LMFDB - Embedded newform 930.2.v.a.401.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(401,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 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("930.401");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.v (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			401.4
Character	$\chi$	$=$	930.401
Dual form			930.2.v.a.821.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 + 0.809017i) q^{2} +(-0.922996 - 1.46563i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.72824 + 0.114757i) q^{6} +(0.0841834 + 0.259090i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.29616 + 2.70555i) q^{9} +O(q^{10})$	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.922996 - 1.46563i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.72824 + 0.114757i) q^{6} +(0.0841834 + 0.259090i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.29616 + 2.70555i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.177677 - 0.546834i) q^{11} +(-1.10868 + 1.33073i) q^{12} +(3.97653 + 5.47323i) q^{13} +(-0.259090 - 0.0841834i) q^{14} +(-1.46563 + 0.922996i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.82647 - 5.62130i) q^{17} +(-1.42697 - 2.63889i) q^{18} +(1.95325 + 1.41912i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(0.302029 - 0.362521i) q^{21} +(0.546834 + 0.177677i) q^{22} +(-1.63581 + 5.03452i) q^{23} +(-0.424916 - 1.67912i) q^{24} -1.00000 q^{25} -6.76528 q^{26} +(5.16168 - 0.597520i) q^{27} +(0.220395 - 0.160126i) q^{28} +(1.97255 + 1.43314i) q^{29} +(0.114757 - 1.72824i) q^{30} +(0.919844 + 5.49126i) q^{31} -1.00000i q^{32} +(-0.637462 + 0.765135i) q^{33} +(3.47416 + 4.78177i) q^{34} +(0.259090 - 0.0841834i) q^{35} +(2.97366 + 0.396658i) q^{36} -9.86212i q^{37} +(-2.29618 + 0.746074i) q^{38} +(4.35141 - 10.8799i) q^{39} +(0.309017 - 0.951057i) q^{40} +(4.40895 - 6.06840i) q^{41} +(0.115757 + 0.457431i) q^{42} +(1.26819 - 1.74551i) q^{43} +(-0.465165 + 0.337962i) q^{44} +(2.70555 + 1.29616i) q^{45} +(-3.11150 - 4.28262i) q^{46} +(-7.33436 - 10.0949i) q^{47} +(1.60820 + 0.643198i) q^{48} +(5.60308 - 4.07087i) q^{49} +(0.587785 - 0.809017i) q^{50} +(-9.92459 + 2.51150i) q^{51} +(3.97653 - 5.47323i) q^{52} +(3.15692 - 9.71600i) q^{53} +(-2.55056 + 4.52710i) q^{54} +(-0.546834 + 0.177677i) q^{55} +0.272423i q^{56} +(0.277064 - 4.17258i) q^{57} +(-2.31887 + 0.753446i) q^{58} +(7.48784 + 10.3061i) q^{59} +(1.33073 + 1.10868i) q^{60} +10.5251i q^{61} +(-4.98319 - 2.48351i) q^{62} +(-0.810094 - 0.108059i) q^{63} +(0.809017 + 0.587785i) q^{64} +(5.47323 - 3.97653i) q^{65} +(-0.244316 - 0.965453i) q^{66} +9.75486 q^{67} -5.91059 q^{68} +(8.88860 - 2.24934i) q^{69} +(-0.0841834 + 0.259090i) q^{70} +(4.16863 + 1.35447i) q^{71} +(-2.06878 + 2.17259i) q^{72} +(11.2674 - 3.66099i) q^{73} +(7.97862 + 5.79681i) q^{74} +(0.922996 + 1.46563i) q^{75} +(0.746074 - 2.29618i) q^{76} +(0.126722 - 0.0920686i) q^{77} +(6.24433 + 9.91541i) q^{78} +(-5.47101 - 1.77764i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-5.63996 - 7.01362i) q^{81} +(2.31792 + 7.13383i) q^{82} +(-7.86138 - 5.71163i) q^{83} +(-0.438110 - 0.175222i) q^{84} +(-5.62130 - 1.82647i) q^{85} +(0.666726 + 2.05197i) q^{86} +(0.279802 - 4.21381i) q^{87} -0.574975i q^{88} +(4.69430 + 14.4476i) q^{89} +(-2.63889 + 1.42697i) q^{90} +(-1.08330 + 1.49103i) q^{91} +5.29360 q^{92} +(7.19915 - 6.41656i) q^{93} +12.4780 q^{94} +(1.41912 - 1.95325i) q^{95} +(-1.46563 + 0.922996i) q^{96} +(0.889534 + 2.73770i) q^{97} +6.92579i q^{98} +(1.70978 + 0.228069i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	$ 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) $ 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$2$	−0.587785	+	0.809017i	−0.415627	+	0.572061i
$3$	−0.922996	−	1.46563i	−0.532892	−	0.846183i
$3$	−0.922996	−	1.46563i	−0.532892	−	0.846183i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	1.72824	+	0.114757i	0.705553	+	0.0468495i
$7$	0.0841834	+	0.259090i	0.0318183	+	0.0979267i	0.965704	−	0.259644i	$-0.0836052\pi$
$7$	0.0841834	+	0.259090i	0.0318183	+	0.0979267i	−0.933886	+	0.357571i	$0.883605\pi$
$8$	0.951057	+	0.309017i	0.336249	+	0.109254i
$9$	−1.29616	+	2.70555i	−0.432052	+	0.901849i
$10$	0.809017	+	0.587785i	0.255834	+	0.185874i
$11$	−0.177677	−	0.546834i	−0.0535717	−	0.164877i	0.920691	−	0.390292i	$-0.127626\pi$
$11$	−0.177677	−	0.546834i	−0.0535717	−	0.164877i	−0.974263	+	0.225416i	$0.927626\pi$
$12$	−1.10868	+	1.33073i	−0.320048	+	0.384148i
$13$	3.97653	+	5.47323i	1.10289	+	1.51800i	0.831495	+	0.555532i	$0.187485\pi$
$13$	3.97653	+	5.47323i	1.10289	+	1.51800i	0.271396	+	0.962468i	$0.412515\pi$
$14$	−0.259090	−	0.0841834i	−0.0692447	−	0.0224990i
$15$	−1.46563	+	0.922996i	−0.378425	+	0.238317i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	1.82647	−	5.62130i	0.442985	−	1.36337i	−0.441694	−	0.897166i	$-0.645622\pi$
$17$	1.82647	−	5.62130i	0.442985	−	1.36337i	0.884679	−	0.466201i	$-0.154378\pi$
$18$	−1.42697	−	2.63889i	−0.336340	−	0.621993i
$19$	1.95325	+	1.41912i	0.448106	+	0.325568i	0.788847	−	0.614589i	$-0.210678\pi$
$19$	1.95325	+	1.41912i	0.448106	+	0.325568i	−0.340742	+	0.940157i	$0.610678\pi$
$20$	−0.951057	+	0.309017i	−0.212663	+	0.0690983i
$21$	0.302029	−	0.362521i	0.0659082	−	0.0791085i
$22$	0.546834	+	0.177677i	0.116585	+	0.0378809i
$23$	−1.63581	+	5.03452i	−0.341091	+	1.04977i	0.622553	+	0.782578i	$0.286096\pi$
$23$	−1.63581	+	5.03452i	−0.341091	+	1.04977i	−0.963643	+	0.267192i	$0.913904\pi$
$24$	−0.424916	−	1.67912i	−0.0867357	−	0.342749i
$25$	−1.00000			−0.200000
$26$	−6.76528			−1.32678
$27$	5.16168	−	0.597520i	0.993366	−	0.114993i
$28$	0.220395	−	0.160126i	0.0416507	−	0.0302610i
$29$	1.97255	+	1.43314i	0.366293	+	0.266127i	0.755672	−	0.654950i	$-0.227310\pi$
$29$	1.97255	+	1.43314i	0.366293	+	0.266127i	−0.389379	+	0.921078i	$0.627310\pi$
$30$	0.114757	−	1.72824i	0.0209517	−	0.315533i
$31$	0.919844	+	5.49126i	0.165209	+	0.986259i
$31$	0.919844	+	5.49126i	0.165209	+	0.986259i
$32$		−	1.00000i		−	0.176777i
$33$	−0.637462	+	0.765135i	−0.110968	+	0.133193i
$34$	3.47416	+	4.78177i	0.595813	+	0.820066i
$35$	0.259090	−	0.0841834i	0.0437942	−	0.0142296i
$36$	2.97366	+	0.396658i	0.495610	+	0.0661097i
$37$		−	9.86212i		−	1.62132i	−0.585515	−	0.810661i	$-0.699108\pi$
$37$		−	9.86212i		−	1.62132i	0.585515	−	0.810661i	$-0.300892\pi$
$38$	−2.29618	+	0.746074i	−0.372490	+	0.121029i
$39$	4.35141	−	10.8799i	0.696784	−	1.74218i
$40$	0.309017	−	0.951057i	0.0488599	−	0.150375i
$41$	4.40895	−	6.06840i	0.688562	−	0.947724i	−0.311435	−	0.950268i	$-0.600810\pi$
$41$	4.40895	−	6.06840i	0.688562	−	0.947724i	0.999997	+	0.00254313i	$0.000809505\pi$
$42$	0.115757	+	0.457431i	0.0178617	+	0.0705832i
$43$	1.26819	−	1.74551i	0.193397	−	0.266188i	−0.701296	−	0.712871i	$-0.747395\pi$
$43$	1.26819	−	1.74551i	0.193397	−	0.266188i	0.894693	+	0.446683i	$0.147395\pi$
$44$	−0.465165	+	0.337962i	−0.0701262	+	0.0509497i
$45$	2.70555	+	1.29616i	0.403319	+	0.193220i
$46$	−3.11150	−	4.28262i	−0.458766	−	0.631437i
$47$	−7.33436	−	10.0949i	−1.06983	−	1.47249i	−0.870252	−	0.492607i	$-0.836044\pi$
$47$	−7.33436	−	10.0949i	−1.06983	−	1.47249i	−0.199575	−	0.979883i	$-0.563956\pi$
$48$	1.60820	+	0.643198i	0.232123	+	0.0928376i
$49$	5.60308	−	4.07087i	0.800440	−	0.581554i
$50$	0.587785	−	0.809017i	0.0831254	−	0.114412i
$51$	−9.92459	+	2.51150i	−1.38972	+	0.351681i
$52$	3.97653	−	5.47323i	0.551446	−	0.759000i
$53$	3.15692	−	9.71600i	0.433636	−	1.33460i	−0.460841	−	0.887483i	$-0.652452\pi$
$53$	3.15692	−	9.71600i	0.433636	−	1.33460i	0.894478	−	0.447113i	$-0.147548\pi$
$54$	−2.55056	+	4.52710i	−0.347087	+	0.616061i
$55$	−0.546834	+	0.177677i	−0.0737351	+	0.0239580i
$56$			0.272423i			0.0364041i
$57$	0.277064	−	4.17258i	0.0366981	−	0.552672i
$58$	−2.31887	+	0.753446i	−0.304482	+	0.0989323i
$59$	7.48784	+	10.3061i	0.974834	+	1.34174i	0.939567	+	0.342366i	$0.111228\pi$
$59$	7.48784	+	10.3061i	0.974834	+	1.34174i	0.0352676	+	0.999378i	$0.488772\pi$
$60$	1.33073	+	1.10868i	0.171796	+	0.143130i
$61$			10.5251i			1.34760i	0.738914	+	0.673799i	$0.235339\pi$
$61$			10.5251i			1.34760i	−0.738914	+	0.673799i	$0.764661\pi$
$62$	−4.98319	−	2.48351i	−0.632866	−	0.315406i
$63$	−0.810094	−	0.108059i	−0.102062	−	0.0136141i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	5.47323	−	3.97653i	0.678870	−	0.493228i
$66$	−0.244316	−	0.965453i	−0.0300733	−	0.118839i
$67$	9.75486			1.19175			0.595873	−	0.803079i	$-0.296806\pi$
$67$	9.75486			1.19175			0.595873	+	0.803079i	$0.296806\pi$
$68$	−5.91059			−0.716764
$69$	8.88860	−	2.24934i	1.07006	−	0.270789i
$70$	−0.0841834	+	0.259090i	−0.0100618	+	0.0309671i
$71$	4.16863	+	1.35447i	0.494725	+	0.160746i	0.545744	−	0.837952i	$-0.316247\pi$
$71$	4.16863	+	1.35447i	0.494725	+	0.160746i	−0.0510193	+	0.998698i	$0.516247\pi$
$72$	−2.06878	+	2.17259i	−0.243808	+	0.256043i
$73$	11.2674	−	3.66099i	1.31874	−	0.428486i	0.436681	−	0.899617i	$-0.356154\pi$
$73$	11.2674	−	3.66099i	1.31874	−	0.428486i	0.882064	+	0.471131i	$0.156154\pi$
$74$	7.97862	+	5.79681i	0.927496	+	0.673865i
$75$	0.922996	+	1.46563i	0.106578	+	0.169237i
$76$	0.746074	−	2.29618i	0.0855806	−	0.263390i
$77$	0.126722	−	0.0920686i	0.0144413	−	0.0104922i
