LMFDB - Embedded newform 630.2.cd.a.263.45

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			263.45
Character	$\chi$	$=$	630.263
Dual form			630.2.cd.a.527.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.57648 - 0.717442i) q^{3} +1.00000i q^{4} +(1.60334 + 1.55862i) q^{5} +(1.62204 + 0.607429i) q^{6} +(2.55854 + 0.673710i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.97055 - 2.26206i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.57648 - 0.717442i) q^{3} +1.00000i q^{4} +(1.60334 + 1.55862i) q^{5} +(1.62204 + 0.607429i) q^{6} +(2.55854 + 0.673710i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.97055 - 2.26206i) q^{9} +(0.0316170 + 2.23584i) q^{10} +(-4.13272 + 2.38603i) q^{11} +(0.717442 + 1.57648i) q^{12} +(0.348786 - 1.30169i) q^{13} +(1.33277 + 2.28554i) q^{14} +(3.64585 + 1.30683i) q^{15} -1.00000 q^{16} +(-4.94748 + 1.32567i) q^{17} +(2.99291 - 0.206125i) q^{18} +(1.62774 - 0.939777i) q^{19} +(-1.55862 + 1.60334i) q^{20} +(4.51682 - 0.773514i) q^{21} +(-4.60945 - 1.23510i) q^{22} +(-1.33972 - 4.99991i) q^{23} +(-0.607429 + 1.62204i) q^{24} +(0.141382 + 4.99800i) q^{25} +(1.16706 - 0.673803i) q^{26} +(1.48364 - 4.97984i) q^{27} +(-0.673710 + 2.55854i) q^{28} +(4.90075 - 8.48834i) q^{29} +(1.65393 + 3.50207i) q^{30} -2.30702 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.80330 + 6.72650i) q^{33} +(-4.43579 - 2.56100i) q^{34} +(3.05214 + 5.06798i) q^{35} +(2.26206 + 1.97055i) q^{36} +(-3.39853 - 0.910632i) q^{37} +(1.81551 + 0.486464i) q^{38} +(-0.384032 - 2.30231i) q^{39} +(-2.23584 + 0.0316170i) q^{40} +(-4.61203 + 2.66276i) q^{41} +(3.74083 + 2.64692i) q^{42} +(0.375353 - 0.100575i) q^{43} +(-2.38603 - 4.13272i) q^{44} +(6.68516 - 0.555491i) q^{45} +(2.58814 - 4.48280i) q^{46} +(1.56599 + 1.56599i) q^{47} +(-1.57648 + 0.717442i) q^{48} +(6.09223 + 3.44742i) q^{49} +(-3.43415 + 3.63409i) q^{50} +(-6.84849 + 5.63942i) q^{51} +(1.30169 + 0.348786i) q^{52} +(-0.0260397 - 0.0971817i) q^{53} +(4.57037 - 2.47219i) q^{54} +(-10.3451 - 2.61575i) q^{55} +(-2.28554 + 1.33277i) q^{56} +(1.89186 - 2.64935i) q^{57} +(9.46751 - 2.53681i) q^{58} -1.49375 q^{59} +(-1.30683 + 3.64585i) q^{60} +13.4441 q^{61} +(-1.63131 - 1.63131i) q^{62} +(6.56571 - 4.45998i) q^{63} -1.00000i q^{64} +(2.58806 - 1.54342i) q^{65} +(-8.15280 + 1.35991i) q^{66} +(2.59071 - 2.59071i) q^{67} +(-1.32567 - 4.94748i) q^{68} +(-5.69918 - 6.92106i) q^{69} +(-1.42542 + 5.74179i) q^{70} +14.1744i q^{71} +(0.206125 + 2.99291i) q^{72} +(5.55636 - 1.48882i) q^{73} +(-1.75921 - 3.04704i) q^{74} +(3.80866 + 7.77780i) q^{75} +(0.939777 + 1.62774i) q^{76} +(-12.1812 + 3.32048i) q^{77} +(1.35643 - 1.89953i) q^{78} -3.85958i q^{79} +(-1.60334 - 1.55862i) q^{80} +(-1.23383 - 8.91502i) q^{81} +(-5.14406 - 1.37835i) q^{82} +(-1.17029 - 4.36758i) q^{83} +(0.773514 + 4.51682i) q^{84} +(-9.99871 - 5.58576i) q^{85} +(0.336532 + 0.194297i) q^{86} +(1.63602 - 16.8977i) q^{87} +(1.23510 - 4.60945i) q^{88} +(-7.07233 - 12.2496i) q^{89} +(5.11992 + 4.33433i) q^{90} +(1.76934 - 3.09544i) q^{91} +(4.99991 - 1.33972i) q^{92} +(-3.63697 + 1.65515i) q^{93} +2.21464i q^{94} +(4.07458 + 1.03026i) q^{95} +(-1.62204 - 0.607429i) q^{96} +(-2.94420 - 10.9879i) q^{97} +(1.87016 + 6.74555i) 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 $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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
$3$	1.57648	−	0.717442i	0.910179	−	0.414215i
$3$	1.57648	−	0.717442i	0.910179	−	0.414215i
$4$			1.00000i			0.500000i
$5$	1.60334	+	1.55862i	0.717034	+	0.697038i
$5$	1.60334	+	1.55862i	0.717034	+	0.697038i
$6$	1.62204	+	0.607429i	0.662197	+	0.247982i
$7$	2.55854	+	0.673710i	0.967036	+	0.254638i
$7$	2.55854	+	0.673710i	0.967036	+	0.254638i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	1.97055	−	2.26206i	0.656852	−	0.754020i
$10$	0.0316170	+	2.23584i	0.00999818	+	0.707036i
$11$	−4.13272	+	2.38603i	−1.24606	+	0.719414i	−0.970322	−	0.241818i	$-0.922256\pi$
$11$	−4.13272	+	2.38603i	−1.24606	+	0.719414i	−0.275740	+	0.961232i	$0.588923\pi$
$12$	0.717442	+	1.57648i	0.207108	+	0.455089i
$13$	0.348786	−	1.30169i	0.0967359	−	0.361023i	−0.900541	−	0.434771i	$-0.856829\pi$
$13$	0.348786	−	1.30169i	0.0967359	−	0.361023i	0.997277	+	0.0737478i	$0.0234960\pi$
$14$	1.33277	+	2.28554i	0.356199	+	0.610837i
$15$	3.64585	+	1.30683i	0.941353	+	0.337423i
$16$	−1.00000			−0.250000
$17$	−4.94748	+	1.32567i	−1.19994	+	0.321523i	−0.802808	−	0.596238i	$-0.796661\pi$
$17$	−4.94748	+	1.32567i	−1.19994	+	0.321523i	−0.397133	+	0.917761i	$0.629995\pi$
$18$	2.99291	−	0.206125i	0.705436	−	0.0485841i
$19$	1.62774	−	0.939777i	0.373429	−	0.215600i	−0.301526	−	0.953458i	$-0.597496\pi$
$19$	1.62774	−	0.939777i	0.373429	−	0.215600i	0.674956	+	0.737858i	$0.264163\pi$
$20$	−1.55862	+	1.60334i	−0.348519	+	0.358517i
$21$	4.51682	−	0.773514i	0.985651	−	0.168795i
$22$	−4.60945	−	1.23510i	−0.982738	−	0.263324i
$23$	−1.33972	−	4.99991i	−0.279351	−	1.04255i	−0.952869	−	0.303382i	$-0.901884\pi$
$23$	−1.33972	−	4.99991i	−0.279351	−	1.04255i	0.673518	−	0.739171i	$-0.264782\pi$
$24$	−0.607429	+	1.62204i	−0.123991	+	0.331099i
$25$	0.141382	+	4.99800i	0.0282763	+	0.999600i
$26$	1.16706	−	0.673803i	0.228880	−	0.132144i
$27$	1.48364	−	4.97984i	0.285526	−	0.958371i
$28$	−0.673710	+	2.55854i	−0.127319	+	0.483518i
$29$	4.90075	−	8.48834i	0.910046	−	1.57625i	0.0960483	−	0.995377i	$-0.469380\pi$
$29$	4.90075	−	8.48834i	0.910046	−	1.57625i	0.813997	−	0.580869i	$-0.197287\pi$
$30$	1.65393	+	3.50207i	0.301965	+	0.639388i
$31$	−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
$33$	−4.80330	+	6.72650i	−0.836147	+	1.17093i
$34$	−4.43579	−	2.56100i	−0.760732	−	0.439209i
$35$	3.05214	+	5.06798i	0.515906	+	0.856645i
$36$	2.26206	+	1.97055i	0.377010	+	0.328426i
$37$	−3.39853	−	0.910632i	−0.558714	−	0.149707i	−0.0315987	−	0.999501i	$-0.510060\pi$
$37$	−3.39853	−	0.910632i	−0.558714	−	0.149707i	−0.527116	+	0.849794i	$0.676727\pi$
$38$	1.81551	+	0.486464i	0.294514	+	0.0789149i
$39$	−0.384032	−	2.30231i	−0.0614943	−	0.368665i
$40$	−2.23584	+	0.0316170i	−0.353518	+	0.00499909i
$41$	−4.61203	+	2.66276i	−0.720279	+	0.415853i	−0.814855	−	0.579664i	$-0.803184\pi$
$41$	−4.61203	+	2.66276i	−0.720279	+	0.415853i	0.0945765	+	0.995518i	$0.469850\pi$
$42$	3.74083	+	2.64692i	0.577223	+	0.408428i
$43$	0.375353	−	0.100575i	0.0572408	−	0.0153376i	−0.230085	−	0.973171i	$-0.573900\pi$
$43$	0.375353	−	0.100575i	0.0572408	−	0.0153376i	0.287326	+	0.957833i	$0.407234\pi$
$44$	−2.38603	−	4.13272i	−0.359707	−	0.623031i
$45$	6.68516	−	0.555491i	0.996566	−	0.0828076i
$46$	2.58814	−	4.48280i	0.381601	−	0.660952i
$47$	1.56599	+	1.56599i	0.228423	+	0.228423i	0.812033	−	0.583611i	$-0.198361\pi$
$47$	1.56599	+	1.56599i	0.228423	+	0.228423i	−0.583611	+	0.812033i	$0.698361\pi$
$48$	−1.57648	+	0.717442i	−0.227545	+	0.103554i
$49$	6.09223	+	3.44742i	0.870319	+	0.492489i
$50$	−3.43415	+	3.63409i	−0.485662	+	0.513938i
$51$	−6.84849	+	5.63942i	−0.958981	+	0.789677i
$52$	1.30169	+	0.348786i	0.180512	+	0.0483679i
$53$	−0.0260397	−	0.0971817i	−0.00357683	−	0.0133489i	0.964114	−	0.265487i	$-0.0855328\pi$
$53$	−0.0260397	−	0.0971817i	−0.00357683	−	0.0133489i	−0.967691	+	0.252138i	$0.918866\pi$
$54$	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
$57$	1.89186	−	2.64935i	0.250583	−	0.350914i
$58$	9.46751	−	2.53681i	1.24315	−	0.333100i
$59$	−1.49375			−0.194469			−0.0972347	−	0.995261i	$-0.531000\pi$
$59$	−1.49375			−0.194469			−0.0972347	+	0.995261i	$0.531000\pi$
$60$	−1.30683	+	3.64585i	−0.168711	+	0.470677i
$61$	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
$63$	6.56571	−	4.45998i	0.827202	−	0.561905i
$64$		−	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	$0.178153\pi$
$68$	−1.32567	−	4.94748i	−0.160762	−	0.599970i
$69$	−5.69918	−	6.92106i	−0.686101	−	0.833198i
$70$	−1.42542	+	5.74179i	−0.170370	+	0.686276i
$71$			14.1744i			1.68220i	0.540882	+	0.841099i	$0.318091\pi$
$71$			14.1744i			1.68220i	−0.540882	+	0.841099i	$0.681909\pi$
$72$	0.206125	+	2.99291i	0.0242921	+	0.352718i
$73$	5.55636	−	1.48882i	0.650323	−	0.174254i	0.0814481	−	0.996678i	$-0.474046\pi$
$73$	5.55636	−	1.48882i	0.650323	−	0.174254i	0.568875	+	0.822424i	$0.307379\pi$
$74$	−1.75921	−	3.04704i	−0.204504	−	0.354211i
$75$	3.80866	+	7.77780i	0.439786	+	0.898103i
$76$	0.939777	+	1.62774i	0.107800	+	0.186715i
