LMFDB - Embedded newform 510.2.l.f.137.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(137,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("510.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			137.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	510.137
Dual form			510.2.l.f.443.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(0.599900 - 1.62484i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(0.724745 + 1.57313i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.28024 - 1.94949i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.599900 - 1.62484i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(0.724745 + 1.57313i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.28024 - 1.94949i) q^{9} +(0.224745 - 2.22474i) q^{10} +1.41421i q^{11} +(-1.62484 - 0.599900i) q^{12} +(-4.22474 + 4.22474i) q^{13} +1.41421 q^{14} +(1.25882 + 3.66270i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(2.99087 - 0.233875i) q^{18} +7.44949i q^{19} +(1.41421 + 1.73205i) q^{20} +(-2.22474 + 1.02494i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-1.73205 - 1.73205i) q^{23} +(1.57313 - 0.724745i) q^{24} +(1.00000 - 4.89898i) q^{25} -5.97469i q^{26} +(-4.53553 + 2.53553i) q^{27} +(-1.00000 + 1.00000i) q^{28} -3.78194 q^{29} +(-3.48004 - 1.69980i) q^{30} +3.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.29788 + 0.848387i) q^{33} +1.00000i q^{34} +(3.14626 + 0.317837i) q^{35} +(-1.94949 + 2.28024i) q^{36} +(2.89898 + 2.89898i) q^{37} +(-5.26758 - 5.26758i) q^{38} +(4.33013 + 9.39898i) q^{39} +(-2.22474 - 0.224745i) q^{40} +8.34242i q^{41} +(0.848387 - 2.29788i) q^{42} +(-7.44949 + 7.44949i) q^{43} +1.41421 q^{44} +(6.70648 + 0.151870i) q^{45} +2.44949 q^{46} +(-3.53553 + 3.53553i) q^{47} +(-0.599900 + 1.62484i) q^{48} -5.00000i q^{49} +(2.75699 + 4.17121i) q^{50} +(-0.724745 - 1.57313i) q^{51} +(4.22474 + 4.22474i) q^{52} +(-9.36736 - 9.36736i) q^{53} +(1.41421 - 5.00000i) q^{54} +(-2.00000 - 2.44949i) q^{55} -1.41421i q^{56} +(12.1043 + 4.46895i) q^{57} +(2.67423 - 2.67423i) q^{58} +3.14626 q^{59} +(3.66270 - 1.25882i) q^{60} -6.34847 q^{61} +(-2.12132 + 2.12132i) q^{62} +(0.330749 + 4.22973i) q^{63} +1.00000i q^{64} +(1.34278 - 13.2922i) q^{65} +(-2.22474 + 1.02494i) q^{66} +(-5.55051 - 5.55051i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(-3.85337 + 1.77526i) q^{69} +(-2.44949 + 2.00000i) q^{70} +1.09638i q^{71} +(-0.233875 - 2.99087i) q^{72} +(7.67423 - 7.67423i) q^{73} -4.09978 q^{74} +(-7.36018 - 4.56374i) q^{75} +7.44949 q^{76} +(1.41421 - 1.41421i) q^{77} +(-9.70794 - 3.58422i) q^{78} +2.89898i q^{79} +(1.73205 - 1.41421i) q^{80} +(1.39898 + 8.89060i) q^{81} +(-5.89898 - 5.89898i) q^{82} +(-5.65685 - 5.65685i) q^{83} +(1.02494 + 2.22474i) q^{84} +(-0.224745 + 2.22474i) q^{85} -10.5352i q^{86} +(-2.26879 + 6.14506i) q^{87} +(-1.00000 + 1.00000i) q^{88} +12.4101 q^{89} +(-4.84959 + 4.63481i) q^{90} +8.44949 q^{91} +(-1.73205 + 1.73205i) q^{92} +(1.79970 - 4.87453i) q^{93} -5.00000i q^{94} +(-10.5352 - 12.9029i) q^{95} +(-0.724745 - 1.57313i) q^{96} +(-8.12372 - 8.12372i) q^{97} +(3.53553 + 3.53553i) q^{98} +(2.75699 - 3.22474i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) $ 8 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	$ 8 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 24 q^{13} + 8 q^{15} - 8 q^{16} + 8 q^{18} - 8 q^{21} - 8 q^{22} + 8 q^{25} - 8 q^{27} - 8 q^{28} - 8 q^{30} + 24 q^{31} - 4 q^{33} + 4 q^{36} - 16 q^{37} - 8 q^{40} + 4 q^{42} - 40 q^{43} + 12 q^{45} - 4 q^{48} + 4 q^{51} + 24 q^{52} - 16 q^{55} + 32 q^{57} - 8 q^{58} + 16 q^{60} + 8 q^{61} + 4 q^{63} - 8 q^{66} - 64 q^{67} - 8 q^{72} + 32 q^{73} - 20 q^{75} + 40 q^{76} - 28 q^{81} - 8 q^{82} + 8 q^{85} + 40 q^{87} - 8 q^{88} - 20 q^{90} + 48 q^{91} + 12 q^{93} + 4 q^{96} - 16 q^{97}+O(q^{100}) $ 8 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 24 * q^13 + 8 * q^15 - 8 * q^16 + 8 * q^18 - 8 * q^21 - 8 * q^22 + 8 * q^25 - 8 * q^27 - 8 * q^28 - 8 * q^30 + 24 * q^31 - 4 * q^33 + 4 * q^36 - 16 * q^37 - 8 * q^40 + 4 * q^42 - 40 * q^43 + 12 * q^45 - 4 * q^48 + 4 * q^51 + 24 * q^52 - 16 * q^55 + 32 * q^57 - 8 * q^58 + 16 * q^60 + 8 * q^61 + 4 * q^63 - 8 * q^66 - 64 * q^67 - 8 * q^72 + 32 * q^73 - 20 * q^75 + 40 * q^76 - 28 * q^81 - 8 * q^82 + 8 * q^85 + 40 * q^87 - 8 * q^88 - 20 * q^90 + 48 * q^91 + 12 * q^93 + 4 * q^96 - 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.599900	−	1.62484i	0.346353	−	0.938104i
$3$	0.599900	−	1.62484i	0.346353	−	0.938104i
$4$		−	1.00000i		−	0.500000i
$5$	−1.73205	+	1.41421i	−0.774597	+	0.632456i
$5$	−1.73205	+	1.41421i	−0.774597	+	0.632456i
$6$	0.724745	+	1.57313i	0.295876	+	0.642229i
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−2.28024	−	1.94949i	−0.760080	−	0.649830i
$10$	0.224745	−	2.22474i	0.0710706	−	0.703526i
$11$			1.41421i			0.426401i	0.977008	+	0.213201i	$0.0683888\pi$
$11$			1.41421i			0.426401i	−0.977008	+	0.213201i	$0.931611\pi$
$12$	−1.62484	−	0.599900i	−0.469052	−	0.173176i
$13$	−4.22474	+	4.22474i	−1.17173	+	1.17173i	−0.189937	+	0.981796i	$0.560828\pi$
$13$	−4.22474	+	4.22474i	−1.17173	+	1.17173i	−0.981796	+	0.189937i	$0.939172\pi$
$14$	1.41421			0.377964
$15$	1.25882	+	3.66270i	0.325026	+	0.945705i
$16$	−1.00000			−0.250000
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$17$	0.707107	−	0.707107i	0.171499	−	0.171499i
$18$	2.99087	−	0.233875i	0.704955	−	0.0551249i
$19$			7.44949i			1.70903i	0.519427	+	0.854515i	$0.326146\pi$
$19$			7.44949i			1.70903i	−0.519427	+	0.854515i	$0.673854\pi$
$20$	1.41421	+	1.73205i	0.316228	+	0.387298i
$21$	−2.22474	+	1.02494i	−0.485479	+	0.223661i
$22$	−1.00000	−	1.00000i	−0.213201	−	0.213201i
$23$	−1.73205	−	1.73205i	−0.361158	−	0.361158i	0.503081	−	0.864239i	$-0.332200\pi$
$23$	−1.73205	−	1.73205i	−0.361158	−	0.361158i	−0.864239	+	0.503081i	$0.832200\pi$
$24$	1.57313	−	0.724745i	0.321114	−	0.147938i
$25$	1.00000	−	4.89898i	0.200000	−	0.979796i
$26$		−	5.97469i		−	1.17173i
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$	−3.78194			−0.702288			−0.351144	−	0.936321i	$-0.614207\pi$
$29$	−3.78194			−0.702288			−0.351144	+	0.936321i	$0.614207\pi$
$30$	−3.48004	−	1.69980i	−0.635365	−	0.310340i
$31$	3.00000			0.538816			0.269408	−	0.963026i	$-0.413172\pi$
$31$	3.00000			0.538816			0.269408	+	0.963026i	$0.413172\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	2.29788	+	0.848387i	0.400009	+	0.147685i
$34$			1.00000i			0.171499i
$35$	3.14626	+	0.317837i	0.531816	+	0.0537243i
$36$	−1.94949	+	2.28024i	−0.324915	+	0.380040i
$37$	2.89898	+	2.89898i	0.476589	+	0.476589i	0.904039	−	0.427450i	$-0.140588\pi$
$37$	2.89898	+	2.89898i	0.476589	+	0.476589i	−0.427450	+	0.904039i	$0.640588\pi$
$38$	−5.26758	−	5.26758i	−0.854515	−	0.854515i
$39$	4.33013	+	9.39898i	0.693375	+	1.50504i
$40$	−2.22474	−	0.224745i	−0.351763	−	0.0355353i
$41$			8.34242i			1.30287i	0.758706	+	0.651433i	$0.225832\pi$
$41$			8.34242i			1.30287i	−0.758706	+	0.651433i	$0.774168\pi$
$42$	0.848387	−	2.29788i	0.130909	−	0.354570i
$43$	−7.44949	+	7.44949i	−1.13604	+	1.13604i	−0.146883	+	0.989154i	$0.546924\pi$
$43$	−7.44949	+	7.44949i	−1.13604	+	1.13604i	−0.989154	+	0.146883i	$0.953076\pi$
$44$	1.41421			0.213201
$45$	6.70648	+	0.151870i	0.999744	+	0.0226395i
$46$	2.44949			0.361158
$47$	−3.53553	+	3.53553i	−0.515711	+	0.515711i	−0.916271	−	0.400560i	$-0.868816\pi$
$47$	−3.53553	+	3.53553i	−0.515711	+	0.515711i	0.400560	+	0.916271i	$0.368816\pi$
$48$	−0.599900	+	1.62484i	−0.0865882	+	0.234526i
$49$		−	5.00000i		−	0.714286i
$50$	2.75699	+	4.17121i	0.389898	+	0.589898i
$51$	−0.724745	−	1.57313i	−0.101485	−	0.220283i
$52$	4.22474	+	4.22474i	0.585867	+	0.585867i
$53$	−9.36736	−	9.36736i	−1.28671	−	1.28671i	−0.936776	−	0.349930i	$-0.886205\pi$
$53$	−9.36736	−	9.36736i	−1.28671	−	1.28671i	−0.349930	−	0.936776i	$-0.613795\pi$
$54$	1.41421	−	5.00000i	0.192450	−	0.680414i
$55$	−2.00000	−	2.44949i	−0.269680	−	0.330289i
$56$		−	1.41421i		−	0.188982i
$57$	12.1043	+	4.46895i	1.60325	+	0.591927i
$58$	2.67423	−	2.67423i	0.351144	−	0.351144i
$59$	3.14626			0.409609			0.204804	−	0.978803i	$-0.434344\pi$
$59$	3.14626			0.409609			0.204804	+	0.978803i	$0.434344\pi$
$60$	3.66270	−	1.25882i	0.472853	−	0.162513i
$61$	−6.34847			−0.812838			−0.406419	−	0.913687i	$-0.633223\pi$
$61$	−6.34847			−0.812838			−0.406419	+	0.913687i	$0.633223\pi$
$62$	−2.12132	+	2.12132i	−0.269408	+	0.269408i
$63$	0.330749	+	4.22973i	0.0416705	+	0.532896i
$64$			1.00000i			0.125000i
$65$	1.34278	−	13.2922i	0.166552	−	1.64869i
$66$	−2.22474	+	1.02494i	−0.273847	+	0.126162i
$67$	−5.55051	−	5.55051i	−0.678103	−	0.678103i	0.281468	−	0.959571i	$-0.409179\pi$
