LMFDB - Embedded newform 580.2.j.a.273.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [580,2,Mod(17,580)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("580.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(580, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 580 = 2^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	580.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.63132331723$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			273.3
Character	$\chi$	$=$	580.273
Dual form			580.2.j.a.17.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.94358i q^{3} +(1.60038 + 1.56166i) q^{5} +(-2.43648 + 2.43648i) q^{7} -0.777490 q^{9} +(3.63262 + 3.63262i) q^{11} +(1.85204 - 1.85204i) q^{13} +(3.03520 - 3.11047i) q^{15} +1.85970 q^{17} +(-4.62783 + 4.62783i) q^{19} +(4.73549 + 4.73549i) q^{21} +(3.50523 + 3.50523i) q^{23} +(0.122448 + 4.99850i) q^{25} -4.31962i q^{27} +(1.62696 - 5.13352i) q^{29} +(0.975698 + 0.975698i) q^{31} +(7.06027 - 7.06027i) q^{33} +(-7.70426 + 0.0943513i) q^{35} -5.83374i q^{37} +(-3.59959 - 3.59959i) q^{39} +(4.19030 - 4.19030i) q^{41} +1.57107i q^{43} +(-1.24428 - 1.21417i) q^{45} -4.93141i q^{47} -4.87290i q^{49} -3.61448i q^{51} +(-6.32215 - 6.32215i) q^{53} +(0.140671 + 11.4865i) q^{55} +(8.99454 + 8.99454i) q^{57} +14.1373i q^{59} +(3.44633 + 3.44633i) q^{61} +(1.89434 - 1.89434i) q^{63} +(5.85623 - 0.0717192i) q^{65} +(-9.16458 - 9.16458i) q^{67} +(6.81269 - 6.81269i) q^{69} +4.34190i q^{71} +8.46750 q^{73} +(9.71497 - 0.237987i) q^{75} -17.7016 q^{77} +(8.92349 - 8.92349i) q^{79} -10.7280 q^{81} +(3.60727 + 3.60727i) q^{83} +(2.97624 + 2.90422i) q^{85} +(-9.97738 - 3.16212i) q^{87} +(-7.20998 + 7.20998i) q^{89} +9.02494i q^{91} +(1.89634 - 1.89634i) q^{93} +(-14.6334 + 0.179210i) q^{95} +13.8125i q^{97} +(-2.82432 - 2.82432i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) $ 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/580\mathbb{Z}\right)^\times$.

$n$	$117$	$291$	$321$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		−	1.94358i		−	1.12212i	−0.827774	−	0.561062i	$-0.810393\pi$
$3$		−	1.94358i		−	1.12212i	0.827774	−	0.561062i	$-0.189607\pi$
$4$		0			0
$5$	1.60038	+	1.56166i	0.715713	+	0.698395i
$5$	1.60038	+	1.56166i	0.715713	+	0.698395i
$6$		0			0
$7$	−2.43648	+	2.43648i	−0.920904	+	0.920904i	−0.997093	−	0.0761893i	$-0.975725\pi$
$7$	−2.43648	+	2.43648i	−0.920904	+	0.920904i	0.0761893	+	0.997093i	$0.475725\pi$
$8$		0			0
$9$	−0.777490			−0.259163
$10$		0			0
$11$	3.63262	+	3.63262i	1.09528	+	1.09528i	0.994955	+	0.100320i	$0.0319866\pi$
$11$	3.63262	+	3.63262i	1.09528	+	1.09528i	0.100320	+	0.994955i	$0.468013\pi$
$12$		0			0
$13$	1.85204	−	1.85204i	0.513664	−	0.513664i	−0.401983	−	0.915647i	$-0.631679\pi$
$13$	1.85204	−	1.85204i	0.513664	−	0.513664i	0.915647	+	0.401983i	$0.131679\pi$
$14$		0			0
$15$	3.03520	−	3.11047i	0.783686	−	0.803119i
$16$		0			0
$17$	1.85970			0.451044			0.225522	−	0.974238i	$-0.427591\pi$
$17$	1.85970			0.451044			0.225522	+	0.974238i	$0.427591\pi$
$18$		0			0
$19$	−4.62783	+	4.62783i	−1.06170	+	1.06170i	−0.0637294	+	0.997967i	$0.520299\pi$
$19$	−4.62783	+	4.62783i	−1.06170	+	1.06170i	−0.997967	+	0.0637294i	$0.979701\pi$
$20$		0			0
$21$	4.73549	+	4.73549i	1.03337	+	1.03337i
$22$		0			0
$23$	3.50523	+	3.50523i	0.730892	+	0.730892i	0.970796	−	0.239905i	$-0.0771161\pi$
$23$	3.50523	+	3.50523i	0.730892	+	0.730892i	−0.239905	+	0.970796i	$0.577116\pi$
$24$		0			0
$25$	0.122448	+	4.99850i	0.0244896	+	0.999700i
$26$		0			0
$27$		−	4.31962i		−	0.831311i
$28$		0			0
$29$	1.62696	−	5.13352i	0.302119	−	0.953270i
$29$	1.62696	−	5.13352i	0.302119	−	0.953270i
$30$		0			0
$31$	0.975698	+	0.975698i	0.175241	+	0.175241i	0.789277	−	0.614037i	$-0.210455\pi$
$31$	0.975698	+	0.975698i	0.175241	+	0.175241i	−0.614037	+	0.789277i	$0.710455\pi$
$32$		0			0
$33$	7.06027	−	7.06027i	1.22903	−	1.22903i
$34$		0			0
$35$	−7.70426	+	0.0943513i	−1.30226	+	0.0159483i
$36$		0			0
$37$		−	5.83374i		−	0.959061i	−0.877525	−	0.479530i	$-0.840807\pi$
$37$		−	5.83374i		−	0.959061i	0.877525	−	0.479530i	$-0.159193\pi$
$38$		0			0
$39$	−3.59959	−	3.59959i	−0.576395	−	0.576395i
$40$		0			0
$41$	4.19030	−	4.19030i	0.654414	−	0.654414i	−0.299639	−	0.954053i	$-0.596866\pi$
$41$	4.19030	−	4.19030i	0.654414	−	0.654414i	0.954053	+	0.299639i	$0.0968661\pi$
$42$		0			0
$43$			1.57107i			0.239585i	0.992799	+	0.119793i	$0.0382230\pi$
$43$			1.57107i			0.239585i	−0.992799	+	0.119793i	$0.961777\pi$
$44$		0			0
$45$	−1.24428	−	1.21417i	−0.185487	−	0.180998i
$46$		0			0
$47$		−	4.93141i		−	0.719320i	−0.933083	−	0.359660i	$-0.882893\pi$
$47$		−	4.93141i		−	0.719320i	0.933083	−	0.359660i	$-0.117107\pi$
$48$		0			0
$49$		−	4.87290i		−	0.696129i
$50$		0			0
$51$		−	3.61448i		−	0.506128i
$52$		0			0
$53$	−6.32215	−	6.32215i	−0.868414	−	0.868414i	0.123883	−	0.992297i	$-0.460465\pi$
$53$	−6.32215	−	6.32215i	−0.868414	−	0.868414i	−0.992297	+	0.123883i	$0.960465\pi$
$54$		0			0
$55$	0.140671	+	11.4865i	0.0189680	+	1.54884i
$56$		0			0
$57$	8.99454	+	8.99454i	1.19136	+	1.19136i
$58$		0			0
$59$			14.1373i			1.84052i	0.391309	+	0.920259i	$0.372022\pi$
$59$			14.1373i			1.84052i	−0.391309	+	0.920259i	$0.627978\pi$
$60$		0			0
$61$	3.44633	+	3.44633i	0.441257	+	0.441257i	0.892434	−	0.451177i	$-0.148996\pi$
$61$	3.44633	+	3.44633i	0.441257	+	0.441257i	−0.451177	+	0.892434i	$0.648996\pi$
$62$		0			0
$63$	1.89434	−	1.89434i	0.238665	−	0.238665i
$64$		0			0
$65$	5.85623	−	0.0717192i	0.726376	−	0.00889567i
$66$		0			0
$67$	−9.16458	−	9.16458i	−1.11963	−	1.11963i	−0.991795	−	0.127836i	$-0.959197\pi$
$67$	−9.16458	−	9.16458i	−1.11963	−	1.11963i	−0.127836	−	0.991795i	$-0.540803\pi$
$68$		0			0
$69$	6.81269	−	6.81269i	0.820152	−	0.820152i
$70$		0			0
$71$			4.34190i			0.515288i	0.966240	+	0.257644i	$0.0829462\pi$
$71$			4.34190i			0.515288i	−0.966240	+	0.257644i	$0.917054\pi$
$72$		0			0
$73$	8.46750			0.991046			0.495523	−	0.868595i	$-0.334976\pi$
$73$	8.46750			0.991046			0.495523	+	0.868595i	$0.334976\pi$
$74$		0			0
$75$	9.71497	−	0.237987i	1.12179	−	0.0274804i
$76$		0			0
$77$	−17.7016			−2.01729
$78$		0			0
$79$	8.92349	−	8.92349i	1.00397	−	1.00397i	0.00397952	−	0.999992i	$-0.498733\pi$
