LMFDB - Embedded newform 380.3.b.a.191.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,3,Mod(191,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("380.191");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	380.b (of order $2$, degree $1$, 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:	$10.3542500457$
Analytic rank:	$0$
Dimension:	$72$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			191.17
Character	$\chi$	$=$	380.191
Dual form			380.3.b.a.191.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32631 - 1.49696i) q^{2} +0.452282i q^{3} +(-0.481798 + 3.97088i) q^{4} +2.23607 q^{5} +(0.677050 - 0.599867i) q^{6} -5.37605i q^{7} +(6.58327 - 4.54539i) q^{8} +8.79544 q^{9} +O(q^{10})$	\(q+(-1.32631 - 1.49696i) q^{2} +0.452282i q^{3} +(-0.481798 + 3.97088i) q^{4} +2.23607 q^{5} +(0.677050 - 0.599867i) q^{6} -5.37605i q^{7} +(6.58327 - 4.54539i) q^{8} +8.79544 q^{9} +(-2.96572 - 3.34731i) q^{10} +19.9587i q^{11} +(-1.79596 - 0.217909i) q^{12} -2.92852 q^{13} +(-8.04775 + 7.13031i) q^{14} +1.01133i q^{15} +(-15.5357 - 3.82632i) q^{16} -7.25985 q^{17} +(-11.6655 - 13.1665i) q^{18} -4.35890i q^{19} +(-1.07733 + 8.87915i) q^{20} +2.43149 q^{21} +(29.8775 - 26.4715i) q^{22} +1.55287i q^{23} +(2.05580 + 2.97750i) q^{24} +5.00000 q^{25} +(3.88413 + 4.38388i) q^{26} +8.04856i q^{27} +(21.3476 + 2.59017i) q^{28} +43.0057 q^{29} +(1.51393 - 1.34134i) q^{30} +47.4060i q^{31} +(14.8774 + 28.3313i) q^{32} -9.02697 q^{33} +(9.62882 + 10.8677i) q^{34} -12.0212i q^{35} +(-4.23763 + 34.9256i) q^{36} +53.1828 q^{37} +(-6.52511 + 5.78126i) q^{38} -1.32452i q^{39} +(14.7206 - 10.1638i) q^{40} +18.8168 q^{41} +(-3.22491 - 3.63985i) q^{42} -9.23507i q^{43} +(-79.2536 - 9.61607i) q^{44} +19.6672 q^{45} +(2.32459 - 2.05959i) q^{46} -21.2337i q^{47} +(1.73058 - 7.02654i) q^{48} +20.0981 q^{49} +(-6.63156 - 7.48482i) q^{50} -3.28350i q^{51} +(1.41095 - 11.6288i) q^{52} +85.9678 q^{53} +(12.0484 - 10.6749i) q^{54} +44.6290i q^{55} +(-24.4362 - 35.3920i) q^{56} +1.97145 q^{57} +(-57.0389 - 64.3779i) q^{58} -109.477i q^{59} +(-4.01588 - 0.487259i) q^{60} +5.04294 q^{61} +(70.9650 - 62.8751i) q^{62} -47.2847i q^{63} +(22.6789 - 59.8470i) q^{64} -6.54837 q^{65} +(11.9726 + 13.5130i) q^{66} +93.4609i q^{67} +(3.49778 - 28.8280i) q^{68} -0.702335 q^{69} +(-17.9953 + 15.9439i) q^{70} +59.3817i q^{71} +(57.9028 - 39.9787i) q^{72} -125.788 q^{73} +(-70.5369 - 79.6127i) q^{74} +2.26141i q^{75} +(17.3087 + 2.10011i) q^{76} +107.299 q^{77} +(-1.98275 + 1.75672i) q^{78} +78.8437i q^{79} +(-34.7390 - 8.55592i) q^{80} +75.5187 q^{81} +(-24.9570 - 28.1681i) q^{82} -18.4528i q^{83} +(-1.17149 + 9.65516i) q^{84} -16.2335 q^{85} +(-13.8246 + 12.2486i) q^{86} +19.4507i q^{87} +(90.7200 + 131.394i) q^{88} -106.043 q^{89} +(-26.0848 - 29.4411i) q^{90} +15.7439i q^{91} +(-6.16625 - 0.748168i) q^{92} -21.4409 q^{93} +(-31.7861 + 28.1625i) q^{94} -9.74679i q^{95} +(-12.8138 + 6.72877i) q^{96} +40.1417 q^{97} +(-26.6563 - 30.0861i) q^{98} +175.546i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	$ 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) $ 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.32631	−	1.49696i	−0.663156	−	0.748482i
$2$	−1.32631	−	1.49696i	−0.663156	−	0.748482i
$3$			0.452282i			0.150761i	0.997155	+	0.0753804i	$0.0240171\pi$
$3$			0.452282i			0.150761i	−0.997155	+	0.0753804i	$0.975983\pi$
$4$	−0.481798	+	3.97088i	−0.120449	+	0.992719i
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$	0.677050	−	0.599867i	0.112842	−	0.0999778i
$7$		−	5.37605i		−	0.768007i	−0.923332	−	0.384004i	$-0.874545\pi$
$7$		−	5.37605i		−	0.768007i	0.923332	−	0.384004i	$-0.125455\pi$
$8$	6.58327	−	4.54539i	0.822909	−	0.568173i
$9$	8.79544			0.977271
$10$	−2.96572	−	3.34731i	−0.296572	−	0.334731i
$11$			19.9587i			1.81443i	0.420669	+	0.907214i	$0.361795\pi$
$11$			19.9587i			1.81443i	−0.420669	+	0.907214i	$0.638205\pi$
$12$	−1.79596	−	0.217909i	−0.149663	−	0.0181591i
$13$	−2.92852			−0.225271			−0.112635	−	0.993636i	$-0.535929\pi$
$13$	−2.92852			−0.225271			−0.112635	+	0.993636i	$0.535929\pi$
$14$	−8.04775	+	7.13031i	−0.574839	+	0.509308i
$15$			1.01133i			0.0674223i
$16$	−15.5357	−	3.82632i	−0.970984	−	0.239145i
$17$	−7.25985			−0.427050			−0.213525	−	0.976938i	$-0.568494\pi$
$17$	−7.25985			−0.427050			−0.213525	+	0.976938i	$0.568494\pi$
$18$	−11.6655	−	13.1665i	−0.648083	−	0.731470i
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	−1.07733	+	8.87915i	−0.0538666	+	0.443958i
$21$	2.43149			0.115785
$22$	29.8775	−	26.4715i	1.35807	−	1.20325i
$23$			1.55287i			0.0675160i	0.999430	+	0.0337580i	$0.0107475\pi$
$23$			1.55287i			0.0675160i	−0.999430	+	0.0337580i	$0.989252\pi$
$24$	2.05580	+	2.97750i	0.0856582	+	0.124062i
$25$	5.00000			0.200000
$26$	3.88413	+	4.38388i	0.149389	+	0.168611i
$27$			8.04856i			0.298095i
$28$	21.3476	+	2.59017i	0.762415	+	0.0925061i
$29$	43.0057			1.48295			0.741477	−	0.670979i	$-0.234126\pi$
$29$	43.0057			1.48295			0.741477	+	0.670979i	$0.234126\pi$
$30$	1.51393	−	1.34134i	0.0504643	−	0.0447114i
$31$			47.4060i			1.52923i	0.644490	+	0.764613i	$0.277070\pi$
$31$			47.4060i			1.52923i	−0.644490	+	0.764613i	$0.722930\pi$
$32$	14.8774	+	28.3313i	0.464918	+	0.885354i
$33$	−9.02697			−0.273545
$34$	9.62882	+	10.8677i	0.283201	+	0.319639i
$35$		−	12.0212i		−	0.343463i
$36$	−4.23763	+	34.9256i	−0.117712	+	0.970156i
$37$	53.1828			1.43737			0.718687	−	0.695334i	$-0.244744\pi$
$37$	53.1828			1.43737			0.718687	+	0.695334i	$0.244744\pi$
$38$	−6.52511	+	5.78126i	−0.171713	+	0.152138i
$39$		−	1.32452i		−	0.0339620i
$40$	14.7206	−	10.1638i	0.368016	−	0.254095i
$41$	18.8168			0.458947			0.229474	−	0.973315i	$-0.426300\pi$
$41$	18.8168			0.458947			0.229474	+	0.973315i	$0.426300\pi$
$42$	−3.22491	−	3.63985i	−0.0767837	−	0.0866632i
$43$		−	9.23507i		−	0.214769i	−0.994218	−	0.107385i	$-0.965752\pi$
$43$		−	9.23507i		−	0.214769i	0.994218	−	0.107385i	$-0.0342476\pi$
$44$	−79.2536	−	9.61607i	−1.80122	−	0.218547i
$45$	19.6672			0.437049
$46$	2.32459	−	2.05959i	0.0505345	−	0.0447736i
$47$		−	21.2337i		−	0.451781i	−0.974153	−	0.225891i	$-0.927471\pi$
$47$		−	21.2337i		−	0.451781i	0.974153	−	0.225891i	$-0.0725292\pi$
$48$	1.73058	−	7.02654i	0.0360537	−	0.146386i
$49$	20.0981			0.410165
$50$	−6.63156	−	7.48482i	−0.132631	−	0.149696i
$51$		−	3.28350i		−	0.0643824i
$52$	1.41095	−	11.6288i	0.0271337	−	0.223631i
$53$	85.9678			1.62203			0.811017	−	0.585022i	$-0.198914\pi$
$53$	85.9678			1.62203			0.811017	+	0.585022i	$0.198914\pi$
$54$	12.0484	−	10.6749i	0.223119	−	0.197683i
$55$			44.6290i			0.811437i
$56$	−24.4362	−	35.3920i	−0.436361	−	0.632000i
$57$	1.97145			0.0345869
$58$	−57.0389	−	64.3779i	−0.983429	−	1.10996i
$59$		−	109.477i		−	1.85555i	−0.373142	−	0.927774i	$-0.621720\pi$
$59$		−	109.477i		−	1.85555i	0.373142	−	0.927774i	$-0.378280\pi$
$60$	−4.01588	−	0.487259i	−0.0669314	−	0.00812098i
$61$	5.04294			0.0826711			0.0413355	−	0.999145i	$-0.486839\pi$
$61$	5.04294			0.0826711			0.0413355	+	0.999145i	$0.486839\pi$
$62$	70.9650	−	62.8751i	1.14460	−	1.01411i
$63$		−	47.2847i		−	0.750551i
$64$	22.6789	−	59.8470i	0.354359	−	0.935110i
$65$	−6.54837			−0.100744
$66$	11.9726	+	13.5130i	0.181403	+	0.204743i
$67$			93.4609i			1.39494i	0.716615	+	0.697469i	$0.245691\pi$
$67$			93.4609i			1.39494i	−0.716615	+	0.697469i	$0.754309\pi$
$68$	3.49778	−	28.8280i	0.0514380	−	0.423941i
$69$	−0.702335			−0.0101788
$70$	−17.9953	+	15.9439i	−0.257076	+	0.227770i
$71$			59.3817i			0.836361i	0.908364	+	0.418181i	$0.137332\pi$
$71$			59.3817i			0.836361i	−0.908364	+	0.418181i	$0.862668\pi$
$72$	57.9028	−	39.9787i	0.804205	−	0.555259i
$73$	−125.788			−1.72312			−0.861562	−	0.507653i	$-0.830513\pi$
$73$	−125.788			−1.72312			−0.861562	+	0.507653i	$0.830513\pi$
$74$	−70.5369	−	79.6127i	−0.953202	−	1.07585i
$75$			2.26141i			0.0301521i
