LMFDB - Embedded newform 507.2.t.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(4,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.t (of order $78$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$14$ over $\Q(\zeta_{78})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{78}]$

Embedding invariants

Embedding label			4.3
Character	$\chi$	$=$	507.4
Dual form			507.2.t.a.127.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.22635 - 0.0897189i) q^{2} +(0.278217 - 0.960518i) q^{3} +(2.95507 + 0.238558i) q^{4} +(1.89329 + 0.718032i) q^{5} +(-0.705586 + 2.11349i) q^{6} +(-0.669684 - 1.57181i) q^{7} +(-2.13381 - 0.259091i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(-4.15072 - 1.76846i) q^{10} +(2.15305 + 3.40478i) q^{11} +(1.05129 - 2.77203i) q^{12} +(3.56212 - 0.557956i) q^{13} +(1.34993 + 3.55947i) q^{14} +(1.21643 - 1.61877i) q^{15} +(-1.12524 - 0.182869i) q^{16} +(3.74310 - 1.59478i) q^{17} +(1.83374 + 1.26574i) q^{18} +(0.892394 - 0.515224i) q^{19} +(5.42353 + 2.57350i) q^{20} +(-1.69607 + 0.205940i) q^{21} +(-4.48797 - 7.77339i) q^{22} +(-4.45782 + 7.72116i) q^{23} +(-0.842524 + 1.97748i) q^{24} +(-0.673560 - 0.596722i) q^{25} +(-7.98058 + 0.922618i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(-1.60400 - 4.80456i) q^{28} +(-0.183582 + 4.55555i) q^{29} +(-2.85344 + 3.49482i) q^{30} +(-0.0212241 - 0.0239571i) q^{31} +(6.70084 + 1.36799i) q^{32} +(3.86936 - 1.12077i) q^{33} +(-8.47653 + 3.21472i) q^{34} +(-0.139302 - 3.45674i) q^{35} +(-2.37010 - 1.78101i) q^{36} +(6.15543 - 1.25664i) q^{37} +(-2.03301 + 1.06700i) q^{38} +(0.455116 - 3.57671i) q^{39} +(-3.85389 - 2.02268i) q^{40} +(-0.0212979 - 0.00616901i) q^{41} +(3.79451 - 0.306325i) q^{42} +(0.529302 - 2.59269i) q^{43} +(5.55018 + 10.5750i) q^{44} +(-1.21643 - 1.61877i) q^{45} +(10.6174 - 16.7901i) q^{46} +(9.53495 - 6.58150i) q^{47} +(-0.488710 + 1.02993i) q^{48} +(2.82697 - 2.94319i) q^{49} +(1.44604 + 1.38894i) q^{50} +(-0.490424 - 4.03901i) q^{51} +(10.6594 - 0.799030i) q^{52} +(1.09724 - 9.03658i) q^{53} +(1.72594 - 1.40919i) q^{54} +(1.63162 + 7.99220i) q^{55} +(1.02173 + 3.52744i) q^{56} +(-0.246602 - 1.00050i) q^{57} +(0.817438 - 10.1258i) q^{58} +(-0.390147 - 2.40067i) q^{59} +(3.98081 - 4.49341i) q^{60} +(-2.75425 + 2.06969i) q^{61} +(0.0451029 + 0.0552410i) q^{62} +(-0.274066 + 1.68640i) q^{63} +(-12.5819 - 3.10117i) q^{64} +(7.14477 + 1.50134i) q^{65} +(-8.71512 + 2.14808i) q^{66} +(0.426683 + 5.28542i) q^{67} +(11.4416 - 3.81976i) q^{68} +(6.17608 + 6.42998i) q^{69} +7.70843i q^{70} +(5.75046 - 5.52339i) q^{71} +(1.66500 + 1.35943i) q^{72} +(6.03415 - 11.4971i) q^{73} +(-13.8169 + 2.24546i) q^{74} +(-0.760558 + 0.480948i) q^{75} +(2.76000 - 1.30964i) q^{76} +(3.90978 - 5.66430i) q^{77} +(-1.33415 + 7.92218i) q^{78} +(4.55874 + 6.60447i) q^{79} +(-1.99910 - 1.15418i) q^{80} +(0.428693 + 0.903450i) q^{81} +(0.0468631 + 0.0156452i) q^{82} +(-3.37692 + 13.7007i) q^{83} +(-5.06113 + 0.203957i) q^{84} +(8.23189 - 0.331734i) q^{85} +(-1.41103 + 5.72475i) q^{86} +(4.32461 + 1.44377i) q^{87} +(-3.71204 - 7.82296i) q^{88} +(-11.3092 - 6.52934i) q^{89} +(2.56297 + 3.71310i) q^{90} +(-3.26249 - 5.22530i) q^{91} +(-15.0151 + 21.7532i) q^{92} +(-0.0289161 + 0.0137209i) q^{93} +(-21.8186 + 13.7973i) q^{94} +(2.05951 - 0.334703i) q^{95} +(3.17827 - 6.05568i) q^{96} +(6.12974 + 5.00478i) q^{97} +(-6.55790 + 6.29895i) q^{98} -4.02841i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31}+ \cdots + 104 q^{98}+O(q^{100}) $ 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{78}\right)$

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 $

$2$	−2.22635	−	0.0897189i	−1.57427	−	0.0634408i	−0.762331	−	0.647187i	$-0.775945\pi$
$2$	−2.22635	−	0.0897189i	−1.57427	−	0.0634408i	−0.811936	+	0.583746i	$0.801586\pi$
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$3$	0.278217	−	0.960518i	0.160629	−	0.554555i
$4$	2.95507	+	0.238558i	1.47754	+	0.119279i
$5$	1.89329	+	0.718032i	0.846707	+	0.321114i	0.739528	−	0.673126i	$-0.235049\pi$
$5$	1.89329	+	0.718032i	0.846707	+	0.321114i	0.107179	+	0.994240i	$0.465818\pi$
$6$	−0.705586	+	2.11349i	−0.288054	+	0.862828i
$7$	−0.669684	−	1.57181i	−0.253117	−	0.594087i	0.744147	−	0.668016i	$-0.232856\pi$
$7$	−0.669684	−	1.57181i	−0.253117	−	0.594087i	−0.997263	+	0.0739295i	$0.976446\pi$
$8$	−2.13381	−	0.259091i	−0.754414	−	0.0916025i
$9$	−0.845190	−	0.534466i	−0.281730	−	0.178155i
$10$	−4.15072	−	1.76846i	−1.31257	−	0.559235i
$11$	2.15305	+	3.40478i	0.649169	+	1.02658i	0.996061	+	0.0886732i	$0.0282627\pi$
$11$	2.15305	+	3.40478i	0.649169	+	1.02658i	−0.346892	+	0.937905i	$0.612763\pi$
$12$	1.05129	−	2.77203i	0.303482	−	0.800217i
$13$	3.56212	−	0.557956i	0.987954	−	0.154749i
$13$	3.56212	−	0.557956i	0.987954	−	0.154749i
$14$	1.34993	+	3.55947i	0.360784	+	0.951309i
$15$	1.21643	−	1.61877i	0.314081	−	0.417966i
$16$	−1.12524	−	0.182869i	−0.281309	−	0.0457172i
$17$	3.74310	−	1.59478i	0.907834	−	0.386792i	0.112983	−	0.993597i	$-0.463959\pi$
$17$	3.74310	−	1.59478i	0.907834	−	0.386792i	0.794851	+	0.606805i	$0.207549\pi$
$18$	1.83374	+	1.26574i	0.432216	+	0.298337i
$19$	0.892394	−	0.515224i	0.204729	−	0.118200i	−0.394130	−	0.919055i	$-0.628954\pi$
$19$	0.892394	−	0.515224i	0.204729	−	0.118200i	0.598859	+	0.800854i	$0.295621\pi$
$20$	5.42353	+	2.57350i	1.21274	+	0.575452i
$21$	−1.69607	+	0.205940i	−0.370112	+	0.0449397i
$22$	−4.48797	−	7.77339i	−0.956839	−	1.65729i
$23$	−4.45782	+	7.72116i	−0.929519	+	1.60997i	−0.145392	+	0.989374i	$0.546444\pi$
$23$	−4.45782	+	7.72116i	−0.929519	+	1.60997i	−0.784127	+	0.620600i	$0.786889\pi$
$24$	−0.842524	+	1.97748i	−0.171979	+	0.403650i
$25$	−0.673560	−	0.596722i	−0.134712	−	0.119344i
$26$	−7.98058	+	0.922618i	−1.56512	+	0.180940i
$27$	−0.748511	+	0.663123i	−0.144051	+	0.127618i
$28$	−1.60400	−	4.80456i	−0.303127	−	0.907977i
$29$	−0.183582	+	4.55555i	−0.0340904	+	0.845945i	0.888202	+	0.459453i	$0.151954\pi$
$29$	−0.183582	+	4.55555i	−0.0340904	+	0.845945i	−0.922293	+	0.386492i	$0.873687\pi$
$30$	−2.85344	+	3.49482i	−0.520964	+	0.638065i
$31$	−0.0212241	−	0.0239571i	−0.00381196	−	0.00430282i	0.746602	−	0.665271i	$-0.231684\pi$
$31$	−0.0212241	−	0.0239571i	−0.00381196	−	0.00430282i	−0.750414	+	0.660969i	$0.770146\pi$
$32$	6.70084	+	1.36799i	1.18455	+	0.241828i
$33$	3.86936	−	1.12077i	0.673570	−	0.195102i
$34$	−8.47653	+	3.21472i	−1.45371	+	0.551320i
$35$	−0.139302	−	3.45674i	−0.0235463	−	0.584297i
$36$	−2.37010	−	1.78101i	−0.395016	−	0.296836i
$37$	6.15543	−	1.25664i	1.01195	−	0.206590i	0.334683	−	0.942331i	$-0.391371\pi$
$37$	6.15543	−	1.25664i	1.01195	−	0.206590i	0.677263	+	0.735741i	$0.263166\pi$
$38$	−2.03301	+	1.06700i	−0.329797	+	0.173091i
$39$	0.455116	−	3.57671i	0.0728769	−	0.572732i
$40$	−3.85389	−	2.02268i	−0.609353	−	0.319813i
$41$	−0.0212979	−	0.00616901i	−0.00332617	−	0.000963437i	0.276554	−	0.960998i	$-0.410808\pi$
$41$	−0.0212979	−	0.00616901i	−0.00332617	−	0.000963437i	−0.279880	+	0.960035i	$0.590295\pi$
$42$	3.79451	−	0.306325i	0.585506	−	0.0472669i
$43$	0.529302	−	2.59269i	0.0807178	−	0.395382i	−0.919281	−	0.393603i	$-0.871229\pi$
$43$	0.529302	−	2.59269i	0.0807178	−	0.395382i	0.999998	−	0.00177910i	$-0.000566304\pi$
$44$	5.55018	+	10.5750i	0.836722	+	1.59424i
$45$	−1.21643	−	1.61877i	−0.181335	−	0.241313i
$46$	10.6174	−	16.7901i	1.56545	−	2.47556i
$47$	9.53495	−	6.58150i	1.39082	−	0.960011i	0.391612	−	0.920131i	$-0.371918\pi$
$47$	9.53495	−	6.58150i	1.39082	−	0.960011i	0.999204	−	0.0398804i	$-0.0126977\pi$
$48$	−0.488710	+	1.02993i	−0.0705391	+	0.148658i
$49$	2.82697	−	2.94319i	0.403853	−	0.420456i
$50$	1.44604	+	1.38894i	0.204501	+	0.196426i
$51$	−0.490424	−	4.03901i	−0.0686732	−	0.565574i
$52$	10.6594	−	0.799030i	1.47820	−	0.110806i
$53$	1.09724	−	9.03658i	0.150717	−	1.24127i	−0.699421	−	0.714710i	$-0.746559\pi$
$53$	1.09724	−	9.03658i	0.150717	−	1.24127i	0.850138	−	0.526560i	$-0.176518\pi$
$54$	1.72594	−	1.40919i	0.234871	−	0.191766i
$55$	1.63162	+	7.99220i	0.220007	+	1.07767i
$56$	1.02173	+	3.52744i	0.136535	+	0.471374i
$57$	−0.246602	−	1.00050i	−0.0326633	−	0.132520i
$58$	0.817438	−	10.1258i	0.107335	−	1.32958i
$59$	−0.390147	−	2.40067i	−0.0507928	−	0.312541i	0.949205	−	0.314659i	$-0.101890\pi$
$59$	−0.390147	−	2.40067i	−0.0507928	−	0.312541i	−0.999998	+	0.00211773i	$0.999326\pi$
$60$	3.98081	−	4.49341i	0.513921	−	0.580097i
$61$	−2.75425	+	2.06969i	−0.352646	+	0.264996i	−0.762271	−	0.647258i	$-0.775916\pi$
$61$	−2.75425	+	2.06969i	−0.352646	+	0.264996i	0.409626	+	0.912254i	$0.365659\pi$
$62$	0.0451029	+	0.0552410i	0.00572807	+	0.00701562i
$63$	−0.274066	+	1.68640i	−0.0345291	+	0.212466i
$64$	−12.5819	−	3.10117i	−1.57274	−	0.387646i
$65$	7.14477	+	1.50134i	0.886199	+	0.186218i
$66$	−8.71512	+	2.14808i	−1.07276	+	0.264411i
$67$	0.426683	+	5.28542i	0.0521276	+	0.645717i	0.969084	+	0.246730i	$0.0793560\pi$
$67$	0.426683	+	5.28542i	0.0521276	+	0.645717i	−0.916957	+	0.398987i	$0.869362\pi$
$68$	11.4416	−	3.81976i	1.38750	−	0.463214i
$69$	6.17608	+	6.42998i	0.743512	+	0.774078i
$70$			7.70843i			0.921333i
$71$	5.75046	−	5.52339i	0.682454	−	0.655506i	−0.269056	−	0.963125i	$-0.586712\pi$
$71$	5.75046	−	5.52339i	0.682454	−	0.655506i	0.951510	+	0.307618i	$0.0995320\pi$
$72$	1.66500	+	1.35943i	0.196222	+	0.160210i
$73$	6.03415	−	11.4971i	0.706244	−	1.34564i	−0.222506	−	0.974931i	$-0.571424\pi$
$73$	6.03415	−	11.4971i	0.706244	−	1.34564i	0.928751	−	0.370705i	$-0.120884\pi$
$74$	−13.8169	+	2.24546i	−1.60618	+	0.261030i
$75$	−0.760558	+	0.480948i	−0.0878217	+	0.0555351i
