LMFDB - Embedded newform 841.2.e.b.196.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(63,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("841.63");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.e (of order $14$, degree $6$, not 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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{14})$
Coefficient field:	$\Q(\zeta_{28})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			196.1
Root			$0.974928 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	841.196
Dual form			841.2.e.b.236.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.433884 + 0.0990311i) q^{2} +(-0.541044 + 1.12349i) q^{3} +(-1.62349 + 0.781831i) q^{4} +(0.153989 + 0.674671i) q^{5} +(0.123490 - 0.541044i) q^{6} +(-0.321552 - 0.154851i) q^{7} +(1.32288 - 1.05496i) q^{8} +(0.900969 + 1.12978i) q^{9} +O(q^{10})$	\(q+(-0.433884 + 0.0990311i) q^{2} +(-0.541044 + 1.12349i) q^{3} +(-1.62349 + 0.781831i) q^{4} +(0.153989 + 0.674671i) q^{5} +(0.123490 - 0.541044i) q^{6} +(-0.321552 - 0.154851i) q^{7} +(1.32288 - 1.05496i) q^{8} +(0.900969 + 1.12978i) q^{9} +(-0.133627 - 0.277479i) q^{10} +(3.86147 + 3.07942i) q^{11} -2.24698i q^{12} +(3.52446 - 4.41953i) q^{13} +(0.154851 + 0.0353438i) q^{14} +(-0.841301 - 0.192021i) q^{15} +(1.77748 - 2.22889i) q^{16} +4.49396i q^{17} +(-0.502799 - 0.400969i) q^{18} +(1.02262 + 2.12349i) q^{19} +(-0.777479 - 0.974928i) q^{20} +(0.347948 - 0.277479i) q^{21} +(-1.98039 - 0.953703i) q^{22} +(-0.510885 + 2.23833i) q^{23} +(0.469501 + 2.05702i) q^{24} +(4.07338 - 1.96163i) q^{25} +(-1.09153 + 2.26659i) q^{26} +(-5.40391 + 1.23341i) q^{27} +0.643104 q^{28} +0.384043 q^{30} +(-6.52424 + 1.48911i) q^{31} +(-2.01877 + 4.19202i) q^{32} +(-5.54892 + 2.67222i) q^{33} +(-0.445042 - 1.94986i) q^{34} +(0.0549581 - 0.240787i) q^{35} +(-2.34601 - 1.12978i) q^{36} +(-3.86147 + 3.07942i) q^{37} +(-0.653989 - 0.820077i) q^{38} +(3.05841 + 6.35086i) q^{39} +(0.915458 + 0.730054i) q^{40} -3.10992i q^{41} +(-0.123490 + 0.154851i) q^{42} +(3.32042 + 0.757865i) q^{43} +(-8.67664 - 1.98039i) q^{44} +(-0.623490 + 0.781831i) q^{45} -1.02177i q^{46} +(5.03894 + 4.01842i) q^{47} +(1.54244 + 3.20291i) q^{48} +(-4.28501 - 5.37323i) q^{49} +(-1.57311 + 1.25451i) q^{50} +(-5.04892 - 2.43143i) q^{51} +(-2.26659 + 9.93060i) q^{52} +(1.04407 + 4.57438i) q^{53} +(2.22252 - 1.07031i) q^{54} +(-1.48297 + 3.07942i) q^{55} +(-0.588735 + 0.134375i) q^{56} -2.93900 q^{57} -12.4940 q^{59} +(1.51597 - 0.346011i) q^{60} +(-0.712916 + 1.48039i) q^{61} +(2.68329 - 1.29221i) q^{62} +(-0.114761 - 0.502799i) q^{63} +(-0.807979 + 3.53999i) q^{64} +(3.52446 + 1.69729i) q^{65} +(2.14295 - 1.70895i) q^{66} +(1.44839 + 1.81623i) q^{67} +(-3.51352 - 7.29590i) q^{68} +(-2.23833 - 1.78501i) q^{69} +0.109916i q^{70} +(4.57338 - 5.73483i) q^{71} +(2.38374 + 0.544073i) q^{72} +(5.48460 + 1.25182i) q^{73} +(1.37047 - 1.71851i) q^{74} +5.63773i q^{75} +(-3.32042 - 2.64795i) q^{76} +(-0.764811 - 1.58815i) q^{77} +(-1.95593 - 2.45265i) q^{78} +(3.64715 - 2.90850i) q^{79} +(1.77748 + 0.855989i) q^{80} +(0.573376 - 2.51212i) q^{81} +(0.307979 + 1.34934i) q^{82} +(-4.01357 + 1.93284i) q^{83} +(-0.347948 + 0.722521i) q^{84} +(-3.03194 + 0.692021i) q^{85} -1.51573 q^{86} +8.35690 q^{88} +(-5.53753 + 1.26391i) q^{89} +(0.193096 - 0.400969i) q^{90} +(-1.81767 + 0.875342i) q^{91} +(-0.920583 - 4.03334i) q^{92} +(1.85690 - 8.13559i) q^{93} +(-2.58426 - 1.24451i) q^{94} +(-1.27518 + 1.01693i) q^{95} +(-3.61745 - 4.53614i) q^{96} +(-0.0783611 - 0.162718i) q^{97} +(2.39131 + 1.90701i) q^{98} +7.13706i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 12 q^{5} - 8 q^{6} - 12 q^{7} + 2 q^{9}+O(q^{10}) $ 12 * q - 10 * q^4 + 12 * q^5 - 8 * q^6 - 12 * q^7 + 2 * q^9	$ 12 q - 10 q^{4} + 12 q^{5} - 8 q^{6} - 12 q^{7} + 2 q^{9} + 24 q^{13} + 22 q^{16} - 10 q^{20} + 2 q^{22} - 14 q^{24} - 6 q^{25} + 24 q^{28} - 36 q^{30} - 30 q^{33} - 4 q^{34} + 2 q^{35} - 18 q^{36} - 18 q^{38} + 8 q^{42} + 2 q^{45} - 2 q^{49} - 24 q^{51} - 34 q^{52} + 20 q^{53} + 26 q^{54} + 4 q^{57} - 112 q^{59} - 20 q^{62} + 40 q^{63} - 30 q^{64} + 24 q^{65} + 60 q^{67} - 12 q^{74} - 16 q^{78} + 22 q^{80} - 48 q^{81} + 24 q^{82} - 36 q^{83} + 32 q^{86} + 84 q^{88} + 46 q^{91} - 28 q^{92} + 6 q^{93} + 30 q^{94} + 4 q^{96}+O(q^{100}) $ 12 * q - 10 * q^4 + 12 * q^5 - 8 * q^6 - 12 * q^7 + 2 * q^9 + 24 * q^13 + 22 * q^16 - 10 * q^20 + 2 * q^22 - 14 * q^24 - 6 * q^25 + 24 * q^28 - 36 * q^30 - 30 * q^33 - 4 * q^34 + 2 * q^35 - 18 * q^36 - 18 * q^38 + 8 * q^42 + 2 * q^45 - 2 * q^49 - 24 * q^51 - 34 * q^52 + 20 * q^53 + 26 * q^54 + 4 * q^57 - 112 * q^59 - 20 * q^62 + 40 * q^63 - 30 * q^64 + 24 * q^65 + 60 * q^67 - 12 * q^74 - 16 * q^78 + 22 * q^80 - 48 * q^81 + 24 * q^82 - 36 * q^83 + 32 * q^86 + 84 * q^88 + 46 * q^91 - 28 * q^92 + 6 * q^93 + 30 * q^94 + 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{14}\right)$

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 $

$2$	−0.433884	+	0.0990311i	−0.306802	+	0.0700256i	−0.373150	−	0.927771i	$-0.621722\pi$
$2$	−0.433884	+	0.0990311i	−0.306802	+	0.0700256i	0.0663480	+	0.997797i	$0.478865\pi$
$3$	−0.541044	+	1.12349i	−0.312372	+	0.648647i	−0.996757	−	0.0804740i	$-0.974357\pi$
$3$	−0.541044	+	1.12349i	−0.312372	+	0.648647i	0.684385	+	0.729121i	$0.260071\pi$
$4$	−1.62349	+	0.781831i	−0.811745	+	0.390916i
$5$	0.153989	+	0.674671i	0.0688661	+	0.301722i	0.997618	−	0.0689797i	$-0.0219744\pi$
$5$	0.153989	+	0.674671i	0.0688661	+	0.301722i	−0.928752	+	0.370702i	$0.879117\pi$
$6$	0.123490	−	0.541044i	0.0504145	−	0.220880i
$7$	−0.321552	−	0.154851i	−0.121535	−	0.0585283i	0.372128	−	0.928181i	$-0.378628\pi$
$7$	−0.321552	−	0.154851i	−0.121535	−	0.0585283i	−0.493663	+	0.869653i	$0.664342\pi$
$8$	1.32288	−	1.05496i	0.467707	−	0.372984i
$9$	0.900969	+	1.12978i	0.300323	+	0.376593i
$10$	−0.133627	−	0.277479i	−0.0422565	−	0.0877466i
$11$	3.86147	+	3.07942i	1.16428	+	0.928479i	0.998336	−	0.0576568i	$-0.0183629\pi$
$11$	3.86147	+	3.07942i	1.16428	+	0.928479i	0.165940	+	0.986136i	$0.446934\pi$
$12$		−	2.24698i		−	0.648647i
$13$	3.52446	−	4.41953i	0.977509	−	1.22576i	0.00332670	−	0.999994i	$-0.498941\pi$
$13$	3.52446	−	4.41953i	0.977509	−	1.22576i	0.974182	−	0.225763i	$-0.0724875\pi$
$14$	0.154851	+	0.0353438i	0.0413858	+	0.00944603i
$15$	−0.841301	−	0.192021i	−0.217223	−	0.0495797i
$16$	1.77748	−	2.22889i	0.444370	−	0.557222i
$17$			4.49396i			1.08995i	0.838454	+	0.544973i	$0.183460\pi$
$17$			4.49396i			1.08995i	−0.838454	+	0.544973i	$0.816540\pi$
$18$	−0.502799	−	0.400969i	−0.118511	−	0.0945093i
$19$	1.02262	+	2.12349i	0.234605	+	0.487162i	0.984720	−	0.174145i	$-0.0557162\pi$
$19$	1.02262	+	2.12349i	0.234605	+	0.487162i	−0.750115	+	0.661307i	$0.770002\pi$
$20$	−0.777479	−	0.974928i	−0.173850	−	0.218001i
$21$	0.347948	−	0.277479i	0.0759284	−	0.0605509i
$22$	−1.98039	−	0.953703i	−0.422220	−	0.203330i
$23$	−0.510885	+	2.23833i	−0.106527	+	0.466725i	0.893323	+	0.449415i	$0.148367\pi$
$23$	−0.510885	+	2.23833i	−0.106527	+	0.466725i	−0.999850	+	0.0173102i	$0.994490\pi$
$24$	0.469501	+	2.05702i	0.0958364	+	0.419887i
$25$	4.07338	−	1.96163i	0.814675	−	0.392327i
$26$	−1.09153	+	2.26659i	−0.214067	+	0.444516i
$27$	−5.40391	+	1.23341i	−1.03998	+	0.237369i
$28$	0.643104			0.121535
$29$		0			0
$29$		0			0
$30$	0.384043			0.0701163
$31$	−6.52424	+	1.48911i	−1.17179	+	0.267453i	−0.763750	−	0.645512i	$-0.776644\pi$
$31$	−6.52424	+	1.48911i	−1.17179	+	0.267453i	−0.408038	+	0.912965i	$0.633787\pi$
$32$	−2.01877	+	4.19202i	−0.356872	+	0.741052i
$33$	−5.54892	+	2.67222i	−0.965943	+	0.465173i
$34$	−0.445042	−	1.94986i	−0.0763241	−	0.334398i
$35$	0.0549581	−	0.240787i	0.00928962	−	0.0407005i
$36$	−2.34601	−	1.12978i	−0.391002	−	0.188297i
$37$	−3.86147	+	3.07942i	−0.634821	+	0.506253i	−0.887206	−	0.461374i	$-0.847357\pi$
$37$	−3.86147	+	3.07942i	−0.634821	+	0.506253i	0.252385	+	0.967627i	$0.418785\pi$
$38$	−0.653989	−	0.820077i	−0.106091	−	0.133034i
$39$	3.05841	+	6.35086i	0.489738	+	1.01695i
$40$	0.915458	+	0.730054i	0.144747	+	0.115432i
$41$		−	3.10992i		−	0.485687i	−0.970065	−	0.242844i	$-0.921920\pi$
$41$		−	3.10992i		−	0.485687i	0.970065	−	0.242844i	$-0.0780802\pi$
$42$	−0.123490	+	0.154851i	−0.0190549	+	0.0238941i
$43$	3.32042	+	0.757865i	0.506360	+	0.115573i	0.468066	−	0.883693i	$-0.344951\pi$
$43$	3.32042	+	0.757865i	0.506360	+	0.115573i	0.0382932	+	0.999267i	$0.487808\pi$
$44$	−8.67664	−	1.98039i	−1.30805	−	0.298554i
$45$	−0.623490	+	0.781831i	−0.0929444	+	0.116549i
$46$		−	1.02177i		−	0.150652i
$47$	5.03894	+	4.01842i	0.735004	+	0.586146i	0.917818	−	0.397001i	$-0.129949\pi$
$47$	5.03894	+	4.01842i	0.735004	+	0.586146i	−0.182814	+	0.983148i	$0.558521\pi$
$48$	1.54244	+	3.20291i	0.222632	+	0.462300i
$49$	−4.28501	−	5.37323i	−0.612145	−	0.767605i
$50$	−1.57311	+	1.25451i	−0.222471	+	0.177415i
$51$	−5.04892	−	2.43143i	−0.706990	−	0.340468i
$52$	−2.26659	+	9.93060i	−0.314320	+	1.37713i
$53$	1.04407	+	4.57438i	0.143414	+	0.628340i	0.994627	+	0.103519i	$0.0330104\pi$
$53$	1.04407	+	4.57438i	0.143414	+	0.628340i	−0.851213	+	0.524820i	$0.824132\pi$
$54$	2.22252	−	1.07031i	0.302447	−	0.145651i
$55$	−1.48297	+	3.07942i	−0.199963	+	0.415228i
$56$	−0.588735	+	0.134375i	−0.0786730	+	0.0179566i
$57$	−2.93900			−0.389280
$58$		0			0
$59$	−12.4940			−1.62657			−0.813287	−	0.581862i	$-0.802324\pi$
$59$	−12.4940			−1.62657			−0.813287	+	0.581862i	$0.802324\pi$
$60$	1.51597	−	0.346011i	0.195711	−	0.0446698i
$61$	−0.712916	+	1.48039i	−0.0912796	+	0.189544i	−0.941610	−	0.336705i	$-0.890688\pi$
