−	0.409630i
$466$	5.83251	−	10.1022i	0.270186	−	0.467975i
$467$	22.2005	−	5.94861i	1.02732	−	0.275269i	0.294469	−	0.955661i	$-0.404857\pi$
$467$	22.2005	−	5.94861i	1.02732	−	0.275269i	0.732848	+	0.680392i	$0.238190\pi$
$468$	−2.25719	+	3.35402i	−0.104339	+	0.155040i
$469$	−8.37383	−	4.88305i	−0.386668	−	0.225478i
$470$	1.34920	+	4.76474i	0.0622339	+	0.219781i
$471$	5.64190	+	15.0658i	0.259965	+	0.694196i
$472$	1.05624	−	1.05624i	0.0486174	−	0.0486174i
$473$	1.31125	−	1.31125i	0.0602914	−	0.0602914i
$474$	−2.34442	−	6.26042i	−0.107683	−	0.287550i
$475$	−9.39401	+	0.265734i	−0.431027	+	0.0121927i
$476$	−0.0586192	+	13.5514i	−0.00268681	+	0.621129i
$477$	0.132598	+	0.271143i	0.00607126	+	0.0124148i
$478$	−0.440678	+	0.118079i	−0.0201561	+	0.00540082i
$479$	19.5180	−	33.8062i	0.891801	−	1.54464i	0.0540866	−	0.998536i	$-0.482775\pi$
$479$	19.5180	−	33.8062i	0.891801	−	1.54464i	0.837714	−	0.546109i	$-0.183891\pi$
$480$	−3.11973	+	2.29505i	−0.142396	+	0.104754i
$481$	−2.37072	−	4.10620i	−0.108095	−	0.187227i
$482$	−17.3324	+	4.64420i	−0.789468	+	0.211537i
$483$	−21.5474	−	9.91878i	−0.980441	−	0.451320i
$484$	−10.1953	+	5.88624i	−0.463421	+	0.267556i
$485$	25.4338	−	0.359660i	1.15489	−	0.0163313i
$486$	3.41392	+	15.2100i	0.154859	+	0.689941i
$487$	−10.4032	−	2.78753i	−0.471414	−	0.126315i	0.0152880	−	0.999883i	$-0.495133\pi$
$487$	−10.4032	−	2.78753i	−0.471414	−	0.126315i	−0.486702	+	0.873568i	$0.661800\pi$
$488$	9.50639	−	9.50639i	0.430334	−	0.430334i
$489$	−2.20041	+	13.1917i	−0.0995061	+	0.596550i
$490$	15.6522	−	0.0859119i	0.707096	−	0.00388110i
$491$	25.7279	+	14.8540i	1.16108	+	0.670352i	0.951563	−	0.307453i	$-0.0994766\pi$
$491$	25.7279	+	14.8540i	1.16108	+	0.670352i	0.209520	+	0.977804i	$0.432810\pi$
$492$	5.36039	+	7.50664i	0.241665	+	0.338426i
$493$	48.4927	−	12.9936i	2.18400	−	0.585201i
$494$	−1.26645	−	2.19355i	−0.0569802	−	0.0986927i
$495$	14.4685	+	28.5556i	0.650312	+	1.28348i
$496$	2.30702			0.103588
$497$	−36.2659	+	9.54946i	−1.62675	+	0.428352i
$498$	−7.79528	+	0.754734i	−0.349315	+	0.0338204i
$499$	27.6676	−	15.9739i	1.23857	−	0.715090i	0.269770	−	0.962925i	$-0.413052\pi$
$499$	27.6676	−	15.9739i	1.23857	−	0.715090i	0.968802	+	0.247834i	$0.0797189\pi$
$500$	8.23384	+	7.56332i	0.368229	+	0.338242i
$501$	−6.33831	+	37.9989i	−0.283175	+	1.69766i
$502$	1.95265	−	1.95265i	0.0871511	−	0.0871511i
$503$	−8.12773	+	8.12773i	−0.362398	+	0.362398i	−0.864695	−	0.502297i	$-0.832488\pi$
$503$	−8.12773	+	8.12773i	−0.362398	+	0.362398i	0.502297	+	0.864695i	$0.332488\pi$
$504$	1.48897	+	7.79634i	0.0663242	+	0.347277i
$505$	−19.8816	−	5.02706i	−0.884719	−	0.223701i
$506$		−	24.7015i		−	1.09812i
$507$	−1.86677	−	19.2810i	−0.0829064	−	0.856300i
$508$	−8.38188	−	8.38188i	−0.371886	−	0.371886i
$509$	14.7879	+	25.6134i	0.655463	+	1.13530i	0.981777	+	0.190034i	$0.0608600\pi$
$509$	14.7879	+	25.6134i	0.655463	+	1.13530i	−0.326314	+	0.945261i	$0.605807\pi$
$510$	7.21897	+	18.4773i	0.319661	+	0.818189i
$511$	15.2192	+	0.0658334i	0.673258	+	0.00291230i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−9.50018	−	2.26496i	−0.419443	−	0.100001i
$514$	−17.9823	+	10.3821i	−0.793166	+	0.457935i
$515$	−0.306926	−	21.7047i	−0.0135248	−	0.956424i
$516$	0.427849	−	0.519578i	0.0188350	−	0.0228731i
$517$	2.73530	+	10.2083i	0.120298	+	0.448959i
$518$	−8.98115	−	2.44818i	−0.394609	−	0.107567i
$519$	0.329523	+	0.879939i	0.0144644	+	0.0386251i
$520$	−0.738676	+	2.92140i	−0.0323931	+	0.128112i
$521$	−28.7925	+	16.6234i	−1.26142	+	0.728283i	−0.973350	−	0.229325i	$-0.926348\pi$
$521$	−28.7925	+	16.6234i	−1.26142	+	0.728283i	−0.288073	+	0.957608i	$0.593015\pi$
$522$	26.4150	−	12.9178i	1.15615	−	0.565398i
$523$	−5.44141	+	1.45802i	−0.237936	+	0.0637548i	−0.375817	−	0.926694i	$-0.622638\pi$
$523$	−5.44141	+	1.45802i	−0.237936	+	0.0637548i	0.137880	+	0.990449i	$0.455971\pi$
$524$	−9.42856	−	16.3307i	−0.411889	−	0.713412i
$525$	21.2590	−	8.54718i	0.927819	−	0.373030i
$526$	0.740355	−	1.28233i	0.0322810	−	0.0559123i
$527$	3.05836	−	11.4140i	0.133224	−	0.497200i
$528$	−6.72650	+	4.80330i	−0.292733	+	0.209037i
$529$	3.28565	+	1.89697i	0.142854	+	0.0824769i
$530$	0.161312	+	0.156813i	0.00700693	+	0.00681152i
$531$	−2.94351	−	3.37895i	−0.127738	−	0.146634i
$532$	−4.79777	−	1.30783i	−0.208010	−	0.0567016i
$533$	6.93216	+	1.85747i	0.300265	+	0.0804558i
$534$	4.03085	−	24.1654i	0.174432	−	1.04574i
$535$	−31.1496	+	18.5764i	−1.34671	+	0.803127i
$536$		−	3.66382i		−	0.158253i
$537$	−44.1836	+	4.27782i	−1.90666	+	0.184602i
$538$	2.17416	−	8.11408i	0.0937348	−	0.349823i
$539$	33.4031	+	0.288988i	1.43877	+	0.0124476i
$540$	6.22582	+	9.81015i	0.267917	+	0.422162i
$541$	−14.0679	+	24.3664i	−0.604827	+	1.04759i	0.387251	+	0.921974i	$0.373425\pi$
$541$	−14.0679	+	24.3664i	−0.604827	+	1.04759i	−0.992079	+	0.125618i	$0.959909\pi$
$542$	−22.9232	+	6.14224i	−0.984634	+	0.263832i
