LMFDB - Embedded newform 380.2.f.a.151.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(151,380)]

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, 1]))

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

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

chi := DirichletCharacter("380.151");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.f (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:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} + x^{16} - 9x^{14} + 20x^{12} - 24x^{10} + 80x^{8} - 144x^{6} + 64x^{4} - 256x^{2} + 1024 $ x^20 - x^18 + x^16 - 9x^14 + 20x^12 - 24x^10 + 80x^8 - 144x^6 + 64x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			151.13
Root			$-0.611950 - 1.27496i$ of defining polynomial
Character	$\chi$	$=$	380.151
Dual form			380.2.f.a.151.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.611950 - 1.27496i) q^{2} -3.21061 q^{3} +(-1.25103 - 1.56042i) q^{4} -1.00000 q^{5} +(-1.96474 + 4.09340i) q^{6} +3.02772i q^{7} +(-2.75504 + 0.640115i) q^{8} +7.30804 q^{9} +O(q^{10})$	\(q+(0.611950 - 1.27496i) q^{2} -3.21061 q^{3} +(-1.25103 - 1.56042i) q^{4} -1.00000 q^{5} +(-1.96474 + 4.09340i) q^{6} +3.02772i q^{7} +(-2.75504 + 0.640115i) q^{8} +7.30804 q^{9} +(-0.611950 + 1.27496i) q^{10} -0.488592i q^{11} +(4.01659 + 5.00991i) q^{12} -0.943033i q^{13} +(3.86021 + 1.85281i) q^{14} +3.21061 q^{15} +(-0.869829 + 3.90428i) q^{16} +3.16706 q^{17} +(4.47216 - 9.31745i) q^{18} +(2.58768 - 3.50769i) q^{19} +(1.25103 + 1.56042i) q^{20} -9.72083i q^{21} +(-0.622934 - 0.298994i) q^{22} +7.08696i q^{23} +(8.84538 - 2.05516i) q^{24} +1.00000 q^{25} +(-1.20233 - 0.577089i) q^{26} -13.8315 q^{27} +(4.72451 - 3.78777i) q^{28} +8.80545i q^{29} +(1.96474 - 4.09340i) q^{30} +3.66325 q^{31} +(4.44550 + 3.49822i) q^{32} +1.56868i q^{33} +(1.93809 - 4.03787i) q^{34} -3.02772i q^{35} +(-9.14261 - 11.4036i) q^{36} +1.11751i q^{37} +(-2.88863 - 5.44572i) q^{38} +3.02772i q^{39} +(2.75504 - 0.640115i) q^{40} +1.56868i q^{41} +(-12.3936 - 5.94866i) q^{42} +3.58788i q^{43} +(-0.762409 + 0.611245i) q^{44} -7.30804 q^{45} +(9.03557 + 4.33687i) q^{46} +0.471362i q^{47} +(2.79269 - 12.5351i) q^{48} -2.16706 q^{49} +(0.611950 - 1.27496i) q^{50} -10.1682 q^{51} +(-1.47153 + 1.17977i) q^{52} +12.4070i q^{53} +(-8.46417 + 17.6345i) q^{54} +0.488592i q^{55} +(-1.93809 - 8.34148i) q^{56} +(-8.30804 + 11.2618i) q^{57} +(11.2266 + 5.38850i) q^{58} +8.65611 q^{59} +(-4.01659 - 5.00991i) q^{60} -8.62030 q^{61} +(2.24173 - 4.67049i) q^{62} +22.1267i q^{63} +(7.18051 - 3.52709i) q^{64} +0.943033i q^{65} +(2.00000 + 0.959954i) q^{66} +6.59410 q^{67} +(-3.96210 - 4.94195i) q^{68} -22.7535i q^{69} +(-3.86021 - 1.85281i) q^{70} -13.9287 q^{71} +(-20.1340 + 4.67799i) q^{72} -11.6960 q^{73} +(1.42477 + 0.683858i) q^{74} -3.21061 q^{75} +(-8.71075 + 0.350370i) q^{76} +1.47932 q^{77} +(3.86021 + 1.85281i) q^{78} +10.5317 q^{79} +(0.869829 - 3.90428i) q^{80} +22.4834 q^{81} +(2.00000 + 0.959954i) q^{82} -18.0674i q^{83} +(-15.1686 + 12.1611i) q^{84} -3.16706 q^{85} +(4.57439 + 2.19560i) q^{86} -28.2709i q^{87} +(0.312755 + 1.34609i) q^{88} +9.83998i q^{89} +(-4.47216 + 9.31745i) q^{90} +2.85524 q^{91} +(11.0586 - 8.86602i) q^{92} -11.7613 q^{93} +(0.600967 + 0.288450i) q^{94} +(-2.58768 + 3.50769i) q^{95} +(-14.2728 - 11.2314i) q^{96} -1.71549i q^{97} +(-1.32614 + 2.76291i) q^{98} -3.57065i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9}+O(q^{10}) $ 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9	$ 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9} - 2 q^{16} + 20 q^{17} - 2 q^{20} + 26 q^{24} + 20 q^{25} - 14 q^{26} - 14 q^{28} + 6 q^{30} - 4 q^{36} + 10 q^{38} - 42 q^{42} + 8 q^{44} - 16 q^{45} - 30 q^{54} - 36 q^{57} + 62 q^{58} - 24 q^{61} - 40 q^{62} + 50 q^{64} + 40 q^{66} + 6 q^{68} - 36 q^{73} - 36 q^{74} - 28 q^{76} - 32 q^{77} + 2 q^{80} + 60 q^{81} + 40 q^{82} - 20 q^{85} + 26 q^{92} - 122 q^{96}+O(q^{100}) $ 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9 - 2 * q^16 + 20 * q^17 - 2 * q^20 + 26 * q^24 + 20 * q^25 - 14 * q^26 - 14 * q^28 + 6 * q^30 - 4 * q^36 + 10 * q^38 - 42 * q^42 + 8 * q^44 - 16 * q^45 - 30 * q^54 - 36 * q^57 + 62 * q^58 - 24 * q^61 - 40 * q^62 + 50 * q^64 + 40 * q^66 + 6 * q^68 - 36 * q^73 - 36 * q^74 - 28 * q^76 - 32 * q^77 + 2 * q^80 + 60 * q^81 + 40 * q^82 - 20 * q^85 + 26 * q^92 - 122 * q^96

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 $

$2$	0.611950	−	1.27496i	0.432714	−	0.901531i
$2$	0.611950	−	1.27496i	0.432714	−	0.901531i
$3$	−3.21061			−1.85365			−0.926825	−	0.375495i	$-0.877473\pi$
$3$	−3.21061			−1.85365			−0.926825	+	0.375495i	$0.877473\pi$
$4$	−1.25103	−	1.56042i	−0.625517	−	0.780211i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.96474	+	4.09340i	−0.802100	+	1.67112i
$7$			3.02772i			1.14437i	0.820125	+	0.572185i	$0.193904\pi$
$7$			3.02772i			1.14437i	−0.820125	+	0.572185i	$0.806096\pi$
$8$	−2.75504	+	0.640115i	−0.974054	+	0.226315i
$9$	7.30804			2.43601
$10$	−0.611950	+	1.27496i	−0.193516	+	0.403177i
$11$		−	0.488592i		−	0.147316i	−0.997284	−	0.0736580i	$-0.976533\pi$
$11$		−	0.488592i		−	0.147316i	0.997284	−	0.0736580i	$-0.0234673\pi$
$12$	4.01659	+	5.00991i	1.15949	+	1.44624i
$13$		−	0.943033i		−	0.261550i	−0.991412	−	0.130775i	$-0.958253\pi$
$13$		−	0.943033i		−	0.261550i	0.991412	−	0.130775i	$-0.0417466\pi$
$14$	3.86021	+	1.85281i	1.03168	+	0.495185i
$15$	3.21061			0.828977
$16$	−0.869829	+	3.90428i	−0.217457	+	0.976070i
$17$	3.16706			0.768126			0.384063	−	0.923307i	$-0.374525\pi$
$17$	3.16706			0.768126			0.384063	+	0.923307i	$0.374525\pi$
$18$	4.47216	−	9.31745i	1.05410	−	2.19614i
$19$	2.58768	−	3.50769i	0.593655	−	0.804720i
$19$	2.58768	−	3.50769i	0.593655	−	0.804720i
$20$	1.25103	+	1.56042i	0.279740	+	0.348921i
$21$		−	9.72083i		−	2.12126i
$22$	−0.622934	−	0.298994i	−0.132810	−	0.0637457i
$23$			7.08696i			1.47773i	0.673852	+	0.738866i	$0.264639\pi$
$23$			7.08696i			1.47773i	−0.673852	+	0.738866i	$0.735361\pi$
$24$	8.84538	−	2.05516i	1.80555	−	0.419508i
$25$	1.00000			0.200000
$26$	−1.20233	−	0.577089i	−0.235796	−	0.113177i
$27$	−13.8315			−2.66187
$28$	4.72451	−	3.78777i	0.892849	−	0.715822i
$29$			8.80545i			1.63513i	0.575835	+	0.817566i	$0.304677\pi$
$29$			8.80545i			1.63513i	−0.575835	+	0.817566i	$0.695323\pi$
$30$	1.96474	−	4.09340i	0.358710	−	0.747349i
$31$	3.66325			0.657939			0.328969	−	0.944341i	$-0.393299\pi$
$31$	3.66325			0.657939			0.328969	+	0.944341i	$0.393299\pi$
$32$	4.44550	+	3.49822i	0.785861	+	0.618404i
$33$			1.56868i			0.273072i
$34$	1.93809	−	4.03787i	0.332379	−	0.692489i
$35$		−	3.02772i		−	0.511777i
$36$	−9.14261	−	11.4036i	−1.52377	−	1.90060i
$37$			1.11751i			0.183717i	0.995772	+	0.0918584i	$0.0292807\pi$
$37$			1.11751i			0.183717i	−0.995772	+	0.0918584i	$0.970719\pi$
$38$	−2.88863	−	5.44572i	−0.468597	−	0.883412i
$39$			3.02772i			0.484823i
$40$	2.75504	−	0.640115i	0.435610	−	0.101211i
$41$			1.56868i			0.244987i	0.992469	+	0.122493i	$0.0390890\pi$
$41$			1.56868i			0.244987i	−0.992469	+	0.122493i	$0.960911\pi$
$42$	−12.3936	−	5.94866i	−1.91238	−	0.917899i
$43$			3.58788i			0.547147i	0.961851	+	0.273573i	$0.0882056\pi$
$43$			3.58788i			0.547147i	−0.961851	+	0.273573i	$0.911794\pi$
$44$	−0.762409	+	0.611245i	−0.114937	+	0.0921486i
$45$	−7.30804			−1.08942
$46$	9.03557	+	4.33687i	1.33222	+	0.639436i
$47$			0.471362i			0.0687552i	0.999409	+	0.0343776i	$0.0109449\pi$
$47$			0.471362i			0.0687552i	−0.999409	+	0.0343776i	$0.989055\pi$
$48$	2.79269	−	12.5351i	0.403090	−	1.80929i
$49$	−2.16706			−0.309581
$50$	0.611950	−	1.27496i	0.0865428	−	0.180306i
$51$	−10.1682			−1.42384
$52$	−1.47153	+	1.17977i	−0.204064	+	0.163604i
$53$			12.4070i			1.70423i	0.523351	+	0.852117i	$0.324682\pi$
$53$			12.4070i			1.70423i	−0.523351	+	0.852117i	$0.675318\pi$
$54$	−8.46417	+	17.6345i	−1.15183	+	2.39976i
$55$			0.488592i			0.0658817i
$56$	−1.93809	−	8.34148i	−0.258988	−	1.11468i
$57$	−8.30804	+	11.2618i	−1.10043	+	1.49167i
