LMFDB - Embedded newform 183.2.g.c.11.13

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			11.13
Character	$\chi$	$=$	183.11
Dual form			183.2.g.c.50.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.53906 - 1.53906i) q^{2} +(1.73072 + 0.0678001i) q^{3} -2.73741i q^{4} -3.09885 q^{5} +(2.76803 - 2.55934i) q^{6} +(1.25340 + 1.25340i) q^{7} +(-1.13492 - 1.13492i) q^{8} +(2.99081 + 0.234686i) q^{9} +O(q^{10})$	\(q+(1.53906 - 1.53906i) q^{2} +(1.73072 + 0.0678001i) q^{3} -2.73741i q^{4} -3.09885 q^{5} +(2.76803 - 2.55934i) 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} +(4.96423 - 4.24183i) q^{18} +7.74511i q^{19} +8.48283i q^{20} +(2.08430 + 2.25426i) q^{21} -6.96660 q^{22} +(-1.17745 + 1.17745i) q^{23} +(-1.88728 - 2.04118i) 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} +(-8.57774 + 7.93102i) q^{30} +(-0.319670 + 0.319670i) q^{31} +(5.31934 - 5.31934i) q^{32} +(-3.76363 - 4.07053i) 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} +(1.74531 + 1.88763i) q^{51} +11.5261i q^{52} +(-5.28133 + 5.28133i) q^{53} +(8.87930 - 7.00486i) 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} +(3.45451 + 4.04282i) 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} +(-2.11767 + 1.95800i) q^{69} -11.9557 q^{70} +(10.0641 + 10.0641i) q^{71} +(-3.12797 - 3.66067i) q^{72} +4.20765 q^{73} -20.6218i q^{74} +(7.96635 + 0.312077i) q^{75} +21.2015 q^{76} -5.67353i q^{77} +(-11.6551 + 10.7763i) 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} +(6.17084 - 5.70559i) q^{84} +(-3.25238 - 3.25238i) q^{85} +6.34294i q^{86} +(-9.58692 - 10.3687i) q^{87} +5.13723i q^{88} +(-1.44252 - 1.44252i) q^{89} +(-15.3834 + 13.1448i) q^{90} +(-5.27755 - 5.27755i) q^{91} +(3.22316 + 3.22316i) q^{92} +(-0.574935 + 0.531587i) q^{93} +(-12.6211 - 12.6211i) q^{94} -24.0010i q^{95} +(9.56696 - 8.84565i) q^{96} +14.1801i q^{97} +(-5.93768 - 5.93768i) q^{98} +(-6.23783 - 7.30014i) 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	$-0.470491\pi$
$2$	1.53906	−	1.53906i	1.08828	−	1.08828i	0.995706	−	0.0925737i	$-0.0295094\pi$
$3$	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	$-0.743678\pi$
$5$	−3.09885			−1.38585			−0.692925	+	0.721010i	$0.743678\pi$
$6$	2.76803	−	2.55934i	1.13005	−	1.04485i
$7$	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	0.278141	−	0.960540i	$-0.410282\pi$
$11$	−2.26326	−	2.26326i	−0.682400	−	0.682400i	−0.960540	+	0.278141i	$0.910282\pi$
$12$	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	$-0.192392\pi$
$17$	1.04954	+	1.04954i	0.254551	+	0.254551i	−0.568282	+	0.822834i	$0.692392\pi$
$18$	4.96423	−	4.24183i	1.17008	−	0.999810i
$19$			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
$21$	2.08430	+	2.25426i	0.454832	+	0.491921i
$22$	−6.96660			−1.48528
$23$	−1.17745	+	1.17745i	−0.245515	+	0.245515i	−0.819127	−	0.573612i	$-0.805542\pi$
$23$	−1.17745	+	1.17745i	−0.245515	+	0.245515i	0.573612	+	0.819127i	$0.305542\pi$
$24$	−1.88728	−	2.04118i	−0.385239	−	0.416653i
$25$	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	$-0.976667\pi$
$29$	−5.76510	−	5.76510i	−1.07055	−	1.07055i	−0.0732376	−	0.997315i	$-0.523333\pi$
$30$	−8.57774	+	7.93102i	−1.56607	+	1.44800i
$31$	−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
$33$	−3.76363	−	4.07053i	−0.655165	−	0.708589i
$34$	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	$-0.452368\pi$
$41$	1.90920			0.298167			0.149084	+	0.988825i	$0.452368\pi$
$42$	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	$-0.795928\pi$
$47$		−	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
$51$	1.74531	+	1.88763i	0.244392	+	0.264321i
$52$			11.5261i			1.59839i
$53$	−5.28133	+	5.28133i	−0.725446	+	0.725446i	−0.969709	−	0.244263i	$-0.921454\pi$
$53$	−5.28133	+	5.28133i	−0.725446	+	0.725446i	0.244263	+	0.969709i	$0.421454\pi$
$54$	8.87930	−	7.00486i	1.20832	−	0.953241i
$55$	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	$-0.233668\pi$
$59$	0.557124	+	0.557124i	0.0725314	+	0.0725314i	−0.669910	+	0.742442i	$0.733668\pi$
$60$	−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