$76$	2.76000	−	1.30964i	0.316594	−	0.150226i
$77$	3.90978	−	5.66430i	0.445561	−	0.645507i
$78$	−1.33415	+	7.92218i	−0.151062	+	0.897011i
$79$	4.55874	+	6.60447i	0.512898	+	0.743061i	0.990797	−	0.135354i	$-0.0432171\pi$
$79$	4.55874	+	6.60447i	0.512898	+	0.743061i	−0.477899	+	0.878415i	$0.658602\pi$
$80$	−1.99910	−	1.15418i	−0.223506	−	0.129041i
$81$	0.428693	+	0.903450i	0.0476325	+	0.100383i
$82$	0.0468631	+	0.0156452i	0.00517516	+	0.00172772i
$83$	−3.37692	+	13.7007i	−0.370665	+	1.50385i	0.428947	+	0.903330i	$0.358885\pi$
$83$	−3.37692	+	13.7007i	−0.370665	+	1.50385i	−0.799612	+	0.600517i	$0.794962\pi$
$84$	−5.06113	+	0.203957i	−0.552214	+	0.0222535i
$85$	8.23189	−	0.331734i	0.892874	−	0.0359816i
$86$	−1.41103	+	5.72475i	−0.152155	+	0.617316i
$87$	4.32461	+	1.44377i	0.463647	+	0.154788i
$88$	−3.71204	−	7.82296i	−0.395705	−	0.833931i
$89$	−11.3092	−	6.52934i	−1.19877	−	0.692109i	−0.238487	−	0.971146i	$-0.576652\pi$
$89$	−11.3092	−	6.52934i	−1.19877	−	0.692109i	−0.960280	+	0.279037i	$0.909985\pi$
$90$	2.56297	+	3.71310i	0.270160	+	0.391395i
$91$	−3.26249	−	5.22530i	−0.342002	−	0.547761i
$92$	−15.0151	+	21.7532i	−1.56544	+	2.26792i
$93$	−0.0289161	+	0.0137209i	−0.00299846	+	0.00142279i
$94$	−21.8186	+	13.7973i	−2.25042	+	1.42308i
$95$	2.05951	−	0.334703i	0.211301	−	0.0343398i
$96$	3.17827	−	6.05568i	0.324381	−	0.618056i
$97$	6.12974	+	5.00478i	0.622381	+	0.508158i	0.890354	−	0.455268i	$-0.150457\pi$
$97$	6.12974	+	5.00478i	0.622381	+	0.508158i	−0.267974	+	0.963426i	$0.586354\pi$
$98$	−6.55790	+	6.29895i	−0.662448	+	0.636290i
$99$		−	4.02841i		−	0.404871i
$100$	−1.84807	−	1.92404i	−0.184807	−	0.192404i
$101$	−14.4874	+	4.83662i	−1.44156	+	0.481262i	−0.926630	−	0.375974i	$-0.877308\pi$
$101$	−14.4874	+	4.83662i	−1.44156	+	0.481262i	−0.514925	+	0.857235i	$0.672180\pi$
$102$	0.729482	+	9.03625i	0.0722294	+	0.894722i
$103$	−5.14535	+	1.26821i	−0.506986	+	0.124961i	−0.484509	−	0.874786i	$-0.661002\pi$
$103$	−5.14535	+	1.26821i	−0.506986	+	0.124961i	−0.0224775	+	0.999747i	$0.507155\pi$
$104$	−7.74543	+	0.267658i	−0.759502	+	0.0262460i
$105$	−3.35902	−	0.827925i	−0.327807	−	0.0807972i
$106$	−3.25359	+	20.0202i	−0.316017	+	1.94453i
$107$	5.79400	+	7.09636i	0.560127	+	0.686031i	0.974580	−	0.224040i	$-0.0719245\pi$
$107$	5.79400	+	7.09636i	0.560127	+	0.686031i	−0.414453	+	0.910071i	$0.636027\pi$
$108$	−2.37010	+	1.78101i	−0.228063	+	0.171378i
$109$	3.46625	−	3.91259i	0.332007	−	0.374758i	−0.558674	−	0.829387i	$-0.688690\pi$
$109$	3.46625	−	3.91259i	0.332007	−	0.374758i	0.890681	+	0.454629i	$0.150228\pi$
$110$	−2.91551	−	17.9398i	−0.277983	−	1.71050i
$111$	0.505522	−	6.26202i	0.0479821	−	0.594365i
$112$	0.466119	+	1.89112i	0.0440441	+	0.178694i
$113$	−4.99376	−	17.2404i	−0.469773	−	1.62184i	−0.749668	−	0.661814i	$-0.769787\pi$
$113$	−4.99376	−	17.2404i	−0.469773	−	1.62184i	0.279895	−	0.960031i	$-0.409700\pi$
$114$	0.459259	+	2.24960i	0.0430136	+	0.210694i
$115$	−13.9840	+	11.4176i	−1.30401	+	1.06470i
$116$	−1.62926	+	13.4182i	−0.151273	+	1.24585i
$117$	−3.30888	−	1.43225i	−0.305906	−	0.132412i
$118$	0.653219	+	5.37974i	0.0601337	+	0.495245i
$119$	−5.01338	−	4.81542i	−0.459576	−	0.441429i
$120$	−3.01504	+	3.13898i	−0.275234	+	0.286549i
$121$	−2.24125	+	4.72334i	−0.203750	+	0.429395i
$122$	6.31762	−	4.36074i	0.571970	−	0.394803i
$123$	−0.0118509	+	0.0187407i	−0.00106856	+	0.00168979i
$124$	−0.0570037	−	0.0758581i	−0.00511908	−	0.00681226i
$125$	−5.55182	−	10.5781i	−0.496570	−	0.946135i
$126$	0.761469	−	3.72992i	0.0678371	−	0.332288i
$127$	5.71692	−	0.461517i	0.507294	−	0.0409530i	0.175830	−	0.984421i	$-0.443739\pi$
$127$	5.71692	−	0.461517i	0.507294	−	0.0409530i	0.331465	+	0.943468i	$0.392457\pi$
$128$	14.5955	+	4.22764i	1.29007	+	0.373675i
$129$	−2.34307	−	1.22974i	−0.206296	−	0.108272i
$130$	−15.7721	−	3.98353i	−1.38330	−	0.349378i
$131$	−13.6260	+	7.15147i	−1.19051	+	0.624826i	−0.939297	−	0.343106i	$-0.888521\pi$
$131$	−13.6260	+	7.15147i	−1.19051	+	0.624826i	−0.251211	+	0.967932i	$0.580829\pi$
$132$	11.7016	−	2.38890i	1.01850	−	0.207927i
$133$	−1.40745	−	1.05763i	−0.122042	−	0.0917084i
$134$	−0.475745	−	11.8055i	−0.0410981	−	1.01984i
$135$	−1.89329	+	0.718032i	−0.162949	+	0.0617983i
$136$	−8.40023	+	2.43316i	−0.720314	+	0.208642i
$137$	7.62673	+	1.55701i	0.651596	+	0.133024i	0.514441	−	0.857526i	$-0.327999\pi$
$137$	7.62673	+	1.55701i	0.651596	+	0.133024i	0.137154	+	0.990550i	$0.456204\pi$
$138$	−13.1732	−	14.8695i	−1.12138	−	1.26578i
$139$	−6.50918	+	7.97229i	−0.552101	+	0.676201i	−0.972973	−	0.230919i	$-0.925827\pi$
$139$	−6.50918	+	7.97229i	−0.552101	+	0.676201i	0.420872	+	0.907120i	$0.361724\pi$
$140$	0.412987	−	10.2482i	0.0349038	−	0.866129i
$141$	−3.66886	−	10.9896i	−0.308974	−	0.925490i
$142$	−13.2981	+	11.7811i	−1.11595	+	0.988647i
$143$	9.56913	+	10.9269i	0.800211	+	0.913754i
$144$	0.853302	+	0.755960i	0.0711085	+	0.0629967i
$145$	−3.61861	+	8.49318i	−0.300509	+	0.705320i
$146$	−14.4657	+	25.0552i	−1.19719	+	2.07359i
$147$	−2.04048	−	3.53421i	−0.168296	−	0.291497i
$148$	18.4895	−	2.24504i	1.51983	−	0.184541i
$149$	9.80453	+	4.65231i	0.803219	+	0.381132i	0.785617	−	0.618713i	$-0.212346\pi$
$149$	9.80453	+	4.65231i	0.803219	+	0.381132i	0.0176016	+	0.999845i	$0.494397\pi$
$150$	1.73642	−	1.00252i	0.141778	−	0.0818556i
$151$	−13.5120	−	9.32669i	−1.09960	−	0.758996i	−0.127093	−	0.991891i	$-0.540565\pi$
$151$	−13.5120	−	9.32669i	−1.09960	−	0.758996i	−0.972502	+	0.232895i	$0.925180\pi$
$152$	−2.03769	+	0.868176i	−0.165278	+	0.0704184i
$153$	−4.01599	−	0.652661i	−0.324673	−	0.0527645i
$154$	−9.21274	+	12.2599i	−0.742384	+	0.987934i
$155$	−0.0229815	−	0.0605974i	−0.00184592	−	0.00486730i
$156$	2.19816	−	10.4609i	0.175993	−	0.837541i
$157$	−0.944181	+	2.48960i	−0.0753539	+	0.198692i	−0.967400	−	0.253252i	$-0.918500\pi$
$157$	−0.944181	+	2.48960i	−0.0753539	+	0.198692i	0.892047	+	0.451944i	$0.149269\pi$
$158$	−9.55680	−	15.1129i	−0.760298	−	1.20232i
$159$	−8.37453	−	3.56805i	−0.664143	−	0.282965i
$160$	11.7044	+	7.40142i	0.925315	+	0.585134i
$161$	15.1215	+	1.83608i	1.19174	+	0.144704i
$162$	−0.873364	−	2.04986i	−0.0686179	−	0.161052i
$163$	−2.78486	+	8.34167i	−0.218127	+	0.653370i	0.781441	+	0.623979i	$0.214485\pi$
$163$	−2.78486	+	8.34167i	−0.218127	+	0.653370i	−0.999568	+	0.0293910i	$0.990643\pi$
$164$	−0.0614652	−	0.0233107i	−0.00479963	−	0.00182026i
$165$	8.13060	+	0.656370i	0.632966	+	0.0510983i
$166$	8.74741	−	30.1996i	0.678931	−	2.34394i
$167$	−18.0362	−	0.726833i	−1.39568	−	0.0562440i	−0.669022	−	0.743242i	$-0.733287\pi$
$167$	−18.0362	−	0.726833i	−1.39568	−	0.0562440i	−0.726659	+	0.686998i	$0.758928\pi$
$168$	3.67243			0.283334
$169$	12.3774	−	3.97501i	0.952105	−	0.305770i
$170$	−18.3568			−1.40791
$171$	−1.02961	−	0.0414919i	−0.0787364	−	0.00317297i
$172$	2.18263	−	7.53533i	0.166424	−	0.574563i
$173$	−9.13876	−	0.737757i	−0.694807	−	0.0560907i	−0.271983	−	0.962302i	$-0.587679\pi$
$173$	−9.13876	−	0.737757i	−0.694807	−	0.0560907i	−0.422825	+	0.906211i	$0.638961\pi$
$174$	−9.49857	−	3.60233i	−0.720085	−	0.273092i
$175$	−0.486859	+	1.45832i	−0.0368031	+	0.110239i
$176$	−1.80006	−	4.22491i	−0.135685	−	0.318464i
$177$	−2.41443	−	0.293165i	−0.181480	−	0.0220357i
$178$	24.5923	+	15.5513i	1.84327	+	1.16562i
$179$	4.05727	+	1.72864i	0.303255	+	0.129205i	0.538234	−	0.842796i	$-0.319092\pi$
$179$	4.05727	+	1.72864i	0.303255	+	0.129205i	−0.234979	+	0.972001i	$0.575502\pi$
$180$	−3.20847	−	5.07379i	−0.239145	−	0.378178i
$181$	−7.72401	+	20.3665i	−0.574121	+	1.51383i	0.261878	+	0.965101i	$0.415658\pi$
$181$	−7.72401	+	20.3665i	−0.574121	+	1.51383i	−0.835999	+	0.548732i	$0.815111\pi$
$182$	6.79464	+	11.9261i	0.503652	+	0.884019i
$183$	1.22169	+	3.22133i	0.0903099	+	0.238128i
$184$	11.5126	−	15.3205i	0.848720	−	1.12944i
$185$	12.5563	+	2.04060i	0.923161	+	0.150028i
$186$	0.0656084	−	0.0279531i	0.00481064	−	0.00204962i
$187$	13.4890	+	9.31075i	0.986410	+	0.680870i
$188$	29.7466	−	17.1742i	2.16949	−	1.25256i
$189$	1.54357	+	0.732431i	0.112278	+	0.0532765i
$190$	−4.61522	+	0.560390i	−0.334824	+	0.0406549i
$191$	0.958313	+	1.65985i	0.0693411	+	0.120102i	0.898611	−	0.438745i	$-0.144577\pi$
$191$	0.958313	+	1.65985i	0.0693411	+	0.120102i	−0.829270	+	0.558848i	$0.811244\pi$
$192$	−6.47925	+	11.2224i	−0.467600	+	0.809906i
$193$	3.08359	−	7.23746i	0.221962	−	0.520964i	−0.771352	−	0.636409i	$-0.780419\pi$
$193$	3.08359	−	7.23746i	0.221962	−	0.520964i	0.993314	+	0.115445i	$0.0368294\pi$
$194$	−13.1979	−	11.6923i	−0.947556	−	0.839461i
$195$	3.42986	−	6.44498i	0.245618	−	0.461535i
$196$	9.05604	−	8.02295i	0.646860	−	0.573068i
$197$	7.62387	+	22.8363i	0.543178	+	1.62702i	0.759365	+	0.650665i	$0.225510\pi$
$197$	7.62387	+	22.8363i	0.543178	+	1.62702i	−0.216187	+	0.976352i	$0.569362\pi$
$198$	−0.361425	+	8.96866i	−0.0256853	+	0.637375i
$199$	4.02038	−	4.92407i	0.284997	−	0.349058i	−0.612188	−	0.790712i	$-0.709711\pi$
$199$	4.02038	−	4.92407i	0.284997	−	0.349058i	0.897186	+	0.441654i	$0.145608\pi$
$200$	1.28264	+	1.44780i	0.0906964	+	0.102375i
$201$	5.19545	+	1.06066i	0.366459	+	0.0748131i
$202$	32.6881	−	9.46822i	2.29993	−	0.666182i
$203$	7.28338	−	2.76222i	0.511193	−	0.193870i
$204$	−0.485702	−	12.0526i	−0.0340059	−	0.843848i
$205$	−0.0358936	−	0.0269723i	−0.00250692	−	0.00188383i
$206$	11.5691	−	2.36186i	0.806060	−	0.164558i
$207$	7.89440	−	4.14330i	0.548699	−	0.287979i
$208$	−4.11026	−	0.0235671i	−0.284995	−	0.00163408i
$209$	3.67559	+	1.92910i	0.254246	+	0.133439i
$210$	7.40408	+	2.14462i	0.510930	+	0.147993i