$58$	11.2266	+	5.38850i	1.47412	+	0.707545i
$59$	8.65611			1.12693			0.563465	−	0.826140i	$-0.309468\pi$
$59$	8.65611			1.12693			0.563465	+	0.826140i	$0.309468\pi$
$60$	−4.01659	−	5.00991i	−0.518539	−	0.646777i
$61$	−8.62030			−1.10372			−0.551858	−	0.833938i	$-0.686081\pi$
$61$	−8.62030			−1.10372			−0.551858	+	0.833938i	$0.686081\pi$
$62$	2.24173	−	4.67049i	0.284699	−	0.593152i
$63$			22.1267i			2.78770i
$64$	7.18051	−	3.52709i	0.897563	−	0.440886i
$65$			0.943033i			0.116969i
$66$	2.00000	+	0.959954i	0.246183	+	0.118162i
$67$	6.59410			0.805598			0.402799	−	0.915288i	$-0.368037\pi$
$67$	6.59410			0.805598			0.402799	+	0.915288i	$0.368037\pi$
$68$	−3.96210	−	4.94195i	−0.480476	−	0.599300i
$69$		−	22.7535i		−	2.73920i
$70$	−3.86021	−	1.85281i	−0.461383	−	0.221453i
$71$	−13.9287			−1.65304			−0.826518	−	0.562911i	$-0.809682\pi$
$71$	−13.9287			−1.65304			−0.826518	+	0.562911i	$0.809682\pi$
$72$	−20.1340	+	4.67799i	−2.37281	+	0.551306i
$73$	−11.6960			−1.36892			−0.684458	−	0.729053i	$-0.739961\pi$
$73$	−11.6960			−1.36892			−0.684458	+	0.729053i	$0.739961\pi$
$74$	1.42477	+	0.683858i	0.165626	+	0.0794969i
$75$	−3.21061			−0.370730
$76$	−8.71075	+	0.350370i	−0.999192	+	0.0401902i
$77$	1.47932			0.168584
$78$	3.86021	+	1.85281i	0.437083	+	0.209790i
$79$	10.5317			1.18491			0.592456	−	0.805603i	$-0.298159\pi$
$79$	10.5317			1.18491			0.592456	+	0.805603i	$0.298159\pi$
$80$	0.869829	−	3.90428i	0.0972499	−	0.436512i
$81$	22.4834			2.49815
$82$	2.00000	+	0.959954i	0.220863	+	0.106009i
$83$		−	18.0674i		−	1.98316i	−0.129499	−	0.991580i	$-0.541337\pi$
$83$		−	18.0674i		−	1.98316i	0.129499	−	0.991580i	$-0.458663\pi$
$84$	−15.1686	+	12.1611i	−1.65503	+	1.32688i
$85$	−3.16706			−0.343516
$86$	4.57439	+	2.19560i	0.493270	+	0.236758i
$87$		−	28.2709i		−	3.03096i
$88$	0.312755	+	1.34609i	0.0333398	+	0.143494i
$89$			9.83998i			1.04304i	0.853240	+	0.521518i	$0.174634\pi$
$89$			9.83998i			1.04304i	−0.853240	+	0.521518i	$0.825366\pi$
$90$	−4.47216	+	9.31745i	−0.471407	+	0.982145i
$91$	2.85524			0.299310
$92$	11.0586	−	8.86602i	1.15294	−	0.924347i
$93$	−11.7613			−1.21959
$94$	0.600967	+	0.288450i	0.0619850	+	0.0297514i
$95$	−2.58768	+	3.50769i	−0.265490	+	0.359882i
$96$	−14.2728	−	11.2314i	−1.45671	−	1.14630i
$97$		−	1.71549i		−	0.174182i	−0.996200	−	0.0870910i	$-0.972243\pi$
$97$		−	1.71549i		−	0.174182i	0.996200	−	0.0870910i	$-0.0277571\pi$
$98$	−1.32614	+	2.76291i	−0.133960	+	0.279096i
$99$		−	3.57065i		−	0.358864i
$100$	−1.25103	−	1.56042i	−0.125103	−	0.156042i
$101$	9.47511			0.942808			0.471404	−	0.881917i	$-0.343747\pi$
$101$	9.47511			0.942808			0.471404	+	0.881917i	$0.343747\pi$
$102$	−6.22244	+	12.9640i	−0.616114	+	1.28363i
$103$	−5.44549			−0.536560			−0.268280	−	0.963341i	$-0.586455\pi$
$103$	−5.44549			−0.536560			−0.268280	+	0.963341i	$0.586455\pi$
$104$	0.603649	+	2.59810i	0.0591927	+	0.254764i
$105$			9.72083i			0.948656i
$106$	15.8184	+	7.59248i	1.53642	+	0.737446i
$107$	−3.47686			−0.336121			−0.168060	−	0.985777i	$-0.553750\pi$
$107$	−3.47686			−0.336121			−0.168060	+	0.985777i	$0.553750\pi$
$108$	17.3036	+	21.5829i	1.66504	+	2.07682i
$109$		−	12.5538i		−	1.20244i	−0.799084	−	0.601219i	$-0.794682\pi$
$109$		−	12.5538i		−	1.20244i	0.799084	−	0.601219i	$-0.205318\pi$
$110$	0.622934	+	0.298994i	0.0593944	+	0.0285079i
$111$		−	3.58788i		−	0.340546i
$112$	−11.8210	−	2.63360i	−1.11698	−	0.248851i
$113$			10.0974i			0.949886i	0.880016	+	0.474943i	$0.157531\pi$
$113$			10.0974i			0.949886i	−0.880016	+	0.474943i	$0.842469\pi$
$114$	9.27427	+	17.4841i	0.868615	+	1.63754i
$115$		−	7.08696i		−	0.660862i
$116$	13.7402	−	11.0159i	1.27575	−	1.02280i
$117$		−	6.89173i		−	0.637141i
$118$	5.29711	−	11.0362i	0.487638	−	1.01596i
$119$			9.58897i			0.879019i
$120$	−8.84538	+	2.05516i	−0.807469	+	0.187610i
$121$	10.7613			0.978298
$122$	−5.27519	+	10.9905i	−0.477594	+	0.995034i
$123$		−	5.03643i		−	0.454119i
$124$	−4.58285	−	5.71621i	−0.411552	−	0.513331i
$125$	−1.00000			−0.0894427
$126$	28.2106	+	13.5404i	2.51320	+	1.20628i
$127$	4.63898			0.411643			0.205822	−	0.978590i	$-0.434013\pi$
$127$	4.63898			0.411643			0.205822	+	0.978590i	$0.434013\pi$
$128$	−0.102771	−	11.3132i	−0.00908376	−	0.999959i
$129$		−	11.5193i		−	1.01422i
$130$	1.20233	+	0.577089i	0.105451	+	0.0506141i
$131$			21.6381i			1.89053i	0.326306	+	0.945264i	$0.394196\pi$
$131$			21.6381i			1.89053i	−0.326306	+	0.945264i	$0.605804\pi$
$132$	2.44780	−	1.96247i	0.213054	−	0.170811i
$133$	10.6203	+	7.83476i	0.920897	+	0.679360i
$134$	4.03526	−	8.40720i	0.348594	−	0.726272i
$135$	13.8315			1.19042
$136$	−8.72539	+	2.02728i	−0.748196	+	0.173838i
$137$	12.5508			1.07229			0.536145	−	0.844126i	$-0.319880\pi$
$137$	12.5508			1.07229			0.536145	+	0.844126i	$0.319880\pi$
$138$	−29.0097	−	13.9240i	−2.46947	−	1.18529i
$139$			5.97381i			0.506692i	0.967376	+	0.253346i	$0.0815310\pi$
$139$			5.97381i			0.506692i	−0.967376	+	0.253346i	$0.918469\pi$
$140$	−4.72451	+	3.78777i	−0.399294	+	0.320125i
$141$		−	1.51336i		−	0.127448i
$142$	−8.52369	+	17.7585i	−0.715292	+	1.49026i
$143$	−0.460758			−0.0385305
$144$	−6.35675	+	28.5326i	−0.529729	+	2.37772i
$145$		−	8.80545i		−	0.731253i
$146$	−7.15738	+	14.9119i	−0.592349	+	1.23412i
$147$	6.95761			0.573854
$148$	1.74378	−	1.39804i	0.143338	−	0.114918i
$149$	−20.3382			−1.66617			−0.833085	−	0.553146i	$-0.813427\pi$
$149$	−20.3382			−1.66617			−0.833085	+	0.553146i	$0.813427\pi$
$150$	−1.96474	+	4.09340i	−0.160420	+	0.334224i
$151$	1.35251			0.110066			0.0550330	−	0.998485i	$-0.482474\pi$
$151$	1.35251			0.110066			0.0550330	+	0.998485i	$0.482474\pi$
$152$	−4.88384	+	11.3203i	−0.396132	+	0.918194i
$153$	23.1450			1.87117
$154$	0.905268	−	1.88607i	0.0729486	−	0.151984i
$155$	−3.66325			−0.294239
$156$	4.72451	−	3.78777i	0.378264	−	0.303265i
$157$	6.52895			0.521067			0.260534	−	0.965465i	$-0.416102\pi$
$157$	6.52895			0.521067			0.260534	+	0.965465i	$0.416102\pi$
$158$	6.44489	−	13.4275i	0.512728	−	1.06823i
$159$		−	39.8341i		−	3.15905i
$160$	−4.44550	−	3.49822i	−0.351448	−	0.276559i
$161$	−21.4573			−1.69107
$162$	13.7587	−	28.6654i	1.08099	−	2.25216i
$163$			9.64331i			0.755322i	0.925944	+	0.377661i	$0.123272\pi$
$163$			9.64331i			0.755322i	−0.925944	+	0.377661i	$0.876728\pi$
$164$	2.44780	−	1.96247i	0.191141	−	0.153243i
$165$		−	1.56868i		−	0.122122i
$166$	−23.0352	−	11.0564i	−1.78788	−	0.858141i
$167$	−0.429732			−0.0332536			−0.0166268	−	0.999862i	$-0.505293\pi$
$167$	−0.429732			−0.0332536			−0.0166268	+	0.999862i	$0.505293\pi$
$168$	6.22244	+	26.7813i	0.480072	+	2.06622i
$169$	12.1107			0.931591
$170$	−1.93809	+	4.03787i	−0.148644	+	0.309691i
$171$	18.9109	−	25.6344i	1.44615	−	1.96031i
$172$	5.59860	−	4.48856i	0.426890	−	0.342249i
$173$		−	17.1044i		−	1.30042i	−0.759753	−	0.650212i	$-0.774680\pi$
$173$		−	17.1044i		−	1.30042i	0.759753	−	0.650212i	$-0.225320\pi$
$174$	−36.0442	−	17.3004i	−2.73251	−	1.31154i
$175$			3.02772i			0.228874i
$176$	1.90760	+	0.424991i	0.143791	+	0.0320349i
$177$	−27.7914			−2.08893
$178$	12.5456	+	6.02158i	0.940330	+	0.451337i
$179$	−11.9559			−0.893622			−0.446811	−	0.894628i	$-0.647440\pi$
$179$	−11.9559			−0.893622			−0.446811	+	0.894628i	$0.647440\pi$
$180$	9.14261	+	11.4036i	0.681450	+	0.849976i
$181$			17.8046i			1.32341i	0.749765	+	0.661704i	$0.230166\pi$
$181$			17.8046i			1.32341i	−0.749765	+	0.661704i	$0.769834\pi$
$182$	1.74726	−	3.64031i	0.129516	−	0.269837i
$183$	27.6765			2.04590
$184$	−4.53647	−	19.5249i	−0.334433	−	1.43939i
$185$		−	1.11751i		−	0.0821606i
$186$	−7.19732	+	14.9951i	−0.527733	+	1.09950i
$187$		−	1.54740i		−	0.113157i
$188$	0.735524	−	0.589690i	0.0536436	−	0.0430076i
$189$		−	41.8778i		−	3.04616i
$190$	2.88863	+	5.44572i	0.209563	+	0.395074i
$191$		−	0.848579i		−	0.0614010i	−0.999529	−	0.0307005i	$-0.990226\pi$
$191$		−	0.848579i		−	0.0614010i	0.999529	−	0.0307005i	$-0.00977381\pi$
$192$	−23.0538	+	11.3241i	−1.66377	+	0.817247i
$193$		−	23.0432i		−	1.65869i	−0.558739	−	0.829343i	$-0.688715\pi$
$193$		−	23.0432i		−	1.65869i	0.558739	−	0.829343i	$-0.311285\pi$
