LMFDB - Embedded newform 183.2.g.c.50.2

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			50.2
Character	$\chi$	$=$	183.50
Dual form			183.2.g.c.11.2

$q$-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 $\left(\mathbb{Z}/183\mathbb{Z}\right)^\times$.

$n$	$62$	$124$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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	−0.995706	−	0.0925737i	$-0.970491\pi$
$2$	−1.53906	−	1.53906i	−1.08828	−	1.08828i	−0.0925737	−	0.995706i	$-0.529509\pi$
$3$	−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	−0.429383	−	0.903122i	$-0.641269\pi$
$7$	1.25340	−	1.25340i	0.473739	−	0.473739i	0.903122	+	0.429383i	$0.141269\pi$
$8$	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	−0.278141	−	0.960540i	$-0.589718\pi$
$11$	2.26326	−	2.26326i	0.682400	−	0.682400i	0.960540	+	0.278141i	$0.0897181\pi$
$12$	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	−0.822834	−	0.568282i	$-0.807608\pi$
$17$	−1.04954	+	1.04954i	−0.254551	+	0.254551i	0.568282	+	0.822834i	$0.307608\pi$
$18$	−4.24183	−	4.96423i	−0.999810	−	1.17008i
$19$		−	7.74511i		−	1.77685i	−0.459021	−	0.888425i	$-0.651800\pi$
$19$		−	7.74511i		−	1.77685i	0.459021	−	0.888425i	$-0.348200\pi$
$20$			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	0.819127	−	0.573612i	$-0.194458\pi$
$23$	1.17745	+	1.17745i	0.245515	+	0.245515i	−0.573612	+	0.819127i	$0.694458\pi$
$24$	−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	0.0732376	−	0.997315i	$-0.476667\pi$
$29$	5.76510	−	5.76510i	1.07055	−	1.07055i	0.997315	−	0.0732376i	$-0.0233331\pi$
$30$	7.93102	+	8.57774i	1.44800	+	1.56607i
$31$	−0.319670	−	0.319670i	−0.0574145	−	0.0574145i	0.677817	−	0.735231i	$-0.262926\pi$
$31$	−0.319670	−	0.319670i	−0.0574145	−	0.0574145i	−0.735231	+	0.677817i	$0.762926\pi$
$32$	−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	0.994244	+	0.107143i	$0.0341703\pi$
$37$	6.69947	+	6.69947i	1.10139	+	1.10139i	0.107143	+	0.994244i	$0.465830\pi$
$38$	−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	0.532305	−	0.846552i	$-0.321326\pi$
$43$	−2.06066	−	2.06066i	−0.314247	−	0.314247i	−0.846552	+	0.532305i	$0.821326\pi$
$44$	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	$-0.795928\pi$
$47$		−	8.20055i		−	1.19617i	0.801431	−	0.598087i	$-0.204072\pi$
$48$	−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	0.969709	−	0.244263i	$-0.0785460\pi$
$53$	5.28133	+	5.28133i	0.725446	+	0.725446i	−0.244263	+	0.969709i	$0.578546\pi$
$54$	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	−0.742442	−	0.669910i	$-0.766332\pi$
$59$	−0.557124	+	0.557124i	−0.0725314	+	0.0725314i	0.669910	+	0.742442i	$0.266332\pi$
$60$	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	0.792187	−	0.610278i	$-0.208942\pi$
$67$	1.48899	+	1.48899i	0.181909	+	0.181909i	−0.610278	+	0.792187i	$0.708942\pi$
$68$	−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	−0.218574	+	0.975820i	$0.570140\pi$
$71$	−10.0641	+	10.0641i	−1.19439	+	1.19439i	−0.975820	+	0.218574i	$0.929860\pi$
$72$	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	−0.999998	−	0.00178995i	$-0.999430\pi$
$79$	−8.87227	+	8.87227i	−0.998208	+	0.998208i	0.00178995	+	0.999998i	$0.499430\pi$
$80$	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	$0.0239753\pi$