$211$	−8.88466	+	0.717244i	−0.611645	+	0.0493771i	−0.382408	−	0.923994i	$-0.624905\pi$
$211$	−8.88466	+	0.717244i	−0.611645	+	0.0493771i	−0.229237	+	0.973371i	$0.573623\pi$
$212$	5.39818	−	26.4420i	0.370748	−	1.81604i
$213$	−3.70544	−	7.06013i	−0.253893	−	0.483752i
$214$	−12.2628	−	16.3188i	−0.838267	−	1.11553i
$215$	2.86376	−	4.52867i	0.195307	−	0.308853i
$216$	1.76899	−	1.22104i	0.120364	−	0.0830814i
$217$	−0.0234424	+	0.0494038i	−0.00159137	+	0.00335375i
$218$	−8.06813	+	8.39981i	−0.546443	+	0.568907i
$219$	−9.36438	−	8.99461i	−0.632786	−	0.607800i
$220$	2.91495	+	24.0068i	0.196526	+	1.61854i
$221$	12.4435	−	7.76929i	0.837042	−	0.522619i
$222$	−1.68729	+	13.8961i	−0.113244	+	0.932645i
$223$	−8.00117	+	6.53276i	−0.535798	+	0.437466i	−0.861316	−	0.508070i	$-0.830359\pi$
$223$	−8.00117	+	6.53276i	−0.535798	+	0.437466i	0.325517	+	0.945536i	$0.394462\pi$
$224$	−2.33724	−	11.4485i	−0.156163	−	0.764938i
$225$	0.250359	+	0.864338i	0.0166906	+	0.0576225i
$226$	9.57106	+	38.8313i	0.636657	+	2.58302i
$227$	−1.47259	+	18.2413i	−0.0977395	+	1.21072i	0.743004	+	0.669287i	$0.233400\pi$
$227$	−1.47259	+	18.2413i	−0.0977395	+	1.21072i	−0.840744	+	0.541434i	$0.817882\pi$
$228$	−0.490049	−	3.01540i	−0.0324543	−	0.199699i
$229$	−1.22841	+	1.38658i	−0.0811754	+	0.0916281i	−0.787695	−	0.616065i	$-0.788726\pi$
$229$	−1.22841	+	1.38658i	−0.0811754	+	0.0916281i	0.706520	+	0.707693i	$0.250264\pi$
$230$	32.1577	−	24.1649i	2.12041	−	1.59339i
$231$	−4.35289	−	5.33132i	−0.286399	−	0.350775i
$232$	1.57203	−	9.67310i	0.103209	−	0.635070i
$233$	−25.5213	−	6.29045i	−1.67196	−	0.412101i	−0.714262	−	0.699879i	$-0.753237\pi$
$233$	−25.5213	−	6.29045i	−1.67196	−	0.412101i	−0.957697	+	0.287778i	$0.907083\pi$
$234$	7.23822	+	3.48556i	0.473177	+	0.227858i
$235$	22.7782	−	5.61432i	1.48589	−	0.366238i
$236$	−0.580214	−	7.18724i	−0.0377687	−	0.467849i
$237$	7.61203	−	2.54127i	0.494455	−	0.165073i
$238$	10.7295	+	11.1706i	0.695491	+	0.724083i
$239$			3.46545i			0.224161i	0.993699	+	0.112081i	$0.0357515\pi$
$239$			3.46545i			0.224161i	−0.993699	+	0.112081i	$0.964249\pi$
$240$	−1.66480	+	1.59906i	−0.107462	+	0.103219i
$241$	−5.27265	−	4.30499i	−0.339641	−	0.277309i	0.447239	−	0.894415i	$-0.352407\pi$
$241$	−5.27265	−	4.30499i	−0.339641	−	0.277309i	−0.786880	+	0.617106i	$0.788305\pi$
$242$	5.41359	−	10.3147i	0.347999	−	0.663056i
$243$	0.987050	−	0.160411i	0.0633193	−	0.0102904i
$244$	−8.63276	+	5.45903i	−0.552656	+	0.349478i
$245$	7.46560	−	3.54247i	0.476960	−	0.226320i
$246$	0.0280656	−	0.0406601i	0.00178940	−	0.00259239i
$247$	2.89134	−	2.33321i	0.183972	−	0.148458i
$248$	0.0390811	+	0.0566187i	0.00248165	+	0.00359529i
$249$	12.2202	+	7.05536i	0.774427	+	0.447115i
$250$	11.4112	+	24.0487i	0.721711	+	1.52097i
$251$	−23.6148	−	7.88377i	−1.49055	−	0.497619i	−0.549386	−	0.835568i	$-0.685138\pi$
$251$	−23.6148	−	7.88377i	−1.49055	−	0.497619i	−0.941164	+	0.337950i	$0.890267\pi$
$252$	−1.21219	+	4.91805i	−0.0763608	+	0.309808i
$253$	−35.8867	+	1.44619i	−2.25618	+	0.0909209i
$254$	−12.7693	+	0.514584i	−0.801215	+	0.0322879i
$255$	1.97162	−	7.99917i	0.123468	−	0.500928i
$256$	−7.53224	−	2.51463i	−0.470765	−	0.157165i
$257$	−2.77746	−	5.85338i	−0.173253	−	0.365124i	0.798186	−	0.602411i	$-0.205793\pi$
$257$	−2.77746	−	5.85338i	−0.173253	−	0.365124i	−0.971440	+	0.237287i	$0.923742\pi$
$258$	5.10616	+	2.94804i	0.317896	+	0.183537i
$259$	−6.09738	−	8.83358i	−0.378873	−	0.548892i
$260$	20.7552	+	6.14101i	1.28718	+	0.380849i
$261$	2.58995	−	3.75219i	0.160314	−	0.232255i
$262$	30.9778	−	14.6992i	1.91382	−	0.908117i
$263$	0.339191	−	0.214491i	0.0209154	−	0.0132261i	−0.523967	−	0.851738i	$-0.675549\pi$
$263$	0.339191	−	0.214491i	0.0209154	−	0.0132261i	0.544883	+	0.838512i	$0.316574\pi$
$264$	−8.54685	+	1.38900i	−0.526023	+	0.0854870i
$265$	8.56595	−	16.3211i	0.526202	−	1.00259i
$266$	3.03860	+	2.48094i	0.186308	+	0.152116i
$267$	−9.41796	+	9.04607i	−0.576370	+	0.553610i
$268$			15.7206i			0.960288i
$269$	−0.981150	−	1.02149i	−0.0598218	−	0.0622811i	0.690619	−	0.723219i	$-0.257338\pi$
$269$	−0.981150	−	1.02149i	−0.0598218	−	0.0622811i	−0.750441	+	0.660938i	$0.770159\pi$
$270$	4.27956	−	1.42873i	0.260446	−	0.0869495i
$271$	−0.699565	−	8.66567i	−0.0424956	−	0.526402i	−0.982627	−	0.185591i	$-0.940580\pi$
$271$	−0.699565	−	8.66567i	−0.0424956	−	0.526402i	0.940132	−	0.340812i	$-0.110702\pi$
$272$	−4.50351	+	1.11002i	−0.273065	+	0.0673046i
$273$	−5.92668	+	1.67991i	−0.358699	+	0.101673i
$274$	−16.8401	−	4.15071i	−1.01735	−	0.250753i
$275$	0.581496	−	3.57809i	0.0350656	−	0.215767i
$276$	16.7168	+	20.4744i	1.00624	+	1.23241i
$277$	11.9745	−	8.99828i	0.719480	−	0.540654i	−0.176743	−	0.984257i	$-0.556556\pi$
$277$	11.9745	−	8.99828i	0.719480	−	0.540654i	0.896224	+	0.443603i	$0.146300\pi$
$278$	15.2070	−	17.1651i	0.912054	−	1.02950i
$279$	0.00513417	+	0.0315918i	0.000307375	+	0.00189135i
$280$	−0.598368	+	7.41211i	−0.0357593	+	0.442959i
$281$	4.66356	+	18.9208i	0.278205	+	1.12872i	0.929182	+	0.369623i	$0.120513\pi$
$281$	4.66356	+	18.9208i	0.278205	+	1.12872i	−0.650977	+	0.759097i	$0.725641\pi$
$282$	7.18220	+	24.7958i	0.427694	+	1.47657i
$283$	−5.09805	−	24.9719i	−0.303048	−	1.48443i	−0.791141	−	0.611634i	$-0.790513\pi$
$283$	−5.09805	−	24.9719i	−0.303048	−	1.48443i	0.488093	−	0.872791i	$-0.337693\pi$
$284$	18.3107	−	14.9502i	1.08654	−	0.887132i
$285$	0.251504	−	2.07132i	0.0148978	−	0.122694i
$286$	−20.3239	−	25.1857i	−1.20178	−	1.48926i
$287$	0.00456637	+	0.0376074i	0.000269544	+	0.00221990i
$288$	−4.93234	−	4.73758i	−0.290641	−	0.279165i
$289$	−0.308881	+	0.321579i	−0.0181695	+	0.0189164i
$290$	8.81829	−	18.5841i	0.517828	−	1.09130i
$291$	6.51258	−	4.49531i	0.381774	−	0.263520i
$292$	20.5741	−	32.5353i	1.20401	−	1.90399i
$293$	4.75217	+	6.32399i	0.277625	+	0.369452i	0.916620	−	0.399759i	$-0.130906\pi$
$293$	4.75217	+	6.32399i	0.277625	+	0.369452i	−0.638995	+	0.769210i	$0.720650\pi$
$294$	4.22573	+	8.05146i	0.246450	+	0.469570i
$295$	0.985095	−	4.82532i	0.0573545	−	0.280941i
$296$	−13.4601	+	1.08661i	−0.782351	+	0.0631579i
$297$	−3.86936	−	1.12077i	−0.224523	−	0.0650340i
$298$	−21.4109	−	11.2373i	−1.24030	−	0.650961i
$299$	−11.5712	+	29.9910i	−0.669180	+	1.73442i
$300$	−2.36224	+	1.23980i	−0.136384	+	0.0715799i
$301$	−4.42967	+	0.904324i	−0.255322	+	0.0521244i
$302$	29.2458	+	21.9768i	1.68291	+	1.26462i
$303$	0.615001	+	15.2611i	0.0353309	+	0.876727i
$304$	−1.09837	+	0.416558i	−0.0629960	+	0.0238912i
$305$	−6.70071	+	1.94088i	−0.383681	+	0.111135i
$306$	8.88244	+	1.81336i	0.507775	+	0.103663i
$307$	6.79999	+	7.67560i	0.388096	+	0.438070i	0.909794	−	0.415061i	$-0.136240\pi$
$307$	6.79999	+	7.67560i	0.388096	+	0.438070i	−0.521698	+	0.853130i	$0.674701\pi$
$308$	12.9050	−	15.8057i	0.735329	−	0.900614i
$309$	−0.213383	+	5.29504i	−0.0121389	+	0.301224i
$310$	0.0457283	+	0.136973i	0.00259719	+	0.00777954i
$311$	5.38198	−	4.76802i	0.305184	−	0.270369i	−0.496605	−	0.867977i	$-0.665420\pi$
$311$	5.38198	−	4.76802i	0.305184	−	0.270369i	0.801789	+	0.597607i	$0.203882\pi$
$312$	−1.89782	+	7.51409i	−0.107443	+	0.425402i
$313$	5.86000	+	5.19151i	0.331227	+	0.293441i	0.812301	−	0.583239i	$-0.198215\pi$
$313$	5.86000	+	5.19151i	0.331227	+	0.293441i	−0.481074	+	0.876680i	$0.659753\pi$
$314$	2.32544	−	5.45802i	0.131232	−	0.308014i
$315$	−1.72978	+	2.99606i	−0.0974618	+	0.168809i
$316$	11.8959	+	20.6042i	0.669194	+	1.15908i
$317$	8.06500	−	0.979269i	0.452976	−	0.0550012i	0.109130	−	0.994027i	$-0.465193\pi$
$317$	8.06500	−	0.979269i	0.452976	−	0.0550012i	0.343845	+	0.939026i	$0.388270\pi$
$318$	18.3245	+	8.69509i	1.02759	+	0.487597i
$319$	−15.9059	+	9.18327i	−0.890559	+	0.514164i
$320$	−21.5946	−	14.9057i	−1.20717	−	0.833252i
$321$	8.42817	−	3.59091i	0.470415	−	0.200425i
$322$	−33.5010	−	5.44445i	−1.86694	−	0.303407i
$323$	2.51865	−	3.35171i	0.140141	−	0.186494i
$324$	1.05129	+	2.77203i	0.0584052	+	0.154002i
$325$	−2.73224	−	1.74978i	−0.151558	−	0.0970601i
$326$	6.94848	−	18.3216i	0.384841	−	1.01474i
$327$	−2.79374	−	4.41795i	−0.154494	−	0.244313i
$328$	0.0438472	+	0.0186816i	0.00242106	+	0.00103152i
$329$	−16.7302	−	10.5796i	−0.922368	−	0.583270i
$330$	−18.0427	−	2.19078i	−0.993217	−	0.120598i
$331$	−5.32909	−	12.5078i	−0.292913	−	0.687493i	0.706890	−	0.707323i	$-0.250098\pi$
$331$	−5.32909	−	12.5078i	−0.292913	−	0.687493i	−0.999803	+	0.0198306i	$0.993687\pi$
$332$	−13.2475	+	39.6810i	−0.727049	+	2.17778i
$333$	−5.87414	−	2.22777i	−0.321901	−	0.122081i
$334$	40.0897	+	3.23637i	2.19361	+	0.177086i
$335$	−2.98726	+	10.3132i	−0.163212	+	0.563472i
$336$	1.94614	+	0.0784266i	0.106170	+	0.00427852i
$337$	3.23037			0.175969			0.0879847	−	0.996122i	$-0.471957\pi$
$337$	3.23037			0.175969			0.0879847	+	0.996122i	$0.471957\pi$
$338$	−27.9130	+	7.73929i	−1.51827	+	0.420962i
$339$	−17.9491			−0.974862
$340$	24.4050	+	0.983487i	1.32355	+	0.0533371i
$341$	0.0358719	−	0.123844i	0.00194257	−	0.00670653i
$342$	2.28856	+	0.184751i	0.123751	+	0.00999020i
$343$	−17.7018	−	6.71340i	−0.955806	−	0.362489i
$344$	−1.80117	+	5.39516i	−0.0971126	+	0.290888i
$345$	7.07620	+	16.6085i	0.380970	+	0.894169i
$346$	20.2799	+	2.46243i	1.09025	+	0.132381i
$347$	10.2546	+	6.48460i	0.550495	+	0.348112i	0.780577	−	0.625059i	$-0.214925\pi$
$347$	10.2546	+	6.48460i	0.550495	+	0.348112i	−0.230083	+	0.973171i	$0.573900\pi$
$348$	12.4351	+	5.29812i	0.666593	+	0.284009i
$349$	1.22984	+	1.94484i	0.0658320	+	0.104105i	0.876502	−	0.481399i	$-0.159871\pi$
$349$	1.22984	+	1.94484i	0.0658320	+	0.104105i	−0.810670	+	0.585504i	$0.800897\pi$
$350$	1.21476	−	3.20305i	0.0649315	−	0.171210i
