LMFDB - Embedded newform 900.3.p.f.401.3

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			401.3
Character	$\chi$	$=$	900.401
Dual form			900.3.p.f.101.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.55773 + 1.56781i) q^{3} +(5.75148 + 9.96186i) q^{7} +(4.08395 - 8.02006i) q^{9} +O(q^{10})$	\(q+(-2.55773 + 1.56781i) q^{3} +(5.75148 + 9.96186i) q^{7} +(4.08395 - 8.02006i) q^{9} +(-13.2043 + 7.62351i) q^{11} +(-8.52085 + 14.7585i) q^{13} -10.4260i q^{17} +23.1507 q^{19} +(-30.3290 - 16.4625i) q^{21} +(12.0908 + 6.98060i) q^{23} +(2.12830 + 26.9160i) q^{27} +(-38.8276 + 22.4171i) q^{29} +(-2.72391 + 4.71796i) q^{31} +(21.8208 - 40.2007i) q^{33} +50.7314 q^{37} +(-1.34456 - 51.1074i) q^{39} +(-36.9497 - 21.3329i) q^{41} +(-3.07449 - 5.32518i) q^{43} +(27.7935 - 16.0466i) q^{47} +(-41.6591 + 72.1557i) q^{49} +(16.3460 + 26.6669i) q^{51} +16.7365i q^{53} +(-59.2131 + 36.2958i) q^{57} +(-16.9286 - 9.77374i) q^{59} +(-3.29969 - 5.71522i) q^{61} +(103.383 - 5.44352i) q^{63} +(-17.7813 + 30.7981i) q^{67} +(-41.8691 + 1.10152i) q^{69} -65.5016i q^{71} -104.118 q^{73} +(-151.889 - 87.6930i) q^{77} +(-75.2628 - 130.359i) q^{79} +(-47.6427 - 65.5070i) q^{81} +(-70.5455 + 40.7295i) q^{83} +(64.1646 - 118.211i) q^{87} -14.3858i q^{89} -196.030 q^{91} +(-0.429826 - 16.3378i) q^{93} +(-13.4333 - 23.2672i) q^{97} +(7.21531 + 137.033i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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
$3$	−2.55773	+	1.56781i	−0.852576	+	0.522603i
$3$	−2.55773	+	1.56781i	−0.852576	+	0.522603i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	5.75148	+	9.96186i	0.821641	+	1.42312i	0.904460	+	0.426559i	$0.140274\pi$
$7$	5.75148	+	9.96186i	0.821641	+	1.42312i	−0.0828194	+	0.996565i	$0.526392\pi$
$8$		0			0
$9$	4.08395	−	8.02006i	0.453772	−	0.891118i
$10$		0			0
$11$	−13.2043	+	7.62351i	−1.20039	+	0.693047i	−0.960642	−	0.277788i	$-0.910399\pi$
$11$	−13.2043	+	7.62351i	−1.20039	+	0.693047i	−0.239750	+	0.970835i	$0.577065\pi$
$12$		0			0
$13$	−8.52085	+	14.7585i	−0.655450	+	1.13527i	0.326331	+	0.945256i	$0.394188\pi$
$13$	−8.52085	+	14.7585i	−0.655450	+	1.13527i	−0.981781	+	0.190017i	$0.939146\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	10.4260i		−	0.613294i	−0.951823	−	0.306647i	$-0.900793\pi$
$17$		−	10.4260i		−	0.613294i	0.951823	−	0.306647i	$-0.0992071\pi$
$18$		0			0
$19$	23.1507			1.21846			0.609228	−	0.792995i	$-0.291479\pi$
$19$	23.1507			1.21846			0.609228	+	0.792995i	$0.291479\pi$
$20$		0			0
$21$	−30.3290	−	16.4625i	−1.44424	−	0.783929i
$22$		0			0
$23$	12.0908	+	6.98060i	0.525685	+	0.303504i	0.739258	−	0.673423i	$-0.235177\pi$
$23$	12.0908	+	6.98060i	0.525685	+	0.303504i	−0.213572	+	0.976927i	$0.568510\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	2.12830	+	26.9160i	0.0788258	+	0.996888i
$28$		0			0
$29$	−38.8276	+	22.4171i	−1.33888	+	0.773004i	−0.986642	−	0.162906i	$-0.947913\pi$
$29$	−38.8276	+	22.4171i	−1.33888	+	0.773004i	−0.352240	+	0.935910i	$0.614580\pi$
$30$		0			0
$31$	−2.72391	+	4.71796i	−0.0878682	+	0.152192i	−0.906610	−	0.421970i	$-0.861339\pi$
$31$	−2.72391	+	4.71796i	−0.0878682	+	0.152192i	0.818742	+	0.574162i	$0.194672\pi$
$32$		0			0
$33$	21.8208	−	40.2007i	0.661237	−	1.21820i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	50.7314			1.37112			0.685559	−	0.728017i	$-0.259558\pi$
$37$	50.7314			1.37112			0.685559	+	0.728017i	$0.259558\pi$
$38$		0			0
$39$	−1.34456	−	51.1074i	−0.0344760	−	1.31045i
$40$		0			0
$41$	−36.9497	−	21.3329i	−0.901211	−	0.520315i	−0.0236184	−	0.999721i	$-0.507519\pi$
$41$	−36.9497	−	21.3329i	−0.901211	−	0.520315i	−0.877593	+	0.479406i	$0.840852\pi$
$42$		0			0
$43$	−3.07449	−	5.32518i	−0.0714998	−	0.123841i	0.828059	−	0.560641i	$-0.189445\pi$
$43$	−3.07449	−	5.32518i	−0.0714998	−	0.123841i	−0.899559	+	0.436800i	$0.856112\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	27.7935	−	16.0466i	0.591351	−	0.341417i	−0.174280	−	0.984696i	$-0.555760\pi$
$47$	27.7935	−	16.0466i	0.591351	−	0.341417i	0.765632	+	0.643279i	$0.222427\pi$
$48$		0			0
$49$	−41.6591	+	72.1557i	−0.850186	+	1.47257i
$50$		0			0
$51$	16.3460	+	26.6669i	0.320509	+	0.522880i
$52$		0			0
$53$			16.7365i			0.315783i	0.987456	+	0.157892i	$0.0504696\pi$
$53$			16.7365i			0.315783i	−0.987456	+	0.157892i	$0.949530\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−59.2131	+	36.2958i	−1.03883	+	0.636769i
$58$		0			0
$59$	−16.9286	−	9.77374i	−0.286926	−	0.165657i	0.349629	−	0.936888i	$-0.386308\pi$
$59$	−16.9286	−	9.77374i	−0.286926	−	0.165657i	−0.636555	+	0.771232i	$0.719641\pi$
$60$		0			0
$61$	−3.29969	−	5.71522i	−0.0540932	−	0.0936922i	0.837711	−	0.546114i	$-0.183893\pi$
$61$	−3.29969	−	5.71522i	−0.0540932	−	0.0936922i	−0.891804	+	0.452422i	$0.850560\pi$
$62$		0			0
$63$	103.383	−	5.44352i	1.64101	−	0.0864051i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−17.7813	+	30.7981i	−0.265392	+	0.459673i	−0.967666	−	0.252234i	$-0.918835\pi$
$67$	−17.7813	+	30.7981i	−0.265392	+	0.459673i	0.702274	+	0.711907i	$0.252168\pi$
$68$		0			0
$69$	−41.8691	+	1.10152i	−0.606799	+	0.0159640i
$70$		0			0
$71$		−	65.5016i		−	0.922557i	−0.887255	−	0.461279i	$-0.847391\pi$
$71$		−	65.5016i		−	0.922557i	0.887255	−	0.461279i	$-0.152609\pi$
$72$		0			0
$73$	−104.118			−1.42628			−0.713139	−	0.701023i	$-0.752727\pi$
$73$	−104.118			−1.42628			−0.713139	+	0.701023i	$0.752727\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−151.889	−	87.6930i	−1.97258	−	1.13887i
$78$		0			0
$79$	−75.2628	−	130.359i	−0.952694	−	1.65011i	−0.739560	−	0.673091i	$-0.764966\pi$
$79$	−75.2628	−	130.359i	−0.952694	−	1.65011i	−0.213133	−	0.977023i	$-0.568367\pi$
$80$		0			0
$81$	−47.6427	−	65.5070i	−0.588182	−	0.808729i
$82$		0			0
$83$	−70.5455	+	40.7295i	−0.849946	+	0.490716i	−0.860633	−	0.509227i	$-0.829932\pi$
$83$	−70.5455	+	40.7295i	−0.849946	+	0.490716i	0.0106869	+	0.999943i	$0.496598\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	64.1646	−	118.211i	0.737525	−	1.35875i
$88$		0			0
$89$		−	14.3858i		−	0.161638i	−0.996729	−	0.0808189i	$-0.974246\pi$
$89$		−	14.3858i		−	0.161638i	0.996729	−	0.0808189i	$-0.0257536\pi$
