LMFDB - Embedded newform 900.2.w.c.469.5

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			469.5
Character	$\chi$	$=$	900.469
Dual form			900.2.w.c.829.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.921600 + 2.03732i) q^{5} +4.41540i q^{7} +O(q^{10})$	$q+(0.921600 + 2.03732i) q^{5} +4.41540i q^{7} +(-1.37568 - 4.23392i) q^{11} +(5.46646 + 1.77616i) q^{13} +(-3.86196 + 5.31553i) q^{17} +(-2.25162 - 1.63590i) q^{19} +(-1.25059 + 0.406341i) q^{23} +(-3.30131 + 3.75518i) q^{25} +(3.91985 - 2.84794i) q^{29} +(0.159486 + 0.115873i) q^{31} +(-8.99556 + 4.06923i) q^{35} +(-7.80690 - 2.53662i) q^{37} +(-2.42573 + 7.46564i) q^{41} +0.412792i q^{43} +(4.58154 + 6.30595i) q^{47} -12.4958 q^{49} +(0.185420 + 0.255208i) q^{53} +(7.35800 - 6.70469i) q^{55} +(0.778419 - 2.39573i) q^{59} +(2.88348 + 8.87444i) q^{61} +(1.41929 + 12.7738i) q^{65} +(7.02151 - 9.66428i) q^{67} +(0.411990 - 0.299328i) q^{71} +(14.9990 - 4.87346i) q^{73} +(18.6945 - 6.07420i) q^{77} +(-2.77617 + 2.01700i) q^{79} +(-3.15732 + 4.34568i) q^{83} +(-14.3886 - 2.96923i) q^{85} +(3.50585 + 10.7899i) q^{89} +(-7.84246 + 24.1366i) q^{91} +(1.25774 - 6.09490i) q^{95} +(2.98572 + 4.10948i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{10}\right)$

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
$5$	0.921600	+	2.03732i	0.412152	+	0.911115i
$5$	0.921600	+	2.03732i	0.412152	+	0.911115i
$6$		0			0
$7$			4.41540i			1.66886i	0.551111	+	0.834432i	$0.314204\pi$
$7$			4.41540i			1.66886i	−0.551111	+	0.834432i	$0.685796\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.37568	−	4.23392i	−0.414785	−	1.27658i	−0.912443	−	0.409203i	$-0.865807\pi$
$11$	−1.37568	−	4.23392i	−0.414785	−	1.27658i	0.497659	−	0.867373i	$-0.334193\pi$
$12$		0			0
$13$	5.46646	+	1.77616i	1.51612	+	0.492619i	0.944672	−	0.328017i	$-0.106380\pi$
$13$	5.46646	+	1.77616i	1.51612	+	0.492619i	0.571452	+	0.820635i	$0.306380\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.86196	+	5.31553i	−0.936662	+	1.28921i	0.0205412	+	0.999789i	$0.493461\pi$
$17$	−3.86196	+	5.31553i	−0.936662	+	1.28921i	−0.957203	+	0.289416i	$0.906539\pi$
$18$		0			0
$19$	−2.25162	−	1.63590i	−0.516557	−	0.375301i	0.298748	−	0.954332i	$-0.403431\pi$
$19$	−2.25162	−	1.63590i	−0.516557	−	0.375301i	−0.815305	+	0.579031i	$0.803431\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.25059	+	0.406341i	−0.260766	+	0.0847280i	−0.436482	−	0.899713i	$-0.643776\pi$
$23$	−1.25059	+	0.406341i	−0.260766	+	0.0847280i	0.175716	+	0.984441i	$0.443776\pi$
$24$		0			0
$25$	−3.30131	+	3.75518i	−0.660261	+	0.751036i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.91985	−	2.84794i	0.727899	−	0.528849i	−0.160999	−	0.986954i	$-0.551472\pi$
$29$	3.91985	−	2.84794i	0.727899	−	0.528849i	0.888898	+	0.458105i	$0.151472\pi$
$30$		0			0
$31$	0.159486	+	0.115873i	0.0286446	+	0.0208115i	0.602015	−	0.798484i	$-0.294365\pi$
$31$	0.159486	+	0.115873i	0.0286446	+	0.0208115i	−0.573371	+	0.819296i	$0.694365\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−8.99556	+	4.06923i	−1.52053	+	0.687826i
$36$		0			0
$37$	−7.80690	−	2.53662i	−1.28345	−	0.417017i	−0.413654	−	0.910434i	$-0.635748\pi$
$37$	−7.80690	−	2.53662i	−1.28345	−	0.417017i	−0.869793	+	0.493417i	$0.835748\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.42573	+	7.46564i	−0.378836	+	1.16594i	0.562018	+	0.827125i	$0.310025\pi$
$41$	−2.42573	+	7.46564i	−0.378836	+	1.16594i	−0.940854	+	0.338813i	$0.889975\pi$
$42$		0			0
$43$			0.412792i			0.0629502i	0.999505	+	0.0314751i	$0.0100205\pi$
$43$			0.412792i			0.0629502i	−0.999505	+	0.0314751i	$0.989980\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.58154	+	6.30595i	0.668287	+	0.919818i	0.999720	−	0.0236610i	$-0.00753223\pi$
$47$	4.58154	+	6.30595i	0.668287	+	0.919818i	−0.331433	+	0.943479i	$0.607532\pi$
$48$		0			0
$49$	−12.4958			−1.78511
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.185420	+	0.255208i	0.0254694	+	0.0350556i	0.821562	−	0.570120i	$-0.193103\pi$
$53$	0.185420	+	0.255208i	0.0254694	+	0.0350556i	−0.796092	+	0.605175i	$0.793103\pi$
$54$		0			0
$55$	7.35800	−	6.70469i	0.992153	−	0.904060i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.778419	−	2.39573i	0.101342	−	0.311897i	−0.887513	−	0.460783i	$-0.847569\pi$
$59$	0.778419	−	2.39573i	0.101342	−	0.311897i	0.988854	+	0.148886i	$0.0475687\pi$
$60$		0			0
$61$	2.88348	+	8.87444i	0.369192	+	1.13626i	0.947314	+	0.320305i	$0.103786\pi$
$61$	2.88348	+	8.87444i	0.369192	+	1.13626i	−0.578123	+	0.815950i	$0.696214\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.41929	+	12.7738i	0.176042	+	1.58440i
$66$		0			0
$67$	7.02151	−	9.66428i	0.857814	−	1.18068i	−0.124273	−	0.992248i	$-0.539660\pi$
$67$	7.02151	−	9.66428i	0.857814	−	1.18068i	0.982086	−	0.188431i	$-0.0603403\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.411990	−	0.299328i	0.0488942	−	0.0355237i	−0.563070	−	0.826409i	$-0.690380\pi$
$71$	0.411990	−	0.299328i	0.0488942	−	0.0355237i	0.611964	+	0.790886i	$0.290380\pi$
$72$		0			0
$73$	14.9990	−	4.87346i	1.75549	−	0.570395i	0.758777	−	0.651351i	$-0.225797\pi$
$73$	14.9990	−	4.87346i	1.75549	−	0.570395i	0.996718	+	0.0809557i	$0.0257972\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	18.6945	−	6.07420i	2.13043	−	0.692219i
$78$		0			0
$79$	−2.77617	+	2.01700i	−0.312343	+	0.226930i	−0.732901	−	0.680335i	$-0.761834\pi$
$79$	−2.77617	+	2.01700i	−0.312343	+	0.226930i	0.420558	+	0.907266i	$0.361834\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.15732	+	4.34568i	−0.346561	+	0.477000i	−0.946343	−	0.323163i	$-0.895254\pi$
$83$	−3.15732	+	4.34568i	−0.346561	+	0.477000i	0.599783	+	0.800163i	$0.295254\pi$
$84$		0			0
$85$	−14.3886	−	2.96923i	−1.56066	−	0.322058i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.50585	+	10.7899i	0.371619	+	1.14373i	0.945731	+	0.324950i	$0.105347\pi$
$89$	3.50585	+	10.7899i	0.371619	+	1.14373i	−0.574112	+	0.818777i	$0.694653\pi$
