LMFDB - Embedded newform 280.2.br.a.123.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(67,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 6, 3, 8]))

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

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

chi := DirichletCharacter("280.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			123.34
Character	$\chi$	$=$	280.123
Dual form			280.2.br.a.107.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.949136 + 1.04840i) q^{2} +(0.357022 - 0.0956638i) q^{3} +(-0.198283 + 1.99015i) q^{4} +(-2.11588 + 0.723237i) q^{5} +(0.439157 + 0.283504i) q^{6} +(1.60674 + 2.10200i) q^{7} +(-2.27467 + 1.68104i) q^{8} +(-2.47976 + 1.43169i) q^{9} +O(q^{10})$	\(q+(0.949136 + 1.04840i) q^{2} +(0.357022 - 0.0956638i) q^{3} +(-0.198283 + 1.99015i) q^{4} +(-2.11588 + 0.723237i) q^{5} +(0.439157 + 0.283504i) q^{6} +(1.60674 + 2.10200i) q^{7} +(-2.27467 + 1.68104i) q^{8} +(-2.47976 + 1.43169i) q^{9} +(-2.76649 - 1.53183i) q^{10} +(-0.466681 + 0.808315i) q^{11} +(0.119594 + 0.729495i) q^{12} +(4.27704 - 4.27704i) q^{13} +(-0.678723 + 3.67958i) q^{14} +(-0.686227 + 0.460624i) q^{15} +(-3.92137 - 0.789223i) q^{16} +(1.52523 + 5.69224i) q^{17} +(-3.85462 - 1.24091i) q^{18} +(4.55363 - 2.62904i) q^{19} +(-1.01981 - 4.35431i) q^{20} +(0.774726 + 0.596754i) q^{21} +(-1.29038 + 0.277933i) q^{22} +(-2.48608 - 0.666144i) q^{23} +(-0.651292 + 0.817772i) q^{24} +(3.95386 - 3.06056i) q^{25} +(8.54355 + 0.424555i) q^{26} +(-1.53244 + 1.53244i) q^{27} +(-4.50187 + 2.78085i) q^{28} +5.15709 q^{29} +(-1.13424 - 0.282245i) q^{30} +(-1.23225 - 0.711441i) q^{31} +(-2.89449 - 4.86024i) q^{32} +(-0.0892890 + 0.333231i) q^{33} +(-4.52009 + 7.00176i) q^{34} +(-4.91990 - 3.28552i) q^{35} +(-2.35758 - 5.21897i) q^{36} +(0.432338 - 1.61351i) q^{37} +(7.07830 + 2.27871i) q^{38} +(1.11784 - 1.93616i) q^{39} +(3.59712 - 5.20199i) q^{40} +6.12368 q^{41} +(0.109684 + 1.37862i) q^{42} +(-7.08536 - 7.08536i) q^{43} +(-1.51613 - 1.08904i) q^{44} +(4.21142 - 4.82274i) q^{45} +(-1.66124 - 3.23867i) q^{46} +(2.45559 - 9.16440i) q^{47} +(-1.47552 + 0.0933627i) q^{48} +(-1.83680 + 6.75472i) q^{49} +(6.96143 + 1.24033i) q^{50} +(1.08908 + 1.88635i) q^{51} +(7.66388 + 9.36001i) q^{52} +(2.06081 + 7.69103i) q^{53} +(-3.06111 - 0.152116i) q^{54} +(0.402835 - 2.04782i) q^{55} +(-7.18833 - 2.08036i) q^{56} +(1.37424 - 1.37424i) q^{57} +(4.89478 + 5.40669i) q^{58} +(0.873827 + 0.504505i) q^{59} +(-0.780643 - 1.45703i) q^{60} +(2.84724 - 1.64386i) q^{61} +(-0.423700 - 1.96715i) q^{62} +(-6.99374 - 2.91211i) q^{63} +(2.34821 - 7.64761i) q^{64} +(-5.95638 + 12.1430i) q^{65} +(-0.434107 + 0.222671i) q^{66} +(0.526202 + 1.96381i) q^{67} +(-11.6308 + 1.90676i) q^{68} -0.951312 q^{69} +(-1.22512 - 8.27642i) q^{70} +12.5416i q^{71} +(3.23390 - 7.42520i) q^{72} +(-3.20705 + 0.859326i) q^{73} +(2.10195 - 1.07818i) q^{74} +(1.11883 - 1.47093i) q^{75} +(4.32927 + 9.58369i) q^{76} +(-2.44891 + 0.317787i) q^{77} +(3.09085 - 0.665733i) q^{78} +(2.02447 + 3.50648i) q^{79} +(8.86792 - 1.16618i) q^{80} +(3.89456 - 6.74557i) q^{81} +(5.81220 + 6.42006i) q^{82} +(-9.21676 - 9.21676i) q^{83} +(-1.34124 + 1.42349i) q^{84} +(-7.34403 - 10.9410i) q^{85} +(0.703319 - 14.1532i) q^{86} +(1.84120 - 0.493347i) q^{87} +(-0.297267 - 2.62316i) q^{88} +(10.3405 - 5.97011i) q^{89} +(9.05336 - 0.162186i) q^{90} +(15.8624 + 2.11826i) q^{91} +(1.81867 - 4.81558i) q^{92} +(-0.508001 - 0.136118i) q^{93} +(11.9386 - 6.12382i) q^{94} +(-7.73350 + 8.85608i) q^{95} +(-1.49835 - 1.45832i) q^{96} +(-4.41264 + 4.41264i) q^{97} +(-8.82501 + 4.48545i) q^{98} -2.67257i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	$ 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) $ 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.949136	+	1.04840i	0.671140	+	0.741330i
$2$	0.949136	+	1.04840i	0.671140	+	0.741330i
$3$	0.357022	−	0.0956638i	0.206127	−	0.0552315i	−0.154278	−	0.988027i	$-0.549305\pi$
$3$	0.357022	−	0.0956638i	0.206127	−	0.0552315i	0.360405	+	0.932796i	$0.382638\pi$
$4$	−0.198283	+	1.99015i	−0.0991414	+	0.995073i
$5$	−2.11588	+	0.723237i	−0.946248	+	0.323441i
$5$	−2.11588	+	0.723237i	−0.946248	+	0.323441i
$6$	0.439157	+	0.283504i	0.179285	+	0.115740i
$7$	1.60674	+	2.10200i	0.607289	+	0.794481i
$7$	1.60674	+	2.10200i	0.607289	+	0.794481i
$8$	−2.27467	+	1.68104i	−0.804216	+	0.594337i
$9$	−2.47976	+	1.43169i	−0.826588	+	0.477231i
$10$	−2.76649	−	1.53183i	−0.874842	−	0.484408i
$11$	−0.466681	+	0.808315i	−0.140710	+	0.243716i	−0.927764	−	0.373167i	$-0.878272\pi$
$11$	−0.466681	+	0.808315i	−0.140710	+	0.243716i	0.787054	+	0.616884i	$0.211605\pi$
$12$	0.119594	+	0.729495i	0.0345237	+	0.210587i
$13$	4.27704	−	4.27704i	1.18624	−	1.18624i	0.208140	−	0.978099i	$-0.433259\pi$
$13$	4.27704	−	4.27704i	1.18624	−	1.18624i	0.978099	−	0.208140i	$-0.0667408\pi$
$14$	−0.678723	+	3.67958i	−0.181396	+	0.983410i
$15$	−0.686227	+	0.460624i	−0.177183	+	0.118933i
$16$	−3.92137	−	0.789223i	−0.980342	−	0.197306i
$17$	1.52523	+	5.69224i	0.369923	+	1.38057i	0.860623	+	0.509242i	$0.170074\pi$
$17$	1.52523	+	5.69224i	0.369923	+	1.38057i	−0.490701	+	0.871328i	$0.663259\pi$
$18$	−3.85462	−	1.24091i	−0.908542	−	0.292486i
$19$	4.55363	−	2.62904i	1.04467	−	0.603143i	0.123521	−	0.992342i	$-0.460581\pi$
$19$	4.55363	−	2.62904i	1.04467	−	0.603143i	0.921154	+	0.389199i	$0.127248\pi$
$20$	−1.01981	−	4.35431i	−0.228036	−	0.973653i
$21$	0.774726	+	0.596754i	0.169059	+	0.130222i
$22$	−1.29038	+	0.277933i	−0.275110	+	0.0592555i
$23$	−2.48608	−	0.666144i	−0.518384	−	0.138901i	−0.00986492	−	0.999951i	$-0.503140\pi$
$23$	−2.48608	−	0.666144i	−0.518384	−	0.138901i	−0.508519	+	0.861051i	$0.669807\pi$
$24$	−0.651292	+	0.817772i	−0.132944	+	0.166927i
$25$	3.95386	−	3.06056i	0.790771	−	0.612112i
$26$	8.54355	+	0.424555i	1.67553	+	0.0832621i
$27$	−1.53244	+	1.53244i	−0.294919	+	0.294919i
$28$	−4.50187	+	2.78085i	−0.850774	+	0.525532i
$29$	5.15709			0.957648			0.478824	−	0.877911i	$-0.341063\pi$
$29$	5.15709			0.957648			0.478824	+	0.877911i	$0.341063\pi$
$30$	−1.13424	−	0.282245i	−0.207083	−	0.0515306i
$31$	−1.23225	−	0.711441i	−0.221319	−	0.127779i	0.385242	−	0.922816i	$-0.374118\pi$
$31$	−1.23225	−	0.711441i	−0.221319	−	0.127779i	−0.606561	+	0.795037i	$0.707451\pi$
$32$	−2.89449	−	4.86024i	−0.511678	−	0.859177i
$33$	−0.0892890	+	0.333231i	−0.0155432	+	0.0580081i
$34$	−4.52009	+	7.00176i	−0.775189	+	1.20079i
$35$	−4.91990	−	3.28552i	−0.831614	−	0.555353i
$36$	−2.35758	−	5.21897i	−0.392930	−	0.869829i
$37$	0.432338	−	1.61351i	0.0710760	−	0.265259i	−0.921239	−	0.388997i	$-0.872822\pi$
$37$	0.432338	−	1.61351i	0.0710760	−	0.265259i	0.992315	+	0.123738i	$0.0394882\pi$
$38$	7.07830	+	2.27871i	1.14825	+	0.369655i
$39$	1.11784	−	1.93616i	0.178998	−	0.310033i
$40$	3.59712	−	5.20199i	0.568754	−	0.822507i
$41$	6.12368			0.956358			0.478179	−	0.878262i	$-0.341297\pi$
$41$	6.12368			0.956358			0.478179	+	0.878262i	$0.341297\pi$
$42$	0.109684	+	1.37862i	0.0169246	+	0.212726i
$43$	−7.08536	−	7.08536i	−1.08051	−	1.08051i	−0.996462	−	0.0840448i	$-0.973216\pi$
$43$	−7.08536	−	7.08536i	−1.08051	−	1.08051i	−0.0840448	−	0.996462i	$-0.526784\pi$
$44$	−1.51613	−	1.08904i	−0.228565	−	0.164179i
$45$	4.21142	−	4.82274i	0.627801	−	0.718931i
$46$	−1.66124	−	3.23867i	−0.244937	−	0.477515i
$47$	2.45559	−	9.16440i	0.358185	−	1.33677i	−0.518243	−	0.855233i	$-0.673414\pi$
$47$	2.45559	−	9.16440i	0.358185	−	1.33677i	0.876429	−	0.481532i	$-0.159919\pi$
$48$	−1.47552	+	0.0933627i	−0.212972	+	0.0134758i
$49$	−1.83680	+	6.75472i	−0.262399	+	0.964959i
$50$	6.96143	+	1.24033i	0.984496	+	0.175410i
$51$	1.08908	+	1.88635i	0.152502	+	0.264141i
$52$	7.66388	+	9.36001i	1.06279	+	1.29800i
$53$	2.06081	+	7.69103i	0.283073	+	1.05644i	0.950236	+	0.311532i	$0.100842\pi$
$53$	2.06081	+	7.69103i	0.283073	+	1.05644i	−0.667162	+	0.744912i	$0.732491\pi$
$54$	−3.06111	−	0.152116i	−0.416565	−	0.0207004i
$55$	0.402835	−	2.04782i	0.0543183	−	0.276127i
$56$	−7.18833	−	2.08036i	−0.960581	−	0.277999i
$57$	1.37424	−	1.37424i	0.182023	−	0.182023i
$58$	4.89478	+	5.40669i	0.642716	+	0.709933i
$59$	0.873827	+	0.504505i	0.113763	+	0.0656809i	0.555802	−	0.831315i	$-0.312411\pi$
$59$	0.873827	+	0.504505i	0.113763	+	0.0656809i	−0.442039	+	0.896996i	$0.645745\pi$
$60$	−0.780643	−	1.45703i	−0.100781	−	0.188101i
$61$	2.84724	−	1.64386i	0.364552	−	0.210474i	−0.306524	−	0.951863i	$-0.599166\pi$
$61$	2.84724	−	1.64386i	0.364552	−	0.210474i	0.671076	+	0.741389i	$0.265832\pi$
$62$	−0.423700	−	1.96715i	−0.0538100	−	0.249828i
$63$	−6.99374	−	2.91211i	−0.881128	−	0.366891i
$64$	2.34821	−	7.64761i	0.293526	−	0.955951i
$65$	−5.95638	+	12.1430i	−0.738797	+	1.50615i
$66$	−0.434107	+	0.222671i	−0.0534348	+	0.0274089i
$67$	0.526202	+	1.96381i	0.0642859	+	0.239918i	0.990591	−	0.136856i	$-0.0436999\pi$
$67$	0.526202	+	1.96381i	0.0642859	+	0.239918i	−0.926305	+	0.376774i	$0.877033\pi$
$68$	−11.6308	+	1.90676i	−1.41044	+	0.231229i
$69$	−0.951312			−0.114525
$70$	−1.22512	−	8.27642i	−0.146430	−	0.989221i
$71$			12.5416i			1.48841i	0.667950	+	0.744206i	$0.267172\pi$
$71$			12.5416i			1.48841i	−0.667950	+	0.744206i	$0.732828\pi$
$72$	3.23390	−	7.42520i	0.381119	−	0.875068i
$73$	−3.20705	+	0.859326i	−0.375356	+	0.100576i	−0.441565	−	0.897229i	$-0.645576\pi$
$73$	−3.20705	+	0.859326i	−0.375356	+	0.100576i	0.0662084	+	0.997806i	$0.478910\pi$
$74$	2.10195	−	1.07818i	0.244347	−	0.125335i
$75$	1.11883	−	1.47093i	0.129191	−	0.169848i
$76$	4.32927	+	9.58369i	0.496601	+	1.09932i