$67$	−5.55051	−	5.55051i	−0.678103	−	0.678103i	−0.959571	+	0.281468i	$0.909179\pi$
$68$	−0.707107	−	0.707107i	−0.0857493	−	0.0857493i
$69$	−3.85337	+	1.77526i	−0.463891	+	0.213716i
$70$	−2.44949	+	2.00000i	−0.292770	+	0.239046i
$71$			1.09638i			0.130116i	0.997881	+	0.0650580i	$0.0207232\pi$
$71$			1.09638i			0.130116i	−0.997881	+	0.0650580i	$0.979277\pi$
$72$	−0.233875	−	2.99087i	−0.0275624	−	0.352477i
$73$	7.67423	−	7.67423i	0.898201	−	0.898201i	−0.0970758	−	0.995277i	$-0.530949\pi$
$73$	7.67423	−	7.67423i	0.898201	−	0.898201i	0.995277	+	0.0970758i	$0.0309489\pi$
$74$	−4.09978			−0.476589
$75$	−7.36018	−	4.56374i	−0.849880	−	0.526976i
$76$	7.44949			0.854515
$77$	1.41421	−	1.41421i	0.161165	−	0.161165i
$78$	−9.70794	−	3.58422i	−1.09921	−	0.405833i
$79$			2.89898i			0.326161i	0.986613	+	0.163080i	$0.0521430\pi$
$79$			2.89898i			0.326161i	−0.986613	+	0.163080i	$0.947857\pi$
$80$	1.73205	−	1.41421i	0.193649	−	0.158114i
$81$	1.39898	+	8.89060i	0.155442	+	0.987845i
$82$	−5.89898	−	5.89898i	−0.651433	−	0.651433i
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	0.324846	−	0.945767i	$-0.394687\pi$
$83$	−5.65685	−	5.65685i	−0.620920	−	0.620920i	−0.945767	+	0.324846i	$0.894687\pi$
$84$	1.02494	+	2.22474i	0.111831	+	0.242740i
$85$	−0.224745	+	2.22474i	−0.0243770	+	0.241307i
$86$		−	10.5352i		−	1.13604i
$87$	−2.26879	+	6.14506i	−0.243239	+	0.658820i
$88$	−1.00000	+	1.00000i	−0.106600	+	0.106600i
$89$	12.4101			1.31547			0.657733	−	0.753251i	$-0.271515\pi$
$89$	12.4101			1.31547			0.657733	+	0.753251i	$0.271515\pi$
$90$	−4.84959	+	4.63481i	−0.511192	+	0.488552i
$91$	8.44949			0.885747
$92$	−1.73205	+	1.73205i	−0.180579	+	0.180579i
$93$	1.79970	−	4.87453i	0.186620	−	0.505466i
$94$		−	5.00000i		−	0.515711i
$95$	−10.5352	−	12.9029i	−1.08089	−	1.32381i
$96$	−0.724745	−	1.57313i	−0.0739690	−	0.160557i
$97$	−8.12372	−	8.12372i	−0.824839	−	0.824839i	0.161958	−	0.986798i	$-0.448219\pi$
$97$	−8.12372	−	8.12372i	−0.824839	−	0.824839i	−0.986798	+	0.161958i	$0.948219\pi$
$98$	3.53553	+	3.53553i	0.357143	+	0.357143i
$99$	2.75699	−	3.22474i	0.277088	−	0.324099i
$100$	−4.89898	−	1.00000i	−0.489898	−	0.100000i
$101$			2.04989i			0.203971i	0.994786	+	0.101986i	$0.0325196\pi$
$101$			2.04989i			0.203971i	−0.994786	+	0.101986i	$0.967480\pi$
$102$	1.62484	+	0.599900i	0.160884	+	0.0593990i
$103$	−7.79796	+	7.79796i	−0.768356	+	0.768356i	−0.977817	−	0.209461i	$-0.932829\pi$
$103$	−7.79796	+	7.79796i	−0.768356	+	0.768356i	0.209461	+	0.977817i	$0.432829\pi$
$104$	−5.97469			−0.585867
$105$	2.40388	−	4.92152i	0.234595	−	0.480291i
$106$	13.2474			1.28671
$107$	12.5851	−	12.5851i	1.21664	−	1.21664i	0.247843	−	0.968800i	$-0.420278\pi$
$107$	12.5851	−	12.5851i	1.21664	−	1.21664i	0.968800	−	0.247843i	$-0.0797218\pi$
$108$	2.53553	+	4.53553i	0.243982	+	0.436432i
$109$			10.3485i			0.991204i	0.868550	+	0.495602i	$0.165052\pi$
$109$			10.3485i			0.991204i	−0.868550	+	0.495602i	$0.834948\pi$
$110$	3.14626	+	0.317837i	0.299985	+	0.0303046i
$111$	6.44949	−	2.97129i	0.612158	−	0.282023i
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	−1.97846	−	1.97846i	−0.186117	−	0.186117i	0.607898	−	0.794015i	$-0.292013\pi$
$113$	−1.97846	−	1.97846i	−0.186117	−	0.186117i	−0.794015	+	0.607898i	$0.792013\pi$
$114$	−11.7190	+	5.39898i	−1.09759	+	0.505661i
$115$	5.44949	+	0.550510i	0.508168	+	0.0513353i
$116$			3.78194i			0.351144i
$117$	17.8695	−	1.39733i	1.65204	−	0.129183i
$118$	−2.22474	+	2.22474i	−0.204804	+	0.204804i
$119$	−1.41421			−0.129641
$120$	−1.69980	+	3.48004i	−0.155170	+	0.317683i
$121$	9.00000			0.818182
$122$	4.48905	−	4.48905i	0.406419	−	0.406419i
$123$	13.5551	+	5.00462i	1.22222	+	0.451251i
$124$		−	3.00000i		−	0.269408i
$125$	5.19615	+	9.89949i	0.464758	+	0.885438i
$126$	−3.22474	−	2.75699i	−0.287283	−	0.245613i
$127$	−1.22474	−	1.22474i	−0.108679	−	0.108679i	0.650677	−	0.759355i	$-0.274485\pi$
$127$	−1.22474	−	1.22474i	−0.108679	−	0.108679i	−0.759355	+	0.650677i	$0.774485\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	7.63531	+	16.5732i	0.672252	+	1.45919i
$130$	8.44949	+	10.3485i	0.741069	+	0.907621i
$131$			4.73545i			0.413738i	0.978369	+	0.206869i	$0.0663274\pi$
$131$			4.73545i			0.413738i	−0.978369	+	0.206869i	$0.933673\pi$
$132$	0.848387	−	2.29788i	0.0738426	−	0.200005i
$133$	7.44949	−	7.44949i	0.645953	−	0.645953i
$134$	7.84961			0.678103
$135$	4.26999	−	10.8059i	0.367502	−	0.930023i
$136$	1.00000			0.0857493
$137$	10.2173	−	10.2173i	0.872926	−	0.872926i	−0.119865	−	0.992790i	$-0.538246\pi$
$137$	10.2173	−	10.2173i	0.872926	−	0.872926i	0.992790	+	0.119865i	$0.0382461\pi$
$138$	1.46945	−	3.98004i	0.125088	−	0.338803i
$139$			1.79796i			0.152501i	0.997089	+	0.0762504i	$0.0242949\pi$
$139$			1.79796i			0.152501i	−0.997089	+	0.0762504i	$0.975705\pi$
$140$	0.317837	−	3.14626i	0.0268622	−	0.265908i
$141$	3.62372	+	7.86566i	0.305173	+	0.662408i
$142$	−0.775255	−	0.775255i	−0.0650580	−	0.0650580i
$143$	−5.97469	−	5.97469i	−0.499629	−	0.499629i
$144$	2.28024	+	1.94949i	0.190020	+	0.162457i
$145$	6.55051	−	5.34847i	0.543990	−	0.444166i
$146$			10.8530i			0.898201i
$147$	−8.12422	−	2.99950i	−0.670075	−	0.247395i
$148$	2.89898	−	2.89898i	0.238295	−	0.238295i
$149$	−18.0990			−1.48273			−0.741366	−	0.671101i	$-0.765822\pi$
$149$	−18.0990			−1.48273			−0.741366	+	0.671101i	$0.765822\pi$
$150$	8.43149	−	1.97738i	0.688428	−	0.161452i
$151$	0.651531			0.0530208			0.0265104	−	0.999649i	$-0.491560\pi$
$151$	0.651531			0.0530208			0.0265104	+	0.999649i	$0.491560\pi$
$152$	−5.26758	+	5.26758i	−0.427258	+	0.427258i
$153$	−2.99087	+	0.233875i	−0.241797	+	0.0189077i
$154$			2.00000i			0.161165i
$155$	−5.19615	+	4.24264i	−0.417365	+	0.340777i
$156$	9.39898	−	4.33013i	0.752521	−	0.346688i
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	−2.04989	−	2.04989i	−0.163080	−	0.163080i
$159$	−20.8400	+	9.60102i	−1.65272	+	0.761410i
$160$	−0.224745	+	2.22474i	−0.0177676	+	0.175882i
$161$			3.46410i			0.273009i
$162$	−7.27583	−	5.29738i	−0.571644	−	0.416201i
$163$	−2.44949	+	2.44949i	−0.191859	+	0.191859i	−0.796499	−	0.604640i	$-0.793317\pi$
$163$	−2.44949	+	2.44949i	−0.191859	+	0.191859i	0.604640	+	0.796499i	$0.293317\pi$
$164$	8.34242			0.651433
$165$	−5.17984	+	1.78024i	−0.403250	+	0.138591i
$166$	8.00000			0.620920
$167$	10.5352	−	10.5352i	0.815236	−	0.815236i	−0.170178	−	0.985413i	$-0.554434\pi$
$167$	10.5352	−	10.5352i	0.815236	−	0.815236i	0.985413	+	0.170178i	$0.0544341\pi$
$168$	−2.29788	−	0.848387i	−0.177285	−	0.0654545i
$169$		−	22.6969i		−	1.74592i
$170$	−1.41421	−	1.73205i	−0.108465	−	0.132842i
$171$	14.5227	−	16.9866i	1.11058	−	1.29900i
$172$	7.44949	+	7.44949i	0.568018	+	0.568018i
$173$	12.2672	+	12.2672i	0.932659	+	0.932659i	0.997871	−	0.0652120i	$-0.0207723\pi$
$173$	12.2672	+	12.2672i	0.932659	+	0.932659i	−0.0652120	+	0.997871i	$0.520772\pi$
$174$	−2.74094	−	5.94949i	−0.207790	−	0.451030i
$175$	−5.89898	+	3.89898i	−0.445921	+	0.294735i
$176$		−	1.41421i		−	0.106600i
$177$	1.88745	−	5.11219i	0.141869	−	0.384256i
$178$	−8.77526	+	8.77526i	−0.657733	+	0.657733i
$179$	14.4921			1.08319			0.541594	−	0.840640i	$-0.317821\pi$
$179$	14.4921			1.08319			0.541594	+	0.840640i	$0.317821\pi$
$180$	0.151870	−	6.70648i	0.0113198	−	0.499872i
$181$	8.69694			0.646438			0.323219	−	0.946324i	$-0.395235\pi$
$181$	8.69694			0.646438			0.323219	+	0.946324i	$0.395235\pi$
$182$	−5.97469	+	5.97469i	−0.442874	+	0.442874i
$183$	−3.80845	+	10.3153i	−0.281529	+	0.762527i
$184$		−	2.44949i		−	0.180579i
$185$	−9.12096	−	0.921404i	−0.670586	−	0.0677429i
$186$	2.17423	+	4.71940i	0.159423	+	0.346043i
$187$	1.00000	+	1.00000i	0.0731272	+	0.0731272i
$188$	3.53553	+	3.53553i	0.257855	+	0.257855i
$189$	7.07107	+	2.00000i	0.514344	+	0.145479i
$190$	16.5732	+	1.67423i	1.20235	+	0.121462i
$191$			2.82843i			0.204658i	0.994751	+	0.102329i	$0.0326294\pi$
$191$			2.82843i			0.204658i	−0.994751	+	0.102329i	$0.967371\pi$
$192$	1.62484	+	0.599900i	0.117263	+	0.0432941i
$193$	−15.3485	+	15.3485i	−1.10481	+	1.10481i	−0.110985	+	0.993822i	$0.535401\pi$
$193$	−15.3485	+	15.3485i	−1.10481	+	1.10481i	−0.993822	+	0.110985i	$0.964599\pi$
$194$	11.4887			0.824839
$195$	−20.7922	−	10.1558i	−1.48896	−	0.727271i
$196$	−5.00000			−0.357143
$197$	−1.73205	+	1.73205i	−0.123404	+	0.123404i	−0.766111	−	0.642708i	$-0.777811\pi$
$197$	−1.73205	+	1.73205i	−0.123404	+	0.123404i	0.642708	+	0.766111i	$0.277811\pi$
$198$	0.330749	+	4.22973i	0.0235053	+	0.300594i
$199$		−	2.79796i		−	0.198342i	−0.995070	−	0.0991710i	$-0.968381\pi$
$199$		−	2.79796i		−	0.198342i	0.995070	−	0.0991710i	$-0.0316191\pi$
$200$	4.17121	−	2.75699i	0.294949	−	0.194949i
$201$	−12.3485	+	5.68896i	−0.870994	+	0.401268i
$202$	−1.44949	−	1.44949i	−0.101986	−	0.101986i
$203$	3.78194	+	3.78194i	0.265440	+	0.265440i