$61$	−0.712916	+	1.48039i	−0.0912796	+	0.189544i	0.850331	+	0.526249i	$0.176402\pi$
$62$	2.68329	−	1.29221i	0.340778	−	0.164110i
$63$	−0.114761	−	0.502799i	−0.0144585	−	0.0633467i
$64$	−0.807979	+	3.53999i	−0.100997	+	0.442498i
$65$	3.52446	+	1.69729i	0.437155	+	0.210523i
$66$	2.14295	−	1.70895i	0.263779	−	0.210357i
$67$	1.44839	+	1.81623i	0.176950	+	0.221888i	0.862395	−	0.506237i	$-0.168964\pi$
$67$	1.44839	+	1.81623i	0.176950	+	0.221888i	−0.685445	+	0.728124i	$0.740392\pi$
$68$	−3.51352	−	7.29590i	−0.426077	−	0.884757i
$69$	−2.23833	−	1.78501i	−0.269464	−	0.214890i
$70$			0.109916i			0.0131375i
$71$	4.57338	−	5.73483i	0.542760	−	0.680599i	−0.432507	−	0.901631i	$-0.642371\pi$
$71$	4.57338	−	5.73483i	0.542760	−	0.680599i	0.975267	+	0.221031i	$0.0709423\pi$
$72$	2.38374	+	0.544073i	0.280926	+	0.0641196i
$73$	5.48460	+	1.25182i	0.641924	+	0.146515i	0.531078	−	0.847323i	$-0.321787\pi$
$73$	5.48460	+	1.25182i	0.641924	+	0.146515i	0.110845	+	0.993838i	$0.464644\pi$
$74$	1.37047	−	1.71851i	0.159314	−	0.199773i
$75$			5.63773i			0.650989i
$76$	−3.32042	−	2.64795i	−0.380879	−	0.303741i
$77$	−0.764811	−	1.58815i	−0.0871583	−	0.180986i
$78$	−1.95593	−	2.45265i	−0.221465	−	0.277708i
$79$	3.64715	−	2.90850i	0.410336	−	0.327232i	−0.396471	−	0.918047i	$-0.629765\pi$
$79$	3.64715	−	2.90850i	0.410336	−	0.327232i	0.806807	+	0.590815i	$0.201194\pi$
$80$	1.77748	+	0.855989i	0.198728	+	0.0957025i
$81$	0.573376	−	2.51212i	0.0637084	−	0.279125i
$82$	0.307979	+	1.34934i	0.0340105	+	0.149010i
$83$	−4.01357	+	1.93284i	−0.440547	+	0.212156i	−0.640990	−	0.767549i	$-0.721476\pi$
$83$	−4.01357	+	1.93284i	−0.440547	+	0.212156i	0.200443	+	0.979705i	$0.435762\pi$
$84$	−0.347948	+	0.722521i	−0.0379642	+	0.0788335i
$85$	−3.03194	+	0.692021i	−0.328861	+	0.0750603i
$86$	−1.51573			−0.163445
$87$		0			0
$88$	8.35690			0.890848
$89$	−5.53753	+	1.26391i	−0.586977	+	0.133974i	−0.505687	−	0.862717i	$-0.668761\pi$
$89$	−5.53753	+	1.26391i	−0.586977	+	0.133974i	−0.0812898	+	0.996691i	$0.525904\pi$
$90$	0.193096	−	0.400969i	0.0203542	−	0.0422658i
$91$	−1.81767	+	0.875342i	−0.190543	+	0.0917608i
$92$	−0.920583	−	4.03334i	−0.0959774	−	0.420505i
$93$	1.85690	−	8.13559i	0.192551	−	0.843622i
$94$	−2.58426	−	1.24451i	−0.266546	−	0.128362i
$95$	−1.27518	+	1.01693i	−0.130831	+	0.104334i
$96$	−3.61745	−	4.53614i	−0.369204	−	0.462968i
$97$	−0.0783611	−	0.162718i	−0.00795636	−	0.0165216i	0.896953	−	0.442126i	$-0.145776\pi$
$97$	−0.0783611	−	0.162718i	−0.00795636	−	0.0165216i	−0.904909	+	0.425605i	$0.860061\pi$
$98$	2.39131	+	1.90701i	0.241559	+	0.192637i
$99$			7.13706i			0.717302i
$100$	−5.07942	+	6.36939i	−0.507942	+	0.636939i
$101$	−3.14855	−	0.718636i	−0.313292	−	0.0715070i	0.0629836	−	0.998015i	$-0.479938\pi$
$101$	−3.14855	−	0.718636i	−0.313292	−	0.0715070i	−0.376276	+	0.926508i	$0.622796\pi$
$102$	2.43143	+	0.554958i	0.240747	+	0.0549490i
$103$	−8.51238	+	10.6742i	−0.838749	+	1.05176i	0.159168	+	0.987252i	$0.449119\pi$
$103$	−8.51238	+	10.6742i	−0.838749	+	1.05176i	−0.997917	+	0.0645070i	$0.979453\pi$
$104$		−	9.56465i		−	0.937891i
$105$	0.240787	+	0.192021i	0.0234984	+	0.0187394i
$106$	−0.906013	−	1.88135i	−0.0879997	−	0.182733i
$107$	10.1283	+	12.7005i	0.979143	+	1.22781i	0.973703	+	0.227821i	$0.0731602\pi$
$107$	10.1283	+	12.7005i	0.979143	+	1.22781i	0.00544006	+	0.999985i	$0.498268\pi$
$108$	7.80887	−	6.22737i	0.751409	−	0.599229i
$109$	4.92543	+	2.37196i	0.471770	+	0.227193i	0.654634	−	0.755946i	$-0.272823\pi$
$109$	4.92543	+	2.37196i	0.471770	+	0.227193i	−0.182864	+	0.983138i	$0.558537\pi$
$110$	0.338478	−	1.48297i	0.0322726	−	0.141396i
$111$	−1.37047	−	6.00442i	−0.130079	−	0.569914i
$112$	−0.916698	+	0.441459i	−0.0866199	+	0.0417139i
$113$	4.63152	−	9.61745i	0.435697	−	0.904733i	−0.561324	−	0.827596i	$-0.689708\pi$
$113$	4.63152	−	9.61745i	0.435697	−	0.904733i	0.997020	−	0.0771372i	$-0.0245780\pi$
$114$	1.27518	−	0.291053i	0.119432	−	0.0272596i
$115$	−1.58881			−0.148157
$116$		0			0
$117$	8.16852			0.755180
$118$	5.42093	−	1.23729i	0.499037	−	0.113902i
$119$	0.695895	−	1.44504i	0.0637926	−	0.132467i
$120$	−1.31551	+	0.633517i	−0.120089	+	0.0578319i
$121$	2.98039	+	13.0579i	0.270944	+	1.18708i
$122$	0.162718	−	0.712916i	0.0147318	−	0.0645444i
$123$	3.49396	+	1.68260i	0.315040	+	0.151715i
$124$	9.42780	−	7.51842i	0.846641	−	0.675174i
$125$	4.10806	+	5.15134i	0.367436	+	0.460750i
$126$	0.0995855	+	0.206791i	0.00887178	+	0.0184224i
$127$	−0.810631	−	0.646457i	−0.0719319	−	0.0573637i	0.586864	−	0.809686i	$-0.300362\pi$
$127$	−0.810631	−	0.646457i	−0.0719319	−	0.0573637i	−0.658796	+	0.752322i	$0.728934\pi$
$128$		−	10.9215i		−	0.965337i
$129$	−2.64795	+	3.32042i	−0.233139	+	0.292347i
$130$	−1.69729	−	0.387395i	−0.148862	−	0.0339768i
$131$	7.82065	+	1.78501i	0.683293	+	0.155957i	0.550057	−	0.835127i	$-0.314606\pi$
$131$	7.82065	+	1.78501i	0.683293	+	0.155957i	0.133236	+	0.991084i	$0.457463\pi$
$132$	6.91939	−	8.67664i	0.602255	−	0.755204i
$133$		−	0.841166i		−	0.0729384i
$134$	−0.808298	−	0.644596i	−0.0698263	−	0.0556846i
$135$	−1.66429	−	3.45593i	−0.143239	−	0.297439i
$136$	4.74094	+	5.94495i	0.406532	+	0.509775i
$137$	−13.4729	+	10.7443i	−1.15107	+	0.917947i	−0.997533	−	0.0701964i	$-0.977637\pi$
$137$	−13.4729	+	10.7443i	−1.15107	+	0.917947i	−0.153536	+	0.988143i	$0.549066\pi$
$138$	1.14795	+	0.552823i	0.0977199	+	0.0470594i
$139$	3.70895	−	16.2500i	0.314589	−	1.37830i	−0.532310	−	0.846550i	$-0.678676\pi$
$139$	3.70895	−	16.2500i	0.314589	−	1.37830i	0.846899	−	0.531754i	$-0.178467\pi$
$140$	0.0990311	+	0.433884i	0.00836966	+	0.0366699i
$141$	−7.24094	+	3.48705i	−0.609797	+	0.293663i
$142$	−1.41639	+	2.94116i	−0.118861	+	0.246816i
$143$	27.2192	−	6.21260i	2.27618	−	0.519523i
$144$	4.11960			0.343300
$145$		0			0
$146$	−2.50365			−0.207203
$147$	8.35516	−	1.90701i	0.689122	−	0.157288i
$148$	3.86147	−	8.01842i	0.317411	−	0.659110i
$149$	16.7642	−	8.07321i	1.37338	−	0.661383i	0.405800	−	0.913962i	$-0.366993\pi$
$149$	16.7642	−	8.07321i	1.37338	−	0.661383i	0.967576	+	0.252578i	$0.0812785\pi$
$150$	−0.558311	−	2.44612i	−0.0455859	−	0.199725i
$151$	−1.67510	+	7.33907i	−0.136317	+	0.597245i	0.859909	+	0.510448i	$0.170520\pi$
$151$	−1.67510	+	7.33907i	−0.136317	+	0.597245i	−0.996226	+	0.0867973i	$0.972337\pi$
$152$	3.59299	+	1.73029i	0.291430	+	0.140345i
$153$	−5.07718	+	4.04892i	−0.410466	+	0.327336i
$154$	0.489115	+	0.613331i	0.0394140	+	0.0494236i
$155$	−2.00933	−	4.17241i	−0.161393	−	0.335136i
$156$	−9.93060	−	7.91939i	−0.795084	−	0.634058i
$157$			18.2392i			1.45565i	0.685764	+	0.727824i	$0.259468\pi$
$157$			18.2392i			1.45565i	−0.685764	+	0.727824i	$0.740532\pi$
$158$	−1.29440	+	1.62313i	−0.102977	+	0.129129i
$159$	−5.70416	−	1.30194i	−0.452369	−	0.103250i
$160$	−3.13910	−	0.716480i	−0.248168	−	0.0566427i
$161$	0.510885	−	0.640630i	0.0402634	−	0.0504887i
$162$			1.14675i			0.0900973i
$163$	−9.88291	−	7.88135i	−0.774089	−	0.617315i	0.154684	−	0.987964i	$-0.450564\pi$
$163$	−9.88291	−	7.88135i	−0.774089	−	0.617315i	−0.928773	+	0.370649i	$0.879135\pi$
$164$	2.43143	+	5.04892i	0.189863	+	0.394254i
$165$	−2.65734	−	3.33220i	−0.206874	−	0.259411i
$166$	1.55001	−	1.23609i	0.120304	−	0.0959395i
$167$	−0.717677	−	0.345615i	−0.0555355	−	0.0267445i	0.405910	−	0.913913i	$-0.366955\pi$
$167$	−0.717677	−	0.345615i	−0.0555355	−	0.0267445i	−0.461445	+	0.887169i	$0.652669\pi$
$168$	0.167563	−	0.734141i	0.0129278	−	0.0566402i
$169$	−4.21768	−	18.4788i	−0.324437	−	1.42145i
$170$	1.24698	−	0.600514i	0.0956390	−	0.0460573i
$171$	−1.47773	+	3.06853i	−0.113005	+	0.234656i
$172$	−5.98319	+	1.36563i	−0.456214	+	0.104128i
$173$	9.15346			0.695924			0.347962	−	0.937509i	$-0.386874\pi$
$173$	9.15346			0.695924			0.347962	+	0.937509i	$0.386874\pi$
$174$		0			0
$175$	−1.61356			−0.121974
$176$	13.7274	−	3.13318i	1.03474	−	0.236172i
$177$	6.75978	−	14.0368i	0.508096	−	1.05507i
$178$	2.27748	−	1.09678i	0.170704	−	0.0822068i
$179$	0.757865	+	3.32042i	0.0566455	+	0.248180i	0.995321	−	0.0966211i	$-0.0308035\pi$
$179$	0.757865	+	3.32042i	0.0566455	+	0.248180i	−0.938676	+	0.344801i	$0.887946\pi$
$180$	0.400969	−	1.75676i	0.0298865	−	0.130941i
$181$	−11.4194	−	5.49929i	−0.848796	−	0.408759i	−0.0416657	−	0.999132i	$-0.513266\pi$
$181$	−11.4194	−	5.49929i	−0.848796	−	0.408759i	−0.807131	+	0.590373i	$0.798981\pi$
$182$	0.701970	−	0.559802i	0.0520335	−	0.0414953i
$183$	−1.27748	−	1.60191i	−0.0944340	−	0.118416i
$184$	1.68551	+	3.50000i	0.124258	+	0.258023i
$185$	−2.67222	−	2.13102i	−0.196465	−	0.156676i
$186$			3.71379i			0.272308i
$187$	−13.8388	+	17.3533i	−1.01199	+	1.26900i
$188$	−11.3224	−	2.58426i	−0.825770	−	0.188477i
$189$	1.92863	+	0.440198i	0.140287	+	0.0320197i
$190$	0.452575	−	0.567511i	0.0328332	−	0.0411715i
$191$		−	10.6703i		−	0.772072i	−0.922484	−	0.386036i	$-0.873844\pi$
$191$		−	10.6703i		−	0.772072i	0.922484	−	0.386036i	$-0.126156\pi$
$192$	−3.53999	−	2.82304i	−0.255476	−	0.203736i
$193$	−9.86168	−	20.4780i	−0.709859	−	1.47404i	−0.873146	−	0.487459i	$-0.837924\pi$
$193$	−9.86168	−	20.4780i	−0.709859	−	1.47404i	0.163286	−	0.986579i	$-0.447791\pi$
$194$	0.0501138	+	0.0628407i	0.00359796	+	0.00451170i
$195$	−3.81378	+	3.04138i	−0.273110	+	0.217798i
$196$	11.1576	+	5.37323i	0.796974	+	0.383802i
$197$	4.35205	−	19.0676i	0.310071	−	1.35851i	−0.544320	−	0.838878i	$-0.683212\pi$
$197$	4.35205	−	19.0676i	0.310071	−	1.35851i	0.854391	−	0.519631i	$-0.173931\pi$
$198$	−0.706791	−	3.09666i	−0.0502295	−	0.220070i
$199$	0.788364	−	0.379656i	0.0558857	−	0.0269131i	−0.405732	−	0.913992i	$-0.632983\pi$
$199$	0.788364	−	0.379656i	0.0558857	−	0.0269131i	0.461618	+	0.887079i	$0.347269\pi$
