LMFDB - Embedded newform 630.2.bt.a.473.46

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(317,630)]

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([2, 3, 4]))

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

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

chi := DirichletCharacter("630.317");

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.bt (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			473.46
Character	$\chi$	$=$	630.473
Dual form			630.2.bt.a.317.46

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(1.72399 - 0.166915i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.548139 + 2.16784i) q^{5} +(1.62204 - 0.607429i) q^{6} +(-1.86272 + 1.87890i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.94428 - 0.575521i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(1.72399 - 0.166915i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.548139 + 2.16784i) q^{5} +(1.62204 - 0.607429i) q^{6} +(-1.86272 + 1.87890i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.94428 - 0.575521i) q^{9} +(0.0316170 + 2.23584i) q^{10} +4.77205i q^{11} +(1.40956 - 1.00655i) q^{12} +(-1.30169 + 0.348786i) q^{13} +(-1.31295 + 2.29699i) q^{14} +(-0.583140 + 3.82883i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.94748 - 1.32567i) q^{17} +(2.69500 - 1.31795i) q^{18} +(1.62774 - 0.939777i) q^{19} +(0.609219 + 2.15148i) q^{20} +(-2.89769 + 3.55013i) q^{21} +(1.23510 + 4.60945i) q^{22} +(3.66019 - 3.66019i) q^{23} +(1.10102 - 1.33707i) q^{24} +(-4.39909 - 2.37656i) q^{25} +(-1.16706 + 0.673803i) q^{26} +(4.97984 - 1.48364i) q^{27} +(-0.673710 + 2.55854i) q^{28} +(-4.90075 - 8.48834i) q^{29} +(0.427704 + 3.84929i) q^{30} +(1.15351 + 1.99794i) q^{31} +(0.258819 - 0.965926i) q^{32} +(0.796529 + 8.22697i) 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} +(1.32905 - 1.32905i) q^{38} +(-2.18588 + 0.818575i) q^{39} +(1.14530 + 1.92049i) q^{40} +(-4.61203 - 2.66276i) q^{41} +(-1.88011 + 4.17914i) q^{42} +(-0.100575 + 0.375353i) q^{43} +(2.38603 + 4.13272i) q^{44} +(-0.366237 + 6.69820i) q^{45} +(2.58814 - 4.48280i) q^{46} +(2.13918 - 0.573191i) q^{47} +(0.717442 - 1.57648i) q^{48} +(-0.0605584 - 6.99974i) q^{49} +(-4.86429 - 1.15701i) q^{50} +(8.30813 - 3.11126i) q^{51} +(-0.952902 + 0.952902i) q^{52} +(0.0260397 + 0.0971817i) q^{53} +(4.42616 - 2.72196i) q^{54} +(-10.3451 - 2.61575i) q^{55} +(0.0114446 + 2.64573i) q^{56} +(2.64935 - 1.89186i) q^{57} +(-6.93070 - 6.93070i) q^{58} +(-0.746874 - 1.29362i) q^{59} +(1.40940 + 3.60744i) q^{60} +(-6.72203 + 11.6429i) q^{61} +(1.63131 + 1.63131i) q^{62} +(-4.40301 + 6.60405i) q^{63} -1.00000i q^{64} +(-0.0426073 - 3.01304i) q^{65} +(2.89868 + 7.74048i) q^{66} +(-3.53898 - 0.948267i) q^{67} +(3.62181 - 3.62181i) q^{68} +(5.69918 - 6.92106i) q^{69} +(-4.25983 - 4.10534i) q^{70} -14.1744i q^{71} +(1.67496 - 2.48887i) q^{72} +(5.55636 - 1.48882i) q^{73} -3.51841 q^{74} +(-7.98066 - 3.36289i) q^{75} +(0.939777 - 1.62774i) q^{76} +(-8.96623 - 8.88899i) q^{77} +(-1.89953 + 1.35643i) q^{78} +(3.34250 + 1.92979i) q^{79} +(1.60334 + 1.55862i) q^{80} +(8.33755 - 3.38899i) q^{81} +(-5.14406 - 1.37835i) q^{82} +(-4.36758 - 1.17029i) q^{83} +(-0.734409 + 4.52334i) q^{84} +(0.161943 + 11.4520i) q^{85} +0.388594i q^{86} +(-9.86567 - 13.8158i) q^{87} +(3.37435 + 3.37435i) 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} +(2.32213 + 3.25189i) q^{93} +(1.91793 - 1.10732i) q^{94} +(1.14506 + 4.04382i) q^{95} +(0.284973 - 1.70845i) q^{96} +(10.9879 + 2.94420i) 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} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) $ 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$281$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	1.72399	−	0.166915i	0.995346	−	0.0963686i
$3$	1.72399	−	0.166915i	0.995346	−	0.0963686i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−0.548139	+	2.16784i	−0.245135	+	0.969489i
$5$	−0.548139	+	2.16784i	−0.245135	+	0.969489i
$6$	1.62204	−	0.607429i	0.662197	−	0.247982i
$7$	−1.86272	+	1.87890i	−0.704041	+	0.710159i
$7$	−1.86272	+	1.87890i	−0.704041	+	0.710159i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	2.94428	−	0.575521i	0.981426	−	0.191840i
$10$	0.0316170	+	2.23584i	0.00999818	+	0.707036i
$11$			4.77205i			1.43883i	0.694582	+	0.719414i	$0.255589\pi$
$11$			4.77205i			1.43883i	−0.694582	+	0.719414i	$0.744411\pi$
$12$	1.40956	−	1.00655i	0.406905	−	0.290565i
$13$	−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	$0.476504\pi$
$14$	−1.31295	+	2.29699i	−0.350901	+	0.613896i
$15$	−0.583140	+	3.82883i	−0.150566	+	0.988600i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	4.94748	−	1.32567i	1.19994	−	0.321523i	0.397133	−	0.917761i	$-0.370005\pi$
$17$	4.94748	−	1.32567i	1.19994	−	0.321523i	0.802808	+	0.596238i	$0.203339\pi$
$18$	2.69500	−	1.31795i	0.635217	−	0.310643i
$19$	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	$0.264163\pi$
$20$	0.609219	+	2.15148i	0.136225	+	0.481085i
$21$	−2.89769	+	3.55013i	−0.632328	+	0.774701i
$22$	1.23510	+	4.60945i	0.263324	+	0.982738i
$23$	3.66019	−	3.66019i	0.763202	−	0.763202i	−0.213698	−	0.976900i	$-0.568551\pi$
$23$	3.66019	−	3.66019i	0.763202	−	0.763202i	0.976900	+	0.213698i	$0.0685509\pi$
$24$	1.10102	−	1.33707i	0.224744	−	0.272929i
$25$	−4.39909	−	2.37656i	−0.879817	−	0.475312i
$26$	−1.16706	+	0.673803i	−0.228880	+	0.132144i
$27$	4.97984	−	1.48364i	0.958371	−	0.285526i
$28$	−0.673710	+	2.55854i	−0.127319	+	0.483518i
$29$	−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	$-0.530620\pi$
$30$	0.427704	+	3.84929i	0.0780878	+	0.702782i
$31$	1.15351	+	1.99794i	0.207177	+	0.358841i	0.950824	−	0.309731i	$-0.100239\pi$
$31$	1.15351	+	1.99794i	0.207177	+	0.358841i	−0.743647	+	0.668572i	$0.766906\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	0.796529	+	8.22697i	0.138658	+	1.43213i
$34$	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	$0.676727\pi$
$38$	1.32905	−	1.32905i	0.215600	−	0.215600i
$39$	−2.18588	+	0.818575i	−0.350021	+	0.131077i
$40$	1.14530	+	1.92049i	0.181088	+	0.303656i
$41$	−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	$0.803184\pi$
$42$	−1.88011	+	4.17914i	−0.290108	+	0.644855i
$43$	−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
$45$	−0.366237	+	6.69820i	−0.0545953	+	0.998509i
$46$	2.58814	−	4.48280i	0.381601	−	0.660952i
$47$	2.13918	−	0.573191i	0.312031	−	0.0836084i	−0.0994052	−	0.995047i	$-0.531694\pi$
$47$	2.13918	−	0.573191i	0.312031	−	0.0836084i	0.411436	+	0.911439i	$0.365027\pi$
$48$	0.717442	−	1.57648i	0.103554	−	0.227545i
$49$	−0.0605584	−	6.99974i	−0.00865120	−	0.999963i
$50$	−4.86429	−	1.15701i	−0.687915	−	0.163626i
$51$	8.30813	−	3.11126i	1.16337	−	0.435663i
$52$	−0.952902	+	0.952902i	−0.132144	+	0.132144i
$53$	0.0260397	+	0.0971817i	0.00357683	+	0.0133489i	0.967691	−	0.252138i	$-0.0811338\pi$
$53$	0.0260397	+	0.0971817i	0.00357683	+	0.0133489i	−0.964114	+	0.265487i	$0.914467\pi$
$54$	4.42616	−	2.72196i	0.602325	−	0.370412i
$55$	−10.3451	−	2.61575i	−1.39493	−	0.352708i
$56$	0.0114446	+	2.64573i	0.00152934	+	0.353550i
$57$	2.64935	−	1.89186i	0.350914	−	0.250583i
$58$	−6.93070	−	6.93070i	−0.910046	−	0.910046i
$59$	−0.746874	−	1.29362i	−0.0972347	−	0.168416i	0.813304	−	0.581838i	$-0.197666\pi$
$59$	−0.746874	−	1.29362i	−0.0972347	−	0.168416i	−0.910539	+	0.413423i	$0.864333\pi$
$60$	1.40940	+	3.60744i	0.181953	+	0.465718i
$61$	−6.72203	+	11.6429i	−0.860668	+	1.49072i	0.0106174	+	0.999944i	$0.496620\pi$
$61$	−6.72203	+	11.6429i	−0.860668	+	1.49072i	−0.871285	+	0.490777i	$0.836713\pi$
$62$	1.63131	+	1.63131i	0.207177	+	0.207177i
$63$	−4.40301	+	6.60405i	−0.554728	+	0.832032i
$64$		−	1.00000i		−	0.125000i
$65$	−0.0426073	−	3.01304i	−0.00528479	−	0.373721i
$66$	2.89868	+	7.74048i	0.356803	+	0.952787i
$67$	−3.53898	−	0.948267i	−0.432355	−	0.115849i	0.0360762	−	0.999349i	$-0.488514\pi$
$67$	−3.53898	−	0.948267i	−0.432355	−	0.115849i	−0.468432	+	0.883500i	$0.655181\pi$
$68$	3.62181	−	3.62181i	0.439209	−	0.439209i
$69$	5.69918	−	6.92106i	0.686101	−	0.833198i
$70$	−4.25983	−	4.10534i	−0.509147	−	0.490682i
$71$		−	14.1744i		−	1.68220i	−0.540882	−	0.841099i	$-0.681909\pi$
$71$		−	14.1744i		−	1.68220i	0.540882	−	0.841099i	$-0.318091\pi$