$77$	−2.44891	+	0.317787i	−0.279079	+	0.0362152i
$78$	3.09085	−	0.665733i	0.349970	−	0.0753794i
$79$	2.02447	+	3.50648i	0.227770	+	0.394510i	0.957147	−	0.289603i	$-0.0935231\pi$
$79$	2.02447	+	3.50648i	0.227770	+	0.394510i	−0.729377	+	0.684112i	$0.760190\pi$
$80$	8.86792	−	1.16618i	0.991464	−	0.130383i
$81$	3.89456	−	6.74557i	0.432729	−	0.749508i
$82$	5.81220	+	6.42006i	0.641851	+	0.708977i
$83$	−9.21676	−	9.21676i	−1.01167	−	1.01167i	−0.999931	−	0.0117394i	$-0.996263\pi$
$83$	−9.21676	−	9.21676i	−1.01167	−	1.01167i	−0.0117394	−	0.999931i	$-0.503737\pi$
$84$	−1.34124	+	1.42349i	−0.146342	+	0.155316i
$85$	−7.34403	−	10.9410i	−0.796572	−	1.18671i
$86$	0.703319	−	14.1532i	0.0758408	−	1.52618i
$87$	1.84120	−	0.493347i	0.197397	−	0.0528924i
$88$	−0.297267	−	2.62316i	−0.0316888	−	0.279630i
$89$	10.3405	−	5.97011i	1.09609	−	0.632831i	0.160902	−	0.986970i	$-0.448560\pi$
$89$	10.3405	−	5.97011i	1.09609	−	0.632831i	0.935192	+	0.354140i	$0.115226\pi$
$90$	9.05336	−	0.162186i	0.954308	−	0.0170959i
$91$	15.8624	+	2.11826i	1.66283	+	0.222054i
$92$	1.81867	−	4.81558i	0.189610	−	0.502059i
$93$	−0.508001	−	0.136118i	−0.0526772	−	0.0141148i
$94$	11.9386	−	6.12382i	1.23138	−	0.631623i
$95$	−7.73350	+	8.85608i	−0.793440	+	0.908614i
$96$	−1.49835	−	1.45832i	−0.152924	−	0.148839i
$97$	−4.41264	+	4.41264i	−0.448035	+	0.448035i	−0.894701	−	0.446666i	$-0.852611\pi$
$97$	−4.41264	+	4.41264i	−0.448035	+	0.448035i	0.446666	+	0.894701i	$0.352611\pi$
$98$	−8.82501	+	4.48545i	−0.891460	+	0.453099i
$99$		−	2.67257i		−	0.268604i
$100$	5.30698	+	8.47561i	0.530698	+	0.847561i
$101$	−1.30911	−	0.755818i	−0.130262	−	0.0752067i	0.433453	−	0.901176i	$-0.357295\pi$
$101$	−1.30911	−	0.755818i	−0.130262	−	0.0752067i	−0.563715	+	0.825969i	$0.690628\pi$
$102$	−0.943957	+	2.93219i	−0.0934657	+	0.290330i
$103$	4.45140	+	1.19275i	0.438609	+	0.117525i	0.471365	−	0.881938i	$-0.343762\pi$
$103$	4.45140	+	1.19275i	0.438609	+	0.117525i	−0.0327554	+	0.999463i	$0.510428\pi$
$104$	−2.53896	+	16.9187i	−0.248966	+	1.65902i
$105$	−2.07082	−	0.702346i	−0.202091	−	0.0685419i
$106$	−6.10729	+	9.46038i	−0.593192	+	0.918873i
$107$	−12.1549	−	3.25690i	−1.17506	−	0.314856i	−0.382095	−	0.924123i	$-0.624797\pi$
$107$	−12.1549	−	3.25690i	−1.17506	−	0.314856i	−0.792965	+	0.609267i	$0.791464\pi$
$108$	−2.74593	−	3.35365i	−0.264227	−	0.322705i
$109$	2.15167	−	3.72680i	0.206092	−	0.356962i	−0.744388	−	0.667747i	$-0.767259\pi$
$109$	2.15167	−	3.72680i	0.206092	−	0.356962i	0.950480	+	0.310785i	$0.100592\pi$
$110$	2.52927	−	1.52132i	0.241157	−	0.145052i
$111$		−	0.617418i		−	0.0586027i
$112$	−4.64166	−	9.51078i	−0.438596	−	0.898685i
$113$	−3.26855	−	3.26855i	−0.307479	−	0.307479i	0.536452	−	0.843931i	$-0.319764\pi$
$113$	−3.26855	−	3.26855i	−0.307479	−	0.307479i	−0.843931	+	0.536452i	$0.819764\pi$
$114$	2.74510	+	0.136413i	0.257102	+	0.0127762i
$115$	5.74202	−	0.388550i	0.535446	−	0.0362325i
$116$	−1.02256	+	10.2634i	−0.0949425	+	0.952930i
$117$	−4.48265	+	16.7295i	−0.414421	+	1.54664i
$118$	0.300459	+	1.39496i	0.0276595	+	0.128417i
$119$	−9.51443	+	12.3520i	−0.872186	+	1.13230i
$120$	0.786609	−	2.20134i	0.0718072	−	0.200954i
$121$	5.06442	+	8.77183i	0.460402	+	0.797439i
$122$	4.42584	+	1.42481i	0.400697	+	0.128996i
$123$	2.18629	−	0.585815i	0.197131	−	0.0528211i
$124$	1.66021	−	2.31130i	0.149091	−	0.207561i
$125$	−6.15236	+	9.33534i	−0.550283	+	0.834978i
$126$	−3.58496	−	10.0962i	−0.319373	−	0.899442i
$127$	−5.01136	−	5.01136i	−0.444686	−	0.444686i	0.448897	−	0.893583i	$-0.351817\pi$
$127$	−5.01136	−	5.01136i	−0.444686	−	0.444686i	−0.893583	+	0.448897i	$0.851817\pi$
$128$	10.2465	−	4.79676i	0.905673	−	0.423977i
$129$	−3.20744	−	1.85182i	−0.282400	−	0.163043i
$130$	−18.3841	+	5.28070i	−1.61240	+	0.463148i
$131$	−2.74939	−	4.76208i	−0.240215	−	0.416065i	0.720560	−	0.693392i	$-0.243885\pi$
$131$	−2.74939	−	4.76208i	−0.240215	−	0.416065i	−0.960775	+	0.277327i	$0.910551\pi$
$132$	−0.645474	−	0.243772i	−0.0561813	−	0.0212176i
$133$	12.8427	+	5.34755i	1.11361	+	0.463691i
$134$	−1.55942	+	2.41560i	−0.134714	+	0.208676i
$135$	2.13414	−	4.35078i	0.183678	−	0.374456i
$136$	−13.0383	−	10.3840i	−1.11802	−	0.890418i
$137$	0.307968	+	1.14935i	0.0263115	+	0.0981959i	0.977833	−	0.209387i	$-0.0671467\pi$
$137$	0.307968	+	1.14935i	0.0263115	+	0.0981959i	−0.951521	+	0.307582i	$0.900480\pi$
$138$	−0.902925	−	0.997355i	−0.0768620	−	0.0849005i
$139$		−	7.23581i		−	0.613734i	−0.951752	−	0.306867i	$-0.900719\pi$
$139$		−	7.23581i		−	0.613734i	0.951752	−	0.306867i	$-0.0992806\pi$
$140$	7.51419	−	9.13986i	0.635065	−	0.772459i
$141$		−	3.50681i		−	0.295326i
$142$	−13.1486	+	11.9037i	−1.10340	+	0.998933i
$143$	1.46119	+	5.45322i	0.122190	+	0.456021i
$144$	10.8540	−	3.65710i	0.904499	−	0.304759i
$145$	−10.9118	+	3.72980i	−0.906172	+	0.309743i
$146$	−3.94484	−	2.54665i	−0.326477	−	0.210762i
$147$	−0.00959489	+	2.58730i	−0.000791373	+	0.213397i
$148$	3.12539	+	1.18035i	0.256906	+	0.0970240i
$149$	−1.62968	−	2.82269i	−0.133509	−	0.231244i	0.791518	−	0.611146i	$-0.209291\pi$
$149$	−1.62968	−	2.82269i	−0.133509	−	0.231244i	−0.925027	+	0.379902i	$0.875958\pi$
$150$	2.60404	−	0.223130i	0.212619	−	0.0182185i
$151$	−15.5929	−	9.00258i	−1.26893	−	0.732620i	−0.294148	−	0.955760i	$-0.595036\pi$
$151$	−15.5929	−	9.00258i	−1.26893	−	0.732620i	−0.974786	+	0.223140i	$0.928369\pi$
$152$	−5.93847	+	13.6350i	−0.481673	+	1.10595i
$153$	−11.9317	−	11.9317i	−0.964624	−	0.964624i
$154$	−2.65752	−	2.26581i	−0.214149	−	0.182585i
$155$	3.12183	+	0.614110i	0.250752	+	0.0493265i
$156$	3.63159	+	2.60858i	0.290760	+	0.208853i
$157$	−16.5963	+	4.44696i	−1.32453	+	0.354906i	−0.850672	−	0.525696i	$-0.823805\pi$
$157$	−16.5963	+	4.44696i	−1.32453	+	0.354906i	−0.473856	+	0.880603i	$0.657138\pi$
$158$	−1.75470	+	5.45058i	−0.139596	+	0.433625i
$159$	1.47151	+	2.54872i	0.116698	+	0.202127i
$160$	9.63948	+	8.19026i	0.762068	+	0.647497i
$161$	−2.59425	−	6.29606i	−0.204455	−	0.496199i
$162$	10.7685	−	2.31941i	0.846055	−	0.182230i
$163$	−6.27040	+	23.4014i	−0.491135	+	1.83294i	0.0595442	+	0.998226i	$0.481035\pi$
$163$	−6.27040	+	23.4014i	−0.491135	+	1.83294i	−0.550680	+	0.834717i	$0.685631\pi$
$164$	−1.21422	+	12.1870i	−0.0948147	+	0.951647i
$165$	−0.0520807	−	0.769653i	−0.00405448	−	0.0599174i
$166$	0.914889	−	18.4108i	0.0710092	−	1.42895i
$167$	0.324222	+	0.324222i	0.0250891	+	0.0250891i	0.719540	−	0.694451i	$-0.244353\pi$
$167$	0.324222	+	0.324222i	0.0250891	+	0.0250891i	−0.694451	+	0.719540i	$0.744353\pi$
$168$	−2.76541	−	0.0550701i	−0.213356	−	0.00424875i
$169$		−	23.5862i		−	1.81432i
$170$	4.50001	−	18.0839i	0.345135	−	1.38697i
$171$	−7.52795	+	13.0388i	−0.575677	+	0.997101i
$172$	15.5058	−	12.6960i	1.18231	−	0.968061i
$173$	−11.2669	−	3.01895i	−0.856605	−	0.229526i	−0.196318	−	0.980540i	$-0.562898\pi$
$173$	−11.2669	−	3.01895i	−0.856605	−	0.229526i	−0.660287	+	0.751014i	$0.729565\pi$
$174$	2.26477	+	1.46206i	0.171692	+	0.110838i
$175$	12.7861	+	3.39349i	0.966538	+	0.256524i
$176$	2.46797	−	2.80139i	0.186030	−	0.211162i
$177$	0.360239	+	0.0965257i	0.0270772	+	0.00725531i
$178$	16.0736	+	5.17457i	1.20477	+	0.387850i
$179$	8.91929	+	5.14955i	0.666659	+	0.384896i	0.794810	−	0.606859i	$-0.207571\pi$
$179$	8.91929	+	5.14955i	0.666659	+	0.384896i	−0.128151	+	0.991755i	$0.540904\pi$
$180$	8.76290	+	9.33760i	0.653148	+	0.695984i
$181$			4.32971i			0.321825i	0.986969	+	0.160912i	$0.0514436\pi$
$181$			4.32971i			0.321825i	−0.986969	+	0.160912i	$0.948556\pi$
$182$	12.8348	+	18.6407i	0.951380	+	1.38174i
$183$	0.859272	−	0.859272i	0.0635192	−	0.0635192i
$184$	6.77482	−	2.66395i	0.499446	−	0.196389i
$185$	0.252175	+	3.72667i	0.0185403	+	0.273990i
$186$	−0.339455	−	0.661783i	−0.0248901	−	0.0485243i
$187$	−5.31292	−	1.42359i	−0.388519	−	0.104103i
$188$	17.7516	+	6.70413i	1.29467	+	0.488949i
$189$	−5.68343	−	0.758962i	−0.413409	−	0.0552063i
$190$	−16.6248	+	0.297825i	−1.20609	+	0.0216065i
$191$	−18.9512	+	10.9415i	−1.37126	+	0.791696i	−0.991086	−	0.133221i	$-0.957468\pi$
$191$	−18.9512	+	10.9415i	−1.37126	+	0.791696i	−0.380171	+	0.924916i	$0.624135\pi$
$192$	0.106764	−	2.95501i	0.00770501	−	0.213259i
$193$	21.2377	−	5.69064i	1.52873	−	0.409621i	0.606123	−	0.795371i	$-0.292724\pi$
$193$	21.2377	−	5.69064i	1.52873	−	0.409621i	0.922603	+	0.385750i	$0.126057\pi$
$194$	−8.81440	−	0.438015i	−0.632837	−	0.0314476i
$195$	−0.964912	+	4.90513i	−0.0690988	+	0.351264i
$196$	−13.0787	−	4.99484i	−0.934191	−	0.356774i
$197$	−0.857585	−	0.857585i	−0.0611004	−	0.0611004i	0.675896	−	0.736997i	$-0.263757\pi$
$197$	−0.857585	−	0.857585i	−0.0611004	−	0.0611004i	−0.736997	+	0.675896i	$0.763757\pi$
$198$	2.80193	−	2.53664i	0.199124	−	0.180271i
$199$	4.95165	−	8.57652i	0.351013	−	0.607973i	−0.635414	−	0.772172i	$-0.719170\pi$
$199$	4.95165	−	8.57652i	0.351013	−	0.607973i	0.986427	+	0.164199i	$0.0525038\pi$
$200$	−3.84878	+	13.6083i	−0.272150	+	0.962255i
$201$	0.375732	+	0.650787i	0.0265021	+	0.0459030i
$202$	−0.450129	−	2.08985i	−0.0316709	−	0.147041i
$203$	8.28609	+	10.8402i	0.581569	+	0.760833i
$204$	−3.97005	+	1.79340i	−0.277959	+	0.125563i
$205$	−12.9569	+	4.42887i	−0.904952	+	0.309326i
$206$	2.97450	+	5.79892i	0.207243	+	0.404030i
$207$	7.11861	−	1.90742i	0.494777	−	0.132575i
$208$	−20.1474	+	13.3963i	−1.39697	+	0.928868i
$209$			4.90769i			0.339472i
$210$	−1.22915	−	2.83767i	−0.0848193	−	0.195818i
$211$	18.4290			1.26871			0.634354	−	0.773043i	$-0.281266\pi$
$211$	18.4290			1.26871			0.634354	+	0.773043i	$0.281266\pi$
$212$	−15.7149	+	2.57631i	−1.07930	+	0.176941i
