LMFDB - Embedded newform 770.2.bd.a.527.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [770,2,Mod(263,770)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(770, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 8, 6]))

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

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

chi := DirichletCharacter("770.263");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.bd (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.43
Character	$\chi$	$=$	770.527
Dual form			770.2.bd.a.263.43

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(1.68009 + 0.450179i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.17405 + 0.522991i) q^{5} +1.73936i q^{6} +(-2.63950 - 0.181786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.0219675 + 0.0126829i) q^{9} +O(q^{10})$	\(q+(0.258819 + 0.965926i) q^{2} +(1.68009 + 0.450179i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.17405 + 0.522991i) q^{5} +1.73936i q^{6} +(-2.63950 - 0.181786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.0219675 + 0.0126829i) q^{9} +(-1.06786 - 1.96461i) q^{10} +(1.55872 - 2.92752i) q^{11} +(-1.68009 + 0.450179i) q^{12} +(-3.32403 - 3.32403i) q^{13} +(-0.507560 - 2.59661i) q^{14} +(-3.88804 - 0.100038i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-7.82461 - 2.09660i) q^{17} +(-0.00656516 + 0.0245015i) q^{18} +(-2.87862 + 4.98591i) q^{19} +(1.62128 - 1.53995i) q^{20} +(-4.35276 - 1.49366i) q^{21} +(3.23120 + 0.747908i) q^{22} +(2.10302 + 7.84857i) q^{23} +(-0.869679 - 1.50633i) q^{24} +(4.45296 - 2.27401i) q^{25} +(2.35044 - 4.07109i) q^{26} +(-3.65854 - 3.65854i) q^{27} +(2.37677 - 1.16232i) q^{28} +1.91105 q^{29} +(-0.909668 - 3.78145i) q^{30} +(2.56804 + 4.44798i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.93670 - 4.21680i) q^{33} -8.10063i q^{34} +(5.83347 - 0.985221i) q^{35} -0.0253658 q^{36} +(-1.00374 + 0.268950i) q^{37} +(-5.56106 - 1.49008i) q^{38} +(-4.08826 - 7.08108i) q^{39} +(1.90709 + 1.16747i) q^{40} -0.282644i q^{41} +(0.316191 - 4.59103i) q^{42} +(-4.39175 - 4.39175i) q^{43} +(0.113872 + 3.31467i) q^{44} +(-0.0543914 - 0.0160845i) q^{45} +(-7.03684 + 4.06272i) q^{46} +(8.11458 - 2.17429i) q^{47} +(1.22991 - 1.22991i) q^{48} +(6.93391 + 0.959649i) q^{49} +(3.34904 + 3.71267i) q^{50} +(-12.2022 - 7.04495i) q^{51} +(4.54071 + 1.21668i) q^{52} +(-3.53731 - 0.947818i) q^{53} +(2.58698 - 4.48078i) q^{54} +(-1.85766 + 7.17977i) q^{55} +(1.73787 + 1.99495i) q^{56} +(-7.08088 + 7.08088i) q^{57} +(0.494615 + 1.84593i) q^{58} +(-11.9752 + 6.91389i) q^{59} +(3.41716 - 1.85738i) q^{60} +(4.42027 + 2.55205i) q^{61} +(-3.63176 + 3.63176i) q^{62} +(-0.0556775 - 0.0374699i) q^{63} +1.00000i q^{64} +(8.96503 + 5.48816i) q^{65} +(5.09201 + 2.71117i) q^{66} +(1.30017 - 4.85229i) q^{67} +(7.82461 - 2.09660i) q^{68} +14.1331i q^{69} +(2.46146 + 5.37970i) q^{70} -4.68194 q^{71} +(-0.00656516 - 0.0245015i) q^{72} +(1.35742 - 5.06597i) q^{73} +(-0.519572 - 0.899924i) q^{74} +(8.50509 - 1.81592i) q^{75} -5.75723i q^{76} +(-4.64642 + 7.44384i) q^{77} +(5.78168 - 5.78168i) q^{78} +(-7.16404 + 12.4085i) q^{79} +(-0.634100 + 2.14428i) q^{80} +(-4.53773 - 7.85957i) q^{81} +(0.273013 - 0.0731537i) q^{82} +(-2.14298 - 2.14298i) q^{83} +(4.51643 - 0.882829i) q^{84} +(18.1076 + 0.465904i) q^{85} +(3.10544 - 5.37877i) q^{86} +(3.21073 + 0.860313i) q^{87} +(-3.17225 + 0.967892i) q^{88} +(-11.2164 - 6.47579i) q^{89} +(0.00145890 - 0.0567010i) q^{90} +(8.16951 + 9.37803i) q^{91} +(-5.74556 - 5.74556i) q^{92} +(2.31216 + 8.62908i) q^{93} +(4.20041 + 7.27533i) q^{94} +(3.65066 - 12.3451i) q^{95} +(1.50633 + 0.869679i) q^{96} +(-6.51550 - 6.51550i) q^{97} +(0.867677 + 6.94602i) q^{98} +(0.0713707 - 0.0445412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 8 q^{5}+O(q^{10}) $ 192 * q + 8 * q^5	$ 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) $ 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	1.68009	+	0.450179i	0.970001	+	0.259911i	0.708828	−	0.705381i	$-0.249224\pi$
$3$	1.68009	+	0.450179i	0.970001	+	0.259911i	0.261173	+	0.965292i	$0.415891\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−2.17405	+	0.522991i	−0.972263	+	0.233889i
$5$	−2.17405	+	0.522991i	−0.972263	+	0.233889i
$6$			1.73936i			0.710090i
$7$	−2.63950	−	0.181786i	−0.997637	−	0.0687088i
$7$	−2.63950	−	0.181786i	−0.997637	−	0.0687088i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.0219675	+	0.0126829i	0.00732249	+	0.00422764i
$10$	−1.06786	−	1.96461i	−0.337685	−	0.621264i
$11$	1.55872	−	2.92752i	0.469971	−	0.882682i
$11$	1.55872	−	2.92752i	0.469971	−	0.882682i
$12$	−1.68009	+	0.450179i	−0.485000	+	0.129955i
$13$	−3.32403	−	3.32403i	−0.921920	−	0.921920i	0.0752454	−	0.997165i	$-0.476026\pi$
$13$	−3.32403	−	3.32403i	−0.921920	−	0.921920i	−0.997165	+	0.0752454i	$0.976026\pi$
$14$	−0.507560	−	2.59661i	−0.135651	−	0.693973i
$15$	−3.88804	−	0.100038i	−1.00389	−	0.0258298i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−7.82461	−	2.09660i	−1.89775	−	0.508500i	−0.997291	−	0.0735524i	$-0.976566\pi$
$17$	−7.82461	−	2.09660i	−1.89775	−	0.508500i	−0.900456	−	0.434947i	$-0.856767\pi$
$18$	−0.00656516	+	0.0245015i	−0.00154742	+	0.00577506i
$19$	−2.87862	+	4.98591i	−0.660400	+	1.14385i	0.320111	+	0.947380i	$0.396280\pi$
$19$	−2.87862	+	4.98591i	−0.660400	+	1.14385i	−0.980511	+	0.196466i	$0.937054\pi$
$20$	1.62128	−	1.53995i	0.362530	−	0.344343i
$21$	−4.35276	−	1.49366i	−0.949850	−	0.325944i
$22$	3.23120	+	0.747908i	0.688894	+	0.159454i
$23$	2.10302	+	7.84857i	0.438510	+	1.63654i	0.732525	+	0.680740i	$0.238342\pi$
$23$	2.10302	+	7.84857i	0.438510	+	1.63654i	−0.294015	+	0.955801i	$0.594992\pi$
$24$	−0.869679	−	1.50633i	−0.177522	−	0.307478i
$25$	4.45296	−	2.27401i	0.890592	−	0.454803i
$26$	2.35044	−	4.07109i	0.460960	−	0.798406i
$27$	−3.65854	−	3.65854i	−0.704086	−	0.704086i
$28$	2.37677	−	1.16232i	0.449167	−	0.219657i
$29$	1.91105			0.354873			0.177436	−	0.984132i	$-0.443220\pi$
$29$	1.91105			0.354873			0.177436	+	0.984132i	$0.443220\pi$
$30$	−0.909668	−	3.78145i	−0.166082	−	0.690394i
$31$	2.56804	+	4.44798i	0.461234	+	0.798880i	0.999023	−	0.0441991i	$-0.0140736\pi$
$31$	2.56804	+	4.44798i	0.461234	+	0.798880i	−0.537789	+	0.843080i	$0.680740\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	3.93670	−	4.21680i	0.685291	−	0.734051i
$34$		−	8.10063i		−	1.38925i
$35$	5.83347	−	0.985221i	0.986036	−	0.166533i
$36$	−0.0253658			−0.00422764
$37$	−1.00374	+	0.268950i	−0.165013	+	0.0442151i	−0.340380	−	0.940288i	$-0.610556\pi$
$37$	−1.00374	+	0.268950i	−0.165013	+	0.0442151i	0.175367	+	0.984503i	$0.443889\pi$
$38$	−5.56106	−	1.49008i	−0.902123	−	0.241723i
$39$	−4.08826	−	7.08108i	−0.654646	−	1.13388i
$40$	1.90709	+	1.16747i	0.301538	+	0.184594i
$41$		−	0.282644i		−	0.0441416i	−0.999756	−	0.0220708i	$-0.992974\pi$
$41$		−	0.282644i		−	0.0441416i	0.999756	−	0.0220708i	$-0.00702592\pi$
$42$	0.316191	−	4.59103i	0.0487894	−	0.708412i
$43$	−4.39175	−	4.39175i	−0.669736	−	0.669736i	0.287919	−	0.957655i	$-0.407037\pi$
$43$	−4.39175	−	4.39175i	−0.669736	−	0.669736i	−0.957655	+	0.287919i	$0.907037\pi$
$44$	0.113872	+	3.31467i	0.0171669	+	0.499705i
$45$	−0.0543914	−	0.0160845i	−0.00810818	−	0.00239773i
$46$	−7.03684	+	4.06272i	−1.03753	+	0.599016i
$47$	8.11458	−	2.17429i	1.18363	−	0.317153i	0.387266	−	0.921968i	$-0.373419\pi$
$47$	8.11458	−	2.17429i	1.18363	−	0.317153i	0.796366	+	0.604814i	$0.206753\pi$
$48$	1.22991	−	1.22991i	0.177522	−	0.177522i
$49$	6.93391	+	0.959649i	0.990558	+	0.137093i
$50$	3.34904	+	3.71267i	0.473626	+	0.525051i
$51$	−12.2022	−	7.04495i	−1.70865	−	0.986491i
$52$	4.54071	+	1.21668i	0.629683	+	0.168723i
$53$	−3.53731	−	0.947818i	−0.485886	−	0.130193i	0.00755589	−	0.999971i	$-0.497595\pi$
$53$	−3.53731	−	0.947818i	−0.485886	−	0.130193i	−0.493442	+	0.869779i	$0.664262\pi$
$54$	2.58698	−	4.48078i	0.352043	−	0.609756i
$55$	−1.85766	+	7.17977i	−0.250487	+	0.968120i
$56$	1.73787	+	1.99495i	0.232232	+	0.266586i
$57$	−7.08088	+	7.08088i	−0.937886	+	0.937886i
$58$	0.494615	+	1.84593i	0.0649462	+	0.242382i
$59$	−11.9752	+	6.91389i	−1.55904	+	0.900111i	−0.561690	+	0.827348i	$0.689848\pi$
$59$	−11.9752	+	6.91389i	−1.55904	+	0.900111i	−0.997349	+	0.0727634i	$0.976818\pi$
$60$	3.41716	−	1.85738i	0.441153	−	0.239787i
$61$	4.42027	+	2.55205i	0.565958	+	0.326756i	0.755533	−	0.655110i	$-0.227378\pi$
$61$	4.42027	+	2.55205i	0.565958	+	0.326756i	−0.189575	+	0.981866i	$0.560711\pi$
$62$	−3.63176	+	3.63176i	−0.461234	+	0.461234i
$63$	−0.0556775	−	0.0374699i	−0.00701471	−	0.00472077i
$64$			1.00000i			0.125000i
$65$	8.96503	+	5.48816i	1.11198	+	0.680722i
$66$	5.09201	+	2.71117i	0.626783	+	0.333722i
$67$	1.30017	−	4.85229i	0.158841	−	0.592801i	−0.839905	−	0.542733i	$-0.817390\pi$
$67$	1.30017	−	4.85229i	0.158841	−	0.592801i	0.998746	−	0.0500680i	$-0.0159438\pi$
$68$	7.82461	−	2.09660i	0.948874	−	0.254250i
$69$			14.1331i			1.70142i
$70$	2.46146	+	5.37970i	0.294201	+	0.642997i
$71$	−4.68194			−0.555644			−0.277822	−	0.960633i	$-0.589613\pi$
$71$	−4.68194			−0.555644			−0.277822	+	0.960633i	$0.589613\pi$
$72$	−0.00656516	−	0.0245015i	−0.000773712	−	0.00288753i
$73$	1.35742	−	5.06597i	0.158874	−	0.592927i	−0.839868	−	0.542791i	$-0.817368\pi$
$73$	1.35742	−	5.06597i	0.158874	−	0.592927i	0.998742	−	0.0501366i	$-0.0159657\pi$