$72$	1.67496	−	2.48887i	0.197396	−	0.293317i
$73$	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	$0.307379\pi$
$74$	−3.51841			−0.409007
$75$	−7.98066	−	3.36289i	−0.921528	−	0.388313i
$76$	0.939777	−	1.62774i	0.107800	−	0.186715i
$77$	−8.96623	−	8.88899i	−1.02180	−	1.01299i
$78$	−1.89953	+	1.35643i	−0.215080	+	0.153585i
$79$	3.34250	+	1.92979i	0.376060	+	0.217118i	0.676103	−	0.736807i	$-0.263668\pi$
$79$	3.34250	+	1.92979i	0.376060	+	0.217118i	−0.300043	+	0.953926i	$0.597001\pi$
$80$	1.60334	+	1.55862i	0.179259	+	0.174259i
$81$	8.33755	−	3.38899i	0.926395	−	0.376554i
$82$	−5.14406	−	1.37835i	−0.568066	−	0.152213i
$83$	−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	$0.663159\pi$
$84$	−0.734409	+	4.52334i	−0.0801306	+	0.493537i
$85$	0.161943	+	11.4520i	0.0175652	+	1.24215i
$86$			0.388594i			0.0419032i
$87$	−9.86567	−	13.8158i	−1.05771	−	1.48121i
$88$	3.37435	+	3.37435i	0.359707	+	0.359707i
$89$	7.07233	+	12.2496i	0.749665	+	1.29846i	0.947983	+	0.318321i	$0.103119\pi$
$89$	7.07233	+	12.2496i	0.749665	+	1.29846i	−0.198318	+	0.980138i	$0.563548\pi$
$90$	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
$93$	2.32213	+	3.25189i	0.240794	+	0.337205i
$94$	1.91793	−	1.10732i	0.197820	−	0.114211i
$95$	1.14506	+	4.04382i	0.117481	+	0.414887i
$96$	0.284973	−	1.70845i	0.0290850	−	0.174368i
$97$	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	$0.387360\pi$
$98$	−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
$101$			9.17114i			0.912563i	0.889836	+	0.456281i	$0.150819\pi$
$101$			9.17114i			0.912563i	−0.889836	+	0.456281i	$0.849181\pi$
$102$	7.21978	−	5.15555i	0.714865	−	0.510475i
$103$	6.86432	+	6.86432i	0.676362	+	0.676362i	0.959175	−	0.282813i	$-0.0912676\pi$
$103$	6.86432	+	6.86432i	0.676362	+	0.676362i	−0.282813	+	0.959175i	$0.591268\pi$
$104$	−0.673803	+	1.16706i	−0.0660718	+	0.114440i
$105$	−6.10778	−	8.22770i	−0.596058	−	0.802941i
$106$	0.0503049	+	0.0871307i	0.00488605	+	0.00846288i
$107$	4.19794	−	15.6669i	0.405831	−	1.51458i	−0.396688	−	0.917953i	$-0.629841\pi$
$107$	4.19794	−	15.6669i	0.405831	−	1.51458i	0.802519	−	0.596627i	$-0.203493\pi$
$108$	3.57085	−	3.77479i	0.343605	−	0.363229i
$109$	−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	$0.780634\pi$
$110$	−10.6696	+	0.150878i	−1.01730	+	0.0143857i
$111$	−6.01102	−	1.00265i	−0.570541	−	0.0951677i
$112$	0.695819	+	2.55261i	0.0657487	+	0.241199i
$113$	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	$0.650980\pi$
$114$	2.06942	−	2.51310i	0.193819	−	0.235373i
$115$	5.92842	+	9.94100i	0.552828	+	0.927003i
$116$	−8.48834	−	4.90075i	−0.788123	−	0.455023i
$117$	−3.63180	+	1.77607i	−0.335760	+	0.164198i
$118$	−1.05624	−	1.05624i	−0.0972347	−	0.0972347i
$119$	−6.72495	+	11.7652i	−0.616475	+	1.07851i
$120$	2.29505	+	3.11973i	0.209508	+	0.284792i
$121$	−11.7725			−1.07023
$122$	−3.47958	+	12.9860i	−0.315026	+	1.17569i
$123$	−8.39555	−	3.82075i	−0.757002	−	0.344505i
$124$	1.99794	+	1.15351i	0.179420	+	0.103588i
$125$	7.56332	−	8.23384i	0.676484	−	0.736457i
$126$	−2.54373	+	7.51861i	−0.226614	+	0.669811i
$127$	−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	$0.426281\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	−0.110739	+	0.663892i	−0.00975002	+	0.0584524i
$130$	−0.820987	−	2.89934i	−0.0720053	−	0.254289i
$131$		−	18.8571i		−	1.64755i	−0.566914	−	0.823777i	$-0.691863\pi$
$131$		−	18.8571i		−	1.64755i	0.566914	−	0.823777i	$-0.308137\pi$
$132$	4.80330	+	6.72650i	0.418073	+	0.585466i
$133$	−1.26627	+	4.80891i	−0.109800	+	0.416985i
$134$	−3.66382			−0.316506
$135$	0.486644	+	11.6088i	0.0418837	+	0.999122i
$136$	2.56100	−	4.43579i	0.219604	−	0.380366i
$137$	−5.75003	−	5.75003i	−0.491258	−	0.491258i	0.417444	−	0.908702i	$-0.362926\pi$
$137$	−5.75003	−	5.75003i	−0.491258	−	0.491258i	−0.908702	+	0.417444i	$0.862926\pi$
$138$	3.71368	−	8.16029i	0.316130	−	0.694650i
$139$	−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	$0.682526\pi$
$140$	−5.17722	−	2.86293i	−0.437555	−	0.241962i
$141$	3.59224	−	1.34524i	0.302521	−	0.113289i
$142$	−3.66862	−	13.6915i	−0.307863	−	1.14896i
$143$	−1.66443	−	6.21172i	−0.139186	−	0.519450i
$144$	0.973724	−	2.83758i	0.0811436	−	0.236465i
$145$	21.0877	−	5.97125i	1.75124	−	0.495886i
$146$	4.98170	−	2.87618i	0.412288	−	0.238035i
$147$	−1.27277	−	12.0574i	−0.104976	−	0.994475i
$148$	−3.39853	+	0.910632i	−0.279357	+	0.0748535i
$149$	−13.3748			−1.09571			−0.547853	−	0.836574i	$-0.684555\pi$
$149$	−13.3748			−1.09571			−0.547853	+	0.836574i	$0.684555\pi$
$150$	−8.57911	−	1.18275i	−0.700481	−	0.0965715i
$151$	2.76104			0.224690			0.112345	−	0.993669i	$-0.464164\pi$
$151$	2.76104			0.224690			0.112345	+	0.993669i	$0.464164\pi$
$152$	0.486464	−	1.81551i	0.0394575	−	0.147257i
$153$	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
$156$	−1.48374	+	1.80185i	−0.118794	+	0.144263i
$157$	−8.97167	−	2.40395i	−0.716017	−	0.191856i	−0.117623	−	0.993058i	$-0.537528\pi$
$157$	−8.97167	−	2.40395i	−0.716017	−	0.191856i	−0.598394	+	0.801202i	$0.704194\pi$
$158$	3.72807	+	0.998933i	0.296589	+	0.0794709i
$159$	0.0611134	+	0.163194i	0.00484660	+	0.0129421i
$160$	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
$163$	−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	$0.985547\pi$
$164$	−5.32552			−0.415853
$165$	−18.2714	−	2.78277i	−1.42242	−	0.216639i
$166$	−4.52165			−0.350948
$167$	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	$0.0867807\pi$
$168$	0.461343	+	4.55929i	0.0355934	+	0.351757i
$169$	−9.68559	+	5.59198i	−0.745045	+	0.430152i
$170$	3.12042	+	11.0199i	0.239326	+	0.845187i
$171$	4.25166	−	3.70376i	0.325133	−	0.283234i
$172$	0.100575	+	0.375353i	0.00766881	+	0.0286204i
$173$	0.140406	+	0.524003i	0.0106749	+	0.0398392i	0.971058	−	0.238844i	$-0.0767686\pi$
$173$	0.140406	+	0.524003i	0.0106749	+	0.0398392i	−0.960383	+	0.278684i	$0.910102\pi$
$174$	−13.1053	−	10.7916i	−0.993510	−	0.818110i
$175$	12.6596	−	3.83860i	0.956975	−	0.290171i
$176$	4.13272	+	2.38603i	0.311515	+	0.179853i
$177$	−1.50353	−	2.10553i	−0.113012	−	0.158261i
$178$	10.0018	+	10.0018i	0.749665	+	0.749665i
$179$	12.8143	−	22.1951i	0.957789	−	1.65894i	0.229936	−	0.973206i	$-0.426148\pi$
$179$	12.8143	−	22.1951i	0.957789	−	1.65894i	0.727853	−	0.685734i	$-0.240518\pi$
$180$	3.03193	+	5.98393i	0.225987	+	0.446016i
$181$	−18.7914			−1.39676			−0.698378	−	0.715729i	$-0.746095\pi$
$181$	−18.7914			−1.39676			−0.698378	+	0.715729i	$0.746095\pi$
$182$	0.907896	−	3.44790i	0.0672977	−	0.255575i
$183$	−9.64533	+	21.1942i	−0.713003	+	1.56672i
$184$		−	5.17629i		−	0.381601i
$185$	3.83697	−	6.86832i	0.282100	−	0.504969i
$186$	3.08466	+	2.54007i	0.226178	+	0.186247i
$187$	6.32618	+	23.6096i	0.462616	+	1.72651i
$188$	1.56599	−	1.56599i	0.114211	−	0.114211i
$189$	−6.48843	+	12.1202i	−0.471964	+	0.881618i
$190$	2.15266	+	3.60966i	0.156170	+	0.261872i
$191$	−0.160121	−	0.0924456i	−0.0115859	−	0.00668913i	0.494196	−	0.869351i	$-0.335463\pi$
$191$	−0.160121	−	0.0924456i	−0.0115859	−	0.00668913i	−0.505782	+	0.862661i	$0.668796\pi$
$192$	−0.166915	−	1.72399i	−0.0120461	−	0.124418i
$193$	1.75761	−	6.55948i	0.126515	−	0.472162i	−0.873374	−	0.487051i	$-0.838073\pi$
$193$	1.75761	−	6.55948i	0.126515	−	0.472162i	0.999889	+	0.0148887i	$0.00473938\pi$
$194$	11.3755			0.816713
$195$	−0.576377	−	5.18733i	−0.0412752	−	0.371473i
$196$	−3.55231	−	6.03167i	−0.253737	−	0.430834i
$197$	−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	$0.997341\pi$
$198$	6.28930	+	12.8607i	0.446961	+	0.913968i
$199$	−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	$0.958471\pi$
$200$	−4.79111	+	1.43014i	−0.338782	+	0.101126i
$201$	−6.25945	−	1.04409i	−0.441507	−	0.0736446i
$202$	2.37367	+	8.85864i	0.167011	+	0.623292i
$203$	25.0775	+	6.60336i	1.76009	+	0.463465i
$204$	5.63942	−	6.84849i	0.394839	−	0.479490i
$205$	8.30048	−	8.53860i	0.579731	−	0.596362i
$206$	8.40704	+	4.85381i	0.585747	+	0.338181i
$207$	8.67010	−	12.8831i	0.602613	−	0.895439i
$208$	−0.348786	+	1.30169i	−0.0241840	+	0.0902558i
$209$	4.48466	+	7.76766i	0.310211	+	0.537301i
$210$	−8.02915	−	6.36654i	−0.554064	−	0.439333i
$211$	−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	$0.247047\pi$
$212$	0.0711419	+	0.0711419i	0.00488605	+	0.00488605i
