LMFDB - Embedded newform 570.2.bc.a.139.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(139,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 14]))

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

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

chi := DirichletCharacter("570.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bc (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			139.9
Character	$\chi$	$=$	570.139
Dual form			570.2.bc.a.529.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.22203 - 1.87260i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-3.95160 - 2.28146i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.22203 - 1.87260i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-3.95160 - 2.28146i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(2.22000 - 0.267559i) q^{10} +(-2.24659 - 3.89121i) q^{11} +(0.866025 + 0.500000i) q^{12} +(0.0949418 + 0.260851i) q^{13} +(-0.792342 - 4.49360i) q^{14} +(-1.34171 - 1.78880i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-2.12818 - 2.53626i) q^{17} -1.00000i q^{18} +(1.90108 + 3.92249i) q^{19} +(1.63195 + 1.52864i) q^{20} +(-3.49540 + 2.93299i) q^{21} +(1.53676 - 4.22221i) q^{22} +(-1.73438 - 0.305817i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-2.01329 - 4.57675i) q^{25} +(-0.138796 + 0.240401i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(2.93299 - 3.49540i) q^{28} +(8.06721 + 6.76920i) q^{29} +(0.507863 - 2.17763i) q^{30} +(4.93003 - 8.53907i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-4.42492 + 0.780234i) q^{33} +(0.574924 - 3.26056i) q^{34} +(-9.10124 + 4.61178i) q^{35} +(0.766044 - 0.642788i) q^{36} +4.60745i q^{37} +(-1.78281 + 3.97764i) q^{38} +0.277591 q^{39} +(-0.122006 + 2.23274i) q^{40} +(5.56646 + 2.02603i) q^{41} +(-4.49360 - 0.792342i) q^{42} +(-6.39239 + 1.12715i) q^{43} +(4.22221 - 1.53676i) q^{44} +(-2.13981 + 0.648993i) q^{45} +(-0.880565 - 1.52518i) q^{46} +(5.60594 - 6.68089i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(6.91010 + 11.9686i) q^{49} +(2.21187 - 4.48415i) q^{50} +(-3.11119 + 1.13238i) q^{51} +(-0.273374 + 0.0482032i) q^{52} +(0.0358120 + 0.00631463i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(-10.0321 - 0.548194i) q^{55} +4.56292 q^{56} +(4.33614 - 0.444863i) q^{57} +10.5310i q^{58} +(7.58989 - 6.36868i) q^{59} +(1.99461 - 1.01071i) q^{60} +(1.82237 - 10.3352i) q^{61} +(9.71027 - 1.71218i) q^{62} +(1.56061 + 4.28774i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.604492 + 0.140978i) q^{65} +(-3.44198 - 2.88816i) q^{66} +(3.96292 - 4.72282i) q^{67} +(2.86729 - 1.65543i) q^{68} +(-0.880565 + 1.52518i) q^{69} +(-9.38299 - 4.00756i) q^{70} +(2.08816 + 11.8426i) q^{71} +(0.984808 + 0.173648i) q^{72} +(3.62366 - 9.95594i) q^{73} +(-3.52951 + 2.96161i) q^{74} +(-4.98933 + 0.326536i) q^{75} +(-4.19301 + 1.19107i) q^{76} +20.5020i q^{77} +(0.178432 + 0.212647i) q^{78} +(-10.0990 - 3.67572i) q^{79} +(-1.78880 + 1.34171i) q^{80} +(0.173648 + 0.984808i) q^{81} +(2.02603 + 5.56646i) q^{82} +(1.27349 + 0.735249i) q^{83} +(-2.28146 - 3.95160i) q^{84} +(-7.35011 + 0.885848i) q^{85} +(-4.97240 - 4.17234i) q^{86} +(9.12011 - 5.26550i) q^{87} +(3.89121 + 2.24659i) q^{88} +(7.51517 - 2.73530i) q^{89} +(-1.87260 - 1.22203i) q^{90} +(0.219947 - 1.24738i) q^{91} +(0.602342 - 1.65492i) q^{92} +(-6.33793 - 7.55325i) q^{93} +8.72129 q^{94} +(9.66844 + 1.23342i) q^{95} -1.00000 q^{96} +(-1.78839 - 2.13132i) q^{97} +(-4.72679 + 12.9867i) q^{98} +(-0.780234 + 4.42492i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{5}+O(q^{10}) $ 60 * q - 6 * q^5	$ 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) $ 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$2$	0.642788	+	0.766044i	0.454519	+	0.541675i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$3$	0.342020	−	0.939693i	0.197465	−	0.542532i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	1.22203	−	1.87260i	0.546508	−	0.837454i
$5$	1.22203	−	1.87260i	0.546508	−	0.837454i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	−3.95160	−	2.28146i	−1.49356	−	0.862310i	−0.493592	−	0.869694i	$-0.664316\pi$
$7$	−3.95160	−	2.28146i	−1.49356	−	0.862310i	−0.999973	+	0.00738345i	$0.997650\pi$
$8$	−0.866025	+	0.500000i	−0.306186	+	0.176777i
$9$	−0.766044	−	0.642788i	−0.255348	−	0.214263i
$10$	2.22000	−	0.267559i	0.702027	−	0.0846095i
$11$	−2.24659	−	3.89121i	−0.677373	−	1.17324i	−0.975769	−	0.218803i	$-0.929785\pi$
$11$	−2.24659	−	3.89121i	−0.677373	−	1.17324i	0.298396	−	0.954442i	$-0.403548\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	0.0949418	+	0.260851i	0.0263321	+	0.0723469i	0.952162	−	0.305593i	$-0.0988547\pi$
$13$	0.0949418	+	0.260851i	0.0263321	+	0.0723469i	−0.925830	+	0.377940i	$0.876633\pi$
$14$	−0.792342	−	4.49360i	−0.211762	−	1.20096i
$15$	−1.34171	−	1.78880i	−0.346429	−	0.461866i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	−2.12818	−	2.53626i	−0.516159	−	0.615134i	0.443509	−	0.896270i	$-0.353733\pi$
$17$	−2.12818	−	2.53626i	−0.516159	−	0.615134i	−0.959668	+	0.281136i	$0.909289\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.90108	+	3.92249i	0.436138	+	0.899880i
$19$	1.90108	+	3.92249i	0.436138	+	0.899880i
$20$	1.63195	+	1.52864i	0.364916	+	0.341814i
$21$	−3.49540	+	2.93299i	−0.762758	+	0.640030i
$22$	1.53676	−	4.22221i	0.327638	−	0.900179i
$23$	−1.73438	−	0.305817i	−0.361642	−	0.0637673i	−0.0101251	−	0.999949i	$-0.503223\pi$
$23$	−1.73438	−	0.305817i	−0.361642	−	0.0637673i	−0.351517	+	0.936181i	$0.614334\pi$
$24$	0.173648	+	0.984808i	0.0354458	+	0.201023i
$25$	−2.01329	−	4.57675i	−0.402659	−	0.915350i
$26$	−0.138796	+	0.240401i	−0.0272201	+	0.0471466i
$27$	−0.866025	+	0.500000i	−0.166667	+	0.0962250i
$28$	2.93299	−	3.49540i	0.554282	−	0.660568i
$29$	8.06721	+	6.76920i	1.49804	+	1.25701i	0.883775	+	0.467911i	$0.154993\pi$
$29$	8.06721	+	6.76920i	1.49804	+	1.25701i	0.614269	+	0.789097i	$0.289451\pi$
$30$	0.507863	−	2.17763i	0.0927226	−	0.397579i
$31$	4.93003	−	8.53907i	0.885460	−	1.53366i	0.0402741	−	0.999189i	$-0.487177\pi$
$31$	4.93003	−	8.53907i	0.885460	−	1.53366i	0.845186	−	0.534473i	$-0.179490\pi$
$32$	−0.342020	−	0.939693i	−0.0604612	−	0.166116i
$33$	−4.42492	+	0.780234i	−0.770280	+	0.135821i
$34$	0.574924	−	3.26056i	0.0985987	−	0.559181i
$35$	−9.10124	+	4.61178i	−1.53839	+	0.779533i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$			4.60745i			0.757460i	0.925507	+	0.378730i	$0.123639\pi$
$37$			4.60745i			0.757460i	−0.925507	+	0.378730i	$0.876361\pi$
$38$	−1.78281	+	3.97764i	−0.289209	+	0.645258i
$39$	0.277591			0.0444502
$40$	−0.122006	+	2.23274i	−0.0192908	+	0.353027i
$41$	5.56646	+	2.02603i	0.869336	+	0.316412i	0.737898	−	0.674912i	$-0.235819\pi$
$41$	5.56646	+	2.02603i	0.869336	+	0.316412i	0.131438	+	0.991324i	$0.458041\pi$
$42$	−4.49360	−	0.792342i	−0.693377	−	0.122261i
$43$	−6.39239	+	1.12715i	−0.974830	+	0.171889i	−0.638303	−	0.769785i	$-0.720363\pi$
$43$	−6.39239	+	1.12715i	−0.974830	+	0.171889i	−0.336527	+	0.941674i	$0.609252\pi$
$44$	4.22221	−	1.53676i	0.636523	−	0.231675i
$45$	−2.13981	+	0.648993i	−0.318985	+	0.0967462i
$46$	−0.880565	−	1.52518i	−0.129832	−	0.224876i
$47$	5.60594	−	6.68089i	0.817710	−	0.974509i	−0.182252	−	0.983252i	$-0.558339\pi$
$47$	5.60594	−	6.68089i	0.817710	−	0.974509i	0.999962	+	0.00874326i	$0.00278310\pi$
$48$	−0.642788	+	0.766044i	−0.0927784	+	0.110569i
$49$	6.91010	+	11.9686i	0.987157	+	1.70981i
$50$	2.21187	−	4.48415i	0.312806	−	0.634155i
$51$	−3.11119	+	1.13238i	−0.435653	+	0.158565i
$52$	−0.273374	+	0.0482032i	−0.0379102	+	0.00668459i
$53$	0.0358120	+	0.00631463i	0.00491916	+	0.000867381i	0.176107	−	0.984371i	$-0.443649\pi$
$53$	0.0358120	+	0.00631463i	0.00491916	+	0.000867381i	−0.171188	+	0.985238i	$0.554761\pi$
$54$	−0.939693	−	0.342020i	−0.127876	−	0.0465430i
$55$	−10.0321	−	0.548194i	−1.35273	−	0.0739184i
$56$	4.56292			0.609745
$57$	4.33614	−	0.444863i	0.574336	−	0.0589235i
$58$			10.5310i			1.38279i
$59$	7.58989	−	6.36868i	0.988120	−	0.829131i	0.00282536	−	0.999996i	$-0.499101\pi$
$59$	7.58989	−	6.36868i	0.988120	−	0.829131i	0.985294	+	0.170865i	$0.0546562\pi$
$60$	1.99461	−	1.01071i	0.257503	−	0.130482i
$61$	1.82237	−	10.3352i	0.233330	−	1.32328i	−0.612772	−	0.790260i	$-0.709946\pi$
$61$	1.82237	−	10.3352i	0.233330	−	1.32328i	0.846102	−	0.533021i	$-0.178943\pi$
$62$	9.71027	−	1.71218i	1.23321	−	0.217447i
$63$	1.56061	+	4.28774i	0.196618	+	0.540204i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	0.604492	+	0.140978i	0.0749779	+	0.0174862i
$66$	−3.44198	−	2.88816i	−0.423678	−	0.355508i
$67$	3.96292	−	4.72282i	0.484148	−	0.576985i	−0.467571	−	0.883955i	$-0.654871\pi$
$67$	3.96292	−	4.72282i	0.484148	−	0.576985i	0.951719	+	0.306971i	$0.0993154\pi$
$68$	2.86729	−	1.65543i	0.347709	−	0.200750i
$69$	−0.880565	+	1.52518i	−0.106008	+	0.183611i
$70$	−9.38299	−	4.00756i	−1.12148	−	0.478995i
$71$	2.08816	+	11.8426i	0.247819	+	1.40545i	0.813852	+	0.581072i	$0.197366\pi$
$71$	2.08816	+	11.8426i	0.247819	+	1.40545i	−0.566033	+	0.824383i	$0.691523\pi$
$72$	0.984808	+	0.173648i	0.116061	+	0.0204646i
$73$	3.62366	−	9.95594i	0.424118	−	1.16525i	−0.525212	−	0.850972i	$-0.676014\pi$
$73$	3.62366	−	9.95594i	0.424118	−	1.16525i	0.949329	−	0.314283i	$-0.101764\pi$
$74$	−3.52951	+	2.96161i	−0.410298	+	0.344280i
$75$	−4.98933	+	0.326536i	−0.576118	+	0.0377051i
