LMFDB - Embedded newform 900.3.p.f.401.8

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			401.8
Character	$\chi$	$=$	900.401
Dual form			900.3.p.f.101.8

$q$-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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

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

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
$3$	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	0.888894	−	0.458114i	$-0.151475\pi$
$7$	0.333962	+	0.578439i	0.0477088	+	0.0826342i	−0.841185	+	0.540748i	$0.818141\pi$
$8$		0			0
$9$	−7.20401	+	5.39464i	−0.800446	+	0.599405i
$10$		0			0
$11$	16.8529	−	9.73004i	1.53208	−	0.884549i	0.532819	−	0.846230i	$-0.321133\pi$
$11$	16.8529	−	9.73004i	1.53208	−	0.884549i	0.999266	−	0.0383196i	$-0.0122005\pi$
$12$		0			0
$13$	10.0251	−	17.3639i	0.771158	−	1.33568i	−0.165771	−	0.986164i	$-0.553011\pi$
$13$	10.0251	−	17.3639i	0.771158	−	1.33568i	0.936929	−	0.349520i	$-0.113655\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	16.3370i		−	0.960998i	−0.876995	−	0.480499i	$-0.840456\pi$
$17$		−	16.3370i		−	0.960998i	0.876995	−	0.480499i	$-0.159544\pi$
$18$		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	−0.314800	−	0.949158i	$-0.601937\pi$
$23$	−29.7665	−	17.1857i	−1.29419	−	0.747203i	−0.979395	+	0.201955i	$0.935271\pi$
$24$		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	−0.583203	−	0.812327i	$-0.698201\pi$
$29$	−4.96794	+	2.86824i	−0.171308	+	0.0989048i	0.411894	+	0.911232i	$0.364867\pi$
$30$		0			0
$31$	13.4261	−	23.2546i	0.433099	−	0.750149i	−0.564039	−	0.825748i	$-0.690753\pi$
$31$	13.4261	−	23.2546i	0.433099	−	0.750149i	0.997138	+	0.0755984i	$0.0240867\pi$
$32$		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	0.776027	−	0.630700i	$-0.217232\pi$
$41$	25.3314	+	14.6251i	0.617839	+	0.356709i	−0.158188	+	0.987409i	$0.550565\pi$
$42$		0			0
$43$	−17.0624	−	29.5529i	−0.396799	−	0.687276i	0.596530	−	0.802591i	$-0.296546\pi$
$43$	−17.0624	−	29.5529i	−0.396799	−	0.687276i	−0.993329	+	0.115315i	$0.963212\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	58.8885	−	33.9993i	1.25295	−	0.723389i	0.281254	−	0.959633i	$-0.409250\pi$
$47$	58.8885	−	33.9993i	1.25295	−	0.723389i	0.971694	+	0.236244i	$0.0759165\pi$
$48$		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	$0.113729\pi$
$53$			37.0720i			0.699471i	−0.936848	+	0.349736i	$0.886271\pi$
$54$		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	0.633116	−	0.774057i	$-0.281775\pi$
$59$	16.4800	+	9.51473i	0.279322	+	0.161267i	−0.353794	+	0.935323i	$0.615109\pi$
$60$		0			0
$61$	56.7812	+	98.3479i	0.930839	+	1.61226i	0.781891	+	0.623415i	$0.214255\pi$
$61$	56.7812	+	98.3479i	0.930839	+	1.61226i	0.148948	+	0.988845i	$0.452411\pi$
$62$		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	0.125545	+	0.992088i	$0.459932\pi$
$67$	−53.3588	+	92.4202i	−0.796401	+	1.37941i	−0.921946	+	0.387318i	$0.873401\pi$
$68$		0			0
$69$	20.7099	−	101.013i	0.300144	−	1.46396i
$70$		0			0
$71$		−	37.0887i		−	0.522376i	−0.965288	−	0.261188i	$-0.915886\pi$
$71$		−	37.0887i		−	0.522376i	0.965288	−	0.261188i	$-0.0841142\pi$
$72$		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	0.914192	−	0.405280i	$-0.132826\pi$
$79$	8.38293	+	14.5197i	0.106113	+	0.183793i	−0.808079	+	0.589074i	$0.799493\pi$
$80$		0			0
$81$	22.7956	−	77.7262i	0.281427	−	0.959583i
$82$		0			0
