LMFDB - Embedded newform 580.2.j.a.273.4

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			273.4
Character	$\chi$	$=$	580.273
Dual form			580.2.j.a.17.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.61432i q^{3} +(-1.66951 + 1.48752i) q^{5} +(1.96009 - 1.96009i) q^{7} +0.393986 q^{9} +(1.97757 + 1.97757i) q^{11} +(1.79751 - 1.79751i) q^{13} +(2.40133 + 2.69512i) q^{15} -3.77934 q^{17} +(3.84455 - 3.84455i) q^{19} +(-3.16420 - 3.16420i) q^{21} +(-3.28633 - 3.28633i) q^{23} +(0.574554 - 4.96688i) q^{25} -5.47896i q^{27} +(0.143119 - 5.38326i) q^{29} +(6.28310 + 6.28310i) q^{31} +(3.19243 - 3.19243i) q^{33} +(-0.356719 + 6.18807i) q^{35} -2.84861i q^{37} +(-2.90174 - 2.90174i) q^{39} +(-0.715885 + 0.715885i) q^{41} -1.15641i q^{43} +(-0.657765 + 0.586063i) q^{45} +1.02010i q^{47} -0.683883i q^{49} +6.10105i q^{51} +(-1.96686 - 1.96686i) q^{53} +(-6.24328 - 0.359902i) q^{55} +(-6.20632 - 6.20632i) q^{57} -6.60253i q^{59} +(-2.62953 - 2.62953i) q^{61} +(0.772246 - 0.772246i) q^{63} +(-0.327131 + 5.67479i) q^{65} +(5.70401 + 5.70401i) q^{67} +(-5.30517 + 5.30517i) q^{69} +10.2338i q^{71} +12.4381 q^{73} +(-8.01811 - 0.927511i) q^{75} +7.75244 q^{77} +(-8.41306 + 8.41306i) q^{79} -7.66282 q^{81} +(2.10823 + 2.10823i) q^{83} +(6.30966 - 5.62185i) q^{85} +(-8.69028 - 0.231039i) q^{87} +(-2.72236 + 2.72236i) q^{89} -7.04653i q^{91} +(10.1429 - 10.1429i) q^{93} +(-0.699676 + 12.1374i) q^{95} +1.98353i q^{97} +(0.779136 + 0.779136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$		−	1.61432i		−	0.932025i	−0.884778	−	0.466013i	$-0.845690\pi$
$3$		−	1.61432i		−	0.932025i	0.884778	−	0.466013i	$-0.154310\pi$
$4$		0			0
$5$	−1.66951	+	1.48752i	−0.746629	+	0.665240i
$5$	−1.66951	+	1.48752i	−0.746629	+	0.665240i
$6$		0			0
$7$	1.96009	−	1.96009i	0.740843	−	0.740843i	−0.231897	−	0.972740i	$-0.574493\pi$
$7$	1.96009	−	1.96009i	0.740843	−	0.740843i	0.972740	+	0.231897i	$0.0744933\pi$
$8$		0			0
$9$	0.393986			0.131329
$10$		0			0
$11$	1.97757	+	1.97757i	0.596261	+	0.596261i	0.939316	−	0.343054i	$-0.111462\pi$
$11$	1.97757	+	1.97757i	0.596261	+	0.596261i	−0.343054	+	0.939316i	$0.611462\pi$
$12$		0			0
$13$	1.79751	−	1.79751i	0.498538	−	0.498538i	−0.412444	−	0.910983i	$-0.635325\pi$
$13$	1.79751	−	1.79751i	0.498538	−	0.498538i	0.910983	+	0.412444i	$0.135325\pi$
$14$		0			0
$15$	2.40133	+	2.69512i	0.620021	+	0.695878i
$16$		0			0
$17$	−3.77934			−0.916625			−0.458312	−	0.888791i	$-0.651546\pi$
$17$	−3.77934			−0.916625			−0.458312	+	0.888791i	$0.651546\pi$
$18$		0			0
$19$	3.84455	−	3.84455i	0.882001	−	0.882001i	−0.111737	−	0.993738i	$-0.535641\pi$
$19$	3.84455	−	3.84455i	0.882001	−	0.882001i	0.993738	+	0.111737i	$0.0356413\pi$
$20$		0			0
$21$	−3.16420	−	3.16420i	−0.690485	−	0.690485i
$22$		0			0
$23$	−3.28633	−	3.28633i	−0.685246	−	0.685246i	0.275931	−	0.961177i	$-0.411014\pi$
$23$	−3.28633	−	3.28633i	−0.685246	−	0.685246i	−0.961177	+	0.275931i	$0.911014\pi$
$24$		0			0
$25$	0.574554	−	4.96688i	0.114911	−	0.993376i
$26$		0			0
$27$		−	5.47896i		−	1.05443i
$28$		0			0
$29$	0.143119	−	5.38326i	0.0265765	−	0.999647i
$29$	0.143119	−	5.38326i	0.0265765	−	0.999647i
$30$		0			0
$31$	6.28310	+	6.28310i	1.12848	+	1.12848i	0.990425	+	0.138052i	$0.0440842\pi$
$31$	6.28310	+	6.28310i	1.12848	+	1.12848i	0.138052	+	0.990425i	$0.455916\pi$
$32$		0			0
$33$	3.19243	−	3.19243i	0.555731	−	0.555731i
$34$		0			0
$35$	−0.356719	+	6.18807i	−0.0602965	+	1.04597i
$36$		0			0
$37$		−	2.84861i		−	0.468309i	−0.972199	−	0.234154i	$-0.924768\pi$
$37$		−	2.84861i		−	0.468309i	0.972199	−	0.234154i	$-0.0752321\pi$
$38$		0			0
$39$	−2.90174	−	2.90174i	−0.464650	−	0.464650i
$40$		0			0
$41$	−0.715885	+	0.715885i	−0.111802	+	0.111802i	−0.760795	−	0.648992i	$-0.775191\pi$
$41$	−0.715885	+	0.715885i	−0.111802	+	0.111802i	0.648992	+	0.760795i	$0.275191\pi$
$42$		0			0
$43$		−	1.15641i		−	0.176351i	−0.996105	−	0.0881756i	$-0.971896\pi$
$43$		−	1.15641i		−	0.176351i	0.996105	−	0.0881756i	$-0.0281037\pi$
$44$		0			0
$45$	−0.657765	+	0.586063i	−0.0980538	+	0.0873651i
$46$		0			0
$47$			1.02010i			0.148796i	0.997229	+	0.0743982i	$0.0237036\pi$
$47$			1.02010i			0.148796i	−0.997229	+	0.0743982i	$0.976296\pi$
$48$		0			0
$49$		−	0.683883i		−	0.0976975i
$50$		0			0
$51$			6.10105i			0.854318i
$52$		0			0
$53$	−1.96686	−	1.96686i	−0.270168	−	0.270168i	0.559000	−	0.829168i	$-0.311185\pi$
$53$	−1.96686	−	1.96686i	−0.270168	−	0.270168i	−0.829168	+	0.559000i	$0.811185\pi$
$54$		0			0
$55$	−6.24328	−	0.359902i	−0.841843	−	0.0485291i
$56$		0			0
$57$	−6.20632	−	6.20632i	−0.822048	−	0.822048i
$58$		0			0
$59$		−	6.60253i		−	0.859576i	−0.902930	−	0.429788i	$-0.858588\pi$
$59$		−	6.60253i		−	0.859576i	0.902930	−	0.429788i	$-0.141412\pi$
$60$		0			0
$61$	−2.62953	−	2.62953i	−0.336676	−	0.336676i	0.518439	−	0.855115i	$-0.326513\pi$
$61$	−2.62953	−	2.62953i	−0.336676	−	0.336676i	−0.855115	+	0.518439i	$0.826513\pi$
$62$		0			0
$63$	0.772246	−	0.772246i	0.0972939	−	0.0972939i
$64$		0			0
$65$	−0.327131	+	5.67479i	−0.0405756	+	0.703871i
$66$		0			0
$67$	5.70401	+	5.70401i	0.696856	+	0.696856i	0.963731	−	0.266875i	$-0.0859910\pi$
$67$	5.70401	+	5.70401i	0.696856	+	0.696856i	−0.266875	+	0.963731i	$0.585991\pi$
$68$		0			0
$69$	−5.30517	+	5.30517i	−0.638667	+	0.638667i
$70$		0			0
$71$			10.2338i			1.21452i	0.794502	+	0.607262i	$0.207732\pi$
$71$			10.2338i			1.21452i	−0.794502	+	0.607262i	$0.792268\pi$
$72$		0			0
$73$	12.4381			1.45577			0.727886	−	0.685698i	$-0.240503\pi$
$73$	12.4381			1.45577			0.727886	+	0.685698i	$0.240503\pi$
$74$		0			0
$75$	−8.01811	−	0.927511i	−0.925852	−	0.107100i
$76$		0			0
$77$	7.75244			0.883472
$78$		0			0
$79$	−8.41306	+	8.41306i	−0.946544	+	0.946544i	−0.998642	−	0.0520983i	$-0.983409\pi$
$79$	−8.41306	+	8.41306i	−0.946544	+	0.946544i	0.0520983	+	0.998642i	$0.483409\pi$
$80$		0			0
$81$	−7.66282			−0.851424
$82$		0			0
$83$	2.10823	+	2.10823i	0.231408	+	0.231408i	0.813280	−	0.581872i	$-0.197680\pi$
$83$	2.10823	+	2.10823i	0.231408	+	0.231408i	−0.581872	+	0.813280i	$0.697680\pi$
$84$		0			0
$85$	6.30966	−	5.62185i	0.684379	−	0.609776i
$86$		0			0
$87$	−8.69028	−	0.231039i	−0.931696	−	0.0247699i
$88$		0			0