$204$	−1.57313	+	0.724745i	−0.110141	+	0.0507423i
$205$	−11.7980	−	14.4495i	−0.824005	−	1.00920i
$206$		−	11.0280i		−	0.768356i
$207$	0.572874	+	7.32611i	0.0398175	+	0.509199i
$208$	4.22474	−	4.22474i	0.292933	−	0.292933i
$209$	−10.5352			−0.728733
$210$	1.78024	+	5.17984i	0.122848	+	0.357443i
$211$	−20.4495			−1.40780			−0.703900	−	0.710299i	$-0.748560\pi$
$211$	−20.4495			−1.40780			−0.703900	+	0.710299i	$0.748560\pi$
$212$	−9.36736	+	9.36736i	−0.643353	+	0.643353i
$213$	1.78144	+	0.657717i	0.122062	+	0.0450660i
$214$			17.7980i			1.21664i
$215$	2.36773	−	23.4381i	0.161478	−	1.59846i
$216$	−5.00000	−	1.41421i	−0.340207	−	0.0962250i
$217$	−3.00000	−	3.00000i	−0.203653	−	0.203653i
$218$	−7.31747	−	7.31747i	−0.495602	−	0.495602i
$219$	−7.86566	−	17.0732i	−0.531512	−	1.15370i
$220$	−2.44949	+	2.00000i	−0.165145	+	0.134840i
$221$			5.97469i			0.401901i
$222$	−2.45946	+	6.66150i	−0.165068	+	0.447091i
$223$	−20.1237	+	20.1237i	−1.34758	+	1.34758i	−0.459306	+	0.888278i	$0.651902\pi$
$223$	−20.1237	+	20.1237i	−1.34758	+	1.34758i	−0.888278	+	0.459306i	$0.848098\pi$
$224$	−1.41421			−0.0944911
$225$	−11.8307	+	9.22135i	−0.788717	+	0.614757i
$226$	2.79796			0.186117
$227$	−13.1172	+	13.1172i	−0.870619	+	0.870619i	−0.992540	−	0.121921i	$-0.961094\pi$
$227$	−13.1172	+	13.1172i	−0.870619	+	0.870619i	0.121921	+	0.992540i	$0.461094\pi$
$228$	4.46895	−	12.1043i	0.295964	−	0.801624i
$229$		−	19.7980i		−	1.30829i	−0.756371	−	0.654143i	$-0.773029\pi$
$229$		−	19.7980i		−	1.30829i	0.756371	−	0.654143i	$-0.226971\pi$
$230$	−4.24264	+	3.46410i	−0.279751	+	0.228416i
$231$	−1.44949	−	3.14626i	−0.0953694	−	0.207009i
$232$	−2.67423	−	2.67423i	−0.175572	−	0.175572i
$233$	4.80688	+	4.80688i	0.314909	+	0.314909i	0.846808	−	0.531899i	$-0.178521\pi$
$233$	4.80688	+	4.80688i	0.314909	+	0.314909i	−0.531899	+	0.846808i	$0.678521\pi$
$234$	−11.6476	+	13.6237i	−0.761427	+	0.890611i
$235$	1.12372	−	11.1237i	0.0733037	−	0.725632i
$236$		−	3.14626i		−	0.204804i
$237$	4.71039	+	1.73910i	0.305973	+	0.112967i
$238$	1.00000	−	1.00000i	0.0648204	−	0.0648204i
$239$	−22.9774			−1.48628			−0.743141	−	0.669135i	$-0.766665\pi$
$239$	−22.9774			−1.48628			−0.743141	+	0.669135i	$0.766665\pi$
$240$	−1.25882	−	3.66270i	−0.0812564	−	0.236426i
$241$	22.4495			1.44610			0.723049	−	0.690796i	$-0.242740\pi$
$241$	22.4495			1.44610			0.723049	+	0.690796i	$0.242740\pi$
$242$	−6.36396	+	6.36396i	−0.409091	+	0.409091i
$243$	15.2851	+	3.06035i	0.980540	+	0.196322i
$244$			6.34847i			0.406419i
$245$	7.07107	+	8.66025i	0.451754	+	0.553283i
$246$	−13.1237	+	6.04612i	−0.836738	+	0.385487i
$247$	−31.4722	−	31.4722i	−2.00253	−	2.00253i
$248$	2.12132	+	2.12132i	0.134704	+	0.134704i
$249$	−12.5851	+	5.79796i	−0.797546	+	0.367431i
$250$	−10.6742	−	3.32577i	−0.675098	−	0.210340i
$251$			12.8708i			0.812397i	0.913785	+	0.406198i	$0.133146\pi$
$251$			12.8708i			0.812397i	−0.913785	+	0.406198i	$0.866854\pi$
$252$	4.22973	−	0.330749i	0.266448	−	0.0208352i
$253$	2.44949	−	2.44949i	0.153998	−	0.153998i
$254$	1.73205			0.108679
$255$	3.48004	+	1.69980i	0.217929	+	0.106446i
$256$	1.00000			0.0625000
$257$	−10.2173	+	10.2173i	−0.637340	+	0.637340i	−0.949898	−	0.312559i	$-0.898814\pi$
$257$	−10.2173	+	10.2173i	−0.637340	+	0.637340i	0.312559	+	0.949898i	$0.398814\pi$
$258$	−17.1180	−	6.32005i	−1.06572	−	0.393469i
$259$		−	5.79796i		−	0.360268i
$260$	−13.2922	−	1.34278i	−0.824345	−	0.0832758i
$261$	8.62372	+	7.37285i	0.533795	+	0.456368i
$262$	−3.34847	−	3.34847i	−0.206869	−	0.206869i
$263$	15.1992	+	15.1992i	0.937222	+	0.937222i	0.998143	−	0.0609206i	$-0.0194036\pi$
$263$	15.1992	+	15.1992i	0.937222	+	0.937222i	−0.0609206	+	0.998143i	$0.519404\pi$
$264$	1.02494	+	2.22474i	0.0630809	+	0.136924i
$265$	29.4722	+	2.97730i	1.81046	+	0.182894i
$266$			10.5352i			0.645953i
$267$	7.44482	−	20.1645i	0.455615	−	1.23404i
$268$	−5.55051	+	5.55051i	−0.339051	+	0.339051i
$269$	2.51059			0.153073			0.0765367	−	0.997067i	$-0.475614\pi$
$269$	2.51059			0.153073			0.0765367	+	0.997067i	$0.475614\pi$
$270$	4.62158	+	10.6603i	0.281260	+	0.648762i
$271$	−22.2474			−1.35144			−0.675718	−	0.737160i	$-0.736166\pi$
$271$	−22.2474			−1.35144			−0.675718	+	0.737160i	$0.736166\pi$
$272$	−0.707107	+	0.707107i	−0.0428746	+	0.0428746i
$273$	5.06885	−	13.7291i	0.306781	−	0.830923i
$274$			14.4495i			0.872926i
$275$	6.92820	+	1.41421i	0.417786	+	0.0852803i
$276$	1.77526	+	3.85337i	0.106858	+	0.231946i
$277$	−1.34847	−	1.34847i	−0.0810217	−	0.0810217i	0.665435	−	0.746456i	$-0.268246\pi$
$277$	−1.34847	−	1.34847i	−0.0810217	−	0.0810217i	−0.746456	+	0.665435i	$0.768246\pi$
$278$	−1.27135	−	1.27135i	−0.0762504	−	0.0762504i
$279$	−6.84072	−	5.84847i	−0.409543	−	0.350139i
$280$	2.00000	+	2.44949i	0.119523	+	0.146385i
$281$			19.6882i			1.17450i	0.809405	+	0.587251i	$0.199790\pi$
$281$			19.6882i			1.17450i	−0.809405	+	0.587251i	$0.800210\pi$
$282$	−8.12422	−	2.99950i	−0.483790	−	0.178618i
$283$	−4.22474	+	4.22474i	−0.251135	+	0.251135i	−0.821436	−	0.570301i	$-0.806827\pi$
$283$	−4.22474	+	4.22474i	−0.251135	+	0.251135i	0.570301	+	0.821436i	$0.306827\pi$
$284$	1.09638			0.0650580
$285$	−27.2852	+	9.37756i	−1.61624	+	0.555479i
$286$	8.44949			0.499629
$287$	8.34242	−	8.34242i	0.492437	−	0.492437i
$288$	−2.99087	+	0.233875i	−0.176239	+	0.0137812i
$289$		−	1.00000i		−	0.0588235i
$290$	−0.849971	+	8.41385i	−0.0499120	+	0.494078i
$291$	−18.0732	+	8.32636i	−1.05947	+	0.488100i
$292$	−7.67423	−	7.67423i	−0.449101	−	0.449101i
$293$	12.1958	+	12.1958i	0.712486	+	0.712486i	0.967055	−	0.254569i	$-0.0819336\pi$
$293$	12.1958	+	12.1958i	0.712486	+	0.712486i	−0.254569	+	0.967055i	$0.581934\pi$
$294$	7.86566	−	3.62372i	0.458735	−	0.211340i
$295$	−5.44949	+	4.44949i	−0.317282	+	0.259059i
$296$			4.09978i			0.238295i
$297$	−3.58579	−	6.41421i	−0.208068	−	0.372190i
$298$	12.7980	−	12.7980i	0.741366	−	0.741366i
$299$	14.6349			0.846361
$300$	−4.56374	+	7.36018i	−0.263488	+	0.424940i
$301$	14.8990			0.858763
$302$	−0.460702	+	0.460702i	−0.0265104	+	0.0265104i
$303$	3.33075	+	1.22973i	0.191347	+	0.0706461i
$304$		−	7.44949i		−	0.427258i
$305$	10.9959	−	8.97809i	0.629622	−	0.514084i
$306$	1.94949	−	2.28024i	0.111445	−	0.130353i
$307$	−12.0000	−	12.0000i	−0.684876	−	0.684876i	0.276219	−	0.961095i	$-0.410919\pi$
$307$	−12.0000	−	12.0000i	−0.684876	−	0.684876i	−0.961095	+	0.276219i	$0.910919\pi$
$308$	−1.41421	−	1.41421i	−0.0805823	−	0.0805823i
$309$	7.99247	+	17.3485i	0.454676	+	0.986920i
$310$	0.674235	−	6.67423i	0.0382940	−	0.379071i
$311$		−	9.47090i		−	0.537046i	−0.963273	−	0.268523i	$-0.913465\pi$
$311$		−	9.47090i		−	0.537046i	0.963273	−	0.268523i	$-0.0865355\pi$
$312$	−3.58422	+	9.70794i	−0.202916	+	0.549604i
$313$	14.6969	−	14.6969i	0.830720	−	0.830720i	−0.156895	−	0.987615i	$-0.550148\pi$
$313$	14.6969	−	14.6969i	0.830720	−	0.830720i	0.987615	+	0.156895i	$0.0501485\pi$
$314$		0			0
$315$	−6.55461	−	6.85835i	−0.369311	−	0.386425i
$316$	2.89898			0.163080
$317$	−20.4347	+	20.4347i	−1.14773	+	1.14773i	−0.160726	+	0.986999i	$0.551384\pi$
$317$	−20.4347	+	20.4347i	−1.14773	+	1.14773i	−0.986999	+	0.160726i	$0.948616\pi$
$318$	7.94715	−	21.5250i	0.445654	−	1.20706i
$319$		−	5.34847i		−	0.299457i
$320$	−1.41421	−	1.73205i	−0.0790569	−	0.0968246i
$321$	−12.8990	−	27.9985i	−0.719951	−	1.56273i
$322$	−2.44949	−	2.44949i	−0.136505	−	0.136505i
$323$	5.26758	+	5.26758i	0.293096	+	0.293096i
$324$	8.89060	−	1.39898i	0.493922	−	0.0777211i
$325$	16.4722	+	24.9217i	0.913713	+	1.38241i
$326$		−	3.46410i		−	0.191859i
$327$	16.8147	+	6.20805i	0.929852	+	0.343306i
$328$	−5.89898	+	5.89898i	−0.325717	+	0.325717i
$329$	7.07107			0.389841
$330$	2.40388	−	4.92152i	0.132329	−	0.270921i
$331$	23.0454			1.26669			0.633345	−	0.773870i	$-0.281681\pi$
$331$	23.0454			1.26669			0.633345	+	0.773870i	$0.281681\pi$
$332$	−5.65685	+	5.65685i	−0.310460	+	0.310460i
$333$	−0.958835	−	12.2619i	−0.0525438	−	0.671948i
$334$			14.8990i			0.815236i
$335$	17.4634	+	1.76416i	0.954126	+	0.0963863i
$336$	2.22474	−	1.02494i	0.121370	−	0.0559153i
$337$	7.47219	+	7.47219i	0.407036	+	0.407036i	0.880704	−	0.473667i	$-0.157070\pi$
$337$	7.47219	+	7.47219i	0.407036	+	0.407036i	−0.473667	+	0.880704i	$0.657070\pi$
$338$	16.0492	+	16.0492i	0.872959	+	0.872959i
$339$	−4.40156	+	2.02781i	−0.239060	+	0.110135i
$340$	2.22474	+	0.224745i	0.120654	+	0.0121885i
$341$			4.24264i			0.229752i
$342$	1.74225	+	22.2805i	0.0942101	+	1.20479i
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	−10.5352			−0.568018
$345$	4.16364	−	8.52432i	0.224163	−	0.458934i
$346$	−17.3485			−0.932659
$347$	−15.5170	+	15.5170i	−0.832998	+	0.832998i	−0.987926	−	0.154928i	$-0.950485\pi$
$347$	−15.5170	+	15.5170i	−0.832998	+	0.832998i	0.154928	+	0.987926i	$0.450485\pi$
