LMFDB - Embedded newform 252.2.bi.c.139.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.12
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.07529 + 0.918559i) q^{2} +(0.476707 + 1.66516i) q^{3} +(0.312499 - 1.97544i) q^{4} +(-0.0753642 - 0.0435115i) q^{5} +(-2.04214 - 1.35264i) q^{6} +(2.31226 + 1.28587i) q^{7} +(1.47853 + 2.41122i) q^{8} +(-2.54550 + 1.58759i) q^{9} +O(q^{10})$	\(q+(-1.07529 + 0.918559i) q^{2} +(0.476707 + 1.66516i) q^{3} +(0.312499 - 1.97544i) q^{4} +(-0.0753642 - 0.0435115i) q^{5} +(-2.04214 - 1.35264i) q^{6} +(2.31226 + 1.28587i) q^{7} +(1.47853 + 2.41122i) q^{8} +(-2.54550 + 1.58759i) q^{9} +(0.121006 - 0.0224389i) q^{10} +(-1.68051 + 0.970240i) q^{11} +(3.43838 - 0.421344i) q^{12} +(3.30872 + 1.91029i) q^{13} +(-3.66750 + 0.741269i) q^{14} +(0.0365269 - 0.146236i) q^{15} +(-3.80469 - 1.23464i) q^{16} +3.56266i q^{17} +(1.27886 - 4.04531i) q^{18} -0.00157027 q^{19} +(-0.109506 + 0.135280i) q^{20} +(-1.03890 + 4.46326i) q^{21} +(0.915809 - 2.58693i) q^{22} +(-3.54164 - 2.04477i) q^{23} +(-3.31023 + 3.61142i) q^{24} +(-2.49621 - 4.32357i) q^{25} +(-5.31255 + 0.985138i) q^{26} +(-3.85704 - 3.48185i) q^{27} +(3.26272 - 4.16589i) q^{28} +(1.71473 + 2.96999i) q^{29} +(0.0950489 + 0.190798i) q^{30} +(-1.51690 + 2.62736i) q^{31} +(5.22524 - 2.16723i) q^{32} +(-2.41671 - 2.33579i) q^{33} +(-3.27251 - 3.83089i) q^{34} +(-0.118312 - 0.197518i) q^{35} +(2.34071 + 5.52459i) q^{36} -0.230504 q^{37} +(0.00168850 - 0.00144239i) q^{38} +(-1.60364 + 6.42019i) q^{39} +(-0.00651223 - 0.246052i) q^{40} +(5.09104 + 2.93931i) q^{41} +(-2.98265 - 5.75359i) q^{42} +(7.75595 - 4.47790i) q^{43} +(1.39149 + 3.62293i) q^{44} +(0.260918 - 0.00888846i) q^{45} +(5.68653 - 1.05449i) q^{46} +(-1.45112 - 2.51342i) q^{47} +(0.242154 - 6.92397i) q^{48} +(3.69310 + 5.94651i) q^{49} +(6.65561 + 2.35617i) q^{50} +(-5.93238 + 1.69834i) q^{51} +(4.80763 - 5.93920i) q^{52} +7.09519 q^{53} +(7.34572 + 0.201079i) q^{54} +0.168867 q^{55} +(0.318240 + 7.47654i) q^{56} +(-0.000748561 - 0.00261475i) q^{57} +(-4.57195 - 1.61853i) q^{58} +(5.77529 - 10.0031i) q^{59} +(-0.277464 - 0.117855i) q^{60} +(-5.32949 + 3.07698i) q^{61} +(-0.782268 - 4.21854i) q^{62} +(-7.92728 + 0.397742i) q^{63} +(-3.62792 + 7.13009i) q^{64} +(-0.166239 - 0.287935i) q^{65} +(4.74422 + 0.291756i) q^{66} +(9.82677 + 5.67349i) q^{67} +(7.03780 + 1.11333i) q^{68} +(1.71654 - 6.87215i) q^{69} +(0.308652 + 0.103713i) q^{70} -15.1314i q^{71} +(-7.59160 - 3.79046i) q^{72} -16.6300i q^{73} +(0.247859 - 0.211732i) q^{74} +(6.00946 - 6.21767i) q^{75} +(-0.000490709 + 0.00310197i) q^{76} +(-5.13336 + 0.0825454i) q^{77} +(-4.17294 - 8.37662i) q^{78} +(4.29129 - 2.47758i) q^{79} +(0.233016 + 0.258596i) q^{80} +(3.95914 - 8.08240i) q^{81} +(-8.17427 + 1.51580i) q^{82} +(6.31136 + 10.9316i) q^{83} +(8.49223 + 3.44704i) q^{84} +(0.155017 - 0.268497i) q^{85} +(-4.22668 + 11.9393i) q^{86} +(-4.12809 + 4.27111i) q^{87} +(-4.82413 - 2.61754i) q^{88} -9.06131i q^{89} +(-0.272398 + 0.249226i) q^{90} +(5.19425 + 8.67166i) q^{91} +(-5.14607 + 6.35730i) q^{92} +(-5.09808 - 1.27341i) q^{93} +(3.86910 + 1.36971i) q^{94} +(0.000118342 + 6.83250e-5i) q^{95} +(6.09969 + 7.66771i) q^{96} +(-10.6191 + 6.13095i) q^{97} +(-9.43338 - 3.00190i) q^{98} +(2.73739 - 5.13769i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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 $

$2$	−1.07529	+	0.918559i	−0.760345	+	0.649519i
$2$	−1.07529	+	0.918559i	−0.760345	+	0.649519i
$3$	0.476707	+	1.66516i	0.275227	+	0.961379i
$3$	0.476707	+	1.66516i	0.275227	+	0.961379i
$4$	0.312499	−	1.97544i	0.156250	−	0.987718i
$5$	−0.0753642	−	0.0435115i	−0.0337039	−	0.0194590i	0.483053	−	0.875591i	$-0.339528\pi$
$5$	−0.0753642	−	0.0435115i	−0.0337039	−	0.0194590i	−0.516757	+	0.856132i	$0.672861\pi$
$6$	−2.04214	−	1.35264i	−0.833702	−	0.552215i
$7$	2.31226	+	1.28587i	0.873953	+	0.486011i
$7$	2.31226	+	1.28587i	0.873953	+	0.486011i
$8$	1.47853	+	2.41122i	0.522738	+	0.852493i
$9$	−2.54550	+	1.58759i	−0.848500	+	0.529195i
$10$	0.121006	−	0.0224389i	0.0382656	−	0.00709581i
$11$	−1.68051	+	0.970240i	−0.506691	+	0.292538i	−0.731473	−	0.681871i	$-0.761167\pi$
$11$	−1.68051	+	0.970240i	−0.506691	+	0.292538i	0.224781	+	0.974409i	$0.427833\pi$
$12$	3.43838	−	0.421344i	0.992575	−	0.121631i
$13$	3.30872	+	1.91029i	0.917674	+	0.529820i	0.882892	−	0.469575i	$-0.155593\pi$
$13$	3.30872	+	1.91029i	0.917674	+	0.529820i	0.0347820	+	0.999395i	$0.488926\pi$
$14$	−3.66750	+	0.741269i	−0.980179	+	0.198113i
$15$	0.0365269	−	0.146236i	0.00943121	−	0.0377579i
$16$	−3.80469	−	1.23464i	−0.951172	−	0.308661i
$17$			3.56266i			0.864071i	0.901857	+	0.432035i	$0.142204\pi$
$17$			3.56266i			0.864071i	−0.901857	+	0.432035i	$0.857796\pi$
$18$	1.27886	−	4.04531i	0.301431	−	0.953488i
$19$	−0.00157027			−0.000360246			−0.000180123	−	1.00000i	$-0.500057\pi$
$19$	−0.00157027			−0.000360246			−0.000180123		1.00000i	$0.500057\pi$
$20$	−0.109506	+	0.135280i	−0.0244862	+	0.0302495i
$21$	−1.03890	+	4.46326i	−0.226706	+	0.973963i
$22$	0.915809	−	2.58693i	0.195251	−	0.551536i
$23$	−3.54164	−	2.04477i	−0.738484	−	0.426364i	0.0830341	−	0.996547i	$-0.473539\pi$
$23$	−3.54164	−	2.04477i	−0.738484	−	0.426364i	−0.821518	+	0.570183i	$0.806872\pi$
$24$	−3.31023	+	3.61142i	−0.675698	+	0.737179i
$25$	−2.49621	−	4.32357i	−0.499243	−	0.864714i
$26$	−5.31255	+	0.985138i	−1.04188	+	0.193201i
$27$	−3.85704	−	3.48185i	−0.742287	−	0.670082i
$28$	3.26272	−	4.16589i	0.616597	−	0.787279i
$29$	1.71473	+	2.96999i	0.318417	+	0.551514i	0.980158	−	0.198218i	$-0.0635155\pi$
$29$	1.71473	+	2.96999i	0.318417	+	0.551514i	−0.661741	+	0.749732i	$0.730182\pi$
$30$	0.0950489	+	0.190798i	0.0173535	+	0.0348348i
$31$	−1.51690	+	2.62736i	−0.272444	+	0.471887i	−0.969487	−	0.245142i	$-0.921165\pi$
$31$	−1.51690	+	2.62736i	−0.272444	+	0.471887i	0.697043	+	0.717029i	$0.254499\pi$
$32$	5.22524	−	2.16723i	0.923700	−	0.383116i
$33$	−2.41671	−	2.33579i	−0.420696	−	0.406608i
$34$	−3.27251	−	3.83089i	−0.561231	−	0.656992i
$35$	−0.118312	−	0.197518i	−0.0199983	−	0.0333867i
$36$	2.34071	+	5.52459i	0.390118	+	0.920765i
$37$	−0.230504			−0.0378947			−0.0189473	−	0.999820i	$-0.506031\pi$
$37$	−0.230504			−0.0378947			−0.0189473	+	0.999820i	$0.506031\pi$
$38$	0.00168850	−	0.00144239i	0.000273911	−	0.000233986i
$39$	−1.60364	+	6.42019i	−0.256789	+	1.02805i
$40$	−0.00651223	−	0.246052i	−0.00102967	−	0.0389043i
$41$	5.09104	+	2.93931i	0.795086	+	0.459043i	0.841750	−	0.539867i	$-0.181526\pi$
$41$	5.09104	+	2.93931i	0.795086	+	0.459043i	−0.0466638	+	0.998911i	$0.514859\pi$
$42$	−2.98265	−	5.75359i	−0.460233	−	0.887798i
$43$	7.75595	−	4.47790i	1.18277	−	0.682873i	0.226117	−	0.974100i	$-0.427397\pi$
$43$	7.75595	−	4.47790i	1.18277	−	0.682873i	0.956654	+	0.291227i	$0.0940636\pi$
$44$	1.39149	+	3.62293i	0.209775	+	0.546177i
$45$	0.260918	−	0.00888846i	0.0388953	−	0.00132501i
$46$	5.68653	−	1.05449i	0.838434	−	0.155476i
$47$	−1.45112	−	2.51342i	−0.211668	−	0.366620i	0.740569	−	0.671981i	$-0.234556\pi$
$47$	−1.45112	−	2.51342i	−0.211668	−	0.366620i	−0.952237	+	0.305361i	$0.901223\pi$
$48$	0.242154	−	6.92397i	0.0349520	−	0.999389i
$49$	3.69310	+	5.94651i	0.527586	+	0.849502i
$50$	6.65561	+	2.35617i	0.941245	+	0.333213i
$51$	−5.93238	+	1.69834i	−0.830700	+	0.237816i
$52$	4.80763	−	5.93920i	0.666698	−	0.823619i
$53$	7.09519			0.974599			0.487299	−	0.873235i	$-0.337982\pi$
$53$	7.09519			0.974599			0.487299	+	0.873235i	$0.337982\pi$
$54$	7.34572	+	0.201079i	0.999626	+	0.0273634i
$55$	0.168867			0.0227700
$56$	0.318240	+	7.47654i	0.0425266	+	0.999095i
$57$	−0.000748561	−	0.00261475i	−9.91493e−5	−	0.000346333i
$58$	−4.57195	−	1.61853i	−0.600326	−	0.212523i
$59$	5.77529	−	10.0031i	0.751879	−	1.30229i	−0.195032	−	0.980797i	$-0.562481\pi$
$59$	5.77529	−	10.0031i	0.751879	−	1.30229i	0.946911	−	0.321495i	$-0.104185\pi$
$60$	−0.277464	−	0.117855i	−0.0358205	−	0.0152150i
$61$	−5.32949	+	3.07698i	−0.682371	+	0.393967i	−0.800748	−	0.599002i	$-0.795564\pi$
$61$	−5.32949	+	3.07698i	−0.682371	+	0.393967i	0.118377	+	0.992969i	$0.462231\pi$
$62$	−0.782268	−	4.21854i	−0.0993481	−	0.535755i
$63$	−7.92728	+	0.397742i	−0.998744	+	0.0501108i
$64$	−3.62792	+	7.13009i	−0.453490	+	0.891261i
$65$	−0.166239	−	0.287935i	−0.0206195	−	0.0357140i
$66$	4.74422	+	0.291756i	0.583974	+	0.0359127i
$67$	9.82677	+	5.67349i	1.20053	+	0.693127i	0.960673	−	0.277681i	$-0.0895657\pi$
$67$	9.82677	+	5.67349i	1.20053	+	0.693127i	0.239858	+	0.970808i	$0.422899\pi$
$68$	7.03780	+	1.11333i	0.853458	+	0.135011i
$69$	1.71654	−	6.87215i	0.206647	−	0.827310i
$70$	0.308652	+	0.103713i	0.0368909	+	0.0123961i
$71$		−	15.1314i		−	1.79577i	−0.440231	−	0.897885i	$-0.645103\pi$
$71$		−	15.1314i		−	1.79577i	0.440231	−	0.897885i	$-0.354897\pi$
$72$	−7.59160	−	3.79046i	−0.894679	−	0.446710i
$73$		−	16.6300i		−	1.94639i	−0.229982	−	0.973195i	$-0.573867\pi$
$73$		−	16.6300i		−	1.94639i	0.229982	−	0.973195i	$-0.426133\pi$
$74$	0.247859	−	0.211732i	0.0288130	−	0.0246133i
$75$	6.00946	−	6.21767i	0.693913	−	0.717954i
$76$	−0.000490709		0.00310197i	−5.62882e−5		0.000355821i
$77$	−5.13336	+	0.0825454i	−0.585001	+	0.00940692i
$78$	−4.17294	−	8.37662i	−0.472493	−	0.948465i
$79$	4.29129	−	2.47758i	0.482808	−	0.278749i	−0.238778	−	0.971074i	$-0.576747\pi$
