LMFDB - Embedded newform 900.3.u.c.149.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,3,Mod(149,900)]

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, 5, 3]))

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

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

chi := DirichletCharacter("900.149");

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.u (of order $6$, degree $2$, not 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			149.3
Character	$\chi$	$=$	900.149
Dual form			900.3.u.c.749.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39478 + 2.65605i) q^{3} +(2.45229 - 1.41583i) q^{7} +(-5.10917 - 7.40921i) q^{9} +O(q^{10})$	\(q+(-1.39478 + 2.65605i) q^{3} +(2.45229 - 1.41583i) q^{7} +(-5.10917 - 7.40921i) q^{9} +(-0.949152 + 0.547993i) q^{11} +(3.63097 + 2.09634i) q^{13} +7.85770 q^{17} -13.3580 q^{19} +(0.340105 + 8.48818i) q^{21} +(12.3679 - 21.4218i) q^{23} +(26.8054 - 3.23598i) q^{27} +(2.43628 - 1.40659i) q^{29} +(12.0630 - 20.8937i) q^{31} +(-0.131636 - 3.28532i) q^{33} -49.9138i q^{37} +(-10.6324 + 6.72010i) q^{39} +(-18.9104 - 10.9179i) q^{41} +(42.4611 - 24.5149i) q^{43} +(33.8220 + 58.5815i) q^{47} +(-20.4908 + 35.4912i) q^{49} +(-10.9598 + 20.8704i) q^{51} +49.8418 q^{53} +(18.6315 - 35.4795i) q^{57} +(86.8838 + 50.1624i) q^{59} +(-41.5597 - 71.9835i) q^{61} +(-23.0194 - 10.9358i) q^{63} +(49.8405 + 28.7754i) q^{67} +(39.6468 + 62.7284i) q^{69} -14.2317i q^{71} +71.5532i q^{73} +(-1.55173 + 2.68768i) q^{77} +(54.4107 + 94.2421i) q^{79} +(-28.7927 + 75.7098i) q^{81} +(-40.2871 - 69.7793i) q^{83} +(0.337884 + 8.43276i) q^{87} +65.6139i q^{89} +11.8723 q^{91} +(38.6694 + 61.1820i) q^{93} +(134.102 - 77.4238i) q^{97} +(8.90957 + 4.23267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 52 q^{9}+O(q^{10}) $ 24 * q - 52 * q^9	$ 24 q - 52 q^{9} + 96 q^{11} - 144 q^{19} - 256 q^{21} - 300 q^{29} - 24 q^{31} - 80 q^{39} + 180 q^{41} - 96 q^{49} - 288 q^{51} - 96 q^{59} - 156 q^{61} + 300 q^{69} - 240 q^{79} + 868 q^{81} + 240 q^{91} + 240 q^{99}+O(q^{100}) $ 24 * q - 52 * q^9 + 96 * q^11 - 144 * q^19 - 256 * q^21 - 300 * q^29 - 24 * q^31 - 80 * q^39 + 180 * q^41 - 96 * q^49 - 288 * q^51 - 96 * q^59 - 156 * q^61 + 300 * q^69 - 240 * q^79 + 868 * q^81 + 240 * q^91 + 240 * 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
$3$	−1.39478	+	2.65605i	−0.464927	+	0.885349i
$3$	−1.39478	+	2.65605i	−0.464927	+	0.885349i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.45229	−	1.41583i	0.350327	−	0.202262i	−0.314502	−	0.949257i	$-0.601838\pi$
$7$	2.45229	−	1.41583i	0.350327	−	0.202262i	0.664829	+	0.746995i	$0.268504\pi$
$8$		0			0
$9$	−5.10917	−	7.40921i	−0.567686	−	0.823245i
$10$		0			0
$11$	−0.949152	+	0.547993i	−0.0862865	+	0.0498175i	−0.542522	−	0.840041i	$-0.682531\pi$
$11$	−0.949152	+	0.547993i	−0.0862865	+	0.0498175i	0.456236	+	0.889859i	$0.349197\pi$
$12$		0			0
$13$	3.63097	+	2.09634i	0.279306	+	0.161257i	0.633109	−	0.774063i	$-0.281778\pi$
$13$	3.63097	+	2.09634i	0.279306	+	0.161257i	−0.353803	+	0.935320i	$0.615112\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.85770			0.462218			0.231109	−	0.972928i	$-0.425765\pi$
$17$	7.85770			0.462218			0.231109	+	0.972928i	$0.425765\pi$
$18$		0			0
$19$	−13.3580			−0.703053			−0.351527	−	0.936178i	$-0.614337\pi$
$19$	−13.3580			−0.703053			−0.351527	+	0.936178i	$0.614337\pi$
$20$		0			0
$21$	0.340105	+	8.48818i	0.0161955	+	0.404199i
$22$		0			0
$23$	12.3679	−	21.4218i	0.537734	−	0.931383i	−0.461292	−	0.887249i	$-0.652614\pi$
$23$	12.3679	−	21.4218i	0.537734	−	0.931383i	0.999026	−	0.0441340i	$-0.0140529\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	26.8054	−	3.23598i	0.992792	−	0.119851i
$28$		0			0
$29$	2.43628	−	1.40659i	0.0840097	−	0.0485030i	−0.457407	−	0.889258i	$-0.651222\pi$
$29$	2.43628	−	1.40659i	0.0840097	−	0.0485030i	0.541416	+	0.840755i	$0.317888\pi$
$30$		0			0
$31$	12.0630	−	20.8937i	0.389128	−	0.673990i	−0.603204	−	0.797587i	$-0.706110\pi$
$31$	12.0630	−	20.8937i	0.389128	−	0.673990i	0.992333	+	0.123597i	$0.0394429\pi$
$32$		0			0
$33$	−0.131636	−	3.28532i	−0.00398898	−	0.0995552i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	49.9138i		−	1.34902i	−0.738264	−	0.674511i	$-0.764354\pi$
$37$		−	49.9138i		−	1.34902i	0.738264	−	0.674511i	$-0.235646\pi$
$38$		0			0
$39$	−10.6324	+	6.72010i	−0.272626	+	0.172310i
$40$		0			0
$41$	−18.9104	−	10.9179i	−0.461229	−	0.266291i	0.251332	−	0.967901i	$-0.419131\pi$
$41$	−18.9104	−	10.9179i	−0.461229	−	0.266291i	−0.712561	+	0.701610i	$0.752465\pi$
$42$		0			0
$43$	42.4611	−	24.5149i	0.987467	−	0.570114i	0.0829506	−	0.996554i	$-0.473566\pi$
$43$	42.4611	−	24.5149i	0.987467	−	0.570114i	0.904516	+	0.426439i	$0.140232\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	33.8220	+	58.5815i	0.719618	+	1.24641i	0.961151	+	0.276022i	$0.0890164\pi$
$47$	33.8220	+	58.5815i	0.719618	+	1.24641i	−0.241533	+	0.970393i	$0.577650\pi$
$48$		0			0
$49$	−20.4908	+	35.4912i	−0.418180	+	0.724310i
$50$		0			0
$51$	−10.9598	+	20.8704i	−0.214897	+	0.409224i
$52$		0			0
$53$	49.8418			0.940412			0.470206	−	0.882557i	$-0.344180\pi$
$53$	49.8418			0.940412			0.470206	+	0.882557i	$0.344180\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	18.6315	−	35.4795i	0.326869	−	0.622448i
$58$		0			0
$59$	86.8838	+	50.1624i	1.47261	+	0.850210i	0.999525	−	0.0308088i	$-0.00980829\pi$
$59$	86.8838	+	50.1624i	1.47261	+	0.850210i	0.473081	+	0.881019i	$0.343142\pi$
$60$		0			0
$61$	−41.5597	−	71.9835i	−0.681307	−	1.18006i	−0.974582	−	0.224030i	$-0.928079\pi$
$61$	−41.5597	−	71.9835i	−0.681307	−	1.18006i	0.293276	−	0.956028i	$-0.405255\pi$
$62$		0			0
$63$	−23.0194	−	10.9358i	−0.365387	−	0.173584i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	49.8405	+	28.7754i	0.743888	+	0.429484i	0.823481	−	0.567343i	$-0.192029\pi$
$67$	49.8405	+	28.7754i	0.743888	+	0.429484i	−0.0795931	+	0.996827i	$0.525362\pi$
$68$		0			0
$69$	39.6468	+	62.7284i	0.574592	+	0.909107i
$70$		0			0
$71$		−	14.2317i		−	0.200446i	−0.994965	−	0.100223i	$-0.968044\pi$
$71$		−	14.2317i		−	0.200446i	0.994965	−	0.100223i	$-0.0319556\pi$
$72$		0			0
$73$			71.5532i			0.980180i	0.871672	+	0.490090i	$0.163036\pi$
$73$			71.5532i			0.980180i	−0.871672	+	0.490090i	$0.836964\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.55173	+	2.68768i	−0.0201524	+	0.0349049i