$194$	−2.18718	−	1.04980i	−0.157030	−	0.0753710i
$195$		−	3.02772i		−	0.216819i
$196$	2.71107	+	3.38153i	0.193648	+	0.241538i
$197$	1.14519			0.0815914			0.0407957	−	0.999168i	$-0.487011\pi$
$197$	1.14519			0.0815914			0.0407957	+	0.999168i	$0.487011\pi$
$198$	−4.55243	−	2.18506i	−0.323527	−	0.155285i
$199$		−	1.56194i		−	0.110723i	−0.998466	−	0.0553615i	$-0.982369\pi$
$199$		−	1.56194i		−	0.110723i	0.998466	−	0.0553615i	$-0.0176311\pi$
$200$	−2.75504	+	0.640115i	−0.194811	+	0.0452629i
$201$	−21.1711			−1.49330
$202$	5.79829	−	12.0804i	0.407967	−	0.849971i
$203$	−26.6604			−1.87119
$204$	12.7208	+	15.8667i	0.890633	+	1.11089i
$205$		−	1.56868i		−	0.109561i
$206$	−3.33237	+	6.94277i	−0.232177	+	0.483726i
$207$			51.7918i			3.59978i
$208$	3.68187	+	0.820278i	0.255291	+	0.0568760i
$209$	−1.71383	−	1.26432i	−0.118548	−	0.0874548i
$210$	12.3936	+	5.94866i	0.855243	+	0.410497i
$211$	9.54786			0.657302			0.328651	−	0.944451i	$-0.393406\pi$
$211$	9.54786			0.657302			0.328651	+	0.944451i	$0.393406\pi$
$212$	19.3602	−	15.5216i	1.32966	−	1.06603i
$213$	44.7198			3.06415
$214$	−2.12767	+	4.43285i	−0.145444	+	0.303023i
$215$		−	3.58788i		−	0.244691i
$216$	38.1063	−	8.85373i	2.59280	−	0.602420i
$217$			11.0913i			0.752925i
$218$	−16.0056	−	7.68232i	−1.08404	−	0.520312i
$219$	37.5514			2.53749
$220$	0.762409	−	0.611245i	0.0514016	−	0.0412101i
$221$		−	2.98665i		−	0.200904i
$222$	−4.57439	−	2.19560i	−0.307013	−	0.147359i
$223$	8.65072			0.579295			0.289647	−	0.957133i	$-0.406462\pi$
$223$	8.65072			0.579295			0.289647	+	0.957133i	$0.406462\pi$
$224$	−10.5916	+	13.4597i	−0.707682	+	0.899314i
$225$	7.30804			0.487203
$226$	12.8738	+	6.17913i	0.856352	+	0.411029i
$227$	2.31886			0.153908			0.0769541	−	0.997035i	$-0.475481\pi$
$227$	2.31886			0.153908			0.0769541	+	0.997035i	$0.475481\pi$
$228$	27.9669	−	1.12490i	1.85215	−	0.0744986i
$229$	−16.7074			−1.10406			−0.552029	−	0.833825i	$-0.686146\pi$
$229$	−16.7074			−1.10406			−0.552029	+	0.833825i	$0.686146\pi$
$230$	−9.03557	−	4.33687i	−0.595788	−	0.285964i
$231$	−4.74952			−0.312495
$232$	−5.63650	−	24.2594i	−0.370054	−	1.59271i
$233$	−20.0432			−1.31308			−0.656538	−	0.754293i	$-0.727980\pi$
$233$	−20.0432			−1.31308			−0.656538	+	0.754293i	$0.727980\pi$
$234$	−8.78666	−	4.21740i	−0.574402	−	0.275700i
$235$		−	0.471362i		−	0.0307483i
$236$	−10.8291	−	13.5072i	−0.704913	−	0.879242i
$237$	−33.8133			−2.19641
$238$	12.2255	+	5.86797i	0.792463	+	0.380364i
$239$			19.1162i			1.23652i	0.785972	+	0.618262i	$0.212163\pi$
$239$			19.1162i			1.23652i	−0.785972	+	0.618262i	$0.787837\pi$
$240$	−2.79269	+	12.5351i	−0.180267	+	0.809139i
$241$		−	10.4803i		−	0.675093i	−0.941309	−	0.337546i	$-0.890403\pi$
$241$		−	10.4803i		−	0.675093i	0.941309	−	0.337546i	$-0.109597\pi$
$242$	6.58537	−	13.7202i	0.423323	−	0.881966i
$243$	−30.6910			−1.96883
$244$	10.7843	+	13.4513i	0.690393	+	0.861131i
$245$	2.16706			0.138449
$246$	−6.42123	−	3.08204i	−0.409403	−	0.196504i
$247$	−3.30787	−	2.44027i	−0.210475	−	0.155271i
$248$	−10.0924	+	2.34490i	−0.640868	+	0.148901i
$249$			58.0076i			3.67608i
$250$	−0.611950	+	1.27496i	−0.0387031	+	0.0806354i
$251$			25.7318i			1.62418i	0.583535	+	0.812088i	$0.301669\pi$
$251$			25.7318i			1.62418i	−0.583535	+	0.812088i	$0.698331\pi$
$252$	34.5269	−	27.6812i	2.17499	−	1.74375i
$253$	3.46263			0.217694
$254$	2.83883	−	5.91451i	0.178124	−	0.371109i
$255$	10.1682			0.636759
$256$	−14.4868	−	6.79211i	−0.905425	−	0.424507i
$257$		−	10.3042i		−	0.642757i	−0.946951	−	0.321379i	$-0.895854\pi$
$257$		−	10.3042i		−	0.642757i	0.946951	−	0.321379i	$-0.104146\pi$
$258$	−14.6866	−	7.04924i	−0.914349	−	0.438866i
$259$	−3.38349			−0.210240
$260$	1.47153	−	1.17977i	0.0912604	−	0.0731660i
$261$			64.3506i			3.98320i
$262$	27.5876	+	13.2414i	1.70437	+	0.818059i
$263$		−	3.62234i		−	0.223363i	−0.993744	−	0.111681i	$-0.964376\pi$
$263$		−	3.62234i		−	0.223363i	0.993744	−	0.111681i	$-0.0356236\pi$
$264$	−1.00413	−	4.32178i	−0.0618002	−	0.265987i
$265$		−	12.4070i		−	0.762157i
$266$	16.4881	−	8.74594i	1.01095	−	0.536248i
$267$		−	31.5924i		−	1.93342i
$268$	−8.24945	−	10.2896i	−0.503915	−	0.628536i
$269$			14.9871i			0.913778i	0.889524	+	0.456889i	$0.151036\pi$
$269$			14.9871i			0.913778i	−0.889524	+	0.456889i	$0.848964\pi$
$270$	8.46417	−	17.6345i	0.515113	−	1.07320i
$271$		−	2.44027i		−	0.148236i	−0.997249	−	0.0741179i	$-0.976386\pi$
$271$		−	2.44027i		−	0.148236i	0.997249	−	0.0741179i	$-0.0236141\pi$
$272$	−2.75480	+	12.3651i	−0.167035	+	0.749744i
$273$	−9.16706			−0.554816
$274$	7.68048	−	16.0018i	0.463995	−	0.966702i
$275$		−	0.488592i		−	0.0294632i
$276$	−35.5050	+	28.4654i	−2.13715	+	1.71341i
$277$	22.7032			1.36410			0.682052	−	0.731303i	$-0.261088\pi$
$277$	22.7032			1.36410			0.682052	+	0.731303i	$0.261088\pi$
$278$	7.61635	+	3.65567i	0.456798	+	0.219253i
$279$	26.7712			1.60275
$280$	1.93809	+	8.34148i	0.115823	+	0.498499i
$281$		−	7.97768i		−	0.475908i	−0.971276	−	0.237954i	$-0.923523\pi$
$281$		−	7.97768i		−	0.475908i	0.971276	−	0.237954i	$-0.0764768\pi$
$282$	−1.92947	−	0.926102i	−0.114898	−	0.0551486i
$283$		−	6.56125i		−	0.390026i	−0.980801	−	0.195013i	$-0.937525\pi$
$283$		−	6.56125i		−	0.390026i	0.980801	−	0.195013i	$-0.0624749\pi$
$284$	17.4253	+	21.7347i	1.03400	+	1.28972i
$285$	8.30804	−	11.2618i	0.492126	−	0.667094i
$286$	−0.281961	+	0.587447i	−0.0166727	+	0.0347365i
$287$	−4.74952			−0.280355
$288$	32.4879	+	25.5651i	1.91437	+	1.50644i
$289$	−6.96971			−0.409983
$290$	−11.2266	−	5.38850i	−0.659247	−	0.316424i
$291$			5.50779i			0.322872i
$292$	14.6321	+	18.2507i	0.856280	+	1.06804i
$293$			7.47982i			0.436976i	0.975840	+	0.218488i	$0.0701124\pi$
$293$			7.47982i			0.436976i	−0.975840	+	0.218488i	$0.929888\pi$
$294$	4.25771	−	8.87065i	0.248315	−	0.517347i
$295$	−8.65611			−0.503978
$296$	−0.715332	−	3.07877i	−0.0415778	−	0.178950i
$297$			6.75794i			0.392136i
$298$	−12.4460	+	25.9303i	−0.720975	+	1.50210i
$299$	6.68324			0.386502
$300$	4.01659	+	5.00991i	0.231898	+	0.289247i
$301$	−10.8631			−0.626138
$302$	0.827671	−	1.72440i	0.0476271	−	0.0992279i
$303$	−30.4209			−1.74764
$304$	11.4442	+	13.1541i	0.656368	+	0.754441i
$305$	8.62030			0.493597
$306$	14.1636	−	29.5089i	0.809680	−	1.68691i
$307$	−12.2926			−0.701574			−0.350787	−	0.936455i	$-0.614086\pi$
$307$	−12.2926			−0.701574			−0.350787	+	0.936455i	$0.614086\pi$
$308$	−1.85068	−	2.30836i	−0.105452	−	0.131531i
$309$	17.4834			0.994595
$310$	−2.24173	+	4.67049i	−0.127321	+	0.265266i
$311$			2.03330i			0.115298i	0.998337	+	0.0576490i	$0.0183604\pi$
$311$			2.03330i			0.115298i	−0.998337	+	0.0576490i	$0.981640\pi$
$312$	−1.93809	−	8.34148i	−0.109722	−	0.472243i
$313$	23.5095			1.32883			0.664417	−	0.747362i	$-0.268680\pi$
$313$	23.5095			1.32883			0.664417	+	0.747362i	$0.268680\pi$
$314$	3.99539	−	8.32414i	0.225473	−	0.469758i
$315$		−	22.1267i		−	1.24670i
$316$	−13.1755	−	16.4339i	−0.741182	−	0.924480i
$317$		−	10.5447i		−	0.592250i	−0.955149	−	0.296125i	$-0.904306\pi$
$317$		−	10.5447i		−	0.592250i	0.955149	−	0.296125i	$-0.0956944\pi$
$318$	−50.7868	−	24.3765i	−2.84798	−	1.36697i
$319$	4.30227			0.240881
$320$	−7.18051	+	3.52709i	−0.401403	+	0.197170i
$321$	11.1629			0.623050
$322$	−13.1308	+	27.3571i	−0.731751	+	1.52455i
$323$	8.19535	−	11.1091i	0.456001	−	0.618126i
$324$	−28.1275	−	35.0835i	−1.56264	−	1.94909i
$325$		−	0.943033i		−	0.0523101i
$326$	12.2948	+	5.90123i	0.680947	+	0.326839i
$327$			40.3055i			2.22890i
$328$	−1.00413	−	4.32178i	−0.0554441	−	0.238630i
$329$	−1.42715			−0.0786814
$330$	−2.00000	−	0.959954i	−0.110096	−	0.0528437i
$331$	−1.08262			−0.0595061			−0.0297531	−	0.999557i	$-0.509472\pi$
$331$	−1.08262			−0.0595061			−0.0297531	+	0.999557i	$0.509472\pi$
$332$	−28.1928	+	22.6030i	−1.54728	+	1.24050i
$333$			8.16678i			0.447537i
$334$	−0.262974	+	0.547890i	−0.0143893	+	0.0299792i
$335$	−6.59410			−0.360274
$336$	37.9528	+	8.45546i	2.07050	+	0.461283i
$337$			0.257449i			0.0140241i	0.999975	+	0.00701206i	$0.00223203\pi$