$77$	−12.1812	+	3.32048i	−1.38818	+	0.378404i
$78$	1.35643	−	1.89953i	0.153585	−	0.215080i
$79$		−	3.85958i		−	0.434237i	−0.976145	−	0.217118i	$-0.930334\pi$
$79$		−	3.85958i		−	0.434237i	0.976145	−	0.217118i	$-0.0696658\pi$
$80$	−1.60334	−	1.55862i	−0.179259	−	0.174259i
$81$	−1.23383	−	8.91502i	−0.137092	−	0.990558i
$82$	−5.14406	−	1.37835i	−0.568066	−	0.152213i
$83$	−1.17029	−	4.36758i	−0.128456	−	0.479404i	0.871483	−	0.490425i	$-0.163159\pi$
$83$	−1.17029	−	4.36758i	−0.128456	−	0.479404i	−0.999939	+	0.0110209i	$0.996492\pi$
$84$	0.773514	+	4.51682i	0.0843973	+	0.492826i
$85$	−9.99871	−	5.58576i	−1.08451	−	0.605861i
$86$	0.336532	+	0.194297i	0.0362892	+	0.0209516i
$87$	1.63602	−	16.8977i	0.175400	−	1.81162i
$88$	1.23510	−	4.60945i	0.131662	−	0.491369i
$89$	−7.07233	−	12.2496i	−0.749665	−	1.29846i	−0.947983	−	0.318321i	$-0.896881\pi$
$89$	−7.07233	−	12.2496i	−0.749665	−	1.29846i	0.198318	−	0.980138i	$-0.436452\pi$
$90$	5.11992	+	4.33433i	0.539687	+	0.456879i
$91$	1.76934	−	3.09544i	0.185478	−	0.324490i
$92$	4.99991	−	1.33972i	0.521276	−	0.139676i
$93$	−3.63697	+	1.65515i	−0.377136	+	0.171632i
$94$			2.21464i			0.228423i
$95$	4.07458	+	1.03026i	0.418043	+	0.105702i
$96$	−1.62204	−	0.607429i	−0.165549	−	0.0619955i
$97$	−2.94420	−	10.9879i	−0.298938	−	1.11565i	−0.938039	−	0.346529i	$-0.887360\pi$
$97$	−2.94420	−	10.9879i	−0.298938	−	1.11565i	0.639102	−	0.769122i	$-0.279306\pi$
$98$	1.87016	+	6.74555i	0.188915	+	0.681404i
$99$	−2.74641	+	14.0502i	−0.276025	+	1.41210i
$100$	−4.99800	+	0.141382i	−0.499800	+	0.0141382i
$101$	−7.94244	+	4.58557i	−0.790302	+	0.456281i	−0.840069	−	0.542480i	$-0.817486\pi$
$101$	−7.94244	+	4.58557i	−0.790302	+	0.456281i	0.0497666	+	0.998761i	$0.484152\pi$
$102$	−8.83029	−	0.854942i	−0.874329	−	0.0846519i
$103$	−9.37684	+	2.51252i	−0.923927	+	0.247566i	−0.689263	−	0.724511i	$-0.742066\pi$
$103$	−9.37684	+	2.51252i	−0.923927	+	0.247566i	−0.234664	+	0.972077i	$0.575399\pi$
$104$	0.673803	+	1.16706i	0.0660718	+	0.114440i
$105$	8.44761	+	5.79982i	0.824402	+	0.566005i
$106$	0.0503049	−	0.0871307i	0.00488605	−	0.00846288i
$107$	−4.19794	+	15.6669i	−0.405831	+	1.51458i	0.396688	+	0.917953i	$0.370159\pi$
$107$	−4.19794	+	15.6669i	−0.405831	+	1.51458i	−0.802519	+	0.596627i	$0.796507\pi$
$108$	4.97984	+	1.48364i	0.479185	+	0.142763i
$109$	−6.33702	−	3.65868i	−0.606977	−	0.350438i	0.164805	−	0.986326i	$-0.447301\pi$
$109$	−6.33702	−	3.65868i	−0.606977	−	0.350438i	−0.771781	+	0.635888i	$0.780634\pi$
$110$	−5.46545	−	9.16468i	−0.521110	−	0.873817i
$111$	−6.01102	+	1.00265i	−0.570541	+	0.0951677i
$112$	−2.55854	−	0.673710i	−0.241759	−	0.0636596i
$113$	15.2187	+	4.07785i	1.43166	+	0.383612i	0.889604	−	0.456732i	$-0.150980\pi$
$113$	15.2187	+	4.07785i	1.43166	+	0.383612i	0.542054	+	0.840344i	$0.317647\pi$
$114$	3.21112	−	0.535623i	0.300749	−	0.0501657i
$115$	5.64495	−	10.1047i	0.526395	−	0.942265i
$116$	8.48834	+	4.90075i	0.788123	+	0.455023i
$117$	−2.25719	−	3.35402i	−0.208678	−	0.310079i
$118$	−1.05624	−	1.05624i	−0.0972347	−	0.0972347i
$119$	−13.5514	+	0.0586192i	−1.24226	+	0.00537361i
$120$	−3.50207	+	1.65393i	−0.319694	+	0.150983i
$121$	5.88624	−	10.1953i	0.535113	−	0.926842i
$122$	9.50639	+	9.50639i	0.860668	+	0.860668i
$123$	−5.36039	+	7.50664i	−0.483330	+	0.676851i
$124$		−	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	−0.429955	−	0.902850i	$-0.641471\pi$
$131$	−16.3307	−	9.42856i	−1.42682	−	0.823777i	−0.996869	+	0.0790734i	$0.974804\pi$
$132$	−6.72650	−	4.80330i	−0.585466	−	0.418073i
$133$	4.79777	−	1.30783i	0.416020	−	0.113403i
$134$	3.66382			0.316506
$135$	10.1405	−	5.67193i	0.872753	−	0.488162i
$136$	2.56100	−	4.43579i	0.219604	−	0.380366i
$137$	2.10466	−	7.85469i	0.179813	−	0.671071i	−0.815869	−	0.578237i	$-0.803741\pi$
$137$	2.10466	−	7.85469i	0.179813	−	0.671071i	0.995682	−	0.0928338i	$-0.0295925\pi$
$138$	0.864002	−	8.92386i	0.0735487	−	0.759650i
$139$	1.01702	−	0.587175i	0.0862623	−	0.0498036i	−0.456248	−	0.889852i	$-0.650807\pi$
$139$	1.01702	−	0.587175i	0.0862623	−	0.0498036i	0.542511	+	0.840049i	$0.317474\pi$
$140$	−5.06798	+	3.05214i	−0.428323	+	0.257953i
$141$	3.59224	+	1.34524i	0.302521	+	0.113289i
$142$	−10.0228	+	10.0228i	−0.841099	+	0.841099i
$143$	1.66443	+	6.21172i	0.139186	+	0.519450i
$144$	−1.97055	+	2.26206i	−0.164213	+	0.188505i
$145$	21.0877	−	5.97125i	1.75124	−	0.495886i
$146$	4.98170	+	2.87618i	0.412288	+	0.238035i
$147$	12.0776	+	1.06396i	0.996142	+	0.0877541i
$148$	0.910632	−	3.39853i	0.0748535	−	0.279357i
$149$	−6.68740	+	11.5829i	−0.547853	+	0.948910i	0.450568	+	0.892742i	$0.351221\pi$
$149$	−6.68740	+	11.5829i	−0.547853	+	0.948910i	−0.998421	+	0.0561675i	$0.982112\pi$
$150$	−2.80660	+	8.19286i	−0.229158	+	0.668944i
$151$	−1.38052	−	2.39113i	−0.112345	−	0.194587i	0.804370	−	0.594128i	$-0.202503\pi$
$151$	−1.38052	−	2.39113i	−0.112345	−	0.194587i	−0.916715	+	0.399541i	$0.869170\pi$
$152$	−0.486464	+	1.81551i	−0.0394575	+	0.147257i
$153$	−6.75053	+	13.8038i	−0.545748	+	1.11597i
$154$	−10.9613	−	6.26547i	−0.883291	−	0.504886i
$155$	−3.69894	−	3.59578i	−0.297106	−	0.288820i
$156$	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
$160$	−0.0316170	−	2.23584i	−0.00249955	−	0.176759i
$161$	−0.0592403	−	13.6950i	−0.00466879	−	1.07932i
$162$	5.43143	−	7.17632i	0.426733	−	0.563825i
$163$	−1.99846	+	7.45837i	−0.156532	+	0.584184i	0.842438	+	0.538794i	$0.181120\pi$
$163$	−1.99846	+	7.45837i	−0.156532	+	0.584184i	−0.998969	+	0.0453904i	$0.985547\pi$
$164$	−2.66276	−	4.61203i	−0.207927	−	0.360139i
$165$	−18.1854	+	3.29831i	−1.41573	+	0.256773i
$166$	2.26083	−	3.91587i	0.175474	−	0.303930i
$167$	5.75659	−	21.4839i	0.445458	−	1.66247i	−0.269265	−	0.963066i	$-0.586781\pi$
$167$	5.75659	−	21.4839i	0.445458	−	1.66247i	0.714723	−	0.699407i	$-0.246553\pi$
$168$	−2.64692	+	3.74083i	−0.204214	+	0.288611i
$169$	9.68559	+	5.59198i	0.745045	+	0.430152i
$170$	−3.12042	−	11.0199i	−0.239326	−	0.845187i
$171$	1.08172	−	5.53393i	0.0827213	−	0.423190i
$172$	0.100575	+	0.375353i	0.00766881	+	0.0286204i
$173$	−0.383597	+	0.383597i	−0.0291643	+	0.0291643i	−0.721539	−	0.692374i	$-0.756565\pi$
$173$	−0.383597	+	0.383597i	−0.0291643	+	0.0291643i	0.692374	+	0.721539i	$0.256565\pi$
$174$	13.1053	−	10.7916i	0.993510	−	0.818110i
$175$	−3.00547	+	12.8828i	−0.227192	+	0.973850i
$176$	4.13272	−	2.38603i	0.311515	−	0.179853i
$177$	−2.35486	+	1.07168i	−0.177002	+	0.0805522i
$178$	3.66091	−	13.6627i	0.274397	−	1.02406i
$179$	−12.8143	+	22.1951i	−0.957789	+	1.65894i	−0.229936	+	0.973206i	$0.573852\pi$
$179$	−12.8143	+	22.1951i	−0.957789	+	1.65894i	−0.727853	+	0.685734i	$0.759482\pi$
$180$	0.555491	+	6.68516i	0.0414038	+	0.498283i
$181$	−18.7914			−1.39676			−0.698378	−	0.715729i	$-0.746095\pi$
$181$	−18.7914			−1.39676			−0.698378	+	0.715729i	$0.746095\pi$
$182$	3.43992	−	0.937690i	0.254984	−	0.0695062i
$183$	21.1942	−	9.64533i	1.56672	−	0.713003i
$184$	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	$-0.997871\pi$
$191$		−	0.184891i		−	0.0133783i	0.999978	−	0.00668913i	$-0.00212923\pi$
$192$	−0.717442	−	1.57648i	−0.0517769	−	0.113772i
$193$	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
$195$	2.97271	−	4.28995i	0.212880	−	0.307210i
$196$	−3.44742	+	6.09223i	−0.246245	+	0.435159i
$197$	13.9180	+	13.9180i	0.991613	+	0.991613i	0.999965	−	0.00835192i	$-0.00265853\pi$
$197$	13.9180	+	13.9180i	0.991613	+	0.991613i	−0.00835192	+	0.999965i	$0.502659\pi$
$198$	−11.8770	+	7.99302i	−0.844064	+	0.568039i
$199$	−19.3909	−	11.1953i	−1.37458	−	0.793617i	−0.383083	−	0.923714i	$-0.625138\pi$
$199$	−19.3909	−	11.1953i	−1.37458	−	0.793617i	−0.991501	+	0.130097i	$0.958471\pi$
$200$	−3.63409	−	3.43415i	−0.256969	−	0.242831i
$201$	2.22551	−	5.94289i	0.156976	−	0.419179i
$202$	−8.85864	−	2.37367i	−0.623292	−	0.167011i
$203$	18.2574	−	18.4161i	1.28142	−	1.29255i
$204$	−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
$207$	−13.9501	−	6.82206i	−0.969598	−	0.474166i
$208$	−0.348786	+	1.30169i	−0.0241840	+	0.0902558i
$209$	−4.48466	+	7.76766i	−0.310211	+	0.537301i
$210$	1.87227	+	10.0745i	0.129199	+	0.695203i
$211$	−3.62926	−	6.28605i	−0.249848	−	0.432750i	0.713635	−	0.700517i	$-0.247047\pi$
$211$	−3.62926	−	6.28605i	−0.249848	−	0.432750i	−0.963484	+	0.267768i	$0.913714\pi$
$212$	0.0971817	−	0.0260397i	0.00667446	−	0.00178842i
$213$	10.1693	+	22.3457i	0.696792	+	1.53110i
$214$	−14.0466	+	8.10981i	−0.960206	+	0.554375i