$543$	13.4818	−	29.6243i	0.578558	−	1.27130i
$544$	−4.43579	+	2.56100i	−0.190183	+	0.109802i
$545$	11.4050	−	11.7322i	0.488537	−	0.502552i
$546$	4.75021	+	3.94619i	0.203290	+	0.168881i
$547$	−39.9889	−	10.7150i	−1.70980	−	0.458141i	−0.734427	−	0.678687i	$-0.762549\pi$
$547$	−39.9889	−	10.7150i	−1.70980	−	0.458141i	−0.975376	+	0.220547i	$0.929216\pi$
$548$	2.10466	+	7.85469i	0.0899065	+	0.335536i
$549$	−26.4923	−	30.4113i	−1.13066	−	1.29792i
$550$	17.3421	+	16.3879i	0.739469	+	0.698784i
$551$			18.4224i			0.784822i
$552$	−0.864002	−	8.92386i	−0.0367744	−	0.379825i
$553$	−9.87489	+	2.60024i	−0.419923	+	0.110573i
$554$	−5.14010	+	8.90291i	−0.218382	+	0.378248i
$555$	−13.5434	+	1.50484i	−0.574886	+	0.0638769i
$556$	0.587175	−	1.01702i	0.0249018	−	0.0431311i
$557$	1.18103	−	4.40768i	0.0500420	−	0.186759i	−0.936381	−	0.350986i	$-0.885846\pi$
$557$	1.18103	−	4.40768i	0.0500420	−	0.186759i	0.986423	+	0.164227i	$0.0525130\pi$
$558$	0.475535	−	6.90471i	0.0201310	−	0.292300i
$559$		−	0.523672i		−	0.0221489i
$560$	3.00818	+	5.09420i	0.127119	+	0.215269i
$561$	14.8471	+	39.6468i	0.626844	+	1.67389i
$562$	17.9989	+	4.82279i	0.759237	+	0.203437i
$563$	14.8846	−	14.8846i	0.627310	−	0.627310i	−0.320080	−	0.947391i	$-0.603710\pi$
$563$	14.8846	−	14.8846i	0.627310	−	0.627310i	0.947391	+	0.320080i	$0.103710\pi$
$564$	1.34524	+	3.59224i	0.0566447	+	0.151261i
$565$	18.0449	+	30.2585i	0.759156	+	1.27298i
$566$		−	3.95597i		−	0.166282i
$567$	23.6407	−	2.84935i	0.992815	−	0.119661i
$568$	−10.0228	−	10.0228i	−0.420549	−	0.420549i
$569$	−9.45533			−0.396388			−0.198194	−	0.980163i	$-0.563508\pi$
$569$	−9.45533			−0.396388			−0.198194	+	0.980163i	$0.563508\pi$
$570$	−7.23496	+	0.803893i	−0.303039	+	0.0336714i
$571$	21.1794			0.886331			0.443165	−	0.896440i	$-0.353855\pi$
$571$	21.1794			0.886331			0.443165	+	0.896440i	$0.353855\pi$
$572$	−1.66443	+	6.21172i	−0.0695931	+	0.259725i
$573$	−0.291477	−	0.132649i	−0.0121766	−	0.00554148i
$574$	12.2327	−	6.99215i	0.510581	−	0.291847i
$575$	−24.8001	+	7.40282i	−1.03424	+	0.308719i
$576$	−2.26206	+	1.97055i	−0.0942525	+	0.0821064i
$577$	19.3461	+	5.18377i	0.805389	+	0.215803i	0.637949	−	0.770079i	$-0.279783\pi$
$577$	19.3461	+	5.18377i	0.805389	+	0.215803i	0.167440	+	0.985882i	$0.446450\pi$
$578$	2.39019	+	8.92031i	0.0994188	+	0.371036i
$579$	−11.0151	+	4.12498i	−0.457772	+	0.171428i
$580$	15.2768	−	15.7151i	0.634336	−	0.652534i
$581$	−0.0517484	+	11.9631i	−0.00214688	+	0.496311i
$582$	19.6112	−	1.89875i	0.812912	−	0.0787055i
$583$	0.339493	+	0.339493i	0.0140604	+	0.0140604i
$584$	2.87618	+	4.98170i	0.119017	+	0.206144i
$585$	8.59123	+	2.81297i	0.355203	+	0.116302i
$586$	15.2368	−	26.3910i	0.629428	−	1.09020i
$587$	−4.74776	+	17.7189i	−0.195961	+	0.731336i	0.796055	+	0.605224i	$0.206917\pi$
$587$	−4.74776	+	17.7189i	−0.195961	+	0.731336i	−0.992016	+	0.126112i	$0.959750\pi$
$588$	12.0776	−	1.06396i	0.498071	−	0.0438771i
$589$	3.75524	+	2.16809i	0.154732	+	0.0893345i
$590$	−2.91596	−	1.62899i	−0.120048	−	0.0670646i
$591$	31.9266	−	11.9560i	1.31329	−	0.491804i
$592$	−0.910632	−	3.39853i	−0.0374268	−	0.139679i
$593$	3.20616	+	11.9655i	0.131661	+	0.491366i	0.999989	−	0.00462398i	$-0.00147186\pi$
$593$	3.20616	+	11.9655i	0.131661	+	0.491366i	−0.868328	+	0.495990i	$0.834805\pi$
$594$	12.9893	+	21.1219i	0.532959	+	0.866641i
$595$	29.1913	−	8.12967i	1.19673	−	0.333284i
$596$	−11.5829	+	6.68740i	−0.474455	+	0.273927i
$597$	3.73735	+	38.6013i	0.152960	+	1.57985i
$598$	−4.93249	−	4.93249i	−0.201705	−	0.201705i
$599$	−11.1364			−0.455021			−0.227511	−	0.973776i	$-0.573059\pi$
$599$	−11.1364			−0.455021			−0.227511	+	0.973776i	$0.573059\pi$
$600$	6.83835	+	5.31385i	0.279174	+	0.216937i
$601$	−5.99957	−	10.3916i	−0.244728	−	0.423881i	0.717327	−	0.696736i	$-0.245365\pi$
$601$	−5.99957	−	10.3916i	−0.244728	−	0.423881i	−0.962055	+	0.272856i	$0.912032\pi$
$602$	−0.723841	−	0.730130i	−0.0295016	−	0.0297579i
$603$	−10.9655	−	0.755206i	−0.446550	−	0.0307544i
$604$	−2.39113	−	1.38052i	−0.0972936	−	0.0561725i
$605$	18.8752	+	18.3489i	0.767388	+	0.745987i
$606$	−15.6684	−	2.61353i	−0.636485	−	0.106167i
$607$	−13.5202	−	3.62272i	−0.548767	−	0.147042i	−0.0262262	−	0.999656i	$-0.508349\pi$
$607$	−13.5202	−	3.62272i	−0.548767	−	0.147042i	−0.522541	+	0.852614i	$0.675016\pi$
$608$	−0.486464	−	1.81551i	−0.0197287	−	0.0736286i
$609$	−15.5699	−	42.1311i	−0.630926	−	1.70724i
$610$	−26.2442	−	14.6613i	−1.06260	−	0.593619i
$611$	2.58462	+	1.49223i	0.104562	+	0.0603692i
$612$	6.75053	+	13.8038i	0.272874	+	0.557986i
$613$	−2.10709	+	7.86376i	−0.0851045	+	0.317614i	−0.995334	−	0.0964899i	$-0.969238\pi$
$613$	−2.10709	+	7.86376i	−0.0851045	+	0.317614i	0.910229	+	0.414104i	$0.135905\pi$
$614$	6.40484			0.258478
$615$	12.8847	−	16.1059i	0.519562	−	0.649454i
$616$	6.26547	+	10.9613i	0.252443	+	0.441645i
