LMFDB - Embedded newform 504.2.cs.a.85.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(85,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2, 0]))

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

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

chi := DirichletCharacter("504.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cs (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			85.7
Character	$\chi$	$=$	504.85
Dual form			504.2.cs.a.421.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20390 + 0.742040i) q^{2} +(-1.50659 + 0.854512i) q^{3} +(0.898754 - 1.78668i) q^{4} +(3.20115 + 1.84819i) q^{5} +(1.17970 - 2.14670i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.243781 + 2.81790i) q^{8} +(1.53962 - 2.57480i) q^{9} +O(q^{10})$	\(q+(-1.20390 + 0.742040i) q^{2} +(-1.50659 + 0.854512i) q^{3} +(0.898754 - 1.78668i) q^{4} +(3.20115 + 1.84819i) q^{5} +(1.17970 - 2.14670i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.243781 + 2.81790i) q^{8} +(1.53962 - 2.57480i) q^{9} +(-5.22530 + 0.150350i) q^{10} +(1.82566 - 1.05405i) q^{11} +(0.172691 + 3.45979i) q^{12} +(1.52763 + 0.881980i) q^{13} +(-1.24458 - 0.671589i) q^{14} +(-6.40212 - 0.0490330i) q^{15} +(-2.38448 - 3.21158i) q^{16} +5.70313 q^{17} +(0.0570536 + 4.24226i) q^{18} -7.31960i q^{19} +(6.17918 - 4.05839i) q^{20} +(-1.49332 - 0.877488i) q^{21} +(-1.41577 + 2.62368i) q^{22} +(3.76218 - 6.51629i) q^{23} +(-2.77521 - 4.03711i) q^{24} +(4.33159 + 7.50253i) q^{25} +(-2.49358 + 0.0717490i) q^{26} +(-0.119377 + 5.19478i) q^{27} +(1.99669 - 0.114999i) q^{28} +(-3.94605 + 2.27825i) q^{29} +(7.74390 - 4.69160i) q^{30} +(-3.33335 + 5.77353i) q^{31} +(5.25380 + 2.09704i) q^{32} +(-1.84982 + 3.14806i) q^{33} +(-6.86600 + 4.23195i) q^{34} +3.69637i q^{35} +(-3.21661 - 5.06492i) q^{36} +1.33066i q^{37} +(5.43143 + 8.81207i) q^{38} +(-3.05518 - 0.0233992i) q^{39} +(-4.42763 + 9.47109i) q^{40} +(0.715411 - 1.23913i) q^{41} +(2.44894 - 0.0516970i) q^{42} +(-7.02960 + 4.05854i) q^{43} +(-0.242427 - 4.20921i) q^{44} +(9.68726 - 5.39682i) q^{45} +(0.306053 + 10.6367i) q^{46} +(4.86691 + 8.42973i) q^{47} +(6.33677 + 2.80096i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-10.7820 - 5.81809i) q^{50} +(-8.59226 + 4.87339i) q^{51} +(2.94879 - 1.93672i) q^{52} -2.92710i q^{53} +(-3.71102 - 6.34258i) q^{54} +7.79229 q^{55} +(-2.31848 + 1.62007i) q^{56} +(6.25469 + 11.0276i) q^{57} +(3.06010 - 5.67092i) q^{58} +(4.09591 + 2.36477i) q^{59} +(-5.84154 + 11.3945i) q^{60} +(1.91970 - 1.10834i) q^{61} +(-0.271168 - 9.42423i) q^{62} +(2.99965 + 0.0459505i) q^{63} +(-7.88114 + 1.37390i) q^{64} +(3.26013 + 5.64671i) q^{65} +(-0.108982 - 5.16260i) q^{66} +(-8.89797 - 5.13725i) q^{67} +(5.12571 - 10.1897i) q^{68} +(-0.0998119 + 13.0322i) q^{69} +(-2.74286 - 4.45007i) q^{70} -9.43810 q^{71} +(7.63085 + 3.71081i) q^{72} -1.98930 q^{73} +(-0.987405 - 1.60199i) q^{74} +(-12.9369 - 7.60183i) q^{75} +(-13.0778 - 6.57852i) q^{76} +(1.82566 + 1.05405i) q^{77} +(3.69549 - 2.23889i) q^{78} +(7.60348 + 13.1696i) q^{79} +(-1.69750 - 14.6877i) q^{80} +(-4.25915 - 7.92841i) q^{81} +(0.0581986 + 2.02265i) q^{82} +(3.30347 - 1.90726i) q^{83} +(-2.90992 + 1.87945i) q^{84} +(18.2566 + 10.5404i) q^{85} +(5.45134 - 10.1023i) q^{86} +(3.99828 - 6.80434i) q^{87} +(3.41526 + 4.88758i) q^{88} -7.94314 q^{89} +(-7.65785 + 13.6856i) q^{90} +1.76396i q^{91} +(-8.26128 - 12.5784i) q^{92} +(0.0884348 - 11.5467i) q^{93} +(-12.1145 - 6.53712i) q^{94} +(13.5280 - 23.4312i) q^{95} +(-9.70726 + 1.33006i) q^{96} +(-9.64428 - 16.7044i) q^{97} +(-0.0406750 - 1.41363i) q^{98} +(0.0968678 - 6.32353i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	$ 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) $ 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.20390	+	0.742040i	−0.851286	+	0.524701i
$2$	−1.20390	+	0.742040i	−0.851286	+	0.524701i
$3$	−1.50659	+	0.854512i	−0.869829	+	0.493353i
$3$	−1.50659	+	0.854512i	−0.869829	+	0.493353i
$4$	0.898754	−	1.78668i	0.449377	−	0.893342i
$5$	3.20115	+	1.84819i	1.43160	+	0.826534i	0.997243	−	0.0742069i	$-0.0236425\pi$
$5$	3.20115	+	1.84819i	1.43160	+	0.826534i	0.434356	+	0.900741i	$0.356976\pi$
$6$	1.17970	−	2.14670i	0.481611	−	0.876385i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	0.243781	+	2.81790i	0.0861895	+	0.996279i
$9$	1.53962	−	2.57480i	0.513206	−	0.858265i
$10$	−5.22530	+	0.150350i	−1.65238	+	0.0475448i
$11$	1.82566	−	1.05405i	0.550457	−	0.317807i	−0.198849	−	0.980030i	$-0.563720\pi$
$11$	1.82566	−	1.05405i	0.550457	−	0.317807i	0.749306	+	0.662223i	$0.230387\pi$
$12$	0.172691	+	3.45979i	0.0498516	+	0.998757i
$13$	1.52763	+	0.881980i	0.423689	+	0.244617i	0.696655	−	0.717407i	$-0.254671\pi$
$13$	1.52763	+	0.881980i	0.423689	+	0.244617i	−0.272965	+	0.962024i	$0.588004\pi$
$14$	−1.24458	−	0.671589i	−0.332627	−	0.179490i
$15$	−6.40212	−	0.0490330i	−1.65302	−	0.0126603i
$16$	−2.38448	−	3.21158i	−0.596121	−	0.802895i
$17$	5.70313			1.38321			0.691606	−	0.722275i	$-0.256904\pi$
$17$	5.70313			1.38321			0.691606	+	0.722275i	$0.256904\pi$
$18$	0.0570536	+	4.24226i	0.0134477	+	0.999910i
$19$		−	7.31960i		−	1.67923i	−0.543181	−	0.839616i	$-0.682780\pi$
$19$		−	7.31960i		−	1.67923i	0.543181	−	0.839616i	$-0.317220\pi$
$20$	6.17918	−	4.05839i	1.38171	−	0.907483i
$21$	−1.49332	−	0.877488i	−0.325870	−	0.191484i
$22$	−1.41577	+	2.62368i	−0.301843	+	0.559370i
$23$	3.76218	−	6.51629i	0.784470	−	1.35874i	−0.144846	−	0.989454i	$-0.546269\pi$
$23$	3.76218	−	6.51629i	0.784470	−	1.35874i	0.929315	−	0.369287i	$-0.120398\pi$
$24$	−2.77521	−	4.03711i	−0.566487	−	0.824071i
$25$	4.33159	+	7.50253i	0.866318	+	1.50051i
$26$	−2.49358	+	0.0717490i	−0.489032	+	0.0140711i
$27$	−0.119377	+	5.19478i	−0.0229741	+	0.999736i
$28$	1.99669	−	0.114999i	0.377339	−	0.0217327i
$29$	−3.94605	+	2.27825i	−0.732763	+	0.423061i	−0.819432	−	0.573176i	$-0.805711\pi$
$29$	−3.94605	+	2.27825i	−0.732763	+	0.423061i	0.0866689	+	0.996237i	$0.472378\pi$
$30$	7.74390	−	4.69160i	1.41384	−	0.856564i
$31$	−3.33335	+	5.77353i	−0.598687	+	1.03696i	0.394328	+	0.918970i	$0.370977\pi$
$31$	−3.33335	+	5.77353i	−0.598687	+	1.03696i	−0.993015	+	0.117987i	$0.962356\pi$
$32$	5.25380	+	2.09704i	0.928749	+	0.370708i
$33$	−1.84982	+	3.14806i	−0.322013	+	0.548007i
$34$	−6.86600	+	4.23195i	−1.17751	+	0.725773i
$35$			3.69637i			0.624801i
$36$	−3.21661	−	5.06492i	−0.536102	−	0.844153i
$37$			1.33066i			0.218760i	0.994000	+	0.109380i	$0.0348865\pi$
$37$			1.33066i			0.218760i	−0.994000	+	0.109380i	$0.965114\pi$
$38$	5.43143	+	8.81207i	0.881095	+	1.42951i
$39$	−3.05518	−	0.0233992i	−0.489220	−	0.00374687i
$40$	−4.42763	+	9.47109i	−0.700070	+	1.49751i
$41$	0.715411	−	1.23913i	0.111728	−	0.193519i	−0.804739	−	0.593629i	$-0.797695\pi$
$41$	0.715411	−	1.23913i	0.111728	−	0.193519i	0.916467	+	0.400110i	$0.131028\pi$
$42$	2.44894	−	0.0516970i	0.377880	−	0.00797702i
$43$	−7.02960	+	4.05854i	−1.07200	+	0.618922i	−0.928728	−	0.370761i	$-0.879097\pi$
$43$	−7.02960	+	4.05854i	−1.07200	+	0.618922i	−0.143276	+	0.989683i	$0.545764\pi$
$44$	−0.242427	−	4.20921i	−0.0365473	−	0.634562i
$45$	9.68726	−	5.39682i	1.44409	−	0.804510i
$46$	0.306053	+	10.6367i	0.0451251	+	1.56829i
$47$	4.86691	+	8.42973i	0.709911	+	1.22960i	0.964890	+	0.262656i	$0.0845984\pi$
$47$	4.86691	+	8.42973i	0.709911	+	1.22960i	−0.254978	+	0.966947i	$0.582068\pi$
$48$	6.33677	+	2.80096i	0.914634	+	0.404284i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−10.7820	−	5.81809i	−1.52480	−	0.822802i
$51$	−8.59226	+	4.87339i	−1.20316	+	0.682411i
$52$	2.94879	−	1.93672i	0.408923	−	0.268574i
$53$		−	2.92710i		−	0.402068i	−0.979584	−	0.201034i	$-0.935570\pi$
$53$		−	2.92710i		−	0.402068i	0.979584	−	0.201034i	$-0.0644302\pi$
$54$	−3.71102	−	6.34258i	−0.505005	−	0.863116i
$55$	7.79229			1.05071
$56$	−2.31848	+	1.62007i	−0.309820	+	0.216491i
$57$	6.25469	+	11.0276i	0.828453	+	1.46064i
$58$	3.06010	−	5.67092i	0.401811	−	0.744628i
$59$	4.09591	+	2.36477i	0.533242	+	0.307867i	0.742335	−	0.670028i	$-0.233718\pi$
$59$	4.09591	+	2.36477i	0.533242	+	0.307867i	−0.209094	+	0.977896i	$0.567051\pi$
$60$	−5.84154	+	11.3945i	−0.754139	+	1.47102i
$61$	1.91970	−	1.10834i	0.245792	−	0.141908i	−0.372044	−	0.928215i	$-0.621343\pi$
$61$	1.91970	−	1.10834i	0.245792	−	0.141908i	0.617836	+	0.786307i	$0.288010\pi$
$62$	−0.271168	−	9.42423i	−0.0344383	−	1.19688i
$63$	2.99965	+	0.0459505i	0.377920	+	0.00578922i
$64$	−7.88114	+	1.37390i	−0.985143	+	0.171737i
$65$	3.26013	+	5.64671i	0.404369	+	0.700388i
$66$	−0.108982	−	5.16260i	−0.0134148	−	0.635472i
$67$	−8.89797	−	5.13725i	−1.08706	−	0.627614i	−0.154268	−	0.988029i	$-0.549302\pi$
$67$	−8.89797	−	5.13725i	−1.08706	−	0.627614i	−0.932792	+	0.360415i	$0.882635\pi$
$68$	5.12571	−	10.1897i	0.621583	−	1.23568i
$69$	−0.0998119	+	13.0322i	−0.0120159	+	1.56889i
$70$	−2.74286	−	4.45007i	−0.327834	−	0.531885i
$71$	−9.43810			−1.12010			−0.560048	−	0.828460i	$-0.689217\pi$
$71$	−9.43810			−1.12010			−0.560048	+	0.828460i	$0.689217\pi$
$72$	7.63085	+	3.71081i	0.899305	+	0.437323i
$73$	−1.98930			−0.232830			−0.116415	−	0.993201i	$-0.537140\pi$
$73$	−1.98930			−0.232830			−0.116415	+	0.993201i	$0.537140\pi$
$74$	−0.987405	−	1.60199i	−0.114784	−	0.186227i
