LMFDB - Embedded newform 276.2.o.a.167.36

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			167.36
Character	$\chi$	$=$	276.167
Dual form			276.2.o.a.119.36

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12083 + 0.862408i) q^{2} +(0.414750 - 1.68166i) q^{3} +(0.512503 + 1.93322i) q^{4} +(0.963734 + 1.49960i) q^{5} +(1.91514 - 1.52717i) q^{6} +(1.51856 + 0.218336i) q^{7} +(-1.09280 + 2.60879i) q^{8} +(-2.65596 - 1.39494i) q^{9} +O(q^{10})$	\(q+(1.12083 + 0.862408i) q^{2} +(0.414750 - 1.68166i) q^{3} +(0.512503 + 1.93322i) q^{4} +(0.963734 + 1.49960i) q^{5} +(1.91514 - 1.52717i) q^{6} +(1.51856 + 0.218336i) q^{7} +(-1.09280 + 2.60879i) q^{8} +(-2.65596 - 1.39494i) q^{9} +(-0.213089 + 2.51192i) q^{10} +(0.389727 + 0.853382i) q^{11} +(3.46358 - 0.0600535i) q^{12} +(-0.592791 - 4.12295i) q^{13} +(1.51375 + 1.55434i) q^{14} +(2.92153 - 0.998715i) q^{15} +(-3.47468 + 1.98156i) q^{16} +(1.29554 + 1.12259i) q^{17} +(-1.77387 - 3.85401i) q^{18} +(-1.48571 + 1.28737i) q^{19} +(-2.40514 + 2.63166i) q^{20} +(0.996990 - 2.46315i) q^{21} +(-0.299148 + 1.29260i) q^{22} +(-1.67032 - 4.49556i) q^{23} +(3.93386 + 2.91971i) q^{24} +(0.757059 - 1.65773i) q^{25} +(2.89125 - 5.13234i) q^{26} +(-3.44737 + 3.88788i) q^{27} +(0.356175 + 3.04761i) q^{28} +(2.40675 + 2.08546i) q^{29} +(4.13582 + 1.40016i) q^{30} +(0.492015 + 1.67565i) q^{31} +(-5.60343 - 0.775606i) q^{32} +(1.59674 - 0.301448i) q^{33} +(0.483941 + 2.37551i) q^{34} +(1.13607 + 2.48765i) q^{35} +(1.33553 - 5.84948i) q^{36} +(-4.75096 - 3.05325i) q^{37} +(-2.77546 + 0.161634i) q^{38} +(-7.17927 - 0.713121i) q^{39} +(-4.96531 + 0.875421i) q^{40} +(-1.19717 - 1.86284i) q^{41} +(3.24169 - 1.90095i) q^{42} +(0.604010 - 2.05707i) q^{43} +(-1.45004 + 1.19079i) q^{44} +(-0.467797 - 5.32723i) q^{45} +(2.00486 - 6.47924i) q^{46} -11.1593 q^{47} +(1.89119 + 6.66509i) q^{48} +(-4.45810 - 1.30902i) q^{49} +(2.27817 - 1.20513i) q^{50} +(2.42514 - 1.71306i) q^{51} +(7.66677 - 3.25902i) q^{52} +(-13.0479 - 1.87600i) q^{53} +(-7.21685 + 1.38460i) q^{54} +(-0.904139 + 1.40687i) q^{55} +(-2.22907 + 3.72301i) q^{56} +(1.54873 + 3.03239i) q^{57} +(0.899029 + 4.41304i) q^{58} +(1.78992 + 12.4492i) q^{59} +(3.42803 + 5.13611i) q^{60} +(8.79525 - 2.58252i) q^{61} +(-0.893631 + 2.30243i) q^{62} +(-3.72868 - 2.69819i) q^{63} +(-5.61158 - 5.70177i) q^{64} +(5.61149 - 4.86238i) q^{65} +(2.04964 + 1.03917i) q^{66} +(9.23061 + 4.21548i) q^{67} +(-1.50624 + 3.07989i) q^{68} +(-8.25277 + 0.944386i) q^{69} +(-0.872031 + 3.76798i) q^{70} +(1.24015 - 2.71554i) q^{71} +(6.54153 - 5.40447i) q^{72} +(4.83868 + 5.58413i) q^{73} +(-2.69184 - 7.51943i) q^{74} +(-2.47375 - 1.96066i) q^{75} +(-3.25020 - 2.21241i) q^{76} +(0.405499 + 1.38100i) q^{77} +(-7.43171 - 6.99075i) q^{78} +(13.5576 - 1.94928i) q^{79} +(-6.32022 - 3.30093i) q^{80} +(5.10830 + 7.40981i) q^{81} +(0.264704 - 3.12037i) q^{82} +(-5.56778 - 3.57819i) q^{83} +(5.27277 + 0.665029i) q^{84} +(-0.434881 + 3.02466i) q^{85} +(2.45103 - 1.78472i) q^{86} +(4.50523 - 3.18239i) q^{87} +(-2.65219 + 0.0841406i) q^{88} +(2.03727 - 6.93831i) q^{89} +(4.06993 - 6.37434i) q^{90} -6.39038i q^{91} +(7.83485 - 5.53309i) q^{92} +(3.02194 - 0.132427i) q^{93} +(-12.5076 - 9.62385i) q^{94} +(-3.36237 - 0.987280i) q^{95} +(-3.62833 + 9.10139i) q^{96} +(-5.32915 + 3.42483i) q^{97} +(-3.86785 - 5.31188i) q^{98} +(0.155315 - 2.81020i) 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 $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$-1$	$-1$

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 $

$2$	1.12083	+	0.862408i	0.792544	+	0.609815i
$2$	1.12083	+	0.862408i	0.792544	+	0.609815i
$3$	0.414750	−	1.68166i	0.239456	−	0.970907i
$3$	0.414750	−	1.68166i	0.239456	−	0.970907i
$4$	0.512503	+	1.93322i	0.256252	+	0.966610i
$5$	0.963734	+	1.49960i	0.430995	+	0.670642i	0.987033	−	0.160515i	$-0.0513156\pi$
$5$	0.963734	+	1.49960i	0.430995	+	0.670642i	−0.556038	+	0.831157i	$0.687679\pi$
$6$	1.91514	−	1.52717i	0.781853	−	0.623463i
$7$	1.51856	+	0.218336i	0.573962	+	0.0825232i	0.423183	−	0.906044i	$-0.360913\pi$
$7$	1.51856	+	0.218336i	0.573962	+	0.0825232i	0.150779	+	0.988568i	$0.451822\pi$
$8$	−1.09280	+	2.60879i	−0.386363	+	0.922347i
$9$	−2.65596	−	1.39494i	−0.885322	−	0.464979i
$10$	−0.213089	+	2.51192i	−0.0673846	+	0.794340i
$11$	0.389727	+	0.853382i	0.117507	+	0.257304i	0.959242	−	0.282587i	$-0.0911926\pi$
$11$	0.389727	+	0.853382i	0.117507	+	0.257304i	−0.841735	+	0.539891i	$0.818465\pi$
$12$	3.46358	−	0.0600535i	0.999850	−	0.0173359i
$13$	−0.592791	−	4.12295i	−0.164411	−	1.14350i	−0.890195	−	0.455579i	$-0.849432\pi$
$13$	−0.592791	−	4.12295i	−0.164411	−	1.14350i	0.725784	−	0.687922i	$-0.241477\pi$
$14$	1.51375	+	1.55434i	0.404566	+	0.415414i
$15$	2.92153	−	0.998715i	0.754335	−	0.257867i
$16$	−3.47468	+	1.98156i	−0.868670	+	0.495391i
$17$	1.29554	+	1.12259i	0.314214	+	0.272268i	0.797661	−	0.603106i	$-0.206070\pi$
$17$	1.29554	+	1.12259i	0.314214	+	0.272268i	−0.483448	+	0.875373i	$0.660616\pi$
$18$	−1.77387	−	3.85401i	−0.418105	−	0.908399i
$19$	−1.48571	+	1.28737i	−0.340844	+	0.295343i	−0.808416	−	0.588612i	$-0.799675\pi$
$19$	−1.48571	+	1.28737i	−0.340844	+	0.295343i	0.467571	+	0.883955i	$0.345129\pi$
$20$	−2.40514	+	2.63166i	−0.537806	+	0.588457i
$21$	0.996990	−	2.46315i	0.217561	−	0.537503i
$22$	−0.299148	+	1.29260i	−0.0637786	+	0.275583i
$23$	−1.67032	−	4.49556i	−0.348287	−	0.937388i
$23$	−1.67032	−	4.49556i	−0.348287	−	0.937388i
$24$	3.93386	+	2.91971i	0.802996	+	0.595984i
$25$	0.757059	−	1.65773i	0.151412	−	0.331546i
$26$	2.89125	−	5.13234i	0.567022	−	1.00654i
$27$	−3.44737	+	3.88788i	−0.663447	+	0.748223i
$28$	0.356175	+	3.04761i	0.0673108	+	0.575944i
$29$	2.40675	+	2.08546i	0.446922	+	0.387260i	0.849041	−	0.528327i	$-0.177181\pi$
$29$	2.40675	+	2.08546i	0.446922	+	0.387260i	−0.402119	+	0.915587i	$0.631726\pi$
$30$	4.13582	+	1.40016i	0.755095	+	0.255634i
$31$	0.492015	+	1.67565i	0.0883685	+	0.300956i	0.991804	−	0.127768i	$-0.0407814\pi$
$31$	0.492015	+	1.67565i	0.0883685	+	0.300956i	−0.903435	+	0.428724i	$0.858963\pi$
$32$	−5.60343	−	0.775606i	−0.990556	−	0.137109i
$33$	1.59674	−	0.301448i	0.277956	−	0.0524753i
$34$	0.483941	+	2.37551i	0.0829952	+	0.407396i
$35$	1.13607	+	2.48765i	0.192031	+	0.420490i
$36$	1.33553	−	5.84948i	0.222588	−	0.974913i
$37$	−4.75096	−	3.05325i	−0.781052	−	0.501952i	0.0883304	−	0.996091i	$-0.471847\pi$
$37$	−4.75096	−	3.05325i	−0.781052	−	0.501952i	−0.869383	+	0.494139i	$0.835483\pi$
$38$	−2.77546	+	0.161634i	−0.450239	+	0.0262206i
$39$	−7.17927	−	0.713121i	−1.14960	−	0.114191i
$40$	−4.96531	+	0.875421i	−0.785085	+	0.138416i
$41$	−1.19717	−	1.86284i	−0.186967	−	0.290926i	0.735098	−	0.677960i	$-0.237136\pi$
$41$	−1.19717	−	1.86284i	−0.186967	−	0.290926i	−0.922065	+	0.387034i	$0.873500\pi$
$42$	3.24169	−	1.90095i	0.500204	−	0.293323i
$43$	0.604010	−	2.05707i	0.0921107	−	0.313700i	−0.900530	−	0.434793i	$-0.856822\pi$
$43$	0.604010	−	2.05707i	0.0921107	−	0.313700i	0.992641	+	0.121093i	$0.0386398\pi$
$44$	−1.45004	+	1.19079i	−0.218602	+	0.179518i
$45$	−0.467797	−	5.32723i	−0.0697350	−	0.794137i
$46$	2.00486	−	6.47924i	0.295601	−	0.955312i
$47$	−11.1593			−1.62775			−0.813874	−	0.581042i	$-0.802645\pi$
$47$	−11.1593			−1.62775			−0.813874	+	0.581042i	$0.802645\pi$
$48$	1.89119	+	6.66509i	0.272970	+	0.962022i
$49$	−4.45810	−	1.30902i	−0.636871	−	0.187002i
$50$	2.27817	−	1.20513i	0.322182	−	0.170431i
$51$	2.42514	−	1.71306i	0.339587	−	0.239876i
$52$	7.66677	−	3.25902i	1.06319	−	0.451945i
$53$	−13.0479	−	1.87600i	−1.79226	−	0.257688i	−0.835693	−	0.549196i	$-0.814934\pi$
$53$	−13.0479	−	1.87600i	−1.79226	−	0.257688i	−0.956568	+	0.291508i	$0.905843\pi$
$54$	−7.21685	+	1.38460i	−0.982089	+	0.188420i
$55$	−0.904139	+	1.40687i	−0.121914	+	0.189702i
$56$	−2.22907	+	3.72301i	−0.297872	+	0.497508i
$57$	1.54873	+	3.03239i	0.205134	+	0.401650i
$58$	0.899029	+	4.41304i	0.118048	+	0.579460i
$59$	1.78992	+	12.4492i	0.233027	+	1.62074i	0.684885	+	0.728651i	$0.259853\pi$
$59$	1.78992	+	12.4492i	0.233027	+	1.62074i	−0.451857	+	0.892090i	$0.649238\pi$
$60$	3.42803	+	5.13611i	0.442557	+	0.663069i
$61$	8.79525	−	2.58252i	1.12612	−	0.330658i	0.334936	−	0.942241i	$-0.391285\pi$
$61$	8.79525	−	2.58252i	1.12612	−	0.330658i	0.791180	+	0.611583i	$0.209467\pi$
$62$	−0.893631	+	2.30243i	−0.113491	+	0.292409i
$63$	−3.72868	−	2.69819i	−0.469769	−	0.339940i
$64$	−5.61158	−	5.70177i	−0.701448	−	0.712721i
$65$	5.61149	−	4.86238i	0.696019	−	0.603104i
$66$	2.04964	+	1.03917i	0.252293	+	0.127913i
$67$	9.23061	+	4.21548i	1.12770	+	0.515003i	0.889829	−	0.456294i	$-0.150824\pi$
$67$	9.23061	+	4.21548i	1.12770	+	0.515003i	0.237870	+	0.971297i	$0.423551\pi$
$68$	−1.50624	+	3.07989i	−0.182659	+	0.373491i
$69$	−8.25277	+	0.944386i	−0.993516	+	0.113691i
$70$	−0.872031	+	3.76798i	−0.104228	+	0.450360i
$71$	1.24015	−	2.71554i	0.147178	−	0.322276i	−0.821657	−	0.569983i	$-0.806950\pi$
$71$	1.24015	−	2.71554i	0.147178	−	0.322276i	0.968835	+	0.247707i	$0.0796771\pi$
$72$	6.54153	−	5.40447i	0.770927	−	0.636923i
$73$	4.83868	+	5.58413i	0.566325	+	0.653573i	0.964608	−	0.263689i	$-0.0849393\pi$
$73$	4.83868	+	5.58413i	0.566325	+	0.653573i	−0.398283	+	0.917263i	$0.630394\pi$
$74$	−2.69184	−	7.51943i	−0.312921	−	0.874116i
$75$	−2.47375	−	1.96066i	−0.285644	−	0.226397i
$76$	−3.25020	−	2.21241i	−0.372824	−	0.253781i