$83$	78.3060	−	45.2100i	0.943446	−	0.544699i	0.0524070	−	0.998626i	$-0.483311\pi$
$83$	78.3060	−	45.2100i	0.943446	−	0.544699i	0.891039	+	0.453927i	$0.149977\pi$
$84$		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	$-0.949551\pi$
$89$		−	28.0932i		−	0.315654i	0.987467	−	0.157827i	$-0.0504488\pi$
$90$		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	0.840699	−	0.541503i	$-0.182145\pi$
$97$	−4.71479	−	8.16625i	−0.0486061	−	0.0841882i	−0.889305	+	0.457315i	$0.848811\pi$
$98$		0			0
$99$	−68.9186	+	161.011i	−0.696147	+	1.62637i
$100$		0			0
$101$	81.1675	−	46.8621i	0.803639	−	0.463981i	−0.0411032	−	0.999155i	$-0.513087\pi$
$101$	81.1675	−	46.8621i	0.803639	−	0.463981i	0.844742	+	0.535174i	$0.179754\pi$
$102$		0			0
$103$	−50.8741	+	88.1165i	−0.493923	+	0.855500i	−0.999975	−	0.00700275i	$-0.997771\pi$
$103$	−50.8741	+	88.1165i	−0.493923	+	0.855500i	0.506052	+	0.862503i	$0.331104\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			48.7944i			0.456022i	0.973659	+	0.228011i	$0.0732223\pi$
$107$			48.7944i			0.456022i	−0.973659	+	0.228011i	$0.926778\pi$
$108$		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	0.704235	−	0.709967i	$-0.251290\pi$
$113$	49.8898	+	28.8039i	0.441503	+	0.254902i	−0.262732	+	0.964869i	$0.584624\pi$
$114$		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	0.878455	−	0.477825i	$-0.158575\pi$
$131$	118.408	+	68.3627i	0.903875	+	0.521852i	0.0254194	+	0.999677i	$0.491908\pi$
$132$		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	−0.683574	−	0.729881i	$-0.739575\pi$
$137$	−53.8775	+	31.1062i	−0.393266	+	0.227052i	0.290308	+	0.956933i	$0.406242\pi$
$138$		0			0
$139$	−85.8890	+	148.764i	−0.617907	+	1.07025i	0.371960	+	0.928249i	$0.378686\pi$
$139$	−85.8890	+	148.764i	−0.617907	+	1.07025i	−0.989867	+	0.141997i	$0.954648\pi$
$140$		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	0.761042	−	0.648703i	$-0.224688\pi$
$149$	86.3858	+	49.8748i	0.579770	+	0.334731i	−0.181272	+	0.983433i	$0.558021\pi$
$150$		0			0
$151$	−23.8819	−	41.3646i	−0.158158	−	0.273938i	0.776046	−	0.630676i	$-0.217222\pi$
$151$	−23.8819	−	41.3646i	−0.158158	−	0.273938i	−0.934204	+	0.356738i	$0.883889\pi$
$152$		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	−0.512334	−	0.858786i	$-0.671219\pi$
$157$	76.5474	−	132.584i	0.487563	−	0.844484i	0.999898	+	0.0143016i	$0.00455249\pi$
$158$		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	0.118842	−	0.992913i	$-0.462082\pi$
$167$	−113.832	−	65.7207i	−0.681626	−	0.393537i	−0.800467	+	0.599376i	$0.795415\pi$
$168$		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	0.170166	−	0.985415i	$-0.445570\pi$
$173$	191.795	−	110.733i	1.10864	−	0.640075i	0.938478	+	0.345340i	$0.112236\pi$
$174$		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	$-0.938678\pi$
$179$		−	68.5428i		−	0.382921i	0.981500	−	0.191460i	$-0.0613223\pi$
$180$		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	−0.965814	−	0.259236i	$-0.916529\pi$
$191$	−233.825	+	134.999i	−1.22422	+	0.706802i	−0.258402	+	0.966037i	$0.583196\pi$
$192$		0			0
$193$	−25.8488	+	44.7715i	−0.133932	+	0.231976i	−0.925189	−	0.379507i	$-0.876094\pi$
$193$	−25.8488	+	44.7715i	−0.133932	+	0.231976i	0.791257	+	0.611484i	$0.209427\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	293.145i		−	1.48805i	−0.668153	−	0.744024i	$-0.732915\pi$
$197$		−	293.145i		−	1.48805i	0.668153	−	0.744024i	$-0.267085\pi$