$83$			1.37111i			0.150499i	−0.997165	+	0.0752493i	$0.976025\pi$
$84$	−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	−0.626508	−	0.779415i	$-0.715517\pi$
$89$	1.44252	−	1.44252i	0.152906	−	0.152906i	0.779415	+	0.626508i	$0.215517\pi$
$90$	−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	$-0.744194\pi$
$97$		−	14.1801i		−	1.43977i	0.694091	−	0.719887i	$-0.255806\pi$
$98$	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	0.989038	+	0.147659i	$0.0471738\pi$
$101$	11.4237	+	11.4237i	1.13670	+	1.13670i	0.147659	+	0.989038i	$0.452826\pi$
$102$	−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	$-0.812245\pi$
$109$		−	11.6145i		−	1.11247i	0.831024	−	0.556236i	$-0.187755\pi$
$110$	−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	$0.180105\pi$
$127$			12.0832i			1.07221i	−0.844151	+	0.536106i	$0.819895\pi$
$128$	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	$0.114503\pi$
$131$			8.05793i			0.704025i	−0.935995	+	0.352012i	$0.885497\pi$
$132$	−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	$0.0675748\pi$
$137$			4.93240i			0.421403i	−0.977550	+	0.210702i	$0.932425\pi$
$138$	−0.245730	+	6.27270i	−0.0209179	+	0.533968i
$139$	12.6647	+	12.6647i	1.07420	+	1.07420i	0.997017	+	0.0771863i	$0.0245936\pi$
$139$	12.6647	+	12.6647i	1.07420	+	1.07420i	0.0771863	+	0.997017i	$0.475406\pi$
$140$	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	0.827314	−	0.561739i	$-0.189868\pi$
$151$	3.26344	+	3.26344i	0.265575	+	0.265575i	−0.561739	+	0.827314i	$0.689868\pi$
$152$	−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	0.590902	−	0.806743i	$-0.298772\pi$
$157$	−2.70448	−	2.70448i	−0.215841	−	0.215841i	−0.806743	+	0.590902i	$0.798772\pi$
$158$	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	$0.0828295\pi$
$163$			6.56971i			0.514580i	−0.966334	+	0.257290i	$0.917171\pi$
$164$		−	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	0.974259	−	0.225431i	$-0.0723790\pi$
$173$	9.84930	+	9.84930i	0.748828	+	0.748828i	−0.225431	+	0.974259i	$0.572379\pi$
$174$	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	$0.0705091\pi$
$179$			5.87887i			0.439407i	−0.975567	+	0.219704i	$0.929491\pi$
$180$	−1.99081	+	25.3705i	−0.148386	+	1.89101i
$181$	3.41593	+	3.41593i	0.253904	+	0.253904i	0.822569	−	0.568665i	$-0.192540\pi$
$181$	3.41593	+	3.41593i	0.253904	+	0.253904i	−0.568665	+	0.822569i	$0.692540\pi$
$182$	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	−0.941768	−	0.336264i	$-0.890836\pi$
$191$	−8.36822	+	8.36822i	−0.605504	+	0.605504i	0.336264	+	0.941768i	$0.390836\pi$
$192$	0.841450	−	21.4796i	0.0607264	−	1.55015i
$193$	−14.1415	−	14.1415i	−1.01793	−	1.01793i	−0.999836	−	0.0180945i	$-0.994240\pi$
$193$	−14.1415	−	14.1415i	−1.01793	−	1.01793i	−0.0180945	−	0.999836i	$-0.505760\pi$
$194$	−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	0.983283	−	0.182082i	$-0.0582835\pi$
$211$	11.6381	+	11.6381i	0.801202	+	0.801202i	−0.182082	+	0.983283i	$0.558284\pi$
$212$	−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	−0.735941	−	0.677046i	$-0.763260\pi$
$223$	−0.879490	+	0.879490i	−0.0588950	+	0.0588950i	0.677046	+	0.735941i	$0.263260\pi$
$224$	−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	−0.971726	−	0.236113i	$-0.924127\pi$
