LMFDB - Embedded newform 183.2.g.c.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [183,2,Mod(11,183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(183, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("183.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 183 = 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	183.g (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:	$1.46126235699$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	183.11
Dual form			183.2.g.c.50.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53906 + 1.53906i) q^{2} +(-1.73072 + 0.0678001i) q^{3} -2.73741i q^{4} +3.09885 q^{5} +(2.55934 - 2.76803i) q^{6} +(1.25340 + 1.25340i) q^{7} +(1.13492 + 1.13492i) q^{8} +(2.99081 - 0.234686i) q^{9} +O(q^{10})$	\(q+(-1.53906 + 1.53906i) q^{2} +(-1.73072 + 0.0678001i) q^{3} -2.73741i q^{4} +3.09885 q^{5} +(2.55934 - 2.76803i) q^{6} +(1.25340 + 1.25340i) q^{7} +(1.13492 + 1.13492i) q^{8} +(2.99081 - 0.234686i) q^{9} +(-4.76932 + 4.76932i) q^{10} +(2.26326 + 2.26326i) q^{11} +(0.185597 + 4.73770i) q^{12} -4.21059 q^{13} -3.85810 q^{14} +(-5.36326 + 0.210103i) q^{15} +1.98141 q^{16} +(-1.04954 - 1.04954i) q^{17} +(-4.24183 + 4.96423i) q^{18} +7.74511i q^{19} -8.48283i q^{20} +(-2.25426 - 2.08430i) q^{21} -6.96660 q^{22} +(1.17745 - 1.17745i) q^{23} +(-2.04118 - 1.88728i) q^{24} +4.60290 q^{25} +(6.48036 - 6.48036i) q^{26} +(-5.16035 + 0.608954i) q^{27} +(3.43106 - 3.43106i) q^{28} +(5.76510 + 5.76510i) q^{29} +(7.93102 - 8.57774i) q^{30} +(-0.319670 + 0.319670i) q^{31} +(-5.31934 + 5.31934i) q^{32} +(-4.07053 - 3.76363i) q^{33} +3.23062 q^{34} +(3.88409 + 3.88409i) q^{35} +(-0.642433 - 8.18706i) q^{36} +(6.69947 - 6.69947i) q^{37} +(-11.9202 - 11.9202i) q^{38} +(7.28737 - 0.285479i) q^{39} +(3.51694 + 3.51694i) q^{40} -1.90920 q^{41} +(6.67731 - 0.261580i) q^{42} +(-2.06066 + 2.06066i) q^{43} +(6.19548 - 6.19548i) q^{44} +(9.26807 - 0.727259i) q^{45} +3.62432i q^{46} +8.20055i q^{47} +(-3.42927 + 0.134340i) q^{48} -3.85799i q^{49} +(-7.08414 + 7.08414i) q^{50} +(1.88763 + 1.74531i) q^{51} +11.5261i q^{52} +(5.28133 - 5.28133i) q^{53} +(7.00486 - 8.87930i) q^{54} +(7.01353 + 7.01353i) q^{55} +2.84500i q^{56} +(-0.525119 - 13.4046i) q^{57} -17.7457 q^{58} +(-0.557124 - 0.557124i) q^{59} +(0.575137 + 14.6814i) q^{60} +(-5.45457 - 5.58996i) q^{61} -0.983984i q^{62} +(4.04282 + 3.45451i) q^{63} -12.4107i q^{64} -13.0480 q^{65} +(12.0572 - 0.472336i) q^{66} +(1.48899 - 1.48899i) q^{67} +(-2.87303 + 2.87303i) q^{68} +(-1.95800 + 2.11767i) q^{69} -11.9557 q^{70} +(-10.0641 - 10.0641i) q^{71} +(3.66067 + 3.12797i) q^{72} +4.20765 q^{73} +20.6218i q^{74} +(-7.96635 + 0.312077i) q^{75} +21.2015 q^{76} +5.67353i q^{77} +(-10.7763 + 11.6551i) q^{78} +(-8.87227 - 8.87227i) q^{79} +6.14010 q^{80} +(8.88984 - 1.40380i) q^{81} +(2.93838 - 2.93838i) q^{82} -1.37111i q^{83} +(-5.70559 + 6.17084i) q^{84} +(-3.25238 - 3.25238i) q^{85} -6.34294i q^{86} +(-10.3687 - 9.58692i) q^{87} +5.13723i q^{88} +(1.44252 + 1.44252i) q^{89} +(-13.1448 + 15.3834i) q^{90} +(-5.27755 - 5.27755i) q^{91} +(-3.22316 - 3.22316i) q^{92} +(0.531587 - 0.574935i) q^{93} +(-12.6211 - 12.6211i) q^{94} +24.0010i q^{95} +(8.84565 - 9.56696i) q^{96} +14.1801i q^{97} +(5.93768 + 5.93768i) q^{98} +(7.30014 + 6.23783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9	$ 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{13} - 40 q^{15} + 12 q^{16} - 4 q^{18} - 18 q^{21} - 48 q^{22} + 14 q^{24} + 36 q^{25} - 24 q^{28} - 22 q^{30} + 32 q^{31} + 2 q^{33} + 96 q^{34} + 8 q^{37} + 28 q^{40} + 20 q^{42} - 32 q^{43} - 24 q^{51} - 2 q^{54} - 40 q^{55} - 16 q^{57} - 56 q^{58} + 64 q^{61} + 40 q^{63} - 12 q^{67} - 30 q^{69} - 24 q^{70} + 44 q^{72} - 72 q^{73} + 128 q^{76} - 66 q^{78} + 28 q^{81} - 28 q^{82} + 46 q^{84} - 44 q^{85} - 12 q^{87} - 56 q^{90} - 64 q^{91} + 36 q^{93} - 16 q^{94} + 54 q^{96} + 32 q^{99}+O(q^{100}) $ 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^13 - 40 * q^15 + 12 * q^16 - 4 * q^18 - 18 * q^21 - 48 * q^22 + 14 * q^24 + 36 * q^25 - 24 * q^28 - 22 * q^30 + 32 * q^31 + 2 * q^33 + 96 * q^34 + 8 * q^37 + 28 * q^40 + 20 * q^42 - 32 * q^43 - 24 * q^51 - 2 * q^54 - 40 * q^55 - 16 * q^57 - 56 * q^58 + 64 * q^61 + 40 * q^63 - 12 * q^67 - 30 * q^69 - 24 * q^70 + 44 * q^72 - 72 * q^73 + 128 * q^76 - 66 * q^78 + 28 * q^81 - 28 * q^82 + 46 * q^84 - 44 * q^85 - 12 * q^87 - 56 * q^90 - 64 * q^91 + 36 * q^93 - 16 * q^94 + 54 * q^96 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/183\mathbb{Z}\right)^\times$.

$n$	$62$	$124$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.53906	+	1.53906i	−1.08828	+	1.08828i	−0.0925737	+	0.995706i	$0.529509\pi$
$2$	−1.53906	+	1.53906i	−1.08828	+	1.08828i	−0.995706	+	0.0925737i	$0.970491\pi$
$3$	−1.73072	+	0.0678001i	−0.999234	+	0.0391444i
$3$	−1.73072	+	0.0678001i	−0.999234	+	0.0391444i
$4$		−	2.73741i		−	1.36870i
$5$	3.09885			1.38585			0.692925	−	0.721010i	$-0.256322\pi$
$5$	3.09885			1.38585			0.692925	+	0.721010i	$0.256322\pi$
$6$	2.55934	−	2.76803i	1.04485	−	1.13005i
$7$	1.25340	+	1.25340i	0.473739	+	0.473739i	0.903122	−	0.429383i	$-0.141269\pi$
$7$	1.25340	+	1.25340i	0.473739	+	0.473739i	−0.429383	+	0.903122i	$0.641269\pi$
$8$	1.13492	+	1.13492i	0.401254	+	0.401254i
$9$	2.99081	−	0.234686i	0.996935	−	0.0782288i
$10$	−4.76932	+	4.76932i	−1.50819	+	1.50819i
$11$	2.26326	+	2.26326i	0.682400	+	0.682400i	0.960540	−	0.278141i	$-0.0897181\pi$
$11$	2.26326	+	2.26326i	0.682400	+	0.682400i	−0.278141	+	0.960540i	$0.589718\pi$
$12$	0.185597	+	4.73770i	0.0535771	+	1.36766i
$13$	−4.21059			−1.16781			−0.583904	−	0.811822i	$-0.698476\pi$
$13$	−4.21059			−1.16781			−0.583904	+	0.811822i	$0.698476\pi$
$14$	−3.85810			−1.03112
$15$	−5.36326	+	0.210103i	−1.38479	+	0.0542483i
$16$	1.98141			0.495352
$17$	−1.04954	−	1.04954i	−0.254551	−	0.254551i	0.568282	−	0.822834i	$-0.307608\pi$
$17$	−1.04954	−	1.04954i	−0.254551	−	0.254551i	−0.822834	+	0.568282i	$0.807608\pi$
$18$	−4.24183	+	4.96423i	−0.999810	+	1.17008i
$19$			7.74511i			1.77685i	0.459021	+	0.888425i	$0.348200\pi$
$19$			7.74511i			1.77685i	−0.459021	+	0.888425i	$0.651800\pi$
$20$		−	8.48283i		−	1.89682i
$21$	−2.25426	−	2.08430i	−0.491921	−	0.454832i
$22$	−6.96660			−1.48528
$23$	1.17745	−	1.17745i	0.245515	−	0.245515i	−0.573612	−	0.819127i	$-0.694458\pi$
$23$	1.17745	−	1.17745i	0.245515	−	0.245515i	0.819127	+	0.573612i	$0.194458\pi$
$24$	−2.04118	−	1.88728i	−0.416653	−	0.385239i
$25$	4.60290			0.920580
$26$	6.48036	−	6.48036i	1.27090	−	1.27090i
$27$	−5.16035	+	0.608954i	−0.993109	+	0.117193i
$28$	3.43106	−	3.43106i	0.648409	−	0.648409i
$29$	5.76510	+	5.76510i	1.07055	+	1.07055i	0.997315	+	0.0732376i	$0.0233331\pi$
$29$	5.76510	+	5.76510i	1.07055	+	1.07055i	0.0732376	+	0.997315i	$0.476667\pi$
$30$	7.93102	−	8.57774i	1.44800	−	1.56607i
$31$	−0.319670	+	0.319670i	−0.0574145	+	0.0574145i	−0.735231	−	0.677817i	$-0.762926\pi$
$31$	−0.319670	+	0.319670i	−0.0574145	+	0.0574145i	0.677817	+	0.735231i	$0.262926\pi$
$32$	−5.31934	+	5.31934i	−0.940335	+	0.940335i
$33$	−4.07053	−	3.76363i	−0.708589	−	0.655165i
$34$	3.23062			0.554046
$35$	3.88409	+	3.88409i	0.656532	+	0.656532i
$36$	−0.642433	−	8.18706i	−0.107072	−	1.36451i
$37$	6.69947	−	6.69947i	1.10139	−	1.10139i	0.107143	−	0.994244i	$-0.465830\pi$
$37$	6.69947	−	6.69947i	1.10139	−	1.10139i	0.994244	−	0.107143i	$-0.0341703\pi$
$38$	−11.9202	−	11.9202i	−1.93371	−	1.93371i
$39$	7.28737	−	0.285479i	1.16691	−	0.0457132i
$40$	3.51694	+	3.51694i	0.556078	+	0.556078i
$41$	−1.90920			−0.298167			−0.149084	−	0.988825i	$-0.547632\pi$
$41$	−1.90920			−0.298167			−0.149084	+	0.988825i	$0.547632\pi$
$42$	6.67731	−	0.261580i	1.03033	−	0.0403627i
$43$	−2.06066	+	2.06066i	−0.314247	+	0.314247i	−0.846552	−	0.532305i	$-0.821326\pi$
$43$	−2.06066	+	2.06066i	−0.314247	+	0.314247i	0.532305	+	0.846552i	$0.321326\pi$
$44$	6.19548	−	6.19548i	0.934004	−	0.934004i
$45$	9.26807	−	0.727259i	1.38160	−	0.108413i
$46$			3.62432i			0.534377i
$47$			8.20055i			1.19617i	0.801431	+	0.598087i	$0.204072\pi$
$47$			8.20055i			1.19617i	−0.801431	+	0.598087i	$0.795928\pi$
$48$	−3.42927	+	0.134340i	−0.494972	+	0.0193903i
$49$		−	3.85799i		−	0.551142i
$50$	−7.08414	+	7.08414i	−1.00185	+	1.00185i
$51$	1.88763	+	1.74531i	0.264321	+	0.244392i
$52$			11.5261i			1.59839i
$53$	5.28133	−	5.28133i	0.725446	−	0.725446i	−0.244263	−	0.969709i	$-0.578546\pi$
$53$	5.28133	−	5.28133i	0.725446	−	0.725446i	0.969709	+	0.244263i	$0.0785460\pi$
$54$	7.00486	−	8.87930i	0.953241	−	1.20832i
$55$	7.01353	+	7.01353i	0.945704	+	0.945704i
$56$			2.84500i			0.380180i
$57$	−0.525119	−	13.4046i	−0.0695538	−	1.77549i
