LMFDB - Embedded newform 731.2.m.c.87.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(87,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7, 0]))

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

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

chi := DirichletCharacter("731.87");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.m (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			87.3
Character	$\chi$	$=$	731.87
Dual form			731.2.m.c.689.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73249 - 1.73249i) q^{2} +(2.93607 - 1.21616i) q^{3} +4.00305i q^{4} +(0.137451 + 0.331835i) q^{5} +(-7.19370 - 2.97973i) q^{6} +(-0.639449 + 1.54377i) q^{7} +(3.47026 - 3.47026i) q^{8} +(5.02014 - 5.02014i) q^{9} +O(q^{10})$	\(q+(-1.73249 - 1.73249i) q^{2} +(2.93607 - 1.21616i) q^{3} +4.00305i q^{4} +(0.137451 + 0.331835i) q^{5} +(-7.19370 - 2.97973i) q^{6} +(-0.639449 + 1.54377i) q^{7} +(3.47026 - 3.47026i) q^{8} +(5.02014 - 5.02014i) q^{9} +(0.336769 - 0.813033i) q^{10} +(-4.27974 - 1.77273i) q^{11} +(4.86834 + 11.7532i) q^{12} -4.60128i q^{13} +(3.78240 - 1.56672i) q^{14} +(0.807129 + 0.807129i) q^{15} -4.01830 q^{16} +(3.41504 - 2.31031i) q^{17} -17.3947 q^{18} +(2.56658 + 2.56658i) q^{19} +(-1.32835 + 0.550221i) q^{20} +5.31028i q^{21} +(4.34338 + 10.4858i) q^{22} +(-1.45643 - 0.603271i) q^{23} +(5.96854 - 14.4093i) q^{24} +(3.44431 - 3.44431i) q^{25} +(-7.97168 + 7.97168i) q^{26} +(4.98570 - 12.0365i) q^{27} +(-6.17978 - 2.55975i) q^{28} +(-1.54114 - 3.72065i) q^{29} -2.79669i q^{30} +(2.01425 - 0.834328i) q^{31} +(0.0211394 + 0.0211394i) q^{32} -14.7215 q^{33} +(-9.91911 - 1.91393i) q^{34} -0.600169 q^{35} +(20.0958 + 20.0958i) q^{36} +(-3.93237 + 1.62884i) q^{37} -8.89315i q^{38} +(-5.59589 - 13.5097i) q^{39} +(1.62854 + 0.674565i) q^{40} +(-0.381172 + 0.920231i) q^{41} +(9.20001 - 9.20001i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(7.09631 - 17.1320i) q^{44} +(2.35588 + 0.975837i) q^{45} +(1.47808 + 3.56840i) q^{46} -12.1145i q^{47} +(-11.7980 + 4.88689i) q^{48} +(2.97543 + 2.97543i) q^{49} -11.9345 q^{50} +(7.21708 - 10.9365i) q^{51} +18.4192 q^{52} +(5.65186 + 5.65186i) q^{53} +(-29.4909 + 12.2155i) q^{54} -1.66383i q^{55} +(3.13822 + 7.57633i) q^{56} +(10.6570 + 4.41428i) q^{57} +(-3.77597 + 9.11600i) q^{58} +(6.05376 - 6.05376i) q^{59} +(-3.23098 + 3.23098i) q^{60} +(-1.72990 + 4.17634i) q^{61} +(-4.93513 - 2.04420i) q^{62} +(4.53980 + 10.9600i) q^{63} +7.96335i q^{64} +(1.52687 - 0.632449i) q^{65} +(25.5049 + 25.5049i) q^{66} +2.08192 q^{67} +(9.24827 + 13.6706i) q^{68} -5.00984 q^{69} +(1.03979 + 1.03979i) q^{70} +(-7.30247 + 3.02478i) q^{71} -34.8424i q^{72} +(2.66629 + 6.43700i) q^{73} +(9.63475 + 3.99084i) q^{74} +(5.92390 - 14.3016i) q^{75} +(-10.2741 + 10.2741i) q^{76} +(5.47336 - 5.47336i) q^{77} +(-13.7106 + 33.1002i) q^{78} +(-6.09528 - 2.52475i) q^{79} +(-0.552318 - 1.33341i) q^{80} -20.1049i q^{81} +(2.25467 - 0.933914i) q^{82} +(-6.67871 - 6.67871i) q^{83} -21.2573 q^{84} +(1.23604 + 0.815676i) q^{85} +2.45011 q^{86} +(-9.04980 - 9.04980i) q^{87} +(-21.0037 + 8.70000i) q^{88} +11.2275i q^{89} +(-2.39091 - 5.77216i) q^{90} +(7.10331 + 2.94229i) q^{91} +(2.41492 - 5.83014i) q^{92} +(4.89929 - 4.89929i) q^{93} +(-20.9882 + 20.9882i) q^{94} +(-0.498903 + 1.20446i) q^{95} +(0.0877757 + 0.0363579i) q^{96} +(4.60112 + 11.1081i) q^{97} -10.3098i q^{98} +(-30.3842 + 12.5856i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	$ 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) $ 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/731\mathbb{Z}\right)^\times$.

$n$	$173$	$562$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.73249	−	1.73249i	−1.22506	−	1.22506i	−0.965812	−	0.259244i	$-0.916527\pi$
$2$	−1.73249	−	1.73249i	−1.22506	−	1.22506i	−0.259244	−	0.965812i	$-0.583473\pi$
$3$	2.93607	−	1.21616i	1.69514	−	0.702150i	0.695278	−	0.718741i	$-0.255281\pi$
$3$	2.93607	−	1.21616i	1.69514	−	0.702150i	0.999862	+	0.0165912i	$0.00528139\pi$
$4$			4.00305i			2.00152i
$5$	0.137451	+	0.331835i	0.0614698	+	0.148401i	0.951630	−	0.307247i	$-0.0994076\pi$
$5$	0.137451	+	0.331835i	0.0614698	+	0.148401i	−0.890160	+	0.455648i	$0.849408\pi$
$6$	−7.19370	−	2.97973i	−2.93681	−	1.21647i
$7$	−0.639449	+	1.54377i	−0.241689	+	0.583489i	−0.997451	−	0.0713576i	$-0.977267\pi$
$7$	−0.639449	+	1.54377i	−0.241689	+	0.583489i	0.755762	+	0.654847i	$0.227267\pi$
$8$	3.47026	−	3.47026i	1.22692	−	1.22692i
$9$	5.02014	−	5.02014i	1.67338	−	1.67338i
$10$	0.336769	−	0.813033i	0.106496	−	0.257104i
$11$	−4.27974	−	1.77273i	−1.29039	−	0.534497i	−0.371289	−	0.928517i	$-0.621084\pi$
$11$	−4.27974	−	1.77273i	−1.29039	−	0.534497i	−0.919102	+	0.394020i	$0.871084\pi$
$12$	4.86834	+	11.7532i	1.40537	+	3.39286i
$13$		−	4.60128i		−	1.27617i	−0.769967	−	0.638083i	$-0.779728\pi$
$13$		−	4.60128i		−	1.27617i	0.769967	−	0.638083i	$-0.220272\pi$
$14$	3.78240	−	1.56672i	1.01089	−	0.418724i
$15$	0.807129	+	0.807129i	0.208400	+	0.208400i
$16$	−4.01830			−1.00457
$17$	3.41504	−	2.31031i	0.828268	−	0.560332i
$17$	3.41504	−	2.31031i	0.828268	−	0.560332i
$18$	−17.3947			−4.09996
$19$	2.56658	+	2.56658i	0.588814	+	0.588814i	0.937310	−	0.348497i	$-0.113308\pi$
$19$	2.56658	+	2.56658i	0.588814	+	0.588814i	−0.348497	+	0.937310i	$0.613308\pi$
$20$	−1.32835	+	0.550221i	−0.297029	+	0.123033i
$21$			5.31028i			1.15880i
$22$	4.34338	+	10.4858i	0.926012	+	2.23559i
$23$	−1.45643	−	0.603271i	−0.303686	−	0.125791i	0.225637	−	0.974212i	$-0.427554\pi$
$23$	−1.45643	−	0.603271i	−0.303686	−	0.125791i	−0.529322	+	0.848421i	$0.677554\pi$
$24$	5.96854	−	14.4093i	1.21832	−	2.94129i
$25$	3.44431	−	3.44431i	0.688862	−	0.688862i
$26$	−7.97168	+	7.97168i	−1.56338	+	1.56338i
$27$	4.98570	−	12.0365i	0.959498	−	2.31643i
$28$	−6.17978	−	2.55975i	−1.16787	−	0.483747i
$29$	−1.54114	−	3.72065i	−0.286183	−	0.690907i	0.713772	−	0.700378i	$-0.246985\pi$
$29$	−1.54114	−	3.72065i	−0.286183	−	0.690907i	−0.999955	+	0.00947112i	$0.996985\pi$
$30$		−	2.79669i		−	0.510603i
$31$	2.01425	−	0.834328i	0.361769	−	0.149850i	−0.194392	−	0.980924i	$-0.562274\pi$
$31$	2.01425	−	0.834328i	0.361769	−	0.149850i	0.556162	+	0.831074i	$0.312274\pi$
$32$	0.0211394	+	0.0211394i	0.00373696	+	0.00373696i
$33$	−14.7215			−2.56269
$34$	−9.91911	−	1.91393i	−1.70111	−	0.328237i
$35$	−0.600169			−0.101447
$36$	20.0958	+	20.0958i	3.34931	+	3.34931i
$37$	−3.93237	+	1.62884i	−0.646478	+	0.267780i	−0.681736	−	0.731598i	$-0.738775\pi$
$37$	−3.93237	+	1.62884i	−0.646478	+	0.267780i	0.0352580	+	0.999378i	$0.488775\pi$
$38$		−	8.89315i		−	1.44266i
$39$	−5.59589	−	13.5097i	−0.896060	−	2.16328i
$40$	1.62854	+	0.674565i	0.257496	+	0.106658i
$41$	−0.381172	+	0.920231i	−0.0595291	+	0.143716i	−0.950845	−	0.309666i	$-0.899783\pi$
$41$	−0.381172	+	0.920231i	−0.0595291	+	0.143716i	0.891316	+	0.453382i	$0.149783\pi$
$42$	9.20001	−	9.20001i	1.41959	−	1.41959i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$43$	−0.707107	+	0.707107i	−0.107833	+	0.107833i
$44$	7.09631	−	17.1320i	1.06981	−	2.58275i
$45$	2.35588	+	0.975837i	0.351194	+	0.145469i
$46$	1.47808	+	3.56840i	0.217931	+	0.526133i
$47$		−	12.1145i		−	1.76708i	−0.468355	−	0.883540i	$-0.655153\pi$
$47$		−	12.1145i		−	1.76708i	0.468355	−	0.883540i	$-0.344847\pi$
$48$	−11.7980	+	4.88689i	−1.70289	+	0.705362i
$49$	2.97543	+	2.97543i	0.425061	+	0.425061i
$50$	−11.9345			−1.68779
$51$	7.21708	−	10.9365i	1.01059	−	1.53141i
$52$	18.4192			2.55428
$53$	5.65186	+	5.65186i	0.776342	+	0.776342i	0.979207	−	0.202865i	$-0.0650251\pi$
$53$	5.65186	+	5.65186i	0.776342	+	0.776342i	−0.202865	+	0.979207i	$0.565025\pi$
$54$	−29.4909	+	12.2155i	−4.01320	+	1.66232i
$55$		−	1.66383i		−	0.224351i
$56$	3.13822	+	7.57633i	0.419362	+	1.01243i
$57$	10.6570	+	4.41428i	1.41156	+	0.584686i
$58$	−3.77597	+	9.11600i	−0.495809	+	1.19699i
$59$	6.05376	−	6.05376i	0.788133	−	0.788133i	−0.193055	−	0.981188i	$-0.561840\pi$
$59$	6.05376	−	6.05376i	0.788133	−	0.788133i	0.981188	+	0.193055i	$0.0618396\pi$
$60$	−3.23098	+	3.23098i	−0.417117	+	0.417117i
$61$	−1.72990	+	4.17634i	−0.221491	+	0.534726i	−0.995093	−	0.0989457i	$-0.968453\pi$
$61$	−1.72990	+	4.17634i	−0.221491	+	0.534726i	0.773602	+	0.633672i	$0.218453\pi$
$62$	−4.93513	−	2.04420i	−0.626762	−	0.259613i
$63$	4.53980	+	10.9600i	0.571961	+	1.38084i
$64$			7.96335i			0.995419i
$65$	1.52687	−	0.632449i	0.189385	−	0.0784457i
$66$	25.5049	+	25.5049i	3.13944	+	3.13944i
$67$	2.08192			0.254347			0.127174	−	0.991880i	$-0.459409\pi$
$67$	2.08192			0.254347			0.127174	+	0.991880i	$0.459409\pi$
$68$	9.24827	+	13.6706i	1.12152	+	1.65780i
$69$	−5.00984			−0.603114
$70$	1.03979	+	1.03979i	0.124278	+	0.124278i
$71$	−7.30247	+	3.02478i	−0.866643	+	0.358975i	−0.771302	−	0.636469i	$-0.780394\pi$
$71$	−7.30247	+	3.02478i	−0.866643	+	0.358975i	−0.0953413	+	0.995445i	$0.530394\pi$
$72$		−	34.8424i		−	4.10621i
$73$	2.66629	+	6.43700i	0.312066	+	0.753394i	0.999628	+	0.0272683i	$0.00868084\pi$