$213$	1.19978	+	4.47762i	0.0822073	+	0.306802i
$214$	−8.12213	−	15.8344i	−0.555217	−	1.08242i
$215$	20.1161	+	9.86734i	1.37191	+	0.672947i
$216$	0.909699	−	6.06190i	0.0618972	−	0.412460i
$217$	−0.484457	−	3.73329i	−0.0328871	−	0.253432i
$218$	5.94939	−	1.28143i	0.402944	−	0.0867893i
$219$	−1.06278	+	0.613597i	−0.0718161	+	0.0414630i
$220$	3.99558	+	1.20775i	0.269382	+	0.0814264i
$221$	30.8694	+	17.8225i	2.07650	+	1.19887i
$222$	0.647300	−	0.586013i	0.0434440	−	0.0393306i
$223$	15.5226	−	15.5226i	1.03947	−	1.03947i	0.0402785	−	0.999188i	$-0.487175\pi$
$223$	15.5226	−	15.5226i	1.03947	−	1.03947i	0.999188	−	0.0402785i	$-0.0128245\pi$
$224$	5.56554	−	13.8933i	0.371863	−	0.928288i
$225$	−5.42285	+	13.2502i	−0.361523	+	0.883344i
$226$	0.324448	−	6.52904i	0.0215820	−	0.434305i
$227$	−5.45937	−	20.3746i	−0.362351	−	1.35231i	−0.870977	−	0.491325i	$-0.836513\pi$
$227$	−5.45937	−	20.3746i	−0.362351	−	1.35231i	0.508625	−	0.860988i	$-0.330154\pi$
$228$	2.46246	+	3.00744i	0.163080	+	0.199172i
$229$	−5.62790	−	9.74781i	−0.371902	−	0.644153i	0.617956	−	0.786213i	$-0.287961\pi$
$229$	−5.62790	−	9.74781i	−0.371902	−	0.644153i	−0.989858	+	0.142059i	$0.954628\pi$
$230$	5.85731	+	5.65114i	0.386220	+	0.372625i
$231$	−0.843915	+	0.347729i	−0.0555255	+	0.0228789i
$232$	−11.7307	+	8.66928i	−0.770155	+	0.569166i
$233$	4.07176	−	15.1960i	0.266750	−	0.995523i	−0.694421	−	0.719569i	$-0.744340\pi$
$233$	4.07176	−	15.1960i	0.266750	−	0.995523i	0.961171	−	0.275954i	$-0.0889938\pi$
$234$	−21.7938	+	11.1789i	−1.42471	+	0.730789i
$235$	1.43230	+	21.1667i	0.0934332	+	1.38076i
$236$	−1.17730	+	1.63901i	−0.0766359	+	0.106690i
$237$	1.05822	+	1.05822i	0.0687390	+	0.0687390i
$238$	−21.9803	+	1.74876i	−1.42477	+	0.113355i
$239$	13.7719			0.890831			0.445415	−	0.895324i	$-0.353056\pi$
$239$	13.7719			0.890831			0.445415	+	0.895324i	$0.353056\pi$
$240$	3.05448	−	1.26469i	0.197166	−	0.0816355i
$241$	−0.456648	+	0.790937i	−0.0294153	+	0.0509487i	−0.880358	−	0.474309i	$-0.842698\pi$
$241$	−0.456648	+	0.790937i	−0.0294153	+	0.0509487i	0.850943	+	0.525258i	$0.176031\pi$
$242$	−4.38956	+	13.6352i	−0.282172	+	0.876503i
$243$	2.42788	−	9.06096i	0.155748	−	0.581261i
$244$	2.70696	+	5.99238i	0.173295	+	0.383623i
$245$	−0.998831	−	15.6206i	−0.0638130	−	0.997962i
$246$	2.68925	+	1.73609i	0.171461	+	0.110689i
$247$	8.23156	−	30.7206i	0.523762	−	1.95471i
$248$	3.99892	−	0.453174i	0.253932	−	0.0287766i
$249$	−4.17230	−	2.40888i	−0.264409	−	0.152656i
$250$	−15.6266	+	2.41037i	−0.988312	+	0.152445i
$251$	0.192874			0.0121741			0.00608705	−	0.999981i	$-0.498062\pi$
$251$	0.192874			0.0121741			0.00608705	+	0.999981i	$0.498062\pi$
$252$	7.18226	−	13.3411i	0.452440	−	0.840413i
$253$	1.69866	−	1.69866i	0.106794	−	0.106794i
$254$	0.497446	−	10.0104i	0.0312126	−	0.628106i
$255$	−3.66864	−	3.20361i	−0.229739	−	0.200618i
$256$	14.7543	+	6.18967i	0.922141	+	0.386854i
$257$	18.6795	+	5.00515i	1.16519	+	0.312213i	0.789039	−	0.614343i	$-0.210579\pi$
$257$	18.6795	+	5.00515i	1.16519	+	0.312213i	0.376156	+	0.926556i	$0.377246\pi$
$258$	−1.10285	−	5.12031i	−0.0686607	−	0.318776i
$259$	4.08625	−	1.68371i	0.253907	−	0.104621i
$260$	−22.9853	−	14.2618i	−1.42549	−	0.884480i
$261$	−12.7884	+	7.38336i	−0.791580	+	0.457019i
$262$	2.38302	−	7.40232i	0.147223	−	0.457317i
$263$	−5.24206	−	19.5636i	−0.323239	−	1.20635i	−0.916070	−	0.401018i	$-0.868656\pi$
$263$	−5.24206	−	19.5636i	−0.323239	−	1.20635i	0.592831	−	0.805327i	$-0.298010\pi$
$264$	−0.357072	−	0.908088i	−0.0219763	−	0.0558889i
$265$	−9.92285	−	14.7828i	−0.609556	−	0.908101i
$266$	6.58312	+	18.5399i	0.403637	+	1.13675i
$267$	3.12068	−	3.12068i	0.190982	−	0.190982i
$268$	−4.01262	+	0.657830i	−0.245110	+	0.0401833i
$269$	2.29596	−	3.97672i	0.139987	−	0.242465i	−0.787504	−	0.616309i	$-0.788627\pi$
$269$	2.29596	−	3.97672i	0.139987	−	0.242465i	0.927491	+	0.373844i	$0.121961\pi$
$270$	6.58695	−	1.89205i	0.400869	−	0.115147i
$271$	18.4195	−	10.6345i	1.11890	−	0.645999i	0.177782	−	0.984070i	$-0.443108\pi$
$271$	18.4195	−	10.6345i	1.11890	−	0.645999i	0.941121	+	0.338071i	$0.109774\pi$
$272$	−1.48854	−	23.5251i	−0.0902561	−	1.42642i
$273$	5.86588	−	0.761195i	0.355019	−	0.0460696i
$274$	−0.912678	+	1.41377i	−0.0551369	+	0.0854087i
$275$	0.628707	+	4.62427i	0.0379125	+	0.278854i
$276$	0.188629	−	1.89325i	0.0113541	−	0.113960i
$277$	15.4644	−	4.14367i	0.929164	−	0.248969i	0.237666	−	0.971347i	$-0.423618\pi$
$277$	15.4644	−	4.14367i	0.929164	−	0.248969i	0.691498	+	0.722378i	$0.256951\pi$
$278$	7.58602	−	6.86777i	0.454979	−	0.411901i
$279$	4.07426			0.243920
$280$	16.7142	−	0.797095i	0.998865	−	0.0476355i
$281$	−18.0107			−1.07443			−0.537214	−	0.843446i	$-0.680523\pi$
$281$	−18.0107			−1.07443			−0.537214	+	0.843446i	$0.680523\pi$
$282$	3.67653	−	3.32844i	0.218934	−	0.198205i
$283$	3.61970	−	0.969897i	0.215169	−	0.0576544i	−0.149624	−	0.988743i	$-0.547806\pi$
$283$	3.61970	−	0.969897i	0.215169	−	0.0576544i	0.364793	+	0.931089i	$0.381140\pi$
$284$	−24.9596	−	2.48678i	−1.48108	−	0.147563i
$285$	−1.91382	+	3.90163i	−0.113365	+	0.231113i
$286$	−4.33029	+	6.70775i	−0.256055	+	0.396638i
$287$	9.83914	+	12.8720i	0.580786	+	0.759808i
$288$	14.1360	+	7.90823i	0.832973	+	0.465997i
$289$	−15.3528	+	8.86395i	−0.903106	+	0.521409i
$290$	−14.2671	−	7.89980i	−0.837791	−	0.463892i
$291$	−1.15328	+	1.99754i	−0.0676065	+	0.117098i
$292$	−1.07428	−	6.55288i	−0.0628676	−	0.383478i
$293$	6.03311	−	6.03311i	0.352458	−	0.352458i	−0.508565	−	0.861023i	$-0.669824\pi$
$293$	6.03311	−	6.03311i	0.352458	−	0.352458i	0.861023	+	0.508565i	$0.169824\pi$
$294$	−2.72163	+	2.44564i	−0.158729	+	0.142633i
$295$	−2.21379	−	0.435484i	−0.128892	−	0.0253549i
$296$	1.72895	+	4.39697i	0.100493	+	0.255569i
$297$	−0.523536	−	1.95386i	−0.0303786	−	0.113375i
$298$	1.41252	−	4.38767i	0.0818250	−	0.254171i
$299$	−13.4822	+	7.78396i	−0.779696	+	0.450158i
$300$	2.70552	+	2.51830i	0.156203	+	0.145394i
$301$	3.50911	−	26.2777i	0.202262	−	1.51462i
$302$	−5.36150	−	24.8923i	−0.308520	−	1.43239i
$303$	−0.539687	−	0.144609i	−0.0310042	−	0.00830756i
$304$	−19.9314	+	6.71560i	−1.14314	+	0.385166i
$305$	−4.83551	+	5.53743i	−0.276881	+	0.317072i
$306$	1.18439	−	23.8341i	0.0677070	−	1.36250i
$307$	−14.8970	+	14.8970i	−0.850215	+	0.850215i	−0.990159	−	0.139944i	$-0.955308\pi$
$307$	−14.8970	+	14.8970i	−0.850215	+	0.850215i	0.139944	+	0.990159i	$0.455308\pi$
$308$	−0.146866	−	4.93671i	−0.00836845	−	0.281295i
$309$	1.70335			0.0969002
$310$	2.31921	+	3.85580i	0.131722	+	0.218995i
$311$	3.12920	+	1.80664i	0.177441	+	0.102445i	0.586090	−	0.810246i	$-0.300667\pi$
$311$	3.12920	+	1.80664i	0.177441	+	0.102445i	−0.408649	+	0.912692i	$0.634000\pi$
$312$	0.712043	+	6.28325i	0.0403115	+	0.355719i
$313$	0.450144	−	1.67996i	0.0254437	−	0.0949570i	−0.952036	−	0.305985i	$-0.901014\pi$
$313$	0.450144	−	1.67996i	0.0254437	−	0.0949570i	0.977480	+	0.211028i	$0.0676810\pi$
$314$	−20.4143	−	13.1788i	−1.15205	−	0.743721i
$315$	16.9040	+	1.10352i	0.952434	+	0.0621764i
$316$	−7.37983	+	3.33371i	−0.415148	+	0.187536i
$317$	0.369498	−	1.37898i	0.0207531	−	0.0774515i	−0.954773	−	0.297337i	$-0.903902\pi$
$317$	0.369498	−	1.37898i	0.0207531	−	0.0774515i	0.975526	+	0.219885i	$0.0705683\pi$
$318$	−1.27542	+	3.96181i	−0.0715221	+	0.222167i
$319$	−2.40672	+	4.16856i	−0.134750	+	0.233394i
$320$	0.562515	+	17.8797i	0.0314455	+	0.999505i
$321$	−4.65114			−0.259601
$322$	4.13849	−	8.69562i	0.230629	−	0.484588i
$323$	21.9105	+	21.9105i	1.21913	+	1.21913i
$324$	12.6525	+	9.08827i	0.702914	+	0.504904i
$325$	3.82067	−	30.0010i	0.211933	−	1.66415i
$326$	−30.4855	+	15.6373i	−1.68844	+	0.866068i
$327$	0.411673	−	1.53639i	0.0227656	−	0.0849623i
$328$	−13.9293	+	10.2942i	−0.769119	+	0.568399i
$329$	23.2090	−	9.56312i	1.27956	−	0.527232i
$330$	0.757472	−	0.785106i	0.0416974	−	0.0432187i
$331$	4.50741	+	7.80706i	0.247750	+	0.429115i	0.962901	−	0.269855i	$-0.0869757\pi$
$331$	4.50741	+	7.80706i	0.247750	+	0.429115i	−0.715152	+	0.698969i	$0.753642\pi$
$332$	20.1702	−	16.5152i	1.10698	−	0.906388i
$333$	1.23795	+	4.62010i	0.0678393	+	0.253180i
$334$	−0.0321835	+	0.647645i	−0.00176100	+	0.0354376i
$335$	−2.53368	−	3.77462i	−0.138430	−	0.206229i
$336$	−2.56701	−	2.95152i	−0.140042	−	0.161019i
$337$	−14.5042	+	14.5042i	−0.790093	+	0.790093i	−0.981509	−	0.191416i	$-0.938692\pi$
$337$	−14.5042	+	14.5042i	−0.790093	+	0.790093i	0.191416	+	0.981509i	$0.438692\pi$
$338$	24.7278	−	22.3865i	1.34501	−	1.21767i
$339$	−1.47963	−	0.854263i	−0.0803623	−	0.0463972i
$340$	23.2303	−	12.4463i	1.25984	−	0.674996i
$341$	1.15014	−	0.664033i	0.0622835	−	0.0359594i
$342$	−20.8149	+	4.48328i	−1.12554	+	0.242428i
$343$	−17.1496	+	6.99211i	−0.925994	+	0.377538i
$344$	28.0276	+	4.20605i	1.51115	+	0.226775i
$345$	2.01286	−	0.688024i	0.108369	−	0.0370420i
$346$	−7.52873	−	14.6776i	−0.404747	−	0.789071i
$347$	−4.33964	−	16.1957i	−0.232964	−	0.869433i	−0.979056	−	0.203590i	$-0.934739\pi$
$347$	−4.33964	−	16.1957i	−0.232964	−	0.869433i	0.746092	−	0.665842i	$-0.231928\pi$
$348$	0.616756	+	3.76207i	0.0330616	+	0.201668i
$349$	2.69468			0.144243			0.0721214	−	0.997396i	$-0.477023\pi$
$349$	2.69468			0.144243			0.0721214	+	0.997396i	$0.477023\pi$
$350$	8.57801	+	16.6258i	0.458514	+	0.888687i
$351$			13.1087i			0.699689i
$352$	5.27941	−	0.0714778i	0.281394	−	0.00380978i
$353$	−8.71218	+	2.33442i	−0.463703	+	0.124249i	−0.483104	−	0.875563i	$-0.660491\pi$
$353$	−8.71218	+	2.33442i	−0.463703	+	0.124249i	0.0194013	+	0.999812i	$0.493824\pi$
$354$	0.240718	+	0.469290i	0.0127940	+	0.0249425i
