LMFDB - Embedded newform 900.3.p.f.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(101,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("900.101");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	900.p (of order $6$, degree $2$, 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:	$24.5232237924$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 180)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	900.101
Dual form			900.3.p.f.401.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0930019 + 2.99856i) q^{3} +(3.67363 - 6.36292i) q^{7} +(-8.98270 - 0.557743i) q^{9} +O(q^{10})$	\(q+(-0.0930019 + 2.99856i) q^{3} +(3.67363 - 6.36292i) q^{7} +(-8.98270 - 0.557743i) q^{9} +(-8.35448 - 4.82346i) q^{11} +(8.34294 + 14.4504i) q^{13} -15.4743i q^{17} +17.4865 q^{19} +(18.7379 + 11.6074i) q^{21} +(-9.16415 + 5.29093i) q^{23} +(2.50783 - 26.8833i) q^{27} +(36.2049 + 20.9029i) q^{29} +(24.3641 + 42.1998i) q^{31} +(15.2404 - 24.6028i) q^{33} +20.4792 q^{37} +(-44.1063 + 23.6729i) q^{39} +(24.1640 - 13.9511i) q^{41} +(15.1046 - 26.1619i) q^{43} +(36.4814 + 21.0626i) q^{47} +(-2.49113 - 4.31476i) q^{49} +(46.4005 + 1.43914i) q^{51} -90.4314i q^{53} +(-1.62628 + 52.4344i) q^{57} +(48.0096 - 27.7184i) q^{59} +(-58.3790 + 101.115i) q^{61} +(-36.5480 + 55.1072i) q^{63} +(-8.64187 - 14.9682i) q^{67} +(-15.0129 - 27.9713i) q^{69} +38.4861i q^{71} -7.38815 q^{73} +(-61.3825 + 35.4392i) q^{77} +(11.8497 - 20.5242i) q^{79} +(80.3778 + 10.0201i) q^{81} +(3.69783 + 2.13494i) q^{83} +(-66.0456 + 106.618i) q^{87} +145.034i q^{89} +122.596 q^{91} +(-128.804 + 69.1324i) q^{93} +(-51.3498 + 88.9405i) q^{97} +(72.3555 + 47.9874i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^9	$ 24 q - 2 q^{9} - 18 q^{11} - 26 q^{21} - 36 q^{29} + 30 q^{31} - 6 q^{39} - 36 q^{41} - 108 q^{49} + 124 q^{51} + 306 q^{59} + 48 q^{61} + 268 q^{69} - 114 q^{79} - 14 q^{81} - 84 q^{91} - 418 q^{99}+O(q^{100}) $ 24 * q - 2 * q^9 - 18 * q^11 - 26 * q^21 - 36 * q^29 + 30 * q^31 - 6 * q^39 - 36 * q^41 - 108 * q^49 + 124 * q^51 + 306 * q^59 + 48 * q^61 + 268 * q^69 - 114 * q^79 - 14 * q^81 - 84 * q^91 - 418 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0930019	+	2.99856i	−0.0310006	+	0.999519i
$3$	−0.0930019	+	2.99856i	−0.0310006	+	0.999519i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.67363	−	6.36292i	0.524804	−	0.908988i	−0.474778	−	0.880105i	$-0.657472\pi$
$7$	3.67363	−	6.36292i	0.524804	−	0.908988i	0.999583	−	0.0288825i	$-0.00919487\pi$
$8$		0			0
$9$	−8.98270	−	0.557743i	−0.998078	−	0.0619715i
$10$		0			0
$11$	−8.35448	−	4.82346i	−0.759498	−	0.438496i	0.0696175	−	0.997574i	$-0.477822\pi$
$11$	−8.35448	−	4.82346i	−0.759498	−	0.438496i	−0.829115	+	0.559077i	$0.811155\pi$
$12$		0			0
$13$	8.34294	+	14.4504i	0.641765	+	1.11157i	0.985039	+	0.172334i	$0.0551309\pi$
$13$	8.34294	+	14.4504i	0.641765	+	1.11157i	−0.343274	+	0.939235i	$0.611536\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	15.4743i		−	0.910251i	−0.890427	−	0.455125i	$-0.849594\pi$
$17$		−	15.4743i		−	0.910251i	0.890427	−	0.455125i	$-0.150406\pi$
$18$		0			0
$19$	17.4865			0.920344			0.460172	−	0.887830i	$-0.347788\pi$
$19$	17.4865			0.920344			0.460172	+	0.887830i	$0.347788\pi$
$20$		0			0
$21$	18.7379	+	11.6074i	0.892282	+	0.552731i
$22$		0			0
$23$	−9.16415	+	5.29093i	−0.398441	+	0.230040i	−0.685811	−	0.727779i	$-0.740552\pi$
$23$	−9.16415	+	5.29093i	−0.398441	+	0.230040i	0.287370	+	0.957820i	$0.407219\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.50783	−	26.8833i	0.0928827	−	0.995677i
$28$		0			0
$29$	36.2049	+	20.9029i	1.24844	+	0.720789i	0.970799	−	0.239895i	$-0.0771130\pi$
$29$	36.2049	+	20.9029i	1.24844	+	0.720789i	0.277644	+	0.960684i	$0.410446\pi$
$30$		0			0
$31$	24.3641	+	42.1998i	0.785937	+	1.36128i	0.928438	+	0.371489i	$0.121153\pi$
$31$	24.3641	+	42.1998i	0.785937	+	1.36128i	−0.142500	+	0.989795i	$0.545514\pi$
$32$		0			0
$33$	15.2404	−	24.6028i	0.461831	−	0.745539i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	20.4792			0.553492			0.276746	−	0.960943i	$-0.410744\pi$
$37$	20.4792			0.553492			0.276746	+	0.960943i	$0.410744\pi$
$38$		0			0
$39$	−44.1063	+	23.6729i	−1.13093	+	0.606997i
$40$		0			0
$41$	24.1640	−	13.9511i	0.589365	−	0.340270i	−0.175482	−	0.984483i	$-0.556148\pi$
$41$	24.1640	−	13.9511i	0.589365	−	0.340270i	0.764846	+	0.644213i	$0.222815\pi$
$42$		0			0
$43$	15.1046	−	26.1619i	0.351269	−	0.608416i	−0.635203	−	0.772345i	$-0.719084\pi$
$43$	15.1046	−	26.1619i	0.351269	−	0.608416i	0.986472	+	0.163930i	$0.0524170\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	36.4814	+	21.0626i	0.776200	+	0.448139i	0.835082	−	0.550126i	$-0.185420\pi$
$47$	36.4814	+	21.0626i	0.776200	+	0.448139i	−0.0588817	+	0.998265i	$0.518753\pi$
$48$		0			0
$49$	−2.49113	−	4.31476i	−0.0508393	−	0.0880562i
$50$		0			0
$51$	46.4005	+	1.43914i	0.909813	+	0.0282183i
$52$		0			0
$53$		−	90.4314i		−	1.70625i	−0.521704	−	0.853127i	$-0.674703\pi$
$53$		−	90.4314i		−	1.70625i	0.521704	−	0.853127i	$-0.325297\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−1.62628	+	52.4344i	−0.0285312	+	0.919901i
$58$		0			0
$59$	48.0096	−	27.7184i	0.813722	−	0.469803i	−0.0345248	−	0.999404i	$-0.510992\pi$
$59$	48.0096	−	27.7184i	0.813722	−	0.469803i	0.848247	+	0.529601i	$0.177658\pi$
$60$		0			0
$61$	−58.3790	+	101.115i	−0.957034	+	1.65763i	−0.227389	+	0.973804i	$0.573019\pi$
$61$	−58.3790	+	101.115i	−0.957034	+	1.65763i	−0.729644	+	0.683827i	$0.760314\pi$
$62$		0			0
$63$	−36.5480	+	55.1072i	−0.580127	+	0.874718i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−8.64187	−	14.9682i	−0.128983	−	0.223405i	0.794300	−	0.607526i	$-0.207838\pi$
$67$	−8.64187	−	14.9682i	−0.128983	−	0.223405i	−0.923283	+	0.384121i	$0.874505\pi$
$68$		0			0
$69$	−15.0129	−	27.9713i	−0.217578	−	0.405381i
$70$		0			0
$71$			38.4861i			0.542058i	0.962571	+	0.271029i	$0.0873640\pi$
$71$			38.4861i			0.542058i	−0.962571	+	0.271029i	$0.912636\pi$
$72$		0			0
$73$	−7.38815			−0.101208			−0.0506038	−	0.998719i	$-0.516115\pi$
$73$	−7.38815			−0.101208			−0.0506038	+	0.998719i	$0.516115\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−61.3825	+	35.4392i	−0.797176	+	0.460250i
$78$		0			0
$79$	11.8497	−	20.5242i	0.149996	−	0.259800i	−0.781230	−	0.624244i	$-0.785407\pi$
