LMFDB - Embedded newform 900.2.w.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(109,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("900.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.w (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			289.1
Character	$\chi$	$=$	900.289
Dual form			900.2.w.c.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23394 - 0.0974182i) q^{5} +1.31873i q^{7} +O(q^{10})$	$q+(-2.23394 - 0.0974182i) q^{5} +1.31873i q^{7} +(1.25737 - 0.913532i) q^{11} +(1.42727 - 1.96447i) q^{13} +(1.25004 - 0.406161i) q^{17} +(0.315522 + 0.971077i) q^{19} +(2.94350 + 4.05137i) q^{23} +(4.98102 + 0.435254i) q^{25} +(-1.82443 + 5.61503i) q^{29} +(2.73547 + 8.41891i) q^{31} +(0.128468 - 2.94596i) q^{35} +(-2.95370 + 4.06542i) q^{37} +(6.43499 + 4.67529i) q^{41} -6.84831i q^{43} +(7.37336 + 2.39575i) q^{47} +5.26096 q^{49} +(3.75685 + 1.22067i) q^{53} +(-2.89789 + 1.91829i) q^{55} +(6.35355 + 4.61613i) q^{59} +(2.83287 - 2.05820i) q^{61} +(-3.37982 + 4.24947i) q^{65} +(-7.92426 + 2.57475i) q^{67} +(4.00454 - 12.3247i) q^{71} +(-7.47339 - 10.2862i) q^{73} +(1.20470 + 1.65812i) q^{77} +(0.386585 - 1.18979i) q^{79} +(7.80521 - 2.53607i) q^{83} +(-2.83208 + 0.785565i) q^{85} +(-7.74667 + 5.62829i) q^{89} +(2.59059 + 1.88218i) q^{91} +(-0.610258 - 2.20007i) q^{95} +(-15.4769 - 5.02874i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5}+O(q^{10}) $ 24 * q + 2 * q^5	$ 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.23394	−	0.0974182i	−0.999051	−	0.0435667i
$5$	−2.23394	−	0.0974182i	−0.999051	−	0.0435667i
$6$		0			0
$7$			1.31873i			0.498431i	0.968448	+	0.249216i	$0.0801728\pi$
$7$			1.31873i			0.498431i	−0.968448	+	0.249216i	$0.919827\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.25737	−	0.913532i	0.379111	−	0.275440i	−0.381868	−	0.924217i	$-0.624719\pi$
$11$	1.25737	−	0.913532i	0.379111	−	0.275440i	0.760979	+	0.648777i	$0.224719\pi$
$12$		0			0
$13$	1.42727	−	1.96447i	0.395854	−	0.544846i	−0.563844	−	0.825882i	$-0.690678\pi$
$13$	1.42727	−	1.96447i	0.395854	−	0.544846i	0.959697	+	0.281036i	$0.0906780\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.25004	−	0.406161i	0.303178	−	0.0985085i	−0.153477	−	0.988152i	$-0.549047\pi$
$17$	1.25004	−	0.406161i	0.303178	−	0.0985085i	0.456655	+	0.889644i	$0.349047\pi$
$18$		0			0
$19$	0.315522	+	0.971077i	0.0723857	+	0.222780i	0.980704	−	0.195500i	$-0.0626330\pi$
$19$	0.315522	+	0.971077i	0.0723857	+	0.222780i	−0.908318	+	0.418280i	$0.862633\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.94350	+	4.05137i	0.613761	+	0.844770i	0.996880	−	0.0789291i	$-0.0251501\pi$
$23$	2.94350	+	4.05137i	0.613761	+	0.844770i	−0.383119	+	0.923699i	$0.625150\pi$
$24$		0			0
$25$	4.98102	+	0.435254i	0.996204	+	0.0870507i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.82443	+	5.61503i	−0.338789	+	1.04268i	0.626037	+	0.779794i	$0.284676\pi$
$29$	−1.82443	+	5.61503i	−0.338789	+	1.04268i	−0.964825	+	0.262891i	$0.915324\pi$
$30$		0			0
$31$	2.73547	+	8.41891i	0.491305	+	1.51208i	0.822637	+	0.568567i	$0.192502\pi$
$31$	2.73547	+	8.41891i	0.491305	+	1.51208i	−0.331332	+	0.943514i	$0.607498\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.128468	−	2.94596i	0.0217150	−	0.497958i
$36$		0			0
$37$	−2.95370	+	4.06542i	−0.485586	+	0.668352i	−0.979566	−	0.201121i	$-0.935541\pi$
$37$	−2.95370	+	4.06542i	−0.485586	+	0.668352i	0.493981	+	0.869473i	$0.335541\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	6.43499	+	4.67529i	1.00498	+	0.730158i	0.963150	−	0.268967i	$-0.0866821\pi$
$41$	6.43499	+	4.67529i	1.00498	+	0.730158i	0.0418271	+	0.999125i	$0.486682\pi$
$42$		0			0
$43$		−	6.84831i		−	1.04436i	−0.852836	−	0.522179i	$-0.825119\pi$
$43$		−	6.84831i		−	1.04436i	0.852836	−	0.522179i	$-0.174881\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	7.37336	+	2.39575i	1.07552	+	0.349456i	0.792633	−	0.609698i	$-0.208709\pi$
$47$	7.37336	+	2.39575i	1.07552	+	0.349456i	0.282882	+	0.959155i	$0.408709\pi$
$48$		0			0
$49$	5.26096			0.751566
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.75685	+	1.22067i	0.516043	+	0.167673i	0.555449	−	0.831551i	$-0.312546\pi$
$53$	3.75685	+	1.22067i	0.516043	+	0.167673i	−0.0394057	+	0.999223i	$0.512546\pi$
$54$		0			0
$55$	−2.89789	+	1.91829i	−0.390751	+	0.258662i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.35355	+	4.61613i	0.827162	+	0.600969i	0.918755	−	0.394828i	$-0.129196\pi$
$59$	6.35355	+	4.61613i	0.827162	+	0.600969i	−0.0915928	+	0.995797i	$0.529196\pi$
$60$		0			0
$61$	2.83287	−	2.05820i	0.362711	−	0.263525i	−0.391471	−	0.920191i	$-0.628034\pi$
$61$	2.83287	−	2.05820i	0.362711	−	0.263525i	0.754182	+	0.656665i	$0.228034\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.37982	+	4.24947i	−0.419215	+	0.527082i
$66$		0			0
$67$	−7.92426	+	2.57475i	−0.968102	+	0.314555i	−0.750050	−	0.661382i	$-0.769970\pi$
$67$	−7.92426	+	2.57475i	−0.968102	+	0.314555i	−0.218052	+	0.975937i	$0.569970\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.00454	−	12.3247i	0.475252	−	1.46267i	−0.370366	−	0.928886i	$-0.620768\pi$
$71$	4.00454	−	12.3247i	0.475252	−	1.46267i	0.845618	−	0.533788i	$-0.179232\pi$
$72$		0			0
$73$	−7.47339	−	10.2862i	−0.874694	−	1.20391i	−0.977862	−	0.209249i	$-0.932898\pi$
$73$	−7.47339	−	10.2862i	−0.874694	−	1.20391i	0.103168	−	0.994664i	$-0.467102\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.20470	+	1.65812i	0.137288	+	0.188961i
$78$		0			0
$79$	0.386585	−	1.18979i	0.0434942	−	0.133861i	−0.926951	−	0.375182i	$-0.877580\pi$
$79$	0.386585	−	1.18979i	0.0434942	−	0.133861i	0.970446	+	0.241320i	$0.0775804\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.80521	−	2.53607i	0.856734	−	0.278370i	0.152470	−	0.988308i	$-0.451277\pi$
$83$	7.80521	−	2.53607i	0.856734	−	0.278370i	0.704264	+	0.709939i	$0.251277\pi$
$84$		0			0
$85$	−2.83208	+	0.785565i	−0.307182	+	0.0852065i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−7.74667	+	5.62829i	−0.821146	+	0.596597i	−0.917040	−	0.398794i	$-0.869429\pi$