$200$	3.31913	−	6.89224i	0.234698	−	0.487355i
$201$	−2.82416	+	0.644596i	−0.199201	+	0.0454663i
$202$	1.43727			0.101126
$203$		0			0
$204$	10.0978			0.706990
$205$	2.09817	−	0.478894i	0.146543	−	0.0334474i
$206$	2.63631	−	5.47434i	0.183680	−	0.381416i
$207$	−2.98911	+	1.43948i	−0.207758	+	0.100051i
$208$	−3.58599	−	15.7112i	−0.248644	−	1.08938i
$209$	−2.59030	+	11.3489i	−0.179175	+	0.785017i
$210$	−0.123490	−	0.0594696i	−0.00852161	−	0.00410379i
$211$	−14.2831	+	11.3904i	−0.983288	+	0.784146i	−0.976431	−	0.215830i	$-0.930754\pi$
$211$	−14.2831	+	11.3904i	−0.983288	+	0.784146i	−0.00685718	+	0.999976i	$0.502183\pi$
$212$	−5.27144	−	6.61017i	−0.362044	−	0.453989i
$213$	3.96863	+	8.24094i	0.271926	+	0.564660i
$214$	−5.65227	−	4.50753i	−0.386381	−	0.308129i
$215$			2.35690i			0.160739i
$216$	−5.84750	+	7.33254i	−0.397872	+	0.498916i
$217$	2.32847	+	0.531459i	0.158067	+	0.0360778i
$218$	−2.37196	−	0.541385i	−0.160649	−	0.0366672i
$219$	−4.37382	+	5.48460i	−0.295555	+	0.370615i
$220$		−	6.15883i		−	0.415228i
$221$	19.8612	+	15.8388i	1.33601	+	1.06543i
$222$	1.18925	+	2.46950i	0.0798172	+	0.165742i
$223$	−1.13371	−	1.42163i	−0.0759189	−	0.0951993i	0.742422	−	0.669933i	$-0.233677\pi$
$223$	−1.13371	−	1.42163i	−0.0759189	−	0.0951993i	−0.818341	+	0.574734i	$0.805106\pi$
$224$	1.29828	−	1.03534i	0.0867450	−	0.0691768i
$225$	5.88620	+	2.83464i	0.392413	+	0.188976i
$226$	−1.05711	+	4.63152i	−0.0703182	+	0.308084i
$227$	3.08330	+	13.5088i	0.204646	+	0.896612i	0.968063	+	0.250707i	$0.0806630\pi$
$227$	3.08330	+	13.5088i	0.204646	+	0.896612i	−0.763417	+	0.645906i	$0.776480\pi$
$228$	4.77144	−	2.29780i	0.315996	−	0.152176i
$229$	5.54174	−	11.5075i	0.366208	−	0.760439i	−0.633706	−	0.773574i	$-0.718467\pi$
$229$	5.54174	−	11.5075i	0.366208	−	0.760439i	0.999914	+	0.0131352i	$0.00418118\pi$
$230$	0.689359	−	0.157342i	0.0454550	−	0.0103748i
$231$	2.19806			0.144622
$232$		0			0
$233$	−8.86592			−0.580826			−0.290413	−	0.956901i	$-0.593793\pi$
$233$	−8.86592			−0.580826			−0.290413	+	0.956901i	$0.593793\pi$
$234$	−3.54419	+	0.808938i	−0.231691	+	0.0528819i
$235$	−1.93517	+	4.01842i	−0.126236	+	0.262133i
$236$	20.2838	−	9.76817i	1.32036	−	0.635854i
$237$	1.29440	+	5.67116i	0.0840806	+	0.368381i
$238$	−0.158834	+	0.695895i	−0.0102957	+	0.0451082i
$239$	23.0330	+	11.0921i	1.48988	+	0.717487i	0.988984	−	0.148022i	$-0.0472905\pi$
$239$	23.0330	+	11.0921i	1.48988	+	0.717487i	0.500894	+	0.865509i	$0.333005\pi$
$240$	−1.92339	+	1.53385i	−0.124154	+	0.0990097i
$241$	−6.06734	−	7.60820i	−0.390831	−	0.490087i	0.547022	−	0.837118i	$-0.315761\pi$
$241$	−6.06734	−	7.60820i	−0.390831	−	0.490087i	−0.937854	+	0.347031i	$0.887190\pi$
$242$	−2.58628	−	5.37047i	−0.166252	−	0.345227i
$243$	−10.4887	−	8.36443i	−0.672848	−	0.536578i
$244$		−	2.96077i		−	0.189544i
$245$	2.96532	−	3.71839i	0.189447	−	0.237559i
$246$	−1.68260	−	0.384043i	−0.107279	−	0.0244857i
$247$	12.9890	+	2.96466i	0.826471	+	0.188637i
$248$	−7.05980	+	8.85271i	−0.448298	+	0.562148i
$249$		−	5.55496i		−	0.352031i
$250$	−2.29256	−	1.82826i	−0.144994	−	0.115629i
$251$	4.23484	+	8.79374i	0.267301	+	0.555056i	0.990810	−	0.135258i	$-0.0431865\pi$
$251$	4.23484	+	8.79374i	0.267301	+	0.555056i	−0.723509	+	0.690314i	$0.757472\pi$
$252$	0.579417	+	0.726566i	0.0364998	+	0.0457693i
$253$	−8.86553	+	7.07002i	−0.557371	+	0.444489i
$254$	0.415739	+	0.200209i	0.0260858	+	0.0125622i
$255$	0.862937	−	3.78077i	0.0540392	−	0.236761i
$256$	−0.534384	−	2.34129i	−0.0333990	−	0.146331i
$257$	−14.7371	+	7.09699i	−0.919272	+	0.442698i	−0.832811	−	0.553557i	$-0.813270\pi$
$257$	−14.7371	+	7.09699i	−0.919272	+	0.442698i	−0.0864609	+	0.996255i	$0.527556\pi$
$258$	0.820077	−	1.70291i	0.0510557	−	0.106018i
$259$	1.71851	−	0.392240i	0.106783	−	0.0243726i
$260$	−7.04892			−0.437155
$261$		0			0
$262$	−3.57002			−0.220557
$263$	23.1287	−	5.27897i	1.42618	−	0.325515i	0.561346	−	0.827581i	$-0.310284\pi$
$263$	23.1287	−	5.27897i	1.42618	−	0.325515i	0.864829	+	0.502066i	$0.167426\pi$
$264$	−4.52145	+	9.38889i	−0.278276	+	0.577846i
$265$	−2.92543	+	1.40881i	−0.179708	+	0.0865426i
$266$	0.0833017	+	0.364968i	0.00510755	+	0.0223776i
$267$	1.57606	−	6.90519i	0.0964536	−	0.422591i
$268$	−3.77144	−	1.81623i	−0.230377	−	0.110944i
$269$	19.8229	−	15.8083i	1.20863	−	0.963847i	0.208726	−	0.977974i	$-0.433068\pi$
$269$	19.8229	−	15.8083i	1.20863	−	0.963847i	0.999900	+	0.0141266i	$0.00449679\pi$
$270$	1.06435	+	1.33465i	0.0647744	+	0.0812245i
$271$	−0.522153	−	1.08426i	−0.0317185	−	0.0658642i	0.884508	−	0.466526i	$-0.154495\pi$
$271$	−0.522153	−	1.08426i	−0.0317185	−	0.0658642i	−0.916226	+	0.400662i	$0.868780\pi$
$272$	10.0165	+	7.98792i	0.607342	+	0.484339i
$273$		−	2.51573i		−	0.152259i
$274$	4.78166	−	5.99601i	0.288871	−	0.362232i
$275$	21.7699	+	4.96884i	1.31277	+	0.299632i
$276$	5.02949	+	1.14795i	0.302740	+	0.0690984i
$277$	6.64944	−	8.33813i	0.399526	−	0.500990i	−0.540853	−	0.841117i	$-0.681899\pi$
$277$	6.64944	−	8.33813i	0.399526	−	0.500990i	0.940380	+	0.340127i	$0.110470\pi$
$278$			7.41789i			0.444896i
$279$	−7.56051	−	6.02930i	−0.452636	−	0.360965i
$280$	−0.181318	−	0.376510i	−0.0108358	−	0.0225008i
$281$	−10.1501	−	12.7278i	−0.605504	−	0.759279i	0.380720	−	0.924690i	$-0.375676\pi$
$281$	−10.1501	−	12.7278i	−0.605504	−	0.759279i	−0.986225	+	0.165412i	$0.947105\pi$
$282$	2.79640	−	2.23005i	0.166523	−	0.132798i
$283$	−4.72737	−	2.27658i	−0.281013	−	0.135329i	0.288069	−	0.957610i	$-0.406987\pi$
$283$	−4.72737	−	2.27658i	−0.281013	−	0.135329i	−0.569081	+	0.822281i	$0.692701\pi$
$284$	−2.94116	+	12.8861i	−0.174526	+	0.764646i
$285$	−0.452575	−	1.98286i	−0.0268082	−	0.117454i
$286$	−11.1947	+	5.39109i	−0.661957	+	0.318782i
$287$	−0.481575	+	1.00000i	−0.0284265	+	0.0590281i
$288$	−6.55491	+	1.49612i	−0.386252	+	0.0881594i
$289$	−3.19567			−0.187981
$290$		0			0
$291$	0.225209			0.0132020
$292$	−9.88291	+	2.25571i	−0.578353	+	0.132005i
$293$	2.93469	−	6.09395i	0.171447	−	0.356012i	−0.797486	−	0.603337i	$-0.793837\pi$
$293$	2.93469	−	6.09395i	0.171447	−	0.356012i	0.968933	+	0.247325i	$0.0795515\pi$
$294$	−3.43631	+	1.65484i	−0.200410	+	0.0965123i
$295$	−1.92394	−	8.42931i	−0.112016	−	0.490774i
$296$	−1.85958	+	8.14737i	−0.108086	+	0.473556i
$297$	−24.6652	−	11.8781i	−1.43122	−	0.689238i
$298$	−6.47421	+	5.16301i	−0.375041	+	0.299085i
$299$	8.09179	+	10.1468i	0.467961	+	0.586804i
$300$	−4.40775	−	9.15279i	−0.254482	−	0.528437i
$301$	−0.950332	−	0.757865i	−0.0547762	−	0.0436826i
$302$		−	3.35019i		−	0.192782i
$303$	2.51089	−	3.14855i	0.144247	−	0.180879i
$304$	6.55070	+	1.49516i	0.375709	+	0.0857531i
$305$	−1.10855	−	0.253020i	−0.0634757	−	0.0144879i
$306$	1.80194	−	2.25956i	0.103010	−	0.129170i
$307$			4.51812i			0.257863i	0.991654	+	0.128931i	$0.0411547\pi$
$307$			4.51812i			0.257863i	−0.991654	+	0.128931i	$0.958845\pi$
$308$	2.48333	+	1.98039i	0.141501	+	0.112843i
$309$	−7.38676	−	15.3388i	−0.420218	−	0.872592i
$310$	1.28501	+	1.61135i	0.0729838	+	0.0915187i
$311$	9.86401	−	7.86629i	0.559337	−	0.446056i	−0.302567	−	0.953128i	$-0.597844\pi$
$311$	9.86401	−	7.86629i	0.559337	−	0.446056i	0.861904	+	0.507072i	$0.169272\pi$
$312$	10.7458	+	5.17490i	0.608360	+	0.292971i
$313$	−4.28136	+	18.7579i	−0.241997	+	1.06026i	0.697199	+	0.716877i	$0.254429\pi$
$313$	−4.28136	+	18.7579i	−0.241997	+	1.06026i	−0.939196	+	0.343381i	$0.888428\pi$
$314$	−1.80625	−	7.91370i	−0.101933	−	0.446596i
$315$	0.321552	−	0.154851i	0.0181174	−	0.00872488i
$316$	−3.64715	+	7.57338i	−0.205168	+	0.426036i
$317$	−2.79640	+	0.638260i	−0.157061	+	0.0358482i	−0.300329	−	0.953836i	$-0.597096\pi$
$317$	−2.79640	+	0.638260i	−0.157061	+	0.0358482i	0.143267	+	0.989684i	$0.454239\pi$
$318$	2.60388			0.146018
$319$		0			0
$320$	−2.51275			−0.140467
$321$	−19.7488	+	4.50753i	−1.10227	+	0.251586i
$322$	−0.158222	+	0.328552i	−0.00881739	+	0.0183095i
$323$	−9.54288	+	4.59561i	−0.530980	+	0.255706i
$324$	1.03319	+	4.52669i	0.0573993	+	0.251483i
$325$	5.68694	−	24.9161i	0.315455	−	1.38210i
$326$	5.06853	+	2.44088i	0.280720	+	0.135188i
$327$	−5.32975	+	4.25033i	−0.294736	+	0.235044i
$328$	−3.28083	−	4.11403i	−0.181154	−	0.227159i
$329$	−0.998023	−	2.07242i	−0.0550228	−	0.114256i
$330$	1.48297	+	1.18263i	0.0816348	+	0.0651015i
$331$		−	3.13408i		−	0.172265i	−0.996284	−	0.0861323i	$-0.972549\pi$
$331$		−	3.13408i		−	0.172265i	0.996284	−	0.0861323i	$-0.0274508\pi$
$332$	5.00484	−	6.27588i	0.274677	−	0.344433i
$333$	−6.95812	−	1.58815i	−0.381303	−	0.0870299i
$334$	0.345615	+	0.0788843i	0.0189112	+	0.00431636i
$335$	−1.00232	+	1.25687i	−0.0547626	+	0.0686701i
$336$		−	1.26875i		−	0.0692160i
$337$	−3.89551	−	3.10656i	−0.212202	−	0.169225i	0.511621	−	0.859211i	$-0.329045\pi$
$337$	−3.89551	−	3.10656i	−0.212202	−	0.169225i	−0.723823	+	0.689986i	$0.757617\pi$
$338$	3.65996	+	7.59999i	0.199076	+	0.413385i
$339$	8.29925	+	10.4069i	0.450753	+	0.565227i
$340$	4.38129	−	3.49396i	0.237609	−	0.189487i
$341$	−29.7787	−	14.3407i	−1.61261	−	0.776591i
$342$	0.337282	−	1.47773i	0.0182381	−	0.0799063i
$343$	1.10172	+	4.82695i	0.0594873	+	0.260631i
$344$	5.19202	−	2.50035i	0.279935	−	0.134810i
$345$	0.859616	−	1.78501i	0.0462802	−	0.0961018i
$346$	−3.97154	+	0.906477i	−0.213511	+	0.0487325i
$347$	−20.1172			−1.07995			−0.539974	−	0.841682i	$-0.681566\pi$
$347$	−20.1172			−1.07995			−0.539974	+	0.841682i	$0.681566\pi$
$348$		0			0
$349$	20.4892			1.09676			0.548380	−	0.836229i	$-0.315245\pi$
$349$	20.4892			1.09676			0.548380	+	0.836229i	$0.315245\pi$
$350$	0.700099	−	0.159793i	0.0374219	−	0.00854130i
$351$	−13.5948	+	28.2298i	−0.725635	+	1.50680i