$78$		0			0
$79$	54.4107	+	94.2421i	0.688743	+	1.19294i	0.972245	+	0.233966i	$0.0751704\pi$
$79$	54.4107	+	94.2421i	0.688743	+	1.19294i	−0.283502	+	0.958972i	$0.591496\pi$
$80$		0			0
$81$	−28.7927	+	75.7098i	−0.355466	+	0.934689i
$82$		0			0
$83$	−40.2871	−	69.7793i	−0.485387	−	0.840715i	0.514472	−	0.857507i	$-0.327988\pi$
$83$	−40.2871	−	69.7793i	−0.485387	−	0.840715i	−0.999859	+	0.0167923i	$0.994655\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	0.337884	+	8.43276i	0.00388373	+	0.0969283i
$88$		0			0
$89$			65.6139i			0.737235i	0.929581	+	0.368617i	$0.120169\pi$
$89$			65.6139i			0.737235i	−0.929581	+	0.368617i	$0.879831\pi$
$90$		0			0
$91$	11.8723			0.130465
$92$		0			0
$93$	38.6694	+	61.1820i	0.415800	+	0.657871i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	134.102	−	77.4238i	1.38249	−	0.798184i	0.390040	−	0.920798i	$-0.372461\pi$
$97$	134.102	−	77.4238i	1.38249	−	0.798184i	0.992454	+	0.122614i	$0.0391277\pi$
$98$		0			0
$99$	8.90957	+	4.23267i	0.0899957	+	0.0427543i
$100$		0			0
$101$	124.917	−	72.1209i	1.23680	−	0.714068i	0.268363	−	0.963318i	$-0.413517\pi$
$101$	124.917	−	72.1209i	1.23680	−	0.714068i	0.968439	+	0.249250i	$0.0801841\pi$
$102$		0			0
$103$	−17.5708	−	10.1445i	−0.170590	−	0.0984901i	0.412274	−	0.911060i	$-0.364735\pi$
$103$	−17.5708	−	10.1445i	−0.170590	−	0.0984901i	−0.582864	+	0.812570i	$0.698068\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	156.290			1.46065			0.730325	−	0.683100i	$-0.239369\pi$
$107$	156.290			1.46065			0.730325	+	0.683100i	$0.239369\pi$
$108$		0			0
$109$	−55.5439			−0.509577			−0.254788	−	0.966997i	$-0.582006\pi$
$109$	−55.5439			−0.509577			−0.254788	+	0.966997i	$0.582006\pi$
$110$		0			0
$111$	132.574	+	69.6189i	1.19436	+	0.627197i
$112$		0			0
$113$	−55.7238	+	96.5164i	−0.493131	+	0.854127i	−0.999969	−	0.00791409i	$-0.997481\pi$
$113$	−55.7238	+	96.5164i	−0.493131	+	0.854127i	0.506838	+	0.862041i	$0.330814\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−3.01902	−	37.6132i	−0.0258036	−	0.321481i
$118$		0			0
$119$	19.2694	−	11.1252i	0.161928	−	0.0934889i
$120$		0			0
$121$	−59.8994	+	103.749i	−0.495036	+	0.857428i
$122$		0			0
$123$	55.3743	−	34.9988i	0.450198	−	0.284543i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	144.448i		−	1.13739i	−0.822549	−	0.568694i	$-0.807449\pi$
$127$		−	144.448i		−	1.13739i	0.822549	−	0.568694i	$-0.192551\pi$
$128$		0			0
$129$	5.88886	+	146.972i	0.0456501	+	1.13931i
$130$		0			0
$131$	166.658	+	96.2201i	1.27220	+	0.734504i	0.975401	−	0.220436i	$-0.0707480\pi$
$131$	166.658	+	96.2201i	1.27220	+	0.734504i	0.296797	+	0.954940i	$0.404081\pi$
$132$		0			0
$133$	−32.7578	+	18.9127i	−0.246299	+	0.142201i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	16.4505	+	28.4931i	0.120077	+	0.207979i	0.919798	−	0.392393i	$-0.128353\pi$
$137$	16.4505	+	28.4931i	0.120077	+	0.207979i	−0.799721	+	0.600372i	$0.795019\pi$
$138$		0			0
$139$	80.1236	−	138.778i	0.576429	−	0.998404i	−0.419456	−	0.907776i	$-0.637779\pi$
$139$	80.1236	−	138.778i	0.576429	−	0.998404i	0.995885	−	0.0906285i	$-0.0288876\pi$
$140$		0			0
$141$	−202.770	+	8.12458i	−1.43808	+	0.0576211i
$142$		0			0
$143$	−4.59513			−0.0321338
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−65.6860	−	103.927i	−0.446844	−	0.706987i
$148$		0			0
$149$	−39.1186	−	22.5851i	−0.262541	−	0.151578i	0.362952	−	0.931808i	$-0.381769\pi$
$149$	−39.1186	−	22.5851i	−0.262541	−	0.151578i	−0.625493	+	0.780230i	$0.715102\pi$
$150$		0			0
$151$	−134.134	−	232.328i	−0.888307	−	1.53859i	−0.841875	−	0.539672i	$-0.818548\pi$
$151$	−134.134	−	232.328i	−0.888307	−	1.53859i	−0.0464318	−	0.998921i	$-0.514785\pi$
$152$		0			0
$153$	−40.1463	−	58.2193i	−0.262394	−	0.380519i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	180.403	+	104.156i	1.14906	+	0.663412i	0.948659	−	0.316302i	$-0.102441\pi$
$157$	180.403	+	104.156i	1.14906	+	0.663412i	0.200404	+	0.979713i	$0.435774\pi$
$158$		0			0
$159$	−69.5184	+	132.382i	−0.437223	+	0.832593i
$160$		0			0
$161$		−	70.0433i		−	0.435052i
$162$		0			0
$163$		−	24.6396i		−	0.151163i	−0.997140	−	0.0755815i	$-0.975919\pi$
$163$		−	24.6396i		−	0.151163i	0.997140	−	0.0755815i	$-0.0240813\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−44.6359	+	77.3116i	−0.267281	+	0.462944i	−0.968159	−	0.250337i	$-0.919458\pi$
$167$	−44.6359	+	77.3116i	−0.267281	+	0.462944i	0.700878	+	0.713281i	$0.252792\pi$
$168$		0			0
$169$	−75.7107	−	131.135i	−0.447992	−	0.775945i
$170$		0			0
$171$	68.2484	+	98.9723i	0.399113	+	0.578785i
$172$		0			0
$173$	30.5959	+	52.9937i	0.176855	+	0.306322i	0.940802	−	0.338958i	$-0.110074\pi$
$173$	30.5959	+	52.9937i	0.176855	+	0.306322i	−0.763947	+	0.645279i	$0.776741\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−254.418	+	160.802i	−1.43739	+	0.908485i
$178$		0			0
$179$		−	131.909i		−	0.736924i	−0.929643	−	0.368462i	$-0.879885\pi$
$179$		−	131.909i		−	0.736924i	0.929643	−	0.368462i	$-0.120115\pi$
$180$		0			0
$181$	−311.741			−1.72233			−0.861163	−	0.508328i	$-0.830264\pi$
$181$	−311.741			−1.72233			−0.861163	+	0.508328i	$0.830264\pi$
$182$		0			0
$183$	249.158	−	9.98329i	1.36152	−	0.0545535i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−7.45815	+	4.30596i	−0.0398832	+	0.0230265i
$188$		0			0
$189$	61.1530	−	45.8875i	0.323561	−	0.242791i
$190$		0			0
$191$	303.129	−	175.012i	1.58706	−	0.916291i	0.593274	−	0.805000i	$-0.297835\pi$
$191$	303.129	−	175.012i	1.58706	−	0.916291i	0.993788	−	0.111290i	$-0.0354983\pi$
$192$		0			0
$193$	−171.510	−	99.0214i	−0.888653	−	0.513064i	−0.0151517	−	0.999885i	$-0.504823\pi$
$193$	−171.510	−	99.0214i	−0.888653	−	0.513064i	−0.873502	+	0.486821i	$0.838156\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−32.5493			−0.165225			−0.0826124	−	0.996582i	$-0.526326\pi$
$197$	−32.5493			−0.165225			−0.0826124	+	0.996582i	$0.526326\pi$
$198$		0			0
$199$	−128.299			−0.644717			−0.322358	−	0.946618i	$-0.604476\pi$
$199$	−128.299			−0.644717			−0.322358	+	0.946618i	$0.604476\pi$
$200$		0			0
$201$	−145.946	+	92.2433i	−0.726097	+	0.458922i
$202$		0			0
$203$	3.98298	−	6.89873i	0.0196206	−	0.0339839i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−221.908	+	17.8115i	−1.07202	+	0.0860457i
$208$		0			0
$209$	12.6788	−	7.32010i	0.0606640	−	0.0350244i
$210$		0			0