$77$	0.405499	+	1.38100i	0.0462109	+	0.157380i
$78$	−7.43171	−	6.99075i	−0.841476	−	0.791546i
$79$	13.5576	−	1.94928i	1.52535	−	0.219312i	0.671958	−	0.740589i	$-0.265453\pi$
$79$	13.5576	−	1.94928i	1.52535	−	0.219312i	0.853387	+	0.521277i	$0.174544\pi$
$80$	−6.32022	−	3.30093i	−0.706622	−	0.369055i
$81$	5.10830	+	7.40981i	0.567589	+	0.823312i
$82$	0.264704	−	3.12037i	0.0292317	−	0.344587i
$83$	−5.56778	−	3.57819i	−0.611143	−	0.392758i	0.198143	−	0.980173i	$-0.436509\pi$
$83$	−5.56778	−	3.57819i	−0.611143	−	0.392758i	−0.809286	+	0.587415i	$0.800145\pi$
$84$	5.27277	+	0.665029i	0.575306	+	0.0725607i
$85$	−0.434881	+	3.02466i	−0.0471695	+	0.328071i
$86$	2.45103	−	1.78472i	0.264301	−	0.192451i
$87$	4.50523	−	3.18239i	0.483012	−	0.341188i
$88$	−2.65219	+	0.0841406i	−0.282724	+	0.00896942i
$89$	2.03727	−	6.93831i	0.215950	−	0.735459i	−0.778254	−	0.627950i	$-0.783894\pi$
$89$	2.03727	−	6.93831i	0.215950	−	0.735459i	0.994204	−	0.107509i	$-0.0342876\pi$
$90$	4.06993	−	6.37434i	0.429009	−	0.671914i
$91$		−	6.39038i		−	0.669894i
$92$	7.83485	−	5.53309i	0.816840	−	0.576864i
$93$	3.02194	−	0.132427i	0.313360	−	0.0137320i
$94$	−12.5076	−	9.62385i	−1.29006	−	0.992624i
$95$	−3.36237	−	0.987280i	−0.344972	−	0.101293i
$96$	−3.62833	+	9.10139i	−0.370315	+	0.928906i
$97$	−5.32915	+	3.42483i	−0.541093	+	0.347739i	−0.782466	−	0.622693i	$-0.786039\pi$
$97$	−5.32915	+	3.42483i	−0.541093	+	0.347739i	0.241373	+	0.970432i	$0.422402\pi$
$98$	−3.86785	−	5.31188i	−0.390712	−	0.536581i
$99$	0.155315	−	2.81020i	0.0156097	−	0.282435i
$100$	3.59275	+	0.613971i	0.359275	+	0.0613971i
$101$	−7.45106	+	11.5941i	−0.741408	+	1.15365i	0.241650	+	0.970363i	$0.422311\pi$
$101$	−7.45106	+	11.5941i	−0.741408	+	1.15365i	−0.983059	+	0.183291i	$0.941325\pi$
$102$	4.19551	+	0.171417i	0.415418	+	0.0169728i
$103$	12.1593	−	5.55295i	1.19809	−	0.547149i	0.286431	−	0.958101i	$-0.407531\pi$
$103$	12.1593	−	5.55295i	1.19809	−	0.547149i	0.911657	+	0.410952i	$0.134804\pi$
$104$	11.4037	+	2.95909i	1.11823	+	0.290163i
$105$	4.65457	−	0.878734i	0.454239	−	0.0857557i
$106$	−13.0065	−	13.3553i	−1.26330	−	1.29718i
$107$	15.1676	−	4.45362i	1.46631	−	0.430548i	0.551413	−	0.834233i	$-0.314089\pi$
$107$	15.1676	−	4.45362i	1.46631	−	0.430548i	0.914898	+	0.403685i	$0.132271\pi$
$108$	−9.28292	−	4.67198i	−0.893249	−	0.449561i
$109$	−6.60017	+	7.61700i	−0.632181	+	0.729576i	−0.977972	−	0.208735i	$-0.933065\pi$
$109$	−6.60017	+	7.61700i	−0.632181	+	0.729576i	0.345791	+	0.938312i	$0.387611\pi$
$110$	−2.22668	+	0.797117i	−0.212305	+	0.0760021i
$111$	−7.10499	+	6.72316i	−0.674376	+	0.638134i
$112$	−5.70916	+	2.25047i	−0.539465	+	0.212650i
$113$	15.7129	+	7.17585i	1.47815	+	0.675047i	0.981246	−	0.192759i	$-0.0617437\pi$
$113$	15.7129	+	7.17585i	1.47815	+	0.675047i	0.496902	+	0.867807i	$0.334471\pi$
$114$	−0.879307	+	4.73442i	−0.0823546	+	0.443419i
$115$	5.13179	−	6.83734i	0.478542	−	0.637585i
$116$	−2.79819	+	5.72158i	−0.259805	+	0.531235i
$117$	−4.17683	+	11.7773i	−0.386148	+	1.08881i
$118$	−8.73007	+	15.4970i	−0.803668	+	1.42661i
$119$	1.72225	+	1.98758i	0.157878	+	0.182201i
$120$	−0.587201	+	8.71305i	−0.0536039	+	0.795389i
$121$	6.62709	−	7.64807i	0.602463	−	0.695279i
$122$	12.0851	+	4.69054i	1.09414	+	0.424662i
$123$	−3.62919	+	1.24063i	−0.327233	+	0.111864i
$124$	−2.98724	+	1.80995i	−0.268262	+	0.162538i
$125$	12.0377	−	1.73076i	1.07668	−	0.154804i
$126$	−1.85226	−	6.23984i	−0.165012	−	0.555889i
$127$	−6.45918	+	2.94981i	−0.573160	+	0.261753i	−0.680840	−	0.732432i	$-0.738385\pi$
$127$	−6.45918	+	2.94981i	−0.573160	+	0.261753i	0.107680	+	0.994186i	$0.465658\pi$
$128$	−1.37236	−	11.2302i	−0.121301	−	0.992616i
$129$	−3.20878	−	1.86891i	−0.282517	−	0.164548i
$130$	10.4829	−	0.610491i	0.919408	−	0.0535436i
$131$	−0.900636	+	6.26406i	−0.0786890	+	0.547294i	0.911899	+	0.410415i	$0.134616\pi$
$131$	−0.900636	+	6.26406i	−0.0786890	+	0.547294i	−0.990588	+	0.136879i	$0.956293\pi$
$132$	1.40110	+	2.93235i	0.121950	+	0.255229i
$133$	−2.53721	+	1.63057i	−0.220004	+	0.141388i
$134$	6.71045	+	12.6854i	0.579695	+	1.09585i
$135$	−9.15262	−	1.42279i	−0.787732	−	0.122455i
$136$	−4.34436	+	2.15302i	−0.372526	+	0.184620i
$137$		−	4.22981i		−	0.361377i	−0.983540	−	0.180688i	$-0.942167\pi$
$137$		−	4.22981i		−	0.361377i	0.983540	−	0.180688i	$-0.0578326\pi$
$138$	−10.0644	−	6.05876i	−0.856735	−	0.515756i
$139$			15.8527i			1.34461i	0.740275	+	0.672304i	$0.234695\pi$
$139$			15.8527i			1.34461i	−0.740275	+	0.672304i	$0.765305\pi$
$140$	−4.22694	+	3.47121i	−0.357241	+	0.293370i
$141$	−4.62831	+	18.7661i	−0.389774	+	1.58039i
$142$	3.73190	−	1.97414i	0.313174	−	0.165666i
$143$	3.28743	−	2.11270i	0.274909	−	0.176673i
$144$	11.9928	−	0.416000i	0.999399	−	0.0346667i
$145$	−0.807888	+	5.61899i	−0.0670915	+	0.466632i
$146$	0.607515	+	10.4318i	0.0502783	+	0.863339i
$147$	−4.05032	+	6.95409i	−0.334064	+	0.573564i
$148$	3.46773	−	10.7494i	0.285046	−	0.883599i
$149$	−12.6683	+	5.78544i	−1.03783	+	0.473962i	−0.860104	−	0.510118i	$-0.829602\pi$
$149$	−12.6683	+	5.78544i	−1.03783	+	0.473962i	−0.177727	+	0.984080i	$0.556874\pi$
$150$	−1.08175	−	4.33094i	−0.0883245	−	0.353620i
$151$	−0.815402	+	0.117237i	−0.0663564	+	0.00954062i	−0.175413	−	0.984495i	$-0.556126\pi$
$151$	−0.815402	+	0.117237i	−0.0663564	+	0.00954062i	0.109057	+	0.994036i	$0.465217\pi$
$152$	−1.73491	−	5.28273i	−0.140719	−	0.428486i
$153$	−1.87496	−	4.78875i	−0.151581	−	0.387147i
$154$	−0.736495	+	1.89757i	−0.0593484	+	0.152911i
$155$	−2.03863	+	2.35271i	−0.163747	+	0.188974i
$156$	−2.30078	−	14.2446i	−0.184210	−	1.14048i
$157$	6.04164	+	6.97243i	0.482176	+	0.556460i	0.943758	−	0.330637i	$-0.107264\pi$
$157$	6.04164	+	6.97243i	0.482176	+	0.556460i	−0.461582	+	0.887097i	$0.652718\pi$
$158$	16.8768	+	9.50735i	1.34264	+	0.756364i
$159$	−8.56640	+	21.1640i	−0.679359	+	1.67841i
$160$	−4.23712	−	9.15038i	−0.334974	−	0.723401i
$161$	−1.55494	−	7.19146i	−0.122547	−	0.566767i
$162$	−0.664766	+	12.7106i	−0.0522290	+	0.998635i
$163$	−14.4370	−	6.59316i	−1.13079	−	0.516416i	−0.239976	−	0.970779i	$-0.577140\pi$
$163$	−14.4370	−	6.59316i	−1.13079	−	0.516416i	−0.890817	+	0.454363i	$0.849867\pi$
$164$	2.98772	−	3.26911i	0.233302	−	0.255275i
$165$	1.99088	+	2.10395i	0.154990	+	0.163793i
$166$	−3.15465	−	8.81223i	−0.244848	−	0.683962i
$167$	7.79316	−	8.99379i	0.603053	−	0.695960i	−0.369344	−	0.929293i	$-0.620418\pi$
$167$	7.79316	−	8.99379i	0.603053	−	0.695960i	0.972397	+	0.233332i	$0.0749630\pi$
$168$	5.33633	+	5.29266i	0.411707	+	0.408338i
$169$	−4.17394	+	1.22558i	−0.321072	+	0.0942752i
$170$	−3.09592	+	3.01508i	−0.237446	+	0.231246i
$171$	5.74178	−	1.34675i	0.439085	−	0.102988i
$172$	4.28633	+	0.113430i	0.326829	+	0.00864894i
$173$	−15.4129	+	7.03886i	−1.17182	+	0.535154i	−0.903673	−	0.428223i	$-0.859140\pi$
$173$	−15.4129	+	7.03886i	−1.17182	+	0.535154i	−0.268151	+	0.963377i	$0.586413\pi$
$174$	7.79410	+	0.318445i	0.590869	+	0.0241413i
$175$	1.51158	−	2.35207i	0.114265	−	0.177799i
$176$	−3.04521	−	2.19296i	−0.229541	−	0.165301i
$177$	21.6776	+	2.15325i	1.62939	+	0.161848i
$178$	8.26709	−	6.01968i	0.619644	−	0.451194i
$179$	18.1702	−	11.6773i	1.35810	−	0.872799i	0.359915	−	0.932985i	$-0.382806\pi$
$179$	18.1702	−	11.6773i	1.35810	−	0.872799i	0.998187	+	0.0601860i	$0.0191694\pi$
$180$	10.0590	−	3.63458i	0.749751	−	0.270905i
$181$	9.52840	+	2.79779i	0.708240	+	0.207958i	0.615963	−	0.787775i	$-0.288767\pi$
$181$	9.52840	+	2.79779i	0.708240	+	0.207958i	0.0922774	+	0.995733i	$0.470585\pi$
$182$	5.51112	−	7.16251i	0.408511	−	0.530920i
$183$	−0.695090	−	15.8617i	−0.0513825	−	1.17253i
$184$	13.5533	+	0.555211i	0.999162	+	0.0409307i
$185$		−	10.0671i		−	0.740145i
$186$	3.50127	+	2.45772i	0.256726	+	0.180209i
$187$	−0.453092	+	1.54309i	−0.0331334	+	0.112842i
$188$	−5.71916	−	21.5733i	−0.417113	−	1.57340i
$189$	−6.08391	+	5.15130i	−0.442539	+	0.374702i
$190$	−2.91719	−	4.00630i	−0.211635	−	0.290648i
$191$	2.11528	−	14.7121i	0.153057	−	1.06453i	−0.758001	−	0.652253i	$-0.773824\pi$
$191$	2.11528	−	14.7121i	0.153057	−	1.06453i	0.911058	−	0.412279i	$-0.135267\pi$
$192$	−11.9158	+	7.07197i	−0.859952	+	0.510376i
$193$	8.37722	+	5.38371i	0.603006	+	0.387528i	0.806228	−	0.591604i	$-0.201505\pi$
$193$	8.37722	+	5.38371i	0.603006	+	0.387528i	−0.203223	+	0.979133i	$0.565142\pi$
$194$	−8.92665	−	0.757257i	−0.640896	−	0.0543678i
$195$	−5.84951	−	11.4533i	−0.418892	−	0.820187i
$196$	0.245826	−	9.28936i	0.0175590	−	0.663526i
$197$	1.71631	−	0.246768i	0.122282	−	0.0175815i	−0.0809021	−	0.996722i	$-0.525780\pi$
$197$	1.71631	−	0.246768i	0.122282	−	0.0175815i	0.203184	+	0.979141i	$0.434871\pi$
$198$	2.59762	−	3.01580i	0.184605	−	0.214323i
$199$	4.89268	+	16.6629i	0.346833	+	1.18120i	0.929601	+	0.368566i	$0.120151\pi$
$199$	4.89268	+	16.6629i	0.346833	+	1.18120i	−0.582769	+	0.812638i	$0.698031\pi$
$200$	3.49735	+	3.78657i	0.247300	+	0.267751i
$201$	10.9174	−	13.7744i	0.770054	−	0.971571i
$202$	−18.3502	+	6.56909i	−1.29111	+	0.462200i
$203$	3.19946	+	3.69237i	0.224558	+	0.259154i
$204$	4.55461	+	3.81037i	0.318886	+	0.266780i
$205$	1.63975	−	3.59056i	0.114525	−	0.250776i
$206$	18.4173	+	4.26236i	1.28320	+	0.296973i
$207$	−1.83470	+	14.2700i	−0.127520	+	0.991836i
$208$	10.2297	+	13.1513i	0.709299	+	0.911878i
$209$	−1.67764	−	0.766152i	−0.116045	−	0.0529958i
$210$	5.97479	+	3.02923i	0.412300	+	0.209037i
$211$	−8.04458	+	6.97067i	−0.553812	+	0.479881i	−0.886226	−	0.463253i	$-0.846682\pi$
