LMFDB - Embedded newform 429.2.j.a.122.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(122,429)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("429.122");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.j (of order $4$, degree $2$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			122.8
Character	$\chi$	$=$	429.122
Dual form			429.2.j.a.320.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43577 - 1.43577i) q^{2} +(-1.73083 - 0.0650121i) q^{3} +2.12285i q^{4} +(-1.59194 - 1.59194i) q^{5} +(2.39173 + 2.57841i) q^{6} +(1.33791 + 1.33791i) q^{7} +(0.176380 - 0.176380i) q^{8} +(2.99155 + 0.225050i) q^{9} +O(q^{10})$	\(q+(-1.43577 - 1.43577i) q^{2} +(-1.73083 - 0.0650121i) q^{3} +2.12285i q^{4} +(-1.59194 - 1.59194i) q^{5} +(2.39173 + 2.57841i) q^{6} +(1.33791 + 1.33791i) q^{7} +(0.176380 - 0.176380i) q^{8} +(2.99155 + 0.225050i) q^{9} +4.57130i q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.138011 - 3.67429i) q^{12} +(-2.05741 + 2.96092i) q^{13} -3.84185i q^{14} +(2.65188 + 2.85887i) q^{15} +3.73921 q^{16} +5.94126 q^{17} +(-3.97204 - 4.61828i) q^{18} +(-2.46772 + 2.46772i) q^{19} +(3.37944 - 3.37944i) q^{20} +(-2.22872 - 2.40268i) q^{21} +2.03048 q^{22} -0.808524 q^{23} +(-0.316751 + 0.293818i) q^{24} +0.0685372i q^{25} +(7.20515 - 1.29723i) q^{26} +(-5.16323 - 0.584009i) q^{27} +(-2.84018 + 2.84018i) q^{28} -5.12953i q^{29} +(0.297190 - 7.91215i) q^{30} +(6.56068 - 6.56068i) q^{31} +(-5.72140 - 5.72140i) q^{32} +(1.26985 - 1.17791i) q^{33} +(-8.53026 - 8.53026i) q^{34} -4.25974i q^{35} +(-0.477746 + 6.35060i) q^{36} +(5.17706 + 5.17706i) q^{37} +7.08614 q^{38} +(3.75353 - 4.99110i) q^{39} -0.561573 q^{40} +(5.79232 + 5.79232i) q^{41} +(-0.249767 + 6.64960i) q^{42} -6.08422i q^{43} +(-1.50108 - 1.50108i) q^{44} +(-4.40409 - 5.12062i) q^{45} +(1.16085 + 1.16085i) q^{46} +(-6.46036 + 6.46036i) q^{47} +(-6.47194 - 0.243094i) q^{48} -3.41999i q^{49} +(0.0984033 - 0.0984033i) q^{50} +(-10.2833 - 0.386254i) q^{51} +(-6.28558 - 4.36757i) q^{52} -4.64016i q^{53} +(6.57469 + 8.25169i) q^{54} +2.25134 q^{55} +0.471962 q^{56} +(4.43164 - 4.11077i) q^{57} +(-7.36480 + 7.36480i) q^{58} +(-1.07306 + 1.07306i) q^{59} +(-6.06895 + 5.62954i) q^{60} +8.34079 q^{61} -18.8392 q^{62} +(3.70133 + 4.30352i) q^{63} +8.95074i q^{64} +(7.98888 - 1.43833i) q^{65} +(-3.51442 - 0.132006i) q^{66} +(2.38684 - 2.38684i) q^{67} +12.6124i q^{68} +(1.39942 + 0.0525638i) q^{69} +(-6.11600 + 6.11600i) q^{70} +(7.67850 + 7.67850i) q^{71} +(0.567344 - 0.487956i) q^{72} +(2.21842 + 2.21842i) q^{73} -14.8661i q^{74} +(0.00445574 - 0.118626i) q^{75} +(-5.23859 - 5.23859i) q^{76} -1.89209 q^{77} +(-12.5552 + 1.77686i) q^{78} +8.33607 q^{79} +(-5.95260 - 5.95260i) q^{80} +(8.89871 + 1.34649i) q^{81} -16.6328i q^{82} +(7.81391 + 7.81391i) q^{83} +(5.10052 - 4.73123i) q^{84} +(-9.45813 - 9.45813i) q^{85} +(-8.73551 + 8.73551i) q^{86} +(-0.333481 + 8.87834i) q^{87} +0.249439i q^{88} +(1.90101 - 1.90101i) q^{89} +(-1.02877 + 13.6753i) q^{90} +(-6.71408 + 1.20882i) q^{91} -1.71637i q^{92} +(-11.7819 + 10.9289i) q^{93} +18.5511 q^{94} +7.85692 q^{95} +(9.53081 + 10.2747i) q^{96} +(-8.73321 + 8.73321i) q^{97} +(-4.91030 + 4.91030i) q^{98} +(-2.27448 + 1.95621i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) $ 96 * q + 12 * q^6 - 16 * q^7	$ 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) $ 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−1.43577	−	1.43577i	−1.01524	−	1.01524i	−0.999882	−	0.0153578i	$-0.995111\pi$
$2$	−1.43577	−	1.43577i	−1.01524	−	1.01524i	−0.0153578	−	0.999882i	$-0.504889\pi$
$3$	−1.73083	−	0.0650121i	−0.999295	−	0.0375347i
$3$	−1.73083	−	0.0650121i	−0.999295	−	0.0375347i
$4$			2.12285i			1.06142i
$5$	−1.59194	−	1.59194i	−0.711937	−	0.711937i	0.255004	−	0.966940i	$-0.417923\pi$
$5$	−1.59194	−	1.59194i	−0.711937	−	0.711937i	−0.966940	+	0.255004i	$0.917923\pi$
$6$	2.39173	+	2.57841i	0.976418	+	1.05263i
$7$	1.33791	+	1.33791i	0.505683	+	0.505683i	0.913198	−	0.407515i	$-0.133605\pi$
$7$	1.33791	+	1.33791i	0.505683	+	0.505683i	−0.407515	+	0.913198i	$0.633605\pi$
$8$	0.176380	−	0.176380i	0.0623599	−	0.0623599i
$9$	2.99155	+	0.225050i	0.997182	+	0.0750166i
$10$			4.57130i			1.44557i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$11$	−0.707107	+	0.707107i	−0.213201	+	0.213201i
$12$	0.138011	−	3.67429i	0.0398403	−	1.06068i
$13$	−2.05741	+	2.96092i	−0.570623	+	0.821212i
$13$	−2.05741	+	2.96092i	−0.570623	+	0.821212i
$14$		−	3.84185i		−	1.02678i
$15$	2.65188	+	2.85887i	0.684713	+	0.738157i
$16$	3.73921			0.934803
$17$	5.94126			1.44097			0.720484	−	0.693471i	$-0.243920\pi$
$17$	5.94126			1.44097			0.720484	+	0.693471i	$0.243920\pi$
$18$	−3.97204	−	4.61828i	−0.936219	−	1.08854i
$19$	−2.46772	+	2.46772i	−0.566134	+	0.566134i	−0.931043	−	0.364909i	$-0.881100\pi$
$19$	−2.46772	+	2.46772i	−0.566134	+	0.566134i	0.364909	+	0.931043i	$0.381100\pi$
$20$	3.37944	−	3.37944i	0.755666	−	0.755666i
$21$	−2.22872	−	2.40268i	−0.486346	−	0.524307i
$22$	2.03048			0.432900
$23$	−0.808524			−0.168589			−0.0842944	−	0.996441i	$-0.526864\pi$
$23$	−0.808524			−0.168589			−0.0842944	+	0.996441i	$0.526864\pi$
$24$	−0.316751	+	0.293818i	−0.0646566	+	0.0599752i
$25$			0.0685372i			0.0137074i
$26$	7.20515	−	1.29723i	1.41305	−	0.254407i
$27$	−5.16323	−	0.584009i	−0.993664	−	0.112393i
$28$	−2.84018	+	2.84018i	−0.536744	+	0.536744i
$29$		−	5.12953i		−	0.952529i	−0.879302	−	0.476265i	$-0.841990\pi$
$29$		−	5.12953i		−	0.952529i	0.879302	−	0.476265i	$-0.158010\pi$
$30$	0.297190	−	7.91215i	0.0542592	−	1.44455i
$31$	6.56068	−	6.56068i	1.17833	−	1.17833i	0.198163	−	0.980169i	$-0.436502\pi$
$31$	6.56068	−	6.56068i	1.17833	−	1.17833i	0.980169	−	0.198163i	$-0.0634975\pi$
$32$	−5.72140	−	5.72140i	−1.01141	−	1.01141i
$33$	1.26985	−	1.17791i	0.221053	−	0.205048i
$34$	−8.53026	−	8.53026i	−1.46293	−	1.46293i
$35$		−	4.25974i		−	0.720028i
$36$	−0.477746	+	6.35060i	−0.0796244	+	1.05843i
$37$	5.17706	+	5.17706i	0.851104	+	0.851104i	0.990269	−	0.139166i	$-0.0444420\pi$
$37$	5.17706	+	5.17706i	0.851104	+	0.851104i	−0.139166	+	0.990269i	$0.544442\pi$
$38$	7.08614			1.14952
$39$	3.75353	−	4.99110i	0.601045	−	0.799215i
$40$	−0.561573			−0.0887925
$41$	5.79232	+	5.79232i	0.904609	+	0.904609i	0.995831	−	0.0912219i	$-0.0290773\pi$
$41$	5.79232	+	5.79232i	0.904609	+	0.904609i	−0.0912219	+	0.995831i	$0.529077\pi$
$42$	−0.249767	+	6.64960i	−0.0385399	+	1.02606i
$43$		−	6.08422i		−	0.927835i	−0.885878	−	0.463917i	$-0.846443\pi$
$43$		−	6.08422i		−	0.927835i	0.885878	−	0.463917i	$-0.153557\pi$
$44$	−1.50108	−	1.50108i	−0.226296	−	0.226296i
$45$	−4.40409	−	5.12062i	−0.656524	−	0.763338i
$46$	1.16085	+	1.16085i	0.171158	+	0.171158i
$47$	−6.46036	+	6.46036i	−0.942340	+	0.942340i	−0.998426	−	0.0560856i	$-0.982138\pi$
$47$	−6.46036	+	6.46036i	−0.942340	+	0.942340i	0.0560856	+	0.998426i	$0.482138\pi$
$48$	−6.47194	−	0.243094i	−0.934145	−	0.0350876i
$49$		−	3.41999i		−	0.488570i
$50$	0.0984033	−	0.0984033i	0.0139163	−	0.0139163i
$51$	−10.2833	−	0.386254i	−1.43995	−	0.0540864i
$52$	−6.28558	−	4.36757i	−0.871654	−	0.605673i
$53$		−	4.64016i		−	0.637376i	−0.947860	−	0.318688i	$-0.896758\pi$
$53$		−	4.64016i		−	0.637376i	0.947860	−	0.318688i	$-0.103242\pi$
$54$	6.57469	+	8.25169i	0.894702	+	1.12291i
$55$	2.25134			0.303571
$56$	0.471962			0.0630686
$57$	4.43164	−	4.11077i	0.586984	−	0.544485i
$58$	−7.36480	+	7.36480i	−0.967046	+	0.967046i
$59$	−1.07306	+	1.07306i	−0.139701	+	0.139701i	−0.773499	−	0.633798i	$-0.781495\pi$
$59$	−1.07306	+	1.07306i	−0.139701	+	0.139701i	0.633798	+	0.773499i	$0.281495\pi$
$60$	−6.06895	+	5.62954i	−0.783498	+	0.726770i
$61$	8.34079			1.06793			0.533964	−	0.845507i	$-0.320702\pi$
$61$	8.34079			1.06793			0.533964	+	0.845507i	$0.320702\pi$
$62$	−18.8392			−2.39258
$63$	3.70133	+	4.30352i	0.466323	+	0.542193i
$64$			8.95074i			1.11884i
$65$	7.98888	−	1.43833i	0.990898	−	0.178403i
$66$	−3.51442	−	0.132006i	−0.432595	−	0.0162488i
$67$	2.38684	−	2.38684i	0.291600	−	0.291600i	−0.546112	−	0.837712i	$-0.683893\pi$
$67$	2.38684	−	2.38684i	0.291600	−	0.291600i	0.837712	+	0.546112i	$0.183893\pi$
$68$			12.6124i			1.52948i
$69$	1.39942	+	0.0525638i	0.168470	+	0.00632794i
$70$	−6.11600	+	6.11600i	−0.731001	+	0.731001i
$71$	7.67850	+	7.67850i	0.911270	+	0.911270i	0.996372	−	0.0851021i	$-0.0271216\pi$
$71$	7.67850	+	7.67850i	0.911270	+	0.911270i	−0.0851021	+	0.996372i	$0.527122\pi$
$72$	0.567344	−	0.487956i	0.0668622	−	0.0575061i
$73$	2.21842	+	2.21842i	0.259647	+	0.259647i	0.824910	−	0.565264i	$-0.191226\pi$