$211$	18.0757	−	31.3080i	0.0856668	−	0.148379i	−0.820008	−	0.572352i	$-0.806031\pi$
$211$	18.0757	−	31.3080i	0.0856668	−	0.148379i	0.905675	+	0.423972i	$0.139365\pi$
$212$		0			0
$213$	37.8000	+	19.8500i	0.177465	+	0.0931927i
$214$		0			0
$215$		0			0
$216$		0			0
$217$		−	68.3166i		−	0.314823i
$218$		0			0
$219$	−190.049	−	99.8010i	−0.867802	−	0.455712i
$220$		0			0
$221$	28.5311	+	16.4724i	0.129100	+	0.0745359i
$222$		0			0
$223$	151.500	−	87.4685i	0.679372	−	0.392236i	−0.120246	−	0.992744i	$-0.538368\pi$
$223$	151.500	−	87.4685i	0.679372	−	0.392236i	0.799618	+	0.600508i	$0.205035\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	68.1296	+	118.004i	0.300130	+	0.519841i	0.976165	−	0.217028i	$-0.0696364\pi$
$227$	68.1296	+	118.004i	0.300130	+	0.519841i	−0.676035	+	0.736870i	$0.736303\pi$
$228$		0			0
$229$	97.1240	−	168.224i	0.424122	−	0.734601i	−0.572216	−	0.820103i	$-0.693916\pi$
$229$	97.1240	−	168.224i	0.424122	−	0.734601i	0.996338	+	0.0855017i	$0.0272493\pi$
$230$		0			0
$231$	−4.97427	−	7.87019i	−0.0215336	−	0.0340701i
$232$		0			0
$233$	196.013			0.841258			0.420629	−	0.907233i	$-0.361809\pi$
$233$	196.013			0.841258			0.420629	+	0.907233i	$0.361809\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−326.202	+	13.0703i	−1.37638	+	0.0551489i
$238$		0			0
$239$	−43.8109	−	25.2943i	−0.183309	−	0.105834i	0.405537	−	0.914079i	$-0.367084\pi$
$239$	−43.8109	−	25.2943i	−0.183309	−	0.105834i	−0.588847	+	0.808245i	$0.700418\pi$
$240$		0			0
$241$	−104.678	−	181.308i	−0.434351	−	0.752317i	0.562892	−	0.826531i	$-0.309689\pi$
$241$	−104.678	−	181.308i	−0.434351	−	0.752317i	−0.997242	+	0.0742134i	$0.976355\pi$
$242$		0			0
$243$	−160.929	−	182.073i	−0.662261	−	0.749273i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−48.5026	−	28.0030i	−0.196367	−	0.113372i
$248$		0			0
$249$	241.529	−	9.67759i	0.969996	−	0.0388658i
$250$		0			0
$251$			179.480i			0.715061i	0.933901	+	0.357531i	$0.116381\pi$
$251$			179.480i			0.715061i	−0.933901	+	0.357531i	$0.883619\pi$
$252$		0			0
$253$			27.1100i			0.107154i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−225.194	+	390.047i	−0.876241	+	1.51769i	−0.0208064	+	0.999784i	$0.506623\pi$
$257$	−225.194	+	390.047i	−0.876241	+	1.51769i	−0.855435	+	0.517911i	$0.826710\pi$
$258$		0			0
$259$	−70.6696	−	122.403i	−0.272856	−	0.472600i
$260$		0			0
$261$	−22.8691	−	10.8644i	−0.0876210	−	0.0416261i
$262$		0			0
$263$	−197.837	−	342.665i	−0.752234	−	1.30291i	−0.946738	−	0.322005i	$-0.895643\pi$
$263$	−197.837	−	342.665i	−0.752234	−	1.30291i	0.194504	−	0.980902i	$-0.437690\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−174.274	−	91.5170i	−0.652710	−	0.342760i
$268$		0			0
$269$		−	374.710i		−	1.39298i	−0.717569	−	0.696488i	$-0.754745\pi$
$269$		−	374.710i		−	1.39298i	0.717569	−	0.696488i	$-0.245255\pi$
$270$		0			0
$271$	41.1748			0.151936			0.0759682	−	0.997110i	$-0.475795\pi$
$271$	41.1748			0.151936			0.0759682	+	0.997110i	$0.475795\pi$
$272$		0			0
$273$	−16.5592	+	31.5333i	−0.0606565	+	0.115507i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	16.9981	−	9.81388i	0.0613651	−	0.0354292i	−0.469004	−	0.883196i	$-0.655387\pi$
$277$	16.9981	−	9.81388i	0.0613651	−	0.0354292i	0.530369	+	0.847767i	$0.322054\pi$
$278$		0			0
$279$	−216.438	+	17.3724i	−0.775762	+	0.0622665i
$280$		0			0
$281$	316.627	−	182.805i	1.12679	−	0.650551i	0.183663	−	0.982989i	$-0.441205\pi$
$281$	316.627	−	182.805i	1.12679	−	0.650551i	0.943125	+	0.332438i	$0.107871\pi$
$282$		0			0
$283$	−20.8524	−	12.0391i	−0.0736832	−	0.0425410i	0.462706	−	0.886512i	$-0.346879\pi$
$283$	−20.8524	−	12.0391i	−0.0736832	−	0.0425410i	−0.536389	+	0.843971i	$0.680212\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−61.8317			−0.215441
$288$		0			0
$289$	−227.257			−0.786355
$290$		0			0
$291$	18.5984	+	464.171i	0.0639121	+	1.59509i
$292$		0			0
$293$	−170.352	+	295.058i	−0.581406	+	1.00703i	0.413907	+	0.910319i	$0.364164\pi$
$293$	−170.352	+	295.058i	−0.581406	+	1.00703i	−0.995313	+	0.0967059i	$0.969169\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−23.6691	+	17.7606i	−0.0796939	+	0.0598000i
$298$		0			0
$299$	89.8149	−	51.8547i	0.300384	−	0.173427i
$300$		0			0
$301$	69.4180	−	120.235i	0.230624	−	0.399453i
$302$		0			0
$303$	17.3246	+	432.378i	0.0571767	+	1.42699i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	401.187i		−	1.30680i	−0.757014	−	0.653399i	$-0.773342\pi$
$307$		−	401.187i		−	1.30680i	0.757014	−	0.653399i	$-0.226658\pi$
$308$		0			0
$309$	51.4516	−	32.5194i	0.166510	−	0.105241i
$310$		0			0
$311$	78.7894	+	45.4891i	0.253342	+	0.146267i	0.621294	−	0.783578i	$-0.286607\pi$
$311$	78.7894	+	45.4891i	0.253342	+	0.146267i	−0.367951	+	0.929845i	$0.619941\pi$
$312$		0			0
$313$	−402.942	+	232.638i	−1.28735	+	0.743254i	−0.978181	−	0.207752i	$-0.933385\pi$
$313$	−402.942	+	232.638i	−1.28735	+	0.743254i	−0.309172	+	0.951006i	$0.600052\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	96.7678	+	167.607i	0.305261	+	0.528728i	0.977319	−	0.211770i	$-0.0679229\pi$
$317$	96.7678	+	167.607i	0.305261	+	0.528728i	−0.672058	+	0.740498i	$0.734590\pi$
$318$		0			0
$319$	−1.54160	+	2.67013i	−0.00483261	+	0.00837032i
$320$		0			0
$321$	−217.990	+	415.112i	−0.679096	+	1.29318i
$322$		0			0
$323$	−104.963			−0.324964
$324$		0			0
$325$		0			0
$326$		0			0
$327$	77.4715	−	147.527i	0.236916	−	0.451153i
$328$		0			0
$329$	165.883	+	95.7726i	0.504204	+	0.291102i
$330$		0			0
$331$	−65.9739	−	114.270i	−0.199317	−	0.345227i	0.748990	−	0.662581i	$-0.230539\pi$
$331$	−65.9739	−	114.270i	−0.199317	−	0.345227i	−0.948307	+	0.317354i	$0.897206\pi$
$332$		0			0
$333$	−369.822	+	255.018i	−1.11058	+	0.765821i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−303.562	−	175.261i	−0.900777	−	0.520064i	−0.0233245	−	0.999728i	$-0.507425\pi$
$337$	−303.562	−	175.261i	−0.900777	−	0.520064i	−0.877452	+	0.479664i	$0.840758\pi$
$338$		0			0
$339$	−178.630	−	282.624i	−0.526931	−	0.833699i
$340$		0			0
$341$			26.4417i			0.0775417i
$342$		0			0
$343$			254.798i			0.742851i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−114.673	+	198.620i	−0.330470	+	0.572392i	−0.982604	−	0.185712i	$-0.940541\pi$
$347$	−114.673	+	198.620i	−0.330470	+	0.572392i	0.652134	+	0.758104i	$0.273874\pi$
$348$		0			0
$349$	−167.325	−	289.815i	−0.479440	−	0.830415i	0.520282	−	0.853995i	$-0.325827\pi$