$76$	17.3087	+	2.10011i	0.227745	+	0.0276330i
$77$	107.299			1.39349
$78$	−1.98275	+	1.75672i	−0.0254199	+	0.0225221i
$79$			78.8437i			0.998021i	0.866596	+	0.499011i	$0.166303\pi$
$79$			78.8437i			0.998021i	−0.866596	+	0.499011i	$0.833697\pi$
$80$	−34.7390	−	8.55592i	−0.434237	−	0.106949i
$81$	75.5187			0.932330
$82$	−24.9570	−	28.1681i	−0.304353	−	0.343513i
$83$		−	18.4528i		−	0.222323i	−0.993802	−	0.111161i	$-0.964543\pi$
$83$		−	18.4528i		−	0.222323i	0.993802	−	0.111161i	$-0.0354570\pi$
$84$	−1.17149	+	9.65516i	−0.0139463	+	0.114942i
$85$	−16.2335			−0.190983
$86$	−13.8246	+	12.2486i	−0.160751	+	0.142425i
$87$			19.4507i			0.223571i
$88$	90.7200	+	131.394i	1.03091	+	1.49311i
$89$	−106.043			−1.19149			−0.595745	−	0.803174i	$-0.703143\pi$
$89$	−106.043			−1.19149			−0.595745	+	0.803174i	$0.703143\pi$
$90$	−26.0848	−	29.4411i	−0.289831	−	0.327123i
$91$			15.7439i			0.173009i
$92$	−6.16625	−	0.748168i	−0.0670244	−	0.00813227i
$93$	−21.4409			−0.230547
$94$	−31.7861	+	28.1625i	−0.338150	+	0.299601i
$95$		−	9.74679i		−	0.102598i
$96$	−12.8138	+	6.72877i	−0.133477	+	0.0700913i
$97$	40.1417			0.413832			0.206916	−	0.978359i	$-0.433657\pi$
$97$	40.1417			0.413832			0.206916	+	0.978359i	$0.433657\pi$
$98$	−26.6563	−	30.0861i	−0.272003	−	0.307001i
$99$			175.546i			1.77319i
$100$	−2.40899	+	19.8544i	−0.0240899	+	0.198544i
$101$	−101.280			−1.00278			−0.501388	−	0.865223i	$-0.667177\pi$
$101$	−101.280			−1.00278			−0.501388	+	0.865223i	$0.667177\pi$
$102$	−4.91528	+	4.35494i	−0.0481890	+	0.0426955i
$103$			81.3104i			0.789421i	0.918806	+	0.394711i	$0.129155\pi$
$103$			81.3104i			0.789421i	−0.918806	+	0.394711i	$0.870845\pi$
$104$	−19.2792	+	13.3112i	−0.185377	+	0.127993i
$105$	5.43698			0.0517808
$106$	−114.020	−	128.691i	−1.07566	−	1.21406i
$107$		−	151.457i		−	1.41548i	−0.706472	−	0.707741i	$-0.749715\pi$
$107$		−	151.457i		−	1.41548i	0.706472	−	0.707741i	$-0.250285\pi$
$108$	−31.9599	−	3.87778i	−0.295925	−	0.0359054i
$109$	23.1332			0.212232			0.106116	−	0.994354i	$-0.466159\pi$
$109$	23.1332			0.212232			0.106116	+	0.994354i	$0.466159\pi$
$110$	66.8080	−	59.1920i	0.607346	−	0.538109i
$111$			24.0536i			0.216699i
$112$	−20.5705	+	83.5209i	−0.183665	+	0.745722i
$113$	139.258			1.23238			0.616188	−	0.787599i	$-0.288676\pi$
$113$	139.258			1.23238			0.616188	+	0.787599i	$0.288676\pi$
$114$	−2.61476	−	2.95119i	−0.0229365	−	0.0258877i
$115$			3.47232i			0.0301941i
$116$	−20.7200	+	170.770i	−0.178621	+	1.47216i
$117$	−25.7576			−0.220151
$118$	−163.884	+	145.201i	−1.38884	+	1.23052i
$119$			39.0293i			0.327977i
$120$	4.59690	+	6.65789i	0.0383075	+	0.0554824i
$121$	−277.350			−2.29215
$122$	−6.68850	−	7.54909i	−0.0548238	−	0.0618778i
$123$			8.51052i			0.0691912i
$124$	−188.243	−	22.8401i	−1.51809	−	0.184194i
$125$	11.1803			0.0894427
$126$	−70.7835	+	62.7142i	−0.561774	+	0.497732i
$127$		−	113.055i		−	0.890197i	−0.895482	−	0.445099i	$-0.853169\pi$
$127$		−	113.055i		−	0.890197i	0.895482	−	0.445099i	$-0.146831\pi$
$128$	−119.668	+	45.4262i	−0.934907	+	0.354892i
$129$	4.17686			0.0323787
$130$	8.68517	+	9.80266i	0.0668090	+	0.0754051i
$131$		−	97.0078i		−	0.740517i	−0.928929	−	0.370259i	$-0.879269\pi$
$131$		−	97.0078i		−	0.740517i	0.928929	−	0.370259i	$-0.120731\pi$
$132$	4.34918	−	35.8450i	0.0329483	−	0.271553i
$133$	−23.4337			−0.176193
$134$	139.907	−	123.958i	1.04409	−	0.925061i
$135$			17.9971i			0.133312i
$136$	−47.7936	+	32.9988i	−0.351423	+	0.242638i
$137$	174.535			1.27398			0.636989	−	0.770873i	$-0.280180\pi$
$137$	174.535			1.27398			0.636989	+	0.770873i	$0.280180\pi$
$138$	0.931514	+	1.05137i	0.00675010	+	0.00761862i
$139$			241.279i			1.73582i	0.496723	+	0.867909i	$0.334537\pi$
$139$			241.279i			1.73582i	−0.496723	+	0.867909i	$0.665463\pi$
$140$	47.7348	+	5.79179i	0.340963	+	0.0413700i
$141$	9.60364			0.0681109
$142$	88.8922	−	78.7585i	0.626001	−	0.554638i
$143$		−	58.4495i		−	0.408737i
$144$	−136.644	−	33.6542i	−0.948915	−	0.233710i
$145$	96.1636			0.663197
$146$	166.834	+	188.300i	1.14270	+	1.28973i
$147$			9.09001i			0.0618368i
$148$	−25.6234	+	211.182i	−0.173131	+	1.42691i
$149$	−45.9539			−0.308416			−0.154208	−	0.988038i	$-0.549283\pi$
$149$	−45.9539			−0.308416			−0.154208	+	0.988038i	$0.549283\pi$
$150$	3.38525	−	2.99933i	0.0225683	−	0.0199956i
$151$		−	107.754i		−	0.713603i	−0.934180	−	0.356801i	$-0.883867\pi$
$151$		−	107.754i		−	0.713603i	0.934180	−	0.356801i	$-0.116133\pi$
$152$	−19.8129	−	28.6958i	−0.130348	−	0.188788i
$153$	−63.8536			−0.417344
$154$	−142.312	−	160.623i	−0.924103	−	1.04300i
$155$			106.003i			0.683890i
$156$	5.25949	+	0.638150i	0.0337147	+	0.00409070i
$157$	8.96346			0.0570921			0.0285461	−	0.999592i	$-0.490912\pi$
$157$	8.96346			0.0570921			0.0285461	+	0.999592i	$0.490912\pi$
$158$	118.026	−	104.571i	0.747001	−	0.661843i
$159$			38.8817i			0.244539i
$160$	33.2668	+	63.3508i	0.207917	+	0.395942i
$161$	8.34829			0.0518528
$162$	−100.161	−	113.049i	−0.618280	−	0.697832i
$163$		−	57.2983i		−	0.351524i	−0.984433	−	0.175762i	$-0.943761\pi$
$163$		−	57.2983i		−	0.351524i	0.984433	−	0.175762i	$-0.0562388\pi$
$164$	−9.06591	+	74.7193i	−0.0552799	+	0.455606i
$165$	−20.1849			−0.122333
$166$	−27.6231	+	24.4741i	−0.166404	+	0.147434i
$167$			81.3682i			0.487235i	0.969871	+	0.243617i	$0.0783341\pi$
$167$			81.3682i			0.487235i	−0.969871	+	0.243617i	$0.921666\pi$
$168$	16.0072	−	11.0521i	0.0952808	−	0.0657861i
$169$	−160.424			−0.949253
$170$	21.5307	+	24.3010i	0.126651	+	0.142947i
$171$		−	38.3384i		−	0.224201i
$172$	36.6713	+	4.44944i	0.213205	+	0.0258688i
$173$	−332.247			−1.92050			−0.960251	−	0.279137i	$-0.909952\pi$
$173$	−332.247			−1.92050			−0.960251	+	0.279137i	$0.909952\pi$
$174$	29.1170	−	25.7977i	0.167339	−	0.148262i
$175$		−	26.8802i		−	0.153601i
$176$	76.3685	−	310.073i	0.433912	−	1.76178i
$177$	49.5147			0.279744
$178$	140.646	+	158.742i	0.790143	+	0.891809i
$179$		−	2.70546i		−	0.0151143i	−0.999971	−	0.00755714i	$-0.997594\pi$
$179$		−	2.70546i		−	0.0151143i	0.999971	−	0.00755714i	$-0.00240554\pi$
$180$	−9.47562	+	78.0961i	−0.0526423	+	0.433867i
$181$	−241.518			−1.33436			−0.667178	−	0.744898i	$-0.732498\pi$
$181$	−241.518			−1.33436			−0.667178	+	0.744898i	$0.732498\pi$
$182$	23.5680	−	20.8813i	0.129494	−	0.114732i
$183$			2.28083i			0.0124636i
$184$	7.05838	+	10.2230i	0.0383608	+	0.0555595i
$185$	118.920			0.642813
$186$	28.4373	+	32.0962i	0.152889	+	0.172560i
$187$		−	144.897i		−	0.774852i
$188$	84.3165	+	10.2304i	0.448492	+	0.0544168i
$189$	43.2695			0.228939
$190$	−14.5906	+	12.9273i	−0.0767926	+	0.0680383i
$191$			14.4233i			0.0755148i	0.999287	+	0.0377574i	$0.0120214\pi$
$191$			14.4233i			0.0755148i	−0.999287	+	0.0377574i	$0.987979\pi$
$192$	27.0677	+	10.2573i	0.140978	+	0.0534234i
$193$	−169.765			−0.879609			−0.439805	−	0.898094i	$-0.644952\pi$
$193$	−169.765			−0.879609			−0.439805	+	0.898094i	$0.644952\pi$
$194$	−53.2404	−	60.0906i	−0.274435	−	0.309746i
$195$		−	2.96171i		−	0.0151883i
$196$	−9.68322	+	79.8071i	−0.0494042	+	0.407179i
$197$	−85.6593			−0.434819			−0.217409	−	0.976081i	$-0.569761\pi$
$197$	−85.6593			−0.434819			−0.217409	+	0.976081i	$0.569761\pi$
$198$	262.785	−	232.828i	1.32720	−	1.17590i
$199$		−	192.414i		−	0.966905i	−0.875371	−	0.483452i	$-0.839383\pi$
$199$		−	192.414i		−	0.966905i	0.875371	−	0.483452i	$-0.160617\pi$
$200$	32.9164	−	22.7269i	0.164582	−	0.113635i
$201$	−42.2707			−0.210302
$202$	134.329	+	151.613i	0.664996	+	0.750559i
$203$		−	231.200i		−	1.13892i
$204$	13.0384	+	1.58198i	0.0639136	+	0.00775482i
$205$	42.0757			0.205247
$206$	121.719	−	107.843i	0.590867	−	0.523509i
$207$			13.6582i			0.0659814i
$208$	45.4967	+	11.2055i	0.218734	+	0.0538724i
$209$	86.9980			0.416258
$210$	−7.21113	−	8.13896i	−0.0343387	−	0.0387570i
$211$		−	191.096i		−	0.905669i	−0.891595	−	0.452834i	$-0.850413\pi$
$211$		−	191.096i		−	0.905669i	0.891595	−	0.452834i	$-0.149587\pi$