$617$	14.6158	−	3.91629i	0.588410	−	0.157664i	0.0476836	−	0.998862i	$-0.484816\pi$
$617$	14.6158	−	3.91629i	0.588410	−	0.157664i	0.540726	+	0.841199i	$0.318149\pi$
$618$	−1.62035	−	16.7358i	−0.0651801	−	0.673214i
$619$	19.5656	+	11.2962i	0.786407	+	0.454032i	0.838696	−	0.544600i	$-0.183318\pi$
$619$	19.5656	+	11.2962i	0.786407	+	0.454032i	−0.0522894	+	0.998632i	$0.516652\pi$
$620$	−1.40548	−	4.96351i	−0.0564455	−	0.199339i
$621$	−26.8864	+	0.746448i	−1.07891	+	0.0299539i
$622$	−15.3491	+	15.3491i	−0.615443	+	0.615443i
$623$	−36.1058	−	9.84212i	−1.44655	−	0.394316i
$624$	−0.384032	+	2.30231i	−0.0153736	+	0.0921663i
$625$	11.2561	−	22.3226i	0.450244	−	0.892906i
$626$			33.5292i			1.34010i
$627$	−15.4630	+	1.49712i	−0.617534	+	0.0597892i
$628$	6.56772	+	6.56772i	0.262080	+	0.262080i
$629$	−18.0213			−0.718558
$630$	15.8665	−	7.95317i	0.632138	−	0.316862i
$631$	5.51476			0.219539			0.109770	−	0.993957i	$-0.464989\pi$
$631$	5.51476			0.219539			0.109770	+	0.993957i	$0.464989\pi$
$632$	−2.72914	−	2.72914i	−0.108559	−	0.108559i
$633$	−7.30604	−	10.2313i	−0.290389	−	0.406658i
$634$			33.7945i			1.34215i
$635$	−12.9270	+	23.1398i	−0.512993	+	0.918276i
$636$	0.134523	+	0.110773i	0.00533417	+	0.00439244i
$637$	6.72777	−	6.61236i	0.266564	−	0.261991i
$638$	33.0737	−	33.0737i	1.30940	−	1.30940i
$639$	−32.0634	+	27.9315i	−1.26841	+	1.10495i
$640$	−1.09054	+	1.95211i	−0.0431074	+	0.0771638i
$641$	39.7628	+	22.9571i	1.57054	+	0.906750i	0.996103	+	0.0882004i	$0.0281116\pi$
$641$	39.7628	+	22.9571i	1.57054	+	0.906750i	0.574435	+	0.818550i	$0.305222\pi$
$642$	−22.8625	+	16.3258i	−0.902312	+	0.644328i
$643$	−10.4650	+	2.80408i	−0.412698	+	0.110582i	−0.459193	−	0.888336i	$-0.651861\pi$
$643$	−10.4650	+	2.80408i	−0.412698	+	0.110582i	0.0464953	+	0.998919i	$0.485195\pi$
$644$	−13.6950	−	0.0592403i	−0.539660	−	0.00233440i
$645$	−1.37851	−	0.603970i	−0.0542789	−	0.0237813i
$646$	−9.62709			−0.378773
$647$	1.94813	−	7.27052i	0.0765889	−	0.285834i	−0.917000	−	0.398887i	$-0.869397\pi$
$647$	1.94813	−	7.27052i	0.0765889	−	0.285834i	0.993589	+	0.113054i	$0.0360632\pi$
$648$	5.43143	+	7.17632i	0.213367	+	0.281913i
$649$	−6.17324	−	3.56412i	−0.242321	−	0.139904i
$650$	6.73534	−	0.190527i	0.264182	−	0.00747307i
$651$	−10.4204	−	1.78452i	−0.408408	−	0.0699407i
$652$	1.99846	+	7.45837i	0.0782658	+	0.292092i
$653$	−13.5308	−	3.62558i	−0.529503	−	0.141880i	−0.0158440	−	0.999874i	$-0.505044\pi$
$653$	−13.5308	−	3.62558i	−0.529503	−	0.141880i	−0.513659	+	0.857995i	$0.671710\pi$
$654$	8.05655	−	9.78384i	0.315036	−	0.382578i
$655$	−29.3912	+	30.2343i	−1.14841	+	1.18135i
$656$	4.61203	+	2.66276i	0.180070	+	0.103963i
$657$	15.5026	−	7.58131i	0.604815	−	0.295775i
$658$	5.66624	−	1.49202i	0.220893	−	0.0581651i
$659$	−5.17959	−	8.97131i	−0.201768	−	0.349473i	0.747330	−	0.664453i	$-0.231335\pi$
$659$	−5.17959	−	8.97131i	−0.201768	−	0.349473i	−0.949098	+	0.314980i	$0.898002\pi$
$660$	14.4321	+	11.5456i	0.561768	+	0.449414i
$661$	−18.7910			−0.730885			−0.365442	−	0.930834i	$-0.619082\pi$
$661$	−18.7910			−0.730885			−0.365442	+	0.930834i	$0.619082\pi$
$662$	7.27649	+	7.27649i	0.282809	+	0.282809i
$663$	10.8816	+	4.95211i	0.422605	+	0.192324i
$664$	−3.91587	+	2.26083i	−0.151965	+	0.0877371i
$665$	0.109130	+	11.1191i	0.00423189	+	0.431178i
$666$	−10.3592	+	2.02492i	−0.401410	+	0.0784640i
$667$	13.1313	+	49.0066i	0.508445	+	1.89754i
$668$	5.75659	+	21.4839i	0.222729	+	0.831237i
$669$	−15.8137	−	13.0219i	−0.611394	−	0.503455i
$670$	−7.88263	+	2.23207i	−0.304533	+	0.0862324i
$671$	−55.5605	−	32.0779i	−2.14489	−	1.23835i
$672$	2.64692	+	3.74083i	0.102107	+	0.144306i
$673$	1.06797	−	3.98572i	0.0411673	−	0.153638i	−0.942283	−	0.334818i	$-0.891325\pi$
$673$	1.06797	−	3.98572i	0.0411673	−	0.153638i	0.983450	+	0.181180i	$0.0579917\pi$
$674$	−9.70091	+	16.8025i	−0.373665	+	0.647207i
$675$	17.3134	−	19.3712i	0.666394	−	0.745600i
$676$	−5.59198	−	9.68559i	−0.215076	−	0.372523i
$677$	25.1112	+	25.1112i	0.965101	+	0.965101i	0.999411	−	0.0343103i	$-0.0109235\pi$
$677$	25.1112	+	25.1112i	0.965101	+	0.965101i	−0.0343103	+	0.999411i	$0.510923\pi$
$678$	15.8588	+	22.2085i	0.609052	+	0.852911i
$679$	0.130188	−	30.0965i	0.00499614	−	1.15500i
$680$	8.21231	+	7.98329i	0.314928	+	0.306145i
$681$	5.00054	−	29.9788i	0.191621	−	1.14879i
$682$	−2.84940	−	10.6341i	−0.109109	−	0.407201i
$683$	−6.91910	−	1.85397i	−0.264752	−	0.0709401i	0.124001	−	0.992282i	$-0.460427\pi$
$683$	−6.91910	−	1.85397i	−0.264752	−	0.0709401i	−0.388753	+	0.921342i	$0.627094\pi$
$684$	−5.53393	+	1.08172i	−0.211595	+	0.0413607i
$685$	15.6170	−	9.31334i	0.596694	−	0.355845i
$686$	0.240330	−	18.5187i	0.00917584	−	0.707047i
$687$	−2.46627	−	25.4729i	−0.0940940	−	0.971852i
$688$	0.100575	−	0.375353i	0.00383440	−	0.0143102i
$689$	0.135583			0.00516528
$690$	−18.6731	+	7.29546i	−0.710873	+	0.277734i
$691$	12.3634			0.470326			0.235163	−	0.971956i	$-0.424438\pi$
