LMFDB - Embedded newform 276.2.o.a.35.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (of order $22$, degree $10$, 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:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.9
Character	$\chi$	$=$	276.35
Dual form			276.2.o.a.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12871 - 0.852070i) q^{2} +(1.60391 - 0.653824i) q^{3} +(0.547953 + 1.92347i) q^{4} +(0.250263 + 0.852318i) q^{5} +(-2.36744 - 0.628665i) q^{6} +(-1.73353 + 1.50211i) q^{7} +(1.02046 - 2.63793i) q^{8} +(2.14503 - 2.09735i) q^{9} +O(q^{10})$	\(q+(-1.12871 - 0.852070i) q^{2} +(1.60391 - 0.653824i) q^{3} +(0.547953 + 1.92347i) q^{4} +(0.250263 + 0.852318i) q^{5} +(-2.36744 - 0.628665i) q^{6} +(-1.73353 + 1.50211i) q^{7} +(1.02046 - 2.63793i) q^{8} +(2.14503 - 2.09735i) q^{9} +(0.443761 - 1.17526i) q^{10} +(3.94293 + 2.53397i) q^{11} +(2.13648 + 2.72680i) q^{12} +(4.32888 - 4.99580i) q^{13} +(3.23655 - 0.218353i) q^{14} +(0.958664 + 1.20341i) q^{15} +(-3.39950 + 2.10794i) q^{16} +(-3.69390 + 1.68695i) q^{17} +(-4.20819 + 0.539572i) q^{18} +(3.94170 + 1.80011i) q^{19} +(-1.50228 + 0.948404i) q^{20} +(-1.79830 + 3.54267i) q^{21} +(-2.29129 - 6.21976i) q^{22} +(-3.68990 + 3.06344i) q^{23} +(-0.0880263 - 4.89819i) q^{24} +(3.54245 - 2.27660i) q^{25} +(-9.14281 + 1.95027i) q^{26} +(2.06913 - 4.76642i) q^{27} +(-3.83916 - 2.51131i) q^{28} +(5.83444 - 2.66450i) q^{29} +(-0.0566610 - 2.17514i) q^{30} +(-5.38279 + 0.773929i) q^{31} +(5.63315 + 0.517360i) q^{32} +(7.98087 + 1.48626i) q^{33} +(5.60672 + 1.24339i) q^{34} +(-1.71411 - 1.10159i) q^{35} +(5.20956 + 2.97666i) q^{36} +(-8.50962 - 2.49865i) q^{37} +(-2.91520 - 5.39041i) q^{38} +(3.67675 - 10.8431i) q^{39} +(2.50374 + 0.209577i) q^{40} +(-0.885944 - 3.01725i) q^{41} +(5.04835 - 2.46635i) q^{42} +(-4.37045 - 0.628375i) q^{43} +(-2.71348 + 8.97262i) q^{44} +(2.32443 + 1.30336i) q^{45} +(6.77507 - 0.313669i) q^{46} -2.31745 q^{47} +(-4.07424 + 5.60362i) q^{48} +(-0.247420 + 1.72084i) q^{49} +(-5.93821 - 0.448812i) q^{50} +(-4.82169 + 5.12086i) q^{51} +(11.9813 + 5.58903i) q^{52} +(-6.44542 + 5.58499i) q^{53} +(-6.39675 + 3.61684i) q^{54} +(-1.17298 + 3.99479i) q^{55} +(2.19347 + 6.10577i) q^{56} +(7.49908 + 0.310033i) q^{57} +(-8.85570 - 1.96392i) q^{58} +(0.264424 - 0.305161i) q^{59} +(-1.78942 + 2.50338i) q^{60} +(-0.544015 - 3.78371i) q^{61} +(6.73503 + 3.71298i) q^{62} +(-0.568020 + 6.85788i) q^{63} +(-5.91734 - 5.38378i) q^{64} +(5.34137 + 2.43932i) q^{65} +(-7.74165 - 8.47781i) q^{66} +(1.39761 + 2.17473i) q^{67} +(-5.26888 - 6.18074i) q^{68} +(-3.91530 + 7.32601i) q^{69} +(0.996095 + 2.70392i) q^{70} +(-2.91111 + 1.87085i) q^{71} +(-3.34374 - 7.79868i) q^{72} +(-4.87452 + 10.6737i) q^{73} +(7.47583 + 10.0710i) q^{74} +(4.19327 - 5.96759i) q^{75} +(-1.30261 + 8.56813i) q^{76} +(-10.6415 + 1.53002i) q^{77} +(-13.3891 + 9.10585i) q^{78} +(-8.85470 - 7.67265i) q^{79} +(-2.64741 - 2.36991i) q^{80} +(0.202282 - 8.99773i) q^{81} +(-1.57094 + 4.16047i) q^{82} +(2.87504 + 0.844189i) q^{83} +(-7.79961 - 1.51777i) q^{84} +(-2.36226 - 2.72619i) q^{85} +(4.39753 + 4.43318i) q^{86} +(7.61577 - 8.08830i) q^{87} +(10.7080 - 7.81537i) q^{88} +(8.15231 + 1.17212i) q^{89} +(-1.51304 - 3.45168i) q^{90} +15.1628i q^{91} +(-7.91433 - 5.41880i) q^{92} +(-8.12748 + 4.76071i) q^{93} +(2.61572 + 1.97463i) q^{94} +(-0.547807 + 3.81008i) q^{95} +(9.37330 - 2.85329i) q^{96} +(-5.89808 + 1.73183i) q^{97} +(1.74554 - 1.73151i) q^{98} +(13.7723 - 2.83426i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$

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 $

$2$	−1.12871	−	0.852070i	−0.798115	−	0.602505i
$2$	−1.12871	−	0.852070i	−0.798115	−	0.602505i
$3$	1.60391	−	0.653824i	0.926015	−	0.377486i
$3$	1.60391	−	0.653824i	0.926015	−	0.377486i
$4$	0.547953	+	1.92347i	0.273976	+	0.961736i
$5$	0.250263	+	0.852318i	0.111921	+	0.381168i	0.996335	−	0.0855349i	$-0.0272599\pi$
$5$	0.250263	+	0.852318i	0.111921	+	0.381168i	−0.884414	+	0.466703i	$0.845442\pi$
$6$	−2.36744	−	0.628665i	−0.966504	−	0.256651i
$7$	−1.73353	+	1.50211i	−0.655212	+	0.567745i	−0.917741	−	0.397179i	$-0.869989\pi$
$7$	−1.73353	+	1.50211i	−0.655212	+	0.567745i	0.262529	+	0.964924i	$0.415444\pi$
$8$	1.02046	−	2.63793i	0.360786	−	0.932649i
$9$	2.14503	−	2.09735i	0.715009	−	0.699115i
$10$	0.443761	−	1.17526i	0.140330	−	0.371649i
$11$	3.94293	+	2.53397i	1.18884	+	0.764021i	0.976991	−	0.213282i	$-0.0684152\pi$
$11$	3.94293	+	2.53397i	1.18884	+	0.764021i	0.211849	+	0.977302i	$0.432052\pi$
$12$	2.13648	+	2.72680i	0.616748	+	0.787161i
$13$	4.32888	−	4.99580i	1.20062	−	1.38559i	0.298322	−	0.954465i	$-0.403573\pi$
$13$	4.32888	−	4.99580i	1.20062	−	1.38559i	0.902294	−	0.431120i	$-0.141882\pi$
$14$	3.23655	−	0.218353i	0.865004	−	0.0583573i
$15$	0.958664	+	1.20341i	0.247526	+	0.310719i
$16$	−3.39950	+	2.10794i	−0.849874	+	0.526986i
$17$	−3.69390	+	1.68695i	−0.895901	+	0.409144i	−0.809503	−	0.587116i	$-0.800263\pi$
$17$	−3.69390	+	1.68695i	−0.895901	+	0.409144i	−0.0863987	+	0.996261i	$0.527536\pi$
$18$	−4.20819	+	0.539572i	−0.991880	+	0.127178i
$19$	3.94170	+	1.80011i	0.904288	+	0.412975i	0.812606	−	0.582814i	$-0.198048\pi$
$19$	3.94170	+	1.80011i	0.904288	+	0.412975i	0.0916824	+	0.995788i	$0.470776\pi$
$20$	−1.50228	+	0.948404i	−0.335919	+	0.212070i
$21$	−1.79830	+	3.54267i	−0.392421	+	0.773074i
$22$	−2.29129	−	6.21976i	−0.488505	−	1.32606i
$23$	−3.68990	+	3.06344i	−0.769397	+	0.638771i
$23$	−3.68990	+	3.06344i	−0.769397	+	0.638771i
$24$	−0.0880263	−	4.89819i	−0.0179683	−	0.999839i
$25$	3.54245	−	2.27660i	0.708491	−	0.455319i
$26$	−9.14281	+	1.95027i	−1.79305	+	0.382480i
$27$	2.06913	−	4.76642i	0.398203	−	0.917297i
$28$	−3.83916	−	2.51131i	−0.725534	−	0.474593i
$29$	5.83444	−	2.66450i	1.08343	−	0.494785i	0.207997	−	0.978129i	$-0.433305\pi$
$29$	5.83444	−	2.66450i	1.08343	−	0.494785i	0.875430	+	0.483345i	$0.160578\pi$
$30$	−0.0566610	−	2.17514i	−0.0103448	−	0.397125i
$31$	−5.38279	+	0.773929i	−0.966778	+	0.139002i	−0.607579	−	0.794259i	$-0.707859\pi$
$31$	−5.38279	+	0.773929i	−0.966778	+	0.139002i	−0.359199	+	0.933261i	$0.616950\pi$
$32$	5.63315	+	0.517360i	0.995809	+	0.0914573i
$33$	7.98087	+	1.48626i	1.38929	+	0.258725i
$34$	5.60672	+	1.24339i	0.961544	+	0.213240i
$35$	−1.71411	−	1.10159i	−0.289738	−	0.186203i
$36$	5.20956	+	2.97666i	0.868260	+	0.496109i
$37$	−8.50962	−	2.49865i	−1.39897	−	0.410775i	−0.506641	−	0.862157i	$-0.669113\pi$
$37$	−8.50962	−	2.49865i	−1.39897	−	0.410775i	−0.892331	+	0.451382i	$0.850931\pi$
$38$	−2.91520	−	5.39041i	−0.472907	−	0.874439i
$39$	3.67675	−	10.8431i	0.588751	−	1.73629i
$40$	2.50374	+	0.209577i	0.395875	+	0.0331370i
$41$	−0.885944	−	3.01725i	−0.138361	−	0.471215i	0.860935	−	0.508714i	$-0.169879\pi$
$41$	−0.885944	−	3.01725i	−0.138361	−	0.471215i	−0.999297	+	0.0374992i	$0.988061\pi$
$42$	5.04835	−	2.46635i	0.778978	−	0.380566i
$43$	−4.37045	−	0.628375i	−0.666487	−	0.0958263i	−0.199236	−	0.979951i	$-0.563846\pi$
$43$	−4.37045	−	0.628375i	−0.666487	−	0.0958263i	−0.467250	+	0.884125i	$0.654755\pi$
$44$	−2.71348	+	8.97262i	−0.409073	+	1.35267i
$45$	2.32443	+	1.30336i	0.346505	+	0.194293i
$46$	6.77507	−	0.313669i	0.998930	−	0.0462480i
$47$	−2.31745			−0.338034			−0.169017	−	0.985613i	$-0.554059\pi$
$47$	−2.31745			−0.338034			−0.169017	+	0.985613i	$0.554059\pi$
$48$	−4.07424	+	5.60362i	−0.588067	+	0.808813i
$49$	−0.247420	+	1.72084i	−0.0353457	+	0.245835i
$50$	−5.93821	−	0.448812i	−0.839789	−	0.0634716i
$51$	−4.82169	+	5.12086i	−0.675172	+	0.717064i
$52$	11.9813	+	5.58903i	1.66151	+	0.775059i
$53$	−6.44542	+	5.58499i	−0.885346	+	0.767157i	−0.973437	−	0.228955i	$-0.926469\pi$
$53$	−6.44542	+	5.58499i	−0.885346	+	0.767157i	0.0880904	+	0.996112i	$0.471924\pi$
$54$	−6.39675	+	3.61684i	−0.870488	+	0.492190i
$55$	−1.17298	+	3.99479i	−0.158164	+	0.538658i
$56$	2.19347	+	6.10577i	0.293115	+	0.815917i
$57$	7.49908	+	0.310033i	0.993277	+	0.0410649i
$58$	−8.85570	−	1.96392i	−1.16281	−	0.257875i
$59$	0.264424	−	0.305161i	0.0344250	−	0.0397286i	−0.738276	−	0.674499i	$-0.764360\pi$
$59$	0.264424	−	0.305161i	0.0344250	−	0.0397286i	0.772701	+	0.634770i	$0.218905\pi$
$60$	−1.78942	+	2.50338i	−0.231013	+	0.323184i
$61$	−0.544015	−	3.78371i	−0.0696540	−	0.484454i	−0.994552	−	0.104240i	$-0.966759\pi$
$61$	−0.544015	−	3.78371i	−0.0696540	−	0.484454i	0.924898	−	0.380215i	$-0.124150\pi$
$62$	6.73503	+	3.71298i	0.855350	+	0.471549i
$63$	−0.568020	+	6.85788i	−0.0715638	+	0.864012i
$64$	−5.91734	−	5.38378i	−0.739667	−	0.672973i
$65$	5.34137	+	2.43932i	0.662515	+	0.302560i
$66$	−7.74165	−	8.47781i	−0.952931	−	1.04355i
$67$	1.39761	+	2.17473i	0.170746	+	0.265686i	0.916072	−	0.401015i	$-0.131342\pi$
$67$	1.39761	+	2.17473i	0.170746	+	0.265686i	−0.745326	+	0.666700i	$0.767706\pi$
$68$	−5.26888	−	6.18074i	−0.638945	−	0.749525i
$69$	−3.91530	+	7.32601i	−0.471346	+	0.881948i
$70$	0.996095	+	2.70392i	0.119056	+	0.323180i
$71$	−2.91111	+	1.87085i	−0.345485	+	0.222030i	−0.701863	−	0.712312i	$-0.747648\pi$
$71$	−2.91111	+	1.87085i	−0.345485	+	0.222030i	0.356378	+	0.934342i	$0.384012\pi$
$72$	−3.34374	−	7.79868i	−0.394064	−	0.919083i
$73$	−4.87452	+	10.6737i	−0.570520	+	1.24926i	0.376001	+	0.926619i	$0.377299\pi$
$73$	−4.87452	+	10.6737i	−0.570520	+	1.24926i	−0.946520	+	0.322644i	$0.895428\pi$
$74$	7.47583	+	10.0710i	0.869047	+	1.17073i