$90$		0			0
$91$	−7.84246	+	24.1366i	−0.822114	+	2.53021i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.25774	−	6.09490i	0.129042	−	0.625324i
$96$		0			0
$97$	2.98572	+	4.10948i	0.303153	+	0.417255i	0.933231	−	0.359277i	$-0.116977\pi$
$97$	2.98572	+	4.10948i	0.303153	+	0.417255i	−0.630077	+	0.776532i	$0.716977\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	11.1860			1.11305			0.556525	−	0.830831i	$-0.312134\pi$
$101$	11.1860			1.11305			0.556525	+	0.830831i	$0.312134\pi$
$102$		0			0
$103$	−1.84898	−	2.54490i	−0.182185	−	0.250757i	0.708150	−	0.706062i	$-0.249530\pi$
$103$	−1.84898	−	2.54490i	−0.182185	−	0.250757i	−0.890335	+	0.455305i	$0.849530\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			7.74013i			0.748266i	0.927375	+	0.374133i	$0.122060\pi$
$107$			7.74013i			0.748266i	−0.927375	+	0.374133i	$0.877940\pi$
$108$		0			0
$109$	3.20477	−	9.86326i	0.306961	−	0.944729i	−0.671977	−	0.740572i	$-0.734555\pi$
$109$	3.20477	−	9.86326i	0.306961	−	0.944729i	0.978938	−	0.204157i	$-0.0654453\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−9.72574	−	3.16009i	−0.914921	−	0.297276i	−0.186539	−	0.982447i	$-0.559727\pi$
$113$	−9.72574	−	3.16009i	−0.914921	−	0.297276i	−0.728382	+	0.685172i	$0.759727\pi$
$114$		0			0
$115$	−1.98039	−	2.17336i	−0.184672	−	0.202667i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−23.4702	−	17.0521i	−2.15151	−	1.56316i
$120$		0			0
$121$	−7.13440	+	5.18344i	−0.648582	+	0.471222i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.6930	−	3.26502i	−0.956408	−	0.292032i
$126$		0			0
$127$	10.7590	−	3.49582i	0.954709	−	0.310204i	0.210081	−	0.977684i	$-0.432627\pi$
$127$	10.7590	−	3.49582i	0.954709	−	0.310204i	0.744628	+	0.667480i	$0.232627\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−7.64816	−	5.55671i	−0.668223	−	0.485492i	0.201207	−	0.979549i	$-0.435514\pi$
$131$	−7.64816	−	5.55671i	−0.668223	−	0.485492i	−0.869430	+	0.494056i	$0.835514\pi$
$132$		0			0
$133$	7.22314	−	9.94180i	0.626326	−	0.862063i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−7.99861	−	2.59891i	−0.683367	−	0.222039i	−0.0532983	−	0.998579i	$-0.516973\pi$
$137$	−7.99861	−	2.59891i	−0.683367	−	0.222039i	−0.630069	+	0.776539i	$0.716973\pi$
$138$		0			0
$139$	−3.65307	−	11.2430i	−0.309849	−	0.953617i	−0.977823	−	0.209433i	$-0.932838\pi$
$139$	−3.65307	−	11.2430i	−0.309849	−	0.953617i	0.667974	−	0.744185i	$-0.267162\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	25.5880i		−	2.13978i
$144$		0			0
$145$	9.41469	+	5.36131i	0.781847	+	0.445233i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	10.6355			0.871294			0.435647	−	0.900118i	$-0.356520\pi$
$149$	10.6355			0.871294			0.435647	+	0.900118i	$0.356520\pi$
$150$		0			0
$151$	4.41657			0.359415			0.179707	−	0.983720i	$-0.442485\pi$
$151$	4.41657			0.359415			0.179707	+	0.983720i	$0.442485\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.0890883	+	0.431713i	−0.00715574	+	0.0346760i
$156$		0			0
$157$			13.5289i			1.07972i	0.841754	+	0.539861i	$0.181523\pi$
$157$			13.5289i			1.07972i	−0.841754	+	0.539861i	$0.818477\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.79416	−	5.52186i	−0.141400	−	0.435183i
$162$		0			0
$163$	−13.8458	−	4.49876i	−1.08448	−	0.352370i	−0.288371	−	0.957519i	$-0.593114\pi$
$163$	−13.8458	−	4.49876i	−1.08448	−	0.352370i	−0.796112	+	0.605149i	$0.793114\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.85918	−	8.06448i	0.453397	−	0.624048i	−0.519726	−	0.854333i	$-0.673966\pi$
$167$	5.85918	−	8.06448i	0.453397	−	0.624048i	0.973123	+	0.230285i	$0.0739659\pi$
$168$		0			0
$169$	16.2103	+	11.7774i	1.24694	+	0.905957i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	10.3427	−	3.36056i	0.786344	−	0.255499i	0.111798	−	0.993731i	$-0.464339\pi$
$173$	10.3427	−	3.36056i	0.786344	−	0.255499i	0.674547	+	0.738232i	$0.264339\pi$
$174$		0			0
$175$	−16.5806	−	14.5766i	−1.25338	−	1.10189i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	20.3662	−	14.7969i	1.52224	−	1.10597i	0.561875	−	0.827222i	$-0.310080\pi$
$179$	20.3662	−	14.7969i	1.52224	−	1.10597i	0.960364	−	0.278749i	$-0.0899198\pi$
$180$		0			0
$181$	6.14184	+	4.46231i	0.456520	+	0.331681i	0.792164	−	0.610308i	$-0.208954\pi$
$181$	6.14184	+	4.46231i	0.456520	+	0.331681i	−0.335645	+	0.941989i	$0.608954\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.02696	−	18.2429i	−0.149025	−	1.34124i
$186$		0			0
$187$	27.8184	+	9.03874i	2.03428	+	0.660978i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.00373697	−	0.0115012i	0.000270398	−	0.000832198i	−0.950921	−	0.309433i	$-0.899861\pi$
$191$	0.00373697	−	0.0115012i	0.000270398	−	0.000832198i	0.951192	+	0.308601i	$0.0998607\pi$
$192$		0			0
$193$		−	12.7841i		−	0.920219i	−0.887862	−	0.460110i	$-0.847810\pi$
$193$		−	12.7841i		−	0.920219i	0.887862	−	0.460110i	$-0.152190\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	5.79877	+	7.98132i	0.413145	+	0.568646i	0.963982	−	0.265967i	$-0.0856914\pi$
$197$	5.79877	+	7.98132i	0.413145	+	0.568646i	−0.550837	+	0.834613i	$0.685691\pi$
$198$		0			0
$199$	0.295640			0.0209573			0.0104787	−	0.999945i	$-0.496664\pi$
$199$	0.295640			0.0209573			0.0104787	+	0.999945i	$0.496664\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	12.5748	+	17.3077i	0.882578	+	1.21476i
$204$		0			0
$205$	−17.4454	+	1.93835i	−1.21844	+	0.135381i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−3.82874	+	11.7837i	−0.264840	+	0.815093i
$210$		0			0
$211$	−3.90836	−	12.0287i	−0.269062	−	0.828089i	−0.990730	−	0.135849i	$-0.956624\pi$
$211$	−3.90836	−	12.0287i	−0.269062	−	0.828089i	0.721667	−	0.692240i	$-0.243376\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.840987	+	0.380429i	−0.0573548	+	0.0259450i
$216$		0			0
$217$	−0.511628	+	0.704195i	−0.0347315	+	0.0478039i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−30.5525	+	22.1977i	−2.05518	+	1.49318i
$222$		0			0
