LMFDB - Embedded newform 228.2.v.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [228,2,Mod(23,228)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(228, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 2]))

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

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

chi := DirichletCharacter("228.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 228 = 2^{2} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	228.v (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.82058916609$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$36$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			23.2
Character	$\chi$	$=$	228.23
Dual form			228.2.v.a.119.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40660 - 0.146591i) q^{2} +(0.0483859 + 1.73137i) q^{3} +(1.95702 + 0.412388i) q^{4} +(2.52711 + 3.01169i) q^{5} +(0.185744 - 2.44244i) q^{6} +(1.60040 + 0.923992i) q^{7} +(-2.69229 - 0.866945i) q^{8} +(-2.99532 + 0.167548i) q^{9} +O(q^{10})$	\(q+(-1.40660 - 0.146591i) q^{2} +(0.0483859 + 1.73137i) q^{3} +(1.95702 + 0.412388i) q^{4} +(2.52711 + 3.01169i) q^{5} +(0.185744 - 2.44244i) q^{6} +(1.60040 + 0.923992i) q^{7} +(-2.69229 - 0.866945i) q^{8} +(-2.99532 + 0.167548i) q^{9} +(-3.11313 - 4.60668i) q^{10} +(-0.408467 - 0.707485i) q^{11} +(-0.619306 + 3.40829i) q^{12} +(0.986301 - 5.59359i) q^{13} +(-2.11567 - 1.53429i) q^{14} +(-5.09208 + 4.52109i) q^{15} +(3.65987 + 1.61411i) q^{16} +(-0.175324 + 0.481699i) q^{17} +(4.23776 + 0.203414i) q^{18} +(-0.444555 + 4.33617i) q^{19} +(3.70362 + 6.93609i) q^{20} +(-1.52234 + 2.81560i) q^{21} +(0.470837 + 1.05502i) q^{22} +(-1.99250 - 1.67190i) q^{23} +(1.37074 - 4.70330i) q^{24} +(-1.81576 + 10.2977i) q^{25} +(-2.20730 + 7.72334i) q^{26} +(-0.435020 - 5.17791i) q^{27} +(2.75098 + 2.46826i) q^{28} +(-2.32390 - 6.38485i) q^{29} +(7.82525 - 5.61289i) q^{30} +(6.46502 + 3.73258i) q^{31} +(-4.91135 - 2.80690i) q^{32} +(1.20516 - 0.741442i) q^{33} +(0.317222 - 0.651854i) q^{34} +(1.26161 + 7.15494i) q^{35} +(-5.93100 - 0.907338i) q^{36} -3.47952 q^{37} +(1.26095 - 6.03407i) q^{38} +(9.73233 + 1.43701i) q^{39} +(-4.19272 - 10.2992i) q^{40} +(4.77942 - 0.842740i) q^{41} +(2.55406 - 3.73725i) q^{42} +(-4.25838 - 5.07495i) q^{43} +(-0.507620 - 1.55301i) q^{44} +(-8.07409 - 8.59755i) q^{45} +(2.55755 + 2.64378i) q^{46} +(4.34889 - 1.58287i) q^{47} +(-2.61754 + 6.41471i) q^{48} +(-1.79248 - 3.10466i) q^{49} +(4.06358 - 14.2185i) q^{50} +(-0.842484 - 0.280244i) q^{51} +(4.23695 - 10.5400i) q^{52} +(-4.78294 + 5.70009i) q^{53} +(-0.147137 + 7.34700i) q^{54} +(1.09849 - 3.01806i) q^{55} +(-3.50769 - 3.87511i) q^{56} +(-7.52905 - 0.559881i) q^{57} +(2.33282 + 9.32157i) q^{58} +(3.44431 + 1.25363i) q^{59} +(-11.8298 + 6.74796i) q^{60} +(5.68183 + 4.76762i) q^{61} +(-8.54651 - 6.19795i) q^{62} +(-4.94852 - 2.49951i) q^{63} +(6.49681 + 4.66813i) q^{64} +(19.3386 - 11.1652i) q^{65} +(-1.80386 + 0.866243i) q^{66} +(-2.82204 - 7.75348i) q^{67} +(-0.541760 + 0.870393i) q^{68} +(2.79828 - 3.53066i) q^{69} +(-0.725724 - 10.2490i) q^{70} +(-3.25296 + 2.72956i) q^{71} +(8.20951 + 2.14569i) q^{72} +(-0.252680 - 1.43302i) q^{73} +(4.89428 + 0.510067i) q^{74} +(-17.9170 - 2.64549i) q^{75} +(-2.65819 + 8.30265i) q^{76} -1.50968i q^{77} +(-13.4788 - 3.44796i) q^{78} +(-1.10397 + 0.194660i) q^{79} +(4.38770 + 15.1014i) q^{80} +(8.94386 - 1.00372i) q^{81} +(-6.84624 + 0.484775i) q^{82} +(5.35043 - 9.26722i) q^{83} +(-4.14038 + 4.88240i) q^{84} +(-1.89379 + 0.689282i) q^{85} +(5.24588 + 7.76264i) q^{86} +(10.9421 - 4.33247i) q^{87} +(0.486359 + 2.25887i) q^{88} +(8.32500 + 1.46792i) q^{89} +(10.0967 + 13.2769i) q^{90} +(6.74692 - 8.04066i) q^{91} +(-3.20989 - 4.09364i) q^{92} +(-6.14968 + 11.3740i) q^{93} +(-6.34916 + 1.58895i) q^{94} +(-14.1826 + 9.61910i) q^{95} +(4.62215 - 8.63920i) q^{96} +(4.79715 + 1.74602i) q^{97} +(2.06617 + 4.62976i) q^{98} +(1.34203 + 2.05071i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	$ 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) $ 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/228\mathbb{Z}\right)^\times$.

$n$	$77$	$97$	$115$
$\chi(n)$	$-1$	$e\left(\frac{1}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.40660	−	0.146591i	−0.994613	−	0.103655i
$2$	−1.40660	−	0.146591i	−0.994613	−	0.103655i
$3$	0.0483859	+	1.73137i	0.0279356	+	0.999610i
$3$	0.0483859	+	1.73137i	0.0279356	+	0.999610i
$4$	1.95702	+	0.412388i	0.978511	+	0.206194i
$5$	2.52711	+	3.01169i	1.13016	+	1.34687i	0.930196	+	0.367063i	$0.119637\pi$
$5$	2.52711	+	3.01169i	1.13016	+	1.34687i	0.199960	+	0.979804i	$0.435919\pi$
$6$	0.185744	−	2.44244i	0.0758298	−	0.997121i
$7$	1.60040	+	0.923992i	0.604895	+	0.349236i	0.770965	−	0.636878i	$-0.219774\pi$
$7$	1.60040	+	0.923992i	0.604895	+	0.349236i	−0.166070	+	0.986114i	$0.553108\pi$
$8$	−2.69229	−	0.866945i	−0.951867	−	0.306511i
$9$	−2.99532	+	0.167548i	−0.998439	+	0.0558495i
$10$	−3.11313	−	4.60668i	−0.984458	−	1.45676i
$11$	−0.408467	−	0.707485i	−0.123157	−	0.213315i	0.797854	−	0.602851i	$-0.205969\pi$
$11$	−0.408467	−	0.707485i	−0.123157	−	0.213315i	−0.921011	+	0.389536i	$0.872635\pi$
$12$	−0.619306	+	3.40829i	−0.178778	+	0.983889i
$13$	0.986301	−	5.59359i	0.273551	−	1.55138i	−0.469977	−	0.882679i	$-0.655738\pi$
$13$	0.986301	−	5.59359i	0.273551	−	1.55138i	0.743528	−	0.668705i	$-0.233151\pi$
$14$	−2.11567	−	1.53429i	−0.565436	−	0.410056i
$15$	−5.09208	+	4.52109i	−1.31477	+	1.16734i
$16$	3.65987	+	1.61411i	0.914968	+	0.403527i
$17$	−0.175324	+	0.481699i	−0.0425223	+	0.116829i	−0.959136	−	0.282944i	$-0.908689\pi$
$17$	−0.175324	+	0.481699i	−0.0425223	+	0.116829i	0.916614	+	0.399773i	$0.130911\pi$
$18$	4.23776	+	0.203414i	0.998850	+	0.0479450i
$19$	−0.444555	+	4.33617i	−0.101988	+	0.994786i
$19$	−0.444555	+	4.33617i	−0.101988	+	0.994786i
$20$	3.70362	+	6.93609i	0.828154	+	1.55096i
$21$	−1.52234	+	2.81560i	−0.332202	+	0.614415i
$22$	0.470837	+	1.05502i	0.100383	+	0.224932i
$23$	−1.99250	−	1.67190i	−0.415464	−	0.348616i	0.410970	−	0.911649i	$-0.365190\pi$
$23$	−1.99250	−	1.67190i	−0.415464	−	0.348616i	−0.826435	+	0.563033i	$0.809634\pi$
$24$	1.37074	−	4.70330i	0.279801	−	0.960058i
$25$	−1.81576	+	10.2977i	−0.363151	+	2.05953i
$26$	−2.20730	+	7.72334i	−0.432887	+	1.51467i
$27$	−0.435020	−	5.17791i	−0.0837197	−	0.996489i
$28$	2.75098	+	2.46826i	0.519886	+	0.466457i
$29$	−2.32390	−	6.38485i	−0.431537	−	1.18564i	−0.944869	−	0.327448i	$-0.893811\pi$
$29$	−2.32390	−	6.38485i	−0.431537	−	1.18564i	0.513332	−	0.858190i	$-0.328411\pi$
$30$	7.82525	−	5.61289i	1.42869	−	1.02477i
$31$	6.46502	+	3.73258i	1.16115	+	0.670392i	0.951580	−	0.307402i	$-0.0994595\pi$
$31$	6.46502	+	3.73258i	1.16115	+	0.670392i	0.209572	+	0.977793i	$0.432793\pi$
$32$	−4.91135	−	2.80690i	−0.868212	−	0.496194i
$33$	1.20516	−	0.741442i	0.209791	−	0.129068i
$34$	0.317222	−	0.651854i	0.0544032	−	0.111792i
$35$	1.26161	+	7.15494i	0.213251	+	1.20940i
$36$	−5.93100	−	0.907338i	−0.988500	−	0.151223i
$37$	−3.47952			−0.572030			−0.286015	−	0.958225i	$-0.592331\pi$
$37$	−3.47952			−0.572030			−0.286015	+	0.958225i	$0.592331\pi$
$38$	1.26095	−	6.03407i	0.204553	−	0.978855i
$39$	9.73233	+	1.43701i	1.55842	+	0.230105i
$40$	−4.19272	−	10.2992i	−0.662928	−	1.62844i
$41$	4.77942	−	0.842740i	0.746419	−	0.131614i	0.212514	−	0.977158i	$-0.431835\pi$
$41$	4.77942	−	0.842740i	0.746419	−	0.131614i	0.533905	+	0.845544i	$0.320724\pi$
$42$	2.55406	−	3.73725i	0.394100	−	0.576671i
$43$	−4.25838	−	5.07495i	−0.649398	−	0.773922i	0.336426	−	0.941710i	$-0.390782\pi$
$43$	−4.25838	−	5.07495i	−0.649398	−	0.773922i	−0.985823	+	0.167788i	$0.946338\pi$
$44$	−0.507620	−	1.55301i	−0.0765266	−	0.234125i
$45$	−8.07409	−	8.59755i	−1.20361	−	1.28165i
$46$	2.55755	+	2.64378i	0.377091	+	0.389803i
$47$	4.34889	−	1.58287i	0.634351	−	0.230885i	−0.00477306	−	0.999989i	$-0.501519\pi$
$47$	4.34889	−	1.58287i	0.634351	−	0.230885i	0.639124	+	0.769104i	$0.279297\pi$
$48$	−2.61754	+	6.41471i	−0.377809	+	0.925884i
$49$	−1.79248	−	3.10466i	−0.256068	−	0.443523i
$50$	4.06358	−	14.2185i	0.574677	−	2.01080i
$51$	−0.842484	−	0.280244i	−0.117971	−	0.0392420i
$52$	4.23695	−	10.5400i	0.587559	−	1.46164i
$53$	−4.78294	+	5.70009i	−0.656987	+	0.782967i	−0.986950	−	0.161027i	$-0.948519\pi$
$53$	−4.78294	+	5.70009i	−0.656987	+	0.782967i	0.329963	+	0.943994i	$0.392964\pi$
$54$	−0.147137	+	7.34700i	−0.0200228	+	0.999800i
$55$	1.09849	−	3.01806i	0.148120	−	0.406956i
$56$	−3.50769	−	3.87511i	−0.468735	−	0.517834i
$57$	−7.52905	−	0.559881i	−0.997247	−	0.0741580i
$58$	2.33282	+	9.32157i	0.306314	+	1.22398i
$59$	3.44431	+	1.25363i	0.448411	+	0.163208i	0.556348	−	0.830950i	$-0.312202\pi$
$59$	3.44431	+	1.25363i	0.448411	+	0.163208i	−0.107937	+	0.994158i	$0.534424\pi$
$60$	−11.8298	+	6.74796i	−1.52722	+	0.871158i
$61$	5.68183	+	4.76762i	0.727484	+	0.610431i	0.929444	−	0.368962i	$-0.120287\pi$
$61$	5.68183	+	4.76762i	0.727484	+	0.610431i	−0.201961	+	0.979394i	$0.564731\pi$
$62$	−8.54651	−	6.19795i	−1.08541	−	0.787140i
$63$	−4.94852	−	2.49951i	−0.623456	−	0.314908i
$64$	6.49681	+	4.66813i	0.812102	+	0.583516i
$65$	19.3386	−	11.1652i	2.39866	−	1.38487i
$66$	−1.80386	+	0.866243i	−0.222040	+	0.106627i
$67$	−2.82204	−	7.75348i	−0.344767	−	0.947238i	−0.983991	−	0.178218i	$-0.942967\pi$
$67$	−2.82204	−	7.75348i	−0.344767	−	0.947238i	0.639225	−	0.769020i	$-0.279255\pi$
$68$	−0.541760	+	0.870393i	−0.0656980	+	0.105551i
$69$	2.79828	−	3.53066i	0.336874	−	0.425041i
$70$	−0.725724	−	10.2490i	−0.0867406	−	1.22499i