$691$	12.3634			0.470326			0.235163	+	0.971956i	$0.424438\pi$
$692$	0.383597	+	0.383597i	0.0145822	+	0.0145822i
$693$	34.0978	−	16.4926i	1.29527	−	0.626502i
$694$			11.6370i			0.441735i
$695$	−2.54581	−	0.643708i	−0.0965680	−	0.0244172i
$696$	10.7916	−	13.1053i	0.409055	−	0.496755i
$697$	19.2880	−	19.2880i	0.730585	−	0.730585i
$698$	18.4412	+	4.94131i	0.698010	+	0.187031i
$699$	−19.9291	−	3.32422i	−0.753786	−	0.125734i
$700$	9.12741	−	9.57551i	0.344984	−	0.361920i
$701$		−	19.0727i		−	0.720365i	−0.932882	−	0.360183i	$-0.882714\pi$
$701$		−	19.0727i		−	0.720365i	0.932882	−	0.360183i	$-0.117286\pi$
$702$	6.81146	+	1.62394i	0.257082	+	0.0612916i
$703$	1.71158	−	6.38771i	0.0645535	−	0.240917i
$704$	−2.38603	+	4.13272i	−0.0899267	+	0.155758i
$705$	6.90908	−	5.08271i	0.260211	−	0.191426i
$706$	−6.67742	+	11.5656i	−0.251308	+	0.435278i
$707$	−6.38145	+	23.4104i	−0.239999	+	0.880438i
$708$	−2.35486	−	1.07168i	−0.0885010	−	0.0402761i
$709$			16.9288i			0.635773i	0.948129	+	0.317887i	$0.102973\pi$
$709$			16.9288i			0.635773i	−0.948129	+	0.317887i	$0.897027\pi$
$710$	−15.4578	+	27.6700i	−0.580121	+	1.03844i
$711$	−8.73060	+	7.60552i	−0.327423	+	0.285229i
$712$	−3.66091	−	13.6627i	−0.137198	−	0.512031i
$713$	11.5349	+	3.09077i	0.431986	+	0.115750i
$714$	22.0166	−	8.13646i	0.823952	−	0.304499i
$715$	14.3784	−	0.203324i	0.537721	−	0.00760390i
$716$	−22.1951	+	12.8143i	−0.829470	+	0.478895i
$717$	0.459211	+	0.643075i	0.0171495	+	0.0240161i
$718$	−9.34797	+	2.50478i	−0.348863	+	0.0934776i
$719$	21.5142	−	37.2636i	0.802343	−	1.38970i	−0.115727	−	0.993281i	$-0.536920\pi$
$719$	21.5142	−	37.2636i	0.802343	−	1.38970i	0.918070	−	0.396418i	$-0.129747\pi$
$720$	5.61769	+	3.66627i	0.209359	+	0.136634i
$721$	−25.6837	−	0.111099i	−0.956511	−	0.00413756i
$722$	−4.00323	+	14.9402i	−0.148985	+	0.556018i
$723$	18.0613	+	25.2929i	0.671706	+	0.940652i
$724$		−	18.7914i		−	0.698378i
$725$	−43.1176	−	23.2938i	−1.60135	−	0.865111i
$726$	15.7406	+	12.9617i	0.584190	+	0.481054i
$727$	28.2353	+	7.56562i	1.04719	+	0.280593i	0.741089	−	0.671406i	$-0.234309\pi$
$727$	28.2353	+	7.56562i	1.04719	+	0.280593i	0.306099	+	0.952000i	$0.400976\pi$
$728$	3.43992	+	0.937690i	0.127492	+	0.0347531i
$729$	22.5976	−	14.7766i	0.836950	−	0.547280i
$730$	8.96578	−	9.22299i	0.331838	−	0.341358i
$731$	−1.72372	−	0.995191i	−0.0637541	−	0.0368085i
$732$	−21.1942	−	9.64533i	−0.783362	−	0.356502i
$733$	−2.19738	+	8.20072i	−0.0811620	+	0.302901i	−0.994560	−	0.104168i	$-0.966782\pi$
$733$	−2.19738	+	8.20072i	−0.0811620	+	0.302901i	0.913398	+	0.407068i	$0.133449\pi$
$734$	9.13805	−	15.8276i	0.337292	−	0.584206i
$735$	−9.64698	−	25.3365i	−0.355834	−	0.934549i
$736$	−2.58814	−	4.48280i	−0.0954002	−	0.165238i
$737$	−16.8882	+	4.52518i	−0.622085	+	0.166687i
$738$	8.92006	−	13.2545i	0.328352	−	0.487906i
$739$	−21.2221	+	12.2526i	−0.780668	+	0.450719i	−0.836667	−	0.547712i	$-0.815499\pi$
$739$	−21.2221	+	12.2526i	−0.780668	+	0.450719i	0.0559990	+	0.998431i	$0.482166\pi$
$740$	−6.75708	+	4.02965i	−0.248395	+	0.148133i
$741$	−2.78877	+	3.38667i	−0.102448	+	0.124412i
$742$	0.189036	−	0.187408i	0.00693974	−	0.00687996i
$743$	−4.42277	−	16.5060i	−0.162256	−	0.605546i	−0.998374	−	0.0569978i	$-0.981847\pi$
$743$	−4.42277	−	16.5060i	−0.162256	−	0.605546i	0.836119	−	0.548549i	$-0.184819\pi$
$744$	−1.40135	−	3.74210i	−0.0513761	−	0.137192i
$745$	21.4443	+	20.8463i	0.785659	+	0.763749i
$746$	−11.9712	+	6.91157i	−0.438296	+	0.253050i
$747$	5.95929	+	12.1859i	0.218039	+	0.445857i
$748$	17.2835	+	17.2835i	0.631946	+	0.631946i
$749$	21.2956	+	37.2563i	0.778123	+	1.36131i
$750$	7.26657	−	17.9498i	0.265338	−	0.655436i
$751$	7.34232	+	12.7173i	0.267925	+	0.464060i	0.968326	−	0.249690i	$-0.0803287\pi$
$751$	7.34232	+	12.7173i	0.267925	+	0.464060i	−0.700401	+	0.713750i	$0.746995\pi$
$752$	1.56599	+	1.56599i	0.0571056	+	0.0571056i
$753$	−4.35339	−	1.98119i	−0.158646	−	0.0721986i
$754$		−	13.2086i		−	0.481027i
$755$	−1.51343	+	5.98550i	−0.0550795	+	0.217834i
$756$	11.7416	−	7.15091i	0.427037	−	0.260076i
$757$	−19.7572	+	19.7572i	−0.718089	+	0.718089i	−0.968214	−	0.250125i	$-0.919528\pi$
$757$	−19.7572	+	19.7572i	−0.718089	+	0.718089i	0.250125	+	0.968214i	$0.419528\pi$
$758$	7.13611	−	7.13611i	0.259195	−	0.259195i
$759$	−40.0669	+	15.0044i	−1.45434	+	0.544626i
$760$	−3.60966	+	2.15266i	−0.130936	+	0.0780851i
$761$	21.7013	−	12.5293i	0.786673	−	0.454186i	−0.0521170	−	0.998641i	$-0.516597\pi$
$761$	21.7013	−	12.5293i	0.786673	−	0.454186i	0.838790	+	0.544455i	$0.183264\pi$
$762$	−8.50439	+	18.6872i	−0.308082	+	0.676966i
$763$	−13.6302	−	13.7486i	−0.493446	−	0.497733i
$764$	−0.184891			−0.00668913
$765$	25.5860	−	22.9332i	0.925065	−	0.829150i
$766$	2.84938	+	4.93526i	0.102952	+	0.178318i
$767$	−1.94439	+	0.520999i	−0.0702080	+	0.0188122i
$768$	−0.717442	+	1.57648i	−0.0258884	+	0.0568862i