$198$		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	0.320433	+	0.947271i	$0.396172\pi$
$211$	−139.290	+	241.258i	−0.660144	+	1.14340i	−0.980577	+	0.196132i	$0.937162\pi$
$212$		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	0.945053	−	0.326918i	$-0.106010\pi$
$223$	42.2379	+	73.1581i	0.189407	+	0.328063i	−0.755645	+	0.654981i	$0.772677\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−21.5888	+	12.4643i	−0.0951049	+	0.0549089i	−0.546798	−	0.837264i	$-0.684153\pi$
$227$	−21.5888	+	12.4643i	−0.0951049	+	0.0549089i	0.451693	+	0.892173i	$0.350820\pi$
$228$		0			0
$229$	−132.591	+	229.654i	−0.578998	+	1.00285i	0.416596	+	0.909092i	$0.363223\pi$
$229$	−132.591	+	229.654i	−0.578998	+	1.00285i	−0.995595	+	0.0937628i	$0.970110\pi$
$230$		0			0
$231$	−7.83165	+	38.1990i	−0.0339032	+	0.165364i
$232$		0			0
$233$		−	290.507i		−	1.24681i	−0.781899	−	0.623405i	$-0.785749\pi$
$233$		−	290.507i		−	1.24681i	0.781899	−	0.623405i	$-0.214251\pi$
$234$		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	0.680934	−	0.732344i	$-0.261574\pi$
$239$	92.5343	+	53.4247i	0.387173	+	0.223534i	−0.293762	+	0.955879i	$0.594907\pi$
$240$		0			0
$241$	62.9953	+	109.111i	0.261391	+	0.452743i	0.966612	−	0.256245i	$-0.0824854\pi$
$241$	62.9953	+	109.111i	0.261391	+	0.452743i	−0.705221	+	0.708988i	$0.749152\pi$
$242$		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	$0.131669\pi$
$251$			201.781i			0.803908i	−0.915660	+	0.401954i	$0.868331\pi$
$252$		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	0.859080	−	0.511842i	$-0.171037\pi$
$257$	217.255	+	125.432i	0.845351	+	0.488064i	−0.0137283	+	0.999906i	$0.504370\pi$
$258$		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	0.223453	−	0.974715i	$-0.428267\pi$
$263$	310.158	−	179.070i	1.17931	−	0.680873i	0.955854	+	0.293841i	$0.0949338\pi$
$264$		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	$-0.761060\pi$
$269$		−	366.978i		−	1.36423i	0.731245	−	0.682115i	$-0.238940\pi$
$270$		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	0.943238	−	0.332117i	$-0.107763\pi$
$277$	50.9671	+	88.2776i	0.183997	+	0.318692i	−0.759241	+	0.650809i	$0.774430\pi$
$278$		0			0
$279$	28.7289	+	239.956i	0.102971	+	0.860056i
$280$		0			0
$281$	−157.270	+	90.7996i	−0.559678	+	0.323130i	−0.753016	−	0.658002i	$-0.771402\pi$
$281$	−157.270	+	90.7996i	−0.559678	+	0.323130i	0.193338	+	0.981132i	$0.438069\pi$
$282$		0			0
$283$	−133.963	+	232.031i	−0.473368	+	0.819897i	−0.999535	−	0.0304839i	$-0.990295\pi$
$283$	−133.963	+	232.031i	−0.473368	+	0.819897i	0.526167	+	0.850381i	$0.323628\pi$
$284$		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	0.841997	−	0.539482i	$-0.181380\pi$
$293$	233.167	+	134.619i	0.795791	+	0.459450i	−0.0462064	+	0.998932i	$0.514713\pi$
$294$		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	0.533210	−	0.845983i	$-0.320986\pi$
$311$	20.8905	+	12.0612i	0.0671722	+	0.0387819i	−0.466038	+	0.884765i	$0.654319\pi$
$312$		0			0
$313$	−217.601	−	376.897i	−0.695212	−	1.20414i	−0.970109	−	0.242669i	$-0.921977\pi$
$313$	−217.601	−	376.897i	−0.695212	−	1.20414i	0.274897	−	0.961474i	$-0.411356\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	340.217	−	196.425i	1.07324	−	0.619636i	0.144175	−	0.989552i	$-0.453947\pi$
$317$	340.217	−	196.425i	1.07324	−	0.619636i	0.929065	+	0.369916i	$0.120614\pi$
$318$		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	−0.996070	−	0.0885746i	$-0.971769\pi$