$89$	−7.74667	+	5.62829i	−0.821146	+	0.596597i	0.0958948	+	0.995391i	$0.469429\pi$
$90$		0			0
$91$	2.59059	+	1.88218i	0.271568	+	0.197306i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.610258	−	2.20007i	−0.0626112	−	0.225722i
$96$		0			0
$97$	−15.4769	−	5.02874i	−1.57144	−	0.510591i	−0.611604	−	0.791164i	$-0.709476\pi$
$97$	−15.4769	−	5.02874i	−1.57144	−	0.510591i	−0.959833	+	0.280573i	$0.909476\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.63722			−0.560925			−0.280462	−	0.959865i	$-0.590488\pi$
$101$	−5.63722			−0.560925			−0.280462	+	0.959865i	$0.590488\pi$
$102$		0			0
$103$	8.00179	+	2.59994i	0.788439	+	0.256179i	0.675439	−	0.737415i	$-0.263954\pi$
$103$	8.00179	+	2.59994i	0.788439	+	0.256179i	0.113000	+	0.993595i	$0.463954\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	2.06196i		−	0.199337i	−0.995021	−	0.0996687i	$-0.968222\pi$
$107$		−	2.06196i		−	0.199337i	0.995021	−	0.0996687i	$-0.0317783\pi$
$108$		0			0
$109$	11.3052	+	8.21372i	1.08284	+	0.786731i	0.978176	−	0.207776i	$-0.0666226\pi$
$109$	11.3052	+	8.21372i	1.08284	+	0.786731i	0.104666	+	0.994507i	$0.466623\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−3.50093	+	4.81862i	−0.329340	+	0.453297i	−0.941290	−	0.337599i	$-0.890385\pi$
$113$	−3.50093	+	4.81862i	−0.329340	+	0.453297i	0.611950	+	0.790896i	$0.290385\pi$
$114$		0			0
$115$	−6.18093	−	9.33730i	−0.576375	−	0.870707i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.535615	+	1.64845i	0.0490997	+	0.151113i
$120$		0			0
$121$	−2.65275	+	8.16433i	−0.241159	+	0.742211i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.0849	−	1.45757i	−0.991465	−	0.130369i
$126$		0			0
$127$	−1.42406	−	1.96004i	−0.126364	−	0.173926i	0.741147	−	0.671342i	$-0.234282\pi$
$127$	−1.42406	−	1.96004i	−0.126364	−	0.173926i	−0.867512	+	0.497417i	$0.834282\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.37948	−	10.4010i	−0.295267	−	0.908737i	−0.983132	−	0.182899i	$-0.941452\pi$
$131$	−3.37948	−	10.4010i	−0.295267	−	0.908737i	0.687865	−	0.725839i	$-0.258548\pi$
$132$		0			0
$133$	−1.28058	+	0.416087i	−0.111041	+	0.0360793i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.19602	+	3.02256i	−0.187618	+	0.258235i	−0.892456	−	0.451134i	$-0.851020\pi$
$137$	−2.19602	+	3.02256i	−0.187618	+	0.258235i	0.704838	+	0.709368i	$0.251020\pi$
$138$		0			0
$139$	−1.73765	+	1.26247i	−0.147385	+	0.107082i	−0.659034	−	0.752113i	$-0.729035\pi$
$139$	−1.73765	+	1.26247i	−0.147385	+	0.107082i	0.511649	+	0.859194i	$0.329035\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	3.77392i		−	0.315591i
$144$		0			0
$145$	4.62269	−	12.3659i	0.383894	−	1.02693i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.85344			−0.643379			−0.321690	−	0.946845i	$-0.604251\pi$
$149$	−7.85344			−0.643379			−0.321690	+	0.946845i	$0.604251\pi$
$150$		0			0
$151$	22.5124			1.83203			0.916016	−	0.401141i	$-0.131386\pi$
$151$	22.5124			1.83203			0.916016	+	0.401141i	$0.131386\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.29073	−	19.0739i	−0.424962	−	1.53205i
$156$		0			0
$157$			19.4083i			1.54895i	0.632602	+	0.774477i	$0.281987\pi$
$157$			19.4083i			1.54895i	−0.632602	+	0.774477i	$0.718013\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−5.34265	+	3.88166i	−0.421060	+	0.305918i
$162$		0			0
$163$	8.89817	−	12.2473i	0.696959	−	0.959281i	−0.303022	−	0.952984i	$-0.597995\pi$
$163$	8.89817	−	12.2473i	0.696959	−	0.959281i	0.999980	−	0.00629741i	$-0.00200454\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−17.9807	+	5.84227i	−1.39139	+	0.452089i	−0.906395	−	0.422431i	$-0.861177\pi$
$167$	−17.9807	+	5.84227i	−1.39139	+	0.452089i	−0.484990	+	0.874519i	$0.661177\pi$
$168$		0			0
$169$	2.19518	+	6.75608i	0.168860	+	0.519698i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−14.1479	−	19.4729i	−1.07564	−	1.48050i	−0.864228	−	0.503100i	$-0.832193\pi$
$173$	−14.1479	−	19.4729i	−1.07564	−	1.48050i	−0.211415	−	0.977396i	$-0.567807\pi$
$174$		0			0
$175$	−0.573980	+	6.56860i	−0.0433888	+	0.496539i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.461162	−	1.41931i	0.0344689	−	0.106084i	−0.932342	−	0.361578i	$-0.882238\pi$
$179$	0.461162	−	1.41931i	0.0344689	−	0.106084i	0.966811	+	0.255494i	$0.0822381\pi$
$180$		0			0
$181$	−0.809018	−	2.48990i	−0.0601338	−	0.185073i	0.916477	−	0.400087i	$-0.131020\pi$
$181$	−0.809018	−	2.48990i	−0.0601338	−	0.185073i	−0.976611	+	0.215014i	$0.931020\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.99446	−	8.79419i	0.514243	−	0.646562i
$186$		0			0
$187$	1.20071	−	1.65264i	0.0878050	−	0.120853i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	16.6599	+	12.1041i	1.20547	+	0.875824i	0.994811	−	0.101736i	$-0.0324398\pi$
$191$	16.6599	+	12.1041i	1.20547	+	0.875824i	0.210657	+	0.977560i	$0.432440\pi$
$192$		0			0
$193$			5.15953i			0.371391i	0.982607	+	0.185696i	$0.0594539\pi$
$193$			5.15953i			0.371391i	−0.982607	+	0.185696i	$0.940546\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.99630	−	3.24799i	−0.712207	−	0.231410i	−0.0695657	−	0.997577i	$-0.522161\pi$
$197$	−9.99630	−	3.24799i	−0.712207	−	0.231410i	−0.642641	+	0.766167i	$0.722161\pi$
$198$		0			0
$199$	−3.65216			−0.258895			−0.129447	−	0.991586i	$-0.541320\pi$
$199$	−3.65216			−0.258895			−0.129447	+	0.991586i	$0.541320\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.40468	−	2.40593i	−0.519707	−	0.168863i
$204$		0			0
$205$	−13.9200	−	11.0712i	−0.972212	−	0.773249i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.28384	+	0.932763i	0.0888049	+	0.0645206i
$210$		0			0
$211$	21.3259	−	15.4941i	1.46813	−	1.06666i	0.486983	−	0.873411i	$-0.338097\pi$
$211$	21.3259	−	15.4941i	1.46813	−	1.06666i	0.981150	−	0.193249i	$-0.0619026\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.667150	+	15.2988i	−0.0454993	+	1.04337i
$216$		0			0