$75$	−12.9369	−	7.60183i	−1.49383	−	0.877784i
$76$	−13.0778	−	6.57852i	−1.50013	−	0.754608i
$77$	1.82566	+	1.05405i	0.208053	+	0.120120i
$78$	3.69549	−	2.23889i	0.418432	−	0.253505i
$79$	7.60348	+	13.1696i	0.855459	+	1.48170i	0.876219	+	0.481913i	$0.160058\pi$
$79$	7.60348	+	13.1696i	0.855459	+	1.48170i	−0.0207602	+	0.999784i	$0.506609\pi$
$80$	−1.69750	−	14.6877i	−0.189786	−	1.64214i
$81$	−4.25915	−	7.92841i	−0.473239	−	0.880934i
$82$	0.0581986	+	2.02265i	0.00642696	+	0.223364i
$83$	3.30347	−	1.90726i	0.362602	−	0.209349i	−0.307619	−	0.951510i	$-0.599532\pi$
$83$	3.30347	−	1.90726i	0.362602	−	0.209349i	0.670222	+	0.742161i	$0.266199\pi$
$84$	−2.90992	+	1.87945i	−0.317499	+	0.205065i
$85$	18.2566	+	10.5404i	1.98020	+	1.14327i
$86$	5.45134	−	10.1023i	0.587834	−	1.08936i
$87$	3.99828	−	6.80434i	0.428661	−	0.729502i
$88$	3.41526	+	4.88758i	0.364068	+	0.521017i
$89$	−7.94314			−0.841971			−0.420985	−	0.907067i	$-0.638316\pi$
$89$	−7.94314			−0.841971			−0.420985	+	0.907067i	$0.638316\pi$
$90$	−7.65785	+	13.6856i	−0.807208	+	1.44258i
$91$			1.76396i			0.184913i
$92$	−8.26128	−	12.5784i	−0.861298	−	1.31139i
$93$	0.0884348	−	11.5467i	0.00917026	−	1.19734i
$94$	−12.1145	−	6.53712i	−1.24951	−	0.674253i
$95$	13.5280	−	23.4312i	1.38794	−	2.40399i
$96$	−9.70726	+	1.33006i	−0.990743	+	0.135748i
$97$	−9.64428	−	16.7044i	−0.979228	−	1.69607i	−0.665210	−	0.746656i	$-0.731658\pi$
$97$	−9.64428	−	16.7044i	−0.979228	−	1.69607i	−0.314019	−	0.949417i	$-0.601675\pi$
$98$	−0.0406750	−	1.41363i	−0.00410879	−	0.142798i
$99$	0.0968678	−	6.32353i	0.00973559	−	0.635539i
$100$	17.2977	−	0.996253i	1.72977	−	0.0996253i
$101$	1.90658	−	1.10076i	0.189711	−	0.109530i	−0.402136	−	0.915580i	$-0.631732\pi$
$101$	1.90658	−	1.10076i	0.189711	−	0.109530i	0.591847	+	0.806050i	$0.298399\pi$
$102$	6.72798	−	12.2429i	0.666170	−	1.21223i
$103$	3.53121	−	6.11624i	0.347940	−	0.602651i	−0.637943	−	0.770084i	$-0.720214\pi$
$103$	3.53121	−	6.11624i	0.347940	−	0.602651i	0.985883	+	0.167433i	$0.0535478\pi$
$104$	−2.11293	+	4.51973i	−0.207189	+	0.443196i
$105$	−3.15860	−	5.56891i	−0.308247	−	0.543470i
$106$	2.17202	+	3.52394i	0.210966	+	0.342275i
$107$			8.05972i			0.779163i	0.920992	+	0.389581i	$0.127380\pi$
$107$			8.05972i			0.779163i	−0.920992	+	0.389581i	$0.872620\pi$
$108$	9.17414	+	4.88212i	0.882782	+	0.469782i
$109$		−	11.4582i		−	1.09750i	−0.835987	−	0.548750i	$-0.815104\pi$
$109$		−	11.4582i		−	1.09750i	0.835987	−	0.548750i	$-0.184896\pi$
$110$	−9.38114	+	5.78219i	−0.894457	+	0.551310i
$111$	−1.13707	−	2.00476i	−0.107926	−	0.190284i
$112$	1.58907	−	3.67081i	0.150153	−	0.346859i
$113$	−6.45116	+	11.1737i	−0.606874	+	1.05114i	0.384878	+	0.922967i	$0.374243\pi$
$113$	−6.45116	+	11.1737i	−0.606874	+	1.05114i	−0.991752	+	0.128169i	$0.959090\pi$
$114$	−15.7130	−	8.63494i	−1.47165	−	0.808736i
$115$	24.0867	−	13.9064i	2.24609	−	1.29678i
$116$	0.523992	+	9.09794i	0.0486514	+	0.844722i
$117$	4.62289	−	2.57543i	0.427386	−	0.238099i
$118$	−6.68582	+	0.192374i	−0.615480	+	0.0177095i
$119$	2.85156	+	4.93905i	0.261402	+	0.452762i
$120$	−1.42254	−	18.0525i	−0.129860	−	1.64796i
$121$	−3.27798	+	5.67762i	−0.297998	+	0.516147i
$122$	−1.48869	+	2.75882i	−0.134780	+	0.249772i
$123$	−0.0189801	+	2.47818i	−0.00171138	+	0.223450i
$124$	7.31961	+	11.1446i	0.657321	+	1.00082i
$125$			13.5405i			1.21110i
$126$	−3.64538	+	2.17054i	−0.324756	+	0.193367i
$127$	−0.672471			−0.0596722			−0.0298361	−	0.999555i	$-0.509499\pi$
$127$	−0.672471			−0.0596722			−0.0298361	+	0.999555i	$0.509499\pi$
$128$	8.46862	−	7.50216i	0.748528	−	0.663104i
$129$	7.12265	−	12.1214i	0.627114	−	1.06723i
$130$	−8.11495	−	4.37893i	−0.711728	−	0.384057i
$131$	−0.385690	−	0.222679i	−0.0336979	−	0.0194555i	0.483056	−	0.875589i	$-0.339527\pi$
$131$	−0.385690	−	0.222679i	−0.0336979	−	0.0194555i	−0.516754	+	0.856134i	$0.672860\pi$
$132$	3.96206	+	6.13438i	0.344853	+	0.533930i
$133$	6.33896	−	3.65980i	0.549658	−	0.317345i
$134$	14.5243	−	0.417915i	1.25471	−	0.0361023i
$135$	−9.98307	+	16.4087i	−0.859206	+	1.41223i
$136$	1.39031	+	16.0708i	0.119218	+	1.37806i
$137$	5.70863	+	9.88763i	0.487721	+	0.844757i	0.999900	−	0.0141211i	$-0.00449504\pi$
$137$	5.70863	+	9.88763i	0.487721	+	0.844757i	−0.512179	+	0.858879i	$0.671162\pi$
$138$	−9.55025	−	15.7635i	−0.812971	−	1.34188i
$139$	−12.2179	−	7.05401i	−1.03631	−	0.598313i	−0.117524	−	0.993070i	$-0.537496\pi$
$139$	−12.2179	−	7.05401i	−1.03631	−	0.598313i	−0.918786	+	0.394757i	$0.870829\pi$
$140$	6.60425	+	3.32213i	0.558161	+	0.280771i
$141$	−14.5357	−	8.54131i	−1.22413	−	0.719308i
$142$	11.3625	−	7.00345i	0.953523	−	0.587716i
$143$	3.71859			0.310964
$144$	−11.9404	+	1.19495i	−0.995030	+	0.0995793i
$145$	−16.8426			−1.39870
$146$	2.39492	−	1.47614i	0.198205	−	0.122166i
$147$	0.0132652	−	1.73200i	0.00109409	−	0.142853i
$148$	2.37748	+	1.19594i	0.195427	+	0.0983056i
$149$	0.956636	+	0.552314i	0.0783707	+	0.0452473i	0.538673	−	0.842515i	$-0.318926\pi$
$149$	0.956636	+	0.552314i	0.0783707	+	0.0452473i	−0.460303	+	0.887762i	$0.652259\pi$
$150$	21.2156	−	0.447860i	1.73225	−	0.0365677i
$151$	−0.581912	−	1.00790i	−0.0473554	−	0.0820219i	0.841376	−	0.540450i	$-0.181746\pi$
$151$	−0.581912	−	1.00790i	−0.0473554	−	0.0820219i	−0.888731	+	0.458428i	$0.848413\pi$
$152$	20.6259	−	1.78438i	1.67298	−	0.144732i
$153$	8.78064	−	14.6844i	0.709872	−	1.18716i
$154$	−2.98006	+	0.0857465i	−0.240140	+	0.00690965i
$155$	−21.3411	+	12.3213i	−1.71416	+	0.989671i
$156$	−2.78766	+	5.43761i	−0.223191	+	0.435357i
$157$	−4.37117	−	2.52369i	−0.348857	−	0.201413i	0.315325	−	0.948984i	$-0.397887\pi$
$157$	−4.37117	−	2.52369i	−0.348857	−	0.201413i	−0.664182	+	0.747571i	$0.731220\pi$
$158$	−18.9262	−	10.2128i	−1.50569	−	0.812489i
$159$	2.50124	+	4.40993i	0.198361	+	0.349730i
$160$	12.9425	+	16.4230i	1.02319	+	1.29835i
$161$	7.52437			0.593003
$162$	11.0108	+	6.38456i	0.865089	+	0.501618i
$163$		−	6.35787i		−	0.497987i	−0.968505	−	0.248993i	$-0.919900\pi$
$163$		−	6.35787i		−	0.497987i	0.968505	−	0.248993i	$-0.0800998\pi$
$164$	−1.57095	−	2.39188i	−0.122671	−	0.186775i
$165$	−11.7398	+	6.65861i	−0.913940	+	0.518372i
$166$	−2.56178	+	4.74745i	−0.198833	+	0.368474i
$167$	−2.44102	+	4.22797i	−0.188892	+	0.327170i	−0.944881	−	0.327414i	$-0.893823\pi$
$167$	−2.44102	+	4.22797i	−0.188892	+	0.327170i	0.755989	+	0.654584i	$0.227156\pi$
$168$	2.10863	−	4.42195i	0.162684	−	0.341161i
$169$	−4.94422	−	8.56365i	−0.380325	−	0.658742i
$170$	−29.8005	+	0.857464i	−2.28560	+	0.0657645i
$171$	−18.8465	−	11.2694i	−1.44123	−	0.861792i
$172$	0.933453	+	16.2073i	0.0711752	+	1.23580i
$173$	11.3782	−	6.56920i	0.865068	−	0.499447i	−0.000638366	−	1.00000i	$-0.500203\pi$
$173$	11.3782	−	6.56920i	0.865068	−	0.499447i	0.865706	+	0.500553i	$0.166870\pi$
$174$	0.235558	+	11.1586i	0.0178576	+	0.845934i
$175$	−4.33159	+	7.50253i	−0.327437	+	0.567138i
$176$	−7.73841	−	3.34990i	−0.583304	−	0.252508i
$177$	−8.19157	−	0.0627382i	−0.615716	−	0.00471569i
$178$	9.56275	−	5.89412i	0.716758	−	0.441783i
$179$		−	0.931011i		−	0.0695870i	−0.999395	−	0.0347935i	$-0.988923\pi$
$179$		−	0.931011i		−	0.0695870i	0.999395	−	0.0347935i	$-0.0110774\pi$
$180$	−0.935945	−	22.1585i	−0.0697612	−	1.65160i
$181$		−	9.17468i		−	0.681948i	−0.940073	−	0.340974i	$-0.889243\pi$
$181$		−	9.17468i		−	0.681948i	0.940073	−	0.340974i	$-0.110757\pi$
$182$	−1.30893	−	2.12363i	−0.0970242	−	0.157414i
$183$	−1.94510	+	3.31021i	−0.143786	+	0.244698i
$184$	19.2794	+	9.01292i	1.42130	+	0.664441i
$185$	−2.45931	+	4.25966i	−0.180812	+	0.313176i
$186$	8.46166	+	13.9667i	0.620439	+	1.02409i
$187$	10.4120	−	6.01135i	0.761399	−	0.439594i
$188$	19.4354	−	1.11937i	1.41747	−	0.0816388i
$189$	−4.55850	+	2.49401i	−0.331582	+	0.181412i
$190$	1.10050	+	38.2471i	0.0798387	+	2.77474i
$191$	−2.57593	−	4.46164i	−0.186387	−	0.322833i	0.757656	−	0.652654i	$-0.226345\pi$
$191$	−2.57593	−	4.46164i	−0.186387	−	0.322833i	−0.944043	+	0.329822i	$0.893011\pi$
$192$	10.6996	−	8.80443i	0.772179	−	0.635405i
$193$	1.56819	−	2.71618i	0.112881	−	0.195515i	−0.804050	−	0.594562i	$-0.797326\pi$
$193$	1.56819	−	2.71618i	0.112881	−	0.195515i	0.916931	+	0.399047i	$0.130659\pi$
$194$	24.0061	+	12.9540i	1.72354	+	0.930042i
$195$	−9.73685	−	5.72144i	−0.697270	−	0.409721i
$196$	1.09794	+	1.67169i	0.0784241	+	0.119406i
$197$			24.8869i			1.77312i	0.462612	+	0.886561i	$0.346912\pi$
$197$			24.8869i			1.77312i	−0.462612	+	0.886561i	$0.653088\pi$
$198$	4.57569	+	7.68478i	0.325180	+	0.546134i
$199$	−3.45782			−0.245118			−0.122559	−	0.992461i	$-0.539110\pi$
$199$	−3.45782			−0.245118			−0.122559	+	0.992461i	$0.539110\pi$
$200$	−20.0854	+	14.0350i	−1.42025	+	0.992422i
$201$	17.7954	+	0.136293i	1.25519	+	0.00961335i
$202$	−1.47852	+	2.73996i	−0.104028	+	0.192783i
$203$	−3.94605	−	2.27825i	−0.276959	−	0.159902i
$204$	0.984879	+	19.7316i	0.0689553	+	1.38149i
$205$	4.58028	−	2.64443i	0.319901	−	0.184695i
$206$	0.287264	+	9.98364i	0.0200146	+	0.695593i
$207$	−10.9858	−	19.7195i	−0.763566	−	1.37060i
$208$	−0.810069	−	7.00918i	−0.0561682	−	0.485999i
$209$	−7.71519	−	13.3631i	−0.533671	−	0.924345i
$210$	7.93499	+	4.36062i	0.547566	+	0.300911i
$211$	9.67270	+	5.58454i	0.665896	+	0.384455i	0.794520	−	0.607238i	$-0.207723\pi$