$76$	−4.19301	+	1.19107i	−0.480972	+	0.136625i
$77$			20.5020i			2.33642i
$78$	0.178432	+	0.212647i	0.0202035	+	0.0240776i
$79$	−10.0990	−	3.67572i	−1.13622	−	0.413551i	−0.295674	−	0.955289i	$-0.595544\pi$
$79$	−10.0990	−	3.67572i	−1.13622	−	0.413551i	−0.840547	+	0.541738i	$0.817766\pi$
$80$	−1.78880	+	1.34171i	−0.199994	+	0.150008i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	2.02603	+	5.56646i	0.223737	+	0.614713i
$83$	1.27349	+	0.735249i	0.139784	+	0.0807040i	0.568261	−	0.822848i	$-0.307616\pi$
$83$	1.27349	+	0.735249i	0.139784	+	0.0807040i	−0.428477	+	0.903553i	$0.640950\pi$
$84$	−2.28146	−	3.95160i	−0.248927	−	0.431155i
$85$	−7.35011	+	0.885848i	−0.797231	+	0.0960838i
$86$	−4.97240	−	4.17234i	−0.536187	−	0.449914i
$87$	9.12011	−	5.26550i	0.977779	−	0.564521i
$88$	3.89121	+	2.24659i	0.414805	+	0.239488i
$89$	7.51517	−	2.73530i	0.796606	−	0.289941i	0.0885270	−	0.996074i	$-0.471784\pi$
$89$	7.51517	−	2.73530i	0.796606	−	0.289941i	0.708079	+	0.706133i	$0.249562\pi$
$90$	−1.87260	−	1.22203i	−0.197390	−	0.128813i
$91$	0.219947	−	1.24738i	0.0230567	−	0.130761i
$92$	0.602342	−	1.65492i	0.0627985	−	0.172537i
$93$	−6.33793	−	7.55325i	−0.657212	−	0.783235i
$94$	8.72129			0.899532
$95$	9.66844	+	1.23342i	0.991961	+	0.126546i
$96$	−1.00000			−0.102062
$97$	−1.78839	−	2.13132i	−0.181583	−	0.216403i	0.667573	−	0.744545i	$-0.267333\pi$
$97$	−1.78839	−	2.13132i	−0.181583	−	0.216403i	−0.849156	+	0.528142i	$0.822889\pi$
$98$	−4.72679	+	12.9867i	−0.477478	+	1.31186i
$99$	−0.780234	+	4.42492i	−0.0784164	+	0.444722i
$100$	4.85682	−	1.18796i	0.485682	−	0.118796i
$101$	−13.6202	+	4.95734i	−1.35526	+	0.493274i	−0.914585	−	0.404393i	$-0.867483\pi$
$101$	−13.6202	+	4.95734i	−1.35526	+	0.493274i	−0.440674	+	0.897667i	$0.645261\pi$
$102$	−2.86729	−	1.65543i	−0.283904	−	0.163912i
$103$	−9.37046	+	5.41004i	−0.923298	+	0.533067i	−0.884686	−	0.466188i	$-0.845627\pi$
$103$	−9.37046	+	5.41004i	−0.923298	+	0.533067i	−0.0386126	+	0.999254i	$0.512294\pi$
$104$	−0.212647	−	0.178432i	−0.0208518	−	0.0174967i
$105$	1.22085	+	10.1297i	0.119143	+	0.988556i
$106$	0.0181822	+	0.0314926i	0.00176602	+	0.00305883i
$107$	9.65849	+	5.57633i	0.933721	+	0.539084i	0.887987	−	0.459870i	$-0.152104\pi$
$107$	9.65849	+	5.57633i	0.933721	+	0.539084i	0.0457346	+	0.998954i	$0.485437\pi$
$108$	−0.342020	−	0.939693i	−0.0329109	−	0.0904220i
$109$	0.223452	+	1.26726i	0.0214028	+	0.121381i	0.993637	−	0.112627i	$-0.0359267\pi$
$109$	0.223452	+	1.26726i	0.0214028	+	0.121381i	−0.972234	+	0.234009i	$0.924816\pi$
$110$	−6.02857	−	8.03741i	−0.574802	−	0.766337i
$111$	4.32959	+	1.57584i	0.410946	+	0.149572i
$112$	2.93299	+	3.49540i	0.277141	+	0.330284i
$113$			14.1299i			1.32923i	0.747184	+	0.664617i	$0.231405\pi$
$113$			14.1299i			1.32923i	−0.747184	+	0.664617i	$0.768595\pi$
$114$	3.12800	+	3.03572i	0.292964	+	0.284321i
$115$	−2.69213	+	2.87408i	−0.251042	+	0.268009i
$116$	−8.06721	+	6.76920i	−0.749022	+	0.628504i
$117$	0.0949418	−	0.260851i	0.00877738	−	0.0241156i
$118$	9.75738	+	1.72049i	0.898239	+	0.158384i
$119$	2.62333	+	14.8776i	0.240480	+	1.36383i
$120$	2.05636	+	0.878289i	0.187719	+	0.0801764i
$121$	−4.59436	+	7.95766i	−0.417669	+	0.723424i
$122$	9.08858	−	5.24729i	0.822841	−	0.475068i
$123$	3.80769	−	4.53782i	0.343327	−	0.409162i
$124$	7.55325	+	6.33793i	0.678302	+	0.569163i
$125$	−11.0307	−	1.82282i	−0.986620	−	0.163038i
$126$	−2.28146	+	3.95160i	−0.203248	+	0.352037i
$127$	−0.650069	−	1.78605i	−0.0576843	−	0.158486i	0.907503	−	0.420045i	$-0.137986\pi$
$127$	−0.650069	−	1.78605i	−0.0576843	−	0.158486i	−0.965188	+	0.261559i	$0.915763\pi$
$128$	0.984808	−	0.173648i	0.0870455	−	0.0153485i
$129$	−1.12715	+	6.39239i	−0.0992401	+	0.562818i
$130$	0.280564	+	0.553686i	0.0246071	+	0.0485615i
$131$	−0.868613	+	0.728853i	−0.0758911	+	0.0636802i	−0.679944	−	0.733264i	$-0.737996\pi$
$131$	−0.868613	+	0.728853i	−0.0758911	+	0.0636802i	0.604053	+	0.796944i	$0.293552\pi$
$132$		−	4.49319i		−	0.391082i
$133$	1.43667	−	19.8373i	0.124575	−	1.72012i
$134$	6.16521			0.532593
$135$	−0.122006	+	2.23274i	−0.0105006	+	0.192163i
$136$	3.11119	+	1.13238i	0.266782	+	0.0971007i
$137$	−0.358234	−	0.0631663i	−0.0306060	−	0.00539666i	0.158324	−	0.987387i	$-0.449391\pi$
$137$	−0.358234	−	0.0631663i	−0.0306060	−	0.00539666i	−0.188930	+	0.981991i	$0.560502\pi$
$138$	−1.73438	+	0.305817i	−0.147640	+	0.0260329i
$139$	−12.7969	+	4.65769i	−1.08542	+	0.395060i	−0.821922	−	0.569600i	$-0.807098\pi$
$139$	−12.7969	+	4.65769i	−1.08542	+	0.395060i	−0.263497	+	0.964660i	$0.584876\pi$
$140$	−2.96130	−	9.76380i	−0.250276	−	0.825191i
$141$	−4.36064	−	7.55286i	−0.367232	−	0.636065i
$142$	−7.72969	+	9.21188i	−0.648661	+	0.773044i
$143$	0.801729	−	0.955464i	0.0670440	−	0.0798999i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	22.5344	−	6.83455i	1.87138	−	0.567578i
$146$	9.95594	−	3.62366i	0.823959	−	0.299897i
$147$	13.6102	−	2.39985i	1.12255	−	0.197937i
$148$	−4.53745	−	0.800076i	−0.372976	−	0.0657658i
$149$	−6.10162	−	2.22081i	−0.499864	−	0.181936i	0.0797686	−	0.996813i	$-0.474582\pi$
$149$	−6.10162	−	2.22081i	−0.499864	−	0.181936i	−0.579633	+	0.814878i	$0.696804\pi$
$150$	−3.45722	−	3.61215i	−0.282281	−	0.294931i
$151$	−17.6013			−1.43238			−0.716189	−	0.697907i	$-0.754115\pi$
$151$	−17.6013			−1.43238			−0.716189	+	0.697907i	$0.754115\pi$
$152$	−3.60763	−	2.44643i	−0.292617	−	0.198432i
$153$			3.31086i			0.267667i
$154$	−15.7055	+	13.1785i	−1.26558	+	1.06195i
$155$	−9.96565	−	19.6670i	−0.800460	−	1.57969i
$156$	−0.0482032	+	0.273374i	−0.00385935	+	0.0218874i
$157$	−5.93556	+	1.04660i	−0.473709	+	0.0835277i	−0.405406	−	0.914137i	$-0.632870\pi$
$157$	−5.93556	+	1.04660i	−0.473709	+	0.0835277i	−0.0683034	+	0.997665i	$0.521759\pi$
$158$	−3.67572	−	10.0990i	−0.292425	−	0.803430i
$159$	0.0181822	−	0.0314926i	0.00144195	−	0.00249752i
$160$	−2.17763	−	0.507863i	−0.172157	−	0.0401501i
$161$	6.15585	+	5.16537i	0.485149	+	0.407088i
$162$	−0.642788	+	0.766044i	−0.0505022	+	0.0601861i
$163$	17.7277	−	10.2351i	1.38854	−	0.801675i	0.395390	−	0.918513i	$-0.370609\pi$
$163$	17.7277	−	10.2351i	1.38854	−	0.801675i	0.993151	+	0.116839i	$0.0372760\pi$
$164$	−2.96185	+	5.13008i	−0.231282	+	0.400592i
$165$	−3.94631	+	9.23960i	−0.307220	+	0.719302i
$166$	0.255349	+	1.44816i	0.0198189	+	0.112399i
$167$	0.930482	+	0.164069i	0.0720028	+	0.0126960i	0.209534	−	0.977801i	$-0.432805\pi$
$167$	0.930482	+	0.164069i	0.0720028	+	0.0126960i	−0.137531	+	0.990498i	$0.543917\pi$
$168$	1.56061	−	4.28774i	0.120404	−	0.330806i
$169$	9.89955	−	8.30671i	0.761504	−	0.638978i
$170$	−5.40316	−	5.06110i	−0.414403	−	0.388169i
$171$	1.06501	−	4.22679i	0.0814435	−	0.323231i
$172$		−	6.49100i		−	0.494934i
$173$	8.81893	+	10.5100i	0.670491	+	0.799060i	0.988851	−	0.148910i	$-0.0475764\pi$
$173$	8.81893	+	10.5100i	0.670491	+	0.799060i	−0.318360	+	0.947970i	$0.603132\pi$
$174$	9.89590	+	3.60181i	0.750206	+	0.273053i
$175$	−2.48593	+	22.6787i	−0.187919	+	1.71435i
$176$	0.780234	+	4.42492i	0.0588123	+	0.333541i
$177$	−3.38870	−	9.31038i	−0.254710	−	0.699811i
$178$	6.92602	+	3.99874i	0.519127	+	0.299718i
$179$	−3.47408	−	6.01728i	−0.259665	−	0.449752i	0.706487	−	0.707726i	$-0.250279\pi$
$179$	−3.47408	−	6.01728i	−0.259665	−	0.449752i	−0.966152	+	0.257973i	$0.916945\pi$
$180$	−0.267559	−	2.22000i	−0.0199426	−	0.165469i
$181$	−1.39131	−	1.16745i	−0.103415	−	0.0867756i	0.589614	−	0.807685i	$-0.299280\pi$
$181$	−1.39131	−	1.16745i	−0.103415	−	0.0867756i	−0.693029	+	0.720910i	$0.743724\pi$
$182$	1.09693	−	0.633313i	0.0813099	−	0.0469443i
$183$	−9.08858	−	5.24729i	−0.671847	−	0.387891i
$184$	1.65492	−	0.602342i	0.122002	−	0.0444053i
$185$	8.62793	+	5.63044i	0.634338	+	0.413958i
$186$	1.71218	−	9.71027i	0.125543	−	0.711991i
$187$	−5.08799	+	13.9791i	−0.372071	+	1.02226i
$188$	5.60594	+	6.68089i	0.408855	+	0.487254i
$189$	4.56292			0.331903
$190$	5.26990	+	8.19928i	0.382319	+	0.594838i
$191$	−1.84493			−0.133494			−0.0667471	−	0.997770i	$-0.521262\pi$
$191$	−1.84493			−0.133494			−0.0667471	+	0.997770i	$0.521262\pi$
$192$	−0.642788	−	0.766044i	−0.0463892	−	0.0552845i
$193$	−2.42423	+	6.66051i	−0.174500	+	0.479434i	−0.995852	−	0.0909873i	$-0.970998\pi$
$193$	−2.42423	+	6.66051i	−0.174500	+	0.479434i	0.821352	+	0.570421i	$0.193220\pi$
$194$	0.483131	−	2.73997i	0.0346868	−	0.196718i
$195$	0.339225	−	0.519819i	0.0242924	−	0.0372250i
$196$	−12.9867	+	4.72679i	−0.927624	+	0.337628i
$197$	−10.3657	−	5.98466i	−0.738528	−	0.426389i	0.0830061	−	0.996549i	$-0.473548\pi$
$197$	−10.3657	−	5.98466i	−0.738528	−	0.426389i	−0.821534	+	0.570160i	$0.806881\pi$
$198$	−3.89121	+	2.24659i	−0.276536	+	0.159658i
$199$	2.08639	+	1.75069i	0.147900	+	0.124103i	0.713736	−	0.700415i	$-0.247002\pi$
$199$	2.08639	+	1.75069i	0.147900	+	0.124103i	−0.565835	+	0.824518i	$0.691446\pi$
$200$	4.03194	+	2.95694i	0.285101	+	0.209087i
$201$	−3.08260	−	5.33923i	−0.217430	−	0.376600i
$202$	−12.5524	−	7.24715i	−0.883186	−	0.509908i
$203$	−16.4348	−	45.1542i	−1.15350	−	3.16920i
$204$	−0.574924	−	3.26056i	−0.0402527	−	0.228285i
$205$	10.5963	−	7.94792i	0.740079	−	0.555107i
$206$	−10.1675	−	3.70068i	−0.708406	−	0.257839i
$207$	1.13203	+	1.34910i	0.0786817	+	0.0937692i
$208$		−	0.277591i		−	0.0192475i
$209$	10.9923	−	16.2097i	0.760351	−	1.12125i
$210$	−6.97504	+	7.44646i	−0.481324	+	0.513855i
$211$	3.15935	−	2.65101i	0.217499	−	0.182503i	−0.527528	−	0.849538i	$-0.676881\pi$