$331$	−190.240	−	329.505i	−0.574743	−	0.995483i	0.421327	−	0.906909i	$-0.361565\pi$
$332$		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	−0.189525	+	0.981876i	$0.560695\pi$
$337$	−318.496	+	551.651i	−0.945092	+	1.63695i	−0.755567	+	0.655072i	$0.772638\pi$
$338$		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	0.363111	−	0.931746i	$-0.381715\pi$
$347$	−91.0005	−	52.5392i	−0.262249	−	0.151410i	−0.625360	+	0.780336i	$0.715048\pi$
$348$		0			0
$349$	−173.224	−	300.033i	−0.496344	−	0.859693i	0.503647	−	0.863910i	$-0.331991\pi$
$349$	−173.224	−	300.033i	−0.496344	−	0.859693i	−0.999991	+	0.00421630i	$0.998658\pi$
$350$		0			0
$351$	−489.666	+	230.847i	−1.39506	+	0.657683i
$352$		0			0
$353$	−186.075	+	107.430i	−0.527124	+	0.304335i	−0.739845	−	0.672778i	$-0.765101\pi$
$353$	−186.075	+	107.430i	−0.527124	+	0.304335i	0.212720	+	0.977113i	$0.431768\pi$
$354$		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	$0.0996719\pi$
$359$			221.170i			0.616073i	−0.951375	+	0.308037i	$0.900328\pi$
$360$		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	0.987176	+	0.159633i	$0.0510310\pi$
$367$	231.883	+	401.633i	0.631834	+	1.09437i	−0.355342	+	0.934736i	$0.615636\pi$
$368$		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	−0.821475	−	0.570244i	$-0.806849\pi$
$373$	30.9994	−	53.6925i	0.0831083	−	0.143948i	0.904584	+	0.426296i	$0.140182\pi$
$374$		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	−0.186027	−	0.982545i	$-0.559561\pi$
$383$	−432.771	−	249.860i	−1.12995	−	0.652377i	−0.943922	+	0.330168i	$0.892895\pi$
$384$		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	−0.384155	−	0.923269i	$-0.625507\pi$
$389$	86.8798	−	50.1601i	0.223341	−	0.128946i	0.607496	+	0.794322i	$0.292174\pi$
$390$		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	0.993647	+	0.112540i	$0.0358986\pi$
$401$	636.761	+	367.634i	1.58793	+	0.916794i	0.594286	+	0.804254i	$0.297435\pi$
$402$		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	0.166836	−	0.985985i	$-0.446645\pi$
$409$	383.358	−	663.996i	0.937306	−	1.62346i	0.770470	−	0.637476i	$-0.220022\pi$
$410$		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	0.844651	−	0.535317i	$-0.179808\pi$
$419$	336.616	+	194.345i	0.803379	+	0.463831i	−0.0412725	+	0.999148i	$0.513141\pi$
$420$		0			0
$421$	66.7729	+	115.654i	0.158605	+	0.274713i	0.934366	−	0.356315i	$-0.115967\pi$
$421$	66.7729	+	115.654i	0.158605	+	0.274713i	−0.775761	+	0.631027i	$0.782634\pi$
$422$		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	$-0.998367\pi$
$431$		−	4.42143i		−	0.0102585i	0.999987	−	0.00512927i	$-0.00163270\pi$
$432$		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	0.817000	+	0.576638i	$0.195636\pi$
$439$	398.561	+	690.327i	0.907883	+	1.57250i	0.0908834	+	0.995862i	$0.471031\pi$
$440$		0			0
$441$	51.9474	+	433.886i	0.117795	+	0.983869i
$442$		0			0
$443$	−44.3069	+	25.5806i	−0.100016	+	0.0577440i	−0.549173	−	0.835708i	$-0.685057\pi$
$443$	−44.3069	+	25.5806i	−0.100016	+	0.0577440i	0.449158	+	0.893452i	$0.351724\pi$
$444$		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	$-0.848941\pi$
$449$		−	410.343i		−	0.913904i	0.889491	−	0.456952i	$-0.151059\pi$
$450$		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	−0.984182	−	0.177162i	$-0.943308\pi$
$457$	−295.002	−	510.958i	−0.645518	−	1.11807i	0.338664	−	0.940907i	$-0.390025\pi$
$458$		0			0