$223$	4.98335	−	1.61919i	0.333710	−	0.108429i	−0.137369	−	0.990520i	$-0.543865\pi$
$223$	4.98335	−	1.61919i	0.333710	−	0.108429i	0.471079	+	0.882091i	$0.343865\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.38873	−	2.40074i	0.490407	−	0.159343i	−0.0533663	−	0.998575i	$-0.516995\pi$
$227$	7.38873	−	2.40074i	0.490407	−	0.159343i	0.543773	+	0.839232i	$0.316995\pi$
$228$		0			0
$229$	−4.84757	+	3.52196i	−0.320336	+	0.232738i	−0.736319	−	0.676635i	$-0.763438\pi$
$229$	−4.84757	+	3.52196i	−0.320336	+	0.232738i	0.415983	+	0.909373i	$0.363438\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	8.73631	−	12.0245i	0.572334	−	0.787751i	−0.420494	−	0.907295i	$-0.638143\pi$
$233$	8.73631	−	12.0245i	0.572334	−	0.787751i	0.992829	+	0.119544i	$0.0381434\pi$
$234$		0			0
$235$	−8.62486	+	15.1456i	−0.562624	+	0.987991i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.55140	−	20.1631i	−0.423775	−	1.30424i	−0.904163	−	0.427188i	$-0.859504\pi$
$239$	−6.55140	−	20.1631i	−0.423775	−	1.30424i	0.480388	−	0.877056i	$-0.340496\pi$
$240$		0			0
$241$	4.96162	−	15.2703i	0.319606	−	0.983647i	−0.654210	−	0.756313i	$-0.726999\pi$
$241$	4.96162	−	15.2703i	0.319606	−	0.983647i	0.973817	−	0.227334i	$-0.0730010\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.5161	−	25.4578i	−0.735736	−	1.62644i
$246$		0			0
$247$	−9.40278	−	12.9418i	−0.598284	−	0.823468i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	24.1371			1.52352			0.761761	−	0.647858i	$-0.224335\pi$
$251$	24.1371			1.52352			0.761761	+	0.647858i	$0.224335\pi$
$252$		0			0
$253$	3.44084	+	4.73590i	0.216323	+	0.297744i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	4.22940i		−	0.263823i	−0.991262	−	0.131911i	$-0.957889\pi$
$257$		−	4.22940i		−	0.263823i	0.991262	−	0.131911i	$-0.0421114\pi$
$258$		0			0
$259$	11.2002	−	34.4706i	0.695945	−	2.14190i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.97729	+	2.59198i	0.491901	+	0.159828i	0.544455	−	0.838790i	$-0.316736\pi$
$263$	7.97729	+	2.59198i	0.491901	+	0.159828i	−0.0525547	+	0.998618i	$0.516736\pi$
$264$		0			0
$265$	−0.349057	+	0.612958i	−0.0214424	+	0.0376537i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.47812	+	3.25354i	0.273036	+	0.198372i	0.715874	−	0.698229i	$-0.246028\pi$
$269$	4.47812	+	3.25354i	0.273036	+	0.198372i	−0.442838	+	0.896601i	$0.646028\pi$
$270$		0			0
$271$	−12.8227	+	9.31623i	−0.778923	+	0.565921i	−0.904656	−	0.426144i	$-0.859872\pi$
$271$	−12.8227	+	9.31623i	−0.778923	+	0.565921i	0.125733	+	0.992064i	$0.459872\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	20.4407	+	8.81152i	1.23262	+	0.531355i
$276$		0			0
$277$	8.26699	−	2.68611i	0.496715	−	0.161393i	−0.0499369	−	0.998752i	$-0.515902\pi$
$277$	8.26699	−	2.68611i	0.496715	−	0.161393i	0.546652	+	0.837360i	$0.315902\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	8.72120	+	6.33633i	0.520263	+	0.377994i	0.816703	−	0.577058i	$-0.195799\pi$
$281$	8.72120	+	6.33633i	0.520263	+	0.377994i	−0.296440	+	0.955052i	$0.595799\pi$
$282$		0			0
$283$	−5.78686	+	7.96493i	−0.343993	+	0.473466i	−0.945602	−	0.325324i	$-0.894527\pi$
$283$	−5.78686	+	7.96493i	−0.343993	+	0.473466i	0.601609	+	0.798791i	$0.294527\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−32.9638	−	10.7106i	−1.94579	−	0.632226i
$288$		0			0
$289$	−8.08684	−	24.8887i	−0.475696	−	1.46404i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			9.77733i			0.571198i	0.958349	+	0.285599i	$0.0921925\pi$
$293$			9.77733i			0.571198i	−0.958349	+	0.285599i	$0.907808\pi$
$294$		0			0
$295$	5.59824	−	0.622019i	0.325942	−	0.0362153i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.55803			−0.437092
$300$		0			0
$301$	−1.82264			−0.105055
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−15.4226	+	14.0532i	−0.883096	+	0.804686i
$306$		0			0
$307$			32.7301i			1.86801i	0.357265	+	0.934003i	$0.383709\pi$
$307$			32.7301i			1.86801i	−0.357265	+	0.934003i	$0.616291\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.60939	+	23.4193i	0.431489	+	1.32799i	0.896642	+	0.442756i	$0.145999\pi$
$311$	7.60939	+	23.4193i	0.431489	+	1.32799i	−0.465153	+	0.885230i	$0.654001\pi$
$312$		0			0
$313$	21.4458	+	6.96817i	1.21219	+	0.393864i	0.844232	−	0.535979i	$-0.180057\pi$
$313$	21.4458	+	6.96817i	1.21219	+	0.393864i	0.367957	+	0.929843i	$0.380057\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−0.954767	+	1.31412i	−0.0536251	+	0.0738086i	−0.834987	−	0.550269i	$-0.814525\pi$
$317$	−0.954767	+	1.31412i	−0.0536251	+	0.0738086i	0.781362	+	0.624078i	$0.214525\pi$
$318$		0			0
$319$	−17.4504	−	12.6785i	−0.977037	−	0.709859i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	17.3913	−	5.65078i	0.967679	−	0.314418i
$324$		0			0
$325$	−24.7163	+	14.6639i	−1.37101	+	0.813407i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−27.8433	+	20.2293i	−1.53505	+	1.11528i
$330$		0			0
$331$	7.29178	+	5.29779i	0.400793	+	0.291193i	0.769864	−	0.638208i	$-0.220324\pi$
$331$	7.29178	+	5.29779i	0.400793	+	0.291193i	−0.369071	+	0.929401i	$0.620324\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	26.1602	+	5.39842i	1.42928	+	0.294947i
$336$		0			0
$337$	25.6482	+	8.33361i	1.39715	+	0.453961i	0.908267	−	0.418390i	$-0.137406\pi$
$337$	25.6482	+	8.33361i	1.39715	+	0.453961i	0.488880	+	0.872351i	$0.337406\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.271197	−	0.834657i	0.0146861	−	0.0451992i
$342$		0			0
$343$		−	24.2660i		−	1.31024i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.4263	−	21.2325i	−0.828127	−	1.13982i	−0.988269	−	0.152725i	$-0.951195\pi$
$347$	−15.4263	−	21.2325i	−0.828127	−	1.13982i	0.160142	−	0.987094i	$-0.448805\pi$
$348$		0			0
$349$	−18.2310			−0.975885			−0.487943	−	0.872876i	$-0.662252\pi$
$349$	−18.2310			−0.975885			−0.487943	+	0.872876i	$0.662252\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.61542	−	3.59982i	−0.139205	−	0.191599i	0.733723	−	0.679449i	$-0.237781\pi$