$352$	−20.7044	+	9.97071i	−1.10355	+	0.531441i
$353$	4.00484	+	17.5464i	0.213156	+	0.933899i	0.962407	+	0.271612i	$0.0875568\pi$
$353$	4.00484	+	17.5464i	0.213156	+	0.933899i	−0.749250	+	0.662287i	$0.769586\pi$
$354$	−1.54288	+	6.75978i	−0.0820030	+	0.359278i
$355$	4.57338	+	2.20242i	0.242730	+	0.116892i
$356$	8.00197	−	6.38135i	0.424103	−	0.338211i
$357$	1.24698	+	1.56366i	0.0659972	+	0.0827578i
$358$	−0.657650	−	1.36563i	−0.0347579	−	0.0721755i
$359$	18.4736	+	14.7322i	0.975000	+	0.777536i	0.974941	−	0.222464i	$-0.0714099\pi$
$359$	18.4736	+	14.7322i	0.975000	+	0.777536i	5.86917e−5		1.00000i	$0.499981\pi$
$360$			1.69202i			0.0891774i
$361$	8.38285	−	10.5118i	0.441202	−	0.553250i
$362$	5.49929	+	1.25518i	0.289036	+	0.0659706i
$363$	−16.2830	−	3.71648i	−0.854634	−	0.195065i
$364$	2.26659	−	2.84222i	0.118802	−	0.148973i
$365$			3.89307i			0.203772i
$366$	0.712916	+	0.568532i	0.0372647	+	0.0297176i
$367$	12.8617	+	26.7075i	0.671373	+	1.39412i	0.906521	+	0.422161i	$0.138728\pi$
$367$	12.8617	+	26.7075i	0.671373	+	1.39412i	−0.235148	+	0.971960i	$0.575557\pi$
$368$	4.08091	+	5.11730i	0.212732	+	0.266758i
$369$	3.51352	−	2.80194i	0.182906	−	0.145863i
$370$	1.37047	+	0.659983i	0.0712473	+	0.0343109i
$371$	0.372625	−	1.63258i	0.0193457	−	0.0847592i
$372$	3.34601	+	14.6598i	0.173483	+	0.760077i
$373$	22.6935	−	10.9286i	1.17503	−	0.565862i	0.258567	−	0.965993i	$-0.416750\pi$
$373$	22.6935	−	10.9286i	1.17503	−	0.565862i	0.916458	+	0.400131i	$0.131035\pi$
$374$	4.28590	−	8.89977i	0.221619	−	0.460196i
$375$	−8.01012	+	1.82826i	−0.413641	+	0.0944108i
$376$	10.9051			0.562390
$377$		0			0
$378$	−0.880395			−0.0452826
$379$	−26.2325	+	5.98739i	−1.34747	+	0.307551i	−0.834572	−	0.550898i	$-0.814285\pi$
$379$	−26.2325	+	5.98739i	−1.34747	+	0.307551i	−0.512898	+	0.858450i	$0.671428\pi$
$380$	1.27518	−	2.64795i	0.0654156	−	0.135837i
$381$	1.16487	−	0.560974i	0.0596783	−	0.0287396i
$382$	1.05669	+	4.62965i	0.0540648	+	0.236873i
$383$	−4.37681	+	19.1760i	−0.223644	+	0.979850i	0.731065	+	0.682308i	$0.239024\pi$
$383$	−4.37681	+	19.1760i	−0.223644	+	0.979850i	−0.954709	+	0.297542i	$0.903833\pi$
$384$	12.2702	+	5.90904i	0.626163	+	0.301544i
$385$	0.953703	−	0.760553i	0.0486052	−	0.0387614i
$386$	6.30678	+	7.90845i	0.321007	+	0.402530i
$387$	2.13538	+	4.43416i	0.108547	+	0.225401i
$388$	0.254437	+	0.202907i	0.0129171	+	0.0103010i
$389$		−	24.8552i		−	1.26021i	−0.776511	−	0.630103i	$-0.783012\pi$
$389$		−	24.8552i		−	1.26021i	0.776511	−	0.630103i	$-0.216988\pi$
$390$	1.35354	−	1.69729i	0.0685393	−	0.0859456i
$391$	−10.0590	−	2.29590i	−0.508705	−	0.116108i
$392$	−11.3371	−	2.58761i	−0.572609	−	0.130694i
$393$	−6.23676	+	7.82065i	−0.314603	+	0.394499i
$394$			8.70410i			0.438506i
$395$	2.52390	+	2.01275i	0.126991	+	0.101272i
$396$	−5.57998	−	11.5869i	−0.280405	−	0.582266i
$397$	−2.49061	−	3.12312i	−0.125000	−	0.156745i	0.715393	−	0.698722i	$-0.246247\pi$
$397$	−2.49061	−	3.12312i	−0.125000	−	0.156745i	−0.840393	+	0.541977i	$0.817676\pi$
$398$	−0.304461	+	0.242799i	−0.0152612	+	0.0121704i
$399$	0.945042	+	0.455108i	0.0473113	+	0.0227839i
$400$	2.86808	−	12.5659i	0.143404	−	0.628293i
$401$	5.54234	+	24.2826i	0.276771	+	1.21261i	0.901849	+	0.432052i	$0.142210\pi$
$401$	5.54234	+	24.2826i	0.276771	+	1.21261i	−0.625077	+	0.780563i	$0.714933\pi$
$402$	1.16152	−	0.559360i	0.0579315	−	0.0278983i
$403$	−16.4132	+	34.0824i	−0.817601	+	1.69777i
$404$	5.67349	−	1.29494i	0.282267	−	0.0644255i
$405$	1.78315			0.0886055
$406$		0			0
$407$	−24.3937			−1.20915
$408$	−9.24415	+	2.10992i	−0.457653	+	0.104456i
$409$	0.122886	−	0.255176i	0.00607634	−	0.0126177i	−0.897909	−	0.440182i	$-0.854914\pi$
$409$	0.122886	−	0.255176i	0.00607634	−	0.0126177i	0.903985	+	0.427564i	$0.140628\pi$
$410$	−0.862937	+	0.415568i	−0.0426174	+	0.0205235i
$411$	−4.78166	−	20.9498i	−0.235862	−	1.03338i
$412$	5.47434	−	23.9847i	0.269702	−	1.18164i
$413$	4.01746	+	1.93471i	0.197686	+	0.0952007i
$414$	1.15437	−	0.920583i	0.0567344	−	0.0452442i
$415$	−1.92208	−	2.41021i	−0.0943510	−	0.118312i
$416$	11.4117	+	23.6966i	0.559504	+	1.16182i
$417$	16.2500	+	12.9589i	0.795764	+	0.634601i
$418$		−	5.18060i		−	0.253392i
$419$	16.5154	−	20.7096i	0.806828	−	1.01173i	−0.192707	−	0.981256i	$-0.561727\pi$
$419$	16.5154	−	20.7096i	0.806828	−	1.01173i	0.999536	−	0.0304743i	$-0.00970176\pi$
$420$	−0.541044	−	0.123490i	−0.0264003	−	0.00602569i
$421$	−17.1413	−	3.91239i	−0.835415	−	0.190678i	−0.216645	−	0.976250i	$-0.569512\pi$
$421$	−17.1413	−	3.91239i	−0.835415	−	0.190678i	−0.618770	+	0.785572i	$0.712369\pi$
$422$	5.06920	−	6.35657i	0.246765	−	0.309433i
$423$			9.31336i			0.452831i
$424$	6.20696	+	4.94989i	0.301437	+	0.240388i
$425$	8.81551	+	18.3056i	0.427615	+	0.887951i
$426$	−2.53803	−	3.18259i	−0.122968	−	0.154197i
$427$	0.458479	−	0.365625i	0.0221874	−	0.0176938i
$428$	−26.3729	−	12.7005i	−1.27478	−	0.613903i
$429$	−7.74698	+	33.9417i	−0.374028	+	1.63872i
$430$	−0.233406	−	1.02262i	−0.0112558	−	0.0493151i
$431$	25.0426	−	12.0599i	1.20626	−	0.580905i	0.280807	−	0.959764i	$-0.409398\pi$
$431$	25.0426	−	12.0599i	1.20626	−	0.580905i	0.925454	+	0.378859i	$0.123684\pi$
$432$	−6.85620	+	14.2371i	−0.329869	+	0.684981i
$433$	−5.72830	+	1.30745i	−0.275284	+	0.0628318i	−0.357934	−	0.933747i	$-0.616519\pi$
$433$	−5.72830	+	1.30745i	−0.275284	+	0.0628318i	0.0826499	+	0.996579i	$0.473662\pi$
$434$	−1.06292			−0.0510217
$435$		0			0
$436$	−9.85086			−0.471770
$437$	−5.27552	+	1.20410i	−0.252362	+	0.0576001i
$438$	1.35458	−	2.81282i	0.0647245	−	0.134402i
$439$	−14.1821	+	6.82974i	−0.676875	+	0.325966i	−0.740546	−	0.672005i	$-0.765433\pi$
$439$	−14.1821	+	6.82974i	−0.676875	+	0.325966i	0.0636718	+	0.997971i	$0.479719\pi$
$440$	1.28687	+	5.63816i	0.0613492	+	0.268789i
$441$	2.20991	−	9.68223i	0.105234	−	0.461059i
$442$	−10.1860	−	4.90531i	−0.484498	−	0.233322i
$443$	5.26841	−	4.20141i	0.250310	−	0.199615i	−0.490295	−	0.871557i	$-0.663111\pi$
$443$	5.26841	−	4.20141i	0.250310	−	0.199615i	0.740604	+	0.671942i	$0.234539\pi$
$444$	6.91939	+	8.67664i	0.328380	+	0.411775i
$445$	−1.70544	−	3.54138i	−0.0808457	−	0.167878i
$446$	0.632684	+	0.504549i	0.0299585	+	0.0238911i
$447$			23.2024i			1.09743i
$448$	0.807979	−	1.01317i	0.0381734	−	0.0478679i
$449$	−12.0112	−	2.74147i	−0.566842	−	0.129378i	−0.0705106	−	0.997511i	$-0.522463\pi$
$449$	−12.0112	−	2.74147i	−0.566842	−	0.129378i	−0.496332	+	0.868133i	$0.665320\pi$
$450$	−2.83464	−	0.646989i	−0.133626	−	0.0304994i
$451$	9.57673	−	12.0088i	0.450951	−	0.565474i
$452$			19.2349i			0.904733i
$453$	−7.33907	−	5.85272i	−0.344820	−	0.274985i
$454$	−2.67559	−	5.55592i	−0.125572	−	0.260752i
$455$	−0.870469	−	1.09153i	−0.0408082	−	0.0511719i
$456$	−3.88793	+	3.10052i	−0.182069	+	0.145195i
$457$	12.3095	+	5.92793i	0.575813	+	0.277297i	0.699041	−	0.715082i	$-0.253610\pi$
$457$	12.3095	+	5.92793i	0.575813	+	0.277297i	−0.123228	+	0.992378i	$0.539325\pi$
$458$	−1.26487	+	5.54174i	−0.0591033	+	0.258948i
$459$	−5.54288	−	24.2849i	−0.258719	−	1.13352i
$460$	2.57942	−	1.24218i	0.120266	−	0.0579170i
$461$	−5.03660	+	10.4586i	−0.234578	+	0.487106i	−0.984714	−	0.174177i	$-0.944274\pi$
$461$	−5.03660	+	10.4586i	−0.234578	+	0.487106i	0.750136	+	0.661283i	$0.229988\pi$
$462$	−0.953703	+	0.217677i	−0.0443703	+	0.0101272i
$463$	7.24267			0.336595			0.168298	−	0.985736i	$-0.446173\pi$
$463$	7.24267			0.336595			0.168298	+	0.985736i	$0.446173\pi$
$464$		0			0
$465$	5.77479			0.267800
$466$	3.84678	−	0.878002i	0.178199	−	0.0406727i
$467$	−0.895272	+	1.85905i	−0.0414283	+	0.0860267i	−0.920656	−	0.390376i	$-0.872345\pi$
$467$	−0.895272	+	1.85905i	−0.0414283	+	0.0860267i	0.879227	+	0.476402i	$0.158059\pi$
$468$	−13.2615	+	6.38641i	−0.613014	+	0.295212i
$469$	−0.184489	−	0.808298i	−0.00851890	−	0.0373237i
$470$	0.441689	−	1.93517i	0.0203736	−	0.0892626i
$471$	−20.4916	−	9.86822i	−0.944202	−	0.454703i
$472$	−16.5280	+	13.1806i	−0.760761	+	0.606686i
$473$	10.4879	+	13.1514i	0.482235	+	0.604704i
$474$	−1.12324	−	2.33244i	−0.0515922	−	0.107132i
$475$	8.33102	+	6.64377i	0.382253	+	0.304837i
$476$			2.89008i			0.132467i
$477$	−4.22737	+	5.30095i	−0.193558	+	0.242714i
$478$	−11.0921	−	2.53170i	−0.507340	−	0.115797i
$479$	−3.79151	−	0.865388i	−0.173239	−	0.0395406i	0.135022	−	0.990843i	$-0.456890\pi$
$479$	−3.79151	−	0.865388i	−0.173239	−	0.0395406i	−0.308260	+	0.951302i	$0.599747\pi$
$480$	2.50335	−	3.13910i	0.114262	−	0.143280i
$481$			27.9191i			1.27300i
$482$	3.38597	+	2.70022i	0.154227	+	0.122992i
$483$	0.443330	+	0.920583i	0.0201722	+	0.0418880i
$484$	−15.0477	−	18.8692i	−0.683987	−	0.857693i
$485$	0.0977147	−	0.0779248i	0.00443699	−	0.00353839i
$486$	5.37920	+	2.59049i	0.244005	+	0.117507i
$487$	−2.19083	+	9.59863i	−0.0992758	+	0.434956i	0.900724	+	0.434392i	$0.143037\pi$
$487$	−2.19083	+	9.59863i	−0.0992758	+	0.434956i	−1.00000		0.000563841i	$0.999821\pi$
$488$	0.618645	+	2.71046i	0.0280048	+	0.122697i
$489$	14.2017	−	6.83918i	0.642224	−	0.309279i
$490$	−0.918367	+	1.90701i	−0.0414876	+	0.0861499i
$491$	−7.59584	+	1.73370i	−0.342796	+	0.0782409i	−0.390453	−	0.920623i	$-0.627682\pi$
$491$	−7.59584	+	1.73370i	−0.342796	+	0.0782409i	0.0476574	+	0.998864i	$0.484824\pi$
$492$	−6.98792			−0.315040
$493$		0			0
$494$	−5.92931			−0.266772
$495$	−4.81517	+	1.09903i	−0.216426	+	0.0493978i
$496$	−8.27763	+	17.1887i	−0.371676	+	0.771794i
$497$	−2.35862	+	1.13585i	−0.105799	+	0.0509500i
$498$	0.550114	+	2.41021i	0.0246512	+	0.108004i
$499$	−4.57620	+	20.0496i	−0.204859	+	0.897544i	0.763069	+	0.646317i	$0.223691\pi$