$212$	−41.4191	+	341.368i	−0.195373	+	1.61023i
$213$	−26.8573			−0.126090
$214$	−226.725	+	200.878i	−1.05946	+	0.938684i
$215$		−	20.6502i		−	0.0960476i
$216$	36.5838	+	52.9859i	0.169370	+	0.245305i
$217$	254.857			1.17446
$218$	−30.6819	−	34.6296i	−0.140743	−	0.158851i
$219$		−	56.8917i		−	0.259779i
$220$	−177.216	−	21.5022i	−0.805529	−	0.0977372i
$221$	21.2606			0.0962018
$222$	36.0074	−	31.9026i	0.162196	−	0.143705i
$223$			54.7539i			0.245533i	0.992436	+	0.122767i	$0.0391766\pi$
$223$			54.7539i			0.245533i	−0.992436	+	0.122767i	$0.960823\pi$
$224$	152.311	−	79.9814i	0.679958	−	0.357060i
$225$	43.9772			0.195454
$226$	−184.700	−	208.465i	−0.817257	−	0.922411i
$227$		−	103.744i		−	0.457024i	−0.973541	−	0.228512i	$-0.926614\pi$
$227$		−	103.744i		−	0.457024i	0.973541	−	0.228512i	$-0.0733860\pi$
$228$	−0.949842	+	7.82840i	−0.00416597	+	0.0343351i
$229$	261.392			1.14145			0.570725	−	0.821142i	$-0.306662\pi$
$229$	261.392			1.14145			0.570725	+	0.821142i	$0.306662\pi$
$230$	5.19793	−	4.60537i	0.0225997	−	0.0200234i
$231$			48.5294i			0.210084i
$232$	283.118	−	195.477i	1.22034	−	0.842574i
$233$	−249.042			−1.06885			−0.534424	−	0.845217i	$-0.679471\pi$
$233$	−249.042			−1.06885			−0.534424	+	0.845217i	$0.679471\pi$
$234$	34.1626	+	38.5582i	0.145994	+	0.164779i
$235$		−	47.4801i		−	0.202043i
$236$	434.721	+	52.7460i	1.84204	+	0.223500i
$237$	−35.6596			−0.150462
$238$	58.4254	−	51.7650i	0.245485	−	0.217500i
$239$		−	64.4735i		−	0.269764i	−0.990862	−	0.134882i	$-0.956935\pi$
$239$		−	64.4735i		−	0.269764i	0.990862	−	0.134882i	$-0.0430655\pi$
$240$	3.86969	−	15.7118i	0.0161237	−	0.0654659i
$241$	59.8797			0.248463			0.124232	−	0.992253i	$-0.460353\pi$
$241$	59.8797			0.248463			0.124232	+	0.992253i	$0.460353\pi$
$242$	367.853	+	415.183i	1.52005	+	1.71563i
$243$			106.593i			0.438654i
$244$	−2.42968	+	20.0249i	−0.00995769	+	0.0820692i
$245$	44.9407			0.183431
$246$	12.7399	−	11.2876i	0.0517883	−	0.0458845i
$247$			12.7651i			0.0516806i
$248$	215.478	+	312.086i	0.868865	+	1.25841i
$249$	8.34586			0.0335175
$250$	−14.8286	−	16.7366i	−0.0593144	−	0.0669462i
$251$		−	90.7793i		−	0.361671i	−0.983513	−	0.180835i	$-0.942120\pi$
$251$		−	90.7793i		−	0.361671i	0.983513	−	0.180835i	$-0.0578801\pi$
$252$	187.762	+	22.7817i	0.745087	+	0.0904035i
$253$	−30.9932			−0.122503
$254$	−169.239	+	149.946i	−0.666296	+	0.590339i
$255$		−	7.34213i		−	0.0287927i
$256$	226.719	+	118.889i	0.885619	+	0.464412i
$257$	176.740			0.687706			0.343853	−	0.939023i	$-0.388268\pi$
$257$	176.740			0.687706			0.343853	+	0.939023i	$0.388268\pi$
$258$	−5.53981	−	6.25260i	−0.0214721	−	0.0242349i
$259$		−	285.913i		−	1.10391i
$260$	3.15499	−	26.0028i	0.0121346	−	0.100011i
$261$	378.254			1.44925
$262$	−145.217	+	128.663i	−0.554264	+	0.491078i
$263$		−	303.564i		−	1.15424i	−0.816661	−	0.577118i	$-0.804177\pi$
$263$		−	303.564i		−	1.15424i	0.816661	−	0.577118i	$-0.195823\pi$
$264$	−59.4270	+	41.0311i	−0.225102	+	0.155421i
$265$	192.230			0.725396
$266$	31.0803	+	35.0793i	0.116843	+	0.131877i
$267$		−	47.9612i		−	0.179630i
$268$	−371.122	−	45.0292i	−1.38478	−	0.168020i
$269$	135.167			0.502479			0.251240	−	0.967925i	$-0.419162\pi$
$269$	135.167			0.502479			0.251240	+	0.967925i	$0.419162\pi$
$270$	26.9410	−	23.8698i	0.0997816	−	0.0884066i
$271$		−	25.9451i		−	0.0957384i	−0.998854	−	0.0478692i	$-0.984757\pi$
$271$		−	25.9451i		−	0.0957384i	0.998854	−	0.0478692i	$-0.0152431\pi$
$272$	112.787	+	27.7785i	0.414659	+	0.102127i
$273$	−7.12067			−0.0260830
$274$	−231.488	−	261.273i	−0.844846	−	0.953549i
$275$			99.7936i			0.362886i
$276$	0.338383	−	2.78888i	0.00122603	−	0.0101047i
$277$	−371.739			−1.34202			−0.671010	−	0.741448i	$-0.734139\pi$
$277$	−371.739			−1.34202			−0.671010	+	0.741448i	$0.734139\pi$
$278$	361.185	−	320.011i	1.29923	−	1.15112i
$279$			416.957i			1.49447i
$280$	−54.6410	−	79.1389i	−0.195147	−	0.282639i
$281$	383.830			1.36594			0.682971	−	0.730445i	$-0.260687\pi$
$281$	383.830			1.36594			0.682971	+	0.730445i	$0.260687\pi$
$282$	−12.7374	−	14.3763i	−0.0451681	−	0.0509798i
$283$		−	33.5443i		−	0.118531i	−0.998242	−	0.0592656i	$-0.981124\pi$
$283$		−	33.5443i		−	0.118531i	0.998242	−	0.0592656i	$-0.0188759\pi$
$284$	−235.797	−	28.6100i	−0.830272	−	0.100739i
$285$	4.40830			0.0154677
$286$	−87.4967	+	77.5222i	−0.305932	+	0.271056i
$287$		−	101.160i		−	0.352475i
$288$	130.853	+	249.187i	0.454351	+	0.865231i
$289$	−236.295			−0.817628
$290$	−127.543	−	143.953i	−0.439803	−	0.496391i
$291$			18.1554i			0.0623896i
$292$	60.6044	−	499.489i	0.207549	−	1.71058i
$293$	−223.997			−0.764494			−0.382247	−	0.924060i	$-0.624850\pi$
$293$	−223.997			−0.764494			−0.382247	+	0.924060i	$0.624850\pi$
$294$	13.6074	−	12.0562i	0.0462837	−	0.0410074i
$295$		−	244.799i		−	0.829827i
$296$	350.117	−	241.736i	1.18283	−	0.816677i
$297$	−160.639			−0.540872
$298$	60.9492	+	68.7913i	0.204528	+	0.230843i
$299$		−	4.54760i		−	0.0152094i
$300$	−8.97979	−	1.08954i	−0.0299326	−	0.00363181i
$301$	−49.6482			−0.164944
$302$	−161.304	+	142.915i	−0.534119	+	0.473230i
$303$		−	45.8073i		−	0.151179i
$304$	−16.6785	+	67.7187i	−0.0548636	+	0.222759i
$305$	11.2763			0.0369716
$306$	84.6897	+	95.5865i	0.276764	+	0.312374i
$307$			461.673i			1.50382i	0.659265	+	0.751910i	$0.270867\pi$
$307$			461.673i			1.50382i	−0.659265	+	0.751910i	$0.729133\pi$
$308$	−51.6964	+	426.071i	−0.167846	+	1.38335i
$309$	−36.7752			−0.119014
$310$	158.683	−	140.593i	0.511879	−	0.453526i
$311$			241.481i			0.776466i	0.921561	+	0.388233i	$0.126914\pi$
$311$			241.481i			0.776466i	−0.921561	+	0.388233i	$0.873086\pi$
$312$	−6.02044	−	8.71966i	−0.0192963	−	0.0279476i
$313$	−387.340			−1.23751			−0.618754	−	0.785585i	$-0.712362\pi$
$313$	−387.340			−1.23751			−0.618754	+	0.785585i	$0.712362\pi$
$314$	−11.8883	−	13.4180i	−0.0378610	−	0.0427324i
$315$		−	105.732i		−	0.335657i
$316$	−313.079	−	37.9867i	−0.990755	−	0.120211i
$317$	71.7688			0.226400			0.113200	−	0.993572i	$-0.463890\pi$
$317$	71.7688			0.226400			0.113200	+	0.993572i	$0.463890\pi$
$318$	58.2045	−	51.5693i	0.183033	−	0.162167i
$319$			858.337i			2.69071i
$320$	50.7117	−	133.822i	0.158474	−	0.418194i
$321$	68.5011			0.213399
$322$	−11.0724	−	12.4971i	−0.0343864	−	0.0388108i
$323$			31.6450i			0.0979720i
$324$	−36.3848	+	299.876i	−0.112299	+	0.925542i
$325$	−14.6426			−0.0450541
$326$	−85.7735	+	75.9954i	−0.263109	+	0.233115i
$327$			10.4628i			0.0319962i
$328$	123.876	−	85.5297i	0.377672	−	0.260761i
$329$	−114.154			−0.346971
$330$	26.7715	+	30.2161i	0.0811257	+	0.0915639i
$331$		−	585.826i		−	1.76987i	−0.465717	−	0.884934i	$-0.654204\pi$
$331$		−	585.826i		−	1.76987i	0.465717	−	0.884934i	$-0.345796\pi$
$332$	73.2737	+	8.89051i	0.220704	+	0.0267786i
$333$	467.766			1.40470
$334$	121.805	−	107.920i	0.364686	−	0.323112i
$335$			208.985i			0.623835i
$336$	−37.7750	−	9.30367i	−0.112426	−	0.0276895i
$337$	−41.2728			−0.122471			−0.0612356	−	0.998123i	$-0.519504\pi$
$337$	−41.2728			−0.122471			−0.0612356	+	0.998123i	$0.519504\pi$
$338$	212.772	+	240.149i	0.629502	+	0.710499i
$339$			62.9841i			0.185794i
$340$	7.82128	−	64.4613i	0.0230038	−	0.189592i
$341$	−946.162			−2.77467
$342$	−57.3912	+	50.8487i	−0.167811	+	0.148680i
$343$		−	371.475i		−	1.08302i
$344$	−41.9769	−	60.7970i	−0.122026	−	0.176735i
$345$	−1.57047			−0.00455208
$346$	440.663	+	497.362i	1.27359	+	1.43746i
$347$		−	485.733i		−	1.39981i	−0.714237	−	0.699904i	$-0.753226\pi$
$347$		−	485.733i		−	1.39981i	0.714237	−	0.699904i	$-0.246774\pi$
$348$	−77.2363	−	9.37130i	−0.221943	−	0.0269290i
$349$	62.3883			0.178763			0.0893815	−	0.995997i	$-0.471511\pi$
$349$	62.3883			0.178763			0.0893815	+	0.995997i	$0.471511\pi$
$350$	−40.2387	+	35.6516i	−0.114968	+	0.101862i
$351$		−	23.5704i		−	0.0671520i
$352$	−565.457	+	296.933i	−1.60641	+	0.843560i
$353$	−496.586			−1.40676			−0.703379	−	0.710815i	$-0.748327\pi$