$353$	−2.61542	−	3.59982i	−0.139205	−	0.191599i	−0.872927	+	0.487850i	$0.837781\pi$
$354$		0			0
$355$	0.989516	+	0.563492i	0.0525181	+	0.0299071i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.98964	+	30.7449i	−0.527233	+	1.62266i	0.232625	+	0.972567i	$0.425269\pi$
$359$	−9.98964	+	30.7449i	−0.527233	+	1.62266i	−0.759858	+	0.650089i	$0.774731\pi$
$360$		0			0
$361$	−3.47769	−	10.7032i	−0.183036	−	0.563328i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	23.7518	+	26.0662i	1.24323	+	1.36437i
$366$		0			0
$367$	−3.37390	+	4.64378i	−0.176116	+	0.242403i	−0.887945	−	0.459950i	$-0.847867\pi$
$367$	−3.37390	+	4.64378i	−0.176116	+	0.242403i	0.711829	+	0.702353i	$0.247867\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.12685	+	0.818702i	−0.0585030	+	0.0425049i
$372$		0			0
$373$	0.990868	−	0.321953i	0.0513052	−	0.0166701i	−0.283252	−	0.959046i	$-0.591413\pi$
$373$	0.990868	−	0.321953i	0.0513052	−	0.0166701i	0.334557	+	0.942375i	$0.391413\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	26.4861	−	8.60587i	1.36411	−	0.443225i
$378$		0			0
$379$	−3.84230	+	2.79159i	−0.197366	+	0.143395i	−0.682079	−	0.731279i	$-0.738924\pi$
$379$	−3.84230	+	2.79159i	−0.197366	+	0.143395i	0.484713	+	0.874673i	$0.338924\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	6.47739	−	8.91536i	0.330979	−	0.455553i	−0.610801	−	0.791784i	$-0.709152\pi$
$383$	6.47739	−	8.91536i	0.330979	−	0.455553i	0.941780	+	0.336231i	$0.109152\pi$
$384$		0			0
$385$	29.6039	+	32.4885i	1.50875	+	1.65577i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−10.2628	−	31.5856i	−0.520344	−	1.60145i	−0.773344	−	0.633987i	$-0.781417\pi$
$389$	−10.2628	−	31.5856i	−0.520344	−	1.60145i	0.253000	−	0.967466i	$-0.418583\pi$
$390$		0			0
$391$	2.66981	−	8.21682i	0.135018	−	0.415542i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−6.66778	−	3.79705i	−0.335493	−	0.191050i
$396$		0			0
$397$	−1.61299	−	2.22008i	−0.0809534	−	0.111423i	0.766620	−	0.642101i	$-0.221937\pi$
$397$	−1.61299	−	2.22008i	−0.0809534	−	0.111423i	−0.847573	+	0.530678i	$0.821937\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.11503			0.105619			0.0528097	−	0.998605i	$-0.483182\pi$
$401$	2.11503			0.105619			0.0528097	+	0.998605i	$0.483182\pi$
$402$		0			0
$403$	0.666015	+	0.916691i	0.0331766	+	0.0456636i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			36.5434i			1.81139i
$408$		0			0
$409$	2.03102	−	6.25083i	0.100427	−	0.309084i	−0.888203	−	0.459452i	$-0.848046\pi$
$409$	2.03102	−	6.25083i	0.100427	−	0.309084i	0.988630	+	0.150368i	$0.0480459\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	10.5781	+	3.43703i	0.520514	+	0.169125i
$414$		0			0
$415$	−11.7633	−	2.42748i	−0.577438	−	0.119160i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−28.5125	−	20.7155i	−1.39293	−	1.01202i	−0.995537	−	0.0943704i	$-0.969916\pi$
$419$	−28.5125	−	20.7155i	−1.39293	−	1.01202i	−0.397389	−	0.917650i	$-0.630084\pi$
$420$		0			0
$421$	−5.07520	+	3.68735i	−0.247350	+	0.179710i	−0.704552	−	0.709653i	$-0.748852\pi$
$421$	−5.07520	+	3.68735i	−0.247350	+	0.179710i	0.457201	+	0.889363i	$0.348852\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.21127	−	32.0505i	−0.349798	−	1.55468i
$426$		0			0
$427$	−39.1842	+	12.7317i	−1.89626	+	0.616131i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−11.0609	−	8.03624i	−0.532787	−	0.387092i	0.288612	−	0.957446i	$-0.406806\pi$
$431$	−11.0609	−	8.03624i	−0.532787	−	0.387092i	−0.821399	+	0.570354i	$0.806806\pi$
$432$		0			0
$433$	3.98412	−	5.48367i	0.191465	−	0.263529i	−0.702482	−	0.711701i	$-0.747925\pi$
$433$	3.98412	−	5.48367i	0.191465	−	0.263529i	0.893947	+	0.448173i	$0.147925\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.48059	+	1.13091i	0.166499	+	0.0540988i
$438$		0			0
$439$	5.23618	+	16.1153i	0.249909	+	0.769142i	0.994790	+	0.101944i	$0.0325063\pi$
$439$	5.23618	+	16.1153i	0.249909	+	0.769142i	−0.744881	+	0.667197i	$0.767494\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			23.8927i			1.13517i	0.823313	+	0.567587i	$0.192123\pi$
$443$			23.8927i			1.13517i	−0.823313	+	0.567587i	$0.807877\pi$
$444$		0			0
$445$	−18.7514	+	17.0865i	−0.888902	+	0.809977i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	6.39281			0.301695			0.150848	−	0.988557i	$-0.451800\pi$
$449$	6.39281			0.301695			0.150848	+	0.988557i	$0.451800\pi$
$450$		0			0
$451$	34.9460			1.64554
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−56.4015	+	6.26675i	−2.64414	+	0.293790i
$456$		0			0
$457$		−	5.89482i		−	0.275748i	−0.990450	−	0.137874i	$-0.955973\pi$
$457$		−	5.89482i		−	0.275748i	0.990450	−	0.137874i	$-0.0440269\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.60801	+	23.4151i	0.354340	+	1.09055i	0.956391	+	0.292090i	$0.0943506\pi$
$461$	7.60801	+	23.4151i	0.354340	+	1.09055i	−0.602050	+	0.798458i	$0.705649\pi$
$462$		0			0
$463$	−28.3995	−	9.22757i	−1.31984	−	0.428842i	−0.437399	−	0.899267i	$-0.644100\pi$
$463$	−28.3995	−	9.22757i	−1.31984	−	0.428842i	−0.882440	+	0.470426i	$0.844100\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−15.3714	+	21.1569i	−0.711301	+	0.979022i	0.288467	+	0.957490i	$0.406855\pi$
$467$	−15.3714	+	21.1569i	−0.711301	+	0.979022i	−0.999768	+	0.0215325i	$0.993145\pi$
$468$		0			0
$469$	42.6716	+	31.0028i	1.97039	+	1.43157i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.74773	−	0.567871i	0.0803606	−	0.0261108i
$474$		0			0
$475$	13.5764	−	3.05464i	0.622927	−	0.140157i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.25147	+	0.909247i	−0.0571812	+	0.0415446i	−0.616009	−	0.787739i	$-0.711251\pi$
$479$	−1.25147	+	0.909247i	−0.0571812	+	0.0415446i	0.558827	+	0.829284i	$0.311251\pi$
$480$		0			0
$481$	−38.1707	−	27.7326i	−1.74043	−	1.26450i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.62068	+	9.87015i	−0.255222	+	0.448180i
$486$		0			0
$487$	11.8681	+	3.85619i	0.537797	+	0.174741i	0.565307	−	0.824881i	$-0.308758\pi$