$349$	−167.325	−	289.815i	−0.479440	−	0.830415i	−0.999722	+	0.0235800i	$0.992494\pi$
$350$		0			0
$351$	104.113	+	44.4435i	0.296619	+	0.126620i
$352$		0			0
$353$	14.5209	+	25.1509i	0.0411356	+	0.0712489i	0.885860	−	0.463952i	$-0.153569\pi$
$353$	14.5209	+	25.1509i	0.0411356	+	0.0712489i	−0.844725	+	0.535201i	$0.820236\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	2.67244	+	66.6976i	0.00748583	+	0.186828i
$358$		0			0
$359$			293.412i			0.817304i	0.912690	+	0.408652i	$0.134001\pi$
$359$			293.412i			0.817304i	−0.912690	+	0.408652i	$0.865999\pi$
$360$		0			0
$361$	−182.563			−0.505716
$362$		0			0
$363$	−192.015	−	303.803i	−0.528967	−	0.836922i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	49.5815	−	28.6259i	0.135099	−	0.0779997i	−0.430927	−	0.902387i	$-0.641813\pi$
$367$	49.5815	−	28.6259i	0.135099	−	0.0779997i	0.566026	+	0.824387i	$0.308480\pi$
$368$		0			0
$369$	15.7233	+	195.892i	0.0426106	+	0.530874i
$370$		0			0
$371$	122.227	−	70.5676i	0.329452	−	0.190209i
$372$		0			0
$373$	260.297	+	150.282i	0.697847	+	0.402902i	0.806545	−	0.591173i	$-0.201335\pi$
$373$	260.297	+	150.282i	0.697847	+	0.402902i	−0.108698	+	0.994075i	$0.534668\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.7948			0.0312859
$378$		0			0
$379$	198.314			0.523255			0.261627	−	0.965169i	$-0.415741\pi$
$379$	198.314			0.523255			0.261627	+	0.965169i	$0.415741\pi$
$380$		0			0
$381$	383.662	+	201.474i	1.00699	+	0.528803i
$382$		0			0
$383$	28.1798	−	48.8088i	0.0735765	−	0.127438i	−0.826890	−	0.562364i	$-0.809892\pi$
$383$	28.1798	−	48.8088i	0.0735765	−	0.127438i	0.900466	+	0.434926i	$0.143225\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−398.577	−	189.352i	−1.02991	−	0.489282i
$388$		0			0
$389$	620.660	−	358.338i	1.59553	−	0.921179i	0.603194	−	0.797595i	$-0.293895\pi$
$389$	620.660	−	358.338i	1.59553	−	0.921179i	0.992334	−	0.123584i	$-0.0394388\pi$
$390$		0			0
$391$	97.1831	−	168.326i	0.248550	−	0.430501i
$392$		0			0
$393$	−488.017	+	308.446i	−1.24177	+	0.784849i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			310.467i			0.782032i	0.920384	+	0.391016i	$0.127876\pi$
$397$			310.467i			0.782032i	−0.920384	+	0.391016i	$0.872124\pi$
$398$		0			0
$399$	−4.54313	−	113.385i	−0.0113863	−	0.284173i
$400$		0			0
$401$	−426.833	−	246.432i	−1.06442	−	0.614544i	−0.137770	−	0.990464i	$-0.543993\pi$
$401$	−426.833	−	246.432i	−1.06442	−	0.614544i	−0.926652	+	0.375920i	$0.877327\pi$
$402$		0			0
$403$	87.6008	−	50.5763i	0.217372	−	0.125500i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	27.3524	+	47.3758i	0.0672050	+	0.116402i
$408$		0			0
$409$	−341.160	+	590.906i	−0.834132	+	1.44476i	0.0606037	+	0.998162i	$0.480697\pi$
$409$	−341.160	+	590.906i	−0.834132	+	1.44476i	−0.894735	+	0.446597i	$0.852636\pi$
$410$		0			0
$411$	−98.6240	+	3.95167i	−0.239961	+	0.00961477i
$412$		0			0
$413$	284.086			0.687859
$414$		0			0
$415$		0			0
$416$		0			0
$417$	256.847	+	406.377i	0.615939	+	0.974526i
$418$		0			0
$419$	192.209	+	110.972i	0.458732	+	0.264849i	0.711511	−	0.702675i	$-0.248011\pi$
$419$	192.209	+	110.972i	0.458732	+	0.264849i	−0.252779	+	0.967524i	$0.581345\pi$
$420$		0			0
$421$	−76.5614	−	132.608i	−0.181856	−	0.314984i	0.760657	−	0.649155i	$-0.224877\pi$
$421$	−76.5614	−	132.608i	−0.181856	−	0.314984i	−0.942513	+	0.334171i	$0.891544\pi$
$422$		0			0
$423$	261.240	−	549.898i	0.617588	−	1.29999i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−203.833	−	117.683i	−0.477361	−	0.275604i
$428$		0			0
$429$	6.40920	−	12.2049i	0.0149399	−	0.0284496i
$430$		0			0
$431$			328.398i			0.761944i	0.924587	+	0.380972i	$0.124411\pi$
$431$			328.398i			0.761944i	−0.924587	+	0.380972i	$0.875589\pi$
$432$		0			0
$433$		−	171.691i		−	0.396515i	−0.980150	−	0.198258i	$-0.936472\pi$
$433$		−	171.691i		−	0.396515i	0.980150	−	0.198258i	$-0.0635283\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−165.210	+	286.153i	−0.378056	+	0.654812i
$438$		0			0
$439$	49.2459	+	85.2965i	0.112178	+	0.194297i	0.916648	−	0.399695i	$-0.130884\pi$
$439$	49.2459	+	85.2965i	0.112178	+	0.194297i	−0.804470	+	0.593993i	$0.797551\pi$
$440$		0			0
$441$	367.653	−	29.5096i	0.833680	−	0.0669153i
$442$		0			0
$443$	−377.907	−	654.554i	−0.853063	−	1.47755i	−0.878430	−	0.477871i	$-0.841409\pi$
$443$	−377.907	−	654.554i	−0.853063	−	1.47755i	0.0253671	−	0.999678i	$-0.491925\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	114.549	−	72.3994i	0.256262	−	0.161967i
$448$		0			0
$449$			167.336i			0.372686i	0.982485	+	0.186343i	$0.0596635\pi$
$449$			167.336i			0.372686i	−0.982485	+	0.186343i	$0.940336\pi$
$450$		0			0
$451$	23.9318			0.0530638
$452$		0			0
$453$	804.161	−	32.2212i	1.77519	−	0.0711284i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	317.924	−	183.553i	0.695676	−	0.401648i	−0.110059	−	0.993925i	$-0.535104\pi$
$457$	317.924	−	183.553i	0.695676	−	0.401648i	0.805735	+	0.592277i	$0.201771\pi$
$458$		0			0
$459$	210.629	−	25.4274i	0.458886	−	0.0553973i
$460$		0			0
$461$	467.957	−	270.175i	1.01509	−	0.586063i	0.102413	−	0.994742i	$-0.467344\pi$
$461$	467.957	−	270.175i	1.01509	−	0.586063i	0.912678	+	0.408679i	$0.134010\pi$
$462$		0			0
$463$	155.651	+	89.8654i	0.336180	+	0.194094i	0.658582	−	0.752509i	$-0.271157\pi$
$463$	155.651	+	89.8654i	0.336180	+	0.194094i	−0.322401	+	0.946603i	$0.604490\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	56.0646			0.120053			0.0600264	−	0.998197i	$-0.480882\pi$
$467$	56.0646			0.120053			0.0600264	+	0.998197i	$0.480882\pi$
$468$		0			0
$469$	162.965			0.347473
$470$		0			0
$471$	−528.265	+	333.884i	−1.12158	+	0.708884i
$472$		0			0
$473$	−26.8680	+	46.5367i	−0.0568034	+	0.0983863i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−254.650	−	369.288i	−0.533858	−	0.774190i
$478$		0			0
$479$	−497.782	+	287.395i	−1.03921	+	0.599989i	−0.919610	−	0.392833i	$-0.871495\pi$
$479$	−497.782	+	287.395i	−1.03921	+	0.599989i	−0.119601	+	0.992822i	$0.538162\pi$
$480$		0			0
$481$	104.637	−	181.236i	0.217540	−	0.376790i
$482$		0			0
$483$	186.038	+	97.6951i	0.385173	+	0.202267i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			190.185i			0.390524i	0.980751	+	0.195262i	$0.0625557\pi$
$487$			190.185i			0.390524i	−0.980751	+	0.195262i	$0.937444\pi$
$488$		0			0
$489$	65.4438	+	34.3668i	0.133832	+	0.0702797i
$490$		0			0