$73$	2.21842	+	2.21842i	0.259647	+	0.259647i	−0.565264	+	0.824910i	$0.691226\pi$
$74$		−	14.8661i		−	1.72815i
$75$	0.00445574	−	0.118626i	0.000514505	−	0.0136978i
$76$	−5.23859	−	5.23859i	−0.600908	−	0.600908i
$77$	−1.89209			−0.215624
$78$	−12.5552	+	1.77686i	−1.42160	+	0.201190i
$79$	8.33607			0.937881			0.468941	−	0.883230i	$-0.344636\pi$
$79$	8.33607			0.937881			0.468941	+	0.883230i	$0.344636\pi$
$80$	−5.95260	−	5.95260i	−0.665521	−	0.665521i
$81$	8.89871	+	1.34649i	0.988745	+	0.149610i
$82$		−	16.6328i		−	1.83679i
$83$	7.81391	+	7.81391i	0.857688	+	0.857688i	0.991065	−	0.133377i	$-0.0425822\pi$
$83$	7.81391	+	7.81391i	0.857688	+	0.857688i	−0.133377	+	0.991065i	$0.542582\pi$
$84$	5.10052	−	4.73123i	0.556512	−	0.516219i
$85$	−9.45813	−	9.45813i	−1.02588	−	1.02588i
$86$	−8.73551	+	8.73551i	−0.941975	+	0.941975i
$87$	−0.333481	+	8.87834i	−0.0357529	+	0.951858i
$88$			0.249439i			0.0265903i
$89$	1.90101	−	1.90101i	0.201506	−	0.201506i	−0.599139	−	0.800645i	$-0.704490\pi$
$89$	1.90101	−	1.90101i	0.201506	−	0.201506i	0.800645	+	0.599139i	$0.204490\pi$
$90$	−1.02877	+	13.6753i	−0.108442	+	1.44150i
$91$	−6.71408	+	1.20882i	−0.703827	+	0.126718i
$92$		−	1.71637i		−	0.178944i
$93$	−11.7819	+	10.9289i	−1.22173	+	1.13327i
$94$	18.5511			1.91340
$95$	7.85692			0.806103
$96$	9.53081	+	10.2747i	0.972734	+	1.04866i
$97$	−8.73321	+	8.73321i	−0.886723	+	0.886723i	−0.994207	−	0.107484i	$-0.965721\pi$
$97$	−8.73321	+	8.73321i	−0.886723	+	0.886723i	0.107484	+	0.994207i	$0.465721\pi$
$98$	−4.91030	+	4.91030i	−0.496015	+	0.496015i
$99$	−2.27448	+	1.95621i	−0.228594	+	0.196606i
$100$	−0.145494			−0.0145494
$101$	12.3057			1.22446			0.612230	−	0.790680i	$-0.290273\pi$
$101$	12.3057			1.22446			0.612230	+	0.790680i	$0.290273\pi$
$102$	14.2099	+	15.3190i	1.40699	+	1.51681i
$103$			0.219707i			0.0216484i	0.999941	+	0.0108242i	$0.00344552\pi$
$103$			0.219707i			0.0216484i	−0.999941	+	0.0108242i	$0.996554\pi$
$104$	0.159361	+	0.885135i	0.0156267	+	0.0867946i
$105$	−0.276935	+	7.37290i	−0.0270261	+	0.719521i
$106$	−6.66219	+	6.66219i	−0.647089	+	0.647089i
$107$			19.3508i			1.87071i	0.353712	+	0.935354i	$0.384919\pi$
$107$			19.3508i			1.87071i	−0.353712	+	0.935354i	$0.615081\pi$
$108$	1.23976	−	10.9607i	0.119296	−	1.05470i
$109$	8.98090	−	8.98090i	0.860214	−	0.860214i	−0.131149	−	0.991363i	$-0.541867\pi$
$109$	8.98090	−	8.98090i	0.860214	−	0.860214i	0.991363	+	0.131149i	$0.0418665\pi$
$110$	−3.23240	−	3.23240i	−0.308197	−	0.308197i
$111$	−8.62404	−	9.29718i	−0.818558	−	0.882450i
$112$	5.00274	+	5.00274i	0.472714	+	0.472714i
$113$		−	7.35849i		−	0.692228i	−0.938192	−	0.346114i	$-0.887501\pi$
$113$		−	7.35849i		−	0.692228i	0.938192	−	0.346114i	$-0.112499\pi$
$114$	−12.2649	−	0.460684i	−1.14871	−	0.0431470i
$115$	1.28712	+	1.28712i	0.120025	+	0.120025i
$116$	10.8892			1.01104
$117$	−6.82120	+	8.39472i	−0.630620	+	0.776092i
$118$	3.08134			0.283660
$119$	7.94888	+	7.94888i	0.728673	+	0.728673i
$120$	0.971988	+	0.0365090i	0.0887299	+	0.00333280i
$121$		−	1.00000i		−	0.0909091i
$122$	−11.9754	−	11.9754i	−1.08420	−	1.08420i
$123$	−9.64895	−	10.4021i	−0.870017	−	0.937925i
$124$	13.9273	+	13.9273i	1.25071	+	1.25071i
$125$	−7.85059	+	7.85059i	−0.702178	+	0.702178i
$126$	0.864608	−	11.4931i	0.0770254	−	1.02389i
$127$			16.6392i			1.47649i	0.674533	+	0.738245i	$0.264345\pi$
$127$			16.6392i			1.47649i	−0.674533	+	0.738245i	$0.735655\pi$
$128$	1.40838	−	1.40838i	0.124484	−	0.124484i
$129$	−0.395548	+	10.5308i	−0.0348260	+	0.927181i
$130$	−13.5353	−	9.40505i	−1.18712	−	0.824878i
$131$		−	9.24333i		−	0.807593i	−0.914849	−	0.403797i	$-0.867690\pi$
$131$		−	9.24333i		−	0.807593i	0.914849	−	0.403797i	$-0.132310\pi$
$132$	2.50053	+	2.69570i	0.217643	+	0.234631i
$133$	−6.60318			−0.572568
$134$	−6.85390			−0.592087
$135$	7.28984	+	9.14925i	0.627409	+	0.787442i
$136$	1.04792	−	1.04792i	0.0898586	−	0.0898586i
$137$	10.7552	−	10.7552i	0.918877	−	0.918877i	−0.0780704	−	0.996948i	$-0.524876\pi$
$137$	10.7552	−	10.7552i	0.918877	−	0.918877i	0.996948	+	0.0780704i	$0.0248759\pi$
$138$	−1.93377	−	2.08471i	−0.164613	−	0.177462i
$139$	10.3460			0.877534			0.438767	−	0.898601i	$-0.355415\pi$
$139$	10.3460			0.877534			0.438767	+	0.898601i	$0.355415\pi$
$140$	9.04279			0.764255
$141$	11.6018	−	10.7618i	0.977047	−	0.906306i
$142$		−	22.0491i		−	1.85032i
$143$	−0.638878	−	3.54850i	−0.0534256	−	0.296740i
$144$	11.1860	+	0.841509i	0.932169	+	0.0701257i
$145$	−8.16589	+	8.16589i	−0.678141	+	0.678141i
$146$		−	6.37027i		−	0.527207i
$147$	−0.222340	+	5.91942i	−0.0183383	+	0.488225i
$148$	−10.9901	+	10.9901i	−0.903381	+	0.903381i
$149$	−2.11903	−	2.11903i	−0.173597	−	0.173597i	0.614960	−	0.788558i	$-0.289172\pi$
$149$	−2.11903	−	2.11903i	−0.173597	−	0.173597i	−0.788558	+	0.614960i	$0.789172\pi$
$150$	−0.176717	+	0.163922i	−0.0144289	+	0.0133842i
$151$	−0.534299	−	0.534299i	−0.0434806	−	0.0434806i	0.685032	−	0.728513i	$-0.259788\pi$
$151$	−0.534299	−	0.534299i	−0.0434806	−	0.0434806i	−0.728513	+	0.685032i	$0.759788\pi$
$152$			0.870514i			0.0706080i
$153$	17.7736	+	1.33708i	1.43691	+	0.108096i
$154$	2.71660	+	2.71660i	0.218910	+	0.218910i
$155$	−20.8884			−1.67780
$156$	10.5953	+	7.96816i	0.848306	+	0.637964i
$157$	14.0635			1.12239			0.561194	−	0.827684i	$-0.310342\pi$
$157$	14.0635			1.12239			0.561194	+	0.827684i	$0.310342\pi$
$158$	−11.9686	−	11.9686i	−0.952174	−	0.952174i
$159$	−0.301667	+	8.03134i	−0.0239237	+	0.636926i
$160$			18.2162i			1.44012i
$161$	−1.08173	−	1.08173i	−0.0852525	−	0.0852525i
$162$	−10.8432	−	14.7097i	−0.851923	−	1.15570i
$163$	−9.22582	−	9.22582i	−0.722622	−	0.722622i	0.246517	−	0.969139i	$-0.420714\pi$
$163$	−9.22582	−	9.22582i	−0.722622	−	0.722622i	−0.969139	+	0.246517i	$0.920714\pi$
$164$	−12.2962	+	12.2962i	−0.960173	+	0.960173i
$165$	−3.89669	−	0.146364i	−0.303357	−	0.0113944i
$166$		−	22.4379i		−	1.74152i
$167$	7.87009	−	7.87009i	0.609006	−	0.609006i	−0.333680	−	0.942686i	$-0.608291\pi$
$167$	7.87009	−	7.87009i	0.609006	−	0.609006i	0.942686	+	0.333680i	$0.108291\pi$
$168$	−0.816887	−	0.0306832i	−0.0630242	−	0.00236726i
$169$	−4.53411	−	12.1837i	−0.348778	−	0.937205i
$170$			27.1593i			2.08302i
$171$	−7.93766	+	6.82694i	−0.607008	+	0.522069i
$172$	12.9159			0.984826
$173$	4.50776			0.342719			0.171359	−	0.985209i	$-0.445184\pi$
$173$	4.50776			0.342719			0.171359	+	0.985209i	$0.445184\pi$
$174$	13.2260	−	12.2684i	1.00266	−	0.930067i
$175$	−0.0916966	+	0.0916966i	−0.00693161	+	0.00693161i
$176$	−2.64402	+	2.64402i	−0.199301	+	0.199301i
$177$	1.92706	−	1.78753i	0.144846	−	0.134359i
$178$	−5.45880			−0.409154
$179$	−19.9301			−1.48964			−0.744821	−	0.667264i	$-0.767465\pi$
$179$	−19.9301			−1.48964			−0.744821	+	0.667264i	$0.767465\pi$
$180$	10.8703	−	9.34922i	0.810225	−	0.696850i
$181$		−	0.659700i		−	0.0490351i	−0.999699	−	0.0245176i	$-0.992195\pi$
$181$		−	0.659700i		−	0.0490351i	0.999699	−	0.0245176i	$-0.00780497\pi$
$182$	11.3754	+	7.90428i	0.843203	+	0.585904i
$183$	−14.4365	−	0.542252i	−1.06718	−	0.0400844i
$184$	−0.142608	+	0.142608i	−0.0105132	+	0.0105132i
$185$		−	16.4831i		−	1.21186i
$186$	32.6074	+	1.22477i	2.39089	+	0.0898048i
$187$	−4.20111	+	4.20111i	−0.307215	+	0.307215i
$188$	−13.7144	−	13.7144i	−1.00022	−	1.00022i
$189$	−6.12659	−	7.68929i	−0.445644	−	0.559314i
$190$	−11.2807	−	11.2807i	−0.818387	−	0.818387i
$191$			9.84556i			0.712399i	0.934410	+	0.356200i	$0.115928\pi$
$191$			9.84556i			0.712399i	−0.934410	+	0.356200i	$0.884072\pi$
$192$	0.581906	−	15.4922i	0.0419955	−	1.11805i
$193$	−16.1341	−	16.1341i	−1.16136	−	1.16136i	−0.984179	−	0.177176i	$-0.943304\pi$
$193$	−16.1341	−	16.1341i	−1.16136	−	1.16136i	−0.177176	−	0.984179i	$-0.556696\pi$
$194$	25.0777			1.80047
$195$	−13.9209	+	1.97013i	−0.996897	+	0.141084i
$196$	7.26011			0.518579
$197$	−0.879493	−	0.879493i	−0.0626613	−	0.0626613i	0.675082	−	0.737743i	$-0.264108\pi$
$197$	−0.879493	−	0.879493i	−0.0626613	−	0.0626613i	−0.737743	+	0.675082i	$0.764108\pi$
$198$	6.07427	+	0.456959i	0.431680	+	0.0324746i
$199$		−	6.49836i		−	0.460657i	−0.973113	−	0.230328i	$-0.926020\pi$
$199$		−	6.49836i		−	0.460657i	0.973113	−	0.230328i	$-0.0739800\pi$
$200$	0.0120886	+	0.0120886i	0.000854793	+	0.000854793i
$201$	−4.28640	+	3.97605i	−0.302339	+	0.280449i
$202$	−17.6681	−	17.6681i	−1.24312	−	1.24312i
$203$	6.86285	−	6.86285i	0.481678	−	0.481678i
$204$	0.819958	−	21.8299i	0.0574085	−	1.52840i
$205$		−	18.4420i		−	1.28805i
$206$	0.315449	−	0.315449i	0.0219783	−	0.0219783i
$207$	−2.41874	−	0.181958i	−0.168114	−	0.0126470i
$208$	−7.69310	+	11.0715i	−0.533421	+	0.767672i
$209$		−	3.48988i		−	0.241400i