$211$	3.15935	−	2.65101i	0.217499	−	0.182503i	0.745027	+	0.667034i	$0.232437\pi$
$212$	−0.0124374	+	0.0341714i	−0.000854203	+	0.00234690i
$213$	11.8426	+	2.08816i	0.811439	+	0.143079i
$214$	1.93664	+	10.9832i	0.132386	+	0.750798i
$215$	−5.70097	+	13.3478i	−0.388803	+	0.910314i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−38.9630	+	22.4953i	−2.64498	+	1.52708i
$218$	−0.827144	+	0.985752i	−0.0560213	+	0.0667635i
$219$	−8.11615	−	6.81026i	−0.548439	−	0.460195i
$220$	2.28192	−	9.78450i	0.153847	−	0.659671i
$221$	0.459533	−	0.795934i	0.0309115	−	0.0535403i
$222$	1.57584	+	4.32959i	0.105764	+	0.290583i
$223$	−7.35808	+	1.29743i	−0.492733	+	0.0868822i	−0.414493	−	0.910052i	$-0.636041\pi$
$223$	−7.35808	+	1.29743i	−0.492733	+	0.0868822i	−0.0782400	+	0.996935i	$0.524930\pi$
$224$	−0.792342	+	4.49360i	−0.0529406	+	0.300241i
$225$	−1.39961	+	4.80011i	−0.0933071	+	0.320008i
$226$	−10.8242	+	9.08256i	−0.720013	+	0.604163i
$227$			13.7120i			0.910100i	0.890466	+	0.455050i	$0.150379\pi$
$227$			13.7120i			0.910100i	−0.890466	+	0.455050i	$0.849621\pi$
$228$	−0.314858	+	4.34751i	−0.0208520	+	0.287921i
$229$	22.7206			1.50142			0.750711	−	0.660631i	$-0.229711\pi$
$229$	22.7206			1.50142			0.750711	+	0.660631i	$0.229711\pi$
$230$	−3.93214	−	0.214868i	−0.259278	−	0.0141680i
$231$	19.2656	+	7.01211i	1.26758	+	0.461363i
$232$	−10.3710	−	1.82869i	−0.680890	−	0.120059i
$233$	18.1538	−	3.20101i	1.18930	−	0.209705i	0.456230	−	0.889862i	$-0.349199\pi$
$233$	18.1538	−	3.20101i	1.18930	−	0.209705i	0.733067	+	0.680157i	$0.238088\pi$
$234$	0.260851	−	0.0949418i	0.0170523	−	0.00620654i
$235$	−5.66006	−	18.6619i	−0.369221	−	1.21737i
$236$	4.95395	+	8.58049i	0.322475	+	0.558543i
$237$	−6.90809	+	8.23275i	−0.448729	+	0.534774i
$238$	−9.71069	+	11.5728i	−0.629451	+	0.750150i
$239$	8.45797	+	14.6496i	0.547101	+	0.947606i	0.998471	+	0.0552695i	$0.0176018\pi$
$239$	8.45797	+	14.6496i	0.547101	+	0.947606i	−0.451371	+	0.892336i	$0.649065\pi$
$240$	0.648993	+	2.13981i	0.0418923	+	0.138124i
$241$	3.77043	−	1.37232i	0.242875	−	0.0883991i	−0.217715	−	0.976012i	$-0.569860\pi$
$241$	3.77043	−	1.37232i	0.242875	−	0.0883991i	0.460589	+	0.887613i	$0.347638\pi$
$242$	−9.04912	+	1.59560i	−0.581700	+	0.102569i
$243$	0.984808	+	0.173648i	0.0631754	+	0.0111395i
$244$	9.86169	+	3.58936i	0.631330	+	0.229785i
$245$	30.8569	+	1.68614i	1.97137	+	0.107724i
$246$	5.92371			0.377682
$247$	−0.842690	+	0.868306i	−0.0536191	+	0.0552490i
$248$			9.86006i			0.626115i
$249$	1.12647	−	0.945218i	0.0713869	−	0.0599007i
$250$	−5.69407	−	9.62173i	−0.360124	−	0.608531i
$251$	2.34362	−	13.2913i	0.147928	−	0.838942i	−0.817041	−	0.576579i	$-0.804387\pi$
$251$	2.34362	−	13.2913i	0.147928	−	0.838942i	0.964969	−	0.262363i	$-0.0845017\pi$
$252$	−4.49360	+	0.792342i	−0.283070	+	0.0499129i
$253$	2.70644	+	7.43587i	0.170152	+	0.467489i
$254$	0.950337	−	1.64603i	0.0596294	−	0.103281i
$255$	−1.68146	+	7.20982i	−0.105297	+	0.451497i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	5.85072	−	6.97262i	0.364958	−	0.434940i	−0.552049	−	0.833812i	$-0.686154\pi$
$257$	5.85072	−	6.97262i	0.364958	−	0.434940i	0.917007	+	0.398872i	$0.130598\pi$
$258$	−5.62137	+	3.24550i	−0.349971	+	0.202056i
$259$	10.5117	−	18.2068i	0.653166	−	1.13132i
$260$	−0.243805	+	0.570827i	−0.0151202	+	0.0354012i
$261$	−1.82869	−	10.3710i	−0.113193	−	0.641949i
$262$	−1.11667	−	0.196899i	−0.0689880	−	0.0121644i
$263$	10.4087	−	28.5976i	0.641827	−	1.76340i	−0.00408463	−	0.999992i	$-0.501300\pi$
$263$	10.4087	−	28.5976i	0.641827	−	1.76340i	0.645911	−	0.763413i	$-0.276478\pi$
$264$	3.44198	−	2.88816i	0.211839	−	0.177754i
$265$	0.0555881	−	0.0593451i	0.00341475	−	0.00364554i
$266$	16.1198	−	11.6506i	0.988366	−	0.714346i
$267$		−	7.99748i		−	0.489438i
$268$	3.96292	+	4.72282i	0.242074	+	0.288492i
$269$	18.3078	+	6.66351i	1.11625	+	0.406281i	0.833282	−	0.552848i	$-0.186459\pi$
$269$	18.3078	+	6.66351i	1.11625	+	0.406281i	0.282967	+	0.959130i	$0.408681\pi$
$270$	−1.78880	+	1.34171i	−0.108863	+	0.0816541i
$271$	−2.51902	−	14.2861i	−0.153020	−	0.867817i	−0.960574	−	0.278024i	$-0.910320\pi$
$271$	−2.51902	−	14.2861i	−0.153020	−	0.867817i	0.807554	−	0.589793i	$-0.200791\pi$
$272$	1.13238	+	3.11119i	0.0686606	+	0.188643i
$273$	−1.09693	−	0.633313i	−0.0663892	−	0.0383299i
$274$	−0.181880	−	0.315025i	−0.0109878	−	0.0190314i
$275$	−13.2861	+	18.1162i	−0.801180	+	1.09245i
$276$	−1.34910	−	1.13203i	−0.0812065	−	0.0681404i
$277$	3.87701	−	2.23839i	0.232947	−	0.134492i	−0.378984	−	0.925403i	$-0.623726\pi$
$277$	3.87701	−	2.23839i	0.232947	−	0.134492i	0.611931	+	0.790911i	$0.290393\pi$
$278$	−11.7937	−	6.80909i	−0.707338	−	0.408382i
$279$	−9.26543	+	3.37234i	−0.554707	+	0.201897i
$280$	5.57601	−	8.54454i	0.333231	−	0.510634i
$281$	−0.342386	+	1.94177i	−0.0204251	+	0.115836i	−0.993316	−	0.115429i	$-0.963176\pi$
$281$	−0.342386	+	1.94177i	−0.0204251	+	0.115836i	0.972891	+	0.231266i	$0.0742867\pi$
$282$	2.98286	−	8.19533i	0.177627	−	0.488025i
$283$	19.0236	+	22.6715i	1.13084	+	1.34768i	0.929786	+	0.368100i	$0.119992\pi$
$283$	19.0236	+	22.6715i	1.13084	+	1.34768i	0.201052	+	0.979581i	$0.435564\pi$
$284$	−12.0253			−0.713568
$285$	4.46583	−	8.66351i	0.264533	−	0.513182i
$286$	1.24727			0.0737526
$287$	−17.3741	−	20.7057i	−1.02556	−	1.22222i
$288$	−0.342020	+	0.939693i	−0.0201537	+	0.0553719i
$289$	1.04853	−	5.94650i	0.0616781	−	0.349794i
$290$	19.7204	+	12.8692i	1.15802	+	0.755704i
$291$	−2.61445	+	0.951582i	−0.153262	+	0.0557827i
$292$	9.17544	+	5.29744i	0.536952	+	0.310009i
$293$	−7.01843	+	4.05209i	−0.410021	+	0.236726i	−0.690799	−	0.723047i	$-0.742741\pi$
$293$	−7.01843	+	4.05209i	−0.410021	+	0.236726i	0.280778	+	0.959773i	$0.409408\pi$
$294$	10.5869	+	8.88346i	0.617440	+	0.518094i
$295$	−2.65095	−	21.9956i	−0.154344	−	1.28063i
$296$	−2.30373	−	3.99017i	−0.133901	−	0.231924i
$297$	3.89121	+	2.24659i	0.225791	+	0.130361i
$298$	−2.22081	−	6.10162i	−0.128648	−	0.353458i
$299$	−0.0848922	−	0.481448i	−0.00490944	−	0.0278428i
$300$	0.544813	−	4.97023i	0.0314548	−	0.286956i
$301$	27.8317	+	10.1299i	1.60419	+	0.583879i
$302$	−11.3139	−	13.4834i	−0.651043	−	0.775883i
$303$			14.4943i			0.832676i
$304$	−0.444863	−	4.33614i	−0.0255146	−	0.248695i
$305$	−17.1267	−	16.0424i	−0.980670	−	0.918586i
$306$	−2.53626	+	2.12818i	−0.144989	+	0.121660i
$307$	−2.79417	+	7.67693i	−0.159472	+	0.438145i	−0.993535	−	0.113523i	$-0.963786\pi$
$307$	−2.79417	+	7.67693i	−0.159472	+	0.438145i	0.834063	+	0.551668i	$0.186009\pi$
$308$	−20.1906	−	3.56014i	−1.15046	−	0.202858i
$309$	1.87889	+	10.6557i	0.106886	+	0.606181i
$310$	8.65998	−	20.2758i	0.491854	−	1.15159i
$311$	1.76688	−	3.06033i	0.100191	−	0.173536i	−0.811572	−	0.584252i	$-0.801388\pi$
$311$	1.76688	−	3.06033i	0.100191	−	0.173536i	0.911763	+	0.410716i	$0.134721\pi$
$312$	−0.240401	+	0.138796i	−0.0136100	+	0.00785776i
$313$	14.2519	−	16.9847i	0.805563	−	0.960033i	−0.194218	−	0.980958i	$-0.562217\pi$
$313$	14.2519	−	16.9847i	0.805563	−	0.960033i	0.999781	+	0.0209256i	$0.00666131\pi$
$314$	−4.61704	−	3.87416i	−0.260555	−	0.218631i
$315$	9.93635	+	2.31733i	0.559850	+	0.130567i
$316$	5.37354	−	9.30725i	0.302285	−	0.523574i
$317$	−0.974307	−	2.67689i	−0.0547225	−	0.150349i	0.909320	−	0.416098i	$-0.136603\pi$
$317$	−0.974307	−	2.67689i	−0.0547225	−	0.150349i	−0.964042	+	0.265749i	$0.914381\pi$
$318$	0.0358120	−	0.00631463i	0.00200824	−	0.000354107i
$319$	8.21664	−	46.5989i	0.460043	−	2.60904i
$320$	−1.01071	−	1.99461i	−0.0565003	−	0.111502i
$321$	8.54343	−	7.16879i	0.476848	−	0.400123i
$322$			8.03589i			0.447823i
$323$	5.90262	−	13.1694i	0.328430	−	0.732764i
$324$	−1.00000			−0.0555556
$325$	1.00270	−	0.959694i	0.0556199	−	0.0532342i
$326$	19.2357	+	7.00122i	1.06537	+	0.387762i
$327$	1.26726	+	0.223452i	0.0700795	+	0.0123569i
$328$	−5.83371	+	1.02864i	−0.322113	+	0.0567972i
$329$	−37.3946	+	13.6105i	−2.06163	+	0.750372i
$330$	−9.61459	+	2.91605i	−0.529266	+	0.160523i
$331$	−4.65678	−	8.06578i	−0.255960	−	0.443335i	0.709196	−	0.705011i	$-0.249058\pi$
$331$	−4.65678	−	8.06578i	−0.255960	−	0.443335i	−0.965156	+	0.261676i	$0.915725\pi$
$332$	−0.945218	+	1.12647i	−0.0518756	+	0.0618229i
$333$	2.96161	−	3.52951i	0.162295	−	0.193416i
$334$	0.472418	+	0.818252i	0.0258496	+	0.0447728i
$335$	−4.00118	−	13.1924i	−0.218608	−	0.720778i
$336$	4.28774	−	1.56061i	0.233915	−	0.0851382i
$337$	4.21183	−	0.742660i	0.229433	−	0.0404553i	−0.0577494	−	0.998331i	$-0.518392\pi$
$337$	4.21183	−	0.742660i	0.229433	−	0.0404553i	0.287183	+	0.957876i	$0.407281\pi$
$338$	12.7266	+	2.24405i	0.692237	+	0.122060i
$339$	13.2778	+	4.83273i	0.721152	+	0.262478i
$340$	0.403943	−	7.39227i	0.0219069	−	0.400902i
$341$	−44.3031			−2.39915
$342$	3.92249	−	1.90108i	0.212104	−	0.102799i
$343$		−	31.1200i		−	1.68032i
$344$	4.97240	−	4.17234i	0.268094	−	0.224957i
$345$	1.77999	+	3.51277i	0.0958314	+	0.189121i
$346$	−2.38242	+	13.5114i	−0.128080	+	0.726377i
$347$	26.2267	−	4.62447i	1.40792	−	0.248254i	0.582527	−	0.812812i	$-0.302064\pi$
$347$	26.2267	−	4.62447i	1.40792	−	0.248254i	0.825394	+	0.564557i	$0.190953\pi$
$348$	3.60181	+	9.89590i	0.193078	+	0.530476i
$349$	−11.6011	+	20.0937i	−0.620993	+	1.07559i	0.368308	+	0.929704i	$0.379937\pi$
$349$	−11.6011	+	20.0937i	−0.620993	+	1.07559i	−0.989301	+	0.145888i	$0.953396\pi$
$350$	−18.9708	+	12.6733i	−1.01403	+	0.677415i
$351$	−0.212647	−	0.178432i	−0.0113503	−	0.00952401i