$499$	−4.57620	+	20.0496i	−0.204859	+	0.897544i	−0.967928	+	0.251228i	$0.919166\pi$
$500$	−10.6969	−	5.15134i	−0.478378	−	0.230375i
$501$	0.776589	−	0.619309i	0.0346955	−	0.0276687i
$502$	−2.70828	−	3.39608i	−0.120877	−	0.151574i
$503$	3.57299	+	7.41939i	0.159312	+	0.330814i	0.965311	−	0.261102i	$-0.0840859\pi$
$503$	3.57299	+	7.41939i	0.159312	+	0.330814i	−0.806000	+	0.591916i	$0.798372\pi$
$504$	−0.682246	−	0.544073i	−0.0303897	−	0.0242349i
$505$		−	2.23490i		−	0.0994517i
$506$	3.14646	−	3.94553i	0.139877	−	0.175400i
$507$	23.0427	+	5.25936i	1.02336	+	0.233576i
$508$	1.82147	+	0.415739i	0.0808147	+	0.0184454i
$509$	4.93565	−	6.18911i	0.218769	−	0.274327i	−0.660321	−	0.750983i	$-0.729580\pi$
$509$	4.93565	−	6.18911i	0.218769	−	0.274327i	0.879090	+	0.476656i	$0.158151\pi$
$510$			1.72587i			0.0764230i
$511$	−1.56974	−	1.25182i	−0.0694411	−	0.0553774i
$512$	9.94108	+	20.6429i	0.439338	+	0.912294i
$513$	−8.14526	−	10.2138i	−0.359622	−	0.450952i
$514$	5.69135	−	4.53870i	0.251034	−	0.200193i
$515$	−8.51238	−	4.09934i	−0.375100	−	0.180639i
$516$	1.70291	−	7.46092i	0.0749663	−	0.328449i
$517$	7.08330	+	31.0340i	0.311523	+	1.36487i
$518$	−0.706791	+	0.340373i	−0.0310546	+	0.0149551i
$519$	−4.95242	+	10.2838i	−0.217387	+	0.451409i
$520$	6.45299	−	1.47285i	0.282982	−	0.0645889i
$521$	3.52542			0.154451			0.0772257	−	0.997014i	$-0.475394\pi$
$521$	3.52542			0.154451			0.0772257	+	0.997014i	$0.475394\pi$
$522$		0			0
$523$	10.0301			0.438587			0.219294	−	0.975659i	$-0.429625\pi$
$523$	10.0301			0.438587			0.219294	+	0.975659i	$0.429625\pi$
$524$	−14.0923	+	3.21648i	−0.615626	+	0.140513i
$525$	0.873009	−	1.81282i	0.0381013	−	0.0791181i
$526$	−9.51238	+	4.58092i	−0.414759	+	0.199738i
$527$	−6.69202	−	29.3197i	−0.291509	−	1.27718i
$528$	−3.90701	+	17.1177i	−0.170031	+	0.744953i
$529$	15.9731	+	7.69226i	0.694485	+	0.334446i
$530$	1.12978	−	0.900969i	0.0490745	−	0.0391356i
$531$	−11.2567	−	14.1154i	−0.488498	−	0.612557i
$532$	0.657650	+	1.36563i	0.0285128	+	0.0592074i
$533$	−13.7444	−	10.9608i	−0.595335	−	0.474764i
$534$			3.15213i			0.136406i
$535$	−7.00902	+	8.78904i	−0.303027	+	0.379983i
$536$	3.83209	+	0.874650i	0.165521	+	0.0377791i
$537$	−4.14050	−	0.945042i	−0.178676	−	0.0407816i
$538$	−7.03534	+	8.82204i	−0.303315	+	0.380345i
$539$		−	33.9439i		−	1.46207i
$540$	5.40391	+	4.30947i	0.232547	+	0.185450i
$541$	−3.56832	−	7.40970i	−0.153414	−	0.318568i	0.810070	−	0.586333i	$-0.199429\pi$
$541$	−3.56832	−	7.40970i	−0.153414	−	0.318568i	−0.963484	+	0.267765i	$0.913715\pi$
$542$	0.333929	+	0.418734i	0.0143435	+	0.0179862i
$543$	12.3568	−	9.85421i	0.530280	−	0.422885i
$544$	−18.8388	−	9.07228i	−0.807706	−	0.388971i
$545$	−0.841830	+	3.68830i	−0.0360601	+	0.157989i
$546$	0.249136	+	1.09153i	0.0106620	+	0.0467133i
$547$	−23.3017	+	11.2215i	−0.996309	+	0.479797i	−0.859684	−	0.510826i	$-0.829340\pi$
$547$	−23.3017	+	11.2215i	−0.996309	+	0.479797i	−0.136625	+	0.990623i	$0.543625\pi$
$548$	13.4729	−	27.9768i	0.575534	−	1.19511i
$549$	−2.31482	+	0.528344i	−0.0987943	+	0.0225492i
$550$	−9.93767			−0.423744
$551$		0			0
$552$	−4.84415			−0.206181
$553$	−1.62313	+	0.370469i	−0.0690226	+	0.0157540i
$554$	−2.05935	+	4.27628i	−0.0874934	+	0.181682i
$555$	3.83997	−	1.84923i	0.162998	−	0.0784955i
$556$	6.68329	+	29.2814i	0.283435	+	1.24181i
$557$	5.12014	−	22.4328i	0.216947	−	0.950508i	−0.742771	−	0.669545i	$-0.766489\pi$
$557$	5.12014	−	22.4328i	0.216947	−	0.950508i	0.959719	−	0.280963i	$-0.0906537\pi$
$558$	3.87747	+	1.86729i	0.164146	+	0.0790487i
$559$	15.0521	−	12.0036i	0.636636	−	0.507700i
$560$	−0.439001	−	0.550490i	−0.0185512	−	0.0232624i
$561$	−12.0088	−	24.9366i	−0.507014	−	1.05282i
$562$	5.66442	+	4.51722i	0.238939	+	0.190547i
$563$		−	43.1159i		−	1.81712i	−0.417757	−	0.908559i	$-0.637184\pi$
$563$		−	43.1159i		−	1.81712i	0.417757	−	0.908559i	$-0.362816\pi$
$564$	9.02930	−	11.3224i	0.380202	−	0.476759i
$565$	7.20182	+	1.64377i	0.302983	+	0.0691538i
$566$	2.27658	+	0.519614i	0.0956918	+	0.0218410i
$567$	−0.573376	+	0.718991i	−0.0240795	+	0.0301948i
$568$		−	12.4112i		−	0.520762i
$569$	19.0081	+	15.1585i	0.796862	+	0.635476i	0.934884	−	0.354953i	$-0.115503\pi$
$569$	19.0081	+	15.1585i	0.796862	+	0.635476i	−0.138022	+	0.990429i	$0.544075\pi$
$570$	0.392730	+	0.815511i	0.0164496	+	0.0341580i
$571$	11.5274	+	14.4550i	0.482408	+	0.604921i	0.962161	−	0.272483i	$-0.0878448\pi$
$571$	11.5274	+	14.4550i	0.482408	+	0.604921i	−0.479752	+	0.877404i	$0.659273\pi$
$572$	−39.3328	+	31.3669i	−1.64459	+	1.31152i
$573$	11.9879	+	5.77308i	0.500802	+	0.241174i
$574$	0.109916	−	0.481575i	0.00458782	−	0.0201005i
$575$	2.30977	+	10.1197i	0.0963239	+	0.422023i
$576$	−4.72737	+	2.27658i	−0.196974	+	0.0948575i
$577$	16.4260	−	34.1090i	0.683825	−	1.41998i	−0.212760	−	0.977105i	$-0.568245\pi$
$577$	16.4260	−	34.1090i	0.683825	−	1.41998i	0.896585	−	0.442872i	$-0.146041\pi$
$578$	1.38655	−	0.316471i	0.0576728	−	0.0131634i
$579$	28.3424			1.17787
$580$		0			0
$581$	1.58987			0.0659591
$582$	−0.0977147	+	0.0223027i	−0.00405040	+	0.000924478i
$583$	−10.0548	+	20.8790i	−0.416426	+	0.864718i
$584$	8.57606	−	4.13001i	0.354880	−	0.170901i
$585$	1.25786	+	5.51107i	0.0520063	+	0.227855i
$586$	−0.669824	+	2.93469i	−0.0276702	+	0.121231i
$587$	13.0058	+	6.26327i	0.536807	+	0.258513i	0.682587	−	0.730804i	$-0.260855\pi$
$587$	13.0058	+	6.26327i	0.536807	+	0.258513i	−0.145780	+	0.989317i	$0.546569\pi$
$588$	−12.0735	+	9.62833i	−0.497905	+	0.397066i
$589$	−9.83393	−	12.3314i	−0.405200	−	0.508105i
$590$	1.66953	+	3.46681i	0.0687334	+	0.142726i
$591$	19.0676	+	15.2059i	0.784336	+	0.625487i
$592$			14.0804i			0.578700i
$593$	8.10656	−	10.1653i	0.332897	−	0.417439i	−0.587008	−	0.809581i	$-0.699694\pi$
$593$	8.10656	−	10.1653i	0.332897	−	0.417439i	0.919905	+	0.392142i	$0.128266\pi$
$594$	11.8781	+	2.71110i	0.487365	+	0.111238i
$595$	1.08209	+	0.246980i	0.0443613	+	0.0101252i
$596$	−20.9046	+	26.2136i	−0.856286	+	1.07375i
$597$			1.09113i			0.0446570i
$598$	−4.51575	−	3.60119i	−0.184663	−	0.147263i
$599$	−5.24718	−	10.8959i	−0.214394	−	0.445194i	0.765841	−	0.643030i	$-0.222323\pi$
$599$	−5.24718	−	10.8959i	−0.214394	−	0.445194i	−0.980235	+	0.197836i	$0.936609\pi$
$600$	5.94757	+	7.45801i	0.242808	+	0.304472i
$601$	17.4718	−	13.9333i	0.712688	−	0.568349i	−0.198620	−	0.980077i	$-0.563646\pi$
$601$	17.4718	−	13.9333i	0.712688	−	0.568349i	0.911307	+	0.411727i	$0.135074\pi$
$602$	0.487386	+	0.234713i	0.0198644	+	0.00956618i
$603$	−0.746980	+	3.27273i	−0.0304194	+	0.133276i
$604$	−3.01842	−	13.2246i	−0.122818	−	0.538099i
$605$	−8.35086	+	4.02156i	−0.339511	+	0.163500i
$606$	−0.777628	+	1.61476i	−0.0315890	+	0.0655952i
$607$	−40.4290	+	9.22766i	−1.64096	+	0.374539i	−0.940672	−	0.339318i	$-0.889804\pi$
$607$	−40.4290	+	9.22766i	−1.64096	+	0.374539i	−0.700292	+	0.713857i	$0.746947\pi$
$608$	−10.9661			−0.444736
$609$		0			0
$610$	0.506041			0.0204890
$611$	35.5190	−	8.10699i	1.43695	−	0.327974i
$612$	5.07718	−	10.5429i	0.205233	−	0.426171i
$613$	23.2310	−	11.1875i	0.938292	−	0.451858i	0.0987255	−	0.995115i	$-0.468523\pi$
$613$	23.2310	−	11.1875i	0.938292	−	0.451858i	0.839566	+	0.543257i	$0.182809\pi$
$614$	−0.447435	−	1.96034i	−0.0180570	−	0.0791129i
$615$	−0.597171	+	2.61638i	−0.0240802	+	0.105502i
$616$	−2.68718	−	1.29408i	−0.108269	−	0.0521398i
$617$	6.93119	−	5.52744i	0.279039	−	0.222526i	−0.473962	−	0.880545i	$-0.657177\pi$
$617$	6.93119	−	5.52744i	0.279039	−	0.222526i	0.753002	+	0.658019i	$0.228605\pi$
$618$	4.72401	+	5.92372i	0.190028	+	0.238287i
$619$	12.7784	+	26.5347i	0.513608	+	1.06652i	0.983013	+	0.183536i	$0.0587543\pi$
$619$	12.7784	+	26.5347i	0.513608	+	1.06652i	−0.469405	+	0.882983i	$0.655531\pi$
$620$	6.52424	+	5.20291i	0.262020	+	0.208954i
$621$		−	12.7259i		−	0.510672i
$622$	−3.50083	+	4.38990i	−0.140370	+	0.176019i
$623$	1.97632	+	0.451083i	0.0791797	+	0.0180722i
$624$	19.5916	+	4.47166i	0.784292	+	0.179010i
$625$	11.2515	−	14.1089i	0.450058	−	0.564355i
$626$		−	8.56273i		−	0.342235i
$627$	−11.3489	−	9.05041i	−0.453230	−	0.361439i
$628$	−14.2600	−	29.6112i	−0.569035	−	1.18161i
$629$	−13.8388	−	17.3533i	−0.551788	−	0.691920i
$630$	−0.124181	+	0.0990311i	−0.00494749	+	0.00394549i
$631$	21.4170	+	10.3139i	0.852597	+	0.410589i	0.808541	−	0.588440i	$-0.200258\pi$
$631$	21.4170	+	10.3139i	0.852597	+	0.410589i	0.0440561	+	0.999029i	$0.485972\pi$
$632$	1.75637	−	7.69517i	0.0698648	−	0.306098i
$633$	−5.06920	−	22.2096i	−0.201482	−	0.882752i
$634$	1.15010	−	0.553861i	0.0456765	−	0.0219966i
$635$	0.311317	−	0.646457i	0.0123542	−	0.0256538i
$636$	10.2785	−	2.34601i	0.407571	−	0.0930254i
$637$	−38.8495			−1.53927
$638$		0			0
$639$	10.5996			0.419312
$640$	7.36845	−	1.68180i	0.291264	−	0.0664790i
$641$	12.3507	−	25.6465i	0.487824	−	1.01298i	−0.501215	−	0.865323i	$-0.667114\pi$
$641$	12.3507	−	25.6465i	0.487824	−	1.01298i	0.989039	−	0.147654i	$-0.0471722\pi$
$642$	8.12229	−	3.91149i	0.320561	−	0.154374i
$643$	−4.30505	−	18.8617i	−0.169775	−	0.743832i	−0.986088	−	0.166223i	$-0.946843\pi$
$643$	−4.30505	−	18.8617i	−0.169775	−	0.743832i	0.816314	−	0.577609i	$-0.196014\pi$
$644$	−0.328552	+	1.43948i	−0.0129468	+	0.0567235i
$645$	−2.64795	−	1.27518i	−0.104263	−	0.0502104i
$646$	3.68539	−	2.93900i	0.145000	−	0.115633i
$647$	−14.1622	−	17.7588i	−0.556773	−	0.698171i	0.421185	−	0.906975i	$-0.361614\pi$
$647$	−14.1622	−	17.7588i	−0.556773	−	0.698171i	−0.977958	+	0.208804i	$0.933043\pi$
$648$	−1.89168	−	3.92812i	−0.0743122	−	0.154311i
$649$	−48.2450	−	38.4741i	−1.89378	−	1.51024i
$650$			11.3739i			0.446120i
$651$	−1.85690	+	2.32847i	−0.0727775	+	0.0912601i