$79$	11.8497	−	20.5242i	0.149996	−	0.259800i	0.931226	+	0.364443i	$0.118741\pi$
$80$		0			0
$81$	80.3778	+	10.0201i	0.992319	+	0.123705i
$82$		0			0
$83$	3.69783	+	2.13494i	0.0445522	+	0.0257222i	0.522111	−	0.852878i	$-0.325145\pi$
$83$	3.69783	+	2.13494i	0.0445522	+	0.0257222i	−0.477558	+	0.878600i	$0.658478\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−66.0456	+	106.618i	−0.759145	+	1.22550i
$88$		0			0
$89$			145.034i			1.62959i	0.579746	+	0.814797i	$0.303152\pi$
$89$			145.034i			1.62959i	−0.579746	+	0.814797i	$0.696848\pi$
$90$		0			0
$91$	122.596			1.34720
$92$		0			0
$93$	−128.804	+	69.1324i	−1.38499	+	0.743359i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−51.3498	+	88.9405i	−0.529379	+	0.916912i	0.470033	+	0.882649i	$0.344242\pi$
$97$	−51.3498	+	88.9405i	−0.529379	+	0.916912i	−0.999413	+	0.0342635i	$0.989091\pi$
$98$		0			0
$99$	72.3555	+	47.9874i	0.730864	+	0.484721i
$100$		0			0
$101$	96.0083	+	55.4304i	0.950577	+	0.548816i	0.893260	−	0.449540i	$-0.148412\pi$
$101$	96.0083	+	55.4304i	0.950577	+	0.548816i	0.0573168	+	0.998356i	$0.481745\pi$
$102$		0			0
$103$	93.9245	+	162.682i	0.911888	+	1.57944i	0.811394	+	0.584499i	$0.198709\pi$
$103$	93.9245	+	162.682i	0.911888	+	1.57944i	0.100494	+	0.994938i	$0.467958\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	121.767i		−	1.13801i	−0.822334	−	0.569005i	$-0.807328\pi$
$107$		−	121.767i		−	1.13801i	0.822334	−	0.569005i	$-0.192672\pi$
$108$		0			0
$109$	45.3350			0.415918			0.207959	−	0.978138i	$-0.433318\pi$
$109$	45.3350			0.415918			0.207959	+	0.978138i	$0.433318\pi$
$110$		0			0
$111$	−1.90461	+	61.4081i	−0.0171586	+	0.553226i
$112$		0			0
$113$	−16.6356	+	9.60459i	−0.147218	+	0.0849963i	−0.571800	−	0.820393i	$-0.693755\pi$
$113$	−16.6356	+	9.60459i	−0.147218	+	0.0849963i	0.424582	+	0.905390i	$0.360421\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−66.8826	−	134.457i	−0.571646	−	1.14920i
$118$		0			0
$119$	−98.4614	−	56.8467i	−0.827407	−	0.477704i
$120$		0			0
$121$	−13.9685	−	24.1941i	−0.115442	−	0.199951i
$122$		0			0
$123$	39.5858	+	73.7545i	0.321836	+	0.599630i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	179.244			1.41137			0.705684	−	0.708527i	$-0.250640\pi$
$127$	179.244			1.41137			0.705684	+	0.708527i	$0.250640\pi$
$128$		0			0
$129$	77.0431	+	47.7250i	0.597234	+	0.369961i
$130$		0			0
$131$	−73.6059	+	42.4964i	−0.561877	+	0.324400i	−0.753899	−	0.656991i	$-0.771829\pi$
$131$	−73.6059	+	42.4964i	−0.561877	+	0.324400i	0.192021	+	0.981391i	$0.438496\pi$
$132$		0			0
$133$	64.2390	−	111.265i	0.483000	−	0.836581i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−57.2217	−	33.0370i	−0.417677	−	0.241146i	0.276406	−	0.961041i	$-0.410856\pi$
$137$	−57.2217	−	33.0370i	−0.417677	−	0.241146i	−0.694083	+	0.719895i	$0.744190\pi$
$138$		0			0
$139$	−4.71021	−	8.15832i	−0.0338864	−	0.0586929i	0.848585	−	0.529059i	$-0.177455\pi$
$139$	−4.71021	−	8.15832i	−0.0338864	−	0.0586929i	−0.882471	+	0.470366i	$0.844122\pi$
$140$		0			0
$141$	−66.5501	+	107.433i	−0.471987	+	0.761935i
$142$		0			0
$143$		−	160.967i		−	1.12565i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	13.1697	−	7.06850i	0.0895900	−	0.0480851i
$148$		0			0
$149$	−108.044	+	62.3792i	−0.725128	+	0.418653i	−0.816637	−	0.577152i	$-0.804164\pi$
$149$	−108.044	+	62.3792i	−0.725128	+	0.418653i	0.0915094	+	0.995804i	$0.470831\pi$
$150$		0			0
$151$	145.981	−	252.847i	0.966763	−	1.67448i	0.261961	−	0.965078i	$-0.415631\pi$
$151$	145.981	−	252.847i	0.966763	−	1.67448i	0.704802	−	0.709404i	$-0.251036\pi$
$152$		0			0
$153$	−8.63066	+	139.001i	−0.0564096	+	0.908501i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−71.6347	−	124.075i	−0.456272	−	0.790286i	0.542489	−	0.840063i	$-0.317482\pi$
$157$	−71.6347	−	124.075i	−0.456272	−	0.790286i	−0.998760	+	0.0497773i	$0.984149\pi$
$158$		0			0
$159$	271.164	+	8.41029i	1.70543	+	0.0528949i
$160$		0			0
$161$			77.7476i			0.482904i
$162$		0			0
$163$	228.204			1.40002			0.700011	−	0.714132i	$-0.253178\pi$
$163$	228.204			1.40002			0.700011	+	0.714132i	$0.253178\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	52.6156	−	30.3776i	0.315063	−	0.181902i	−0.334127	−	0.942528i	$-0.608441\pi$
$167$	52.6156	−	30.3776i	0.315063	−	0.181902i	0.649190	+	0.760626i	$0.275108\pi$
$168$		0			0
$169$	−54.7094	+	94.7595i	−0.323725	+	0.560707i
$170$		0			0
$171$	−157.076	−	9.75299i	−0.918575	−	0.0570350i
$172$		0			0
$173$	−240.435	−	138.815i	−1.38980	−	0.802400i	−0.396506	−	0.918032i	$-0.629777\pi$
$173$	−240.435	−	138.815i	−1.38980	−	0.802400i	−0.993292	+	0.115632i	$0.963111\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	78.6501	+	146.537i	0.444351	+	0.827895i
$178$		0			0
$179$		−	272.749i		−	1.52374i	−0.647731	−	0.761869i	$-0.724282\pi$
$179$		−	272.749i		−	1.52374i	0.647731	−	0.761869i	$-0.275718\pi$
$180$		0			0
$181$	−110.378			−0.609824			−0.304912	−	0.952380i	$-0.598627\pi$
$181$	−110.378			−0.609824			−0.304912	+	0.952380i	$0.598627\pi$
$182$		0			0
$183$	−297.771	−	184.457i	−1.62717	−	1.00796i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−74.6395	+	129.279i	−0.399142	+	0.691334i
$188$		0			0
$189$	−161.843	−	114.716i	−0.856313	−	0.606965i
$190$		0			0
$191$	29.1046	+	16.8036i	0.152380	+	0.0879768i	0.574251	−	0.818679i	$-0.305293\pi$
$191$	29.1046	+	16.8036i	0.152380	+	0.0879768i	−0.421871	+	0.906656i	$0.638627\pi$
$192$		0			0
$193$	135.342	+	234.419i	0.701255	+	1.21461i	0.968026	+	0.250849i	$0.0807097\pi$
$193$	135.342	+	234.419i	0.701255	+	1.21461i	−0.266772	+	0.963760i	$0.585957\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	63.0978i		−	0.320293i	−0.987093	−	0.160147i	$-0.948803\pi$
$197$		−	63.0978i		−	0.320293i	0.987093	−	0.160147i	$-0.0511967\pi$
$198$		0			0
$199$	−283.032			−1.42227			−0.711135	−	0.703056i	$-0.751818\pi$
$199$	−283.032			−1.42227			−0.711135	+	0.703056i	$0.751818\pi$
$200$		0			0
$201$	45.6866	−	24.5211i	0.227297	−	0.121995i
$202$		0			0
$203$	266.007	−	153.579i	1.31038	−	0.756547i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	85.2698	−	42.4156i	0.411931	−	0.204906i
$208$		0			0
$209$	−146.091	−	84.3456i	−0.698999	−	0.403567i
$210$		0			0
$211$	−56.9312	−	98.6078i	−0.269816	−	0.467336i	0.698998	−	0.715124i	$-0.253630\pi$