$227$	−18.1979	−	18.1979i	−1.20784	−	1.20784i	−0.236113	−	0.971726i	$-0.575873\pi$
$228$	−36.6940	−	1.43747i	−2.43012	−	0.0951986i
$229$		−	24.3206i		−	1.60715i	−0.595205	−	0.803574i	$-0.702929\pi$
$229$		−	24.3206i		−	1.60715i	0.595205	−	0.803574i	$-0.297071\pi$
$230$		−	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	0.536322	−	0.844013i	$-0.319813\pi$
$233$	−4.69671	−	4.69671i	−0.307692	−	0.307692i	−0.844013	+	0.536322i	$0.819813\pi$
$234$	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	$0.149371\pi$
$239$			13.9825i			0.904455i	−0.891903	+	0.452228i	$0.850629\pi$
$240$	−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	0.898983	−	0.437983i	$-0.144307\pi$
$251$	7.30363	+	7.30363i	0.461001	+	0.461001i	−0.437983	+	0.898983i	$0.644307\pi$
$252$	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	$0.131043\pi$
$257$			12.8299i			0.800307i	−0.916448	+	0.400154i	$0.868957\pi$
$258$	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	$-0.885617\pi$
$269$		−	11.5353i		−	0.703321i	0.936128	−	0.351660i	$-0.114383\pi$
$270$	21.7071	+	27.5157i	1.32105	+	1.67455i
$271$		−	21.4321i		−	1.30191i	−0.759117	−	0.650955i	$-0.774369\pi$
$271$		−	21.4321i		−	1.30191i	0.759117	−	0.650955i	$-0.225631\pi$
$272$	−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	−0.709168	−	0.705040i	$-0.750929\pi$
$277$	−0.0686958	+	0.0686958i	−0.00412753	+	0.00412753i	0.705040	+	0.709168i	$0.250929\pi$
$278$		−	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	−0.883757	−	0.467946i	$-0.844994\pi$
$281$	−6.97026	+	6.97026i	−0.415811	+	0.415811i	0.467946	+	0.883757i	$0.344994\pi$
$282$	22.6994	−	20.9880i	1.35173	−	1.24982i
$283$		−	16.4744i		−	0.979299i	−0.871919	−	0.489649i	$-0.837125\pi$
$283$		−	16.4744i		−	0.979299i	0.871919	−	0.489649i	$-0.162875\pi$
$284$	−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	−0.997198	−	0.0748109i	$-0.976165\pi$
$307$	−16.1615	+	16.1615i	−0.922387	+	0.922387i	0.0748109	+	0.997198i	$0.476165\pi$
$308$	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	−0.407774	−	0.913083i	$-0.633695\pi$
$311$	8.91123	−	8.91123i	0.505309	−	0.505309i	0.913083	+	0.407774i	$0.133695\pi$
$312$	8.59456	−	7.94657i	0.486571	−	0.449886i
$313$	8.45895	+	8.45895i	0.478128	+	0.478128i	0.904533	−	0.426404i	$-0.140220\pi$
$313$	8.45895	+	8.45895i	0.478128	+	0.478128i	−0.426404	+	0.904533i	$0.640220\pi$
$314$			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	$-0.988041\pi$
$317$		−	1.33753i		−	0.0751234i	0.999294	−	0.0375617i	$-0.0119591\pi$
$318$	−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	−0.759594	−	0.650398i	$-0.774602\pi$
$331$	−1.98665	+	1.98665i	−0.109196	+	0.109196i	0.650398	+	0.759594i	$0.274602\pi$
$332$	−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	−0.669050	−	0.743217i	$-0.733299\pi$
$337$	1.36153	−	1.36153i	0.0741672	−	0.0741672i	0.743217	+	0.669050i	$0.233299\pi$
$338$	−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	$-0.677239\pi$
$347$		−	31.6282i		−	1.69789i	0.528483	−	0.848944i	$-0.322761\pi$
$348$	−26.2433	−	28.3833i	−1.40679	−	1.52150i
$349$	−6.11174	+	6.11174i	−0.327154	+	0.327154i	−0.851503	−	0.524349i	$-0.824309\pi$
$349$	−6.11174	+	6.11174i	−0.327154	+	0.327154i	0.524349	+	0.851503i	$0.324309\pi$
$350$	−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	−0.899471	−	0.436981i	$-0.856048\pi$