$459$	−251.482	+	362.387i	−0.547891	+	0.789514i
$460$		0			0
$461$	−143.139	+	82.6413i	−0.310497	+	0.179265i	−0.647149	−	0.762364i	$-0.724039\pi$
$461$	−143.139	+	82.6413i	−0.310497	+	0.179265i	0.336652	+	0.941629i	$0.390705\pi$
$462$		0			0
$463$	1.68648	−	2.92107i	0.00364251	−	0.00630902i	−0.864198	−	0.503151i	$-0.832174\pi$
$463$	1.68648	−	2.92107i	0.00364251	−	0.00630902i	0.867841	+	0.496842i	$0.165507\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	553.128i		−	1.18443i	−0.805781	−	0.592214i	$-0.798254\pi$
$467$		−	553.128i		−	1.18443i	0.805781	−	0.592214i	$-0.201746\pi$
$468$		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	−0.749860	−	0.661596i	$-0.769879\pi$
$479$	−264.327	+	152.609i	−0.551831	+	0.318600i	0.198029	+	0.980196i	$0.436546\pi$
$480$		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	−0.0663453	−	0.997797i	$-0.521134\pi$
$491$	−473.145	−	273.170i	−0.963635	−	0.556355i	−0.897290	+	0.441442i	$0.854467\pi$
$492$		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	−0.329438	−	0.944177i	$-0.606859\pi$
$499$	325.828	−	564.351i	0.652963	−	1.13096i	0.982400	−	0.186787i	$-0.0598075\pi$
$500$		0			0
$501$	79.1978	−	386.289i	0.158079	−	0.771036i
$502$		0			0
$503$			188.144i			0.374045i	0.982356	+	0.187022i	$0.0598837\pi$
$503$			188.144i			0.374045i	−0.982356	+	0.187022i	$0.940116\pi$
$504$		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	0.685474	−	0.728097i	$-0.259595\pi$
$509$	202.409	+	116.861i	0.397660	+	0.229589i	−0.287814	+	0.957686i	$0.592928\pi$
$510$		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	$0.144032\pi$
$521$			455.570i			0.874415i	−0.899361	+	0.437207i	$0.855968\pi$
$522$		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	0.854105	+	0.520101i	$0.174106\pi$
$547$	479.978	+	831.346i	0.877473	+	1.51983i	0.0233685	+	0.999727i	$0.492561\pi$
$548$		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	$0.260417\pi$
$557$			813.070i			1.45973i	−0.683591	+	0.729865i	$0.739583\pi$
$558$		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	0.938332	−	0.345735i	$-0.112370\pi$
$563$	623.851	+	360.180i	1.10808	+	0.639752i	0.169751	+	0.985487i	$0.445704\pi$
$564$		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	−0.943437	−	0.331551i	$-0.892428\pi$
$569$	−641.846	+	370.570i	−1.12802	+	0.651265i	−0.184587	+	0.982816i	$0.559095\pi$
$570$		0			0
$571$	69.9039	−	121.077i	0.122424	−	0.212044i	−0.798299	−	0.602261i	$-0.794267\pi$
$571$	69.9039	−	121.077i	0.122424	−	0.212044i	0.920723	+	0.390217i	$0.127600\pi$
$572$		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	−0.828814	−	0.559525i	$-0.810984\pi$
$587$	−445.332	+	257.113i	−0.758658	+	0.438011i	0.0701559	+	0.997536i	$0.477650\pi$
$588$		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	$0.0869413\pi$
$593$			319.924i			0.539501i	−0.962930	+	0.269751i	$0.913059\pi$
$594$		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	0.998536	−	0.0540973i	$-0.0172281\pi$
$599$	869.121	+	501.787i	1.45095	+	0.837709i	0.452418	+	0.891806i	$0.350561\pi$
$600$		0			0
$601$	41.6656	+	72.1669i	0.0693271	+	0.120078i	0.898605	−	0.438758i	$-0.144581\pi$
$601$	41.6656	+	72.1669i	0.0693271	+	0.120078i	−0.829278	+	0.558836i	$0.811248\pi$
$602$		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	−0.886149	−	0.463400i	$-0.846629\pi$
$607$	−25.3472	+	43.9026i	−0.0417581	+	0.0723272i	0.844391	+	0.535727i	$0.179963\pi$