$769$	−45.1967	−	26.0943i	−1.62983	−	0.940985i	−0.984141	−	0.177388i	$-0.943235\pi$
$769$	−45.1967	−	26.0943i	−1.62983	−	0.940985i	−0.645693	−	0.763597i	$-0.723431\pi$
$770$	19.7660	−	20.1579i	0.712319	−	0.726440i
$771$	27.7632	+	22.8617i	0.999868	+	0.823346i
$772$	−4.80188	+	4.80188i	−0.172823	+	0.172823i
$773$	−15.7566	−	4.22197i	−0.566725	−	0.151854i	−0.0359309	−	0.999354i	$-0.511440\pi$
$773$	−15.7566	−	4.22197i	−0.566725	−	0.151854i	−0.530794	+	0.847501i	$0.678106\pi$
$774$	−1.10267	−	0.378383i	−0.0396345	−	0.0136007i
$775$	−9.82262	+	6.04772i	−0.352839	+	0.217241i
$776$	9.85147	−	5.68775i	0.353647	−	0.204178i
$777$	1.48436	+	16.0549i	0.0532510	+	0.575967i
$778$	−32.1773	+	8.62188i	−1.15361	+	0.309109i
$779$	5.00480	+	8.66856i	0.179316	+	0.310584i
$780$	5.18733	−	0.576377i	0.185736	−	0.0206376i
$781$	−33.8206	+	58.5790i	−1.21020	+	2.09612i
$782$	−25.6096	+	6.86207i	−0.915797	+	0.245387i
$783$	−36.9986	−	34.9997i	−1.32222	−	1.25079i
$784$	6.09223	−	3.44742i	0.217580	−	0.123122i
$785$	10.1291	−	18.1315i	0.361524	−	0.647140i
$786$	−20.7620	+	25.2133i	−0.740557	+	0.899329i
$787$	8.27748	−	8.27748i	0.295060	−	0.295060i	−0.544015	−	0.839075i	$-0.683097\pi$
$787$	8.27748	−	8.27748i	0.295060	−	0.295060i	0.839075	+	0.544015i	$0.183097\pi$
$788$	13.9180	−	13.9180i	0.495807	−	0.495807i
$789$	−2.52971	−	0.421963i	−0.0900601	−	0.0150223i
$790$	−4.20903	+	7.53432i	−0.149751	+	0.268059i
$791$	36.1904	−	20.6863i	1.28678	−	0.735521i
$792$	11.8770	+	7.99302i	0.422032	+	0.284020i
$793$	−17.5000	+	4.68910i	−0.621442	+	0.166515i
$794$	−5.99089	+	10.3765i	−0.212609	+	0.368249i
$795$	0.156372	−	0.356907i	0.00554595	−	0.0126582i
$796$	11.1953	+	19.3909i	0.396808	+	0.687292i
$797$	−18.2238	+	4.88305i	−0.645520	+	0.172967i	−0.566703	−	0.823922i	$-0.691781\pi$
$797$	−18.2238	+	4.88305i	−0.645520	+	0.172967i	−0.0788175	+	0.996889i	$0.525114\pi$
$798$	0.792950	+	8.57662i	0.0280701	+	0.303609i
$799$	9.82367	−	5.67170i	0.347537	−	0.200650i
$800$	4.86429	+	1.15701i	0.171979	+	0.0409066i
$801$	−41.6458	+	8.14054i	−1.47148	+	0.287632i
$802$	−37.1883	−	9.96457i	−1.31316	−	0.351861i
$803$	19.4105	−	19.4105i	0.684982	−	0.684982i
$804$	−5.94289	+	2.22551i	−0.209589	+	0.0784878i
$805$	8.21582	+	29.5006i	0.289570	+	1.03976i
$806$	−2.69244	−	1.55448i	−0.0948371	−	0.0547542i
$807$	−14.4821	+	1.40214i	−0.509792	+	0.0493577i
$808$	−8.85864	+	2.37367i	−0.311646	+	0.0835053i
$809$	−19.1875	−	33.2338i	−0.674598	−	1.16844i	−0.976586	−	0.215127i	$-0.930984\pi$
$809$	−19.1875	−	33.2338i	−0.674598	−	1.16844i	0.301988	−	0.953312i	$-0.402350\pi$
$810$	12.1308	−	16.0575i	0.426232	−	0.564204i
$811$	27.8982			0.979639			0.489819	−	0.871824i	$-0.337063\pi$
$811$	27.8982			0.979639			0.489819	+	0.871824i	$0.337063\pi$
$812$	−18.2574	−	18.4161i	−0.640710	−	0.646277i
$813$	23.8872	+	33.4514i	0.837760	+	1.17319i
$814$	−14.5406	+	8.39502i	−0.509648	+	0.294245i
$815$	14.8290	−	8.84342i	0.519437	−	0.309772i
$816$	6.84849	+	5.63942i	0.239745	+	0.197419i
$817$	0.516459	−	0.516459i	0.0180686	−	0.0180686i
$818$	−3.88157	+	3.88157i	−0.135716	+	0.135716i
$819$	3.51548	−	10.1021i	0.122841	−	0.352995i
$820$	2.91913	−	11.5449i	0.101940	−	0.403165i
$821$		−	41.3416i		−	1.44283i	−0.692502	−	0.721416i	$-0.743492\pi$
$821$		−	41.3416i		−	1.44283i	0.692502	−	0.721416i	$-0.256508\pi$
$822$	11.4622	−	8.18501i	0.399791	−	0.285485i
$823$	−17.9232	−	17.9232i	−0.624764	−	0.624764i	0.321982	−	0.946746i	$-0.395651\pi$
$823$	−17.9232	−	17.9232i	−0.624764	−	0.624764i	−0.946746	+	0.321982i	$0.895651\pi$
$824$	−4.85381	−	8.40704i	−0.169090	−	0.292873i
$825$	16.0479	−	38.0841i	0.558716	−	1.32592i
$826$	−1.99083	+	3.41403i	−0.0692698	+	0.118789i
$827$	−21.3177	−	21.3177i	−0.741288	−	0.741288i	0.231538	−	0.972826i	$-0.425624\pi$
$827$	−21.3177	−	21.3177i	−0.741288	−	0.741288i	−0.972826	+	0.231538i	$0.925624\pi$
$828$	−13.9501	+	6.82206i	−0.484799	+	0.237083i
$829$	7.89081	−	4.55576i	0.274059	−	0.158228i	−0.356672	−	0.934230i	$-0.616089\pi$
$829$	7.89081	−	4.55576i	0.274059	−	0.158228i	0.630731	+	0.776002i	$0.282755\pi$
$830$	7.24974	+	7.04756i	0.251642	+	0.244624i
$831$	17.5632	+	2.92958i	0.609259	+	0.101626i
$832$	0.348786	+	1.30169i	0.0120920	+	0.0451279i
$833$	−8.97976	−	34.7114i	−0.311130	−	1.20268i
$834$	−2.00632	−	0.334659i	−0.0694730	−	0.0115883i
$835$	42.7151	−	25.4736i	1.47822	−	0.881549i
$836$	−7.76766	+	4.48466i	−0.268650	+	0.155105i
$837$	−11.4886	+	3.42278i	−0.397104	+	0.118309i
$838$	−10.0463	+	2.69190i	−0.347043	+	0.0929900i
$839$	5.10398	+	8.84035i	0.176209	+	0.305203i	0.940579	−	0.339575i	$-0.110283\pi$
$839$	5.10398	+	8.84035i	0.176209	+	0.305203i	−0.764370	+	0.644778i	$0.776950\pi$
$840$	6.43576	−	7.97377i	0.222055	−	0.275121i
$841$	−33.5346	+	58.0837i	−1.15637	+	2.00288i
$842$	1.37252	−	5.12230i	0.0473000	−	0.176526i
$843$	−3.11027	−	32.1245i	−0.107123	−	1.10643i
$844$	−6.28605	−	3.62926i	−0.216375	−	0.124924i