$352$	−2.88816	+	3.44198i	−0.153940	+	0.183458i
$353$	−8.61958	+	4.97652i	−0.458774	+	0.264873i	−0.711529	−	0.702657i	$-0.751997\pi$
$353$	−8.61958	+	4.97652i	−0.458774	+	0.264873i	0.252755	+	0.967530i	$0.418663\pi$
$354$	4.95395	−	8.58049i	0.263299	−	0.456048i
$355$	24.7282	+	10.5616i	1.31244	+	0.560554i
$356$	1.38875	+	7.87598i	0.0736035	+	0.417426i
$357$	14.8776	+	2.62333i	0.787409	+	0.138841i
$358$	2.37641	−	6.52913i	0.125597	−	0.345075i
$359$	1.74971	−	1.46818i	0.0923459	−	0.0774874i	−0.595446	−	0.803395i	$-0.703025\pi$
$359$	1.74971	−	1.46818i	0.0923459	−	0.0774874i	0.687792	+	0.725908i	$0.258580\pi$
$360$	1.52864	−	1.63195i	0.0805663	−	0.0860114i
$361$	−11.7718	+	14.9139i	−0.619567	+	0.784943i
$362$		−	1.81622i		−	0.0954587i
$363$	5.90640	+	7.03897i	0.310005	+	0.369450i
$364$	1.19024	+	0.433212i	0.0623855	+	0.0227065i
$365$	−14.2153	−	18.9521i	−0.744063	−	0.992000i
$366$	−1.82237	−	10.3352i	−0.0952566	−	0.540227i
$367$	−1.36591	−	3.75280i	−0.0712997	−	0.195894i	0.898924	−	0.438104i	$-0.144350\pi$
$367$	−1.36591	−	3.75280i	−0.0712997	−	0.195894i	−0.970224	+	0.242210i	$0.922128\pi$
$368$	1.52518	+	0.880565i	0.0795057	+	0.0459026i
$369$	−2.96185	−	5.13008i	−0.154188	−	0.267061i
$370$	1.23276	+	10.2286i	0.0640883	+	0.531757i
$371$	−0.127108	−	0.106657i	−0.00659913	−	0.00553733i
$372$	8.53907	−	4.93003i	0.442730	−	0.255610i
$373$	−29.7610	−	17.1825i	−1.54097	−	0.889677i	−0.998778	−	0.0494196i	$-0.984263\pi$
$373$	−29.7610	−	17.1825i	−1.54097	−	0.889677i	−0.542188	−	0.840257i	$-0.682404\pi$
$374$	−13.9791	+	5.08799i	−0.722844	+	0.263094i
$375$	−5.48563	+	9.74207i	−0.283277	+	0.503078i
$376$	−1.51444	+	8.58879i	−0.0781011	+	0.442933i
$377$	−0.999833	+	2.74702i	−0.0514940	+	0.141479i
$378$	2.93299	+	3.49540i	0.150857	+	0.179784i
$379$	−10.0230			−0.514846			−0.257423	−	0.966299i	$-0.582873\pi$
$379$	−10.0230			−0.514846			−0.257423	+	0.966299i	$0.582873\pi$
$380$	−2.89358	+	9.30737i	−0.148438	+	0.477458i
$381$	−1.90067			−0.0973745
$382$	−1.18590	−	1.41330i	−0.0606757	−	0.0723105i
$383$	−10.8423	+	29.7890i	−0.554015	+	1.52214i	0.274165	+	0.961683i	$0.411599\pi$
$383$	−10.8423	+	29.7890i	−0.554015	+	1.52214i	−0.828180	+	0.560462i	$0.810624\pi$
$384$	0.173648	−	0.984808i	0.00886145	−	0.0502558i
$385$	38.3922	+	25.0541i	1.95665	+	1.27687i
$386$	−6.66051	+	2.42423i	−0.339011	+	0.123390i
$387$	5.62137	+	3.24550i	0.285750	+	0.164978i
$388$	2.40949	−	1.39112i	0.122323	−	0.0706234i
$389$	10.7859	+	9.05043i	0.546866	+	0.458875i	0.873878	−	0.486145i	$-0.161597\pi$
$389$	10.7859	+	9.05043i	0.546866	+	0.458875i	−0.327012	+	0.945020i	$0.606042\pi$
$390$	0.616254	−	0.0742720i	0.0312052	−	0.00376091i
$391$	2.91543	+	5.04966i	0.147439	+	0.255373i
$392$	−11.9686	−	6.91010i	−0.604508	−	0.349013i
$393$	0.387815	+	1.06551i	0.0195627	+	0.0537480i
$394$	−2.07845	−	11.7875i	−0.104711	−	0.593844i
$395$	−19.2244	+	14.4195i	−0.967284	+	0.725525i
$396$	−4.22221	−	1.53676i	−0.212174	−	0.0772251i
$397$	6.63992	+	7.91314i	0.333248	+	0.397149i	0.906484	−	0.422241i	$-0.138756\pi$
$397$	6.63992	+	7.91314i	0.333248	+	0.397149i	−0.573236	+	0.819391i	$0.694312\pi$
$398$			2.72359i			0.136521i
$399$	−18.1496	−	8.13480i	−0.908618	−	0.407249i
$400$	0.326536	+	4.98933i	0.0163268	+	0.249466i
$401$	−7.23499	+	6.07087i	−0.361298	+	0.303165i	−0.805308	−	0.592857i	$-0.798000\pi$
$401$	−7.23499	+	6.07087i	−0.361298	+	0.303165i	0.444010	+	0.896022i	$0.353556\pi$
$402$	2.10863	−	5.79340i	0.105169	−	0.288949i
$403$	2.69549	+	0.475287i	0.134272	+	0.0236757i
$404$	−2.51691	−	14.2741i	−0.125221	−	0.710163i
$405$	2.05636	+	0.878289i	0.102181	+	0.0436425i
$406$	24.0260	−	41.6143i	1.19239	−	2.06528i
$407$	17.9286	−	10.3511i	0.888687	−	0.513083i
$408$	2.12818	−	2.53626i	0.105360	−	0.125564i
$409$	7.40637	+	6.21468i	0.366221	+	0.307296i	0.807265	−	0.590190i	$-0.200947\pi$
$409$	7.40637	+	6.21468i	0.366221	+	0.307296i	−0.441043	+	0.897486i	$0.645391\pi$
$410$	12.8996	+	3.00843i	0.637068	+	0.148576i
$411$	−0.181880	+	0.315025i	−0.00897148	+	0.0155391i
$412$	−3.70068	−	10.1675i	−0.182320	−	0.500919i
$413$	−44.5221	+	7.85045i	−2.19079	+	0.386295i
$414$	−0.305817	+	1.73438i	−0.0150301	+	0.0852399i
$415$	2.93307	−	1.48624i	0.143979	−	0.0729569i
$416$	0.212647	−	0.178432i	0.0104259	−	0.00874836i
$417$			13.6182i			0.666885i
$418$	19.4831	−	1.99885i	0.952948	−	0.0977670i
$419$	−18.9308			−0.924831			−0.462415	−	0.886663i	$-0.653017\pi$
$419$	−18.9308			−0.924831			−0.462415	+	0.886663i	$0.653017\pi$
$420$	−10.1878	−	0.556701i	−0.497113	−	0.0271642i
$421$	35.0729	+	12.7655i	1.70935	+	0.622153i	0.996835	−	0.0795037i	$-0.0253336\pi$
$421$	35.0729	+	12.7655i	1.70935	+	0.622153i	0.712516	+	0.701656i	$0.247556\pi$
$422$	4.06159	+	0.716167i	0.197715	+	0.0348625i
$423$	−8.58879	+	1.51444i	−0.417601	+	0.0736344i
$424$	−0.0341714	+	0.0124374i	−0.00165951	+	0.000604013i
$425$	−7.32320	+	14.8464i	−0.355227	+	0.720155i
$426$	6.01263	+	10.4142i	0.291313	+	0.504569i
$427$	−30.7805	+	36.6827i	−1.48957	+	1.77520i
$428$	−7.16879	+	8.54343i	−0.346517	+	0.412962i
$429$	−0.623635	−	1.08017i	−0.0301094	−	0.0521510i
$430$	−13.8895	+	4.21262i	−0.669813	+	0.203150i
$431$	16.9976	−	6.18662i	0.818746	−	0.297999i	0.101514	−	0.994834i	$-0.467631\pi$
$431$	16.9976	−	6.18662i	0.818746	−	0.297999i	0.717232	+	0.696835i	$0.245409\pi$
$432$	0.984808	−	0.173648i	0.0473816	−	0.00835465i
$433$	15.3260	+	2.70239i	0.736520	+	0.129868i	0.529311	−	0.848428i	$-0.322451\pi$
$433$	15.3260	+	2.70239i	0.736520	+	0.129868i	0.207210	+	0.978297i	$0.433562\pi$
$434$	−42.2774	−	15.3877i	−2.02938	−	0.738633i
$435$	1.28484	−	23.5130i	0.0616034	−	1.12736i
$436$	−1.28681			−0.0616269
$437$	−2.09762	−	7.38444i	−0.100343	−	0.353246i
$438$		−	10.5949i		−	0.506243i
$439$	−19.8308	+	16.6400i	−0.946471	+	0.794183i	−0.978700	−	0.205297i	$-0.934184\pi$
$439$	−19.8308	+	16.6400i	−0.946471	+	0.794183i	0.0322288	+	0.999481i	$0.489739\pi$
$440$	8.96215	−	4.54130i	0.427254	−	0.216498i
$441$	2.39985	−	13.6102i	0.114279	−	0.648107i
$442$	0.905102	−	0.159594i	0.0430513	−	0.00759111i
$443$	−7.28933	−	20.0273i	−0.346327	−	0.951525i	−0.983517	−	0.180818i	$-0.942126\pi$
$443$	−7.28933	−	20.0273i	−0.346327	−	0.951525i	0.637190	−	0.770707i	$-0.280097\pi$
$444$	−2.30373	+	3.99017i	−0.109330	+	0.189365i
$445$	4.06162	−	17.4156i	0.192539	−	0.825576i
$446$	−5.72357	−	4.80264i	−0.271019	−	0.227412i
$447$	−4.17376	+	4.97409i	−0.197412	+	0.235266i
$448$	−3.95160	+	2.28146i	−0.186696	+	0.107789i
$449$	6.18910	−	10.7198i	0.292082	−	0.505901i	−0.682220	−	0.731147i	$-0.738985\pi$
$449$	6.18910	−	10.7198i	0.292082	−	0.505901i	0.974302	+	0.225246i	$0.0723187\pi$
$450$	−4.57675	+	2.01329i	−0.215750	+	0.0949075i
$451$	−4.62187	−	26.2120i	−0.217636	−	1.23427i
$452$	−13.9153	−	2.45364i	−0.654520	−	0.115410i
$453$	−6.02001	+	16.5399i	−0.282845	+	0.777110i
$454$	−10.5040	+	8.81393i	−0.492979	+	0.413658i
$455$	−2.06707	−	1.93621i	−0.0969059	−	0.0907710i
$456$	−3.53277	+	2.55333i	−0.165437	+	0.119571i
$457$			12.3900i			0.579580i	0.957090	+	0.289790i	$0.0935855\pi$
$457$			12.3900i			0.579580i	−0.957090	+	0.289790i	$0.906415\pi$
$458$	14.6045	+	17.4050i	0.682425	+	0.813283i
$459$	3.11119	+	1.13238i	0.145218	+	0.0528549i
$460$	−2.36293	−	3.15031i	−0.110172	−	0.146884i
$461$	0.716002	+	4.06065i	0.0333475	+	0.189123i	0.996931	−	0.0782841i	$-0.0249441\pi$
$461$	0.716002	+	4.06065i	0.0333475	+	0.189123i	−0.963584	+	0.267407i	$0.913833\pi$
$462$	7.01211	+	19.2656i	0.326233	+	0.896317i
$463$	−14.9754	−	8.64607i	−0.695968	−	0.401817i	0.109876	−	0.993945i	$-0.464955\pi$
$463$	−14.9754	−	8.64607i	−0.695968	−	0.401817i	−0.805844	+	0.592128i	$0.798288\pi$
$464$	−5.26550	−	9.12011i	−0.244445	−	0.423391i
$465$	−21.8894	+	2.63815i	−1.01510	+	0.122341i
$466$	14.1212	+	11.8491i	0.654150	+	0.548897i
$467$	20.0449	−	11.5729i	0.927567	−	0.535531i	0.0415258	−	0.999137i	$-0.486778\pi$
$467$	20.0449	−	11.5729i	0.927567	−	0.535531i	0.886041	+	0.463606i	$0.153445\pi$
$468$	0.240401	+	0.138796i	0.0111125	+	0.00641583i
$469$	−26.4348	+	9.62148i	−1.22065	+	0.444279i
$470$	10.6577	−	16.3315i	0.491601	−	0.753317i
$471$	−1.04660	+	5.93556i	−0.0482247	+	0.273496i
$472$	−3.38870	+	9.31038i	−0.155978	+	0.428545i
$473$	18.7471	+	22.3419i	0.861992	+	1.02728i
$474$	−10.7471			−0.493630
$475$	14.1248	−	16.5979i	0.648091	−	0.761563i
$476$	−15.1072			−0.692435
$477$	−0.0233746	−	0.0278568i	−0.00107025	−	0.00127548i
$478$	−5.78559	+	15.8958i	−0.264627	+	0.727056i
$479$	−4.10976	+	23.3076i	−0.187780	+	1.06495i	0.734552	+	0.678552i	$0.237392\pi$
$479$	−4.10976	+	23.3076i	−0.187780	+	1.06495i	−0.922332	+	0.386399i	$0.873719\pi$
$480$	−1.22203	+	1.87260i	−0.0557777	+	0.0854723i
$481$	−1.20186	+	0.437440i	−0.0547999	+	0.0199455i
$482$	3.47484	+	2.00620i	0.158275	+	0.0913800i
$483$	6.95929	−	4.01795i	0.316658	−	0.182823i
$484$	−7.03897	−	5.90640i	−0.319953	−	0.268473i
$485$	−6.17658	+	0.744412i	−0.280464	+	0.0338020i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−11.7410	−	6.77868i	−0.532036	−	0.307171i	0.209809	−	0.977742i	$-0.432716\pi$
$487$	−11.7410	−	6.77868i	−0.532036	−	0.307171i	−0.741845	+	0.670571i	$0.766049\pi$
$488$	3.58936	+	9.86169i	0.162483	+	0.446418i
$489$	−3.55461	−	20.1592i	−0.160745	−	0.911631i
$490$	18.5428	+	24.7216i	0.837677	+	1.11681i
$491$	10.5979	+	3.85732i	0.478276	+	0.174078i	0.569898	−	0.821716i	$-0.306983\pi$
