LMFDB - Embedded newform 900.3.p.f.101.8

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			101.8
Character	$\chi$	$=$	900.101
Dual form			900.3.p.f.401.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.947625 - 2.84640i) q^{3} +(0.333962 - 0.578439i) q^{7} +(-7.20401 - 5.39464i) q^{9} +O(q^{10})$	\(q+(0.947625 - 2.84640i) q^{3} +(0.333962 - 0.578439i) q^{7} +(-7.20401 - 5.39464i) q^{9} +(16.8529 + 9.73004i) q^{11} +(10.0251 + 17.3639i) q^{13} +16.3370i q^{17} -2.43805 q^{19} +(-1.33000 - 1.49873i) q^{21} +(-29.7665 + 17.1857i) q^{23} +(-22.1820 + 15.3934i) q^{27} +(-4.96794 - 2.86824i) q^{29} +(13.4261 + 23.2546i) q^{31} +(43.6659 - 38.7498i) q^{33} +11.3929 q^{37} +(58.9246 - 12.0809i) q^{39} +(25.3314 - 14.6251i) q^{41} +(-17.0624 + 29.5529i) q^{43} +(58.8885 + 33.9993i) q^{47} +(24.2769 + 42.0489i) q^{49} +(46.5016 + 15.4813i) q^{51} -37.0720i q^{53} +(-2.31036 + 6.93968i) q^{57} +(16.4800 - 9.51473i) q^{59} +(56.7812 - 98.3479i) q^{61} +(-5.52634 + 2.36548i) q^{63} +(-53.3588 - 92.4202i) q^{67} +(20.7099 + 101.013i) q^{69} +37.0887i q^{71} -115.846 q^{73} +(11.2565 - 6.49893i) q^{77} +(8.38293 - 14.5197i) q^{79} +(22.7956 + 77.7262i) q^{81} +(78.3060 + 45.2100i) q^{83} +(-12.8719 + 11.4227i) q^{87} +28.0932i q^{89} +13.3919 q^{91} +(78.9149 - 16.1793i) q^{93} +(-4.71479 + 8.16625i) q^{97} +(-68.9186 - 161.011i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.947625	−	2.84640i	0.315875	−	0.948801i
$3$	0.947625	−	2.84640i	0.315875	−	0.948801i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.333962	−	0.578439i	0.0477088	−	0.0826342i	−0.841185	−	0.540748i	$-0.818141\pi$
$7$	0.333962	−	0.578439i	0.0477088	−	0.0826342i	0.888894	+	0.458114i	$0.151475\pi$
$8$		0			0
$9$	−7.20401	−	5.39464i	−0.800446	−	0.599405i
$10$		0			0
$11$	16.8529	+	9.73004i	1.53208	+	0.884549i	0.999266	+	0.0383196i	$0.0122005\pi$
$11$	16.8529	+	9.73004i	1.53208	+	0.884549i	0.532819	+	0.846230i	$0.321133\pi$
$12$		0			0
$13$	10.0251	+	17.3639i	0.771158	+	1.33568i	0.936929	+	0.349520i	$0.113655\pi$
$13$	10.0251	+	17.3639i	0.771158	+	1.33568i	−0.165771	+	0.986164i	$0.553011\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			16.3370i			0.960998i	0.876995	+	0.480499i	$0.159544\pi$
$17$			16.3370i			0.960998i	−0.876995	+	0.480499i	$0.840456\pi$
$18$		0			0
$19$	−2.43805			−0.128319			−0.0641593	−	0.997940i	$-0.520437\pi$
$19$	−2.43805			−0.128319			−0.0641593	+	0.997940i	$0.520437\pi$
$20$		0			0
$21$	−1.33000	−	1.49873i	−0.0633333	−	0.0713683i
$22$		0			0
$23$	−29.7665	+	17.1857i	−1.29419	+	0.747203i	−0.979395	−	0.201955i	$-0.935271\pi$
$23$	−29.7665	+	17.1857i	−1.29419	+	0.747203i	−0.314800	+	0.949158i	$0.601937\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−22.1820	+	15.3934i	−0.821557	+	0.570127i
$28$		0			0
$29$	−4.96794	−	2.86824i	−0.171308	−	0.0989048i	0.411894	−	0.911232i	$-0.364867\pi$
$29$	−4.96794	−	2.86824i	−0.171308	−	0.0989048i	−0.583203	+	0.812327i	$0.698201\pi$
$30$		0			0
$31$	13.4261	+	23.2546i	0.433099	+	0.750149i	0.997138	−	0.0755984i	$-0.0240867\pi$
$31$	13.4261	+	23.2546i	0.433099	+	0.750149i	−0.564039	+	0.825748i	$0.690753\pi$
$32$		0			0
$33$	43.6659	−	38.7498i	1.32321	−	1.17424i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	11.3929			0.307916			0.153958	−	0.988077i	$-0.450798\pi$
$37$	11.3929			0.307916			0.153958	+	0.988077i	$0.450798\pi$
$38$		0			0
$39$	58.9246	−	12.0809i	1.51089	−	0.309766i
$40$		0			0
$41$	25.3314	−	14.6251i	0.617839	−	0.356709i	−0.158188	−	0.987409i	$-0.550565\pi$
$41$	25.3314	−	14.6251i	0.617839	−	0.356709i	0.776027	+	0.630700i	$0.217232\pi$
$42$		0			0
$43$	−17.0624	+	29.5529i	−0.396799	+	0.687276i	−0.993329	−	0.115315i	$-0.963212\pi$
$43$	−17.0624	+	29.5529i	−0.396799	+	0.687276i	0.596530	+	0.802591i	$0.296546\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	58.8885	+	33.9993i	1.25295	+	0.723389i	0.971694	−	0.236244i	$-0.0759165\pi$
$47$	58.8885	+	33.9993i	1.25295	+	0.723389i	0.281254	+	0.959633i	$0.409250\pi$
$48$		0			0
$49$	24.2769	+	42.0489i	0.495448	+	0.858141i
$50$		0			0
$51$	46.5016	+	15.4813i	0.911796	+	0.303555i
$52$		0			0
$53$		−	37.0720i		−	0.699471i	−0.936848	−	0.349736i	$-0.886271\pi$
$53$		−	37.0720i		−	0.699471i	0.936848	−	0.349736i	$-0.113729\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.31036	+	6.93968i	−0.0405327	+	0.121749i
$58$		0			0
$59$	16.4800	−	9.51473i	0.279322	−	0.161267i	−0.353794	−	0.935323i	$-0.615109\pi$
$59$	16.4800	−	9.51473i	0.279322	−	0.161267i	0.633116	+	0.774057i	$0.281775\pi$
$60$		0			0
$61$	56.7812	−	98.3479i	0.930839	−	1.61226i	0.148948	−	0.988845i	$-0.452411\pi$
$61$	56.7812	−	98.3479i	0.930839	−	1.61226i	0.781891	−	0.623415i	$-0.214255\pi$
$62$		0			0
$63$	−5.52634	+	2.36548i	−0.0877197	+	0.0375472i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−53.3588	−	92.4202i	−0.796401	−	1.37941i	−0.921946	−	0.387318i	$-0.873401\pi$
$67$	−53.3588	−	92.4202i	−0.796401	−	1.37941i	0.125545	−	0.992088i	$-0.459932\pi$
$68$		0			0
$69$	20.7099	+	101.013i	0.300144	+	1.46396i
$70$		0			0
$71$			37.0887i			0.522376i	0.965288	+	0.261188i	$0.0841142\pi$
$71$			37.0887i			0.522376i	−0.965288	+	0.261188i	$0.915886\pi$
$72$		0			0
$73$	−115.846			−1.58694			−0.793468	−	0.608612i	$-0.791727\pi$
$73$	−115.846			−1.58694			−0.793468	+	0.608612i	$0.791727\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	11.2565	−	6.49893i	0.146188	−	0.0844016i
$78$		0			0
$79$	8.38293	−	14.5197i	0.106113	−	0.183793i	−0.808079	−	0.589074i	$-0.799493\pi$
$79$	8.38293	−	14.5197i	0.106113	−	0.183793i	0.914192	+	0.405280i	$0.132826\pi$
$80$		0			0
$81$	22.7956	+	77.7262i	0.281427	+	0.959583i
$82$		0			0
$83$	78.3060	+	45.2100i	0.943446	+	0.544699i	0.891039	−	0.453927i	$-0.149977\pi$
$83$	78.3060	+	45.2100i	0.943446	+	0.544699i	0.0524070	+	0.998626i	$0.483311\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−12.8719	+	11.4227i	−0.147953	+	0.131296i
$88$		0			0
$89$			28.0932i			0.315654i	0.987467	+	0.157827i	$0.0504488\pi$
$89$			28.0932i			0.315654i	−0.987467	+	0.157827i	$0.949551\pi$
$90$		0			0
$91$	13.3919			0.147164
$92$		0			0