$211$	9.67270	+	5.58454i	0.665896	+	0.384455i	−0.128624	+	0.991693i	$0.541056\pi$
$212$	−5.22980	−	2.63074i	−0.359184	−	0.180680i
$213$	14.2193	−	8.06497i	0.974293	−	0.552603i
$214$	−5.98063	−	9.70311i	−0.408828	−	0.663291i
$215$	−30.0038			−2.04624
$216$	−14.6675	+	0.929994i	−0.997996	+	0.0632781i
$217$	−6.66670			−0.452565
$218$	8.50246	+	13.7946i	0.575859	+	0.934286i
$219$	2.99706	−	1.69988i	0.202523	−	0.114867i
$220$	7.00335	−	13.9224i	0.472166	−	0.938646i
$221$	8.71229	+	5.03004i	0.586052	+	0.338357i
$222$	2.85653	+	1.56978i	0.191718	+	0.105357i
$223$	−1.06276	−	1.84076i	−0.0711678	−	0.123266i	0.828246	−	0.560365i	$-0.189339\pi$
$223$	−1.06276	−	1.84076i	−0.0711678	−	0.123266i	−0.899413	+	0.437099i	$0.856006\pi$
$224$	0.810809	+	5.59845i	0.0541745	+	0.374062i
$225$	25.9865	+	0.398077i	1.73243	+	0.0265385i
$226$	−0.524801	−	18.2391i	−0.0349093	−	1.21325i
$227$	−8.02221	+	4.63162i	−0.532453	+	0.307412i	−0.742015	−	0.670384i	$-0.766130\pi$
$227$	−8.02221	+	4.63162i	−0.532453	+	0.307412i	0.209562	+	0.977795i	$0.432796\pi$
$228$	25.3243	−	1.26403i	1.67714	−	0.0837124i
$229$	−5.33825	−	3.08204i	−0.352761	−	0.203667i	0.313139	−	0.949707i	$-0.398619\pi$
$229$	−5.33825	−	3.08204i	−0.352761	−	0.203667i	−0.665901	+	0.746040i	$0.731953\pi$
$230$	−18.6788	+	34.6152i	−1.23164	+	2.28246i
$231$	−3.65121	−	0.0279642i	−0.240232	−	0.00183991i
$232$	−7.38187	−	10.5642i	−0.484643	−	0.693573i
$233$	−19.1191			−1.25253			−0.626266	−	0.779609i	$-0.715418\pi$
$233$	−19.1191			−1.25253			−0.626266	+	0.779609i	$0.715418\pi$
$234$	−3.65443	+	6.53094i	−0.238897	+	0.426941i
$235$			35.9798i			2.34706i
$236$	7.90631	−	5.19274i	0.514657	−	0.338019i
$237$	−22.7089	−	13.3439i	−1.47510	−	0.866781i
$238$	−7.09797	−	3.83015i	−0.460093	−	0.248272i
$239$	4.56059	−	7.89918i	0.295000	−	0.510956i	−0.679985	−	0.733226i	$-0.738014\pi$
$239$	4.56059	−	7.89918i	0.295000	−	0.510956i	0.974985	+	0.222271i	$0.0713469\pi$
$240$	15.1083	+	20.6778i	0.975235	+	1.33475i
$241$	−6.72639	−	11.6504i	−0.433285	−	0.750471i	0.563869	−	0.825864i	$-0.309312\pi$
$241$	−6.72639	−	11.6504i	−0.433285	−	0.750471i	−0.997154	+	0.0753931i	$0.975979\pi$
$242$	−0.266663	−	9.26768i	−0.0171418	−	0.595749i
$243$	13.1917	+	8.30535i	0.846248	+	0.532789i
$244$	−0.254914	−	4.42601i	−0.0163192	−	0.283346i
$245$	−3.20115	+	1.84819i	−0.204514	+	0.118076i
$246$	−1.81606	−	2.99757i	−0.115788	−	0.191118i
$247$	6.45574	−	11.1817i	0.410769	−	0.711473i
$248$	−17.0818	−	7.98557i	−1.08470	−	0.507084i
$249$	−3.34719	+	5.69630i	−0.212120	+	0.360989i
$250$	−10.0476	−	16.3014i	−0.635464	−	1.03099i
$251$			0.969726i			0.0612085i	0.999532	+	0.0306043i	$0.00974316\pi$
$251$			0.969726i			0.0612085i	−0.999532	+	0.0306043i	$0.990257\pi$
$252$	2.77804	−	5.31813i	0.175000	−	0.335010i
$253$		−	15.8621i		−	0.997239i
$254$	0.809589	−	0.499000i	0.0507981	−	0.0313101i
$255$	−36.5121	−	0.279641i	−2.28648	−	0.0175118i
$256$	−4.62848	+	15.3159i	−0.289280	+	0.957244i
$257$	−7.16500	+	12.4101i	−0.446940	+	0.774123i	−0.998185	−	0.0602202i	$-0.980820\pi$
$257$	−7.16500	+	12.4101i	−0.446940	+	0.774123i	0.551245	+	0.834344i	$0.314153\pi$
$258$	0.419629	+	19.8783i	0.0261250	+	1.23757i
$259$	−1.15239	+	0.665332i	−0.0716059	+	0.0413417i
$260$	13.0189	−	0.749820i	0.807400	−	0.0465019i
$261$	−0.209374	+	13.6679i	−0.0129599	+	0.846023i
$262$	0.629569	−	0.0181149i	0.0388949	−	0.00111914i
$263$	0.325206	+	0.563274i	0.0200531	+	0.0347330i	0.875878	−	0.482533i	$-0.160283\pi$
$263$	0.325206	+	0.563274i	0.0200531	+	0.0347330i	−0.855825	+	0.517266i	$0.826950\pi$
$264$	−9.32188	−	4.44519i	−0.573722	−	0.273582i
$265$	5.40982	−	9.37009i	0.332323	−	0.575600i
$266$	−4.91576	+	9.10980i	−0.301405	+	0.558557i
$267$	11.9670	−	6.78751i	0.732371	−	0.415389i
$268$	−17.1757	+	11.2807i	−1.04917	+	0.689081i
$269$		−	27.4138i		−	1.67145i	−0.549148	−	0.835725i	$-0.685048\pi$
$269$		−	27.4138i		−	1.67145i	0.549148	−	0.835725i	$-0.314952\pi$
$270$	−0.157254	−	27.1622i	−0.00957015	−	1.65304i
$271$	16.8566			1.02397			0.511984	−	0.858995i	$-0.328911\pi$
$271$	16.8566			1.02397			0.511984	+	0.858995i	$0.328911\pi$
$272$	−13.5990	−	18.3160i	−0.824561	−	1.11057i
$273$	−1.50732	−	2.65756i	−0.0912275	−	0.160843i
$274$	−14.2096	−	7.66770i	−0.858436	−	0.463223i
$275$	15.8160	+	9.13138i	0.953742	+	0.550643i
$276$	23.1947	+	11.8911i	1.39616	+	0.715759i
$277$	−5.94050	+	3.42975i	−0.356930	+	0.206074i	−0.667733	−	0.744401i	$-0.732735\pi$
$277$	−5.94050	+	3.42975i	−0.356930	+	0.206074i	0.310803	+	0.950474i	$0.399402\pi$
$278$	19.9435	−	0.573843i	1.19613	−	0.0344168i
$279$	9.73358	+	17.4717i	0.582734	+	1.04600i
$280$	−10.4160	+	0.901104i	−0.622476	+	0.0538513i
$281$	1.40580	+	2.43492i	0.0838630	+	0.145255i	0.904906	−	0.425611i	$-0.139941\pi$
$281$	1.40580	+	2.43492i	0.0838630	+	0.145255i	−0.821043	+	0.570866i	$0.806608\pi$
$282$	23.8376	−	0.503209i	1.41951	−	0.0299657i
$283$	10.0078	+	5.77802i	0.594903	+	0.343468i	0.767034	−	0.641607i	$-0.221732\pi$
$283$	10.0078	+	5.77802i	0.594903	+	0.343468i	−0.172131	+	0.985074i	$0.555065\pi$
$284$	−8.48253	+	16.8629i	−0.503346	+	1.00063i
$285$	−0.358902	+	46.8609i	−0.0212595	+	2.77580i
$286$	−4.47681	+	2.75934i	−0.264719	+	0.163163i
$287$	1.43082			0.0844587
$288$	13.4883	−	10.2988i	0.794806	−	0.606864i
$289$	15.5256			0.913273
$290$	20.2768	−	12.4978i	1.19069	−	0.733899i
$291$	28.8041	+	16.9255i	1.68852	+	0.992189i
$292$	−1.78789	+	3.55425i	−0.104629	+	0.207997i
$293$	15.3367	+	8.85468i	0.895982	+	0.517296i	0.875895	−	0.482503i	$-0.160272\pi$
$293$	15.3367	+	8.85468i	0.895982	+	0.517296i	0.0200879	+	0.999798i	$0.493605\pi$
$294$	1.26924	+	2.09500i	0.0740238	+	0.122183i
$295$	8.74108	+	15.1400i	0.508925	+	0.881485i
$296$	−3.74968	+	0.324390i	−0.217946	+	0.0188548i
$297$	5.25759	+	9.60973i	0.305076	+	0.557613i
$298$	−1.56153	+	0.0449307i	−0.0904572	+	0.00260277i
$299$	11.4945	−	6.63634i	0.664743	−	0.383790i
$300$	−25.2092	+	16.2820i	−1.45545	+	0.940043i
$301$	−7.02960	−	4.05854i	−0.405180	−	0.233931i
$302$	1.44847	+	0.781611i	0.0833500	+	0.0449767i
$303$	−1.93181	+	3.28759i	−0.110980	+	0.188867i
$304$	−23.5075	+	17.4535i	−1.34825	+	1.00102i
$305$	8.19365			0.469167
$306$	0.325384	+	24.1941i	0.0186010	+	1.38309i
$307$			31.6581i			1.80682i	0.428776	+	0.903411i	$0.358945\pi$
$307$			31.6581i			1.80682i	−0.428776	+	0.903411i	$0.641055\pi$
$308$	3.52407	−	2.31455i	0.200802	−	0.131884i
$309$	−0.0936841	+	12.2321i	−0.00532950	+	0.695861i
$310$	16.5497	−	30.6696i	0.939959	−	1.74192i
$311$	13.1849	−	22.8369i	0.747647	−	1.29496i	−0.201301	−	0.979529i	$-0.564517\pi$
$311$	13.1849	−	22.8369i	0.747647	−	1.29496i	0.948948	−	0.315433i	$-0.102150\pi$
$312$	−0.678857	−	8.61490i	−0.0384327	−	0.487723i
$313$	−1.35975	−	2.35515i	−0.0768576	−	0.133121i	0.825035	−	0.565082i	$-0.191155\pi$
$313$	−1.35975	−	2.35515i	−0.0768576	−	0.133121i	−0.901893	+	0.431960i	$0.857822\pi$
$314$	7.13513	−	0.205302i	0.402659	−	0.0115859i
$315$	9.51741	+	5.69100i	0.536245	+	0.320652i
$316$	30.3636	−	1.74878i	1.70809	−	0.0983765i
$317$	−1.07153	+	0.618651i	−0.0601834	+	0.0347469i	−0.529790	−	0.848129i	$-0.677729\pi$
$317$	−1.07153	+	0.618651i	−0.0601834	+	0.0347469i	0.469606	+	0.882876i	$0.344396\pi$
$318$	−6.28359	−	3.45310i	−0.352366	−	0.193640i
$319$	−4.80277	+	8.31863i	−0.268903	+	0.465754i
$320$	−27.7680	−	10.1678i	−1.55228	−	0.568395i
$321$	−6.88713	−	12.1427i	−0.384402	−	0.677739i
$322$	−9.05859	+	5.58338i	−0.504816	+	0.311150i
$323$		−	41.7446i		−	2.32273i
$324$	−17.9935	+	0.484072i	−0.999638	+	0.0268929i
$325$			15.2815i			0.847665i
$326$	4.71779	+	7.65424i	0.261294	+	0.423929i
$327$	9.79119	+	17.2628i	0.541454	+	0.954637i
$328$	3.66614	+	1.71388i	0.202429	+	0.0946333i
$329$	−4.86691	+	8.42973i	−0.268321	+	0.464746i
$330$	9.19257	−	16.7277i	0.506035	−	0.920829i
$331$	11.6233	−	6.71069i	0.638872	−	0.368853i	−0.145308	−	0.989386i	$-0.546417\pi$
$331$	11.6233	−	6.71069i	0.638872	−	0.368853i	0.784180	+	0.620534i	$0.213084\pi$
$332$	−0.438664	−	7.61641i	−0.0240748	−	0.418005i
$333$	3.42619	+	2.04871i	0.187754	+	0.112269i
$334$	−0.198577	−	6.90138i	−0.0108656	−	0.377627i
$335$	−18.9892	−	32.8902i	−1.03749	−	1.79698i
$336$	0.742682	+	6.88828i	0.0405166	+	0.375787i
$337$	7.99212	−	13.8428i	0.435359	−	0.754063i	−0.561966	−	0.827160i	$-0.689955\pi$
$337$	7.99212	−	13.8428i	0.435359	−	0.754063i	0.997325	+	0.0730970i	$0.0232883\pi$
$338$	12.3069	+	6.64097i	0.669408	+	0.361221i
$339$	0.171151	−	22.3468i	0.00929566	−	1.21371i
$340$	35.2406	−	23.1455i	1.91119	−	1.25524i
$341$			14.0540i			0.761067i
$342$	31.0516	−	0.417610i	1.67908	−	0.0225817i
$343$	−1.00000			−0.0539949
$344$	−13.1503	−	18.8193i	−0.709014	−	1.01467i
$345$	−24.4055	+	41.5336i	−1.31395	+	2.23609i
$346$	−8.82360	+	16.3517i	−0.474360	+	0.879075i
$347$	−2.17063	−	1.25321i	−0.116526	−	0.0672761i	0.440604	−	0.897701i	$-0.354764\pi$
$347$	−2.17063	−	1.25321i	−0.116526	−	0.0672761i	−0.557130	+	0.830425i	$0.688097\pi$
$348$	−8.56374	−	13.2591i	−0.459065	−	0.710762i
$349$	22.8599	−	13.1982i	1.22366	−	0.706481i	0.257965	−	0.966154i	$-0.416948\pi$
$349$	22.8599	−	13.1982i	1.22366	−	0.706481i	0.965697	+	0.259673i	$0.0836148\pi$
$350$	−0.352374	−	12.2465i	−0.0188352	−	0.654604i
$351$	−4.76406	+	7.83044i	−0.254287	+	0.417958i
