LMFDB - Embedded newform 360.2.br.e.77.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(77,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 10, 3]))

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

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

chi := DirichletCharacter("360.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.br (of order $12$, degree $4$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			77.14
Character	$\chi$	$=$	360.77
Dual form			360.2.br.e.173.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.11754 - 0.866661i) q^{2} +(-0.925695 - 1.46393i) q^{3} +(0.497797 + 1.93706i) q^{4} +(0.274171 - 2.21920i) q^{5} +(-0.234228 + 2.43827i) q^{6} +(0.362508 - 1.35290i) q^{7} +(1.12247 - 2.59616i) q^{8} +(-1.28618 + 2.71030i) q^{9} +O(q^{10})$	\(q+(-1.11754 - 0.866661i) q^{2} +(-0.925695 - 1.46393i) q^{3} +(0.497797 + 1.93706i) q^{4} +(0.274171 - 2.21920i) q^{5} +(-0.234228 + 2.43827i) q^{6} +(0.362508 - 1.35290i) q^{7} +(1.12247 - 2.59616i) q^{8} +(-1.28618 + 2.71030i) q^{9} +(-2.22969 + 2.24243i) q^{10} +(-1.98069 - 3.43065i) q^{11} +(2.37491 - 2.52187i) q^{12} +(2.82558 - 0.757112i) q^{13} +(-1.57762 + 1.19775i) q^{14} +(-3.50254 + 1.65293i) q^{15} +(-3.50440 + 1.92852i) q^{16} +(1.31735 - 1.31735i) q^{17} +(3.78627 - 1.91420i) q^{18} -2.06739 q^{19} +(4.43520 - 0.573623i) q^{20} +(-2.31612 + 0.721686i) q^{21} +(-0.759712 + 5.55047i) q^{22} +(-3.03544 + 0.813345i) q^{23} +(-4.83966 + 0.760047i) q^{24} +(-4.84966 - 1.21688i) q^{25} +(-3.81386 - 1.60272i) q^{26} +(5.15830 - 0.626043i) q^{27} +(2.80110 + 0.0287310i) q^{28} +(-1.85856 + 1.07304i) q^{29} +(5.34677 + 1.18830i) q^{30} +(-2.84205 + 4.92257i) q^{31} +(5.58768 + 0.881920i) q^{32} +(-3.18871 + 6.07532i) q^{33} +(-2.61390 + 0.330498i) q^{34} +(-2.90296 - 1.17540i) q^{35} +(-5.89027 - 1.14222i) q^{36} +(-7.93663 + 7.93663i) q^{37} +(2.31039 + 1.79173i) q^{38} +(-3.72398 - 3.43559i) q^{39} +(-5.45365 - 3.20276i) q^{40} +(3.68264 + 2.12617i) q^{41} +(3.21382 + 1.20078i) q^{42} +(2.94123 - 10.9768i) q^{43} +(5.65939 - 5.54447i) q^{44} +(5.66206 + 3.59737i) q^{45} +(4.09713 + 1.72176i) q^{46} +(-7.22530 - 1.93601i) q^{47} +(6.06723 + 3.34496i) q^{48} +(4.36325 + 2.51912i) q^{49} +(4.36507 + 5.56292i) q^{50} +(-3.14798 - 0.709044i) q^{51} +(2.87313 + 5.09643i) q^{52} +(4.33765 - 4.33765i) q^{53} +(-6.30718 - 3.77087i) q^{54} +(-8.15633 + 3.45494i) q^{55} +(-3.10545 - 2.45971i) q^{56} +(1.91377 + 3.02651i) q^{57} +(3.00698 + 0.411575i) q^{58} +(2.91329 + 1.68199i) q^{59} +(-4.94538 - 5.96181i) q^{60} +(-2.46738 + 1.42455i) q^{61} +(7.44231 - 3.03808i) q^{62} +(3.20052 + 2.72258i) q^{63} +(-5.48014 - 5.82821i) q^{64} +(-0.905487 - 6.47809i) q^{65} +(8.82876 - 4.02588i) q^{66} +(-1.23200 - 4.59790i) q^{67} +(3.20757 + 1.89602i) q^{68} +(4.00058 + 3.69077i) q^{69} +(2.22550 + 3.82944i) q^{70} -9.27042i q^{71} +(5.59271 + 6.38135i) q^{72} +(11.3570 - 11.3570i) q^{73} +(15.7479 - 1.99114i) q^{74} +(2.70788 + 8.22602i) q^{75} +(-1.02914 - 4.00465i) q^{76} +(-5.35934 + 1.43603i) q^{77} +(1.18421 + 7.06685i) q^{78} +(14.4576 - 8.34709i) q^{79} +(3.31897 + 8.30569i) q^{80} +(-5.69150 - 6.97186i) q^{81} +(-2.27283 - 5.56769i) q^{82} +(-14.5118 - 3.88841i) q^{83} +(-2.55091 - 4.12721i) q^{84} +(-2.56229 - 3.28465i) q^{85} +(-12.8001 + 9.71801i) q^{86} +(3.29132 + 1.72749i) q^{87} +(-11.1298 + 1.29140i) q^{88} +3.86335 q^{89} +(-3.20989 - 8.92729i) q^{90} -4.09719i q^{91} +(-3.08653 - 5.47496i) q^{92} +(9.83717 - 0.396244i) q^{93} +(6.39670 + 8.42546i) q^{94} +(-0.566818 + 4.58794i) q^{95} +(-3.88142 - 8.99636i) q^{96} +(2.60272 - 9.71349i) q^{97} +(-2.69289 - 6.59669i) q^{98} +(11.8456 - 0.955839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) $ 256 * q + 6 * q^2 - 8 * q^6	$ 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) $ 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.11754	−	0.866661i	−0.790221	−	0.612822i
$2$	−1.11754	−	0.866661i	−0.790221	−	0.612822i
$3$	−0.925695	−	1.46393i	−0.534450	−	0.845200i
$3$	−0.925695	−	1.46393i	−0.534450	−	0.845200i
$4$	0.497797	+	1.93706i	0.248898	+	0.968530i
$5$	0.274171	−	2.21920i	0.122613	−	0.992455i
$5$	0.274171	−	2.21920i	0.122613	−	0.992455i
$6$	−0.234228	+	2.43827i	−0.0956232	+	0.995418i
$7$	0.362508	−	1.35290i	0.137015	−	0.511348i	−0.862966	−	0.505262i	$-0.831396\pi$
$7$	0.362508	−	1.35290i	0.137015	−	0.511348i	0.999981	−	0.00608637i	$-0.00193736\pi$
$8$	1.12247	−	2.59616i	0.396851	−	0.917883i
$9$	−1.28618	+	2.71030i	−0.428726	+	0.903435i
$10$	−2.22969	+	2.24243i	−0.705089	+	0.709118i
$11$	−1.98069	−	3.43065i	−0.597199	−	1.03438i	−0.993232	−	0.116143i	$-0.962947\pi$
$11$	−1.98069	−	3.43065i	−0.597199	−	1.03438i	0.396033	−	0.918236i	$-0.370386\pi$
$12$	2.37491	−	2.52187i	0.685577	−	0.728000i
$13$	2.82558	−	0.757112i	0.783675	−	0.209985i	0.155271	−	0.987872i	$-0.450375\pi$
$13$	2.82558	−	0.757112i	0.783675	−	0.209985i	0.628404	+	0.777887i	$0.283708\pi$
$14$	−1.57762	+	1.19775i	−0.421638	+	0.320112i
$15$	−3.50254	+	1.65293i	−0.904353	+	0.426785i
$16$	−3.50440	+	1.92852i	−0.876099	+	0.482131i
$17$	1.31735	−	1.31735i	0.319505	−	0.319505i	−0.529072	−	0.848577i	$-0.677460\pi$
$17$	1.31735	−	1.31735i	0.319505	−	0.319505i	0.848577	+	0.529072i	$0.177460\pi$
$18$	3.78627	−	1.91420i	0.892433	−	0.451181i
$19$	−2.06739			−0.474292			−0.237146	−	0.971474i	$-0.576212\pi$
$19$	−2.06739			−0.474292			−0.237146	+	0.971474i	$0.576212\pi$
$20$	4.43520	−	0.573623i	0.991740	−	0.128266i
$21$	−2.31612	+	0.721686i	−0.505419	+	0.157485i
$22$	−0.759712	+	5.55047i	−0.161971	+	1.18337i
$23$	−3.03544	+	0.813345i	−0.632934	+	0.169594i	−0.561001	−	0.827815i	$-0.689584\pi$
$23$	−3.03544	+	0.813345i	−0.632934	+	0.169594i	−0.0719333	+	0.997409i	$0.522917\pi$
$24$	−4.83966	+	0.760047i	−0.987892	+	0.155144i
$25$	−4.84966	−	1.21688i	−0.969932	−	0.243376i
$26$	−3.81386	−	1.60272i	−0.747960	−	0.314319i
$27$	5.15830	−	0.626043i	0.992716	−	0.120482i
$28$	2.80110	+	0.0287310i	0.529359	+	0.00542965i
$29$	−1.85856	+	1.07304i	−0.345126	+	0.199259i	−0.662536	−	0.749030i	$-0.730520\pi$
$29$	−1.85856	+	1.07304i	−0.345126	+	0.199259i	0.317410	+	0.948288i	$0.397187\pi$
$30$	5.34677	+	1.18830i	0.976182	+	0.216953i
$31$	−2.84205	+	4.92257i	−0.510447	+	0.884120i	0.489480	+	0.872015i	$0.337187\pi$
$31$	−2.84205	+	4.92257i	−0.510447	+	0.884120i	−0.999927	+	0.0121055i	$0.996147\pi$
$32$	5.58768	+	0.881920i	0.987772	+	0.155903i
$33$	−3.18871	+	6.07532i	−0.555084	+	1.05758i
$34$	−2.61390	+	0.330498i	−0.448279	+	0.0566799i
$35$	−2.90296	−	1.17540i	−0.490690	−	0.198679i
$36$	−5.89027	−	1.14222i	−0.981712	−	0.190370i
$37$	−7.93663	+	7.93663i	−1.30477	+	1.30477i	−0.379638	+	0.925135i	$0.623952\pi$
$37$	−7.93663	+	7.93663i	−1.30477	+	1.30477i	−0.925135	+	0.379638i	$0.876048\pi$
$38$	2.31039	+	1.79173i	0.374795	+	0.290656i
$39$	−3.72398	−	3.43559i	−0.596315	−	0.550135i
$40$	−5.45365	−	3.20276i	−0.862298	−	0.506401i
$41$	3.68264	+	2.12617i	0.575132	+	0.332053i	0.759196	−	0.650862i	$-0.225592\pi$
$41$	3.68264	+	2.12617i	0.575132	+	0.332053i	−0.184065	+	0.982914i	$0.558926\pi$
$42$	3.21382	+	1.20078i	0.495903	+	0.185284i
$43$	2.94123	−	10.9768i	0.448534	−	1.67395i	−0.257900	−	0.966172i	$-0.583030\pi$
$43$	2.94123	−	10.9768i	0.448534	−	1.67395i	0.706433	−	0.707779i	$-0.250303\pi$
$44$	5.65939	−	5.54447i	0.853185	−	0.835860i
$45$	5.66206	+	3.59737i	0.844051	+	0.536264i
$46$	4.09713	+	1.72176i	0.604089	+	0.253859i
$47$	−7.22530	−	1.93601i	−1.05392	−	0.282396i	−0.310048	−	0.950721i	$-0.600345\pi$
$47$	−7.22530	−	1.93601i	−1.05392	−	0.282396i	−0.743870	+	0.668325i	$0.767012\pi$
$48$	6.06723	+	3.34496i	0.875729	+	0.482804i
$49$	4.36325	+	2.51912i	0.623322	+	0.359875i
$50$	4.36507	+	5.56292i	0.617315	+	0.786716i
$51$	−3.14798	−	0.709044i	−0.440805	−	0.0992861i
$52$	2.87313	+	5.09643i	0.398432	+	0.706747i
$53$	4.33765	−	4.33765i	0.595822	−	0.595822i	−0.343376	−	0.939198i	$-0.611571\pi$
$53$	4.33765	−	4.33765i	0.595822	−	0.595822i	0.939198	+	0.343376i	$0.111571\pi$
$54$	−6.30718	−	3.77087i	−0.858299	−	0.513150i
$55$	−8.15633	+	3.45494i	−1.09980	+	0.465865i
$56$	−3.10545	−	2.45971i	−0.414983	−	0.328693i
$57$	1.91377	+	3.02651i	0.253485	+	0.400871i
$58$	3.00698	+	0.411575i	0.394836	+	0.0540425i
$59$	2.91329	+	1.68199i	0.379278	+	0.218976i	0.677504	−	0.735519i	$-0.263062\pi$
$59$	2.91329	+	1.68199i	0.379278	+	0.218976i	−0.298226	+	0.954495i	$0.596395\pi$
$60$	−4.94538	−	5.96181i	−0.638446	−	0.769667i
$61$	−2.46738	+	1.42455i	−0.315916	+	0.182394i	−0.649571	−	0.760301i	$-0.725051\pi$
$61$	−2.46738	+	1.42455i	−0.315916	+	0.182394i	0.333655	+	0.942695i	$0.391718\pi$
$62$	7.44231	−	3.03808i	0.945174	−	0.385837i
$63$	3.20052	+	2.72258i	0.403228	+	0.343012i
$64$	−5.48014	−	5.82821i	−0.685018	−	0.728526i
$65$	−0.905487	−	6.47809i	−0.112312	−	0.803509i
$66$	8.82876	−	4.02588i	1.08675	−	0.495552i
$67$	−1.23200	−	4.59790i	−0.150513	−	0.561723i	−0.999448	−	0.0332254i	$-0.989422\pi$
$67$	−1.23200	−	4.59790i	−0.150513	−	0.561723i	0.848935	−	0.528498i	$-0.177245\pi$
$68$	3.20757	+	1.89602i	0.388975	+	0.229926i
$69$	4.00058	+	3.69077i	0.481613	+	0.444316i
$70$	2.22550	+	3.82944i	0.265998	+	0.457706i
$71$		−	9.27042i		−	1.10020i	−0.835100	−	0.550098i	$-0.814590\pi$
$71$		−	9.27042i		−	1.10020i	0.835100	−	0.550098i	$-0.185410\pi$
$72$	5.59271	+	6.38135i	0.659107	+	0.752049i
$73$	11.3570	−	11.3570i	1.32924	−	1.32924i	0.423205	−	0.906034i	$-0.360905\pi$
$73$	11.3570	−	11.3570i	1.32924	−	1.32924i	0.906034	−	0.423205i	$-0.139095\pi$