$491$	−340.176	−	196.401i	−0.692822	−	0.400001i	0.111846	−	0.993726i	$-0.464324\pi$
$491$	−340.176	−	196.401i	−0.692822	−	0.400001i	−0.804668	+	0.593724i	$0.797657\pi$
$492$		0			0
$493$	19.1436	−	11.0525i	0.0388308	−	0.0224190i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−20.1496	−	34.9002i	−0.0405425	−	0.0702217i
$498$		0			0
$499$	150.303	−	260.332i	0.301208	−	0.521707i	−0.675202	−	0.737633i	$-0.735944\pi$
$499$	150.303	−	260.332i	0.301208	−	0.521707i	0.976410	+	0.215926i	$0.0692769\pi$
$500$		0			0
$501$	−143.086	−	226.388i	−0.285601	−	0.451872i
$502$		0			0
$503$	484.676			0.963572			0.481786	−	0.876289i	$-0.339988\pi$
$503$	484.676			0.963572			0.481786	+	0.876289i	$0.339988\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	453.900	−	18.1869i	0.895266	−	0.0358716i
$508$		0			0
$509$	−467.647	−	269.996i	−0.918755	−	0.530444i	−0.0355177	−	0.999369i	$-0.511308\pi$
$509$	−467.647	−	269.996i	−0.918755	−	0.530444i	−0.883238	+	0.468925i	$0.844641\pi$
$510$		0			0
$511$	101.307	+	175.469i	0.198253	+	0.343384i
$512$		0			0
$513$	−358.067	+	43.2263i	−0.697986	+	0.0842617i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−64.2045	−	37.0685i	−0.124187	−	0.0716992i
$518$		0			0
$519$	−183.428	+	7.34962i	−0.353426	+	0.0141611i
$520$		0			0
$521$			103.769i			0.199172i	0.995029	+	0.0995862i	$0.0317519\pi$
$521$			103.769i			0.199172i	−0.995029	+	0.0995862i	$0.968248\pi$
$522$		0			0
$523$		−	142.380i		−	0.272237i	−0.990693	−	0.136119i	$-0.956537\pi$
$523$		−	142.380i		−	0.272237i	0.990693	−	0.136119i	$-0.0434629\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	94.7873	−	164.176i	0.179862	−	0.311530i
$528$		0			0
$529$	−41.4290	−	71.7571i	−0.0783157	−	0.135647i
$530$		0			0
$531$	−72.2407	−	900.028i	−0.136047	−	1.69497i
$532$		0			0
$533$	−45.7754	−	79.2853i	−0.0858826	−	0.148753i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	350.357	+	183.985i	0.652435	+	0.342616i
$538$		0			0
$539$		−	44.9154i		−	0.0833309i
$540$		0			0
$541$	−708.521			−1.30965			−0.654826	−	0.755780i	$-0.727258\pi$
$541$	−708.521			−1.30965			−0.654826	+	0.755780i	$0.727258\pi$
$542$		0			0
$543$	434.811	−	827.999i	0.800756	−	1.52486i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	419.382	−	242.130i	0.766695	−	0.442652i	−0.0649994	−	0.997885i	$-0.520705\pi$
$547$	419.382	−	242.130i	0.766695	−	0.442652i	0.831694	+	0.555234i	$0.187371\pi$
$548$		0			0
$549$	−321.005	+	675.701i	−0.584709	+	1.23078i
$550$		0			0
$551$	−32.5439	+	18.7892i	−0.0590633	+	0.0341002i
$552$		0			0
$553$	266.862	+	154.073i	0.482571	+	0.278612i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	687.468			1.23423			0.617117	−	0.786871i	$-0.288301\pi$
$557$	687.468			1.23423			0.617117	+	0.786871i	$0.288301\pi$
$558$		0			0
$559$	205.567			0.367740
$560$		0			0
$561$	−1.03436	−	25.8151i	−0.00184378	−	0.0460162i
$562$		0			0
$563$	−415.869	+	720.306i	−0.738666	+	1.27941i	0.214431	+	0.976739i	$0.431210\pi$
$563$	−415.869	+	720.306i	−0.738666	+	1.27941i	−0.953096	+	0.302667i	$0.902123\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	36.5842	+	226.428i	0.0645224	+	0.399344i
$568$		0			0
$569$	−250.103	+	144.397i	−0.439548	+	0.253773i	−0.703406	−	0.710788i	$-0.748338\pi$
$569$	−250.103	+	144.397i	−0.439548	+	0.253773i	0.263858	+	0.964562i	$0.415005\pi$
$570$		0			0
$571$	−164.400	+	284.750i	−0.287917	+	0.498686i	−0.973312	−	0.229485i	$-0.926296\pi$
$571$	−164.400	+	284.750i	−0.287917	+	0.498686i	0.685396	+	0.728171i	$0.259629\pi$
$572$		0			0
$573$	42.0405	+	1049.23i	0.0733691	+	1.83111i
$574$		0			0
$575$		0			0
$576$		0			0
$577$			297.033i			0.514788i	0.966307	+	0.257394i	$0.0828638\pi$
$577$			297.033i			0.514788i	−0.966307	+	0.257394i	$0.917136\pi$
$578$		0			0
$579$	502.225	−	317.426i	0.867400	−	0.548231i
$580$		0			0
$581$	−197.592	−	114.080i	−0.340089	−	0.196350i
$582$		0			0
$583$	−47.3074	+	27.3130i	−0.0811449	+	0.0468490i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−458.054	−	793.373i	−0.780331	−	1.35157i	−0.931749	−	0.363103i	$-0.881717\pi$
$587$	−458.054	−	793.373i	−0.780331	−	1.35157i	0.151419	−	0.988470i	$-0.451616\pi$
$588$		0			0
$589$	−161.137	+	279.098i	−0.273578	+	0.473851i
$590$		0			0
$591$	45.3991	−	86.4524i	0.0768174	−	0.146282i
$592$		0			0
$593$	620.630			1.04659			0.523297	−	0.852150i	$-0.324702\pi$
$593$	620.630			1.04659			0.523297	+	0.852150i	$0.324702\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	178.948	−	340.767i	0.299746	−	0.570799i
$598$		0			0
$599$	230.407	+	133.026i	0.384653	+	0.222079i	0.679841	−	0.733360i	$-0.262049\pi$
$599$	230.407	+	133.026i	0.384653	+	0.222079i	−0.295188	+	0.955439i	$0.595382\pi$
$600$		0			0
$601$	504.140	+	873.197i	0.838836	+	1.45291i	0.890869	+	0.454261i	$0.150097\pi$
$601$	504.140	+	873.197i	0.838836	+	1.45291i	−0.0520330	+	0.998645i	$0.516570\pi$
$602$		0			0
$603$	−41.4406	−	516.297i	−0.0687240	−	0.856215i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	998.861	+	576.693i	1.64557	+	0.950071i	0.978803	+	0.204805i	$0.0656562\pi$
$607$	998.861	+	576.693i	1.64557	+	0.950071i	0.666768	+	0.745265i	$0.267677\pi$
$608$		0			0
$609$	12.7680	+	20.2012i	0.0209655	+	0.0331711i
$610$		0			0
$611$			283.611i			0.464174i
$612$		0			0
$613$		−	1168.56i		−	1.90629i	−0.302515	−	0.953145i	$-0.597826\pi$
$613$		−	1168.56i		−	1.90629i	0.302515	−	0.953145i	$-0.402174\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	458.134	−	793.512i	0.742519	−	1.28608i	−0.208826	−	0.977953i	$-0.566964\pi$
$617$	458.134	−	793.512i	0.742519	−	1.28608i	0.951345	−	0.308128i	$-0.0997024\pi$
$618$		0			0
$619$	83.6253	+	144.843i	0.135097	+	0.233995i	0.925635	−	0.378418i	$-0.123532\pi$
$619$	83.6253	+	144.843i	0.135097	+	0.233995i	−0.790537	+	0.612414i	$0.790199\pi$
$620$		0			0
$621$	262.205	−	614.242i	0.422231	−	0.989117i
$622$		0			0
$623$	92.8982	+	160.904i	0.149114	+	0.258274i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	1.75840	+	43.8854i	0.00280447	+	0.0699926i
$628$		0			0
$629$		−	392.208i		−	0.623542i
$630$		0			0
$631$	542.994			0.860530			0.430265	−	0.902703i	$-0.358420\pi$
$631$	542.994			0.860530			0.430265	+	0.902703i	$0.358420\pi$
$632$		0			0
$633$	57.9439	+	91.6777i	0.0915386	+	0.144831i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−148.803	+	85.9117i	−0.233600	+	0.134869i
$638$		0			0
$639$	−105.445	+	72.7120i	−0.165016	+	0.113790i