$89$	−2.72236	+	2.72236i	−0.288570	+	0.288570i	−0.836515	−	0.547945i	$-0.815410\pi$
$89$	−2.72236	+	2.72236i	−0.288570	+	0.288570i	0.547945	+	0.836515i	$0.315410\pi$
$90$		0			0
$91$		−	7.04653i		−	0.738677i
$92$		0			0
$93$	10.1429	−	10.1429i	1.05177	−	1.05177i
$94$		0			0
$95$	−0.699676	+	12.1374i	−0.0717852	+	1.24527i
$96$		0			0
$97$			1.98353i			0.201397i	0.994917	+	0.100699i	$0.0321078\pi$
$97$			1.98353i			0.201397i	−0.994917	+	0.100699i	$0.967892\pi$
$98$		0			0
$99$	0.779136	+	0.779136i	0.0783061	+	0.0783061i
$100$		0			0
$101$	12.5084	+	12.5084i	1.24464	+	1.24464i	0.958057	+	0.286579i	$0.0925182\pi$
$101$	12.5084	+	12.5084i	1.24464	+	1.24464i	0.286579	+	0.958057i	$0.407482\pi$
$102$		0			0
$103$	3.19708	+	3.19708i	0.315017	+	0.315017i	0.846850	−	0.531832i	$-0.178496\pi$
$103$	3.19708	+	3.19708i	0.315017	+	0.315017i	−0.531832	+	0.846850i	$0.678496\pi$
$104$		0			0
$105$	9.98949	+	0.575857i	0.974874	+	0.0561979i
$106$		0			0
$107$	−7.37362	+	7.37362i	−0.712835	+	0.712835i	−0.967127	−	0.254293i	$-0.918157\pi$
$107$	−7.37362	+	7.37362i	−0.712835	+	0.712835i	0.254293	+	0.967127i	$0.418157\pi$
$108$		0			0
$109$	−3.62667			−0.347372			−0.173686	−	0.984801i	$-0.555568\pi$
$109$	−3.62667			−0.347372			−0.173686	+	0.984801i	$0.555568\pi$
$110$		0			0
$111$	−4.59856			−0.436476
$112$		0			0
$113$	12.0264			1.13135			0.565676	−	0.824628i	$-0.308615\pi$
$113$	12.0264			1.13135			0.565676	+	0.824628i	$0.308615\pi$
$114$		0			0
$115$	10.3751	+	0.598083i	0.967478	+	0.0557716i
$116$		0			0
$117$	0.708191	−	0.708191i	0.0654723	−	0.0654723i
$118$		0			0
$119$	−7.40784	+	7.40784i	−0.679075	+	0.679075i
$120$		0			0
$121$		−	3.17840i		−	0.288945i
$122$		0			0
$123$	1.15566	+	1.15566i	0.104203	+	0.104203i
$124$		0			0
$125$	6.42912	+	9.14694i	0.575038	+	0.818127i
$126$		0			0
$127$	−21.7471			−1.92974			−0.964870	−	0.262727i	$-0.915378\pi$
$127$	−21.7471			−1.92974			−0.964870	+	0.262727i	$0.915378\pi$
$128$		0			0
$129$	−1.86681			−0.164364
$130$		0			0
$131$	9.63670	−	9.63670i	0.841962	−	0.841962i	−0.147151	−	0.989114i	$-0.547010\pi$
$131$	9.63670	−	9.63670i	0.841962	−	0.841962i	0.989114	+	0.147151i	$0.0470105\pi$
$132$		0			0
$133$		−	15.0713i		−	1.30685i
$134$		0			0
$135$	8.15008	+	9.14721i	0.701447	+	0.787266i
$136$		0			0
$137$	−0.608748			−0.0520088			−0.0260044	−	0.999662i	$-0.508278\pi$
$137$	−0.608748			−0.0520088			−0.0260044	+	0.999662i	$0.508278\pi$
$138$		0			0
$139$			6.25065i			0.530174i	0.964225	+	0.265087i	$0.0854006\pi$
$139$			6.25065i			0.530174i	−0.964225	+	0.265087i	$0.914599\pi$
$140$		0			0
$141$	1.64676			0.138682
$142$		0			0
$143$	7.10940			0.594518
$144$		0			0
$145$	7.76879	+	9.20032i	0.645163	+	0.764045i
$146$		0			0
$147$	−1.10400			−0.0910566
$148$		0			0
$149$	−19.0372			−1.55959			−0.779795	−	0.626035i	$-0.784677\pi$
$149$	−19.0372			−1.55959			−0.779795	+	0.626035i	$0.784677\pi$
$150$		0			0
$151$			17.7201i			1.44204i	0.692915	+	0.721019i	$0.256326\pi$
$151$			17.7201i			1.44204i	−0.692915	+	0.721019i	$0.743674\pi$
$152$		0			0
$153$	−1.48901			−0.120379
$154$		0			0
$155$	−19.8360	−	1.14347i	−1.59326	−	0.0918457i
$156$		0			0
$157$		−	22.1034i		−	1.76404i	−0.471209	−	0.882022i	$-0.656182\pi$
$157$		−	22.1034i		−	1.76404i	0.471209	−	0.882022i	$-0.343818\pi$
$158$		0			0
$159$	−3.17513	+	3.17513i	−0.251804	+	0.251804i
$160$		0			0
$161$	−12.8830			−1.01532
$162$		0			0
$163$	0.940929			0.0736992			0.0368496	−	0.999321i	$-0.488268\pi$
$163$	0.940929			0.0736992			0.0368496	+	0.999321i	$0.488268\pi$
$164$		0			0
$165$	−0.580995	+	10.0786i	−0.0452304	+	0.784619i
$166$		0			0
$167$	7.07665	+	7.07665i	0.547607	+	0.547607i	0.925748	−	0.378141i	$-0.123436\pi$
$167$	7.07665	+	7.07665i	0.547607	+	0.547607i	−0.378141	+	0.925748i	$0.623436\pi$
$168$		0			0
$169$			6.53795i			0.502919i
$170$		0			0
$171$	1.51470	−	1.51470i	0.115832	−	0.115832i
$172$		0			0
$173$	−14.9169	+	14.9169i	−1.13411	+	1.13411i	−0.144624	+	0.989487i	$0.546197\pi$
$173$	−14.9169	+	14.9169i	−1.13411	+	1.13411i	−0.989487	+	0.144624i	$0.953803\pi$
$174$		0			0
$175$	−8.60934	−	10.8617i	−0.650805	−	0.821067i
$176$		0			0
$177$	−10.6586			−0.801147
$178$		0			0
$179$	11.9746			0.895022			0.447511	−	0.894279i	$-0.352311\pi$
$179$	11.9746			0.895022			0.447511	+	0.894279i	$0.352311\pi$
$180$		0			0
$181$	−26.3827			−1.96101			−0.980506	−	0.196490i	$-0.937046\pi$
$181$	−26.3827			−1.96101			−0.980506	+	0.196490i	$0.937046\pi$
$182$		0			0
$183$	−4.24488	+	4.24488i	−0.313791	+	0.313791i
$184$		0			0
$185$	4.23737	+	4.75580i	0.311538	+	0.349653i
$186$		0			0
$187$	−7.47393	−	7.47393i	−0.546548	−	0.546548i
$188$		0			0
$189$	−10.7392	−	10.7392i	−0.781165	−	0.781165i
$190$		0			0
$191$	−12.1388	−	12.1388i	−0.878334	−	0.878334i	0.115028	−	0.993362i	$-0.463304\pi$
$191$	−12.1388	−	12.1388i	−0.878334	−	0.878334i	−0.993362	+	0.115028i	$0.963304\pi$
$192$		0			0
$193$			14.0307i			1.00995i	0.863134	+	0.504975i	$0.168498\pi$
$193$			14.0307i			1.00995i	−0.863134	+	0.504975i	$0.831502\pi$
$194$		0			0
$195$	9.16090	+	0.528092i	0.656026	+	0.0378175i
$196$		0			0
$197$	−6.03169	+	6.03169i	−0.429740	+	0.429740i	−0.888540	−	0.458800i	$-0.848280\pi$
$197$	−6.03169	+	6.03169i	−0.429740	+	0.429740i	0.458800	+	0.888540i	$0.348280\pi$
$198$		0			0
$199$			9.22916i			0.654238i	0.944983	+	0.327119i	$0.106078\pi$
$199$			9.22916i			0.654238i	−0.944983	+	0.327119i	$0.893922\pi$
$200$		0			0
$201$	9.20808	−	9.20808i	0.649488	−	0.649488i
$202$		0			0
$203$	−10.2711	−	10.8322i	−0.720893	−	0.760271i
$204$		0			0
$205$	0.130285	−	2.26008i	0.00909950	−	0.157851i
$206$		0			0
$207$	−1.29477	−	1.29477i	−0.0899924	−	0.0899924i
$208$		0			0
$209$	15.2058			1.05181
$210$		0			0
$211$	−1.89612	+	1.89612i	−0.130534	+	0.130534i	−0.769355	−	0.638821i	$-0.779422\pi$
$211$	−1.89612	+	1.89612i	−0.130534	+	0.130534i	0.638821	+	0.769355i	$0.279422\pi$
$212$		0			0
$213$	16.5205			1.13197
$214$		0			0
$215$	1.72019	+	1.93065i	0.117316	+	0.131669i
$216$		0			0
$217$	24.6308			1.67205
$218$		0			0
$219$		−	20.0790i		−	1.35682i
$220$		0			0
$221$	−6.79338	+	6.79338i	−0.456973	+	0.456973i
$222$		0			0