$63$	3.45451	+	4.04282i	0.435228	+	0.509348i
$64$		−	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
$69$	−2.11767	+	1.95800i	−0.254937	+	0.235716i
$70$	−11.9557			−1.42898
$71$	10.0641	+	10.0641i	1.19439	+	1.19439i	0.975820	+	0.218574i	$0.0701405\pi$
$71$	10.0641	+	10.0641i	1.19439	+	1.19439i	0.218574	+	0.975820i	$0.429860\pi$
$72$	−3.12797	−	3.66067i	−0.368635	−	0.431414i
$73$	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
$78$	−11.6551	+	10.7763i	−1.31968	+	1.22018i
$79$	−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	$0.0239753\pi$
$83$			1.37111i			0.150499i	−0.997165	+	0.0752493i	$0.976025\pi$
$84$	6.17084	−	5.70559i	0.673294	−	0.622531i
$85$	−3.25238	−	3.25238i	−0.352770	−	0.352770i
$86$			6.34294i			0.683977i
$87$	−9.58692	−	10.3687i	−1.02783	−	1.11164i
$88$			5.13723i			0.547631i
$89$	−1.44252	−	1.44252i	−0.152906	−	0.152906i	0.626508	−	0.779415i	$-0.284483\pi$
$89$	−1.44252	−	1.44252i	−0.152906	−	0.152906i	−0.779415	+	0.626508i	$0.784483\pi$
$90$	−15.3834	+	13.1448i	−1.62155	+	1.38559i
$91$	−5.27755	−	5.27755i	−0.553237	−	0.553237i
$92$	3.22316	+	3.22316i	0.336037	+	0.336037i
$93$	−0.574935	+	0.531587i	−0.0596179	+	0.0551230i
$94$	−12.6211	−	12.6211i	−1.30177	−	1.30177i
$95$		−	24.0010i		−	2.46245i
$96$	9.56696	−	8.84565i	0.976424	−	0.902806i
$97$			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
$99$	−6.23783	−	7.30014i	−0.626925	−	0.733692i
$100$		−	12.6000i		−	1.26000i
$101$	−11.4237	+	11.4237i	−1.13670	+	1.13670i	−0.147659	+	0.989038i	$0.547174\pi$
$101$	−11.4237	+	11.4237i	−1.13670	+	1.13670i	−0.989038	+	0.147659i	$0.952826\pi$
$102$	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
$105$	−6.45895	−	6.98563i	−0.630329	−	0.681728i
$106$			16.2566i			1.57898i
$107$	−11.3308			−1.09539			−0.547694	−	0.836679i	$-0.684494\pi$
$107$	−11.3308			−1.09539			−0.547694	+	0.836679i	$0.684494\pi$
$108$	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
$111$	12.0492	−	11.1407i	1.14366	−	1.05743i
$112$	2.48349	+	2.48349i	0.234668	+	0.234668i
$113$	6.41867			0.603818			0.301909	−	0.953337i	$-0.402376\pi$
$113$	6.41867			0.603818			0.301909	+	0.953337i	$0.402376\pi$
$114$	19.8224	+	21.4387i	1.85653	+	2.00792i
$115$	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
$120$	5.84841	+	6.32531i	0.533884	+	0.577419i
$121$		−	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
$129$	−3.70614	+	3.42671i	−0.326307	+	0.301705i
$130$	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	$0.885497\pi$
$132$	−11.1427	+	10.3026i	−0.969849	+	0.896727i
$133$	−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	0.0771863	−	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	$-0.133849\pi$
$149$	22.2864			1.82577			0.912885	+	0.408216i	$0.133849\pi$
$150$	12.7410	−	11.7804i	1.04030	−	0.961864i
$151$	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
$153$	2.89266	+	3.38529i	0.233858	+	0.273685i
$154$	−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
$159$	−9.49859	+	8.78244i	−0.753287	+	0.696493i
$160$	−16.4839	+	16.4839i	−1.30316	+	1.30316i
$161$	−2.95162			−0.232620
$162$	15.8425	−	11.5215i	1.24471	−	0.905212i
$163$		−	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
$165$	11.6630	+	12.6140i	0.907960	+	0.981998i
$166$	2.11022	+	2.11022i	0.163785	+	0.163785i
$167$	11.6931			0.904837			0.452419	−	0.891806i	$-0.350561\pi$
$167$	11.6931			0.904837			0.452419	+	0.891806i	$0.350561\pi$
$168$	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	$-0.927621\pi$
$173$	−9.84930	+	9.84930i	−0.748828	+	0.748828i	0.225431	+	0.974259i	$0.427621\pi$
$174$	−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
$177$	0.926455	+	1.00200i	0.0696366	+	0.0753150i
$178$	−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	−0.568665	−	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
$183$	−9.06135	−	10.0445i	−0.669834	−	0.742511i
$184$	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
$189$	5.70470	+	7.23122i	0.414956	+	0.525994i
$190$	−36.9389	−	36.9389i	−2.67983	−	2.67983i
$191$	8.36822	+	8.36822i	0.605504	+	0.605504i	0.941768	−	0.336264i	$-0.109164\pi$