$211$	−8.04458	+	6.97067i	−0.553812	+	0.479881i	0.332414	+	0.943133i	$0.392137\pi$
$212$	−3.06035	−	26.1858i	−0.210186	−	1.79845i
$213$	−4.05227	−	3.21178i	−0.277657	−	0.220067i
$214$	20.8411	+	8.08896i	1.42467	+	0.552950i
$215$	3.66689	−	1.07670i	0.250080	−	0.0734300i
$216$	−6.37539	−	13.2421i	−0.433790	−	0.901014i
$217$	0.381300	+	2.65200i	0.0258843	+	0.180029i
$218$	−13.9666	+	2.84529i	−0.945938	+	0.192708i
$219$	11.3975	−	5.82100i	0.770169	−	0.393347i
$220$	−3.18316	−	1.02688i	−0.214609	−	0.0692319i
$221$	3.86040	−	6.00690i	0.259678	−	0.404068i
$222$	−13.7616	+	1.40808i	−0.923616	+	0.0945044i
$223$	−13.4457	−	1.93321i	−0.900393	−	0.129457i	−0.323454	−	0.946244i	$-0.604844\pi$
$223$	−13.4457	−	1.93321i	−0.900393	−	0.129457i	−0.576939	+	0.816787i	$0.695753\pi$
$224$	−8.33980	−	2.40123i	−0.557226	−	0.160439i
$225$	−4.32315	+	3.34682i	−0.288210	+	0.223121i
$226$	11.4229	+	21.5938i	0.759843	+	1.43640i
$227$	−21.3135	−	6.25821i	−1.41463	−	0.415372i	−0.516946	−	0.856018i	$-0.672931\pi$
$227$	−21.3135	−	6.25821i	−1.41463	−	0.415372i	−0.897681	+	0.440646i	$0.854750\pi$
$228$	−5.06855	+	4.54814i	−0.335673	+	0.301208i
$229$	−13.3516			−0.882297			−0.441149	−	0.897434i	$-0.645429\pi$
$229$	−13.3516			−0.882297			−0.441149	+	0.897434i	$0.645429\pi$
$230$	11.6484	−	3.23777i	0.768074	−	0.213492i
$231$	2.49056	−	0.109141i	0.163867	−	0.00718094i
$232$	−8.07062	+	3.99972i	−0.529862	+	0.262594i
$233$	−0.577056	+	1.96527i	−0.0378042	+	0.128749i	−0.976233	−	0.216723i	$-0.930463\pi$
$233$	−0.577056	+	1.96527i	−0.0378042	+	0.128749i	0.938429	+	0.345472i	$0.112281\pi$
$234$	−14.8384	+	9.59820i	−0.970014	+	0.627454i
$235$	−10.7546	−	16.7344i	−0.701551	−	1.09163i
$236$	−23.1496	+	9.84054i	−1.50691	+	0.640564i
$237$	2.34497	−	23.6077i	0.152322	−	1.53348i
$238$	0.216235	+	3.71301i	0.0140164	+	0.240679i
$239$	11.4557	+	7.36214i	0.741008	+	0.476217i	0.855887	−	0.517162i	$-0.173012\pi$
$239$	11.4557	+	7.36214i	0.741008	+	0.476217i	−0.114879	+	0.993379i	$0.536648\pi$
$240$	−8.17236	+	9.25941i	−0.527523	+	0.597692i
$241$	−6.69055	−	14.6503i	−0.430976	−	0.943707i	−0.993167	−	0.116699i	$-0.962769\pi$
$241$	−6.69055	−	14.6503i	−0.430976	−	0.943707i	0.562191	−	0.827008i	$-0.309959\pi$
$242$	14.0236	−	2.85690i	0.901470	−	0.183649i
$243$	14.5795	−	5.51721i	0.935272	−	0.353929i
$244$	9.50017	+	15.6796i	0.608186	+	1.00378i
$245$	−2.33342	−	7.94691i	−0.149077	−	0.507709i
$246$	−5.13762	−	1.73932i	−0.327563	−	0.110895i
$247$	6.18849	+	5.36235i	0.393764	+	0.341198i
$248$	−4.90909	−	0.547583i	−0.311728	−	0.0347715i
$249$	−8.32654	+	7.87906i	−0.527673	+	0.499315i
$250$	14.9848	+	8.44153i	0.947722	+	0.533890i
$251$	−12.0659	+	26.4206i	−0.761592	+	1.66765i	−0.0172540	+	0.999851i	$0.505492\pi$
$251$	−12.0659	+	26.4206i	−0.761592	+	1.66765i	−0.744338	+	0.667803i	$0.767235\pi$
$252$	3.30523	−	8.59118i	0.208210	−	0.541194i
$253$	3.18546	−	3.17746i	0.200268	−	0.199765i
$254$	−9.78356	−	2.26423i	−0.613875	−	0.142070i
$255$	4.90609	+	1.98580i	0.307231	+	0.124356i
$256$	8.14681	−	13.7706i	0.509176	−	0.860662i
$257$	13.2001	−	11.4380i	0.823403	−	0.713482i	−0.137460	−	0.990507i	$-0.543894\pi$
$257$	13.2001	−	11.4380i	0.823403	−	0.713482i	0.960863	+	0.277025i	$0.0893484\pi$
$258$	−1.98472	−	4.86200i	−0.123563	−	0.302695i
$259$	−6.54798	−	5.67385i	−0.406871	−	0.352556i
$260$	12.2760	+	8.35626i	0.761323	+	0.518233i
$261$	−3.48315	−	8.89617i	−0.215602	−	0.550659i
$262$	−6.41164	+	6.24421i	−0.396112	+	0.385769i
$263$	0.531928	+	3.69964i	0.0328001	+	0.228130i	0.999627	−	0.0273020i	$-0.00869156\pi$
$263$	0.531928	+	3.69964i	0.0328001	+	0.228130i	−0.966827	+	0.255432i	$0.917782\pi$
$264$	−0.958499	+	4.49498i	−0.0589915	+	0.276647i
$265$	−9.76143	−	21.3745i	−0.599640	−	1.31303i
$266$	−4.24999	−	0.360531i	−0.260584	−	0.0221056i
$267$	−10.8229	−	6.30366i	−0.662352	−	0.385778i
$268$	−3.41873	+	20.0053i	−0.208832	+	1.22202i
$269$	−3.54256	−	0.509343i	−0.215993	−	0.0310552i	0.0334685	−	0.999440i	$-0.489345\pi$
$269$	−3.54256	−	0.509343i	−0.215993	−	0.0310552i	−0.249462	+	0.968385i	$0.580254\pi$
$270$	−9.03147	−	9.48800i	−0.549637	−	0.577421i
$271$	−7.88982	−	12.2768i	−0.479272	−	0.745762i	0.514464	−	0.857512i	$-0.327991\pi$
$271$	−7.88982	−	12.2768i	−0.479272	−	0.745762i	−0.993736	+	0.111750i	$0.964355\pi$
$272$	−6.72605	−	1.33345i	−0.407827	−	0.0808523i
$273$	−10.7464	−	2.65041i	−0.650405	−	0.160410i
$274$	3.64782	−	4.74088i	0.220373	−	0.286407i
$275$	1.70972			0.103100
$276$	−6.05527	−	15.4704i	−0.364485	−	0.931209i
$277$	−0.0461311			−0.00277175			−0.00138587	−	0.999999i	$-0.500441\pi$
$277$	−0.0461311			−0.00277175			−0.00138587	+	0.999999i	$0.500441\pi$
$278$	−13.6715	+	17.7681i	−0.819962	+	1.06566i
$279$	1.03065	−	5.13680i	0.0617035	−	0.307532i
$280$	−7.73126	+	0.245274i	−0.462031	+	0.0146579i
$281$	6.54270	+	10.1806i	0.390305	+	0.607326i	0.979688	−	0.200528i	$-0.0642657\pi$
$281$	6.54270	+	10.1806i	0.390305	+	0.607326i	−0.589384	+	0.807853i	$0.700629\pi$
$282$	−21.3716	+	17.0421i	−1.27266	+	1.01484i
$283$	24.2713	+	3.48969i	1.44278	+	0.207441i	0.818836	−	0.574027i	$-0.194620\pi$
$283$	24.2713	+	3.48969i	1.44278	+	0.207441i	0.623945	+	0.781468i	$0.285529\pi$
$284$	5.88532	+	1.00575i	0.349230	+	0.0596804i
$285$	−3.05481	+	5.24489i	−0.180951	+	0.310680i
$286$	5.50665	+	0.467134i	0.325615	+	0.0276222i
$287$	−1.41125	−	3.09022i	−0.0833037	−	0.182410i
$288$	13.8006	+	9.87642i	0.813208	+	0.581973i
$289$	−2.00114	−	13.9183i	−0.117714	−	0.818721i
$290$	−5.75137	+	5.60118i	−0.337732	+	0.328913i
$291$	3.54915	+	10.3823i	0.208055	+	0.608619i
$292$	−8.31552	+	12.2161i	−0.486629	+	0.714894i
$293$	−20.3118	−	17.6003i	−1.18663	−	1.02822i	−0.998942	−	0.0459911i	$-0.985355\pi$
$293$	−20.3118	−	17.6003i	−1.18663	−	1.02822i	−0.187687	−	0.982229i	$-0.560099\pi$
$294$	−10.5370	+	4.30130i	−0.614528	+	0.250857i
$295$	−16.9437	+	14.6818i	−0.986503	+	0.854810i
$296$	13.1571	−	9.05766i	0.764743	−	0.526466i
$297$	−4.66138	−	1.42672i	−0.270481	−	0.0827864i
$298$	−19.1884	−	4.44082i	−1.11156	−	0.257250i
$299$	−17.5448	+	9.55159i	−1.01464	+	0.552383i
$300$	2.52258	−	5.78714i	0.145641	−	0.334121i
$301$	1.36636	−	2.99191i	0.0787556	−	0.172451i
$302$	−1.01503	−	0.571807i	−0.0584084	−	0.0329038i
$303$	16.4070	+	17.3388i	0.942556	+	0.996088i
$304$	2.61135	−	7.41722i	0.149771	−	0.425407i
$305$	12.3490	+	10.7005i	0.707103	+	0.612709i
$306$	2.02835	−	6.98433i	0.115953	−	0.399268i
$307$	−2.63299	−	8.96713i	−0.150273	−	0.511781i	0.849605	−	0.527419i	$-0.176840\pi$
$307$	−2.63299	−	8.96713i	−0.150273	−	0.511781i	−0.999878	+	0.0156380i	$0.995022\pi$
$308$	−2.46196	+	1.49169i	−0.140283	+	0.0849968i
$309$	−4.29512	−	22.7509i	−0.244341	−	1.29425i
$310$	−4.31395	+	0.878842i	−0.245016	+	0.0499149i
$311$	−1.08811	−	2.38263i	−0.0617011	−	0.135107i	0.876270	−	0.481821i	$-0.160025\pi$
$311$	−1.08811	−	2.38263i	−0.0617011	−	0.135107i	−0.937971	+	0.346715i	$0.887297\pi$
$312$	9.70588	−	17.9499i	0.549487	−	1.01621i
$313$	15.1727	+	9.75090i	0.857612	+	0.551154i	0.893940	−	0.448186i	$-0.147930\pi$
$313$	15.1727	+	9.75090i	0.857612	+	0.551154i	−0.0363284	+	0.999340i	$0.511566\pi$
$314$	0.758552	+	13.0252i	0.0428076	+	0.735057i
$315$	0.452749	−	8.19186i	0.0255095	−	0.461559i
$316$	10.7167	+	25.2108i	0.602861	+	1.41822i
$317$	4.33627	+	6.74737i	0.243549	+	0.378970i	0.941410	−	0.337263i	$-0.109501\pi$
$317$	4.33627	+	6.74737i	0.243549	+	0.378970i	−0.697861	+	0.716233i	$0.745865\pi$
$318$	−27.8535	+	16.3334i	−1.56194	+	0.915934i
$319$	−0.841720	+	2.86663i	−0.0471273	+	0.160501i
$320$	3.14229	−	13.9101i	0.175659	−	0.777599i
$321$	−1.19870	−	27.3540i	−0.0669049	−	1.52675i
$322$	4.45915	−	9.40138i	0.248499	−	0.523918i
$323$	−3.36997			−0.187510
$324$	−11.7068	+	13.6730i	−0.650376	+	0.759612i
$325$	−7.28351	−	2.13863i	−0.404017	−	0.118630i
$326$	−10.4954	−	19.8404i	−0.581285	−	1.09886i
$327$	10.0718	+	14.2584i	0.556971	+	0.788491i
$328$	6.16802	−	1.08747i	0.340572	−	0.0600454i
$329$	−16.9460	−	2.43647i	−0.934265	−	0.134327i
$330$	0.416966	+	4.07512i	0.0229532	+	0.224328i
$331$	−9.63739	+	14.9961i	−0.529719	+	0.824259i	−0.998247	−	0.0591901i	$-0.981148\pi$
$331$	−9.63739	+	14.9961i	−0.529719	+	0.824259i	0.468528	+	0.883449i	$0.344785\pi$
$332$	4.06393	−	12.5976i	0.223037	−	0.691382i
$333$	8.35927	+	14.7366i	0.458085	+	0.807562i
$334$	16.4911	−	3.35959i	0.902353	−	0.183828i
$335$	2.57433	+	17.9048i	0.140650	+	0.978245i
$336$	1.41666	+	10.5342i	0.0772852	+	0.574690i
$337$	1.22849	−	0.360718i	0.0669203	−	0.0196496i	−0.248101	−	0.968734i	$-0.579807\pi$
$337$	1.22849	−	0.360718i	0.0669203	−	0.0196496i	0.315021	+	0.949085i	$0.397988\pi$
$338$	−5.73521	−	2.22598i	−0.311954	−	0.121077i
$339$	18.5843	−	23.4476i	1.00936	−	1.27350i
$340$	−6.07022	+	0.709429i	−0.329204	+	0.0384742i
$341$	−1.23822	+	1.07292i	−0.0670533	+	0.0581020i
$342$	7.59699	+	3.44229i	0.410798	+	0.186138i
$343$	−16.2528	−	7.42242i	−0.877570	−	0.400773i
$344$	4.70641	+	3.82370i	0.253752	+	0.206160i
$345$	−9.36967	−	11.4657i	−0.504446	−	0.617293i
$346$	−23.3456	−	5.40292i	−1.25507	−	0.290463i
$347$	8.32615	−	18.2317i	0.446971	−	0.978731i	−0.543295	−	0.839542i	$-0.682823\pi$
$347$	8.32615	−	18.2317i	0.446971	−	0.978731i	0.990266	−	0.139189i	$-0.0444494\pi$
$348$	8.46121	+	7.07862i	0.453568	+	0.379454i
$349$	−17.9340	−	20.6970i	−0.959986	−	1.10788i	−0.994100	−	0.108466i	$-0.965406\pi$