$75$	4.19327	−	5.96759i	0.484197	−	0.689078i
$76$	−1.30261	+	8.56813i	−0.149419	+	0.982832i
$77$	−10.6415	+	1.53002i	−1.21271	+	0.174362i
$78$	−13.3891	+	9.10585i	−1.51601	+	1.03103i
$79$	−8.85470	−	7.67265i	−0.996232	−	0.863240i	−0.00562573	−	0.999984i	$-0.501791\pi$
$79$	−8.85470	−	7.67265i	−0.996232	−	0.863240i	−0.990606	+	0.136744i	$0.956336\pi$
$80$	−2.64741	−	2.36991i	−0.295989	−	0.264964i
$81$	0.202282	−	8.99773i	0.0224758	−	0.999747i
$82$	−1.57094	+	4.16047i	−0.173481	+	0.459447i
$83$	2.87504	+	0.844189i	0.315577	+	0.0926618i	0.435685	−	0.900099i	$-0.356506\pi$
$83$	2.87504	+	0.844189i	0.315577	+	0.0926618i	−0.120108	+	0.992761i	$0.538324\pi$
$84$	−7.79961	−	1.51777i	−0.851007	−	0.165602i
$85$	−2.36226	−	2.72619i	−0.256223	−	0.295697i
$86$	4.39753	+	4.43318i	0.474197	+	0.478042i
$87$	7.61577	−	8.08830i	0.816496	−	0.867157i
$88$	10.7080	−	7.81537i	1.14148	−	0.833122i
$89$	8.15231	+	1.17212i	0.864143	+	0.124245i	0.560112	−	0.828417i	$-0.310758\pi$
$89$	8.15231	+	1.17212i	0.864143	+	0.124245i	0.304031	+	0.952662i	$0.401667\pi$
$90$	−1.51304	−	3.45168i	−0.159489	−	0.363839i
$91$			15.1628i			1.58950i
$92$	−7.91433	−	5.41880i	−0.825126	−	0.564949i
$93$	−8.12748	+	4.76071i	−0.842781	+	0.493663i
$94$	2.61572	+	1.97463i	0.269790	+	0.203667i
$95$	−0.547807	+	3.81008i	−0.0562038	+	0.390906i
$96$	9.37330	−	2.85329i	0.956658	−	0.291213i
$97$	−5.89808	+	1.73183i	−0.598859	+	0.175841i	−0.567092	−	0.823654i	$-0.691932\pi$
$97$	−5.89808	+	1.73183i	−0.598859	+	0.175841i	−0.0317671	+	0.999495i	$0.510113\pi$
$98$	1.74554	−	1.73151i	0.176326	−	0.174908i
$99$	13.7723	−	2.83426i	1.38417	−	0.284854i
$100$	6.32007	+	5.56635i	0.632007	+	0.556635i
$101$	−1.80579	+	6.14996i	−0.179683	+	0.611944i	0.819558	+	0.572996i	$0.194219\pi$
$101$	−1.80579	+	6.14996i	−0.179683	+	0.611944i	−0.999241	+	0.0389480i	$0.987599\pi$
$102$	9.80561	−	1.67152i	0.970900	−	0.165505i
$103$	3.61601	−	5.62662i	0.356296	−	0.554407i	−0.616123	−	0.787650i	$-0.711297\pi$
$103$	3.61601	−	5.62662i	0.356296	−	0.554407i	0.972418	+	0.233243i	$0.0749338\pi$
$104$	−8.76112	−	16.5173i	−0.859099	−	1.61965i
$105$	−3.46953	−	0.646124i	−0.338591	−	0.0630552i
$106$	12.0338	−	0.811857i	1.16882	−	0.0788545i
$107$	−0.444508	−	3.09162i	−0.0429722	−	0.298879i	−0.999962	−	0.00875572i	$-0.997213\pi$
$107$	−0.444508	−	3.09162i	−0.0429722	−	0.298879i	0.956989	−	0.290123i	$-0.0936962\pi$
$108$	10.3019	+	1.36814i	0.991296	+	0.131649i
$109$	2.11393	+	4.62887i	0.202478	+	0.443365i	0.983445	−	0.181207i	$-0.0580005\pi$
$109$	2.11393	+	4.62887i	0.202478	+	0.443365i	−0.780967	+	0.624573i	$0.785273\pi$
$110$	4.72779	−	3.50948i	0.450777	−	0.334616i
$111$	−15.2823	+	1.55620i	−1.45053	+	0.147708i
$112$	2.72676	−	8.76060i	0.257654	−	0.827799i
$113$	−7.37040	−	11.4686i	−0.693349	−	1.07887i	−0.992210	−	0.124576i	$-0.960243\pi$
$113$	−7.37040	−	11.4686i	−0.693349	−	1.07887i	0.298861	−	0.954297i	$-0.403393\pi$
$114$	−8.20008	−	6.73968i	−0.768008	−	0.631228i
$115$	−3.53447	−	2.37830i	−0.329591	−	0.221777i
$116$	8.32208	+	9.76236i	0.772686	+	0.906412i
$117$	−1.19234	−	19.7953i	−0.110232	−	1.83008i
$118$	−0.558475	+	0.119130i	−0.0514118	+	0.0109668i
$119$	3.86950	−	8.47301i	0.354716	−	0.776720i
$120$	4.15278	−	1.30086i	0.379095	−	0.118752i
$121$	4.55616	+	9.97661i	0.414197	+	0.906964i
$122$	−2.60995	+	4.73423i	−0.236294	+	0.428617i
$123$	−3.39372	−	4.26013i	−0.306002	−	0.384123i
$124$	−4.43815	−	9.92958i	−0.398557	−	0.891703i
$125$	6.18359	+	5.35811i	0.553077	+	0.479244i
$126$	6.48452	−	7.25653i	0.577687	−	0.646463i
$127$	−1.62784	+	2.53297i	−0.144447	+	0.224765i	−0.905937	−	0.423413i	$-0.860832\pi$
$127$	−1.62784	+	2.53297i	−0.144447	+	0.224765i	0.761489	+	0.648177i	$0.224468\pi$
$128$	2.09157	+	11.1187i	0.184870	+	0.982763i
$129$	−7.42063	+	1.84965i	−0.653350	+	0.162853i
$130$	−3.95036	−	7.30449i	−0.346469	−	0.640647i
$131$	0.0700022	+	0.0807869i	0.00611612	+	0.00705838i	0.758799	−	0.651324i	$-0.225786\pi$
$131$	0.0700022	+	0.0807869i	0.00611612	+	0.00705838i	−0.752683	+	0.658383i	$0.771241\pi$
$132$	1.51435	+	16.1654i	0.131808	+	1.40702i
$133$	−9.53703	+	2.80032i	−0.826965	+	0.242819i
$134$	0.275528	−	3.64550i	0.0238020	−	0.314923i
$135$	4.58033	+	0.570694i	0.394212	+	0.0491175i
$136$	0.680582	+	11.4657i	0.0583595	+	0.983175i
$137$		−	18.0708i		−	1.54390i	−0.635685	−	0.771948i	$-0.719282\pi$
$137$		−	18.0708i		−	1.54390i	0.635685	−	0.771948i	$-0.280718\pi$
$138$	10.6615	−	4.93280i	0.907567	−	0.419908i
$139$		−	8.29312i		−	0.703414i	−0.936110	−	0.351707i	$-0.885601\pi$
$139$		−	8.29312i		−	0.703414i	0.936110	−	0.351707i	$-0.114399\pi$
$140$	1.17963	−	3.90067i	0.0996972	−	0.329667i
$141$	−3.71697	+	1.51520i	−0.313025	+	0.127603i
$142$	4.87988	+	0.368823i	0.409511	+	0.0309510i
$143$	29.7277	−	8.72885i	2.48596	−	0.729943i
$144$	−2.87092	+	11.6515i	−0.239244	+	0.970960i
$145$	3.73114	+	4.30597i	0.309854	+	0.357591i
$146$	14.5967	−	7.89405i	1.20803	−	0.653316i
$147$	0.728291	+	2.92184i	0.0600684	+	0.240989i
$148$	0.143216	−	17.7372i	0.0117723	−	1.45799i
$149$	4.39832	−	6.84392i	0.360324	−	0.560676i	−0.613007	−	0.790077i	$-0.710040\pi$
$149$	4.39832	−	6.84392i	0.360324	−	0.560676i	0.973332	+	0.229401i	$0.0736768\pi$
$150$	−9.81777	+	3.16269i	−0.801618	+	0.258233i
$151$	15.3350	+	13.2879i	1.24795	+	1.08135i	0.993449	+	0.114277i	$0.0364551\pi$
$151$	15.3350	+	13.2879i	1.24795	+	1.08135i	0.254496	+	0.967074i	$0.418090\pi$
$152$	8.77091	−	8.56099i	0.711415	−	0.694388i
$153$	−4.38540	+	11.3659i	−0.354538	+	0.918880i
$154$	13.3148	+	7.34036i	1.07294	+	0.591503i
$155$	−2.00675	−	4.39416i	−0.161186	−	0.352948i
$156$	22.8711	+	1.13061i	1.83116	+	0.0905208i
$157$	−2.50609	+	5.48757i	−0.200008	+	0.437956i	−0.982885	−	0.184220i	$-0.941024\pi$
$157$	−2.50609	+	5.48757i	−0.200008	+	0.437956i	0.782877	+	0.622176i	$0.213751\pi$
$158$	3.45672	+	16.2050i	0.275002	+	1.28920i
$159$	−6.68624	+	13.1720i	−0.530254	+	1.04460i
$160$	0.968813	+	4.93071i	0.0765914	+	0.389807i
$161$	1.79492	−	10.8532i	0.141459	−	0.855352i
$162$	−7.89501	+	9.98343i	−0.620291	+	0.784372i
$163$	−6.54722	−	10.1877i	−0.512818	−	0.797960i	0.484214	−	0.874950i	$-0.339106\pi$
$163$	−6.54722	−	10.1877i	−0.512818	−	0.797960i	−0.997032	+	0.0769893i	$0.975469\pi$
$164$	5.31814	−	3.35740i	0.415277	−	0.262169i
$165$	0.730549	+	7.17419i	0.0568731	+	0.558510i
$166$	−2.52577	−	3.40258i	−0.196038	−	0.264091i
$167$	0.285226	+	0.624557i	0.0220714	+	0.0483297i	0.920347	−	0.391104i	$-0.127907\pi$
$167$	0.285226	+	0.624557i	0.0220714	+	0.0483297i	−0.898275	+	0.439433i	$0.855179\pi$
$168$	7.51022	+	8.35893i	0.579426	+	0.644905i
$169$	−4.36868	−	30.3848i	−0.336052	−	2.33729i
$170$	0.343388	+	5.08988i	0.0263366	+	0.390376i
$171$	12.2305	−	4.40582i	0.935291	−	0.336921i
$172$	−1.18613	−	8.75075i	−0.0904419	−	0.667239i
$173$	−1.22464	+	1.90558i	−0.0931077	+	0.144878i	−0.884683	−	0.466194i	$-0.845625\pi$
$173$	−1.22464	+	1.90558i	−0.0931077	+	0.144878i	0.791575	+	0.611072i	$0.209261\pi$
$174$	−15.4878	+	2.64014i	−1.17412	+	0.200148i
$175$	−2.72124	+	9.26771i	−0.205707	+	0.700573i
$176$	−18.7455	−	0.302734i	−1.41299	−	0.0228194i
$177$	0.224589	−	0.662336i	0.0168811	−	0.0497842i
$178$	−8.20282	−	8.26932i	−0.614827	−	0.619812i
$179$	−22.8358	+	6.70518i	−1.70682	+	0.501169i	−0.982178	−	0.187952i	$-0.939815\pi$
$179$	−22.8358	+	6.70518i	−1.70682	+	0.501169i	−0.724646	+	0.689121i	$0.757997\pi$
$180$	−1.23329	+	5.18515i	−0.0919244	+	0.386478i
$181$	0.312619	−	2.17431i	0.0232368	−	0.161615i	−0.974899	−	0.222647i	$-0.928530\pi$
$181$	0.312619	−	2.17431i	0.0232368	−	0.161615i	0.998136	+	0.0610321i	$0.0194392\pi$
$182$	12.9198	−	17.1144i	0.957679	−	1.26860i
$183$	−3.34643	−	5.71302i	−0.247375	−	0.422319i
$184$	4.31575	+	12.8598i	0.318162	+	0.948036i
$185$		−	7.87821i		−	0.579218i
$186$	13.2300	+	1.55174i	0.970070	+	0.113779i
$187$	−18.8395	−	2.70871i	−1.37768	−	0.198080i
$188$	−1.26985	−	4.45755i	−0.0926134	−	0.325100i
$189$	3.57280	+	11.3708i	0.259883	+	0.827102i
$190$	3.86477	−	3.83369i	0.280380	−	0.278125i
$191$	−10.0775	−	11.6301i	−0.729185	−	0.841524i	0.263195	−	0.964743i	$-0.415224\pi$
$191$	−10.0775	−	11.6301i	−0.729185	−	0.841524i	−0.992380	+	0.123218i	$0.960678\pi$
$192$	−13.0109	−	4.76618i	−0.938981	−	0.343970i
$193$	7.34887	+	2.15782i	0.528983	+	0.155323i	0.535309	−	0.844657i	$-0.320195\pi$
$193$	7.34887	+	2.15782i	0.528983	+	0.155323i	−0.00632552	+	0.999980i	$0.502013\pi$
$194$	8.13284	+	3.07085i	0.583904	+	0.220474i
$195$	10.1619	+	0.420124i	0.727711	+	0.0300857i
$196$	−3.44557	+	0.467035i	−0.246112	+	0.0333596i
$197$	−1.03947	−	0.900704i	−0.0740590	−	0.0641725i	0.617045	−	0.786928i	$-0.288330\pi$
$197$	−1.03947	−	0.900704i	−0.0740590	−	0.0641725i	−0.691104	+	0.722756i	$0.742875\pi$
$198$	−17.9599	−	8.53593i	−1.27635	−	0.606622i
$199$	−18.5334	+	2.66470i	−1.31380	+	0.188896i	−0.763356	−	0.645978i	$-0.776450\pi$
$199$	−18.5334	+	2.66470i	−1.31380	+	0.188896i	−0.550442	+	0.834874i	$0.685541\pi$
$200$	−2.39058	−	11.6679i	−0.169040	−	0.825046i
$201$	3.66353	+	2.57427i	0.258406	+	0.181575i
$202$	7.27840	−	5.40283i	0.512107	−	0.380142i
$203$	−6.11179	+	13.3830i	−0.428964	+	0.939299i
$204$	−12.4919	−	6.46841i	−0.874608	−	0.452879i
$205$	2.34994	−	1.51021i	0.164127	−	0.105478i
$206$	−8.87568	+	3.26970i	−0.618398	+	0.227811i
$207$	−1.48984	+	14.3101i	−0.103551	+	0.994624i
$208$	−4.18516	+	26.1082i	−0.290189	+	1.81028i
$209$	10.9804	+	17.0859i	0.759532	+	1.18186i