$845$	−17.4316	+	17.9317i	−0.599665	+	0.616868i
$846$	5.00964	−	4.36407i	0.172235	−	0.150040i
$847$	22.1193	−	21.9288i	0.760030	−	0.753483i
$848$	0.0971817	+	0.0260397i	0.00333723	+	0.000894209i
$849$	−6.41676	+	2.40297i	−0.220223	+	0.0824697i
$850$	12.1728	−	22.5322i	0.417522	−	0.772847i
$851$		−	18.2123i		−	0.624310i
$852$	−10.1693	+	22.3457i	−0.348396	+	0.765550i
$853$	−0.544167	+	2.03086i	−0.0186319	+	0.0695353i	−0.974616	−	0.223884i	$-0.928126\pi$
$853$	−0.544167	+	2.03086i	−0.0186319	+	0.0695353i	0.955984	+	0.293419i	$0.0947931\pi$
$854$	−17.9179	+	30.7270i	−0.613138	+	1.05146i
$855$	5.69867	+	11.2471i	0.194891	+	0.384643i
$856$	−8.10981	+	14.0466i	−0.277187	+	0.480103i
$857$	27.8367	−	7.45882i	0.950883	−	0.254788i	0.250146	−	0.968208i	$-0.419521\pi$
$857$	27.8367	−	7.45882i	0.950883	−	0.254788i	0.700737	+	0.713420i	$0.252855\pi$
$858$	11.0867	−	1.07341i	0.378494	−	0.0366455i
$859$	35.9780	−	20.7719i	1.22755	−	0.708728i	0.261035	−	0.965329i	$-0.415936\pi$
$859$	35.9780	−	20.7719i	1.22755	−	0.708728i	0.966517	+	0.256602i	$0.0826028\pi$
$860$	−0.868835	+	0.0122862i	−0.0296270	+	0.000418955i
$861$	−18.7721	−	15.5947i	−0.639750	−	0.531465i
$862$	31.5675	+	8.45850i	1.07519	+	0.288098i
$863$	1.23868	+	4.62283i	0.0421653	+	0.157363i	0.983799	−	0.179278i	$-0.0573760\pi$
$863$	1.23868	+	4.62283i	0.0421653	+	0.157363i	−0.941633	+	0.336640i	$0.890709\pi$
$864$	4.57037	+	2.47219i	0.155487	+	0.0841056i
$865$	0.591605	−	1.05899i	0.0201152	−	0.0360069i
$866$			26.4079i			0.897375i
$867$	13.0173	−	9.29545i	0.442090	−	0.315690i
$868$	−5.90261	+	1.55426i	−0.200348	+	0.0527552i
$869$	−9.20906	+	15.9506i	−0.312396	+	0.541086i
$870$	−34.7702	−	15.2339i	−1.17882	−	0.516478i
$871$	−2.46870	+	4.27591i	−0.0836486	+	0.144884i
$872$	1.89387	−	7.06803i	0.0641346	−	0.239354i
$873$	−14.9923	−	30.6570i	−0.507412	−	1.03758i
$874$		−	9.72911i		−	0.329092i
$875$	−26.1621	−	13.8038i	−0.884440	−	0.466654i
$876$	6.33346	−	7.69133i	0.213988	−	0.259866i
$877$	−51.2307	−	13.7272i	−1.72994	−	0.463536i	−0.749769	−	0.661699i	$-0.769835\pi$
$877$	−51.2307	−	13.7272i	−1.72994	−	0.463536i	−0.980169	+	0.198164i	$0.936502\pi$
$878$	16.8094	−	16.8094i	0.567288	−	0.567288i
$879$	−52.0627	−	8.68419i	−1.75603	−	0.292911i
$880$	10.3451	+	2.61575i	0.348732	+	0.0881769i
$881$		−	33.1736i		−	1.11765i	−0.829286	−	0.558824i	$-0.811253\pi$
$881$		−	33.1736i		−	1.11765i	0.829286	−	0.558824i	$-0.188747\pi$
$882$	−9.06207	−	18.9441i	−0.305136	−	0.637881i
$883$	15.6225	+	15.6225i	0.525738	+	0.525738i	0.919299	−	0.393561i	$-0.128757\pi$
$883$	15.6225	+	15.6225i	0.525738	+	0.525738i	−0.393561	+	0.919299i	$0.628757\pi$
$884$	6.90245			0.232155
$885$	−0.871065	+	5.71931i	−0.0292805	+	0.192253i
$886$	21.2227			0.712990
$887$	9.06515	−	33.8316i	0.304378	−	1.13595i	−0.629101	−	0.777323i	$-0.716577\pi$
$887$	9.06515	−	33.8316i	0.304378	−	1.13595i	0.933479	−	0.358631i	$-0.116756\pi$
$888$	−4.95942	+	3.54145i	−0.166427	+	0.118843i
$889$	27.0923	+	15.7984i	0.908647	+	0.529862i
$890$	−27.1647	+	16.1999i	−0.910562	+	0.543023i
$891$	26.3705	−	33.8993i	0.883446	−	1.13567i
$892$	−11.4241	−	3.06109i	−0.382508	−	0.102493i
$893$	1.07734	+	4.02070i	0.0360519	+	0.134547i
$894$	17.8831	+	14.7259i	0.598099	+	0.492507i
$895$	41.0914	+	39.9455i	1.37354	+	1.33523i
$896$	2.28554	+	1.33277i	0.0763547	+	0.0445249i
$897$	−5.00458	+	10.9969i	−0.167098	+	0.367175i
$898$	5.77320	+	5.77320i	0.192654	+	0.192654i
$899$	11.3061	+	19.5828i	0.377081	+	0.653123i
$900$	4.46549	−	14.3199i	0.148850	−	0.477330i
$901$	0.257662	−	0.446284i	0.00858398	−	0.0148679i
$902$	6.57754	−	24.5477i	0.219008	−	0.817349i
$903$	−0.744622	+	1.61761i	−0.0247795	+	0.0538305i
$904$	13.6447	+	7.87780i	0.453817	+	0.262012i
$905$	−40.4293	+	11.4481i	−1.34392	+	0.380548i
$906$	−0.786822	+	4.71708i	−0.0261404	+	0.156715i
$907$	−12.5042	−	46.6661i	−0.415194	−	1.54952i	−0.784448	−	0.620195i	$-0.787053\pi$
$907$	−12.5042	−	46.6661i	−0.415194	−	1.54952i	0.369254	−	0.929328i	$-0.379613\pi$
$908$	−4.54160	−	16.9495i	−0.150718	−	0.562488i
$909$	5.27818	+	27.0024i	0.175066	+	0.895613i
$910$	−0.0782444	−	7.97216i	−0.00259378	−	0.264275i
$911$	43.3450	−	25.0252i	1.43608	−	0.829123i	0.438509	−	0.898727i	$-0.355507\pi$
$911$	43.3450	−	25.0252i	1.43608	−	0.829123i	0.997575	+	0.0696035i	$0.0221734\pi$
$912$	−2.64935	+	1.89186i	−0.0877286	+	0.0626457i
$913$	15.2576	+	15.2576i	0.504954	+	0.504954i
$914$	−33.4656			−1.10694
$915$	−7.83977	+	51.4750i	−0.259175	+	1.70171i
$916$	−7.38778	−	12.7960i	−0.244099	−	0.422792i
$917$	35.1255	+	35.4307i	1.15995	+	1.17003i
$918$	18.2899	−	19.3345i	0.603658	−	0.638134i
$919$	−8.90171	−	5.13941i	−0.293640	−	0.169533i	0.345942	−	0.938256i	$-0.387559\pi$
$919$	−8.90171	−	5.13941i	−0.293640	−	0.169533i	−0.639582	+	0.768723i	$0.720893\pi$
$920$	−8.06788	+	8.29933i	−0.265990	+	0.273621i
$921$	−3.89049	−	10.3889i	−0.128196	−	0.342327i