$71$	−3.25296	+	2.72956i	−0.386055	+	0.323939i	−0.815074	−	0.579357i	$-0.803304\pi$
$71$	−3.25296	+	2.72956i	−0.386055	+	0.323939i	0.429019	+	0.903296i	$0.358859\pi$
$72$	8.20951	+	2.14569i	0.967500	+	0.252872i
$73$	−0.252680	−	1.43302i	−0.0295739	−	0.167722i	0.966444	−	0.256878i	$-0.0826940\pi$
$73$	−0.252680	−	1.43302i	−0.0295739	−	0.167722i	−0.996018	+	0.0891565i	$0.971583\pi$
$74$	4.89428	+	0.510067i	0.568949	+	0.0592940i
$75$	−17.9170	−	2.64549i	−2.06887	−	0.305475i
$76$	−2.65819	+	8.30265i	−0.304915	+	0.952380i
$77$		−	1.50968i		−	0.172044i
$78$	−13.4788	−	3.44796i	−1.52617	−	0.390404i
$79$	−1.10397	+	0.194660i	−0.124207	+	0.0219010i	−0.235406	−	0.971897i	$-0.575642\pi$
$79$	−1.10397	+	0.194660i	−0.124207	+	0.0219010i	0.111199	+	0.993798i	$0.464531\pi$
$80$	4.38770	+	15.1014i	0.490560	+	1.68839i
$81$	8.94386	−	1.00372i	0.993762	−	0.111525i
$82$	−6.84624	+	0.484775i	−0.756041	+	0.0535345i
$83$	5.35043	−	9.26722i	0.587286	−	1.01721i	−0.407300	−	0.913295i	$-0.633530\pi$
$83$	5.35043	−	9.26722i	0.587286	−	1.01721i	0.994586	−	0.103915i	$-0.0331371\pi$
$84$	−4.14038	+	4.88240i	−0.451752	+	0.532714i
$85$	−1.89379	+	0.689282i	−0.205410	+	0.0747632i
$86$	5.24588	+	7.76264i	0.565678	+	0.837067i
$87$	10.9421	−	4.33247i	1.17312	−	0.464490i
$88$	0.486359	+	2.25887i	0.0518460	+	0.240797i
$89$	8.32500	+	1.46792i	0.882449	+	0.155600i	0.596469	−	0.802636i	$-0.296570\pi$
$89$	8.32500	+	1.46792i	0.882449	+	0.155600i	0.285980	+	0.958236i	$0.407681\pi$
$90$	10.0967	+	13.2769i	1.06428	+	1.39950i
$91$	6.74692	−	8.04066i	0.707269	−	0.842890i
$92$	−3.20989	−	4.09364i	−0.334654	−	0.426791i
$93$	−6.14968	+	11.3740i	−0.637692	+	1.17943i
$94$	−6.34916	+	1.58895i	−0.654866	+	0.163887i
$95$	−14.1826	+	9.61910i	−1.45511	+	0.986899i
$96$	4.62215	−	8.63920i	0.471747	−	0.881734i
$97$	4.79715	+	1.74602i	0.487076	+	0.177281i	0.573872	−	0.818945i	$-0.305441\pi$
$97$	4.79715	+	1.74602i	0.487076	+	0.177281i	−0.0867959	+	0.996226i	$0.527663\pi$
$98$	2.06617	+	4.62976i	0.208715	+	0.467677i
$99$	1.34203	+	2.05071i	0.134879	+	0.206104i
$100$	−7.80011	+	19.4040i	−0.780011	+	1.94040i
$101$	6.89433	+	1.21566i	0.686011	+	0.120962i	0.505781	−	0.862662i	$-0.331205\pi$
$101$	6.89433	+	1.21566i	0.686011	+	0.120962i	0.180231	+	0.983624i	$0.442316\pi$
$102$	1.14395	+	0.517690i	0.113268	+	0.0512590i
$103$	−12.2928	+	7.09723i	−1.21124	+	0.699311i	−0.963030	−	0.269395i	$-0.913176\pi$
$103$	−12.2928	+	7.09723i	−1.21124	+	0.699311i	−0.248212	+	0.968706i	$0.579843\pi$
$104$	−7.50475	+	14.2045i	−0.735901	+	1.39286i
$105$	−12.3268	+	2.53051i	−1.20298	+	0.246953i
$106$	7.56324	−	7.31658i	0.734607	−	0.710649i
$107$	3.69987	−	6.40836i	0.357680	−	0.619520i	−0.629893	−	0.776682i	$-0.716901\pi$
$107$	3.69987	−	6.40836i	0.357680	−	0.619520i	0.987573	+	0.157162i	$0.0502346\pi$
$108$	1.28397	−	10.3127i	0.123550	−	0.992338i
$109$	−2.64734	+	2.22138i	−0.253569	+	0.212769i	−0.760707	−	0.649095i	$-0.775148\pi$
$109$	−2.64734	+	2.22138i	−0.253569	+	0.212769i	0.507139	+	0.861865i	$0.330703\pi$
$110$	−1.98755	+	4.08417i	−0.189505	+	0.389410i
$111$	−0.168360	−	6.02436i	−0.0159800	−	0.571807i
$112$	4.36584	+	5.96491i	0.412533	+	0.563631i
$113$			2.18899i			0.205923i	0.994685	+	0.102961i	$0.0328318\pi$
$113$			2.18899i			0.205923i	−0.994685	+	0.102961i	$0.967168\pi$
$114$	10.5082	+	1.89122i	0.984188	+	0.177129i
$115$		−	10.2259i		−	0.953566i
$116$	−1.91488	−	13.4537i	−0.177792	−	1.24914i
$117$	−2.01709	+	16.9198i	−0.186480	+	1.56424i
$118$	−4.66098	−	2.26825i	−0.429078	−	0.208809i
$119$	−0.725674	+	0.608913i	−0.0665225	+	0.0558190i
$120$	17.6289	−	7.75751i	1.60929	−	0.708161i
$121$	5.16631	−	8.94831i	0.469665	−	0.813483i
$122$	−7.29315	−	7.53902i	−0.660290	−	0.682551i
$123$	1.69036	+	8.23418i	0.152414	+	0.742451i
$124$	11.1129	+	9.97085i	0.997970	+	0.895408i
$125$	−18.5781	+	10.7261i	−1.66168	+	0.959371i
$126$	6.59417	+	4.24120i	0.587455	+	0.377836i
$127$	13.6507	+	2.40698i	1.21130	+	0.213585i	0.742577	−	0.669760i	$-0.233603\pi$
$127$	13.6507	+	2.40698i	1.21130	+	0.213585i	0.468723	+	0.883345i	$0.344714\pi$
$128$	−8.45408	−	7.51854i	−0.747242	−	0.664552i
$129$	8.58059	−	7.61842i	0.755478	−	0.670764i
$130$	−28.8384	+	12.8700i	−2.52929	+	1.12877i
$131$	6.47249	+	2.35579i	0.565504	+	0.205826i	0.608921	−	0.793231i	$-0.291602\pi$
$131$	6.47249	+	2.35579i	0.565504	+	0.205826i	−0.0434178	+	0.999057i	$0.513825\pi$
$132$	2.66428	−	0.954024i	0.231896	−	0.0830372i
$133$	−4.71805	+	6.52885i	−0.409107	+	0.566123i
$134$	2.83287	+	11.3197i	0.244723	+	0.977873i
$135$	14.4949	−	14.3953i	1.24752	−	1.23895i
$136$	0.889628	−	1.14487i	0.0762850	−	0.0981722i
$137$	−3.41574	+	4.07072i	−0.291826	+	0.347785i	−0.891960	−	0.452115i	$-0.850670\pi$
$137$	−3.41574	+	4.07072i	−0.291826	+	0.347785i	0.600134	+	0.799900i	$0.295114\pi$
$138$	−4.45362	+	4.55600i	−0.379117	+	0.387833i
$139$	−5.51638	−	0.972686i	−0.467893	−	0.0825022i	−0.0652692	−	0.997868i	$-0.520791\pi$
$139$	−5.51638	−	0.972686i	−0.467893	−	0.0825022i	−0.402624	+	0.915366i	$0.631902\pi$
$140$	−0.481616	+	14.5226i	−0.0407040	+	1.22739i
$141$	2.95096	+	7.45297i	0.248516	+	0.627653i
$142$	4.97573	−	3.36253i	0.417554	−	0.282177i
$143$	−4.36026	+	1.58700i	−0.364623	+	0.132712i
$144$	−11.2329	−	4.22155i	−0.936077	−	0.351796i
$145$	13.3565	−	23.1341i	1.10919	−	1.92118i
$146$	0.145351	+	2.05272i	0.0120293	+	0.169884i
$147$	5.28860	−	3.25367i	0.436196	−	0.268358i
$148$	−6.80951	−	1.43492i	−0.559738	−	0.117949i
$149$	−2.84582	+	0.501794i	−0.233138	+	0.0411086i	−0.288997	−	0.957330i	$-0.593322\pi$
$149$	−2.84582	+	0.501794i	−0.233138	+	0.0411086i	0.0558582	+	0.998439i	$0.482211\pi$
$150$	24.8141	+	6.34760i	2.02607	+	0.518280i
$151$			3.31156i			0.269491i	0.990880	+	0.134746i	$0.0430217\pi$
$151$			3.31156i			0.269491i	−0.990880	+	0.134746i	$0.956978\pi$
$152$	4.95609	−	11.2888i	0.401992	−	0.915643i
$153$	0.444443	−	1.47222i	0.0359311	−	0.119022i
$154$	−0.221306	+	2.12351i	−0.0178333	+	0.171117i
$155$	5.09642	+	28.9033i	0.409355	+	2.32156i
$156$	18.4538	+	6.82575i	1.47748	+	0.546498i
$157$	8.21209	−	6.89076i	0.655396	−	0.549942i	−0.253307	−	0.967386i	$-0.581518\pi$
$157$	8.21209	−	6.89076i	0.655396	−	0.549942i	0.908703	+	0.417444i	$0.137074\pi$
$158$	1.58138	−	0.111976i	0.125808	−	0.00890830i
$159$	−10.1004	−	8.00526i	−0.801015	−	0.634858i
$160$	−3.95799	−	21.8848i	−0.312907	−	1.73014i
$161$	−1.64397	−	4.51677i	−0.129563	−	0.355971i
$162$	−12.7275	+	0.100742i	−0.999969	+	0.00791504i
$163$	−9.60165	+	5.54352i	−0.752059	+	0.434202i	−0.826438	−	0.563028i	$-0.809636\pi$
$163$	−9.60165	+	5.54352i	−0.752059	+	0.434202i	0.0743781	+	0.997230i	$0.476303\pi$
$164$	9.70096	+	0.321714i	0.757518	+	0.0251217i
$165$	5.27855	+	1.75586i	0.410935	+	0.136693i
$166$	−8.88439	+	12.2509i	−0.689562	+	0.950855i
$167$	−15.7324	−	13.2011i	−1.21741	−	1.02153i	−0.998956	−	0.0456823i	$-0.985454\pi$
$167$	−15.7324	−	13.2011i	−1.21741	−	1.02153i	−0.218455	−	0.975847i	$-0.570102\pi$
$168$	6.53955	−	6.26063i	0.504537	−	0.483018i
$169$	−18.0995	−	6.58768i	−1.39227	−	0.506744i
$170$	2.76484	−	0.691929i	0.212053	−	0.0530686i
$171$	0.605064	−	13.0627i	0.0462704	−	0.998929i
$172$	−6.24091	−	11.6879i	−0.475865	−	0.891193i
$173$	−1.92424	+	5.28679i	−0.146297	+	0.401948i	−0.991098	−	0.133133i	$-0.957496\pi$
$173$	−1.92424	+	5.28679i	−0.146297	+	0.401948i	0.844801	+	0.535080i	$0.179719\pi$
$174$	−16.0263	+	4.49002i	−1.21495	+	0.340388i
$175$	−12.4209	+	14.8027i	−0.938932	+	1.11898i
$176$	−0.352980	−	3.24861i	−0.0266069	−	0.244874i
$177$	−2.00384	+	6.02405i	−0.150618	+	0.452795i
$178$	−11.4947	−	3.28514i	−0.861566	−	0.246232i
$179$	−11.4019	−	19.7487i	−0.852219	−	1.47609i	−0.879202	−	0.476450i	$-0.841923\pi$
$179$	−11.4019	−	19.7487i	−0.852219	−	1.47609i	0.0269830	−	0.999636i	$-0.491410\pi$
$180$	−12.2556	−	20.1552i	−0.913481	−	1.50228i
$181$	−16.4902	+	6.00196i	−1.22571	+	0.446122i	−0.872126	−	0.489281i	$-0.837259\pi$
$181$	−16.4902	+	6.00196i	−1.22571	+	0.446122i	−0.353584	+	0.935403i	$0.615037\pi$
$182$	−10.6689	+	10.3209i	−0.790829	+	0.765038i
$183$	−7.97962	+	10.0681i	−0.589870	+	0.744253i
$184$	3.91493	+	6.22863i	0.288612	+	0.459181i
$185$	−8.79313	−	10.4792i	−0.646483	−	0.770449i
$186$	10.3174	−	15.0971i	0.756511	−	1.10697i
$187$	0.412409	−	0.0727188i	0.0301583	−	0.00531772i
$188$	9.16363	−	1.30427i	0.668326	−	0.0951239i
$189$	4.08814	−	8.68869i	0.297369	−	0.632009i
$190$	21.3593	−	11.4511i	1.54957	−	0.830753i
$191$	14.7243			1.06541			0.532707	−	0.846300i	$-0.321175\pi$
$191$	14.7243			1.06541			0.532707	+	0.846300i	$0.321175\pi$
$192$	−7.76793	+	11.4743i	−0.560602	+	0.828085i
$193$	−0.731757	−	4.15000i	−0.0526730	−	0.298724i	0.947079	−	0.321001i	$-0.104019\pi$
$193$	−0.731757	−	4.15000i	−0.0526730	−	0.298724i	−0.999752	+	0.0222775i	$0.992908\pi$
$194$	−6.49169	−	3.15916i	−0.466076	−	0.226814i
$195$	20.2668	+	32.9422i	1.45134	+	2.35904i
$196$	−2.22759	−	6.81508i	−0.159114	−	0.486792i
$197$	3.50625	+	2.02433i	0.249810	+	0.144228i	0.619677	−	0.784857i	$-0.287264\pi$
$197$	3.50625	+	2.02433i	0.249810	+	0.144228i	−0.369867	+	0.929085i	$0.620597\pi$
$198$	−1.58707	−	3.08124i	−0.112788	−	0.218974i
$199$	−5.28054	−	14.5082i	−0.374328	−	1.02846i	−0.973670	−	0.227964i	$-0.926793\pi$
$199$	−5.28054	−	14.5082i	−0.374328	−	1.02846i	0.599342	−	0.800493i	$-0.295429\pi$
$200$	13.8160	−	26.1501i	0.976942	−	1.84909i
$201$	13.2876	−	5.26116i	0.937237	−	0.371094i
$202$	−9.51933	−	2.72058i	−0.669777	−	0.191419i
$203$	2.18039	−	12.3656i	0.153033	−	0.867895i
$204$	−1.53319	−	0.895874i	−0.107345	−	0.0627237i
$205$	14.6162	+	12.2644i	1.02084	+	0.856584i