$351$	−2.29629	+	2.77976i	−0.122567	+	0.148372i
$352$	9.76956	+	25.7602i	0.520719	+	1.37302i
$353$	−3.13445	+	4.17119i	−0.166830	+	0.222010i	−0.875113	−	0.483918i	$-0.839213\pi$
$353$	−3.13445	+	4.17119i	−0.166830	+	0.222010i	0.708284	+	0.705928i	$0.249470\pi$
$354$	5.34908	+	0.869309i	0.284300	+	0.0462033i
$355$	14.8533	−	6.32839i	0.788331	−	0.335876i
$356$	−31.8618	−	21.9926i	−1.68867	−	1.16560i
$357$	−6.02011	+	3.47571i	−0.318618	+	0.183954i
$358$	−8.87783	−	4.21258i	−0.469208	−	0.222642i
$359$	−30.5149	+	3.70518i	−1.61052	+	0.195552i	−0.875748	−	0.482768i	$-0.839632\pi$
$359$	−30.5149	+	3.70518i	−1.61052	+	0.195552i	−0.734767	+	0.678320i	$0.762708\pi$
$360$	2.17622	+	3.76932i	0.114697	+	0.198660i
$361$	−8.96909	+	15.5349i	−0.472057	+	0.817627i
$362$	19.0236	−	44.6501i	0.999859	−	2.34676i
$363$	3.91330	+	3.46688i	0.205395	+	0.181964i
$364$	−8.39437	−	16.2195i	−0.439984	−	0.850130i
$365$	19.6797	−	17.4347i	1.03008	−	0.912575i
$366$	−2.43090	−	7.28142i	−0.127065	−	0.380606i
$367$	1.11647	−	27.7049i	0.0582792	−	1.44618i	−0.660438	−	0.750881i	$-0.729629\pi$
$367$	1.11647	−	27.7049i	0.0582792	−	1.44618i	0.718717	−	0.695303i	$-0.244730\pi$
$368$	6.42806	−	7.87295i	0.335086	−	0.410406i
$369$	0.0147036	+	0.0165970i	0.000765441	+	0.000864004i
$370$	−27.7718	−	5.66964i	−1.44378	−	0.294751i
$371$	−14.9385	+	4.32700i	−0.775571	+	0.224647i
$372$	−0.0887225	+	0.0336480i	−0.00460005	+	0.00174457i
$373$	0.969835	+	24.0662i	0.0502162	+	1.24610i	0.806252	+	0.591572i	$0.201492\pi$
$373$	0.969835	+	24.0662i	0.0502162	+	1.24610i	−0.756036	+	0.654530i	$0.772867\pi$
$374$	−29.1958	−	21.9392i	−1.50968	−	1.13445i
$375$	−11.7051	+	2.38961i	−0.604448	+	0.123399i
$376$	−22.0509	+	11.5732i	−1.13719	+	0.596844i
$377$	1.88786	+	16.3298i	0.0972296	+	0.841030i
$378$	−3.37081	−	1.76914i	−0.173376	−	0.0909945i
$379$	16.1782	+	4.68606i	0.831016	+	0.240707i	0.666347	−	0.745642i	$-0.267857\pi$
$379$	16.1782	+	4.68606i	0.831016	+	0.240707i	0.164669	+	0.986349i	$0.447344\pi$
$380$	6.16586	−	0.497759i	0.316302	−	0.0255345i
$381$	1.14725	−	5.61961i	0.0587754	−	0.287901i
$382$	−1.98462	−	3.78138i	−0.101542	−	0.193472i
$383$	4.41254	+	5.87203i	0.225471	+	0.300047i	0.897975	−	0.440046i	$-0.145038\pi$
$383$	4.41254	+	5.87203i	0.225471	+	0.300047i	−0.672505	+	0.740093i	$0.734782\pi$
$384$	8.12146	−	12.8431i	0.414446	−	0.655395i
$385$	11.4695	−	7.91683i	0.584541	−	0.403479i
$386$	−7.51450	+	15.8365i	−0.382478	+	0.806055i
$387$	−1.83307	+	1.90842i	−0.0931800	+	0.0970106i
$388$	16.9199	+	16.2518i	0.858978	+	0.825060i
$389$	−2.95652	−	24.3491i	−0.149902	−	1.23455i	−0.852410	−	0.522874i	$-0.824860\pi$
$389$	−2.95652	−	24.3491i	−0.149902	−	1.23455i	0.702508	−	0.711676i	$-0.252063\pi$
$390$	−8.21431	+	14.0411i	−0.415948	+	0.710997i
$391$	−4.37244	+	36.0103i	−0.221124	+	1.82112i
$392$	−6.79477	+	5.54776i	−0.343188	+	0.280204i
$393$	3.07813	+	15.0777i	0.155271	+	0.760567i
$394$	−14.9246	−	51.5256i	−0.751889	−	2.59582i
$395$	3.88881	+	15.7775i	0.195667	+	0.793853i
$396$	0.961011	−	11.9043i	0.0482926	−	0.598212i
$397$	−2.14012	−	13.1687i	−0.107410	−	0.660918i	−0.983794	−	0.179305i	$-0.942615\pi$
$397$	−2.14012	−	13.1687i	−0.107410	−	0.660918i	0.876384	−	0.481613i	$-0.159949\pi$
$398$	−9.39256	+	10.6020i	−0.470806	+	0.531431i
$399$	−1.40745	+	1.05763i	−0.0704608	+	0.0529479i
$400$	0.648793	+	0.794627i	0.0324396	+	0.0397313i
$401$	2.23181	−	13.7329i	0.111451	−	0.685787i	−0.869851	−	0.493315i	$-0.835785\pi$
$401$	2.23181	−	13.7329i	0.111451	−	0.685787i	0.981302	−	0.192473i	$-0.0616507\pi$
$402$	−11.4717	−	2.82753i	−0.572158	−	0.141024i
$403$	−0.0889698	−	0.0734958i	−0.00443190	−	0.00366108i
$404$	−43.9653	+	10.8365i	−2.18736	+	0.539135i
$405$	0.162935	+	2.01831i	0.00809631	+	0.100291i
$406$	−16.4632	+	5.49622i	−0.817054	+	0.272773i
$407$	17.5315	+	18.2522i	0.869005	+	0.904730i
$408$			8.74552i			0.432968i
$409$	−20.7512	+	19.9318i	−1.02608	+	0.985563i	−0.999901	−	0.0140948i	$-0.995513\pi$
$409$	−20.7512	+	19.9318i	−1.02608	+	0.985563i	−0.0261786	+	0.999657i	$0.508334\pi$
$410$	0.0774919	+	0.0632702i	0.00382705	+	0.00312469i
$411$	3.61742	−	6.89243i	0.178434	−	0.339978i
$412$	−15.5074	+	2.52020i	−0.763996	+	0.124161i
$413$	−3.51211	+	2.22093i	−0.172820	+	0.109285i
$414$	−17.9474	+	8.51617i	−0.882069	+	0.418547i
$415$	−16.2310	+	23.5147i	−0.796750	+	1.15429i
$416$	24.6325	+	1.13415i	1.20771	+	0.0556064i
$417$	5.84657	+	8.47021i	0.286308	+	0.414788i
$418$	−8.01008	−	4.62462i	−0.391786	−	0.226198i
$419$	−16.0906	−	33.9103i	−0.786079	−	1.65663i	−0.753761	−	0.657148i	$-0.771763\pi$
$419$	−16.0906	−	33.9103i	−0.786079	−	1.65663i	−0.0323175	−	0.999478i	$-0.510289\pi$
$420$	−9.72865	−	3.24790i	−0.474710	−	0.158481i
$421$	−5.26219	+	21.3496i	−0.256464	+	1.04051i	0.691561	+	0.722318i	$0.256923\pi$
$421$	−5.26219	+	21.3496i	−0.256464	+	1.04051i	−0.948025	+	0.318196i	$0.896923\pi$
$422$	19.8447	−	0.799715i	0.966026	−	0.0389295i
$423$	−11.5764	+	0.466515i	−0.562866	+	0.0226827i
$424$	−4.68259	+	18.9980i	−0.227407	+	0.922626i
$425$	−3.47284	−	1.15940i	−0.168458	−	0.0562394i
$426$	7.61618	+	16.0508i	0.369005	+	0.777662i
$427$	5.09762	+	2.94311i	0.246691	+	0.142427i
$428$	15.4288	+	22.3525i	0.745779	+	1.08045i
$429$	13.1578	−	6.15127i	0.635264	−	0.296986i
$430$	−6.78204	+	9.82548i	−0.327059	+	0.473827i
$431$	11.5944	−	5.50162i	0.558484	−	0.265004i	−0.128460	−	0.991715i	$-0.541003\pi$
$431$	11.5944	−	5.50162i	0.558484	−	0.265004i	0.686943	+	0.726711i	$0.258952\pi$
$432$	0.963517	−	0.609291i	0.0463572	−	0.0293145i
$433$	23.7762	−	3.86400i	1.14261	−	0.185692i	0.440494	−	0.897756i	$-0.354803\pi$
$433$	23.7762	−	3.86400i	1.14261	−	0.185692i	0.702115	+	0.712064i	$0.252239\pi$
$434$	0.0566235	−	0.107887i	0.00271801	−	0.00517874i
$435$	7.15110	+	5.83869i	0.342869	+	0.279944i
$436$	11.1764	−	10.7351i	0.535253	−	0.514118i
$437$			9.18709i			0.439478i
$438$	20.0414	+	20.8653i	0.957616	+	0.996984i
$439$	34.3468	−	11.4666i	1.63928	−	0.547273i	0.660261	−	0.751036i	$-0.270445\pi$
$439$	34.3468	−	11.4666i	1.63928	−	0.547273i	0.979020	+	0.203763i	$0.0653173\pi$
$440$	−1.41085	−	17.4765i	−0.0672597	−	0.833161i
$441$	−3.96237	+	0.976636i	−0.188684	+	0.0465065i
$442$	−28.4007	+	16.1808i	−1.35088	+	0.769640i
$443$	−12.6497	−	3.11786i	−0.601004	−	0.148134i	−0.0729365	−	0.997337i	$-0.523237\pi$
$443$	−12.6497	−	3.11786i	−0.601004	−	0.148134i	−0.528067	+	0.849202i	$0.677083\pi$
$444$	2.98771	−	18.3841i	0.141791	−	0.872473i
$445$	−16.7233	−	20.4823i	−0.792760	−	0.970954i
$446$	18.3995	−	13.8264i	0.871243	−	0.654697i
$447$	7.19642	−	8.12308i	0.340379	−	0.384208i
$448$	3.55149	+	21.8532i	0.167792	+	1.03247i
$449$	−3.11090	+	38.5354i	−0.146812	+	1.81860i	0.334886	+	0.942259i	$0.391302\pi$
$449$	−3.11090	+	38.5354i	−0.146812	+	1.81860i	−0.481698	+	0.876337i	$0.659980\pi$
$450$	−0.479839	−	1.94678i	−0.0226198	−	0.0917722i
$451$	−0.0248513	−	0.0857967i	−0.00117020	−	0.00404001i
$452$	−10.6441	−	52.1381i	−0.500655	−	2.45237i
$453$	−12.7177	+	10.3837i	−0.597532	+	0.487870i
$454$	4.91510	−	40.4795i	0.230677	−	1.89980i
$455$	−2.42492	−	12.2356i	−0.113682	−	0.573614i
$456$	0.266980	+	2.19878i	0.0125025	+	0.102967i
$457$	−28.6714	−	27.5392i	−1.34119	−	1.28823i	−0.925512	−	0.378719i	$-0.876365\pi$
$457$	−28.6714	−	27.5392i	−1.34119	−	1.28823i	−0.415678	−	0.909512i	$-0.636456\pi$
$458$	2.85927	−	2.97681i	0.133605	−	0.139097i
$459$	−1.74421	+	3.67585i	−0.0814128	+	0.171574i
$460$	−44.0475	+	30.4038i	−2.05373	+	1.41759i
$461$	−20.6561	+	32.6650i	−0.962051	+	1.52136i	−0.112636	+	0.993636i	$0.535929\pi$
$461$	−20.6561	+	32.6650i	−0.962051	+	1.52136i	−0.849415	+	0.527726i	$0.823045\pi$
$462$	9.21274	+	12.2599i	0.428616	+	0.570384i
$463$	−17.9984	−	34.2931i	−0.836457	−	1.59374i	−0.804278	−	0.594253i	$-0.797448\pi$
$463$	−17.9984	−	34.2931i	−0.836457	−	1.59374i	−0.0321792	−	0.999482i	$-0.510245\pi$
$464$	1.03964	−	5.09250i	0.0482642	−	0.236414i
$465$	−0.0645987	+	0.00521495i	−0.00299569	+	0.000241837i
$466$	56.2551	+	16.2945i	2.60597	+	0.754828i
$467$	−27.4987	−	14.4324i	−1.27249	−	0.667853i	−0.313040	−	0.949740i	$-0.601347\pi$
$467$	−27.4987	−	14.4324i	−1.27249	−	0.667853i	−0.959448	+	0.281887i	$0.909040\pi$
$468$	−9.43630	−	5.02177i	−0.436193	−	0.232131i
$469$	8.02191	−	4.21022i	0.370417	−	0.194410i
$470$	−51.2160	+	10.4558i	−2.36242	+	0.482291i
$471$	2.12862	+	1.59955i	0.0980816	+	0.0737036i
$472$	0.210506	+	5.22365i	0.00968932	+	0.240438i
$473$	9.96715	−	3.78004i	0.458290	−	0.173806i
$474$	−17.1751	+	4.97482i	−0.788876	+	0.228501i
$475$	−0.908526	−	0.185477i	−0.0416860	−	0.00851026i
$476$	−13.6662	−	15.4259i	−0.626387	−	0.707045i
$477$	−5.75712	+	7.05119i	−0.263600	+	0.322852i
$478$	0.310916	−	7.71530i	0.0142210	−	0.352889i
$479$	4.03101	+	12.0744i	0.184182	+	0.551692i	0.999632	−	0.0271359i	$-0.00863869\pi$
$479$	4.03101	+	12.0744i	0.184182	+	0.551692i	−0.815450	+	0.578827i	$0.803510\pi$
$480$	10.3656	−	9.18309i	0.473121	−	0.419149i
$481$	21.2252	−	7.91076i	0.967786	−	0.360700i
$482$	11.3525	+	10.0575i	0.517094	+	0.458105i
$483$	5.97065	−	14.0136i	0.271674	−	0.637643i
$484$	−7.74987	+	13.4232i	−0.352267	+	0.610144i
$485$	8.01181	+	13.8769i	0.363798	+	0.630116i
$486$	−2.21191	+	0.268575i	−0.100334	+	0.0121828i
$487$	−5.35313	−	2.54009i	−0.242573	−	0.115102i	0.303525	−	0.952823i	$-0.401836\pi$
$487$	−5.35313	−	2.54009i	−0.242573	−	0.115102i	−0.546099	+	0.837721i	$0.683888\pi$
$488$	6.41327	−	3.70271i	0.290315	−	0.167614i
$489$	7.23753	+	4.99571i	0.327292	+	0.225914i
$490$	−16.9389	+	7.21698i	−0.765220	+	0.326030i