$355$	−9.07054	−	26.5364i	−0.481414	−	1.40841i
$356$	9.83105	+	21.7630i	0.521045	+	1.15343i
$357$	−2.21523	+	5.32011i	−0.117242	+	0.281570i
$358$	3.06683	+	14.2386i	0.162087	+	0.752534i
$359$	7.69847	+	13.3341i	0.406310	+	0.703749i	0.994473	−	0.104993i	$-0.0334821\pi$
$359$	7.69847	+	13.3341i	0.406310	+	0.703749i	−0.588163	+	0.808742i	$0.700149\pi$
$360$	−1.47235	+	18.0497i	−0.0775997	+	0.951301i
$361$	4.32370	−	7.48887i	0.227563	−	0.394151i
$362$	−4.53926	+	4.10948i	−0.238578	+	0.215989i
$363$	2.64726	+	2.64726i	0.138945	+	0.138945i
$364$	−7.36089	+	31.1485i	−0.385815	+	1.63263i
$365$	6.16421	−	4.13768i	0.322650	−	0.216576i
$366$	1.71643	+	0.0852945i	0.0897190	+	0.00445841i
$367$	6.35657	−	1.70324i	0.331810	−	0.0889083i	−0.0890677	−	0.996026i	$-0.528389\pi$
$367$	6.35657	−	1.70324i	0.331810	−	0.0889083i	0.420878	+	0.907117i	$0.361722\pi$
$368$	9.22310	+	4.57427i	0.480788	+	0.238450i
$369$	−15.1853	+	8.76722i	−0.790514	+	0.456403i
$370$	−3.66769	+	3.80149i	−0.190674	+	0.197630i
$371$	−12.8554	+	16.6893i	−0.667417	+	0.866464i
$372$	0.371623	−	0.984006i	0.0192678	−	0.0510183i
$373$	1.83269	+	0.491068i	0.0948931	+	0.0254265i	0.305953	−	0.952047i	$-0.401025\pi$
$373$	1.83269	+	0.491068i	0.0948931	+	0.0254265i	−0.211060	+	0.977473i	$0.567692\pi$
$374$	−3.55019	−	6.92124i	−0.183576	−	0.357889i
$375$	−1.30347	+	3.92148i	−0.0673111	+	0.202504i
$376$	9.82007	+	24.9739i	0.506431	+	1.28793i
$377$	22.0571	−	22.0571i	1.13600	−	1.13600i
$378$	−4.59865	−	6.67886i	−0.236529	−	0.343524i
$379$			8.18575i			0.420473i	0.977651	+	0.210237i	$0.0674235\pi$
$379$			8.18575i			0.420473i	−0.977651	+	0.210237i	$0.932577\pi$
$380$	−16.0915	−	17.1468i	−0.825475	−	0.879612i
$381$	−2.26857	−	1.30976i	−0.116223	−	0.0671011i
$382$	−29.4582	−	9.48345i	−1.50721	−	0.485216i
$383$	−34.8240	−	9.33107i	−1.77943	−	0.476796i	−0.788947	−	0.614462i	$-0.789373\pi$
$383$	−34.8240	−	9.33107i	−1.77943	−	0.476796i	−0.990479	+	0.137666i	$0.956040\pi$
$384$	3.19936	−	2.69277i	0.163267	−	0.137415i
$385$	4.95176	−	2.44354i	0.252365	−	0.124534i
$386$	26.1236	+	16.8645i	1.32965	+	0.858378i
$387$	27.7141	+	7.42596i	1.40878	+	0.377483i
$388$	−7.90685	−	9.65674i	−0.401409	−	0.490247i
$389$	−4.99176	+	8.64599i	−0.253092	+	0.438369i	−0.964376	−	0.264537i	$-0.914781\pi$
$389$	−4.99176	+	8.64599i	−0.253092	+	0.438369i	0.711283	+	0.702906i	$0.248114\pi$
$390$	−6.05837	+	3.64403i	−0.306778	+	0.184522i
$391$		−	15.1674i		−	0.767048i
$392$	−7.17685	−	18.4524i	−0.362486	−	0.931989i
$393$	−1.43715	−	1.43715i	−0.0724947	−	0.0724947i
$394$	0.0851271	−	1.71306i	0.00428864	−	0.0863025i
$395$	−6.81954	−	5.95510i	−0.343128	−	0.299634i
$396$	5.31881	+	0.529925i	0.267281	+	0.0266297i
$397$	−6.36274	+	23.7461i	−0.319337	+	1.19178i	0.600547	+	0.799589i	$0.294949\pi$
$397$	−6.36274	+	23.7461i	−0.319337	+	1.19178i	−0.919884	+	0.392191i	$0.871717\pi$
$398$	13.6914	−	2.94897i	0.686288	−	0.147818i
$399$	5.09671	+	0.680611i	0.255154	+	0.0340731i
$400$	−17.9200	+	8.88110i	−0.895999	+	0.444055i
$401$	−0.336778	−	0.583317i	−0.0168179	−	0.0291295i	0.857494	−	0.514494i	$-0.172020\pi$
$401$	−0.336778	−	0.583317i	−0.0168179	−	0.0291295i	−0.874312	+	0.485365i	$0.838687\pi$
$402$	−0.325664	+	1.01160i	−0.0162426	+	0.0504541i
$403$	−8.31327	+	2.22753i	−0.414113	+	0.110961i
$404$	1.76376	−	2.45546i	0.0877505	−	0.122164i
$405$	−3.36175	+	17.0895i	−0.167047	+	0.849183i
$406$	−3.50024	+	18.9759i	−0.173714	+	0.941760i
$407$	1.10246	+	1.10246i	0.0546469	+	0.0546469i
$408$	−5.64832	−	2.46002i	−0.279634	−	0.121789i
$409$	−16.9971	−	9.81326i	−0.840450	−	0.485234i	0.0169669	−	0.999856i	$-0.494599\pi$
$409$	−16.9971	−	9.81326i	−0.840450	−	0.485234i	−0.857417	+	0.514622i	$0.827932\pi$
$410$	−16.9411	−	9.38045i	−0.836663	−	0.463268i
$411$	0.219903	+	0.380883i	0.0108470	+	0.0187876i
$412$	−3.25638	+	8.62243i	−0.160430	+	0.424797i
$413$	0.343543	+	2.64739i	0.0169046	+	0.130270i
$414$	8.75627	+	5.65274i	0.430347	+	0.277817i
$415$	26.1674	+	12.8356i	1.28451	+	0.630075i
$416$	−33.1673	−	8.40760i	−1.62616	−	0.412217i
$417$	−0.692206	−	2.58335i	−0.0338975	−	0.126507i
$418$	−5.14522	+	4.65807i	−0.251661	+	0.227834i
$419$		−	18.0799i		−	0.883263i	−0.897197	−	0.441631i	$-0.854400\pi$
$419$		−	18.0799i		−	0.883263i	0.897197	−	0.441631i	$-0.145600\pi$
$420$	1.80838	−	3.98197i	0.0882398	−	0.194300i
$421$			16.5073i			0.804518i	0.915526	+	0.402259i	$0.131775\pi$
$421$			16.5073i			0.804518i	−0.915526	+	0.402259i	$0.868225\pi$
$422$	17.4917	+	19.3210i	0.851481	+	0.940531i
$423$	7.03131	+	26.2412i	0.341874	+	1.27589i
$424$	−17.6166	−	14.0302i	−0.855537	−	0.681368i
$425$	23.4520	+	17.8382i	1.13759	+	0.865281i
$426$	−3.55559	+	5.50772i	−0.172269	+	0.266850i
$427$	8.03016	+	3.34366i	0.388606	+	0.161811i
$428$	8.89182	−	23.5443i	0.429802	−	1.13806i
$429$	1.04335	+	1.80714i	0.0503735	+	0.0872494i
$430$	8.74802	+	30.4552i	0.421867	+	1.46868i
$431$	−14.3957	−	8.31135i	−0.693416	−	0.400344i	0.111475	−	0.993767i	$-0.464443\pi$
$431$	−14.3957	−	8.31135i	−0.693416	−	0.400344i	−0.804890	+	0.593423i	$0.797776\pi$
$432$	7.21872	−	4.79984i	0.347311	−	0.230932i
$433$	18.2234	+	18.2234i	0.875760	+	0.875760i	0.993093	−	0.117332i	$-0.0374343\pi$
$433$	18.2234	+	18.2234i	0.875760	+	0.875760i	−0.117332	+	0.993093i	$0.537434\pi$
$434$	3.45417	−	4.05130i	0.165805	−	0.194469i
$435$	−3.53893	+	2.37548i	−0.169679	+	0.113896i
$436$	6.99023	+	5.02109i	0.334771	+	0.240467i
$437$	−13.0720	+	3.50264i	−0.625319	+	0.167554i
$438$	−1.65202	−	0.531832i	−0.0789365	−	0.0254119i
$439$	−0.223132	−	0.386476i	−0.0106495	−	0.0184455i	0.860652	−	0.509194i	$-0.170057\pi$
$439$	−0.223132	−	0.386476i	−0.0106495	−	0.0184455i	−0.871301	+	0.490749i	$0.836723\pi$
$440$	2.52614	+	5.33528i	0.120429	+	0.254349i
$441$	−5.11585	−	19.3798i	−0.243612	−	0.922848i
$442$	10.6142	+	49.2794i	0.504866	+	2.34398i
$443$	10.0048	−	37.3383i	0.475341	−	1.77400i	−0.144753	−	0.989468i	$-0.546239\pi$
$443$	10.0048	−	37.3383i	0.475341	−	1.77400i	0.620094	−	0.784528i	$-0.287095\pi$
$444$	1.22875	+	0.122423i	0.0583140	+	0.00580995i
$445$	−17.5615	+	20.1107i	−0.832494	+	0.953337i
$446$	31.0068	+	1.54083i	1.46822	+	0.0729602i
$447$	−0.851862	−	0.851862i	−0.0402917	−	0.0402917i
$448$	19.8482	−	7.35176i	0.937740	−	0.347338i
$449$			31.7000i			1.49602i	0.663689	+	0.748008i	$0.268990\pi$
$449$			31.7000i			1.49602i	−0.663689	+	0.748008i	$0.731010\pi$
$450$	−19.0385	+	6.89089i	−0.897483	+	0.324840i
$451$	−2.85781	+	4.94987i	−0.134569	+	0.233080i
$452$	7.15299	−	5.85680i	0.336448	−	0.275480i
$453$	−6.42824	−	1.72244i	−0.302025	−	0.0809274i
$454$	16.1791	−	25.0619i	0.759322	−	1.17621i
$455$	−35.0949	+	6.99033i	−1.64527	+	0.327712i
$456$	−0.815787	+	5.43610i	−0.0382027	+	0.254569i
$457$	27.1592	+	7.27728i	1.27045	+	0.340417i	0.830205	−	0.557459i	$-0.188224\pi$
$457$	27.1592	+	7.27728i	1.27045	+	0.340417i	0.440249	+	0.897876i	$0.354890\pi$
$458$	4.87796	−	15.1523i	0.227932	−	0.708019i
$459$	−11.0604	−	6.38571i	−0.516254	−	0.298059i
$460$	−0.365272	+	11.5045i	−0.0170309	+	0.536400i
$461$		−	3.03886i		−	0.141534i	−0.997493	−	0.0707669i	$-0.977455\pi$
$461$		−	3.03886i		−	0.141534i	0.997493	−	0.0707669i	$-0.0225447\pi$
$462$	−1.16555	−	0.554718i	−0.0542263	−	0.0258078i
$463$	−4.72295	+	4.72295i	−0.219494	+	0.219494i	−0.808285	−	0.588791i	$-0.799604\pi$
$463$	−4.72295	+	4.72295i	−0.219494	+	0.219494i	0.588791	+	0.808285i	$0.299604\pi$
$464$	−20.2229	−	4.07010i	−0.938822	−	0.188950i
$465$	1.17331	−	0.0793955i	0.0544111	−	0.00368188i
$466$	19.7961	−	10.1542i	0.917038	−	0.470386i
$467$	−10.6525	−	2.85433i	−0.492939	−	0.132082i	0.00378232	−	0.999993i	$-0.498796\pi$
$467$	−10.6525	−	2.85433i	−0.492939	−	0.132082i	−0.496721	+	0.867910i	$0.665463\pi$
$468$	−32.4053	−	12.2383i	−1.49793	−	0.565715i
$469$	−3.28247	+	4.26141i	−0.151570	+	0.196774i
$470$	−20.8317	+	21.5917i	−0.960895	+	0.995951i
$471$	−5.49983	+	3.17533i	−0.253419	+	0.146311i
$472$	−2.83576	+	0.321360i	−0.130526	+	0.0147918i
$473$	9.03381	−	2.42060i	0.415375	−	0.111299i
$474$	−0.105043	+	2.11384i	−0.00482479	+	0.0970918i
$475$	9.95807	−	24.3315i	0.456908	−	1.11641i
$476$	−22.6957	−	21.3843i	−1.04025	−	0.980147i
$477$	−16.1215	−	16.1215i	−0.738153	−	0.738153i
$478$	13.0714	+	14.4385i	0.597872	+	0.660400i
$479$	−4.81272	+	8.33587i	−0.219899	+	0.380876i	−0.954777	−	0.297323i	$-0.903906\pi$
$479$	−4.81272	+	8.33587i	−0.219899	+	0.380876i	0.734878	+	0.678199i	$0.237239\pi$
$480$	4.22502	+	2.00196i	0.192845	+	0.0913763i
$481$	−5.05192	−	8.75018i	−0.230348	−	0.398974i
$482$	−1.26264	+	0.271957i	−0.0575116	+	0.0123873i
$483$	−1.52851	−	1.99966i	−0.0695495	−	0.0909876i
$484$	−18.4614	+	8.33963i	−0.839155	+	0.379074i
$485$	6.14521	−	12.5280i	0.279039	−	0.568866i
$486$	11.8039	−	6.05470i	0.535436	−	0.274647i
$487$	−31.8333	+	8.52972i	−1.44251	+	0.386518i	−0.893410	−	0.449241i	$-0.851694\pi$
$487$	−31.8333	+	8.52972i	−1.44251	+	0.386518i	−0.549096	+	0.835760i	$0.685028\pi$
$488$	−3.71314	+	8.52556i	−0.168086	+	0.385934i
$489$			8.95469i			0.404945i
$490$	15.4286	−	15.8732i	0.696992	−	0.717079i
$491$	−29.0829			−1.31250			−0.656248	−	0.754546i	$-0.727857\pi$
$491$	−29.0829			−1.31250			−0.656248	+	0.754546i	$0.727857\pi$
$492$	0.732354	+	4.46720i	0.0330171	+	0.201397i
$493$	7.86575	+	29.3554i	0.354256	+	1.32210i
$494$	40.0203	−	20.5281i	1.80060	−	0.923601i
$495$	1.93290	+	5.65483i	0.0868776	+	0.254166i
$496$	4.27063	+	3.76235i	0.191757	+	0.168934i
$497$	−26.3624	+	20.1510i	−1.18251	+	0.903897i
$498$	−1.43461	−	6.66059i	−0.0642865	−	0.298468i