$213$	−2.36593	−	24.4366i	−0.162111	−	1.67437i
$214$		−	16.2196i		−	1.10875i
$215$	−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
$218$	−7.06803	−	1.89387i	−0.478707	−	0.128269i
$219$	9.33060	−	3.49416i	0.630504	−	0.236113i
$220$	−10.2670	+	2.90722i	−0.692198	+	0.196005i
$221$	−5.97770	+	3.45123i	−0.402104	+	0.232155i
$222$	−6.06571	+	0.587277i	−0.407104	+	0.0394155i
$223$	−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
$227$	12.4079	+	12.4079i	0.823540	+	0.823540i	0.986614	−	0.163074i	$-0.0521409\pi$
$227$	12.4079	+	12.4079i	0.823540	+	0.823540i	−0.163074	+	0.986614i	$0.552141\pi$
$228$	1.34847	−	2.96307i	0.0893046	−	0.196234i
$229$		−	14.7756i		−	0.976397i	−0.872733	−	0.488198i	$-0.837654\pi$
$229$		−	14.7756i		−	0.976397i	0.872733	−	0.488198i	$-0.162346\pi$
$230$	8.29933	+	8.06788i	0.547242	+	0.531981i
$231$	−16.9414	−	13.8279i	−1.11466	−	0.909810i
$232$	−9.46751	−	2.53681i	−0.621573	−	0.166550i
$233$	−11.2675	−	3.01913i	−0.738161	−	0.197790i	−0.129900	−	0.991527i	$-0.541466\pi$
$233$	−11.2675	−	3.01913i	−0.738161	−	0.197790i	−0.608261	+	0.793737i	$0.708132\pi$
$234$	−3.04837	+	2.65553i	−0.199278	+	0.173598i
$235$	0.0700203	+	4.95159i	0.00456762	+	0.323006i
$236$	−1.29362	−	0.746874i	−0.0842078	−	0.0486174i
$237$	6.08454	+	2.76902i	0.395233	+	0.179867i
$238$	−3.45075	+	13.1049i	−0.223679	+	0.849462i
$239$	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	$0.161970\pi$
$240$	3.02429	+	2.41943i	0.195217	+	0.156174i
$241$	−17.9438			−1.15586			−0.577931	−	0.816086i	$-0.696140\pi$
$241$	−17.9438			−1.15586			−0.577931	+	0.816086i	$0.696140\pi$
$242$	−11.3713	+	3.04694i	−0.730977	+	0.195865i
$243$	13.8082	−	7.23424i	0.885795	−	0.464077i
$244$			13.4441i			0.860668i
$245$	15.2075	+	3.70555i	0.971573	+	0.236739i
$246$	−9.09836	−	1.51763i	−0.580091	−	0.0967606i
$247$	−1.79103	+	1.79103i	−0.113960	+	0.113960i
$248$	2.22841	+	0.597102i	0.141504	+	0.0379160i
$249$	−7.72500	−	1.28855i	−0.489552	−	0.0816586i
$250$	5.17453	−	9.91081i	0.327266	−	0.626815i
$251$			2.76147i			0.174302i	0.996195	+	0.0871511i	$0.0277763\pi$
$251$			2.76147i			0.174302i	−0.996195	+	0.0871511i	$0.972224\pi$
$252$	−0.511098	+	7.92078i	−0.0321961	+	0.498962i
$253$	17.4666	+	17.4666i	1.09812	+	1.09812i
$254$	−5.92689	+	10.2657i	−0.371886	+	0.644125i
$255$	2.19071	+	19.7161i	0.137187	+	1.23467i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	14.6825	+	14.6825i	0.915870	+	0.915870i	0.996726	−	0.0808562i	$-0.0257654\pi$
$257$	14.6825	+	14.6825i	0.915870	+	0.915870i	−0.0808562	+	0.996726i	$0.525765\pi$
$258$	0.0648623	+	0.669932i	0.00403815	+	0.0417081i
$259$	8.04149	−	4.68925i	0.499674	−	0.291376i
$260$	−1.54342	−	2.58806i	−0.0957187	−	0.160505i
$261$	−19.3144	−	22.1716i	−1.19553	−	1.37238i
$262$	−4.88058	−	18.2146i	−0.301523	−	1.12530i
$263$	1.04702	−	1.04702i	0.0645620	−	0.0645620i	−0.674089	−	0.738651i	$-0.735463\pi$
$263$	1.04702	−	1.04702i	0.0645620	−	0.0645620i	0.738651	+	0.674089i	$0.235463\pi$
$264$	6.38057	+	5.25411i	0.392697	+	0.323368i
$265$	−0.224948	+	0.00318099i	−0.0138184	+	0.000195406i
$266$	0.0215107	+	4.97278i	0.00131890	+	0.304901i
$267$	14.2373	+	19.9378i	0.871307	+	1.22017i
$268$	−3.53898	+	0.948267i	−0.216178	+	0.0579247i
$269$	4.20016	−	7.27489i	0.256088	−	0.443558i	−0.709102	−	0.705106i	$-0.750900\pi$
$269$	4.20016	−	7.27489i	0.256088	−	0.443558i	0.965190	+	0.261548i	$0.0842329\pi$
$270$	3.47463	+	11.0872i	0.211459	+	0.674748i
$271$	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	$0.577107\pi$
$272$	1.32567	−	4.94748i	0.0803808	−	0.299985i
$273$	2.53365	−	5.63183i	0.153344	−	0.340854i
$274$	−7.04232	−	4.06588i	−0.425442	−	0.245629i
$275$	11.3411	−	20.9927i	0.683892	−	1.26591i
$276$	1.47510	−	8.84341i	0.0887908	−	0.532311i
$277$	−7.26919	+	7.26919i	−0.436763	+	0.436763i	−0.890921	−	0.454158i	$-0.849940\pi$
$277$	−7.26919	+	7.26919i	−0.436763	+	0.436763i	0.454158	+	0.890921i	$0.349940\pi$
$278$	−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	−0.896995	−	0.442041i	$-0.854255\pi$
$281$	−16.1374	+	9.31691i	−0.962674	+	0.555800i	−0.0656791	+	0.997841i	$0.520921\pi$
$282$	3.12167	−	2.22914i	0.185893	−	0.132743i
$283$	1.02388	−	3.82117i	0.0608634	−	0.227145i	−0.928794	−	0.370596i	$-0.879153\pi$
$283$	1.02388	−	3.82117i	0.0608634	−	0.227145i	0.989657	+	0.143451i	$0.0458200\pi$
$284$	−7.08722	−	12.2754i	−0.420549	−	0.728413i
$285$	2.64905	+	6.78037i	0.156916	+	0.401634i
$286$	−3.21542	−	5.56928i	−0.190132	−	0.329318i
$287$	13.5940	−	3.70560i	0.802428	−	0.218734i
$288$	0.206125	−	2.99291i	0.0121460	−	0.176359i
$289$	7.99773	−	4.61749i	0.470455	−	0.271617i
$290$	18.8237	−	11.2257i	1.10536	−	0.659195i
$291$	19.4344	+	3.24171i	1.13927	+	0.190033i
$292$	4.06754	−	4.06754i	0.238035	−	0.238035i
$293$	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	$0.567269\pi$
$294$	−4.35007	−	11.3171i	−0.253701	−	0.660027i
$295$	3.21376	−	0.910020i	0.187113	−	0.0529834i
$296$	−3.04704	+	1.75921i	−0.177105	+	0.102252i
$297$	7.07999	+	23.7641i	0.410823	+	1.37893i
$298$	−12.9191	+	3.46165i	−0.748381	+	0.200528i
$299$	−3.48780	+	6.04104i	−0.201705	+	0.349363i
$300$	−8.59290	+	1.07798i	−0.496111	+	0.0622374i
$301$	−0.517908	−	0.888148i	−0.0298517	−	0.0511920i
$302$	2.66696	−	0.714609i	0.153466	−	0.0411211i
$303$	1.53080	+	15.8109i	0.0879424	+	0.908315i
$304$		−	1.87955i		−	0.107800i
$305$	−21.5554	−	20.9542i	−1.23426	−	1.19984i
$306$	11.5863	−	10.0932i	0.662344	−	0.576990i
$307$	−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	$0.308507\pi$
$308$	−12.2095	−	3.21498i	−0.695699	−	0.183190i
$309$	12.9798	+	10.6883i	0.738394	+	0.608034i
$310$	−4.43061	+	2.64224i	−0.251642	+	0.150069i
$311$	−18.7988	+	10.8535i	−1.06598	+	0.615443i	−0.927080	−	0.374863i	$-0.877690\pi$
$311$	−18.7988	+	10.8535i	−1.06598	+	0.615443i	−0.138899	+	0.990307i	$0.544356\pi$
$312$	−0.966829	+	2.12447i	−0.0547359	+	0.120274i
$313$	32.3867	−	8.67800i	1.83061	−	0.490509i	0.832614	−	0.553853i	$-0.186843\pi$
$313$	32.3867	−	8.67800i	1.83061	−	0.490509i	0.997992	+	0.0633439i	$0.0201765\pi$
$314$	−9.28816			−0.524161
$315$	−11.9031	−	13.1650i	−0.670662	−	0.741763i
$316$	3.85958			0.217118
$317$	32.6430	−	8.74667i	1.83341	−	0.491262i	0.835143	−	0.550034i	$-0.185385\pi$
$317$	32.6430	−	8.74667i	1.83341	−	0.491262i	0.998271	+	0.0587717i	$0.0187184\pi$
$318$	0.101269	+	0.141816i	0.00567886	+	0.00795263i
$319$	40.5068	−	23.3866i	2.26795	−	1.30940i
$320$	2.16784	+	0.548139i	0.121186	+	0.0306419i
$321$	4.62216	−	27.7103i	0.257984	−	1.54664i
$322$	3.60176	+	13.2131i	0.200718	+	0.736335i
$323$	6.80738	−	6.80738i	0.378773	−	0.378773i
$324$	5.52604	−	7.10372i	0.307002	−	0.394651i
$325$	6.55515	+	1.55920i	0.363614	+	0.0864888i
$326$			7.72147i			0.427653i
$327$	−11.5356	−	5.24978i	−0.637923	−	0.290314i
$328$	−5.14406	+	1.37835i	−0.284033	+	0.0761064i
$329$	−2.90771	+	5.08700i	−0.160307	+	0.280455i
$330$	−18.3690	+	2.04103i	−1.01118	+	0.112355i
$331$	5.14525	−	8.91184i	0.282809	−	0.489839i	−0.689267	−	0.724508i	$-0.742067\pi$
$331$	5.14525	−	8.91184i	0.282809	−	0.489839i	0.972075	+	0.234669i	$0.0754005\pi$
$332$	−4.36758	+	1.17029i	−0.239702	+	0.0642280i
$333$	−10.5303	−	0.725233i	−0.577057	−	0.0397425i
$334$	19.2619	−	11.1209i	1.05397	−	0.608507i
$335$	3.99555	−	7.15217i	0.218300	−	0.390765i
$336$	1.62566	+	4.28454i	0.0886868	+	0.233741i
$337$	−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	$-0.260557\pi$
$338$	−7.90825	+	7.90825i	−0.430152	+	0.430152i
$339$	9.57041	+	25.5563i	0.519793	+	1.38803i
$340$	5.86626	+	9.83677i	0.318142	+	0.533474i
$341$	−9.53428	+	5.50462i	−0.516310	+	0.298092i
$342$	3.14819	−	4.67797i	0.170234	−	0.252956i
$343$	13.2646	+	12.9248i	0.716223	+	0.697871i
$344$	0.194297	+	0.336532i	0.0104758	+	0.0181446i
$345$	11.8798	+	16.1486i	0.639589	+	0.869414i
$346$	0.271244	+	0.469808i	0.0145822	+	0.0252570i
$347$	−3.01188	+	11.2405i	−0.161686	+	0.603421i	0.836754	+	0.547580i	$0.184451\pi$
$347$	−3.01188	+	11.2405i	−0.161686	+	0.603421i	−0.998440	+	0.0558412i	$0.982216\pi$
$348$	−15.4518	−	7.03200i	−0.828304	−	0.376955i
$349$	−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	$0.504050\pi$
$350$	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