$90$		0			0
$91$	−196.030			−2.15418
$92$		0			0
$93$	−0.429826	−	16.3378i	−0.00462178	−	0.175676i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−13.4333	−	23.2672i	−0.138488	−	0.239868i	0.788437	−	0.615116i	$-0.210891\pi$
$97$	−13.4333	−	23.2672i	−0.138488	−	0.239868i	−0.926924	+	0.375248i	$0.877557\pi$
$98$		0			0
$99$	7.21531	+	137.033i	0.0728819	+	1.38418i
$100$		0			0
$101$	−82.7052	+	47.7499i	−0.818863	+	0.472771i	−0.850024	−	0.526743i	$-0.823413\pi$
$101$	−82.7052	+	47.7499i	−0.818863	+	0.472771i	0.0311610	+	0.999514i	$0.490080\pi$
$102$		0			0
$103$	−28.8922	+	50.0428i	−0.280507	+	0.485852i	−0.971510	−	0.237000i	$-0.923836\pi$
$103$	−28.8922	+	50.0428i	−0.280507	+	0.485852i	0.691003	+	0.722852i	$0.257169\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			64.8388i			0.605970i	0.952995	+	0.302985i	$0.0979833\pi$
$107$			64.8388i			0.605970i	−0.952995	+	0.302985i	$0.902017\pi$
$108$		0			0
$109$	40.9173			0.375388			0.187694	−	0.982228i	$-0.439899\pi$
$109$	40.9173			0.375388			0.187694	+	0.982228i	$0.439899\pi$
$110$		0			0
$111$	−129.757	+	79.5371i	−1.16898	+	0.716550i
$112$		0			0
$113$	−187.445	−	108.221i	−1.65880	−	0.957709i	−0.973269	−	0.229667i	$-0.926236\pi$
$113$	−187.445	−	108.221i	−1.65880	−	0.957709i	−0.685532	−	0.728043i	$-0.740430\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	83.5657	+	128.611i	0.714237	+	1.09924i
$118$		0			0
$119$	103.862	−	59.9650i	0.872793	−	0.503907i
$120$		0			0
$121$	55.7359	−	96.5374i	0.460627	−	0.797830i
$122$		0			0
$123$	127.953	−	3.36627i	1.04027	−	0.0273680i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−128.534			−1.01208			−0.506041	−	0.862510i	$-0.668891\pi$
$127$	−128.534			−1.01208			−0.506041	+	0.862510i	$0.668891\pi$
$128$		0			0
$129$	16.2126	+	8.80014i	0.125679	+	0.0682181i
$130$		0			0
$131$	−23.1907	−	13.3892i	−0.177028	−	0.102207i	0.408867	−	0.912594i	$-0.365924\pi$
$131$	−23.1907	−	13.3892i	−0.177028	−	0.102207i	−0.585896	+	0.810386i	$0.699257\pi$
$132$		0			0
$133$	133.151	+	230.624i	1.00113	+	1.73401i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	86.4703	−	49.9236i	0.631170	−	0.364406i	−0.150035	−	0.988681i	$-0.547939\pi$
$137$	86.4703	−	49.9236i	0.631170	−	0.364406i	0.781205	+	0.624275i	$0.214605\pi$
$138$		0			0
$139$	−7.69396	+	13.3263i	−0.0553522	+	0.0958729i	−0.892374	−	0.451297i	$-0.850962\pi$
$139$	−7.69396	+	13.3263i	−0.0553522	+	0.0958729i	0.837022	+	0.547170i	$0.184295\pi$
$140$		0			0
$141$	−45.9302	+	84.6177i	−0.325746	+	0.600126i
$142$		0			0
$143$		−	259.835i		−	1.81703i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−6.57369	−	249.868i	−0.0447190	−	1.69978i
$148$		0			0
$149$	104.146	+	60.1287i	0.698966	+	0.403548i	0.806962	−	0.590603i	$-0.201110\pi$
$149$	104.146	+	60.1287i	0.698966	+	0.403548i	−0.107996	+	0.994151i	$0.534443\pi$
$150$		0			0
$151$	22.1568	+	38.3766i	0.146733	+	0.254150i	0.930018	−	0.367513i	$-0.119791\pi$
$151$	22.1568	+	38.3766i	0.146733	+	0.254150i	−0.783285	+	0.621663i	$0.786457\pi$
$152$		0			0
$153$	−83.6171	−	42.5792i	−0.546517	−	0.278296i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−29.7724	+	51.5673i	−0.189633	+	0.328454i	−0.945128	−	0.326701i	$-0.894063\pi$
$157$	−29.7724	+	51.5673i	−0.189633	+	0.328454i	0.755495	+	0.655154i	$0.227396\pi$
$158$		0			0
$159$	−26.2396	−	42.8074i	−0.165029	−	0.269229i
$160$		0			0
$161$			160.595i			0.997486i
$162$		0			0
$163$	200.140			1.22785			0.613927	−	0.789363i	$-0.289589\pi$
$163$	200.140			1.22785			0.613927	+	0.789363i	$0.289589\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	66.7931	+	38.5630i	0.399959	+	0.230916i	0.686466	−	0.727162i	$-0.259161\pi$
$167$	66.7931	+	38.5630i	0.399959	+	0.230916i	−0.286508	+	0.958078i	$0.592494\pi$
$168$		0			0
$169$	−60.7097	−	105.152i	−0.359229	−	0.622203i
$170$		0			0
$171$	94.5462	−	185.670i	0.552902	−	1.08579i
$172$		0			0
$173$	224.050	−	129.355i	1.29509	−	0.747718i	0.315535	−	0.948914i	$-0.397816\pi$
$173$	224.050	−	129.355i	1.29509	−	0.747718i	0.979551	+	0.201195i	$0.0644826\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	58.6222	−	1.54227i	0.331199	−	0.00871338i
$178$		0			0
$179$		−	174.572i		−	0.975261i	−0.873050	−	0.487630i	$-0.837861\pi$
$179$		−	174.572i		−	0.975261i	0.873050	−	0.487630i	$-0.162139\pi$
$180$		0			0
$181$	−22.3291			−0.123365			−0.0616825	−	0.998096i	$-0.519647\pi$
$181$	−22.3291			−0.123365			−0.0616825	+	0.998096i	$0.519647\pi$
$182$		0			0
$183$	17.4001	+	9.44471i	0.0950824	+	0.0516104i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	79.4827	+	137.668i	0.425041	+	0.736193i
$188$		0			0
$189$	−255.892	+	176.009i	−1.35393	+	0.931263i
$190$		0			0
$191$	190.213	−	109.819i	0.995879	−	0.574971i	0.0888528	−	0.996045i	$-0.471680\pi$
$191$	190.213	−	109.819i	0.995879	−	0.574971i	0.907026	+	0.421074i	$0.138347\pi$
$192$		0			0
$193$	−170.724	+	295.702i	−0.884579	+	1.53214i	−0.0383835	+	0.999263i	$0.512221\pi$
$193$	−170.724	+	295.702i	−0.884579	+	1.53214i	−0.846195	+	0.532873i	$0.821112\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			200.719i			1.01888i	0.860507	+	0.509439i	$0.170147\pi$
$197$			200.719i			1.01888i	−0.860507	+	0.509439i	$0.829853\pi$
$198$		0			0
$199$	79.9313			0.401665			0.200833	−	0.979626i	$-0.435635\pi$
$199$	79.9313			0.401665			0.200833	+	0.979626i	$0.435635\pi$
$200$		0			0
$201$	−2.80584	−	106.651i	−0.0139594	−	0.530601i
$202$		0			0
$203$	−446.632	−	257.863i	−2.20016	−	1.27026i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	105.363	−	68.4602i	0.508999	−	0.330726i
$208$		0			0
$209$	−305.689	+	176.489i	−1.46263	+	0.844447i
$210$		0			0
$211$	35.9481	−	62.2639i	0.170370	−	0.295089i	−0.768179	−	0.640235i	$-0.778837\pi$
$211$	35.9481	−	62.2639i	0.170370	−	0.295089i	0.938549	+	0.345145i	$0.112170\pi$
$212$		0			0
$213$	102.694	+	167.535i	0.482131	+	0.786550i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−62.6662			−0.288784
$218$		0			0
$219$	266.306	−	163.238i	1.21601	−	0.745377i
$220$		0			0
$221$	153.873	+	88.8383i	0.696256	+	0.401983i
$222$		0			0