$79$	8.92349	−	8.92349i	1.00397	−	1.00397i	0.999992	−	0.00397952i	$-0.00126673\pi$
$80$		0			0
$81$	−10.7280			−1.19200
$82$		0			0
$83$	3.60727	+	3.60727i	0.395949	+	0.395949i	0.876802	−	0.480852i	$-0.159673\pi$
$83$	3.60727	+	3.60727i	0.395949	+	0.395949i	−0.480852	+	0.876802i	$0.659673\pi$
$84$		0			0
$85$	2.97624	+	2.90422i	0.322818	+	0.315007i
$86$		0			0
$87$	−9.97738	−	3.16212i	−1.06969	−	0.339015i
$88$		0			0
$89$	−7.20998	+	7.20998i	−0.764256	+	0.764256i	−0.977089	−	0.212832i	$-0.931731\pi$
$89$	−7.20998	+	7.20998i	−0.764256	+	0.764256i	0.212832	+	0.977089i	$0.431731\pi$
$90$		0			0
$91$			9.02494i			0.946071i
$92$		0			0
$93$	1.89634	−	1.89634i	0.196642	−	0.196642i
$94$		0			0
$95$	−14.6334	+	0.179210i	−1.50135	+	0.0183865i
$96$		0			0
$97$			13.8125i			1.40245i	0.712940	+	0.701225i	$0.247363\pi$
$97$			13.8125i			1.40245i	−0.712940	+	0.701225i	$0.752637\pi$
$98$		0			0
$99$	−2.82432	−	2.82432i	−0.283855	−	0.283855i
$100$		0			0
$101$	−1.66033	−	1.66033i	−0.165209	−	0.165209i	0.619661	−	0.784870i	$-0.287270\pi$
$101$	−1.66033	−	1.66033i	−0.165209	−	0.165209i	−0.784870	+	0.619661i	$0.787270\pi$
$102$		0			0
$103$	−9.73759	−	9.73759i	−0.959474	−	0.959474i	0.0397366	−	0.999210i	$-0.487348\pi$
$103$	−9.73759	−	9.73759i	−0.959474	−	0.959474i	−0.999210	+	0.0397366i	$0.987348\pi$
$104$		0			0
$105$	0.183379	+	14.9738i	0.0178959	+	1.46129i
$106$		0			0
$107$	3.26393	−	3.26393i	0.315536	−	0.315536i	−0.531514	−	0.847050i	$-0.678377\pi$
$107$	3.26393	−	3.26393i	0.315536	−	0.315536i	0.847050	+	0.531514i	$0.178377\pi$
$108$		0			0
$109$	−7.79752			−0.746867			−0.373434	−	0.927657i	$-0.621820\pi$
$109$	−7.79752			−0.746867			−0.373434	+	0.927657i	$0.621820\pi$
$110$		0			0
$111$	−11.3383			−1.07619
$112$		0			0
$113$	−12.4613			−1.17226			−0.586130	−	0.810217i	$-0.699349\pi$
$113$	−12.4613			−1.17226			−0.586130	+	0.810217i	$0.699349\pi$
$114$		0			0
$115$	0.135738	+	11.0837i	0.0126576	+	1.03356i
$116$		0			0
$117$	−1.43994	+	1.43994i	−0.133123	+	0.133123i
$118$		0			0
$119$	−4.53114	+	4.53114i	−0.415369	+	0.415369i
$120$		0			0
$121$			15.3918i			1.39926i
$122$		0			0
$123$	−8.14416	−	8.14416i	−0.734334	−	0.734334i
$124$		0			0
$125$	−7.60998	+	8.19073i	−0.680658	+	0.732602i
$126$		0			0
$127$	2.27172			0.201583			0.100791	−	0.994908i	$-0.467863\pi$
$127$	2.27172			0.201583			0.100791	+	0.994908i	$0.467863\pi$
$128$		0			0
$129$	3.05349			0.268844
$130$		0			0
$131$	6.69477	−	6.69477i	0.584925	−	0.584925i	−0.351328	−	0.936253i	$-0.614270\pi$
$131$	6.69477	−	6.69477i	0.584925	−	0.584925i	0.936253	+	0.351328i	$0.114270\pi$
$132$		0			0
$133$		−	22.5513i		−	1.95544i
$134$		0			0
$135$	6.74577	−	6.91304i	0.580583	−	0.594980i
$136$		0			0
$137$	−1.76165			−0.150508			−0.0752540	−	0.997164i	$-0.523977\pi$
$137$	−1.76165			−0.150508			−0.0752540	+	0.997164i	$0.523977\pi$
$138$		0			0
$139$		−	11.9232i		−	1.01131i	−0.862735	−	0.505656i	$-0.831251\pi$
$139$		−	11.9232i		−	1.01131i	0.862735	−	0.505656i	$-0.168749\pi$
$140$		0			0
$141$	−9.58457			−0.807166
$142$		0			0
$143$	13.4555			1.12521
$144$		0			0
$145$	10.6206	−	5.67484i	0.881989	−	0.471269i
$146$		0			0
$147$	−9.47085			−0.781143
$148$		0			0
$149$	−6.99569			−0.573109			−0.286554	−	0.958064i	$-0.592510\pi$
$149$	−6.99569			−0.573109			−0.286554	+	0.958064i	$0.592510\pi$
$150$		0			0
$151$		−	9.79368i		−	0.796999i	−0.917169	−	0.398499i	$-0.869531\pi$
$151$		−	9.79368i		−	0.796999i	0.917169	−	0.398499i	$-0.130469\pi$
$152$		0			0
$153$	−1.44590			−0.116894
$154$		0			0
$155$	0.0377833	+	3.08520i	0.00303483	+	0.247809i
$156$		0			0
$157$		−	0.907729i		−	0.0724447i	−0.999344	−	0.0362223i	$-0.988468\pi$
$157$		−	0.907729i		−	0.0724447i	0.999344	−	0.0362223i	$-0.0115324\pi$
$158$		0			0
$159$	−12.2876	+	12.2876i	−0.974468	+	0.974468i
$160$		0			0
$161$	−17.0809			−1.34616
$162$		0			0
$163$	5.16727			0.404732			0.202366	−	0.979310i	$-0.435137\pi$
$163$	5.16727			0.404732			0.202366	+	0.979310i	$0.435137\pi$
$164$		0			0
$165$	22.3249	−	0.273404i	1.73799	−	0.0212845i
$166$		0			0
$167$	−13.2215	−	13.2215i	−1.02311	−	1.02311i	−0.999727	−	0.0233839i	$-0.992556\pi$
$167$	−13.2215	−	13.2215i	−1.02311	−	1.02311i	−0.0233839	−	0.999727i	$-0.507444\pi$
$168$		0			0
$169$			6.13988i			0.472298i
$170$		0			0
$171$	3.59809	−	3.59809i	0.275153	−	0.275153i
$172$		0			0
$173$	13.0083	−	13.0083i	0.989005	−	0.989005i	−0.0109353	−	0.999940i	$-0.503481\pi$
$173$	13.0083	−	13.0083i	0.989005	−	0.989005i	0.999940	+	0.0109353i	$0.00348087\pi$
$174$		0			0
$175$	−12.4771	−	11.8804i	−0.943180	−	0.898075i
$176$		0			0
$177$	27.4769			2.06529
$178$		0			0
$179$	−20.1366			−1.50508			−0.752539	−	0.658548i	$-0.771171\pi$
$179$	−20.1366			−1.50508			−0.752539	+	0.658548i	$0.771171\pi$
$180$		0			0
$181$	22.7180			1.68862			0.844309	−	0.535857i	$-0.180011\pi$
$181$	22.7180			1.68862			0.844309	+	0.535857i	$0.180011\pi$
$182$		0			0
$183$	6.69821	−	6.69821i	0.495146	−	0.495146i
$184$		0			0
$185$	9.11030	−	9.33621i	0.669803	−	0.686412i
$186$		0			0
$187$	6.75559	+	6.75559i	0.494018	+	0.494018i
$188$		0			0
$189$	10.5247	+	10.5247i	0.765558	+	0.765558i
$190$		0			0
$191$	−17.2693	−	17.2693i	−1.24956	−	1.24956i	−0.955912	−	0.293652i	$-0.905129\pi$
$191$	−17.2693	−	17.2693i	−1.24956	−	1.24956i	−0.293652	−	0.955912i	$-0.594871\pi$
$192$		0			0
$193$			23.4530i			1.68818i	0.536200	+	0.844091i	$0.319859\pi$
$193$			23.4530i			1.68818i	−0.536200	+	0.844091i	$0.680141\pi$
$194$		0			0
$195$	−0.139392	−	11.3820i	−0.00998205	−	0.815085i
$196$		0			0
$197$	7.13393	−	7.13393i	0.508271	−	0.508271i	−0.405724	−	0.913996i	$-0.632981\pi$
$197$	7.13393	−	7.13393i	0.508271	−	0.508271i	0.913996	+	0.405724i	$0.132981\pi$
$198$		0			0
$199$			21.3233i			1.51157i	0.654821	+	0.755784i	$0.272744\pi$
$199$			21.3233i			1.51157i	−0.654821	+	0.755784i	$0.727256\pi$
$200$		0			0
$201$	−17.8121	+	17.8121i	−1.25637	+	1.25637i
$202$		0			0
$203$	8.54367	+	16.4718i	0.599648	+	1.15609i
$204$		0			0
$205$	13.2499	−	0.162267i	0.925412	−	0.0113332i
$206$		0			0
$207$	−2.72528	−	2.72528i	−0.189420	−	0.189420i
$208$		0			0
$209$	−33.6223			−2.32570
$210$		0			0
$211$	12.3746	−	12.3746i	0.851903	−	0.851903i	−0.138465	−	0.990367i	$-0.544217\pi$