$359$	−8.76293	+	8.76293i	−0.462490	+	0.462490i	0.436981	+	0.899471i	$0.356048\pi$
$360$	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	−0.393311	−	0.919405i	$-0.628670\pi$
$373$	10.1606	−	10.1606i	0.526094	−	0.526094i	0.919405	+	0.393311i	$0.128670\pi$
$374$	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	−0.789887	−	0.613253i	$-0.789861\pi$
$383$	−3.45679	+	3.45679i	−0.176634	+	0.176634i	0.613253	+	0.789887i	$0.289861\pi$
$384$	−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	0.938287	−	0.345859i	$-0.112412\pi$
$389$	11.6845	+	11.6845i	0.592428	+	0.592428i	−0.345859	+	0.938287i	$0.612412\pi$
$390$	−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	0.913493	−	0.406854i	$-0.133374\pi$
$397$	10.0947	+	10.0947i	0.506640	+	0.506640i	−0.406854	+	0.913493i	$0.633374\pi$
$398$	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	−0.0601887	−	0.998187i	$-0.519170\pi$
$401$	18.7834	−	18.7834i	0.937998	−	0.937998i	0.998187	+	0.0601887i	$0.0191703\pi$
$402$	−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	0.726807	−	0.686842i	$-0.241004\pi$
$409$	0.808239	+	0.808239i	0.0399649	+	0.0399649i	−0.686842	+	0.726807i	$0.741004\pi$
$410$	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	0.455213	−	0.890383i	$-0.349563\pi$
$419$	−8.90771	−	8.90771i	−0.435170	−	0.435170i	−0.890383	+	0.455213i	$0.849563\pi$
$420$	−17.6808	−	19.1225i	−0.862734	−	0.933085i
$421$	18.6194	−	18.6194i	0.907452	−	0.907452i	−0.0886143	−	0.996066i	$-0.528244\pi$
$421$	18.6194	−	18.6194i	0.907452	−	0.907452i	0.996066	+	0.0886143i	$0.0282439\pi$
$422$		−	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	0.991194	+	0.132421i	$0.0422750\pi$
$433$	23.3809	+	23.3809i	1.12361	+	1.12361i	0.132421	+	0.991194i	$0.457725\pi$
$434$	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	$-0.879988\pi$
$443$		−	15.4977i		−	0.736317i	0.929763	−	0.368158i	$-0.120012\pi$
$444$	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	$-0.966765\pi$
$449$		−	4.41687i		−	0.208445i	0.994554	−	0.104222i	$-0.0332354\pi$
$450$	−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	−0.960881	−	0.276963i	$-0.910672\pi$
$457$	−14.6205	+	14.6205i	−0.683917	+	0.683917i	0.276963	+	0.960881i	$0.410672\pi$
$458$	−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	$0.0167064\pi$
$461$			2.25276i			0.104921i	−0.998623	+	0.0524607i	$0.983294\pi$
$462$	15.7045	−	14.5205i	0.730641	−	0.675555i
$463$			13.3522i			0.620530i	0.950650	+	0.310265i	$0.100418\pi$
$463$			13.3522i			0.620530i	−0.950650	+	0.310265i	$0.899582\pi$
$464$	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	0.600717	−	0.799462i	$-0.294882\pi$
$467$	−4.29490	−	4.29490i	−0.198744	−	0.198744i	−0.799462	+	0.600717i	$0.794882\pi$
$468$	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	$0.110777\pi$
$487$			15.0519i			0.682068i	−0.940051	+	0.341034i	$0.889223\pi$
$488$	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	0.478217	−	0.878242i	$-0.341283\pi$
$499$	−8.93588	−	8.93588i	−0.400025	−	0.400025i	−0.878242	+	0.478217i	$0.841283\pi$
$500$		−	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	$-0.904387\pi$
$503$		−	13.2718i		−	0.591760i	0.955225	−	0.295880i	$-0.0956128\pi$
$504$	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	−0.390365	−	0.920660i	$-0.627651\pi$