$652$	22.2067	+	5.06853i	0.869681	+	0.198499i
$653$	22.3563	+	5.10268i	0.874870	+	0.199683i	0.636300	−	0.771442i	$-0.280464\pi$
$653$	22.3563	+	5.10268i	0.874870	+	0.199683i	0.238570	+	0.971125i	$0.423321\pi$
$654$	1.89158	−	2.37196i	0.0739665	−	0.0927510i
$655$			5.55124i			0.216905i
$656$	−6.93166	−	5.52781i	−0.270636	−	0.215825i
$657$	3.52717	+	7.32424i	0.137608	+	0.285746i
$658$	0.638260	+	0.800352i	0.0248820	+	0.0312010i
$659$	14.9941	−	11.9574i	0.584088	−	0.465795i	−0.286314	−	0.958136i	$-0.592430\pi$
$659$	14.9941	−	11.9574i	0.584088	−	0.465795i	0.870402	+	0.492341i	$0.163859\pi$
$660$	6.91939	+	3.33220i	0.269337	+	0.129706i
$661$	0.753553	−	3.30153i	0.0293098	−	0.128415i	−0.958156	−	0.286245i	$-0.907593\pi$
$661$	0.753553	−	3.30153i	0.0293098	−	0.128415i	0.987466	+	0.157831i	$0.0504500\pi$
$662$	0.310371	+	1.35983i	0.0120629	+	0.0528511i
$663$	−28.5405	+	13.7444i	−1.10842	+	0.533787i
$664$	−3.27040	+	6.79105i	−0.126916	+	0.263544i
$665$	0.567511	−	0.129531i	0.0220071	−	0.00502298i
$666$	3.17629			0.123079
$667$		0			0
$668$	1.43535			0.0555355
$669$	2.21057	−	0.504549i	0.0854657	−	0.0195070i
$670$	0.310421	−	0.644596i	0.0119926	−	0.0249029i
$671$	−7.31163	+	3.52109i	−0.282262	+	0.135930i
$672$	0.460771	+	2.01877i	0.0177746	+	0.0778758i
$673$	1.06153	−	4.65087i	0.0409190	−	0.179278i	−0.950339	−	0.311217i	$-0.899263\pi$
$673$	1.06153	−	4.65087i	0.0409190	−	0.179278i	0.991258	+	0.131939i	$0.0421204\pi$
$674$	1.99784	+	0.962111i	0.0769541	+	0.0370591i
$675$	−19.5926	+	15.6246i	−0.754121	+	0.601392i
$676$	21.2947	+	26.7027i	0.819027	+	1.02703i
$677$	−18.6961	−	38.8228i	−0.718549	−	1.49208i	−0.864416	−	0.502778i	$-0.832312\pi$
$677$	−18.6961	−	38.8228i	−0.718549	−	1.49208i	0.145867	−	0.989304i	$-0.453403\pi$
$678$	−4.63152	−	3.69351i	−0.177872	−	0.141849i
$679$			0.0644568i			0.00247362i
$680$	−3.28083	+	4.11403i	−0.125814	+	0.157766i
$681$	−16.8452	−	3.84481i	−0.645511	−	0.147334i
$682$	14.3407	+	3.27317i	0.549133	+	0.125336i
$683$	14.6102	−	18.3206i	0.559044	−	0.701019i	−0.419337	−	0.907831i	$-0.637737\pi$
$683$	14.6102	−	18.3206i	0.559044	−	0.701019i	0.978381	+	0.206812i	$0.0663087\pi$
$684$		−	6.13706i		−	0.234656i
$685$	−9.32355	−	7.43528i	−0.356234	−	0.284087i
$686$	−0.956036	−	1.98523i	−0.0365016	−	0.0757964i
$687$	9.93027	+	12.4522i	0.378864	+	0.475080i
$688$	7.59118	−	6.05376i	0.289411	−	0.230798i
$689$	23.8964	+	11.5079i	0.910381	+	0.438416i
$690$	−0.196202	+	0.859616i	−0.00746928	+	0.0327250i
$691$	−9.59903	−	42.0561i	−0.365164	−	1.59989i	−0.739873	−	0.672747i	$-0.765114\pi$
$691$	−9.59903	−	42.0561i	−0.365164	−	1.59989i	0.374708	−	0.927143i	$-0.377743\pi$
$692$	−14.8605	+	7.15646i	−0.564913	+	0.272048i
$693$	1.10518	−	2.29494i	0.0419825	−	0.0871775i
$694$	8.72853	−	1.99223i	0.331331	−	0.0756240i
$695$	11.5345			0.437529
$696$		0			0
$697$	13.9758			0.529373
$698$	−8.88992	+	2.02907i	−0.336488	+	0.0768013i
$699$	4.79685	−	9.96077i	0.181434	−	0.376751i
$700$	2.61960	−	1.26154i	0.0990118	−	0.0476816i
$701$	0.941453	+	4.12477i	0.0355582	+	0.155791i	0.989590	−	0.143914i	$-0.0459690\pi$
$701$	0.941453	+	4.12477i	0.0355582	+	0.155791i	−0.954032	+	0.299705i	$0.903112\pi$
$702$	3.10292	−	13.5948i	0.117112	−	0.513101i
$703$	−10.4879	−	5.05072i	−0.395559	−	0.190491i
$704$	−14.0211	+	11.1814i	−0.528439	+	0.421416i
$705$	−3.46764	−	4.34828i	−0.130599	−	0.163766i
$706$	−3.47527	−	7.21648i	−0.130794	−	0.271596i
$707$	0.901141	+	0.718636i	0.0338909	+	0.0270271i
$708$			28.0737i			1.05507i
$709$	−8.91819	+	11.1831i	−0.334930	+	0.419989i	−0.920567	−	0.390585i	$-0.872273\pi$
$709$	−8.91819	+	11.1831i	−0.334930	+	0.419989i	0.585637	+	0.810573i	$0.300844\pi$
$710$	−2.20242	−	0.502688i	−0.0826554	−	0.0188656i
$711$	6.57193	+	1.50000i	0.246467	+	0.0562544i
$712$	−5.99210	+	7.51385i	−0.224563	+	0.281594i
$713$		−	15.3642i		−	0.575393i
$714$	−0.695895	−	0.554958i	−0.0260432	−	0.0207688i
$715$	8.38292	+	17.4073i	0.313503	+	0.650996i
$716$	−3.82640	−	4.79815i	−0.142999	−	0.179315i
$717$	−24.9237	+	19.8760i	−0.930792	+	0.742282i
$718$	−9.47434	−	4.56260i	−0.353579	−	0.170275i
$719$	5.21605	−	22.8530i	0.194526	−	0.852274i	−0.779602	−	0.626276i	$-0.784578\pi$
$719$	5.21605	−	22.8530i	0.194526	−	0.852274i	0.974128	−	0.225998i	$-0.0725644\pi$
$720$	0.634375	+	2.77938i	0.0236418	+	0.103581i
$721$	4.39008	−	2.11415i	0.163495	−	0.0787352i
$722$	−2.59619	+	5.39104i	−0.0966202	+	0.200634i
$723$	11.8304	−	2.70022i	0.439978	−	0.100422i
$724$	22.8388			0.848796
$725$		0			0
$726$	7.43296			0.275863
$727$	50.6939	−	11.5706i	1.88013	−	0.429128i	0.881094	−	0.472942i	$-0.156808\pi$
$727$	50.6939	−	11.5706i	1.88013	−	0.429128i	0.999040	+	0.0438137i	$0.0139508\pi$
$728$	−1.48110	+	3.07553i	−0.0548931	+	0.113987i
$729$	22.0368	−	10.6124i	0.816179	−	0.393051i
$730$	−0.385535	−	1.68914i	−0.0142693	−	0.0625178i
$731$	−3.40581	+	14.9218i	−0.125969	+	0.551904i
$732$	3.32640	+	1.60191i	0.122947	+	0.0592082i
$733$	26.7310	−	21.3173i	0.987334	−	0.787372i	0.0101892	−	0.999948i	$-0.496757\pi$
$733$	26.7310	−	21.3173i	0.987334	−	0.787372i	0.977145	+	0.212576i	$0.0681852\pi$
$734$	−8.22534	−	10.3143i	−0.303603	−	0.380706i
$735$	2.57321	+	5.34332i	0.0949142	+	0.197091i
$736$	−8.35178	−	6.66033i	−0.307851	−	0.245503i
$737$			11.4735i			0.422632i
$738$	−1.24698	+	1.56366i	−0.0459020	+	0.0575592i
$739$	−38.7758	−	8.85032i	−1.42639	−	0.325564i	−0.561480	−	0.827490i	$-0.689768\pi$
$739$	−38.7758	−	8.85032i	−1.42639	−	0.325564i	−0.864911	+	0.501926i	$0.832625\pi$
$740$	6.00442	+	1.37047i	0.220727	+	0.0503795i
$741$	−10.3584	+	12.9890i	−0.380525	+	0.477163i
$742$			0.745251i			0.0273590i
$743$	−5.61215	−	4.47554i	−0.205890	−	0.164192i	0.515116	−	0.857120i	$-0.327749\pi$
$743$	−5.61215	−	4.47554i	−0.205890	−	0.164192i	−0.721006	+	0.692929i	$0.756320\pi$
$744$	−6.12627	−	12.7213i	−0.224600	−	0.466386i
$745$	8.02827	+	10.0671i	0.294133	+	0.368831i
$746$	−8.76407	+	6.98911i	−0.320876	+	0.255890i
$747$	−5.79978	−	2.79303i	−0.212203	−	0.102192i
$748$	8.89977	−	38.9925i	0.325408	−	1.42571i
$749$	−1.29009	−	5.65227i	−0.0471390	−	0.206529i
$750$	3.29440	−	1.58650i	0.120295	−	0.0579309i
$751$	11.7880	−	24.4780i	0.430150	−	0.893215i	−0.567413	−	0.823433i	$-0.692056\pi$
$751$	11.7880	−	24.4780i	0.430150	−	0.893215i	0.997562	−	0.0697812i	$-0.0222301\pi$
$752$	17.9132	−	4.08857i	0.653228	−	0.149095i
$753$	−12.1709			−0.443533
$754$		0			0
$755$	−5.20941			−0.189590
$756$	−3.47527	+	0.793209i	−0.126394	+	0.0288487i
$757$	10.2798	−	21.3463i	0.373627	−	0.775845i	−0.626366	−	0.779529i	$-0.715458\pi$
$757$	10.2798	−	21.3463i	0.373627	−	0.775845i	0.999993	+	0.00368433i	$0.00117276\pi$
$758$	10.7889	−	5.19566i	0.391870	−	0.188715i
$759$	−3.14646	−	13.7855i	−0.114209	−	0.500383i
$760$	−0.614097	+	2.69053i	−0.0222756	+	0.0975959i
$761$	12.8427	+	6.18470i	0.465546	+	0.224195i	0.651926	−	0.758283i	$-0.273961\pi$
$761$	12.8427	+	6.18470i	0.465546	+	0.224195i	−0.186380	+	0.982478i	$0.559676\pi$
$762$	−0.449866	+	0.358756i	−0.0162969	+	0.0129964i
$763$	−1.21648	−	1.52542i	−0.0440395	−	0.0552238i
$764$	8.34234	+	17.3230i	0.301815	+	0.626726i
$765$	−3.51352	−	2.80194i	−0.127032	−	0.101304i
$766$		−	8.75361i		−	0.316281i
$767$	−44.0344	+	55.2174i	−1.58999	+	1.99379i
$768$	2.91954	+	0.666366i	0.105350	+	0.0240454i
$769$	−43.5857	−	9.94816i	−1.57174	−	0.358740i	−0.654182	−	0.756337i	$-0.726987\pi$
$769$	−43.5857	−	9.94816i	−1.57174	−	0.358740i	−0.917560	+	0.397598i	$0.869844\pi$
$770$	−0.338478	+	0.424438i	−0.0121979	+	0.0152957i
$771$		−	20.3967i		−	0.734570i
$772$	32.0207	+	25.5356i	1.15245	+	0.919048i
$773$	−9.95706	−	20.6761i	−0.358131	−	0.743666i	0.641596	−	0.767043i	$-0.278273\pi$
$773$	−9.95706	−	20.6761i	−0.358131	−	0.743666i	−0.999727	+	0.0233767i	$0.992558\pi$
$774$	−1.36563	−	1.71244i	−0.0490864	−	0.0615524i
$775$	−23.6546	+	18.8639i	−0.849698	+	0.677611i
$776$	−0.275323	−	0.132589i	−0.00988352	−	0.00475965i
$777$	−0.489115	+	2.14295i	−0.0175469	+	0.0768780i
$778$	2.46144	+	10.7843i	0.0882467	+	0.386634i
$779$	6.60388	−	3.18026i	0.236608	−	0.113945i
$780$	3.81378	−	7.91939i	0.136555	−	0.283560i
$781$	35.3199	−	8.06153i	1.26384	−	0.288464i
$782$	4.59179			0.164202
$783$		0			0
$784$	−19.5929			−0.699745
$785$	−12.3055	+	2.80864i	−0.439201	+	0.100245i
$786$	1.93154	−	4.01089i	0.0688958	−	0.143064i
$787$	12.9133	−	6.21874i	0.460311	−	0.221674i	−0.189333	−	0.981913i	$-0.560632\pi$
$787$	12.9133	−	6.21874i	0.460311	−	0.221674i	0.649644	+	0.760239i	$0.274918\pi$
$788$	7.84213	+	34.3586i	0.279364	+	1.22397i
$789$	−6.58277	+	28.8410i	−0.234353	+	1.02677i
$790$	−1.29440	−	0.623353i	−0.0460529	−	0.0221779i
$791$	−2.97855	+	2.37531i	−0.105905	+	0.0844564i
$792$	7.52930	+	9.44145i	0.267542	+	0.335487i
$793$	4.02997	+	8.36831i	0.143108	+	0.297168i
$794$	1.38992	+	1.10842i	0.0493264	+	0.0393365i
$795$		−	4.04892i		−	0.143600i
$796$	−0.983074	+	1.23274i	−0.0348441	+	0.0436932i
$797$	−9.93771	−	2.26822i	−0.352012	−	0.0803444i	0.0428588	−	0.999081i	$-0.486353\pi$
$797$	−9.93771	−	2.26822i	−0.352012	−	0.0803444i	−0.394871	+	0.918737i	$0.629211\pi$
$798$	−0.455108	−	0.103875i	−0.0161107	−	0.00367715i
$799$	−18.0586	+	22.6448i	−0.638868	+	0.801115i
$800$			21.0358i			0.743727i
$801$	−6.41708	−	5.11745i	−0.226736	−	0.180816i
$802$	−4.80947	−	9.98696i	−0.169828	−	0.352652i
$803$	17.3237	+	21.7232i	0.611340	+	0.766597i
$804$	4.08103	−	3.25451i	0.143927	−	0.114778i
$805$	0.510885	+	0.246029i	0.0180063	+	0.00867139i
$806$	3.74621	−	16.4132i	0.131955	−	0.578131i
$807$	7.03534	+	30.8239i	0.247656	+	1.08505i
$808$	−4.92327	+	2.37092i	−0.173200	+	0.0834088i