$191$	8.36822	+	8.36822i	0.605504	+	0.605504i	−0.336264	+	0.941768i	$0.609164\pi$
$192$	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	$-0.624300\pi$
$197$	−10.6854			−0.761302			−0.380651	+	0.924719i	$0.624300\pi$
$198$	−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
$201$	2.67798	−	2.47608i	0.188890	−	0.174649i
$202$			35.1634i			2.47409i
$203$		−	14.4519i		−	1.01433i
$204$	5.16721	−	4.77762i	0.361777	−	0.334500i
$205$	−5.91634			−0.413215
$206$	11.9636	−	11.9636i	0.833545	−	0.833545i
$207$	−3.79785	+	3.24519i	−0.263969	+	0.225556i
$208$	−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
$213$	16.7359	+	18.1006i	1.14672	+	1.24023i
$214$	−17.4388	+	17.4388i	−1.19209	+	1.19209i
$215$	6.38567	−	6.38567i	0.435499	−	0.435499i
$216$	−5.16545	−	6.54768i	−0.351465	−	0.445513i
$217$	−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	$-0.424127\pi$
$227$	18.1979	−	18.1979i	1.20784	−	1.20784i	0.971726	−	0.236113i	$-0.0758734\pi$
$228$	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	−0.536322	−	0.844013i	$-0.680187\pi$
$233$	4.69671	−	4.69671i	0.307692	−	0.307692i	0.844013	+	0.536322i	$0.180187\pi$
$234$	−20.9023	+	17.8606i	−1.36643	+	1.16759i
$235$			25.4123i			1.65772i
$236$	1.52508	−	1.52508i	0.0992741	−	0.0992741i
$237$	−14.7539	−	15.9570i	−0.958369	−	1.03652i
$238$	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
$246$	5.28474	−	4.88629i	0.336943	−	0.311539i
$247$		−	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	$-0.855693\pi$
$251$	−7.30363	+	7.30363i	−0.461001	+	0.461001i	0.437983	+	0.898983i	$0.355693\pi$
$252$	11.0669	−	9.45641i	0.697147	−	0.595698i
$253$	5.32975			0.335078
$254$	−18.5968	−	18.5968i	−1.16687	−	1.16687i
$255$	−5.40846	−	5.84948i	−0.338691	−	0.366309i
$256$	−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
$261$	−15.8893	−	18.5953i	−0.983523	−	1.15102i
$262$	12.4016	+	12.4016i	0.766176	+	0.766176i
$263$	−14.1525			−0.872679			−0.436339	−	0.899782i	$-0.643725\pi$
$263$	−14.1525			−0.872679			−0.436339	+	0.899782i	$0.643725\pi$
$264$	−0.348305	+	8.89113i	−0.0214367	+	0.547211i
$265$	16.3661	−	16.3661i	1.00536	−	1.00536i
$266$			29.8815i			1.83215i
$267$	−2.39879	−	2.59440i	−0.146804	−	0.158775i
$268$	−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	$-0.114383\pi$
$270$	−27.5157	+	21.7071i	−1.67455	+	1.32105i
$271$			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
$273$	−8.77615	−	9.49179i	−0.531157	−	0.574469i
$274$	7.59125	+	7.59125i	0.458604	+	0.458604i
$275$	−10.4176	−	10.4176i	−0.628204	−	0.628204i
$276$	5.35986	+	5.79692i	0.322626	+	0.348934i
$277$	−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
$279$	−1.03109	+	0.881050i	−0.0617300	+	0.0527471i
$280$			8.81625i			0.526872i
$281$	6.97026	+	6.97026i	0.415811	+	0.415811i	0.883757	−	0.467946i	$-0.155006\pi$
$281$	6.97026	+	6.97026i	0.415811	+	0.415811i	−0.467946	+	0.883757i	$0.655006\pi$
$282$	−20.9880	−	22.6994i	−1.24982	−	1.35173i
$283$			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
$288$	17.1575	−	14.6607i	1.01101	−	0.863892i
$289$		−	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	$-0.608471\pi$
$293$	−11.4417			−0.668429			−0.334214	+	0.942497i	$0.608471\pi$
$294$	−9.87391	−	10.6791i	−0.575858	−	0.622815i
$295$	−1.72645	−	1.72645i	−0.100518	−	0.100518i
$296$	−15.2067			−0.883871
$297$	−10.3010	−	13.0574i	−0.597725	−	0.757670i
$298$	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
$303$	−20.5457	+	18.9967i	−1.18032	+	1.09133i
$304$			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	0.407774	−	0.913083i	$-0.366305\pi$
$311$	−8.91123	−	8.91123i	−0.505309	−	0.505309i	−0.913083	+	0.407774i	$0.866305\pi$
$312$	7.94657	+	8.59456i	0.449886	+	0.486571i
$313$	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
$315$	−10.7050	−	12.5281i	−0.603160	−	0.705880i
$316$	−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	0.650398	−	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
$333$	21.6091	−	18.4646i	1.18417	−	1.01185i
$334$	17.9963	−	17.9963i	0.984716	−	0.984716i
$335$	−4.61416	+	4.61416i	−0.252099	+	0.252099i