$608$		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	0.720685	−	0.693263i	$-0.243827\pi$
$617$	296.558	+	171.218i	0.480645	+	0.277500i	−0.240040	+	0.970763i	$0.577161\pi$
$618$		0			0
$619$	272.901	+	472.679i	0.440875	+	0.763617i	0.997755	−	0.0669756i	$-0.0213350\pi$
$619$	272.901	+	472.679i	0.440875	+	0.763617i	−0.556880	+	0.830593i	$0.688002\pi$
$620$		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	0.159374	−	0.987218i	$-0.449052\pi$
$641$	701.265	−	404.875i	1.09402	−	0.631631i	0.934643	+	0.355587i	$0.115719\pi$
$642$		0			0
$643$	−212.657	+	368.333i	−0.330726	+	0.572835i	−0.982654	−	0.185446i	$-0.940627\pi$
$643$	−212.657	+	368.333i	−0.330726	+	0.572835i	0.651928	+	0.758281i	$0.273960\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	782.663i		−	1.20968i	−0.796347	−	0.604840i	$-0.793237\pi$
$647$		−	782.663i		−	1.20968i	0.796347	−	0.604840i	$-0.206763\pi$
$648$		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	0.990126	−	0.140179i	$-0.0447678\pi$
$653$	890.555	+	514.162i	1.36379	+	0.787385i	0.373665	+	0.927564i	$0.378101\pi$
$654$		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	−0.314797	−	0.949159i	$-0.601936\pi$
$659$	230.519	−	133.090i	0.349801	−	0.201958i	0.664598	+	0.747201i	$0.268603\pi$
$660$		0			0
$661$	254.653	−	441.071i	0.385254	−	0.667279i	−0.606551	−	0.795045i	$-0.707447\pi$
$661$	254.653	−	441.071i	0.385254	−	0.667279i	0.991804	+	0.127766i	$0.0407806\pi$
$662$		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	0.994024	+	0.109164i	$0.0348174\pi$
$673$	398.114	+	689.553i	0.591551	+	1.02460i	−0.402473	+	0.915432i	$0.631849\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1094.70	+	632.023i	−1.61698	+	0.933565i	−0.629287	+	0.777173i	$0.716653\pi$
$677$	−1094.70	+	632.023i	−1.61698	+	0.933565i	−0.987695	+	0.156392i	$0.950014\pi$
$678$		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	$-0.938543\pi$
$683$		−	262.103i		−	0.383753i	0.981419	−	0.191876i	$-0.0614573\pi$
$684$		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	−0.998677	−	0.0514255i	$-0.983624\pi$
$691$	−375.817	−	650.934i	−0.543874	−	0.942018i	0.454803	−	0.890592i	$-0.349710\pi$
$692$		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	$0.146052\pi$
$701$			620.953i			0.885810i	−0.896569	+	0.442905i	$0.853948\pi$
$702$		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	0.687833	−	0.725869i	$-0.258562\pi$
$709$	−201.855	−	349.623i	−0.284704	−	0.493122i	−0.972537	+	0.232747i	$0.925229\pi$
$710$		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	$-0.929287\pi$
$719$		−	316.833i		−	0.440658i	0.975426	−	0.220329i	$-0.0707132\pi$
$720$		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	0.991547	−	0.129747i	$-0.0414166\pi$
$727$	278.738	+	482.789i	0.383409	+	0.664084i	−0.608138	+	0.793831i	$0.708083\pi$
$728$		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	−0.672462	−	0.740132i	$-0.734763\pi$
$733$	223.376	−	386.899i	0.304742	−	0.527829i	0.977204	+	0.212303i	$0.0680963\pi$
$734$		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	0.526308	−	0.850294i	$-0.323576\pi$
$743$	39.4427	+	22.7722i	0.0530857	+	0.0306490i	−0.473222	+	0.880943i	$0.656909\pi$
$744$		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	−0.871732	−	0.489983i	$-0.837003\pi$
$751$	−8.65769	+	14.9956i	−0.0115282	+	0.0199675i	0.860204	+	0.509951i	$0.170336\pi$
$752$		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	−0.328889	−	0.944369i	$-0.606674\pi$