$353$	−9.44329	+	9.44329i	−0.502616	+	0.502616i	−0.912250	−	0.409634i	$-0.865656\pi$
$353$	−9.44329	+	9.44329i	−0.502616	+	0.502616i	0.409634	+	0.912250i	$0.365656\pi$
$354$	−1.99725	−	1.64464i	−0.106153	−	0.0874118i
$355$	30.7280	+	7.76957i	1.63087	+	0.412366i
$356$	12.2496	+	7.07233i	0.649229	+	0.374833i
$357$	−9.62995	+	21.4056i	−0.509671	+	1.13290i
$358$	6.63319	−	24.7554i	0.350575	−	1.30836i
$359$	4.83887	+	8.38116i	0.255386	+	0.442341i	0.965000	−	0.262249i	$-0.0844642\pi$
$359$	4.83887	+	8.38116i	0.255386	+	0.442341i	−0.709615	+	0.704590i	$0.751131\pi$
$360$	4.47737	+	4.99531i	0.235978	+	0.263276i
$361$	−7.73364	+	13.3951i	−0.407034	+	0.705003i
$362$	−18.1511	+	4.86358i	−0.954002	+	0.255624i
$363$	−20.2956	+	1.96501i	−1.06524	+	0.103136i
$364$	−0.0154228	−	3.56540i	−0.000808373	−	0.186878i
$365$	0.181873	+	12.8614i	0.00951966	+	0.673197i
$366$	−3.83120	+	22.9685i	−0.200260	+	1.20058i
$367$	12.9232	−	12.9232i	0.674583	−	0.674583i	−0.284186	−	0.958769i	$-0.591723\pi$
$367$	12.9232	−	12.9232i	0.674583	−	0.674583i	0.958769	+	0.284186i	$0.0917233\pi$
$368$	−1.33972	−	4.99991i	−0.0698378	−	0.260638i
$369$	−15.1116	−	5.18558i	−0.786678	−	0.269951i
$370$	1.92858	−	7.62737i	0.100262	−	0.396528i
$371$	−0.231100	−	0.132096i	−0.0119981	−	0.00685808i
$372$	3.63697	+	1.65515i	0.188568	+	0.0858158i
$373$	9.77443	+	9.77443i	0.506101	+	0.506101i	0.913327	−	0.407226i	$-0.133504\pi$
$373$	9.77443	+	9.77443i	0.506101	+	0.506101i	−0.407226	+	0.913327i	$0.633504\pi$
$374$	12.2212	+	21.1678i	0.631946	+	1.09456i
$375$	11.6647	−	15.4575i	0.602364	−	0.798221i
$376$	1.10732	−	1.91793i	0.0571056	−	0.0989098i
$377$	9.33986	+	9.33986i	0.481027	+	0.481027i
$378$	−3.13040	+	13.3866i	−0.161010	+	0.688532i
$379$			10.0920i			0.518391i	0.965825	+	0.259195i	$0.0834573\pi$
$379$			10.0920i			0.518391i	−0.965825	+	0.259195i	$0.916543\pi$
$380$	3.01356	+	2.92952i	0.154592	+	0.150281i
$381$	−13.0512	+	15.8493i	−0.668634	+	0.811986i
$382$	−0.178591	−	0.0478534i	−0.00913752	−	0.00244839i
$383$	4.02962	−	4.02962i	0.205904	−	0.205904i	−0.596620	−	0.802524i	$-0.703490\pi$
$383$	4.02962	−	4.02962i	0.205904	−	0.205904i	0.802524	+	0.596620i	$0.203490\pi$
$384$	−0.607429	−	1.62204i	−0.0309977	−	0.0827746i
$385$	24.1847	−	14.5650i	1.23257	−	0.742299i
$386$		−	6.79088i		−	0.345647i
$387$	−0.0800989	+	1.16303i	−0.00407166	+	0.0591200i
$388$	10.9879	−	2.94420i	0.557826	−	0.149469i
$389$	−33.3124			−1.68901			−0.844503	−	0.535551i	$-0.820104\pi$
$389$	−33.3124			−1.68901			−0.844503	+	0.535551i	$0.820104\pi$
$390$	−1.89932	−	4.86140i	−0.0961757	−	0.246167i
$391$	13.2565	−	22.9609i	0.670410	−	1.16118i
$392$	−4.99238	−	4.90674i	−0.252153	−	0.247828i
$393$	−3.14754	−	32.5095i	−0.158773	−	1.63989i
$394$	−17.0459	−	9.84148i	−0.858762	−	0.495807i
$395$	−6.01564	+	6.18821i	−0.302680	+	0.311363i
$396$	9.40359	+	10.7947i	0.472548	+	0.542452i
$397$	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	$0.486122\pi$
$398$	−21.6277	−	5.79514i	−1.08410	−	0.290484i
$399$	−1.38036	+	8.50187i	−0.0691045	+	0.425626i
$400$	−4.25770	+	2.62144i	−0.212885	+	0.131072i
$401$			38.5001i			1.92261i	0.275495	+	0.961303i	$0.411158\pi$
$401$			38.5001i			1.92261i	−0.275495	+	0.961303i	$0.588842\pi$
$402$	−6.31639	+	0.611549i	−0.315033	+	0.0305013i
$403$	−2.19837	−	2.19837i	−0.109508	−	0.109508i
$404$	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
$408$	3.67474	−	8.07473i	0.181927	−	0.399759i
$409$	−4.75393	+	2.74468i	−0.235067	+	0.135716i	−0.612907	−	0.790155i	$-0.710000\pi$
$409$	−4.75393	+	2.74468i	−0.235067	+	0.135716i	0.377841	+	0.925871i	$0.376667\pi$
$410$	5.80770	−	10.3960i	0.286822	−	0.513421i
$411$	−10.8728	−	8.95322i	−0.536314	−	0.441630i
$412$	9.37684	+	2.51252i	0.461964	+	0.123783i
$413$	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
$416$			1.34761i			0.0660718i
$417$	−1.85134	−	0.842528i	−0.0906603	−	0.0412588i
$418$	6.34227	+	6.34227i	0.310211	+	0.310211i
$419$	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	$0.0849028\pi$
$420$	−9.40334	−	4.07151i	−0.458836	−	0.198669i
$421$	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	$0.792084\pi$
$422$	−1.87864	+	7.01118i	−0.0914508	+	0.341299i
$423$	5.96845	−	2.91877i	0.290196	−	0.141916i
$424$	0.0871307	+	0.0503049i	0.00423144	+	0.00244302i
$425$	−24.9149	−	5.92624i	−1.20855	−	0.287465i
$426$	−8.60997	−	22.9916i	−0.417154	−	1.11395i
$427$	−9.35463	−	34.3175i	−0.452702	−	1.66074i
$428$	−4.19794	−	15.6669i	−0.202915	−	0.757290i
$429$	−3.90628	−	10.4311i	−0.188597	−	0.503619i
$430$	−0.842410	−	0.213004i	−0.0406246	−	0.0102719i
$431$	28.3027	+	16.3406i	1.36329	+	0.787097i	0.990061	−	0.140641i	$-0.0449163\pi$
$431$	28.3027	+	16.3406i	1.36329	+	0.787097i	0.373232	+	0.927738i	$0.378250\pi$
$432$	1.20505	−	5.05449i	0.0579782	−	0.243184i
$433$	−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	$0.968811\pi$
$434$	−6.10375	+	0.0264029i	−0.292990	+	0.00126738i
$435$	35.3582	−	13.8142i	1.69530	−	0.662342i
$436$	−7.31736			−0.350438
$437$	2.51808	−	9.39760i	0.120456	−	0.449548i
$438$	8.10831	−	5.79003i	0.387430	−	0.276659i
$439$	−20.5872	−	11.8860i	−0.982572	−	0.567288i	−0.0795263	−	0.996833i	$-0.525341\pi$
$439$	−20.5872	−	11.8860i	−0.982572	−	0.567288i	−0.903046	+	0.429545i	$0.858674\pi$
$440$	−9.16468	+	5.46545i	−0.436909	+	0.260555i
$441$	−4.20679	−	20.5743i	−0.200324	−	0.979730i
$442$	−4.88077	+	4.88077i	−0.232155	+	0.232155i
$443$	−5.49283	−	20.4995i	−0.260972	−	0.973962i	−0.964670	−	0.263462i	$-0.915136\pi$
$443$	−5.49283	−	20.4995i	−0.260972	−	0.973962i	0.703697	−	0.710500i	$-0.251531\pi$
$444$	−5.70702	+	2.13719i	−0.270843	+	0.101426i
$445$	−30.4319	+	8.61719i	−1.44261	+	0.408494i
$446$			11.8271i			0.560031i
$447$	−23.0580	+	2.23246i	−1.09061	+	0.105592i
$448$	1.87890	+	1.86272i	0.0887699	+	0.0880052i
$449$	−8.16454			−0.385309			−0.192654	−	0.981267i	$-0.561710\pi$
$449$	−8.16454			−0.385309			−0.192654	+	0.981267i	$0.561710\pi$
$450$	−14.9877	−	0.607071i	−0.706527	−	0.0286176i
$451$	12.7068	−	22.0089i	0.598341	−	1.03636i
$452$	11.1409	+	11.1409i	0.524023	+	0.524023i
$453$	4.76000	−	0.460860i	0.223644	−	0.0216531i
$454$	15.1965	+	8.77370i	0.713206	+	0.411770i
$455$	5.74057	+	5.53239i	0.269122	+	0.259362i
$456$	0.535623	−	3.21112i	0.0250828	−	0.150374i
$457$	8.66154	+	32.3253i	0.405170	+	1.51211i	0.803742	+	0.594978i	$0.202839\pi$
$457$	8.66154	+	32.3253i	0.405170	+	1.51211i	−0.398572	+	0.917137i	$0.630494\pi$
$458$	−3.82420	−	14.2721i	−0.178693	−	0.666891i
$459$	22.6709	−	13.9419i	1.05818	−	0.650753i
$460$	10.1047	+	5.64495i	0.471132	+	0.263197i
$461$	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	$0.148251\pi$
$462$	−19.9431	−	8.97199i	−0.927835	−	0.417415i
$463$	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	$0.143868\pi$
$464$	−9.80149			−0.455023
$465$	−8.32244	+	3.25152i	−0.385944	+	0.150786i
$466$	−11.6650			−0.540371
$467$	−5.94861	+	22.2005i	−0.275269	+	1.02732i	0.680392	+	0.732848i	$0.261810\pi$
$467$	−5.94861	+	22.2005i	−0.275269	+	1.02732i	−0.955661	+	0.294469i	$0.904857\pi$
$468$	−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
$471$	−15.8683	−	2.64688i	−0.731174	−	0.121962i
$472$	−1.44285	−	0.386611i	−0.0664126	−	0.0177952i
$473$	−1.79120	−	0.479951i	−0.0823596	−	0.0220682i
$474$	6.59389	+	1.09988i	0.302867	+	0.0505191i
$475$	−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
$478$	0.118079	−	0.440678i	0.00540082	−	0.0201561i
$479$	−39.0360			−1.78360			−0.891801	−	0.452428i	$-0.850558\pi$
$479$	−39.0360			−1.78360			−0.891801	+	0.452428i	$0.850558\pi$
$480$	3.54744	+	1.55424i	0.161918	+	0.0709412i
$481$	4.74144			0.216191
$482$	−17.3324	+	4.64420i	−0.789468	+	0.211537i
$483$	2.38804	+	23.6002i	0.108660	+	1.07385i
$484$	−10.1953	+	5.88624i	−0.463421	+	0.267556i
$485$	−12.4054	+	22.2062i	−0.563302	+	1.00833i
$486$	11.4653	−	10.5616i	0.520077	−	0.479082i
$487$	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	$0.838200\pi$
$488$	3.47958	+	12.9860i	0.157513	+	0.587847i
$489$	−2.20041	+	13.1917i	−0.0995061	+	0.596550i
$490$	15.6484	−	0.356710i	0.706923	−	0.0161145i
$491$	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	$0.432810\pi$
$492$	−9.18114	+	0.888911i	−0.413918	+	0.0400752i
$493$	−35.4991	−	35.4991i	−1.59880	−	1.59880i