$353$	−496.586			−1.40676			−0.703379	+	0.710815i	$0.748327\pi$
$354$	−65.6718	−	74.1216i	−0.185514	−	0.209383i
$355$			132.781i			0.374032i
$356$	51.0911	−	421.082i	0.143514	−	1.18282i
$357$	−17.6523			−0.0494461
$358$	−4.04997	+	3.58828i	−0.0113128	+	0.0100231i
$359$		−	128.882i		−	0.359003i	−0.983758	−	0.179501i	$-0.942552\pi$
$359$		−	128.882i		−	0.359003i	0.983758	−	0.179501i	$-0.0574484\pi$
$360$	129.475	−	89.3950i	0.359652	−	0.248319i
$361$	−19.0000			−0.0526316
$362$	320.329	+	361.544i	0.884885	+	0.998741i
$363$		−	125.441i		−	0.345566i
$364$	−62.5169	−	7.58536i	−0.171750	−	0.0208389i
$365$	−281.270			−0.770604
$366$	3.41432	−	3.02509i	0.00932874	−	0.00826527i
$367$			443.800i			1.20927i	0.796504	+	0.604633i	$0.206680\pi$
$367$			443.800i			1.20927i	−0.796504	+	0.604633i	$0.793320\pi$
$368$	5.94177	−	24.1250i	0.0161461	−	0.0655569i
$369$	165.502			0.448516
$370$	−157.725	−	178.019i	−0.426285	−	0.481134i
$371$		−	462.167i		−	1.24573i
$372$	10.3302	−	85.1391i	0.0277693	−	0.228869i
$373$	698.461			1.87255			0.936274	−	0.351270i	$-0.114250\pi$
$373$	698.461			1.87255			0.936274	+	0.351270i	$0.114250\pi$
$374$	−216.906	+	192.179i	−0.579962	+	0.513847i
$375$			5.05667i			0.0134845i
$376$	−96.5155	−	139.787i	−0.256690	−	0.371775i
$377$	−125.943			−0.334066
$378$	−57.3888	−	64.7728i	−0.151822	−	0.171357i
$379$			222.962i			0.588290i	0.955761	+	0.294145i	$0.0950349\pi$
$379$			222.962i			0.588290i	−0.955761	+	0.294145i	$0.904965\pi$
$380$	38.7033	+	4.69599i	0.101851	+	0.0123579i
$381$	51.1328			0.134207
$382$	21.5912	−	19.1298i	0.0565214	−	0.0500780i
$383$		−	233.014i		−	0.608392i	−0.952609	−	0.304196i	$-0.901612\pi$
$383$		−	233.014i		−	0.608392i	0.952609	−	0.304196i	$-0.0983878\pi$
$384$	−20.5455	−	54.1238i	−0.0535038	−	0.140947i
$385$	239.928			0.623189
$386$	225.161	+	254.131i	0.583318	+	0.658371i
$387$		−	81.2265i		−	0.209888i
$388$	−19.3402	+	159.398i	−0.0498458	+	0.410819i
$389$	609.049			1.56568			0.782839	−	0.622225i	$-0.213771\pi$
$389$	609.049			1.56568			0.782839	+	0.622225i	$0.213771\pi$
$390$	−4.43357	+	3.92815i	−0.0113681	+	0.0100722i
$391$		−	11.2736i		−	0.0288327i
$392$	132.311	−	91.3536i	0.337529	−	0.233045i
$393$	43.8749			0.111641
$394$	113.611	+	128.229i	0.288352	+	0.325454i
$395$			176.300i			0.446329i
$396$	−697.070	−	84.5775i	−1.76028	−	0.213580i
$397$	−684.318			−1.72372			−0.861861	−	0.507144i	$-0.830701\pi$
$397$	−684.318			−1.72372			−0.861861	+	0.507144i	$0.830701\pi$
$398$	−288.037	+	255.201i	−0.723711	+	0.641208i
$399$		−	10.5986i		−	0.0265630i
$400$	−77.6787	−	19.1316i	−0.194197	−	0.0478290i
$401$	−154.155			−0.384427			−0.192214	−	0.981353i	$-0.561567\pi$
$401$	−154.155			−0.384427			−0.192214	+	0.981353i	$0.561567\pi$
$402$	56.0641	+	63.2777i	0.139463	+	0.157407i
$403$		−	138.829i		−	0.344490i
$404$	48.7966	−	402.172i	0.120784	−	0.995474i
$405$	168.865			0.416951
$406$	−346.099	+	306.644i	−0.852460	+	0.755280i
$407$			1061.46i			2.60801i
$408$	−14.9248	−	21.6162i	−0.0365803	−	0.0529808i
$409$	173.840			0.425037			0.212518	−	0.977157i	$-0.431833\pi$
$409$	173.840			0.425037			0.212518	+	0.977157i	$0.431833\pi$
$410$	−55.8055	−	62.9858i	−0.136111	−	0.153624i
$411$			78.9391i			0.192066i
$412$	−322.874	−	39.1752i	−0.783674	−	0.0950854i
$413$	−588.556			−1.42507
$414$	20.4458	−	18.1150i	0.0493859	−	0.0437559i
$415$		−	41.2616i		−	0.0994257i
$416$	−43.5686	−	82.9688i	−0.104732	−	0.199444i
$417$	−109.126			−0.261693
$418$	−115.386	−	130.233i	−0.276044	−	0.311562i
$419$		−	318.734i		−	0.760701i	−0.924842	−	0.380351i	$-0.875803\pi$
$419$		−	318.734i		−	0.760701i	0.924842	−	0.380351i	$-0.124197\pi$
$420$	−2.61953	+	21.5896i	−0.00623697	+	0.0514038i
$421$	159.793			0.379555			0.189778	−	0.981827i	$-0.439223\pi$
$421$	159.793			0.379555			0.189778	+	0.981827i	$0.439223\pi$
$422$	−286.064	+	253.453i	−0.677876	+	0.600599i
$423$		−	186.760i		−	0.441513i
$424$	565.950	−	390.757i	1.33479	−	0.921596i
$425$	−36.2992			−0.0854100
$426$	35.6211	+	40.2043i	0.0836176	+	0.0943764i
$427$		−	27.1111i		−	0.0634920i
$428$	601.415	+	72.9714i	1.40518	+	0.170494i
$429$	26.4357			0.0616216
$430$	−30.9127	+	27.3886i	−0.0718899	+	0.0636945i
$431$			351.834i			0.816320i	0.912910	+	0.408160i	$0.133829\pi$
$431$			351.834i			0.816320i	−0.912910	+	0.408160i	$0.866171\pi$
$432$	30.7964	−	125.040i	0.0712879	−	0.289445i
$433$	−60.7379			−0.140272			−0.0701362	−	0.997537i	$-0.522343\pi$
$433$	−60.7379			−0.140272			−0.0701362	+	0.997537i	$0.522343\pi$
$434$	−338.020	−	381.511i	−0.778847	−	0.879059i
$435$			43.4931i			0.0999841i
$436$	−11.1455	+	91.8593i	−0.0255632	+	0.210686i
$437$	6.76879			0.0154892
$438$	−85.1647	+	75.4561i	−0.194440	+	0.172274i
$439$			505.457i			1.15138i	0.817667	+	0.575691i	$0.195267\pi$
$439$			505.457i			1.15138i	−0.817667	+	0.575691i	$0.804733\pi$
$440$	202.856	+	293.805i	0.461037	+	0.667739i
$441$	176.772			0.400843
$442$	−28.1982	−	31.8263i	−0.0637968	−	0.0720053i
$443$			29.6312i			0.0668877i	0.999441	+	0.0334438i	$0.0106475\pi$
$443$			29.6312i			0.0668877i	−0.999441	+	0.0334438i	$0.989353\pi$
$444$	−95.5141	−	11.5890i	−0.215122	−	0.0261013i
$445$	−237.119			−0.532851
$446$	81.9645	−	72.6207i	0.183777	−	0.162827i
$447$		−	20.7841i		−	0.0464970i
$448$	−321.740	−	121.923i	−0.718171	−	0.272150i
$449$	28.2407			0.0628968			0.0314484	−	0.999505i	$-0.489988\pi$
$449$	28.2407			0.0628968			0.0314484	+	0.999505i	$0.489988\pi$
$450$	−58.3275	−	65.8323i	−0.129617	−	0.146294i
$451$			375.560i			0.832727i
$452$	−67.0945	+	552.978i	−0.148439	+	1.22340i
$453$	48.7352			0.107583
$454$	−155.302	+	137.597i	−0.342074	+	0.303078i
$455$			35.2043i			0.0773722i
$456$	12.9786	−	8.96101i	0.0284619	−	0.0196513i
$457$	−809.461			−1.77125			−0.885625	−	0.464401i	$-0.846270\pi$
$457$	−809.461			−1.77125			−0.885625	+	0.464401i	$0.846270\pi$
$458$	−346.687	−	391.294i	−0.756958	−	0.854354i
$459$		−	58.4313i		−	0.127301i
$460$	−13.7881	−	1.67296i	−0.0299742	−	0.00363686i
$461$	914.082			1.98282			0.991412	−	0.130778i	$-0.0417474\pi$
$461$	914.082			1.98282			0.991412	+	0.130778i	$0.0417474\pi$
$462$	72.6468	−	64.3651i	0.157244	−	0.139318i
$463$			158.475i			0.342278i	0.985247	+	0.171139i	$0.0547447\pi$
$463$			158.475i			0.342278i	−0.985247	+	0.171139i	$0.945255\pi$
$464$	−668.125	−	164.553i	−1.43992	−	0.354641i
$465$	−47.9433			−0.103104
$466$	330.307	+	372.806i	0.708812	+	0.800013i
$467$		−	665.468i		−	1.42498i	−0.701680	−	0.712492i	$-0.747566\pi$
$467$		−	665.468i		−	1.42498i	0.701680	−	0.712492i	$-0.252434\pi$
$468$	12.4100	−	102.280i	0.0265170	−	0.218548i
$469$	502.450			1.07132
$470$	−71.0759	+	62.9733i	−0.151225	+	0.133986i
$471$			4.05402i			0.00860725i
$472$	−497.617	−	720.719i	−1.05427	−	1.52695i
$473$	184.320			0.389683
$474$	47.2957	+	53.3811i	0.0997800	+	0.112618i
$475$		−	21.7945i		−	0.0458831i
$476$	−154.981	−	18.8042i	−0.325590	−	0.0395047i
$477$	756.125			1.58517
$478$	−96.5144	+	85.5119i	−0.201913	+	0.178895i
$479$			678.464i			1.41642i	0.706003	+	0.708209i	$0.250496\pi$
$479$			678.464i			1.41642i	−0.706003	+	0.708209i	$0.749504\pi$
$480$	−28.6524	+	15.0460i	−0.0596926	+	0.0313458i
$481$	−155.747			−0.323798
$482$	−79.4191	−	89.6377i	−0.164770	−	0.185970i
$483$			3.77578i			0.00781736i
$484$	133.627	−	1101.32i	0.276088	−	2.27546i
$485$	89.7596			0.185071
$486$	159.566	−	141.375i	0.328324	−	0.290896i
$487$		−	123.146i		−	0.252866i	−0.991975	−	0.126433i	$-0.959647\pi$
$487$		−	123.146i		−	0.252866i	0.991975	−	0.126433i	$-0.0403529\pi$
$488$	33.1990	−	22.9221i	0.0680308	−	0.0469715i
$489$	25.9150			0.0529960
$490$	−59.6054	−	67.2746i	−0.121644	−	0.137295i
$491$		−	813.654i		−	1.65714i	−0.559888	−	0.828568i	$-0.689156\pi$
$491$		−	813.654i		−	1.65714i	0.559888	−	0.828568i	$-0.310844\pi$
$492$	−33.7942	−	4.10035i	−0.0686875	−	0.00833405i
$493$	−312.215			−0.633295
$494$	19.1089	−	16.9305i	0.0386820	−	0.0342723i