$210$	10.9834	−	10.1881i	0.757924	−	0.703048i
$211$	−21.8200			−1.50215			−0.751076	−	0.660216i	$-0.770465\pi$
$211$	−21.8200			−1.50215			−0.751076	+	0.660216i	$0.770465\pi$
$212$	9.85036			0.676526
$213$	−12.7910	−	13.7894i	−0.876424	−	0.944832i
$214$	27.7832	−	27.7832i	1.89922	−	1.89922i
$215$	−9.68570	+	9.68570i	−0.660560	+	0.660560i
$216$	−1.01370	+	0.807684i	−0.0689735	+	0.0549559i
$217$	17.5552			1.19172
$218$	−25.7889			−1.74665
$219$	−3.69549	−	3.98393i	−0.249718	−	0.269209i
$220$			4.77925i			0.322217i
$221$	−12.2236	+	17.5916i	−0.822250	+	1.18334i
$222$	−0.966475	+	25.7307i	−0.0648656	+	1.72693i
$223$	−4.85663	+	4.85663i	−0.325224	+	0.325224i	−0.850767	−	0.525543i	$-0.823862\pi$
$223$	−4.85663	+	4.85663i	−0.325224	+	0.325224i	0.525543	+	0.850767i	$0.323862\pi$
$224$		−	15.3094i		−	1.02290i
$225$	−0.0154243	+	0.205032i	−0.00102828	+	0.0136688i
$226$	−10.5651	+	10.5651i	−0.702778	+	0.702778i
$227$	8.99284	+	8.99284i	0.596876	+	0.596876i	0.939480	−	0.342604i	$-0.111309\pi$
$227$	8.99284	+	8.99284i	0.596876	+	0.596876i	−0.342604	+	0.939480i	$0.611309\pi$
$228$	8.72654	+	9.40769i	0.577929	+	0.623039i
$229$	−0.967793	−	0.967793i	−0.0639536	−	0.0639536i	0.674407	−	0.738360i	$-0.264400\pi$
$229$	−0.967793	−	0.967793i	−0.0639536	−	0.0639536i	−0.738360	+	0.674407i	$0.764400\pi$
$230$		−	3.69601i		−	0.243707i
$231$	3.27489	+	0.123009i	0.215472	+	0.00809339i
$232$	−0.904748	−	0.904748i	−0.0593996	−	0.0593996i
$233$	18.1180			1.18695			0.593473	−	0.804854i	$-0.297756\pi$
$233$	18.1180			1.18695			0.593473	+	0.804854i	$0.297756\pi$
$234$	21.8465	−	2.25920i	1.42815	−	0.147689i
$235$	20.5690			1.34177
$236$	−2.27795	−	2.27795i	−0.148282	−	0.148282i
$237$	−14.4283	−	0.541945i	−0.937220	−	0.0352031i
$238$		−	22.8255i		−	1.47956i
$239$	1.80992	+	1.80992i	0.117074	+	0.117074i	0.763217	−	0.646143i	$-0.223619\pi$
$239$	1.80992	+	1.80992i	0.117074	+	0.117074i	−0.646143	+	0.763217i	$0.723619\pi$
$240$	9.91595	+	10.6899i	0.640072	+	0.690032i
$241$	−0.298552	−	0.298552i	−0.0192314	−	0.0192314i	0.697426	−	0.716657i	$-0.254329\pi$
$241$	−0.298552	−	0.298552i	−0.0192314	−	0.0192314i	−0.716657	+	0.697426i	$0.754329\pi$
$242$	−1.43577	+	1.43577i	−0.0922945	+	0.0922945i
$243$	−15.3146	−	2.90907i	−0.982433	−	0.186617i
$244$			17.7062i			1.13352i
$245$	−5.44441	+	5.44441i	−0.347831	+	0.347831i
$246$	−1.08133	+	28.7886i	−0.0689434	+	1.83550i
$247$	−2.22961	−	12.3838i	−0.141867	−	0.787965i
$248$		−	2.31435i		−	0.146961i
$249$	−13.0166	−	14.0326i	−0.824891	−	0.889277i
$250$	22.5432			1.42576
$251$	19.7624			1.24739			0.623695	−	0.781667i	$-0.285631\pi$
$251$	19.7624			1.24739			0.623695	+	0.781667i	$0.285631\pi$
$252$	−9.13572	+	7.85735i	−0.575496	+	0.494967i
$253$	0.571713	−	0.571713i	0.0359433	−	0.0359433i
$254$	23.8900	−	23.8900i	1.49899	−	1.49899i
$255$	15.7555	+	16.9853i	0.986649	+	1.06366i
$256$	13.8573			0.866080
$257$	−5.28192			−0.329477			−0.164739	−	0.986337i	$-0.552678\pi$
$257$	−5.28192			−0.329477			−0.164739	+	0.986337i	$0.552678\pi$
$258$	15.6876	−	14.5518i	0.976668	−	0.905954i
$259$			13.8529i			0.860777i
$260$	3.05336	+	16.9592i	0.189361	+	1.05176i
$261$	1.15440	−	15.3452i	0.0714555	−	0.949845i
$262$	−13.2713	+	13.2713i	−0.819901	+	0.819901i
$263$		−	1.25809i		−	0.0775772i	−0.999247	−	0.0387886i	$-0.987650\pi$
$263$		−	1.25809i		−	0.0775772i	0.999247	−	0.0387886i	$-0.0123499\pi$
$264$	0.0162166	−	0.431737i	0.000998061	−	0.0265716i
$265$	−7.38686	+	7.38686i	−0.453771	+	0.453771i
$266$	9.48062	+	9.48062i	0.581294	+	0.581294i
$267$	−3.41391	+	3.16673i	−0.208928	+	0.193801i
$268$	5.06691	+	5.06691i	0.309511	+	0.309511i
$269$			10.7370i			0.654648i	0.944912	+	0.327324i	$0.106147\pi$
$269$			10.7370i			0.654648i	−0.944912	+	0.327324i	$0.893853\pi$
$270$	2.66968	−	23.6027i	0.162472	−	1.43641i
$271$	12.4997	+	12.4997i	0.759306	+	0.759306i	0.976196	−	0.216890i	$-0.0695914\pi$
$271$	12.4997	+	12.4997i	0.759306	+	0.759306i	−0.216890	+	0.976196i	$0.569591\pi$
$272$	22.2157			1.34702
$273$	11.6995	−	1.65576i	0.708088	−	0.100211i
$274$	−30.8839			−1.86576
$275$	−0.0484631	−	0.0484631i	−0.00292243	−	0.00292243i
$276$	−0.111585	+	2.97075i	−0.00671662	+	0.178818i
$277$			28.1615i			1.69206i	0.533136	+	0.846030i	$0.321014\pi$
$277$			28.1615i			1.69206i	−0.533136	+	0.846030i	$0.678986\pi$
$278$	−14.8544	−	14.8544i	−0.890908	−	0.890908i
$279$	21.1030	−	18.1501i	1.26341	−	1.08662i
$280$	−0.751335	−	0.751335i	−0.0449009	−	0.0449009i
$281$	−1.96439	+	1.96439i	−0.117185	+	0.117185i	−0.763268	−	0.646082i	$-0.776406\pi$
$281$	−1.96439	+	1.96439i	−0.117185	+	0.117185i	0.646082	+	0.763268i	$0.276406\pi$
$282$	−32.1089	−	1.20605i	−1.91205	−	0.0718191i
$283$			12.6405i			0.751399i	0.926741	+	0.375700i	$0.122598\pi$
$283$			12.6405i			0.751399i	−0.926741	+	0.375700i	$0.877402\pi$
$284$	−16.3003	+	16.3003i	−0.967244	+	0.967244i
$285$	−13.5990	−	0.510794i	−0.805535	−	0.0302568i
$286$	−4.17753	+	6.01209i	−0.247023	+	0.355502i
$287$			15.4992i			0.914890i
$288$	−15.8282	−	18.4034i	−0.932687	−	1.08443i
$289$	18.2986			1.07639
$290$	23.4486			1.37695
$291$	15.6835	−	14.5479i	0.919381	−	0.852815i
$292$	−4.70937	+	4.70937i	−0.275595	+	0.275595i
$293$	5.21608	−	5.21608i	0.304727	−	0.304727i	−0.538133	−	0.842860i	$-0.680870\pi$
$293$	5.21608	−	5.21608i	0.304727	−	0.304727i	0.842860	+	0.538133i	$0.180870\pi$
$294$	8.81813	−	8.17967i	0.514284	−	0.477048i
$295$	3.41651			0.198917
$296$	1.82626			0.106149
$297$	4.06391	−	3.23800i	0.235812	−	0.187888i
$298$			6.08485i			0.352486i
$299$	1.66347	−	2.39398i	0.0962008	−	0.138447i
$300$	0.251825	+	0.00945886i	0.0145391	+	0.000546108i
$301$	8.14014	−	8.14014i	0.469190	−	0.469190i
$302$			1.53426i			0.0882865i
$303$	−21.2990	−	0.800017i	−1.22360	−	0.0459598i
$304$	−9.22733	+	9.22733i	−0.529224	+	0.529224i
$305$	−13.2780	−	13.2780i	−0.760297	−	0.760297i
$306$	−23.5990	−	27.4384i	−1.34906	−	1.56855i
$307$	17.3917	+	17.3917i	0.992595	+	0.992595i	0.999973	−	0.00737737i	$-0.00234831\pi$
$307$	17.3917	+	17.3917i	0.992595	+	0.992595i	−0.00737737	+	0.999973i	$0.502348\pi$
$308$		−	4.01662i		−	0.228868i
$309$	0.0142836	−	0.380276i	0.000812568	−	0.0216332i
$310$	29.9908	+	29.9908i	1.70336	+	1.70336i
$311$	4.35195			0.246776			0.123388	−	0.992358i	$-0.460624\pi$
$311$	4.35195			0.246776			0.123388	+	0.992358i	$0.460624\pi$
$312$	−0.218283	−	1.54238i	−0.0123578	−	0.0873200i
$313$	−14.1848			−0.801771			−0.400885	−	0.916128i	$-0.631297\pi$
$313$	−14.1848			−0.801771			−0.400885	+	0.916128i	$0.631297\pi$
$314$	−20.1919	−	20.1919i	−1.13949	−	1.13949i
$315$	0.958654	−	12.7432i	0.0540140	−	0.717999i
$316$			17.6962i			0.995490i
$317$	−22.1988	−	22.1988i	−1.24681	−	1.24681i	−0.957120	−	0.289691i	$-0.906447\pi$
$317$	−22.1988	−	22.1988i	−1.24681	−	1.24681i	−0.289691	−	0.957120i	$-0.593553\pi$
$318$	11.9642	−	11.0980i	0.670921	−	0.622345i
$319$	3.62712	+	3.62712i	0.203080	+	0.203080i
$320$	14.2490	−	14.2490i	0.796545	−	0.796545i
$321$	1.25803	−	33.4929i	0.0702165	−	1.86939i
$322$			3.10623i			0.173103i
$323$	−14.6614	+	14.6614i	−0.815781	+	0.815781i
$324$	−2.85840	+	18.8906i	−0.158800	+	1.04948i
$325$	−0.202933	−	0.141009i	−0.0112567	−	0.00782178i
$326$			26.4922i			1.46727i
$327$	−16.1283	+	14.9605i	−0.891896	+	0.827320i
$328$	2.04330			0.112823
$329$	−17.2868			−0.953051
$330$	5.38459	+	5.80488i	0.296412	+	0.319548i
$331$	−20.1546	+	20.1546i	−1.10780	+	1.10780i	−0.114359	+	0.993439i	$0.536481\pi$
$331$	−20.1546	+	20.1546i	−1.10780	+	1.10780i	−0.993439	+	0.114359i	$0.963519\pi$
$332$	−16.5877	+	16.5877i	−0.910371	+	0.910371i
$333$	14.3223	+	16.6525i	0.784858	+	0.912552i
$334$	−22.5992			−1.23657
$335$	−7.59942			−0.415201
$336$	−8.33365	−	8.98412i	−0.454638	−	0.490124i
$337$		−	25.4303i		−	1.38528i	−0.721284	−	0.692639i	$-0.756448\pi$
$337$		−	25.4303i		−	1.38528i	0.721284	−	0.692639i	$-0.243552\pi$
$338$	−10.9830	+	24.0028i	−0.597395	+	1.30558i
$339$	−0.478390	+	12.7363i	−0.0259826	+	0.691740i
$340$	20.0782	−	20.0782i	1.08889	−	1.08889i
$341$			9.27820i			0.502442i
$342$	21.1985	+	1.59473i	1.14628	+	0.0862333i
$343$	13.9410	−	13.9410i	0.752744	−	0.752744i
$344$	−1.07314	−	1.07314i	−0.0578596	−	0.0578596i
$345$	−2.14411	−	2.31147i	−0.115435	−	0.124445i
$346$	−6.47209	−	6.47209i	−0.347942	−	0.347942i
$347$		−	10.5051i		−	0.563942i	−0.959423	−	0.281971i	$-0.909012\pi$
$347$		−	10.5051i		−	0.563942i	0.959423	−	0.281971i	$-0.0909882\pi$
$348$	−18.8474	−	0.707930i	−1.01032	−	0.0379490i
$349$	−11.1101	−	11.1101i	−0.594709	−	0.594709i	0.344191	−	0.938900i	$-0.388153\pi$
$349$	−11.1101	−	11.1101i	−0.594709	−	0.594709i	−0.938900	+	0.344191i	$0.888153\pi$