$210$	3.36553	+	3.68556i	0.232244	+	0.254328i
$211$	8.93806	+	4.08188i	0.615322	+	0.281008i	0.698593	−	0.715519i	$-0.253810\pi$
$211$	8.93806	+	4.08188i	0.615322	+	0.281008i	−0.0832718	+	0.996527i	$0.526537\pi$
$212$	−14.2744	−	9.33728i	−0.980367	−	0.641287i
$213$	−3.44593	+	4.90403i	−0.236111	+	0.336018i
$214$	−2.13256	+	3.86829i	−0.145779	+	0.264431i
$215$	−0.558186	−	3.88227i	−0.0380679	−	0.264768i
$216$	−10.4620	−	10.3221i	−0.711850	−	0.702332i
$217$	8.16870	−	9.42719i	0.554528	−	0.639959i
$218$	1.55811	−	7.02585i	0.105529	−	0.475851i
$219$	−0.839538	+	20.3067i	−0.0567307	+	1.37220i
$220$	−8.32661	−	0.0672318i	−0.561380	−	0.00453277i
$221$	−7.56281	+	25.7566i	−0.508730	+	1.73257i
$222$	18.5752	+	11.2651i	1.24669	+	0.756064i
$223$	4.18574	−	3.62697i	0.280298	−	0.242880i	−0.503353	−	0.864081i	$-0.667901\pi$
$223$	4.18574	−	3.62697i	0.280298	−	0.242880i	0.783651	+	0.621201i	$0.213355\pi$
$224$	−10.5424	+	7.56475i	−0.704391	+	0.505441i
$225$	2.82385	−	12.3131i	0.188257	−	0.820874i
$226$	−1.45301	+	19.2247i	−0.0966530	+	1.27881i
$227$	2.62249	−	18.2398i	0.174061	−	1.21062i	−0.696134	−	0.717912i	$-0.745098\pi$
$227$	2.62249	−	18.2398i	0.174061	−	1.21062i	0.870195	−	0.492708i	$-0.163993\pi$
$228$	3.51280	+	14.5942i	0.232641	+	0.966521i
$229$	8.71139			0.575665			0.287832	−	0.957681i	$-0.407065\pi$
$229$	8.71139			0.575665			0.287832	+	0.957681i	$0.407065\pi$
$230$	1.96290	+	5.69601i	0.129430	+	0.375584i
$231$	−16.0676	+	9.41167i	−1.05717	+	0.619243i
$232$	−1.07497	−	18.1098i	−0.0705750	−	1.18897i
$233$	−1.86147	−	0.267639i	−0.121949	−	0.0175336i	0.0810700	−	0.996708i	$-0.474166\pi$
$233$	−1.86147	−	0.267639i	−0.121949	−	0.0175336i	−0.203019	+	0.979175i	$0.565075\pi$
$234$	−15.5212	+	23.3590i	−1.01465	+	1.52703i
$235$	−0.579971	−	1.97520i	−0.0378332	−	0.128848i
$236$	0.731861	+	0.341398i	0.0476401	+	0.0222231i
$237$	−19.2187	−	6.51678i	−1.24839	−	0.423310i
$238$	−11.5871	+	6.26646i	−0.751082	+	0.406194i
$239$	4.69479	+	1.37851i	0.303681	+	0.0891686i	0.430023	−	0.902818i	$-0.358506\pi$
$239$	4.69479	+	1.37851i	0.303681	+	0.0891686i	−0.126342	+	0.991987i	$0.540324\pi$
$240$	−5.79569	−	2.07017i	−0.374110	−	0.133629i
$241$	14.6964	+	9.44482i	0.946680	+	0.608394i	0.920281	−	0.391257i	$-0.127960\pi$
$241$	14.6964	+	9.44482i	0.946680	+	0.608394i	0.0263987	+	0.999651i	$0.491596\pi$
$242$	3.35820	−	15.1428i	0.215873	−	0.973417i
$243$	−5.55849	−	14.5638i	−0.356577	−	0.934266i
$244$	6.97977	−	3.11969i	0.446834	−	0.199718i
$245$	−1.52862	+	0.219783i	−0.0976602	+	0.0140414i
$246$	0.200583	+	7.70012i	0.0127887	+	0.490942i
$247$	26.0562	−	11.8995i	1.65792	−	0.757144i
$248$	−3.45134	+	14.9892i	−0.219160	+	0.951814i
$249$	5.16325	−	0.525775i	0.327208	−	0.0333196i
$250$	−2.41397	−	11.3166i	−0.152673	−	0.715724i
$251$	−22.7468	+	14.6185i	−1.43576	+	0.922709i	−0.436022	+	0.899936i	$0.643613\pi$
$251$	−22.7468	+	14.6185i	−1.43576	+	0.922709i	−0.999741	+	0.0227727i	$0.992751\pi$
$252$	−13.5022	+	2.66522i	−0.850558	+	0.167893i
$253$	−22.3117	+	2.72885i	−1.40272	+	0.171561i
$254$	3.99562	−	1.47194i	0.250707	−	0.0923578i
$255$	−5.57129	−	2.82805i	−0.348888	−	0.177100i
$256$	7.11314	−	14.3319i	0.444571	−	0.895743i
$257$	19.3644	+	8.84345i	1.20792	+	0.551639i	0.914594	−	0.404373i	$-0.132510\pi$
$257$	19.3644	+	8.84345i	1.20792	+	0.551639i	0.293327	+	0.956012i	$0.405238\pi$
$258$	9.95174	+	4.23519i	0.619568	+	0.263671i
$259$	18.5049	−	8.45091i	1.14984	−	0.525114i
$260$	−1.76515	+	11.6106i	−0.109470	+	0.720059i
$261$	6.92665	−	17.9522i	0.428749	−	1.11122i
$262$	−0.0101758	−	0.150831i	−0.000628664	−	0.00931840i
$263$	9.80172	−	11.3118i	0.604400	−	0.697514i	−0.368267	−	0.929720i	$-0.620049\pi$
$263$	9.80172	−	11.3118i	0.604400	−	0.697514i	0.972667	+	0.232206i	$0.0745942\pi$
$264$	12.0648	−	19.5363i	0.742536	−	1.20238i
$265$	−6.37323	−	4.09583i	−0.391505	−	0.251605i
$266$	13.1506	+	4.96547i	0.806313	+	0.304453i
$267$	13.8419	−	3.45020i	0.847110	−	0.211149i
$268$	−3.41721	+	3.87992i	−0.208739	+	0.237004i
$269$	2.01516	−	1.74614i	0.122866	−	0.106464i	−0.591260	−	0.806481i	$-0.701369\pi$
$269$	2.01516	−	1.74614i	0.122866	−	0.106464i	0.714127	+	0.700016i	$0.246824\pi$
$270$	−4.68357	−	4.54690i	−0.285033	−	0.276716i
$271$	−1.07047	−	3.64570i	−0.0650266	−	0.221460i	0.920569	−	0.390580i	$-0.127726\pi$
$271$	−1.07047	−	3.64570i	−0.0650266	−	0.221460i	−0.985595	+	0.169120i	$0.945907\pi$
$272$	9.00140	−	13.5213i	0.545790	−	0.819849i
$273$	9.91383	+	24.3198i	0.600012	+	1.47190i
$274$	−15.3976	+	20.3967i	−0.930205	+	1.23221i
$275$	19.7365			1.19016
$276$	−16.2368	−	3.51666i	−0.977339	−	0.211678i
$277$	−0.860661			−0.0517121			−0.0258561	−	0.999666i	$-0.508231\pi$
$277$	−0.860661			−0.0517121			−0.0258561	+	0.999666i	$0.508231\pi$
$278$	−7.06632	+	9.36050i	−0.423810	+	0.561405i
$279$	−9.92304	+	12.9497i	−0.594077	+	0.775277i
$280$	−4.65511	+	3.39758i	−0.278196	+	0.203044i
$281$	3.28155	+	11.1759i	0.195761	+	0.666701i	0.997605	+	0.0691674i	$0.0220343\pi$
$281$	3.28155	+	11.1759i	0.195761	+	0.666701i	−0.801844	+	0.597533i	$0.796148\pi$
$282$	5.48642	+	1.45690i	0.326712	+	0.0867570i
$283$	11.7480	−	10.1797i	0.698349	−	0.605123i	−0.231600	−	0.972811i	$-0.574396\pi$
$283$	11.7480	−	10.1797i	0.698349	−	0.605123i	0.929949	+	0.367688i	$0.119851\pi$
$284$	−5.19369	−	4.57430i	−0.308189	−	0.271434i
$285$	1.61249	+	6.46918i	0.0955159	+	0.383201i
$286$	−40.9914	−	15.4778i	−2.42387	−	0.915222i
$287$	6.06805	+	3.89970i	0.358186	+	0.230192i
$288$	13.1683	−	10.7049i	0.775952	−	0.630792i
$289$	−0.333549	+	0.384936i	−0.0196205	+	0.0226433i
$290$	−0.542374	−	8.03936i	−0.0318493	−	0.472088i
$291$	−8.32765	+	6.63400i	−0.488175	+	0.388892i
$292$	−23.2016	−	3.52732i	−1.35777	−	0.206421i
$293$	0.00187563		0.000856573i	0.000109576		5.00415e-5i	−0.415360	−	0.909657i	$-0.636344\pi$
$293$	0.00187563		0.000856573i	0.000109576		5.00415e-5i	0.415470	+	0.909607i	$0.363617\pi$
$294$	1.66758	−	3.91845i	0.0972555	−	0.228529i
$295$	0.326270	+	0.149002i	0.0189961	+	0.00867525i
$296$	−15.2750	+	19.8980i	−0.887838	+	1.15655i
$297$	20.2364	−	13.5506i	1.17423	−	0.786284i
$298$	−10.7959	+	3.97709i	−0.625390	+	0.230387i
$299$	−0.668813	+	31.6953i	−0.0386784	+	1.83298i
$300$	13.7762	+	4.79568i	0.795370	+	0.276879i
$301$	8.52018	−	5.47559i	0.491095	−	0.315608i
$302$	−5.98652	−	28.0646i	−0.344485	−	1.61494i
$303$	1.12468	+	11.0446i	0.0646109	+	0.634497i
$304$	−17.1943	+	2.18940i	−0.986163	+	0.125571i
$305$	3.08878	−	1.41060i	0.176863	−	0.0807705i
$306$	14.6344	−	9.09211i	0.836592	−	0.519761i
$307$	0.568643	−	0.0817585i	0.0324541	−	0.00466620i	−0.126069	−	0.992022i	$-0.540236\pi$
$307$	0.568643	−	0.0817585i	0.0324541	−	0.00466620i	0.158523	+	0.987355i	$0.449327\pi$
$308$	−8.77398	−	19.6303i	−0.499944	−	1.11854i
$309$	2.12091	−	11.3888i	0.120655	−	0.647886i
$310$	−1.47911	+	6.66961i	−0.0840078	+	0.378808i
$311$	−6.29953	−	4.04846i	−0.357213	−	0.229567i	0.349709	−	0.936858i	$-0.386281\pi$
$311$	−6.29953	−	4.04846i	−0.357213	−	0.229567i	−0.706922	+	0.707291i	$0.749917\pi$
$312$	−24.8514	−	20.7639i	−1.40693	−	1.17553i
$313$	22.7153	+	6.66982i	1.28395	+	0.377000i	0.851355	−	0.524590i	$-0.175781\pi$
$313$	22.7153	+	6.66982i	1.28395	+	0.377000i	0.432590	+	0.901591i	$0.357600\pi$
$314$	7.50444	−	4.05849i	0.423500	−	0.229034i
$315$	−5.98725	+	1.23214i	−0.337343	+	0.0694232i
$316$	9.90617	−	21.2360i	0.557265	−	1.19462i
$317$	4.95415	+	16.8723i	0.278253	+	0.947642i	0.973465	+	0.228837i	$0.0734924\pi$
$317$	4.95415	+	16.8723i	0.278253	+	0.947642i	−0.695212	+	0.718805i	$0.744689\pi$
$318$	18.7702	−	9.17012i	1.05258	−	0.514235i
$319$	29.7566	+	4.27835i	1.66605	+	0.239541i
$320$	3.10780	−	6.39081i	0.173731	−	0.357257i
$321$	−2.73433	−	4.66804i	−0.152615	−	0.260545i
$322$	−11.2736	+	10.7207i	−0.628254	+	0.597440i
$323$	−17.5969			−0.979119
$324$	17.4177	−	4.54124i	0.967651	−	0.252291i
$325$	3.96145	−	27.5525i	0.219742	−	1.52834i
$326$	−1.29073	+	17.0776i	−0.0714869	+	0.945840i
$327$	6.41702	+	6.04213i	0.354862	+	0.334131i
$328$	−8.86336	−	0.741914i	−0.489397	−	0.0409653i
$329$	4.01736	−	3.48106i	0.221484	−	0.191917i
$330$	5.28834	−	8.72003i	0.291113	−	0.480022i
$331$	1.16675	−	3.97358i	0.0641303	−	0.218408i	−0.921193	−	0.389106i	$-0.872784\pi$
$331$	1.16675	−	3.97358i	0.0641303	−	0.218408i	0.985323	+	0.170698i	$0.0546022\pi$
$332$	−0.0483866	+	5.99265i	−0.00265556	+	0.328889i
$333$	−23.4939	+	12.4879i	−1.28746	+	0.684335i
$334$	0.210231	−	0.947974i	0.0115033	−	0.0518708i
$335$	−1.50379	+	1.73547i	−0.0821608	+	0.0948186i
$336$	−1.35444	−	15.8340i	−0.0738906	−	0.863816i
$337$	1.96050	+	13.6356i	0.106795	+	0.742777i	0.970903	+	0.239471i	$0.0769741\pi$
$337$	1.96050	+	13.6356i	0.106795	+	0.742777i	−0.864108	+	0.503306i	$0.832117\pi$
$338$	−20.9590	+	38.0179i	−1.14002	+	2.06790i
$339$	−19.3199	−	13.5756i	−1.04931	−	0.737323i
$340$	3.94935	−	6.03757i	0.214184	−	0.327433i
$341$	−23.1851	−	10.5883i	−1.25554	−	0.573388i
$342$	−17.5587	−	5.44839i	−0.949467	−	0.294615i
$343$	−10.8368	−	16.8624i	−0.585132	−	0.910483i
$344$	−6.11746	+	10.8877i	−0.329831	+	0.587025i
$345$	−7.22394	−	1.50365i	−0.388924	−	0.0809535i
$346$	3.00595	−	1.10736i	0.161601	−	0.0595319i
$347$	1.78063	−	1.14434i	0.0955894	−	0.0614315i	−0.491973	−	0.870611i	$-0.663724\pi$
$347$	1.78063	−	1.14434i	0.0955894	−	0.0614315i	0.587562	+	0.809179i	$0.300088\pi$
$348$	19.7307	+	10.2167i	1.05768	+	0.547674i