$491$	15.0207	+	2.44111i	0.677876	+	0.110166i	0.489595	−	0.871950i	$-0.337144\pi$
$491$	15.0207	+	2.44111i	0.677876	+	0.110166i	0.188281	+	0.982115i	$0.439709\pi$
$492$	−0.0394910	+	0.0525530i	−0.00178039	+	0.00236927i
$493$	6.57795	+	17.3446i	0.296256	+	0.781163i
$494$	−6.64647	+	4.93513i	−0.299039	+	0.222042i
$495$	2.89253	−	7.62697i	0.130010	−	0.342807i
$496$	0.0195012	+	0.0308386i	0.000875628	+	0.00138469i
$497$	−12.5327	−	5.33968i	−0.562168	−	0.239517i
$498$	−26.5736	−	16.8041i	−1.19079	−	0.753010i
$499$	−13.2574	−	1.60973i	−0.593481	−	0.0720616i	−0.181715	−	0.983351i	$-0.558165\pi$
$499$	−13.2574	−	1.60973i	−0.593481	−	0.0720616i	−0.411766	+	0.911290i	$0.635088\pi$
$500$	−13.8826	−	32.5835i	−0.620847	−	1.45718i
$501$	−5.71612	+	17.1219i	−0.255377	+	0.764948i
$502$	51.8674	+	19.6707i	2.31496	+	0.877947i
$503$	11.8900	+	0.959862i	0.530150	+	0.0427981i	0.342644	−	0.939465i	$-0.388678\pi$
$503$	11.8900	+	0.959862i	0.530150	+	0.0427981i	0.187506	+	0.982263i	$0.439960\pi$
$504$	1.02173	−	3.52744i	0.0455117	−	0.157125i
$505$	−30.9019	−	1.24530i	−1.37511	−	0.0554152i
$506$	80.0262			3.55760
$507$	−0.374472	−	12.9946i	−0.0166309	−	0.577111i
$508$	17.0040			0.754431
$509$	20.3992	+	0.822058i	0.904177	+	0.0364371i	0.487997	−	0.872845i	$-0.337728\pi$
$509$	20.3992	+	0.822058i	0.904177	+	0.0364371i	0.416180	+	0.909282i	$0.363369\pi$
$510$	−5.10719	+	17.6321i	−0.226150	+	0.780761i
$511$	−22.1122	−	1.78508i	−0.978187	−	0.0789674i
$512$	−11.8722	−	4.50254i	−0.524683	−	0.198986i
$513$	−0.326310	+	0.977417i	−0.0144069	+	0.0431540i
$514$	5.65845	+	13.2809i	0.249584	+	0.585794i
$515$	−10.6523	−	1.29342i	−0.469395	−	0.0569949i
$516$	−6.63057	−	4.19292i	−0.291895	−	0.184583i
$517$	42.9378	+	18.2941i	1.88840	+	0.804572i
$518$	12.7824	+	20.2137i	0.561625	+	0.888139i
$519$	−3.25119	+	8.57269i	−0.142712	+	0.376299i
$520$	−14.8566	−	5.05471i	−0.651503	−	0.221664i
$521$	7.79251	+	20.5471i	0.341396	+	0.900187i	0.990253	+	0.139277i	$0.0444779\pi$
$521$	7.79251	+	20.5471i	0.341396	+	0.900187i	−0.648858	+	0.760910i	$0.724753\pi$
$522$	−6.10278	+	8.12132i	−0.267111	+	0.355461i
$523$	−7.81741	−	1.27045i	−0.341832	−	0.0555530i	−0.0129277	−	0.999916i	$-0.504115\pi$
$523$	−7.81741	−	1.27045i	−0.341832	−	0.0555530i	−0.328904	+	0.944363i	$0.606679\pi$
$524$	−41.9718	+	17.8825i	−1.83355	+	0.781202i
$525$	1.26529	+	0.873367i	0.0552218	+	0.0381168i
$526$	−0.774402	+	0.447101i	−0.0337655	+	0.0194945i
$527$	−0.117650	−	0.0558257i	−0.00512492	−	0.00243181i
$528$	−4.55891	+	0.553552i	−0.198401	+	0.0240902i
$529$	−28.2443	−	48.9205i	−1.22801	−	2.12698i
$530$	−20.5351	+	35.5679i	−0.891989	+	1.54497i
$531$	−0.953328	+	2.23754i	−0.0413709	+	0.0971011i
$532$	−3.90682	−	3.46114i	−0.169382	−	0.150060i
$533$	−0.0793076	−	0.0100914i	−0.00343520	−	0.000437109i
$534$	21.7793	−	19.2948i	0.942482	−	0.834966i
$535$	5.87433	+	17.5958i	0.253970	+	0.760732i
$536$	0.458945	−	11.3886i	0.0198234	−	0.491913i
$537$	2.78920	−	3.41615i	0.120363	−	0.147418i
$538$	2.09274	+	2.36221i	0.0902244	+	0.101842i
$539$	16.1075	+	3.28837i	0.693800	+	0.141640i
$540$	−5.76612	+	1.67018i	−0.248134	+	0.0718730i
$541$	37.4400	−	14.1991i	1.60967	−	0.610468i	0.624346	−	0.781148i	$-0.285366\pi$
$541$	37.4400	−	14.1991i	1.60967	−	0.610468i	0.985327	+	0.170680i	$0.0545964\pi$
$542$	0.780004	+	19.3556i	0.0335040	+	0.831394i
$543$	17.4135	+	13.0854i	0.747284	+	0.561547i
$544$	27.2635	−	5.56589i	1.16891	−	0.238636i
$545$	9.37200	−	4.91881i	0.401453	−	0.210699i
$546$	13.3456	−	3.20834i	0.571138	−	0.137304i
$547$	2.99737	+	1.57314i	0.128158	+	0.0672626i	0.527584	−	0.849503i	$-0.323098\pi$
$547$	2.99737	+	1.57314i	0.128158	+	0.0672626i	−0.399426	+	0.916766i	$0.630790\pi$
$548$	22.1661	+	6.42050i	0.946890	+	0.274270i
$549$	3.43404	−	0.277225i	0.146561	−	0.0118317i
$550$	−1.61564	+	7.91392i	−0.0688910	+	0.337450i
$551$	2.18330	+	4.15993i	0.0930117	+	0.177219i
$552$	−11.5126	−	15.3205i	−0.490009	−	0.652083i
$553$	7.32803	−	11.5884i	0.311620	−	0.492787i
$554$	−27.4668	+	18.9590i	−1.16695	+	0.805490i
$555$	5.45343	−	11.4929i	0.231485	−	0.487845i
$556$	−21.1370	+	22.0059i	−0.896407	+	0.933258i
$557$	−2.04490	−	1.96415i	−0.0866452	−	0.0832239i	0.648151	−	0.761512i	$-0.275543\pi$
$557$	−2.04490	−	1.96415i	−0.0866452	−	0.0832239i	−0.734796	+	0.678288i	$0.762722\pi$
$558$	−0.00859609	−	0.0707951i	−0.000363901	−	0.00299700i
$559$	0.438827	−	9.53080i	0.0185604	−	0.403110i
$560$	−0.475383	+	3.91513i	−0.0200886	+	0.165445i
$561$	12.6960	−	10.3660i	0.536026	−	0.437652i
$562$	−8.68517	−	42.5428i	−0.366362	−	1.79456i
$563$	−7.31385	−	25.2504i	−0.308242	−	1.06418i	−0.953795	−	0.300459i	$-0.902860\pi$
$563$	−7.31385	−	25.2504i	−0.308242	−	1.06418i	0.645552	−	0.763716i	$-0.276627\pi$
$564$	−8.22011	−	33.3503i	−0.346129	−	1.40430i
$565$	2.92454	−	36.2269i	0.123036	−	1.52408i
$566$	9.10960	+	56.0536i	0.382905	+	2.35611i
$567$	1.13296	−	1.27885i	0.0475798	−	0.0537065i
$568$	−13.7014	+	10.2960i	−0.574899	+	0.432009i
$569$	22.6781	+	27.7757i	0.950717	+	1.16442i	0.986285	+	0.165050i	$0.0527785\pi$
$569$	22.6781	+	27.7757i	0.950717	+	1.16442i	−0.0355681	+	0.999367i	$0.511324\pi$
$570$	−0.745772	+	4.58892i	−0.0312369	+	0.192209i
$571$	22.0140	+	5.42597i	0.921258	+	0.227070i	0.671299	−	0.741187i	$-0.265737\pi$
$571$	22.0140	+	5.42597i	0.921258	+	0.227070i	0.249959	+	0.968256i	$0.419583\pi$
$572$	25.6708	+	34.5726i	1.07335	+	1.44555i
$573$	1.86093	−	0.458679i	0.0777416	−	0.0191616i
$574$	−0.00679224	−	0.0841370i	−0.000283503	−	0.00351181i
$575$	7.60999	−	2.54059i	0.317359	−	0.105950i
$576$	8.97667	+	9.34570i	0.374028	+	0.389404i
$577$			17.2423i			0.717807i	0.933375	+	0.358903i	$0.116849\pi$
$577$			17.2423i			0.717807i	−0.933375	+	0.358903i	$0.883151\pi$
$578$	0.716530	−	0.688236i	0.0298037	−	0.0286268i
$579$	−6.09380	−	4.97544i	−0.253250	−	0.206772i
$580$	−12.7194	+	24.2347i	−0.528143	+	1.00629i
$581$	23.7963	−	3.86727i	0.987236	−	0.160442i
$582$	−14.9026	+	9.42384i	−0.617733	+	0.390631i
$583$	33.1299	−	15.7203i	1.37210	−	0.651070i
$584$	−15.8545	+	22.9692i	−0.656064	+	0.950473i
$585$	−5.23627	−	5.08755i	−0.216493	−	0.210344i
$586$	−10.0126	−	14.5058i	−0.413618	−	0.599228i
$587$	−9.68966	−	5.59433i	−0.399935	−	0.230903i	0.286521	−	0.958074i	$-0.407501\pi$
$587$	−9.68966	−	5.59433i	−0.399935	−	0.230903i	−0.686456	+	0.727171i	$0.740835\pi$
$588$	−5.18664	−	10.9306i	−0.213894	−	0.450771i
$589$	−0.0312835	−	0.0104440i	−0.00128901	−	0.000430336i
$590$	−2.62609	+	10.6545i	−0.108114	+	0.438637i
$591$	24.0558	−	0.969414i	0.989521	−	0.0398763i
$592$	−7.15612	+	0.288382i	−0.294115	+	0.0118524i
$593$	8.47190	−	34.3719i	0.347899	−	1.41148i	−0.492876	−	0.870099i	$-0.664054\pi$
$593$	8.47190	−	34.3719i	0.347899	−	1.41148i	0.840776	−	0.541384i	$-0.182099\pi$
$594$	8.51401	+	2.84239i	0.349334	+	0.116625i
$595$	−6.03418	−	12.7168i	−0.247377	−	0.521337i
$596$	27.8633	+	16.0869i	1.14132	+	0.658944i
$597$	−3.61112	−	5.23161i	−0.147793	−	0.214116i
$598$	28.4523	−	65.7323i	1.16350	−	2.68799i
$599$	−25.4106	+	36.8137i	−1.03825	+	1.50417i	−0.184948	+	0.982748i	$0.559212\pi$
$599$	−25.4106	+	36.8137i	−1.03825	+	1.50417i	−0.853302	+	0.521417i	$0.825404\pi$
$600$	1.74749	−	0.829196i	0.0713411	−	0.0338518i
$601$	−21.2311	+	13.4257i	−0.866033	+	0.547646i	−0.892010	−	0.452017i	$-0.850705\pi$
$601$	−21.2311	+	13.4257i	−0.866033	+	0.547646i	0.0259767	+	0.999663i	$0.491730\pi$
$602$	9.94314	−	1.61592i	0.405252	−	0.0658599i
$603$	2.46425	−	4.69523i	0.100352	−	0.191205i
$604$	−37.7042	−	30.7845i	−1.53416	−	1.25260i
$605$	−7.63486	+	7.33339i	−0.310401	+	0.298145i
$606$		−	34.0317i		−	1.38244i
$607$	22.4817	+	23.4060i	0.912506	+	0.950019i	0.998930	−	0.0462390i	$-0.0147236\pi$
$607$	22.4817	+	23.4060i	0.912506	+	0.950019i	−0.0864244	+	0.996258i	$0.527544\pi$
$608$	6.68461	−	2.23165i	0.271097	−	0.0905054i
$609$	−0.626801	−	7.76432i	−0.0253992	−	0.314626i
$610$	15.0923	−	3.71991i	0.611068	−	0.150615i
$611$	30.2924	−	28.7642i	1.22550	−	1.16367i
$612$	−11.7118	−	2.88671i	−0.473423	−	0.116688i
$613$	1.91997	−	11.8140i	0.0775468	−	0.477164i	−0.919009	−	0.394237i	$-0.871009\pi$
$613$	1.91997	−	11.8140i	0.0775468	−	0.477164i	0.996556	−	0.0829274i	$-0.0264270\pi$
$614$	−14.4505	−	17.6987i	−0.583176	−	0.714260i
$615$	−0.0358936	+	0.0269723i	−0.00144737	+	0.00108763i
$616$	−9.81028	+	11.0735i	−0.395268	+	0.446165i
$617$	−5.57548	−	34.3073i	−0.224461	−	1.38116i	−0.817473	−	0.575967i	$-0.804625\pi$
$617$	−5.57548	−	34.3073i	−0.224461	−	1.38116i	0.593012	−	0.805194i	$-0.297939\pi$
$618$	0.950130	−	11.7695i	0.0382198	−	0.473437i
$619$	1.93308	+	7.84283i	0.0776972	+	0.315230i	0.996912	−	0.0785264i	$-0.0250215\pi$
$619$	1.93308	+	7.84283i	0.0776972	+	0.315230i	−0.919215	+	0.393756i	$0.871175\pi$
$620$	−0.0534562	−	0.184552i	−0.00214685	−	0.00741179i
$621$	−1.78336	−	8.73545i	−0.0715636	−	0.350542i
$622$	−12.4100	+	10.1324i	−0.497594	+	0.406273i
$623$	−2.68930	+	22.1484i	−0.107745	+	0.887356i
$624$	−1.16618	+	3.94142i	−0.0466847	+	0.157783i
$625$	−2.37348	−	19.5473i	−0.0949391	−	0.781894i
$626$	−12.5806	−	12.0839i	−0.502823	−	0.482968i
$627$	2.87555	−	2.99376i	0.114838	−	0.119559i
$628$	−3.38404	+	7.13172i	−0.135038	+	0.284586i
$629$	21.0363	−	14.5203i	0.838772	−	0.578962i
$630$	4.11989	−	6.51508i	0.164140	−	0.259567i
$631$	−2.09714	−	2.79078i	−0.0834858	−	0.111099i	0.755768	−	0.654840i	$-0.227264\pi$
$631$	−2.09714	−	2.79078i	−0.0834858	−	0.111099i	−0.839253	+	0.543741i	$0.817008\pi$
$632$	−8.01630	−	15.2738i	−0.318871	−	0.607558i
$633$	−1.78294	+	8.73343i	−0.0708656	+	0.347123i