$491$	10.5979	+	3.85732i	0.478276	+	0.174078i	−0.0916216	+	0.995794i	$0.529205\pi$
$492$	3.80769	+	4.53782i	0.171664	+	0.204581i
$493$		−	34.8666i		−	1.57031i
$494$	−1.20683	−	0.0874019i	−0.0542979	−	0.00393240i
$495$	7.33266	+	6.86845i	0.329579	+	0.308714i
$496$	−7.55325	+	6.33793i	−0.339151	+	0.284581i
$497$	18.7667	−	51.5612i	0.841803	−	2.31283i
$498$	1.44816	+	0.255349i	0.0648935	+	0.0114425i
$499$	2.74858	+	15.5880i	0.123043	+	0.697813i	0.982451	+	0.186522i	$0.0597215\pi$
$499$	2.74858	+	15.5880i	0.123043	+	0.697813i	−0.859408	+	0.511291i	$0.829167\pi$
$500$	3.71059	−	10.5466i	0.165943	−	0.471660i
$501$	0.472418	−	0.818252i	0.0211061	−	0.0365568i
$502$	11.6882	−	6.74819i	0.521670	−	0.301187i
$503$	0.890786	−	1.06160i	0.0397182	−	0.0473343i	−0.745820	−	0.666148i	$-0.767942\pi$
$503$	0.890786	−	1.06160i	0.0397182	−	0.0473343i	0.785538	+	0.618814i	$0.212386\pi$
$504$	−3.49540	−	2.93299i	−0.155697	−	0.130646i
$505$	−7.36112	+	31.5632i	−0.327565	+	1.40455i
$506$	−3.95654	+	6.85293i	−0.175890	+	0.304650i
$507$	−4.41991	−	12.1436i	−0.196295	−	0.539316i
$508$	1.87180	−	0.330049i	0.0830476	−	0.0146435i
$509$	−3.46463	+	19.6489i	−0.153567	+	0.870921i	0.806517	+	0.591210i	$0.201350\pi$
$509$	−3.46463	+	19.6489i	−0.153567	+	0.870921i	−0.960084	+	0.279711i	$0.909761\pi$
$510$	−6.60387	+	3.34631i	−0.292424	+	0.148177i
$511$	−37.0333	+	31.0747i	−1.63826	+	1.37466i
$512$			1.00000i			0.0441942i
$513$	−3.60763	−	2.44643i	−0.159281	−	0.108013i
$514$	9.10211			0.401477
$515$	−1.32011	+	24.1584i	−0.0581709	+	1.06455i
$516$	−6.09955	−	2.22005i	−0.268518	−	0.0977324i
$517$	−38.5910	−	6.80464i	−1.69723	−	0.299268i
$518$	20.7040	−	3.65068i	0.909682	−	0.160402i
$519$	12.8924	−	4.69246i	0.565914	−	0.205976i
$520$	−0.593994	+	0.180155i	−0.0260484	+	0.00790032i
$521$	1.97001	+	3.41216i	0.0863076	+	0.149489i	0.905948	−	0.423390i	$-0.139160\pi$
$521$	1.97001	+	3.41216i	0.0863076	+	0.149489i	−0.819640	+	0.572879i	$0.805827\pi$
$522$	6.76920	−	8.06721i	0.296280	−	0.353092i
$523$	−1.62685	+	1.93881i	−0.0711373	+	0.0847781i	−0.800439	−	0.599414i	$-0.795400\pi$
$523$	−1.62685	+	1.93881i	−0.0711373	+	0.0847781i	0.729302	+	0.684192i	$0.239845\pi$
$524$	−0.566947	−	0.981981i	−0.0247672	−	0.0428980i
$525$	20.4608	+	10.0926i	0.892983	+	0.440477i
$526$	28.5976	−	10.4087i	1.24692	−	0.453840i
$527$	−32.1493	+	5.66879i	−1.40045	+	0.246936i
$528$	4.42492	+	0.780234i	0.192570	+	0.0339553i
$529$	−18.6984	−	6.80566i	−0.812974	−	0.295898i
$530$	0.0811923	+	0.00443667i	0.00352677	+	0.000192717i
$531$	−9.90790			−0.429966
$532$	19.2865	+	4.85956i	0.836175	+	0.210689i
$533$			1.64437i			0.0712256i
$534$	6.12642	−	5.14068i	0.265116	−	0.222459i
$535$	22.2452	−	11.2721i	0.961744	−	0.487335i
$536$	−1.07058	+	6.07154i	−0.0462419	+	0.262251i
$537$	−6.84259	+	1.20653i	−0.295280	+	0.0520658i
$538$	6.66351	+	18.3078i	0.287284	+	0.789307i
$539$	31.0484	−	53.7774i	1.33735	−	2.31635i
$540$	−2.17763	−	0.507863i	−0.0937103	−	0.0218549i
$541$	−9.33208	−	7.83054i	−0.401217	−	0.336661i	0.419747	−	0.907641i	$-0.362119\pi$
$541$	−9.33208	−	7.83054i	−0.401217	−	0.336661i	−0.820964	+	0.570980i	$0.806563\pi$
$542$	9.32457	−	11.1126i	0.400525	−	0.477327i
$543$	−1.57290	+	0.908112i	−0.0674995	+	0.0389708i
$544$	−1.65543	+	2.86729i	−0.0709759	+	0.122934i
$545$	2.64614	+	1.13019i	0.113348	+	0.0484120i
$546$	−0.219947	−	1.24738i	−0.00941288	−	0.0533831i
$547$	36.5981	+	6.45322i	1.56482	+	0.275920i	0.887865	−	0.460105i	$-0.152188\pi$
$547$	36.5981	+	6.45322i	1.56482	+	0.275920i	0.676955	+	0.736024i	$0.263299\pi$
$548$	0.124413	−	0.341823i	0.00531467	−	0.0146019i
$549$	−8.03932	+	6.74579i	−0.343110	+	0.287903i
$550$	−22.4180	+	1.46719i	−0.955905	+	0.0625610i
$551$	−11.2156	+	44.5123i	−0.477803	+	1.89629i
$552$		−	1.76113i		−	0.0749587i
$553$	31.5211	+	37.5653i	1.34041	+	1.59744i
$554$	4.20681	+	1.53115i	0.178730	+	0.0650524i
$555$	8.24181	−	6.18188i	0.349845	−	0.262406i
$556$	−2.36477	−	13.4113i	−0.100289	−	0.568765i
$557$	0.0530530	+	0.145762i	0.00224793	+	0.00617613i	0.940812	−	0.338930i	$-0.110065\pi$
$557$	0.0530530	+	0.145762i	0.00224793	+	0.00617613i	−0.938564	+	0.345106i	$0.887843\pi$
$558$	−8.53907	−	4.93003i	−0.361487	−	0.208705i
$559$	−0.900923	−	1.56044i	−0.0381050	−	0.0659998i
$560$	10.1297	−	1.22085i	0.428057	−	0.0515902i
$561$	11.3959	+	9.56230i	0.481135	+	0.403720i
$562$	−1.70756	+	0.985862i	−0.0720292	+	0.0415861i
$563$	33.3761	+	19.2697i	1.40664	+	0.812121i	0.995062	−	0.0992553i	$-0.0316460\pi$
$563$	33.3761	+	19.2697i	1.40664	+	0.812121i	0.411573	+	0.911377i	$0.364979\pi$
$564$	8.19533	−	2.98286i	0.345086	−	0.125601i
$565$	26.4598	+	17.2672i	1.11317	+	0.726437i
$566$	−5.13921	+	29.1459i	−0.216017	+	1.22509i
$567$	1.56061	−	4.28774i	0.0655394	−	0.180068i
$568$	−7.72969	−	9.21188i	−0.324330	−	0.386522i
$569$	10.2096			0.428008			0.214004	−	0.976833i	$-0.431349\pi$
$569$	10.2096			0.428008			0.214004	+	0.976833i	$0.431349\pi$
$570$	9.50721	−	2.14777i	0.398213	−	0.0899601i
$571$	14.9185			0.624319			0.312159	−	0.950030i	$-0.398948\pi$
$571$	14.9185			0.624319			0.312159	+	0.950030i	$0.398948\pi$
$572$	0.801729	+	0.955464i	0.0335220	+	0.0399500i
$573$	−0.631002	+	1.73366i	−0.0263605	+	0.0724249i
$574$	4.69360	−	26.6187i	0.195907	−	1.11104i
$575$	2.09216	+	8.55350i	0.0872490	+	0.356706i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−2.67960	−	1.54707i	−0.111553	−	0.0644053i	0.443185	−	0.896430i	$-0.353848\pi$
$577$	−2.67960	−	1.54707i	−0.111553	−	0.0644053i	−0.554739	+	0.832025i	$0.687182\pi$
$578$	5.22926	−	3.01912i	0.217509	−	0.125579i
$579$	5.42969	+	4.55605i	0.225650	+	0.189343i
$580$	2.81766	+	23.3788i	0.116997	+	0.970754i
$581$	−3.35488	−	5.81082i	−0.139184	−	0.241073i
$582$	−2.40949	−	1.39112i	−0.0998766	−	0.0576638i
$583$	−0.0558835	−	0.153539i	−0.00231446	−	0.00635892i
$584$	1.83978	+	10.4339i	0.0761308	+	0.431759i
$585$	−0.372448	−	0.496555i	−0.0153988	−	0.0205300i
$586$	−7.61544	−	2.77179i	−0.314591	−	0.114502i
$587$	18.3079	+	21.8185i	0.755648	+	0.900546i	0.997564	−	0.0697508i	$-0.0222204\pi$
$587$	18.3079	+	21.8185i	0.755648	+	0.900546i	−0.241916	+	0.970297i	$0.577776\pi$
$588$			13.8202i			0.569936i
$589$	42.8667	+	3.10452i	1.76629	+	0.127920i
$590$	15.1456	−	16.1692i	0.623534	−	0.665676i
$591$	−9.16902	+	7.69373i	−0.377163	+	0.316478i
$592$	1.57584	−	4.32959i	0.0647667	−	0.177945i
$593$	6.48974	+	1.14432i	0.266502	+	0.0469915i	0.305302	−	0.952256i	$-0.401243\pi$
$593$	6.48974	+	1.14432i	0.266502	+	0.0469915i	−0.0388003	+	0.999247i	$0.512354\pi$
$594$	0.780234	+	4.42492i	0.0320134	+	0.181557i
$595$	31.0657	+	13.2684i	1.27357	+	0.543953i
$596$	3.24661	−	5.62329i	0.132986	−	0.230339i
$597$	2.35870	−	1.36179i	0.0965351	−	0.0557345i
$598$	0.314243	−	0.374500i	0.0128503	−	0.0153144i
$599$	−20.5271	−	17.2243i	−0.838714	−	0.703765i	0.118560	−	0.992947i	$-0.462172\pi$
$599$	−20.5271	−	17.2243i	−0.838714	−	0.703765i	−0.957274	+	0.289182i	$0.906617\pi$
$600$	4.15762	−	2.77745i	0.169734	−	0.113389i
$601$	−5.99896	+	10.3905i	−0.244703	+	0.423838i	−0.962048	−	0.272880i	$-0.912024\pi$
$601$	−5.99896	+	10.3905i	−0.244703	+	0.423838i	0.717345	+	0.696718i	$0.245357\pi$
$602$	10.1299	+	27.8317i	0.412865	+	1.13434i
$603$	−6.07154	+	1.07058i	−0.247252	+	0.0435973i
$604$	3.05644	−	17.3339i	0.124365	−	0.705308i
$605$	9.28712	+	18.3279i	0.377575	+	0.745135i
$606$	−11.1033	+	9.31676i	−0.451040	+	0.378467i
$607$			42.9179i			1.74198i	0.491298	+	0.870992i	$0.336523\pi$
$607$			42.9179i			1.74198i	−0.491298	+	0.870992i	$0.663477\pi$
$608$	3.03572	−	3.12800i	0.123115	−	0.126857i
$609$	−48.0521			−1.94717
$610$	1.28040	−	23.4317i	0.0518418	−	0.948720i
$611$	2.27495	+	0.828015i	0.0920347	+	0.0334979i
$612$	−3.26056	−	0.574924i	−0.131800	−	0.0232399i
$613$	5.59392	−	0.986359i	0.225936	−	0.0398387i	−0.0595338	−	0.998226i	$-0.518961\pi$
$613$	5.59392	−	0.986359i	0.225936	−	0.0398387i	0.285470	+	0.958388i	$0.407850\pi$
$614$	−7.67693	+	2.79417i	−0.309816	+	0.112764i
$615$	−3.84445	−	12.6756i	−0.155023	−	0.511131i
$616$	−10.2510	−	17.7553i	−0.413025	−	0.715381i
$617$	−20.7244	+	24.6984i	−0.834333	+	0.994319i	0.165634	+	0.986187i	$0.447033\pi$
$617$	−20.7244	+	24.6984i	−0.834333	+	0.994319i	−0.999967	+	0.00813164i	$0.997412\pi$
$618$	−6.95501	+	8.28865i	−0.279771	+	0.333419i
$619$	−4.75604	−	8.23771i	−0.191161	−	0.331101i	0.754474	−	0.656330i	$-0.227892\pi$
$619$	−4.75604	−	8.23771i	−0.191161	−	0.331101i	−0.945635	+	0.325229i	$0.894559\pi$
$620$	21.0987	−	6.39912i	0.847345	−	0.256995i
$621$	1.65492	−	0.602342i	0.0664097	−	0.0241712i
$622$	3.48008	−	0.613632i	0.139539	−	0.0246044i
$623$	−35.9374	−	6.33674i	−1.43980	−	0.253876i
$624$	−0.260851	−	0.0949418i	−0.0104424	−	0.00380072i
$625$	−16.8933	+	18.4287i	−0.675732	+	0.737147i
$626$	22.1720			0.886170
$627$	−11.4726	−	15.8734i	−0.458171	−	0.633923i
$628$		−	6.02712i		−	0.240508i
$629$	11.6857	−	9.80547i	0.465940	−	0.390970i
$630$	4.61178	+	9.10124i	0.183738	+	0.362602i
$631$	−5.23668	+	29.6987i	−0.208469	+	1.18229i	0.683418	+	0.730027i	$0.260493\pi$
$631$	−5.23668	+	29.6987i	−0.208469	+	1.18229i	−0.891887	+	0.452258i	$0.850619\pi$
$632$	10.5838	−	1.86621i	0.421002	−	0.0742339i
$633$	−1.41057	−	3.87552i	−0.0560653	−	0.154038i
$634$	1.42434	−	2.46703i	0.0565678	−	0.0979784i
$635$	−4.13897	−	0.965281i	−0.164250	−	0.0383060i
$636$	0.0278568	+	0.0233746i	0.00110459	+	0.000926865i