$79$	4.29129	−	2.47758i	0.482808	−	0.278749i	0.721586	+	0.692325i	$0.243413\pi$
$80$	0.233016	+	0.258596i	0.0260520	+	0.0289119i
$81$	3.95914	−	8.08240i	0.439905	−	0.898044i
$82$	−8.17427	+	1.51580i	−0.902698	+	0.167392i
$83$	6.31136	+	10.9316i	0.692762	+	1.19990i	0.970929	+	0.239366i	$0.0769396\pi$
$83$	6.31136	+	10.9316i	0.692762	+	1.19990i	−0.278168	+	0.960533i	$0.589727\pi$
$84$	8.49223	+	3.44704i	0.926578	+	0.376103i
$85$	0.155017	−	0.268497i	0.0168139	−	0.0291226i
$86$	−4.22668	+	11.9393i	−0.455775	+	1.28745i
$87$	−4.12809	+	4.27111i	−0.442577	+	0.457911i
$88$	−4.82413	−	2.61754i	−0.514254	−	0.279030i
$89$		−	9.06131i		−	0.960496i	−0.877133	−	0.480248i	$-0.840547\pi$
$89$		−	9.06131i		−	0.960496i	0.877133	−	0.480248i	$-0.159453\pi$
$90$	−0.272398	+	0.249226i	−0.0287133	+	0.0262707i
$91$	5.19425	+	8.67166i	0.544506	+	0.909037i
$92$	−5.14607	+	6.35730i	−0.536515	+	0.662794i
$93$	−5.09808	−	1.27341i	−0.528646	−	0.132046i
$94$	3.86910	+	1.36971i	0.399067	+	0.141275i
$95$	0.000118342	0	6.83250e-5i	1.21417e−5	0	7.01000e-6i
$96$	6.09969	+	7.66771i	0.622547	+	0.782583i
$97$	−10.6191	+	6.13095i	−1.07821	+	0.622504i	−0.930413	−	0.366514i	$-0.880551\pi$
$97$	−10.6191	+	6.13095i	−1.07821	+	0.622504i	−0.147796	+	0.989018i	$0.547218\pi$
$98$	−9.43338	−	3.00190i	−0.952915	−	0.303237i
$99$	2.73739	−	5.13769i	0.275118	−	0.516358i
$100$	−9.32099	+	3.58000i	−0.932099	+	0.358000i
$101$	−11.7157	+	6.76406i	−1.16576	+	0.673049i	−0.952676	−	0.303986i	$-0.901682\pi$
$101$	−11.7157	+	6.76406i	−1.16576	+	0.673049i	−0.213079	+	0.977035i	$0.568349\pi$
$102$	4.81901	−	7.27546i	0.477153	−	0.720378i
$103$	−9.46167	+	16.3881i	−0.932286	+	1.61477i	−0.152882	+	0.988245i	$0.548855\pi$
$103$	−9.46167	+	16.3881i	−0.932286	+	1.61477i	−0.779404	+	0.626522i	$0.784478\pi$
$104$	0.285907	+	10.8025i	0.0280355	+	1.05927i
$105$	0.272499	−	0.291166i	0.0265932	−	0.0284149i
$106$	−7.62939	+	6.51735i	−0.741032	+	0.633021i
$107$		−	5.97361i		−	0.577491i	−0.957406	−	0.288745i	$-0.906762\pi$
$107$		−	5.97361i		−	0.577491i	0.957406	−	0.288745i	$-0.0932381\pi$
$108$	−8.08348	+	6.53126i	−0.777834	+	0.628470i
$109$	12.7788			1.22399			0.611993	−	0.790863i	$-0.290368\pi$
$109$	12.7788			1.22399			0.611993	+	0.790863i	$0.290368\pi$
$110$	−0.181581	+	0.155114i	−0.0173130	+	0.0147895i
$111$	−0.109883	−	0.383826i	−0.0104296	−	0.0364311i
$112$	−7.20985	−	7.74714i	−0.681267	−	0.732035i
$113$	5.70148	−	9.87525i	0.536350	−	0.928986i	−0.462747	−	0.886491i	$-0.653136\pi$
$113$	5.70148	−	9.87525i	0.536350	−	0.928986i	0.999097	−	0.0424949i	$-0.0135306\pi$
$114$	0.00320673	+	0.00212402i	0.000300337	+	0.000198933i
$115$	0.177942	+	0.308205i	0.0165932	+	0.0287402i
$116$	6.40288	−	2.45921i	0.594493	−	0.228332i
$117$	−11.4551	+	0.390231i	−1.05902	+	0.0360769i
$118$	2.97832	+	16.0612i	0.274176	+	1.47855i
$119$	−4.58109	+	8.23779i	−0.419948	+	0.755157i
$120$	0.406612	−	0.128139i	0.0371184	−	0.0116974i
$121$	−3.61727	+	6.26529i	−0.328843	+	0.569572i
$122$	2.90436	−	8.20410i	0.262948	−	0.742764i
$123$	−2.46748	+	9.87857i	−0.222485	+	0.890721i
$124$	4.71614	+	3.81759i	0.423522	+	0.342830i
$125$			0.869572i			0.0777769i
$126$	8.15878	−	7.70936i	0.726842	−	0.686805i
$127$		−	7.53989i		−	0.669057i	−0.942386	−	0.334529i	$-0.891423\pi$
$127$		−	7.53989i		−	0.669057i	0.942386	−	0.334529i	$-0.108577\pi$
$128$	−2.64834	−	10.9994i	−0.234082	−	0.972217i
$129$	11.1537	+	10.7802i	0.982030	+	0.949146i
$130$	0.443241	+	0.156913i	0.0388748	+	0.0137622i
$131$	7.59210	−	13.1499i	0.663325	−	1.14891i	−0.316412	−	0.948622i	$-0.602478\pi$
$131$	7.59210	−	13.1499i	0.663325	−	1.14891i	0.979737	−	0.200290i	$-0.0641885\pi$
$132$	−5.36941	+	4.04413i	−0.467347	+	0.351996i
$133$	−0.00363088	−	0.00201916i	−0.000314837	−	0.000175083i
$134$	−15.7781	+	2.92582i	−1.36302	+	0.252752i
$135$	0.139182	+	0.430232i	0.0119789	+	0.0370285i
$136$	−8.59033	+	5.26748i	−0.736615	+	0.451683i
$137$	−8.24542	−	14.2815i	−0.704454	−	1.22015i	−0.966888	−	0.255200i	$-0.917859\pi$
$137$	−8.24542	−	14.2815i	−0.704454	−	1.22015i	0.262434	−	0.964950i	$-0.415475\pi$
$138$	4.46670	+	8.96630i	0.380231	+	0.763262i
$139$	4.86419	−	8.42502i	0.412575	−	0.714601i	−0.582595	−	0.812762i	$-0.697963\pi$
$139$	4.86419	−	8.42502i	0.412575	−	0.714601i	0.995171	+	0.0981613i	$0.0312961\pi$
$140$	−0.427157	+	0.171993i	−0.0361013	+	0.0145361i
$141$	3.49348	−	3.61451i	0.294204	−	0.304397i
$142$	13.8991	+	16.2707i	1.16639	+	1.36540i
$143$	−7.41377			−0.619970
$144$	11.6449	−	2.89748i	0.970412	−	0.241457i
$145$		−	0.298442i		−	0.0247842i
$146$	15.2756	+	17.8820i	1.26422	+	1.47993i
$147$	−8.14135	+	8.98434i	−0.671487	+	0.741016i
$148$	−0.0720324	+	0.455346i	−0.00592103	+	0.0374292i
$149$	−3.57700	+	6.19555i	−0.293039	+	0.507559i	−0.974527	−	0.224271i	$-0.928000\pi$
$149$	−3.57700	+	6.19555i	−0.293039	+	0.507559i	0.681488	+	0.731830i	$0.261333\pi$
$150$	−0.750624	+	12.2058i	−0.0612882	+	0.996603i
$151$	−13.0331	+	7.52468i	−1.06062	+	0.612350i	−0.925604	−	0.378493i	$-0.876442\pi$
$151$	−13.0331	+	7.52468i	−1.06062	+	0.612350i	−0.135017	+	0.990843i	$0.543109\pi$
$152$	−0.00232169	−	0.00378627i	−0.000188314	−	0.000307107i
$153$	−5.65602	−	9.06874i	−0.457262	−	0.733164i
$154$	5.44404	−	4.80406i	0.438693	−	0.387122i
$155$	0.228641	−	0.132006i	0.0183649	−	0.0106030i
$156$	12.1815	+	5.17420i	0.975304	+	0.414268i
$157$	−9.63504	−	5.56279i	−0.768960	−	0.443959i	0.0635435	−	0.997979i	$-0.479760\pi$
$157$	−9.63504	−	5.56279i	−0.768960	−	0.443959i	−0.832503	+	0.554020i	$0.813093\pi$
$158$	−2.33858	+	6.60592i	−0.186048	+	0.525539i
$159$	3.38233	+	11.8146i	0.268236	+	0.936959i
$160$	−0.488095	−	0.0640267i	−0.0385873	−	0.00506175i
$161$	−5.55991	−	9.28211i	−0.438182	−	0.731533i
$162$	3.16693	+	12.3276i	0.248817	+	0.968550i
$163$		−	5.32460i		−	0.417055i	−0.978017	−	0.208527i	$-0.933133\pi$
$163$		−	5.32460i		−	0.417055i	0.978017	−	0.208527i	$-0.0668670\pi$
$164$	7.39736	−	9.13848i	0.577637	−	0.713595i
$165$	0.0804999	+	0.281190i	0.00626691	+	0.0218906i
$166$	−16.8279	−	5.95729i	−1.30610	−	0.462375i
$167$	−4.56646	+	7.90935i	−0.353364	+	0.612044i	−0.986836	−	0.161721i	$-0.948295\pi$
$167$	−4.56646	+	7.90935i	−0.353364	+	0.612044i	0.633473	+	0.773765i	$0.281629\pi$
$168$	−12.2979	+	4.09404i	−0.948805	+	0.315862i
$169$	0.798427	+	1.38292i	0.0614175	+	0.106378i
$170$	0.0799421	+	0.431104i	0.00613128	+	0.0330642i
$171$	0.00399713	−	0.00249294i	0.000305668	−	0.000190640i
$172$	−6.42207	−	16.7207i	−0.489678	−	1.27494i
$173$	17.6303	−	10.1789i	1.34041	−	0.773885i	0.353541	−	0.935419i	$-0.384977\pi$
$173$	17.6303	−	10.1789i	1.34041	−	0.773885i	0.986867	+	0.161534i	$0.0516440\pi$
$174$	0.515627	−	8.38457i	0.0390896	−	0.635633i
$175$	−0.212371	−	13.2070i	−0.0160537	−	0.998356i
$176$	7.59170	−	1.61664i	0.572246	−	0.121859i
$177$	19.4099	+	4.84822i	1.45893	+	0.364415i
$178$	8.32334	+	9.74354i	0.623861	+	0.730309i
$179$			13.7290i			1.02616i	0.858342	+	0.513079i	$0.171495\pi$
$179$			13.7290i			1.02616i	−0.858342	+	0.513079i	$0.828505\pi$
$180$	0.0639781	−	0.518204i	0.00476864	−	0.0386247i
$181$			1.29204i			0.0960368i	0.998846	+	0.0480184i	$0.0152906\pi$
$181$			1.29204i			0.0960368i	−0.998846	+	0.0480184i	$0.984709\pi$
$182$	−13.5508	−	4.55333i	−1.00445	−	0.337515i
$183$	−7.66426	−	7.40762i	−0.566559	−	0.547587i
$184$	−0.306034	−	11.5629i	−0.0225611	−	0.852429i
$185$	0.0173718	+	0.0100296i	0.00127720	+	0.000737390i
$186$	6.65162	−	3.31361i	0.487720	−	0.242965i
$187$	−3.45663	−	5.98706i	−0.252774	−	0.437817i
$188$	−5.41857	+	2.08116i	−0.395190	+	0.151784i
$189$	−4.44130	−	13.0106i	−0.323057	−	0.946380i
$190$	−0.000190013	0	3.52352e-5i	−1.37850e−5	0	2.55623e-6i
$191$	5.19073	−	2.99687i	0.375588	−	0.216846i	−0.300309	−	0.953842i	$-0.597090\pi$
$191$	5.19073	−	2.99687i	0.375588	−	0.216846i	0.675897	+	0.736996i	$0.263756\pi$
$192$	−13.6022	−	2.64210i	−0.981653	−	0.190677i
$193$	−6.79084	+	11.7621i	−0.488816	+	0.846654i	−0.999917	−	0.0128667i	$-0.995904\pi$
$193$	−6.79084	+	11.7621i	−0.488816	+	0.846654i	0.511102	+	0.859520i	$0.329238\pi$
$194$	5.78700	−	16.3468i	0.415482	−	1.17364i
$195$	0.400210	−	0.414076i	0.0286596	−	0.0296526i
$196$	12.9010	−	5.43720i	0.921503	−	0.388372i
$197$	−12.0508			−0.858584			−0.429292	−	0.903166i	$-0.641237\pi$
$197$	−12.0508			−0.858584			−0.429292	+	0.903166i	$0.641237\pi$
$198$	1.77579	+	8.03896i	0.126200	+	0.571304i
$199$	8.41280			0.596368			0.298184	−	0.954508i	$-0.403619\pi$
$199$	8.41280			0.596368			0.298184	+	0.954508i	$0.403619\pi$
$200$	6.73434	−	12.4114i	0.476190	−	0.877620i
$201$	−4.76276	+	19.0677i	−0.335939	+	1.34493i
$202$	6.38459	−	18.0349i	0.449218	−	1.26893i
$203$	0.145884	+	9.07231i	0.0102391	+	0.636751i
$204$	1.50110	+	12.2498i	0.105098	+	0.857656i
$205$	−0.255788	−	0.443038i	−0.0178650	−	0.0309431i
$206$	−4.87938	−	26.3131i	−0.339963	−	1.83332i
$207$	12.2615	−	0.417702i	0.852233	−	0.0290323i
$208$	−10.2301	−	11.3532i	−0.709332	−	0.787200i
$209$	0.00263885	−	0.00152354i	0.000182533	−	0.000105386i
$210$	−0.0255624	+	0.563395i	−0.00176397	+	0.0388779i
$211$	−12.1289	−	7.00263i	−0.834988	−	0.482081i	0.0205694	−	0.999788i	$-0.493452\pi$
$211$	−12.1289	−	7.00263i	−0.834988	−	0.482081i	−0.855557	+	0.517708i	$0.826785\pi$
$212$	2.21724	−	14.0161i	0.152281	−	0.962628i
$213$	25.1962	−	7.21326i	1.72642	−	0.494244i
$214$	5.48711	+	6.42337i	0.375091	+	0.439092i
$215$	−0.779361			−0.0531520
