LMFDB - Embedded newform 360.2.br.e.77.3

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			77.3
Character	$\chi$	$=$	360.77
Dual form			360.2.br.e.173.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40115 + 0.191780i) q^{2} +(0.925695 + 1.46393i) q^{3} +(1.92644 - 0.537425i) q^{4} +(-0.274171 + 2.21920i) q^{5} +(-1.57779 - 1.87365i) q^{6} +(0.362508 - 1.35290i) q^{7} +(-2.59616 + 1.12247i) q^{8} +(-1.28618 + 2.71030i) q^{9} +O(q^{10})$	\(q+(-1.40115 + 0.191780i) q^{2} +(0.925695 + 1.46393i) q^{3} +(1.92644 - 0.537425i) q^{4} +(-0.274171 + 2.21920i) q^{5} +(-1.57779 - 1.87365i) q^{6} +(0.362508 - 1.35290i) q^{7} +(-2.59616 + 1.12247i) q^{8} +(-1.28618 + 2.71030i) q^{9} +(-0.0414427 - 3.16201i) q^{10} +(1.98069 + 3.43065i) q^{11} +(2.57005 + 2.32268i) q^{12} +(-2.82558 + 0.757112i) q^{13} +(-0.248469 + 1.96514i) q^{14} +(-3.50254 + 1.65293i) q^{15} +(3.42235 - 2.07063i) q^{16} +(1.31735 - 1.31735i) q^{17} +(1.28234 - 4.04420i) q^{18} +2.06739 q^{19} +(0.664477 + 4.42250i) q^{20} +(2.31612 - 0.721686i) q^{21} +(-3.43317 - 4.42700i) q^{22} +(-3.03544 + 0.813345i) q^{23} +(-4.04647 - 2.76154i) q^{24} +(-4.84966 - 1.21688i) q^{25} +(3.81386 - 1.60272i) q^{26} +(-5.15830 + 0.626043i) q^{27} +(-0.0287310 - 2.80110i) q^{28} +(1.85856 - 1.07304i) q^{29} +(4.59059 - 2.98772i) q^{30} +(-2.84205 + 4.92257i) q^{31} +(-4.39812 + 3.55761i) q^{32} +(-3.18871 + 6.07532i) q^{33} +(-1.59317 + 2.09845i) q^{34} +(2.90296 + 1.17540i) q^{35} +(-1.02116 + 5.91246i) q^{36} +(7.93663 - 7.93663i) q^{37} +(-2.89672 + 0.396484i) q^{38} +(-3.72398 - 3.43559i) q^{39} +(-1.77918 - 6.06915i) q^{40} +(3.68264 + 2.12617i) q^{41} +(-3.10683 + 1.45538i) 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} +(6.19931 + 3.09330i) q^{48} +(4.36325 + 2.51912i) q^{49} +(7.02847 + 0.774961i) q^{50} +(3.14798 + 0.709044i) q^{51} +(-5.03642 + 2.97707i) q^{52} +(-4.33765 + 4.33765i) q^{53} +(7.10749 - 1.86644i) q^{54} +(-8.15633 + 3.45494i) q^{55} +(0.577452 + 3.91925i) q^{56} +(1.91377 + 3.02651i) q^{57} +(-2.39833 + 1.85992i) q^{58} +(-2.91329 - 1.68199i) q^{59} +(-5.85912 + 5.06663i) q^{60} +(2.46738 - 1.42455i) q^{61} +(3.03808 - 7.44231i) q^{62} +(3.20052 + 2.72258i) q^{63} +(5.48014 - 5.82821i) q^{64} +(-0.905487 - 6.47809i) q^{65} +(3.30274 - 9.12396i) q^{66} +(1.23200 + 4.59790i) q^{67} +(1.82982 - 3.24578i) q^{68} +(-4.00058 - 3.69077i) q^{69} +(-4.29290 - 1.09019i) q^{70} -9.27042i q^{71} +(0.296905 - 8.48009i) q^{72} +(11.3570 - 11.3570i) q^{73} +(-9.59832 + 12.6425i) q^{74} +(-2.70788 - 8.22602i) q^{75} +(3.98270 - 1.11107i) q^{76} +(5.35934 - 1.43603i) q^{77} +(5.87674 + 4.09960i) q^{78} +(14.4576 - 8.34709i) q^{79} +(3.65683 + 8.16257i) q^{80} +(-5.69150 - 6.97186i) q^{81} +(-5.56769 - 2.27283i) q^{82} +(14.5118 + 3.88841i) q^{83} +(4.07402 - 2.63503i) q^{84} +(2.56229 + 3.28465i) q^{85} +(2.01597 - 15.9443i) q^{86} +(3.29132 + 1.72749i) q^{87} +(-8.99297 - 6.68328i) q^{88} +3.86335 q^{89} +(8.62330 + 3.95458i) q^{90} +4.09719i q^{91} +(-5.41049 + 3.19818i) q^{92} +(-9.83717 + 0.396244i) q^{93} +(10.4950 + 1.32698i) q^{94} +(-0.566818 + 4.58794i) q^{95} +(-9.27940 - 3.14527i) q^{96} +(2.60272 - 9.71349i) q^{97} +(-6.59669 - 2.69289i) 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 $

$2$	−1.40115	+	0.191780i	−0.990762	+	0.135609i
$2$	−1.40115	+	0.191780i	−0.990762	+	0.135609i
$3$	0.925695	+	1.46393i	0.534450	+	0.845200i
$3$	0.925695	+	1.46393i	0.534450	+	0.845200i
$4$	1.92644	−	0.537425i	0.963220	−	0.268712i
$5$	−0.274171	+	2.21920i	−0.122613	+	0.992455i
$5$	−0.274171	+	2.21920i	−0.122613	+	0.992455i
$6$	−1.57779	−	1.87365i	−0.644130	−	0.764916i
$7$	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	$-0.00193736\pi$
$8$	−2.59616	+	1.12247i	−0.917883	+	0.396851i
$9$	−1.28618	+	2.71030i	−0.428726	+	0.903435i
$10$	−0.0414427	−	3.16201i	−0.0131053	−	0.999914i
$11$	1.98069	+	3.43065i	0.597199	+	1.03438i	0.993232	+	0.116143i	$0.0370531\pi$
$11$	1.98069	+	3.43065i	0.597199	+	1.03438i	−0.396033	+	0.918236i	$0.629614\pi$
$12$	2.57005	+	2.32268i	0.741909	+	0.670500i
$13$	−2.82558	+	0.757112i	−0.783675	+	0.209985i	−0.628404	−	0.777887i	$-0.716292\pi$
$13$	−2.82558	+	0.757112i	−0.783675	+	0.209985i	−0.155271	+	0.987872i	$0.549625\pi$
$14$	−0.248469	+	1.96514i	−0.0664063	+	0.525205i
$15$	−3.50254	+	1.65293i	−0.904353	+	0.426785i
$16$	3.42235	−	2.07063i	0.855587	−	0.517659i
$17$	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	$0.177460\pi$
$18$	1.28234	−	4.04420i	0.302252	−	0.953228i
$19$	2.06739			0.474292			0.237146	−	0.971474i	$-0.423788\pi$
$19$	2.06739			0.474292			0.237146	+	0.971474i	$0.423788\pi$
$20$	0.664477	+	4.42250i	0.148582	+	0.988900i
$21$	2.31612	−	0.721686i	0.505419	−	0.157485i
$22$	−3.43317	−	4.42700i	−0.731954	−	0.943839i
$23$	−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	$0.522917\pi$
$24$	−4.04647	−	2.76154i	−0.825982	−	0.563697i
$25$	−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
$28$	−0.0287310	−	2.80110i	−0.00542965	−	0.529359i
$29$	1.85856	−	1.07304i	0.345126	−	0.199259i	−0.317410	−	0.948288i	$-0.602813\pi$
$29$	1.85856	−	1.07304i	0.345126	−	0.199259i	0.662536	+	0.749030i	$0.269480\pi$
$30$	4.59059	−	2.98772i	0.838123	−	0.545481i
$31$	−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	$0.996147\pi$
$32$	−4.39812	+	3.55761i	−0.777485	+	0.628902i
$33$	−3.18871	+	6.07532i	−0.555084	+	1.05758i
$34$	−1.59317	+	2.09845i	−0.273226	+	0.359881i
$35$	2.90296	+	1.17540i	0.490690	+	0.198679i
$36$	−1.02116	+	5.91246i	−0.170193	+	0.985411i
$37$	7.93663	−	7.93663i	1.30477	−	1.30477i	0.379638	−	0.925135i	$-0.376048\pi$
$37$	7.93663	−	7.93663i	1.30477	−	1.30477i	0.925135	−	0.379638i	$-0.123952\pi$
$38$	−2.89672	+	0.396484i	−0.469910	+	0.0643182i
$39$	−3.72398	−	3.43559i	−0.596315	−	0.550135i
$40$	−1.77918	−	6.06915i	−0.281313	−	0.959616i
$41$	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	$0.558926\pi$
$42$	−3.10683	+	1.45538i	−0.479394	+	0.224569i
$43$	−2.94123	+	10.9768i	−0.448534	+	1.67395i	0.257900	+	0.966172i	$0.416970\pi$
$43$	−2.94123	+	10.9768i	−0.448534	+	1.67395i	−0.706433	+	0.707779i	$0.749697\pi$
$44$	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	$0.767012\pi$
$48$	6.19931	+	3.09330i	0.894794	+	0.446479i
$49$	4.36325	+	2.51912i	0.623322	+	0.359875i
$50$	7.02847	+	0.774961i	0.993976	+	0.109596i
$51$	3.14798	+	0.709044i	0.440805	+	0.0992861i
$52$	−5.03642	+	2.97707i	−0.698426	+	0.412845i
$53$	−4.33765	+	4.33765i	−0.595822	+	0.595822i	−0.939198	−	0.343376i	$-0.888429\pi$
$53$	−4.33765	+	4.33765i	−0.595822	+	0.595822i	0.343376	+	0.939198i	$0.388429\pi$
$54$	7.10749	−	1.86644i	0.967207	−	0.253990i
$55$	−8.15633	+	3.45494i	−1.09980	+	0.465865i
$56$	0.577452	+	3.91925i	0.0771652	+	0.523732i
$57$	1.91377	+	3.02651i	0.253485	+	0.400871i
$58$	−2.39833	+	1.85992i	−0.314917	+	0.244220i
$59$	−2.91329	−	1.68199i	−0.379278	−	0.218976i	0.298226	−	0.954495i	$-0.403605\pi$
$59$	−2.91329	−	1.68199i	−0.379278	−	0.218976i	−0.677504	+	0.735519i	$0.736938\pi$
$60$	−5.85912	+	5.06663i	−0.756409	+	0.654099i
$61$	2.46738	−	1.42455i	0.315916	−	0.182394i	−0.333655	−	0.942695i	$-0.608282\pi$
$61$	2.46738	−	1.42455i	0.315916	−	0.182394i	0.649571	+	0.760301i	$0.274949\pi$
$62$	3.03808	−	7.44231i	0.385837	−	0.945174i
$63$	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
$66$	3.30274	−	9.12396i	0.406540	−	1.12308i
$67$	1.23200	+	4.59790i	0.150513	+	0.561723i	0.999448	+	0.0332254i	$0.0105779\pi$
$67$	1.23200	+	4.59790i	0.150513	+	0.561723i	−0.848935	+	0.528498i	$0.822755\pi$
$68$	1.82982	−	3.24578i	0.221899	−	0.393609i
$69$	−4.00058	−	3.69077i	−0.481613	−	0.444316i
$70$	−4.29290	−	1.09019i	−0.513100	−	0.130302i
$71$		−	9.27042i		−	1.10020i	−0.835100	−	0.550098i	$-0.814590\pi$
$71$		−	9.27042i		−	1.10020i	0.835100	−	0.550098i	$-0.185410\pi$
$72$	0.296905	−	8.48009i	0.0349906	−	0.999388i
$73$	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	$-0.139095\pi$