$217$	−11.1022	+	3.60733i	−0.753669	+	0.244882i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.986247	−	3.03536i	0.0663422	−	0.204180i
$222$		0			0
$223$	−10.8706	−	14.9621i	−0.727950	−	1.00194i	−0.999222	−	0.0394348i	$-0.987444\pi$
$223$	−10.8706	−	14.9621i	−0.727950	−	1.00194i	0.271272	−	0.962503i	$-0.412556\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−10.9690	−	15.0976i	−0.728039	−	1.00206i	−0.999218	−	0.0395311i	$-0.987414\pi$
$227$	−10.9690	−	15.0976i	−0.728039	−	1.00206i	0.271179	−	0.962529i	$-0.412586\pi$
$228$		0			0
$229$	−8.63423	+	26.5734i	−0.570566	+	1.75602i	0.0802368	+	0.996776i	$0.474432\pi$
$229$	−8.63423	+	26.5734i	−0.570566	+	1.75602i	−0.650803	+	0.759247i	$0.725568\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	23.5456	−	7.65043i	1.54252	−	0.501196i	0.590452	−	0.807073i	$-0.298950\pi$
$233$	23.5456	−	7.65043i	1.54252	−	0.501196i	0.952071	+	0.305877i	$0.0989495\pi$
$234$		0			0
$235$	−16.2383	−	6.07028i	−1.05927	−	0.395981i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.47102	−	6.88110i	0.612629	−	0.445101i	−0.237710	−	0.971336i	$-0.576397\pi$
$239$	9.47102	−	6.88110i	0.612629	−	0.445101i	0.850339	+	0.526235i	$0.176397\pi$
$240$		0			0
$241$	−24.1221	−	17.5257i	−1.55384	−	1.12893i	−0.940842	−	0.338846i	$-0.889963\pi$
$241$	−24.1221	−	17.5257i	−1.55384	−	1.12893i	−0.612998	−	0.790084i	$-0.710037\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.7527	−	0.512514i	−0.750853	−	0.0327433i
$246$		0			0
$247$	2.35799	+	0.766156i	0.150035	+	0.0487493i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.87297			0.181340			0.0906700	−	0.995881i	$-0.471099\pi$
$251$	2.87297			0.181340			0.0906700	+	0.995881i	$0.471099\pi$
$252$		0			0
$253$	7.40212	+	2.40510i	0.465367	+	0.151207i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			8.11716i			0.506334i	0.967423	+	0.253167i	$0.0814723\pi$
$257$			8.11716i			0.506334i	−0.967423	+	0.253167i	$0.918528\pi$
$258$		0			0
$259$	−5.36118	−	3.89512i	−0.333127	−	0.242031i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.1117	+	18.0467i	−0.808501	+	1.11281i	0.183051	+	0.983103i	$0.441403\pi$
$263$	−13.1117	+	18.0467i	−0.808501	+	1.11281i	−0.991553	+	0.129703i	$0.958597\pi$
$264$		0			0
$265$	−8.27368	−	3.09291i	−0.508248	−	0.189996i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.53369	−	7.79789i	−0.154482	−	0.475446i	0.843626	−	0.536931i	$-0.180416\pi$
$269$	−2.53369	−	7.79789i	−0.154482	−	0.475446i	−0.998108	+	0.0614851i	$0.980416\pi$
$270$		0			0
$271$	−2.93158	+	9.02246i	−0.178081	+	0.548075i	−0.999761	−	0.0218733i	$-0.993037\pi$
$271$	−2.93158	+	9.02246i	−0.178081	+	0.548075i	0.821680	+	0.569949i	$0.193037\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.66060	−	4.00305i	0.401649	−	0.241393i
$276$		0			0
$277$	0.270190	+	0.371885i	0.0162341	+	0.0223444i	0.817057	−	0.576557i	$-0.195604\pi$
$277$	0.270190	+	0.371885i	0.0162341	+	0.0223444i	−0.800823	+	0.598901i	$0.795604\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4.71493	+	14.5111i	0.281269	+	0.865658i	0.987492	+	0.157668i	$0.0503977\pi$
$281$	4.71493	+	14.5111i	0.281269	+	0.865658i	−0.706223	+	0.707990i	$0.749602\pi$
$282$		0			0
$283$	10.1502	−	3.29800i	0.603366	−	0.196046i	0.00862506	−	0.999963i	$-0.497255\pi$
$283$	10.1502	−	3.29800i	0.603366	−	0.196046i	0.594741	+	0.803917i	$0.297255\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.16543	+	8.48598i	−0.363934	+	0.500912i
$288$		0			0
$289$	−12.3557	+	8.97692i	−0.726804	+	0.528054i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	30.8334i		−	1.80130i	−0.434541	−	0.900652i	$-0.643089\pi$
$293$		−	30.8334i		−	1.80130i	0.434541	−	0.900652i	$-0.356911\pi$
$294$		0			0
$295$	−13.7438	−	10.9311i	−0.800195	−	0.636435i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	12.1600			0.703229
$300$		0			0
$301$	9.03104			0.520541
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.52897	+	4.32193i	−0.373848	+	0.247473i
$306$		0			0
$307$		−	17.8634i		−	1.01952i	−0.860318	−	0.509758i	$-0.829735\pi$
$307$		−	17.8634i		−	1.01952i	0.860318	−	0.509758i	$-0.170265\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.75942	+	7.09063i	−0.553406	+	0.402073i	−0.829040	−	0.559190i	$-0.811112\pi$
$311$	−9.75942	+	7.09063i	−0.553406	+	0.402073i	0.275634	+	0.961263i	$0.411112\pi$
$312$		0			0
$313$	11.0264	−	15.1766i	0.623250	−	0.857830i	−0.374335	−	0.927294i	$-0.622129\pi$
$313$	11.0264	−	15.1766i	0.623250	−	0.857830i	0.997584	+	0.0694641i	$0.0221289\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.1912	−	3.31133i	0.572395	−	0.185983i	−0.00849553	−	0.999964i	$-0.502704\pi$
$317$	10.1912	−	3.31133i	0.572395	−	0.185983i	0.580891	+	0.813981i	$0.302704\pi$
$318$		0			0
$319$	2.83552	+	8.72685i	0.158759	+	0.488610i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	0.788827	+	1.08573i	0.0438915	+	0.0604115i
$324$		0			0
$325$	7.96430	−	9.16383i	0.441780	−	0.508318i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.15934	+	9.72344i	−0.174180	+	0.536071i
$330$		0			0
$331$	0.671547	+	2.06681i	0.0369116	+	0.113602i	0.967815	−	0.251664i	$-0.0809779\pi$
$331$	0.671547	+	2.06681i	0.0369116	+	0.113602i	−0.930903	+	0.365266i	$0.880978\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	17.9532	−	4.97988i	0.980887	−	0.272080i
$336$		0			0
$337$	−5.91844	+	8.14603i	−0.322398	+	0.443743i	−0.939197	−	0.343378i	$-0.888429\pi$
$337$	−5.91844	+	8.14603i	−0.322398	+	0.443743i	0.616800	+	0.787120i	$0.288429\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.1304	+	8.08674i	0.602747	+	0.437922i
$342$		0			0
$343$			16.1688i			0.873035i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.9570	−	4.53489i	−0.749249	−	0.243446i	−0.0905912	−	0.995888i	$-0.528876\pi$
$347$	−13.9570	−	4.53489i	−0.749249	−	0.243446i	−0.658658	+	0.752442i	$0.728876\pi$
$348$		0			0
$349$	−18.5685			−0.993949			−0.496974	−	0.867765i	$-0.665556\pi$
$349$	−18.5685			−0.993949			−0.496974	+	0.867765i	$0.665556\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.5663	−	5.70763i	−0.934959	−	0.303787i	−0.198370	−	0.980127i	$-0.563565\pi$