$495$			392.532i			0.792994i
$496$	181.391	−	736.487i	0.365707	−	1.48485i
$497$	319.239			0.642331
$498$	−11.0692	−	12.4934i	−0.0222273	−	0.0250872i
$499$		−	519.764i		−	1.04161i	−0.853675	−	0.520806i	$-0.825632\pi$
$499$		−	519.764i		−	1.04161i	0.853675	−	0.520806i	$-0.174368\pi$
$500$	−5.38666	+	44.3958i	−0.0107733	+	0.0887915i
$501$	−36.8014			−0.0734559
$502$	−135.893	+	120.402i	−0.270704	+	0.239844i
$503$			552.197i			1.09781i	0.835886	+	0.548903i	$0.184955\pi$
$503$			552.197i			1.09781i	−0.835886	+	0.548903i	$0.815045\pi$
$504$	−214.927	−	311.288i	−0.426443	−	0.617635i
$505$	−226.470			−0.448455
$506$	41.1067	+	46.3957i	0.0812385	+	0.0916912i
$507$		−	72.5568i		−	0.143110i
$508$	448.928	+	54.4697i	0.883716	+	0.107224i
$509$	306.248			0.601667			0.300833	−	0.953677i	$-0.402735\pi$
$509$	306.248			0.601667			0.300833	+	0.953677i	$0.402735\pi$
$510$	−10.9909	+	9.73795i	−0.0215508	+	0.0190940i
$511$			676.242i			1.32337i
$512$	−122.726	−	497.074i	−0.239699	−	0.970847i
$513$	35.0829			0.0683877
$514$	−234.413	−	264.574i	−0.456056	−	0.514735i
$515$			181.816i			0.353040i
$516$	−2.01240	+	16.5858i	−0.00390000	+	0.0321430i
$517$	423.798			0.819725
$518$	−428.002	+	379.210i	−0.826258	+	0.732066i
$519$		−	150.269i		−	0.289536i
$520$	−43.1097	+	29.7648i	−0.0829032	+	0.0572401i
$521$	−578.272			−1.10993			−0.554964	−	0.831875i	$-0.687268\pi$
$521$	−578.272			−1.10993			−0.554964	+	0.831875i	$0.687268\pi$
$522$	−501.682	−	566.232i	−0.961077	−	1.08474i
$523$		−	450.830i		−	0.862008i	−0.902350	−	0.431004i	$-0.858160\pi$
$523$		−	450.830i		−	0.862008i	0.902350	−	0.431004i	$-0.141840\pi$
$524$	385.206	+	46.7382i	0.735126	+	0.0891950i
$525$	12.1575			0.0231571
$526$	−454.424	+	402.620i	−0.863924	+	0.765438i
$527$		−	344.160i		−	0.653056i
$528$	140.241	+	34.5401i	0.265607	+	0.0654168i
$529$	526.589			0.995442
$530$	−254.957	−	287.761i	−0.481050	−	0.542945i
$531$		−	962.902i		−	1.81337i
$532$	11.2903	−	93.0522i	0.0212223	−	0.174910i
$533$	−55.1054			−0.103387
$534$	−71.7962	+	63.6115i	−0.134450	+	0.119123i
$535$		−	338.667i		−	0.633023i
$536$	424.816	+	615.278i	0.792566	+	1.14791i
$537$	1.22363			0.00227864
$538$	−179.273	−	202.340i	−0.333222	−	0.376097i
$539$			401.132i			0.744215i
$540$	−71.4644	−	8.67098i	−0.132342	−	0.0160574i
$541$	−601.186			−1.11125			−0.555625	−	0.831433i	$-0.687521\pi$
$541$	−601.186			−1.11125			−0.555625	+	0.831433i	$0.687521\pi$
$542$	−38.8389	+	34.4113i	−0.0716584	+	0.0634894i
$543$		−	109.234i		−	0.201168i
$544$	−108.007	−	205.681i	−0.198543	−	0.378090i
$545$	51.7275			0.0949128
$546$	9.44422	+	10.6594i	0.0172971	+	0.0195227i
$547$			594.491i			1.08682i	0.839467	+	0.543410i	$0.182867\pi$
$547$			594.491i			1.08682i	−0.839467	+	0.543410i	$0.817133\pi$
$548$	−84.0906	+	693.057i	−0.153450	+	1.26470i
$549$	44.3548			0.0807921
$550$	149.387	−	132.357i	0.271613	−	0.240650i
$551$		−	187.457i		−	0.340213i
$552$	−4.62366	+	3.19238i	−0.00837619	+	0.00578330i
$553$	423.868			0.766487
$554$	493.042	+	556.480i	0.889968	+	1.00448i
$555$			53.7856i			0.0969109i
$556$	−958.089	−	116.248i	−1.72318	−	0.209078i
$557$	−455.032			−0.816934			−0.408467	−	0.912773i	$-0.633937\pi$
$557$	−455.032			−0.816934			−0.408467	+	0.912773i	$0.633937\pi$
$558$	624.169	−	553.014i	1.11858	−	0.991065i
$559$			27.0451i			0.0483812i
$560$	−45.9970	+	186.758i	−0.0821375	+	0.333497i
$561$	65.5345			0.116817
$562$	−509.078	−	574.579i	−0.905833	−	1.02238i
$563$		−	645.025i		−	1.14569i	−0.819663	−	0.572846i	$-0.805839\pi$
$563$		−	645.025i		−	1.14569i	0.819663	−	0.572846i	$-0.194161\pi$
$564$	−4.62701	+	38.1349i	−0.00820392	+	0.0676150i
$565$	311.391			0.551135
$566$	−50.2146	+	44.4902i	−0.0887184	+	0.0786046i
$567$		−	405.992i		−	0.716036i
$568$	269.913	+	390.926i	0.475198	+	0.688249i
$569$	−41.0473			−0.0721394			−0.0360697	−	0.999349i	$-0.511484\pi$
$569$	−41.0473			−0.0721394			−0.0360697	+	0.999349i	$0.511484\pi$
$570$	−5.84678	−	6.59907i	−0.0102575	−	0.0115773i
$571$			951.239i			1.66592i	0.553335	+	0.832959i	$0.313355\pi$
$571$			951.239i			1.66592i	−0.553335	+	0.832959i	$0.686645\pi$
$572$	232.096	+	28.1608i	0.405762	+	0.0492322i
$573$	−6.52341			−0.0113847
$574$	−151.433	+	134.170i	−0.263821	+	0.233745i
$575$			7.76434i			0.0135032i
$576$	199.471	−	526.381i	0.346304	−	0.913856i
$577$	822.148			1.42487			0.712433	−	0.701740i	$-0.247593\pi$
$577$	822.148			1.42487			0.712433	+	0.701740i	$0.247593\pi$
$578$	313.400	+	353.724i	0.542215	+	0.611980i
$579$		−	76.7815i		−	0.132611i
$580$	−46.3314	+	381.854i	−0.0798817	+	0.658369i
$581$	−99.2030			−0.170745
$582$	27.1779	−	24.0797i	0.0466975	−	0.0413740i
$583$			1715.81i			2.94307i
$584$	−828.097	+	571.755i	−1.41797	+	0.979032i
$585$	−57.5958			−0.0984543
$586$	297.089	+	335.315i	0.506978	+	0.572209i
$587$			481.621i			0.820478i	0.911978	+	0.410239i	$0.134555\pi$
$587$			481.621i			0.820478i	−0.911978	+	0.410239i	$0.865445\pi$
$588$	−36.0953	−	4.37955i	−0.0613866	−	0.00744821i
$589$	206.638			0.350828
$590$	−366.455	+	324.679i	−0.621110	+	0.550304i
$591$		−	38.7422i		−	0.0655536i
$592$	−826.234	−	203.495i	−1.39567	−	0.343741i
$593$	775.433			1.30764			0.653822	−	0.756648i	$-0.273164\pi$
$593$	775.433			1.30764			0.653822	+	0.756648i	$0.273164\pi$
$594$	213.057	+	240.471i	0.358682	+	0.404833i
$595$			87.2722i			0.146676i
$596$	22.1405	−	182.477i	0.0371485	−	0.306170i
$597$	87.0255			0.145771
$598$	−6.80759	+	6.03153i	−0.0113839	+	0.0100862i
$599$		−	83.6347i		−	0.139624i	−0.997560	−	0.0698119i	$-0.977760\pi$
$599$		−	83.6347i		−	0.139624i	0.997560	−	0.0698119i	$-0.0222399\pi$
$600$	10.2790	+	14.8875i	0.0171316	+	0.0248125i
$601$	415.183			0.690821			0.345411	−	0.938452i	$-0.387740\pi$
$601$	415.183			0.690821			0.345411	+	0.938452i	$0.387740\pi$
$602$	65.8489	+	74.3215i	0.109384	+	0.123458i
$603$			822.029i			1.36323i
$604$	427.878	+	51.9157i	0.708407	+	0.0859531i
$605$	−620.174			−1.02508
$606$	−68.5718	+	60.7547i	−0.113155	+	0.100255i
$607$		−	137.485i		−	0.226500i	−0.993567	−	0.113250i	$-0.963874\pi$
$607$		−	137.485i		−	0.226500i	0.993567	−	0.113250i	$-0.0361260\pi$
$608$	123.493	−	64.8489i	0.203114	−	0.106659i
$609$	104.568			0.171704
$610$	−14.9559	−	16.8803i	−0.0245179	−	0.0276726i
$611$			62.1834i			0.101773i
$612$	30.7645	−	253.555i	0.0502688	−	0.414305i
$613$	−204.676			−0.333892			−0.166946	−	0.985966i	$-0.553391\pi$
$613$	−204.676			−0.333892			−0.166946	+	0.985966i	$0.553391\pi$
$614$	691.107	−	612.322i	1.12558	−	0.997267i
$615$			19.0301i			0.0309432i
$616$	706.379	−	487.715i	1.14672	−	0.791746i
$617$	−113.317			−0.183657			−0.0918287	−	0.995775i	$-0.529271\pi$
$617$	−113.317			−0.183657			−0.0918287	+	0.995775i	$0.529271\pi$
$618$	48.7754	+	55.0512i	0.0789246	+	0.0890796i
$619$			203.382i			0.328565i	0.986413	+	0.164282i	$0.0525308\pi$
$619$			203.382i			0.328565i	−0.986413	+	0.164282i	$0.947469\pi$
$620$	−420.925	−	51.0720i	−0.678911	−	0.0823742i
$621$	−12.4984			−0.0201262
$622$	361.488	−	320.279i	0.581171	−	0.514918i
$623$			570.090i			0.915073i
$624$	−5.06803	+	20.5774i	−0.00812184	+	0.0329765i
$625$	25.0000			0.0400000
$626$	513.733	+	579.833i	0.820660	+	0.926252i
$627$			39.3477i			0.0627554i
$628$	−4.31858	+	35.5928i	−0.00687672	+	0.0566765i
$629$	−386.099			−0.613830
$630$	−158.277	+	140.233i	−0.251233	+	0.222593i
$631$			191.883i			0.304093i	0.988373	+	0.152046i	$0.0485863\pi$
$631$			191.883i			0.304093i	−0.988373	+	0.152046i	$0.951414\pi$
$632$	358.375	+	519.050i	0.567049	+	0.821281i
$633$	86.4294			0.136539
$634$	−95.1878	−	107.435i	−0.150138	−	0.169456i
$635$		−	252.799i		−	0.398108i
$636$	−154.395	−	18.7331i	−0.242759	−	0.0294546i
$637$	−58.8576			−0.0923982
$638$	1284.90	−	1138.42i	2.01395	−	1.78436i
$639$			522.288i			0.817352i
$640$	−267.586	+	101.576i	−0.418103	+	0.158713i
$641$	−448.831			−0.700205			−0.350102	−	0.936711i	$-0.613853\pi$