$93$	78.9149	−	16.1793i	0.848548	−	0.173971i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−4.71479	+	8.16625i	−0.0486061	+	0.0841882i	−0.889305	−	0.457315i	$-0.848811\pi$
$97$	−4.71479	+	8.16625i	−0.0486061	+	0.0841882i	0.840699	+	0.541503i	$0.182145\pi$
$98$		0			0
$99$	−68.9186	−	161.011i	−0.696147	−	1.62637i
$100$		0			0
$101$	81.1675	+	46.8621i	0.803639	+	0.463981i	0.844742	−	0.535174i	$-0.179754\pi$
$101$	81.1675	+	46.8621i	0.803639	+	0.463981i	−0.0411032	+	0.999155i	$0.513087\pi$
$102$		0			0
$103$	−50.8741	−	88.1165i	−0.493923	−	0.855500i	0.506052	−	0.862503i	$-0.331104\pi$
$103$	−50.8741	−	88.1165i	−0.493923	−	0.855500i	−0.999975	+	0.00700275i	$0.997771\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	48.7944i		−	0.456022i	−0.973659	−	0.228011i	$-0.926778\pi$
$107$		−	48.7944i		−	0.456022i	0.973659	−	0.228011i	$-0.0732223\pi$
$108$		0			0
$109$	78.0486			0.716042			0.358021	−	0.933713i	$-0.383452\pi$
$109$	78.0486			0.716042			0.358021	+	0.933713i	$0.383452\pi$
$110$		0			0
$111$	10.7962	−	32.4288i	0.0972631	−	0.292151i
$112$		0			0
$113$	49.8898	−	28.8039i	0.441503	−	0.254902i	−0.262732	−	0.964869i	$-0.584624\pi$
$113$	49.8898	−	28.8039i	0.441503	−	0.254902i	0.704235	+	0.709967i	$0.251290\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	21.4515	−	179.171i	0.183346	−	1.53138i
$118$		0			0
$119$	9.44994	+	5.45592i	0.0794112	+	0.0458481i
$120$		0			0
$121$	128.847	+	223.170i	1.06485	+	1.84438i
$122$		0			0
$123$	−17.6242	−	85.9624i	−0.143286	−	0.698881i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−78.7342			−0.619954			−0.309977	−	0.950744i	$-0.600321\pi$
$127$	−78.7342			−0.619954			−0.309977	+	0.950744i	$0.600321\pi$
$128$		0			0
$129$	67.9506	+	76.5714i	0.526749	+	0.593577i
$130$		0			0
$131$	118.408	−	68.3627i	0.903875	−	0.521852i	0.0254194	−	0.999677i	$-0.491908\pi$
$131$	118.408	−	68.3627i	0.903875	−	0.521852i	0.878455	+	0.477825i	$0.158575\pi$
$132$		0			0
$133$	−0.814217	+	1.41027i	−0.00612193	+	0.0106035i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−53.8775	−	31.1062i	−0.393266	−	0.227052i	0.290308	−	0.956933i	$-0.406242\pi$
$137$	−53.8775	−	31.1062i	−0.393266	−	0.227052i	−0.683574	+	0.729881i	$0.739575\pi$
$138$		0			0
$139$	−85.8890	−	148.764i	−0.617907	−	1.07025i	−0.989867	−	0.141997i	$-0.954648\pi$
$139$	−85.8890	−	148.764i	−0.617907	−	1.07025i	0.371960	−	0.928249i	$-0.378686\pi$
$140$		0			0
$141$	152.580	−	135.402i	1.08213	−	0.960297i
$142$		0			0
$143$			390.177i			2.72851i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	142.694	−	29.2554i	0.970704	−	0.199016i
$148$		0			0
$149$	86.3858	−	49.8748i	0.579770	−	0.334731i	−0.181272	−	0.983433i	$-0.558021\pi$
$149$	86.3858	−	49.8748i	0.579770	−	0.334731i	0.761042	+	0.648703i	$0.224688\pi$
$150$		0			0
$151$	−23.8819	+	41.3646i	−0.158158	+	0.273938i	−0.934204	−	0.356738i	$-0.883889\pi$
$151$	−23.8819	+	41.3646i	−0.158158	+	0.273938i	0.776046	+	0.630676i	$0.217222\pi$
$152$		0			0
$153$	88.1321	−	117.692i	0.576027	−	0.769227i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	76.5474	+	132.584i	0.487563	+	0.844484i	0.999898	−	0.0143016i	$-0.00455249\pi$
$157$	76.5474	+	132.584i	0.487563	+	0.844484i	−0.512334	+	0.858786i	$0.671219\pi$
$158$		0			0
$159$	−105.522	−	35.1303i	−0.663659	−	0.220945i
$160$		0			0
$161$			22.9575i			0.142593i
$162$		0			0
$163$	−162.445			−0.996595			−0.498298	−	0.867006i	$-0.666041\pi$
$163$	−162.445			−0.996595			−0.498298	+	0.867006i	$0.666041\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−113.832	+	65.7207i	−0.681626	+	0.393537i	−0.800467	−	0.599376i	$-0.795415\pi$
$167$	−113.832	+	65.7207i	−0.681626	+	0.393537i	0.118842	+	0.992913i	$0.462082\pi$
$168$		0			0
$169$	−116.503	+	201.790i	−0.689369	+	1.19402i
$170$		0			0
$171$	17.5638	+	13.1524i	0.102712	+	0.0769148i
$172$		0			0
$173$	191.795	+	110.733i	1.10864	+	0.640075i	0.938478	−	0.345340i	$-0.112236\pi$
$173$	191.795	+	110.733i	1.10864	+	0.640075i	0.170166	+	0.985415i	$0.445570\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−11.4659	−	55.9251i	−0.0647790	−	0.315961i
$178$		0			0
$179$			68.5428i			0.382921i	0.981500	+	0.191460i	$0.0613223\pi$
$179$			68.5428i			0.382921i	−0.981500	+	0.191460i	$0.938678\pi$
$180$		0			0
$181$	−197.707			−1.09230			−0.546152	−	0.837686i	$-0.683908\pi$
$181$	−197.707			−1.09230			−0.546152	+	0.837686i	$0.683908\pi$
$182$		0			0
$183$	−226.130	−	254.819i	−1.23568	−	1.39245i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−158.959	+	275.326i	−0.850050	+	1.47233i
$188$		0			0
$189$	1.49620	+	17.9718i	0.00791640	+	0.0950887i
$190$		0			0
$191$	−233.825	−	134.999i	−1.22422	−	0.706802i	−0.258402	−	0.966037i	$-0.583196\pi$
$191$	−233.825	−	134.999i	−1.22422	−	0.706802i	−0.965814	+	0.259236i	$0.916529\pi$
$192$		0			0
$193$	−25.8488	−	44.7715i	−0.133932	−	0.231976i	0.791257	−	0.611484i	$-0.209427\pi$
$193$	−25.8488	−	44.7715i	−0.133932	−	0.231976i	−0.925189	+	0.379507i	$0.876094\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			293.145i			1.48805i	0.668153	+	0.744024i	$0.267085\pi$
$197$			293.145i			1.48805i	−0.668153	+	0.744024i	$0.732915\pi$
$198$		0			0
$199$	216.611			1.08850			0.544248	−	0.838924i	$-0.316815\pi$
$199$	216.611			1.08850			0.544248	+	0.838924i	$0.316815\pi$
$200$		0			0
$201$	−313.629	+	64.3010i	−1.56034	+	0.319906i
$202$		0			0
$203$	−3.31820	+	1.91577i	−0.0163458	+	0.00943727i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	307.149	+	36.7737i	1.48381	+	0.177651i
$208$		0			0
$209$	−41.0883	−	23.7224i	−0.196595	−	0.113504i
$210$		0			0
$211$	−139.290	−	241.258i	−0.660144	−	1.14340i	−0.980577	−	0.196132i	$-0.937162\pi$
$211$	−139.290	−	241.258i	−0.660144	−	1.14340i	0.320433	−	0.947271i	$-0.396172\pi$
$212$		0			0
$213$	105.569	+	35.1462i	0.495631	+	0.165005i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	17.9352			0.0826506
$218$		0			0
$219$	−109.779	+	329.745i	−0.501273	+	1.50569i
$220$		0			0
$221$	−283.673	+	163.779i	−1.28359	+	0.741081i
$222$		0			0
$223$	42.2379	−	73.1581i	0.189407	−	0.328063i	−0.755645	−	0.654981i	$-0.772677\pi$