$349$	−3.80212	+	8.32549i	−0.203523	+	0.445653i	−0.983679	−	0.179932i	$-0.942412\pi$
$349$	−3.80212	+	8.32549i	−0.203523	+	0.445653i	0.780156	+	0.625585i	$0.215140\pi$
$350$	10.9682	−	8.14182i	0.586276	−	0.435199i
$351$	−14.8551	−	30.9702i	−0.792904	−	1.65307i
$352$	20.9002	+	16.3141i	1.11398	+	0.869547i
$353$	10.0978	−	1.45184i	0.537452	−	0.0772739i	0.131756	−	0.991282i	$-0.457938\pi$
$353$	10.0978	−	1.45184i	0.537452	−	0.0772739i	0.405696	+	0.914008i	$0.367029\pi$
$354$	−0.817851	+	0.556217i	−0.0434683	+	0.0295626i
$355$	−2.32310	−	2.01298i	−0.123298	−	0.106838i
$356$	2.21253	+	16.3230i	0.117264	+	0.865118i
$357$	0.666442	−	16.1199i	0.0352719	−	0.853155i
$358$	31.4881	+	11.8895i	1.66420	+	0.628379i
$359$	27.7679	+	8.15338i	1.46553	+	0.430319i	0.914644	−	0.404261i	$-0.132471\pi$
$359$	27.7679	+	8.15338i	1.46553	+	0.430319i	0.550887	+	0.834580i	$0.314289\pi$
$360$	5.81014	−	4.80165i	0.306221	−	0.253069i
$361$	−0.145759	−	0.168215i	−0.00767154	−	0.00885343i
$362$	−2.20552	+	2.18778i	−0.115920	+	0.114987i
$363$	13.8306	+	13.0226i	0.725919	+	0.683509i
$364$	−29.1653	+	8.30851i	−1.52868	+	0.435485i
$365$	−10.3173	−	1.48340i	−0.540033	−	0.0776450i
$366$	−1.09076	+	9.29972i	−0.0570150	+	0.486104i
$367$			26.0405i			1.35930i	0.733536	+	0.679651i	$0.237869\pi$
$367$			26.0405i			1.35930i	−0.733536	+	0.679651i	$0.762131\pi$
$368$	6.08623	−	18.1922i	0.317267	−	0.948336i
$369$	−8.22859	−	4.61395i	−0.428363	−	0.240193i
$370$	−6.71279	+	8.89218i	−0.348981	+	0.462283i
$371$	2.78405	−	19.3635i	0.144541	−	1.00530i
$372$	−13.6106	−	13.0243i	−0.705675	−	0.675281i
$373$	8.78438	−	2.57933i	0.454838	−	0.133553i	−0.0462855	−	0.998928i	$-0.514738\pi$
$373$	8.78438	−	2.57933i	0.454838	−	0.133553i	0.501124	+	0.865376i	$0.332920\pi$
$374$	18.9562	+	19.1099i	0.980202	+	0.988148i
$375$	13.4212	+	4.55092i	0.693066	+	0.235009i
$376$	−2.36485	+	6.11326i	−0.121958	+	0.315267i
$377$	11.9453	−	40.6820i	0.615215	−	2.09523i
$378$	5.65606	−	15.8785i	0.290916	−	0.816704i
$379$	−9.90513	+	15.4127i	−0.508792	+	0.791696i	−0.996698	−	0.0812001i	$-0.974125\pi$
$379$	−9.90513	+	15.4127i	−0.508792	+	0.791696i	0.487905	+	0.872896i	$0.337761\pi$
$380$	−7.62876	+	1.03405i	−0.391347	+	0.0530458i
$381$	−0.954785	+	5.12696i	−0.0489151	+	0.262662i
$382$	1.46491	+	21.7137i	0.0749515	+	1.11097i
$383$	1.18343	+	8.23092i	0.0604703	+	0.420580i	0.997460	+	0.0712242i	$0.0226906\pi$
$383$	1.18343	+	8.23092i	0.0604703	+	0.420580i	−0.936990	+	0.349356i	$0.886400\pi$
$384$	10.6244	+	16.4658i	0.542172	+	0.840268i
$385$	−3.96723	−	8.68703i	−0.202189	−	0.442732i
$386$	−6.45609	−	8.69730i	−0.328606	−	0.442681i
$387$	−10.6926	+	7.81845i	−0.543538	+	0.397434i
$388$	−6.56300	−	10.3958i	−0.333186	−	0.527768i
$389$	−0.146121	−	0.227369i	−0.00740865	−	0.0115281i	0.837529	−	0.546392i	$-0.183999\pi$
$389$	−0.146121	−	0.227369i	−0.00740865	−	0.0115281i	−0.844938	+	0.534864i	$0.820363\pi$
$390$	−11.1119	−	9.13288i	−0.562671	−	0.462461i
$391$	8.46224	−	17.5407i	0.427954	−	0.887070i
$392$	4.28698	+	2.40872i	0.216525	+	0.121659i
$393$	0.165097	+	0.0838054i	0.00832806	+	0.00422742i
$394$	0.405790	+	1.90233i	0.0204434	+	0.0958380i
$395$	4.32353	−	9.46720i	0.217540	−	0.476347i
$396$	12.9982	+	24.9376i	0.653184	+	1.25316i
$397$	5.67966	+	12.4367i	0.285054	+	0.624181i	0.996945	−	0.0781088i	$-0.0248882\pi$
$397$	5.67966	+	12.4367i	0.285054	+	0.624181i	−0.711891	+	0.702290i	$0.752161\pi$
$398$	23.1893	+	12.7841i	1.16237	+	0.640809i
$399$	−13.4656	+	10.7270i	−0.674122	+	0.537022i
$400$	−7.24362	+	15.2066i	−0.362181	+	0.760329i
$401$	−8.25156	−	7.15002i	−0.412063	−	0.357055i	0.424024	−	0.905651i	$-0.360617\pi$
$401$	−8.25156	−	7.15002i	−0.412063	−	0.357055i	−0.836088	+	0.548596i	$0.815163\pi$
$402$	−1.94159	−	6.02718i	−0.0968379	−	0.300608i
$403$	−19.4351	+	30.2416i	−0.968131	+	1.50644i
$404$	−12.8188	−	0.103503i	−0.637757	−	0.00514947i
$405$	7.71954	−	2.07939i	0.383587	−	0.103326i
$406$	18.3016	−	9.89774i	0.908295	−	0.491217i
$407$	−27.2214	−	31.4151i	−1.34931	−	1.55719i
$408$	8.58814	+	17.9449i	0.425176	+	0.888405i
$409$	−3.07234	+	0.902120i	−0.151917	+	0.0446069i	−0.356807	−	0.934178i	$-0.616135\pi$
$409$	−3.07234	+	0.902120i	−0.151917	+	0.0446069i	0.204890	+	0.978785i	$0.434316\pi$
$410$	−3.93919	−	0.297725i	−0.194543	−	0.0147036i
$411$	−11.8152	−	28.9839i	−0.582799	−	1.42967i
$412$	12.8040	+	3.87217i	0.630810	+	0.190768i
$413$			0.926199i			0.0455753i
$414$	13.8748	−	14.8825i	0.681911	−	0.731435i
$415$			2.66172i			0.130659i
$416$	26.9699	−	25.9025i	1.32231	−	1.26997i
$417$	−5.42225	−	13.3014i	−0.265529	−	0.651372i
$418$	2.16470	−	28.6410i	0.105879	−	1.40088i
$419$	−23.2355	+	6.82255i	−1.13513	+	0.333303i	−0.794721	−	0.606975i	$-0.792383\pi$
$419$	−23.2355	+	6.82255i	−1.13513	+	0.333303i	−0.340406	+	0.940279i	$0.610565\pi$
$420$	−0.658336	−	7.02759i	−0.0321235	−	0.342911i
$421$	17.8620	+	20.6138i	0.870540	+	1.00466i	0.999915	+	0.0130605i	$0.00415740\pi$
$421$	17.8620	+	20.6138i	0.870540	+	1.00466i	−0.129375	+	0.991596i	$0.541297\pi$
$422$	−6.61040	−	12.2231i	−0.321789	−	0.595011i
$423$	−4.97099	+	4.86049i	−0.241698	+	0.236325i
$424$	8.15553	+	22.7018i	0.396068	+	1.10250i
$425$	−9.24496	+	14.3854i	−0.448447	+	0.697796i
$426$	8.06802	−	2.59903i	0.390897	−	0.125923i
$427$	6.62662	+	5.74200i	0.320685	+	0.277875i
$428$	5.70308	−	2.54906i	0.275669	−	0.123214i
$429$	41.9733	−	33.4370i	2.02649	−	1.61435i
$430$	−2.67794	+	4.85755i	−0.129142	+	0.234252i
$431$	12.2133	+	26.7433i	0.588292	+	1.28818i	0.936469	+	0.350751i	$0.114074\pi$
$431$	12.2133	+	26.7433i	0.588292	+	1.28818i	−0.348176	+	0.937429i	$0.613199\pi$
$432$	3.01336	+	20.5650i	0.144980	+	0.989435i
$433$	−1.97709	+	4.32923i	−0.0950130	+	0.208049i	−0.951171	−	0.308665i	$-0.900118\pi$
$433$	−1.97709	+	4.32923i	−0.0950130	+	0.208049i	0.856158	+	0.516714i	$0.172845\pi$
$434$	−17.2527	+	3.68021i	−0.828155	+	0.176656i
$435$	8.79975	+	4.46685i	0.421915	+	0.214169i
$436$	−7.74517	+	6.60250i	−0.370926	+	0.316202i
$437$	−20.0590	+	5.43292i	−0.959553	+	0.259892i
$438$	18.2503	−	22.2050i	0.872035	−	1.06099i
$439$	−12.7838	−	19.8920i	−0.610139	−	0.949394i	−0.999598	−	0.0283506i	$-0.990975\pi$
$439$	−12.7838	−	19.8920i	−0.610139	−	0.949394i	0.389459	−	0.921044i	$-0.372662\pi$
$440$	9.34100	+	7.17074i	0.445315	+	0.341852i
$441$	3.07848	+	4.21018i	0.146594	+	0.200485i
$442$	30.4826	−	22.6275i	1.44991	−	1.07628i
$443$	9.52306	+	20.8526i	0.452454	+	0.990737i	0.989143	+	0.146956i	$0.0469477\pi$
$443$	9.52306	+	20.8526i	0.452454	+	0.990737i	−0.536689	+	0.843780i	$0.680325\pi$
$444$	−11.3673	−	28.5424i	−0.539467	−	1.35456i
$445$	1.04120	+	7.24169i	0.0493575	+	0.343289i
$446$	−7.81490	+	0.527231i	−0.370046	+	0.0249651i
$447$	2.57977	−	13.8527i	0.122019	−	0.655212i
$448$	18.3449	+	0.444446i	0.866716	+	0.0209981i
$449$	−20.0327	+	31.1714i	−0.945400	+	1.47107i	−0.0644162	+	0.997923i	$0.520519\pi$
$449$	−20.0327	+	31.1714i	−0.945400	+	1.47107i	−0.880983	+	0.473147i	$0.843118\pi$
$450$	−13.6789	+	11.4918i	−0.644831	+	0.541727i
$451$	4.15240	−	14.1418i	0.195529	−	0.665910i
$452$	18.0209	−	20.4610i	0.847630	−	0.962405i
$453$	33.2838	+	11.2861i	1.56381	+	0.530266i
$454$	−18.5016	+	18.3529i	−0.868325	+	0.861342i
$455$	−12.9235	+	3.79470i	−0.605865	+	0.177898i
$456$	8.47033	−	19.4657i	0.396659	−	0.911563i
$457$	−0.701717	+	4.88055i	−0.0328249	+	0.228302i	−0.999630	−	0.0272141i	$-0.991336\pi$
$457$	−0.701717	+	4.88055i	−0.0328249	+	0.228302i	0.966805	+	0.255516i	$0.0822455\pi$
$458$	−9.83259	−	7.42271i	−0.459447	−	0.346841i
$459$	0.397552	+	21.0971i	0.0185561	+	0.984731i
$460$	2.63787	−	8.10165i	0.122991	−	0.377741i
$461$		−	28.4522i		−	1.32515i	−0.748994	−	0.662576i	$-0.769463\pi$
$461$		−	28.4522i		−	1.32515i	0.748994	−	0.662576i	$-0.230537\pi$
$462$	26.1550	+	3.06771i	1.21684	+	0.142723i
$463$	16.7543	+	2.40891i	0.778640	+	0.111951i	0.520164	−	0.854066i	$-0.325871\pi$
$463$	16.7543	+	2.40891i	0.778640	+	0.111951i	0.258476	+	0.966018i	$0.416780\pi$
$464$	−14.2175	+	21.3566i	−0.660032	+	0.991456i
$465$	−6.09165	−	5.73576i	−0.282493	−	0.265990i
$466$	1.87301	+	1.88819i	0.0867653	+	0.0874687i
$467$	7.16079	+	8.26399i	0.331362	+	0.382412i	0.896843	−	0.442349i	$-0.145855\pi$
$467$	7.16079	+	8.26399i	0.331362	+	0.382412i	−0.565481	+	0.824761i	$0.691309\pi$
$468$	37.4224	−	13.1403i	1.72985	−	0.607412i
$469$	−5.68949	−	1.67059i	−0.262716	−	0.0771405i
$470$	−1.02839	+	2.72360i	−0.0474362	+	0.125630i
$471$	−0.431623	+	10.4401i	−0.0198882	+	0.481054i
$472$	−0.535160	−	1.00893i	−0.0246328	−	0.0464400i
$473$	−15.6401	−	13.5522i	−0.719132	−	0.623132i
$474$	16.1395	+	23.7312i	0.741311	+	1.09001i
$475$	18.0614	−	2.59684i	0.828715	−	0.119151i
$476$	18.4179	+	2.80006i	0.844184	+	0.128340i
$477$	−2.11195	+	25.4982i	−0.0966995	+	1.16748i
$478$	−4.12444	−	5.55622i	−0.188648	−	0.254136i
$479$	7.10529	−	15.5584i	0.324649	−	0.710882i	−0.674988	−	0.737829i	$-0.735851\pi$
$479$	7.10529	−	15.5584i	0.324649	−	0.710882i	0.999637	+	0.0269468i	$0.00857848\pi$
$480$	4.77770	+	7.27495i	0.218071	+	0.332055i
$481$	−49.3199	+	31.6960i	−2.24879	+	1.44521i
$482$	−8.54029	−	23.1828i	−0.389000	−	1.05595i
$483$	−4.21721	−	18.5811i	−0.191890	−	0.845468i
$484$	−16.6932	+	14.2304i	−0.758780	+	0.646835i
$485$	−2.95214	−	4.59362i	−0.134050	−	0.208586i
$486$	−6.13545	+	21.1744i	−0.278309	+	0.960491i
$487$	25.3053	+	11.5565i	1.14669	+	0.523677i	0.895853	−	0.444351i	$-0.146566\pi$