$922$	−22.7817	−	6.10433i	−0.750275	−	0.201036i
$923$	4.94385	+	18.4507i	0.162729	+	0.607312i
$924$	13.9740	−	16.8211i	0.459710	−	0.553374i
$925$	12.7862	+	12.0828i	0.420409	+	0.397278i
$926$	−28.1717	−	16.2649i	−0.925780	−	0.534499i
$927$	−26.1620	+	12.7941i	−0.859274	+	0.420214i
$928$	2.53681	−	9.46751i	0.0832750	−	0.310786i
$929$	−27.6679			−0.907754			−0.453877	−	0.891064i	$-0.649959\pi$
$929$	−27.6679			−0.907754			−0.453877	+	0.891064i	$0.649959\pi$
$930$	−7.19730	+	5.29473i	−0.236009	+	0.173621i
$931$	13.1564	+	0.113823i	0.431183	+	0.00373039i
$932$	−11.2675	+	3.01913i	−0.369081	+	0.0988948i
$933$	34.2205	+	15.5735i	1.12033	+	0.509852i
$934$	−19.9044	−	11.4918i	−0.651293	−	0.376024i
$935$	26.6555	−	47.7144i	0.871729	−	1.56043i
$936$	3.96773	−	0.775575i	0.129689	−	0.0253505i
$937$	−20.7758	+	20.7758i	−0.678715	+	0.678715i	−0.959709	−	0.280995i	$-0.909336\pi$
$937$	−20.7758	+	20.7758i	−0.678715	+	0.678715i	0.280995	+	0.959709i	$0.409336\pi$
$938$	2.46835	+	9.37403i	0.0805946	+	0.306073i
$939$	54.3859	−	20.3666i	1.77482	−	0.664639i
$940$	2.41515	−	4.32321i	0.0787736	−	0.141008i
$941$		−	21.7685i		−	0.709634i	−0.934936	−	0.354817i	$-0.884543\pi$
$941$		−	21.7685i		−	0.709634i	0.934936	−	0.354817i	$-0.115457\pi$
$942$	6.66371	−	14.6426i	0.217115	−	0.477080i
$943$	19.4924	+	19.4924i	0.634760	+	0.634760i
$944$	−1.49375			−0.0486174
$945$	−22.5382	−	20.9052i	−0.733168	−	0.680048i
$946$	−1.85439			−0.0602914
$947$	−8.35258	−	8.35258i	−0.271422	−	0.271422i	0.558250	−	0.829673i	$-0.311473\pi$
$947$	−8.35258	−	8.35258i	−0.271422	−	0.271422i	−0.829673	+	0.558250i	$0.811473\pi$
$948$	−2.76902	+	6.08454i	−0.0899337	+	0.197617i
$949$		−	7.75193i		−	0.251638i
$950$	6.83047	+	6.45467i	0.221610	+	0.209417i
$951$	54.8162	−	20.5278i	1.77754	−	0.665659i
$952$	9.62376	−	9.54086i	0.311908	−	0.309221i
$953$	8.22163	−	8.22163i	0.266325	−	0.266325i	−0.561293	−	0.827617i	$-0.689696\pi$
$953$	8.22163	−	8.22163i	0.266325	−	0.266325i	0.827617	+	0.561293i	$0.189696\pi$
$954$	0.0979662	−	0.285489i	0.00317177	−	0.00924303i
$955$	0.112639	+	0.397789i	0.00364492	+	0.0128722i
$956$	0.395101	+	0.228112i	0.0127785	+	0.00737766i
$957$	−73.7369	−	33.5571i	−2.38357	−	1.08475i
$958$	−37.7059	+	10.1033i	−1.21822	+	0.326422i
$959$	−10.6766	−	18.6786i	−0.344766	−	0.603163i
$960$	3.82883	+	0.583140i	0.123575	+	0.0188208i
$961$	−25.6776			−0.828311
$962$	−1.22717	+	4.57988i	−0.0395657	+	0.147661i
$963$	40.3686	+	27.1673i	1.30086	+	0.875453i
$964$	15.5398	+	8.97190i	0.500503	+	0.288965i
$965$	13.2565	+	7.40573i	0.426742	+	0.238399i
$966$	8.22267	+	22.2500i	0.264560	+	0.715880i
$967$	1.64500	+	6.13923i	0.0528997	+	0.197424i	0.987319	−	0.158752i	$-0.0507470\pi$
$967$	1.64500	+	6.13923i	0.0528997	+	0.197424i	−0.934419	+	0.356176i	$0.884080\pi$
$968$	11.3713	+	3.04694i	0.365489	+	0.0979324i
$969$	5.84778	+	15.6156i	0.187858	+	0.501645i
$970$	−18.2388	−	17.7301i	−0.585611	−	0.569280i
$971$	−2.34429	−	1.35348i	−0.0752320	−	0.0434352i	0.461912	−	0.886926i	$-0.347164\pi$
$971$	−2.34429	−	1.35348i	−0.0752320	−	0.0434352i	−0.537144	+	0.843490i	$0.680497\pi$
$972$	8.34111	−	13.1691i	0.267541	−	0.422400i
$973$	−0.817136	+	2.99766i	−0.0261962	+	0.0961007i
$974$	5.38509	+	9.32725i	0.172549	+	0.298864i
$975$	−4.40028	−	10.8093i	−0.140922	−	0.346174i
$976$	−13.4441			−0.430334
$977$	33.0476	+	33.0476i	1.05729	+	1.05729i	0.998256	+	0.0590317i	$0.0188013\pi$
$977$	33.0476	+	33.0476i	1.05729	+	1.05729i	0.0590317	+	0.998256i	$0.481199\pi$
$978$	10.8839	−	7.77203i	0.348028	−	0.248522i
$979$	−58.4559	+	33.7495i	−1.86826	+	1.07864i
$980$	−11.1286	−	11.0071i	−0.355489	−	0.351608i
$981$	−20.7636	−	7.12509i	−0.662931	−	0.227487i
$982$	−7.68900	−	28.6957i	−0.245366	−	0.915717i
$983$	15.4002	+	57.4742i	0.491189	+	1.83314i	0.550405	+	0.834898i	$0.314473\pi$
$983$	15.4002	+	57.4742i	0.491189	+	1.83314i	−0.0592153	+	0.998245i	$0.518860\pi$
$984$	1.51763	−	9.09836i	0.0483803	−	0.290045i
$985$	−38.4232	−	21.4651i	−1.22427	−	0.683934i
$986$	−43.4774	−	25.1017i	−1.38460	−	0.799400i
$987$	−5.86197	−	8.28459i	−0.186588	−	0.263701i
$988$	−0.655562	+	2.44659i	−0.0208562	+	0.0778365i
$989$	1.00574	−	1.74199i	0.0319806	−	0.0553919i
$990$	9.96108	−	30.4227i	0.316584	−	0.966896i
$991$	−18.5277	−	32.0909i	−0.588552	−	1.01940i	−0.994422	−	0.105472i	$-0.966365\pi$
$991$	−18.5277	−	32.0909i	−0.588552	−	1.01940i	0.405870	−	0.913931i	$-0.366969\pi$
$992$	−1.63131	−	1.63131i	−0.0517942	−	0.0517942i
$993$	7.38284	−	16.2227i	0.234287	−	0.514813i
$994$	32.3963	+	18.8913i	1.02755	+	0.599197i
$995$	34.8987	−	35.8998i	1.10636	−	1.13810i
$996$	6.04577	+	4.97842i	0.191568	+	0.157747i
$997$	3.64514	+	13.6039i	0.115443	+	0.430838i	0.999320	−	0.0368813i	$-0.0117423\pi$
$997$	3.64514	+	13.6039i	0.115443	+	0.430838i	−0.883877	+	0.467720i	$0.845076\pi$
$998$	−30.8592	−	8.26870i	−0.976832	−	0.261741i