$352$	11.8020	−	1.70926i	0.629050	−	0.0911038i
$353$	8.17057	+	14.1518i	0.434876	+	0.753227i	0.997285	−	0.0736320i	$-0.0234590\pi$
$353$	8.17057	+	14.1518i	0.434876	+	0.753227i	−0.562410	+	0.826859i	$0.690126\pi$
$354$	9.90839	−	6.00294i	0.526625	−	0.319053i
$355$	−30.2128	−	17.4434i	−1.60353	−	0.925798i
$356$	−7.13893	+	14.1919i	−0.378362	+	0.752168i
$357$	−8.51661	−	5.00442i	−0.450747	−	0.264862i
$358$	0.690847	+	1.12084i	0.0365124	+	0.0592385i
$359$	−17.7720			−0.937970			−0.468985	−	0.883206i	$-0.655380\pi$
$359$	−17.7720			−0.937970			−0.468985	+	0.883206i	$0.655380\pi$
$360$	17.5693	+	25.9821i	0.925981	+	1.36938i
$361$	−34.5765			−1.81982
$362$	6.80798	+	11.0454i	0.357819	+	0.580533i
$363$	0.0869658	−	11.3549i	0.00456452	−	0.595978i
$364$	3.15164	+	1.58537i	0.165191	+	0.0830957i
$365$	−6.36806	−	3.67660i	−0.333319	−	0.192442i
$366$	−0.114595	−	5.42851i	−0.00599000	−	0.283753i
$367$	8.04577	+	13.9357i	0.419986	+	0.727436i	0.995937	−	0.0900473i	$-0.0287018\pi$
$367$	8.04577	+	13.9357i	0.419986	+	0.727436i	−0.575952	+	0.817484i	$0.695368\pi$
$368$	−29.8985	+	3.45544i	−1.55857	+	0.180127i
$369$	−2.08904	−	3.74982i	−0.108751	−	0.195208i
$370$	−0.200065	−	6.95311i	−0.0104009	−	0.361475i
$371$	2.53494	−	1.46355i	0.131608	−	0.0759837i
$372$	−20.5509	−	10.5357i	−1.06551	−	0.546249i
$373$	−25.0832	−	14.4818i	−1.29876	−	0.749840i	−0.318571	−	0.947899i	$-0.603203\pi$
$373$	−25.0832	−	14.4818i	−1.29876	−	0.749840i	−0.980190	+	0.198059i	$0.936536\pi$
$374$	−8.07431	+	14.9632i	−0.417513	+	0.773727i
$375$	−11.5705	−	20.3999i	−0.597498	−	1.05345i
$376$	−22.5677	+	15.7695i	−1.16384	+	0.813249i
$377$	−8.03750			−0.413952
$378$	3.63733	−	6.38513i	0.187084	−	0.328415i
$379$			4.88786i			0.251073i	0.992089	+	0.125536i	$0.0400651\pi$
$379$			4.88786i			0.251073i	−0.992089	+	0.125536i	$0.959935\pi$
$380$	−29.7058	−	45.2291i	−1.52387	−	2.32020i
$381$	1.01314	−	0.574635i	0.0519046	−	0.0294394i
$382$	6.41187	+	3.45993i	0.328060	+	0.177025i
$383$	13.4288	−	23.2593i	0.686179	−	1.18850i	−0.286886	−	0.957965i	$-0.592620\pi$
$383$	13.4288	−	23.2593i	0.686179	−	1.18850i	0.973065	−	0.230532i	$-0.0740466\pi$
$384$	−6.34805	+	18.5392i	−0.323947	+	0.946075i
$385$	3.89615	+	6.74832i	0.198566	+	0.343926i
$386$	0.127572	+	4.43367i	0.00649325	+	0.225668i
$387$	−0.372984	+	24.3484i	−0.0189599	+	1.23770i
$388$	−38.5133	+	2.21816i	−1.95522	+	0.112610i
$389$	7.27664	−	4.20117i	0.368940	−	0.213008i	−0.304055	−	0.952654i	$-0.598341\pi$
$389$	7.27664	−	4.20117i	0.368940	−	0.213008i	0.672995	+	0.739647i	$0.265007\pi$
$390$	15.9677	−	0.337078i	0.808558	−	0.0170686i
$391$	21.4562	−	37.1632i	1.08509	−	1.87943i
$392$	−2.56226	−	1.19783i	−0.129414	−	0.0604996i
$393$	0.771358	+	0.00590773i	0.0389099	+	0.000298006i
$394$	−18.4671	−	29.9614i	−0.930359	−	1.50943i
$395$			56.2106i			2.82826i
$396$	−11.2111	−	5.85637i	−0.563379	−	0.294294i
$397$			24.6696i			1.23813i	0.785339	+	0.619066i	$0.212489\pi$
$397$			24.6696i			1.23813i	−0.785339	+	0.619066i	$0.787511\pi$
$398$	4.16287	−	2.56584i	0.208666	−	0.128614i
$399$	−6.42286	+	10.9305i	−0.321545	+	0.547211i
$400$	13.7664	−	31.8009i	0.688319	−	1.59004i
$401$	10.4696	−	18.1339i	0.522828	−	0.905565i	−0.476819	−	0.879001i	$-0.658210\pi$
$401$	10.4696	−	18.1339i	0.522828	−	0.905565i	0.999647	−	0.0265633i	$-0.00845637\pi$
$402$	−21.5251	+	13.0408i	−1.07357	+	0.650417i
$403$	−10.1843	+	5.87989i	−0.507315	+	0.292898i
$404$	−0.253172	−	4.39576i	−0.0125958	−	0.218697i
$405$	1.01898	−	33.2518i	0.0506336	−	1.65229i
$406$	6.44121	−	0.185336i	0.319672	−	0.00919806i
$407$	1.40258	+	2.42934i	0.0695233	+	0.120418i
$408$	−15.8274	−	23.0241i	−0.783571	−	1.13986i
$409$	3.76418	−	6.51974i	0.186126	−	0.322381i	−0.757829	−	0.652453i	$-0.773740\pi$
$409$	3.76418	−	6.51974i	0.186126	−	0.322381i	0.943956	+	0.330073i	$0.107073\pi$
$410$	−3.55193	+	6.58238i	−0.175417	+	0.325080i
$411$	−17.0497	−	10.0185i	−0.840997	−	0.494176i
$412$	−7.75409	−	11.8061i	−0.382017	−	0.581647i
$413$			4.72954i			0.232726i
$414$	27.8584	+	15.5884i	1.36917	+	0.766127i
$415$	14.0999			0.692135
$416$	6.17634	+	7.83726i	0.302820	+	0.384253i
$417$	24.4351	+	0.187145i	1.19659	+	0.00916454i
$418$	19.2043	+	10.3629i	0.939312	+	0.506865i
$419$	−13.1594	−	7.59760i	−0.642880	−	0.371167i	0.142843	−	0.989745i	$-0.454376\pi$
$419$	−13.1594	−	7.59760i	−0.642880	−	0.371167i	−0.785723	+	0.618578i	$0.787709\pi$
$420$	−12.7887	+	0.638331i	−0.624024	+	0.0311474i
$421$	−21.3769	+	12.3419i	−1.04184	+	0.601509i	−0.920355	−	0.391083i	$-0.872100\pi$
$421$	−21.3769	+	12.3419i	−1.04184	+	0.601509i	−0.121490	+	0.992593i	$0.538767\pi$
$422$	−15.7889	+	0.454302i	−0.768593	+	0.0221151i
$423$	29.1980	+	0.447274i	1.41966	+	0.0217472i
$424$	8.24828	−	0.713570i	0.400572	−	0.0346540i
$425$	24.7036	+	42.7879i	1.19830	+	2.07552i
$426$	−11.1341	+	20.2607i	−0.539451	+	0.981636i
$427$	1.91970	+	1.10834i	0.0929006	+	0.0536362i
$428$	14.4002	+	7.24371i	0.696059	+	0.350138i
$429$	−5.60238	+	3.17758i	−0.270486	+	0.153415i
$430$	36.1216	−	22.2640i	1.74194	−	1.07367i
$431$	5.37379			0.258846			0.129423	−	0.991589i	$-0.458687\pi$
$431$	5.37379			0.258846			0.129423	+	0.991589i	$0.458687\pi$
$432$	16.9681	−	12.0035i	0.816378	−	0.577518i
$433$	24.4754			1.17621			0.588106	−	0.808784i	$-0.299874\pi$
$433$	24.4754			1.17621			0.588106	+	0.808784i	$0.299874\pi$
$434$	8.02604	−	4.94695i	0.385262	−	0.237461i
$435$	25.3748	−	14.3922i	1.21663	−	0.690051i
$436$	−20.4722	−	10.2981i	−0.980442	−	0.493191i
$437$	−47.6967	−	27.5377i	−2.28164	−	1.31731i
$438$	−2.34678	+	4.27043i	−0.112134	+	0.204049i
$439$	−10.2626	−	17.7753i	−0.489807	−	0.848370i	0.510124	−	0.860101i	$-0.329599\pi$
$439$	−10.2626	−	17.7753i	−0.489807	−	0.848370i	−0.999931	+	0.0117303i	$0.996266\pi$
$440$	1.89961	+	21.9579i	0.0905603	+	1.04680i
$441$	1.46003	+	2.62075i	0.0695252	+	0.124797i
$442$	−14.2212	+	0.409194i	−0.676434	+	0.0194634i
$443$	23.4941	−	13.5643i	1.11624	−	0.644460i	0.175800	−	0.984426i	$-0.443749\pi$
$443$	23.4941	−	13.5643i	1.11624	−	0.644460i	0.940438	+	0.339966i	$0.110415\pi$
$444$	−4.60382	+	0.229794i	−0.218488	+	0.0109055i
$445$	−25.4272	−	14.6804i	−1.20536	−	0.695918i
$446$	2.64538	+	1.42748i	0.125262	+	0.0675930i
$447$	−1.91322	−	0.0146531i	−0.0904920	−	0.000693066i
$448$	−5.13040	−	6.13832i	−0.242389	−	0.290008i
$449$	−39.9124			−1.88358			−0.941791	−	0.336199i	$-0.890858\pi$
$449$	−39.9124			−1.88358			−0.941791	+	0.336199i	$0.890858\pi$
$450$	−31.5805	+	18.8038i	−1.48872	+	0.886418i
$451$		−	3.01630i		−	0.142032i
$452$	14.1659	+	21.5686i	0.666310	+	1.01450i
$453$	1.73797	+	1.02124i	0.0816568	+	0.0479821i
$454$	6.22109	−	11.5288i	0.291970	−	0.541074i
$455$	−3.26013	+	5.64671i	−0.152837	+	0.264722i
$456$	−29.5500	+	20.3134i	−1.38381	+	0.951263i
$457$	3.95030	+	6.84211i	0.184787	+	0.320061i	0.943505	−	0.331359i	$-0.107507\pi$
$457$	3.95030	+	6.84211i	0.184787	+	0.320061i	−0.758718	+	0.651420i	$0.774174\pi$
$458$	8.71372	−	0.250724i	0.407165	−	0.0117155i
$459$	−0.680822	+	29.6265i	−0.0317781	+	1.38285i
$460$	−3.19844	−	55.5337i	−0.149128	−	2.58927i
$461$	−23.8593	+	13.7751i	−1.11124	+	0.641573i	−0.939149	−	0.343509i	$-0.888384\pi$
$461$	−23.8593	+	13.7751i	−1.11124	+	0.641573i	−0.172087	+	0.985082i	$0.555051\pi$
$462$	4.41645	−	2.67568i	0.205472	−	0.124484i
$463$	−14.9150	+	25.8335i	−0.693158	+	1.20058i	0.277640	+	0.960685i	$0.410448\pi$
$463$	−14.9150	+	25.8335i	−0.693158	+	1.20058i	−0.970798	+	0.239899i	$0.922886\pi$
$464$	16.7261	+	7.24060i	0.776489	+	0.336136i
$465$	21.6236	−	36.7994i	1.00277	−	1.70653i
$466$	23.0175	−	14.1871i	1.06626	−	0.657205i
$467$		−	28.1862i		−	1.30430i	−0.758089	−	0.652151i	$-0.773867\pi$
$467$		−	28.1862i		−	1.30430i	0.758089	−	0.652151i	$-0.226133\pi$
$468$	−0.446646	−	10.5743i	−0.0206462	−	0.488799i
$469$		−	10.2745i		−	0.474432i
$470$	−26.6985	−	43.3161i	−1.23151	−	1.99802i
$471$	8.74208	+	0.0669544i	0.402814	+	0.00308510i
$472$	−5.66519	+	12.1183i	−0.260762	+	0.557792i
$473$	−8.55578	+	14.8190i	−0.393395	+	0.681380i
$474$	37.2410	−	0.786155i	1.71054	−	0.0361093i
$475$	54.9155	−	31.7055i	2.51970	−	1.45475i
$476$	11.3874	−	0.655851i	0.521940	−	0.0300609i
$477$	−7.53668	−	4.50661i	−0.345081	−	0.206344i
$478$	0.371004	+	12.8940i	0.0169693	+	0.589757i
$479$	17.7642	+	30.7685i	0.811667	+	1.40585i	0.911697	+	0.410863i	$0.134773\pi$
$479$	17.7642	+	30.7685i	0.811667	+	1.40585i	−0.100030	+	0.994984i	$0.531894\pi$
$480$	−33.5326	−	13.6831i	−1.53055	−	0.624546i
$481$	−1.17362	+	2.03277i	−0.0535124	+	0.0926862i
$482$	16.7430	+	9.03473i	0.762622	+	0.411521i
$483$	−11.3361	+	6.42966i	−0.515812	+	0.292560i
$484$	7.19803	+	10.9595i	0.327183	+	0.498159i
$485$		−	71.2977i		−	3.23746i
$486$	−22.0444	−	0.210047i	−0.999955	−	0.00952794i
$487$	14.1250			0.640063			0.320032	−	0.947407i	$-0.396306\pi$
$487$	14.1250			0.640063			0.320032	+	0.947407i	$0.396306\pi$
$488$	3.59117	+	5.13932i	0.162565	+	0.232646i
$489$	5.43288	+	9.57870i	0.245683	+	0.433164i
$490$	2.48244	−	4.60042i	0.112145	−	0.207826i
$491$	−19.2986	−	11.1421i	−0.870934	−	0.502834i	−0.00327542	−	0.999995i	$-0.501043\pi$
$491$	−19.2986	−	11.1421i	−0.870934	−	0.502834i	−0.867658	+	0.497161i	$0.834376\pi$
$492$	4.41067	+	2.26119i	0.198849	+	0.101942i