$58$	−17.7457			−2.33012
$59$	−0.557124	−	0.557124i	−0.0725314	−	0.0725314i	0.669910	−	0.742442i	$-0.266332\pi$
$59$	−0.557124	−	0.557124i	−0.0725314	−	0.0725314i	−0.742442	+	0.669910i	$0.766332\pi$
$60$	0.575137	+	14.6814i	0.0742499	+	1.89537i
$61$	−5.45457	−	5.58996i	−0.698386	−	0.715721i
$61$	−5.45457	−	5.58996i	−0.698386	−	0.715721i
$62$		−	0.983984i		−	0.124966i
$63$	4.04282	+	3.45451i	0.509348	+	0.435228i
$64$		−	12.4107i		−	1.55134i
$65$	−13.0480			−1.61841
$66$	12.0572	−	0.472336i	1.48414	−	0.0581405i
$67$	1.48899	−	1.48899i	0.181909	−	0.181909i	−0.610278	−	0.792187i	$-0.708942\pi$
$67$	1.48899	−	1.48899i	0.181909	−	0.181909i	0.792187	+	0.610278i	$0.208942\pi$
$68$	−2.87303	+	2.87303i	−0.348406	+	0.348406i
$69$	−1.95800	+	2.11767i	−0.235716	+	0.254937i
$70$	−11.9557			−1.42898
$71$	−10.0641	−	10.0641i	−1.19439	−	1.19439i	−0.975820	−	0.218574i	$-0.929860\pi$
$71$	−10.0641	−	10.0641i	−1.19439	−	1.19439i	−0.218574	−	0.975820i	$-0.570140\pi$
$72$	3.66067	+	3.12797i	0.431414	+	0.368635i
$73$	4.20765			0.492468			0.246234	−	0.969210i	$-0.420807\pi$
$73$	4.20765			0.492468			0.246234	+	0.969210i	$0.420807\pi$
$74$			20.6218i			2.39723i
$75$	−7.96635	+	0.312077i	−0.919875	+	0.0360356i
$76$	21.2015			2.43198
$77$			5.67353i			0.646559i
$78$	−10.7763	+	11.6551i	−1.22018	+	1.31968i
$79$	−8.87227	−	8.87227i	−0.998208	−	0.998208i	0.00178995	−	0.999998i	$-0.499430\pi$
$79$	−8.87227	−	8.87227i	−0.998208	−	0.998208i	−0.999998	+	0.00178995i	$0.999430\pi$
$80$	6.14010			0.686484
$81$	8.88984	−	1.40380i	0.987761	−	0.155978i
$82$	2.93838	−	2.93838i	0.324489	−	0.324489i
$83$		−	1.37111i		−	0.150499i	−0.997165	−	0.0752493i	$-0.976025\pi$
$83$		−	1.37111i		−	0.150499i	0.997165	−	0.0752493i	$-0.0239753\pi$
$84$	−5.70559	+	6.17084i	−0.622531	+	0.673294i
$85$	−3.25238	−	3.25238i	−0.352770	−	0.352770i
$86$		−	6.34294i		−	0.683977i
$87$	−10.3687	−	9.58692i	−1.11164	−	1.02783i
$88$			5.13723i			0.547631i
$89$	1.44252	+	1.44252i	0.152906	+	0.152906i	0.779415	−	0.626508i	$-0.215517\pi$
$89$	1.44252	+	1.44252i	0.152906	+	0.152906i	−0.626508	+	0.779415i	$0.715517\pi$
$90$	−13.1448	+	15.3834i	−1.38559	+	1.62155i
$91$	−5.27755	−	5.27755i	−0.553237	−	0.553237i
$92$	−3.22316	−	3.22316i	−0.336037	−	0.336037i
$93$	0.531587	−	0.574935i	0.0551230	−	0.0596179i
$94$	−12.6211	−	12.6211i	−1.30177	−	1.30177i
$95$			24.0010i			2.46245i
$96$	8.84565	−	9.56696i	0.902806	−	0.976424i
$97$			14.1801i			1.43977i	0.694091	+	0.719887i	$0.255806\pi$
$97$			14.1801i			1.43977i	−0.694091	+	0.719887i	$0.744194\pi$
$98$	5.93768	+	5.93768i	0.599796	+	0.599796i
$99$	7.30014	+	6.23783i	0.733692	+	0.626925i
$100$		−	12.6000i		−	1.26000i
$101$	11.4237	−	11.4237i	1.13670	−	1.13670i	0.147659	−	0.989038i	$-0.452826\pi$
$101$	11.4237	−	11.4237i	1.13670	−	1.13670i	0.989038	−	0.147659i	$-0.0471738\pi$
$102$	−5.59130	+	0.219036i	−0.553621	+	0.0216878i
$103$	7.77333			0.765929			0.382965	−	0.923763i	$-0.374903\pi$
$103$	7.77333			0.765929			0.382965	+	0.923763i	$0.374903\pi$
$104$	−4.77868	−	4.77868i	−0.468588	−	0.468588i
$105$	−6.98563	−	6.45895i	−0.681728	−	0.630329i
$106$			16.2566i			1.57898i
$107$	11.3308			1.09539			0.547694	−	0.836679i	$-0.315506\pi$
$107$	11.3308			1.09539			0.547694	+	0.836679i	$0.315506\pi$
$108$	1.66696	+	14.1260i	0.160403	+	1.35927i
$109$			11.6145i			1.11247i	0.831024	+	0.556236i	$0.187755\pi$
$109$			11.6145i			1.11247i	−0.831024	+	0.556236i	$0.812245\pi$
$110$	−21.5885			−2.05838
$111$	−11.1407	+	12.0492i	−1.05743	+	1.14366i
$112$	2.48349	+	2.48349i	0.234668	+	0.234668i
$113$	−6.41867			−0.603818			−0.301909	−	0.953337i	$-0.597624\pi$
$113$	−6.41867			−0.603818			−0.301909	+	0.953337i	$0.597624\pi$
$114$	21.4387	+	19.8224i	2.00792	+	1.85653i
$115$	3.64874	−	3.64874i	0.340247	−	0.340247i
$116$	15.7814	−	15.7814i	1.46527	−	1.46527i
$117$	−12.5931	+	0.988169i	−1.16423	+	0.0913563i
$118$	1.71489			0.157869
$119$		−	2.63099i		−	0.241182i
$120$	−6.32531	−	5.84841i	−0.577419	−	0.533884i
$121$		−	0.755275i		−	0.0686613i
$122$	16.9982	+	0.208382i	1.53894	+	0.0188660i
$123$	3.30430	−	0.129444i	0.297939	−	0.0116716i
$124$	0.875069	+	0.875069i	0.0785835	+	0.0785835i
$125$	−1.23055			−0.110064
$126$	−11.5388	+	0.905445i	−1.02796	+	0.0806634i
$127$		−	12.0832i		−	1.07221i	−0.844151	−	0.536106i	$-0.819895\pi$
$127$		−	12.0832i		−	1.07221i	0.844151	−	0.536106i	$-0.180105\pi$
$128$	8.46220	+	8.46220i	0.747960	+	0.747960i
$129$	3.42671	−	3.70614i	0.301705	−	0.326307i
$130$	20.0817	−	20.0817i	1.76128	−	1.76128i
$131$		−	8.05793i		−	0.704025i	−0.935995	−	0.352012i	$-0.885497\pi$
$131$		−	8.05793i		−	0.704025i	0.935995	−	0.352012i	$-0.114503\pi$
$132$	−10.3026	+	11.1427i	−0.896727	+	0.969849i
$133$	−9.70770	+	9.70770i	−0.841764	+	0.841764i
$134$			4.58329i			0.395936i
$135$	−15.9912	+	1.88706i	−1.37630	+	0.162412i
$136$		−	2.38229i		−	0.204279i
$137$		−	4.93240i		−	0.421403i	−0.977550	−	0.210702i	$-0.932425\pi$
$137$		−	4.93240i		−	0.421403i	0.977550	−	0.210702i	$-0.0675748\pi$
$138$	−0.245730	−	6.27270i	−0.0209179	−	0.533968i
$139$	12.6647	−	12.6647i	1.07420	−	1.07420i	0.0771863	−	0.997017i	$-0.475406\pi$
$139$	12.6647	−	12.6647i	1.07420	−	1.07420i	0.997017	−	0.0771863i	$-0.0245936\pi$
$140$	10.6324	−	10.6324i	0.898598	−	0.898598i
$141$	−0.555998	−	14.1929i	−0.0468235	−	1.19526i
$142$	30.9786			2.59967
$143$	−9.52969	−	9.52969i	−0.796912	−	0.796912i
$144$	5.92601	−	0.465010i	0.493834	−	0.0387508i
$145$	17.8652	+	17.8652i	1.48362	+	1.48362i
$146$	−6.47583	+	6.47583i	−0.535943	+	0.535943i
$147$	0.261572	+	6.67712i	0.0215741	+	0.550719i
$148$	−18.3392	−	18.3392i	−1.50747	−	1.50747i
$149$	−22.2864			−1.82577			−0.912885	−	0.408216i	$-0.866151\pi$
$149$	−22.2864			−1.82577			−0.912885	+	0.408216i	$0.866151\pi$
$150$	11.7804	−	12.7410i	0.961864	−	1.04030i
$151$	3.26344	−	3.26344i	0.265575	−	0.265575i	−0.561739	−	0.827314i	$-0.689868\pi$
$151$	3.26344	−	3.26344i	0.265575	−	0.265575i	0.827314	+	0.561739i	$0.189868\pi$
$152$	−8.79006	+	8.79006i	−0.712968	+	0.712968i
$153$	−3.38529	−	2.89266i	−0.273685	−	0.233858i
$154$	−8.73191	−	8.73191i	−0.703637	−	0.703637i
$155$	−0.990612	+	0.990612i	−0.0795679	+	0.0795679i
$156$	−0.781472	−	19.9485i	−0.0625679	−	1.59716i
$157$	−2.70448	+	2.70448i	−0.215841	+	0.215841i	−0.806743	−	0.590902i	$-0.798772\pi$
$157$	−2.70448	+	2.70448i	−0.215841	+	0.215841i	0.590902	+	0.806743i	$0.298772\pi$
$158$	27.3099			2.17266
$159$	−8.78244	+	9.49859i	−0.696493	+	0.753287i
$160$	−16.4839	+	16.4839i	−1.30316	+	1.30316i
$161$	2.95162			0.232620
$162$	−11.5215	+	15.8425i	−0.905212	+	1.24471i
$163$		−	6.56971i		−	0.514580i	−0.966334	−	0.257290i	$-0.917171\pi$
$163$		−	6.56971i		−	0.514580i	0.966334	−	0.257290i	$-0.0828295\pi$
$164$			5.22627i			0.408103i
$165$	−12.6140	−	11.6630i	−0.981998	−	0.907960i
$166$	2.11022	+	2.11022i	0.163785	+	0.163785i
$167$	−11.6931			−0.904837			−0.452419	−	0.891806i	$-0.649439\pi$
$167$	−11.6931			−0.904837			−0.452419	+	0.891806i	$0.649439\pi$
$168$	−0.192892	−	4.92391i	−0.0148819	−	0.379888i
$169$	4.72911			0.363777
$170$	10.0112			0.767825
$171$	1.81767	+	23.1641i	0.139001	+	1.77141i
$172$	5.64086	+	5.64086i	0.430111	+	0.430111i
$173$	9.84930	−	9.84930i	0.748828	−	0.748828i	−0.225431	−	0.974259i	$-0.572379\pi$
$173$	9.84930	−	9.84930i	0.748828	−	0.748828i	0.974259	+	0.225431i	$0.0723790\pi$
$174$	30.7128	−	1.20316i	2.32833	−	0.0912112i
$175$	5.76926	+	5.76926i	0.436115	+	0.436115i
$176$	4.48445	+	4.48445i	0.338028	+	0.338028i
$177$	1.00200	+	0.926455i	0.0753150	+	0.0696366i
$178$	−4.44024			−0.332810
$179$		−	5.87887i		−	0.439407i	−0.975567	−	0.219704i	$-0.929491\pi$
$179$		−	5.87887i		−	0.439407i	0.975567	−	0.219704i	$-0.0705091\pi$
$180$	−1.99081	−	25.3705i	−0.148386	−	1.89101i
$181$	3.41593	−	3.41593i	0.253904	−	0.253904i	−0.568665	−	0.822569i	$-0.692540\pi$
$181$	3.41593	−	3.41593i	0.253904	−	0.253904i	0.822569	+	0.568665i	$0.192540\pi$
$182$	16.2449			1.20415
$183$	9.81935	+	9.30486i	0.725867	+	0.687835i
$184$	2.67261			0.197028
$185$	20.7607	−	20.7607i	1.52636	−	1.52636i
$186$	0.0667142	+	1.70300i	0.00489172	+	0.124870i
$187$		−	4.75078i		−	0.347412i
$188$	22.4483			1.63721
$189$	−7.23122	−	5.70470i	−0.525994	−	0.414956i
$190$	−36.9389	−	36.9389i	−2.67983	−	2.67983i
$191$	−8.36822	−	8.36822i	−0.605504	−	0.605504i	0.336264	−	0.941768i	$-0.390836\pi$
$191$	−8.36822	−	8.36822i	−0.605504	−	0.605504i	−0.941768	+	0.336264i	$0.890836\pi$
$192$	0.841450	+	21.4796i	0.0607264	+	1.55015i
$193$	−14.1415	+	14.1415i	−1.01793	+	1.01793i	−0.0180945	+	0.999836i	$0.505760\pi$
$193$	−14.1415	+	14.1415i	−1.01793	+	1.01793i	−0.999836	+	0.0180945i	$0.994240\pi$