$499$	−2.03353	+	1.17406i	−0.0910334	+	0.0525581i	−0.544826	−	0.838549i	$-0.683404\pi$
$499$	−2.03353	+	1.17406i	−0.0910334	+	0.0525581i	0.453792	+	0.891108i	$0.350071\pi$
$500$	−17.3588	−	14.0951i	−0.776308	−	0.630353i
$501$	0.146771	+	0.0847382i	0.00655724	+	0.00378583i
$502$	0.183064	+	0.202209i	0.00817052	+	0.00902502i
$503$	3.87893	−	3.87893i	0.172953	−	0.172953i	−0.615322	−	0.788276i	$-0.710974\pi$
$503$	3.87893	−	3.87893i	0.172953	−	0.172953i	0.788276	+	0.615322i	$0.210974\pi$
$504$	20.8038	−	5.13269i	0.926674	−	0.228628i
$505$	3.31656	+	0.652416i	0.147585	+	0.0290321i
$506$	3.39314	+	0.168615i	0.150843	+	0.00749587i
$507$	−2.25635	−	8.42080i	−0.100208	−	0.373981i
$508$	10.9670	−	8.97968i	0.486582	−	0.398409i
$509$	−6.06913	−	10.5120i	−0.269009	−	0.465938i	0.699597	−	0.714538i	$-0.253363\pi$
$509$	−6.06913	−	10.5120i	−0.269009	−	0.465938i	−0.968606	+	0.248600i	$0.920030\pi$
$510$	−0.123374	−	6.88686i	−0.00546311	−	0.304955i
$511$	−6.95918	−	5.36050i	−0.307856	−	0.237134i
$512$	7.51454	+	21.3432i	0.332099	+	0.943245i
$513$	−2.94933	+	11.0070i	−0.130216	+	0.485973i
$514$	12.4820	+	24.3341i	0.550556	+	1.07333i
$515$	−10.2812	+	0.695709i	−0.453046	+	0.0306566i
$516$	4.32137	−	6.01610i	0.190238	−	0.264844i
$517$	6.26175	+	6.26175i	0.275391	+	0.275391i
$518$	5.64360	+	2.68595i	0.247966	+	0.118014i
$519$	−4.31133			−0.189246
$520$	−6.86412	−	37.6342i	−0.301012	−	1.65037i
$521$	−2.07706	+	3.59757i	−0.0909976	+	0.157612i	−0.907931	−	0.419119i	$-0.862339\pi$
$521$	−2.07706	+	3.59757i	−0.0909976	+	0.157612i	0.816934	+	0.576732i	$0.195672\pi$
$522$	−19.8786	−	6.39950i	−0.870063	−	0.280098i
$523$	−1.35236	+	5.04706i	−0.0591344	+	0.220693i	−0.989169	−	0.146778i	$-0.953110\pi$
$523$	−1.35236	+	5.04706i	−0.0591344	+	0.220693i	0.930035	+	0.367471i	$0.119776\pi$
$524$	10.0224	−	4.52745i	0.437830	−	0.197782i
$525$	4.88956	−	0.0116162i	0.213398	−	0.000506973i
$526$	15.5351	−	24.0643i	0.677362	−	1.04925i
$527$	2.17022	−	8.09939i	0.0945364	−	0.352815i
$528$	0.613129	−	1.23625i	0.0266830	−	0.0538010i
$529$	−14.1817	−	8.18783i	−0.616597	−	0.355992i
$530$	6.08016	−	24.4340i	0.264105	−	1.06135i
$531$	−2.88918			−0.125380
$532$	−13.1889	+	24.4986i	−0.571811	+	1.06215i
$533$	26.1913	−	26.1913i	1.13447	−	1.13447i
$534$	6.23366	+	0.309770i	0.269757	+	0.0134051i
$535$	28.0738	−	1.89969i	1.21374	−	0.0821309i
$536$	−4.49819	−	3.58245i	−0.194292	−	0.154738i
$537$	3.67701	+	0.985252i	0.158675	+	0.0425168i
$538$	6.34836	−	1.36736i	0.273697	−	0.0589512i
$539$	−4.60274	−	4.63701i	−0.198254	−	0.199730i
$540$	8.23553	+	5.10994i	0.354401	+	0.219897i
$541$	17.3067	−	9.99202i	0.744073	−	0.429591i	−0.0794756	−	0.996837i	$-0.525325\pi$
$541$	17.3067	−	9.99202i	0.744073	−	0.429591i	0.823548	+	0.567246i	$0.191991\pi$
$542$	28.6318	+	9.21739i	1.22984	+	0.395921i
$543$	0.414196	+	1.54580i	0.0177749	+	0.0663367i
$544$	23.2509	−	23.8891i	0.996873	−	1.02424i
$545$	−1.85730	+	9.44160i	−0.0795580	+	0.404434i
$546$	6.36555	+	5.42731i	0.272420	+	0.232267i
$547$	11.1516	−	11.1516i	0.476807	−	0.476807i	−0.427302	−	0.904109i	$-0.640536\pi$
$547$	11.1516	−	11.1516i	0.476807	−	0.476807i	0.904109	+	0.427302i	$0.140536\pi$
$548$	−2.34845	+	0.385005i	−0.100321	+	0.0164466i
$549$	−4.70699	+	8.15275i	−0.200890	+	0.347951i
$550$	−4.25135	+	5.04819i	−0.181278	+	0.215256i
$551$	23.4835	−	13.5582i	1.00043	−	0.577599i
$552$	2.16392	−	1.59919i	0.0921025	−	0.0680662i
$553$	−4.11783	+	9.88942i	−0.175108	+	0.420541i
$554$	19.0220	+	12.2799i	0.808168	+	0.521725i
$555$	0.446539	+	1.30638i	0.0189545	+	0.0554527i
$556$	14.4003	+	1.43474i	0.610710	+	0.0608464i
$557$	8.94229	−	2.39608i	0.378897	−	0.101525i	−0.0643436	−	0.997928i	$-0.520495\pi$
$557$	8.94229	−	2.39608i	0.378897	−	0.101525i	0.443241	+	0.896403i	$0.353829\pi$
$558$	3.86702	+	4.27145i	0.163704	+	0.180825i
$559$	−60.6088			−2.56348
$560$	16.6997	+	16.7666i	0.705692	+	0.708519i
$561$	−2.03302			−0.0858340
$562$	−17.0946	−	18.8824i	−0.721093	−	0.796507i
$563$	−26.2394	+	7.03083i	−1.10586	+	0.296314i	−0.765149	−	0.643854i	$-0.777334\pi$
$563$	−26.2394	+	7.03083i	−1.10586	+	0.296314i	−0.340711	+	0.940168i	$0.610668\pi$
$564$	6.97906	+	0.695339i	0.293871	+	0.0292791i
$565$	9.27978	+	4.55191i	0.390403	+	0.191500i
$566$	4.45243	+	2.87433i	0.187150	+	0.120817i
$567$	20.4367	−	2.65200i	0.858261	−	0.111374i
$568$	−21.0829	−	28.5279i	−0.884619	−	1.19700i
$569$	3.24556	−	1.87383i	0.136061	−	0.0785549i	−0.430424	−	0.902627i	$-0.641636\pi$
$569$	3.24556	−	1.87383i	0.136061	−	0.0785549i	0.566485	+	0.824072i	$0.308303\pi$
$570$	−5.90695	+	1.69673i	−0.247415	+	0.0710680i
$571$	0.0783914	−	0.135778i	0.00328058	−	0.00568213i	−0.864380	−	0.502838i	$-0.832289\pi$
$571$	0.0783914	−	0.135778i	0.00328058	−	0.00568213i	0.867661	+	0.497156i	$0.165622\pi$
$572$	−11.1424	+	1.82669i	−0.465888	+	0.0763779i
$573$	−5.71928	+	5.71928i	−0.238926	+	0.238926i
$574$	−4.15628	+	22.5326i	−0.173480	+	0.940492i
$575$	−11.8684	+	4.97496i	−0.494946	+	0.207470i
$576$	5.12601	+	22.3262i	0.213584	+	0.930257i
$577$	−6.79286	−	25.3513i	−0.282791	−	1.05539i	−0.950439	−	0.310912i	$-0.899366\pi$
$577$	−6.79286	−	25.3513i	−0.282791	−	1.05539i	0.667648	−	0.744477i	$-0.267301\pi$
$578$	−23.8649	−	7.68278i	−0.992647	−	0.319562i
$579$	7.03796	−	4.06337i	0.292488	−	0.168868i
$580$	−5.25923	−	22.4556i	−0.218378	−	0.932416i
$581$	4.56471	−	34.1825i	0.189376	−	1.41813i
$582$	−3.18884	+	0.686838i	−0.132182	+	0.0284704i
$583$	−7.17852	−	1.92348i	−0.297304	−	0.0796623i
$584$	5.85040	−	7.34585i	0.242091	−	0.303974i
$585$	−2.61465	−	38.6395i	−0.108102	−	1.59755i
$586$	12.0514	+	0.598869i	0.497837	+	0.0247390i
$587$	−16.2301	+	16.2301i	−0.669886	+	0.669886i	−0.957689	−	0.287803i	$-0.907075\pi$
$587$	−16.2301	+	16.2301i	−0.669886	+	0.669886i	0.287803	+	0.957689i	$0.407075\pi$
$588$	−5.14720	−	0.532112i	−0.212267	−	0.0219439i
$589$	−7.48163			−0.308275
$590$	−1.64462	−	2.73427i	−0.0677080	−	0.112568i
$591$	−0.388217	−	0.224137i	−0.0159691	−	0.00921977i
$592$	−2.96878	+	5.98595i	−0.122016	+	0.246021i
$593$	−11.9395	+	44.5589i	−0.490297	+	1.82981i	0.0646222	+	0.997910i	$0.479416\pi$
$593$	−11.9395	+	44.5589i	−0.490297	+	1.82981i	−0.554919	+	0.831904i	$0.687251\pi$
$594$	1.55152	−	2.40335i	0.0636597	−	0.0986108i
$595$	11.1980	−	33.0164i	0.459071	−	1.35354i
$596$	5.94071	−	2.68361i	0.243341	−	0.109925i
$597$	0.947388	−	3.53570i	0.0387740	−	0.144707i
$598$	−20.9571	−	6.74671i	−0.857001	−	0.275893i
$599$	12.3081	−	21.3182i	0.502894	−	0.871038i	−0.497101	−	0.867693i	$-0.665602\pi$
$599$	12.3081	−	21.3182i	0.502894	−	0.871038i	0.999994	−	0.00334470i	$-0.00106465\pi$
$600$	−0.0722743	+	5.22667i	−0.00295059	+	0.213378i
$601$	12.8434			0.523893			0.261947	−	0.965082i	$-0.415636\pi$
$601$	12.8434			0.523893			0.261947	+	0.965082i	$0.415636\pi$
$602$	30.8802	−	21.2622i	1.25858	−	0.866581i
$603$	−4.11643	−	4.11643i	−0.167634	−	0.167634i
$604$	21.0083	−	29.2472i	0.854814	−	1.19005i
$605$	−17.0598	−	14.8973i	−0.693579	−	0.605662i
$606$	−0.360629	−	0.703061i	−0.0146495	−	0.0285599i
$607$	1.58993	−	5.93369i	0.0645332	−	0.240841i	−0.926124	−	0.377220i	$-0.876880\pi$
$607$	1.58993	−	5.93369i	0.0645332	−	0.240841i	0.990657	+	0.136379i	$0.0435466\pi$
$608$	−25.9582	−	14.5220i	−1.05274	−	0.588945i
$609$	3.99533	+	3.07751i	0.161899	+	0.124707i
$610$	−10.3950	+	0.186221i	−0.420881	+	0.00753987i
$611$	−28.6939	−	49.6992i	−1.16083	−	2.01062i
$612$	26.1118	−	21.3801i	1.05551	−	0.864237i
$613$	0.885426	+	3.30445i	0.0357620	+	0.133466i	0.981499	−	0.191468i	$-0.0613248\pi$
$613$	0.885426	+	3.30445i	0.0357620	+	0.133466i	−0.945737	+	0.324933i	$0.894658\pi$
$614$	−29.7572	−	1.47873i	−1.20090	−	0.0596766i
$615$	−4.20224	+	2.82072i	−0.169450	+	0.113742i
$616$	5.03624	−	4.83958i	0.202916	−	0.194992i
$617$	14.8719	−	14.8719i	0.598718	−	0.598718i	−0.341253	−	0.939971i	$-0.610851\pi$
$617$	14.8719	−	14.8719i	0.598718	−	0.598718i	0.939971	+	0.341253i	$0.110851\pi$
$618$	1.61671	+	1.78579i	0.0650337	+	0.0718351i
$619$	35.1024	+	20.2664i	1.41088	+	0.814574i	0.995472	−	0.0950590i	$-0.0303040\pi$
$619$	35.1024	+	20.2664i	1.41088	+	0.814574i	0.415412	+	0.909633i	$0.363637\pi$
$620$	−1.84118	+	6.09114i	−0.0739434	+	0.244626i
$621$	4.83061	−	2.78895i	0.193846	−	0.111917i
$622$	1.07595	+	4.99540i	0.0431417	+	0.200297i
$623$	29.1637	+	12.1434i	1.16842	+	0.486515i
$624$	−5.91153	+	6.71016i	−0.236651	+	0.268622i
$625$	6.26596	−	24.2020i	0.250638	−	0.968081i
$626$	2.18852	−	1.12258i	0.0874708	−	0.0448673i
$627$	0.469489	+	1.75216i	0.0187496	+	0.0699744i
$628$	−5.55935	−	33.9108i	−0.221842	−	1.35319i
$629$	9.84389			0.392502
$630$	14.8873	+	18.7696i	0.593123	+	0.747797i
$631$			40.4404i			1.60991i	0.593339	+	0.804953i	$0.297809\pi$
$631$			40.4404i			1.60991i	−0.593339	+	0.804953i	$0.702191\pi$
$632$	−10.4995	−	4.57286i	−0.417648	−	0.181899i
$633$	6.57958	−	1.76299i	0.261515	−	0.0700727i
$634$	1.79643	−	0.921462i	0.0713453	−	0.0365959i
$635$	14.2278	+	6.97901i	0.564614	+	0.276954i
$636$	−5.36411	+	2.42315i	−0.212701	+	0.0960840i
$637$	21.0342	+	36.7463i	0.833404	+	1.45594i
$638$	−6.65461	+	1.43332i	−0.263459	+	0.0567459i
$639$	−17.9557	−	31.1002i	−0.710316	−	1.23030i
$640$	−18.2112	+	17.5600i	−0.719859	+	0.694120i
$641$	−7.27169	+	12.5949i	−0.287214	+	0.497470i	−0.973144	−	0.230198i	$-0.926063\pi$
$641$	−7.27169	+	12.5949i	−0.287214	+	0.497470i	0.685929	+	0.727668i	$0.259396\pi$
$642$	−4.41457	−	4.87626i	−0.174229	−	0.192450i
$643$	8.71355	+	8.71355i	0.343629	+	0.343629i	0.857730	−	0.514101i	$-0.171874\pi$