$78$	6.24433	+	9.91541i	0.707031	+	1.12270i
$79$	−5.47101	−	1.77764i	−0.615537	−	0.200000i	−0.0153793	−	0.999882i	$-0.504896\pi$
$79$	−5.47101	−	1.77764i	−0.615537	−	0.200000i	−0.600158	+	0.799882i	$0.704896\pi$
$80$	0.587785	+	0.809017i	0.0657164	+	0.0904508i
$81$	−5.63996	−	7.01362i	−0.626662	−	0.779291i
$82$	2.31792	+	7.13383i	0.255972	+	0.787800i
$83$	−7.86138	−	5.71163i	−0.862899	−	0.626933i	0.0657732	−	0.997835i	$-0.479049\pi$
$83$	−7.86138	−	5.71163i	−0.862899	−	0.626933i	−0.928672	+	0.370902i	$0.879049\pi$
$84$	−0.438110	−	0.175222i	−0.0478017	−	0.0191183i
$85$	−5.62130	−	1.82647i	−0.609716	−	0.198109i
$86$	0.666726	+	2.05197i	0.0718949	+	0.221270i
$87$	0.279802	−	4.21381i	0.0299979	−	0.451768i
$88$		−	0.574975i		−	0.0612926i
$89$	4.69430	+	14.4476i	0.497595	+	1.53144i	0.812874	+	0.582440i	$0.197902\pi$
$89$	4.69430	+	14.4476i	0.497595	+	1.53144i	−0.315279	+	0.948999i	$0.602098\pi$
$90$	−2.63889	+	1.42697i	−0.278164	+	0.150416i
$91$	−1.08330	+	1.49103i	−0.113561	+	0.156303i
$92$	5.29360			0.551896
$93$	7.19915	−	6.41656i	0.746517	−	0.665366i
$94$	12.4780			1.28700
$95$	1.41912	−	1.95325i	0.145598	−	0.200399i
$96$	−1.46563	+	0.922996i	−0.149585	+	0.0942029i
$97$	0.889534	+	2.73770i	0.0903185	+	0.277972i	0.986005	−	0.166714i	$-0.0533155\pi$
$97$	0.889534	+	2.73770i	0.0903185	+	0.277972i	−0.895687	+	0.444685i	$0.853316\pi$
$98$			6.92579i			0.699610i
$99$	1.70978	+	0.228069i	0.171840	+	0.0229218i
$100$	0.309017	+	0.951057i	0.0309017	+	0.0951057i
$101$	−11.5306	−	3.74652i	−1.14734	−	0.372793i	−0.327198	−	0.944956i	$-0.606105\pi$
$101$	−11.5306	−	3.74652i	−1.14734	−	0.372793i	−0.820140	+	0.572163i	$0.806105\pi$
$102$	3.80168	−	9.50539i	0.376422	−	0.941174i
$103$	−0.119088	−	0.0865226i	−0.0117341	−	0.00852532i	0.581903	−	0.813258i	$-0.302308\pi$
$103$	−0.119088	−	0.0865226i	−0.0117341	−	0.00852532i	−0.593637	+	0.804733i	$0.702308\pi$
$104$	2.09059	+	6.43416i	0.204999	+	0.630922i
$105$	−0.362521	−	0.302029i	−0.0353784	−	0.0294751i
$106$	6.00482	+	8.26492i	0.583240	+	0.802760i
$107$	−1.96127	−	0.637255i	−0.189603	−	0.0616057i	0.212676	−	0.977123i	$-0.431782\pi$
$107$	−1.96127	−	0.637255i	−0.189603	−	0.0616057i	−0.402279	+	0.915517i	$0.631782\pi$
$108$	−2.16332	−	4.72441i	−0.208166	−	0.454606i
$109$	−3.65032	+	2.65211i	−0.349637	+	0.254026i	−0.748717	−	0.662890i	$-0.769330\pi$
$109$	−3.65032	+	2.65211i	−0.349637	+	0.254026i	0.399080	+	0.916916i	$0.369330\pi$
$110$	0.177677	−	0.546834i	0.0169408	−	0.0521386i
$111$	−14.4542	+	9.10270i	−1.37194	+	0.863990i
$112$	−0.220395	−	0.160126i	−0.0208254	−	0.0151305i
$113$	9.15830	−	2.97571i	0.861541	−	0.279931i	0.155269	−	0.987872i	$-0.450376\pi$
$113$	9.15830	−	2.97571i	0.861541	−	0.279931i	0.706272	+	0.707941i	$0.250376\pi$
$114$	3.21284	+	2.67673i	0.300910	+	0.250699i
$115$	5.03452	+	1.63581i	0.469471	+	0.152540i
$116$	0.753446	−	2.31887i	0.0699557	−	0.215301i
$117$	−19.9623	+	3.66453i	−1.84551	+	0.338786i
$118$	−12.7391			−1.17273
$119$	1.61018			0.147605
$120$	−1.67912	+	0.424916i	−0.153282	+	0.0387894i
$121$	8.63173	−	6.27132i	0.784703	−	0.570120i
$122$	−8.51497	−	6.18649i	−0.770909	−	0.560098i
$123$	−12.9635	−	0.860790i	−1.16888	−	0.0776148i
$124$	4.93825	−	2.57172i	0.443468	−	0.230947i
$125$			1.00000i			0.0894427i
$126$	0.563583	−	0.591864i	0.0502079	−	0.0527275i
$127$	12.0711	+	16.6145i	1.07114	+	1.47430i	0.868916	+	0.494959i	$0.164817\pi$
$127$	12.0711	+	16.6145i	1.07114	+	1.47430i	0.202224	+	0.979339i	$0.435183\pi$
$128$	−0.951057	+	0.309017i	−0.0840623	+	0.0273135i
$129$	−3.72881	−	0.247597i	−0.328304	−	0.0217997i
$130$			6.76528i			0.593354i
$131$	13.9409	−	4.52968i	1.21802	−	0.395760i	0.371661	−	0.928368i	$-0.378788\pi$
$131$	13.9409	−	4.52968i	1.21802	−	0.395760i	0.846362	+	0.532609i	$0.178788\pi$
$132$	0.924673	+	0.369823i	0.0804825	+	0.0321890i
$133$	−0.203248	+	0.625533i	−0.0176238	+	0.0542406i
$134$	−5.73376	+	7.89184i	−0.495321	+	0.681751i
$135$	−0.597520	−	5.16168i	−0.0514264	−	0.444247i
$136$	3.47416	−	4.78177i	0.297906	−	0.410033i
$137$	2.83623	−	2.06064i	0.242315	−	0.176052i	−0.459999	−	0.887919i	$-0.652150\pi$
$137$	2.83623	−	2.06064i	0.242315	−	0.176052i	0.702314	+	0.711867i	$0.252150\pi$
$138$	−3.40484	+	8.51316i	−0.289839	+	0.724688i
$139$	−5.77462	−	7.94809i	−0.489797	−	0.674148i	0.490553	−	0.871411i	$-0.336795\pi$
$139$	−5.77462	−	7.94809i	−0.489797	−	0.674148i	−0.980351	+	0.197263i	$0.936795\pi$
$140$	−0.160126	−	0.220395i	−0.0135331	−	0.0186268i
$141$	−8.02580	+	20.0670i	−0.675894	+	1.68995i
$142$	−3.54605	+	2.57635i	−0.297578	+	0.216203i
$143$	2.28641	−	3.14697i	0.191199	−	0.263163i
$144$	−0.541668	−	2.95069i	−0.0451390	−	0.245891i
$145$	1.43314	−	1.97255i	0.119016	−	0.163811i
$146$	−3.66099	+	11.2674i	−0.302985	+	0.932493i
$147$	−11.1380	−	4.45465i	−0.918649	−	0.367413i
$148$	−9.37944	+	3.04756i	−0.770985	+	0.250508i
$149$		−	5.35932i		−	0.439053i	−0.975607	−	0.219526i	$-0.929549\pi$
$149$		−	5.35932i		−	0.439053i	0.975607	−	0.219526i	$-0.0704512\pi$
$150$	−1.72824	−	0.114757i	−0.141111	−	0.00936991i
$151$	−5.27676	+	1.71452i	−0.429417	+	0.139526i	−0.515748	−	0.856741i	$-0.672486\pi$
$151$	−5.27676	+	1.71452i	−0.429417	+	0.139526i	0.0863309	+	0.996267i	$0.472486\pi$
$152$	1.41912	+	1.95325i	0.115106	+	0.158429i
$153$	12.8413	+	12.2277i	1.03816	+	0.988550i
$154$			0.156637i			0.0126221i
$155$	5.49126	−	0.919844i	0.441068	−	0.0738837i
$156$	−11.6921	−	0.776366i	−0.936114	−	0.0621590i
$157$	−9.92446	−	7.21054i	−0.792058	−	0.575464i	0.116515	−	0.993189i	$-0.462828\pi$
$157$	−9.92446	−	7.21054i	−0.792058	−	0.575464i	−0.908573	+	0.417725i	$0.862828\pi$
$158$	4.65392	−	3.38127i	0.370246	−	0.269000i
$159$	−17.1539	+	4.34095i	−1.36039	+	0.344260i
$160$	−1.00000			−0.0790569
$161$	−1.44210			−0.113653
$162$	8.98922	−	0.440320i	0.706260	−	0.0345948i
$163$	−2.71134	+	8.34464i	−0.212368	+	0.653602i	0.786962	+	0.617002i	$0.211653\pi$
$163$	−2.71134	+	8.34464i	−0.212368	+	0.653602i	−0.999330	+	0.0366006i	$0.988347\pi$
$164$	−7.13383	−	2.31792i	−0.557058	−	0.180999i
$165$	0.765135	+	0.637462i	0.0595657	+	0.0496264i
$166$	9.24161	−	3.00278i	0.717288	−	0.233061i
$167$	−2.32193	−	1.68698i	−0.179676	−	0.130542i	0.494312	−	0.869285i	$-0.335420\pi$
$167$	−2.32193	−	1.68698i	−0.179676	−	0.130542i	−0.673988	+	0.738742i	$0.735420\pi$
$168$	0.399272	−	0.251445i	0.0308045	−	0.0193994i
$169$	−10.1262	+	31.1652i	−0.778937	+	2.39732i
$170$	4.78177	−	3.47416i	0.366745	−	0.266456i
$171$	−6.37120	+	3.44520i	−0.487218	+	0.263461i
$172$	−2.05197	−	0.666726i	−0.156461	−	0.0508374i
$173$	3.91051	+	5.38236i	0.297311	+	0.409213i	0.931372	−	0.364070i	$-0.118613\pi$
$173$	3.91051	+	5.38236i	0.297311	+	0.409213i	−0.634061	+	0.773283i	$0.718613\pi$
$174$	3.24458	+	2.70318i	0.245971	+	0.204928i
$175$	−0.0841834	−	0.259090i	−0.00636366	−	0.0195853i
$176$	0.465165	+	0.337962i	0.0350631	+	0.0254748i
$177$	8.19375	−	20.4869i	0.615880	−	1.53989i
$178$	−14.4476	−	4.69430i	−1.08289	−	0.351853i
$179$	−2.31705	−	7.13114i	−0.173184	−	0.533006i	0.826362	−	0.563140i	$-0.190407\pi$
$179$	−2.31705	−	7.13114i	−0.173184	−	0.533006i	−0.999546	+	0.0301336i	$0.990407\pi$
$180$	0.396658	−	2.97366i	0.0295651	−	0.221644i
$181$			21.5693i			1.60324i	0.597837	+	0.801618i	$0.296027\pi$
$181$			21.5693i			1.60324i	−0.597837	+	0.801618i	$0.703973\pi$
$182$	−0.569524	−	1.75281i	−0.0422159	−	0.129927i
$183$	15.4259	−	9.71461i	1.14032	−	0.718125i
$184$	−3.11150	+	4.28262i	−0.229383	+	0.315719i
$185$	−9.86212			−0.725078
$186$	0.959554	+	9.59579i	0.0703579	+	0.703598i
$187$	−3.39844			−0.248519
$188$	−7.33436	+	10.0949i	−0.534913	+	0.736245i
$189$	0.589339	+	1.28704i	0.0428681	+	0.0936182i
$190$	0.746074	+	2.29618i	0.0541259	+	0.166582i
$191$		−	6.34878i		−	0.459381i	−0.973264	−	0.229691i	$-0.926229\pi$
$191$		−	6.34878i		−	0.459381i	0.973264	−	0.229691i	$-0.0737715\pi$
$192$	0.114757	−	1.72824i	0.00828191	−	0.124725i
$193$	2.75980	+	8.49380i	0.198655	+	0.611397i	0.999914	+	0.0130801i	$0.00416366\pi$
$193$	2.75980	+	8.49380i	0.198655	+	0.611397i	−0.801259	+	0.598317i	$0.795836\pi$
$194$	−2.73770	−	0.889534i	−0.196556	−	0.0638648i
$195$	−10.8799	−	4.35141i	−0.779126	−	0.311611i
$196$	−5.60308	−	4.07087i	−0.400220	−	0.290777i
$197$	−3.37007	−	10.3720i	−0.240107	−	0.738975i	−0.996403	−	0.0847442i	$-0.972993\pi$
$197$	−3.37007	−	10.3720i	−0.240107	−	0.738975i	0.756295	−	0.654230i	$-0.227007\pi$
$198$	−1.18950	+	1.24919i	−0.0845338	+	0.0887759i
$199$	−7.79987	−	10.7356i	−0.552918	−	0.761027i	0.437486	−	0.899225i	$-0.355869\pi$
$199$	−7.79987	−	10.7356i	−0.552918	−	0.761027i	−0.990405	+	0.138198i	$0.955869\pi$
$200$	−0.951057	−	0.309017i	−0.0672499	−	0.0218508i
$201$	−9.00369	−	14.2970i	−0.635072	−	1.00843i
$202$	9.80852	−	7.12631i	0.690125	−	0.501405i
$203$	−0.205256	+	0.631713i	−0.0144061	+	0.0443376i
$204$	5.45545	+	8.66275i	0.381958	+	0.606514i
$205$	−6.06840	−	4.40895i	−0.423835	−	0.307934i
$206$	0.139996	−	0.0454876i	0.00975402	−	0.00316927i
$207$	−11.5008	−	10.9513i	−0.799364	−	0.761167i
$208$	−6.43416	−	2.09059i	−0.446129	−	0.144956i
$209$	0.428974	−	1.32025i	0.0296728	−	0.0913234i
$210$	0.457431	−	0.115757i	0.0315658	−	0.00798799i
$211$	−7.31822			−0.503807			−0.251904	−	0.967752i	$-0.581057\pi$
$211$	−7.31822			−0.503807			−0.251904	+	0.967752i	$0.581057\pi$