$223$	14.1110	+	14.1110i	0.944944	+	0.944944i	0.998562	−	0.0536178i	$-0.0170753\pi$
$223$	14.1110	+	14.1110i	0.944944	+	0.944944i	−0.0536178	+	0.998562i	$0.517075\pi$
$224$		0			0
$225$	0.226366	−	1.95688i	0.0150911	−	0.130459i
$226$		0			0
$227$	19.1329	−	19.1329i	1.26990	−	1.26990i	0.323758	−	0.946140i	$-0.395054\pi$
$227$	19.1329	−	19.1329i	1.26990	−	1.26990i	0.946140	−	0.323758i	$-0.104946\pi$
$228$		0			0
$229$	−4.05720	−	4.05720i	−0.268107	−	0.268107i	0.560230	−	0.828337i	$-0.310713\pi$
$229$	−4.05720	−	4.05720i	−0.268107	−	0.268107i	−0.828337	+	0.560230i	$0.810713\pi$
$230$		0			0
$231$		−	12.5149i		−	0.823419i
$232$		0			0
$233$	−1.60471	−	1.60471i	−0.105128	−	0.105128i	0.652586	−	0.757714i	$-0.273684\pi$
$233$	−1.60471	−	1.60471i	−0.105128	−	0.105128i	−0.757714	+	0.652586i	$0.773684\pi$
$234$		0			0
$235$	−1.51742	−	1.70307i	−0.0989854	−	0.111096i
$236$		0			0
$237$	13.5813	+	13.5813i	0.882203	+	0.882203i
$238$		0			0
$239$			11.2091i			0.725054i	0.931973	+	0.362527i	$0.118086\pi$
$239$			11.2091i			0.725054i	−0.931973	+	0.362527i	$0.881914\pi$
$240$		0			0
$241$		−	19.6793i		−	1.26765i	−0.773476	−	0.633826i	$-0.781483\pi$
$241$		−	19.6793i		−	1.26765i	0.773476	−	0.633826i	$-0.218517\pi$
$242$		0			0
$243$		−	4.06669i		−	0.260878i
$244$		0			0
$245$	1.01729	+	1.14175i	0.0649923	+	0.0729438i
$246$		0			0
$247$		−	13.8212i		−	0.879423i
$248$		0			0
$249$	3.40334	−	3.40334i	0.215678	−	0.215678i
$250$		0			0
$251$	16.4261	+	16.4261i	1.03680	+	1.03680i	0.999296	+	0.0375077i	$0.0119419\pi$
$251$	16.4261	+	16.4261i	1.03680	+	1.03680i	0.0375077	+	0.999296i	$0.488058\pi$
$252$		0			0
$253$		−	12.9979i		−	0.817172i
$254$		0			0
$255$	−9.07545	−	10.1858i	−0.568326	−	0.637859i
$256$		0			0
$257$	13.8175	−	13.8175i	0.861909	−	0.861909i	−0.129650	−	0.991560i	$-0.541385\pi$
$257$	13.8175	−	13.8175i	0.861909	−	0.861909i	0.991560	+	0.129650i	$0.0413855\pi$
$258$		0			0
$259$	−5.58353	−	5.58353i	−0.346943	−	0.346943i
$260$		0			0
$261$	0.0563867	−	2.12093i	0.00349025	−	0.131282i
$262$		0			0
$263$			5.10568i			0.314830i	0.987533	+	0.157415i	$0.0503160\pi$
$263$			5.10568i			0.314830i	−0.987533	+	0.157415i	$0.949684\pi$
$264$		0			0
$265$	6.20944	+	0.357951i	0.381443	+	0.0219888i
$266$		0			0
$267$	4.39475	+	4.39475i	0.268954	+	0.268954i
$268$		0			0
$269$	0.193739	+	0.193739i	0.0118125	+	0.0118125i	0.712988	−	0.701176i	$-0.247341\pi$
$269$	0.193739	+	0.193739i	0.0118125	+	0.0118125i	−0.701176	+	0.712988i	$0.747341\pi$
$270$		0			0
$271$	13.8823	−	13.8823i	0.843292	−	0.843292i	−0.145994	−	0.989285i	$-0.546638\pi$
$271$	13.8823	−	13.8823i	0.843292	−	0.843292i	0.989285	+	0.145994i	$0.0466380\pi$
$272$		0			0
$273$	−11.3753			−0.688466
$274$		0			0
$275$	10.9586	−	8.68615i	0.660828	−	0.523795i
$276$		0			0
$277$	−21.1060	+	21.1060i	−1.26814	+	1.26814i	−0.321087	+	0.947050i	$0.604048\pi$
$277$	−21.1060	+	21.1060i	−1.26814	+	1.26814i	−0.947050	+	0.321087i	$0.895952\pi$
$278$		0			0
$279$	2.47545	+	2.47545i	0.148201	+	0.148201i
$280$		0			0
$281$	−6.65924			−0.397257			−0.198628	−	0.980075i	$-0.563649\pi$
$281$	−6.65924			−0.397257			−0.198628	+	0.980075i	$0.563649\pi$
$282$		0			0
$283$	−6.41389	+	6.41389i	−0.381266	+	0.381266i	−0.871558	−	0.490292i	$-0.836890\pi$
$283$	−6.41389	+	6.41389i	−0.381266	+	0.381266i	0.490292	+	0.871558i	$0.336890\pi$
$284$		0			0
$285$	19.5936	+	1.12950i	1.16062	+	0.0669057i
$286$		0			0
$287$			2.80639i			0.165656i
$288$		0			0
$289$	−2.71658			−0.159799
$290$		0			0
$291$	3.20205			0.187707
$292$		0			0
$293$		−	29.6043i		−	1.72950i	−0.502203	−	0.864750i	$-0.667477\pi$
$293$		−	29.6043i		−	1.72950i	0.502203	−	0.864750i	$-0.332523\pi$
$294$		0			0
$295$	9.82142	+	11.0230i	0.571825	+	0.641785i
$296$		0			0
$297$	10.8351	−	10.8351i	0.628714	−	0.628714i
$298$		0			0
$299$	−11.8144			−0.683243
$300$		0			0
$301$	−2.26667	−	2.26667i	−0.130649	−	0.130649i
$302$		0			0
$303$	20.1926	−	20.1926i	1.16003	−	1.16003i
$304$		0			0
$305$	8.30151	+	0.478551i	0.475343	+	0.0274018i
$306$		0			0
$307$	−22.8054			−1.30157			−0.650786	−	0.759261i	$-0.725560\pi$
$307$	−22.8054			−1.30157			−0.650786	+	0.759261i	$0.725560\pi$
$308$		0			0
$309$	5.16109	−	5.16109i	0.293604	−	0.293604i
$310$		0			0
$311$	3.18453	+	3.18453i	0.180578	+	0.180578i	0.791608	−	0.611030i	$-0.209244\pi$
$311$	3.18453	+	3.18453i	0.180578	+	0.180578i	−0.611030	+	0.791608i	$0.709244\pi$
$312$		0			0
$313$	3.76785	+	3.76785i	0.212972	+	0.212972i	0.805529	−	0.592557i	$-0.201881\pi$
$313$	3.76785	+	3.76785i	0.212972	+	0.212972i	−0.592557	+	0.805529i	$0.701881\pi$
$314$		0			0
$315$	−0.140542	+	2.43801i	−0.00791866	+	0.137366i
$316$		0			0
$317$		−	12.0726i		−	0.678062i	−0.940775	−	0.339031i	$-0.889901\pi$
$317$		−	12.0726i		−	0.678062i	0.940775	−	0.339031i	$-0.110099\pi$
$318$		0			0
$319$	10.9288	−	10.3628i	0.611897	−	0.580204i
$320$		0			0
$321$	11.9033	+	11.9033i	0.664380	+	0.664380i
$322$		0			0
$323$	−14.5299	+	14.5299i	−0.808464	+	0.808464i
$324$		0			0
$325$	−7.89523	−	9.96075i	−0.437948	−	0.552523i
$326$		0			0
$327$			5.85459i			0.323759i
$328$		0			0
$329$	1.99948	+	1.99948i	0.110235	+	0.110235i
$330$		0			0
$331$	4.13328	−	4.13328i	0.227186	−	0.227186i	−0.584330	−	0.811516i	$-0.698643\pi$
$331$	4.13328	−	4.13328i	0.227186	−	0.227186i	0.811516	+	0.584330i	$0.198643\pi$
$332$		0			0
$333$		−	1.12231i		−	0.0615023i
$334$		0			0
$335$	−18.0078	−	1.03808i	−0.983870	−	0.0567165i
$336$		0			0
$337$		−	1.20250i		−	0.0655043i	−0.999464	−	0.0327522i	$-0.989573\pi$
$337$		−	1.20250i		−	0.0655043i	0.999464	−	0.0327522i	$-0.0104272\pi$
$338$		0			0
$339$		−	19.4145i		−	1.05445i
$340$		0			0
$341$			24.8506i			1.34573i
$342$		0			0
$343$	12.3801	+	12.3801i	0.668465	+	0.668465i
$344$		0			0
$345$	0.965495	−	16.7486i	0.0519805	−	0.901715i
$346$		0			0
$347$	11.2920	+	11.2920i	0.606187	+	0.606187i	0.941947	−	0.335761i	$-0.108993\pi$
$347$	11.2920	+	11.2920i	0.606187	+	0.606187i	−0.335761	+	0.941947i	$0.608993\pi$
$348$		0			0
$349$			10.5990i			0.567353i	0.958920	+	0.283676i	$0.0915541\pi$
$349$			10.5990i			0.567353i	−0.958920	+	0.283676i	$0.908446\pi$
$350$		0			0
$351$	−9.84847	−	9.84847i	−0.525672	−	0.525672i
$352$		0			0