$74$	15.7479	−	1.99114i	1.83065	−	0.231465i
$75$	2.70788	+	8.22602i	0.312679	+	0.949859i
$76$	−1.02914	−	4.00465i	−0.118050	−	0.459365i
$77$	−5.35934	+	1.43603i	−0.610753	+	0.163651i
$78$	1.18421	+	7.06685i	0.134085	+	0.800163i
$79$	14.4576	−	8.34709i	1.62661	−	0.939121i	0.641509	−	0.767115i	$-0.278308\pi$
$79$	14.4576	−	8.34709i	1.62661	−	0.939121i	0.985096	−	0.172006i	$-0.0550248\pi$
$80$	3.31897	+	8.30569i	0.371072	+	0.928604i
$81$	−5.69150	−	6.97186i	−0.632389	−	0.774651i
$82$	−2.27283	−	5.56769i	−0.250992	−	0.614848i
$83$	−14.5118	−	3.88841i	−1.59287	−	0.426809i	−0.649992	−	0.759941i	$-0.725228\pi$
$83$	−14.5118	−	3.88841i	−1.59287	−	0.426809i	−0.942880	+	0.333133i	$0.891894\pi$
$84$	−2.55091	−	4.12721i	−0.278327	−	0.450316i
$85$	−2.56229	−	3.28465i	−0.277919	−	0.356270i
$86$	−12.8001	+	9.71801i	−1.38028	+	1.04792i
$87$	3.29132	+	1.72749i	0.352866	+	0.185207i
$88$	−11.1298	+	1.29140i	−1.18644	+	0.137664i
$89$	3.86335			0.409514			0.204757	−	0.978813i	$-0.434360\pi$
$89$	3.86335			0.409514			0.204757	+	0.978813i	$0.434360\pi$
$90$	−3.20989	−	8.92729i	−0.338352	−	0.941020i
$91$		−	4.09719i		−	0.429502i
$92$	−3.08653	−	5.47496i	−0.321793	−	0.570804i
$93$	9.83717	−	0.396244i	1.02007	−	0.0410885i
$94$	6.39670	+	8.42546i	0.659769	+	0.869019i
$95$	−0.566818	+	4.58794i	−0.0581543	+	0.470713i
$96$	−3.88142	−	8.99636i	−0.396146	−	0.918187i
$97$	2.60272	−	9.71349i	0.264266	−	0.986256i	−0.698431	−	0.715677i	$-0.746118\pi$
$97$	2.60272	−	9.71349i	0.264266	−	0.986256i	0.962698	−	0.270579i	$-0.0872151\pi$
$98$	−2.69289	−	6.59669i	−0.272023	−	0.666366i
$99$	11.8456	−	0.955839i	1.19053	−	0.0960654i
$100$	−0.0569800	−	9.99984i	−0.00569800	−	0.999984i
$101$	3.84696	+	6.66314i	0.382787	+	0.663007i	0.991460	−	0.130415i	$-0.0416309\pi$
$101$	3.84696	+	6.66314i	0.382787	+	0.663007i	−0.608672	+	0.793422i	$0.708298\pi$
$102$	2.90350	+	3.52062i	0.287489	+	0.348593i
$103$	2.06290	+	7.69884i	0.203263	+	0.758589i	0.989972	+	0.141265i	$0.0451168\pi$
$103$	2.06290	+	7.69884i	0.203263	+	0.758589i	−0.786709	+	0.617325i	$0.788217\pi$
$104$	1.20603	−	8.18550i	0.118261	−	0.802654i
$105$	0.966549	+	5.33779i	0.0943256	+	0.520915i
$106$	−8.60677	+	1.08823i	−0.835963	+	0.105698i
$107$	−1.77242	−	1.77242i	−0.171347	−	0.171347i	0.616224	−	0.787571i	$-0.288662\pi$
$107$	−1.77242	−	1.77242i	−0.171347	−	0.171347i	−0.787571	+	0.616224i	$0.788662\pi$
$108$	3.78047	+	9.68029i	0.363776	+	0.931487i
$109$	0.548826			0.0525680			0.0262840	−	0.999655i	$-0.491633\pi$
$109$	0.548826			0.0525680			0.0262840	+	0.999655i	$0.491633\pi$
$110$	12.1093	+	3.20773i	1.15458	+	0.305845i
$111$	18.9656	+	4.27176i	1.80013	+	0.405458i
$112$	1.33873	+	5.44020i	0.126498	+	0.514051i
$113$	12.7126	−	3.40633i	1.19590	−	0.320441i	0.394686	−	0.918816i	$-0.370853\pi$
$113$	12.7126	−	3.40633i	1.19590	−	0.320441i	0.801216	+	0.598375i	$0.204187\pi$
$114$	0.484241	−	5.04084i	0.0453533	−	0.472118i
$115$	0.972741	+	6.95924i	0.0907085	+	0.648953i
$116$	−3.00373	−	3.06599i	−0.278889	−	0.284670i
$117$	−1.58219	+	8.63196i	−0.146274	+	0.798025i
$118$	−1.79801	−	4.40453i	−0.165520	−	0.405469i
$119$	−1.30470	−	2.25980i	−0.119601	−	0.207155i
$120$	0.359798	+	10.9485i	0.0328449	+	0.999460i
$121$	−2.34623	+	4.06379i	−0.213294	+	0.369436i
$122$	3.99200	+	0.546398i	0.361419	+	0.0494686i
$123$	−0.296435	−	7.35931i	−0.0267286	−	0.663567i
$124$	−10.9501	−	3.05478i	−0.983346	−	0.274327i
$125$	−4.03013	+	10.4287i	−0.360466	+	0.932773i
$126$	−1.21716	−	5.81636i	−0.108433	−	0.518162i
$127$	10.8941	+	10.8941i	0.966699	+	0.966699i	0.999463	−	0.0327638i	$-0.0104309\pi$
$127$	10.8941	+	10.8941i	0.966699	+	0.966699i	−0.0327638	+	0.999463i	$0.510431\pi$
$128$	1.07320	+	11.2627i	0.0948585	+	0.995491i
$129$	−18.7920	+	5.85544i	−1.65454	+	0.515543i
$130$	−4.60239	+	8.02429i	−0.403656	+	0.703776i
$131$	−3.24235	+	5.61591i	−0.283285	+	0.490665i	−0.972192	−	0.234186i	$-0.924758\pi$
$131$	−3.24235	+	5.61591i	−0.283285	+	0.490665i	0.688907	+	0.724850i	$0.258091\pi$
$132$	−13.3556	−	3.15246i	−1.16245	−	0.274386i
$133$	−0.749446	+	2.79697i	−0.0649852	+	0.242528i
$134$	−2.60801	+	6.20608i	−0.225298	+	0.536124i
$135$	0.0249449	−	11.6189i	0.00214691	−	0.999998i
$136$	−1.94138	−	4.89875i	−0.166472	−	0.420064i
$137$	−13.2375	−	3.54697i	−1.13095	−	0.303038i	−0.355646	−	0.934621i	$-0.615739\pi$
$137$	−13.2375	−	3.54697i	−1.13095	−	0.303038i	−0.775309	+	0.631582i	$0.782406\pi$
$138$	−1.27216	−	7.59173i	−0.108294	−	0.646251i
$139$	5.63375	−	9.75794i	0.477849	−	0.827658i	−0.521829	−	0.853050i	$-0.674750\pi$
$139$	5.63375	−	9.75794i	0.477849	−	0.827658i	0.999678	+	0.0253921i	$0.00808343\pi$
$140$	0.831741	−	6.20832i	0.0702949	−	0.524699i
$141$	3.85424	+	12.3695i	0.324585	+	1.04170i
$142$	−8.03431	+	10.3601i	−0.674224	+	0.869398i
$143$	−8.19397	−	8.19397i	−0.685214	−	0.685214i
$144$	−0.719611	−	11.9784i	−0.0599676	−	0.998200i
$145$	1.87172	+	4.41871i	0.155438	+	0.366954i
$146$	−22.5346	+	2.84925i	−1.86498	+	0.235806i
$147$	−0.351221	−	8.71943i	−0.0289682	−	0.719167i
$148$	−19.3245	−	11.4229i	−1.58847	−	0.938956i
$149$	−6.89791	−	3.98251i	−0.565099	−	0.326260i	0.190090	−	0.981767i	$-0.439122\pi$
$149$	−6.89791	−	3.98251i	−0.565099	−	0.326260i	−0.755190	+	0.655506i	$0.772455\pi$
$150$	4.10300	−	11.5397i	0.335008	−	0.942215i
$151$	5.68023	+	9.83845i	0.462251	+	0.800642i	0.999073	−	0.0430539i	$-0.0137087\pi$
$151$	5.68023	+	9.83845i	0.462251	+	0.800642i	−0.536822	+	0.843695i	$0.680375\pi$
$152$	−2.32057	+	5.36728i	−0.188223	+	0.435344i
$153$	1.87608	+	5.26478i	0.151672	+	0.425632i
$154$	7.23383	+	3.03991i	0.582919	+	0.244963i
$155$	10.1449	+	7.65669i	0.814862	+	0.615000i
$156$	4.80116	−	8.92380i	0.384401	−	0.714476i
$157$	−0.644729	−	2.40616i	−0.0514550	−	0.192033i	0.935414	−	0.353553i	$-0.115027\pi$
$157$	−0.644729	−	2.40616i	−0.0514550	−	0.192033i	−0.986869	+	0.161521i	$0.948360\pi$
$158$	−23.3910	−	3.20161i	−1.86089	−	0.254706i
$159$	−10.3653	−	2.33467i	−0.822026	−	0.185151i
$160$	3.48913	−	12.1584i	0.275840	−	0.961204i
$161$			4.40150i			0.346887i
$162$	0.318240	+	12.7239i	0.0250033	+	0.999687i
$163$	8.93471	+	8.93471i	0.699821	+	0.699821i	0.964372	−	0.264551i	$-0.0852238\pi$
$163$	8.93471	+	8.93471i	0.699821	+	0.699821i	−0.264551	+	0.964372i	$0.585224\pi$
$164$	−2.28532	+	8.19190i	−0.178453	+	0.639680i
$165$	12.6081	+	8.74206i	0.981537	+	0.680568i
$166$	12.8475	+	16.9222i	0.997163	+	1.31342i
$167$	−1.63542	−	6.10349i	−0.126553	−	0.472302i	0.873337	−	0.487116i	$-0.161951\pi$
$167$	−1.63542	−	6.10349i	−0.126553	−	0.472302i	−0.999890	+	0.0148140i	$0.995284\pi$
$168$	−0.726151	+	6.82310i	−0.0560238	+	0.526414i
$169$	−3.84765	+	2.22144i	−0.295973	+	0.170880i
$170$	0.0167846	+	5.89136i	0.00128732	+	0.451847i
$171$	2.65903	−	5.60325i	0.203341	−	0.428491i
$172$	22.7269	+	0.233111i	1.73291	+	0.0177745i
$173$	−7.18387	−	1.92491i	−0.546179	−	0.146348i	−0.0248300	−	0.999692i	$-0.507904\pi$
$173$	−7.18387	−	1.92491i	−0.546179	−	0.146348i	−0.521349	+	0.853343i	$0.674571\pi$
$174$	−2.18103	−	4.78300i	−0.165343	−	0.362598i
$175$	−3.40436	+	6.11998i	−0.257345	+	0.462627i
$176$	13.5572	+	8.20255i	1.02191	+	0.618291i
$177$	−0.234506	−	5.82186i	−0.0176265	−	0.437598i
$178$	−4.31745	−	3.34822i	−0.323607	−	0.250959i
$179$			7.49932i			0.560525i	0.959923	+	0.280263i	$0.0904215\pi$
$179$			7.49932i			0.560525i	−0.959923	+	0.280263i	$0.909578\pi$
$180$	−4.14975	+	12.7585i	−0.309304	+	0.950963i
$181$		−	23.0395i		−	1.71251i	−0.516552	−	0.856256i	$-0.672785\pi$
$181$		−	23.0395i		−	1.71251i	0.516552	−	0.856256i	$-0.327215\pi$
$182$	−3.55087	+	4.57877i	−0.263208	+	0.339401i
$183$	4.36948	+	2.29338i	0.323001	+	0.169532i
$184$	−1.29560	+	8.79347i	−0.0955132	+	0.648263i
$185$	15.4369	+	19.7889i	1.13495	+	1.45491i
$186$	−11.3369	−	8.08267i	−0.831258	−	0.592650i
$187$	−7.12864	−	1.91011i	−0.521298	−	0.139681i
$188$	0.153441	−	14.9596i	0.0111908	−	1.09104i
$189$	1.02295	−	7.20561i	0.0744090	−	0.524131i
$190$	4.60963	−	4.63597i	0.334418	−	0.336329i
$191$	4.38752	−	2.53313i	0.317470	−	0.183291i	−0.332795	−	0.942999i	$-0.607992\pi$
$191$	4.38752	−	2.53313i	0.317470	−	0.183291i	0.650264	+	0.759708i	$0.274658\pi$
$192$	−3.45915	+	13.4177i	−0.249642	+	0.968338i
$193$	−5.80657	−	21.6704i	−0.417966	−	1.55987i	−0.778819	−	0.627249i	$-0.784181\pi$
$193$	−5.80657	−	21.6704i	−0.417966	−	1.55987i	0.360853	−	0.932623i	$-0.382486\pi$
$194$	−11.3270	+	8.59955i	−0.813228	+	0.617412i
$195$	−8.64526	+	7.32231i	−0.619100	+	0.524361i
$196$	−2.70768	+	9.70589i	−0.193406	+	0.693278i
$197$	−0.144636	−	0.144636i	−0.0103049	−	0.0103049i	0.701936	−	0.712240i	$-0.252319\pi$
$197$	−0.144636	−	0.144636i	−0.0103049	−	0.0103049i	−0.712240	+	0.701936i	$0.752319\pi$
$198$	−14.0663	−	9.19794i	−0.999652	−	0.653669i
$199$			1.78089i			0.126244i	0.998006	+	0.0631220i	$0.0201057\pi$
$199$			1.78089i			0.126244i	−0.998006	+	0.0631220i	$0.979894\pi$
$200$	−8.60279	+	11.2246i	−0.608309	+	0.793700i
$201$	−5.59055	+	6.05983i	−0.394327	+	0.427427i
$202$	1.47554	−	10.7803i	0.103819	−	0.758502i
$203$	0.777972	+	2.90343i	0.0546030	+	0.203781i
$204$	−0.193593	−	6.45078i	−0.0135542	−	0.451645i
$205$	5.72807	−	7.58957i	0.400066	−	0.530078i
$206$	4.36691	−	10.3916i	0.304257	−	0.724017i
$207$	1.69971	−	9.27308i	0.118138	−	0.644524i
$208$	−8.44184	+	8.10242i	−0.585337	+	0.561802i
$209$	4.09485	+	7.09248i	0.283247	+	0.490597i
$210$	3.54590	−	6.80287i	0.244690	−	0.469443i
$211$	6.03211	+	3.48264i	0.415267	+	0.239755i	0.693050	−	0.720889i	$-0.256266\pi$