$74$	−0.519572	−	0.899924i	−0.0603990	−	0.104614i
$75$	8.50509	−	1.81592i	0.982083	−	0.209684i
$76$		−	5.75723i		−	0.660400i
$77$	−4.64642	+	7.44384i	−0.529509	+	0.848305i
$78$	5.78168	−	5.78168i	0.654646	−	0.654646i
$79$	−7.16404	+	12.4085i	−0.806017	+	1.39606i	0.109585	+	0.993977i	$0.465048\pi$
$79$	−7.16404	+	12.4085i	−0.806017	+	1.39606i	−0.915602	+	0.402085i	$0.868286\pi$
$80$	−0.634100	+	2.14428i	−0.0708946	+	0.239737i
$81$	−4.53773	−	7.85957i	−0.504192	−	0.873286i
$82$	0.273013	−	0.0731537i	0.0301493	−	0.00807847i
$83$	−2.14298	−	2.14298i	−0.235222	−	0.235222i	0.579646	−	0.814868i	$-0.303191\pi$
$83$	−2.14298	−	2.14298i	−0.235222	−	0.235222i	−0.814868	+	0.579646i	$0.803191\pi$
$84$	4.51643	−	0.882829i	0.492783	−	0.0963246i
$85$	18.1076	+	0.465904i	1.96404	+	0.0505344i
$86$	3.10544	−	5.37877i	0.334868	−	0.580008i
$87$	3.21073	+	0.860313i	0.344227	+	0.0922353i
$88$	−3.17225	+	0.967892i	−0.338163	+	0.103178i
$89$	−11.2164	−	6.47579i	−1.18894	−	0.686433i	−0.230871	−	0.972984i	$-0.574158\pi$
$89$	−11.2164	−	6.47579i	−1.18894	−	0.686433i	−0.958065	+	0.286552i	$0.907491\pi$
$90$	0.00145890	−	0.0567010i	0.000153782	−	0.00597681i
$91$	8.16951	+	9.37803i	0.856397	+	0.983085i
$92$	−5.74556	−	5.74556i	−0.599016	−	0.599016i
$93$	2.31216	+	8.62908i	0.239759	+	0.894794i
$94$	4.20041	+	7.27533i	0.433240	+	0.750393i
$95$	3.65066	−	12.3451i	0.374550	−	1.26658i
$96$	1.50633	+	0.869679i	0.153739	+	0.0887612i
$97$	−6.51550	−	6.51550i	−0.661549	−	0.661549i	0.294196	−	0.955745i	$-0.404948\pi$
$97$	−6.51550	−	6.51550i	−0.661549	−	0.661549i	−0.955745	+	0.294196i	$0.904948\pi$
$98$	0.867677	+	6.94602i	0.0876486	+	0.701654i
$99$	0.0713707	−	0.0445412i	0.00717302	−	0.00447656i
$100$	−2.71937	+	4.19583i	−0.271937	+	0.419583i
$101$	−8.15892	+	4.71056i	−0.811843	+	0.468718i	−0.847596	−	0.530643i	$-0.821951\pi$
$101$	−8.15892	+	4.71056i	−0.811843	+	0.468718i	0.0357524	+	0.999361i	$0.488617\pi$
$102$	3.64674	−	13.6098i	0.361081	−	1.34757i
$103$	−1.10683	−	4.13074i	−0.109059	−	0.407014i	0.889715	−	0.456517i	$-0.150903\pi$
$103$	−1.10683	−	4.13074i	−0.109059	−	0.407014i	−0.998774	+	0.0495024i	$0.984236\pi$
$104$			4.70089i			0.460960i
$105$	10.2443	+	0.970843i	0.999739	+	0.0947446i
$106$		−	3.66209i		−	0.355693i
$107$	1.16172	+	4.33559i	0.112307	+	0.419137i	0.999071	−	0.0430856i	$-0.0137188\pi$
$107$	1.16172	+	4.33559i	0.112307	+	0.419137i	−0.886764	+	0.462222i	$0.847052\pi$
$108$	4.99766	+	1.33912i	0.480900	+	0.128857i
$109$	0.644830	+	1.11688i	0.0617635	+	0.106978i	0.895254	−	0.445557i	$-0.146994\pi$
$109$	0.644830	+	1.11688i	0.0617635	+	0.106978i	−0.833490	+	0.552534i	$0.813661\pi$
$110$	−7.41592	+	0.0638997i	−0.707081	+	0.00609260i
$111$	−1.80744			−0.171555
$112$	−1.47718	+	2.19498i	−0.139580	+	0.207406i
$113$	3.82720	−	3.82720i	0.360033	−	0.360033i	−0.503792	−	0.863825i	$-0.668062\pi$
$113$	3.82720	−	3.82720i	0.360033	−	0.360033i	0.863825	+	0.503792i	$0.168062\pi$
$114$	−8.67228	−	5.00694i	−0.812233	−	0.468943i
$115$	−8.67679	−	15.9633i	−0.809115	−	1.48859i
$116$	−1.65502	+	0.955524i	−0.153664	+	0.0887181i
$117$	−0.0308621	−	0.115179i	−0.00285320	−	0.0106483i
$118$	−9.77771	−	9.77771i	−0.900111	−	0.900111i
$119$	20.2719	+	6.95638i	1.85832	+	0.637690i
$120$	2.67852	+	2.81999i	0.244514	+	0.257429i
$121$	−6.14079	−	9.12637i	−0.558254	−	0.829670i
$122$	−1.32104	+	4.93017i	−0.119601	+	0.446357i
$123$	0.127240	−	0.474868i	0.0114729	−	0.0428174i
$124$	−4.44798	−	2.56804i	−0.399440	−	0.230617i
$125$	−8.49166	+	7.27267i	−0.759517	+	0.650487i
$126$	0.0217828	−	0.0634783i	0.00194056	−	0.00565509i
$127$	2.22040	−	2.22040i	0.197029	−	0.197029i	−0.601696	−	0.798725i	$-0.705508\pi$
$127$	2.22040	−	2.22040i	0.197029	−	0.197029i	0.798725	+	0.601696i	$0.205508\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−5.40146	−	9.35561i	−0.475572	−	0.823716i
$130$	−2.98083	+	10.0800i	−0.261436	+	0.884074i
$131$	7.80247	+	4.50476i	0.681705	+	0.393583i	0.800497	−	0.599336i	$-0.204569\pi$
$131$	7.80247	+	4.50476i	0.681705	+	0.393583i	−0.118792	+	0.992919i	$0.537902\pi$
$132$	−1.30088	+	5.62021i	−0.113227	+	0.489176i
$133$	8.50447	−	12.6370i	0.737431	−	1.09577i
$134$	5.02346			0.433960
$135$	9.86721	+	6.04045i	0.849235	+	0.519879i
$136$	4.05032	+	7.01536i	0.347312	+	0.601562i
$137$	−3.21036	+	11.9812i	−0.274280	+	1.02363i	0.682043	+	0.731312i	$0.261092\pi$
$137$	−3.21036	+	11.9812i	−0.274280	+	1.02363i	−0.956323	+	0.292313i	$0.905575\pi$
$138$	−13.6515	+	3.65790i	−1.16209	+	0.311381i
$139$	18.3015			1.55231			0.776157	−	0.630540i	$-0.217166\pi$
$139$	18.3015			1.55231			0.776157	+	0.630540i	$0.217166\pi$
$140$	−4.55932	+	3.76996i	−0.385333	+	0.318620i
$141$	14.6120			1.23056
$142$	−1.21177	−	4.52240i	−0.101690	−	0.379512i
$143$	−14.9124	+	4.54995i	−1.24704	+	0.380486i
$144$	0.0219675	−	0.0126829i	0.00183062	−	0.00105691i
$145$	−4.15471	+	0.999460i	−0.345030	+	0.0830006i
$146$	5.24468			0.434053
$147$	11.2176	+	4.73380i	0.925210	+	0.390437i
$148$	0.734785	−	0.734785i	0.0603990	−	0.0603990i
$149$	−3.78879	+	6.56238i	−0.310390	+	0.537611i	−0.978447	−	0.206499i	$-0.933793\pi$
$149$	−3.78879	+	6.56238i	−0.310390	+	0.537611i	0.668057	+	0.744110i	$0.267126\pi$
$150$	3.95532	+	7.74529i	0.322951	+	0.632401i
$151$	11.4953	−	6.63684i	0.935478	−	0.540098i	0.0469380	−	0.998898i	$-0.485054\pi$
$151$	11.4953	−	6.63684i	0.935478	−	0.540098i	0.888540	+	0.458799i	$0.151720\pi$
$152$	5.56106	−	1.49008i	0.451061	−	0.120862i
$153$	−0.145296	−	0.145296i	−0.0117465	−	0.0117465i
$154$	−8.39278	−	2.56149i	−0.676310	−	0.206411i
$155$	−7.90929	−	8.32705i	−0.635290	−	0.668845i
$156$	7.08108	+	4.08826i	0.566940	+	0.327323i
$157$	−0.484159	+	1.80690i	−0.0386401	+	0.144207i	−0.982551	−	0.185994i	$-0.940450\pi$
$157$	−0.484159	+	1.80690i	−0.0386401	+	0.144207i	0.943911	+	0.330200i	$0.107116\pi$
$158$	−13.8399	−	3.70838i	−1.10104	−	0.295023i
$159$	−5.51631	−	3.18484i	−0.437472	−	0.252574i
$160$	−2.23533	−	0.0575145i	−0.176718	−	0.00454692i
$161$	−4.12415	−	21.0986i	−0.325029	−	1.66280i
$162$	6.41732	−	6.41732i	0.504192	−	0.504192i
$163$	−3.44510	−	12.8573i	−0.269841	−	1.00706i	−0.959220	−	0.282659i	$-0.908783\pi$
$163$	−3.44510	−	12.8573i	−0.269841	−	1.00706i	0.689380	−	0.724400i	$-0.257883\pi$
$164$	0.141322	+	0.244777i	0.0110354	+	0.0191139i
$165$	−6.35322	+	11.2264i	−0.494597	+	0.873973i
$166$	1.51531	−	2.62460i	0.117611	−	0.203709i
$167$	1.75418	−	1.75418i	0.135742	−	0.135742i	−0.635971	−	0.771713i	$-0.719400\pi$
$167$	1.75418	−	1.75418i	0.135742	−	0.135742i	0.771713	+	0.635971i	$0.219400\pi$
$168$	2.02169	+	4.13405i	0.155977	+	0.318949i
$169$			9.09833i			0.699872i
$170$	4.23656	+	17.6112i	0.324929	+	1.35071i
$171$	−0.126472	+	0.0730185i	−0.00967154	+	0.00558386i
$172$	5.99924	+	1.60749i	0.457438	+	0.122570i
$173$	−16.5331	+	4.43002i	−1.25699	+	0.336808i	−0.825031	−	0.565087i	$-0.808843\pi$
$173$	−16.5331	+	4.43002i	−1.25699	+	0.336808i	−0.431955	+	0.901895i	$0.642176\pi$
$174$			3.32400i			0.251991i
$175$	−12.1670	+	5.19277i	−0.919737	+	0.392536i
$176$	−1.75595	−	2.81365i	−0.132360	−	0.212087i
$177$	−23.2319	+	6.22497i	−1.74622	+	0.467898i
$178$	3.35212	−	12.5103i	0.251252	−	0.937685i
$179$	13.3768	−	7.72312i	0.999832	−	0.577253i	0.0916333	−	0.995793i	$-0.470791\pi$
$179$	13.3768	−	7.72312i	0.999832	−	0.577253i	0.908199	+	0.418540i	$0.137458\pi$
$180$	0.0551465	−	0.0132661i	0.00411038	−	0.000988797i
$181$	13.6190			1.01229			0.506145	−	0.862448i	$-0.331070\pi$
$181$	13.6190			1.01229			0.506145	+	0.862448i	$0.331070\pi$
$182$	−6.94406	+	10.3184i	−0.514728	+	0.764847i
$183$	6.27758	+	6.27758i	0.464052	+	0.464052i
$184$	4.06272	−	7.03684i	0.299508	−	0.518763i
$185$	2.04151	−	1.10965i	0.150095	−	0.0815834i
$186$	−7.73663	+	4.46674i	−0.567277	+	0.327517i
$187$	−18.3342	+	19.6387i	−1.34073	+	1.43613i
$188$	−5.94028	+	5.94028i	−0.433240	+	0.433240i
$189$	8.99163	+	10.3218i	0.654045	+	0.750799i
$190$	12.8693	+	0.331124i	0.933637	+	0.0240223i
$191$	−7.30596	+	12.6543i	−0.528641	+	0.915632i	0.470802	+	0.882239i	$0.343965\pi$
$191$	−7.30596	+	12.6543i	−0.528641	+	0.915632i	−0.999442	+	0.0333933i	$0.989369\pi$
$192$	−0.450179	+	1.68009i	−0.0324889	+	0.121250i
$193$	2.55333	−	9.52915i	0.183793	−	0.685923i	−0.811093	−	0.584917i	$-0.801127\pi$
$193$	2.55333	−	9.52915i	0.183793	−	0.685923i	0.994886	−	0.101006i	$-0.0322062\pi$
$194$	4.60715	−	7.97982i	0.330774	−	0.572918i
$195$	12.5914	+	13.2565i	0.901690	+	0.949316i
$196$	−6.48476	+	2.63587i	−0.463197	+	0.188277i
$197$	1.86369	−	1.86369i	0.132783	−	0.132783i	−0.637592	−	0.770374i	$-0.720069\pi$
$197$	1.86369	−	1.86369i	0.132783	−	0.132783i	0.770374	+	0.637592i	$0.220069\pi$
$198$	0.0614956	+	0.0574107i	0.00437030	+	0.00408000i
$199$	−7.04161	+	4.06547i	−0.499166	+	0.288194i	−0.728369	−	0.685185i	$-0.759721\pi$
$199$	−7.04161	+	4.06547i	−0.499166	+	0.288194i	0.229203	+	0.973379i	$0.426388\pi$
$200$	−4.75669	−	1.54075i	−0.336349	−	0.108947i
$201$	4.36879	−	7.56697i	0.308151	−	0.533733i
$202$	−6.66173	−	6.66173i	−0.468718	−	0.468718i
$203$	−5.04421	−	0.347402i	−0.354034	−	0.0243829i
$204$	14.0899			0.986491
$205$	0.147820	+	0.614482i	0.0103242	+	0.0429173i
$206$	3.70352	−	2.13823i	0.258037	−	0.148978i
$207$	−0.0533449	+	0.199086i	−0.00370772	+	0.0138374i
$208$	−4.54071	+	1.21668i	−0.314841	+	0.0843615i
$209$	10.1094	+	16.1988i	0.699283	+	1.12050i
$210$	1.71365	+	10.1465i	0.118253	+	0.700174i