$216$	2.69275	−	14.4482i	0.183218	−	0.983072i
$217$	−6.88590	+	4.12460i	−0.467446	+	0.279996i
$218$	−13.7409	+	11.7381i	−0.930652	+	0.795002i
$219$	27.6915	−	7.92762i	1.87122	−	0.535699i
$220$	0.0527707	−	0.333585i	0.00355780	−	0.0224903i
$221$	−6.80571	+	11.7878i	−0.457802	+	0.792936i
$222$	0.470723	+	0.311790i	0.0315928	+	0.0209260i
$223$	−2.41887	−	4.18961i	−0.161980	−	0.280557i	0.773599	−	0.633676i	$-0.218455\pi$
$223$	−2.41887	−	4.18961i	−0.161980	−	0.280557i	−0.935579	+	0.353118i	$0.885121\pi$
$224$	14.8689	+	1.70775i	0.993469	+	0.114104i
$225$	13.2181	+	7.04269i	0.881210	+	0.469513i
$226$	2.94025	+	15.8559i	0.195583	+	1.05472i
$227$	−3.48794	−	6.04129i	−0.231503	−	0.400975i	0.726748	−	0.686904i	$-0.241031\pi$
$227$	−3.48794	−	6.04129i	−0.231503	−	0.400975i	−0.958251	+	0.285930i	$0.907698\pi$
$228$	−0.00539920		0.000661625i	−0.000357571		4.38172e-5i
$229$	22.3529	+	12.9055i	1.47712	+	0.852818i	0.999666	−	0.0258374i	$-0.00822520\pi$
$229$	22.3529	+	12.9055i	1.47712	+	0.852818i	0.477457	+	0.878655i	$0.341559\pi$
$230$	−0.474444	−	0.167959i	−0.0312839	−	0.0110749i
$231$	−2.58456	−	8.50851i	−0.170052	−	0.559819i
$232$	−4.62603	+	8.52579i	−0.303714	+	0.559746i
$233$	2.59217			0.169819			0.0849094	−	0.996389i	$-0.472940\pi$
$233$	2.59217			0.169819			0.0849094	+	0.996389i	$0.472940\pi$
$234$	11.9591	−	10.9418i	0.781792	−	0.715288i
$235$			0.252562i			0.0164753i
$236$	−17.9557	−	14.5347i	−1.16882	−	0.946127i
$237$	6.17125	+	5.96460i	0.400866	+	0.387442i
$238$	−2.64089	−	13.0660i	−0.171183	−	0.846944i
$239$	4.42624	+	2.55549i	0.286310	+	0.165301i	0.636276	−	0.771461i	$-0.280474\pi$
$239$	4.42624	+	2.55549i	0.286310	+	0.165301i	−0.349967	+	0.936762i	$0.613807\pi$
$240$	−0.319522	+	0.511283i	−0.0206251	+	0.0330032i
$241$	−6.37110	+	3.67836i	−0.410399	+	0.236944i	−0.690961	−	0.722892i	$-0.742812\pi$
$241$	−6.37110	+	3.67836i	−0.410399	+	0.236944i	0.280562	+	0.959836i	$0.409479\pi$
$242$	−1.86543	−	10.0597i	−0.119914	−	0.646661i
$243$	15.3458	+	2.73966i	0.984435	+	0.175749i
$244$	4.41292	+	11.4896i	0.282508	+	0.735547i
$245$	−0.0195858	−	0.608847i	−0.00125129	−	0.0388978i
$246$	−6.42079	−	12.8889i	−0.409374	−	0.821764i
$247$	−0.00519560	−	0.00299968i	−0.000330588	−	0.000190865i
$248$	−8.57790	+	0.227030i	−0.544697	+	0.0144164i
$249$	−15.1942	+	15.7206i	−0.962891	+	0.996251i
$250$	−0.798753	−	0.935042i	−0.0505176	−	0.0591373i
$251$	−6.83111			−0.431176			−0.215588	−	0.976484i	$-0.569167\pi$
$251$	−6.83111			−0.431176			−0.215588	+	0.976484i	$0.569167\pi$
$252$	−1.69156	+	15.7841i	−0.106558	+	0.994306i
$253$	7.93567			0.498911
$254$	6.92584	+	8.10758i	0.434566	+	0.508715i
$255$	0.520987	+	0.130133i	0.0326255	+	0.00814924i
$256$	12.9513	+	9.39487i	0.809457	+	0.587179i
$257$	16.9529	+	9.78775i	1.05749	+	0.610543i	0.924737	−	0.380606i	$-0.124285\pi$
$257$	16.9529	+	9.78775i	1.05749	+	0.610543i	0.132754	+	0.991149i	$0.457618\pi$
$258$	−21.8958	−	1.34653i	−1.36317	−	0.0838311i
$259$	−0.532986	−	0.296397i	−0.0331181	−	0.0184172i
$260$	−0.620747	+	0.238416i	−0.0384971	+	0.0147859i
$261$	−9.07996	−	4.83785i	−0.562035	−	0.299455i
$262$	3.91525	+	21.1138i	0.241885	+	1.30441i
$263$	1.91788	−	1.10729i	0.118262	−	0.0682784i	−0.439702	−	0.898144i	$-0.644916\pi$
$263$	1.91788	−	1.10729i	0.118262	−	0.0682784i	0.557964	+	0.829865i	$0.311583\pi$
$264$	2.05891	−	9.28073i	0.126717	−	0.571190i
$265$	−0.534723	−	0.308723i	−0.0328478	−	0.0189647i
$266$	0.00575897	−	0.00116400i	0.000353105	−	7.13692e-5i
$267$	15.0885	−	4.31959i	0.923401	−	0.264355i
$268$	14.2785	−	17.6392i	0.872197	−	1.07749i
$269$			22.7144i			1.38492i	0.721455	+	0.692461i	$0.243473\pi$
$269$			22.7144i			1.38492i	−0.721455	+	0.692461i	$0.756527\pi$
$270$	−0.544855	−	0.334778i	−0.0331588	−	0.0203739i
$271$	−29.2323			−1.77574			−0.887868	−	0.460098i	$-0.847814\pi$
$271$	−29.2323			−1.77574			−0.887868	+	0.460098i	$0.847814\pi$
$272$	4.39861	−	13.5548i	0.266705	−	0.821880i
$273$	−11.9635	+	12.7831i	−0.724067	+	0.773668i
$274$	21.9846	+	7.78284i	1.32814	+	0.470179i
$275$	8.38980	+	4.84385i	0.505924	+	0.292095i
$276$	−13.0391	−	5.53845i	−0.784860	−	0.333375i
$277$	−4.13808	−	7.16737i	−0.248633	−	0.430645i	0.714514	−	0.699622i	$-0.246648\pi$
$277$	−4.13808	−	7.16737i	−0.248633	−	0.430645i	−0.963147	+	0.268976i	$0.913315\pi$
$278$	2.50846	+	13.5274i	0.150448	+	0.811319i
$279$	−0.309871	−	9.09615i	−0.0185515	−	0.544572i
$280$	0.301332	−	0.577311i	0.0180080	−	0.0345009i
$281$	7.55145	+	13.0795i	0.450482	+	0.780257i	0.998416	−	0.0562642i	$-0.0179189\pi$
$281$	7.55145	+	13.0795i	0.450482	+	0.780257i	−0.547934	+	0.836521i	$0.684586\pi$
$282$	−0.436360	+	7.09561i	−0.0259848	+	0.422538i
$283$	3.68016	−	6.37423i	0.218763	−	0.378909i	−0.735667	−	0.677343i	$-0.763131\pi$
$283$	3.68016	−	6.37423i	0.218763	−	0.378909i	0.954430	+	0.298435i	$0.0964645\pi$
$284$	−29.8911	−	4.72856i	−1.77371	−	0.280588i
$285$	−5.73573e−5	0	0.000229630i	−3.39755e−6	0	1.36021e-5i
$286$	7.97195	−	6.80998i	0.471391	−	0.402683i
$287$	7.99225	+	13.3428i	0.471767	+	0.787603i
$288$	−9.86018	+	13.8122i	−0.581017	+	0.813891i
$289$	4.30748			0.253381
$290$	0.274136	+	0.320912i	0.0160978	+	0.0188446i
$291$	−15.2712	−	14.7598i	−0.895215	−	0.865237i
$292$	−32.8514	−	5.19685i	−1.92248	−	0.304123i
$293$	−15.3641	−	8.87049i	−0.897583	−	0.518220i	−0.0211675	−	0.999776i	$-0.506738\pi$
$293$	−15.3641	−	8.87049i	−0.897583	−	0.518220i	−0.876415	+	0.481556i	$0.840072\pi$
$294$	0.501670	−	17.1391i	0.0292580	−	0.999572i
$295$	−0.870500	+	0.502584i	−0.0506825	+	0.0292616i
$296$	−0.340806	−	0.555795i	−0.0198090	−	0.0323049i
$297$	9.86000	+	2.10901i	0.572135	+	0.122377i
$298$	−1.84466	−	9.94770i	−0.106858	−	0.576255i
$299$	−7.81221	−	13.5311i	−0.451792	−	0.782526i
$300$	−10.4046	−	13.8143i	−0.600712	−	0.797570i
$301$	23.6917	−	0.380967i	1.36557	−	0.0219586i
$302$	7.10254	−	20.0629i	0.408705	−	1.15449i
$303$	−16.8482	−	16.2840i	−0.967903	−	0.935491i
$304$	0.00597440	+	0.00193873i	0.000342655	+	0.000111194i
$305$	0.535537			0.0306648
$306$	14.4120	+	4.55614i	0.823881	+	0.260457i
$307$	11.5790			0.660849			0.330425	−	0.943832i	$-0.392808\pi$
$307$	11.5790			0.660849			0.330425	+	0.943832i	$0.392808\pi$
$308$	−1.44111	+	10.1664i	−0.0821148	+	0.579286i
$309$	−31.7992	−	7.94285i	−1.80899	−	0.451853i
$310$	−0.124600	+	0.351964i	−0.00707681	+	0.0199902i
$311$	−13.4363	+	23.2724i	−0.761905	+	1.31966i	0.179963	+	0.983673i	$0.442402\pi$
$311$	−13.4363	+	23.2724i	−0.761905	+	1.31966i	−0.941868	+	0.335984i	$0.890931\pi$
$312$	−17.8515	+	5.62569i	−1.01064	+	0.318492i
$313$	3.50952	−	2.02622i	0.198370	−	0.114529i	−0.397525	−	0.917591i	$-0.630131\pi$
$313$	3.50952	−	2.02622i	0.198370	−	0.114529i	0.595895	+	0.803062i	$0.296798\pi$
$314$	15.4702	−	2.86873i	0.873035	−	0.161892i
$315$	0.614740	+	0.314953i	0.0346367	+	0.0177456i
$316$	−3.55327	−	9.25141i	−0.199887	−	0.520432i
$317$	0.536393	+	0.929060i	0.0301268	+	0.0521812i	0.880696	−	0.473682i	$-0.157076\pi$
$317$	0.536393	+	0.929060i	0.0301268	+	0.0521812i	−0.850569	+	0.525864i	$0.823742\pi$
$318$	−14.4894	−	9.59727i	−0.812525	−	0.538188i
$319$	−5.76322	−	3.32739i	−0.322678	−	0.186298i
$320$	0.583657	−	0.379497i	0.0326274	−	0.0212145i
$321$	9.94700	−	2.84766i	0.555188	−	0.158941i
$322$	14.5047	+	4.87387i	0.808314	+	0.271610i
$323$		−	0.00559434i		−	0.000311278i
$324$	−14.7290	−	10.3468i	−0.818279	−	0.574821i
$325$		−	19.0740i		−	1.05803i
$326$	4.89096	+	5.72549i	0.270885	+	0.317106i
$327$	6.09174	+	21.2787i	0.336874	+	1.17671i
$328$	0.439917	+	16.6214i	0.0242903	+	0.917765i
$329$	−0.123458	−	7.67762i	−0.00680644	−	0.423281i
$330$	−0.344850	−	0.228416i	−0.0189834	−	0.0125739i
$331$	−15.1087	+	8.72301i	−0.830449	+	0.479460i	−0.854007	−	0.520262i	$-0.825834\pi$
$331$	−15.1087	+	8.72301i	−0.830449	+	0.479460i	0.0235571	+	0.999722i	$0.492501\pi$
$332$	23.5670	−	9.05157i	1.29340	−	0.496769i
$333$	0.586748	−	0.365945i	0.0321536	−	0.0200537i
$334$	−2.35493	−	12.6994i	−0.128856	−	0.694881i
$335$	−0.493725	−	0.855156i	−0.0269751	−	0.0467222i
$336$	9.46322	−	15.6986i	0.516261	−	0.856431i
$337$	−4.93338	+	8.54486i	−0.268738	+	0.465468i	−0.968536	−	0.248873i	$-0.919940\pi$
$337$	−4.93338	+	8.54486i	−0.268738	+	0.465468i	0.699798	+	0.714341i	$0.253273\pi$
$338$	−2.12883	−	0.753634i	−0.115793	−	0.0409923i
$339$	19.1618	+	4.78626i	1.04073	+	0.259954i
$340$	−0.481955	−	0.390130i	−0.0261377	−	0.0211578i
$341$		−	5.88705i		−	0.318801i
$342$	−0.00200816	+	0.00635224i	−0.000108589	+	0.000343490i
$343$	0.893004	+	18.4987i	0.0482177	+	0.998837i
$344$	22.2645	+	12.0806i	1.20042	+	0.651341i
$345$	−0.428383	+	0.443225i	−0.0230634	+	0.0238624i
$346$	−9.60782	+	27.1397i	−0.516520	+	1.45904i
$347$	2.01004	+	1.16050i	0.107905	+	0.0622988i	0.552981	−	0.833194i	$-0.313490\pi$
$347$	2.01004	+	1.16050i	0.107905	+	0.0622988i	−0.445076	+	0.895493i	$0.646823\pi$
$348$	7.14728	+	9.48949i	0.383134	+	0.508690i
$349$	4.37081	−	2.52349i	0.233964	−	0.135079i	−0.378435	−	0.925628i	$-0.623538\pi$
$349$	4.37081	−	2.52349i	0.233964	−	0.135079i	0.612400	+	0.790548i	$0.290204\pi$
$350$	12.3598	+	14.0063i	0.660658	+	0.748668i
$351$	−6.11053	−	18.8885i	−0.326156	−	1.00820i
$352$	−6.67831	+	8.71178i	−0.355955	+	0.464339i
$353$	−17.5065	+	10.1074i	−0.931777	+	0.537962i	−0.887373	−	0.461052i	$-0.847472\pi$