$73$	2.66629	+	6.43700i	0.312066	+	0.753394i	−0.687562	+	0.726125i	$0.741319\pi$
$74$	9.63475	+	3.99084i	1.12002	+	0.463926i
$75$	5.92390	−	14.3016i	0.684034	−	1.65140i
$76$	−10.2741	+	10.2741i	−1.17852	+	1.17852i
$77$	5.47336	−	5.47336i	0.623747	−	0.623747i
$78$	−13.7106	+	33.1002i	−1.55242	+	3.74786i
$79$	−6.09528	−	2.52475i	−0.685773	−	0.284056i	0.0124649	−	0.999922i	$-0.496032\pi$
$79$	−6.09528	−	2.52475i	−0.685773	−	0.284056i	−0.698238	+	0.715866i	$0.746032\pi$
$80$	−0.552318	−	1.33341i	−0.0617510	−	0.149080i
$81$		−	20.1049i		−	2.23388i
$82$	2.25467	−	0.933914i	0.248986	−	0.103134i
$83$	−6.67871	−	6.67871i	−0.733084	−	0.733084i	0.238146	−	0.971229i	$-0.423460\pi$
$83$	−6.67871	−	6.67871i	−0.733084	−	0.733084i	−0.971229	+	0.238146i	$0.923460\pi$
$84$	−21.2573			−2.31936
$85$	1.23604	+	0.815676i	0.134067	+	0.0884725i
$86$	2.45011			0.264202
$87$	−9.04980	−	9.04980i	−0.970240	−	0.970240i
$88$	−21.0037	+	8.70000i	−2.23900	+	0.927423i
$89$			11.2275i			1.19011i	0.803686	+	0.595054i	$0.202869\pi$
$89$			11.2275i			1.19011i	−0.803686	+	0.595054i	$0.797131\pi$
$90$	−2.39091	−	5.77216i	−0.252024	−	0.608440i
$91$	7.10331	+	2.94229i	0.744629	+	0.308436i
$92$	2.41492	−	5.83014i	0.251773	−	0.607834i
$93$	4.89929	−	4.89929i	0.508033	−	0.508033i
$94$	−20.9882	+	20.9882i	−2.16477	+	2.16477i
$95$	−0.498903	+	1.20446i	−0.0511864	+	0.123575i
$96$	0.0877757	+	0.0363579i	0.00895857	+	0.00371076i
$97$	4.60112	+	11.1081i	0.467173	+	1.12786i	0.965392	+	0.260805i	$0.0839879\pi$
$97$	4.60112	+	11.1081i	0.467173	+	1.12786i	−0.498218	+	0.867052i	$0.666012\pi$
$98$		−	10.3098i		−	1.04145i
$99$	−30.3842	+	12.5856i	−3.05373	+	1.26490i
$100$	13.7877	+	13.7877i	1.37877	+	1.37877i
$101$	−13.3944			−1.33279			−0.666397	−	0.745597i	$-0.732165\pi$
$101$	−13.3944			−1.33279			−0.666397	+	0.745597i	$0.732165\pi$
$102$	−31.4508	+	6.44377i	−3.11410	+	0.638029i
$103$	−0.681348			−0.0671352			−0.0335676	−	0.999436i	$-0.510687\pi$
$103$	−0.681348			−0.0671352			−0.0335676	+	0.999436i	$0.510687\pi$
$104$	−15.9677	−	15.9677i	−1.56576	−	1.56576i
$105$	−1.76214	+	0.729901i	−0.171967	+	0.0712311i
$106$		−	19.5836i		−	1.90213i
$107$	7.02754	+	16.9660i	0.679378	+	1.64016i	0.765153	+	0.643849i	$0.222663\pi$
$107$	7.02754	+	16.9660i	0.679378	+	1.64016i	−0.0857751	+	0.996315i	$0.527337\pi$
$108$	48.1829	+	19.9580i	4.63640	+	1.92046i
$109$	−6.26783	+	15.1319i	−0.600349	+	1.44937i	0.272873	+	0.962050i	$0.412026\pi$
$109$	−6.26783	+	15.1319i	−0.600349	+	1.44937i	−0.873222	+	0.487322i	$0.837974\pi$
$110$	−2.88257	+	2.88257i	−0.274843	+	0.274843i
$111$	−9.56478	+	9.56478i	−0.907849	+	0.907849i
$112$	2.56950	−	6.20332i	0.242795	−	0.586158i
$113$	6.22400	+	2.57807i	0.585505	+	0.242524i	0.655715	−	0.755008i	$-0.272367\pi$
$113$	6.22400	+	2.57807i	0.585505	+	0.242524i	−0.0702107	+	0.997532i	$0.522367\pi$
$114$	−10.8155	−	26.1109i	−1.01296	−	2.44551i
$115$		−	0.566213i		−	0.0527996i
$116$	14.8939	−	6.16927i	1.38287	−	0.572802i
$117$	−23.0991	−	23.0991i	−2.13551	−	2.13551i
$118$	−20.9762			−1.93101
$119$	1.38283	+	6.74935i	0.126764	+	0.618712i
$120$	5.60190			0.511381
$121$	7.39546	+	7.39546i	0.672314	+	0.672314i
$122$	10.2325	−	4.23844i	0.926408	−	0.383731i
$123$			3.16543i			0.285417i
$124$	3.33986	+	8.06312i	0.299928	+	0.724090i
$125$	3.27554	+	1.35677i	0.292973	+	0.121354i
$126$	11.1230	−	26.8533i	0.990917	−	2.39228i
$127$	15.5456	−	15.5456i	1.37945	−	1.37945i	0.533897	−	0.845549i	$-0.320727\pi$
$127$	15.5456	−	15.5456i	1.37945	−	1.37945i	0.845549	−	0.533897i	$-0.179273\pi$
$128$	13.8387	−	13.8387i	1.22318	−	1.22318i
$129$	−1.21616	+	2.93607i	−0.107077	+	0.258506i
$130$	−3.74100	−	1.54957i	−0.328107	−	0.135906i
$131$	6.10267	+	14.7332i	0.533193	+	1.28724i	0.929398	+	0.369080i	$0.120327\pi$
$131$	6.10267	+	14.7332i	0.533193	+	1.28724i	−0.396205	+	0.918162i	$0.629673\pi$
$132$		−	58.9310i		−	5.12929i
$133$	−5.60340	+	2.32100i	−0.485876	+	0.201256i
$134$	−3.60691	−	3.60691i	−0.311590	−	0.311590i
$135$	4.67943			0.402742
$136$	3.83370	−	19.8684i	0.328737	−	1.70371i
$137$	15.4739			1.32203			0.661014	−	0.750374i	$-0.270126\pi$
$137$	15.4739			1.32203			0.661014	+	0.750374i	$0.270126\pi$
$138$	8.67950	+	8.67950i	0.738848	+	0.738848i
$139$	−2.29638	+	0.951193i	−0.194777	+	0.0806791i	−0.477940	−	0.878393i	$-0.658616\pi$
$139$	−2.29638	+	0.951193i	−0.194777	+	0.0806791i	0.283163	+	0.959072i	$0.408616\pi$
$140$		−	2.40251i		−	0.203049i
$141$	−14.7332	−	35.5690i	−1.24076	−	2.99545i
$142$	17.8919	+	7.41105i	1.50145	+	0.621922i
$143$	−8.15682	+	19.6923i	−0.682108	+	1.64675i
$144$	−20.1724	+	20.1724i	−1.68103	+	1.68103i
$145$	1.02281	−	1.02281i	0.0849398	−	0.0849398i
$146$	6.53271	−	15.7714i	0.540651	−	1.30525i
$147$	12.3546	+	5.11746i	1.01899	+	0.422081i
$148$	−6.52033	−	15.7415i	−0.535968	−	1.29394i
$149$		−	1.73929i		−	0.142488i	−0.997459	−	0.0712441i	$-0.977303\pi$
$149$		−	1.73929i		−	0.142488i	0.997459	−	0.0712441i	$-0.0226969\pi$
$150$	−35.0404	+	14.5142i	−2.86104	+	1.18508i
$151$	−13.7432	−	13.7432i	−1.11840	−	1.11840i	−0.991976	−	0.126426i	$-0.959649\pi$
$151$	−13.7432	−	13.7432i	−1.11840	−	1.11840i	−0.126426	−	0.991976i	$-0.540351\pi$
$152$	17.8134			1.44486
$153$	5.54589	−	28.7420i	0.448359	−	2.32365i
$154$	−18.9651			−1.52825
$155$	0.553719	+	0.553719i	0.0444758	+	0.0444758i
$156$	54.0799	−	22.4006i	4.32986	−	1.79349i
$157$			20.3358i			1.62297i	0.584372	+	0.811486i	$0.301341\pi$
$157$			20.3358i			1.62297i	−0.584372	+	0.811486i	$0.698659\pi$
$158$	6.18592	+	14.9341i	0.492125	+	1.18810i
$159$	23.4678	+	9.72068i	1.86112	+	0.770900i
$160$	−0.00410918	+	0.00992043i	−0.000324859	+	0.000784279i
$161$	1.86262	−	1.86262i	0.146795	−	0.146795i
$162$	−34.8315	+	34.8315i	−2.73662	+	2.73662i
$163$	−1.51967	+	3.66881i	−0.119030	+	0.287363i	−0.972153	−	0.234346i	$-0.924705\pi$
$163$	−1.51967	+	3.66881i	−0.119030	+	0.287363i	0.853124	+	0.521709i	$0.174705\pi$
$164$	−3.68373	−	1.52585i	−0.287651	−	0.119149i
$165$	−2.02348	−	4.88512i	−0.157528	−	0.380306i
$166$			23.1416i			1.79614i
$167$	−0.683976	+	0.283312i	−0.0529277	+	0.0219234i	−0.408990	−	0.912539i	$-0.634119\pi$
$167$	−0.683976	+	0.283312i	−0.0529277	+	0.0219234i	0.356063	+	0.934462i	$0.384119\pi$
$168$	18.4281	+	18.4281i	1.42176	+	1.42176i
$169$	−8.17181			−0.628601
$170$	−0.728277	−	3.55458i	−0.0558563	−	0.272624i
$171$	25.7691			1.97062
$172$	−2.83058	−	2.83058i	−0.215830	−	0.215830i
$173$	18.3456	−	7.59901i	1.39479	−	0.577742i	0.446398	−	0.894835i	$-0.352707\pi$
$173$	18.3456	−	7.59901i	1.39479	−	0.577742i	0.948395	+	0.317093i	$0.102707\pi$
$174$			31.3574i			2.37720i
$175$	3.11475	+	7.51968i	0.235453	+	0.568434i
$176$	17.1973	+	7.12335i	1.29629	+	0.536942i
$177$	10.4119	−	25.1366i	0.782608	−	1.88938i
$178$	19.4515	−	19.4515i	1.45795	−	1.45795i
$179$	7.03958	−	7.03958i	0.526163	−	0.526163i	−0.393263	−	0.919426i	$-0.628654\pi$
$179$	7.03958	−	7.03958i	0.526163	−	0.526163i	0.919426	+	0.393263i	$0.128654\pi$
$180$	−3.90632	+	9.43069i	−0.291160	+	0.702922i
$181$	21.1522	+	8.76154i	1.57223	+	0.651240i	0.987159	−	0.159740i	$-0.0510656\pi$
$181$	21.1522	+	8.76154i	1.57223	+	0.651240i	0.585074	+	0.810980i	$0.301066\pi$
$182$	−7.20893	−	17.4039i	−0.534362	−	1.29006i
$183$			14.3659i			1.06196i
$184$	−7.14769	+	2.96067i	−0.526934	+	0.218263i
$185$	−1.08101	−	1.08101i	−0.0794777	−	0.0794777i
$186$	−16.9759			−1.24474
$187$	−18.7110	+	3.83359i	−1.36829	+	0.280340i
$188$	48.4949			3.53685
$189$	15.3935	+	15.3935i	1.11971	+	1.11971i
$190$	2.95106	−	1.22237i	0.214092	−	0.0886799i
$191$			13.0708i			0.945773i	0.881123	+	0.472886i	$0.156788\pi$
$191$			13.0708i			0.945773i	−0.881123	+	0.472886i	$0.843212\pi$
$192$	9.68470	+	23.3809i	0.698933	+	1.68737i
$193$	−9.29480	−	3.85003i	−0.669055	−	0.277132i	0.0221884	−	0.999754i	$-0.492937\pi$
$193$	−9.29480	−	3.85003i	−0.669055	−	0.277132i	−0.691243	+	0.722622i	$0.742937\pi$
$194$	11.2733	−	27.2161i	0.809374	−	1.95400i
$195$	3.71383	−	3.71383i	0.265953	−	0.265953i
$196$	−11.9108	+	11.9108i	−0.850769	+	0.850769i
$197$	−7.13544	+	17.2265i	−0.508379	+	1.22734i	0.436437	+	0.899735i	$0.356240\pi$
$197$	−7.13544	+	17.2265i	−0.508379	+	1.22734i	−0.944816	+	0.327601i	$0.893760\pi$
$198$	74.4447	+	30.8360i	5.29056	+	2.19142i
$199$	−4.23600	−	10.2266i	−0.300282	−	0.724944i	−0.999945	−	0.0104717i	$-0.996667\pi$
$199$	−4.23600	−	10.2266i	−0.300282	−	0.724944i	0.699663	−	0.714473i	$-0.253333\pi$
$200$		−	23.9053i		−	1.69036i
$201$	6.11267	−	2.53195i	0.431154	−	0.178590i
$202$	23.2057	+	23.2057i	1.63275	+	1.63275i
$203$	6.72930			0.472304
$204$	43.7791	+	28.8903i	3.06515	+	2.02273i
$205$	−0.357757			−0.0249868
$206$	1.18043	+	1.18043i	0.0822444	+	0.0822444i
$207$	−10.3400	+	4.28295i	−0.718676	+	0.297686i
$208$			18.4893i			1.28200i
$209$	−6.43445	−	15.5341i	−0.445080	−	1.07452i
$210$	4.31743	+	1.78834i	0.297931	+	0.123407i
$211$	−6.83523	+	16.5017i	−0.470557	+	1.13602i	0.493361	+	0.869824i	$0.335768\pi$