$223$	176.565	+	305.820i	0.791773	+	1.37139i	0.924868	+	0.380288i	$0.124175\pi$
$223$	176.565	+	305.820i	0.791773	+	1.37139i	−0.133095	+	0.991103i	$0.542492\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−148.439	+	85.7010i	−0.653914	+	0.377538i	−0.789954	−	0.613166i	$-0.789896\pi$
$227$	−148.439	+	85.7010i	−0.653914	+	0.377538i	0.136040	+	0.990703i	$0.456562\pi$
$228$		0			0
$229$	−82.9005	+	143.588i	−0.362011	+	0.627021i	−0.988292	−	0.152576i	$-0.951243\pi$
$229$	−82.9005	+	143.588i	−0.362011	+	0.627021i	0.626281	+	0.779597i	$0.284576\pi$
$230$		0			0
$231$	525.976	−	13.8377i	2.27695	−	0.0599035i
$232$		0			0
$233$			6.09276i			0.0261492i	0.999915	+	0.0130746i	$0.00416189\pi$
$233$			6.09276i			0.0261492i	−0.999915	+	0.0130746i	$0.995838\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	396.880	+	215.425i	1.67460	+	0.908967i
$238$		0			0
$239$	30.7721	+	17.7663i	0.128754	+	0.0743360i	0.562994	−	0.826461i	$-0.309650\pi$
$239$	30.7721	+	17.7663i	0.128754	+	0.0743360i	−0.434240	+	0.900797i	$0.642983\pi$
$240$		0			0
$241$	150.152	+	260.071i	0.623038	+	1.07913i	0.988917	+	0.148471i	$0.0474352\pi$
$241$	150.152	+	260.071i	0.623038	+	1.07913i	−0.365879	+	0.930663i	$0.619232\pi$
$242$		0			0
$243$	224.560	+	92.8544i	0.924114	+	0.382117i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−197.263	+	341.670i	−0.798637	+	1.38328i
$248$		0			0
$249$	116.580	−	214.777i	0.468193	−	0.862557i
$250$		0			0
$251$		−	240.776i		−	0.959268i	−0.877469	−	0.479634i	$-0.840770\pi$
$251$		−	240.776i		−	0.959268i	0.877469	−	0.479634i	$-0.159230\pi$
$252$		0			0
$253$	−212.867			−0.841371
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−116.091	−	67.0253i	−0.451717	−	0.260799i	0.256838	−	0.966454i	$-0.417319\pi$
$257$	−116.091	−	67.0253i	−0.451717	−	0.260799i	−0.708555	+	0.705656i	$0.750653\pi$
$258$		0			0
$259$	291.781	+	505.379i	1.12657	+	1.95127i
$260$		0			0
$261$	21.2168	+	402.950i	0.0812903	+	1.54387i
$262$		0			0
$263$	−378.584	+	218.575i	−1.43948	+	0.831085i	−0.997813	−	0.0660933i	$-0.978947\pi$
$263$	−378.584	+	218.575i	−1.43948	+	0.831085i	−0.441668	+	0.897178i	$0.645613\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	22.5541	+	36.7949i	0.0844725	+	0.137809i
$268$		0			0
$269$		−	39.0128i		−	0.145029i	−0.997367	−	0.0725146i	$-0.976898\pi$
$269$		−	39.0128i		−	0.145029i	0.997367	−	0.0725146i	$-0.0231024\pi$
$270$		0			0
$271$	225.452			0.831925			0.415963	−	0.909382i	$-0.363445\pi$
$271$	225.452			0.831925			0.415963	+	0.909382i	$0.363445\pi$
$272$		0			0
$273$	501.392	−	307.338i	1.83660	−	1.12578i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−114.044	−	197.530i	−0.411712	−	0.713106i	0.583365	−	0.812210i	$-0.301736\pi$
$277$	−114.044	−	197.530i	−0.411712	−	0.713106i	−0.995077	+	0.0991038i	$0.968402\pi$
$278$		0			0
$279$	26.7140	+	41.1138i	0.0957490	+	0.147361i
$280$		0			0
$281$	−208.527	+	120.393i	−0.742089	+	0.428445i	−0.822828	−	0.568290i	$-0.807605\pi$
$281$	−208.527	+	120.393i	−0.742089	+	0.428445i	0.0807396	+	0.996735i	$0.474272\pi$
$282$		0			0
$283$	−23.2378	+	40.2490i	−0.0821123	+	0.142223i	−0.904157	−	0.427200i	$-0.859500\pi$
$283$	−23.2378	+	40.2490i	−0.0821123	+	0.142223i	0.822045	+	0.569423i	$0.192833\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	490.783i		−	1.71005i
$288$		0			0
$289$	180.299			0.623871
$290$		0			0
$291$	70.8372	+	38.4502i	0.243427	+	0.132131i
$292$		0			0
$293$	−83.6062	−	48.2701i	−0.285345	−	0.164744i	0.350495	−	0.936564i	$-0.386013\pi$
$293$	−83.6062	−	48.2701i	−0.285345	−	0.164744i	−0.635841	+	0.771820i	$0.719347\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−233.297	−	339.182i	−0.785512	−	1.14203i
$298$		0			0
$299$	−206.047	+	118.961i	−0.689120	+	0.397864i
$300$		0			0
$301$	35.3658	−	61.2554i	0.117494	−	0.203506i
$302$		0			0
$303$	136.675	−	251.797i	0.451072	−	0.831014i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	398.954			1.29952			0.649762	−	0.760138i	$-0.274869\pi$
$307$	398.954			1.29952			0.649762	+	0.760138i	$0.274869\pi$
$308$		0			0
$309$	−4.55910	−	173.293i	−0.0147544	−	0.560820i
$310$		0			0
$311$	346.600	+	200.110i	1.11447	+	0.643440i	0.939984	−	0.341220i	$-0.110840\pi$
$311$	346.600	+	200.110i	1.11447	+	0.643440i	0.174487	+	0.984659i	$0.444173\pi$
$312$		0			0
$313$	−103.400	−	179.093i	−0.330350	−	0.572183i	0.652230	−	0.758021i	$-0.273833\pi$
$313$	−103.400	−	179.093i	−0.330350	−	0.572183i	−0.982580	+	0.185838i	$0.940500\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−54.3839	+	31.3986i	−0.171558	+	0.0990491i	−0.583320	−	0.812242i	$-0.698247\pi$
$317$	−54.3839	+	31.3986i	−0.171558	+	0.0990491i	0.411762	+	0.911291i	$0.364913\pi$
$318$		0			0
$319$	341.794	−	592.005i	1.07146	−	1.85582i
$320$		0			0
$321$	−101.655	−	165.840i	−0.316682	−	0.516636i
$322$		0			0
$323$		−	241.369i		−	0.747272i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−104.655	+	64.1505i	−0.320047	+	0.196179i
$328$		0			0
$329$	319.708	+	184.583i	0.971756	+	0.561044i
$330$		0			0
$331$	120.382	+	208.509i	0.363693	+	0.629935i	0.988566	−	0.150792i	$-0.0481823\pi$
$331$	120.382	+	208.509i	0.363693	+	0.629935i	−0.624872	+	0.780727i	$0.714849\pi$
$332$		0			0
$333$	207.184	−	406.869i	0.622175	−	1.22183i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	171.439	−	296.941i	0.508720	−	0.881130i	−0.491229	−	0.871031i	$-0.663452\pi$
$337$	171.439	−	296.941i	0.508720	−	0.881130i	0.999949	−	0.0100989i	$-0.00321463\pi$
$338$		0			0
$339$	649.102	−	17.0770i	1.91476	−	0.0503746i
$340$		0			0
$341$		−	83.0632i		−	0.243587i
$342$		0			0
$343$	−394.762			−1.15091
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−79.1222	−	45.6812i	−0.228018	−	0.131646i	0.381639	−	0.924311i	$-0.375360\pi$
$347$	−79.1222	−	45.6812i	−0.228018	−	0.131646i	−0.609657	+	0.792665i	$0.708693\pi$
$348$		0			0
$349$	−31.0445	−	53.7706i	−0.0889526	−	0.154070i	0.818116	−	0.575053i	$-0.195019\pi$
$349$	−31.0445	−	53.7706i	−0.0889526	−	0.154070i	−0.907069	+	0.420983i	$0.861685\pi$
$350$		0			0
$351$	−415.376	−	197.936i	−1.18341	−	0.563922i
$352$		0			0
$353$	−114.478	+	66.0940i	−0.324301	+	0.187235i	−0.653308	−	0.757092i	$-0.726619\pi$