$350$	0.263310			0.0140745
$351$	12.3521	−	14.0864i	0.659306	−	0.751875i
$352$	8.09128			0.431266
$353$	12.9257	+	12.9257i	0.687967	+	0.687967i	0.961782	−	0.273815i	$-0.0882857\pi$
$353$	12.9257	+	12.9257i	0.687967	+	0.687967i	−0.273815	+	0.961782i	$0.588286\pi$
$354$	−5.33328	−	0.200324i	−0.283460	−	0.0106471i
$355$		−	24.4474i		−	1.29753i
$356$	4.03555	+	4.03555i	0.213884	+	0.213884i
$357$	−13.2414	−	14.2749i	−0.700809	−	0.755510i
$358$	28.6149	+	28.6149i	1.51234	+	1.51234i
$359$	5.05627	−	5.05627i	0.266860	−	0.266860i	−0.560974	−	0.827834i	$-0.689573\pi$
$359$	5.05627	−	5.05627i	0.266860	−	0.266860i	0.827834	+	0.560974i	$0.189573\pi$
$360$	−1.67997	−	0.126382i	−0.0885423	−	0.00666091i
$361$			6.82072i			0.358985i
$362$	−0.947175	+	0.947175i	−0.0497824	+	0.0497824i
$363$	−0.0650121	+	1.73083i	−0.00341225	+	0.0908450i
$364$	−2.56613	−	14.2530i	−0.134502	−	0.747059i
$365$		−	7.06318i		−	0.369704i
$366$	19.9489	+	21.5060i	1.04274	+	1.12413i
$367$	−11.3223			−0.591019			−0.295510	−	0.955340i	$-0.595489\pi$
$367$	−11.3223			−0.591019			−0.295510	+	0.955340i	$0.595489\pi$
$368$	−3.02324			−0.157597
$369$	16.0244	+	18.6316i	0.834199	+	0.969920i
$370$	−23.6659	+	23.6659i	−1.23033	+	1.23033i
$371$	6.20813	−	6.20813i	0.322310	−	0.322310i
$372$	−23.2004	−	25.0113i	−1.20288	−	1.29677i
$373$	20.7274			1.07322			0.536612	−	0.843829i	$-0.319704\pi$
$373$	20.7274			1.07322			0.536612	+	0.843829i	$0.319704\pi$
$374$	12.0636			0.623795
$375$	14.0984	−	13.0776i	0.728039	−	0.675327i
$376$			2.27896i			0.117528i
$377$	15.1881	+	10.5536i	0.782228	+	0.543536i
$378$	−2.24368	+	19.8364i	−0.115402	+	1.02027i
$379$	−9.54285	+	9.54285i	−0.490183	+	0.490183i	−0.908364	−	0.418181i	$-0.862668\pi$
$379$	−9.54285	+	9.54285i	−0.490183	+	0.490183i	0.418181	+	0.908364i	$0.362668\pi$
$380$			16.6790i			0.855616i
$381$	1.08175	−	28.7996i	0.0554196	−	1.47545i
$382$	14.1359	−	14.1359i	0.723256	−	0.723256i
$383$	−11.0397	−	11.0397i	−0.564105	−	0.564105i	0.366366	−	0.930471i	$-0.380602\pi$
$383$	−11.0397	−	11.0397i	−0.564105	−	0.564105i	−0.930471	+	0.366366i	$0.880602\pi$
$384$	−2.52923	+	2.34611i	−0.129069	+	0.119724i
$385$	3.01209	+	3.01209i	0.153511	+	0.153511i
$386$			46.3295i			2.35811i
$387$	1.36925	−	18.2012i	0.0696030	−	0.925220i
$388$	−18.5393	−	18.5393i	−0.941189	−	0.941189i
$389$	29.8511			1.51351			0.756757	−	0.653697i	$-0.226783\pi$
$389$	29.8511			1.51351			0.756757	+	0.653697i	$0.226783\pi$
$390$	22.8158	+	17.1585i	1.15532	+	0.868855i
$391$	−4.80365			−0.242931
$392$	−0.603218	−	0.603218i	−0.0304671	−	0.0304671i
$393$	−0.600928	+	15.9986i	−0.0303128	+	0.807024i
$394$			2.52549i			0.127232i
$395$	−13.2705	−	13.2705i	−0.667712	−	0.667712i
$396$	−4.15273	−	4.82837i	−0.208683	−	0.242635i
$397$	18.0127	+	18.0127i	0.904030	+	0.904030i	0.995782	−	0.0917522i	$-0.0292468\pi$
$397$	18.0127	+	18.0127i	0.904030	+	0.904030i	−0.0917522	+	0.995782i	$0.529247\pi$
$398$	−9.33013	+	9.33013i	−0.467677	+	0.467677i
$399$	11.4290	+	0.429286i	0.572165	+	0.0214912i
$400$			0.256275i			0.0128138i
$401$	0.856457	−	0.856457i	0.0427694	−	0.0427694i	−0.685399	−	0.728168i	$-0.740372\pi$
$401$	0.856457	−	0.856457i	0.0427694	−	0.0427694i	0.728168	+	0.685399i	$0.240372\pi$
$402$	11.8629	+	0.445586i	0.591670	+	0.0222238i
$403$	5.92763	+	32.9237i	0.295276	+	1.64004i
$404$			26.1231i			1.29967i
$405$	−12.0227	−	16.3097i	−0.597411	−	0.810437i
$406$	−19.7069			−0.978037
$407$	−7.32147			−0.362912
$408$	−1.88190	+	1.74565i	−0.0931681	+	0.0864224i
$409$	−12.7740	+	12.7740i	−0.631635	+	0.631635i	−0.948478	−	0.316843i	$-0.897377\pi$
$409$	−12.7740	+	12.7740i	−0.631635	+	0.631635i	0.316843	+	0.948478i	$0.397377\pi$
$410$	−26.4785	+	26.4785i	−1.30768	+	1.30768i
$411$	−19.3146	+	17.9162i	−0.952720	+	0.883740i
$412$	−0.466405			−0.0229781
$413$	−2.87133			−0.141289
$414$	3.21149	+	3.73399i	0.157836	+	0.183516i
$415$		−	24.8785i		−	1.22124i
$416$	28.7119	−	5.16934i	1.40772	−	0.253448i
$417$	−17.9071	−	0.672613i	−0.876916	−	0.0329380i
$418$	−5.01065	+	5.01065i	−0.245079	+	0.245079i
$419$			29.8330i			1.45744i	0.684814	+	0.728718i	$0.259883\pi$
$419$			29.8330i			1.45744i	−0.684814	+	0.728718i	$0.740117\pi$
$420$	−15.6515	−	0.587890i	−0.763717	−	0.0286861i
$421$	−13.5610	+	13.5610i	−0.660923	+	0.660923i	−0.955598	−	0.294674i	$-0.904789\pi$
$421$	−13.5610	+	13.5610i	−0.660923	+	0.660923i	0.294674	+	0.955598i	$0.404789\pi$
$422$	31.3284	+	31.3284i	1.52504	+	1.52504i
$423$	−20.7804	+	17.8726i	−1.01038	+	0.868994i
$424$	−0.818434	−	0.818434i	−0.0397466	−	0.0397466i
$425$			0.407197i			0.0197520i
$426$	−1.43345	+	38.1632i	−0.0694511	+	1.84901i
$427$	11.1592	+	11.1592i	0.540033	+	0.540033i
$428$	−41.0787			−1.98561
$429$	0.875094	+	6.18338i	0.0422499	+	0.298536i
$430$	27.8128			1.34125
$431$	−8.09111	−	8.09111i	−0.389735	−	0.389735i	0.484858	−	0.874593i	$-0.338871\pi$
$431$	−8.09111	−	8.09111i	−0.389735	−	0.389735i	−0.874593	+	0.484858i	$0.838871\pi$
$432$	−19.3064	−	2.18374i	−0.928880	−	0.105065i
$433$			2.38252i			0.114497i	0.998360	+	0.0572484i	$0.0182327\pi$
$433$			2.38252i			0.114497i	−0.998360	+	0.0572484i	$0.981767\pi$
$434$	−25.2052	−	25.2052i	−1.20989	−	1.20989i
$435$	14.6647	−	13.6029i	0.703116	−	0.652209i
$436$	19.0651	+	19.0651i	0.913052	+	0.913052i
$437$	1.99521	−	1.99521i	0.0954438	−	0.0954438i
$438$	−0.414144	+	11.0259i	−0.0197886	+	0.526836i
$439$			23.3582i			1.11483i	0.830236	+	0.557413i	$0.188206\pi$
$439$			23.3582i			1.11483i	−0.830236	+	0.557413i	$0.811794\pi$
$440$	0.397092	−	0.397092i	0.0189306	−	0.0189306i
$441$	0.769667	−	10.2311i	0.0366508	−	0.487193i
$442$	42.8077	−	7.70717i	2.03616	−	0.366593i
$443$		−	32.6213i		−	1.54989i	−0.632032	−	0.774943i	$-0.717779\pi$
$443$		−	32.6213i		−	1.54989i	0.632032	−	0.774943i	$-0.282221\pi$
$444$	19.7365	−	18.3075i	0.936653	−	0.868837i
$445$	−6.05257			−0.286919
$446$	13.9460			0.660360
$447$	3.52991	+	3.80544i	0.166959	+	0.179991i
$448$	−11.9753	+	11.9753i	−0.565780	+	0.565780i
$449$	−14.7169	+	14.7169i	−0.694534	+	0.694534i	−0.963226	−	0.268692i	$-0.913409\pi$
$449$	−14.7169	+	14.7169i	−0.694534	+	0.694534i	0.268692	+	0.963226i	$0.413409\pi$
$450$	0.316524	−	0.272232i	0.0149211	−	0.0128332i
$451$	−8.19158			−0.385726
$452$	15.6209			0.734748
$453$	0.890045	+	0.959516i	0.0418179	+	0.0450820i
$454$		−	25.8232i		−	1.21194i
$455$	12.6128	+	8.76405i	0.591296	+	0.410865i
$456$	0.0565939	−	1.50671i	0.00265025	−	0.0705583i
$457$	21.8413	−	21.8413i	1.02169	−	1.02169i	0.0219331	−	0.999759i	$-0.493018\pi$
$457$	21.8413	−	21.8413i	1.02169	−	1.02169i	0.999759	−	0.0219331i	$-0.00698209\pi$
$458$			2.77905i			0.129856i
$459$	−30.6761	−	3.46975i	−1.43184	−	0.161954i
$460$	−2.73236	+	2.73236i	−0.127397	+	0.127397i
$461$	−26.2030	−	26.2030i	−1.22039	−	1.22039i	−0.967492	−	0.252901i	$-0.918615\pi$
$461$	−26.2030	−	26.2030i	−1.22039	−	1.22039i	−0.252901	−	0.967492i	$-0.581385\pi$
$462$	−4.52536	−	4.87859i	−0.210539	−	0.226972i
$463$	−18.0526	−	18.0526i	−0.838976	−	0.838976i	0.149748	−	0.988724i	$-0.452154\pi$
$463$	−18.0526	−	18.0526i	−0.838976	−	0.838976i	−0.988724	+	0.149748i	$0.952154\pi$
$464$		−	19.1804i		−	0.890428i
$465$	36.1542	+	1.35800i	1.67661	+	0.0629756i
$466$	−26.0131	−	26.0131i	−1.20504	−	1.20504i
$467$	−9.23398			−0.427298			−0.213649	−	0.976911i	$-0.568535\pi$
$467$	−9.23398			−0.427298			−0.213649	+	0.976911i	$0.568535\pi$
$468$	−17.8207	−	14.4804i	−0.823762	−	0.669355i
$469$	6.38677			0.294914
$470$	−29.5323	−	29.5323i	−1.36222	−	1.36222i
$471$	−24.3415	−	0.914297i	−1.12160	−	0.0421286i
$472$			0.378535i			0.0174235i
$473$	4.30219	+	4.30219i	0.197815	+	0.197815i
$474$	19.9376	+	21.4938i	0.915764	+	0.987243i
$475$	−0.169130	−	0.169130i	−0.00776024	−	0.00776024i
$476$	−16.8743	+	16.8743i	−0.773431	+	0.773431i
$477$	1.04427	−	13.8813i	0.0478137	−	0.635580i
$478$		−	5.19725i		−	0.237717i
$479$	−7.27499	+	7.27499i	−0.332403	+	0.332403i	−0.853498	−	0.521096i	$-0.825523\pi$
$479$	−7.27499	+	7.27499i	−0.332403	+	0.332403i	0.521096	+	0.853498i	$0.325523\pi$
$480$	1.18427	−	31.5292i	0.0540545	−	1.43910i
$481$	−25.9802	+	4.67752i	−1.18460	+	0.213277i
$482$			0.857302i			0.0390490i
$483$	1.80197	+	1.94262i	0.0819925	+	0.0883924i
$484$	2.12285			0.0964931
$485$	27.8055			1.26258
$486$	17.8114	+	26.1649i	0.807944	+	1.18687i
$487$	−3.72175	+	3.72175i	−0.168648	+	0.168648i	−0.786385	−	0.617737i	$-0.788050\pi$
$487$	−3.72175	+	3.72175i	−0.168648	+	0.168648i	0.617737	+	0.786385i	$0.288050\pi$
$488$	1.47115	−	1.47115i	0.0665959	−	0.0665959i
$489$	15.3685	+	16.5681i	0.694989	+	0.749236i
$490$	15.6338			0.706263