$74$	−9.59832	+	12.6425i	−1.11578	+	1.46966i
$75$	−2.70788	−	8.22602i	−0.312679	−	0.949859i
$76$	3.98270	−	1.11107i	0.456847	−	0.127448i
$77$	5.35934	−	1.43603i	0.610753	−	0.163651i
$78$	5.87674	+	4.09960i	0.665409	+	0.464188i
$79$	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	$-0.0550248\pi$
$80$	3.65683	+	8.16257i	0.408847	+	0.912603i
$81$	−5.69150	−	6.97186i	−0.632389	−	0.774651i
$82$	−5.56769	−	2.27283i	−0.614848	−	0.250992i
$83$	14.5118	+	3.88841i	1.59287	+	0.426809i	0.942880	−	0.333133i	$-0.108106\pi$
$83$	14.5118	+	3.88841i	1.59287	+	0.426809i	0.649992	+	0.759941i	$0.274772\pi$
$84$	4.07402	−	2.63503i	0.444512	−	0.287505i
$85$	2.56229	+	3.28465i	0.277919	+	0.356270i
$86$	2.01597	−	15.9443i	0.217388	−	1.71931i
$87$	3.29132	+	1.72749i	0.352866	+	0.185207i
$88$	−8.99297	−	6.68328i	−0.958654	−	0.712440i
$89$	3.86335			0.409514			0.204757	−	0.978813i	$-0.434360\pi$
$89$	3.86335			0.409514			0.204757	+	0.978813i	$0.434360\pi$
$90$	8.62330	+	3.95458i	0.908976	+	0.416849i
$91$			4.09719i			0.429502i
$92$	−5.41049	+	3.19818i	−0.564083	+	0.333434i
$93$	−9.83717	+	0.396244i	−1.02007	+	0.0410885i
$94$	10.4950	+	1.32698i	1.08248	+	0.136867i
$95$	−0.566818	+	4.58794i	−0.0581543	+	0.470713i
$96$	−9.27940	−	3.14527i	−0.947075	−	0.321013i
$97$	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	$-0.0872151\pi$
$98$	−6.59669	−	2.69289i	−0.666366	−	0.272023i
$99$	−11.8456	+	0.955839i	−1.19053	+	0.0960654i
$100$	−9.99657	+	0.262084i	−0.999657	+	0.0262084i
$101$	−3.84696	−	6.66314i	−0.382787	−	0.663007i	0.608672	−	0.793422i	$-0.291702\pi$
$101$	−3.84696	−	6.66314i	−0.382787	−	0.663007i	−0.991460	+	0.130415i	$0.958369\pi$
$102$	−4.54677	−	0.389758i	−0.450197	−	0.0385918i
$103$	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	$0.788217\pi$
$104$	6.48584	−	5.13720i	0.635989	−	0.503744i
$105$	0.966549	+	5.33779i	0.0943256	+	0.520915i
$106$	5.24582	−	6.90957i	0.509519	−	0.671117i
$107$	1.77242	+	1.77242i	0.171347	+	0.171347i	0.787571	−	0.616224i	$-0.211338\pi$
$107$	1.77242	+	1.77242i	0.171347	+	0.171347i	−0.616224	+	0.787571i	$0.711338\pi$
$108$	−9.60071	+	3.97823i	−0.923829	+	0.382806i
$109$	−0.548826			−0.0525680			−0.0262840	−	0.999655i	$-0.508367\pi$
$109$	−0.548826			−0.0525680			−0.0262840	+	0.999655i	$0.508367\pi$
$110$	10.7656	−	6.40512i	1.02646	−	0.610704i
$111$	18.9656	+	4.27176i	1.80013	+	0.405458i
$112$	−1.56073	−	5.38072i	−0.147475	−	0.508430i
$113$	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	$0.204187\pi$
$114$	−3.26190	−	3.87357i	−0.305505	−	0.362793i
$115$	−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
$118$	4.40453	+	1.79801i	0.405469	+	0.165520i
$119$	−1.30470	−	2.25980i	−0.119601	−	0.207155i
$120$	7.23782	−	8.22277i	0.660720	−	0.750633i
$121$	−2.34623	+	4.06379i	−0.213294	+	0.369436i
$122$	−3.18398	+	2.46920i	−0.288264	+	0.223550i
$123$	0.296435	+	7.35931i	0.0267286	+	0.663567i
$124$	−2.82953	+	11.0104i	−0.254099	+	0.988766i
$125$	4.03013	−	10.4287i	0.360466	−	0.932773i
$126$	−5.00654	−	3.20094i	−0.446018	−	0.285163i
$127$	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	$0.510431\pi$
$128$	−6.56077	+	9.21718i	−0.579895	+	0.814691i
$129$	−18.7920	+	5.85544i	−1.65454	+	0.515543i
$130$	2.51109	+	8.90312i	0.220237	+	0.780856i
$131$	3.24235	−	5.61591i	0.283285	−	0.490665i	−0.688907	−	0.724850i	$-0.741909\pi$
$131$	3.24235	−	5.61591i	0.283285	−	0.490665i	0.972192	+	0.234186i	$0.0752423\pi$
$132$	−2.87784	+	13.4174i	−0.250484	+	1.16784i
$133$	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	$0.782406\pi$
$138$	6.31322	+	4.40409i	0.537417	+	0.374901i
$139$	−5.63375	+	9.75794i	−0.477849	+	0.827658i	−0.999678	−	0.0253921i	$-0.991917\pi$
$139$	−5.63375	+	9.75794i	−0.477849	+	0.827658i	0.521829	+	0.853050i	$0.325250\pi$
$140$	6.22407	+	0.704221i	0.526030	+	0.0595176i
$141$	−3.85424	−	12.3695i	−0.324585	−	1.04170i
$142$	1.77788	+	12.9892i	0.149196	+	1.09003i
$143$	−8.19397	−	8.19397i	−0.685214	−	0.685214i
$144$	1.21030	+	11.9388i	0.100859	+	0.994901i
$145$	1.87172	+	4.41871i	0.155438	+	0.366954i
$146$	−13.7348	+	18.0909i	−1.13670	+	1.49722i
$147$	0.351221	+	8.71943i	0.0289682	+	0.719167i
$148$	11.0241	−	19.5548i	0.906176	−	1.60739i
$149$	6.89791	+	3.98251i	0.565099	+	0.326260i	0.755190	−	0.655506i	$-0.227545\pi$
$149$	6.89791	+	3.98251i	0.565099	+	0.326260i	−0.190090	+	0.981767i	$0.560878\pi$
$150$	5.37173	+	11.0066i	0.438600	+	0.898682i
$151$	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	$0.680375\pi$
$152$	−5.36728	+	2.32057i	−0.435344	+	0.188223i
$153$	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
$156$	−9.02041	−	4.61711i	−0.722211	−	0.369664i
$157$	0.644729	+	2.40616i	0.0514550	+	0.192033i	0.986869	−	0.161521i	$-0.0516399\pi$
$157$	0.644729	+	2.40616i	0.0514550	+	0.192033i	−0.935414	+	0.353553i	$0.884973\pi$
$158$	−18.6564	+	14.4682i	−1.48423	+	1.15103i
$159$	−10.3653	−	2.33467i	−0.822026	−	0.185151i
$160$	−6.68919	−	10.7357i	−0.528827	−	0.848730i
$161$			4.40150i			0.346887i
$162$	9.31170	+	8.67711i	0.731596	+	0.681738i
$163$	−8.93471	−	8.93471i	−0.699821	−	0.699821i	0.264551	−	0.964372i	$-0.414776\pi$
$163$	−8.93471	−	8.93471i	−0.699821	−	0.699821i	−0.964372	+	0.264551i	$0.914776\pi$
$164$	8.23705	+	2.11681i	0.643205	+	0.165295i
$165$	−12.6081	−	8.74206i	−0.981537	−	0.680568i
$166$	−21.0789	−	2.66518i	−1.63604	−	0.206858i
$167$	−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	$0.995284\pi$
$168$	−5.20297	+	4.47338i	−0.401418	+	0.345129i
$169$	−3.84765	+	2.22144i	−0.295973	+	0.170880i
$170$	−4.22007	−	4.11088i	−0.323665	−	0.315290i
$171$	−2.65903	+	5.60325i	−0.203341	+	0.428491i
$172$	0.233111	+	22.7269i	0.0177745	+	1.73291i
$173$	7.18387	+	1.92491i	0.546179	+	0.146348i	0.521349	−	0.853343i	$-0.325429\pi$
$173$	7.18387	+	1.92491i	0.546179	+	0.146348i	0.0248300	+	0.999692i	$0.492096\pi$
$174$	−4.94292	−	1.78927i	−0.374722	−	0.135644i
$175$	−3.40436	+	6.11998i	−0.257345	+	0.462627i
$176$	13.8822	+	7.63960i	1.04641	+	0.575856i
$177$	−0.234506	−	5.82186i	−0.0176265	−	0.437598i
$178$	−5.41313	+	0.740913i	−0.405732	+	0.0555338i
$179$		−	7.49932i		−	0.560525i	−0.959923	−	0.280263i	$-0.909578\pi$
$179$		−	7.49932i		−	0.560525i	0.959923	−	0.280263i	$-0.0904215\pi$
$180$	−12.8409	−	3.88718i	−0.957107	−	0.289733i
$181$			23.0395i			1.71251i	0.516552	+	0.856256i	$0.327215\pi$
$181$			23.0395i			1.71251i	−0.516552	+	0.856256i	$0.672785\pi$
$182$	−0.785758	−	5.74077i	−0.0582443	−	0.425534i
$183$	4.36948	+	2.29338i	0.323001	+	0.169532i
$184$	6.96756	−	5.51876i	0.513656	−	0.406848i
$185$	15.4369	+	19.7889i	1.13495	+	1.45491i
$186$	13.7074	−	2.44177i	1.00507	−	0.179039i
$187$	7.12864	+	1.91011i	0.521298	+	0.139681i
$188$	−14.9596	+	0.153441i	−1.09104	+	0.0111908i
$189$	−1.02295	+	7.20561i	−0.0744090	+	0.524131i
$190$	−0.0856781	−	6.53710i	−0.00621574	−	0.474251i
$191$	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	$0.274658\pi$
$192$	13.6050	+	2.62739i	0.981858	+	0.189616i
$193$	−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	$-0.382486\pi$
$194$	−1.78395	+	14.1092i	−0.128080	+	1.01298i
$195$	8.64526	−	7.32231i	0.619100	−	0.524361i
$196$	9.75939	+	2.50802i	0.697099	+	0.179145i
$197$	0.144636	+	0.144636i	0.0103049	+	0.0103049i	0.712240	−	0.701936i	$-0.247681\pi$
$197$	0.144636	+	0.144636i	0.0103049	+	0.0103049i	−0.701936	+	0.712240i	$0.747681\pi$
$198$	16.4142	−	3.61102i	1.16650	−	0.256624i
$199$			1.78089i			0.126244i	0.998006	+	0.0631220i	$0.0201057\pi$
$199$			1.78089i			0.126244i	−0.998006	+	0.0631220i	$0.979894\pi$
$200$	13.9564	−	2.28436i	0.986868	−	0.161529i
$201$	−5.59055	+	6.05983i	−0.394327	+	0.427427i
$202$	6.66803	+	8.59828i	0.469161	+	0.604973i
$203$	−0.777972	−	2.90343i	−0.0546030	−	0.203781i
$204$	6.44545	−	0.325870i	0.451272	−	0.0228155i
$205$	−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
$208$	−8.10242	+	8.44184i	−0.561802	+	0.585337i
$209$	4.09485	+	7.09248i	0.283247	+	0.490597i