$353$	−114.478	+	66.0940i	−0.324301	+	0.187235i	0.329007	+	0.944327i	$0.393286\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−171.638	+	316.210i	−0.480779	+	0.885743i
$358$		0			0
$359$		−	299.807i		−	0.835118i	−0.908650	−	0.417559i	$-0.862886\pi$
$359$		−	299.807i		−	0.835118i	0.908650	−	0.417559i	$-0.137114\pi$
$360$		0			0
$361$	174.954			0.484637
$362$		0			0
$363$	8.79496	+	334.300i	0.0242285	+	0.920936i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	214.235	+	371.066i	0.583747	+	1.01108i	0.995030	+	0.0995722i	$0.0317474\pi$
$367$	214.235	+	371.066i	0.583747	+	1.01108i	−0.411283	+	0.911508i	$0.634919\pi$
$368$		0			0
$369$	−321.992	+	209.216i	−0.872606	+	0.566981i
$370$		0			0
$371$	−166.727	+	96.2597i	−0.449398	+	0.259460i
$372$		0			0
$373$	−209.555	+	362.959i	−0.561809	+	0.973081i	0.435530	+	0.900174i	$0.356561\pi$
$373$	−209.555	+	362.959i	−0.561809	+	0.973081i	−0.997339	+	0.0729068i	$0.976772\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	764.051i		−	2.02666i
$378$		0			0
$379$	−394.789			−1.04166			−0.520830	−	0.853660i	$-0.674378\pi$
$379$	−394.789			−1.04166			−0.520830	+	0.853660i	$0.674378\pi$
$380$		0			0
$381$	328.756	−	201.517i	0.862876	−	0.528917i
$382$		0			0
$383$	446.655	+	257.876i	1.16620	+	0.673307i	0.952782	−	0.303654i	$-0.0982067\pi$
$383$	446.655	+	257.876i	1.16620	+	0.673307i	0.213419	+	0.976961i	$0.431540\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−55.2643	+	2.90987i	−0.142802	+	0.00751904i
$388$		0			0
$389$	94.1463	−	54.3554i	0.242021	−	0.139731i	−0.374084	−	0.927395i	$-0.622043\pi$
$389$	94.1463	−	54.3554i	0.242021	−	0.139731i	0.616105	+	0.787664i	$0.288710\pi$
$390$		0			0
$391$	72.7797	−	126.058i	0.186137	−	0.322400i
$392$		0			0
$393$	80.3071	−	2.11277i	0.204344	−	0.00537600i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−319.633			−0.805121			−0.402560	−	0.915393i	$-0.631880\pi$
$397$	−319.633			−0.805121			−0.402560	+	0.915393i	$0.631880\pi$
$398$		0			0
$399$	−702.138	−	381.118i	−1.75974	−	0.955183i
$400$		0			0
$401$	74.7066	+	43.1319i	0.186301	+	0.107561i	0.590250	−	0.807221i	$-0.299029\pi$
$401$	74.7066	+	43.1319i	0.186301	+	0.107561i	−0.403949	+	0.914782i	$0.632363\pi$
$402$		0			0
$403$	−46.4201	−	80.4020i	−0.115186	−	0.199509i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−669.873	+	386.751i	−1.64588	+	0.950249i
$408$		0			0
$409$	−335.486	+	581.079i	−0.820260	+	1.42073i	0.0852283	+	0.996361i	$0.472838\pi$
$409$	−335.486	+	581.079i	−0.820260	+	1.42073i	−0.905488	+	0.424371i	$0.860495\pi$
$410$		0			0
$411$	−142.897	+	263.260i	−0.347681	+	0.640535i
$412$		0			0
$413$		−	224.854i		−	0.544441i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.21408	−	46.1478i	−0.00291147	−	0.110666i
$418$		0			0
$419$	617.394	+	356.453i	1.47349	+	0.850723i	0.999555	−	0.0298344i	$-0.00949798\pi$
$419$	617.394	+	356.453i	1.47349	+	0.850723i	0.473940	+	0.880557i	$0.342831\pi$
$420$		0			0
$421$	−205.862	−	356.564i	−0.488983	−	0.846944i	0.510936	−	0.859619i	$-0.329299\pi$
$421$	−205.862	−	356.564i	−0.488983	−	0.846944i	−0.999920	+	0.0126744i	$0.995966\pi$
$422$		0			0
$423$	−15.1874	−	288.439i	−0.0359039	−	0.681889i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	37.9562	−	65.7420i	0.0888903	−	0.153963i
$428$		0			0
$429$	407.372	+	664.588i	0.949585	+	1.54916i
$430$		0			0
$431$			165.609i			0.384243i	0.981371	+	0.192122i	$0.0615368\pi$
$431$			165.609i			0.384243i	−0.981371	+	0.192122i	$0.938463\pi$
$432$		0			0
$433$	227.973			0.526497			0.263248	−	0.964728i	$-0.415206\pi$
$433$	227.973			0.526497			0.263248	+	0.964728i	$0.415206\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	279.909	+	161.606i	0.640525	+	0.369807i
$438$		0			0
$439$	−238.105	−	412.410i	−0.542380	−	0.939430i	−0.998767	−	0.0496487i	$-0.984190\pi$
$439$	−238.105	−	412.410i	−0.542380	−	0.939430i	0.456386	−	0.889782i	$-0.349144\pi$
$440$		0			0
$441$	408.560	+	628.789i	0.926439	+	1.42583i
$442$		0			0
$443$	−468.565	+	270.526i	−1.05771	+	0.610669i	−0.924798	−	0.380459i	$-0.875766\pi$
$443$	−468.565	+	270.526i	−1.05771	+	0.610669i	−0.132912	+	0.991128i	$0.542433\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−360.648	+	9.48813i	−0.806818	+	0.0212262i
$448$		0			0
$449$			98.6418i			0.219692i	0.993949	+	0.109846i	$0.0350358\pi$
$449$			98.6418i			0.219692i	−0.993949	+	0.109846i	$0.964964\pi$
$450$		0			0
$451$	650.527			1.44241
$452$		0			0
$453$	−116.838	−	63.4194i	−0.257921	−	0.139999i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	137.957	+	238.948i	0.301874	+	0.522862i	0.976561	−	0.215243i	$-0.0690544\pi$
$457$	137.957	+	238.948i	0.301874	+	0.522862i	−0.674686	+	0.738105i	$0.735721\pi$
$458$		0			0
$459$	280.626	−	22.1896i	0.611386	−	0.0483434i
$460$		0			0
$461$	686.984	−	396.631i	1.49020	−	0.860370i	0.490267	−	0.871572i	$-0.336899\pi$
$461$	686.984	−	396.631i	1.49020	−	0.860370i	0.999937	+	0.0112022i	$0.00356585\pi$
$462$		0			0
$463$	−389.599	+	674.806i	−0.841468	+	1.45746i	0.0471863	+	0.998886i	$0.484975\pi$
$463$	−389.599	+	674.806i	−0.841468	+	1.45746i	−0.888654	+	0.458579i	$0.848359\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	233.839i		−	0.500726i	−0.968152	−	0.250363i	$-0.919450\pi$
$467$		−	233.839i		−	0.500726i	0.968152	−	0.250363i	$-0.0805500\pi$
$468$		0			0
$469$	−409.075			−0.872229
$470$		0			0
$471$	−4.69799	−	178.572i	−0.00997450	−	0.379135i
$472$		0			0
$473$	81.1931	+	46.8769i	0.171656	+	0.0991054i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	134.228	+	68.3510i	0.281400	+	0.143294i
$478$		0			0
$479$	−83.5159	+	48.2179i	−0.174355	+	0.100664i	−0.584638	−	0.811295i	$-0.698763\pi$
$479$	−83.5159	+	48.2179i	−0.174355	+	0.100664i	0.410283	+	0.911958i	$0.365430\pi$
$480$		0			0
$481$	−432.274	+	748.721i	−0.898699	+	1.55659i
$482$		0			0
$483$	−251.783	−	410.759i	−0.521289	−	0.850433i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	171.674			0.352513			0.176256	−	0.984344i	$-0.443601\pi$
$487$	171.674			0.352513			0.176256	+	0.984344i	$0.443601\pi$
$488$		0			0
$489$	−511.905	+	313.782i	−1.04684	+	0.641681i
$490$		0			0