$491$	17.5271			0.790985			0.395493	−	0.918469i	$-0.370574\pi$
$491$	17.5271			0.790985			0.395493	+	0.918469i	$0.370574\pi$
$492$	22.0821	−	20.4833i	0.995536	−	0.923457i
$493$		−	30.4759i		−	1.37256i
$494$	−14.5791	+	20.9815i	−0.655945	+	0.944002i
$495$	6.73499	+	0.506664i	0.302715	+	0.0227728i
$496$	24.5318	−	24.5318i	1.10151	−	1.10151i
$497$			20.5463i			0.921627i
$498$	−1.45873	+	38.8362i	−0.0653674	+	1.74029i
$499$	16.8825	−	16.8825i	0.755763	−	0.755763i	−0.219786	−	0.975548i	$-0.570536\pi$
$499$	16.8825	−	16.8825i	0.755763	−	0.755763i	0.975548	+	0.219786i	$0.0705358\pi$
$500$	−16.6656	−	16.6656i	−0.745308	−	0.745308i
$501$	−14.1334	+	13.1101i	−0.631436	+	0.585718i
$502$	−28.3742	−	28.3742i	−1.26640	−	1.26640i
$503$		−	4.61727i		−	0.205874i	−0.994688	−	0.102937i	$-0.967176\pi$
$503$		−	4.61727i		−	0.205874i	0.994688	−	0.102937i	$-0.0328240\pi$
$504$	1.41190	+	0.106215i	0.0628909	+	0.00473119i
$505$	−19.5899	−	19.5899i	−0.871738	−	0.871738i
$506$	−1.64169			−0.0729821
$507$	7.05569	+	21.3826i	0.313354	+	0.949636i
$508$	−35.3225			−1.56718
$509$	−9.55041	−	9.55041i	−0.423315	−	0.423315i	0.463029	−	0.886343i	$-0.346763\pi$
$509$	−9.55041	−	9.55041i	−0.423315	−	0.423315i	−0.886343	+	0.463029i	$0.846763\pi$
$510$	1.76568	−	47.0082i	0.0781858	−	2.08156i
$511$			5.93610i			0.262598i
$512$	−22.7126	−	22.7126i	−1.00376	−	1.00376i
$513$	14.1826	−	11.3002i	0.626176	−	0.498917i
$514$	7.58360	+	7.58360i	0.334498	+	0.334498i
$515$	0.349761	−	0.349761i	0.0154123	−	0.0154123i
$516$	−22.3552	−	0.839687i	−0.984132	−	0.0369652i
$517$		−	9.13633i		−	0.401815i
$518$	19.8895	−	19.8895i	0.873895	−	0.873895i
$519$	−7.80217	−	0.293059i	−0.342477	−	0.0128639i
$520$	1.15539	−	1.66277i	0.0506671	−	0.0729175i
$521$			41.1736i			1.80385i	0.431894	+	0.901925i	$0.357846\pi$
$521$			41.1736i			1.80385i	−0.431894	+	0.901925i	$0.642154\pi$
$522$	−23.6896	+	20.3747i	−1.03687	+	0.891776i
$523$	−14.0362			−0.613760			−0.306880	−	0.951748i	$-0.599285\pi$
$523$	−14.0362			−0.613760			−0.306880	+	0.951748i	$0.599285\pi$
$524$	19.6222			0.857199
$525$	0.164673	−	0.152750i	0.00718691	−	0.00666655i
$526$	−1.80632	+	1.80632i	−0.0787595	+	0.0787595i
$527$	38.9787	−	38.9787i	1.69794	−	1.69794i
$528$	4.74825	−	4.40446i	0.206641	−	0.191680i
$529$	−22.3463			−0.971578
$530$	21.2116			0.921373
$531$	−3.45162	+	2.96863i	−0.149787	+	0.128828i
$532$		−	14.0175i		−	0.607738i
$533$	−29.0678	+	5.23342i	−1.25907	+	0.226684i
$534$	9.44826	+	0.354888i	0.408866	+	0.0153575i
$535$	30.8052	−	30.8052i	1.33183	−	1.33183i
$536$		−	0.841985i		−	0.0363682i
$537$	34.4955	+	1.29569i	1.48859	+	0.0559133i
$538$	15.4159	−	15.4159i	0.664625	−	0.664625i
$539$	2.41830	+	2.41830i	0.104163	+	0.104163i
$540$	−19.4225	+	15.4752i	−0.835810	+	0.665947i
$541$	−6.96858	−	6.96858i	−0.299602	−	0.299602i	0.541256	−	0.840858i	$-0.317949\pi$
$541$	−6.96858	−	6.96858i	−0.299602	−	0.299602i	−0.840858	+	0.541256i	$0.817949\pi$
$542$		−	35.8934i		−	1.54175i
$543$	−0.0428885	+	1.14183i	−0.00184052	+	0.0490006i
$544$	−33.9923	−	33.9923i	−1.45741	−	1.45741i
$545$	−28.5941			−1.22484
$546$	−19.1751	−	14.4205i	−0.820617	−	0.617141i
$547$	−11.2135			−0.479454			−0.239727	−	0.970840i	$-0.577058\pi$
$547$	−11.2135			−0.479454			−0.239727	+	0.970840i	$0.577058\pi$
$548$	22.8316	+	22.8316i	0.975318	+	0.975318i
$549$	24.9519	+	1.87709i	1.06492	+	0.0801123i
$550$			0.139163i			0.00593394i
$551$	12.6582	+	12.6582i	0.539259	+	0.539259i
$552$	0.256101	−	0.237558i	0.0109004	−	0.0101112i
$553$	11.1529	+	11.1529i	0.474271	+	0.474271i
$554$	40.4333	−	40.4333i	1.71785	−	1.71785i
$555$	−1.07160	+	28.5295i	−0.0454870	+	1.21101i
$556$			21.9629i			0.931436i
$557$	5.09175	−	5.09175i	0.215745	−	0.215745i	−0.590958	−	0.806702i	$-0.701250\pi$
$557$	5.09175	−	5.09175i	0.215745	−	0.215745i	0.806702	+	0.590958i	$0.201250\pi$
$558$	−56.3583	−	4.23975i	−2.38584	−	0.179483i
$559$	18.0149	+	12.5177i	0.761949	+	0.529444i
$560$		−	15.9281i		−	0.673085i
$561$	7.54453	−	6.99828i	0.318530	−	0.295468i
$562$	5.64080			0.237943
$563$	−36.2204			−1.52651			−0.763255	−	0.646098i	$-0.776400\pi$
$563$	−36.2204			−1.52651			−0.763255	+	0.646098i	$0.776400\pi$
$564$	22.8456	+	24.6288i	0.961975	+	1.03706i
$565$	−11.7143	+	11.7143i	−0.492823	+	0.492823i
$566$	18.1488	−	18.1488i	0.762851	−	0.762851i
$567$	10.1042	+	13.7072i	0.424336	+	0.575647i
$568$	2.70867			0.113653
$569$	19.6747			0.824807			0.412404	−	0.911001i	$-0.364689\pi$
$569$	19.6747			0.824807			0.412404	+	0.911001i	$0.364689\pi$
$570$	18.7916	+	20.2583i	0.787093	+	0.848529i
$571$		−	10.1981i		−	0.426779i	−0.976967	−	0.213389i	$-0.931550\pi$
$571$		−	10.1981i		−	0.426779i	0.976967	−	0.213389i	$-0.0684503\pi$
$572$	7.53292	−	1.35624i	0.314967	−	0.0567072i
$573$	0.640080	−	17.0410i	0.0267397	−	0.711897i
$574$	22.2533	−	22.2533i	0.928833	−	0.928833i
$575$		−	0.0554139i		−	0.00231092i
$576$	−2.01436	+	26.7766i	−0.0839318	+	1.11569i
$577$	0.128356	−	0.128356i	0.00534353	−	0.00534353i	−0.704430	−	0.709773i	$-0.748797\pi$
$577$	0.128356	−	0.128356i	0.00534353	−	0.00534353i	0.709773	+	0.704430i	$0.248797\pi$
$578$	−26.2725	−	26.2725i	−1.09279	−	1.09279i
$579$	26.8764	+	28.9742i	1.11695	+	1.20413i
$580$	−17.3349	−	17.3349i	−0.719794	−	0.719794i
$581$			20.9086i			0.867436i
$582$	−43.4052	−	1.63035i	−1.79920	−	0.0675803i
$583$	3.28109	+	3.28109i	0.135889	+	0.135889i
$584$	0.782572			0.0323830
$585$	24.2228	−	2.50494i	1.00149	−	0.103567i
$586$	−14.9781			−0.618741
$587$	−10.3530	−	10.3530i	−0.427313	−	0.427313i	0.460399	−	0.887712i	$-0.347706\pi$
$587$	−10.3530	−	10.3530i	−0.427313	−	0.427313i	−0.887712	+	0.460399i	$0.847706\pi$
$588$	−12.5660	−	0.471995i	−0.518214	−	0.0194647i
$589$			32.3798i			1.33419i
$590$	−4.90530	−	4.90530i	−0.201948	−	0.201948i
$591$	1.46508	+	1.57943i	0.0602651	+	0.0649691i
$592$	19.3581	+	19.3581i	0.795614	+	0.795614i
$593$	10.7607	−	10.7607i	0.441889	−	0.441889i	−0.450757	−	0.892647i	$-0.648846\pi$
$593$	10.7607	−	10.7607i	0.441889	−	0.441889i	0.892647	+	0.450757i	$0.148846\pi$
$594$	−10.4838	−	1.18582i	−0.430157	−	0.0486548i
$595$		−	25.3083i		−	1.03754i
$596$	4.49837	−	4.49837i	0.184261	−	0.184261i
$597$	−0.422472	+	11.2476i	−0.0172906	+	0.460332i
$598$	−5.82554	+	1.04884i	−0.238224	+	0.0428902i
$599$		−	36.9829i		−	1.51108i	−0.655101	−	0.755541i	$-0.727374\pi$
$599$		−	36.9829i		−	1.51108i	0.655101	−	0.755541i	$-0.272626\pi$
$600$	−0.0201374	−	0.0217092i	−0.000822107	−	0.000886275i
$601$	−26.5895			−1.08461			−0.542304	−	0.840182i	$-0.682448\pi$
$601$	−26.5895			−1.08461			−0.542304	+	0.840182i	$0.682448\pi$
$602$	−23.3747			−0.952681
$603$	7.67752	−	6.60320i	0.312653	−	0.268903i
$604$	1.13423	−	1.13423i	0.0461514	−	0.0461514i
$605$	−1.59194	+	1.59194i	−0.0647215	+	0.0647215i
$606$	29.4318	+	31.7290i	1.19558	+	1.28890i
$607$	−18.9328			−0.768458			−0.384229	−	0.923238i	$-0.625533\pi$
$607$	−18.9328			−0.768458			−0.384229	+	0.923238i	$0.625533\pi$
$608$	28.2376			1.14519
$609$	−12.3246	+	11.4323i	−0.499418	+	0.463259i
$610$			38.1283i			1.54377i
$611$	−5.83700	−	32.4202i	−0.236140	−	1.31158i
$612$	−2.83842	+	37.7306i	−0.114736	+	1.52517i
$613$	−6.30253	+	6.30253i	−0.254557	+	0.254557i	−0.822836	−	0.568279i	$-0.807609\pi$
$613$	−6.30253	+	6.30253i	−0.254557	+	0.254557i	0.568279	+	0.822836i	$0.307609\pi$
$614$		−	49.9408i		−	2.01544i
$615$	−1.19896	+	31.9200i	−0.0483465	+	1.28714i
$616$	−0.333728	+	0.333728i	−0.0134463	+	0.0134463i
$617$	−28.2292	−	28.2292i	−1.13647	−	1.13647i	−0.989079	−	0.147386i	$-0.952914\pi$
$617$	−28.2292	−	28.2292i	−1.13647	−	1.13647i	−0.147386	−	0.989079i	$-0.547086\pi$
$618$	−0.566496	+	0.525480i	−0.0227878	+	0.0211379i
$619$	−21.2163	−	21.2163i	−0.852756	−	0.852756i	0.137716	−	0.990472i	$-0.456024\pi$
$619$	−21.2163	−	21.2163i	−0.852756	−	0.852756i	−0.990472	+	0.137716i	$0.956024\pi$
$620$		−	44.3429i		−	1.78085i
$621$	4.17459	+	0.472186i	0.167521	+	0.0189482i
$622$	−6.24838	−	6.24838i	−0.250537	−	0.250537i
$623$	5.08675			0.203797
$624$	14.0352	−	18.6628i	0.561859	−	0.747109i
$625$	25.3380			1.01352
$626$	20.3660	+	20.3660i	0.813990	+	0.813990i
$627$	−0.226884	+	6.04039i	−0.00906089	+	0.241230i
$628$			29.8546i			1.19133i
$629$	30.7583	+	30.7583i	1.22641	+	1.22641i
$630$	−19.6727	+	16.9199i	−0.783779	+	0.674104i
$631$	−9.80024	−	9.80024i	−0.390141	−	0.390141i	0.484597	−	0.874738i	$-0.338966\pi$
$631$	−9.80024	−	9.80024i	−0.390141	−	0.390141i	−0.874738	+	0.484597i	$0.838966\pi$
$632$	1.47032	−	1.47032i	0.0584861	−	0.0584861i
$633$	37.7667	+	1.41856i	1.50109	+	0.0563828i
$634$			63.7447i			2.53163i
$635$	26.4886	−	26.4886i	1.05117	−	1.05117i