$211$	12.3746	−	12.3746i	0.851903	−	0.851903i	0.990367	+	0.138465i	$0.0442168\pi$
$212$		0			0
$213$	8.43881			0.578218
$214$		0			0
$215$	−2.45347	+	2.51431i	−0.167325	+	0.171474i
$216$		0			0
$217$	−4.75454			−0.322759
$218$		0			0
$219$		−	16.4572i		−	1.11208i
$220$		0			0
$221$	3.44425	−	3.44425i	0.231685	−	0.231685i
$222$		0			0
$223$	−8.13887	−	8.13887i	−0.545019	−	0.545019i	0.379977	−	0.924996i	$-0.375932\pi$
$223$	−8.13887	−	8.13887i	−0.545019	−	0.545019i	−0.924996	+	0.379977i	$0.875932\pi$
$224$		0			0
$225$	−0.0952021	−	3.88628i	−0.00634681	−	0.259086i
$226$		0			0
$227$	−8.77793	+	8.77793i	−0.582612	+	0.582612i	−0.935620	−	0.353008i	$-0.885159\pi$
$227$	−8.77793	+	8.77793i	−0.582612	+	0.582612i	0.353008	+	0.935620i	$0.385159\pi$
$228$		0			0
$229$	−4.06560	−	4.06560i	−0.268662	−	0.268662i	0.559899	−	0.828561i	$-0.310840\pi$
$229$	−4.06560	−	4.06560i	−0.268662	−	0.268662i	−0.828561	+	0.559899i	$0.810840\pi$
$230$		0			0
$231$			34.4045i			2.26365i
$232$		0			0
$233$	−4.15853	−	4.15853i	−0.272434	−	0.272434i	0.557645	−	0.830079i	$-0.311705\pi$
$233$	−4.15853	−	4.15853i	−0.272434	−	0.272434i	−0.830079	+	0.557645i	$0.811705\pi$
$234$		0			0
$235$	7.70117	−	7.89214i	0.502369	−	0.514826i
$236$		0			0
$237$	−17.3435	−	17.3435i	−1.12658	−	1.12658i
$238$		0			0
$239$		−	21.3164i		−	1.37885i	−0.724359	−	0.689423i	$-0.757864\pi$
$239$		−	21.3164i		−	1.37885i	0.724359	−	0.689423i	$-0.242136\pi$
$240$		0			0
$241$			3.57287i			0.230149i	0.993357	+	0.115074i	$0.0367106\pi$
$241$			3.57287i			0.230149i	−0.993357	+	0.115074i	$0.963289\pi$
$242$		0			0
$243$			7.89179i			0.506259i
$244$		0			0
$245$	7.60980	−	7.79850i	0.486173	−	0.498228i
$246$		0			0
$247$			17.1419i			1.09071i
$248$		0			0
$249$	7.01100	−	7.01100i	0.444304	−	0.444304i
$250$		0			0
$251$	−2.49699	−	2.49699i	−0.157609	−	0.157609i	0.623897	−	0.781506i	$-0.285548\pi$
$251$	−2.49699	−	2.49699i	−0.157609	−	0.157609i	−0.781506	+	0.623897i	$0.785548\pi$
$252$		0			0
$253$			25.4663i			1.60106i
$254$		0			0
$255$	5.64458	−	5.78454i	0.353477	−	0.362242i
$256$		0			0
$257$	18.6910	−	18.6910i	1.16591	−	1.16591i	0.182751	−	0.983159i	$-0.441500\pi$
$257$	18.6910	−	18.6910i	1.16591	−	1.16591i	0.983159	−	0.182751i	$-0.0585001\pi$
$258$		0			0
$259$	14.2138	+	14.2138i	0.883203	+	0.883203i
$260$		0			0
$261$	−1.26494	+	3.99126i	−0.0782981	+	0.247053i
$262$		0			0
$263$			15.0919i			0.930605i	0.885152	+	0.465302i	$0.154054\pi$
$263$			15.0919i			0.930605i	−0.885152	+	0.465302i	$0.845946\pi$
$264$		0			0
$265$	−0.244821	−	19.9909i	−0.0150392	−	1.22803i
$266$		0			0
$267$	14.0132	+	14.0132i	0.857591	+	0.857591i
$268$		0			0
$269$	7.60089	+	7.60089i	0.463435	+	0.463435i	0.899780	−	0.436345i	$-0.143727\pi$
$269$	7.60089	+	7.60089i	0.463435	+	0.463435i	−0.436345	+	0.899780i	$0.643727\pi$
$270$		0			0
$271$	18.4585	−	18.4585i	1.12127	−	1.12127i	0.129725	−	0.991550i	$-0.458591\pi$
$271$	18.4585	−	18.4585i	1.12127	−	1.12127i	0.991550	−	0.129725i	$-0.0414094\pi$
$272$		0			0
$273$	17.5407			1.06161
$274$		0			0
$275$	−17.7128	+	18.6024i	−1.06812	+	1.12177i
$276$		0			0
$277$	4.41033	−	4.41033i	0.264991	−	0.264991i	−0.562087	−	0.827078i	$-0.690001\pi$
$277$	4.41033	−	4.41033i	0.264991	−	0.264991i	0.827078	+	0.562087i	$0.190001\pi$
$278$		0			0
$279$	−0.758595	−	0.758595i	−0.0454159	−	0.0454159i
$280$		0			0
$281$	−28.1452			−1.67900			−0.839502	−	0.543357i	$-0.817153\pi$
$281$	−28.1452			−1.67900			−0.839502	+	0.543357i	$0.817153\pi$
$282$		0			0
$283$	11.7512	−	11.7512i	0.698539	−	0.698539i	−0.265556	−	0.964095i	$-0.585556\pi$
$283$	11.7512	−	11.7512i	0.698539	−	0.698539i	0.964095	+	0.265556i	$0.0855556\pi$
$284$		0			0
$285$	0.348308	+	28.4411i	0.0206320	+	1.68471i
$286$		0			0
$287$			20.4192i			1.20531i
$288$		0			0
$289$	−13.5415			−0.796559
$290$		0			0
$291$	26.8457			1.57372
$292$		0			0
$293$			7.37524i			0.430866i	0.976519	+	0.215433i	$0.0691163\pi$
$293$			7.37524i			0.430866i	−0.976519	+	0.215433i	$0.930884\pi$
$294$		0			0
$295$	−22.0776	+	22.6251i	−1.28541	+	1.31728i
$296$		0			0
$297$	15.6915	−	15.6915i	0.910514	−	0.910514i
$298$		0			0
$299$	12.9837			0.750866
$300$		0			0
$301$	−3.82787	−	3.82787i	−0.220635	−	0.220635i
$302$		0			0
$303$	−3.22699	+	3.22699i	−0.185385	+	0.185385i
$304$		0			0
$305$	0.133457	+	10.8974i	0.00764172	+	0.623985i
$306$		0			0
$307$	21.0042			1.19877			0.599387	−	0.800460i	$-0.295411\pi$
$307$	21.0042			1.19877			0.599387	+	0.800460i	$0.295411\pi$
$308$		0			0
$309$	−18.9258	+	18.9258i	−1.07665	+	1.07665i
$310$		0			0
$311$	5.15195	+	5.15195i	0.292140	+	0.292140i	0.837925	−	0.545785i	$-0.183768\pi$
$311$	5.15195	+	5.15195i	0.292140	+	0.292140i	−0.545785	+	0.837925i	$0.683768\pi$
$312$		0			0
$313$	−8.00389	−	8.00389i	−0.452406	−	0.452406i	0.443746	−	0.896153i	$-0.353649\pi$
$313$	−8.00389	−	8.00389i	−0.452406	−	0.452406i	−0.896153	+	0.443746i	$0.853649\pi$
$314$		0			0
$315$	5.98998	−	0.0733572i	0.337497	−	0.00413321i
$316$		0			0
$317$		−	10.1101i		−	0.567840i	−0.958848	−	0.283920i	$-0.908365\pi$
$317$		−	10.1101i		−	0.567840i	0.958848	−	0.283920i	$-0.0916351\pi$
$318$		0			0
$319$	24.5582	−	12.7380i	1.37500	−	0.713190i
$320$		0			0
$321$	−6.34369	−	6.34369i	−0.354070	−	0.354070i
$322$		0			0
$323$	−8.60639	+	8.60639i	−0.478872	+	0.478872i
$324$		0			0
$325$	9.48421	+	9.03066i	0.526089	+	0.500931i
$326$		0			0
$327$			15.1551i			0.838078i
$328$		0			0
$329$	12.0153	+	12.0153i	0.662424	+	0.662424i
$330$		0			0
$331$	6.36944	−	6.36944i	0.350096	−	0.350096i	−0.510049	−	0.860145i	$-0.670373\pi$
$331$	6.36944	−	6.36944i	0.350096	−	0.350096i	0.860145	+	0.510049i	$0.170373\pi$
$332$		0			0
$333$			4.53567i			0.248553i
$334$		0			0
$335$	−0.354892	−	28.9788i	−0.0193898	−	1.58328i
$336$		0			0
$337$		−	4.84578i		−	0.263967i	−0.991252	−	0.131983i	$-0.957865\pi$
$337$		−	4.84578i		−	0.263967i	0.991252	−	0.131983i	$-0.0421345\pi$
$338$		0			0
$339$			24.2195i			1.31542i
$340$		0			0
$341$			7.08867i			0.383873i
$342$		0			0
$343$	−5.18264	−	5.18264i	−0.279836	−	0.279836i
$344$		0			0
$345$	21.5420	−	0.263817i	1.15978	−	0.0142034i
$346$		0			0
$347$	−13.7213	−	13.7213i	−0.736599	−	0.736599i	0.235319	−	0.971918i	$-0.424386\pi$