$487$	11.8681	+	3.85619i	0.537797	+	0.174741i	−0.0275101	+	0.999622i	$0.508758\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	5.46864	−	16.8307i	0.246796	−	0.759561i	−0.748540	−	0.663090i	$-0.769245\pi$
$491$	5.46864	−	16.8307i	0.246796	−	0.759561i	0.995336	−	0.0964706i	$-0.0307554\pi$
$492$		0			0
$493$			31.8347i			1.43376i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.32165	+	1.81910i	0.0592843	+	0.0815978i
$498$		0			0
$499$	30.9281			1.38453			0.692267	−	0.721642i	$-0.256612\pi$
$499$	30.9281			1.38453			0.692267	+	0.721642i	$0.256612\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−18.5467	−	25.5273i	−0.826956	−	1.13821i	−0.988482	−	0.151338i	$-0.951642\pi$
$503$	−18.5467	−	25.5273i	−0.826956	−	1.13821i	0.161526	−	0.986868i	$-0.448358\pi$
$504$		0			0
$505$	10.3090	+	22.7894i	0.458746	+	1.01412i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.23276	+	6.87172i	−0.0989652	+	0.304583i	−0.988267	−	0.152738i	$-0.951191\pi$
$509$	−2.23276	+	6.87172i	−0.0989652	+	0.304583i	0.889302	+	0.457321i	$0.151191\pi$
$510$		0			0
$511$	21.5183	+	66.2264i	0.951912	+	2.92968i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.48075	−	6.11234i	0.153380	−	0.269342i
$516$		0			0
$517$	20.3962	−	28.0729i	0.897022	−	1.23464i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−7.67413	+	5.57558i	−0.336210	+	0.244271i	−0.743061	−	0.669224i	$-0.766627\pi$
$521$	−7.67413	+	5.57558i	−0.336210	+	0.244271i	0.406851	+	0.913494i	$0.366627\pi$
$522$		0			0
$523$	−19.3589	+	6.29007i	−0.846504	+	0.275046i	−0.699981	−	0.714162i	$-0.746808\pi$
$523$	−19.3589	+	6.29007i	−0.846504	+	0.275046i	−0.146523	+	0.989207i	$0.546808\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.23186	+	0.400255i	−0.0536606	+	0.0174354i
$528$		0			0
$529$	−17.2085	+	12.5027i	−0.748197	+	0.543597i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−26.5204	+	36.5022i	−1.14873	+	1.58108i
$534$		0			0
$535$	−15.7691	+	7.13330i	−0.681757	+	0.308400i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	17.1902	+	52.9061i	0.740435	+	2.27883i
$540$		0			0
$541$	9.54086	−	29.3638i	0.410194	−	1.26245i	−0.506286	−	0.862366i	$-0.668982\pi$
$541$	9.54086	−	29.3638i	0.410194	−	1.26245i	0.916480	−	0.400081i	$-0.131018\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	23.0481	−	2.56086i	0.987271	−	0.109695i
$546$		0			0
$547$	9.01637	+	12.4100i	0.385512	+	0.530612i	0.957034	−	0.289975i	$-0.0936469\pi$
$547$	9.01637	+	12.4100i	0.385512	+	0.530612i	−0.571522	+	0.820587i	$0.693647\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−13.4850			−0.574478
$552$		0			0
$553$	−8.90587	−	12.2579i	−0.378716	−	0.521258i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	28.6722i		−	1.21488i	−0.794365	−	0.607441i	$-0.792196\pi$
$557$		−	28.6722i		−	1.21488i	0.794365	−	0.607441i	$-0.207804\pi$
$558$		0			0
$559$	−0.733185	+	2.25651i	−0.0310104	+	0.0954403i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.99026	+	2.27127i	0.294604	+	0.0957227i	0.452590	−	0.891719i	$-0.350500\pi$
$563$	6.99026	+	2.27127i	0.294604	+	0.0957227i	−0.157986	+	0.987441i	$0.550500\pi$
$564$		0			0
$565$	−2.52516	−	22.7267i	−0.106234	−	0.956121i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	25.1830	+	18.2965i	1.05572	+	0.767029i	0.973293	−	0.229568i	$-0.0737312\pi$
$569$	25.1830	+	18.2965i	1.05572	+	0.767029i	0.0824322	+	0.996597i	$0.473731\pi$
$570$		0			0
$571$	−10.5055	+	7.63268i	−0.439641	+	0.319418i	−0.785492	−	0.618872i	$-0.787590\pi$
$571$	−10.5055	+	7.63268i	−0.439641	+	0.319418i	0.345851	+	0.938289i	$0.387590\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.60269	−	6.03765i	0.108540	−	0.251787i
$576$		0			0
$577$	20.7231	−	6.73333i	0.862712	−	0.280312i	0.155951	−	0.987765i	$-0.450156\pi$
$577$	20.7231	−	6.73333i	0.862712	−	0.280312i	0.706761	+	0.707453i	$0.250156\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−19.1879	−	13.9408i	−0.796048	−	0.578363i
$582$		0			0
$583$	0.825453	−	1.13614i	0.0341868	−	0.0470541i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	25.3208	+	8.22724i	1.04510	+	0.339575i	0.780745	−	0.624850i	$-0.214840\pi$
$587$	25.3208	+	8.22724i	1.04510	+	0.339575i	0.264358	+	0.964425i	$0.414840\pi$
$588$		0			0
$589$	−0.169545	−	0.521806i	−0.00698598	−	0.0215006i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	5.23169i		−	0.214840i	−0.994214	−	0.107420i	$-0.965741\pi$
$593$		−	5.23169i		−	0.214840i	0.994214	−	0.107420i	$-0.0342589\pi$
$594$		0			0
$595$	13.1103	−	63.5314i	0.537472	−	2.60453i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	39.5405			1.61558			0.807790	−	0.589471i	$-0.200664\pi$
$599$	39.5405			1.61558			0.807790	+	0.589471i	$0.200664\pi$
$600$		0			0
$601$	−45.5789			−1.85920			−0.929602	−	0.368565i	$-0.879849\pi$
$601$	−45.5789			−1.85920			−0.929602	+	0.368565i	$0.879849\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−17.1354	−	9.75796i	−0.696652	−	0.396717i
$606$		0			0
$607$			18.6524i			0.757078i	0.925585	+	0.378539i	$0.123573\pi$
$607$			18.6524i			0.757078i	−0.925585	+	0.378539i	$0.876427\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	13.8444	+	42.6088i	0.560086	+	1.72377i
$612$		0			0
$613$	10.1837	+	3.30887i	0.411314	+	0.133644i	0.507363	−	0.861733i	$-0.330620\pi$
$613$	10.1837	+	3.30887i	0.411314	+	0.133644i	−0.0960485	+	0.995377i	$0.530620\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.83565	+	13.5376i	−0.395968	+	0.545004i	−0.959726	−	0.280936i	$-0.909355\pi$
$617$	−9.83565	+	13.5376i	−0.395968	+	0.545004i	0.563758	+	0.825940i	$0.309355\pi$
$618$		0			0
$619$	18.5531	+	13.4796i	0.745711	+	0.541791i	0.894495	−	0.447079i	$-0.147536\pi$
$619$	18.5531	+	13.4796i	0.745711	+	0.541791i	−0.148783	+	0.988870i	$0.547536\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−47.6417	+	15.4797i	−1.90872	+	0.620182i
$624$		0			0
$625$	−3.20277	−	24.7940i	−0.128111	−	0.991760i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	43.6334	−	31.7015i	1.73978	−	1.26402i