$212$	−10.2160			−0.701638
$213$	−1.86247	−	7.35984i	−0.127615	−	0.504288i
$214$	1.66835	−	1.21213i	0.114046	−	0.0828595i
$215$	−1.74551	−	1.26819i	−0.119043	−	0.0864897i
$216$	5.09370	+	1.02677i	0.346582	+	0.0698630i
$217$	−1.34529	+	0.700595i	−0.0913244	+	0.0475595i
$218$		−	4.51204i		−	0.305594i
$219$	−15.7654	−	13.1347i	−1.06533	−	0.887562i
$220$	0.337962	+	0.465165i	0.0227854	+	0.0313614i
$221$	38.0297	−	12.3566i	2.55815	−	0.831194i
$222$	1.13175	−	17.0442i	0.0759582	−	1.14393i
$223$		−	20.2280i		−	1.35457i	−0.735722	−	0.677284i	$-0.763157\pi$
$223$		−	20.2280i		−	1.35457i	0.735722	−	0.677284i	$-0.236843\pi$
$224$	0.259090	−	0.0841834i	0.0173112	−	0.00562474i
$225$	1.29616	−	2.70555i	0.0864104	−	0.180370i
$226$	−2.97571	+	9.15830i	−0.197941	+	0.609201i
$227$	−1.80469	+	2.48394i	−0.119781	+	0.164865i	−0.864697	−	0.502294i	$-0.832490\pi$
$227$	−1.80469	+	2.48394i	−0.119781	+	0.164865i	0.744916	+	0.667158i	$0.232490\pi$
$228$	−4.05398	+	1.02590i	−0.268481	+	0.0679416i
$229$	16.0074	−	22.0323i	1.05780	−	1.45593i	0.175950	−	0.984399i	$-0.443700\pi$
$229$	16.0074	−	22.0323i	1.05780	−	1.45593i	0.881848	−	0.471534i	$-0.156300\pi$
$230$	−4.28262	+	3.11150i	−0.282387	+	0.205166i
$231$	−0.251902	−	0.100748i	−0.0165740	−	0.00662875i
$232$	1.43314	+	1.97255i	0.0940902	+	0.129504i
$233$	13.0839	+	18.0084i	0.857155	+	1.17977i	0.982240	+	0.187627i	$0.0600795\pi$
$233$	13.0839	+	18.0084i	0.857155	+	1.17977i	−0.125085	+	0.992146i	$0.539920\pi$
$234$	8.76886	−	18.3038i	0.573238	−	1.19656i
$235$	−10.0949	+	7.33436i	−0.658517	+	0.478441i
$236$	7.48784	−	10.3061i	0.487417	−	0.670872i
$237$	2.44436	+	9.65925i	0.158778	+	0.627436i
$238$	−0.946440	+	1.30266i	−0.0613486	+	0.0844391i
$239$	−6.70715	+	20.6425i	−0.433850	+	1.33525i	0.460411	+	0.887706i	$0.347702\pi$
$239$	−6.70715	+	20.6425i	−0.433850	+	1.33525i	−0.894261	+	0.447546i	$0.852298\pi$
$240$	0.643198	−	1.60820i	0.0415182	−	0.103809i
$241$	1.13921	−	0.370152i	0.0733830	−	0.0238436i	−0.272095	−	0.962270i	$-0.587717\pi$
$241$	1.13921	−	0.370152i	0.0733830	−	0.0238436i	0.345478	+	0.938427i	$0.387717\pi$
$242$			10.6694i			0.685855i
$243$	−5.07373	+	14.7397i	−0.325480	+	0.945549i
$244$	10.0099	−	3.25243i	0.640821	−	0.208215i
$245$	−4.07087	−	5.60308i	−0.260079	−	0.357968i
$246$	8.31614	−	9.98172i	0.530218	−	0.636411i
$247$			16.3337i			1.03929i
$248$	−0.822067	+	5.50674i	−0.0522013	+	0.349678i
$249$	−1.11512	+	16.7937i	−0.0706680	+	1.06426i
$250$	−0.809017	−	0.587785i	−0.0511667	−	0.0371748i
$251$	−15.7948	+	11.4756i	−0.996962	+	0.724335i	−0.961435	−	0.275034i	$-0.911311\pi$
$251$	−15.7948	+	11.4756i	−0.996962	+	0.724335i	−0.0355272	+	0.999369i	$0.511311\pi$
$252$	0.147563	+	0.803837i	0.00929558	+	0.0506370i
$253$	3.04369			0.191355
$254$	−20.5366			−1.28858
$255$	2.51150	+	9.92459i	0.157277	+	0.621502i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	12.9290	+	4.20089i	0.806490	+	0.262044i	0.683110	−	0.730315i	$-0.260627\pi$
$257$	12.9290	+	4.20089i	0.806490	+	0.262044i	0.123379	+	0.992360i	$0.460627\pi$
$258$	2.39205	−	2.87114i	0.148923	−	0.178749i
$259$	2.55517	−	0.830227i	0.158771	−	0.0515878i
$260$	−5.47323	−	3.97653i	−0.339435	−	0.246614i
$261$	−6.43415	+	3.47924i	−0.398264	+	0.215360i
$262$	−4.52968	+	13.9409i	−0.279844	+	0.861272i
$263$	−24.4841	+	17.7887i	−1.50975	+	1.09690i	−0.543465	+	0.839432i	$0.682888\pi$
$263$	−24.4841	+	17.7887i	−1.50975	+	1.09690i	−0.966287	+	0.257467i	$0.917112\pi$
$264$	−0.842702	+	0.530700i	−0.0518647	+	0.0326623i
$265$	−9.71600	−	3.15692i	−0.596849	−	0.193928i
$266$	−0.386600	−	0.532110i	−0.0237040	−	0.0326257i
$267$	16.8420	−	20.2152i	1.03071	−	1.23715i
$268$	−3.01442	−	9.27742i	−0.184135	−	0.566709i
$269$	13.1662	+	9.56581i	0.802758	+	0.583238i	0.911722	−	0.410808i	$-0.134753\pi$
$269$	13.1662	+	9.56581i	0.802758	+	0.583238i	−0.108964	+	0.994046i	$0.534753\pi$
$270$	4.52710	+	2.55056i	0.275511	+	0.155222i
$271$	−3.42289	−	1.11217i	−0.207926	−	0.0675593i	0.203202	−	0.979137i	$-0.434865\pi$
$271$	−3.42289	−	1.11217i	−0.207926	−	0.0675593i	−0.411128	+	0.911578i	$0.634865\pi$
$272$	1.82647	+	5.62130i	0.110746	+	0.340842i
$273$	3.18519	+	0.211500i	0.192776	+	0.0128006i
$274$			3.50577i			0.211791i
$275$	0.177677	+	0.546834i	0.0107143	+	0.0329753i
$276$	−4.88598	−	7.75848i	−0.294101	−	0.467005i
$277$	11.2011	−	15.4171i	0.673012	−	0.926321i	−0.326812	−	0.945089i	$-0.605974\pi$
$277$	11.2011	−	15.4171i	0.673012	−	0.926321i	0.999824	+	0.0187683i	$0.00597448\pi$
$278$	9.82438			0.589227
$279$	−16.0491	−	4.62884i	−0.960835	−	0.277122i
$280$	0.272423			0.0162804
$281$	0.237292	−	0.326604i	0.0141556	−	0.0194835i	−0.801881	−	0.597484i	$-0.796167\pi$
$281$	0.237292	−	0.326604i	0.0141556	−	0.0194835i	0.816036	+	0.578001i	$0.196167\pi$
$282$	−11.5171	−	18.2881i	−0.685834	−	1.08904i
$283$	3.76791	+	11.5964i	0.223979	+	0.689336i	0.998394	+	0.0566581i	$0.0180445\pi$
$283$	3.76791	+	11.5964i	0.223979	+	0.689336i	−0.774415	+	0.632678i	$0.781956\pi$
$284$		−	4.38315i		−	0.260092i
$285$	−4.17258	−	0.277064i	−0.247163	−	0.0164119i
$286$	1.20204	+	3.69948i	0.0710778	+	0.218755i
$287$	1.94342	+	0.631455i	0.114716	+	0.0372736i
$288$	2.70555	+	1.29616i	0.159426	+	0.0763767i
$289$	−14.5098	−	10.5420i	−0.853515	−	0.620115i
$290$	0.753446	+	2.31887i	0.0442439	+	0.136169i
$291$	3.19143	−	3.83062i	0.187085	−	0.224555i
$292$	−6.96361	−	9.58459i	−0.407514	−	0.560895i
$293$	−30.0501	−	9.76386i	−1.75554	−	0.570411i	−0.758821	−	0.651299i	$-0.774224\pi$
$293$	−30.0501	−	9.76386i	−1.75554	−	0.570411i	−0.996723	+	0.0808880i	$0.974224\pi$
$294$	10.1507	−	6.39247i	0.591998	−	0.372817i
$295$	10.3061	−	7.48784i	0.600046	−	0.435959i
$296$	3.04756	−	9.37944i	0.177136	−	0.545169i
$297$	−1.24386	−	2.71642i	−0.0721759	−	0.157623i
$298$	4.33578	+	3.15013i	0.251165	+	0.182482i
$299$	−34.0599	+	11.0667i	−1.96974	+	0.640006i
$300$	1.10868	−	1.33073i	0.0640095	−	0.0768295i
$301$	0.559005	+	0.181632i	0.0322205	+	0.0104691i
$302$	1.71452	−	5.27676i	0.0986598	−	0.303644i
$303$	5.15168	+	20.3577i	0.295957	+	1.16952i
$304$	−2.41435			−0.138472
$305$	10.5251			0.602664
$306$	−17.4403	+	3.20157i	−0.996998	+	0.183022i
$307$	−4.70346	+	3.41726i	−0.268441	+	0.195034i	−0.713860	−	0.700289i	$-0.753055\pi$
$307$	−4.70346	+	3.41726i	−0.268441	+	0.195034i	0.445419	+	0.895322i	$0.353055\pi$
$308$	−0.126722	−	0.0920686i	−0.00722063	−	0.00524610i
$309$	−0.0168924	+	0.254399i	−0.000960976	+	0.0144723i
$310$	−2.48351	+	4.98319i	−0.141054	+	0.283026i
$311$			11.0311i			0.625515i	0.949833	+	0.312758i	$0.101253\pi$
$311$			11.0311i			0.625515i	−0.949833	+	0.312758i	$0.898747\pi$
$312$	7.50051	−	9.00274i	0.424633	−	0.509680i
$313$	−0.259803	−	0.357588i	−0.0146849	−	0.0202121i	0.801611	−	0.597845i	$-0.203976\pi$
$313$	−0.259803	−	0.357588i	−0.0146849	−	0.0202121i	−0.816296	+	0.577633i	$0.803976\pi$
$314$	11.6669	−	3.79081i	0.658401	−	0.213928i
$315$	−0.108059	+	0.810094i	−0.00608842	+	0.0456436i
$316$			5.75256i			0.323607i
$317$	2.34400	−	0.761611i	0.131652	−	0.0427763i	−0.242450	−	0.970164i	$-0.577951\pi$
$317$	2.34400	−	0.761611i	0.131652	−	0.0427763i	0.374102	+	0.927388i	$0.377951\pi$
$318$	6.57091	−	16.4293i	0.368479	−	0.921312i
$319$	0.433213	−	1.33329i	0.0242553	−	0.0746500i
$320$	0.587785	−	0.809017i	0.0328582	−	0.0452254i
$321$	0.876262	+	3.46268i	0.0489082	+	0.193268i
$322$	0.847645	−	1.16668i	0.0472374	−	0.0650167i
$323$	11.5448	−	8.38782i	0.642372	−	0.466711i
$324$	−4.92751	+	7.53125i	−0.273750	+	0.418403i
$325$	−3.97653	−	5.47323i	−0.220578	−	0.303600i
$326$	−5.15727	−	7.09837i	−0.285635	−	0.393143i
$327$	7.25625	+	2.90213i	0.401271	+	0.160488i
$328$	6.06840	−	4.40895i	0.335071	−	0.243443i
$329$	1.99805	−	2.75008i	0.110156	−	0.151617i
$330$	−0.965453	+	0.244316i	−0.0531464	+	0.0134492i
$331$	18.1780	−	25.0198i	0.999151	−	1.37521i	0.0733066	−	0.997309i	$-0.476645\pi$
$331$	18.1780	−	25.0198i	0.999151	−	1.37521i	0.925845	−	0.377904i	$-0.123355\pi$
$332$	−3.00278	+	9.24161i	−0.164799	+	0.507199i
$333$	26.6824	+	12.7829i	1.46219	+	0.700496i
$334$	2.72959	−	0.886897i	0.149356	−	0.0485288i
$335$		−	9.75486i		−	0.532965i
$336$	−0.0312626	+	0.470814i	−0.00170551	+	0.0256850i
$337$	−0.372547	+	0.121048i	−0.0202939	+	0.00659390i	−0.319146	−	0.947705i	$-0.603396\pi$
$337$	−0.372547	+	0.121048i	−0.0202939	+	0.00659390i	0.298852	+	0.954299i	$0.403396\pi$
$338$	−19.2611	−	26.5107i	−1.04767	−	1.44199i
$339$	−12.8144	−	10.6761i	−0.695981	−	0.579848i
$340$			5.91059i			0.320547i
$341$	2.83937	−	1.47867i	0.153760	−	0.0800746i
$342$	0.957670	−	7.17945i	0.0517849	−	0.388220i
$343$	3.06917	+	2.22988i	0.165720	+	0.120402i
$344$	1.74551	−	1.26819i	0.0941117	−	0.0683761i
$345$	−2.24934	−	8.88860i	−0.121100	−	0.478546i
$346$	−6.65296			−0.357665
$347$	−20.4773			−1.09928			−0.549640	−	0.835401i	$-0.685235\pi$
$347$	−20.4773			−1.09928			−0.549640	+	0.835401i	$0.685235\pi$
$348$	−4.09403	+	1.03603i	−0.219463	+	0.0555371i
$349$	−6.38250	+	19.6433i	−0.341647	+	1.05148i	0.621707	+	0.783250i	$0.286440\pi$
$349$	−6.38250	+	19.6433i	−0.341647	+	1.05148i	−0.963354	+	0.268233i	$0.913560\pi$
$350$	0.259090	+	0.0841834i	0.0138489	+	0.00449979i
$351$	23.7960	+	25.8750i	1.27013	+	1.38111i
$352$	−0.546834	+	0.177677i	−0.0291463	+	0.00947022i