$194$	−21.8241	−	21.8241i	−1.56688	−	1.56688i
$195$	22.5825	−	0.884657i	1.61717	−	0.0633516i
$196$	−10.5609			−0.754351
$197$	10.6854			0.761302			0.380651	−	0.924719i	$-0.375700\pi$
$197$	10.6854			0.761302			0.380651	+	0.924719i	$0.375700\pi$
$198$	−20.8357	+	1.63497i	−1.48073	+	0.116192i
$199$	−11.5371			−0.817841			−0.408921	−	0.912570i	$-0.634095\pi$
$199$	−11.5371			−0.817841			−0.408921	+	0.912570i	$0.634095\pi$
$200$	5.22391	+	5.22391i	0.369386	+	0.369386i
$201$	−2.47608	+	2.67798i	−0.174649	+	0.188890i
$202$			35.1634i			2.47409i
$203$			14.4519i			1.01433i
$204$	4.77762	−	5.16721i	0.334500	−	0.361777i
$205$	−5.91634			−0.413215
$206$	−11.9636	+	11.9636i	−0.833545	+	0.833545i
$207$	3.24519	−	3.79785i	0.225556	−	0.263969i
$208$	−8.34291			−0.578476
$209$	−17.5292	+	17.5292i	−1.21252	+	1.21252i
$210$	20.6920	−	0.810598i	1.42789	−	0.0559366i
$211$	11.6381	−	11.6381i	0.801202	−	0.801202i	−0.182082	−	0.983283i	$-0.558284\pi$
$211$	11.6381	−	11.6381i	0.801202	−	0.801202i	0.983283	+	0.182082i	$0.0582835\pi$
$212$	−14.4572	−	14.4572i	−0.992921	−	0.992921i
$213$	18.1006	+	16.7359i	1.24023	+	1.14672i
$214$	−17.4388	+	17.4388i	−1.19209	+	1.19209i
$215$	−6.38567	+	6.38567i	−0.435499	+	0.435499i
$216$	−6.54768	−	5.16545i	−0.445513	−	0.351465i
$217$	−0.801348			−0.0543990
$218$	−17.8755	−	17.8755i	−1.21068	−	1.21068i
$219$	−7.28228	+	0.285279i	−0.492091	+	0.0192774i
$220$	19.1989	−	19.1989i	1.29439	−	1.29439i
$221$	4.41920	+	4.41920i	0.297267	+	0.297267i
$222$	−1.39816	−	35.6906i	−0.0938383	−	2.39540i
$223$	−0.879490	−	0.879490i	−0.0588950	−	0.0588950i	0.677046	−	0.735941i	$-0.263260\pi$
$223$	−0.879490	−	0.879490i	−0.0588950	−	0.0588950i	−0.735941	+	0.677046i	$0.763260\pi$
$224$	−13.3345			−0.890948
$225$	13.7664	−	1.08024i	0.917759	−	0.0720159i
$226$	9.87871	−	9.87871i	0.657122	−	0.657122i
$227$	−18.1979	+	18.1979i	−1.20784	+	1.20784i	−0.236113	+	0.971726i	$0.575873\pi$
$227$	−18.1979	+	18.1979i	−1.20784	+	1.20784i	−0.971726	+	0.236113i	$0.924127\pi$
$228$	−36.6940	+	1.43747i	−2.43012	+	0.0951986i
$229$			24.3206i			1.60715i	0.595205	+	0.803574i	$0.297071\pi$
$229$			24.3206i			1.60715i	−0.595205	+	0.803574i	$0.702929\pi$
$230$			11.2313i			0.740567i
$231$	−0.384666	−	9.81932i	−0.0253092	−	0.646064i
$232$			13.0858i			0.859126i
$233$	−4.69671	+	4.69671i	−0.307692	+	0.307692i	−0.844013	−	0.536322i	$-0.819813\pi$
$233$	−4.69671	+	4.69671i	−0.307692	+	0.307692i	0.536322	+	0.844013i	$0.319813\pi$
$234$	17.8606	−	20.9023i	1.16759	−	1.36643i
$235$			25.4123i			1.65772i
$236$	−1.52508	+	1.52508i	−0.0992741	+	0.0992741i
$237$	15.9570	+	14.7539i	1.03652	+	0.958369i
$238$	4.04924	+	4.04924i	0.262473	+	0.262473i
$239$		−	13.9825i		−	0.904455i	−0.891903	−	0.452228i	$-0.850629\pi$
$239$		−	13.9825i		−	0.904455i	0.891903	−	0.452228i	$-0.149371\pi$
$240$	−10.6268	+	0.416299i	−0.685957	+	0.0268720i
$241$	−14.7165			−0.947971			−0.473985	−	0.880533i	$-0.657185\pi$
$241$	−14.7165			−0.947971			−0.473985	+	0.880533i	$0.657185\pi$
$242$	1.16241	+	1.16241i	0.0747227	+	0.0747227i
$243$	−15.2907	+	3.03233i	−0.980898	+	0.194524i
$244$	−15.3020	+	14.9314i	−0.979611	+	0.955884i
$245$		−	11.9554i		−	0.763800i
$246$	−4.88629	+	5.28474i	−0.311539	+	0.336943i
$247$		−	32.6115i		−	2.07502i
$248$	−0.725599			−0.0460756
$249$	0.0929612	+	2.37301i	0.00589118	+	0.150383i
$250$	1.89389	−	1.89389i	0.119780	−	0.119780i
$251$	7.30363	−	7.30363i	0.461001	−	0.461001i	−0.437983	−	0.898983i	$-0.644307\pi$
$251$	7.30363	−	7.30363i	0.461001	−	0.461001i	0.898983	+	0.437983i	$0.144307\pi$
$252$	9.45641	−	11.0669i	0.595698	−	0.697147i
$253$	5.32975			0.335078
$254$	18.5968	+	18.5968i	1.16687	+	1.16687i
$255$	5.84948	+	5.40846i	0.366309	+	0.338691i
$256$	−1.22617			−0.0766357
$257$		−	12.8299i		−	0.800307i	−0.916448	−	0.400154i	$-0.868957\pi$
$257$		−	12.8299i		−	0.800307i	0.916448	−	0.400154i	$-0.131043\pi$
$258$	0.430052	+	10.9779i	0.0267739	+	0.683453i
$259$	16.7942			1.04354
$260$			35.7178i			2.21512i
$261$	18.5953	+	15.8893i	1.15102	+	0.983523i
$262$	12.4016	+	12.4016i	0.766176	+	0.766176i
$263$	14.1525			0.872679			0.436339	−	0.899782i	$-0.356275\pi$
$263$	14.1525			0.872679			0.436339	+	0.899782i	$0.356275\pi$
$264$	−0.348305	−	8.89113i	−0.0214367	−	0.547211i
$265$	16.3661	−	16.3661i	1.00536	−	1.00536i
$266$		−	29.8815i		−	1.83215i
$267$	−2.59440	−	2.39879i	−0.158775	−	0.146804i
$268$	−4.07598	−	4.07598i	−0.248980	−	0.248980i
$269$			11.5353i			0.703321i	0.936128	+	0.351660i	$0.114383\pi$
$269$			11.5353i			0.703321i	−0.936128	+	0.351660i	$0.885617\pi$
$270$	21.7071	−	27.5157i	1.32105	−	1.67455i
$271$			21.4321i			1.30191i	0.759117	+	0.650955i	$0.225631\pi$
$271$			21.4321i			1.30191i	−0.759117	+	0.650955i	$0.774369\pi$
$272$	−2.07957	−	2.07957i	−0.126093	−	0.126093i
$273$	9.49179	+	8.77615i	0.574469	+	0.531157i
$274$	7.59125	+	7.59125i	0.458604	+	0.458604i
$275$	10.4176	+	10.4176i	0.628204	+	0.628204i
$276$	5.79692	+	5.35986i	0.348934	+	0.322626i
$277$	−0.0686958	−	0.0686958i	−0.00412753	−	0.00412753i	0.705040	−	0.709168i	$-0.250929\pi$
$277$	−0.0686958	−	0.0686958i	−0.00412753	−	0.00412753i	−0.709168	+	0.705040i	$0.750929\pi$
$278$			38.9834i			2.33807i
$279$	−0.881050	+	1.03109i	−0.0527471	+	0.0617300i
$280$			8.81625i			0.526872i
$281$	−6.97026	−	6.97026i	−0.415811	−	0.415811i	0.467946	−	0.883757i	$-0.344994\pi$
$281$	−6.97026	−	6.97026i	−0.415811	−	0.415811i	−0.883757	+	0.467946i	$0.844994\pi$
$282$	22.6994	+	20.9880i	1.35173	+	1.24982i
$283$			16.4744i			0.979299i	0.871919	+	0.489649i	$0.162875\pi$
$283$			16.4744i			0.979299i	−0.871919	+	0.489649i	$0.837125\pi$
$284$	−27.5497	+	27.5497i	−1.63477	+	1.63477i
$285$	−1.62727	−	41.5391i	−0.0963911	−	2.46056i
$286$	29.3335			1.73453
$287$	−2.39299	−	2.39299i	−0.141254	−	0.141254i
$288$	−14.6607	+	17.1575i	−0.863892	+	1.01101i
$289$		−	14.7969i		−	0.870407i
$290$	−54.9912			−3.22920
$291$	−0.961414	−	24.5419i	−0.0563591	−	1.43867i
$292$		−	11.5181i		−	0.674044i
$293$	11.4417			0.668429			0.334214	−	0.942497i	$-0.391529\pi$
$293$	11.4417			0.668429			0.334214	+	0.942497i	$0.391529\pi$
$294$	−10.6791	−	9.87391i	−0.622815	−	0.575858i
$295$	−1.72645	−	1.72645i	−0.100518	−	0.100518i
$296$	15.2067			0.883871
$297$	−13.0574	−	10.3010i	−0.757670	−	0.597725i
$298$	34.3001	−	34.3001i	1.98695	−	1.98695i
$299$	−4.95775	+	4.95775i	−0.286714	+	0.286714i
$300$	0.854283	+	21.8072i	0.0493221	+	1.25904i
$301$	−5.16564			−0.297742
$302$			10.0452i			0.578039i
$303$	−18.9967	+	20.5457i	−1.09133	+	1.18032i
$304$			15.3462i			0.880167i
$305$	−16.9029	−	17.3225i	−0.967858	−	0.991883i
$306$	9.66215	−	0.758182i	0.552348	−	0.0433424i
$307$	−16.1615	−	16.1615i	−0.922387	−	0.922387i	0.0748109	−	0.997198i	$-0.476165\pi$
$307$	−16.1615	−	16.1615i	−0.922387	−	0.922387i	−0.997198	+	0.0748109i	$0.976165\pi$
$308$	15.5308			0.884949
$309$	−13.4535	+	0.527033i	−0.765342	+	0.0299818i
$310$		−	3.04922i		−	0.173184i
$311$	8.91123	+	8.91123i	0.505309	+	0.505309i	0.913083	−	0.407774i	$-0.133695\pi$
$311$	8.91123	+	8.91123i	0.505309	+	0.505309i	−0.407774	+	0.913083i	$0.633695\pi$
$312$	8.59456	+	7.94657i	0.486571	+	0.449886i
$313$	8.45895	−	8.45895i	0.478128	−	0.478128i	−0.426404	−	0.904533i	$-0.640220\pi$
$313$	8.45895	−	8.45895i	0.478128	−	0.478128i	0.904533	+	0.426404i	$0.140220\pi$
$314$		−	8.32471i		−	0.469790i
$315$	12.5281	+	10.7050i	0.705880	+	0.603160i
$316$	−24.2870	+	24.2870i	−1.36625	+	1.36625i
$317$			1.33753i			0.0751234i	0.999294	+	0.0375617i	$0.0119591\pi$
$317$			1.33753i			0.0751234i	−0.999294	+	0.0375617i	$0.988041\pi$
$318$	−1.10220	−	28.1356i	−0.0618081	−	1.57777i
$319$			26.0959i			1.46109i
$320$		−	38.4591i		−	2.14993i
$321$	−19.6104	+	0.768228i	−1.09455	+	0.0428783i
$322$	−4.54272	+	4.54272i	−0.253156	+	0.253156i
$323$	8.12882	−	8.12882i	0.452300	−	0.452300i
$324$	−3.84278	−	24.3351i	−0.213488	−	1.35195i
$325$	−19.3809			−1.07506
$326$	10.1112	+	10.1112i	0.560006	+	0.560006i
$327$	−0.787467	−	20.1016i	−0.0435471	−	1.11162i
$328$	−2.16679	−	2.16679i	−0.119641	−	0.119641i
$329$	−10.2785	+	10.2785i	−0.566674	+	0.566674i
$330$	37.3637	−	1.46370i	2.05680	−	0.0805741i
$331$	−1.98665	−	1.98665i	−0.109196	−	0.109196i	0.650398	−	0.759594i	$-0.274602\pi$
$331$	−1.98665	−	1.98665i	−0.109196	−	0.109196i	−0.759594	+	0.650398i	$0.774602\pi$
$332$	−3.75328			−0.205988
$333$	18.4646	−	21.6091i	1.01185	−	1.18417i
$334$	17.9963	−	17.9963i	0.984716	−	0.984716i
$335$	4.61416	−	4.61416i	0.252099	−	0.252099i
$336$	−4.46662	−	4.12985i	−0.243674	−	0.225302i
$337$	1.36153	+	1.36153i	0.0741672	+	0.0741672i	0.743217	−	0.669050i	$-0.233299\pi$
$337$	1.36153	+	1.36153i	0.0741672	+	0.0741672i	−0.669050	+	0.743217i	$0.733299\pi$