$636$	−17.0493	−	0.640392i	−0.676049	−	0.0253932i
$637$	10.1263	+	7.03632i	0.401219	+	0.278789i
$638$		−	10.4154i		−	0.412350i
$639$	21.2425	+	24.6986i	0.840342	+	0.977063i
$640$	−4.48411			−0.177250
$641$	1.46545			0.0578817			0.0289409	−	0.999581i	$-0.490787\pi$
$641$	1.46545			0.0578817			0.0289409	+	0.999581i	$0.490787\pi$
$642$	−49.8942	+	46.2817i	−1.96917	+	1.82659i
$643$	6.81498	−	6.81498i	0.268757	−	0.268757i	−0.559842	−	0.828599i	$-0.689138\pi$
$643$	6.81498	−	6.81498i	0.268757	−	0.268757i	0.828599	+	0.559842i	$0.189138\pi$
$644$	2.29635	−	2.29635i	0.0904890	−	0.0904890i
$645$	17.3940	−	16.1346i	0.684888	−	0.635300i
$646$	42.1006			1.65643
$647$	30.3672			1.19386			0.596928	−	0.802295i	$-0.296388\pi$
$647$	30.3672			1.19386			0.596928	+	0.802295i	$0.296388\pi$
$648$	1.80705	−	1.33206i	0.0709877	−	0.0523283i
$649$		−	1.51754i		−	0.0595688i
$650$	0.0889083	+	0.493821i	0.00348727	+	0.0193692i
$651$	−30.3851	−	1.14130i	−1.19088	−	0.0447311i
$652$	19.5850	−	19.5850i	0.767008	−	0.767008i
$653$			32.7119i			1.28012i	0.768326	+	0.640058i	$0.221090\pi$
$653$			32.7119i			1.28012i	−0.768326	+	0.640058i	$0.778910\pi$
$654$	44.6363	+	1.67659i	1.74542	+	0.0655599i
$655$	−14.7148	+	14.7148i	−0.574955	+	0.574955i
$656$	21.6587	+	21.6587i	0.845631	+	0.845631i
$657$	6.13726	+	7.13577i	0.239437	+	0.278393i
$658$	24.8198	+	24.8198i	0.967575	+	0.967575i
$659$			38.9430i			1.51700i	0.651672	+	0.758501i	$0.274068\pi$
$659$			38.9430i			1.51700i	−0.651672	+	0.758501i	$0.725932\pi$
$660$	0.310709	−	8.27208i	0.0120943	−	0.321990i
$661$	28.7697	+	28.7697i	1.11901	+	1.11901i	0.991887	+	0.127126i	$0.0405753\pi$
$661$	28.7697	+	28.7697i	1.11901	+	1.11901i	0.127126	+	0.991887i	$0.459425\pi$
$662$	57.8747			2.24936
$663$	22.3007	−	29.6534i	0.866087	−	1.15164i
$664$	2.75644			0.106971
$665$	10.5119	+	10.5119i	0.407632	+	0.407632i
$666$	3.34561	−	44.4726i	0.129640	−	1.72328i
$667$			4.14735i			0.160586i
$668$	16.7070	+	16.7070i	0.646413	+	0.646413i
$669$	8.72174	−	8.09026i	0.337202	−	0.312787i
$670$	10.9110	+	10.9110i	0.421528	+	0.421528i
$671$	−5.89783	+	5.89783i	−0.227683	+	0.227683i
$672$	−0.995298	+	26.4980i	−0.0383945	+	1.02218i
$673$			9.94571i			0.383379i	0.981456	+	0.191690i	$0.0613967\pi$
$673$			9.94571i			0.383379i	−0.981456	+	0.191690i	$0.938603\pi$
$674$	−36.5120	+	36.5120i	−1.40639	+	1.40639i
$675$	0.0400263	−	0.353873i	0.00154061	−	0.0136206i
$676$	25.8641	−	9.62523i	0.994772	−	0.370201i
$677$		−	40.8169i		−	1.56872i	−0.620305	−	0.784360i	$-0.712991\pi$
$677$		−	40.8169i		−	1.56872i	0.620305	−	0.784360i	$-0.287009\pi$
$678$	18.9732	−	17.5995i	0.728661	−	0.675904i
$679$	−23.3685			−0.896801
$680$	−3.33645			−0.127947
$681$	−14.9804	−	16.1497i	−0.574051	−	0.618859i
$682$	13.3213	−	13.3213i	0.510100	−	0.510100i
$683$	36.2434	−	36.2434i	1.38681	−	1.38681i	0.554890	−	0.831924i	$-0.312760\pi$
$683$	36.2434	−	36.2434i	1.38681	−	1.38681i	0.831924	−	0.554890i	$-0.187240\pi$
$684$	−14.4926	−	16.8504i	−0.554137	−	0.644293i
$685$	−34.2432			−1.30836
$686$	−40.0321			−1.52843
$687$	1.61217	+	1.73800i	0.0615080	+	0.0663090i
$688$		−	22.7502i		−	0.867343i
$689$	13.7392	+	9.54673i	0.523420	+	0.363701i
$690$	−0.240285	+	6.39716i	−0.00914749	+	0.243536i
$691$	15.4886	−	15.4886i	0.589214	−	0.589214i	−0.348205	−	0.937419i	$-0.613209\pi$
$691$	15.4886	−	15.4886i	0.589214	−	0.589214i	0.937419	+	0.348205i	$0.113209\pi$
$692$			9.56929i			0.363770i
$693$	−5.66028	−	0.425815i	−0.215016	−	0.0161754i
$694$	−15.0828	+	15.0828i	−0.572536	+	0.572536i
$695$	−16.4702	−	16.4702i	−0.624749	−	0.624749i
$696$	1.50715	+	1.62478i	0.0571282	+	0.0615873i
$697$	34.4137	+	34.4137i	1.30351	+	1.30351i
$698$			31.9029i			1.20754i
$699$	−31.3591	−	1.17789i	−1.18611	−	0.0445517i
$700$	−0.194658	−	0.194658i	−0.00735738	−	0.00735738i
$701$	0.523590			0.0197757			0.00988785	−	0.999951i	$-0.496853\pi$
$701$	0.523590			0.0197757			0.00988785	+	0.999951i	$0.496853\pi$
$702$	−37.9594	+	2.49001i	−1.43269	+	0.0939793i
$703$	−25.5511			−0.963677
$704$	−6.32913	−	6.32913i	−0.238538	−	0.238538i
$705$	−35.6014	−	1.33723i	−1.34083	−	0.0503631i
$706$		−	37.1166i		−	1.39690i
$707$	16.4639	+	16.4639i	0.619188	+	0.619188i
$708$	3.79466	+	4.09085i	0.142612	+	0.153743i
$709$	−8.56339	−	8.56339i	−0.321605	−	0.321605i	0.527778	−	0.849383i	$-0.323025\pi$
$709$	−8.56339	−	8.56339i	−0.321605	−	0.321605i	−0.849383	+	0.527778i	$0.823025\pi$
$710$	−35.1007	+	35.1007i	−1.31731	+	1.31731i
$711$	24.9377	+	1.87603i	0.935239	+	0.0703566i
$712$		−	0.670600i		−	0.0251318i
$713$	−5.30446	+	5.30446i	−0.198654	+	0.198654i
$714$	−1.48393	+	39.5070i	−0.0555347	+	1.47851i
$715$	−4.63194	+	6.66604i	−0.173225	+	0.249296i
$716$		−	42.3085i		−	1.58114i
$717$	−3.01500	−	3.25034i	−0.112597	−	0.121386i
$718$	−14.5192			−0.541853
$719$	−11.5025			−0.428972			−0.214486	−	0.976727i	$-0.568808\pi$
$719$	−11.5025			−0.428972			−0.214486	+	0.976727i	$0.568808\pi$
$720$	−16.4678	−	19.1471i	−0.613720	−	0.713571i
$721$	−0.293949	+	0.293949i	−0.0109472	+	0.0109472i
$722$	9.79296	−	9.79296i	0.364456	−	0.364456i
$723$	0.497334	+	0.536152i	0.0184960	+	0.0199397i
$724$	1.40044			0.0520471
$725$	0.351563			0.0130567
$726$	2.57841	−	2.39173i	0.0956937	−	0.0887652i
$727$		−	27.3315i		−	1.01367i	−0.862044	−	0.506834i	$-0.830816\pi$
$727$		−	27.3315i		−	1.01367i	0.862044	−	0.506834i	$-0.169184\pi$
$728$	−0.971021	+	1.39744i	−0.0359884	+	0.0517927i
$729$	26.3179	+	6.03075i	0.974736	+	0.223361i
$730$	−10.1411	+	10.1411i	−0.375338	+	0.375338i
$731$		−	36.1480i		−	1.33698i
$732$	1.15112	−	30.6465i	0.0425466	−	1.13273i
$733$	9.41825	−	9.41825i	0.347871	−	0.347871i	−0.511445	−	0.859316i	$-0.670890\pi$
$733$	9.41825	−	9.41825i	0.347871	−	0.347871i	0.859316	+	0.511445i	$0.170890\pi$
$734$	16.2562	+	16.2562i	0.600026	+	0.600026i
$735$	9.77730	−	9.06940i	0.360641	−	0.334530i
$736$	4.62588	+	4.62588i	0.170512	+	0.170512i
$737$			3.37551i			0.124338i
$738$	3.74321	−	49.7579i	0.137790	−	1.83161i
$739$	−19.9099	−	19.9099i	−0.732399	−	0.732399i	0.238696	−	0.971094i	$-0.423280\pi$
$739$	−19.9099	−	19.9099i	−0.732399	−	0.732399i	−0.971094	+	0.238696i	$0.923280\pi$
$740$	34.9912			1.28630
$741$	3.05397	+	21.5793i	0.112191	+	0.792735i
$742$	−17.8268			−0.654444
$743$	27.2359	+	27.2359i	0.999187	+	0.999187i	1.00000		0.000812252i	$-0.000258548\pi$
$743$	27.2359	+	27.2359i	0.999187	+	0.999187i	−0.000812252		1.00000i	$0.500259\pi$
$744$	−0.150461	+	4.00574i	−0.00551615	+	0.146858i
$745$			6.74672i			0.247181i
$746$	−29.7597	−	29.7597i	−1.08958	−	1.08958i
$747$	21.6172	+	25.1342i	0.790931	+	0.919612i
$748$	−8.91831	−	8.91831i	−0.326086	−	0.326086i
$749$	−25.8896	+	25.8896i	−0.945985	+	0.945985i
$750$	−39.0185	−	1.46558i	−1.42475	−	0.0535154i
$751$		−	42.4363i		−	1.54852i	−0.632866	−	0.774261i	$-0.718122\pi$
$751$		−	42.4363i		−	1.54852i	0.632866	−	0.774261i	$-0.281878\pi$
$752$	−24.1567	+	24.1567i	−0.880903	+	0.880903i
$753$	−34.2053	−	1.28479i	−1.24651	−	0.0468205i
$754$	−6.65417	−	36.9590i	−0.242330	−	1.34597i
$755$			1.70114i			0.0619109i
$756$	16.3232	−	13.0058i	0.593669	−	0.473017i
$757$	19.0517			0.692447			0.346224	−	0.938152i	$-0.387464\pi$
$757$	19.0517			0.692447			0.346224	+	0.938152i	$0.387464\pi$
$758$	27.4026			0.995307
$759$	−1.02671	+	0.952369i	−0.0372671	+	0.0345688i
$760$	1.38581	−	1.38581i	0.0502684	−	0.0502684i
$761$	−20.7318	+	20.7318i	−0.751526	+	0.751526i	−0.974764	−	0.223238i	$-0.928337\pi$
$761$	−20.7318	+	20.7318i	−0.751526	+	0.751526i	0.223238	+	0.974764i	$0.428337\pi$
$762$	−42.9026	+	39.7964i	−1.55420	+	1.44167i
$763$	24.0313			0.869991
$764$	−20.9006			−0.756158
$765$	−26.1659	−	30.4230i	−0.946030	−	1.09995i
$766$			31.7010i			1.14540i
$767$	−0.969524	−	5.38500i	−0.0350075	−	0.194441i
$768$	−23.9846	−	0.900890i	−0.865470	−	0.0325081i
$769$	−22.9142	+	22.9142i	−0.826306	+	0.826306i	−0.987004	−	0.160698i	$-0.948626\pi$
$769$	−22.9142	+	22.9142i	−0.826306	+	0.826306i	0.160698	+	0.987004i	$0.448626\pi$
$770$		−	8.64932i		−	0.311700i
$771$	9.14211	+	0.343389i	0.329245	+	0.0123668i
$772$	34.2502	−	34.2502i	1.23269	−	1.23269i
$773$	−7.44427	−	7.44427i	−0.267752	−	0.267752i	0.560442	−	0.828194i	$-0.310631\pi$
$773$	−7.44427	−	7.44427i	−0.267752	−	0.267752i	−0.828194	+	0.560442i	$0.810631\pi$
$774$	−28.0986	+	24.1668i	−1.00998	+	0.868657i
$775$	0.449650	+	0.449650i	0.0161519	+	0.0161519i
$776$			3.08073i			0.110592i
$777$	0.900605	−	23.9770i	0.0323090	−	0.860170i
$778$	−42.8593	−	42.8593i	−1.53658	−	1.53658i
$779$	−28.5877			−1.02426
$780$	−4.18229	−	29.5520i	−0.149750	−	1.05813i
$781$	−10.8590			−0.388567