$211$	−56.9312	−	98.6078i	−0.269816	−	0.467336i	−0.968814	+	0.247788i	$0.920296\pi$
$212$		0			0
$213$	−115.403	−	3.57928i	−0.541798	−	0.0168042i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	358.018			1.64985
$218$		0			0
$219$	0.687112	−	22.1538i	0.00313750	−	0.101159i
$220$		0			0
$221$	223.609	−	129.101i	1.01181	−	0.584167i
$222$		0			0
$223$	108.929	−	188.670i	0.488471	−	0.846056i	−0.511441	−	0.859318i	$-0.670888\pi$
$223$	108.929	−	188.670i	0.488471	−	0.846056i	0.999912	+	0.0132622i	$0.00422163\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−45.8299	−	26.4599i	−0.201894	−	0.116563i	0.395645	−	0.918404i	$-0.370521\pi$
$227$	−45.8299	−	26.4599i	−0.201894	−	0.116563i	−0.597539	+	0.801840i	$0.703855\pi$
$228$		0			0
$229$	195.660	+	338.894i	0.854413	+	1.47989i	0.877189	+	0.480146i	$0.159416\pi$
$229$	195.660	+	338.894i	0.854413	+	1.47989i	−0.0227762	+	0.999741i	$0.507251\pi$
$230$		0			0
$231$	−100.558	−	187.355i	−0.435315	−	0.811061i
$232$		0			0
$233$		−	178.384i		−	0.765596i	−0.923832	−	0.382798i	$-0.874961\pi$
$233$		−	178.384i		−	0.765596i	0.923832	−	0.382798i	$-0.125039\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	60.4411	+	37.4407i	0.255026	+	0.157978i
$238$		0			0
$239$	314.501	−	181.577i	1.31591	−	0.759738i	0.332838	−	0.942984i	$-0.391994\pi$
$239$	314.501	−	181.577i	1.31591	−	0.759738i	0.983067	+	0.183246i	$0.0586604\pi$
$240$		0			0
$241$	−90.3219	+	156.442i	−0.374780	+	0.649137i	−0.990294	−	0.138988i	$-0.955615\pi$
$241$	−90.3219	+	156.442i	−0.374780	+	0.649137i	0.615514	+	0.788126i	$0.288948\pi$
$242$		0			0
$243$	−37.5211	+	240.086i	−0.154408	+	0.988007i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	145.889	+	252.687i	0.590644	+	1.02303i
$248$		0			0
$249$	−6.74566	+	10.8896i	−0.0270910	+	0.0437334i
$250$		0			0
$251$			73.5509i			0.293032i	0.989208	+	0.146516i	$0.0468059\pi$
$251$			73.5509i			0.293032i	−0.989208	+	0.146516i	$0.953194\pi$
$252$		0			0
$253$	102.082			0.403487
$254$		0			0
$255$		0			0
$256$		0			0
$257$	125.532	−	72.4759i	0.488451	−	0.282007i	−0.235481	−	0.971879i	$-0.575666\pi$
$257$	125.532	−	72.4759i	0.488451	−	0.282007i	0.723932	+	0.689872i	$0.242333\pi$
$258$		0			0
$259$	75.2331	−	130.308i	0.290475	−	0.503118i
$260$		0			0
$261$	−313.559	−	207.957i	−1.20138	−	0.796772i
$262$		0			0
$263$	−284.803	−	164.431i	−1.08290	−	0.625213i	−0.151223	−	0.988500i	$-0.548321\pi$
$263$	−284.803	−	164.431i	−1.08290	−	0.625213i	−0.931677	+	0.363287i	$0.881654\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−434.892	−	13.4884i	−1.62881	−	0.0505184i
$268$		0			0
$269$			355.832i			1.32280i	0.750035	+	0.661398i	$0.230037\pi$
$269$			355.832i			1.32280i	−0.750035	+	0.661398i	$0.769963\pi$
$270$		0			0
$271$	−128.345			−0.473599			−0.236799	−	0.971559i	$-0.576098\pi$
$271$	−128.345			−0.473599			−0.236799	+	0.971559i	$0.576098\pi$
$272$		0			0
$273$	−11.4016	+	367.610i	−0.0417642	+	1.34656i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	135.277	−	234.307i	0.488365	−	0.845872i	−0.511546	−	0.859256i	$-0.670927\pi$
$277$	135.277	−	234.307i	0.488365	−	0.845872i	0.999910	+	0.0133837i	$0.00426031\pi$
$278$		0			0
$279$	−195.318	−	392.657i	−0.700066	−	1.40737i
$280$		0			0
$281$	−454.766	−	262.559i	−1.61838	−	0.934374i	−0.987339	−	0.158627i	$-0.949293\pi$
$281$	−454.766	−	262.559i	−1.61838	−	0.934374i	−0.631044	−	0.775747i	$-0.717373\pi$
$282$		0			0
$283$	104.798	+	181.516i	0.370311	+	0.641398i	0.989613	−	0.143755i	$-0.0459177\pi$
$283$	104.798	+	181.516i	0.370311	+	0.641398i	−0.619302	+	0.785153i	$0.712584\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	205.004i		−	0.714300i
$288$		0			0
$289$	49.5472			0.171444
$290$		0			0
$291$	−261.918	−	162.247i	−0.900060	−	0.557550i
$292$		0			0
$293$	103.694	−	59.8679i	0.353905	−	0.204327i	−0.312499	−	0.949918i	$-0.601166\pi$
$293$	103.694	−	59.8679i	0.353905	−	0.204327i	0.666404	+	0.745591i	$0.267833\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−150.622	+	212.499i	−0.507145	+	0.715486i
$298$		0			0
$299$	−152.912	−	88.2838i	−0.511411	−	0.295264i
$300$		0			0
$301$	−110.977	−	192.218i	−0.368695	−	0.638598i
$302$		0			0
$303$	−175.140	+	282.731i	−0.578021	+	0.933106i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−435.735			−1.41933			−0.709666	−	0.704538i	$-0.751154\pi$
$307$	−435.735			−1.41933			−0.709666	+	0.704538i	$0.751154\pi$
$308$		0			0
$309$	−496.547	+	266.508i	−1.60695	+	0.862487i
$310$		0			0
$311$	59.2451	−	34.2052i	0.190499	−	0.109985i	−0.401717	−	0.915764i	$-0.631587\pi$
$311$	59.2451	−	34.2052i	0.190499	−	0.109985i	0.592216	+	0.805779i	$0.298253\pi$
$312$		0			0
$313$	21.9685	−	38.0506i	0.0701870	−	0.121567i	−0.828796	−	0.559551i	$-0.810974\pi$
$313$	21.9685	−	38.0506i	0.0701870	−	0.121567i	0.898983	+	0.437983i	$0.144307\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−231.691	−	133.767i	−0.730885	−	0.421977i	0.0878609	−	0.996133i	$-0.471997\pi$
$317$	−231.691	−	133.767i	−0.730885	−	0.421977i	−0.818746	+	0.574156i	$0.805330\pi$
$318$		0			0
$319$	−201.648	−	349.265i	−0.632127	−	1.09488i
$320$		0			0
$321$	365.126	+	11.3246i	1.13746	+	0.0352791i
$322$		0			0
$323$		−	270.591i		−	0.837743i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−4.21625	+	135.940i	−0.0128937	+	0.415718i
$328$		0			0
$329$	268.038	−	154.752i	0.814707	−	0.470371i
$330$		0			0
$331$	−36.0615	+	62.4604i	−0.108947	+	0.188702i	−0.915344	−	0.402673i	$-0.868081\pi$
$331$	−36.0615	+	62.4604i	−0.108947	+	0.188702i	0.806397	+	0.591375i	$0.201415\pi$
$332$		0			0
$333$	−183.959	−	11.4221i	−0.552429	−	0.0343007i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−97.8962	−	169.561i	−0.290493	−	0.503149i	0.683433	−	0.730013i	$-0.260486\pi$
$337$	−97.8962	−	169.561i	−0.290493	−	0.503149i	−0.973926	+	0.226864i	$0.927153\pi$
$338$		0			0
$339$	−27.2528	−	50.7762i	−0.0803916	−	0.149782i
$340$		0			0
$341$		−	470.076i		−	1.37852i
$342$		0			0
$343$	323.410			0.942886
$344$		0			0
$345$		0			0
$346$		0			0
$347$	109.827	−	63.4084i	0.316503	−	0.182733i	−0.333330	−	0.942810i	$-0.608172\pi$
$347$	109.827	−	63.4084i	0.316503	−	0.182733i	0.649833	+	0.760077i	$0.274839\pi$
$348$		0			0
$349$	65.2764	−	113.062i	0.187038	−	0.323960i	−0.757223	−	0.653156i	$-0.773444\pi$