$348$	6.14506	+	2.26879i	0.329410	+	0.121620i
$349$		−	13.5505i		−	0.725342i	−0.931917	−	0.362671i	$-0.881865\pi$
$349$		−	13.5505i		−	0.725342i	0.931917	−	0.362671i	$-0.118135\pi$
$350$	1.41421	−	6.92820i	0.0755929	−	0.370328i
$351$	8.44949	−	29.8735i	0.451000	−	1.59453i
$352$	1.00000	+	1.00000i	0.0533002	+	0.0533002i
$353$	−4.56048	−	4.56048i	−0.242730	−	0.242730i	0.575249	−	0.817979i	$-0.304905\pi$
$353$	−4.56048	−	4.56048i	−0.242730	−	0.242730i	−0.817979	+	0.575249i	$0.804905\pi$
$354$	2.28024	+	4.94949i	0.121193	+	0.263062i
$355$	−1.55051	−	1.89898i	−0.0822925	−	0.100787i
$356$		−	12.4101i		−	0.657733i
$357$	−0.848387	+	2.29788i	−0.0449014	+	0.121617i
$358$	−10.2474	+	10.2474i	−0.541594	+	0.541594i
$359$	−13.9993			−0.738853			−0.369427	−	0.929260i	$-0.620446\pi$
$359$	−13.9993			−0.738853			−0.369427	+	0.929260i	$0.620446\pi$
$360$	4.63481	+	4.84959i	0.244276	+	0.255596i
$361$	−36.4949			−1.92078
$362$	−6.14966	+	6.14966i	−0.323219	+	0.323219i
$363$	5.39910	−	14.6236i	0.283379	−	0.767540i
$364$		−	8.44949i		−	0.442874i
$365$	−2.43916	+	24.1452i	−0.127671	+	1.26382i
$366$	−4.60102	−	9.98698i	−0.240499	−	0.522028i
$367$	18.2474	+	18.2474i	0.952509	+	0.952509i	0.998922	−	0.0464133i	$-0.0147791\pi$
$367$	18.2474	+	18.2474i	0.952509	+	0.952509i	−0.0464133	+	0.998922i	$0.514779\pi$
$368$	1.73205	+	1.73205i	0.0902894	+	0.0902894i
$369$	16.2635	−	19.0227i	0.846642	−	0.990282i
$370$	7.10102	−	5.79796i	0.369164	−	0.301422i
$371$			18.7347i			0.972658i
$372$	−4.87453	−	1.79970i	−0.252733	−	0.0933102i
$373$	7.10102	−	7.10102i	0.367677	−	0.367677i	−0.498952	−	0.866629i	$-0.666282\pi$
$373$	7.10102	−	7.10102i	0.367677	−	0.367677i	0.866629	+	0.498952i	$0.166282\pi$
$374$	−1.41421			−0.0731272
$375$	19.2023	−	2.50423i	0.991603	−	0.129318i
$376$	−5.00000			−0.257855
$377$	15.9777	−	15.9777i	0.822895	−	0.822895i
$378$	−6.41421	+	3.58579i	−0.329912	+	0.184433i
$379$			23.5959i			1.21204i	0.795449	+	0.606020i	$0.207235\pi$
$379$			23.5959i			1.21204i	−0.795449	+	0.606020i	$0.792765\pi$
$380$	−12.9029	+	10.5352i	−0.661905	+	0.540443i
$381$	−2.72474	+	1.25529i	−0.139593	+	0.0643107i
$382$	−2.00000	−	2.00000i	−0.102329	−	0.102329i
$383$	−2.89986	−	2.89986i	−0.148176	−	0.148176i	0.629127	−	0.777303i	$-0.283413\pi$
$383$	−2.89986	−	2.89986i	−0.148176	−	0.148176i	−0.777303	+	0.629127i	$0.783413\pi$
$384$	−1.57313	+	0.724745i	−0.0802786	+	0.0369845i
$385$	−0.449490	+	4.44949i	−0.0229081	+	0.226767i
$386$		−	21.7060i		−	1.10481i
$387$	31.5093	−	2.46391i	1.60171	−	0.125248i
$388$	−8.12372	+	8.12372i	−0.412420	+	0.412420i
$389$	−8.62815			−0.437464			−0.218732	−	0.975785i	$-0.570192\pi$
$389$	−8.62815			−0.437464			−0.218732	+	0.975785i	$0.570192\pi$
$390$	21.8835	−	7.52106i	1.10811	−	0.380843i
$391$	−2.44949			−0.123876
$392$	3.53553	−	3.53553i	0.178571	−	0.178571i
$393$	7.69437	+	2.84080i	0.388130	+	0.143299i
$394$		−	2.44949i		−	0.123404i
$395$	−4.09978	−	5.02118i	−0.206282	−	0.252643i
$396$	−3.22474	−	2.75699i	−0.162050	−	0.138544i
$397$	27.6969	+	27.6969i	1.39007	+	1.39007i	0.825137	+	0.564932i	$0.191098\pi$
$397$	27.6969	+	27.6969i	1.39007	+	1.39007i	0.564932	+	0.825137i	$0.308902\pi$
$398$	1.97846	+	1.97846i	0.0991710	+	0.0991710i
$399$	−7.63531	−	16.5732i	−0.382244	−	0.829698i
$400$	−1.00000	+	4.89898i	−0.0500000	+	0.244949i
$401$		−	5.16404i		−	0.257880i	−0.991652	−	0.128940i	$-0.958843\pi$
$401$		−	5.16404i		−	0.257880i	0.991652	−	0.128940i	$-0.0411575\pi$
$402$	4.70898	−	12.7544i	0.234863	−	0.636131i
$403$	−12.6742	+	12.6742i	−0.631349	+	0.631349i
$404$	2.04989			0.101986
$405$	−14.9963	−	13.4205i	−0.745173	−	0.666871i
$406$	−5.34847			−0.265440
$407$	−4.09978	+	4.09978i	−0.203218	+	0.203218i
$408$	0.599900	−	1.62484i	0.0296995	−	0.0804418i
$409$		−	25.0000i		−	1.23617i	−0.786111	−	0.618085i	$-0.787909\pi$
$409$		−	25.0000i		−	1.23617i	0.786111	−	0.618085i	$-0.212091\pi$
$410$	18.5597	+	1.87492i	0.916601	+	0.0925955i
$411$	−10.4722	−	22.7310i	−0.516555	−	1.12124i
$412$	7.79796	+	7.79796i	0.384178	+	0.384178i
$413$	−3.14626	−	3.14626i	−0.154818	−	0.154818i
$414$	−5.58542	−	4.77526i	−0.274509	−	0.234691i
$415$	17.7980	+	1.79796i	0.873667	+	0.0882583i
$416$			5.97469i			0.292933i
$417$	2.92140	+	1.07860i	0.143062	+	0.0528191i
$418$	7.44949	−	7.44949i	0.364366	−	0.364366i
$419$	14.6349			0.714964			0.357482	−	0.933920i	$-0.383635\pi$
$419$	14.6349			0.714964			0.357482	+	0.933920i	$0.383635\pi$
$420$	−4.92152	−	2.40388i	−0.240146	−	0.117297i
$421$	7.10102			0.346083			0.173041	−	0.984915i	$-0.444641\pi$
$421$	7.10102			0.346083			0.173041	+	0.984915i	$0.444641\pi$
$422$	14.4600	−	14.4600i	0.703900	−	0.703900i
$423$	14.9543	−	1.16938i	0.727105	−	0.0568570i
$424$		−	13.2474i		−	0.643353i
$425$	−2.75699	−	4.17121i	−0.133734	−	0.202333i
$426$	−1.72474	+	0.794593i	−0.0835642	+	0.0384982i
$427$	6.34847	+	6.34847i	0.307224	+	0.307224i
$428$	−12.5851	−	12.5851i	−0.608322	−	0.608322i
$429$	−13.2922	+	6.12372i	−0.641752	+	0.295656i
$430$	14.8990	+	18.2474i	0.718493	+	0.879970i
$431$			11.5994i			0.558725i	0.960186	+	0.279363i	$0.0901232\pi$
$431$			11.5994i			0.558725i	−0.960186	+	0.279363i	$0.909877\pi$
$432$	4.53553	−	2.53553i	0.218216	−	0.121991i
$433$	−4.10102	+	4.10102i	−0.197082	+	0.197082i	−0.798748	−	0.601666i	$-0.794504\pi$
$433$	−4.10102	+	4.10102i	−0.197082	+	0.197082i	0.601666	+	0.798748i	$0.294504\pi$
$434$	4.24264			0.203653
$435$	−4.76078	−	13.8521i	−0.228262	−	0.664158i
$436$	10.3485			0.495602
$437$	12.9029	−	12.9029i	0.617229	−	0.617229i
$438$	17.6344	+	6.51072i	0.842607	+	0.311094i
$439$		−	2.89898i		−	0.138361i	−0.997604	−	0.0691804i	$-0.977962\pi$
$439$		−	2.89898i		−	0.138361i	0.997604	−	0.0691804i	$-0.0220384\pi$
$440$	0.317837	−	3.14626i	0.0151523	−	0.149992i
$441$	−9.74745	+	11.4012i	−0.464164	+	0.542914i
$442$	−4.22474	−	4.22474i	−0.200951	−	0.200951i
$443$	−6.11756	−	6.11756i	−0.290654	−	0.290654i	0.546685	−	0.837339i	$-0.315890\pi$
$443$	−6.11756	−	6.11756i	−0.290654	−	0.290654i	−0.837339	+	0.546685i	$0.815890\pi$
$444$	−2.97129	−	6.44949i	−0.141011	−	0.306079i
$445$	−21.4949	+	17.5505i	−1.01896	+	0.831974i
$446$		−	28.4592i		−	1.34758i
$447$	−10.8576	+	29.4081i	−0.513548	+	1.39096i
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	24.3916			1.15111			0.575555	−	0.817763i	$-0.304786\pi$
$449$	24.3916			1.15111			0.575555	+	0.817763i	$0.304786\pi$
$450$	1.84512	−	14.8861i	0.0869798	−	0.701737i
$451$	−11.7980			−0.555544
$452$	−1.97846	+	1.97846i	−0.0930587	+	0.0930587i
$453$	0.390854	−	1.05864i	0.0183639	−	0.0497391i
$454$		−	18.5505i		−	0.870619i
$455$	−14.6349	+	11.9494i	−0.686097	+	0.560196i
$456$	5.39898	+	11.7190i	0.252830	+	0.548794i
$457$	−1.20204	−	1.20204i	−0.0562291	−	0.0562291i	0.678433	−	0.734662i	$-0.262659\pi$
$457$	−1.20204	−	1.20204i	−0.0562291	−	0.0562291i	−0.734662	+	0.678433i	$0.762659\pi$
$458$	13.9993	+	13.9993i	0.654143	+	0.654143i
$459$	−1.41421	+	5.00000i	−0.0660098	+	0.233380i
$460$	0.550510	−	5.44949i	0.0256677	−	0.254084i
$461$		−	20.0061i		−	0.931776i	−0.884844	−	0.465888i	$-0.845735\pi$
$461$		−	20.0061i		−	0.931776i	0.884844	−	0.465888i	$-0.154265\pi$
$462$	3.24969	+	1.19980i	0.151189	+	0.0558198i
$463$	−9.92168	+	9.92168i	−0.461100	+	0.461100i	−0.899016	−	0.437916i	$-0.855717\pi$
$463$	−9.92168	+	9.92168i	−0.461100	+	0.461100i	0.437916	+	0.899016i	$0.355717\pi$
$464$	3.78194			0.175572
$465$	3.77646	+	10.9881i	0.175129	+	0.509561i
$466$	−6.79796			−0.314909
$467$	12.1244	−	12.1244i	0.561048	−	0.561048i	−0.368557	−	0.929605i	$-0.620148\pi$
$467$	12.1244	−	12.1244i	0.561048	−	0.561048i	0.929605	+	0.368557i	$0.120148\pi$
$468$	−1.39733	−	17.8695i	−0.0645917	−	0.826019i
$469$			11.1010i			0.512598i
$470$	7.07107	+	8.66025i	0.326164	+	0.399468i
$471$		0			0
$472$	2.22474	+	2.22474i	0.102402	+	0.102402i
$473$	−10.5352	−	10.5352i	−0.484408	−	0.484408i
$474$	−4.56048	+	2.10102i	−0.209470	+	0.0965031i
$475$	36.4949	+	7.44949i	1.67450	+	0.341806i
$476$			1.41421i			0.0648204i
$477$	3.09825	+	39.6214i	0.141859	+	1.81414i
$478$	16.2474	−	16.2474i	0.743141	−	0.743141i
$479$	−35.3874			−1.61689			−0.808447	−	0.588569i	$-0.799691\pi$
$479$	−35.3874			−1.61689			−0.808447	+	0.588569i	$0.799691\pi$
$480$	3.48004	+	1.69980i	0.158841	+	0.0775849i
$481$	−24.4949			−1.11687
$482$	−15.8742	+	15.8742i	−0.723049	+	0.723049i
$483$	5.62863	+	2.07812i	0.256111	+	0.0945576i
$484$		−	9.00000i		−	0.409091i
$485$	25.5594	+	2.58202i	1.16059	+	0.117244i
$486$	−12.9722	+	8.64420i	−0.588431	+	0.392109i
$487$	29.3485	+	29.3485i	1.32991	+	1.32991i	0.905447	+	0.424459i	$0.139536\pi$
$487$	29.3485	+	29.3485i	1.32991	+	1.32991i	0.424459	+	0.905447i	$0.360464\pi$
$488$	−4.48905	−	4.48905i	−0.203210	−	0.203210i