$347$	−13.7213	−	13.7213i	−0.736599	−	0.736599i	−0.971918	+	0.235319i	$0.924386\pi$
$348$		0			0
$349$		−	2.22026i		−	0.118848i	−0.998233	−	0.0594238i	$-0.981074\pi$
$349$		−	2.22026i		−	0.118848i	0.998233	−	0.0594238i	$-0.0189263\pi$
$350$		0			0
$351$	−8.00012	−	8.00012i	−0.427015	−	0.427015i
$352$		0			0
$353$	4.35182	−	4.35182i	0.231624	−	0.231624i	−0.581746	−	0.813370i	$-0.697630\pi$
$353$	4.35182	−	4.35182i	0.231624	−	0.231624i	0.813370	+	0.581746i	$0.197630\pi$
$354$		0			0
$355$	−6.78056	+	6.94870i	−0.359875	+	0.368798i
$356$		0			0
$357$	8.80661	+	8.80661i	0.466095	+	0.466095i
$358$		0			0
$359$	8.72309	−	8.72309i	0.460387	−	0.460387i	−0.438395	−	0.898782i	$-0.644453\pi$
$359$	8.72309	−	8.72309i	0.460387	−	0.460387i	0.898782	+	0.438395i	$0.144453\pi$
$360$		0			0
$361$		−	23.8336i		−	1.25440i
$362$		0			0
$363$	29.9152			1.57014
$364$		0			0
$365$	13.5512	+	13.2233i	0.709305	+	0.692142i
$366$		0			0
$367$	−29.2092			−1.52471			−0.762355	−	0.647159i	$-0.775957\pi$
$367$	−29.2092			−1.52471			−0.762355	+	0.647159i	$0.775957\pi$
$368$		0			0
$369$	−3.25791	+	3.25791i	−0.169600	+	0.169600i
$370$		0			0
$371$	30.8076			1.59945
$372$		0			0
$373$	0.0133883	+	0.0133883i	0.000693220	+	0.000693220i	0.707453	−	0.706760i	$-0.249844\pi$
$373$	0.0133883	+	0.0133883i	0.000693220	+	0.000693220i	−0.706760	+	0.707453i	$0.749844\pi$
$374$		0			0
$375$	15.9193	+	14.7906i	0.822070	+	0.763783i
$376$		0			0
$377$	−6.49429	−	12.5207i	−0.334473	−	0.644848i
$378$		0			0
$379$	24.5683	−	24.5683i	1.26199	−	1.26199i	0.311862	−	0.950127i	$-0.399047\pi$
$379$	24.5683	−	24.5683i	1.26199	−	1.26199i	0.950127	−	0.311862i	$-0.100953\pi$
$380$		0			0
$381$		−	4.41526i		−	0.226201i
$382$		0			0
$383$	−6.84046	+	6.84046i	−0.349531	+	0.349531i	−0.859935	−	0.510404i	$-0.829496\pi$
$383$	−6.84046	+	6.84046i	−0.349531	+	0.349531i	0.510404	+	0.859935i	$0.329496\pi$
$384$		0			0
$385$	−28.3294	−	27.6439i	−1.44380	−	1.40886i
$386$		0			0
$387$		−	1.22149i		−	0.0620917i
$388$		0			0
$389$	9.46706	+	9.46706i	0.479999	+	0.479999i	0.905131	−	0.425132i	$-0.139772\pi$
$389$	9.46706	+	9.46706i	0.479999	+	0.479999i	−0.425132	+	0.905131i	$0.639772\pi$
$390$		0			0
$391$	6.51870	+	6.51870i	0.329665	+	0.329665i
$392$		0			0
$393$	−13.0118	−	13.0118i	−0.656358	−	0.656358i
$394$		0			0
$395$	28.2165	−	0.345557i	1.41972	−	0.0173868i
$396$		0			0
$397$	−5.65219	+	5.65219i	−0.283675	+	0.283675i	−0.834573	−	0.550898i	$-0.814285\pi$
$397$	−5.65219	+	5.65219i	−0.283675	+	0.283675i	0.550898	+	0.834573i	$0.314285\pi$
$398$		0			0
$399$	−43.8301			−2.19425
$400$		0			0
$401$	23.4797			1.17252			0.586261	−	0.810122i	$-0.300599\pi$
$401$	23.4797			1.17252			0.586261	+	0.810122i	$0.300599\pi$
$402$		0			0
$403$	3.61407			0.180030
$404$		0			0
$405$	−17.1689	−	16.7534i	−0.853128	−	0.832485i
$406$		0			0
$407$	21.1917	−	21.1917i	1.05044	−	1.05044i
$408$		0			0
$409$	19.3373	−	19.3373i	0.956170	−	0.956170i	−0.0429090	−	0.999079i	$-0.513663\pi$
$409$	19.3373	−	19.3373i	0.956170	−	0.956170i	0.999079	+	0.0429090i	$0.0136626\pi$
$410$		0			0
$411$			3.42390i			0.168889i
$412$		0			0
$413$	−34.4453	−	34.4453i	−1.69494	−	1.69494i
$414$		0			0
$415$	0.139689	+	11.4063i	0.00685707	+	0.559915i
$416$		0			0
$417$	−23.1736			−1.13482
$418$		0			0
$419$	5.08083			0.248215			0.124107	−	0.992269i	$-0.460393\pi$
$419$	5.08083			0.248215			0.124107	+	0.992269i	$0.460393\pi$
$420$		0			0
$421$	−3.42631	+	3.42631i	−0.166988	+	0.166988i	−0.785654	−	0.618666i	$-0.787673\pi$
$421$	−3.42631	+	3.42631i	−0.166988	+	0.166988i	0.618666	+	0.785654i	$0.287673\pi$
$422$		0			0
$423$			3.83412i			0.186421i
$424$		0			0
$425$	0.227717	+	9.29573i	0.0110459	+	0.450909i
$426$		0			0
$427$	−16.7939			−0.812712
$428$		0			0
$429$		−	26.1518i		−	1.26262i
$430$		0			0
$431$	−1.28177			−0.0617408			−0.0308704	−	0.999523i	$-0.509828\pi$
$431$	−1.28177			−0.0617408			−0.0308704	+	0.999523i	$0.509828\pi$
$432$		0			0
$433$	2.55122			0.122604			0.0613019	−	0.998119i	$-0.480475\pi$
$433$	2.55122			0.122604			0.0613019	+	0.998119i	$0.480475\pi$
$434$		0			0
$435$	−11.0295	−	20.6419i	−0.528823	−	0.989702i
$436$		0			0
$437$	−32.4432			−1.55197
$438$		0			0
$439$	−11.2877			−0.538732			−0.269366	−	0.963038i	$-0.586814\pi$
$439$	−11.2877			−0.538732			−0.269366	+	0.963038i	$0.586814\pi$
$440$		0			0
$441$			3.78863i			0.180411i
$442$		0			0
$443$	−26.4961			−1.25887			−0.629435	−	0.777053i	$-0.716713\pi$
$443$	−26.4961			−1.25887			−0.629435	+	0.777053i	$0.716713\pi$
$444$		0			0
$445$	−22.7983	+	0.279202i	−1.08074	+	0.0132354i
$446$		0			0
$447$			13.5967i			0.643100i
$448$		0			0
$449$	−17.5874	+	17.5874i	−0.830000	+	0.830000i	−0.987516	−	0.157516i	$-0.949651\pi$
$449$	−17.5874	+	17.5874i	−0.830000	+	0.830000i	0.157516	+	0.987516i	$0.449651\pi$
$450$		0			0
$451$	30.4435			1.43353
$452$		0			0
$453$	−19.0348			−0.894332
$454$		0			0
$455$	−14.0939	+	14.4434i	−0.660731	+	0.677115i
$456$		0			0
$457$	9.95447	+	9.95447i	0.465650	+	0.465650i	0.900502	−	0.434852i	$-0.143199\pi$
$457$	9.95447	+	9.95447i	0.465650	+	0.465650i	−0.434852	+	0.900502i	$0.643199\pi$
$458$		0			0
$459$		−	8.03321i		−	0.374958i
$460$		0			0
$461$	−5.31637	+	5.31637i	−0.247608	+	0.247608i	−0.819988	−	0.572380i	$-0.806020\pi$
$461$	−5.31637	+	5.31637i	−0.247608	+	0.247608i	0.572380	+	0.819988i	$0.306020\pi$
$462$		0			0
$463$	−1.84057	+	1.84057i	−0.0855386	+	0.0855386i	−0.748581	−	0.663043i	$-0.769265\pi$
$463$	−1.84057	+	1.84057i	−0.0855386	+	0.0855386i	0.663043	+	0.748581i	$0.269265\pi$
$464$		0			0
$465$	5.99632	−	0.0734347i	0.278072	−	0.00340545i
$466$		0			0
$467$	20.4894			0.948137			0.474068	−	0.880488i	$-0.342785\pi$
$467$	20.4894			0.948137			0.474068	+	0.880488i	$0.342785\pi$
$468$		0			0
$469$	44.6587			2.06215
$470$		0			0
$471$	−1.76424			−0.0812919
$472$		0			0
$473$	−5.70708	+	5.70708i	−0.262412	+	0.262412i
$474$		0			0
$475$	−23.6989	−	22.5655i	−1.08738	−	1.03538i
$476$		0			0
$477$	4.91541	+	4.91541i	0.225061	+	0.225061i
$478$		0			0
$479$	27.5649	+	27.5649i	1.25947	+	1.25947i	0.951346	+	0.308125i	$0.0997016\pi$
$479$	27.5649	+	27.5649i	1.25947	+	1.25947i	0.308125	+	0.951346i	$0.400298\pi$
$480$		0			0
$481$	−10.8043	−	10.8043i	−0.492635	−	0.492635i