$637$	−2.46597	+	2.93883i	−0.0977053	+	0.116441i
$638$	40.9784	−	23.6589i	1.62235	−	0.936664i
$639$	6.01263	−	10.4142i	0.237856	−	0.411979i
$640$	0.878289	−	2.05636i	0.0347174	−	0.0812847i
$641$	−5.49066	−	31.1391i	−0.216868	−	1.22992i	−0.877635	−	0.479329i	$-0.840880\pi$
$641$	−5.49066	−	31.1391i	−0.216868	−	1.22992i	0.660767	−	0.750591i	$-0.270231\pi$
$642$	10.9832	+	1.93664i	0.433473	+	0.0764330i
$643$	−10.8395	+	29.7812i	−0.427466	+	1.17445i	0.519879	+	0.854240i	$0.325977\pi$
$643$	−10.8395	+	29.7812i	−0.427466	+	1.17445i	−0.947345	+	0.320214i	$0.896245\pi$
$644$	−6.15585	+	5.16537i	−0.242574	+	0.203544i
$645$	10.5930	+	9.92239i	0.417099	+	0.390694i
$646$	13.8825	−	3.94345i	0.546198	−	0.155153i
$647$			21.1592i			0.831853i	0.909398	+	0.415927i	$0.136543\pi$
$647$			21.1592i			0.831853i	−0.909398	+	0.415927i	$0.863457\pi$
$648$	−0.642788	−	0.766044i	−0.0252511	−	0.0300931i
$649$	−41.8333	−	15.2261i	−1.64210	−	0.597675i
$650$	1.37969	+	0.151235i	0.0541160	+	0.00593193i
$651$	7.81254	+	44.3071i	0.306198	+	1.73653i
$652$	7.00122	+	19.2357i	0.274189	+	0.753328i
$653$	−22.2950	−	12.8720i	−0.872469	−	0.503720i	−0.00430125	−	0.999991i	$-0.501369\pi$
$653$	−22.2950	−	12.8720i	−0.872469	−	0.503720i	−0.868168	+	0.496270i	$0.834702\pi$
$654$	0.643404	+	1.11441i	0.0251591	+	0.0435768i
$655$	0.303383	+	2.51725i	0.0118542	+	0.0983570i
$656$	−4.53782	−	3.80769i	−0.177172	−	0.148665i
$657$	−9.17544	+	5.29744i	−0.357968	+	0.206673i
$658$	−34.4631	−	19.8973i	−1.34351	−	0.775676i
$659$	−9.33861	+	3.39897i	−0.363780	+	0.132405i	−0.517442	−	0.855718i	$-0.673116\pi$
$659$	−9.33861	+	3.39897i	−0.363780	+	0.132405i	0.153662	+	0.988124i	$0.450893\pi$
$660$	−8.41396	−	5.49080i	−0.327513	−	0.213729i
$661$	3.30706	−	18.7553i	0.128630	−	0.729495i	−0.850456	−	0.526046i	$-0.823674\pi$
$661$	3.30706	−	18.7553i	0.128630	−	0.729495i	0.979086	−	0.203449i	$-0.0652151\pi$
$662$	3.18543	−	8.75189i	0.123805	−	0.340152i
$663$	−0.590764	−	0.704045i	−0.0229434	−	0.0273428i
$664$	−1.47050			−0.0570664
$665$	−35.3918	−	26.9321i	−1.37244	−	1.04438i
$666$	4.60745			0.178535
$667$	−11.9214	−	14.2074i	−0.461600	−	0.550113i
$668$	−0.323153	+	0.887855i	−0.0125032	+	0.0343522i
$669$	−1.29743	+	7.35808i	−0.0501614	+	0.284480i
$670$	7.53406	−	11.5450i	0.291066	−	0.446022i
$671$	−44.3104	+	16.1277i	−1.71058	+	0.622602i
$672$	3.95160	+	2.28146i	0.152436	+	0.0880092i
$673$	4.36437	−	2.51977i	0.168234	−	0.0971299i	−0.413519	−	0.910496i	$-0.635700\pi$
$673$	4.36437	−	2.51977i	0.168234	−	0.0971299i	0.581753	+	0.813366i	$0.302367\pi$
$674$	3.27622	+	2.74908i	0.126195	+	0.105891i
$675$	4.03194	+	2.95694i	0.155189	+	0.113813i
$676$	6.46147	+	11.1916i	0.248518	+	0.430446i
$677$	−15.1116	−	8.72470i	−0.580787	−	0.335317i	0.180659	−	0.983546i	$-0.442177\pi$
$677$	−15.1116	−	8.72470i	−0.580787	−	0.335317i	−0.761446	+	0.648228i	$0.775510\pi$
$678$	4.83273	+	13.2778i	0.185600	+	0.509931i
$679$	2.20449	+	12.5023i	0.0846004	+	0.479793i
$680$	5.92246	−	4.44222i	0.227116	−	0.170351i
$681$	12.8851	+	4.68979i	0.493758	+	0.179713i
$682$	−28.4775	−	33.9381i	−1.09046	−	1.29956i
$683$			11.0615i			0.423255i	0.977350	+	0.211628i	$0.0678764\pi$
$683$			11.0615i			0.423255i	−0.977350	+	0.211628i	$0.932124\pi$
$684$	3.97764	+	1.78281i	0.152089	+	0.0681673i
$685$	−0.556057	+	0.593639i	−0.0212459	+	0.0226818i
$686$	23.8393	−	20.0036i	0.910189	−	0.763739i
$687$	7.77091	−	21.3504i	0.296479	−	0.814569i
$688$	6.39239	+	1.12715i	0.243708	+	0.0429722i
$689$	0.00175289	+	0.00994111i	6.67796e−5	+	0.000378726i
$690$	−1.54678	+	3.62152i	−0.0588850	+	0.137869i
$691$	−2.51568	+	4.35729i	−0.0957012	+	0.165759i	−0.909901	−	0.414825i	$-0.863843\pi$
$691$	−2.51568	+	4.35729i	−0.0957012	+	0.165759i	0.814200	+	0.580585i	$0.197176\pi$
$692$	−11.8817	+	6.85991i	−0.451675	+	0.260775i
$693$	13.1785	−	15.7055i	0.500608	−	0.596601i
$694$	20.4007	+	17.1182i	0.774401	+	0.649799i
$695$	−6.91616	+	29.6554i	−0.262345	+	1.12489i
$696$	−5.26550	+	9.12011i	−0.199588	+	0.345697i
$697$	−6.70788	−	18.4298i	−0.254079	−	0.698077i
$698$	−22.8497	+	4.02902i	−0.864875	+	0.152501i
$699$	3.20101	−	18.1538i	0.121073	−	0.686641i
$700$	−21.9025	−	6.38629i	−0.827837	−	0.241379i
$701$	7.59710	−	6.37472i	0.286938	−	0.240770i	−0.487945	−	0.872875i	$-0.662253\pi$
$701$	7.59710	−	6.37472i	0.286938	−	0.240770i	0.774883	+	0.632105i	$0.217809\pi$
$702$		−	0.277591i		−	0.0104770i
$703$	−18.0727	+	8.75914i	−0.681623	+	0.330357i
$704$	−4.49319			−0.169343
$705$	−19.4723	−	1.06405i	−0.733371	−	0.0400743i
$706$	−9.35280	−	3.40414i	−0.351997	−	0.128116i
$707$	65.1315	+	11.4844i	2.44952	+	0.431917i
$708$	9.75738	−	1.72049i	0.366705	−	0.0646599i
$709$	−32.2245	+	11.7288i	−1.21022	+	0.440483i	−0.866779	−	0.498692i	$-0.833814\pi$
$709$	−32.2245	+	11.7288i	−1.21022	+	0.440483i	−0.343439	+	0.939175i	$0.611592\pi$
$710$	7.80431	+	25.7318i	0.292891	+	0.965698i
$711$	5.37354	+	9.30725i	0.201524	+	0.349049i
$712$	−5.14068	+	6.12642i	−0.192655	+	0.229597i
$713$	−11.1619	+	13.3023i	−0.418017	+	0.498173i
$714$	7.55358	+	13.0832i	0.282686	+	0.489626i
$715$	−0.809470	−	2.66893i	−0.0302725	−	0.0998122i
$716$	6.52913	−	2.37641i	0.244005	−	0.0888105i
$717$	16.6589	−	2.93742i	0.622140	−	0.109700i
$718$	2.24938	+	0.396626i	0.0839460	+	0.0148020i
$719$	1.95418	+	0.711264i	0.0728786	+	0.0265257i	0.378202	−	0.925723i	$-0.376542\pi$
$719$	1.95418	+	0.711264i	0.0728786	+	0.0265257i	−0.305324	+	0.952249i	$0.598765\pi$
$720$	2.23274	+	0.122006i	0.0832092	+	0.00454688i
$721$	49.3711			1.83867
$722$	−18.9915	+	0.568778i	−0.706790	+	0.0211677i
$723$		−	4.01241i		−	0.149223i
$724$	1.39131	−	1.16745i	0.0517076	−	0.0433878i
$725$	14.7393	−	50.5500i	0.547402	−	1.87738i
$726$	−1.59560	+	9.04912i	−0.0592184	+	0.335844i
$727$	19.9917	−	3.52508i	0.741451	−	0.130738i	0.209851	−	0.977733i	$-0.432702\pi$
$727$	19.9917	−	3.52508i	0.741451	−	0.130738i	0.531600	+	0.846995i	$0.321591\pi$
$728$	0.433212	+	1.19024i	0.0160559	+	0.0441132i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	5.38075	−	23.0717i	0.199150	−	0.853924i
$731$	16.4629	+	13.8140i	0.608902	+	0.510929i
$732$	6.74579	−	8.03932i	0.249332	−	0.297142i
$733$	18.3168	−	10.5752i	0.676546	−	0.390604i	−0.122006	−	0.992529i	$-0.538933\pi$
$733$	18.3168	−	10.5752i	0.676546	−	0.390604i	0.798552	+	0.601925i	$0.205599\pi$
$734$	1.99682	−	3.45860i	0.0737040	−	0.127659i
$735$	12.1381	−	28.4193i	0.447722	−	1.04826i
$736$	0.305817	+	1.73438i	0.0112726	+	0.0639299i
$737$	−27.2806	−	4.81030i	−1.00489	−	0.177190i
$738$	2.02603	−	5.56646i	0.0745791	−	0.204904i
$739$	−30.9400	+	25.9618i	−1.13815	+	0.955019i	−0.999377	−	0.0353054i	$-0.988760\pi$
$739$	−30.9400	+	25.9618i	−1.13815	+	0.955019i	−0.138771	+	0.990325i	$0.544315\pi$
$740$	−7.04312	+	7.51914i	−0.258910	+	0.276409i
$741$	0.527724	+	1.08885i	0.0193864	+	0.0399998i
$742$		−	0.165928i		−	0.00609141i
$743$	12.0085	+	14.3111i	0.440548	+	0.525024i	0.939935	−	0.341355i	$-0.110886\pi$
$743$	12.0085	+	14.3111i	0.440548	+	0.525024i	−0.499387	+	0.866379i	$0.666441\pi$
$744$	9.26543	+	3.37234i	0.339687	+	0.123636i
$745$	−11.6151	+	8.71203i	−0.425543	+	0.319184i
$746$	−5.96743	−	33.8430i	−0.218483	−	1.23908i
$747$	−0.502940	−	1.38182i	−0.0184016	−	0.0505580i
$748$	−12.8832	−	7.43815i	−0.471058	−	0.271966i
$749$	−25.4443	−	44.0709i	−0.929715	−	1.61031i
$750$	−10.9890	+	2.05985i	−0.401260	+	0.0752150i
$751$	−22.1308	−	18.5699i	−0.807564	−	0.677627i	0.142461	−	0.989800i	$-0.454499\pi$
$751$	−22.1308	−	18.5699i	−0.807564	−	0.677627i	−0.950025	+	0.312173i	$0.898943\pi$
$752$	−7.55286	+	4.36064i	−0.275424	+	0.159016i
$753$	−11.6882	−	6.74819i	−0.425942	−	0.245918i
$754$	−2.74702	+	0.999833i	−0.100040	+	0.0364118i
$755$	−21.5093	+	32.9604i	−0.782805	+	1.19955i
$756$	−0.792342	+	4.49360i	−0.0288172	+	0.163430i
$757$	8.52446	−	23.4208i	0.309827	−	0.851242i	−0.682863	−	0.730547i	$-0.739265\pi$
$757$	8.52446	−	23.4208i	0.309827	−	0.851242i	0.992690	−	0.120695i	$-0.0385124\pi$
$758$	−6.44265	−	7.67805i	−0.234007	−	0.278879i
$759$	7.91309			0.287227
$760$	−8.98982	+	3.76605i	−0.326095	+	0.136609i
$761$	33.3183			1.20779			0.603894	−	0.797065i	$-0.293615\pi$
$761$	33.3183			1.20779			0.603894	+	0.797065i	$0.293615\pi$
$762$	−1.22173	−	1.45600i	−0.0442586	−	0.0527453i
$763$	2.00820	−	5.51749i	0.0727018	−	0.199747i
$764$	0.320368	−	1.81690i	0.0115905	−	0.0657331i
$765$	6.19992	+	4.04596i	0.224159	+	0.146282i
$766$	−29.7890	+	10.8423i	−1.07632	+	0.391748i
$767$	2.38187	+	1.37517i	0.0860044	+	0.0496547i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−40.8622	−	34.2875i	−1.47353	−	1.23644i	−0.912779	−	0.408453i	$-0.866068\pi$
$769$	−40.8622	−	34.2875i	−1.47353	−	1.23644i	−0.560750	−	0.827985i	$-0.689487\pi$
$770$	5.48550	+	45.5146i	0.197684	+	1.64023i
$771$	−4.55106	−	7.88266i	−0.163902	−	0.283887i
$772$	−6.13836	−	3.54398i	−0.220924	−	0.127551i
$773$	2.48175	+	6.81856i	0.0892625	+	0.245247i	0.976289	−	0.216472i	$-0.0694551\pi$
$773$	2.48175	+	6.81856i	0.0892625	+	0.245247i	−0.887026	+	0.461719i	$0.847233\pi$
$774$	1.12715	+	6.39239i	0.0405146	+	0.229770i
$775$	−49.0068	−	5.37189i	−1.76038	−	0.192964i
$776$	2.61445	+	0.951582i	0.0938533	+	0.0341598i
$777$	−13.5136	−	16.1049i	−0.484797	−	0.577759i
$778$			14.0800i			0.504792i
$779$	2.63524	+	25.6860i	0.0944172	+	0.920297i
$780$	0.453016	+	0.424337i	0.0162206	+	0.0151937i
$781$	41.3907	−	34.7309i	1.48108	−	1.24277i