$353$	19.7050	+	14.3165i	1.04879	+	0.761990i	0.971982	−	0.235056i	$-0.0755274\pi$
$353$	19.7050	+	14.3165i	1.04879	+	0.761990i	0.0768072	+	0.997046i	$0.475527\pi$
$354$	11.7581	+	18.6708i	0.624937	+	0.992342i
$355$	1.35447	−	4.16863i	0.0718878	−	0.221248i
$356$	12.2898	−	8.92909i	0.651360	−	0.473241i
$357$	−1.48619	−	2.35993i	−0.0786575	−	0.124901i
$358$	7.13114	+	2.31705i	0.376892	+	0.122460i
$359$	18.0363	+	24.8248i	0.951918	+	1.31020i	0.950670	+	0.310204i	$0.100397\pi$
$359$	18.0363	+	24.8248i	0.951918	+	1.31020i	0.00124802	+	0.999999i	$0.499603\pi$
$360$	2.17259	+	2.06878i	0.114506	+	0.109034i
$361$	−4.07004	−	12.5263i	−0.214213	−	0.659279i
$362$	−17.4499	−	12.6781i	−0.917149	−	0.666348i
$363$	−17.1585	−	6.86254i	−0.900588	−	0.360190i
$364$	1.75281	+	0.569524i	0.0918724	+	0.0298512i
$365$	−3.66099	−	11.2674i	−0.191625	−	0.589760i
$366$	−1.20783	+	18.1899i	−0.0631344	+	0.950802i
$367$		−	31.2674i		−	1.63215i	−0.577949	−	0.816073i	$-0.696147\pi$
$367$		−	31.2674i		−	1.63215i	0.577949	−	0.816073i	$-0.303853\pi$
$368$	−1.63581	−	5.03452i	−0.0852727	−	0.262442i
$369$	10.7036	+	19.7942i	0.557209	+	1.03045i
$370$	5.79681	−	7.97862i	0.301362	−	0.414789i
$371$	2.78308			0.144490
$372$	−8.32717	−	4.86397i	−0.431744	−	0.252185i
$373$	−10.1885			−0.527540			−0.263770	−	0.964586i	$-0.584966\pi$
$373$	−10.1885			−0.527540			−0.263770	+	0.964586i	$0.584966\pi$
$374$	1.99755	−	2.74940i	0.103291	−	0.142168i
$375$	1.46563	−	0.922996i	0.0756849	−	0.0476633i
$376$	−3.85590	−	11.8672i	−0.198853	−	0.612006i
$377$			16.4951i			0.849542i
$378$	−1.38764	−	0.279716i	−0.0713725	−	0.0143871i
$379$	10.2591	+	31.5742i	0.526974	+	1.62186i	0.760379	+	0.649480i	$0.225013\pi$
$379$	10.2591	+	31.5742i	0.526974	+	1.62186i	−0.233405	+	0.972380i	$0.574987\pi$
$380$	−2.29618	−	0.746074i	−0.117792	−	0.0382728i
$381$	13.2091	−	33.0270i	0.676724	−	1.69202i
$382$	5.13627	+	3.73172i	0.262794	+	0.190931i
$383$	6.57595	+	20.2387i	0.336015	+	1.03415i	0.966220	+	0.257720i	$0.0829711\pi$
$383$	6.57595	+	20.2387i	0.336015	+	1.03415i	−0.630204	+	0.776429i	$0.717029\pi$
$384$	1.33073	+	1.10868i	0.0679084	+	0.0565770i
$385$	−0.0920686	−	0.126722i	−0.00469225	−	0.00645833i
$386$	−8.49380	−	2.75980i	−0.432323	−	0.140470i
$387$	3.07879	+	5.69360i	0.156504	+	0.289422i
$388$	2.32883	−	1.69199i	0.118228	−	0.0858980i
$389$	0.493699	−	1.51945i	0.0250315	−	0.0770391i	−0.937760	−	0.347283i	$-0.887104\pi$
$389$	0.493699	−	1.51945i	0.0250315	−	0.0770391i	0.962792	+	0.270244i	$0.0871043\pi$
$390$	9.91541	−	6.24433i	0.502086	−	0.316194i
$391$	25.3128	+	18.3908i	1.28012	+	0.930063i
$392$	6.58681	−	2.14019i	0.332684	−	0.108096i
$393$	−19.5062	−	16.2514i	−0.983960	−	0.819773i
$394$	10.3720	+	3.37007i	0.522534	+	0.169782i
$395$	−1.77764	+	5.47101i	−0.0894428	+	0.275277i
$396$	−0.311446	−	1.69658i	−0.0156507	−	0.0852562i
$397$	−13.9033			−0.697788			−0.348894	−	0.937162i	$-0.613443\pi$
$397$	−13.9033			−0.697788			−0.348894	+	0.937162i	$0.613443\pi$
$398$	13.2699			0.665162
$399$	1.10440	−	0.279478i	0.0552890	−	0.0139914i
$400$	0.809017	−	0.587785i	0.0404508	−	0.0293893i
$401$	27.4172	+	19.9197i	1.36915	+	0.994744i	0.997803	+	0.0662494i	$0.0211033\pi$
$401$	27.4172	+	19.9197i	1.36915	+	0.994744i	0.371345	+	0.928495i	$0.378897\pi$
$402$	16.8588	+	1.11944i	0.840840	+	0.0558327i
$403$	−26.3971	+	26.8707i	−1.31493	+	1.33852i
$404$			12.1240i			0.603192i
$405$	−7.01362	+	5.63996i	−0.348510	+	0.280252i
$406$	−0.390420	−	0.537367i	−0.0193762	−	0.0266691i
$407$	−5.39294	+	1.75227i	−0.267318	+	0.0868570i
$408$	−10.2149	−	0.678284i	−0.505715	−	0.0335801i
$409$		−	2.33373i		−	0.115396i	−0.998334	−	0.0576979i	$-0.981624\pi$
$409$		−	2.33373i		−	0.115396i	0.998334	−	0.0576979i	$-0.0183760\pi$
$410$	7.13383	−	2.31792i	0.352315	−	0.114474i
$411$	−5.63796	−	2.25490i	−0.278100	−	0.111226i
$412$	−0.0454876	+	0.139996i	−0.00224101	+	0.00689713i
$413$	−2.03986	+	2.80763i	−0.100375	+	0.138154i
$414$	15.6198	−	2.86737i	0.767672	−	0.140924i
$415$	−5.71163	+	7.86138i	−0.280373	+	0.385900i
$416$	5.47323	−	3.97653i	0.268347	−	0.194965i
$417$	−6.31902	+	15.7995i	−0.309444	+	0.773706i
$418$	0.815958	+	1.12307i	0.0399098	+	0.0549311i
$419$	−11.8558	−	16.3181i	−0.579193	−	0.797191i	0.414413	−	0.910089i	$-0.363987\pi$
$419$	−11.8558	−	16.3181i	−0.579193	−	0.797191i	−0.993607	+	0.112898i	$0.963987\pi$
$420$	−0.175222	+	0.438110i	−0.00854996	+	0.0213776i
$421$	9.13913	−	6.63996i	0.445414	−	0.323612i	−0.342369	−	0.939566i	$-0.611229\pi$
$421$	9.13913	−	6.63996i	0.445414	−	0.323612i	0.787782	+	0.615954i	$0.211229\pi$
$422$	4.30154	−	5.92057i	0.209396	−	0.288209i
$423$	36.8186	−	6.75891i	1.79018	−	0.328629i
$424$	6.00482	−	8.26492i	0.291620	−	0.401380i
$425$	−1.82647	+	5.62130i	−0.0885969	+	0.272673i
$426$	7.04897	+	2.81924i	0.341524	+	0.136592i
$427$	−2.72694	+	0.886037i	−0.131966	+	0.0428783i
$428$			2.06220i			0.0996802i
$429$	−6.72264	−	0.446391i	−0.324572	−	0.0215520i
$430$	2.05197	−	0.666726i	0.0989549	−	0.0321524i
$431$	2.39496	+	3.29639i	0.115361	+	0.158781i	0.862793	−	0.505558i	$-0.168713\pi$
$431$	2.39496	+	3.29639i	0.115361	+	0.158781i	−0.747432	+	0.664339i	$0.768713\pi$
$432$	−3.82468	+	3.51737i	−0.184015	+	0.169229i
$433$			15.7273i			0.755806i	0.925845	+	0.377903i	$0.123355\pi$
$433$			15.7273i			0.755806i	−0.925845	+	0.377903i	$0.876645\pi$
$434$	0.223950	−	1.50016i	0.0107499	−	0.0720102i
$435$	−4.21381	−	0.279802i	−0.202037	−	0.0134155i
$436$	3.65032	+	2.65211i	0.174818	+	0.127013i
$437$	−10.3397	+	7.51225i	−0.494616	+	0.359360i
$438$	19.8929	−	5.03407i	0.950518	−	0.240537i
$439$	−9.19440			−0.438825			−0.219413	−	0.975632i	$-0.570414\pi$
$439$	−9.19440			−0.438825			−0.219413	+	0.975632i	$0.570414\pi$
$440$	−0.574975			−0.0274109
$441$	3.75147	+	20.4359i	0.178642	+	0.973137i
$442$	−12.3566	+	38.0297i	−0.587743	+	1.80889i
$443$	6.60622	+	2.14649i	0.313871	+	0.101983i	0.461716	−	0.887028i	$-0.347234\pi$
$443$	6.60622	+	2.14649i	0.313871	+	0.101983i	−0.147845	+	0.989010i	$0.547234\pi$
$444$	13.1238	+	10.9339i	0.622828	+	0.518901i
$445$	14.4476	−	4.69430i	0.684880	−	0.222531i
$446$	16.3648	+	11.8897i	0.774896	+	0.562995i
$447$	−7.85479	+	4.94663i	−0.371519	+	0.233968i
$448$	−0.0841834	+	0.259090i	−0.00397729	+	0.0122408i
$449$	7.96546	−	5.78725i	0.375913	−	0.273117i	−0.383745	−	0.923439i	$-0.625366\pi$
$449$	7.96546	−	5.78725i	0.375913	−	0.273117i	0.759659	+	0.650322i	$0.225366\pi$
$450$	1.42697	+	2.63889i	0.0672681	+	0.124399i
$451$	−4.10178	−	1.33275i	−0.193145	−	0.0627566i
$452$	−5.66014	−	7.79052i	−0.266231	−	0.366435i
$453$	7.38329	+	6.15129i	0.346897	+	0.289013i
$454$	−0.948779	−	2.92004i	−0.0445284	−	0.137044i
$455$	1.49103	+	1.08330i	0.0699007	+	0.0507858i
$456$	1.55290	−	3.88275i	0.0727214	−	0.181826i
$457$	−1.52689	−	0.496118i	−0.0714250	−	0.0232074i	0.273087	−	0.961989i	$-0.411955\pi$
$457$	−1.52689	−	0.496118i	−0.0714250	−	0.0232074i	−0.344512	+	0.938782i	$0.611955\pi$
$458$	8.41558	+	25.9005i	0.393234	+	1.21025i
$459$	6.06883	−	30.1067i	0.283269	−	1.40526i
$460$		−	5.29360i		−	0.246816i
$461$	−7.60371	−	23.4018i	−0.354140	−	1.08993i	−0.956506	−	0.291712i	$-0.905775\pi$
$461$	−7.60371	−	23.4018i	−0.354140	−	1.08993i	0.602366	−	0.798220i	$-0.294225\pi$
$462$	0.229572	−	0.144575i	0.0106806	−	0.00672623i
$463$	16.2602	−	22.3802i	0.755674	−	1.04010i	−0.241888	−	0.970304i	$-0.577767\pi$
$463$	16.2602	−	22.3802i	0.755674	−	1.04010i	0.997562	−	0.0697916i	$-0.0222334\pi$
$464$	−2.43820			−0.113191
$465$	−6.41656	−	7.19915i	−0.297561	−	0.333853i
$466$	−22.2597			−1.03116
$467$	1.49867	−	2.06274i	0.0693501	−	0.0954522i	−0.772933	−	0.634488i	$-0.781211\pi$
$467$	1.49867	−	2.06274i	0.0693501	−	0.0954522i	0.842283	+	0.539035i	$0.181211\pi$
$468$	9.65386	+	17.8528i	0.446250	+	0.825248i
$469$	0.821197	+	2.52738i	0.0379193	+	0.116704i
$470$		−	12.4780i		−	0.575565i
$471$	−1.40776	+	21.2009i	−0.0648664	+	0.976886i
$472$	3.93659	+	12.1156i	0.181196	+	0.557665i
$473$	−1.17983	−	0.383351i	−0.0542488	−	0.0176265i
$474$	−9.25125	−	3.70004i	−0.424924	−	0.169948i
$475$	−1.95325	−	1.41912i	−0.0896212	−	0.0651136i
$476$	−0.497573	−	1.53137i	−0.0228062	−	0.0701904i
$477$	22.1952	+	21.1346i	1.01625	+	0.967689i
$478$	−12.7578	−	17.5596i	−0.583526	−	0.803155i
$479$	17.8946	+	5.81431i	0.817625	+	0.265663i	0.687824	−	0.725877i	$-0.258566\pi$
$479$	17.8946	+	5.81431i	0.817625	+	0.265663i	0.129801	+	0.991540i	$0.458566\pi$
$480$	0.922996	+	1.46563i	0.0421288	+	0.0668967i
$481$	53.9776	−	39.2170i	2.46117	−	1.78814i
$482$	−0.370152	+	1.13921i	−0.0168600	+	0.0518896i
$483$	1.33105	+	2.11359i	0.0605650	+	0.0961716i
$484$	−8.63173	−	6.27132i	−0.392351	−	0.285060i
$485$	2.73770	−	0.889534i	0.124313	−	0.0403917i
$486$	−8.94237	−	12.7685i	−0.405634	−	0.579190i
$487$	−22.5834	−	7.33778i	−1.02335	−	0.332507i	−0.251192	−	0.967937i	$-0.580823\pi$
$487$	−22.5834	−	7.33778i	−1.02335	−	0.332507i	−0.772158	+	0.635431i	$0.780823\pi$
$488$	−3.25243	+	10.0099i	−0.147231	+	0.453129i
$489$	14.7327	−	3.72825i	0.666237	−	0.168597i
$490$	6.92579			0.312875
$491$	−20.3125			−0.916691			−0.458345	−	0.888774i	$-0.651558\pi$
$491$	−20.3125			−0.916691			−0.458345	+	0.888774i	$0.651558\pi$
$492$	3.18728	+	12.5950i	0.143694	+	0.567827i