$353$	−17.5065	+	10.1074i	−0.931777	+	0.537962i	−0.0444039	+	0.999014i	$0.514139\pi$
$354$	−25.3246	+	12.6158i	−1.34599	+	0.670525i
$355$	−0.658392	+	1.14037i	−0.0349438	+	0.0605244i
$356$	−17.9000	−	2.83165i	−0.948699	−	0.150077i
$357$	−15.9011	−	3.70123i	−0.841573	−	0.195890i
$358$	−12.6109	−	14.7627i	−0.666509	−	0.780234i
$359$			22.2990i			1.17690i	0.808535	+	0.588448i	$0.200261\pi$
$359$			22.2990i			1.17690i	−0.808535	+	0.588448i	$0.799739\pi$
$360$	0.407206	+	0.615988i	0.0214616	+	0.0324654i
$361$	−19.0000			−1.00000
$362$	−1.18682	−	1.38932i	−0.0623778	−	0.0730212i
$363$	−12.1571	−	3.03661i	−0.638081	−	0.159381i
$364$	18.7535	−	7.55102i	0.982951	−	0.395781i
$365$	−0.723595	+	1.25330i	−0.0378747	+	0.0656009i
$366$	15.0456	+	0.925264i	0.786448	+	0.0483643i
$367$	2.04752	+	3.54641i	0.106880	+	0.185121i	0.914505	−	0.404576i	$-0.132581\pi$
$367$	2.04752	+	3.54641i	0.106880	+	0.185121i	−0.807625	+	0.589696i	$0.799247\pi$
$368$	10.9503	+	12.1524i	0.570823	+	0.633486i
$369$	−17.6256	+	0.600437i	−0.917554	+	0.0312575i
$370$	−0.0278925	+	0.00517226i	−0.00145006	+	0.000268893i
$371$	16.4059	+	9.12345i	0.851753	+	0.473666i
$372$	−4.10868	+	9.67299i	−0.213025	+	0.501521i
$373$	12.0913	−	20.9428i	0.626064	−	1.08438i	−0.362270	−	0.932073i	$-0.617998\pi$
$373$	12.0913	−	20.9428i	0.626064	−	1.08438i	0.988334	−	0.152302i	$-0.0486686\pi$
$374$	9.21635	+	3.26271i	0.476566	+	0.168711i
$375$	−1.44797	+	0.414531i	−0.0747731	+	0.0214063i
$376$	3.91487	−	7.21512i	0.201894	−	0.372091i
$377$			13.1025i			0.674814i
$378$	16.7267	+	9.91055i	0.860326	+	0.509744i
$379$			4.84485i			0.248863i	0.992228	+	0.124432i	$0.0397107\pi$
$379$			4.84485i			0.248863i	−0.992228	+	0.124432i	$0.960289\pi$
$380$	0.000171954	0	0.000212426i	8.82103e−6	0	1.08972e-5i
$381$	12.5551	−	3.59432i	0.643218	−	0.184143i
$382$	−2.82874	+	7.99050i	−0.144731	+	0.408830i
$383$	−0.601970	+	1.04264i	−0.0307592	+	0.0532765i	−0.880995	−	0.473125i	$-0.843126\pi$
$383$	−0.601970	+	1.04264i	−0.0307592	+	0.0532765i	0.850236	+	0.526402i	$0.176459\pi$
$384$	17.0532	−	9.65338i	0.870243	−	0.492622i
$385$	0.390464	+	0.217140i	0.0198999	+	0.0110665i
$386$	−3.50204	−	18.8855i	−0.178249	−	0.961244i
$387$	−12.6337	+	23.7117i	−0.642208	+	1.20533i
$388$	8.79283	+	22.8933i	0.446389	+	1.16223i
$389$	10.3048	+	17.8485i	0.522475	+	0.904954i	0.999658	+	0.0261497i	$0.00832467\pi$
$389$	10.3048	+	17.8485i	0.522475	+	0.904954i	−0.477183	+	0.878804i	$0.658342\pi$
$390$	−0.0499890	+	0.812868i	−0.00253129	+	0.0411612i
$391$	7.28481	−	12.6177i	0.368408	−	0.638102i
$392$	−8.87797	+	17.6969i	−0.448405	+	0.893830i
$393$	25.5159	+	6.37339i	1.28711	+	0.321495i
$394$	12.9581	−	11.0694i	0.652820	−	0.557667i
$395$	−0.431213			−0.0216967
$396$	−9.29375	−	7.01306i	−0.467028	−	0.352419i
$397$			6.96805i			0.349717i	0.984594	+	0.174858i	$0.0559467\pi$
$397$			6.96805i			0.349717i	−0.984594	+	0.174858i	$0.944053\pi$
$398$	−9.04621	+	7.72765i	−0.453445	+	0.387352i
$399$	0.00163135	−	0.00700854i	8.16698e−5	−	0.000350866i
$400$	4.15925	+	19.5318i	0.207962	+	0.976588i
$401$	11.9068	−	20.6233i	0.594600	−	1.02988i	−0.399004	−	0.916949i	$-0.630644\pi$
$401$	11.9068	−	20.6233i	0.594600	−	1.02988i	0.993603	−	0.112927i	$-0.0360227\pi$
$402$	−12.3935	−	24.8782i	−0.618130	−	1.24081i
$403$	−10.0380	+	5.79546i	−0.500030	+	0.288692i
$404$	9.70081	+	25.2574i	0.482634	+	1.25660i
$405$	−0.650056	+	0.436855i	−0.0323015	+	0.0217075i
$406$	−8.49032	−	9.62137i	−0.421368	−	0.477500i
$407$	0.387363	−	0.223644i	0.0192009	−	0.0110856i
$408$	−12.8663	−	11.7932i	−0.636975	−	0.583851i
$409$	−19.4544	−	11.2320i	−0.961960	−	0.555388i	−0.0651845	−	0.997873i	$-0.520764\pi$
$409$	−19.4544	−	11.2320i	−0.961960	−	0.555388i	−0.896776	+	0.442485i	$0.854097\pi$
$410$	0.682003	+	0.241438i	0.0336817	+	0.0119238i
$411$	19.8503	−	20.5380i	0.979142	−	1.01307i
$412$	29.4168	+	23.8122i	1.44926	+	1.17314i
$413$	26.2166	−	15.7035i	1.29004	−	0.772720i
$414$	−12.8010	+	11.7121i	−0.629134	+	0.575616i
$415$		−	1.09847i		−	0.0539217i
$416$	21.4289	+	2.81097i	1.05064	+	0.137819i
$417$	16.3478	+	4.08337i	0.800554	+	0.199964i
$418$	−0.00143807	+	0.00406219i	−7.03383e−5	+	0.000198688i
$419$	−6.66611	+	11.5460i	−0.325661	+	0.564061i	−0.981646	−	0.190713i	$-0.938920\pi$
$419$	−6.66611	+	11.5460i	−0.325661	+	0.564061i	0.655985	+	0.754774i	$0.272253\pi$
$420$	−0.490024	−	0.629293i	−0.0239107	−	0.0307064i
$421$	−11.6922	−	20.2516i	−0.569845	−	0.987001i	−0.996581	−	0.0826243i	$-0.973670\pi$
$421$	−11.6922	−	20.2516i	−0.569845	−	0.987001i	0.426736	−	0.904376i	$-0.359663\pi$
$422$	19.4744	−	3.61126i	0.948000	−	0.175793i
$423$	7.68410	+	4.09412i	0.373614	+	0.199063i
$424$	10.4904	+	17.1080i	0.509460	+	0.830839i
$425$	15.4034	−	8.89315i	0.747174	−	0.431381i
$426$	−20.4674	+	30.9005i	−0.991650	+	1.49714i
$427$	−16.2797	+	0.261781i	−0.787832	+	0.0126685i
$428$	−11.8005	−	1.86675i	−0.570398	−	0.0902327i
$429$	−3.53420	−	12.3451i	−0.170633	−	0.596027i
$430$	0.838039	−	0.715889i	0.0404138	−	0.0345232i
$431$			6.30522i			0.303712i	0.988403	+	0.151856i	$0.0485250\pi$
$431$			6.30522i			0.303712i	−0.988403	+	0.151856i	$0.951475\pi$
$432$	10.3760	+	18.0094i	0.499215	+	0.866478i
$433$		−	26.7657i		−	1.28628i	−0.765749	−	0.643139i	$-0.777632\pi$
$433$		−	26.7657i		−	1.28628i	0.765749	−	0.643139i	$-0.222368\pi$
$434$	3.61566	−	10.7602i	0.173557	−	0.516508i
$435$	0.496953	−	0.142269i	0.0238271	−	0.00682129i
$436$	3.99336	−	25.2437i	0.191247	−	1.20895i
$437$	0.00556135	+	0.00321085i	0.000266035	+	0.000153596i
$438$	−22.4944	+	33.9608i	−1.07483	+	1.62271i
$439$	4.07359	+	7.05566i	0.194422	+	0.336749i	0.946711	−	0.322085i	$-0.104384\pi$
$439$	4.07359	+	7.05566i	0.194422	+	0.336749i	−0.752289	+	0.658833i	$0.771050\pi$
$440$	0.249674	+	0.407174i	0.0119027	+	0.0194112i
$441$	−18.8414	−	9.27373i	−0.897209	−	0.441606i
$442$	−3.50971	−	18.9268i	−0.166940	−	0.900256i
$443$	−3.25881	+	1.88148i	−0.154831	+	0.0893916i	−0.575414	−	0.817863i	$-0.695159\pi$
$443$	−3.25881	+	1.88148i	−0.154831	+	0.0893916i	0.420583	+	0.907254i	$0.361826\pi$
$444$	−0.792561	+	0.0971215i	−0.0376133	+	0.00460918i
$445$	−0.394271	+	0.682898i	−0.0186903	+	0.0323725i
$446$	6.44940	+	2.28317i	0.305388	+	0.108111i
$447$	−12.0217	−	3.00281i	−0.568609	−	0.142028i
$448$	−17.5570	+	11.8216i	−0.829492	+	0.558519i
$449$	−9.04263			−0.426748			−0.213374	−	0.976971i	$-0.568445\pi$
$449$	−9.04263			−0.426748			−0.213374	+	0.976971i	$0.568445\pi$
$450$	−20.6825	+	4.56870i	−0.974981	+	0.215371i
$451$	−11.4074			−0.537151
$452$	−17.7262	−	14.3489i	−0.833771	−	0.674916i
$453$	−18.7428	−	18.1152i	−0.880612	−	0.851124i
$454$	9.29983	+	3.29226i	0.436463	+	0.154514i
$455$	−0.0141432	−	0.879543i	−0.000663044	−	0.0412336i
$456$	0.00519797	−	0.00567092i	0.000243417	−	0.000265565i
$457$	−3.96610	−	6.86948i	−0.185526	−	0.321341i	0.758227	−	0.651990i	$-0.226066\pi$
$457$	−3.96610	−	6.86948i	−0.185526	−	0.321341i	−0.943754	+	0.330649i	$0.892732\pi$
$458$	−35.8903	+	6.65535i	−1.67705	+	0.310984i
$459$	12.4046	−	13.7413i	0.578998	−	0.641389i
$460$	0.664445	−	0.255199i	0.0309799	−	0.0118987i
$461$	−28.3973	+	16.3952i	−1.32259	+	0.763600i	−0.984142	−	0.177383i	$-0.943237\pi$
$461$	−28.3973	+	16.3952i	−1.32259	+	0.763600i	−0.338452	+	0.940984i	$0.609903\pi$
$462$	10.5947	+	6.77505i	0.492911	+	0.315204i
$463$	1.28928	+	0.744365i	0.0599179	+	0.0345936i	0.529660	−	0.848210i	$-0.322320\pi$
$463$	1.28928	+	0.744365i	0.0599179	+	0.0345936i	−0.469742	+	0.882804i	$0.655653\pi$
$464$	−2.85712	−	13.4170i	−0.132638	−	0.622868i
$465$	0.328805	+	0.317795i	0.0152480	+	0.0147374i
$466$	−2.78734	+	2.38106i	−0.129121	+	0.110301i
$467$	2.31036			0.106911			0.0534554	−	0.998570i	$-0.482977\pi$
$467$	2.31036			0.106911			0.0534554	+	0.998570i	$0.482977\pi$
$468$	−2.80884	+	22.7508i	−0.129838	+	1.05165i
$469$	15.4267	+	25.7545i	0.712340	+	1.18923i
$470$	−0.231993	−	0.271578i	−0.0107011	−	0.0125269i
$471$	4.66983	−	18.6957i	0.215175	−	0.861452i
$472$	32.6585	−	0.864368i	1.50323	−	0.0397858i
$473$	−8.68927	+	15.0503i	−0.399533	+	0.692012i
$474$	−12.1147	−	0.745020i	−0.556447	−	0.0342199i
$475$	0.00391974	+	0.00678919i	0.000179850	+	0.000311509i
$476$	14.8416	+	11.6240i	0.680265	+	0.532783i
$477$	−18.0608	+	11.2642i	−0.826947	+	0.515753i
$478$	−7.10686	+	1.31787i	−0.325060	+	0.0602778i
$479$	−12.7223	−	22.0356i	−0.581295	−	1.00683i	−0.995326	−	0.0965702i	$-0.969213\pi$
$479$	−12.7223	−	22.0356i	−0.581295	−	1.00683i	0.414031	−	0.910263i	$-0.364121\pi$
$480$	−0.126064	−	0.843278i	−0.00575401	−	0.0384902i
$481$	−0.762674	−	0.440330i	−0.0347750	−	0.0200773i
$482$	3.47200	−	9.80754i	0.158145	−	0.446721i
$483$	12.8057	−	13.6830i	0.582681	−	0.622597i
$484$	11.2463	+	9.10358i	0.511195	+	0.413799i
$485$	1.06707			0.0484531
$486$	−19.0178	+	11.1501i	−0.862663	+	0.505779i
$487$		−	25.9203i		−	1.17456i	−0.809384	−	0.587280i	$-0.800199\pi$
$487$		−	25.9203i		−	1.17456i	0.809384	−	0.587280i	$-0.199801\pi$
$488$	−15.2991	−	8.30115i	−0.692556	−	0.375775i
$489$	8.86629	−	2.53827i	0.400948	−	0.114785i
$490$	0.580322	+	0.636696i	0.0262163	+	0.0287630i
$491$	13.2651	+	7.65861i	0.598645	+	0.345628i	0.768508	−	0.639840i	$-0.220999\pi$
$491$	13.2651	+	7.65861i	0.598645	+	0.345628i	−0.169863	+	0.985468i	$0.554333\pi$
$492$	18.7434	+	7.96140i	0.845017	+	0.358928i
$493$	−10.5811	+	6.10898i	−0.476547	+	0.275135i
$494$	0.00834216	−	0.00154694i	0.000375332	−	6.95999e-5i