$223$	42.2379	−	73.1581i	0.189407	−	0.328063i	0.945053	+	0.326918i	$0.106010\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−21.5888	−	12.4643i	−0.0951049	−	0.0549089i	0.451693	−	0.892173i	$-0.350820\pi$
$227$	−21.5888	−	12.4643i	−0.0951049	−	0.0549089i	−0.546798	+	0.837264i	$0.684153\pi$
$228$		0			0
$229$	−132.591	−	229.654i	−0.578998	−	1.00285i	−0.995595	−	0.0937628i	$-0.970110\pi$
$229$	−132.591	−	229.654i	−0.578998	−	1.00285i	0.416596	−	0.909092i	$-0.363223\pi$
$230$		0			0
$231$	−7.83165	−	38.1990i	−0.0339032	−	0.165364i
$232$		0			0
$233$			290.507i			1.24681i	0.781899	+	0.623405i	$0.214251\pi$
$233$			290.507i			1.24681i	−0.781899	+	0.623405i	$0.785749\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−33.3849	−	37.6204i	−0.140865	−	0.158736i
$238$		0			0
$239$	92.5343	−	53.4247i	0.387173	−	0.223534i	−0.293762	−	0.955879i	$-0.594907\pi$
$239$	92.5343	−	53.4247i	0.387173	−	0.223534i	0.680934	+	0.732344i	$0.261574\pi$
$240$		0			0
$241$	62.9953	−	109.111i	0.261391	−	0.452743i	−0.705221	−	0.708988i	$-0.749152\pi$
$241$	62.9953	−	109.111i	0.261391	−	0.452743i	0.966612	+	0.256245i	$0.0824854\pi$
$242$		0			0
$243$	242.842	+	8.76980i	0.999349	+	0.0360897i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−24.4416	−	42.3341i	−0.0989539	−	0.171393i
$248$		0			0
$249$	202.891	−	180.048i	0.814822	−	0.723085i
$250$		0			0
$251$		−	201.781i		−	0.803908i	−0.915660	−	0.401954i	$-0.868331\pi$
$251$		−	201.781i		−	0.803908i	0.915660	−	0.401954i	$-0.131669\pi$
$252$		0			0
$253$	−668.869			−2.64375
$254$		0			0
$255$		0			0
$256$		0			0
$257$	217.255	−	125.432i	0.845351	−	0.488064i	−0.0137283	−	0.999906i	$-0.504370\pi$
$257$	217.255	−	125.432i	0.845351	−	0.488064i	0.859080	+	0.511842i	$0.171037\pi$
$258$		0			0
$259$	3.80480	−	6.59010i	0.0146903	−	0.0254444i
$260$		0			0
$261$	20.3159	+	47.4631i	0.0778389	+	0.181851i
$262$		0			0
$263$	310.158	+	179.070i	1.17931	+	0.680873i	0.955854	−	0.293841i	$-0.0949338\pi$
$263$	310.158	+	179.070i	1.17931	+	0.680873i	0.223453	+	0.974715i	$0.428267\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	79.9645	+	26.6218i	0.299493	+	0.0997072i
$268$		0			0
$269$			366.978i			1.36423i	0.731245	+	0.682115i	$0.238940\pi$
$269$			366.978i			1.36423i	−0.731245	+	0.682115i	$0.761060\pi$
$270$		0			0
$271$	7.74235			0.0285695			0.0142848	−	0.999898i	$-0.495453\pi$
$271$	7.74235			0.0285695			0.0142848	+	0.999898i	$0.495453\pi$
$272$		0			0
$273$	12.6905	−	38.1189i	0.0464855	−	0.139630i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	50.9671	−	88.2776i	0.183997	−	0.318692i	−0.759241	−	0.650809i	$-0.774430\pi$
$277$	50.9671	−	88.2776i	0.183997	−	0.318692i	0.943238	+	0.332117i	$0.107763\pi$
$278$		0			0
$279$	28.7289	−	239.956i	0.102971	−	0.860056i
$280$		0			0
$281$	−157.270	−	90.7996i	−0.559678	−	0.323130i	0.193338	−	0.981132i	$-0.438069\pi$
$281$	−157.270	−	90.7996i	−0.559678	−	0.323130i	−0.753016	+	0.658002i	$0.771402\pi$
$282$		0			0
$283$	−133.963	−	232.031i	−0.473368	−	0.819897i	0.526167	−	0.850381i	$-0.323628\pi$
$283$	−133.963	−	232.031i	−0.473368	−	0.819897i	−0.999535	+	0.0304839i	$0.990295\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	19.5369i		−	0.0680728i
$288$		0			0
$289$	22.1036			0.0764830
$290$		0			0
$291$	18.7766	+	21.1587i	0.0645244	+	0.0727104i
$292$		0			0
$293$	233.167	−	134.619i	0.795791	−	0.459450i	−0.0462064	−	0.998932i	$-0.514713\pi$
$293$	233.167	−	134.619i	0.795791	−	0.459450i	0.841997	+	0.539482i	$0.181380\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−523.611	+	43.5920i	−1.76300	+	0.146775i
$298$		0			0
$299$	−596.821	−	344.575i	−1.99606	−	1.15242i
$300$		0			0
$301$	11.3964	+	19.7391i	0.0378617	+	0.0655783i
$302$		0			0
$303$	210.305	−	186.628i	0.694075	−	0.615933i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−409.604			−1.33422			−0.667108	−	0.744961i	$-0.732468\pi$
$307$	−409.604			−1.33422			−0.667108	+	0.744961i	$0.732468\pi$
$308$		0			0
$309$	−299.025	+	61.3067i	−0.967717	+	0.198404i
$310$		0			0
$311$	20.8905	−	12.0612i	0.0671722	−	0.0387819i	−0.466038	−	0.884765i	$-0.654319\pi$
$311$	20.8905	−	12.0612i	0.0671722	−	0.0387819i	0.533210	+	0.845983i	$0.320986\pi$
$312$		0			0
$313$	−217.601	+	376.897i	−0.695212	+	1.20414i	0.274897	+	0.961474i	$0.411356\pi$
$313$	−217.601	+	376.897i	−0.695212	+	1.20414i	−0.970109	+	0.242669i	$0.921977\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	340.217	+	196.425i	1.07324	+	0.619636i	0.929065	−	0.369916i	$-0.120614\pi$
$317$	340.217	+	196.425i	1.07324	+	0.619636i	0.144175	+	0.989552i	$0.453947\pi$
$318$		0			0
$319$	−55.8162	−	96.6764i	−0.174972	−	0.303061i
$320$		0			0
$321$	−138.888	−	46.2388i	−0.432674	−	0.144046i
$322$		0			0
$323$		−	39.8304i		−	0.123314i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	73.9608	−	222.158i	0.226180	−	0.679382i
$328$		0			0
$329$	39.3331	−	22.7089i	0.119553	−	0.0690242i
$330$		0			0
$331$	−190.240	+	329.505i	−0.574743	+	0.995483i	0.421327	+	0.906909i	$0.361565\pi$
$331$	−190.240	+	329.505i	−0.574743	+	0.995483i	−0.996070	+	0.0885746i	$0.971769\pi$
$332$		0			0
$333$	−82.0746	−	61.4607i	−0.246470	−	0.184567i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−318.496	−	551.651i	−0.945092	−	1.63695i	−0.755567	−	0.655072i	$-0.772638\pi$
$337$	−318.496	−	551.651i	−0.945092	−	1.63695i	−0.189525	−	0.981876i	$-0.560695\pi$
$338$		0			0
$339$	−34.7107	−	169.302i	−0.102391	−	0.499415i
$340$		0			0
$341$			522.545i			1.53239i
$342$		0			0
$343$	65.1586			0.189967
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−91.0005	+	52.5392i	−0.262249	+	0.151410i	−0.625360	−	0.780336i	$-0.715048\pi$
$347$	−91.0005	+	52.5392i	−0.262249	+	0.151410i	0.363111	+	0.931746i	$0.381715\pi$
$348$		0			0
$349$	−173.224	+	300.033i	−0.496344	+	0.859693i	−0.999991	−	0.00421630i	$-0.998658\pi$
$349$	−173.224	+	300.033i	−0.496344	+	0.859693i	0.503647	+	0.863910i	$0.331991\pi$
$350$		0			0
$351$	−489.666	−	230.847i	−1.39506	−	0.657683i
$352$		0			0
$353$	−186.075	−	107.430i	−0.527124	−	0.304335i	0.212720	−	0.977113i	$-0.431768\pi$
$353$	−186.075	−	107.430i	−0.527124	−	0.304335i	−0.739845	+	0.672778i	$0.765101\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	24.4848	−	21.7282i	0.0685847	−	0.0608632i