$215$	0.758577	+	0.423778i	0.0517345	+	0.0289014i
$216$	2.47219	+	4.57037i	0.168211	+	0.310974i
$217$	−5.90261	−	1.55426i	−0.400695	−	0.105510i
$218$	−1.89387	−	7.06803i	−0.128269	−	0.478707i
$219$	7.69133	−	6.33346i	0.519732	−	0.427976i
$220$	2.61575	−	10.3451i	0.176354	−	0.697464i
$221$			6.90245i			0.464309i
$222$	−4.95942	−	3.54145i	−0.332854	−	0.237687i
$223$	11.4241	−	3.06109i	0.765016	−	0.204986i	0.144848	−	0.989454i	$-0.453731\pi$
$223$	11.4241	−	3.06109i	0.765016	−	0.204986i	0.620169	+	0.784468i	$0.287064\pi$
$224$	−1.33277	−	2.28554i	−0.0890497	−	0.152709i
$225$	11.5844	+	9.52902i	0.772292	+	0.635268i
$226$	7.87780	+	13.6447i	0.524023	+	0.907635i
$227$	−4.54160	+	16.9495i	−0.301437	+	1.12498i	0.634533	+	0.772896i	$0.281192\pi$
$227$	−4.54160	+	16.9495i	−0.301437	+	1.12498i	−0.935970	+	0.352081i	$0.885474\pi$
$228$	2.64935	+	1.89186i	0.175457	+	0.125291i
$229$	12.7960	+	7.38778i	0.845585	+	0.488198i	0.859159	−	0.511709i	$-0.170988\pi$
$229$	12.7960	+	7.38778i	0.845585	+	0.488198i	−0.0135741	+	0.999908i	$0.504321\pi$
$230$	11.1367	−	3.15349i	0.734330	−	0.207935i
$231$	−16.8211	+	13.9740i	−1.10675	+	0.919420i
$232$	2.53681	+	9.46751i	0.166550	+	0.621573i
$233$	11.2675	+	3.01913i	0.738161	+	0.197790i	0.608261	−	0.793737i	$-0.291868\pi$
$233$	11.2675	+	3.01913i	0.738161	+	0.197790i	0.129900	+	0.991527i	$0.458534\pi$
$234$	0.775575	−	3.96773i	0.0507010	−	0.259379i
$235$	0.0700203	+	4.95159i	0.00456762	+	0.323006i
$236$		−	1.49375i		−	0.0972347i
$237$	−2.76902	−	6.08454i	−0.179867	−	0.395233i
$238$	−9.62376	−	9.54086i	−0.623816	−	0.618442i
$239$	−0.228112	−	0.395101i	−0.0147553	−	0.0255570i	0.858553	−	0.512724i	$-0.171364\pi$
$239$	−0.228112	−	0.395101i	−0.0147553	−	0.0255570i	−0.873309	+	0.487167i	$0.838030\pi$
$240$	−3.64585	−	1.30683i	−0.235338	−	0.0843557i
$241$	8.97190	+	15.5398i	0.577931	+	1.00101i	0.995716	+	0.0924598i	$0.0294730\pi$
$241$	8.97190	+	15.5398i	0.577931	+	1.00101i	−0.417786	+	0.908546i	$0.637194\pi$
$242$	11.3713	−	3.04694i	0.730977	−	0.195865i
$243$	−8.34111	−	13.1691i	−0.535083	−	0.844800i
$244$			13.4441i			0.860668i
$245$	4.39466	+	15.0229i	0.280765	+	0.959777i
$246$	−9.09836	+	1.51763i	−0.580091	+	0.0967606i
$247$	−0.655562	−	2.44659i	−0.0417124	−	0.155673i
$248$	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	$-0.972224\pi$
$251$		−	2.76147i		−	0.174302i	0.996195	−	0.0871511i	$-0.0277763\pi$
$252$	4.45998	+	6.56571i	0.280953	+	0.413601i
$253$	17.4666	+	17.4666i	1.09812	+	1.09812i
$254$	−11.8538			−0.743772
$255$	−19.7702	−	1.63233i	−1.23806	−	0.102220i
$256$	1.00000			0.0625000
$257$	20.0567	−	5.37417i	1.25110	−	0.335232i	0.428339	−	0.903618i	$-0.359099\pi$
$257$	20.0567	−	5.37417i	1.25110	−	0.335232i	0.822762	+	0.568386i	$0.192432\pi$
$258$	0.669932	+	0.0648623i	0.0417081	+	0.00403815i
$259$	−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
$262$	−4.88058	−	18.2146i	−0.301523	−	1.12530i
$263$	1.43026	+	0.383236i	0.0881933	+	0.0236313i	0.302646	−	0.953103i	$-0.402130\pi$
$263$	1.43026	+	0.383236i	0.0881933	+	0.0236313i	−0.214453	+	0.976734i	$0.568797\pi$
$264$	−1.35991	−	8.15280i	−0.0836965	−	0.501770i
$265$	0.109719	−	0.196401i	0.00674000	−	0.0120648i
$266$	4.31731	+	2.46776i	0.264711	+	0.151308i
$267$	−19.9378	−	14.2373i	−1.22017	−	0.871307i
$268$	2.59071	+	2.59071i	0.158253	+	0.158253i
$269$	−4.20016	+	7.27489i	−0.256088	+	0.443558i	−0.965190	−	0.261548i	$-0.915767\pi$
$269$	−4.20016	+	7.27489i	−0.256088	+	0.443558i	0.709102	+	0.705106i	$0.249100\pi$
$270$	11.1811	+	3.15973i	0.680458	+	0.192295i
$271$	11.8659	+	20.5523i	0.720802	+	1.24847i	0.960679	+	0.277663i	$0.0895598\pi$
$271$	11.8659	+	20.5523i	0.720802	+	1.24847i	−0.239876	+	0.970803i	$0.577107\pi$
$272$	4.94748	−	1.32567i	0.299985	−	0.0803808i
$273$	0.568531	−	6.14928i	0.0344091	−	0.372172i
$274$	7.04232	−	4.06588i	0.425442	−	0.245629i
$275$	−12.5096	−	20.3180i	−0.754360	−	1.22522i
$276$	6.92106	−	5.69918i	0.416599	−	0.343050i
$277$	9.92990	+	2.66071i	0.596630	+	0.159867i	0.544482	−	0.838773i	$-0.316726\pi$
$277$	9.92990	+	2.66071i	0.596630	+	0.159867i	0.0521485	+	0.998639i	$0.483393\pi$
$278$	1.13434	+	0.303944i	0.0680329	+	0.0182294i
$279$	−4.54612	+	5.21862i	−0.272169	+	0.312431i
$280$	−5.74179	−	1.42542i	−0.343138	−	0.0851850i
$281$	−16.1374	−	9.31691i	−0.962674	−	0.555800i	−0.0656791	−	0.997841i	$-0.520921\pi$
$281$	−16.1374	−	9.31691i	−0.962674	−	0.555800i	−0.896995	+	0.442041i	$0.854255\pi$
$282$	1.58887	+	3.49132i	0.0946161	+	0.207905i
$283$	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
$285$	7.16262	−	1.29910i	0.424277	−	0.0769518i
$286$	−3.21542	+	5.56928i	−0.190132	+	0.329318i
$287$	−13.5940	+	3.70560i	−0.802428	+	0.218734i
$288$	−2.99291	+	0.206125i	−0.176359	+	0.0121460i
$289$	7.99773	−	4.61749i	0.470455	−	0.271617i
$290$	19.1336	+	10.6889i	1.12356	+	0.627676i
$291$	−12.5246	−	15.2099i	−0.734206	−	0.891618i
$292$	1.48882	+	5.55636i	0.0871268	+	0.325161i
$293$	29.4353	+	7.88717i	1.71963	+	0.460774i	0.977753	−	0.209761i	$-0.0672688\pi$
$293$	29.4353	+	7.88717i	1.71963	+	0.460774i	0.741878	+	0.670535i	$0.233935\pi$
$294$	7.78781	+	9.29247i	0.454194	+	0.541948i
$295$	−2.39498	−	2.32819i	−0.139441	−	0.135553i
$296$	3.04704	−	1.75921i	0.177105	−	0.102252i
$297$	5.75058	+	24.1203i	0.333682	+	1.39960i
$298$	−12.9191	+	3.46165i	−0.748381	+	0.200528i
$299$	−6.97560			−0.403409
$300$	−7.77780	+	3.80866i	−0.449051	+	0.219893i
$301$	1.02811	−	0.00444729i	0.0592594	−	0.000256337i
$302$	0.714609	−	2.66696i	0.0411211	−	0.153466i
$303$	−9.23119	+	12.9273i	−0.530318	+	0.742653i
$304$	−1.62774	+	0.939777i	−0.0933574	+	0.0538999i
$305$	21.5554	+	20.9542i	1.23426	+	1.19984i
$306$	−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	$0.308507\pi$
$308$	−3.32048	−	12.1812i	−0.189202	−	0.694088i
$309$	−12.9798	+	10.6883i	−0.738394	+	0.608034i
$310$	−0.0729412	−	5.15815i	−0.00414278	−	0.292963i
$311$			21.7069i			1.23089i	0.788181	+	0.615443i	$0.211023\pi$
$311$			21.7069i			1.23089i	−0.788181	+	0.615443i	$0.788977\pi$
$312$	1.89953	+	1.35643i	0.107540	+	0.0767927i
$313$	−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
$315$	17.4785	+	3.08262i	0.984801	+	0.173686i
$316$	3.85958			0.217118
$317$	23.8963	+	23.8963i	1.34215	+	1.34215i	0.893914	+	0.448238i	$0.147948\pi$
$317$	23.8963	+	23.8963i	1.34215	+	1.34215i	0.448238	+	0.893914i	$0.352052\pi$
$318$	0.0167933	−	0.173450i	0.000941723	−	0.00972661i
$319$			46.7732i			2.61880i
$320$	1.55862	−	1.60334i	0.0871297	−	0.0896293i
$321$	4.62216	+	27.7103i	0.257984	+	1.54664i
$322$	9.64196	−	9.72574i	0.537326	−	0.541994i
$323$	−6.80738	+	6.80738i	−0.378773	+	0.378773i
$324$	8.91502	−	1.23383i	0.495279	−	0.0685460i
$325$	6.55515	+	1.55920i	0.363614	+	0.0864888i
$326$	−6.68699	+	3.86073i	−0.370358	+	0.213826i
$327$	−12.6151	−	1.22138i	−0.697614	−	0.0675425i
$328$	1.37835	−	5.14406i	0.0761064	−	0.284033i
$329$	2.95161	+	5.06165i	0.162728	+	0.279058i
$330$	−15.1913	−	10.5268i	−0.836252	−	0.579479i
$331$	−10.2905			−0.565617			−0.282809	−	0.959176i	$-0.591266\pi$
$331$	−10.2905			−0.565617			−0.282809	+	0.959176i	$0.591266\pi$
$332$	4.36758	−	1.17029i	0.239702	−	0.0642280i
$333$	−8.75689	+	5.89322i	−0.479874	+	0.322946i
$334$	19.2619	−	11.1209i	1.05397	−	0.608507i
$335$	8.19174	−	0.115839i	0.447563	−	0.00632897i
$336$	−4.51682	+	0.773514i	−0.246413	+	0.0421987i
$337$	18.7407	+	5.02156i	1.02087	+	0.273542i	0.730166	−	0.683270i	$-0.239443\pi$
$337$	18.7407	+	5.02156i	1.02087	+	0.273542i	0.290707	+	0.956812i	$0.406110\pi$
$338$	2.89462	+	10.8029i	0.157447	+	0.587599i
$339$	26.9176	−	4.48992i	1.46196	−	0.243859i
$340$	5.58576	−	9.99871i	0.302930	−	0.542256i
$341$	9.53428	−	5.50462i	0.516310	−	0.298092i
$342$	4.67797	−	3.14819i	0.252956	−	0.170234i
$343$	13.2646	+	12.9248i	0.716223	+	0.697871i
$344$	−0.194297	+	0.336532i	−0.0104758	+	0.0181446i
$345$	1.64963	−	19.9797i	0.0888130	−	1.07567i
$346$	−0.542488			−0.0291643
$347$	8.22861	+	8.22861i	0.441735	+	0.441735i	0.892595	−	0.450860i	$-0.148883\pi$
$347$	8.22861	+	8.22861i	0.441735	+	0.441735i	−0.450860	+	0.892595i	$0.648883\pi$
$348$	16.8977	+	1.63602i	0.905810	+	0.0876999i
$349$	16.5339	+	9.54588i	0.885042	+	0.510979i	0.872317	−	0.488940i	$-0.162616\pi$
$349$	16.5339	+	9.54588i	0.885042	+	0.510979i	0.0127243	+	0.999919i	$0.495950\pi$
$350$	−11.2347	+	6.98434i	−0.600521	+	0.373329i