$495$	−0.429850	+	0.268090i	−0.0193203	+	0.0120498i
$496$	9.01520	−	8.12343i	0.404794	−	0.364753i
$497$	19.4570	−	34.9878i	0.872764	−	1.56942i
$498$	1.89786	−	30.8609i	0.0850450	−	1.38291i
$499$	6.53183	+	3.77115i	0.292405	+	0.168820i	0.639026	−	0.769185i	$-0.279338\pi$
$499$	6.53183	+	3.77115i	0.292405	+	0.168820i	−0.346621	+	0.938005i	$0.612671\pi$
$500$	1.71778	+	0.271741i	0.0768216	+	0.0121526i
$501$	−15.3472	−	3.83344i	−0.685661	−	0.171265i
$502$	7.34543	−	6.27477i	0.327842	−	0.280057i
$503$	13.5508			0.604198			0.302099	−	0.953277i	$-0.402313\pi$
$503$	13.5508			0.604198			0.302099	+	0.953277i	$0.402313\pi$
$504$	−12.6797	−	18.5263i	−0.564800	−	0.825228i
$505$	1.17726			0.0523873
$506$	−8.53315	+	7.28938i	−0.379345	+	0.324052i
$507$	−1.92216	+	1.98875i	−0.0853660	+	0.0883236i
$508$	−14.8946	−	2.35621i	−0.660840	−	0.104540i
$509$	−31.0586	−	17.9317i	−1.37665	−	0.794807i	−0.384892	−	0.922962i	$-0.625761\pi$
$509$	−31.0586	−	17.9317i	−1.37665	−	0.794807i	−0.991754	+	0.128155i	$0.959095\pi$
$510$	−0.679747	+	0.338627i	−0.0300997	+	0.0149946i
$511$	21.3839	−	38.4528i	0.945967	−	1.70105i
$512$	−22.5562	+	1.79432i	−0.996851	+	0.0792986i
$513$	0.00605661	+	0.00546745i	0.000267406	+	0.000241394i
$514$	−27.2199	+	5.04754i	−1.20062	+	0.222638i
$515$	1.42614	−	0.823384i	0.0628433	−	0.0362826i
$516$	24.7812	−	18.6646i	1.09093	−	0.821665i
$517$	4.87724	+	2.81587i	0.214501	+	0.123842i
$518$	0.845373	−	0.170866i	0.0371436	−	0.00750741i
$519$	25.3539	+	24.5049i	1.11291	+	1.07565i
$520$	0.448485	−	0.826559i	0.0196673	−	0.0362470i
$521$			24.2360i			1.06180i	0.847436	+	0.530898i	$0.178145\pi$
$521$			24.2360i			1.06180i	−0.847436	+	0.530898i	$0.821855\pi$
$522$	14.2074	−	3.13839i	0.621843	−	0.137363i
$523$	7.57054			0.331037			0.165518	−	0.986207i	$-0.447070\pi$
$523$	7.57054			0.331037			0.165518	+	0.986207i	$0.447070\pi$
$524$	−23.6043	−	19.1070i	−1.03116	−	0.834695i
$525$	21.8905	−	6.64951i	0.955381	−	0.290208i
$526$	−1.04517	+	2.95234i	−0.0455715	+	0.128728i
$527$	−9.36036	−	5.40421i	−0.407744	−	0.235411i
$528$	6.31097	+	11.8707i	0.274650	+	0.516607i
$529$	−3.13784	−	5.43491i	−0.136428	−	0.236300i
$530$	0.858563	−	0.159208i	0.0372936	−	0.00691556i
$531$	1.17977	+	34.6317i	0.0511975	+	1.50289i
$532$	−0.00512337	+	0.00654159i	−0.000222126	+	0.000283614i
$533$	11.2299	+	19.4507i	0.486420	+	0.842505i
$534$	−12.2567	+	18.5045i	−0.530400	+	0.800768i
$535$	−0.259921	+	0.450196i	−0.0112374	+	0.0194637i
$536$	0.849132	+	32.0829i	0.0366769	+	1.38577i
$537$	−22.8610	+	6.54474i	−0.986526	+	0.282426i
$538$	−20.8645	−	24.4246i	−0.899533	−	1.05302i
$539$	−11.9758	−	6.40995i	−0.515835	−	0.276096i
$540$	0.893390	−	0.140498i	0.0384454	−	0.00604607i
$541$	7.30387			0.314018			0.157009	−	0.987597i	$-0.449815\pi$
$541$	7.30387			0.314018			0.157009	+	0.987597i	$0.449815\pi$
$542$	31.4332	−	26.8516i	1.35017	−	1.15338i
$543$	−2.15146	+	0.615927i	−0.0923278	+	0.0264319i
$544$	7.72109	+	18.6157i	0.331039	+	0.798143i
$545$	−0.963063	−	0.556025i	−0.0412531	−	0.0238175i
$546$	1.12227	−	24.7348i	0.0480286	−	1.05855i
$547$	1.89577	−	1.09452i	0.0810571	−	0.0467983i	−0.458924	−	0.888476i	$-0.651765\pi$
$547$	1.89577	−	1.09452i	0.0810571	−	0.0467983i	0.539981	+	0.841677i	$0.318432\pi$
$548$	−30.7888	+	11.8253i	−1.31523	+	0.505154i
$549$	8.68124	−	16.2935i	0.370506	−	0.695389i
$550$	−13.4708	+	2.49798i	−0.574398	+	0.106514i
$551$	−0.00269259	−	0.00466370i	−0.000114708	−	0.000198681i
$552$	19.1082	−	6.02172i	0.813298	−	0.256301i
$553$	13.1084	−	0.210786i	0.557427	−	0.00896352i
$554$	11.0333	+	3.90593i	0.468759	+	0.165947i
$555$	−0.00841961	+	0.0337079i	−0.000357393	+	0.00143082i
$556$	−15.1230	−	12.2417i	−0.641359	−	0.519164i
$557$	0.120599			0.00510995			0.00255497	−	0.999997i	$-0.499187\pi$
$557$	0.120599			0.00510995			0.00255497	+	0.999997i	$0.499187\pi$
$558$	8.68855	+	9.49637i	0.367816	+	0.402013i
$559$	34.2164			1.44720
$560$	0.206275	+	0.897568i	0.00871669	+	0.0379292i
$561$	8.32160	−	8.60991i	0.351338	−	0.363511i
$562$	−20.1343	−	7.12780i	−0.849314	−	0.300668i
$563$	6.89903	−	11.9495i	0.290759	−	0.503610i	−0.683230	−	0.730203i	$-0.739425\pi$
$563$	6.89903	−	11.9495i	0.290759	−	0.503610i	0.973989	+	0.226593i	$0.0727588\pi$
$564$	−6.04852	−	8.03067i	−0.254689	−	0.338152i
$565$	−0.859375	+	0.496160i	−0.0361542	+	0.0208736i
$566$	1.89786	+	10.2346i	0.0797730	+	0.430192i
$567$	19.5475	−	13.5977i	0.820916	−	0.571049i
$568$	36.4851	−	22.3722i	1.53088	−	0.938717i
$569$	−5.08023	−	8.79921i	−0.212974	−	0.368882i	0.739670	−	0.672970i	$-0.234982\pi$
$569$	−5.08023	−	8.79921i	−0.212974	−	0.368882i	−0.952644	+	0.304088i	$0.901648\pi$
$570$	−0.000149253	0	0.000299605i	−6.25151e−6	0	1.25491e-5i
$571$	13.0923	+	7.55883i	0.547895	+	0.316327i	0.748272	−	0.663392i	$-0.230884\pi$
$571$	13.0923	+	7.55883i	0.547895	+	0.316327i	−0.200378	+	0.979719i	$0.564217\pi$
$572$	−2.31680	+	14.6454i	−0.0968701	+	0.612356i
$573$	7.46473	+	7.21476i	0.311843	+	0.301401i
$574$	−20.8502	−	7.00608i	−0.870269	−	0.292428i
$575$			20.4167i			0.851436i
$576$	−2.08475	−	23.9093i	−0.0868647	−	0.996220i
$577$		−	26.7948i		−	1.11548i	−0.830016	−	0.557740i	$-0.811669\pi$
$577$		−	26.7948i		−	1.11548i	0.830016	−	0.557740i	$-0.188331\pi$
$578$	−4.63180	+	3.95668i	−0.192657	+	0.164576i
$579$	−22.8230	−	5.70076i	−0.948491	−	0.236915i
$580$	−0.589552	−	0.0932628i	−0.0244798	−	0.00387253i
$581$	0.536954	+	33.3923i	0.0222766	+	1.38534i
$582$	29.9788	+	1.84361i	1.24266	+	0.0764200i
$583$	−11.9235	+	6.88403i	−0.493821	+	0.285108i
$584$	40.0984	−	24.5878i	1.65928	−	1.01745i
$585$	0.880284	+	0.469020i	0.0363953	+	0.0193916i
$586$	24.6690	−	4.57451i	1.01907	−	0.188971i
$587$	−6.49971	−	11.2578i	−0.268272	−	0.464660i	0.700144	−	0.714002i	$-0.253119\pi$
$587$	−6.49971	−	11.2578i	−0.268272	−	0.464660i	−0.968416	+	0.249342i	$0.919786\pi$
$588$	15.2038	+	18.8903i	0.626995	+	0.779023i
$589$	0.00238196	−	0.00412567i	9.81468e−5	−	0.000169995i
$590$	0.474388	−	1.34003i	0.0195303	−	0.0551681i
$591$	−5.74470	−	20.0665i	−0.236306	−	0.825425i
$592$	0.876997	+	0.284591i	0.0360443	+	0.0116966i
$593$		−	37.6206i		−	1.54489i	−0.635081	−	0.772446i	$-0.719033\pi$
$593$		−	37.6206i		−	1.54489i	0.635081	−	0.772446i	$-0.280967\pi$
$594$	−12.5396	+	6.78920i	−0.514507	+	0.278564i
$595$	0.703690	−	0.421504i	0.0288485	−	0.0172800i
$596$	11.1211	+	9.00224i	0.455538	+	0.368746i
$597$	4.01044	+	14.0086i	0.164137	+	0.573336i
$598$	20.8295	+	7.37393i	0.851783	+	0.301543i
$599$	−24.0839	−	13.9048i	−0.984040	−	0.568136i	−0.0805528	−	0.996750i	$-0.525669\pi$
$599$	−24.0839	−	13.9048i	−0.984040	−	0.568136i	−0.903488	+	0.428614i	$0.859002\pi$
$600$	23.8773	+	5.29712i	0.974786	+	0.216254i
$601$	13.7188	−	7.92056i	0.559602	−	0.323086i	−0.193384	−	0.981123i	$-0.561946\pi$
$601$	13.7188	−	7.92056i	0.559602	−	0.323086i	0.752986	+	0.658037i	$0.228613\pi$
$602$	−25.1256	+	22.1719i	−1.02404	+	0.903660i
$603$	−34.0212	+	1.15897i	−1.38545	+	0.0471969i
$604$	10.7917	+	28.0976i	0.439107	+	1.14327i
$605$	0.545225	−	0.314786i	0.0221666	−	0.0127979i
$606$	33.0745	+	2.03399i	1.34356	+	0.0826251i
$607$	2.94759	−	5.10537i	0.119639	−	0.207221i	−0.799986	−	0.600019i	$-0.795160\pi$
$607$	2.94759	−	5.10537i	0.119639	−	0.207221i	0.919625	+	0.392798i	$0.128493\pi$
$608$	−0.00820505	+	0.00340314i	−0.000332759	+	0.000138016i
$609$	−15.0373	+	4.56776i	−0.609342	+	0.185095i
$610$	−0.575858	+	0.491922i	−0.0233158	+	0.0199173i
$611$		−	11.0883i		−	0.448583i
$612$	−19.6822	+	8.33913i	−0.795606	+	0.337089i
$613$	32.1607			1.29896			0.649480	−	0.760379i	$-0.274987\pi$
$613$	32.1607			1.29896			0.649480	+	0.760379i	$0.274987\pi$
$614$	−12.4508	+	10.6360i	−0.502474	+	0.429234i
$615$	0.615792	−	0.637127i	0.0248311	−	0.0256914i
$616$	−7.78885	−	12.2556i	−0.313822	−	0.493792i
$617$	22.5725	−	39.0968i	0.908736	−	1.57398i	0.0929129	−	0.995674i	$-0.470382\pi$
$617$	22.5725	−	39.0968i	0.908736	−	1.57398i	0.815823	−	0.578302i	$-0.196284\pi$
$618$	41.4893	−	20.6686i	1.66895	−	0.831412i
$619$	−15.6805	−	27.1595i	−0.630253	−	1.09163i	−0.987500	−	0.157621i	$-0.949618\pi$
$619$	−15.6805	−	27.1595i	−0.630253	−	1.09163i	0.357246	−	0.934010i	$-0.383716\pi$
$620$	−0.189319	−	0.492916i	−0.00760322	−	0.0197960i
$621$	6.54068	+	20.2182i	0.262469	+	0.811329i
$622$	−6.92912	−	37.3667i	−0.277832	−	1.49827i
$623$	11.6516	−	20.9521i	0.466812	−	0.839428i
$624$	14.0280	−	22.4469i	0.561570	−	0.898595i
$625$	−12.4432	+	21.5523i	−0.497729	+	0.862092i
$626$	−1.91255	+	5.40248i	−0.0764408	+	0.215926i
$627$	0.00379490	+	0.00366782i	0.000151554	+	0.000146479i
$628$	−13.9999	+	17.2950i	−0.558656	+	0.690147i
$629$		−	0.821207i		−	0.0327437i
$630$	−0.950326	+	0.226009i	−0.0378619	+	0.00900441i
$631$			35.0020i			1.39341i	0.717360	+	0.696703i	$0.245351\pi$
$631$			35.0020i			1.39341i	−0.717360	+	0.696703i	$0.754649\pi$
$632$	12.3188	+	6.68407i	0.490014	+	0.265878i
$633$	5.87854	−	23.5347i	0.233651	−	0.935422i
$634$	−1.43017	−	0.506301i	−0.0567995	−	0.0201078i
$635$	−0.328072	+	0.568238i	−0.0130192	+	0.0225498i
$636$	24.3960	−	2.98951i	0.967363	−	0.118542i
$637$	0.859877	+	26.7303i	0.0340696	+	1.05909i
$638$	9.25354	−	1.71594i	0.366351	−	0.0679346i
$639$	24.0224	+	38.5170i	0.950312	+	1.52371i
$640$	−0.279010	+	0.944193i	−0.0110288	+	0.0373225i