$211$		−	14.3166i		−	0.985595i	−0.870144	−	0.492798i	$-0.835974\pi$
$211$		−	14.3166i		−	0.985595i	0.870144	−	0.492798i	$-0.164026\pi$
$212$	3.53731	−	0.947818i	0.242943	−	0.0650964i
$213$	−7.86608	−	2.10771i	−0.538975	−	0.144418i
$214$	−3.88718	+	2.24426i	−0.265722	+	0.153415i
$215$	11.8447	+	7.25103i	0.807803	+	0.494516i
$216$			5.17395i			0.352043i
$217$	−5.96976	−	12.2073i	−0.405254	−	0.828683i
$218$	−0.911927	+	0.911927i	−0.0617635	+	0.0617635i
$219$	4.56119	−	7.90021i	0.308217	−	0.533847i
$220$	−1.98110	−	7.14669i	−0.133566	−	0.481830i
$221$	19.0401	+	32.9784i	1.28077	+	2.21837i
$222$	−0.467800	−	1.74585i	−0.0313967	−	0.117174i
$223$	1.59917	−	1.59917i	0.107089	−	0.107089i	−0.651532	−	0.758621i	$-0.725874\pi$
$223$	1.59917	−	1.59917i	0.107089	−	0.107089i	0.758621	+	0.651532i	$0.225874\pi$
$224$	−2.50251	−	0.858745i	−0.167206	−	0.0573773i
$225$	0.126661	+	0.00652226i	0.00844409	+	0.000434817i
$226$	4.68735	+	2.70624i	0.311798	+	0.180016i
$227$	5.48410	+	1.46946i	0.363992	+	0.0975315i	0.436180	−	0.899860i	$-0.356331\pi$
$227$	5.48410	+	1.46946i	0.363992	+	0.0975315i	−0.0721871	+	0.997391i	$0.522998\pi$
$228$	2.59178	−	9.67267i	0.171645	−	0.640588i
$229$	−11.9304	−	6.88803i	−0.788385	−	0.455174i	0.0510089	−	0.998698i	$-0.483756\pi$
$229$	−11.9304	−	6.88803i	−0.788385	−	0.455174i	−0.839394	+	0.543524i	$0.817090\pi$
$230$	13.1737	−	12.5127i	0.868645	−	0.825066i
$231$	−11.1575	+	10.4146i	−0.734107	+	0.685231i
$232$	−1.35131	−	1.35131i	−0.0887181	−	0.0887181i
$233$	−4.43074	+	1.18721i	−0.290267	+	0.0777769i	−0.401014	−	0.916072i	$-0.631342\pi$
$233$	−4.43074	+	1.18721i	−0.290267	+	0.0777769i	0.110747	+	0.993849i	$0.464676\pi$
$234$	0.103267	−	0.0596210i	0.00675075	−	0.00389755i
$235$	−16.5043	+	8.97087i	−1.07662	+	0.585195i
$236$	6.91389	−	11.9752i	0.450056	−	0.779519i
$237$	−17.6223	+	17.6223i	−1.14469	+	1.14469i
$238$	−1.47258	+	21.3816i	−0.0954535	+	1.38596i
$239$	3.83109			0.247813			0.123906	−	0.992294i	$-0.460458\pi$
$239$	3.83109			0.247813			0.123906	+	0.992294i	$0.460458\pi$
$240$	−2.03065	+	3.31712i	−0.131078	+	0.214119i
$241$	3.12758	−	1.80571i	0.201465	−	0.116316i	−0.395873	−	0.918305i	$-0.629558\pi$
$241$	3.12758	−	1.80571i	0.201465	−	0.116316i	0.597339	+	0.801989i	$0.296225\pi$
$242$	7.22604	−	8.29363i	0.464508	−	0.533135i
$243$	−0.0682254	−	0.254620i	−0.00437666	−	0.0163339i
$244$	−5.10409			−0.326756
$245$	−15.5765	+	1.54005i	−0.995148	+	0.0983899i
$246$	0.491619			0.0313445
$247$	26.1419	−	7.00470i	1.66337	−	0.445698i
$248$	1.32932	−	4.96107i	0.0844117	−	0.315029i
$249$	−2.63567	−	4.56512i	−0.167029	−	0.289303i
$250$	−9.22266	−	6.32001i	−0.583292	−	0.399712i
$251$	−30.7760			−1.94256			−0.971281	−	0.237934i	$-0.923530\pi$
$251$	−30.7760			−1.94256			−0.971281	+	0.237934i	$0.923530\pi$
$252$	0.0669531	+	0.00461116i	0.00421765	+	0.000290476i
$253$	26.2549	+	6.07708i	1.65063	+	0.382063i
$254$	2.71943	+	1.57006i	0.170632	+	0.0985144i
$255$	30.2126	+	8.93441i	1.89199	+	0.559495i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.7814	+	3.15681i	−0.734901	+	0.196916i	−0.606811	−	0.794846i	$-0.707551\pi$
$257$	−11.7814	+	3.15681i	−0.734901	+	0.196916i	−0.128090	+	0.991763i	$0.540885\pi$
$258$	7.63882	−	7.63882i	0.475572	−	0.475572i
$259$	2.69825	−	0.527428i	0.167661	−	0.0327728i
$260$	−10.5080	−	0.270369i	−0.651680	−	0.0167676i
$261$	0.0419809	+	0.0242377i	0.00259855	+	0.00150027i
$262$	−2.33184	+	8.70253i	−0.144061	+	0.537644i
$263$	−2.29040	+	8.54790i	−0.141232	+	0.527086i	0.858662	+	0.512542i	$0.171296\pi$
$263$	−2.29040	+	8.54790i	−0.141232	+	0.527086i	−0.999894	+	0.0145438i	$0.995370\pi$
$264$	−5.76540	+	0.198064i	−0.354836	+	0.0121900i
$265$	8.18597	+	0.210623i	0.502860	+	0.0129385i
$266$	14.4075	+	4.94399i	0.883382	+	0.303136i
$267$	−15.9293	−	15.9293i	−0.974858	−	0.974858i
$268$	1.30017	+	4.85229i	0.0794203	+	0.296401i
$269$	19.3240	−	11.1567i	1.17820	−	0.680235i	0.222604	−	0.974909i	$-0.428544\pi$
$269$	19.3240	−	11.1567i	1.17820	−	0.680235i	0.955598	+	0.294673i	$0.0952109\pi$
$270$	−3.28081	+	11.0944i	−0.199663	+	0.675183i
$271$	−11.4164	−	6.59129i	−0.693500	−	0.400392i	0.111422	−	0.993773i	$-0.464459\pi$
$271$	−11.4164	−	6.59129i	−0.693500	−	0.400392i	−0.804922	+	0.593381i	$0.797793\pi$
$272$	−5.72801	+	5.72801i	−0.347312	+	0.347312i
$273$	9.50372	+	19.4337i	0.575191	+	1.17618i
$274$	−12.4039			−0.749346
$275$	0.283687	−	16.5807i	0.0171069	−	0.999854i
$276$	−7.06653	−	12.2396i	−0.425355	−	0.736736i
$277$	10.1006	+	2.70645i	0.606886	+	0.162615i	0.549159	−	0.835718i	$-0.314948\pi$
$277$	10.1006	+	2.70645i	0.606886	+	0.162615i	0.0577267	+	0.998332i	$0.481615\pi$
$278$	4.73678	+	17.6779i	0.284093	+	1.06025i
$279$			0.130281i			0.00779972i
$280$	−4.82154	−	3.42823i	−0.288142	−	0.204876i
$281$			16.1771i			0.965043i	0.875884	+	0.482522i	$0.160279\pi$
$281$			16.1771i			0.965043i	−0.875884	+	0.482522i	$0.839721\pi$
$282$	3.78188	+	14.1142i	0.225207	+	0.840486i
$283$	−0.510950	+	1.90689i	−0.0303728	+	0.113353i	−0.979448	−	0.201697i	$-0.935354\pi$
$283$	−0.510950	+	1.90689i	−0.0303728	+	0.113353i	0.949075	+	0.315050i	$0.102021\pi$
$284$	4.05468	−	2.34097i	0.240601	−	0.138911i
$285$	11.6909	−	19.0974i	0.692512	−	1.13123i
$286$	−8.25453	−	13.2267i	−0.488100	−	0.782109i
$287$	−0.0513808	+	0.746039i	−0.00303291	+	0.0440373i
$288$	0.0179364	+	0.0179364i	0.00105691	+	0.00105691i
$289$	42.1064	+	24.3101i	2.47685	+	1.43001i
$290$	−2.04072	−	3.75446i	−0.119835	−	0.220469i
$291$	−8.01349	−	13.8798i	−0.469759	−	0.813647i
$292$	1.35742	+	5.06597i	0.0794372	+	0.296464i
$293$	−9.93175	−	9.93175i	−0.580219	−	0.580219i	0.354744	−	0.934963i	$-0.384568\pi$
$293$	−9.93175	−	9.93175i	−0.580219	−	0.580219i	−0.934963	+	0.354744i	$0.884568\pi$
$294$	−1.66917	+	12.0605i	−0.0973482	+	0.703385i
$295$	22.4188	−	21.2940i	1.30527	−	1.23979i
$296$	0.899924	+	0.519572i	0.0523070	+	0.0301995i
$297$	−16.4131	+	5.00783i	−0.952384	+	0.290584i
$298$	−7.31938	−	1.96122i	−0.424000	−	0.113611i
$299$	19.0984	−	33.0794i	1.10449	−	1.91303i
$300$	−6.45767	+	5.82518i	−0.372834	+	0.336317i
$301$	10.7937	+	12.3904i	0.622136	+	0.714169i
$302$	9.38591	+	9.38591i	0.540098	+	0.540098i
$303$	−15.8283	+	4.24119i	−0.909313	+	0.243650i
$304$	2.87862	+	4.98591i	0.165100	+	0.285961i
$305$	−10.9446	−	3.23651i	−0.626685	−	0.185322i
$306$	0.102740	−	0.177950i	0.00587324	−	0.0101727i
$307$	−11.8385	+	11.8385i	−0.675659	+	0.675659i	−0.959015	−	0.283356i	$-0.908552\pi$
$307$	−11.8385	+	11.8385i	−0.675659	+	0.675659i	0.283356	+	0.959015i	$0.408552\pi$
$308$	0.301996	−	8.76977i	0.0172078	−	0.499704i
$309$		−	7.43830i		−	0.423150i
$310$	5.99624	−	9.79499i	0.340563	−	0.556318i
$311$	−5.47980	−	9.49129i	−0.310731	−	0.538202i	0.667790	−	0.744350i	$-0.267240\pi$
$311$	−5.47980	−	9.49129i	−0.310731	−	0.538202i	−0.978521	+	0.206148i	$0.933907\pi$
$312$	−2.11624	+	7.89792i	−0.119809	+	0.447131i
$313$	6.06109	+	22.6203i	0.342593	+	1.27857i	0.895399	+	0.445265i	$0.146890\pi$
$313$	6.06109	+	22.6203i	0.342593	+	1.27857i	−0.552806	+	0.833310i	$0.686443\pi$
$314$	−1.87065			−0.105567
$315$	0.140642	+	0.0523426i	0.00792428	+	0.00294917i
$316$		−	14.3281i		−	0.806017i
$317$	−27.5619	+	7.38519i	−1.54803	+	0.414793i	−0.928850	−	0.370456i	$-0.879201\pi$
$317$	−27.5619	+	7.38519i	−1.54803	+	0.414793i	−0.619180	+	0.785249i	$0.712535\pi$
$318$	1.64859	−	6.15264i	0.0924486	−	0.345023i
$319$	2.97879	−	5.59464i	0.166780	−	0.313240i
$320$	−0.522991	−	2.17405i	−0.0292361	−	0.121533i
$321$			7.80716i			0.435753i
$322$	19.3123	−	9.44435i	1.07623	−	0.526313i
$323$	32.9775	−	32.9775i	1.83492	−	1.83492i
$324$	7.85957	+	4.53773i	0.436643	+	0.252096i
$325$	−22.3607	−	7.24289i	−1.24035	−	0.401763i
$326$	11.5275	−	6.65541i	0.638450	−	0.368609i
$327$	0.580578	+	2.16675i	0.0321060	+	0.119821i
$328$	−0.199860	+	0.199860i	−0.0110354	+	0.0110354i
$329$	−21.8137	+	4.26393i	−1.20263	+	0.235078i
$330$	−12.4882	−	3.23114i	−0.687452	−	0.177868i
$331$	14.3480	−	24.8514i	0.788636	−	1.36596i	−0.138167	−	0.990409i	$-0.544121\pi$
$331$	14.3480	−	24.8514i	0.788636	−	1.36596i	0.926803	−	0.375549i	$-0.122546\pi$
$332$	2.92736	+	0.784385i	0.160660	+	0.0430487i
$333$	−0.0254606	−	0.00682214i	−0.00139523	−	0.000373851i
$334$	2.14842	+	1.24039i	0.117556	+	0.0678712i
$335$	−0.288922	+	11.2291i	−0.0157855	+	0.613510i
$336$	−3.46993	+	3.02277i	−0.189300	+	0.164906i
$337$	8.31174	−	8.31174i	0.452770	−	0.452770i	−0.443503	−	0.896273i	$-0.646265\pi$
$337$	8.31174	−	8.31174i	0.452770	−	0.452770i	0.896273	+	0.443503i	$0.146265\pi$
$338$	−8.78832	+	2.35482i	−0.478021	+	0.128085i
$339$	8.15297	−	4.70712i	0.442809	−	0.255656i
$340$	−15.9146	+	8.65030i	−0.863089	+	0.469129i
$341$	17.0244	−	0.584856i	0.921924	−	0.0316717i
$342$	−0.103264	−	0.103264i	−0.00558386	−	0.00558386i
$343$	−18.1276	−	3.79348i	−0.978798	−	0.204829i
$344$			6.21087i			0.334868i
$345$	−7.39146	−	30.7259i	−0.397943	−	1.65423i
$346$	−8.55815	−	14.8231i	−0.460089	−	0.796897i
$347$	−10.2051	−	2.73446i	−0.547840	−	0.146793i	−0.0257261	−	0.999669i	$-0.508190\pi$
$347$	−10.2051	−	2.73446i	−0.547840	−	0.146793i	−0.522114	+	0.852876i	$0.674856\pi$
$348$	−3.21073	+	0.860313i	−0.172113	+	0.0461176i
$349$	−4.40151			−0.235607			−0.117804	−	0.993037i	$-0.537585\pi$
$349$	−4.40151			−0.235607			−0.117804	+	0.993037i	$0.537585\pi$
$350$	−8.16487	−	10.4084i	−0.436431	−	0.556353i