$643$	8.71355	+	8.71355i	0.343629	+	0.343629i	−0.514101	+	0.857730i	$0.671874\pi$
$644$	13.0445	−	3.91453i	0.514024	−	0.154254i
$645$	8.12585	+	1.59847i	0.319955	+	0.0629399i
$646$	−2.17491	+	43.7669i	−0.0855708	+	1.72199i
$647$	−30.9101	+	8.28233i	−1.21520	+	0.325612i	−0.808800	−	0.588083i	$-0.799883\pi$
$647$	−30.9101	+	8.28233i	−1.21520	+	0.325612i	−0.406400	+	0.913695i	$0.633216\pi$
$648$	2.48076	+	21.8908i	0.0974534	+	0.859953i
$649$	−0.815598	+	0.470886i	−0.0320150	+	0.0184839i
$650$	35.0793	−	24.4694i	1.37592	−	0.959769i
$651$	−0.530103	−	1.28652i	−0.0207764	−	0.0504228i
$652$	−45.3290	−	17.1191i	−1.77522	−	0.670436i
$653$	−28.5721	−	7.65587i	−1.11811	−	0.299597i	−0.347993	−	0.937497i	$-0.613137\pi$
$653$	−28.5721	−	7.65587i	−1.11811	−	0.299597i	−0.770119	+	0.637900i	$0.779803\pi$
$654$	2.00148	−	1.02664i	0.0782640	−	0.0401448i
$655$	9.26147	+	8.08751i	0.361876	+	0.316005i
$656$	−24.0132	−	4.83295i	−0.937558	−	0.188695i
$657$	6.72243	−	6.72243i	0.262267	−	0.262267i
$658$	32.0545	+	15.2557i	1.24961	+	0.594727i
$659$			19.7431i			0.769080i	0.923108	+	0.384540i	$0.125640\pi$
$659$			19.7431i			0.769080i	−0.923108	+	0.384540i	$0.874360\pi$
$660$	1.54205	+	0.0489606i	0.0600242	+	0.00190579i
$661$	−7.75340	−	4.47643i	−0.301572	−	0.174113i	0.341577	−	0.939854i	$-0.389039\pi$
$661$	−7.75340	−	4.47643i	−0.301572	−	0.174113i	−0.643149	+	0.765741i	$0.722372\pi$
$662$	−3.90678	+	12.1355i	−0.151841	+	0.471661i
$663$	12.7260	+	3.40993i	0.494238	+	0.132431i
$664$	36.4588	+	5.47131i	1.41487	+	0.212328i
$665$	−31.0411	−	2.02642i	−1.20372	−	0.0785810i
$666$	−3.66872	+	5.68296i	−0.142160	+	0.220210i
$667$	−12.8209	−	3.43536i	−0.496429	−	0.133018i
$668$	−0.709538	+	0.580962i	−0.0274528	+	0.0224781i
$669$	4.05695	−	7.02684i	0.156851	−	0.271673i
$670$	1.55250	−	6.23894i	0.0599782	−	0.241031i
$671$			3.06863i			0.118463i
$672$	0.657930	−	5.49265i	0.0253802	−	0.211884i
$673$	4.21226	+	4.21226i	0.162371	+	0.162371i	0.783616	−	0.621245i	$-0.213373\pi$
$673$	4.21226	+	4.21226i	0.162371	+	0.162371i	−0.621245	+	0.783616i	$0.713373\pi$
$674$	−28.9726	−	1.43974i	−1.11598	−	0.0554566i
$675$	−1.36893	+	10.7492i	−0.0526901	+	0.413737i
$676$	46.9400	+	4.67674i	1.80539	+	0.179875i
$677$	5.40838	−	20.1844i	0.207861	−	0.775748i	−0.780697	−	0.624909i	$-0.785136\pi$
$677$	5.40838	−	20.1844i	0.207861	−	0.775748i	0.988558	−	0.150839i	$-0.0481974\pi$
$678$	−0.508758	−	2.36205i	−0.0195387	−	0.0907140i
$679$	−16.3653	−	2.18541i	−0.628043	−	0.0838684i
$680$	35.0974	+	12.5414i	1.34592	+	0.480941i
$681$	−3.89823	−	6.75194i	−0.149381	−	0.258735i
$682$	1.78781	+	0.575547i	0.0684587	+	0.0220388i
$683$	−43.0488	+	11.5349i	−1.64722	+	0.441370i	−0.958831	−	0.283977i	$-0.908346\pi$
$683$	−43.0488	+	11.5349i	−1.64722	+	0.441370i	−0.688384	+	0.725347i	$0.741680\pi$
$684$	−24.4564	−	17.5671i	−0.935116	−	0.671695i
$685$	−1.48288	−	2.20915i	−0.0566578	−	0.0844074i
$686$	−23.6079	−	11.3432i	−0.901352	−	0.433086i
$687$	−2.94180	−	2.94180i	−0.112237	−	0.112237i
$688$	22.1924	+	33.3762i	0.846076	+	1.27246i
$689$	41.7090	+	24.0807i	1.58899	+	0.917403i
$690$	2.63180	+	1.45725i	0.100191	+	0.0554766i
$691$	−0.909913	−	1.57602i	−0.0346147	−	0.0599544i	0.848199	−	0.529678i	$-0.177687\pi$
$691$	−0.909913	−	1.57602i	−0.0346147	−	0.0599544i	−0.882814	+	0.469723i	$0.844354\pi$
$692$	8.24218	−	21.8241i	0.313321	−	0.829629i
$693$	5.61775	−	4.29412i	0.213401	−	0.163120i
$694$	12.8607	−	19.9216i	0.488186	−	0.756215i
$695$	5.23321	+	15.3101i	0.198507	+	0.580744i
$696$	−3.35877	+	4.21732i	−0.127314	+	0.159857i
$697$	9.34002	+	34.8574i	0.353779	+	1.32032i
$698$	2.55762	+	2.82510i	0.0968072	+	0.106932i
$699$		−	5.81483i		−	0.219937i
$700$	−9.28880	+	24.7733i	−0.351084	+	0.936344i
$701$			5.61667i			0.212139i	0.994359	+	0.106069i	$0.0338266\pi$
$701$			5.61667i			0.212139i	−0.994359	+	0.106069i	$0.966173\pi$
$702$	−13.7431	+	12.4419i	−0.518701	+	0.469589i
$703$	−2.27327	−	8.48396i	−0.0857380	−	0.319979i
$704$	5.08581	+	5.46709i	0.191679	+	0.206049i
$705$	2.53625	+	7.41996i	0.0955208	+	0.279452i
$706$	−10.7164	−	6.91816i	−0.403319	−	0.260368i
$707$	−0.514675	−	3.96616i	−0.0193563	−	0.149163i
$708$	−0.263529	+	0.697788i	−0.00990404	+	0.0262245i
$709$	23.2036	+	40.1899i	0.871431	+	1.50936i	0.860517	+	0.509422i	$0.170141\pi$
$709$	23.2036	+	40.1899i	0.871431	+	1.50936i	0.0109136	+	0.999940i	$0.496526\pi$
$710$	19.2116	−	34.6962i	0.720999	−	1.30213i
$711$	−10.0404	−	5.79683i	−0.376544	−	0.217398i
$712$	−13.4853	+	30.9629i	−0.505382	+	1.16038i
$713$	2.58956	+	2.58956i	0.0969797	+	0.0969797i
$714$	−7.68015	+	2.72706i	−0.287423	+	0.102058i
$715$	−7.03565	−	10.4815i	−0.263119	−	0.391988i
$716$	−12.0169	+	16.7296i	−0.449093	+	0.625215i
$717$	4.91688	−	1.31747i	0.183624	−	0.0492019i
$718$	−6.67261	+	20.7270i	−0.249020	+	0.773524i
$719$	4.65550	+	8.06357i	0.173621	+	0.300720i	0.939683	−	0.342046i	$-0.111120\pi$
$719$	4.65550	+	8.06357i	0.173621	+	0.300720i	−0.766062	+	0.642766i	$0.777787\pi$
$720$	−20.3207	+	15.5880i	−0.757309	+	0.580930i
$721$	4.64507	+	11.2733i	0.172991	+	0.419838i
$722$	11.9551	−	2.57499i	0.444923	−	0.0958312i
$723$	−0.0873694	+	0.326067i	−0.00324930	+	0.0121266i
$724$	−8.61675	−	0.858506i	−0.320239	−	0.0319061i
$725$	20.3904	−	15.7836i	0.757280	−	0.586187i
$726$	−0.262776	+	5.28799i	−0.00975255	+	0.196256i
$727$	25.4562	+	25.4562i	0.944119	+	0.944119i	0.998519	−	0.0543998i	$-0.0173245\pi$
$727$	25.4562	+	25.4562i	0.944119	+	0.944119i	−0.0543998	+	0.998519i	$0.517325\pi$
$728$	−39.6426	+	21.8470i	−1.46925	+	0.809705i
$729$			19.9001i			0.737042i
$730$	10.1886	+	2.53534i	0.377098	+	0.0938371i
$731$	29.5247	−	51.1383i	1.09201	−	1.89142i
$732$	1.53970	+	1.88046i	0.0569089	+	0.0695036i
$733$	−21.3118	−	5.71047i	−0.787168	−	0.210921i	−0.157225	−	0.987563i	$-0.550255\pi$
$733$	−21.3118	−	5.71047i	−0.787168	−	0.210921i	−0.629943	+	0.776642i	$0.716922\pi$
$734$	7.81892	+	5.04762i	0.288602	+	0.186311i
$735$	−1.85093	−	5.48134i	−0.0682725	−	0.202182i
$736$	3.95832	+	14.0111i	0.145906	+	0.516456i
$737$	−1.83295	−	0.491138i	−0.0675176	−	0.0180913i
$738$	−23.6044	−	7.59895i	−0.868891	−	0.279721i
$739$	18.0851	+	10.4414i	0.665270	+	0.384094i	0.794282	−	0.607549i	$-0.207847\pi$
$739$	18.0851	+	10.4414i	0.665270	+	0.384094i	−0.129012	+	0.991643i	$0.541181\pi$
$740$	−7.46662	−	0.237068i	−0.274478	−	0.00871478i
$741$		−	11.7554i		−	0.431845i
$742$	−29.6985	+	2.36283i	−1.09027	+	0.0867421i
$743$	−19.7220	+	19.7220i	−0.723531	+	0.723531i	−0.969323	−	0.245792i	$-0.920952\pi$
$743$	−19.7220	+	19.7220i	−0.723531	+	0.723531i	0.245792	+	0.969323i	$0.420952\pi$
$744$	1.38435	−	0.544346i	0.0507528	−	0.0199567i
$745$	5.48968	+	4.79382i	0.201126	+	0.175632i
$746$	1.22464	+	2.38748i	0.0448371	+	0.0874119i
$747$	36.0509	+	9.65982i	1.31903	+	0.353434i
$748$	3.88662	−	10.2912i	0.142109	−	0.376284i
$749$	−12.6837	−	30.7826i	−0.463454	−	1.12477i
$750$	−5.34845	+	2.35546i	−0.195298	+	0.0860091i
$751$	−11.7027	+	6.75653i	−0.427036	+	0.246549i	−0.698083	−	0.716017i	$-0.745963\pi$
$751$	−11.7027	+	6.75653i	−0.427036	+	0.246549i	0.271047	+	0.962566i	$0.412630\pi$
$752$	−16.8620	+	33.9990i	−0.614896	+	1.23981i
$753$	0.0688603	−	0.0184511i	0.00250941	−	0.000672394i
$754$	44.0598	+	2.18947i	1.60456	+	0.0797358i
$755$	39.5037	+	7.77095i	1.43769	+	0.282814i
$756$	2.63737	−	11.1604i	0.0959203	−	0.405899i
$757$	−17.4013	−	17.4013i	−0.632459	−	0.632459i	0.316225	−	0.948684i	$-0.397585\pi$
$757$	−17.4013	−	17.4013i	−0.632459	−	0.632459i	−0.948684	+	0.316225i	$0.897585\pi$
$758$	−8.58193	+	7.76938i	−0.311710	+	0.282197i
$759$	0.443960	−	0.768961i	0.0161147	−	0.0279115i
$760$	2.70370	−	33.1449i	0.0980736	−	1.20229i
$761$	−8.67408	−	15.0240i	−0.314435	−	0.544618i	0.664882	−	0.746948i	$-0.268482\pi$
$761$	−8.67408	−	15.0240i	−0.314435	−	0.544618i	−0.979317	+	0.202330i	$0.935148\pi$
$762$	−0.780031	−	3.62151i	−0.0282575	−	0.131194i
$763$	11.2909	−	1.46518i	0.408757	−	0.0530430i
$764$	−18.0174	−	39.8851i	−0.651847	−	1.44299i
$765$	33.8755	+	16.6166i	1.22477	+	0.600774i
$766$	−23.2701	−	45.3660i	−0.840781	−	1.63914i
$767$	5.89519	−	1.57961i	0.212863	−	0.0570364i
$768$	5.85972	+	0.798402i	0.211445	+	0.0288099i
$769$			33.6019i			1.21171i	0.795573	+	0.605857i	$0.207170\pi$
$769$			33.6019i			1.21171i	−0.795573	+	0.605857i	$0.792830\pi$
$770$	7.26170	+	2.87217i	0.261693	+	0.103506i
$771$	7.14781			0.257422
$772$	7.11413	+	43.3946i	0.256043	+	1.56181i
$773$	5.43743	+	20.2928i	0.195571	+	0.729880i	0.992118	+	0.125304i	$0.0399907\pi$
$773$	5.43743	+	20.2928i	0.195571	+	0.729880i	−0.796548	+	0.604576i	$0.793343\pi$
$774$	18.5190	+	36.1036i	0.665653	+	1.29772i
$775$	−7.04956	+	0.958445i	−0.253228	+	0.0344284i
$776$	2.61946	−	17.4551i	0.0940330	−	0.626601i
$777$	1.29781	−	0.992028i	0.0465587	−	0.0355888i
$778$	−13.8023	+	2.97285i	−0.494837	+	0.106582i
$779$	27.8850	−	16.0994i	0.999083	−	0.576821i
$780$	−9.57061	−	2.89292i	−0.342683	−	0.103583i
$781$	−10.1376	−	5.85292i	−0.362750	−	0.209434i
$782$	15.9015	−	14.3959i	0.568636	−	0.514797i
$783$	−7.90296	+	7.90296i	−0.282429	+	0.282429i
$784$	12.5337	−	25.0381i	0.447633	−	0.894217i
$785$	31.8995	−	21.4123i	1.13854	−	0.764236i
$786$	0.142657	−	2.87076i	0.00508841	−	0.102397i
$787$	4.00750	+	14.9562i	0.142852	+	0.533130i	0.999842	+	0.0177970i	$0.00566526\pi$
$787$	4.00750	+	14.9562i	0.142852	+	0.533130i	−0.856990	+	0.515333i	$0.827668\pi$
$788$	1.87676	−	1.53668i	0.0668570	−	0.0547418i
$789$	−3.74306	−	6.48318i	−0.133257	−	0.230807i
$790$	−0.229338	−	12.8018i	−0.00815947	−	0.455468i
$791$	1.61879	−	12.1222i	0.0575575	−	0.431015i