$338$	−7.27838	+	7.27838i	−0.395892	+	0.395892i
$339$	11.1089	−	0.435186i	0.603355	−	0.0236361i
$340$	−8.90309	+	8.90309i	−0.482838	+	0.482838i
$341$	−1.44700			−0.0783593
$342$	−38.4485	−	32.8535i	−2.07906	−	1.77651i
$343$	13.6094	−	13.6094i	0.734837	−	0.734837i
$344$	−4.67735			−0.252186
$345$	−6.06757	+	6.56234i	−0.326667	+	0.353305i
$346$			30.3173i			1.62987i
$347$			31.6282i			1.69789i	0.528483	+	0.848944i	$0.322761\pi$
$347$			31.6282i			1.69789i	−0.528483	+	0.848944i	$0.677239\pi$
$348$	−26.2433	+	28.3833i	−1.40679	+	1.52150i
$349$	−6.11174	−	6.11174i	−0.327154	−	0.327154i	0.524349	−	0.851503i	$-0.324309\pi$
$349$	−6.11174	−	6.11174i	−0.327154	−	0.327154i	−0.851503	+	0.524349i	$0.824309\pi$
$350$	−17.7585			−0.949230
$351$	21.7281	−	2.56406i	1.15976	−	0.136859i
$352$	−24.0781			−1.28337
$353$	20.1415			1.07202			0.536012	−	0.844211i	$-0.319930\pi$
$353$	20.1415			1.07202			0.536012	+	0.844211i	$0.319930\pi$
$354$	−2.96801	+	0.116270i	−0.157748	+	0.00617968i
$355$	−31.1873	−	31.1873i	−1.65525	−	1.65525i
$356$	3.94876	−	3.94876i	0.209284	−	0.209284i
$357$	0.178381	+	4.55351i	0.00944093	+	0.240997i
$358$	9.04793	+	9.04793i	0.478198	+	0.478198i
$359$	−8.76293	−	8.76293i	−0.462490	−	0.462490i	0.436981	−	0.899471i	$-0.356048\pi$
$359$	−8.76293	−	8.76293i	−0.462490	−	0.462490i	−0.899471	+	0.436981i	$0.856048\pi$
$360$	11.3439	+	9.69312i	0.597875	+	0.510872i
$361$	−40.9868			−2.15720
$362$			10.5146i			0.552638i
$363$	0.0512077	+	1.30717i	0.00268771	+	0.0686087i
$364$	−14.4468	+	14.4468i	−0.757218	+	0.757218i
$365$	13.0389			0.682487
$366$	−29.4333	+	0.791827i	−1.53850	+	0.0413895i
$367$	−35.0371			−1.82892			−0.914461	−	0.404675i	$-0.867385\pi$
$367$	−35.0371			−1.82892			−0.914461	+	0.404675i	$0.867385\pi$
$368$	2.33300	−	2.33300i	0.121616	−	0.121616i
$369$	−5.71005	+	0.448064i	−0.297254	+	0.0233253i
$370$			63.9039i			3.32221i
$371$	13.2392			0.687345
$372$	−1.57383	−	1.45517i	−0.0815994	−	0.0754472i
$373$	10.1606	+	10.1606i	0.526094	+	0.526094i	0.919405	−	0.393311i	$-0.128670\pi$
$373$	10.1606	+	10.1606i	0.526094	+	0.526094i	−0.393311	+	0.919405i	$0.628670\pi$
$374$	7.31174	+	7.31174i	0.378081	+	0.378081i
$375$	2.12975	−	0.0834316i	0.109980	−	0.00430839i
$376$	−9.30695	+	9.30695i	−0.479969	+	0.479969i
$377$	−24.2745	−	24.2745i	−1.25020	−	1.25020i
$378$	19.9092	−	2.34941i	1.02402	−	0.120841i
$379$	12.7493			0.654886			0.327443	−	0.944871i	$-0.393813\pi$
$379$	12.7493			0.654886			0.327443	+	0.944871i	$0.393813\pi$
$380$	65.7005			3.37036
$381$	0.819244	+	20.9127i	0.0419711	+	1.07139i
$382$	25.7584			1.31791
$383$	−3.45679	−	3.45679i	−0.176634	−	0.176634i	0.613253	−	0.789887i	$-0.289861\pi$
$383$	−3.45679	−	3.45679i	−0.176634	−	0.176634i	−0.789887	+	0.613253i	$0.789861\pi$
$384$	−15.2195	−	14.0720i	−0.776665	−	0.718108i
$385$			17.5815i			0.896034i
$386$		−	43.5294i		−	2.21559i
$387$	−5.67941	+	6.64663i	−0.288701	+	0.337867i
$388$	38.8168			1.97063
$389$	11.6845	−	11.6845i	0.592428	−	0.592428i	−0.345859	−	0.938287i	$-0.612412\pi$
$389$	11.6845	−	11.6845i	0.592428	−	0.592428i	0.938287	+	0.345859i	$0.112412\pi$
$390$	−33.3943	+	36.1174i	−1.69099	+	1.82887i
$391$	−2.47156			−0.124992
$392$	4.37850	−	4.37850i	0.221148	−	0.221148i
$393$	0.546329	+	13.9461i	0.0275586	+	0.703485i
$394$	−16.4455	+	16.4455i	−0.828510	+	0.828510i
$395$	−27.4939	−	27.4939i	−1.38337	−	1.38337i
$396$	17.0755	−	19.9835i	0.858075	−	1.00421i
$397$	10.0947	−	10.0947i	0.506640	−	0.506640i	−0.406854	−	0.913493i	$-0.633374\pi$
$397$	10.0947	−	10.0947i	0.506640	−	0.506640i	0.913493	+	0.406854i	$0.133374\pi$
$398$	17.7562	−	17.7562i	0.890040	−	0.890040i
$399$	16.1432	−	17.4595i	0.808169	−	0.874069i
$400$	9.12023			0.456011
$401$	18.7834	+	18.7834i	0.937998	+	0.937998i	0.998187	−	0.0601887i	$-0.0191703\pi$
$401$	18.7834	+	18.7834i	0.937998	+	0.937998i	−0.0601887	+	0.998187i	$0.519170\pi$
$402$	−0.310747	−	7.93240i	−0.0154987	−	0.395632i
$403$	1.34600	−	1.34600i	0.0670491	−	0.0670491i
$404$	−31.2713	−	31.2713i	−1.55580	−	1.55580i
$405$	27.5483	−	4.35018i	1.36889	−	0.216162i
$406$	−22.2424	−	22.2424i	−1.10387	−	1.10387i
$407$	30.3254			1.50317
$408$	0.161519	+	4.12308i	0.00799640	+	0.204123i
$409$	0.808239	−	0.808239i	0.0399649	−	0.0399649i	−0.686842	−	0.726807i	$-0.741004\pi$
$409$	0.808239	−	0.808239i	0.0399649	−	0.0399649i	0.726807	+	0.686842i	$0.241004\pi$
$410$	9.10560	−	9.10560i	0.449694	−	0.449694i
$411$	0.334417	+	8.53662i	0.0164956	+	0.421080i
$412$		−	21.2788i		−	1.04833i
$413$		−	1.39660i		−	0.0687220i
$414$	0.850580	+	10.8397i	0.0418037	+	0.532740i
$415$		−	4.24886i		−	0.208569i
$416$	22.3976	−	22.3976i	1.09813	−	1.09813i
$417$	−21.0604	+	22.7777i	−1.03133	+	1.11543i
$418$		−	53.9571i		−	2.63913i
$419$	−8.90771	+	8.90771i	−0.435170	+	0.435170i	−0.890383	−	0.455213i	$-0.849563\pi$
$419$	−8.90771	+	8.90771i	−0.435170	+	0.435170i	0.455213	+	0.890383i	$0.349563\pi$
$420$	−17.6808	+	19.1225i	−0.862734	+	0.933085i
$421$	18.6194	+	18.6194i	0.907452	+	0.907452i	0.996066	−	0.0886143i	$-0.0282439\pi$
$421$	18.6194	+	18.6194i	0.907452	+	0.907452i	−0.0886143	+	0.996066i	$0.528244\pi$
$422$			35.8235i			1.74386i
$423$	1.92456	+	24.5263i	0.0935752	+	1.19251i
$424$	11.9877			0.582176
$425$	−4.83094	−	4.83094i	−0.234335	−	0.234335i
$426$	−53.6155	+	2.10036i	−2.59768	+	0.101763i
$427$	0.169705	−	13.8432i	0.00821258	−	0.669918i
$428$		−	31.0170i		−	1.49926i
$429$	17.1394	+	15.8471i	0.827496	+	0.765107i
$430$		−	19.6559i		−	0.947890i
$431$	35.0743			1.68947			0.844735	−	0.535185i	$-0.179758\pi$
$431$	35.0743			1.68947			0.844735	+	0.535185i	$0.179758\pi$
$432$	−10.2248	+	1.20659i	−0.491939	+	0.0580519i
$433$	23.3809	−	23.3809i	1.12361	−	1.12361i	0.132421	−	0.991194i	$-0.457725\pi$
$433$	23.3809	−	23.3809i	1.12361	−	1.12361i	0.991194	−	0.132421i	$-0.0422750\pi$
$434$	1.23332	−	1.23332i	0.0592013	−	0.0592013i
$435$	−32.1310	−	29.7085i	−1.54056	−	1.42441i
$436$	31.7938			1.52265
$437$	9.11946	+	9.11946i	0.436243	+	0.436243i
$438$	10.7688	−	11.6469i	0.514553	−	0.556512i
$439$	4.57740			0.218467			0.109234	−	0.994016i	$-0.465160\pi$
$439$	4.57740			0.218467			0.109234	+	0.994016i	$0.465160\pi$
$440$			15.9195i			0.758934i
$441$	−0.905419	−	11.5385i	−0.0431152	−	0.549453i
$442$	−13.6028			−0.647020
$443$			15.4977i			0.736317i	0.929763	+	0.368158i	$0.120012\pi$
$443$			15.4977i			0.736317i	−0.929763	+	0.368158i	$0.879988\pi$
$444$	32.9835	+	30.4967i	1.56533	+	1.44731i
$445$	4.47015	+	4.47015i	0.211905	+	0.211905i
$446$	2.70717			0.128188
$447$	38.5715	−	1.51102i	1.82437	−	0.0714687i
$448$	15.5556	−	15.5556i	0.734933	−	0.734933i
$449$			4.41687i			0.208445i	0.994554	+	0.104222i	$0.0332354\pi$
$449$			4.41687i			0.208445i	−0.994554	+	0.104222i	$0.966765\pi$
$450$	−19.5247	+	22.8498i	−0.920405	+	1.07715i
$451$	−4.32103	−	4.32103i	−0.203469	−	0.203469i
$452$			17.5705i			0.826448i
$453$	−5.42684	+	5.86937i	−0.254975	+	0.275767i
$454$		−	56.0154i		−	2.62893i
$455$	−16.3543	−	16.3543i	−0.766704	−	0.766704i
$456$	14.6172	−	15.8091i	0.684513	−	0.740330i
$457$	−14.6205	−	14.6205i	−0.683917	−	0.683917i	0.276963	−	0.960881i	$-0.410672\pi$
$457$	−14.6205	−	14.6205i	−0.683917	−	0.683917i	−0.960881	+	0.276963i	$0.910672\pi$
$458$	−37.4308	−	37.4308i	−1.74903	−	1.74903i
$459$	6.05512	+	4.77688i	0.282629	+	0.222966i
$460$	−9.98809	−	9.98809i	−0.465697	−	0.465697i
$461$		−	2.25276i		−	0.104921i	−0.998623	−	0.0524607i	$-0.983294\pi$
$461$		−	2.25276i		−	0.104921i	0.998623	−	0.0524607i	$-0.0167064\pi$
$462$	15.7045	+	14.5205i	0.730641	+	0.675555i
$463$		−	13.3522i		−	0.620530i	−0.950650	−	0.310265i	$-0.899582\pi$
$463$		−	13.3522i		−	0.620530i	0.950650	−	0.310265i	$-0.100418\pi$
$464$	11.4230	+	11.4230i	0.530300	+	0.530300i
$465$	1.64731	−	1.78164i	0.0763923	−	0.0826215i
$466$		−	14.4570i		−	0.669709i
$467$	−4.29490	+	4.29490i	−0.198744	+	0.198744i	−0.799462	−	0.600717i	$-0.794882\pi$
$467$	−4.29490	+	4.29490i	−0.198744	+	0.198744i	0.600717	+	0.799462i	$0.294882\pi$
$468$	2.70502	+	34.4724i	0.125040	+	1.59349i
$469$	3.73259			0.172355
$470$	−39.1111	−	39.1111i	−1.80406	−	1.80406i
$471$	4.49734	−	4.86407i	0.207226	−	0.224124i
$472$		−	1.26458i		−	0.0582070i
$473$	−9.32761			−0.428884
$474$	−47.2659	+	1.85161i	−2.17099	+	0.0850475i
$475$			35.6500i			1.63573i
$476$	−7.20208			−0.330107
$477$	14.5560	−	17.0349i	0.666472	−	0.779974i
$478$	21.5200	+	21.5200i	0.984300	+	0.984300i
$479$	−14.2150			−0.649499			−0.324749	−	0.945800i	$-0.605280\pi$
$479$	−14.2150			−0.649499			−0.324749	+	0.945800i	$0.605280\pi$
$480$	27.4114	−	29.6466i	1.25115	−	1.35318i
$481$	−28.2088	+	28.2088i	−1.28621	+	1.28621i
$482$	22.6495	−	22.6495i	1.03166	−	1.03166i