$482$		0			0
$483$			33.1980i			1.51056i
$484$		0			0
$485$	−21.5705	+	22.1053i	−0.979464	+	1.00375i
$486$		0			0
$487$	−26.5791	+	26.5791i	−1.20442	+	1.20442i	−0.231606	+	0.972810i	$0.574398\pi$
$487$	−26.5791	+	26.5791i	−1.20442	+	1.20442i	−0.972810	+	0.231606i	$0.925602\pi$
$488$		0			0
$489$		−	10.0430i		−	0.454159i
$490$		0			0
$491$	−9.98666	+	9.98666i	−0.450692	+	0.450692i	−0.895584	−	0.444892i	$-0.853242\pi$
$491$	−9.98666	+	9.98666i	−0.450692	+	0.450692i	0.444892	+	0.895584i	$0.353242\pi$
$492$		0			0
$493$	3.02566	−	9.54682i	0.136269	−	0.429967i
$494$		0			0
$495$	−0.109370	−	8.93062i	−0.00491582	−	0.401402i
$496$		0			0
$497$	−10.5790	−	10.5790i	−0.474531	−	0.474531i
$498$		0			0
$499$	20.2373			0.905947			0.452974	−	0.891524i	$-0.350363\pi$
$499$	20.2373			0.905947			0.452974	+	0.891524i	$0.350363\pi$
$500$		0			0
$501$	−25.6970	+	25.6970i	−1.14806	+	1.14806i
$502$		0			0
$503$	−7.32269			−0.326503			−0.163251	−	0.986585i	$-0.552198\pi$
$503$	−7.32269			−0.326503			−0.163251	+	0.986585i	$0.552198\pi$
$504$		0			0
$505$	−0.0642954	−	5.25004i	−0.00286111	−	0.233624i
$506$		0			0
$507$	11.9333			0.529978
$508$		0			0
$509$		−	19.7924i		−	0.877282i	−0.898662	−	0.438641i	$-0.855460\pi$
$509$		−	19.7924i		−	0.877282i	0.898662	−	0.438641i	$-0.144540\pi$
$510$		0			0
$511$	−20.6309	+	20.6309i	−0.912659	+	0.912659i
$512$		0			0
$513$	19.9905	+	19.9905i	0.882600	+	0.882600i
$514$		0			0
$515$	−0.377082	−	30.7907i	−0.0166162	−	1.35680i
$516$		0			0
$517$	17.9139	−	17.9139i	0.787853	−	0.787853i
$518$		0			0
$519$	−25.2827	−	25.2827i	−1.10979	−	1.10979i
$520$		0			0
$521$		−	19.7931i		−	0.867153i	−0.901117	−	0.433576i	$-0.857251\pi$
$521$		−	19.7931i		−	0.867153i	0.901117	−	0.433576i	$-0.142749\pi$
$522$		0			0
$523$	23.0220	+	23.0220i	1.00668	+	1.00668i	0.999978	+	0.00670228i	$0.00213342\pi$
$523$	23.0220	+	23.0220i	1.00668	+	1.00668i	0.00670228	+	0.999978i	$0.497867\pi$
$524$		0			0
$525$	−23.0905	+	24.2502i	−1.00775	+	1.05837i
$526$		0			0
$527$	1.81451	+	1.81451i	0.0790413	+	0.0790413i
$528$		0			0
$529$			1.57334i			0.0684061i
$530$		0			0
$531$		−	10.9916i		−	0.476995i
$532$		0			0
$533$		−	15.5212i		−	0.672298i
$534$		0			0
$535$	10.3207	−	0.126393i	0.446201	−	0.00546446i
$536$		0			0
$537$			39.1370i			1.68888i
$538$		0			0
$539$	17.7014	−	17.7014i	0.762452	−	0.762452i
$540$		0			0
$541$	−20.6991	−	20.6991i	−0.889924	−	0.889924i	0.104591	−	0.994515i	$-0.466646\pi$
$541$	−20.6991	−	20.6991i	−0.889924	−	0.889924i	−0.994515	+	0.104591i	$0.966646\pi$
$542$		0			0
$543$		−	44.1542i		−	1.89484i
$544$		0			0
$545$	−12.4790	−	12.1771i	−0.534542	−	0.521608i
$546$		0			0
$547$	−11.5561	+	11.5561i	−0.494103	+	0.494103i	−0.909596	−	0.415493i	$-0.863609\pi$
$547$	−11.5561	+	11.5561i	−0.494103	+	0.494103i	0.415493	+	0.909596i	$0.363609\pi$
$548$		0			0
$549$	−2.67949	−	2.67949i	−0.114358	−	0.114358i
$550$		0			0
$551$	16.2277	+	31.2863i	0.691325	+	1.33284i
$552$		0			0
$553$			43.4839i			1.84912i
$554$		0			0
$555$	−18.1456	−	17.7066i	−0.770240	−	0.751602i
$556$		0			0
$557$	27.1837	+	27.1837i	1.15181	+	1.15181i	0.986190	+	0.165619i	$0.0529621\pi$
$557$	27.1837	+	27.1837i	1.15181	+	1.15181i	0.165619	+	0.986190i	$0.447038\pi$
$558$		0			0
$559$	2.90968	+	2.90968i	0.123066	+	0.123066i
$560$		0			0
$561$	13.1300	−	13.1300i	0.554349	−	0.554349i
$562$		0			0
$563$	−30.3017			−1.27707			−0.638533	−	0.769594i	$-0.720458\pi$
$563$	−30.3017			−1.27707			−0.638533	+	0.769594i	$0.720458\pi$
$564$		0			0
$565$	−19.9428	−	19.4603i	−0.839001	−	0.818700i
$566$		0			0
$567$	26.1385	−	26.1385i	1.09772	−	1.09772i
$568$		0			0
$569$	20.8497	+	20.8497i	0.874066	+	0.874066i	0.992913	−	0.118847i	$-0.0379197\pi$
$569$	20.8497	+	20.8497i	0.874066	+	0.874066i	−0.118847	+	0.992913i	$0.537920\pi$
$570$		0			0
$571$	−36.5008			−1.52751			−0.763756	−	0.645505i	$-0.776647\pi$
$571$	−36.5008			−1.52751			−0.763756	+	0.645505i	$0.776647\pi$
$572$		0			0
$573$	−33.5643	+	33.5643i	−1.40217	+	1.40217i
$574$		0			0
$575$	−17.0917	+	17.9501i	−0.712774	+	0.748572i
$576$		0			0
$577$			26.3322i			1.09622i	0.836405	+	0.548111i	$0.184653\pi$
$577$			26.3322i			1.09622i	−0.836405	+	0.548111i	$0.815347\pi$
$578$		0			0
$579$	45.5826			1.89435
$580$		0			0
$581$	−17.5781			−0.729263
$582$		0			0
$583$		−	45.9319i		−	1.90230i
$584$		0			0
$585$	−4.55316	+	0.0557609i	−0.188250	+	0.00230543i
$586$		0			0
$587$	11.5897	−	11.5897i	0.478358	−	0.478358i	−0.426248	−	0.904606i	$-0.640165\pi$
$587$	11.5897	−	11.5897i	0.478358	−	0.478358i	0.904606	+	0.426248i	$0.140165\pi$
$588$		0			0
$589$	−9.03072			−0.372105
$590$		0			0
$591$	−13.8653	−	13.8653i	−0.570344	−	0.570344i
$592$		0			0
$593$	−2.66114	+	2.66114i	−0.109280	+	0.109280i	−0.759632	−	0.650353i	$-0.774621\pi$
$593$	−2.66114	+	2.66114i	−0.109280	+	0.109280i	0.650353	+	0.759632i	$0.274621\pi$
$594$		0			0
$595$	−14.3276	+	0.175465i	−0.587376	+	0.00719338i
$596$		0			0
$597$	41.4434			1.69617
$598$		0			0
$599$	−2.71139	+	2.71139i	−0.110784	+	0.110784i	−0.760326	−	0.649542i	$-0.774961\pi$
$599$	−2.71139	+	2.71139i	−0.110784	+	0.110784i	0.649542	+	0.760326i	$0.274961\pi$
$600$		0			0
$601$	14.2843	+	14.2843i	0.582670	+	0.582670i	0.935636	−	0.352966i	$-0.114827\pi$
$601$	14.2843	+	14.2843i	0.582670	+	0.582670i	−0.352966	+	0.935636i	$0.614827\pi$
$602$		0			0
$603$	7.12537	+	7.12537i	0.290167	+	0.290167i
$604$		0			0
$605$	−24.0367	+	24.6328i	−0.977232	+	1.00146i
$606$		0			0
$607$			42.4254i			1.72199i	0.508610	+	0.860997i	$0.330159\pi$
$607$			42.4254i			1.72199i	−0.508610	+	0.860997i	$0.669841\pi$
$608$		0			0
$609$	32.0142	−	16.6053i	1.29728	−	0.672880i
$610$		0			0
$611$	−9.13318	−	9.13318i	−0.369489	−	0.369489i
$612$		0			0
$613$	4.55331	−	4.55331i	0.183906	−	0.183906i	−0.609149	−	0.793056i	$-0.708489\pi$
$613$	4.55331	−	4.55331i	0.183906	−	0.183906i	0.793056	+	0.609149i	$0.208489\pi$
$614$		0			0
$615$	−0.315377	−	25.7522i	−0.0127172	−	1.03843i
$616$		0			0
$617$		−	41.5158i		−	1.67136i	−0.549214	−	0.835682i	$-0.685073\pi$
$617$		−	41.5158i		−	1.67136i	0.549214	−	0.835682i	$-0.314927\pi$
$618$		0			0
$619$	−21.1434	−	21.1434i	−0.849823	−	0.849823i	0.140288	−	0.990111i	$-0.455197\pi$