$210$	−2.37796	−	7.29368i	−0.164095	−	0.503312i
$211$	−6.03211	−	3.48264i	−0.415267	−	0.239755i	0.277783	−	0.960644i	$-0.410400\pi$
$211$	−6.03211	−	3.48264i	−0.415267	−	0.239755i	−0.693050	+	0.720889i	$0.743734\pi$
$212$	−6.02506	+	10.6874i	−0.413803	+	0.734012i
$213$	13.5712	−	8.58158i	0.929886	−	0.588000i
$214$	−2.82334	−	2.14351i	−0.193000	−	0.146528i
$215$	−23.5533	−	9.53670i	−1.60632	−	0.650398i
$216$	12.6891	−	7.41533i	0.863383	−	0.504549i
$217$	5.62948	+	5.62948i	0.382154	+	0.382154i
$218$	0.768987	−	0.105254i	0.0520824	−	0.00712869i
$219$	27.1390	+	6.11274i	1.83388	+	0.413060i
$220$	−13.8559	+	11.0392i	−0.934165	+	0.744260i
$221$	−2.72490	+	4.71967i	−0.183297	+	0.317479i
$222$	−27.3928	−	2.34817i	−1.83849	−	0.157599i
$223$	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	$-0.755636\pi$
$227$	3.77930	−	14.1046i	0.250841	−	0.936152i	0.970357	−	0.241676i	$-0.0776971\pi$
$228$	5.31329	+	4.80189i	0.351881	+	0.318013i
$229$	−6.35644	+	11.0097i	−0.420046	+	0.727540i	−0.995943	−	0.0899814i	$-0.971319\pi$
$229$	−6.35644	+	11.0097i	−0.420046	+	0.727540i	0.575898	+	0.817522i	$0.304653\pi$
$230$	2.69760	+	9.56439i	0.177874	+	0.630657i
$231$	7.06336	+	6.51637i	0.464735	+	0.428745i
$232$	−3.62068	+	4.87196i	−0.237709	+	0.319860i
$233$	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	$0.579466\pi$
$234$	−0.561452	+	12.3981i	−0.0367033	+	0.810489i
$235$	6.27736	−	15.5035i	0.409490	−	1.01134i
$236$	−6.51622	−	1.67458i	−0.424170	−	0.109006i
$237$	25.6029	+	13.4380i	1.66308	+	0.872893i
$238$	2.26146	+	2.91610i	0.146589	+	0.189023i
$239$	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	$0.0680787\pi$
$240$	−8.56431	+	12.9094i	−0.552824	+	0.833298i
$241$	−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	$-0.352044\pi$
$242$	2.50807	−	6.14394i	0.161225	−	0.394947i
$243$	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
$246$	−1.82672	−	10.2547i	−0.116467	−	0.653813i
$247$	−5.84157	+	1.56524i	−0.371690	+	0.0995941i
$248$	1.85301	−	15.9699i	0.117666	−	1.01409i
$249$	7.74110	+	24.8437i	0.490572	+	1.57440i
$250$	−3.64679	+	15.3851i	−0.230644	+	0.973038i
$251$	−23.9116			−1.50929			−0.754643	−	0.656136i	$-0.772190\pi$
$251$	−23.9116			−1.50929			−0.754643	+	0.656136i	$0.772190\pi$
$252$	7.62879	+	3.52484i	0.480569	+	0.222044i
$253$	−8.80256	−	8.80256i	−0.553412	−	0.553412i
$254$	−17.3536	−	13.1751i	−1.08886	−	0.826676i
$255$	−2.43659	+	6.79158i	−0.152585	+	0.425305i
$256$	7.42494	−	14.1729i	0.464059	−	0.885804i
$257$	−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	$-0.424223\pi$
$258$	25.2074	−	11.8083i	1.56935	−	0.735151i
$259$	−7.86037	−	13.6146i	−0.488419	−	0.845967i
$260$	−5.22586	−	11.9930i	−0.324094	−	0.743776i
$261$	0.517828	+	6.41738i	0.0320527	+	0.397226i
$262$	−3.46600	+	8.49055i	−0.214130	+	0.524548i
$263$	−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	$0.814705\pi$
$264$	1.45909	−	19.3517i	0.0898011	−	1.19102i
$265$	−8.43683	−	10.8153i	−0.518270	−	0.664381i
$266$	−0.513683	+	4.06270i	−0.0314959	+	0.249100i
$267$	3.57629	+	5.65567i	0.218865	+	0.346122i
$268$	4.84441	+	8.19548i	0.295920	+	0.500619i
$269$		−	25.2891i		−	1.54190i	−0.636895	−	0.770950i	$-0.719782\pi$
$269$		−	25.2891i		−	1.54190i	0.636895	−	0.770950i	$-0.280218\pi$
$270$	2.19333	+	16.2846i	0.133482	+	0.991051i
$271$	−12.8895			−0.782981			−0.391490	−	0.920182i	$-0.628040\pi$
$271$	−12.8895			−0.782981			−0.391490	+	0.920182i	$0.628040\pi$
$272$	1.78069	−	7.23620i	0.107970	−	0.438759i
$273$	−5.99799	+	3.79274i	−0.363015	+	0.229547i
$274$	19.2279	+	2.43116i	1.16160	+	0.146872i
$275$	−5.43097	−	19.0477i	−0.327500	−	1.14862i
$276$	−9.69038	−	4.96003i	−0.583293	−	0.298559i
$277$	−13.3573	−	3.57907i	−0.802560	−	0.215045i	−0.165852	−	0.986151i	$-0.553037\pi$
$277$	−13.3573	−	3.57907i	−0.802560	−	0.215045i	−0.636708	+	0.771105i	$0.719704\pi$
$278$	6.02235	−	14.7528i	0.361197	−	0.884813i
$279$	−9.68629	−	14.0341i	−0.579903	−	0.840201i
$280$	−8.85591	+	0.206933i	−0.529242	+	0.0123666i
$281$	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	$0.292815\pi$
$282$	7.77258	+	16.5923i	0.462850	+	0.988058i
$283$	−18.3652	+	4.92094i	−1.09170	+	0.292519i	−0.759379	−	0.650648i	$-0.774497\pi$
$283$	−18.3652	+	4.92094i	−1.09170	+	0.292519i	−0.332318	+	0.943167i	$0.607831\pi$
$284$	−4.98215	−	17.8589i	−0.295636	−	1.05973i
$285$	−7.24112	+	3.41725i	−0.428927	+	0.202421i
$286$	13.0524	+	9.90954i	0.771806	+	0.585963i
$287$	4.21149	−	4.21149i	0.248596	−	0.248596i
$288$	−3.98544	−	16.4959i	−0.234844	−	0.972033i
$289$			13.5292i			0.795833i
$290$	−3.46998	−	5.83231i	−0.203764	−	0.342485i
$291$	16.6292	−	5.18153i	0.974821	−	0.303747i
$292$	15.7751	−	27.9822i	0.923167	−	1.63753i
$293$	2.08189	+	7.76971i	0.121625	+	0.453912i	0.999697	−	0.0246175i	$-0.00783679\pi$
$293$	2.08189	+	7.76971i	0.121625	+	0.453912i	−0.878072	+	0.478529i	$0.841170\pi$
$294$	−2.16433	−	12.1499i	−0.126226	−	0.708595i
$295$	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
$298$	−10.4288	−	4.25721i	−0.604123	−	0.246614i
$299$	7.96110	−	4.59634i	0.460402	−	0.265813i
$300$	−9.63744	−	14.3917i	−0.556418	−	0.830902i
$301$	13.7843	+	7.95839i	0.794516	+	0.458714i
$302$	−9.84567	−	12.6958i	−0.566555	−	0.730560i
$303$	6.19324	−	11.7997i	0.355793	−	0.677876i
$304$	7.07533	−	4.28081i	0.405798	−	0.245521i
$305$	2.48486	+	5.86618i	0.142283	+	0.335896i
$306$	−3.63835	−	7.01695i	−0.207990	−	0.401132i
$307$	4.70909	−	4.70909i	0.268762	−	0.268762i	−0.559839	−	0.828601i	$-0.689137\pi$
$307$	4.70909	−	4.70909i	0.268762	−	0.268762i	0.828601	+	0.559839i	$0.189137\pi$
$308$	9.55269	−	5.64667i	0.544315	−	0.321749i
$309$	−9.36094	+	10.1467i	−0.532525	+	0.577226i
$310$	15.6830	+	8.78257i	0.890734	+	0.498817i
$311$	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	$0.573614\pi$
$312$	13.5244	+	4.73932i	0.765669	+	0.268311i
$313$	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	$0.419617\pi$
$317$	−8.02391	+	29.9456i	−0.450668	+	1.68191i	−0.700522	+	0.713631i	$0.747049\pi$
$318$	14.9711	+	1.28336i	0.839540	+	0.0719670i
$319$	7.36245	+	4.25071i	0.412218	+	0.237994i
$320$	11.4314	+	13.7594i	0.639037	+	0.769176i
$321$	−0.953978	+	4.23542i	−0.0532459	+	0.236398i
$322$	−0.844119	−	6.16716i	−0.0470409	−	0.343682i
$323$	2.72348	−	2.72348i	0.151539	−	0.151539i
$324$	−14.7112	−	10.3721i	−0.817288	−	0.576229i
$325$	14.6244	−	0.233348i	0.811217	−	0.0129438i
$326$	14.2324	+	10.8054i	0.788258	+	0.598454i
$327$	−0.508046	−	0.803442i	−0.0280950	−	0.0444305i
$328$	−11.9473	−	1.38626i	−0.659679	−	0.0765434i
$329$	−5.23846	+	9.07328i	−0.288806	+	0.500226i
$330$	19.3423	+	9.83096i	1.06476	+	0.541176i
$331$	−27.3462	+	15.7884i	−1.50309	+	0.867807i	−0.503091	+	0.864233i	$0.667804\pi$
$331$	−27.3462	+	15.7884i	−1.50309	+	0.867807i	−0.999994	+	0.00357340i	$0.998863\pi$
$332$	30.0458	−	0.308181i	1.64898	−	0.0169136i
$333$	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
$336$	6.43223	−	7.26570i	0.350907	−	0.396377i
$337$	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	$0.346702\pi$
$338$	4.96510	−	3.85047i	0.270066	−	0.209438i
$339$	16.7546	+	15.4571i	0.909987	+	0.839517i
$340$	6.70134	+	4.95064i	0.363431	+	0.268486i
$341$	−22.5168			−1.21935
$342$	2.65111	−	8.36094i	0.143355	−	0.452108i
$343$	11.9226	−	11.9226i	0.643759	−	0.643759i
$344$	−4.68519	−	31.7991i	−0.252608	−	1.71449i
$345$	9.28738	−	7.86616i	0.500016	−	0.423500i
$346$	−10.4348	−	1.31937i	−0.560980	−	0.0709296i
$347$	−8.87313	+	2.37755i	−0.476335	+	0.127633i	−0.488995	−	0.872286i	$-0.662637\pi$
$347$	−8.87313	+	2.37755i	−0.476335	+	0.127633i	0.0126608	+	0.999920i	$0.495970\pi$
$348$	7.26892	+	1.55908i	0.389655	+	0.0835753i
$349$	−12.9698	−	22.4644i	−0.694260	−	1.20249i	−0.970429	−	0.241385i	$-0.922398\pi$
$349$	−12.9698	−	22.4644i	−0.694260	−	1.20249i	0.276169	−	0.961109i	$-0.410935\pi$
$350$	3.59633	−	9.22789i	0.192232	−	0.493251i
$351$	14.1012	−	5.67434i	0.752667	−	0.302874i