$337$			0.257449i			0.0140241i	−0.999975	+	0.00701206i	$0.997768\pi$
$338$	7.41114	−	15.4406i	0.403113	−	0.839859i
$339$		−	32.4190i		−	1.76076i
$340$	3.96210	+	4.94195i	0.214875	+	0.268015i
$341$		−	1.78983i		−	0.0969249i
$342$	−21.1102	−	39.7975i	−1.14151	−	2.15200i
$343$			14.6328i			0.790095i
$344$	−2.29665	−	9.88476i	−0.123827	−	0.532950i
$345$			22.7535i			1.22501i
$346$	−21.8074	−	10.4671i	−1.17237	−	0.562712i
$347$		−	16.9053i		−	0.907523i	−0.891123	−	0.453762i	$-0.850082\pi$
$347$		−	16.9053i		−	0.907523i	0.891123	−	0.453762i	$-0.149918\pi$
$348$	−44.1145	+	35.3679i	−2.36479	+	1.89592i
$349$	−15.4709			−0.828138			−0.414069	−	0.910245i	$-0.635893\pi$
$349$	−15.4709			−0.828138			−0.414069	+	0.910245i	$0.635893\pi$
$350$	3.86021	+	1.85281i	0.206337	+	0.0990369i
$351$			13.0435i			0.696212i
$352$	1.70920	−	2.17203i	0.0911007	−	0.115770i
$353$	−16.0568			−0.854620			−0.427310	−	0.904105i	$-0.640539\pi$
$353$	−16.0568			−0.854620			−0.427310	+	0.904105i	$0.640539\pi$
$354$	−17.0070	+	35.4329i	−0.903910	+	1.88324i
$355$	13.9287			0.739260
$356$	15.3545	−	12.3102i	0.813788	−	0.652437i
$357$		−	30.7865i		−	1.62939i
$358$	−7.31639	+	15.2432i	−0.386683	+	0.805629i
$359$		−	8.15765i		−	0.430544i	−0.976554	−	0.215272i	$-0.930936\pi$
$359$		−	8.15765i		−	0.430544i	0.976554	−	0.215272i	$-0.0690639\pi$
$360$	20.1340	−	4.67799i	1.06115	−	0.246552i
$361$	−5.60782	−	18.1536i	−0.295148	−	0.955451i
$362$	22.7002	+	10.8955i	1.19309	+	0.572657i
$363$	−34.5503			−1.81342
$364$	−3.57200	−	4.45537i	−0.187224	−	0.233525i
$365$	11.6960			0.612197
$366$	16.9366	−	35.2863i	0.885291	−	1.84444i
$367$		−	3.05212i		−	0.159319i	−0.996822	−	0.0796597i	$-0.974617\pi$
$367$		−	3.05212i		−	0.159319i	0.996822	−	0.0796597i	$-0.0253834\pi$
$368$	−27.6695	−	6.16444i	−1.44237	−	0.321344i
$369$			11.4640i			0.596791i
$370$	−1.42477	−	0.683858i	−0.0740704	−	0.0355521i
$371$	−37.5649			−1.95027
$372$	14.7138	+	18.3525i	0.762873	+	0.951535i
$373$			22.1917i			1.14904i	0.818490	+	0.574521i	$0.194812\pi$
$373$			22.1917i			1.14904i	−0.818490	+	0.574521i	$0.805188\pi$
$374$	−1.97287	−	0.946933i	−0.102015	−	0.0489647i
$375$	3.21061			0.165795
$376$	−0.301726	−	1.29862i	−0.0155603	−	0.0669713i
$377$	8.30384			0.427669
$378$	−53.3924	−	25.6271i	−2.74621	−	1.31812i
$379$	−23.4631			−1.20522			−0.602609	−	0.798037i	$-0.705872\pi$
$379$	−23.4631			−1.20522			−0.602609	+	0.798037i	$0.705872\pi$
$380$	8.71075	−	0.350370i	0.446852	−	0.0179736i
$381$	−14.8940			−0.763042
$382$	−1.08190	−	0.519288i	−0.0553549	−	0.0265691i
$383$	−8.91696			−0.455636			−0.227818	−	0.973704i	$-0.573159\pi$
$383$	−8.91696			−0.455636			−0.227818	+	0.973704i	$0.573159\pi$
$384$	0.329958	+	36.3225i	0.0168381	+	1.85357i
$385$	−1.47932			−0.0753930
$386$	−29.3791	−	14.1013i	−1.49536	−	0.717737i
$387$			26.2204i			1.33286i
$388$	−2.67689	+	2.14614i	−0.135899	+	0.108954i
$389$	17.8050			0.902751			0.451375	−	0.892334i	$-0.350934\pi$
$389$	17.8050			0.902751			0.451375	+	0.892334i	$0.350934\pi$
$390$	−3.86021	−	1.85281i	−0.195469	−	0.0938208i
$391$			22.4448i			1.13508i
$392$	5.97035	−	1.38717i	0.301548	−	0.0700626i
$393$		−	69.4716i		−	3.50438i
$394$	0.700799	−	1.46007i	0.0353058	−	0.0735572i
$395$	−10.5317			−0.529908
$396$	−5.57172	+	4.46700i	−0.279989	+	0.224475i
$397$	14.6683			0.736179			0.368089	−	0.929790i	$-0.380012\pi$
$397$	14.6683			0.736179			0.368089	+	0.929790i	$0.380012\pi$
$398$	−1.99141	−	0.955830i	−0.0998203	−	0.0479114i
$399$	−34.0977	−	25.1544i	−1.70702	−	1.25929i
$400$	−0.869829	+	3.90428i	−0.0434915	+	0.195214i
$401$		−	18.1350i		−	0.905621i	−0.891607	−	0.452810i	$-0.850421\pi$
$401$		−	18.1350i		−	0.905621i	0.891607	−	0.452810i	$-0.149579\pi$
$402$	−12.9557	+	26.9923i	−0.646170	+	1.34625i
$403$		−	3.45457i		−	0.172084i
$404$	−11.8537	−	14.7852i	−0.589743	−	0.735589i
$405$	−22.4834			−1.11721
$406$	−16.3148	+	33.9909i	−0.809692	+	1.68694i
$407$	0.546004			0.0270644
$408$	28.0139	−	6.50883i	1.38689	−	0.322235i
$409$			6.24316i			0.308704i	0.988016	+	0.154352i	$0.0493290\pi$
$409$			6.24316i			0.308704i	−0.988016	+	0.154352i	$0.950671\pi$
$410$	−2.00000	−	0.959954i	−0.0987730	−	0.0474087i
$411$	−40.2959			−1.98765
$412$	6.81250	+	8.49726i	0.335628	+	0.418630i
$413$			26.2082i			1.28962i
$414$	66.0323	+	31.6940i	3.24531	+	1.55768i
$415$			18.0674i			0.886896i
$416$	3.29894	−	4.19225i	0.161744	−	0.205542i
$417$		−	19.1796i		−	0.939228i
$418$	−2.66073	+	1.41136i	−0.130141	+	0.0690319i
$419$			4.64669i			0.227006i	0.993538	+	0.113503i	$0.0362071\pi$
$419$			4.64669i			0.227006i	−0.993538	+	0.113503i	$0.963793\pi$
$420$	15.1686	−	12.1611i	0.740151	−	0.593400i
$421$			15.7441i			0.767320i	0.923474	+	0.383660i	$0.125337\pi$
$421$			15.7441i			0.767320i	−0.923474	+	0.383660i	$0.874663\pi$
$422$	5.84282	−	12.1731i	0.284424	−	0.592578i
$423$			3.44474i			0.167489i
$424$	−7.94191	−	34.1818i	−0.385693	−	1.66002i
$425$	3.16706			0.153625
$426$	27.3663	−	57.0158i	1.32590	−	2.76242i
$427$		−	26.0998i		−	1.26306i
$428$	4.34967	+	5.42537i	0.210249	+	0.262245i
$429$	1.47932			0.0714221
$430$	−4.57439	−	2.19560i	−0.220597	−	0.105881i
$431$	14.2220			0.685050			0.342525	−	0.939509i	$-0.388718\pi$
$431$	14.2220			0.685050			0.342525	+	0.939509i	$0.388718\pi$
$432$	12.0310	−	54.0019i	0.578843	−	2.59817i
$433$		−	30.9395i		−	1.48686i	−0.668815	−	0.743429i	$-0.733198\pi$
$433$		−	30.9395i		−	1.48686i	0.668815	−	0.743429i	$-0.266802\pi$
$434$	14.1409	+	6.78731i	0.678785	+	0.325801i
$435$			28.2709i			1.35549i
$436$	−19.5893	+	15.7053i	−0.938155	+	0.752146i
$437$	24.8589	+	18.3388i	1.18916	+	0.877263i
$438$	22.9796	−	47.8764i	1.09801	−	2.28762i
$439$	24.9444			1.19053			0.595266	−	0.803529i	$-0.297047\pi$
$439$	24.9444			1.19053			0.595266	+	0.803529i	$0.297047\pi$
$440$	−0.312755	−	1.34609i	−0.0149100	−	0.0641723i
$441$	−15.8370			−0.754143
$442$	−3.80785	−	1.82768i	−0.181121	−	0.0869338i
$443$			23.4764i			1.11540i	0.830044	+	0.557698i	$0.188315\pi$
$443$			23.4764i			1.11540i	−0.830044	+	0.557698i	$0.811685\pi$
$444$	−5.59860	+	4.48856i	−0.265698	+	0.213018i
$445$		−	9.83998i		−	0.466460i
$446$	5.29381	−	11.0293i	0.250669	−	0.522252i
$447$	65.2981			3.08849
$448$	10.6790	+	21.7405i	0.504536	+	1.02714i
$449$		−	1.97053i		−	0.0929951i	−0.998918	−	0.0464976i	$-0.985194\pi$
$449$		−	1.97053i		−	0.0929951i	0.998918	−	0.0464976i	$-0.0148060\pi$
$450$	4.47216	−	9.31745i	0.210820	−	0.439229i
$451$	0.766444			0.0360904
$452$	15.7562	−	12.6322i	0.741112	−	0.594170i
$453$	−4.34240			−0.204024
$454$	1.41903	−	2.95645i	0.0665982	−	0.138753i
$455$	−2.85524			−0.133856
$456$	15.6801	−	36.3450i	0.734289	−	1.70201i
$457$	−9.40564			−0.439977			−0.219989	−	0.975502i	$-0.570602\pi$
$457$	−9.40564			−0.439977			−0.219989	+	0.975502i	$0.570602\pi$
$458$	−10.2241	+	21.3013i	−0.477742	+	0.995343i
$459$	−43.8051			−2.04465
$460$	−11.0586	+	8.86602i	−0.515612	+	0.413380i
$461$	18.2902			0.851861			0.425930	−	0.904756i	$-0.359947\pi$
$461$	18.2902			0.851861			0.425930	+	0.904756i	$0.359947\pi$
$462$	−2.90647	+	6.05543i	−0.135221	+	0.281724i
$463$		−	8.89549i		−	0.413409i	−0.978403	−	0.206704i	$-0.933726\pi$
$463$		−	8.89549i		−	0.413409i	0.978403	−	0.206704i	$-0.0662738\pi$
$464$	−34.3790	−	7.65924i	−1.59600	−	0.355571i
$465$	11.7613			0.545416
$466$	−12.2655	+	25.5543i	−0.568187	+	1.18378i
$467$			0.513185i			0.0237474i	0.999930	+	0.0118737i	$0.00377960\pi$
$467$			0.513185i			0.0237474i	−0.999930	+	0.0118737i	$0.996220\pi$
$468$	−10.7540	+	8.62178i	−0.497104	+	0.398542i
$469$			19.9651i			0.921901i
$470$	−0.600967	−	0.288450i	−0.0277205	−	0.0133052i
$471$	−20.9619			−0.965876
$472$	−23.8479	+	5.54090i	−1.09769	+	0.255041i
$473$	1.75301			0.0806034
$474$	−20.6921	+	43.1105i	−0.950418	+	1.98013i
$475$	2.58768	−	3.50769i	0.118731	−	0.160944i
$476$	14.9628	−	11.9961i	0.685820	−	0.549841i
$477$			90.6710i			4.15154i
$478$	24.3723	+	11.6982i	1.11476	+	0.535061i
$479$		−	20.5748i		−	0.940086i	−0.882643	−	0.470043i	$-0.844238\pi$