$353$	−25.7160	+	25.7160i	−1.36872	+	1.36872i	−0.506462	+	0.862262i	$0.669047\pi$
$353$	−25.7160	+	25.7160i	−1.36872	+	1.36872i	−0.862262	+	0.506462i	$0.830953\pi$
$354$		0			0
$355$	−15.2230	−	17.0854i	−0.807950	−	0.906799i
$356$		0			0
$357$	11.9586	+	11.9586i	0.632915	+	0.632915i
$358$		0			0
$359$	−0.396828	+	0.396828i	−0.0209438	+	0.0209438i	−0.717501	−	0.696557i	$-0.754714\pi$
$359$	−0.396828	+	0.396828i	−0.0209438	+	0.0209438i	0.696557	+	0.717501i	$0.254714\pi$
$360$		0			0
$361$		−	10.5612i		−	0.555852i
$362$		0			0
$363$	−5.13094			−0.269304
$364$		0			0
$365$	−20.7656	+	18.5020i	−1.08692	+	0.968438i
$366$		0			0
$367$	−2.84554			−0.148536			−0.0742679	−	0.997238i	$-0.523662\pi$
$367$	−2.84554			−0.148536			−0.0742679	+	0.997238i	$0.523662\pi$
$368$		0			0
$369$	−0.282049	+	0.282049i	−0.0146829	+	0.0146829i
$370$		0			0
$371$	−7.71042			−0.400305
$372$		0			0
$373$	−11.3309	−	11.3309i	−0.586692	−	0.586692i	0.350042	−	0.936734i	$-0.386167\pi$
$373$	−11.3309	−	11.3309i	−0.586692	−	0.586692i	−0.936734	+	0.350042i	$0.886167\pi$
$374$		0			0
$375$	14.7660	−	10.3786i	0.762515	−	0.535950i
$376$		0			0
$377$	−9.41919	−	9.93370i	−0.485113	−	0.511612i
$378$		0			0
$379$	22.5172	−	22.5172i	1.15663	−	1.15663i	0.171437	−	0.985195i	$-0.445159\pi$
$379$	22.5172	−	22.5172i	1.15663	−	1.15663i	0.985195	−	0.171437i	$-0.0548410\pi$
$380$		0			0
$381$			35.1066i			1.79857i
$382$		0			0
$383$	2.20602	−	2.20602i	0.112723	−	0.112723i	−0.648496	−	0.761218i	$-0.724602\pi$
$383$	2.20602	−	2.20602i	0.112723	−	0.112723i	0.761218	+	0.648496i	$0.224602\pi$
$384$		0			0
$385$	−12.9428	+	11.5319i	−0.659626	+	0.587721i
$386$		0			0
$387$		−	0.455610i		−	0.0231600i
$388$		0			0
$389$	−5.99292	−	5.99292i	−0.303853	−	0.303853i	0.538666	−	0.842519i	$-0.318928\pi$
$389$	−5.99292	−	5.99292i	−0.303853	−	0.303853i	−0.842519	+	0.538666i	$0.818928\pi$
$390$		0			0
$391$	12.4201	+	12.4201i	0.628114	+	0.628114i
$392$		0			0
$393$	−15.5567	−	15.5567i	−0.784730	−	0.784730i
$394$		0			0
$395$	1.53111	−	26.5604i	0.0770383	−	1.33640i
$396$		0			0
$397$	6.67342	−	6.67342i	0.334930	−	0.334930i	−0.519525	−	0.854455i	$-0.673891\pi$
$397$	6.67342	−	6.67342i	0.334930	−	0.334930i	0.854455	+	0.519525i	$0.173891\pi$
$398$		0			0
$399$	−24.3299			−1.21802
$400$		0			0
$401$	−18.0031			−0.899030			−0.449515	−	0.893273i	$-0.648403\pi$
$401$	−18.0031			−0.899030			−0.449515	+	0.893273i	$0.648403\pi$
$402$		0			0
$403$	22.5878			1.12518
$404$		0			0
$405$	12.7932	−	11.3986i	0.635698	−	0.566402i
$406$		0			0
$407$	5.63334	−	5.63334i	0.279234	−	0.279234i
$408$		0			0
$409$	5.72639	−	5.72639i	0.283152	−	0.283152i	−0.551213	−	0.834365i	$-0.685835\pi$
$409$	5.72639	−	5.72639i	0.283152	−	0.283152i	0.834365	+	0.551213i	$0.185835\pi$
$410$		0			0
$411$			0.982711i			0.0484736i
$412$		0			0
$413$	−12.9415	−	12.9415i	−0.636811	−	0.636811i
$414$		0			0
$415$	−6.65575	−	0.383680i	−0.326718	−	0.0188341i
$416$		0			0
$417$	10.0905			0.494135
$418$		0			0
$419$	11.5150			0.562547			0.281273	−	0.959628i	$-0.409243\pi$
$419$	11.5150			0.562547			0.281273	+	0.959628i	$0.409243\pi$
$420$		0			0
$421$	24.7177	−	24.7177i	1.20467	−	1.20467i	0.231935	−	0.972731i	$-0.425494\pi$
$421$	24.7177	−	24.7177i	1.20467	−	1.20467i	0.972731	−	0.231935i	$-0.0745057\pi$
$422$		0			0
$423$			0.401904i			0.0195412i
$424$		0			0
$425$	−2.17143	+	18.7715i	−0.105330	+	0.910553i
$426$		0			0
$427$	−10.3082			−0.498849
$428$		0			0
$429$		−	11.4768i		−	0.554106i
$430$		0			0
$431$	20.6075			0.992629			0.496314	−	0.868143i	$-0.334686\pi$
$431$	20.6075			0.992629			0.496314	+	0.868143i	$0.334686\pi$
$432$		0			0
$433$	−15.8626			−0.762309			−0.381155	−	0.924511i	$-0.624473\pi$
$433$	−15.8626			−0.762309			−0.381155	+	0.924511i	$0.624473\pi$
$434$		0			0
$435$	14.8522	−	12.5413i	0.712110	−	0.601308i
$436$		0			0
$437$	−25.2689			−1.20878
$438$		0			0
$439$	−4.13619			−0.197409			−0.0987047	−	0.995117i	$-0.531470\pi$
$439$	−4.13619			−0.197409			−0.0987047	+	0.995117i	$0.531470\pi$
$440$		0			0
$441$		−	0.269440i		−	0.0128305i
$442$		0			0
$443$	−19.9797			−0.949266			−0.474633	−	0.880184i	$-0.657419\pi$
$443$	−19.9797			−0.949266			−0.474633	+	0.880184i	$0.657419\pi$
$444$		0			0
$445$	0.495447	−	8.59459i	0.0234864	−	0.407423i
$446$		0			0
$447$			30.7321i			1.45358i
$448$		0			0
$449$	−13.4467	+	13.4467i	−0.634591	+	0.634591i	−0.949216	−	0.314625i	$-0.898121\pi$
$449$	−13.4467	+	13.4467i	−0.634591	+	0.634591i	0.314625	+	0.949216i	$0.398121\pi$
$450$		0			0
$451$	−2.83143			−0.133327
$452$		0			0
$453$	28.6058			1.34402
$454$		0			0
$455$	10.4819	+	11.7643i	0.491398	+	0.551518i
$456$		0			0
$457$	14.5618	+	14.5618i	0.681173	+	0.681173i	0.960265	−	0.279091i	$-0.0900332\pi$
$457$	14.5618	+	14.5618i	0.681173	+	0.681173i	−0.279091	+	0.960265i	$0.590033\pi$
$458$		0			0
$459$			20.7069i			0.966514i
$460$		0			0
$461$	−20.1277	+	20.1277i	−0.937441	+	0.937441i	−0.998155	−	0.0607141i	$-0.980662\pi$
$461$	−20.1277	+	20.1277i	−0.937441	+	0.937441i	0.0607141	+	0.998155i	$0.480662\pi$
$462$		0			0
$463$	19.1317	−	19.1317i	0.889125	−	0.889125i	−0.105314	−	0.994439i	$-0.533585\pi$
$463$	19.1317	−	19.1317i	0.889125	−	0.889125i	0.994439	+	0.105314i	$0.0335849\pi$
$464$		0			0
$465$	−1.84592	+	32.0215i	−0.0856025	+	1.48496i
$466$		0			0
$467$	23.2734			1.07696			0.538481	−	0.842637i	$-0.318998\pi$
$467$	23.2734			1.07696			0.538481	+	0.842637i	$0.318998\pi$
$468$		0			0
$469$	22.3607			1.03252
$470$		0			0
$471$	−35.6819			−1.64413
$472$		0			0
$473$	2.28689	−	2.28689i	0.105151	−	0.105151i
$474$		0			0
$475$	−16.8865	−	21.3043i	−0.774807	−	0.977510i
$476$		0			0
$477$	−0.774913	−	0.774913i	−0.0354808	−	0.0354808i
$478$		0			0
$479$	16.0347	+	16.0347i	0.732643	+	0.732643i	0.971143	−	0.238500i	$-0.0766556\pi$
$479$	16.0347	+	16.0347i	0.732643	+	0.732643i	−0.238500	+	0.971143i	$0.576656\pi$
$480$		0			0
$481$	−5.12039	−	5.12039i	−0.233470	−	0.233470i
$482$		0			0
$483$			20.7972i			0.946304i
$484$		0			0
$485$	−2.95055	−	3.31153i	−0.133977	−	0.150369i
$486$		0			0
$487$	−27.3306	+	27.3306i	−1.23847	+	1.23847i	−0.277844	+	0.960626i	$0.589620\pi$
$487$	−27.3306	+	27.3306i	−1.23847	+	1.23847i	−0.960626	+	0.277844i	$0.910380\pi$