$349$	65.2764	−	113.062i	0.187038	−	0.323960i	0.944261	+	0.329196i	$0.106778\pi$
$350$		0			0
$351$	409.397	−	188.047i	1.16637	−	0.535745i
$352$		0			0
$353$	226.254	+	130.628i	0.640947	+	0.370051i	0.784979	−	0.619522i	$-0.212674\pi$
$353$	226.254	+	130.628i	0.640947	+	0.370051i	−0.144032	+	0.989573i	$0.546007\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	179.615	−	289.955i	0.503124	−	0.812200i
$358$		0			0
$359$			390.386i			1.08743i	0.839271	+	0.543713i	$0.182982\pi$
$359$			390.386i			1.08743i	−0.839271	+	0.543713i	$0.817018\pi$
$360$		0			0
$361$	−55.2213			−0.152968
$362$		0			0
$363$	73.8465	−	39.6352i	0.203434	−	0.109188i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	42.1665	−	73.0345i	0.114895	−	0.199004i	−0.802843	−	0.596191i	$-0.796680\pi$
$367$	42.1665	−	73.0345i	0.114895	−	0.199004i	0.917738	+	0.397187i	$0.130013\pi$
$368$		0			0
$369$	−224.839	+	111.841i	−0.609319	+	0.303092i
$370$		0			0
$371$	−575.407	−	332.212i	−1.55096	−	0.895449i
$372$		0			0
$373$	88.5806	+	153.426i	0.237482	+	0.411330i	0.959991	−	0.280031i	$-0.0903447\pi$
$373$	88.5806	+	153.426i	0.237482	+	0.411330i	−0.722509	+	0.691361i	$0.757011\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			697.566i			1.85031i
$378$		0			0
$379$	291.976			0.770386			0.385193	−	0.922836i	$-0.374135\pi$
$379$	291.976			0.770386			0.385193	+	0.922836i	$0.374135\pi$
$380$		0			0
$381$	−16.6700	+	537.473i	−0.0437533	+	1.41069i
$382$		0			0
$383$	−236.884	+	136.765i	−0.618497	+	0.357090i	−0.776284	−	0.630384i	$-0.782898\pi$
$383$	−236.884	+	136.765i	−0.618497	+	0.357090i	0.157786	+	0.987473i	$0.449564\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−150.271	+	226.580i	−0.388298	+	0.585478i
$388$		0			0
$389$	−206.095	−	118.989i	−0.529808	−	0.305885i	0.211130	−	0.977458i	$-0.432286\pi$
$389$	−206.095	−	118.989i	−0.529808	−	0.305885i	−0.740938	+	0.671573i	$0.765619\pi$
$390$		0			0
$391$	81.8732	+	141.808i	0.209394	+	0.362682i
$392$		0			0
$393$	−120.582	−	224.664i	−0.306826	−	0.571664i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	76.9037			0.193712			0.0968560	−	0.995298i	$-0.469121\pi$
$397$	76.9037			0.193712			0.0968560	+	0.995298i	$0.469121\pi$
$398$		0			0
$399$	327.661	+	202.972i	0.821206	+	0.508703i
$400$		0			0
$401$	−473.107	+	273.149i	−1.17982	+	0.681169i	−0.955973	−	0.293456i	$-0.905195\pi$
$401$	−473.107	+	273.149i	−1.17982	+	0.681169i	−0.223846	+	0.974625i	$0.571861\pi$
$402$		0			0
$403$	−406.536	+	704.141i	−1.00877	+	1.74725i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−171.093	−	98.7807i	−0.420376	−	0.242704i
$408$		0			0
$409$	−281.051	−	486.795i	−0.687166	−	1.19021i	−0.972751	−	0.231853i	$-0.925521\pi$
$409$	−281.051	−	486.795i	−0.687166	−	1.19021i	0.285585	−	0.958353i	$-0.407812\pi$
$410$		0			0
$411$	104.385	−	168.510i	0.253978	−	0.410000i
$412$		0			0
$413$		−	407.308i		−	0.986218i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	24.9012	−	13.3651i	0.0597152	−	0.0320506i
$418$		0			0
$419$	209.645	−	121.038i	0.500345	−	0.288874i	−0.228511	−	0.973541i	$-0.573386\pi$
$419$	209.645	−	121.038i	0.500345	−	0.288874i	0.728856	+	0.684667i	$0.240052\pi$
$420$		0			0
$421$	−8.10023	+	14.0300i	−0.0192405	+	0.0333255i	−0.875485	−	0.483245i	$-0.839458\pi$
$421$	−8.10023	+	14.0300i	−0.0192405	+	0.0333255i	0.856245	+	0.516570i	$0.172791\pi$
$422$		0			0
$423$	−315.954	−	209.546i	−0.746937	−	0.495380i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	428.926	+	742.922i	1.00451	+	1.73986i
$428$		0			0
$429$	482.670	+	14.9703i	1.12511	+	0.0348957i
$430$		0			0
$431$		−	50.0624i		−	0.116154i	−0.998312	−	0.0580770i	$-0.981503\pi$
$431$		−	50.0624i		−	0.116154i	0.998312	−	0.0580770i	$-0.0184969\pi$
$432$		0			0
$433$	452.725			1.04556			0.522778	−	0.852469i	$-0.324896\pi$
$433$	452.725			1.04556			0.522778	+	0.852469i	$0.324896\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−160.249	+	92.5199i	−0.366703	+	0.211716i
$438$		0			0
$439$	115.139	−	199.426i	0.262275	−	0.454274i	−0.704571	−	0.709634i	$-0.748860\pi$
$439$	115.139	−	199.426i	0.262275	−	0.454274i	0.966846	+	0.255360i	$0.0821938\pi$
$440$		0			0
$441$	19.9705	+	40.1476i	0.0452846	+	0.0910376i
$442$		0			0
$443$	−517.751	−	298.924i	−1.16874	−	0.674772i	−0.215356	−	0.976536i	$-0.569091\pi$
$443$	−517.751	−	298.924i	−1.16874	−	0.674772i	−0.953383	+	0.301764i	$0.902425\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−176.999	−	329.778i	−0.395972	−	0.737758i
$448$		0			0
$449$			642.091i			1.43005i	0.699101	+	0.715023i	$0.253584\pi$
$449$			642.091i			1.43005i	−0.699101	+	0.715023i	$0.746416\pi$
$450$		0			0
$451$	−269.170			−0.596828
$452$		0			0
$453$	744.600	+	461.248i	1.64371	+	1.01821i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−44.2091	+	76.5724i	−0.0967376	+	0.167554i	−0.910332	−	0.413878i	$-0.864174\pi$
$457$	−44.2091	+	76.5724i	−0.0967376	+	0.167554i	0.813595	+	0.581432i	$0.197507\pi$
$458$		0			0
$459$	−415.999	−	38.8069i	−0.906316	−	0.0845466i
$460$		0			0
$461$	421.874	+	243.569i	0.915127	+	0.528349i	0.882077	−	0.471105i	$-0.156145\pi$
$461$	421.874	+	243.569i	0.915127	+	0.528349i	0.0330498	+	0.999454i	$0.489478\pi$
$462$		0			0
$463$	−313.941	−	543.761i	−0.678058	−	1.17443i	−0.975565	−	0.219711i	$-0.929488\pi$
$463$	−313.941	−	543.761i	−0.678058	−	1.17443i	0.297507	−	0.954720i	$-0.403845\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	323.410i		−	0.692527i	−0.938137	−	0.346263i	$-0.887450\pi$
$467$		−	323.410i		−	0.692527i	0.938137	−	0.346263i	$-0.112550\pi$
$468$		0			0
$469$	−126.988			−0.270764
$470$		0			0
$471$	378.708	−	203.261i	0.804051	−	0.431553i
$472$		0			0
$473$	−252.381	+	145.713i	−0.533576	+	0.308060i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−50.4375	+	812.318i	−0.105739	+	1.70297i
$478$		0			0
$479$	−137.174	−	79.1972i	−0.286375	−	0.165339i	0.349931	−	0.936776i	$-0.386205\pi$
$479$	−137.174	−	79.1972i	−0.286375	−	0.165339i	−0.636306	+	0.771437i	$0.719538\pi$
$480$		0			0
$481$	170.857	+	295.933i	0.355212	+	0.615245i
$482$		0			0
$483$	−233.131	−	7.23068i	−0.482672	−	0.0149703i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	108.301			0.222385			0.111192	−	0.993799i	$-0.464533\pi$
$487$	108.301			0.222385			0.111192	+	0.993799i	$0.464533\pi$
$488$		0			0