$619$	−21.1434	−	21.1434i	−0.849823	−	0.849823i	−0.990111	+	0.140288i	$0.955197\pi$
$620$		0			0
$621$	15.1413	−	15.1413i	0.607599	−	0.607599i
$622$		0			0
$623$		−	35.1340i		−	1.40761i
$624$		0			0
$625$	−24.9700	+	1.22411i	−0.998801	+	0.0489645i
$626$		0			0
$627$			65.3474i			2.60972i
$628$		0			0
$629$		−	10.8490i		−	0.432579i
$630$		0			0
$631$			19.2485i			0.766271i	0.923692	+	0.383135i	$0.125156\pi$
$631$			19.2485i			0.766271i	−0.923692	+	0.383135i	$0.874844\pi$
$632$		0			0
$633$	−24.0510	−	24.0510i	−0.955941	−	0.955941i
$634$		0			0
$635$	3.63562	+	3.54765i	0.144275	+	0.140784i
$636$		0			0
$637$	−9.02482	−	9.02482i	−0.357576	−	0.357576i
$638$		0			0
$639$		−	3.37578i		−	0.133544i
$640$		0			0
$641$	−12.9533	−	12.9533i	−0.511626	−	0.511626i	0.403399	−	0.915024i	$-0.367829\pi$
$641$	−12.9533	−	12.9533i	−0.511626	−	0.511626i	−0.915024	+	0.403399i	$0.867829\pi$
$642$		0			0
$643$	−31.4880	+	31.4880i	−1.24176	+	1.24176i	−0.282495	+	0.959269i	$0.591162\pi$
$643$	−31.4880	+	31.4880i	−1.24176	+	1.24176i	−0.959269	+	0.282495i	$0.908838\pi$
$644$		0			0
$645$	4.88674	+	4.76850i	0.192415	+	0.187760i
$646$		0			0
$647$	−1.10518	−	1.10518i	−0.0434492	−	0.0434492i	0.685048	−	0.728498i	$-0.259781\pi$
$647$	−1.10518	−	1.10518i	−0.0434492	−	0.0434492i	−0.728498	+	0.685048i	$0.759781\pi$
$648$		0			0
$649$	−51.3554	+	51.3554i	−2.01587	+	2.01587i
$650$		0			0
$651$			9.24082i			0.362176i
$652$		0			0
$653$	−46.0257			−1.80113			−0.900563	−	0.434725i	$-0.856846\pi$
$653$	−46.0257			−1.80113			−0.900563	+	0.434725i	$0.856846\pi$
$654$		0			0
$655$	21.1691	−	0.259251i	0.827147	−	0.0101298i
$656$		0			0
$657$	−6.58340			−0.256843
$658$		0			0
$659$	20.1694	−	20.1694i	0.785689	−	0.785689i	−0.195095	−	0.980784i	$-0.562502\pi$
$659$	20.1694	−	20.1694i	0.785689	−	0.785689i	0.980784	+	0.195095i	$0.0625016\pi$
$660$		0			0
$661$	7.27755			0.283064			0.141532	−	0.989934i	$-0.454797\pi$
$661$	7.27755			0.283064			0.141532	+	0.989934i	$0.454797\pi$
$662$		0			0
$663$	−6.69416	−	6.69416i	−0.259980	−	0.259980i
$664$		0			0
$665$	35.2173	−	36.0906i	1.36567	−	1.39953i
$666$		0			0
$667$	23.6971	−	12.2913i	0.917554	−	0.475921i
$668$		0			0
$669$	−15.8185	+	15.8185i	−0.611580	+	0.611580i
$670$		0			0
$671$			25.0384i			0.966597i
$672$		0			0
$673$	−21.2481	+	21.2481i	−0.819055	+	0.819055i	−0.985971	−	0.166916i	$-0.946619\pi$
$673$	−21.2481	+	21.2481i	−0.819055	+	0.819055i	0.166916	+	0.985971i	$0.446619\pi$
$674$		0			0
$675$	21.5916	−	0.528929i	0.831062	−	0.0203585i
$676$		0			0
$677$			14.0763i			0.540995i	0.962721	+	0.270498i	$0.0871883\pi$
$677$			14.0763i			0.540995i	−0.962721	+	0.270498i	$0.912812\pi$
$678$		0			0
$679$	−33.6540	−	33.6540i	−1.29152	−	1.29152i
$680$		0			0
$681$	17.0606	+	17.0606i	0.653763	+	0.653763i
$682$		0			0
$683$	5.54044	+	5.54044i	0.211999	+	0.211999i	0.805116	−	0.593117i	$-0.202103\pi$
$683$	5.54044	+	5.54044i	0.211999	+	0.211999i	−0.593117	+	0.805116i	$0.702103\pi$
$684$		0			0
$685$	−2.81931	−	2.75110i	−0.107720	−	0.105114i
$686$		0			0
$687$	−7.90180	+	7.90180i	−0.301473	+	0.301473i
$688$		0			0
$689$	−23.4178			−0.892146
$690$		0			0
$691$	12.8445			0.488627			0.244313	−	0.969696i	$-0.421437\pi$
$691$	12.8445			0.488627			0.244313	+	0.969696i	$0.421437\pi$
$692$		0			0
$693$	13.7628			0.522807
$694$		0			0
$695$	18.6199	−	19.0817i	0.706295	−	0.723809i
$696$		0			0
$697$	7.79271	−	7.79271i	0.295170	−	0.295170i
$698$		0			0
$699$	−8.08242	+	8.08242i	−0.305705	+	0.305705i
$700$		0			0
$701$		−	31.8398i		−	1.20257i	−0.799034	−	0.601286i	$-0.794655\pi$
$701$		−	31.8398i		−	1.20257i	0.799034	−	0.601286i	$-0.205345\pi$
$702$		0			0
$703$	26.9975	+	26.9975i	1.01823	+	1.01823i
$704$		0			0
$705$	−15.3390	−	14.9678i	−0.577699	−	0.563721i
$706$		0			0
$707$	8.09075			0.304284
$708$		0			0
$709$	23.0793			0.866760			0.433380	−	0.901211i	$-0.357321\pi$
$709$	23.0793			0.866760			0.433380	+	0.901211i	$0.357321\pi$
$710$		0			0
$711$	−6.93793	+	6.93793i	−0.260193	+	0.260193i
$712$		0			0
$713$			6.84010i			0.256164i
$714$		0			0
$715$	21.5340	+	21.0129i	0.805325	+	0.785839i
$716$		0			0
$717$	−41.4301			−1.54724
$718$		0			0
$719$			3.34874i			0.124887i	0.998049	+	0.0624435i	$0.0198893\pi$
$719$			3.34874i			0.124887i	−0.998049	+	0.0624435i	$0.980111\pi$
$720$		0			0
$721$	47.4510			1.76717
$722$		0			0
$723$	6.94415			0.258256
$724$		0			0
$725$	25.8591	+	7.50377i	0.960383	+	0.278683i
$726$		0			0
$727$	−50.1808			−1.86110			−0.930552	−	0.366159i	$-0.880673\pi$
$727$	−50.1808			−1.86110			−0.930552	+	0.366159i	$0.880673\pi$
$728$		0			0
$729$	−16.8456			−0.623912
$730$		0			0
$731$			2.92172i			0.108064i
$732$		0			0
$733$	45.2699			1.67208			0.836040	−	0.548668i	$-0.184865\pi$
$733$	45.2699			1.67208			0.836040	+	0.548668i	$0.184865\pi$
$734$		0			0
$735$	−15.1570	−	14.7902i	−0.559074	−	0.545546i
$736$		0			0
$737$		−	66.5828i		−	2.45261i
$738$		0			0
$739$	−12.2936	+	12.2936i	−0.452227	+	0.452227i	−0.896093	−	0.443866i	$-0.853607\pi$
$739$	−12.2936	+	12.2936i	−0.452227	+	0.452227i	0.443866	+	0.896093i	$0.353607\pi$
$740$		0			0
$741$	33.3165			1.22391
$742$		0			0
$743$	24.9417			0.915022			0.457511	−	0.889204i	$-0.348741\pi$
$743$	24.9417			0.915022			0.457511	+	0.889204i	$0.348741\pi$
$744$		0			0
$745$	−11.1958	−	10.9249i	−0.410181	−	0.400256i
$746$		0			0
$747$	−2.80462	−	2.80462i	−0.102616	−	0.102616i
$748$		0			0
$749$			15.9050i			0.581156i
$750$		0			0
$751$	34.8278	−	34.8278i	1.27088	−	1.27088i	0.325258	−	0.945625i	$-0.394549\pi$
$751$	34.8278	−	34.8278i	1.27088	−	1.27088i	0.945625	−	0.325258i	$-0.105451\pi$
$752$		0			0
$753$	−4.85310	+	4.85310i	−0.176857	+	0.176857i
$754$		0			0
$755$	15.2944	−	15.6736i	0.556620	−	0.570422i
$756$		0			0
$757$	−5.15668			−0.187423			−0.0937114	−	0.995599i	$-0.529873\pi$
$757$	−5.15668			−0.187423			−0.0937114	+	0.995599i	$0.529873\pi$
$758$		0			0
$759$	49.4958			1.79658
$760$		0			0
$761$	−43.6585			−1.58262			−0.791309	−	0.611416i	$-0.790600\pi$
$761$	−43.6585			−1.58262			−0.791309	+	0.611416i	$0.790600\pi$
$762$		0			0
$763$	18.9985	−	18.9985i	0.687793	−	0.687793i
$764$		0			0
$765$	−2.31399	−	2.25800i	−0.0836626	−	0.0816383i
$766$		0			0
$767$	26.1829	+	26.1829i	0.945408	+	0.945408i