$479$		−	20.5748i		−	0.940086i	0.882643	−	0.470043i	$-0.155762\pi$
$480$	14.2728	+	11.2314i	0.651460	+	0.512643i
$481$	1.05384			0.0480512
$482$	−13.3619	−	6.41340i	−0.608617	−	0.292122i
$483$	68.8911			3.13465
$484$	−13.4627	−	16.7921i	−0.611942	−	0.763279i
$485$			1.71549i			0.0778965i
$486$	−18.7814	+	39.1298i	−0.851941	+	1.77496i
$487$	−1.51600			−0.0686965			−0.0343482	−	0.999410i	$-0.510936\pi$
$487$	−1.51600			−0.0686965			−0.0343482	+	0.999410i	$0.510936\pi$
$488$	23.7493	−	5.51798i	1.07508	−	0.249787i
$489$		−	30.9610i		−	1.40010i
$490$	1.32614	−	2.76291i	0.0599087	−	0.124816i
$491$		−	18.4129i		−	0.830962i	−0.909602	−	0.415481i	$-0.863613\pi$
$491$		−	18.4129i		−	0.830962i	0.909602	−	0.415481i	$-0.136387\pi$
$492$	−7.85895	+	6.30074i	−0.354309	+	0.284059i
$493$			27.8874i			1.25599i
$494$	−5.13549	+	2.72407i	−0.231057	+	0.122562i
$495$			3.57065i			0.160489i
$496$	−3.18640	+	14.3023i	−0.143074	+	0.642194i
$497$		−	42.1722i		−	1.89168i
$498$	73.9572	+	35.4978i	3.31410	+	1.59069i
$499$		−	8.98900i		−	0.402403i	−0.979550	−	0.201202i	$-0.935515\pi$
$499$		−	8.98900i		−	0.402403i	0.979550	−	0.201202i	$-0.0644846\pi$
$500$	1.25103	+	1.56042i	0.0559479	+	0.0697842i
$501$	1.37970			0.0616406
$502$	32.8069	+	15.7466i	1.46425	+	0.702804i
$503$			10.0185i			0.446703i	0.974738	+	0.223352i	$0.0716998\pi$
$503$			10.0185i			0.446703i	−0.974738	+	0.223352i	$0.928300\pi$
$504$	−14.1636	−	60.9599i	−0.630898	−	2.71537i
$505$	−9.47511			−0.421637
$506$	2.11896	−	4.41471i	0.0941991	−	0.196258i
$507$	−38.8827			−1.72684
$508$	−5.80353	−	7.23877i	−0.257490	−	0.321168i
$509$		−	17.0538i		−	0.755898i	−0.925826	−	0.377949i	$-0.876629\pi$
$509$		−	17.0538i		−	0.755898i	0.925826	−	0.377949i	$-0.123371\pi$
$510$	6.22244	−	12.9640i	0.275534	−	0.574058i
$511$		−	35.4122i		−	1.56654i
$512$	−17.5249	+	14.3136i	−0.774496	+	0.632578i
$513$	−35.7914	+	48.5165i	−1.58023	+	2.14206i
$514$	−13.1374	−	6.30565i	−0.579466	−	0.278130i
$515$	5.44549			0.239957
$516$	−17.9750	+	14.4110i	−0.791303	+	0.634410i
$517$	0.230304			0.0101287
$518$	−2.07053	+	4.31381i	−0.0909738	+	0.189538i
$519$			54.9157i			2.41053i
$520$	−0.603649	−	2.59810i	−0.0264718	−	0.113934i
$521$		−	15.1017i		−	0.661618i	−0.943698	−	0.330809i	$-0.892678\pi$
$521$		−	15.1017i		−	0.661618i	0.943698	−	0.330809i	$-0.107322\pi$
$522$	82.0443	+	39.3794i	3.59098	+	1.72359i
$523$	−3.49037			−0.152623			−0.0763117	−	0.997084i	$-0.524314\pi$
$523$	−3.49037			−0.152623			−0.0763117	+	0.997084i	$0.524314\pi$
$524$	33.7645	−	27.0700i	1.47501	−	1.18256i
$525$		−	9.72083i		−	0.424252i
$526$	−4.61833	−	2.21669i	−0.201369	−	0.0966523i
$527$	11.6017			0.505380
$528$	−6.12456	−	1.36448i	−0.266537	−	0.0593815i
$529$	−27.2250			−1.18369
$530$	−15.8184	−	7.59248i	−0.687108	−	0.329796i
$531$	63.2592			2.74522
$532$	−1.06082	−	26.3737i	−0.0459924	−	1.14344i
$533$	1.47932			0.0640763
$534$	−40.2790	−	19.3330i	−1.74304	−	0.836620i
$535$	3.47686			0.150318
$536$	−18.1670	+	4.22098i	−0.784696	+	0.182319i
$537$	38.3856			1.65646
$538$	19.1079	+	9.17134i	0.823799	+	0.395405i
$539$			1.05881i			0.0456061i
$540$	−17.3036	−	21.5829i	−0.744630	−	0.928781i
$541$	−0.859019			−0.0369321			−0.0184661	−	0.999829i	$-0.505878\pi$
$541$	−0.859019			−0.0369321			−0.0184661	+	0.999829i	$0.505878\pi$
$542$	−3.11124	−	1.49332i	−0.133639	−	0.0641437i
$543$		−	57.1638i		−	2.45313i
$544$	14.0792	+	11.0791i	0.603640	+	0.475012i
$545$			12.5538i			0.537747i
$546$	−5.60979	+	11.6876i	−0.240077	+	0.500184i
$547$	16.9704			0.725600			0.362800	−	0.931867i	$-0.381821\pi$
$547$	16.9704			0.725600			0.362800	+	0.931867i	$0.381821\pi$
$548$	−15.7015	−	19.5846i	−0.670735	−	0.836612i
$549$	−62.9975			−2.68867
$550$	−0.622934	−	0.298994i	−0.0265620	−	0.0127491i
$551$	30.8868	+	22.7857i	1.31582	+	0.970703i
$552$	14.5648	+	62.6868i	0.619921	+	2.66813i
$553$			31.8871i			1.35598i
$554$	13.8932	−	28.9456i	0.590267	−	1.22978i
$555$			3.58788i			0.152297i
$556$	9.32165	−	7.47343i	0.395326	−	0.316944i
$557$	32.6593			1.38382			0.691910	−	0.721984i	$-0.256769\pi$
$557$	32.6593			1.38382			0.691910	+	0.721984i	$0.256769\pi$
$558$	16.3826	−	34.1321i	0.693532	−	1.44493i
$559$	3.38349			0.143106
$560$	11.8210	+	2.63360i	0.499530	+	0.111290i
$561$			4.96811i			0.209754i
$562$	−10.1712	−	4.88194i	−0.429046	−	0.205932i
$563$	9.10359			0.383671			0.191835	−	0.981427i	$-0.438556\pi$
$563$	9.10359			0.383671			0.191835	+	0.981427i	$0.438556\pi$
$564$	−2.36148	+	1.89327i	−0.0994364	+	0.0797209i
$565$		−	10.0974i		−	0.424802i
$566$	−8.36532	−	4.01516i	−0.351621	−	0.168770i
$567$			68.0733i			2.85881i
$568$	38.3742	−	8.91598i	1.61015	−	0.374106i
$569$			29.8666i			1.25207i	0.779794	+	0.626037i	$0.215324\pi$
$569$			29.8666i			1.25207i	−0.779794	+	0.626037i	$0.784676\pi$
$570$	−9.27427	−	17.4841i	−0.388456	−	0.732328i
$571$		−	28.8364i		−	1.20677i	−0.797451	−	0.603383i	$-0.793819\pi$
$571$		−	28.8364i		−	1.20677i	0.797451	−	0.603383i	$-0.206181\pi$
$572$	0.576424	+	0.718977i	0.0241015	+	0.0300619i
$573$			2.72446i			0.113816i
$574$	−2.90647	+	6.05543i	−0.121314	+	0.252749i
$575$			7.08696i			0.295547i
$576$	52.4755	−	25.7761i	2.18648	−	1.07400i
$577$	24.1255			1.00436			0.502180	−	0.864763i	$-0.332532\pi$
$577$	24.1255			1.00436			0.502180	+	0.864763i	$0.332532\pi$
$578$	−4.26511	+	8.88608i	−0.177405	+	0.369612i
$579$			73.9829i			3.07462i
$580$	−13.7402	+	11.0159i	−0.570531	+	0.457411i
$581$	54.7031			2.26947
$582$	7.02220	+	3.37049i	0.291079	+	0.139711i
$583$	6.06196			0.251061
$584$	32.2230	−	7.48679i	1.33340	−	0.309806i
$585$			6.89173i			0.284938i
$586$	9.53645	+	4.57728i	0.393947	+	0.189086i
$587$		−	1.98430i		−	0.0819010i	−0.999161	−	0.0409505i	$-0.986961\pi$
$587$		−	1.98430i		−	0.0819010i	0.999161	−	0.0409505i	$-0.0130386\pi$
$588$	−8.70420	−	10.8568i	−0.358955	−	0.447727i
$589$	9.47932	−	12.8496i	0.390588	−	0.529457i
$590$	−5.29711	+	11.0362i	−0.218078	+	0.454352i
$591$	−3.67676			−0.151242
$592$	−4.36305	−	0.972039i	−0.179320	−	0.0399506i
$593$	−37.8922			−1.55604			−0.778022	−	0.628237i	$-0.783777\pi$
$593$	−37.8922			−1.55604			−0.778022	+	0.628237i	$0.783777\pi$
$594$	8.61609	+	4.13552i	0.353522	+	0.169683i
$595$		−	9.58897i		−	0.393109i
$596$	25.4438	+	31.7361i	1.04222	+	1.29996i
$597$			5.01479i			0.205242i
$598$	4.08981	−	8.52084i	0.167245	−	0.348443i
$599$	−35.0029			−1.43018			−0.715091	−	0.699032i	$-0.753615\pi$
$599$	−35.0029			−1.43018			−0.715091	+	0.699032i	$0.753615\pi$
$600$	8.84538	−	2.05516i	0.361111	−	0.0839016i
$601$		−	13.3793i		−	0.545753i	−0.962049	−	0.272877i	$-0.912025\pi$
$601$		−	13.3793i		−	0.545753i	0.962049	−	0.272877i	$-0.0879751\pi$
$602$	−6.64766	+	13.8500i	−0.270939	+	0.564482i
$603$	48.1900			1.96245
$604$	−1.69204	−	2.11049i	−0.0688481	−	0.0858746i
$605$	−10.7613			−0.437508
$606$	−18.6161	+	38.7854i	−0.756227	+	1.57555i
$607$	−28.7047			−1.16509			−0.582543	−	0.812800i	$-0.697942\pi$
$607$	−28.7047			−1.16509			−0.582543	+	0.812800i	$0.697942\pi$
$608$	23.7742	−	6.54117i	0.964172	−	0.265279i
$609$	85.5963			3.46854
$610$	5.27519	−	10.9905i	0.213586	−	0.444993i
$611$	0.444510			0.0179830
$612$	−28.9552	−	36.1160i	−1.17045	−	1.45990i
$613$	−9.72631			−0.392842			−0.196421	−	0.980520i	$-0.562932\pi$
$613$	−9.72631			−0.392842			−0.196421	+	0.980520i	$0.562932\pi$
$614$	−7.52244	+	15.6725i	−0.303581	+	0.632491i
$615$			5.03643i			0.203088i
$616$	−4.07558	+	0.946933i	−0.164210	+	0.0381530i
$617$	9.50602			0.382698			0.191349	−	0.981522i	$-0.438714\pi$
$617$	9.50602			0.382698			0.191349	+	0.981522i	$0.438714\pi$
$618$	10.6990	−	22.2906i	0.430375	−	0.896658i
$619$			37.7438i			1.51705i	0.651643	+	0.758526i	$0.274080\pi$
$619$			37.7438i			1.51705i	−0.651643	+	0.758526i	$0.725920\pi$
$620$	4.58285	+	5.71621i	0.184052	+	0.229569i
$621$		−	98.0230i		−	3.93353i
$622$	2.59237	+	1.24428i	0.103945	+	0.0498911i
$623$	−29.7927			−1.19362
$624$	−11.8210	−	2.63360i	−0.473221	−	0.105428i
$625$	1.00000			0.0400000
$626$	14.3866	−	29.9736i	0.575005	−	1.19798i
$627$	5.50245	+	4.05924i	0.219747	+	0.162111i