$641$	−448.831			−0.700205			−0.350102	+	0.936711i	$0.613853\pi$
$642$	−90.8538	−	102.544i	−0.141517	−	0.159725i
$643$		−	514.967i		−	0.800882i	−0.916323	−	0.400441i	$-0.868857\pi$
$643$		−	514.967i		−	0.800882i	0.916323	−	0.400441i	$-0.131143\pi$
$644$	−4.02219	+	33.1501i	−0.00624564	+	0.0514752i
$645$	9.33974			0.0144802
$646$	47.3713	−	41.9710i	0.0733302	−	0.0649707i
$647$		−	770.414i		−	1.19075i	−0.803449	−	0.595374i	$-0.797004\pi$
$647$		−	770.414i		−	1.19075i	0.803449	−	0.595374i	$-0.202996\pi$
$648$	497.160	−	343.262i	0.767223	−	0.529725i
$649$	2185.03			3.36676
$650$	19.4206	+	21.9194i	0.0298779	+	0.0337222i
$651$			115.267i			0.177062i
$652$	227.525	+	27.6062i	0.348964	+	0.0423408i
$653$	−1057.09			−1.61882			−0.809409	−	0.587245i	$-0.800213\pi$
$653$	−1057.09			−1.61882			−0.809409	+	0.587245i	$0.800213\pi$
$654$	15.6624	−	13.8769i	0.0239486	−	0.0212184i
$655$		−	216.916i		−	0.331169i
$656$	−292.333	−	71.9992i	−0.445630	−	0.109755i
$657$	−1106.36			−1.68396
$658$	151.403	+	170.884i	0.230096	+	0.259702i
$659$		−	663.737i		−	1.00719i	−0.863940	−	0.503594i	$-0.832011\pi$
$659$		−	663.737i		−	1.00719i	0.863940	−	0.503594i	$-0.167989\pi$
$660$	9.72505	−	80.1519i	0.0147349	−	0.121442i
$661$	−490.161			−0.741544			−0.370772	−	0.928724i	$-0.620907\pi$
$661$	−490.161			−0.741544			−0.370772	+	0.928724i	$0.620907\pi$
$662$	−876.960	+	776.988i	−1.32471	+	1.17370i
$663$			9.61579i			0.0145035i
$664$	−83.8749	−	121.480i	−0.126318	−	0.182951i
$665$	−52.3992			−0.0787959
$666$	−620.403	−	700.229i	−0.931537	−	1.05139i
$667$			66.7821i			0.100123i
$668$	−323.103	−	39.2030i	−0.483687	−	0.0586872i
$669$	−24.7642			−0.0370167
$670$	312.843	−	277.179i	0.466929	−	0.413700i
$671$			100.650i			0.150001i
$672$	36.1742	+	68.8874i	0.0538306	+	0.102511i
$673$	116.377			0.172922			0.0864611	−	0.996255i	$-0.472444\pi$
$673$	116.377			0.172922			0.0864611	+	0.996255i	$0.472444\pi$
$674$	54.7406	+	61.7838i	0.0812174	+	0.0916674i
$675$			40.2428i			0.0596190i
$676$	77.2919	−	637.023i	0.114337	−	0.942342i
$677$	48.8264			0.0721216			0.0360608	−	0.999350i	$-0.488519\pi$
$677$	48.8264			0.0721216			0.0360608	+	0.999350i	$0.488519\pi$
$678$	94.2849	−	83.5366i	0.139063	−	0.123210i
$679$		−	215.804i		−	0.317826i
$680$	−106.870	+	73.7876i	−0.157161	+	0.108511i
$681$	46.9218			0.0689013
$682$	1254.91	+	1416.37i	1.84004	+	2.07679i
$683$			267.660i			0.391889i	0.980615	+	0.195945i	$0.0627773\pi$
$683$			267.660i			0.391889i	−0.980615	+	0.195945i	$0.937223\pi$
$684$	152.237	+	18.4714i	0.222569	+	0.0270049i
$685$	390.272			0.569740
$686$	−556.084	+	492.691i	−0.810618	+	0.718209i
$687$			118.223i			0.172086i
$688$	−35.3363	+	143.474i	−0.0513610	+	0.208537i
$689$	−251.758			−0.365397
$690$	2.08293	+	2.35093i	0.00301874	+	0.00340715i
$691$			1147.02i			1.65994i	0.557811	+	0.829968i	$0.311641\pi$
$691$			1147.02i			1.65994i	−0.557811	+	0.829968i	$0.688359\pi$
$692$	160.076	−	1319.31i	0.231324	−	1.90652i
$693$	943.742			1.36182
$694$	−727.125	+	644.233i	−1.04773	+	0.928290i
$695$			539.516i			0.776282i
$696$	88.4109	+	128.049i	0.127027	+	0.183979i
$697$	−136.607			−0.195993
$698$	−82.7462	−	93.3929i	−0.118548	−	0.133801i
$699$		−	112.637i		−	0.161140i
$700$	106.738	+	12.9508i	0.152483	+	0.0185012i
$701$	754.074			1.07571			0.537856	−	0.843037i	$-0.319235\pi$
$701$	754.074			1.07571			0.537856	+	0.843037i	$0.319235\pi$
$702$	−35.2840	+	31.2616i	−0.0502621	+	0.0445322i
$703$		−	231.818i		−	0.329756i
$704$	1194.47	+	452.643i	1.69669	+	0.642958i
$705$	21.4744			0.0304601
$706$	658.627	+	743.371i	0.932900	+	1.05293i
$707$			544.488i			0.770138i
$708$	−23.8561	+	196.617i	−0.0336950	+	0.277707i
$709$	211.999			0.299011			0.149505	−	0.988761i	$-0.452232\pi$
$709$	211.999			0.299011			0.149505	+	0.988761i	$0.452232\pi$
$710$	198.769	−	176.109i	0.279956	−	0.248041i
$711$			693.465i			0.975338i
$712$	−698.108	+	482.005i	−0.980488	+	0.676973i
$713$	−73.6152			−0.103247
$714$	23.4124	+	26.4248i	0.0327905	+	0.0370095i
$715$		−	130.697i		−	0.182793i
$716$	10.7430	+	1.30348i	0.0150042	+	0.00182051i
$717$	29.1602			0.0406698
$718$	−192.932	+	170.938i	−0.268707	+	0.238075i
$719$		−	256.689i		−	0.357008i	−0.983939	−	0.178504i	$-0.942874\pi$
$719$		−	256.689i		−	0.357008i	0.983939	−	0.178504i	$-0.0571258\pi$
$720$	−305.545	−	75.2530i	−0.424367	−	0.104518i
$721$	437.129			0.606281
$722$	25.1999	+	28.4423i	0.0349029	+	0.0393938i
$723$			27.0825i			0.0374585i
$724$	116.363	−	959.040i	0.160722	−	1.32464i
$725$	215.028			0.296591
$726$	−187.780	+	166.373i	−0.258650	+	0.229164i
$727$		−	1231.59i		−	1.69407i	−0.531537	−	0.847035i	$-0.678385\pi$
$727$		−	1231.59i		−	1.69407i	0.531537	−	0.847035i	$-0.321615\pi$
$728$	71.5619	+	103.646i	0.0982993	+	0.142371i
$729$	631.459			0.866198
$730$	373.052	+	421.052i	0.511030	+	0.576783i
$731$			67.0452i			0.0917171i
$732$	−9.05690	−	1.09890i	−0.0123728	−	0.00150123i
$733$	467.514			0.637808			0.318904	−	0.947787i	$-0.396685\pi$
$733$	467.514			0.637808			0.318904	+	0.947787i	$0.396685\pi$
$734$	664.353	−	588.618i	0.905113	−	0.801931i
$735$			20.3259i			0.0276543i
$736$	−43.9948	+	23.1026i	−0.0597755	+	0.0313894i
$737$	−1865.36			−2.53102
$738$	−219.508	−	247.751i	−0.297436	−	0.335706i
$739$		−	1085.03i		−	1.46824i	−0.679017	−	0.734122i	$-0.737594\pi$
$739$		−	1085.03i		−	1.46824i	0.679017	−	0.734122i	$-0.262406\pi$
$740$	−57.2956	+	472.218i	−0.0774265	+	0.638133i
$741$	−5.77344			−0.00779141
$742$	−691.847	+	612.978i	−0.932409	+	0.826115i
$743$		−	1081.13i		−	1.45509i	−0.686061	−	0.727544i	$-0.740662\pi$
$743$		−	1081.13i		−	1.45509i	0.686061	−	0.727544i	$-0.259338\pi$
$744$	−141.151	+	97.4571i	−0.189719	+	0.130991i
$745$	−102.756			−0.137928
$746$	−926.376	−	1045.57i	−1.24179	−	1.40157i
$747$		−	162.300i		−	0.217269i
$748$	575.369	+	69.8112i	0.769210	+	0.0933305i
$749$	−814.238			−1.08710
$750$	7.56965	−	6.70672i	0.0100929	−	0.00894229i
$751$		−	355.154i		−	0.472908i	−0.971643	−	0.236454i	$-0.924015\pi$
$751$		−	355.154i		−	0.472908i	0.971643	−	0.236454i	$-0.0759852\pi$
$752$	−81.2471	+	329.882i	−0.108041	+	0.438673i
$753$	41.0579			0.0545257
$754$	167.039	+	188.532i	0.221538	+	0.250042i
$755$		−	240.945i		−	0.319133i
$756$	−20.8471	+	171.818i	−0.0275756	+	0.227272i
$757$	943.171			1.24593			0.622966	−	0.782249i	$-0.285927\pi$
$757$	943.171			1.24593			0.622966	+	0.782249i	$0.285927\pi$
$758$	333.766	−	295.717i	0.440324	−	0.390128i
$759$		−	14.0177i		−	0.0184686i
$760$	−44.3029	−	64.1658i	−0.0582933	−	0.0844287i
$761$	1210.44			1.59059			0.795295	−	0.606222i	$-0.207316\pi$
$761$	1210.44			1.59059			0.795295	+	0.606222i	$0.207316\pi$
$762$	−67.8180	−	76.5439i	−0.0890000	−	0.100451i
$763$		−	124.365i		−	0.162995i
$764$	−57.2732	−	6.94913i	−0.0749650	−	0.00909571i
$765$	−142.781			−0.186642
$766$	−348.814	+	309.049i	−0.455370	+	0.403459i
$767$			320.606i			0.418001i
$768$	−53.7716	+	102.541i	−0.0700151	+	0.133517i
$769$	−770.817			−1.00236			−0.501181	−	0.865342i	$-0.667101\pi$
$769$	−770.817			−1.00236			−0.501181	+	0.865342i	$0.667101\pi$
$770$	−318.219	−	359.163i	−0.413271	−	0.466446i
$771$			79.9366i			0.103679i
$772$	81.7922	−	674.114i	0.105948	−	0.873205i
$773$	114.709			0.148395			0.0741973	−	0.997244i	$-0.476361\pi$
$773$	114.709			0.148395			0.0741973	+	0.997244i	$0.476361\pi$
$774$	−121.593	+	107.732i	−0.157097	+	0.139188i
$775$			237.030i			0.305845i
$776$	264.264	−	182.459i	0.340546	−	0.235128i
$777$	129.314			0.166427
$778$	−807.788	−	911.723i	−1.03829	−	1.17188i
$779$		−	82.0207i		−	0.105290i
$780$	11.7606	+	1.42695i	0.0150777	+	0.00182942i
$781$	−1185.18			−1.51752
$782$	−16.8761	+	14.9523i	−0.0215807	+	0.0191206i
$783$			346.134i			0.442061i
$784$	−312.239	−	76.9018i	−0.398264	−	0.0980890i
$785$	20.0429			0.0255324
$786$	−58.1918	−	65.6791i	−0.0740353	−	0.0835612i
$787$		−	825.982i		−	1.04953i	−0.851246	−	0.524766i	$-0.824153\pi$