$349$	−17.9340	−	20.6970i	−0.959986	−	1.10788i	0.0341137	−	0.999418i	$-0.489139\pi$
$350$	3.72266	−	1.33266i	0.198985	−	0.0712335i
$351$	18.0731	+	11.9087i	0.964672	+	0.635637i
$352$	−1.52192	−	5.08414i	−0.0811185	−	0.270986i
$353$	5.84620	+	19.9103i	0.311162	+	1.05972i	0.955503	+	0.294981i	$0.0953134\pi$
$353$	5.84620	+	19.9103i	0.311162	+	1.05972i	−0.644341	+	0.764738i	$0.722868\pi$
$354$	22.4399	+	21.1084i	1.19267	+	1.12190i
$355$	5.26740	−	0.757338i	0.279565	−	0.0401953i
$356$	14.4574	+	0.382588i	0.766240	+	0.0202771i
$357$	4.05674	−	2.07189i	0.214705	−	0.109656i
$358$	30.4362	+	2.58193i	1.60860	+	0.136459i
$359$	−12.9463	−	8.32008i	−0.683279	−	0.439117i	0.152412	−	0.988317i	$-0.451296\pi$
$359$	−12.9463	−	8.32008i	−0.683279	−	0.439117i	−0.835691	+	0.549200i	$0.814932\pi$
$360$	14.4088	+	4.60121i	0.759413	+	0.242505i
$361$	−2.15399	+	14.9813i	−0.113368	+	0.788489i
$362$	8.26684	+	11.3532i	0.434495	+	0.596711i
$363$	−10.1129	−	14.3166i	−0.530788	−	0.751425i
$364$	12.3540	−	3.27509i	0.647526	−	0.171661i
$365$	−3.71077	+	12.6377i	−0.194230	+	0.661488i
$366$	12.9002	−	18.3777i	0.674305	−	0.960617i
$367$		−	23.1470i		−	1.20826i	−0.796885	−	0.604131i	$-0.793520\pi$
$367$		−	23.1470i		−	1.20826i	0.796885	−	0.604131i	$-0.206480\pi$
$368$	14.7121	+	12.3108i	0.766920	+	0.641743i
$369$	0.581108	+	6.61761i	0.0302513	+	0.344499i
$370$	8.68192	−	11.2834i	0.451351	−	0.586597i
$371$	−19.4044	−	5.69763i	−1.00742	−	0.295806i
$372$	1.80476	+	5.77420i	0.0935726	+	0.299378i
$373$	20.8657	−	13.4096i	1.08038	−	0.694320i	0.125738	−	0.992064i	$-0.459870\pi$
$373$	20.8657	−	13.4096i	1.08038	−	0.694320i	0.954646	+	0.297743i	$0.0962339\pi$
$374$	−1.83861	+	1.33879i	−0.0950723	+	0.0692269i
$375$	2.08209	−	20.9612i	0.107518	−	1.08243i
$376$	12.1948	−	29.1122i	0.628901	−	1.50135i
$377$	7.17155	−	11.1592i	0.369354	−	0.574726i
$378$	−11.2615	+	0.526895i	−0.579230	+	0.0271006i
$379$	−31.9784	+	14.6040i	−1.64262	+	0.750159i	−0.999873	−	0.0159203i	$-0.994932\pi$
$379$	−31.9784	+	14.6040i	−1.64262	+	0.750159i	−0.642746	+	0.766079i	$0.722205\pi$
$380$	0.185406	−	7.00618i	0.00951112	−	0.359410i
$381$	2.28163	+	12.0856i	0.116892	+	0.619163i
$382$	15.0587	−	14.6655i	0.770472	−	0.750352i
$383$	18.3504	−	5.38816i	0.937661	−	0.275322i	0.223020	−	0.974814i	$-0.428408\pi$
$383$	18.3504	−	5.38816i	0.937661	−	0.275322i	0.714641	+	0.699492i	$0.246590\pi$
$384$	−19.4545	−	2.34987i	−0.992784	−	0.119916i
$385$	−1.68016	+	1.93901i	−0.0856288	+	0.0988209i
$386$	4.74645	+	13.2588i	0.241588	+	0.674855i
$387$	−4.47372	+	4.62095i	−0.227412	+	0.234896i
$388$	−9.35216	−	8.54717i	−0.474784	−	0.433917i
$389$	7.16560	+	3.27242i	0.363311	+	0.165918i	0.588702	−	0.808350i	$-0.299639\pi$
$389$	7.16560	+	3.27242i	0.363311	+	0.165918i	−0.225392	+	0.974268i	$0.572366\pi$
$390$	3.32113	−	17.8818i	0.168172	−	0.905481i
$391$	2.88269	−	7.69924i	0.145784	−	0.389367i
$392$	8.28675	−	10.1998i	0.418544	−	0.515165i
$393$	10.1605	+	4.11258i	0.512529	+	0.207452i
$394$	2.13650	+	1.20357i	0.107635	+	0.0606352i
$395$	15.9890	+	18.4523i	0.804496	+	0.928438i
$396$	5.51233	−	1.13998i	0.277005	−	0.0572860i
$397$	−11.7266	+	13.5332i	−0.588539	+	0.679211i	−0.969418	−	0.245414i	$-0.921076\pi$
$397$	−11.7266	+	13.5332i	−0.588539	+	0.679211i	0.380879	+	0.924625i	$0.375621\pi$
$398$	−8.88642	+	22.8958i	−0.445436	+	1.14766i
$399$	1.68975	+	4.94301i	0.0845934	+	0.247460i
$400$	0.654354	+	7.26024i	0.0327177	+	0.363012i
$401$	19.8231	−	2.85013i	0.989917	−	0.142329i	0.371714	−	0.928347i	$-0.378770\pi$
$401$	19.8231	−	2.85013i	0.989917	−	0.142329i	0.618203	+	0.786019i	$0.287861\pi$
$402$	24.1157	−	6.02344i	1.20278	−	0.300422i
$403$	6.61696	−	3.02187i	0.329614	−	0.150530i
$404$	−26.2326	−	8.46254i	−1.30512	−	0.421027i
$405$	−6.18871	+	14.8015i	−0.307519	+	0.735492i
$406$	0.401705	+	6.89775i	0.0199363	+	0.342330i
$407$	0.754019	−	5.24431i	0.0373753	−	0.259951i
$408$	1.81883	+	8.19870i	0.0900454	+	0.405896i
$409$	−9.23862	+	5.93730i	−0.456820	+	0.293581i	−0.748742	−	0.662862i	$-0.769342\pi$
$409$	−9.23862	+	5.93730i	−0.456820	+	0.293581i	0.291922	+	0.956442i	$0.405705\pi$
$410$	4.93441	−	2.61026i	0.243693	−	0.128911i
$411$	−7.11310	−	1.75431i	−0.350864	−	0.0865339i
$412$	16.9667	+	20.6606i	0.835891	+	1.01788i
$413$			19.2956i			0.949474i
$414$	−14.3630	+	14.4120i	−0.705902	+	0.708310i
$415$		−	11.7979i		−	0.579135i
$416$	0.123877	+	23.5625i	0.00607356	+	1.15524i
$417$	26.6589	+	6.57491i	1.30549	+	0.321975i
$418$	−1.21961	−	2.30553i	−0.0596529	−	0.112767i
$419$	−12.9321	+	8.31093i	−0.631773	+	0.406016i	−0.816965	−	0.576687i	$-0.804345\pi$
$419$	−12.9321	+	8.31093i	−0.631773	+	0.406016i	0.185193	+	0.982702i	$0.440709\pi$
$420$	4.08427	+	8.54795i	0.199292	+	0.417097i
$421$	−2.07917	+	14.4610i	−0.101333	+	0.704784i	0.874302	+	0.485383i	$0.161320\pi$
$421$	−2.07917	+	14.4610i	−0.101333	+	0.704784i	−0.975635	+	0.219402i	$0.929589\pi$
$422$	−15.0281	+	0.875195i	−0.731559	+	0.0426038i
$423$	29.6386	+	15.5665i	1.44108	+	0.756868i
$424$	19.1528	−	31.9891i	0.930141	−	1.55353i
$425$	2.84174	−	1.29778i	0.137845	−	0.0629516i
$426$	−1.77203	−	7.09456i	−0.0858550	−	0.343733i
$427$	13.9200	−	2.00139i	0.673635	−	0.0968540i
$428$	16.3833	+	27.0399i	0.791916	+	1.30702i
$429$	−2.18939	−	6.40458i	−0.105705	−	0.309216i
$430$	5.03850	+	1.95557i	0.242978	+	0.0943058i
$431$	−5.31256	+	6.13102i	−0.255897	+	0.295321i	−0.869132	−	0.494579i	$-0.835322\pi$
$431$	−5.31256	+	6.13102i	−0.255897	+	0.295321i	0.613236	+	0.789900i	$0.289868\pi$
$432$	4.27444	−	20.3403i	0.205654	−	0.978625i
$433$	13.7330	+	15.8487i	0.659965	+	0.761640i	0.982772	−	0.184825i	$-0.0591717\pi$
$433$	13.7330	+	15.8487i	0.659965	+	0.761640i	−0.322806	+	0.946465i	$0.604626\pi$
$434$	−1.85974	+	3.30127i	−0.0892702	+	0.158466i
$435$	9.11416	+	3.68907i	0.436990	+	0.176877i
$436$	−18.1079	−	8.85584i	−0.867213	−	0.424118i
$437$	8.26906	+	4.52875i	0.395563	+	0.216639i
$438$	17.7947	+	3.30494i	0.850261	+	0.157916i
$439$	−18.3498	−	8.38009i	−0.875790	−	0.399960i	−0.0737829	−	0.997274i	$-0.523507\pi$
$439$	−18.3498	−	8.38009i	−0.875790	−	0.399960i	−0.802007	+	0.597314i	$0.796234\pi$
$440$	−2.68218	−	3.89613i	−0.127868	−	0.185741i
$441$	10.0146	+	9.69547i	0.476884	+	0.461689i
$442$	9.50723	−	3.40345i	0.452213	−	0.161885i
$443$	−7.81772	+	9.02213i	−0.371431	+	0.428654i	−0.910437	−	0.413648i	$-0.864255\pi$
$443$	−7.81772	+	9.02213i	−0.371431	+	0.428654i	0.539006	+	0.842302i	$0.318800\pi$
$444$	−16.6387	−	10.2899i	−0.789637	−	0.488336i
$445$	12.3681	−	3.63160i	0.586303	−	0.172154i
$446$	−13.4031	−	13.7625i	−0.634656	−	0.651674i
$447$	4.47495	+	23.7034i	0.211658	+	1.12113i
$448$	−7.27662	−	9.88368i	−0.343788	−	0.466960i
$449$	−11.4323	+	5.22094i	−0.539522	+	0.246392i	−0.666488	−	0.745516i	$-0.732203\pi$
$449$	−11.4323	+	5.22094i	−0.539522	+	0.246392i	0.126966	+	0.991907i	$0.459476\pi$
$450$	−7.73182	+	0.0228808i	−0.364482	+	0.00107861i
$451$	1.12314	−	1.74764i	0.0528867	−	0.0822933i
$452$	−5.81958	+	34.0542i	−0.273730	+	1.60177i
$453$	−0.141035	+	1.41985i	−0.00662640	+	0.0667105i
$454$	−18.4916	−	25.3953i	−0.867854	−	1.19186i
$455$	9.58301	−	6.15863i	0.449259	−	0.288721i
$456$	−9.60332	+	0.726510i	−0.449717	+	0.0340219i
$457$	10.4747	+	3.07565i	0.489987	+	0.143873i	0.517387	−	0.855751i	$-0.326905\pi$
$457$	10.4747	+	3.07565i	0.489987	+	0.143873i	−0.0274005	+	0.999625i	$0.508723\pi$
$458$	−14.9648	−	11.5145i	−0.699259	−	0.538038i
$459$	−8.83069	+	1.16691i	−0.412181	+	0.0544667i
$460$	15.8481	+	6.41672i	0.738923	+	0.299181i
$461$			8.44304i			0.393232i	0.980481	+	0.196616i	$0.0629952\pi$
$461$			8.44304i			0.393232i	−0.980481	+	0.196616i	$0.937005\pi$
$462$	2.88561	+	2.02555i	0.134251	+	0.0942372i
$463$	−7.05257	+	24.0189i	−0.327761	+	1.11625i	0.616583	+	0.787290i	$0.288517\pi$
$463$	−7.05257	+	24.0189i	−0.327761	+	1.11625i	−0.944344	+	0.328961i	$0.893302\pi$
$464$	−12.4951	−	2.47718i	−0.580073	−	0.115000i
$465$	3.11093	+	4.40407i	0.144266	+	0.204234i
$466$	−2.34165	+	1.70507i	−0.108475	+	0.0789859i
$467$	1.78195	−	12.3937i	0.0824588	−	0.573514i	−0.906144	−	0.422969i	$-0.860988\pi$
$467$	1.78195	−	12.3937i	0.0824588	−	0.573514i	0.988603	−	0.150545i	$-0.0481029\pi$
$468$	−24.9088	−	2.03881i	−1.15141	−	0.0942442i
$469$	13.0968	+	8.41683i	0.604756	+	0.388653i
$470$	2.37792	−	28.0312i	0.109685	−	1.29298i
$471$	14.2310	−	7.26818i	0.655731	−	0.334900i
$472$	−34.4333	−	8.93489i	−1.58492	−	0.411262i
$473$	1.99087	−	0.286243i	0.0915401	−	0.0131615i
$474$	22.9878	−	24.4378i	1.05586	−	1.12247i
$475$	1.00934	+	3.43751i	0.0463119	+	0.157724i
$476$	−2.95977	+	4.34813i	−0.135661	+	0.199296i
$477$	32.0378	+	23.1835i	1.46691	+	1.06150i
$478$	6.49069	+	18.1312i	0.296877	+	0.829301i
$479$	−26.6453	−	30.7503i	−1.21745	−	1.40502i	−0.887365	−	0.461068i	$-0.847467\pi$
$479$	−26.6453	−	30.7503i	−1.21745	−	1.40502i	−0.330089	−	0.943950i	$-0.607079\pi$
$480$	−17.1452	+	3.33028i	−0.782567	+	0.152006i
$481$	−9.77210	+	21.3979i	−0.445569	+	0.975661i
$482$	5.13557	−	22.1904i	0.233919	−	1.01074i
$483$	−12.7385	−	0.367769i	−0.579622	−	0.0167341i
$484$	18.1818	+	8.89197i	0.826446	+	0.404180i
$485$	−10.2718	−	4.69096i	−0.466417	−	0.213005i
$486$	21.0991	+	6.38961i	0.957076	+	0.289839i
$487$	4.91385	−	4.25787i	0.222668	−	0.192943i	−0.536382	−	0.843975i	$-0.680209\pi$
$487$	4.91385	−	4.25787i	0.222668	−	0.192943i	0.759050	+	0.651033i	$0.225664\pi$
$488$	−2.87418	+	25.7671i	−0.130108	+	1.16642i