$491$	18.7250	+	10.8109i	0.0381364	+	0.0220181i	0.518947	−	0.854806i	$-0.326324\pi$
$491$	18.7250	+	10.8109i	0.0381364	+	0.0220181i	−0.480811	+	0.876824i	$0.659658\pi$
$492$		0			0
$493$	233.721	+	404.816i	0.474079	+	0.821128i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	652.518	−	376.731i	1.31291	−	0.758010i
$498$		0			0
$499$	259.979	−	450.298i	0.521001	−	0.902400i	−0.478701	−	0.877978i	$-0.658892\pi$
$499$	259.979	−	450.298i	0.521001	−	0.902400i	0.999702	−	0.0244219i	$-0.00777450\pi$
$500$		0			0
$501$	−231.298	+	6.08513i	−0.461673	+	0.0121460i
$502$		0			0
$503$		−	362.526i		−	0.720727i	−0.932812	−	0.360363i	$-0.882653\pi$
$503$		−	362.526i		−	0.720727i	0.932812	−	0.360363i	$-0.117347\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	320.138	+	173.770i	0.631435	+	0.342741i
$508$		0			0
$509$	−391.066	−	225.782i	−0.768303	−	0.443580i	0.0639662	−	0.997952i	$-0.479625\pi$
$509$	−391.066	−	225.782i	−0.768303	−	0.443580i	−0.832269	+	0.554372i	$0.812958\pi$
$510$		0			0
$511$	−598.835	−	1037.21i	−1.17189	−	2.02977i
$512$		0			0
$513$	49.2715	+	623.123i	0.0960458	+	1.21467i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−244.663	+	423.768i	−0.473235	+	0.819668i
$518$		0			0
$519$	−370.254	+	682.123i	−0.713400	+	1.31430i
$520$		0			0
$521$		−	901.613i		−	1.73054i	−0.501303	−	0.865272i	$-0.667146\pi$
$521$		−	901.613i		−	1.73054i	0.501303	−	0.865272i	$-0.332854\pi$
$522$		0			0
$523$	292.527			0.559326			0.279663	−	0.960098i	$-0.409777\pi$
$523$	292.527			0.559326			0.279663	+	0.960098i	$0.409777\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	49.1894	+	28.3995i	0.0933385	+	0.0538890i
$528$		0			0
$529$	−167.042	−	289.326i	−0.315770	−	0.546930i
$530$		0			0
$531$	−147.522	+	95.8531i	−0.277818	+	0.180514i
$532$		0			0
$533$	629.685	−	363.549i	1.18140	−	0.682080i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	273.695	+	446.507i	0.509674	+	0.831484i
$538$		0			0
$539$		−	1270.36i		−	2.35688i
$540$		0			0
$541$	−790.789			−1.46172			−0.730858	−	0.682529i	$-0.760880\pi$
$541$	−790.789			−1.46172			−0.730858	+	0.682529i	$0.760880\pi$
$542$		0			0
$543$	57.1117	−	35.0077i	0.105178	−	0.0644710i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	79.1123	+	137.027i	0.144629	+	0.250506i	0.929235	−	0.369490i	$-0.120468\pi$
$547$	79.1123	+	137.027i	0.144629	+	0.250506i	−0.784605	+	0.619996i	$0.787134\pi$
$548$		0			0
$549$	−59.3122	+	3.12300i	−0.108037	+	0.00568853i
$550$		0			0
$551$	−898.885	+	518.971i	−1.63137	+	0.941872i
$552$		0			0
$553$	865.745	−	1499.52i	1.56554	−	2.71160i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			1011.82i			1.81655i	0.418378	+	0.908273i	$0.362599\pi$
$557$			1011.82i			1.81655i	−0.418378	+	0.908273i	$0.637401\pi$
$558$		0			0
$559$	104.789			0.187458
$560$		0			0
$561$	−419.133	−	227.504i	−0.747117	−	0.405533i
$562$		0			0
$563$	70.1223	+	40.4851i	0.124551	+	0.0719096i	0.560981	−	0.827829i	$-0.310424\pi$
$563$	70.1223	+	40.4851i	0.124551	+	0.0719096i	−0.436430	+	0.899738i	$0.643757\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	378.555	−	851.373i	0.667646	−	1.50154i
$568$		0			0
$569$	−668.982	+	386.237i	−1.17572	+	0.678800i	−0.955020	−	0.296543i	$-0.904166\pi$
$569$	−668.982	+	386.237i	−1.17572	+	0.678800i	−0.220696	+	0.975343i	$0.570833\pi$
$570$		0			0
$571$	−384.389	+	665.781i	−0.673185	+	1.16599i	0.303811	+	0.952732i	$0.401741\pi$
$571$	−384.389	+	665.781i	−0.673185	+	1.16599i	−0.976996	+	0.213258i	$0.931592\pi$
$572$		0			0
$573$	−314.337	+	579.106i	−0.548581	+	1.01066i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−188.653			−0.326955			−0.163477	−	0.986547i	$-0.552271\pi$
$577$	−188.653			−0.326955			−0.163477	+	0.986547i	$0.552271\pi$
$578$		0			0
$579$	−26.9397	−	1023.99i	−0.0465280	−	1.76855i
$580$		0			0
$581$	−811.482	−	468.510i	−1.39670	−	0.806385i
$582$		0			0
$583$	−127.591	−	220.994i	−0.218852	−	0.379063i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−482.078	+	278.328i	−0.821258	+	0.474153i	−0.850850	−	0.525409i	$-0.823912\pi$
$587$	−482.078	+	278.328i	−0.821258	+	0.474153i	0.0295923	+	0.999562i	$0.490579\pi$
$588$		0			0
$589$	−63.0604	+	109.224i	−0.107064	+	0.185440i
$590$		0			0
$591$	−314.689	−	513.385i	−0.532469	−	0.868671i
$592$		0			0
$593$			715.570i			1.20670i	0.797478	+	0.603348i	$0.206167\pi$
$593$			715.570i			1.20670i	−0.797478	+	0.603348i	$0.793833\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−204.443	+	125.317i	−0.342450	+	0.209911i
$598$		0			0
$599$	1014.24	+	585.573i	1.69323	+	0.977585i	0.951884	+	0.306458i	$0.0991440\pi$
$599$	1014.24	+	585.573i	1.69323	+	0.977585i	0.741343	+	0.671127i	$0.234189\pi$
$600$		0			0
$601$	−114.910	−	199.030i	−0.191198	−	0.331164i	0.754450	−	0.656358i	$-0.227904\pi$
$601$	−114.910	−	199.030i	−0.191198	−	0.331164i	−0.945647	+	0.325194i	$0.894571\pi$
$602$		0			0
$603$	174.385	+	268.385i	0.289195	+	0.445083i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	517.211	−	895.835i	0.852077	−	1.47584i	−0.0272535	−	0.999629i	$-0.508676\pi$
$607$	517.211	−	895.835i	0.852077	−	1.47584i	0.879330	−	0.476212i	$-0.157991\pi$
$608$		0			0
$609$	1546.64	−	40.6901i	2.53965	−	0.0668146i
$610$		0			0
$611$			546.922i			0.895126i
$612$		0			0
$613$	−69.5129			−0.113398			−0.0566989	−	0.998391i	$-0.518058\pi$
$613$	−69.5129			−0.113398			−0.0566989	+	0.998391i	$0.518058\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	896.050	+	517.335i	1.45227	+	0.838468i	0.998610	−	0.0527077i	$-0.0167852\pi$
$617$	896.050	+	517.335i	1.45227	+	0.838468i	0.453659	+	0.891175i	$0.350118\pi$
$618$		0			0
$619$	488.346	+	845.840i	0.788927	+	1.36646i	0.926625	+	0.375987i	$0.122696\pi$
$619$	488.346	+	845.840i	0.788927	+	1.36646i	−0.137698	+	0.990474i	$0.543970\pi$
$620$		0			0
$621$	−162.157	+	340.292i	−0.261123	+	0.547973i
$622$		0			0
$623$	143.309	−	82.7395i	0.230031	−	0.132808i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	505.167	−	930.674i	0.805689	−	1.48433i
$628$		0			0
$629$		−	528.925i		−	0.840898i
$630$		0			0
$631$	257.928			0.408761			0.204380	−	0.978892i	$-0.434482\pi$