$640$		0			0
$641$	−90.6386	+	52.3302i	−0.141402	+	0.0816384i	−0.569032	−	0.822315i	$-0.692682\pi$
$641$	−90.6386	+	52.3302i	−0.141402	+	0.0816384i	0.427630	+	0.903954i	$0.359349\pi$
$642$		0			0
$643$	−182.276	−	105.237i	−0.283478	−	0.163666i	0.351519	−	0.936181i	$-0.385665\pi$
$643$	−182.276	−	105.237i	−0.283478	−	0.163666i	−0.634997	+	0.772515i	$0.718999\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	899.002			1.38949			0.694747	−	0.719254i	$-0.255516\pi$
$647$	899.002			1.38949			0.694747	+	0.719254i	$0.255516\pi$
$648$		0			0
$649$	−109.955			−0.169421
$650$		0			0
$651$	181.452	+	95.2867i	0.278728	+	0.146370i
$652$		0			0
$653$	−220.178	+	381.359i	−0.337179	+	0.584011i	−0.983901	−	0.178715i	$-0.942806\pi$
$653$	−220.178	+	381.359i	−0.337179	+	0.584011i	0.646722	+	0.762726i	$0.276139\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	530.152	−	365.577i	0.806929	−	0.556434i
$658$		0			0
$659$	−779.837	+	450.239i	−1.18336	+	0.683215i	−0.956790	−	0.290779i	$-0.906086\pi$
$659$	−779.837	+	450.239i	−1.18336	+	0.683215i	−0.226573	+	0.973994i	$0.572752\pi$
$660$		0			0
$661$	268.406	−	464.893i	0.406060	−	0.703317i	−0.588384	−	0.808582i	$-0.700236\pi$
$661$	268.406	−	464.893i	0.406060	−	0.703317i	0.994444	+	0.105264i	$0.0335689\pi$
$662$		0			0
$663$	−83.5462	+	52.8045i	−0.126012	+	0.0796448i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	69.5861i		−	0.104327i
$668$		0			0
$669$	21.0113	+	524.390i	0.0314070	+	0.783842i
$670$		0			0
$671$	78.8929	+	45.5488i	0.117575	+	0.0678820i
$672$		0			0
$673$	−127.704	+	73.7299i	−0.189753	+	0.109554i	−0.591867	−	0.806036i	$-0.701609\pi$
$673$	−127.704	+	73.7299i	−0.189753	+	0.109554i	0.402114	+	0.915590i	$0.368276\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−439.279	−	760.854i	−0.648861	−	1.12386i	−0.983395	−	0.181477i	$-0.941912\pi$
$677$	−439.279	−	760.854i	−0.648861	−	1.12386i	0.334534	−	0.942384i	$-0.391421\pi$
$678$		0			0
$679$	219.238	−	379.732i	0.322884	−	0.559251i
$680$		0			0
$681$	−408.450	+	16.3658i	−0.599780	+	0.0240320i
$682$		0			0
$683$	395.518			0.579090			0.289545	−	0.957164i	$-0.406496\pi$
$683$	395.518			0.579090			0.289545	+	0.957164i	$0.406496\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	311.343	+	492.601i	0.453193	+	0.717032i
$688$		0			0
$689$	180.974	+	104.486i	0.262662	+	0.151648i
$690$		0			0
$691$	370.319	+	641.412i	0.535918	+	0.928237i	0.999118	+	0.0419833i	$0.0133676\pi$
$691$	370.319	+	641.412i	0.535918	+	0.928237i	−0.463201	+	0.886253i	$0.653299\pi$
$692$		0			0
$693$	27.8416	−	2.23471i	0.0401755	−	0.00322469i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−148.592	−	85.7897i	−0.213188	−	0.123084i
$698$		0			0
$699$	−273.395	+	520.620i	−0.391124	+	0.744807i
$700$		0			0
$701$			1221.15i			1.74201i	0.491275	+	0.871004i	$0.336531\pi$
$701$			1221.15i			1.74201i	−0.491275	+	0.871004i	$0.663469\pi$
$702$		0			0
$703$			666.750i			0.948435i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	204.222	−	353.723i	0.288857	−	0.500315i
$708$		0			0
$709$	371.624	+	643.672i	0.524153	+	0.907859i	0.999605	+	0.0281175i	$0.00895127\pi$
$709$	371.624	+	643.672i	0.524153	+	0.907859i	−0.475452	+	0.879742i	$0.657715\pi$
$710$		0			0
$711$	420.265	−	884.639i	0.591091	−	1.24422i
$712$		0			0
$713$	−298.387	−	516.822i	−0.418495	−	0.724855i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	128.289	−	81.0840i	0.178925	−	0.113088i
$718$		0			0
$719$			1187.47i			1.65156i	0.563993	+	0.825779i	$0.309264\pi$
$719$			1187.47i			1.65156i	−0.563993	+	0.825779i	$0.690736\pi$
$720$		0			0
$721$	−57.4515			−0.0796831
$722$		0			0
$723$	627.567	−	25.1454i	0.868005	−	0.0347793i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−156.825	+	90.5432i	−0.215716	+	0.124544i	−0.603965	−	0.797011i	$-0.706413\pi$
$727$	−156.825	+	90.5432i	−0.215716	+	0.124544i	0.388249	+	0.921554i	$0.373080\pi$
$728$		0			0
$729$	708.057	−	173.483i	0.971271	−	0.237974i
$730$		0			0
$731$	333.646	−	192.631i	0.456425	−	0.263517i
$732$		0			0
$733$	−439.932	−	253.995i	−0.600180	−	0.346514i	0.168932	−	0.985628i	$-0.445968\pi$
$733$	−439.932	−	253.995i	−0.600180	−	0.346514i	−0.769112	+	0.639114i	$0.779301\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−63.0749			−0.0855834
$738$		0			0
$739$	1428.58			1.93313			0.966566	−	0.256418i	$-0.0825423\pi$
$739$	1428.58			1.93313			0.966566	+	0.256418i	$0.0825423\pi$
$740$		0			0
$741$	142.028	−	89.7672i	0.191670	−	0.121143i
$742$		0			0
$743$	−358.142	+	620.319i	−0.482021	+	0.834885i	−0.999787	−	0.0206374i	$-0.993430\pi$
$743$	−358.142	+	620.319i	−0.482021	+	0.834885i	0.517766	+	0.855522i	$0.326764\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−311.176	+	655.010i	−0.416567	+	0.876854i
$748$		0			0
$749$	383.268	−	221.280i	0.511706	−	0.295433i
$750$		0			0
$751$	−265.708	+	460.219i	−0.353805	+	0.612809i	−0.986913	−	0.161255i	$-0.948446\pi$
$751$	−265.708	+	460.219i	−0.353805	+	0.612809i	0.633108	+	0.774064i	$0.281779\pi$
$752$		0			0
$753$	−476.708	−	250.336i	−0.633079	−	0.332451i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			952.388i			1.25811i	0.777362	+	0.629054i	$0.216558\pi$
$757$			952.388i			1.25811i	−0.777362	+	0.629054i	$0.783442\pi$
$758$		0			0
$759$	−72.0056	−	37.8126i	−0.0948690	−	0.0498189i
$760$		0			0
$761$	−1203.10	−	694.609i	−1.58094	−	0.912758i	−0.994722	−	0.102606i	$-0.967282\pi$
$761$	−1203.10	−	694.609i	−1.58094	−	0.912758i	−0.586220	−	0.810152i	$-0.699385\pi$
$762$		0			0
$763$	−136.210	+	78.6407i	−0.178519	+	0.103068i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	210.315	+	364.277i	0.274205	+	0.474937i
$768$		0			0
$769$	−511.731	+	886.345i	−0.665450	+	1.15259i	0.313713	+	0.949518i	$0.398427\pi$
$769$	−511.731	+	886.345i	−0.665450	+	1.15259i	−0.979163	+	0.203076i	$0.934906\pi$
$770$		0			0
$771$	−721.888	−	1142.16i	−0.936301	−	1.48140i
$772$		0			0
$773$	1030.13			1.33264			0.666320	−	0.745666i	$-0.267868\pi$
$773$	1030.13			1.33264			0.666320	+	0.745666i	$0.267868\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	423.678	−	16.9759i	0.545274	−	0.0218481i
$778$		0			0
$779$	252.605	+	145.842i	0.324268	+	0.187216i
$780$		0			0
$781$	7.79885	+	13.5080i	0.00998572	+	0.0172958i
$782$		0			0