$358$		0			0
$359$		−	221.170i		−	0.616073i	−0.951375	−	0.308037i	$-0.900328\pi$
$359$		−	221.170i		−	0.616073i	0.951375	−	0.308037i	$-0.0996719\pi$
$360$		0			0
$361$	−355.056			−0.983534
$362$		0			0
$363$	757.331	−	155.270i	2.08631	−	0.427740i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	231.883	−	401.633i	0.631834	−	1.09437i	−0.355342	−	0.934736i	$-0.615636\pi$
$367$	231.883	−	401.633i	0.631834	−	1.09437i	0.987176	−	0.159633i	$-0.0510310\pi$
$368$		0			0
$369$	−261.385	−	31.2945i	−0.708360	−	0.0848091i
$370$		0			0
$371$	−21.4439	−	12.3806i	−0.0578002	−	0.0333710i
$372$		0			0
$373$	30.9994	+	53.6925i	0.0831083	+	0.143948i	0.904584	−	0.426296i	$-0.140182\pi$
$373$	30.9994	+	53.6925i	0.0831083	+	0.143948i	−0.821475	+	0.570244i	$0.806849\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	115.017i		−	0.305085i
$378$		0			0
$379$	−560.650			−1.47929			−0.739644	−	0.672998i	$-0.765006\pi$
$379$	−560.650			−1.47929			−0.739644	+	0.672998i	$0.765006\pi$
$380$		0			0
$381$	−74.6105	+	224.109i	−0.195828	+	0.588213i
$382$		0			0
$383$	−432.771	+	249.860i	−1.12995	+	0.652377i	−0.943922	−	0.330168i	$-0.892895\pi$
$383$	−432.771	+	249.860i	−1.12995	+	0.652377i	−0.186027	+	0.982545i	$0.559561\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	282.345	−	120.854i	0.729573	−	0.312284i
$388$		0			0
$389$	86.8798	+	50.1601i	0.223341	+	0.128946i	0.607496	−	0.794322i	$-0.292174\pi$
$389$	86.8798	+	50.1601i	0.223341	+	0.128946i	−0.384155	+	0.923269i	$0.625507\pi$
$390$		0			0
$391$	−280.762	−	486.294i	−0.718061	−	1.24372i
$392$		0			0
$393$	−82.3816	−	401.818i	−0.209622	−	1.02244i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	467.421			1.17738			0.588692	−	0.808357i	$-0.299643\pi$
$397$	467.421			1.17738			0.588692	+	0.808357i	$0.299643\pi$
$398$		0			0
$399$	3.24261	+	3.65399i	0.00812684	+	0.00915788i
$400$		0			0
$401$	636.761	−	367.634i	1.58793	−	0.916794i	0.594286	−	0.804254i	$-0.297435\pi$
$401$	636.761	−	367.634i	1.58793	−	0.916794i	0.993647	−	0.112540i	$-0.0358986\pi$
$402$		0			0
$403$	−269.194	+	466.258i	−0.667975	+	1.15697i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	192.004	+	110.853i	0.471754	+	0.272367i
$408$		0			0
$409$	383.358	+	663.996i	0.937306	+	1.62346i	0.770470	+	0.637476i	$0.220022\pi$
$409$	383.358	+	663.996i	0.937306	+	1.62346i	0.166836	+	0.985985i	$0.446645\pi$
$410$		0			0
$411$	−139.596	+	123.880i	−0.339650	+	0.301411i
$412$		0			0
$413$		−	12.7102i		−	0.0307754i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−504.833	+	103.502i	−1.21063	+	0.248206i
$418$		0			0
$419$	336.616	−	194.345i	0.803379	−	0.463831i	−0.0412725	−	0.999148i	$-0.513141\pi$
$419$	336.616	−	194.345i	0.803379	−	0.463831i	0.844651	+	0.535317i	$0.179808\pi$
$420$		0			0
$421$	66.7729	−	115.654i	0.158605	−	0.274713i	−0.775761	−	0.631027i	$-0.782634\pi$
$421$	66.7729	−	115.654i	0.158605	−	0.274713i	0.934366	+	0.356315i	$0.115967\pi$
$422$		0			0
$423$	−240.820	−	562.614i	−0.569313	−	1.33006i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−37.9255	−	65.6889i	−0.0888185	−	0.153838i
$428$		0			0
$429$	1110.60	+	369.741i	2.58881	+	0.861868i
$430$		0			0
$431$			4.42143i			0.0102585i	0.999987	+	0.00512927i	$0.00163270\pi$
$431$			4.42143i			0.0102585i	−0.999987	+	0.00512927i	$0.998367\pi$
$432$		0			0
$433$	503.803			1.16352			0.581759	−	0.813361i	$-0.302365\pi$
$433$	503.803			1.16352			0.581759	+	0.813361i	$0.302365\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	72.5723	−	41.8996i	0.166069	−	0.0958801i
$438$		0			0
$439$	398.561	−	690.327i	0.907883	−	1.57250i	0.0908834	−	0.995862i	$-0.471031\pi$
$439$	398.561	−	690.327i	0.907883	−	1.57250i	0.817000	−	0.576638i	$-0.195636\pi$
$440$		0			0
$441$	51.9474	−	433.886i	0.117795	−	0.983869i
$442$		0			0
$443$	−44.3069	−	25.5806i	−0.100016	−	0.0577440i	0.449158	−	0.893452i	$-0.351724\pi$
$443$	−44.3069	−	25.5806i	−0.100016	−	0.0577440i	−0.549173	+	0.835708i	$0.685057\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−60.1026	−	293.151i	−0.134458	−	0.655819i
$448$		0			0
$449$			410.343i			0.913904i	0.889491	+	0.456952i	$0.151059\pi$
$449$			410.343i			0.913904i	−0.889491	+	0.456952i	$0.848941\pi$
$450$		0			0
$451$	569.211			1.26211
$452$		0			0
$453$	95.1093	+	107.176i	0.209954	+	0.236591i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−295.002	+	510.958i	−0.645518	+	1.11807i	0.338664	+	0.940907i	$0.390025\pi$
$457$	−295.002	+	510.958i	−0.645518	+	1.11807i	−0.984182	+	0.177162i	$0.943308\pi$
$458$		0			0
$459$	−251.482	−	362.387i	−0.547891	−	0.789514i
$460$		0			0
$461$	−143.139	−	82.6413i	−0.310497	−	0.179265i	0.336652	−	0.941629i	$-0.390705\pi$
$461$	−143.139	−	82.6413i	−0.310497	−	0.179265i	−0.647149	+	0.762364i	$0.724039\pi$
$462$		0			0
$463$	1.68648	+	2.92107i	0.00364251	+	0.00630902i	0.867841	−	0.496842i	$-0.165507\pi$
$463$	1.68648	+	2.92107i	0.00364251	+	0.00630902i	−0.864198	+	0.503151i	$0.832174\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			553.128i			1.18443i	0.805781	+	0.592214i	$0.201746\pi$
$467$			553.128i			1.18443i	−0.805781	+	0.592214i	$0.798254\pi$
$468$		0			0
$469$	−71.2793			−0.151981
$470$		0			0
$471$	449.926	−	92.2448i	0.955257	−	0.195849i
$472$		0			0
$473$	−575.101	+	332.035i	−1.21586	+	0.701976i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−199.990	+	267.067i	−0.419267	+	0.559889i
$478$		0			0
$479$	−264.327	−	152.609i	−0.551831	−	0.318600i	0.198029	−	0.980196i	$-0.436546\pi$
$479$	−264.327	−	152.609i	−0.551831	−	0.318600i	−0.749860	+	0.661596i	$0.769879\pi$
$480$		0			0
$481$	114.214	+	197.825i	0.237452	+	0.411279i
$482$		0			0
$483$	65.3461	+	21.7551i	0.135292	+	0.0450415i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−263.256			−0.540566			−0.270283	−	0.962781i	$-0.587117\pi$
$487$	−263.256			−0.540566			−0.270283	+	0.962781i	$0.587117\pi$
$488$		0			0
$489$	−153.937	+	462.384i	−0.314800	+	0.945571i
$490$		0			0
$491$	−473.145	+	273.170i	−0.963635	+	0.556355i	−0.897290	−	0.441442i	$-0.854467\pi$
$491$	−473.145	+	273.170i	−0.963635	+	0.556355i	−0.0663453	+	0.997797i	$0.521134\pi$