$509$	11.9640	−	11.9640i	0.530295	−	0.530295i	0.920660	+	0.390365i	$0.127651\pi$
$510$	−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	0.301358	−	0.953511i	$-0.402560\pi$
$521$	−14.8857	−	14.8857i	−0.652153	−	0.652153i	−0.953511	+	0.301358i	$0.902560\pi$
$522$	−53.0738	−	4.16467i	−2.32298	−	0.182283i
$523$	1.30481	+	1.30481i	0.0570552	+	0.0570552i	0.735059	−	0.678003i	$-0.237155\pi$
$523$	1.30481	+	1.30481i	0.0570552	+	0.0570552i	−0.678003	+	0.735059i	$0.737155\pi$
$524$	−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	−0.268341	−	0.963324i	$-0.586475\pi$
$541$	16.1649	−	16.1649i	0.694983	−	0.694983i	0.963324	+	0.268341i	$0.0864753\pi$
$542$	−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	0.598962	−	0.800777i	$-0.295580\pi$
$547$	−4.72006	−	4.72006i	−0.201815	−	0.201815i	−0.800777	+	0.598962i	$0.795580\pi$
$548$	−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	−0.457439	−	0.889241i	$-0.651233\pi$
$557$	10.1909	−	10.1909i	0.431802	−	0.431802i	0.889241	+	0.457439i	$0.151233\pi$
$558$	−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	$0.329844\pi$
$569$			41.0519i			1.72098i	−0.509463	+	0.860492i	$0.670156\pi$
$570$	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	0.0619817	−	0.998077i	$-0.480258\pi$
$577$	−22.4858	−	22.4858i	−0.936096	−	0.936096i	−0.998077	+	0.0619817i	$0.980258\pi$
$578$	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	−0.915793	−	0.401650i	$-0.868437\pi$
$587$	−12.4567	+	12.4567i	−0.514143	+	0.514143i	0.401650	+	0.915793i	$0.368437\pi$
$588$	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	0.539056	−	0.842270i	$-0.318781\pi$
$593$	−7.38376	−	7.38376i	−0.303215	−	0.303215i	−0.842270	+	0.539056i	$0.818781\pi$
$594$	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	0.376053	−	0.926598i	$-0.377281\pi$
$599$	−13.4743	−	13.4743i	−0.550546	−	0.550546i	−0.926598	+	0.376053i	$0.877281\pi$
$600$	−9.39533	+	8.68696i	−0.383563	+	0.354644i
$601$		−	11.4467i		−	0.466922i	−0.972366	−	0.233461i	$-0.924995\pi$
$601$		−	11.4467i		−	0.466922i	0.972366	−	0.233461i	$-0.0750052\pi$
$602$	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	$-0.806146\pi$
$613$		−	28.3269i		−	1.14411i	0.820214	−	0.572057i	$-0.193854\pi$
$614$	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	0.432400	−	0.901682i	$-0.357667\pi$
$617$	−11.6567	−	11.6567i	−0.469281	−	0.469281i	−0.901682	+	0.432400i	$0.857667\pi$
$618$	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	0.813496	−	0.581570i	$-0.197562\pi$
$631$	5.82591	+	5.82591i	0.231926	+	0.231926i	−0.581570	+	0.813496i	$0.697562\pi$
$632$			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	−0.0312278	+	0.999512i	$0.509942\pi$
$641$	−26.0963	+	26.0963i	−1.03074	+	1.03074i	−0.999512	+	0.0312278i	$0.990058\pi$
$642$	28.9993	+	31.3640i	1.14451	+	1.23784i
$643$	−17.6595	+	17.6595i	−0.696421	+	0.696421i	−0.963637	−	0.267216i	$-0.913896\pi$
$643$	−17.6595	+	17.6595i	−0.696421	+	0.696421i	0.267216	+	0.963637i	$0.413896\pi$
$644$			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	−0.814946	−	0.579537i	$-0.803234\pi$
$647$	−5.98792	+	5.98792i	−0.235409	+	0.235409i	0.579537	+	0.814946i	$0.303234\pi$
$648$	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	−0.373094	−	0.927794i	$-0.621703\pi$