$489$	2.51059	+	5.44949i	0.113533	+	0.246434i
$490$	−11.1237	−	1.12372i	−0.502519	−	0.0507647i
$491$		−	2.86054i		−	0.129094i	−0.997915	−	0.0645471i	$-0.979440\pi$
$491$		−	2.86054i		−	0.129094i	0.997915	−	0.0645471i	$-0.0205603\pi$
$492$	5.00462	−	13.5551i	0.225626	−	0.611112i
$493$	−2.67423	+	2.67423i	−0.120441	+	0.120441i
$494$	44.5084			2.00253
$495$	−0.214777	+	9.48440i	−0.00965352	+	0.426292i
$496$	−3.00000			−0.134704
$497$	1.09638	−	1.09638i	0.0491792	−	0.0491792i
$498$	4.79920	−	12.9988i	0.215057	−	0.582488i
$499$			19.1464i			0.857112i	0.903515	+	0.428556i	$0.140978\pi$
$499$			19.1464i			0.857112i	−0.903515	+	0.428556i	$0.859022\pi$
$500$	9.89949	−	5.19615i	0.442719	−	0.232379i
$501$	−10.7980	−	23.4381i	−0.482417	−	1.04714i
$502$	−9.10102	−	9.10102i	−0.406198	−	0.406198i
$503$	16.0171	+	16.0171i	0.714165	+	0.714165i	0.967404	−	0.253239i	$-0.0814958\pi$
$503$	16.0171	+	16.0171i	0.714165	+	0.714165i	−0.253239	+	0.967404i	$0.581496\pi$
$504$	−2.75699	+	3.22474i	−0.122806	+	0.143642i
$505$	−2.89898	−	3.55051i	−0.129003	−	0.157996i
$506$			3.46410i			0.153998i
$507$	−36.8790	−	13.6159i	−1.63785	−	0.604703i
$508$	−1.22474	+	1.22474i	−0.0543393	+	0.0543393i
$509$	−5.94258			−0.263400			−0.131700	−	0.991290i	$-0.542044\pi$
$509$	−5.94258			−0.263400			−0.131700	+	0.991290i	$0.542044\pi$
$510$	−3.66270	+	1.25882i	−0.162187	+	0.0557414i
$511$	−15.3485			−0.678976
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−18.8884	−	33.7874i	−0.833945	−	1.49175i
$514$		−	14.4495i		−	0.637340i
$515$	2.47848	−	24.5344i	0.109215	−	1.08112i
$516$	16.5732	−	7.63531i	0.729595	−	0.336126i
$517$	−5.00000	−	5.00000i	−0.219900	−	0.219900i
$518$	4.09978	+	4.09978i	0.180134	+	0.180134i
$519$	27.2914	−	12.5732i	1.19796	−	0.551903i
$520$	10.3485	−	8.44949i	0.453810	−	0.370535i
$521$			5.94258i			0.260349i	0.991491	+	0.130175i	$0.0415538\pi$
$521$			5.94258i			0.260349i	−0.991491	+	0.130175i	$0.958446\pi$
$522$	−11.3113	+	0.884501i	−0.495082	+	0.0387136i
$523$	−2.24745	+	2.24745i	−0.0982741	+	0.0982741i	−0.754534	−	0.656260i	$-0.772137\pi$
$523$	−2.24745	+	2.24745i	−0.0982741	+	0.0982741i	0.656260	+	0.754534i	$0.272137\pi$
$524$	4.73545			0.206869
$525$	2.79643	+	11.9239i	0.122046	+	0.520403i
$526$	−21.4949			−0.937222
$527$	2.12132	−	2.12132i	0.0924062	−	0.0924062i
$528$	−2.29788	−	0.848387i	−0.100002	−	0.0369213i
$529$		−	17.0000i		−	0.739130i
$530$	−22.9453	+	18.7347i	−0.996678	+	0.813784i
$531$	−7.17423	−	6.13361i	−0.311335	−	0.266176i
$532$	−7.44949	−	7.44949i	−0.322976	−	0.322976i
$533$	−35.2446	−	35.2446i	−1.52661	−	1.52661i
$534$	8.99415	+	19.5227i	0.389215	+	0.844830i
$535$	−4.00000	+	39.5959i	−0.172935	+	1.71188i
$536$		−	7.84961i		−	0.339051i
$537$	8.69381	−	23.5474i	0.375165	−	1.01614i
$538$	−1.77526	+	1.77526i	−0.0765367	+	0.0765367i
$539$	7.07107			0.304572
$540$	−10.8059	−	4.26999i	−0.465011	−	0.183751i
$541$	−8.89898			−0.382597			−0.191299	−	0.981532i	$-0.561270\pi$
$541$	−8.89898			−0.382597			−0.191299	+	0.981532i	$0.561270\pi$
$542$	15.7313	−	15.7313i	0.675718	−	0.675718i
$543$	5.21730	−	14.1312i	0.223896	−	0.606427i
$544$		−	1.00000i		−	0.0428746i
$545$	−14.6349	−	17.9241i	−0.626892	−	0.767783i
$546$	6.12372	+	13.2922i	0.262071	+	0.568852i
$547$	25.5732	+	25.5732i	1.09343	+	1.09343i	0.995160	+	0.0982721i	$0.0313315\pi$
$547$	25.5732	+	25.5732i	1.09343	+	1.09343i	0.0982721	+	0.995160i	$0.468668\pi$
$548$	−10.2173	−	10.2173i	−0.436463	−	0.436463i
$549$	14.4760	+	12.3763i	0.617822	+	0.528207i
$550$	−5.89898	+	3.89898i	−0.251533	+	0.166253i
$551$		−	28.1735i		−	1.20023i
$552$	−3.98004	−	1.46945i	−0.169402	−	0.0625439i
$553$	2.89898	−	2.89898i	0.123277	−	0.123277i
$554$	1.90702			0.0810217
$555$	−6.96880	+	14.2674i	−0.295809	+	0.605617i
$556$	1.79796			0.0762504
$557$	26.8307	−	26.8307i	1.13685	−	1.13685i	0.147844	−	0.989011i	$-0.452767\pi$
$557$	26.8307	−	26.8307i	1.13685	−	1.13685i	0.989011	−	0.147844i	$-0.0472333\pi$
$558$	8.97261	−	0.701625i	0.379841	−	0.0297022i
$559$		−	62.9444i		−	2.66226i
$560$	−3.14626	−	0.317837i	−0.132954	−	0.0134311i
$561$	2.22474	−	1.02494i	0.0939288	−	0.0432732i
$562$	−13.9217	−	13.9217i	−0.587251	−	0.587251i
$563$	5.97469	+	5.97469i	0.251803	+	0.251803i	0.821710	−	0.569906i	$-0.193021\pi$
$563$	5.97469	+	5.97469i	0.251803	+	0.251803i	−0.569906	+	0.821710i	$0.693021\pi$
$564$	7.86566	−	3.62372i	0.331204	−	0.152586i
$565$	6.22474	+	0.628827i	0.261877	+	0.0264549i
$566$		−	5.97469i		−	0.251135i
$567$	7.49163	−	10.2896i	0.314619	−	0.432122i
$568$	−0.775255	+	0.775255i	−0.0325290	+	0.0325290i
$569$	−34.7518			−1.45687			−0.728435	−	0.685115i	$-0.759752\pi$
$569$	−34.7518			−1.45687			−0.728435	+	0.685115i	$0.759752\pi$
$570$	12.6626	−	25.9245i	0.530380	−	1.08586i
$571$	23.7980			0.995914			0.497957	−	0.867202i	$-0.334084\pi$
$571$	23.7980			0.995914			0.497957	+	0.867202i	$0.334084\pi$
$572$	−5.97469	+	5.97469i	−0.249814	+	0.249814i
$573$	4.59575	+	1.69677i	0.191990	+	0.0708838i
$574$			11.7980i			0.492437i
$575$	−10.2173	+	6.75323i	−0.426092	+	0.281629i
$576$	1.94949	−	2.28024i	0.0812287	−	0.0950100i
$577$	−15.7980	−	15.7980i	−0.657678	−	0.657678i	0.297152	−	0.954830i	$-0.403963\pi$
$577$	−15.7980	−	15.7980i	−0.657678	−	0.657678i	−0.954830	+	0.297152i	$0.903963\pi$
$578$	0.707107	+	0.707107i	0.0294118	+	0.0294118i
$579$	15.7313	+	34.1464i	0.653771	+	1.41908i
$580$	−5.34847	−	6.55051i	−0.222083	−	0.271995i
$581$			11.3137i			0.469372i
$582$	6.89206	−	18.6673i	0.285685	−	0.773785i
$583$	13.2474	−	13.2474i	0.548653	−	0.548653i
$584$	10.8530			0.449101
$585$	−28.9748	+	27.6916i	−1.19796	+	1.14491i
$586$	−17.2474			−0.712486
$587$	−21.7381	+	21.7381i	−0.897228	+	0.897228i	−0.995190	−	0.0979619i	$-0.968768\pi$
$587$	−21.7381	+	21.7381i	−0.897228	+	0.897228i	0.0979619	+	0.995190i	$0.468768\pi$
$588$	−2.99950	+	8.12422i	−0.123697	+	0.335037i
$589$			22.3485i			0.920853i
$590$	0.707107	−	6.99964i	0.0291111	−	0.288170i
$591$	1.77526	+	3.85337i	0.0730242	+	0.158507i
$592$	−2.89898	−	2.89898i	−0.119147	−	0.119147i
$593$	23.4702	+	23.4702i	0.963804	+	0.963804i	0.999367	−	0.0355630i	$-0.0113224\pi$
$593$	23.4702	+	23.4702i	0.963804	+	0.963804i	−0.0355630	+	0.999367i	$0.511322\pi$
$594$	7.07107	+	2.00000i	0.290129	+	0.0820610i
$595$	2.44949	−	2.00000i	0.100419	−	0.0819920i
$596$			18.0990i			0.741366i
$597$	−4.54625	−	1.67850i	−0.186066	−	0.0686963i
$598$	−10.3485	+	10.3485i	−0.423180	+	0.423180i
$599$	0.142865			0.00583729			0.00291864	−	0.999996i	$-0.499071\pi$
$599$	0.142865			0.00583729			0.00291864	+	0.999996i	$0.499071\pi$
$600$	−1.97738	−	8.43149i	−0.0807261	−	0.344214i
$601$	0.853572			0.0348179			0.0174090	−	0.999848i	$-0.494458\pi$
$601$	0.853572			0.0348179			0.0174090	+	0.999848i	$0.494458\pi$
$602$	−10.5352	+	10.5352i	−0.429381	+	0.429381i
$603$	1.83583	+	23.4772i	0.0747607	+	0.956064i
$604$		−	0.651531i		−	0.0265104i
$605$	−15.5885	+	12.7279i	−0.633761	+	0.517464i
$606$	−3.22474	+	1.48565i	−0.130996	+	0.0603502i
$607$	−0.797959	−	0.797959i	−0.0323882	−	0.0323882i	0.690727	−	0.723115i	$-0.257291\pi$
$607$	−0.797959	−	0.797959i	−0.0323882	−	0.0323882i	−0.723115	+	0.690727i	$0.757291\pi$
$608$	5.26758	+	5.26758i	0.213629	+	0.213629i
$609$	8.41385	−	3.87628i	0.340946	−	0.157075i
$610$	−1.42679	+	14.1237i	−0.0577689	+	0.571853i
$611$		−	29.8735i		−	1.20855i
$612$	0.233875	+	2.99087i	0.00945384	+	0.120899i
$613$	2.92168	−	2.92168i	0.118006	−	0.118006i	−0.645638	−	0.763644i	$-0.723408\pi$
$613$	2.92168	−	2.92168i	0.118006	−	0.118006i	0.763644	+	0.645638i	$0.223408\pi$
$614$	16.9706			0.684876
$615$	−30.5558	+	10.5016i	−1.23213	+	0.423465i
$616$	2.00000			0.0805823
$617$	−4.02834	+	4.02834i	−0.162175	+	0.162175i	−0.783530	−	0.621355i	$-0.786583\pi$
$617$	−4.02834	+	4.02834i	−0.162175	+	0.162175i	0.621355	+	0.783530i	$0.286583\pi$
$618$	−17.9188	−	6.61569i	−0.720798	−	0.266122i
$619$		−	16.6969i		−	0.671107i	−0.942021	−	0.335553i	$-0.891077\pi$
$619$		−	16.6969i		−	0.671107i	0.942021	−	0.335553i	$-0.108923\pi$
$620$	4.24264	+	5.19615i	0.170389	+	0.208683i
$621$	12.2474	+	3.46410i	0.491473	+	0.139010i
$622$	6.69694	+	6.69694i	0.268523	+	0.268523i
$623$	−12.4101	−	12.4101i	−0.497200	−	0.497200i
$624$	−4.33013	−	9.39898i	−0.173344	−	0.376260i
$625$	−23.0000	−	9.79796i	−0.920000	−	0.391918i
$626$			20.7846i			0.830720i
$627$	−6.32005	+	17.1180i	−0.252399	+	0.683628i
$628$		0			0
$629$	4.09978			0.163469
$630$	9.48440	+	0.214777i	0.377868	+	0.00855693i
$631$	39.6413			1.57810			0.789048	−	0.614331i	$-0.210574\pi$
$631$	39.6413			1.57810			0.789048	+	0.614331i	$0.210574\pi$
$632$	−2.04989	+	2.04989i	−0.0815402	+	0.0815402i
$633$	−12.2677	+	33.2272i	−0.487596	+	1.32066i
$634$		−	28.8990i		−	1.14773i