$211$	−6.83523	+	16.5017i	−0.470557	+	1.13602i	−0.963918	+	0.266200i	$0.914232\pi$
$212$	−22.6247	+	22.6247i	−1.55387	+	1.55387i
$213$	−17.7619	+	17.7619i	−1.21703	+	1.21703i
$214$	17.2183	−	41.5685i	1.17702	−	2.84157i
$215$	−0.331835	−	0.137451i	−0.0226310	−	0.00937405i
$216$	−24.4683	−	59.0716i	−1.66486	−	4.01932i
$217$			3.64304i			0.247306i
$218$	37.0748	−	15.3569i	2.51102	−	1.04010i
$219$	15.6568	+	15.6568i	1.05799	+	1.05799i
$220$	6.66040			0.449044
$221$	−10.6304	−	15.7136i	−0.715077	−	1.05701i
$222$	33.1418			2.22433
$223$	3.85642	+	3.85642i	0.258245	+	0.258245i	0.824340	−	0.566095i	$-0.191547\pi$
$223$	3.85642	+	3.85642i	0.258245	+	0.258245i	−0.566095	+	0.824340i	$0.691547\pi$
$224$	−0.0461519	+	0.0191168i	−0.00308366	+	0.00127729i
$225$		−	34.5818i		−	2.30545i
$226$	−6.31655	−	15.2495i	−0.420171	−	1.01438i
$227$	−5.17959	−	2.14546i	−0.343781	−	0.142399i	0.204111	−	0.978948i	$-0.434570\pi$
$227$	−5.17959	−	2.14546i	−0.343781	−	0.142399i	−0.547892	+	0.836549i	$0.684570\pi$
$228$	−17.6706	+	42.6606i	−1.17026	+	2.82526i
$229$	−1.63233	+	1.63233i	−0.107868	+	0.107868i	−0.758981	−	0.651113i	$-0.774302\pi$
$229$	−1.63233	+	1.63233i	−0.107868	+	0.107868i	0.651113	+	0.758981i	$0.274302\pi$
$230$	−0.980959	+	0.980959i	−0.0646825	+	0.0646825i
$231$	9.41368	−	22.7266i	0.619374	−	1.49530i
$232$	−18.2598	−	7.56345i	−1.19881	−	0.496565i
$233$	−9.71089	−	23.4442i	−0.636181	−	1.53588i	−0.831728	−	0.555183i	$-0.812648\pi$
$233$	−9.71089	−	23.4442i	−0.636181	−	1.53588i	0.195547	−	0.980694i	$-0.437352\pi$
$234$			80.0378i			5.23224i
$235$	4.02001	−	1.66514i	0.262237	−	0.108622i
$236$	24.2335	+	24.2335i	1.57747	+	1.57747i
$237$	−20.9667			−1.36193
$238$	9.29744	−	14.0889i	0.602663	−	0.913250i
$239$	−11.8765			−0.768225			−0.384113	−	0.923286i	$-0.625493\pi$
$239$	−11.8765			−0.768225			−0.384113	+	0.923286i	$0.625493\pi$
$240$	−3.24328	−	3.24328i	−0.209353	−	0.209353i
$241$	8.26055	−	3.42163i	0.532109	−	0.220407i	−0.100418	−	0.994945i	$-0.532018\pi$
$241$	8.26055	−	3.42163i	0.532109	−	0.220407i	0.632527	+	0.774539i	$0.282018\pi$
$242$		−	25.6251i		−	1.64725i
$243$	−9.49365	−	22.9197i	−0.609018	−	1.47030i
$244$	−16.7181	−	6.92486i	−1.07027	−	0.443319i
$245$	−0.578377	+	1.39632i	−0.0369511	+	0.0892079i
$246$	5.48407	−	5.48407i	0.349652	−	0.349652i
$247$	11.8096	−	11.8096i	0.751424	−	0.751424i
$248$	4.09463	−	9.88530i	0.260009	−	0.627717i
$249$	−27.7315	−	11.4868i	−1.75741	−	0.727945i
$250$	−3.32425	−	8.02545i	−0.210244	−	0.507574i
$251$		−	7.65242i		−	0.483016i	−0.970399	−	0.241508i	$-0.922358\pi$
$251$		−	7.65242i		−	0.483016i	0.970399	−	0.241508i	$-0.0776421\pi$
$252$	−43.8736	+	18.1730i	−2.76378	+	1.14479i
$253$	5.16369	+	5.16369i	0.324638	+	0.324638i
$254$	−53.8651			−3.37980
$255$	4.62109	+	0.891659i	0.289384	+	0.0558379i
$256$	−32.0242			−2.00151
$257$	0.232300	+	0.232300i	0.0144905	+	0.0144905i	0.714315	−	0.699824i	$-0.246738\pi$
$257$	0.232300	+	0.232300i	0.0144905	+	0.0144905i	−0.699824	+	0.714315i	$0.746738\pi$
$258$	7.19370	−	2.97973i	0.447860	−	0.185510i
$259$		−	7.11223i		−	0.441932i
$260$	2.53173	+	6.11213i	0.157011	+	0.379058i
$261$	−26.4149	−	10.9414i	−1.63504	−	0.677256i
$262$	14.9522	−	36.0979i	0.923752	−	2.23013i
$263$	−10.1427	+	10.1427i	−0.625426	+	0.625426i	−0.946914	−	0.321487i	$-0.895817\pi$
$263$	−10.1427	+	10.1427i	−0.625426	+	0.625426i	0.321487	+	0.946914i	$0.395817\pi$
$264$	−51.0876	+	51.0876i	−3.14422	+	3.14422i
$265$	−1.09863	+	2.65234i	−0.0674885	+	0.162932i
$266$	13.7290	+	5.68672i	0.841776	+	0.348675i
$267$	13.6544	+	32.9646i	0.835634	+	2.01740i
$268$			8.33404i			0.509082i
$269$	−2.16338	+	0.896100i	−0.131903	+	0.0546362i	−0.447659	−	0.894204i	$-0.647742\pi$
$269$	−2.16338	+	0.896100i	−0.131903	+	0.0546362i	0.315755	+	0.948841i	$0.397742\pi$
$270$	−8.10708	−	8.10708i	−0.493381	−	0.493381i
$271$	13.9447			0.847079			0.423540	−	0.905878i	$-0.360787\pi$
$271$	13.9447			0.847079			0.423540	+	0.905878i	$0.360787\pi$
$272$	−13.7226	+	9.28350i	−0.832057	+	0.562895i
$273$	24.4341			1.47882
$274$	−26.8085	−	26.8085i	−1.61956	−	1.61956i
$275$	−20.8466	+	8.63494i	−1.25710	+	0.520707i
$276$		−	20.0546i		−	1.20715i
$277$	−1.64216	−	3.96452i	−0.0986676	−	0.238205i	0.866836	−	0.498593i	$-0.166150\pi$
$277$	−1.64216	−	3.96452i	−0.0986676	−	0.238205i	−0.965504	+	0.260388i	$0.916150\pi$
$278$	5.62639	+	2.33053i	0.337449	+	0.139776i
$279$	5.92335	−	14.3002i	0.354622	−	0.856132i
$280$	−2.08274	+	2.08274i	−0.124468	+	0.124468i
$281$	15.0109	−	15.0109i	0.895472	−	0.895472i	−0.0995594	−	0.995032i	$-0.531743\pi$
$281$	15.0109	−	15.0109i	0.895472	−	0.895472i	0.995032	+	0.0995594i	$0.0317433\pi$
$282$	−36.0979	+	87.1480i	−2.14960	+	5.18959i
$283$	−16.8696	−	6.98761i	−1.00279	−	0.415370i	−0.179972	−	0.983672i	$-0.557601\pi$
$283$	−16.8696	−	6.98761i	−1.00279	−	0.415370i	−0.822820	+	0.568301i	$0.807601\pi$
$284$	−12.1083	−	29.2321i	−0.718498	−	1.73461i
$285$			4.14312i			0.245417i
$286$	48.2484	−	19.9851i	2.85299	−	1.18175i
$287$	−1.17688	−	1.17688i	−0.0694691	−	0.0694691i
$288$	0.212245			0.0125067
$289$	6.32496	−	15.7796i	0.372056	−	0.928210i
$290$	−3.54402			−0.208112
$291$	27.0184	+	27.0184i	1.58385	+	1.58385i
$292$	−25.7676	+	10.6733i	−1.50794	+	0.624607i
$293$		−	5.66868i		−	0.331168i	−0.986196	−	0.165584i	$-0.947049\pi$
$293$		−	5.66868i		−	0.331168i	0.986196	−	0.165584i	$-0.0529508\pi$
$294$	−12.5384	−	30.2703i	−0.731252	−	1.76540i
$295$	2.84094	+	1.17676i	0.165406	+	0.0685135i
$296$	−7.99385	+	19.2989i	−0.464633	+	1.12172i
$297$	−42.6750	+	42.6750i	−2.47626	+	2.47626i
$298$	−3.01330	+	3.01330i	−0.174556	+	0.174556i
$299$	−2.77582	+	6.70143i	−0.160530	+	0.387553i
$300$	57.2499	+	23.7137i	3.30532	+	1.36911i
$301$	−0.639449	−	1.54377i	−0.0368572	−	0.0889813i
$302$			47.6198i			2.74021i
$303$	−39.3269	+	16.2898i	−2.25927	+	0.935822i
$304$	−10.3133	−	10.3133i	−0.591507	−	0.591507i
$305$	−1.62363			−0.0929690
$306$	−59.4035	+	40.1870i	−3.39587	+	2.29734i
$307$	−21.3068			−1.21605			−0.608023	−	0.793920i	$-0.708037\pi$
$307$	−21.3068			−1.21605			−0.608023	+	0.793920i	$0.708037\pi$
$308$	21.9101	+	21.9101i	1.24844	+	1.24844i
$309$	−2.00049	+	0.828628i	−0.113804	+	0.0471390i
$310$		−	1.91863i		−	0.108971i
$311$	−11.8155	−	28.5251i	−0.669994	−	1.61751i	−0.781618	−	0.623757i	$-0.785605\pi$
$311$	−11.8155	−	28.5251i	−0.669994	−	1.61751i	0.111625	−	0.993750i	$-0.464395\pi$
$312$	−66.3014	−	27.4629i	−3.75358	−	1.55478i
$313$	7.68068	−	18.5428i	0.434138	−	1.04810i	−0.543802	−	0.839214i	$-0.683016\pi$
$313$	7.68068	−	18.5428i	0.434138	−	1.04810i	0.977940	−	0.208888i	$-0.0669843\pi$
$314$	35.2315	−	35.2315i	1.98823	−	1.98823i
$315$	−3.01293	+	3.01293i	−0.169759	+	0.169759i
$316$	10.1067	−	24.3997i	0.568546	−	1.37259i
$317$	16.4095	+	6.79705i	0.921651	+	0.381760i	0.792505	−	0.609865i	$-0.208777\pi$
$317$	16.4095	+	6.79705i	0.921651	+	0.381760i	0.129146	+	0.991626i	$0.458777\pi$
$318$	−23.8168	−	57.4987i	−1.33558	−	3.22437i
$319$			18.6554i			1.04450i
$320$	−2.64252	+	1.09457i	−0.147721	+	0.0611882i
$321$	41.2667	+	41.2667i	2.30328	+	2.30328i
$322$	−6.45394			−0.359664
$323$	14.6945	+	2.83538i	0.817626	+	0.157765i
$324$	80.4808			4.47116
$325$	−15.8483	−	15.8483i	−0.879103	−	0.879103i
$326$	8.98899	−	3.72336i	0.497854	−	0.206218i
$327$			52.0509i			2.87842i
$328$	1.87067	+	4.51621i	0.103291	+	0.249366i
$329$	18.7020	+	7.74660i	1.03107	+	0.427084i
$330$	−4.95776	+	11.9691i	−0.272916	+	0.658877i
$331$	23.6989	−	23.6989i	1.30261	−	1.30261i	0.375981	−	0.926628i	$-0.377306\pi$
$331$	23.6989	−	23.6989i	1.30261	−	1.30261i	0.926628	−	0.375981i	$-0.122694\pi$
$332$	26.7352	−	26.7352i	1.46728	−	1.46728i
$333$	−11.5640	+	27.9180i	−0.633705	+	1.52990i
$334$	1.67582	+	0.694147i	0.0916967	+	0.0379820i
$335$	0.286162	+	0.690855i	0.0156347	+	0.0377454i
$336$		−	21.3383i		−	1.16410i
$337$	12.5546	−	5.20028i	0.683892	−	0.283277i	−0.0135606	−	0.999908i	$-0.504317\pi$
$337$	12.5546	−	5.20028i	0.683892	−	0.283277i	0.697453	+	0.716631i	$0.254317\pi$
$338$	14.1576	+	14.1576i	0.770071	+	0.770071i
$339$	21.4094			1.16280
$340$	−3.26519	+	4.94793i	−0.177080	+	0.268339i
$341$	−10.0995			−0.546918
$342$	−44.6448	−	44.6448i	−2.41411	−	2.41411i
$343$	−17.3024	+	7.16688i	−0.934240	+	0.386975i
$344$			4.90769i			0.264605i
$345$	−0.688605	−	1.66244i	−0.0370733	−	0.0895028i
$346$	−44.9488	−	18.6184i	−2.41646	−	1.00093i
$347$	−7.56148	+	18.2550i	−0.405921	+	0.979981i	0.580278	+	0.814418i	$0.302944\pi$
$347$	−7.56148	+	18.2550i	−0.405921	+	0.979981i	−0.986199	+	0.165562i	$0.947056\pi$
$348$	36.2268	−	36.2268i	1.94196	−	1.94196i
$349$	−10.8223	+	10.8223i	−0.579302	+	0.579302i	−0.934711	−	0.355409i	$-0.884342\pi$
$349$	−10.8223	+	10.8223i	−0.579302	+	0.579302i	0.355409	+	0.934711i	$0.384342\pi$
$350$	7.63149	−	18.4241i	0.407921	−	0.984807i
$351$	−55.3835	−	22.9406i	−2.95615	−	1.22448i
$352$	−0.0529968	−	0.127946i	−0.00282474	−	0.00681953i