$351$	−5.96473	−	3.66813i	−0.318374	−	0.195790i
$352$	4.60945	+	1.23510i	0.245684	+	0.0658309i
$353$	−12.8998	−	3.45648i	−0.686586	−	0.183970i	−0.101371	−	0.994849i	$-0.532323\pi$
$353$	−12.8998	−	3.45648i	−0.686586	−	0.183970i	−0.585214	+	0.810879i	$0.698990\pi$
$354$	−2.42293	−	0.907346i	−0.128777	−	0.0482249i
$355$	−22.0926	+	22.7264i	−1.17256	+	1.20619i
$356$	12.2496	−	7.07233i	0.649229	−	0.374833i
$357$	−21.3215	+	9.81478i	−1.12845	+	0.519453i
$358$	−24.7554	+	6.63319i	−1.30836	+	0.350575i
$359$	−4.83887	−	8.38116i	−0.255386	−	0.442341i	0.709615	−	0.704590i	$-0.248869\pi$
$359$	−4.83887	−	8.38116i	−0.255386	−	0.442341i	−0.965000	+	0.262249i	$0.915536\pi$
$360$	−4.33433	+	5.11992i	−0.228439	+	0.269843i
$361$	−7.73364	+	13.3951i	−0.407034	+	0.705003i
$362$	−13.2876	−	13.2876i	−0.698378	−	0.698378i
$363$	1.96501	−	20.2956i	0.103136	−	1.06524i
$364$	3.09544	+	1.76934i	0.162245	+	0.0927388i
$365$	11.2292	+	6.27319i	0.587765	+	0.328354i
$366$	21.8069	+	8.16632i	1.13986	+	0.426860i
$367$	−17.6534	−	4.73020i	−0.921498	−	0.246915i	−0.233272	−	0.972411i	$-0.574943\pi$
$367$	−17.6534	−	4.73020i	−0.921498	−	0.246915i	−0.688225	+	0.725497i	$0.741610\pi$
$368$	1.33972	+	4.99991i	0.0698378	+	0.260638i
$369$	−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
$372$	−1.65515	−	3.63697i	−0.0858158	−	0.188568i
$373$	−13.3521	+	3.57769i	−0.691347	+	0.185246i	−0.587351	−	0.809332i	$-0.699829\pi$
$373$	−13.3521	+	3.57769i	−0.691347	+	0.185246i	−0.103995	+	0.994578i	$0.533163\pi$
$374$	24.4425			1.26389
$375$	−6.01610	+	18.4067i	−0.310670	+	0.950518i
$376$	−2.21464			−0.114211
$377$	−9.33986	−	9.33986i	−0.481027	−	0.481027i
$378$	13.3590	−	3.24609i	0.687113	−	0.166961i
$379$			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
$383$	−1.47495	−	5.50457i	−0.0753662	−	0.281270i	0.917950	−	0.396696i	$-0.129843\pi$
$383$	−1.47495	−	5.50457i	−0.0753662	−	0.281270i	−0.993316	+	0.115426i	$0.963177\pi$
$384$	0.607429	−	1.62204i	0.0309977	−	0.0827746i
$385$	−24.7060	−	13.6621i	−1.25913	−	0.696283i
$386$			6.79088i			0.345647i
$387$	0.512146	−	1.04726i	0.0260338	−	0.0532352i
$388$	10.9879	−	2.94420i	0.557826	−	0.149469i
$389$	−16.6562	−	28.8494i	−0.844503	−	1.46272i	−0.886052	−	0.463585i	$-0.846563\pi$
$389$	−16.6562	−	28.8494i	−0.844503	−	1.46272i	0.0415495	−	0.999136i	$-0.486771\pi$
$390$	5.13547	−	0.931428i	0.260045	−	0.0471647i
$391$	13.2565	+	22.9609i	0.670410	+	1.16118i
$392$	−6.74555	+	1.87016i	−0.340702	+	0.0944574i
$393$	−32.5095	−	3.14754i	−1.63989	−	0.158773i
$394$			19.6830i			0.991613i
$395$	6.01564	−	6.18821i	0.302680	−	0.311363i
$396$	−14.0502	−	2.74641i	−0.706052	−	0.138013i
$397$	11.5735	+	3.10111i	0.580858	+	0.155640i	0.537272	−	0.843409i	$-0.319455\pi$
$397$	11.5735	+	3.10111i	0.580858	+	0.155640i	0.0435861	+	0.999050i	$0.486122\pi$
$398$	−5.79514	−	21.6277i	−0.290484	−	1.08410i
$399$	6.62529	−	5.50388i	0.331679	−	0.275539i
$400$	−0.141382	−	4.99800i	−0.00706908	−	0.249900i
$401$	33.3421	+	19.2501i	1.66502	+	0.961303i	0.970260	+	0.242066i	$0.0778249\pi$
$401$	33.3421	+	19.2501i	1.66502	+	0.961303i	0.694765	+	0.719237i	$0.255508\pi$
$402$	5.77593	−	2.62858i	0.288077	−	0.131102i
$403$	−0.804658	+	3.00302i	−0.0400829	+	0.149591i
$404$	−4.58557	−	7.94244i	−0.228141	−	0.395151i
$405$	11.9169	−	16.2169i	0.592157	−	0.805823i
$406$	25.9321	−	0.112174i	1.28699	−	0.00556709i
$407$	16.2179	−	4.34558i	0.803894	−	0.215403i
$408$	0.854942	−	8.83029i	0.0423259	−	0.437165i
$409$		−	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
$412$	−2.51252	−	9.37684i	−0.123783	−	0.461964i
$413$	−3.82181	−	1.00635i	−0.188059	−	0.0495194i
$414$	−5.04027	−	14.6881i	−0.247716	−	0.721882i
$415$	4.93105	−	8.82675i	0.242056	−	0.433288i
$416$	−1.16706	+	0.673803i	−0.0572199	+	0.0330359i
$417$	1.18204	−	1.65532i	0.0578847	−	0.0810613i
$418$	−8.66370	+	2.32143i	−0.423756	+	0.113545i
$419$	−5.20034	−	9.00726i	−0.254053	−	0.440033i	0.710585	−	0.703612i	$-0.248431\pi$
$419$	−5.20034	−	9.00726i	−0.254053	−	0.440033i	−0.964638	+	0.263578i	$0.915097\pi$
$420$	−5.79982	+	8.44761i	−0.283002	+	0.412201i
$421$	2.65150	−	4.59253i	0.129226	−	0.223826i	−0.794151	−	0.607721i	$-0.792084\pi$
$421$	2.65150	−	4.59253i	0.129226	−	0.223826i	0.923377	+	0.383895i	$0.125417\pi$
$422$	1.87864	−	7.01118i	0.0914508	−	0.341299i
$423$	6.62821	−	0.456492i	0.322275	−	0.0221954i
$424$	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
$427$	34.3971	+	9.05740i	1.66459	+	0.438318i
$428$	−15.6669	−	4.19794i	−0.757290	−	0.202915i
$429$	7.08048	+	8.59850i	0.341849	+	0.415140i
$430$	0.236739	+	0.836051i	0.0114166	+	0.0403179i
$431$	−28.3027	−	16.3406i	−1.36329	−	0.787097i	−0.373232	−	0.927738i	$-0.621750\pi$
$431$	−28.3027	−	16.3406i	−1.36329	−	0.787097i	−0.990061	+	0.140641i	$0.955084\pi$
$432$	−1.48364	+	4.97984i	−0.0713815	+	0.239593i
$433$	−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
$435$	28.9602	−	24.5427i	1.38854	−	1.17673i
$436$	3.65868	−	6.33702i	0.175219	−	0.303488i
$437$	−6.87952	−	6.87952i	−0.329092	−	0.329092i
$438$	9.91702	+	0.960159i	0.473854	+	0.0458782i
$439$			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	−0.254170	−	0.967160i	$-0.581802\pi$
$443$	15.0067	−	15.0067i	0.712990	−	0.712990i	0.967160	+	0.254170i	$0.0818023\pi$
$444$	−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
$447$	−2.23246	+	23.0580i	−0.105592	+	1.09061i
$448$	0.673710	−	2.55854i	0.0318298	−	0.120880i
$449$	8.16454			0.385309			0.192654	−	0.981267i	$-0.438290\pi$
$449$	8.16454			0.385309			0.192654	+	0.981267i	$0.438290\pi$
$450$	1.45336	+	14.9294i	0.0685118	+	0.703780i
$451$	12.7068	−	22.0089i	0.598341	−	1.03636i
$452$	−4.07785	+	15.2187i	−0.191806	+	0.715829i
$453$	−3.89185	−	2.77912i	−0.182855	−	0.130574i
$454$	−15.1965	+	8.77370i	−0.713206	+	0.411770i
$455$	7.66148	−	2.20529i	0.359176	−	0.103386i
$456$	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	$-0.0361725\pi$
$458$	3.82420	+	14.2721i	0.178693	+	0.666891i
$459$	−0.738621	+	26.6045i	−0.0344759	+	1.24179i
$460$	10.1047	+	5.64495i	0.471132	+	0.263197i
$461$	20.4255	+	11.7927i	0.951310	+	0.549239i	0.893488	−	0.449088i	$-0.148251\pi$
$461$	20.4255	+	11.7927i	0.951310	+	0.549239i	0.0578226	+	0.998327i	$0.481584\pi$
$462$	−21.7754	−	2.01324i	−1.01308	−	0.0936646i
$463$	−8.41936	+	31.4215i	−0.391281	+	1.46028i	0.436743	+	0.899586i	$0.356132\pi$
$463$	−8.41936	+	31.4215i	−0.391281	+	1.46028i	−0.828024	+	0.560693i	$0.810535\pi$
$464$	−4.90075	+	8.48834i	−0.227511	+	0.394061i
$465$	−8.41105	−	3.01489i	−0.390053	−	0.139812i
$466$	5.83251	+	10.1022i	0.270186	+	0.467975i
$467$	5.94861	−	22.2005i	0.275269	−	1.02732i	−0.680392	−	0.732848i	$-0.738190\pi$
$467$	5.94861	−	22.2005i	0.275269	−	1.02732i	0.955661	−	0.294469i	$-0.0951429\pi$
$468$	3.35402	−	2.25719i	0.155040	−	0.104339i
$469$	8.37383	−	4.88305i	0.386668	−	0.225478i
$470$	−3.45179	+	3.55081i	−0.159219	+	0.163787i
$471$	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
$475$	4.92714	+	8.00258i	0.226073	+	0.367184i
$476$	−0.0586192	−	13.5514i	−0.00268681	−	0.621129i
$477$	−0.271143	−	0.132598i	−0.0124148	−	0.00607126i
$478$	0.118079	−	0.440678i	0.00540082	−	0.0201561i
$479$	−19.5180	−	33.8062i	−0.891801	−	1.54464i	−0.837714	−	0.546109i	$-0.816109\pi$
$479$	−19.5180	−	33.8062i	−0.891801	−	1.54464i	−0.0540866	−	0.998536i	$-0.517225\pi$
$480$	−1.65393	−	3.50207i	−0.0754913	−	0.159847i
$481$	−2.37072	+	4.10620i	−0.108095	+	0.187227i
$482$	−4.64420	+	17.3324i	−0.211537	+	0.789468i
$483$	−9.91878	−	21.5474i	−0.451320	−	0.980441i
$484$	10.1953	+	5.88624i	0.463421	+	0.267556i
$485$	12.4054	−	22.2062i	0.563302	−	1.00833i
$486$	3.41392	−	15.2100i	0.154859	−	0.689941i
$487$	2.78753	+	10.4032i	0.126315	+	0.471414i	0.999883	−	0.0152880i	$-0.00486651\pi$
$487$	2.78753	+	10.4032i	0.126315	+	0.471414i	−0.873568	+	0.486702i	$0.838200\pi$
$488$	−9.50639	+	9.50639i	−0.430334	+	0.430334i
$489$	2.20041	+	13.1917i	0.0995061	+	0.596550i
$490$	−7.51529	+	13.7303i	−0.339506	+	0.620271i
$491$	25.7279	−	14.8540i	1.16108	−	0.670352i	0.209520	−	0.977804i	$-0.432810\pi$
$491$	25.7279	−	14.8540i	1.16108	−	0.670352i	0.951563	+	0.307453i	$0.0994766\pi$
$492$	−7.50664	−	5.36039i	−0.338426	−	0.241665i
$493$	−12.9936	+	48.4927i	−0.585201	+	2.18400i
$494$	1.26645	−	2.19355i	0.0569802	−	0.0986927i
$495$	−26.3025	+	18.2467i	−1.18221	+	0.820126i
$496$	2.30702			0.103588
$497$	−9.54946	+	36.2659i	−0.428352	+	1.62675i