$353$	−17.5663	−	5.70763i	−0.934959	−	0.303787i	−0.736589	+	0.676340i	$0.763565\pi$
$354$		0			0
$355$	−10.1466	+	27.1426i	−0.538524	+	1.44058i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	19.9550	+	14.4981i	1.05318	+	0.765182i	0.972815	−	0.231583i	$-0.0743906\pi$
$359$	19.9550	+	14.4981i	1.05318	+	0.765182i	0.0803676	+	0.996765i	$0.474391\pi$
$360$		0			0
$361$	14.5279	−	10.5551i	0.764626	−	0.555533i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.6931	+	23.7069i	0.821413	+	1.24088i
$366$		0			0
$367$	12.4469	−	4.04423i	0.649721	−	0.211107i	0.0344301	−	0.999407i	$-0.489038\pi$
$367$	12.4469	−	4.04423i	0.649721	−	0.211107i	0.615291	+	0.788300i	$0.289038\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.60973	+	4.95425i	−0.0835733	+	0.257212i
$372$		0			0
$373$	−0.174079	−	0.239599i	−0.00901348	−	0.0124060i	0.804486	−	0.593971i	$-0.202441\pi$
$373$	−0.174079	−	0.239599i	−0.00901348	−	0.0124060i	−0.813500	+	0.581565i	$0.802441\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.42659	+	11.5982i	0.433992	+	0.597338i
$378$		0			0
$379$	−2.41901	+	7.44495i	−0.124256	+	0.382421i	−0.993765	−	0.111496i	$-0.964436\pi$
$379$	−2.41901	+	7.44495i	−0.124256	+	0.382421i	0.869509	+	0.493918i	$0.164436\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	19.8293	−	6.44294i	1.01323	−	0.329219i	0.245090	−	0.969500i	$-0.421182\pi$
$383$	19.8293	−	6.44294i	1.01323	−	0.329219i	0.768140	+	0.640282i	$0.221182\pi$
$384$		0			0
$385$	−2.52970	−	3.82152i	−0.128925	−	0.194763i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	22.6010	−	16.4206i	1.14592	−	0.832558i	0.157985	−	0.987441i	$-0.449500\pi$
$389$	22.6010	−	16.4206i	1.14592	−	0.832558i	0.987933	+	0.154883i	$0.0495001\pi$
$390$		0			0
$391$	5.32498	+	3.86883i	0.269296	+	0.195655i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−0.979517	+	2.62026i	−0.0492848	+	0.131839i
$396$		0			0
$397$	30.6358	+	9.95418i	1.53757	+	0.499586i	0.950704	−	0.310100i	$-0.100363\pi$
$397$	30.6358	+	9.95418i	1.53757	+	0.499586i	0.586863	+	0.809686i	$0.300363\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.3441			0.516562			0.258281	−	0.966070i	$-0.416844\pi$
$401$	10.3441			0.516562			0.258281	+	0.966070i	$0.416844\pi$
$402$		0			0
$403$	20.4429	+	6.64232i	1.01834	+	0.330877i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			7.81004i			0.387129i
$408$		0			0
$409$	29.7399	+	21.6073i	1.47054	+	1.06841i	0.980456	+	0.196739i	$0.0630351\pi$
$409$	29.7399	+	21.6073i	1.47054	+	1.06841i	0.490087	+	0.871673i	$0.336965\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.08740	+	8.37859i	−0.299542	+	0.412284i
$414$		0			0
$415$	−17.6835	+	4.90507i	−0.868048	+	0.240780i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.74262	−	26.9070i	−0.427105	−	1.31449i	−0.900964	−	0.433894i	$-0.857139\pi$
$419$	−8.74262	−	26.9070i	−0.427105	−	1.31449i	0.473859	−	0.880601i	$-0.342861\pi$
$420$		0			0
$421$	0.392142	−	1.20689i	0.0191118	−	0.0588202i	−0.941046	−	0.338279i	$-0.890155\pi$
$421$	0.392142	−	1.20689i	0.0191118	−	0.0588202i	0.960158	+	0.279459i	$0.0901551\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.40323	−	1.47901i	0.310602	−	0.0717427i
$426$		0			0
$427$	2.71420	+	3.73577i	0.131349	+	0.180787i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.24011	−	6.89434i	−0.107902	−	0.332089i	0.882498	−	0.470315i	$-0.155860\pi$
$431$	−2.24011	−	6.89434i	−0.107902	−	0.332089i	−0.990401	+	0.138226i	$0.955860\pi$
$432$		0			0
$433$	3.64988	−	1.18592i	0.175402	−	0.0569916i	−0.219999	−	0.975500i	$-0.570606\pi$
$433$	3.64988	−	1.18592i	0.175402	−	0.0569916i	0.395401	+	0.918508i	$0.370606\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.00546	+	4.13666i	−0.143771	+	0.197883i
$438$		0			0
$439$	25.5358	−	18.5528i	1.21876	−	0.885479i	0.222761	−	0.974873i	$-0.428493\pi$
$439$	25.5358	−	18.5528i	1.21876	−	0.885479i	0.995996	+	0.0893940i	$0.0284930\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			2.65284i			0.126040i	0.998012	+	0.0630200i	$0.0200732\pi$
$443$			2.65284i			0.126040i	−0.998012	+	0.0630200i	$0.979927\pi$
$444$		0			0
$445$	17.8539	−	11.8186i	0.846358	−	0.560256i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−27.3646			−1.29142			−0.645709	−	0.763584i	$-0.723438\pi$
$449$	−27.3646			−1.29142			−0.645709	+	0.763584i	$0.723438\pi$
$450$		0			0
$451$	12.3622			0.582113
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−5.60389	−	4.45705i	−0.262714	−	0.208950i
$456$		0			0
$457$			1.66698i			0.0779781i	0.999240	+	0.0389891i	$0.0124138\pi$
$457$			1.66698i			0.0779781i	−0.999240	+	0.0389891i	$0.987586\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−27.8272	+	20.2176i	−1.29604	+	0.941630i	−0.999909	−	0.0135170i	$-0.995697\pi$
$461$	−27.8272	+	20.2176i	−1.29604	+	0.941630i	−0.296133	+	0.955147i	$0.595697\pi$
$462$		0			0
$463$	−20.7939	+	28.6204i	−0.966377	+	1.33010i	−0.0225205	+	0.999746i	$0.507169\pi$
$463$	−20.7939	+	28.6204i	−0.966377	+	1.33010i	−0.943856	+	0.330357i	$0.892831\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−22.9613	+	7.46057i	−1.06252	+	0.345234i	−0.787571	−	0.616224i	$-0.788662\pi$
$467$	−22.9613	+	7.46057i	−1.06252	+	0.345234i	−0.274951	+	0.961458i	$0.588662\pi$
$468$		0			0
$469$	−3.39538	−	10.4499i	−0.156784	−	0.482532i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−6.25615	−	8.61086i	−0.287658	−	0.395928i
$474$		0			0
$475$	1.14896	+	4.97428i	0.0527177	+	0.228236i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.03656	+	21.6563i	−0.321509	+	0.989502i	0.651483	+	0.758663i	$0.274147\pi$
$479$	−7.03656	+	21.6563i	−0.321509	+	0.989502i	−0.972992	+	0.230839i	$0.925853\pi$
$480$		0			0
$481$	3.77067	+	11.6049i	0.171928	+	0.529139i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	34.0846	+	12.7416i	1.54770	+	0.578568i
$486$		0			0
$487$	−5.49973	+	7.56973i	−0.249217	+	0.343017i	−0.915237	−	0.402917i	$-0.867996\pi$