$494$	−1.26645	+	2.19355i	−0.0569802	+	0.0986927i
$495$	−31.9642	−	1.74770i	−1.43668	−	0.0785533i
$496$	2.30702			0.103588
$497$	26.6324	+	26.4030i	1.19463	+	1.18434i
$498$	−7.79528	+	0.754734i	−0.349315	+	0.0338204i
$499$			31.9478i			1.43018i	0.699032	+	0.715090i	$0.253614\pi$
$499$			31.9478i			1.43018i	−0.699032	+	0.715090i	$0.746386\pi$
$500$	2.43311	−	10.9124i	0.108812	−	0.488016i
$501$	36.0771	−	13.5103i	1.61181	−	0.603595i
$502$	0.714720	+	2.66737i	0.0318995	+	0.119051i
$503$	−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	$0.332488\pi$
$504$	1.55637	+	7.78317i	0.0693261	+	0.346690i
$505$	−19.8816	−	5.02706i	−0.884719	−	0.223701i
$506$	21.3921	+	12.3508i	0.950996	+	0.549058i
$507$	−15.7645	+	11.2572i	−0.700125	+	0.499949i
$508$	−3.06798	+	11.4499i	−0.136120	+	0.508006i
$509$	−29.5759			−1.31093			−0.655463	−	0.755227i	$-0.727527\pi$
$509$	−29.5759			−1.31093			−0.655463	+	0.755227i	$0.727527\pi$
$510$	7.21897	+	18.4773i	0.319661	+	0.818189i
$511$	−7.55258	+	13.2131i	−0.334107	+	0.584514i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	6.71161	−	7.09492i	0.296325	−	0.313248i
$514$	17.9823	+	10.3821i	0.793166	+	0.457935i
$515$	−18.6434	+	11.1182i	−0.821525	+	0.489925i
$516$	0.236043	+	0.630317i	0.0103912	+	0.0277481i
$517$	2.73530	+	10.2083i	0.120298	+	0.448959i
$518$	6.55381	−	6.61076i	0.287958	−	0.290460i
$519$	0.329523	+	0.879939i	0.0144644	+	0.0386251i
$520$	−2.16067	−	2.10041i	−0.0947516	−	0.0921092i
$521$	28.7925	+	16.6234i	1.26142	+	0.728283i	0.973350	−	0.229325i	$-0.0736520\pi$
$521$	28.7925	+	16.6234i	1.26142	+	0.728283i	0.288073	+	0.957608i	$0.406985\pi$
$522$	−24.3947	−	16.4172i	−1.06773	−	0.718559i
$523$	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
$525$	21.1843	−	8.73078i	0.924558	−	0.381042i
$526$	0.740355	−	1.28233i	0.0322810	−	0.0559123i
$527$	8.35560	+	8.35560i	0.363975	+	0.363975i
$528$	7.52303	+	3.42367i	0.327398	+	0.148996i
$529$		−	3.79394i		−	0.164954i
$530$	−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
$533$	6.93216	+	1.85747i	0.300265	+	0.0804558i
$534$	18.9124	+	15.5735i	0.818420	+	0.673932i
$535$	31.6624	+	17.6882i	1.36889	+	0.764726i
$536$	−3.17296	+	1.83191i	−0.137051	+	0.0791265i
$537$	18.3871	−	40.4030i	0.793461	−	1.74352i
$538$	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	−0.992079	−	0.125618i	$-0.959909\pi$
$541$	−14.0679	−	24.3664i	−0.604827	−	1.04759i	0.387251	−	0.921974i	$-0.373425\pi$
$542$	16.7809	+	16.7809i	0.720802	+	0.720802i
$543$	−32.3962	+	3.13658i	−1.39026	+	0.134604i
$544$		−	5.12201i		−	0.219604i
$545$	11.4050	−	11.7322i	0.488537	−	0.502552i
$546$	0.989695	−	6.09569i	0.0423550	−	0.260871i
$547$	−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	$0.929216\pi$
$548$	−7.85469	−	2.10466i	−0.335536	−	0.0899065i
$549$	−13.0908	+	38.1486i	−0.558702	+	1.62814i
$550$	5.52133	−	23.2126i	0.235430	−	0.989790i
$551$	−15.9543	−	9.21121i	−0.679676	−	0.392411i
$552$	−0.864002	−	8.92386i	−0.0367744	−	0.379825i
$553$	−9.85202	+	2.68557i	−0.418951	+	0.114202i
$554$	−5.14010	+	8.90291i	−0.218382	+	0.378248i
$555$	5.46847	−	12.4814i	0.232124	−	0.529804i
$556$	−1.17435			−0.0498036
$557$	−4.40768	+	1.18103i	−0.186759	+	0.0500420i	−0.350986	−	0.936381i	$-0.614154\pi$
$557$	−4.40768	+	1.18103i	−0.186759	+	0.0500420i	0.164227	+	0.986423i	$0.447487\pi$
$558$	5.74189	+	3.86418i	0.243074	+	0.163584i
$559$		−	0.523672i		−	0.0221489i
$560$	−5.91507	+	0.109238i	−0.249957	+	0.00461616i
$561$	14.8471	+	39.6468i	0.626844	+	1.67389i
$562$	−13.1761	+	13.1761i	−0.555800	+	0.555800i
$563$	−20.3327	−	5.44814i	−0.856922	−	0.229612i	−0.196498	−	0.980504i	$-0.562957\pi$
$563$	−20.3327	−	5.44814i	−0.856922	−	0.229612i	−0.660424	+	0.750893i	$0.729624\pi$
$564$	2.43836	−	2.96113i	0.102673	−	0.124686i
$565$	−35.2271	+	0.498145i	−1.48201	+	0.0209571i
$566$		−	3.95597i		−	0.166282i
$567$	−9.16293	+	21.9782i	−0.384807	+	0.922997i
$568$	−10.0228	−	10.0228i	−0.420549	−	0.420549i
$569$	4.72767	−	8.18856i	0.198194	−	0.343282i	−0.749749	−	0.661723i	$-0.769826\pi$
$569$	4.72767	−	8.18856i	0.198194	−	0.343282i	0.947943	+	0.318440i	$0.103159\pi$
$570$	4.31367	+	5.86371i	0.180680	+	0.245604i
$571$	−10.5897	−	18.3419i	−0.443165	−	0.767585i	0.554757	−	0.832012i	$-0.312811\pi$
$571$	−10.5897	−	18.3419i	−0.443165	−	0.767585i	−0.997922	+	0.0644275i	$0.979478\pi$
$572$	−4.54730	−	4.54730i	−0.190132	−	0.190132i
$573$	−0.291477	−	0.132649i	−0.0121766	−	0.00554148i
$574$	12.1717	−	7.09772i	0.508037	−	0.296253i
$575$	−24.8001	+	7.40282i	−1.03424	+	0.308719i
$576$	−0.575521	−	2.94428i	−0.0239800	−	0.122678i
$577$	−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	$-0.220217\pi$
$578$	6.53012	−	6.53012i	0.271617	−	0.271617i
$579$	1.93522	−	11.6019i	0.0804250	−	0.482156i
$580$	15.2768	−	15.7151i	0.634336	−	0.652534i
$581$	10.3344	−	6.02634i	0.428745	−	0.250015i
$582$	19.6112	−	1.89875i	0.812912	−	0.0787055i
$583$	−0.463756	+	0.124263i	−0.0192068	+	0.00514645i
$584$	2.87618	−	4.98170i	0.119017	−	0.206144i
$585$	−1.85951	−	8.84670i	−0.0768814	−	0.365766i
$586$	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	$0.959750\pi$
$588$	−7.13093	−	9.80560i	−0.294075	−	0.404376i
$589$	3.75524	+	2.16809i	0.154732	+	0.0893345i
$590$	2.86873	−	1.71080i	0.118104	−	0.0704323i
$591$	−26.3175	−	21.6713i	−1.08256	−	0.891438i
$592$	−2.48789	+	2.48789i	−0.102252	+	0.102252i
$593$	−11.9655	−	3.20616i	−0.491366	−	0.131661i	0.00462398	−	0.999989i	$-0.498528\pi$
$593$	−11.9655	−	3.20616i	−0.491366	−	0.131661i	−0.495990	+	0.868328i	$0.665195\pi$
$594$	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
$597$	−35.2984	−	16.0640i	−1.44467	−	0.657456i
$598$	−1.80542	+	6.73791i	−0.0738290	+	0.275534i
$599$	5.56820	+	9.64441i	0.227511	+	0.394060i	0.957070	−	0.289858i	$-0.0936080\pi$
$599$	5.56820	+	9.64441i	0.227511	+	0.394060i	−0.729559	+	0.683918i	$0.760275\pi$
$600$	−8.02110	+	3.26526i	−0.327460	+	0.133304i
$601$	−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	$0.912032\pi$
$602$	−0.730130	−	0.723841i	−0.0297579	−	0.0295016i
$603$	−10.9655	−	0.755206i	−0.446550	−	0.0307544i
$604$	2.39113	−	1.38052i	0.0972936	−	0.0561725i
$605$	6.45296	−	25.5209i	0.262350	−	1.03757i
$606$	5.57082	+	14.8760i	0.226299	+	0.604296i
$607$	9.89745	−	9.89745i	0.401725	−	0.401725i	−0.477115	−	0.878841i	$-0.658318\pi$
$607$	9.89745	−	9.89745i	0.401725	−	0.401725i	0.878841	+	0.477115i	$0.158318\pi$
$608$	−0.486464	−	1.81551i	−0.0197287	−	0.0736286i
$609$	44.3355	+	7.19831i	1.79657	+	0.291690i
$610$	−26.2442	−	14.6613i	−1.06260	−	0.593619i
$611$	−2.58462	+	1.49223i	−0.104562	+	0.0603692i
$612$	8.57919	−	12.7480i	0.346793	−	0.515309i
$613$	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	$0.364095\pi$
$614$	−3.20242	+	5.54675i	−0.129239	+	0.223849i
$615$	12.8847	−	16.1059i	0.519562	−	0.649454i
$616$	−12.6255	+	0.0546140i	−0.508698	+	0.00220046i
$617$	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	$0.318149\pi$
$618$	15.3038	+	6.96465i	0.615610	+	0.280159i
$619$		−	22.5924i		−	0.908064i	−0.890985	−	0.454032i	$-0.849985\pi$
$619$		−	22.5924i		−	0.908064i	0.890985	−	0.454032i	$-0.150015\pi$
$620$	−3.59578	+	3.69894i	−0.144410	+	0.148553i
$621$	12.7968	−	23.6575i	0.513516	−	0.949344i
$622$	−15.3491	+	15.3491i	−0.615443	+	0.615443i
$623$	−36.1896	−	9.52939i	−1.44991	−	0.381787i
$624$	−0.384032	+	2.30231i	−0.0153736	+	0.0921663i
$625$	13.7039	+	20.9094i	0.548157	+	0.836376i
$626$	29.0371	−	16.7646i	1.16056	−	0.670048i
$627$	9.02805	+	12.6428i	0.360546	+	0.504905i
$628$	−8.97167	+	2.40395i	−0.358009	+	0.0959281i
$629$	−18.0213			−0.718558
$630$	−14.9048	−	9.63566i	−0.593823	−	0.383894i
$631$	5.51476			0.219539			0.109770	−	0.993957i	$-0.464989\pi$
$631$	5.51476			0.219539			0.109770	+	0.993957i	$0.464989\pi$
$632$	3.72807	−	0.998933i	0.148295	−	0.0397354i
$633$	−5.20756	+	11.4429i	−0.206982	+	0.454813i
$634$	29.2669	−	16.8973i	1.16234	−	0.671076i
$635$	−13.5762	−	22.7650i	−0.538754	−	0.903403i
$636$	0.134523	+	0.110773i	0.00533417	+	0.00439244i
$637$	2.52024	+	9.09035i	0.0998556	+	0.360173i
$638$	33.0737	−	33.0737i	1.30940	−	1.30940i
$639$	−8.15769	−	41.7335i	−0.322713	−	1.65095i
$640$	2.23584	−	0.0316170i	0.0883795	−	0.00124977i