$630$		0			0
$631$	−11.7443	−	8.53273i	−0.467533	−	0.339683i	0.328946	−	0.944349i	$-0.393307\pi$
$631$	−11.7443	−	8.53273i	−0.467533	−	0.339683i	−0.796479	+	0.604666i	$0.793307\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	17.0376	+	18.6978i	0.676117	+	0.741999i
$636$		0			0
$637$	−68.3076	−	22.1945i	−2.70645	−	0.879377i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.81208	−	30.1985i	0.387554	−	1.19277i	−0.547057	−	0.837095i	$-0.684252\pi$
$641$	9.81208	−	30.1985i	0.387554	−	1.19277i	0.934611	−	0.355672i	$-0.115748\pi$
$642$		0			0
$643$		−	3.63816i		−	0.143475i	−0.997424	−	0.0717376i	$-0.977146\pi$
$643$		−	3.63816i		−	0.143475i	0.997424	−	0.0717376i	$-0.0228544\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.60932	−	9.09695i	−0.259839	−	0.357638i	0.659088	−	0.752066i	$-0.270943\pi$
$647$	−6.60932	−	9.09695i	−0.259839	−	0.357638i	−0.918927	+	0.394428i	$0.870943\pi$
$648$		0			0
$649$	−11.2142			−0.440195
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.18866	+	1.63604i	0.0465157	+	0.0640233i	0.831641	−	0.555313i	$-0.187402\pi$
$653$	1.18866	+	1.63604i	0.0465157	+	0.0640233i	−0.785126	+	0.619337i	$0.787402\pi$
$654$		0			0
$655$	4.27223	−	20.7028i	0.166930	−	0.808925i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.245610	+	0.755909i	−0.00956760	+	0.0294460i	−0.955726	−	0.294257i	$-0.904928\pi$
$659$	−0.245610	+	0.755909i	−0.00956760	+	0.0294460i	0.946159	+	0.323703i	$0.104928\pi$
$660$		0			0
$661$	12.6628	+	38.9722i	0.492527	+	1.51584i	0.820776	+	0.571250i	$0.193541\pi$
$661$	12.6628	+	38.9722i	0.492527	+	1.51584i	−0.328249	+	0.944591i	$0.606459\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	26.9114	+	5.55345i	1.04358	+	0.215353i
$666$		0			0
$667$	−3.74489	+	5.15440i	−0.145003	+	0.199579i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	33.6069	−	24.4169i	1.29738	−	0.942602i
$672$		0			0
$673$	−33.3834	+	10.8469i	−1.28683	+	0.418118i	−0.870982	−	0.491314i	$-0.836517\pi$
$673$	−33.3834	+	10.8469i	−1.28683	+	0.418118i	−0.415852	+	0.909432i	$0.636517\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	36.5079	−	11.8621i	1.40311	−	0.455899i	0.492916	−	0.870077i	$-0.335931\pi$
$677$	36.5079	−	11.8621i	1.40311	−	0.455899i	0.910196	+	0.414178i	$0.135931\pi$
$678$		0			0
$679$	−18.1450	+	13.1831i	−0.696342	+	0.505922i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.91673	−	6.76730i	0.188134	−	0.258944i	−0.704523	−	0.709681i	$-0.748839\pi$
$683$	4.91673	−	6.76730i	0.188134	−	0.258944i	0.892657	+	0.450738i	$0.148839\pi$
$684$		0			0
$685$	−2.07673	−	18.6908i	−0.0793479	−	0.714140i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.560299	+	1.72442i	0.0213457	+	0.0656953i
$690$		0			0
$691$	1.80183	−	5.54547i	0.0685450	−	0.210960i	−0.910917	−	0.412590i	$-0.864624\pi$
$691$	1.80183	−	5.54547i	0.0685450	−	0.210960i	0.979462	+	0.201631i	$0.0646241\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	19.5388	−	17.8040i	0.741150	−	0.675344i
$696$		0			0
$697$	−30.3158	−	41.7261i	−1.14829	−	1.58049i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−50.6649			−1.91359			−0.956793	−	0.290770i	$-0.906089\pi$
$701$	−50.6649			−1.91359			−0.956793	+	0.290770i	$0.906089\pi$
$702$		0			0
$703$	13.4285	+	18.4828i	0.506467	+	0.697091i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			49.3907i			1.85753i
$708$		0			0
$709$	3.00734	−	9.25565i	0.112943	−	0.347603i	−0.878569	−	0.477615i	$-0.841501\pi$
$709$	3.00734	−	9.25565i	0.112943	−	0.347603i	0.991512	+	0.130012i	$0.0415015\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−0.246536	−	0.0801044i	−0.00923285	−	0.00299993i
$714$		0			0
$715$	52.1309	−	23.5819i	1.94958	−	0.881914i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.1579	−	11.0129i	−0.565294	−	0.410710i	0.268099	−	0.963391i	$-0.413605\pi$
$719$	−15.1579	−	11.0129i	−0.565294	−	0.410710i	−0.833393	+	0.552681i	$0.813605\pi$
$720$		0			0
$721$	11.2368	−	8.16399i	0.418479	−	0.304043i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.24610	+	24.1217i	−0.0834181	+	0.895857i
$726$		0			0
$727$	36.1247	−	11.7376i	1.33979	−	0.435324i	0.450544	−	0.892754i	$-0.351230\pi$
$727$	36.1247	−	11.7376i	1.33979	−	0.435324i	0.889246	+	0.457430i	$0.151230\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.19421	−	1.59418i	−0.0811557	−	0.0589630i
$732$		0			0
$733$	15.4951	−	21.3271i	0.572323	−	0.787735i	−0.420505	−	0.907290i	$-0.638147\pi$
$733$	15.4951	−	21.3271i	0.572323	−	0.787735i	0.992828	+	0.119555i	$0.0381469\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−50.5772	−	16.4335i	−1.86303	−	0.605337i
$738$		0			0
$739$	10.2081	+	31.4174i	0.375513	+	1.15571i	0.943132	+	0.332418i	$0.107864\pi$
$739$	10.2081	+	31.4174i	0.375513	+	1.15571i	−0.567619	+	0.823291i	$0.692136\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			40.2017i			1.47486i	0.675425	+	0.737428i	$0.263960\pi$
$743$			40.2017i			1.47486i	−0.675425	+	0.737428i	$0.736040\pi$
$744$		0			0
$745$	9.80168	+	21.6679i	0.359106	+	0.793849i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−34.1758			−1.24876
$750$		0			0
$751$	30.5937			1.11638			0.558190	−	0.829713i	$-0.311496\pi$
$751$	30.5937			1.11638			0.558190	+	0.829713i	$0.311496\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	4.07031	+	8.99793i	0.148134	+	0.327468i
$756$		0			0
$757$		−	24.4003i		−	0.886845i	−0.896313	−	0.443422i	$-0.853764\pi$
$757$		−	24.4003i		−	0.886845i	0.896313	−	0.443422i	$-0.146236\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.75574	−	26.9474i	−0.317395	−	0.976842i	−0.974757	−	0.223267i	$-0.928328\pi$
$761$	−8.75574	−	26.9474i	−0.317395	−	0.976842i	0.657362	−	0.753575i	$-0.271672\pi$
$762$		0			0
$763$	43.5502	+	14.1503i	1.57662	+	0.512276i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	8.51040	−	11.7136i	0.307293	−	0.422952i
$768$		0			0
$769$	−33.2679	−	24.1706i	−1.19967	−	0.871613i	−0.205420	−	0.978674i	$-0.565856\pi$