$809$	−3.89317	+	8.08426i	−0.136877	+	0.284227i	−0.958129	−	0.286338i	$-0.907562\pi$
$809$	−3.89317	+	8.08426i	−0.136877	+	0.284227i	0.821252	+	0.570566i	$0.193276\pi$
$810$	−0.773680	+	0.176587i	−0.0271844	+	0.00620465i
$811$	28.5628			1.00298			0.501489	−	0.865164i	$-0.332786\pi$
$811$	28.5628			1.00298			0.501489	+	0.865164i	$0.332786\pi$
$812$		0			0
$813$	1.50066			0.0526306
$814$	10.5840	−	2.41574i	0.370971	−	0.0846716i
$815$	3.79546	−	7.88135i	0.132949	−	0.276072i
$816$	−14.3937	+	6.93166i	−0.503881	+	0.242656i
$817$	1.78621	+	7.82589i	0.0624915	+	0.273793i
$818$	−0.0280480	+	0.122886i	−0.000980676	+	0.00429662i
$819$	−2.62661	−	1.26491i	−0.0917810	−	0.0441994i
$820$	−3.03194	+	2.41789i	−0.105880	+	0.0844365i
$821$	−7.06734	−	8.86216i	−0.246652	−	0.309291i	0.643059	−	0.765817i	$-0.277665\pi$
$821$	−7.06734	−	8.86216i	−0.246652	−	0.309291i	−0.889710	+	0.456526i	$0.849094\pi$
$822$	4.14937	+	8.61625i	0.144726	+	0.300526i
$823$	4.43468	+	3.53654i	0.154583	+	0.123276i	0.697727	−	0.716364i	$-0.254195\pi$
$823$	4.43468	+	3.53654i	0.154583	+	0.123276i	−0.543144	+	0.839640i	$0.682766\pi$
$824$			23.1008i			0.804755i
$825$	−17.3609	+	21.7699i	−0.604429	+	0.757930i
$826$	−1.93471	−	0.441584i	−0.0673170	−	0.0153647i
$827$	−2.83044	−	0.646030i	−0.0984241	−	0.0224646i	0.173025	−	0.984917i	$-0.444646\pi$
$827$	−2.83044	−	0.646030i	−0.0984241	−	0.0224646i	−0.271449	+	0.962453i	$0.587503\pi$
$828$	3.72737	−	4.67397i	0.129535	−	0.162432i
$829$		−	45.2137i		−	1.57034i	−0.619282	−	0.785169i	$-0.712576\pi$
$829$		−	45.2137i		−	1.57034i	0.619282	−	0.785169i	$-0.287424\pi$
$830$	1.07264	+	0.855404i	0.0372320	+	0.0296915i
$831$	5.77017	+	11.9819i	0.200165	+	0.415647i
$832$	12.7974	+	16.0474i	0.443670	+	0.556344i
$833$	24.1471	−	19.2567i	0.836647	−	0.667204i
$834$	−8.33393	−	4.01341i	−0.288580	−	0.138973i
$835$	0.122662	−	0.537417i	0.00424489	−	0.0185981i
$836$	−4.66756	−	20.4499i	−0.161431	−	0.707276i
$837$	33.4197	−	16.0941i	1.15515	−	0.556292i
$838$	−5.11485	+	10.6211i	−0.176690	+	0.366900i
$839$	44.4817	−	10.1527i	1.53568	−	0.350509i	0.630721	−	0.776009i	$-0.282759\pi$
$839$	44.4817	−	10.1527i	1.53568	−	0.350509i	0.904958	+	0.425501i	$0.139902\pi$
$840$	0.521106			0.0179799
$841$		0			0
$842$	7.82477			0.269659
$843$	19.7912	−	4.51722i	0.681647	−	0.155581i
$844$	14.2831	−	29.6591i	0.491644	−	1.02091i
$845$	11.8177	−	5.69109i	0.406540	−	0.195779i
$846$	−0.922312	−	4.04091i	−0.0317097	−	0.138929i
$847$	1.06369	−	4.66032i	0.0365487	−	0.160130i
$848$	12.0516	+	5.80375i	0.413854	+	0.199302i
$849$	5.11543	−	4.07942i	0.175561	−	0.140005i
$850$	−5.63773	−	7.06949i	−0.193372	−	0.242481i
$851$	−4.92000	−	10.2165i	−0.168655	−	0.350216i
$852$	−12.8861	−	10.2763i	−0.441469	−	0.352060i
$853$			36.9288i			1.26442i	0.774797	+	0.632210i	$0.217852\pi$
$853$			36.9288i			1.26442i	−0.774797	+	0.632210i	$0.782148\pi$
$854$	−0.162718	+	0.204042i	−0.00556811	+	0.00698219i
$855$	−2.29780	−	0.524459i	−0.0785832	−	0.0179361i
$856$	26.7971	+	6.11625i	0.915904	+	0.209049i
$857$	22.1652	−	27.7942i	0.757148	−	0.949433i	−0.242638	−	0.970117i	$-0.578013\pi$
$857$	22.1652	−	27.7942i	0.757148	−	0.949433i	0.999786	+	0.0206835i	$0.00658425\pi$
$858$		−	15.4940i		−	0.528955i
$859$	−33.1349	−	26.4242i	−1.13055	−	0.901583i	−0.134547	−	0.990907i	$-0.542958\pi$
$859$	−33.1349	−	26.4242i	−1.13055	−	0.901583i	−0.996003	+	0.0893241i	$0.971529\pi$
$860$	−1.84270	−	3.82640i	−0.0628354	−	0.130479i
$861$	−0.862937	−	1.08209i	−0.0294088	−	0.0368775i
$862$	−9.67129	+	7.71260i	−0.329405	+	0.262692i
$863$	44.8500	+	21.5986i	1.52671	+	0.735225i	0.993825	−	0.110962i	$-0.0353933\pi$
$863$	44.8500	+	21.5986i	1.52671	+	0.735225i	0.532886	+	0.846187i	$0.321108\pi$
$864$	5.73878	−	25.1433i	0.195237	−	0.855391i
$865$	1.40953	+	6.17557i	0.0479256	+	0.209976i
$866$	2.35594	−	1.13456i	0.0800580	−	0.0385539i
$867$	1.72900	−	3.59030i	0.0587199	−	0.121933i
$868$	−4.19576	+	0.957656i	−0.142414	+	0.0325050i
$869$	23.0398			0.781572
$870$		0			0
$871$	13.1317			0.444950
$872$	9.01805	−	2.05831i	0.305390	−	0.0697032i
$873$	0.113235	−	0.235135i	0.00383243	−	0.00795811i
$874$	2.16972	−	1.04488i	0.0733918	−	0.0353436i
$875$	−0.523262	−	2.29256i	−0.0176895	−	0.0775027i
$876$	2.81282	−	12.3238i	0.0950365	−	0.416382i
$877$	−19.7250	−	9.49905i	−0.666065	−	0.320760i	0.0701218	−	0.997538i	$-0.477661\pi$
$877$	−19.7250	−	9.49905i	−0.666065	−	0.320760i	−0.736187	+	0.676778i	$0.763376\pi$
$878$	5.47702	−	4.36778i	0.184841	−	0.147405i
$879$	5.25869	+	6.59419i	0.177371	+	0.222417i
$880$	4.22773	+	8.77897i	0.142517	+	0.295939i
$881$	−26.2154	−	20.9061i	−0.883220	−	0.704345i	0.0728937	−	0.997340i	$-0.476777\pi$
$881$	−26.2154	−	20.9061i	−0.883220	−	0.704345i	−0.956114	+	0.292995i	$0.905348\pi$
$882$			4.41981i			0.148823i
$883$	10.0553	−	12.6089i	0.338386	−	0.424323i	−0.583301	−	0.812256i	$-0.698239\pi$
$883$	10.0553	−	12.6089i	0.338386	−	0.424323i	0.921688	+	0.387933i	$0.126811\pi$
$884$	−44.6277	−	10.1860i	−1.50099	−	0.342592i
$885$	10.5112	+	2.39911i	0.353329	+	0.0806451i
$886$	−1.86981	+	2.34466i	−0.0628173	+	0.0787705i
$887$			52.7391i			1.77081i	0.464823	+	0.885403i	$0.346118\pi$
$887$			52.7391i			1.77081i	−0.464823	+	0.885403i	$0.653882\pi$
$888$	−8.14737	−	6.49731i	−0.273408	−	0.218036i
$889$	0.160555	+	0.333397i	0.00538485	+	0.0111818i
$890$	1.09067	+	1.36766i	0.0365594	+	0.0458440i
$891$	9.94995	−	7.93482i	0.333336	−	0.265826i
$892$	2.95204	+	1.42163i	0.0988417	+	0.0475996i
$893$	−3.38016	+	14.8094i	−0.113113	+	0.495579i
$894$	−2.29776	−	10.0671i	−0.0768485	−	0.336695i
$895$	−2.12349	+	1.02262i	−0.0709804	+	0.0341824i
$896$	−1.69122	+	3.51184i	−0.0564995	+	0.117322i
$897$	−15.7778	+	3.60119i	−0.526806	+	0.120240i
$898$	5.48294			0.182968
$899$		0			0
$900$	−11.7724			−0.392413
$901$	−20.5571	+	4.69202i	−0.684856	+	0.156314i
$902$	−2.96594	+	6.15883i	−0.0987549	+	0.205067i
$903$	1.36563	−	0.657650i	0.0454452	−	0.0218852i
$904$	−4.01908	−	17.6087i	−0.133673	−	0.585658i
$905$	1.95175	−	8.55116i	0.0648783	−	0.284250i
$906$	3.76391	+	1.81260i	0.125047	+	0.0602196i
$907$	−23.3327	+	18.6072i	−0.774750	+	0.617843i	−0.928954	−	0.370196i	$-0.879290\pi$
$907$	−23.3327	+	18.6072i	−0.774750	+	0.617843i	0.154203	+	0.988039i	$0.450719\pi$
$908$	−15.5673	−	19.5208i	−0.516620	−	0.647821i
$909$	−2.02485	−	4.20464i	−0.0671599	−	0.139459i
$910$	0.485778	+	0.387395i	0.0161034	+	0.0128420i
$911$			9.34050i			0.309465i	0.987956	+	0.154732i	$0.0494515\pi$
$911$			9.34050i			0.309465i	−0.987956	+	0.154732i	$0.950548\pi$
$912$	−5.22401	+	6.55070i	−0.172984	+	0.216916i
$913$	−21.4503	−	4.89589i	−0.709901	−	0.162030i
$914$	−5.92793	−	1.35301i	−0.196078	−	0.0447536i
$915$	0.884043	−	1.10855i	0.0292256	−	0.0366477i
$916$			23.0151i			0.760439i
$917$	−2.23833	−	1.78501i	−0.0739163	−	0.0589463i
$918$	4.80993	+	9.98792i	0.158751	+	0.329650i
$919$	−11.4852	−	14.4020i	−0.378863	−	0.475079i	0.555441	−	0.831556i	$-0.312549\pi$
$919$	−11.4852	−	14.4020i	−0.378863	−	0.475079i	−0.934304	+	0.356477i	$0.883978\pi$
$920$	−2.10180	+	1.67613i	−0.0692942	+	0.0552603i
$921$	−5.07606	−	2.44450i	−0.167262	−	0.0805491i
$922$	1.14957	−	5.03660i	0.0378591	−	0.165872i
$923$	−9.22660	−	40.4244i	−0.303697	−	1.33058i
$924$	−3.56853	+	1.71851i	−0.117396	+	0.0565350i
$925$	−9.68851	+	20.1184i	−0.318556	+	0.661489i
$926$	−3.14248	+	0.717250i	−0.103268	+	0.0235703i
$927$	−19.7289			−0.647981
$928$		0			0
$929$	−4.84654			−0.159010			−0.0795050	−	0.996834i	$-0.525334\pi$
$929$	−4.84654			−0.159010			−0.0795050	+	0.996834i	$0.525334\pi$
$930$	−2.50559	+	0.571884i	−0.0821615	+	0.0187528i
$931$	7.02808	−	14.5939i	0.230336	−	0.478297i
$932$	14.3937	−	6.93166i	0.471482	−	0.227054i
$933$	3.50083	+	15.3381i	0.114612	+	0.502148i
$934$	0.204340	−	0.895272i	0.00668621	−	0.0292942i
$935$	−13.8388	−	6.66440i	−0.452576	−	0.217949i
$936$	10.8059	−	8.61745i	0.353203	−	0.281670i
$937$	27.8790	+	34.9591i	0.910766	+	1.14206i	0.989408	+	0.145161i	$0.0463702\pi$
$937$	27.8790	+	34.9591i	0.910766	+	1.14206i	−0.0786420	+	0.996903i	$0.525058\pi$
$938$	0.160093	+	0.332437i	0.00522723	+	0.0108545i
$939$	−18.7579	−	14.9589i	−0.612140	−	0.488166i
$940$		−	8.03684i		−	0.262133i
$941$	−8.47016	+	10.6213i	−0.276119	+	0.346243i	−0.900483	−	0.434891i	$-0.856787\pi$
$941$	−8.47016	+	10.6213i	−0.276119	+	0.346243i	0.624364	+	0.781134i	$0.285358\pi$
$942$	9.86822	+	2.25236i	0.321524	+	0.0733857i
$943$	6.96103	+	1.58881i	0.226682	+	0.0517388i
$944$	−22.2078	+	27.8476i	−0.722801	+	0.906363i
$945$			1.36898i			0.0445328i
$946$	−5.85294	−	4.66756i	−0.190295	−	0.151756i
$947$	−6.51329	−	13.5250i	−0.211654	−	0.439503i	0.767932	−	0.640532i	$-0.221286\pi$
$947$	−6.51329	−	13.5250i	−0.211654	−	0.439503i	−0.979585	+	0.201028i	$0.935572\pi$
$948$	−6.53534	−	8.19506i	−0.212258	−	0.266163i
$949$	24.8627	−	19.8274i	0.807078	−	0.643623i
$950$	−4.27263	−	2.05759i	−0.138623	−	0.0667571i
$951$	0.795897	−	3.48705i	0.0258087	−	0.113075i
$952$	−0.603875	−	2.64575i	−0.0195717	−	0.0857493i
$953$	−46.7105	+	22.4946i	−1.51310	+	0.728671i	−0.992166	−	0.124925i	$-0.960131\pi$
$953$	−46.7105	+	22.4946i	−1.51310	+	0.728671i	−0.520935	+	0.853596i	$0.674417\pi$
$954$	1.30923	−	2.71864i	0.0423878	−	0.0880191i
$955$	7.19891	−	1.64310i	0.232951	−	0.0531696i
$956$	−46.0659			−1.48988
$957$		0			0
$958$	1.73078			0.0559188
$959$	5.99601	−	1.36855i	0.193621	−	0.0441928i
$960$	1.35951	−	2.82304i	0.0438779	−	0.0911134i
$961$	12.4182	−	5.98029i	0.400587	−	0.192912i
$962$	−2.76487	−	12.1137i	−0.0891428	−	0.390560i
$963$	−5.22348	+	22.8856i	−0.168324	+	0.737477i
$964$	15.7986	+	7.60820i	0.508838	+	0.245044i