$493$	−22.5048	+	12.9932i	−1.01357	+	0.585183i
$494$	0.525174	+	18.2520i	0.0236287	+	0.821198i
$495$	11.9972	−	20.0636i	0.539232	−	0.901790i
$496$	26.4905	−	3.06157i	1.18946	−	0.137469i
$497$	−4.71905	−	8.17364i	−0.211678	−	0.366638i
$498$	−0.197199	−	9.34153i	−0.00883670	−	0.418604i
$499$	−8.54058	−	4.93091i	−0.382329	−	0.220738i	0.296502	−	0.955032i	$-0.404180\pi$
$499$	−8.54058	−	4.93091i	−0.382329	−	0.220738i	−0.678831	+	0.734294i	$0.737513\pi$
$500$	24.1925	+	12.1695i	1.08192	+	0.544239i
$501$	0.0647610	−	8.45568i	0.00289331	−	0.377772i
$502$	−0.719575	−	1.16745i	−0.0321162	−	0.0521060i
$503$	3.34001			0.148924			0.0744619	−	0.997224i	$-0.476276\pi$
$503$	3.34001			0.148924			0.0744619	+	0.997224i	$0.476276\pi$
$504$	0.601772	+	8.46392i	0.0268051	+	0.377013i
$505$	8.13765			0.362121
$506$	11.7703	+	19.0963i	0.523253	+	0.848936i
$507$	14.7666	+	8.67699i	0.655810	+	0.385359i
$508$	−0.604386	+	1.20149i	−0.0268153	+	0.0533077i
$509$	7.09491	+	4.09625i	0.314476	+	0.181563i	0.648928	−	0.760850i	$-0.275218\pi$
$509$	7.09491	+	4.09625i	0.314476	+	0.181563i	−0.334451	+	0.942413i	$0.608551\pi$
$510$	44.1644	−	26.7568i	1.95563	−	1.18481i
$511$	−0.994651	−	1.72279i	−0.0440008	−	0.0762116i
$512$	−5.79278	−	21.8734i	−0.256007	−	0.966675i
$513$	38.0237	+	0.873793i	1.67879	+	0.0385789i
$514$	−0.582872	−	20.2573i	−0.0257094	−	0.893511i
$515$	22.6079	−	13.0527i	0.996223	−	0.575169i
$516$	−15.2557	−	23.6201i	−0.671594	−	1.03982i
$517$	17.7706	+	10.2599i	0.781552	+	0.451229i
$518$	0.893658	−	1.65611i	0.0392651	−	0.0727653i
$519$	−11.5288	+	19.6199i	−0.506058	+	0.861217i
$520$	−15.1171	+	10.5633i	−0.662929	+	0.463230i
$521$	−18.9174			−0.828785			−0.414393	−	0.910098i	$-0.636006\pi$
$521$	−18.9174			−0.828785			−0.414393	+	0.910098i	$0.636006\pi$
$522$	−9.89007	−	16.6102i	−0.432877	−	0.727008i
$523$		−	27.7020i		−	1.21133i	−0.795722	−	0.605663i	$-0.792908\pi$
$523$		−	27.7020i		−	1.21133i	0.795722	−	0.605663i	$-0.207092\pi$
$524$	−0.744497	+	0.488974i	−0.0325235	+	0.0213609i
$525$	0.114918	−	15.0046i	0.00501545	−	0.654855i
$526$	−0.809488	−	0.436810i	−0.0352954	−	0.0190458i
$527$	−19.0105	+	32.9272i	−0.828111	+	1.43433i
$528$	14.5211	−	1.56564i	0.631951	−	0.0681358i
$529$	−16.8081	−	29.1124i	−0.730785	−	1.26576i
$530$	0.440089	+	15.2950i	0.0191162	+	0.664371i
$531$	12.3949	−	6.90528i	0.537895	−	0.299663i
$532$	−0.841744	−	14.6150i	−0.0364942	−	0.633640i
$533$	2.18577	−	1.26196i	0.0946763	−	0.0546614i
$534$	−9.37053	+	17.0515i	−0.405502	+	0.737891i
$535$	−14.8959	+	25.8004i	−0.644005	+	1.11545i
$536$	12.3071	−	26.3260i	0.531586	−	1.13711i
$537$	0.795560	+	1.40265i	0.0343309	+	0.0605288i
$538$	20.3421	+	33.0035i	0.877012	+	1.42288i
$539$			2.10809i			0.0908019i
$540$	20.3448	+	32.5839i	0.875500	+	1.40219i
$541$			6.92931i			0.297914i	0.988844	+	0.148957i	$0.0475917\pi$
$541$			6.92931i			0.297914i	−0.988844	+	0.148957i	$0.952408\pi$
$542$	−20.2937	+	12.5083i	−0.871689	+	0.537277i
$543$	7.83987	+	13.8225i	0.336441	+	0.593179i
$544$	29.9631	+	11.9597i	1.28466	+	0.512767i
$545$	21.1769	−	36.6795i	0.907120	−	1.57118i
$546$	3.78669	+	2.08095i	0.162055	+	0.0890562i
$547$	−18.0823	+	10.4398i	−0.773145	+	0.446376i	−0.833995	−	0.551771i	$-0.813952\pi$
$547$	−18.0823	+	10.4398i	−0.773145	+	0.446376i	0.0608502	+	0.998147i	$0.480619\pi$
$548$	22.7967	−	1.31297i	0.973828	−	0.0560872i
$549$	0.101857	−	6.64924i	0.00434716	−	0.283783i
$550$	−25.8168	+	0.742837i	−1.10083	+	0.0316747i
$551$	16.6759	+	28.8835i	0.710418	+	1.23048i
$552$	−36.7478	+	2.89574i	−1.56409	+	0.123251i
$553$	−7.60348	+	13.1696i	−0.323333	+	0.560029i
$554$	4.60676	−	8.53717i	0.195723	−	0.362709i
$555$	0.0652464	−	8.51906i	0.00276955	−	0.361614i
$556$	−23.5842	+	15.4897i	−1.00019	+	0.656911i
$557$		−	15.2760i		−	0.647264i	−0.946183	−	0.323632i	$-0.895096\pi$
$557$		−	15.2760i		−	0.647264i	0.946183	−	0.323632i	$-0.104904\pi$
$558$	−24.6830	−	13.8115i	−1.04491	−	0.584688i
$559$	−14.3182			−0.605596
$560$	11.8712	−	8.81394i	0.501650	−	0.372457i
$561$	−10.5498	+	17.9538i	−0.445412	+	0.758010i
$562$	−3.49925	−	1.88824i	−0.147607	−	0.0796506i
$563$	34.8152	+	20.1006i	1.46729	+	0.847139i	0.999330	−	0.0366125i	$-0.0116567\pi$
$563$	34.8152	+	20.1006i	1.46729	+	0.847139i	0.467957	+	0.883751i	$0.344990\pi$
$564$	−28.3247	+	18.2942i	−1.19268	+	0.770326i
$565$	−41.3023	+	23.8459i	−1.73760	+	1.00320i
$566$	−16.3359	+	0.470041i	−0.686651	+	0.0197573i
$567$	4.73663	−	7.65274i	0.198920	−	0.321385i
$568$	−2.30083	−	26.5956i	−0.0965405	−	1.11593i
$569$	9.39368	+	16.2703i	0.393803	+	0.682088i	0.992948	−	0.118554i	$-0.0378257\pi$
$569$	9.39368	+	16.2703i	0.393803	+	0.682088i	−0.599144	+	0.800641i	$0.704492\pi$
$570$	−34.3406	−	56.6822i	−1.43837	−	2.37416i
$571$	−15.3022	−	8.83476i	−0.640379	−	0.369723i	0.144381	−	0.989522i	$-0.453881\pi$
$571$	−15.3022	−	8.83476i	−0.640379	−	0.369723i	−0.784761	+	0.619799i	$0.787214\pi$
$572$	3.34209	−	6.64394i	0.139740	−	0.277797i
$573$	7.69338	+	4.52069i	0.321396	+	0.188854i
$574$	−1.72257	+	1.06173i	−0.0718986	+	0.0443156i
$575$	65.1849			2.71840
$576$	−8.59644	+	22.4076i	−0.358185	+	0.933651i
$577$	−41.0555			−1.70916			−0.854581	−	0.519317i	$-0.826186\pi$
$577$	−41.0555			−1.70916			−0.854581	+	0.519317i	$0.826186\pi$
$578$	−18.6913	+	11.5206i	−0.777457	+	0.479195i
$579$	−0.0416045	+	5.43221i	−0.00172903	+	0.225755i
$580$	−15.1373	+	30.0923i	−0.628543	+	1.24952i
$581$	3.30347	+	1.90726i	0.137051	+	0.0791264i
$582$	−47.2366	+	0.997161i	−1.95802	+	0.0413337i
$583$	−3.08529	−	5.34389i	−0.127780	−	0.221321i
$584$	−0.484953	−	5.60566i	−0.0200675	−	0.231964i
$585$	19.5585	+	0.299609i	0.808643	+	0.0123873i
$586$	−25.0344	+	0.720327i	−1.03416	+	0.0297564i
$587$	−15.2546	+	8.80727i	−0.629627	+	0.363515i	−0.780607	−	0.625022i	$-0.785090\pi$
$587$	−15.2546	+	8.80727i	−0.629627	+	0.363515i	0.150981	+	0.988537i	$0.451757\pi$
$588$	−3.08262	−	1.58034i	−0.127125	−	0.0651722i
$589$	42.2599	+	24.3988i	1.74129	+	1.00533i
$590$	−21.7579	−	11.7408i	−0.895758	−	0.483362i
$591$	−21.2662	−	37.4944i	−0.874774	−	1.54231i
$592$	4.27353	−	3.17294i	0.175641	−	0.130407i
$593$	33.9863			1.39565			0.697825	−	0.716269i	$-0.254151\pi$
$593$	33.9863			1.39565			0.697825	+	0.716269i	$0.254151\pi$
$594$	−13.4604	−	7.66782i	−0.552288	−	0.314615i
$595$			21.0809i			0.864232i
$596$	1.84659	−	1.21281i	0.0756393	−	0.0496787i
$597$	5.20951	−	2.95474i	0.213211	−	0.120930i
$598$	−8.91378	+	16.5189i	−0.364512	+	0.675506i
$599$	−16.5568	+	28.6773i	−0.676494	+	1.17172i	0.299536	+	0.954085i	$0.403168\pi$
$599$	−16.5568	+	28.6773i	−0.676494	+	1.17172i	−0.976030	+	0.217636i	$0.930165\pi$
$600$	18.2674	−	38.3082i	0.745765	−	1.56392i
$601$	17.7413	+	30.7288i	0.723683	+	1.25346i	0.959514	+	0.281661i	$0.0908855\pi$
$601$	17.7413	+	30.7288i	0.723683	+	1.25346i	−0.235831	+	0.971794i	$0.575781\pi$
$602$	11.4745	−	0.330162i	0.467668	−	0.0134564i
$603$	−26.9268	+	15.0011i	−1.09655	+	0.610890i
$604$	−2.32380	+	0.133838i	−0.0945540	+	0.00544580i
$605$	−20.9866	+	12.1166i	−0.853227	+	0.492611i
$606$	−0.113812	−	5.39141i	−0.00462331	−	0.219011i
$607$	−12.6279	+	21.8721i	−0.512549	+	0.887761i	0.487345	+	0.873210i	$0.337965\pi$
$607$	−12.6279	+	21.8721i	−0.512549	+	0.887761i	−0.999894	+	0.0145518i	$0.995368\pi$
$608$	15.3495	−	38.4557i	0.622505	−	1.55959i
$609$	7.89187	+	0.0604428i	0.319795	+	0.00244927i
$610$	−9.86434	+	6.08001i	−0.399396	+	0.246173i
$611$			17.1701i			0.694626i
$612$	−18.3447	−	28.8859i	−0.741542	−	1.16764i
$613$		−	36.2121i		−	1.46259i	−0.682061	−	0.731296i	$-0.738916\pi$
$613$		−	36.2121i		−	1.46259i	0.682061	−	0.731296i	$-0.261084\pi$
$614$	−23.4916	−	38.1132i	−0.948042	−	1.53812i
$615$	−4.64090	+	7.89797i	−0.187139	+	0.318477i
$616$	−2.52514	+	5.40149i	−0.101741	+	0.217632i
$617$	−10.9391	+	18.9471i	−0.440391	+	0.762780i	−0.997718	−	0.0675128i	$-0.978494\pi$
$617$	−10.9391	+	18.9471i	−0.440391	+	0.762780i	0.557327	+	0.830293i	$0.311827\pi$
$618$	−8.96393	−	14.7958i	−0.360582	−	0.595173i
$619$	−8.91092	+	5.14472i	−0.358160	+	0.206784i	−0.668273	−	0.743916i	$-0.732966\pi$
$619$	−8.91092	+	5.14472i	−0.358160	+	0.206784i	0.310113	+	0.950700i	$0.399633\pi$
$620$	2.83386	+	49.2037i	0.113811	+	1.97607i
$621$	33.4016	+	20.3216i	1.34036	+	0.815479i
$622$	1.07259	+	37.2771i	0.0430070	+	1.49468i
$623$	−3.97157	−	6.87896i	−0.159118	−	0.275600i
$624$	7.20987	+	9.86774i	0.288626	+	0.395026i
$625$	−3.36737	+	5.83246i	−0.134695	+	0.233298i
$626$	3.38462	+	1.82638i	0.135277	+	0.0729970i
$627$	23.0426	+	13.5400i	0.920231	+	0.540734i
$628$	−8.43765	+	5.54172i	−0.336699	+	0.221139i
$629$			7.58894i			0.302591i
$630$	−15.6810	+	0.210891i	−0.624745	+	0.00840212i
$631$	12.6914			0.505235			0.252617	−	0.967566i	$-0.418709\pi$
$631$	12.6914			0.505235			0.252617	+	0.967566i	$0.418709\pi$
$632$	−35.2571	+	24.6364i	−1.40245	+	0.979982i
$633$	−19.3448	−	0.148160i	−0.768888	−	0.00588881i
$634$	0.830958	−	1.53992i	0.0330016	−	0.0611579i
$635$	−2.15268	−	1.24285i	−0.0854266	−	0.0493211i
$636$	10.1272	−	0.505484i	0.401568	−	0.0200437i
$637$	−1.52763	+	0.881980i	−0.0605271	+	0.0349453i
$638$	−0.390705	−	13.5787i	−0.0154681	−	0.537584i
$639$	−14.5311	+	24.3012i	−0.574840	+	0.961340i
$640$	40.9748	−	8.36396i	1.61967	−	0.330615i