$211$	6.03211	+	3.48264i	0.415267	+	0.239755i	−0.277783	+	0.960644i	$0.589600\pi$
$212$	10.5615	+	6.24301i	0.725370	+	0.428772i
$213$	−13.5712	+	8.58158i	−0.929886	+	0.588000i
$214$	0.444666	+	3.51685i	0.0303967	+	0.240407i
$215$	−23.5533	−	9.53670i	−1.60632	−	0.650398i
$216$	4.16470	−	14.0945i	0.283372	−	0.959010i
$217$	5.62948	+	5.62948i	0.382154	+	0.382154i
$218$	−0.613336	−	0.475646i	−0.0415403	−	0.0322148i
$219$	−27.1390	−	6.11274i	−1.83388	−	0.413060i
$220$	−10.7526	−	14.0794i	−0.724942	−	0.949235i
$221$	2.72490	−	4.71967i	0.183297	−	0.317479i
$222$	−17.4926	−	21.2106i	−1.17403	−	1.42356i
$223$	1.24958	+	0.334823i	0.0836778	+	0.0224214i	0.300415	−	0.953809i	$-0.402875\pi$
$223$	1.24958	+	0.334823i	0.0836778	+	0.0224214i	−0.216737	+	0.976230i	$0.569541\pi$
$224$	3.21873	−	7.23987i	0.215061	−	0.483734i
$225$	9.53563	−	11.5789i	0.635709	−	0.771929i
$226$	−17.1590	−	7.21081i	−1.14140	−	0.479656i
$227$	−3.77930	+	14.1046i	−0.250841	+	0.936152i	0.719516	+	0.694476i	$0.244364\pi$
$227$	−3.77930	+	14.1046i	−0.250841	+	0.936152i	−0.970357	+	0.241676i	$0.922303\pi$
$228$	−4.90986	+	5.21368i	−0.325164	+	0.345284i
$229$	6.35644	−	11.0097i	0.420046	−	0.727540i	−0.575898	−	0.817522i	$-0.695347\pi$
$229$	6.35644	−	11.0097i	0.420046	−	0.727540i	0.995943	+	0.0899814i	$0.0286808\pi$
$230$	4.94423	−	8.62028i	0.326013	−	0.568404i
$231$	7.06336	+	6.51637i	0.464735	+	0.428745i
$232$	0.699620	+	6.02958i	0.0459323	+	0.395861i
$233$	11.0198	+	11.0198i	0.721933	+	0.721933i	0.968999	−	0.247066i	$-0.0794665\pi$
$233$	11.0198	+	11.0198i	0.721933	+	0.721933i	−0.247066	+	0.968999i	$0.579466\pi$
$234$	9.24915	−	8.27535i	0.604636	−	0.540976i
$235$	−6.27736	+	15.5035i	−0.409490	+	1.01134i
$236$	−1.80788	+	6.48050i	−0.117683	+	0.421845i
$237$	−25.6029	−	13.4380i	−1.66308	−	0.872893i
$238$	−0.500429	+	3.65615i	−0.0324380	+	0.236993i
$239$	4.71202	−	8.16145i	0.304795	−	0.527921i	−0.672421	−	0.740169i	$-0.734745\pi$
$239$	4.71202	−	8.16145i	0.304795	−	0.527921i	0.977216	+	0.212249i	$0.0680787\pi$
$240$	9.08659	−	12.5473i	0.586537	−	0.809923i
$241$	−8.53851	−	14.7891i	−0.550014	−	0.952652i	−0.998273	−	0.0587480i	$-0.981289\pi$
$241$	−8.53851	−	14.7891i	−0.550014	−	0.952652i	0.448259	−	0.893904i	$-0.352044\pi$
$242$	6.14394	−	2.50807i	0.394947	−	0.161225i
$243$	−4.93772	+	14.7858i	−0.316755	+	0.948507i
$244$	−3.98768	−	4.07034i	−0.255285	−	0.260577i
$245$	6.78671	−	8.99224i	0.433587	−	0.574493i
$246$	−6.04675	+	8.48125i	−0.385527	+	0.540744i
$247$	−5.84157	+	1.56524i	−0.371690	+	0.0995941i
$248$	9.58971	+	12.9038i	0.608947	+	0.819395i
$249$	7.74110	+	24.8437i	0.490572	+	1.57440i
$250$	13.5420	−	8.16176i	0.856471	−	0.516195i
$251$	23.9116			1.50929			0.754643	−	0.656136i	$-0.227810\pi$
$251$	23.9116			1.50929			0.754643	+	0.656136i	$0.227810\pi$
$252$	−3.68058	+	7.55489i	−0.231855	+	0.475913i
$253$	8.80256	+	8.80256i	0.553412	+	0.553412i
$254$	−2.73312	−	21.6162i	−0.171491	−	1.35632i
$255$	−2.43659	+	6.79158i	−0.152585	+	0.425305i
$256$	8.56159	−	13.5166i	0.535099	−	0.844789i
$257$	−7.28307	−	27.1808i	−0.454305	−	1.69549i	−0.690122	−	0.723693i	$-0.742443\pi$
$257$	−7.28307	−	27.1808i	−0.454305	−	1.69549i	0.235817	−	0.971798i	$-0.424223\pi$
$258$	26.0755	+	9.74259i	1.62339	+	0.606547i
$259$	7.86037	+	13.6146i	0.488419	+	0.845967i
$260$	12.0977	−	4.97876i	0.750268	−	0.308769i
$261$	−0.517828	−	6.41738i	−0.0320527	−	0.397226i
$262$	8.49055	−	3.46600i	0.524548	−	0.214130i
$263$	−6.27296	+	23.4110i	−0.386807	+	1.44358i	0.448491	+	0.893787i	$0.351962\pi$
$263$	−6.27296	+	23.4110i	−0.386807	+	1.44358i	−0.835298	+	0.549797i	$0.814705\pi$
$264$	12.1933	+	15.0978i	0.750446	+	0.929203i
$265$	−8.43683	−	10.8153i	−0.518270	−	0.664381i
$266$	3.26156	−	2.47621i	0.199979	−	0.151826i
$267$	−3.57629	−	5.65567i	−0.218865	−	0.346122i
$268$	8.29312	−	4.67529i	0.506583	−	0.285589i
$269$			25.2891i			1.54190i	0.636895	+	0.770950i	$0.280218\pi$
$269$			25.2891i			1.54190i	−0.636895	+	0.770950i	$0.719782\pi$
$270$	−10.0975	+	12.9630i	−0.614517	+	0.788903i
$271$	−12.8895			−0.782981			−0.391490	−	0.920182i	$-0.628040\pi$
$271$	−12.8895			−0.782981			−0.391490	+	0.920182i	$0.628040\pi$
$272$	−2.07598	+	7.15708i	−0.125875	+	0.433961i
$273$	−5.99799	+	3.79274i	−0.363015	+	0.229547i
$274$	11.7194	+	15.4363i	0.707995	+	0.932541i
$275$	5.43097	+	19.0477i	0.327500	+	1.14862i
$276$	−5.15776	+	9.58660i	−0.310461	+	0.577046i
$277$	13.3573	+	3.57907i	0.802560	+	0.215045i	0.636708	−	0.771105i	$-0.280296\pi$
$277$	13.3573	+	3.57907i	0.802560	+	0.215045i	0.165852	+	0.986151i	$0.446963\pi$
$278$	−14.7528	+	6.02235i	−0.884813	+	0.361197i
$279$	−9.68629	−	14.0341i	−0.579903	−	0.840201i
$280$	−6.31001	+	6.21721i	−0.377095	+	0.371550i
$281$	3.68587	−	2.12804i	0.219880	−	0.126948i	−0.386015	−	0.922493i	$-0.626149\pi$
$281$	3.68587	−	2.12804i	0.219880	−	0.126948i	0.605895	+	0.795545i	$0.292815\pi$
$282$	6.41288	−	17.1637i	0.381881	−	1.02208i
$283$	18.3652	−	4.92094i	1.09170	−	0.292519i	0.332318	−	0.943167i	$-0.392169\pi$
$283$	18.3652	−	4.92094i	1.09170	−	0.292519i	0.759379	+	0.650648i	$0.225503\pi$
$284$	17.9573	−	4.61478i	1.06557	−	0.273837i
$285$	7.24112	−	3.41725i	0.428927	−	0.202421i
$286$	2.05570	+	16.2585i	0.121556	+	0.961385i
$287$	4.21149	−	4.21149i	0.248596	−	0.248596i
$288$	−9.57702	+	14.0100i	−0.564331	+	0.825548i
$289$			13.5292i			0.795833i
$290$	1.73779	−	6.56024i	0.102047	−	0.385230i
$291$	−16.6292	+	5.18153i	−0.974821	+	0.303747i
$292$	27.6527	+	16.3457i	1.61825	+	0.956562i
$293$	−2.08189	−	7.76971i	−0.121625	−	0.453912i	0.878072	−	0.478529i	$-0.158830\pi$
$293$	−2.08189	−	7.76971i	−0.121625	−	0.453912i	−0.999697	+	0.0246175i	$0.992163\pi$
$294$	−7.16429	+	10.0487i	−0.417830	+	0.586053i
$295$	4.53140	−	6.00401i	0.263828	−	0.349567i
$296$	11.6962	+	29.5134i	0.679828	+	1.71543i
$297$	−12.3647	−	16.4563i	−0.717473	−	0.954893i
$298$	4.25721	+	10.4288i	0.246614	+	0.604123i
$299$	−7.96110	+	4.59634i	−0.460402	+	0.265813i
$300$	−14.5863	+	9.34022i	−0.842141	+	0.539258i
$301$	−13.7843	−	7.95839i	−0.794516	−	0.458714i
$302$	2.17871	−	15.9177i	0.125371	−	0.915961i
$303$	6.19324	−	11.7997i	0.355793	−	0.677876i
$304$	7.24495	−	3.98701i	0.415526	−	0.228671i
$305$	2.48486	+	5.86618i	0.142283	+	0.335896i
$306$	2.46618	−	7.50953i	0.140982	−	0.429291i
$307$	−4.70909	+	4.70909i	−0.268762	+	0.268762i	−0.828601	−	0.559839i	$-0.810863\pi$
$307$	−4.70909	+	4.70909i	−0.268762	+	0.268762i	0.559839	+	0.828601i	$0.310863\pi$
$308$	−5.44954	−	9.66650i	−0.310516	−	0.550800i
$309$	9.36094	−	10.1467i	0.532525	−	0.577226i
$310$	−4.70164	−	17.3489i	−0.267035	−	0.985351i
$311$	8.80269	+	5.08224i	0.499155	+	0.288187i	0.728364	−	0.685190i	$-0.240281\pi$
$311$	8.80269	+	5.08224i	0.499155	+	0.288187i	−0.229210	+	0.973377i	$0.573614\pi$
$312$	−13.0994	+	5.81174i	−0.741608	+	0.329025i
$313$	13.3079	+	3.56583i	0.752205	+	0.201553i	0.614496	−	0.788920i	$-0.289359\pi$
$313$	13.3079	+	3.56583i	0.752205	+	0.201553i	0.137709	+	0.990473i	$0.456026\pi$
$314$	−1.36482	+	3.24775i	−0.0770210	+	0.183281i
$315$	6.91942	−	6.35613i	0.389865	−	0.358127i
$316$	23.3657	+	23.8500i	1.31443	+	1.34167i
$317$	8.02391	−	29.9456i	0.450668	−	1.68191i	−0.249854	−	0.968284i	$-0.580383\pi$
$317$	8.02391	−	29.9456i	0.450668	−	1.68191i	0.700522	−	0.713631i	$-0.252951\pi$
$318$	9.56034	+	11.5923i	0.536117	+	0.650066i
$319$	7.36245	+	4.25071i	0.412218	+	0.237994i
$320$	−14.4364	+	10.5636i	−0.807021	+	0.590522i
$321$	−0.953978	+	4.23542i	−0.0532459	+	0.236398i
$322$	3.81461	−	4.91885i	0.212580	−	0.274117i
$323$	−2.72348	+	2.72348i	−0.151539	+	0.151539i
$324$	10.6717	−	14.4953i	0.592872	−	0.805296i
$325$	−14.6244	+	0.233348i	−0.811217	+	0.0129438i
$326$	−2.24154	−	17.7283i	−0.124147	−	0.981878i
$327$	−0.508046	−	0.803442i	−0.0280950	−	0.0444305i
$328$	9.65353	−	7.17419i	0.533027	−	0.396128i
$329$	−5.23846	+	9.07328i	−0.288806	+	0.500226i
$330$	−6.51363	−	20.6965i	−0.358564	−	1.13931i
$331$	27.3462	−	15.7884i	1.50309	−	0.867807i	0.503091	−	0.864233i	$-0.332196\pi$
$331$	27.3462	−	15.7884i	1.50309	−	0.867807i	0.999994	−	0.00357340i	$-0.00113745\pi$
$332$	0.308181	−	30.0458i	0.0169136	−	1.64898i
$333$	−11.3028	−	31.7186i	−0.619388	−	1.73817i
$334$	−3.46200	+	8.23825i	−0.189432	+	0.450777i
$335$	−10.5414	+	1.47345i	−0.575940	+	0.0805030i
$336$	6.72482	−	6.99577i	0.366869	−	0.381651i
$337$	7.73245	−	2.07190i	0.421214	−	0.112864i	−0.0419853	−	0.999118i	$-0.513368\pi$
$337$	7.73245	−	2.07190i	0.421214	−	0.112864i	0.463199	+	0.886254i	$0.346702\pi$
$338$	6.22514	+	0.852056i	0.338603	+	0.0463457i
$339$	−16.7546	−	15.4571i	−0.909987	−	0.839517i
$340$	5.08706	−	6.59838i	0.275884	−	0.357848i
$341$	22.5168			1.21935
$342$	−7.82770	+	3.95739i	−0.423273	+	0.213991i
$343$	11.9226	−	11.9226i	0.643759	−	0.643759i
$344$	−25.1962	−	19.9570i	−1.35849	−	1.07601i
$345$	9.28738	−	7.86616i	0.500016	−	0.423500i
$346$	6.36002	+	8.37714i	0.341917	+	0.450358i
$347$	8.87313	−	2.37755i	0.476335	−	0.127633i	−0.0126608	−	0.999920i	$-0.504030\pi$
$347$	8.87313	−	2.37755i	0.476335	−	0.127633i	0.488995	+	0.872286i	$0.337363\pi$
$348$	−1.70785	+	7.23541i	−0.0915503	+	0.387859i
$349$	12.9698	+	22.4644i	0.694260	+	1.20249i	0.970429	+	0.241385i	$0.0776016\pi$
$349$	12.9698	+	22.4644i	0.694260	+	1.20249i	−0.276169	+	0.961109i	$0.589065\pi$
$350$	9.10846	−	3.88890i	0.486867	−	0.207871i
$351$	14.1012	−	5.67434i	0.752667	−	0.302874i
$352$	−8.04189	−	20.9162i	−0.428634	−	1.11484i
$353$	1.08646	−	4.05471i	0.0578262	−	0.215810i	−0.930967	−	0.365104i	$-0.881033\pi$