$653$	14.1747	−	14.1747i	0.554699	−	0.554699i	0.927794	+	0.373094i	$0.121703\pi$
$654$	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	−0.483820	−	0.875167i	$-0.660751\pi$
$661$	10.0615	−	10.0615i	0.391347	−	0.391347i	0.875167	+	0.483820i	$0.160751\pi$
$662$	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	−0.952317	−	0.305112i	$-0.901306\pi$
$673$	−16.7900	+	16.7900i	−0.647205	+	0.647205i	0.305112	+	0.952317i	$0.401306\pi$
$674$	−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	−0.309539	−	0.950887i	$-0.600175\pi$
$677$	16.6874	−	16.6874i	0.641348	−	0.641348i	0.950887	+	0.309539i	$0.100175\pi$
$678$	−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	$-0.972528\pi$
$683$		−	4.50543i		−	0.172395i	0.996278	−	0.0861977i	$-0.0274717\pi$
$684$	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	0.0589435	−	0.998261i	$-0.481227\pi$
$701$	−24.8698	−	24.8698i	−0.939318	−	0.939318i	−0.998261	+	0.0589435i	$0.981227\pi$
$702$	−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	0.788225	+	0.615388i	$0.211000\pi$
$709$	37.3741	+	37.3741i	1.40361	+	1.40361i	0.615388	+	0.788225i	$0.289000\pi$
$710$	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	0.150414	−	0.988623i	$-0.451939\pi$
$739$	30.9642	−	30.9642i	1.13904	−	1.13904i	0.988623	−	0.150414i	$-0.0480607\pi$
$740$	−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	−0.510105	−	0.860112i	$-0.670394\pi$
$743$	9.54048	−	9.54048i	0.350006	−	0.350006i	0.860112	+	0.510105i	$0.170394\pi$
$744$	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	$0.121315\pi$
$751$			20.3868i			0.743923i	−0.928248	+	0.371962i	$0.878685\pi$
$752$		−	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	−0.454659	−	0.890665i	$-0.650239\pi$
$761$	12.0278	−	12.0278i	0.436006	−	0.436006i	0.890665	+	0.454659i	$0.150239\pi$
$762$	−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	0.548678	−	0.836034i	$-0.315131\pi$
$769$	−7.96860	−	7.96860i	−0.287355	−	0.287355i	−0.836034	+	0.548678i	$0.815131\pi$
$770$	−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	−0.227540	+	0.973769i	$0.573068\pi$
$787$	−33.7009	+	33.7009i	−1.20131	+	1.20131i	−0.973769	+	0.227540i	$0.926932\pi$
$788$			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	$-0.951591\pi$
$809$		−	8.61799i		−	0.302992i	0.988458	−	0.151496i	$-0.0484091\pi$
$810$	−35.7033	−	49.0937i	−1.25449	−	1.72498i
$811$	−31.2190	+	31.2190i	−1.09625	+	1.09625i	−0.101401	+	0.994846i	$0.532333\pi$
$811$	−31.2190	+	31.2190i	−1.09625	+	1.09625i	−0.994846	+	0.101401i	$0.967667\pi$
$812$	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	−0.317791	+	0.948161i	$0.602941\pi$
$821$	−36.2734	+	36.2734i	−1.26595	+	1.26595i	−0.948161	+	0.317791i	$0.897059\pi$
$822$	−13.6530	+	12.6237i	−0.476205	+	0.440301i
$823$	24.8152	−	24.8152i	0.865003	−	0.865003i	−0.126912	−	0.991914i	$-0.540506\pi$
$823$	24.8152	−	24.8152i	0.865003	−	0.865003i	0.991914	+	0.126912i	$0.0405064\pi$
$824$	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	$0.0440829\pi$
$827$			7.93987i			0.276096i	−0.990426	+	0.138048i	$0.955917\pi$
$828$	−10.3963	+	8.88340i	−0.361295	+	0.308720i
$829$		−	27.4393i		−	0.953005i	−0.879173	−	0.476502i	$-0.841904\pi$
$829$		−	27.4393i		−	0.953005i	0.879173	−	0.476502i	$-0.158096\pi$