$492$		0			0
$493$	46.8583	−	81.1610i	0.0950473	−	0.164627i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	21.4535	+	12.3862i	0.0431661	+	0.0249220i
$498$		0			0
$499$	325.828	+	564.351i	0.652963	+	1.13096i	0.982400	+	0.186787i	$0.0598075\pi$
$499$	325.828	+	564.351i	0.652963	+	1.13096i	−0.329438	+	0.944177i	$0.606859\pi$
$500$		0			0
$501$	79.1978	+	386.289i	0.158079	+	0.771036i
$502$		0			0
$503$		−	188.144i		−	0.374045i	−0.982356	−	0.187022i	$-0.940116\pi$
$503$		−	188.144i		−	0.374045i	0.982356	−	0.187022i	$-0.0598837\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	463.973	+	522.836i	0.915135	+	1.03124i
$508$		0			0
$509$	202.409	−	116.861i	0.397660	−	0.229589i	−0.287814	−	0.957686i	$-0.592928\pi$
$509$	202.409	−	116.861i	0.397660	−	0.229589i	0.685474	+	0.728097i	$0.259595\pi$
$510$		0			0
$511$	−38.6883	+	67.0100i	−0.0757109	+	0.131135i
$512$		0			0
$513$	54.0810	−	37.5300i	0.105421	−	0.0731579i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	661.629	+	1145.98i	1.27975	+	2.21659i
$518$		0			0
$519$	496.941	−	440.993i	0.957497	−	0.849698i
$520$		0			0
$521$		−	455.570i		−	0.874415i	−0.899361	−	0.437207i	$-0.855968\pi$
$521$		−	455.570i		−	0.874415i	0.899361	−	0.437207i	$-0.144032\pi$
$522$		0			0
$523$	−176.002			−0.336523			−0.168261	−	0.985742i	$-0.553815\pi$
$523$	−176.002			−0.336523			−0.168261	+	0.985742i	$0.553815\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−379.910	+	219.341i	−0.720892	+	0.416207i
$528$		0			0
$529$	326.195	−	564.987i	0.616626	−	1.06803i
$530$		0			0
$531$	−170.051	−	20.3595i	−0.320246	−	0.0383418i
$532$		0			0
$533$	507.897	+	293.234i	0.952902	+	0.550158i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	195.100	+	64.9529i	0.363315	+	0.120955i
$538$		0			0
$539$			944.862i			1.75299i
$540$		0			0
$541$	409.786			0.757461			0.378730	−	0.925507i	$-0.376361\pi$
$541$	409.786			0.757461			0.378730	+	0.925507i	$0.376361\pi$
$542$		0			0
$543$	−187.352	+	562.754i	−0.345032	+	1.03638i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	479.978	−	831.346i	0.877473	−	1.51983i	0.0233685	−	0.999727i	$-0.492561\pi$
$547$	479.978	−	831.346i	0.877473	−	1.51983i	0.854105	−	0.520101i	$-0.174106\pi$
$548$		0			0
$549$	−939.604	+	402.185i	−1.71148	+	0.732578i
$550$		0			0
$551$	12.1121	+	6.99292i	0.0219820	+	0.0126913i
$552$		0			0
$553$	−5.59916	−	9.69803i	−0.0101251	−	0.0175371i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	813.070i		−	1.45973i	−0.683591	−	0.729865i	$-0.739583\pi$
$557$		−	813.070i		−	1.45973i	0.683591	−	0.729865i	$-0.260417\pi$
$558$		0			0
$559$	−684.204			−1.22398
$560$		0			0
$561$	633.054	+	713.368i	1.12844	+	1.27160i
$562$		0			0
$563$	623.851	−	360.180i	1.10808	−	0.639752i	0.169751	−	0.985487i	$-0.445704\pi$
$563$	623.851	−	360.180i	1.10808	−	0.639752i	0.938332	+	0.345735i	$0.112370\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	52.5727	+	12.7717i	0.0927209	+	0.0225251i
$568$		0			0
$569$	−641.846	−	370.570i	−1.12802	−	0.651265i	−0.184587	−	0.982816i	$-0.559095\pi$
$569$	−641.846	−	370.570i	−1.12802	−	0.651265i	−0.943437	+	0.331551i	$0.892428\pi$
$570$		0			0
$571$	69.9039	+	121.077i	0.122424	+	0.212044i	0.920723	−	0.390217i	$-0.127600\pi$
$571$	69.9039	+	121.077i	0.122424	+	0.212044i	−0.798299	+	0.602261i	$0.794267\pi$
$572$		0			0
$573$	−605.841	+	537.632i	−1.05731	+	0.938276i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−696.659			−1.20738			−0.603690	−	0.797219i	$-0.706304\pi$
$577$	−696.659			−1.20738			−0.603690	+	0.797219i	$0.706304\pi$
$578$		0			0
$579$	−151.933	+	31.1496i	−0.262405	+	0.0537989i
$580$		0			0
$581$	52.3025	−	30.1968i	0.0900214	−	0.0519739i
$582$		0			0
$583$	360.712	−	624.771i	0.618717	−	1.07165i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−445.332	−	257.113i	−0.758658	−	0.438011i	0.0701559	−	0.997536i	$-0.477650\pi$
$587$	−445.332	−	257.113i	−0.758658	−	0.438011i	−0.828814	+	0.559525i	$0.810984\pi$
$588$		0			0
$589$	−32.7335	−	56.6961i	−0.0555747	−	0.0962582i
$590$		0			0
$591$	834.409	+	277.792i	1.41186	+	0.470037i
$592$		0			0
$593$		−	319.924i		−	0.539501i	−0.962930	−	0.269751i	$-0.913059\pi$
$593$		−	319.924i		−	0.539501i	0.962930	−	0.269751i	$-0.0869413\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	205.266	−	616.561i	0.343829	−	1.03277i
$598$		0			0
$599$	869.121	−	501.787i	1.45095	−	0.837709i	0.452418	−	0.891806i	$-0.350561\pi$
$599$	869.121	−	501.787i	1.45095	−	0.837709i	0.998536	+	0.0540973i	$0.0172281\pi$
$600$		0			0
$601$	41.6656	−	72.1669i	0.0693271	−	0.120078i	−0.829278	−	0.558836i	$-0.811248\pi$
$601$	41.6656	−	72.1669i	0.0693271	−	0.120078i	0.898605	+	0.438758i	$0.144581\pi$
$602$		0			0
$603$	−114.176	+	953.649i	−0.189347	+	1.58151i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−25.3472	−	43.9026i	−0.0417581	−	0.0723272i	0.844391	−	0.535727i	$-0.179963\pi$
$607$	−25.3472	−	43.9026i	−0.0417581	−	0.0723272i	−0.886149	+	0.463400i	$0.846629\pi$
$608$		0			0
$609$	2.30863	+	11.2604i	0.00379085	+	0.0184899i
$610$		0			0
$611$			1363.38i			2.23139i
$612$		0			0
$613$	262.022			0.427442			0.213721	−	0.976895i	$-0.431442\pi$
$613$	262.022			0.427442			0.213721	+	0.976895i	$0.431442\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	296.558	−	171.218i	0.480645	−	0.277500i	−0.240040	−	0.970763i	$-0.577161\pi$
$617$	296.558	−	171.218i	0.480645	−	0.277500i	0.720685	+	0.693263i	$0.243827\pi$
$618$		0			0
$619$	272.901	−	472.679i	0.440875	−	0.763617i	−0.556880	−	0.830593i	$-0.688002\pi$
$619$	272.901	−	472.679i	0.440875	−	0.763617i	0.997755	+	0.0669756i	$0.0213350\pi$
$620$		0			0
$621$	395.734	−	839.421i	0.637254	−	1.35172i
$622$		0			0
$623$	16.2502	+	9.38206i	0.0260838	+	0.0150595i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−106.460	+	94.4740i	−0.169792	+	0.150676i
$628$		0			0
$629$			186.125i			0.295907i
$630$		0			0
$631$	906.405			1.43646			0.718229	−	0.695807i	$-0.244953\pi$
$631$	906.405			1.43646			0.718229	+	0.695807i	$0.244953\pi$
$632$		0			0
$633$	−818.713	+	167.854i	−1.29339	+	0.265173i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−486.755	+	843.085i	−0.764137	+	1.32352i