$483$	−5.10843	+	0.200120i	−0.232442	+	0.00910578i
$484$	−2.06750			−0.0939771
$485$			43.9422i			1.99531i
$486$	18.8663	−	28.2002i	0.855795	−	1.27919i
$487$		−	15.0519i		−	0.682068i	−0.940051	−	0.341034i	$-0.889223\pi$
$487$		−	15.0519i		−	0.682068i	0.940051	−	0.341034i	$-0.110777\pi$
$488$	0.153663	−	12.5346i	0.00695600	−	0.567416i
$489$	0.445427	+	11.3704i	0.0201429	+	0.514185i
$490$	18.4000	+	18.4000i	0.831228	+	0.831228i
$491$	4.75692			0.214677			0.107339	−	0.994223i	$-0.465767\pi$
$491$	4.75692			0.214677			0.107339	+	0.994223i	$0.465767\pi$
$492$	−0.354342	−	9.04522i	−0.0159749	−	0.407790i
$493$		−	12.1014i		−	0.545021i
$494$	50.1911	+	50.1911i	2.25820	+	2.25820i
$495$	22.6221	+	19.3301i	1.01679	+	0.868824i
$496$	−0.633397	+	0.633397i	−0.0284404	+	0.0284404i
$497$		−	25.2287i		−	1.13166i
$498$	−3.79527	−	3.50913i	−0.170070	−	0.157248i
$499$	−8.93588	+	8.93588i	−0.400025	+	0.400025i	−0.878242	−	0.478217i	$-0.841283\pi$
$499$	−8.93588	+	8.93588i	−0.400025	+	0.400025i	0.478217	+	0.878242i	$0.341283\pi$
$500$			3.36853i			0.150645i
$501$	20.2375	−	0.792792i	0.904144	−	0.0354193i
$502$			22.4814i			1.00340i
$503$			13.2718i			0.591760i	0.955225	+	0.295880i	$0.0956128\pi$
$503$			13.2718i			0.591760i	−0.955225	+	0.295880i	$0.904387\pi$
$504$	0.667684	+	8.50885i	0.0297410	+	0.379014i
$505$	35.4003	−	35.4003i	1.57529	−	1.57529i
$506$	−8.20280	+	8.20280i	−0.364659	+	0.364659i
$507$	−8.18477	+	0.320634i	−0.363499	+	0.0142399i
$508$	−33.0767			−1.46754
$509$	11.9640	+	11.9640i	0.530295	+	0.530295i	0.920660	−	0.390365i	$-0.127651\pi$
$509$	11.9640	+	11.9640i	0.530295	+	0.530295i	−0.390365	+	0.920660i	$0.627651\pi$
$510$	−17.3266	+	0.678761i	−0.767236	+	0.0300560i
$511$	5.27386	+	5.27386i	0.233302	+	0.233302i
$512$	−15.0373	+	15.0373i	−0.664559	+	0.664559i
$513$	−4.71642	−	39.9675i	−0.208235	−	1.76461i
$514$	19.7460	+	19.7460i	0.870958	+	0.870958i
$515$	24.0884			1.06146
$516$	−10.1452	−	9.38031i	−0.446618	−	0.412945i
$517$	−18.5600	+	18.5600i	−0.816268	+	0.816268i
$518$	−25.8473	+	25.8473i	−1.13566	+	1.13566i
$519$	−16.3786	+	17.7142i	−0.718942	+	0.777567i
$520$	−14.8084	−	14.8084i	−0.649392	−	0.649392i
$521$	−14.8857	+	14.8857i	−0.652153	+	0.652153i	−0.953511	−	0.301358i	$-0.902560\pi$
$521$	−14.8857	+	14.8857i	−0.652153	+	0.652153i	0.301358	+	0.953511i	$0.402560\pi$
$522$	−53.0738	+	4.16467i	−2.32298	+	0.182283i
$523$	1.30481	−	1.30481i	0.0570552	−	0.0570552i	−0.678003	−	0.735059i	$-0.737155\pi$
$523$	1.30481	−	1.30481i	0.0570552	−	0.0570552i	0.735059	+	0.678003i	$0.237155\pi$
$524$	−22.0579			−0.963602
$525$	−10.3762	−	9.59384i	−0.452852	−	0.418709i
$526$	−21.7815	+	21.7815i	−0.949718	+	0.949718i
$527$	0.671015			0.0292299
$528$	−8.06539	−	7.45729i	−0.351001	−	0.324537i
$529$			20.2272i			0.879445i
$530$			50.3767i			2.18822i
$531$	−1.79700	−	1.53550i	−0.0779832	−	0.0666351i
$532$	26.5739	+	26.5739i	1.15213	+	1.15213i
$533$	8.03888			0.348202
$534$	7.68482	−	0.301049i	0.332555	−	0.0130276i
$535$	35.1124			1.51804
$536$	3.37976			0.145983
$537$	0.398588	+	10.1747i	0.0172003	+	0.439071i
$538$	−17.7535	−	17.7535i	−0.765409	−	0.765409i
$539$	8.73166	−	8.73166i	0.376099	−	0.376099i
$540$	5.16566	+	43.7744i	0.222295	+	1.88375i
$541$	16.1649	+	16.1649i	0.694983	+	0.694983i	0.963324	−	0.268341i	$-0.0864753\pi$
$541$	16.1649	+	16.1649i	0.694983	+	0.694983i	−0.268341	+	0.963324i	$0.586475\pi$
$542$	−32.9853	−	32.9853i	−1.41684	−	1.41684i
$543$	−5.68043	+	6.14364i	−0.243771	+	0.263649i
$544$	11.1657			0.478727
$545$			35.9918i			1.54172i
$546$	−28.1155	+	1.10141i	−1.20323	+	0.0471359i
$547$	−4.72006	+	4.72006i	−0.201815	+	0.201815i	−0.800777	−	0.598962i	$-0.795580\pi$
$547$	−4.72006	+	4.72006i	−0.201815	+	0.201815i	0.598962	+	0.800777i	$0.295580\pi$
$548$	−13.5020			−0.576777
$549$	−17.6254	−	15.4384i	−0.752236	−	0.658894i
$550$	−32.0666			−1.36732
$551$	−44.6513	+	44.6513i	−1.90221	+	1.90221i
$552$	−4.62555	+	0.181203i	−0.196876	+	0.00771253i
$553$		−	22.2410i		−	0.945781i
$554$	0.211454			0.00898382
$555$	−34.5234	+	37.3386i	−1.46544	+	1.58494i
$556$	−34.6684	−	34.6684i	−1.47027	−	1.47027i
$557$	10.1909	+	10.1909i	0.431802	+	0.431802i	0.889241	−	0.457439i	$-0.151233\pi$
$557$	10.1909	+	10.1909i	0.431802	+	0.431802i	−0.457439	+	0.889241i	$0.651233\pi$
$558$	−0.230928	−	2.94290i	−0.00977594	−	0.124583i
$559$	8.67658	−	8.67658i	0.366980	−	0.366980i
$560$	7.69598	+	7.69598i	0.325214	+	0.325214i
$561$	0.322103	+	8.22229i	0.0135992	+	0.347145i
$562$	21.4553			0.905036
$563$	24.2049			1.02012			0.510058	−	0.860140i	$-0.329624\pi$
$563$	24.2049			1.02012			0.510058	+	0.860140i	$0.329624\pi$
$564$	−38.8517	+	1.52199i	−1.63595	+	0.0640875i
$565$	−19.8905			−0.836801
$566$	−25.3550	−	25.3550i	−1.06575	−	1.06575i
$567$	12.9020	+	9.38298i	0.541834	+	0.394048i
$568$		−	22.8439i		−	0.958511i
$569$		−	41.0519i		−	1.72098i	−0.509463	−	0.860492i	$-0.670156\pi$
$569$		−	41.0519i		−	1.72098i	0.509463	−	0.860492i	$-0.329844\pi$
$570$	66.4355	+	61.4266i	2.78268	+	2.57288i
$571$	−17.5775			−0.735597			−0.367799	−	0.929905i	$-0.619888\pi$
$571$	−17.5775			−0.735597			−0.367799	+	0.929905i	$0.619888\pi$
$572$	−26.0867	+	26.0867i	−1.09074	+	1.09074i
$573$	15.0504	+	13.9157i	0.628742	+	0.581337i
$574$	7.36590			0.307447
$575$	5.41967	−	5.41967i	0.226016	−	0.226016i
$576$	−2.91263	−	37.1181i	−0.121360	−	1.54659i
$577$	−22.4858	+	22.4858i	−0.936096	+	0.936096i	−0.998077	−	0.0619817i	$-0.980258\pi$
$577$	−22.4858	+	22.4858i	−0.936096	+	0.936096i	0.0619817	+	0.998077i	$0.480258\pi$
$578$	22.7733	+	22.7733i	0.947246	+	0.947246i
$579$	23.5163	−	25.4339i	0.977304	−	1.05700i
$580$	48.9044	−	48.9044i	2.03064	−	2.03064i
$581$	1.71854	−	1.71854i	0.0712971	−	0.0712971i
$582$	39.2511	+	36.2918i	1.62701	+	1.50434i
$583$	23.9061			0.990088
$584$	4.77534	+	4.77534i	0.197605	+	0.197605i
$585$	−39.0241	+	3.06219i	−1.61345	+	0.126606i
$586$	−17.6094	+	17.6094i	−0.727438	+	0.727438i
$587$	−12.4567	−	12.4567i	−0.514143	−	0.514143i	0.401650	−	0.915793i	$-0.368437\pi$
$587$	−12.4567	−	12.4567i	−0.514143	−	0.514143i	−0.915793	+	0.401650i	$0.868437\pi$
$588$	18.2780	−	0.716031i	0.753772	−	0.0295286i
$589$	−2.47588	−	2.47588i	−0.102017	−	0.102017i
$590$	5.31421			0.218783
$591$	−18.4935	+	0.724470i	−0.760719	+	0.0298007i
$592$	13.2744	−	13.2744i	0.545574	−	0.545574i
$593$	−7.38376	+	7.38376i	−0.303215	+	0.303215i	−0.842270	−	0.539056i	$-0.818781\pi$
$593$	−7.38376	+	7.38376i	−0.303215	+	0.303215i	0.539056	+	0.842270i	$0.318781\pi$
$594$	35.9500	−	4.24234i	1.47505	−	0.174065i
$595$		−	8.15304i		−	0.334242i
$596$			61.0069i			2.49894i
$597$	19.9675	−	0.782214i	0.817214	−	0.0320139i
$598$		−	15.2606i		−	0.624051i
$599$	−13.4743	+	13.4743i	−0.550546	+	0.550546i	−0.926598	−	0.376053i	$-0.877281\pi$
$599$	−13.4743	+	13.4743i	−0.550546	+	0.550546i	0.376053	+	0.926598i	$0.377281\pi$
$600$	−9.39533	−	8.68696i	−0.383563	−	0.354644i
$601$			11.4467i			0.466922i	0.972366	+	0.233461i	$0.0750052\pi$
$601$			11.4467i			0.466922i	−0.972366	+	0.233461i	$0.924995\pi$
$602$	7.95022	−	7.95022i	0.324027	−	0.324027i
$603$	4.10383	−	4.80273i	0.167121	−	0.195582i
$604$	−8.93336	−	8.93336i	−0.363493	−	0.363493i
$605$		−	2.34049i		−	0.0951543i
$606$	−2.38408	−	60.8581i	−0.0968467	−	2.47219i
$607$	−8.78637			−0.356628			−0.178314	−	0.983974i	$-0.557064\pi$
$607$	−8.78637			−0.356628			−0.178314	+	0.983974i	$0.557064\pi$
$608$	−41.1989	−	41.1989i	−1.67084	−	1.67084i
$609$	−0.979841	−	25.0123i	−0.0397052	−	1.01355i
$610$	52.6749	+	0.645746i	2.13275	+	0.0261455i
$611$		−	34.5292i		−	1.39690i
$612$	−7.91841	+	9.26693i	−0.320083	+	0.374593i
$613$			28.3269i			1.14411i	0.820214	+	0.572057i	$0.193854\pi$
$613$			28.3269i			1.14411i	−0.820214	+	0.572057i	$0.806146\pi$
$614$	49.7471			2.00763
$615$	10.2395	−	0.401128i	0.412898	−	0.0161751i
$616$	−6.43899	+	6.43899i	−0.259434	+	0.259434i
$617$	−11.6567	+	11.6567i	−0.469281	+	0.469281i	−0.901682	−	0.432400i	$-0.857667\pi$
$617$	−11.6567	+	11.6567i	−0.469281	+	0.469281i	0.432400	+	0.901682i	$0.357667\pi$
$618$	19.8946	−	21.5169i	0.800277	−	0.865535i
$619$	−0.0927367			−0.00372740			−0.00186370	−	0.999998i	$-0.500593\pi$
$619$	−0.0927367			−0.00372740			−0.00186370	+	0.999998i	$0.500593\pi$
$620$	2.71171	+	2.71171i	0.108905	+	0.108905i
$621$	−5.35903	+	6.79305i	−0.215050	+	0.272596i
$622$	−27.4298			−1.09984
$623$			3.61609i			0.144876i
$624$	14.4393	−	0.565650i	0.578033	−	0.0226441i
$625$	−26.8278			−1.07311
$626$			26.0377i			1.04067i
$627$	29.1498	−	31.5267i	1.16413	−	1.25906i
$628$	7.40327	+	7.40327i	0.295422	+	0.295422i
$629$	−14.0628			−0.560719
$630$	−35.7572	+	2.80584i	−1.42460	+	0.111787i