$353$	1.08646	−	4.05471i	0.0578262	−	0.215810i	0.988793	+	0.149294i	$0.0477000\pi$
$354$	−4.78351	+	6.70940i	−0.254241	+	0.356601i
$355$	−20.5729	−	2.54168i	−1.09189	−	0.134898i
$356$	1.92316	+	7.48354i	0.101927	+	0.396627i
$357$	−2.10044	+	4.00187i	−0.111167	+	0.211801i
$358$	6.49937	−	8.38079i	0.343502	−	0.442939i
$359$	−1.04667			−0.0552413			−0.0276206	−	0.999618i	$-0.508793\pi$
$359$	−1.04667			−0.0552413			−0.0276206	+	0.999618i	$0.508793\pi$
$360$	15.6948	−	10.6617i	0.827190	−	0.561922i
$361$	−14.7259			−0.775048
$362$	−19.9674	+	25.7476i	−1.04946	+	1.35326i
$363$	8.12100	−	0.327116i	0.426242	−	0.0171691i
$364$	7.93649	−	2.03957i	0.415985	−	0.106902i
$365$	−22.0897	−	28.3172i	−1.15623	−	1.48219i
$366$	−2.89549	−	6.34981i	−0.151350	−	0.331910i
$367$	−1.07130	+	3.99813i	−0.0559213	+	0.208701i	−0.988233	−	0.152954i	$-0.951121\pi$
$367$	−1.07130	+	3.99813i	−0.0559213	+	0.208701i	0.932312	+	0.361655i	$0.117788\pi$
$368$	9.06885	−	8.70421i	0.472746	−	0.453738i
$369$	−10.4991	+	7.24644i	−0.546562	+	0.377235i
$370$	−0.101122	−	35.4935i	−0.00525707	−	1.84522i
$371$	−4.29597	−	7.44084i	−0.223036	−	0.386309i
$372$	5.66446	+	18.8579i	0.293689	+	0.977738i
$373$	−31.4295	+	8.42151i	−1.62736	+	0.436049i	−0.953151	−	0.302494i	$-0.902181\pi$
$373$	−31.4295	+	8.42151i	−1.62736	+	0.436049i	−0.674207	+	0.738543i	$0.735514\pi$
$374$	6.31113	+	8.31274i	0.326341	+	0.429842i
$375$	18.9976	−	3.75399i	0.981030	−	0.193855i
$376$	−13.1364	+	16.5849i	−0.677456	+	0.855303i
$377$	−4.43910	+	4.43910i	−0.228625	+	0.228625i
$378$	−7.38802	+	7.16601i	−0.379999	+	0.368580i
$379$	−15.2502			−0.783348			−0.391674	−	0.920104i	$-0.628104\pi$
$379$	−15.2502			−0.783348			−0.391674	+	0.920104i	$0.628104\pi$
$380$	−9.16927	+	1.18590i	−0.470374	+	0.0608355i
$381$	5.86360	−	26.0329i	0.300401	−	1.33371i
$382$	−7.09860	−	0.971609i	−0.363196	−	0.0497118i
$383$	−30.8755	+	8.27307i	−1.57766	+	0.422734i	−0.938202	−	0.346088i	$-0.887510\pi$
$383$	−30.8755	+	8.27307i	−1.57766	+	0.422734i	−0.639463	+	0.768822i	$0.720843\pi$
$384$	15.4943	−	11.9969i	0.790692	−	0.612215i
$385$	1.71746	+	12.2871i	0.0875297	+	0.626211i
$386$	−12.2918	+	29.2499i	−0.625638	+	1.48878i
$387$	25.9676	+	22.0898i	1.32001	+	1.12289i
$388$	20.1112	+	0.206282i	1.02099	+	0.0104724i
$389$	20.0659	−	11.5850i	1.01738	−	0.587385i	0.104037	−	0.994573i	$-0.466824\pi$
$389$	20.0659	−	11.5850i	1.01738	−	0.587385i	0.913344	+	0.407188i	$0.133491\pi$
$390$	16.0074	−	0.690467i	0.810566	−	0.0349631i
$391$	−2.92729	+	5.07022i	−0.148039	+	0.256412i
$392$	11.4377	−	8.50009i	0.577689	−	0.429319i
$393$	11.2227	−	0.452054i	0.566112	−	0.0228031i
$394$	0.0362862	+	0.286986i	0.00182807	+	0.0144582i
$395$	−14.5600	−	34.3727i	−0.732592	−	1.72948i
$396$	7.74822	+	22.4698i	0.389363	+	1.12915i
$397$	−1.89719	+	1.89719i	−0.0952172	+	0.0952172i	−0.753111	−	0.657894i	$-0.771448\pi$
$397$	−1.89719	+	1.89719i	−0.0952172	+	0.0952172i	0.657894	+	0.753111i	$0.271448\pi$
$398$	1.54343	−	1.99022i	0.0773651	−	0.0997606i
$399$	4.78832	−	1.49201i	0.239716	−	0.0746937i
$400$	19.3419	−	5.08826i	0.967096	−	0.254413i
$401$	6.77526	+	3.91170i	0.338340	+	0.195341i	0.659538	−	0.751671i	$-0.270752\pi$
$401$	6.77526	+	3.91170i	0.338340	+	0.195341i	−0.321197	+	0.947012i	$0.604085\pi$
$402$	11.4995	−	1.92700i	0.573542	−	0.0961098i
$403$	−4.30350	+	16.0609i	−0.214372	+	0.800049i
$404$	−10.9919	+	10.7687i	−0.546867	+	0.535762i
$405$	−17.0324	+	10.7191i	−0.846345	+	0.532635i
$406$	1.64688	−	3.91894i	0.0817331	−	0.194494i
$407$	42.9477	+	11.5078i	2.12884	+	0.570421i
$408$	−5.37429	+	7.37680i	−0.266067	+	0.365206i
$409$	−30.1115	−	17.3849i	−1.48892	−	0.859627i	−0.488997	−	0.872285i	$-0.662637\pi$
$409$	−30.1115	−	17.3849i	−1.48892	−	0.859627i	−0.999920	+	0.0126586i	$0.995971\pi$
$410$	−12.9789	+	3.51736i	−0.640984	+	0.173710i
$411$	7.06136	+	22.6622i	0.348311	+	1.11784i
$412$	−13.8862	+	7.82841i	−0.684124	+	0.385678i
$413$	3.33165	−	3.33165i	0.163940	−	0.163940i
$414$	−9.93612	+	8.88998i	−0.488333	+	0.436919i
$415$	−12.6078	+	31.1383i	−0.618895	+	1.52852i
$416$	16.4562	−	1.73857i	0.806830	−	0.0852403i
$417$	−19.5001	+	0.785468i	−0.954923	+	0.0384645i
$418$	1.57062	−	11.4750i	0.0768215	−	0.561260i
$419$	7.44813	+	4.30018i	0.363865	+	0.210078i	0.670775	−	0.741661i	$-0.265962\pi$
$419$	7.44813	+	4.30018i	0.363865	+	0.210078i	−0.306910	+	0.951739i	$0.599295\pi$
$420$	−9.85848	+	4.52940i	−0.481044	+	0.221012i
$421$	−12.3451	+	7.12747i	−0.601665	+	0.347372i	−0.769696	−	0.638410i	$-0.779592\pi$
$421$	−12.3451	+	7.12747i	−0.601665	+	0.347372i	0.168031	+	0.985782i	$0.446259\pi$
$422$	−3.72286	−	9.11979i	−0.181226	−	0.443944i
$423$	14.5402	−	17.0927i	0.706968	−	0.831075i
$424$	−6.39239	−	16.1301i	−0.310442	−	0.783347i
$425$	−7.99178	+	4.78566i	−0.387658	+	0.232139i
$426$	22.6037	+	2.17139i	1.09515	+	0.105204i
$427$	1.03282	+	3.85453i	0.0499816	+	0.186534i
$428$	2.55098	−	4.31559i	0.123306	−	0.208602i
$429$	−4.41027	+	19.5805i	−0.212930	+	0.945356i
$430$	18.0567	+	31.0704i	0.870773	+	1.49835i
$431$			2.21175i			0.106536i	0.998580	+	0.0532681i	$0.0169638\pi$
$431$			2.21175i			0.106536i	−0.998580	+	0.0532681i	$0.983036\pi$
$432$	−16.8694	+	12.1418i	−0.811629	+	0.584173i
$433$	−12.7158	+	12.7158i	−0.611084	+	0.611084i	−0.943228	−	0.332145i	$-0.892228\pi$
$433$	−12.7158	+	12.7158i	−0.611084	+	0.611084i	0.332145	+	0.943228i	$0.392228\pi$
$434$	−1.41232	−	11.1700i	−0.0677938	−	0.536179i
$435$	4.73603	−	6.83045i	0.227075	−	0.327495i
$436$	0.273204	+	1.06311i	0.0130841	+	0.0509137i
$437$	6.27545	−	1.68150i	0.300195	−	0.0804371i
$438$	25.0313	+	30.3516i	1.19604	+	1.45025i
$439$	−10.7793	+	6.22342i	−0.514467	+	0.297028i	−0.734668	−	0.678427i	$-0.762662\pi$
$439$	−10.7793	+	6.22342i	−0.514467	+	0.297028i	0.220201	+	0.975455i	$0.429329\pi$
$440$	−0.185589	+	25.0532i	−0.00884762	+	1.19437i
$441$	−12.4395	+	8.58570i	−0.592358	+	0.408843i
$442$	−7.13555	+	2.91286i	−0.339403	+	0.138551i
$443$	−12.0072	−	3.21732i	−0.570479	−	0.152859i	−0.0379625	−	0.999279i	$-0.512087\pi$
$443$	−12.0072	−	3.21732i	−0.570479	−	0.152859i	−0.532516	+	0.846420i	$0.678753\pi$
$444$	1.16634	+	38.8639i	0.0553519	+	1.84440i
$445$	1.05922	−	8.57353i	0.0502118	−	0.406424i
$446$	−1.10627	−	1.45714i	−0.0523836	−	0.0689975i
$447$	0.555249	+	13.7847i	0.0262624	+	0.651992i
$448$	−9.87158	+	5.30131i	−0.466388	+	0.250463i
$449$	18.9764			0.895551			0.447776	−	0.894146i	$-0.352216\pi$
$449$	18.9764			0.895551			0.447776	+	0.894146i	$0.352216\pi$
$450$	−20.6915	+	4.67577i	−0.975406	+	0.220418i
$451$		−	16.8451i		−	0.793206i
$452$	12.9266	+	22.9294i	0.608015	+	1.07851i
$453$	9.14463	−	17.4229i	0.429652	−	0.818597i
$454$	16.4474	−	12.4870i	0.771915	−	0.586046i
$455$	−9.09246	−	1.12333i	−0.426261	−	0.0526625i
$456$	10.0055	−	1.57131i	0.468549	−	0.0735835i
$457$	3.41263	−	12.7361i	0.159636	−	0.595770i	−0.839027	−	0.544089i	$-0.816875\pi$
$457$	3.41263	−	12.7361i	0.159636	−	0.595770i	0.998664	−	0.0516813i	$-0.0164580\pi$
$458$	−16.6452	+	6.79489i	−0.777781	+	0.317504i
$459$	5.97059	−	7.62003i	0.278683	−	0.355672i
$460$	−12.9962	+	5.34855i	−0.605953	+	0.249377i
$461$	14.8666	+	25.7497i	0.692406	+	1.19928i	0.971047	+	0.238888i	$0.0767828\pi$
$461$	14.8666	+	25.7497i	0.692406	+	1.19928i	−0.278641	+	0.960395i	$0.589884\pi$
$462$	−2.24612	−	13.4038i	−0.104499	−	0.623603i
$463$	−6.78888	−	25.3364i	−0.315506	−	1.17748i	−0.923518	−	0.383556i	$-0.874699\pi$
$463$	−6.78888	−	25.3364i	−0.315506	−	1.17748i	0.608012	−	0.793928i	$-0.291967\pi$
$464$	4.44375	−	7.34464i	0.206296	−	0.340966i
$465$	1.81772	−	21.9392i	0.0842950	−	1.01741i
$466$	−2.76465	−	21.8656i	−0.128070	−	1.01290i
$467$	−15.9845	−	15.9845i	−0.739674	−	0.739674i	0.232841	−	0.972515i	$-0.425198\pi$
$467$	−15.9845	−	15.9845i	−0.739674	−	0.739674i	−0.972515	+	0.232841i	$0.925198\pi$
$468$	−17.5082	+	1.23216i	−0.809318	+	0.0569567i
$469$	−6.66712			−0.307859
$470$	20.4515	−	11.8855i	0.943359	−	0.548238i
$471$	−2.92563	+	3.17121i	−0.134806	+	0.146122i
$472$	7.63678	−	5.67540i	0.351511	−	0.261232i
$473$	−43.4833	+	11.6513i	−1.99936	+	0.535728i
$474$	16.9660	+	37.2065i	0.779276	+	1.70895i
$475$	10.0261	+	2.51576i	0.460031	+	0.115431i
$476$	3.72789	−	3.65219i	0.170868	−	0.167398i
$477$	6.17736	+	17.3353i	0.282842	+	0.793730i
$478$	−12.3391	+	5.03704i	−0.564377	+	0.230389i
$479$	0.365317	+	0.632748i	0.0166918	+	0.0289110i	0.874251	−	0.485475i	$-0.161353\pi$
$479$	0.365317	+	0.632748i	0.0166918	+	0.0289110i	−0.857559	+	0.514386i	$0.828020\pi$
$480$	−21.0289	+	6.14710i	−0.959832	+	0.280575i
$481$	−16.4167	+	28.4345i	−0.748535	+	1.29650i
$482$	−3.27503	+	23.9275i	−0.149174	+	1.08987i
$483$	6.44348	−	4.07444i	0.293188	−	0.185394i
$484$	−9.03975	−	2.52185i	−0.410898	−	0.114629i
$485$	−20.8426	−	8.43911i	−0.946412	−	0.383200i
$486$	18.3324	−	12.2444i	0.831573	−	0.555416i
$487$	14.5262	+	14.5262i	0.658243	+	0.658243i	0.954964	−	0.296721i	$-0.0958933\pi$
$487$	14.5262	+	14.5262i	0.658243	+	0.658243i	−0.296721	+	0.954964i	$0.595893\pi$
$488$	0.928800	+	8.00474i	0.0420448	+	0.362358i
$489$	4.80897	−	21.3506i	0.217469	−	0.965508i
$490$	−15.3777	+	4.16742i	−0.694692	+	0.188265i
$491$	1.56899	−	2.71756i	0.0708073	−	0.122642i	−0.828448	−	0.560066i	$-0.810776\pi$
$491$	1.56899	−	2.71756i	0.0708073	−	0.122642i	0.899255	+	0.437424i	$0.144109\pi$
$492$	14.1079	−	4.23766i	0.636032	−	0.191048i
$493$	−1.03481	+	3.86195i	−0.0466054	+	0.173934i
$494$	7.88473	+	3.31344i	0.354751	+	0.149079i