$489$	−21.2234	+	684.282i	−0.0434016	+	1.39935i
$490$		0			0
$491$	588.153	−	339.570i	1.19787	−	0.691589i	0.237788	−	0.971317i	$-0.423578\pi$
$491$	588.153	−	339.570i	1.19787	−	0.691589i	0.960079	+	0.279728i	$0.0902444\pi$
$492$		0			0
$493$	323.457	−	560.243i	0.656099	−	1.13640i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	244.884	+	141.384i	0.492725	+	0.284475i
$498$		0			0
$499$	−37.1564	−	64.3568i	−0.0744618	−	0.128972i	0.826390	−	0.563098i	$-0.190391\pi$
$499$	−37.1564	−	64.3568i	−0.0744618	−	0.128972i	−0.900852	+	0.434126i	$0.857057\pi$
$500$		0			0
$501$	86.1957	+	160.596i	0.172047	+	0.320551i
$502$		0			0
$503$			278.694i			0.554063i	0.960861	+	0.277031i	$0.0893506\pi$
$503$			278.694i			0.554063i	−0.960861	+	0.277031i	$0.910649\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−279.054	−	172.862i	−0.550402	−	0.340951i
$508$		0			0
$509$	−239.428	+	138.234i	−0.470390	+	0.271580i	−0.716403	−	0.697687i	$-0.754213\pi$
$509$	−239.428	+	138.234i	−0.470390	+	0.271580i	0.246013	+	0.969267i	$0.420879\pi$
$510$		0			0
$511$	−27.1413	+	47.0102i	−0.0531141	+	0.0919964i
$512$		0			0
$513$	43.8533	−	470.095i	0.0854840	−	0.916365i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−203.189	−	351.933i	−0.393015	−	0.680722i
$518$		0			0
$519$	438.607	−	708.049i	0.845099	−	1.36426i
$520$		0			0
$521$			929.478i			1.78403i	0.452008	+	0.892014i	$0.350708\pi$
$521$			929.478i			1.78403i	−0.452008	+	0.892014i	$0.649292\pi$
$522$		0			0
$523$	217.275			0.415439			0.207719	−	0.978188i	$-0.433396\pi$
$523$	217.275			0.415439			0.207719	+	0.978188i	$0.433396\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	653.011	−	377.016i	1.23911	−	0.715400i
$528$		0			0
$529$	−208.512	+	361.154i	−0.394163	+	0.682710i
$530$		0			0
$531$	−446.716	+	222.209i	−0.841272	+	0.418472i
$532$		0			0
$533$	403.197	+	232.786i	0.756467	+	0.436747i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	817.854	+	25.3662i	1.52301	+	0.0472368i
$538$		0			0
$539$			48.0634i			0.0891714i
$540$		0			0
$541$	393.139			0.726690			0.363345	−	0.931655i	$-0.381635\pi$
$541$	393.139			0.726690			0.363345	+	0.931655i	$0.381635\pi$
$542$		0			0
$543$	10.2654	−	330.975i	0.0189049	−	0.609531i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	438.342	−	759.230i	0.801356	−	1.38799i	−0.117368	−	0.993088i	$-0.537446\pi$
$547$	438.342	−	759.230i	0.801356	−	1.38799i	0.918724	−	0.394900i	$-0.129221\pi$
$548$		0			0
$549$	580.798	−	875.730i	1.05792	−	1.59514i
$550$		0			0
$551$	633.097	+	365.519i	1.14900	+	0.663374i
$552$		0			0
$553$	−87.0626	−	150.797i	−0.157437	−	0.272689i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	546.180i		−	0.980575i	−0.871561	−	0.490287i	$-0.836892\pi$
$557$		−	546.180i		−	0.980575i	0.871561	−	0.490287i	$-0.163108\pi$
$558$		0			0
$559$	504.066			0.901728
$560$		0			0
$561$	−380.710	−	235.834i	−0.678628	−	0.420382i
$562$		0			0
$563$	821.569	−	474.333i	1.45927	−	0.842510i	0.460294	−	0.887766i	$-0.347744\pi$
$563$	821.569	−	474.333i	1.45927	−	0.842510i	0.998975	+	0.0452567i	$0.0144106\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	359.035	−	474.627i	0.633219	−	0.837085i
$568$		0			0
$569$	−101.288	−	58.4785i	−0.178010	−	0.102774i	0.408347	−	0.912827i	$-0.366105\pi$
$569$	−101.288	−	58.4785i	−0.178010	−	0.102774i	−0.586357	+	0.810052i	$0.699439\pi$
$570$		0			0
$571$	71.9220	+	124.573i	0.125958	+	0.218166i	0.922107	−	0.386935i	$-0.126466\pi$
$571$	71.9220	+	124.573i	0.125958	+	0.218166i	−0.796149	+	0.605101i	$0.793133\pi$
$572$		0			0
$573$	−53.0933	+	85.7092i	−0.0926584	+	0.149580i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−665.087			−1.15266			−0.576332	−	0.817216i	$-0.695516\pi$
$577$	−665.087			−1.15266			−0.576332	+	0.817216i	$0.695516\pi$
$578$		0			0
$579$	−715.507	+	384.030i	−1.23576	+	0.663264i
$580$		0			0
$581$	27.1689	−	15.6860i	0.0467624	−	0.0269983i
$582$		0			0
$583$	−436.192	+	755.507i	−0.748186	+	1.29590i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	193.390	+	111.654i	0.329454	+	0.190210i	0.655599	−	0.755109i	$-0.272416\pi$
$587$	193.390	+	111.654i	0.329454	+	0.190210i	−0.326145	+	0.945320i	$0.605750\pi$
$588$		0			0
$589$	426.043	+	737.928i	0.723332	+	1.25285i
$590$		0			0
$591$	189.202	+	5.86822i	0.320140	+	0.00992930i
$592$		0			0
$593$			320.932i			0.541200i	0.962692	+	0.270600i	$0.0872221\pi$
$593$			320.932i			0.541200i	−0.962692	+	0.270600i	$0.912778\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	26.3225	−	848.687i	0.0440913	−	1.42159i
$598$		0			0
$599$	536.544	−	309.774i	0.895732	−	0.517151i	0.0199193	−	0.999802i	$-0.493659\pi$
$599$	536.544	−	309.774i	0.895732	−	0.517151i	0.875813	+	0.482650i	$0.160326\pi$
$600$		0			0
$601$	291.655	−	505.162i	0.485283	−	0.840535i	−0.514574	−	0.857446i	$-0.672050\pi$
$601$	291.655	−	505.162i	0.485283	−	0.840535i	0.999857	+	0.0169108i	$0.00538313\pi$
$602$		0			0
$603$	69.2790	+	139.274i	0.114890	+	0.230969i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	74.8229	+	129.597i	0.123267	+	0.213504i	0.921054	−	0.389435i	$-0.127330\pi$
$607$	74.8229	+	129.597i	0.123267	+	0.213504i	−0.797787	+	0.602939i	$0.793996\pi$
$608$		0			0
$609$	435.776	+	811.919i	0.715560	+	1.33320i
$610$		0			0
$611$			702.895i			1.15040i
$612$		0			0
$613$	−775.281			−1.26473			−0.632367	−	0.774669i	$-0.717916\pi$
$613$	−775.281			−1.26473			−0.632367	+	0.774669i	$0.717916\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1035.34	+	597.754i	−1.67802	+	0.968807i	−0.715103	+	0.699019i	$0.753620\pi$
$617$	−1035.34	+	597.754i	−1.67802	+	0.968807i	−0.962920	+	0.269787i	$0.913047\pi$
$618$		0			0
$619$	−417.536	+	723.194i	−0.674533	+	1.16833i	0.302072	+	0.953285i	$0.402322\pi$
$619$	−417.536	+	723.194i	−0.674533	+	1.16833i	−0.976605	+	0.215041i	$0.931011\pi$
$620$		0			0
$621$	119.255	+	259.631i	0.192037	+	0.418086i
$622$		0			0
$623$	922.838	+	532.801i	1.48128	+	0.855218i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	266.502	−	430.217i	0.425043	−	0.686152i
$628$		0			0
$629$		−	316.901i		−	0.503817i
$630$		0			0
$631$	378.090			0.599191			0.299596	−	0.954066i	$-0.403148\pi$
$631$	378.090			0.599191			0.299596	+	0.954066i	$0.403148\pi$
$632$		0			0