$787$		−	825.982i		−	1.04953i	0.851246	−	0.524766i	$-0.175847\pi$
$788$	41.2705	−	340.143i	0.0523737	−	0.431653i
$789$	137.297			0.174013
$790$	263.914	−	233.828i	0.334069	−	0.295985i
$791$		−	748.660i		−	0.946473i
$792$	797.923	+	1155.66i	1.00748	+	1.45917i
$793$	−14.7683			−0.0186234
$794$	907.618	+	1024.40i	1.14310	+	1.29017i
$795$			86.9422i			0.109361i
$796$	764.053	+	92.7047i	0.959865	+	0.116463i
$797$	1008.08			1.26484			0.632421	−	0.774625i	$-0.282061\pi$
$797$	1008.08			1.26484			0.632421	+	0.774625i	$0.282061\pi$
$798$	−15.8658	+	14.0571i	−0.0198819	+	0.0176154i
$799$			154.154i			0.192933i
$800$	74.3868	+	141.657i	0.0929835	+	0.177071i
$801$	−932.692			−1.16441
$802$	204.458	+	230.765i	0.254935	+	0.287737i
$803$		−	2510.57i		−	3.12648i
$804$	20.3659	−	167.852i	0.0253308	−	0.208771i
$805$	18.6674			0.0231893
$806$	−207.822	+	184.131i	−0.257844	+	0.228450i
$807$			61.1336i			0.0757542i
$808$	−666.756	+	460.358i	−0.825193	+	0.569750i
$809$	492.443			0.608705			0.304353	−	0.952559i	$-0.401560\pi$
$809$	492.443			0.608705			0.304353	+	0.952559i	$0.401560\pi$
$810$	−223.968	−	252.785i	−0.276503	−	0.312080i
$811$		−	899.626i		−	1.10928i	−0.832090	−	0.554640i	$-0.812856\pi$
$811$		−	899.626i		−	1.10928i	0.832090	−	0.554640i	$-0.187144\pi$
$812$	918.069	+	111.392i	1.13063	+	0.137182i
$813$	11.7345			0.0144336
$814$	1588.97	−	1407.83i	1.95205	−	1.72952i
$815$		−	128.123i		−	0.157206i
$816$	−12.5637	+	51.0116i	−0.0153967	+	0.0625142i
$817$	−40.2547			−0.0492714
$818$	−230.566	−	260.232i	−0.281866	−	0.318132i
$819$			138.474i			0.169077i
$820$	−20.2720	+	167.078i	−0.0247219	+	0.203753i
$821$	−134.016			−0.163235			−0.0816176	−	0.996664i	$-0.526009\pi$
$821$	−134.016			−0.163235			−0.0816176	+	0.996664i	$0.526009\pi$
$822$	118.169	−	104.698i	0.143758	−	0.127370i
$823$		−	953.605i		−	1.15869i	−0.815081	−	0.579347i	$-0.803308\pi$
$823$		−	953.605i		−	1.15869i	0.815081	−	0.579347i	$-0.196692\pi$
$824$	369.587	+	535.288i	0.448528	+	0.649622i
$825$	−45.1349			−0.0547089
$826$	780.608	+	881.046i	0.945046	+	1.06664i
$827$		−	355.736i		−	0.430152i	−0.976597	−	0.215076i	$-0.931000\pi$
$827$		−	355.736i		−	0.430152i	0.976597	−	0.215076i	$-0.0690000\pi$
$828$	−54.2349	−	6.58047i	−0.0655010	−	0.00794743i
$829$	−783.264			−0.944829			−0.472415	−	0.881376i	$-0.656618\pi$
$829$	−783.264			−0.944829			−0.472415	+	0.881376i	$0.656618\pi$
$830$	−61.7672	+	54.7258i	−0.0744183	+	0.0659347i
$831$		−	168.131i		−	0.202324i
$832$	−66.4157	+	175.263i	−0.0798266	+	0.210653i
$833$	−145.909			−0.175161
$834$	144.735	+	163.358i	0.173543	+	0.195873i
$835$			181.945i			0.217898i
$836$	−41.9155	+	345.458i	−0.0501381	+	0.413228i
$837$	−381.550			−0.455854
$838$	−477.133	+	422.740i	−0.569371	+	0.504463i
$839$			535.378i			0.638115i	0.947735	+	0.319057i	$0.103366\pi$
$839$			535.378i			0.638115i	−0.947735	+	0.319057i	$0.896634\pi$
$840$	35.7931	−	24.7132i	0.0426109	−	0.0294204i
$841$	1008.49			1.19915
$842$	−211.935	−	239.204i	−0.251704	−	0.284090i
$843$			173.599i			0.205931i
$844$	758.819	+	92.0697i	0.899075	+	0.109087i
$845$	−358.718			−0.424519
$846$	−279.573	+	247.702i	−0.330464	+	0.292792i
$847$			1491.05i			1.76039i
$848$	−1335.57	−	328.941i	−1.57497	−	0.387902i
$849$	15.1715			0.0178699
$850$	48.1441	+	54.3386i	0.0566401	+	0.0639278i
$851$			82.5859i			0.0970457i
$852$	12.9398	−	106.647i	0.0151875	−	0.125172i
$853$	225.665			0.264554			0.132277	−	0.991213i	$-0.457771\pi$
$853$	225.665			0.264554			0.132277	+	0.991213i	$0.457771\pi$
$854$	−40.5843	+	35.9577i	−0.0475226	+	0.0421050i
$855$		−	85.7274i		−	0.100266i
$856$	−688.428	−	997.079i	−0.804239	−	1.16481i
$857$	−659.385			−0.769411			−0.384705	−	0.923039i	$-0.625697\pi$
$857$	−659.385			−0.769411			−0.384705	+	0.923039i	$0.625697\pi$
$858$	−35.0619	−	39.5732i	−0.0408647	−	0.0461226i
$859$		−	480.420i		−	0.559278i	−0.960105	−	0.279639i	$-0.909785\pi$
$859$		−	480.420i		−	0.559278i	0.960105	−	0.279639i	$-0.0902148\pi$
$860$	81.9996	+	9.94924i	0.0953484	+	0.0115689i
$861$	45.7530			0.0531393
$862$	526.683	−	466.641i	0.611001	−	0.541347i
$863$			537.592i			0.622934i	0.950257	+	0.311467i	$0.100820\pi$
$863$			537.592i			0.622934i	−0.950257	+	0.311467i	$0.899180\pi$
$864$	−228.026	+	119.741i	−0.263919	+	0.138590i
$865$	−742.927			−0.858875
$866$	80.5574	+	90.9224i	0.0930224	+	0.104991i
$867$		−	106.872i		−	0.123266i
$868$	−122.790	+	1012.01i	−0.141463	+	1.16591i
$869$	−1573.62			−1.81084
$870$	65.1075	−	57.6853i	0.0748362	−	0.0663050i
$871$		−	273.702i		−	0.314239i
$872$	152.292	−	105.149i	0.174647	−	0.120584i
$873$	353.064			0.404426
$874$	−8.97753	−	10.1326i	−0.0102718	−	0.0115934i
$875$		−	60.1061i		−	0.0686926i
$876$	225.910	+	27.4103i	0.257888	+	0.0312903i
$877$	217.717			0.248252			0.124126	−	0.992266i	$-0.460387\pi$
$877$	217.717			0.248252			0.124126	+	0.992266i	$0.460387\pi$
$878$	756.650	−	670.393i	0.861788	−	0.763545i
$879$		−	101.310i		−	0.115256i
$880$	170.765	−	693.345i	0.194051	−	0.787892i
$881$	121.206			0.137577			0.0687886	−	0.997631i	$-0.478087\pi$
$881$	121.206			0.137577			0.0687886	+	0.997631i	$0.478087\pi$
$882$	−234.454	−	264.621i	−0.265821	−	0.300023i
$883$			685.393i			0.776209i	0.921615	+	0.388105i	$0.126870\pi$
$883$			685.393i			0.776209i	−0.921615	+	0.388105i	$0.873130\pi$
$884$	−10.2433	+	84.4233i	−0.0115875	+	0.0955014i
$885$	110.718			0.125105
$886$	44.3569	−	39.3002i	0.0500642	−	0.0443569i
$887$		−	778.930i		−	0.878162i	−0.898447	−	0.439081i	$-0.855304\pi$
$887$		−	778.930i		−	0.878162i	0.898447	−	0.439081i	$-0.144696\pi$
$888$	109.333	+	158.352i	0.123123	+	0.178324i
$889$	−607.790			−0.683678
$890$	314.493	+	354.958i	0.353363	+	0.398829i
$891$			1507.26i			1.69165i
$892$	−217.421	−	26.3803i	−0.243745	−	0.0295743i
$893$	−92.5557			−0.103646
$894$	−31.1131	+	27.5662i	−0.0348021	+	0.0308347i
$895$		−	6.04959i		−	0.00675932i
$896$	244.214	+	643.342i	0.272560	+	0.718015i
$897$	2.05680			0.00229298
$898$	−37.4559	−	42.2753i	−0.0417104	−	0.0470771i
$899$			2038.73i			2.26777i
$900$	−21.1881	+	174.628i	−0.0235424	+	0.194031i
$901$	−624.113			−0.692690
$902$	562.199	−	498.109i	0.623281	−	0.552227i
$903$		−	22.4550i		−	0.0248671i
$904$	916.776	−	632.983i	1.01413	−	0.700203i
$905$	−540.052			−0.596742
$906$	−64.6381	−	72.9548i	−0.0713444	−	0.0805241i
$907$			232.414i			0.256245i	0.991758	+	0.128122i	$0.0408950\pi$
$907$			232.414i			0.256245i	−0.991758	+	0.128122i	$0.959105\pi$
$908$	411.956	+	49.9838i	0.453696	+	0.0550483i
$909$	−890.805			−0.979983
$910$	52.6996	−	46.6919i	0.0579116	−	0.0513098i
$911$		−	241.478i		−	0.265069i	−0.991178	−	0.132535i	$-0.957688\pi$
$911$		−	241.478i		−	0.265069i	0.991178	−	0.132535i	$-0.0423116\pi$
$912$	−30.6280	−	7.54341i	−0.0335833	−	0.00827128i
$913$	368.294			0.403388
$914$	1073.60	+	1211.73i	1.17461	+	1.32575i
$915$			5.10009i			0.00557387i
$916$	−125.938	+	1037.96i	−0.137487	+	1.13314i
$917$	−521.519			−0.568723
$918$	−87.4696	+	77.4981i	−0.0952828	+	0.0844206i
$919$		−	59.0495i		−	0.0642540i	−0.999484	−	0.0321270i	$-0.989772\pi$
$919$		−	59.0495i		−	0.0642540i	0.999484	−	0.0321270i	$-0.0102281\pi$
$920$	15.7830	+	22.8592i	0.0171555	+	0.0248470i
$921$	−208.806			−0.226717
$922$	−1212.36	−	1368.35i	−1.31492	−	1.48411i
$923$		−	173.900i		−	0.188408i
$924$	−192.704	−	23.3814i	−0.208555	−	0.0253045i
$925$	265.914			0.287475
$926$	237.231	−	210.187i	0.256188	−	0.226983i
$927$			715.161i			0.771479i
$928$	639.811	+	1218.41i	0.689451	+	1.31294i
$929$	−375.029			−0.403691			−0.201845	−	0.979417i	$-0.564694\pi$
$929$	−375.029			−0.403691			−0.201845	+	0.979417i	$0.564694\pi$
$930$	63.5877	+	71.7693i	0.0683739	+	0.0771713i
$931$		−	87.6056i		−	0.0940984i
$932$	119.988	−	988.913i	0.128742	−	1.06107i
$933$	−109.218			−0.117061
$934$	−996.181	+	882.617i	−1.06657	+	0.944987i
$935$		−	324.000i		−	0.346524i
$936$	−169.569	+	117.078i	−0.181164	+	0.125084i