$498$	0.754734	−	7.79528i	0.0338204	−	0.349315i
$499$	−27.6676	−	15.9739i	−1.23857	−	0.715090i	−0.269770	−	0.962925i	$-0.586948\pi$
$499$	−27.6676	−	15.9739i	−1.23857	−	0.715090i	−0.968802	+	0.247834i	$0.920281\pi$
$500$	−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	−0.502297	−	0.864695i	$-0.667512\pi$
$503$	8.12773	−	8.12773i	0.362398	−	0.362398i	0.864695	+	0.502297i	$0.167512\pi$
$504$	−1.48897	+	7.79634i	−0.0663242	+	0.347277i
$505$	−19.8816	−	5.02706i	−0.884719	−	0.223701i
$506$			24.7015i			1.09812i
$507$	19.2810	+	1.86677i	0.856300	+	0.0829064i
$508$	−8.38188	−	8.38188i	−0.371886	−	0.371886i
$509$	−14.7879	+	25.6134i	−0.655463	+	1.13530i	0.326314	+	0.945261i	$0.394193\pi$
$509$	−14.7879	+	25.6134i	−0.655463	+	1.13530i	−0.981777	+	0.190034i	$0.939140\pi$
$510$	−12.8254	−	15.1339i	−0.567918	−	0.670139i
$511$	15.2192	−	0.0658334i	0.673258	−	0.00291230i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.26496	−	9.50018i	−0.100001	−	0.419443i
$514$	17.9823	+	10.3821i	0.793166	+	0.457935i
$515$	−18.9503	−	10.5866i	−0.835050	−	0.466499i
$516$	0.427849	+	0.519578i	0.0188350	+	0.0228731i
$517$	−10.2083	−	2.73530i	−0.448959	−	0.120298i
$518$	−2.44818	−	8.98115i	−0.107567	−	0.394609i
$519$	−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	−0.288073	−	0.957608i	$-0.593015\pi$
$521$	−28.7925	−	16.6234i	−1.26142	−	0.728283i	−0.973350	+	0.229325i	$0.926348\pi$
$522$	12.9178	−	26.4150i	0.565398	−	1.15615i
$523$	1.45802	−	5.44141i	0.0637548	−	0.237936i	−0.926694	−	0.375817i	$-0.877362\pi$
$523$	1.45802	−	5.44141i	0.0637548	−	0.237936i	0.990449	+	0.137880i	$0.0440290\pi$
$524$	9.42856	−	16.3307i	0.411889	−	0.713412i
$525$	4.50462	+	22.4657i	0.196598	+	0.980484i
$526$	0.740355	+	1.28233i	0.0322810	+	0.0559123i
$527$	11.4140	−	3.05836i	0.497200	−	0.133224i
$528$	4.80330	−	6.72650i	0.209037	−	0.292733i
$529$	−3.28565	+	1.89697i	−0.142854	+	0.0824769i
$530$	0.216460	−	0.0612934i	0.00940241	−	0.00266242i
$531$	−2.94351	+	3.37895i	−0.127738	+	0.146634i
$532$	1.30783	+	4.79777i	0.0567016	+	0.208010i
$533$	1.85747	+	6.93216i	0.0804558	+	0.300265i
$534$	−4.03085	−	24.1654i	−0.174432	−	1.04574i
$535$	−31.1496	+	18.5764i	−1.34671	+	0.803127i
$536$			3.66382i			0.158253i
$537$	−4.27782	+	44.1836i	−0.184602	+	1.90666i
$538$	−8.11408	+	2.17416i	−0.349823	+	0.0937348i
$539$	−33.4031	+	0.288988i	−1.43877	+	0.0124476i
$540$	5.67193	+	10.1405i	0.244081	+	0.436376i
$541$	−14.0679	−	24.3664i	−0.604827	−	1.04759i	−0.992079	−	0.125618i	$-0.959909\pi$
$541$	−14.0679	−	24.3664i	−0.604827	−	1.04759i	0.387251	−	0.921974i	$-0.373425\pi$
$542$	−6.14224	+	22.9232i	−0.263832	+	0.984634i
$543$	−29.6243	+	13.4818i	−1.27130	+	0.578558i
$544$	4.43579	+	2.56100i	0.190183	+	0.109802i
$545$	−4.45788	−	15.7431i	−0.190954	−	0.674362i
$546$	4.75021	−	3.94619i	0.203290	−	0.168881i
$547$	10.7150	+	39.9889i	0.458141	+	1.70980i	0.678687	+	0.734427i	$0.262549\pi$
$547$	10.7150	+	39.9889i	0.458141	+	1.70980i	−0.220547	+	0.975376i	$0.570784\pi$
$548$	7.85469	+	2.10466i	0.335536	+	0.0899065i
$549$	26.4923	−	30.4113i	1.13066	−	1.29792i
$550$	5.52133	−	23.2126i	0.235430	−	0.989790i
$551$		−	18.4224i		−	0.784822i
$552$	8.92386	+	0.864002i	0.379825	+	0.0367744i
$553$	2.60024	−	9.87489i	0.110573	−	0.419923i
$554$	5.14010	+	8.90291i	0.218382	+	0.378248i
$555$	−11.2005	−	7.76133i	−0.475433	−	0.329450i
$556$	0.587175	+	1.01702i	0.0249018	+	0.0431311i
$557$	4.40768	−	1.18103i	0.186759	−	0.0500420i	−0.164227	−	0.986423i	$-0.552513\pi$
$557$	4.40768	−	1.18103i	0.186759	−	0.0500420i	0.350986	+	0.936381i	$0.385846\pi$
$558$	−6.90471	+	0.475535i	−0.292300	+	0.0201310i
$559$		−	0.523672i		−	0.0221489i
$560$	−3.05214	−	5.06798i	−0.128976	−	0.214161i
$561$	14.8471	−	39.6468i	0.626844	−	1.67389i
$562$	−4.82279	−	17.9989i	−0.203437	−	0.759237i
$563$	−14.8846	+	14.8846i	−0.627310	+	0.627310i	−0.947391	−	0.320080i	$-0.896290\pi$
$563$	−14.8846	+	14.8846i	−0.627310	+	0.627310i	0.320080	+	0.947391i	$0.396290\pi$
$564$	−1.34524	+	3.59224i	−0.0566447	+	0.151261i
$565$	18.0449	+	30.2585i	0.759156	+	1.27298i
$566$			3.95597i			0.166282i
$567$	2.84935	−	23.6407i	0.119661	−	0.992815i
$568$	−10.0228	−	10.0228i	−0.420549	−	0.420549i
$569$	9.45533			0.396388			0.198194	−	0.980163i	$-0.436492\pi$
$569$	9.45533			0.396388			0.198194	+	0.980163i	$0.436492\pi$
$570$	5.98334	+	4.14614i	0.250614	+	0.173663i
$571$	21.1794			0.886331			0.443165	−	0.896440i	$-0.353855\pi$
$571$	21.1794			0.886331			0.443165	+	0.896440i	$0.353855\pi$
$572$	−6.21172	+	1.66443i	−0.259725	+	0.0695931i
$573$	−0.132649	−	0.291477i	−0.00554148	−	0.0121766i
$574$	−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
$577$	−5.18377	−	19.3461i	−0.215803	−	0.805389i	−0.985882	−	0.167440i	$-0.946450\pi$
$577$	−5.18377	−	19.3461i	−0.215803	−	0.805389i	0.770079	−	0.637949i	$-0.220217\pi$
$578$	8.92031	+	2.39019i	0.371036	+	0.0994188i
$579$	11.0151	+	4.12498i	0.457772	+	0.171428i
$580$	5.97125	+	21.0877i	0.247943	+	0.875618i
$581$	−0.0517484	−	11.9631i	−0.00214688	−	0.496311i
$582$	1.89875	−	19.6112i	0.0787055	−	0.812912i
$583$	0.339493	+	0.339493i	0.0140604	+	0.0140604i
$584$	−2.87618	+	4.98170i	−0.119017	+	0.206144i
$585$	1.60862	−	8.89575i	0.0665082	−	0.367794i
$586$	15.2368	+	26.3910i	0.629428	+	1.09020i
$587$	−17.7189	+	4.74776i	−0.731336	+	0.195961i	−0.605224	−	0.796055i	$-0.706917\pi$
$587$	−17.7189	+	4.74776i	−0.731336	+	0.195961i	−0.126112	+	0.992016i	$0.540250\pi$
$588$	−1.06396	+	12.0776i	−0.0438771	+	0.498071i
$589$	−3.75524	+	2.16809i	−0.154732	+	0.0893345i
$590$	−0.0472279	−	3.33979i	−0.00194434	−	0.137497i
$591$	31.9266	+	11.9560i	1.31329	+	0.491804i
$592$	3.39853	+	0.910632i	0.139679	+	0.0374268i
$593$	11.9655	+	3.20616i	0.491366	+	0.131661i	0.495990	−	0.868328i	$-0.334805\pi$
$593$	11.9655	+	3.20616i	0.491366	+	0.131661i	−0.00462398	+	0.999989i	$0.501472\pi$
$594$	−12.9893	+	21.1219i	−0.532959	+	0.866641i
$595$	−21.8189	−	21.0276i	−0.894487	−	0.862048i
$596$	−11.5829	−	6.68740i	−0.474455	−	0.273927i
$597$	−38.6013	−	3.73735i	−1.57985	−	0.152960i
$598$	−4.93249	−	4.93249i	−0.201705	−	0.201705i
$599$	11.1364			0.455021			0.227511	−	0.973776i	$-0.426941\pi$
$599$	11.1364			0.455021			0.227511	+	0.973776i	$0.426941\pi$
$600$	−8.19286	−	2.80660i	−0.334472	−	0.114579i
$601$	−5.99957	+	10.3916i	−0.244728	+	0.423881i	−0.962055	−	0.272856i	$-0.912032\pi$
$601$	−5.99957	+	10.3916i	−0.244728	+	0.423881i	0.717327	+	0.696736i	$0.245365\pi$
$602$	0.730130	+	0.723841i	0.0297579	+	0.0295016i
$603$	−0.755206	−	10.9655i	−0.0307544	−	0.446550i
$604$	2.39113	−	1.38052i	0.0972936	−	0.0561725i
$605$	25.3282	−	7.17201i	1.02974	−	0.291584i
$606$	−15.6684	+	2.61353i	−0.636485	+	0.106167i
$607$	3.62272	+	13.5202i	0.147042	+	0.548767i	0.999656	+	0.0262262i	$0.00834903\pi$
$607$	3.62272	+	13.5202i	0.147042	+	0.548767i	−0.852614	+	0.522541i	$0.824984\pi$
$608$	−1.81551	−	0.486464i	−0.0736286	−	0.0197287i
$609$	15.5699	−	42.1311i	0.630926	−	1.70724i
$610$	0.425061	+	30.0588i	0.0172102	+	1.21705i
$611$	2.58462	−	1.49223i	0.104562	−	0.0603692i
$612$	−13.8038	−	6.75053i	−0.557986	−	0.272874i
$613$	7.86376	−	2.10709i	0.317614	−	0.0851045i	−0.0964899	−	0.995334i	$-0.530762\pi$
$613$	7.86376	−	2.10709i	0.317614	−	0.0851045i	0.414104	+	0.910229i	$0.364095\pi$
$614$	−6.40484			−0.258478
$615$	−20.2945	+	3.68085i	−0.818355	+	0.148426i
$616$	6.26547	−	10.9613i	0.252443	−	0.441645i
$617$	3.91629	−	14.6158i	0.157664	−	0.588410i	−0.841199	−	0.540726i	$-0.818149\pi$
$617$	3.91629	−	14.6158i	0.157664	−	0.588410i	0.998862	−	0.0476836i	$-0.0151839\pi$
$618$	−16.7358	−	1.62035i	−0.673214	−	0.0651801i
$619$	−19.5656	+	11.2962i	−0.786407	+	0.454032i	−0.838696	−	0.544600i	$-0.816682\pi$
$619$	−19.5656	+	11.2962i	−0.786407	+	0.454032i	0.0522894	+	0.998632i	$0.483348\pi$
$620$	3.59578	−	3.69894i	0.144410	−	0.148553i
$621$	−26.8864	−	0.746448i	−1.07891	−	0.0299539i
$622$	−15.3491	+	15.3491i	−0.615443	+	0.615443i
$623$	−9.84212	−	36.1058i	−0.394316	−	1.44655i
$624$	0.384032	+	2.30231i	0.0153736	+	0.0921663i
$625$	−24.9600	+	1.41325i	−0.998401	+	0.0565300i
$626$		−	33.5292i		−	1.34010i
$627$	−1.49712	+	15.4630i	−0.0597892	+	0.617534i
$628$	6.56772	+	6.56772i	0.262080	+	0.262080i
$629$	18.0213			0.718558
$630$	10.1794	+	14.5389i	0.405558	+	0.579243i
$631$	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