$830$	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	$0.242813\pi$
$853$			40.3608i			1.38193i	−0.722890	+	0.690963i	$0.757187\pi$
$854$	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	$-0.942952\pi$
$859$		−	10.4494i		−	0.356528i	0.983983	−	0.178264i	$-0.0570481\pi$
$860$	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	$0.227603\pi$
$863$			38.5215i			1.31129i	−0.755070	+	0.655644i	$0.772397\pi$
$864$	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	−0.204141	−	0.978941i	$-0.565440\pi$
$877$	22.9451	−	22.9451i	0.774800	−	0.774800i	0.978941	+	0.204141i	$0.0654402\pi$
$878$	−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	0.852764	−	0.522296i	$-0.174925\pi$
$883$	9.81995	+	9.81995i	0.330468	+	0.330468i	−0.522296	+	0.852764i	$0.674925\pi$
$884$	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	0.693723	−	0.720242i	$-0.255969\pi$
$887$	−0.789783	−	0.789783i	−0.0265183	−	0.0265183i	−0.720242	+	0.693723i	$0.755969\pi$
$888$	−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	−0.961200	−	0.275853i	$-0.911040\pi$
$907$	−20.6402	+	20.6402i	−0.685347	+	0.685347i	0.275853	+	0.961200i	$0.411040\pi$
$908$	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	$-0.989151\pi$
$911$		−	2.05701i		−	0.0681517i	0.999419	−	0.0340758i	$-0.0108488\pi$
$912$	−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	$-0.737852\pi$
$919$		−	44.4765i		−	1.46714i	0.679612	−	0.733572i	$-0.262148\pi$
$920$	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	0.866083	−	0.499900i	$-0.166630\pi$
$941$	11.2329	+	11.2329i	0.366183	+	0.366183i	−0.499900	+	0.866083i	$0.666630\pi$
$942$	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	0.619204	−	0.785230i	$-0.287455\pi$
$947$	−5.10916	−	5.10916i	−0.166025	−	0.166025i	−0.785230	+	0.619204i	$0.787455\pi$
$948$	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	−0.637248	−	0.770659i	$-0.719927\pi$
$953$	4.11848	−	4.11848i	0.133411	−	0.133411i	0.770659	+	0.637248i	$0.219927\pi$
$954$	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	$0.112393\pi$
$967$			21.5065i			0.691604i	−0.938308	+	0.345802i	$0.887607\pi$
$968$	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	$-0.990560\pi$
$971$		−	1.84790i		−	0.0593018i	0.999560	−	0.0296509i	$-0.00943956\pi$
$972$	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	$-0.948695\pi$
$977$		−	10.0325i		−	0.320968i	0.987038	−	0.160484i	$-0.0513055\pi$
$978$	−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	0.254293	−	0.967127i	$-0.418157\pi$
$983$	−22.3494	−	22.3494i	−0.712835	−	0.712835i	−0.967127	+	0.254293i	$0.918157\pi$
$984$	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	0.801092	−	0.598542i	$-0.204253\pi$
$997$	6.39558	+	6.39558i	0.202550	+	0.202550i	−0.598542	+	0.801092i	$0.704253\pi$
$998$			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.50.2	yes	28
3.2	odd	2	inner	183.2.g.c.50.13	yes	28
61.11	odd	4	inner	183.2.g.c.11.13	yes	28
183.11	even	4	inner	183.2.g.c.11.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
183.2.g.c.11.2	✓	28	183.11	even	4	inner
183.2.g.c.11.13	yes	28	61.11	odd	4	inner
183.2.g.c.50.2	yes	28	1.1	even	1	trivial
183.2.g.c.50.13	yes	28	3.2	odd	2	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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