$487$	−5.49973	+	7.56973i	−0.249217	+	0.343017i	0.666020	+	0.745934i	$0.267996\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	14.7363	+	10.7066i	0.665042	+	0.483181i	0.868362	−	0.495931i	$-0.165173\pi$
$491$	14.7363	+	10.7066i	0.665042	+	0.483181i	−0.203320	+	0.979112i	$0.565173\pi$
$492$		0			0
$493$			7.76000i			0.349493i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	16.2529	+	5.28089i	0.729043	+	0.236880i
$498$		0			0
$499$	−6.14936			−0.275283			−0.137642	−	0.990482i	$-0.543952\pi$
$499$	−6.14936			−0.275283			−0.137642	+	0.990482i	$0.543952\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	15.0653	+	4.89502i	0.671730	+	0.218258i	0.624971	−	0.780648i	$-0.285111\pi$
$503$	15.0653	+	4.89502i	0.671730	+	0.218258i	0.0467590	+	0.998906i	$0.485111\pi$
$504$		0			0
$505$	12.5932	+	0.549168i	0.560392	+	0.0244377i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.09898	+	2.97808i	0.181684	+	0.132001i	0.674910	−	0.737900i	$-0.264182\pi$
$509$	4.09898	+	2.97808i	0.181684	+	0.132001i	−0.493226	+	0.869901i	$0.664182\pi$
$510$		0			0
$511$	13.5647	−	9.85535i	0.600068	−	0.435975i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−17.6223	−	6.58764i	−0.776530	−	0.290286i
$516$		0			0
$517$	11.4596	−	3.72346i	0.503994	−	0.163758i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.2578	−	34.6481i	0.493215	−	1.51796i	−0.326505	−	0.945195i	$-0.605871\pi$
$521$	11.2578	−	34.6481i	0.493215	−	1.51796i	0.819720	−	0.572764i	$-0.194129\pi$
$522$		0			0
$523$	−6.80572	−	9.36727i	−0.297593	−	0.409602i	0.633869	−	0.773441i	$-0.281466\pi$
$523$	−6.80572	−	9.36727i	−0.297593	−	0.409602i	−0.931462	+	0.363839i	$0.881466\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.83887	+	9.41289i	0.297906	+	0.410032i
$528$		0			0
$529$	−0.642075	+	1.97610i	−0.0279163	+	0.0859175i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.3689	−	5.96843i	0.795647	−	0.258521i
$534$		0			0
$535$	−0.200873	+	4.60631i	−0.00868448	+	0.199148i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.61498	−	4.80606i	0.284927	−	0.207012i
$540$		0			0
$541$	−17.2715	−	12.5485i	−0.742559	−	0.539500i	0.150953	−	0.988541i	$-0.451766\pi$
$541$	−17.2715	−	12.5485i	−0.742559	−	0.539500i	−0.893511	+	0.449041i	$0.851766\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−24.4550	−	19.4503i	−1.04754	−	0.833160i
$546$		0			0
$547$	−24.1049	−	7.83217i	−1.03065	−	0.334879i	−0.255604	−	0.966781i	$-0.582274\pi$
$547$	−24.1049	−	7.83217i	−1.03065	−	0.334879i	−0.775048	+	0.631902i	$0.782274\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.02827			−0.256813
$552$		0			0
$553$	1.56900	+	0.509800i	0.0667207	+	0.0216789i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			0.953134i			0.0403856i	0.999796	+	0.0201928i	$0.00642800\pi$
$557$			0.953134i			0.0403856i	−0.999796	+	0.0201928i	$0.993572\pi$
$558$		0			0
$559$	−13.4533	−	9.77439i	−0.569014	−	0.413413i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−17.9315	+	24.6806i	−0.755723	+	1.04016i	0.241835	+	0.970317i	$0.422251\pi$
$563$	−17.9315	+	24.6806i	−0.755723	+	1.04016i	−0.997558	+	0.0698461i	$0.977749\pi$
$564$		0			0
$565$	8.29030	−	10.4235i	0.348776	−	0.438519i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	9.81510	+	30.2078i	0.411471	+	1.26638i	0.915370	+	0.402614i	$0.131898\pi$
$569$	9.81510	+	30.2078i	0.411471	+	1.26638i	−0.503899	+	0.863762i	$0.668102\pi$
$570$		0			0
$571$	−8.65796	+	26.6465i	−0.362324	+	1.11512i	0.589315	+	0.807903i	$0.299398\pi$
$571$	−8.65796	+	26.6465i	−0.362324	+	1.11512i	−0.951640	+	0.307217i	$0.900602\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	12.8982	+	21.4611i	0.537893	+	0.894991i
$576$		0			0
$577$	−3.33187	−	4.58593i	−0.138708	−	0.190915i	0.734012	−	0.679137i	$-0.237646\pi$
$577$	−3.33187	−	4.58593i	−0.138708	−	0.190915i	−0.872719	+	0.488222i	$0.837646\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.34438	+	10.2929i	0.138748	+	0.427023i
$582$		0			0
$583$	5.83888	−	1.89717i	0.241822	−	0.0785726i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	19.9949	−	27.5206i	0.825278	−	1.13590i	−0.163506	−	0.986542i	$-0.552280\pi$
$587$	19.9949	−	27.5206i	0.825278	−	1.13590i	0.988784	−	0.149355i	$-0.0477197\pi$
$588$		0			0
$589$	−7.31231	+	5.31270i	−0.301298	+	0.218906i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			22.9225i			0.941313i	0.882316	+	0.470657i	$0.155983\pi$
$593$			22.9225i			0.941313i	−0.882316	+	0.470657i	$0.844017\pi$
$594$		0			0
$595$	−1.03594	−	3.73473i	−0.0424696	−	0.153109i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−17.7017			−0.723270			−0.361635	−	0.932320i	$-0.617781\pi$
$599$	−17.7017			−0.723270			−0.361635	+	0.932320i	$0.617781\pi$
$600$		0			0
$601$	−28.8773			−1.17793			−0.588964	−	0.808159i	$-0.700464\pi$
$601$	−28.8773			−1.17793			−0.588964	+	0.808159i	$0.700464\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.72145	−	17.9802i	0.273266	−	0.731000i
$606$		0			0
$607$		−	11.5926i		−	0.470528i	−0.971932	−	0.235264i	$-0.924405\pi$
$607$		−	11.5926i		−	0.470528i	0.971932	−	0.235264i	$-0.0755954\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	15.2302	−	11.0654i	0.616146	−	0.447657i
$612$		0			0
$613$	−7.48123	+	10.2970i	−0.302164	+	0.415893i	−0.932917	−	0.360090i	$-0.882746\pi$
$613$	−7.48123	+	10.2970i	−0.302164	+	0.415893i	0.630754	+	0.775983i	$0.282746\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	40.7643	−	13.2451i	1.64111	−	0.533229i	0.664323	−	0.747446i	$-0.268720\pi$
$617$	40.7643	−	13.2451i	1.64111	−	0.533229i	0.976786	+	0.214217i	$0.0687199\pi$
$618$		0			0
$619$	−4.30448	−	13.2478i	−0.173012	−	0.532475i	0.826525	−	0.562899i	$-0.190314\pi$
$619$	−4.30448	−	13.2478i	−0.173012	−	0.532475i	−0.999537	+	0.0304242i	$0.990314\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.42216	−	10.2157i	−0.297363	−	0.409285i
$624$		0			0
$625$	24.6211	+	4.33601i	0.984844	+	0.173441i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.04102	+	6.28160i	−0.0813806	+	0.250464i