$495$	1.12653	−	26.5498i	0.0506337	−	1.19332i
$496$	0.466367	−	22.7316i	0.0209405	−	1.02068i
$497$	−12.5419	−	3.36060i	−0.562583	−	0.150744i
$498$	12.8800	−	34.4727i	0.577168	−	1.54476i
$499$	−8.15826	+	14.1305i	−0.365214	+	0.632569i	−0.988810	−	0.149178i	$-0.952337\pi$
$499$	−8.15826	+	14.1305i	−0.365214	+	0.632569i	0.623597	+	0.781746i	$0.285671\pi$
$500$	−22.2072	−	2.61522i	−0.993137	−	0.116956i
$501$	−7.42117	+	8.04411i	−0.331553	+	0.359384i
$502$	−26.7222	−	20.7232i	−1.19267	−	0.924924i
$503$	23.5670	+	23.5670i	1.05080	+	1.05080i	0.998639	+	0.0521617i	$0.0166111\pi$
$503$	23.5670	+	23.5670i	1.05080	+	1.05080i	0.0521617	+	0.998639i	$0.483389\pi$
$504$	10.6607	−	5.25308i	0.474867	−	0.233991i
$505$	15.8415	−	6.71033i	0.704939	−	0.298606i
$506$	−2.20839	−	17.4661i	−0.0981748	−	0.776461i
$507$	6.81378	+	3.57631i	0.302611	+	0.158829i
$508$	−15.6795	+	26.5257i	−0.695667	+	1.17689i
$509$	3.78199	+	2.18353i	0.167634	+	0.0967834i	0.581470	−	0.813568i	$-0.302478\pi$
$509$	3.78199	+	2.18353i	0.167634	+	0.0967834i	−0.413836	+	0.910352i	$0.635811\pi$
$510$	8.60900	−	5.47817i	0.381213	−	0.242578i
$511$	−11.2479	−	19.4819i	−0.497578	−	0.861830i
$512$	−21.2823	+	7.68539i	−0.940552	+	0.339649i
$513$	−10.6642	+	1.29427i	−0.470837	+	0.0571436i
$514$	−15.4174	+	36.6876i	−0.680032	+	1.61822i
$515$	17.6508	−	2.46718i	0.777788	−	0.108717i
$516$	−20.6969	−	33.4864i	−0.911132	−	1.47416i
$517$	7.66926	+	28.6221i	0.337294	+	1.25880i
$518$	3.01492	−	22.0271i	0.132468	−	0.967815i
$519$	3.83214	+	12.2986i	0.168212	+	0.539846i
$520$	−17.8346	−	4.92064i	−0.782098	−	0.215784i
$521$		−	33.7498i		−	1.47861i	−0.673373	−	0.739303i	$-0.735155\pi$
$521$		−	33.7498i		−	1.47861i	0.673373	−	0.739303i	$-0.264845\pi$
$522$	−4.98300	+	7.62047i	−0.218100	+	0.333539i
$523$	0.0847849	+	0.0847849i	0.00370738	+	0.00370738i	0.708958	−	0.705251i	$-0.249166\pi$
$523$	0.0847849	+	0.0847849i	0.00370738	+	0.00370738i	−0.705251	+	0.708958i	$0.749166\pi$
$524$	−12.4924	−	3.48504i	−0.545732	−	0.152245i
$525$	12.1106	−	0.681494i	0.528550	−	0.0297428i
$526$	27.2997	−	20.7262i	1.19032	−	0.903707i
$527$	2.74079	+	10.2288i	0.119390	+	0.445571i
$528$	−0.541873	−	27.4398i	−0.0235820	−	1.19417i
$529$	−11.3662	+	6.56227i	−0.494182	+	0.285316i
$530$	0.0552667	+	19.3985i	0.00240063	+	0.842616i
$531$	−8.30570	+	5.73256i	−0.360437	+	0.248772i
$532$	−5.79097	−	0.0593982i	−0.251070	−	0.00257524i
$533$	12.0153	+	3.21950i	0.520442	+	0.139452i
$534$	−0.904905	+	9.41987i	−0.0391591	+	0.407638i
$535$	−4.41930	+	3.44741i	−0.191063	+	0.149044i
$536$	−13.3198	−	1.96250i	−0.575328	−	0.0847672i
$537$	10.9785	−	6.94208i	0.473756	−	0.299573i
$538$	21.9170	−	28.2616i	0.944911	−	1.21844i
$539$		−	19.9584i		−	0.859668i
$540$	22.5190	−	5.73554i	0.969062	−	0.246818i
$541$			15.3742i			0.660986i	0.943808	+	0.330493i	$0.107215\pi$
$541$			15.3742i			0.660986i	−0.943808	+	0.330493i	$0.892785\pi$
$542$	14.4045	+	11.1708i	0.618728	+	0.479828i
$543$	−33.7282	+	21.3275i	−1.44741	+	0.915252i
$544$	8.52276	−	6.19916i	0.365410	−	0.265787i
$545$	0.150472	−	1.21795i	0.00644552	−	0.0521714i
$546$	9.99002	+	0.959676i	0.427534	+	0.0410703i
$547$	−36.7514	−	9.84751i	−1.57138	−	0.421049i	−0.635134	−	0.772402i	$-0.719055\pi$
$547$	−36.7514	−	9.84751i	−1.57138	−	0.421049i	−0.936243	+	0.351353i	$0.885722\pi$
$548$	0.281119	−	27.4075i	0.0120088	−	1.17079i
$549$	−0.687457	−	8.51958i	−0.0293399	−	0.363607i
$550$	10.4386	−	25.9934i	0.445103	−	1.10836i
$551$	3.84237	−	2.21839i	0.163690	−	0.0945067i
$552$	14.0723	−	6.24340i	0.598959	−	0.265737i
$553$	−6.05178	−	22.5856i	−0.257348	−	0.960435i
$554$	−11.8254	−	15.5760i	−0.502415	−	0.661760i
$555$	14.6797	−	40.9171i	0.623118	−	1.73683i
$556$	21.7062	+	6.05544i	0.920547	+	0.256808i
$557$	−13.7557	−	13.7557i	−0.582847	−	0.582847i	0.352838	−	0.935684i	$-0.385217\pi$
$557$	−13.7557	−	13.7557i	−0.582847	−	0.582847i	−0.935684	+	0.352838i	$0.885217\pi$
$558$	−1.33799	+	24.0784i	−0.0566418	+	1.01932i
$559$		−	33.2428i		−	1.40602i
$560$	12.4399	−	1.47935i	0.525682	−	0.0625139i
$561$	3.80268	+	12.2040i	0.160549	+	0.515253i
$562$	−5.96339	−	0.816229i	−0.251550	−	0.0344305i
$563$	10.6947	+	39.9133i	0.450730	+	1.68215i	0.700348	+	0.713801i	$0.253028\pi$
$563$	10.6947	+	39.9133i	0.450730	+	1.68215i	−0.249619	+	0.968344i	$0.580305\pi$
$564$	−22.0418	+	13.6234i	−0.928126	+	0.573647i
$565$	−4.07389	−	29.1457i	−0.171390	−	1.22617i
$566$	−24.7886	−	10.4170i	−1.04194	−	0.437861i
$567$	−11.4954	+	5.17267i	−0.482763	+	0.217232i
$568$	−24.0675	−	10.4057i	−1.00985	−	0.436614i
$569$	13.8900	+	24.0583i	0.582301	+	1.00857i	0.995206	+	0.0978005i	$0.0311807\pi$
$569$	13.8900	+	24.0583i	0.582301	+	1.00857i	−0.412905	+	0.910774i	$0.635486\pi$
$570$	−11.0539	−	2.45668i	−0.462995	−	0.102899i
$571$	−8.21072	−	4.74046i	−0.343608	−	0.198382i	0.318258	−	0.948004i	$-0.396902\pi$
$571$	−8.21072	−	4.74046i	−0.343608	−	0.198382i	−0.661866	+	0.749622i	$0.730235\pi$
$572$	11.7933	−	19.9511i	0.493101	−	0.834199i
$573$	−7.76983	−	4.07810i	−0.324589	−	0.170365i
$574$	−8.35645	+	1.05658i	−0.348791	+	0.0441007i
$575$	15.7106	−	0.250680i	0.655178	−	0.0104541i
$576$	22.8447	−	7.35674i	0.951861	−	0.306531i
$577$	3.40629	+	3.40629i	0.141806	+	0.141806i	0.774446	−	0.632640i	$-0.218029\pi$
$577$	3.40629	+	3.40629i	0.141806	+	0.141806i	−0.632640	+	0.774446i	$0.718029\pi$
$578$	11.7252	−	15.1194i	0.487704	−	0.628884i
$579$	−26.3489	+	28.5606i	−1.09502	+	1.18694i
$580$	−7.62756	+	5.82526i	−0.316717	+	0.241881i
$581$	−10.5213	+	18.2234i	−0.436496	+	0.756032i
$582$	23.0744	+	8.62130i	0.956466	+	0.357364i
$583$	−23.4725	−	6.28943i	−0.972130	−	0.260481i
$584$	−16.7368	−	42.2326i	−0.692575	−	1.74760i
$585$	18.7222	+	5.87783i	0.774068	+	0.243018i
$586$	−4.40711	+	10.4873i	−0.182056	+	0.433225i
$587$	−6.78111	+	25.3074i	−0.279886	+	1.04455i	0.672609	+	0.739998i	$0.265173\pi$
$587$	−6.78111	+	25.3074i	−0.279886	+	1.04455i	−0.952496	+	0.304552i	$0.901493\pi$
$588$	16.7152	−	5.02084i	0.689324	−	0.207056i
$589$	5.87562	−	10.1769i	0.242101	−	0.419331i
$590$	−10.2675	+	2.78254i	−0.422705	+	0.114555i
$591$	−0.0778478	+	0.345625i	−0.00320223	+	0.0142171i
$592$	12.5071	−	43.1191i	0.514039	−	1.77218i
$593$	12.5128	+	12.5128i	0.513838	+	0.513838i	0.915700	−	0.401862i	$-0.131637\pi$
$593$	12.5128	+	12.5128i	0.513838	+	0.513838i	−0.401862	+	0.915700i	$0.631637\pi$
$594$	−0.443986	+	29.1066i	−0.0182170	+	1.19426i
$595$	−5.37265	+	2.27580i	−0.220257	+	0.0932988i
$596$	4.28060	−	15.3442i	0.175340	−	0.628521i
$597$	2.60710	−	1.64856i	0.106701	−	0.0674711i
$598$	12.8803	+	1.76297i	0.526716	+	0.0720933i
$599$	22.7210	−	39.3540i	0.928357	−	1.60796i	0.142285	−	0.989826i	$-0.454555\pi$
$599$	22.7210	−	39.3540i	0.928357	−	1.60796i	0.786072	−	0.618135i	$-0.212112\pi$
$600$	24.3956	+	2.20331i	0.995946	+	0.0899498i
$601$	−9.12969	−	15.8131i	−0.372408	−	0.645029i	0.617527	−	0.786549i	$-0.288134\pi$
$601$	−9.12969	−	15.8131i	−0.372408	−	0.645029i	−0.989935	+	0.141520i	$0.954801\pi$
$602$	8.50733	+	20.8402i	0.346733	+	0.849382i
$603$	14.0463	+	2.57461i	0.572009	+	0.104846i
$604$	−16.2301	+	15.9005i	−0.660392	+	0.646982i
$605$	8.37508	+	6.32092i	0.340495	+	0.256982i
$606$	−17.1476	+	7.81922i	−0.696572	+	0.317634i
$607$	−29.7175	+	7.96277i	−1.20620	+	0.323199i	−0.805268	−	0.592911i	$-0.797979\pi$
$607$	−29.7175	+	7.96277i	−1.20620	+	0.323199i	−0.400927	+	0.916110i	$0.631312\pi$
$608$	−11.5519	−	1.82327i	−0.468492	−	0.0739434i
$609$	3.53025	−	3.82659i	0.143053	−	0.155061i
$610$	2.30706	−	8.70923i	0.0934100	−	0.352626i
$611$	−21.8814			−0.885228
$612$	−9.26428	+	6.25486i	−0.374486	+	0.252838i
$613$	9.05061	+	9.05061i	0.365551	+	0.365551i	0.865852	−	0.500301i	$-0.166777\pi$
$613$	9.05061	+	9.05061i	0.365551	+	0.365551i	−0.500301	+	0.865852i	$0.666777\pi$
$614$	9.34378	−	1.18142i	0.377084	−	0.0476781i
$615$	−16.4130	−	1.35986i	−0.661837	−	0.0548350i
$616$	−2.28750	+	15.5256i	−0.0921660	+	0.625545i
$617$	8.84442	+	33.0078i	0.356063	+	1.32885i	0.879142	+	0.476561i	$0.158117\pi$
$617$	8.84442	+	33.0078i	0.356063	+	1.32885i	−0.523078	+	0.852285i	$0.675217\pi$
$618$	−19.2550	+	3.22661i	−0.774550	+	0.129793i
$619$	17.3425	+	30.0381i	0.697055	+	1.20733i	0.969483	+	0.245158i	$0.0788400\pi$
$619$	17.3425	+	30.0381i	0.697055	+	1.20733i	−0.272428	+	0.962176i	$0.587827\pi$
$620$	−9.78134	+	23.4628i	−0.392828	+	0.942290i
$621$	−15.1485	+	6.09580i	−0.607890	+	0.244616i
$622$	−5.43279	−	13.3086i	−0.217835	−	0.533625i
$623$	1.40050	−	5.22673i	0.0561097	−	0.209404i
$624$	19.6759	+	4.85789i	0.787668	+	0.194471i
$625$	22.0384	+	11.8029i	0.881537	+	0.472116i
$626$	−11.7817	−	15.5184i	−0.470892	−	0.620239i
$627$	6.59231	−	12.5600i	0.263272	−	0.501600i
$628$	4.33993	−	2.44666i	0.173182	−	0.0976323i
$629$			20.9107i			0.833764i
$630$	−13.2413	+	1.10644i	−0.527548	+	0.0440817i
$631$	−5.01823			−0.199773			−0.0998863	−	0.994999i	$-0.531848\pi$
$631$	−5.01823			−0.199773			−0.0998863	+	0.994999i	$0.531848\pi$
$632$	−5.44228	−	46.9036i	−0.216482	−	1.86572i
$633$	−0.485556	−	12.0544i	−0.0192991	−	0.479121i
$634$	−34.9198	+	26.5115i	−1.38684	+	1.05291i
$635$	27.1631	−	21.1894i	1.07794	−	0.840875i
$636$	−0.637444	−	21.2405i	−0.0252763	−	0.842240i
$637$	14.2360	+	3.81452i	0.564050	+	0.151137i
$638$	−4.54391	−	11.1311i	−0.179895	−	0.440684i
$639$	25.1257	+	11.9234i	0.993955	+	0.471682i
$640$	25.2884	+	0.706261i	0.999610	+	0.0279174i
$641$	33.2605	−	19.2030i	1.31371	−	0.758471i	0.331002	−	0.943630i	$-0.392613\pi$
$641$	33.2605	−	19.2030i	1.31371	−	0.758471i	0.982709	+	0.185159i	$0.0592799\pi$