$792$	4.49270	+	6.07921i	0.159641	+	0.216015i
$793$	5.14694	−	19.2086i	0.182773	−	0.682119i
$794$	−30.9345	+	15.8675i	−1.09782	+	0.563118i
$795$	−4.95686	−	4.32854i	−0.175802	−	0.153517i
$796$	16.0867	+	11.5551i	0.570178	+	0.409559i
$797$	2.17089	+	2.17089i	0.0768969	+	0.0768969i	0.744509	−	0.667612i	$-0.232684\pi$
$797$	2.17089	+	2.17089i	0.0768969	+	0.0768969i	−0.667612	+	0.744509i	$0.732684\pi$
$798$	4.12391	+	5.98937i	0.145985	+	0.212022i
$799$	55.9113			1.97800
$800$	−26.3194	−	10.3579i	−0.930533	−	0.366208i
$801$	−17.0947	+	29.6089i	−0.604012	+	1.04618i
$802$	0.291901	−	0.906725i	0.0103074	−	0.0320176i
$803$	0.802062	−	2.99334i	0.0283042	−	0.105633i
$804$	−1.36966	+	0.618722i	−0.0483043	+	0.0218206i
$805$	10.0426	+	11.4454i	0.353957	+	0.403398i
$806$	−10.2258	−	6.60139i	−0.360187	−	0.232524i
$807$	0.439280	−	1.63942i	0.0154634	−	0.0577102i
$808$	4.24836	−	0.481441i	0.149457	−	0.0169370i
$809$	−18.0260	−	10.4073i	−0.633762	−	0.365902i	0.148446	−	0.988921i	$-0.452573\pi$
$809$	−18.0260	−	10.4073i	−0.633762	−	0.365902i	−0.782207	+	0.623018i	$0.785906\pi$
$810$	−21.1074	+	12.6958i	−0.741637	+	0.446084i
$811$	−55.0469			−1.93296			−0.966480	−	0.256743i	$-0.917351\pi$
$811$	−55.0469			−1.93296			−0.966480	+	0.256743i	$0.917351\pi$
$812$	−23.2166	+	14.3411i	−0.814742	+	0.503274i
$813$	5.55882	−	5.55882i	0.194956	−	0.194956i
$814$	−0.109434	+	2.20220i	−0.00383567	+	0.0771872i
$815$	−3.65741	−	54.0495i	−0.128114	−	1.89327i
$816$	−2.78194	−	8.25659i	−0.0973875	−	0.289038i
$817$	−50.8918	−	13.6364i	−1.78048	−	0.477078i
$818$	−5.84430	−	27.1338i	−0.204341	−	0.948712i
$819$	−42.3677	+	17.4573i	−1.48045	+	0.610008i
$820$	−6.24497	−	26.6644i	−0.218084	−	0.931161i
$821$	−29.5682	+	17.0712i	−1.03194	+	0.595790i	−0.917539	−	0.397645i	$-0.869827\pi$
$821$	−29.5682	+	17.0712i	−1.03194	+	0.595790i	−0.114399	+	0.993435i	$0.536494\pi$
$822$	−0.190600	+	0.592056i	−0.00664794	+	0.0206503i
$823$	−8.20422	−	30.6186i	−0.285981	−	1.06730i	−0.948119	−	0.317914i	$-0.897018\pi$
$823$	−8.20422	−	30.6186i	−0.285981	−	1.06730i	0.662138	−	0.749382i	$-0.269649\pi$
$824$	−12.1305	+	4.76987i	−0.422586	+	0.166166i
$825$	0.666838	+	1.59082i	0.0232163	+	0.0553853i
$826$	−2.44945	+	2.87290i	−0.0852274	+	0.0999611i
$827$	13.8807	−	13.8807i	0.482680	−	0.482680i	−0.423306	−	0.905987i	$-0.639131\pi$
$827$	13.8807	−	13.8807i	0.482680	−	0.482680i	0.905987	+	0.423306i	$0.139131\pi$
$828$	2.38456	+	14.5453i	0.0828691	+	0.505483i
$829$	18.0996	−	31.3494i	0.628625	−	1.08881i	−0.359203	−	0.933260i	$-0.616951\pi$
$829$	18.0996	−	31.3494i	0.628625	−	1.08881i	0.987828	−	0.155551i	$-0.0497153\pi$
$830$	11.3796	+	39.6166i	0.394991	+	1.37511i
$831$	5.12473	−	2.95876i	0.177775	−	0.102638i
$832$	−22.6658	−	42.7526i	−0.785794	−	1.48218i
$833$	−41.2510	−	0.152977i	−1.42926	−	0.00530036i
$834$	2.05138	−	3.17765i	0.0710335	−	0.110033i
$835$	−0.920503	−	0.451524i	−0.0318553	−	0.0156256i
$836$	−9.76703	−	0.973111i	−0.337800	−	0.0336557i
$837$	2.97860	−	0.798114i	0.102956	−	0.0275869i
$838$	18.9550	−	17.1603i	0.654789	−	0.592793i
$839$	36.3979			1.25660			0.628298	−	0.777973i	$-0.283752\pi$
$839$	36.3979			1.25660			0.628298	+	0.777973i	$0.283752\pi$
$840$	5.89109	−	1.88353i	0.203262	−	0.0649878i
$841$	−2.40441			−0.0829108
$842$	−17.3063	+	15.6677i	−0.596413	+	0.539944i
$843$	−6.43022	+	1.72297i	−0.221469	+	0.0593424i
$844$	−3.65416	+	36.6765i	−0.125781	+	1.26246i
$845$	17.0584	+	49.9055i	0.586828	+	1.71680i
$846$	−20.8376	+	32.2781i	−0.716411	+	1.10974i
$847$	−10.3012	+	24.7394i	−0.353953	+	0.850056i
$848$	−2.01124	−	31.7858i	−0.0690661	−	1.09153i
$849$	1.19953	−	0.692550i	0.0411678	−	0.0237682i
$850$	3.55751	+	41.5179i	0.122022	+	1.42405i
$851$	−2.14966	+	3.72332i	−0.0736893	+	0.127634i
$852$	−9.14902	+	1.49989i	−0.313440	+	0.0513855i
$853$	−26.4581	+	26.4581i	−0.905908	+	0.905908i	−0.995939	−	0.0900314i	$-0.971303\pi$
$853$	−26.4581	+	26.4581i	−0.905908	+	0.905908i	0.0900314	+	0.995939i	$0.471303\pi$
$854$	4.11622	+	11.5924i	0.140854	+	0.396684i
$855$	6.49806	−	33.0329i	0.222229	−	1.12970i
$856$	33.1233	−	13.0245i	1.13213	−	0.445170i
$857$	1.36367	+	5.08927i	0.0465820	+	0.173846i	0.985298	−	0.170846i	$-0.0546500\pi$
$857$	1.36367	+	5.08927i	0.0465820	+	0.173846i	−0.938716	+	0.344692i	$0.887983\pi$
$858$	−0.904320	+	2.80907i	−0.0308730	+	0.0959000i
$859$	−44.5451	+	25.7181i	−1.51986	+	0.877492i	−0.520134	+	0.854085i	$0.674118\pi$
$859$	−44.5451	+	25.7181i	−1.51986	+	0.877492i	−0.999726	+	0.0234068i	$0.992549\pi$
$860$	−23.6261	+	38.0775i	−0.805644	+	1.29843i
$861$	4.74417	+	3.65433i	0.161681	+	0.124539i
$862$	−4.94984	−	22.9810i	−0.168592	−	0.782737i
$863$	21.7264	+	5.82157i	0.739575	+	0.198169i	0.608889	−	0.793255i	$-0.291615\pi$
$863$	21.7264	+	5.82157i	0.739575	+	0.198169i	0.130686	+	0.991424i	$0.458282\pi$
$864$	11.8837	+	3.01240i	0.404291	+	0.102484i
$865$	26.0227	−	1.76090i	0.884799	−	0.0598724i
$866$	−1.80892	+	36.4019i	−0.0614696	+	1.23699i
$867$	−4.63333	+	4.63333i	−0.157356	+	0.157356i
$868$	7.52586	−	0.223892i	0.255444	−	0.00759940i
$869$	−3.77912			−0.128198
$870$	−5.84938	−	1.45556i	−0.198313	−	0.0493482i
$871$	10.6499	+	6.14873i	0.360859	+	0.208342i
$872$	1.37057	+	12.0943i	0.0464133	+	0.409563i
$873$	4.62476	−	17.2598i	0.156524	−	0.584157i
$874$	−16.0793	−	10.3802i	−0.543890	−	0.351116i
$875$	−29.5081	+	2.06718i	−0.997555	+	0.0698835i
$876$	−1.01042	−	2.23676i	−0.0341388	−	0.0755730i
$877$	6.75014	−	25.1919i	0.227936	−	0.850668i	−0.753271	−	0.657710i	$-0.771525\pi$
$877$	6.75014	−	25.1919i	0.227936	−	0.850668i	0.981207	−	0.192958i	$-0.0618082\pi$
$878$	0.193399	−	0.600750i	0.00652689	−	0.0202743i
$879$	1.57680	−	2.73111i	0.0531843	−	0.0921179i
$880$	−3.19585	+	7.71231i	−0.107732	+	0.259982i
$881$	42.2555			1.42362			0.711812	−	0.702370i	$-0.247875\pi$
$881$	42.2555			1.42362			0.711812	+	0.702370i	$0.247875\pi$
$882$	15.4622	−	23.7575i	0.520638	−	0.799958i
$883$	−23.2185	−	23.2185i	−0.781366	−	0.781366i	0.198695	−	0.980061i	$-0.436330\pi$
$883$	−23.2185	−	23.2185i	−0.781366	−	0.781366i	−0.980061	+	0.198695i	$0.936330\pi$
$884$	−41.5902	+	57.9008i	−1.39883	+	1.94741i
$885$	−0.832031	+	0.0563017i	−0.0279684	+	0.00189256i
$886$	48.6413	−	24.9501i	1.63414	−	0.838215i
$887$	1.36155	−	5.08138i	0.0457164	−	0.170616i	−0.939293	−	0.343116i	$-0.888518\pi$
$887$	1.36155	−	5.08138i	0.0457164	−	0.170616i	0.985010	+	0.172500i	$0.0551844\pi$
$888$	1.03790	+	1.40442i	0.0348298	+	0.0471292i
$889$	2.48194	−	18.5858i	0.0832415	−	0.623348i
$890$	−37.7522	+	0.676312i	−1.26546	+	0.0226700i
$891$	3.63503	+	6.29606i	0.121778	+	0.210926i
$892$	27.8143	+	33.9700i	0.931292	+	1.13740i
$893$	−12.9117	−	48.1871i	−0.432074	−	1.61252i
$894$	0.0845590	−	1.70162i	0.00282807	−	0.0569108i
$895$	−22.5965	−	4.44505i	−0.755316	−	0.148582i
$896$	26.5462	+	13.8310i	0.886847	+	0.462063i
$897$	−4.06881	+	4.06881i	−0.135853	+	0.135853i
$898$	−33.2343	+	30.0876i	−1.10904	+	1.00404i
$899$	−6.35484	−	3.66897i	−0.211946	−	0.122367i
$900$	−25.2945	−	13.4195i	−0.843150	−	0.447318i
$901$	−40.6360	+	23.4612i	−1.35378	+	0.781606i
$902$	−7.90188	+	1.70197i	−0.263104	+	0.0566695i
$903$	−1.26100	−	9.71742i	−0.0419633	−	0.323376i
$904$	12.9294	+	1.94030i	0.430026	+	0.0645333i
$905$	−3.13141	−	9.16112i	−0.104091	−	0.304526i
$906$	−4.29547	−	8.37420i	−0.142707	−	0.278214i
$907$	10.7351	+	40.0638i	0.356452	+	1.33030i	0.878648	+	0.477470i	$0.158446\pi$
$907$	10.7351	+	40.0638i	0.356452	+	1.33030i	−0.522196	+	0.852825i	$0.674887\pi$
$908$	41.6310	−	6.82501i	1.38157	−	0.226496i
$909$	4.32839			0.143564
$910$	−40.6385	−	30.1587i	−1.34715	−	0.999752i
$911$		−	56.2856i		−	1.86483i	−0.361394	−	0.932413i	$-0.617699\pi$
$911$		−	56.2856i		−	1.86483i	0.361394	−	0.932413i	$-0.382301\pi$
$912$	−6.47350	+	4.30433i	−0.214359	+	0.142531i
$913$	11.7513	−	3.14876i	0.388912	−	0.104209i
$914$	18.1483	+	35.3808i	0.600291	+	1.17029i
$915$	−1.19665	+	2.43957i	−0.0395602	+	0.0806497i
$916$	20.5155	−	9.26752i	0.677851	−	0.306208i
$917$	5.59234	−	13.4306i	0.184675	−	0.443518i
$918$	−3.80302	−	17.6566i	−0.125518	−	0.582754i
$919$	10.6286	+	18.4093i	0.350606	+	0.607267i	0.986356	−	0.164628i	$-0.0526424\pi$
$919$	10.6286	+	18.4093i	0.350606	+	0.607267i	−0.635750	+	0.771895i	$0.719309\pi$
$920$	−12.4080	+	10.5364i	−0.409080	+	0.347374i
$921$	−3.89345	+	6.74365i	−0.128294	+	0.222211i
$922$	3.18594	−	2.88429i	0.104923	−	0.0949891i
$923$	53.6409	+	53.6409i	1.76561	+	1.76561i
$924$	−0.524698	−	1.74846i	−0.0172613	−	0.0575202i
$925$	−3.22884	−	7.70278i	−0.106163	−	0.253266i
$926$	−9.43426	−	0.468817i	−0.310029	−	0.0154063i
$927$	−12.7461	+	3.41530i	−0.418635	+	0.112173i
$928$	−14.9271	−	25.0647i	−0.490007	−	0.822789i
$929$	44.9633	−	25.9596i	1.47520	−	0.851706i	0.475589	−	0.879668i	$-0.342235\pi$
$929$	44.9633	−	25.9596i	1.47520	−	0.851706i	0.999609	+	0.0279615i	$0.00890157\pi$
$930$	1.19687	+	1.15474i	0.0392469	+	0.0378655i
$931$	9.39433	+	35.5875i	0.307887	+	1.16633i
$932$	29.4349	+	11.1165i	0.964172	+	0.364133i
$933$	1.29002	+	0.345661i	0.0422335	+	0.0113164i
$934$	−7.11819	−	13.8772i	−0.232914	−	0.454076i
$935$	12.2711	−	0.830356i	0.401307	−	0.0271556i
$936$	−17.9264	−	45.5895i	−0.585942	−	1.49014i
$937$	−18.6851	+	18.6851i	−0.610416	+	0.610416i	−0.943055	−	0.332638i	$-0.892061\pi$
$937$	−18.6851	+	18.6851i	−0.610416	+	0.610416i	0.332638	+	0.943055i	$0.392061\pi$
$938$	−7.58317	+	0.603320i	−0.247599	+	0.0196991i
$939$		−	0.642846i		−	0.0209785i
$940$	−42.4088	−	1.34650i	−1.38322	−	0.0439178i