$641$	−18.6549	−	32.3112i	−0.736823	−	1.27622i	−0.953919	−	0.300065i	$-0.902992\pi$
$641$	−18.6549	−	32.3112i	−0.736823	−	1.27622i	0.217095	−	0.976150i	$-0.430342\pi$
$642$	−8.08017	+	12.1990i	−0.318899	+	0.481455i
$643$	−17.6289	+	30.5341i	−0.695216	+	1.20415i	0.274892	+	0.961475i	$0.411358\pi$
$643$	−17.6289	+	30.5341i	−0.695216	+	1.20415i	−0.970108	+	0.242674i	$0.921975\pi$
$644$	−20.0737	+	8.08258i	−0.791014	+	0.318498i
$645$	−0.371527	−	1.29776i	−0.0146289	−	0.0510992i
$646$	0.00513874	+	0.00601555i	0.000202181	+	0.000236678i
$647$	19.9790			0.785455			0.392727	−	0.919655i	$-0.371532\pi$
$647$	19.9790			0.785455			0.392727	+	0.919655i	$0.371532\pi$
$648$	25.3421	−	2.40369i	0.995532	−	0.0944257i
$649$			22.4137i			0.879814i
$650$	17.5206	+	20.5101i	0.687213	+	0.804471i
$651$	−10.1507	−	9.49989i	−0.397836	−	0.372330i
$652$	−10.5184	−	1.66393i	−0.411932	−	0.0651646i
$653$	−5.59236	+	9.68626i	−0.218846	+	0.379052i	−0.954455	−	0.298353i	$-0.903563\pi$
$653$	−5.59236	+	9.68626i	−0.218846	+	0.379052i	0.735609	+	0.677406i	$0.236896\pi$
$654$	−26.0961	−	17.2852i	−1.02044	−	0.675903i
$655$	−1.14435	+	0.660688i	−0.0447133	+	0.0258152i
$656$	−15.7408	−	17.4688i	−0.614575	−	0.682041i
$657$	26.4015	+	42.3316i	1.03002	+	1.65151i
$658$	7.18510	+	8.14227i	0.280104	+	0.317419i
$659$	−27.2085	+	15.7088i	−1.05989	+	0.611929i	−0.925402	−	0.378986i	$-0.876273\pi$
$659$	−27.2085	+	15.7088i	−1.05989	+	0.611929i	−0.134490	+	0.990915i	$0.542939\pi$
$660$	0.580628	−	0.0711509i	0.0226009	−	0.00276954i
$661$	−21.5855	−	12.4624i	−0.839577	−	0.484730i	0.0175436	−	0.999846i	$-0.494415\pi$
$661$	−21.5855	−	12.4624i	−0.839577	−	0.484730i	−0.857120	+	0.515116i	$0.827749\pi$
$662$	8.23364	−	23.2580i	0.320010	−	0.903948i
$663$	−22.8729	−	5.71323i	−0.888311	−	0.221884i
$664$	−17.0269	+	31.3807i	−0.660773	+	1.21781i
$665$	0.000185782	0	0.000310158i	7.20431e−6	0	1.20274e-5i
$666$	−0.294783	+	0.932460i	−0.0114226	+	0.0361321i
$667$		−	14.0249i		−	0.543046i
$668$	14.1974	+	11.4924i	0.549313	+	0.444655i
$669$	5.82327	−	6.02502i	0.225141	−	0.232941i
$670$	1.31641	+	0.466026i	0.0508573	+	0.0180042i
$671$	5.97082	−	10.3418i	0.230501	−	0.399239i
$672$	4.24443	+	25.5731i	0.163732	+	0.986505i
$673$	17.3140	+	29.9887i	0.667405	+	1.15598i	0.978627	+	0.205643i	$0.0659284\pi$
$673$	17.3140	+	29.9887i	0.667405	+	1.15598i	−0.311222	+	0.950337i	$0.600738\pi$
$674$	−2.54414	−	13.7198i	−0.0979967	−	0.528467i
$675$	−5.42601	+	25.3676i	−0.208847	+	0.976399i
$676$	2.98137	−	1.14508i	0.114668	−	0.0440416i
$677$	−8.13000	+	4.69386i	−0.312461	+	0.180400i	−0.648027	−	0.761617i	$-0.724406\pi$
$677$	−8.13000	+	4.69386i	−0.312461	+	0.180400i	0.335566	+	0.942017i	$0.391072\pi$
$678$	−25.0009	+	12.4546i	−0.960156	+	0.478316i
$679$	−32.4378	+	0.521605i	−1.24485	+	0.0200174i
$680$	0.876600	−	0.0232008i	0.0336161	−	0.000889711i
$681$	8.39698	−	8.68790i	0.321773	−	0.332921i
$682$	5.40760	+	6.33028i	0.207068	+	0.242399i
$683$		−	36.4991i		−	1.39660i	−0.715806	−	0.698300i	$-0.753940\pi$
$683$		−	36.4991i		−	1.39660i	0.715806	−	0.698300i	$-0.246060\pi$
$684$	−0.00367555	−	0.00867512i	−0.000140538	−	0.000331701i
$685$			1.43508i			0.0548317i
$686$	−17.9524	−	19.0712i	−0.685426	−	0.728142i
$687$	−10.8338	+	43.3733i	−0.413337	+	1.65479i
$688$	−35.0376	+	7.46117i	−1.33579	+	0.284455i
$689$	23.4760	+	13.5539i	0.894364	+	0.516361i
$690$	0.0535081	−	0.870091i	0.00203702	−	0.0331238i
$691$	13.6934	+	23.7176i	0.520921	+	0.902261i	0.999704	+	0.0243280i	$0.00774462\pi$
$691$	13.6934	+	23.7176i	0.520921	+	0.902261i	−0.478783	+	0.877933i	$0.658922\pi$
$692$	−14.5982	−	38.0084i	−0.554942	−	1.44486i
$693$	12.9359	−	8.35977i	0.491395	−	0.317562i
$694$	−3.22737	+	0.598469i	−0.122509	+	0.0227176i
$695$	−0.733171	+	0.423297i	−0.0278108	+	0.0160566i
$696$	−16.4020	−	3.63876i	−0.621718	−	0.137927i
$697$	−10.4718	+	18.1376i	−0.396646	+	0.687011i
$698$	−2.38192	+	6.72834i	−0.0901570	+	0.254671i
$699$	1.23571	+	4.31638i	0.0467387	+	0.163260i
$700$	−26.1560	−	3.70766i	−0.988603	−	0.140136i
$701$	−45.2968			−1.71084			−0.855418	−	0.517939i	$-0.826699\pi$
$701$	−45.2968			−1.71084			−0.855418	+	0.517939i	$0.826699\pi$
$702$	23.9208	+	14.6978i	0.902833	+	0.554732i
$703$	0.000361955	0		1.36514e−5	0
$704$	−0.821159	−	15.5021i	−0.0309486	−	0.584258i
$705$	−0.420556	+	0.120398i	−0.0158391	+	0.00453446i
$706$	9.54035	−	26.9491i	0.359056	−	1.01424i
$707$	−35.7874	+	0.575468i	−1.34592	+	0.0216427i
$708$	15.6429	−	36.8278i	0.587897	−	1.38408i
$709$	3.51774	+	6.09291i	0.132112	+	0.228824i	0.924490	−	0.381205i	$-0.124491\pi$
$709$	3.51774	+	6.09291i	0.132112	+	0.228824i	−0.792379	+	0.610029i	$0.791158\pi$
$710$	−0.339533	−	1.83100i	−0.0127424	−	0.0687161i
$711$	−6.99012	+	13.1195i	−0.262150	+	0.492019i
$712$	21.8488	−	13.3974i	0.818817	−	0.502088i
$713$	10.7447	−	6.20344i	0.402391	−	0.232321i
$714$	20.4981	−	10.6262i	0.767121	−	0.397674i
$715$	0.558733	+	0.322584i	0.0208954	+	0.0120640i
$716$	27.1208	+	4.29032i	1.01355	+	0.160337i
$717$	−2.14527	+	8.58861i	−0.0801167	+	0.320747i
$718$	−20.4829	−	23.9779i	−0.764417	−	0.894848i
$719$	26.6362			0.993364			0.496682	−	0.867933i	$-0.334551\pi$
$719$	26.6362			0.993364			0.496682	+	0.867933i	$0.334551\pi$
$720$	−1.00369	−	0.288323i	−0.0374052	−	0.0107452i
$721$	−42.9507	+	25.7271i	−1.59957	+	0.958128i
$722$	20.4305	−	17.4526i	0.760345	−	0.649519i
$723$	−9.16220	−	8.85539i	−0.340746	−	0.329336i
$724$	2.55235	+	0.403763i	0.0948573	+	0.0150057i
$725$	8.56065	−	14.8275i	0.317935	−	0.550679i
$726$	15.8617	−	7.90175i	0.588683	−	0.293262i
$727$	2.70743	+	4.68941i	0.100413	+	0.173921i	0.911855	−	0.410513i	$-0.134650\pi$
$727$	2.70743	+	4.68941i	0.100413	+	0.173921i	−0.811442	+	0.584433i	$0.801317\pi$
$728$	−13.2294	+	25.3457i	−0.490315	+	0.939376i
$729$	2.75349	+	26.8592i	0.101981	+	0.994786i
$730$	−0.373158	−	2.01233i	−0.0138112	−	0.0744797i
$731$	15.9532	+	27.6318i	0.590051	+	1.02200i
$732$	−17.0283	+	12.8254i	−0.629386	+	0.474040i
$733$	10.2787	+	5.93443i	0.379654	+	0.219193i	0.677668	−	0.735368i	$-0.262991\pi$
$733$	10.2787	+	5.93443i	0.379654	+	0.219193i	−0.298014	+	0.954562i	$0.596324\pi$
$734$	−5.45926	−	1.93265i	−0.201505	−	0.0713354i
$735$	1.00449	−	0.322855i	0.0370511	−	0.0119087i
$736$	−22.9374	−	3.00885i	−0.845484	−	0.110908i
$737$	−22.0186			−0.811065
$738$	18.4011	−	16.8358i	0.677356	−	0.619736i
$739$		−	35.3536i		−	1.30050i	−0.759718	−	0.650252i	$-0.774663\pi$
$739$		−	35.3536i		−	1.30050i	0.759718	−	0.650252i	$-0.225337\pi$
$740$	0.0252415	−	0.0311826i	0.000927895	−	0.00114629i
$741$	0.00251816	−	0.0100815i	9.25070e−5	−	0.000370352i
$742$	−26.0216	+	5.25944i	−0.955282	+	0.193080i
$743$	−13.2573	−	7.65413i	−0.486365	−	0.280803i	0.236700	−	0.971583i	$-0.423934\pi$
$743$	−13.2573	−	7.65413i	−0.486365	−	0.280803i	−0.723065	+	0.690780i	$0.757267\pi$
$744$	−4.46719	−	14.1753i	−0.163775	−	0.519693i
$745$	0.539156	−	0.311282i	0.0197531	−	0.0114045i
$746$	6.23549	+	33.6261i	0.228298	+	1.23114i
$747$	−33.4204	−	17.8066i	−1.22279	−	0.651508i
$748$	−12.9072	+	4.95740i	−0.471936	+	0.181260i
$749$	7.68126	−	13.8125i	0.280667	−	0.504699i
$750$	1.17622	−	1.77579i	0.0429495	−	0.0648427i
$751$	37.1811	+	21.4665i	1.35676	+	0.783325i	0.989186	−	0.146669i	$-0.0468553\pi$
$751$	37.1811	+	21.4665i	1.35676	+	0.783325i	0.367574	+	0.929994i	$0.380189\pi$
$752$	2.41789	+	11.3544i	0.0881714	+	0.414052i
$753$	−3.25644	−	11.3749i	−0.118671	−	0.414523i
$754$	−12.0354	−	14.0890i	−0.438305	−	0.513092i
$755$	1.30964			0.0476628
$756$	−27.0894	+	4.70770i	−0.985233	+	0.171217i
$757$	−30.0701			−1.09292			−0.546459	−	0.837486i	$-0.684025\pi$
$757$	−30.0701			−1.09292			−0.546459	+	0.837486i	$0.684025\pi$
$758$	−4.45028	−	5.20962i	−0.161641	−	0.189222i
$759$	3.78299	+	13.2141i	0.137314	+	0.479643i
$760$	1.02260e−5	0	0.000386370i	3.70935e−7	0	1.40151e-5i
$761$	−0.115802	−	0.0668580i	−0.00419780	−	0.00242360i	0.497900	−	0.867235i	$-0.334105\pi$
$761$	−0.115802	−	0.0668580i	−0.00419780	−	0.00242360i	−0.502097	+	0.864811i	$0.667438\pi$
$762$	−10.1988	+	15.3975i	−0.369463	+	0.557794i
$763$	29.5479	+	16.4318i	1.06971	+	0.594871i
$764$	−4.29803	−	11.1905i	−0.155497	−	0.404857i
$765$	0.0316665	+	0.929561i	0.00114491	+	0.0336083i
$766$	−0.310436	−	1.67409i	−0.0112165	−	0.0604872i
$767$	38.2177	−	22.0650i	1.37996	−	0.796720i
$768$	−9.46996	+	26.0446i	−0.341718	+	0.939803i
$769$	−29.4369	−	16.9954i	−1.06152	−	0.612869i	−0.135668	−	0.990754i	$-0.543318\pi$
$769$	−29.4369	−	16.9954i	−1.06152	−	0.612869i	−0.925852	+	0.377886i	$0.876651\pi$
$770$	−0.619317	+	0.125176i	−0.0223187	+	0.00451102i
$771$	−8.21659	+	32.8951i	−0.295913	+	1.18469i
$772$	21.1131	+	17.0905i	0.759877	+	0.615101i
$773$			35.3881i			1.27282i	0.771351	+	0.636410i	$0.219582\pi$
$773$			35.3881i			1.27282i	−0.771351	+	0.636410i	$0.780418\pi$
$774$	−8.19569	−	37.1018i	−0.294588	−	1.33360i
$775$	15.1461			0.544063
$776$	−30.4837	−	16.5402i	−1.09430	−	0.593759i
$777$	0.239470	−	1.02880i	0.00859094	−	0.0369080i
$778$	−27.4756	−	9.72671i	−0.985047	−	0.348720i
$779$	−0.00799432	−	0.00461552i	−0.000286426	−	0.000165368i
$780$	−0.692915	−	0.919987i	−0.0248103	−	0.0329408i
$781$	14.6811	+	25.4284i	0.525331	+	0.909901i
$782$	3.75678	+	20.2592i	0.134342	+	0.724466i
$783$	3.72730	−	17.4258i	0.133203	−	0.622747i
$784$	−6.70928	−	27.1843i	−0.239617	−	0.970867i
$785$	0.484092	+	0.838471i	0.0172780	+	0.0299263i