$635$	3.85337	+	0.389270i	0.152916	+	0.0154477i
$636$	9.60102	+	20.8400i	0.380705	+	0.826359i
$637$	21.1237	+	21.1237i	0.836952	+	0.836952i
$638$	3.78194	+	3.78194i	0.149728	+	0.149728i
$639$	2.13737	−	2.50000i	0.0845532	−	0.0988985i
$640$	2.22474	+	0.224745i	0.0879408	+	0.00888382i
$641$		−	3.46410i		−	0.136824i	−0.997657	−	0.0684119i	$-0.978207\pi$
$641$		−	3.46410i		−	0.136824i	0.997657	−	0.0684119i	$-0.0217932\pi$
$642$	28.9189	+	10.6770i	1.14134	+	0.421388i
$643$	18.4949	−	18.4949i	0.729368	−	0.729368i	−0.241126	−	0.970494i	$-0.577517\pi$
$643$	18.4949	−	18.4949i	0.729368	−	0.729368i	0.970494	+	0.241126i	$0.0775168\pi$
$644$	3.46410			0.136505
$645$	−36.6628	−	17.9077i	−1.44360	−	0.705115i
$646$	−7.44949			−0.293096
$647$	−6.99964	+	6.99964i	−0.275184	+	0.275184i	−0.831183	−	0.555999i	$-0.812336\pi$
$647$	−6.99964	+	6.99964i	−0.275184	+	0.275184i	0.555999	+	0.831183i	$0.312336\pi$
$648$	−5.29738	+	7.27583i	−0.208101	+	0.285822i
$649$			4.44949i			0.174658i
$650$	−29.2699	−	5.97469i	−1.14806	−	0.234347i
$651$	−6.67423	+	3.07483i	−0.261584	+	0.120512i
$652$	2.44949	+	2.44949i	0.0959294	+	0.0959294i
$653$	−33.5125	−	33.5125i	−1.31145	−	1.31145i	−0.920349	−	0.391097i	$-0.872096\pi$
$653$	−33.5125	−	33.5125i	−1.31145	−	1.31145i	−0.391097	−	0.920349i	$-0.627904\pi$
$654$	−16.2795	+	7.50000i	−0.636579	+	0.293273i
$655$	−6.69694	−	8.20204i	−0.261671	−	0.320480i
$656$		−	8.34242i		−	0.325717i
$657$	−32.4599	+	2.53825i	−1.26638	+	0.0990265i
$658$	−5.00000	+	5.00000i	−0.194920	+	0.194920i
$659$	−10.3602			−0.403576			−0.201788	−	0.979429i	$-0.564675\pi$
$659$	−10.3602			−0.403576			−0.201788	+	0.979429i	$0.564675\pi$
$660$	1.78024	+	5.17984i	0.0692957	+	0.201625i
$661$	−16.8990			−0.657294			−0.328647	−	0.944453i	$-0.606593\pi$
$661$	−16.8990			−0.657294			−0.328647	+	0.944453i	$0.606593\pi$
$662$	−16.2956	+	16.2956i	−0.633345	+	0.633345i
$663$	9.70794	+	3.58422i	0.377025	+	0.139200i
$664$		−	8.00000i		−	0.310460i
$665$	−2.36773	+	23.4381i	−0.0918164	+	0.908889i
$666$	9.34847	+	7.99247i	0.362246	+	0.309702i
$667$	6.55051	+	6.55051i	0.253637	+	0.253637i
$668$	−10.5352	−	10.5352i	−0.407618	−	0.407618i
$669$	20.6257	+	44.7702i	0.797435	+	1.73091i
$670$	−13.5959	+	11.1010i	−0.525256	+	0.428870i
$671$		−	8.97809i		−	0.346595i
$672$	−0.848387	+	2.29788i	−0.0327273	+	0.0886425i
$673$	−2.07832	+	2.07832i	−0.0801132	+	0.0801132i	−0.746028	−	0.665915i	$-0.768041\pi$
$673$	−2.07832	+	2.07832i	−0.0801132	+	0.0801132i	0.665915	+	0.746028i	$0.268041\pi$
$674$	−10.5673			−0.407036
$675$	7.88599	+	24.7550i	0.303532	+	0.952821i
$676$	−22.6969			−0.872959
$677$	34.8946	−	34.8946i	1.34111	−	1.34111i	0.446153	−	0.894957i	$-0.352794\pi$
$677$	34.8946	−	34.8946i	1.34111	−	1.34111i	0.894957	−	0.446153i	$-0.147206\pi$
$678$	1.67850	−	4.54625i	0.0644623	−	0.174598i
$679$			16.2474i			0.623520i
$680$	−1.73205	+	1.41421i	−0.0664211	+	0.0542326i
$681$	13.4444	+	29.1824i	0.515190	+	1.11827i
$682$	−3.00000	−	3.00000i	−0.114876	−	0.114876i
$683$	27.8950	+	27.8950i	1.06737	+	1.06737i	0.997560	+	0.0698124i	$0.0222401\pi$
$683$	27.8950	+	27.8950i	1.06737	+	1.06737i	0.0698124	+	0.997560i	$0.477760\pi$
$684$	−16.9866	−	14.5227i	−0.649500	−	0.555289i
$685$	−3.24745	+	32.1464i	−0.124079	+	1.22825i
$686$		−	16.9706i		−	0.647939i
$687$	−32.1686	−	11.8768i	−1.22731	−	0.453128i
$688$	7.44949	−	7.44949i	0.284009	−	0.284009i
$689$	79.1494			3.01535
$690$	3.08346	+	8.97175i	0.117385	+	0.341549i
$691$	2.69694			0.102596			0.0512982	−	0.998683i	$-0.483664\pi$
$691$	2.69694			0.102596			0.0512982	+	0.998683i	$0.483664\pi$
$692$	12.2672	−	12.2672i	0.466330	−	0.466330i
$693$	−5.98174	+	0.467750i	−0.227228	+	0.0177684i
$694$		−	21.9444i		−	0.832998i
$695$	−2.54270	−	3.11416i	−0.0964500	−	0.118127i
$696$	−5.94949	+	2.74094i	−0.225515	+	0.103895i
$697$	5.89898	+	5.89898i	0.223440	+	0.223440i
$698$	9.58166	+	9.58166i	0.362671	+	0.362671i
$699$	10.6941	−	4.92679i	0.404488	−	0.186348i
$700$	3.89898	+	5.89898i	0.147368	+	0.222960i
$701$		−	9.47090i		−	0.357711i	−0.983875	−	0.178856i	$-0.942761\pi$
$701$		−	9.47090i		−	0.357711i	0.983875	−	0.178856i	$-0.0572395\pi$
$702$	15.1490	+	27.0984i	0.571763	+	1.02276i
$703$	−21.5959	+	21.5959i	−0.814505	+	0.814505i
$704$	−1.41421			−0.0533002
$705$	−17.4002	−	8.49900i	−0.655329	−	0.320091i
$706$	6.44949			0.242730
$707$	2.04989	−	2.04989i	0.0770940	−	0.0770940i
$708$	−5.11219	−	1.88745i	−0.192128	−	0.0709345i
$709$			7.24745i			0.272184i	0.990696	+	0.136092i	$0.0434542\pi$
$709$			7.24745i			0.272184i	−0.990696	+	0.136092i	$0.956546\pi$
$710$	2.43916	+	0.246405i	0.0915400	+	0.00924741i
$711$	5.65153	−	6.61037i	0.211949	−	0.247908i
$712$	8.77526	+	8.77526i	0.328867	+	0.328867i
$713$	−5.19615	−	5.19615i	−0.194597	−	0.194597i
$714$	−1.02494	−	2.22474i	−0.0383576	−	0.0832590i
$715$	18.7980	+	1.89898i	0.703004	+	0.0710178i
$716$		−	14.4921i		−	0.541594i
$717$	−13.7841	+	37.3346i	−0.514778	+	1.39429i
$718$	9.89898	−	9.89898i	0.369427	−	0.369427i
$719$	14.3171			0.533938			0.266969	−	0.963705i	$-0.413978\pi$
$719$	14.3171			0.533938			0.266969	+	0.963705i	$0.413978\pi$
$720$	−6.70648	−	0.151870i	−0.249936	−	0.00565988i
$721$	15.5959			0.580822
$722$	25.8058	−	25.8058i	0.960392	−	0.960392i
$723$	13.4675	−	36.4769i	0.500860	−	1.35659i
$724$		−	8.69694i		−	0.323219i
$725$	−3.78194	+	18.5276i	−0.140458	+	0.688099i
$726$	6.52270	+	14.1582i	0.242080	+	0.525460i
$727$	0.371173	+	0.371173i	0.0137660	+	0.0137660i	0.713956	−	0.700190i	$-0.246902\pi$
$727$	0.371173	+	0.371173i	0.0137660	+	0.0137660i	−0.700190	+	0.713956i	$0.746902\pi$
$728$	5.97469	+	5.97469i	0.221437	+	0.221437i
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	−15.3485	−	18.7980i	−0.568072	−	0.695744i
$731$			10.5352i			0.389657i
$732$	10.3153	+	3.80845i	0.381264	+	0.140764i
$733$	35.3939	−	35.3939i	1.30730	−	1.30730i	0.383948	−	0.923355i	$-0.374564\pi$
$733$	35.3939	−	35.3939i	1.30730	−	1.30730i	0.923355	−	0.383948i	$-0.125436\pi$
$734$	−25.8058			−0.952509
$735$	18.3135	−	6.29410i	0.675504	−	0.232161i
$736$	−2.44949			−0.0902894
$737$	7.84961	−	7.84961i	0.289144	−	0.289144i
$738$	1.95108	+	24.9511i	0.0718204	+	0.918462i
$739$		−	21.0454i		−	0.774168i	−0.922044	−	0.387084i	$-0.873482\pi$
$739$		−	21.0454i		−	0.774168i	0.922044	−	0.387084i	$-0.126518\pi$
$740$	−0.921404	+	9.12096i	−0.0338715	+	0.335293i
$741$	−70.0176	+	32.2572i	−2.57216	+	1.18500i
$742$	−13.2474	−	13.2474i	−0.486329	−	0.486329i
$743$	14.9528	+	14.9528i	0.548564	+	0.548564i	0.926025	−	0.377461i	$-0.123203\pi$
$743$	14.9528	+	14.9528i	0.548564	+	0.548564i	−0.377461	+	0.926025i	$0.623203\pi$
$744$	4.71940	−	2.17423i	0.173021	−	0.0797113i
$745$	31.3485	−	25.5959i	1.14852	−	0.937762i
$746$			10.0424i			0.367677i
$747$	1.87100	+	23.9270i	0.0684563	+	0.875442i
$748$	1.00000	−	1.00000i	0.0365636	−	0.0365636i
$749$	−25.1701			−0.919696
$750$	−11.8073	+	15.3488i	−0.431143	+	0.560460i
$751$	−15.0000			−0.547358			−0.273679	−	0.961821i	$-0.588241\pi$
$751$	−15.0000			−0.547358			−0.273679	+	0.961821i	$0.588241\pi$
$752$	3.53553	−	3.53553i	0.128928	−	0.128928i
$753$	20.9130	+	7.72119i	0.762113	+	0.281376i
$754$			22.5959i			0.822895i
$755$	−1.12848	+	0.921404i	−0.0410698	+	0.0335333i
$756$	2.00000	−	7.07107i	0.0727393	−	0.257172i
$757$	−3.37117	−	3.37117i	−0.122527	−	0.122527i	0.643184	−	0.765712i	$-0.277613\pi$
$757$	−3.37117	−	3.37117i	−0.122527	−	0.122527i	−0.765712	+	0.643184i	$0.777613\pi$
$758$	−16.6848	−	16.6848i	−0.606020	−	0.606020i
$759$	−2.51059	−	5.44949i	−0.0911286	−	0.197804i
$760$	1.67423	−	16.5732i	0.0607309	−	0.601174i
$761$			47.8617i			1.73499i	0.497449	+	0.867494i	$0.334270\pi$
$761$			47.8617i			1.73499i	−0.497449	+	0.867494i	$0.665730\pi$
$762$	1.03906	−	2.81431i	0.0376411	−	0.101952i
$763$	10.3485	−	10.3485i	0.374640	−	0.374640i
$764$	2.82843			0.102329
$765$	4.84959	−	4.63481i	0.175337	−	0.167572i
$766$	4.10102			0.148176
$767$	−13.2922	+	13.2922i	−0.479952	+	0.479952i
$768$	0.599900	−	1.62484i	0.0216470	−	0.0586315i
$769$		−	8.39388i		−	0.302691i	−0.988481	−	0.151345i	$-0.951639\pi$
$769$		−	8.39388i		−	0.302691i	0.988481	−	0.151345i	$-0.0483606\pi$
$770$	−2.82843	−	3.46410i	−0.101929	−	0.124838i
$771$	10.4722	+	22.7310i	0.377147	+	0.818635i
$772$	15.3485	+	15.3485i	0.552403	+	0.552403i
$773$	−23.1202	−	23.1202i	−0.831577	−	0.831577i	0.156156	−	0.987732i	$-0.450090\pi$
$773$	−23.1202	−	23.1202i	−0.831577	−	0.831577i	−0.987732	+	0.156156i	$0.950090\pi$
$774$	−20.5382	+	24.0227i	−0.738231	+	0.863478i
$775$	3.00000	−	14.6969i	0.107763	−	0.527930i
$776$		−	11.4887i		−	0.412420i
$777$	−9.42078	−	3.47820i	−0.337969	−	0.124780i
$778$	6.10102	−	6.10102i	0.218732	−	0.218732i
$779$	−62.1467			−2.22664
$780$	−10.1558	+	20.7922i	−0.363635	+	0.744479i