$769$	−33.2679	−	24.1706i	−1.19967	−	0.871613i	−0.994252	+	0.107061i	$0.965856\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.58131	+	1.48856i	−0.164778	+	0.0535397i	−0.390244	−	0.920711i	$-0.627609\pi$
$773$	−4.58131	+	1.48856i	−0.164778	+	0.0535397i	0.225466	+	0.974251i	$0.427609\pi$
$774$		0			0
$775$	−0.961638	+	0.216366i	−0.0345431	+	0.00777208i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	17.6749	−	12.8415i	0.633268	−	0.460096i
$780$		0			0
$781$	−1.83410	−	1.33255i	−0.0656293	−	0.0476825i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−27.5626	+	12.4682i	−0.983751	+	0.445010i
$786$		0			0
$787$	−38.3447	−	12.4590i	−1.36684	−	0.444114i	−0.468520	−	0.883453i	$-0.655213\pi$
$787$	−38.3447	−	12.4590i	−1.36684	−	0.444114i	−0.898321	+	0.439339i	$0.855213\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	13.9530	−	42.9430i	0.496113	−	1.52688i
$792$		0			0
$793$			53.6333i			1.90457i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.7487	−	24.4289i	−0.628690	−	0.865318i	0.369259	−	0.929326i	$-0.379611\pi$
$797$	−17.7487	−	24.4289i	−0.628690	−	0.865318i	−0.997949	+	0.0640088i	$0.979611\pi$
$798$		0			0
$799$	−51.2132			−1.81179
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−41.2677	−	56.8001i	−1.45630	−	2.00443i
$804$		0			0
$805$	9.59626	−	8.74421i	0.338224	−	0.308193i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.36218	−	10.3477i	0.118208	−	0.363807i	−0.874395	−	0.485216i	$-0.838741\pi$
$809$	3.36218	−	10.3477i	0.118208	−	0.363807i	0.992603	+	0.121409i	$0.0387411\pi$
$810$		0			0
$811$	−14.6035	−	44.9451i	−0.512799	−	1.57823i	−0.787250	−	0.616633i	$-0.788496\pi$
$811$	−14.6035	−	44.9451i	−0.512799	−	1.57823i	0.274451	−	0.961601i	$-0.411504\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.59486	−	32.3542i	−0.125923	−	1.13332i
$816$		0			0
$817$	0.675285	−	0.929450i	0.0236252	−	0.0325173i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	20.1200	−	14.6180i	0.702191	−	0.510172i	−0.178454	−	0.983948i	$-0.557110\pi$
$821$	20.1200	−	14.6180i	0.702191	−	0.510172i	0.880645	+	0.473777i	$0.157110\pi$
$822$		0			0
$823$	−21.6451	+	7.03293i	−0.754502	+	0.245152i	−0.660917	−	0.750459i	$-0.729833\pi$
$823$	−21.6451	+	7.03293i	−0.754502	+	0.245152i	−0.0935845	+	0.995611i	$0.529833\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	44.5530	−	14.4761i	1.54926	−	0.503385i	0.595346	−	0.803469i	$-0.297015\pi$
$827$	44.5530	−	14.4761i	1.54926	−	0.503385i	0.953913	+	0.300084i	$0.0970148\pi$
$828$		0			0
$829$	−11.1652	+	8.11202i	−0.387785	+	0.281742i	−0.764547	−	0.644568i	$-0.777037\pi$
$829$	−11.1652	+	8.11202i	−0.387785	+	0.281742i	0.376762	+	0.926310i	$0.377037\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	48.2581	−	66.4215i	1.67204	−	2.30137i
$834$		0			0
$835$	21.8297	+	4.50478i	0.755448	+	0.155894i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.27210	−	10.0705i	−0.112966	−	0.347672i	0.878552	−	0.477647i	$-0.158510\pi$
$839$	−3.27210	−	10.0705i	−0.112966	−	0.347672i	−0.991517	+	0.129975i	$0.958510\pi$
$840$		0			0
$841$	−1.70701	+	5.25362i	−0.0588623	+	0.181159i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−9.05497	+	43.8795i	−0.311501	+	1.50950i
$846$		0			0
$847$	−22.8870	−	31.5012i	−0.786406	−	1.08239i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.7940			0.370012
$852$		0			0
$853$	−13.3131	−	18.3240i	−0.455834	−	0.627401i	0.517805	−	0.855499i	$-0.326749\pi$
$853$	−13.3131	−	18.3240i	−0.455834	−	0.627401i	−0.973638	+	0.228098i	$0.926749\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			39.4749i			1.34844i	0.738533	+	0.674218i	$0.235519\pi$
$857$			39.4749i			1.34844i	−0.738533	+	0.674218i	$0.764481\pi$
$858$		0			0
$859$	−13.7012	+	42.1679i	−0.467478	+	1.43875i	0.388361	+	0.921507i	$0.373041\pi$
$859$	−13.7012	+	42.1679i	−0.467478	+	1.43875i	−0.855839	+	0.517242i	$0.826959\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.78917	−	1.55610i	−0.163025	−	0.0529701i	0.226367	−	0.974042i	$-0.427315\pi$
$863$	−4.78917	−	1.55610i	−0.163025	−	0.0529701i	−0.389393	+	0.921072i	$0.627315\pi$
$864$		0			0
$865$	16.3784	+	17.9743i	0.556882	+	0.611146i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	12.3590	+	8.97931i	0.419249	+	0.304602i
$870$		0			0
$871$	55.5481	−	40.3581i	1.88218	−	1.36748i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	14.4164	−	47.2137i	0.487363	−	1.59612i
$876$		0			0
$877$	−16.6380	+	5.40602i	−0.561826	+	0.182548i	−0.576143	−	0.817349i	$-0.695443\pi$
$877$	−16.6380	+	5.40602i	−0.561826	+	0.182548i	0.0143164	+	0.999898i	$0.495443\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−43.8856	−	31.8848i	−1.47855	−	1.07423i	−0.978022	−	0.208503i	$-0.933141\pi$
$881$	−43.8856	−	31.8848i	−1.47855	−	1.07423i	−0.500523	−	0.865723i	$-0.666859\pi$
$882$		0			0
$883$	−17.8419	+	24.5572i	−0.600427	+	0.826416i	−0.995747	−	0.0921269i	$-0.970633\pi$
$883$	−17.8419	+	24.5572i	−0.600427	+	0.826416i	0.395321	+	0.918543i	$0.370633\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−50.0705	−	16.2689i	−1.68120	−	0.546256i	−0.696058	−	0.717985i	$-0.745065\pi$
$887$	−50.0705	−	16.2689i	−1.68120	−	0.546256i	−0.985144	+	0.171729i	$0.945065\pi$
$888$		0			0
$889$	15.4354	+	47.5054i	0.517688	+	1.59328i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	21.6935i		−	0.725947i
$894$		0			0
$895$	48.9154	+	27.8555i	1.63506	+	0.931106i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	0.955163			0.0318565
$900$		0			0
$901$	−2.07265			−0.0690500
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.43081	+	16.6253i	−0.114044	+	0.552645i
$906$		0			0
$907$			8.79799i			0.292133i	0.989275	+	0.146066i	$0.0466613\pi$
$907$			8.79799i			0.292133i	−0.989275	+	0.146066i	$0.953339\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.73942	+	29.9749i	0.322682	+	0.993112i	0.972476	+	0.233002i	$0.0748548\pi$
$911$	9.73942	+	29.9749i	0.322682	+	0.993112i	−0.649795	+	0.760110i	$0.725145\pi$