$628$	−8.16794	−	10.1879i	−0.325936	−	0.406542i
$629$			3.53921i			0.141118i
$630$	−28.2106	−	13.5404i	−1.12394	−	0.539464i
$631$		−	24.8879i		−	0.990773i	−0.868673	−	0.495386i	$-0.835027\pi$
$631$		−	24.8879i		−	0.990773i	0.868673	−	0.495386i	$-0.164973\pi$
$632$	−29.0153	+	6.74151i	−1.15417	+	0.268163i
$633$	−30.6545			−1.21841
$634$	−13.4441	−	6.45284i	−0.533932	−	0.256275i
$635$	−4.63898			−0.184092
$636$	−62.1580	+	49.8338i	−2.46473	+	1.97604i
$637$			2.04361i			0.0809709i
$638$	2.63278	−	5.48521i	0.104233	−	0.217162i
$639$	−101.792			−4.02682
$640$	0.102771	+	11.3132i	0.00406238	+	0.447195i
$641$			17.6954i			0.698925i	0.936950	+	0.349463i	$0.113636\pi$
$641$			17.6954i			0.698925i	−0.936950	+	0.349463i	$0.886364\pi$
$642$	6.83111	−	14.2322i	0.269602	−	0.561699i
$643$			10.2796i			0.405389i	0.979242	+	0.202695i	$0.0649699\pi$
$643$			10.2796i			0.405389i	−0.979242	+	0.202695i	$0.935030\pi$
$644$	26.8438	+	33.4824i	1.05779	+	1.31939i
$645$			11.5193i			0.453572i
$646$	−9.14847	−	17.2469i	−0.359942	−	0.678571i
$647$		−	31.9257i		−	1.25513i	−0.778565	−	0.627564i	$-0.784052\pi$
$647$		−	31.9257i		−	1.25513i	0.778565	−	0.627564i	$-0.215948\pi$
$648$	−61.9426	+	14.3919i	−2.43334	+	0.565369i
$649$		−	4.22930i		−	0.166015i
$650$	−1.20233	−	0.577089i	−0.0471592	−	0.0226353i
$651$		−	35.6098i		−	1.39566i
$652$	15.0476	−	12.0641i	0.589311	−	0.472467i
$653$	5.72631			0.224088			0.112044	−	0.993703i	$-0.464260\pi$
$653$	5.72631			0.224088			0.112044	+	0.993703i	$0.464260\pi$
$654$	51.3878	+	24.6650i	2.00942	+	0.964476i
$655$		−	21.6381i		−	0.845470i
$656$	−6.12456	−	1.36448i	−0.239124	−	0.0532741i
$657$	−85.4750			−3.33470
$658$	−0.873345	+	1.81956i	−0.0340465	+	0.0709337i
$659$	0.928171			0.0361564			0.0180782	−	0.999837i	$-0.494245\pi$
$659$	0.928171			0.0361564			0.0180782	+	0.999837i	$0.494245\pi$
$660$	−2.44780	+	1.96247i	−0.0952805	+	0.0763891i
$661$		−	15.5689i		−	0.605560i	−0.953060	−	0.302780i	$-0.902085\pi$
$661$		−	15.5689i		−	0.605560i	0.953060	−	0.302780i	$-0.0979147\pi$
$662$	−0.662509	+	1.38029i	−0.0257491	+	0.0536466i
$663$			9.58897i			0.372405i
$664$	11.5652	+	49.7765i	0.448818	+	1.93170i
$665$	−10.6203	−	7.83476i	−0.411837	−	0.303819i
$666$	10.4123	+	4.99766i	0.403468	+	0.193656i
$667$	−62.4039			−2.41629
$668$	0.537609	+	0.670562i	0.0208007	+	0.0259448i
$669$	−27.7741			−1.07381
$670$	−4.03526	+	8.40720i	−0.155896	+	0.324799i
$671$			4.21181i			0.162595i
$672$	34.0056	−	43.2139i	1.31179	−	1.66701i
$673$		−	14.6637i		−	0.565244i	−0.959231	−	0.282622i	$-0.908796\pi$
$673$		−	14.6637i		−	0.565244i	0.959231	−	0.282622i	$-0.0912041\pi$
$674$	0.328236	+	0.157546i	0.0126432	+	0.00606843i
$675$	−13.8315			−0.532373
$676$	−15.1509	−	18.8978i	−0.582726	−	0.726838i
$677$		−	20.0120i		−	0.769123i	−0.923099	−	0.384562i	$-0.874353\pi$
$677$		−	20.0120i		−	0.769123i	0.923099	−	0.384562i	$-0.125647\pi$
$678$	−41.3328	−	19.8388i	−1.58738	−	0.761904i
$679$	5.19403			0.199328
$680$	8.72539	−	2.02728i	0.334603	−	0.0777428i
$681$	−7.44496			−0.285292
$682$	−2.28196	−	1.09529i	−0.0873808	−	0.0419408i
$683$	39.0637			1.49473			0.747366	−	0.664412i	$-0.231318\pi$
$683$	39.0637			1.49473			0.747366	+	0.664412i	$0.231318\pi$
$684$	−63.6586	+	2.56052i	−2.43405	+	0.0979040i
$685$	−12.5508			−0.479542
$686$	18.6561	+	8.95452i	0.712295	+	0.341885i
$687$	53.6411			2.04654
$688$	−14.0081	−	3.12084i	−0.534053	−	0.118981i
$689$	11.7002			0.445743
$690$	29.0097	+	13.9240i	1.10438	+	0.530078i
$691$		−	36.4683i		−	1.38732i	−0.720302	−	0.693660i	$-0.755997\pi$
$691$		−	36.4683i		−	1.38732i	0.720302	−	0.693660i	$-0.244003\pi$
$692$	−26.6901	+	21.3982i	−1.01461	+	0.813438i
$693$	10.8109			0.410673
$694$	−21.5535	−	10.3452i	−0.818161	−	0.392698i
$695$		−	5.97381i		−	0.226599i
$696$	18.0966	+	77.8875i	0.685951	+	2.95232i
$697$			4.96811i			0.188181i
$698$	−9.46742	+	19.7247i	−0.358347	+	0.746592i
$699$	64.3511			2.43398
$700$	4.72451	−	3.78777i	0.178570	−	0.143164i
$701$	−32.9543			−1.24467			−0.622333	−	0.782753i	$-0.713815\pi$
$701$	−32.9543			−1.24467			−0.622333	+	0.782753i	$0.713815\pi$
$702$	16.6300	+	7.98199i	0.627657	+	0.301261i
$703$	3.91987	+	2.89175i	0.147841	+	0.109064i
$704$	−1.72330	−	3.50834i	−0.0649495	−	0.132225i
$705$			1.51336i			0.0569965i
$706$	−9.82599	+	20.4718i	−0.369806	+	0.770466i
$707$			28.6879i			1.07892i
$708$	34.7680	+	43.3663i	1.30666	+	1.62981i
$709$	0.863080			0.0324137			0.0162068	−	0.999869i	$-0.494841\pi$
$709$	0.863080			0.0324137			0.0162068	+	0.999869i	$0.494841\pi$
$710$	8.52369	−	17.7585i	0.319888	−	0.666466i
$711$	76.9663			2.88646
$712$	−6.29872	−	27.1096i	−0.236054	−	1.01597i
$713$			25.9613i			0.972258i
$714$	−39.2515	−	18.8398i	−1.46895	−	0.705062i
$715$	0.460758			0.0172314
$716$	14.9572	+	18.6562i	0.558976	+	0.697214i
$717$		−	61.3747i		−	2.29208i
$718$	−10.4007	−	4.99208i	−0.388149	−	0.186303i
$719$		−	30.5363i		−	1.13881i	−0.822057	−	0.569405i	$-0.807173\pi$
$719$		−	30.5363i		−	1.13881i	0.822057	−	0.569405i	$-0.192827\pi$
$720$	6.35675	−	28.5326i	0.236902	−	1.06335i
$721$		−	16.4874i		−	0.614023i
$722$	−26.5767	−	3.95936i	−0.989084	−	0.147352i
$723$			33.6481i			1.25139i
$724$	27.7827	−	22.2742i	1.03254	−	0.827814i
$725$			8.80545i			0.327026i
$726$	−21.1431	+	44.0502i	−0.784693	+	1.63486i
$727$		−	5.68270i		−	0.210760i	−0.994432	−	0.105380i	$-0.966394\pi$
$727$		−	5.68270i		−	0.210760i	0.994432	−	0.105380i	$-0.0336058\pi$
$728$	−7.86630	+	1.82768i	−0.291544	+	0.0677383i
$729$	31.0870			1.15137
$730$	7.15738	−	14.9119i	0.264907	−	0.551915i
$731$			11.3630i			0.420277i
$732$	−34.6242	−	43.1869i	−1.27975	−	1.59623i
$733$	25.1533			0.929059			0.464529	−	0.885558i	$-0.346224\pi$
$733$	25.1533			0.929059			0.464529	+	0.885558i	$0.346224\pi$
$734$	−3.89132	−	1.86775i	−0.143631	−	0.0689398i
$735$	−6.95761			−0.256635
$736$	−24.7917	+	31.5051i	−0.913836	+	1.16129i
$737$		−	3.22182i		−	0.118677i
$738$	14.6161	+	7.01539i	0.538026	+	0.258240i
$739$		−	29.1790i		−	1.07337i	−0.843784	−	0.536683i	$-0.819677\pi$
$739$		−	29.1790i		−	1.07337i	0.843784	−	0.536683i	$-0.180323\pi$
$740$	−1.74378	+	1.39804i	−0.0641026	+	0.0513929i
$741$	10.6203	+	7.83476i	0.390146	+	0.287817i
$742$	−22.9879	+	47.8937i	−0.843911	+	1.75823i
$743$	42.1946			1.54797			0.773985	−	0.633204i	$-0.218260\pi$
$743$	42.1946			1.54797			0.773985	+	0.633204i	$0.218260\pi$
$744$	32.4028	−	7.52857i	1.18794	−	0.276011i
$745$	20.3382			0.745134
$746$	28.2934	+	13.5802i	1.03590	+	0.497207i
$747$		−	132.038i		−	4.83101i
$748$	−2.41460	+	1.93585i	−0.0882864	+	0.0707817i
$749$		−	10.5269i		−	0.384646i
$750$	1.96474	−	4.09340i	0.0717420	−	0.149470i
$751$	37.9019			1.38306			0.691529	−	0.722348i	$-0.256937\pi$
$751$	37.9019			1.38306			0.691529	+	0.722348i	$0.256937\pi$
$752$	−1.84033	−	0.410005i	−0.0671099	−	0.0149513i
$753$		−	82.6149i		−	3.01065i
$754$	5.08153	−	10.5870i	0.185059	−	0.385557i
$755$	−1.35251			−0.0492230
$756$	−65.3469	+	52.3905i	−2.37665	+	1.90542i
$757$	9.06683			0.329540			0.164770	−	0.986332i	$-0.447312\pi$
$757$	9.06683			0.329540			0.164770	+	0.986332i	$0.447312\pi$
$758$	−14.3582	+	29.9144i	−0.521515	+	1.08654i
$759$	−11.1172			−0.403528
$760$	4.88384	−	11.3203i	0.177156	−	0.410629i
$761$	35.1190			1.27306			0.636531	−	0.771251i	$-0.280369\pi$
$761$	35.1190			1.27306			0.636531	+	0.771251i	$0.280369\pi$
$762$	−9.11438	+	18.9892i	−0.330179	+	0.687906i
$763$	38.0094			1.37603
$764$	−1.32414	+	1.06160i	−0.0479057	+	0.0384074i
$765$	−23.1450			−0.836811
$766$	−5.45674	+	11.3687i	−0.197160	+	0.410770i
$767$		−	8.16300i		−	0.294749i
$768$	46.5115	+	21.8069i	1.67834	+	0.786887i
$769$	−34.2519			−1.23515			−0.617577	−	0.786511i	$-0.711886\pi$
$769$	−34.2519			−1.23515			−0.617577	+	0.786511i	$0.711886\pi$
$770$	−0.905268	+	1.88607i	−0.0326236	+	0.0679691i
$771$			33.0828i			1.19145i
$772$	−35.9571	+	28.8278i	−1.29413	+	1.03754i
$773$		−	9.33048i		−	0.335594i	−0.985822	−	0.167797i	$-0.946335\pi$
$773$		−	9.33048i		−	0.335594i	0.985822	−	0.167797i	$-0.0536653\pi$