$633$	300.976	−	161.541i	0.475475	−	0.255199i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	41.5666	−	71.9955i	0.0652538	−	0.113023i
$638$		0			0
$639$	21.4654	−	345.710i	0.0335922	−	0.541017i
$640$		0			0
$641$	70.5646	+	40.7405i	0.110085	+	0.0635577i	0.554032	−	0.832496i	$-0.313089\pi$
$641$	70.5646	+	40.7405i	0.110085	+	0.0635577i	−0.443947	+	0.896053i	$0.646422\pi$
$642$		0			0
$643$	−424.883	−	735.919i	−0.660783	−	1.14451i	−0.980410	−	0.196966i	$-0.936891\pi$
$643$	−424.883	−	735.919i	−0.660783	−	1.14451i	0.319628	−	0.947543i	$-0.396442\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			569.387i			0.880042i	0.897988	+	0.440021i	$0.145029\pi$
$647$			569.387i			0.880042i	−0.897988	+	0.440021i	$0.854971\pi$
$648$		0			0
$649$	−534.793			−0.824027
$650$		0			0
$651$	−33.2964	+	1073.54i	−0.0511465	+	1.64906i
$652$		0			0
$653$	−814.403	+	470.196i	−1.24717	+	0.720055i	−0.970544	−	0.240922i	$-0.922550\pi$
$653$	−814.403	+	470.196i	−1.24717	+	0.720055i	−0.276627	+	0.960977i	$0.589217\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	66.3655	+	4.12069i	0.101013	+	0.00627198i
$658$		0			0
$659$	−1094.20	−	631.738i	−1.66040	−	0.958631i	−0.972525	−	0.232800i	$-0.925211\pi$
$659$	−1094.20	−	631.738i	−1.66040	−	0.958631i	−0.687873	−	0.725831i	$-0.741456\pi$
$660$		0			0
$661$	−65.8107	−	113.987i	−0.0995623	−	0.172447i	0.811941	−	0.583739i	$-0.198411\pi$
$661$	−65.8107	−	113.987i	−0.0995623	−	0.172447i	−0.911504	+	0.411292i	$0.865078\pi$
$662$		0			0
$663$	366.320	+	682.512i	0.552520	+	1.02943i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−442.382			−0.663242
$668$		0			0
$669$	555.609	+	344.176i	0.830506	+	0.514464i
$670$		0			0
$671$	975.453	−	563.178i	1.45373	−	0.839311i
$672$		0			0
$673$	−119.398	+	206.803i	−0.177411	+	0.307285i	−0.940993	−	0.338426i	$-0.890106\pi$
$673$	−119.398	+	206.803i	−0.177411	+	0.307285i	0.763582	+	0.645711i	$0.223439\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−304.426	−	175.760i	−0.449669	−	0.259617i	0.258021	−	0.966139i	$-0.416930\pi$
$677$	−304.426	−	175.760i	−0.449669	−	0.259617i	−0.707691	+	0.706523i	$0.750263\pi$
$678$		0			0
$679$	377.280	+	653.469i	0.555641	+	0.962399i
$680$		0			0
$681$	83.6039	−	134.963i	0.122766	−	0.198183i
$682$		0			0
$683$			1067.52i			1.56299i	0.623911	+	0.781495i	$0.285543\pi$
$683$			1067.52i			1.56299i	−0.623911	+	0.781495i	$0.714457\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−1034.39	+	555.182i	−1.50566	+	0.808125i
$688$		0			0
$689$	1306.77	−	754.464i	1.89662	−	1.09501i
$690$		0			0
$691$	−231.293	+	400.611i	−0.334722	+	0.579755i	−0.983431	−	0.181281i	$-0.941976\pi$
$691$	−231.293	+	400.611i	−0.334722	+	0.579755i	0.648709	+	0.761036i	$0.275309\pi$
$692$		0			0
$693$	571.147	−	284.104i	0.824166	−	0.409963i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−215.882	−	373.919i	−0.309731	−	0.536470i
$698$		0			0
$699$	534.894	+	16.5900i	0.765228	+	0.0237340i
$700$		0			0
$701$			519.309i			0.740812i	0.928870	+	0.370406i	$0.120781\pi$
$701$			519.309i			0.740812i	−0.928870	+	0.370406i	$0.879219\pi$
$702$		0			0
$703$	358.110			0.509403
$704$		0			0
$705$		0			0
$706$		0			0
$707$	705.398	−	407.262i	0.997734	−	0.576042i
$708$		0			0
$709$	−312.572	+	541.391i	−0.440863	+	0.763598i	−0.997754	−	0.0669881i	$-0.978661\pi$
$709$	−312.572	+	541.391i	−0.440863	+	0.763598i	0.556890	+	0.830586i	$0.311994\pi$
$710$		0			0
$711$	−117.889	+	177.754i	−0.165808	+	0.250006i
$712$		0			0
$713$	−446.552	−	257.817i	−0.626300	−	0.361594i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	515.221	+	959.938i	0.718579	+	1.33883i
$718$		0			0
$719$			1385.24i			1.92662i	0.268400	+	0.963308i	$0.413505\pi$
$719$			1385.24i			1.92662i	−0.268400	+	0.963308i	$0.586495\pi$
$720$		0			0
$721$	1380.18			1.91425
$722$		0			0
$723$	−460.701	−	285.385i	−0.637207	−	0.394723i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−679.246	+	1176.49i	−0.934314	+	1.61828i	−0.158461	+	0.987365i	$0.550653\pi$
$727$	−679.246	+	1176.49i	−0.934314	+	1.61828i	−0.775853	+	0.630914i	$0.782680\pi$
$728$		0			0
$729$	−716.422	−	134.838i	−0.982746	−	0.184962i
$730$		0			0
$731$	−404.836	−	233.732i	−0.553811	−	0.319743i
$732$		0			0
$733$	−463.215	−	802.313i	−0.631945	−	1.09456i	−0.987154	−	0.159773i	$-0.948924\pi$
$733$	−463.215	−	802.313i	−0.631945	−	1.09456i	0.355209	−	0.934787i	$-0.384410\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			166.735i			0.226235i
$738$		0			0
$739$	693.908			0.938983			0.469491	−	0.882937i	$-0.344437\pi$
$739$	693.908			0.938983			0.469491	+	0.882937i	$0.344437\pi$
$740$		0			0
$741$	−771.266	+	413.957i	−1.04084	+	0.558646i
$742$		0			0
$743$	86.9306	−	50.1894i	0.116999	−	0.0675497i	−0.440358	−	0.897822i	$-0.645149\pi$
$743$	86.9306	−	50.1894i	0.116999	−	0.0675497i	0.557358	+	0.830272i	$0.311815\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−32.0258	−	21.2400i	−0.0428725	−	0.0284337i
$748$		0			0
$749$	−774.794	−	447.328i	−1.03444	−	0.597233i
$750$		0			0
$751$	−2.35903	−	4.08596i	−0.00314118	−	0.00544069i	0.864451	−	0.502718i	$-0.167667\pi$
$751$	−2.35903	−	4.08596i	−0.00314118	−	0.00544069i	−0.867592	+	0.497277i	$0.834333\pi$
$752$		0			0
$753$	−220.547	−	6.84038i	−0.292891	−	0.00908417i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−133.356			−0.176163			−0.0880816	−	0.996113i	$-0.528074\pi$
$757$	−133.356			−0.176163			−0.0880816	+	0.996113i	$0.528074\pi$
$758$		0			0
$759$	−9.49384	+	306.100i	−0.0125084	+	0.403293i
$760$		0			0
$761$	−190.293	+	109.866i	−0.250057	+	0.144371i	−0.619790	−	0.784767i	$-0.712782\pi$
$761$	−190.293	+	109.866i	−0.250057	+	0.144371i	0.369733	+	0.929138i	$0.379449\pi$
$762$		0			0
$763$	166.544	−	288.463i	0.218276	−	0.378064i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	801.083	+	462.505i	1.04444	+	0.603006i
$768$		0			0
$769$	−319.416	−	553.246i	−0.415366	−	0.719435i	0.580101	−	0.814545i	$-0.303013\pi$
$769$	−319.416	−	553.246i	−0.415366	−	0.719435i	−0.995467	+	0.0951097i	$0.969680\pi$
$770$		0			0
$771$	205.648	+	383.155i	0.266729	+	0.496958i
$772$		0			0
$773$			1244.36i			1.60978i	0.593426	+	0.804888i	$0.297775\pi$
$773$			1244.36i			1.60978i	−0.593426	+	0.804888i	$0.702225\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	383.738	+	237.710i	0.493871	+	0.305933i
$778$		0			0