$782$	−1.99427	+	5.47921i	−0.0713149	+	0.195936i
$783$	−10.3710	−	1.82869i	−0.370630	−	0.0653520i
$784$	−2.39985	−	13.6102i	−0.0857090	−	0.486080i
$785$	−5.29355	+	12.3939i	−0.188935	+	0.442358i
$786$	−0.566947	+	0.981981i	−0.0202223	+	0.0350261i
$787$	−3.03527	+	1.75241i	−0.108196	+	0.0624668i	−0.553121	−	0.833101i	$-0.686563\pi$
$787$	−3.03527	+	1.75241i	−0.108196	+	0.0624668i	0.444926	+	0.895567i	$0.353230\pi$
$788$	7.69373	−	9.16902i	0.274078	−	0.326633i
$789$	−23.3130	−	19.5619i	−0.829964	−	0.696423i
$790$	−23.4032	−	5.45804i	−0.832648	−	0.194189i
$791$	32.2369	−	55.8359i	1.14621	−	1.98530i
$792$	−1.53676	−	4.22221i	−0.0546064	−	0.150030i
$793$	2.86895	−	0.505873i	0.101879	−	0.0179641i
$794$	−1.79376	+	10.1729i	−0.0636583	+	0.361024i
$795$	−0.0367539	−	0.0725330i	−0.00130353	−	0.00257248i
$796$	−2.08639	+	1.75069i	−0.0739502	+	0.0620515i
$797$		−	21.0188i		−	0.744525i	−0.928128	−	0.372262i	$-0.878582\pi$
$797$		−	21.0188i		−	0.744525i	0.928128	−	0.372262i	$-0.121418\pi$
$798$	−5.43474	−	19.1324i	−0.192388	−	0.677278i
$799$	−28.8749			−1.02152
$800$	−3.61215	+	3.45722i	−0.127709	+	0.122231i
$801$	−7.51517	−	2.73530i	−0.265535	−	0.0966470i
$802$	−9.30112	−	1.64004i	−0.328434	−	0.0579118i
$803$	−46.8816	+	8.26649i	−1.65441	+	0.291718i
$804$	5.79340	−	2.10863i	0.204317	−	0.0743655i
$805$	17.1953	−	5.21524i	0.606055	−	0.183813i
$806$	1.36853	+	2.37037i	0.0482046	+	0.0834928i
$807$	12.5233	−	14.9247i	0.440841	−	0.525374i
$808$	9.31676	−	11.1033i	0.327762	−	0.390612i
$809$	5.90084	+	10.2206i	0.207463	+	0.359336i	0.950915	−	0.309454i	$-0.100146\pi$
$809$	5.90084	+	10.2206i	0.207463	+	0.359336i	−0.743452	+	0.668789i	$0.766813\pi$
$810$	0.648993	+	2.13981i	0.0228033	+	0.0751854i
$811$	23.4450	−	8.53328i	0.823265	−	0.299644i	0.104173	−	0.994559i	$-0.466780\pi$
$811$	23.4450	−	8.53328i	0.823265	−	0.299644i	0.719092	+	0.694915i	$0.244558\pi$
$812$	47.3221	−	8.34415i	1.66068	−	0.292822i
$813$	−14.2861	−	2.51902i	−0.501035	−	0.0883459i
$814$	19.4536	+	7.08055i	0.681850	+	0.248173i
$815$	2.49748	−	45.7046i	0.0874828	−	1.60096i
$816$	3.31086			0.115903
$817$	−16.5737	−	22.9312i	−0.579840	−	0.802263i
$818$			9.66833i			0.338045i
$819$	−0.970292	+	0.814172i	−0.0339047	+	0.0284495i
$820$	5.98714	+	11.8155i	0.209080	+	0.412615i
$821$	1.88850	−	10.7102i	0.0659089	−	0.373788i	−0.933957	−	0.357387i	$-0.883668\pi$
$821$	1.88850	−	10.7102i	0.0659089	−	0.373788i	0.999865	−	0.0164016i	$-0.00522103\pi$
$822$	−0.358234	+	0.0631663i	−0.0124948	+	0.00220318i
$823$	14.5530	+	39.9840i	0.507285	+	1.39375i	0.884027	+	0.467436i	$0.154822\pi$
$823$	14.5530	+	39.9840i	0.507285	+	1.39375i	−0.376742	+	0.926318i	$0.622956\pi$
$824$	5.41004	−	9.37046i	0.188468	−	0.326435i
$825$	12.4796	+	18.6809i	0.434484	+	0.650387i
$826$	−34.6320	−	29.0597i	−1.20500	−	1.01112i
$827$	13.9737	−	16.6532i	0.485912	−	0.579088i	−0.466261	−	0.884647i	$-0.654399\pi$
$827$	13.9737	−	16.6532i	0.485912	−	0.579088i	0.952173	+	0.305560i	$0.0988436\pi$
$828$	−1.52518	+	0.880565i	−0.0530038	+	0.0306018i
$829$	5.96024	−	10.3234i	0.207008	−	0.358548i	−0.743763	−	0.668444i	$-0.766961\pi$
$829$	5.96024	−	10.3234i	0.207008	−	0.358548i	0.950771	+	0.309896i	$0.100294\pi$
$830$	3.02387	+	1.29152i	0.104960	+	0.0448294i
$831$	−0.777386	−	4.40878i	−0.0269672	−	0.152939i
$832$	0.273374	+	0.0482032i	0.00947754	+	0.00167115i
$833$	15.6497	−	42.9972i	0.542230	−	1.48977i
$834$	−10.4321	+	8.75360i	−0.361235	+	0.303112i
$835$	1.44431	−	1.54193i	0.0499825	−	0.0533606i
$836$	14.0547	+	13.6401i	0.486092	+	0.471752i
$837$			9.86006i			0.340814i
$838$	−12.1685	−	14.5018i	−0.420354	−	0.500958i
$839$	6.12043	+	2.22766i	0.211301	+	0.0769072i	0.445502	−	0.895281i	$-0.353025\pi$
$839$	6.12043	+	2.22766i	0.211301	+	0.0769072i	−0.234201	+	0.972188i	$0.575247\pi$
$840$	−6.12213	−	8.16214i	−0.211234	−	0.281621i
$841$	14.2221	+	80.6577i	0.490418	+	2.78130i
$842$	12.7655	+	35.0729i	0.439928	+	1.20869i
$843$	1.70756	+	0.985862i	0.0588116	+	0.0339549i
$844$	2.06212	+	3.57170i	0.0709811	+	0.122943i
$845$	−3.45765	−	28.6890i	−0.118947	−	0.986931i
$846$	−6.68089	−	5.60594i	−0.229694	−	0.192736i
$847$	36.3102	−	20.9637i	1.24763	−	0.720321i
$848$	−0.0314926	−	0.0181822i	−0.00108146	−	0.000624381i
$849$	27.8107	−	10.1223i	0.954461	−	0.347395i
$850$	−16.0802	+	3.93317i	−0.551548	+	0.134907i
$851$	1.40904	−	7.99105i	0.0483012	−	0.273930i
$852$	−4.11288	+	11.3000i	−0.140905	+	0.387133i
$853$	−14.3915	−	17.1511i	−0.492755	−	0.587243i	0.461161	−	0.887317i	$-0.347433\pi$
$853$	−14.3915	−	17.1511i	−0.492755	−	0.587243i	−0.953916	+	0.300074i	$0.902989\pi$
$854$	−47.8859			−1.63862
$855$	−6.61363	−	7.15960i	−0.226181	−	0.244853i
$856$	−11.1527			−0.381190
$857$	15.5902	+	18.5796i	0.532550	+	0.634668i	0.963500	−	0.267708i	$-0.0862661\pi$
$857$	15.5902	+	18.5796i	0.532550	+	0.634668i	−0.430951	+	0.902376i	$0.641822\pi$
$858$	0.426591	−	1.17205i	0.0145636	−	0.0400131i
$859$	8.16872	−	46.3271i	0.278713	−	1.58066i	−0.448202	−	0.893932i	$-0.647935\pi$
$859$	8.16872	−	46.3271i	0.278713	−	1.58066i	0.726915	−	0.686728i	$-0.240953\pi$
$860$	−12.1551	−	7.93219i	−0.414485	−	0.270485i
$861$	−25.3993	+	9.24459i	−0.865606	+	0.315055i
$862$	15.6651	+	9.04424i	0.533555	+	0.308048i
$863$	20.1854	−	11.6541i	0.687120	−	0.396709i	−0.115412	−	0.993318i	$-0.536819\pi$
$863$	20.1854	−	11.6541i	0.687120	−	0.396709i	0.802532	+	0.596609i	$0.203486\pi$
$864$	0.766044	+	0.642788i	0.0260614	+	0.0218681i
$865$	30.4580	−	3.67086i	1.03560	−	0.124813i
$866$	7.78121	+	13.4775i	0.264416	+	0.457983i
$867$	−5.22926	−	3.01912i	−0.177595	−	0.102535i
$868$	−15.3877	−	42.2774i	−0.522293	−	1.43499i
$869$	8.38524	+	47.5550i	0.284450	+	1.61319i
$870$	18.8378	−	14.1296i	0.638663	−	0.479038i
$871$	1.60820	+	0.585336i	0.0544917	+	0.0198334i
$872$	−0.827144	−	0.985752i	−0.0280106	−	0.0333818i
$873$			2.78224i			0.0941645i
$874$	4.30849	−	6.35350i	0.145737	−	0.214910i
$875$	39.4304	+	32.3692i	1.33299	+	1.09428i
$876$	8.11615	−	6.81026i	0.274219	−	0.230097i
$877$	−3.08942	+	8.48810i	−0.104322	+	0.286623i	−0.980861	−	0.194708i	$-0.937624\pi$
$877$	−3.08942	+	8.48810i	−0.104322	+	0.286623i	0.876539	+	0.481331i	$0.159846\pi$
$878$	−25.4939	−	4.49527i	−0.860379	−	0.151708i
$879$	1.40728	+	7.98106i	0.0474663	+	0.269195i
$880$	9.23960	+	3.94631i	0.311467	+	0.133030i
$881$	−2.62778	+	4.55145i	−0.0885323	+	0.153342i	−0.906891	−	0.421365i	$-0.861551\pi$
$881$	−2.62778	+	4.55145i	−0.0885323	+	0.153342i	0.818359	+	0.574708i	$0.194884\pi$
$882$	11.9686	−	6.91010i	0.403005	−	0.232675i
$883$	−8.32617	+	9.92274i	−0.280198	+	0.333927i	−0.887727	−	0.460371i	$-0.847716\pi$
$883$	−8.32617	+	9.92274i	−0.280198	+	0.333927i	0.607529	+	0.794298i	$0.292161\pi$
$884$	0.704045	+	0.590764i	0.0236796	+	0.0198695i
$885$	−21.5757	−	5.03185i	−0.725261	−	0.169144i
$886$	10.6563	−	18.4572i	0.358005	−	0.620083i
$887$	15.9173	+	43.7323i	0.534449	+	1.46839i	0.853725	+	0.520725i	$0.174338\pi$
$887$	15.9173	+	43.7323i	0.534449	+	1.46839i	−0.319275	+	0.947662i	$0.603440\pi$
$888$	−4.53745	+	0.800076i	−0.152267	+	0.0268488i
$889$	−1.50598	+	8.54086i	−0.0505091	+	0.286451i
$890$	15.9518	−	8.08312i	0.534707	−	0.270947i
$891$	3.44198	−	2.88816i	0.115311	−	0.0967571i
$892$		−	7.47159i		−	0.250167i
$893$	36.8630	+	9.28828i	1.23357	+	0.310820i
$894$	−6.49321			−0.217166
$895$	−15.5134	−	0.847713i	−0.518556	−	0.0283359i
$896$	−4.28774	−	1.56061i	−0.143243	−	0.0521363i
$897$	−0.481448	−	0.0848922i	−0.0160751	−	0.00283447i
$898$	12.1902	−	2.14945i	0.406791	−	0.0717282i
$899$	97.5742	−	35.5141i	3.25428	−	1.18446i
$900$	−4.48415	−	2.21187i	−0.149472	−	0.0737292i
$901$	−0.0601988	−	0.104267i	−0.00200551	−	0.00347365i
$902$	17.1086	−	20.3893i	0.569655	−	0.678889i
$903$	19.0380	−	22.6886i	0.633545	−	0.755030i
$904$	−7.06497	−	12.2369i	−0.234978	−	0.406993i
$905$	−3.88639	+	1.17872i	−0.129188	+	0.0391819i
$906$	−16.5399	+	6.02001i	−0.549500	+	0.200002i
$907$	−23.4183	+	4.12927i	−0.777591	+	0.137110i	−0.548338	−	0.836257i	$-0.684739\pi$
$907$	−23.4183	+	4.12927i	−0.777591	+	0.137110i	−0.229253	+	0.973367i	$0.573628\pi$
$908$	−13.5037	−	2.38107i	−0.448137	−	0.0790186i
$909$	13.6202	+	4.95734i	0.451753	+	0.164425i
$910$	0.154535	−	2.82804i	0.00512280	−	0.0937487i
$911$	−7.91887			−0.262364			−0.131182	−	0.991358i	$-0.541877\pi$
$911$	−7.91887			−0.262364			−0.131182	+	0.991358i	$0.541877\pi$
$912$	−4.22679	−	1.06501i	−0.139963	−	0.0352661i
$913$		−	6.60722i		−	0.218667i
$914$	−9.49129	+	7.96414i	−0.313944	+	0.263430i
$915$	−20.9326	+	10.6070i	−0.692011	+	0.350656i
$916$	−3.94540	+	22.3755i	−0.130360	+	0.739306i
$917$	5.09526	−	0.898432i	0.168260	−	0.0296688i
$918$	1.13238	+	3.11119i	0.0373741	+	0.102684i
$919$	−13.3750	+	23.1663i	−0.441202	+	0.764185i	−0.997779	−	0.0666116i	$-0.978781\pi$
$919$	−13.3750	+	23.1663i	−0.441202	+	0.764185i	0.556577	+	0.830796i	$0.312114\pi$
$920$	0.894413	−	3.83509i	0.0294879	−	0.126439i
$921$	6.25829	+	5.25133i	0.206218	+	0.173037i
$922$	−2.65040	+	3.15863i	−0.0872863	+	0.104024i
$923$	−2.89089	+	1.66905i	−0.0951547	+	0.0549376i
$924$	−10.2510	+	17.7553i	−0.337234	+	0.584106i
$925$	21.0872	−	9.27615i	0.693342	−	0.304998i
$926$	−3.00275	−	17.0294i	−0.0986765	−	0.559622i
$927$	10.6557	+	1.87889i	0.349979	+	0.0617107i
$928$	3.60181	−	9.89590i	0.118235	−	0.324849i
$929$	35.4578	−	29.7526i	1.16333	−	0.976151i	0.163386	−	0.986562i	$-0.447759\pi$