$633$	−10.2313	−	7.30604i	−0.406658	−	0.290389i
$634$			33.7945i			1.34215i
$635$	−26.5032	+	0.374781i	−1.05175	+	0.0148727i
$636$	0.134523	−	0.110773i	0.00533417	−	0.00439244i
$637$	6.61236	−	6.72777i	0.261991	−	0.266564i
$638$	−33.0737	+	33.0737i	−1.30940	+	1.30940i
$639$	32.0634	+	27.9315i	1.26841	+	1.10495i
$640$	2.23584	−	0.0316170i	0.0883795	−	0.00124977i
$641$	39.7628	−	22.9571i	1.57054	−	0.906750i	0.574435	−	0.818550i	$-0.305222\pi$
$641$	39.7628	−	22.9571i	1.57054	−	0.906750i	0.996103	−	0.0882004i	$-0.0281116\pi$
$642$	−16.3258	+	22.8625i	−0.644328	+	0.902312i
$643$	2.80408	−	10.4650i	0.110582	−	0.412698i	−0.888336	−	0.459193i	$-0.848139\pi$
$643$	2.80408	−	10.4650i	0.110582	−	0.412698i	0.998919	+	0.0464953i	$0.0148052\pi$
$644$	13.6950	−	0.0592403i	0.539660	−	0.00233440i
$645$	1.49991	+	0.123841i	0.0590590	+	0.00487622i
$646$	−9.62709			−0.378773
$647$	7.27052	−	1.94813i	0.285834	−	0.0765889i	−0.113054	−	0.993589i	$-0.536063\pi$
$647$	7.27052	−	1.94813i	0.285834	−	0.0765889i	0.398887	+	0.917000i	$0.369397\pi$
$648$	7.17632	+	5.43143i	0.281913	+	0.213367i
$649$	6.17324	−	3.56412i	0.242321	−	0.139904i
$650$	3.53267	+	5.73771i	0.138563	+	0.225052i
$651$	−10.4204	+	1.78452i	−0.408408	+	0.0699407i
$652$	−7.45837	−	1.99846i	−0.292092	−	0.0782658i
$653$	−3.62558	−	13.5308i	−0.141880	−	0.529503i	−0.999874	−	0.0158440i	$-0.994956\pi$
$653$	−3.62558	−	13.5308i	−0.141880	−	0.529503i	0.857995	−	0.513659i	$-0.171710\pi$
$654$	−8.05655	−	9.78384i	−0.315036	−	0.382578i
$655$	−11.4881	−	40.5707i	−0.448878	−	1.58523i
$656$	4.61203	−	2.66276i	0.180070	−	0.103963i
$657$	7.58131	−	15.5026i	0.295775	−	0.604815i
$658$	−1.49202	+	5.66624i	−0.0581651	+	0.220893i
$659$	5.17959	−	8.97131i	0.201768	−	0.349473i	−0.747330	−	0.664453i	$-0.768665\pi$
$659$	5.17959	−	8.97131i	0.201768	−	0.349473i	0.949098	+	0.314980i	$0.101998\pi$
$660$	−3.29831	−	18.1854i	−0.128387	−	0.707865i
$661$	−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
$663$	4.95211	+	10.8816i	0.192324	+	0.422605i
$664$	3.91587	+	2.26083i	0.151965	+	0.0877371i
$665$	9.73086	+	5.38103i	0.377347	+	0.208668i
$666$	−10.3592	−	2.02492i	−0.401410	−	0.0784640i
$667$	−49.0066	−	13.1313i	−1.89754	−	0.508445i
$668$	21.4839	+	5.75659i	0.831237	+	0.222729i
$669$	15.8137	−	13.0219i	0.611394	−	0.503455i
$670$	5.87435	+	5.71052i	0.226946	+	0.220617i
$671$	−55.5605	+	32.0779i	−2.14489	+	1.23835i
$672$	−3.74083	−	2.64692i	−0.144306	−	0.102107i
$673$	−3.98572	+	1.06797i	−0.153638	+	0.0411673i	−0.334818	−	0.942283i	$-0.608675\pi$
$673$	−3.98572	+	1.06797i	−0.153638	+	0.0411673i	0.181180	+	0.983450i	$0.442008\pi$
$674$	9.70091	+	16.8025i	0.373665	+	0.647207i
$675$	25.0990	+	6.71116i	0.966061	+	0.258313i
$676$	−5.59198	+	9.68559i	−0.215076	+	0.372523i
$677$	−25.1112	−	25.1112i	−0.965101	−	0.965101i	0.0343103	−	0.999411i	$-0.489077\pi$
$677$	−25.1112	−	25.1112i	−0.965101	−	0.965101i	−0.999411	+	0.0343103i	$0.989077\pi$
$678$	22.2085	+	15.8588i	0.852911	+	0.609052i
$679$	−0.130188	−	30.0965i	−0.00499614	−	1.15500i
$680$	11.0199	−	3.12042i	0.422593	−	0.119663i
$681$	5.00054	+	29.9788i	0.191621	+	1.14879i
$682$	10.6341	+	2.84940i	0.407201	+	0.109109i
$683$	−1.85397	−	6.91910i	−0.0709401	−	0.264752i	0.921342	−	0.388753i	$-0.127094\pi$
$683$	−1.85397	−	6.91910i	−0.0709401	−	0.264752i	−0.992282	+	0.124001i	$0.960427\pi$
$684$	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
$687$	25.4729	+	2.46627i	0.971852	+	0.0940940i
$688$	−0.375353	+	0.100575i	−0.0143102	+	0.00383440i
$689$	−0.135583			−0.00516528
$690$	15.2942	−	12.9613i	0.582241	−	0.493429i
$691$	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
$693$	−16.4926	+	34.0978i	−0.626502	+	1.29527i
$694$			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
$698$	4.94131	+	18.4412i	0.187031	+	0.698010i
$699$	19.9291	−	3.32422i	0.753786	−	0.125734i
$700$	−12.8828	−	3.00547i	−0.486925	−	0.113596i
$701$			19.0727i			0.720365i	0.932882	+	0.360183i	$0.117286\pi$
$701$			19.0727i			0.720365i	−0.932882	+	0.360183i	$0.882714\pi$
$702$	−1.62394	−	6.81146i	−0.0612916	−	0.257082i
$703$	−6.38771	+	1.71158i	−0.240917	+	0.0645535i
$704$	2.38603	+	4.13272i	0.0899267	+	0.155758i
$705$	3.66286	+	7.75582i	0.137951	+	0.292101i
$706$	−6.67742	−	11.5656i	−0.251308	−	0.435278i
$707$	−23.4104	+	6.38145i	−0.880438	+	0.239999i
$708$	−1.07168	−	2.35486i	−0.0402761	−	0.0885010i
$709$			16.9288i			0.635773i	0.948129	+	0.317887i	$0.102973\pi$
$709$			16.9288i			0.635773i	−0.948129	+	0.317887i	$0.897027\pi$
$710$	−31.6919	+	0.448154i	−1.18937	+	0.0168189i
$711$	−8.73060	−	7.60552i	−0.327423	−	0.285229i
$712$	13.6627	+	3.66091i	0.512031	+	0.137198i
$713$	3.09077	+	11.5349i	0.115750	+	0.431986i
$714$	−22.0166	−	8.13646i	−0.823952	−	0.304499i
$715$	−7.01310	+	12.5537i	−0.262275	+	0.469482i
$716$	−22.1951	−	12.8143i	−0.829470	−	0.478895i
$717$	−0.643075	−	0.459211i	−0.0240161	−	0.0171495i
$718$	2.50478	−	9.34797i	0.0934776	−	0.348863i
$719$	−21.5142	−	37.2636i	−0.802343	−	1.38970i	−0.918070	−	0.396418i	$-0.870253\pi$
$719$	−21.5142	−	37.2636i	−0.802343	−	1.38970i	0.115727	−	0.993281i	$-0.463080\pi$
$720$	−6.68516	+	0.555491i	−0.249141	+	0.0207019i
$721$	−25.6837	+	0.111099i	−0.956511	+	0.00413756i
$722$	−14.9402	+	4.00323i	−0.556018	+	0.148985i
$723$	25.2929	+	18.0613i	0.940652	+	0.671706i
$724$		−	18.7914i		−	0.698378i
$725$	43.1176	+	23.2938i	1.60135	+	0.865111i
$726$	15.7406	−	12.9617i	0.584190	−	0.481054i
$727$	−7.56562	−	28.2353i	−0.280593	−	1.04719i	−0.952000	−	0.306099i	$-0.900976\pi$
$727$	−7.56562	−	28.2353i	−0.280593	−	1.04719i	0.671406	−	0.741089i	$-0.265691\pi$
$728$	0.937690	+	3.43992i	0.0347531	+	0.127492i
$729$	−22.5976	−	14.7766i	−0.836950	−	0.547280i
$730$	3.50445	+	12.3761i	0.129706	+	0.458060i
$731$	−1.72372	+	0.995191i	−0.0637541	+	0.0368085i
$732$	9.64533	+	21.1942i	0.356502	+	0.783362i
$733$	8.20072	−	2.19738i	0.302901	−	0.0811620i	−0.104168	−	0.994560i	$-0.533218\pi$
$733$	8.20072	−	2.19738i	0.302901	−	0.0811620i	0.407068	+	0.913398i	$0.366551\pi$
$734$	−9.13805	−	15.8276i	−0.337292	−	0.584206i
$735$	17.7061	+	20.5303i	0.653100	+	0.757272i
$736$	−2.58814	+	4.48280i	−0.0954002	+	0.165238i
$737$	−4.52518	+	16.8882i	−0.166687	+	0.622085i
$738$	−13.2545	+	8.92006i	−0.487906	+	0.328352i
$739$	21.2221	+	12.2526i	0.780668	+	0.450719i	0.836667	−	0.547712i	$-0.184501\pi$
$739$	21.2221	+	12.2526i	0.780668	+	0.450719i	−0.0559990	+	0.998431i	$0.517834\pi$
$740$	6.75708	−	4.02965i	0.248395	−	0.148133i
$741$	−2.78877	−	3.38667i	−0.102448	−	0.124412i
$742$	0.187408	−	0.189036i	0.00687996	−	0.00693974i
$743$	−16.5060	−	4.42277i	−0.605546	−	0.162256i	−0.0569978	−	0.998374i	$-0.518153\pi$
$743$	−16.5060	−	4.42277i	−0.605546	−	0.162256i	−0.548549	+	0.836119i	$0.684819\pi$
$744$	1.40135	−	3.74210i	0.0513761	−	0.137192i
$745$	−28.7756	+	8.14818i	−1.05426	+	0.298526i
$746$	−11.9712	−	6.91157i	−0.438296	−	0.253050i
$747$	−12.1859	−	5.95929i	−0.445857	−	0.218039i
$748$	17.2835	+	17.2835i	0.631946	+	0.631946i
$749$	−21.2956	+	37.2563i	−0.778123	+	1.36131i
$750$	−17.2695	+	8.76148i	−0.630594	+	0.319924i
$751$	7.34232	−	12.7173i	0.267925	−	0.464060i	−0.700401	−	0.713750i	$-0.746995\pi$
$751$	7.34232	−	12.7173i	0.267925	−	0.464060i	0.968326	+	0.249690i	$0.0803287\pi$
$752$	−1.56599	−	1.56599i	−0.0571056	−	0.0571056i
$753$	−1.98119	−	4.35339i	−0.0721986	−	0.158646i
$754$		−	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	0.838790	−	0.544455i	$-0.183264\pi$
$761$	21.7013	+	12.5293i	0.786673	+	0.454186i	−0.0521170	+	0.998641i	$0.516597\pi$
$762$	−18.6872	+	8.50439i	−0.676966	+	0.308082i
$763$	−13.7486	−	13.6302i	−0.497733	−	0.493446i
$764$	0.184891			0.00668913
$765$	−32.3383	+	11.6106i	−1.16919	+	0.419783i
$766$	2.84938	−	4.93526i	0.102952	−	0.178318i
$767$	−0.520999	+	1.94439i	−0.0188122	+	0.0702080i
$768$	1.57648	−	0.717442i	0.0568862	−	0.0258884i
$769$	45.1967	−	26.0943i	1.62983	−	0.940985i	0.645693	−	0.763597i	$-0.276569\pi$
$769$	45.1967	−	26.0943i	1.62983	−	0.940985i	0.984141	−	0.177388i	$-0.0567646\pi$
$770$	−7.80922	−	27.1303i	−0.281425	−	0.977708i
$771$	27.7632	−	22.8617i	0.999868	−	0.823346i
$772$	−4.80188	+	4.80188i	−0.172823	+	0.172823i
$773$	−4.22197	−	15.7566i	−0.151854	−	0.566725i	−0.999354	−	0.0359309i	$-0.988560\pi$
$773$	−4.22197	−	15.7566i	−0.151854	−	0.566725i	0.847501	−	0.530794i	$-0.178106\pi$
$774$	1.10267	−	0.378383i	0.0396345	−	0.0136007i