$493$	11.6589	−	8.47069i	0.525091	−	0.381501i
$494$	−13.2143	−	9.60073i	−0.594538	−	0.431957i
$495$	0.228069	−	1.70978i	0.0102509	−	0.0768490i
$496$	−3.97185	−	3.90185i	−0.178341	−	0.175198i
$497$			1.19407i			0.0535615i
$498$	−12.9309	−	10.7732i	−0.579449	−	0.482761i
$499$	−9.68099	−	13.3247i	−0.433381	−	0.596497i	0.535344	−	0.844634i	$-0.320182\pi$
$499$	−9.68099	−	13.3247i	−0.433381	−	0.596497i	−0.968725	+	0.248136i	$0.920182\pi$
$500$	0.951057	−	0.309017i	0.0425325	−	0.0138197i
$501$	−0.329361	+	4.96016i	−0.0147147	+	0.221604i
$502$		−	19.5235i		−	0.871377i
$503$	17.9498	−	5.83225i	0.800343	−	0.260047i	0.119840	−	0.992793i	$-0.461762\pi$
$503$	17.9498	−	5.83225i	0.800343	−	0.260047i	0.680502	+	0.732746i	$0.261762\pi$
$504$	−0.737053	−	0.353103i	−0.0328310	−	0.0157285i
$505$	−3.74652	+	11.5306i	−0.166718	+	0.513105i
$506$	−1.78904	+	2.46240i	−0.0795324	+	0.109467i
$507$	55.0231	−	13.9241i	2.44366	−	0.618390i
$508$	12.0711	−	16.6145i	0.535570	−	0.737149i
$509$	−34.9656	+	25.4040i	−1.54982	+	1.12601i	−0.606047	+	0.795429i	$0.707246\pi$
$509$	−34.9656	+	25.4040i	−1.54982	+	1.12601i	−0.943777	+	0.330584i	$0.892754\pi$
$510$	−9.50539	−	3.80168i	−0.420906	−	0.168341i
$511$	1.89705	+	2.61106i	0.0839205	+	0.115507i
$512$	0.587785	+	0.809017i	0.0259767	+	0.0357538i
$513$	10.9300	+	6.15793i	0.482571	+	0.271879i
$514$	−10.9981	+	7.99057i	−0.485104	+	0.352449i
$515$	−0.0865226	+	0.119088i	−0.00381264	+	0.00524765i
$516$	0.916787	+	3.62282i	0.0403593	+	0.159486i
$517$	−4.21708	+	5.80431i	−0.185467	+	0.255273i
$518$	−0.830227	+	2.55517i	−0.0364781	+	0.112268i
$519$	4.27917	−	10.6993i	0.187835	−	0.469646i
$520$	6.43416	−	2.09059i	0.282157	−	0.0916783i
$521$			11.0722i			0.485080i	0.970141	+	0.242540i	$0.0779806\pi$
$521$			11.0722i			0.485080i	−0.970141	+	0.242540i	$0.922019\pi$
$522$	0.967132	−	7.25039i	0.0423302	−	0.317341i
$523$	−3.63433	+	1.18086i	−0.158918	+	0.0516356i	−0.387396	−	0.921914i	$-0.626625\pi$
$523$	−3.63433	+	1.18086i	−0.158918	+	0.0516356i	0.228478	+	0.973549i	$0.426625\pi$
$524$	−8.61596	−	11.8588i	−0.376390	−	0.518056i
$525$	−0.302029	+	0.362521i	−0.0131816	+	0.0158217i
$526$		−	30.2640i		−	1.31957i
$527$	32.5481	+	4.85890i	1.41782	+	0.211657i
$528$	0.0659827	−	0.993698i	0.00287153	−	0.0432452i
$529$	−4.06309	−	2.95200i	−0.176656	−	0.128348i
$530$	8.26492	−	6.00482i	0.359005	−	0.260833i
$531$	−37.5891	+	6.90035i	−1.63123	+	0.299450i
$532$	0.657724			0.0285159
$533$	50.7460			2.19805
$534$	6.45493	+	25.5076i	0.279332	+	1.10382i
$535$	−0.637255	+	1.96127i	−0.0275509	+	0.0847930i
$536$	9.27742	+	3.01442i	0.400723	+	0.130203i
$537$	−8.31300	+	9.97795i	−0.358732	+	0.430580i
$538$	−15.4778	+	5.02904i	−0.667296	+	0.216818i
$539$	−3.22163	−	2.34065i	−0.138765	−	0.100819i
$540$	−4.72441	+	2.16332i	−0.203306	+	0.0930946i
$541$	−7.56557	+	23.2844i	−0.325269	+	1.00108i	0.646050	+	0.763295i	$0.276420\pi$
$541$	−7.56557	+	23.2844i	−0.325269	+	1.00108i	−0.971319	+	0.237780i	$0.923580\pi$
$542$	2.91169	−	2.11546i	0.125068	−	0.0908670i
$543$	31.6127	−	19.9084i	1.35663	−	0.854351i
$544$	−5.62130	−	1.82647i	−0.241011	−	0.0783093i
$545$	2.65211	+	3.65032i	0.113604	+	0.156362i
$546$	−2.04331	+	2.45255i	−0.0874457	+	0.104960i
$547$	2.30956	+	7.10808i	0.0987495	+	0.303920i	0.988213	−	0.153087i	$-0.0489215\pi$
$547$	2.30956	+	7.10808i	0.0987495	+	0.303920i	−0.889463	+	0.457007i	$0.848922\pi$
$548$	−2.83623	−	2.06064i	−0.121158	−	0.0880261i
$549$	−28.4761	−	13.6421i	−1.21533	−	0.582233i
$550$	−0.546834	−	0.177677i	−0.0233171	−	0.00757618i
$551$	1.81908	+	5.59855i	0.0774954	+	0.238506i
$552$	9.14865	+	0.607481i	0.389392	+	0.0258561i
$553$		−	1.56713i		−	0.0666412i
$554$	5.88879	+	18.1238i	0.250191	+	0.770008i
$555$	9.10270	+	14.4542i	0.386388	+	0.613549i
$556$	−5.77462	+	7.94809i	−0.244899	+	0.337074i
$557$	−37.5044			−1.58911			−0.794557	−	0.607189i	$-0.792297\pi$
$557$	−37.5044			−1.58911			−0.794557	+	0.607189i	$0.792297\pi$
$558$	13.1782	−	10.2632i	0.557879	−	0.434477i
$559$	14.5966			0.617369
$560$	−0.160126	+	0.220395i	−0.00676657	+	0.00931338i
$561$	3.13675	+	4.98087i	0.132434	+	0.210292i
$562$	0.124752	+	0.383946i	0.00526233	+	0.0161958i
$563$		−	5.63067i		−	0.237305i	−0.992936	−	0.118652i	$-0.962143\pi$
$563$		−	5.63067i		−	0.237305i	0.992936	−	0.118652i	$-0.0378574\pi$
$564$	21.5650	+	1.43194i	0.908049	+	0.0602955i
$565$	−2.97571	−	9.15830i	−0.125189	−	0.385293i
$566$	−11.5964	−	3.76791i	−0.487434	−	0.158377i
$567$	1.34237	−	2.05169i	0.0563741	−	0.0861627i
$568$	3.54605	+	2.57635i	0.148789	+	0.108101i
$569$	−8.57619	−	26.3948i	−0.359533	−	1.10653i	−0.953334	−	0.301916i	$-0.902374\pi$
$569$	−8.57619	−	26.3948i	−0.359533	−	1.10653i	0.593802	−	0.804611i	$-0.297626\pi$
$570$	2.67673	−	3.21284i	0.112116	−	0.134571i
$571$	−2.07688	−	2.85858i	−0.0869148	−	0.119628i	0.763345	−	0.645991i	$-0.223555\pi$
$571$	−2.07688	−	2.85858i	−0.0869148	−	0.119628i	−0.850260	+	0.526363i	$0.823555\pi$
$572$	−3.69948	−	1.20204i	−0.154683	−	0.0502596i
$573$	−9.30497	+	5.85990i	−0.388721	+	0.244801i
$574$	−1.65317	+	1.20110i	−0.0690020	+	0.0501329i
$575$	1.63581	−	5.03452i	0.0682182	−	0.209954i
$576$	−2.63889	+	1.42697i	−0.109954	+	0.0594571i
$577$	−2.86965	−	2.08492i	−0.119465	−	0.0867965i	0.526448	−	0.850207i	$-0.323523\pi$
$577$	−2.86965	−	2.08492i	−0.119465	−	0.0867965i	−0.645914	+	0.763411i	$0.723523\pi$
$578$	17.0572	−	5.54224i	0.709488	−	0.230527i
$579$	9.90150	−	11.8846i	0.411492	−	0.493907i
$580$	−2.31887	−	0.753446i	−0.0962857	−	0.0312851i
$581$	0.818027	−	2.51763i	0.0339375	−	0.104449i
$582$	1.22316	+	4.83350i	0.0507016	+	0.200355i
$583$	−5.87395			−0.243274
$584$	11.8472			0.490241
$585$	3.66453	+	19.9623i	0.151510	+	0.825338i
$586$	25.5621	−	18.5720i	1.05596	−	0.767201i
$587$	−17.0600	−	12.3948i	−0.704141	−	0.511588i	0.177137	−	0.984186i	$-0.443316\pi$
$587$	−17.0600	−	12.3948i	−0.704141	−	0.511588i	−0.881278	+	0.472598i	$0.843316\pi$
$588$	−0.794786	+	11.9695i	−0.0327764	+	0.493612i
$589$	−5.99605	+	12.0312i	−0.247063	+	0.495735i
$590$			12.7391i			0.524460i
$591$	−12.0910	+	14.5126i	−0.497357	+	0.596969i
$592$	5.79681	+	7.97862i	0.238247	+	0.327919i
$593$	−1.11746	+	0.363083i	−0.0458884	+	0.0149100i	−0.331871	−	0.943325i	$-0.607680\pi$
$593$	−1.11746	+	0.363083i	−0.0458884	+	0.0149100i	0.285983	+	0.958235i	$0.407680\pi$
$594$	2.92875	+	0.590369i	0.120168	+	0.0242231i
$595$		−	1.61018i		−	0.0660110i
$596$	−5.09702	+	1.65612i	−0.208782	+	0.0678374i
$597$	−8.53520	+	21.3407i	−0.349322	+	0.873416i
$598$	11.0667	−	34.0599i	0.452553	−	1.39281i
$599$	−10.6296	+	14.6304i	−0.434313	+	0.597781i	−0.968937	−	0.247310i	$-0.920454\pi$
$599$	−10.6296	+	14.6304i	−0.434313	+	0.597781i	0.534623	+	0.845091i	$0.320454\pi$
$600$	0.424916	+	1.67912i	0.0173471	+	0.0685498i
$601$	6.85803	−	9.43927i	0.279745	−	0.385036i	−0.645904	−	0.763418i	$-0.723520\pi$
$601$	6.85803	−	9.43927i	0.279745	−	0.385036i	0.925649	+	0.378382i	$0.123520\pi$
$602$	−0.475518	+	0.345484i	−0.0193807	+	0.0140809i
$603$	−12.6438	+	26.3922i	−0.514896	+	1.07477i
$604$	3.26122	+	4.48868i	0.132697	+	0.182642i
$605$	−6.27132	−	8.63173i	−0.254965	−	0.350930i
$606$	−19.4978	−	7.79813i	−0.792043	−	0.316777i
$607$	24.9014	−	18.0919i	1.01071	−	0.734327i	0.0463559	−	0.998925i	$-0.485239\pi$
$607$	24.9014	−	18.0919i	1.01071	−	0.734327i	0.964359	+	0.264598i	$0.0852392\pi$
$608$	1.41912	−	1.95325i	0.0575528	−	0.0792147i
$609$	1.11531	−	0.282239i	0.0451946	−	0.0114369i
$610$	−6.18649	+	8.51497i	−0.250484	+	0.344761i
$611$	26.0863	−	80.2852i	1.05534	−	3.24799i
$612$	7.66104	−	15.9914i	0.309679	−	0.646413i
$613$	−3.50002	+	1.13722i	−0.141364	+	0.0459321i	−0.378845	−	0.925460i	$-0.623679\pi$
$613$	−3.50002	+	1.13722i	−0.141364	+	0.0459321i	0.237480	+	0.971392i	$0.423679\pi$
$614$		−	5.81380i		−	0.234626i
$615$	−0.860790	+	12.9635i	−0.0347104	+	0.522738i
$616$	0.148970	−	0.0484034i	0.00600218	−	0.00195023i
$617$	5.33631	+	7.34480i	0.214832	+	0.295691i	0.902809	−	0.430042i	$-0.141501\pi$
$617$	5.33631	+	7.34480i	0.214832	+	0.295691i	−0.687977	+	0.725732i	$0.741501\pi$
$618$	−0.195884	−	0.163198i	−0.00787962	−	0.00656480i
$619$		−	20.0124i		−	0.804366i	−0.915559	−	0.402183i	$-0.868251\pi$
$619$		−	20.0124i		−	0.804366i	0.915559	−	0.402183i	$-0.131749\pi$
$620$	−2.57172	−	4.93825i	−0.103283	−	0.198325i
$621$	−5.43533	+	26.9640i	−0.218112	+	1.08203i
$622$	−8.92434	−	6.48391i	−0.357833	−	0.259981i
$623$	−3.34803	+	2.43249i	−0.134136	+	0.0974556i
$624$	2.87468	+	11.3597i	0.115079	+	0.454753i
$625$	1.00000			0.0400000
$626$	0.442003			0.0176660
$627$	−2.33094	+	0.589864i	−0.0930887	+	0.0235569i
$628$	−3.79081	+	11.6669i	−0.151270	+	0.465560i
$629$	−55.4380	−	18.0129i	−2.21046	−	0.718221i
$630$	−0.591864	−	0.563583i	−0.0235804	−	0.0224537i
$631$	−22.7939	+	7.40618i	−0.907409	+	0.294835i	−0.725292	−	0.688442i	$-0.758295\pi$
$631$	−22.7939	+	7.40618i	−0.907409	+	0.294835i	−0.182118	+	0.983277i	$0.558295\pi$
$632$	−4.65392	−	3.38127i	−0.185123	−	0.134500i
$633$	6.75469	+	10.7258i	0.268475	+	0.426313i
$634$	−0.761611	+	2.34400i	−0.0302474	+	0.0930921i
$635$	16.6145	−	12.0711i	0.659326	−	0.479028i
$636$	9.42934	+	14.9729i	0.373897	+	0.593715i
$637$	44.5616	+	14.4790i	1.76560	+	0.573677i
$638$	0.824019	+	1.13417i	0.0326232	+	0.0449020i