$929$	35.4578	−	29.7526i	1.16333	−	0.976151i	0.999946	+	0.0104113i	$0.00331408\pi$
$930$	−16.0912	−	15.0725i	−0.527650	−	0.494245i
$931$	−33.8102	+	49.8581i	−1.10808	+	1.63403i
$932$			18.4339i			0.603822i
$933$	−2.27146	−	2.70702i	−0.0743643	−	0.0886240i
$934$	21.7500	+	7.91635i	0.711681	+	0.259031i
$935$	19.9597	+	26.6107i	0.652753	+	0.870263i
$936$	0.0482032	+	0.273374i	0.00157557	+	0.00893551i
$937$	2.74470	+	7.54100i	0.0896655	+	0.246354i	0.976417	−	0.215892i	$-0.0692659\pi$
$937$	2.74470	+	7.54100i	0.0896655	+	0.246354i	−0.886752	+	0.462246i	$0.847044\pi$
$938$	−24.3624	−	14.0657i	−0.795462	−	0.459260i
$939$	−11.0860	−	19.2015i	−0.361777	−	0.626617i
$940$	19.3613	−	2.33346i	0.631495	−	0.0761090i
$941$	−19.4818	−	16.3472i	−0.635088	−	0.532902i	0.267417	−	0.963581i	$-0.413830\pi$
$941$	−19.4818	−	16.3472i	−0.635088	−	0.532902i	−0.902505	+	0.430679i	$0.858274\pi$
$942$	−5.21964	+	3.01356i	−0.170065	+	0.0981871i
$943$	−9.03474	−	5.21621i	−0.294212	−	0.169863i
$944$	−9.31038	+	3.38870i	−0.303027	+	0.110293i
$945$	5.57601	−	8.54454i	0.181388	−	0.277954i
$946$	−5.06450	+	28.7222i	−0.164661	+	0.933839i
$947$	15.7627	−	43.3076i	0.512218	−	1.40731i	−0.366702	−	0.930339i	$-0.619513\pi$
$947$	15.7627	−	43.3076i	0.512218	−	1.40731i	0.878920	−	0.476969i	$-0.158265\pi$
$948$	−6.90809	−	8.23275i	−0.224364	−	0.267387i
$949$	2.94105			0.0954705
$950$	21.7940	+	0.151312i	0.707090	+	0.00490922i
$951$	−2.84868			−0.0923749
$952$	−9.71069	−	11.5728i	−0.314725	−	0.375075i
$953$	15.9442	−	43.8062i	0.516482	−	1.41902i	−0.357889	−	0.933764i	$-0.616503\pi$
$953$	15.9442	−	43.8062i	0.516482	−	1.41902i	0.874371	−	0.485259i	$-0.161275\pi$
$954$	0.00631463	−	0.0358120i	0.000204444	−	0.00115946i
$955$	−2.25455	+	3.45482i	−0.0729556	+	0.111795i
$956$	−15.8958	+	5.78559i	−0.514106	+	0.187119i
$957$	−40.9784	−	23.6589i	−1.32464	−	0.764783i
$958$	−20.4963	+	11.8336i	−0.662207	+	0.382325i
$959$	1.27149	+	1.06690i	0.0410584	+	0.0344521i
$960$	−2.22000	+	0.267559i	−0.0716503	+	0.00863542i
$961$	−33.1104	−	57.3489i	−1.06808	−	1.84997i
$962$	−1.10764	−	0.639494i	−0.0357116	−	0.0206181i
$963$	−3.81443	−	10.4801i	−0.122918	−	0.337716i
$964$	0.696747	+	3.95145i	0.0224407	+	0.127268i
$965$	9.51002	+	12.6789i	0.306138	+	0.408150i
$966$	7.55127	+	2.74844i	0.242958	+	0.0884295i
$967$	14.0718	+	16.7701i	0.452518	+	0.539290i	0.943278	−	0.332005i	$-0.107725\pi$
$967$	14.0718	+	16.7701i	0.452518	+	0.539290i	−0.490759	+	0.871295i	$0.663281\pi$
$968$		−	9.18872i		−	0.295337i
$969$	−10.3564	−	10.0508i	−0.332694	−	0.322880i
$970$	−4.54048	−	4.25303i	−0.145786	−	0.136557i
$971$	43.7768	−	36.7331i	1.40486	−	1.17882i	0.445972	−	0.895047i	$-0.352858\pi$
$971$	43.7768	−	36.7331i	1.40486	−	1.17882i	0.958891	−	0.283774i	$-0.0915865\pi$
$972$	−0.342020	+	0.939693i	−0.0109703	+	0.0301407i
$973$	61.1946	+	10.7903i	1.96181	+	0.345920i
$974$	−2.35421	−	13.3514i	−0.0754338	−	0.427806i
$975$	−0.558873	−	1.27047i	−0.0178983	−	0.0406875i
$976$	−5.24729	+	9.08858i	−0.167962	+	0.290918i
$977$	−10.7313	+	6.19571i	−0.343324	+	0.198218i	−0.661741	−	0.749732i	$-0.730182\pi$
$977$	−10.7313	+	6.19571i	−0.343324	+	0.198218i	0.318417	+	0.947951i	$0.396849\pi$
$978$	13.1580	−	15.6811i	0.420746	−	0.501426i
$979$	−27.5272	−	23.0980i	−0.879772	−	0.738216i
$980$	−7.01877	+	30.0953i	−0.224206	+	0.961359i
$981$	0.643404	−	1.11441i	0.0205423	−	0.0355803i
$982$	3.85732	+	10.5979i	0.123092	+	0.338192i
$983$	−31.9038	+	5.62550i	−1.01757	+	0.179425i	−0.657465	−	0.753485i	$-0.728371\pi$
$983$	−31.9038	+	5.62550i	−1.01757	+	0.179425i	−0.360108	+	0.932911i	$0.617260\pi$
$984$	−1.02864	+	5.83371i	−0.0327919	+	0.185972i
$985$	−23.8741	+	12.0975i	−0.760692	+	0.385458i
$986$	26.7094	−	22.4118i	0.850600	−	0.713738i
$987$			39.7945i			1.26667i
$988$	−0.708783	−	0.980668i	−0.0225494	−	0.0311992i
$989$	11.4315			0.363501
$990$	−0.548194	+	10.0321i	−0.0174227	+	0.318841i
$991$	−18.0125	−	6.55601i	−0.572186	−	0.208259i	0.0396906	−	0.999212i	$-0.487363\pi$
$991$	−18.0125	−	6.55601i	−0.572186	−	0.208259i	−0.611876	+	0.790953i	$0.709585\pi$
$992$	−9.71027	−	1.71218i	−0.308301	−	0.0543618i
$993$	−9.17207	+	1.61728i	−0.291067	+	0.0513229i
$994$	51.5612	−	18.7667i	1.63542	−	0.595244i
$995$	5.82798	−	1.76759i	0.184759	−	0.0560364i
$996$	0.735249	+	1.27349i	0.0232973	+	0.0403520i
$997$	27.9353	−	33.2920i	0.884720	−	1.05437i	−0.113429	−	0.993546i	$-0.536183\pi$
$997$	27.9353	−	33.2920i	0.884720	−	1.05437i	0.998149	−	0.0608219i	$-0.0193722\pi$
$998$	−10.1743	+	12.1253i	−0.322063	+	0.383819i
$999$	−2.30373	−	3.99017i	−0.0728867	−	0.126243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bc.a.139.9	yes	60
5.4	even	2	inner	570.2.bc.a.139.2	✓	60
19.16	even	9	inner	570.2.bc.a.529.2	yes	60
95.54	even	18	inner	570.2.bc.a.529.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bc.a.139.2	✓	60	5.4	even	2	inner
570.2.bc.a.139.9	yes	60	1.1	even	1	trivial
570.2.bc.a.529.2	yes	60	19.16	even	9	inner
570.2.bc.a.529.9	yes	60	95.54	even	18	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.22203 - 1.87260i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-3.95160 - 2.28146i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.642788 + 0.766044i) q^{2} +(0.342020 - 0.939693i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(1.22203 - 1.87260i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-3.95160 - 2.28146i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(-0.766044 - 0.642788i) q^{9} +(2.22000 - 0.267559i) q^{10} +(-2.24659 - 3.89121i) q^{11} +(0.866025 + 0.500000i) q^{12} +(0.0949418 + 0.260851i) q^{13} +(-0.792342 - 4.49360i) q^{14} +(-1.34171 - 1.78880i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(-2.12818 - 2.53626i) q^{17} -1.00000i q^{18} +(1.90108 + 3.92249i) q^{19} +(1.63195 + 1.52864i) q^{20} +(-3.49540 + 2.93299i) q^{21} +(1.53676 - 4.22221i) q^{22} +(-1.73438 - 0.305817i) q^{23} +(0.173648 + 0.984808i) q^{24} +(-2.01329 - 4.57675i) q^{25} +(-0.138796 + 0.240401i) q^{26} +(-0.866025 + 0.500000i) q^{27} +(2.93299 - 3.49540i) q^{28} +(8.06721 + 6.76920i) q^{29} +(0.507863 - 2.17763i) q^{30} +(4.93003 - 8.53907i) q^{31} +(-0.342020 - 0.939693i) q^{32} +(-4.42492 + 0.780234i) q^{33} +(0.574924 - 3.26056i) q^{34} +(-9.10124 + 4.61178i) q^{35} +(0.766044 - 0.642788i) q^{36} +4.60745i q^{37} +(-1.78281 + 3.97764i) q^{38} +0.277591 q^{39} +(-0.122006 + 2.23274i) q^{40} +(5.56646 + 2.02603i) q^{41} +(-4.49360 - 0.792342i) q^{42} +(-6.39239 + 1.12715i) q^{43} +(4.22221 - 1.53676i) q^{44} +(-2.13981 + 0.648993i) q^{45} +(-0.880565 - 1.52518i) q^{46} +(5.60594 - 6.68089i) q^{47} +(-0.642788 + 0.766044i) q^{48} +(6.91010 + 11.9686i) q^{49} +(2.21187 - 4.48415i) q^{50} +(-3.11119 + 1.13238i) q^{51} +(-0.273374 + 0.0482032i) q^{52} +(0.0358120 + 0.00631463i) q^{53} +(-0.939693 - 0.342020i) q^{54} +(-10.0321 - 0.548194i) q^{55} +4.56292 q^{56} +(4.33614 - 0.444863i) q^{57} +10.5310i q^{58} +(7.58989 - 6.36868i) q^{59} +(1.99461 - 1.01071i) q^{60} +(1.82237 - 10.3352i) q^{61} +(9.71027 - 1.71218i) q^{62} +(1.56061 + 4.28774i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.604492 + 0.140978i) q^{65} +(-3.44198 - 2.88816i) q^{66} +(3.96292 - 4.72282i) q^{67} +(2.86729 - 1.65543i) q^{68} +(-0.880565 + 1.52518i) q^{69} +(-9.38299 - 4.00756i) q^{70} +(2.08816 + 11.8426i) q^{71} +(0.984808 + 0.173648i) q^{72} +(3.62366 - 9.95594i) q^{73} +(-3.52951 + 2.96161i) q^{74} +(-4.98933 + 0.326536i) q^{75} +(-4.19301 + 1.19107i) q^{76} +20.5020i q^{77} +(0.178432 + 0.212647i) q^{78} +(-10.0990 - 3.67572i) q^{79} +(-1.78880 + 1.34171i) q^{80} +(0.173648 + 0.984808i) q^{81} +(2.02603 + 5.56646i) q^{82} +(1.27349 + 0.735249i) q^{83} +(-2.28146 - 3.95160i) q^{84} +(-7.35011 + 0.885848i) q^{85} +(-4.97240 - 4.17234i) q^{86} +(9.12011 - 5.26550i) q^{87} +(3.89121 + 2.24659i) q^{88} +(7.51517 - 2.73530i) q^{89} +(-1.87260 - 1.22203i) q^{90} +(0.219947 - 1.24738i) q^{91} +(0.602342 - 1.65492i) q^{92} +(-6.33793 - 7.55325i) q^{93} +8.72129 q^{94} +(9.66844 + 1.23342i) q^{95} -1.00000 q^{96} +(-1.78839 - 2.13132i) q^{97} +(-4.72679 + 12.9867i) q^{98} +(-0.780234 + 4.42492i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{5}+O(q^{10}) \) 60 * q - 6 * q^5	\( 60 q - 6 q^{5} - 6 q^{10} - 12 q^{11} + 24 q^{14} + 12 q^{15} + 24 q^{19} + 12 q^{20} - 30 q^{21} + 18 q^{25} - 6 q^{26} + 36 q^{29} - 6 q^{30} + 36 q^{31} + 30 q^{35} + 12 q^{39} + 6 q^{40} + 42 q^{41} - 6 q^{44} - 6 q^{45} + 12 q^{46} + 66 q^{49} + 18 q^{55} - 24 q^{56} - 12 q^{59} + 6 q^{60} + 84 q^{61} + 30 q^{64} - 24 q^{65} + 12 q^{66} + 12 q^{69} - 72 q^{71} - 42 q^{74} + 6 q^{76} - 72 q^{79} - 6 q^{80} + 12 q^{84} - 138 q^{85} - 36 q^{86} - 180 q^{89} - 12 q^{90} - 60 q^{94} + 24 q^{95} - 60 q^{96} - 6 q^{99}+O(q^{100}) \) 60 * q - 6 * q^5 - 6 * q^10 - 12 * q^11 + 24 * q^14 + 12 * q^15 + 24 * q^19 + 12 * q^20 - 30 * q^21 + 18 * q^25 - 6 * q^26 + 36 * q^29 - 6 * q^30 + 36 * q^31 + 30 * q^35 + 12 * q^39 + 6 * q^40 + 42 * q^41 - 6 * q^44 - 6 * q^45 + 12 * q^46 + 66 * q^49 + 18 * q^55 - 24 * q^56 - 12 * q^59 + 6 * q^60 + 84 * q^61 + 30 * q^64 - 24 * q^65 + 12 * q^66 + 12 * q^69 - 72 * q^71 - 42 * q^74 + 6 * q^76 - 72 * q^79 - 6 * q^80 + 12 * q^84 - 138 * q^85 - 36 * q^86 - 180 * q^89 - 12 * q^90 - 60 * q^94 + 24 * q^95 - 60 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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