$631$	257.928			0.408761			0.204380	+	0.978892i	$0.434482\pi$
$632$		0			0
$633$	5.67250	+	215.614i	0.00896129	+	0.340622i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−709.942	−	1229.66i	−1.11451	−	1.93039i
$638$		0			0
$639$	−525.327	−	267.505i	−0.822107	−	0.418631i
$640$		0			0
$641$	−654.916	+	378.116i	−1.02171	+	0.589885i	−0.914599	−	0.404362i	$-0.867494\pi$
$641$	−654.916	+	378.116i	−1.02171	+	0.589885i	−0.107111	+	0.994247i	$0.534160\pi$
$642$		0			0
$643$	124.784	−	216.133i	0.194066	−	0.336132i	−0.752528	−	0.658560i	$-0.771166\pi$
$643$	124.784	−	216.133i	0.194066	−	0.336132i	0.946594	+	0.322428i	$0.104499\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1210.85i			1.87149i	0.352682	+	0.935743i	$0.385270\pi$
$647$			1210.85i			1.87149i	−0.352682	+	0.935743i	$0.614730\pi$
$648$		0			0
$649$	298.041			0.459231
$650$		0			0
$651$	160.283	−	98.2486i	0.246211	−	0.150920i
$652$		0			0
$653$	−718.130	−	414.612i	−1.09974	−	0.634935i	−0.163587	−	0.986529i	$-0.552306\pi$
$653$	−718.130	−	414.612i	−1.09974	−	0.634935i	−0.936153	+	0.351594i	$0.885640\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−425.214	+	835.035i	−0.647205	+	1.27098i
$658$		0			0
$659$	−1048.49	+	605.347i	−1.59104	+	0.918585i	−0.597905	+	0.801567i	$0.704000\pi$
$659$	−1048.49	+	605.347i	−1.59104	+	0.918585i	−0.993130	+	0.117018i	$0.962666\pi$
$660$		0			0
$661$	122.502	−	212.180i	0.185329	−	0.320999i	−0.758358	−	0.651838i	$-0.773998\pi$
$661$	122.502	−	212.180i	0.185329	−	0.320999i	0.943687	+	0.330839i	$0.107332\pi$
$662$		0			0
$663$	−532.846	+	14.0184i	−0.803689	+	0.0211439i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−625.940			−0.938440
$668$		0			0
$669$	−931.074	−	505.384i	−1.39174	−	0.755432i
$670$		0			0
$671$	87.1402	+	50.3104i	0.129866	+	0.0749782i
$672$		0			0
$673$	−588.395	−	1019.13i	−0.874287	−	1.51431i	−0.857520	−	0.514451i	$-0.827996\pi$
$673$	−588.395	−	1019.13i	−0.874287	−	1.51431i	−0.0167673	−	0.999859i	$-0.505337\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	634.940	−	366.583i	0.937873	−	0.541481i	0.0485799	−	0.998819i	$-0.484530\pi$
$677$	634.940	−	366.583i	0.937873	−	0.541481i	0.889293	+	0.457338i	$0.151197\pi$
$678$		0			0
$679$	154.523	−	267.641i	0.227574	−	0.394170i
$680$		0			0
$681$	245.303	−	451.923i	0.360209	−	0.663617i
$682$		0			0
$683$			770.725i			1.12844i	0.825624	+	0.564221i	$0.190823\pi$
$683$			770.725i			1.12844i	−0.825624	+	0.564221i	$0.809177\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−13.0814	−	497.231i	−0.0190414	−	0.723771i
$688$		0			0
$689$	−247.006	−	142.609i	−0.358500	−	0.206980i
$690$		0			0
$691$	83.3176	+	144.310i	0.120575	+	0.208843i	0.919995	−	0.391931i	$-0.128193\pi$
$691$	83.3176	+	144.310i	0.120575	+	0.208843i	−0.799419	+	0.600773i	$0.794859\pi$
$692$		0			0
$693$	−1323.61	+	860.023i	−1.90997	+	1.24101i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−222.417	+	385.237i	−0.319106	+	0.552708i
$698$		0			0
$699$	−9.55228	−	15.5836i	−0.0136656	−	0.0222942i
$700$		0			0
$701$			857.331i			1.22301i	0.791240	+	0.611506i	$0.209436\pi$
$701$			857.331i			1.22301i	−0.791240	+	0.611506i	$0.790564\pi$
$702$		0			0
$703$	1174.47			1.67065
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−951.355	−	549.265i	−1.34562	−	0.776896i
$708$		0			0
$709$	562.074	+	973.541i	0.792770	+	1.37312i	0.924245	+	0.381799i	$0.124695\pi$
$709$	562.074	+	973.541i	0.792770	+	1.37312i	−0.131475	+	0.991319i	$0.541971\pi$
$710$		0			0
$711$	−1352.86	+	71.2328i	−1.90275	+	0.100187i
$712$		0			0
$713$	−65.8684	+	38.0291i	−0.0923820	+	0.0533368i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−106.561	+	2.80347i	−0.148621	+	0.00391000i
$718$		0			0
$719$			772.421i			1.07430i	0.843487	+	0.537150i	$0.180499\pi$
$719$			772.421i			1.07430i	−0.843487	+	0.537150i	$0.819501\pi$
$720$		0			0
$721$	−664.692			−0.921903
$722$		0			0
$723$	−791.790	−	429.781i	−1.09515	−	0.594442i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	130.564	+	226.144i	0.179593	+	0.311065i	0.941741	−	0.336338i	$-0.109189\pi$
$727$	130.564	+	226.144i	0.179593	+	0.311065i	−0.762148	+	0.647403i	$0.775855\pi$
$728$		0			0
$729$	−719.941	+	114.570i	−0.987573	+	0.157161i
$730$		0			0
$731$	−55.5203	+	32.0547i	−0.0759512	+	0.0438504i
$732$		0			0
$733$	−258.692	+	448.068i	−0.352923	+	0.611280i	−0.986760	−	0.162186i	$-0.948145\pi$
$733$	−258.692	+	448.068i	−0.352923	+	0.611280i	0.633838	+	0.773466i	$0.281479\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	542.224i		−	0.735717i
$738$		0			0
$739$	−396.875			−0.537044			−0.268522	−	0.963274i	$-0.586535\pi$
$739$	−396.875			−0.537044			−0.268522	+	0.963274i	$0.586535\pi$
$740$		0			0
$741$	−31.1276	−	1183.17i	−0.0420075	−	1.59672i
$742$		0			0
$743$	672.933	+	388.518i	0.905698	+	0.522905i	0.879044	−	0.476740i	$-0.158182\pi$
$743$	672.933	+	388.518i	0.905698	+	0.522905i	0.0266533	+	0.999645i	$0.491515\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	38.5486	+	732.116i	0.0516045	+	0.980075i
$748$		0			0
$749$	−645.915	+	372.919i	−0.862370	+	0.497890i
$750$		0			0
$751$	234.632	−	406.395i	0.312426	−	0.541138i	−0.666461	−	0.745540i	$-0.732192\pi$
$751$	234.632	−	406.395i	0.312426	−	0.541138i	0.978887	+	0.204402i	$0.0655250\pi$
$752$		0			0
$753$	377.491	+	615.840i	0.501316	+	0.817849i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−578.062			−0.763622			−0.381811	−	0.924240i	$-0.624699\pi$
$757$	−578.062			−0.763622			−0.381811	+	0.924240i	$0.624699\pi$
$758$		0			0
$759$	544.456	−	333.735i	0.717333	−	0.439703i
$760$		0			0
$761$	693.715	+	400.517i	0.911584	+	0.526303i	0.880940	−	0.473227i	$-0.156911\pi$
$761$	693.715	+	400.517i	0.911584	+	0.526303i	0.0306434	+	0.999530i	$0.490244\pi$
$762$		0			0
$763$	235.335	+	407.612i	0.308434	+	0.534223i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	288.492	−	166.561i	0.376131	−	0.217159i
$768$		0			0
$769$	310.124	−	537.150i	0.403282	−	0.698504i	−0.590838	−	0.806790i	$-0.701203\pi$
$769$	310.124	−	537.150i	0.403282	−	0.698504i	0.994120	+	0.108286i	$0.0345362\pi$
$770$		0			0
$771$	402.013	−	10.5764i	0.521417	−	0.0137178i
$772$		0			0