$779$	422.544	−	243.956i	0.542418	−	0.313165i
$780$		0			0
$781$	185.636	−	321.532i	0.237691	−	0.411692i
$782$		0			0
$783$	652.734	−	920.884i	0.833632	−	1.17610i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	569.367	+	986.173i	0.723466	+	1.25308i	0.959602	+	0.281359i	$0.0907853\pi$
$787$	569.367	+	986.173i	0.723466	+	1.25308i	−0.236137	+	0.971720i	$0.575881\pi$
$788$		0			0
$789$	519.543	−	838.705i	0.658483	−	1.06300i
$790$		0			0
$791$			141.135i			0.178426i
$792$		0			0
$793$	−1948.21			−2.45676
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1182.74	+	682.858i	−1.48400	+	0.856785i	−0.999834	−	0.0181932i	$-0.994209\pi$
$797$	−1182.74	+	682.858i	−1.48400	+	0.856785i	−0.484161	+	0.874979i	$0.660875\pi$
$798$		0			0
$799$	325.927	−	564.523i	0.407919	−	0.706537i
$800$		0			0
$801$	80.8916	−	1302.80i	0.100988	−	1.62646i
$802$		0			0
$803$	61.7241	+	35.6364i	0.0768669	+	0.0443791i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1066.98	−	33.0931i	−1.32216	−	0.0410075i
$808$		0			0
$809$		−	504.881i		−	0.624080i	−0.950069	−	0.312040i	$-0.898988\pi$
$809$		−	504.881i		−	0.624080i	0.950069	−	0.312040i	$-0.101012\pi$
$810$		0			0
$811$	−1484.09			−1.82995			−0.914974	−	0.403514i	$-0.867789\pi$
$811$	−1484.09			−1.82995			−0.914974	+	0.403514i	$0.867789\pi$
$812$		0			0
$813$	11.9363	−	384.851i	0.0146819	−	0.473371i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	264.126	−	457.480i	0.323288	−	0.559951i
$818$		0			0
$819$	−1101.24	−	68.3769i	−1.34461	−	0.0834882i
$820$		0			0
$821$	343.313	+	198.212i	0.418165	+	0.241428i	0.694292	−	0.719694i	$-0.255718\pi$
$821$	343.313	+	198.212i	0.418165	+	0.241428i	−0.276127	+	0.961121i	$0.589051\pi$
$822$		0			0
$823$	355.569	+	615.863i	0.432040	+	0.748315i	0.997049	−	0.0767697i	$-0.0244606\pi$
$823$	355.569	+	615.863i	0.432040	+	0.748315i	−0.565009	+	0.825085i	$0.691127\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			296.720i			0.358791i	0.983777	+	0.179396i	$0.0574142\pi$
$827$			296.720i			0.358791i	−0.983777	+	0.179396i	$0.942586\pi$
$828$		0			0
$829$	−252.785			−0.304928			−0.152464	−	0.988309i	$-0.548721\pi$
$829$	−252.785			−0.304928			−0.152464	+	0.988309i	$0.548721\pi$
$830$		0			0
$831$	690.001	+	427.427i	0.830326	+	0.514352i
$832$		0			0
$833$	−66.7677	+	38.5483i	−0.0801533	+	0.0462765i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1195.57	−	549.156i	1.42840	−	0.656100i
$838$		0			0
$839$	252.022	+	145.505i	0.300384	+	0.173427i	0.642615	−	0.766189i	$-0.277849\pi$
$839$	252.022	+	145.505i	0.300384	+	0.173427i	−0.342231	+	0.939616i	$0.611183\pi$
$840$		0			0
$841$	453.361	+	785.244i	0.539074	+	0.933703i
$842$		0			0
$843$	829.592	−	1339.22i	0.984095	−	1.58864i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−205.260			−0.242338
$848$		0			0
$849$	−554.032	+	297.362i	−0.652570	+	0.350250i
$850$		0			0
$851$	−187.675	+	108.354i	−0.220534	+	0.127326i
$852$		0			0
$853$	21.8099	−	37.7759i	0.0255685	−	0.0442859i	−0.852958	−	0.521980i	$-0.825194\pi$
$853$	21.8099	−	37.7759i	0.0255685	−	0.0442859i	0.878527	+	0.477694i	$0.158527\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	297.359	+	171.680i	0.346977	+	0.200327i	0.663353	−	0.748307i	$-0.269133\pi$
$857$	297.359	+	171.680i	0.346977	+	0.200327i	−0.316376	+	0.948634i	$0.602466\pi$
$858$		0			0
$859$	7.74411	+	13.4132i	0.00901526	+	0.0156149i	0.870498	−	0.492172i	$-0.163797\pi$
$859$	7.74411	+	13.4132i	0.00901526	+	0.0156149i	−0.861483	+	0.507787i	$0.830464\pi$
$860$		0			0
$861$	614.717	+	19.0658i	0.713957	+	0.0221438i
$862$		0			0
$863$		−	880.604i		−	1.02040i	−0.860056	−	0.510199i	$-0.829572\pi$
$863$		−	880.604i		−	1.02040i	0.860056	−	0.510199i	$-0.170428\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−4.60798	+	148.570i	−0.00531486	+	0.171361i
$868$		0			0
$869$	−197.996	+	114.313i	−0.227843	+	0.131545i
$870$		0			0
$871$	144.197	−	249.757i	0.165554	−	0.286748i
$872$		0			0
$873$	510.866	−	770.286i	0.585184	−	0.882343i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−621.717	−	1076.84i	−0.708913	−	1.22787i	−0.965261	−	0.261289i	$-0.915853\pi$
$877$	−621.717	−	1076.84i	−0.708913	−	1.22787i	0.256348	−	0.966585i	$-0.417481\pi$
$878$		0			0
$879$	169.874	+	316.501i	0.193258	+	0.360069i
$880$		0			0
$881$		−	1006.63i		−	1.14260i	−0.820742	−	0.571299i	$-0.806440\pi$
$881$		−	1006.63i		−	1.14260i	0.820742	−	0.571299i	$-0.193560\pi$
$882$		0			0
$883$	−765.263			−0.866662			−0.433331	−	0.901235i	$-0.642662\pi$
$883$	−765.263			−0.866662			−0.433331	+	0.901235i	$0.642662\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−586.263	+	338.479i	−0.660951	+	0.381600i	−0.792639	−	0.609691i	$-0.791294\pi$
$887$	−586.263	+	338.479i	−0.660951	+	0.381600i	0.131688	+	0.991291i	$0.457960\pi$
$888$		0			0
$889$	658.475	−	1140.51i	0.740692	−	1.28292i
$890$		0			0
$891$	−623.183	−	471.412i	−0.699420	−	0.529082i
$892$		0			0
$893$	637.933	+	368.311i	0.714371	+	0.412442i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	278.945	−	450.305i	0.310976	−	0.502012i
$898$		0			0
$899$			2037.12i			2.26598i
$900$		0			0
$901$	−1399.36			−1.55312
$902$		0			0
$903$	586.698	−	314.895i	0.649721	−	0.348721i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	11.7176	−	20.2956i	0.0129191	−	0.0223766i	−0.859494	−	0.511147i	$-0.829221\pi$
$907$	11.7176	−	20.2956i	0.0129191	−	0.0223766i	0.872413	+	0.488770i	$0.162554\pi$
$908$		0			0
$909$	−831.498	−	551.463i	−0.914739	−	0.606670i
$910$		0			0
$911$	−1085.84	−	626.910i	−1.19192	−	0.688156i	−0.233179	−	0.972434i	$-0.574913\pi$
$911$	−1085.84	−	626.910i	−1.19192	−	0.688156i	−0.958742	+	0.284278i	$0.908246\pi$
$912$		0			0
$913$	−20.5956	−	35.6727i	−0.0225582	−	0.0390719i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			624.464i			0.680986i
$918$		0			0
$919$	−1113.99			−1.21217			−0.606087	−	0.795398i	$-0.707262\pi$
$919$	−1113.99			−1.21217			−0.606087	+	0.795398i	$0.707262\pi$
$920$		0			0
$921$	40.5242	−	1306.58i	0.0440002	−	1.41865i
$922$		0			0
$923$	−556.140	+	321.088i	−0.602536	+	0.347874i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−752.961	−	1513.71i	−0.812256	−	1.63291i
$928$		0			0
$929$	550.765	+	317.984i	0.592858	+	0.342286i	0.766227	−	0.642570i	$-0.222132\pi$
$929$	550.765	+	317.984i	0.592858	+	0.342286i	−0.173369	+	0.984857i	$0.555465\pi$