$206$	18.3313	−	8.18093i	1.27720	−	0.569992i
$207$	6.24829	+	4.67404i	0.434286	+	0.324869i
$208$	12.6384	−	18.8798i	0.876315	−	1.30908i
$209$	3.24936	−	1.45667i	0.224763	−	0.100760i
$210$	17.7098	−	1.75241i	1.22209	−	0.120928i
$211$	−8.50175	+	23.3584i	−0.585285	+	1.60806i	0.193733	+	0.981054i	$0.437940\pi$
$211$	−8.50175	+	23.3584i	−0.585285	+	1.60806i	−0.779018	+	0.627002i	$0.784282\pi$
$212$	−11.7110	+	9.18277i	−0.804313	+	0.630675i
$213$	−4.88329	−	5.50002i	−0.334597	−	0.376855i
$214$	−6.14363	+	8.47160i	−0.419970	+	0.579107i
$215$	4.52276	−	25.6498i	0.308450	−	1.74930i
$216$	−3.31777	+	14.3176i	−0.225745	+	0.974186i
$217$	6.89775	+	11.9473i	0.468250	+	0.811033i
$218$	4.04936	−	2.73651i	0.274258	−	0.185340i
$219$	2.46886	−	0.506821i	0.166830	−	0.0342478i
$220$	3.39438	−	5.45342i	0.228849	−	0.367669i
$221$	2.52150	+	1.45579i	0.169615	+	0.0979271i
$222$	−0.646302	+	8.49852i	−0.0433770	+	0.570383i
$223$	5.63487	+	6.71538i	0.377339	+	0.449695i	0.920972	−	0.389628i	$-0.127396\pi$
$223$	5.63487	+	6.71538i	0.377339	+	0.449695i	−0.543634	+	0.839323i	$0.682952\pi$
$224$	−5.26657	−	9.03021i	−0.351888	−	0.603356i
$225$	3.71341	−	31.1490i	0.247561	−	2.07660i
$226$	0.320886	−	3.07902i	0.0213450	−	0.204813i
$227$	−10.4925			−0.696415			−0.348207	−	0.937418i	$-0.613209\pi$
$227$	−10.4925			−0.696415			−0.348207	+	0.937418i	$0.613209\pi$
$228$	−14.5036	−	4.20059i	−0.960526	−	0.278191i
$229$	−11.3656			−0.751060			−0.375530	−	0.926810i	$-0.622539\pi$
$229$	−11.3656			−0.751060			−0.375530	+	0.926810i	$0.622539\pi$
$230$	−1.49902	+	14.3836i	−0.0988423	+	0.948430i
$231$	2.61382	−	0.0730473i	0.171977	−	0.00480616i
$232$	0.721277	+	19.2045i	0.0473542	+	1.26084i
$233$	−11.5311	−	13.7422i	−0.755428	−	0.900284i	0.242122	−	0.970246i	$-0.422157\pi$
$233$	−11.5311	−	13.7422i	−0.755428	−	0.900284i	−0.997550	+	0.0699619i	$0.977712\pi$
$234$	5.31752	−	23.5037i	0.347617	−	1.53648i
$235$	15.7572	+	9.09743i	1.02789	+	0.593451i
$236$	6.22361	+	3.87377i	0.405122	+	0.252161i
$237$	−0.390446	−	1.90197i	−0.0253622	−	0.123546i
$238$	1.10999	−	0.750117i	0.0719501	−	0.0486229i
$239$	12.1523	+	21.0485i	0.786070	+	1.36151i	0.928358	+	0.371688i	$0.121221\pi$
$239$	12.1523	+	21.0485i	0.786070	+	1.36151i	−0.142288	+	0.989825i	$0.545446\pi$
$240$	−25.9339	+	8.32745i	−1.67403	+	0.537535i
$241$	−2.79534	+	15.8532i	−0.180064	+	1.02119i	0.752071	+	0.659082i	$0.229055\pi$
$241$	−2.79534	+	15.8532i	−0.180064	+	1.02119i	−0.932135	+	0.362111i	$0.882056\pi$
$242$	−8.57865	+	11.8293i	−0.551456	+	0.760418i
$243$	2.17057	+	15.4366i	0.139242	+	0.990258i
$244$	9.15335	+	11.6735i	0.585983	+	0.747317i
$245$	4.82049	−	13.2442i	0.307970	−	0.846140i
$246$	−1.17059	−	11.8300i	−0.0746341	−	0.754250i
$247$	23.8163	+	6.76343i	1.51540	+	0.430347i
$248$	−14.1697	−	15.6540i	−0.899780	−	0.994030i
$249$	16.3039	+	8.81520i	1.03322	+	0.558641i
$250$	27.7043	−	12.3639i	1.75217	−	0.781961i
$251$	7.18164	+	6.02611i	0.453301	+	0.380365i	0.840659	−	0.541565i	$-0.182168\pi$
$251$	7.18164	+	6.02611i	0.453301	+	0.380365i	−0.387358	+	0.921929i	$0.626612\pi$
$252$	−8.65361	−	6.93230i	−0.545126	−	0.436694i
$253$	−0.368978	+	2.09258i	−0.0231975	+	0.131559i
$254$	−18.8481	−	5.38671i	−1.18264	−	0.337992i
$255$	−1.28504	−	3.24550i	−0.0804722	−	0.203241i
$256$	10.7893	+	11.8148i	0.674333	+	0.738428i
$257$	5.52550	+	15.1812i	0.344671	+	0.946976i	0.984020	+	0.178059i	$0.0569819\pi$
$257$	5.52550	+	15.1812i	0.344671	+	0.946976i	−0.639349	+	0.768917i	$0.720796\pi$
$258$	−13.1862	+	9.45819i	−0.820937	+	0.588841i
$259$	−5.56864	−	3.21505i	−0.346018	−	0.199774i
$260$	42.4505	−	13.8755i	2.63267	−	0.860519i
$261$	8.03058	+	18.7353i	0.497081	+	1.15969i
$262$	−8.75883	−	4.26245i	−0.541122	−	0.263335i
$263$	1.95883	+	11.1091i	0.120787	+	0.685016i	0.983721	+	0.179700i	$0.0575128\pi$
$263$	1.95883	+	11.1091i	0.120787	+	0.685016i	−0.862935	+	0.505316i	$0.831376\pi$
$264$	−3.88742	+	0.951367i	−0.239254	+	0.0585526i
$265$	−29.2539			−1.79705
$266$	7.59346	−	8.49183i	0.465585	−	0.520667i
$267$	−2.13871	+	14.4847i	−0.130887	+	0.886451i
$268$	−2.32534	−	16.3375i	−0.142043	−	0.997972i
$269$	−31.6617	+	5.58281i	−1.93045	+	0.340390i	−0.999682	−	0.0252273i	$-0.991969\pi$
$269$	−31.6617	+	5.58281i	−1.93045	+	0.340390i	−0.930765	+	0.365617i	$0.880858\pi$
$270$	−22.4987	+	18.1235i	−1.36923	+	1.10296i
$271$	−11.1445	−	13.2815i	−0.676978	−	0.806791i	0.312738	−	0.949840i	$-0.398754\pi$
$271$	−11.1445	−	13.2815i	−0.676978	−	0.806791i	−0.989716	+	0.143049i	$0.954309\pi$
$272$	−1.41918	+	1.47996i	−0.0860502	+	0.0897360i
$273$	14.2479	+	11.2924i	0.862319	+	0.683446i
$274$	5.40129	−	5.22514i	0.326304	−	0.315662i
$275$	8.02712	−	2.92163i	0.484054	−	0.176181i
$276$	6.93231	−	5.75559i	0.417276	−	0.346446i
$277$	−7.66188	−	13.2708i	−0.460358	−	0.797363i	0.538621	−	0.842548i	$-0.318946\pi$
$277$	−7.66188	−	13.2708i	−0.460358	−	0.797363i	−0.998979	+	0.0451851i	$0.985612\pi$
$278$	7.61673	+	2.17683i	0.456821	+	0.130557i
$279$	−19.9902	−	10.0971i	−1.19678	−	0.604495i
$280$	2.80633	−	20.3569i	0.167710	−	1.21656i
$281$	8.39113	−	10.0002i	0.500573	−	0.596560i	−0.455301	−	0.890338i	$-0.650468\pi$
$281$	8.39113	−	10.0002i	0.500573	−	0.596560i	0.955874	+	0.293778i	$0.0949127\pi$
$282$	−3.05827	−	10.9159i	−0.182117	−	0.650032i
$283$	2.99418	−	8.22644i	0.177986	−	0.489011i	−0.818333	−	0.574745i	$-0.805101\pi$
$283$	2.99418	−	8.22644i	0.177986	−	0.489011i	0.996318	+	0.0857338i	$0.0273235\pi$
$284$	−7.49175	+	4.00032i	−0.444554	+	0.237375i
$285$	−17.3405	−	24.0900i	−1.02716	−	1.42697i
$286$	6.36576	−	1.59310i	0.376415	−	0.0942019i
$287$	8.42767	+	3.06742i	0.497470	+	0.181064i
$288$	15.1813	+	7.58466i	0.894569	+	0.446931i
$289$	12.8215	+	10.7585i	0.754204	+	0.632852i
$290$	−22.1784	+	30.5823i	−1.30236	+	1.79586i
$291$	−2.79090	+	8.39014i	−0.163605	+	0.491839i
$292$	0.0964599	−	2.90865i	0.00564489	−	0.170216i
$293$	−15.5573	+	8.98199i	−0.908865	+	0.524733i	−0.880066	−	0.474852i	$-0.842502\pi$
$293$	−15.5573	+	8.98199i	−0.908865	+	0.524733i	−0.0287989	+	0.999585i	$0.509168\pi$
$294$	−7.91588	+	3.80134i	−0.461663	+	0.221699i
$295$	4.92860	+	13.5412i	0.286954	+	0.788401i
$296$	9.36788	+	3.01656i	0.544497	+	0.175334i
$297$	−3.48560	+	2.42278i	−0.202255	+	0.140584i
$298$	4.07647	−	0.288651i	0.236144	−	0.0167211i
$299$	−11.3172	+	9.49622i	−0.654488	+	0.549181i
$300$	−33.9729	−	12.5660i	−1.96143	−	0.725500i
$301$	−2.12592	−	12.0567i	−0.122536	−	0.694935i
$302$	0.485445	−	4.65803i	0.0279342	−	0.268040i
$303$	−1.77117	+	11.9955i	−0.101751	+	0.689123i
$304$	−8.62605	+	15.1523i	−0.494738	+	0.869042i
$305$			29.1602i			1.66971i
$306$	−0.840965	+	2.00566i	−0.0480748	+	0.114656i
$307$	−7.67258	+	1.35288i	−0.437897	+	0.0772131i	−0.388251	−	0.921554i	$-0.626921\pi$
$307$	−7.67258	+	1.35288i	−0.437897	+	0.0772131i	−0.0496465	+	0.998767i	$0.515809\pi$
$308$	0.622575	−	2.95448i	0.0354745	−	0.168347i
$309$	−12.8828	−	20.9400i	−0.732875	−	1.19123i
$310$	−2.93165	−	41.4023i	−0.166507	−	2.35149i
$311$	−9.56080	+	16.5598i	−0.542143	+	0.939020i	0.456637	+	0.889653i	$0.349054\pi$
$311$	−9.56080	+	16.5598i	−0.542143	+	0.939020i	−0.998781	+	0.0493669i	$0.984280\pi$
$312$	−24.9564	−	12.3062i	−1.41288	−	0.696703i
$313$	11.5650	−	4.20932i	0.653694	−	0.237925i	0.00618244	−	0.999981i	$-0.498032\pi$
$313$	11.5650	−	4.20932i	0.653694	−	0.237925i	0.647511	+	0.762056i	$0.275810\pi$
$314$	−12.5612	+	8.48869i	−0.708870	+	0.479045i
$315$	−4.97771	−	21.2199i	−0.280462	−	1.19561i
$316$	−2.24077	−	0.0743110i	−0.126053	−	0.00418032i
$317$	−16.5656	−	2.92096i	−0.930417	−	0.164058i	−0.312157	−	0.950031i	$-0.601051\pi$
$317$	−16.5656	−	2.92096i	−0.930417	−	0.164058i	−0.618261	+	0.785973i	$0.712162\pi$
$318$	13.0337	+	12.7408i	0.730893	+	0.714468i
$319$	−3.56796	+	4.25212i	−0.199767	+	0.238073i
$320$	2.35918	+	31.3632i	0.131882	+	1.75326i
$321$	11.2743	+	6.09578i	0.629270	+	0.340234i
$322$	1.65028	+	6.59426i	0.0919667	+	0.367484i
$323$	−2.01079	−	0.974376i	−0.111883	−	0.0542157i
$324$	17.9172	+	1.72404i	0.995403	+	0.0957798i
$325$	55.8101	+	20.3132i	3.09579	+	1.12677i
$326$	14.3183	−	6.38997i	0.793016	−	0.353908i
$327$	−3.97413	−	4.47605i	−0.219770	−	0.247526i
$328$	−13.5982	−	1.87459i	−0.750833	−	0.103507i
$329$	8.42253	+	1.48512i	0.464349	+	0.0818773i
$330$	−7.16739	−	3.24357i	−0.394552	−	0.178553i
$331$	8.46976	−	4.89002i	0.465540	−	0.268780i	−0.248831	−	0.968547i	$-0.580046\pi$
$331$	8.46976	−	4.89002i	0.465540	−	0.268780i	0.714371	+	0.699767i	$0.246713\pi$
$332$	14.2926	−	15.9297i	0.784409	−	0.874256i
$333$	10.4223	−	0.582989i	0.571137	−	0.0319476i
$334$	20.1940	+	20.8748i	1.10497	+	1.14222i
$335$	16.2195	−	28.0929i	0.886164	−	1.53488i
$336$	−10.1163	+	7.84753i	−0.551887	+	0.428118i
$337$	−20.6586	+	17.3346i	−1.12534	+	0.944275i	−0.998862	−	0.0476940i	$-0.984813\pi$
$337$	−20.6586	+	17.3346i	−1.12534	+	0.944275i	−0.126481	+	0.991969i	$0.540368\pi$
$338$	24.4930	+	11.9194i	1.33224	+	0.648331i
$339$	−3.78996	+	0.105916i	−0.205842	+	0.00575258i
$340$	−3.99044	+	0.567965i	−0.216412	+	0.0308022i
$341$		−	6.09854i		−	0.330255i
$342$	−2.76595	+	18.2852i	−0.149566	+	0.988752i
$343$		−	19.5608i		−	1.05619i
$344$	7.06509	+	17.3550i	0.380924	+	0.935718i
$345$	17.7048	−	0.494788i	0.953194	−	0.0266385i
$346$	3.48162	−	7.15431i	0.187173	−	0.384618i
$347$	6.85601	−	5.75288i	0.368050	−	0.308831i	−0.439940	−	0.898027i	$-0.645000\pi$
$347$	6.85601	−	5.75288i	0.368050	−	0.308831i	0.807990	+	0.589197i	$0.200556\pi$
$348$	23.2007	−	3.96634i	1.24369	−	0.212618i
$349$	0.418101	−	0.724172i	0.0223804	−	0.0387640i	−0.854618	−	0.519257i	$-0.826209\pi$