$773$		−	261.647i		−	0.338483i	−0.985575	−	0.169241i	$-0.945868\pi$
$773$		−	261.647i		−	0.338483i	0.985575	−	0.169241i	$-0.0541318\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1538.63	−	835.165i	−1.98022	−	1.07486i
$778$		0			0
$779$	−855.410	−	493.871i	−1.09809	−	0.633981i
$780$		0			0
$781$	499.352	+	864.903i	0.639375	+	1.10743i
$782$		0			0
$783$	−686.015	−	997.372i	−0.876137	−	1.27378i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	3.76150	−	6.51512i	0.00477955	−	0.00827842i	−0.863626	−	0.504133i	$-0.831812\pi$
$787$	3.76150	−	6.51512i	0.00477955	−	0.00827842i	0.868405	+	0.495855i	$0.165145\pi$
$788$		0			0
$789$	625.630	−	1152.60i	0.792940	−	1.46084i
$790$		0			0
$791$		−	2489.73i		−	3.14757i
$792$		0			0
$793$	112.464			0.141822
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−293.332	−	169.355i	−0.368045	−	0.212491i	0.304559	−	0.952494i	$-0.401491\pi$
$797$	−293.332	−	169.355i	−0.368045	−	0.212491i	−0.672604	+	0.740002i	$0.734824\pi$
$798$		0			0
$799$	−167.302	−	289.775i	−0.209389	−	0.362672i
$800$		0			0
$801$	−115.375	−	58.7507i	−0.144038	−	0.0733468i
$802$		0			0
$803$	1374.81	−	793.747i	1.71209	−	0.988477i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	61.1647	+	99.7842i	0.0757927	+	0.123648i
$808$		0			0
$809$		−	1370.18i		−	1.69367i	−0.531857	−	0.846834i	$-0.678506\pi$
$809$		−	1370.18i		−	1.69367i	0.531857	−	0.846834i	$-0.321494\pi$
$810$		0			0
$811$	395.829			0.488075			0.244037	−	0.969766i	$-0.421528\pi$
$811$	395.829			0.488075			0.244037	+	0.969766i	$0.421528\pi$
$812$		0			0
$813$	−576.644	+	353.465i	−0.709279	+	0.434767i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−71.1766	−	123.281i	−0.0871195	−	0.150895i
$818$		0			0
$819$	−800.577	+	1572.17i	−0.977505	+	1.91962i
$820$		0			0
$821$	−828.903	+	478.567i	−1.00963	+	0.582908i	−0.911082	−	0.412225i	$-0.864752\pi$
$821$	−828.903	+	478.567i	−1.00963	+	0.582908i	−0.0985439	+	0.995133i	$0.531418\pi$
$822$		0			0
$823$	648.461	−	1123.17i	0.787923	−	1.36472i	−0.139314	−	0.990248i	$-0.544490\pi$
$823$	648.461	−	1123.17i	0.787923	−	1.36472i	0.927237	−	0.374475i	$-0.122177\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1097.08i			1.32658i	0.748361	+	0.663291i	$0.230841\pi$
$827$			1097.08i			1.32658i	−0.748361	+	0.663291i	$0.769159\pi$
$828$		0			0
$829$	−286.317			−0.345376			−0.172688	−	0.984977i	$-0.555245\pi$
$829$	−286.317			−0.345376			−0.172688	+	0.984977i	$0.555245\pi$
$830$		0			0
$831$	601.384	+	326.430i	0.723688	+	0.392815i
$832$		0			0
$833$	752.295	+	434.338i	0.903116	+	0.521414i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−132.786	−	63.2756i	−0.158645	−	0.0755981i
$838$		0			0
$839$	−291.527	+	168.313i	−0.347470	+	0.200612i	−0.663570	−	0.748114i	$-0.730960\pi$
$839$	−291.527	+	168.313i	−0.347470	+	0.200612i	0.316100	+	0.948726i	$0.397626\pi$
$840$		0			0
$841$	584.554	−	1012.48i	0.695070	−	1.20390i
$842$		0			0
$843$	344.602	−	634.863i	0.408780	−	0.753100i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	1282.26			1.51388
$848$		0			0
$849$	−3.66685	−	139.379i	−0.00431903	−	0.164168i
$850$		0			0
$851$	613.381	+	354.135i	0.720776	+	0.416140i
$852$		0			0
$853$	−609.006	−	1054.83i	−0.713958	−	1.23661i	−0.963360	−	0.268212i	$-0.913567\pi$
$853$	−609.006	−	1054.83i	−0.713958	−	1.23661i	0.249402	−	0.968400i	$-0.419766\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1044.64	−	603.121i	1.21894	−	0.703758i	0.254252	−	0.967138i	$-0.418171\pi$
$857$	1044.64	−	603.121i	1.21894	−	0.703758i	0.964692	+	0.263380i	$0.0848372\pi$
$858$		0			0
$859$	−779.669	+	1350.43i	−0.907647	+	1.57209i	−0.0903231	+	0.995913i	$0.528790\pi$
$859$	−779.669	+	1350.43i	−0.907647	+	1.57209i	−0.817324	+	0.576178i	$0.804543\pi$
$860$		0			0
$861$	769.455	+	1255.29i	0.893676	+	1.45794i
$862$		0			0
$863$			1124.20i			1.30266i	0.758793	+	0.651332i	$0.225789\pi$
$863$			1124.20i			1.30266i	−0.758793	+	0.651332i	$0.774211\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−461.155	+	282.674i	−0.531897	+	0.326037i
$868$		0			0
$869$	1987.59	+	1147.53i	2.28721	+	1.32052i
$870$		0			0
$871$	−303.023	−	524.852i	−0.347903	−	0.602585i
$872$		0			0
$873$	−241.465	+	12.7140i	−0.276592	+	0.0145636i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	575.390	−	996.604i	0.656088	−	1.13638i	−0.325531	−	0.945531i	$-0.605543\pi$
$877$	575.390	−	996.604i	0.656088	−	1.13638i	0.981620	−	0.190847i	$-0.0611235\pi$
$878$		0			0
$879$	289.520	−	7.61687i	0.329375	−	0.00866539i
$880$		0			0
$881$		−	234.506i		−	0.266181i	−0.991104	−	0.133091i	$-0.957510\pi$
$881$		−	234.506i		−	0.266181i	0.991104	−	0.133091i	$-0.0424902\pi$
$882$		0			0
$883$	−1211.86			−1.37243			−0.686215	−	0.727399i	$-0.740729\pi$
$883$	−1211.86			−1.37243			−0.686215	+	0.727399i	$0.740729\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1145.78	−	661.516i	−1.29175	−	0.745790i	−0.312783	−	0.949825i	$-0.601261\pi$
$887$	−1145.78	−	661.516i	−1.29175	−	0.745790i	−0.978964	+	0.204034i	$0.934595\pi$
$888$		0			0
$889$	−739.263	−	1280.44i	−0.831567	−	1.44032i
$890$		0			0
$891$	1128.48	+	501.770i	1.26654	+	0.563154i
$892$		0			0
$893$	643.438	−	371.489i	0.720536	−	0.416001i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	340.504	−	627.313i	0.379603	−	0.699346i
$898$		0			0
$899$		−	244.249i		−	0.271690i
$900$		0			0
$901$	174.495			0.193668
$902$		0			0
$903$	5.58062	+	212.121i	0.00618009	+	0.234907i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	247.366	+	428.451i	0.272730	+	0.472383i	0.969560	−	0.244854i	$-0.0787400\pi$
$907$	247.366	+	428.451i	0.272730	+	0.472383i	−0.696830	+	0.717237i	$0.745407\pi$
$908$		0			0
$909$	45.1931	+	858.309i	0.0497174	+	0.944234i
$910$		0			0
$911$	149.606	−	86.3753i	0.164222	−	0.0948137i	−0.415636	−	0.909531i	$-0.636441\pi$
$911$	149.606	−	86.3753i	0.164222	−	0.0948137i	0.579859	+	0.814717i	$0.303108\pi$
$912$		0			0
$913$	621.003	−	1075.61i	0.680179	−	1.17810i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	308.030i		−	0.335911i
$918$		0			0
$919$	−414.019			−0.450510			−0.225255	−	0.974300i	$-0.572321\pi$
$919$	−414.019			−0.450510			−0.225255	+	0.974300i	$0.572321\pi$