$638$		0			0
$639$	200.080	−	267.187i	0.313115	−	0.418134i
$640$		0			0
$641$	701.265	+	404.875i	1.09402	+	0.631631i	0.934643	−	0.355587i	$-0.115719\pi$
$641$	701.265	+	404.875i	1.09402	+	0.631631i	0.159374	+	0.987218i	$0.449052\pi$
$642$		0			0
$643$	−212.657	−	368.333i	−0.330726	−	0.572835i	0.651928	−	0.758281i	$-0.273960\pi$
$643$	−212.657	−	368.333i	−0.330726	−	0.572835i	−0.982654	+	0.185446i	$0.940627\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			782.663i			1.20968i	0.796347	+	0.604840i	$0.206763\pi$
$647$			782.663i			1.20968i	−0.796347	+	0.604840i	$0.793237\pi$
$648$		0			0
$649$	370.315			0.570593
$650$		0			0
$651$	16.9958	−	51.0508i	0.0261073	−	0.0784190i
$652$		0			0
$653$	890.555	−	514.162i	1.36379	−	0.787385i	0.373665	−	0.927564i	$-0.378101\pi$
$653$	890.555	−	514.162i	1.36379	−	0.787385i	0.990126	+	0.140179i	$0.0447678\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	834.559	+	624.950i	1.27026	+	0.951217i
$658$		0			0
$659$	230.519	+	133.090i	0.349801	+	0.201958i	0.664598	−	0.747201i	$-0.268603\pi$
$659$	230.519	+	133.090i	0.349801	+	0.201958i	−0.314797	+	0.949159i	$0.601936\pi$
$660$		0			0
$661$	254.653	+	441.071i	0.385254	+	0.667279i	0.991804	−	0.127766i	$-0.0407806\pi$
$661$	254.653	+	441.071i	0.385254	+	0.667279i	−0.606551	+	0.795045i	$0.707447\pi$
$662$		0			0
$663$	197.365	+	962.650i	0.297684	+	1.45196i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	197.171			0.295608
$668$		0			0
$669$	−168.212	−	189.552i	−0.251438	−	0.283337i
$670$		0			0
$671$	1913.86	−	1104.97i	2.85225	−	1.64675i
$672$		0			0
$673$	398.114	−	689.553i	0.591551	−	1.02460i	−0.402473	−	0.915432i	$-0.631849\pi$
$673$	398.114	−	689.553i	0.591551	−	1.02460i	0.994024	−	0.109164i	$-0.0348174\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1094.70	−	632.023i	−1.61698	−	0.933565i	−0.987695	−	0.156392i	$-0.950014\pi$
$677$	−1094.70	−	632.023i	−1.61698	−	0.933565i	−0.629287	−	0.777173i	$-0.716653\pi$
$678$		0			0
$679$	3.14912	+	5.45443i	0.00463788	+	0.00803304i
$680$		0			0
$681$	−55.9366	+	49.6390i	−0.0821388	+	0.0728913i
$682$		0			0
$683$			262.103i			0.383753i	0.981419	+	0.191876i	$0.0614573\pi$
$683$			262.103i			0.383753i	−0.981419	+	0.191876i	$0.938543\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−779.333	+	159.781i	−1.13440	+	0.232577i
$688$		0			0
$689$	643.714	−	371.648i	0.934273	−	0.539403i
$690$		0			0
$691$	−375.817	+	650.934i	−0.543874	+	0.942018i	0.454803	+	0.890592i	$0.349710\pi$
$691$	−375.817	+	650.934i	−0.543874	+	0.942018i	−0.998677	+	0.0514255i	$0.983624\pi$
$692$		0			0
$693$	−116.151	−	13.9063i	−0.167606	−	0.0200668i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	238.929	+	413.838i	0.342797	+	0.593742i
$698$		0			0
$699$	826.900	+	275.292i	1.18297	+	0.393836i
$700$		0			0
$701$		−	620.953i		−	0.885810i	−0.896569	−	0.442905i	$-0.853948\pi$
$701$		−	620.953i		−	0.885810i	0.896569	−	0.442905i	$-0.146052\pi$
$702$		0			0
$703$	−27.7765			−0.0395114
$704$		0			0
$705$		0			0
$706$		0			0
$707$	54.2137	−	31.3003i	0.0766814	−	0.0442720i
$708$		0			0
$709$	−201.855	+	349.623i	−0.284704	+	0.493122i	−0.972537	−	0.232747i	$-0.925229\pi$
$709$	−201.855	+	349.623i	−0.284704	+	0.493122i	0.687833	+	0.725869i	$0.258562\pi$
$710$		0			0
$711$	−138.719	+	59.3769i	−0.195104	+	0.0835119i
$712$		0			0
$713$	−799.293	−	461.472i	−1.12103	−	0.647226i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−64.3804	−	314.016i	−0.0897913	−	0.437959i
$718$		0			0
$719$			316.833i			0.440658i	0.975426	+	0.220329i	$0.0707132\pi$
$719$			316.833i			0.440658i	−0.975426	+	0.220329i	$0.929287\pi$
$720$		0			0
$721$	−67.9600			−0.0942580
$722$		0			0
$723$	−250.878	−	282.706i	−0.346996	−	0.391018i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	278.738	−	482.789i	0.383409	−	0.664084i	−0.608138	−	0.793831i	$-0.708083\pi$
$727$	278.738	−	482.789i	0.383409	−	0.664084i	0.991547	+	0.129747i	$0.0414166\pi$
$728$		0			0
$729$	255.085	−	682.915i	0.349911	−	0.936783i
$730$		0			0
$731$	−482.804	−	278.747i	−0.660471	−	0.381323i
$732$		0			0
$733$	223.376	+	386.899i	0.304742	+	0.527829i	0.977204	−	0.212303i	$-0.0680963\pi$
$733$	223.376	+	386.899i	0.304742	+	0.527829i	−0.672462	+	0.740132i	$0.734763\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	2076.73i		−	2.81782i
$738$		0			0
$739$	−209.090			−0.282937			−0.141468	−	0.989943i	$-0.545182\pi$
$739$	−209.090			−0.282937			−0.141468	+	0.989943i	$0.545182\pi$
$740$		0			0
$741$	−143.661	+	29.4538i	−0.193875	+	0.0397487i
$742$		0			0
$743$	39.4427	−	22.7722i	0.0530857	−	0.0306490i	−0.473222	−	0.880943i	$-0.656909\pi$
$743$	39.4427	−	22.7722i	0.0530857	−	0.0306490i	0.526308	+	0.850294i	$0.323576\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−320.226	−	748.126i	−0.428682	−	1.00151i
$748$		0			0
$749$	−28.2246	−	16.2955i	−0.0376830	−	0.0217563i
$750$		0			0
$751$	−8.65769	−	14.9956i	−0.0115282	−	0.0199675i	0.860204	−	0.509951i	$-0.170336\pi$
$751$	−8.65769	−	14.9956i	−0.0115282	−	0.0199675i	−0.871732	+	0.489983i	$0.837003\pi$
$752$		0			0
$753$	−574.349	−	191.213i	−0.762748	−	0.253934i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	1269.99			1.67767			0.838834	−	0.544388i	$-0.183238\pi$
$757$	1269.99			1.67767			0.838834	+	0.544388i	$0.183238\pi$
$758$		0			0
$759$	−633.838	+	1903.87i	−0.835096	+	2.50839i
$760$		0			0
$761$	−997.808	+	576.085i	−1.31118	+	0.757010i	−0.982292	−	0.187358i	$-0.940007\pi$
$761$	−997.808	+	576.085i	−1.31118	+	0.757010i	−0.328889	+	0.944369i	$0.606674\pi$
$762$		0			0
$763$	26.0653	−	45.1464i	0.0341616	−	0.0591696i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	330.426	+	190.771i	0.430803	+	0.248724i
$768$		0			0
$769$	−253.059	−	438.311i	−0.329076	−	0.569976i	0.653253	−	0.757140i	$-0.273404\pi$
$769$	−253.059	−	438.311i	−0.329076	−	0.569976i	−0.982329	+	0.187164i	$0.940070\pi$
$770$		0			0
$771$	−151.155	−	737.259i	−0.196050	−	0.956237i
$772$		0			0
$773$		−	374.490i		−	0.484463i	−0.970218	−	0.242232i	$-0.922121\pi$
$773$		−	374.490i		−	0.484463i	0.970218	−	0.242232i	$-0.0778794\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−15.1526	−	17.0749i	−0.0195014	−	0.0219754i