$487$	25.3053	+	11.5565i	1.14669	+	0.523677i	0.250840	+	0.968028i	$0.419293\pi$
$488$	−10.5363	−	2.42604i	−0.476956	−	0.109822i
$489$	−17.1621	−	12.0593i	−0.776096	−	0.545342i
$490$	1.91264	+	1.05442i	0.0864041	+	0.0476341i
$491$	5.23087	+	36.3815i	0.236066	+	1.64187i	0.671033	+	0.741427i	$0.265851\pi$
$491$	5.23087	+	36.3815i	0.236066	+	1.64187i	−0.434967	+	0.900446i	$0.643240\pi$
$492$	6.33465	−	8.86208i	0.285588	−	0.399534i
$493$	−17.0569	+	19.6848i	−0.768206	+	0.886557i
$494$	−39.5489	−	8.77071i	−1.77939	−	0.394613i
$495$	5.86239	+	11.0291i	0.263495	+	0.495720i
$496$	16.6674	−	13.9776i	0.748388	−	0.627613i
$497$	2.23626	−	7.61599i	0.100310	−	0.341624i
$498$	−6.27579	−	3.80601i	−0.281225	−	0.170551i
$499$	30.0834	−	26.0674i	1.34672	−	1.16694i	0.376026	−	0.926609i	$-0.377290\pi$
$499$	30.0834	−	26.0674i	1.34672	−	1.16694i	0.970692	−	0.240329i	$-0.0772552\pi$
$500$	−6.91787	+	14.8300i	−0.309376	+	0.663216i
$501$	0.865826	+	0.815243i	0.0386823	+	0.0364224i
$502$	38.1303	+	2.88190i	1.70184	+	0.128626i
$503$	5.06328	−	35.2159i	0.225761	−	1.57020i	−0.489917	−	0.871769i	$-0.662973\pi$
$503$	5.06328	−	35.2159i	0.225761	−	1.57020i	0.715677	−	0.698431i	$-0.246118\pi$
$504$	17.5110	+	8.49656i	0.780000	+	0.378467i
$505$	−5.69364			−0.253364
$506$	27.5085	+	15.9311i	1.22290	+	0.708222i
$507$	−26.8733	−	45.8780i	−1.19348	−	2.03751i
$508$	−5.76408	−	1.74316i	−0.255740	−	0.0773402i
$509$	40.1023	+	5.76583i	1.77750	+	0.255566i	0.951401	−	0.307956i	$-0.0996450\pi$
$509$	40.1023	+	5.76583i	1.77750	+	0.255566i	0.826101	+	0.563522i	$0.190554\pi$
$510$	3.87865	+	7.93917i	0.171749	+	0.351552i
$511$	−7.58298	−	25.8253i	−0.335451	−	1.14244i
$512$	−20.2404	+	10.1156i	−0.894509	+	0.447050i
$513$	16.7360	−	15.0631i	0.738911	−	0.665053i
$514$	−14.3215	−	26.4815i	−0.631695	−	1.16805i
$515$	5.70062	+	1.67385i	0.251199	+	0.0737587i
$516$	−7.62390	−	13.2599i	−0.335624	−	0.583733i
$517$	−9.13754	−	5.87234i	−0.401869	−	0.258265i
$518$	−28.0874	−	6.22890i	−1.23409	−	0.273682i
$519$	−0.718295	+	3.85707i	−0.0315296	+	0.169306i
$520$	11.8854	−	11.6009i	0.521209	−	0.508734i
$521$	−35.1375	+	5.05201i	−1.53940	+	0.221333i	−0.859180	−	0.511674i	$-0.829026\pi$
$521$	−35.1375	+	5.05201i	−1.53940	+	0.221333i	−0.680222	+	0.733006i	$0.738116\pi$
$522$	−23.1147	+	14.3608i	−1.01170	+	0.628556i
$523$	−2.39162	+	1.09222i	−0.104578	+	0.0477592i	−0.467017	−	0.884248i	$-0.654671\pi$
$523$	−2.39162	+	1.09222i	−0.104578	+	0.0477592i	0.362439	+	0.932007i	$0.381944\pi$
$524$	−0.117033	+	0.178915i	−0.00511263	+	0.00781593i
$525$	1.69483	+	16.6437i	0.0739687	+	0.726393i
$526$	−20.7017	+	4.41592i	−0.902636	+	0.192543i
$527$	18.5779	−	11.9393i	0.809266	−	0.520084i
$528$	−30.2639	+	11.7707i	−1.31707	+	0.512253i
$529$	4.23068	−	22.6076i	0.183943	−	0.982937i
$530$	3.70357	+	10.0534i	0.160873	+	0.436693i
$531$	−0.0728325	−	1.20917i	−0.00316066	−	0.0524733i
$532$	−10.6122	−	16.8098i	−0.460097	−	0.728796i
$533$	−18.9087	−	8.63532i	−0.819028	−	0.374037i
$534$	−18.5632	−	7.90001i	−0.803310	−	0.341867i
$535$	2.52380	−	1.15258i	0.109113	−	0.0498304i
$536$	7.16299	−	1.46759i	0.309394	−	0.0633902i
$537$	−32.2424	+	25.6851i	−1.39136	+	1.10839i
$538$	−3.76236	+	0.253827i	−0.162207	+	0.0109432i
$539$	−5.33612	+	6.15821i	−0.229843	+	0.265253i
$540$	1.41209	+	9.12284i	0.0607666	+	0.392585i
$541$	−19.4244	−	12.4833i	−0.835122	−	0.536700i	0.0517800	−	0.998659i	$-0.483511\pi$
$541$	−19.4244	−	12.4833i	−0.835122	−	0.536700i	−0.886902	+	0.461959i	$0.847147\pi$
$542$	−1.89814	+	5.02704i	−0.0815321	+	0.215930i
$543$	−0.920207	−	3.69179i	−0.0394899	−	0.158430i
$544$	−21.6810	+	7.59174i	−0.929566	+	0.325493i
$545$	−3.41623	+	2.96018i	−0.146335	+	0.126800i
$546$	9.53234	−	35.8971i	0.407946	−	1.53625i
$547$	−7.54307	−	25.6893i	−0.322518	−	1.09840i	−0.948030	−	0.318182i	$-0.896928\pi$
$547$	−7.54307	−	25.6893i	−0.322518	−	1.09840i	0.625511	−	0.780215i	$-0.284890\pi$
$548$	34.7588	−	9.90197i	1.48482	−	0.422991i
$549$	−9.10268	−	6.97517i	−0.388493	−	0.297693i
$550$	−22.2767	−	16.8169i	−0.949881	−	0.717074i
$551$	27.7940			1.18406
$552$	15.3301	+	17.8041i	0.652493	+	0.757795i
$553$	26.8751			1.14284
$554$	0.971433	+	0.733344i	0.0412722	+	0.0311568i
$555$	−5.15097	−	12.6359i	−0.218646	−	0.536365i
$556$	15.9516	−	4.54424i	0.676498	−	0.192719i
$557$	−0.255938	−	0.871646i	−0.0108445	−	0.0369328i	0.953893	−	0.300147i	$-0.0970357\pi$
$557$	−0.255938	−	0.871646i	−0.0108445	−	0.0369328i	−0.964737	+	0.263214i	$0.915217\pi$
$558$	22.2342	−	6.16125i	0.941250	−	0.260826i
$559$	−22.0584	+	19.1137i	−0.932971	+	0.808424i
$560$	8.14922	+	0.131608i	0.344368	+	0.00556144i
$561$	−31.9877	+	7.97319i	−1.35052	+	0.336628i
$562$	5.81878	−	15.4105i	0.245450	−	0.650051i
$563$	6.85435	+	4.40502i	0.288876	+	0.185650i	0.677051	−	0.735936i	$-0.263258\pi$
$563$	6.85435	+	4.40502i	0.288876	+	0.185650i	−0.388174	+	0.921586i	$0.626894\pi$
$564$	−4.95118	−	6.31923i	−0.208482	−	0.266087i
$565$	7.93033	−	9.15208i	0.333631	−	0.385031i
$566$	−21.9339	+	1.47977i	−0.921952	+	0.0621993i
$567$	13.1649	+	15.9017i	0.552875	+	0.667807i
$568$	1.96452	+	9.58842i	0.0824296	+	0.402321i
$569$	38.8936	−	17.7621i	1.63050	−	0.744626i	0.630989	−	0.775792i	$-0.282649\pi$
$569$	38.8936	−	17.7621i	1.63050	−	0.744626i	0.999514	+	0.0311661i	$0.00992208\pi$
$570$	3.69217	−	8.67576i	0.154648	−	0.363388i
$571$	−33.8816	−	15.4732i	−1.41790	−	0.647534i	−0.448673	−	0.893696i	$-0.648103\pi$
$571$	−33.8816	−	15.4732i	−1.41790	−	0.647534i	−0.969229	+	0.246162i	$0.920831\pi$
$572$	33.0791	+	52.3975i	1.38311	+	2.19085i
$573$	−23.7675	−	12.0646i	−0.992900	−	0.504008i
$574$	−3.52623	−	9.57202i	−0.147182	−	0.399529i
$575$	−6.09707	+	19.2525i	−0.254266	+	0.802885i
$576$	−23.9845	+	0.862339i	−0.999354	+	0.0359308i
$577$	0.641384	−	0.412192i	0.0267012	−	0.0171598i	−0.527222	−	0.849727i	$-0.676766\pi$
$577$	0.641384	−	0.412192i	0.0267012	−	0.0171598i	0.553923	+	0.832568i	$0.313130\pi$
$578$	0.704472	−	0.150272i	0.0293022	−	0.00625051i
$579$	13.1977	−	1.34393i	0.548479	−	0.0558517i
$580$	−6.23792	+	9.53621i	−0.259016	+	0.395970i
$581$	−6.25204	+	2.85521i	−0.259378	+	0.118454i
$582$	15.0521	−	0.392097i	0.623930	−	0.0162529i
$583$	−39.5661	+	5.68874i	−1.63866	+	0.235604i
$584$	23.1823	+	23.7507i	0.959289	+	0.982811i
$585$	16.5735	−	5.97028i	0.685229	−	0.246841i
$586$	−0.00284690		0.000631352i	−0.000117604		2.60809e-5i
$587$	9.99654	+	6.42438i	0.412601	+	0.265163i	0.730433	−	0.682984i	$-0.239318\pi$
$587$	9.99654	+	6.42438i	0.412601	+	0.265163i	−0.317832	+	0.948147i	$0.602955\pi$
$588$	−5.22101	+	3.00188i	−0.215311	+	0.123795i
$589$	−22.6105	−	6.63905i	−0.931651	−	0.273557i
$590$	−0.241302	−	0.446184i	−0.00993424	−	0.0183691i
$591$	−2.25611	−	0.765015i	−0.0928040	−	0.0314685i
$592$	34.1954	−	9.44365i	1.40542	−	0.388132i
$593$	11.1415	+	37.9444i	0.457526	+	1.55819i	0.788796	+	0.614655i	$0.210705\pi$
$593$	11.1415	+	37.9444i	0.457526	+	1.55819i	−0.331270	+	0.943536i	$0.607477\pi$
$594$	−34.3869	−	1.94822i	−1.41091	−	0.0799364i
$595$	8.19009	+	1.17756i	0.335761	+	0.0482751i
$596$	15.5742	+	4.70991i	0.637943	+	0.192925i
$597$	−27.9836	+	16.3915i	−1.14529	+	0.670860i
$598$	27.7615	−	35.2047i	1.13525	−	1.43963i
$599$	−32.7381			−1.33764			−0.668822	−	0.743422i	$-0.733201\pi$
$599$	−32.7381			−1.33764			−0.668822	+	0.743422i	$0.733201\pi$
$600$	−11.4630	−	17.1512i	−0.467976	−	0.700195i
$601$	−3.14662	+	21.8852i	−0.128353	+	0.892718i	0.819288	+	0.573382i	$0.194369\pi$
$601$	−3.14662	+	21.8852i	−0.128353	+	0.892718i	−0.947642	+	0.319336i	$0.896540\pi$
$602$	−14.2824	−	1.07947i	−0.582106	−	0.0439957i
$603$	7.55908	+	1.73358i	0.307830	+	0.0705966i
$604$	−17.1560	+	36.7776i	−0.698067	+	1.49646i
$605$	−7.36300	+	6.38007i	−0.299348	+	0.259387i
$606$	8.14137	−	13.4244i	0.330720	−	0.545330i
$607$	−3.61645	+	12.3165i	−0.146787	+	0.499911i	−0.999757	−	0.0220494i	$-0.992981\pi$
$607$	−3.61645	+	12.3165i	−0.146787	+	0.499911i	0.852970	+	0.521960i	$0.174799\pi$
$608$	21.2729	+	12.1796i	0.862729	+	0.493948i
$609$	−1.05263	+	25.4610i	−0.0426548	+	1.03173i
$610$	−4.68825	−	1.03971i	−0.189822	−	0.0420964i
$611$	−10.0320	+	11.5775i	−0.405850	+	0.468376i
$612$	−24.2650	−	2.20721i	−0.980856	−	0.0892211i
$613$	−0.00585301	−	0.0407086i	−0.000236401	−	0.00164420i	0.989703	−	0.143137i	$-0.0457189\pi$
$613$	−0.00585301	−	0.0407086i	−0.000236401	−	0.00164420i	−0.989939	+	0.141493i	$0.954810\pi$
$614$	−0.711494	−	0.392242i	−0.0287136	−	0.0158296i
$615$	2.78166	−	3.95868i	0.112167	−	0.159629i
$616$	−6.82311	+	29.6328i	−0.274911	+	1.19394i
$617$	−36.6351	−	16.7307i	−1.47487	−	0.673552i	−0.494225	−	0.869334i	$-0.664548\pi$
$617$	−36.6351	−	16.7307i	−1.47487	−	0.673552i	−0.980647	+	0.195782i	$0.937276\pi$
$618$	−12.0979	+	11.0474i	−0.486651	+	0.444393i
$619$	3.17418	+	4.93912i	0.127581	+	0.198520i	0.899168	−	0.437604i	$-0.144173\pi$
$619$	3.17418	+	4.93912i	0.127581	+	0.198520i	−0.771587	+	0.636124i	$0.780537\pi$
$620$	7.35245	−	6.26772i	0.295282	−	0.251718i
$621$	6.96677	+	23.9262i	0.279567	+	0.960126i
$622$	3.66074	+	9.93716i	0.146782	+	0.398444i
$623$	−15.8929	+	10.2138i	−0.636736	+	0.409206i
$624$	10.3576	+	44.6115i	0.414636	+	1.78589i
$625$	5.72712	−	12.5406i	0.229085	−	0.501625i
$626$	−19.9557	−	26.8833i	−0.797592	−	1.07447i
$627$	28.7828	+	20.2249i	1.14947	+	0.807704i
$628$	−11.9284	−	1.81347i	−0.475996	−	0.0723652i