$781$	−1.55051			−0.0554816
$782$	1.73205	−	1.73205i	0.0619380	−	0.0619380i
$783$	17.1531	−	9.58923i	0.613002	−	0.342691i
$784$			5.00000i			0.178571i
$785$		0			0
$786$	−7.44949	+	3.43199i	−0.265714	+	0.122415i
$787$	−26.9217	−	26.9217i	−0.959654	−	0.959654i	0.0395627	−	0.999217i	$-0.487404\pi$
$787$	−26.9217	−	26.9217i	−0.959654	−	0.959654i	−0.999217	+	0.0395627i	$0.987404\pi$
$788$	1.73205	+	1.73205i	0.0617018	+	0.0617018i
$789$	33.8143	−	15.5783i	1.20382	−	0.554603i
$790$	6.44949	+	0.651531i	0.229463	+	0.0231804i
$791$			3.95691i			0.140692i
$792$	4.22973	−	0.330749i	0.150297	−	0.0117527i
$793$	26.8207	−	26.8207i	0.952430	−	0.952430i
$794$	−39.1694			−1.39007
$795$	22.5180	−	46.1016i	0.798632	−	1.63506i
$796$	−2.79796			−0.0991710
$797$	0.921404	−	0.921404i	0.0326378	−	0.0326378i	−0.690600	−	0.723237i	$-0.742653\pi$
$797$	0.921404	−	0.921404i	0.0326378	−	0.0326378i	0.723237	+	0.690600i	$0.242653\pi$
$798$	17.1180	+	6.32005i	0.605971	+	0.223727i
$799$			5.00000i			0.176887i
$800$	−2.75699	−	4.17121i	−0.0974745	−	0.147474i
$801$	−28.2980	−	24.1933i	−0.999859	−	0.854829i
$802$	3.65153	+	3.65153i	0.128940	+	0.128940i
$803$	10.8530	+	10.8530i	0.382994	+	0.382994i
$804$	5.68896	+	12.3485i	0.200634	+	0.435497i
$805$	−4.89898	−	6.00000i	−0.172666	−	0.211472i
$806$		−	17.9241i		−	0.631349i
$807$	1.50610	−	4.07932i	0.0530174	−	0.143599i
$808$	−1.44949	+	1.44949i	−0.0509929	+	0.0509929i
$809$	−31.7484			−1.11621			−0.558107	−	0.829769i	$-0.688472\pi$
$809$	−31.7484			−1.11621			−0.558107	+	0.829769i	$0.688472\pi$
$810$	20.0937	−	1.11425i	0.706022	−	0.0391509i
$811$	12.0454			0.422971			0.211486	−	0.977381i	$-0.432170\pi$
$811$	12.0454			0.422971			0.211486	+	0.977381i	$0.432170\pi$
$812$	3.78194	−	3.78194i	0.132720	−	0.132720i
$813$	−13.3463	+	36.1486i	−0.468074	+	1.26779i
$814$		−	5.79796i		−	0.203218i
$815$	0.778539	−	7.70674i	0.0272710	−	0.269955i
$816$	0.724745	+	1.57313i	0.0253711	+	0.0550706i
$817$	−55.4949	−	55.4949i	−1.94152	−	1.94152i
$818$	17.6777	+	17.6777i	0.618085	+	0.618085i
$819$	−19.2669	−	16.4722i	−0.673238	−	0.575585i
$820$	−14.4495	+	11.7980i	−0.504598	+	0.412003i
$821$			26.4094i			0.921693i	0.887480	+	0.460846i	$0.152454\pi$
$821$			26.4094i			0.921693i	−0.887480	+	0.460846i	$0.847546\pi$
$822$	23.4782	+	8.66826i	0.818895	+	0.302340i
$823$	8.44949	−	8.44949i	0.294531	−	0.294531i	−0.544336	−	0.838867i	$-0.683218\pi$
$823$	8.44949	−	8.44949i	0.294531	−	0.294531i	0.838867	+	0.544336i	$0.183218\pi$
$824$	−11.0280			−0.384178
$825$	6.45411	−	10.4089i	0.224703	−	0.362390i
$826$	4.44949			0.154818
$827$	−31.1769	+	31.1769i	−1.08413	+	1.08413i	−0.0880078	+	0.996120i	$0.528050\pi$
$827$	−31.1769	+	31.1769i	−1.08413	+	1.08413i	−0.996120	+	0.0880078i	$0.971950\pi$
$828$	7.32611	−	0.572874i	0.254600	−	0.0199088i
$829$			13.1464i			0.456594i	0.973591	+	0.228297i	$0.0733158\pi$
$829$			13.1464i			0.456594i	−0.973591	+	0.228297i	$0.926684\pi$
$830$	−13.8564	+	11.3137i	−0.480963	+	0.392705i
$831$	−3.00000	+	1.38211i	−0.104069	+	0.0479447i
$832$	−4.22474	−	4.22474i	−0.146467	−	0.146467i
$833$	−3.53553	−	3.53553i	−0.122499	−	0.122499i
$834$	−2.82843	+	1.30306i	−0.0979404	+	0.0451213i
$835$	−3.34847	+	33.1464i	−0.115879	+	1.14708i
$836$			10.5352i			0.364366i
$837$	−13.6066	+	7.60660i	−0.470313	+	0.262923i
$838$	−10.3485	+	10.3485i	−0.357482	+	0.357482i
$839$	15.5242			0.535956			0.267978	−	0.963425i	$-0.413644\pi$
$839$	15.5242			0.535956			0.267978	+	0.963425i	$0.413644\pi$
$840$	5.17984	−	1.78024i	0.178721	−	0.0614241i
$841$	−14.6969			−0.506791
$842$	−5.02118	+	5.02118i	−0.173041	+	0.173041i
$843$	31.9903	+	11.8110i	1.10181	+	0.406792i
$844$			20.4495i			0.703900i
$845$	32.0983	+	39.3123i	1.10422	+	1.35238i
$846$	−9.74745	+	11.4012i	−0.335124	+	0.391981i
$847$	−9.00000	−	9.00000i	−0.309244	−	0.309244i
$848$	9.36736	+	9.36736i	0.321676	+	0.321676i
$849$	4.33013	+	9.39898i	0.148610	+	0.322572i
$850$	4.89898	+	1.00000i	0.168034	+	0.0342997i
$851$		−	10.0424i		−	0.344248i
$852$	0.657717	−	1.78144i	0.0225330	−	0.0610312i
$853$	7.14643	−	7.14643i	0.244689	−	0.244689i	−0.574098	−	0.818787i	$-0.694647\pi$
$853$	7.14643	−	7.14643i	0.244689	−	0.244689i	0.818787	+	0.574098i	$0.194647\pi$
$854$	−8.97809			−0.307224
$855$	−1.13136	+	49.9599i	−0.0386916	+	1.70859i
$856$	17.7980			0.608322
$857$	25.8772	−	25.8772i	0.883949	−	0.883949i	−0.109984	−	0.993933i	$-0.535080\pi$
$857$	25.8772	−	25.8772i	0.883949	−	0.883949i	0.993933	+	0.109984i	$0.0350800\pi$
$858$	5.06885	−	13.7291i	0.173048	−	0.468704i
$859$			39.2474i			1.33911i	0.742764	+	0.669553i	$0.233514\pi$
$859$			39.2474i			1.33911i	−0.742764	+	0.669553i	$0.766486\pi$
$860$	−23.4381	−	2.36773i	−0.799231	−	0.0807388i
$861$	−8.55051	−	18.5597i	−0.291401	−	0.632515i
$862$	−8.20204	−	8.20204i	−0.279363	−	0.279363i
$863$	−13.8564	−	13.8564i	−0.471678	−	0.471678i	0.430780	−	0.902457i	$-0.358239\pi$
$863$	−13.8564	−	13.8564i	−0.471678	−	0.471678i	−0.902457	+	0.430780i	$0.858239\pi$
$864$	−1.41421	+	5.00000i	−0.0481125	+	0.170103i
$865$	−38.5959	−	3.89898i	−1.31230	−	0.132569i
$866$		−	5.79972i		−	0.197082i
$867$	−1.62484	−	0.599900i	−0.0551826	−	0.0203737i
$868$	−3.00000	+	3.00000i	−0.101827	+	0.101827i
$869$	−4.09978			−0.139075
$870$	13.1613	+	6.42854i	0.446210	+	0.217948i
$871$	46.8990			1.58911
$872$	−7.31747	+	7.31747i	−0.247801	+	0.247801i
$873$	2.68692	+	34.3612i	0.0909383	+	1.16295i
$874$			18.2474i			0.617229i
$875$	4.70334	−	15.0956i	0.159002	−	0.510326i
$876$	−17.0732	+	7.86566i	−0.576850	+	0.265756i
$877$	−21.0000	−	21.0000i	−0.709120	−	0.709120i	0.257230	−	0.966350i	$-0.417190\pi$
$877$	−21.0000	−	21.0000i	−0.709120	−	0.709120i	−0.966350	+	0.257230i	$0.917190\pi$
$878$	2.04989	+	2.04989i	0.0691804	+	0.0691804i
$879$	27.1325	−	12.5000i	0.915157	−	0.421615i
$880$	2.00000	+	2.44949i	0.0674200	+	0.0825723i
$881$		−	41.5050i		−	1.39834i	−0.714956	−	0.699170i	$-0.753553\pi$
$881$		−	41.5050i		−	1.39834i	0.714956	−	0.699170i	$-0.246447\pi$
$882$	−1.16938	−	14.9543i	−0.0393749	−	0.503539i
$883$	−22.0454	+	22.0454i	−0.741887	+	0.741887i	−0.972941	−	0.231054i	$-0.925783\pi$
$883$	−22.0454	+	22.0454i	−0.741887	+	0.741887i	0.231054	+	0.972941i	$0.425783\pi$
$884$	5.97469			0.200951
$885$	3.96058	+	11.5238i	0.133133	+	0.387369i
$886$	8.65153			0.290654
$887$	−13.3636	+	13.3636i	−0.448706	+	0.448706i	−0.894924	−	0.446218i	$-0.852770\pi$
$887$	−13.3636	+	13.3636i	−0.448706	+	0.448706i	0.446218	+	0.894924i	$0.352770\pi$
$888$	6.66150	+	2.45946i	0.223545	+	0.0825340i
$889$			2.44949i			0.0821532i
$890$	2.78910	−	27.6093i	0.0934909	−	0.925465i
$891$	−12.5732	+	1.97846i	−0.421219	+	0.0662808i
$892$	20.1237	+	20.1237i	0.673792	+	0.673792i
$893$	−26.3379	−	26.3379i	−0.881365	−	0.881365i
$894$	−13.1172	−	28.4722i	−0.438705	−	0.952253i
$895$	−25.1010	+	20.4949i	−0.839035	+	0.685069i
$896$			1.41421i			0.0472456i
$897$	8.77951	−	23.7795i	0.293139	−	0.793975i
$898$	−17.2474	+	17.2474i	−0.575555	+	0.575555i
$899$	−11.3458			−0.378404
$900$	9.22135	+	11.8307i	0.307378	+	0.394358i
$901$	−13.2474			−0.441337
$902$	8.34242	−	8.34242i	0.277772	−	0.277772i
$903$	8.93790	−	24.2085i	0.297435	−	0.805609i
$904$		−	2.79796i		−	0.0930587i
$905$	−15.0635	+	12.2993i	−0.500729	+	0.408844i
$906$	0.472194	+	1.02494i	0.0156876	+	0.0340515i
$907$	−38.9671	−	38.9671i	−1.29388	−	1.29388i	−0.932366	−	0.361515i	$-0.882260\pi$
$907$	−38.9671	−	38.9671i	−1.29388	−	1.29388i	−0.361515	−	0.932366i	$-0.617740\pi$
$908$	13.1172	+	13.1172i	0.435309	+	0.435309i
$909$	3.99624	−	4.67423i	0.132547	−	0.155035i
$910$	1.89898	−	18.7980i	0.0629506	−	0.623146i
$911$			53.8043i			1.78262i	0.453397	+	0.891309i	$0.350212\pi$
$911$			53.8043i			1.78262i	−0.453397	+	0.891309i	$0.649788\pi$
$912$	−12.1043	−	4.46895i	−0.400812	−	0.147982i
$913$	8.00000	−	8.00000i	0.264761	−	0.264761i
$914$	1.69994			0.0562291
$915$	−7.99157	−	23.2525i	−0.264193	−	0.768705i
$916$	−19.7980			−0.654143
$917$	4.73545	−	4.73545i	0.156378	−	0.156378i
$918$	−2.53553	−	4.53553i	−0.0836851	−	0.149695i
$919$			21.1918i			0.699054i	0.936926	+	0.349527i	$0.113658\pi$
$919$			21.1918i			0.699054i	−0.936926	+	0.349527i	$0.886342\pi$
$920$	3.46410	+	4.24264i	0.114208	+	0.139876i
$921$	−26.6969	+	12.2993i	−0.879694	+	0.405277i
$922$	14.1464	+	14.1464i	0.465888	+	0.465888i
$923$	−4.63191	−	4.63191i	−0.152461	−	0.152461i
$924$	−3.14626	+	1.44949i	−0.103504	+	0.0476847i
$925$	17.1010	−	11.3031i	0.562278	−	0.371642i
$926$		−	14.0314i		−	0.461100i
$927$	32.9833	−	2.57917i	1.08331	−	0.0847110i
$928$	−2.67423	+	2.67423i	−0.0877861	+	0.0877861i
$929$	−17.8920			−0.587016			−0.293508	−	0.955957i	$-0.594823\pi$
$929$	−17.8920			−0.587016			−0.293508	+	0.955957i	$0.594823\pi$