$488$		0			0
$489$		−	1.51896i		−	0.0686896i
$490$		0			0
$491$	−3.65833	+	3.65833i	−0.165098	+	0.165098i	−0.784821	−	0.619723i	$-0.787245\pi$
$491$	−3.65833	+	3.65833i	−0.165098	+	0.165098i	0.619723	+	0.784821i	$0.287245\pi$
$492$		0			0
$493$	−0.540894	+	20.3452i	−0.0243606	+	0.916301i
$494$		0			0
$495$	−2.45976	−	0.141796i	−0.110558	−	0.00637326i
$496$		0			0
$497$	20.0591	+	20.0591i	0.899772	+	0.899772i
$498$		0			0
$499$	−22.1752			−0.992699			−0.496350	−	0.868123i	$-0.665327\pi$
$499$	−22.1752			−0.992699			−0.496350	+	0.868123i	$0.665327\pi$
$500$		0			0
$501$	11.4239	−	11.4239i	0.510384	−	0.510384i
$502$		0			0
$503$	2.57000			0.114591			0.0572954	−	0.998357i	$-0.481752\pi$
$503$	2.57000			0.114591			0.0572954	+	0.998357i	$0.481752\pi$
$504$		0			0
$505$	−39.4896	−	2.27643i	−1.75726	−	0.101300i
$506$		0			0
$507$	10.5543			0.468734
$508$		0			0
$509$			43.1784i			1.91385i	0.290334	+	0.956925i	$0.406234\pi$
$509$			43.1784i			1.91385i	−0.290334	+	0.956925i	$0.593766\pi$
$510$		0			0
$511$	24.3798	−	24.3798i	1.07850	−	1.07850i
$512$		0			0
$513$	−21.0642	−	21.0642i	−0.930006	−	0.930006i
$514$		0			0
$515$	−10.0933	−	0.581841i	−0.444764	−	0.0256390i
$516$		0			0
$517$	−2.01732	+	2.01732i	−0.0887216	+	0.0887216i
$518$		0			0
$519$	24.0806	+	24.0806i	1.05702	+	1.05702i
$520$		0			0
$521$		−	19.8679i		−	0.870427i	−0.900327	−	0.435214i	$-0.856673\pi$
$521$		−	19.8679i		−	0.870427i	0.900327	−	0.435214i	$-0.143327\pi$
$522$		0			0
$523$	−10.1370	−	10.1370i	−0.443258	−	0.443258i	0.449847	−	0.893105i	$-0.351478\pi$
$523$	−10.1370	−	10.1370i	−0.443258	−	0.443258i	−0.893105	+	0.449847i	$0.851478\pi$
$524$		0			0
$525$	−17.5342	+	13.8982i	−0.765255	+	0.606567i
$526$		0			0
$527$	−23.7460	−	23.7460i	−1.03439	−	1.03439i
$528$		0			0
$529$		−	1.40012i		−	0.0608749i
$530$		0			0
$531$		−	2.60130i		−	0.112887i
$532$		0			0
$533$			2.57361i			0.111476i
$534$		0			0
$535$	1.34194	−	23.2788i	0.0580169	−	1.00643i
$536$		0			0
$537$		−	19.3307i		−	0.834183i
$538$		0			0
$539$	1.35243	−	1.35243i	0.0582532	−	0.0582532i
$540$		0			0
$541$	27.2063	+	27.2063i	1.16969	+	1.16969i	0.982282	+	0.187407i	$0.0600082\pi$
$541$	27.2063	+	27.2063i	1.16969	+	1.16969i	0.187407	+	0.982282i	$0.439992\pi$
$542$		0			0
$543$			42.5900i			1.82771i
$544$		0			0
$545$	6.05477	−	5.39475i	0.259358	−	0.231086i
$546$		0			0
$547$	−13.0148	+	13.0148i	−0.556475	+	0.556475i	−0.928302	−	0.371827i	$-0.878731\pi$
$547$	−13.0148	+	13.0148i	−0.556475	+	0.556475i	0.371827	+	0.928302i	$0.378731\pi$
$548$		0			0
$549$	−1.03600	−	1.03600i	−0.0442152	−	0.0442152i
$550$		0			0
$551$	−20.1460	−	21.2465i	−0.858249	−	0.905130i
$552$		0			0
$553$			32.9807i			1.40248i
$554$		0			0
$555$	7.67736	−	6.84046i	0.325886	−	0.290361i
$556$		0			0
$557$	−2.92063	−	2.92063i	−0.123751	−	0.123751i	0.642519	−	0.766270i	$-0.277889\pi$
$557$	−2.92063	−	2.92063i	−0.123751	−	0.123751i	−0.766270	+	0.642519i	$0.777889\pi$
$558$		0			0
$559$	−2.07866	−	2.07866i	−0.0879178	−	0.0879178i
$560$		0			0
$561$	−12.0653	+	12.0653i	−0.509396	+	0.509396i
$562$		0			0
$563$	5.85586			0.246795			0.123397	−	0.992357i	$-0.460621\pi$
$563$	5.85586			0.246795			0.123397	+	0.992357i	$0.460621\pi$
$564$		0			0
$565$	−20.0783	+	17.8896i	−0.844701	+	0.752621i
$566$		0			0
$567$	−15.0198	+	15.0198i	−0.630772	+	0.630772i
$568$		0			0
$569$	14.9312	+	14.9312i	0.625947	+	0.625947i	0.947046	−	0.321099i	$-0.104052\pi$
$569$	14.9312	+	14.9312i	0.625947	+	0.625947i	−0.321099	+	0.947046i	$0.604052\pi$
$570$		0			0
$571$	38.1793			1.59775			0.798876	−	0.601495i	$-0.205428\pi$
$571$	38.1793			1.59775			0.798876	+	0.601495i	$0.205428\pi$
$572$		0			0
$573$	−19.5959	+	19.5959i	−0.818630	+	0.818630i
$574$		0			0
$575$	−18.2110	+	14.4346i	−0.759449	+	0.601965i
$576$		0			0
$577$		−	14.5914i		−	0.607449i	−0.952760	−	0.303724i	$-0.901770\pi$
$577$		−	14.5914i		−	0.607449i	0.952760	−	0.303724i	$-0.0982302\pi$
$578$		0			0
$579$	22.6499			0.941298
$580$		0			0
$581$	8.26462			0.342874
$582$		0			0
$583$		−	7.77921i		−	0.322182i
$584$		0			0
$585$	−0.128885	+	2.23579i	−0.00532873	+	0.0924384i
$586$		0			0
$587$	−12.0313	+	12.0313i	−0.496587	+	0.496587i	−0.910374	−	0.413787i	$-0.864206\pi$
$587$	−12.0313	+	12.0313i	−0.496587	+	0.496587i	0.413787	+	0.910374i	$0.364206\pi$
$588$		0			0
$589$	48.3114			1.99064
$590$		0			0
$591$	9.73705	+	9.73705i	0.400529	+	0.400529i
$592$		0			0
$593$	−11.6124	+	11.6124i	−0.476865	+	0.476865i	−0.904128	−	0.427263i	$-0.859478\pi$
$593$	−11.6124	+	11.6124i	−0.476865	+	0.476865i	0.427263	+	0.904128i	$0.359478\pi$
$594$		0			0
$595$	1.34816	−	23.3868i	0.0552693	−	0.958766i
$596$		0			0
$597$	14.8988			0.609767
$598$		0			0
$599$	26.8052	−	26.8052i	1.09523	−	1.09523i	0.100271	−	0.994960i	$-0.468029\pi$
$599$	26.8052	−	26.8052i	1.09523	−	1.09523i	0.994960	−	0.100271i	$-0.0319708\pi$
$600$		0			0
$601$	−8.61367	−	8.61367i	−0.351359	−	0.351359i	0.509256	−	0.860615i	$-0.329921\pi$
$601$	−8.61367	−	8.61367i	−0.351359	−	0.351359i	−0.860615	+	0.509256i	$0.829921\pi$
$602$		0			0
$603$	2.24730	+	2.24730i	0.0915172	+	0.0915172i
$604$		0			0
$605$	4.72794	+	5.30638i	0.192218	+	0.215735i
$606$		0			0
$607$			18.3784i			0.745956i	0.927840	+	0.372978i	$0.121663\pi$
$607$			18.3784i			0.745956i	−0.927840	+	0.372978i	$0.878337\pi$
$608$		0			0
$609$	−17.4866	+	16.5809i	−0.708592	+	0.671890i
$610$		0			0
$611$	1.83363	+	1.83363i	0.0741807	+	0.0741807i
$612$		0			0
$613$	−17.9986	+	17.9986i	−0.726959	+	0.726959i	−0.970013	−	0.243054i	$-0.921851\pi$
$613$	−17.9986	+	17.9986i	−0.726959	+	0.726959i	0.243054	+	0.970013i	$0.421851\pi$
$614$		0			0
$615$	−3.64847	−	0.210321i	−0.147121	−	0.00848096i
$616$		0			0
$617$			28.4106i			1.14377i	0.820335	+	0.571883i	$0.193787\pi$
$617$			28.4106i			1.14377i	−0.820335	+	0.571883i	$0.806213\pi$
$618$		0			0
$619$	9.49374	+	9.49374i	0.381586	+	0.381586i	0.871673	−	0.490088i	$-0.163035\pi$
$619$	9.49374	+	9.49374i	0.381586	+	0.381586i	−0.490088	+	0.871673i	$0.663035\pi$
$620$		0			0
$621$	−18.0057	+	18.0057i	−0.722542	+	0.722542i
$622$		0			0
$623$			10.6721i			0.427570i
$624$		0			0
$625$	−24.3398	−	5.70748i	−0.973591	−	0.228299i