$782$	6.89692	+	6.89692i	0.246633	+	0.246633i
$783$	−2.99569	+	26.4849i	−0.107057	+	0.946494i
$784$		−	12.7881i		−	0.456717i
$785$	−22.3882	−	22.3882i	−0.799070	−	0.799070i
$786$	23.8331	−	22.1075i	0.850098	−	0.788548i
$787$	2.70791	+	2.70791i	0.0965264	+	0.0965264i	0.753721	−	0.657195i	$-0.228257\pi$
$787$	2.70791	+	2.70791i	0.0965264	+	0.0965264i	−0.657195	+	0.753721i	$0.728257\pi$
$788$	1.86703	−	1.86703i	0.0665102	−	0.0665102i
$789$	−0.0817911	+	2.17754i	−0.00291184	+	0.0775225i
$790$			38.1067i			1.35578i
$791$	9.84500	−	9.84500i	0.350048	−	0.350048i
$792$	−0.0561363	+	0.746210i	−0.00199472	+	0.0265154i
$793$	−17.1604	+	24.6964i	−0.609385	+	0.876996i
$794$		−	51.7239i		−	1.83561i
$795$	13.2656	−	12.3052i	0.470483	−	0.436419i
$796$	13.7950			0.488952
$797$	3.00031			0.106277			0.0531383	−	0.998587i	$-0.483078\pi$
$797$	3.00031			0.106277			0.0531383	+	0.998587i	$0.483078\pi$
$798$	−15.7930	−	17.0257i	−0.559066	−	0.602703i
$799$	−38.3827	+	38.3827i	−1.35788	+	1.35788i
$800$	0.392128	−	0.392128i	0.0138638	−	0.0138638i
$801$	6.11477	−	5.25913i	0.216055	−	0.185822i
$802$	−2.45934			−0.0868424
$803$	−3.13732			−0.110714
$804$	−8.44055	−	9.09937i	−0.297675	−	0.320910i
$805$			3.44411i			0.121389i
$806$	38.7600	−	55.7814i	1.36526	−	1.96481i
$807$	0.698037	−	18.5840i	0.0245721	−	0.654187i
$808$	2.17048	−	2.17048i	0.0763571	−	0.0763571i
$809$			16.1882i			0.569148i	0.958654	+	0.284574i	$0.0918521\pi$
$809$			16.1882i			0.569148i	−0.958654	+	0.284574i	$0.908148\pi$
$810$	−6.15523	+	40.6787i	−0.216273	+	1.42930i
$811$	4.02134	−	4.02134i	0.141208	−	0.141208i	−0.632969	−	0.774177i	$-0.718164\pi$
$811$	4.02134	−	4.02134i	0.141208	−	0.141208i	0.774177	+	0.632969i	$0.218164\pi$
$812$	14.5688	+	14.5688i	0.511264	+	0.511264i
$813$	−20.8223	−	22.4476i	−0.730270	−	0.787271i
$814$	10.5119	+	10.5119i	0.368442	+	0.368442i
$815$			29.3739i			1.02892i
$816$	−38.4515	−	1.44429i	−1.34607	−	0.0505601i
$817$	15.0141	+	15.0141i	0.525279	+	0.525279i
$818$	36.6810			1.28252
$819$	−20.3575	+	2.10523i	−0.711350	+	0.0735625i
$820$	39.1496			1.36716
$821$	20.8379	+	20.8379i	0.727249	+	0.727249i	0.970071	−	0.242822i	$-0.0780730\pi$
$821$	20.8379	+	20.8379i	0.727249	+	0.727249i	−0.242822	+	0.970071i	$0.578073\pi$
$822$	53.4547	+	2.00782i	1.86445	+	0.0700309i
$823$		−	3.89412i		−	0.135741i	−0.997694	−	0.0678703i	$-0.978380\pi$
$823$		−	3.89412i		−	0.135741i	0.997694	−	0.0678703i	$-0.0216204\pi$
$824$	0.0387521	+	0.0387521i	0.00134999	+	0.00134999i
$825$	0.0807307	+	0.0870321i	0.00281068	+	0.00303007i
$826$	4.12256	+	4.12256i	0.143442	+	0.143442i
$827$	12.6103	−	12.6103i	0.438502	−	0.438502i	−0.453005	−	0.891508i	$-0.649648\pi$
$827$	12.6103	−	12.6103i	0.438502	−	0.438502i	0.891508	+	0.453005i	$0.149648\pi$
$828$	0.386269	−	5.13461i	0.0134238	−	0.178440i
$829$		−	47.1893i		−	1.63895i	−0.573113	−	0.819476i	$-0.694264\pi$
$829$		−	47.1893i		−	1.63895i	0.573113	−	0.819476i	$-0.305736\pi$
$830$	−35.7197	+	35.7197i	−1.23985	+	1.23985i
$831$	1.83084	−	48.7427i	0.0635110	−	1.69087i
$832$	−26.5024	−	18.4154i	−0.918807	−	0.638438i
$833$		−	20.3190i		−	0.704013i
$834$	24.7447	+	26.6762i	0.856840	+	0.923720i
$835$	−25.0574			−0.867147
$836$	7.40849			0.256228
$837$	−37.7058	+	30.0428i	−1.30330	+	1.03843i
$838$	42.8331	−	42.8331i	1.47965	−	1.47965i
$839$	−36.9591	+	36.9591i	−1.27597	+	1.27597i	−0.333064	+	0.942904i	$0.608083\pi$
$839$	−36.9591	+	36.9591i	−1.27597	+	1.27597i	−0.942904	+	0.333064i	$0.891917\pi$
$840$	1.25159	+	1.34928i	0.0431839	+	0.0465546i
$841$	2.68794			0.0926877
$842$	38.9409			1.34199
$843$	3.52773	−	3.27231i	0.121501	−	0.112704i
$844$		−	46.3205i		−	1.59442i
$845$	−12.1776	+	26.6137i	−0.418923	+	0.915539i
$846$	55.4966	+	4.17493i	1.90801	+	0.143537i
$847$	1.33791	−	1.33791i	0.0459712	−	0.0459712i
$848$		−	17.3506i		−	0.595821i
$849$	0.821785	−	21.8785i	0.0282036	−	0.750870i
$850$	0.584640	−	0.584640i	0.0200530	−	0.0200530i
$851$	−4.18578	−	4.18578i	−0.143487	−	0.143487i
$852$	29.2727	−	27.1533i	1.00287	−	0.930257i
$853$	31.2710	+	31.2710i	1.07070	+	1.07070i	0.997303	+	0.0733967i	$0.0233839\pi$
$853$	31.2710	+	31.2710i	1.07070	+	1.07070i	0.0733967	+	0.997303i	$0.476616\pi$
$854$		−	32.0441i		−	1.09653i
$855$	23.5043	+	1.76820i	0.803831	+	0.0604710i
$856$	3.41309	+	3.41309i	0.116657	+	0.116657i
$857$	35.8252			1.22377			0.611883	−	0.790948i	$-0.290412\pi$
$857$	35.8252			1.22377			0.611883	+	0.790948i	$0.290412\pi$
$858$	7.62146	−	10.1343i	0.260192	−	0.345980i
$859$	−7.65699			−0.261253			−0.130627	−	0.991432i	$-0.541699\pi$
$859$	−7.65699			−0.261253			−0.130627	+	0.991432i	$0.541699\pi$
$860$	−20.5613	−	20.5613i	−0.701134	−	0.701134i
$861$	1.00764	−	26.8265i	0.0343402	−	0.914245i
$862$			23.2339i			0.791349i
$863$	26.4363	+	26.4363i	0.899901	+	0.899901i	0.995427	−	0.0955257i	$-0.0304532\pi$
$863$	26.4363	+	26.4363i	0.899901	+	0.899901i	−0.0955257	+	0.995427i	$0.530453\pi$
$864$	26.1995	+	32.8822i	0.891326	+	1.11868i
$865$	−7.17608	−	7.17608i	−0.243994	−	0.243994i
$866$	3.42075	−	3.42075i	0.116242	−	0.116242i
$867$	−31.6718	−	1.18963i	−1.07563	−	0.0404020i
$868$			37.2670i			1.26492i
$869$	−5.89449	+	5.89449i	−0.199957	+	0.199957i
$870$	−40.5856	−	1.52444i	−1.37598	−	0.0516835i
$871$	2.15654	+	11.9780i	0.0730715	+	0.405858i
$872$		−	3.16811i		−	0.107286i
$873$	−28.0912	+	24.1604i	−0.950744	+	0.817706i
$874$	−5.72931			−0.193797
$875$	−21.0068			−0.710159
$876$	8.45729	−	7.84495i	0.285745	−	0.265056i
$877$	−26.7626	+	26.7626i	−0.903708	+	0.903708i	−0.995755	−	0.0920467i	$-0.970659\pi$
$877$	−26.7626	+	26.7626i	−0.903708	+	0.903708i	0.0920467	+	0.995755i	$0.470659\pi$
$878$	33.5369	−	33.5369i	1.13182	−	1.13182i
$879$	−9.36726	+	8.68904i	−0.315950	+	0.293074i
$880$	8.41825			0.283779
$881$	−35.8635			−1.20827			−0.604136	−	0.796882i	$-0.706481\pi$
$881$	−35.8635			−1.20827			−0.604136	+	0.796882i	$0.706481\pi$
$882$	−15.7945	+	13.5843i	−0.531827	+	0.457408i
$883$		−	1.32600i		−	0.0446234i	−0.999751	−	0.0223117i	$-0.992897\pi$
$883$		−	1.32600i		−	0.0446234i	0.999751	−	0.0223117i	$-0.00710263\pi$
$884$	−37.3443	−	25.9489i	−1.25603	−	0.872756i
$885$	−5.91339	−	0.222114i	−0.198777	−	0.00746629i
$886$	−46.8366	+	46.8366i	−1.57351	+	1.57351i
$887$		−	4.04050i		−	0.135667i	−0.997697	−	0.0678333i	$-0.978391\pi$
$887$		−	4.04050i		−	0.135667i	0.997697	−	0.0678333i	$-0.0216086\pi$
$888$	−3.16095	−	0.118729i	−0.106075	−	0.00398429i
$889$	−22.2618	+	22.2618i	−0.746635	+	0.746635i
$890$	8.69007	+	8.69007i	0.291292	+	0.291292i
$891$	−7.24445	+	5.34022i	−0.242698	+	0.178904i
$892$	−10.3099	−	10.3099i	−0.345200	−	0.345200i
$893$		−	31.8847i		−	1.06698i
$894$	0.395589	−	10.5319i	0.0132305	−	0.352238i
$895$	31.7274	+	31.7274i	1.06053	+	1.06053i
$896$	3.76858			0.125899
$897$	−3.03482	+	4.03542i	−0.101330	+	0.134739i
$898$	42.2601			1.41024
$899$	−33.6532	−	33.6532i	−1.12240	−	1.12240i
$900$	−0.435252	−	0.0327434i	−0.0145084	−	0.00109145i
$901$		−	27.5684i		−	0.918438i
$902$	11.7612	+	11.7612i	0.391605	+	0.391605i
$903$	−14.6184	+	13.5600i	−0.486470	+	0.451249i
$904$	−1.29789	−	1.29789i	−0.0431673	−	0.0431673i
$905$	−1.05020	+	1.05020i	−0.0349099	+	0.0349099i
$906$	0.0997451	−	2.65554i	0.00331381	−	0.0882243i
$907$		−	17.6046i		−	0.584552i	−0.956334	−	0.292276i	$-0.905587\pi$
$907$		−	17.6046i		−	0.584552i	0.956334	−	0.292276i	$-0.0944126\pi$
$908$	−19.0904	+	19.0904i	−0.633538	+	0.633538i
$909$	36.8130	+	2.76939i	1.22101	+	0.0918548i
$910$	−5.52586	−	30.6921i	−0.183180	−	1.01743i
$911$		−	10.6654i		−	0.353359i	−0.984268	−	0.176680i	$-0.943464\pi$
$911$		−	10.6654i		−	0.353359i	0.984268	−	0.176680i	$-0.0565357\pi$
$912$	16.5708	−	15.3711i	0.548715	−	0.508986i
$913$	−11.0505			−0.365719
$914$	−62.7180			−2.07453
$915$	22.1188	+	23.8452i	0.731224	+	0.788299i
$916$	2.05448	−	2.05448i	0.0678818	−	0.0678818i
$917$	12.3667	−	12.3667i	0.408386	−	0.408386i
$918$	39.0620	+	49.0255i	1.28924	+	1.61808i
$919$	24.9929			0.824440			0.412220	−	0.911084i	$-0.364753\pi$
$919$	24.9929			0.824440			0.412220	+	0.911084i	$0.364753\pi$
$920$	0.454045			0.0149694
$921$	−28.9714	−	31.2327i	−0.954639	−	1.02915i
$922$			75.2426i			2.47798i
$923$	−38.5333	+	6.93760i	−1.26834	+	0.228354i
$924$	−0.261129	+	6.95209i	−0.00859051	+	0.228707i
$925$	−0.354821	+	0.354821i	−0.0116664	+	0.0116664i
$926$			51.8386i			1.70352i
$927$	−0.0494451	+	0.657265i	−0.00162399	+	0.0215874i
$928$	−29.3481	+	29.3481i	−0.963397	+	0.963397i
$929$	15.3186	+	15.3186i	0.502588	+	0.502588i	0.912241	−	0.409653i	$-0.134350\pi$
$929$	15.3186	+	15.3186i	0.502588	+	0.502588i	−0.409653	+	0.912241i	$0.634350\pi$