$639$	−9.06777	+	9.52281i	−0.358715	+	0.376717i
$640$	0.309017	+	0.951057i	0.0122150	+	0.0375938i
$641$	−17.7151	−	12.8707i	−0.699703	−	0.508364i	0.180133	−	0.983642i	$-0.442347\pi$
$641$	−17.7151	−	12.8707i	−0.699703	−	0.508364i	−0.879835	+	0.475278i	$0.842347\pi$
$642$	−3.31642	−	1.32640i	−0.130889	−	0.0523489i
$643$	3.59837	+	1.16918i	0.141906	+	0.0461080i	0.379109	−	0.925352i	$-0.376231\pi$
$643$	3.59837	+	1.16918i	0.141906	+	0.0461080i	−0.237203	+	0.971460i	$0.576231\pi$
$644$	0.445633	+	1.37152i	0.0175604	+	0.0540454i
$645$	−0.247597	+	3.72881i	−0.00974914	+	0.146822i
$646$			14.2702i			0.561454i
$647$	−3.65933	−	11.2623i	−0.143863	−	0.442766i	0.853000	−	0.521911i	$-0.174781\pi$
$647$	−3.65933	−	11.2623i	−0.143863	−	0.442766i	−0.996863	+	0.0791456i	$0.974781\pi$
$648$	−3.19659	−	8.41319i	−0.125574	−	0.330501i
$649$	4.30532	−	5.92577i	0.168999	−	0.232607i
$650$	6.76528			0.265356
$651$	2.26851	+	1.32506i	0.0889101	+	0.0519331i
$652$	8.77407			0.343619
$653$	−24.7860	+	34.1149i	−0.969950	+	1.33502i	−0.0278773	+	0.999611i	$0.508875\pi$
$653$	−24.7860	+	34.1149i	−0.969950	+	1.33502i	−0.942072	+	0.335410i	$0.891125\pi$
$654$	−6.61299	+	4.16459i	−0.258588	+	0.162849i
$655$	−4.52968	−	13.9409i	−0.176989	−	0.544716i
$656$			7.50095i			0.292863i
$657$	−4.69929	+	35.2296i	−0.183337	+	1.37444i
$658$	1.05044	+	3.23291i	0.0409503	+	0.126032i
$659$	14.6108	+	4.74735i	0.569158	+	0.184931i	0.579438	−	0.815017i	$-0.303272\pi$
$659$	14.6108	+	4.74735i	0.569158	+	0.184931i	−0.0102798	+	0.999947i	$0.503272\pi$
$660$	0.369823	−	0.924673i	0.0143953	−	0.0359929i
$661$	−5.49157	−	3.98986i	−0.213597	−	0.155187i	0.475843	−	0.879530i	$-0.342143\pi$
$661$	−5.49157	−	3.98986i	−0.213597	−	0.155187i	−0.689440	+	0.724343i	$0.742143\pi$
$662$	9.55672	+	29.4126i	0.371433	+	1.14315i
$663$	−53.2115	−	44.3324i	−2.06656	−	1.72173i
$664$	−5.71163	−	7.86138i	−0.221654	−	0.305081i
$665$	0.625533	+	0.203248i	0.0242571	+	0.00788161i
$666$	−26.0251	+	14.0730i	−1.00845	+	0.545316i
$667$	−10.4419	+	7.58647i	−0.404311	+	0.293749i
$668$	−0.886897	+	2.72959i	−0.0343151	+	0.105611i
$669$	−29.6468	+	18.6704i	−1.14621	+	0.721838i
$670$	7.89184	+	5.73376i	0.304889	+	0.221514i
$671$	5.75547	−	1.87007i	0.222188	−	0.0721931i
$672$	−0.362521	−	0.302029i	−0.0139845	−	0.0116510i
$673$	−8.03401	−	2.61041i	−0.309688	−	0.100624i	0.150050	−	0.988678i	$-0.452057\pi$
$673$	−8.03401	−	2.61041i	−0.309688	−	0.100624i	−0.459738	+	0.888055i	$0.652057\pi$
$674$	0.121048	−	0.372547i	0.00466259	−	0.0143500i
$675$	−5.16168	+	0.597520i	−0.198673	+	0.0229986i
$676$	32.7690			1.26035
$677$	−6.74264			−0.259141			−0.129570	−	0.991570i	$-0.541360\pi$
$677$	−6.74264			−0.259141			−0.129570	+	0.991570i	$0.541360\pi$
$678$	16.1693	−	4.09178i	0.620977	−	0.157144i
$679$	−0.634427	+	0.460938i	−0.0243471	+	0.0176892i
$680$	−4.78177	−	3.47416i	−0.183372	−	0.133228i
$681$	5.30626	+	0.352341i	0.203336	+	0.0135018i
$682$	−0.472668	+	3.16624i	−0.0180994	+	0.121242i
$683$		−	47.6805i		−	1.82444i	−0.409698	−	0.912221i	$-0.634366\pi$
$683$		−	47.6805i		−	1.82444i	0.409698	−	0.912221i	$-0.365634\pi$
$684$	5.24539	+	4.99475i	0.200563	+	0.190979i
$685$	−2.06064	−	2.83623i	−0.0787330	−	0.108367i
$686$	−3.60803	+	1.17232i	−0.137755	+	0.0447594i
$687$	−47.0660	−	3.12523i	−1.79568	−	0.119235i
$688$			2.15757i			0.0822566i
$689$	65.7315	−	21.3574i	2.50417	−	0.813654i
$690$	8.51316	+	3.40484i	0.324090	+	0.129620i
$691$	2.02193	−	6.22285i	0.0769177	−	0.236728i	−0.905203	−	0.424979i	$-0.860282\pi$
$691$	2.02193	−	6.22285i	0.0769177	−	0.236728i	0.982121	+	0.188250i	$0.0602816\pi$
$692$	3.91051	−	5.38236i	0.148655	−	0.204606i
$693$	0.0848450	+	0.462187i	0.00322299	+	0.0175570i
$694$	12.0363	−	16.5665i	0.456891	−	0.628856i
$695$	−7.94809	+	5.77462i	−0.301488	+	0.219044i
$696$	1.56825	−	3.92111i	0.0594442	−	0.148629i
$697$	−26.0595	−	35.8678i	−0.987073	−	1.35859i
$698$	−12.1402	−	16.7096i	−0.459515	−	0.632468i
$699$	14.3174	−	35.7979i	0.541533	−	1.35400i
$700$	−0.220395	+	0.160126i	−0.00833014	+	0.00605220i
$701$	1.02376	−	1.40909i	0.0386670	−	0.0532205i	−0.789246	−	0.614077i	$-0.789528\pi$
$701$	1.02376	−	1.40909i	0.0386670	−	0.0532205i	0.827913	+	0.560857i	$0.189528\pi$
$702$	−34.9202	+	4.04239i	−1.31798	+	0.152570i
$703$	13.9955	−	19.2632i	0.527851	−	0.726524i
$704$	0.177677	−	0.546834i	0.00669646	−	0.0206096i
$705$	20.0670	+	8.02580i	0.755767	+	0.302269i
$706$	−23.1646	+	7.52662i	−0.871810	+	0.283268i
$707$		−	3.30286i		−	0.124217i
$708$	−22.0163	−	1.46190i	−0.827421	−	0.0549417i
$709$	7.51338	−	2.44125i	0.282171	−	0.0916829i	−0.164512	−	0.986375i	$-0.552605\pi$
$709$	7.51338	−	2.44125i	0.282171	−	0.0916829i	0.446683	+	0.894692i	$0.352605\pi$
$710$	2.57635	+	3.54605i	0.0966888	+	0.133081i
$711$	11.9008	−	12.4980i	0.446314	−	0.468711i
$712$			15.1911i			0.569309i
$713$	−29.1505	−	4.35170i	−1.09170	−	0.162972i
$714$	2.78279	+	0.184780i	0.104143	+	0.00691523i
$715$	−3.14697	−	2.28641i	−0.117690	−	0.0855068i
$716$	−6.06611	+	4.40728i	−0.226701	+	0.164708i
$717$	36.4450	−	9.22272i	1.36106	−	0.344429i
$718$	−30.6851			−1.14516
$719$	−2.84950			−0.106268			−0.0531341	−	0.998587i	$-0.516921\pi$
$719$	−2.84950			−0.106268			−0.0531341	+	0.998587i	$0.516921\pi$
$720$	−2.95069	+	0.541668i	−0.109966	+	0.0201868i
$721$	0.0123919	−	0.0381383i	0.000461498	−	0.00142034i
$722$	12.5263	+	4.07004i	0.466180	+	0.151471i
$723$	−1.59399	−	1.32801i	−0.0592812	−	0.0493894i
$724$	20.5136	−	6.66529i	0.762384	−	0.247713i
$725$	−1.97255	−	1.43314i	−0.0732585	−	0.0532254i
$726$	15.6374	−	9.84782i	0.580359	−	0.365487i
$727$	−3.73632	+	11.4992i	−0.138573	+	0.426483i	−0.996129	−	0.0879081i	$-0.971982\pi$
$727$	−3.73632	+	11.4992i	−0.138573	+	0.426483i	0.857556	+	0.514391i	$0.171982\pi$
$728$	−1.49103	+	1.08330i	−0.0552614	+	0.0401497i
$729$	26.2859	−	6.16842i	0.973553	−	0.228460i
$730$	11.2674	+	3.66099i	0.417024	+	0.135499i
$731$	−7.49574	−	10.3170i	−0.277240	−	0.381588i
$732$	−14.0060	−	11.6689i	−0.517677	−	0.431296i
$733$	−5.32642	−	16.3930i	−0.196736	−	0.605491i	−0.999952	−	0.00980314i	$-0.996880\pi$
$733$	−5.32642	−	16.3930i	−0.196736	−	0.605491i	0.803216	−	0.595688i	$-0.203120\pi$
$734$	25.2959	+	18.3785i	0.933688	+	0.678364i
$735$	−4.45465	+	11.1380i	−0.164312	+	0.410832i
$736$	5.03452	+	1.63581i	0.185575	+	0.0602969i
$737$	−1.73321	−	5.33429i	−0.0638438	−	0.196491i
$738$	−22.3053	−	2.97531i	−0.821069	−	0.109523i
$739$		−	26.3577i		−	0.969582i	−0.874630	−	0.484791i	$-0.838896\pi$
$739$		−	26.3577i		−	0.969582i	0.874630	−	0.484791i	$-0.161104\pi$
$740$	3.04756	+	9.37944i	0.112031	+	0.344795i
$741$	23.9392	−	15.0760i	0.879430	−	0.553830i
$742$	−1.63585	+	2.25156i	−0.0600540	+	0.0826572i
$743$	−33.2316			−1.21915			−0.609575	−	0.792729i	$-0.708660\pi$
$743$	−33.2316			−1.21915			−0.609575	+	0.792729i	$0.708660\pi$
$744$	8.82962	−	3.87785i	0.323710	−	0.142169i
$745$	−5.35932			−0.196350
$746$	5.98864	−	8.24266i	0.219260	−	0.301785i
$747$	25.6427	−	13.8662i	0.938216	−	0.507337i
$748$	1.05018	+	3.23211i	0.0383982	+	0.118178i
$749$		−	0.561791i		−	0.0205274i
$750$	−0.114757	+	1.72824i	−0.00419035	+	0.0631066i
$751$	5.30118	+	16.3153i	0.193443	+	0.595355i	0.999991	+	0.00418756i	$0.00133294\pi$
$751$	5.30118	+	16.3153i	0.193443	+	0.595355i	−0.806549	+	0.591168i	$0.798667\pi$
$752$	11.8672	+	3.85590i	0.432754	+	0.140610i
$753$	31.3976	+	12.5575i	1.14419	+	0.457620i
$754$	−13.3448	−	9.69558i	−0.485990	−	0.353092i
$755$	1.71452	+	5.27676i	0.0623979	+	0.192041i
$756$	1.04193	−	0.958212i	0.0378946	−	0.0348498i
$757$	−8.11950	−	11.1755i	−0.295108	−	0.406182i	0.635557	−	0.772054i	$-0.280771\pi$
$757$	−8.11950	−	11.1755i	−0.295108	−	0.406182i	−0.930665	+	0.365873i	$0.880771\pi$
$758$	−31.5742	−	10.2591i	−1.14683	−	0.372627i
$759$	−2.80932	−	4.46093i	−0.101972	−	0.161922i
$760$	1.95325	−	1.41912i	0.0708518	−	0.0514768i
$761$	8.81869	−	27.1411i	0.319677	−	0.983865i	−0.654109	−	0.756400i	$-0.726956\pi$
$761$	8.81869	−	27.1411i	0.319677	−	0.983865i	0.973786	−	0.227465i	$-0.0730437\pi$
$762$	18.9552	+	30.0992i	0.686676	+	1.09038i
$763$	−0.994430	−	0.722496i	−0.0360008	−	0.0261561i
$764$	−6.03805	+	1.96188i	−0.218449	+	0.0709783i
$765$	12.2277	−	12.8413i	0.442093	−	0.464278i
$766$	−20.2387	−	6.57595i	−0.731254	−	0.237599i
$767$	−26.6321	+	81.9653i	−0.961631	+	2.95960i
$768$	−1.67912	+	0.424916i	−0.0605900	+	0.0153328i
$769$	−10.5150			−0.379182			−0.189591	−	0.981863i	$-0.560716\pi$
$769$	−10.5150			−0.379182			−0.189591	+	0.981863i	$0.560716\pi$
$770$	0.156637			0.00564479
$771$	−5.77647	−	22.8266i	−0.208034	−	0.822079i
$772$	7.22526	−	5.24946i	0.260043	−	0.188932i
$773$	−16.3826	−	11.9026i	−0.589240	−	0.428108i	0.252803	−	0.967518i	$-0.418647\pi$
$773$	−16.3826	−	11.9026i	−0.589240	−	0.428108i	−0.842044	+	0.539410i	$0.818647\pi$
$774$	−6.41589	−	0.855818i	−0.230614	−	0.0307617i
$775$	−0.919844	−	5.49126i	−0.0330418	−	0.197252i
$776$			2.87859i			0.103335i
$777$	−3.57522	−	2.97865i	−0.128260	−	0.106859i
$778$	0.939071	+	1.29252i	0.0336673	+	0.0463391i
$779$	17.2235	−	5.59627i	0.617097	−	0.200507i
$780$	−0.776366	+	11.6921i	−0.0277984	+	0.418643i
$781$		−	2.52021i		−	0.0901800i
$782$	−29.7570	+	9.66862i	−1.06411	+	0.345749i
$783$	11.0380	+	6.21877i	0.394466	+	0.222241i