$634$	−18.0434	+	1.45661i	−0.716595	+	0.0578495i
$635$	11.1552	+	3.23114i	0.442680	+	0.128224i
$636$	−23.8962	−	12.5417i	−0.947545	−	0.497310i
$637$	8.42784	−	12.0613i	0.333923	−	0.477887i
$638$	36.2360	−	19.0181i	1.43460	−	0.752935i
$639$	−7.81230	+	1.59489i	−0.309050	+	0.0630930i
$640$	24.5980	+	18.4842i	0.972323	+	0.730653i
$641$	0.0398216	+	0.988164i	0.00157286	+	0.0390301i	0.999785	−	0.0207432i	$-0.00660324\pi$
$641$	0.0398216	+	0.988164i	0.00157286	+	0.0390301i	−0.998212	+	0.0597733i	$0.980962\pi$
$642$	−19.0862	+	7.23846i	−0.753274	+	0.285679i
$643$	−39.8133	+	11.5321i	−1.57008	+	0.454780i	−0.945350	−	0.326058i	$-0.894280\pi$
$643$	−39.8133	+	11.5321i	−1.57008	+	0.454780i	−0.624734	+	0.780838i	$0.714792\pi$
$644$	44.2471	+	9.03312i	1.74358	+	0.355955i
$645$	−3.55313	−	4.01065i	−0.139904	−	0.157919i
$646$	−5.90810	+	7.23611i	−0.232451	+	0.284701i
$647$	0.0100739	−	0.249980i	0.000396044	−	0.00982774i	−0.998979	−	0.0451793i	$-0.985614\pi$
$647$	0.0100739	−	0.249980i	0.000396044	−	0.00982774i	0.999375	+	0.0353516i	$0.0112551\pi$
$648$	−0.680671	−	2.03886i	−0.0267393	−	0.0800939i
$649$	7.33374	−	6.49713i	0.287874	−	0.255035i
$650$	5.92595	+	4.14075i	0.232435	+	0.162414i
$651$	0.0409312	+	0.0362619i	0.00160422	+	0.00142121i
$652$	−10.2194	+	23.9859i	−0.400224	+	0.939361i
$653$	13.6520	−	23.6459i	0.534243	−	0.925335i	−0.464957	−	0.885333i	$-0.653930\pi$
$653$	13.6520	−	23.6459i	0.534243	−	0.925335i	0.999200	−	0.0400020i	$-0.0127364\pi$
$654$	5.82348	+	10.0866i	0.227716	+	0.394416i
$655$	−30.9330	+	3.75594i	−1.20865	+	0.146757i
$656$	0.0228371	+	0.0108363i	0.000891638	+	0.000423087i
$657$	−11.2448	+	6.49220i	−0.438702	+	0.253285i
$658$	36.2982	+	25.0549i	1.41505	+	0.976740i
$659$	−21.4138	+	9.12358i	−0.834164	+	0.355404i	−0.766453	−	0.642301i	$-0.777980\pi$
$659$	−21.4138	+	9.12358i	−0.834164	+	0.355404i	−0.0677114	+	0.997705i	$0.521570\pi$
$660$	23.8699	+	3.87924i	0.929136	+	0.150999i
$661$	7.05912	−	9.39398i	0.274568	−	0.365384i	−0.641004	−	0.767537i	$-0.721482\pi$
$661$	7.05912	−	9.39398i	0.274568	−	0.365384i	0.915572	+	0.402154i	$0.131738\pi$
$662$	10.7422	+	28.3250i	0.417509	+	1.10088i
$663$	−4.00054	−	14.1138i	−0.155368	−	0.548134i
$664$	10.7554	−	28.3597i	0.417391	−	1.10057i
$665$	−1.90531	−	3.01301i	−0.0738847	−	0.116839i
$666$	12.8780	+	5.48681i	0.499013	+	0.212610i
$667$	−34.3558	−	21.7253i	−1.33026	−	0.841206i
$668$	−53.1249	−	6.45053i	−2.05546	−	0.249578i
$669$	4.04876	+	9.50280i	0.156534	+	0.367399i
$670$	7.57599	−	22.6928i	0.292686	−	0.876701i
$671$	−12.9769	−	4.92147i	−0.500966	−	0.189991i
$672$	−11.6468	−	0.940226i	−0.449285	−	0.0362700i
$673$	−7.40495	+	25.5648i	−0.285440	+	0.985452i	0.681790	+	0.731548i	$0.261202\pi$
$673$	−7.40495	+	25.5648i	−0.285440	+	0.985452i	−0.967229	+	0.253904i	$0.918285\pi$
$674$	−7.19194	−	0.289825i	−0.277023	−	0.0111636i
$675$	0.899866			0.0346359
$676$	37.5243	−	8.79374i	1.44324	−	0.338221i
$677$	−36.6209			−1.40745			−0.703727	−	0.710470i	$-0.748482\pi$
$677$	−36.6209			−1.40745			−0.703727	+	0.710470i	$0.748482\pi$
$678$	39.9610	+	1.61037i	1.53469	+	0.0618460i
$679$	3.76155	−	12.9864i	0.144355	−	0.498371i
$680$	−17.6512	−	1.42495i	−0.676893	−	0.0546444i
$681$	17.1114	+	6.48951i	0.655712	+	0.248679i
$682$	−0.0909745	+	0.272502i	−0.00348359	+	0.0104346i
$683$	−15.0871	−	35.4106i	−0.577290	−	1.35495i	−0.911051	−	0.412293i	$-0.864728\pi$
$683$	−15.0871	−	35.4106i	−0.577290	−	1.35495i	0.333761	−	0.942658i	$-0.391682\pi$
$684$	−3.03268	−	0.368234i	−0.115957	−	0.0140798i
$685$	13.3217	+	8.42411i	0.508995	+	0.321869i
$686$	38.8081	+	16.5346i	1.48170	+	0.631293i
$687$	0.990075	+	1.56568i	0.0377737	+	0.0597344i
$688$	−1.06971	+	2.82060i	−0.0407824	+	0.107534i
$689$	−1.13352	−	32.8016i	−0.0431837	−	1.24964i
$690$	−14.2640	−	37.6111i	−0.543022	−	1.43183i
$691$	−0.330018	+	0.439174i	−0.0125545	+	0.0167070i	−0.805676	−	0.592356i	$-0.798198\pi$
$691$	−0.330018	+	0.439174i	−0.0125545	+	0.0167070i	0.793122	+	0.609063i	$0.208454\pi$
$692$	−26.8297	−	4.36026i	−1.01991	−	0.165752i
$693$	−6.33188	+	2.69776i	−0.240528	+	0.102480i
$694$	−22.2485	−	15.3570i	−0.844541	−	0.582945i
$695$	−18.0481	+	10.4201i	−0.684605	+	0.395257i
$696$	−8.85382	−	4.20119i	−0.335603	−	0.159246i
$697$	−0.0895583	+	0.0108743i	−0.00339226	+	0.000411895i
$698$	−2.56357	−	4.44024i	−0.0970326	−	0.168065i
$699$	−13.1426	+	22.7636i	−0.497098	+	0.860998i
$700$	−1.78660	+	4.19330i	−0.0675271	+	0.158492i
$701$	8.91900	+	7.90155i	0.336866	+	0.298437i	0.814549	−	0.580095i	$-0.196985\pi$
$701$	8.91900	+	7.90155i	0.336866	+	0.298437i	−0.477683	+	0.878532i	$0.658523\pi$
$702$	5.36174	−	5.98270i	0.202366	−	0.225802i
$703$	4.84562	−	4.29284i	0.182756	−	0.161908i
$704$	−16.5308	−	49.5157i	−0.623027	−	1.86619i
$705$	0.944635	−	23.4409i	0.0355770	−	0.882835i
$706$	7.35262	−	9.00532i	0.276719	−	0.338920i
$707$	17.3042	+	19.5324i	0.650793	+	0.734593i
$708$	−7.06490	−	1.44231i	−0.265515	−	0.0542053i
$709$	28.0598	−	8.12761i	1.05381	−	0.305239i	0.294283	−	0.955718i	$-0.404919\pi$
$709$	28.0598	−	8.12761i	1.05381	−	0.305239i	0.759524	+	0.650480i	$0.225432\pi$
$710$	−33.6364	+	12.7566i	−1.26235	+	0.478747i
$711$	−0.323135	−	8.01852i	−0.0121185	−	0.300718i
$712$	22.4398	+	16.8624i	0.840969	+	0.631947i
$713$	0.279590	−	0.0570786i	0.0104707	−	0.00213761i
$714$	13.7147	−	7.19803i	0.513260	−	0.269380i
$715$	10.2713	+	27.5588i	0.384126	+	1.03064i
$716$	11.5772	+	6.07617i	0.432659	+	0.227077i
$717$	3.32862	+	0.964147i	0.124310	+	0.0360067i
$718$	68.2693	−	5.51127i	2.54779	−	0.205679i
$719$	−6.16005	+	30.1739i	−0.229731	+	1.12530i	0.687267	+	0.726405i	$0.258810\pi$
$719$	−6.16005	+	30.1739i	−0.229731	+	1.12530i	−0.916998	+	0.398892i	$0.869395\pi$
$720$	1.07275	+	2.04395i	0.0399790	+	0.0761736i
$721$	5.43914	+	7.23818i	0.202564	+	0.269564i
$722$	21.3621	−	33.7815i	0.795016	−	1.25722i
$723$	−5.60196	+	3.86675i	−0.208339	+	0.143806i
$724$	−27.6836	+	58.3420i	−1.02885	+	2.16826i
$725$	2.84205	−	2.95889i	0.105551	−	0.109890i
$726$	−8.40134	−	8.06959i	−0.311803	−	0.299491i
$727$	1.47743	+	12.1677i	0.0547948	+	0.451276i	0.994123	+	0.108256i	$0.0345267\pi$
$727$	1.47743	+	12.1677i	0.0547948	+	0.451276i	−0.939328	+	0.343020i	$0.888550\pi$
$728$	5.60769	+	11.9951i	0.207835	+	0.444567i
$729$	0.120537	−	0.992709i	0.00446432	−	0.0367670i
$730$	−45.3782	+	37.0502i	−1.67952	+	1.37129i
$731$	−2.15356	−	10.5488i	−0.0796522	−	0.390162i
$732$	2.84171	+	9.81072i	0.105033	+	0.362615i
$733$	10.3607	+	42.0349i	0.382680	+	1.55259i	0.774513	+	0.632558i	$0.217995\pi$
$733$	10.3607	+	42.0349i	0.382680	+	1.55259i	−0.391833	+	0.920036i	$0.628159\pi$
$734$	−4.97130	+	61.5807i	−0.183494	+	2.27298i
$735$	−1.32555	−	8.15642i	−0.0488936	−	0.300854i
$736$	−40.4336	+	45.6401i	−1.49040	+	1.68232i
$737$	−17.0770	+	12.8325i	−0.629039	+	0.472692i
$738$	−0.0312464	−	0.0382699i	−0.00115020	−	0.00140873i
$739$	−3.55364	+	21.8664i	−0.130723	+	0.804370i	0.836035	+	0.548676i	$0.184868\pi$
$739$	−3.55364	+	21.8664i	−0.130723	+	0.804370i	−0.966758	+	0.255694i	$0.917696\pi$
$740$	36.6181	+	9.02556i	1.34611	+	0.331786i
$741$	−1.43666	−	3.42632i	−0.0527772	−	0.125869i
$742$	33.6467	−	8.29316i	1.23521	−	0.304451i
$743$	4.11584	+	50.9839i	0.150996	+	1.87042i	0.420331	+	0.907371i	$0.361914\pi$
$743$	4.11584	+	50.9839i	0.150996	+	1.87042i	−0.269336	+	0.963046i	$0.586804\pi$
$744$	0.0652563	−	0.0217858i	0.00239241	−	0.000798705i
$745$	15.2224	+	15.8482i	0.557704	+	0.580632i
$746$		−	53.6669i		−	1.96488i
$747$	10.1767	−	9.77484i	0.372346	−	0.357643i
$748$	37.6397	+	30.7319i	1.37624	+	1.12367i
$749$	7.27395	−	13.8594i	0.265784	−	0.506410i
$750$	26.2740	−	4.26994i	0.959391	−	0.155916i
$751$	−23.3552	+	14.7689i	−0.852243	+	0.538926i	−0.887688	−	0.460446i	$-0.847690\pi$
$751$	−23.3552	+	14.7689i	−0.852243	+	0.538926i	0.0354448	+	0.999372i	$0.488715\pi$
$752$	−11.9326	+	5.66211i	−0.435139	+	0.206476i
$753$	−14.1425	+	20.4890i	−0.515383	+	0.746661i
$754$	−2.73794	−	36.5253i	−0.0997098	−	1.33017i
$755$	−18.8854	−	27.3603i	−0.687311	−	0.995742i
$756$	4.38662	+	2.53262i	0.159540	+	0.0921104i
$757$	−3.31712	−	6.99067i	−0.120563	−	0.254080i	0.834193	−	0.551473i	$-0.185934\pi$
$757$	−3.31712	−	6.99067i	−0.120563	−	0.254080i	−0.954755	+	0.297393i	$0.903883\pi$
$758$	−35.5978	−	11.8843i	−1.29297	−	0.431657i
$759$	−8.59523	+	34.8722i	−0.311987	+	1.26578i
$760$	−4.48132	+	0.180591i	−0.162554	+	0.00655072i
$761$	−19.8117	+	0.798385i	−0.718175	+	0.0289414i	−0.396663	−	0.917964i	$-0.629832\pi$
$761$	−19.8117	+	0.798385i	−0.718175	+	0.0289414i	−0.321511	+	0.946906i	$0.604191\pi$
$762$	−3.05837	+	12.4083i	−0.110793	+	0.449505i
$763$	−8.47113	−	2.82808i	−0.306675	−	0.102383i
$764$	2.43592	+	5.13359i	0.0881284	+	0.185727i
$765$	−7.13481	−	4.11929i	−0.257960	−	0.148933i
$766$	−9.29704	−	13.4691i	−0.335916	−	0.486658i
$767$	−2.72922	−	8.33379i	−0.0985464	−	0.300916i
$768$	−4.51095	+	6.53524i	−0.162775	+	0.235820i
$769$	−44.8909	+	21.3010i	−1.61881	+	0.768133i	−0.999850	−	0.0172934i	$-0.994495\pi$
$769$	−44.8909	+	21.3010i	−1.61881	+	0.768133i	−0.618955	+	0.785426i	$0.712444\pi$
$770$	−26.2455	+	16.5966i	−0.945821	+	0.598101i
$771$	−6.39502	+	1.03929i	−0.230311	+	0.0374292i
$772$	10.8388	−	20.6516i	0.390097	−	0.743268i
$773$	−2.42759	−	1.98207i	−0.0873143	−	0.0712899i	0.587783	−	0.809019i	$-0.300001\pi$
$773$	−2.42759	−	1.98207i	−0.0873143	−	0.0712899i	−0.675097	+	0.737729i	$0.735898\pi$
$774$	4.25227	−	4.08436i	0.152845	−	0.146809i
$775$			0.0288014i			0.00103458i
$776$	−11.7830	−	12.2674i	−0.422984	−	0.440373i