$912$		0			0
$913$	22.7427	+	7.38956i	0.752675	+	0.244559i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.5351	−	33.7697i	0.810221	−	1.11517i
$918$		0			0
$919$	−27.0858	−	19.6790i	−0.893478	−	0.649150i	0.0433046	−	0.999062i	$-0.486211\pi$
$919$	−27.0858	−	19.6790i	−0.893478	−	0.649150i	−0.936782	+	0.349912i	$0.886211\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.78378	−	0.904506i	0.0916294	−	0.0297722i
$924$		0			0
$925$	35.2984	−	20.9422i	1.16060	−	0.688575i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.51966	−	1.10410i	0.0498585	−	0.0362244i	−0.562577	−	0.826745i	$-0.690190\pi$
$929$	1.51966	−	1.10410i	0.0498585	−	0.0362244i	0.612435	+	0.790521i	$0.290190\pi$
$930$		0			0
$931$	28.1357	+	20.4418i	0.922110	+	0.669952i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	7.22267	+	65.0049i	0.236207	+	2.12589i
$936$		0			0
$937$	−2.17621	−	0.707094i	−0.0710937	−	0.0230997i	0.273254	−	0.961942i	$-0.411900\pi$
$937$	−2.17621	−	0.707094i	−0.0710937	−	0.0230997i	−0.344348	+	0.938842i	$0.611900\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	18.5837	−	57.1947i	0.605811	−	1.86449i	0.114691	−	0.993401i	$-0.463412\pi$
$941$	18.5837	−	57.1947i	0.605811	−	1.86449i	0.491119	−	0.871092i	$-0.336588\pi$
$942$		0			0
$943$		−	10.3221i		−	0.336135i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.4333	+	35.0060i	0.826472	+	1.13754i	0.988569	+	0.150766i	$0.0481740\pi$
$947$	25.4333	+	35.0060i	0.826472	+	1.13754i	−0.162098	+	0.986775i	$0.551826\pi$
$948$		0			0
$949$	90.6473			2.94253
$950$		0			0
$951$		0			0
$952$		0			0
$953$	20.4875	+	28.1986i	0.663654	+	0.913441i	0.999595	−	0.0284419i	$-0.00905456\pi$
$953$	20.4875	+	28.1986i	0.663654	+	0.913441i	−0.335942	+	0.941883i	$0.609055\pi$
$954$		0			0
$955$	0.0268756	−	0.00298613i	0.000869673	−	9.66290e-5i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11.4752	−	35.3171i	0.370554	−	1.14045i
$960$		0			0
$961$	−9.56752	−	29.4458i	−0.308630	−	0.949864i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	26.0452	−	11.7818i	0.838426	−	0.379271i
$966$		0			0
$967$	−20.5577	+	28.2952i	−0.661090	+	0.909912i	−0.999517	−	0.0310806i	$-0.990105\pi$
$967$	−20.5577	+	28.2952i	−0.661090	+	0.909912i	0.338427	+	0.940993i	$0.390105\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−48.1194	+	34.9608i	−1.54422	+	1.12194i	−0.596607	+	0.802533i	$0.703485\pi$
$971$	−48.1194	+	34.9608i	−1.54422	+	1.12194i	−0.947616	+	0.319411i	$0.896515\pi$
$972$		0			0
$973$	49.6423	−	16.1297i	1.59146	−	0.517096i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	14.6616	−	4.76386i	0.469067	−	0.152409i	−0.0649398	−	0.997889i	$-0.520686\pi$
$977$	14.6616	−	4.76386i	0.469067	−	0.152409i	0.534007	+	0.845480i	$0.320686\pi$
$978$		0			0
$979$	40.8606	−	29.6870i	1.30591	−	0.948800i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−34.5324	+	47.5297i	−1.10141	+	1.51596i	−0.267912	+	0.963443i	$0.586334\pi$
$983$	−34.5324	+	47.5297i	−1.10141	+	1.51596i	−0.833500	+	0.552520i	$0.813666\pi$
$984$		0			0
$985$	−10.9163	+	19.1695i	−0.347823	+	0.610791i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−0.167734	−	0.516233i	−0.00533364	−	0.0164153i
$990$		0			0
$991$	0.529181	−	1.62865i	0.0168100	−	0.0517358i	−0.942300	−	0.334771i	$-0.891341\pi$
$991$	0.529181	−	1.62865i	0.0168100	−	0.0517358i	0.959110	+	0.283035i	$0.0913412\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.272462	+	0.602311i	0.00863762	+	0.0190945i
$996$		0			0
$997$	−6.93389	−	9.54368i	−0.219598	−	0.302251i	0.684977	−	0.728564i	$-0.259812\pi$
$997$	−6.93389	−	9.54368i	−0.219598	−	0.302251i	−0.904576	+	0.426313i	$0.859812\pi$
$998$		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.469.5		24
3.2	odd	2		300.2.o.a.169.4	✓	24
15.2	even	4		1500.2.m.d.901.1		24
15.8	even	4		1500.2.m.c.901.6		24
15.14	odd	2		1500.2.o.c.349.3		24
25.4	even	10	inner	900.2.w.c.829.5		24
75.2	even	20		7500.2.a.m.1.2		12
75.11	odd	10		7500.2.d.g.1249.11		24
75.14	odd	10		7500.2.d.g.1249.14		24
75.23	even	20		7500.2.a.n.1.11		12
75.29	odd	10		300.2.o.a.229.4	yes	24
75.47	even	20		1500.2.m.d.601.1		24
75.53	even	20		1500.2.m.c.601.6		24
75.71	odd	10		1500.2.o.c.649.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.4	✓	24	3.2	odd	2
300.2.o.a.229.4	yes	24	75.29	odd	10
900.2.w.c.469.5		24	1.1	even	1	trivial
900.2.w.c.829.5		24	25.4	even	10	inner
1500.2.m.c.601.6		24	75.53	even	20
1500.2.m.c.901.6		24	15.8	even	4
1500.2.m.d.601.1		24	75.47	even	20
1500.2.m.d.901.1		24	15.2	even	4
1500.2.o.c.349.3		24	15.14	odd	2
1500.2.o.c.649.3		24	75.71	odd	10
7500.2.a.m.1.2		12	75.2	even	20
7500.2.a.n.1.11		12	75.23	even	20
7500.2.d.g.1249.11		24	75.11	odd	10
7500.2.d.g.1249.14		24	75.14	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)

\(f(q)\)	\(=\)	\(q+(0.921600 + 2.03732i) q^{5} +4.41540i q^{7} +O(q^{10})\)	\(q+(0.921600 + 2.03732i) q^{5} +4.41540i q^{7} +(-1.37568 - 4.23392i) q^{11} +(5.46646 + 1.77616i) q^{13} +(-3.86196 + 5.31553i) q^{17} +(-2.25162 - 1.63590i) q^{19} +(-1.25059 + 0.406341i) q^{23} +(-3.30131 + 3.75518i) q^{25} +(3.91985 - 2.84794i) q^{29} +(0.159486 + 0.115873i) q^{31} +(-8.99556 + 4.06923i) q^{35} +(-7.80690 - 2.53662i) q^{37} +(-2.42573 + 7.46564i) q^{41} +0.412792i q^{43} +(4.58154 + 6.30595i) q^{47} -12.4958 q^{49} +(0.185420 + 0.255208i) q^{53} +(7.35800 - 6.70469i) q^{55} +(0.778419 - 2.39573i) q^{59} +(2.88348 + 8.87444i) q^{61} +(1.41929 + 12.7738i) q^{65} +(7.02151 - 9.66428i) q^{67} +(0.411990 - 0.299328i) q^{71} +(14.9990 - 4.87346i) q^{73} +(18.6945 - 6.07420i) q^{77} +(-2.77617 + 2.01700i) q^{79} +(-3.15732 + 4.34568i) q^{83} +(-14.3886 - 2.96923i) q^{85} +(3.50585 + 10.7899i) q^{89} +(-7.84246 + 24.1366i) q^{91} +(1.25774 - 6.09490i) q^{95} +(2.98572 + 4.10948i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 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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