$784$	−2.14019	+	6.58681i	−0.0764352	+	0.235243i
$785$	−7.21054	+	9.92446i	−0.257355	+	0.354219i
$786$	24.6131	−	6.22857i	0.877921	−	0.222166i
$787$	11.1098	−	15.2913i	0.396021	−	0.545077i	−0.563718	−	0.825967i	$-0.690630\pi$
$787$	11.1098	−	15.2913i	0.396021	−	0.545077i	0.959740	+	0.280890i	$0.0906297\pi$
$788$	−8.82295	+	6.41025i	−0.314305	+	0.228356i
$789$	48.6704	+	19.4657i	1.73271	+	0.692998i
$790$	−3.38127	−	4.65392i	−0.120300	−	0.165579i
$791$	1.54195	+	2.12232i	0.0548255	+	0.0754609i
$792$	1.55562	+	0.745258i	0.0552766	+	0.0264816i
$793$	−57.6061	+	41.8533i	−2.04565	+	1.48625i
$794$	8.17217	−	11.2480i	0.290019	−	0.399177i
$795$	4.34095	+	17.1539i	0.153958	+	0.608386i
$796$	−7.79987	+	10.7356i	−0.276459	+	0.380513i
$797$	2.86628	−	8.82151i	0.101529	−	0.312474i	−0.887371	−	0.461056i	$-0.847471\pi$
$797$	2.86628	−	8.82151i	0.101529	−	0.312474i	0.988900	+	0.148582i	$0.0474708\pi$
$798$	−0.423047	+	1.05775i	−0.0149757	+	0.0374439i
$799$	−70.1424	+	22.7906i	−2.48146	+	0.806275i
$800$			1.00000i			0.0353553i
$801$	−45.1731	−	6.02566i	−1.59611	−	0.212906i
$802$	−32.2308	+	10.4724i	−1.13811	+	0.369794i
$803$	−4.00390	−	5.51090i	−0.141295	−	0.194475i
$804$	−10.8150	+	12.9810i	−0.381415	+	0.457806i
$805$			1.44210i			0.0508274i
$806$	−6.22300	−	37.1499i	−0.219196	−	1.30855i
$807$	1.86760	−	28.1260i	0.0657427	−	0.990083i
$808$	−9.80852	−	7.12631i	−0.345063	−	0.250703i
$809$	17.0191	−	12.3651i	0.598359	−	0.434733i	−0.246937	−	0.969032i	$-0.579424\pi$
$809$	17.0191	−	12.3651i	0.598359	−	0.434733i	0.845296	+	0.534298i	$0.179424\pi$
$810$	−0.440320	−	8.98922i	−0.0154713	−	0.315849i
$811$	−29.7279			−1.04389			−0.521943	−	0.852980i	$-0.674793\pi$
$811$	−29.7279			−1.04389			−0.521943	+	0.852980i	$0.674793\pi$
$812$	0.664222			0.0233096
$813$	1.52929	+	6.04323i	0.0536346	+	0.211945i
$814$	1.75227	−	5.39294i	0.0614172	−	0.189023i
$815$	8.34464	+	2.71134i	0.292300	+	0.0949740i
$816$	6.55294	−	7.86538i	0.229399	−	0.275343i
$817$	4.95417	−	1.60971i	0.173325	−	0.0563166i
$818$	1.88803	+	1.37173i	0.0660134	+	0.0479616i
$819$	−2.62993	−	4.86353i	−0.0918973	−	0.169945i
$820$	−2.31792	+	7.13383i	−0.0809453	+	0.249124i
$821$	−16.0714	+	11.6766i	−0.560897	+	0.407515i	−0.831787	−	0.555095i	$-0.812682\pi$
$821$	−16.0714	+	11.6766i	−0.560897	+	0.407515i	0.270890	+	0.962610i	$0.412682\pi$
$822$	5.13817	−	3.23581i	0.179214	−	0.112862i
$823$	−0.0423440	−	0.0137584i	−0.00147602	−	0.000479587i	0.308279	−	0.951296i	$-0.400247\pi$
$823$	−0.0423440	−	0.0137584i	−0.00147602	−	0.000479587i	−0.309755	+	0.950816i	$0.600247\pi$
$824$	−0.0865226	−	0.119088i	−0.00301416	−	0.00414863i
$825$	0.637462	−	0.765135i	0.0221936	−	0.0266386i
$826$	−1.07242	−	3.30057i	−0.0373142	−	0.114841i
$827$	19.7735	+	14.3663i	0.687591	+	0.499564i	0.875867	−	0.482552i	$-0.160290\pi$
$827$	19.7735	+	14.3663i	0.687591	+	0.499564i	−0.188277	+	0.982116i	$0.560290\pi$
$828$	−6.86134	+	14.3221i	−0.238448	+	0.497727i
$829$	10.4128	+	3.38334i	0.361653	+	0.117508i	0.484206	−	0.874954i	$-0.339108\pi$
$829$	10.4128	+	3.38334i	0.361653	+	0.117508i	−0.122554	+	0.992462i	$0.539108\pi$
$830$	−3.00278	−	9.24161i	−0.104228	−	0.320781i
$831$	−32.9343	−	2.18688i	−1.14248	−	0.0758620i
$832$			6.76528i			0.234544i
$833$	−12.6498	−	38.9319i	−0.438288	−	1.34891i
$834$	−9.06786	−	14.3989i	−0.313994	−	0.498594i
$835$	−1.68698	+	2.32193i	−0.0583803	+	0.0803535i
$836$	−1.38819			−0.0480116
$837$	8.02908	+	27.7945i	0.277526	+	0.960718i
$838$	20.1703			0.696771
$839$	3.03160	−	4.17264i	0.104663	−	0.144056i	−0.753473	−	0.657479i	$-0.771623\pi$
$839$	3.03160	−	4.17264i	0.104663	−	0.144056i	0.858136	+	0.513423i	$0.171623\pi$
$840$	−0.251445	−	0.399272i	−0.00867569	−	0.0137762i
$841$	−7.12444	−	21.9268i	−0.245670	−	0.756096i
$842$			11.2966i			0.389306i
$843$	−0.697700	−	0.0463281i	−0.0240301	−	0.00159562i
$844$	2.26146	+	6.96005i	0.0778425	+	0.239575i
$845$	31.1652	+	10.1262i	1.07211	+	0.348351i
$846$	−16.1734	+	33.7597i	−0.556052	+	1.16068i
$847$	2.35148	+	1.70845i	0.0807979	+	0.0587031i
$848$	3.15692	+	9.71600i	0.108409	+	0.333649i
$849$	13.5183	−	16.2258i	0.463948	−	0.556869i
$850$	−3.47416	−	4.78177i	−0.119163	−	0.164013i
$851$	49.6510	+	16.1326i	1.70202	+	0.553018i
$852$	−6.42409	+	4.04563i	−0.220086	+	0.138601i
$853$	−31.8862	+	23.1667i	−1.09176	+	0.793212i	−0.979696	−	0.200489i	$-0.935747\pi$
$853$	−31.8862	+	23.1667i	−1.09176	+	0.793212i	−0.112067	+	0.993701i	$0.535747\pi$
$854$	0.886037	−	2.72694i	0.0303196	−	0.0933140i
$855$	3.44520	+	6.37120i	0.117823	+	0.217891i
$856$	−1.66835	−	1.21213i	−0.0570232	−	0.0414298i
$857$	−9.16016	+	2.97632i	−0.312905	+	0.101669i	−0.461260	−	0.887265i	$-0.652602\pi$
$857$	−9.16016	+	2.97632i	−0.312905	+	0.101669i	0.148354	+	0.988934i	$0.452602\pi$
$858$	4.31261	−	5.17635i	0.147230	−	0.176718i
$859$	−26.4938	−	8.60837i	−0.903958	−	0.293714i	−0.180088	−	0.983650i	$-0.557638\pi$
$859$	−26.4938	−	8.60837i	−0.903958	−	0.293714i	−0.723870	+	0.689937i	$0.757638\pi$
$860$	−0.666726	+	2.05197i	−0.0227352	+	0.0699717i
$861$	−0.868288	−	3.43117i	−0.0295912	−	0.116934i
$862$	−4.07456			−0.138780
$863$	−6.83641			−0.232714			−0.116357	−	0.993207i	$-0.537122\pi$
$863$	−6.83641			−0.232714			−0.116357	+	0.993207i	$0.537122\pi$
$864$	−0.597520	−	5.16168i	−0.0203281	−	0.175604i
$865$	5.38236	−	3.91051i	0.183006	−	0.132961i
$866$	−12.7237	−	9.24428i	−0.432368	−	0.314133i
$867$	−2.05818	+	30.9962i	−0.0698995	+	1.05268i
$868$	1.08202	+	1.06295i	0.0367263	+	0.0360790i
$869$			3.30758i			0.112202i
$870$	2.70318	−	3.24458i	0.0916464	−	0.110002i
$871$	38.7905	+	53.3905i	1.31437	+	1.80907i
$872$	−4.29120	+	1.39430i	−0.145318	+	0.0472168i
$873$	−8.55996	−	1.14182i	−0.289711	−	0.0386446i
$874$		−	12.7806i		−	0.432310i
$875$	−0.259090	+	0.0841834i	−0.00875883	+	0.00284592i
$876$	−7.62009	+	19.0526i	−0.257459	+	0.643729i
$877$	−8.81729	+	27.1368i	−0.297739	+	0.916346i	0.684549	+	0.728967i	$0.259999\pi$
$877$	−8.81729	+	27.1368i	−0.297739	+	0.916346i	−0.982288	+	0.187379i	$0.940001\pi$
$878$	5.40434	−	7.43843i	0.182387	−	0.251035i
$879$	13.4259	+	53.0544i	0.452844	+	1.78948i
$880$	0.337962	−	0.465165i	0.0113927	−	0.0156807i
$881$	14.1432	−	10.2756i	0.476496	−	0.346195i	−0.323471	−	0.946238i	$-0.604850\pi$
$881$	14.1432	−	10.2756i	0.476496	−	0.346195i	0.799968	+	0.600043i	$0.204850\pi$
$882$	−18.7380	−	8.97690i	−0.630942	−	0.302268i
$883$	−19.7215	−	27.1443i	−0.663682	−	0.913480i	0.335915	−	0.941892i	$-0.390955\pi$
$883$	−19.7215	−	27.1443i	−0.663682	−	0.913480i	−0.999596	+	0.0284129i	$0.990955\pi$
$884$	−23.5036	−	32.3500i	−0.790513	−	1.08805i
$885$	−20.4869	−	8.19375i	−0.688661	−	0.275430i
$886$	−5.61958	+	4.08287i	−0.188794	+	0.137167i
$887$	−16.9048	+	23.2675i	−0.567609	+	0.781247i	−0.992269	−	0.124106i	$-0.960394\pi$
$887$	−16.9048	+	23.2675i	−0.567609	+	0.781247i	0.424660	+	0.905353i	$0.360394\pi$
$888$	−16.5597	+	4.19058i	−0.555707	+	0.140627i
$889$	−3.28846	+	4.52617i	−0.110291	+	0.151803i
$890$	−4.69430	+	14.4476i	−0.157353	+	0.484284i
$891$	−2.83319	+	4.33028i	−0.0949156	+	0.145070i
$892$	−19.2380	+	6.25080i	−0.644135	+	0.209292i
$893$		−	30.1261i		−	1.00813i
$894$	0.615022	−	9.26222i	0.0205694	−	0.309775i
$895$	−7.13114	+	2.31705i	−0.238368	+	0.0774503i
$896$	−0.160126	−	0.220395i	−0.00534944	−	0.00736288i
$897$	47.6569	+	39.7048i	1.59122	+	1.32570i
$898$			9.84585i			0.328560i
$899$	−6.05530	+	12.1500i	−0.201955	+	0.405226i
$900$	−2.97366	−	0.396658i	−0.0991220	−	0.0132219i
$901$	−48.8506	−	35.4920i	−1.62745	−	1.18241i
$902$	3.48918	−	2.53504i	0.116177	−	0.0844075i
$903$	−0.249754	−	0.986941i	−0.00831129	−	0.0328433i
$904$	9.62961			0.320276
$905$	21.5693			0.716988
$906$	−9.31629	+	2.35757i	−0.309513	+	0.0783250i
$907$	−2.20593	+	6.78916i	−0.0732468	+	0.225430i	−0.980977	−	0.194124i	$-0.937814\pi$
$907$	−2.20593	+	6.78916i	−0.0732468	+	0.225430i	0.907730	+	0.419554i	$0.137814\pi$
$908$	2.92004	+	0.948779i	0.0969050	+	0.0314863i
$909$	25.0819	−	26.3405i	0.831913	−	0.873660i
$910$	−1.75281	+	0.569524i	−0.0581052	+	0.0188795i
$911$	33.3882	+	24.2579i	1.10620	+	0.803702i	0.982061	−	0.188563i	$-0.0603831\pi$
$911$	33.3882	+	24.2579i	1.10620	+	0.803702i	0.124139	+	0.992265i	$0.460383\pi$
$912$	2.22843	+	3.53855i	0.0737908	+	0.117173i
$913$	−1.72652	+	5.31370i	−0.0571396	+	0.175858i
$914$	1.29885	−	0.943672i	0.0429622	−	0.0312139i
$915$	−9.71461	−	15.4259i	−0.321155	−	0.509964i
$916$	−25.9005	−	8.41558i	−0.855776	−	0.278059i
$917$	2.34719	+	3.23062i	0.0775109	+	0.106685i
$918$	20.7897	+	22.6061i	0.686162	+	0.746112i
$919$	−2.27348	−	6.99706i	−0.0749953	−	0.230812i	0.906531	−	0.422139i	$-0.138721\pi$
$919$	−2.27348	−	6.99706i	−0.0749953	−	0.230812i	−0.981526	+	0.191328i	$0.938721\pi$
$920$	4.28262	+	3.11150i	0.141194	+	0.102583i
$921$	9.34973	+	3.73942i	0.308084	+	0.123218i
$922$	23.4018	+	7.60371i	0.770698	+	0.250415i
$923$	9.16336	+	28.2019i	0.301616	+	0.928278i
$924$	−0.0179752	+	0.270706i	−0.000591341	+	0.00890558i
$925$			9.86212i			0.324265i
$926$	8.54847	+	26.3095i	0.280920	+	0.864584i
$927$	0.388448	−	0.210052i	0.0127583	−	0.00689900i
$928$	1.43314	−	1.97255i	0.0470451	−	0.0647520i
$929$	−49.3429			−1.61889			−0.809444	−	0.587197i	$-0.800231\pi$
$929$	−49.3429			−1.61889			−0.809444	+	0.587197i	$0.800231\pi$