$630$		0			0
$631$	−2.66089	−	8.18939i	−0.105928	−	0.326014i	0.884019	−	0.467451i	$-0.154828\pi$
$631$	−2.66089	−	8.18939i	−0.105928	−	0.326014i	−0.989947	+	0.141437i	$0.954828\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	2.99032	+	4.51736i	0.118667	+	0.179266i
$636$		0			0
$637$	7.50882	−	10.3350i	0.297510	−	0.409488i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−17.0591	−	12.3942i	−0.673794	−	0.489540i	0.197499	−	0.980303i	$-0.436718\pi$
$641$	−17.0591	−	12.3942i	−0.673794	−	0.489540i	−0.871293	+	0.490763i	$0.836718\pi$
$642$		0			0
$643$			12.2412i			0.482747i	0.970432	+	0.241374i	$0.0775979\pi$
$643$			12.2412i			0.482747i	−0.970432	+	0.241374i	$0.922402\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−10.7461	−	3.49162i	−0.422472	−	0.137270i	0.0900623	−	0.995936i	$-0.471293\pi$
$647$	−10.7461	−	3.49162i	−0.422472	−	0.137270i	−0.512535	+	0.858667i	$0.671293\pi$
$648$		0			0
$649$	12.2057			0.479117
$650$		0			0
$651$		0			0
$652$		0			0
$653$	20.2319	+	6.57373i	0.791734	+	0.257250i	0.676842	−	0.736128i	$-0.263348\pi$
$653$	20.2319	+	6.57373i	0.791734	+	0.257250i	0.114892	+	0.993378i	$0.463348\pi$
$654$		0			0
$655$	6.53633	+	23.5644i	0.255396	+	0.920738i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	14.9986	+	10.8971i	0.584263	+	0.424492i	0.840258	−	0.542186i	$-0.182403\pi$
$659$	14.9986	+	10.8971i	0.584263	+	0.424492i	−0.255995	+	0.966678i	$0.582403\pi$
$660$		0			0
$661$	−16.0800	+	11.6828i	−0.625441	+	0.454409i	−0.854818	−	0.518928i	$-0.826331\pi$
$661$	−16.0800	+	11.6828i	−0.625441	+	0.454409i	0.229377	+	0.973338i	$0.426331\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.90129	−	0.804763i	0.112507	−	0.0312074i
$666$		0			0
$667$	−28.1188	+	9.13635i	−1.08876	+	0.353761i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.68173	−	5.17583i	0.0649224	−	0.199811i
$672$		0			0
$673$	−25.6055	−	35.2430i	−0.987021	−	1.35852i	−0.932960	−	0.359980i	$-0.882784\pi$
$673$	−25.6055	−	35.2430i	−0.987021	−	1.35852i	−0.0540603	−	0.998538i	$-0.517216\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.73904	+	3.76996i	0.105270	+	0.144891i	0.858402	−	0.512978i	$-0.171458\pi$
$677$	2.73904	+	3.76996i	0.105270	+	0.144891i	−0.753132	+	0.657870i	$0.771458\pi$
$678$		0			0
$679$	6.63152	−	20.4097i	0.254494	−	0.783253i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	37.0242	−	12.0299i	1.41669	−	0.460311i	0.502141	−	0.864786i	$-0.332546\pi$
$683$	37.0242	−	12.0299i	1.41669	−	0.460311i	0.914549	+	0.404475i	$0.132546\pi$
$684$		0			0
$685$	5.20024	−	6.53830i	0.198691	−	0.249816i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.76002	−	5.63798i	0.295633	−	0.214790i
$690$		0			0
$691$	7.81060	+	5.67473i	0.297129	+	0.215877i	0.726354	−	0.687321i	$-0.241213\pi$
$691$	7.81060	+	5.67473i	0.297129	+	0.215877i	−0.429225	+	0.903198i	$0.641213\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.00479	−	2.65102i	0.151910	−	0.100559i
$696$		0			0
$697$	9.94289	+	3.23064i	0.376614	+	0.122369i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.6430			−0.704135			−0.352068	−	0.935975i	$-0.614521\pi$
$701$	−18.6430			−0.704135			−0.352068	+	0.935975i	$0.614521\pi$
$702$		0			0
$703$	−4.87980	−	1.58554i	−0.184045	−	0.0597999i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	7.43395i		−	0.279582i
$708$		0			0
$709$	−9.85935	−	7.16324i	−0.370276	−	0.269021i	0.387050	−	0.922059i	$-0.373494\pi$
$709$	−9.85935	−	7.16324i	−0.370276	−	0.269021i	−0.757325	+	0.653038i	$0.773494\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−26.0563	+	35.8634i	−0.975817	+	1.34310i
$714$		0			0
$715$	−0.367649	+	8.43073i	−0.0137493	+	0.315291i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−13.2311	−	40.7210i	−0.493435	−	1.51864i	−0.819382	−	0.573248i	$-0.805683\pi$
$719$	−13.2311	−	40.7210i	−0.493435	−	1.51864i	0.325947	−	0.945388i	$-0.394317\pi$
$720$		0			0
$721$	−3.42860	+	10.5522i	−0.127688	+	0.392983i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−11.5315	+	27.1745i	−0.428269	+	1.00923i
$726$		0			0
$727$	0.631037	+	0.868548i	0.0234039	+	0.0322126i	0.820559	−	0.571562i	$-0.193663\pi$
$727$	0.631037	+	0.868548i	0.0234039	+	0.0322126i	−0.797155	+	0.603775i	$0.793663\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.78152	−	8.56063i	−0.102878	−	0.316626i
$732$		0			0
$733$	0.773538	−	0.251338i	0.0285713	−	0.00928337i	−0.294696	−	0.955591i	$-0.595219\pi$
$733$	0.773538	−	0.251338i	0.0285713	−	0.00928337i	0.323268	+	0.946308i	$0.395219\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.61160	+	10.4765i	−0.280377	+	0.385906i
$738$		0			0
$739$	30.6000	−	22.2322i	1.12564	−	0.817824i	0.140585	−	0.990069i	$-0.455102\pi$
$739$	30.6000	−	22.2322i	1.12564	−	0.817824i	0.985054	+	0.172244i	$0.0551018\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			45.7517i			1.67847i	0.543772	+	0.839233i	$0.316996\pi$
$743$			45.7517i			1.67847i	−0.543772	+	0.839233i	$0.683004\pi$
$744$		0			0
$745$	17.5442	+	0.765068i	0.642768	+	0.0280299i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.71916			0.0993560
$750$		0			0
$751$	−39.1925			−1.43016			−0.715078	−	0.699045i	$-0.753609\pi$
$751$	−39.1925			−1.43016			−0.715078	+	0.699045i	$0.753609\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−50.2915	−	2.19312i	−1.83029	−	0.0798157i
$756$		0			0
$757$			4.48615i			0.163052i	0.996671	+	0.0815259i	$0.0259793\pi$
$757$			4.48615i			0.163052i	−0.996671	+	0.0815259i	$0.974021\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	17.2776	−	12.5529i	0.626312	−	0.455043i	−0.228808	−	0.973471i	$-0.573483\pi$
$761$	17.2776	−	12.5529i	0.626312	−	0.455043i	0.855121	+	0.518429i	$0.173483\pi$
$762$		0			0
$763$	−10.8316	+	14.9085i	−0.392131	+	0.539723i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	18.1365	−	5.89290i	0.654870	−	0.212780i
$768$		0			0
$769$	−7.94179	−	24.4423i	−0.286388	−	0.881413i	−0.985979	−	0.166869i	$-0.946634\pi$