$626$		0			0
$627$		−	24.5469i		−	0.980310i
$628$		0			0
$629$			10.7659i			0.429264i
$630$		0			0
$631$			38.3228i			1.52561i	0.646630	+	0.762804i	$0.276178\pi$
$631$			38.3228i			1.52561i	−0.646630	+	0.762804i	$0.723822\pi$
$632$		0			0
$633$	3.06094	+	3.06094i	0.121661	+	0.121661i
$634$		0			0
$635$	36.3070	−	32.3493i	1.44080	−	1.28374i
$636$		0			0
$637$	−1.22928	−	1.22928i	−0.0487059	−	0.0487059i
$638$		0			0
$639$			4.03196i			0.159502i
$640$		0			0
$641$	−14.9702	−	14.9702i	−0.591286	−	0.591286i	0.346693	−	0.937979i	$-0.387305\pi$
$641$	−14.9702	−	14.9702i	−0.591286	−	0.591286i	−0.937979	+	0.346693i	$0.887305\pi$
$642$		0			0
$643$	1.96517	−	1.96517i	0.0774987	−	0.0774987i	−0.667295	−	0.744794i	$-0.732548\pi$
$643$	1.96517	−	1.96517i	0.0774987	−	0.0774987i	0.744794	+	0.667295i	$0.232548\pi$
$644$		0			0
$645$	3.11667	−	2.77693i	0.122719	−	0.109341i
$646$		0			0
$647$	−22.5149	−	22.5149i	−0.885152	−	0.885152i	0.108901	−	0.994053i	$-0.465267\pi$
$647$	−22.5149	−	22.5149i	−0.885152	−	0.885152i	−0.994053	+	0.108901i	$0.965267\pi$
$648$		0			0
$649$	13.0570	−	13.0570i	0.512532	−	0.512532i
$650$		0			0
$651$		−	39.7619i		−	1.55839i
$652$		0			0
$653$	26.8513			1.05077			0.525386	−	0.850864i	$-0.323921\pi$
$653$	26.8513			1.05077			0.525386	+	0.850864i	$0.323921\pi$
$654$		0			0
$655$	−1.75380	+	30.4234i	−0.0685265	+	1.18874i
$656$		0			0
$657$	4.90044			0.191184
$658$		0			0
$659$	21.5709	−	21.5709i	0.840282	−	0.840282i	−0.148613	−	0.988895i	$-0.547481\pi$
$659$	21.5709	−	21.5709i	0.840282	−	0.840282i	0.988895	+	0.148613i	$0.0474810\pi$
$660$		0			0
$661$	44.9398			1.74795			0.873977	−	0.485967i	$-0.161532\pi$
$661$	44.9398			1.74795			0.873977	+	0.485967i	$0.161532\pi$
$662$		0			0
$663$	10.9667	+	10.9667i	0.425910	+	0.425910i
$664$		0			0
$665$	22.4189	+	25.1618i	0.869369	+	0.975732i
$666$		0			0
$667$	−18.1615	+	17.2208i	−0.703216	+	0.666793i
$668$		0			0
$669$	22.7796	−	22.7796i	0.880712	−	0.880712i
$670$		0			0
$671$		−	10.4002i		−	0.401494i
$672$		0			0
$673$	−24.6538	+	24.6538i	−0.950335	+	0.950335i	−0.998824	−	0.0484883i	$-0.984560\pi$
$673$	−24.6538	+	24.6538i	−0.950335	+	0.950335i	0.0484883	+	0.998824i	$0.484560\pi$
$674$		0			0
$675$	−27.2133	−	3.14796i	−1.04744	−	0.121165i
$676$		0			0
$677$			2.78008i			0.106847i	0.998572	+	0.0534235i	$0.0170133\pi$
$677$			2.78008i			0.106847i	−0.998572	+	0.0534235i	$0.982987\pi$
$678$		0			0
$679$	3.88790	+	3.88790i	0.149204	+	0.149204i
$680$		0			0
$681$	−30.8866	−	30.8866i	−1.18358	−	1.18358i
$682$		0			0
$683$	−24.9472	−	24.9472i	−0.954577	−	0.954577i	0.0444355	−	0.999012i	$-0.485851\pi$
$683$	−24.9472	−	24.9472i	−0.954577	−	0.954577i	−0.999012	+	0.0444355i	$0.985851\pi$
$684$		0			0
$685$	1.01631	−	0.905526i	0.0388313	−	0.0345984i
$686$		0			0
$687$	−6.54960	+	6.54960i	−0.249883	+	0.249883i
$688$		0			0
$689$	−7.07087			−0.269379
$690$		0			0
$691$	17.0310			0.647891			0.323945	−	0.946076i	$-0.394991\pi$
$691$	17.0310			0.647891			0.323945	+	0.946076i	$0.394991\pi$
$692$		0			0
$693$	3.05435			0.116025
$694$		0			0
$695$	−9.29799	−	10.4356i	−0.352693	−	0.395843i
$696$		0			0
$697$	2.70557	−	2.70557i	0.102481	−	0.102481i
$698$		0			0
$699$	−2.59050	+	2.59050i	−0.0979819	+	0.0979819i
$700$		0			0
$701$		−	28.6390i		−	1.08168i	−0.841125	−	0.540841i	$-0.818106\pi$
$701$		−	28.6390i		−	1.08168i	0.841125	−	0.540841i	$-0.181894\pi$
$702$		0			0
$703$	−10.9516	−	10.9516i	−0.413049	−	0.413049i
$704$		0			0
$705$	−2.74929	+	2.44959i	−0.103544	+	0.0922569i
$706$		0			0
$707$	49.0352			1.84416
$708$		0			0
$709$	0.203100			0.00762757			0.00381378	−	0.999993i	$-0.498786\pi$
$709$	0.203100			0.00762757			0.00381378	+	0.999993i	$0.498786\pi$
$710$		0			0
$711$	−3.31463	+	3.31463i	−0.124308	+	0.124308i
$712$		0			0
$713$		−	41.2966i		−	1.54657i
$714$		0			0
$715$	−11.8692	+	10.5754i	−0.443885	+	0.395497i
$716$		0			0
$717$	18.0950			0.675769
$718$		0			0
$719$		−	34.6022i		−	1.29044i	−0.763995	−	0.645222i	$-0.776765\pi$
$719$		−	34.6022i		−	1.29044i	0.763995	−	0.645222i	$-0.223235\pi$
$720$		0			0
$721$	12.5331			0.466757
$722$		0			0
$723$	−31.7685			−1.18148
$724$		0			0
$725$	−26.6558	−	3.80383i	−0.989971	−	0.141271i
$726$		0			0
$727$	−16.1265			−0.598100			−0.299050	−	0.954237i	$-0.596670\pi$
$727$	−16.1265			−0.598100			−0.299050	+	0.954237i	$0.596670\pi$
$728$		0			0
$729$	−29.5534			−1.09457
$730$		0			0
$731$			4.37048i			0.161648i
$732$		0			0
$733$	−26.3707			−0.974025			−0.487012	−	0.873395i	$-0.661913\pi$
$733$	−26.3707			−0.974025			−0.487012	+	0.873395i	$0.661913\pi$
$734$		0			0
$735$	1.84315	−	1.64223i	0.0679855	−	0.0605745i
$736$		0			0
$737$			22.5602i			0.831017i
$738$		0			0
$739$	−18.9424	+	18.9424i	−0.696806	+	0.696806i	−0.963720	−	0.266914i	$-0.913996\pi$
$739$	−18.9424	+	18.9424i	−0.696806	+	0.696806i	0.266914	+	0.963720i	$0.413996\pi$
$740$		0			0
$741$	−22.3118			−0.819644
$742$		0			0
$743$	3.57379			0.131110			0.0655548	−	0.997849i	$-0.479118\pi$
$743$	3.57379			0.131110			0.0655548	+	0.997849i	$0.479118\pi$
$744$		0			0
$745$	31.7829	−	28.3183i	1.16444	−	1.03750i
$746$		0			0
$747$	0.830612	+	0.830612i	0.0303905	+	0.0303905i
$748$		0			0
$749$			28.9059i			1.05620i
$750$		0			0
$751$	−11.8193	+	11.8193i	−0.431294	+	0.431294i	−0.889068	−	0.457775i	$-0.848647\pi$
$751$	−11.8193	+	11.8193i	−0.431294	+	0.431294i	0.457775	+	0.889068i	$0.348647\pi$
$752$		0			0
$753$	26.5168	−	26.5168i	0.966328	−	0.966328i
$754$		0			0
$755$	−26.3590	−	29.5839i	−0.959302	−	1.07667i
$756$		0			0
$757$	28.9459			1.05206			0.526029	−	0.850467i	$-0.323680\pi$
$757$	28.9459			1.05206			0.526029	+	0.850467i	$0.323680\pi$
$758$		0			0
$759$	−20.9827			−0.761625
$760$		0			0
$761$	−4.54292			−0.164681			−0.0823404	−	0.996604i	$-0.526239\pi$
$761$	−4.54292			−0.164681			−0.0823404	+	0.996604i	$0.526239\pi$
$762$		0			0
$763$	−7.10859	+	7.10859i	−0.257348	+	0.257348i
$764$		0			0
$765$	2.48592	−	2.21493i	0.0898785	−	0.0800810i
$766$		0			0
$767$	−11.8681	−	11.8681i	−0.428532	−	0.428532i
$768$		0			0
$769$	−4.63210	−	4.63210i	−0.167038	−	0.167038i	0.618638	−	0.785676i	$-0.287685\pi$
$769$	−4.63210	−	4.63210i	−0.167038	−	0.167038i	−0.785676	+	0.618638i	$0.787685\pi$