$930$	9.59579	−	0.959554i	0.314658	−	0.0314650i
$931$	16.7213			0.548017
$932$	13.0839	−	18.0084i	0.428578	−	0.589886i
$933$	16.1675	−	10.1816i	0.529301	−	0.333332i
$934$	0.787896	+	2.42490i	0.0257808	+	0.0793450i
$935$			3.39844i			0.111141i
$936$	−20.1176	−	2.68350i	−0.657566	−	0.0877130i
$937$	3.23354	+	9.95182i	0.105635	+	0.325112i	0.989879	−	0.141914i	$-0.0453256\pi$
$937$	3.23354	+	9.95182i	0.105635	+	0.325112i	−0.884244	+	0.467026i	$0.845326\pi$
$938$	−2.52738	−	0.821197i	−0.0825220	−	0.0268130i
$939$	−0.284295	+	0.710828i	−0.00927763	+	0.0231970i
$940$	10.0949	+	7.33436i	0.329259	+	0.239220i
$941$	−12.2349	−	37.6553i	−0.398847	−	1.22753i	−0.925924	−	0.377709i	$-0.876712\pi$
$941$	−12.2349	−	37.6553i	−0.398847	−	1.22753i	0.527077	−	0.849818i	$-0.323288\pi$
$942$	−16.3244	−	13.6005i	−0.531879	−	0.443128i
$943$	23.3392	+	32.1237i	0.760030	+	1.04609i
$944$	−12.1156	−	3.93659i	−0.394329	−	0.128125i
$945$	1.28704	−	0.589339i	0.0418673	−	0.0191712i
$946$	1.00363	−	0.729177i	0.0326307	−	0.0237076i
$947$	−17.0527	+	52.4827i	−0.554137	+	1.70546i	0.144074	+	0.989567i	$0.453980\pi$
$947$	−17.0527	+	52.4827i	−0.554137	+	1.70546i	−0.698211	+	0.715892i	$0.746020\pi$
$948$	8.43114	−	5.30959i	0.273831	−	0.172448i
$949$	64.8424	+	47.1108i	2.10487	+	1.52928i
$950$	2.29618	−	0.746074i	0.0744979	−	0.0242058i
$951$	−3.27974	−	2.73248i	−0.106353	−	0.0886066i
$952$	1.53137	+	0.497573i	0.0496321	+	0.0161264i
$953$	−5.76782	+	17.7515i	−0.186838	+	0.575028i	−0.999975	−	0.00704391i	$-0.997758\pi$
$953$	−5.76782	+	17.7515i	−0.186838	+	0.575028i	0.813137	+	0.582072i	$0.197758\pi$
$954$	−30.1443	+	5.53368i	−0.975958	+	0.179160i
$955$	−6.34878			−0.205442
$956$	21.7048			0.701983
$957$	−2.35397	+	0.595692i	−0.0760930	+	0.0192560i
$958$	−15.2221	+	11.0595i	−0.491803	+	0.357315i
$959$	0.772653	+	0.561366i	0.0249503	+	0.0181274i
$960$	−1.72824	−	0.114757i	−0.0557789	−	0.00370378i
$961$	−29.3078	+	10.1022i	−0.945412	+	0.325877i
$962$			66.7200i			2.15114i
$963$	4.26623	−	4.48032i	0.137477	−	0.144376i
$964$	−0.704071	−	0.969070i	−0.0226766	−	0.0312116i
$965$	8.49380	−	2.75980i	0.273425	−	0.0888412i
$966$	−2.49230	−	0.165492i	−0.0801885	−	0.00532461i
$967$		−	50.4717i		−	1.62306i	−0.584311	−	0.811530i	$-0.698635\pi$
$967$		−	50.4717i		−	1.62306i	0.584311	−	0.811530i	$-0.301365\pi$
$968$	10.1472	−	3.29703i	0.326144	−	0.105970i
$969$	−22.9493	−	9.17857i	−0.737238	−	0.294858i
$970$	−0.889534	+	2.73770i	−0.0285612	+	0.0879024i
$971$	2.82800	−	3.89240i	0.0907547	−	0.124913i	−0.761225	−	0.648488i	$-0.775402\pi$
$971$	2.82800	−	3.89240i	0.0907547	−	0.124913i	0.851980	+	0.523574i	$0.175402\pi$
$972$	15.5861	+	0.270599i	0.499925	+	0.00867948i
$973$	1.57314	−	2.16524i	0.0504326	−	0.0694145i
$974$	19.2106	−	13.9573i	0.615546	−	0.447220i
$975$	−4.35141	+	10.8799i	−0.139357	+	0.348436i
$976$	−6.18649	−	8.51497i	−0.198025	−	0.272558i
$977$	4.46834	+	6.15014i	0.142955	+	0.196761i	0.874490	−	0.485043i	$-0.161196\pi$
$977$	4.46834	+	6.15014i	0.142955	+	0.196761i	−0.731536	+	0.681803i	$0.761196\pi$
$978$	−5.64346	+	14.1104i	−0.180458	+	0.451202i
$979$	7.06635	−	5.13400i	0.225842	−	0.164083i
$980$	−4.07087	+	5.60308i	−0.130039	+	0.178984i
$981$	−2.44403	−	13.3136i	−0.0780317	−	0.425072i
$982$	11.9394	−	16.4332i	0.381001	−	0.524403i
$983$	2.89303	−	8.90383i	0.0922733	−	0.283988i	−0.894260	−	0.447547i	$-0.852298\pi$
$983$	2.89303	−	8.90383i	0.0922733	−	0.283988i	0.986533	+	0.163559i	$0.0522975\pi$
$984$	−12.0630	−	4.82460i	−0.384555	−	0.153803i
$985$	−10.3720	+	3.37007i	−0.330479	+	0.107379i
$986$			14.4112i			0.458946i
$987$	−5.87480	−	0.390093i	−0.186997	−	0.0124168i
$988$	15.5343	−	5.04740i	0.494212	−	0.160579i
$989$	6.71329	+	9.24005i	0.213470	+	0.293816i
$990$	1.24919	+	1.18950i	0.0397018	+	0.0378047i
$991$			45.4947i			1.44519i	0.691273	+	0.722594i	$0.257050\pi$
$991$			45.4947i			1.44519i	−0.691273	+	0.722594i	$0.742950\pi$
$992$	5.49126	−	0.919844i	0.174348	−	0.0292051i
$993$	−53.4480	−	3.54901i	−1.69612	−	0.112624i
$994$	−0.966025	−	0.701858i	−0.0306404	−	0.0222616i
$995$	−10.7356	+	7.79987i	−0.340342	+	0.247273i
$996$	16.3164	−	4.12900i	0.517004	−	0.130832i
$997$	−49.1597			−1.55690			−0.778452	−	0.627704i	$-0.783995\pi$
$997$	−49.1597			−1.55690			−0.778452	+	0.627704i	$0.783995\pi$
$998$	16.4703			0.521358
$999$	−5.89282	−	50.9051i	−0.186441	−	1.61057i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.v.a.401.4	✓	80
3.2	odd	2	inner	930.2.v.a.401.13	yes	80
31.15	odd	10	inner	930.2.v.a.821.13	yes	80
93.77	even	10	inner	930.2.v.a.821.4	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.v.a.401.4	✓	80	1.1	even	1	trivial
930.2.v.a.401.13	yes	80	3.2	odd	2	inner
930.2.v.a.821.4	yes	80	93.77	even	10	inner
930.2.v.a.821.13	yes	80	31.15	odd	10	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.v (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.922996 - 1.46563i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.72824 + 0.114757i) q^{6} +(0.0841834 + 0.259090i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.29616 + 2.70555i) q^{9} +O(q^{10})\)	\(q+(-0.587785 + 0.809017i) q^{2} +(-0.922996 - 1.46563i) q^{3} +(-0.309017 - 0.951057i) q^{4} -1.00000i q^{5} +(1.72824 + 0.114757i) q^{6} +(0.0841834 + 0.259090i) q^{7} +(0.951057 + 0.309017i) q^{8} +(-1.29616 + 2.70555i) q^{9} +(0.809017 + 0.587785i) q^{10} +(-0.177677 - 0.546834i) q^{11} +(-1.10868 + 1.33073i) q^{12} +(3.97653 + 5.47323i) q^{13} +(-0.259090 - 0.0841834i) q^{14} +(-1.46563 + 0.922996i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(1.82647 - 5.62130i) q^{17} +(-1.42697 - 2.63889i) q^{18} +(1.95325 + 1.41912i) q^{19} +(-0.951057 + 0.309017i) q^{20} +(0.302029 - 0.362521i) q^{21} +(0.546834 + 0.177677i) q^{22} +(-1.63581 + 5.03452i) q^{23} +(-0.424916 - 1.67912i) q^{24} -1.00000 q^{25} -6.76528 q^{26} +(5.16168 - 0.597520i) q^{27} +(0.220395 - 0.160126i) q^{28} +(1.97255 + 1.43314i) q^{29} +(0.114757 - 1.72824i) q^{30} +(0.919844 + 5.49126i) q^{31} -1.00000i q^{32} +(-0.637462 + 0.765135i) q^{33} +(3.47416 + 4.78177i) q^{34} +(0.259090 - 0.0841834i) q^{35} +(2.97366 + 0.396658i) q^{36} -9.86212i q^{37} +(-2.29618 + 0.746074i) q^{38} +(4.35141 - 10.8799i) q^{39} +(0.309017 - 0.951057i) q^{40} +(4.40895 - 6.06840i) q^{41} +(0.115757 + 0.457431i) q^{42} +(1.26819 - 1.74551i) q^{43} +(-0.465165 + 0.337962i) q^{44} +(2.70555 + 1.29616i) q^{45} +(-3.11150 - 4.28262i) q^{46} +(-7.33436 - 10.0949i) q^{47} +(1.60820 + 0.643198i) q^{48} +(5.60308 - 4.07087i) q^{49} +(0.587785 - 0.809017i) q^{50} +(-9.92459 + 2.51150i) q^{51} +(3.97653 - 5.47323i) q^{52} +(3.15692 - 9.71600i) q^{53} +(-2.55056 + 4.52710i) q^{54} +(-0.546834 + 0.177677i) q^{55} +0.272423i q^{56} +(0.277064 - 4.17258i) q^{57} +(-2.31887 + 0.753446i) q^{58} +(7.48784 + 10.3061i) q^{59} +(1.33073 + 1.10868i) q^{60} +10.5251i q^{61} +(-4.98319 - 2.48351i) q^{62} +(-0.810094 - 0.108059i) q^{63} +(0.809017 + 0.587785i) q^{64} +(5.47323 - 3.97653i) q^{65} +(-0.244316 - 0.965453i) q^{66} +9.75486 q^{67} -5.91059 q^{68} +(8.88860 - 2.24934i) q^{69} +(-0.0841834 + 0.259090i) q^{70} +(4.16863 + 1.35447i) q^{71} +(-2.06878 + 2.17259i) q^{72} +(11.2674 - 3.66099i) q^{73} +(7.97862 + 5.79681i) q^{74} +(0.922996 + 1.46563i) q^{75} +(0.746074 - 2.29618i) q^{76} +(0.126722 - 0.0920686i) q^{77} +(6.24433 + 9.91541i) q^{78} +(-5.47101 - 1.77764i) q^{79} +(0.587785 + 0.809017i) q^{80} +(-5.63996 - 7.01362i) q^{81} +(2.31792 + 7.13383i) q^{82} +(-7.86138 - 5.71163i) q^{83} +(-0.438110 - 0.175222i) q^{84} +(-5.62130 - 1.82647i) q^{85} +(0.666726 + 2.05197i) q^{86} +(0.279802 - 4.21381i) q^{87} -0.574975i q^{88} +(4.69430 + 14.4476i) q^{89} +(-2.63889 + 1.42697i) q^{90} +(-1.08330 + 1.49103i) q^{91} +5.29360 q^{92} +(7.19915 - 6.41656i) q^{93} +12.4780 q^{94} +(1.41912 - 1.95325i) q^{95} +(-1.46563 + 0.922996i) q^{96} +(0.889534 + 2.73770i) q^{97} +6.92579i q^{98} +(1.70978 + 0.228069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9}+O(q^{10}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9	\( 80 q + 20 q^{4} + 12 q^{7} - 8 q^{9} + 20 q^{10} - 10 q^{13} - 20 q^{16} - 12 q^{18} - 12 q^{19} + 30 q^{21} + 10 q^{22} - 80 q^{25} + 18 q^{28} + 16 q^{31} + 72 q^{33} + 10 q^{34} + 8 q^{36} + 54 q^{39} - 20 q^{40} + 50 q^{43} + 8 q^{45} - 10 q^{46} + 8 q^{49} - 44 q^{51} - 10 q^{52} - 10 q^{55} + 30 q^{58} + 28 q^{63} + 20 q^{64} + 66 q^{66} + 60 q^{67} + 20 q^{69} - 12 q^{70} + 12 q^{72} - 20 q^{73} - 18 q^{76} + 8 q^{78} + 40 q^{79} + 16 q^{81} - 4 q^{82} - 60 q^{84} - 72 q^{87} - 12 q^{90} + 10 q^{91} + 104 q^{93} - 12 q^{94} - 178 q^{97}+O(q^{100}) \) 80 * q + 20 * q^4 + 12 * q^7 - 8 * q^9 + 20 * q^10 - 10 * q^13 - 20 * q^16 - 12 * q^18 - 12 * q^19 + 30 * q^21 + 10 * q^22 - 80 * q^25 + 18 * q^28 + 16 * q^31 + 72 * q^33 + 10 * q^34 + 8 * q^36 + 54 * q^39 - 20 * q^40 + 50 * q^43 + 8 * q^45 - 10 * q^46 + 8 * q^49 - 44 * q^51 - 10 * q^52 - 10 * q^55 + 30 * q^58 + 28 * q^63 + 20 * q^64 + 66 * q^66 + 60 * q^67 + 20 * q^69 - 12 * q^70 + 12 * q^72 - 20 * q^73 - 18 * q^76 + 8 * q^78 + 40 * q^79 + 16 * q^81 - 4 * q^82 - 60 * q^84 - 72 * q^87 - 12 * q^90 + 10 * q^91 + 104 * q^93 - 12 * q^94 - 178 * q^97

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