$786$	−33.2913	+	16.5846i	−1.18746	+	0.591552i
$787$	−1.02046	+	1.76749i	−0.0363755	+	0.0630043i	−0.883640	−	0.468167i	$-0.844915\pi$
$787$	−1.02046	+	1.76749i	−0.0363755	+	0.0630043i	0.847264	+	0.531171i	$0.178248\pi$
$788$	−3.76587	+	23.8056i	−0.134153	+	0.848039i
$789$	2.75808	+	2.66572i	0.0981902	+	0.0949022i
$790$	0.463679	−	0.396095i	0.0164970	−	0.0140924i
$791$	25.8815	−	15.5028i	0.920242	−	0.551217i
$792$	16.4354	−	0.995780i	0.584006	−	0.0353835i
$793$	−23.5117			−0.834926
$794$	−6.40057	−	7.49268i	−0.227148	−	0.265905i
$795$	0.259165	−	1.03757i	0.00919165	−	0.0367988i
$796$	2.62899	−	16.6189i	0.0931822	−	0.589043i
$797$	19.3409	+	11.1665i	0.685089	+	0.395536i	0.801770	−	0.597633i	$-0.203892\pi$
$797$	19.3409	+	11.1665i	0.685089	+	0.395536i	−0.116681	+	0.993169i	$0.537225\pi$
$798$	0.00468358	+	0.00903471i	0.000165797	+	0.000319825i
$799$	8.95444	−	5.16985i	0.316785	−	0.182896i
$800$	−22.4135	−	17.1818i	−0.792436	−	0.607469i
$801$	14.3856	+	23.0656i	0.508290	+	0.814981i
$802$	6.14036	+	33.1131i	0.216824	+	1.16927i
$803$	16.1351	+	27.9467i	0.569394	+	0.986219i
$804$	36.1787	+	15.3672i	1.27592	+	0.541959i
$805$	0.0151388	+	0.941459i	0.000533574	+	0.0331821i
$806$	5.47033	−	15.4523i	0.192684	−	0.544285i
$807$	−37.8231	+	10.8281i	−1.33143	+	0.381168i
$808$	−33.6316	−	18.2482i	−1.18315	−	0.641970i
$809$	23.9415			0.841738			0.420869	−	0.907121i	$-0.361725\pi$
$809$	23.9415			0.841738			0.420869	+	0.907121i	$0.361725\pi$
$810$	0.297721	−	1.06686i	0.0104609	−	0.0374857i
$811$	−47.1365			−1.65519			−0.827594	−	0.561328i	$-0.810291\pi$
$811$	−47.1365			−1.65519			−0.827594	+	0.561328i	$0.810291\pi$
$812$	17.9674	+	2.54691i	0.630530	+	0.0893788i
$813$	−13.9353	−	48.6764i	−0.488731	−	1.70716i
$814$	−0.211098	+	0.596299i	−0.00739897	+	0.0209003i
$815$	−0.231681	+	0.401284i	−0.00811545	+	0.0140564i
$816$	24.6677	+	0.862713i	0.863543	+	0.0302010i
$817$	−0.0121790	+	0.00703152i	−0.000426088	+	0.000246002i
$818$	31.2365	−	5.79236i	1.09216	−	0.202525i
$819$	−26.9890	−	13.8274i	−0.943071	−	0.483169i
$820$	−0.955126	+	0.366844i	−0.0333544	+	0.0128107i
$821$	24.5881	+	42.5878i	0.858130	+	1.48632i	0.873711	+	0.486446i	$0.161707\pi$
$821$	24.5881	+	42.5878i	0.858130	+	1.48632i	−0.0155813	+	0.999879i	$0.504960\pi$
$822$	−2.47944	+	40.3180i	−0.0864804	+	1.40625i
$823$	39.1098	+	22.5800i	1.36328	+	0.787091i	0.990059	−	0.140651i	$-0.0449195\pi$
$823$	39.1098	+	22.5800i	1.36328	+	0.787091i	0.373222	+	0.927742i	$0.378253\pi$
$824$	−53.5045	+	1.41610i	−1.86392	+	0.0493320i
$825$	−4.06630	+	16.2794i	−0.141570	+	0.566777i
$826$	−13.7659	+	40.9674i	−0.478976	+	1.42544i
$827$		−	15.7743i		−	0.548526i	−0.961655	−	0.274263i	$-0.911566\pi$
$827$		−	15.7743i		−	0.548526i	0.961655	−	0.274263i	$-0.0884339\pi$
$828$	3.00657	−	24.3523i	0.104485	−	0.846302i
$829$			24.0257i			0.834447i	0.908804	+	0.417223i	$0.136997\pi$
$829$			24.0257i			0.834447i	−0.908804	+	0.417223i	$0.863003\pi$
$830$	1.00901	+	1.18117i	0.0350232	+	0.0409991i
$831$	9.96214	−	10.3073i	0.345583	−	0.357556i
$832$	−25.6243	+	16.6611i	−0.888364	+	0.577620i
$833$	−21.1854	+	13.1573i	−0.734030	+	0.455872i
$834$	−21.3294	+	10.6256i	−0.738578	+	0.367934i
$835$	0.688296	−	0.397388i	0.0238195	−	0.0137522i
$836$	−0.00218502	−	0.00568899i	−7.55705e−5	−	0.000196758i
$837$	14.9988	−	4.85218i	0.518435	−	0.167716i
$838$	−3.43771	−	18.5386i	−0.118754	−	0.640404i
$839$	−19.2798	−	33.3935i	−0.665611	−	1.15287i	−0.979119	−	0.203287i	$-0.934838\pi$
$839$	−19.2798	−	33.3935i	−0.665611	−	1.15287i	0.313508	−	0.949586i	$-0.398496\pi$
$840$	1.10496	+	0.226557i	0.0381248	+	0.00781697i
$841$	8.61942	−	14.9293i	0.297221	−	0.514803i
$842$	31.1748	+	11.0363i	1.07435	+	0.380336i
$843$	−18.1796	+	18.8094i	−0.626138	+	0.647832i
$844$	−17.6235	+	21.7715i	−0.606626	+	0.749408i
$845$		−	0.138963i		−	0.00478048i
$846$	−12.0233	+	2.65592i	−0.413371	+	0.0913125i
$847$	−16.4204	+	9.83567i	−0.564211	+	0.337958i
$848$	−26.9950	−	8.76003i	−0.927011	−	0.300821i
$849$	12.3685	+	3.08941i	0.424484	+	0.106028i
$850$	−8.39423	+	23.7116i	−0.287920	+	0.813302i
$851$	0.816363	+	0.471328i	0.0279846	+	0.0161569i
$852$	−6.37553	−	52.0276i	−0.218422	−	1.78244i
$853$	16.7546	−	9.67325i	0.573665	−	0.331206i	−0.184947	−	0.982749i	$-0.559211\pi$
$853$	16.7546	−	9.67325i	0.573665	−	0.331206i	0.758612	+	0.651543i	$0.225878\pi$
$854$	17.2650	−	15.2354i	0.590796	−	0.521345i
$855$	−0.000409713	0	1.39573e-5i	−1.40119e−5	0	4.77330e-7i
$856$	14.4037	−	8.83214i	0.492307	−	0.301876i
$857$	−2.04423	+	1.18024i	−0.0698296	+	0.0403161i	−0.534508	−	0.845163i	$-0.679503\pi$
$857$	−2.04423	+	1.18024i	−0.0698296	+	0.0403161i	0.464679	+	0.885479i	$0.346170\pi$
$858$	15.1400	+	10.0282i	0.516870	+	0.342357i
$859$	8.10933	−	14.0458i	0.276687	−	0.479235i	−0.693873	−	0.720098i	$-0.744097\pi$
$859$	8.10933	−	14.0458i	0.276687	−	0.479235i	0.970559	+	0.240862i	$0.0774302\pi$
$860$	−0.243550	+	1.53958i	−0.00830498	+	0.0524991i
$861$	−18.4080	+	19.6690i	−0.627342	+	0.670317i
$862$	−5.79172	−	6.77994i	−0.197267	−	0.230926i
$863$		−	36.2730i		−	1.23475i	−0.786671	−	0.617373i	$-0.788197\pi$
$863$		−	36.2730i		−	1.23475i	0.786671	−	0.617373i	$-0.211803\pi$
$864$	−27.6999	−	9.83439i	−0.942370	−	0.334573i
$865$	−1.77159			−0.0602360
$866$	24.5859	+	28.7809i	0.835463	+	0.978016i
$867$	2.05341	+	7.17264i	0.0697374	+	0.243596i
$868$	5.99604	+	14.8916i	0.203519	+	0.505454i
$869$	−4.80769	+	8.32717i	−0.163090	+	0.282480i
$870$	−0.403686	+	0.609461i	−0.0136862	+	0.0206627i
$871$	21.6760	+	37.5440i	0.734465	+	1.27213i
$872$	18.8938	+	30.8124i	0.639824	+	1.04344i
$873$	17.2976	−	32.4651i	0.585434	−	1.09878i
$874$	−0.00892942	+	0.00165583i	−0.000302042	+	5.60094e-5i
$875$	−1.11815	+	2.01068i	−0.0378004	+	0.0679733i
$876$	−7.00693	−	57.1802i	−0.236742	−	1.93194i
$877$	−10.9980	+	19.0490i	−0.371375	+	0.643240i	−0.989777	−	0.142621i	$-0.954447\pi$
$877$	−10.9980	+	19.0490i	−0.371375	+	0.643240i	0.618402	+	0.785862i	$0.287780\pi$
$878$	−10.8613	−	3.84506i	−0.366552	−	0.129764i
$879$	7.44657	−	29.8123i	0.251167	−	1.00555i
$880$	−0.642485	−	0.208490i	−0.0216582	−	0.00702820i
$881$			17.8109i			0.600063i	0.953929	+	0.300031i	$0.0969972\pi$
$881$			17.8109i			0.600063i	−0.953929	+	0.300031i	$0.903003\pi$
$882$	28.7784	−	7.33497i	0.969020	−	0.246981i
$883$			55.9070i			1.88142i	0.339211	+	0.940710i	$0.389840\pi$
$883$			55.9070i			1.88142i	−0.339211	+	0.940710i	$0.610160\pi$
$884$	21.1593	+	17.1279i	0.711665	+	0.576075i
$885$	−1.25185	−	1.20994i	−0.0420806	−	0.0406715i
$886$	1.77592	−	5.01654i	0.0596633	−	0.168534i
$887$	−9.91067	+	17.1658i	−0.332768	+	0.576371i	−0.983053	−	0.183319i	$-0.941316\pi$
$887$	−9.91067	+	17.1658i	−0.332768	+	0.576371i	0.650286	+	0.759690i	$0.274649\pi$
$888$	0.763022	−	0.832448i	0.0256053	−	0.0279351i
$889$	9.69529	−	17.4342i	0.325169	−	0.584724i
$890$	−0.203326	−	1.09648i	−0.00681550	−	0.0367539i
$891$	1.18850	+	17.4238i	0.0398164	+	0.583720i
$892$	−9.03220	+	3.46908i	−0.302420	+	0.116153i
$893$	0.00227866	+	0.00394675i	7.62524e−5	+	0.000132073i
$894$	15.6851	−	7.81379i	0.524589	−	0.261332i
$895$	0.597372	−	1.03468i	0.0199679	−	0.0345855i
$896$	8.02007	−	28.8388i	0.267932	−	0.963438i
$897$	18.8073	−	19.4589i	0.627959	−	0.649715i
$898$	9.72345	−	8.30619i	0.324476	−	0.277181i
$899$	−10.4043			−0.347003
$900$	18.0430	−	23.9108i	0.601435	−	0.797025i
$901$			25.2777i			0.842123i
$902$	12.2662	−	10.4783i	0.408420	−	0.348890i
$903$	11.9284	+	39.2689i	0.396952	+	1.30679i
$904$	32.2411	−	0.853321i	1.07232	−	0.0283810i
$905$	0.0562188	−	0.0973739i	0.00186878	−	0.00323682i
$906$	36.7938	+	2.26271i	1.22239	+	0.0751735i
$907$	24.1992	−	13.9714i	0.803522	−	0.463914i	−0.0411792	−	0.999152i	$-0.513111\pi$
$907$	24.1992	−	13.9714i	0.803522	−	0.463914i	0.844701	+	0.535238i	$0.179778\pi$
$908$	−13.0242	+	5.00230i	−0.432222	+	0.166007i
$909$	19.0838	−	35.8176i	0.632969	−	1.18799i
$910$	0.823120	+	0.932773i	0.0272862	+	0.0309211i
$911$	−2.33738	+	1.34949i	−0.0774408	+	0.0447105i	−0.538220	−	0.842804i	$-0.680903\pi$
$911$	−2.33738	+	1.34949i	−0.0774408	+	0.0447105i	0.460780	+	0.887515i	$0.347570\pi$
$912$	−0.000380249		0.0108725i	−1.25913e−5		0.000360025i
$913$	−21.2125	−	12.2471i	−0.702033	−	0.405319i
$914$	10.5747	+	3.74360i	0.349781	+	0.123827i
$915$	0.255294	+	0.891753i	0.00843977	+	0.0294805i
$916$	32.4792	−	40.1238i	1.07314	−	1.32573i
$917$	34.4639	−	20.6436i	1.13810	−	0.681711i
$918$	−0.716376	+	26.1703i	−0.0236439	+	0.863747i
$919$		−	42.6049i		−	1.40541i	−0.711483	−	0.702703i	$-0.751976\pi$
$919$		−	42.6049i		−	1.40541i	0.711483	−	0.702703i	$-0.248024\pi$
$920$	−0.480056	+	0.884745i	−0.0158270	+	0.0291692i
$921$	5.51980	+	19.2809i	0.181884	+	0.635327i
$922$	15.4754	−	43.7142i	0.509655	−	1.43965i
$923$	28.9054	−	50.0657i	0.951434	−	1.64793i
$924$	−17.6157	+	2.44673i	−0.579514	+	0.0804916i
$925$	0.575388	+	0.996601i	0.0189186	+	0.0327680i
$926$	−2.07009	+	0.383869i	−0.0680275	+	0.0126147i
$927$	−1.93281	−	56.7371i	−0.0634819	−	1.86349i
$928$	15.3965	+	11.8027i	0.505416	+	0.387443i
$929$	7.43599	−	4.29317i	0.243967	−	0.140854i	−0.373032	−	0.927819i	$-0.621682\pi$
$929$	7.43599	−	4.29317i	0.243967	−	0.140854i	0.616999	+	0.786964i	$0.288348\pi$
$930$	−0.645474	−	0.0396948i	−0.0211659	−	0.00130164i
$931$	−0.00579918	−	0.00933765i	−0.000190060	−	0.000306029i