$336$	4.12985	+	4.46662i	0.225302	+	0.243674i
$337$	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
$342$	32.8535	+	38.4485i	1.77651	+	2.07906i
$343$	13.6094	−	13.6094i	0.734837	−	0.734837i
$344$	4.67735			0.252186
$345$	6.56234	−	6.06757i	0.353305	−	0.326667i
$346$			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	$-0.322761\pi$
$348$	−28.3833	+	26.2433i	−1.52150	+	1.40679i
$349$	−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	$-0.680070\pi$
$353$	−20.1415			−1.07202			−0.536012	+	0.844211i	$0.680070\pi$
$354$	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	$-0.143952\pi$
$359$	8.76293	+	8.76293i	0.462490	+	0.462490i	−0.436981	+	0.899471i	$0.643952\pi$
$360$	9.69312	+	11.3439i	0.510872	+	0.597875i
$361$	−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
$366$	−29.4050	−	1.51313i	−1.53703	−	0.0790926i
$367$	−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
$372$	1.45517	+	1.57383i	0.0754472	+	0.0815994i
$373$	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	0.789887	−	0.613253i	$-0.210139\pi$
$383$	3.45679	+	3.45679i	0.176634	+	0.176634i	−0.613253	+	0.789887i	$0.710139\pi$
$384$	−14.0720	−	15.2195i	−0.718108	−	0.776665i
$385$			17.5815i			0.896034i
$386$			43.5294i			2.21559i
$387$	−6.64663	+	5.67941i	−0.337867	+	0.288701i
$388$	38.8168			1.97063
$389$	−11.6845	+	11.6845i	−0.592428	+	0.592428i	−0.938287	−	0.345859i	$-0.887588\pi$
$389$	−11.6845	+	11.6845i	−0.592428	+	0.592428i	0.345859	+	0.938287i	$0.387588\pi$
$390$	36.1174	−	33.3943i	1.82887	−	1.69099i
$391$	−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
$396$	−19.9835	+	17.0755i	−1.00421	+	0.858075i
$397$	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
$399$	−17.4595	+	16.1432i	−0.874069	+	0.808169i
$400$	9.12023			0.456011
$401$	−18.7834	−	18.7834i	−0.937998	−	0.937998i	0.0601887	−	0.998187i	$-0.480830\pi$
$401$	−18.7834	−	18.7834i	−0.937998	−	0.937998i	−0.998187	+	0.0601887i	$0.980830\pi$
$402$	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
$417$	22.7777	−	21.0604i	1.11543	−	1.03133i
$418$		−	53.9571i		−	2.63913i
$419$	8.90771	−	8.90771i	0.435170	−	0.435170i	−0.455213	−	0.890383i	$-0.650437\pi$
$419$	8.90771	−	8.90771i	0.435170	−	0.435170i	0.890383	+	0.455213i	$0.150437\pi$
$420$	−19.1225	+	17.6808i	−0.933085	+	0.862734i
$421$	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
$429$	15.8471	+	17.1394i	0.765107	+	0.827496i
$430$		−	19.6559i		−	0.947890i
$431$	−35.0743			−1.68947			−0.844735	−	0.535185i	$-0.820242\pi$
$431$	−35.0743			−1.68947			−0.844735	+	0.535185i	$0.820242\pi$
$432$	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
$435$	29.7085	+	32.1310i	1.42441	+	1.54056i
$436$	31.7938			1.52265
$437$	−9.11946	−	9.11946i	−0.436243	−	0.436243i
$438$	11.6469	−	10.7688i	0.556512	−	0.514553i
$439$	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	$-0.120012\pi$
$444$	−30.4967	−	32.9835i	−1.44731	−	1.56533i
$445$	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	$-0.0332354\pi$
$450$	22.8498	−	19.5247i	1.07715	−	0.920405i
$451$	−4.32103	−	4.32103i	−0.203469	−	0.203469i
$452$		−	17.5705i		−	0.826448i
$453$	5.86937	−	5.42684i	0.275767	−	0.254975i
$454$		−	56.0154i		−	2.62893i
$455$	16.3543	+	16.3543i	0.766704	+	0.766704i
$456$	15.8091	−	14.6172i	0.740330	−	0.684513i
$457$	−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
$459$	4.77688	+	6.05512i	0.222966	+	0.282629i
$460$	−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	$0.983294\pi$
$462$	−14.5205	−	15.7045i	−0.675555	−	0.730641i
$463$		−	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
$465$	1.78164	−	1.64731i	0.0826215	−	0.0763923i
$466$		−	14.4570i		−	0.669709i
$467$	4.29490	−	4.29490i	0.198744	−	0.198744i	−0.600717	−	0.799462i	$-0.705118\pi$
$467$	4.29490	−	4.29490i	0.198744	−	0.198744i	0.799462	+	0.600717i	$0.205118\pi$
$468$	−2.70502	+	34.4724i	−0.125040	+	1.59349i
$469$	3.73259			0.172355
$470$	39.1111	+	39.1111i	1.80406	+	1.80406i
$471$	−4.86407	+	4.49734i	−0.224124	+	0.207226i
$472$		−	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
$477$	−17.0349	+	14.5560i	−0.779974	+	0.666472i