$941$	47.6790	+	27.5275i	1.55429	+	0.897370i	0.997785	+	0.0665261i	$0.0211916\pi$
$941$	47.6790	+	27.5275i	1.55429	+	0.897370i	0.556506	+	0.830844i	$0.312142\pi$
$942$	−8.54910	−	2.75220i	−0.278545	−	0.0896716i
$943$	−15.2240	−	4.07925i	−0.495761	−	0.132839i
$944$	−3.02843	−	2.66799i	−0.0985671	−	0.0868358i
$945$	12.5743	−	2.50460i	0.409043	−	0.0814747i
$946$	11.1121	+	7.17356i	0.361284	+	0.233232i
$947$	−3.47532	−	0.931210i	−0.112933	−	0.0302603i	0.201910	−	0.979404i	$-0.435285\pi$
$947$	−3.47532	−	0.931210i	−0.112933	−	0.0302603i	−0.314843	+	0.949144i	$0.601952\pi$
$948$	−2.31585	+	1.89619i	−0.0752152	+	0.0615855i
$949$	−10.0413	+	17.3921i	−0.325955	+	0.564570i
$950$	34.9607	−	12.6539i	1.13427	−	0.410546i
$951$		−	0.527676i		−	0.0171111i
$952$	0.878018	−	44.0907i	0.0284567	−	1.42899i
$953$	−9.00314	−	9.00314i	−0.291640	−	0.291640i	0.546088	−	0.837728i	$-0.316117\pi$
$953$	−9.00314	−	9.00314i	−0.291640	−	0.291640i	−0.837728	+	0.546088i	$0.816117\pi$
$954$	1.60028	−	32.2033i	0.0518110	−	1.04262i
$955$	32.1850	−	36.8569i	1.04148	−	1.19266i
$956$	−2.73073	+	27.4081i	−0.0883181	+	0.886442i
$957$	−0.460472	+	1.71850i	−0.0148849	+	0.0555513i
$958$	−13.3072	+	2.86622i	−0.429938	+	0.0926035i
$959$	−1.92112	+	2.49406i	−0.0620360	+	0.0805373i
$960$	1.91127	+	6.32964i	0.0616860	+	0.204288i
$961$	−14.4877	−	25.0934i	−0.467345	−	0.809466i
$962$	4.37873	−	13.6015i	0.141176	−	0.438531i
$963$	34.8042	−	9.32575i	1.12155	−	0.300518i
$964$	−1.48354	−	1.06563i	−0.0477815	−	0.0343215i
$965$	−40.8207	+	27.4006i	−1.31407	+	0.882057i
$966$	0.645678	−	3.50043i	0.0207743	−	0.112625i
$967$	4.36956	+	4.36956i	0.140516	+	0.140516i	0.773866	−	0.633350i	$-0.218321\pi$
$967$	4.36956	+	4.36956i	0.140516	+	0.140516i	−0.633350	+	0.773866i	$0.718321\pi$
$968$	−26.2657	−	11.4395i	−0.844210	−	0.367679i
$969$	9.91856	+	5.72648i	0.318630	+	0.183961i
$970$	18.9670	−	5.44812i	0.608992	−	0.174928i
$971$	9.24578	+	16.0142i	0.296711	+	0.513919i	0.975382	−	0.220524i	$-0.0707768\pi$
$971$	9.24578	+	16.0142i	0.296711	+	0.513919i	−0.678670	+	0.734443i	$0.737443\pi$
$972$	17.5512	+	6.62847i	0.562956	+	0.212608i
$973$	15.2097	−	11.6260i	0.487600	−	0.372714i
$974$	−39.1567	−	25.2782i	−1.25466	−	0.809965i
$975$	−1.50594	−	11.0765i	−0.0482288	−	0.354732i
$976$	−12.4625	+	4.19906i	−0.398914	+	0.134409i
$977$	1.57145	+	5.86472i	0.0502750	+	0.187629i	0.986497	−	0.163781i	$-0.0523690\pi$
$977$	1.57145	+	5.86472i	0.0502750	+	0.187629i	−0.936222	+	0.351410i	$0.885702\pi$
$978$	−9.38809	+	8.49921i	−0.300198	+	0.271775i
$979$			11.1446i			0.356182i
$980$	31.2853	+	1.10947i	0.999372	+	0.0354407i
$981$			12.3221i			0.393414i
$982$	−27.6037	−	30.4905i	−0.880868	−	0.972992i
$983$	7.68312	+	28.6738i	0.245054	+	0.914552i	0.973357	+	0.229297i	$0.0736427\pi$
$983$	7.68312	+	28.6738i	0.245054	+	0.914552i	−0.728303	+	0.685255i	$0.759691\pi$
$984$	−3.98830	+	5.00777i	−0.127142	+	0.159642i
$985$	2.43478	+	1.19431i	0.0775785	+	0.0380537i
$986$	−23.3105	+	36.1087i	−0.742358	+	1.14994i
$987$	7.37130	−	5.63451i	0.234631	−	0.179349i
$988$	59.5063	+	22.4734i	1.89315	+	0.714973i
$989$	12.8949	+	22.3346i	0.410034	+	0.710200i
$990$	−4.09394	+	7.39366i	−0.130114	+	0.234986i
$991$	44.4018	+	25.6354i	1.41047	+	0.814336i	0.995432	−	0.0954681i	$-0.0304348\pi$
$991$	44.4018	+	25.6354i	1.41047	+	0.814336i	0.415038	+	0.909804i	$0.363768\pi$
$992$	0.108966	+	8.04830i	0.00345967	+	0.255534i
$993$	2.35610	+	2.35610i	0.0747685	+	0.0747685i
$994$	−46.1478	−	8.51226i	−1.46372	−	0.269992i
$995$	−4.27423	+	21.7281i	−0.135502	+	0.688826i
$996$	5.62131	−	7.82585i	0.178118	−	0.247971i
$997$	4.03325	−	1.08071i	0.127734	−	0.0342263i	−0.194385	−	0.980925i	$-0.562271\pi$
$997$	4.03325	−	1.08071i	0.127734	−	0.0342263i	0.322120	+	0.946699i	$0.395605\pi$
$998$	−3.16098	−	1.01761i	−0.100059	−	0.0322119i
$999$	1.81008	+	3.13515i	0.0572684	+	0.0991917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.br.a.123.34	yes	176
5.2	odd	4	inner	280.2.br.a.67.11	✓	176
7.2	even	3	inner	280.2.br.a.163.26	yes	176
8.3	odd	2	inner	280.2.br.a.123.40	yes	176
35.2	odd	12	inner	280.2.br.a.107.40	yes	176
40.27	even	4	inner	280.2.br.a.67.26	yes	176
56.51	odd	6	inner	280.2.br.a.163.11	yes	176
280.107	even	12	inner	280.2.br.a.107.34	yes	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.br.a.67.11	✓	176	5.2	odd	4	inner
280.2.br.a.67.26	yes	176	40.27	even	4	inner
280.2.br.a.107.34	yes	176	280.107	even	12	inner
280.2.br.a.107.40	yes	176	35.2	odd	12	inner
280.2.br.a.123.34	yes	176	1.1	even	1	trivial
280.2.br.a.123.40	yes	176	8.3	odd	2	inner
280.2.br.a.163.11	yes	176	56.51	odd	6	inner
280.2.br.a.163.26	yes	176	7.2	even	3	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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.br (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.949136 + 1.04840i) q^{2} +(0.357022 - 0.0956638i) q^{3} +(-0.198283 + 1.99015i) q^{4} +(-2.11588 + 0.723237i) q^{5} +(0.439157 + 0.283504i) q^{6} +(1.60674 + 2.10200i) q^{7} +(-2.27467 + 1.68104i) q^{8} +(-2.47976 + 1.43169i) q^{9} +O(q^{10})\)	\(q+(0.949136 + 1.04840i) q^{2} +(0.357022 - 0.0956638i) q^{3} +(-0.198283 + 1.99015i) q^{4} +(-2.11588 + 0.723237i) q^{5} +(0.439157 + 0.283504i) q^{6} +(1.60674 + 2.10200i) q^{7} +(-2.27467 + 1.68104i) q^{8} +(-2.47976 + 1.43169i) q^{9} +(-2.76649 - 1.53183i) q^{10} +(-0.466681 + 0.808315i) q^{11} +(0.119594 + 0.729495i) q^{12} +(4.27704 - 4.27704i) q^{13} +(-0.678723 + 3.67958i) q^{14} +(-0.686227 + 0.460624i) q^{15} +(-3.92137 - 0.789223i) q^{16} +(1.52523 + 5.69224i) q^{17} +(-3.85462 - 1.24091i) q^{18} +(4.55363 - 2.62904i) q^{19} +(-1.01981 - 4.35431i) q^{20} +(0.774726 + 0.596754i) q^{21} +(-1.29038 + 0.277933i) q^{22} +(-2.48608 - 0.666144i) q^{23} +(-0.651292 + 0.817772i) q^{24} +(3.95386 - 3.06056i) q^{25} +(8.54355 + 0.424555i) q^{26} +(-1.53244 + 1.53244i) q^{27} +(-4.50187 + 2.78085i) q^{28} +5.15709 q^{29} +(-1.13424 - 0.282245i) q^{30} +(-1.23225 - 0.711441i) q^{31} +(-2.89449 - 4.86024i) q^{32} +(-0.0892890 + 0.333231i) q^{33} +(-4.52009 + 7.00176i) q^{34} +(-4.91990 - 3.28552i) q^{35} +(-2.35758 - 5.21897i) q^{36} +(0.432338 - 1.61351i) q^{37} +(7.07830 + 2.27871i) q^{38} +(1.11784 - 1.93616i) q^{39} +(3.59712 - 5.20199i) q^{40} +6.12368 q^{41} +(0.109684 + 1.37862i) q^{42} +(-7.08536 - 7.08536i) q^{43} +(-1.51613 - 1.08904i) q^{44} +(4.21142 - 4.82274i) q^{45} +(-1.66124 - 3.23867i) q^{46} +(2.45559 - 9.16440i) q^{47} +(-1.47552 + 0.0933627i) q^{48} +(-1.83680 + 6.75472i) q^{49} +(6.96143 + 1.24033i) q^{50} +(1.08908 + 1.88635i) q^{51} +(7.66388 + 9.36001i) q^{52} +(2.06081 + 7.69103i) q^{53} +(-3.06111 - 0.152116i) q^{54} +(0.402835 - 2.04782i) q^{55} +(-7.18833 - 2.08036i) q^{56} +(1.37424 - 1.37424i) q^{57} +(4.89478 + 5.40669i) q^{58} +(0.873827 + 0.504505i) q^{59} +(-0.780643 - 1.45703i) q^{60} +(2.84724 - 1.64386i) q^{61} +(-0.423700 - 1.96715i) q^{62} +(-6.99374 - 2.91211i) q^{63} +(2.34821 - 7.64761i) q^{64} +(-5.95638 + 12.1430i) q^{65} +(-0.434107 + 0.222671i) q^{66} +(0.526202 + 1.96381i) q^{67} +(-11.6308 + 1.90676i) q^{68} -0.951312 q^{69} +(-1.22512 - 8.27642i) q^{70} +12.5416i q^{71} +(3.23390 - 7.42520i) q^{72} +(-3.20705 + 0.859326i) q^{73} +(2.10195 - 1.07818i) q^{74} +(1.11883 - 1.47093i) q^{75} +(4.32927 + 9.58369i) q^{76} +(-2.44891 + 0.317787i) q^{77} +(3.09085 - 0.665733i) q^{78} +(2.02447 + 3.50648i) q^{79} +(8.86792 - 1.16618i) q^{80} +(3.89456 - 6.74557i) q^{81} +(5.81220 + 6.42006i) q^{82} +(-9.21676 - 9.21676i) q^{83} +(-1.34124 + 1.42349i) q^{84} +(-7.34403 - 10.9410i) q^{85} +(0.703319 - 14.1532i) q^{86} +(1.84120 - 0.493347i) q^{87} +(-0.297267 - 2.62316i) q^{88} +(10.3405 - 5.97011i) q^{89} +(9.05336 - 0.162186i) q^{90} +(15.8624 + 2.11826i) q^{91} +(1.81867 - 4.81558i) q^{92} +(-0.508001 - 0.136118i) q^{93} +(11.9386 - 6.12382i) q^{94} +(-7.73350 + 8.85608i) q^{95} +(-1.49835 - 1.45832i) q^{96} +(-4.41264 + 4.41264i) q^{97} +(-8.82501 + 4.48545i) q^{98} -2.67257i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8}+O(q^{10}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8	\( 176 q - 2 q^{2} - 4 q^{3} - 16 q^{6} - 20 q^{8} - 2 q^{10} - 8 q^{11} - 14 q^{12} + 4 q^{16} - 4 q^{17} - 16 q^{18} + 8 q^{20} - 4 q^{25} - 20 q^{26} - 40 q^{27} - 34 q^{28} - 12 q^{30} + 18 q^{32} + 20 q^{33} - 32 q^{35} - 48 q^{36} - 16 q^{38} - 22 q^{40} - 32 q^{41} + 30 q^{42} - 16 q^{43} + 20 q^{46} + 36 q^{48} + 68 q^{50} - 8 q^{51} - 32 q^{52} - 52 q^{56} - 40 q^{57} - 14 q^{58} - 50 q^{60} + 56 q^{62} - 4 q^{65} - 60 q^{66} - 28 q^{67} - 40 q^{68} + 64 q^{70} - 48 q^{72} - 4 q^{73} - 4 q^{75} - 144 q^{76} + 184 q^{78} - 40 q^{80} + 32 q^{81} + 74 q^{82} - 16 q^{83} - 56 q^{86} - 64 q^{88} - 56 q^{90} + 16 q^{91} + 44 q^{92} - 104 q^{96} - 48 q^{97} + 70 q^{98}+O(q^{100}) \) 176 * q - 2 * q^2 - 4 * q^3 - 16 * q^6 - 20 * q^8 - 2 * q^10 - 8 * q^11 - 14 * q^12 + 4 * q^16 - 4 * q^17 - 16 * q^18 + 8 * q^20 - 4 * q^25 - 20 * q^26 - 40 * q^27 - 34 * q^28 - 12 * q^30 + 18 * q^32 + 20 * q^33 - 32 * q^35 - 48 * q^36 - 16 * q^38 - 22 * q^40 - 32 * q^41 + 30 * q^42 - 16 * q^43 + 20 * q^46 + 36 * q^48 + 68 * q^50 - 8 * q^51 - 32 * q^52 - 52 * q^56 - 40 * q^57 - 14 * q^58 - 50 * q^60 + 56 * q^62 - 4 * q^65 - 60 * q^66 - 28 * q^67 - 40 * q^68 + 64 * q^70 - 48 * q^72 - 4 * q^73 - 4 * q^75 - 144 * q^76 + 184 * q^78 - 40 * q^80 + 32 * q^81 + 74 * q^82 - 16 * q^83 - 56 * q^86 - 64 * q^88 - 56 * q^90 + 16 * q^91 + 44 * q^92 - 104 * q^96 - 48 * q^97 + 70 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more