$930$	−10.4401	−	5.09940i	−0.342345	−	0.167216i
$931$	37.2474			1.22074
$932$	4.80688	−	4.80688i	0.157455	−	0.157455i
$933$	−15.3887	−	5.68160i	−0.503805	−	0.186007i
$934$			17.1464i			0.561048i
$935$	−3.14626	−	0.317837i	−0.102894	−	0.0103944i
$936$	13.6237	+	11.6476i	0.445305	+	0.380714i
$937$	26.8990	+	26.8990i	0.878751	+	0.878751i	0.993405	−	0.114654i	$-0.0365760\pi$
$937$	26.8990	+	26.8990i	0.878751	+	0.878751i	−0.114654	+	0.993405i	$0.536576\pi$
$938$	−7.84961	−	7.84961i	−0.256299	−	0.256299i
$939$	−15.0635	−	32.6969i	−0.491580	−	1.06702i
$940$	−11.1237	−	1.12372i	−0.362816	−	0.0366518i
$941$		−	40.5515i		−	1.32194i	−0.750412	−	0.660970i	$-0.770145\pi$
$941$		−	40.5515i		−	1.32194i	0.750412	−	0.660970i	$-0.229855\pi$
$942$		0			0
$943$	14.4495	−	14.4495i	0.470540	−	0.470540i
$944$	−3.14626			−0.102402
$945$	−15.0759	+	6.53590i	−0.490418	+	0.212613i
$946$	14.8990			0.484408
$947$	−37.2230	+	37.2230i	−1.20959	+	1.20959i	−0.238425	+	0.971161i	$0.576631\pi$
$947$	−37.2230	+	37.2230i	−1.20959	+	1.20959i	−0.971161	+	0.238425i	$0.923369\pi$
$948$	1.73910	−	4.71039i	0.0564833	−	0.152986i
$949$			64.8434i			2.10490i
$950$	−31.0734	+	20.5382i	−1.00815	+	0.666347i
$951$	20.9444	+	45.4619i	0.679168	+	1.47420i
$952$	−1.00000	−	1.00000i	−0.0324102	−	0.0324102i
$953$	−27.7128	−	27.7128i	−0.897706	−	0.897706i	0.0975268	−	0.995233i	$-0.468907\pi$
$953$	−27.7128	−	27.7128i	−0.897706	−	0.897706i	−0.995233	+	0.0975268i	$0.968907\pi$
$954$	−30.2073	−	25.8258i	−0.977999	−	0.836140i
$955$	−4.00000	−	4.89898i	−0.129437	−	0.158527i
$956$			22.9774i			0.743141i
$957$	−8.69043	−	3.20855i	−0.280922	−	0.103718i
$958$	25.0227	−	25.0227i	0.808447	−	0.808447i
$959$	−20.4347			−0.659870
$960$	−3.66270	+	1.25882i	−0.118213	+	0.0406282i
$961$	−22.0000			−0.709677
$962$	17.3205	−	17.3205i	0.558436	−	0.558436i
$963$	−53.2314	+	4.16250i	−1.71536	+	0.134135i
$964$		−	22.4495i		−	0.723049i
$965$	4.87832	−	48.2903i	0.157039	−	1.55452i
$966$	−5.44949	+	2.51059i	−0.175334	+	0.0807769i
$967$	18.4949	+	18.4949i	0.594756	+	0.594756i	0.938912	−	0.344156i	$-0.111835\pi$
$967$	18.4949	+	18.4949i	0.594756	+	0.594756i	−0.344156	+	0.938912i	$0.611835\pi$
$968$	6.36396	+	6.36396i	0.204545	+	0.204545i
$969$	11.7190	−	5.39898i	0.376470	−	0.173440i
$970$	−19.8990	+	16.2474i	−0.638918	+	0.521674i
$971$		−	23.2310i		−	0.745518i	−0.927928	−	0.372759i	$-0.878412\pi$
$971$		−	23.2310i		−	0.745518i	0.927928	−	0.372759i	$-0.121588\pi$
$972$	3.06035	−	15.2851i	0.0981609	−	0.490270i
$973$	1.79796	−	1.79796i	0.0576399	−	0.0576399i
$974$	−41.5050			−1.32991
$975$	50.3755	−	11.8142i	1.61331	−	0.378358i
$976$	6.34847			0.203210
$977$	20.7525	−	20.7525i	0.663931	−	0.663931i	−0.292373	−	0.956304i	$-0.594445\pi$
$977$	20.7525	−	20.7525i	0.663931	−	0.663931i	0.956304	+	0.292373i	$0.0944449\pi$
$978$	−5.62863	−	2.07812i	−0.179984	−	0.0664508i
$979$			17.5505i			0.560917i
$980$	8.66025	−	7.07107i	0.276642	−	0.225877i
$981$	20.1742	−	23.5970i	0.644114	−	0.753394i
$982$	2.02270	+	2.02270i	0.0645471	+	0.0645471i
$983$	19.0205	+	19.0205i	0.606658	+	0.606658i	0.942071	−	0.335413i	$-0.108876\pi$
$983$	19.0205	+	19.0205i	0.606658	+	0.606658i	−0.335413	+	0.942071i	$0.608876\pi$
$984$	6.04612	+	13.1237i	0.192743	+	0.418369i
$985$	0.550510	−	5.44949i	0.0175407	−	0.173635i
$986$		−	3.78194i		−	0.120441i
$987$	4.24194	−	11.4894i	0.135022	−	0.365711i
$988$	−31.4722	+	31.4722i	−1.00126	+	1.00126i
$989$	25.8058			0.820576
$990$	−6.55461	−	6.85835i	−0.208319	−	0.217973i
$991$	−56.3939			−1.79141			−0.895705	−	0.444648i	$-0.853329\pi$
$991$	−56.3939			−1.79141			−0.895705	+	0.444648i	$0.853329\pi$
$992$	2.12132	−	2.12132i	0.0673520	−	0.0673520i
$993$	13.8249	−	37.4452i	0.438722	−	1.18829i
$994$			1.55051i			0.0491792i
$995$	3.95691	+	4.84621i	0.125443	+	0.153635i
$996$	5.79796	+	12.5851i	0.183715	+	0.398773i
$997$	−22.8434	−	22.8434i	−0.723457	−	0.723457i	0.245851	−	0.969308i	$-0.420933\pi$
$997$	−22.8434	−	22.8434i	−0.723457	−	0.723457i	−0.969308	+	0.245851i	$0.920933\pi$
$998$	−13.5386	−	13.5386i	−0.428556	−	0.428556i
$999$	−20.4989	−	5.79796i	−0.648556	−	0.183439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.l.f.137.1	✓	8
3.2	odd	2	inner	510.2.l.f.137.4	yes	8
5.3	odd	4	inner	510.2.l.f.443.4	yes	8
15.8	even	4	inner	510.2.l.f.443.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.l.f.137.1	✓	8	1.1	even	1	trivial
510.2.l.f.137.4	yes	8	3.2	odd	2	inner
510.2.l.f.443.1	yes	8	15.8	even	4	inner
510.2.l.f.443.4	yes	8	5.3	odd	4	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.599900 - 1.62484i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(0.724745 + 1.57313i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.28024 - 1.94949i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.599900 - 1.62484i) q^{3} -1.00000i q^{4} +(-1.73205 + 1.41421i) q^{5} +(0.724745 + 1.57313i) q^{6} +(-1.00000 - 1.00000i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.28024 - 1.94949i) q^{9} +(0.224745 - 2.22474i) q^{10} +1.41421i q^{11} +(-1.62484 - 0.599900i) q^{12} +(-4.22474 + 4.22474i) q^{13} +1.41421 q^{14} +(1.25882 + 3.66270i) q^{15} -1.00000 q^{16} +(0.707107 - 0.707107i) q^{17} +(2.99087 - 0.233875i) q^{18} +7.44949i q^{19} +(1.41421 + 1.73205i) q^{20} +(-2.22474 + 1.02494i) q^{21} +(-1.00000 - 1.00000i) q^{22} +(-1.73205 - 1.73205i) q^{23} +(1.57313 - 0.724745i) q^{24} +(1.00000 - 4.89898i) q^{25} -5.97469i q^{26} +(-4.53553 + 2.53553i) q^{27} +(-1.00000 + 1.00000i) q^{28} -3.78194 q^{29} +(-3.48004 - 1.69980i) q^{30} +3.00000 q^{31} +(0.707107 - 0.707107i) q^{32} +(2.29788 + 0.848387i) q^{33} +1.00000i q^{34} +(3.14626 + 0.317837i) q^{35} +(-1.94949 + 2.28024i) q^{36} +(2.89898 + 2.89898i) q^{37} +(-5.26758 - 5.26758i) q^{38} +(4.33013 + 9.39898i) q^{39} +(-2.22474 - 0.224745i) q^{40} +8.34242i q^{41} +(0.848387 - 2.29788i) q^{42} +(-7.44949 + 7.44949i) q^{43} +1.41421 q^{44} +(6.70648 + 0.151870i) q^{45} +2.44949 q^{46} +(-3.53553 + 3.53553i) q^{47} +(-0.599900 + 1.62484i) q^{48} -5.00000i q^{49} +(2.75699 + 4.17121i) q^{50} +(-0.724745 - 1.57313i) q^{51} +(4.22474 + 4.22474i) q^{52} +(-9.36736 - 9.36736i) q^{53} +(1.41421 - 5.00000i) q^{54} +(-2.00000 - 2.44949i) q^{55} -1.41421i q^{56} +(12.1043 + 4.46895i) q^{57} +(2.67423 - 2.67423i) q^{58} +3.14626 q^{59} +(3.66270 - 1.25882i) q^{60} -6.34847 q^{61} +(-2.12132 + 2.12132i) q^{62} +(0.330749 + 4.22973i) q^{63} +1.00000i q^{64} +(1.34278 - 13.2922i) q^{65} +(-2.22474 + 1.02494i) q^{66} +(-5.55051 - 5.55051i) q^{67} +(-0.707107 - 0.707107i) q^{68} +(-3.85337 + 1.77526i) q^{69} +(-2.44949 + 2.00000i) q^{70} +1.09638i q^{71} +(-0.233875 - 2.99087i) q^{72} +(7.67423 - 7.67423i) q^{73} -4.09978 q^{74} +(-7.36018 - 4.56374i) q^{75} +7.44949 q^{76} +(1.41421 - 1.41421i) q^{77} +(-9.70794 - 3.58422i) q^{78} +2.89898i q^{79} +(1.73205 - 1.41421i) q^{80} +(1.39898 + 8.89060i) q^{81} +(-5.89898 - 5.89898i) q^{82} +(-5.65685 - 5.65685i) q^{83} +(1.02494 + 2.22474i) q^{84} +(-0.224745 + 2.22474i) q^{85} -10.5352i q^{86} +(-2.26879 + 6.14506i) q^{87} +(-1.00000 + 1.00000i) q^{88} +12.4101 q^{89} +(-4.84959 + 4.63481i) q^{90} +8.44949 q^{91} +(-1.73205 + 1.73205i) q^{92} +(1.79970 - 4.87453i) q^{93} -5.00000i q^{94} +(-10.5352 - 12.9029i) q^{95} +(-0.724745 - 1.57313i) q^{96} +(-8.12372 - 8.12372i) q^{97} +(3.53553 + 3.53553i) q^{98} +(2.75699 - 3.22474i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 4 q^{6} - 8 q^{7}+O(q^{10}) \) 8 * q + 4 * q^3 - 4 * q^6 - 8 * q^7	\( 8 q + 4 q^{3} - 4 q^{6} - 8 q^{7} - 8 q^{10} - 4 q^{12} - 24 q^{13} + 8 q^{15} - 8 q^{16} + 8 q^{18} - 8 q^{21} - 8 q^{22} + 8 q^{25} - 8 q^{27} - 8 q^{28} - 8 q^{30} + 24 q^{31} - 4 q^{33} + 4 q^{36} - 16 q^{37} - 8 q^{40} + 4 q^{42} - 40 q^{43} + 12 q^{45} - 4 q^{48} + 4 q^{51} + 24 q^{52} - 16 q^{55} + 32 q^{57} - 8 q^{58} + 16 q^{60} + 8 q^{61} + 4 q^{63} - 8 q^{66} - 64 q^{67} - 8 q^{72} + 32 q^{73} - 20 q^{75} + 40 q^{76} - 28 q^{81} - 8 q^{82} + 8 q^{85} + 40 q^{87} - 8 q^{88} - 20 q^{90} + 48 q^{91} + 12 q^{93} + 4 q^{96} - 16 q^{97}+O(q^{100}) \) 8 * q + 4 * q^3 - 4 * q^6 - 8 * q^7 - 8 * q^10 - 4 * q^12 - 24 * q^13 + 8 * q^15 - 8 * q^16 + 8 * q^18 - 8 * q^21 - 8 * q^22 + 8 * q^25 - 8 * q^27 - 8 * q^28 - 8 * q^30 + 24 * q^31 - 4 * q^33 + 4 * q^36 - 16 * q^37 - 8 * q^40 + 4 * q^42 - 40 * q^43 + 12 * q^45 - 4 * q^48 + 4 * q^51 + 24 * q^52 - 16 * q^55 + 32 * q^57 - 8 * q^58 + 16 * q^60 + 8 * q^61 + 4 * q^63 - 8 * q^66 - 64 * q^67 - 8 * q^72 + 32 * q^73 - 20 * q^75 + 40 * q^76 - 28 * q^81 - 8 * q^82 + 8 * q^85 + 40 * q^87 - 8 * q^88 - 20 * q^90 + 48 * q^91 + 12 * q^93 + 4 * q^96 - 16 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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