$478$	21.5200	+	21.5200i	0.984300	+	0.984300i
$479$	14.2150			0.649499			0.324749	−	0.945800i	$-0.394720\pi$
$479$	14.2150			0.649499			0.324749	+	0.945800i	$0.394720\pi$
$480$	−29.6466	+	27.4114i	−1.35318	+	1.25115i
$481$	−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
$486$	28.2002	−	18.8663i	1.27919	−	0.855795i
$487$		−	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	$-0.534233\pi$
$491$	−4.75692			−0.214677			−0.107339	+	0.994223i	$0.534233\pi$
$492$	0.354342	−	9.04522i	0.0159749	−	0.407790i
$493$		−	12.1014i		−	0.545021i
$494$	−50.1911	−	50.1911i	−2.25820	−	2.25820i
$495$	19.3301	+	22.6221i	0.868824	+	1.01679i
$496$	−0.633397	+	0.633397i	−0.0284404	+	0.0284404i
$497$			25.2287i			1.13166i
$498$	3.50913	+	3.79527i	0.157248	+	0.170070i
$499$	−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	$-0.904387\pi$
$503$		−	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	$-0.372349\pi$
$509$	−11.9640	−	11.9640i	−0.530295	−	0.530295i	−0.920660	+	0.390365i	$0.872349\pi$
$510$	−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
$516$	9.38031	+	10.1452i	0.412945	+	0.446618i
$517$	−18.5600	+	18.5600i	−0.816268	+	0.816268i
$518$	25.8473	−	25.8473i	1.13566	−	1.13566i
$519$	−17.7142	+	16.3786i	−0.777567	+	0.718942i
$520$	−14.8084	−	14.8084i	−0.649392	−	0.649392i
$521$	14.8857	−	14.8857i	0.652153	−	0.652153i	−0.301358	−	0.953511i	$-0.597440\pi$
$521$	14.8857	−	14.8857i	0.652153	−	0.652153i	0.953511	+	0.301358i	$0.0974400\pi$
$522$	−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
$525$	9.59384	+	10.3762i	0.418709	+	0.452852i
$526$	−21.7815	+	21.7815i	−0.949718	+	0.949718i
$527$	−0.671015			−0.0292299
$528$	−7.45729	−	8.06539i	−0.324537	−	0.351001i
$529$			20.2272i			0.879445i
$530$		−	50.3767i		−	2.18822i
$531$	1.53550	+	1.79700i	0.0666351	+	0.0779832i
$532$	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
$543$	6.14364	−	5.68043i	0.263649	−	0.243771i
$544$	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
$549$	−15.0017	−	17.9986i	−0.640256	−	0.768162i
$550$	−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
$555$	−37.3386	+	34.5234i	−1.58494	+	1.46544i
$556$	−34.6684	−	34.6684i	−1.47027	−	1.47027i
$557$	−10.1909	−	10.1909i	−0.431802	−	0.431802i	0.457439	−	0.889241i	$-0.348767\pi$
$557$	−10.1909	−	10.1909i	−0.431802	−	0.431802i	−0.889241	+	0.457439i	$0.848767\pi$
$558$	−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	$-0.670376\pi$
$563$	−24.2049			−1.02012			−0.510058	+	0.860140i	$0.670376\pi$
$564$	−38.8517	−	1.52199i	−1.63595	−	0.0640875i
$565$	−19.8905			−0.836801
$566$	25.3550	+	25.3550i	1.06575	+	1.06575i
$567$	9.38298	+	12.9020i	0.394048	+	0.541834i
$568$		−	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	$0.670156\pi$
$570$	−61.4266	−	66.4355i	−2.57288	−	2.78268i
$571$	−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
$573$	13.9157	+	15.0504i	0.581337	+	0.628742i
$574$	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
$579$	−25.4339	+	23.5163i	−1.05700	+	0.977304i
$580$	48.9044	−	48.9044i	2.03064	−	2.03064i
$581$	−1.71854	+	1.71854i	−0.0712971	+	0.0712971i
$582$	36.2918	+	39.2511i	1.50434	+	1.62701i
$583$	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	$-0.131563\pi$
$587$	12.4567	+	12.4567i	0.514143	+	0.514143i	−0.401650	+	0.915793i	$0.631563\pi$
$588$	−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	$-0.681219\pi$
$593$	7.38376	−	7.38376i	0.303215	−	0.303215i	0.842270	+	0.539056i	$0.181219\pi$
$594$	−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	$-0.622719\pi$
$599$	13.4743	−	13.4743i	0.550546	−	0.550546i	0.926598	+	0.376053i	$0.122719\pi$
$600$	−8.68696	−	9.39533i	−0.354644	−	0.383563i
$601$			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
$603$	4.80273	−	4.10383i	0.195582	−	0.167121i
$604$	−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
$612$	9.26693	−	7.91841i	0.374593	−	0.320083i
$613$			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	−0.432400	−	0.901682i	$-0.642333\pi$
$617$	11.6567	−	11.6567i	0.469281	−	0.469281i	0.901682	+	0.432400i	$0.142333\pi$