$777$	−10.1812	+	3.39899i	−0.365249	+	0.121938i
$778$	4.39767	+	54.4750i	0.157664	+	1.95302i
$779$	−0.0221845	+	0.00546800i	−0.000794843	+	0.000195911i
$780$	11.6730	−	18.2272i	0.417961	−	0.652638i
$781$	31.1869	+	7.68689i	1.11596	+	0.275059i
$782$	12.9654	−	79.7793i	0.463642	−	2.85290i
$783$	−2.88348	−	3.53162i	−0.103047	−	0.126210i
$784$	−3.71924	+	2.79482i	−0.132830	+	0.0998151i
$785$	−3.57523	+	4.03560i	−0.127605	+	0.144037i
$786$	−5.50024	−	33.8443i	−0.196187	−	1.20719i
$787$	2.27976	−	28.2399i	0.0812647	−	1.00664i	−0.819712	−	0.572776i	$-0.805866\pi$
$787$	2.27976	−	28.2399i	0.0812647	−	1.00664i	0.900977	−	0.433868i	$-0.142852\pi$
$788$	17.0813	+	69.3016i	0.608497	+	2.46877i
$789$	−0.111654	−	0.385474i	−0.00397499	−	0.0137232i
$790$	−7.24231	−	35.4752i	−0.257670	−	1.26215i
$791$	−23.7544	+	19.3949i	−0.844609	+	0.689602i
$792$	−1.04373	+	8.59585i	−0.0370872	+	0.305440i
$793$	−8.65617	+	8.90922i	−0.307390	+	0.316376i
$794$	3.58318	+	29.5101i	0.127162	+	1.04728i
$795$	−13.2935	−	12.7686i	−0.471471	−	0.452854i
$796$	13.0552	−	13.5919i	0.462729	−	0.481752i
$797$	10.2933	−	21.6926i	0.364606	−	0.768391i	−0.635387	−	0.772194i	$-0.719159\pi$
$797$	10.2933	−	21.6926i	0.364606	−	0.768391i	0.999993	+	0.00380300i	$0.00121053\pi$
$798$	3.22837	−	2.22839i	0.114283	−	0.0788840i
$799$	25.1942	−	39.8414i	0.891306	−	1.40949i
$800$	−3.69711	−	4.91996i	−0.130713	−	0.173947i
$801$	6.06867	+	11.5629i	0.214426	+	0.408555i
$802$	−6.20089	+	30.3740i	−0.218961	+	1.07254i
$803$	52.1369	−	4.20893i	1.83987	−	0.148530i
$804$	15.0999	+	4.37374i	0.532533	+	0.154250i
$805$	27.3111	+	14.3340i	0.962589	+	0.505206i
$806$	0.191484	+	0.171610i	0.00674473	+	0.00604469i
$807$	−1.25413	+	0.658217i	−0.0441474	+	0.0231704i
$808$	32.1665	−	6.56684i	1.13161	−	0.231021i
$809$	−17.5278	−	13.1713i	−0.616244	−	0.463077i	0.246207	−	0.969217i	$-0.420816\pi$
$809$	−17.5278	−	13.1713i	−0.616244	−	0.463077i	−0.862451	+	0.506140i	$0.831072\pi$
$810$	−0.181670	−	4.50809i	−0.00638323	−	0.158398i
$811$	−2.78917	+	1.05779i	−0.0979412	+	0.0371442i	−0.403089	−	0.915161i	$-0.632063\pi$
$811$	−2.78917	+	1.05779i	−0.0979412	+	0.0371442i	0.305148	+	0.952305i	$0.401294\pi$
$812$	22.1819	−	6.42506i	0.778432	−	0.225476i
$813$	−8.51817	−	1.73900i	−0.298745	−	0.0609893i
$814$	−37.3937	−	42.2088i	−1.31065	−	1.47942i
$815$	−11.2621	+	13.7936i	−0.394496	+	0.483169i
$816$	−0.186765	+	4.63453i	−0.00653808	+	0.162241i
$817$	−0.863471	−	2.58641i	−0.0302090	−	0.0904871i
$818$	47.9876	−	42.5133i	1.67785	−	1.48644i
$819$	−0.0353201	+	6.16006i	−0.00123418	+	0.215250i
$820$	−0.0996339	−	0.0882679i	−0.00347937	−	0.00308245i
$821$	11.5563	−	27.1236i	0.403317	−	0.946620i	−0.587227	−	0.809423i	$-0.699780\pi$
$821$	11.5563	−	27.1236i	0.403317	−	0.946620i	0.990544	−	0.137197i	$-0.0438094\pi$
$822$	−8.67204	+	15.0204i	−0.302472	+	0.523897i
$823$	0.691219	+	1.19723i	0.0240944	+	0.0417327i	0.877821	−	0.478988i	$-0.158996\pi$
$823$	0.691219	+	1.19723i	0.0240944	+	0.0417327i	−0.853727	+	0.520721i	$0.825663\pi$
$824$	11.3078	−	1.37301i	0.393924	−	0.0478311i
$825$	−3.27504	−	1.55403i	−0.114022	−	0.0541042i
$826$	8.01846	−	4.62946i	0.278998	−	0.161079i
$827$	12.5693	+	8.67596i	0.437078	+	0.301693i	0.766209	−	0.642591i	$-0.222141\pi$
$827$	12.5693	+	8.67596i	0.437078	+	0.301693i	−0.329132	+	0.944284i	$0.606756\pi$
$828$	24.3170	−	10.3605i	0.845073	−	0.360052i
$829$	−0.109349	−	0.0177710i	−0.00379786	−	0.000617212i	0.158512	−	0.987357i	$-0.449330\pi$
$829$	−0.109349	−	0.0177710i	−0.00379786	−	0.000617212i	−0.162310	+	0.986740i	$0.551894\pi$
$830$	38.2457	−	50.8958i	1.32753	−	1.76662i
$831$	−5.31149	−	14.0052i	−0.184253	−	0.485836i
$832$	−46.5487	−	4.02656i	−1.61379	−	0.139596i
$833$	5.88788	−	15.5251i	0.204003	−	0.537912i
$834$	−12.2566	−	19.3822i	−0.424410	−	0.671151i
$835$	−33.6259	−	14.3267i	−1.16367	−	0.495794i
$836$	10.4014	+	6.57747i	0.359741	+	0.227487i
$837$	0.0317729	+	0.00385793i	0.00109823	+	0.000133350i
$838$	32.7810	+	76.9398i	1.13240	+	2.65784i
$839$	−12.0557	+	36.1112i	−0.416209	+	1.24670i	0.506848	+	0.862036i	$0.330811\pi$
$839$	−12.0557	+	36.1112i	−0.416209	+	1.24670i	−0.923057	+	0.384663i	$0.874318\pi$
$840$	6.95299	+	2.63692i	0.239901	+	0.0909825i
$841$	8.18662	+	0.660892i	0.282297	+	0.0227894i
$842$	13.6309	−	47.0595i	0.469753	−	1.62178i
$843$	19.4713	+	0.784665i	0.670626	+	0.0270253i
$844$	−26.4259			−0.909618
$845$	26.2882	+	1.36148i	0.904341	+	0.0468362i
$846$	25.8151			0.887540
$847$	8.92511	+	0.359670i	0.306670	+	0.0123584i
$848$	−2.88716	+	9.96765i	−0.0991456	+	0.342290i
$849$	−25.4043	−	2.05085i	−0.871874	−	0.0703850i
$850$	7.62774	+	2.89282i	0.261629	+	0.0992230i
$851$	−17.7370	+	53.1289i	−0.608018	+	1.82124i
$852$	−9.26560	−	21.7472i	−0.317434	−	0.745046i
$853$	−0.694915	−	0.0843779i	−0.0237934	−	0.00288905i	0.108631	−	0.994082i	$-0.465353\pi$
$853$	−0.694915	−	0.0843779i	−0.0237934	−	0.00288905i	−0.132425	+	0.991193i	$0.542276\pi$
$854$	−11.0850	−	7.00975i	−0.379322	−	0.239869i
$855$	−1.91957	−	0.817851i	−0.0656478	−	0.0279699i
$856$	−10.5247	−	16.6434i	−0.359726	−	0.568861i
$857$	6.91749	−	18.2399i	0.236297	−	0.623063i	−0.763443	−	0.645875i	$-0.776493\pi$
$857$	6.91749	−	18.2399i	0.236297	−	0.623063i	0.999740	+	0.0228118i	$0.00726185\pi$
$858$	−29.8457	+	12.5144i	−1.01892	+	0.427234i
$859$	−14.4869	−	38.1988i	−0.494287	−	1.30333i	−0.917658	−	0.397371i	$-0.869923\pi$
$859$	−14.4869	−	38.1988i	−0.494287	−	1.30333i	0.423371	−	0.905956i	$-0.360847\pi$
$860$	9.54298	−	12.6994i	0.325413	−	0.433046i
$861$	0.0373931	+	0.00607696i	0.00127435	+	0.000207102i
$862$	−26.3069	+	11.2083i	−0.896015	+	0.381756i
$863$	37.2444	+	25.7079i	1.26781	+	0.875109i	0.996183	−	0.0872928i	$-0.0278216\pi$
$863$	37.2444	+	25.7079i	1.26781	+	0.875109i	0.271631	+	0.962401i	$0.412437\pi$
$864$	−5.92280	+	3.41953i	−0.201498	+	0.116335i
$865$	−16.7726	−	7.95872i	−0.570287	−	0.270604i
$866$	−53.2807	+	6.46945i	−1.81055	+	0.219841i
$867$	0.222947	+	0.386155i	0.00757167	+	0.0131145i
$868$	−0.0810597	+	0.140400i	−0.00275135	+	0.00476547i
$869$	−12.6715	+	29.7412i	−0.429853	+	1.00890i
$870$	−15.3970	−	13.6406i	−0.522007	−	0.462458i
$871$	4.46893	+	18.5892i	0.151424	+	0.629872i
$872$	−8.41003	+	7.45063i	−0.284799	+	0.252310i
$873$	−2.50591	−	7.50613i	−0.0848123	−	0.254044i
$874$	0.824256	−	20.4537i	0.0278809	−	0.691857i
$875$	−12.9088	+	15.8104i	−0.436396	+	0.534488i
$876$	−25.5267	−	28.8137i	−0.862468	−	0.973525i
$877$	31.6431	+	6.45999i	1.06851	+	0.218138i	0.701929	−	0.712247i	$-0.252322\pi$
$877$	31.6431	+	6.45999i	1.06851	+	0.218138i	0.366583	+	0.930385i	$0.380528\pi$
$878$	−77.4967	+	22.4472i	−2.61539	+	0.757556i
$879$	7.39645	−	2.80510i	0.249476	−	0.0946137i
$880$	−0.374434	−	9.29149i	−0.0126222	−	0.313216i
$881$	−32.7788	−	24.6317i	−1.10435	−	0.829863i	−0.117751	−	0.993043i	$-0.537568\pi$
$881$	−32.7788	−	24.6317i	−1.10435	−	0.829863i	−0.986596	+	0.163180i	$0.947825\pi$
$882$	8.90924	−	1.81883i	0.299990	−	0.0612433i
$883$	−30.7108	+	16.1183i	−1.03350	+	0.542424i	−0.894126	−	0.447816i	$-0.852202\pi$
$883$	−30.7108	+	16.1183i	−1.03350	+	0.542424i	−0.139376	+	0.990239i	$0.544510\pi$
$884$	38.6250	−	19.9903i	1.29910	−	0.672348i
$885$	−4.36073	−	2.28869i	−0.146584	−	0.0769334i
$886$	27.8829	+	8.07637i	0.936744	+	0.271331i
$887$	−35.3997	+	2.85776i	−1.18860	+	0.0959541i	−0.658902	−	0.752229i	$-0.728979\pi$
$887$	−35.3997	+	2.85776i	−1.18860	+	0.0959541i	−0.529703	+	0.848183i	$0.677697\pi$
$888$	−2.70112	+	13.2310i	−0.0906436	+	0.444002i
$889$	−4.55394	−	8.67681i	−0.152734	−	0.291011i
$890$	35.3942	+	47.1012i	1.18642	+	1.57884i
$891$	−2.15305	+	3.40478i	−0.0721299	+	0.114064i
$892$	−25.2025	+	17.3960i	−0.843843	+	0.582462i
$893$	5.11799	−	10.7859i	0.171267	−	0.360937i
$894$	−16.7505	+	17.4392i	−0.560222	+	0.583253i
$895$	6.44039	+	6.18608i	0.215279	+	0.206778i
$896$	−3.12935	−	25.7725i	−0.104544	−	0.860999i
$897$	25.5876	+	19.4584i	0.854344	+	0.649696i
$898$	10.3833	−	85.5141i	0.346495	−	2.85364i
$899$	0.113034	−	0.0922894i	0.00376989	−	0.00307802i
$900$	0.533633	+	2.61391i	0.0177878	+	0.0871303i
$901$	−10.3043	−	35.5746i	−0.343287	−	1.18516i
$902$	0.0476302	+	0.193243i	0.00158591	+	0.00643430i
$903$	−0.363793	+	4.50638i	−0.0121063	+	0.149963i
$904$	6.18886	+	38.0816i	0.205838	+	1.26658i
$905$	−29.2476	+	33.0138i	−0.972225	+	1.09741i
$906$	29.2458	−	21.9768i	0.971626	−	0.730130i
$907$	13.9699	+	17.1100i	0.463862	+	0.568127i	0.952570	−	0.304320i	$-0.0984292\pi$
$907$	13.9699	+	17.1100i	0.463862	+	0.568127i	−0.488708	+	0.872447i	$0.662532\pi$
$908$	−8.70325	+	53.5532i	−0.288827	+	1.77723i
$909$	14.8297	+	3.65518i	0.491869	+	0.121235i
$910$	4.30097	+	27.4583i	0.142576	+	0.910234i
$911$	25.0867	−	6.18333i	0.831161	−	0.204863i	0.199294	−	0.979940i	$-0.436135\pi$
$911$	25.0867	−	6.18333i	0.831161	−	0.204863i	0.631867	+	0.775077i	$0.282289\pi$
$912$	0.0945249	+	1.17090i	0.00313003	+	0.0387724i
$913$	−53.9184	+	18.0006i	−1.78444	+	0.595734i
$914$	61.3617	+	63.8843i	2.02967	+	2.11311i
$915$			6.97614i			0.230624i
$916$	−3.96081	+	3.80441i	−0.130869	+	0.125701i
$917$	20.3658	+	16.6282i	0.672538	+	0.549111i
$918$	4.21302	−	8.02723i	0.139050	−	0.264938i
$919$	10.3409	−	1.68056i	0.341114	−	0.0554365i	0.0125588	−	0.999921i	$-0.496002\pi$
$919$	10.3409	−	1.68056i	0.341114	−	0.0554365i	0.328555	+	0.944485i	$0.393438\pi$
$920$	32.7973	−	20.7398i	1.08130	−	0.683770i
$921$	9.26443	−	4.39603i	0.305273	−	0.144854i
$922$	48.9184	−	70.8706i	1.61104	−	2.33400i
$923$	17.4020	−	22.8835i	0.572794	−	0.753219i
$924$	−11.5913	−	16.7929i	−0.381325	−	0.552445i