$930$	−49.9593	−	53.8588i	−1.63823	−	1.76610i
$931$	8.43957	+	8.43957i	0.276596	+	0.276596i
$932$			38.4617i			1.25985i
$933$	−7.53248	−	0.282929i	−0.246602	−	0.00926269i
$934$	13.2578	+	13.2578i	0.433810	+	0.433810i
$935$	13.3758			0.437436
$936$	0.277537	+	2.68379i	0.00907159	+	0.0877223i
$937$	15.3687			0.502073			0.251036	−	0.967978i	$-0.419229\pi$
$937$	15.3687			0.502073			0.251036	+	0.967978i	$0.419229\pi$
$938$	−9.16991	−	9.16991i	−0.299408	−	0.299408i
$939$	24.5514	+	0.922181i	0.801206	+	0.0300942i
$940$			43.6648i			1.42419i
$941$	26.5102	+	26.5102i	0.864207	+	0.864207i	0.991824	−	0.127617i	$-0.0407327\pi$
$941$	26.5102	+	26.5102i	0.864207	+	0.864207i	−0.127617	+	0.991824i	$0.540733\pi$
$942$	33.6360	+	36.2614i	1.09592	+	1.18146i
$943$	−4.68323	−	4.68323i	−0.152507	−	0.152507i
$944$	−4.01242	+	4.01242i	−0.130593	+	0.130593i
$945$	−2.48773	+	21.9940i	−0.0809259	+	0.715466i
$946$		−	12.3539i		−	0.401659i
$947$	5.05234	−	5.05234i	0.164179	−	0.164179i	−0.620236	−	0.784415i	$-0.712963\pi$
$947$	5.05234	−	5.05234i	0.164179	−	0.164179i	0.784415	+	0.620236i	$0.212963\pi$
$948$	1.15047	−	30.6291i	0.0373654	−	0.994788i
$949$	−11.1328	+	2.00436i	−0.361385	+	0.0650644i
$950$			0.485664i			0.0157570i
$951$	36.9792	+	39.8656i	1.19913	+	1.29273i
$952$	2.80405			0.0908799
$953$	−42.4331			−1.37454			−0.687271	−	0.726401i	$-0.741191\pi$
$953$	−42.4331			−1.37454			−0.687271	+	0.726401i	$0.741191\pi$
$954$	−21.4296	+	18.4309i	−0.693808	+	0.596723i
$955$	15.6735	−	15.6735i	0.507183	−	0.507183i
$956$	−3.84219	+	3.84219i	−0.124265	+	0.124265i
$957$	−6.04213	−	6.51374i	−0.195314	−	0.210559i
$958$	20.8904			0.674937
$959$	28.7790			0.929321
$960$	−25.5890	+	23.7363i	−0.825882	+	0.766086i
$961$		−	55.0849i		−	1.77693i
$962$	44.0173	+	30.5857i	1.41918	+	0.986122i
$963$	−4.35488	+	57.8887i	−0.140334	+	1.86544i
$964$	0.633781	−	0.633781i	0.0204127	−	0.0204127i
$965$			51.3689i			1.65362i
$966$	0.201942	−	5.37636i	0.00649739	−	0.172981i
$967$	0.0403125	−	0.0403125i	0.00129636	−	0.00129636i	−0.706458	−	0.707755i	$-0.749708\pi$
$967$	0.0403125	−	0.0403125i	0.00129636	−	0.00129636i	0.707755	+	0.706458i	$0.249708\pi$
$968$	−0.176380	−	0.176380i	−0.00566908	−	0.00566908i
$969$	26.3295	−	24.4232i	0.845826	−	0.784586i
$970$	−39.9221	−	39.9221i	−1.28182	−	1.28182i
$971$		−	41.5020i		−	1.33186i	−0.746012	−	0.665932i	$-0.768034\pi$
$971$		−	41.5020i		−	1.33186i	0.746012	−	0.665932i	$-0.231966\pi$
$972$	6.17552	−	32.5106i	0.198080	−	1.04278i
$973$	13.8420	+	13.8420i	0.443754	+	0.443754i
$974$	10.6871			0.342437
$975$	0.342076	+	0.257256i	0.0109552	+	0.00823879i
$976$	31.1880			0.998303
$977$	−0.505411	−	0.505411i	−0.0161695	−	0.0161695i	0.698976	−	0.715145i	$-0.253640\pi$
$977$	−0.505411	−	0.505411i	−0.0161695	−	0.0161695i	−0.715145	+	0.698976i	$0.753640\pi$
$978$	1.72231	−	45.8535i	0.0550735	−	1.46623i
$979$			2.68843i			0.0859226i
$980$	−11.5577	−	11.5577i	−0.369196	−	0.369196i
$981$	28.8879	−	24.8456i	0.922321	−	0.793260i
$982$	−25.1648	−	25.1648i	−0.803040	−	0.803040i
$983$	14.7864	−	14.7864i	0.471613	−	0.471613i	−0.430823	−	0.902436i	$-0.641777\pi$
$983$	14.7864	−	14.7864i	0.471613	−	0.471613i	0.902436	+	0.430823i	$0.141777\pi$
$984$	−3.53661	−	0.132839i	−0.112743	−	0.00423476i
$985$			2.80020i			0.0892217i
$986$	−43.7562	+	43.7562i	−1.39348	+	1.39348i
$987$	29.9205	+	1.12385i	0.952379	+	0.0357725i
$988$	26.2890	−	4.73312i	0.836365	−	0.150581i
$989$			4.91924i			0.156423i
$990$	−8.94242	−	10.3973i	−0.284209	−	0.330449i
$991$	53.9383			1.71341			0.856703	−	0.515809i	$-0.172509\pi$
$991$	53.9383			1.71341			0.856703	+	0.515809i	$0.172509\pi$
$992$	−75.0724			−2.38355
$993$	36.1945	−	33.5739i	1.14860	−	1.06544i
$994$	29.4997	−	29.4997i	0.935673	−	0.935673i
$995$	−10.3450	+	10.3450i	−0.327958	+	0.327958i
$996$	29.7890	−	27.6322i	0.943900	−	0.875559i
$997$	−52.5725			−1.66499			−0.832495	−	0.554033i	$-0.813088\pi$
$997$	−52.5725			−1.66499			−0.832495	+	0.554033i	$0.813088\pi$
$998$	−48.4785			−1.53456
$999$	−23.7069	−	29.7538i	−0.750053	−	0.941369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.j.a.122.8	✓	96
3.2	odd	2	inner	429.2.j.a.122.41	yes	96
13.8	odd	4	inner	429.2.j.a.320.41	yes	96
39.8	even	4	inner	429.2.j.a.320.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.j.a.122.8	✓	96	1.1	even	1	trivial
429.2.j.a.122.41	yes	96	3.2	odd	2	inner
429.2.j.a.320.8	yes	96	39.8	even	4	inner
429.2.j.a.320.41	yes	96	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.43577 - 1.43577i) q^{2} +(-1.73083 - 0.0650121i) q^{3} +2.12285i q^{4} +(-1.59194 - 1.59194i) q^{5} +(2.39173 + 2.57841i) q^{6} +(1.33791 + 1.33791i) q^{7} +(0.176380 - 0.176380i) q^{8} +(2.99155 + 0.225050i) q^{9} +O(q^{10})\)	\(q+(-1.43577 - 1.43577i) q^{2} +(-1.73083 - 0.0650121i) q^{3} +2.12285i q^{4} +(-1.59194 - 1.59194i) q^{5} +(2.39173 + 2.57841i) q^{6} +(1.33791 + 1.33791i) q^{7} +(0.176380 - 0.176380i) q^{8} +(2.99155 + 0.225050i) q^{9} +4.57130i q^{10} +(-0.707107 + 0.707107i) q^{11} +(0.138011 - 3.67429i) q^{12} +(-2.05741 + 2.96092i) q^{13} -3.84185i q^{14} +(2.65188 + 2.85887i) q^{15} +3.73921 q^{16} +5.94126 q^{17} +(-3.97204 - 4.61828i) q^{18} +(-2.46772 + 2.46772i) q^{19} +(3.37944 - 3.37944i) q^{20} +(-2.22872 - 2.40268i) q^{21} +2.03048 q^{22} -0.808524 q^{23} +(-0.316751 + 0.293818i) q^{24} +0.0685372i q^{25} +(7.20515 - 1.29723i) q^{26} +(-5.16323 - 0.584009i) q^{27} +(-2.84018 + 2.84018i) q^{28} -5.12953i q^{29} +(0.297190 - 7.91215i) q^{30} +(6.56068 - 6.56068i) q^{31} +(-5.72140 - 5.72140i) q^{32} +(1.26985 - 1.17791i) q^{33} +(-8.53026 - 8.53026i) q^{34} -4.25974i q^{35} +(-0.477746 + 6.35060i) q^{36} +(5.17706 + 5.17706i) q^{37} +7.08614 q^{38} +(3.75353 - 4.99110i) q^{39} -0.561573 q^{40} +(5.79232 + 5.79232i) q^{41} +(-0.249767 + 6.64960i) q^{42} -6.08422i q^{43} +(-1.50108 - 1.50108i) q^{44} +(-4.40409 - 5.12062i) q^{45} +(1.16085 + 1.16085i) q^{46} +(-6.46036 + 6.46036i) q^{47} +(-6.47194 - 0.243094i) q^{48} -3.41999i q^{49} +(0.0984033 - 0.0984033i) q^{50} +(-10.2833 - 0.386254i) q^{51} +(-6.28558 - 4.36757i) q^{52} -4.64016i q^{53} +(6.57469 + 8.25169i) q^{54} +2.25134 q^{55} +0.471962 q^{56} +(4.43164 - 4.11077i) q^{57} +(-7.36480 + 7.36480i) q^{58} +(-1.07306 + 1.07306i) q^{59} +(-6.06895 + 5.62954i) q^{60} +8.34079 q^{61} -18.8392 q^{62} +(3.70133 + 4.30352i) q^{63} +8.95074i q^{64} +(7.98888 - 1.43833i) q^{65} +(-3.51442 - 0.132006i) q^{66} +(2.38684 - 2.38684i) q^{67} +12.6124i q^{68} +(1.39942 + 0.0525638i) q^{69} +(-6.11600 + 6.11600i) q^{70} +(7.67850 + 7.67850i) q^{71} +(0.567344 - 0.487956i) q^{72} +(2.21842 + 2.21842i) q^{73} -14.8661i q^{74} +(0.00445574 - 0.118626i) q^{75} +(-5.23859 - 5.23859i) q^{76} -1.89209 q^{77} +(-12.5552 + 1.77686i) q^{78} +8.33607 q^{79} +(-5.95260 - 5.95260i) q^{80} +(8.89871 + 1.34649i) q^{81} -16.6328i q^{82} +(7.81391 + 7.81391i) q^{83} +(5.10052 - 4.73123i) q^{84} +(-9.45813 - 9.45813i) q^{85} +(-8.73551 + 8.73551i) q^{86} +(-0.333481 + 8.87834i) q^{87} +0.249439i q^{88} +(1.90101 - 1.90101i) q^{89} +(-1.02877 + 13.6753i) q^{90} +(-6.71408 + 1.20882i) q^{91} -1.71637i q^{92} +(-11.7819 + 10.9289i) q^{93} +18.5511 q^{94} +7.85692 q^{95} +(9.53081 + 10.2747i) q^{96} +(-8.73321 + 8.73321i) q^{97} +(-4.91030 + 4.91030i) q^{98} +(-2.27448 + 1.95621i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 12 q^{6} - 16 q^{7}+O(q^{10}) \) 96 * q + 12 * q^6 - 16 * q^7	\( 96 q + 12 q^{6} - 16 q^{7} + 16 q^{13} - 16 q^{15} - 120 q^{16} - 28 q^{18} - 24 q^{19} + 24 q^{24} - 24 q^{27} + 56 q^{28} + 48 q^{31} - 16 q^{34} - 16 q^{37} + 80 q^{40} + 52 q^{42} + 4 q^{45} - 56 q^{46} + 28 q^{48} + 4 q^{54} + 4 q^{57} + 48 q^{58} + 4 q^{60} - 96 q^{61} - 36 q^{63} + 20 q^{66} - 16 q^{67} + 48 q^{70} - 16 q^{72} - 16 q^{73} - 88 q^{76} + 80 q^{78} + 16 q^{79} + 32 q^{81} + 52 q^{84} - 8 q^{85} - 48 q^{87} - 16 q^{91} - 36 q^{93} - 16 q^{94} - 108 q^{96} - 48 q^{97}+O(q^{100}) \) 96 * q + 12 * q^6 - 16 * q^7 + 16 * q^13 - 16 * q^15 - 120 * q^16 - 28 * q^18 - 24 * q^19 + 24 * q^24 - 24 * q^27 + 56 * q^28 + 48 * q^31 - 16 * q^34 - 16 * q^37 + 80 * q^40 + 52 * q^42 + 4 * q^45 - 56 * q^46 + 28 * q^48 + 4 * q^54 + 4 * q^57 + 48 * q^58 + 4 * q^60 - 96 * q^61 - 36 * q^63 + 20 * q^66 - 16 * q^67 + 48 * q^70 - 16 * q^72 - 16 * q^73 - 88 * q^76 + 80 * q^78 + 16 * q^79 + 32 * q^81 + 52 * q^84 - 8 * q^85 - 48 * q^87 - 16 * q^91 - 36 * q^93 - 16 * q^94 - 108 * q^96 - 48 * q^97

Introduction

L-functions

Modular forms

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Database

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