$770$		0			0
$771$	−22.3057	−	22.3057i	−0.803322	−	0.803322i
$772$		0			0
$773$			23.2773i			0.837226i	0.908165	+	0.418613i	$0.137484\pi$
$773$			23.2773i			0.837226i	−0.908165	+	0.418613i	$0.862516\pi$
$774$		0			0
$775$	34.8174	−	27.5974i	1.25068	−	0.991328i
$776$		0			0
$777$	−9.01357	+	9.01357i	−0.323360	+	0.323360i
$778$		0			0
$779$			5.50452i			0.197220i
$780$		0			0
$781$	−20.2380	+	20.2380i	−0.724174	+	0.724174i
$782$		0			0
$783$	−29.4947	−	0.784142i	−1.05405	−	0.0280229i
$784$		0			0
$785$	32.8793	+	36.9019i	1.17351	+	1.31709i
$786$		0			0
$787$	27.3371	+	27.3371i	0.974463	+	0.974463i	0.999682	−	0.0252189i	$-0.00802827\pi$
$787$	27.3371	+	27.3371i	0.974463	+	0.974463i	−0.0252189	+	0.999682i	$0.508028\pi$
$788$		0			0
$789$	8.24218			0.293429
$790$		0			0
$791$	23.5729	−	23.5729i	0.838154	−	0.838154i
$792$		0			0
$793$	−9.45317			−0.335692
$794$		0			0
$795$	0.577846	−	10.0240i	0.0204941	−	0.355514i
$796$		0			0
$797$	37.4688			1.32721			0.663606	−	0.748082i	$-0.269025\pi$
$797$	37.4688			1.32721			0.663606	+	0.748082i	$0.269025\pi$
$798$		0			0
$799$		−	3.85530i		−	0.136391i
$800$		0			0
$801$	−1.07257	+	1.07257i	−0.0378975	+	0.0378975i
$802$		0			0
$803$	24.5973	+	24.5973i	0.868020	+	0.868020i
$804$		0			0
$805$	21.5083	−	19.1637i	0.758068	−	0.675432i
$806$		0			0
$807$	0.312756	−	0.312756i	0.0110095	−	0.0110095i
$808$		0			0
$809$	2.68633	+	2.68633i	0.0944463	+	0.0944463i	0.752751	−	0.658305i	$-0.228726\pi$
$809$	2.68633	+	2.68633i	0.0944463	+	0.0944463i	−0.658305	+	0.752751i	$0.728726\pi$
$810$		0			0
$811$		−	7.94175i		−	0.278872i	−0.990231	−	0.139436i	$-0.955471\pi$
$811$		−	7.94175i		−	0.278872i	0.990231	−	0.139436i	$-0.0445290\pi$
$812$		0			0
$813$	−22.4105	−	22.4105i	−0.785969	−	0.785969i
$814$		0			0
$815$	−1.57089	+	1.39965i	−0.0550260	+	0.0490277i
$816$		0			0
$817$	−4.44589	−	4.44589i	−0.155542	−	0.155542i
$818$		0			0
$819$		−	2.77623i		−	0.0970095i
$820$		0			0
$821$		−	39.1659i		−	1.36690i	−0.729998	−	0.683449i	$-0.760479\pi$
$821$		−	39.1659i		−	1.36690i	0.729998	−	0.683449i	$-0.239521\pi$
$822$		0			0
$823$			17.0068i			0.592821i	0.955061	+	0.296411i	$0.0957897\pi$
$823$			17.0068i			0.592821i	−0.955061	+	0.296411i	$0.904210\pi$
$824$		0			0
$825$	−14.0222	−	17.6906i	−0.488190	−	0.615909i
$826$		0			0
$827$		−	22.6233i		−	0.786691i	−0.919391	−	0.393345i	$-0.871318\pi$
$827$		−	22.6233i		−	0.786691i	0.919391	−	0.393345i	$-0.128682\pi$
$828$		0			0
$829$	34.8056	−	34.8056i	1.20885	−	1.20885i	0.237450	−	0.971400i	$-0.423688\pi$
$829$	34.8056	−	34.8056i	1.20885	−	1.20885i	0.971400	−	0.237450i	$-0.0763117\pi$
$830$		0			0
$831$	34.0717	+	34.0717i	1.18194	+	1.18194i
$832$		0			0
$833$			2.58463i			0.0895520i
$834$		0			0
$835$	−22.3412	−	1.28789i	−0.773150	−	0.0445692i
$836$		0			0
$837$	34.4249	−	34.4249i	1.18990	−	1.18990i
$838$		0			0
$839$	−24.3908	−	24.3908i	−0.842064	−	0.842064i	0.147063	−	0.989127i	$-0.453018\pi$
$839$	−24.3908	−	24.3908i	−0.842064	−	0.842064i	−0.989127	+	0.147063i	$0.953018\pi$
$840$		0			0
$841$	−28.9590	−	1.54089i	−0.998587	−	0.0531341i
$842$		0			0
$843$			10.7501i			0.370253i
$844$		0			0
$845$	−9.72535	−	10.9152i	−0.334562	−	0.375494i
$846$		0			0
$847$	−6.22994	−	6.22994i	−0.214063	−	0.214063i
$848$		0			0
$849$	10.3540	+	10.3540i	0.355350	+	0.355350i
$850$		0			0
$851$	−9.36147	+	9.36147i	−0.320907	+	0.320907i
$852$		0			0
$853$	−36.0783			−1.23530			−0.617648	−	0.786455i	$-0.711914\pi$
$853$	−36.0783			−1.23530			−0.617648	+	0.786455i	$0.711914\pi$
$854$		0			0
$855$	−0.275662	+	4.78196i	−0.00942746	+	0.163540i
$856$		0			0
$857$	26.5320	−	26.5320i	0.906316	−	0.906316i	−0.0896568	−	0.995973i	$-0.528577\pi$
$857$	26.5320	−	26.5320i	0.906316	−	0.906316i	0.995973	+	0.0896568i	$0.0285770\pi$
$858$		0			0
$859$	−9.99547	−	9.99547i	−0.341041	−	0.341041i	0.515718	−	0.856759i	$-0.327525\pi$
$859$	−9.99547	−	9.99547i	−0.341041	−	0.341041i	−0.856759	+	0.515718i	$0.827525\pi$
$860$		0			0
$861$	4.53041			0.154396
$862$		0			0
$863$	4.24981	−	4.24981i	0.144665	−	0.144665i	−0.631065	−	0.775730i	$-0.717382\pi$
$863$	4.24981	−	4.24981i	0.144665	−	0.144665i	0.775730	+	0.631065i	$0.217382\pi$
$864$		0			0
$865$	2.71475	−	47.0932i	0.0923042	−	1.60122i
$866$		0			0
$867$			4.38542i			0.148937i
$868$		0			0
$869$	−33.2749			−1.12877
$870$		0			0
$871$	20.5060			0.694819
$872$		0			0
$873$			0.781483i			0.0264492i
$874$		0			0
$875$	30.5304	+	5.32716i	1.03212	+	0.180091i
$876$		0			0
$877$	−6.45331	+	6.45331i	−0.217913	+	0.217913i	−0.807618	−	0.589706i	$-0.799244\pi$
$877$	−6.45331	+	6.45331i	−0.217913	+	0.217913i	0.589706	+	0.807618i	$0.299244\pi$
$878$		0			0
$879$	−47.7906			−1.61194
$880$		0			0
$881$	21.5282	+	21.5282i	0.725303	+	0.725303i	0.969680	−	0.244377i	$-0.0785836\pi$
$881$	21.5282	+	21.5282i	0.725303	+	0.725303i	−0.244377	+	0.969680i	$0.578584\pi$
$882$		0			0
$883$	20.4272	−	20.4272i	0.687429	−	0.687429i	−0.274234	−	0.961663i	$-0.588424\pi$
$883$	20.4272	−	20.4272i	0.687429	−	0.687429i	0.961663	+	0.274234i	$0.0884242\pi$
$884$		0			0
$885$	17.7946	−	15.8549i	0.598160	−	0.532955i
$886$		0			0
$887$	39.3078			1.31983			0.659913	−	0.751342i	$-0.270593\pi$
$887$	39.3078			1.31983			0.659913	+	0.751342i	$0.270593\pi$
$888$		0			0
$889$	−42.6262	+	42.6262i	−1.42964	+	1.42964i
$890$		0			0
$891$	−15.1538	−	15.1538i	−0.507671	−	0.507671i
$892$		0			0
$893$	3.92182	+	3.92182i	0.131239	+	0.131239i
$894$		0			0
$895$	−19.9917	+	17.8124i	−0.668249	+	0.595404i
$896$		0			0
$897$			19.0721i			0.636800i
$898$		0			0
$899$	34.7228	−	32.9243i	1.15807	−	1.09809i
$900$		0			0
$901$	7.43342	+	7.43342i	0.247643	+	0.247643i
$902$		0			0
$903$	−3.65912	+	3.65912i	−0.121768	+	0.121768i
$904$		0			0
$905$	44.0463	−	39.2449i	1.46415	−	1.30454i
$906$		0			0
$907$			57.9918i			1.92559i	0.270237	+	0.962794i	$0.412898\pi$
$907$			57.9918i			1.92559i	−0.270237	+	0.962794i	$0.587102\pi$
$908$		0			0
$909$	4.92815	+	4.92815i	0.163456	+	0.163456i
$910$		0			0
$911$	−18.3105	+	18.3105i	−0.606653	+	0.606653i	−0.942070	−	0.335417i	$-0.891123\pi$
$911$	−18.3105	+	18.3105i	−0.606653	+	0.606653i	0.335417	+	0.942070i	$0.391123\pi$