$783$	60.7538	−	45.5879i	0.0775910	−	0.0582221i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−711.419	−	410.738i	−0.903963	−	0.521903i	−0.0254790	−	0.999675i	$-0.508111\pi$
$787$	−711.419	−	410.738i	−0.903963	−	0.521903i	−0.878484	+	0.477772i	$0.841444\pi$
$788$		0			0
$789$	1186.07	−	47.5236i	1.50326	−	0.0602327i
$790$		0			0
$791$			315.582i			0.398966i
$792$		0			0
$793$		−	348.494i		−	0.439462i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−85.5591	+	148.193i	−0.107351	+	0.185938i	−0.914696	−	0.404142i	$-0.867570\pi$
$797$	−85.5591	+	148.193i	−0.107351	+	0.185938i	0.807345	+	0.590080i	$0.200904\pi$
$798$		0			0
$799$	265.763	+	460.316i	0.332620	+	0.576115i
$800$		0			0
$801$	486.147	−	335.233i	0.606925	−	0.418518i
$802$		0			0
$803$	−39.2106	−	67.9148i	−0.0488302	−	0.0845763i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	995.248	+	522.639i	1.23327	+	0.647632i
$808$		0			0
$809$		−	605.283i		−	0.748186i	−0.927391	−	0.374093i	$-0.877954\pi$
$809$		−	605.283i		−	0.748186i	0.927391	−	0.374093i	$-0.122046\pi$
$810$		0			0
$811$	1570.18			1.93610			0.968050	−	0.250756i	$-0.0806791\pi$
$811$	1570.18			1.93610			0.968050	+	0.250756i	$0.0806791\pi$
$812$		0			0
$813$	−57.4298	+	109.362i	−0.0706393	+	0.134517i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−567.196	+	327.471i	−0.694242	+	0.400821i
$818$		0			0
$819$	−60.6575	−	87.9642i	−0.0740629	−	0.107404i
$820$		0			0
$821$	−1386.41	+	800.446i	−1.68869	+	0.974965i	−0.733166	+	0.680050i	$0.761958\pi$
$821$	−1386.41	+	800.446i	−1.68869	+	0.974965i	−0.955523	+	0.294915i	$0.904709\pi$
$822$		0			0
$823$	323.616	+	186.840i	0.393215	+	0.227023i	0.683552	−	0.729902i	$-0.260434\pi$
$823$	323.616	+	186.840i	0.393215	+	0.227023i	−0.290337	+	0.956924i	$0.593768\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1490.30			−1.80205			−0.901027	−	0.433764i	$-0.857185\pi$
$827$	−1490.30			−1.80205			−0.901027	+	0.433764i	$0.857185\pi$
$828$		0			0
$829$	85.8287			0.103533			0.0517664	−	0.998659i	$-0.483515\pi$
$829$	85.8287			0.103533			0.0517664	+	0.998659i	$0.483515\pi$
$830$		0			0
$831$	2.35745	+	58.8360i	0.00283688	+	0.0708015i
$832$		0			0
$833$	−161.011	+	278.879i	−0.193290	+	0.334789i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	255.741	−	599.099i	0.305545	−	0.715769i
$838$		0			0
$839$	−1114.95	+	643.717i	−1.32890	+	0.767243i	−0.985130	−	0.171810i	$-0.945039\pi$
$839$	−1114.95	+	643.717i	−1.32890	+	0.767243i	−0.343774	+	0.939053i	$0.611705\pi$
$840$		0			0
$841$	−416.543	+	721.474i	−0.495295	+	0.857876i
$842$		0			0
$843$	43.9126	+	1095.95i	0.0520909	+	1.30006i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			339.230i			0.400508i
$848$		0			0
$849$	61.0609	−	38.5929i	0.0719210	−	0.0454569i
$850$		0			0
$851$	−1069.24	−	617.329i	−1.25646	−	0.725415i
$852$		0			0
$853$	908.783	−	524.686i	1.06540	−	0.615107i	0.138477	−	0.990366i	$-0.455779\pi$
$853$	908.783	−	524.686i	1.06540	−	0.615107i	0.926920	+	0.375259i	$0.122446\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−351.333	−	608.526i	−0.409957	−	0.710066i	0.584928	−	0.811085i	$-0.301123\pi$
$857$	−351.333	−	608.526i	−0.409957	−	0.710066i	−0.994884	+	0.101020i	$0.967789\pi$
$858$		0			0
$859$	152.845	−	264.735i	0.177934	−	0.308190i	−0.763239	−	0.646116i	$-0.776392\pi$
$859$	152.845	−	264.735i	0.177934	−	0.308190i	0.941173	+	0.337926i	$0.109725\pi$
$860$		0			0
$861$	86.2417	−	164.228i	0.100165	−	0.190741i
$862$		0			0
$863$	−975.875			−1.13079			−0.565397	−	0.824819i	$-0.691277\pi$
$863$	−975.875			−1.13079			−0.565397	+	0.824819i	$0.691277\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	316.973	−	603.604i	0.365598	−	0.696198i
$868$		0			0
$869$	−103.288	−	59.6333i	−0.118858	−	0.0686229i
$870$		0			0
$871$	120.646	+	208.966i	0.138515	+	0.239915i
$872$		0			0
$873$	−1258.80	−	598.018i	−1.44192	−	0.685015i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−307.716	−	177.660i	−0.350874	−	0.202577i	0.314196	−	0.949358i	$-0.398265\pi$
$877$	−307.716	−	177.660i	−0.350874	−	0.202577i	−0.665070	+	0.746781i	$0.731598\pi$
$878$		0			0
$879$	−546.085	−	864.005i	−0.621257	−	0.982941i
$880$		0			0
$881$		−	645.657i		−	0.732869i	−0.930444	−	0.366434i	$-0.880578\pi$
$881$		−	645.657i		−	0.732869i	0.930444	−	0.366434i	$-0.119422\pi$
$882$		0			0
$883$			1069.33i			1.21101i	0.795840	+	0.605507i	$0.207030\pi$
$883$			1069.33i			1.21101i	−0.795840	+	0.605507i	$0.792970\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	142.678	−	247.125i	0.160854	−	0.278608i	−0.774321	−	0.632793i	$-0.781908\pi$
$887$	142.678	−	247.125i	0.160854	−	0.278608i	0.935175	+	0.354185i	$0.115242\pi$
$888$		0			0
$889$	−204.515	−	354.230i	−0.230050	−	0.398459i
$890$		0			0
$891$	−14.1598	−	87.6383i	−0.0158920	−	0.0983595i
$892$		0			0
$893$	−451.795	−	782.533i	−0.505930	−	0.876296i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	12.4563	+	310.879i	0.0138866	+	0.346576i
$898$		0			0
$899$		−	67.8706i		−	0.0754957i
$900$		0			0
$901$	391.642			0.434675
$902$		0			0
$903$	222.528	+	352.079i	0.246432	+	0.389900i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−1075.37	+	620.865i	−1.18563	+	0.684526i	−0.957311	−	0.289059i	$-0.906658\pi$
$907$	−1075.37	+	620.865i	−1.18563	+	0.684526i	−0.228323	+	0.973585i	$0.573324\pi$
$908$		0			0
$909$	−1172.58	−	557.058i	−1.28997	−	0.612825i
$910$		0			0
$911$	−123.752	+	71.4483i	−0.135842	+	0.0784285i	−0.566381	−	0.824144i	$-0.691657\pi$
$911$	−123.752	+	71.4483i	−0.135842	+	0.0784285i	0.430539	+	0.902572i	$0.358324\pi$
$912$		0			0
$913$	76.4772	+	44.1541i	0.0837647	+	0.0483616i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	544.926			0.594248
$918$		0			0
$919$	−976.872			−1.06297			−0.531487	−	0.847067i	$-0.678366\pi$
$919$	−976.872			−1.06297			−0.531487	+	0.847067i	$0.678366\pi$
$920$		0			0
$921$	1065.57	+	559.568i	1.15697	+	0.607566i
$922$		0			0
$923$	29.8345	−	51.6748i	0.0323233	−	0.0559857i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	14.6094	+	182.015i	0.0157599	+	0.196349i
$928$		0			0
$929$	784.088	−	452.693i	0.844013	−	0.487291i	−0.0146135	−	0.999893i	$-0.504652\pi$
$929$	784.088	−	452.693i	0.844013	−	0.487291i	0.858626	+	0.512602i	$0.171318\pi$
$930$		0			0
$931$	273.717	−	474.092i	0.294003	−	0.509229i
$932$		0			0
$933$	−230.715	+	145.821i	−0.247283	+	0.156293i
$934$		0			0
$935$		0			0
$936$		0			0
$937$		−	601.348i		−	0.641780i	−0.947116	−	0.320890i	$-0.896018\pi$