$618$	21.5169	−	19.8946i	0.865535	−	0.800277i
$619$	−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
$621$	−6.79305	+	5.35903i	−0.272596	+	0.215050i
$622$	−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
$627$	31.5267	−	29.1498i	1.25906	−	1.16413i
$628$	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
$633$	20.9314	−	19.3533i	0.831950	−	0.769225i
$634$	−2.05854	−	2.05854i	−0.0817553	−	0.0817553i
$635$			37.4441i			1.48593i
$636$	24.0411	+	26.0015i	0.953293	+	1.03103i
$637$			16.2444i			0.643628i
$638$	40.1631	+	40.1631i	1.59007	+	1.59007i
$639$	27.7380	+	32.4618i	1.09730	+	1.28417i
$640$	26.2231	+	26.2231i	1.03656	+	1.03656i
$641$	26.0963	+	26.0963i	1.03074	+	1.03074i	0.999512	+	0.0312278i	$0.00994175\pi$
$641$	26.0963	+	26.0963i	1.03074	+	1.03074i	0.0312278	+	0.999512i	$0.490058\pi$
$642$	−31.3640	+	28.9993i	−1.23784	+	1.14451i
$643$	−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
$645$	11.4848	−	10.6189i	0.452213	−	0.418118i
$646$			25.0215i			0.984457i
$647$	5.98792	+	5.98792i	0.235409	+	0.235409i	0.814946	−	0.579537i	$-0.196766\pi$
$647$	5.98792	+	5.98792i	0.235409	+	0.235409i	−0.579537	+	0.814946i	$0.696766\pi$
$648$	−8.49604	−	11.6824i	−0.333756	−	0.458930i
$649$		−	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	$-0.378297\pi$
$653$	−14.1747	−	14.1747i	−0.554699	−	0.554699i	−0.927794	+	0.373094i	$0.878297\pi$
$654$	29.7256	+	32.1495i	1.16236	+	1.25714i
$655$		−	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	$-0.462473\pi$
$659$	6.03891			0.235242			0.117621	+	0.993059i	$0.462473\pi$
$660$	34.5297	−	31.9263i	1.34407	−	1.24273i
$661$	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
$663$	−7.34878	−	7.94803i	−0.285403	−	0.308676i
$664$	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
$669$	−1.46252	−	1.58178i	−0.0565444	−	0.0611553i
$670$			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	0.309539	−	0.950887i	$-0.399825\pi$
$677$	−16.6874	−	16.6874i	−0.641348	−	0.641348i	−0.950887	+	0.309539i	$0.899825\pi$
$678$	17.7671	−	16.4275i	0.682341	−	0.630896i
$679$	−17.7733	+	17.7733i	−0.682078	+	0.682078i
$680$			7.38236i			0.283101i
$681$	32.7294	−	30.2617i	1.25419	−	1.15963i
$682$	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
$699$	8.44714	−	7.81026i	0.319500	−	0.295411i
$700$	15.7928	−	15.7928i	0.596913	−	0.596913i
$701$	24.8698	−	24.8698i	0.939318	−	0.939318i	−0.0589435	−	0.998261i	$-0.518773\pi$
$701$	24.8698	−	24.8698i	0.939318	−	0.939318i	0.998261	+	0.0589435i	$0.0187732\pi$
$702$	−37.3871	+	29.4946i	−1.41109	+	1.11320i
$703$	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
$708$	2.74289	−	2.53609i	0.103084	−	0.0953119i
$709$	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
$711$	−24.4530	−	28.6174i	−0.917061	−	1.07324i
$712$			3.27427i			0.122709i
$713$		−	0.752790i		−	0.0281922i
$714$	6.73358	+	7.28266i	0.251998	+	0.272547i
$715$	−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	$-0.304800\pi$
$719$	30.8641			1.15104			0.575519	+	0.817788i	$0.304800\pi$
$720$	−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
$726$	−1.93300	−	2.09063i	−0.0717405	−	0.0775904i
$727$	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
$732$	−27.4959	+	24.8046i	−1.01628	+	0.916805i
$733$	−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
$738$	9.47771	−	8.09852i	0.348879	−	0.298111i
$739$	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	0.510105	−	0.860112i	$-0.329606\pi$
$743$	−9.54048	−	9.54048i	−0.350006	−	0.350006i	−0.860112	+	0.510105i	$0.829606\pi$
$744$	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
$750$	3.40621	−	3.14940i	0.124377	−	0.115000i
$751$		−	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
$753$	−13.1357	+	12.1454i	−0.478693	+	0.442602i
$754$	74.7198			2.72113
$755$	−10.1129	+	10.1129i	−0.368047	+	0.368047i
$756$	19.7948	−	15.6161i	0.719931	−	0.567952i
$757$	−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	$-0.349761\pi$
$761$	−12.0278	−	12.0278i	−0.436006	−	0.436006i	−0.890665	+	0.454659i	$0.849761\pi$
$762$	−30.9250	−	33.4468i	−1.12030	−	1.21165i
$763$	−14.5576	+	14.5576i	−0.527022	+	0.527022i