$642$	4.73679	−	3.90649i	0.186946	−	0.154177i
$643$	6.58055	−	1.76325i	0.259511	−	0.0695359i	−0.126717	−	0.991939i	$-0.540444\pi$
$643$	6.58055	−	1.76325i	0.259511	−	0.0695359i	0.386229	+	0.922403i	$0.373777\pi$
$644$	−8.52596	+	2.19105i	−0.335970	+	0.0863395i
$645$	7.84215	+	43.3085i	0.308785	+	1.70527i
$646$	5.40394	−	0.683267i	0.212615	−	0.0268828i
$647$	−30.1337	+	30.1337i	−1.18468	+	1.18468i	−0.206158	+	0.978519i	$0.566096\pi$
$647$	−30.1337	+	30.1337i	−1.18468	+	1.18468i	−0.978519	+	0.206158i	$0.933904\pi$
$648$	−24.4886	+	6.95039i	−0.962004	+	0.273037i
$649$		−	13.3260i		−	0.523090i
$650$	16.5456	+	12.4136i	0.648973	+	0.486903i
$651$	3.02998	−	13.4523i	0.118754	−	0.527239i
$652$	−12.8594	+	21.7547i	−0.503613	+	0.851981i
$653$	5.32699	+	19.8806i	0.208461	+	0.777988i	0.988367	+	0.152091i	$0.0486006\pi$
$653$	5.32699	+	19.8806i	0.208461	+	0.777988i	−0.779905	+	0.625898i	$0.784733\pi$
$654$	−0.128550	+	1.33818i	−0.00502672	+	0.0523271i
$655$	11.5739	+	8.73513i	0.452228	+	0.341310i
$656$	−17.0058	−	0.348895i	−0.663965	−	0.0136221i
$657$	16.1738	+	45.3881i	0.631002	+	1.77076i
$658$	13.7177	−	5.59979i	0.534770	−	0.218303i
$659$	12.7489	−	7.36058i	0.496627	−	0.286727i	−0.230693	−	0.973027i	$-0.574099\pi$
$659$	12.7489	−	7.36058i	0.496627	−	0.286727i	0.727319	+	0.686299i	$0.240766\pi$
$660$	−10.6576	+	28.7743i	−0.414848	+	1.12004i
$661$	15.6457	+	9.03307i	0.608549	+	0.351346i	0.772397	−	0.635140i	$-0.219057\pi$
$661$	15.6457	+	9.03307i	0.608549	+	0.351346i	−0.163848	+	0.986486i	$0.552391\pi$
$662$	−44.2437	−	6.05578i	−1.71958	−	0.235365i
$663$	−9.43169	+	0.379911i	−0.366297	+	0.0147545i
$664$	−26.3839	+	33.3103i	−1.02389	+	1.29269i
$665$	6.00155	+	2.43002i	0.232730	+	0.0942320i
$666$	−14.8580	+	45.2425i	−0.575734	+	1.75311i
$667$	4.76881	−	4.76881i	0.184649	−	0.184649i
$668$	11.0087	−	6.20621i	0.425940	−	0.240125i
$669$	−0.666570	−	2.13924i	−0.0257711	−	0.0827076i
$670$	13.0575	+	7.48921i	0.504454	+	0.289333i
$671$	9.77423	+	5.64315i	0.377330	+	0.217851i
$672$	−13.5782	+	1.98992i	−0.523791	+	0.0767629i
$673$	39.2766	+	10.5241i	1.51400	+	0.405676i	0.917762	−	0.397130i	$-0.129994\pi$
$673$	39.2766	+	10.5241i	1.51400	+	0.405676i	0.596241	+	0.802806i	$0.296660\pi$
$674$	−10.4370	−	4.38598i	−0.402017	−	0.168942i
$675$	−25.7778	−	3.24093i	−0.992189	−	0.124743i
$676$	−6.21841	−	6.34730i	−0.239170	−	0.244127i
$677$	8.12253	−	30.3137i	0.312174	−	1.16505i	−0.614418	−	0.788981i	$-0.710609\pi$
$677$	8.12253	−	30.3137i	0.312174	−	1.16505i	0.926592	−	0.376069i	$-0.122724\pi$
$678$	5.32790	+	31.7946i	0.204617	+	1.22106i
$679$	−12.1979	−	7.04245i	−0.468111	−	0.270264i
$680$	−11.4036	+	2.96521i	−0.437306	+	0.113711i
$681$	24.1466	−	7.52388i	0.925298	−	0.288316i
$682$	−25.1635	−	19.5145i	−0.963559	−	0.747247i
$683$	22.8499	−	22.8499i	0.874327	−	0.874327i	−0.118613	−	0.992941i	$-0.537845\pi$
$683$	22.8499	−	22.8499i	0.874327	−	0.874327i	0.992941	+	0.118613i	$0.0378448\pi$
$684$	12.1775	+	2.36141i	0.465618	+	0.0902909i
$685$	−11.5008	+	28.4041i	−0.439422	+	1.08526i
$686$	−23.6568	+	2.99114i	−0.903221	+	0.114202i
$687$	−22.0015	+	0.886226i	−0.839410	+	0.0338116i
$688$	10.8618	+	44.1394i	0.414104	+	1.68280i
$689$	8.97228	−	15.5405i	0.341817	−	0.592044i
$690$	−17.1963	+	0.741750i	−0.654653	+	0.0282379i
$691$	−0.0596721	+	0.0344517i	−0.00227003	+	0.00131060i	−0.501135	−	0.865369i	$-0.667084\pi$
$691$	−0.0596721	+	0.0344517i	−0.00227003	+	0.00131060i	0.498865	+	0.866680i	$0.333751\pi$
$692$	0.152561	−	14.8738i	0.00579950	−	0.565417i
$693$	3.00098	−	16.3724i	0.113998	−	0.621937i
$694$	−11.9766	−	5.03299i	−0.454626	−	0.191050i
$695$	−20.1102	−	15.1777i	−0.762823	−	0.575725i
$696$	8.17924	−	6.60575i	0.310033	−	0.250390i
$697$	7.65226	−	2.05042i	0.289850	−	0.0776651i
$698$	4.97471	−	36.3454i	0.188296	−	1.37569i
$699$	5.93124	−	26.3332i	0.224340	−	0.996014i
$700$	−13.5494	−	3.54794i	−0.512120	−	0.134099i
$701$	−8.86219			−0.334720			−0.167360	−	0.985896i	$-0.553524\pi$
$701$	−8.86219			−0.334720			−0.167360	+	0.985896i	$0.553524\pi$
$702$	−20.6764	−	5.87965i	−0.780381	−	0.221913i
$703$	16.4081	−	16.4081i	0.618843	−	0.618843i
$704$	−9.14010	+	30.3443i	−0.344481	+	1.14364i
$705$	28.5070	−	5.16195i	1.07364	−	0.194410i
$706$	−4.72822	+	3.58971i	−0.177949	+	0.135101i
$707$	10.4091	−	2.78911i	0.391475	−	0.104895i
$708$	11.1605	−	3.35235i	0.419439	−	0.125989i
$709$	−5.02429	−	8.70232i	−0.188691	−	0.326822i	0.756123	−	0.654429i	$-0.227091\pi$
$709$	−5.02429	−	8.70232i	−0.188691	−	0.326822i	−0.944814	+	0.327607i	$0.893758\pi$
$710$	20.7883	+	20.6701i	0.780169	+	0.775737i
$711$	4.02814	+	49.9203i	0.151067	+	1.87216i
$712$	4.33648	−	10.0299i	0.162516	−	0.375886i
$713$	4.62313	−	17.2538i	0.173138	−	0.646159i
$714$	5.81559	−	2.65189i	0.217643	−	0.0992443i
$715$	−20.4306	+	15.9375i	−0.764060	+	0.596028i
$716$	−14.5266	+	3.73314i	−0.542885	+	0.139514i
$717$	−16.3097	+	0.656958i	−0.609096	+	0.0245345i
$718$	1.16970	+	0.907111i	0.0436528	+	0.0338531i
$719$	5.56512			0.207544			0.103772	−	0.994601i	$-0.466909\pi$
$719$	5.56512			0.207544			0.103772	+	0.994601i	$0.466909\pi$
$720$	−26.7797	−	1.68717i	−0.998021	−	0.0628772i
$721$	11.1636			0.415753
$722$	16.4568	+	12.7624i	0.612459	+	0.474966i
$723$	−13.7462	+	26.1900i	−0.511226	+	0.974016i
$724$	44.6289	−	11.4690i	1.65862	−	0.426241i
$725$	10.3191	−	2.94224i	0.383243	−	0.109272i
$726$	−9.35905	−	6.67259i	−0.347347	−	0.247643i
$727$	2.55731	−	9.54403i	0.0948456	−	0.353968i	−0.902150	−	0.431422i	$-0.858012\pi$
$727$	2.55731	−	9.54403i	0.0948456	−	0.353968i	0.996996	+	0.0774532i	$0.0246788\pi$
$728$	−10.6370	−	4.59895i	−0.394232	−	0.170448i
$729$	26.2161	−	6.45864i	0.970968	−	0.239209i
$730$	0.144702	+	50.7899i	0.00535565	+	1.87982i
$731$	−10.5857	−	18.3350i	−0.391527	−	0.678145i
$732$	−2.26730	+	9.60558i	−0.0838019	+	0.355032i
$733$	15.5973	−	4.17927i	0.576098	−	0.154365i	0.0410061	−	0.999159i	$-0.486944\pi$
$733$	15.5973	−	4.17927i	0.576098	−	0.154365i	0.535092	+	0.844794i	$0.320277\pi$
$734$	4.66225	−	3.53963i	0.172087	−	0.130650i
$735$	−19.4464	−	1.61119i	−0.717292	−	0.0594296i
$736$	−17.6784	+	1.86770i	−0.651635	+	0.0688442i
$737$	−13.3336	+	13.3336i	−0.491149	+	0.491149i
$738$	18.0134	+	1.00097i	0.663082	+	0.0368463i
$739$	−0.382628			−0.0140752			−0.00703759	−	0.999975i	$-0.502240\pi$
$739$	−0.382628			−0.0140752			−0.00703759	+	0.999975i	$0.502240\pi$
$740$	−30.6479	+	39.7531i	−1.12664	+	1.46135i
$741$	7.69892	+	7.10271i	0.282827	+	0.260925i
$742$	−1.64776	+	12.0386i	−0.0604912	+	0.441951i
$743$	11.6345	−	3.11745i	0.426827	−	0.114368i	−0.0390091	−	0.999239i	$-0.512420\pi$
$743$	11.6345	−	3.11745i	0.426827	−	0.114368i	0.465837	+	0.884871i	$0.345753\pi$
$744$	10.0132	−	25.9837i	0.367101	−	0.952608i
$745$	−10.7292	+	14.2159i	−0.393087	+	0.520831i
$746$	42.4224	+	17.8273i	1.55319	+	0.652705i
$747$	29.2035	−	34.3301i	1.06850	−	1.25607i
$748$	0.151388	−	14.7594i	0.00553530	−	0.539659i
$749$	−3.04043	+	1.75539i	−0.111095	+	0.0641406i
$750$	−24.4840	−	12.2692i	−0.894029	−	0.448009i
$751$	18.2653	−	31.6365i	0.666512	−	1.15443i	−0.312361	−	0.949963i	$-0.601120\pi$
$751$	18.2653	−	31.6365i	0.666512	−	1.15443i	0.978873	−	0.204469i	$-0.0655467\pi$
$752$	29.0539	−	7.14960i	1.05949	−	0.260719i
$753$	−22.1348	−	35.0049i	−0.806638	−	1.27565i
$754$	8.80807	−	1.11368i	0.320771	−	0.0405579i
$755$	23.3908	−	9.90813i	0.851278	−	0.360594i
$756$	14.4669	−	1.60541i	0.526157	−	0.0583881i
$757$	11.2246	−	11.2246i	0.407964	−	0.407964i	−0.473064	−	0.881028i	$-0.656852\pi$
$757$	11.2246	−	11.2246i	0.407964	−	0.407964i	0.881028	+	0.473064i	$0.156852\pi$
$758$	17.0427	+	13.2167i	0.619018	+	0.480053i
$759$	4.73784	−	21.0348i	0.171973	−	0.763515i
$760$	11.2748	+	6.62136i	0.408981	+	0.240182i
$761$	−30.9170	−	17.8499i	−1.12074	−	0.647060i	−0.179151	−	0.983822i	$-0.557335\pi$
$761$	−30.9170	−	17.8499i	−1.12074	−	0.647060i	−0.941590	+	0.336762i	$0.890668\pi$
$762$	−29.1145	+	24.0111i	−1.05471	+	0.869831i
$763$	0.198954	−	0.742507i	0.00720262	−	0.0268805i
$764$	7.09092	+	7.23789i	0.256541	+	0.261858i
$765$	12.1979	−	2.71994i	0.441017	−	0.0983395i
$766$	41.6746	+	17.5131i	1.50576	+	0.632774i
$767$	9.50518	+	2.54691i	0.343212	+	0.0919634i
$768$	−27.7128	−	0.0212902i	−1.00000	−	0.000768245i
$769$	27.9354	+	16.1285i	1.00737	+	0.581608i	0.910422	−	0.413681i	$-0.135757\pi$
$769$	27.9354	+	16.1285i	1.00737	+	0.581608i	0.0969530	+	0.995289i	$0.469090\pi$
$770$	8.72946	−	15.2198i	0.314588	−	0.548485i
$771$	−33.0488	+	35.8230i	−1.19022	+	1.29013i
$772$	39.0864	−	22.0351i	1.40675	−	0.793062i
$773$	−27.7925	+	27.7925i	−0.999628	+	0.999628i	−1.00000		0.000372119i	$-0.999882\pi$
$773$	−27.7925	+	27.7925i	−0.999628	+	0.999628i	0.000372119		1.00000i	$0.499882\pi$
$774$	−9.87551	−	47.1914i	−0.354968	−	1.69626i
$775$	19.7731	−	20.4144i	0.710272	−	0.733306i
$776$	−22.2964	−	17.6602i	−0.800393	−	0.633963i
$777$	12.6544	−	24.1099i	0.453976	−	0.864939i
$778$	−32.4648	−	4.44356i	−1.16392	−	0.159309i
$779$	−7.61345	−	4.39563i	−0.272780	−	0.157490i
$780$	−18.4873	−	13.1014i	−0.661953	−	0.469104i
$781$	−31.8035	+	18.3618i	−1.13802	+	0.657036i
$782$	7.66553	−	3.12921i	0.274119	−	0.111900i
$783$	−8.91525	+	6.69860i	−0.318605	+	0.239389i
$784$	−20.1488	−	0.413377i	−0.719599	−	0.0147635i
$785$	−5.51651	+	0.771080i	−0.196893	+	0.0275210i
$786$	−12.9336	−	9.22111i	−0.461328	−	0.328906i
$787$	−0.748914	−	2.79499i	−0.0266959	−	0.0996305i	0.951292	−	0.308290i	$-0.0997567\pi$