$351$			24.3222i			1.29822i
$352$	2.26331	−	2.42434i	0.120635	−	0.129218i
$353$	−29.8708	−	8.00387i	−1.58986	−	0.426003i	−0.647903	−	0.761723i	$-0.724354\pi$
$353$	−29.8708	−	8.00387i	−1.58986	−	0.426003i	−0.941962	+	0.335720i	$0.891020\pi$
$354$	−12.0257	−	20.8292i	−0.639160	−	1.10706i
$355$	10.1788	−	2.44861i	0.540232	−	0.129959i
$356$	12.9516			0.686433
$357$	30.9271	+	20.8133i	1.63683	+	1.10156i
$358$	10.9221	+	10.9221i	0.577253	+	0.577253i
$359$	−0.722549	+	1.25149i	−0.0381347	+	0.0660512i	−0.884463	−	0.466611i	$-0.845475\pi$
$359$	−0.722549	+	1.25149i	−0.0381347	+	0.0660512i	0.846328	+	0.532662i	$0.178808\pi$
$360$	0.0270870	+	0.0498339i	0.00142761	+	0.00262648i
$361$	−7.07285	−	12.2505i	−0.372255	−	0.644765i
$362$	3.52485	+	13.1549i	0.185262	+	0.691407i
$363$	−6.20859	−	18.0976i	−0.325866	−	0.949877i
$364$	−11.7640	−	4.03686i	−0.616602	−	0.211589i
$365$	−0.301645	+	11.7236i	−0.0157888	+	0.613640i
$366$	−4.43892	+	7.68844i	−0.232026	+	0.401881i
$367$	5.47421	−	20.4300i	0.285751	−	1.06644i	−0.662537	−	0.749029i	$-0.730520\pi$
$367$	5.47421	−	20.4300i	0.285751	−	1.06644i	0.948289	−	0.317409i	$-0.102813\pi$
$368$	7.84857	+	2.10302i	0.409135	+	0.109627i
$369$	0.00358475	−	0.00620898i	0.000186615	−	0.000323226i
$370$	1.60023	+	1.68475i	0.0831917	+	0.0875858i
$371$	9.16441	+	3.14480i	0.475793	+	0.163270i
$372$	−6.31693	−	6.31693i	−0.327517	−	0.327517i
$373$	−26.2934	+	7.04530i	−1.36142	+	0.364792i	−0.864338	−	0.502911i	$-0.832262\pi$
$373$	−26.2934	+	7.04530i	−1.36142	+	0.364792i	−0.497083	+	0.867703i	$0.665596\pi$
$374$	−23.7148	−	12.6266i	−1.22626	−	0.652906i
$375$	−17.5408	+	8.39598i	−0.905801	+	0.433566i
$376$	−7.27533	−	4.20041i	−0.375197	−	0.216620i
$377$	−6.35238	−	6.35238i	−0.327164	−	0.327164i
$378$	−7.64287	+	11.3567i	−0.393107	+	0.584127i
$379$		−	10.6497i		−	0.547040i	−0.961866	−	0.273520i	$-0.911812\pi$
$379$		−	10.6497i		−	0.547040i	0.961866	−	0.273520i	$-0.0881880\pi$
$380$	3.01098	+	12.5165i	0.154460	+	0.642082i
$381$	4.73006	−	2.73090i	0.242328	−	0.139908i
$382$	−14.1140	−	3.78184i	−0.722136	−	0.193496i
$383$	0.177248	+	0.661500i	0.00905697	+	0.0338011i	0.970306	−	0.241879i	$-0.0777637\pi$
$383$	0.177248	+	0.661500i	0.00905697	+	0.0338011i	−0.961249	+	0.275680i	$0.911097\pi$
$384$	−1.73936			−0.0887612
$385$	6.20847	−	18.6133i	0.316413	−	0.948621i
$386$	9.86530			0.502131
$387$	−0.0407754	−	0.152176i	−0.00207273	−	0.00773553i
$388$	8.90034	+	2.38484i	0.451846	+	0.121072i
$389$	9.13720	−	5.27536i	0.463274	−	0.267472i	−0.250146	−	0.968208i	$-0.580479\pi$
$389$	9.13720	−	5.27536i	0.463274	−	0.267472i	0.713420	+	0.700737i	$0.247145\pi$
$390$	−9.54587	+	15.5934i	−0.483374	+	0.789602i
$391$		−	65.8212i		−	3.32872i
$392$	−4.22444	−	5.58159i	−0.213366	−	0.281913i
$393$	11.0809	+	11.0809i	0.558958	+	0.558958i
$394$	2.28255	+	1.31783i	0.114993	+	0.0663913i
$395$	9.08544	−	30.7233i	0.457138	−	1.54586i
$396$	−0.0395382	+	0.0742591i	−0.00198687	+	0.00373166i
$397$	−8.52135	+	2.28329i	−0.427674	+	0.114595i	−0.466234	−	0.884661i	$-0.654390\pi$
$397$	−8.52135	+	2.28329i	−0.427674	+	0.114595i	0.0385599	+	0.999256i	$0.487723\pi$
$398$	−5.74945	−	5.74945i	−0.288194	−	0.288194i
$399$	19.9772	−	17.4028i	1.00011	−	0.871229i
$400$	0.257128	−	4.99338i	0.0128564	−	0.249669i
$401$	4.74031	−	8.21045i	0.236720	−	0.410011i	−0.723051	−	0.690794i	$-0.757261\pi$
$401$	4.74031	−	8.21045i	0.236720	−	0.410011i	0.959771	+	0.280784i	$0.0905944\pi$
$402$	8.43986	+	2.26145i	0.420942	+	0.112791i
$403$	6.24896	−	23.3215i	0.311283	−	1.16172i
$404$	4.71056	−	8.15892i	0.234359	−	0.405922i
$405$	13.9757	+	14.7139i	0.694459	+	0.731139i
$406$	−0.969972	−	4.96224i	−0.0481389	−	0.246272i
$407$	−0.777183	+	3.35768i	−0.0385235	+	0.166434i
$408$	3.64674	+	13.6098i	0.180540	+	0.673786i
$409$	−4.54606	−	7.87401i	−0.224788	−	0.389345i	0.731468	−	0.681876i	$-0.238836\pi$
$409$	−4.54606	−	7.87401i	−0.224788	−	0.389345i	−0.956256	+	0.292532i	$0.905502\pi$
$410$	−0.555285	+	0.301823i	−0.0274236	+	0.0149060i
$411$	−10.7874	+	18.6843i	−0.532103	+	0.921629i
$412$	3.02391	+	3.02391i	0.148978	+	0.148978i
$413$	32.8654	−	16.0723i	1.61720	−	0.790865i
$414$	−0.206109			−0.0101297
$415$	5.77969	+	3.53818i	0.283714	+	0.173682i
$416$	−2.35044	−	4.07109i	−0.115240	−	0.199601i
$417$	30.7482	+	8.23895i	1.50575	+	0.403463i
$418$	−13.0304	+	13.9575i	−0.637336	+	0.682684i
$419$		−	36.2513i		−	1.77099i	−0.464647	−	0.885496i	$-0.653819\pi$
$419$		−	36.2513i		−	1.77099i	0.464647	−	0.885496i	$-0.346181\pi$
$420$	−9.35723	+	4.28137i	−0.456586	+	0.208909i
$421$	−11.3011			−0.550784			−0.275392	−	0.961332i	$-0.588808\pi$
$421$	−11.3011			−0.550784			−0.275392	+	0.961332i	$0.588808\pi$
$422$	13.8288	−	3.70541i	0.673174	−	0.180376i
$423$	0.205833	+	0.0551528i	0.0100079	+	0.00268162i
$424$	1.83104	+	3.17146i	0.0889234	+	0.154020i
$425$	−39.6104	+	8.45720i	−1.92139	+	0.410234i
$426$		−	8.14357i		−	0.394557i
$427$	−11.2034	−	7.53967i	−0.542170	−	0.364870i
$428$	−3.17387	−	3.17387i	−0.153415	−	0.153415i
$429$	−27.1025	+	0.931077i	−1.30852	+	0.0449528i
$430$	−3.93832	+	13.3178i	−0.189922	+	0.642242i
$431$	−23.9851	+	13.8478i	−1.15532	+	0.667025i	−0.950178	−	0.311708i	$-0.899099\pi$
$431$	−23.9851	+	13.8478i	−1.15532	+	0.667025i	−0.205142	+	0.978732i	$0.565766\pi$
$432$	−4.99766	+	1.33912i	−0.240450	+	0.0644283i
$433$	8.45486	−	8.45486i	0.406315	−	0.406315i	−0.474137	−	0.880451i	$-0.657240\pi$
$433$	8.45486	−	8.45486i	0.406315	−	0.406315i	0.880451	+	0.474137i	$0.157240\pi$
$434$	10.2462	−	8.92582i	0.491835	−	0.428453i
$435$	−7.43022	−	0.191178i	−0.356252	−	0.00916629i
$436$	−1.11688	−	0.644830i	−0.0534888	−	0.0308818i
$437$	−45.1860	−	12.1076i	−2.16154	−	0.579183i
$438$	8.81154	+	2.36105i	0.421032	+	0.112815i
$439$	1.81101	−	3.13676i	0.0864349	−	0.149710i	−0.819567	−	0.572984i	$-0.805786\pi$
$439$	1.81101	−	3.13676i	0.0864349	−	0.149710i	0.906002	+	0.423274i	$0.139119\pi$
$440$	6.39043	−	3.76330i	0.304652	−	0.179408i
$441$	0.140149	+	0.109023i	0.00667377	+	0.00519158i
$442$	−26.9267	+	26.9267i	−1.28077	+	1.28077i
$443$	−4.07481	−	15.2074i	−0.193600	−	0.722525i	−0.992625	−	0.121227i	$-0.961317\pi$
$443$	−4.07481	−	15.2074i	−0.193600	−	0.722525i	0.799025	−	0.601298i	$-0.205350\pi$
$444$	1.56529	−	0.903721i	0.0742854	−	0.0428887i
$445$	27.7718	+	8.21260i	1.31651	+	0.389315i
$446$	1.95858	+	1.13079i	0.0927414	+	0.0535443i
$447$	−9.31976	+	9.31976i	−0.440809	+	0.440809i
$448$	0.181786	−	2.63950i	0.00858860	−	0.124705i
$449$			14.6105i			0.689512i	0.938692	+	0.344756i	$0.112038\pi$
$449$			14.6105i			0.689512i	−0.938692	+	0.344756i	$0.887962\pi$
$450$	0.0264824	+	0.124034i	0.00124839	+	0.00584700i
$451$	−0.827448	−	0.440563i	−0.0389630	−	0.0207453i
$452$	−1.40085	+	5.22805i	−0.0658906	+	0.245907i
$453$	22.3010	−	5.97553i	1.04779	−	0.280755i
$454$			5.67756i			0.266461i
$455$	−22.6655	−	16.1157i	−1.06258	−	0.755516i
$456$	10.0139			0.468943
$457$	3.58178	+	13.3674i	0.167549	+	0.625300i	0.997701	+	0.0677639i	$0.0215864\pi$
$457$	3.58178	+	13.3674i	0.167549	+	0.625300i	−0.830153	+	0.557536i	$0.811747\pi$
$458$	3.56551	−	13.3067i	0.166605	−	0.621779i
$459$	20.9562	+	36.2971i	0.978149	+	1.69420i
$460$	15.4960	+	9.48624i	0.722504	+	0.442298i
$461$			25.9122i			1.20685i	0.797419	+	0.603427i	$0.206198\pi$
$461$			25.9122i			1.20685i	−0.797419	+	0.603427i	$0.793802\pi$
$462$	−12.9475	−	8.08179i	−0.602372	−	0.375999i
$463$	−2.72852	+	2.72852i	−0.126805	+	0.126805i	−0.767661	−	0.640856i	$-0.778580\pi$
$463$	−2.72852	+	2.72852i	−0.126805	+	0.126805i	0.640856	+	0.767661i	$0.278580\pi$
$464$	0.955524	−	1.65502i	0.0443591	−	0.0768322i
$465$	−9.53967	−	17.5508i	−0.442392	−	0.813899i
$466$	−2.29352	−	3.97249i	−0.106245	−	0.184022i
$467$	21.7629	−	5.83134i	1.00707	−	0.269842i	0.282663	−	0.959219i	$-0.408782\pi$
$467$	21.7629	−	5.83134i	1.00707	−	0.269842i	0.724403	+	0.689377i	$0.242116\pi$
$468$	0.0843168	+	0.0843168i	0.00389755	+	0.00389755i
$469$	−4.31387	+	12.5712i	−0.199196	+	0.580486i
$470$	−12.9368	−	13.6201i	−0.596731	−	0.628250i
$471$	−1.62686	+	2.81781i	−0.0749618	+	0.129838i
$472$	13.3566	+	3.57889i	0.614788	+	0.164732i
$473$	−19.7025	+	6.01145i	−0.905920	+	0.276407i
$474$	−21.5828	−	12.4608i	−0.991330	−	0.572345i
$475$	−1.48034	+	28.7481i	−0.0679228	+	1.31905i
$476$	−21.0342	+	4.11156i	−0.964100	+	0.188453i
$477$	−0.0656845	−	0.0656845i	−0.00300749	−	0.00300749i
$478$	0.991560	+	3.70055i	0.0453529	+	0.169259i
$479$	10.3942	+	18.0033i	0.474924	+	0.822593i	0.999588	−	0.0287167i	$-0.00914207\pi$
$479$	10.3942	+	18.0033i	0.474924	+	0.822593i	−0.524663	+	0.851310i	$0.675809\pi$
$480$	−3.72966	−	1.10293i	−0.170235	−	0.0503415i
$481$	4.23044	+	2.44245i	0.192892	+	0.111366i
$482$	2.55366	+	2.55366i	0.116316	+	0.116316i
$483$	2.56920	−	37.3042i	0.116902	−	1.69740i
$484$	9.88127	+	4.83327i	0.449149	+	0.219694i
$485$	17.5725	+	10.7575i	0.797928	+	0.488471i
$486$	0.228286	−	0.131801i	0.0103553	−	0.00597863i
$487$	4.39351	−	16.3968i	0.199089	−	0.743009i	−0.792082	−	0.610415i	$-0.791003\pi$
$487$	4.39351	−	16.3968i	0.199089	−	0.743009i	0.991170	−	0.132594i	$-0.0423307\pi$
$488$	−1.32104	−	4.93017i	−0.0598005	−	0.223179i
$489$		−	23.1523i		−	1.04698i
$490$	−5.51907	−	14.6472i	−0.249326	−	0.661692i
$491$			3.84105i			0.173344i	0.996237	+	0.0866722i	$0.0276233\pi$
$491$			3.84105i			0.173344i	−0.996237	+	0.0866722i	$0.972377\pi$