$352$	−20.9162	−	8.04189i	−1.11484	−	0.428634i
$353$	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	$0.0477000\pi$
$354$	1.44509	+	8.11232i	0.0768058	+	0.431165i
$355$	20.5729	+	2.54168i	1.09189	+	0.134898i
$356$	7.44252	−	2.07626i	0.394453	−	0.110042i
$357$	2.10044	−	4.00187i	0.111167	−	0.211801i
$358$	1.43822	+	10.5077i	0.0760122	+	0.555347i
$359$	−1.04667			−0.0552413			−0.0276206	−	0.999618i	$-0.508793\pi$
$359$	−1.04667			−0.0552413			−0.0276206	+	0.999618i	$0.508793\pi$
$360$	18.7376	+	2.98388i	0.987557	+	0.157264i
$361$	−14.7259			−0.775048
$362$	−4.41851	−	32.2818i	−0.232232	−	1.69669i
$363$	−8.12100	+	0.327116i	−0.426242	+	0.0171691i
$364$	2.20193	+	7.89299i	0.115412	+	0.413705i
$365$	22.0897	+	28.3172i	1.15623	+	1.48219i
$366$	−6.56212	−	2.37539i	−0.343007	−	0.124164i
$367$	−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	$0.117788\pi$
$368$	−8.70421	+	9.06885i	−0.453738	+	0.472746i
$369$	−10.4991	+	7.24644i	−0.546562	+	0.377235i
$370$	−25.4246	−	24.7667i	−1.32176	−	1.28756i
$371$	4.29597	+	7.44084i	0.223036	+	0.386309i
$372$	−18.7378	+	6.05008i	−0.971508	+	0.313682i
$373$	31.4295	−	8.42151i	1.62736	−	0.436049i	0.674207	−	0.738543i	$-0.264486\pi$
$373$	31.4295	−	8.42151i	1.62736	−	0.436049i	0.953151	+	0.302494i	$0.0978191\pi$
$374$	−10.3546	−	1.30922i	−0.535424	−	0.0676984i
$375$	18.9976	−	3.75399i	0.981030	−	0.193855i
$376$	20.9312	−	3.08394i	1.07944	−	0.159042i
$377$	−4.43910	+	4.43910i	−0.228625	+	0.228625i
$378$	0.0514201	−	10.2923i	0.00264477	−	0.529380i
$379$	15.2502			0.783348			0.391674	−	0.920104i	$-0.371896\pi$
$379$	15.2502			0.783348			0.391674	+	0.920104i	$0.371896\pi$
$380$	1.37373	+	9.14302i	0.0704710	+	0.469027i
$381$	−5.86360	+	26.0329i	−0.300401	+	1.33371i
$382$	−5.66176	+	4.39074i	−0.289681	+	0.224650i
$383$	−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	$0.720843\pi$
$384$	−19.5666	−	1.07220i	−0.998502	−	0.0547155i
$385$	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
$388$	−0.206282	−	20.1112i	−0.0104724	−	1.02099i
$389$	−20.0659	+	11.5850i	−1.01738	+	0.587385i	−0.913344	−	0.407188i	$-0.866509\pi$
$389$	−20.0659	+	11.5850i	−1.01738	+	0.587385i	−0.104037	+	0.994573i	$0.533176\pi$
$390$	−10.7090	+	11.9176i	−0.542273	+	0.603473i
$391$	−2.92729	+	5.07022i	−0.148039	+	0.256412i
$392$	−14.1554	−	1.64246i	−0.714953	−	0.0829569i
$393$	11.2227	−	0.452054i	0.566112	−	0.0228031i
$394$	−0.230394	−	0.174918i	−0.0116071	−	0.00881224i
$395$	14.5600	+	34.3727i	0.732592	+	1.72948i
$396$	−22.3062	+	8.20749i	−1.12093	+	0.412442i
$397$	1.89719	−	1.89719i	0.0952172	−	0.0952172i	−0.657894	−	0.753111i	$-0.728552\pi$
$397$	1.89719	−	1.89719i	0.0952172	−	0.0952172i	0.753111	+	0.657894i	$0.228552\pi$
$398$	−0.341539	−	2.49529i	−0.0171198	−	0.125078i
$399$	4.78832	−	1.49201i	0.239716	−	0.0746937i
$400$	−19.1169	+	5.87729i	−0.955847	+	0.293865i
$401$	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	$0.604085\pi$
$402$	6.67104	−	9.56288i	0.332721	−	0.476953i
$403$	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
$408$	−8.96855	+	1.69270i	−0.444009	+	0.0838013i
$409$	−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	$0.995971\pi$
$410$	6.57036	−	11.7326i	0.324487	−	0.579434i
$411$	−7.06136	−	22.6622i	−0.348311	−	1.11784i
$412$	8.11160	+	13.7227i	0.399630	+	0.676069i
$413$	−3.33165	+	3.33165i	−0.163940	+	0.163940i
$414$	−0.603153	+	13.3189i	−0.0296433	+	0.654591i
$415$	−12.6078	+	31.1383i	−0.618895	+	1.52852i
$416$	9.73372	−	13.3822i	0.477235	−	0.656115i
$417$	−19.5001	+	0.785468i	−0.954923	+	0.0384645i
$418$	−7.09769	−	9.15232i	−0.347159	−	0.447655i
$419$	−7.44813	−	4.30018i	−0.363865	−	0.210078i	0.306910	−	0.951739i	$-0.400705\pi$
$419$	−7.44813	−	4.30018i	−0.363865	−	0.210078i	−0.670775	+	0.741661i	$0.734038\pi$
$420$	4.73066	+	9.76350i	0.230833	+	0.476410i
$421$	12.3451	−	7.12747i	0.601665	−	0.347372i	−0.168031	−	0.985782i	$-0.553741\pi$
$421$	12.3451	−	7.12747i	0.601665	−	0.347372i	0.769696	+	0.638410i	$0.220408\pi$
$422$	9.11979	+	3.72286i	0.443944	+	0.181226i
$423$	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
$426$	−17.3696	+	14.6268i	−0.841558	+	0.708669i
$427$	−1.03282	−	3.85453i	−0.0499816	−	0.186534i
$428$	4.36701	+	2.46192i	0.211087	+	0.119002i
$429$	4.41027	−	19.5805i	0.212930	−	0.945356i
$430$	34.8307	+	8.84529i	1.67969	+	0.426558i
$431$			2.21175i			0.106536i	0.998580	+	0.0532681i	$0.0169638\pi$
$431$			2.21175i			0.106536i	−0.998580	+	0.0532681i	$0.983036\pi$
$432$	−16.3572	+	12.8235i	−0.786986	+	0.616971i
$433$	−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	$0.392228\pi$
$434$	−8.96737	−	6.80812i	−0.430447	−	0.326800i
$435$	−4.73603	+	6.83045i	−0.227075	+	0.327495i
$436$	−1.05728	+	0.294953i	−0.0506346	+	0.0141257i
$437$	−6.27545	+	1.68150i	−0.300195	+	0.0804371i
$438$	−39.1981	−	3.36014i	−1.87296	−	0.160554i
$439$	−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	$0.429329\pi$
$440$	17.2971	−	18.1248i	0.824607	−	0.864066i
$441$	−12.4395	+	8.58570i	−0.592358	+	0.408843i
$442$	2.91286	−	7.13555i	0.138551	−	0.339403i
$443$	12.0072	+	3.21732i	0.570479	+	0.152859i	0.532516	−	0.846420i	$-0.321247\pi$
$443$	12.0072	+	3.21732i	0.570479	+	0.152859i	0.0379625	+	0.999279i	$0.487913\pi$
$444$	38.8318	−	1.96326i	1.84287	−	0.0931723i
$445$	−1.05922	+	8.57353i	−0.0502118	+	0.406424i
$446$	−1.81506	−	0.229493i	−0.0859454	−	0.0108668i
$447$	0.555249	+	13.7847i	0.0262624	+	0.651992i
$448$	−5.89839	−	9.52686i	−0.278673	−	0.450102i
$449$	18.9764			0.895551			0.447776	−	0.894146i	$-0.352216\pi$
$449$	18.9764			0.895551			0.447776	+	0.894146i	$0.352216\pi$
$450$	−11.1402	+	18.0526i	−0.525156	+	0.851006i
$451$			16.8451i			0.793206i
$452$	22.6594	−	13.3942i	1.06581	−	0.630009i
$453$	−9.14463	+	17.4229i	−0.429652	+	0.818597i
$454$	−2.59040	+	20.4874i	−0.121573	+	0.961521i
$455$	−9.09246	−	1.12333i	−0.426261	−	0.0526625i
$456$	−8.36562	−	5.70918i	−0.391756	−	0.267357i
$457$	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	$-0.0164580\pi$
$458$	6.79489	−	16.6452i	0.317504	−	0.777781i
$459$	−5.97059	+	7.62003i	−0.278683	+	0.355672i
$460$	−5.61400	−	12.8838i	−0.261754	−	0.600710i
$461$	−14.8666	−	25.7497i	−0.692406	−	1.19928i	−0.971047	−	0.238888i	$-0.923217\pi$
$461$	−14.8666	−	25.7497i	−0.692406	−	1.19928i	0.278641	−	0.960395i	$-0.410116\pi$
$462$	−11.1465	−	7.77579i	−0.518584	−	0.361763i
$463$	−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	$-0.291967\pi$
$464$	4.13877	−	7.52072i	0.192137	−	0.349141i
$465$	1.81772	−	21.9392i	0.0842950	−	1.01741i
$466$	−17.5538	−	13.3270i	−0.813164	−	0.617363i
$467$	15.9845	+	15.9845i	0.739674	+	0.739674i	0.972515	−	0.232841i	$-0.0748022\pi$
$467$	15.9845	+	15.9845i	0.739674	+	0.739674i	−0.232841	+	0.972515i	$0.574802\pi$
$468$	−1.59103	−	17.4793i	−0.0735453	−	0.807980i
$469$	6.66712			0.307859
$470$	−5.82225	+	22.9267i	−0.268560	+	1.05753i
$471$	−2.92563	+	3.17121i	−0.134806	+	0.146122i
$472$	9.45135	+	1.09665i	0.435034	+	0.0504775i
$473$	−43.4833	+	11.6513i	−1.99936	+	0.535728i
$474$	−38.4506	−	13.9186i	−1.76609	−	0.639301i
$475$	−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
$478$	−5.03704	+	12.3391i	−0.230389	+	0.564377i
$479$	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	$0.828020\pi$
$480$	9.52412	−	19.7305i	0.434715	−	0.900568i
$481$	−16.4167	+	28.4345i	−0.748535	+	1.29650i
$482$	14.8000	+	19.0843i	0.674121	+	0.869265i
$483$	−6.44348	+	4.07444i	−0.293188	+	0.185394i
$484$	−2.33589	+	9.08958i	−0.106177	+	0.413163i
$485$	20.8426	+	8.43911i	0.946412	+	0.383200i
$486$	−4.08287	+	21.6640i	−0.185203	+	0.982700i
$487$	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	$0.595893\pi$
$488$	−4.80673	+	6.46791i	−0.217591	+	0.292788i
$489$	4.80897	−	21.3506i	0.217469	−	0.965508i
$490$	7.78466	−	13.9010i	0.351675	−	0.627985i
$491$	−1.56899	+	2.71756i	−0.0708073	+	0.122642i	−0.899255	−	0.437424i	$-0.855891\pi$