$787$	−0.748914	−	2.79499i	−0.0266959	−	0.0996305i	−0.977988	+	0.208659i	$0.933090\pi$
$788$	0.208169	−	0.352167i	0.00741570	−	0.0125454i
$789$	40.0789	−	12.4883i	1.42685	−	0.444595i
$790$	−13.5181	+	51.0315i	−0.480954	+	1.81562i
$791$		−	18.4337i		−	0.655428i
$792$	10.8148	−	31.8261i	0.384286	−	1.13089i
$793$	−5.89325	+	5.89325i	−0.209276	+	0.209276i
$794$	3.76441	−	0.475967i	0.133594	−	0.0168914i
$795$	−8.02297	+	22.3626i	−0.284545	+	0.793121i
$796$	−3.44969	+	0.886521i	−0.122271	+	0.0314219i
$797$	7.74889	−	2.07631i	0.274480	−	0.0735467i	−0.118953	−	0.992900i	$-0.537954\pi$
$797$	7.74889	−	2.07631i	0.274480	−	0.0735467i	0.393433	+	0.919353i	$0.371287\pi$
$798$	−6.64421	−	2.48248i	−0.235203	−	0.0878787i
$799$	−12.0687	+	6.96786i	−0.426959	+	0.246505i
$800$	−26.0252	−	11.0765i	−0.920129	−	0.391615i
$801$	−4.96895	+	10.4709i	−0.175569	+	0.369970i
$802$	−4.18152	−	10.2433i	−0.147654	−	0.361705i
$803$	−61.4566	−	16.4673i	−2.16876	−	0.581117i
$804$	−14.5212	−	7.81266i	−0.512123	−	0.275531i
$805$	9.76778	+	1.20676i	0.344269	+	0.0425328i
$806$	18.7287	−	14.2190i	0.659689	−	0.500843i
$807$	37.0214	−	23.4100i	1.30321	−	0.824069i
$808$	21.6167	−	2.50821i	0.760472	−	0.0882385i
$809$	−20.4056			−0.717424			−0.358712	−	0.933448i	$-0.616784\pi$
$809$	−20.4056			−0.717424			−0.358712	+	0.933448i	$0.616784\pi$
$810$	28.3242	+	2.78230i	0.995210	+	0.0977601i
$811$		−	1.23274i		−	0.0432873i	−0.999766	−	0.0216437i	$-0.993110\pi$
$811$		−	1.23274i		−	0.0432873i	0.999766	−	0.0216437i	$-0.00688993\pi$
$812$	−5.23685	+	2.95230i	−0.183777	+	0.103605i
$813$	11.9317	+	18.8693i	0.418464	+	0.661775i
$814$	−38.0225	−	50.0816i	−1.33269	−	1.75536i
$815$	22.2775	−	17.3782i	0.780347	−	0.608733i
$816$	12.3992	−	3.58618i	0.434058	−	0.125541i
$817$	−6.08067	+	22.6934i	−0.212736	+	0.793941i
$818$	18.5840	+	45.5248i	0.649775	+	1.59174i
$819$	11.1046	+	5.26971i	0.388027	+	0.184138i
$820$	17.5529	+	7.31755i	0.612972	+	0.255540i
$821$	23.9207	+	41.4320i	0.834840	+	1.44599i	0.894161	+	0.447746i	$0.147773\pi$
$821$	23.9207	+	41.4320i	0.834840	+	1.44599i	−0.0593209	+	0.998239i	$0.518894\pi$
$822$	11.7491	−	31.4457i	0.409795	−	1.09679i
$823$	4.15265	+	15.4979i	0.144752	+	0.540223i	0.999766	+	0.0216179i	$0.00688173\pi$
$823$	4.15265	+	15.4979i	0.144752	+	0.540223i	−0.855014	+	0.518605i	$0.826452\pi$
$824$	22.3030	+	3.28606i	0.776961	+	0.114475i
$825$	22.8571	−	25.5829i	0.795782	−	0.890684i
$826$	−6.61067	+	0.835845i	−0.230015	+	0.0290828i
$827$	30.4795	+	30.4795i	1.05988	+	1.05988i	0.998089	+	0.0617866i	$0.0196798\pi$
$827$	30.4795	+	30.4795i	1.05988	+	1.05988i	0.0617866	+	0.998089i	$0.480320\pi$
$828$	18.8086	−	1.32368i	0.653645	−	0.0460010i
$829$	10.6637			0.370365			0.185183	−	0.982704i	$-0.440712\pi$
$829$	10.6637			0.370365			0.185183	+	0.982704i	$0.440712\pi$
$830$	41.0762	−	23.8716i	1.42577	−	0.828596i
$831$	−7.12525	−	22.8672i	−0.247172	−	0.793255i
$832$	−19.8972	−	12.3190i	−0.689811	−	0.427084i
$833$	9.06652	−	2.42937i	0.314136	−	0.0841726i
$834$	22.4729	+	16.0222i	0.778172	+	0.554802i
$835$	−13.9932	+	1.95593i	−0.484255	+	0.0676876i
$836$	−11.7002	+	11.4626i	−0.404658	+	0.396442i
$837$	−11.5784	+	27.1714i	−0.400208	+	0.939180i
$838$	−4.59680	−	11.2606i	−0.158794	−	0.388992i
$839$	15.7340	+	27.2521i	0.543199	+	0.940848i	0.998718	+	0.0506218i	$0.0161203\pi$
$839$	15.7340	+	27.2521i	0.543199	+	0.940848i	−0.455519	+	0.890226i	$0.650546\pi$
$840$	14.9427	+	3.48217i	0.515572	+	0.120146i
$841$	−12.1972	+	21.1261i	−0.420592	+	0.728487i
$842$	19.9733	+	2.73381i	0.688325	+	0.0942134i
$843$	−6.52728	−	3.42593i	−0.224811	−	0.117995i
$844$	−3.74331	+	13.4182i	−0.128850	+	0.461873i
$845$	3.87490	+	9.14774i	0.133301	+	0.314692i
$846$	−31.0628	+	6.50037i	−1.06796	+	0.223487i
$847$	4.64737	+	4.64737i	0.159686	+	0.159686i
$848$	−6.83558	+	23.5661i	−0.234735	+	0.809263i
$849$	−24.2045	−	22.3301i	−0.830695	−	0.766365i
$850$	13.0787	+	1.57799i	0.448595	+	0.0541247i
$851$	17.6360	−	30.5464i	0.604553	−	1.04712i
$852$	−23.3787	−	22.0164i	−0.800943	−	0.754269i
$853$	−4.45982	+	16.6443i	−0.152701	+	0.569889i	0.846590	+	0.532246i	$0.178652\pi$
$853$	−4.45982	+	16.6443i	−0.152701	+	0.569889i	−0.999291	+	0.0376434i	$0.988015\pi$
$854$	2.18636	−	5.20270i	0.0748156	−	0.178033i
$855$	−11.7057	−	7.43715i	−0.400326	−	0.254345i
$856$	−6.59098	+	2.61202i	−0.225275	+	0.0892769i
$857$	17.2039	+	4.60978i	0.587675	+	0.157467i	0.540391	−	0.841414i	$-0.318277\pi$
$857$	17.2039	+	4.60978i	0.587675	+	0.157467i	0.0472848	+	0.998881i	$0.484943\pi$
$858$	21.8983	−	18.0598i	0.747597	−	0.616552i
$859$	19.3208	−	33.4646i	0.659218	−	1.14180i	−0.321601	−	0.946875i	$-0.604221\pi$
$859$	19.3208	−	33.4646i	0.659218	−	1.14180i	0.980818	−	0.194923i	$-0.0624458\pi$
$860$	6.74838	−	50.3716i	0.230118	−	1.71766i
$861$	−10.0639	−	2.26677i	−0.342976	−	0.0772512i
$862$	1.91684	−	2.47172i	0.0652878	−	0.0841872i
$863$	17.7528	+	17.7528i	0.604311	+	0.604311i	0.941454	−	0.337143i	$-0.109460\pi$
$863$	17.7528	+	17.7528i	0.604311	+	0.604311i	−0.337143	+	0.941454i	$0.609460\pi$
$864$	29.3751	+	1.05108i	0.999360	+	0.0357583i
$865$	−6.24136	+	15.4146i	−0.212213	+	0.524114i
$866$	25.2308	−	3.19015i	0.857377	−	0.108406i
$867$	19.8057	−	12.5239i	0.672638	−	0.425333i
$868$	−8.10230	+	13.7070i	−0.275010	+	0.465245i
$869$	−57.2719	−	33.0659i	−1.94281	−	1.12168i
$870$	−11.2124	+	3.52877i	−0.380136	+	0.119637i
$871$	−6.96226	−	12.0590i	−0.235907	−	0.408603i
$872$	0.616038	−	1.42484i	0.0208617	−	0.0482513i
$873$	22.9790	+	19.5474i	0.777720	+	0.661581i
$874$	−8.47036	−	3.55954i	−0.286514	−	0.120403i
$875$	12.6480	+	9.23286i	0.427582	+	0.312127i
$876$	−1.66898	−	55.6128i	−0.0563897	−	1.87898i
$877$	13.6570	+	50.9687i	0.461164	+	1.72109i	0.669303	+	0.742990i	$0.266593\pi$
$877$	13.6570	+	50.9687i	0.461164	+	1.72109i	−0.208138	+	0.978099i	$0.566740\pi$
$878$	17.4399	+	2.38706i	0.588568	+	0.0805592i
$879$	−9.44712	+	10.2401i	−0.318643	+	0.345391i
$880$	21.9201	−	27.8372i	0.738925	−	0.938391i
$881$		−	5.46211i		−	0.184023i	−0.995758	−	0.0920116i	$-0.970670\pi$
$881$		−	5.46211i		−	0.184023i	0.995758	−	0.0920116i	$-0.0293297\pi$
$882$	21.3426	+	1.18597i	0.718641	+	0.0399336i
$883$	8.44443	+	8.44443i	0.284178	+	0.284178i	0.834773	−	0.550595i	$-0.185599\pi$
$883$	8.44443	+	8.44443i	0.284178	+	0.284178i	−0.550595	+	0.834773i	$0.685599\pi$
$884$	10.4987	+	2.92886i	0.353110	+	0.0985083i
$885$	−12.9841	−	1.07577i	−0.436457	−	0.0361616i
$886$	10.6302	+	14.0016i	0.357129	+	0.470394i
$887$	−2.46914	−	9.21495i	−0.0829055	−	0.309408i	0.912004	−	0.410182i	$-0.134535\pi$
$887$	−2.46914	−	9.21495i	−0.0829055	−	0.309408i	−0.994909	+	0.100774i	$0.967868\pi$
$888$	32.3784	−	44.4428i	1.08655	−	1.49140i
$889$	18.6879	−	10.7895i	0.626772	−	0.361867i
$890$	−8.61407	+	8.66329i	−0.288744	+	0.290394i
$891$	−12.6449	+	33.3346i	−0.423621	+	1.11675i
$892$	−0.0265368	+	2.58718i	−0.000888517	+	0.0866251i
$893$	14.9375	+	4.00249i	0.499864	+	0.133938i
$894$	11.3261	−	15.8861i	0.378802	−	0.531312i
$895$	16.6424	+	2.05609i	0.556296	+	0.0687277i
$896$	15.6263	+	2.63089i	0.522039	+	0.0878918i
$897$	14.0983	+	7.39967i	0.470727	+	0.247068i
$898$	−21.2069	−	16.4461i	−0.707683	−	0.548813i
$899$		−	12.1985i		−	0.406844i
$900$	27.1759	+	12.7071i	0.905863	+	0.423571i
$901$		−	11.4284i		−	0.380736i
$902$	−14.5990	+	18.8251i	−0.486094	+	0.626808i
$903$	1.10957	+	27.5463i	0.0369243	+	0.916684i
$904$	5.42606	−	36.8275i	0.180468	−	1.22487i
$905$	−51.1291	−	6.31676i	−1.69959	−	0.209976i
$906$	−25.3192	+	11.5455i	−0.841175	+	0.383572i
$907$	−2.49062	−	0.667360i	−0.0826997	−	0.0221593i	0.217232	−	0.976120i	$-0.430297\pi$
$907$	−2.49062	−	0.667360i	−0.0826997	−	0.0221593i	−0.299932	+	0.953961i	$0.596964\pi$
$908$	−29.2027	−	0.299533i	−0.969125	−	0.00994035i
$909$	−23.0070	+	1.85647i	−0.763094	+	0.0615751i
$910$	9.18765	+	9.13545i	0.304568	+	0.302837i
$911$	−15.3723	+	8.87520i	−0.509307	+	0.294048i	−0.732549	−	0.680715i	$-0.761669\pi$
$911$	−15.3723	+	8.87520i	−0.509307	+	0.294048i	0.223242	+	0.974763i	$0.428336\pi$
$912$	−12.5433	−	6.91534i	−0.415351	−	0.228990i
$913$	15.4034	+	57.4864i	0.509780	+	1.90252i
$914$	−14.8517	+	11.2755i	−0.491249	+	0.372962i
$915$	6.28745	−	9.06795i	0.207857	−	0.299777i
$916$	24.4906	+	6.83222i	0.809193	+	0.225743i
$917$	6.42239	+	6.42239i	0.212086	+	0.212086i
$918$	−13.2764	+	3.34122i	−0.438185	+	0.110277i
$919$		−	22.2926i		−	0.735366i	−0.929951	−	0.367683i	$-0.880151\pi$
$919$		−	22.2926i		−	0.735366i	0.929951	−	0.367683i	$-0.119849\pi$
$920$	19.1592	+	5.28611i	0.631660	+	0.174278i
$921$	11.2529	+	2.53459i	0.370797	+	0.0835176i
$922$	5.70223	−	41.6607i	0.187793	−	1.37202i
$923$	−7.01874	−	26.1943i	−0.231025	−	0.862196i
$924$	−9.10647	+	16.9260i	−0.299581	+	0.556824i
$925$	48.1479	−	28.8320i	1.58309	−	0.947991i
$926$	−14.3712	+	34.1982i	−0.472269	+	1.12382i
$927$	−23.5194	−	4.31099i	−0.772480	−	0.141592i
$928$	−11.3314	+	4.35671i	−0.371971	+	0.143016i
$929$	−20.0135	−	34.6645i	−0.656623	−	1.13730i	−0.981484	−	0.191543i	$-0.938651\pi$
$929$	−20.0135	−	34.6645i	−0.656623	−	1.13730i	0.324861	−	0.945762i	$-0.394682\pi$
$930$	−21.0453	+	22.9427i	−0.690102	+	0.752319i
$931$	−9.02054	−	5.20801i	−0.295636	−	0.170686i
$932$	−15.8604	+	26.8317i	−0.519525	+	0.878901i
$933$	−0.708574	−	17.5911i	−0.0231977	−	0.575907i
$934$	4.01019	+	31.7165i	0.131217	+	1.03779i
$935$	−6.19338	+	15.2961i	−0.202545	+	0.500238i
$936$	20.6340	+	13.7967i	0.674444	+	0.450960i
$937$	−36.1589	−	36.1589i	−1.18126	−	1.18126i	−0.979418	−	0.201843i	$-0.935307\pi$