$629$	35.6487	−	5.12551i	1.42141	−	0.204368i
$630$	7.80771	+	3.71083i	0.311067	+	0.147843i
$631$	−11.4134	−	9.88977i	−0.454360	−	0.393705i	0.397393	−	0.917649i	$-0.369915\pi$
$631$	−11.4134	−	9.88977i	−0.454360	−	0.393705i	−0.851753	+	0.523943i	$0.824460\pi$
$632$	−29.2757	+	15.5285i	−1.16453	+	0.617690i
$633$	17.0046	+	0.703021i	0.675874	+	0.0279426i
$634$	8.78460	−	23.2651i	0.348881	−	0.923977i
$635$	−2.56628	−	0.753528i	−0.101840	−	0.0299029i
$636$	−28.9997	−	5.64319i	−1.14991	−	0.223767i
$637$	7.52593	+	8.68539i	0.298188	+	0.344128i
$638$	−29.9409	−	30.1837i	−1.18537	−	1.19498i
$639$	−2.32057	+	10.1186i	−0.0918005	+	0.400287i
$640$	−8.95321	+	4.56528i	−0.353907	+	0.180458i
$641$	31.4751	+	4.52544i	1.24319	+	0.178744i	0.732348	−	0.680930i	$-0.238424\pi$
$641$	31.4751	+	4.52544i	1.24319	+	0.178744i	0.510843	+	0.859674i	$0.329333\pi$
$642$	−0.891248	+	7.59869i	−0.0351747	+	0.299896i
$643$		−	16.3820i		−	0.646044i	−0.946391	−	0.323022i	$-0.895301\pi$
$643$		−	16.3820i		−	0.646044i	0.946391	−	0.323022i	$-0.104699\pi$
$644$	21.8594	−	2.49457i	0.861379	−	0.0982996i
$645$	−3.43360	−	5.86183i	−0.135198	−	0.230809i
$646$	19.8618	+	14.9938i	0.781450	+	0.589924i
$647$	−1.94462	+	13.5251i	−0.0764510	+	0.531728i	0.915222	+	0.402949i	$0.132015\pi$
$647$	−1.94462	+	13.5251i	−0.0764510	+	0.531728i	−0.991673	+	0.128779i	$0.958894\pi$
$648$	−23.5289	−	9.71540i	−0.924304	−	0.381657i
$649$	1.81587	−	0.533189i	0.0712793	−	0.0209295i
$650$	−27.9480	+	27.7232i	−1.09621	+	1.08740i
$651$	6.93810	−	20.4612i	0.271926	−	0.801938i
$652$	16.0082	−	18.1758i	0.626928	−	0.711818i
$653$	−4.75066	+	16.1793i	−0.185908	+	0.633144i	0.812810	+	0.582528i	$0.197936\pi$
$653$	−4.75066	+	16.1793i	−0.185908	+	0.633144i	−0.998718	+	0.0506154i	$0.983882\pi$
$654$	−2.09461	−	12.2875i	−0.0819057	−	0.480481i
$655$	−0.0513371	+	0.0798821i	−0.00200591	+	0.00312125i
$656$	9.37196	+	8.38960i	0.365913	+	0.327559i
$657$	11.9305	+	33.1190i	0.465453	+	1.29209i
$658$	−7.50053	+	0.506022i	−0.292401	+	0.0197268i
$659$	−6.06585	−	42.1889i	−0.236292	−	1.64345i	−0.669978	−	0.742381i	$-0.733696\pi$
$659$	−6.06585	−	42.1889i	−0.236292	−	1.64345i	0.433686	−	0.901064i	$-0.357213\pi$
$660$	−13.3991	+	5.33631i	−0.521557	+	0.207715i
$661$	5.53444	+	12.1187i	0.215265	+	0.471364i	0.986202	−	0.165547i	$-0.0529391\pi$
$661$	5.53444	+	12.1187i	0.215265	+	0.471364i	−0.770937	+	0.636911i	$0.780212\pi$
$662$	−4.70269	+	3.49085i	−0.182775	+	0.135676i
$663$	4.71024	+	46.2558i	0.182930	+	1.79643i
$664$	5.16077	−	6.72270i	0.200277	−	0.260891i
$665$	−4.77353	−	7.42776i	−0.185110	−	0.288036i
$666$	37.1583	+	5.92324i	1.43985	+	0.229521i
$667$	−13.3659	+	27.7052i	−0.517531	+	1.07275i
$668$	−1.04503	+	0.890852i	−0.0404334	+	0.0344681i
$669$	4.34214	−	8.55405i	0.167877	−	0.330719i
$670$	3.17607	−	0.677496i	0.122702	−	0.0261739i
$671$	7.44279	−	16.2974i	0.287326	−	0.629156i
$672$	−11.9629	+	19.0260i	−0.461480	+	0.733944i
$673$	−13.4724	−	29.5005i	−0.519323	−	1.13716i	−0.969695	−	0.244318i	$-0.921436\pi$
$673$	−13.4724	−	29.5005i	−0.519323	−	1.13716i	0.450372	−	0.892841i	$-0.351291\pi$
$674$	9.40564	−	17.0610i	0.362292	−	0.657167i
$675$	−3.52143	−	21.5954i	−0.135540	−	0.831206i
$676$	56.0505	−	25.0525i	2.15579	−	0.963556i
$677$	−5.05560	−	4.38070i	−0.194303	−	0.168364i	0.552276	−	0.833661i	$-0.313759\pi$
$677$	−5.05560	−	4.38070i	−0.194303	−	0.168364i	−0.746579	+	0.665297i	$0.768305\pi$
$678$	10.2391	+	31.7847i	0.393231	+	1.22068i
$679$	7.62309	−	11.8618i	0.292547	−	0.455212i
$680$	−9.60208	+	3.44951i	−0.368223	+	0.132283i
$681$	−7.71942	−	30.9696i	−0.295809	−	1.18676i
$682$	17.1472	+	31.7064i	0.656601	+	1.21410i
$683$	−29.8954	−	34.5012i	−1.14392	−	1.32015i	−0.940005	−	0.341161i	$-0.889180\pi$
$683$	−29.8954	−	34.5012i	−1.14392	−	1.32015i	−0.203911	−	0.978989i	$-0.565365\pi$
$684$	15.1762	+	21.1109i	0.580277	+	0.807195i
$685$	15.4021	−	4.52246i	0.588484	−	0.172795i
$686$	−2.13638	+	28.2664i	−0.0815674	+	1.07922i
$687$	13.9722	−	5.69572i	0.533074	−	0.217305i
$688$	16.1819	−	7.07650i	0.616929	−	0.269789i
$689$			56.3768i			2.14778i
$690$	6.87249	+	7.85248i	0.261631	+	0.298939i
$691$			35.1017i			1.33533i	0.744461	+	0.667665i	$0.232706\pi$
$691$			35.1017i			1.33533i	−0.744461	+	0.667665i	$0.767294\pi$
$692$	−4.33637	−	1.31140i	−0.164844	−	0.0498518i
$693$	−19.6173	+	25.6008i	−0.745201	+	0.972495i
$694$	−2.98487	−	0.225597i	−0.113304	−	0.00856356i
$695$	7.06837	−	2.07546i	0.268119	−	0.0787268i
$696$	−13.5648	−	28.3436i	−0.514172	−	1.07436i
$697$	8.36252	+	9.65086i	0.316753	+	0.365553i
$698$	11.3854	−	6.15735i	0.430943	−	0.233059i
$699$	−3.16061	+	0.787808i	−0.119545	+	0.0297976i
$700$	−19.3173	−	0.155974i	−0.730125	−	0.00589528i
$701$	4.99350	−	7.77003i	0.188602	−	0.293470i	−0.734057	−	0.679088i	$-0.762375\pi$
$701$	4.99350	−	7.77003i	0.188602	−	0.293470i	0.922658	+	0.385618i	$0.126012\pi$
$702$	−9.62180	+	47.6138i	−0.363152	+	1.79707i
$703$	−29.0445	−	25.1672i	−1.09543	−	0.949199i
$704$	−9.68932	−	36.2223i	−0.365180	−	1.36518i
$705$	−2.22165	−	2.78884i	−0.0836723	−	0.105034i
$706$	−12.6345	−	6.96533i	−0.475506	−	0.262144i
$707$	−6.10753	−	13.3736i	−0.229697	−	0.502967i
$708$	1.39705	+	0.0690613i	0.0525043	+	0.00259548i
$709$	18.4489	−	40.3974i	0.692862	−	1.51716i	−0.155554	−	0.987827i	$-0.549716\pi$
$709$	18.4489	−	40.3974i	0.692862	−	1.51716i	0.848416	−	0.529329i	$-0.177556\pi$
$710$	0.906900	+	4.25151i	0.0340353	+	0.159556i
$711$	−35.0858	+	2.11334i	−1.31582	+	0.0792566i
$712$	11.4111	−	20.3091i	0.427647	−	0.761116i
$713$	17.4911	−	19.3456i	0.655046	−	0.724498i
$714$	−14.4875	+	17.6268i	−0.542181	+	0.659665i
$715$	14.8795	+	23.1529i	0.556462	+	0.865871i
$716$	−25.4101	−	40.2498i	−0.949622	−	1.50421i
$717$	8.43130	−	0.858560i	0.314873	−	0.0320635i
$718$	−24.3945	−	32.8629i	−0.910394	−	1.22643i
$719$	−12.4151	−	27.1852i	−0.463004	−	1.01384i	−0.986792	−	0.161989i	$-0.948209\pi$
$719$	−12.4151	−	27.1852i	−0.463004	−	1.01384i	0.523788	−	0.851849i	$-0.324518\pi$
$720$	−10.6493	+	0.469006i	−0.396875	+	0.0174788i
$721$	2.18335	+	15.1856i	0.0813123	+	0.565539i
$722$	0.0211882	+	0.314062i	0.000788542	+	0.0116882i
$723$	29.7469	+	5.53972i	1.10630	+	0.206024i
$724$	4.35353	−	0.590106i	0.161798	−	0.0219311i
$725$	14.6022	−	22.7215i	0.542313	−	0.843856i
$726$	−4.51451	−	26.4833i	−0.167549	−	0.982889i
$727$	−13.6377	+	46.4459i	−0.505796	+	1.72258i	0.169954	+	0.985452i	$0.445638\pi$
$727$	−13.6377	+	46.4459i	−0.505796	+	1.72258i	−0.675750	+	0.737131i	$0.736180\pi$
$728$	39.9985	+	15.4730i	1.48244	+	0.573468i
$729$	−18.4374	−	19.7246i	−0.682868	−	0.730542i
$730$	10.3812	+	10.4654i	0.384227	+	0.387342i
$731$	17.2040	−	5.05155i	0.636313	−	0.186838i
$732$	9.15516	−	9.56724i	0.338384	−	0.353615i
$733$	0.656047	−	4.56291i	0.0242316	−	0.168535i	−0.974112	−	0.226066i	$-0.927414\pi$
$733$	0.656047	−	4.56291i	0.0242316	−	0.168535i	0.998344	+	0.0575308i	$0.0183227\pi$
$734$	22.1883	−	29.3920i	0.818985	−	1.08488i
$735$	−2.30807	+	1.35196i	−0.0851344	+	0.0498679i
$736$	−22.3706	+	15.3478i	−0.824592	+	0.565727i
$737$			12.1163i			0.446311i
$738$	5.35624	+	12.2191i	0.197166	+	0.449792i
$739$	24.1626	+	3.47406i	0.888837	+	0.127795i	0.571582	−	0.820545i	$-0.306330\pi$
$739$	24.1626	+	3.47406i	0.888837	+	0.127795i	0.317255	+	0.948340i	$0.397239\pi$
$740$	15.1535	−	4.31689i	0.557055	−	0.158692i
$741$	34.0115	−	36.1218i	1.24944	−	1.32697i
$742$	−19.6414	+	19.4835i	−0.721059	+	0.715260i
$743$	−8.55749	−	9.87587i	−0.313944	−	0.362311i	0.576745	−	0.816924i	$-0.304323\pi$
$743$	−8.55749	−	9.87587i	−0.313944	−	0.362311i	−0.890689	+	0.454614i	$0.849777\pi$
$744$	4.26468	+	26.2978i	0.156351	+	0.964125i
$745$	6.93393	+	2.03599i	0.254040	+	0.0745927i
$746$	−12.1128	−	4.57361i	−0.443479	−	0.167452i
$747$	7.93760	−	4.21915i	0.290422	−	0.154371i
$748$	−5.11301	−	37.7214i	−0.186950	−	1.37923i
$749$	5.41453	+	4.69172i	0.197843	+	0.171432i
$750$	−11.2708	−	16.5724i	−0.411553	−	0.605139i
$751$	36.7341	−	5.28156i	1.34045	−	0.192727i	0.565497	−	0.824751i	$-0.308685\pi$
$751$	36.7341	−	5.28156i	1.34045	−	0.192727i	0.774949	+	0.632024i	$0.217775\pi$
$752$	7.87815	−	4.88505i	0.287287	−	0.178139i
$753$	−26.9258	+	38.3190i	−0.981229	+	1.39642i
$754$	−48.1466	+	35.7397i	−1.75340	+	1.30156i
$755$	−7.48769	+	16.3958i	−0.272505	+	0.596703i
$756$	−19.9137	+	13.1028i	−0.724253	+	0.476545i
$757$	36.5744	−	23.5050i	1.32932	−	0.854303i	0.333248	−	0.942839i	$-0.391855\pi$
$757$	36.5744	−	23.5050i	1.32932	−	0.854303i	0.996073	+	0.0885365i	$0.0282190\pi$
$758$	24.3127	−	8.95652i	0.883076	−	0.325315i
$759$	−34.0017	+	18.9647i	−1.23418	+	0.688377i
$760$	9.49171	+	5.33310i	0.344301	+	0.193452i
$761$	0.741379	+	1.15361i	0.0268750	+	0.0418183i	0.854431	−	0.519565i	$-0.173906\pi$
$761$	0.741379	+	1.15361i	0.0268750	+	0.0418183i	−0.827556	+	0.561383i	$0.810269\pi$
$762$	5.44621	−	4.97329i	0.197295	−	0.180163i
$763$	−10.6176	−	4.84892i	−0.384385	−	0.175543i
$764$	16.8482	−	25.7566i	0.609545	−	0.931842i
$765$	−10.7849	−	0.893282i	−0.389928	−	0.0322967i
$766$	5.67758	−	10.2986i	0.205139	−	0.372105i
$767$	−0.379864	−	2.64201i	−0.0137161	−	0.0953976i
$768$	2.03826	−	27.6378i	0.0735495	−	0.997292i
$769$	−3.98474	+	4.59864i	−0.143694	+	0.165831i	−0.823034	−	0.567992i	$-0.807720\pi$
$769$	−3.98474	+	4.59864i	−0.143694	+	0.165831i	0.679341	+	0.733823i	$0.262266\pi$
$770$	−2.92412	+	13.1855i	−0.105378	+	0.475171i