$353$			34.3374i			1.82760i	0.406167	+	0.913799i	$0.366865\pi$
$353$			34.3374i			1.82760i	−0.406167	+	0.913799i	$0.633135\pi$
$354$	−61.5875	+	25.5104i	−3.27334	+	1.35586i
$355$	−2.00746	−	2.00746i	−0.106545	−	0.106545i
$356$	−44.9441			−2.38203
$357$	12.2684	+	18.1348i	0.649311	+	0.959796i
$358$	−24.3920			−1.28916
$359$	1.72341	+	1.72341i	0.0909580	+	0.0909580i	0.751122	−	0.660164i	$-0.229513\pi$
$359$	1.72341	+	1.72341i	0.0909580	+	0.0909580i	−0.660164	+	0.751122i	$0.729513\pi$
$360$	11.5619	−	4.78911i	0.609367	−	0.252408i
$361$		−	5.82535i		−	0.306597i
$362$	−21.4668	−	51.8253i	−1.12827	−	2.72388i
$363$	30.7076	+	12.7195i	1.61173	+	0.667601i
$364$	−11.7781	+	28.4349i	−0.617341	+	1.49039i
$365$	−1.76954	+	1.76954i	−0.0926219	+	0.0926219i
$366$	24.8887	−	24.8887i	1.30095	−	1.30095i
$367$	−11.8763	+	28.6719i	−0.619937	+	1.49666i	0.231840	+	0.972754i	$0.425526\pi$
$367$	−11.8763	+	28.6719i	−0.619937	+	1.49666i	−0.851776	+	0.523905i	$0.824474\pi$
$368$	5.85235	+	2.42412i	0.305075	+	0.126366i
$369$	2.70615	+	6.53322i	0.140876	+	0.340106i
$370$			3.74569i			0.194729i
$371$	−12.3392	+	5.11108i	−0.640621	+	0.265354i
$372$	19.6121	+	19.6121i	1.01684	+	1.01684i
$373$	16.1022			0.833739			0.416870	−	0.908966i	$-0.363127\pi$
$373$	16.1022			0.833739			0.416870	+	0.908966i	$0.363127\pi$
$374$	39.0583	+	25.7750i	2.01966	+	1.33279i
$375$	11.2673			0.581839
$376$	−42.0405	−	42.0405i	−2.16807	−	2.16807i
$377$	−17.1198	+	7.09123i	−0.881712	+	0.365217i
$378$		−	53.3383i		−	2.74342i
$379$	−0.304093	−	0.734147i	−0.0156202	−	0.0377106i	0.915877	−	0.401459i	$-0.131497\pi$
$379$	−0.304093	−	0.734147i	−0.0156202	−	0.0377106i	−0.931497	+	0.363748i	$0.881497\pi$
$380$	−4.82151	−	1.99713i	−0.247338	−	0.102451i
$381$	26.7370	−	64.5488i	1.36978	−	3.30693i
$382$	22.6451	−	22.6451i	1.15862	−	1.15862i
$383$	2.54759	−	2.54759i	0.130176	−	0.130176i	−0.639017	−	0.769193i	$-0.720659\pi$
$383$	2.54759	−	2.54759i	0.130176	−	0.130176i	0.769193	+	0.639017i	$0.220659\pi$
$384$	23.8013	−	57.4615i	1.21461	−	2.93232i
$385$	2.56857	+	1.06394i	0.130906	+	0.0542232i
$386$	9.43301	+	22.7733i	0.480128	+	1.15913i
$387$			7.09954i			0.360890i
$388$	−44.4662	+	18.4185i	−2.25743	+	0.935059i
$389$	−3.77256	−	3.77256i	−0.191276	−	0.191276i	0.604971	−	0.796247i	$-0.293185\pi$
$389$	−3.77256	−	3.77256i	−0.191276	−	0.191276i	−0.796247	+	0.604971i	$0.793185\pi$
$390$	−12.8683			−0.651614
$391$	−6.36749	+	1.30460i	−0.322018	+	0.0659763i
$392$	20.6510			1.04303
$393$	35.8357	+	35.8357i	1.80767	+	1.80767i
$394$	42.2068	−	17.4826i	2.12635	−	0.880763i
$395$		−	2.36966i		−	0.119230i
$396$	−50.3806	−	121.629i	−2.53172	−	6.11211i
$397$	24.2019	+	10.0248i	1.21466	+	0.503128i	0.895708	−	0.444643i	$-0.146669\pi$
$397$	24.2019	+	10.0248i	1.21466	+	0.503128i	0.318951	+	0.947771i	$0.396669\pi$
$398$	−10.3787	+	25.0563i	−0.520235	+	1.25596i
$399$	−13.6292	+	13.6292i	−0.682316	+	0.682316i
$400$	−13.8403	+	13.8403i	−0.692014	+	0.692014i
$401$	7.83386	−	18.9126i	0.391204	−	0.944450i	−0.598474	−	0.801142i	$-0.704226\pi$
$401$	7.83386	−	18.9126i	0.391204	−	0.944450i	0.989678	−	0.143308i	$-0.0457740\pi$
$402$	−14.9767	−	6.20356i	−0.746971	−	0.309405i
$403$	−3.83898	−	9.26812i	−0.191233	−	0.461678i
$404$		−	53.6185i		−	2.66762i
$405$	6.67151	−	2.76343i	0.331510	−	0.137316i
$406$	−11.6584	−	11.6584i	−0.578599	−	0.578599i
$407$	19.7170			0.977337
$408$	−12.9072	−	62.9975i	−0.639001	−	3.11884i
$409$	−17.8123			−0.880761			−0.440381	−	0.897811i	$-0.645157\pi$
$409$	−17.8123			−0.880761			−0.440381	+	0.897811i	$0.645157\pi$
$410$	0.619811	+	0.619811i	0.0306103	+	0.0306103i
$411$	45.4326	−	18.8188i	2.24102	−	0.928262i
$412$		−	2.72747i		−	0.134373i
$413$	5.47453	+	13.2167i	0.269384	+	0.650350i
$414$	25.3340	+	10.4937i	1.24510	+	0.515737i
$415$	1.29824	−	3.13422i	0.0637280	−	0.153853i
$416$	0.0972685	−	0.0972685i	0.00476898	−	0.00476898i
$417$	−5.58553	+	5.58553i	−0.273525	+	0.273525i
$418$	−15.7651	+	38.0604i	−0.771097	+	1.86159i
$419$	−6.21631	−	2.57488i	−0.303687	−	0.125791i	0.225636	−	0.974212i	$-0.427554\pi$
$419$	−6.21631	−	2.57488i	−0.303687	−	0.125791i	−0.529323	+	0.848421i	$0.677554\pi$
$420$	−2.92183	−	7.05392i	−0.142571	−	0.344196i
$421$			11.3071i			0.551072i	0.961291	+	0.275536i	$0.0888554\pi$
$421$			11.3071i			0.551072i	−0.961291	+	0.275536i	$0.911145\pi$
$422$	40.4310	−	16.7471i	1.96815	−	0.815235i
$423$	−60.8164	−	60.8164i	−2.95699	−	2.95699i
$424$	39.2269			1.90502
$425$	3.80503	−	19.7199i	0.184571	−	0.956554i
$426$	61.5448			2.98185
$427$	−5.34112	−	5.34112i	−0.258475	−	0.258475i
$428$	−67.9156	+	28.1316i	−3.28283	+	1.35979i
$429$			67.7380i			3.27042i
$430$	0.336769	+	0.813033i	0.0162405	+	0.0392079i
$431$	−3.60177	−	1.49190i	−0.173491	−	0.0718625i	0.294247	−	0.955729i	$-0.404931\pi$
$431$	−3.60177	−	1.49190i	−0.173491	−	0.0718625i	−0.467739	+	0.883867i	$0.654931\pi$
$432$	−20.0340	+	48.3664i	−0.963887	+	2.32703i
$433$	−6.26661	+	6.26661i	−0.301154	+	0.301154i	−0.841465	−	0.540311i	$-0.818307\pi$
$433$	−6.26661	+	6.26661i	−0.301154	+	0.301154i	0.540311	+	0.841465i	$0.318307\pi$
$434$	6.31153	−	6.31153i	0.302963	−	0.302963i
$435$	1.75914	−	4.24694i	0.0843444	−	0.203625i
$436$	−60.5737	−	25.0904i	−2.90095	−	1.20161i
$437$	−2.18969	−	5.28637i	−0.104747	−	0.252881i
$438$		−	54.2506i		−	2.59220i
$439$	15.8395	−	6.56095i	0.755980	−	0.313137i	0.0288011	−	0.999585i	$-0.490831\pi$
$439$	15.8395	−	6.56095i	0.755980	−	0.313137i	0.727179	+	0.686448i	$0.240831\pi$
$440$	−5.77393	−	5.77393i	−0.275261	−	0.275261i
$441$	29.8741			1.42257
$442$	−8.80655	+	45.6406i	−0.418885	+	2.17090i
$443$	−18.1614			−0.862876			−0.431438	−	0.902143i	$-0.641994\pi$
$443$	−18.1614			−0.862876			−0.431438	+	0.902143i	$0.641994\pi$
$444$	−38.2883	−	38.2883i	−1.81708	−	1.81708i
$445$	−3.72567	+	1.54322i	−0.176613	+	0.0731557i
$446$		−	13.3624i		−	0.632728i
$447$	−2.11525	−	5.10667i	−0.100048	−	0.241537i
$448$	−12.2936	−	5.09216i	−0.580816	−	0.240582i
$449$	−7.75874	+	18.7312i	−0.366157	+	0.883982i	0.628215	+	0.778040i	$0.283786\pi$
$449$	−7.75874	+	18.7312i	−0.366157	+	0.883982i	−0.994372	+	0.105942i	$0.966214\pi$
$450$	−59.9127	+	59.9127i	−2.82431	+	2.82431i
$451$	3.26264	−	3.26264i	0.153632	−	0.153632i
$452$	−10.3201	+	24.9150i	−0.485418	+	1.17190i
$453$	−57.0647	−	23.6370i	−2.68113	−	1.11056i
$454$	5.25661	+	12.6906i	0.246705	+	0.595598i
$455$			2.76155i			0.129463i
$456$	52.3014	−	21.6639i	2.44924	−	1.01451i
$457$	−20.1211	−	20.1211i	−0.941223	−	0.941223i	0.0571428	−	0.998366i	$-0.481801\pi$
$457$	−20.1211	−	20.1211i	−0.941223	−	0.941223i	−0.998366	+	0.0571428i	$0.981801\pi$
$458$	5.65600			0.264288
$459$	−10.7818	−	52.6237i	−0.503250	−	2.45627i
$460$	2.26658			0.105680
$461$	−0.326653	−	0.326653i	−0.0152137	−	0.0152137i	0.699459	−	0.714673i	$-0.253424\pi$
$461$	−0.326653	−	0.326653i	−0.0152137	−	0.0152137i	−0.714673	+	0.699459i	$0.753424\pi$
$462$	−55.6828	+	23.0646i	−2.59060	+	1.07306i
$463$			29.6467i			1.37780i	0.724857	+	0.688899i	$0.241906\pi$
$463$			29.6467i			1.37780i	−0.724857	+	0.688899i	$0.758094\pi$
$464$	6.19277	+	14.9507i	0.287492	+	0.694067i
$465$	2.29917	+	0.952346i	0.106621	+	0.0441640i
$466$	−23.7928	+	57.4408i	−1.10218	+	2.66089i
$467$	−8.70060	+	8.70060i	−0.402616	+	0.402616i	−0.879154	−	0.476538i	$-0.841891\pi$
$467$	−8.70060	+	8.70060i	−0.402616	+	0.402616i	0.476538	+	0.879154i	$0.341891\pi$
$468$	92.4667	−	92.4667i	4.27427	−	4.27427i
$469$	−1.33128	+	3.21400i	−0.0614730	+	0.148409i
$470$	−9.84949	−	4.07979i	−0.454323	−	0.188187i
$471$	24.7316	+	59.7072i	1.13957	+	2.75116i
$472$		−	42.0163i		−	1.93396i
$473$	4.27974	−	1.77273i	0.196783	−	0.0815101i
$474$	36.3246	+	36.3246i	1.66844	+	1.66844i
$475$	17.6802			0.811223
$476$	−27.0180	+	5.53555i	−1.23837	+	0.253722i
$477$	56.7462			2.59823
$478$	20.5759	+	20.5759i	0.941119	+	0.941119i
$479$	−36.5080	+	15.1221i	−1.66809	+	0.690946i	−0.998651	−	0.0519196i	$-0.983466\pi$
$479$	−36.5080	+	15.1221i	−1.66809	+	0.690946i	−0.669440	+	0.742866i	$0.733466\pi$
$480$			0.0341245i			0.00155756i
$481$	7.49476	+	18.0940i	0.341732	+	0.825014i
$482$	−20.2393	−	8.38338i	−0.921874	−	0.381853i
$483$	3.20354	−	7.73402i	0.145766	−	0.351910i
$484$	−29.6044	+	29.6044i	−1.34565	+	1.34565i
$485$	−3.05363	+	3.05363i	−0.138658	+	0.138658i
$486$	−23.2605	+	56.1558i	−1.05512	+	2.54728i
$487$	−7.46746	−	3.09312i	−0.338383	−	0.140163i	0.207020	−	0.978337i	$-0.433623\pi$
$487$	−7.46746	−	3.09312i	−0.338383	−	0.140163i	−0.545403	+	0.838174i	$0.683623\pi$
$488$	8.48981	+	20.4962i	0.384315	+	0.927820i
$489$			12.6200i			0.570698i
$490$	3.42115	−	1.41709i	0.154552	−	0.0640175i
$491$	27.0678	+	27.0678i	1.22155	+	1.22155i	0.967081	+	0.254470i	$0.0819012\pi$
$491$	27.0678	+	27.0678i	1.22155	+	1.22155i	0.254470	+	0.967081i	$0.418099\pi$
$492$	−12.6714			−0.571269
$493$	−13.8589	−	9.14564i	−0.624173	−	0.411899i
$494$	−40.9199			−1.84107
$495$	−8.35266	−	8.35266i	−0.375424	−	0.375424i
$496$	−8.09384	+	3.35258i	−0.363424	+	0.150535i