$930$		0			0
$931$	−43.5611	−	75.4501i	−0.0467896	−	0.0810420i
$932$		0			0
$933$	97.0563	+	180.831i	0.104026	+	0.193817i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−81.1236			−0.0865780			−0.0432890	−	0.999063i	$-0.513784\pi$
$937$	−81.1236			−0.0865780			−0.0432890	+	0.999063i	$0.513784\pi$
$938$		0			0
$939$	112.054	+	69.4127i	0.119333	+	0.0739219i
$940$		0			0
$941$	−292.823	+	169.061i	−0.311183	+	0.179661i	−0.647456	−	0.762103i	$-0.724167\pi$
$941$	−292.823	+	169.061i	−0.311183	+	0.179661i	0.336273	+	0.941765i	$0.390834\pi$
$942$		0			0
$943$	−147.628	+	255.699i	−0.156552	+	0.271155i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−337.557	−	194.889i	−0.356449	−	0.205796i	0.311073	−	0.950386i	$-0.399312\pi$
$947$	−337.557	−	194.889i	−0.356449	−	0.205796i	−0.667522	+	0.744590i	$0.732645\pi$
$948$		0			0
$949$	−61.6389	−	106.762i	−0.0649514	−	0.112499i
$950$		0			0
$951$	422.655	−	682.297i	0.444432	−	0.717452i
$952$		0			0
$953$			1439.63i			1.51063i	0.655363	+	0.755314i	$0.272516\pi$
$953$			1439.63i			1.51063i	−0.655363	+	0.755314i	$0.727484\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	1066.05	−	572.172i	1.11395	−	0.597881i
$958$		0			0
$959$	−420.423	+	242.731i	−0.438397	+	0.253109i
$960$		0			0
$961$	−706.715	+	1224.07i	−0.735395	+	1.27374i
$962$		0			0
$963$	−67.9148	+	1093.80i	−0.0705242	+	1.13582i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−332.808	−	576.441i	−0.344166	−	0.596113i	0.641036	−	0.767511i	$-0.278505\pi$
$967$	−332.808	−	576.441i	−0.344166	−	0.596113i	−0.985202	+	0.171398i	$0.945172\pi$
$968$		0			0
$969$	811.383	+	25.1655i	0.837341	+	0.0259706i
$970$		0			0
$971$		−	437.415i		−	0.450479i	−0.974303	−	0.225239i	$-0.927684\pi$
$971$		−	437.415i		−	0.450479i	0.974303	−	0.225239i	$-0.0723164\pi$
$972$		0			0
$973$	−69.2142			−0.0711349
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1070.94	−	618.306i	1.09615	−	0.632862i	0.160942	−	0.986964i	$-0.448547\pi$
$977$	1070.94	−	618.306i	1.09615	−	0.632862i	0.935207	+	0.354102i	$0.115214\pi$
$978$		0			0
$979$	699.565	−	1211.68i	0.714571	−	1.23767i
$980$		0			0
$981$	−407.231	−	25.2853i	−0.415118	−	0.0257750i
$982$		0			0
$983$	1102.74	+	636.669i	1.12181	+	0.647680i	0.941864	−	0.335996i	$-0.109073\pi$
$983$	1102.74	+	636.669i	1.12181	+	0.647680i	0.179951	+	0.983676i	$0.442406\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	439.105	+	818.121i	0.444889	+	0.828897i
$988$		0			0
$989$			319.668i			0.323224i
$990$		0			0
$991$	443.540			0.447568			0.223784	−	0.974639i	$-0.428159\pi$
$991$	443.540			0.447568			0.223784	+	0.974639i	$0.428159\pi$
$992$		0			0
$993$	−183.937	−	113.942i	−0.185234	−	0.114745i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	278.990	−	483.225i	0.279830	−	0.484679i	−0.691513	−	0.722364i	$-0.743055\pi$
$997$	278.990	−	483.225i	0.279830	−	0.484679i	0.971342	+	0.237685i	$0.0763887\pi$
$998$		0			0
$999$	51.3585	−	550.549i	0.0514099	−	0.551100i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.f.101.6		24
3.2	odd	2		2700.3.p.f.1601.10		24
5.2	odd	4		180.3.t.a.29.12	yes	24
5.3	odd	4		180.3.t.a.29.1	✓	24
5.4	even	2	inner	900.3.p.f.101.7		24
9.4	even	3		2700.3.p.f.2501.10		24
9.5	odd	6	inner	900.3.p.f.401.6		24
15.2	even	4		540.3.t.a.89.7		24
15.8	even	4		540.3.t.a.89.3		24
15.14	odd	2		2700.3.p.f.1601.3		24
45.2	even	12		1620.3.b.b.809.1		24
45.4	even	6		2700.3.p.f.2501.3		24
45.7	odd	12		1620.3.b.b.809.24		24
45.13	odd	12		540.3.t.a.449.7		24
45.14	odd	6	inner	900.3.p.f.401.7		24
45.22	odd	12		540.3.t.a.449.3		24
45.23	even	12		180.3.t.a.149.12	yes	24
45.32	even	12		180.3.t.a.149.1	yes	24
45.38	even	12		1620.3.b.b.809.23		24
45.43	odd	12		1620.3.b.b.809.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.t.a.29.1	✓	24	5.3	odd	4
180.3.t.a.29.12	yes	24	5.2	odd	4
180.3.t.a.149.1	yes	24	45.32	even	12
180.3.t.a.149.12	yes	24	45.23	even	12
540.3.t.a.89.3		24	15.8	even	4
540.3.t.a.89.7		24	15.2	even	4
540.3.t.a.449.3		24	45.22	odd	12
540.3.t.a.449.7		24	45.13	odd	12
900.3.p.f.101.6		24	1.1	even	1	trivial
900.3.p.f.101.7		24	5.4	even	2	inner
900.3.p.f.401.6		24	9.5	odd	6	inner
900.3.p.f.401.7		24	45.14	odd	6	inner
1620.3.b.b.809.1		24	45.2	even	12
1620.3.b.b.809.2		24	45.43	odd	12
1620.3.b.b.809.23		24	45.38	even	12
1620.3.b.b.809.24		24	45.7	odd	12
2700.3.p.f.1601.3		24	15.14	odd	2
2700.3.p.f.1601.10		24	3.2	odd	2
2700.3.p.f.2501.3		24	45.4	even	6
2700.3.p.f.2501.10		24	9.4	even	3

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0930019 + 2.99856i) q^{3} +(3.67363 - 6.36292i) q^{7} +(-8.98270 - 0.557743i) q^{9} +O(q^{10})\)	\(q+(-0.0930019 + 2.99856i) q^{3} +(3.67363 - 6.36292i) q^{7} +(-8.98270 - 0.557743i) q^{9} +(-8.35448 - 4.82346i) q^{11} +(8.34294 + 14.4504i) q^{13} -15.4743i q^{17} +17.4865 q^{19} +(18.7379 + 11.6074i) q^{21} +(-9.16415 + 5.29093i) q^{23} +(2.50783 - 26.8833i) q^{27} +(36.2049 + 20.9029i) q^{29} +(24.3641 + 42.1998i) q^{31} +(15.2404 - 24.6028i) q^{33} +20.4792 q^{37} +(-44.1063 + 23.6729i) q^{39} +(24.1640 - 13.9511i) q^{41} +(15.1046 - 26.1619i) q^{43} +(36.4814 + 21.0626i) q^{47} +(-2.49113 - 4.31476i) q^{49} +(46.4005 + 1.43914i) q^{51} -90.4314i q^{53} +(-1.62628 + 52.4344i) q^{57} +(48.0096 - 27.7184i) q^{59} +(-58.3790 + 101.115i) q^{61} +(-36.5480 + 55.1072i) q^{63} +(-8.64187 - 14.9682i) q^{67} +(-15.0129 - 27.9713i) q^{69} +38.4861i q^{71} -7.38815 q^{73} +(-61.3825 + 35.4392i) q^{77} +(11.8497 - 20.5242i) q^{79} +(80.3778 + 10.0201i) q^{81} +(3.69783 + 2.13494i) q^{83} +(-66.0456 + 106.618i) q^{87} +145.034i q^{89} +122.596 q^{91} +(-128.804 + 69.1324i) q^{93} +(-51.3498 + 88.9405i) q^{97} +(72.3555 + 47.9874i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9}+O(q^{10}) \) 24 * q - 2 * q^9	\( 24 q - 2 q^{9} - 18 q^{11} - 26 q^{21} - 36 q^{29} + 30 q^{31} - 6 q^{39} - 36 q^{41} - 108 q^{49} + 124 q^{51} + 306 q^{59} + 48 q^{61} + 268 q^{69} - 114 q^{79} - 14 q^{81} - 84 q^{91} - 418 q^{99}+O(q^{100}) \) 24 * q - 2 * q^9 - 18 * q^11 - 26 * q^21 - 36 * q^29 + 30 * q^31 - 6 * q^39 - 36 * q^41 - 108 * q^49 + 124 * q^51 + 306 * q^59 + 48 * q^61 + 268 * q^69 - 114 * q^79 - 14 * q^81 - 84 * q^91 - 418 * q^99

Introduction

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