$631$	5.82591	−	5.82591i	0.231926	−	0.231926i	−0.581570	−	0.813496i	$-0.697562\pi$
$631$	5.82591	−	5.82591i	0.231926	−	0.231926i	0.813496	+	0.581570i	$0.197562\pi$
$632$		−	20.1386i		−	0.801070i
$633$	−19.3533	+	20.9314i	−0.769225	+	0.831950i
$634$	−2.05854	−	2.05854i	−0.0817553	−	0.0817553i
$635$		−	37.4441i		−	1.48593i
$636$	26.0015	+	24.0411i	1.03103	+	0.953293i
$637$			16.2444i			0.643628i
$638$	−40.1631	−	40.1631i	−1.59007	−	1.59007i
$639$	−32.4618	−	27.7380i	−1.28417	−	1.09730i
$640$	26.2231	+	26.2231i	1.03656	+	1.03656i
$641$	−26.0963	−	26.0963i	−1.03074	−	1.03074i	−0.999512	−	0.0312278i	$-0.990058\pi$
$641$	−26.0963	−	26.0963i	−1.03074	−	1.03074i	−0.0312278	−	0.999512i	$-0.509942\pi$
$642$	28.9993	−	31.3640i	1.14451	−	1.23784i
$643$	−17.6595	−	17.6595i	−0.696421	−	0.696421i	0.267216	−	0.963637i	$-0.413896\pi$
$643$	−17.6595	−	17.6595i	−0.696421	−	0.696421i	−0.963637	+	0.267216i	$0.913896\pi$
$644$		−	8.07979i		−	0.318388i
$645$	10.6189	−	11.4848i	0.418118	−	0.452213i
$646$			25.0215i			0.984457i
$647$	−5.98792	−	5.98792i	−0.235409	−	0.235409i	0.579537	−	0.814946i	$-0.303234\pi$
$647$	−5.98792	−	5.98792i	−0.235409	−	0.235409i	−0.814946	+	0.579537i	$0.803234\pi$
$648$	11.6824	+	8.49604i	0.458930	+	0.333756i
$649$		−	2.52184i		−	0.0989908i
$650$	29.8284	−	29.8284i	1.16997	−	1.16997i
$651$	1.38691	−	0.0543315i	0.0543573	−	0.00212942i
$652$	−17.9840			−0.704308
$653$	14.1747	+	14.1747i	0.554699	+	0.554699i	0.927794	−	0.373094i	$-0.121703\pi$
$653$	14.1747	+	14.1747i	0.554699	+	0.554699i	−0.373094	+	0.927794i	$0.621703\pi$
$654$	32.1495	+	29.7256i	1.25714	+	1.16236i
$655$		−	24.9704i		−	0.975673i
$656$	−3.78291			−0.147698
$657$	12.5843	−	0.987479i	0.490959	−	0.0385252i
$658$		−	31.6386i		−	1.23340i
$659$	−6.03891			−0.235242			−0.117621	−	0.993059i	$-0.537527\pi$
$659$	−6.03891			−0.235242			−0.117621	+	0.993059i	$0.537527\pi$
$660$	−31.9263	+	34.5297i	−1.24273	+	1.34407i
$661$	10.0615	+	10.0615i	0.391347	+	0.391347i	0.875167	−	0.483820i	$-0.160751\pi$
$661$	10.0615	+	10.0615i	0.391347	+	0.391347i	−0.483820	+	0.875167i	$0.660751\pi$
$662$	6.11515			0.237672
$663$	−7.94803	−	7.34878i	−0.308676	−	0.285403i
$664$	1.55609	−	1.55609i	0.0603882	−	0.0603882i
$665$	−30.0827	+	30.0827i	−1.16656	+	1.16656i
$666$	4.83965	+	61.6757i	0.187533	+	2.38989i
$667$	13.5762			0.525673
$668$			32.0087i			1.23846i
$669$	1.58178	+	1.46252i	0.0611553	+	0.0565444i
$670$			14.2029i			0.548708i
$671$	0.306436	−	24.9967i	0.0118298	−	0.964986i
$672$	23.0783	−	0.904080i	0.890265	−	0.0348756i
$673$	−16.7900	−	16.7900i	−0.647205	−	0.647205i	0.305112	−	0.952317i	$-0.401306\pi$
$673$	−16.7900	−	16.7900i	−0.647205	−	0.647205i	−0.952317	+	0.305112i	$0.901306\pi$
$674$	−4.19095			−0.161429
$675$	−23.7526	+	2.80296i	−0.914237	+	0.107886i
$676$		−	12.9455i		−	0.497904i
$677$	16.6874	+	16.6874i	0.641348	+	0.641348i	0.950887	−	0.309539i	$-0.100175\pi$
$677$	16.6874	+	16.6874i	0.641348	+	0.641348i	−0.309539	+	0.950887i	$0.600175\pi$
$678$	−16.4275	+	17.7671i	−0.630896	+	0.682341i
$679$	−17.7733	+	17.7733i	−0.682078	+	0.682078i
$680$		−	7.38236i		−	0.283101i
$681$	30.2617	−	32.7294i	1.15963	−	1.25419i
$682$	2.22701	−	2.22701i	0.0852768	−	0.0852768i
$683$			4.50543i			0.172395i	0.996278	+	0.0861977i	$0.0274717\pi$
$683$			4.50543i			0.172395i	−0.996278	+	0.0861977i	$0.972528\pi$
$684$	63.4097	−	4.97571i	2.42453	−	0.190251i
$685$		−	15.2848i		−	0.584002i
$686$			41.8913i			1.59942i
$687$	−1.64894	−	42.0922i	−0.0629109	−	1.60592i
$688$	−4.08300	+	4.08300i	−0.155663	+	0.155663i
$689$	−22.2375	+	22.2375i	−0.847182	+	0.847182i
$690$	−0.761480	−	19.4382i	−0.0289891	−	0.739999i
$691$	11.2473			0.427867			0.213933	−	0.976848i	$-0.431372\pi$
$691$	11.2473			0.427867			0.213933	+	0.976848i	$0.431372\pi$
$692$	−26.9616	−	26.9616i	−1.02492	−	1.02492i
$693$	1.33150	+	16.9684i	0.0505796	+	0.644578i
$694$	−48.6776	−	48.6776i	−1.84778	−	1.84778i
$695$	39.2460	−	39.2460i	1.48868	−	1.48868i
$696$	−0.887220	−	22.6479i	−0.0336300	−	0.858468i
$697$	2.00379	+	2.00379i	0.0758989	+	0.0758989i
$698$	18.8127			0.712070
$699$	7.81026	−	8.44714i	0.295411	−	0.319500i
$700$	15.7928	−	15.7928i	0.596913	−	0.596913i
$701$	−24.8698	+	24.8698i	−0.939318	+	0.939318i	−0.998261	−	0.0589435i	$-0.981227\pi$
$701$	−24.8698	+	24.8698i	−0.939318	+	0.939318i	0.0589435	+	0.998261i	$0.481227\pi$
$702$	−29.4946	+	37.3871i	−1.11320	+	1.41109i
$703$	51.8882	+	51.8882i	1.95700	+	1.95700i
$704$	28.0888	−	28.0888i	1.05864	−	1.05864i
$705$	−1.72296	−	43.9817i	−0.0648903	−	1.65645i
$706$	−30.9990	+	30.9990i	−1.16666	+	1.16666i
$707$	28.6368			1.07700
$708$	2.53609	−	2.74289i	0.0953119	−	0.103084i
$709$	37.3741	−	37.3741i	1.40361	−	1.40361i	0.615388	−	0.788225i	$-0.289000\pi$
$709$	37.3741	−	37.3741i	1.40361	−	1.40361i	0.788225	−	0.615388i	$-0.211000\pi$
$710$	95.9983			3.60275
$711$	−28.6174	−	24.4530i	−1.07324	−	0.917061i
$712$			3.27427i			0.122709i
$713$			0.752790i			0.0281922i
$714$	−7.28266	−	6.73358i	−0.272547	−	0.251998i
$715$	−29.5311	−	29.5311i	−1.10440	−	1.10440i
$716$	−16.0929			−0.601419
$717$	0.948018	+	24.1999i	0.0354044	+	0.903762i
$718$	26.9733			1.00664
$719$	−30.8641			−1.15104			−0.575519	−	0.817788i	$-0.695200\pi$
$719$	−30.8641			−1.15104			−0.575519	+	0.817788i	$0.695200\pi$
$720$	18.3638	−	1.44100i	0.684380	−	0.0537028i
$721$	9.74307	+	9.74307i	0.362851	+	0.362851i
$722$	63.0811	−	63.0811i	2.34763	−	2.34763i
$723$	25.4701	−	0.997778i	0.947244	−	0.0371078i
$724$	−9.35081	−	9.35081i	−0.347520	−	0.347520i
$725$	26.5362	+	26.5362i	0.985529	+	0.985529i
$726$	−2.09063	−	1.93300i	−0.0775904	−	0.0717405i
$727$	12.6473			0.469062			0.234531	−	0.972109i	$-0.424645\pi$
$727$	12.6473			0.469062			0.234531	+	0.972109i	$0.424645\pi$
$728$		−	11.9792i		−	0.443977i
$729$	26.2583	−	6.28483i	0.972531	−	0.232771i
$730$	−20.0676	+	20.0676i	−0.742737	+	0.742737i
$731$	4.32549			0.159984
$732$	25.4712	−	26.8796i	0.941443	−	0.993498i
$733$	−8.44053			−0.311758			−0.155879	−	0.987776i	$-0.549821\pi$
$733$	−8.44053			−0.311758			−0.155879	+	0.987776i	$0.549821\pi$
$734$	53.9242	−	53.9242i	1.99038	−	1.99038i
$735$	0.810575	+	20.6914i	0.0298985	+	0.763215i
$736$			12.5265i			0.461732i
$737$	6.73995			0.248269
$738$	8.09852	−	9.47771i	0.298111	−	0.348879i
$739$	30.9642	+	30.9642i	1.13904	+	1.13904i	0.988623	+	0.150414i	$0.0480607\pi$
$739$	30.9642	+	30.9642i	1.13904	+	1.13904i	0.150414	+	0.988623i	$0.451939\pi$
$740$	−56.8305	−	56.8305i	−2.08913	−	2.08913i
$741$	2.21106	+	56.4415i	0.0812255	+	2.07343i
$742$	−20.3759	+	20.3759i	−0.748023	+	0.748023i
$743$	9.54048	+	9.54048i	0.350006	+	0.350006i	0.860112	−	0.510105i	$-0.170394\pi$
$743$	9.54048	+	9.54048i	0.350006	+	0.350006i	−0.510105	+	0.860112i	$0.670394\pi$
$744$	1.25581	−	0.0491957i	0.0460403	−	0.00180360i
$745$	−69.0622			−2.53024
$746$	−31.2755			−1.14508
$747$	−0.321780	−	4.10072i	−0.0117733	−	0.150037i
$748$	−13.0048			−0.475504
$749$	14.2020	+	14.2020i	0.518929	+	0.518929i
$750$	−3.14940	+	3.40621i	−0.115000	+	0.124377i
$751$		−	20.3868i		−	0.743923i	−0.928248	−	0.371962i	$-0.878685\pi$
$751$		−	20.3868i		−	0.743923i	0.928248	−	0.371962i	$-0.121315\pi$
$752$			16.2486i			0.592527i
$753$	−12.1454	+	13.1357i	−0.442602	+	0.478693i
$754$	74.7198			2.72113
$755$	10.1129	−	10.1129i	0.368047	−	0.368047i
$756$	−15.6161	+	19.7948i	−0.567952	+	0.719931i
$757$	−26.4785			−0.962377			−0.481189	−	0.876617i	$-0.659795\pi$
$757$	−26.4785			−0.962377			−0.481189	+	0.876617i	$0.659795\pi$
$758$	−19.6219	+	19.6219i	−0.712699	+	0.712699i
$759$	−9.22432	+	0.361358i	−0.334822	+	0.0131164i
$760$	−27.2391	+	27.2391i	−0.988067	+	0.988067i
$761$	12.0278	+	12.0278i	0.436006	+	0.436006i	0.890665	−	0.454659i	$-0.150239\pi$
$761$	12.0278	+	12.0278i	0.436006	+	0.436006i	−0.454659	+	0.890665i	$0.650239\pi$
$762$	−33.4468	−	30.9250i	−1.21165	−	1.12030i
$763$	−14.5576	+	14.5576i	−0.527022	+	0.527022i
$764$	−22.9073	+	22.9073i	−0.828756	+	0.828756i
$765$	−10.4905	−	8.96395i	−0.379286	−	0.324092i
$766$	10.6404			0.384453
$767$	2.34582	+	2.34582i	0.0847028	+	0.0847028i
$768$	2.12216	−	0.0831345i	0.0765769	−	0.00299986i
$769$	−7.96860	+	7.96860i	−0.287355	+	0.287355i	−0.836034	−	0.548678i	$-0.815131\pi$
$769$	−7.96860	+	7.96860i	−0.287355	+	0.287355i	0.548678	+	0.836034i	$0.315131\pi$
$770$	−27.0589	−	27.0589i	−0.975136	−	0.975136i
$771$	0.869869	+	22.2050i	0.0313275	+	0.799694i
$772$	38.7112	+	38.7112i	1.39325	+	1.39325i
$773$	33.9058			1.21951			0.609753	−	0.792592i	$-0.291269\pi$
$773$	33.9058			1.21951			0.609753	+	0.792592i	$0.291269\pi$
$774$	−1.48860	−	18.9705i	−0.0535067	−	0.681881i
$775$	−1.47141	+	1.47141i	−0.0528546	+	0.0528546i