$489$	−17.0752	+	21.5436i	−0.772167	+	0.974236i
$490$	4.23812	−	10.9195i	0.191459	−	0.493291i
$491$	23.4611	−	6.88880i	1.05878	−	0.310887i	0.294423	−	0.955675i	$-0.404873\pi$
$491$	23.4611	−	6.88880i	1.05878	−	0.310887i	0.764361	+	0.644788i	$0.223054\pi$
$492$	−4.25838	−	6.38020i	−0.191982	−	0.287641i
$493$	0.776917	+	5.40357i	0.0349906	+	0.243365i
$494$	2.31168	+	11.3473i	0.104007	+	0.510538i
$495$	4.36385	−	2.47537i	0.196141	−	0.111260i
$496$	−5.03000	−	4.84739i	−0.225854	−	0.217654i
$497$	2.47614	−	3.85295i	0.111070	−	0.172828i
$498$	−16.1276	+	1.65017i	−0.722694	+	0.0739460i
$499$	5.00199	+	0.719177i	0.223920	+	0.0321948i	0.253361	−	0.967372i	$-0.418464\pi$
$499$	5.00199	+	0.719177i	0.223920	+	0.0321948i	−0.0294417	+	0.999566i	$0.509373\pi$
$500$	9.51530	+	22.3845i	0.425537	+	1.00107i
$501$	−11.8923	−	16.8356i	−0.531308	−	0.752160i
$502$	−36.3091	+	19.2072i	−1.62056	+	0.857259i
$503$	−22.7469	−	6.67909i	−1.01423	−	0.297806i	−0.267949	−	0.963433i	$-0.586346\pi$
$503$	−22.7469	−	6.67909i	−1.01423	−	0.297806i	−0.746284	+	0.665627i	$0.768164\pi$
$504$	11.1137	−	6.77876i	0.495044	−	0.301950i
$505$	−24.5673			−1.09323
$506$	6.31061	−	0.814217i	0.280541	−	0.0361964i
$507$	0.329867	+	7.52745i	0.0146499	+	0.334306i
$508$	−9.01298	−	10.9752i	−0.399886	−	0.486947i
$509$	5.10300	−	17.3792i	0.226187	−	0.770321i	−0.765700	−	0.643197i	$-0.777607\pi$
$509$	5.10300	−	17.3792i	0.226187	−	0.770321i	0.991887	−	0.127123i	$-0.0405744\pi$
$510$	3.78630	+	6.45679i	0.167660	+	0.285912i
$511$	6.12861	+	9.53630i	0.271114	+	0.421861i
$512$	21.0070	−	8.40857i	0.928389	−	0.371610i
$513$	0.116634	−	10.2143i	0.00514953	−	0.450972i
$514$	24.6593	−	1.43608i	1.08767	−	0.0633430i
$515$	20.0455	+	12.8825i	0.883311	+	0.567669i
$516$	1.96850	−	7.16110i	0.0866586	−	0.315250i
$517$	−4.34907	−	9.52312i	−0.191272	−	0.418827i
$518$	−2.44596	−	12.0064i	−0.107469	−	0.527532i
$519$	5.44445	+	28.8387i	0.238985	+	1.26588i
$520$	6.55271	+	19.9528i	0.287356	+	0.874988i
$521$	0.492799	+	1.67832i	0.0215899	+	0.0735285i	0.969583	−	0.244761i	$-0.0787096\pi$
$521$	0.492799	+	1.67832i	0.0215899	+	0.0735285i	−0.947993	+	0.318290i	$0.896891\pi$
$522$	3.76812	−	12.9750i	0.164926	−	0.567899i
$523$	6.61261	+	5.72986i	0.289149	+	0.250549i	0.787341	−	0.616518i	$-0.211457\pi$
$523$	6.61261	+	5.72986i	0.289149	+	0.250549i	−0.498192	+	0.867067i	$0.666003\pi$
$524$	−12.5714	+	1.46922i	−0.549184	+	0.0641834i
$525$	−3.32845	−	3.51749i	−0.145265	−	0.153516i
$526$	−2.59440	+	4.60539i	−0.113121	+	0.200805i
$527$	−1.24364	+	2.72320i	−0.0541739	+	0.118624i
$528$	−4.95082	+	4.21147i	−0.215457	+	0.183281i
$529$	−17.4200	+	15.0181i	−0.757393	+	0.652959i
$530$	7.49272	−	32.3755i	0.325463	−	1.40630i
$531$	12.6118	−	35.5613i	0.547307	−	1.54323i
$532$	−4.45258	−	4.06932i	−0.193044	−	0.176427i
$533$	−6.97072	+	6.04016i	−0.301935	+	0.261629i
$534$	−6.69429	−	16.3991i	−0.289690	−	0.709658i
$535$	21.2962	+	18.4533i	0.920716	+	0.797805i
$536$	−21.0845	+	19.4741i	−0.910712	+	0.841152i
$537$	−12.1011	−	35.3992i	−0.522201	−	1.52759i
$538$	−3.53133	−	3.62602i	−0.152246	−	0.156329i
$539$	−0.620349	−	4.31462i	−0.0267203	−	0.185844i
$540$	−1.94017	−	18.4232i	−0.0834916	−	0.792809i
$541$	−5.09118	−	11.1481i	−0.218887	−	0.479296i	0.768053	−	0.640387i	$-0.221226\pi$
$541$	−5.09118	−	11.1481i	−0.218887	−	0.479296i	−0.986940	+	0.161091i	$0.948499\pi$
$542$	1.74450	−	20.5644i	0.0749326	−	0.883317i
$543$	8.65684	−	14.8631i	0.371500	−	0.637839i
$544$	−6.38876	−	7.29517i	−0.273916	−	0.312778i
$545$	−17.7833	−	2.55685i	−0.761751	−	0.109523i
$546$	−9.75917	−	12.2385i	−0.417654	−	0.523759i
$547$	−12.6877	−	19.7424i	−0.542485	−	0.844123i	0.456474	−	0.889737i	$-0.349112\pi$
$547$	−12.6877	−	19.7424i	−0.542485	−	0.844123i	−0.998959	+	0.0456133i	$0.985476\pi$
$548$	8.17715	−	2.16779i	0.349311	−	0.0926034i
$549$	−26.9623	−	5.40974i	−1.15072	−	0.230882i
$550$	1.91630	+	1.47448i	0.0817113	+	0.0628720i
$551$	−6.26048			−0.266705
$552$	6.55490	−	22.5618i	0.278995	−	0.960292i
$553$	21.0136			0.893588
$554$	−0.0517050	−	0.0397839i	−0.00219673	−	0.00169025i
$555$	−16.9294	−	4.17531i	−0.718612	−	0.177232i
$556$	−30.6468	+	8.12456i	−1.29971	+	0.344558i
$557$	1.09191	+	1.69905i	0.0462657	+	0.0719909i	0.863616	−	0.504150i	$-0.168194\pi$
$557$	1.09191	+	1.69905i	0.0462657	+	0.0719909i	−0.817350	+	0.576141i	$0.804558\pi$
$558$	5.58520	−	4.86861i	0.236440	−	0.206105i
$559$	−8.83926	−	1.27089i	−0.373861	−	0.0537531i
$560$	−8.87692	−	6.39259i	−0.375118	−	0.270136i
$561$	2.40703	+	1.40194i	0.101625	+	0.0591901i
$562$	−1.44664	+	17.0532i	−0.0610228	+	0.719346i
$563$	17.5895	+	38.5157i	0.741310	+	1.62324i	0.781388	+	0.624045i	$0.214512\pi$
$563$	17.5895	+	38.5157i	0.741310	+	1.62324i	−0.0400789	+	0.999197i	$0.512761\pi$
$564$	−38.6510	+	0.670153i	−1.62750	+	0.0282185i
$565$	4.38218	+	30.4787i	0.184360	+	1.28225i
$566$	24.1944	+	24.8431i	1.01697	+	1.04424i
$567$	6.13943	+	12.3676i	0.257832	+	0.519389i
$568$	5.72906	+	6.20283i	0.240386	+	0.260265i
$569$	−25.0169	−	21.6773i	−1.04876	−	0.908760i	−0.0528086	−	0.998605i	$-0.516817\pi$
$569$	−25.0169	−	21.6773i	−1.04876	−	0.908760i	−0.995956	+	0.0898451i	$0.971363\pi$
$570$	−7.94715	+	3.24411i	−0.332869	+	0.135881i
$571$	19.5533	−	16.9430i	0.818280	−	0.709043i	−0.141457	−	0.989944i	$-0.545179\pi$
$571$	19.5533	−	16.9430i	0.818280	−	0.709043i	0.959737	+	0.280901i	$0.0906332\pi$
$572$	5.76914	+	5.27256i	0.241220	+	0.220457i
$573$	−23.8635	−	9.65905i	−0.996912	−	0.403512i
$574$	1.08326	−	4.68067i	0.0452143	−	0.195368i
$575$	−8.71694	−	0.634459i	−0.363522	−	0.0264588i
$576$	6.95056	+	22.9715i	0.289607	+	0.957146i
$577$	4.60367	−	10.0806i	0.191653	−	0.419663i	−0.789273	−	0.614043i	$-0.789542\pi$
$577$	4.60367	−	10.0806i	0.191653	−	0.419663i	0.980926	+	0.194380i	$0.0622695\pi$
$578$	9.76029	−	17.3258i	0.405974	−	0.720656i
$579$	12.5280	−	11.8547i	0.520647	−	0.492667i
$580$	−11.2768	+	1.31792i	−0.468243	+	0.0547238i
$581$	−7.67376	−	6.64935i	−0.318361	−	0.275861i
$582$	−4.97578	+	14.6975i	−0.206253	+	0.609232i
$583$	−3.48415	−	11.8659i	−0.144299	−	0.491437i
$584$	−19.8555	+	6.52077i	−0.821628	+	0.269831i
$585$	−21.6866	+	5.08664i	−0.896632	+	0.210307i
$586$	−7.58738	−	37.2440i	−0.313432	−	1.53853i
$587$	−5.97268	−	13.0783i	−0.246519	−	0.539801i	0.745409	−	0.666608i	$-0.232254\pi$
$587$	−5.97268	−	13.0783i	−0.246519	−	0.539801i	−0.991927	+	0.126807i	$0.959527\pi$
$588$	−15.5196	−	4.26616i	−0.640017	−	0.175933i
$589$	−2.88817	−	1.85612i	−0.119005	−	0.0764799i
$590$	−31.6527	+	1.84336i	−1.30312	+	0.0758900i
$591$	0.296859	−	2.98860i	0.0122111	−	0.122934i
$592$	22.5583	+	1.19476i	0.927139	+	0.0491045i
$593$	−0.231346	−	0.359981i	−0.00950024	−	0.0147827i	0.836471	−	0.548011i	$-0.184615\pi$
$593$	−0.231346	−	0.359981i	−0.00950024	−	0.0147827i	−0.845971	+	0.533229i	$0.820979\pi$
$594$	−3.99419	−	5.61912i	−0.163883	−	0.230555i
$595$	−1.32079	+	4.49818i	−0.0541469	+	0.184407i
$596$	−17.6771	−	21.5256i	−0.724082	−	0.881725i
$597$	30.0507	−	1.31687i	1.22989	−	0.0538961i
$598$	−27.9021	−	4.42512i	−1.14100	−	0.180957i
$599$	−4.64706			−0.189874			−0.0949368	−	0.995483i	$-0.530265\pi$
$599$	−4.64706			−0.189874			−0.0949368	+	0.995483i	$0.530265\pi$
$600$	7.81825	−	4.31088i	0.319179	−	0.175991i
$601$	8.38717	+	2.46270i	0.342120	+	0.100455i	0.448279	−	0.893894i	$-0.352037\pi$
$601$	8.38717	+	2.46270i	0.342120	+	0.100455i	−0.106159	+	0.994349i	$0.533855\pi$
$602$	4.11170	−	2.17505i	0.167580	−	0.0886484i
$603$	−18.6359	−	24.0723i	−0.758911	−	0.980300i
$604$	−0.644541	−	1.51627i	−0.0262260	−	0.0616960i
$605$	17.8558	+	2.56728i	0.725942	+	0.104375i
$606$	3.43624	+	33.5833i	0.139588	+	1.36423i
$607$	1.18468	−	1.84340i	0.0480848	−	0.0748215i	−0.816379	−	0.577517i	$-0.804022\pi$
$607$	1.18468	−	1.84340i	0.0480848	−	0.0748215i	0.864464	+	0.502695i	$0.167658\pi$
$608$	9.32354	−	6.06137i	0.378120	−	0.245821i
$609$	7.53630	−	3.84899i	0.305386	−	0.155969i
$610$	4.61292	+	22.6433i	0.186772	+	0.916801i
$611$	6.61512	+	46.0092i	0.267619	+	1.86133i
$612$	8.29678	−	6.07896i	0.335378	−	0.245727i
$613$	15.3202	−	4.49841i	0.618776	−	0.181689i	0.0427036	−	0.999088i	$-0.486403\pi$
$613$	15.3202	−	4.49841i	0.618776	−	0.181689i	0.576072	+	0.817399i	$0.304585\pi$
$614$	4.78221	−	12.3213i	0.192994	−	0.497247i
$615$	−5.35802	−	4.24670i	−0.216056	−	0.171243i
$616$	−4.04588	−	0.451296i	−0.163013	−	0.0181832i
$617$	−4.37063	+	3.78717i	−0.175955	+	0.152466i	−0.738386	−	0.674378i	$-0.764412\pi$
$617$	−4.37063	+	3.78717i	−0.175955	+	0.152466i	0.562431	+	0.826844i	$0.309866\pi$
$618$	14.8064	−	29.2039i	0.595602	−	1.17475i
$619$	7.13875	+	3.26016i	0.286930	+	0.131037i	0.553681	−	0.832729i	$-0.313223\pi$
$619$	7.13875	+	3.26016i	0.286930	+	0.131037i	−0.266751	+	0.963766i	$0.585950\pi$
$620$	−5.59311	−	2.73536i	−0.224625	−	0.109855i
$621$	23.2364	+	9.00384i	0.932445	+	0.361311i
$622$	0.835217	−	3.60891i	0.0334892	−	0.144704i
$623$	4.60860	−	10.0914i	0.184640	−	0.404305i
$624$	26.3588	−	11.7483i	1.05520	−	0.470309i
$625$	8.22945	+	9.49729i	0.329178	+	0.379892i
$626$	8.59670	+	24.0141i	0.343593	+	0.959798i
$627$	−1.98421	+	2.50346i	−0.0792416	+	0.0999785i
$628$	−10.3829	+	15.2532i	−0.414322	+	0.608670i
$629$	−2.72749	−	9.28897i	−0.108752	−	0.370375i
$630$	7.57218	−	8.79120i	0.301683	−	0.350250i
$631$	−5.02027	+	0.721805i	−0.199854	+	0.0287346i	−0.241515	−	0.970397i	$-0.577644\pi$