$764$	22.9073	−	22.9073i	0.828756	−	0.828756i
$765$	−8.96395	−	10.4905i	−0.324092	−	0.379286i
$766$	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	$-0.708731\pi$
$773$	−33.9058			−1.21951			−0.609753	+	0.792592i	$0.708731\pi$
$774$	−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
$783$	−26.2392	−	33.2606i	−0.937713	−	1.18864i
$784$		−	7.64426i		−	0.273009i
$785$	8.38079	−	8.38079i	0.299123	−	0.299123i
$786$	20.6230	+	22.3046i	0.735597	+	0.795580i
$787$	−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
$795$	29.4348	−	27.2155i	1.04394	−	0.965235i
$796$			31.5817i			1.11938i
$797$	9.91395			0.351170			0.175585	−	0.984464i	$-0.443818\pi$
$797$	9.91395			0.351170			0.175585	+	0.984464i	$0.443818\pi$
$798$	−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
$801$	−3.97575	−	4.65283i	−0.140476	−	0.164400i
$802$	−57.8176			−2.04161
$803$	−9.52302	−	9.52302i	−0.336060	−	0.336060i
$804$	−6.77803	−	7.33074i	−0.239043	−	0.258535i
$805$	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	$-0.0484091\pi$
$810$	−49.0937	+	35.7033i	−1.72498	+	1.25449i
$811$	−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
$816$	3.45817	+	3.74016i	0.121060	+	0.130932i
$817$	−15.9600	−	15.9600i	−0.558370	−	0.558370i
$818$		−	2.48786i		−	0.0869859i
$819$	−14.5455	−	17.0227i	−0.508263	−	0.594821i
$820$			16.1954i			0.565569i
$821$	36.2734	+	36.2734i	1.26595	+	1.26595i	0.948161	+	0.317791i	$0.102941\pi$
$821$	36.2734	+	36.2734i	1.26595	+	1.26595i	0.317791	+	0.948161i	$0.397059\pi$
$822$	12.6237	+	13.6530i	0.440301	+	0.476205i
$823$	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
$825$	−17.3236	−	18.7363i	−0.603131	−	0.652313i
$826$	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	$0.955917\pi$
$828$	8.88340	+	10.3963i	0.308720	+	0.361295i
$829$			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
$831$	−0.114236	−	0.123551i	−0.00396280	−	0.00428594i
$832$			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
$837$	−1.84427	+	1.45495i	−0.0637475	+	0.0502903i
$838$		−	27.4190i		−	0.947173i
$839$	33.4374			1.15439			0.577193	−	0.816608i	$-0.304148\pi$
$839$	33.4374			1.15439			0.577193	+	0.816608i	$0.304148\pi$
$840$	−0.597743	+	15.2585i	−0.0206241	+	0.526468i
$841$			37.4727i			1.29216i
$842$	57.3126			1.97512
$843$	11.5910	+	12.5362i	0.399215	+	0.431769i
$844$	−31.8583	−	31.8583i	−1.09661	−	1.09661i
$845$	−14.6548			−0.504141
$846$	−34.7854	−	40.7094i	−1.19595	−	1.39962i
$847$	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
$852$	49.5488	−	45.8130i	1.69751	−	1.56953i
$853$		−	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	$-0.641045\pi$
$857$	−25.1028			−0.857495			−0.428747	+	0.903424i	$0.641045\pi$
$858$	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
$861$	3.97935	+	4.30384i	0.135616	+	0.146675i
$862$	−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	$0.772397\pi$
$864$	30.6889	−	24.2104i	1.04406	−	0.823655i
$865$	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	$-0.435675\pi$
$881$	11.9148			0.401421			0.200711	+	0.979651i	$0.435675\pi$
$882$	−16.3650	−	19.1519i	−0.551037	−	0.644880i
$883$	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
$885$	−2.87095	−	3.10506i	−0.0965059	−	0.104375i
$886$	−23.8518	−	23.8518i	−0.801318	−	0.801318i
$887$	0.789783	−	0.789783i	0.0265183	−	0.0265183i	−0.693723	−	0.720242i	$-0.744031\pi$
$887$	0.789783	−	0.789783i	0.0265183	−	0.0265183i	0.720242	+	0.693723i	$0.244031\pi$
$888$	−26.3186	−	1.03102i	−0.883194	−	0.0345986i
$889$	15.1451	−	15.1451i	0.507949	−	0.507949i
$890$	13.7597			0.461225
$891$	−16.9429	−	23.2972i	−0.567608	−	0.780487i
$892$	−2.40752	+	2.40752i	−0.0806099	+	0.0806099i
$893$	63.5142			2.12542
$894$	61.6895	−	57.0384i	2.06320	−	1.90765i
$895$		−	18.2178i		−	0.608953i
$896$		−	21.2130i		−	0.708676i
$897$	8.91664	−	8.24436i	0.297718	−	0.275271i
$898$	−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
$909$	−36.8470	+	31.4850i	−1.22214	+	1.04429i
$910$	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
$915$	28.0798	+	31.1264i	0.928290	+	1.02901i