$492$	0.127240	+	0.474868i	0.00573644	+	0.0214087i
$493$	−14.9532	−	4.00670i	−0.673458	−	0.180453i
$494$	13.5320	+	23.4382i	0.608835	+	1.05453i
$495$	−0.131869	+	0.134161i	−0.00592705	+	0.00603008i
$496$	5.13608			0.230617
$497$	12.3580	+	0.851112i	0.554331	+	0.0381776i
$498$	3.72741	−	3.72741i	0.167029	−	0.167029i
$499$	8.45155	+	4.87950i	0.378343	+	0.218437i	0.677097	−	0.735894i	$-0.263238\pi$
$499$	8.45155	+	4.87950i	0.378343	+	0.218437i	−0.298754	+	0.954330i	$0.596571\pi$
$500$	3.71766	−	10.5441i	0.166259	−	0.471549i
$501$	3.73687	−	2.15749i	0.166951	−	0.0963893i
$502$	−7.96541	−	29.7273i	−0.355514	−	1.32680i
$503$	28.1033	+	28.1033i	1.25307	+	1.25307i	0.954339	+	0.298726i	$0.0965617\pi$
$503$	28.1033	+	28.1033i	1.25307	+	1.25307i	0.298726	+	0.954339i	$0.403438\pi$
$504$	0.0128747	+	0.0658652i	0.000573485	+	0.00293387i
$505$	15.2743	−	14.5080i	0.679698	−	0.645598i
$506$	0.925261	+	26.9332i	0.0411329	+	1.19732i
$507$	−4.09588	+	15.2860i	−0.181904	+	0.678876i
$508$	−0.812724	+	3.03313i	−0.0360588	+	0.134573i
$509$	12.3074	+	7.10569i	0.545517	+	0.314954i	0.747312	−	0.664474i	$-0.231344\pi$
$509$	12.3074	+	7.10569i	0.545517	+	0.314954i	−0.201795	+	0.979428i	$0.564678\pi$
$510$	−0.810374	+	31.4956i	−0.0358840	+	1.39465i
$511$	−4.50384	+	13.1249i	−0.199238	+	0.580610i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	28.7727	−	7.70961i	1.27034	−	0.340388i
$514$	−6.09848	−	10.5629i	−0.268992	−	0.465909i
$515$	4.56664	+	8.40157i	0.201230	+	0.370217i
$516$	9.35561	+	5.40146i	0.411858	+	0.237786i
$517$	6.28304	−	27.1447i	0.276328	−	1.19382i
$518$	1.20781	+	2.46980i	0.0530683	+	0.108517i
$519$	−29.7714			−1.30682
$520$	−2.45852	−	10.2199i	−0.107813	−	0.448174i
$521$	12.4114	+	21.4972i	0.543754	+	0.941810i	0.998684	+	0.0512824i	$0.0163309\pi$
$521$	12.4114	+	21.4972i	0.543754	+	0.941810i	−0.454930	+	0.890527i	$0.650336\pi$
$522$	−0.0125463	+	0.0468236i	−0.000549138	+	0.00204941i
$523$	30.1286	−	8.07294i	1.31743	−	0.353005i	0.469417	−	0.882976i	$-0.344464\pi$
$523$	30.1286	−	8.07294i	1.31743	−	0.353005i	0.848016	+	0.529971i	$0.177797\pi$
$524$	−9.00952			−0.393583
$525$	−22.7793	+	3.24701i	−0.994170	+	0.141711i
$526$	−8.84944			−0.385854
$527$	−10.7683	−	40.1879i	−0.469075	−	1.75061i
$528$	−1.68351	−	5.51768i	−0.0732654	−	0.240126i
$529$	−37.2588	+	21.5114i	−1.61995	+	0.935279i
$530$	1.91524	+	7.96155i	0.0831926	+	0.345828i
$531$	−0.350753			−0.0152214
$532$	−1.04659	+	15.1962i	−0.0453752	+	0.658839i
$533$	−0.939517	+	0.939517i	−0.0406950	+	0.0406950i
$534$	11.2637	−	19.5093i	0.487429	−	0.844252i
$535$	−4.79310	−	8.81820i	−0.207224	−	0.381244i
$536$	−4.35044	+	2.51173i	−0.187910	+	0.108490i
$537$	25.9511	−	6.95357i	1.11987	−	0.300069i
$538$	15.7779	+	15.7779i	0.680235	+	0.680235i
$539$	13.6174	−	18.8034i	0.586543	−	0.809918i
$540$	−11.5655	−	0.297578i	−0.497699	−	0.0128057i
$541$	−24.1308	−	13.9319i	−1.03746	−	0.598979i	−0.118349	−	0.992972i	$-0.537760\pi$
$541$	−24.1308	−	13.9319i	−1.03746	−	0.598979i	−0.919113	+	0.393993i	$0.871093\pi$
$542$	3.41190	−	12.7334i	0.146554	−	0.546946i
$543$	22.8811	+	6.13097i	0.981922	+	0.263105i
$544$	−7.01536	−	4.05032i	−0.300781	−	0.173656i
$545$	−1.98601	−	2.09091i	−0.0850712	−	0.0895646i
$546$	−16.3118	+	14.2097i	−0.698079	+	0.608119i
$547$	13.5488	−	13.5488i	0.579304	−	0.579304i	−0.355407	−	0.934711i	$-0.615658\pi$
$547$	13.5488	−	13.5488i	0.579304	−	0.579304i	0.934711	+	0.355407i	$0.115658\pi$
$548$	−3.21036	−	11.9812i	−0.137140	−	0.511813i
$549$	0.0647348	+	0.112124i	0.00276281	+	0.00478533i
$550$	16.0891	−	4.01738i	0.686044	−	0.171302i
$551$	−5.50117	+	9.52831i	−0.234358	+	0.405919i
$552$	9.99358	−	9.99358i	0.425355	−	0.425355i
$553$	21.1652	−	31.4498i	0.900034	−	1.33738i
$554$			10.4569i			0.444271i
$555$	3.92946	−	0.945275i	0.166796	−	0.0401247i
$556$	−15.8496	+	9.15076i	−0.672172	+	0.388078i
$557$	0.165182	+	0.0442603i	0.00699897	+	0.00187537i	0.262317	−	0.964982i	$-0.415513\pi$
$557$	0.165182	+	0.0442603i	0.00699897	+	0.00187537i	−0.255318	+	0.966857i	$0.582180\pi$
$558$	−0.125842	+	0.0337192i	−0.00532731	+	0.00142745i
$559$			29.1966i			1.23488i
$560$	2.06351	−	5.54454i	0.0871991	−	0.234300i
$561$	−39.6441	+	24.7412i	−1.67377	+	1.04457i
$562$	−15.6258	+	4.18693i	−0.659137	+	0.176615i
$563$	−10.8287	+	40.4134i	−0.456376	+	1.70322i	0.227633	+	0.973747i	$0.426901\pi$
$563$	−10.8287	+	40.4134i	−0.456376	+	1.70322i	−0.684010	+	0.729473i	$0.739765\pi$
$564$	−12.6544	+	7.30602i	−0.532847	+	0.307639i
$565$	−6.31893	+	10.3221i	−0.265839	+	0.434254i
$566$	−1.97416			−0.0829802
$567$	10.5486	+	21.5702i	0.442998	+	0.905865i
$568$	3.31063	+	3.31063i	0.138911	+	0.138911i
$569$	−5.37595	+	9.31141i	−0.225371	+	0.390355i	−0.956431	−	0.291959i	$-0.905693\pi$
$569$	−5.37595	+	9.31141i	−0.225371	+	0.390355i	0.731059	+	0.682314i	$0.239026\pi$
$570$	21.4725	+	6.34981i	0.899385	+	0.265964i
$571$	16.0341	−	9.25730i	0.671007	−	0.387406i	−0.125451	−	0.992100i	$-0.540038\pi$
$571$	16.0341	−	9.25730i	0.671007	−	0.387406i	0.796458	+	0.604694i	$0.206705\pi$
$572$	10.6395	−	11.3966i	0.444862	−	0.476515i
$573$	−17.9714	+	17.9714i	−0.750765	+	0.750765i
$574$	−0.733917	+	0.143459i	−0.0306331	+	0.00598786i
$575$	27.2124	+	30.1671i	1.13484	+	1.25806i
$576$	−0.0126829	+	0.0219675i	−0.000528455	+	0.000915311i
$577$	−5.04056	+	18.8116i	−0.209841	+	0.783139i	0.778078	+	0.628168i	$0.216195\pi$
$577$	−5.04056	+	18.8116i	−0.209841	+	0.783139i	−0.987919	+	0.154971i	$0.950472\pi$
$578$	−12.5839	+	46.9636i	−0.523419	+	1.95343i
$579$	8.57965	−	14.8604i	0.356558	−	0.617576i
$580$	3.09835	−	2.94291i	0.128652	−	0.122198i
$581$	5.26683	+	6.04595i	0.218505	+	0.250828i
$582$	11.3328	−	11.3328i	0.469759	−	0.469759i
$583$	−8.28842	+	8.87816i	−0.343271	+	0.367696i
$584$	−4.54203	+	2.62234i	−0.187950	+	0.108513i
$585$	0.127333	+	0.234264i	0.00526458	+	0.00968561i
$586$	7.02281	−	12.1639i	0.290109	−	0.502484i
$587$	−18.4772	−	18.4772i	−0.762635	−	0.762635i	0.214163	−	0.976798i	$-0.431298\pi$
$587$	−18.4772	−	18.4772i	−0.762635	−	0.762635i	−0.976798	+	0.214163i	$0.931298\pi$
$588$	−12.0816	+	1.50920i	−0.498237	+	0.0622384i
$589$	−29.5696			−1.21839
$590$	26.3709	+	16.1436i	1.08567	+	0.664620i
$591$	3.97017	−	2.29218i	0.163311	−	0.0942875i
$592$	−0.268950	+	1.00374i	−0.0110538	+	0.0412533i
$593$	−7.48280	+	2.00501i	−0.307282	+	0.0823359i	−0.409165	−	0.912460i	$-0.634180\pi$
$593$	−7.48280	+	2.00501i	−0.307282	+	0.0823359i	0.101883	+	0.994796i	$0.467513\pi$
$594$	−9.08521	−	14.5577i	−0.372771	−	0.597310i
$595$	−47.7102	−	4.52146i	−1.95593	−	0.185362i
$596$		−	7.57758i		−	0.310390i
$597$	−13.6607	+	3.66038i	−0.559097	+	0.149809i
$598$	36.8953	+	9.88605i	1.50876	+	0.404271i
$599$	24.3743	−	14.0725i	0.995907	−	0.574987i	0.0888726	−	0.996043i	$-0.471674\pi$
$599$	24.3743	−	14.0725i	0.995907	−	0.574987i	0.907035	+	0.421056i	$0.138340\pi$
$600$	−7.29806	−	4.72996i	−0.297942	−	0.193100i
$601$			24.1701i			0.985918i	0.870053	+	0.492959i	$0.164085\pi$
$601$			24.1701i			0.985918i	−0.870053	+	0.492959i	$0.835915\pi$
$602$	−9.17458	+	13.6327i	−0.373928	+	0.555629i
$603$	0.0901025	−	0.0901025i	0.00366926	−	0.00366926i
$604$	−6.63684	+	11.4953i	−0.270049	+	0.467739i
$605$	18.1234	+	16.6296i	0.736820	+	0.676089i
$606$	−8.19334	−	14.1913i	−0.332832	−	0.576482i
$607$	−10.1802	−	37.9929i	−0.413200	−	1.54208i	−0.788413	−	0.615146i	$-0.789097\pi$
$607$	−10.1802	−	37.9929i	−0.413200	−	1.54208i	0.375213	−	0.926939i	$-0.377570\pi$
$608$	−4.07098	+	4.07098i	−0.165100	+	0.165100i
$609$	−8.31833	−	2.85446i	−0.337076	−	0.115669i
$610$	0.293560	−	11.4093i	0.0118859	−	0.461950i
$611$	−34.2005	−	19.7457i	−1.38360	−	0.798824i
$612$	0.198478	+	0.0531820i	0.00802299	+	0.00214975i
$613$	5.10732	−	19.0608i	0.206283	−	0.769858i	−0.782772	−	0.622309i	$-0.786195\pi$
$613$	5.10732	−	19.0608i	0.206283	−	0.769858i	0.989055	−	0.147549i	$-0.0471384\pi$
$614$	−14.4991	−	8.37108i	−0.585138	−	0.337829i
$615$	−0.0282753	+	1.09893i	−0.00114017	+	0.0443132i
$616$	8.54911	−	1.97808i	0.344453	−	0.0796990i
$617$	25.8034	+	25.8034i	1.03881	+	1.03881i	0.999216	+	0.0395893i	$0.0126049\pi$
$617$	25.8034	+	25.8034i	1.03881	+	1.03881i	0.0395893	+	0.999216i	$0.487395\pi$
$618$	7.18484	−	1.92517i	0.289017	−	0.0774418i
$619$	−33.6089	+	19.4041i	−1.35086	+	0.779917i	−0.988370	−	0.152071i	$-0.951406\pi$
$619$	−33.6089	+	19.4041i	−1.35086	+	0.779917i	−0.362487	+	0.931989i	$0.618072\pi$
$620$	11.0132	+	3.25679i	0.442300	+	0.130796i
$621$	21.0203	−	36.4083i	0.843517	−	1.46101i
$622$	7.74961	−	7.74961i	0.310731	−	0.310731i
$623$	28.4285	+	19.1318i	1.13896	+	0.766501i
$624$	−8.17652			−0.327323
$625$	14.6577	−	20.2522i	0.586309	−	0.810087i
$626$	−20.2808	+	11.7091i	−0.810584	+	0.467991i
$627$	9.69235	+	31.7666i	0.387075	+	1.26863i
$628$	−0.484159	−	1.80690i	−0.0193200	−	0.0721034i
$629$	8.41772			0.335636
$630$	−0.0141582	+	0.149397i	−0.000564078	+	0.00595212i
$631$	−6.92402			−0.275641			−0.137821	−	0.990457i	$-0.544010\pi$
$631$	−6.92402			−0.275641			−0.137821	+	0.990457i	$0.544010\pi$
$632$	13.8399	−	3.70838i	0.550520	−	0.147511i
$633$	6.44503	−	24.0532i	0.256167	−	0.956028i
$634$	−14.2671	−	24.7113i	−0.566618	−	0.981412i
$635$	−3.66601	+	5.98851i	−0.145481	+	0.237647i
$636$	6.36968			0.252574
$637$	−19.8586	−	26.2384i	−0.786827	−	1.03960i
$638$	6.17497	+	1.42929i	0.244469	+	0.0565860i