$497$		−	13.2075i		−	0.592438i
$498$	28.1439	+	67.9454i	1.26116	+	3.04470i
$499$	15.9607	+	6.61114i	0.714500	+	0.295955i	0.710165	−	0.704035i	$-0.248620\pi$
$499$	15.9607	+	6.61114i	0.714500	+	0.295955i	0.00433457	+	0.999991i	$0.498620\pi$
$500$	−5.43123	+	13.1122i	−0.242892	+	0.586393i
$501$	−1.66365	+	1.66365i	−0.0743263	+	0.0743263i
$502$	−13.2577	+	13.2577i	−0.591722	+	0.591722i
$503$	13.3204	−	32.1582i	0.593926	−	1.43387i	−0.285755	−	0.958303i	$-0.592244\pi$
$503$	13.3204	−	32.1582i	0.593926	−	1.43387i	0.879682	−	0.475563i	$-0.157756\pi$
$504$	53.7885	+	22.2799i	2.39593	+	0.992427i
$505$	−1.84107	−	4.44474i	−0.0819266	−	0.197788i
$506$		−	17.8921i		−	0.795400i
$507$	−23.9930	+	9.93823i	−1.06557	+	0.441372i
$508$	62.2297	+	62.2297i	2.76100	+	2.76100i
$509$	−5.61443			−0.248855			−0.124428	−	0.992229i	$-0.539709\pi$
$509$	−5.61443			−0.248855			−0.124428	+	0.992229i	$0.539709\pi$
$510$	−6.46121	−	9.55079i	−0.286107	−	0.422916i
$511$	−11.6422			−0.515020
$512$	27.8042	+	27.8042i	1.22878	+	1.22878i
$513$	43.6889	−	18.0965i	1.92891	−	0.798982i
$514$		−	0.804917i		−	0.0355034i
$515$	−0.0936517	−	0.226095i	−0.00412679	−	0.00996295i
$516$	−11.7532	−	4.86834i	−0.517407	−	0.214317i
$517$	−21.4757	+	51.8469i	−0.944500	+	2.28022i
$518$	−12.3219	+	12.3219i	−0.541392	+	0.541392i
$519$	44.6224	−	44.6224i	1.95871	−	1.95871i
$520$	3.10387	−	7.49340i	0.136114	−	0.328607i
$521$	−17.1671	−	7.11087i	−0.752106	−	0.311533i	−0.0265057	−	0.999649i	$-0.508438\pi$
$521$	−17.1671	−	7.11087i	−0.752106	−	0.311533i	−0.725601	+	0.688116i	$0.758438\pi$
$522$	26.8077	+	64.7195i	1.17334	+	2.83269i
$523$		−	16.2866i		−	0.712163i	−0.934455	−	0.356082i	$-0.884113\pi$
$523$		−	16.2866i		−	0.712163i	0.934455	−	0.356082i	$-0.115887\pi$
$524$	−58.9775	+	24.4293i	−2.57645	+	1.06720i
$525$	18.2903	+	18.2903i	0.798252	+	0.798252i
$526$	35.1443			1.53236
$527$	4.95117	−	7.50279i	0.215676	−	0.326827i
$528$	59.1555			2.57441
$529$	−14.5062	−	14.5062i	−0.630705	−	0.630705i
$530$	6.49852	−	2.69178i	0.282278	−	0.116923i
$531$		−	60.7814i		−	2.63769i
$532$	−9.29109	−	22.4307i	−0.402820	−	0.972493i
$533$	4.23424	+	1.75388i	0.183405	+	0.0759690i
$534$	33.4548	−	80.7669i	1.44773	−	3.49513i
$535$	−4.66397	+	4.66397i	−0.201641	+	0.201641i
$536$	7.22482	−	7.22482i	0.312065	−	0.312065i
$537$	12.1074	−	29.2299i	0.522474	−	1.26136i
$538$	5.30052	+	2.19555i	0.228521	+	0.0946567i
$539$	−7.45944	−	18.0087i	−0.321301	−	0.775688i
$540$			18.7320i			0.806097i
$541$	35.4985	−	14.7040i	1.52620	−	0.632173i	0.547378	−	0.836886i	$-0.315626\pi$
$541$	35.4985	−	14.7040i	1.52620	−	0.632173i	0.978822	+	0.204713i	$0.0656261\pi$
$542$	−24.1590	−	24.1590i	−1.03772	−	1.03772i
$543$	72.7598			3.12242
$544$	0.121030	+	0.0233533i	0.00518914	+	0.00100127i
$545$	−5.88281			−0.251992
$546$	−42.3319	−	42.3319i	−1.81164	−	1.81164i
$547$	33.5004	−	13.8763i	1.43237	−	0.593309i	0.474437	−	0.880289i	$-0.342652\pi$
$547$	33.5004	−	13.8763i	1.43237	−	0.593309i	0.957936	+	0.286981i	$0.0926516\pi$
$548$			61.9429i			2.64607i
$549$	12.2815	+	29.6501i	0.524161	+	1.26544i
$550$	51.0765	+	21.1566i	2.17791	+	0.902119i
$551$	5.59387	−	13.5048i	0.238307	−	0.575324i
$552$	−17.3855	+	17.3855i	−0.739974	+	0.739974i
$553$	7.79525	−	7.79525i	0.331488	−	0.331488i
$554$	−4.02347	+	9.71351i	−0.170941	+	0.412687i
$555$	−4.48862	−	1.85925i	−0.190531	−	0.0789206i
$556$	−3.80767	−	9.19253i	−0.161481	−	0.389850i
$557$			11.0520i			0.468288i	0.972202	+	0.234144i	$0.0752287\pi$
$557$			11.0520i			0.468288i	−0.972202	+	0.234144i	$0.924771\pi$
$558$	−35.0372	+	14.5129i	−1.48324	+	0.614379i
$559$	3.25360	+	3.25360i	0.137613	+	0.137613i
$560$	2.41166			0.101911
$561$	−50.2746	+	34.0113i	−2.12260	+	1.43596i
$562$	−52.0123			−2.19401
$563$	−5.28365	−	5.28365i	−0.222679	−	0.222679i	0.586946	−	0.809626i	$-0.300330\pi$
$563$	−5.28365	−	5.28365i	−0.222679	−	0.222679i	−0.809626	+	0.586946i	$0.800330\pi$
$564$	142.384	−	58.9775i	5.99546	−	2.48340i
$565$			2.41970i			0.101797i
$566$	17.1204	+	41.3324i	0.719625	+	1.73733i
$567$	31.0373	+	12.8561i	1.30344	+	0.539904i
$568$	−14.8447	+	35.8383i	−0.622869	+	1.50374i
$569$	−29.6943	+	29.6943i	−1.24485	+	1.24485i	−0.286882	+	0.957966i	$0.592619\pi$
$569$	−29.6943	+	29.6943i	−1.24485	+	1.24485i	−0.957966	+	0.286882i	$0.907381\pi$
$570$	7.17792	−	7.17792i	0.300650	−	0.300650i
$571$	2.05137	−	4.95245i	0.0858473	−	0.207254i	−0.875126	−	0.483895i	$-0.839222\pi$
$571$	2.05137	−	4.95245i	0.0858473	−	0.207254i	0.960973	+	0.276642i	$0.0892215\pi$
$572$	−78.8293	−	32.6521i	−3.29602	−	1.36525i
$573$	15.8962	+	38.3769i	0.664074	+	1.60322i
$574$			4.07787i			0.170207i
$575$	−7.09424	+	2.93853i	−0.295850	+	0.122545i
$576$	39.9771	+	39.9771i	1.66571	+	1.66571i
$577$	29.6355			1.23374			0.616871	−	0.787064i	$-0.288400\pi$
$577$	29.6355			1.23374			0.616871	+	0.787064i	$0.288400\pi$
$578$	−38.2959	+	16.3800i	−1.59290	+	0.681319i
$579$	−31.9724			−1.32873
$580$	4.09436	+	4.09436i	0.170009	+	0.170009i
$581$	14.5811	−	6.03968i	0.604925	−	0.250568i
$582$		−	93.6184i		−	3.88061i
$583$	−14.1693	−	34.2077i	−0.586832	−	1.41674i
$584$	31.5908	+	13.0853i	1.30724	+	0.541475i
$585$	4.49010	−	10.8401i	0.185643	−	0.448181i
$586$	−9.82093	+	9.82093i	−0.405699	+	0.405699i
$587$	−20.9035	+	20.9035i	−0.862781	+	0.862781i	−0.991660	−	0.128879i	$-0.958862\pi$
$587$	−20.9035	+	20.9035i	−0.862781	+	0.862781i	0.128879	+	0.991660i	$0.458862\pi$
$588$	−20.4854	+	49.4562i	−0.844805	+	2.03954i
$589$	7.31109	+	3.02835i	0.301248	+	0.124781i
$590$	−2.88319	−	6.96063i	−0.118699	−	0.286565i
$591$			59.2560i			2.43747i
$592$	15.8014	−	6.54517i	0.649435	−	0.269005i
$593$	26.8548	+	26.8548i	1.10279	+	1.10279i	0.994072	+	0.108720i	$0.0346752\pi$
$593$	26.8548	+	26.8548i	1.10279	+	1.10279i	0.108720	+	0.994072i	$0.465325\pi$
$594$	147.868			6.06710
$595$	−2.04960	+	1.38657i	−0.0840254	+	0.0568440i
$596$	6.96246			0.285193
$597$	−24.8743	−	24.8743i	−1.01804	−	1.01804i
$598$	16.4192	−	6.80107i	0.671433	−	0.278117i
$599$			0.763279i			0.0311868i	0.999878	+	0.0155934i	$0.00496373\pi$
$599$			0.763279i			0.0311868i	−0.999878	+	0.0155934i	$0.995036\pi$
$600$	−29.0727	−	70.1877i	−1.18689	−	2.86540i
$601$	12.7972	+	5.30078i	0.522009	+	0.216223i	0.628099	−	0.778133i	$-0.283833\pi$
$601$	12.7972	+	5.30078i	0.522009	+	0.216223i	−0.106090	+	0.994357i	$0.533833\pi$
$602$	−1.56672	+	3.78240i	−0.0638548	+	0.154159i
$603$	10.4515	−	10.4515i	0.425619	−	0.425619i
$604$	55.0145	−	55.0145i	2.23851	−	2.23851i
$605$	−1.43756	+	3.47058i	−0.0584452	+	0.141099i
$606$	96.3554	+	39.9117i	3.91417	+	1.62130i
$607$	6.25840	+	15.1091i	0.254021	+	0.613260i	0.998521	−	0.0543616i	$-0.0173124\pi$
$607$	6.25840	+	15.1091i	0.254021	+	0.613260i	−0.744501	+	0.667622i	$0.767312\pi$
$608$			0.108512i			0.00440074i
$609$	19.7577	−	8.18390i	0.800621	−	0.331628i
$610$	2.81293	+	2.81293i	0.113892	+	0.113892i
$611$	−55.7422			−2.25509
$612$	115.056	+	22.2005i	4.65085	+	0.897401i
$613$	25.0812			1.01302			0.506511	−	0.862233i	$-0.330935\pi$
$613$	25.0812			1.01302			0.506511	+	0.862233i	$0.330935\pi$
$614$	36.9139	+	36.9139i	1.48972	+	1.48972i
$615$	−1.05040	+	0.435090i	−0.0423562	+	0.0175445i
$616$		−	37.9880i		−	1.53058i
$617$	−11.7052	−	28.2589i	−0.471235	−	1.13766i	−0.963618	−	0.267283i	$-0.913874\pi$
$617$	−11.7052	−	28.2589i	−0.471235	−	1.13766i	0.492383	−	0.870379i	$-0.336126\pi$
$618$	4.90141	+	2.03023i	0.197164	+	0.0816679i
$619$	6.88838	−	16.6300i	0.276867	−	0.668417i	−0.722878	−	0.690975i	$-0.757181\pi$
$619$	6.88838	−	16.6300i	0.276867	−	0.668417i	0.999746	+	0.0225587i	$0.00718127\pi$
$620$	−2.21656	+	2.21656i	−0.0890193	+	0.0890193i
$621$	−14.5226	+	14.5226i	−0.582772	+	0.582772i
$622$	−28.9492	+	69.8896i	−1.16076	+	2.80232i
$623$	−17.3326	−	7.17939i	−0.694415	−	0.287636i
$624$	22.4860	+	54.2859i	0.900159	+	2.17318i
$625$		−	23.0815i		−	0.923261i
$626$	−45.4319	+	18.8185i	−1.81583	+	0.752140i
$627$	−37.7840	−	37.7840i	−1.50895	−	1.50895i
$628$	−81.4051			−3.24842
$629$	−9.66607	+	14.6475i	−0.385411	+	0.584036i
$630$	10.4397			0.415929
$631$	−22.8510	−	22.8510i	−0.909685	−	0.909685i	0.0865617	−	0.996246i	$-0.472412\pi$
$631$	−22.8510	−	22.8510i	−0.909685	−	0.909685i	−0.996246	+	0.0865617i	$0.972412\pi$
$632$	−29.9138	+	12.3907i	−1.18991	+	0.492875i
$633$			56.7629i			2.25612i
$634$	−16.6535	−	40.2052i	−0.661396	−	1.59675i
$635$	7.29532	+	3.02182i	0.289506	+	0.119917i
$636$	−38.9124	+	93.9427i	−1.54298	+	3.72507i
$637$	13.6908	−	13.6908i	0.542448	−	0.542448i
$638$	32.3204	−	32.3204i	1.27958	−	1.27958i
$639$	−21.4746	+	51.8442i	−0.849521	+	2.05092i
$640$	6.49431	+	2.69003i	0.256710	+	0.106333i
$641$	1.69486	+	4.09174i	0.0669428	+	0.161614i	0.953810	−	0.300410i	$-0.0971234\pi$
$641$	1.69486	+	4.09174i	0.0669428	+	0.161614i	−0.886867	+	0.462024i	$0.847123\pi$
$642$		−	142.988i		−	5.64330i
$643$	−20.2537	+	8.38937i	−0.798729	+	0.330844i	−0.744447	−	0.667681i	$-0.767287\pi$