$774$	33.4299	+	16.0456i	1.20161	+	0.576746i
$775$	3.66325			0.131588
$776$	1.09811	+	4.72626i	0.0394199	+	0.169663i
$777$	10.8631			0.389711
$778$	10.8958	−	22.7007i	0.390633	−	0.813858i
$779$	5.50245	+	4.05924i	0.197146	+	0.145437i
$780$	−4.72451	+	3.78777i	−0.169165	+	0.135624i
$781$			6.80546i			0.243519i
$782$	28.6162	+	13.7351i	1.02331	+	0.491167i
$783$		−	121.792i		−	4.35250i
$784$	1.88498	−	8.46082i	0.0673205	−	0.302172i
$785$	−6.52895			−0.233028
$786$	−88.5733	−	42.5131i	−3.15930	−	1.51639i
$787$	−4.73061			−0.168628			−0.0843141	−	0.996439i	$-0.526870\pi$
$787$	−4.73061			−0.168628			−0.0843141	+	0.996439i	$0.526870\pi$
$788$	−1.43267	−	1.78698i	−0.0510368	−	0.0636585i
$789$			11.6299i			0.414037i
$790$	−6.44489	+	13.4275i	−0.229299	+	0.477729i
$791$	−30.5722			−1.08702
$792$	2.28563	+	9.83729i	0.0812162	+	0.349553i
$793$			8.12923i			0.288677i
$794$	8.97624	−	18.7014i	0.318555	−	0.663688i
$795$			39.8341i			1.41277i
$796$	−2.43729	+	1.95404i	−0.0863873	+	0.0692591i
$797$			21.3976i			0.757940i	0.925409	+	0.378970i	$0.123722\pi$
$797$			21.3976i			0.757940i	−0.925409	+	0.378970i	$0.876278\pi$
$798$	−52.9369	+	28.0799i	−1.87395	+	0.994016i
$799$			1.49283i			0.0528127i
$800$	4.44550	+	3.49822i	0.157172	+	0.123681i
$801$			71.9110i			2.54085i
$802$	−23.1214	−	11.0977i	−0.816446	−	0.391875i
$803$			5.71458i			0.201663i
$804$	26.4858	+	33.0359i	0.934082	+	1.16509i
$805$	21.4573			0.756270
$806$	−4.40442	−	2.11402i	−0.155139	−	0.0744632i
$807$		−	48.1177i		−	1.69382i
$808$	−26.1043	+	6.06516i	−0.918347	+	0.213371i
$809$	37.8352			1.33021			0.665107	−	0.746748i	$-0.268386\pi$
$809$	37.8352			1.33021			0.665107	+	0.746748i	$0.268386\pi$
$810$	−13.7587	+	28.6654i	−0.483432	+	1.00720i
$811$	−42.0985			−1.47828			−0.739139	−	0.673552i	$-0.764768\pi$
$811$	−42.0985			−1.47828			−0.739139	+	0.673552i	$0.764768\pi$
$812$	33.3531	+	41.6015i	1.17046	+	1.45993i
$813$			7.83476i			0.274777i
$814$	0.334127	−	0.696132i	0.0117112	−	0.0243994i
$815$		−	9.64331i		−	0.337790i
$816$	8.84462	−	39.6996i	0.309623	−	1.38976i
$817$	12.5852	+	9.28429i	0.440300	+	0.324816i
$818$	7.95976	+	3.82050i	0.278307	+	0.133581i
$819$	20.8662			0.729124
$820$	−2.44780	+	1.96247i	−0.0854809	+	0.0685325i
$821$	29.9355			1.04476			0.522379	−	0.852713i	$-0.325045\pi$
$821$	29.9355			1.04476			0.522379	+	0.852713i	$0.325045\pi$
$822$	−24.6591	+	51.3755i	−0.860084	+	1.79193i
$823$			0.318164i			0.0110905i	0.999985	+	0.00554526i	$0.00176512\pi$
$823$			0.318164i			0.0110905i	−0.999985	+	0.00554526i	$0.998235\pi$
$824$	15.0026	−	3.48574i	0.522639	−	0.121432i
$825$			1.56868i			0.0546144i
$826$	33.4144	+	16.0381i	1.16264	+	0.558038i
$827$	−20.0096			−0.695802			−0.347901	−	0.937531i	$-0.613105\pi$
$827$	−20.0096			−0.695802			−0.347901	+	0.937531i	$0.613105\pi$
$828$	80.8170	−	64.7933i	2.80859	−	2.25172i
$829$		−	3.63983i		−	0.126417i	−0.998000	−	0.0632083i	$-0.979867\pi$
$829$		−	3.63983i		−	0.126417i	0.998000	−	0.0632083i	$-0.0201333\pi$
$830$	23.0352	+	11.0564i	0.799564	+	0.383772i
$831$	−72.8913			−2.52857
$832$	−3.32616	−	6.77146i	−0.115314	−	0.234758i
$833$	−6.86323			−0.237797
$834$	−24.4532	−	11.7370i	−0.846744	−	0.406417i
$835$	0.429732			0.0148715
$836$	0.171188	+	4.25600i	0.00592066	+	0.147197i
$837$	−50.6681			−1.75135
$838$	5.92433	+	2.84354i	0.204653	+	0.0982285i
$839$	35.9639			1.24161			0.620806	−	0.783964i	$-0.286805\pi$
$839$	35.9639			1.24161			0.620806	+	0.783964i	$0.286805\pi$
$840$	−6.22244	−	26.7813i	−0.214695	−	0.924042i
$841$	−48.5360			−1.67366
$842$	20.0731	+	9.63460i	0.691763	+	0.332030i
$843$			25.6132i			0.882167i
$844$	−11.9447	−	14.8987i	−0.411153	−	0.512834i
$845$	−12.1107			−0.416620
$846$	4.39189	+	2.10801i	0.150996	+	0.0724748i
$847$			32.5821i			1.11953i
$848$	−48.4404	−	10.7920i	−1.66345	−	0.370598i
$849$			21.0657i			0.722971i
$850$	1.93809	−	4.03787i	0.0664758	−	0.138498i
$851$	−7.91972			−0.271484
$852$	−55.9459	−	69.7817i	−1.91668	−	2.39068i
$853$	−26.7120			−0.914602			−0.457301	−	0.889312i	$-0.651184\pi$
$853$	−26.7120			−0.914602			−0.457301	+	0.889312i	$0.651184\pi$
$854$	−33.2762	−	15.9718i	−1.13869	−	0.546543i
$855$	−18.9109	+	25.6344i	−0.646739	+	0.876677i
$856$	9.57889	−	2.22559i	0.327400	−	0.0760691i
$857$		−	19.2855i		−	0.658780i	−0.944194	−	0.329390i	$-0.893157\pi$
$857$		−	19.2855i		−	0.658780i	0.944194	−	0.329390i	$-0.106843\pi$
$858$	0.905268	−	1.88607i	0.0309054	−	0.0643892i
$859$		−	27.1922i		−	0.927787i	−0.885891	−	0.463893i	$-0.846452\pi$
$859$		−	27.1922i		−	0.927787i	0.885891	−	0.463893i	$-0.153548\pi$
$860$	−5.59860	+	4.48856i	−0.190911	+	0.153059i
$861$	15.2489			0.519680
$862$	8.70316	−	18.1324i	0.296431	−	0.617593i
$863$	−40.1609			−1.36709			−0.683547	−	0.729907i	$-0.739563\pi$
$863$	−40.1609			−1.36709			−0.683547	+	0.729907i	$0.739563\pi$
$864$	−61.4878	−	48.3855i	−2.09186	−	1.64611i
$865$			17.1044i			0.581568i
$866$	−39.4466	−	18.9334i	−1.34045	−	0.643385i
$867$	22.3770			0.759964
$868$	17.3071	−	13.8756i	0.587440	−	0.470967i
$869$		−	5.14571i		−	0.174556i
$870$	36.0442	+	17.3004i	1.22201	+	0.586538i
$871$		−	6.21846i		−	0.210704i
$872$	8.03589	+	34.5863i	0.272130	+	1.17124i
$873$		−	12.5369i		−	0.424310i
$874$	38.5936	−	20.4716i	1.30545	−	0.692462i
$875$		−	3.02772i		−	0.102355i
$876$	−46.9781	−	58.5960i	−1.58724	−	1.97978i
$877$		−	30.1261i		−	1.01729i	−0.860977	−	0.508644i	$-0.830147\pi$
$877$		−	30.1261i		−	1.01729i	0.860977	−	0.508644i	$-0.169853\pi$
$878$	15.2647	−	31.8030i	0.515160	−	1.07330i
$879$		−	24.0148i		−	0.810000i
$880$	−1.90760	−	0.424991i	−0.0643051	−	0.0143265i
$881$	−34.6286			−1.16667			−0.583333	−	0.812233i	$-0.698252\pi$
$881$	−34.6286			−1.16667			−0.583333	+	0.812233i	$0.698252\pi$
$882$	−9.69145	+	20.1915i	−0.326328	+	0.679883i
$883$			21.0760i			0.709265i	0.935006	+	0.354632i	$0.115394\pi$
$883$			21.0760i			0.709265i	−0.935006	+	0.354632i	$0.884606\pi$
$884$	−4.66043	+	3.73640i	−0.156747	+	0.125669i
$885$	27.7914			0.934198
$886$	29.9314	+	14.3664i	1.00556	+	0.482648i
$887$	26.9404			0.904570			0.452285	−	0.891873i	$-0.350609\pi$
$887$	26.9404			0.904570			0.452285	+	0.891873i	$0.350609\pi$
$888$	2.29665	+	9.88476i	0.0770707	+	0.331711i
$889$			14.0455i			0.471072i
$890$	−12.5456	−	6.02158i	−0.420528	−	0.201844i
$891$		−	10.9852i		−	0.368018i
$892$	−10.8223	−	13.4988i	−0.362359	−	0.451972i
$893$	1.65339	+	1.21973i	0.0553287	+	0.0408169i
$894$	39.9592	−	83.2523i	1.33643	−	2.78437i
$895$	11.9559			0.399640
$896$	34.2533	−	0.311161i	1.14432	−	0.0103952i
$897$	−21.4573			−0.716438
$898$	−2.51234	−	1.20587i	−0.0838380	−	0.0402403i
$899$			32.2566i			1.07582i
$900$	−9.14261	−	11.4036i	−0.304754	−	0.380121i
$901$			39.2938i			1.30907i
$902$	0.469026	−	0.977183i	0.0156168	−	0.0325367i
$903$	34.8772			1.16064
$904$	−6.46351	−	27.8188i	−0.214973	−	0.925241i
$905$		−	17.8046i		−	0.591846i
$906$	−2.65733	+	5.53637i	−0.0882839	+	0.183934i
$907$	−13.8276			−0.459137			−0.229569	−	0.973292i	$-0.573732\pi$
$907$	−13.8276			−0.459137			−0.229569	+	0.973292i	$0.573732\pi$
$908$	−2.90097	−	3.61840i	−0.0962721	−	0.120081i
$909$	69.2445			2.29670
$910$	−1.74726	+	3.64031i	−0.0579212	+	0.120675i
$911$	−4.76877			−0.157996			−0.0789982	−	0.996875i	$-0.525172\pi$
$911$	−4.76877			−0.157996			−0.0789982	+	0.996875i	$0.525172\pi$
$912$	−36.7428	−	42.2328i	−1.21668	−	1.39847i
$913$	−8.82760			−0.292151
$914$	−5.75578	+	11.9918i	−0.190384	+	0.396653i
$915$	−27.6765			−0.914955
$916$	20.9016	+	26.0706i	0.690607	+	0.861398i
$917$	−65.5140			−2.16346
$918$	−26.8066	+	55.8497i	−0.884749	+	1.84331i
$919$			46.6300i			1.53818i	0.639140	+	0.769091i	$0.279291\pi$
$919$			46.6300i			1.53818i	−0.639140	+	0.769091i	$0.720709\pi$
$920$	4.53647	+	19.5249i	0.149563	+	0.643716i
$921$	39.4667			1.30047
$922$	11.1927	−	23.3193i	0.368612	−	0.767979i
$923$			13.1353i			0.432352i
$924$	5.94181	+	7.41125i	0.195471	+	0.243812i
$925$			1.11751i			0.0367434i
$926$	−11.3414	−	5.44360i	−0.372701	−	0.178888i
$927$	−39.7959			−1.30707