$349$	0.418101	−	0.724172i	0.0223804	−	0.0387640i	0.876999	+	0.480493i	$0.159542\pi$
$350$	19.6411	−	19.0006i	1.04986	−	1.01562i
$351$	−29.3922	−	2.67365i	−1.56884	−	0.142709i
$352$	0.0202827	+	4.62123i	0.00108107	+	0.246312i
$353$	14.9057	−	8.60584i	0.793353	−	0.458043i	−0.0477886	−	0.998857i	$-0.515217\pi$
$353$	14.9057	−	8.60584i	0.793353	−	0.458043i	0.841142	+	0.540815i	$0.181884\pi$
$354$	3.70166	−	8.17966i	0.196741	−	0.434744i
$355$	−16.4411	−	2.89902i	−0.872606	−	0.153864i
$356$	15.6869	+	6.30589i	0.831402	+	0.334212i
$357$	−1.08937	−	1.22695i	−0.0576555	−	0.0649372i
$358$	13.1429	+	29.4498i	0.694624	+	1.55647i
$359$	−30.0962	−	10.9541i	−1.58842	−	0.578137i	−0.611405	−	0.791318i	$-0.709395\pi$
$359$	−30.0962	−	10.9541i	−1.58842	−	0.578137i	−0.977013	+	0.213181i	$0.931618\pi$
$360$	14.2842	+	30.1468i	0.752841	+	1.58888i
$361$	−18.6047	−	3.85533i	−0.979197	−	0.202912i
$362$	24.0749	−	6.02501i	1.26535	−	0.316667i
$363$	15.7429	+	8.51185i	0.826286	+	0.446756i
$364$	16.5197	−	12.9534i	0.865870	−	0.678943i
$365$	3.67725	−	4.38238i	0.192476	−	0.229384i
$366$	12.7000	−	12.9920i	0.663839	−	0.679100i
$367$	10.9145	+	1.92451i	0.569730	+	0.100459i	0.451090	−	0.892479i	$-0.351035\pi$
$367$	10.9145	+	1.92451i	0.569730	+	0.100459i	0.118640	+	0.992937i	$0.462146\pi$
$368$	−4.59366	−	9.33506i	−0.239461	−	0.486624i
$369$	−14.1747	+	3.32506i	−0.737904	+	0.173096i
$370$	10.8322	+	16.0290i	0.563140	+	0.833310i
$371$	−12.9215	+	4.70303i	−0.670849	+	0.244169i
$372$	−16.7256	+	19.7231i	−0.867180	+	1.02259i
$373$	6.01501	−	10.4183i	0.311446	−	0.539440i	−0.667230	−	0.744852i	$-0.732520\pi$
$373$	6.01501	−	10.4183i	0.311446	−	0.539440i	0.978676	+	0.205412i	$0.0658535\pi$
$374$	−0.590752	+	0.0418305i	−0.0305471	+	0.00216301i
$375$	−19.4698	−	31.6467i	−1.00542	−	1.63423i
$376$	−13.0807	+	0.491281i	−0.674586	+	0.0253359i
$377$	−38.0063	+	6.70154i	−1.95743	+	0.345147i
$378$	−7.02405	+	11.6222i	−0.361278	+	0.597781i
$379$		−	15.2025i		−	0.780898i	−0.920625	−	0.390449i	$-0.872320\pi$
$379$		−	15.2025i		−	0.780898i	0.920625	−	0.390449i	$-0.127680\pi$
$380$	−31.7225	+	12.9760i	−1.62733	+	0.665657i
$381$	−3.50688	+	23.7509i	−0.179663	+	1.21679i
$382$	−20.7112	−	2.15845i	−1.05968	−	0.110436i
$383$	−3.66018	−	20.7579i	−0.187026	−	1.06068i	−0.923324	−	0.384021i	$-0.874539\pi$
$383$	−3.66018	−	20.7579i	−0.187026	−	1.06068i	0.736298	−	0.676657i	$-0.236572\pi$
$384$	12.6084	−	15.0010i	0.643418	−	0.765515i
$385$	4.54669	−	3.81512i	0.231721	−	0.194437i
$386$	0.420934	+	5.94464i	0.0214250	+	0.302574i
$387$	13.6055	+	14.4876i	0.691607	+	0.736445i
$388$	8.66808	+	5.39528i	0.440055	+	0.273904i
$389$	7.46086	+	20.4985i	0.378281	+	1.03932i	0.972069	+	0.234696i	$0.0754094\pi$
$389$	7.46086	+	20.4985i	0.378281	+	1.03932i	−0.593788	+	0.804621i	$0.702368\pi$
$390$	−23.6782	−	49.3073i	−1.19899	−	2.49677i
$391$	1.15469	−	0.666658i	0.0583950	−	0.0337144i
$392$	2.13429	+	9.91261i	0.107798	+	0.500663i
$393$	−3.76558	+	11.3203i	−0.189948	+	0.571033i
$394$	−4.63513	−	3.36140i	−0.233514	−	0.169345i
$395$	−3.37611	−	2.83289i	−0.169870	−	0.142538i
$396$	1.78069	+	4.56671i	0.0894829	+	0.229486i
$397$	−18.4059	−	6.69921i	−0.923767	−	0.336224i	−0.164031	−	0.986455i	$-0.552450\pi$
$397$	−18.4059	−	6.69921i	−0.923767	−	0.336224i	−0.759736	+	0.650231i	$0.774672\pi$
$398$	5.30082	+	21.1812i	0.265706	+	1.06172i
$399$	−11.5322	−	7.85282i	−0.577331	−	0.393132i
$400$	−23.2670	+	34.7573i	−1.16335	+	1.73787i
$401$	11.0270	−	30.2964i	0.550661	−	1.51293i	−0.282150	−	0.959370i	$-0.591048\pi$
$401$	11.0270	−	30.2964i	0.550661	−	1.51293i	0.832811	−	0.553558i	$-0.186730\pi$
$402$	−19.4616	+	5.45248i	−0.970654	+	0.271945i
$403$	27.2550	−	32.4813i	1.35767	−	1.61801i
$404$	12.9910	+	5.22221i	0.646328	+	0.259814i
$405$	25.6250	+	24.3996i	1.27331	+	1.21243i
$406$	−4.87961	+	17.0738i	−0.242171	+	0.847357i
$407$	1.42127	+	2.46171i	0.0704498	+	0.122023i
$408$	2.02525	+	1.48488i	0.100265	+	0.0735127i
$409$	23.1601	−	8.42959i	1.14519	−	0.416817i	0.301407	−	0.953495i	$-0.402544\pi$
$409$	23.1601	−	8.42959i	1.14519	−	0.416817i	0.843787	+	0.536679i	$0.180321\pi$
$410$	−18.7612	−	19.3937i	−0.926548	−	0.957785i
$411$	−7.21321	−	5.71696i	−0.355801	−	0.281997i
$412$	−26.9840	+	8.82005i	−1.32941	+	0.434532i
$413$	4.35394	+	5.18882i	0.214243	+	0.255325i
$414$	−8.10364	−	7.49043i	−0.398272	−	0.368135i
$415$	41.4311	−	7.30542i	2.03377	−	0.358609i
$416$	−20.5447	+	24.7036i	−1.00729	+	1.21119i
$417$	1.41717	−	9.59798i	0.0693991	−	0.470015i
$418$	−4.78407	+	1.57261i	−0.233997	+	0.0769190i
$419$	1.77830			0.0868756			0.0434378	−	0.999056i	$-0.486169\pi$
$419$	1.77830			0.0868756			0.0434378	+	0.999056i	$0.486169\pi$
$420$	−25.1674	−	0.131167i	−1.22805	−	0.00640028i
$421$	−6.90800	−	39.1772i	−0.336675	−	1.90938i	−0.410024	−	0.912075i	$-0.634480\pi$
$421$	−6.90800	−	39.1772i	−0.336675	−	1.90938i	0.0733486	−	0.997306i	$-0.476631\pi$
$422$	15.3826	−	31.6095i	0.748816	−	1.53873i
$423$	−12.7611	+	5.46984i	−0.620466	+	0.265953i
$424$	17.8187	−	11.1997i	0.865353	−	0.543906i
$425$	−4.64202	−	2.68007i	−0.225171	−	0.130003i
$426$	6.06255	+	8.45215i	0.293732	+	0.409508i
$427$	4.68796	+	12.8801i	0.226866	+	0.623310i
$428$	9.88346	−	11.0155i	0.477735	−	0.532455i
$429$	−2.95867	−	7.47245i	−0.142846	−	0.360773i
$430$	−10.1217	+	35.4160i	−0.488113	+	1.70791i
$431$	−5.93788	+	33.6754i	−0.286017	+	1.62209i	0.415611	+	0.909543i	$0.363568\pi$
$431$	−5.93788	+	33.6754i	−0.286017	+	1.62209i	−0.701628	+	0.712543i	$0.747543\pi$
$432$	6.76558	−	19.6527i	0.325509	−	0.945539i
$433$	−0.798545	−	0.670059i	−0.0383756	−	0.0322010i	0.623398	−	0.781905i	$-0.285752\pi$
$433$	−0.798545	−	0.670059i	−0.0383756	−	0.0322010i	−0.661774	+	0.749704i	$0.730196\pi$
$434$	−7.95099	−	17.8161i	−0.381660	−	0.855201i
$435$	40.7000	+	22.0057i	1.95141	+	1.05509i
$436$	−6.09696	+	3.25556i	−0.291992	+	0.155913i
$437$	8.13543	−	7.89656i	0.389171	−	0.377744i
$438$	−3.54699	+	0.350979i	−0.169482	+	0.0167704i
$439$	−6.29001	+	17.2817i	−0.300206	+	0.824809i	0.694258	+	0.719727i	$0.255733\pi$
$439$	−6.29001	+	17.2817i	−0.300206	+	0.824809i	−0.994464	+	0.105082i	$0.966489\pi$
$440$	−5.57393	+	7.17317i	−0.265727	+	0.341967i
$441$	5.88922	+	8.99912i	0.280439	+	0.428529i
$442$	−3.33333	−	2.41734i	−0.158550	−	0.114981i
$443$	−1.01298	+	5.74488i	−0.0481280	+	0.272948i	−0.999370	−	0.0354989i	$-0.988698\pi$
$443$	−1.01298	+	5.74488i	−0.0481280	+	0.272948i	0.951242	+	0.308447i	$0.0998091\pi$
$444$	2.15489	−	11.8592i	0.102267	−	0.562815i
$445$	16.6172	+	28.7819i	0.787733	+	1.36439i
$446$	−6.94157	−	10.2718i	−0.328693	−	0.486386i
$447$	−1.00649	−	4.90290i	−0.0476054	−	0.231899i
$448$	6.08419	+	13.4739i	0.287451	+	0.636581i
$449$	8.02414	+	4.63274i	0.378683	+	0.218633i	0.677245	−	0.735758i	$-0.263174\pi$
$449$	8.02414	+	4.63274i	0.378683	+	0.218633i	−0.298562	+	0.954390i	$0.596507\pi$
$450$	−9.78942	+	43.2697i	−0.461478	+	2.03975i
$451$	−2.54846	−	3.03714i	−0.120002	−	0.143013i
$452$	−0.902713	+	4.28390i	−0.0424601	+	0.201498i
$453$	−5.73356	+	0.160233i	−0.269386	+	0.00752841i
$454$	14.7588	+	1.53811i	0.692663	+	0.0721871i
$455$	41.2661			1.93459
$456$	19.7850	+	8.03463i	0.926516	+	0.376256i
$457$	8.67588			0.405841			0.202920	−	0.979195i	$-0.434957\pi$
$457$	8.67588			0.405841			0.202920	+	0.979195i	$0.434957\pi$
$458$	15.9868	+	1.66609i	0.747014	+	0.0778514i
$459$	2.57046	+	0.698263i	0.119979	+	0.0325921i
$460$	4.21702	−	20.0122i	0.196620	−	0.933075i
$461$	−2.31241	−	2.75583i	−0.107700	−	0.128352i	0.709502	−	0.704704i	$-0.248920\pi$
$461$	−2.31241	−	2.75583i	−0.107700	−	0.128352i	−0.817201	+	0.576352i	$0.804476\pi$
$462$	−3.68730	−	0.280415i	−0.171549	−	0.0130461i
$463$	−29.8697	−	17.2453i	−1.38816	−	0.801456i	−0.395054	−	0.918658i	$-0.629274\pi$
$463$	−29.8697	−	17.2453i	−1.38816	−	0.801456i	−0.993108	+	0.117202i	$0.962607\pi$
$464$	1.80067	−	27.1188i	0.0835939	−	1.25896i
$465$	−49.7958	+	10.2223i	−2.30922	+	0.474049i
$466$	14.2051	+	21.0201i	0.658039	+	0.973739i
$467$	9.10511	+	15.7705i	0.421334	+	0.729772i	0.996070	−	0.0885667i	$-0.0282287\pi$
$467$	9.10511	+	15.7705i	0.421334	+	0.729772i	−0.574736	+	0.818339i	$0.694895\pi$
$468$	−10.9250	+	32.2807i	−0.505010	+	1.49218i
$469$	2.64776	−	15.0162i	0.122262	−	0.693385i
$470$	−20.8304	−	15.1063i	−0.960835	−	0.696800i
$471$	12.3278	+	13.8848i	0.568037	+	0.639777i
$472$	−8.18624	−	6.36115i	−0.376802	−	0.292796i
$473$	−1.85104	+	5.08569i	−0.0851109	+	0.233840i
$474$	0.270388	+	2.73254i	0.0124193	+	0.125510i
$475$	−43.8452	−	12.4513i	−2.01176	−	0.571305i
$476$	−1.67127	+	0.892397i	−0.0766025	+	0.0409029i
$477$	13.3714	−	17.8749i	0.612234	−	0.818437i
$478$	−14.0079	−	31.3881i	−0.640708	−	1.43566i
$479$	14.7886	+	12.4091i	0.675711	+	0.566988i	0.914749	−	0.404022i	$-0.132388\pi$
$479$	14.7886	+	12.4091i	0.675711	+	0.566988i	−0.239039	+	0.971010i	$0.576832\pi$
$480$	37.6992	−	7.91168i	1.72073	−	0.361117i
$481$	−3.43186	+	19.4630i	−0.156479	+	0.887439i
$482$	6.25585	−	21.8892i	0.284946	−	0.997027i
$483$	7.74068	−	3.06488i	0.352213	−	0.139457i
$484$	13.8008	−	15.3815i	0.627307	−	0.699160i
$485$	6.86443	+	18.8599i	0.311698	+	0.856383i
$486$	−0.790255	−	22.0312i	−0.0358467	−	0.999357i
$487$	30.9096	+	17.8457i	1.40065	+	0.808664i	0.994459	−	0.105125i	$-0.0335244\pi$
$487$	30.9096	+	17.8457i	1.40065	+	0.808664i	0.406188	+	0.913789i	$0.366858\pi$
$488$	−11.1638	−	17.7616i	−0.505364	−	0.804031i
$489$	−10.0625	−	16.3558i	−0.455042	−	0.739636i
$490$	−8.72195	+	17.9226i	−0.394018	+	0.809659i
$491$	−6.54895	−	37.1409i	−0.295550	−	1.67615i	−0.664959	−	0.746879i	$-0.731551\pi$