$641$	−11.4010	−	19.7472i	−0.450314	−	0.779966i	0.548092	−	0.836418i	$-0.315355\pi$
$641$	−11.4010	−	19.7472i	−0.450314	−	0.779966i	−0.998405	+	0.0564521i	$0.982021\pi$
$642$	17.3018	+	9.50806i	0.682847	+	0.375253i
$643$	−12.9990	−	7.50500i	−0.512632	−	0.295968i	0.221283	−	0.975210i	$-0.428976\pi$
$643$	−12.9990	−	7.50500i	−0.512632	−	0.295968i	−0.733915	+	0.679241i	$0.762309\pi$
$644$	6.76256	−	13.4437i	0.266482	−	0.529755i
$645$	45.2034	−	25.6386i	1.77988	−	1.00952i
$646$	30.9762	+	50.2563i	1.21874	+	1.97731i
$647$	−4.13174			−0.162435			−0.0812177	−	0.996696i	$-0.525881\pi$
$647$	−4.13174			−0.162435			−0.0812177	+	0.996696i	$0.525881\pi$
$648$	21.3032	−	13.9347i	0.836868	−	0.547405i
$649$	9.97031			0.391369
$650$	−11.3395	−	18.3974i	−0.444771	−	0.721605i
$651$	10.0440	−	5.69677i	0.393654	−	0.223274i
$652$	−11.3595	−	5.71416i	−0.444873	−	0.223784i
$653$	−14.6869	−	8.47948i	−0.574742	−	0.331828i	0.184299	−	0.982870i	$-0.440999\pi$
$653$	−14.6869	−	8.47948i	−0.574742	−	0.331828i	−0.759041	+	0.651043i	$0.774332\pi$
$654$	−24.5973	−	13.5173i	−0.961832	−	0.528568i
$655$	−0.823103	−	1.42566i	−0.0321613	−	0.0557050i
$656$	−5.68544	+	0.657081i	−0.221979	+	0.0256547i
$657$	−3.06277	+	5.12205i	−0.119490	+	0.199830i
$658$	−0.395923	−	13.7600i	−0.0154347	−	0.536421i
$659$	38.8030	−	22.4029i	1.51155	−	0.872693i	0.511640	−	0.859200i	$-0.329038\pi$
$659$	38.8030	−	22.4029i	1.51155	−	0.872693i	0.999909	−	0.0134937i	$-0.00429530\pi$
$660$	1.34566	+	26.9597i	0.0523797	+	1.04941i
$661$	36.0198	+	20.7960i	1.40101	+	0.808872i	0.994496	−	0.104773i	$-0.0334117\pi$
$661$	36.0198	+	20.7960i	1.40101	+	0.808872i	0.406512	+	0.913646i	$0.366745\pi$
$662$	−9.01365	+	16.7039i	−0.350325	+	0.649217i
$663$	−17.4241	−	0.133449i	−0.676695	−	0.00518271i
$664$	6.17978	+	8.84389i	0.239822	+	0.343210i
$665$	27.0560			1.04919
$666$	−5.64502	+	0.0759192i	−0.218740	+	0.00294181i
$667$			34.2848i			1.32751i
$668$	5.36017	+	8.16123i	0.207391	+	0.315767i
$669$	3.17409	+	1.86512i	0.122718	+	0.0721098i
$670$	47.2669	+	25.5058i	1.82608	+	0.985376i
$671$	2.33647	−	4.04689i	0.0901986	−	0.156229i
$672$	−6.00549	−	7.74171i	−0.231667	−	0.298643i
$673$	−19.7401	−	34.1908i	−0.760924	−	1.31796i	−0.942375	−	0.334559i	$-0.891413\pi$
$673$	−19.7401	−	34.1908i	−0.760924	−	1.31796i	0.181451	−	0.983400i	$-0.441921\pi$
$674$	0.650158	+	22.5958i	0.0250432	+	0.870357i
$675$	−39.4911	+	21.6060i	−1.52001	+	0.831616i
$676$	−19.7442	+	1.13716i	−0.759391	+	0.0437368i
$677$	−15.8487	+	9.15025i	−0.609115	+	0.351673i	−0.772619	−	0.634870i	$-0.781054\pi$
$677$	−15.8487	+	9.15025i	−0.609115	+	0.351673i	0.163504	+	0.986543i	$0.447720\pi$
$678$	16.3762	+	27.0303i	0.628923	+	1.03809i
$679$	9.64428	−	16.7044i	0.370114	−	0.641055i
$680$	−25.2513	+	54.0148i	−0.968344	+	2.07137i
$681$	8.12839	−	13.8330i	0.311481	−	0.530083i
$682$	−10.4286	−	16.9196i	−0.399333	−	0.647886i
$683$		−	44.0803i		−	1.68668i	−0.537377	−	0.843342i	$-0.680585\pi$
$683$		−	44.0803i		−	1.68668i	0.537377	−	0.843342i	$-0.319415\pi$
$684$	−37.0732	+	23.5443i	−1.41753	+	0.900239i
$685$			42.2024i			1.61247i
$686$	1.20390	−	0.742040i	0.0459651	−	0.0283312i
$687$	10.6762	+	0.0817675i	0.407322	+	0.00311962i
$688$	29.7963	+	12.8986i	1.13597	+	0.491755i
$689$	2.58164	−	4.47154i	0.0983527	−	0.170352i
$690$	−1.43784	−	68.1122i	−0.0547378	−	2.59299i
$691$	−26.9982	+	15.5874i	−1.02706	+	0.592973i	−0.916141	−	0.400857i	$-0.868713\pi$
$691$	−26.9982	+	15.5874i	−1.02706	+	0.592973i	−0.110918	+	0.993830i	$0.535379\pi$
$692$	−1.51090	−	26.2333i	−0.0574357	−	0.997241i
$693$	5.52477	−	3.07788i	0.209869	−	0.116919i
$694$	3.54316	−	0.101949i	0.134496	−	0.00386993i
$695$	−26.0743	−	45.1619i	−0.989053	−	1.71309i
$696$	20.1487	+	9.60800i	0.763733	+	0.364190i
$697$	4.08008	−	7.06690i	0.154544	−	0.267678i
$698$	−17.7275	+	32.8522i	−0.670995	+	1.24347i
$699$	28.8046	−	16.3375i	1.08949	−	0.617940i
$700$	9.51162	+	14.4821i	0.359506	+	0.547372i
$701$			30.2679i			1.14320i	0.820532	+	0.571601i	$0.193678\pi$
$701$			30.2679i			1.14320i	−0.820532	+	0.571601i	$0.806322\pi$
$702$	−0.0750435	−	12.9622i	−0.00283234	−	0.489226i
$703$	9.73992			0.367348
$704$	−12.9401	+	10.8154i	−0.487700	+	0.407619i
$705$	−30.7452	−	54.2068i	−1.15793	−	2.04155i
$706$	−20.3378	−	10.9745i	−0.765423	−	0.413032i
$707$	1.90658	+	1.10076i	0.0717041	+	0.0413984i
$708$	−7.47430	+	14.5794i	−0.280901	+	0.547926i
$709$	−36.5181	+	21.0837i	−1.37147	+	0.791817i	−0.991113	−	0.133024i	$-0.957531\pi$
$709$	−36.5181	+	21.0837i	−1.37147	+	0.791817i	−0.380354	+	0.924841i	$0.624198\pi$
$710$	49.3169	−	1.41902i	1.85083	−	0.0532548i
$711$	45.6155	+	0.698768i	1.71072	+	0.0262058i
$712$	−1.93638	−	22.3830i	−0.0725690	−	0.838838i
$713$	25.0813	+	43.4422i	0.939304	+	1.62692i
$714$	13.9666	−	0.294835i	0.522688	−	0.0110339i
$715$	11.9038	+	6.87264i	0.445176	+	0.257022i
$716$	−1.66342	−	0.836749i	−0.0621650	−	0.0312708i
$717$	−0.120994	+	15.7979i	−0.00451860	+	0.589983i
$718$	21.3957	−	13.1875i	0.798481	−	0.492154i
$719$	−13.3338			−0.497266			−0.248633	−	0.968598i	$-0.579981\pi$
$719$	−13.3338			−0.497266			−0.248633	+	0.968598i	$0.579981\pi$
$720$	−40.4314	−	18.2428i	−1.50679	−	0.679868i
$721$	7.06242			0.263018
$722$	41.6267	−	25.6572i	1.54919	−	0.954861i
$723$	20.0893	+	11.8046i	0.747131	+	0.439019i
$724$	−16.3923	−	8.24578i	−0.609213	−	0.306452i
$725$	−34.1853	−	19.7369i	−1.26961	−	0.733011i
$726$	8.32110	+	13.7347i	0.308825	+	0.509743i
$727$	7.02071	+	12.1602i	0.260384	+	0.450998i	0.966344	−	0.257254i	$-0.0828176\pi$
$727$	7.02071	+	12.1602i	0.260384	+	0.450998i	−0.705960	+	0.708251i	$0.749484\pi$
$728$	−4.97067	+	0.430019i	−0.184225	+	0.0159376i
$729$	−26.9715	−	1.24028i	−0.998944	−	0.0459361i
$730$	10.3947	−	0.299091i	0.384725	−	0.0110699i
$731$	−40.0907	+	23.1464i	−1.48281	+	0.856100i
$732$	4.16613	+	6.45035i	0.153985	+	0.238412i
$733$	26.9054	+	15.5338i	0.993773	+	0.573755i	0.906400	−	0.422421i	$-0.138820\pi$
$733$	26.9054	+	15.5338i	0.993773	+	0.573755i	0.0873728	+	0.996176i	$0.472153\pi$
$734$	−20.0271	−	10.8069i	−0.739215	−	0.398890i
$735$	3.24352	−	5.51988i	0.119639	−	0.203604i
$736$	33.4307	−	26.3459i	1.23227	−	0.971121i
$737$	−21.6596			−0.797840
$738$	5.29752	+	2.96426i	0.195004	+	0.109116i
$739$		−	11.7664i		−	0.432835i	−0.976301	−	0.216418i	$-0.930563\pi$
$739$		−	11.7664i		−	0.432835i	0.976301	−	0.216418i	$-0.0694373\pi$
$740$	5.40034	+	8.22240i	0.198521	+	0.302261i
$741$	−0.171273	+	22.3627i	−0.00629186	+	0.821514i
$742$	−1.96581	+	3.64300i	−0.0721670	+	0.133739i
$743$	7.28823	−	12.6236i	0.267379	−	0.463114i	−0.700805	−	0.713353i	$-0.747176\pi$
$743$	7.28823	−	12.6236i	0.267379	−	0.463114i	0.968184	+	0.250239i	$0.0805091\pi$
$744$	32.5591	−	2.56567i	1.19367	−	0.0940619i
$745$	2.04156	+	3.53608i	0.0747970	+	0.129552i
$746$	40.9438	−	1.17809i	1.49906	−	0.0431331i
$747$	0.175279	−	11.4422i	0.00641312	−	0.418648i
$748$	−1.38259	−	24.0056i	−0.0505526	−	0.877733i
$749$	−6.97992	+	4.02986i	−0.255041	+	0.147248i
$750$	29.0673	+	15.9737i	1.06139	+	0.583277i
$751$	12.7168	−	22.0261i	0.464042	−	0.803744i	−0.535116	−	0.844779i	$-0.679732\pi$
$751$	12.7168	−	22.0261i	0.464042	−	0.803744i	0.999158	+	0.0410349i	$0.0130655\pi$
$752$	15.4677	−	35.7310i	0.564049	−	1.30298i
$753$	−0.828642	−	1.46098i	−0.0301974	−	0.0532410i
$754$	9.67635	−	5.96414i	0.352392	−	0.217201i
$755$		−	4.30193i		−	0.156563i
$756$	0.359033	+	10.3861i	0.0130579	+	0.377739i
$757$		−	45.8600i		−	1.66681i	−0.552663	−	0.833405i	$-0.686388\pi$
$757$		−	45.8600i		−	1.66681i	0.552663	−	0.833405i	$-0.313612\pi$
$758$	−3.62699	−	5.88450i	−0.131738	−	0.213735i
$759$	13.5543	+	23.8976i	0.491990	+	0.867427i
$760$	69.3246	+	32.4085i	2.51467	+	1.17558i
$761$	27.3232	−	47.3252i	0.990466	−	1.71554i	0.375931	−	0.926648i	$-0.377323\pi$
$761$	27.3232	−	47.3252i	0.990466	−	1.71554i	0.614535	−	0.788890i	$-0.289344\pi$
$762$	−0.793315	+	1.44359i	−0.0287388	+	0.0522958i
$763$	9.92311	−	5.72911i	0.359241	−	0.207408i
$764$	−10.2867	+	0.592456i	−0.372158	+	0.0214343i
$765$	55.2476	−	30.7787i	1.99748	−	1.11281i
$766$	1.09243	+	37.9666i	0.0394711	+	1.37179i
$767$	4.17136	+	7.22501i	0.150619	+	0.260880i
$768$	−6.11441	−	27.0299i	−0.220635	−	0.975356i
$769$	−8.77268	+	15.1947i	−0.316351	+	0.547936i	−0.979724	−	0.200353i	$-0.935791\pi$
$769$	−8.77268	+	15.1947i	−0.316351	+	0.547936i	0.663373	+	0.748289i	$0.269124\pi$
$770$	−9.69810	−	5.23321i	−0.349495	−	0.188592i
$771$	0.190090	−	24.8196i	0.00684591	−	0.893854i
$772$	−3.44355	−	5.24304i	−0.123936	−	0.188701i
$773$			32.4515i			1.16720i	0.812042	+	0.583599i	$0.198356\pi$
$773$			32.4515i			1.16720i	−0.812042	+	0.583599i	$0.801644\pi$
$774$	−17.6184	−	29.5898i	−0.633282	−	1.06358i
$775$	−57.7548			−2.07461
$776$	44.7202	−	31.2488i	1.60536	−	1.12177i
$777$	1.16764	−	1.98711i	0.0418889	−	0.0712872i
$778$	−5.64292	+	10.4573i	−0.202308	+	0.374914i
$779$	−9.06992	−	5.23652i	−0.324964	−	0.187618i
$780$	−18.9734	+	12.2545i	−0.679358	+	0.438782i
$781$	−17.2308	+	9.94819i	−0.616565	+	0.355974i
$782$	1.74546	+	60.6622i	0.0624176	+	2.16928i
$783$	−11.3640	−	20.7708i	−0.406115	−	0.742289i
$784$	3.97355	−	0.459233i	0.141913	−	0.0164012i
$785$	−9.32852	−	16.1575i	−0.332949	−	0.576685i