$932$	0.810052	−	5.12067i	0.0265341	−	0.167733i
$933$	−45.1574	−	11.2795i	−1.47839	−	0.369274i
$934$	−2.48431	+	2.12220i	−0.0812891	+	0.0694406i
$935$			0.601614i			0.0196749i
$936$	−17.8776	−	27.0438i	−0.584348	−	0.883953i
$937$			11.9278i			0.389666i	0.980836	+	0.194833i	$0.0624165\pi$
$937$			11.9278i			0.389666i	−0.980836	+	0.194833i	$0.937584\pi$
$938$	−40.2452	−	13.5232i	−1.31405	−	0.441549i
$939$	5.04699	+	4.87799i	0.164702	+	0.159187i
$940$	0.498920	+	0.0789255i	0.0162730	+	0.00257427i
$941$	−22.1293	−	12.7763i	−0.721394	−	0.416497i	0.0938716	−	0.995584i	$-0.470076\pi$
$941$	−22.1293	−	12.7763i	−0.721394	−	0.416497i	−0.815266	+	0.579087i	$0.803409\pi$
$942$	12.1517	+	24.3928i	0.395922	+	0.794761i
$943$	−12.0204	−	20.8200i	−0.391439	−	0.677992i
$944$	−34.3234	+	30.9282i	−1.11713	+	1.00663i
$945$	−0.231395	+	1.17378i	−0.00752729	+	0.0381830i
$946$	−4.48106	−	24.1650i	−0.145692	−	0.785672i
$947$	−23.7577	+	13.7165i	−0.772022	+	0.445727i	−0.833595	−	0.552375i	$-0.813722\pi$
$947$	−23.7577	+	13.7165i	−0.772022	+	0.445727i	0.0615733	+	0.998103i	$0.480388\pi$
$948$	13.7112	−	10.3270i	0.445319	−	0.335404i
$949$	31.7681	−	55.0239i	1.03124	−	1.78615i
$950$	−0.0104511	−	0.00369984i	−0.000339079	−	0.000120039i
$951$	−1.29133	+	1.33607i	−0.0418742	+	0.0433250i
$952$	−26.6364	+	1.13378i	−0.863289	+	0.0367460i
$953$	24.0958			0.780539			0.390269	−	0.920701i	$-0.372382\pi$
$953$	24.0958			0.780539			0.390269	+	0.920701i	$0.372382\pi$
$954$	9.07376	−	28.7022i	0.293774	−	0.929268i
$955$	−0.521594			−0.0168784
$956$	6.43140	−	7.94516i	0.208006	−	0.256965i
$957$	2.79327	−	11.1829i	0.0902936	−	0.361490i
$958$	33.9211	+	12.0085i	1.09594	+	0.387978i
$959$	−0.701498	−	43.6250i	−0.0226526	−	1.40873i
$960$	0.910156	+	0.790971i	0.0293752	+	0.0255285i
$961$	10.8980	+	18.8759i	0.351548	+	0.608900i
$962$	1.22457	−	0.227078i	0.0394816	−	0.00732130i
$963$	9.48362	+	15.2058i	0.305605	+	0.490001i
$964$	5.27539	+	13.7352i	0.169909	+	0.442381i
$965$	1.02357	−	0.590960i	0.0329500	−	0.0190237i
$966$	−1.20127	+	26.4760i	−0.0386502	+	0.851851i
$967$	−18.9596	−	10.9463i	−0.609699	−	0.352010i	0.163149	−	0.986601i	$-0.447835\pi$
$967$	−18.9596	−	10.9463i	−0.609699	−	0.352010i	−0.772848	+	0.634592i	$0.781168\pi$
$968$	−20.4552	+	0.541384i	−0.657455	+	0.0174008i
$969$	0.00931547	−	0.00266686i	0.000299256	−	8.56720e-5i
$970$	−1.14741	+	0.980166i	−0.0368411	+	0.0314712i
$971$	−37.7214			−1.21054			−0.605269	−	0.796021i	$-0.706935\pi$
$971$	−37.7214			−1.21054			−0.605269	+	0.796021i	$0.706935\pi$
$972$	10.2076	−	29.4585i	0.327408	−	0.944883i
$973$	22.0807	−	13.2262i	0.707875	−	0.424011i
$974$	23.8093	+	27.8718i	0.762899	+	0.893070i
$975$	31.7612	−	9.09270i	1.01717	−	0.291200i
$976$	24.0760	−	5.12693i	0.770655	−	0.164109i
$977$	6.94206	−	12.0240i	0.222096	−	0.384682i	−0.733348	−	0.679853i	$-0.762043\pi$
$977$	6.94206	−	12.0240i	0.222096	−	0.384682i	0.955444	+	0.295171i	$0.0953768\pi$
$978$	−7.20229	+	10.8736i	−0.230304	+	0.347699i
$979$	8.79164	+	15.2276i	0.280982	+	0.486675i
$980$	−1.20886	−	0.151574i	−0.0386155	−	0.00484184i
$981$	−32.5284	+	20.2874i	−1.03855	+	0.647727i
$982$	−21.2987	+	3.94954i	−0.679669	+	0.126035i
$983$	6.56820	+	11.3765i	0.209493	+	0.362853i	0.951555	−	0.307479i	$-0.0994853\pi$
$983$	6.56820	+	11.3765i	0.209493	+	0.362853i	−0.742062	+	0.670331i	$0.766152\pi$
$984$	−27.4676	+	8.65609i	−0.875635	+	0.275946i
$985$	0.908199	+	0.524349i	0.0289376	+	0.0167072i
$986$	5.76626	−	16.2883i	0.183635	−	0.518724i
$987$	12.7256	−	3.86555i	0.405060	−	0.123042i
$988$	−0.00754930	+	0.00932617i	−0.000240175	+	0.000296705i
$989$	−36.6250			−1.16461
$990$	0.215957	−	0.683117i	0.00686357	−	0.0217109i
$991$			10.7025i			0.339977i	0.985446	+	0.169989i	$0.0543731\pi$
$991$			10.7025i			0.339977i	−0.985446	+	0.169989i	$0.945627\pi$
$992$	−2.23211	+	17.0160i	−0.0708694	+	0.540260i
$993$	−21.7276	−	21.0000i	−0.689505	−	0.666416i
$994$	11.2165	+	55.4944i	0.355764	+	1.76018i
$995$	−0.634024	−	0.366054i	−0.0200999	−	0.0116047i
$996$	26.3068	+	34.9278i	0.833564	+	1.10673i
$997$	40.2843	−	23.2582i	1.27582	−	0.736594i	0.299741	−	0.954021i	$-0.403100\pi$
$997$	40.2843	−	23.2582i	1.27582	−	0.736594i	0.976077	+	0.217427i	$0.0697664\pi$
$998$	−10.4876	+	1.94478i	−0.331981	+	0.0615611i
$999$	0.889064	+	0.802580i	0.0281287	+	0.0253925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.139.12	yes	80
3.2	odd	2		756.2.bi.c.307.30		80
4.3	odd	2	inner	252.2.bi.c.139.37	yes	80
7.6	odd	2	inner	252.2.bi.c.139.11	✓	80
9.2	odd	6		756.2.bi.c.559.3		80
9.7	even	3	inner	252.2.bi.c.223.38	yes	80
12.11	even	2		756.2.bi.c.307.4		80
21.20	even	2		756.2.bi.c.307.29		80
28.27	even	2	inner	252.2.bi.c.139.38	yes	80
36.7	odd	6	inner	252.2.bi.c.223.11	yes	80
36.11	even	6		756.2.bi.c.559.29		80
63.20	even	6		756.2.bi.c.559.4		80
63.34	odd	6	inner	252.2.bi.c.223.37	yes	80
84.83	odd	2		756.2.bi.c.307.3		80
252.83	odd	6		756.2.bi.c.559.30		80
252.223	even	6	inner	252.2.bi.c.223.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.11	✓	80	7.6	odd	2	inner
252.2.bi.c.139.12	yes	80	1.1	even	1	trivial
252.2.bi.c.139.37	yes	80	4.3	odd	2	inner
252.2.bi.c.139.38	yes	80	28.27	even	2	inner
252.2.bi.c.223.11	yes	80	36.7	odd	6	inner
252.2.bi.c.223.12	yes	80	252.223	even	6	inner
252.2.bi.c.223.37	yes	80	63.34	odd	6	inner
252.2.bi.c.223.38	yes	80	9.7	even	3	inner
756.2.bi.c.307.3		80	84.83	odd	2
756.2.bi.c.307.4		80	12.11	even	2
756.2.bi.c.307.29		80	21.20	even	2
756.2.bi.c.307.30		80	3.2	odd	2
756.2.bi.c.559.3		80	9.2	odd	6
756.2.bi.c.559.4		80	63.20	even	6
756.2.bi.c.559.29		80	36.11	even	6
756.2.bi.c.559.30		80	252.83	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.07529 + 0.918559i) q^{2} +(0.476707 + 1.66516i) q^{3} +(0.312499 - 1.97544i) q^{4} +(-0.0753642 - 0.0435115i) q^{5} +(-2.04214 - 1.35264i) q^{6} +(2.31226 + 1.28587i) q^{7} +(1.47853 + 2.41122i) q^{8} +(-2.54550 + 1.58759i) q^{9} +O(q^{10})\)	\(q+(-1.07529 + 0.918559i) q^{2} +(0.476707 + 1.66516i) q^{3} +(0.312499 - 1.97544i) q^{4} +(-0.0753642 - 0.0435115i) q^{5} +(-2.04214 - 1.35264i) q^{6} +(2.31226 + 1.28587i) q^{7} +(1.47853 + 2.41122i) q^{8} +(-2.54550 + 1.58759i) q^{9} +(0.121006 - 0.0224389i) q^{10} +(-1.68051 + 0.970240i) q^{11} +(3.43838 - 0.421344i) q^{12} +(3.30872 + 1.91029i) q^{13} +(-3.66750 + 0.741269i) q^{14} +(0.0365269 - 0.146236i) q^{15} +(-3.80469 - 1.23464i) q^{16} +3.56266i q^{17} +(1.27886 - 4.04531i) q^{18} -0.00157027 q^{19} +(-0.109506 + 0.135280i) q^{20} +(-1.03890 + 4.46326i) q^{21} +(0.915809 - 2.58693i) q^{22} +(-3.54164 - 2.04477i) q^{23} +(-3.31023 + 3.61142i) q^{24} +(-2.49621 - 4.32357i) q^{25} +(-5.31255 + 0.985138i) q^{26} +(-3.85704 - 3.48185i) q^{27} +(3.26272 - 4.16589i) q^{28} +(1.71473 + 2.96999i) q^{29} +(0.0950489 + 0.190798i) q^{30} +(-1.51690 + 2.62736i) q^{31} +(5.22524 - 2.16723i) q^{32} +(-2.41671 - 2.33579i) q^{33} +(-3.27251 - 3.83089i) q^{34} +(-0.118312 - 0.197518i) q^{35} +(2.34071 + 5.52459i) q^{36} -0.230504 q^{37} +(0.00168850 - 0.00144239i) q^{38} +(-1.60364 + 6.42019i) q^{39} +(-0.00651223 - 0.246052i) q^{40} +(5.09104 + 2.93931i) q^{41} +(-2.98265 - 5.75359i) q^{42} +(7.75595 - 4.47790i) q^{43} +(1.39149 + 3.62293i) q^{44} +(0.260918 - 0.00888846i) q^{45} +(5.68653 - 1.05449i) q^{46} +(-1.45112 - 2.51342i) q^{47} +(0.242154 - 6.92397i) q^{48} +(3.69310 + 5.94651i) q^{49} +(6.65561 + 2.35617i) q^{50} +(-5.93238 + 1.69834i) q^{51} +(4.80763 - 5.93920i) q^{52} +7.09519 q^{53} +(7.34572 + 0.201079i) q^{54} +0.168867 q^{55} +(0.318240 + 7.47654i) q^{56} +(-0.000748561 - 0.00261475i) q^{57} +(-4.57195 - 1.61853i) q^{58} +(5.77529 - 10.0031i) q^{59} +(-0.277464 - 0.117855i) q^{60} +(-5.32949 + 3.07698i) q^{61} +(-0.782268 - 4.21854i) q^{62} +(-7.92728 + 0.397742i) q^{63} +(-3.62792 + 7.13009i) q^{64} +(-0.166239 - 0.287935i) q^{65} +(4.74422 + 0.291756i) q^{66} +(9.82677 + 5.67349i) q^{67} +(7.03780 + 1.11333i) q^{68} +(1.71654 - 6.87215i) q^{69} +(0.308652 + 0.103713i) q^{70} -15.1314i q^{71} +(-7.59160 - 3.79046i) q^{72} -16.6300i q^{73} +(0.247859 - 0.211732i) q^{74} +(6.00946 - 6.21767i) q^{75} +(-0.000490709 + 0.00310197i) q^{76} +(-5.13336 + 0.0825454i) q^{77} +(-4.17294 - 8.37662i) q^{78} +(4.29129 - 2.47758i) q^{79} +(0.233016 + 0.258596i) q^{80} +(3.95914 - 8.08240i) q^{81} +(-8.17427 + 1.51580i) q^{82} +(6.31136 + 10.9316i) q^{83} +(8.49223 + 3.44704i) q^{84} +(0.155017 - 0.268497i) q^{85} +(-4.22668 + 11.9393i) q^{86} +(-4.12809 + 4.27111i) q^{87} +(-4.82413 - 2.61754i) q^{88} -9.06131i q^{89} +(-0.272398 + 0.249226i) q^{90} +(5.19425 + 8.67166i) q^{91} +(-5.14607 + 6.35730i) q^{92} +(-5.09808 - 1.27341i) q^{93} +(3.86910 + 1.36971i) q^{94} +(0.000118342 + 6.83250e-5i) q^{95} +(6.09969 + 7.66771i) q^{96} +(-10.6191 + 6.13095i) q^{97} +(-9.43338 - 3.00190i) q^{98} +(2.73739 - 5.13769i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9}+O(q^{10}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44} + 24 q^{46} - 24 q^{49} - 12 q^{50} - 48 q^{53} + 32 q^{56} + 72 q^{57} - 14 q^{58} + 56 q^{60} - 8 q^{64} - 40 q^{65} - 22 q^{70} - 100 q^{72} + 64 q^{74} - 12 q^{77} - 24 q^{78} - 104 q^{81} + 62 q^{84} + 40 q^{85} - 52 q^{86} + 6 q^{88} + 30 q^{92} + 48 q^{93} + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

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