$643$	−20.2537	+	8.38937i	−0.798729	+	0.330844i	−0.0542819	+	0.998526i	$0.517287\pi$
$644$	7.45616	+	7.45616i	0.293814	+	0.293814i
$645$	−1.14145			−0.0449447
$646$	−20.5459	−	30.3704i	−0.808368	−	1.19491i
$647$	−19.3776			−0.761812			−0.380906	−	0.924614i	$-0.624388\pi$
$647$	−19.3776			−0.761812			−0.380906	+	0.924614i	$0.624388\pi$
$648$	−69.7692	−	69.7692i	−2.74079	−	2.74079i
$649$	−36.6402	+	15.1769i	−1.43825	+	0.595744i
$650$			54.9139i			2.15390i
$651$	4.43052	+	10.6962i	0.173646	+	0.419218i
$652$	−14.6864	−	6.08331i	−0.575165	−	0.238241i
$653$	2.77334	−	6.69544i	0.108529	−	0.262013i	−0.860279	−	0.509823i	$-0.829711\pi$
$653$	2.77334	−	6.69544i	0.108529	−	0.262013i	0.968809	+	0.247810i	$0.0797109\pi$
$654$	90.1778	−	90.1778i	3.52623	−	3.52623i
$655$	−4.05016	+	4.05016i	−0.158253	+	0.158253i
$656$	1.53166	−	3.69776i	0.0598014	−	0.144373i
$657$	45.6998	+	18.9295i	1.78292	+	0.738508i
$658$	−18.9800	−	45.8219i	−0.739919	−	1.78632i
$659$			13.7567i			0.535885i	0.963435	+	0.267942i	$0.0863437\pi$
$659$			13.7567i			0.535885i	−0.963435	+	0.267942i	$0.913656\pi$
$660$	19.5554	−	8.10011i	0.761192	−	0.315296i
$661$	6.55171	+	6.55171i	0.254832	+	0.254832i	0.822948	−	0.568116i	$-0.192328\pi$
$661$	6.55171	+	6.55171i	0.254832	+	0.254832i	−0.568116	+	0.822948i	$0.692328\pi$
$662$	−82.1162			−3.19154
$663$	−50.3217	−	33.2078i	−1.95433	−	1.28969i
$664$	−46.3538			−1.79887
$665$	−1.54038	−	1.54038i	−0.0597334	−	0.0597334i
$666$	68.4023	−	28.3332i	2.65054	−	1.09789i
$667$			6.34857i			0.245818i
$668$	−1.13411	−	2.73799i	−0.0438801	−	0.105936i
$669$	16.0127	+	6.63269i	0.619088	+	0.256434i
$670$	0.701128	−	1.69267i	0.0270869	−	0.0653936i
$671$	14.8070	−	14.8070i	0.571619	−	0.571619i
$672$	−0.112256	+	0.112256i	−0.00433038	+	0.00433038i
$673$	−8.98828	+	21.6996i	−0.346473	+	0.836459i	0.650558	+	0.759457i	$0.274535\pi$
$673$	−8.98828	+	21.6996i	−0.346473	+	0.836459i	−0.997031	+	0.0770029i	$0.975465\pi$
$674$	−30.7602	−	12.7413i	−1.18484	−	0.490776i
$675$	−24.2853	−	58.6299i	−0.934742	−	2.25667i
$676$		−	32.7122i		−	1.25816i
$677$	10.2495	−	4.24549i	0.393921	−	0.163167i	−0.176926	−	0.984224i	$-0.556615\pi$
$677$	10.2495	−	4.24549i	0.393921	−	0.163167i	0.570846	+	0.821057i	$0.306615\pi$
$678$	−37.0916	−	37.0916i	−1.42450	−	1.42450i
$679$	−20.0905			−0.771003
$680$	7.11999	−	1.45877i	0.273039	−	0.0559414i
$681$	−17.8169			−0.682743
$682$	17.4973	+	17.4973i	0.670005	+	0.670005i
$683$	6.67963	−	2.76679i	0.255589	−	0.105868i	−0.251210	−	0.967933i	$-0.580829\pi$
$683$	6.67963	−	2.76679i	0.255589	−	0.105868i	0.506799	+	0.862064i	$0.330829\pi$
$684$			103.155i			3.94423i
$685$	2.12690	+	5.13480i	0.0812648	+	0.196191i
$686$	42.3927	+	17.5596i	1.61856	+	0.670430i
$687$	−2.80746	+	6.77782i	−0.107111	+	0.258590i
$688$	2.84137	−	2.84137i	0.108326	−	0.108326i
$689$	26.0058	−	26.0058i	0.990742	−	0.990742i
$690$	−1.68716	+	4.07316i	−0.0642291	+	0.155063i
$691$	24.6904	+	10.2271i	0.939267	+	0.389057i	0.799187	−	0.601083i	$-0.205264\pi$
$691$	24.6904	+	10.2271i	0.939267	+	0.389057i	0.140081	+	0.990140i	$0.455264\pi$
$692$	30.4192	+	73.4384i	1.15636	+	2.79171i
$693$		−	54.9540i		−	2.08753i
$694$	44.7268	−	18.5265i	1.69781	−	0.703255i
$695$	−0.631278	−	0.631278i	−0.0239457	−	0.0239457i
$696$	−62.8104			−2.38082
$697$	0.824299	+	4.02325i	0.0312226	+	0.152391i
$698$	37.4989			1.41935
$699$	−57.0237	−	57.0237i	−2.15683	−	2.15683i
$700$	−30.1016	+	12.4685i	−1.13774	+	0.471265i
$701$		−	31.4077i		−	1.18625i	−0.805110	−	0.593126i	$-0.797894\pi$
$701$		−	31.4077i		−	1.18625i	0.805110	−	0.593126i	$-0.202106\pi$
$702$	56.2071	+	135.696i	2.12140	+	5.12151i
$703$	−14.2733	−	5.91219i	−0.538327	−	0.222983i
$704$	14.1168	−	34.0811i	0.532049	−	1.28448i
$705$	9.77796	−	9.77796i	0.368259	−	0.368259i
$706$	59.4893	−	59.4893i	2.23891	−	2.23891i
$707$	8.56506	−	20.6779i	0.322122	−	0.777671i
$708$	100.623	+	41.6794i	3.78165	+	1.56641i
$709$	9.28446	+	22.4147i	0.348685	+	0.841801i	0.996776	+	0.0802374i	$0.0255678\pi$
$709$	9.28446	+	22.4147i	0.348685	+	0.841801i	−0.648091	+	0.761563i	$0.724432\pi$
$710$			6.95580i			0.261047i
$711$	−43.2737	+	17.9246i	−1.62289	+	0.672224i
$712$	38.9622	+	38.9622i	1.46017	+	1.46017i
$713$	−3.43692			−0.128714
$714$	10.1635	−	52.6732i	0.380360	−	1.97125i
$715$	−7.65576			−0.286309
$716$	28.1798	+	28.1798i	1.05313	+	1.05313i
$717$	−34.8701	+	14.4437i	−1.30225	+	0.539409i
$718$		−	5.97158i		−	0.222857i
$719$	−3.37646	−	8.15149i	−0.125921	−	0.303999i	0.848330	−	0.529468i	$-0.177609\pi$
$719$	−3.37646	−	8.15149i	−0.125921	−	0.303999i	−0.974250	+	0.225469i	$0.927609\pi$
$720$	−9.46662	−	3.92120i	−0.352800	−	0.146135i
$721$	0.435688	−	1.05184i	0.0162259	−	0.0391727i
$722$	−10.0924	+	10.0924i	−0.375599	+	0.375599i
$723$	20.0923	−	20.0923i	0.747240	−	0.747240i
$724$	−35.0729	+	84.6734i	−1.30347	+	3.14686i
$725$	−18.1232	−	7.50689i	−0.673080	−	0.278799i
$726$	−31.1642	−	75.2371i	−1.15661	−	2.79231i
$727$		−	11.9093i		−	0.441690i	−0.975309	−	0.220845i	$-0.929119\pi$
$727$		−	11.9093i		−	0.441690i	0.975309	−	0.220845i	$-0.0708815\pi$
$728$	34.8609	−	14.4398i	1.29203	−	0.535176i
$729$	−13.0991	−	13.0991i	−0.485153	−	0.485153i
$730$	6.13142			0.226934
$731$	−0.781162	+	4.04843i	−0.0288923	+	0.149737i
$732$	−57.5072			−2.12553
$733$	24.5751	+	24.5751i	0.907702	+	0.907702i	0.996086	−	0.0883849i	$-0.0281705\pi$
$733$	24.5751	+	24.5751i	0.907702	+	0.907702i	−0.0883849	+	0.996086i	$0.528171\pi$
$734$	70.2493	−	29.0982i	2.59295	−	1.07403i
$735$			4.80310i			0.177165i
$736$	−0.0180352	−	0.0435408i	−0.000664786	−	0.00160493i
$737$	−8.91009	−	3.69068i	−0.328207	−	0.135948i
$738$	6.63036	−	16.0071i	0.244067	−	0.589230i
$739$	23.7769	−	23.7769i	0.874648	−	0.874648i	−0.118327	−	0.992975i	$-0.537753\pi$
$739$	23.7769	−	23.7769i	0.874648	−	0.874648i	0.992975	+	0.118327i	$0.0377531\pi$
$740$	4.32735	−	4.32735i	0.159077	−	0.159077i
$741$	20.3114	−	49.0360i	0.746157	−	1.80138i
$742$	30.2325	+	12.5227i	1.10987	+	0.459723i
$743$	5.73786	+	13.8524i	0.210502	+	0.508196i	0.993501	−	0.113827i	$-0.0363110\pi$
$743$	5.73786	+	13.8524i	0.210502	+	0.508196i	−0.782999	+	0.622023i	$0.786311\pi$
$744$		−	34.0036i		−	1.24663i
$745$	0.577157	−	0.239066i	0.0211454	−	0.00875871i
$746$	−27.8969	−	27.8969i	−1.02138	−	1.02138i
$747$	−67.0561			−2.45345
$748$	−15.3460	−	74.9011i	−0.561107	−	2.73866i
$749$	−30.6853			−1.12122
$750$	−19.5204	−	19.5204i	−0.712786	−	0.712786i
$751$	−0.796333	+	0.329852i	−0.0290586	+	0.0120365i	−0.397165	−	0.917747i	$-0.630006\pi$
$751$	−0.796333	+	0.329852i	−0.0290586	+	0.0120365i	0.368107	+	0.929784i	$0.380006\pi$
$752$			48.6796i			1.77516i
$753$	−9.30656	−	22.4680i	−0.339150	−	0.818780i
$754$	41.9453	+	17.3743i	1.52756	+	0.632735i
$755$	2.67146	−	6.44947i	0.0972243	−	0.234720i
$756$	−61.6210	+	61.6210i	−2.24113	+	2.24113i
$757$	20.0327	−	20.0327i	0.728102	−	0.728102i	−0.242140	−	0.970241i	$-0.577849\pi$
$757$	20.0327	−	20.0327i	0.728102	−	0.728102i	0.970241	+	0.242140i	$0.0778492\pi$
$758$	−0.745063	+	1.79874i	−0.0270619	+	0.0653332i
$759$	21.4408	+	8.88108i	0.778252	+	0.322363i
$760$	2.44846	+	5.91111i	0.0888151	+	0.214419i
$761$			31.5235i			1.14273i	0.820697	+	0.571363i	$0.193585\pi$
$761$			31.5235i			1.14273i	−0.820697	+	0.571363i	$0.806415\pi$
$762$	−158.152	+	65.5086i	−5.72923	+	2.37313i
$763$	−19.3522	−	19.3522i	−0.700595	−	0.700595i
$764$	−52.3232			−1.89299
$765$	10.2999	−	2.11028i	0.372393	−	0.0762975i
$766$	−8.82735			−0.318945
$767$	−27.8551	−	27.8551i	−1.00579	−	1.00579i
$768$	−94.0251	+	38.9465i	−3.39284	+	1.40536i
$769$			6.90701i			0.249073i	0.992215	+	0.124537i	$0.0397444\pi$
$769$			6.90701i			0.249073i	−0.992215	+	0.124537i	$0.960256\pi$
$770$	−2.60676	−	6.29328i	−0.0939412	−	0.226794i
$771$	0.964565	+	0.399536i	0.0347379	+	0.0143889i
$772$	15.4119	−	37.2075i	0.554685	−	1.33913i
$773$	−10.6689	+	10.6689i	−0.383733	+	0.383733i	−0.872445	−	0.488712i	$-0.837467\pi$
$773$	−10.6689	+	10.6689i	−0.383733	+	0.383733i	0.488712	+	0.872445i	$0.337467\pi$
$774$	12.2999	−	12.2999i	0.442111	−	0.442111i
$775$	4.06401	−	9.81138i	0.145983	−	0.352435i
$776$	54.5151	+	22.5809i	1.95698	+	0.810607i
$777$	−8.64961	−	20.8820i	−0.310303	−	0.749137i
$778$			13.0718i			0.468648i
$779$	−3.34015	+	1.38354i	−0.119673	+	0.0495703i
$780$	14.8666	+	14.8666i	0.532311	+	0.532311i
$781$	36.6148			1.31018
$782$	13.2918	+	8.77141i	0.475314	+	0.313665i
$783$	−52.4674			−1.87503
$784$	−11.9561	−	11.9561i	−0.427005	−	0.427005i
$785$	−6.74813	+	2.79517i	−0.240851	+	0.0997637i
$786$		−	124.170i		−	4.42900i
$787$	13.7585	+	33.2160i	0.490438	+	1.18402i	0.954498	+	0.298217i	$0.0963921\pi$
$787$	13.7585	+	33.2160i	0.490438	+	1.18402i	−0.464060	+	0.885804i	$0.653608\pi$
$788$	−68.9585	−	28.5635i	−2.45654	−	1.01753i
$789$	−17.4445	+	42.1149i	−0.621042	+	1.49933i
$790$	−4.10541	+	4.10541i	−0.146064	+	0.146064i
$791$	−7.95987	+	7.95987i	−0.283020	+	0.283020i
$792$	−61.7660	+	149.116i	−2.19476	+	5.29862i