$639$	−0.102850	−	0.0593806i	−0.00406869	−	0.00234906i
$640$	1.96461	−	1.06786i	0.0776580	−	0.0422107i
$641$	3.14361	+	5.44489i	0.124165	+	0.215060i	0.921406	−	0.388601i	$-0.127041\pi$
$641$	3.14361	+	5.44489i	0.124165	+	0.215060i	−0.797241	+	0.603661i	$0.793708\pi$
$642$	−7.54113	+	2.02064i	−0.297625	+	0.0797483i
$643$	−15.7015	+	15.7015i	−0.619207	+	0.619207i	−0.945328	−	0.326121i	$-0.894258\pi$
$643$	−15.7015	+	15.7015i	−0.619207	+	0.619207i	0.326121	+	0.945328i	$0.394258\pi$
$644$	14.1209	+	16.2098i	0.556442	+	0.638758i
$645$	16.6359	+	17.5146i	0.655039	+	0.689638i
$646$	40.3890	+	23.3186i	1.58908	+	0.917458i
$647$	−4.01264	+	14.9754i	−0.157753	+	0.588743i	0.841101	+	0.540879i	$0.181908\pi$
$647$	−4.01264	+	14.9754i	−0.157753	+	0.588743i	−0.998854	+	0.0478643i	$0.984758\pi$
$648$	−2.34890	+	8.76622i	−0.0922735	+	0.344369i
$649$	1.57460	+	45.8345i	0.0618083	+	1.79916i
$650$	1.20873	−	23.4733i	0.0474102	−	0.920700i
$651$	−4.53428	−	23.1968i	−0.177713	−	0.909153i
$652$	9.41218	+	9.41218i	0.368609	+	0.368609i
$653$	8.82957	+	32.9524i	0.345528	+	1.28953i	0.891994	+	0.452047i	$0.149306\pi$
$653$	8.82957	+	32.9524i	0.345528	+	1.28953i	−0.546467	+	0.837481i	$0.684027\pi$
$654$	−1.94265	+	1.12159i	−0.0759637	+	0.0438576i
$655$	−19.3189	−	5.71294i	−0.754852	−	0.223223i
$656$	−0.244777	−	0.141322i	−0.00955694	−	0.00551770i
$657$	0.0940705	−	0.0940705i	0.00367004	−	0.00367004i
$658$	−9.76443	−	19.9668i	−0.380657	−	0.778387i
$659$	−23.5693			−0.918128			−0.459064	−	0.888403i	$-0.651815\pi$
$659$	−23.5693			−0.918128			−0.459064	+	0.888403i	$0.651815\pi$
$660$	−0.111144	−	12.8989i	−0.00432629	−	0.502091i
$661$	−9.56447	−	16.5662i	−0.372015	−	0.644349i	0.617860	−	0.786288i	$-0.288000\pi$
$661$	−9.56447	−	16.5662i	−0.372015	−	0.644349i	−0.989875	+	0.141939i	$0.954666\pi$
$662$	27.7182	+	7.42706i	1.07730	+	0.288661i
$663$	17.1429	+	63.9781i	0.665775	+	2.48470i
$664$			3.03063i			0.117611i
$665$	−11.8801	+	31.9212i	−0.460690	+	1.23785i
$666$		−	0.0263587i		−	0.00102138i
$667$	4.01897	+	14.9990i	0.155615	+	0.580764i
$668$	−0.642074	+	2.39625i	−0.0248426	+	0.0927138i
$669$	3.40667	−	1.96684i	0.131710	−	0.0760425i
$670$	−10.9212	+	2.62722i	−0.421924	+	0.101498i
$671$	14.3611	−	8.96253i	0.554406	−	0.345995i
$672$	−3.81786	−	2.56935i	−0.147277	−	0.0991147i
$673$	8.99874	+	8.99874i	0.346876	+	0.346876i	0.858945	−	0.512069i	$-0.171121\pi$
$673$	8.99874	+	8.99874i	0.346876	+	0.346876i	−0.512069	+	0.858945i	$0.671121\pi$
$674$	10.1798	+	5.87729i	0.392110	+	0.226385i
$675$	−24.6109	−	7.97176i	−0.947274	−	0.306833i
$676$	−4.54917	−	7.87939i	−0.174968	−	0.303053i
$677$	−11.1509	−	41.6159i	−0.428565	−	1.59943i	−0.756012	−	0.654558i	$-0.772855\pi$
$677$	−11.1509	−	41.6159i	−0.428565	−	1.59943i	0.327447	−	0.944870i	$-0.393812\pi$
$678$	6.65687	+	6.65687i	0.255656	+	0.255656i
$679$	16.0132	+	18.3821i	0.614531	+	0.705440i
$680$	−12.4745	−	13.1334i	−0.478377	−	0.503644i
$681$	8.55227	+	4.93765i	0.327724	+	0.189211i
$682$	4.97117	+	16.2930i	0.190356	+	0.623889i
$683$	−29.3004	−	7.85103i	−1.12115	−	0.300411i	−0.349802	−	0.936824i	$-0.613751\pi$
$683$	−29.3004	−	7.85103i	−1.12115	−	0.300411i	−0.771349	+	0.636412i	$0.780418\pi$
$684$	0.0730185	−	0.126472i	0.00279193	−	0.00483577i
$685$	0.713403	−	27.7267i	0.0272577	−	1.05938i
$686$	−1.02754	−	18.4917i	−0.0392317	−	0.706018i
$687$	−16.9433	−	16.9433i	−0.646429	−	0.646429i
$688$	−5.99924	+	1.60749i	−0.228719	+	0.0612851i
$689$	8.60753	+	14.9087i	0.327921	+	0.567975i
$690$	27.7659	−	15.0921i	1.05703	−	0.574545i
$691$	−5.74469	+	9.95010i	−0.218538	+	0.378520i	−0.954361	−	0.298654i	$-0.903462\pi$
$691$	−5.74469	+	9.95010i	−0.218538	+	0.378520i	0.735823	+	0.677174i	$0.236796\pi$
$692$	12.1030	−	12.1030i	0.460089	−	0.460089i
$693$	−0.196480	+	0.104592i	−0.00746365	+	0.00397313i
$694$		−	10.5651i		−	0.401047i
$695$	−39.7883	+	9.57152i	−1.50926	+	0.363068i
$696$	−1.66200	−	2.87866i	−0.0629979	−	0.109115i
$697$	−0.592591	+	2.21158i	−0.0224460	+	0.0837696i
$698$	−1.13919	−	4.25153i	−0.0431191	−	0.160923i
$699$	−7.97850			−0.301775
$700$	7.94052	−	10.5806i	0.300124	−	0.399907i
$701$		−	40.7560i		−	1.53933i	−0.638447	−	0.769666i	$-0.720423\pi$
$701$		−	40.7560i		−	1.53933i	0.638447	−	0.769666i	$-0.279577\pi$
$702$	−23.4934	+	6.29504i	−0.886702	+	0.237591i
$703$	1.54841	−	5.77873i	0.0583993	−	0.217949i
$704$	2.92752	+	1.55872i	0.110335	+	0.0587464i
$705$	−31.7673	+	7.64197i	−1.19642	+	0.287813i
$706$		−	30.9246i		−	1.16386i
$707$	22.3918	−	10.9503i	0.842130	−	0.411829i
$708$	17.0069	−	17.0069i	0.639160	−	0.639160i
$709$	16.2195	+	9.36434i	0.609137	+	0.351685i	0.772628	−	0.634860i	$-0.218942\pi$
$709$	16.2195	+	9.36434i	0.609137	+	0.351685i	−0.163491	+	0.986545i	$0.552275\pi$
$710$	4.99963	+	9.19817i	0.187633	+	0.345201i
$711$	−0.314751	+	0.181722i	−0.0118041	+	0.00681510i
$712$	3.35212	+	12.5103i	0.125626	+	0.468842i
$713$	−29.5096	+	29.5096i	−1.10514	+	1.10514i
$714$	−12.0996	+	35.2601i	−0.452817	+	1.31958i
$715$	30.0407	−	17.6908i	1.12346	−	0.661600i
$716$	−7.72312	+	13.3768i	−0.288627	+	0.499916i
$717$	6.43658	+	1.72468i	0.240379	+	0.0644093i
$718$	−1.39586	−	0.374019i	−0.0520929	−	0.0139583i
$719$	−43.8605	−	25.3229i	−1.63572	−	0.944384i	−0.982283	−	0.187404i	$-0.939993\pi$
$719$	−43.8605	−	25.3229i	−1.63572	−	0.944384i	−0.653438	−	0.756980i	$-0.726674\pi$
$720$	−0.0411253	+	0.0390620i	−0.00153265	+	0.00145576i
$721$	2.17056	+	11.1043i	0.0808360	+	0.413546i
$722$	10.0025	−	10.0025i	0.372255	−	0.372255i
$723$	6.06752	−	1.62579i	0.225653	−	0.0604637i
$724$	−11.7944	+	6.80949i	−0.438335	+	0.253073i
$725$	8.50982	−	4.34575i	0.316047	−	0.161397i
$726$	15.8740	−	10.6810i	0.589140	−	0.396410i
$727$	−10.5240	−	10.5240i	−0.390315	−	0.390315i	0.484485	−	0.874800i	$-0.339007\pi$
$727$	−10.5240	−	10.5240i	−0.390315	−	0.390315i	−0.874800	+	0.484485i	$0.839007\pi$
$728$	0.854557	−	12.4080i	0.0316720	−	0.459870i
$729$			26.7679i			0.991402i
$730$	−11.4022	+	2.74292i	−0.422014	+	0.101520i
$731$	25.1560	+	43.5715i	0.930428	+	1.61155i
$732$	−8.57534	−	2.29775i	−0.316954	−	0.0849275i
$733$	−28.6741	+	7.68321i	−1.05910	+	0.283786i	−0.746009	−	0.665936i	$-0.768032\pi$
$733$	−28.6741	+	7.68321i	−1.05910	+	0.283786i	−0.313094	+	0.949722i	$0.601366\pi$
$734$	21.1507			0.780687
$735$	−26.8633	−	4.42481i	−0.990867	−	0.163212i
$736$			8.12544i			0.299508i
$737$	−12.1786	−	11.3696i	−0.448604	−	0.418805i
$738$	0.00692521	+	0.00185561i	0.000254921	+	6.83058e-5i
$739$	15.6926	+	27.1803i	0.577260	+	0.999844i	0.995792	+	0.0916421i	$0.0292116\pi$
$739$	15.6926	+	27.1803i	0.577260	+	0.999844i	−0.418532	+	0.908202i	$0.637455\pi$
$740$	−1.21317	+	1.98174i	−0.0445971	+	0.0728503i
$741$	47.0741			1.72931
$742$	−0.665717	+	9.66608i	−0.0244393	+	0.354853i
$743$	−9.15312	−	9.15312i	−0.335795	−	0.335795i	0.518987	−	0.854782i	$-0.326309\pi$
$743$	−9.15312	−	9.15312i	−0.335795	−	0.335795i	−0.854782	+	0.518987i	$0.826309\pi$
$744$	4.46674	−	7.73663i	0.163759	−	0.283638i
$745$	4.80495	−	16.2484i	0.176040	−	0.595296i
$746$	−13.6105	−	23.5740i	−0.498315	−	0.863107i
$747$	−0.0198966	−	0.0742550i	−0.000727978	−	0.00271685i
$748$	6.05853	−	26.1747i	0.221522	−	0.957044i
$749$	−2.27820	−	11.6550i	−0.0832436	−	0.425863i
$750$	−12.6498	−	14.7700i	−0.461904	−	0.539325i
$751$	−0.543994	+	0.942226i	−0.0198506	+	0.0343823i	−0.875780	−	0.482710i	$-0.839652\pi$
$751$	−0.543994	+	0.942226i	−0.0198506	+	0.0343823i	0.855929	+	0.517093i	$0.172986\pi$
$752$	2.17429	−	8.11458i	0.0792884	−	0.295908i
$753$	−51.7064	−	13.8547i	−1.88429	−	0.504893i
$754$	4.49181	−	7.78004i	0.163582	−	0.283332i
$755$	−21.5204	+	20.4408i	−0.783208	+	0.743915i
$756$	−12.9479	−	4.44310i	−0.470910	−	0.161594i
$757$	−6.92816	−	6.92816i	−0.251808	−	0.251808i	0.569903	−	0.821712i	$-0.306981\pi$
$757$	−6.92816	−	6.92816i	−0.251808	−	0.251808i	−0.821712	+	0.569903i	$0.806981\pi$
$758$	10.2869	−	2.75636i	0.373636	−	0.100115i
$759$	41.3748	+	22.0295i	1.50181	+	0.799618i
$760$	−11.3107	+	6.14789i	−0.410282	+	0.223007i
$761$	47.3108	+	27.3149i	1.71502	+	0.990165i	0.927460	+	0.373923i	$0.121988\pi$
$761$	47.3108	+	27.3149i	1.71502	+	0.990165i	0.787557	+	0.616242i	$0.211346\pi$
$762$	3.86208	+	3.86208i	0.139908	+	0.139908i
$763$	−1.49899	−	3.06522i	−0.0542673	−	0.110968i
$764$		−	14.6119i		−	0.528641i
$765$	0.391869	+	0.239892i	0.0141680	+	0.00867330i
$766$	−0.593085	+	0.342418i	−0.0214290	+	0.0123720i
$767$	62.7879	+	16.8240i	2.26714	+	0.607478i
$768$	−0.450179	−	1.68009i	−0.0162444	−	0.0606251i
$769$	31.1289			1.12254			0.561268	−	0.827634i	$-0.310314\pi$
$769$	31.1289			1.12254			0.561268	+	0.827634i	$0.310314\pi$
$770$	19.5859	+	1.17945i	0.705828	+	0.0425044i
$771$	−21.2149			−0.764035
$772$	2.55333	+	9.52915i	0.0918963	+	0.342962i
$773$	15.0883	+	4.04291i	0.542690	+	0.145413i	0.519742	−	0.854323i	$-0.326028\pi$
$773$	15.0883	+	4.04291i	0.542690	+	0.145413i	0.0229480	+	0.999737i	$0.492695\pi$
$774$	0.136437	−	0.0787720i	0.00490413	−	0.00283140i
$775$	21.5501	+	13.9669i	0.774104	+	0.501706i
$776$			9.21431i			0.330774i
$777$	4.77074	+	0.328568i	0.171149	+	0.0117873i
$778$	7.46049	+	7.46049i	0.267472	+	0.267472i
$779$	1.40924	+	0.813624i	0.0504912	+	0.0291511i
$780$	−17.5327	−	5.18474i	−0.627772	−	0.185643i
$781$	−7.29782	+	13.7065i	−0.261137	+	0.490457i
$782$	63.5784	−	17.0358i	2.27356	−	0.609199i
$783$	−6.99164	−	6.99164i	−0.249861	−	0.249861i