$641$		−	45.9142i		−	1.81350i	−0.421668	−	0.906750i	$-0.638555\pi$
$641$		−	45.9142i		−	1.81350i	0.421668	−	0.906750i	$-0.361445\pi$
$642$	−2.70730	−	27.9624i	−0.106849	−	1.10359i
$643$	−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	$0.485195\pi$
$644$	6.89882	+	11.8306i	0.271852	+	0.466192i
$645$	−1.37851	−	0.603970i	−0.0542789	−	0.0237813i
$646$	4.81355	−	8.33731i	0.189386	−	0.328027i
$647$	−7.27052	+	1.94813i	−0.285834	+	0.0765889i	−0.398887	−	0.917000i	$-0.630603\pi$
$647$	−7.27052	+	1.94813i	−0.285834	+	0.0765889i	0.113054	+	0.993589i	$0.463937\pi$
$648$	3.49916	−	8.29191i	0.137460	−	0.325737i
$649$	6.17324	−	3.56412i	0.242321	−	0.139904i
$650$	6.73534	−	0.190527i	0.264182	−	0.00747307i
$651$	−10.4355	−	1.69430i	−0.408998	−	0.0664048i
$652$	1.99846	+	7.45837i	0.0782658	+	0.292092i
$653$	9.90526	−	9.90526i	0.387623	−	0.387623i	−0.486216	−	0.873839i	$-0.661623\pi$
$653$	9.90526	−	9.90526i	0.387623	−	0.387623i	0.873839	+	0.486216i	$0.161623\pi$
$654$	−12.5013	−	2.08525i	−0.488840	−	0.0815399i
$655$	40.8793	+	10.3363i	1.59729	+	0.403874i
$656$	−4.61203	+	2.66276i	−0.180070	+	0.103963i
$657$	15.5026	−	7.58131i	0.604815	−	0.295775i
$658$	−1.49202	+	5.66624i	−0.0581651	+	0.220893i
$659$	−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	$0.898002\pi$
$660$	−17.2149	+	6.72574i	−0.670088	+	0.261799i
$661$	9.39549	+	16.2735i	0.365442	+	0.632965i	0.988847	−	0.148935i	$-0.0475844\pi$
$661$	9.39549	+	16.2735i	0.365442	+	0.632965i	−0.623405	+	0.781899i	$0.714251\pi$
$662$	2.66338	−	9.93987i	0.103515	−	0.386324i
$663$	−9.72943	+	6.94765i	−0.377860	+	0.269824i
$664$	−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
$668$	15.7273	−	15.7273i	0.608507	−	0.608507i
$669$	−3.37042	+	20.2060i	−0.130308	+	0.781210i
$670$	2.00829	−	7.94259i	0.0775869	−	0.306849i
$671$	−55.5605	−	32.0779i	−2.14489	−	1.23835i
$672$	2.67918	+	3.71779i	0.103352	+	0.143417i
$673$	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
$675$	−25.4327	−	5.30825i	−0.978905	−	0.204315i
$676$	−5.59198	+	9.68559i	−0.215076	+	0.372523i
$677$	−34.3025	+	9.19133i	−1.31835	+	0.353251i	−0.848360	−	0.529419i	$-0.822410\pi$
$677$	−34.3025	+	9.19133i	−1.31835	+	0.353251i	−0.469992	+	0.882671i	$0.655743\pi$
$678$	15.8588	+	22.2085i	0.609052	+	0.852911i
$679$	−25.9992	+	15.1610i	−0.997758	+	0.581825i
$680$	8.21231	+	7.98329i	0.314928	+	0.306145i
$681$	23.4621	+	19.3200i	0.899070	+	0.740344i
$682$	−7.78470	+	7.78470i	−0.298092	+	0.298092i
$683$	1.85397	+	6.91910i	0.0709401	+	0.264752i	0.992282	−	0.124001i	$-0.0395726\pi$
$683$	1.85397	+	6.91910i	0.0709401	+	0.264752i	−0.921342	+	0.388753i	$0.872906\pi$
$684$	1.83017	−	5.33338i	0.0699781	−	0.203927i
$685$	15.6170	−	9.31334i	0.596694	−	0.355845i
$686$	16.1578	+	9.05122i	0.616909	+	0.345577i
$687$	−2.46627	−	25.4729i	−0.0940940	−	0.971852i
$688$	0.274777	+	0.274777i	0.0104758	+	0.0104758i
$689$	−0.0677913	−	0.117418i	−0.00258264	−	0.00447327i
$690$	15.6546	+	12.5237i	0.595961	+	0.476768i
$691$	−6.18170	+	10.7070i	−0.235163	+	0.407315i	−0.959320	−	0.282321i	$-0.908896\pi$
$691$	−6.18170	+	10.7070i	−0.235163	+	0.407315i	0.724157	+	0.689635i	$0.242229\pi$
$692$	0.383597	+	0.383597i	0.0145822	+	0.0145822i
$693$	−31.5149	−	21.0114i	−1.19715	−	0.798158i
$694$			11.6370i			0.441735i
$695$	1.83037	−	1.88288i	0.0694299	−	0.0714217i
$696$	−16.7453	−	2.79316i	−0.634730	−	0.105875i
$697$	−26.3479	−	7.05990i	−0.997998	−	0.267413i
$698$	−13.4999	+	13.4999i	−0.510979	+	0.510979i
$699$	−19.9291	−	3.32422i	−0.753786	−	0.125734i
$700$	9.04423	−	9.65412i	0.341840	−	0.364891i
$701$		−	19.0727i		−	0.720365i	−0.932882	−	0.360183i	$-0.882714\pi$
$701$		−	19.0727i		−	0.720365i	0.932882	−	0.360183i	$-0.117286\pi$
$702$	−4.81210	+	5.08693i	−0.181621	+	0.191994i
$703$	−6.38771	+	1.71158i	−0.240917	+	0.0645535i
$704$	4.77205			0.179853
$705$	0.947210	+	8.52480i	0.0356740	+	0.321062i
$706$	−6.67742	+	11.5656i	−0.251308	+	0.435278i
$707$	−17.2317	−	17.0833i	−0.648064	−	0.642482i
$708$	−2.35486	−	1.07168i	−0.0885010	−	0.0402761i
$709$	−14.6607	−	8.46438i	−0.550596	−	0.317887i	0.198767	−	0.980047i	$-0.436306\pi$
$709$	−14.6607	−	8.46438i	−0.550596	−	0.317887i	−0.749362	+	0.662160i	$0.769640\pi$
$710$	31.6919	−	0.448154i	1.18937	−	0.0168189i
$711$	10.9519	+	3.75817i	0.410727	+	0.140942i
$712$	13.6627	+	3.66091i	0.512031	+	0.137198i
$713$	11.5349	+	3.09077i	0.431986	+	0.115750i
$714$	−3.76165	+	23.1686i	−0.140776	+	0.867064i
$715$	14.3784	−	0.203324i	0.537721	−	0.00760390i
$716$		−	25.6287i		−	0.957789i
$717$	0.327314	−	0.719225i	0.0122238	−	0.0268600i
$718$	6.84319	+	6.84319i	0.255386	+	0.255386i
$719$	21.5142	+	37.2636i	0.802343	+	1.38970i	0.918070	+	0.396418i	$0.129747\pi$
$719$	21.5142	+	37.2636i	0.802343	+	1.38970i	−0.115727	+	0.993281i	$0.536920\pi$
$720$	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
$723$	−30.9349	+	2.99510i	−1.15048	+	0.111389i
$724$	−16.2739	+	9.39572i	−0.604813	+	0.349189i
$725$	1.38575	+	48.9879i	0.0514655	+	1.81936i
$726$	−19.0955	+	7.15094i	−0.708700	+	0.265396i
$727$	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	$0.400976\pi$
$728$	−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
$731$			1.99038i			0.0736169i
$732$	2.24402	+	23.1774i	0.0829414	+	0.856662i
$733$	−6.00335	−	6.00335i	−0.221739	−	0.221739i	0.587492	−	0.809230i	$-0.300116\pi$
$733$	−6.00335	−	6.00335i	−0.221739	−	0.221739i	−0.809230	+	0.587492i	$0.800116\pi$
$734$	9.13805	−	15.8276i	0.337292	−	0.584206i
$735$	26.8361	+	3.84996i	0.989866	+	0.142008i
$736$	−2.58814	−	4.48280i	−0.0954002	−	0.165238i
$737$	4.52518	−	16.8882i	0.166687	−	0.622085i
$738$	−15.9388	−	1.09772i	−0.586715	−	0.0404077i
$739$	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	$0.517834\pi$
$740$	−0.111242	−	7.86662i	−0.00408933	−	0.289183i
$741$	−2.78877	+	3.38667i	−0.102448	+	0.124412i
$742$	−0.257414	−	0.0677819i	−0.00944997	−	0.00248835i
$743$	−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	$-0.184819\pi$
$744$	3.94143	+	0.657440i	0.144500	+	0.0241029i
$745$	7.33126	−	28.9945i	0.268596	−	1.06228i
$746$	11.9712	+	6.91157i	0.438296	+	0.253050i
$747$	−13.5329	−	0.932026i	−0.495143	−	0.0341011i
$748$	17.2835	+	17.2835i	0.631946	+	0.631946i
$749$	21.6171	+	37.0706i	0.789871	+	1.35453i
$750$	7.26657	−	17.9498i	0.265338	−	0.655436i
$751$	−14.6846			−0.535850			−0.267925	−	0.963440i	$-0.586338\pi$
$751$	−14.6846			−0.535850			−0.267925	+	0.963440i	$0.586338\pi$
$752$	0.573191	−	2.13918i	0.0209021	−	0.0780077i
$753$	0.460931	+	4.76074i	0.0167973	+	0.173491i
$754$	11.4389	+	6.60428i	0.416582	+	0.240514i
$755$	−1.51343	+	5.98550i	−0.0550795	+	0.217834i
$756$	0.440973	+	13.7407i	0.0160380	+	0.499743i
$757$	−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	$0.419528\pi$
$758$	2.61200	+	9.74811i	0.0948721	+	0.354067i
$759$	33.0277	+	27.1968i	1.19883	+	0.987181i
$760$	3.66909	+	2.04973i	0.133092	+	0.0743515i
$761$			25.0585i			0.908372i	0.890907	+	0.454186i	$0.150070\pi$
$761$			25.0585i			0.908372i	−0.890907	+	0.454186i	$0.849930\pi$
$762$	−8.50439	+	18.6872i	−0.308082	+	0.676966i
$763$	18.6784	−	5.09156i	0.676203	−	0.184327i
$764$	−0.184891			−0.00668913
$765$	7.06768	+	33.6247i	0.255532	+	1.21570i
$766$	2.84938	−	4.93526i	0.102952	−	0.178318i
$767$	1.42340	+	1.42340i	0.0513958	+	0.0513958i
$768$	−1.00655	−	1.40956i	−0.0363207	−	0.0508631i
$769$	−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	$-0.723431\pi$
$770$	19.5909	−	20.3281i	0.706007	−	0.732575i
$771$	27.7632	+	22.8617i	0.999868	+	0.823346i
$772$	−1.75761	−	6.55948i	−0.0632577	−	0.236081i
$773$	4.22197	+	15.7566i	0.151854	+	0.566725i	0.999354	+	0.0359309i	$0.0114396\pi$
$773$	4.22197	+	15.7566i	0.151854	+	0.566725i	−0.847501	+	0.530794i	$0.821894\pi$
$774$	0.223644	+	1.14413i	0.00803871	+	0.0411248i
$775$	−0.326171	−	11.5305i	−0.0117164	−	0.414188i
$776$	9.85147	−	5.68775i	0.353647	−	0.204178i
$777$	13.0807	−	9.42647i	0.469269	−	0.338173i
$778$	−32.1773	+	8.62188i	−1.15361	+	0.309109i
$779$	−10.0096			−0.358631
$780$	−3.09282	−	4.20417i	−0.110741	−	0.150534i
$781$	67.6412			2.42039
$782$	6.86207	−	25.6096i	0.245387	−	0.915797i
$783$	−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
$786$	−11.4544	−	30.5871i	−0.408564	−	1.09101i