$937$	−495.198			−0.528493			−0.264247	−	0.964455i	$-0.585123\pi$
$937$	−495.198			−0.528493			−0.264247	+	0.964455i	$0.585123\pi$
$938$	−666.405	−	752.149i	−0.710453	−	0.801865i
$939$		−	175.187i		−	0.186568i
$940$	188.538	+	22.8758i	0.200572	+	0.0243360i
$941$	1716.88			1.82452			0.912262	−	0.409608i	$-0.134334\pi$
$941$	1716.88			1.82452			0.912262	+	0.409608i	$0.134334\pi$
$942$	6.06871	−	5.37689i	0.00644237	−	0.00570795i
$943$			29.2200i			0.0309863i
$944$	−418.896	+	1700.81i	−0.443745	+	1.80171i
$945$	96.7535			0.102385
$946$	−244.466	−	275.920i	−0.258420	−	0.291671i
$947$			1086.35i			1.14715i	0.819155	+	0.573573i	$0.194443\pi$
$947$			1086.35i			1.14715i	−0.819155	+	0.573573i	$0.805557\pi$
$948$	17.1807	−	141.600i	0.0181231	−	0.149367i
$949$	368.372			0.388169
$950$	−32.6256	+	28.9063i	−0.0343427	+	0.0304277i
$951$			32.4598i			0.0341322i
$952$	177.403	+	256.941i	0.186348	+	0.269896i
$953$	−1472.12			−1.54473			−0.772363	−	0.635181i	$-0.780925\pi$
$953$	−1472.12			−1.54473			−0.772363	+	0.635181i	$0.780925\pi$
$954$	−1002.86	−	1131.89i	−1.05121	−	1.18647i
$955$			32.2515i			0.0337712i
$956$	256.016	+	31.0632i	0.267800	+	0.0324929i
$957$	−388.211			−0.405654
$958$	1015.64	−	899.854i	1.06016	−	0.939305i
$959$		−	938.309i		−	0.978424i
$960$	60.5253	+	22.9360i	0.0630472	+	0.0238917i
$961$	−1286.33			−1.33853
$962$	206.569	+	233.147i	0.214728	+	0.242357i
$963$		−	1332.13i		−	1.38331i
$964$	−28.8499	+	237.775i	−0.0299273	+	0.246654i
$965$	−379.605			−0.393373
$966$	5.65221	−	5.00787i	0.00585115	−	0.00518413i
$967$		−	1208.67i		−	1.24992i	−0.780659	−	0.624958i	$-0.785116\pi$
$967$		−	1208.67i		−	1.24992i	0.780659	−	0.624958i	$-0.214884\pi$
$968$	−1825.87	+	1260.66i	−1.88623	+	1.30234i
$969$	−14.3124			−0.0147703
$970$	−119.049	−	134.367i	−0.122731	−	0.138522i
$971$			347.585i			0.357966i	0.983852	+	0.178983i	$0.0572808\pi$
$971$			347.585i			0.357966i	−0.983852	+	0.178983i	$0.942719\pi$
$972$	−423.267	−	51.3562i	−0.435460	−	0.0528356i
$973$	1297.13			1.33312
$974$	−184.345	+	163.330i	−0.189266	+	0.167690i
$975$		−	6.62258i		−	0.00679239i
$976$	−78.3457	−	19.2959i	−0.0802723	−	0.0197704i
$977$	−451.588			−0.462219			−0.231109	−	0.972928i	$-0.574236\pi$
$977$	−451.588			−0.462219			−0.231109	+	0.972928i	$0.574236\pi$
$978$	−34.3714	−	38.7938i	−0.0351446	−	0.0396665i
$979$		−	2116.47i		−	2.16187i
$980$	−21.6523	+	178.454i	−0.0220942	+	0.182096i
$981$	203.467			0.207408
$982$	−1218.01	+	1079.16i	−1.24034	+	1.09894i
$983$			1307.42i			1.33003i	0.746828	+	0.665017i	$0.231576\pi$
$983$			1307.42i			1.33003i	−0.746828	+	0.665017i	$0.768424\pi$
$984$	38.6836	+	56.0271i	0.0393126	+	0.0569381i
$985$	−191.540			−0.194457
$986$	414.094	+	467.374i	0.419973	+	0.474010i
$987$		−	51.6296i		−	0.0523097i
$988$	−50.6887	−	6.15021i	−0.0513044	−	0.00622491i
$989$	14.3408			0.0145003
$990$	587.606	−	520.620i	0.593541	−	0.525878i
$991$			501.450i			0.506004i	0.967466	+	0.253002i	$0.0814179\pi$
$991$			501.450i			0.506004i	−0.967466	+	0.253002i	$0.918582\pi$
$992$	−1343.07	+	705.276i	−1.35391	+	0.710964i
$993$	264.959			0.266827
$994$	−423.410	−	477.889i	−0.425966	−	0.480773i
$995$		−	430.251i		−	0.432413i
$996$	−4.02102	+	33.1404i	−0.00403717	+	0.0332735i
$997$	−1058.02			−1.06120			−0.530601	−	0.847622i	$-0.678034\pi$
$997$	−1058.02			−1.06120			−0.530601	+	0.847622i	$0.678034\pi$
$998$	−778.068	+	689.369i	−0.779627	+	0.690750i
$999$			428.045i			0.428474i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.3.b.a.191.17	✓	72
4.3	odd	2	inner	380.3.b.a.191.18	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.3.b.a.191.17	✓	72	1.1	even	1	trivial
380.3.b.a.191.18	yes	72	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	380.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32631 - 1.49696i) q^{2} +0.452282i q^{3} +(-0.481798 + 3.97088i) q^{4} +2.23607 q^{5} +(0.677050 - 0.599867i) q^{6} -5.37605i q^{7} +(6.58327 - 4.54539i) q^{8} +8.79544 q^{9} +O(q^{10})\)	\(q+(-1.32631 - 1.49696i) q^{2} +0.452282i q^{3} +(-0.481798 + 3.97088i) q^{4} +2.23607 q^{5} +(0.677050 - 0.599867i) q^{6} -5.37605i q^{7} +(6.58327 - 4.54539i) q^{8} +8.79544 q^{9} +(-2.96572 - 3.34731i) q^{10} +19.9587i q^{11} +(-1.79596 - 0.217909i) q^{12} -2.92852 q^{13} +(-8.04775 + 7.13031i) q^{14} +1.01133i q^{15} +(-15.5357 - 3.82632i) q^{16} -7.25985 q^{17} +(-11.6655 - 13.1665i) q^{18} -4.35890i q^{19} +(-1.07733 + 8.87915i) q^{20} +2.43149 q^{21} +(29.8775 - 26.4715i) q^{22} +1.55287i q^{23} +(2.05580 + 2.97750i) q^{24} +5.00000 q^{25} +(3.88413 + 4.38388i) q^{26} +8.04856i q^{27} +(21.3476 + 2.59017i) q^{28} +43.0057 q^{29} +(1.51393 - 1.34134i) q^{30} +47.4060i q^{31} +(14.8774 + 28.3313i) q^{32} -9.02697 q^{33} +(9.62882 + 10.8677i) q^{34} -12.0212i q^{35} +(-4.23763 + 34.9256i) q^{36} +53.1828 q^{37} +(-6.52511 + 5.78126i) q^{38} -1.32452i q^{39} +(14.7206 - 10.1638i) q^{40} +18.8168 q^{41} +(-3.22491 - 3.63985i) q^{42} -9.23507i q^{43} +(-79.2536 - 9.61607i) q^{44} +19.6672 q^{45} +(2.32459 - 2.05959i) q^{46} -21.2337i q^{47} +(1.73058 - 7.02654i) q^{48} +20.0981 q^{49} +(-6.63156 - 7.48482i) q^{50} -3.28350i q^{51} +(1.41095 - 11.6288i) q^{52} +85.9678 q^{53} +(12.0484 - 10.6749i) q^{54} +44.6290i q^{55} +(-24.4362 - 35.3920i) q^{56} +1.97145 q^{57} +(-57.0389 - 64.3779i) q^{58} -109.477i q^{59} +(-4.01588 - 0.487259i) q^{60} +5.04294 q^{61} +(70.9650 - 62.8751i) q^{62} -47.2847i q^{63} +(22.6789 - 59.8470i) q^{64} -6.54837 q^{65} +(11.9726 + 13.5130i) q^{66} +93.4609i q^{67} +(3.49778 - 28.8280i) q^{68} -0.702335 q^{69} +(-17.9953 + 15.9439i) q^{70} +59.3817i q^{71} +(57.9028 - 39.9787i) q^{72} -125.788 q^{73} +(-70.5369 - 79.6127i) q^{74} +2.26141i q^{75} +(17.3087 + 2.10011i) q^{76} +107.299 q^{77} +(-1.98275 + 1.75672i) q^{78} +78.8437i q^{79} +(-34.7390 - 8.55592i) q^{80} +75.5187 q^{81} +(-24.9570 - 28.1681i) q^{82} -18.4528i q^{83} +(-1.17149 + 9.65516i) q^{84} -16.2335 q^{85} +(-13.8246 + 12.2486i) q^{86} +19.4507i q^{87} +(90.7200 + 131.394i) q^{88} -106.043 q^{89} +(-26.0848 - 29.4411i) q^{90} +15.7439i q^{91} +(-6.16625 - 0.748168i) q^{92} -21.4409 q^{93} +(-31.7861 + 28.1625i) q^{94} -9.74679i q^{95} +(-12.8138 + 6.72877i) q^{96} +40.1417 q^{97} +(-26.6563 - 30.0861i) q^{98} +175.546i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9}+O(q^{10}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9	\( 72 q + 4 q^{2} + 12 q^{4} + 12 q^{6} + 16 q^{8} - 216 q^{9} - 80 q^{12} - 80 q^{14} + 4 q^{16} - 44 q^{18} - 40 q^{20} + 16 q^{21} + 160 q^{22} + 204 q^{24} + 360 q^{25} + 28 q^{26} + 20 q^{28} + 16 q^{29} + 40 q^{30} - 136 q^{32} - 96 q^{34} + 8 q^{36} - 192 q^{37} - 4 q^{42} - 40 q^{44} + 80 q^{45} - 232 q^{46} - 156 q^{48} - 504 q^{49} + 20 q^{50} + 228 q^{52} + 320 q^{53} + 92 q^{54} + 8 q^{56} + 380 q^{58} - 140 q^{60} - 168 q^{62} - 60 q^{64} - 40 q^{66} + 396 q^{68} - 48 q^{69} - 120 q^{70} - 284 q^{72} + 192 q^{74} - 640 q^{77} - 520 q^{78} + 120 q^{80} + 568 q^{81} - 240 q^{82} + 112 q^{84} + 688 q^{86} - 484 q^{88} + 240 q^{89} + 12 q^{92} + 512 q^{93} + 432 q^{94} + 300 q^{96} - 44 q^{98}+O(q^{100}) \) 72 * q + 4 * q^2 + 12 * q^4 + 12 * q^6 + 16 * q^8 - 216 * q^9 - 80 * q^12 - 80 * q^14 + 4 * q^16 - 44 * q^18 - 40 * q^20 + 16 * q^21 + 160 * q^22 + 204 * q^24 + 360 * q^25 + 28 * q^26 + 20 * q^28 + 16 * q^29 + 40 * q^30 - 136 * q^32 - 96 * q^34 + 8 * q^36 - 192 * q^37 - 4 * q^42 - 40 * q^44 + 80 * q^45 - 232 * q^46 - 156 * q^48 - 504 * q^49 + 20 * q^50 + 228 * q^52 + 320 * q^53 + 92 * q^54 + 8 * q^56 + 380 * q^58 - 140 * q^60 - 168 * q^62 - 60 * q^64 - 40 * q^66 + 396 * q^68 - 48 * q^69 - 120 * q^70 - 284 * q^72 + 192 * q^74 - 640 * q^77 - 520 * q^78 + 120 * q^80 + 568 * q^81 - 240 * q^82 + 112 * q^84 + 688 * q^86 - 484 * q^88 + 240 * q^89 + 12 * q^92 + 512 * q^93 + 432 * q^94 + 300 * q^96 - 44 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more