$631$	−5.02027	+	0.721805i	−0.199854	+	0.0287346i	0.0416609	+	0.999132i	$0.486735\pi$
$632$	−9.73041	+	37.4990i	−0.387055	+	1.49163i
$633$	8.38581	+	16.4193i	0.333306	+	0.652610i
$634$	−0.958782	+	11.3023i	−0.0380781	+	0.448870i
$635$	−10.6485	−	6.84335i	−0.422572	−	0.271570i
$636$	−45.3050	−	5.71411i	−1.79646	−	0.226579i
$637$	−2.75429	+	19.1565i	−0.109129	+	0.759008i
$638$	−3.41563	+	2.48709i	−0.135226	+	0.0984650i
$639$	−7.08180	+	5.48246i	−0.280152	+	0.216883i
$640$	15.5182	−	12.8809i	0.613409	−	0.509162i
$641$	−2.85551	+	9.72496i	−0.112786	+	0.384113i	−0.996468	−	0.0839745i	$-0.973239\pi$
$641$	−2.85551	+	9.72496i	−0.112786	+	0.384113i	0.883682	+	0.468087i	$0.155057\pi$
$642$	22.2467	−	31.6928i	0.878009	−	1.25081i
$643$			34.6614i			1.36691i	0.729991	+	0.683457i	$0.239524\pi$
$643$			34.6614i			1.36691i	−0.729991	+	0.683457i	$0.760476\pi$
$644$	13.1058	−	6.69170i	0.516440	−	0.263690i
$645$	−0.289795	−	6.61302i	−0.0114107	−	0.260387i
$646$	−3.77716	−	2.90629i	−0.148610	−	0.114347i
$647$	−33.4345	−	9.81725i	−1.31444	−	0.385956i	−0.451960	−	0.892038i	$-0.649275\pi$
$647$	−33.4345	−	9.81725i	−1.31444	−	0.385956i	−0.862485	+	0.506083i	$0.831093\pi$
$648$	−24.9130	+	5.22906i	−0.978675	+	0.205417i
$649$	−9.92631	+	6.37925i	−0.389642	+	0.250407i
$650$	−6.31918	−	8.67840i	−0.247859	−	0.340395i
$651$	4.61791	+	0.458699i	0.180990	+	0.0179778i
$652$	5.34702	−	31.2889i	0.209405	−	1.22537i
$653$	23.9389	−	37.2497i	0.936802	−	1.45769i	0.0482935	−	0.998833i	$-0.484622\pi$
$653$	23.9389	−	37.2497i	0.936802	−	1.45769i	0.888509	−	0.458860i	$-0.151742\pi$
$654$	−1.00783	+	24.6672i	−0.0394094	+	0.964563i
$655$	−10.2616	+	4.68630i	−0.400952	+	0.183109i
$656$	7.85113	+	4.10049i	0.306535	+	0.160097i
$657$	−5.06185	−	21.5809i	−0.197481	−	0.841952i
$658$	−16.8923	−	17.3453i	−0.658531	−	0.676188i
$659$	41.4690	−	12.1764i	1.61540	−	0.474325i	0.655625	−	0.755086i	$-0.272405\pi$
$659$	41.4690	−	12.1764i	1.61540	−	0.474325i	0.959778	+	0.280761i	$0.0905869\pi$
$660$	−3.04707	+	4.92710i	−0.118607	+	0.191787i
$661$	−18.2646	+	21.0785i	−0.710412	+	0.819859i	−0.990120	−	0.140226i	$-0.955217\pi$
$661$	−18.2646	+	21.0785i	−0.710412	+	0.819859i	0.279707	+	0.960085i	$0.409763\pi$
$662$	−23.7346	+	8.49662i	−0.922471	+	0.330231i
$663$	−8.50046	−	8.98324i	−0.330131	−	0.348880i
$664$	15.4192	−	10.6149i	0.598382	−	0.411939i
$665$	−4.89040	−	2.23337i	−0.189642	−	0.0866064i
$666$	−3.33969	+	23.7263i	−0.129410	+	0.919375i
$667$	5.35525	−	14.3031i	0.207356	−	0.553817i
$668$	21.3810	+	10.4566i	0.827256	+	0.404576i
$669$	−8.82762	+	21.8094i	−0.341295	+	0.843199i
$670$	−12.5559	+	22.2883i	−0.485077	+	0.861073i
$671$	5.63162	+	6.49923i	0.217406	+	0.250900i
$672$	−7.49699	+	13.0288i	−0.289203	+	0.502597i
$673$	24.8523	−	28.6811i	0.957987	−	1.10558i	−0.0363535	−	0.999339i	$-0.511574\pi$
$673$	24.8523	−	28.6811i	0.957987	−	1.10558i	0.994341	−	0.106237i	$-0.0338803\pi$
$674$	1.68801	+	0.655160i	0.0650198	+	0.0252358i
$675$	3.83518	+	8.65816i	0.147616	+	0.333253i
$676$	−4.50847	−	7.44102i	−0.173403	−	0.286193i
$677$	−10.8527	+	1.56038i	−0.417101	+	0.0599701i	−0.347671	−	0.937617i	$-0.613027\pi$
$677$	−10.8527	+	1.56038i	−0.417101	+	0.0599701i	−0.0694305	+	0.997587i	$0.522118\pi$
$678$	41.0512	−	10.2535i	1.57656	−	0.393782i
$679$	−8.84039	+	4.03727i	−0.339263	+	0.154936i
$680$	−7.41548	−	4.43986i	−0.284371	−	0.170261i
$681$	−19.3640	+	33.2465i	−0.742029	+	1.27401i
$682$	−2.31312	+	0.134710i	−0.0885741	+	0.00515829i
$683$	−0.773505	+	5.37985i	−0.0295974	+	0.205854i	−0.999254	−	0.0386162i	$-0.987705\pi$
$683$	−0.773505	+	5.37985i	−0.0295974	+	0.205854i	0.969657	+	0.244470i	$0.0786141\pi$
$684$	5.54624	+	10.4099i	0.212066	+	0.398033i
$685$	6.34302	−	4.07641i	0.242354	−	0.155752i
$686$	−11.8154	−	22.3358i	−0.451116	−	0.852786i
$687$	−5.53757	+	22.4528i	−0.211271	+	0.856629i
$688$	1.97747	+	8.34455i	0.0753904	+	0.318133i
$689$			54.9078i			2.09182i
$690$	−0.613652	−	20.9316i	−0.0233613	−	0.796851i
$691$			14.2914i			0.543672i	0.962344	+	0.271836i	$0.0876307\pi$
$691$			14.2914i			0.543672i	−0.962344	+	0.271836i	$0.912369\pi$
$692$	−21.5068	−	26.1892i	−0.817567	−	0.995563i
$693$	0.849422	−	4.23354i	0.0322669	−	0.160819i
$694$	25.0554	−	13.2541i	0.951089	−	0.503117i
$695$	−23.7727	+	15.2778i	−0.901750	+	0.579520i
$696$	3.37888	+	15.2309i	0.128076	+	0.577327i
$697$	0.540219	−	3.75731i	0.0204623	−	0.142318i
$698$	−2.25169	−	38.6642i	−0.0852276	−	1.46346i
$699$	3.06559	+	1.78551i	0.115951	+	0.0675342i
$700$	5.32175	+	1.71678i	0.201143	+	0.0648881i
$701$	33.4336	−	15.2686i	1.26277	−	0.576688i	0.332342	−	0.943159i	$-0.392161\pi$
$701$	33.4336	−	15.2686i	1.26277	−	0.576688i	0.930430	+	0.366471i	$0.119434\pi$
$702$	9.98671	+	28.9340i	0.376924	+	1.09204i
$703$	10.9892	−	1.58001i	0.414465	−	0.0595911i
$704$	2.67880	−	7.01095i	0.100961	−	0.264235i
$705$	−32.6021	+	11.1449i	−1.22787	+	0.419743i
$706$	−10.6183	+	27.3578i	−0.399623	+	1.02963i
$707$	−13.8463	+	15.9795i	−0.520743	+	0.600970i
$708$	6.94714	+	43.0112i	0.261090	+	1.61646i
$709$	−27.0993	−	31.2743i	−1.01774	−	1.17453i	−0.984554	−	0.175080i	$-0.943982\pi$
$709$	−27.0993	−	31.2743i	−1.01774	−	1.17453i	−0.0331813	−	0.999449i	$-0.510564\pi$
$710$	6.55698	+	3.69381i	0.246079	+	0.138626i
$711$	−38.7276	−	13.7347i	−1.45240	−	0.515093i
$712$	15.8743	+	12.8970i	0.594914	+	0.483335i
$713$	6.71115	−	5.01076i	0.251335	−	0.187654i
$714$	6.33371	+	1.17634i	0.237033	+	0.0440234i
$715$	6.33642	+	2.89374i	0.236969	+	0.108220i
$716$	31.8870	+	29.1423i	1.19167	+	1.08910i
$717$	17.1319	−	16.2112i	0.639801	−	0.605417i
$718$	−7.33524	−	20.4904i	−0.273749	−	0.764693i
$719$	13.7972	−	15.9228i	0.514547	−	0.593819i	−0.437710	−	0.899116i	$-0.644210\pi$
$719$	13.7972	−	15.9228i	0.514547	−	0.593819i	0.952257	+	0.305297i	$0.0987558\pi$
$720$	12.1817	+	17.5835i	0.453985	+	0.655297i
$721$	19.6770	−	5.77768i	0.732809	−	0.215172i
$722$	−15.3342	+	14.9338i	−0.570681	+	0.555779i
$723$	−27.4117	+	5.17504i	−1.01945	+	0.192462i
$724$	−0.525410	+	19.8544i	−0.0195267	+	0.737882i
$725$	5.27917	−	2.41092i	0.196064	−	0.0895392i
$726$	1.01194	−	24.7678i	0.0375568	−	0.919220i
$727$	8.89788	−	13.8454i	0.330004	−	0.513497i	−0.636114	−	0.771595i	$-0.719459\pi$
$727$	8.89788	−	13.8454i	0.330004	−	0.513497i	0.966119	+	0.258098i	$0.0830958\pi$
$728$	16.6712	+	6.98340i	0.617875	+	0.258822i
$729$	−3.23124	−	26.8060i	−0.119676	−	0.992813i
$730$	−15.0580	+	10.9645i	−0.557321	+	0.405814i
$731$	3.09176	−	1.98695i	0.114353	−	0.0734902i
$732$	30.3080	−	9.47295i	1.12021	−	0.350130i
$733$	36.8226	+	10.8121i	1.36007	+	0.399354i	0.878789	−	0.477211i	$-0.158352\pi$
$733$	36.8226	+	10.8121i	1.36007	+	0.399354i	0.481285	+	0.876564i	$0.340170\pi$
$734$	19.9621	−	25.9437i	0.736816	−	0.957600i
$735$	−14.3318	+	0.628045i	−0.528636	+	0.0231658i
$736$	5.87276	+	26.4860i	0.216473	+	0.976289i
$737$			9.52013i			0.350678i
$738$	−5.05577	+	7.91835i	−0.186105	+	0.291478i
$739$	5.39083	−	18.3595i	0.198305	−	0.675364i	−0.798955	−	0.601390i	$-0.794614\pi$
$739$	5.39083	−	18.3595i	0.198305	−	0.675364i	0.997260	−	0.0739737i	$-0.0235681\pi$
$740$	19.4618	−	5.15940i	0.715431	−	0.189663i
$741$	11.5843	−	8.18290i	0.425561	−	0.300606i
$742$	−16.8352	−	23.1205i	−0.618041	−	0.848782i
$743$	5.68902	−	39.5680i	0.208710	−	1.45161i	−0.568663	−	0.822571i	$-0.692539\pi$
$743$	5.68902	−	39.5680i	0.208710	−	1.45161i	0.777373	−	0.629040i	$-0.216552\pi$
$744$	−2.95689	+	8.02832i	−0.108405	+	0.294332i
$745$	−20.8848	−	13.4218i	−0.765159	−	0.491738i
$746$	34.9513	+	2.96495i	1.27966	+	0.108555i
$747$	9.79647	+	17.2703i	0.358434	+	0.631886i
$748$	−3.21534	−	0.0850882i	−0.117565	−	0.00311113i
$749$	24.0053	−	3.45145i	0.877136	−	0.126113i
$750$	20.4107	−	21.6982i	0.745295	−	0.792307i
$751$	−0.572530	−	1.94986i	−0.0208919	−	0.0711513i	0.948387	−	0.317114i	$-0.102714\pi$
$751$	−0.572530	−	1.94986i	−0.0208919	−	0.0711513i	−0.969279	+	0.245963i	$0.920896\pi$
$752$	38.7749	−	22.1128i	1.41398	−	0.806371i
$753$	39.4262	+	31.2487i	1.43677	+	1.13877i
$754$	17.6618	−	6.32266i	0.643205	−	0.230258i
$755$	−0.961639	−	1.10979i	−0.0349976	−	0.0403894i
$756$	−13.0766	−	9.12147i	−0.475592	−	0.331745i
$757$	10.3680	−	22.7028i	0.376832	−	0.825147i	−0.622271	−	0.782802i	$-0.713790\pi$
$757$	10.3680	−	22.7028i	0.376832	−	0.825147i	0.999103	−	0.0423449i	$-0.0134828\pi$
$758$	−48.4369	−	11.2098i	−1.75931	−	0.407160i
$759$	−4.02224	−	6.67471i	−0.145998	−	0.242277i
$760$	6.25000	−	7.69282i	0.226711	−	0.279048i
$761$	−35.9056	−	16.3975i	−1.30158	−	0.594411i	−0.360550	−	0.932740i	$-0.617411\pi$
$761$	−35.9056	−	16.3975i	−1.30158	−	0.594411i	−0.941028	+	0.338329i	$0.890138\pi$
$762$	−7.86539	+	15.5135i	−0.284933	+	0.561996i
$763$	−11.6858	+	10.1258i	−0.423055	+	0.366579i
$764$	29.5259	−	3.45070i	1.06821	−	0.124842i
$765$	5.37424	−	7.42677i	0.194306	−	0.268515i
$766$	25.2144	+	9.78633i	0.911033	+	0.353595i
$767$	50.2662	−	14.7595i	1.81501	−	0.532935i
$768$	−19.7786	−	19.4115i	−0.713698	−	0.700453i
$769$	−0.869254	−	6.04579i	−0.0313461	−	0.218017i	0.968128	−	0.250458i	$-0.0805811\pi$
$769$	−0.869254	−	6.04579i	−0.0313461	−	0.218017i	−0.999474	+	0.0324407i	$0.989672\pi$
$770$	−3.55538	+	0.724306i	−0.128127	+	0.0261022i
$771$	−13.7601	−	26.9421i	−0.495557	−	0.970295i
$772$	−6.11455	+	18.9542i	−0.220067	+	0.682176i
$773$	15.4107	−	23.9795i	0.554285	−	0.862484i	−0.445172	−	0.895445i	$-0.646857\pi$