$786$	−0.933023	+	0.565266i	−0.0332798	+	0.0201624i
$787$	19.5737	+	11.3009i	0.697727	+	0.402833i	0.806500	−	0.591234i	$-0.201359\pi$
$787$	19.5737	+	11.3009i	0.697727	+	0.402833i	−0.108774	+	0.994067i	$0.534692\pi$
$788$	44.4651	+	22.3672i	1.58400	+	0.796800i
$789$	−0.971277	−	0.570729i	−0.0345784	−	0.0203185i
$790$	−41.7105	−	67.6720i	−1.48399	−	2.40766i
$791$	−12.9023			−0.458754
$792$	17.8427	−	1.26859i	0.634013	−	0.0450774i
$793$	3.91012			0.138852
$794$	−18.3058	−	29.6997i	−0.649649	−	1.05400i
$795$	−0.143524	+	18.7396i	−0.00509028	+	0.664626i
$796$	−3.10773	+	6.17803i	−0.110150	+	0.218974i
$797$	−9.94015	−	5.73895i	−0.352098	−	0.203284i	0.313511	−	0.949585i	$-0.398495\pi$
$797$	−9.94015	−	5.73895i	−0.352098	−	0.203284i	−0.665609	+	0.746301i	$0.731828\pi$
$798$	−0.378402	−	17.9253i	−0.0133953	−	0.634548i
$799$	27.7566	+	48.0758i	0.981957	+	1.70080i
$800$	7.02418	+	48.5003i	0.248342	+	1.71475i
$801$	−12.2294	+	20.4520i	−0.432105	+	0.722635i
$802$	0.851703	+	29.6003i	0.0300747	+	1.04522i
$803$	−3.63179	+	2.09681i	−0.128163	+	0.0739950i
$804$	16.2372	−	31.6723i	0.572642	−	1.11700i
$805$	24.0867	+	13.9064i	0.848943	+	0.490138i
$806$	7.89774	−	14.6359i	0.278186	−	0.515529i
$807$	23.4254	+	41.3013i	0.824614	+	1.45388i
$808$	3.56662	+	5.10420i	0.125473	+	0.179565i
$809$	−0.500225			−0.0175870			−0.00879349	−	0.999961i	$-0.502799\pi$
$809$	−0.500225			−0.0175870			−0.00879349	+	0.999961i	$0.502799\pi$
$810$	23.4474	+	40.7879i	0.823857	+	1.43314i
$811$			23.2223i			0.815446i	0.913106	+	0.407723i	$0.133677\pi$
$811$			23.2223i			0.815446i	−0.913106	+	0.407723i	$0.866323\pi$
$812$	−7.61705	+	5.00276i	−0.267306	+	0.175562i
$813$	−25.3960	+	14.4042i	−0.890677	+	0.505177i
$814$	−3.49123	−	1.88391i	−0.122368	−	0.0660311i
$815$	11.7505	−	20.3525i	0.411603	−	0.712918i
$816$	36.1394	+	15.9742i	1.26513	+	0.559210i
$817$	29.7069	+	51.4539i	1.03931	+	1.80014i
$818$	0.306215	+	10.6423i	0.0107066	+	0.372099i
$819$	4.54184	+	2.71582i	0.158705	+	0.0948986i
$820$	−0.608210	−	10.5602i	−0.0212396	−	0.368778i
$821$	13.2321	−	7.63958i	0.461805	−	0.266623i	−0.250998	−	0.967988i	$-0.580759\pi$
$821$	13.2321	−	7.63958i	0.461805	−	0.266623i	0.712803	+	0.701364i	$0.247425\pi$
$822$	27.9602	−	0.590238i	0.975225	−	0.0205869i
$823$	4.54900	−	7.87909i	0.158568	−	0.274648i	−0.775784	−	0.630998i	$-0.782646\pi$
$823$	4.54900	−	7.87909i	0.158568	−	0.274648i	0.934353	+	0.356350i	$0.115979\pi$
$824$	18.0958	+	8.45958i	0.630397	+	0.294704i
$825$	−31.6311	−	0.242258i	−1.10125	−	0.00843436i
$826$	−3.50951	−	5.69390i	−0.122111	−	0.198116i
$827$			39.4647i			1.37232i	0.727450	+	0.686161i	$0.240705\pi$
$827$			39.4647i			1.37232i	−0.727450	+	0.686161i	$0.759295\pi$
$828$	−45.1060	+	1.90522i	−1.56754	+	0.0662109i
$829$			7.12411i			0.247430i	0.992318	+	0.123715i	$0.0394809\pi$
$829$			7.12411i			0.247430i	−0.992318	+	0.123715i	$0.960519\pi$
$830$	−16.9748	+	10.4627i	−0.589205	+	0.363164i
$831$	6.01913	−	10.2435i	0.208801	−	0.355341i
$832$	−13.2513	−	4.85219i	−0.459405	−	0.168220i
$833$	−2.85156	+	4.93905i	−0.0988008	+	0.171128i
$834$	−29.5563	+	17.9065i	−1.02345	+	0.620052i
$835$	−15.6281	+	9.02291i	−0.540834	+	0.312251i
$836$	−30.8097	+	1.77447i	−1.06558	+	0.0613714i
$837$	−29.5943	−	18.0052i	−1.02293	−	0.622352i
$838$	21.4804	−	0.618064i	0.742027	−	0.0213507i
$839$	−14.2144	−	24.6200i	−0.490734	−	0.849976i	0.509209	−	0.860643i	$-0.329938\pi$
$839$	−14.2144	−	24.6200i	−0.490734	−	0.849976i	−0.999943	+	0.0106667i	$0.996605\pi$
$840$	14.9226	−	10.2582i	0.514880	−	0.353942i
$841$	−4.11912	+	7.13452i	−0.142039	+	0.246018i
$842$	16.5774	−	30.7210i	0.571296	−	1.05871i
$843$	−4.19863	−	2.46715i	−0.144609	−	0.0849730i
$844$	18.6712	−	12.2629i	0.642689	−	0.422108i
$845$		−	36.5514i		−	1.25741i
$846$	−35.4834	+	21.1276i	−1.21994	+	0.726383i
$847$	−6.55595			−0.225265
$848$	−9.40061	+	6.97962i	−0.322818	+	0.239681i
$849$	−20.0151	−	0.153293i	−0.686915	−	0.00526099i
$850$	−61.4910	−	33.1813i	−2.10912	−	1.13811i
$851$	8.67099	+	5.00620i	0.297238	+	0.171610i
$852$	−1.62988	−	32.6539i	−0.0558386	−	1.11870i
$853$	1.20861	−	0.697794i	0.0413822	−	0.0238920i	−0.479166	−	0.877724i	$-0.659061\pi$
$853$	1.20861	−	0.697794i	0.0413822	−	0.0238920i	0.520548	+	0.853832i	$0.325728\pi$
$854$	−3.13355	+	0.0901631i	−0.107228	+	0.00308532i
$855$	−39.5025	−	70.9069i	−1.35096	−	2.42496i
$856$	−22.7115	+	1.96480i	−0.776263	+	0.0671556i
$857$	−18.4798	−	32.0080i	−0.631259	−	1.09337i	−0.987295	−	0.158900i	$-0.949205\pi$
$857$	−18.4798	−	32.0080i	−0.631259	−	1.09337i	0.356036	−	0.934472i	$-0.384128\pi$
$858$	4.38682	−	7.98268i	0.149764	−	0.272524i
$859$	−8.98534	−	5.18769i	−0.306576	−	0.177002i	0.338817	−	0.940852i	$-0.389973\pi$
$859$	−8.98534	−	5.18769i	−0.306576	−	0.177002i	−0.645393	+	0.763850i	$0.723306\pi$
$860$	−26.9660	+	53.6073i	−0.919534	+	1.82799i
$861$	−2.15566	+	1.22265i	−0.0734647	+	0.0416680i
$862$	−6.46951	+	3.98756i	−0.220352	+	0.135817i
$863$	12.1268			0.412802			0.206401	−	0.978467i	$-0.433825\pi$
$863$	12.1268			0.412802			0.206401	+	0.978467i	$0.433825\pi$
$864$	−11.5209	+	27.0420i	−0.391947	+	0.919988i
$865$	48.5644			1.65124
$866$	−29.4659	+	18.1617i	−1.00129	+	0.617160i
$867$	−23.3907	+	13.2668i	−0.794391	+	0.450566i
$868$	−5.99172	+	11.9113i	−0.203372	+	0.404295i
$869$	27.7628	+	16.0288i	0.941787	+	0.543741i
$870$	−19.8692	+	36.1558i	−0.673628	+	1.22580i
$871$	−9.06189	−	15.6957i	−0.307051	−	0.531827i
$872$	32.2882	−	2.79329i	1.09341	−	0.0945928i
$873$	−57.8589	−	0.886319i	−1.95823	−	0.0299974i
$874$	77.8561	−	2.24019i	2.63352	−	0.0757755i
$875$	−11.7264	+	6.77023i	−0.396424	+	0.228876i
$876$	−0.343535	−	6.88258i	−0.0116070	−	0.232541i
$877$	8.27364	+	4.77679i	0.279381	+	0.161301i	0.633143	−	0.774035i	$-0.281764\pi$
$877$	8.27364	+	4.77679i	0.279381	+	0.161301i	−0.353762	+	0.935335i	$0.615098\pi$
$878$	25.5452	+	13.7845i	0.862107	+	0.465204i
$879$	−30.6726	−	0.234917i	−1.03456	−	0.00792357i
$880$	−18.5806	−	25.0256i	−0.626351	−	0.843611i
$881$	−5.00905			−0.168759			−0.0843795	−	0.996434i	$-0.526891\pi$
$881$	−5.00905			−0.168759			−0.0843795	+	0.996434i	$0.526891\pi$
$882$	−3.70243	−	2.07172i	−0.124667	−	0.0697584i
$883$		−	50.0439i		−	1.68411i	−0.539389	−	0.842056i	$-0.681345\pi$
$883$		−	50.0439i		−	1.68411i	0.539389	−	0.842056i	$-0.318655\pi$
$884$	16.8173	−	11.0453i	0.565627	−	0.371495i
$885$	−26.1065	−	15.3404i	−0.877561	−	0.515662i
$886$	−18.2193	+	33.7636i	−0.612089	+	1.13431i
$887$	5.06367	−	8.77053i	0.170021	−	0.294485i	−0.768406	−	0.639963i	$-0.778950\pi$
$887$	5.06367	−	8.77053i	0.170021	−	0.294485i	0.938427	+	0.345477i	$0.112283\pi$
$888$	5.37203	−	3.69287i	0.180273	−	0.123925i
$889$	−0.336236	−	0.582377i	−0.0112770	−	0.0195323i
$890$	41.5053	−	1.19425i	1.39126	−	0.0400313i
$891$	−16.1327	−	9.98524i	−0.540465	−	0.334518i
$892$	−4.24401	+	0.244432i	−0.142100	+	0.00818420i
$893$	61.7023	−	35.6238i	2.06479	−	1.19211i
$894$	2.31420	−	1.40204i	0.0773983	−	0.0468913i
$895$	1.72068	−	2.98031i	0.0575160	−	0.0996207i
$896$	10.7314	+	3.58296i	0.358510	+	0.119698i
$897$	−11.6466	+	19.8204i	−0.388869	+	0.661784i
$898$	48.0505	−	29.6166i	1.60347	−	0.988318i
$899$		−	30.3769i		−	1.01312i
$900$	24.0667	−	46.0719i	0.802223	−	1.53573i
$901$		−	16.6936i		−	0.556145i
$902$	2.23822	+	3.63133i	0.0745244	+	0.120910i
$903$	14.0588	+	0.107674i	0.467847	+	0.00358318i
$904$	−33.0592	−	15.4548i	−1.09953	−	0.514019i
$905$	16.9565	−	29.3695i	0.563654	−	0.976277i
$906$	−2.85014	+	0.0601663i	−0.0946896	+	0.00199889i
$907$	−20.7603	+	11.9860i	−0.689334	+	0.397987i	−0.803363	−	0.595490i	$-0.796958\pi$
$907$	−20.7603	+	11.9860i	−0.689334	+	0.397987i	0.114028	+	0.993478i	$0.463625\pi$
$908$	1.06526	+	18.4958i	0.0353519	+	0.613806i
$909$	0.101161	−	6.60380i	0.00335530	−	0.219034i
$910$	−0.265211	−	9.21722i	−0.00879166	−	0.305548i
$911$	−9.16554	−	15.8752i	−0.303668	−	0.525968i	0.673296	−	0.739373i	$-0.264878\pi$
$911$	−9.16554	−	15.8752i	−0.303668	−	0.525968i	−0.976964	+	0.213405i	$0.931545\pi$
$912$	20.5019	−	46.3826i	0.678886	−	1.53588i
$913$	4.02067	−	6.96401i	0.133065	−	0.230475i
$914$	−9.83288	−	5.30595i	−0.325243	−	0.175505i
$915$	−12.3445	+	7.00157i	−0.408095	+	0.231465i
$916$	−10.3044	+	6.76777i	−0.340467	+	0.223613i
$917$		−	0.445357i		−	0.0147070i
$918$	−21.1644	−	36.1725i	−0.698529	−	1.19387i
$919$	26.2739			0.866697			0.433349	−	0.901226i	$-0.357332\pi$
$919$	26.2739			0.866697			0.433349	+	0.901226i	$0.357332\pi$
$920$	45.0588	+	64.4837i	1.48555	+	2.12597i
$921$	−27.0522	−	47.6957i	−0.891401	−	1.57163i
$922$	18.5025	−	34.2884i	0.609346	−	1.12923i
$923$	−14.4180	−	8.32422i	−0.474573	−	0.273995i
$924$	−3.33151	+	6.49843i	−0.109598	+	0.213783i
$925$	−9.98334	+	5.76388i	−0.328250	+	0.189515i
$926$	−1.21333	−	42.1685i	−0.0398726	−	1.38574i
$927$	−10.3113	−	18.5088i	−0.338669	−	0.607909i
$928$	−25.5094	+	3.69446i	−0.837386	+	0.121277i
$929$	−13.6554	−	23.6519i	−0.448020	−	0.775994i	0.550237	−	0.835009i	$-0.314537\pi$
$929$	−13.6554	−	23.6519i	−0.448020	−	0.775994i	−0.998257	+	0.0590147i	$0.981204\pi$
$930$	1.27395	+	60.3484i	0.0417744	+	1.97890i
$931$	6.33896	+	3.65980i	0.207751	+	0.119945i
$932$	−17.1833	+	34.1598i	−0.562859	+	1.11894i
$933$	−0.349800	+	45.6725i	−0.0114519	+	1.49525i