$965$	12.2973	−	9.80678i	0.395865	−	0.315691i
$966$	−0.283520	−	0.355523i	−0.00912210	−	0.0114388i
$967$	−18.0604	−	37.5027i	−0.580782	−	1.20601i	−0.959818	−	0.280625i	$-0.909458\pi$
$967$	−18.0604	−	37.5027i	−0.580782	−	1.20601i	0.379035	−	0.925382i	$-0.376256\pi$
$968$	17.7182	+	14.1298i	0.569486	+	0.454150i
$969$		−	13.2078i		−	0.424294i
$970$	−0.0346798	+	0.0434871i	−0.00111350	+	0.00139629i
$971$	54.3746	+	12.4107i	1.74497	+	0.398277i	0.971777	−	0.235900i	$-0.0758038\pi$
$971$	54.3746	+	12.4107i	1.74497	+	0.398277i	0.773188	+	0.634177i	$0.218661\pi$
$972$	23.5678	+	5.37920i	0.755938	+	0.172538i
$973$	−3.70895	+	4.65087i	−0.118903	+	0.149100i
$974$		−	4.38165i		−	0.140397i
$975$	24.9161	+	19.8699i	0.797954	+	0.636347i
$976$	2.03242	+	4.22037i	0.0650562	+	0.135091i
$977$	30.5250	+	38.2772i	0.976583	+	1.22460i	0.974451	+	0.224598i	$0.0721070\pi$
$977$	30.5250	+	38.2772i	0.976583	+	1.22460i	0.00213146	+	0.999998i	$0.499322\pi$
$978$	−5.48460	+	4.37382i	−0.175378	+	0.139859i
$979$	−25.2751	−	12.1718i	−0.807795	−	0.389014i
$980$	−1.90701	+	8.35516i	−0.0609172	+	0.266896i
$981$	1.75786	+	7.70171i	0.0561243	+	0.245897i
$982$	3.12402	−	1.50445i	0.0996916	−	0.0480089i
$983$	−2.24461	+	4.66099i	−0.0715921	+	0.148662i	−0.933693	−	0.358073i	$-0.883434\pi$
$983$	−2.24461	+	4.66099i	−0.0715921	+	0.148662i	0.862101	+	0.506736i	$0.169148\pi$
$984$	6.39715	−	1.46011i	0.203934	−	0.0465465i
$985$	13.5345			0.431246
$986$		0			0
$987$	2.86831			0.0912994
$988$	−23.4054	+	5.34213i	−0.744624	+	0.169956i
$989$	−3.39271	+	7.04503i	−0.107882	+	0.224019i
$990$	1.98039	−	0.953703i	0.0629408	−	0.0303107i
$991$	−3.75010	−	16.4302i	−0.119126	−	0.521924i	−0.998915	−	0.0465608i	$-0.985174\pi$
$991$	−3.75010	−	16.4302i	−0.119126	−	0.521924i	0.879790	−	0.475363i	$-0.157683\pi$
$992$	6.92854	−	30.3559i	0.219981	−	0.963802i
$993$	3.52111	+	1.69568i	0.111739	+	0.0538106i
$994$	0.910884	−	0.726406i	0.0288915	−	0.0230402i
$995$	0.377543	+	0.473424i	0.0119689	+	0.0150085i
$996$	4.34304	+	9.01842i	0.137615	+	0.285760i
$997$	29.8735	+	23.8233i	0.946104	+	0.754493i	0.969464	−	0.245234i	$-0.0788649\pi$
$997$	29.8735	+	23.8233i	0.946104	+	0.754493i	−0.0233599	+	0.999727i	$0.507436\pi$
$998$		−	9.15239i		−	0.289714i
$999$	17.0688	−	21.4036i	0.540034	−	0.677181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.e.b.196.1		12
29.2	odd	28		841.2.a.e.1.2		3
29.3	odd	28		841.2.d.b.778.1		6
29.4	even	14	inner	841.2.e.b.236.1		12
29.5	even	14		841.2.b.c.840.4		6
29.6	even	14		841.2.e.d.270.1		12
29.7	even	7		841.2.e.c.63.2		12
29.8	odd	28		841.2.d.d.190.1		6
29.9	even	14		841.2.e.d.651.2		12
29.10	odd	28		841.2.d.a.605.1		6
29.11	odd	28		841.2.d.b.574.1		6
29.12	odd	4		841.2.d.a.645.1		6
29.13	even	14		841.2.e.c.267.2		12
29.14	odd	28		29.2.d.a.20.1	yes	6
29.15	odd	28		841.2.d.d.571.1		6
29.16	even	7		841.2.e.c.267.1		12
29.17	odd	4		841.2.d.e.645.1		6
29.18	odd	28		841.2.d.c.574.1		6
29.19	odd	28		841.2.d.e.605.1		6
29.20	even	7		841.2.e.d.651.1		12
29.21	odd	28		29.2.d.a.16.1	✓	6
29.22	even	14		841.2.e.c.63.1		12
29.23	even	7		841.2.e.d.270.2		12
29.24	even	7		841.2.b.c.840.3		6
29.25	even	7	inner	841.2.e.b.236.2		12
29.26	odd	28		841.2.d.c.778.1		6
29.27	odd	28		841.2.a.f.1.2		3
29.28	even	2	inner	841.2.e.b.196.2		12
87.2	even	28		7569.2.a.r.1.2		3
87.14	even	28		261.2.k.a.136.1		6
87.50	even	28		261.2.k.a.190.1		6
87.56	even	28		7569.2.a.p.1.2		3
116.43	even	28		464.2.u.f.49.1		6
116.79	even	28		464.2.u.f.161.1		6
145.14	odd	28		725.2.l.b.426.1		6
145.43	even	28		725.2.r.b.49.1		12
145.72	even	28		725.2.r.b.49.2		12
145.79	odd	28		725.2.l.b.451.1		6
145.108	even	28		725.2.r.b.74.2		12
145.137	even	28		725.2.r.b.74.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.16.1	✓	6	29.21	odd	28
29.2.d.a.20.1	yes	6	29.14	odd	28
261.2.k.a.136.1		6	87.14	even	28
261.2.k.a.190.1		6	87.50	even	28
464.2.u.f.49.1		6	116.43	even	28
464.2.u.f.161.1		6	116.79	even	28
725.2.l.b.426.1		6	145.14	odd	28
725.2.l.b.451.1		6	145.79	odd	28
725.2.r.b.49.1		12	145.43	even	28
725.2.r.b.49.2		12	145.72	even	28
725.2.r.b.74.1		12	145.137	even	28
725.2.r.b.74.2		12	145.108	even	28
841.2.a.e.1.2		3	29.2	odd	28
841.2.a.f.1.2		3	29.27	odd	28
841.2.b.c.840.3		6	29.24	even	7
841.2.b.c.840.4		6	29.5	even	14
841.2.d.a.605.1		6	29.10	odd	28
841.2.d.a.645.1		6	29.12	odd	4
841.2.d.b.574.1		6	29.11	odd	28
841.2.d.b.778.1		6	29.3	odd	28
841.2.d.c.574.1		6	29.18	odd	28
841.2.d.c.778.1		6	29.26	odd	28
841.2.d.d.190.1		6	29.8	odd	28
841.2.d.d.571.1		6	29.15	odd	28
841.2.d.e.605.1		6	29.19	odd	28
841.2.d.e.645.1		6	29.17	odd	4
841.2.e.b.196.1		12	1.1	even	1	trivial
841.2.e.b.196.2		12	29.28	even	2	inner
841.2.e.b.236.1		12	29.4	even	14	inner
841.2.e.b.236.2		12	29.25	even	7	inner
841.2.e.c.63.1		12	29.22	even	14
841.2.e.c.63.2		12	29.7	even	7
841.2.e.c.267.1		12	29.16	even	7
841.2.e.c.267.2		12	29.13	even	14
841.2.e.d.270.1		12	29.6	even	14
841.2.e.d.270.2		12	29.23	even	7
841.2.e.d.651.1		12	29.20	even	7
841.2.e.d.651.2		12	29.9	even	14
7569.2.a.p.1.2		3	87.56	even	28
7569.2.a.r.1.2		3	87.2	even	28

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:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.e (of order \(14\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.433884 + 0.0990311i) q^{2} +(-0.541044 + 1.12349i) q^{3} +(-1.62349 + 0.781831i) q^{4} +(0.153989 + 0.674671i) q^{5} +(0.123490 - 0.541044i) q^{6} +(-0.321552 - 0.154851i) q^{7} +(1.32288 - 1.05496i) q^{8} +(0.900969 + 1.12978i) q^{9} +O(q^{10})\)	\(q+(-0.433884 + 0.0990311i) q^{2} +(-0.541044 + 1.12349i) q^{3} +(-1.62349 + 0.781831i) q^{4} +(0.153989 + 0.674671i) q^{5} +(0.123490 - 0.541044i) q^{6} +(-0.321552 - 0.154851i) q^{7} +(1.32288 - 1.05496i) q^{8} +(0.900969 + 1.12978i) q^{9} +(-0.133627 - 0.277479i) q^{10} +(3.86147 + 3.07942i) q^{11} -2.24698i q^{12} +(3.52446 - 4.41953i) q^{13} +(0.154851 + 0.0353438i) q^{14} +(-0.841301 - 0.192021i) q^{15} +(1.77748 - 2.22889i) q^{16} +4.49396i q^{17} +(-0.502799 - 0.400969i) q^{18} +(1.02262 + 2.12349i) q^{19} +(-0.777479 - 0.974928i) q^{20} +(0.347948 - 0.277479i) q^{21} +(-1.98039 - 0.953703i) q^{22} +(-0.510885 + 2.23833i) q^{23} +(0.469501 + 2.05702i) q^{24} +(4.07338 - 1.96163i) q^{25} +(-1.09153 + 2.26659i) q^{26} +(-5.40391 + 1.23341i) q^{27} +0.643104 q^{28} +0.384043 q^{30} +(-6.52424 + 1.48911i) q^{31} +(-2.01877 + 4.19202i) q^{32} +(-5.54892 + 2.67222i) q^{33} +(-0.445042 - 1.94986i) q^{34} +(0.0549581 - 0.240787i) q^{35} +(-2.34601 - 1.12978i) q^{36} +(-3.86147 + 3.07942i) q^{37} +(-0.653989 - 0.820077i) q^{38} +(3.05841 + 6.35086i) q^{39} +(0.915458 + 0.730054i) q^{40} -3.10992i q^{41} +(-0.123490 + 0.154851i) q^{42} +(3.32042 + 0.757865i) q^{43} +(-8.67664 - 1.98039i) q^{44} +(-0.623490 + 0.781831i) q^{45} -1.02177i q^{46} +(5.03894 + 4.01842i) q^{47} +(1.54244 + 3.20291i) q^{48} +(-4.28501 - 5.37323i) q^{49} +(-1.57311 + 1.25451i) q^{50} +(-5.04892 - 2.43143i) q^{51} +(-2.26659 + 9.93060i) q^{52} +(1.04407 + 4.57438i) q^{53} +(2.22252 - 1.07031i) q^{54} +(-1.48297 + 3.07942i) q^{55} +(-0.588735 + 0.134375i) q^{56} -2.93900 q^{57} -12.4940 q^{59} +(1.51597 - 0.346011i) q^{60} +(-0.712916 + 1.48039i) q^{61} +(2.68329 - 1.29221i) q^{62} +(-0.114761 - 0.502799i) q^{63} +(-0.807979 + 3.53999i) q^{64} +(3.52446 + 1.69729i) q^{65} +(2.14295 - 1.70895i) q^{66} +(1.44839 + 1.81623i) q^{67} +(-3.51352 - 7.29590i) q^{68} +(-2.23833 - 1.78501i) q^{69} +0.109916i q^{70} +(4.57338 - 5.73483i) q^{71} +(2.38374 + 0.544073i) q^{72} +(5.48460 + 1.25182i) q^{73} +(1.37047 - 1.71851i) q^{74} +5.63773i q^{75} +(-3.32042 - 2.64795i) q^{76} +(-0.764811 - 1.58815i) q^{77} +(-1.95593 - 2.45265i) q^{78} +(3.64715 - 2.90850i) q^{79} +(1.77748 + 0.855989i) q^{80} +(0.573376 - 2.51212i) q^{81} +(0.307979 + 1.34934i) q^{82} +(-4.01357 + 1.93284i) q^{83} +(-0.347948 + 0.722521i) q^{84} +(-3.03194 + 0.692021i) q^{85} -1.51573 q^{86} +8.35690 q^{88} +(-5.53753 + 1.26391i) q^{89} +(0.193096 - 0.400969i) q^{90} +(-1.81767 + 0.875342i) q^{91} +(-0.920583 - 4.03334i) q^{92} +(1.85690 - 8.13559i) q^{93} +(-2.58426 - 1.24451i) q^{94} +(-1.27518 + 1.01693i) q^{95} +(-3.61745 - 4.53614i) q^{96} +(-0.0783611 - 0.162718i) q^{97} +(2.39131 + 1.90701i) q^{98} +7.13706i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 12 q^{5} - 8 q^{6} - 12 q^{7} + 2 q^{9}+O(q^{10}) \) 12 * q - 10 * q^4 + 12 * q^5 - 8 * q^6 - 12 * q^7 + 2 * q^9	\( 12 q - 10 q^{4} + 12 q^{5} - 8 q^{6} - 12 q^{7} + 2 q^{9} + 24 q^{13} + 22 q^{16} - 10 q^{20} + 2 q^{22} - 14 q^{24} - 6 q^{25} + 24 q^{28} - 36 q^{30} - 30 q^{33} - 4 q^{34} + 2 q^{35} - 18 q^{36} - 18 q^{38} + 8 q^{42} + 2 q^{45} - 2 q^{49} - 24 q^{51} - 34 q^{52} + 20 q^{53} + 26 q^{54} + 4 q^{57} - 112 q^{59} - 20 q^{62} + 40 q^{63} - 30 q^{64} + 24 q^{65} + 60 q^{67} - 12 q^{74} - 16 q^{78} + 22 q^{80} - 48 q^{81} + 24 q^{82} - 36 q^{83} + 32 q^{86} + 84 q^{88} + 46 q^{91} - 28 q^{92} + 6 q^{93} + 30 q^{94} + 4 q^{96}+O(q^{100}) \) 12 * q - 10 * q^4 + 12 * q^5 - 8 * q^6 - 12 * q^7 + 2 * q^9 + 24 * q^13 + 22 * q^16 - 10 * q^20 + 2 * q^22 - 14 * q^24 - 6 * q^25 + 24 * q^28 - 36 * q^30 - 30 * q^33 - 4 * q^34 + 2 * q^35 - 18 * q^36 - 18 * q^38 + 8 * q^42 + 2 * q^45 - 2 * q^49 - 24 * q^51 - 34 * q^52 + 20 * q^53 + 26 * q^54 + 4 * q^57 - 112 * q^59 - 20 * q^62 + 40 * q^63 - 30 * q^64 + 24 * q^65 + 60 * q^67 - 12 * q^74 - 16 * q^78 + 22 * q^80 - 48 * q^81 + 24 * q^82 - 36 * q^83 + 32 * q^86 + 84 * q^88 + 46 * q^91 - 28 * q^92 + 6 * q^93 + 30 * q^94 + 4 * q^96

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