$761$	−997.808	−	576.085i	−1.31118	−	0.757010i	−0.982292	+	0.187358i	$0.940007\pi$
$762$		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	−0.982329	−	0.187164i	$-0.940070\pi$
$769$	−253.059	+	438.311i	−0.329076	+	0.569976i	0.653253	+	0.757140i	$0.273404\pi$
$770$		0			0
$771$	−151.155	+	737.259i	−0.196050	+	0.956237i
$772$		0			0
$773$			374.490i			0.484463i	0.970218	+	0.242232i	$0.0778794\pi$
$773$			374.490i			0.484463i	−0.970218	+	0.242232i	$0.922121\pi$
$774$		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	0.454466	+	0.890764i	$0.349830\pi$
$787$	−428.278	+	741.800i	−0.544191	+	0.942567i	−0.998657	+	0.0518027i	$0.983503\pi$
$788$		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	0.619709	−	0.784831i	$-0.287251\pi$
$797$	199.154	+	114.982i	0.249880	+	0.144268i	−0.369829	+	0.929100i	$0.620584\pi$
$798$		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	$-0.750874\pi$
$809$		−	1140.95i		−	1.41032i	0.709046	−	0.705162i	$-0.249126\pi$
$810$		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	−0.834332	−	0.551263i	$-0.814146\pi$
$821$	−635.528	+	366.922i	−0.774090	+	0.446921i	0.0602414	+	0.998184i	$0.480813\pi$
$822$		0			0
$823$	167.403	−	289.950i	0.203406	−	0.352309i	−0.746218	−	0.665702i	$-0.768132\pi$
$823$	167.403	−	289.950i	0.203406	−	0.352309i	0.949624	+	0.313393i	$0.101466\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1023.56i		−	1.23768i	−0.785517	−	0.618840i	$-0.787603\pi$
$827$		−	1023.56i		−	1.23768i	0.785517	−	0.618840i	$-0.212397\pi$
$828$		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	−0.971720	−	0.236134i	$-0.924119\pi$
$839$	−1051.34	+	606.989i	−1.25308	+	0.723467i	−0.281362	+	0.959602i	$0.590786\pi$
$840$		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	0.834964	−	0.550305i	$-0.185488\pi$
$853$	−50.4087	−	87.3104i	−0.0590958	−	0.102357i	−0.894060	+	0.447948i	$0.852155\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	119.311	−	68.8840i	0.139219	−	0.0803780i	−0.428773	−	0.903412i	$-0.641054\pi$
$857$	119.311	−	68.8840i	0.139219	−	0.0803780i	0.567992	+	0.823034i	$0.307721\pi$
$858$		0			0
$859$	193.732	−	335.554i	0.225532	−	0.390634i	−0.730947	−	0.682435i	$-0.760921\pi$
$859$	193.732	−	335.554i	0.225532	−	0.390634i	0.956479	+	0.291801i	$0.0942545\pi$
$860$		0			0
$861$	−55.6098	+	18.5136i	−0.0645875	+	0.0215025i
$862$		0			0
$863$			1033.60i			1.19768i	0.800868	+	0.598841i	$0.204372\pi$
$863$			1033.60i			1.19768i	−0.800868	+	0.598841i	$0.795628\pi$
$864$		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	−0.783329	−	0.621608i	$-0.786480\pi$
$877$	128.624	−	222.783i	0.146663	−	0.254029i	0.929992	+	0.367579i	$0.119813\pi$
$878$		0			0
$879$	−162.225	+	791.254i	−0.184556	+	0.900176i
$880$		0			0
$881$		−	861.458i		−	0.977819i	−0.872335	−	0.488909i	$-0.837395\pi$
$881$		−	861.458i		−	0.977819i	0.872335	−	0.488909i	$-0.162605\pi$
$882$		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	−0.288440	−	0.957498i	$-0.593137\pi$
$887$	−1119.29	−	646.220i	−1.26188	−	0.728546i	−0.973438	+	0.228952i	$0.926470\pi$
$888$		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	0.937654	−	0.347570i	$-0.112993\pi$
$907$	152.215	+	263.644i	0.167823	+	0.290677i	−0.769831	+	0.638247i	$0.779660\pi$
$908$		0			0
$909$	−331.927	+	775.465i	−0.365157	+	0.853097i
$910$		0			0
$911$	−219.187	+	126.548i	−0.240601	+	0.138911i	−0.615453	−	0.788174i	$-0.711027\pi$