$491$	−1.56899	+	2.71756i	−0.0708073	+	0.122642i	0.828448	+	0.560066i	$0.189224\pi$
$492$	4.52614	+	14.0180i	0.204054	+	0.631979i
$493$	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
$498$	−15.6110	−	33.3251i	−0.699543	−	1.49333i
$499$	8.15826	−	14.1305i	0.365214	−	0.632569i	−0.623597	−	0.781746i	$-0.714329\pi$
$499$	8.15826	−	14.1305i	0.365214	−	0.632569i	0.988810	+	0.149178i	$0.0476626\pi$
$500$	2.15915	−	22.2562i	0.0965603	−	0.995327i
$501$	7.42117	−	8.04411i	0.331553	−	0.359384i
$502$	33.5037	−	4.58576i	1.49534	−	0.204673i
$503$	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	$0.483389\pi$
$504$	−11.3651	−	3.47578i	−0.506241	−	0.154824i
$505$	15.8415	−	6.71033i	0.704939	−	0.298606i
$506$	14.0219	+	10.6456i	0.623348	+	0.473253i
$507$	−6.81378	−	3.57631i	−0.302611	−	0.158829i
$508$	26.8417	+	15.1321i	1.19091	+	0.671380i
$509$	−3.78199	−	2.18353i	−0.167634	−	0.0967834i	0.413836	−	0.910352i	$-0.364189\pi$
$509$	−3.78199	−	2.18353i	−0.167634	−	0.0967834i	−0.581470	+	0.813568i	$0.697522\pi$
$510$	2.11154	−	9.98332i	0.0935007	−	0.442069i
$511$	−11.2479	−	19.4819i	−0.497578	−	0.861830i
$512$	−7.68539	+	21.2823i	−0.339649	+	0.940552i
$513$	−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
$516$	−33.0548	+	21.3794i	−1.45516	+	0.941178i
$517$	−7.66926	−	28.6221i	−0.337294	−	1.25880i
$518$	13.6245	+	17.5686i	0.598628	+	0.771919i
$519$	3.83214	+	12.2986i	0.168212	+	0.539846i
$520$	9.62223	+	15.8018i	0.421963	+	0.692956i
$521$		−	33.7498i		−	1.47861i	−0.673373	−	0.739303i	$-0.735155\pi$
$521$		−	33.7498i		−	1.47861i	0.673373	−	0.739303i	$-0.264845\pi$
$522$	−1.95628	−	8.89241i	−0.0856240	−	0.389210i
$523$	−0.0847849	−	0.0847849i	−0.00370738	−	0.00370738i	0.705251	−	0.708958i	$-0.250834\pi$
$523$	−0.0847849	−	0.0847849i	−0.00370738	−	0.00370738i	−0.708958	+	0.705251i	$0.750834\pi$
$524$	3.22806	−	12.5612i	0.141019	−	0.548740i
$525$	−12.1106	+	0.681494i	−0.528550	+	0.0297428i
$526$	4.29959	−	34.0054i	0.187471	−	1.48270i
$527$	2.74079	+	10.2288i	0.119390	+	0.445571i
$528$	1.66687	+	27.3945i	0.0725411	+	1.19219i
$529$	−11.3662	+	6.56227i	−0.494182	+	0.285316i
$530$	13.8954	+	13.5359i	0.603579	+	0.587962i
$531$	8.30570	−	5.73256i	0.360437	−	0.248772i
$532$	−0.0593982	−	5.79097i	−0.00257524	−	0.251070i
$533$	−12.0153	−	3.21950i	−0.520442	−	0.139452i
$534$	−6.09556	−	7.23858i	−0.263780	−	0.313244i
$535$	−4.41930	+	3.44741i	−0.191063	+	0.149044i
$536$	−8.35948	−	10.5540i	−0.361074	−	0.455865i
$537$	10.9785	−	6.94208i	0.473756	−	0.299573i
$538$	4.84993	+	35.4337i	0.209095	+	1.52766i
$539$			19.9584i			0.859668i
$540$	−6.19624	−	22.3966i	−0.266644	−	0.963795i
$541$		−	15.3742i		−	0.660986i	−0.943808	−	0.330493i	$-0.892785\pi$
$541$		−	15.3742i		−	0.660986i	0.943808	−	0.330493i	$-0.107215\pi$
$542$	18.0601	−	2.47195i	0.775748	−	0.106179i
$543$	−33.7282	+	21.3275i	−1.44741	+	0.915252i
$544$	−1.10725	+	10.4805i	−0.0474729	+	0.449348i
$545$	0.150472	−	1.21795i	0.00644552	−	0.0521714i
$546$	7.67671	−	6.46450i	0.328533	−	0.276655i
$547$	36.7514	+	9.84751i	1.57138	+	0.421049i	0.936243	−	0.351353i	$-0.114278\pi$
$547$	36.7514	+	9.84751i	1.57138	+	0.421049i	0.635134	+	0.772402i	$0.280945\pi$
$548$	−27.4075	+	0.281119i	−1.17079	+	0.0120088i
$549$	0.687457	+	8.51958i	0.0293399	+	0.363607i
$550$	11.2626	+	25.6472i	0.480238	+	1.09360i
$551$	3.84237	−	2.21839i	0.163690	−	0.0945067i
$552$	14.5289	+	5.09133i	0.618392	+	0.216701i
$553$	−6.05178	−	22.5856i	−0.257348	−	0.960435i
$554$	19.4019	+	2.45315i	0.824308	+	0.104224i
$555$	−14.6797	+	40.9171i	−0.623118	+	1.73683i
$556$	−5.60893	+	21.8258i	−0.237872	+	0.925621i
$557$	13.7557	+	13.7557i	0.582847	+	0.582847i	0.935684	−	0.352838i	$-0.114783\pi$
$557$	13.7557	+	13.7557i	0.582847	+	0.582847i	−0.352838	+	0.935684i	$0.614783\pi$
$558$	16.2634	+	17.8063i	0.688485	+	0.753799i
$559$		−	33.2428i		−	1.40602i
$560$	12.3688	−	1.98833i	0.522676	−	0.0840223i
$561$	3.80268	+	12.2040i	0.160549	+	0.515253i
$562$	−4.75633	+	3.68857i	−0.200634	+	0.155593i
$563$	−10.6947	−	39.9133i	−0.450730	−	1.68215i	−0.700348	−	0.713801i	$-0.746972\pi$
$563$	−10.6947	−	39.9133i	−0.450730	−	1.68215i	0.249619	−	0.968344i	$-0.419695\pi$
$564$	−14.0726	−	21.7577i	−0.592564	−	0.916165i
$565$	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
$568$	10.4057	+	24.0675i	0.436614	+	1.00985i
$569$	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	$0.635486\pi$
$570$	9.49053	−	6.17678i	0.397515	−	0.258717i
$571$	8.21072	+	4.74046i	0.343608	+	0.198382i	0.661866	−	0.749622i	$-0.269765\pi$
$571$	8.21072	+	4.74046i	0.343608	+	0.198382i	−0.318258	+	0.948004i	$0.603098\pi$
$572$	−20.1888	−	11.3816i	−0.844138	−	0.475887i
$573$	7.76983	+	4.07810i	0.324589	+	0.170365i
$574$	−5.09325	+	6.70860i	−0.212588	+	0.280012i
$575$	15.7106	−	0.250680i	0.655178	−	0.0104541i
$576$	8.74779	+	22.3490i	0.364491	+	0.931207i
$577$	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	$0.718029\pi$
$578$	−2.59462	−	18.9564i	−0.107922	−	0.788481i
$579$	26.3489	−	28.5606i	1.09502	−	1.18694i
$580$	5.98049	+	7.50647i	0.248326	+	0.311689i
$581$	10.5213	−	18.2234i	0.436496	−	0.756032i
$582$	−22.3063	+	10.4492i	−0.924625	+	0.433135i
$583$	−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	$-0.734827\pi$
$587$	6.78111	−	25.3074i	0.279886	−	1.04455i	0.952496	−	0.304552i	$-0.0985068\pi$
$588$	5.36265	+	16.6087i	0.221152	+	0.684932i
$589$	−5.87562	+	10.1769i	−0.242101	+	0.419331i
$590$	−5.19772	+	9.28154i	−0.213987	+	0.382115i
$591$	−0.0778478	+	0.345625i	−0.00320223	+	0.0142171i
$592$	10.7281	−	43.5958i	0.440920	−	1.79177i
$593$	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	$0.631637\pi$
$594$	20.4808	+	20.6865i	0.840337	+	0.848776i
$595$	5.37265	−	2.27580i	0.220257	−	0.0932988i
$596$	15.4287	+	3.96496i	0.631985	+	0.162411i
$597$	−2.60710	+	1.64856i	−0.106701	+	0.0674711i
$598$	−10.2732	+	7.96694i	−0.420103	+	0.325793i
$599$	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	$-0.212112\pi$
$600$	16.2635	+	18.3166i	0.663956	+	0.747772i
$601$	−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	$0.954801\pi$
$602$	−20.8402	−	8.50733i	−0.849382	−	0.346733i
$603$	−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
$606$	−6.41471	+	17.7209i	−0.260580	+	0.719863i
$607$	−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	$0.631312\pi$
$608$	−9.09262	+	7.35496i	−0.368754	+	0.298283i
$609$	3.53025	−	3.82659i	0.143053	−	0.155061i
$610$	−4.60668	−	7.74285i	−0.186519	−	0.313499i
$611$	21.8814			0.885228
$612$	6.44358	+	9.13403i	0.260466	+	0.369221i
$613$	−9.05061	−	9.05061i	−0.365551	−	0.365551i	0.500301	−	0.865852i	$-0.333223\pi$
$613$	−9.05061	−	9.05061i	−0.365551	−	0.365551i	−0.865852	+	0.500301i	$0.833223\pi$
$614$	−5.69503	+	7.50124i	−0.229833	+	0.302726i
$615$	−16.4130	−	1.35986i	−0.661837	−	0.0548350i
$616$	−12.3018	+	9.74384i	−0.495655	+	0.392591i
$617$	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	$0.675217\pi$
$618$	11.1701	−	16.0123i	0.449329	−	0.644109i
$619$	−17.3425	−	30.0381i	−0.697055	−	1.20733i	−0.969483	−	0.245158i	$-0.921160\pi$
$619$	−17.3425	−	30.0381i	−0.697055	−	1.20733i	0.272428	−	0.962176i	$-0.412173\pi$
$620$	−23.6585	−	9.29801i	−0.950150	−	0.373417i
$621$	15.1485	−	6.09580i	0.607890	−	0.244616i
$622$	−13.3086	−	5.43279i	−0.533625	−	0.217835i
$623$	1.40050	−	5.22673i	0.0561097	−	0.209404i
$624$	−19.8586	−	4.04679i	−0.794981	−	0.162001i
$625$	22.0384	+	11.8029i	0.881537	+	0.472116i
$626$	−19.3302	−	2.44408i	−0.772589	−	0.0976851i
$627$	−6.59231	+	12.5600i	−0.263272	+	0.501600i
$628$	2.53516	+	4.28883i	0.101164	+	0.171143i
$629$		−	20.9107i		−	0.833764i
$630$	8.47617	−	10.2329i	0.337699	−	0.407688i
$631$	−5.01823			−0.199773			−0.0998863	−	0.994999i	$-0.531848\pi$
$631$	−5.01823			−0.199773			−0.0998863	+	0.994999i	$0.531848\pi$
$632$	−28.1650	+	37.8986i	−1.12034	+	1.50752i
$633$	−0.485556	−	12.0544i	−0.0192991	−	0.479121i
$634$	5.49973	−	43.4972i	0.218422	−	1.72749i