$491$	−6.54895	−	37.1409i	−0.295550	−	1.67615i	0.369410	−	0.929267i	$-0.379560\pi$
$492$	−0.0876179	+	16.8116i	−0.00395012	+	0.757924i
$493$	3.48301			0.156867
$494$	−32.5085	−	13.0047i	−1.46262	−	0.585107i
$495$	−2.78464	+	9.22411i	−0.125160	+	0.414593i
$496$	17.6364	+	24.0960i	0.791896	+	1.08194i
$497$	−7.72813	+	1.36268i	−0.346654	+	0.0611245i
$498$	−21.6408	−	14.7894i	−0.969747	−	0.662730i
$499$	−12.5295	−	14.9321i	−0.560899	−	0.668453i	0.408838	−	0.912607i	$-0.365934\pi$
$499$	−12.5295	−	14.9321i	−0.560899	−	0.668453i	−0.969736	+	0.244154i	$0.921490\pi$
$500$	−40.7812	+	13.3298i	−1.82379	+	0.596127i
$501$	22.0948	−	27.8775i	0.987121	−	1.24547i
$502$	−9.21828	−	9.52906i	−0.411432	−	0.425303i
$503$	−9.58943	+	3.49027i	−0.427571	+	0.155623i	−0.546837	−	0.837239i	$-0.684168\pi$
$503$	−9.58943	+	3.49027i	−0.427571	+	0.155623i	0.119266	+	0.992862i	$0.461946\pi$
$504$	11.1559	+	11.0195i	0.496924	+	0.490847i
$505$	13.7615	+	23.8356i	0.612379	+	1.06067i
$506$	0.825757	−	2.88933i	0.0367094	−	0.128446i
$507$	10.5300	−	31.6558i	0.467653	−	1.40588i
$508$	25.7220	+	10.3399i	1.14123	+	0.458758i
$509$	14.7678	−	17.5996i	0.654571	−	0.780088i	−0.332025	−	0.943271i	$-0.607732\pi$
$509$	14.7678	−	17.5996i	0.654571	−	0.780088i	0.986596	+	0.163183i	$0.0521761\pi$
$510$	1.33177	+	4.75349i	0.0589717	+	0.210488i
$511$	0.919708	−	2.52688i	0.0406855	−	0.111782i
$512$	−13.4443	−	18.2003i	−0.594158	−	0.804348i
$513$	22.6457	+	0.415541i	0.999832	+	0.0183466i
$514$	−5.54672	−	22.1638i	−0.244655	−	0.977602i
$515$	−52.4397	−	19.0865i	−2.31077	−	0.841052i
$516$	19.9341	−	11.3709i	0.877552	−	0.500575i
$517$	−2.89623	−	2.43023i	−0.127376	−	0.106881i
$518$	7.36152	+	5.33859i	0.323447	+	0.234564i
$519$	−9.24653	−	3.07577i	−0.405878	−	0.135011i
$520$	−61.7447	+	13.2943i	−2.70769	+	0.582993i
$521$	−17.1402	+	9.89589i	−0.750925	+	0.433547i	−0.826028	−	0.563629i	$-0.809405\pi$
$521$	−17.1402	+	9.89589i	−0.750925	+	0.433547i	0.0751028	+	0.997176i	$0.476072\pi$
$522$	−8.54936	−	27.5302i	−0.374195	−	1.20496i
$523$	−5.62078	−	15.4430i	−0.245780	−	0.675274i	−0.999830	−	0.0184571i	$-0.994125\pi$
$523$	−5.62078	−	15.4430i	−0.245780	−	0.675274i	0.754050	−	0.656817i	$-0.228098\pi$
$524$	11.6953	+	7.27951i	0.510911	+	0.318007i
$525$	−26.2299	−	20.7890i	−1.14477	−	0.907306i
$526$	−1.12679	−	15.9131i	−0.0491305	−	0.693846i
$527$	−2.93145	+	2.45978i	−0.127696	+	0.107150i
$528$	5.60749	−	0.768328i	0.244035	−	0.0334372i
$529$	−2.81912	−	15.9880i	−0.122571	−	0.695133i
$530$	41.1484	+	4.28835i	1.78737	+	0.186274i
$531$	−10.5268	−	3.17792i	−0.456826	−	0.137910i
$532$	−11.9258	+	10.8314i	−0.517047	+	0.469602i
$533$		−	27.5653i		−	1.19399i
$534$	5.13163	−	20.0606i	0.222067	−	0.868109i
$535$	28.6499	−	5.05176i	1.23864	−	0.218406i
$536$	0.875887	+	23.3211i	0.0378325	+	1.00732i
$537$	33.6407	−	20.6965i	1.45170	−	0.893121i
$538$	45.3536	−	3.21144i	1.95533	−	0.138455i
$539$	−1.46433	+	2.53630i	−0.0630733	+	0.109246i
$540$	34.3033	−	22.1943i	1.47618	−	0.955092i
$541$	−23.2327	+	8.45599i	−0.998850	+	0.363552i	−0.789141	−	0.614212i	$-0.789474\pi$
$541$	−23.2327	+	8.45599i	−0.998850	+	0.363552i	−0.209709	+	0.977764i	$0.567252\pi$
$542$	13.7288	+	20.3153i	0.589703	+	0.872617i
$543$	−11.1895	−	28.2604i	−0.480189	−	1.21277i
$544$	2.21316	−	1.87367i	0.0948883	−	0.0803330i
$545$	−13.3802	−	2.35929i	−0.573144	−	0.101061i
$546$	−18.3856	−	17.9724i	−0.786831	−	0.769149i
$547$	11.8739	−	14.1508i	0.507691	−	0.605043i	−0.449933	−	0.893062i	$-0.648552\pi$
$547$	11.8739	−	14.1508i	0.507691	−	0.605043i	0.957625	+	0.288019i	$0.0929967\pi$
$548$	−8.36339	+	6.55787i	−0.357266	+	0.280139i
$549$	−17.8177	−	13.3286i	−0.760440	−	0.568849i
$550$	−11.7192	+	2.93285i	−0.499708	+	0.125057i
$551$	28.7189	−	7.23840i	1.22347	−	0.308366i
$552$	−10.5947	+	7.07958i	−0.450939	+	0.301327i
$553$	−1.94666	−	0.708527i	−0.0827805	−	0.0301296i
$554$	8.83179	+	19.7898i	0.375227	+	0.840787i
$555$	17.7180	−	15.7312i	0.752088	−	0.667754i
$556$	−10.3945	−	4.17846i	−0.440827	−	0.177206i
$557$	−23.9025	−	4.21465i	−1.01278	−	0.178580i	−0.357457	−	0.933930i	$-0.616356\pi$
$557$	−23.9025	−	4.21465i	−1.01278	−	0.178580i	−0.655322	+	0.755349i	$0.727467\pi$
$558$	26.6380	+	17.1329i	1.12767	+	0.725292i
$559$	−32.5872	+	18.8142i	−1.37829	+	0.795758i
$560$	−6.93150	+	28.2225i	−0.292909	+	1.19262i
$561$	0.145858	+	0.710515i	0.00615814	+	0.0299980i
$562$	−13.2689	+	12.8361i	−0.559713	+	0.541459i
$563$	−9.69314	+	16.7890i	−0.408517	+	0.707573i	−0.994724	−	0.102589i	$-0.967287\pi$
$563$	−9.69314	+	16.7890i	−0.408517	+	0.707573i	0.586207	+	0.810162i	$0.300621\pi$
$564$	2.70158	+	15.8026i	0.113757	+	0.665408i
$565$	−6.59255	+	5.53180i	−0.277351	+	0.232725i
$566$	−5.41752	+	11.1324i	−0.227715	+	0.467928i
$567$	15.2412	+	6.65770i	0.640070	+	0.279597i
$568$	11.1243	−	4.52861i	0.466764	−	0.190016i
$569$			15.5507i			0.651919i	0.945384	+	0.325959i	$0.105687\pi$
$569$			15.5507i			0.651919i	−0.945384	+	0.325959i	$0.894313\pi$
$570$	20.8597	+	36.4269i	0.873717	+	1.52575i
$571$			17.2428i			0.721587i	0.932646	+	0.360794i	$0.117494\pi$
$571$			17.2428i			0.721587i	−0.932646	+	0.360794i	$0.882506\pi$
$572$	−9.18758	+	1.30768i	−0.384152	+	0.0546770i
$573$	0.712450	+	25.4933i	0.0297630	+	1.06500i
$574$	−11.4047	−	5.55004i	−0.476022	−	0.231654i
$575$	20.8346	−	17.4823i	0.868863	−	0.729062i
$576$	−20.2422	−	12.8940i	−0.843423	−	0.537250i
$577$	−0.972885	+	1.68509i	−0.0405017	+	0.0701511i	−0.885566	−	0.464514i	$-0.846229\pi$
$577$	−0.972885	+	1.68509i	−0.0405017	+	0.0701511i	0.845064	+	0.534665i	$0.179562\pi$
$578$	−16.4575	−	17.0123i	−0.684542	−	0.707620i
$579$	7.14980	−	1.46775i	0.297136	−	0.0609975i
$580$	35.6791	−	39.7658i	1.48149	−	1.65119i
$581$	17.1257	−	9.88752i	0.710493	−	0.410203i
$582$	5.15558	−	11.3924i	0.213706	−	0.472231i
$583$	5.98640	+	1.05556i	0.247931	+	0.0437170i
$584$	−0.562061	+	4.07715i	−0.0232583	+	0.168714i
$585$	−56.0547	+	36.6834i	−2.31758	+	1.51667i
$586$	23.1994	−	10.3535i	0.958360	−	0.427698i
$587$	−21.7221	−	7.90620i	−0.896567	−	0.326324i	−0.147691	−	0.989034i	$-0.547184\pi$
$587$	−21.7221	−	7.90620i	−0.896567	−	0.326324i	−0.748876	+	0.662710i	$0.769406\pi$
$588$	11.6917	−	4.18655i	0.482157	−	0.172650i
$589$	−19.0592	+	26.3741i	−0.785319	+	1.08673i
$590$	−4.94753	−	19.7695i	−0.203687	−	0.813898i
$591$	−3.33523	+	6.16858i	−0.137193	+	0.253742i
$592$	−12.7346	−	5.61632i	−0.523389	−	0.230829i
$593$	7.15355	−	8.52526i	0.293761	−	0.350091i	−0.598896	−	0.800826i	$-0.704394\pi$
$593$	7.15355	−	8.52526i	0.293761	−	0.350091i	0.892657	+	0.450736i	$0.148838\pi$
$594$	5.25799	−	2.89691i	0.215738	−	0.118862i
$595$	−3.66771	−	0.646717i	−0.150362	−	0.0265128i
$596$	−5.77626	−	0.191559i	−0.236605	−	0.00784656i
$597$	24.8636	−	9.84459i	1.01760	−	0.402912i
$598$	17.3107	−	11.6984i	0.707888	−	0.478381i
$599$	−9.34469	+	3.40119i	−0.381813	+	0.138969i	−0.525794	−	0.850612i	$-0.676232\pi$
$599$	−9.34469	+	3.40119i	−0.381813	+	0.138969i	0.143981	+	0.989580i	$0.454010\pi$
$600$	45.9441	+	22.6555i	1.87566	+	0.924905i
$601$	20.4943	−	35.4971i	0.835979	−	1.44796i	−0.0572511	−	0.998360i	$-0.518234\pi$
$601$	20.4943	−	35.4971i	0.835979	−	1.44796i	0.893230	−	0.449599i	$-0.148433\pi$
$602$	1.22291	+	17.2705i	0.0498419	+	0.703893i
$603$	9.75198	+	22.7513i	0.397131	+	0.926505i
$604$	−1.36565	+	6.48080i	−0.0555675	+	0.263700i
$605$	40.0053	−	7.05402i	1.62645	−	0.286787i
$606$	4.24975	−	16.6132i	0.172634	−	0.674863i
$607$			20.0981i			0.815758i	0.913036	+	0.407879i	$0.133731\pi$
$607$			20.0981i			0.815758i	−0.913036	+	0.407879i	$0.866269\pi$
$608$	14.3545	−	20.0486i	0.582154	−	0.813079i
$609$	21.5150	+	3.17675i	0.871831	+	0.128728i
$610$	4.27462	−	41.0166i	0.173074	−	1.66071i
$611$	−4.56460	−	25.8871i	−0.184664	−	1.04728i
$612$	1.47691	−	2.69788i	0.0597005	−	0.109055i
$613$	−4.29342	+	3.60261i	−0.173410	+	0.145508i	−0.725362	−	0.688368i	$-0.758328\pi$
$613$	−4.29342	+	3.60261i	−0.173410	+	0.145508i	0.551952	+	0.833876i	$0.313883\pi$
$614$	10.9905	−	0.778229i	0.443542	−	0.0314067i
$615$	−20.5271	+	25.8995i	−0.827732	+	1.04437i
$616$	−1.30881	+	4.06449i	−0.0527335	+	0.163763i
$617$	10.4325	+	28.6630i	0.419996	+	1.15393i	0.951708	+	0.307005i	$0.0993267\pi$
$617$	10.4325	+	28.6630i	0.419996	+	1.15393i	−0.531712	+	0.846925i	$0.678451\pi$
$618$	15.0512	+	31.3426i	0.605449	+	1.26078i
$619$	−24.7871	+	14.3109i	−0.996279	+	0.575202i	−0.907145	−	0.420817i	$-0.861743\pi$
$619$	−24.7871	+	14.3109i	−0.996279	+	0.575202i	−0.0891341	+	0.996020i	$0.528410\pi$
$620$	−1.94555	+	58.6660i	−0.0781351	+	2.35608i
$621$	−7.79019	+	11.0443i	−0.312610	+	0.443192i
$622$	15.8757	−	21.8914i	0.636557	−	0.877765i
$623$	11.9670	+	10.0415i	0.479448	+	0.402304i
$624$	33.2996	+	20.9683i	1.33305	+	0.839403i
$625$	−30.1230	−	10.9639i	−1.20492	−	0.438555i
$626$	−16.8844	+	4.22549i	−0.674835	+	0.168885i
$627$	2.67926	+	5.55538i	0.106999	+	0.221861i
$628$	18.9129	−	10.0988i	0.754707	−	0.402986i
$629$	0.610044	−	1.67608i	0.0243240	−	0.0668298i
$630$	3.89098	+	30.5775i	0.155021	+	1.21824i
$631$	−20.9960	+	25.0221i	−0.835837	+	0.996112i	0.164116	+	0.986441i	$0.447523\pi$
$631$	−20.9960	+	25.0221i	−0.835837	+	0.996112i	−0.999953	+	0.00967104i	$0.996922\pi$
$632$	3.14097	+	0.433002i	0.124941	+	0.0172239i
$633$	−40.8535	−	13.5895i	−1.62378	−	0.540134i
$634$	22.8729	+	6.53698i	0.908400	+	0.259617i
$635$	27.2476	+	47.1942i	1.08129	+	1.87284i
$636$	−16.4655	−	19.8318i	−0.652898	−	0.786380i
$637$	−19.1341	+	6.96425i	−0.758122	+	0.275934i
$638$	5.64199	−	5.45799i	0.223369	−	0.216084i
$639$	9.28632	−	8.72092i	0.367361	−	0.344994i