$771$	36.8408	+	1.52310i	1.32679	+	0.0548533i
$772$	−0.123681	+	15.3177i	−0.00445136	+	0.551297i
$773$	−5.06545	+	17.2513i	−0.182192	+	0.620488i	0.816856	+	0.576842i	$0.195715\pi$
$773$	−5.06545	+	17.2513i	−0.182192	+	0.620488i	−0.999047	+	0.0436452i	$0.986103\pi$
$774$	18.7307	+	0.286151i	0.673262	+	0.0102855i
$775$	−17.3064	+	14.9961i	−0.621663	+	0.538674i
$776$	−1.45028	+	17.3260i	−0.0520621	+	0.621966i
$777$	24.1547	−	25.6534i	0.866546	−	0.920312i
$778$	−0.0288066	+	0.381139i	−0.00103277	+	0.0136645i
$779$	1.93927	−	13.4879i	0.0694814	−	0.483254i
$780$	4.76016	+	19.7764i	0.170441	+	0.708109i
$781$	−16.2190			−0.580361
$782$	−24.4973	+	12.5878i	−0.876021	+	0.450140i
$783$	−0.627926	−	33.3225i	−0.0224402	−	1.19085i
$784$	−2.78634	−	6.37154i	−0.0995120	−	0.227555i
$785$	−5.30434	−	0.762649i	−0.189320	−	0.0272201i
$786$	−0.114938	−	0.235266i	−0.00409971	−	0.00839167i
$787$	8.43135	+	28.7145i	0.300545	+	1.02356i	0.961880	+	0.273472i	$0.0881720\pi$
$787$	8.43135	+	28.7145i	0.300545	+	1.02356i	−0.661335	+	0.750091i	$0.730010\pi$
$788$	1.16290	−	2.49293i	0.0414266	−	0.0888070i
$789$	8.32511	−	24.5516i	0.296382	−	0.874061i
$790$	−12.9467	+	7.00173i	−0.460623	+	0.249111i
$791$	30.0039	+	8.80994i	1.06682	+	0.313245i
$792$	6.57747	−	39.2226i	0.233720	−	1.39372i
$793$	−21.2576	−	13.6615i	−0.754881	−	0.485132i
$794$	4.18630	−	18.8769i	0.148566	−	0.669915i
$795$	−12.9000	−	2.40235i	−0.457516	−	0.0852024i
$796$	−15.2809	−	34.1884i	−0.541617	−	1.21177i
$797$	28.7011	−	4.12659i	1.01664	−	0.146171i	0.386208	−	0.922412i	$-0.373785\pi$
$797$	28.7011	−	4.12659i	1.01664	−	0.146171i	0.630437	+	0.776241i	$0.282876\pi$
$798$	24.3388	−	0.634009i	0.861585	−	0.0224437i
$799$	8.56041	−	3.90941i	0.302846	−	0.138305i
$800$	21.1330	−	10.9917i	0.747164	−	0.388615i
$801$	19.9453	−	14.5840i	0.704731	−	0.515299i
$802$	3.22127	+	15.1012i	0.113747	+	0.533241i
$803$	−46.2668	+	29.7339i	−1.63272	+	1.04929i
$804$	−2.94409	+	8.45729i	−0.103830	+	0.298265i
$805$	9.69957	−	1.18631i	0.341865	−	0.0418121i
$806$	47.7045	−	17.5738i	1.68032	−	0.619011i
$807$	2.09045	−	4.11821i	0.0735874	−	0.144968i
$808$	14.3804	+	11.0393i	0.505901	+	0.388362i
$809$	−34.7776	−	15.8824i	−1.22272	−	0.558396i	−0.303758	−	0.952749i	$-0.598241\pi$
$809$	−34.7776	−	15.8824i	−1.22272	−	0.558396i	−0.918959	+	0.394353i	$0.870969\pi$
$810$	−10.4849	−	4.23057i	−0.368401	−	0.148647i
$811$	−38.7102	+	17.6783i	−1.35930	+	0.620770i	−0.955748	−	0.294187i	$-0.904951\pi$
$811$	−38.7102	+	17.6783i	−1.35930	+	0.620770i	−0.403550	+	0.914958i	$0.632224\pi$
$812$	−29.0907	−	4.42264i	−1.02088	−	0.155204i
$813$	−4.10058	−	5.14745i	−0.143814	−	0.180529i
$814$	3.95701	+	58.6529i	0.138693	+	2.05578i
$815$	7.04461	−	8.12991i	0.246762	−	0.284778i
$816$	5.59684	−	27.5722i	0.195929	−	0.965220i
$817$	−16.0958	−	10.3442i	−0.563122	−	0.361897i
$818$	4.23643	+	1.59962i	0.148123	+	0.0559294i
$819$	31.8017	+	32.5247i	1.11124	+	1.13650i
$820$	4.19250	+	3.69251i	0.146409	+	0.128948i
$821$	11.9775	−	10.3786i	0.418017	−	0.362214i	−0.420311	−	0.907380i	$-0.638079\pi$
$821$	11.9775	−	10.3786i	0.418017	−	0.362214i	0.838328	+	0.545166i	$0.183533\pi$
$822$	−11.3605	+	42.7817i	−0.396243	+	1.49218i
$823$	−1.41454	−	4.81748i	−0.0493078	−	0.167927i	0.931158	−	0.364615i	$-0.118799\pi$
$823$	−1.41454	−	4.81748i	−0.0493078	−	0.167927i	−0.980466	+	0.196688i	$0.936981\pi$
$824$	−11.1526	−	15.2805i	−0.388521	−	0.532321i
$825$	31.6555	−	12.9042i	1.10210	−	0.449267i
$826$	0.789187	−	1.04541i	0.0274593	−	0.0363743i
$827$	14.4254			0.501621			0.250810	−	0.968036i	$-0.419303\pi$
$827$	14.4254			0.501621			0.250810	+	0.968036i	$0.419303\pi$
$828$	−28.3415	+	4.97562i	−0.984937	+	0.172915i
$829$	48.9017			1.69843			0.849213	−	0.528051i	$-0.177077\pi$
$829$	48.9017			1.69843			0.849213	+	0.528051i	$0.177077\pi$
$830$	2.26797	−	3.00430i	0.0787225	−	0.104281i
$831$	−1.38042	+	0.562721i	−0.0478862	+	0.0195206i
$832$	−52.5118	+	6.25605i	−1.82052	+	0.216889i
$833$	−1.98902	−	6.77400i	−0.0689156	−	0.234705i
$834$	−5.21360	+	19.6335i	−0.180532	+	0.679852i
$835$	−0.460940	+	0.399406i	−0.0159515	+	0.0138220i
$836$	−26.8475	+	30.4828i	−0.928540	+	1.05427i
$837$	−7.44881	+	27.2580i	−0.257468	+	0.942174i
$838$	32.0393	+	12.0976i	1.10678	+	0.417905i
$839$	40.5302	+	26.0472i	1.39926	+	0.899249i	0.999846	−	0.0175222i	$-0.00557778\pi$
$839$	40.5302	+	26.0472i	1.39926	+	0.899249i	0.399412	+	0.916771i	$0.369214\pi$
$840$	−5.24493	+	8.49302i	−0.180967	+	0.293037i
$841$	7.95013	−	9.17494i	0.274142	−	0.316377i
$842$	−2.59649	−	38.4866i	−0.0894810	−	1.32634i
$843$	12.5704	+	15.7796i	0.432948	+	0.543478i
$844$	−2.95374	+	19.4288i	−0.101672	+	0.668767i
$845$	24.8042	−	11.3277i	0.853290	−	0.389684i
$846$	9.75226	−	1.25043i	0.335290	−	0.0429907i
$847$	−22.8842	−	10.4509i	−0.786311	−	0.359096i
$848$	10.1383	−	32.5727i	0.348152	−	1.11855i
$849$	12.1870	−	24.0085i	0.418257	−	0.823970i
$850$	22.6922	−	8.35957i	0.778338	−	0.286731i
$851$	39.0541	−	16.8489i	1.33876	−	0.577574i
$852$	−11.3210	−	3.94098i	−0.387850	−	0.135016i
$853$	−41.0748	+	26.3972i	−1.40638	+	0.903823i	−0.999951	−	0.00986166i	$-0.996861\pi$
$853$	−41.0748	+	26.3972i	−1.40638	+	0.903823i	−0.406424	+	0.913684i	$0.633225\pi$
$854$	−2.58692	−	12.1274i	−0.0885225	−	0.414990i
$855$	6.81600	+	9.32167i	0.233102	+	0.318794i
$856$	−8.60908	−	1.98229i	−0.294252	−	0.0677532i
$857$	13.7480	−	6.27850i	0.469623	−	0.214469i	−0.166524	−	0.986037i	$-0.553254\pi$
$857$	13.7480	−	6.27850i	0.469623	−	0.214469i	0.636147	+	0.771568i	$0.280527\pi$
$858$	−75.8662	+	1.97626i	−2.59003	+	0.0674684i
$859$	33.1113	−	4.76068i	1.12974	−	0.162432i	0.448006	−	0.894030i	$-0.352134\pi$
$859$	33.1113	−	4.76068i	1.12974	−	0.162432i	0.681736	+	0.731598i	$0.261225\pi$
$860$	7.16157	−	3.20095i	0.244208	−	0.109152i
$861$	12.2823	+	2.28731i	0.418580	+	0.0779514i
$862$	9.00201	−	40.5919i	0.306610	−	1.38257i
$863$	4.33545	+	2.78622i	0.147580	+	0.0948442i	0.612347	−	0.790589i	$-0.290225\pi$
$863$	4.33545	+	2.78622i	0.147580	+	0.0948442i	−0.464767	+	0.885433i	$0.653862\pi$
$864$	14.1216	−	25.7794i	0.480428	−	0.877034i
$865$	−1.93064	−	0.566887i	−0.0656437	−	0.0192747i
$866$	5.92036	−	3.20180i	0.201182	−	0.108802i
$867$	−0.283301	+	0.835484i	−0.00962140	+	0.0283745i
$868$	22.6090	+	10.5466i	0.767399	+	0.357976i
$869$	−15.4713	−	52.6903i	−0.524827	−	1.78740i
$870$	−6.12625	−	12.5398i	−0.207699	−	0.425138i
$871$	16.9146	+	2.43196i	0.573130	+	0.0824037i
$872$	14.3678	−	0.852847i	0.486556	−	0.0288810i
$873$	−9.01929	+	16.0851i	−0.305257	+	0.544399i
$874$	27.2700	+	10.9595i	0.922420	+	0.370711i
$875$	−18.7679			−0.634471
$876$	−39.5194	+	9.51229i	−1.33524	+	0.321391i
$877$	2.25954	−	15.7154i	0.0762993	−	0.530673i	−0.915445	−	0.402443i	$-0.868161\pi$
$877$	2.25954	−	15.7154i	0.0762993	−	0.530673i	0.991744	−	0.128230i	$-0.0409297\pi$
$878$	−2.52022	+	33.3449i	−0.0850534	+	1.12534i
$879$	0.00244829	−	0.00260020i	8.25788e−5	−	8.77025e-5i
$880$	−4.43327	−	16.0528i	−0.149445	−	0.541141i
$881$	−4.82276	+	4.17895i	−0.162483	+	0.140792i	−0.732308	−	0.680974i	$-0.761557\pi$
$881$	−4.82276	+	4.17895i	−0.162483	+	0.140792i	0.569824	+	0.821766i	$0.307011\pi$
$882$	0.112671	−	7.37513i	0.00379382	−	0.248334i
$883$	−6.68531	+	22.7681i	−0.224979	+	0.766207i	0.767203	+	0.641404i	$0.221648\pi$
$883$	−6.68531	+	22.7681i	−0.224979	+	0.766207i	−0.992182	+	0.124802i	$0.960170\pi$
$884$	−53.6861	−	0.433480i	−1.80566	−	0.0145795i
$885$	0.620727	+	0.0256626i	0.0208655	+	0.000862640i
$886$	7.01914	−	31.6508i	0.235813	−	1.06333i
$887$	15.9094	−	18.3604i	0.534186	−	0.616484i	−0.422939	−	0.906158i	$-0.639002\pi$
$887$	15.9094	−	18.3604i	0.534186	−	0.616484i	0.957125	+	0.289675i	$0.0935471\pi$
$888$	−11.4898	+	41.9016i	−0.385572	+	1.40613i
$889$	−0.982893	−	6.83617i	−0.0329652	−	0.229278i
$890$	4.99522	−	9.06091i	0.167440	−	0.303723i
$891$	23.5976	−	34.9649i	0.790548	−	1.17137i
$892$	9.26996	+	6.06375i	0.310381	+	0.203029i
$893$	−9.13468	−	4.17167i	−0.305681	−	0.139600i
$894$	−14.7153	+	13.4375i	−0.492153	+	0.449418i
$895$	−11.4299	−	17.7853i	−0.382059	−	0.594495i
$896$	−20.3273	−	16.1328i	−0.679088	−	0.538959i
$897$	19.6504	+	51.2735i	0.656109	+	1.71197i
$898$	49.1712	−	18.1141i	1.64086	−	0.604476i
$899$	−29.3434	+	18.8579i	−0.978658	+	0.628946i
$900$	25.2313	−	1.31541i	0.841042	−	0.0438469i
$901$	14.3871	−	31.5034i	0.479305	−	1.04953i
$902$	−16.7366	+	12.4238i	−0.557268	+	0.413666i
$903$	10.0855	−	14.3530i	0.335624	−	0.477639i
$904$	−37.7745	+	7.73942i	−1.25636	+	0.257409i
$905$	1.93144	−	0.277699i	0.0642033	−	0.00923103i
$906$	−27.9511	−	41.0988i	−0.928614	−	1.36542i
$907$	−6.62920	−	5.74423i	−0.220119	−	0.190734i	0.537820	−	0.843060i	$-0.319248\pi$
$907$	−6.62920	−	5.74423i	−0.220119	−	0.190734i	−0.757939	+	0.652326i	$0.773793\pi$
$908$	36.5208	−	4.95027i	1.21199	−	0.164281i
$909$	9.02512	+	16.9792i	0.299344	+	0.563164i
$910$	17.8202	+	6.72868i	0.590735	+	0.223053i
$911$	11.8806	+	3.48847i	0.393623	+	0.115578i	0.472553	−	0.881302i	$-0.343332\pi$
$911$	11.8806	+	3.48847i	0.393623	+	0.115578i	−0.0789307	+	0.996880i	$0.525151\pi$
$912$	−26.1466	+	14.7537i	−0.865801	+	0.488543i
$913$	9.19696	+	10.6139i	0.304375	+	0.351267i
$914$	4.95060	−	4.91079i	0.163751	−	0.162434i
$915$	4.03182	−	4.28198i	0.133288	−	0.141558i
$916$	4.77343	+	16.7561i	0.157719	+	0.553638i
$917$	−0.242702	−	0.0348952i	−0.00801472	−	0.00115234i