$635$	−27.1631	+	21.1894i	−1.07794	+	0.840875i
$636$	−21.2229	+	1.07299i	−0.841544	+	0.0425469i
$637$	−14.2360	−	3.81452i	−0.564050	−	0.151137i
$638$	−11.1311	−	4.54391i	−0.440684	−	0.179895i
$639$	25.1257	+	11.9234i	0.993955	+	0.471682i
$640$	−18.6559	−	17.0867i	−0.737441	−	0.675411i
$641$	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	$0.0592799\pi$
$642$	0.524397	−	6.11742i	0.0206963	−	0.241435i
$643$	−6.58055	+	1.76325i	−0.259511	+	0.0695359i	−0.386229	−	0.922403i	$-0.626223\pi$
$643$	−6.58055	+	1.76325i	−0.259511	+	0.0695359i	0.126717	+	0.991939i	$0.459556\pi$
$644$	2.36547	+	8.47922i	0.0932127	+	0.334128i
$645$	−7.84215	−	43.3085i	−0.308785	−	1.70527i
$646$	−3.29370	+	4.33832i	−0.129589	+	0.170689i
$647$	−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	$0.933904\pi$
$648$	22.6017	+	11.7116i	0.887880	+	0.460075i
$649$		−	13.3260i		−	0.523090i
$650$	−20.4462	+	3.13163i	−0.801968	+	0.122832i
$651$	−3.02998	+	13.4523i	−0.118754	+	0.527239i
$652$	−22.0139	−	12.4105i	−0.862132	−	0.486031i
$653$	−5.32699	−	19.8806i	−0.208461	−	0.777988i	−0.988367	−	0.152091i	$-0.951399\pi$
$653$	−5.32699	−	19.8806i	−0.208461	−	0.777988i	0.779905	−	0.625898i	$-0.215267\pi$
$654$	0.865932	+	1.02831i	0.0338606	+	0.0402101i
$655$	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
$658$	5.59979	−	13.7177i	0.218303	−	0.534770i
$659$	−12.7489	+	7.36058i	−0.496627	+	0.286727i	−0.727319	−	0.686299i	$-0.759234\pi$
$659$	−12.7489	+	7.36058i	−0.496627	+	0.286727i	0.230693	+	0.973027i	$0.425901\pi$
$660$	−28.9869	−	10.0652i	−1.12831	−	0.391786i
$661$	−15.6457	−	9.03307i	−0.608549	−	0.351346i	0.163848	−	0.986486i	$-0.447609\pi$
$661$	−15.6457	−	9.03307i	−0.608549	−	0.351346i	−0.772397	+	0.635140i	$0.780943\pi$
$662$	35.2883	−	27.3663i	1.37152	−	1.06362i
$663$	−9.43169	+	0.379911i	−0.366297	+	0.0147545i
$664$	−42.0395	+	6.19398i	−1.63145	+	0.240373i
$665$	6.00155	+	2.43002i	0.232730	+	0.0942320i
$666$	−21.9199	−	42.2748i	−0.849377	−	1.63812i
$667$	−4.76881	+	4.76881i	−0.184649	+	0.184649i
$668$	−6.43071	−	10.8791i	−0.248812	−	0.420924i
$669$	0.666570	+	2.13924i	0.0257711	+	0.0827076i
$670$	14.4875	−	4.08616i	0.559703	−	0.157862i
$671$	9.77423	+	5.64315i	0.377330	+	0.217851i
$672$	−7.61910	+	11.4139i	−0.293913	+	0.440301i
$673$	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	$0.289391\pi$
$677$	−8.12253	+	30.3137i	−0.312174	+	1.16505i	−0.926592	+	0.376069i	$0.877276\pi$
$678$	−26.4401	−	18.4446i	−1.01543	−	0.708359i
$679$	−12.1979	−	7.04245i	−0.468111	−	0.270264i
$680$	−10.3390	−	5.65140i	−0.396483	−	0.216721i
$681$	24.1466	−	7.52388i	0.925298	−	0.288316i
$682$	31.5494	−	4.31828i	1.20809	−	0.165355i
$683$	−22.8499	+	22.8499i	−0.874327	+	0.874327i	−0.992941	−	0.118613i	$-0.962155\pi$
$683$	−22.8499	+	22.8499i	−0.874327	+	0.874327i	0.118613	+	0.992941i	$0.462155\pi$
$684$	−2.11113	+	12.2234i	−0.0807212	+	0.467372i
$685$	11.5008	−	28.4041i	0.439422	−	1.08526i
$686$	−14.4188	+	18.9918i	−0.550513	+	0.725111i
$687$	−22.0015	+	0.886226i	−0.839410	+	0.0338116i
$688$	12.6631	+	43.6568i	0.482775	+	1.66440i
$689$	8.97228	−	15.5405i	0.341817	−	0.592044i
$690$	−11.5044	+	12.8028i	−0.437966	+	0.487394i
$691$	0.0596721	−	0.0344517i	0.00227003	−	0.00131060i	−0.498865	−	0.866680i	$-0.666249\pi$
$691$	0.0596721	−	0.0344517i	0.00227003	−	0.00131060i	0.501135	+	0.865369i	$0.332916\pi$
$692$	14.8738	−	0.152561i	0.565417	−	0.00579950i
$693$	−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
$696$	−10.4838	−	0.790467i	−0.397389	−	0.0299626i
$697$	7.65226	−	2.05042i	0.289850	−	0.0776651i
$698$	22.4809	+	28.9887i	0.850916	+	1.09724i
$699$	−5.93124	+	26.3332i	−0.224340	+	0.996014i
$700$	−3.26927	+	13.6194i	−0.123567	+	0.514763i
$701$	8.86219			0.334720			0.167360	−	0.985896i	$-0.446476\pi$
$701$	8.86219			0.334720			0.167360	+	0.985896i	$0.446476\pi$
$702$	−18.6697	+	10.6549i	−0.704641	+	0.402145i
$703$	16.4081	−	16.4081i	0.618843	−	0.618843i
$704$	30.8490	+	7.25659i	1.16266	+	0.273493i
$705$	28.5070	−	5.16195i	1.07364	−	0.194410i
$706$	−0.744675	+	5.88961i	−0.0280262	+	0.221658i
$707$	−10.4091	+	2.78911i	−0.391475	+	0.104895i
$708$	−3.58057	−	11.0894i	−0.134566	−	0.416766i
$709$	5.02429	+	8.70232i	0.188691	+	0.326822i	0.944814	−	0.327607i	$-0.106242\pi$
$709$	5.02429	+	8.70232i	0.188691	+	0.326822i	−0.756123	+	0.654429i	$0.772909\pi$
$710$	−29.3131	+	0.384191i	−1.10010	+	0.0144184i
$711$	4.02814	+	49.9203i	0.151067	+	1.87216i
$712$	−10.0299	+	4.33648i	−0.375886	+	0.162516i
$713$	4.62313	−	17.2538i	0.173138	−	0.646159i
$714$	−2.17555	+	6.01004i	−0.0814178	+	0.224920i
$715$	20.4306	−	15.9375i	0.764060	−	0.596028i
$716$	−4.03032	−	14.4470i	−0.150620	−	0.539909i
$717$	16.3097	−	0.656958i	0.609096	−	0.0245345i
$718$	1.46655	−	0.200731i	0.0547310	−	0.00749121i
$719$	5.56512			0.207544			0.103772	−	0.994601i	$-0.466909\pi$
$719$	5.56512			0.207544			0.103772	+	0.994601i	$0.466909\pi$
$720$	−26.8264	−	0.587378i	−0.999760	−	0.0218903i
$721$	11.1636			0.415753
$722$	20.6332	−	2.82413i	0.767888	−	0.105103i
$723$	13.7462	−	26.1900i	0.511226	−	0.974016i
$724$	12.3820	+	44.3842i	0.460173	+	1.64953i
$725$	−10.3191	+	2.94224i	−0.383243	+	0.109272i
$726$	11.3160	−	2.01578i	0.419976	−	0.0748127i
$727$	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	$0.0246788\pi$
$728$	−4.59895	−	10.6370i	−0.170448	−	0.394232i
$729$	26.2161	−	6.45864i	0.970968	−	0.239209i
$730$	−36.3816	−	35.4403i	−1.34654	−	1.31170i
$731$	10.5857	+	18.3350i	0.391527	+	0.678145i
$732$	9.65006	+	2.06980i	0.356677	+	0.0765019i
$733$	−15.5973	+	4.17927i	−0.576098	+	0.154365i	−0.535092	−	0.844794i	$-0.679723\pi$
$733$	−15.5973	+	4.17927i	−0.576098	+	0.154365i	−0.0410061	+	0.999159i	$0.513056\pi$
$734$	0.734285	−	5.80744i	0.0271030	−	0.214356i
$735$	−19.4464	−	1.61119i	−0.717292	−	0.0594296i
$736$	10.4567	−	14.3761i	0.385438	−	0.529910i
$737$	−13.3336	+	13.3336i	−0.491149	+	0.491149i
$738$	13.3211	−	12.1669i	0.490356	−	0.447869i
$739$	0.382628			0.0140752			0.00703759	−	0.999975i	$-0.497760\pi$
$739$	0.382628			0.0140752			0.00703759	+	0.999975i	$0.497760\pi$
$740$	40.3734	+	29.8260i	1.48416	+	1.09643i
$741$	−7.69892	−	7.10271i	−0.282827	−	0.260925i
$742$	−7.44630	−	9.60184i	−0.273362	−	0.352495i
$743$	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	$0.345753\pi$
$744$	25.0941	−	12.0706i	0.919996	−	0.442530i
$745$	−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
$748$	14.7594	−	0.151388i	0.539659	−	0.00553530i
$749$	3.04043	−	1.75539i	0.111095	−	0.0641406i
$750$	−25.8985	+	8.90325i	−0.945679	+	0.325101i
$751$	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	$-0.0655467\pi$
$752$	−28.7363	+	8.33524i	−1.04790	+	0.303955i
$753$	−22.1348	−	35.0049i	−0.806638	−	1.27565i
$754$	5.36851	−	7.07117i	0.195510	−	0.257517i
$755$	−23.3908	+	9.90813i	−0.851278	+	0.360594i
$756$	1.90181	+	14.4309i	0.0691683	+	0.524848i
$757$	−11.2246	+	11.2246i	−0.407964	+	0.407964i	−0.881028	−	0.473064i	$-0.843148\pi$
$757$	−11.2246	+	11.2246i	−0.407964	+	0.407964i	0.473064	+	0.881028i	$0.343148\pi$
$758$	−21.3678	+	2.92467i	−0.776112	+	0.106229i
$759$	4.73784	−	21.0348i	0.171973	−	0.763515i
$760$	−3.67825	−	12.5473i	−0.133424	−	0.455138i
$761$	−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	$0.890668\pi$
$762$	3.22319	−	37.6005i	0.116764	−	1.36212i
$763$	−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
$768$	27.6213	−	2.25016i	0.996698	−	0.0811957i
$769$	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	$0.469090\pi$
$770$	−4.76284	−	16.8867i	−0.171641	−	0.608556i
$771$	33.0488	−	35.8230i	1.19022	−	1.29013i
$772$	−22.8322	−	38.6262i	−0.821751	−	1.39019i
$773$	27.7925	−	27.7925i	0.999628	−	0.999628i	−0.000372119	−	1.00000i	$-0.500118\pi$
$773$	27.7925	−	27.7925i	0.999628	−	0.999628i	1.00000		0.000372119i	$0.000118449\pi$
$774$	40.6209	+	25.9710i	1.46009	+	0.933509i
$775$	19.7731	−	20.4144i	0.710272	−	0.733306i
$776$	4.14596	+	28.1393i	0.148831	+	1.01014i