$937$	−36.1589	−	36.1589i	−1.18126	−	1.18126i	−0.201843	−	0.979418i	$-0.564693\pi$
$938$	7.45078	+	5.77813i	0.243276	+	0.188663i
$939$	−7.09890	−	22.7826i	−0.231664	−	0.743483i
$940$	−33.1561	−	4.44199i	−1.08143	−	0.144882i
$941$	−5.90580	+	10.2291i	−0.192524	+	0.333461i	−0.946086	−	0.323916i	$-0.895001\pi$
$941$	−5.90580	+	10.2291i	−0.192524	+	0.333461i	0.753562	+	0.657376i	$0.228334\pi$
$942$	6.01787	−	1.00843i	0.196073	−	0.0328564i
$943$	−12.9078	−	3.45863i	−0.420335	−	0.112628i
$944$	−13.4531	−	0.276006i	−0.437860	−	0.00898324i
$945$	−15.7102	−	4.24571i	−0.511053	−	0.138113i
$946$	58.6921	+	24.6645i	1.90825	+	0.801911i
$947$	−3.11580	+	11.6283i	−0.101250	+	0.377870i	−0.997893	−	0.0648848i	$-0.979332\pi$
$947$	−3.11580	+	11.6283i	−0.101250	+	0.377870i	0.896643	+	0.442754i	$0.145999\pi$
$948$	13.2852	−	56.2837i	0.431484	−	1.82801i
$949$	23.4916	−	40.6887i	0.762571	−	1.32081i
$950$	−9.02431	−	11.5007i	−0.292787	−	0.373133i
$951$	−51.2660	+	15.9741i	−1.66241	+	0.517996i
$952$	−7.33129	+	0.850658i	−0.237608	+	0.0275700i
$953$	−14.8216	−	14.8216i	−0.480119	−	0.480119i	0.425051	−	0.905170i	$-0.360256\pi$
$953$	−14.8216	−	14.8216i	−0.480119	−	0.480119i	−0.905170	+	0.425051i	$0.860256\pi$
$954$	8.12040	−	24.7266i	0.262908	−	0.800554i
$955$	−4.41859	−	10.4313i	−0.142982	−	0.337548i
$956$	18.1548	+	5.06471i	0.587170	+	0.163804i
$957$	−0.592642	−	14.7130i	−0.0191574	−	0.475603i
$958$	0.140121	−	1.02373i	0.00452710	−	0.0330751i
$959$	−9.59740	+	16.6232i	−0.309916	+	0.536791i
$960$	28.8281	+	11.3553i	0.930422	+	0.366490i
$961$	−0.654484	−	1.13360i	−0.0211124	−	0.0365677i
$962$	42.9894	−	17.5490i	1.38603	−	0.565803i
$963$	7.08345	−	2.52415i	0.228261	−	0.0813398i
$964$	24.3970	−	23.9016i	0.785774	−	0.769818i
$965$	−49.6829	+	6.94452i	−1.59935	+	0.223552i
$966$	−10.7320	−	1.03095i	−0.345297	−	0.0331704i
$967$	35.0720	−	9.39752i	1.12784	−	0.302204i	0.353788	−	0.935326i	$-0.384893\pi$
$967$	35.0720	−	9.39752i	1.12784	−	0.302204i	0.774052	+	0.633122i	$0.218227\pi$
$968$	7.91671	+	10.6527i	0.254453	+	0.342390i
$969$	6.50810	+	1.46587i	0.209070	+	0.0470906i
$970$	15.9786	+	27.4945i	0.513041	+	0.882795i
$971$	−18.6917			−0.599845			−0.299923	−	0.953964i	$-0.596961\pi$
$971$	−18.6917			−0.599845			−0.299923	+	0.953964i	$0.596961\pi$
$972$	−31.0989	−	2.20435i	−0.997497	−	0.0707046i
$973$	−11.1592	−	11.1592i	−0.357749	−	0.357749i
$974$	−3.64432	−	28.8228i	−0.116772	−	0.923543i
$975$	13.8794	+	21.1931i	0.444495	+	0.678722i
$976$	5.89942	−	9.75058i	0.188836	−	0.312108i
$977$	−4.36353	−	16.2849i	−0.139602	−	0.521001i	−0.999936	−	0.0112714i	$-0.996412\pi$
$977$	−4.36353	−	16.2849i	−0.139602	−	0.521001i	0.860335	−	0.509730i	$-0.170255\pi$
$978$	−23.8780	+	19.6924i	−0.763533	+	0.629695i
$979$	−7.65208	−	13.2538i	−0.244562	−	0.423593i
$980$	20.7969	+	8.66995i	0.664333	+	0.276951i
$981$	−0.705888	+	1.48749i	−0.0225373	+	0.0474918i
$982$	−4.10861	+	1.67721i	−0.131111	+	0.0535219i
$983$	5.08598	−	18.9811i	0.162218	−	0.605404i	−0.836161	−	0.548484i	$-0.815205\pi$
$983$	5.08598	−	18.9811i	0.162218	−	0.605404i	0.998379	−	0.0569205i	$-0.0181282\pi$
$984$	−19.4387	−	7.49098i	−0.619684	−	0.238804i
$985$	−0.360630	+	0.281320i	−0.0114906	+	0.00896359i
$986$	4.50345	−	3.41907i	0.143419	−	0.108885i
$987$	18.1319	−	0.730355i	0.577143	−	0.0232475i
$988$	−5.93989	−	10.5363i	−0.188973	−	0.335204i
$989$			35.7118i			1.13557i
$990$	−24.2686	+	28.6942i	−0.771307	+	0.911961i
$991$	−12.5037			−0.397194			−0.198597	−	0.980081i	$-0.563638\pi$
$991$	−12.5037			−0.397194			−0.198597	+	0.980081i	$0.563638\pi$
$992$	−20.2218	+	24.9993i	−0.642042	+	0.793729i
$993$	−48.4273	−	25.4177i	−1.53679	−	0.806608i
$994$	11.1036	+	14.6252i	0.352186	+	0.463884i
$995$	3.95214	+	0.488268i	0.125291	+	0.0154791i
$996$	−44.2701	+	27.3621i	−1.40275	+	0.867000i
$997$	2.64853	+	0.709672i	0.0838798	+	0.0224755i	0.300515	−	0.953777i	$-0.402841\pi$
$997$	2.64853	+	0.709672i	0.0838798	+	0.0224755i	−0.216635	+	0.976253i	$0.569508\pi$
$998$	21.3636	−	8.72099i	0.676251	−	0.276058i
$999$	−35.9708	+	45.9082i	−1.13807	+	1.45247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.br.e.77.14	yes	256
5.3	odd	4	inner	360.2.br.e.293.17	yes	256
8.5	even	2	inner	360.2.br.e.77.3	✓	256
9.2	odd	6	inner	360.2.br.e.317.36	yes	256
40.13	odd	4	inner	360.2.br.e.293.36	yes	256
45.38	even	12	inner	360.2.br.e.173.3	yes	256
72.29	odd	6	inner	360.2.br.e.317.17	yes	256
360.173	even	12	inner	360.2.br.e.173.14	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.br.e.77.3	✓	256	8.5	even	2	inner
360.2.br.e.77.14	yes	256	1.1	even	1	trivial
360.2.br.e.173.3	yes	256	45.38	even	12	inner
360.2.br.e.173.14	yes	256	360.173	even	12	inner
360.2.br.e.293.17	yes	256	5.3	odd	4	inner
360.2.br.e.293.36	yes	256	40.13	odd	4	inner
360.2.br.e.317.17	yes	256	72.29	odd	6	inner
360.2.br.e.317.36	yes	256	9.2	odd	6	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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.11754 - 0.866661i) q^{2} +(-0.925695 - 1.46393i) q^{3} +(0.497797 + 1.93706i) q^{4} +(0.274171 - 2.21920i) q^{5} +(-0.234228 + 2.43827i) q^{6} +(0.362508 - 1.35290i) q^{7} +(1.12247 - 2.59616i) q^{8} +(-1.28618 + 2.71030i) q^{9} +O(q^{10})\)	\(q+(-1.11754 - 0.866661i) q^{2} +(-0.925695 - 1.46393i) q^{3} +(0.497797 + 1.93706i) q^{4} +(0.274171 - 2.21920i) q^{5} +(-0.234228 + 2.43827i) q^{6} +(0.362508 - 1.35290i) q^{7} +(1.12247 - 2.59616i) q^{8} +(-1.28618 + 2.71030i) q^{9} +(-2.22969 + 2.24243i) q^{10} +(-1.98069 - 3.43065i) q^{11} +(2.37491 - 2.52187i) q^{12} +(2.82558 - 0.757112i) q^{13} +(-1.57762 + 1.19775i) q^{14} +(-3.50254 + 1.65293i) q^{15} +(-3.50440 + 1.92852i) q^{16} +(1.31735 - 1.31735i) q^{17} +(3.78627 - 1.91420i) q^{18} -2.06739 q^{19} +(4.43520 - 0.573623i) q^{20} +(-2.31612 + 0.721686i) q^{21} +(-0.759712 + 5.55047i) q^{22} +(-3.03544 + 0.813345i) q^{23} +(-4.83966 + 0.760047i) q^{24} +(-4.84966 - 1.21688i) q^{25} +(-3.81386 - 1.60272i) q^{26} +(5.15830 - 0.626043i) q^{27} +(2.80110 + 0.0287310i) q^{28} +(-1.85856 + 1.07304i) q^{29} +(5.34677 + 1.18830i) q^{30} +(-2.84205 + 4.92257i) q^{31} +(5.58768 + 0.881920i) q^{32} +(-3.18871 + 6.07532i) q^{33} +(-2.61390 + 0.330498i) q^{34} +(-2.90296 - 1.17540i) q^{35} +(-5.89027 - 1.14222i) q^{36} +(-7.93663 + 7.93663i) q^{37} +(2.31039 + 1.79173i) q^{38} +(-3.72398 - 3.43559i) q^{39} +(-5.45365 - 3.20276i) q^{40} +(3.68264 + 2.12617i) q^{41} +(3.21382 + 1.20078i) q^{42} +(2.94123 - 10.9768i) q^{43} +(5.65939 - 5.54447i) q^{44} +(5.66206 + 3.59737i) q^{45} +(4.09713 + 1.72176i) q^{46} +(-7.22530 - 1.93601i) q^{47} +(6.06723 + 3.34496i) q^{48} +(4.36325 + 2.51912i) q^{49} +(4.36507 + 5.56292i) q^{50} +(-3.14798 - 0.709044i) q^{51} +(2.87313 + 5.09643i) q^{52} +(4.33765 - 4.33765i) q^{53} +(-6.30718 - 3.77087i) q^{54} +(-8.15633 + 3.45494i) q^{55} +(-3.10545 - 2.45971i) q^{56} +(1.91377 + 3.02651i) q^{57} +(3.00698 + 0.411575i) q^{58} +(2.91329 + 1.68199i) q^{59} +(-4.94538 - 5.96181i) q^{60} +(-2.46738 + 1.42455i) q^{61} +(7.44231 - 3.03808i) q^{62} +(3.20052 + 2.72258i) q^{63} +(-5.48014 - 5.82821i) q^{64} +(-0.905487 - 6.47809i) q^{65} +(8.82876 - 4.02588i) q^{66} +(-1.23200 - 4.59790i) q^{67} +(3.20757 + 1.89602i) q^{68} +(4.00058 + 3.69077i) q^{69} +(2.22550 + 3.82944i) q^{70} -9.27042i q^{71} +(5.59271 + 6.38135i) q^{72} +(11.3570 - 11.3570i) q^{73} +(15.7479 - 1.99114i) q^{74} +(2.70788 + 8.22602i) q^{75} +(-1.02914 - 4.00465i) q^{76} +(-5.35934 + 1.43603i) q^{77} +(1.18421 + 7.06685i) q^{78} +(14.4576 - 8.34709i) q^{79} +(3.31897 + 8.30569i) q^{80} +(-5.69150 - 6.97186i) q^{81} +(-2.27283 - 5.56769i) q^{82} +(-14.5118 - 3.88841i) q^{83} +(-2.55091 - 4.12721i) q^{84} +(-2.56229 - 3.28465i) q^{85} +(-12.8001 + 9.71801i) q^{86} +(3.29132 + 1.72749i) q^{87} +(-11.1298 + 1.29140i) q^{88} +3.86335 q^{89} +(-3.20989 - 8.92729i) q^{90} -4.09719i q^{91} +(-3.08653 - 5.47496i) q^{92} +(9.83717 - 0.396244i) q^{93} +(6.39670 + 8.42546i) q^{94} +(-0.566818 + 4.58794i) q^{95} +(-3.88142 - 8.99636i) q^{96} +(2.60272 - 9.71349i) q^{97} +(-2.69289 - 6.59669i) q^{98} +(11.8456 - 0.955839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 6 q^{2} - 8 q^{6}+O(q^{10}) \) 256 * q + 6 * q^2 - 8 * q^6	\( 256 q + 6 q^{2} - 8 q^{6} - 10 q^{12} + 28 q^{15} + 12 q^{16} - 28 q^{18} - 54 q^{20} + 14 q^{22} - 28 q^{25} - 32 q^{28} + 14 q^{30} - 32 q^{31} - 114 q^{32} + 4 q^{33} - 40 q^{36} - 30 q^{38} + 46 q^{40} + 24 q^{41} - 10 q^{42} - 16 q^{46} + 24 q^{47} - 2 q^{48} + 78 q^{50} + 38 q^{52} - 8 q^{55} - 96 q^{56} - 80 q^{57} - 18 q^{58} - 2 q^{60} - 144 q^{63} - 84 q^{65} - 4 q^{66} - 30 q^{68} - 30 q^{70} - 86 q^{72} + 64 q^{73} + 16 q^{76} - 82 q^{78} + 72 q^{81} - 64 q^{82} + 48 q^{86} - 4 q^{87} + 38 q^{88} + 78 q^{90} - 108 q^{92} - 24 q^{95} - 116 q^{96} + 36 q^{97}+O(q^{100}) \) 256 * q + 6 * q^2 - 8 * q^6 - 10 * q^12 + 28 * q^15 + 12 * q^16 - 28 * q^18 - 54 * q^20 + 14 * q^22 - 28 * q^25 - 32 * q^28 + 14 * q^30 - 32 * q^31 - 114 * q^32 + 4 * q^33 - 40 * q^36 - 30 * q^38 + 46 * q^40 + 24 * q^41 - 10 * q^42 - 16 * q^46 + 24 * q^47 - 2 * q^48 + 78 * q^50 + 38 * q^52 - 8 * q^55 - 96 * q^56 - 80 * q^57 - 18 * q^58 - 2 * q^60 - 144 * q^63 - 84 * q^65 - 4 * q^66 - 30 * q^68 - 30 * q^70 - 86 * q^72 + 64 * q^73 + 16 * q^76 - 82 * q^78 + 72 * q^81 - 64 * q^82 + 48 * q^86 - 4 * q^87 + 38 * q^88 + 78 * q^90 - 108 * q^92 - 24 * q^95 - 116 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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