$775$	−0.326171	−	11.5305i	−0.0117164	−	0.414188i
$776$	9.85147	+	5.68775i	0.353647	+	0.204178i
$777$	−16.0549	−	1.48436i	−0.575967	−	0.0532510i
$778$	8.62188	−	32.1773i	0.309109	−	1.15361i
$779$	−5.00480	+	8.66856i	−0.179316	+	0.310584i
$780$	4.28995	+	2.97271i	0.153605	+	0.106440i
$781$	−33.8206	−	58.5790i	−1.21020	−	2.09612i
$782$	−6.86207	+	25.6096i	−0.245387	+	0.915797i
$783$	−34.9997	−	36.9986i	−1.25079	−	1.32222i
$784$	−6.09223	−	3.44742i	−0.217580	−	0.123122i
$785$	20.7669	−	0.293664i	0.741201	−	0.0104813i
$786$	−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
$790$	8.62942	−	0.122029i	0.307021	−	0.00434158i
$791$	36.1904	+	20.6863i	1.28678	+	0.735521i
$792$	−7.99302	−	11.8770i	−0.284020	−	0.422032i
$793$	4.68910	−	17.5000i	0.166515	−	0.621442i
$794$	5.99089	+	10.3765i	0.212609	+	0.368249i
$795$	0.0320633	−	0.388339i	0.00113717	−	0.0137730i
$796$	11.1953	−	19.3909i	0.396808	−	0.687292i
$797$	−4.88305	+	18.2238i	−0.172967	+	0.645520i	0.823922	+	0.566703i	$0.191781\pi$
$797$	−4.88305	+	18.2238i	−0.172967	+	0.645520i	−0.996889	+	0.0788175i	$0.974886\pi$
$798$	8.57662	+	0.792950i	0.303609	+	0.0280701i
$799$	−9.82367	−	5.67170i	−0.347537	−	0.200650i
$800$	3.43415	−	3.63409i	0.121415	−	0.128485i
$801$	−41.6458	−	8.14054i	−1.47148	−	0.287632i
$802$	9.96457	+	37.1883i	0.351861	+	1.31316i
$803$	−19.4105	+	19.4105i	−0.684982	+	0.684982i
$804$	5.94289	+	2.22551i	0.209589	+	0.0784878i
$805$	21.2504	−	22.0501i	0.748979	−	0.777164i
$806$	−2.69244	+	1.55448i	−0.0948371	+	0.0547542i
$807$	−1.40214	+	14.4821i	−0.0493577	+	0.509792i
$808$	2.37367	−	8.85864i	0.0835053	−	0.311646i
$809$	19.1875	−	33.2338i	0.674598	−	1.16844i	−0.301988	−	0.953312i	$-0.597650\pi$
$809$	19.1875	−	33.2338i	0.674598	−	1.16844i	0.976586	−	0.215127i	$-0.0690165\pi$
$810$	19.8936	−	3.04051i	0.698990	−	0.106833i
$811$	27.8982			0.979639			0.489819	−	0.871824i	$-0.337063\pi$
$811$	27.8982			0.979639			0.489819	+	0.871824i	$0.337063\pi$
$812$	18.4161	+	18.2574i	0.646277	+	0.640710i
$813$	33.4514	+	23.8872i	1.17319	+	0.837760i
$814$	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	$0.256508\pi$
$821$			41.3416i			1.44283i	−0.692502	+	0.721416i	$0.743492\pi$
$822$	8.18501	−	11.4622i	0.285485	−	0.399791i
$823$	−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
$825$	−34.2981	−	23.0559i	−1.19411	−	0.802703i
$826$	−1.99083	−	3.41403i	−0.0692698	−	0.118789i
$827$	21.3177	+	21.3177i	0.741288	+	0.741288i	0.972826	−	0.231538i	$-0.0743756\pi$
$827$	21.3177	+	21.3177i	0.741288	+	0.741288i	−0.231538	+	0.972826i	$0.574376\pi$
$828$	6.82206	−	13.9501i	0.237083	−	0.484799i
$829$	−7.89081	−	4.55576i	−0.274059	−	0.158228i	0.356672	−	0.934230i	$-0.383911\pi$
$829$	−7.89081	−	4.55576i	−0.274059	−	0.158228i	−0.630731	+	0.776002i	$0.717245\pi$
$830$	9.72823	−	2.75468i	0.337672	−	0.0956162i
$831$	17.5632	−	2.92958i	0.609259	−	0.101626i
$832$	−1.30169	−	0.348786i	−0.0451279	−	0.0120920i
$833$	−34.7114	−	8.97976i	−1.20268	−	0.311130i
$834$	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
$837$	−3.42278	+	11.4886i	−0.118309	+	0.397104i
$838$	2.69190	−	10.0463i	0.0929900	−	0.347043i
$839$	−5.10398	+	8.84035i	−0.176209	+	0.305203i	−0.940579	−	0.339575i	$-0.889717\pi$
$839$	−5.10398	+	8.84035i	−0.176209	+	0.305203i	0.764370	+	0.644778i	$0.223050\pi$
$840$	−10.0745	+	1.87227i	−0.347602	+	0.0645993i
$841$	−33.5346	−	58.0837i	−1.15637	−	2.00288i
$842$	5.12230	−	1.37252i	0.176526	−	0.0473000i
$843$	−32.1245	−	3.11027i	−1.10643	−	0.107123i
$844$	6.28605	−	3.62926i	0.216375	−	0.124924i
$845$	6.81348	+	24.0620i	0.234391	+	0.827759i
$846$	5.00964	+	4.36407i	0.172235	+	0.150040i
$847$	21.9288	−	22.1193i	0.753483	−	0.760030i
$848$	0.0260397	+	0.0971817i	0.000894209	+	0.00333723i
$849$	6.41676	+	2.40297i	0.220223	+	0.0824697i
$850$	12.1728	−	22.5322i	0.417522	−	0.772847i
$851$			18.2123i			0.624310i
$852$	−22.3457	+	10.1693i	−0.765550	+	0.348396i
$853$	2.03086	−	0.544167i	0.0695353	−	0.0186319i	−0.223884	−	0.974616i	$-0.571874\pi$
$853$	2.03086	−	0.544167i	0.0695353	−	0.0186319i	0.293419	+	0.955984i	$0.405207\pi$
$854$	17.9179	+	30.7270i	0.613138	+	1.05146i
$855$	10.3597	−	7.18676i	0.354294	−	0.245782i
$856$	−8.10981	−	14.0466i	−0.277187	−	0.480103i
$857$	7.45882	−	27.8367i	0.254788	−	0.950883i	−0.713420	−	0.700737i	$-0.752855\pi$
$857$	7.45882	−	27.8367i	0.254788	−	0.950883i	0.968208	−	0.250146i	$-0.0804786\pi$
$858$	−1.07341	+	11.0867i	−0.0366455	+	0.378494i
$859$	−35.9780	−	20.7719i	−1.22755	−	0.708728i	−0.261035	−	0.965329i	$-0.584064\pi$
$859$	−35.9780	−	20.7719i	−1.22755	−	0.708728i	−0.966517	+	0.256602i	$0.917397\pi$
$860$	−0.423778	+	0.758577i	−0.0144507	+	0.0258672i
$861$	−18.7721	+	15.5947i	−0.639750	+	0.531465i
$862$	−8.45850	−	31.5675i	−0.288098	−	1.07519i
$863$	4.62283	+	1.23868i	0.157363	+	0.0421653i	0.336640	−	0.941633i	$-0.390709\pi$
$863$	4.62283	+	1.23868i	0.157363	+	0.0421653i	−0.179278	+	0.983799i	$0.557376\pi$
$864$	−4.57037	+	2.47219i	−0.155487	+	0.0841056i
$865$	−1.21292	+	0.0171519i	−0.0412404	+	0.000583180i
$866$		−	26.4079i		−	0.897375i
$867$	9.29545	−	13.0173i	0.315690	−	0.442090i
$868$	1.55426	−	5.90261i	0.0527552	−	0.200348i
$869$	9.20906	+	15.9506i	0.312396	+	0.541086i
$870$	37.8323	+	3.12363i	1.28263	+	0.105901i
$871$	−2.46870	−	4.27591i	−0.0836486	−	0.144884i
$872$	7.06803	−	1.89387i	0.239354	−	0.0641346i
$873$	−30.6570	−	14.9923i	−1.03758	−	0.507412i
$874$		−	9.72911i		−	0.329092i
$875$	−24.8983	+	15.9711i	−0.841715	+	0.539922i
$876$	6.33346	+	7.69133i	0.213988	+	0.259866i
$877$	13.7272	+	51.2307i	0.463536	+	1.72994i	0.661699	+	0.749769i	$0.269835\pi$
$877$	13.7272	+	51.2307i	0.463536	+	1.72994i	−0.198164	+	0.980169i	$0.563498\pi$
$878$	−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	$0.188747\pi$
$881$			33.1736i			1.11765i	−0.829286	+	0.558824i	$0.811253\pi$
$882$	18.9441	+	9.06207i	0.637881	+	0.305136i
$883$	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
$885$	−5.44598	−	1.95208i	−0.183064	−	0.0656184i
$886$	21.2227			0.712990
$887$	33.8316	−	9.06515i	1.13595	−	0.304378i	0.358631	−	0.933479i	$-0.383244\pi$
$887$	33.8316	−	9.06515i	1.13595	−	0.304378i	0.777323	+	0.629101i	$0.216577\pi$
$888$	3.54145	−	4.95942i	0.118843	−	0.166427i
$889$	−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
$892$	3.06109	+	11.4241i	0.102493	+	0.382508i
$893$	4.02070	+	1.07734i	0.134547	+	0.0360519i
$894$	−17.8831	+	14.7259i	−0.598099	+	0.492507i
$895$	−55.1395	+	15.6135i	−1.84311	+	0.521901i
$896$	2.28554	−	1.33277i	0.0763547	−	0.0445249i
$897$	−10.9969	+	5.00458i	−0.367175	+	0.167098i
$898$	5.77320	+	5.77320i	0.192654	+	0.192654i
$899$	−11.3061	+	19.5828i	−0.377081	+	0.653123i
$900$	−9.52902	+	11.5844i	−0.317634	+	0.386146i
$901$	0.257662	+	0.446284i	0.00858398	+	0.0148679i
$902$	24.5477	−	6.57754i	0.817349	−	0.219008i
$903$	1.61761	−	0.744622i	0.0538305	−	0.0247795i
$904$	−13.6447	+	7.87780i	−0.453817	+	0.262012i
$905$	−30.1290	−	29.2888i	−1.00152	−	0.973592i
$906$	−0.786822	−	4.71708i	−0.0261404	−	0.156715i
$907$	46.6661	+	12.5042i	1.54952	+	0.415194i	0.929328	−	0.369254i	$-0.120387\pi$
$907$	46.6661	+	12.5042i	1.54952	+	0.415194i	0.620195	+	0.784448i	$0.287053\pi$
$908$	−16.9495	−	4.54160i	−0.562488	−	0.150718i
$909$	−5.27818	+	27.0024i	−0.175066	+	0.895613i
$910$	6.97686	+	3.85811i	0.231281	+	0.127895i
$911$	43.3450	+	25.0252i	1.43608	+	0.829123i	0.997575	−	0.0696035i	$-0.0221734\pi$
$911$	43.3450	+	25.0252i	1.43608	+	0.829123i	0.438509	+	0.898727i	$0.355507\pi$
$912$	−1.89186	+	2.64935i	−0.0626457	+	0.0877286i
$913$	15.2576	+	15.2576i	0.504954	+	0.504954i
$914$	33.4656			1.10694
$915$	49.0150	+	17.5691i	1.62038	+	0.580818i
$916$	−7.38778	+	12.7960i	−0.244099	+	0.422792i
$917$	−35.4307	−	35.1255i	−1.17003	−	1.15995i
$918$	−19.3345	+	18.2899i	−0.638134	+	0.603658i
$919$	8.90171	−	5.13941i	0.293640	−	0.169533i	−0.345942	−	0.938256i	$-0.612441\pi$
$919$	8.90171	−	5.13941i	0.293640	−	0.169533i	0.639582	+	0.768723i	$0.279107\pi$
$920$	3.15349	+	11.1367i	0.103968	+	0.367165i
$921$	−3.89049	+	10.3889i	−0.128196	+	0.342327i
$922$	6.10433	+	22.7817i	0.201036	+	0.750275i
$923$	18.4507	+	4.94385i	0.607312	+	0.162729i
$924$	−13.9740	−	16.8211i	−0.459710	−	0.553374i
$925$	4.07085	−	17.1146i	0.133849	−	0.562724i
$926$	−28.1717	+	16.2649i	−0.925780	+	0.534499i
$927$	−12.7941	+	26.1620i	−0.420214	+	0.859274i
$928$	−9.46751	+	2.53681i	−0.310786	+	0.0832750i