$640$	1.27915	−	44.4612i	0.0505627	−	1.75748i
$641$	1.01808	+	1.21330i	0.0402117	+	0.0479224i	0.785775	−	0.618512i	$-0.212264\pi$
$641$	1.01808	+	1.21330i	0.0402117	+	0.0479224i	−0.745564	+	0.666434i	$0.767820\pi$
$642$	−14.9648	−	10.2270i	−0.590613	−	0.403628i
$643$	−44.7260	+	7.88640i	−1.76382	+	0.311009i	−0.959190	−	0.282764i	$-0.908749\pi$
$643$	−44.7260	+	7.88640i	−1.76382	+	0.311009i	−0.804633	+	0.593773i	$0.797638\pi$
$644$	−1.35462	−	9.51737i	−0.0533796	−	0.375037i
$645$	44.6283	+	6.58950i	1.75724	+	0.259461i
$646$	2.68553	+	1.66532i	0.105661	+	0.0655210i
$647$	−7.91696			−0.311248			−0.155624	−	0.987816i	$-0.549739\pi$
$647$	−7.91696			−0.311248			−0.155624	+	0.987816i	$0.549739\pi$
$648$	−24.9496	−	5.05153i	−0.980112	−	0.198443i
$649$	−0.519964	−	2.94886i	−0.0204104	−	0.115753i
$650$	−75.5244	−	36.7537i	−2.96231	−	1.44160i
$651$	−20.3514	+	12.5207i	−0.797636	+	0.490724i
$652$	−21.0767	+	6.88918i	−0.825428	+	0.269801i
$653$	−5.90597	−	3.40981i	−0.231119	−	0.133436i	0.379969	−	0.924999i	$-0.375935\pi$
$653$	−5.90597	−	3.40981i	−0.231119	−	0.133436i	−0.611088	+	0.791563i	$0.709268\pi$
$654$	4.93385	+	6.87856i	0.192929	+	0.268973i
$655$	9.26174	+	25.4464i	0.361886	+	0.994274i
$656$	18.8523	+	4.63016i	0.736059	+	0.180778i
$657$	0.996955	+	4.25000i	0.0388949	+	0.165808i
$658$	−11.6294	−	3.32363i	−0.453361	−	0.129569i
$659$	−2.00685	+	11.3814i	−0.0781759	+	0.443357i	0.920446	+	0.390870i	$0.127826\pi$
$659$	−2.00685	+	11.3814i	−0.0781759	+	0.443357i	−0.998622	+	0.0524870i	$0.983285\pi$
$660$	9.60615	+	5.61307i	0.373919	+	0.218488i
$661$	26.8184	+	22.5033i	1.04311	+	0.875276i	0.992353	−	0.123435i	$-0.0393911\pi$
$661$	26.8184	+	22.5033i	1.04311	+	0.875276i	0.0507603	+	0.998711i	$0.483836\pi$
$662$	−12.6304	+	5.63669i	−0.490893	+	0.219076i
$663$	−2.39851	+	4.43611i	−0.0931506	+	0.172284i
$664$	−22.4391	+	20.3115i	−0.870805	+	0.788239i
$665$	−31.5859	+	2.28979i	−1.22485	+	0.0887942i
$666$	−14.7454	−	0.707782i	−0.571372	−	0.0274260i
$667$	−6.04451	+	16.6071i	−0.234044	+	0.643031i
$668$	−25.3447	−	32.3226i	−0.980617	−	1.25060i
$669$	−11.3542	+	10.0810i	−0.438978	+	0.389754i
$670$	−26.9324	+	37.1378i	−1.04049	+	1.43476i
$671$	1.05218	−	5.96723i	0.0406191	−	0.230362i
$672$	15.3799	−	9.55535i	0.593291	−	0.368606i
$673$	3.19840	+	5.53979i	0.123289	+	0.213543i	0.921063	−	0.389414i	$-0.127322\pi$
$673$	3.19840	+	5.53979i	0.123289	+	0.213543i	−0.797774	+	0.602957i	$0.793989\pi$
$674$	31.5993	−	21.3544i	1.21716	−	0.822541i
$675$	54.1103	+	4.92213i	2.08271	+	0.189453i
$676$	−32.7044	−	20.3562i	−1.25786	−	0.782933i
$677$	33.2915	+	19.2209i	1.27950	+	0.738718i	0.976756	−	0.214355i	$-0.0687650\pi$
$677$	33.2915	+	19.2209i	1.27950	+	0.738718i	0.302741	+	0.953073i	$0.402098\pi$
$678$	5.34647	+	0.406592i	0.205330	+	0.0156151i
$679$	6.06405	+	7.22686i	0.232717	+	0.277341i
$680$	5.69619	−	0.213935i	0.218439	−	0.00820404i
$681$	−0.507692	−	18.1665i	−0.0194548	−	0.696143i
$682$	−0.893991	+	8.57819i	−0.0342327	+	0.328476i
$683$	29.1486			1.11534			0.557670	−	0.830063i	$-0.311696\pi$
$683$	29.1486			1.11534			0.557670	+	0.830063i	$0.311696\pi$
$684$	6.57102	−	25.3145i	0.251249	−	0.967922i
$685$	−20.8917			−0.798229
$686$	−2.86744	+	27.5142i	−0.109479	+	1.05050i
$687$	−0.549935	−	19.6781i	−0.0209813	−	0.750767i
$688$	−7.39364	−	25.4471i	−0.281880	−	0.970163i
$689$	27.1665	+	32.3758i	1.03496	+	1.23342i
$690$	−24.9760	−	1.89940i	−0.950821	−	0.0723088i
$691$	37.4771	+	21.6374i	1.42570	+	0.823126i	0.996777	−	0.0802170i	$-0.0255613\pi$
$691$	37.4771	+	21.6374i	1.42570	+	0.823126i	0.428919	+	0.903343i	$0.358895\pi$
$692$	−5.94598	+	9.55284i	−0.226032	+	0.363145i
$693$	0.252945	+	4.52197i	0.00960857	+	0.171776i
$694$	−10.4870	+	7.08694i	−0.398079	+	0.269017i
$695$	−11.0110	−	19.0717i	−0.417673	−	0.723430i
$696$	−33.2154	+	2.17803i	−1.25903	+	0.0825581i
$697$	−0.431999	+	2.44999i	−0.0163631	+	0.0928000i
$698$	−0.694255	+	0.957327i	−0.0262780	+	0.0362353i
$699$	23.2350	−	20.6296i	0.878829	−	0.780283i
$700$	−30.4124	+	23.8469i	−1.14948	+	0.901328i
$701$	−1.49048	+	4.09507i	−0.0562947	+	0.154668i	−0.964652	−	0.263526i	$-0.915115\pi$
$701$	−1.49048	+	4.09507i	−0.0562947	+	0.154668i	0.908358	+	0.418194i	$0.137337\pi$
$702$	40.9510	+	8.06938i	1.54560	+	0.304559i
$703$	1.54684	−	15.0878i	0.0583401	−	0.569048i
$704$	0.648901	−	6.50318i	0.0244564	−	0.245098i
$705$	−14.9886	+	27.7218i	−0.564504	+	1.04406i
$706$	−22.2279	+	9.91989i	−0.836558	+	0.373340i
$707$	9.91044	+	8.31584i	0.372720	+	0.312749i
$708$	−6.40581	+	10.9628i	−0.240745	+	0.412009i
$709$	2.34971	−	13.3259i	0.0882454	−	0.500464i	−0.908364	−	0.418181i	$-0.862668\pi$
$709$	2.34971	−	13.3259i	0.0882454	−	0.500464i	0.996609	−	0.0822832i	$-0.0262212\pi$
$710$	22.7011	+	6.48787i	0.851956	+	0.243485i
$711$	3.27413	−	0.768037i	0.122789	−	0.0288036i
$712$	−21.1407	−	11.1694i	−0.792281	−	0.418591i
$713$	−6.64102	−	18.2461i	−0.248708	−	0.683320i
$714$	1.35244	+	1.88552i	0.0506139	+	0.0705637i
$715$	−15.7984	−	9.12120i	−0.590826	−	0.341114i
$716$	−14.1697	−	43.3506i	−0.529545	−	1.62009i
$717$	−35.8548	+	22.0587i	−1.33902	+	0.823798i
$718$	40.7274	+	19.8199i	1.51993	+	0.739671i
$719$	5.99951	+	34.0249i	0.223744	+	1.26892i	0.865072	+	0.501649i	$0.167273\pi$
$719$	5.99951	+	34.0249i	0.223744	+	1.26892i	−0.641327	+	0.767267i	$0.721616\pi$
$720$	−15.6728	−	44.4984i	−0.584090	−	1.65836i
$721$	−26.2311			−0.976899
$722$	25.6042	+	8.15017i	0.952889	+	0.303318i
$723$	−27.5830	−	4.07271i	−1.02582	−	0.151466i
$724$	−34.7469	+	4.94558i	−1.29136	+	0.183801i
$725$	69.9687	−	12.3374i	2.59857	−	0.458198i
$726$	−20.8961	−	14.2805i	−0.775526	−	0.529999i
$727$	26.1375	+	31.1495i	0.969388	+	1.15527i	0.987845	+	0.155441i	$0.0496800\pi$
$727$	26.1375	+	31.1495i	0.969388	+	1.15527i	−0.0184575	+	0.999830i	$0.505876\pi$
$728$	−25.1354	+	15.7986i	−0.931582	+	0.585533i
$729$	−26.6215	+	4.50499i	−0.985982	+	0.166852i
$730$	−5.81482	+	5.62518i	−0.215216	+	0.208197i
$731$	3.19119	−	1.16150i	0.118030	−	0.0429596i
$732$	−19.7682	+	16.4127i	−0.730655	+	0.606632i
$733$	−9.42813	−	16.3300i	−0.348236	−	0.603163i	0.637700	−	0.770285i	$-0.279886\pi$
$733$	−9.42813	−	16.3300i	−0.348236	−	0.603163i	−0.985936	+	0.167122i	$0.946553\pi$
$734$	−15.0701	−	4.30697i	−0.556248	−	0.158973i
$735$	23.1639	+	7.70524i	0.854413	+	0.284212i
$736$	5.09298	+	13.8040i	0.187730	+	0.508824i
$737$	−4.33276	+	5.16359i	−0.159599	+	0.190203i
$738$	20.4254	−	2.59913i	0.751871	−	0.0956754i
$739$	12.0726	−	33.1691i	0.444096	−	1.22014i	−0.492679	−	0.870211i	$-0.663982\pi$
$739$	12.0726	−	33.1691i	0.444096	−	1.22014i	0.936775	−	0.349933i	$-0.113796\pi$
$740$	−12.8868	−	24.1343i	−0.473729	−	0.887194i
$741$	−10.5577	+	41.5622i	−0.387845	+	1.52683i
$742$	18.8647	−	4.72109i	0.692545	−	0.173317i
$743$	−21.7536	−	7.91768i	−0.798064	−	0.290471i	−0.0893799	−	0.995998i	$-0.528489\pi$
$743$	−21.7536	−	7.91768i	−0.798064	−	0.290471i	−0.708684	+	0.705526i	$0.750711\pi$
$744$	26.4173	−	25.2906i	0.968506	−	0.927197i
$745$	−8.70293	−	7.30262i	−0.318851	−	0.267547i
$746$	−9.98792	+	13.7726i	−0.365684	+	0.504251i
$747$	−14.4735	+	28.6547i	−0.529559	+	1.04842i
$748$	0.837081	+	0.0277602i	0.0306067	+	0.00101501i
$749$	11.8426	−	6.83730i	0.432717	−	0.249830i
$750$	22.7470	+	47.3683i	0.830604	+	1.72964i
$751$	2.21674	+	6.09045i	0.0808901	+	0.222244i	0.973544	−	0.228499i	$-0.0733816\pi$
$751$	2.21674	+	6.09045i	0.0808901	+	0.222244i	−0.892654	+	0.450742i	$0.851159\pi$
$752$	18.4713	+	1.22648i	0.673579	+	0.0447252i
$753$	−10.0860	+	12.7257i	−0.367553	+	0.463750i
$754$	54.4419	−	3.85498i	1.98266	−	0.140390i
$755$	−9.97339	+	8.36867i	−0.362969	+	0.304567i
$756$	11.5837	−	15.3181i	0.421295	−	0.557113i
$757$	−0.985133	−	5.58697i	−0.0358053	−	0.203062i	0.961657	−	0.274254i	$-0.0884308\pi$
$757$	−0.985133	−	5.58697i	−0.0358053	−	0.203062i	−0.997463	+	0.0711920i	$0.977320\pi$
$758$	−2.22854	+	21.3837i	−0.0809443	+	0.776691i
$759$	−3.64089	−	0.537588i	−0.132156	−	0.0195132i
$760$	46.5229	−	13.6018i	1.68756	−	0.493390i
$761$		−	47.9592i		−	1.73852i	−0.494356	−	0.869260i	$-0.664596\pi$
$761$		−	47.9592i		−	1.73852i	0.494356	−	0.869260i	$-0.335404\pi$
$762$	8.41443	−	32.8938i	0.304823	−	1.19162i
$763$	−6.28934	+	1.10898i	−0.227689	+	0.0401478i
$764$	28.8158	+	6.07214i	1.04252	+	0.219682i
$765$	5.55701	−	2.38192i	0.200914	−	0.0861185i
$766$	2.10547	+	29.7345i	0.0760737	+	1.07435i
$767$	10.4094	−	18.0296i	0.375862	−	0.651012i
$768$	−19.9339	+	19.2520i	−0.719302	+	0.694698i
$769$	36.0153	−	13.1085i	1.29874	−	0.472704i	0.402157	−	0.915571i	$-0.368261\pi$
$769$	36.0153	−	13.1085i	1.29874	−	0.472704i	0.896588	+	0.442866i	$0.146038\pi$
$770$	−6.95461	+	4.69983i	−0.250627	+	0.169370i
$771$	−26.0170	+	10.3013i	−0.936978	+	0.370991i
$772$	0.279347	−	8.42341i	0.0100539	−	0.303165i
$773$	33.5684	+	5.91901i	1.20737	+	0.212892i	0.740882	−	0.671635i	$-0.234408\pi$
$773$	33.5684	+	5.91901i	1.20737	+	0.212892i	0.466488	+	0.884527i	$0.345519\pi$
$774$	−17.0137	−	22.3726i	−0.611545	−	0.804167i
$775$	−50.1758	+	59.7972i	−1.80237	+	2.14798i
$776$	−11.4016	−	8.85964i	−0.409293	−	0.318043i
$777$	5.29702	−	9.79696i	0.190030	−	0.351464i
$778$	−7.48951	−	29.9268i	−0.268512	−	1.07293i
$779$	1.52955	+	21.0990i	0.0548019	+	0.755950i
$780$	26.0776	+	72.8264i	0.933729	+	2.60760i
$781$	3.25985	+	1.18649i	0.116647	+	0.0424559i
$782$	−1.72190	+	0.768452i	−0.0615751	+	0.0274798i
$783$	−32.0493	+	14.8105i	−1.14535	+	0.529283i
$784$	−1.54898	−	14.2559i	−0.0553208	−	0.509139i
$785$	41.5056	+	7.31856i	1.48140	+	0.261211i
$786$	6.95610	−	15.3711i	0.248116	−	0.548268i