$911$	−219.187	+	126.548i	−0.240601	+	0.138911i	0.374852	+	0.927085i	$0.377693\pi$
$912$		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	−0.613346	−	0.789814i	$-0.710177\pi$
$929$	−219.262	+	126.591i	−0.236020	+	0.136266i	0.377326	+	0.926080i	$0.376844\pi$
$930$		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	0.810207	−	0.586144i	$-0.199355\pi$
$941$	665.941	+	384.481i	0.707695	+	0.408588i	−0.102512	+	0.994732i	$0.532688\pi$
$942$		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	−0.489266	−	0.872135i	$-0.662735\pi$
$947$	20.2585	−	11.6962i	0.0213923	−	0.0123508i	0.510658	+	0.859784i	$0.329402\pi$
$948$		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	$0.223325\pi$
$953$			1230.20i			1.29087i	−0.763814	+	0.645437i	$0.776675\pi$
$954$		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	0.470016	+	0.882658i	$0.344248\pi$
$967$	−511.926	+	886.681i	−0.529396	+	0.916940i	−0.999412	+	0.0342828i	$0.989085\pi$
$968$		0			0
$969$	−113.373	+	37.7443i	−0.117000	+	0.0389518i
$970$		0			0
$971$		−	180.852i		−	0.186253i	−0.995654	−	0.0931267i	$-0.970314\pi$
$971$		−	180.852i		−	0.186253i	0.995654	−	0.0931267i	$-0.0296862\pi$
$972$		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	0.998759	+	0.0498105i	$0.0158617\pi$
$977$	1505.83	+	869.389i	1.54128	+	0.889856i	0.542516	+	0.840045i	$0.317472\pi$
$978$		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	−0.773450	−	0.633858i	$-0.781470\pi$
$983$	−600.846	+	346.899i	−0.611237	+	0.352898i	0.162212	+	0.986756i	$0.448137\pi$
$984$		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	0.867087	−	0.498157i	$-0.165990\pi$
$997$	2.12093	+	3.67355i	0.00212731	+	0.00368461i	−0.864960	+	0.501841i	$0.832656\pi$
$998$		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.401.8		24
3.2	odd	2		2700.3.p.f.2501.7		24
5.2	odd	4		180.3.t.a.149.11	yes	24
5.3	odd	4		180.3.t.a.149.2	yes	24
5.4	even	2	inner	900.3.p.f.401.5		24
9.2	odd	6	inner	900.3.p.f.101.8		24
9.7	even	3		2700.3.p.f.1601.7		24
15.2	even	4		540.3.t.a.449.8		24
15.8	even	4		540.3.t.a.449.12		24
15.14	odd	2		2700.3.p.f.2501.6		24
45.2	even	12		180.3.t.a.29.2	✓	24
45.7	odd	12		540.3.t.a.89.12		24
45.13	odd	12		1620.3.b.b.809.18		24
45.22	odd	12		1620.3.b.b.809.8		24
45.23	even	12		1620.3.b.b.809.7		24
45.29	odd	6	inner	900.3.p.f.101.5		24
45.32	even	12		1620.3.b.b.809.17		24
45.34	even	6		2700.3.p.f.1601.6		24
45.38	even	12		180.3.t.a.29.11	yes	24
45.43	odd	12		540.3.t.a.89.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.t.a.29.2	✓	24	45.2	even	12
180.3.t.a.29.11	yes	24	45.38	even	12
180.3.t.a.149.2	yes	24	5.3	odd	4
180.3.t.a.149.11	yes	24	5.2	odd	4
540.3.t.a.89.8		24	45.43	odd	12
540.3.t.a.89.12		24	45.7	odd	12
540.3.t.a.449.8		24	15.2	even	4
540.3.t.a.449.12		24	15.8	even	4
900.3.p.f.101.5		24	45.29	odd	6	inner
900.3.p.f.101.8		24	9.2	odd	6	inner
900.3.p.f.401.5		24	5.4	even	2	inner
900.3.p.f.401.8		24	1.1	even	1	trivial
1620.3.b.b.809.7		24	45.23	even	12
1620.3.b.b.809.8		24	45.22	odd	12
1620.3.b.b.809.17		24	45.32	even	12
1620.3.b.b.809.18		24	45.13	odd	12
2700.3.p.f.1601.6		24	45.34	even	6
2700.3.p.f.1601.7		24	9.7	even	3
2700.3.p.f.2501.6		24	15.14	odd	2
2700.3.p.f.2501.7		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)

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

L-functions

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