$912$		0			0
$913$			8.33836i			0.275959i
$914$		0			0
$915$	0.772532	−	13.4012i	0.0255391	−	0.443032i
$916$		0			0
$917$		−	37.7775i		−	1.24752i
$918$		0			0
$919$		−	24.1742i		−	0.797432i	−0.917075	−	0.398716i	$-0.869456\pi$
$919$		−	24.1742i		−	0.797432i	0.917075	−	0.398716i	$-0.130544\pi$
$920$		0			0
$921$			36.8151i			1.21310i
$922$		0			0
$923$	18.3952	+	18.3952i	0.605487	+	0.605487i
$924$		0			0
$925$	−14.1487	−	1.63668i	−0.465207	−	0.0538137i
$926$		0			0
$927$	1.25960	+	1.25960i	0.0413708	+	0.0413708i
$928$		0			0
$929$			33.7664i			1.10784i	0.832570	+	0.553920i	$0.186869\pi$
$929$			33.7664i			1.10784i	−0.832570	+	0.553920i	$0.813131\pi$
$930$		0			0
$931$	−2.62922	−	2.62922i	−0.0861693	−	0.0861693i
$932$		0			0
$933$	5.14083	−	5.14083i	0.168303	−	0.168303i
$934$		0			0
$935$	23.5955	+	1.36019i	0.771654	+	0.0444830i
$936$		0			0
$937$	−20.0508	−	20.0508i	−0.655031	−	0.655031i	0.299169	−	0.954200i	$-0.403291\pi$
$937$	−20.0508	−	20.0508i	−0.655031	−	0.655031i	−0.954200	+	0.299169i	$0.903291\pi$
$938$		0			0
$939$	6.08250	−	6.08250i	0.198495	−	0.198495i
$940$		0			0
$941$		−	36.0818i		−	1.17623i	−0.808776	−	0.588117i	$-0.799869\pi$
$941$		−	36.0818i		−	1.17623i	0.808776	−	0.588117i	$-0.200131\pi$
$942$		0			0
$943$	4.70526			0.153224
$944$		0			0
$945$	33.9042	+	1.95445i	1.10290	+	0.0635783i
$946$		0			0
$947$	4.44219			0.144352			0.0721759	−	0.997392i	$-0.477006\pi$
$947$	4.44219			0.144352			0.0721759	+	0.997392i	$0.477006\pi$
$948$		0			0
$949$	22.3576	−	22.3576i	0.725758	−	0.725758i
$950$		0			0
$951$	−19.4889			−0.631971
$952$		0			0
$953$	−26.7670	−	26.7670i	−0.867067	−	0.867067i	0.125080	−	0.992147i	$-0.460081\pi$
$953$	−26.7670	−	26.7670i	−0.867067	−	0.867067i	−0.992147	+	0.125080i	$0.960081\pi$
$954$		0			0
$955$	38.3227	+	2.20916i	1.24009	+	0.0714868i
$956$		0			0
$957$	−16.7288	−	17.6426i	−0.540765	−	0.570304i
$958$		0			0
$959$	−1.19320	+	1.19320i	−0.0385304	+	0.0385304i
$960$		0			0
$961$			47.9546i			1.54692i
$962$		0			0
$963$	−2.90510	+	2.90510i	−0.0936156	+	0.0936156i
$964$		0			0
$965$	−20.8709	−	23.4244i	−0.671859	−	0.754058i
$966$		0			0
$967$			23.1984i			0.746010i	0.927829	+	0.373005i	$0.121673\pi$
$967$			23.1984i			0.746010i	−0.927829	+	0.373005i	$0.878327\pi$
$968$		0			0
$969$	23.4558	+	23.4558i	0.753509	+	0.753509i
$970$		0			0
$971$	−7.51735	−	7.51735i	−0.241243	−	0.241243i	0.576121	−	0.817364i	$-0.304566\pi$
$971$	−7.51735	−	7.51735i	−0.241243	−	0.241243i	−0.817364	+	0.576121i	$0.804566\pi$
$972$		0			0
$973$	12.2518	+	12.2518i	0.392775	+	0.392775i
$974$		0			0
$975$	−16.0798	+	12.7454i	−0.514966	+	0.408179i
$976$		0			0
$977$	4.14969	−	4.14969i	0.132760	−	0.132760i	−0.637604	−	0.770364i	$-0.720074\pi$
$977$	4.14969	−	4.14969i	0.132760	−	0.132760i	0.770364	+	0.637604i	$0.220074\pi$
$978$		0			0
$979$	−10.7673			−0.344126
$980$		0			0
$981$	−1.42886			−0.0456199
$982$		0			0
$983$	15.4286			0.492095			0.246047	−	0.969258i	$-0.420868\pi$
$983$	15.4286			0.492095			0.246047	+	0.969258i	$0.420868\pi$
$984$		0			0
$985$	1.09772	−	19.0423i	0.0349761	−	0.606737i
$986$		0			0
$987$	3.22779	−	3.22779i	0.102742	−	0.102742i
$988$		0			0
$989$	−3.80035	+	3.80035i	−0.120844	+	0.120844i
$990$		0			0
$991$		−	22.2159i		−	0.705711i	−0.935678	−	0.352856i	$-0.885211\pi$
$991$		−	22.2159i		−	0.705711i	0.935678	−	0.352856i	$-0.114789\pi$
$992$		0			0
$993$	−6.67241	−	6.67241i	−0.211743	−	0.211743i
$994$		0			0
$995$	−13.7286	−	15.4082i	−0.435226	−	0.488473i
$996$		0			0
$997$	−32.3920			−1.02586			−0.512932	−	0.858429i	$-0.671441\pi$
$997$	−32.3920			−1.02586			−0.512932	+	0.858429i	$0.671441\pi$
$998$		0			0
$999$	−15.6074			−0.493798

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	580.2.j.a.273.4	yes	30
5.2	odd	4		580.2.s.a.157.4	yes	30
5.3	odd	4		2900.2.s.d.157.12		30
5.4	even	2		2900.2.j.d.2593.12		30
29.17	odd	4		580.2.s.a.133.4	yes	30
145.17	even	4	inner	580.2.j.a.17.12	✓	30
145.104	odd	4		2900.2.s.d.1293.12		30
145.133	even	4		2900.2.j.d.1757.4		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
580.2.j.a.17.12	✓	30	145.17	even	4	inner
580.2.j.a.273.4	yes	30	1.1	even	1	trivial
580.2.s.a.133.4	yes	30	29.17	odd	4
580.2.s.a.157.4	yes	30	5.2	odd	4
2900.2.j.d.1757.4		30	145.133	even	4
2900.2.j.d.2593.12		30	5.4	even	2
2900.2.s.d.157.12		30	5.3	odd	4
2900.2.s.d.1293.12		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)

\(f(q)\)	\(=\)	\(q-1.61432i q^{3} +(-1.66951 + 1.48752i) q^{5} +(1.96009 - 1.96009i) q^{7} +0.393986 q^{9} +(1.97757 + 1.97757i) q^{11} +(1.79751 - 1.79751i) q^{13} +(2.40133 + 2.69512i) q^{15} -3.77934 q^{17} +(3.84455 - 3.84455i) q^{19} +(-3.16420 - 3.16420i) q^{21} +(-3.28633 - 3.28633i) q^{23} +(0.574554 - 4.96688i) q^{25} -5.47896i q^{27} +(0.143119 - 5.38326i) q^{29} +(6.28310 + 6.28310i) q^{31} +(3.19243 - 3.19243i) q^{33} +(-0.356719 + 6.18807i) q^{35} -2.84861i q^{37} +(-2.90174 - 2.90174i) q^{39} +(-0.715885 + 0.715885i) q^{41} -1.15641i q^{43} +(-0.657765 + 0.586063i) q^{45} +1.02010i q^{47} -0.683883i q^{49} +6.10105i q^{51} +(-1.96686 - 1.96686i) q^{53} +(-6.24328 - 0.359902i) q^{55} +(-6.20632 - 6.20632i) q^{57} -6.60253i q^{59} +(-2.62953 - 2.62953i) q^{61} +(0.772246 - 0.772246i) q^{63} +(-0.327131 + 5.67479i) q^{65} +(5.70401 + 5.70401i) q^{67} +(-5.30517 + 5.30517i) q^{69} +10.2338i q^{71} +12.4381 q^{73} +(-8.01811 - 0.927511i) q^{75} +7.75244 q^{77} +(-8.41306 + 8.41306i) q^{79} -7.66282 q^{81} +(2.10823 + 2.10823i) q^{83} +(6.30966 - 5.62185i) q^{85} +(-8.69028 - 0.231039i) q^{87} +(-2.72236 + 2.72236i) q^{89} -7.04653i q^{91} +(10.1429 - 10.1429i) q^{93} +(-0.699676 + 12.1374i) q^{95} +1.98353i q^{97} +(0.779136 + 0.779136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 38 q^{9} - 4 q^{11} + 6 q^{13} + 14 q^{15} + 12 q^{17} - 4 q^{21} - 2 q^{25} - 4 q^{31} - 4 q^{33} + 16 q^{35} + 12 q^{39} + 10 q^{41} - 20 q^{45} - 18 q^{53} - 2 q^{55} - 24 q^{57} - 22 q^{61} - 24 q^{63}+ \cdots - 60 q^{95}+O(q^{100}) \) 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

L-functions

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Database

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