$768$		0			0
$769$	21.5060	+	21.5060i	0.775528	+	0.775528i	0.979067	−	0.203539i	$-0.0652445\pi$
$769$	21.5060	+	21.5060i	0.775528	+	0.775528i	−0.203539	+	0.979067i	$0.565244\pi$
$770$		0			0
$771$	−36.3273	−	36.3273i	−1.30830	−	1.30830i
$772$		0			0
$773$			31.7441i			1.14176i	0.821034	+	0.570879i	$0.193397\pi$
$773$			31.7441i			1.14176i	−0.821034	+	0.570879i	$0.806603\pi$
$774$		0			0
$775$	−4.75755	+	4.99650i	−0.170896	+	0.179480i
$776$		0			0
$777$	27.6256	−	27.6256i	0.991063	−	0.991063i
$778$		0			0
$779$			38.7839i			1.38958i
$780$		0			0
$781$	−15.7724	+	15.7724i	−0.564383	+	0.564383i
$782$		0			0
$783$	−22.1748	−	7.02785i	−0.792464	−	0.251155i
$784$		0			0
$785$	1.41756	−	1.45271i	0.0505950	−	0.0518496i
$786$		0			0
$787$	11.7538	+	11.7538i	0.418976	+	0.418976i	0.884851	−	0.465875i	$-0.154260\pi$
$787$	11.7538	+	11.7538i	0.418976	+	0.418976i	−0.465875	+	0.884851i	$0.654260\pi$
$788$		0			0
$789$	29.3322			1.04425
$790$		0			0
$791$	30.3617	−	30.3617i	1.07954	−	1.07954i
$792$		0			0
$793$	12.7655			0.453316
$794$		0			0
$795$	−38.8538	+	0.475829i	−1.37800	+	0.0168759i
$796$		0			0
$797$	42.5873			1.50852			0.754260	−	0.656576i	$-0.227996\pi$
$797$	42.5873			1.50852			0.754260	+	0.656576i	$0.227996\pi$
$798$		0			0
$799$		−	9.17096i		−	0.324445i
$800$		0			0
$801$	5.60569	−	5.60569i	0.198067	−	0.198067i
$802$		0			0
$803$	30.7592	+	30.7592i	1.08547	+	1.08547i
$804$		0			0
$805$	−27.3360	−	26.6745i	−0.963466	−	0.940153i
$806$		0			0
$807$	14.7729	−	14.7729i	0.520031	−	0.520031i
$808$		0			0
$809$	3.54567	+	3.54567i	0.124659	+	0.124659i	0.766684	−	0.642025i	$-0.221905\pi$
$809$	3.54567	+	3.54567i	0.124659	+	0.124659i	−0.642025	+	0.766684i	$0.721905\pi$
$810$		0			0
$811$			13.3074i			0.467286i	0.972322	+	0.233643i	$0.0750647\pi$
$811$			13.3074i			0.467286i	−0.972322	+	0.233643i	$0.924935\pi$
$812$		0			0
$813$	−35.8755	−	35.8755i	−1.25821	−	1.25821i
$814$		0			0
$815$	8.26960	+	8.06950i	0.289672	+	0.282662i
$816$		0			0
$817$	−7.27062	−	7.27062i	−0.254367	−	0.254367i
$818$		0			0
$819$		−	7.01680i		−	0.245187i
$820$		0			0
$821$			18.3092i			0.638996i	0.947587	+	0.319498i	$0.103514\pi$
$821$			18.3092i			0.638996i	−0.947587	+	0.319498i	$0.896486\pi$
$822$		0			0
$823$			52.4736i			1.82912i	0.404456	+	0.914558i	$0.367461\pi$
$823$			52.4736i			1.82912i	−0.404456	+	0.914558i	$0.632539\pi$
$824$		0			0
$825$	36.1553	+	34.4262i	1.25876	+	1.19857i
$826$		0			0
$827$			5.44121i			0.189209i	0.995515	+	0.0946047i	$0.0301587\pi$
$827$			5.44121i			0.189209i	−0.995515	+	0.0946047i	$0.969841\pi$
$828$		0			0
$829$	−3.07163	+	3.07163i	−0.106682	+	0.106682i	−0.758433	−	0.651751i	$-0.774035\pi$
$829$	−3.07163	+	3.07163i	−0.106682	+	0.106682i	0.651751	+	0.758433i	$0.274035\pi$
$830$		0			0
$831$	−8.57181	−	8.57181i	−0.297353	−	0.297353i
$832$		0			0
$833$		−	9.06215i		−	0.313985i
$834$		0			0
$835$	−0.511994	−	41.8069i	−0.0177183	−	1.44679i
$836$		0			0
$837$	4.21464	−	4.21464i	0.145679	−	0.145679i
$838$		0			0
$839$	−18.1044	−	18.1044i	−0.625033	−	0.625033i	0.321781	−	0.946814i	$-0.395718\pi$
$839$	−18.1044	−	18.1044i	−0.625033	−	0.625033i	−0.946814	+	0.321781i	$0.895718\pi$
$840$		0			0
$841$	−23.7060	−	16.7041i	−0.817448	−	0.576002i
$842$		0			0
$843$			54.7024i			1.88405i
$844$		0			0
$845$	−9.58839	+	9.82615i	−0.329851	+	0.338030i
$846$		0			0
$847$	−37.5019	−	37.5019i	−1.28858	−	1.28858i
$848$		0			0
$849$	−22.8394	−	22.8394i	−0.783848	−	0.783848i
$850$		0			0
$851$	20.4486	−	20.4486i	0.700970	−	0.700970i
$852$		0			0
$853$	−44.2478			−1.51502			−0.757509	−	0.652825i	$-0.773584\pi$
$853$	−44.2478			−1.51502			−0.757509	+	0.652825i	$0.773584\pi$
$854$		0			0
$855$	11.3773	−	0.139334i	0.389096	−	0.00476511i
$856$		0			0
$857$	−9.83388	+	9.83388i	−0.335919	+	0.335919i	−0.854829	−	0.518910i	$-0.826338\pi$
$857$	−9.83388	+	9.83388i	−0.335919	+	0.335919i	0.518910	+	0.854829i	$0.326338\pi$
$858$		0			0
$859$	16.3239	+	16.3239i	0.556963	+	0.556963i	0.928441	−	0.371479i	$-0.121149\pi$
$859$	16.3239	+	16.3239i	0.556963	+	0.556963i	−0.371479	+	0.928441i	$0.621149\pi$
$860$		0			0
$861$	39.6862			1.35250
$862$		0			0
$863$	−9.34319	+	9.34319i	−0.318046	+	0.318046i	−0.848016	−	0.529970i	$-0.822203\pi$
$863$	−9.34319	+	9.34319i	−0.318046	+	0.318046i	0.529970	+	0.848016i	$0.322203\pi$
$864$		0			0
$865$	41.1329	−	0.503739i	1.39856	−	0.0171276i
$866$		0			0
$867$			26.3189i			0.893838i
$868$		0			0
$869$	64.8313			2.19925
$870$		0			0
$871$	−33.9464			−1.15023
$872$		0			0
$873$		−	10.7391i		−	0.363464i
$874$		0			0
$875$	−1.41499	−	38.4982i	−0.0478353	−	1.30148i
$876$		0			0
$877$	27.3843	−	27.3843i	0.924701	−	0.924701i	−0.0726561	−	0.997357i	$-0.523148\pi$
$877$	27.3843	−	27.3843i	0.924701	−	0.924701i	0.997357	+	0.0726561i	$0.0231476\pi$
$878$		0			0
$879$	14.3343			0.483485
$880$		0			0
$881$	8.60229	+	8.60229i	0.289818	+	0.289818i	0.837008	−	0.547190i	$-0.184302\pi$
$881$	8.60229	+	8.60229i	0.289818	+	0.289818i	−0.547190	+	0.837008i	$0.684302\pi$
$882$		0			0
$883$	8.10629	−	8.10629i	0.272798	−	0.272798i	−0.557427	−	0.830226i	$-0.688211\pi$
$883$	8.10629	−	8.10629i	0.272798	−	0.272798i	0.830226	+	0.557427i	$0.188211\pi$
$884$		0			0
$885$	43.9736	+	42.9095i	1.47815	+	1.44239i
$886$		0			0
$887$	−26.9610			−0.905262			−0.452631	−	0.891698i	$-0.649515\pi$
$887$	−26.9610			−0.905262			−0.452631	+	0.891698i	$0.649515\pi$
$888$		0			0
$889$	−5.53501	+	5.53501i	−0.185638	+	0.185638i
$890$		0			0
$891$	−38.9706	−	38.9706i	−1.30557	−	1.30557i
$892$		0			0
$893$	22.8217	+	22.8217i	0.763699	+	0.763699i
$894$		0			0
$895$	−32.2262	−	31.4464i	−1.07720	−	1.05114i
$896$		0			0
$897$		−	25.2348i		−	0.842565i
$898$		0			0
$899$	6.59618	−	3.42134i	0.219995	−	0.114108i
$900$		0			0
$901$	−11.7573	−	11.7573i	−0.391693	−	0.391693i
$902$		0			0
$903$	−7.43977	+	7.43977i	−0.247580	+	0.247580i
$904$		0			0
$905$	36.3575	+	35.4778i	1.20856	+	1.17932i
$906$		0			0
$907$			3.84036i			0.127517i	0.997965	+	0.0637586i	$0.0203088\pi$
$907$			3.84036i			0.127517i	−0.997965	+	0.0637586i	$0.979691\pi$
$908$		0			0
$909$	1.29089	+	1.29089i	0.0428162	+	0.0428162i
$910$		0			0
$911$	3.60131	−	3.60131i	0.119317	−	0.119317i	−0.644927	−	0.764244i	$-0.723112\pi$