$769$	−7.94179	−	24.4423i	−0.286388	−	0.881413i	0.699591	−	0.714544i	$-0.253366\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−17.4223	−	23.9797i	−0.626636	−	0.862490i	0.371179	−	0.928561i	$-0.378954\pi$
$773$	−17.4223	−	23.9797i	−0.626636	−	0.862490i	−0.997815	+	0.0660712i	$0.978954\pi$
$774$		0			0
$775$	9.96107	+	43.1254i	0.357812	+	1.54911i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.50969	+	7.72403i	−0.0899189	+	0.276742i
$780$		0			0
$781$	−6.22383	−	19.1550i	−0.222706	−	0.685420i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.89073	−	43.3572i	0.0674829	−	1.54748i
$786$		0			0
$787$	−4.72360	+	6.50148i	−0.168378	+	0.231753i	−0.884865	−	0.465848i	$-0.845749\pi$
$787$	−4.72360	+	6.50148i	−0.168378	+	0.231753i	0.716486	+	0.697601i	$0.245749\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.35443	−	4.61676i	−0.225938	−	0.164153i
$792$		0			0
$793$		−	8.50268i		−	0.301939i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.6232	−	5.07628i	−0.553401	−	0.179811i	0.0189486	−	0.999820i	$-0.493968\pi$
$797$	−15.6232	−	5.07628i	−0.553401	−	0.179811i	−0.572350	+	0.820009i	$0.693968\pi$
$798$		0			0
$799$	10.1900			0.360497
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−18.7936	−	6.10642i	−0.663213	−	0.215491i
$804$		0			0
$805$	12.3133	−	8.15095i	0.433988	−	0.287283i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−39.2743	−	28.5344i	−1.38081	−	1.00322i	−0.996804	−	0.0798870i	$-0.974544\pi$
$809$	−39.2743	−	28.5344i	−1.38081	−	1.00322i	−0.384006	−	0.923330i	$-0.625456\pi$
$810$		0			0
$811$	−17.2584	+	12.5390i	−0.606024	+	0.440302i	−0.848012	−	0.529977i	$-0.822201\pi$
$811$	−17.2584	+	12.5390i	−0.606024	+	0.440302i	0.241988	+	0.970279i	$0.422201\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−21.0711	+	26.4929i	−0.738090	+	0.928006i
$816$		0			0
$817$	6.65024	−	2.16079i	0.232662	−	0.0755966i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.922371	+	2.83877i	−0.0321910	+	0.0990736i	−0.965861	−	0.259061i	$-0.916587\pi$
$821$	−0.922371	+	2.83877i	−0.0321910	+	0.0990736i	0.933670	+	0.358134i	$0.116587\pi$
$822$		0			0
$823$	−2.01233	−	2.76974i	−0.0701455	−	0.0965469i	0.772503	−	0.635011i	$-0.219005\pi$
$823$	−2.01233	−	2.76974i	−0.0701455	−	0.0965469i	−0.842648	+	0.538464i	$0.819005\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.58186	−	6.30639i	−0.159327	−	0.219295i	0.721889	−	0.692009i	$-0.243274\pi$
$827$	−4.58186	−	6.30639i	−0.159327	−	0.219295i	−0.881216	+	0.472715i	$0.843274\pi$
$828$		0			0
$829$	6.65047	−	20.4680i	0.230980	−	0.710884i	−0.766649	−	0.642067i	$-0.778077\pi$
$829$	6.65047	−	20.4680i	0.230980	−	0.710884i	0.997629	−	0.0688179i	$-0.0219227\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.57639	−	2.13680i	0.227858	−	0.0740357i
$834$		0			0
$835$	40.7370	−	11.2997i	1.40976	−	0.391041i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.31004	+	2.40488i	−0.114275	+	0.0830258i	−0.643455	−	0.765484i	$-0.722500\pi$
$839$	−3.31004	+	2.40488i	−0.114275	+	0.0830258i	0.529180	+	0.848510i	$0.322500\pi$
$840$		0			0
$841$	−4.73850	−	3.44272i	−0.163397	−	0.118715i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−4.24575	−	15.3066i	−0.146058	−	0.526562i
$846$		0			0
$847$	−10.7665	−	3.49825i	−0.369941	−	0.120201i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−25.1648			−0.862637
$852$		0			0
$853$	−23.8815	−	7.75958i	−0.817688	−	0.265683i	−0.129837	−	0.991535i	$-0.541446\pi$
$853$	−23.8815	−	7.75958i	−0.817688	−	0.265683i	−0.687850	+	0.725852i	$0.741446\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	35.8315i		−	1.22398i	−0.790865	−	0.611991i	$-0.790369\pi$
$857$		−	35.8315i		−	1.22398i	0.790865	−	0.611991i	$-0.209631\pi$
$858$		0			0
$859$	−23.2363	−	16.8821i	−0.792811	−	0.576011i	0.115985	−	0.993251i	$-0.462997\pi$
$859$	−23.2363	−	16.8821i	−0.792811	−	0.576011i	−0.908796	+	0.417240i	$0.862997\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−12.3598	+	17.0119i	−0.420734	+	0.579090i	−0.965795	−	0.259306i	$-0.916506\pi$
$863$	−12.3598	+	17.0119i	−0.420734	+	0.579090i	0.545062	+	0.838396i	$0.316506\pi$
$864$		0			0
$865$	29.7086	+	44.8796i	1.01012	+	1.52595i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−0.600828	−	1.84916i	−0.0203817	−	0.0627284i
$870$		0			0
$871$	−6.25204	+	19.2418i	−0.211842	+	0.651984i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.92214	−	14.6180i	0.0649802	−	0.494177i
$876$		0			0
$877$	4.13682	+	5.69384i	0.139690	+	0.192267i	0.873130	−	0.487487i	$-0.162086\pi$
$877$	4.13682	+	5.69384i	0.139690	+	0.192267i	−0.733440	+	0.679754i	$0.762086\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−15.1220	−	46.5406i	−0.509472	−	1.56799i	−0.793121	−	0.609064i	$-0.791545\pi$
$881$	−15.1220	−	46.5406i	−0.509472	−	1.56799i	0.283649	−	0.958928i	$-0.408455\pi$
$882$		0			0
$883$	−8.09007	+	2.62862i	−0.272252	+	0.0884602i	−0.441961	−	0.897034i	$-0.645717\pi$
$883$	−8.09007	+	2.62862i	−0.272252	+	0.0884602i	0.169709	+	0.985494i	$0.445717\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	19.7983	−	27.2500i	0.664761	−	0.914966i	−0.334866	−	0.942266i	$-0.608691\pi$
$887$	19.7983	−	27.2500i	0.664761	−	0.914966i	0.999627	+	0.0273002i	$0.00869101\pi$
$888$		0			0
$889$	2.58476	−	1.87794i	0.0866901	−	0.0629840i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			7.91602i			0.264899i
$894$		0			0
$895$	−1.16848	+	3.12574i	−0.0390579	+	0.104482i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−52.2631			−1.74307
$900$		0			0
$901$	5.19199			0.172970
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.56474	+	5.64112i	0.0520137	+	0.187517i
$906$		0			0
$907$		−	42.2382i		−	1.40250i	−0.712918	−	0.701248i	$-0.752627\pi$
$907$		−	42.2382i		−	1.40250i	0.712918	−	0.701248i	$-0.247373\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−30.4371	+	22.1138i	−1.00843	+	0.732664i	−0.963878	−	0.266343i	$-0.914185\pi$