$937$		−	601.348i		−	0.641780i	0.947116	−	0.320890i	$-0.103982\pi$
$938$		0			0
$939$	−55.8834	−	1394.71i	−0.0595137	−	1.48532i
$940$		0			0
$941$	430.443	+	248.517i	0.457432	+	0.264098i	0.710964	−	0.703229i	$-0.248259\pi$
$941$	430.443	+	248.517i	0.457432	+	0.264098i	−0.253532	+	0.967327i	$0.581592\pi$
$942$		0			0
$943$	−467.763	+	270.063i	−0.496037	+	0.286387i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−636.420	−	1102.31i	−0.672038	−	1.16400i	−0.977325	−	0.211744i	$-0.932086\pi$
$947$	−636.420	−	1102.31i	−0.672038	−	1.16400i	0.305287	−	0.952260i	$-0.401248\pi$
$948$		0			0
$949$	−150.000	+	259.808i	−0.158061	+	0.273770i
$950$		0			0
$951$	−580.141	+	23.2451i	−0.610033	+	0.0244428i
$952$		0			0
$953$	1562.94			1.64002			0.820009	−	0.572351i	$-0.193968\pi$
$953$	1562.94			1.64002			0.820009	+	0.572351i	$0.193968\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−4.94180	−	7.81881i	−0.00516384	−	0.00817013i
$958$		0			0
$959$	80.6829	+	46.5823i	0.0841324	+	0.0485738i
$960$		0			0
$961$	189.469	+	328.170i	0.197158	+	0.341488i
$962$		0			0
$963$	−798.510	−	1157.98i	−0.829190	−	1.20247i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	322.540	+	186.219i	0.333547	+	0.192574i	0.657415	−	0.753529i	$-0.271650\pi$
$967$	322.540	+	186.219i	0.333547	+	0.192574i	−0.323868	+	0.946102i	$0.604983\pi$
$968$		0			0
$969$	146.401	−	278.787i	0.151084	−	0.287706i
$970$		0			0
$971$			1250.51i			1.28786i	0.765086	+	0.643928i	$0.222696\pi$
$971$			1250.51i			1.28786i	−0.765086	+	0.643928i	$0.777304\pi$
$972$		0			0
$973$		−	453.766i		−	0.466358i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−727.019	+	1259.23i	−0.744134	+	1.28888i	0.206464	+	0.978454i	$0.433804\pi$
$977$	−727.019	+	1259.23i	−0.744134	+	1.28888i	−0.950598	+	0.310424i	$0.899529\pi$
$978$		0			0
$979$	−35.9560	−	62.2775i	−0.0367272	−	0.0636134i
$980$		0			0
$981$	283.783	+	411.536i	0.289279	+	0.419507i
$982$		0			0
$983$	−612.665	−	1061.17i	−0.623261	−	1.07952i	−0.988874	−	0.148752i	$-0.952474\pi$
$983$	−612.665	−	1061.17i	−0.623261	−	1.07952i	0.365614	−	0.930767i	$-0.380859\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−485.747	+	307.011i	−0.492145	+	0.311055i
$988$		0			0
$989$		−	1212.79i		−	1.22628i
$990$		0			0
$991$	847.879			0.855579			0.427790	−	0.903878i	$-0.359292\pi$
$991$	847.879			0.855579			0.427790	+	0.903878i	$0.359292\pi$
$992$		0			0
$993$	395.526	−	15.8480i	0.398314	−	0.0159597i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−1021.68	+	589.869i	−1.02476	+	0.591644i	−0.915479	−	0.402367i	$-0.868188\pi$
$997$	−1021.68	+	589.869i	−1.02476	+	0.591644i	−0.109279	+	0.994011i	$0.534854\pi$
$998$		0			0
$999$	−161.520	−	1337.96i	−0.161682	−	1.33930i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.c.149.3		24
3.2	odd	2		2700.3.u.c.449.9		24
5.2	odd	4		180.3.o.b.41.5	✓	12
5.3	odd	4		900.3.p.c.401.2		12
5.4	even	2	inner	900.3.u.c.149.10		24
9.2	odd	6	inner	900.3.u.c.749.10		24
9.7	even	3		2700.3.u.c.2249.4		24
15.2	even	4		540.3.o.b.341.3		12
15.8	even	4		2700.3.p.c.2501.2		12
15.14	odd	2		2700.3.u.c.449.4		24
20.7	even	4		720.3.bs.b.401.2		12
45.2	even	12		180.3.o.b.101.5	yes	12
45.7	odd	12		540.3.o.b.521.3		12
45.22	odd	12		1620.3.g.b.161.2		12
45.29	odd	6	inner	900.3.u.c.749.3		24
45.32	even	12		1620.3.g.b.161.8		12
45.34	even	6		2700.3.u.c.2249.9		24
45.38	even	12		900.3.p.c.101.2		12
45.43	odd	12		2700.3.p.c.1601.2		12
60.47	odd	4		2160.3.bs.b.881.1		12
180.7	even	12		2160.3.bs.b.1601.1		12
180.47	odd	12		720.3.bs.b.641.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.b.41.5	✓	12	5.2	odd	4
180.3.o.b.101.5	yes	12	45.2	even	12
540.3.o.b.341.3		12	15.2	even	4
540.3.o.b.521.3		12	45.7	odd	12
720.3.bs.b.401.2		12	20.7	even	4
720.3.bs.b.641.2		12	180.47	odd	12
900.3.p.c.101.2		12	45.38	even	12
900.3.p.c.401.2		12	5.3	odd	4
900.3.u.c.149.3		24	1.1	even	1	trivial
900.3.u.c.149.10		24	5.4	even	2	inner
900.3.u.c.749.3		24	45.29	odd	6	inner
900.3.u.c.749.10		24	9.2	odd	6	inner
1620.3.g.b.161.2		12	45.22	odd	12
1620.3.g.b.161.8		12	45.32	even	12
2160.3.bs.b.881.1		12	60.47	odd	4
2160.3.bs.b.1601.1		12	180.7	even	12
2700.3.p.c.1601.2		12	45.43	odd	12
2700.3.p.c.2501.2		12	15.8	even	4
2700.3.u.c.449.4		24	15.14	odd	2
2700.3.u.c.449.9		24	3.2	odd	2
2700.3.u.c.2249.4		24	9.7	even	3
2700.3.u.c.2249.9		24	45.34	even	6

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.u (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39478 + 2.65605i) q^{3} +(2.45229 - 1.41583i) q^{7} +(-5.10917 - 7.40921i) q^{9} +O(q^{10})\)	\(q+(-1.39478 + 2.65605i) q^{3} +(2.45229 - 1.41583i) q^{7} +(-5.10917 - 7.40921i) q^{9} +(-0.949152 + 0.547993i) q^{11} +(3.63097 + 2.09634i) q^{13} +7.85770 q^{17} -13.3580 q^{19} +(0.340105 + 8.48818i) q^{21} +(12.3679 - 21.4218i) q^{23} +(26.8054 - 3.23598i) q^{27} +(2.43628 - 1.40659i) q^{29} +(12.0630 - 20.8937i) q^{31} +(-0.131636 - 3.28532i) q^{33} -49.9138i q^{37} +(-10.6324 + 6.72010i) q^{39} +(-18.9104 - 10.9179i) q^{41} +(42.4611 - 24.5149i) q^{43} +(33.8220 + 58.5815i) q^{47} +(-20.4908 + 35.4912i) q^{49} +(-10.9598 + 20.8704i) q^{51} +49.8418 q^{53} +(18.6315 - 35.4795i) q^{57} +(86.8838 + 50.1624i) q^{59} +(-41.5597 - 71.9835i) q^{61} +(-23.0194 - 10.9358i) q^{63} +(49.8405 + 28.7754i) q^{67} +(39.6468 + 62.7284i) q^{69} -14.2317i q^{71} +71.5532i q^{73} +(-1.55173 + 2.68768i) q^{77} +(54.4107 + 94.2421i) q^{79} +(-28.7927 + 75.7098i) q^{81} +(-40.2871 - 69.7793i) q^{83} +(0.337884 + 8.43276i) q^{87} +65.6139i q^{89} +11.8723 q^{91} +(38.6694 + 61.1820i) q^{93} +(134.102 - 77.4238i) q^{97} +(8.90957 + 4.23267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 52 q^{9}+O(q^{10}) \) 24 * q - 52 * q^9	\( 24 q - 52 q^{9} + 96 q^{11} - 144 q^{19} - 256 q^{21} - 300 q^{29} - 24 q^{31} - 80 q^{39} + 180 q^{41} - 96 q^{49} - 288 q^{51} - 96 q^{59} - 156 q^{61} + 300 q^{69} - 240 q^{79} + 868 q^{81} + 240 q^{91} + 240 q^{99}+O(q^{100}) \) 24 * q - 52 * q^9 + 96 * q^11 - 144 * q^19 - 256 * q^21 - 300 * q^29 - 24 * q^31 - 80 * q^39 + 180 * q^41 - 96 * q^49 - 288 * q^51 - 96 * q^59 - 156 * q^61 + 300 * q^69 - 240 * q^79 + 868 * q^81 + 240 * q^91 + 240 * q^99

Introduction

L-functions

Modular forms

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Database

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