$928$	−30.8034	+	39.1446i	−1.01117	+	1.28499i
$929$	23.0589			0.756537			0.378268	−	0.925696i	$-0.376520\pi$
$929$	23.0589			0.756537			0.378268	+	0.925696i	$0.376520\pi$
$930$	7.19732	−	14.9951i	0.236009	−	0.491710i
$931$	−5.60767	+	7.60139i	−0.183784	+	0.249126i
$932$	25.0748	+	31.2759i	0.821351	+	1.02448i
$933$		−	6.52815i		−	0.213722i
$934$	0.654289	+	0.314044i	0.0214090	+	0.0102758i
$935$			1.54740i			0.0506054i
$936$	4.41150	+	18.9870i	0.144194	+	0.620609i
$937$	8.32894			0.272095			0.136047	−	0.990702i	$-0.456560\pi$
$937$	8.32894			0.272095			0.136047	+	0.990702i	$0.456560\pi$
$938$	25.4546	+	12.2176i	0.831123	+	0.398920i
$939$	−75.4798			−2.46319
$940$	−0.735524	+	0.589690i	−0.0239901	+	0.0192336i
$941$			45.6945i			1.48960i	0.667289	+	0.744799i	$0.267454\pi$
$941$			45.6945i			1.48960i	−0.667289	+	0.744799i	$0.732546\pi$
$942$	−12.8277	+	26.7256i	−0.417948	+	0.870767i
$943$	−11.1172			−0.362025
$944$	−7.52934	+	33.7959i	−0.245059	+	1.09996i
$945$			41.8778i			1.36228i
$946$	1.07275	−	2.23501i	0.0348782	−	0.0726665i
$947$			48.3372i			1.57075i	0.619021	+	0.785375i	$0.287530\pi$
$947$			48.3372i			1.57075i	−0.619021	+	0.785375i	$0.712470\pi$
$948$	42.3016	+	52.7630i	1.37389	+	1.71366i
$949$			11.0297i			0.358040i
$950$	−2.88863	−	5.44572i	−0.0937195	−	0.176682i
$951$			33.8550i			1.09782i
$952$	−6.13804	−	26.4180i	−0.198935	−	0.856213i
$953$		−	4.66986i		−	0.151272i	−0.997136	−	0.0756358i	$-0.975901\pi$
$953$		−	4.66986i		−	0.151272i	0.997136	−	0.0756358i	$-0.0240986\pi$
$954$	115.602	+	55.4861i	3.74274	+	1.79643i
$955$			0.848579i			0.0274594i
$956$	29.8293	−	23.9150i	0.964749	−	0.773467i
$957$	−13.8129			−0.446509
$958$	−26.2320	−	12.5908i	−0.847517	−	0.406789i
$959$			38.0003i			1.22709i
$960$	23.0538	−	11.3241i	0.744059	−	0.365484i
$961$	−17.5806			−0.567116
$962$	0.644901	−	1.34361i	0.0207924	−	0.0433196i
$963$	−25.4090			−0.818795
$964$	−16.3536	+	13.1112i	−0.526715	+	0.422282i
$965$			23.0432i			0.741787i
$966$	42.1579	−	87.8332i	1.35641	−	2.82599i
$967$			4.19050i			0.134757i	0.997727	+	0.0673787i	$0.0214636\pi$
$967$			4.19050i			0.134757i	−0.997727	+	0.0673787i	$0.978536\pi$
$968$	−29.6478	+	6.88845i	−0.952915	+	0.221403i
$969$	−26.3121	+	35.6670i	−0.845267	+	1.14579i
$970$	2.18718	+	1.04980i	0.0702262	+	0.0337069i
$971$	−9.15781			−0.293888			−0.146944	−	0.989145i	$-0.546944\pi$
$971$	−9.15781			−0.293888			−0.146944	+	0.989145i	$0.546944\pi$
$972$	38.3955	+	47.8910i	1.23154	+	1.53610i
$973$	−18.0870			−0.579842
$974$	−0.927716	+	1.93283i	−0.0297259	+	0.0619320i
$975$			3.02772i			0.0969645i
$976$	7.49819	−	33.6560i	0.240011	−	1.07730i
$977$		−	20.6015i		−	0.659099i	−0.944138	−	0.329549i	$-0.893103\pi$
$977$		−	20.6015i		−	0.659099i	0.944138	−	0.329549i	$-0.106897\pi$
$978$	−39.4739	−	18.9466i	−1.26224	−	0.605844i
$979$	4.80773			0.153656
$980$	−2.71107	−	3.38153i	−0.0866019	−	0.108019i
$981$		−	91.7439i		−	2.92916i
$982$	−23.4757	−	11.2678i	−0.749138	−	0.359569i
$983$	−28.8332			−0.919636			−0.459818	−	0.888013i	$-0.652085\pi$
$983$	−28.8332			−0.919636			−0.459818	+	0.888013i	$0.652085\pi$
$984$	3.22389	+	13.8756i	0.102774	+	0.442337i
$985$	−1.14519			−0.0364888
$986$	35.5553	+	17.0657i	1.13231	+	0.543483i
$987$	4.58203			0.145848
$988$	0.330411	+	8.21453i	0.0105118	+	0.261339i
$989$	−25.4272			−0.808536
$990$	4.55243	+	2.18506i	0.144686	+	0.0694458i
$991$	33.2449			1.05606			0.528029	−	0.849226i	$-0.322931\pi$
$991$	33.2449			1.05606			0.528029	+	0.849226i	$0.322931\pi$
$992$	16.2850	+	12.8149i	0.517048	+	0.406872i
$993$	3.47587			0.110303
$994$	−53.7678	−	25.8073i	−1.70541	−	0.818558i
$995$			1.56194i			0.0495168i
$996$	90.5163	−	72.5694i	2.86812	−	2.29945i
$997$	−55.1366			−1.74619			−0.873097	−	0.487546i	$-0.837892\pi$
$997$	−55.1366			−1.74619			−0.873097	+	0.487546i	$0.837892\pi$
$998$	−11.4606	−	5.50082i	−0.362779	−	0.174125i
$999$		−	15.4567i		−	0.489030i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.f.a.151.13	yes	20
4.3	odd	2	inner	380.2.f.a.151.7	✓	20
19.18	odd	2	inner	380.2.f.a.151.8	yes	20
76.75	even	2	inner	380.2.f.a.151.14	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.f.a.151.7	✓	20	4.3	odd	2	inner
380.2.f.a.151.8	yes	20	19.18	odd	2	inner
380.2.f.a.151.13	yes	20	1.1	even	1	trivial
380.2.f.a.151.14	yes	20	76.75	even	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.611950 - 1.27496i) q^{2} -3.21061 q^{3} +(-1.25103 - 1.56042i) q^{4} -1.00000 q^{5} +(-1.96474 + 4.09340i) q^{6} +3.02772i q^{7} +(-2.75504 + 0.640115i) q^{8} +7.30804 q^{9} +O(q^{10})\)	\(q+(0.611950 - 1.27496i) q^{2} -3.21061 q^{3} +(-1.25103 - 1.56042i) q^{4} -1.00000 q^{5} +(-1.96474 + 4.09340i) q^{6} +3.02772i q^{7} +(-2.75504 + 0.640115i) q^{8} +7.30804 q^{9} +(-0.611950 + 1.27496i) q^{10} -0.488592i q^{11} +(4.01659 + 5.00991i) q^{12} -0.943033i q^{13} +(3.86021 + 1.85281i) q^{14} +3.21061 q^{15} +(-0.869829 + 3.90428i) q^{16} +3.16706 q^{17} +(4.47216 - 9.31745i) q^{18} +(2.58768 - 3.50769i) q^{19} +(1.25103 + 1.56042i) q^{20} -9.72083i q^{21} +(-0.622934 - 0.298994i) q^{22} +7.08696i q^{23} +(8.84538 - 2.05516i) q^{24} +1.00000 q^{25} +(-1.20233 - 0.577089i) q^{26} -13.8315 q^{27} +(4.72451 - 3.78777i) q^{28} +8.80545i q^{29} +(1.96474 - 4.09340i) q^{30} +3.66325 q^{31} +(4.44550 + 3.49822i) q^{32} +1.56868i q^{33} +(1.93809 - 4.03787i) q^{34} -3.02772i q^{35} +(-9.14261 - 11.4036i) q^{36} +1.11751i q^{37} +(-2.88863 - 5.44572i) q^{38} +3.02772i q^{39} +(2.75504 - 0.640115i) q^{40} +1.56868i q^{41} +(-12.3936 - 5.94866i) q^{42} +3.58788i q^{43} +(-0.762409 + 0.611245i) q^{44} -7.30804 q^{45} +(9.03557 + 4.33687i) q^{46} +0.471362i q^{47} +(2.79269 - 12.5351i) q^{48} -2.16706 q^{49} +(0.611950 - 1.27496i) q^{50} -10.1682 q^{51} +(-1.47153 + 1.17977i) q^{52} +12.4070i q^{53} +(-8.46417 + 17.6345i) q^{54} +0.488592i q^{55} +(-1.93809 - 8.34148i) q^{56} +(-8.30804 + 11.2618i) q^{57} +(11.2266 + 5.38850i) q^{58} +8.65611 q^{59} +(-4.01659 - 5.00991i) q^{60} -8.62030 q^{61} +(2.24173 - 4.67049i) q^{62} +22.1267i q^{63} +(7.18051 - 3.52709i) q^{64} +0.943033i q^{65} +(2.00000 + 0.959954i) q^{66} +6.59410 q^{67} +(-3.96210 - 4.94195i) q^{68} -22.7535i q^{69} +(-3.86021 - 1.85281i) q^{70} -13.9287 q^{71} +(-20.1340 + 4.67799i) q^{72} -11.6960 q^{73} +(1.42477 + 0.683858i) q^{74} -3.21061 q^{75} +(-8.71075 + 0.350370i) q^{76} +1.47932 q^{77} +(3.86021 + 1.85281i) q^{78} +10.5317 q^{79} +(0.869829 - 3.90428i) q^{80} +22.4834 q^{81} +(2.00000 + 0.959954i) q^{82} -18.0674i q^{83} +(-15.1686 + 12.1611i) q^{84} -3.16706 q^{85} +(4.57439 + 2.19560i) q^{86} -28.2709i q^{87} +(0.312755 + 1.34609i) q^{88} +9.83998i q^{89} +(-4.47216 + 9.31745i) q^{90} +2.85524 q^{91} +(11.0586 - 8.86602i) q^{92} -11.7613 q^{93} +(0.600967 + 0.288450i) q^{94} +(-2.58768 + 3.50769i) q^{95} +(-14.2728 - 11.2314i) q^{96} -1.71549i q^{97} +(-1.32614 + 2.76291i) q^{98} -3.57065i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9}+O(q^{10}) \) 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9	\( 20 q + 2 q^{4} - 20 q^{5} - 6 q^{6} + 16 q^{9} - 2 q^{16} + 20 q^{17} - 2 q^{20} + 26 q^{24} + 20 q^{25} - 14 q^{26} - 14 q^{28} + 6 q^{30} - 4 q^{36} + 10 q^{38} - 42 q^{42} + 8 q^{44} - 16 q^{45} - 30 q^{54} - 36 q^{57} + 62 q^{58} - 24 q^{61} - 40 q^{62} + 50 q^{64} + 40 q^{66} + 6 q^{68} - 36 q^{73} - 36 q^{74} - 28 q^{76} - 32 q^{77} + 2 q^{80} + 60 q^{81} + 40 q^{82} - 20 q^{85} + 26 q^{92} - 122 q^{96}+O(q^{100}) \) 20 * q + 2 * q^4 - 20 * q^5 - 6 * q^6 + 16 * q^9 - 2 * q^16 + 20 * q^17 - 2 * q^20 + 26 * q^24 + 20 * q^25 - 14 * q^26 - 14 * q^28 + 6 * q^30 - 4 * q^36 + 10 * q^38 - 42 * q^42 + 8 * q^44 - 16 * q^45 - 30 * q^54 - 36 * q^57 + 62 * q^58 - 24 * q^61 - 40 * q^62 + 50 * q^64 + 40 * q^66 + 6 * q^68 - 36 * q^73 - 36 * q^74 - 28 * q^76 - 32 * q^77 + 2 * q^80 + 60 * q^81 + 40 * q^82 - 20 * q^85 + 26 * q^92 - 122 * q^96

Introduction

L-functions

Modular forms

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Database

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