$911$	−30.4371	+	22.1138i	−1.00843	+	0.732664i	−0.0445478	+	0.999007i	$0.514185\pi$
$912$		0			0
$913$	7.49726	−	10.3191i	0.248123	−	0.341512i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	13.7160	−	4.45661i	0.452943	−	0.147170i
$918$		0			0
$919$	−11.7537	−	36.1742i	−0.387719	−	1.19328i	−0.934488	−	0.355993i	$-0.884143\pi$
$919$	−11.7537	−	36.1742i	−0.387719	−	1.19328i	0.546769	−	0.837283i	$-0.315857\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−18.4960	−	25.4575i	−0.608802	−	0.837944i
$924$		0			0
$925$	−16.4819	+	18.9643i	−0.541923	+	0.623544i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.91592	+	24.3627i	−0.259713	+	0.799314i	0.733152	+	0.680065i	$0.238049\pi$
$929$	−7.91592	+	24.3627i	−0.259713	+	0.799314i	−0.992864	+	0.119249i	$0.961951\pi$
$930$		0			0
$931$	1.65995	+	5.10880i	0.0544027	+	0.167434i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.84333	+	3.57494i	−0.0929868	+	0.116913i
$936$		0			0
$937$	22.3315	−	30.7367i	0.729538	−	1.00412i	−0.269614	−	0.962968i	$-0.586896\pi$
$937$	22.3315	−	30.7367i	0.729538	−	1.00412i	0.999153	−	0.0411552i	$-0.0131038\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−30.3522	−	22.0522i	−0.989454	−	0.718881i	−0.0296528	−	0.999560i	$-0.509440\pi$
$941$	−30.3522	−	22.0522i	−0.989454	−	0.718881i	−0.959802	+	0.280680i	$0.909440\pi$
$942$		0			0
$943$			39.8323i			1.29712i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	33.4391	+	10.8650i	1.08663	+	0.353066i	0.796942	−	0.604056i	$-0.206450\pi$
$947$	33.4391	+	10.8650i	1.08663	+	0.353066i	0.289684	+	0.957122i	$0.406450\pi$
$948$		0			0
$949$	−30.8735			−1.00220
$950$		0			0
$951$		0			0
$952$		0			0
$953$	49.5641	+	16.1044i	1.60554	+	0.521671i	0.968469	−	0.249134i	$-0.0801459\pi$
$953$	49.5641	+	16.1044i	1.60554	+	0.521671i	0.637071	+	0.770805i	$0.280146\pi$
$954$		0			0
$955$	−36.0381	−	28.6629i	−1.16617	−	0.927511i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.98593	−	2.89594i	−0.128712	−	0.0935149i
$960$		0			0
$961$	−38.3157	+	27.8380i	−1.23599	+	0.898001i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.502632	−	11.5261i	0.0161803	−	0.371039i
$966$		0			0
$967$	39.7277	−	12.9083i	1.27756	−	0.415103i	0.409838	−	0.912158i	$-0.365585\pi$
$967$	39.7277	−	12.9083i	1.27756	−	0.415103i	0.867719	+	0.497055i	$0.165585\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.141561	+	0.435679i	−0.00454289	+	0.0139816i	−0.953302	−	0.302018i	$-0.902340\pi$
$971$	−0.141561	+	0.435679i	−0.00454289	+	0.0139816i	0.948759	+	0.315999i	$0.102340\pi$
$972$		0			0
$973$	−1.66486	−	2.29148i	−0.0533728	−	0.0734614i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.29079	+	3.15300i	0.0732888	+	0.100873i	0.844088	−	0.536205i	$-0.180143\pi$
$977$	2.29079	+	3.15300i	0.0732888	+	0.100873i	−0.770799	+	0.637079i	$0.780143\pi$
$978$		0			0
$979$	−4.59881	+	14.1537i	−0.146979	+	0.452353i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−53.5388	+	17.3958i	−1.70762	+	0.554841i	−0.989935	−	0.141523i	$-0.954800\pi$
$983$	−53.5388	+	17.3958i	−1.70762	+	0.554841i	−0.717689	+	0.696364i	$0.754800\pi$
$984$		0			0
$985$	22.0148	+	8.22966i	0.701449	+	0.262219i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	27.7451	−	20.1580i	0.882242	−	0.640986i
$990$		0			0
$991$	−17.5804	−	12.7729i	−0.558460	−	0.405745i	0.272435	−	0.962174i	$-0.412171\pi$
$991$	−17.5804	−	12.7729i	−0.558460	−	0.405745i	−0.830895	+	0.556429i	$0.812171\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	8.15872	+	0.355786i	0.258649	+	0.0112792i
$996$		0			0
$997$	36.6447	+	11.9066i	1.16055	+	0.377085i	0.825107	−	0.564976i	$-0.191115\pi$
$997$	36.6447	+	11.9066i	1.16055	+	0.377085i	0.335441	+	0.942061i	$0.391115\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.w.c.289.1		24
3.2	odd	2		300.2.o.a.289.6	yes	24
15.2	even	4		1500.2.m.c.301.2		24
15.8	even	4		1500.2.m.d.301.5		24
15.14	odd	2		1500.2.o.c.949.2		24
25.9	even	10	inner	900.2.w.c.109.1		24
75.29	odd	10		7500.2.d.g.1249.4		24
75.38	even	20		1500.2.m.d.1201.5		24
75.41	odd	10		1500.2.o.c.49.2		24
75.47	even	20		7500.2.a.n.1.4		12
75.53	even	20		7500.2.a.m.1.9		12
75.59	odd	10		300.2.o.a.109.6	✓	24
75.62	even	20		1500.2.m.c.1201.2		24
75.71	odd	10		7500.2.d.g.1249.21		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.6	✓	24	75.59	odd	10
300.2.o.a.289.6	yes	24	3.2	odd	2
900.2.w.c.109.1		24	25.9	even	10	inner
900.2.w.c.289.1		24	1.1	even	1	trivial
1500.2.m.c.301.2		24	15.2	even	4
1500.2.m.c.1201.2		24	75.62	even	20
1500.2.m.d.301.5		24	15.8	even	4
1500.2.m.d.1201.5		24	75.38	even	20
1500.2.o.c.49.2		24	75.41	odd	10
1500.2.o.c.949.2		24	15.14	odd	2
7500.2.a.m.1.9		12	75.53	even	20
7500.2.a.n.1.4		12	75.47	even	20
7500.2.d.g.1249.4		24	75.29	odd	10
7500.2.d.g.1249.21		24	75.71	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.23394 - 0.0974182i) q^{5} +1.31873i q^{7} +O(q^{10})\)	\(q+(-2.23394 - 0.0974182i) q^{5} +1.31873i q^{7} +(1.25737 - 0.913532i) q^{11} +(1.42727 - 1.96447i) q^{13} +(1.25004 - 0.406161i) q^{17} +(0.315522 + 0.971077i) q^{19} +(2.94350 + 4.05137i) q^{23} +(4.98102 + 0.435254i) q^{25} +(-1.82443 + 5.61503i) q^{29} +(2.73547 + 8.41891i) q^{31} +(0.128468 - 2.94596i) q^{35} +(-2.95370 + 4.06542i) q^{37} +(6.43499 + 4.67529i) q^{41} -6.84831i q^{43} +(7.37336 + 2.39575i) q^{47} +5.26096 q^{49} +(3.75685 + 1.22067i) q^{53} +(-2.89789 + 1.91829i) q^{55} +(6.35355 + 4.61613i) q^{59} +(2.83287 - 2.05820i) q^{61} +(-3.37982 + 4.24947i) q^{65} +(-7.92426 + 2.57475i) q^{67} +(4.00454 - 12.3247i) q^{71} +(-7.47339 - 10.2862i) q^{73} +(1.20470 + 1.65812i) q^{77} +(0.386585 - 1.18979i) q^{79} +(7.80521 - 2.53607i) q^{83} +(-2.83208 + 0.785565i) q^{85} +(-7.74667 + 5.62829i) q^{89} +(2.59059 + 1.88218i) q^{91} +(-0.610258 - 2.20007i) q^{95} +(-15.4769 - 5.02874i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 24 * q + 2 * q^5	\( 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Introduction

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