$918$	17.5275	−	24.1512i	0.578495	−	0.797109i
$919$		−	11.3029i		−	0.372850i	−0.982469	−	0.186425i	$-0.940310\pi$
$919$		−	11.3029i		−	0.372850i	0.982469	−	0.186425i	$-0.0596901\pi$
$920$	−9.88055	+	6.89672i	−0.325752	+	0.227378i
$921$	0.858593	−	0.502925i	0.0282916	−	0.0165720i
$922$	−24.2433	+	32.1142i	−0.798411	+	1.05762i
$923$	−3.25543	+	22.6420i	−0.107154	+	0.745271i
$924$	−26.9074	−	25.7484i	−0.885188	−	0.847061i
$925$	−35.8333	+	10.5216i	−1.17819	+	0.345949i
$926$	−16.8581	−	16.9948i	−0.553993	−	0.558484i
$927$	−4.04453	−	19.6533i	−0.132840	−	0.645498i
$928$	34.2447	−	11.9910i	1.12414	−	0.393624i
$929$	−4.12231	+	14.0393i	−0.135249	+	0.460615i	−0.999067	−	0.0431887i	$-0.986248\pi$
$929$	−4.12231	+	14.0393i	−0.135249	+	0.460615i	0.863818	+	0.503804i	$0.168067\pi$
$930$	1.98840	+	11.6645i	0.0652022	+	0.382494i
$931$	−4.07297	+	6.33766i	−0.133486	+	0.207708i
$932$	−0.505202	−	3.72714i	−0.0165484	−	0.122087i
$933$	−12.7508	−	2.37456i	−0.417443	−	0.0777397i
$934$	−1.04092	−	15.4291i	−0.0340600	−	0.504856i
$935$	−2.40614	−	16.7351i	−0.0786893	−	0.547296i
$936$	−53.4353	−	17.0549i	−1.74659	−	0.557458i
$937$	−23.5967	−	51.6695i	−0.770870	−	1.68797i	−0.724729	−	0.689034i	$-0.758035\pi$
$937$	−23.5967	−	51.6695i	−0.770870	−	1.68797i	−0.0461403	−	0.998935i	$-0.514692\pi$
$938$	4.99831	+	6.73345i	0.163200	+	0.219855i
$939$	40.7941	−	4.15407i	1.33127	−	0.135563i
$940$	3.48145	−	2.19788i	0.113552	−	0.0716868i
$941$	29.1006	+	45.2815i	0.948654	+	1.47613i	0.878016	+	0.478632i	$0.158867\pi$
$941$	29.1006	+	45.2815i	0.948654	+	1.47613i	0.0706379	+	0.997502i	$0.477497\pi$
$942$	9.38287	−	11.4160i	0.305710	−	0.371954i
$943$	12.5122	+	8.41930i	0.407453	+	0.274170i
$944$	−0.255644	+	1.59478i	−0.00832051	+	0.0519058i
$945$	−8.79737	+	5.89084i	−0.286179	+	0.191629i
$946$	6.10562	+	28.6229i	0.198511	+	0.930612i
$947$	−9.26473	+	20.2869i	−0.301063	+	0.659237i	−0.998342	−	0.0575635i	$-0.981667\pi$
$947$	−9.26473	+	20.2869i	−0.301063	+	0.659237i	0.697278	+	0.716800i	$0.254394\pi$
$948$	2.00392	−	40.5375i	0.0650842	−	1.31660i
$949$	32.2225	+	70.5574i	1.04599	+	2.29039i
$950$	−22.5987	−	12.4585i	−0.733200	−	0.404208i
$951$	18.9775	+	23.8224i	0.615388	+	0.772495i
$952$	−18.4026	−	18.8538i	−0.596430	−	0.611055i
$953$	23.4069	+	20.2822i	0.758223	+	0.657004i	0.945618	−	0.325280i	$-0.105459\pi$
$953$	23.4069	+	20.2822i	0.758223	+	0.657004i	−0.187394	+	0.982285i	$0.560004\pi$
$954$	24.1100	−	26.9805i	0.780592	−	0.873525i
$955$	7.39050	−	11.4998i	0.239151	−	0.372126i
$956$	−0.0790127	+	9.78566i	−0.00255545	+	0.316491i
$957$	50.5240	−	12.5935i	1.63321	−	0.407090i
$958$	−21.2766	+	11.5067i	−0.687417	+	0.371763i
$959$	27.1444	+	31.3263i	0.876539	+	1.01158i
$960$	0.806153	−	12.2822i	0.0260185	−	0.396407i
$961$	−1.36877	+	0.401908i	−0.0441540	+	0.0129648i
$962$	82.6748	+	6.24859i	2.66554	+	0.201463i
$963$	−7.43769	−	5.69933i	−0.239676	−	0.183658i
$964$	−10.1139	+	33.4435i	−0.325747	+	1.07714i
$965$			6.80359i			0.219015i
$966$	−11.0724	+	24.5659i	−0.356248	+	0.790395i
$967$			2.44181i			0.0785233i	0.999229	+	0.0392617i	$0.0125006\pi$
$967$			2.44181i			0.0785233i	−0.999229	+	0.0392617i	$0.987499\pi$
$968$	30.9669	−	1.83814i	0.995315	−	0.0590801i
$969$	−28.2238	+	11.5053i	−0.906680	+	0.369604i
$970$	−0.581990	+	7.70028i	−0.0186866	+	0.247241i
$971$	39.4271	−	11.5769i	1.26528	−	0.371519i	0.420821	−	0.907144i	$-0.361742\pi$
$971$	39.4271	−	11.5769i	1.26528	−	0.371519i	0.844456	+	0.535625i	$0.179924\pi$
$972$	24.9672	−	18.6719i	0.800824	−	0.598900i
$973$	12.4572	+	14.3764i	0.399359	+	0.460885i
$974$	−18.7153	−	34.6058i	−0.599675	−	1.10884i
$975$	−11.6607	−	46.7817i	−0.373442	−	1.49821i
$976$	9.82523	+	11.7160i	0.314498	+	0.375018i
$977$	4.98267	−	7.75318i	0.159410	−	0.248046i	−0.752356	−	0.658756i	$-0.771083\pi$
$977$	4.98267	−	7.75318i	0.159410	−	0.248046i	0.911766	+	0.410710i	$0.134719\pi$
$978$	9.09553	+	28.2347i	0.290843	+	0.902847i
$979$	29.1739	+	25.2793i	0.932401	+	0.807930i
$980$	−1.26036	−	2.81984i	−0.0402607	−	0.0900764i
$981$	14.2428	+	5.49540i	0.454737	+	0.175455i
$982$	25.0955	−	45.5211i	0.800829	−	1.45264i
$983$	−22.6901	−	49.6845i	−0.723703	−	1.58469i	−0.808641	−	0.588303i	$-0.799796\pi$
$983$	−22.6901	−	49.6845i	−0.723703	−	1.58469i	0.0849376	−	0.996386i	$-0.472931\pi$
$984$	−14.7011	+	4.60512i	−0.468653	+	0.146806i
$985$	0.507545	−	1.11137i	0.0161717	−	0.0354112i
$986$	36.0251	−	7.68458i	1.14727	−	0.244727i
$987$	4.16747	−	8.20995i	0.132652	−	0.261326i
$988$	37.1658	+	43.5980i	1.18240	+	1.38704i
$989$	18.0515	−	11.0700i	0.574004	−	0.352004i
$990$	2.78063	−	17.4437i	0.0883742	−	0.554399i
$991$	−11.4186	−	17.7677i	−0.362725	−	0.564411i	0.611145	−	0.791519i	$-0.290709\pi$
$991$	−11.4186	−	17.7677i	−0.362725	−	0.564411i	−0.973870	+	0.227108i	$0.927073\pi$
$992$	−30.7225	+	1.57481i	−0.975439	+	0.0500003i
$993$	−0.726670	−	7.13610i	−0.0230602	−	0.226457i
$994$	−9.01343	+	6.69076i	−0.285889	+	0.212218i
$995$	−6.90939	−	15.1295i	−0.219043	−	0.479636i
$996$	3.84053	+	9.64327i	0.121692	+	0.305559i
$997$	5.53154	+	38.4727i	0.175186	+	1.21844i	0.867718	+	0.497056i	$0.165586\pi$
$997$	5.53154	+	38.4727i	0.175186	+	1.21844i	−0.692533	+	0.721387i	$0.743505\pi$
$998$	−56.1666	+	3.78927i	−1.77792	+	0.119947i
$999$	−29.5171	+	35.3904i	−0.933878	+	1.11970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.35.9	✓	440
3.2	odd	2	inner	276.2.o.a.35.36	yes	440
4.3	odd	2	inner	276.2.o.a.35.20	yes	440
12.11	even	2	inner	276.2.o.a.35.25	yes	440
23.2	even	11	inner	276.2.o.a.71.25	yes	440
69.2	odd	22	inner	276.2.o.a.71.20	yes	440
92.71	odd	22	inner	276.2.o.a.71.36	yes	440
276.71	even	22	inner	276.2.o.a.71.9	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.35.9	✓	440	1.1	even	1	trivial
276.2.o.a.35.20	yes	440	4.3	odd	2	inner
276.2.o.a.35.25	yes	440	12.11	even	2	inner
276.2.o.a.35.36	yes	440	3.2	odd	2	inner
276.2.o.a.71.9	yes	440	276.71	even	22	inner
276.2.o.a.71.20	yes	440	69.2	odd	22	inner
276.2.o.a.71.25	yes	440	23.2	even	11	inner
276.2.o.a.71.36	yes	440	92.71	odd	22	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12871 - 0.852070i) q^{2} +(1.60391 - 0.653824i) q^{3} +(0.547953 + 1.92347i) q^{4} +(0.250263 + 0.852318i) q^{5} +(-2.36744 - 0.628665i) q^{6} +(-1.73353 + 1.50211i) q^{7} +(1.02046 - 2.63793i) q^{8} +(2.14503 - 2.09735i) q^{9} +O(q^{10})\)	\(q+(-1.12871 - 0.852070i) q^{2} +(1.60391 - 0.653824i) q^{3} +(0.547953 + 1.92347i) q^{4} +(0.250263 + 0.852318i) q^{5} +(-2.36744 - 0.628665i) q^{6} +(-1.73353 + 1.50211i) q^{7} +(1.02046 - 2.63793i) q^{8} +(2.14503 - 2.09735i) q^{9} +(0.443761 - 1.17526i) q^{10} +(3.94293 + 2.53397i) q^{11} +(2.13648 + 2.72680i) q^{12} +(4.32888 - 4.99580i) q^{13} +(3.23655 - 0.218353i) q^{14} +(0.958664 + 1.20341i) q^{15} +(-3.39950 + 2.10794i) q^{16} +(-3.69390 + 1.68695i) q^{17} +(-4.20819 + 0.539572i) q^{18} +(3.94170 + 1.80011i) q^{19} +(-1.50228 + 0.948404i) q^{20} +(-1.79830 + 3.54267i) q^{21} +(-2.29129 - 6.21976i) q^{22} +(-3.68990 + 3.06344i) q^{23} +(-0.0880263 - 4.89819i) q^{24} +(3.54245 - 2.27660i) q^{25} +(-9.14281 + 1.95027i) q^{26} +(2.06913 - 4.76642i) q^{27} +(-3.83916 - 2.51131i) q^{28} +(5.83444 - 2.66450i) q^{29} +(-0.0566610 - 2.17514i) q^{30} +(-5.38279 + 0.773929i) q^{31} +(5.63315 + 0.517360i) q^{32} +(7.98087 + 1.48626i) q^{33} +(5.60672 + 1.24339i) q^{34} +(-1.71411 - 1.10159i) q^{35} +(5.20956 + 2.97666i) q^{36} +(-8.50962 - 2.49865i) q^{37} +(-2.91520 - 5.39041i) q^{38} +(3.67675 - 10.8431i) q^{39} +(2.50374 + 0.209577i) q^{40} +(-0.885944 - 3.01725i) q^{41} +(5.04835 - 2.46635i) q^{42} +(-4.37045 - 0.628375i) q^{43} +(-2.71348 + 8.97262i) q^{44} +(2.32443 + 1.30336i) q^{45} +(6.77507 - 0.313669i) q^{46} -2.31745 q^{47} +(-4.07424 + 5.60362i) q^{48} +(-0.247420 + 1.72084i) q^{49} +(-5.93821 - 0.448812i) q^{50} +(-4.82169 + 5.12086i) q^{51} +(11.9813 + 5.58903i) q^{52} +(-6.44542 + 5.58499i) q^{53} +(-6.39675 + 3.61684i) q^{54} +(-1.17298 + 3.99479i) q^{55} +(2.19347 + 6.10577i) q^{56} +(7.49908 + 0.310033i) q^{57} +(-8.85570 - 1.96392i) q^{58} +(0.264424 - 0.305161i) q^{59} +(-1.78942 + 2.50338i) q^{60} +(-0.544015 - 3.78371i) q^{61} +(6.73503 + 3.71298i) q^{62} +(-0.568020 + 6.85788i) q^{63} +(-5.91734 - 5.38378i) q^{64} +(5.34137 + 2.43932i) q^{65} +(-7.74165 - 8.47781i) q^{66} +(1.39761 + 2.17473i) q^{67} +(-5.26888 - 6.18074i) q^{68} +(-3.91530 + 7.32601i) q^{69} +(0.996095 + 2.70392i) q^{70} +(-2.91111 + 1.87085i) q^{71} +(-3.34374 - 7.79868i) q^{72} +(-4.87452 + 10.6737i) q^{73} +(7.47583 + 10.0710i) q^{74} +(4.19327 - 5.96759i) q^{75} +(-1.30261 + 8.56813i) q^{76} +(-10.6415 + 1.53002i) q^{77} +(-13.3891 + 9.10585i) q^{78} +(-8.85470 - 7.67265i) q^{79} +(-2.64741 - 2.36991i) q^{80} +(0.202282 - 8.99773i) q^{81} +(-1.57094 + 4.16047i) q^{82} +(2.87504 + 0.844189i) q^{83} +(-7.79961 - 1.51777i) q^{84} +(-2.36226 - 2.72619i) q^{85} +(4.39753 + 4.43318i) q^{86} +(7.61577 - 8.08830i) q^{87} +(10.7080 - 7.81537i) q^{88} +(8.15231 + 1.17212i) q^{89} +(-1.51304 - 3.45168i) q^{90} +15.1628i q^{91} +(-7.91433 - 5.41880i) q^{92} +(-8.12748 + 4.76071i) q^{93} +(2.61572 + 1.97463i) q^{94} +(-0.547807 + 3.81008i) q^{95} +(9.37330 - 2.85329i) q^{96} +(-5.89808 + 1.73183i) q^{97} +(1.74554 - 1.73151i) q^{98} +(13.7723 - 2.83426i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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