$787$	14.2969	−	8.25433i	0.509630	−	0.294235i	−0.223052	−	0.974807i	$-0.571602\pi$
$787$	14.2969	−	8.25433i	0.509630	−	0.294235i	0.732681	+	0.680572i	$0.238269\pi$
$788$	6.02700	+	5.40760i	0.214703	+	0.192638i
$789$	−19.1392	+	3.92900i	−0.681374	+	0.139876i
$790$	4.33354	+	4.47964i	0.154180	+	0.159378i
$791$	−2.02261	+	3.50326i	−0.0719157	+	0.124562i
$792$	−1.83527	−	6.68455i	−0.0652134	−	0.237525i
$793$	32.2721	−	27.0795i	1.14602	−	0.961622i
$794$	24.9077	+	12.1212i	0.883940	+	0.430166i
$795$	−1.41548	−	50.6494i	−0.0502018	−	1.79635i
$796$	−4.35114	−	30.5704i	−0.154222	−	1.08354i
$797$			21.8763i			0.774897i	0.921891	+	0.387449i	$0.126644\pi$
$797$			21.8763i			0.774897i	−0.921891	+	0.387449i	$0.873356\pi$
$798$	15.0700	+	12.7362i	0.533470	+	0.450858i
$799$			2.37237i			0.0839284i
$800$	37.8223	−	45.4787i	1.33722	−	1.60792i
$801$	−25.1820	−	3.00205i	−0.889761	−	0.106072i
$802$	−19.9517	+	40.9983i	−0.704518	+	1.44770i
$803$	−0.910627	+	0.764107i	−0.0321353	+	0.0269647i
$804$	28.1738	−	4.81654i	0.993614	−	0.169866i
$805$	9.44861	−	16.3655i	0.333020	−	0.576807i
$806$	−43.0982	+	41.6926i	−1.51807	+	1.46856i
$807$	−11.1979	−	54.5481i	−0.394185	−	1.92018i
$808$	−17.5076	−	9.24990i	−0.615915	−	0.325410i
$809$	−32.0292	+	18.4920i	−1.12609	+	0.650145i	−0.942947	−	0.332942i	$-0.891959\pi$
$809$	−32.0292	+	18.4920i	−1.12609	+	0.650145i	−0.183138	+	0.983087i	$0.558625\pi$
$810$	−32.4672	−	38.0767i	−1.14078	−	1.33788i
$811$	13.9136	+	2.45335i	0.488574	+	0.0861488i	0.412508	−	0.910954i	$-0.364653\pi$
$811$	13.9136	+	2.45335i	0.488574	+	0.0861488i	0.0760660	+	0.997103i	$0.475764\pi$
$812$	9.36649	−	23.3006i	0.328700	−	0.817690i
$813$	22.4559	−	19.9379i	0.787564	−	0.699252i
$814$	−1.63829	−	3.67098i	−0.0574220	−	0.128668i
$815$	−40.9597	−	14.9081i	−1.43476	−	0.522209i
$816$	−2.63104	−	2.38552i	−0.0921048	−	0.0835097i
$817$	23.8989	−	16.2090i	0.836117	−	0.567081i
$818$	−33.8126	+	8.46197i	−1.18223	+	0.295866i
$819$	−18.8620	+	25.2148i	−0.659090	+	0.881075i
$820$	23.5464	+	30.0293i	0.822277	+	1.04867i
$821$	−6.90220	+	8.22573i	−0.240889	+	0.287080i	−0.872920	−	0.487863i	$-0.837777\pi$
$821$	−6.90220	+	8.22573i	−0.240889	+	0.287080i	0.632032	+	0.774942i	$0.282221\pi$
$822$	9.30802	+	9.09884i	0.324654	+	0.317358i
$823$	35.9293	+	6.33531i	1.25242	+	0.220835i	0.760230	−	0.649654i	$-0.225086\pi$
$823$	35.9293	+	6.33531i	1.25242	+	0.220835i	0.492188	+	0.870489i	$0.336197\pi$
$824$	39.2486	−	8.45062i	1.36729	−	0.294391i
$825$	5.44684	+	13.7566i	0.189635	+	0.478943i
$826$	−5.36360	−	7.93682i	−0.186623	−	0.276157i
$827$	11.0278	−	4.01381i	0.383476	−	0.139574i	−0.143087	−	0.989710i	$-0.545703\pi$
$827$	11.0278	−	4.01381i	0.383476	−	0.139574i	0.526563	+	0.850136i	$0.323481\pi$
$828$	10.3005	+	11.7239i	0.357968	+	0.407435i
$829$	2.97115	−	5.14618i	0.103192	−	0.178734i	−0.809806	−	0.586698i	$-0.800428\pi$
$829$	2.97115	−	5.14618i	0.103192	−	0.178734i	0.912998	+	0.407964i	$0.133761\pi$
$830$	−59.3477	+	4.20235i	−2.05999	+	0.145866i
$831$	22.6059	−	13.9077i	0.784192	−	0.482453i
$832$	32.5194	−	31.7363i	1.12741	−	1.10026i
$833$	1.80977	−	0.319112i	0.0627050	−	0.0110566i
$834$	−3.40036	+	13.2927i	−0.117745	+	0.460290i
$835$		−	80.7416i		−	2.79418i
$836$	6.95979	−	1.51073i	0.240709	−	0.0522496i
$837$	16.5146	−	35.0991i	0.570827	−	1.21320i
$838$	−2.50135	−	0.260682i	−0.0864076	−	0.00900512i
$839$	2.37420	+	13.4648i	0.0819665	+	0.464855i	0.997970	+	0.0636851i	$0.0202853\pi$
$839$	2.37420	+	13.4648i	0.0819665	+	0.464855i	−0.916004	+	0.401170i	$0.868604\pi$
$840$	35.3812	+	3.87382i	1.22077	+	0.133659i
$841$	−13.1506	+	11.0347i	−0.453468	+	0.380505i
$842$	3.97374	+	56.1192i	0.136944	+	1.93399i
$843$	17.7200	+	14.0443i	0.610311	+	0.483712i
$844$	−26.2708	+	42.2068i	−0.904279	+	1.45282i
$845$	−25.8993	−	71.1578i	−0.890963	−	2.44790i
$846$	18.7515	−	5.82319i	0.644691	−	0.200205i
$847$	16.5363	−	9.54726i	0.568195	−	0.328048i
$848$	−26.7055	+	13.1414i	−0.917070	+	0.451278i
$849$	14.3879	+	4.78600i	0.493792	+	0.164255i
$850$	6.13658	+	4.45026i	0.210483	+	0.152643i
$851$	6.93294	+	5.81743i	0.237658	+	0.199419i
$852$	−7.28855	−	12.7775i	−0.249702	−	0.437749i
$853$	18.3147	+	6.66601i	0.627084	+	0.228240i	0.635961	−	0.771721i	$-0.280604\pi$
$853$	18.3147	+	6.66601i	0.627084	+	0.228240i	−0.00887785	+	0.999961i	$0.502826\pi$
$854$	−4.70597	−	18.8043i	−0.161035	−	0.643469i
$855$	40.8698	−	31.1885i	1.39772	−	1.06663i
$856$	−15.5168	+	14.0456i	−0.530353	+	0.480067i
$857$	1.18455	−	3.25451i	0.0404633	−	0.111172i	−0.917815	−	0.397007i	$-0.870049\pi$
$857$	1.18455	−	3.25451i	0.0404633	−	0.111172i	0.958279	+	0.285835i	$0.0922710\pi$
$858$	3.06626	+	10.9444i	0.104681	+	0.373637i
$859$	−5.35392	+	6.38056i	−0.182673	+	0.217702i	−0.849608	−	0.527414i	$-0.823162\pi$
$859$	−5.35392	+	6.38056i	−0.182673	+	0.217702i	0.666935	+	0.745116i	$0.267606\pi$
$860$	19.4288	−	48.3322i	0.662518	−	1.64811i
$861$	−4.90307	+	14.7399i	−0.167096	+	0.502334i
$862$	13.2887	−	46.4972i	0.452615	−	1.58370i
$863$	14.7765	+	25.5936i	0.502998	+	0.871218i	0.999994	+	0.00346494i	$0.00110293\pi$
$863$	14.7765	+	25.5936i	0.502998	+	0.871218i	−0.496996	+	0.867753i	$0.665564\pi$
$864$	−12.3973	+	26.6516i	−0.421766	+	0.906705i
$865$	−20.7849	+	7.56509i	−0.706708	+	0.257221i
$866$	1.02501	+	1.05956i	0.0348311	+	0.0360054i
$867$	−18.0066	+	22.7193i	−0.611536	+	0.771588i
$868$	8.57215	+	26.2256i	0.290958	+	0.890155i
$869$	0.588655	+	0.701532i	0.0199687	+	0.0237978i
$870$	−54.0226	−	36.9193i	−1.83154	−	1.25168i
$871$	−46.1532	+	8.13805i	−1.56384	+	0.275747i
$872$	9.05320	−	3.68549i	0.306580	−	0.124806i
$873$	−14.6615	−	4.42612i	−0.496217	−	0.149802i
$874$	−12.6008	+	9.91468i	−0.426229	+	0.335369i
$875$	−39.6433			−1.34019
$876$	5.04063	+	0.0262706i	0.170307	+	0.000887600i
$877$	5.31290	+	30.1310i	0.179404	+	1.01745i	0.932937	+	0.360040i	$0.117237\pi$
$877$	5.31290	+	30.1310i	0.179404	+	1.01745i	−0.753533	+	0.657410i	$0.771652\pi$
$878$	11.3808	−	23.3863i	0.384085	−	0.789248i
$879$	−16.3039	−	26.5008i	−0.549918	−	0.893851i
$880$	8.89179	−	9.27266i	0.299742	−	0.312581i
$881$	−24.6197	−	14.2142i	−0.829458	−	0.478888i	0.0242093	−	0.999707i	$-0.492293\pi$
$881$	−24.6197	−	14.2142i	−0.829458	−	0.478888i	−0.853667	+	0.520819i	$0.825627\pi$
$882$	−6.96456	−	13.5214i	−0.234509	−	0.455290i
$883$	−3.07785	−	8.45632i	−0.103578	−	0.284578i	0.877068	−	0.480365i	$-0.159496\pi$
$883$	−3.07785	−	8.45632i	−0.103578	−	0.284578i	−0.980646	+	0.195788i	$0.937274\pi$
$884$	4.33429	+	3.88885i	0.145778	+	0.130796i
$885$	−23.2065	+	9.18847i	−0.780077	+	0.308867i
$886$	2.26700	−	7.93224i	0.0761613	−	0.266489i
$887$	−1.62844	+	9.23534i	−0.0546776	+	0.310092i	−0.999865	−	0.0164364i	$-0.994768\pi$
$887$	−1.62844	+	9.23534i	−0.0546776	+	0.310092i	0.945187	+	0.326529i	$0.105879\pi$
$888$	−4.76952	+	16.3653i	−0.160055	+	0.549182i
$889$	19.6225	+	16.4652i	0.658118	+	0.552226i
$890$	−19.1546	−	42.9204i	−0.642063	−	1.43870i
$891$	−4.36339	−	5.91766i	−0.146179	−	0.198249i
$892$	8.25822	+	15.4659i	0.276506	+	0.517836i
$893$	4.93026	+	19.5612i	0.164985	+	0.654591i
$894$	0.697006	+	7.04393i	0.0233114	+	0.235584i
$895$	30.6630	−	84.2460i	1.02495	−	2.81603i
$896$	−6.58285	−	19.8442i	−0.219918	−	0.662948i
$897$	−16.9891	−	19.1348i	−0.567250	−	0.638891i
$898$	−10.6076	−	7.69266i	−0.353980	−	0.256707i
$899$	8.80795	−	49.9524i	0.293762	−	1.66600i
$900$	20.1127	−	59.4279i	0.670423	−	1.98093i
$901$	−1.90716	−	3.30330i	−0.0635367	−	0.110049i
$902$	3.13943	+	4.64560i	0.104532	+	0.154682i
$903$	20.7717	−	4.26413i	0.691240	−	0.141901i
$904$	1.89773	−	5.89338i	0.0631177	−	0.196011i
$905$	−59.7486	−	34.4959i	−1.98611	−	1.14668i
$906$	8.08829	+	0.615104i	0.268715	+	0.0204355i
$907$	−0.0781550	−	0.0931416i	−0.00259510	−	0.00309271i	0.764745	−	0.644333i	$-0.222865\pi$
$907$	−0.0781550	−	0.0931416i	−0.00259510	−	0.00309271i	−0.767340	+	0.641240i	$0.778420\pi$
$908$	−20.5341	−	4.32700i	−0.681449	−	0.143597i
$909$	−20.8544	−	2.48614i	−0.691696	−	0.0824601i
$910$	−58.0447	−	6.04924i	−1.92416	−	0.200530i
$911$	37.0091			1.22617			0.613083	−	0.790018i	$-0.289929\pi$
$911$	37.0091			1.22617			0.613083	+	0.790018i	$0.289929\pi$
$912$	−26.6516	−	14.2018i	−0.882524	−	0.470268i
$913$	−8.74190			−0.289315
$914$	−12.2035	−	1.27181i	−0.403655	−	0.0420676i
$915$	−50.4872	+	1.41094i	−1.66905	+	0.0466443i
$916$	−22.2427	−	4.68704i	−0.734920	−	0.154864i
$917$	8.18184	+	9.75074i	0.270188	+	0.321998i
$918$	−3.51324	−	1.35898i	−0.115954	−	0.0448530i
$919$	−34.1724	−	19.7294i	−1.12724	−	0.650814i	−0.184003	−	0.982926i	$-0.558906\pi$
$919$	−34.1724	−	19.7294i	−1.12724	−	0.650814i	−0.943240	+	0.332111i	$0.892239\pi$
$920$	−8.86526	+	27.5309i	−0.292279	+	0.907668i
$921$	−2.71359	−	13.2187i	−0.0894159	−	0.435569i
$922$	2.84865	+	4.21531i	0.0938153	+	0.138824i
$923$	12.0596	+	20.8879i	0.396948	+	0.687534i
$924$	5.14543	+	0.934955i	0.169272	+	0.0307578i
$925$	6.31797	−	35.8310i	0.207733	−	1.17812i
$926$	39.4866	+	28.6357i	1.29761	+	0.941029i
$927$	35.6316	−	23.3181i	1.17030	−	0.765867i
$928$	−6.50818	+	37.8812i	−0.213641	+	1.24351i
$929$	−15.8720	+	43.6079i	−0.520743	+	1.43073i	0.348952	+	0.937141i	$0.386538\pi$
$929$	−15.8720	+	43.6079i	−0.520743	+	1.43073i	−0.869695	+	0.493589i	$0.835685\pi$
$930$	71.5410	−	7.07908i	2.34592	−	0.232132i
$931$	14.2592	−	6.39229i	0.467326	−	0.209499i
$932$	−16.8995	−	31.6492i	−0.553561	−	1.03670i
$933$	−29.1338	−	15.7521i	−0.953798	−	0.515700i
$934$	−10.4954	−	23.5175i	−0.343420	−	0.769514i
$935$	1.26121	+	1.05828i	0.0412459	+	0.0346094i
$936$	20.0992	−	43.8044i	0.656961	−	1.43179i