$934$	20.9153	+	33.9334i	0.684369	+	1.11033i
$935$	44.4404			1.45336
$936$	8.38429	+	12.3990i	0.274049	+	0.405274i
$937$	−43.2384			−1.41254			−0.706269	−	0.707944i	$-0.749623\pi$
$937$	−43.2384			−1.41254			−0.706269	+	0.707944i	$0.749623\pi$
$938$	7.62408	+	12.3695i	0.248935	+	0.403877i
$939$	4.06109	+	2.38633i	0.132529	+	0.0778748i
$940$	64.2846	+	32.3370i	2.09673	+	1.05472i
$941$	31.4986	+	18.1857i	1.02683	+	0.592838i	0.916074	−	0.401010i	$-0.131341\pi$
$941$	31.4986	+	18.1857i	1.02683	+	0.592838i	0.110752	+	0.993848i	$0.464674\pi$
$942$	−10.5743	+	6.40636i	−0.344529	+	0.208731i
$943$	−5.38302	−	9.32366i	−0.175295	−	0.303620i
$944$	−2.17196	−	18.7931i	−0.0706914	−	0.611663i
$945$	−19.2018	−	0.441262i	−0.624636	−	0.0143543i
$946$	−0.696012	−	24.1894i	−0.0226293	−	0.786465i
$947$	−36.9895	+	21.3559i	−1.20200	+	0.693973i	−0.960999	−	0.276553i	$-0.910808\pi$
$947$	−36.9895	+	21.3559i	−1.20200	+	0.693973i	−0.240998	+	0.970526i	$0.577475\pi$
$948$	−44.2511	+	28.5808i	−1.43721	+	0.928260i
$949$	−3.03892	−	1.75452i	−0.0986477	−	0.0569543i
$950$	−42.5861	+	78.9198i	−1.38168	+	2.56050i
$951$	1.08572	−	1.84769i	0.0352068	−	0.0599155i
$952$	−13.2226	+	9.23947i	−0.428547	+	0.299453i
$953$	−17.5322			−0.567924			−0.283962	−	0.958836i	$-0.591649\pi$
$953$	−17.5322			−0.567924			−0.283962	+	0.958836i	$0.591649\pi$
$954$	12.4175	−	0.167002i	0.402032	−	0.00540688i
$955$		−	19.0432i		−	0.616223i
$956$	−10.0145	−	15.2478i	−0.323892	−	0.493148i
$957$	0.127419	−	16.6368i	0.00411887	−	0.537791i
$958$	−44.2178	−	23.8605i	−1.42861	−	0.770896i
$959$	−5.70863	+	9.88763i	−0.184341	+	0.319288i
$960$	50.5234	−	8.40943i	1.63063	−	0.271413i
$961$	−6.72242	−	11.6436i	−0.216852	−	0.375599i
$962$	−0.0954738	−	3.31812i	−0.00307820	−	0.106980i
$963$	20.7521	+	12.4089i	0.668728	+	0.399871i
$964$	−26.8610	+	1.54705i	−0.865135	+	0.0498271i
$965$	10.0400	−	5.79661i	0.323200	−	0.186600i
$966$	8.87651	−	16.1525i	0.285597	−	0.519699i
$967$	−14.4214	+	24.9785i	−0.463760	+	0.803256i	−0.999145	−	0.0413527i	$-0.986833\pi$
$967$	−14.4214	+	24.9785i	−0.463760	+	0.803256i	0.535385	+	0.844608i	$0.320167\pi$
$968$	−16.7981	−	7.85292i	−0.539911	−	0.252402i
$969$	35.6713	+	62.8919i	1.14593	+	2.02038i
$970$	52.9058	+	85.8354i	1.69870	+	2.75601i
$971$		−	41.1476i		−	1.32049i	−0.751050	−	0.660245i	$-0.770452\pi$
$971$		−	41.1476i		−	1.32049i	0.751050	−	0.660245i	$-0.229548\pi$
$972$	26.6951	−	16.1050i	0.856247	−	0.516567i
$973$		−	14.1080i		−	0.452282i
$974$	−17.0051	+	10.4813i	−0.544877	+	0.335842i
$975$	−13.0582	−	23.0229i	−0.418198	−	0.737324i
$976$	−8.13699	−	3.52244i	−0.260459	−	0.112751i
$977$	−5.60160	+	9.70225i	−0.179211	+	0.310403i	−0.941611	−	0.336704i	$-0.890688\pi$
$977$	−5.60160	+	9.70225i	−0.179211	+	0.310403i	0.762400	+	0.647107i	$0.224021\pi$
$978$	−13.6484	−	7.50039i	−0.436428	−	0.239836i
$979$	−14.5015	+	8.37243i	−0.463469	+	0.267584i
$980$	0.425078	+	7.38052i	0.0135786	+	0.235762i
$981$	−29.5026	−	17.6413i	−0.941945	−	0.563243i
$982$	31.5015	−	0.906405i	1.00525	−	0.0289246i
$983$	9.36939	+	16.2283i	0.298837	+	0.517601i	0.975870	−	0.218352i	$-0.0700680\pi$
$983$	9.36939	+	16.2283i	0.298837	+	0.517601i	−0.677033	+	0.735953i	$0.736735\pi$
$984$	−6.98790	+	0.550649i	−0.222766	+	0.0175540i
$985$	−45.9957	+	79.6669i	−1.46555	+	2.53840i
$986$	17.4521	−	32.3420i	0.555789	−	1.02998i
$987$	0.129121	−	16.8590i	0.00410995	−	0.536627i
$988$	−14.1760	−	21.5839i	−0.450998	−	0.686677i
$989$			61.0760i			1.94210i
$990$	0.444578	+	33.0569i	0.0141296	+	1.05062i
$991$	−49.7936			−1.58175			−0.790874	−	0.611979i	$-0.790373\pi$
$991$	−49.7936			−1.58175			−0.790874	+	0.611979i	$0.790373\pi$
$992$	−29.6201	+	23.3428i	−0.940438	+	0.741135i
$993$	−11.7771	+	20.0425i	−0.373735	+	0.636028i
$994$	11.7464	+	6.33852i	0.372574	+	0.201046i
$995$	−11.0690	−	6.39069i	−0.350911	−	0.202598i
$996$	7.16920	+	11.0999i	0.227165	+	0.351715i
$997$	16.0637	−	9.27438i	0.508742	−	0.293723i	−0.223574	−	0.974687i	$-0.571772\pi$
$997$	16.0637	−	9.27438i	0.508742	−	0.293723i	0.732317	+	0.680964i	$0.238439\pi$
$998$	13.9409	−	0.401129i	0.441293	−	0.0126975i
$999$	−6.91250	−	0.158851i	−0.218702	−	0.00502581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cs.a.85.7	✓	72
8.5	even	2	inner	504.2.cs.a.85.31	yes	72
9.7	even	3	inner	504.2.cs.a.421.31	yes	72
72.61	even	6	inner	504.2.cs.a.421.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cs.a.85.7	✓	72	1.1	even	1	trivial
504.2.cs.a.85.31	yes	72	8.5	even	2	inner
504.2.cs.a.421.7	yes	72	72.61	even	6	inner
504.2.cs.a.421.31	yes	72	9.7	even	3	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20390 + 0.742040i) q^{2} +(-1.50659 + 0.854512i) q^{3} +(0.898754 - 1.78668i) q^{4} +(3.20115 + 1.84819i) q^{5} +(1.17970 - 2.14670i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.243781 + 2.81790i) q^{8} +(1.53962 - 2.57480i) q^{9} +O(q^{10})\)	\(q+(-1.20390 + 0.742040i) q^{2} +(-1.50659 + 0.854512i) q^{3} +(0.898754 - 1.78668i) q^{4} +(3.20115 + 1.84819i) q^{5} +(1.17970 - 2.14670i) q^{6} +(0.500000 + 0.866025i) q^{7} +(0.243781 + 2.81790i) q^{8} +(1.53962 - 2.57480i) q^{9} +(-5.22530 + 0.150350i) q^{10} +(1.82566 - 1.05405i) q^{11} +(0.172691 + 3.45979i) q^{12} +(1.52763 + 0.881980i) q^{13} +(-1.24458 - 0.671589i) q^{14} +(-6.40212 - 0.0490330i) q^{15} +(-2.38448 - 3.21158i) q^{16} +5.70313 q^{17} +(0.0570536 + 4.24226i) q^{18} -7.31960i q^{19} +(6.17918 - 4.05839i) q^{20} +(-1.49332 - 0.877488i) q^{21} +(-1.41577 + 2.62368i) q^{22} +(3.76218 - 6.51629i) q^{23} +(-2.77521 - 4.03711i) q^{24} +(4.33159 + 7.50253i) q^{25} +(-2.49358 + 0.0717490i) q^{26} +(-0.119377 + 5.19478i) q^{27} +(1.99669 - 0.114999i) q^{28} +(-3.94605 + 2.27825i) q^{29} +(7.74390 - 4.69160i) q^{30} +(-3.33335 + 5.77353i) q^{31} +(5.25380 + 2.09704i) q^{32} +(-1.84982 + 3.14806i) q^{33} +(-6.86600 + 4.23195i) q^{34} +3.69637i q^{35} +(-3.21661 - 5.06492i) q^{36} +1.33066i q^{37} +(5.43143 + 8.81207i) q^{38} +(-3.05518 - 0.0233992i) q^{39} +(-4.42763 + 9.47109i) q^{40} +(0.715411 - 1.23913i) q^{41} +(2.44894 - 0.0516970i) q^{42} +(-7.02960 + 4.05854i) q^{43} +(-0.242427 - 4.20921i) q^{44} +(9.68726 - 5.39682i) q^{45} +(0.306053 + 10.6367i) q^{46} +(4.86691 + 8.42973i) q^{47} +(6.33677 + 2.80096i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-10.7820 - 5.81809i) q^{50} +(-8.59226 + 4.87339i) q^{51} +(2.94879 - 1.93672i) q^{52} -2.92710i q^{53} +(-3.71102 - 6.34258i) q^{54} +7.79229 q^{55} +(-2.31848 + 1.62007i) q^{56} +(6.25469 + 11.0276i) q^{57} +(3.06010 - 5.67092i) q^{58} +(4.09591 + 2.36477i) q^{59} +(-5.84154 + 11.3945i) q^{60} +(1.91970 - 1.10834i) q^{61} +(-0.271168 - 9.42423i) q^{62} +(2.99965 + 0.0459505i) q^{63} +(-7.88114 + 1.37390i) q^{64} +(3.26013 + 5.64671i) q^{65} +(-0.108982 - 5.16260i) q^{66} +(-8.89797 - 5.13725i) q^{67} +(5.12571 - 10.1897i) q^{68} +(-0.0998119 + 13.0322i) q^{69} +(-2.74286 - 4.45007i) q^{70} -9.43810 q^{71} +(7.63085 + 3.71081i) q^{72} -1.98930 q^{73} +(-0.987405 - 1.60199i) q^{74} +(-12.9369 - 7.60183i) q^{75} +(-13.0778 - 6.57852i) q^{76} +(1.82566 + 1.05405i) q^{77} +(3.69549 - 2.23889i) q^{78} +(7.60348 + 13.1696i) q^{79} +(-1.69750 - 14.6877i) q^{80} +(-4.25915 - 7.92841i) q^{81} +(0.0581986 + 2.02265i) q^{82} +(3.30347 - 1.90726i) q^{83} +(-2.90992 + 1.87945i) q^{84} +(18.2566 + 10.5404i) q^{85} +(5.45134 - 10.1023i) q^{86} +(3.99828 - 6.80434i) q^{87} +(3.41526 + 4.88758i) q^{88} -7.94314 q^{89} +(-7.65785 + 13.6856i) q^{90} +1.76396i q^{91} +(-8.26128 - 12.5784i) q^{92} +(0.0884348 - 11.5467i) q^{93} +(-12.1145 - 6.53712i) q^{94} +(13.5280 - 23.4312i) q^{95} +(-9.70726 + 1.33006i) q^{96} +(-9.64428 - 16.7044i) q^{97} +(-0.0406750 - 1.41363i) q^{98} +(0.0968678 - 6.32353i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8}+O(q^{10}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8	\( 72 q - 8 q^{6} + 36 q^{7} + 6 q^{8} + 20 q^{12} + 40 q^{17} - q^{18} + 2 q^{20} - 12 q^{22} + 12 q^{23} + 10 q^{24} + 36 q^{25} - 42 q^{26} + 4 q^{30} + 5 q^{32} + 8 q^{33} + 6 q^{34} - 18 q^{36} - 25 q^{38} - 4 q^{39} - 9 q^{40} + 24 q^{41} - 7 q^{42} + 12 q^{46} - 53 q^{48} - 36 q^{49} + 41 q^{50} - 9 q^{52} + 12 q^{54} + 3 q^{56} + 4 q^{57} + 9 q^{58} - 50 q^{60} + 60 q^{62} - 6 q^{64} - 40 q^{65} - 2 q^{66} + 23 q^{68} - 56 q^{71} + 19 q^{72} + 22 q^{74} - 24 q^{76} - 54 q^{78} - 6 q^{80} - 4 q^{81} - 48 q^{82} + 10 q^{84} - 39 q^{86} - 76 q^{87} - 12 q^{88} - 88 q^{89} - 77 q^{90} + 11 q^{92} + 24 q^{94} - 24 q^{95} + 59 q^{96}+O(q^{100}) \) 72 * q - 8 * q^6 + 36 * q^7 + 6 * q^8 + 20 * q^12 + 40 * q^17 - q^18 + 2 * q^20 - 12 * q^22 + 12 * q^23 + 10 * q^24 + 36 * q^25 - 42 * q^26 + 4 * q^30 + 5 * q^32 + 8 * q^33 + 6 * q^34 - 18 * q^36 - 25 * q^38 - 4 * q^39 - 9 * q^40 + 24 * q^41 - 7 * q^42 + 12 * q^46 - 53 * q^48 - 36 * q^49 + 41 * q^50 - 9 * q^52 + 12 * q^54 + 3 * q^56 + 4 * q^57 + 9 * q^58 - 50 * q^60 + 60 * q^62 - 6 * q^64 - 40 * q^65 - 2 * q^66 + 23 * q^68 - 56 * q^71 + 19 * q^72 + 22 * q^74 - 24 * q^76 - 54 * q^78 - 6 * q^80 - 4 * q^81 - 48 * q^82 + 10 * q^84 - 39 * q^86 - 76 * q^87 - 12 * q^88 - 88 * q^89 - 77 * q^90 + 11 * q^92 + 24 * q^94 - 24 * q^95 + 59 * q^96

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