$777$	12.6544	−	24.1099i	0.453976	−	0.864939i
$778$	25.8935	−	20.0806i	0.928328	−	0.719925i
$779$	7.61345	+	4.39563i	0.272780	+	0.157490i
$780$	12.7194	−	18.7522i	0.455428	−	0.671435i
$781$	31.8035	−	18.3618i	1.13802	−	0.657036i
$782$	3.12921	−	7.66553i	0.111900	−	0.274119i
$783$	−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
$786$	−15.6380	+	2.78569i	−0.557790	+	0.0993623i
$787$	0.748914	+	2.79499i	0.0266959	+	0.0996305i	0.977988	−	0.208659i	$-0.0669100\pi$
$787$	0.748914	+	2.79499i	0.0266959	+	0.0996305i	−0.951292	+	0.308290i	$0.900243\pi$
$788$	0.356363	+	0.200901i	0.0126949	+	0.00715681i
$789$	−40.0789	+	12.4883i	−1.42685	+	0.444595i
$790$	−26.9927	−	45.3690i	−0.960358	−	1.61416i
$791$		−	18.4337i		−	0.655428i
$792$	29.6803	−	15.7778i	1.05464	−	0.560640i
$793$	−5.89325	+	5.89325i	−0.209276	+	0.209276i
$794$	−2.29440	+	3.02209i	−0.0814253	+	0.107250i
$795$	8.02297	−	22.3626i	0.284545	−	0.793121i
$796$	0.957094	+	3.43078i	0.0339233	+	0.121601i
$797$	−7.74889	+	2.07631i	−0.274480	+	0.0735467i	−0.393433	−	0.919353i	$-0.628713\pi$
$797$	−7.74889	+	2.07631i	−0.274480	+	0.0735467i	0.118953	+	0.992900i	$0.462046\pi$
$798$	−6.42302	+	3.00883i	−0.227373	+	0.106511i
$799$	−12.0687	+	6.96786i	−0.426959	+	0.246505i
$800$	25.6585	−	11.9012i	0.907167	−	0.420771i
$801$	−4.96895	+	10.4709i	−0.175569	+	0.369970i
$802$	−10.2433	−	4.18152i	−0.361705	−	0.147654i
$803$	61.4566	+	16.4673i	2.16876	+	0.581117i
$804$	−7.51315	+	14.6784i	−0.264969	+	0.517667i
$805$	−9.76778	−	1.20676i	−0.344269	−	0.0425328i
$806$	−2.94969	+	23.3290i	−0.103898	+	0.821729i
$807$	37.0214	−	23.4100i	1.30321	−	0.824069i
$808$	17.4665	+	12.9805i	0.614469	+	0.456653i
$809$	−20.4056			−0.717424			−0.358712	−	0.933448i	$-0.616784\pi$
$809$	−20.4056			−0.717424			−0.358712	+	0.933448i	$0.616784\pi$
$810$	−21.8092	+	18.2855i	−0.766297	+	0.642486i
$811$			1.23274i			0.0432873i	0.999766	+	0.0216437i	$0.00688993\pi$
$811$			1.23274i			0.0432873i	−0.999766	+	0.0216437i	$0.993110\pi$
$812$	−3.05909	−	5.17519i	−0.107353	−	0.181614i
$813$	−11.9317	−	18.8693i	−0.418464	−	0.661775i
$814$	−62.3832	−	7.88765i	−2.18653	−	0.276462i
$815$	22.2775	−	17.3782i	0.780347	−	0.608733i
$816$	12.2417	−	4.09172i	0.428544	−	0.143239i
$817$	−6.08067	+	22.6934i	−0.212736	+	0.793941i
$818$	45.5248	+	18.5840i	1.59174	+	0.649775i
$819$	−11.1046	−	5.26971i	−0.388027	−	0.184138i
$820$	−6.95597	+	17.6993i	−0.242913	+	0.618085i
$821$	−23.9207	−	41.4320i	−0.834840	−	1.44599i	−0.894161	−	0.447746i	$-0.852227\pi$
$821$	−23.9207	−	41.4320i	−0.834840	−	1.44599i	0.0593209	−	0.998239i	$-0.481106\pi$
$822$	14.2402	+	30.3988i	0.496683	+	1.06028i
$823$	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	$0.826452\pi$
$824$	−13.9973	−	17.6719i	−0.487619	−	0.615631i
$825$	22.8571	−	25.5829i	0.795782	−	0.890684i
$826$	4.02920	−	5.30709i	0.140194	−	0.184657i
$827$	−30.4795	−	30.4795i	−1.05988	−	1.05988i	−0.998089	−	0.0617866i	$-0.980320\pi$
$827$	−30.4795	−	30.4795i	−1.05988	−	1.05988i	−0.0617866	−	0.998089i	$-0.519680\pi$
$828$	−1.70920	−	18.7775i	−0.0593988	−	0.652564i
$829$	−10.6637			−0.370365			−0.185183	−	0.982704i	$-0.559288\pi$
$829$	−10.6637			−0.370365			−0.185183	+	0.982704i	$0.559288\pi$
$830$	11.6938	−	46.0474i	0.405897	−	1.59833i
$831$	−7.12525	−	22.8672i	−0.247172	−	0.793255i
$832$	−11.0720	+	20.6172i	−0.383852	+	0.714771i
$833$	9.06652	−	2.42937i	0.314136	−	0.0841726i
$834$	27.1719	−	4.84028i	0.940885	−	0.167605i
$835$	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
$838$	11.2606	+	4.59680i	0.388992	+	0.158794i
$839$	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	$0.650546\pi$
$840$	−8.50081	−	12.7729i	−0.293306	−	0.440706i
$841$	−12.1972	+	21.1261i	−0.420592	+	0.728487i
$842$	−15.9305	+	12.3542i	−0.549001	+	0.425754i
$843$	6.52728	+	3.42593i	0.224811	+	0.117995i
$844$	−13.4922	−	3.46729i	−0.464419	−	0.119349i
$845$	−3.87490	−	9.14774i	−0.133301	−	0.314692i
$846$	−17.0949	+	26.7379i	−0.587736	+	0.919269i
$847$	4.64737	+	4.64737i	0.159686	+	0.159686i
$848$	−5.86326	+	23.8266i	−0.201345	+	0.818210i
$849$	−24.2045	−	22.3301i	−0.830695	−	0.766365i
$850$	10.2799	−	8.23809i	0.352597	−	0.282564i
$851$	−17.6360	+	30.5464i	−0.604553	+	1.04712i
$852$	21.5322	−	23.8254i	0.737682	−	0.816246i
$853$	4.45982	−	16.6443i	0.152701	−	0.569889i	−0.846590	−	0.532246i	$-0.821348\pi$
$853$	4.45982	−	16.6443i	0.152701	−	0.569889i	0.999291	−	0.0376434i	$-0.0119851\pi$
$854$	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	$0.484943\pi$
$858$	−2.42430	+	28.2810i	−0.0827644	+	0.965498i
$859$	−19.3208	+	33.4646i	−0.659218	+	1.14180i	0.321601	+	0.946875i	$0.395779\pi$
$859$	−19.3208	+	33.4646i	−0.659218	+	1.14180i	−0.980818	+	0.194923i	$0.937554\pi$
$860$	−50.4994	−	5.71374i	−1.72201	−	0.194837i
$861$	10.0639	+	2.26677i	0.342976	+	0.0772512i
$862$	−0.424169	−	3.09899i	−0.0144473	−	0.105552i
$863$	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	$0.609460\pi$
$864$	20.4596	−	21.1046i	0.696050	−	0.717994i
$865$	−6.24136	+	15.4146i	−0.212213	+	0.524114i
$866$	15.3781	−	20.2554i	0.522570	−	0.688307i
$867$	−19.8057	+	12.5239i	−0.672638	+	0.425333i
$868$	13.8703	+	7.81944i	0.470788	+	0.265409i
$869$	57.2719	+	33.0659i	1.94281	+	1.12168i
$870$	5.32594	−	10.4788i	0.180566	−	0.355263i
$871$	−6.96226	−	12.0590i	−0.235907	−	0.408603i
$872$	1.42484	−	0.616038i	0.0482513	−	0.0208617i
$873$	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
$876$	55.5668	−	2.80936i	1.87743	−	0.0949194i
$877$	−13.6570	−	50.9687i	−0.461164	−	1.72109i	−0.669303	−	0.742990i	$-0.733407\pi$
$877$	−13.6570	−	50.9687i	−0.461164	−	1.72109i	0.208138	−	0.978099i	$-0.433260\pi$
$878$	13.9099	−	10.7872i	0.469435	−	0.364050i
$879$	−9.44712	+	10.2401i	−0.318643	+	0.345391i
$880$	−20.7599	+	28.7128i	−0.699815	+	0.967908i
$881$		−	5.46211i		−	0.184023i	−0.995758	−	0.0920116i	$-0.970670\pi$
$881$		−	5.46211i		−	0.184023i	0.995758	−	0.0920116i	$-0.0293297\pi$
$882$	15.7831	−	14.4155i	0.531443	−	0.485395i
$883$	−8.44443	−	8.44443i	−0.284178	−	0.284178i	0.550595	−	0.834773i	$-0.314401\pi$
$883$	−8.44443	−	8.44443i	−0.284178	−	0.284178i	−0.834773	+	0.550595i	$0.814401\pi$
$884$	−2.71290	+	10.5566i	−0.0912446	+	0.355057i
$885$	12.9841	+	1.07577i	0.436457	+	0.0361616i
$886$	−17.4409	−	2.20520i	−0.585938	−	0.0740852i
$887$	−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	$0.967868\pi$
$888$	−54.0326	+	10.1980i	−1.81322	+	0.342222i
$889$	18.6879	−	10.7895i	0.626772	−	0.361867i
$890$	−0.160108	−	12.2159i	−0.00536682	−	0.409479i
$891$	12.6449	−	33.3346i	0.423621	−	1.11675i
$892$	2.58718	−	0.0265368i	0.0866251	−	0.000888517i
$893$	−14.9375	−	4.00249i	−0.499864	−	0.133938i
$894$	−3.42161	−	19.2079i	−0.114436	−	0.642407i
$895$	16.6424	+	2.05609i	0.556296	+	0.0687277i
$896$	10.0916	+	12.2174i	0.337136	+	0.408153i
$897$	14.0983	+	7.39967i	0.470727	+	0.247068i
$898$	−26.5888	+	3.63929i	−0.887279	+	0.121445i
$899$			12.1985i			0.406844i
$900$	12.1470	−	27.4308i	0.404901	−	0.914361i
$901$			11.4284i			0.380736i
$902$	−3.23056	−	23.6025i	−0.107566	−	0.785879i
$903$	1.10957	+	27.5463i	0.0369243	+	0.916684i
$904$	−29.1805	+	23.1129i	−0.970531	+	0.768723i
$905$	−51.1291	−	6.31676i	−1.69959	−	0.209976i
$906$	9.47164	−	26.1658i	0.314674	−	0.869300i
$907$	2.49062	+	0.667360i	0.0826997	+	0.0221593i	0.299932	−	0.953961i	$-0.403036\pi$
$907$	2.49062	+	0.667360i	0.0826997	+	0.0221593i	−0.217232	+	0.976120i	$0.569703\pi$
$908$	−0.299533	−	29.2027i	−0.00994035	−	0.969125i
$909$	23.0070	−	1.85647i	0.763094	−	0.0615751i
$910$	12.9553	−	0.169798i	0.429465	−	0.00562876i
$911$	−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	$0.428336\pi$
$912$	12.8164	+	6.39505i	0.424393	+	0.211761i
$913$	15.4034	+	57.4864i	0.509780	+	1.90252i
$914$	−2.33908	+	18.4997i	−0.0773698	+	0.611915i
$915$	−6.28745	+	9.06795i	−0.207857	+	0.299777i
$916$	−6.32843	+	24.6256i	−0.209097	+	0.813653i