$773$	15.4107	−	23.9795i	0.554285	−	0.862484i	0.999457	+	0.0329614i	$0.0104938\pi$
$774$	−8.99940	+	1.32111i	−0.323477	+	0.0474864i
$775$	3.15026	+	0.452938i	0.113161	+	0.0162700i
$776$	−3.11100	−	17.6453i	−0.111678	−	0.633429i
$777$	−12.2573	+	8.65824i	−0.439727	+	0.310613i
$778$	5.20923	+	9.84749i	0.186760	+	0.353050i
$779$	4.17681	+	1.22642i	0.149650	+	0.0439411i
$780$	19.1438	−	17.1782i	0.685459	−	0.615080i
$781$	2.80071			0.100217
$782$	9.87089	−	6.14345i	0.352982	−	0.219689i
$783$	−16.4050	+	2.16780i	−0.586266	+	0.0774707i
$784$	18.0844	−	4.28559i	0.645870	−	0.153057i
$785$	−4.63331	+	15.7796i	−0.165370	+	0.563199i
$786$	7.84142	+	13.3720i	0.279694	+	0.476963i
$787$	8.03359	+	12.5005i	0.286366	+	0.445595i	0.954398	−	0.298538i	$-0.0964991\pi$
$787$	8.03359	+	12.5005i	0.286366	+	0.445595i	−0.668031	+	0.744133i	$0.732863\pi$
$788$	1.35667	+	3.19153i	0.0483294	+	0.113694i
$789$	6.44216	+	0.639903i	0.229347	+	0.0227812i
$790$	2.00749	+	34.4709i	0.0714231	+	1.22642i
$791$	22.2943	+	14.3277i	0.792693	+	0.509433i
$792$	7.16149	+	3.47616i	0.254472	+	0.123520i
$793$	−15.8613	−	34.7315i	−0.563253	−	1.23335i
$794$	−24.8146	+	5.05525i	−0.880636	+	0.179404i
$795$	−39.9933	+	7.55031i	−1.41842	+	0.267782i
$796$	−29.7056	+	17.9984i	−1.05289	+	0.637938i
$797$	5.05725	+	17.2234i	0.179137	+	0.610085i	0.999281	+	0.0379270i	$0.0120754\pi$
$797$	5.05725	+	17.2234i	0.179137	+	0.610085i	−0.820143	+	0.572158i	$0.806106\pi$
$798$	−2.36897	+	6.99751i	−0.0838608	+	0.247709i
$799$	−14.4572	−	12.5273i	−0.511460	−	0.443183i
$800$	−5.52787	+	8.70178i	−0.195440	+	0.307655i
$801$	−15.0894	+	15.5860i	−0.533159	+	0.550706i
$802$	24.6762	+	13.9011i	0.871347	+	0.490865i
$803$	−2.87964	+	6.30553i	−0.101620	+	0.222517i
$804$	32.2241	+	14.0463i	1.13646	+	0.495376i
$805$	9.28576	−	9.26245i	0.327280	−	0.326459i
$806$	10.0225	+	2.31954i	0.353029	+	0.0817023i
$807$	−2.32582	+	5.74613i	−0.0818726	+	0.202273i
$808$	−22.1040	−	32.1083i	−0.777617	−	1.12956i
$809$	−27.0808	+	23.4657i	−0.952112	+	0.825009i	−0.984664	−	0.174461i	$-0.944182\pi$
$809$	−27.0808	+	23.4657i	−0.952112	+	0.825009i	0.0325525	+	0.999470i	$0.489636\pi$
$810$	−19.7014	+	11.2527i	−0.692237	+	0.395380i
$811$	−14.2910	−	12.3832i	−0.501826	−	0.434834i	0.366803	−	0.930299i	$-0.380452\pi$
$811$	−14.2910	−	12.3832i	−0.501826	−	0.434834i	−0.868628	+	0.495464i	$0.834998\pi$
$812$	−5.49844	+	8.07761i	−0.192957	+	0.283469i
$813$	−23.9177	+	8.17620i	−0.838831	+	0.286752i
$814$	5.36787	−	5.22769i	0.188144	−	0.183231i
$815$	−4.02634	−	28.0038i	−0.141036	−	0.980930i
$816$	−5.03204	+	10.7579i	−0.176157	+	0.376602i
$817$	1.75083	+	3.83379i	0.0612539	+	0.134127i
$818$	−15.4753	−	1.31278i	−0.541080	−	0.0459003i
$819$	−8.91418	+	16.9726i	−0.311487	+	0.593071i
$820$	7.78173	+	1.32983i	0.271750	+	0.0464398i
$821$	−36.0700	−	5.18608i	−1.25885	−	0.180995i	−0.519590	−	0.854416i	$-0.673915\pi$
$821$	−36.0700	−	5.18608i	−1.25885	−	0.180995i	−0.739260	+	0.673420i	$0.764824\pi$
$822$	−6.45962	−	8.10068i	−0.225305	−	0.282544i
$823$	26.0549	+	40.5422i	0.908216	+	1.41321i	0.910634	+	0.413214i	$0.135594\pi$
$823$	26.0549	+	40.5422i	0.908216	+	1.41321i	−0.00241829	+	0.999997i	$0.500770\pi$
$824$	1.19886	+	37.7893i	0.0417644	+	1.31645i
$825$	0.709107	−	2.87517i	0.0246879	−	0.100101i
$826$	−16.6407	+	21.6270i	−0.579003	+	0.752500i
$827$	19.9131			0.692448			0.346224	−	0.938152i	$-0.387464\pi$
$827$	19.9131			0.692448			0.346224	+	0.938152i	$0.387464\pi$
$828$	−28.5274	+	3.76656i	−0.991396	+	0.130897i
$829$	−30.6900			−1.06591			−0.532954	−	0.846144i	$-0.678918\pi$
$829$	−30.6900			−1.06591			−0.532954	+	0.846144i	$0.678918\pi$
$830$	10.1746	−	13.2234i	0.353165	−	0.458990i
$831$	−0.0191329	+	0.0775769i	−0.000663712	+	0.00269111i
$832$	−20.1816	+	26.5163i	−0.699672	+	0.919286i
$833$	−4.30614	−	6.70049i	−0.149199	−	0.232158i
$834$	24.2097	+	30.3602i	0.838313	+	1.05129i
$835$	20.9976	+	3.01900i	0.726653	+	0.104477i
$836$	0.621345	−	3.63590i	0.0214897	−	0.125750i
$837$	−8.21089	−	3.86369i	−0.283810	−	0.133549i
$838$	−21.6620	−	1.83761i	−0.748302	−	0.0634792i
$839$	−0.411375	−	0.900785i	−0.0142022	−	0.0310985i	0.902398	−	0.430904i	$-0.141805\pi$
$839$	−0.411375	−	0.900785i	−0.0142022	−	0.0310985i	−0.916600	+	0.399805i	$0.869078\pi$
$840$	−2.79407	+	13.1031i	−0.0964046	+	0.452099i
$841$	−2.68383	−	18.6665i	−0.0925460	−	0.643672i
$842$	−14.8017	+	14.4151i	−0.510099	+	0.496778i
$843$	19.8340	−	6.78018i	0.683118	−	0.233522i
$844$	−17.5987	−	11.9795i	−0.605773	−	0.412350i
$845$	−5.86044	−	5.07810i	−0.201605	−	0.174692i
$846$	19.7951	+	43.0079i	0.680569	+	1.47864i
$847$	11.7335	−	10.1671i	0.403167	−	0.349347i
$848$	49.0546	−	19.3367i	1.68454	−	0.664024i
$849$	15.9350	−	39.3688i	0.546888	−	1.35113i
$850$	4.30432	+	0.996157i	0.147637	+	0.0341679i
$851$	−5.79044	+	26.4581i	−0.198494	+	0.906972i
$852$	4.13227	−	9.47998i	0.141569	−	0.324779i
$853$	3.38187	−	7.40526i	0.115793	−	0.253551i	−0.842858	−	0.538136i	$-0.819129\pi$
$853$	3.38187	−	7.40526i	0.115793	−	0.253551i	0.958651	+	0.284585i	$0.0918558\pi$
$854$	17.3279	+	9.76149i	0.592948	+	0.334031i
$855$	7.55314	+	7.31247i	0.258312	+	0.250081i
$856$	−4.95660	+	44.4361i	−0.169413	+	1.51879i
$857$	−22.4624	−	19.4637i	−0.767300	−	0.664869i	0.180558	−	0.983564i	$-0.442210\pi$
$857$	−22.4624	−	19.4637i	−0.767300	−	0.664869i	−0.947857	+	0.318696i	$0.896755\pi$
$858$	3.06944	−	9.06657i	0.104789	−	0.309528i
$859$	9.96523	+	33.9385i	0.340009	+	1.15797i	0.935123	+	0.354324i	$0.115289\pi$
$859$	9.96523	+	33.9385i	0.340009	+	1.15797i	−0.595114	+	0.803642i	$0.702893\pi$
$860$	3.96078	+	6.53709i	0.135062	+	0.222913i
$861$	−5.78201	+	1.09158i	−0.197050	+	0.0372011i
$862$	−11.2419	+	2.29021i	−0.382900	+	0.0780049i
$863$	−10.7918	−	23.6307i	−0.367357	−	0.804399i	−0.999562	−	0.0295979i	$-0.990577\pi$
$863$	−10.7918	−	23.6307i	−0.367357	−	0.804399i	0.632205	−	0.774801i	$-0.282150\pi$
$864$	22.3326	−	19.1117i	0.759770	−	0.650192i
$865$	−25.4095	−	16.3297i	−0.863947	−	0.555225i
$866$	1.72423	+	29.6071i	0.0585917	+	1.00609i
$867$	−24.2358	−	2.40735i	−0.823089	−	0.0817580i
$868$	−4.93148	+	2.09629i	−0.167385	+	0.0711529i
$869$	6.94723	+	10.8101i	0.235669	+	0.366707i
$870$	7.03390	+	11.9949i	0.238472	+	0.406666i
$871$	11.9084	−	40.5563i	0.403501	−	1.37420i
$872$	−12.6585	−	25.5423i	−0.428671	−	0.864972i
$873$	18.9315	−	1.66241i	0.640733	−	0.0562642i
$874$	5.36255	+	12.2072i	0.181391	+	0.412916i
$875$	18.6579			0.630751
$876$	17.0945	+	19.0505i	0.577570	+	0.643657i
$877$	−43.6600	−	12.8197i	−1.47429	−	0.432892i	−0.556802	−	0.830646i	$-0.687972\pi$
$877$	−43.6600	−	12.8197i	−1.47429	−	0.432892i	−0.917492	+	0.397754i	$0.869790\pi$
$878$	−13.3399	−	25.2177i	−0.450201	−	0.851056i
$879$	−38.0220	+	26.8579i	−1.28245	+	0.905893i
$880$	0.353797	−	6.68002i	0.0119265	−	0.225184i
$881$	41.6594	+	5.98972i	1.40354	+	0.201799i	0.802135	−	0.597143i	$-0.203698\pi$
$881$	41.6594	+	5.98972i	1.40354	+	0.201799i	0.601408	+	0.798942i	$0.294607\pi$
$882$	2.86313	+	19.5036i	0.0964064	+	0.656719i
$883$	19.6281	−	30.5420i	0.660539	−	1.02782i	−0.335767	−	0.941945i	$-0.608995\pi$
$883$	19.6281	−	30.5420i	0.660539	−	1.02782i	0.996306	−	0.0858742i	$-0.0273683\pi$
$884$	13.5911	+	4.38445i	0.457119	+	0.147465i
$885$	17.6625	+	34.5829i	0.593717	+	1.16249i
$886$	−16.5431	+	3.37017i	−0.555775	+	0.113223i
$887$	−0.385151	−	2.67878i	−0.0129321	−	0.0899447i	0.982333	−	0.187140i	$-0.0599219\pi$
$887$	−0.385151	−	2.67878i	−0.0129321	−	0.0899447i	−0.995265	+	0.0971955i	$0.969013\pi$
$888$	−9.77499	−	25.8825i	−0.328027	−	0.868560i
$889$	−10.4527	+	3.06919i	−0.350572	+	0.102937i
$890$	16.9944	+	6.59595i	0.569653	+	0.221097i
$891$	−4.33256	+	7.24713i	−0.145146	+	0.242788i
$892$	−3.15367	−	26.9843i	−0.105593	−	0.903503i
$893$	16.5794	−	14.3661i	0.554808	−	0.480744i
$894$	−15.4263	+	30.4266i	−0.515934	+	1.01762i
$895$	35.0224	+	15.9942i	1.17067	+	0.534627i
$896$	0.367940	−	17.3533i	0.0122920	−	0.579734i
$897$	8.78583	+	33.4659i	0.293350	+	1.11740i
$898$	−17.3162	−	4.00752i	−0.577848	−	0.133733i
$899$	−2.31034	+	5.05894i	−0.0770542	+	0.168725i
$900$	−8.68576	−	6.64234i	−0.289525	−	0.221411i
$901$	−14.7980	−	17.0778i	−0.492993	−	0.568944i
$902$	2.76603	−	0.990197i	0.0920987	−	0.0329700i
$903$	−4.46468	−	3.53864i	−0.148575	−	0.117759i
$904$	−35.8914	+	33.1500i	−1.19373	+	1.10255i
$905$	4.98728	+	16.9851i	0.165783	+	0.564604i
$906$	−1.38257	+	1.46978i	−0.0459328	+	0.0488301i
$907$	−13.6924	+	1.96867i	−0.454649	+	0.0653686i	−0.365835	−	0.930680i	$-0.619217\pi$
$907$	−13.6924	+	1.96867i	−0.454649	+	0.0653686i	−0.0888136	+	0.996048i	$0.528308\pi$
$908$	1.17526	−	44.4111i	0.0390023	−	1.47383i
$909$	35.9628	−	20.3997i	1.19281	−	0.676615i
$910$	16.0521	+	1.36172i	0.532123	+	0.0451405i
$911$	4.55053	+	2.92445i	0.150766	+	0.0968912i	0.613849	−	0.789424i	$-0.289620\pi$
$911$	4.55053	+	2.92445i	0.150766	+	0.0968912i	−0.463083	+	0.886315i	$0.653257\pi$
$912$	−11.3902	−	7.46769i	−0.377167	−	0.247280i
$913$	0.883656	−	6.14596i	0.0292447	−	0.203402i
$914$	9.08787	+	12.4808i	0.300600	+	0.412827i
$915$	23.1164	−	16.3288i	0.764203	−	0.539815i
$916$	−6.84273	−	25.8115i	−0.226090	−	0.852838i
$917$	−2.73534	+	9.31571i	−0.0903289	+	0.307632i
$918$	−10.9040	−	6.30776i	−0.359886	−	0.208187i
$919$			20.3619i			0.671677i	0.941920	+	0.335839i	$0.109020\pi$
$919$			20.3619i			0.671677i	−0.941920	+	0.335839i	$0.890980\pi$