$776$	−16.0933	+	16.0933i	−0.577715	+	0.577715i
$777$	−29.0661	+	1.13865i	−1.04274	+	0.0408488i
$778$			35.9663i			1.28945i
$779$		−	14.7870i		−	0.529799i
$780$	−2.42167	−	61.8176i	−0.0867097	−	2.21342i
$781$		−	45.5556i		−	1.63011i
$782$	3.80388	−	3.80388i	0.136027	−	0.136027i
$783$	−33.2606	−	26.2392i	−1.18864	−	0.937713i
$784$		−	7.64426i		−	0.273009i
$785$	−8.38079	+	8.38079i	−0.299123	+	0.299123i
$786$	−22.3046	−	20.6230i	−0.795580	−	0.735597i
$787$	−33.7009	−	33.7009i	−1.20131	−	1.20131i	−0.973769	−	0.227540i	$-0.926932\pi$
$787$	−33.7009	−	33.7009i	−1.20131	−	1.20131i	−0.227540	−	0.973769i	$-0.573068\pi$
$788$		−	29.2503i		−	1.04200i
$789$	−24.4940	+	0.959539i	−0.872010	+	0.0341605i
$790$	84.6294			3.01098
$791$	−8.04514	−	8.04514i	−0.286052	−	0.286052i
$792$	1.20564	+	15.3645i	0.0428405	+	0.545953i
$793$	22.9670	+	23.5371i	0.815581	+	0.835826i
$794$			31.0728i			1.10273i
$795$	−27.2155	+	29.4348i	−0.965235	+	1.04394i
$796$			31.5817i			1.11938i
$797$	−9.91395			−0.351170			−0.175585	−	0.984464i	$-0.556182\pi$
$797$	−9.91395			−0.351170			−0.175585	+	0.984464i	$0.556182\pi$
$798$	2.02597	+	51.7165i	0.0717184	+	1.83075i
$799$	8.60682	−	8.60682i	0.304488	−	0.304488i
$800$	−24.4844	+	24.4844i	−0.865654	+	0.865654i
$801$	4.65283	+	3.97575i	0.164400	+	0.140476i
$802$	−57.8176			−2.04161
$803$	9.52302	+	9.52302i	0.336060	+	0.336060i
$804$	7.33074	+	6.77803i	0.258535	+	0.239043i
$805$	9.14664			0.322377
$806$			4.14316i			0.145936i
$807$	−0.782096	−	19.9644i	−0.0275311	−	0.702781i
$808$	25.9298			0.912208
$809$			8.61799i			0.302992i	0.988458	+	0.151496i	$0.0484091\pi$
$809$			8.61799i			0.302992i	−0.988458	+	0.151496i	$0.951591\pi$
$810$	−35.7033	+	49.0937i	−1.25449	+	1.72498i
$811$	−31.2190	−	31.2190i	−1.09625	−	1.09625i	−0.994846	−	0.101401i	$-0.967667\pi$
$811$	−31.2190	−	31.2190i	−1.09625	−	1.09625i	−0.101401	−	0.994846i	$-0.532333\pi$
$812$	39.5608			1.38831
$813$	−1.45310	−	37.0931i	−0.0509625	−	1.30091i
$814$	−46.6725	+	46.6725i	−1.63587	+	1.63587i
$815$		−	20.3586i		−	0.713130i
$816$	3.74016	+	3.45817i	0.130932	+	0.121060i
$817$	−15.9600	−	15.9600i	−0.558370	−	0.558370i
$818$			2.48786i			0.0869859i
$819$	−17.0227	−	14.5455i	−0.594821	−	0.508263i
$820$			16.1954i			0.565569i
$821$	−36.2734	−	36.2734i	−1.26595	−	1.26595i	−0.948161	−	0.317791i	$-0.897059\pi$
$821$	−36.2734	−	36.2734i	−1.26595	−	1.26595i	−0.317791	−	0.948161i	$-0.602941\pi$
$822$	−13.6530	−	12.6237i	−0.476205	−	0.440301i
$823$	24.8152	+	24.8152i	0.865003	+	0.865003i	0.991914	−	0.126912i	$-0.0405064\pi$
$823$	24.8152	+	24.8152i	0.865003	+	0.865003i	−0.126912	+	0.991914i	$0.540506\pi$
$824$	8.82209	+	8.82209i	0.307332	+	0.307332i
$825$	−18.7363	−	17.3236i	−0.652313	−	0.603131i
$826$	2.14944	+	2.14944i	0.0747887	+	0.0747887i
$827$		−	7.93987i		−	0.276096i	−0.990426	−	0.138048i	$-0.955917\pi$
$827$		−	7.93987i		−	0.276096i	0.990426	−	0.138048i	$-0.0440829\pi$
$828$	−10.3963	−	8.88340i	−0.361295	−	0.308720i
$829$			27.4393i			0.953005i	0.879173	+	0.476502i	$0.158096\pi$
$829$			27.4393i			0.953005i	−0.879173	+	0.476502i	$0.841904\pi$
$830$	6.53925	+	6.53925i	0.226981	+	0.226981i
$831$	0.123551	+	0.114236i	0.00428594	+	0.00396280i
$832$			52.2566i			1.81167i
$833$	−4.04913	+	4.04913i	−0.140294	+	0.140294i
$834$	−2.64308	−	67.4694i	−0.0915222	−	2.33627i
$835$	−36.2351			−1.25397
$836$	47.9847	+	47.9847i	1.65959	+	1.65959i
$837$	1.45495	−	1.84427i	0.0502903	−	0.0637475i
$838$		−	27.4190i		−	0.947173i
$839$	−33.4374			−1.15439			−0.577193	−	0.816608i	$-0.695852\pi$
$839$	−33.4374			−1.15439			−0.577193	+	0.816608i	$0.695852\pi$
$840$	−0.597743	−	15.2585i	−0.0206241	−	0.526468i
$841$			37.4727i			1.29216i
$842$	−57.3126			−1.97512
$843$	12.5362	+	11.5910i	0.431769	+	0.399215i
$844$	−31.8583	−	31.8583i	−1.09661	−	1.09661i
$845$	14.6548			0.504141
$846$	−40.7094	−	34.7854i	−1.39962	−	1.19595i
$847$	0.946659	−	0.946659i	0.0325276	−	0.0325276i
$848$	10.4645	−	10.4645i	0.359351	−	0.359351i
$849$	−1.11696	−	28.5125i	−0.0383341	−	0.978548i
$850$	14.8702			0.510044
$851$		−	15.7766i		−	0.540813i
$852$	45.8130	−	49.5488i	1.56953	−	1.69751i
$853$		−	40.3608i		−	1.38193i	−0.722890	−	0.690963i	$-0.757187\pi$
$853$		−	40.3608i		−	1.38193i	0.722890	−	0.690963i	$-0.242813\pi$
$854$	21.0443	+	21.5667i	0.720121	+	0.737996i
$855$	5.63270	+	71.7823i	0.192634	+	2.45490i
$856$	12.8595	+	12.8595i	0.439529	+	0.439529i
$857$	25.1028			0.857495			0.428747	−	0.903424i	$-0.358955\pi$
$857$	25.1028			0.857495			0.428747	+	0.903424i	$0.358955\pi$
$858$	−50.7682	+	1.98882i	−1.73320	+	0.0678970i
$859$			10.4494i			0.356528i	0.983983	+	0.178264i	$0.0570481\pi$
$859$			10.4494i			0.356528i	−0.983983	+	0.178264i	$0.942952\pi$
$860$	17.4802	+	17.4802i	0.596070	+	0.596070i
$861$	4.30384	+	3.97935i	0.146675	+	0.135616i
$862$	−53.9814	+	53.9814i	−1.83861	+	1.83861i
$863$		−	38.5215i		−	1.31129i	−0.755070	−	0.655644i	$-0.772397\pi$
$863$		−	38.5215i		−	1.31129i	0.755070	−	0.655644i	$-0.227603\pi$
$864$	24.2104	−	30.6889i	0.823655	−	1.04406i
$865$	30.5215	−	30.5215i	1.03776	−	1.03776i
$866$			71.9692i			2.44561i
$867$	1.00323	+	25.6094i	0.0340716	+	0.869740i
$868$			2.19362i			0.0744562i
$869$		−	40.1606i		−	1.36235i
$870$	95.1746	−	3.72841i	3.22672	−	0.126405i
$871$	−6.26953	+	6.26953i	−0.212435	+	0.212435i
$872$	−13.1815	+	13.1815i	−0.446384	+	0.446384i
$873$	3.32788	+	42.4100i	0.112632	+	1.43536i
$874$	−28.0708			−0.949509
$875$	−1.54237	−	1.54237i	−0.0521417	−	0.0521417i
$876$	0.780926	+	19.9346i	0.0263850	+	0.673527i
$877$	22.9451	+	22.9451i	0.774800	+	0.774800i	0.978941	−	0.204141i	$-0.0654402\pi$
$877$	22.9451	+	22.9451i	0.774800	+	0.774800i	−0.204141	+	0.978941i	$0.565440\pi$
$878$	−7.04489	+	7.04489i	−0.237753	+	0.237753i
$879$	−19.8023	+	0.775746i	−0.667917	+	0.0261653i
$880$	13.8967	+	13.8967i	0.468456	+	0.468456i
$881$	−11.9148			−0.401421			−0.200711	−	0.979651i	$-0.564325\pi$
$881$	−11.9148			−0.401421			−0.200711	+	0.979651i	$0.564325\pi$
$882$	19.1519	+	16.3650i	0.644880	+	0.551037i
$883$	9.81995	−	9.81995i	0.330468	−	0.330468i	−0.522296	−	0.852764i	$-0.674925\pi$
$883$	9.81995	−	9.81995i	0.330468	−	0.330468i	0.852764	+	0.522296i	$0.174925\pi$
$884$	12.0972	−	12.0972i	0.406871	−	0.406871i
$885$	3.10506	+	2.87095i	0.104375	+	0.0965059i
$886$	−23.8518	−	23.8518i	−0.801318	−	0.801318i
$887$	−0.789783	+	0.789783i	−0.0265183	+	0.0265183i	−0.720242	−	0.693723i	$-0.755969\pi$
$887$	−0.789783	+	0.789783i	−0.0265183	+	0.0265183i	0.693723	+	0.720242i	$0.255969\pi$
$888$	−26.3186	+	1.03102i	−0.883194	+	0.0345986i
$889$	15.1451	−	15.1451i	0.507949	−	0.507949i
$890$	−13.7597			−0.461225
$891$	23.2972	+	16.9429i	0.780487	+	0.567608i
$892$	−2.40752	+	2.40752i	−0.0806099	+	0.0806099i
$893$	−63.5142			−2.12542
$894$	−57.0384	+	61.6895i	−1.90765	+	2.06320i
$895$		−	18.2178i		−	0.608953i
$896$			21.2130i			0.708676i
$897$	8.24436	−	8.91664i	0.275271	−	0.297718i
$898$	−6.79782	−	6.79782i	−0.226846	−	0.226846i
$899$	−3.68586			−0.122930
$900$	−2.95705	−	37.6842i	−0.0985685	−	1.25614i
$901$	−11.0860			−0.369327
$902$	13.3006			0.442863
$903$	8.94029	−	0.350231i	0.297514	−	0.0116549i
$904$	−7.28466	−	7.28466i	−0.242284	−	0.242284i
$905$	10.5855	−	10.5855i	0.351873	−	0.351873i
$906$	−0.681069	−	17.3855i	−0.0226270	−	0.577596i
$907$	−20.6402	−	20.6402i	−0.685347	−	0.685347i	0.275853	−	0.961200i	$-0.411040\pi$
$907$	−20.6402	−	20.6402i	−0.685347	−	0.685347i	−0.961200	+	0.275853i	$0.911040\pi$
$908$	49.8152	+	49.8152i	1.65317	+	1.65317i
$909$	31.4850	−	36.8470i	1.04429	−	1.22214i
$910$	50.3406			1.66878
$911$			2.05701i			0.0681517i	0.999419	+	0.0340758i	$0.0108488\pi$
$911$			2.05701i			0.0681517i	−0.999419	+	0.0340758i	$0.989151\pi$
$912$	−1.04048	−	26.5601i	−0.0344536	−	0.879492i
$913$	3.10318	−	3.10318i	0.102700	−	0.102700i
$914$	45.0036			1.48859
$915$	30.4287	+	28.8344i	1.00594	+	0.953236i
$916$	66.5753			2.19971
$917$	10.0998	−	10.0998i	0.333524	−	0.333524i
$918$	−16.6711	+	1.96730i	−0.550228	+	0.0649305i
$919$			44.4765i			1.46714i	0.679612	+	0.733572i	$0.262148\pi$
$919$			44.4765i			1.46714i	−0.679612	+	0.733572i	$0.737852\pi$
$920$	8.28203			0.273051
$921$	29.0669	+	26.8754i	0.957786	+	0.885574i
$922$	3.46713	+	3.46713i	0.114184	+	0.114184i
$923$	42.3760	+	42.3760i	1.39482	+	1.39482i
$924$	−26.8795	+	1.05299i	−0.884271	+	0.0346408i
$925$	30.8370	−	30.8370i	1.01391	−	1.01391i
$926$	20.5499	+	20.5499i	0.675310	+	0.675310i
$927$	23.2485	−	1.82430i	0.763582	−	0.0599177i
$928$	−61.3330			−2.01336
$929$	−10.8164			−0.354874			−0.177437	−	0.984132i	$-0.556781\pi$
$929$	−10.8164			−0.354874			−0.177437	+	0.984132i	$0.556781\pi$