$784$	4.29803	−	5.52512i	0.153501	−	0.197326i
$785$	0.107589	−	4.18151i	0.00384003	−	0.149244i
$786$	−7.83539	+	13.5713i	−0.279479	+	0.484072i
$787$	12.1217	+	3.24799i	0.432091	+	0.115778i	0.468308	−	0.883566i	$-0.344864\pi$
$787$	12.1217	+	3.24799i	0.432091	+	0.115778i	−0.0362165	+	0.999344i	$0.511531\pi$
$788$	−0.682159	+	2.54585i	−0.0243009	+	0.0906922i
$789$	−7.69617	+	13.3302i	−0.273991	+	0.474566i
$790$	32.0279	+	0.824073i	1.13950	+	0.0293192i
$791$	−10.7976	+	9.40616i	−0.383919	+	0.334445i
$792$	−0.0819620	−	0.0189713i	−0.00291239	−	0.000674116i
$793$	−6.21004	−	23.1762i	−0.220525	−	0.823011i
$794$	−4.41098	−	7.64003i	−0.156540	−	0.271135i
$795$	13.6584	+	4.03902i	0.484412	+	0.143249i
$796$	4.06547	−	7.04161i	0.144097	−	0.249583i
$797$	12.2814	+	12.2814i	0.435029	+	0.435029i	0.890335	−	0.455306i	$-0.150470\pi$
$797$	12.2814	+	12.2814i	0.435029	+	0.435029i	−0.455306	+	0.890335i	$0.650470\pi$
$798$	21.9803	+	14.7923i	0.778093	+	0.523642i
$799$	−68.0520			−2.40751
$800$	4.88979	−	1.04402i	0.172880	−	0.0369116i
$801$	−0.164264	−	0.284514i	−0.00580398	−	0.0100528i
$802$	9.15757	+	2.45376i	0.323365	+	0.0866454i
$803$	−12.7149	−	11.8703i	−0.448700	−	0.418894i
$804$			8.73759i			0.308151i
$805$	20.0005	+	43.7125i	0.704924	+	1.54066i
$806$	24.1441			0.850441
$807$	37.4885	−	10.0450i	1.31966	−	0.353601i
$808$	9.10010	+	2.43836i	0.320140	+	0.0857813i
$809$	−9.08595	−	15.7373i	−0.319445	−	0.553295i	0.660927	−	0.750450i	$-0.270163\pi$
$809$	−9.08595	−	15.7373i	−0.319445	−	0.553295i	−0.980372	+	0.197155i	$0.936830\pi$
$810$	−10.5953	+	17.3077i	−0.372283	+	0.608132i
$811$			48.6609i			1.70872i	0.519685	+	0.854358i	$0.326049\pi$
$811$			48.6609i			1.70872i	−0.519685	+	0.854358i	$0.673951\pi$
$812$	4.54211	−	2.22124i	0.159397	−	0.0779504i
$813$	−16.2134	−	16.2134i	−0.568629	−	0.568629i
$814$	−3.44442	+	0.118329i	−0.120727	+	0.00414744i
$815$	14.2140	+	26.1506i	0.497896	+	0.916014i
$816$	−12.2022	+	7.04495i	−0.427163	+	0.246623i
$817$	34.5390	−	9.25470i	1.20837	−	0.323781i
$818$	6.42910	−	6.42910i	0.224788	−	0.224788i
$819$	0.0605225	+	0.309625i	0.00211483	+	0.0108192i
$820$	−0.435257	−	0.458247i	−0.0151998	−	0.0160027i
$821$	7.98288	+	4.60892i	0.278605	+	0.160852i	0.632792	−	0.774322i	$-0.281909\pi$
$821$	7.98288	+	4.60892i	0.278605	+	0.160852i	−0.354187	+	0.935175i	$0.615242\pi$
$822$	−20.8396	−	5.58396i	−0.726866	−	0.194763i
$823$	27.5408	+	7.37955i	0.960013	+	0.257235i	0.704606	−	0.709599i	$-0.251124\pi$
$823$	27.5408	+	7.37955i	0.960013	+	0.257235i	0.255407	+	0.966834i	$0.417790\pi$
$824$	−2.13823	+	3.70352i	−0.0744888	+	0.129018i
$825$	7.94090	−	27.7294i	0.276467	−	0.965413i
$826$	24.0308	+	27.5857i	0.836139	+	0.959830i
$827$	10.1014	−	10.1014i	0.351261	−	0.351261i	−0.509317	−	0.860579i	$-0.670102\pi$
$827$	10.1014	−	10.1014i	0.351261	−	0.351261i	0.860579	+	0.509317i	$0.170102\pi$
$828$	−0.0533449	−	0.199086i	−0.00185386	−	0.00691871i
$829$	30.7972	−	17.7808i	1.06963	−	0.617552i	0.141551	−	0.989931i	$-0.454791\pi$
$829$	30.7972	−	17.7808i	1.06963	−	0.617552i	0.928081	+	0.372379i	$0.121458\pi$
$830$	−1.92172	+	6.49850i	−0.0667040	+	0.225566i
$831$	15.7515	+	9.09415i	0.546414	+	0.315472i
$832$	3.32403	−	3.32403i	0.115240	−	0.115240i
$833$	−52.2431	−	22.0465i	−1.81012	−	0.763866i
$834$			31.8329i			1.10228i
$835$	−2.89625	+	4.73109i	−0.100229	+	0.163726i
$836$	−16.8544	−	8.97390i	−0.582923	−	0.310369i
$837$	6.87782	−	25.6684i	0.237732	−	0.887229i
$838$	35.0161	−	9.38253i	1.20961	−	0.324114i
$839$			11.4797i			0.396325i	0.980169	+	0.198162i	$0.0634973\pi$
$839$			11.4797i			0.396325i	−0.980169	+	0.198162i	$0.936503\pi$
$840$	−6.55731	−	7.93029i	−0.226249	−	0.273621i
$841$	−25.3479			−0.874065
$842$	−2.92495	−	10.9161i	−0.100800	−	0.376192i
$843$	−7.28258	+	27.1789i	−0.250825	+	0.936093i
$844$	7.15830	+	12.3985i	0.246399	+	0.426775i
$845$	−4.75834	−	19.7802i	−0.163692	−	0.680460i
$846$			0.213094i			0.00732633i
$847$	14.5496	+	25.2054i	0.499929	+	0.866066i
$848$	−2.58949	+	2.58949i	−0.0889234	+	0.0889234i
$849$	−1.71689	+	2.97373i	−0.0589234	+	0.102058i
$850$	−18.4209	−	36.0718i	−0.631833	−	1.23725i
$851$	−4.22175	−	7.31228i	−0.144720	−	0.250662i
$852$	7.86608	−	2.10771i	0.269487	−	0.0722089i
$853$	−15.4002	−	15.4002i	−0.527292	−	0.527292i	0.392472	−	0.919764i	$-0.371620\pi$
$853$	−15.4002	−	15.4002i	−0.527292	−	0.527292i	−0.919764	+	0.392472i	$0.871620\pi$
$854$	4.38311	−	12.7730i	0.149987	−	0.437085i
$855$	0.236768	−	0.224889i	0.00809728	−	0.00769105i
$856$	2.24426	−	3.88718i	0.0767074	−	0.132861i
$857$	−32.0199	−	8.57970i	−1.09378	−	0.293077i	−0.333550	−	0.942732i	$-0.608247\pi$
$857$	−32.0199	−	8.57970i	−1.09378	−	0.293077i	−0.760229	+	0.649655i	$0.774913\pi$
$858$	−7.91399	−	25.9380i	−0.270179	−	0.885509i
$859$	−35.2405	−	20.3461i	−1.20239	−	0.694199i	−0.241303	−	0.970450i	$-0.577575\pi$
$859$	−35.2405	−	20.3461i	−1.20239	−	0.694199i	−0.961086	+	0.276250i	$0.910908\pi$
$860$	−13.8833	−	0.357215i	−0.473418	−	0.0121809i
$861$	−0.422175	+	1.23028i	−0.0143877	+	0.0419279i
$862$	−19.5837	−	19.5837i	−0.667025	−	0.667025i
$863$	−2.22852	−	8.31695i	−0.0758597	−	0.283112i	0.917567	−	0.397581i	$-0.130150\pi$
$863$	−2.22852	−	8.31695i	−0.0758597	−	0.283112i	−0.993427	+	0.114469i	$0.963483\pi$
$864$	−2.58698	−	4.48078i	−0.0880107	−	0.152439i
$865$	33.6268	−	18.2777i	1.14335	−	0.621461i
$866$	10.3550	+	5.97849i	0.351879	+	0.203157i
$867$	59.7987	+	59.7987i	2.03087	+	2.03087i
$868$	11.2736	+	7.58692i	0.382651	+	0.257517i
$869$	25.1594	+	40.3142i	0.853474	+	1.36757i
$870$	−1.73842	−	7.22652i	−0.0589379	−	0.245002i
$871$	−20.4509	+	11.8073i	−0.692953	+	0.400077i
$872$	0.333789	−	1.24572i	0.0113035	−	0.0421853i
$873$	−0.0604934	−	0.225765i	−0.00204739	−	0.00764097i
$874$		−	46.7800i		−	1.58236i
$875$	23.7358	−	17.6525i	0.802416	−	0.596765i
$876$			9.12238i			0.308217i
$877$	−4.23182	−	15.7934i	−0.142898	−	0.533304i	−0.999840	−	0.0178906i	$-0.994305\pi$
$877$	−4.23182	−	15.7934i	−0.142898	−	0.533304i	0.856942	−	0.515414i	$-0.172362\pi$
$878$	3.49861	+	0.937449i	0.118072	+	0.0316374i
$879$	−12.2152	−	21.1573i	−0.412008	−	0.713618i
$880$	5.28903	+	5.19867i	0.178293	+	0.175247i
$881$	−15.7161			−0.529488			−0.264744	−	0.964319i	$-0.585287\pi$
$881$	−15.7161			−0.529488			−0.264744	+	0.964319i	$0.585287\pi$
$882$	−0.0690351	+	0.163591i	−0.00232453	+	0.00550840i
$883$	−35.0853	+	35.0853i	−1.18071	+	1.18071i	−0.201155	+	0.979560i	$0.564469\pi$
$883$	−35.0853	+	35.0853i	−1.18071	+	1.18071i	−0.979560	+	0.201155i	$0.935531\pi$
$884$	−32.9784	−	19.0401i	−1.10918	−	0.640387i
$885$	47.2517	−	25.6835i	1.58835	−	0.863340i
$886$	13.6346	−	7.87193i	0.458063	−	0.264463i
$887$	10.0751	+	37.6010i	0.338290	+	1.26252i	0.900258	+	0.435357i	$0.143378\pi$
$887$	10.0751	+	37.6010i	0.338290	+	1.26252i	−0.561967	+	0.827159i	$0.689955\pi$
$888$	1.27805	+	1.27805i	0.0428887	+	0.0428887i
$889$	−6.26439	+	5.45711i	−0.210101	+	0.183026i
$890$	−0.744905	+	28.9510i	−0.0249693	+	0.970441i
$891$	−30.0821	+	1.03344i	−1.00779	+	0.0346216i
$892$	−0.585338	+	2.18451i	−0.0195986	+	0.0731429i
$893$	−12.5179	+	46.7175i	−0.418896	+	1.56334i
$894$	−11.4143	−	6.59006i	−0.381752	−	0.220405i
$895$	−25.0428	+	23.7864i	−0.837087	+	0.795091i
$896$	2.59661	−	0.507560i	0.0867466	−	0.0169564i
$897$	46.9787	−	46.9787i	1.56857	−	1.56857i
$898$	−14.1126	+	3.78147i	−0.470945	+	0.126189i
$899$	4.90765	+	8.50030i	0.163679	+	0.283501i
$900$	−0.112953	+	0.0576823i	−0.00376510	+	0.00192274i
$901$	25.6908	+	14.8326i	0.855886	+	0.494146i
$902$	0.211392	−	0.913279i	0.00703857	−	0.0304089i
$903$	12.5564	+	25.6760i	0.417852	+	0.854445i
$904$	−5.41248			−0.180016
$905$	−29.6083	+	7.12260i	−0.984213	+	0.236763i
$906$	11.5438	+	19.9945i	0.383518	+	0.664273i
$907$	−10.5996	+	39.5581i	−0.351953	+	1.31351i	0.532323	+	0.846541i	$0.321319\pi$
$907$	−10.5996	+	39.5581i	−0.351953	+	1.31351i	−0.884276	+	0.466964i	$0.845348\pi$
$908$	−5.48410	+	1.46946i	−0.181996	+	0.0487657i
$909$	−0.238974			−0.00792628
$910$	9.70031	−	26.0643i	0.321562	−	0.864022i
$911$	−40.0161			−1.32579			−0.662896	−	0.748711i	$-0.730673\pi$
$911$	−40.0161			−1.32579			−0.662896	+	0.748711i	$0.730673\pi$
$912$	2.59178	+	9.67267i	0.0858225	+	0.320294i
$913$	−9.61392	+	2.93332i	−0.318174	+	0.0970787i
$914$	−11.9849	+	6.91947i	−0.396424	+	0.228876i
$915$	−16.9309	−	10.3646i	−0.559718	−	0.342645i
$916$	13.7761			0.455174
$917$	−19.7757	−	13.3087i	−0.653052	−	0.439492i
$918$	−29.6365	+	29.6365i	−0.978149	+	0.978149i
$919$	16.1595	−	27.9892i	0.533054	−	0.923277i	−0.466201	−	0.884679i	$-0.654378\pi$
$919$	16.1595	−	27.9892i	0.533054	−	0.923277i	0.999255	−	0.0385979i	$-0.0122891\pi$
$920$	−5.15235	+	17.4232i	−0.169868	+	0.574425i
$921$	−25.2192	+	14.5603i	−0.831001	+	0.479778i
$922$	−25.0293	+	6.70658i	−0.824296	+	0.220869i
$923$	15.5629	+	15.5629i	0.512259	+	0.512259i
$924$	4.45535	−	14.5981i	0.146570	−	0.480241i
$925$	−3.85800	+	3.48013i	−0.126850	+	0.114426i
$926$	−3.34175	−	1.92936i	−0.109817	−	0.0634026i
$927$	0.0280757	−	0.104780i	0.000922126	−	0.00344142i
$928$	1.84593	+	0.494615i	0.0605956	+	0.0162365i
$929$	−34.6826	−	20.0240i	−1.13790	−	0.656966i	−0.191990	−	0.981397i	$-0.561494\pi$
$929$	−34.6826	−	20.0240i	−1.13790	−	0.656966i	−0.945909	+	0.324431i	$0.894827\pi$
$930$	14.4837	−	13.7571i	0.474940	−	0.451113i
$931$	−24.7448	+	31.8094i	−0.810977	+	1.04251i