$911$	3.60131	−	3.60131i	0.119317	−	0.119317i	0.764244	+	0.644927i	$0.223112\pi$
$912$		0			0
$913$			26.2077i			0.867347i
$914$		0			0
$915$	21.1800	−	0.259384i	0.700189	−	0.00857497i
$916$		0			0
$917$			32.6234i			1.07732i
$918$		0			0
$919$		−	15.2170i		−	0.501964i	−0.967992	−	0.250982i	$-0.919247\pi$
$919$		−	15.2170i		−	0.501964i	0.967992	−	0.250982i	$-0.0807535\pi$
$920$		0			0
$921$		−	40.8233i		−	1.34517i
$922$		0			0
$923$	8.04138	+	8.04138i	0.264685	+	0.264685i
$924$		0			0
$925$	29.1599	−	0.714330i	0.958773	−	0.0234870i
$926$		0			0
$927$	7.57088	+	7.57088i	0.248660	+	0.248660i
$928$		0			0
$929$			35.3848i			1.16094i	0.814283	+	0.580468i	$0.197131\pi$
$929$			35.3848i			1.16094i	−0.814283	+	0.580468i	$0.802869\pi$
$930$		0			0
$931$	22.5509	+	22.5509i	0.739077	+	0.739077i
$932$		0			0
$933$	10.0132	−	10.0132i	0.327818	−	0.327818i
$934$		0			0
$935$	0.261606	+	21.3615i	0.00855543	+	0.698594i
$936$		0			0
$937$	37.6363	+	37.6363i	1.22953	+	1.22953i	0.964143	+	0.265382i	$0.0854982\pi$
$937$	37.6363	+	37.6363i	1.22953	+	1.22953i	0.265382	+	0.964143i	$0.414502\pi$
$938$		0			0
$939$	−15.5562	+	15.5562i	−0.507656	+	0.507656i
$940$		0			0
$941$			21.5542i			0.702646i	0.936254	+	0.351323i	$0.114268\pi$
$941$			21.5542i			0.702646i	−0.936254	+	0.351323i	$0.885732\pi$
$942$		0			0
$943$	29.3759			0.956612
$944$		0			0
$945$	0.407561	+	33.2795i	0.0132580	+	1.08258i
$946$		0			0
$947$	39.0914			1.27030			0.635151	−	0.772388i	$-0.280938\pi$
$947$	39.0914			1.27030			0.635151	+	0.772388i	$0.280938\pi$
$948$		0			0
$949$	15.6822	−	15.6822i	0.509065	−	0.509065i
$950$		0			0
$951$	−19.6498			−0.637187
$952$		0			0
$953$	−3.52102	−	3.52102i	−0.114057	−	0.114057i	0.647775	−	0.761832i	$-0.275700\pi$
$953$	−3.52102	−	3.52102i	−0.114057	−	0.114057i	−0.761832	+	0.647775i	$0.775700\pi$
$954$		0			0
$955$	−0.668744	−	54.6063i	−0.0216400	−	1.76702i
$956$		0			0
$957$	−24.7572	−	47.7308i	−0.800288	−	1.54292i
$958$		0			0
$959$	4.29223	−	4.29223i	0.138603	−	0.138603i
$960$		0			0
$961$		−	29.0960i		−	0.938582i
$962$		0			0
$963$	−2.53767	+	2.53767i	−0.0817752	+	0.0817752i
$964$		0			0
$965$	−36.6255	+	37.5337i	−1.17902	+	1.20825i
$966$		0			0
$967$			22.4246i			0.721125i	0.932735	+	0.360562i	$0.117415\pi$
$967$			22.4246i			0.721125i	−0.932735	+	0.360562i	$0.882585\pi$
$968$		0			0
$969$	16.7272	+	16.7272i	0.537354	+	0.537354i
$970$		0			0
$971$	−17.2394	−	17.2394i	−0.553238	−	0.553238i	0.374136	−	0.927374i	$-0.377939\pi$
$971$	−17.2394	−	17.2394i	−0.553238	−	0.553238i	−0.927374	+	0.374136i	$0.877939\pi$
$972$		0			0
$973$	29.0506	+	29.0506i	0.931321	+	0.931321i
$974$		0			0
$975$	17.5518	−	18.4333i	0.562107	−	0.590338i
$976$		0			0
$977$	−41.4310	+	41.4310i	−1.32549	+	1.32549i	−0.416240	+	0.909255i	$0.636652\pi$
$977$	−41.4310	+	41.4310i	−1.32549	+	1.32549i	−0.909255	+	0.416240i	$0.863348\pi$
$978$		0			0
$979$	−52.3822			−1.67414
$980$		0			0
$981$	6.06250			0.193561
$982$		0			0
$983$	9.90815			0.316021			0.158010	−	0.987437i	$-0.449492\pi$
$983$	9.90815			0.316021			0.158010	+	0.987437i	$0.449492\pi$
$984$		0			0
$985$	22.5578	−	0.276257i	0.718750	−	0.00880227i
$986$		0			0
$987$	23.3526	−	23.3526i	0.743323	−	0.743323i
$988$		0			0
$989$	−5.50695	+	5.50695i	−0.175111	+	0.175111i
$990$		0			0
$991$			19.1659i			0.608824i	0.952541	+	0.304412i	$0.0984599\pi$
$991$			19.1659i			0.608824i	−0.952541	+	0.304412i	$0.901540\pi$
$992$		0			0
$993$	−12.3795	−	12.3795i	−0.392851	−	0.392851i
$994$		0			0
$995$	−33.2997	+	34.1254i	−1.05567	+	1.08185i
$996$		0			0
$997$	16.5779			0.525027			0.262513	−	0.964928i	$-0.415449\pi$
$997$	16.5779			0.525027			0.262513	+	0.964928i	$0.415449\pi$
$998$		0			0
$999$	−25.1995			−0.797278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	580.2.j.a.273.3	yes	30
5.2	odd	4		580.2.s.a.157.3	yes	30
5.3	odd	4		2900.2.s.d.157.13		30
5.4	even	2		2900.2.j.d.2593.13		30
29.17	odd	4		580.2.s.a.133.3	yes	30
145.17	even	4	inner	580.2.j.a.17.13	✓	30
145.104	odd	4		2900.2.s.d.1293.13		30
145.133	even	4		2900.2.j.d.1757.3		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.2.j.a.17.13	✓	30	145.17	even	4	inner
580.2.j.a.273.3	yes	30	1.1	even	1	trivial
580.2.s.a.133.3	yes	30	29.17	odd	4
580.2.s.a.157.3	yes	30	5.2	odd	4
2900.2.j.d.1757.3		30	145.133	even	4
2900.2.j.d.2593.13		30	5.4	even	2
2900.2.s.d.157.13		30	5.3	odd	4
2900.2.s.d.1293.13		30	145.104	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.94358i q^{3} +(1.60038 + 1.56166i) q^{5} +(-2.43648 + 2.43648i) q^{7} -0.777490 q^{9} +(3.63262 + 3.63262i) q^{11} +(1.85204 - 1.85204i) q^{13} +(3.03520 - 3.11047i) q^{15} +1.85970 q^{17} +(-4.62783 + 4.62783i) q^{19} +(4.73549 + 4.73549i) q^{21} +(3.50523 + 3.50523i) q^{23} +(0.122448 + 4.99850i) q^{25} -4.31962i q^{27} +(1.62696 - 5.13352i) q^{29} +(0.975698 + 0.975698i) q^{31} +(7.06027 - 7.06027i) q^{33} +(-7.70426 + 0.0943513i) q^{35} -5.83374i q^{37} +(-3.59959 - 3.59959i) q^{39} +(4.19030 - 4.19030i) q^{41} +1.57107i q^{43} +(-1.24428 - 1.21417i) q^{45} -4.93141i q^{47} -4.87290i q^{49} -3.61448i q^{51} +(-6.32215 - 6.32215i) q^{53} +(0.140671 + 11.4865i) q^{55} +(8.99454 + 8.99454i) q^{57} +14.1373i q^{59} +(3.44633 + 3.44633i) q^{61} +(1.89434 - 1.89434i) q^{63} +(5.85623 - 0.0717192i) q^{65} +(-9.16458 - 9.16458i) q^{67} +(6.81269 - 6.81269i) q^{69} +4.34190i q^{71} +8.46750 q^{73} +(9.71497 - 0.237987i) q^{75} -17.7016 q^{77} +(8.92349 - 8.92349i) q^{79} -10.7280 q^{81} +(3.60727 + 3.60727i) q^{83} +(2.97624 + 2.90422i) q^{85} +(-9.97738 - 3.16212i) q^{87} +(-7.20998 + 7.20998i) q^{89} +9.02494i q^{91} +(1.89634 - 1.89634i) q^{93} +(-14.6334 + 0.179210i) q^{95} +13.8125i q^{97} +(-2.82432 - 2.82432i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) \) 30 * q - 38 * q^9 - 4 * q^11 + 6 * q^13 + 14 * q^15 + 12 * q^17 - 4 * q^21 - 2 * q^25 - 4 * q^31 - 4 * q^33 + 16 * q^35 + 12 * q^39 + 10 * q^41 - 20 * q^45 - 18 * q^53 - 2 * q^55 - 24 * q^57 - 22 * q^61 - 24 * q^63 - 10 * q^65 - 16 * q^67 + 8 * q^69 - 20 * q^73 + 34 * q^75 + 20 * q^77 + 20 * q^79 + 70 * q^81 + 56 * q^83 + 12 * q^85 + 4 * q^87 + 6 * q^89 - 44 * q^93 - 60 * q^95

Introduction

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