$778$		0			0
$779$	−61.7593	+	35.6567i	−0.0792802	+	0.0457725i
$780$		0			0
$781$	−360.874	+	625.053i	−0.462067	+	0.800324i
$782$		0			0
$783$	154.351	−	12.8501i	0.197128	−	0.0164114i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−428.278	−	741.800i	−0.544191	−	0.942567i	−0.998657	−	0.0518027i	$-0.983503\pi$
$787$	−428.278	−	741.800i	−0.544191	−	0.942567i	0.454466	−	0.890764i	$-0.349830\pi$
$788$		0			0
$789$	803.618	−	713.143i	1.01853	−	0.903857i
$790$		0			0
$791$		−	38.4776i		−	0.0486443i
$792$		0			0
$793$	2276.94			2.87129
$794$		0			0
$795$		0			0
$796$		0			0
$797$	199.154	−	114.982i	0.249880	−	0.144268i	−0.369829	−	0.929100i	$-0.620584\pi$
$797$	199.154	−	114.982i	0.249880	−	0.144268i	0.619709	+	0.784831i	$0.287251\pi$
$798$		0			0
$799$	−555.445	+	962.060i	−0.695176	+	1.20408i
$800$		0			0
$801$	151.553	−	202.384i	0.189204	−	0.252664i
$802$		0			0
$803$	−1952.35	−	1127.19i	−2.43132	−	1.40372i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1044.57	+	347.758i	1.29438	+	0.430926i
$808$		0			0
$809$			1140.95i			1.41032i	0.709046	+	0.705162i	$0.249126\pi$
$809$			1140.95i			1.41032i	−0.709046	+	0.705162i	$0.750874\pi$
$810$		0			0
$811$	−853.740			−1.05270			−0.526350	−	0.850268i	$-0.676440\pi$
$811$	−853.740			−1.05270			−0.526350	+	0.850268i	$0.676440\pi$
$812$		0			0
$813$	7.33684	−	22.0378i	0.00902441	−	0.0271068i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	41.5990	−	72.0515i	0.0509167	−	0.0881903i
$818$		0			0
$819$	−96.4757	−	72.2448i	−0.117797	−	0.0882110i
$820$		0			0
$821$	−635.528	−	366.922i	−0.774090	−	0.446921i	0.0602414	−	0.998184i	$-0.480813\pi$
$821$	−635.528	−	366.922i	−0.774090	−	0.446921i	−0.834332	+	0.551263i	$0.814146\pi$
$822$		0			0
$823$	167.403	+	289.950i	0.203406	+	0.352309i	0.949624	−	0.313393i	$-0.101466\pi$
$823$	167.403	+	289.950i	0.203406	+	0.352309i	−0.746218	+	0.665702i	$0.768132\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1023.56i			1.23768i	0.785517	+	0.618840i	$0.212397\pi$
$827$			1023.56i			1.23768i	−0.785517	+	0.618840i	$0.787603\pi$
$828$		0			0
$829$	1381.98			1.66705			0.833525	−	0.552482i	$-0.186319\pi$
$829$	1381.98			1.66705			0.833525	+	0.552482i	$0.186319\pi$
$830$		0			0
$831$	−202.976	−	228.727i	−0.244255	−	0.275243i
$832$		0			0
$833$	−686.951	+	396.611i	−0.824671	+	0.476124i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−655.786	−	309.162i	−0.783496	−	0.369369i
$838$		0			0
$839$	−1051.34	−	606.989i	−1.25308	−	0.723467i	−0.281362	−	0.959602i	$-0.590786\pi$
$839$	−1051.34	−	606.989i	−1.25308	−	0.723467i	−0.971720	+	0.236134i	$0.924119\pi$
$840$		0			0
$841$	−404.046	−	699.829i	−0.480436	−	0.832139i
$842$		0			0
$843$	−407.485	+	361.608i	−0.483375	+	0.428954i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	172.120			0.203212
$848$		0			0
$849$	−787.400	+	161.435i	−0.927444	+	0.190147i
$850$		0			0
$851$	−339.126	+	195.795i	−0.398503	+	0.230076i
$852$		0			0
$853$	−50.4087	+	87.3104i	−0.0590958	+	0.102357i	−0.894060	−	0.447948i	$-0.852155\pi$
$853$	−50.4087	+	87.3104i	−0.0590958	+	0.102357i	0.834964	+	0.550305i	$0.185488\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	119.311	+	68.8840i	0.139219	+	0.0803780i	0.567992	−	0.823034i	$-0.307721\pi$
$857$	119.311	+	68.8840i	0.139219	+	0.0803780i	−0.428773	+	0.903412i	$0.641054\pi$
$858$		0			0
$859$	193.732	+	335.554i	0.225532	+	0.390634i	0.956479	−	0.291801i	$-0.0942545\pi$
$859$	193.732	+	335.554i	0.225532	+	0.390634i	−0.730947	+	0.682435i	$0.760921\pi$
$860$		0			0
$861$	−55.6098	−	18.5136i	−0.0645875	−	0.0215025i
$862$		0			0
$863$		−	1033.60i		−	1.19768i	−0.800868	−	0.598841i	$-0.795628\pi$
$863$		−	1033.60i		−	1.19768i	0.800868	−	0.598841i	$-0.204372\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	20.9459	−	62.9157i	0.0241591	−	0.0725672i
$868$		0			0
$869$	282.554	−	163.133i	0.325148	−	0.187724i
$870$		0			0
$871$	1069.85	−	1853.04i	1.22830	−	2.12748i
$872$		0			0
$873$	78.0194	−	33.3952i	0.0893693	−	0.0382534i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	128.624	+	222.783i	0.146663	+	0.254029i	0.929992	−	0.367579i	$-0.119813\pi$
$877$	128.624	+	222.783i	0.146663	+	0.254029i	−0.783329	+	0.621608i	$0.786480\pi$
$878$		0			0
$879$	−162.225	−	791.254i	−0.184556	−	0.900176i
$880$		0			0
$881$			861.458i			0.977819i	0.872335	+	0.488909i	$0.162605\pi$
$881$			861.458i			0.977819i	−0.872335	+	0.488909i	$0.837395\pi$
$882$		0			0
$883$	1059.68			1.20009			0.600045	−	0.799967i	$-0.295150\pi$
$883$	1059.68			1.20009			0.600045	+	0.799967i	$0.295150\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−1119.29	+	646.220i	−1.26188	+	0.728546i	−0.973438	−	0.228952i	$-0.926470\pi$
$887$	−1119.29	+	646.220i	−1.26188	+	0.728546i	−0.288440	+	0.957498i	$0.593137\pi$
$888$		0			0
$889$	−26.2942	+	45.5429i	−0.0295773	+	0.0512294i
$890$		0			0
$891$	−372.106	+	1531.72i	−0.417628	+	1.71910i
$892$		0			0
$893$	−143.573	−	82.8921i	−0.160776	−	0.0928243i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−1546.36	+	1372.26i	−1.72392	+	1.52984i
$898$		0			0
$899$		−	154.037i		−	0.171342i
$900$		0			0
$901$	605.643			0.672190
$902$		0			0
$903$	66.9848	−	13.7334i	0.0741803	−	0.0152086i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	152.215	−	263.644i	0.167823	−	0.290677i	−0.769831	−	0.638247i	$-0.779660\pi$
$907$	152.215	−	263.644i	0.167823	−	0.290677i	0.937654	+	0.347570i	$0.112993\pi$
$908$		0			0
$909$	−331.927	−	775.465i	−0.365157	−	0.853097i
$910$		0			0
$911$	−219.187	−	126.548i	−0.240601	−	0.138911i	0.374852	−	0.927085i	$-0.377693\pi$
$911$	−219.187	−	126.548i	−0.240601	−	0.138911i	−0.615453	+	0.788174i	$0.711027\pi$
$912$		0			0
$913$	879.790	+	1523.84i	0.963626	+	1.66905i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	91.3221i		−	0.0995879i
$918$		0			0
$919$	782.852			0.851852			0.425926	−	0.904758i	$-0.359948\pi$
$919$	782.852			0.851852			0.425926	+	0.904758i	$0.359948\pi$
$920$		0			0
$921$	−388.151	+	1165.90i	−0.421445	+	1.26590i
$922$		0			0