$793$	19.2165	+	7.95975i	0.682399	+	0.282659i
$794$	−24.5618	−	59.2974i	−0.871665	−	2.10439i
$795$			9.12355i			0.323579i
$796$	40.9376	−	16.9569i	1.45099	−	0.601021i
$797$	30.3909	+	30.3909i	1.07650	+	1.07650i	0.996821	+	0.0796786i	$0.0253894\pi$
$797$	30.3909	+	30.3909i	1.07650	+	1.07650i	0.0796786	+	0.996821i	$0.474611\pi$
$798$	47.2251			1.67175
$799$	−27.9882	−	41.3714i	−0.990151	−	1.46362i
$800$	0.145622			0.00514850
$801$	56.3634	+	56.3634i	1.99150	+	1.99150i
$802$	−46.3380	+	19.1938i	−1.63625	+	0.677758i
$803$		−	32.2753i		−	1.13897i
$804$	10.1355	+	24.4693i	0.357452	+	0.862966i
$805$	0.874101	+	0.362065i	0.0308080	+	0.0127611i
$806$	−9.40593	+	22.7079i	−0.331310	+	0.799853i
$807$	−5.26202	+	5.26202i	−0.185232	+	0.185232i
$808$	−46.4822	+	46.4822i	−1.63524	+	1.63524i
$809$	−13.9414	+	33.6574i	−0.490152	+	1.18333i	0.464490	+	0.885578i	$0.346238\pi$
$809$	−13.9414	+	33.6574i	−0.490152	+	1.18333i	−0.954643	+	0.297754i	$0.903762\pi$
$810$	−16.3459	−	6.77071i	−0.574338	−	0.237899i
$811$	−0.944867	−	2.28111i	−0.0331788	−	0.0801006i	0.906422	−	0.422374i	$-0.138803\pi$
$811$	−0.944867	−	2.28111i	−0.0331788	−	0.0801006i	−0.939600	+	0.342273i	$0.888803\pi$
$812$			26.9377i			0.945328i
$813$	40.9426	−	16.9590i	1.43592	−	0.594777i
$814$	−34.1596	−	34.1596i	−1.19729	−	1.19729i
$815$	−1.42632			−0.0499618
$816$	−29.0004	+	43.9459i	−1.01522	+	1.53841i
$817$	−3.62969			−0.126987
$818$	30.8596	+	30.8596i	1.07898	+	1.07898i
$819$	50.4303	−	20.8889i	1.76218	−	0.729917i
$820$		−	1.43212i		−	0.0500118i
$821$	−6.97363	−	16.8358i	−0.243381	−	0.587575i	0.754233	−	0.656607i	$-0.228009\pi$
$821$	−6.97363	−	16.8358i	−0.243381	−	0.587575i	−0.997614	+	0.0690322i	$0.978009\pi$
$822$	−111.315	−	46.1081i	−3.88255	−	1.60821i
$823$	−0.503652	+	1.21592i	−0.0175562	+	0.0423844i	−0.932415	−	0.361391i	$-0.882302\pi$
$823$	−0.503652	+	1.21592i	−0.0175562	+	0.0423844i	0.914858	+	0.403775i	$0.132302\pi$
$824$	−2.36446	+	2.36446i	−0.0823698	+	0.0823698i
$825$	−50.7056	+	50.7056i	−1.76534	+	1.76534i
$826$	13.4132	−	32.3823i	0.466705	−	1.12673i
$827$	51.6473	+	21.3930i	1.79595	+	0.743907i	0.987959	+	0.154714i	$0.0494455\pi$
$827$	51.6473	+	21.3930i	1.79595	+	0.743907i	0.807992	+	0.589194i	$0.200554\pi$
$828$	−17.1449	−	41.3913i	−0.595825	−	1.43845i
$829$		−	49.1246i		−	1.70617i	−0.521774	−	0.853084i	$-0.674729\pi$
$829$		−	49.1246i		−	1.70617i	0.521774	−	0.853084i	$-0.325271\pi$
$830$	−7.67920	+	3.18083i	−0.266549	+	0.110408i
$831$	−9.64297	−	9.64297i	−0.334511	−	0.334511i
$832$	36.6416			1.27032
$833$	17.0353	+	3.28704i	0.590239	+	0.113889i
$834$	19.3538			0.670166
$835$	−0.188026	−	0.188026i	−0.00650691	−	0.00650691i
$836$	62.1839	−	25.7574i	2.15068	−	0.890839i
$837$		−	28.4043i		−	0.981795i
$838$	6.30874	+	15.2307i	0.217932	+	0.526134i
$839$	−5.90091	−	2.44424i	−0.203722	−	0.0843844i	0.278489	−	0.960439i	$-0.410166\pi$
$839$	−5.90091	−	2.44424i	−0.203722	−	0.0843844i	−0.482211	+	0.876055i	$0.660166\pi$
$840$	−3.58213	+	8.64803i	−0.123595	+	0.298385i
$841$	9.03800	−	9.03800i	0.311655	−	0.311655i
$842$	19.5894	−	19.5894i	0.675094	−	0.675094i
$843$	25.8173	−	62.3285i	0.889195	−	2.14671i
$844$	−66.0571	−	27.3618i	−2.27378	−	0.941830i
$845$	−1.12322	−	2.71169i	−0.0386400	−	0.0932851i
$846$			210.728i			7.24497i
$847$	−16.1459	+	6.68784i	−0.554779	+	0.229797i
$848$	−22.7108	−	22.7108i	−0.779894	−	0.779894i
$849$	−58.0283			−1.99153
$850$	−40.7567	+	27.5723i	−1.39794	+	0.945722i
$851$	6.70984			0.230010
$852$	−71.1019	−	71.1019i	−2.43591	−	2.43591i
$853$	−10.1637	+	4.20996i	−0.348000	+	0.144146i	−0.549835	−	0.835273i	$-0.685309\pi$
$853$	−10.1637	+	4.20996i	−0.348000	+	0.144146i	0.201835	+	0.979419i	$0.435309\pi$
$854$			18.5069i			0.633292i
$855$	3.54198	+	8.55111i	0.121133	+	0.292442i
$856$	83.2638	+	34.4890i	2.84590	+	1.17881i
$857$	18.0922	−	43.6786i	0.618019	−	1.49203i	−0.235980	−	0.971758i	$-0.575830\pi$
$857$	18.0922	−	43.6786i	0.618019	−	1.49203i	0.854000	−	0.520273i	$-0.174170\pi$
$858$	117.355	−	117.355i	4.00645	−	4.00645i
$859$	0.655570	−	0.655570i	0.0223678	−	0.0223678i	−0.695834	−	0.718202i	$-0.744965\pi$
$859$	0.655570	−	0.655570i	0.0223678	−	0.0223678i	0.718202	+	0.695834i	$0.244965\pi$
$860$	0.550221	−	1.32835i	0.0187624	−	0.0452964i
$861$	−4.88668	−	2.02413i	−0.166538	−	0.0689822i
$862$	3.65533	+	8.82475i	0.124501	+	0.300572i
$863$			2.83426i			0.0964792i	0.998836	+	0.0482396i	$0.0153611\pi$
$863$			2.83426i			0.0964792i	−0.998836	+	0.0482396i	$0.984639\pi$
$864$	0.359840	−	0.149051i	0.0122420	−	0.00507081i
$865$	5.04324	+	5.04324i	0.171475	+	0.171475i
$866$	21.7137			0.737862
$867$	−0.619962	−	54.0221i	−0.0210550	−	1.83469i
$868$	−14.5833			−0.494988
$869$	21.6105	+	21.6105i	0.733088	+	0.733088i
$870$	−10.4055	+	4.31009i	−0.352779	+	0.146126i
$871$		−	9.57952i		−	0.324590i
$872$	30.7606	+	74.2626i	1.04169	+	2.51485i
$873$	78.8624	+	32.6659i	2.66909	+	1.10557i
$874$	−5.36498	+	12.9522i	−0.181473	+	0.438115i
$875$	−4.18909	+	4.18909i	−0.141617	+	0.141617i
$876$	−62.6751	+	62.6751i	−2.11759	+	2.11759i
$877$	−3.76889	+	9.09891i	−0.127266	+	0.307248i	−0.974651	−	0.223732i	$-0.928176\pi$
$877$	−3.76889	+	9.09891i	−0.127266	+	0.307248i	0.847384	+	0.530980i	$0.178176\pi$
$878$	−38.8086	−	16.0751i	−1.30973	−	0.542507i
$879$	−6.89401	−	16.6436i	−0.232529	−	0.561375i
$880$			6.68577i			0.225377i
$881$	17.4062	−	7.20990i	0.586431	−	0.242908i	−0.0696831	−	0.997569i	$-0.522199\pi$
$881$	17.4062	−	7.20990i	0.586431	−	0.242908i	0.656115	+	0.754661i	$0.272199\pi$
$882$	−51.7566	−	51.7566i	−1.74273	−	1.74273i
$883$	−42.8439			−1.44181			−0.720906	−	0.693032i	$-0.756274\pi$
$883$	−42.8439			−1.44181			−0.720906	+	0.693032i	$0.756274\pi$
$884$	62.9021	−	42.5539i	2.11563	−	1.43124i
$885$	9.77233			0.328493
$886$	31.4645	+	31.4645i	1.05707	+	1.05707i
$887$	13.5011	−	5.59233i	0.453322	−	0.187772i	−0.144327	−	0.989530i	$-0.546102\pi$
$887$	13.5011	−	5.59233i	0.453322	−	0.187772i	0.597649	+	0.801758i	$0.296102\pi$
$888$			66.3846i			2.22772i
$889$	14.0581	+	33.9394i	0.471495	+	1.13829i
$890$	9.12830	+	3.78106i	0.305981	+	0.126742i
$891$	−35.6405	+	86.0437i	−1.19400	+	2.88257i
$892$	−15.4374	+	15.4374i	−0.516883	+	0.516883i
$893$	31.0928	−	31.0928i	1.04048	−	1.04048i
$894$	−5.18261	+	12.5119i	−0.173332	+	0.418461i
$895$	3.30357	+	1.36839i	0.110426	+	0.0457401i
$896$	12.5146	+	30.2129i	0.418083	+	1.00934i
$897$			23.0517i			0.769673i
$898$	45.8936	−	19.0098i	1.53149	−	0.634364i
$899$	−6.20848	−	6.20848i	−0.207064	−	0.207064i
$900$	138.433			4.61442
$901$	32.3588	+	6.24377i	1.07803	+	0.208010i
$902$	−11.3050			−0.376414
$903$	−3.75493	−	3.75493i	−0.124956	−	0.124956i
$904$	30.5455	−	12.6524i	1.01593	−	0.420811i
$905$			8.22333i			0.273353i
$906$	57.9132	+	139.815i	1.92404	+	4.64504i
$907$	−46.3585	−	19.2023i	−1.53931	−	0.637603i	−0.557966	−	0.829864i	$-0.688418\pi$
$907$	−46.3585	−	19.2023i	−1.53931	−	0.637603i	−0.981344	+	0.192261i	$0.938418\pi$
$908$	8.58837	−	20.7342i	0.285015	−	0.688087i
$909$	−67.2418	+	67.2418i	−2.23027	+	2.23027i
$910$	4.78436	−	4.78436i	0.158600	−	0.158600i
$911$	−9.73188	+	23.4948i	−0.322431	+	0.778418i	0.676680	+	0.736277i	$0.263418\pi$
$911$	−9.73188	+	23.4948i	−0.322431	+	0.778418i	−0.999112	+	0.0421413i	$0.986582\pi$
$912$	−42.8231	−	17.7379i	−1.41801	−	0.587361i
$913$	16.7436	+	40.4227i	0.554133	+	1.33780i
$914$			69.7191i			2.30610i
$915$	−4.76710	+	1.97460i	−0.157595	+	0.0652782i
$916$	−6.53430	−	6.53430i	−0.215899	−	0.215899i
$917$	−26.6469			−0.879959
$918$	−72.4908	+	109.849i	−2.39255	+	3.62557i
$919$	−24.9716			−0.823738			−0.411869	−	0.911243i	$-0.635124\pi$
$919$	−24.9716			−0.823738			−0.411869	+	0.911243i	$0.635124\pi$
$920$	−1.96491	−	1.96491i	−0.0647811	−	0.0647811i
$921$	−62.5583	+	25.9125i	−2.06137	+	0.853846i
$922$			1.13185i			0.0372754i
$923$	13.9179	+	33.6007i	0.458112	+	1.10598i
$924$	90.9758	+	37.6834i	2.99288	+	1.23969i
$925$	−7.93408	+	19.1546i	−0.260871	+	0.629798i
$926$	51.3626	−	51.3626i	1.68788	−	1.68788i
$927$	−3.42046	+	3.42046i	−0.112343	+	0.112343i
$928$	0.0460735	−	0.111231i	0.00151244	−	0.00365134i
$929$	−47.3905	−	19.6298i	−1.55483	−	0.644032i	−0.570649	−	0.821194i	$-0.693308\pi$
$929$	−47.3905	−	19.6298i	−1.55483	−	0.644032i	−0.984182	+	0.177162i	$0.943308\pi$
$930$	−2.33335	−	5.63322i	−0.0765137	−	0.184720i
$931$			15.2733i			0.500563i
$932$	93.8481	−	38.8731i	3.07410	−	1.27333i
$933$	−69.3820	−	69.3820i	−2.27147	−	2.27147i
$934$	30.1474			0.986454
$935$	−3.84396	−	5.68205i	−0.125711	−	0.185823i
$936$	−160.320			−5.24021
$937$	−27.8436	−	27.8436i	−0.909611	−	0.909611i	0.0866296	−	0.996241i	$-0.472390\pi$
$937$	−27.8436	−	27.8436i	−0.909611	−	0.909611i	−0.996241	+	0.0866296i	$0.972390\pi$
$938$	7.87467	−	3.26180i	0.257117	−	0.106501i
$939$		−	63.7839i		−	2.08151i
$940$	6.66565	+	16.0923i	0.217410	+	0.524873i
$941$	−32.2993	−	13.3788i	−1.05293	−	0.436137i	−0.211992	−	0.977271i	$-0.567995\pi$