$920$	12.2292	+	20.8596i	0.403184	+	0.687720i
$921$	−16.1717	+	0.708674i	−0.532876	+	0.0233516i
$922$	−7.28135	+	9.46318i	−0.239798	+	0.311653i
$923$	−11.9312	−	3.50332i	−0.392721	−	0.115313i
$924$	1.48741	+	4.75886i	0.0489323	+	0.156555i
$925$	−8.65822	+	5.56430i	−0.284680	+	0.182953i
$926$	−28.6188	+	20.8388i	−0.940472	+	0.684805i
$927$	−40.0406	−	2.21297i	−1.31511	−	0.0726836i
$928$	−11.8686	−	13.5524i	−0.389604	−	0.444880i
$929$	26.5474	−	41.3086i	0.870993	−	1.35529i	−0.0630054	−	0.998013i	$-0.520069\pi$
$929$	26.5474	−	41.3086i	0.870993	−	1.35529i	0.933998	−	0.357278i	$-0.116295\pi$
$930$	−0.311295	+	7.61909i	−0.0102078	+	0.249840i
$931$	8.30861	−	3.79442i	0.272304	−	0.124357i
$932$	−4.09505	−	0.108368i	−0.134138	−	0.00354971i
$933$	−4.45807	+	0.841637i	−0.145951	+	0.0275540i
$934$	12.6857	−	12.3545i	0.415089	−	0.404250i
$935$	−2.75068	+	0.807672i	−0.0899568	+	0.0264137i
$936$	−26.1602	−	23.7667i	−0.855071	−	0.776840i
$937$	15.2140	−	17.5579i	0.497020	−	0.573592i	−0.450708	−	0.892672i	$-0.648828\pi$
$937$	15.2140	−	17.5579i	0.497020	−	0.573592i	0.947728	+	0.319080i	$0.103374\pi$
$938$	7.42054	+	20.7286i	0.242289	+	0.676814i
$939$	22.6906	−	21.4711i	0.740479	−	0.700684i
$940$	26.8396	−	29.3674i	0.875412	−	0.957860i
$941$	54.7072	+	24.9839i	1.78340	+	0.814453i	0.973776	+	0.227511i	$0.0730588\pi$
$941$	54.7072	+	24.9839i	1.78340	+	0.814453i	0.809629	+	0.586942i	$0.199669\pi$
$942$	22.2187	+	4.12659i	0.723923	+	0.134452i
$943$	−6.37482	+	8.49350i	−0.207593	+	0.276586i
$944$	−30.8882	−	39.7100i	−1.00532	−	1.29245i
$945$	−13.5882	−	4.15894i	−0.442023	−	0.135290i
$946$	2.47827	+	1.39611i	0.0805756	+	0.0453915i
$947$	4.13366	+	4.77050i	0.134326	+	0.155020i	0.818927	−	0.573897i	$-0.194569\pi$
$947$	4.13366	+	4.77050i	0.134326	+	0.155020i	−0.684601	+	0.728918i	$0.740024\pi$
$948$	46.8407	−	7.56568i	1.52131	−	0.245722i
$949$	20.1548	−	23.2599i	0.654252	−	0.755048i
$950$	−1.83324	+	4.72332i	−0.0594781	+	0.153245i
$951$	13.1453	−	4.49367i	0.426264	−	0.145717i
$952$	−7.06725	+	2.32096i	−0.229051	+	0.0752228i
$953$	−54.7950	+	7.87834i	−1.77499	+	0.255204i	−0.950510	−	0.310694i	$-0.899439\pi$
$953$	−54.7950	+	7.87834i	−1.77499	+	0.255204i	−0.824475	+	0.565898i	$0.808529\pi$
$954$	15.9151	+	53.6144i	0.515270	+	1.73583i
$955$	24.1009	−	11.0065i	0.779886	−	0.356162i
$956$	−8.36154	+	25.9195i	−0.270432	+	0.838297i
$957$	4.47160	+	2.60442i	0.144546	+	0.0841891i
$958$	−3.34542	−	57.4449i	−0.108086	−	1.85596i
$959$	0.923519	−	6.42322i	0.0298220	−	0.207417i
$960$	−22.0888	−	11.0535i	−0.712914	−	0.356750i
$961$	23.5131	−	15.1110i	0.758488	−	0.487451i
$962$	−29.4066	+	15.5558i	−0.948106	+	0.501539i
$963$	−46.4972	−	9.32924i	−1.49835	−	0.300631i
$964$	24.8933	−	20.4426i	0.801758	−	0.658413i
$965$			17.7510i			0.571423i
$966$	−13.9605	−	11.3980i	−0.449171	−	0.366725i
$967$		−	44.8077i		−	1.44092i	−0.693498	−	0.720459i	$-0.743931\pi$
$967$		−	44.8077i		−	1.44092i	0.693498	−	0.720459i	$-0.256069\pi$
$968$	12.7102	+	25.6465i	0.408520	+	0.824310i
$969$	−1.39770	+	5.66715i	−0.0449005	+	0.182055i
$970$	−7.46734	−	14.1162i	−0.239762	−	0.453244i
$971$	13.7659	−	8.84682i	0.441770	−	0.283908i	−0.300787	−	0.953691i	$-0.597249\pi$
$971$	13.7659	−	8.84682i	0.441770	−	0.283908i	0.742557	+	0.669783i	$0.233613\pi$
$972$	18.1380	+	25.3577i	0.581776	+	0.813349i
$973$	−3.46121	+	24.0733i	−0.110961	+	0.771754i
$974$	9.17959	−	0.534592i	0.294133	−	0.0171294i
$975$	−6.61729	+	11.3614i	−0.211923	+	0.363856i
$976$	−25.4433	+	26.4018i	−0.814419	+	0.845100i
$977$	−14.0924	+	6.43578i	−0.450856	+	0.205899i	−0.627884	−	0.778307i	$-0.716079\pi$
$977$	−14.0924	+	6.43578i	−0.450856	+	0.205899i	0.177028	+	0.984206i	$0.443352\pi$
$978$	−37.7177	+	9.42087i	−1.20608	+	0.301246i
$979$	6.71501	−	0.965473i	0.214613	−	0.0308566i
$980$	14.1672	−	8.58383i	0.452556	−	0.274201i
$981$	28.1551	−	11.0237i	0.898922	−	0.351958i
$982$	32.2368	+	12.5119i	1.02872	+	0.399271i
$983$	−0.444984	+	0.513539i	−0.0141928	+	0.0163794i	−0.762802	−	0.646633i	$-0.776177\pi$
$983$	−0.444984	+	0.513539i	−0.0141928	+	0.0163794i	0.748609	+	0.663012i	$0.230722\pi$
$984$	0.729434	−	10.8236i	0.0232535	−	0.345042i
$985$	2.02412	+	2.33596i	0.0644938	+	0.0744298i
$986$	−3.78930	+	6.72649i	−0.120676	+	0.214215i
$987$	−11.1257	+	27.4869i	−0.354134	+	0.874919i
$988$	−7.19499	+	14.7119i	−0.228903	+	0.468049i
$989$	−10.2566	+	0.720611i	−0.326140	+	0.0229141i
$990$	7.02591	+	0.988960i	0.223298	+	0.0314312i
$991$	30.5017	+	13.9296i	0.968917	+	0.442490i	0.836055	−	0.548645i	$-0.184856\pi$
$991$	30.5017	+	13.9296i	0.968917	+	0.442490i	0.132862	+	0.991135i	$0.457583\pi$
$992$	−1.45733	−	9.77100i	−0.0462702	−	0.310229i
$993$	21.2212	+	22.4264i	0.673434	+	0.711682i
$994$	6.09814	−	2.18304i	0.193421	−	0.0692419i
$995$	−20.2725	+	23.3957i	−0.642681	+	0.741694i
$996$	−19.4993	−	12.0590i	−0.617860	−	0.382104i
$997$	18.9143	−	5.55373i	0.599021	−	0.175888i	0.0318559	−	0.999492i	$-0.489858\pi$
$997$	18.9143	−	5.55373i	0.599021	−	0.175888i	0.567165	+	0.823604i	$0.308040\pi$
$998$	4.98613	+	5.11983i	0.157833	+	0.162065i
$999$	28.2490	−	7.94545i	0.893759	−	0.251383i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.167.36	yes	440
3.2	odd	2	inner	276.2.o.a.167.9	yes	440
4.3	odd	2	inner	276.2.o.a.167.42	yes	440
12.11	even	2	inner	276.2.o.a.167.3	yes	440
23.4	even	11	inner	276.2.o.a.119.3	✓	440
69.50	odd	22	inner	276.2.o.a.119.42	yes	440
92.27	odd	22	inner	276.2.o.a.119.9	yes	440
276.119	even	22	inner	276.2.o.a.119.36	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.119.3	✓	440	23.4	even	11	inner
276.2.o.a.119.9	yes	440	92.27	odd	22	inner
276.2.o.a.119.36	yes	440	276.119	even	22	inner
276.2.o.a.119.42	yes	440	69.50	odd	22	inner
276.2.o.a.167.3	yes	440	12.11	even	2	inner
276.2.o.a.167.9	yes	440	3.2	odd	2	inner
276.2.o.a.167.36	yes	440	1.1	even	1	trivial
276.2.o.a.167.42	yes	440	4.3	odd	2	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)

\(f(q)\)	\(=\)	\(q+(1.12083 + 0.862408i) q^{2} +(0.414750 - 1.68166i) q^{3} +(0.512503 + 1.93322i) q^{4} +(0.963734 + 1.49960i) q^{5} +(1.91514 - 1.52717i) q^{6} +(1.51856 + 0.218336i) q^{7} +(-1.09280 + 2.60879i) q^{8} +(-2.65596 - 1.39494i) q^{9} +O(q^{10})\)	\(q+(1.12083 + 0.862408i) q^{2} +(0.414750 - 1.68166i) q^{3} +(0.512503 + 1.93322i) q^{4} +(0.963734 + 1.49960i) q^{5} +(1.91514 - 1.52717i) q^{6} +(1.51856 + 0.218336i) q^{7} +(-1.09280 + 2.60879i) q^{8} +(-2.65596 - 1.39494i) q^{9} +(-0.213089 + 2.51192i) q^{10} +(0.389727 + 0.853382i) q^{11} +(3.46358 - 0.0600535i) q^{12} +(-0.592791 - 4.12295i) q^{13} +(1.51375 + 1.55434i) q^{14} +(2.92153 - 0.998715i) q^{15} +(-3.47468 + 1.98156i) q^{16} +(1.29554 + 1.12259i) q^{17} +(-1.77387 - 3.85401i) q^{18} +(-1.48571 + 1.28737i) q^{19} +(-2.40514 + 2.63166i) q^{20} +(0.996990 - 2.46315i) q^{21} +(-0.299148 + 1.29260i) q^{22} +(-1.67032 - 4.49556i) q^{23} +(3.93386 + 2.91971i) q^{24} +(0.757059 - 1.65773i) q^{25} +(2.89125 - 5.13234i) q^{26} +(-3.44737 + 3.88788i) q^{27} +(0.356175 + 3.04761i) q^{28} +(2.40675 + 2.08546i) q^{29} +(4.13582 + 1.40016i) q^{30} +(0.492015 + 1.67565i) q^{31} +(-5.60343 - 0.775606i) q^{32} +(1.59674 - 0.301448i) q^{33} +(0.483941 + 2.37551i) q^{34} +(1.13607 + 2.48765i) q^{35} +(1.33553 - 5.84948i) q^{36} +(-4.75096 - 3.05325i) q^{37} +(-2.77546 + 0.161634i) q^{38} +(-7.17927 - 0.713121i) q^{39} +(-4.96531 + 0.875421i) q^{40} +(-1.19717 - 1.86284i) q^{41} +(3.24169 - 1.90095i) q^{42} +(0.604010 - 2.05707i) q^{43} +(-1.45004 + 1.19079i) q^{44} +(-0.467797 - 5.32723i) q^{45} +(2.00486 - 6.47924i) q^{46} -11.1593 q^{47} +(1.89119 + 6.66509i) q^{48} +(-4.45810 - 1.30902i) q^{49} +(2.27817 - 1.20513i) q^{50} +(2.42514 - 1.71306i) q^{51} +(7.66677 - 3.25902i) q^{52} +(-13.0479 - 1.87600i) q^{53} +(-7.21685 + 1.38460i) q^{54} +(-0.904139 + 1.40687i) q^{55} +(-2.22907 + 3.72301i) q^{56} +(1.54873 + 3.03239i) q^{57} +(0.899029 + 4.41304i) q^{58} +(1.78992 + 12.4492i) q^{59} +(3.42803 + 5.13611i) q^{60} +(8.79525 - 2.58252i) q^{61} +(-0.893631 + 2.30243i) q^{62} +(-3.72868 - 2.69819i) q^{63} +(-5.61158 - 5.70177i) q^{64} +(5.61149 - 4.86238i) q^{65} +(2.04964 + 1.03917i) q^{66} +(9.23061 + 4.21548i) q^{67} +(-1.50624 + 3.07989i) q^{68} +(-8.25277 + 0.944386i) q^{69} +(-0.872031 + 3.76798i) q^{70} +(1.24015 - 2.71554i) q^{71} +(6.54153 - 5.40447i) q^{72} +(4.83868 + 5.58413i) q^{73} +(-2.69184 - 7.51943i) q^{74} +(-2.47375 - 1.96066i) q^{75} +(-3.25020 - 2.21241i) q^{76} +(0.405499 + 1.38100i) q^{77} +(-7.43171 - 6.99075i) q^{78} +(13.5576 - 1.94928i) q^{79} +(-6.32022 - 3.30093i) q^{80} +(5.10830 + 7.40981i) q^{81} +(0.264704 - 3.12037i) q^{82} +(-5.56778 - 3.57819i) q^{83} +(5.27277 + 0.665029i) q^{84} +(-0.434881 + 3.02466i) q^{85} +(2.45103 - 1.78472i) q^{86} +(4.50523 - 3.18239i) q^{87} +(-2.65219 + 0.0841406i) q^{88} +(2.03727 - 6.93831i) q^{89} +(4.06993 - 6.37434i) q^{90} -6.39038i q^{91} +(7.83485 - 5.53309i) q^{92} +(3.02194 - 0.132427i) q^{93} +(-12.5076 - 9.62385i) q^{94} +(-3.36237 - 0.987280i) q^{95} +(-3.62833 + 9.10139i) q^{96} +(-5.32915 + 3.42483i) q^{97} +(-3.86785 - 5.31188i) q^{98} +(0.155315 - 2.81020i) 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

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Representations

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Database

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