$925$	−4.89591	−	2.82666i	−0.160977	−	0.0929399i
$926$	36.9940	+	77.9633i	1.21570	+	2.56203i
$927$	5.02661	+	1.67813i	0.165096	+	0.0551170i
$928$	−7.46209	+	30.2749i	−0.244955	+	0.993822i
$929$	2.59618	−	0.104622i	0.0851778	−	0.00343255i	0.00235953	−	0.999997i	$-0.499249\pi$
$929$	2.59618	−	0.104622i	0.0851778	−	0.00343255i	0.0828182	+	0.996565i	$0.473608\pi$
$930$	0.144287	−	0.00581458i	0.00473137	−	0.000190668i
$931$	1.00637	−	4.08301i	0.0329825	−	0.133815i
$932$	−73.9168	−	24.6771i	−2.42123	−	0.808324i
$933$	−3.08241	−	6.49603i	−0.100913	−	0.212671i
$934$	59.9269	+	34.5988i	1.96087	+	1.13211i
$935$	18.8531	+	27.3135i	0.616564	+	0.893247i
$936$	6.68941	+	3.91345i	0.218650	+	0.127915i
$937$	−9.89718	+	14.3385i	−0.323327	+	0.468420i	−0.950617	−	0.310366i	$-0.899548\pi$
$937$	−9.89718	+	14.3385i	−0.323327	+	0.468420i	0.627291	+	0.778785i	$0.284164\pi$
$938$	−18.2373	+	8.65372i	−0.595470	+	0.282554i
$939$	6.61689	−	4.18427i	0.215934	−	0.136548i
$940$	68.6506	−	11.1568i	2.23914	−	0.363895i
$941$	23.9946	−	45.7180i	0.782203	−	1.49036i	−0.0871629	−	0.996194i	$-0.527780\pi$
$941$	23.9946	−	45.7180i	0.782203	−	1.49036i	0.869366	−	0.494169i	$-0.164528\pi$
$942$	−4.59554	−	3.75215i	−0.149731	−	0.122252i
$943$	0.142574	−	0.136944i	0.00464285	−	0.00445952i
$944$			2.77267i			0.0902428i
$945$	2.39651	+	2.49504i	0.0779586	+	0.0811635i
$946$	−22.5295	+	7.52145i	−0.732497	+	0.244544i
$947$	−0.0823612	−	1.02023i	−0.00267638	−	0.0331529i	0.995281	−	0.0970319i	$-0.0309349\pi$
$947$	−0.0823612	−	1.02023i	−0.00267638	−	0.0331529i	−0.997958	+	0.0638790i	$0.979653\pi$
$948$	23.1004	−	5.69373i	0.750265	−	0.184924i
$949$	15.0795	−	44.3209i	0.489501	−	1.43872i
$950$	2.00606	+	0.494449i	0.0650851	+	0.0160420i
$951$	1.30322	−	8.01903i	0.0422598	−	0.260035i
$952$	9.44995	+	11.5741i	0.306275	+	0.375118i
$953$	31.8897	−	23.9635i	1.03301	−	0.776255i	0.0579750	−	0.998318i	$-0.481536\pi$
$953$	31.8897	−	23.9635i	1.03301	−	0.776255i	0.975032	+	0.222063i	$0.0712792\pi$
$954$	13.4500	−	15.1819i	0.435460	−	0.491532i
$955$	0.622546	+	3.83068i	0.0201451	+	0.123958i
$956$	−0.826711	+	10.2406i	−0.0267377	+	0.331206i
$957$	4.39540	+	17.8328i	0.142083	+	0.576454i
$958$	−7.89115	−	27.2434i	−0.254952	−	0.880195i
$959$	−2.66018	−	13.0304i	−0.0859018	−	0.420775i
$960$	−20.3252	+	16.5950i	−0.655992	+	0.535601i
$961$	3.73651	−	30.7730i	0.120533	−	0.992676i
$962$	−47.9645	+	15.7078i	−1.54644	+	0.506441i
$963$	−1.10427	−	9.09447i	−0.0355845	−	0.293065i
$964$	−14.5541	−	13.9794i	−0.468756	−	0.450246i
$965$	11.0349	−	11.4885i	0.355225	−	0.369829i
$966$	−14.5501	+	30.6636i	−0.468141	+	0.986585i
$967$	37.6065	−	25.9579i	1.20934	−	0.834749i	0.219319	−	0.975653i	$-0.429616\pi$
$967$	37.6065	−	25.9579i	1.20934	−	0.834749i	0.990023	+	0.140904i	$0.0450010\pi$
$968$	6.00618	−	9.49801i	0.193046	−	0.305278i
$969$	−2.51865	−	3.35171i	−0.0809105	−	0.107672i
$970$	−16.5921	−	31.6136i	−0.532740	−	1.01505i
$971$	6.21950	−	30.4651i	0.199593	−	0.977673i	−0.749337	−	0.662188i	$-0.769628\pi$
$971$	6.21950	−	30.4651i	0.199593	−	0.977673i	0.948931	−	0.315484i	$-0.102167\pi$
$972$	2.95507	−	0.238558i	0.0947841	−	0.00765176i
$973$	16.8900	+	4.89224i	0.541468	+	0.156838i
$974$	11.6900	+	6.13541i	0.374573	+	0.196591i
$975$	−2.44085	+	2.13755i	−0.0781698	+	0.0684564i
$976$	3.47767	−	1.82522i	0.111317	−	0.0584239i
$977$	−22.9678	+	4.68891i	−0.734805	+	0.150011i	−0.552833	−	0.833292i	$-0.686453\pi$
$977$	−22.9678	+	4.68891i	−0.734805	+	0.150011i	−0.181972	+	0.983304i	$0.558248\pi$
$978$	−15.6651	−	11.7715i	−0.500914	−	0.376412i
$979$	−2.11822	−	52.5631i	−0.0676987	−	1.67992i
$980$	22.9065	−	8.68729i	0.731721	−	0.277505i
$981$	−5.02079	+	1.45429i	−0.160301	+	0.0464319i
$982$	−33.2224	−	6.78240i	−1.06017	−	0.216435i
$983$	−13.3371	−	15.0544i	−0.425386	−	0.480161i	0.496271	−	0.868168i	$-0.334702\pi$
$983$	−13.3371	−	15.0544i	−0.425386	−	0.480161i	−0.921657	+	0.388006i	$0.873164\pi$
$984$	0.0301430	−	0.0369185i	0.000960925	−	0.00117692i
$985$	−1.96294	+	48.7100i	−0.0625446	+	1.55203i
$986$	−13.0887	−	39.2054i	−0.416829	−	1.24856i
$987$	−14.8165	+	13.1263i	−0.471615	+	0.417814i
$988$	9.10073	−	6.20504i	0.289533	−	0.197409i
$989$	17.6591	+	15.6446i	0.561526	+	0.497468i
$990$	−7.12407	+	16.7208i	−0.226418	+	0.531422i
$991$	23.4146	−	40.5552i	0.743788	−	1.28828i	−0.206970	−	0.978347i	$-0.566360\pi$
$991$	23.4146	−	40.5552i	0.743788	−	1.28828i	0.950759	−	0.309932i	$-0.100306\pi$
$992$	−0.109446	−	0.189567i	−0.00347493	−	0.00601875i
$993$	−13.4967	+	1.63879i	−0.428303	+	0.0520054i
$994$	27.4231	+	13.0124i	0.869808	+	0.412729i
$995$	11.1474	−	6.43596i	0.353396	−	0.204034i
$996$	34.4286	+	23.7644i	1.09091	+	0.753003i
$997$	−15.0925	+	6.43032i	−0.477985	+	0.203650i	−0.617502	−	0.786569i	$-0.711855\pi$
$997$	−15.0925	+	6.43032i	−0.477985	+	0.203650i	0.139517	+	0.990220i	$0.455445\pi$
$998$	29.3711	+	4.77327i	0.929726	+	0.151095i
$999$	−3.77410	+	5.02241i	−0.119407	+	0.158902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.t.a.4.3	✓	336
169.127	even	78	inner	507.2.t.a.127.3	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.t.a.4.3	✓	336	1.1	even	1	trivial
507.2.t.a.127.3	yes	336	169.127	even	78	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.t (of order \(78\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.22635 - 0.0897189i) q^{2} +(0.278217 - 0.960518i) q^{3} +(2.95507 + 0.238558i) q^{4} +(1.89329 + 0.718032i) q^{5} +(-0.705586 + 2.11349i) q^{6} +(-0.669684 - 1.57181i) q^{7} +(-2.13381 - 0.259091i) q^{8} +(-0.845190 - 0.534466i) q^{9} +(-4.15072 - 1.76846i) q^{10} +(2.15305 + 3.40478i) q^{11} +(1.05129 - 2.77203i) q^{12} +(3.56212 - 0.557956i) q^{13} +(1.34993 + 3.55947i) q^{14} +(1.21643 - 1.61877i) q^{15} +(-1.12524 - 0.182869i) q^{16} +(3.74310 - 1.59478i) q^{17} +(1.83374 + 1.26574i) q^{18} +(0.892394 - 0.515224i) q^{19} +(5.42353 + 2.57350i) q^{20} +(-1.69607 + 0.205940i) q^{21} +(-4.48797 - 7.77339i) q^{22} +(-4.45782 + 7.72116i) q^{23} +(-0.842524 + 1.97748i) q^{24} +(-0.673560 - 0.596722i) q^{25} +(-7.98058 + 0.922618i) q^{26} +(-0.748511 + 0.663123i) q^{27} +(-1.60400 - 4.80456i) q^{28} +(-0.183582 + 4.55555i) q^{29} +(-2.85344 + 3.49482i) q^{30} +(-0.0212241 - 0.0239571i) q^{31} +(6.70084 + 1.36799i) q^{32} +(3.86936 - 1.12077i) q^{33} +(-8.47653 + 3.21472i) q^{34} +(-0.139302 - 3.45674i) q^{35} +(-2.37010 - 1.78101i) q^{36} +(6.15543 - 1.25664i) q^{37} +(-2.03301 + 1.06700i) q^{38} +(0.455116 - 3.57671i) q^{39} +(-3.85389 - 2.02268i) q^{40} +(-0.0212979 - 0.00616901i) q^{41} +(3.79451 - 0.306325i) q^{42} +(0.529302 - 2.59269i) q^{43} +(5.55018 + 10.5750i) q^{44} +(-1.21643 - 1.61877i) q^{45} +(10.6174 - 16.7901i) q^{46} +(9.53495 - 6.58150i) q^{47} +(-0.488710 + 1.02993i) q^{48} +(2.82697 - 2.94319i) q^{49} +(1.44604 + 1.38894i) q^{50} +(-0.490424 - 4.03901i) q^{51} +(10.6594 - 0.799030i) q^{52} +(1.09724 - 9.03658i) q^{53} +(1.72594 - 1.40919i) q^{54} +(1.63162 + 7.99220i) q^{55} +(1.02173 + 3.52744i) q^{56} +(-0.246602 - 1.00050i) q^{57} +(0.817438 - 10.1258i) q^{58} +(-0.390147 - 2.40067i) q^{59} +(3.98081 - 4.49341i) q^{60} +(-2.75425 + 2.06969i) q^{61} +(0.0451029 + 0.0552410i) q^{62} +(-0.274066 + 1.68640i) q^{63} +(-12.5819 - 3.10117i) q^{64} +(7.14477 + 1.50134i) q^{65} +(-8.71512 + 2.14808i) q^{66} +(0.426683 + 5.28542i) q^{67} +(11.4416 - 3.81976i) q^{68} +(6.17608 + 6.42998i) q^{69} +7.70843i q^{70} +(5.75046 - 5.52339i) q^{71} +(1.66500 + 1.35943i) q^{72} +(6.03415 - 11.4971i) q^{73} +(-13.8169 + 2.24546i) q^{74} +(-0.760558 + 0.480948i) q^{75} +(2.76000 - 1.30964i) q^{76} +(3.90978 - 5.66430i) q^{77} +(-1.33415 + 7.92218i) q^{78} +(4.55874 + 6.60447i) q^{79} +(-1.99910 - 1.15418i) q^{80} +(0.428693 + 0.903450i) q^{81} +(0.0468631 + 0.0156452i) q^{82} +(-3.37692 + 13.7007i) q^{83} +(-5.06113 + 0.203957i) q^{84} +(8.23189 - 0.331734i) q^{85} +(-1.41103 + 5.72475i) q^{86} +(4.32461 + 1.44377i) q^{87} +(-3.71204 - 7.82296i) q^{88} +(-11.3092 - 6.52934i) q^{89} +(2.56297 + 3.71310i) q^{90} +(-3.26249 - 5.22530i) q^{91} +(-15.0151 + 21.7532i) q^{92} +(-0.0289161 + 0.0137209i) q^{93} +(-21.8186 + 13.7973i) q^{94} +(2.05951 - 0.334703i) q^{95} +(3.17827 - 6.05568i) q^{96} +(6.12974 + 5.00478i) q^{97} +(-6.55790 + 6.29895i) q^{98} -4.02841i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 14 q^{3} - 12 q^{4} + 14 q^{9} + 4 q^{10} + 24 q^{12} + 26 q^{13} + 4 q^{14} + 8 q^{16} + 4 q^{17} + 72 q^{22} - 48 q^{23} + 68 q^{25} + 39 q^{26} - 28 q^{27} - 45 q^{29} + 4 q^{30} + 26 q^{31}+ \cdots + 104 q^{98}+O(q^{100}) \) 336 * q + 14 * q^3 - 12 * q^4 + 14 * q^9 + 4 * q^10 + 24 * q^12 + 26 * q^13 + 4 * q^14 + 8 * q^16 + 4 * q^17 + 72 * q^22 - 48 * q^23 + 68 * q^25 + 39 * q^26 - 28 * q^27 - 45 * q^29 + 4 * q^30 + 26 * q^31 + 65 * q^32 - 13 * q^33 + 65 * q^34 - 82 * q^35 - 12 * q^36 - 73 * q^38 + 24 * q^40 - 132 * q^42 - 72 * q^43 + 39 * q^44 + 8 * q^48 + 68 * q^49 + 52 * q^50 - 8 * q^51 - 65 * q^52 + 37 * q^53 - 53 * q^55 + 14 * q^56 - 26 * q^57 + 26 * q^58 - 208 * q^59 + 78 * q^60 - 12 * q^61 - 49 * q^62 + 14 * q^64 + 52 * q^65 + 64 * q^66 - 26 * q^67 - 33 * q^68 + 4 * q^69 - 78 * q^71 + 52 * q^73 + 205 * q^74 - 8 * q^75 - 26 * q^76 - 114 * q^77 - 65 * q^78 + 28 * q^79 - 468 * q^80 + 14 * q^81 - 45 * q^82 - 78 * q^83 + 13 * q^85 + 13 * q^86 + 46 * q^87 + 26 * q^88 - 8 * q^90 - 260 * q^91 + 8 * q^92 - 25 * q^94 - 90 * q^95 - 65 * q^96 - 26 * q^97 + 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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