$999$	9.57698	+	15.5731i	0.303002	+	0.492710i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.cd.a.23.10	yes	192
5.2	odd	4	inner	630.2.cd.a.527.45	yes	192
7.4	even	3		630.2.bt.a.473.46	yes	192
9.2	odd	6		630.2.bt.a.443.36	yes	192
35.32	odd	12		630.2.bt.a.347.36	yes	192
45.2	even	12		630.2.bt.a.317.46	✓	192
63.11	odd	6	inner	630.2.cd.a.263.45	yes	192
315.137	even	12	inner	630.2.cd.a.137.10	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.46	✓	192	45.2	even	12
630.2.bt.a.347.36	yes	192	35.32	odd	12
630.2.bt.a.443.36	yes	192	9.2	odd	6
630.2.bt.a.473.46	yes	192	7.4	even	3
630.2.cd.a.23.10	yes	192	1.1	even	1	trivial
630.2.cd.a.137.10	yes	192	315.137	even	12	inner
630.2.cd.a.263.45	yes	192	63.11	odd	6	inner
630.2.cd.a.527.45	yes	192	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.717442 + 1.57648i) q^{3} +1.00000i q^{4} +(2.15148 - 0.609219i) q^{5} +(1.62204 - 0.607429i) q^{6} +(-0.673710 - 2.55854i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.97055 - 2.26206i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.717442 + 1.57648i) q^{3} +1.00000i q^{4} +(2.15148 - 0.609219i) q^{5} +(1.62204 - 0.607429i) q^{6} +(-0.673710 - 2.55854i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-1.97055 - 2.26206i) q^{9} +(-1.95211 - 1.09054i) q^{10} +(-4.13272 - 2.38603i) q^{11} +(-1.57648 - 0.717442i) q^{12} +(-1.30169 + 0.348786i) q^{13} +(-1.33277 + 2.28554i) q^{14} +(-0.583140 + 3.82883i) q^{15} -1.00000 q^{16} +(-1.32567 + 4.94748i) q^{17} +(-0.206125 + 2.99291i) q^{18} +(-1.62774 - 0.939777i) q^{19} +(0.609219 + 2.15148i) q^{20} +(4.51682 + 0.773514i) q^{21} +(1.23510 + 4.60945i) q^{22} +(-4.99991 - 1.33972i) q^{23} +(0.607429 + 1.62204i) q^{24} +(4.25770 - 2.62144i) q^{25} +(1.16706 + 0.673803i) q^{26} +(4.97984 - 1.48364i) q^{27} +(2.55854 - 0.673710i) q^{28} +(-4.90075 - 8.48834i) q^{29} +(3.11973 - 2.29505i) q^{30} -2.30702 q^{31} +(0.707107 + 0.707107i) q^{32} +(6.72650 - 4.80330i) q^{33} +(4.43579 - 2.56100i) q^{34} +(-3.00818 - 5.09420i) q^{35} +(2.26206 - 1.97055i) q^{36} +(0.910632 + 3.39853i) q^{37} +(0.486464 + 1.81551i) q^{38} +(0.384032 - 2.30231i) q^{39} +(1.09054 - 1.95211i) q^{40} +(-4.61203 - 2.66276i) q^{41} +(-2.64692 - 3.74083i) q^{42} +(-0.100575 + 0.375353i) q^{43} +(2.38603 - 4.13272i) q^{44} +(-5.61769 - 3.66627i) q^{45} +(2.58814 + 4.48280i) q^{46} +(-1.56599 - 1.56599i) q^{47} +(0.717442 - 1.57648i) q^{48} +(-6.09223 + 3.44742i) q^{49} +(-4.86429 - 1.15701i) q^{50} +(-6.84849 - 5.63942i) q^{51} +(-0.348786 - 1.30169i) q^{52} +(-0.0971817 - 0.0260397i) q^{53} +(-4.57037 - 2.47219i) q^{54} +(-10.3451 - 2.61575i) q^{55} +(-2.28554 - 1.33277i) q^{56} +(2.64935 - 1.89186i) q^{57} +(-2.53681 + 9.46751i) q^{58} +1.49375 q^{59} +(-3.82883 - 0.583140i) q^{60} +13.4441 q^{61} +(1.63131 + 1.63131i) q^{62} +(-4.45998 + 6.56571i) q^{63} -1.00000i q^{64} +(-2.58806 + 1.54342i) q^{65} +(-8.15280 - 1.35991i) q^{66} +(2.59071 - 2.59071i) q^{67} +(-4.94748 - 1.32567i) q^{68} +(5.69918 - 6.92106i) q^{69} +(-1.47504 + 5.72925i) q^{70} -14.1744i q^{71} +(-2.99291 - 0.206125i) q^{72} +(-1.48882 + 5.55636i) q^{73} +(1.75921 - 3.04704i) q^{74} +(1.07798 + 8.59290i) q^{75} +(0.939777 - 1.62774i) q^{76} +(-3.32048 + 12.1812i) q^{77} +(-1.89953 + 1.35643i) q^{78} -3.85958i q^{79} +(-2.15148 + 0.609219i) q^{80} +(-1.23383 + 8.91502i) q^{81} +(1.37835 + 5.14406i) q^{82} +(-4.36758 - 1.17029i) q^{83} +(-0.773514 + 4.51682i) q^{84} +(0.161943 + 11.4520i) q^{85} +(0.336532 - 0.194297i) q^{86} +(16.8977 - 1.63602i) q^{87} +(-4.60945 + 1.23510i) q^{88} +(7.07233 - 12.2496i) q^{89} +(1.37986 + 6.56475i) q^{90} +(1.76934 + 3.09544i) q^{91} +(1.33972 - 4.99991i) q^{92} +(1.65515 - 3.63697i) q^{93} +2.21464i q^{94} +(-4.07458 - 1.03026i) q^{95} +(-1.62204 + 0.607429i) q^{96} +(10.9879 + 2.94420i) q^{97} +(6.74555 + 1.87016i) q^{98} +(2.74641 + 14.0502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{6}+O(q^{10}) \) 192 * q + 8 * q^6	\( 192 q + 8 q^{6} + 24 q^{11} + 12 q^{15} - 192 q^{16} - 36 q^{17} - 8 q^{18} + 24 q^{23} + 36 q^{27} - 12 q^{30} + 40 q^{33} + 12 q^{41} - 4 q^{42} + 8 q^{45} - 12 q^{46} - 48 q^{50} + 24 q^{51} - 12 q^{56} - 48 q^{57} - 12 q^{58} - 16 q^{60} - 24 q^{61} - 52 q^{63} - 36 q^{68} + 8 q^{72} + 8 q^{75} + 96 q^{77} - 16 q^{78} + 16 q^{81} + 76 q^{87} - 20 q^{90} - 24 q^{92} - 8 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 24 * q^11 + 12 * q^15 - 192 * q^16 - 36 * q^17 - 8 * q^18 + 24 * q^23 + 36 * q^27 - 12 * q^30 + 40 * q^33 + 12 * q^41 - 4 * q^42 + 8 * q^45 - 12 * q^46 - 48 * q^50 + 24 * q^51 - 12 * q^56 - 48 * q^57 - 12 * q^58 - 16 * q^60 - 24 * q^61 - 52 * q^63 - 36 * q^68 + 8 * q^72 + 8 * q^75 + 96 * q^77 - 16 * q^78 + 16 * q^81 + 76 * q^87 - 20 * q^90 - 24 * q^92 - 8 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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