$917$	−6.42239	−	6.42239i	−0.212086	−	0.212086i
$918$	6.90432	−	11.8218i	0.227876	−	0.390179i
$919$		−	22.2926i		−	0.735366i	−0.929951	−	0.367683i	$-0.880151\pi$
$919$		−	22.2926i		−	0.735366i	0.929951	−	0.367683i	$-0.119849\pi$
$920$	10.3369	+	16.9755i	0.340798	+	0.559665i
$921$	11.2529	+	2.53459i	0.370797	+	0.0835176i
$922$	25.7686	+	33.2281i	0.848644	+	1.09431i
$923$	7.01874	+	26.1943i	0.231025	+	0.862196i
$924$	17.1092	+	8.75737i	0.562851	+	0.288096i
$925$	−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
$928$	−4.35671	+	11.3314i	−0.143016	+	0.371971i
$929$	−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	$-0.394682\pi$
$930$	1.66060	+	31.0888i	0.0544533	+	1.01944i
$931$	9.02054	+	5.20801i	0.295636	+	0.170686i
$932$	27.1514	+	15.3067i	0.889373	+	0.501388i
$933$	0.708574	+	17.5911i	0.0231977	+	0.575907i
$934$	−25.4622	−	19.3312i	−0.833147	−	0.632535i
$935$	−6.19338	+	15.2961i	−0.202545	+	0.500238i
$936$	5.58144	+	24.1859i	0.182435	+	0.790542i
$937$	−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	$-0.564693\pi$
$938$	−9.34163	+	1.27862i	−0.305015	+	0.0417484i
$939$	7.09890	+	22.7826i	0.231664	+	0.743483i
$940$	3.76096	−	33.2403i	0.122669	−	1.08418i
$941$	5.90580	−	10.2291i	0.192524	−	0.333461i	−0.753562	−	0.657376i	$-0.771666\pi$
$941$	5.90580	−	10.2291i	0.192524	−	0.333461i	0.946086	+	0.323916i	$0.104999\pi$
$942$	3.49107	−	5.00442i	0.113745	−	0.163053i
$943$	−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	−0.896643	−	0.442754i	$-0.854001\pi$
$947$	3.11580	−	11.6283i	0.101250	−	0.377870i	0.997893	+	0.0648848i	$0.0206680\pi$
$948$	56.5443	+	12.1279i	1.83647	+	0.393897i
$949$	−23.4916	+	40.6887i	−0.762571	+	1.32081i
$950$	14.5306	+	1.60215i	0.471435	+	0.0519805i
$951$	−51.2660	+	15.9741i	−1.66241	+	0.517996i
$952$	5.92375	+	4.40233i	0.191990	+	0.142680i
$953$	−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	$0.860256\pi$
$954$	11.9800	+	23.1047i	0.387866	+	0.748042i
$955$	4.41859	+	10.4313i	0.142982	+	0.337548i
$956$	4.69125	−	18.2549i	0.151726	−	0.590406i
$957$	0.592642	+	14.7130i	0.0191574	+	0.475603i
$958$	−0.633212	−	0.816514i	−0.0204582	−	0.0263804i
$959$	−9.59740	+	16.6232i	−0.309916	+	0.536791i
$960$	−9.56081	+	29.4719i	−0.308574	+	0.951200i
$961$	−0.654484	−	1.13360i	−0.0211124	−	0.0365677i
$962$	17.5490	−	42.9894i	0.565803	−	1.38603i
$963$	−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
$966$	8.24688	−	6.94464i	0.265339	−	0.223440i
$967$	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	$0.218227\pi$
$968$	1.52974	−	13.1838i	0.0491676	−	0.423745i
$969$	6.50810	+	1.46587i	0.209070	+	0.0470906i
$970$	−30.8220	−	7.82727i	−0.989634	−	0.251319i
$971$	18.6917			0.599845			0.299923	−	0.953964i	$-0.403039\pi$
$971$	18.6917			0.599845			0.299923	+	0.953964i	$0.403039\pi$
$972$	1.56599	−	31.1376i	0.0502292	−	0.998738i
$973$	11.1592	+	11.1592i	0.357749	+	0.357749i
$974$	−23.1391	−	17.5675i	−0.741426	−	0.562899i
$975$	13.8794	+	21.1931i	0.444495	+	0.678722i
$976$	5.49454	−	9.98434i	0.175876	−	0.319591i
$977$	−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	$-0.170255\pi$
$978$	−2.64346	+	30.8377i	−0.0845286	+	0.986080i
$979$	7.65208	+	13.2538i	0.244562	+	0.423593i
$980$	−8.24154	+	20.9704i	−0.263266	+	0.669874i
$981$	0.705888	−	1.48749i	0.0225373	−	0.0474918i
$982$	1.67721	−	4.10861i	0.0535219	−	0.131111i
$983$	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	$-0.0181282\pi$
$984$	−9.03017	−	18.7733i	−0.287871	−	0.598469i
$985$	−0.360630	+	0.281320i	−0.0114906	+	0.00896359i
$986$	−0.709275	+	5.60963i	−0.0225879	+	0.178647i
$987$	−18.1319	+	0.730355i	−0.577143	+	0.0232475i
$988$	−10.4122	+	6.15476i	−0.331258	+	0.195809i
$989$		−	35.7118i		−	1.13557i
$990$	3.51328	+	37.4163i	0.111659	+	1.18917i
$991$	−12.5037			−0.397194			−0.198597	−	0.980081i	$-0.563638\pi$
$991$	−12.5037			−0.397194			−0.198597	+	0.980081i	$0.563638\pi$
$992$	−5.01292	−	31.7609i	−0.159160	−	1.00841i
$993$	−48.4273	−	25.4177i	−1.53679	−	0.806608i
$994$	18.2176	+	2.30342i	0.577828	+	0.0730599i
$995$	−3.95214	−	0.488268i	−0.125291	−	0.0154791i
$996$	28.2644	+	43.6996i	0.895591	+	1.38467i
$997$	−2.64853	−	0.709672i	−0.0838798	−	0.0224755i	0.216635	−	0.976253i	$-0.430492\pi$
$997$	−2.64853	−	0.709672i	−0.0838798	−	0.0224755i	−0.300515	+	0.953777i	$0.597159\pi$
$998$	−8.72099	+	21.3636i	−0.276058	+	0.676251i
$999$	−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.77.3	✓	256
5.3	odd	4	inner	360.2.br.e.293.36	yes	256
8.5	even	2	inner	360.2.br.e.77.14	yes	256
9.2	odd	6	inner	360.2.br.e.317.17	yes	256
40.13	odd	4	inner	360.2.br.e.293.17	yes	256
45.38	even	12	inner	360.2.br.e.173.14	yes	256
72.29	odd	6	inner	360.2.br.e.317.36	yes	256
360.173	even	12	inner	360.2.br.e.173.3	yes	256

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

\(f(q)\)	\(=\)	\(q+(-1.40115 + 0.191780i) q^{2} +(0.925695 + 1.46393i) q^{3} +(1.92644 - 0.537425i) q^{4} +(-0.274171 + 2.21920i) q^{5} +(-1.57779 - 1.87365i) q^{6} +(0.362508 - 1.35290i) q^{7} +(-2.59616 + 1.12247i) q^{8} +(-1.28618 + 2.71030i) q^{9} +O(q^{10})\)	\(q+(-1.40115 + 0.191780i) q^{2} +(0.925695 + 1.46393i) q^{3} +(1.92644 - 0.537425i) q^{4} +(-0.274171 + 2.21920i) q^{5} +(-1.57779 - 1.87365i) q^{6} +(0.362508 - 1.35290i) q^{7} +(-2.59616 + 1.12247i) q^{8} +(-1.28618 + 2.71030i) q^{9} +(-0.0414427 - 3.16201i) q^{10} +(1.98069 + 3.43065i) q^{11} +(2.57005 + 2.32268i) q^{12} +(-2.82558 + 0.757112i) q^{13} +(-0.248469 + 1.96514i) q^{14} +(-3.50254 + 1.65293i) q^{15} +(3.42235 - 2.07063i) q^{16} +(1.31735 - 1.31735i) q^{17} +(1.28234 - 4.04420i) q^{18} +2.06739 q^{19} +(0.664477 + 4.42250i) q^{20} +(2.31612 - 0.721686i) q^{21} +(-3.43317 - 4.42700i) q^{22} +(-3.03544 + 0.813345i) q^{23} +(-4.04647 - 2.76154i) q^{24} +(-4.84966 - 1.21688i) q^{25} +(3.81386 - 1.60272i) q^{26} +(-5.15830 + 0.626043i) q^{27} +(-0.0287310 - 2.80110i) q^{28} +(1.85856 - 1.07304i) q^{29} +(4.59059 - 2.98772i) q^{30} +(-2.84205 + 4.92257i) q^{31} +(-4.39812 + 3.55761i) q^{32} +(-3.18871 + 6.07532i) q^{33} +(-1.59317 + 2.09845i) q^{34} +(2.90296 + 1.17540i) q^{35} +(-1.02116 + 5.91246i) q^{36} +(7.93663 - 7.93663i) q^{37} +(-2.89672 + 0.396484i) q^{38} +(-3.72398 - 3.43559i) q^{39} +(-1.77918 - 6.06915i) q^{40} +(3.68264 + 2.12617i) q^{41} +(-3.10683 + 1.45538i) 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} +(6.19931 + 3.09330i) q^{48} +(4.36325 + 2.51912i) q^{49} +(7.02847 + 0.774961i) q^{50} +(3.14798 + 0.709044i) q^{51} +(-5.03642 + 2.97707i) q^{52} +(-4.33765 + 4.33765i) q^{53} +(7.10749 - 1.86644i) q^{54} +(-8.15633 + 3.45494i) q^{55} +(0.577452 + 3.91925i) q^{56} +(1.91377 + 3.02651i) q^{57} +(-2.39833 + 1.85992i) q^{58} +(-2.91329 - 1.68199i) q^{59} +(-5.85912 + 5.06663i) q^{60} +(2.46738 - 1.42455i) q^{61} +(3.03808 - 7.44231i) q^{62} +(3.20052 + 2.72258i) q^{63} +(5.48014 - 5.82821i) q^{64} +(-0.905487 - 6.47809i) q^{65} +(3.30274 - 9.12396i) q^{66} +(1.23200 + 4.59790i) q^{67} +(1.82982 - 3.24578i) q^{68} +(-4.00058 - 3.69077i) q^{69} +(-4.29290 - 1.09019i) q^{70} -9.27042i q^{71} +(0.296905 - 8.48009i) q^{72} +(11.3570 - 11.3570i) q^{73} +(-9.59832 + 12.6425i) q^{74} +(-2.70788 - 8.22602i) q^{75} +(3.98270 - 1.11107i) q^{76} +(5.35934 - 1.43603i) q^{77} +(5.87674 + 4.09960i) q^{78} +(14.4576 - 8.34709i) q^{79} +(3.65683 + 8.16257i) q^{80} +(-5.69150 - 6.97186i) q^{81} +(-5.56769 - 2.27283i) q^{82} +(14.5118 + 3.88841i) q^{83} +(4.07402 - 2.63503i) q^{84} +(2.56229 + 3.28465i) q^{85} +(2.01597 - 15.9443i) q^{86} +(3.29132 + 1.72749i) q^{87} +(-8.99297 - 6.68328i) q^{88} +3.86335 q^{89} +(8.62330 + 3.95458i) q^{90} +4.09719i q^{91} +(-5.41049 + 3.19818i) q^{92} +(-9.83717 + 0.396244i) q^{93} +(10.4950 + 1.32698i) q^{94} +(-0.566818 + 4.58794i) q^{95} +(-9.27940 - 3.14527i) q^{96} +(2.60272 - 9.71349i) q^{97} +(-6.59669 - 2.69289i) 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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