$920$		0			0
$921$	−1020.42	+	625.483i	−1.10794	+	0.679135i
$922$		0			0
$923$	966.708	+	558.129i	1.04735	+	0.604690i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	283.352	+	436.089i	0.305665	+	0.470431i
$928$		0			0
$929$	1148.49	−	663.083i	1.23627	−	0.713760i	0.267939	−	0.963436i	$-0.413657\pi$
$929$	1148.49	−	663.083i	1.23627	−	0.713760i	0.968330	+	0.249676i	$0.0803240\pi$
$930$		0			0
$931$	−964.437	+	1670.45i	−1.03592	+	1.79426i
$932$		0			0
$933$	−1200.24	+	31.5767i	−1.28643	+	0.0338443i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	419.126			0.447306			0.223653	−	0.974669i	$-0.428202\pi$
$937$	419.126			0.447306			0.223653	+	0.974669i	$0.428202\pi$
$938$		0			0
$939$	545.252	+	295.961i	0.580673	+	0.315188i
$940$		0			0
$941$	579.729	+	334.707i	0.616077	+	0.355692i	0.775340	−	0.631544i	$-0.217578\pi$
$941$	579.729	+	334.707i	0.616077	+	0.355692i	−0.159263	+	0.987236i	$0.550912\pi$
$942$		0			0
$943$	−297.833	−	515.862i	−0.315836	−	0.547043i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	262.908	−	151.790i	0.277622	−	0.160285i	−0.354724	−	0.934971i	$-0.615425\pi$
$947$	262.908	−	151.790i	0.277622	−	0.160285i	0.632346	+	0.774686i	$0.282092\pi$
$948$		0			0
$949$	887.176	−	1536.63i	0.934854	−	1.61921i
$950$		0			0
$951$	89.8723	−	165.573i	0.0945029	−	0.174104i
$952$		0			0
$953$			1452.57i			1.52421i	0.647455	+	0.762103i	$0.275833\pi$
$953$			1452.57i			1.52421i	−0.647455	+	0.762103i	$0.724167\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	53.9341	+	2050.06i	0.0563575	+	2.14217i
$958$		0			0
$959$	994.665	+	574.270i	1.03719	+	0.598822i
$960$		0			0
$961$	465.661	+	806.548i	0.484558	+	0.839280i
$962$		0			0
$963$	520.011	+	264.798i	0.539991	+	0.274972i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−20.9429	+	36.2742i	−0.0216576	+	0.0375121i	−0.876651	−	0.481127i	$-0.840228\pi$
$967$	−20.9429	+	36.2742i	−0.0216576	+	0.0375121i	0.854993	+	0.518639i	$0.173561\pi$
$968$		0			0
$969$	378.420	+	617.356i	0.390527	+	0.637106i
$970$		0			0
$971$			513.822i			0.529168i	0.964363	+	0.264584i	$0.0852346\pi$
$971$			513.822i			0.529168i	−0.964363	+	0.264584i	$0.914765\pi$
$972$		0			0
$973$	−177.007			−0.181919
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1492.47	+	861.680i	1.52761	+	0.881965i	0.999462	+	0.0328124i	$0.0104464\pi$
$977$	1492.47	+	861.680i	1.52761	+	0.881965i	0.528147	+	0.849153i	$0.322887\pi$
$978$		0			0
$979$	109.670	+	189.954i	0.112023	+	0.194029i
$980$		0			0
$981$	167.104	−	328.159i	0.170340	−	0.334515i
$982$		0			0
$983$	−690.994	+	398.946i	−0.702944	+	0.405845i	−0.808443	−	0.588574i	$-0.799689\pi$
$983$	−690.994	+	398.946i	−0.702944	+	0.405845i	0.105499	+	0.994419i	$0.466356\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−1107.12	+	29.1267i	−1.12170	+	0.0295103i
$988$		0			0
$989$		−	85.8473i		−	0.0868021i
$990$		0			0
$991$	−920.998			−0.929363			−0.464681	−	0.885478i	$-0.653831\pi$
$991$	−920.998			−0.929363			−0.464681	+	0.885478i	$0.653831\pi$
$992$		0			0
$993$	−634.807	−	344.572i	−0.639282	−	0.347001i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−448.411	−	776.671i	−0.449761	−	0.779008i	0.548610	−	0.836079i	$-0.315157\pi$
$997$	−448.411	−	776.671i	−0.449761	−	0.779008i	−0.998370	+	0.0570705i	$0.981824\pi$
$998$		0			0
$999$	107.971	+	1365.48i	0.108079	+	1.36685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.f.401.3		24
3.2	odd	2		2700.3.p.f.2501.11		24
5.2	odd	4		180.3.t.a.149.9	yes	24
5.3	odd	4		180.3.t.a.149.4	yes	24
5.4	even	2	inner	900.3.p.f.401.10		24
9.2	odd	6	inner	900.3.p.f.101.3		24
9.7	even	3		2700.3.p.f.1601.11		24
15.2	even	4		540.3.t.a.449.9		24
15.8	even	4		540.3.t.a.449.11		24
15.14	odd	2		2700.3.p.f.2501.2		24
45.2	even	12		180.3.t.a.29.4	✓	24
45.7	odd	12		540.3.t.a.89.11		24
45.13	odd	12		1620.3.b.b.809.14		24
45.22	odd	12		1620.3.b.b.809.12		24
45.23	even	12		1620.3.b.b.809.11		24
45.29	odd	6	inner	900.3.p.f.101.10		24
45.32	even	12		1620.3.b.b.809.13		24
45.34	even	6		2700.3.p.f.1601.2		24
45.38	even	12		180.3.t.a.29.9	yes	24
45.43	odd	12		540.3.t.a.89.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.t.a.29.4	✓	24	45.2	even	12
180.3.t.a.29.9	yes	24	45.38	even	12
180.3.t.a.149.4	yes	24	5.3	odd	4
180.3.t.a.149.9	yes	24	5.2	odd	4
540.3.t.a.89.9		24	45.43	odd	12
540.3.t.a.89.11		24	45.7	odd	12
540.3.t.a.449.9		24	15.2	even	4
540.3.t.a.449.11		24	15.8	even	4
900.3.p.f.101.3		24	9.2	odd	6	inner
900.3.p.f.101.10		24	45.29	odd	6	inner
900.3.p.f.401.3		24	1.1	even	1	trivial
900.3.p.f.401.10		24	5.4	even	2	inner
1620.3.b.b.809.11		24	45.23	even	12
1620.3.b.b.809.12		24	45.22	odd	12
1620.3.b.b.809.13		24	45.32	even	12
1620.3.b.b.809.14		24	45.13	odd	12
2700.3.p.f.1601.2		24	45.34	even	6
2700.3.p.f.1601.11		24	9.7	even	3
2700.3.p.f.2501.2		24	15.14	odd	2
2700.3.p.f.2501.11		24	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(-2.55773 + 1.56781i) q^{3} +(5.75148 + 9.96186i) q^{7} +(4.08395 - 8.02006i) q^{9} +O(q^{10})\)	\(q+(-2.55773 + 1.56781i) q^{3} +(5.75148 + 9.96186i) q^{7} +(4.08395 - 8.02006i) q^{9} +(-13.2043 + 7.62351i) q^{11} +(-8.52085 + 14.7585i) q^{13} -10.4260i q^{17} +23.1507 q^{19} +(-30.3290 - 16.4625i) q^{21} +(12.0908 + 6.98060i) q^{23} +(2.12830 + 26.9160i) q^{27} +(-38.8276 + 22.4171i) q^{29} +(-2.72391 + 4.71796i) q^{31} +(21.8208 - 40.2007i) q^{33} +50.7314 q^{37} +(-1.34456 - 51.1074i) q^{39} +(-36.9497 - 21.3329i) q^{41} +(-3.07449 - 5.32518i) q^{43} +(27.7935 - 16.0466i) q^{47} +(-41.6591 + 72.1557i) q^{49} +(16.3460 + 26.6669i) q^{51} +16.7365i q^{53} +(-59.2131 + 36.2958i) q^{57} +(-16.9286 - 9.77374i) q^{59} +(-3.29969 - 5.71522i) q^{61} +(103.383 - 5.44352i) q^{63} +(-17.7813 + 30.7981i) q^{67} +(-41.8691 + 1.10152i) q^{69} -65.5016i q^{71} -104.118 q^{73} +(-151.889 - 87.6930i) q^{77} +(-75.2628 - 130.359i) q^{79} +(-47.6427 - 65.5070i) q^{81} +(-70.5455 + 40.7295i) q^{83} +(64.1646 - 118.211i) q^{87} -14.3858i q^{89} -196.030 q^{91} +(-0.429826 - 16.3378i) q^{93} +(-13.4333 - 23.2672i) q^{97} +(7.21531 + 137.033i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more