$932$	3.24353	−	3.24353i	0.106245	−	0.106245i
$933$	−4.93378	−	18.4131i	−0.161525	−	0.602818i
$934$	11.2653	+	19.5121i	0.368612	+	0.638454i
$935$	29.5886	−	52.2842i	0.967649	−	1.70987i
$936$	−0.0596210	+	0.103267i	−0.00194877	+	0.00337537i
$937$	28.1132	−	28.1132i	0.918417	−	0.918417i	−0.0784971	−	0.996914i	$-0.525012\pi$
$937$	28.1132	−	28.1132i	0.918417	−	0.918417i	0.996914	+	0.0784971i	$0.0250121\pi$
$938$	−13.2594	−	0.913195i	−0.432935	−	0.0298169i
$939$			40.7327i			1.32926i
$940$	9.80774	−	16.0212i	0.319893	−	0.522553i
$941$	5.47546	−	3.16126i	0.178495	−	0.103054i	−0.408090	−	0.912941i	$-0.633805\pi$
$941$	5.47546	−	3.16126i	0.178495	−	0.103054i	0.586585	+	0.809887i	$0.300472\pi$
$942$	−3.14285	−	0.842125i	−0.102400	−	0.0274379i
$943$	2.21835	−	0.594406i	0.0722395	−	0.0193565i
$944$			13.8278i			0.450056i
$945$	−24.9464	−	17.7375i	−0.811507	−	0.577001i
$946$	−10.9060	−	17.4752i	−0.354584	−	0.568169i
$947$	−9.90519	+	2.65409i	−0.321875	+	0.0862462i	−0.416139	−	0.909301i	$-0.636617\pi$
$947$	−9.90519	+	2.65409i	−0.321875	+	0.0862462i	0.0942636	+	0.995547i	$0.469950\pi$
$948$	6.45020	−	24.0725i	0.209493	−	0.781837i
$949$	−21.3516	+	12.3273i	−0.693101	+	0.400162i
$950$	−28.1516	+	6.01064i	−0.913360	+	0.195011i
$951$	−49.6311			−1.60940
$952$	−9.41551	−	19.2533i	−0.305158	−	0.624003i
$953$	2.35459	+	2.35459i	0.0762727	+	0.0762727i	0.744214	−	0.667941i	$-0.232824\pi$
$953$	2.35459	+	2.35459i	0.0762727	+	0.0762727i	−0.667941	+	0.744214i	$0.732824\pi$
$954$	0.0464460	−	0.0804468i	0.00150374	−	0.00260456i
$955$	9.26542	−	31.3320i	0.299822	−	1.01388i
$956$	−3.31782	+	1.91555i	−0.107306	+	0.0619532i
$957$	7.52322	−	8.05851i	0.243191	−	0.260495i
$958$	−14.6997	+	14.6997i	−0.474924	+	0.474924i
$959$	10.6518	−	31.0408i	0.343963	−	1.00236i
$960$	0.100038	−	3.88804i	0.00322872	−	0.125486i
$961$	2.31033	−	4.00160i	0.0745267	−	0.129084i
$962$	−1.26430	+	4.71845i	−0.0407628	+	0.152129i
$963$	−0.0294679	+	0.109976i	−0.000949590	+	0.00354392i
$964$	−1.80571	+	3.12758i	−0.0581581	+	0.100733i
$965$	−0.567398	+	22.0522i	−0.0182652	+	0.709885i
$966$	36.6980	−	7.17338i	1.18074	−	0.230800i
$967$	−25.2478	+	25.2478i	−0.811914	+	0.811914i	−0.984921	−	0.173007i	$-0.944652\pi$
$967$	−25.2478	+	25.2478i	−0.811914	+	0.811914i	0.173007	+	0.984921i	$0.444652\pi$
$968$	−2.11112	+	10.7955i	−0.0678541	+	0.346981i
$969$	70.2510	−	40.5594i	2.25679	−	1.30296i
$970$	−5.84280	+	19.7580i	−0.187601	+	0.634392i
$971$	15.5165	−	26.8753i	0.497948	−	0.862470i	−0.502050	−	0.864839i	$-0.667421\pi$
$971$	15.5165	−	26.8753i	0.497948	−	0.862470i	0.999997	+	0.00236839i	$0.000753884\pi$
$972$	0.186395	+	0.186395i	0.00597863	+	0.00597863i
$973$	−48.3068	−	3.32696i	−1.54865	−	0.106658i
$974$	16.9752			0.543921
$975$	−34.3073	−	22.2350i	−1.09871	−	0.712090i
$976$	4.42027	−	2.55205i	0.141490	−	0.0816890i
$977$	13.2910	−	49.6028i	0.425218	−	1.58693i	−0.338229	−	0.941064i	$-0.609828\pi$
$977$	13.2910	−	49.6028i	0.425218	−	1.58693i	0.763447	−	0.645871i	$-0.223505\pi$
$978$	22.3634	−	5.99225i	0.715103	−	0.191611i
$979$	−36.4413	+	22.7423i	−1.16467	+	0.726849i
$980$	12.7196	−	9.12198i	0.406314	−	0.291391i
$981$			0.0327133i			0.00104446i
$982$	−3.71017	+	0.994138i	−0.118396	+	0.0317242i
$983$	−14.2148	−	3.80883i	−0.453380	−	0.121483i	0.0249003	−	0.999690i	$-0.492073\pi$
$983$	−14.2148	−	3.80883i	−0.453380	−	0.121483i	−0.478281	+	0.878207i	$0.658740\pi$
$984$	−0.425755	+	0.245810i	−0.0135726	+	0.00783613i
$985$	−3.07706	+	5.02645i	−0.0980433	+	0.160156i
$986$		−	15.4807i		−	0.493006i
$987$	−38.5685	−	2.65627i	−1.22765	−	0.0845500i
$988$	−19.1372	+	19.1372i	−0.608835	+	0.608835i
$989$	25.2330	−	43.7049i	0.802364	−	1.38974i
$990$	−0.163719	−	0.0926519i	−0.00520335	−	0.00294467i
$991$	10.6437	+	18.4354i	0.338108	+	0.585620i	0.984077	−	0.177744i	$-0.0568798\pi$
$991$	10.6437	+	18.4354i	0.338108	+	0.585620i	−0.645969	+	0.763364i	$0.723546\pi$
$992$	1.32932	+	4.96107i	0.0422058	+	0.157514i
$993$	35.2935	−	35.2935i	1.12000	−	1.12000i
$994$	2.37637	+	12.1572i	0.0753738	+	0.385602i
$995$	13.1826	−	12.5212i	0.417916	−	0.396950i
$996$	4.56512	+	2.63567i	0.144651	+	0.0835145i
$997$	43.9383	+	11.7732i	1.39154	+	0.372862i	0.875299	−	0.483582i	$-0.160664\pi$
$997$	43.9383	+	11.7732i	1.39154	+	0.372862i	0.516240	+	0.856444i	$0.327331\pi$
$998$	−2.52582	+	9.42648i	−0.0799533	+	0.298390i
$999$	4.65617	+	2.68824i	0.147315	+	0.0850521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	770.2.bd.a.527.43	yes	192
5.3	odd	4	inner	770.2.bd.a.373.30	yes	192
7.4	even	3	inner	770.2.bd.a.417.6	yes	192
11.10	odd	2	inner	770.2.bd.a.527.19	yes	192
35.18	odd	12	inner	770.2.bd.a.263.19	✓	192
55.43	even	4	inner	770.2.bd.a.373.6	yes	192
77.32	odd	6	inner	770.2.bd.a.417.30	yes	192
385.263	even	12	inner	770.2.bd.a.263.43	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
770.2.bd.a.263.19	✓	192	35.18	odd	12	inner
770.2.bd.a.263.43	yes	192	385.263	even	12	inner
770.2.bd.a.373.6	yes	192	55.43	even	4	inner
770.2.bd.a.373.30	yes	192	5.3	odd	4	inner
770.2.bd.a.417.6	yes	192	7.4	even	3	inner
770.2.bd.a.417.30	yes	192	77.32	odd	6	inner
770.2.bd.a.527.19	yes	192	11.10	odd	2	inner
770.2.bd.a.527.43	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.68009 + 0.450179i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.17405 + 0.522991i) q^{5} +1.73936i q^{6} +(-2.63950 - 0.181786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.0219675 + 0.0126829i) q^{9} +O(q^{10})\)	\(q+(0.258819 + 0.965926i) q^{2} +(1.68009 + 0.450179i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.17405 + 0.522991i) q^{5} +1.73936i q^{6} +(-2.63950 - 0.181786i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.0219675 + 0.0126829i) q^{9} +(-1.06786 - 1.96461i) q^{10} +(1.55872 - 2.92752i) q^{11} +(-1.68009 + 0.450179i) q^{12} +(-3.32403 - 3.32403i) q^{13} +(-0.507560 - 2.59661i) q^{14} +(-3.88804 - 0.100038i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-7.82461 - 2.09660i) q^{17} +(-0.00656516 + 0.0245015i) q^{18} +(-2.87862 + 4.98591i) q^{19} +(1.62128 - 1.53995i) q^{20} +(-4.35276 - 1.49366i) q^{21} +(3.23120 + 0.747908i) q^{22} +(2.10302 + 7.84857i) q^{23} +(-0.869679 - 1.50633i) q^{24} +(4.45296 - 2.27401i) q^{25} +(2.35044 - 4.07109i) q^{26} +(-3.65854 - 3.65854i) q^{27} +(2.37677 - 1.16232i) q^{28} +1.91105 q^{29} +(-0.909668 - 3.78145i) q^{30} +(2.56804 + 4.44798i) q^{31} +(0.965926 + 0.258819i) q^{32} +(3.93670 - 4.21680i) q^{33} -8.10063i q^{34} +(5.83347 - 0.985221i) q^{35} -0.0253658 q^{36} +(-1.00374 + 0.268950i) q^{37} +(-5.56106 - 1.49008i) q^{38} +(-4.08826 - 7.08108i) q^{39} +(1.90709 + 1.16747i) q^{40} -0.282644i q^{41} +(0.316191 - 4.59103i) q^{42} +(-4.39175 - 4.39175i) q^{43} +(0.113872 + 3.31467i) q^{44} +(-0.0543914 - 0.0160845i) q^{45} +(-7.03684 + 4.06272i) q^{46} +(8.11458 - 2.17429i) q^{47} +(1.22991 - 1.22991i) q^{48} +(6.93391 + 0.959649i) q^{49} +(3.34904 + 3.71267i) q^{50} +(-12.2022 - 7.04495i) q^{51} +(4.54071 + 1.21668i) q^{52} +(-3.53731 - 0.947818i) q^{53} +(2.58698 - 4.48078i) q^{54} +(-1.85766 + 7.17977i) q^{55} +(1.73787 + 1.99495i) q^{56} +(-7.08088 + 7.08088i) q^{57} +(0.494615 + 1.84593i) q^{58} +(-11.9752 + 6.91389i) q^{59} +(3.41716 - 1.85738i) q^{60} +(4.42027 + 2.55205i) q^{61} +(-3.63176 + 3.63176i) q^{62} +(-0.0556775 - 0.0374699i) q^{63} +1.00000i q^{64} +(8.96503 + 5.48816i) q^{65} +(5.09201 + 2.71117i) q^{66} +(1.30017 - 4.85229i) q^{67} +(7.82461 - 2.09660i) q^{68} +14.1331i q^{69} +(2.46146 + 5.37970i) q^{70} -4.68194 q^{71} +(-0.00656516 - 0.0245015i) q^{72} +(1.35742 - 5.06597i) q^{73} +(-0.519572 - 0.899924i) q^{74} +(8.50509 - 1.81592i) q^{75} -5.75723i q^{76} +(-4.64642 + 7.44384i) q^{77} +(5.78168 - 5.78168i) q^{78} +(-7.16404 + 12.4085i) q^{79} +(-0.634100 + 2.14428i) q^{80} +(-4.53773 - 7.85957i) q^{81} +(0.273013 - 0.0731537i) q^{82} +(-2.14298 - 2.14298i) q^{83} +(4.51643 - 0.882829i) q^{84} +(18.1076 + 0.465904i) q^{85} +(3.10544 - 5.37877i) q^{86} +(3.21073 + 0.860313i) q^{87} +(-3.17225 + 0.967892i) q^{88} +(-11.2164 - 6.47579i) q^{89} +(0.00145890 - 0.0567010i) q^{90} +(8.16951 + 9.37803i) q^{91} +(-5.74556 - 5.74556i) q^{92} +(2.31216 + 8.62908i) q^{93} +(4.20041 + 7.27533i) q^{94} +(3.65066 - 12.3451i) q^{95} +(1.50633 + 0.869679i) q^{96} +(-6.51550 - 6.51550i) q^{97} +(0.867677 + 6.94602i) q^{98} +(0.0713707 - 0.0445412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 8 q^{5}+O(q^{10}) \) 192 * q + 8 * q^5	\( 192 q + 8 q^{5} + 4 q^{11} + 16 q^{15} + 96 q^{16} + 24 q^{22} - 8 q^{23} + 24 q^{25} - 8 q^{26} - 16 q^{33} - 160 q^{36} - 40 q^{37} - 40 q^{42} + 32 q^{45} - 40 q^{47} + 40 q^{53} + 8 q^{55} + 16 q^{56} + 32 q^{58} - 48 q^{67} - 72 q^{70} + 32 q^{71} - 48 q^{75} - 72 q^{77} - 8 q^{80} + 64 q^{81} + 16 q^{82} - 12 q^{88} - 112 q^{91} - 16 q^{92} + 80 q^{93} - 64 q^{97}+O(q^{100}) \) 192 * q + 8 * q^5 + 4 * q^11 + 16 * q^15 + 96 * q^16 + 24 * q^22 - 8 * q^23 + 24 * q^25 - 8 * q^26 - 16 * q^33 - 160 * q^36 - 40 * q^37 - 40 * q^42 + 32 * q^45 - 40 * q^47 + 40 * q^53 + 8 * q^55 + 16 * q^56 + 32 * q^58 - 48 * q^67 - 72 * q^70 + 32 * q^71 - 48 * q^75 - 72 * q^77 - 8 * q^80 + 64 * q^81 + 16 * q^82 - 12 * q^88 - 112 * q^91 - 16 * q^92 + 80 * q^93 - 64 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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