$941$	−32.2993	−	13.3788i	−1.05293	−	0.436137i	−0.840936	+	0.541134i	$0.817995\pi$
$942$	60.5951	−	146.289i	1.97429	−	4.76637i
$943$	1.11030	−	1.11030i	0.0361562	−	0.0361562i
$944$	−24.3258	+	24.3258i	−0.791738	+	0.791738i
$945$	−2.99226	+	7.22396i	−0.0973383	+	0.234995i
$946$	−10.4858	−	4.34338i	−0.340924	−	0.141215i
$947$	3.32154	+	8.01890i	0.107935	+	0.260579i	0.968614	−	0.248569i	$-0.0799604\pi$
$947$	3.32154	+	8.01890i	0.107935	+	0.260579i	−0.860679	+	0.509149i	$0.829960\pi$
$948$		−	83.9306i		−	2.72594i
$949$	29.6185	−	12.2684i	0.961456	−	0.398248i
$950$	−30.6308	−	30.6308i	−0.993794	−	0.993794i
$951$	56.4458			1.83038
$952$	28.2208	+	18.6232i	0.914641	+	0.603582i
$953$	−17.1212			−0.554611			−0.277306	−	0.960782i	$-0.589441\pi$
$953$	−17.1212			−0.554611			−0.277306	+	0.960782i	$0.589441\pi$
$954$	−98.3122	−	98.3122i	−3.18298	−	3.18298i
$955$	−4.33737	+	1.79660i	−0.140354	+	0.0581365i
$956$		−	47.5421i		−	1.53762i
$957$	22.6880	+	54.7736i	0.733398	+	1.77058i
$958$	89.4486	+	37.0508i	2.88995	+	1.19706i
$959$	−9.89480	+	23.8882i	−0.319520	+	0.771389i
$960$	−6.42745	+	6.42745i	−0.207445	+	0.207445i
$961$	−18.5592	+	18.5592i	−0.598685	+	0.598685i
$962$	18.3630	−	44.3322i	0.592047	−	1.42933i
$963$	120.451	+	49.8923i	3.88147	+	1.60776i
$964$	13.6970	+	33.0674i	0.441149	+	1.06503i
$965$		−	3.61353i		−	0.116324i
$966$	−18.9492	+	7.84903i	−0.609681	+	0.252538i
$967$	9.78804	+	9.78804i	0.314762	+	0.314762i	0.846751	−	0.531989i	$-0.178555\pi$
$967$	9.78804	+	9.78804i	0.314762	+	0.314762i	−0.531989	+	0.846751i	$0.678555\pi$
$968$	51.3284			1.64976
$969$	46.5925	−	9.54605i	1.49677	−	0.306663i
$970$	10.5808			0.339728
$971$	22.9117	+	22.9117i	0.735271	+	0.735271i	0.971659	−	0.236388i	$-0.0759635\pi$
$971$	22.9117	+	22.9117i	0.735271	+	0.735271i	−0.236388	+	0.971659i	$0.575963\pi$
$972$	91.7487	−	38.0035i	2.94284	−	1.21896i
$973$		−	4.15332i		−	0.133149i
$974$	7.57849	+	18.2961i	0.242831	+	0.586245i
$975$	−65.8056	−	27.2576i	−2.10747	−	0.872941i
$976$	6.95125	−	16.7818i	0.222504	−	0.537172i
$977$	−6.12002	+	6.12002i	−0.195797	+	0.195797i	−0.798195	−	0.602399i	$-0.794212\pi$
$977$	−6.12002	+	6.12002i	−0.195797	+	0.195797i	0.602399	+	0.798195i	$0.294212\pi$
$978$	21.8641	−	21.8641i	0.699137	−	0.699137i
$979$	19.9032	−	48.0506i	0.636110	−	1.53570i
$980$	−5.58956	−	2.31527i	−0.178552	−	0.0739586i
$981$	44.4987	+	107.429i	1.42074	+	3.42996i
$982$		−	93.7893i		−	2.99294i
$983$	−45.5944	+	18.8858i	−1.45424	+	0.602365i	−0.963203	−	0.268776i	$-0.913381\pi$
$983$	−45.5944	+	18.8858i	−1.45424	+	0.602365i	−0.491034	+	0.871140i	$0.663381\pi$
$984$	10.9849	+	10.9849i	0.350185	+	0.350185i
$985$	−6.69713			−0.213388
$986$	8.16568	+	39.8551i	0.260048	+	1.26925i
$987$	64.3313			2.04769
$988$	47.2742	+	47.2742i	1.50399	+	1.50399i
$989$	1.45643	−	0.603271i	0.0463116	−	0.0191829i
$990$			28.9418i			0.919831i
$991$	−5.66257	−	13.6707i	−0.179877	−	0.434263i	0.808063	−	0.589096i	$-0.200516\pi$
$991$	−5.66257	−	13.6707i	−0.179877	−	0.434263i	−0.987941	+	0.154833i	$0.950516\pi$
$992$	0.0602172	+	0.0249428i	0.00191190	+	0.000791934i
$993$	40.7599	−	98.4031i	1.29348	−	3.12273i
$994$	−22.8819	+	22.8819i	−0.725769	+	0.725769i
$995$	2.81130	−	2.81130i	0.0891243	−	0.0891243i
$996$	45.9821	−	111.011i	1.45700	−	3.51751i
$997$	23.5737	+	9.76456i	0.746588	+	0.309247i	0.723348	−	0.690483i	$-0.242602\pi$
$997$	23.5737	+	9.76456i	0.746588	+	0.309247i	0.0232391	+	0.999730i	$0.492602\pi$
$998$	−16.1980	−	39.1055i	−0.512740	−	1.23786i
$999$			55.4531i			1.75446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.m.c.87.3	✓	128
17.9	even	8	inner	731.2.m.c.689.3	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.m.c.87.3	✓	128	1.1	even	1	trivial
731.2.m.c.689.3	yes	128	17.9	even	8	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:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73249 - 1.73249i) q^{2} +(2.93607 - 1.21616i) q^{3} +4.00305i q^{4} +(0.137451 + 0.331835i) q^{5} +(-7.19370 - 2.97973i) q^{6} +(-0.639449 + 1.54377i) q^{7} +(3.47026 - 3.47026i) q^{8} +(5.02014 - 5.02014i) q^{9} +O(q^{10})\)	\(q+(-1.73249 - 1.73249i) q^{2} +(2.93607 - 1.21616i) q^{3} +4.00305i q^{4} +(0.137451 + 0.331835i) q^{5} +(-7.19370 - 2.97973i) q^{6} +(-0.639449 + 1.54377i) q^{7} +(3.47026 - 3.47026i) q^{8} +(5.02014 - 5.02014i) q^{9} +(0.336769 - 0.813033i) q^{10} +(-4.27974 - 1.77273i) q^{11} +(4.86834 + 11.7532i) q^{12} -4.60128i q^{13} +(3.78240 - 1.56672i) q^{14} +(0.807129 + 0.807129i) q^{15} -4.01830 q^{16} +(3.41504 - 2.31031i) q^{17} -17.3947 q^{18} +(2.56658 + 2.56658i) q^{19} +(-1.32835 + 0.550221i) q^{20} +5.31028i q^{21} +(4.34338 + 10.4858i) q^{22} +(-1.45643 - 0.603271i) q^{23} +(5.96854 - 14.4093i) q^{24} +(3.44431 - 3.44431i) q^{25} +(-7.97168 + 7.97168i) q^{26} +(4.98570 - 12.0365i) q^{27} +(-6.17978 - 2.55975i) q^{28} +(-1.54114 - 3.72065i) q^{29} -2.79669i q^{30} +(2.01425 - 0.834328i) q^{31} +(0.0211394 + 0.0211394i) q^{32} -14.7215 q^{33} +(-9.91911 - 1.91393i) q^{34} -0.600169 q^{35} +(20.0958 + 20.0958i) q^{36} +(-3.93237 + 1.62884i) q^{37} -8.89315i q^{38} +(-5.59589 - 13.5097i) q^{39} +(1.62854 + 0.674565i) q^{40} +(-0.381172 + 0.920231i) q^{41} +(9.20001 - 9.20001i) q^{42} +(-0.707107 + 0.707107i) q^{43} +(7.09631 - 17.1320i) q^{44} +(2.35588 + 0.975837i) q^{45} +(1.47808 + 3.56840i) q^{46} -12.1145i q^{47} +(-11.7980 + 4.88689i) q^{48} +(2.97543 + 2.97543i) q^{49} -11.9345 q^{50} +(7.21708 - 10.9365i) q^{51} +18.4192 q^{52} +(5.65186 + 5.65186i) q^{53} +(-29.4909 + 12.2155i) q^{54} -1.66383i q^{55} +(3.13822 + 7.57633i) q^{56} +(10.6570 + 4.41428i) q^{57} +(-3.77597 + 9.11600i) q^{58} +(6.05376 - 6.05376i) q^{59} +(-3.23098 + 3.23098i) q^{60} +(-1.72990 + 4.17634i) q^{61} +(-4.93513 - 2.04420i) q^{62} +(4.53980 + 10.9600i) q^{63} +7.96335i q^{64} +(1.52687 - 0.632449i) q^{65} +(25.5049 + 25.5049i) q^{66} +2.08192 q^{67} +(9.24827 + 13.6706i) q^{68} -5.00984 q^{69} +(1.03979 + 1.03979i) q^{70} +(-7.30247 + 3.02478i) q^{71} -34.8424i q^{72} +(2.66629 + 6.43700i) q^{73} +(9.63475 + 3.99084i) q^{74} +(5.92390 - 14.3016i) q^{75} +(-10.2741 + 10.2741i) q^{76} +(5.47336 - 5.47336i) q^{77} +(-13.7106 + 33.1002i) q^{78} +(-6.09528 - 2.52475i) q^{79} +(-0.552318 - 1.33341i) q^{80} -20.1049i q^{81} +(2.25467 - 0.933914i) q^{82} +(-6.67871 - 6.67871i) q^{83} -21.2573 q^{84} +(1.23604 + 0.815676i) q^{85} +2.45011 q^{86} +(-9.04980 - 9.04980i) q^{87} +(-21.0037 + 8.70000i) q^{88} +11.2275i q^{89} +(-2.39091 - 5.77216i) q^{90} +(7.10331 + 2.94229i) q^{91} +(2.41492 - 5.83014i) q^{92} +(4.89929 - 4.89929i) q^{93} +(-20.9882 + 20.9882i) q^{94} +(-0.498903 + 1.20446i) q^{95} +(0.0877757 + 0.0363579i) q^{96} +(4.60112 + 11.1081i) q^{97} -10.3098i q^{98} +(-30.3842 + 12.5856i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9}+O(q^{10}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9	\( 128 q + 4 q^{2} + 4 q^{3} + 8 q^{5} - 12 q^{6} + 4 q^{7} - 4 q^{8} + 8 q^{9} - 8 q^{10} - 4 q^{11} + 12 q^{12} + 12 q^{14} - 12 q^{15} - 144 q^{16} - 12 q^{17} + 64 q^{18} - 28 q^{19} - 8 q^{20} - 12 q^{22} + 16 q^{23} - 16 q^{24} - 20 q^{25} + 16 q^{26} - 8 q^{27} + 20 q^{28} + 12 q^{31} - 4 q^{32} - 104 q^{33} + 20 q^{34} + 32 q^{35} - 96 q^{36} - 12 q^{37} + 8 q^{39} + 216 q^{40} + 24 q^{41} - 4 q^{42} + 24 q^{44} - 28 q^{45} - 48 q^{46} + 28 q^{48} - 80 q^{50} - 20 q^{51} + 56 q^{52} - 36 q^{53} - 12 q^{54} - 8 q^{56} + 72 q^{57} - 32 q^{58} + 48 q^{59} - 40 q^{60} - 76 q^{61} - 44 q^{62} + 36 q^{65} - 68 q^{66} - 48 q^{67} + 32 q^{68} + 216 q^{69} - 196 q^{70} + 4 q^{71} + 20 q^{73} + 88 q^{74} + 80 q^{75} + 72 q^{76} + 28 q^{77} - 120 q^{78} + 68 q^{79} - 68 q^{80} + 28 q^{82} - 36 q^{83} - 152 q^{84} + 28 q^{85} - 24 q^{86} - 56 q^{87} + 20 q^{88} - 112 q^{90} + 96 q^{91} - 28 q^{92} + 24 q^{93} - 36 q^{94} - 108 q^{95} + 272 q^{96} + 8 q^{97} - 20 q^{99}+O(q^{100}) \) 128 * q + 4 * q^2 + 4 * q^3 + 8 * q^5 - 12 * q^6 + 4 * q^7 - 4 * q^8 + 8 * q^9 - 8 * q^10 - 4 * q^11 + 12 * q^12 + 12 * q^14 - 12 * q^15 - 144 * q^16 - 12 * q^17 + 64 * q^18 - 28 * q^19 - 8 * q^20 - 12 * q^22 + 16 * q^23 - 16 * q^24 - 20 * q^25 + 16 * q^26 - 8 * q^27 + 20 * q^28 + 12 * q^31 - 4 * q^32 - 104 * q^33 + 20 * q^34 + 32 * q^35 - 96 * q^36 - 12 * q^37 + 8 * q^39 + 216 * q^40 + 24 * q^41 - 4 * q^42 + 24 * q^44 - 28 * q^45 - 48 * q^46 + 28 * q^48 - 80 * q^50 - 20 * q^51 + 56 * q^52 - 36 * q^53 - 12 * q^54 - 8 * q^56 + 72 * q^57 - 32 * q^58 + 48 * q^59 - 40 * q^60 - 76 * q^61 - 44 * q^62 + 36 * q^65 - 68 * q^66 - 48 * q^67 + 32 * q^68 + 216 * q^69 - 196 * q^70 + 4 * q^71 + 20 * q^73 + 88 * q^74 + 80 * q^75 + 72 * q^76 + 28 * q^77 - 120 * q^78 + 68 * q^79 - 68 * q^80 + 28 * q^82 - 36 * q^83 - 152 * q^84 + 28 * q^85 - 24 * q^86 - 56 * q^87 + 20 * q^88 - 112 * q^90 + 96 * q^91 - 28 * q^92 + 24 * q^93 - 36 * q^94 - 108 * q^95 + 272 * q^96 + 8 * q^97 - 20 * q^99

Introduction

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