$916$	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
$921$	−26.8754	−	29.0669i	−0.885574	−	0.957786i
$922$	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	$-0.443219\pi$
$929$	10.8164			0.354874			0.177437	+	0.984132i	$0.443219\pi$
$930$	0.206738	−	5.27736i	0.00677919	−	0.173051i
$931$	29.8806			0.979297
$932$	−12.8568	−	12.8568i	−0.421139	−	0.421139i
$933$	−14.8187	−	16.0271i	−0.485142	−	0.524702i
$934$		−	13.2202i		−	0.432578i
$935$			14.7220i			0.481460i
$936$	13.1706	+	15.4136i	0.430495	+	0.503809i
$937$	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
$939$	15.2136	−	14.0666i	0.496478	−	0.459046i
$940$	69.5639			2.26892
$941$	−11.2329	+	11.2329i	−0.366183	+	0.366183i	−0.866083	−	0.499900i	$-0.833370\pi$
$941$	−11.2329	+	11.2329i	−0.366183	+	0.366183i	0.499900	+	0.866083i	$0.333370\pi$
$942$	−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
$945$	−17.6780	−	22.4085i	−0.575067	−	0.728949i
$946$	14.3558	−	14.3558i	0.466746	−	0.466746i
$947$	5.10916	−	5.10916i	0.166025	−	0.166025i	−0.619204	−	0.785230i	$-0.712545\pi$
$947$	5.10916	−	5.10916i	0.166025	−	0.166025i	0.785230	+	0.619204i	$0.212545\pi$
$948$	−43.6808	+	40.3875i	−1.41869	+	1.31172i
$949$	−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	$-0.280073\pi$
$953$	−4.11848	−	4.11848i	−0.133411	−	0.133411i	−0.770659	+	0.637248i	$0.780073\pi$
$954$	−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
$966$	−8.17018	+	7.55419i	−0.262871	+	0.243052i
$967$		−	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
$969$	−14.6199	+	13.5176i	−0.469658	+	0.434248i
$970$	−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	$-0.0513055\pi$
$978$	−16.8141	−	18.1852i	−0.537656	−	0.581498i
$979$			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	$-0.581843\pi$
$983$	22.3494	−	22.3494i	0.712835	−	0.712835i	0.967127	+	0.254293i	$0.0818427\pi$
$984$	−3.60320	−	3.89702i	−0.114866	−	0.124232i
$985$	33.1125			1.05505
$986$	−18.6248	−	18.6248i	−0.593135	−	0.593135i
$987$	18.4862	−	17.0924i	0.588422	−	0.544058i
$988$	−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
$993$	−3.30365	−	3.57304i	−0.104838	−	0.113387i
$994$	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
$999$	38.6513	−	30.4919i	1.22287	−	0.964722i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.53906 - 1.53906i) q^{2} +(1.73072 + 0.0678001i) q^{3} -2.73741i q^{4} -3.09885 q^{5} +(2.76803 - 2.55934i) q^{6} +(1.25340 + 1.25340i) q^{7} +(-1.13492 - 1.13492i) q^{8} +(2.99081 + 0.234686i) q^{9} +O(q^{10})\)	\(q+(1.53906 - 1.53906i) q^{2} +(1.73072 + 0.0678001i) q^{3} -2.73741i q^{4} -3.09885 q^{5} +(2.76803 - 2.55934i) 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} +(4.96423 - 4.24183i) q^{18} +7.74511i q^{19} +8.48283i q^{20} +(2.08430 + 2.25426i) q^{21} -6.96660 q^{22} +(-1.17745 + 1.17745i) q^{23} +(-1.88728 - 2.04118i) 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} +(-8.57774 + 7.93102i) q^{30} +(-0.319670 + 0.319670i) q^{31} +(5.31934 - 5.31934i) q^{32} +(-3.76363 - 4.07053i) 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} +(1.74531 + 1.88763i) q^{51} +11.5261i q^{52} +(-5.28133 + 5.28133i) q^{53} +(8.87930 - 7.00486i) 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} +(3.45451 + 4.04282i) 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} +(-2.11767 + 1.95800i) q^{69} -11.9557 q^{70} +(10.0641 + 10.0641i) q^{71} +(-3.12797 - 3.66067i) q^{72} +4.20765 q^{73} -20.6218i q^{74} +(7.96635 + 0.312077i) q^{75} +21.2015 q^{76} -5.67353i q^{77} +(-11.6551 + 10.7763i) 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} +(6.17084 - 5.70559i) q^{84} +(-3.25238 - 3.25238i) q^{85} +6.34294i q^{86} +(-9.58692 - 10.3687i) q^{87} +5.13723i q^{88} +(-1.44252 - 1.44252i) q^{89} +(-15.3834 + 13.1448i) q^{90} +(-5.27755 - 5.27755i) q^{91} +(3.22316 + 3.22316i) q^{92} +(-0.574935 + 0.531587i) q^{93} +(-12.6211 - 12.6211i) q^{94} -24.0010i q^{95} +(9.56696 - 8.84565i) q^{96} +14.1801i q^{97} +(-5.93768 - 5.93768i) q^{98} +(-6.23783 - 7.30014i) 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

Related objects

Downloads

Learn more