$923$	−644.004	+	371.816i	−0.697729	+	0.402834i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−108.860	+	909.240i	−0.117432	+	0.980842i
$928$		0			0
$929$	−219.262	−	126.591i	−0.236020	−	0.136266i	0.377326	−	0.926080i	$-0.376844\pi$
$929$	−219.262	−	126.591i	−0.236020	−	0.136266i	−0.613346	+	0.789814i	$0.710177\pi$
$930$		0			0
$931$	−59.1885	−	102.517i	−0.0635752	−	0.110115i
$932$		0			0
$933$	−14.5345	−	70.8923i	−0.0155783	−	0.0759832i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	578.052			0.616918			0.308459	−	0.951238i	$-0.400187\pi$
$937$	578.052			0.616918			0.308459	+	0.951238i	$0.400187\pi$
$938$		0			0
$939$	866.595	+	976.538i	0.922891	+	1.03998i
$940$		0			0
$941$	665.941	−	384.481i	0.707695	−	0.408588i	−0.102512	−	0.994732i	$-0.532688\pi$
$941$	665.941	−	384.481i	0.707695	−	0.408588i	0.810207	+	0.586144i	$0.199355\pi$
$942$		0			0
$943$	−502.684	+	870.674i	−0.533069	+	0.923302i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	20.2585	+	11.6962i	0.0213923	+	0.0123508i	0.510658	−	0.859784i	$-0.329402\pi$
$947$	20.2585	+	11.6962i	0.0213923	+	0.0123508i	−0.489266	+	0.872135i	$0.662735\pi$
$948$		0			0
$949$	−1161.37	−	2011.54i	−1.22378	−	2.11965i
$950$		0			0
$951$	881.502	−	782.258i	0.926921	−	0.822564i
$952$		0			0
$953$		−	1230.20i		−	1.29087i	−0.763814	−	0.645437i	$-0.776675\pi$
$953$		−	1230.20i		−	1.29087i	0.763814	−	0.645437i	$-0.223325\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−328.073	+	67.2622i	−0.342814	+	0.0702845i
$958$		0			0
$959$	−35.9860	+	20.7765i	−0.0375245	+	0.0216648i
$960$		0			0
$961$	119.981	−	207.814i	0.124851	−	0.216247i
$962$		0			0
$963$	−263.228	+	351.515i	−0.273342	+	0.365021i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−511.926	−	886.681i	−0.529396	−	0.916940i	−0.999412	−	0.0342828i	$-0.989085\pi$
$967$	−511.926	−	886.681i	−0.529396	−	0.916940i	0.470016	−	0.882658i	$-0.344248\pi$
$968$		0			0
$969$	−113.373	−	37.7443i	−0.117000	−	0.0389518i
$970$		0			0
$971$			180.852i			0.186253i	0.995654	+	0.0931267i	$0.0296862\pi$
$971$			180.852i			0.186253i	−0.995654	+	0.0931267i	$0.970314\pi$
$972$		0			0
$973$	−114.735			−0.117918
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1505.83	−	869.389i	1.54128	−	0.889856i	0.542516	−	0.840045i	$-0.317472\pi$
$977$	1505.83	−	869.389i	1.54128	−	0.889856i	0.998759	−	0.0498105i	$-0.0158617\pi$
$978$		0			0
$979$	−273.348	+	473.452i	−0.279211	+	0.483608i
$980$		0			0
$981$	−562.263	−	421.045i	−0.573153	−	0.429199i
$982$		0			0
$983$	−600.846	−	346.899i	−0.611237	−	0.352898i	0.162212	−	0.986756i	$-0.448137\pi$
$983$	−600.846	−	346.899i	−0.611237	−	0.352898i	−0.773450	+	0.633858i	$0.781470\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−27.3658	−	133.477i	−0.0277263	−	0.135235i
$988$		0			0
$989$		−	1172.91i		−	1.18596i
$990$		0			0
$991$	−587.142			−0.592474			−0.296237	−	0.955114i	$-0.595732\pi$
$991$	−587.142			−0.592474			−0.296237	+	0.955114i	$0.595732\pi$
$992$		0			0
$993$	757.628	+	853.746i	0.762969	+	0.859765i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	2.12093	−	3.67355i	0.00212731	−	0.00368461i	−0.864960	−	0.501841i	$-0.832656\pi$
$997$	2.12093	−	3.67355i	0.00212731	−	0.00368461i	0.867087	+	0.498157i	$0.165990\pi$
$998$		0			0
$999$	−252.718	+	175.376i	−0.252971	+	0.175551i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.f.101.8		24
3.2	odd	2		2700.3.p.f.1601.7		24
5.2	odd	4		180.3.t.a.29.2	✓	24
5.3	odd	4		180.3.t.a.29.11	yes	24
5.4	even	2	inner	900.3.p.f.101.5		24
9.4	even	3		2700.3.p.f.2501.7		24
9.5	odd	6	inner	900.3.p.f.401.8		24
15.2	even	4		540.3.t.a.89.12		24
15.8	even	4		540.3.t.a.89.8		24
15.14	odd	2		2700.3.p.f.1601.6		24
45.2	even	12		1620.3.b.b.809.8		24
45.4	even	6		2700.3.p.f.2501.6		24
45.7	odd	12		1620.3.b.b.809.17		24
45.13	odd	12		540.3.t.a.449.12		24
45.14	odd	6	inner	900.3.p.f.401.5		24
45.22	odd	12		540.3.t.a.449.8		24
45.23	even	12		180.3.t.a.149.2	yes	24
45.32	even	12		180.3.t.a.149.11	yes	24
45.38	even	12		1620.3.b.b.809.18		24
45.43	odd	12		1620.3.b.b.809.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.t.a.29.2	✓	24	5.2	odd	4
180.3.t.a.29.11	yes	24	5.3	odd	4
180.3.t.a.149.2	yes	24	45.23	even	12
180.3.t.a.149.11	yes	24	45.32	even	12
540.3.t.a.89.8		24	15.8	even	4
540.3.t.a.89.12		24	15.2	even	4
540.3.t.a.449.8		24	45.22	odd	12
540.3.t.a.449.12		24	45.13	odd	12
900.3.p.f.101.5		24	5.4	even	2	inner
900.3.p.f.101.8		24	1.1	even	1	trivial
900.3.p.f.401.5		24	45.14	odd	6	inner
900.3.p.f.401.8		24	9.5	odd	6	inner
1620.3.b.b.809.7		24	45.43	odd	12
1620.3.b.b.809.8		24	45.2	even	12
1620.3.b.b.809.17		24	45.7	odd	12
1620.3.b.b.809.18		24	45.38	even	12
2700.3.p.f.1601.6		24	15.14	odd	2
2700.3.p.f.1601.7		24	3.2	odd	2
2700.3.p.f.2501.6		24	45.4	even	6
2700.3.p.f.2501.7		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)

\(f(q)\)	\(=\)	\(q+(0.947625 - 2.84640i) q^{3} +(0.333962 - 0.578439i) q^{7} +(-7.20401 - 5.39464i) q^{9} +O(q^{10})\)	\(q+(0.947625 - 2.84640i) q^{3} +(0.333962 - 0.578439i) q^{7} +(-7.20401 - 5.39464i) q^{9} +(16.8529 + 9.73004i) q^{11} +(10.0251 + 17.3639i) q^{13} +16.3370i q^{17} -2.43805 q^{19} +(-1.33000 - 1.49873i) q^{21} +(-29.7665 + 17.1857i) q^{23} +(-22.1820 + 15.3934i) q^{27} +(-4.96794 - 2.86824i) q^{29} +(13.4261 + 23.2546i) q^{31} +(43.6659 - 38.7498i) q^{33} +11.3929 q^{37} +(58.9246 - 12.0809i) q^{39} +(25.3314 - 14.6251i) q^{41} +(-17.0624 + 29.5529i) q^{43} +(58.8885 + 33.9993i) q^{47} +(24.2769 + 42.0489i) q^{49} +(46.5016 + 15.4813i) q^{51} -37.0720i q^{53} +(-2.31036 + 6.93968i) q^{57} +(16.4800 - 9.51473i) q^{59} +(56.7812 - 98.3479i) q^{61} +(-5.52634 + 2.36548i) q^{63} +(-53.3588 - 92.4202i) q^{67} +(20.7099 + 101.013i) q^{69} +37.0887i q^{71} -115.846 q^{73} +(11.2565 - 6.49893i) q^{77} +(8.38293 - 14.5197i) q^{79} +(22.7956 + 77.7262i) q^{81} +(78.3060 + 45.2100i) q^{83} +(-12.8719 + 11.4227i) q^{87} +28.0932i q^{89} +13.3919 q^{91} +(78.9149 - 16.1793i) q^{93} +(-4.71479 + 8.16625i) q^{97} +(-68.9186 - 161.011i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9}+O(q^{10}) \) 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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