$787$	−11.3073	−	3.02977i	−0.403060	−	0.108000i	0.0515931	−	0.998668i	$-0.483570\pi$
$787$	−11.3073	−	3.02977i	−0.403060	−	0.108000i	−0.454653	+	0.890669i	$0.650237\pi$
$788$	−19.0123	−	5.09432i	−0.677284	−	0.181478i
$789$	1.63029	−	1.97981i	0.0580397	−	0.0704832i
$790$	−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
$793$	4.68910	−	17.5000i	0.166515	−	0.621442i
$794$	11.9818			0.425217
$795$	−0.387277	+	0.0430313i	−0.0137353	+	0.00152616i
$796$	−22.3907			−0.793617
$797$	−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	$0.525114\pi$
$798$	0.867118	+	8.56944i	0.0306957	+	0.303355i
$799$	9.82367	−	5.67170i	0.347537	−	0.200650i
$800$	−3.43415	+	3.63409i	−0.121415	+	0.128485i
$801$	27.8728	+	31.9961i	0.984838	+	1.13053i
$802$	9.96457	+	37.1883i	0.351861	+	1.31316i
$803$	7.10474	+	26.5152i	0.250721	+	0.935703i
$804$	−5.94289	+	2.22551i	−0.209589	+	0.0784878i
$805$	−29.7212	−	7.37837i	−1.04753	−	0.260053i
$806$	−2.69244	−	1.55448i	−0.0948371	−	0.0547542i
$807$	6.02674	−	13.2429i	0.212151	−	0.466172i
$808$	6.48498	+	6.48498i	0.228141	+	0.228141i
$809$	−19.1875	+	33.2338i	−0.674598	+	1.16844i	0.301988	+	0.953312i	$0.402350\pi$
$809$	−19.1875	+	33.2338i	−0.674598	+	1.16844i	−0.976586	+	0.215127i	$0.930984\pi$
$810$	7.84086	+	18.5343i	0.275500	+	0.651230i
$811$	27.8982			0.979639			0.489819	−	0.871824i	$-0.337063\pi$
$811$	27.8982			0.979639			0.489819	+	0.871824i	$0.337063\pi$
$812$	25.0194	−	6.82006i	0.878009	−	0.239337i
$813$	23.8872	+	33.4514i	0.837760	+	1.17319i
$814$		−	16.7900i		−	0.588491i
$815$	−15.0731	−	8.42058i	−0.527989	−	0.294960i
$816$	1.45964	−	8.75068i	0.0510975	−	0.306335i
$817$	0.189037	+	0.705496i	0.00661357	+	0.0246822i
$818$	−3.88157	+	3.88157i	−0.135716	+	0.135716i
$819$	3.42795	−	10.1321i	0.119782	−	0.354045i
$820$	2.91913	−	11.5449i	0.101940	−	0.403165i
$821$	35.8029	+	20.6708i	1.24953	+	0.721416i	0.971015	−	0.239017i	$-0.0768252\pi$
$821$	35.8029	+	20.6708i	1.24953	+	0.721416i	0.278513	+	0.960432i	$0.410158\pi$
$822$	−12.8195	−	5.83407i	−0.447133	−	0.203487i
$823$	−6.56035	+	24.4836i	−0.228679	+	0.853443i	0.752217	+	0.658915i	$0.228984\pi$
$823$	−6.56035	+	24.4836i	−0.228679	+	0.853443i	−0.980897	+	0.194528i	$0.937682\pi$
$824$	9.70762			0.338181
$825$	16.0479	−	38.0841i	0.558716	−	1.32592i
$826$	3.95205	−	0.0170953i	0.137509	−	0.000594822i
$827$	−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	$0.925624\pi$
$828$	1.06696	−	15.4922i	0.0370795	−	0.538390i
$829$	−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	$0.717245\pi$
$830$	2.47850	−	9.80223i	0.0860299	−	0.340241i
$831$	−11.3187	+	13.7454i	−0.392640	+	0.476821i
$832$	0.348786	+	1.30169i	0.0120920	+	0.0451279i
$833$	−9.57898	−	34.5508i	−0.331892	−	1.19711i
$834$	−2.00632	−	0.334659i	−0.0694730	−	0.0115883i
$835$	0.703219	+	49.7291i	0.0243359	+	1.72095i
$836$	7.76766	+	4.48466i	0.268650	+	0.155105i
$837$	8.70852	+	8.23804i	0.301011	+	0.284748i
$838$	2.69190	−	10.0463i	0.0929900	−	0.347043i
$839$	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	$0.776950\pi$
$840$	−10.1367	−	1.49901i	−0.349750	−	0.0517208i
$841$	−33.5346	+	58.0837i	−1.15637	+	2.00288i
$842$	3.74978	+	3.74978i	0.129226	+	0.129226i
$843$	−26.2655	+	18.7558i	−0.904632	+	0.645985i
$844$			7.25851i			0.249848i
$845$	−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
$848$	0.0971817	+	0.0260397i	0.00333723	+	0.000894209i
$849$	1.12735	−	6.75856i	0.0386904	−	0.231953i
$850$	−25.5998	+	0.724158i	−0.878066	+	0.0248384i
$851$	−15.7723	+	9.10616i	−0.540668	+	0.312155i
$852$	−14.2673	−	19.9797i	−0.488788	−	0.684495i
$853$	−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
$857$	−20.3779	−	20.3779i	−0.696095	−	0.696095i	0.267471	−	0.963566i	$-0.413812\pi$
$857$	−20.3779	−	20.3779i	−0.696095	−	0.696095i	−0.963566	+	0.267471i	$0.913812\pi$
$858$	−6.47295	−	9.06467i	−0.220983	−	0.309463i
$859$			41.5438i			1.41746i	0.705482	+	0.708728i	$0.250731\pi$
$859$			41.5438i			1.41746i	−0.705482	+	0.708728i	$0.749269\pi$
$860$	−0.868835	+	0.0122862i	−0.0296270	+	0.000418955i
$861$	22.8174	−	8.65746i	0.777614	−	0.295045i
$862$	31.5675	+	8.45850i	1.07519	+	0.288098i
$863$	−4.62283	−	1.23868i	−0.157363	−	0.0421653i	0.179278	−	0.983799i	$-0.442624\pi$
$863$	−4.62283	−	1.23868i	−0.157363	−	0.0421653i	−0.336640	+	0.941633i	$0.609291\pi$
$864$	−0.144205	−	5.19415i	−0.00490597	−	0.176709i
$865$	−1.21292	+	0.0171519i	−0.0412404	+	0.000583180i
$866$	−22.8699	−	13.2039i	−0.777150	−	0.448688i
$867$	13.0173	−	9.29545i	0.442090	−	0.315690i
$868$	−5.88894	+	1.60527i	−0.199884	+	0.0544864i
$869$	−9.20906	+	15.9506i	−0.312396	+	0.541086i
$870$	30.5781	−	22.4949i	1.03669	−	0.762649i
$871$	4.93739			0.167297
$872$	−7.06803	+	1.89387i	−0.239354	+	0.0641346i
$873$	34.0458	+	2.34478i	1.15228	+	0.0793586i
$874$		−	9.72911i		−	0.329092i
$875$	1.38225	+	29.5481i	0.0467287	+	0.998908i
$876$	6.33346	−	7.69133i	0.213988	−	0.259866i
$877$	37.5035	−	37.5035i	1.26640	−	1.26640i	0.318469	−	0.947933i	$-0.396831\pi$
$877$	37.5035	−	37.5035i	1.26640	−	1.26640i	0.947933	−	0.318469i	$-0.103169\pi$
$878$	−22.9620	−	6.15265i	−0.774930	−	0.207642i
$879$	18.5106	+	49.4297i	0.624347	+	1.66722i
$880$	−7.43783	+	7.65121i	−0.250729	+	0.257922i
$881$		−	33.1736i		−	1.11765i	−0.829286	−	0.558824i	$-0.811253\pi$
$881$		−	33.1736i		−	1.11765i	0.829286	−	0.558824i	$-0.188747\pi$
$882$	−9.38848	−	18.7845i	−0.316127	−	0.632506i
$883$	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	$0.628757\pi$
$884$	−3.45123	+	5.97770i	−0.116077	+	0.201052i
$885$	5.38860	−	2.10529i	0.181136	−	0.0707686i
$886$	−10.6113	−	18.3794i	−0.356495	−	0.617467i
$887$	24.7665	+	24.7665i	0.831576	+	0.831576i	0.987732	−	0.156156i	$-0.0499103\pi$
$887$	24.7665	+	24.7665i	0.831576	+	0.831576i	−0.156156	+	0.987732i	$0.549910\pi$
$888$	−4.95942	+	3.54145i	−0.166427	+	0.118843i
$889$	−0.135661	−	31.3618i	−0.00454993	−	1.05184i
$890$	−27.1647	+	16.1999i	−0.910562	+	0.543023i
$891$	16.1724	+	39.7872i	0.541796	+	1.33292i
$892$	3.06109	+	11.4241i	0.102493	+	0.382508i
$893$	2.94335	−	2.94335i	0.0984956	−	0.0984956i
$894$	−21.6945	+	8.12424i	−0.725574	+	0.271715i
$895$	41.0914	+	39.9455i	1.37354	+	1.33523i
$896$	2.29699	+	1.31295i	0.0767370	+	0.0438626i
$897$	−5.00458	+	10.9969i	−0.167098	+	0.367175i
$898$	−7.88634	+	2.11314i	−0.263171	+	0.0705164i
$899$	11.3061	−	19.5828i	0.377081	−	0.653123i
$900$	−14.6341	+	3.29272i	−0.487805	+	0.109757i
$901$	0.257662	+	0.446284i	0.00858398	+	0.0148679i
$902$	6.57754	−	24.5477i	0.219008	−	0.817349i
$903$	−1.04111	−	1.44471i	−0.0346461	−	0.0480770i
$904$	13.6447	+	7.87780i	0.453817	+	0.262012i
$905$	10.3003	−	40.7369i	0.342394	−	1.35414i
$906$	4.47853	−	1.67713i	0.148789	−	0.0557191i
$907$	−34.1620	+	34.1620i	−1.13433	+	1.13433i	−0.144881	+	0.989449i	$0.546280\pi$
$907$	−34.1620	+	34.1620i	−1.13433	+	1.13433i	−0.989449	+	0.144881i	$0.953720\pi$
$908$	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	0.438509	−	0.898727i	$-0.355507\pi$
$911$	43.3450	−	25.0252i	1.43608	−	0.829123i	0.997575	+	0.0696035i	$0.0221734\pi$
$912$	−0.313726	−	3.24033i	−0.0103885	−	0.107298i
$913$	5.58468	−	20.8423i	0.184826	−	0.689780i
$914$	16.7328	+	28.9821i	0.553472	+	0.958642i
$915$	−40.6588	−	32.5270i	−1.34414	−	1.07531i
$916$	−7.38778	−	12.7960i	−0.244099	−	0.422792i
$917$	35.4307	+	35.1255i	1.17003	+	1.15995i
$918$	18.2899	−	19.3345i	0.603658	−	0.638134i
$919$	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	$0.279107\pi$
$920$	11.2214	+	2.83733i	0.369958	+	0.0935439i
$921$	−7.05184	+	8.56373i	−0.232366	+	0.282184i
$922$	16.6774	−	16.6774i	0.549239	−	0.549239i
$923$	4.94385	+	18.4507i	0.162729	+	0.607312i
$924$	−21.5856	−	3.50464i	−0.710115	−	0.115294i
$925$	12.7862	+	12.0828i	0.420409	+	0.397278i
$926$	28.1717	−	16.2649i	0.925780	−	0.534499i
$927$	24.1610	+	16.2599i	0.793553	+	0.534046i
$928$	−9.46751	+	2.53681i	−0.310786	+	0.0832750i
$929$	13.8339	−	23.9611i	0.453877	−	0.786138i	−0.544746	−	0.838601i	$-0.683374\pi$
$929$	13.8339	−	23.9611i	0.453877	−	0.786138i	0.998623	+	0.0524634i	$0.0167073\pi$
$930$	−7.19730	+	5.29473i	−0.236009	+	0.173621i
$931$	−6.67676	−	11.3368i	−0.218822	−	0.371550i
$932$	−11.2675	+	3.01913i	−0.369081	+	0.0988948i
$933$	−30.5972	+	21.8491i	−1.00171	+	0.715306i