$929$	27.6679			0.907754			0.453877	−	0.891064i	$-0.350041\pi$
$929$	27.6679			0.907754			0.453877	+	0.891064i	$0.350041\pi$
$930$	−3.81566	−	8.07936i	−0.125120	−	0.264933i
$931$	13.1564	−	0.113823i	0.431183	−	0.00373039i
$932$	−3.01913	+	11.2675i	−0.0988948	+	0.369081i
$933$	15.5735	+	34.2205i	0.509852	+	1.12033i
$934$	19.9044	−	11.4918i	0.651293	−	0.376024i
$935$	54.6496	−	0.772799i	1.78723	−	0.0252732i
$936$	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	$0.409336\pi$
$938$	9.37403	+	2.46835i	0.306073	+	0.0805946i
$939$	−54.3859	−	20.3666i	−1.77482	−	0.664639i
$940$	−4.95159	+	0.0700203i	−0.161503	+	0.00228381i
$941$			21.7685i			0.709634i	0.934936	+	0.354817i	$0.115457\pi$
$941$			21.7685i			0.709634i	−0.934936	+	0.354817i	$0.884543\pi$
$942$	14.6426	−	6.66371i	0.477080	−	0.217115i
$943$	19.4924	+	19.4924i	0.634760	+	0.634760i
$944$	1.49375			0.0486174
$945$	29.7660	−	7.68012i	0.968289	−	0.249834i
$946$	−1.85439			−0.0602914
$947$	8.35258	+	8.35258i	0.271422	+	0.271422i	0.829673	−	0.558250i	$-0.188527\pi$
$947$	8.35258	+	8.35258i	0.271422	+	0.271422i	−0.558250	+	0.829673i	$0.688527\pi$
$948$	6.08454	−	2.76902i	0.197617	−	0.0899337i
$949$		−	7.75193i		−	0.251638i
$950$	−2.17467	+	9.14269i	−0.0705556	+	0.296628i
$951$	54.8162	+	20.5278i	1.77754	+	0.665659i
$952$	9.54086	−	9.62376i	0.309221	−	0.311908i
$953$	−8.22163	+	8.22163i	−0.266325	+	0.266325i	−0.827617	−	0.561293i	$-0.810304\pi$
$953$	−8.22163	+	8.22163i	−0.266325	+	0.266325i	0.561293	+	0.827617i	$0.310304\pi$
$954$	−0.0979662	−	0.285489i	−0.00317177	−	0.00924303i
$955$	0.288176	−	0.296443i	0.00932516	−	0.00959267i
$956$	0.395101	−	0.228112i	0.0127785	−	0.00737766i
$957$	33.5571	+	73.7369i	1.08475	+	2.38357i
$958$	10.1033	−	37.7059i	0.326422	−	1.21822i
$959$	10.6766	−	18.6786i	0.344766	−	0.603163i
$960$	1.30683	−	3.64585i	0.0421778	−	0.117669i
$961$	−25.6776			−0.828311
$962$	−4.57988	+	1.22717i	−0.147661	+	0.0395657i
$963$	27.1673	+	40.3686i	0.875453	+	1.30086i
$964$	−15.5398	+	8.97190i	−0.500503	+	0.288965i
$965$	0.214707	+	15.1833i	0.00691168	+	0.488769i
$966$	8.22267	−	22.2500i	0.264560	−	0.715880i
$967$	−6.13923	−	1.64500i	−0.197424	−	0.0528997i	0.158752	−	0.987319i	$-0.449253\pi$
$967$	−6.13923	−	1.64500i	−0.197424	−	0.0528997i	−0.356176	+	0.934419i	$0.615920\pi$
$968$	3.04694	+	11.3713i	0.0979324	+	0.365489i
$969$	−5.84778	+	15.6156i	−0.187858	+	0.501645i
$970$	24.4741	−	6.93017i	0.785817	−	0.222514i
$971$	−2.34429	+	1.35348i	−0.0752320	+	0.0434352i	−0.537144	−	0.843490i	$-0.680497\pi$
$971$	−2.34429	+	1.35348i	−0.0752320	+	0.0434352i	0.461912	+	0.886926i	$0.347164\pi$
$972$	13.1691	−	8.34111i	0.422400	−	0.267541i
$973$	2.99766	−	0.817136i	0.0961007	−	0.0261962i
$974$	−5.38509	+	9.32725i	−0.172549	+	0.298864i
$975$	11.4527	−	2.24490i	0.366779	−	0.0718942i
$976$	−13.4441			−0.430334
$977$	−33.0476	−	33.0476i	−1.05729	−	1.05729i	−0.998256	−	0.0590317i	$-0.981199\pi$
$977$	−33.0476	−	33.0476i	−1.05729	−	1.05729i	−0.0590317	−	0.998256i	$-0.518801\pi$
$978$	−7.77203	+	10.8839i	−0.248522	+	0.348028i
$979$	58.4559	+	33.7495i	1.86826	+	1.07864i
$980$	−15.0229	+	4.39466i	−0.479888	+	0.140382i
$981$	−20.7636	+	7.12509i	−0.662931	+	0.227487i
$982$	28.6957	+	7.68900i	0.915717	+	0.245366i
$983$	57.4742	+	15.4002i	1.83314	+	0.491189i	0.998245	−	0.0592153i	$-0.0188598\pi$
$983$	57.4742	+	15.4002i	1.83314	+	0.491189i	0.834898	+	0.550405i	$0.185527\pi$
$984$	−1.51763	−	9.09836i	−0.0483803	−	0.290045i
$985$	0.622317	+	44.0080i	0.0198287	+	1.40221i
$986$	−43.4774	+	25.1017i	−1.38460	+	0.799400i
$987$	8.28459	+	5.86197i	0.263701	+	0.186588i
$988$	2.44659	−	0.655562i	0.0778365	−	0.0208562i
$989$	−1.00574	−	1.74199i	−0.0319806	−	0.0553919i
$990$	−31.5010	−	5.69633i	−1.00117	−	0.181041i
$991$	−18.5277	+	32.0909i	−0.588552	+	1.01940i	0.405870	+	0.913931i	$0.366969\pi$
$991$	−18.5277	+	32.0909i	−0.588552	+	1.01940i	−0.994422	+	0.105472i	$0.966365\pi$
$992$	1.63131	+	1.63131i	0.0517942	+	0.0517942i
$993$	−16.2227	+	7.38284i	−0.514813	+	0.234287i
$994$	−32.3963	+	18.8913i	−1.02755	+	0.599197i
$995$	−13.6408	−	48.1730i	−0.432443	−	1.52719i
$996$	6.04577	−	4.97842i	0.191568	−	0.157747i
$997$	−13.6039	−	3.64514i	−0.430838	−	0.115443i	0.0368813	−	0.999320i	$-0.488258\pi$
$997$	−13.6039	−	3.64514i	−0.430838	−	0.115443i	−0.467720	+	0.883877i	$0.654924\pi$
$998$	−8.26870	−	30.8592i	−0.261741	−	0.976832i
$999$	−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.263.45	yes	192
5.2	odd	4	inner	630.2.cd.a.137.10	yes	192
7.2	even	3		630.2.bt.a.443.36	yes	192
9.5	odd	6		630.2.bt.a.473.46	yes	192
35.2	odd	12		630.2.bt.a.317.46	✓	192
45.32	even	12		630.2.bt.a.347.36	yes	192
63.23	odd	6	inner	630.2.cd.a.23.10	yes	192
315.212	even	12	inner	630.2.cd.a.527.45	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.46	✓	192	35.2	odd	12
630.2.bt.a.347.36	yes	192	45.32	even	12
630.2.bt.a.443.36	yes	192	7.2	even	3
630.2.bt.a.473.46	yes	192	9.5	odd	6
630.2.cd.a.23.10	yes	192	63.23	odd	6	inner
630.2.cd.a.137.10	yes	192	5.2	odd	4	inner
630.2.cd.a.263.45	yes	192	1.1	even	1	trivial
630.2.cd.a.527.45	yes	192	315.212	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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.57648 - 0.717442i) q^{3} +1.00000i q^{4} +(1.60334 + 1.55862i) q^{5} +(1.62204 + 0.607429i) q^{6} +(2.55854 + 0.673710i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.97055 - 2.26206i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.57648 - 0.717442i) q^{3} +1.00000i q^{4} +(1.60334 + 1.55862i) q^{5} +(1.62204 + 0.607429i) q^{6} +(2.55854 + 0.673710i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(1.97055 - 2.26206i) q^{9} +(0.0316170 + 2.23584i) q^{10} +(-4.13272 + 2.38603i) q^{11} +(0.717442 + 1.57648i) q^{12} +(0.348786 - 1.30169i) q^{13} +(1.33277 + 2.28554i) q^{14} +(3.64585 + 1.30683i) q^{15} -1.00000 q^{16} +(-4.94748 + 1.32567i) q^{17} +(2.99291 - 0.206125i) q^{18} +(1.62774 - 0.939777i) q^{19} +(-1.55862 + 1.60334i) q^{20} +(4.51682 - 0.773514i) q^{21} +(-4.60945 - 1.23510i) q^{22} +(-1.33972 - 4.99991i) q^{23} +(-0.607429 + 1.62204i) q^{24} +(0.141382 + 4.99800i) q^{25} +(1.16706 - 0.673803i) q^{26} +(1.48364 - 4.97984i) q^{27} +(-0.673710 + 2.55854i) q^{28} +(4.90075 - 8.48834i) q^{29} +(1.65393 + 3.50207i) q^{30} -2.30702 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.80330 + 6.72650i) q^{33} +(-4.43579 - 2.56100i) q^{34} +(3.05214 + 5.06798i) q^{35} +(2.26206 + 1.97055i) q^{36} +(-3.39853 - 0.910632i) q^{37} +(1.81551 + 0.486464i) q^{38} +(-0.384032 - 2.30231i) q^{39} +(-2.23584 + 0.0316170i) q^{40} +(-4.61203 + 2.66276i) q^{41} +(3.74083 + 2.64692i) q^{42} +(0.375353 - 0.100575i) q^{43} +(-2.38603 - 4.13272i) q^{44} +(6.68516 - 0.555491i) q^{45} +(2.58814 - 4.48280i) q^{46} +(1.56599 + 1.56599i) q^{47} +(-1.57648 + 0.717442i) q^{48} +(6.09223 + 3.44742i) q^{49} +(-3.43415 + 3.63409i) q^{50} +(-6.84849 + 5.63942i) q^{51} +(1.30169 + 0.348786i) q^{52} +(-0.0260397 - 0.0971817i) q^{53} +(4.57037 - 2.47219i) q^{54} +(-10.3451 - 2.61575i) q^{55} +(-2.28554 + 1.33277i) q^{56} +(1.89186 - 2.64935i) q^{57} +(9.46751 - 2.53681i) q^{58} -1.49375 q^{59} +(-1.30683 + 3.64585i) q^{60} +13.4441 q^{61} +(-1.63131 - 1.63131i) q^{62} +(6.56571 - 4.45998i) q^{63} -1.00000i q^{64} +(2.58806 - 1.54342i) q^{65} +(-8.15280 + 1.35991i) q^{66} +(2.59071 - 2.59071i) q^{67} +(-1.32567 - 4.94748i) q^{68} +(-5.69918 - 6.92106i) q^{69} +(-1.42542 + 5.74179i) q^{70} +14.1744i q^{71} +(0.206125 + 2.99291i) q^{72} +(5.55636 - 1.48882i) q^{73} +(-1.75921 - 3.04704i) q^{74} +(3.80866 + 7.77780i) q^{75} +(0.939777 + 1.62774i) q^{76} +(-12.1812 + 3.32048i) q^{77} +(1.35643 - 1.89953i) q^{78} -3.85958i q^{79} +(-1.60334 - 1.55862i) q^{80} +(-1.23383 - 8.91502i) q^{81} +(-5.14406 - 1.37835i) q^{82} +(-1.17029 - 4.36758i) q^{83} +(0.773514 + 4.51682i) q^{84} +(-9.99871 - 5.58576i) q^{85} +(0.336532 + 0.194297i) q^{86} +(1.63602 - 16.8977i) q^{87} +(1.23510 - 4.60945i) q^{88} +(-7.07233 - 12.2496i) q^{89} +(5.11992 + 4.33433i) q^{90} +(1.76934 - 3.09544i) q^{91} +(4.99991 - 1.33972i) q^{92} +(-3.63697 + 1.65515i) q^{93} +2.21464i q^{94} +(4.07458 + 1.03026i) q^{95} +(-1.62204 - 0.607429i) q^{96} +(-2.94420 - 10.9879i) q^{97} +(1.87016 + 6.74555i) 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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