$937$	−6.38508	+	36.2116i	−0.208591	+	1.18298i	0.683096	+	0.730329i	$0.260633\pi$
$937$	−6.38508	+	36.2116i	−0.208591	+	1.18298i	−0.891687	+	0.452652i	$0.850478\pi$
$938$	−5.92558	+	20.7336i	−0.193477	+	0.676976i
$939$	7.84750	+	19.8197i	0.256094	+	0.646792i
$940$	27.0855	+	24.3020i	0.883432	+	0.792642i
$941$	−17.6722	−	48.5541i	−0.576098	−	1.58282i	−0.794700	−	0.607003i	$-0.792372\pi$
$941$	−17.6722	−	48.5541i	−0.576098	−	1.58282i	0.218601	−	0.975814i	$-0.429851\pi$
$942$	−15.3049	−	21.3374i	−0.498660	−	0.695211i
$943$	−10.9320	−	6.31157i	−0.355993	−	0.205533i
$944$	10.5822	+	10.1476i	0.344423	+	0.330276i
$945$	36.4988	−	9.64504i	1.18731	−	0.313753i
$946$	3.34918	−	6.88217i	0.108891	−	0.223758i
$947$	0.208972	+	1.18514i	0.00679067	+	0.0385118i	0.988015	−	0.154359i	$-0.0493313\pi$
$947$	0.208972	+	1.18514i	0.00679067	+	0.0385118i	−0.981224	+	0.192871i	$0.938220\pi$
$948$	0.0202384	−	3.88321i	0.000657312	−	0.126121i
$949$	−8.26493			−0.268291
$950$	59.8472	+	23.9413i	1.94170	+	0.776757i
$951$	4.25574	−	28.8226i	0.138002	−	0.934637i
$952$	2.48162	−	1.01025i	0.0804297	−	0.0327423i
$953$	8.13061	−	1.43365i	0.263376	−	0.0464404i	−0.0404005	−	0.999184i	$-0.512863\pi$
$953$	8.13061	−	1.43365i	0.263376	−	0.0464404i	0.303777	+	0.952743i	$0.401752\pi$
$954$	−21.4284	+	23.1827i	−0.693771	+	0.750567i
$955$	37.2099	+	44.3450i	1.20408	+	1.43497i
$956$	15.1023	+	46.2038i	0.488442	+	1.49434i
$957$	−7.53466	−	5.97173i	−0.243561	−	0.193039i
$958$	−18.9826	−	19.6225i	−0.613299	−	0.633975i
$959$	−9.22786	+	3.35867i	−0.297983	+	0.108457i
$960$	−54.1873	+	5.60217i	−1.74889	+	0.180809i
$961$	12.3643	+	21.4157i	0.398850	+	0.690828i
$962$	7.68035	−	26.8736i	0.247624	−	0.866438i
$963$	−10.0086	+	19.8150i	−0.322522	+	0.638529i
$964$	−12.0082	+	29.8722i	−0.386758	+	0.962120i
$965$	10.6493	−	12.6913i	0.342812	−	0.408548i
$966$	−11.3373	+	3.17633i	−0.364771	+	0.102197i
$967$	1.37427	−	3.77577i	0.0441934	−	0.121420i	−0.915633	−	0.402016i	$-0.868310\pi$
$967$	1.37427	−	3.77577i	0.0441934	−	0.121420i	0.959826	+	0.280595i	$0.0905319\pi$
$968$	−21.6669	+	19.6125i	−0.696400	+	0.630370i
$969$	1.58972	−	3.52857i	0.0510690	−	0.113354i
$970$	−6.89079	−	27.5345i	−0.221250	−	0.884079i
$971$	23.1113	+	8.41181i	0.741675	+	0.269948i	0.685098	−	0.728451i	$-0.259759\pi$
$971$	23.1113	+	8.41181i	0.741675	+	0.269948i	0.0565769	+	0.998398i	$0.481981\pi$
$972$	−2.11801	+	31.1049i	−0.0679352	+	0.997690i
$973$	−7.92967	−	6.65378i	−0.254213	−	0.213310i
$974$	−40.8613	−	29.6327i	−1.30928	−	0.949493i
$975$	−32.4693	+	97.6110i	−1.03985	+	3.12605i
$976$	13.0993	+	26.6200i	0.419299	+	0.852084i
$977$	27.6979	−	15.9914i	0.886133	−	0.511609i	0.0134576	−	0.999909i	$-0.495716\pi$
$977$	27.6979	−	15.9914i	0.886133	−	0.511609i	0.872676	+	0.488300i	$0.162383\pi$
$978$	11.7562	+	24.4811i	0.375923	+	0.782820i
$979$	−2.36195	−	6.48942i	−0.0754884	−	0.207403i
$980$	14.8955	−	23.9312i	0.475821	−	0.764456i
$981$	7.55742	−	7.09729i	0.241290	−	0.226599i
$982$	3.76720	+	53.2023i	0.120216	+	1.69775i
$983$	32.1387	−	26.9676i	1.02506	−	0.860131i	0.0348091	−	0.999394i	$-0.488918\pi$
$983$	32.1387	−	26.9676i	1.02506	−	0.860131i	0.990255	+	0.139263i	$0.0444732\pi$
$984$	2.58767	−	23.6342i	0.0824918	−	0.753432i
$985$	2.76400	+	15.6754i	0.0880684	+	0.499461i
$986$	−4.89919	−	0.510578i	−0.156022	−	0.0162601i
$987$	−2.16377	+	14.6544i	−0.0688734	+	0.466455i
$988$	43.8199	+	23.0577i	1.39410	+	0.733565i
$989$			17.2314i			0.547928i
$990$	5.26904	−	12.5664i	0.167461	−	0.399386i
$991$	9.01443	−	1.58949i	0.286353	−	0.0504917i	−0.0286268	−	0.999590i	$-0.509113\pi$
$991$	9.01443	−	1.58949i	0.286353	−	0.0504917i	0.314980	+	0.949098i	$0.398002\pi$
$992$	−21.2750	−	36.4787i	−0.675481	−	1.15820i
$993$	8.87628	+	14.4277i	0.281680	+	0.457850i
$994$	11.0701	−	0.783863i	0.351123	−	0.0248626i
$995$	30.3496	−	52.5670i	0.962146	−	1.66649i
$996$	28.2719	+	23.9751i	0.895828	+	0.759680i
$997$	−20.8455	+	7.58714i	−0.660183	+	0.240287i	−0.650316	−	0.759664i	$-0.725363\pi$
$997$	−20.8455	+	7.58714i	−0.660183	+	0.240287i	−0.00986789	+	0.999951i	$0.503141\pi$
$998$	15.4351	+	22.8402i	0.488589	+	0.722993i
$999$	1.51366	+	18.0167i	0.0478902	+	0.570022i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	228.2.v.a.23.2	✓	216
3.2	odd	2	inner	228.2.v.a.23.35	yes	216
4.3	odd	2	inner	228.2.v.a.23.30	yes	216
12.11	even	2	inner	228.2.v.a.23.7	yes	216
19.5	even	9	inner	228.2.v.a.119.7	yes	216
57.5	odd	18	inner	228.2.v.a.119.30	yes	216
76.43	odd	18	inner	228.2.v.a.119.35	yes	216
228.119	even	18	inner	228.2.v.a.119.2	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.v.a.23.2	✓	216	1.1	even	1	trivial
228.2.v.a.23.7	yes	216	12.11	even	2	inner
228.2.v.a.23.30	yes	216	4.3	odd	2	inner
228.2.v.a.23.35	yes	216	3.2	odd	2	inner
228.2.v.a.119.2	yes	216	228.119	even	18	inner
228.2.v.a.119.7	yes	216	19.5	even	9	inner
228.2.v.a.119.30	yes	216	57.5	odd	18	inner
228.2.v.a.119.35	yes	216	76.43	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 228 = 2^{2} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	228.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40660 - 0.146591i) q^{2} +(0.0483859 + 1.73137i) q^{3} +(1.95702 + 0.412388i) q^{4} +(2.52711 + 3.01169i) q^{5} +(0.185744 - 2.44244i) q^{6} +(1.60040 + 0.923992i) q^{7} +(-2.69229 - 0.866945i) q^{8} +(-2.99532 + 0.167548i) q^{9} +O(q^{10})\)	\(q+(-1.40660 - 0.146591i) q^{2} +(0.0483859 + 1.73137i) q^{3} +(1.95702 + 0.412388i) q^{4} +(2.52711 + 3.01169i) q^{5} +(0.185744 - 2.44244i) q^{6} +(1.60040 + 0.923992i) q^{7} +(-2.69229 - 0.866945i) q^{8} +(-2.99532 + 0.167548i) q^{9} +(-3.11313 - 4.60668i) q^{10} +(-0.408467 - 0.707485i) q^{11} +(-0.619306 + 3.40829i) q^{12} +(0.986301 - 5.59359i) q^{13} +(-2.11567 - 1.53429i) q^{14} +(-5.09208 + 4.52109i) q^{15} +(3.65987 + 1.61411i) q^{16} +(-0.175324 + 0.481699i) q^{17} +(4.23776 + 0.203414i) q^{18} +(-0.444555 + 4.33617i) q^{19} +(3.70362 + 6.93609i) q^{20} +(-1.52234 + 2.81560i) q^{21} +(0.470837 + 1.05502i) q^{22} +(-1.99250 - 1.67190i) q^{23} +(1.37074 - 4.70330i) q^{24} +(-1.81576 + 10.2977i) q^{25} +(-2.20730 + 7.72334i) q^{26} +(-0.435020 - 5.17791i) q^{27} +(2.75098 + 2.46826i) q^{28} +(-2.32390 - 6.38485i) q^{29} +(7.82525 - 5.61289i) q^{30} +(6.46502 + 3.73258i) q^{31} +(-4.91135 - 2.80690i) q^{32} +(1.20516 - 0.741442i) q^{33} +(0.317222 - 0.651854i) q^{34} +(1.26161 + 7.15494i) q^{35} +(-5.93100 - 0.907338i) q^{36} -3.47952 q^{37} +(1.26095 - 6.03407i) q^{38} +(9.73233 + 1.43701i) q^{39} +(-4.19272 - 10.2992i) q^{40} +(4.77942 - 0.842740i) q^{41} +(2.55406 - 3.73725i) q^{42} +(-4.25838 - 5.07495i) q^{43} +(-0.507620 - 1.55301i) q^{44} +(-8.07409 - 8.59755i) q^{45} +(2.55755 + 2.64378i) q^{46} +(4.34889 - 1.58287i) q^{47} +(-2.61754 + 6.41471i) q^{48} +(-1.79248 - 3.10466i) q^{49} +(4.06358 - 14.2185i) q^{50} +(-0.842484 - 0.280244i) q^{51} +(4.23695 - 10.5400i) q^{52} +(-4.78294 + 5.70009i) q^{53} +(-0.147137 + 7.34700i) q^{54} +(1.09849 - 3.01806i) q^{55} +(-3.50769 - 3.87511i) q^{56} +(-7.52905 - 0.559881i) q^{57} +(2.33282 + 9.32157i) q^{58} +(3.44431 + 1.25363i) q^{59} +(-11.8298 + 6.74796i) q^{60} +(5.68183 + 4.76762i) q^{61} +(-8.54651 - 6.19795i) q^{62} +(-4.94852 - 2.49951i) q^{63} +(6.49681 + 4.66813i) q^{64} +(19.3386 - 11.1652i) q^{65} +(-1.80386 + 0.866243i) q^{66} +(-2.82204 - 7.75348i) q^{67} +(-0.541760 + 0.870393i) q^{68} +(2.79828 - 3.53066i) q^{69} +(-0.725724 - 10.2490i) q^{70} +(-3.25296 + 2.72956i) q^{71} +(8.20951 + 2.14569i) q^{72} +(-0.252680 - 1.43302i) q^{73} +(4.89428 + 0.510067i) q^{74} +(-17.9170 - 2.64549i) q^{75} +(-2.65819 + 8.30265i) q^{76} -1.50968i q^{77} +(-13.4788 - 3.44796i) q^{78} +(-1.10397 + 0.194660i) q^{79} +(4.38770 + 15.1014i) q^{80} +(8.94386 - 1.00372i) q^{81} +(-6.84624 + 0.484775i) q^{82} +(5.35043 - 9.26722i) q^{83} +(-4.14038 + 4.88240i) q^{84} +(-1.89379 + 0.689282i) q^{85} +(5.24588 + 7.76264i) q^{86} +(10.9421 - 4.33247i) q^{87} +(0.486359 + 2.25887i) q^{88} +(8.32500 + 1.46792i) q^{89} +(10.0967 + 13.2769i) q^{90} +(6.74692 - 8.04066i) q^{91} +(-3.20989 - 4.09364i) q^{92} +(-6.14968 + 11.3740i) q^{93} +(-6.34916 + 1.58895i) q^{94} +(-14.1826 + 9.61910i) q^{95} +(4.62215 - 8.63920i) q^{96} +(4.79715 + 1.74602i) q^{97} +(2.06617 + 4.62976i) q^{98} +(1.34203 + 2.05071i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9	\( 216 q - 18 q^{4} - 6 q^{6} - 18 q^{9} - 18 q^{10} - 3 q^{12} - 36 q^{13} - 6 q^{16} - 12 q^{18} - 30 q^{21} - 18 q^{24} - 24 q^{25} - 36 q^{28} + 12 q^{33} + 30 q^{34} - 66 q^{36} - 48 q^{37} - 42 q^{40} - 117 q^{42} - 6 q^{45} - 6 q^{46} - 81 q^{48} + 24 q^{49} + 12 q^{52} + 33 q^{54} - 12 q^{57} + 48 q^{58} - 18 q^{60} - 48 q^{61} + 36 q^{64} - 18 q^{66} - 6 q^{69} - 18 q^{70} + 12 q^{72} - 132 q^{73} + 60 q^{76} - 39 q^{78} + 18 q^{81} + 132 q^{82} - 45 q^{84} - 144 q^{85} + 114 q^{88} + 72 q^{90} - 30 q^{93} + 138 q^{96} - 60 q^{97}+O(q^{100}) \) 216 * q - 18 * q^4 - 6 * q^6 - 18 * q^9 - 18 * q^10 - 3 * q^12 - 36 * q^13 - 6 * q^16 - 12 * q^18 - 30 * q^21 - 18 * q^24 - 24 * q^25 - 36 * q^28 + 12 * q^33 + 30 * q^34 - 66 * q^36 - 48 * q^37 - 42 * q^40 - 117 * q^42 - 6 * q^45 - 6 * q^46 - 81 * q^48 + 24 * q^49 + 12 * q^52 + 33 * q^54 - 12 * q^57 + 48 * q^58 - 18 * q^60 - 48 * q^61 + 36 * q^64 - 18 * q^66 - 6 * q^69 - 18 * q^70 + 12 * q^72 - 132 * q^73 + 60 * q^76 - 39 * q^78 + 18 * q^81 + 132 * q^82 - 45 * q^84 - 144 * q^85 + 114 * q^88 + 72 * q^90 - 30 * q^93 + 138 * q^96 - 60 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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