$934$			22.9837i			0.752049i
$935$	−54.6496	+	0.772799i	−1.78723	+	0.0252732i
$936$	−1.31220	+	3.82394i	−0.0428905	+	0.124989i
$937$	−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	$0.409336\pi$
$938$	6.82467	−	6.88397i	0.222833	−	0.224770i
$939$	54.3859	−	20.3666i	1.77482	−	0.664639i
$940$	2.53643	+	4.25319i	0.0827293	+	0.138724i
$941$	−18.8521	+	10.8843i	−0.614561	+	0.354817i	−0.774748	−	0.632270i	$-0.782123\pi$
$941$	−18.8521	+	10.8843i	−0.614561	+	0.354817i	0.160188	+	0.987087i	$0.448790\pi$
$942$	−16.0127	+	1.55034i	−0.521721	+	0.0505127i
$943$	−26.6271	+	7.13471i	−0.867098	+	0.232338i
$944$	−1.49375			−0.0486174
$945$	−22.7182	−	20.7095i	−0.739024	−	0.673680i
$946$	−1.85439			−0.0602914
$947$	11.4098	−	3.05726i	0.370770	−	0.0993474i	−0.0686227	−	0.997643i	$-0.521860\pi$
$947$	11.4098	−	3.05726i	0.370770	−	0.0993474i	0.439392	+	0.898295i	$0.355194\pi$
$948$	6.65388	−	0.644224i	0.216108	−	0.0209234i
$949$	−6.71337	+	3.87597i	−0.217925	+	0.125819i
$950$	−9.00514	+	2.68803i	−0.292165	+	0.0872111i
$951$	54.8162	−	20.5278i	1.77754	−	0.665659i
$952$	3.56399	+	13.0745i	0.115510	+	0.423747i
$953$	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	$0.189696\pi$
$954$	0.198257	+	0.227586i	0.00641882	+	0.00736835i
$955$	0.288176	−	0.296443i	0.00932516	−	0.00959267i
$956$		−	0.456223i		−	0.0147553i
$957$	65.9297	−	47.0795i	2.13120	−	1.52186i
$958$	−37.7059	+	10.1033i	−1.21822	+	0.326422i
$959$	21.5144	−	0.0930646i	0.694737	−	0.00300521i
$960$	3.82883	+	0.583140i	0.123575	+	0.0188208i
$961$	12.8388	−	22.2375i	0.414156	−	0.717338i
$962$	4.57988	−	1.22717i	0.147661	−	0.0395657i
$963$	3.34327	−	48.5438i	0.107735	−	1.56430i
$964$	−15.5398	+	8.97190i	−0.500503	+	0.288965i
$965$	13.2565	+	7.40573i	0.426742	+	0.238399i
$966$	8.41486	+	22.1780i	0.270744	+	0.713565i
$967$	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	$0.884080\pi$
$968$	−8.32440	+	8.32440i	−0.267556	+	0.267556i
$969$	10.5996	−	12.8721i	0.340508	−	0.413512i
$970$	−6.23536	+	24.6603i	−0.200205	+	0.791794i
$971$	2.34429	−	1.35348i	0.0752320	−	0.0434352i	−0.461912	−	0.886926i	$-0.652836\pi$
$971$	2.34429	−	1.35348i	0.0752320	−	0.0434352i	0.537144	+	0.843490i	$0.319503\pi$
$972$	8.34111	−	13.1691i	0.267541	−	0.422400i
$973$	2.99766	−	0.817136i	0.0961007	−	0.0261962i
$974$	5.38509	+	9.32725i	0.172549	+	0.298864i
$975$	11.5613	+	1.59389i	0.370257	+	0.0510453i
$976$	6.72203	+	11.6429i	0.215167	+	0.372680i
$977$	12.0963	−	45.1439i	0.386994	−	1.44428i	−0.448005	−	0.894031i	$-0.647865\pi$
$977$	12.0963	−	45.1439i	0.386994	−	1.44428i	0.834999	−	0.550251i	$-0.185468\pi$
$978$	1.28883	+	13.3117i	0.0412123	+	0.425662i
$979$	−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
$983$	42.0741	−	42.0741i	1.34195	−	1.34195i	0.447841	−	0.894113i	$-0.352193\pi$
$983$	42.0741	−	42.0741i	1.34195	−	1.34195i	0.894113	−	0.447841i	$-0.147807\pi$
$984$	−8.63823	+	3.23488i	−0.275377	+	0.103124i
$985$	37.8009	−	22.5430i	1.20444	−	0.718278i
$986$	−43.4774	−	25.1017i	−1.38460	−	0.799400i
$987$	−4.16377	+	9.25528i	−0.132534	+	0.294599i
$988$	−0.655562	+	2.44659i	−0.0208562	+	0.0778365i
$989$	1.00574	+	1.74199i	0.0319806	+	0.0553919i
$990$	−31.3273	+	6.58478i	−0.995648	+	0.209278i
$991$	−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	$0.966365\pi$
$992$	2.22841	−	0.597102i	0.0707522	−	0.0189580i
$993$	7.38284	−	16.2227i	0.234287	−	0.514813i
$994$	32.5585	+	18.6104i	1.03269	+	0.590285i
$995$	34.8987	−	35.8998i	1.10636	−	1.13810i
$996$	−7.33432	+	2.74658i	−0.232397	+	0.0870288i
$997$	9.95871	−	9.95871i	0.315396	−	0.315396i	−0.531600	−	0.846996i	$-0.678409\pi$
$997$	9.95871	−	9.95871i	0.315396	−	0.315396i	0.846996	+	0.531600i	$0.178409\pi$
$998$	8.26870	+	30.8592i	0.261741	+	0.976832i
$999$	−18.2752	+	0.507374i	−0.578201	+	0.0160526i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.bt.a.317.46	✓	192	315.2	even	12	inner
630.2.bt.a.347.36	yes	192	5.2	odd	4	inner
630.2.bt.a.443.36	yes	192	63.2	odd	6	inner
630.2.bt.a.473.46	yes	192	1.1	even	1	trivial
630.2.cd.a.23.10	yes	192	7.2	even	3
630.2.cd.a.137.10	yes	192	45.2	even	12
630.2.cd.a.263.45	yes	192	9.2	odd	6
630.2.cd.a.527.45	yes	192	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.72399 - 0.166915i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.548139 + 2.16784i) q^{5} +(1.62204 - 0.607429i) q^{6} +(-1.86272 + 1.87890i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.94428 - 0.575521i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(1.72399 - 0.166915i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-0.548139 + 2.16784i) q^{5} +(1.62204 - 0.607429i) q^{6} +(-1.86272 + 1.87890i) q^{7} +(0.707107 - 0.707107i) q^{8} +(2.94428 - 0.575521i) q^{9} +(0.0316170 + 2.23584i) q^{10} +4.77205i q^{11} +(1.40956 - 1.00655i) q^{12} +(-1.30169 + 0.348786i) q^{13} +(-1.31295 + 2.29699i) q^{14} +(-0.583140 + 3.82883i) q^{15} +(0.500000 - 0.866025i) q^{16} +(4.94748 - 1.32567i) q^{17} +(2.69500 - 1.31795i) q^{18} +(1.62774 - 0.939777i) q^{19} +(0.609219 + 2.15148i) q^{20} +(-2.89769 + 3.55013i) q^{21} +(1.23510 + 4.60945i) q^{22} +(3.66019 - 3.66019i) q^{23} +(1.10102 - 1.33707i) q^{24} +(-4.39909 - 2.37656i) q^{25} +(-1.16706 + 0.673803i) q^{26} +(4.97984 - 1.48364i) q^{27} +(-0.673710 + 2.55854i) q^{28} +(-4.90075 - 8.48834i) q^{29} +(0.427704 + 3.84929i) q^{30} +(1.15351 + 1.99794i) q^{31} +(0.258819 - 0.965926i) q^{32} +(0.796529 + 8.22697i) 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} +(1.32905 - 1.32905i) q^{38} +(-2.18588 + 0.818575i) q^{39} +(1.14530 + 1.92049i) q^{40} +(-4.61203 - 2.66276i) q^{41} +(-1.88011 + 4.17914i) q^{42} +(-0.100575 + 0.375353i) q^{43} +(2.38603 + 4.13272i) q^{44} +(-0.366237 + 6.69820i) q^{45} +(2.58814 - 4.48280i) q^{46} +(2.13918 - 0.573191i) q^{47} +(0.717442 - 1.57648i) q^{48} +(-0.0605584 - 6.99974i) q^{49} +(-4.86429 - 1.15701i) q^{50} +(8.30813 - 3.11126i) q^{51} +(-0.952902 + 0.952902i) q^{52} +(0.0260397 + 0.0971817i) q^{53} +(4.42616 - 2.72196i) q^{54} +(-10.3451 - 2.61575i) q^{55} +(0.0114446 + 2.64573i) q^{56} +(2.64935 - 1.89186i) q^{57} +(-6.93070 - 6.93070i) q^{58} +(-0.746874 - 1.29362i) q^{59} +(1.40940 + 3.60744i) q^{60} +(-6.72203 + 11.6429i) q^{61} +(1.63131 + 1.63131i) q^{62} +(-4.40301 + 6.60405i) q^{63} -1.00000i q^{64} +(-0.0426073 - 3.01304i) q^{65} +(2.89868 + 7.74048i) q^{66} +(-3.53898 - 0.948267i) q^{67} +(3.62181 - 3.62181i) q^{68} +(5.69918 - 6.92106i) q^{69} +(-4.25983 - 4.10534i) q^{70} -14.1744i q^{71} +(1.67496 - 2.48887i) q^{72} +(5.55636 - 1.48882i) q^{73} -3.51841 q^{74} +(-7.98066 - 3.36289i) q^{75} +(0.939777 - 1.62774i) q^{76} +(-8.96623 - 8.88899i) q^{77} +(-1.89953 + 1.35643i) q^{78} +(3.34250 + 1.92979i) q^{79} +(1.60334 + 1.55862i) q^{80} +(8.33755 - 3.38899i) q^{81} +(-5.14406 - 1.37835i) q^{82} +(-4.36758 - 1.17029i) q^{83} +(-0.734409 + 4.52334i) q^{84} +(0.161943 + 11.4520i) q^{85} +0.388594i q^{86} +(-9.86567 - 13.8158i) q^{87} +(3.37435 + 3.37435i) 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} +(2.32213 + 3.25189i) q^{93} +(1.91793 - 1.10732i) q^{94} +(1.14506 + 4.04382i) q^{95} +(0.284973 - 1.70845i) q^{96} +(10.9879 + 2.94420i) 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	\( 192 q + 8 q^{6} + 12 q^{15} + 96 q^{16} + 36 q^{17} + 16 q^{18} - 12 q^{21} + 36 q^{27} - 12 q^{30} - 20 q^{33} + 12 q^{41} - 4 q^{42} + 20 q^{45} - 12 q^{46} - 48 q^{50} - 24 q^{51} - 48 q^{57} + 24 q^{58} + 8 q^{60} + 12 q^{61} - 28 q^{63} + 24 q^{65} + 8 q^{72} - 88 q^{75} - 48 q^{77} - 16 q^{78} + 4 q^{81} + 40 q^{87} - 20 q^{90} - 24 q^{92} - 12 q^{93} + 4 q^{96}+O(q^{100}) \) 192 * q + 8 * q^6 + 12 * q^15 + 96 * q^16 + 36 * q^17 + 16 * q^18 - 12 * q^21 + 36 * q^27 - 12 * q^30 - 20 * q^33 + 12 * q^41 - 4 * q^42 + 20 * q^45 - 12 * q^46 - 48 * q^50 - 24 * q^51 - 48 * q^57 + 24 * q^58 + 8 * q^60 + 12 * q^61 - 28 * q^63 + 24 * q^65 + 8 * q^72 - 88 * q^75 - 48 * q^77 - 16 * q^78 + 4 * q^81 + 40 * q^87 - 20 * q^90 - 24 * q^92 - 12 * q^93 + 4 * q^96

Introduction

L-functions

Modular forms

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Representations

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Database

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