$930$	0.206738	+	5.27736i	0.00677919	+	0.173051i
$931$	29.8806			0.979297
$932$	12.8568	+	12.8568i	0.421139	+	0.421139i
$933$	−16.0271	−	14.8187i	−0.524702	−	0.485142i
$934$		−	13.2202i		−	0.432578i
$935$		−	14.7220i		−	0.481460i
$936$	−15.4136	−	13.1706i	−0.503809	−	0.430495i
$937$	9.21774			0.301130			0.150565	−	0.988600i	$-0.451891\pi$
$937$	9.21774			0.301130			0.150565	+	0.988600i	$0.451891\pi$
$938$	−5.74468	+	5.74468i	−0.187570	+	0.187570i
$939$	−14.0666	+	15.2136i	−0.459046	+	0.496478i
$940$	69.5639			2.26892
$941$	11.2329	−	11.2329i	0.366183	−	0.366183i	−0.499900	−	0.866083i	$-0.666630\pi$
$941$	11.2329	−	11.2329i	0.366183	−	0.366183i	0.866083	+	0.499900i	$0.166630\pi$
$942$	0.564416	+	14.4078i	0.0183897	+	0.469430i
$943$	−2.24799	+	2.24799i	−0.0732045	+	0.0732045i
$944$	−1.10389	−	1.10389i	−0.0359286	−	0.0359286i
$945$	−22.4085	−	17.6780i	−0.728949	−	0.575067i
$946$	14.3558	−	14.3558i	0.466746	−	0.466746i
$947$	−5.10916	+	5.10916i	−0.166025	+	0.166025i	−0.785230	−	0.619204i	$-0.787455\pi$
$947$	−5.10916	+	5.10916i	−0.166025	+	0.166025i	0.619204	+	0.785230i	$0.287455\pi$
$948$	40.3875	−	43.6808i	1.31172	−	1.41869i
$949$	−17.7167			−0.575109
$950$	−54.8675	−	54.8675i	−1.78014	−	1.78014i
$951$	−0.0906849	−	2.31490i	−0.00294066	−	0.0750658i
$952$	2.98595	−	2.98595i	0.0967752	−	0.0967752i
$953$	4.11848	+	4.11848i	0.133411	+	0.133411i	0.770659	−	0.637248i	$-0.219927\pi$
$953$	4.11848	+	4.11848i	0.133411	+	0.133411i	−0.637248	+	0.770659i	$0.719927\pi$
$954$	3.81519	+	48.6202i	0.123521	+	1.57414i
$955$	−25.9319	−	25.9319i	−0.839137	−	0.839137i
$956$	−38.2759			−1.23793
$957$	−1.76930	−	45.1647i	−0.0571935	−	1.45997i
$958$	21.8777	−	21.8777i	0.706836	−	0.706836i
$959$	6.18225	−	6.18225i	0.199635	−	0.199635i
$960$	2.60753	+	66.5621i	0.0841577	+	2.14828i
$961$			30.7956i			0.993407i
$962$		−	86.8300i		−	2.79951i
$963$	33.8882	−	2.65918i	1.09203	−	0.0856909i
$964$			40.2850i			1.29749i
$965$	−43.8226	+	43.8226i	−1.41070	+	1.41070i
$966$	7.55419	−	8.17018i	0.243052	−	0.262871i
$967$		−	21.5065i		−	0.691604i	−0.938308	−	0.345802i	$-0.887607\pi$
$967$		−	21.5065i		−	0.691604i	0.938308	−	0.345802i	$-0.112393\pi$
$968$	0.857174	−	0.857174i	0.0275506	−	0.0275506i
$969$	−13.5176	+	14.6199i	−0.434248	+	0.469658i
$970$	−67.6296	−	67.6296i	−2.17146	−	2.17146i
$971$			1.84790i			0.0593018i	0.999560	+	0.0296509i	$0.00943956\pi$
$971$			1.84790i			0.0593018i	−0.999560	+	0.0296509i	$0.990560\pi$
$972$	8.30072	+	41.8569i	0.266246	+	1.34256i
$973$	31.7477			1.01778
$974$	23.1658	+	23.1658i	0.742281	+	0.742281i
$975$	33.5431	−	1.31403i	1.07424	−	0.0420827i
$976$	−10.8077	−	11.0760i	−0.345947	−	0.354534i
$977$			10.0325i			0.320968i	0.987038	+	0.160484i	$0.0513055\pi$
$977$			10.0325i			0.320968i	−0.987038	+	0.160484i	$0.948695\pi$
$978$	−18.1852	−	16.8141i	−0.581498	−	0.537656i
$979$			6.52959i			0.208687i
$980$	−32.7267			−1.04542
$981$	2.72578	+	34.7369i	0.0870274	+	1.10906i
$982$	−7.32119	+	7.32119i	−0.233629	+	0.233629i
$983$	−22.3494	+	22.3494i	−0.712835	+	0.712835i	−0.967127	−	0.254293i	$-0.918157\pi$
$983$	−22.3494	+	22.3494i	−0.712835	+	0.712835i	0.254293	+	0.967127i	$0.418157\pi$
$984$	3.89702	+	3.60320i	0.124232	+	0.114866i
$985$	33.1125			1.05505
$986$	18.6248	+	18.6248i	0.593135	+	0.593135i
$987$	17.0924	−	18.4862i	0.544058	−	0.588422i
$988$	−89.2711			−2.84009
$989$			4.85263i			0.154305i
$990$	−64.5669	+	5.06652i	−2.05207	+	0.161025i
$991$	51.4679			1.63493			0.817465	−	0.575978i	$-0.195379\pi$
$991$	51.4679			1.63493			0.817465	+	0.575978i	$0.195379\pi$
$992$		−	3.40087i		−	0.107978i
$993$	3.57304	+	3.30365i	0.113387	+	0.104838i
$994$	38.8285	+	38.8285i	1.23157	+	1.23157i
$995$	−35.7517			−1.13341
$996$	6.49589	−	0.254473i	0.205830	−	0.00806329i
$997$	6.39558	−	6.39558i	0.202550	−	0.202550i	−0.598542	−	0.801092i	$-0.704253\pi$
$997$	6.39558	−	6.39558i	0.202550	−	0.202550i	0.801092	+	0.598542i	$0.204253\pi$
$998$		−	27.5057i		−	0.870678i
$999$	−30.4919	+	38.6513i	−0.964722	+	1.22287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	183.2.g.c.11.2	✓	28
3.2	odd	2	inner	183.2.g.c.11.13	yes	28
61.50	odd	4	inner	183.2.g.c.50.13	yes	28
183.50	even	4	inner	183.2.g.c.50.2	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.g.c.11.2	✓	28	1.1	even	1	trivial
183.2.g.c.11.13	yes	28	3.2	odd	2	inner
183.2.g.c.50.2	yes	28	183.50	even	4	inner
183.2.g.c.50.13	yes	28	61.50	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:	\( N \)	\(=\)	\( 183 = 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	183.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53906 + 1.53906i) q^{2} +(-1.73072 + 0.0678001i) q^{3} -2.73741i q^{4} +3.09885 q^{5} +(2.55934 - 2.76803i) q^{6} +(1.25340 + 1.25340i) q^{7} +(1.13492 + 1.13492i) q^{8} +(2.99081 - 0.234686i) q^{9} +O(q^{10})\)	\(q+(-1.53906 + 1.53906i) q^{2} +(-1.73072 + 0.0678001i) q^{3} -2.73741i q^{4} +3.09885 q^{5} +(2.55934 - 2.76803i) q^{6} +(1.25340 + 1.25340i) q^{7} +(1.13492 + 1.13492i) q^{8} +(2.99081 - 0.234686i) q^{9} +(-4.76932 + 4.76932i) q^{10} +(2.26326 + 2.26326i) q^{11} +(0.185597 + 4.73770i) q^{12} -4.21059 q^{13} -3.85810 q^{14} +(-5.36326 + 0.210103i) q^{15} +1.98141 q^{16} +(-1.04954 - 1.04954i) q^{17} +(-4.24183 + 4.96423i) q^{18} +7.74511i q^{19} -8.48283i q^{20} +(-2.25426 - 2.08430i) q^{21} -6.96660 q^{22} +(1.17745 - 1.17745i) q^{23} +(-2.04118 - 1.88728i) q^{24} +4.60290 q^{25} +(6.48036 - 6.48036i) q^{26} +(-5.16035 + 0.608954i) q^{27} +(3.43106 - 3.43106i) q^{28} +(5.76510 + 5.76510i) q^{29} +(7.93102 - 8.57774i) q^{30} +(-0.319670 + 0.319670i) q^{31} +(-5.31934 + 5.31934i) q^{32} +(-4.07053 - 3.76363i) q^{33} +3.23062 q^{34} +(3.88409 + 3.88409i) q^{35} +(-0.642433 - 8.18706i) q^{36} +(6.69947 - 6.69947i) q^{37} +(-11.9202 - 11.9202i) q^{38} +(7.28737 - 0.285479i) q^{39} +(3.51694 + 3.51694i) q^{40} -1.90920 q^{41} +(6.67731 - 0.261580i) q^{42} +(-2.06066 + 2.06066i) q^{43} +(6.19548 - 6.19548i) q^{44} +(9.26807 - 0.727259i) q^{45} +3.62432i q^{46} +8.20055i q^{47} +(-3.42927 + 0.134340i) q^{48} -3.85799i q^{49} +(-7.08414 + 7.08414i) q^{50} +(1.88763 + 1.74531i) q^{51} +11.5261i q^{52} +(5.28133 - 5.28133i) q^{53} +(7.00486 - 8.87930i) q^{54} +(7.01353 + 7.01353i) q^{55} +2.84500i q^{56} +(-0.525119 - 13.4046i) q^{57} -17.7457 q^{58} +(-0.557124 - 0.557124i) q^{59} +(0.575137 + 14.6814i) q^{60} +(-5.45457 - 5.58996i) q^{61} -0.983984i q^{62} +(4.04282 + 3.45451i) q^{63} -12.4107i q^{64} -13.0480 q^{65} +(12.0572 - 0.472336i) q^{66} +(1.48899 - 1.48899i) q^{67} +(-2.87303 + 2.87303i) q^{68} +(-1.95800 + 2.11767i) q^{69} -11.9557 q^{70} +(-10.0641 - 10.0641i) q^{71} +(3.66067 + 3.12797i) q^{72} +4.20765 q^{73} +20.6218i q^{74} +(-7.96635 + 0.312077i) q^{75} +21.2015 q^{76} +5.67353i q^{77} +(-10.7763 + 11.6551i) q^{78} +(-8.87227 - 8.87227i) q^{79} +6.14010 q^{80} +(8.88984 - 1.40380i) q^{81} +(2.93838 - 2.93838i) q^{82} -1.37111i q^{83} +(-5.70559 + 6.17084i) q^{84} +(-3.25238 - 3.25238i) q^{85} -6.34294i q^{86} +(-10.3687 - 9.58692i) q^{87} +5.13723i q^{88} +(1.44252 + 1.44252i) q^{89} +(-13.1448 + 15.3834i) q^{90} +(-5.27755 - 5.27755i) q^{91} +(-3.22316 - 3.22316i) q^{92} +(0.531587 - 0.574935i) q^{93} +(-12.6211 - 12.6211i) q^{94} +24.0010i q^{95} +(8.84565 - 9.56696i) q^{96} +14.1801i q^{97} +(5.93768 + 5.93768i) q^{98} +(7.30014 + 6.23783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9	\( 28 q - 6 q^{6} + 4 q^{7} - 4 q^{9} - 16 q^{10} - 16 q^{12} + 16 q^{13} - 40 q^{15} + 12 q^{16} - 4 q^{18} - 18 q^{21} - 48 q^{22} + 14 q^{24} + 36 q^{25} - 24 q^{28} - 22 q^{30} + 32 q^{31} + 2 q^{33} + 96 q^{34} + 8 q^{37} + 28 q^{40} + 20 q^{42} - 32 q^{43} - 24 q^{51} - 2 q^{54} - 40 q^{55} - 16 q^{57} - 56 q^{58} + 64 q^{61} + 40 q^{63} - 12 q^{67} - 30 q^{69} - 24 q^{70} + 44 q^{72} - 72 q^{73} + 128 q^{76} - 66 q^{78} + 28 q^{81} - 28 q^{82} + 46 q^{84} - 44 q^{85} - 12 q^{87} - 56 q^{90} - 64 q^{91} + 36 q^{93} - 16 q^{94} + 54 q^{96} + 32 q^{99}+O(q^{100}) \) 28 * q - 6 * q^6 + 4 * q^7 - 4 * q^9 - 16 * q^10 - 16 * q^12 + 16 * q^13 - 40 * q^15 + 12 * q^16 - 4 * q^18 - 18 * q^21 - 48 * q^22 + 14 * q^24 + 36 * q^25 - 24 * q^28 - 22 * q^30 + 32 * q^31 + 2 * q^33 + 96 * q^34 + 8 * q^37 + 28 * q^40 + 20 * q^42 - 32 * q^43 - 24 * q^51 - 2 * q^54 - 40 * q^55 - 16 * q^57 - 56 * q^58 + 64 * q^61 + 40 * q^63 - 12 * q^67 - 30 * q^69 - 24 * q^70 + 44 * q^72 - 72 * q^73 + 128 * q^76 - 66 * q^78 + 28 * q^81 - 28 * q^82 + 46 * q^84 - 44 * q^85 - 12 * q^87 - 56 * q^90 - 64 * q^91 + 36 * q^93 - 16 * q^94 + 54 * q^96 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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