LMFDB - Embedded newform 900.3.p.f.401.2

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			401.2
Character	$\chi$	$=$	900.401
Dual form			900.3.p.f.101.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.69243 - 1.32320i) q^{3} +(1.36039 + 2.35627i) q^{7} +(5.49831 + 7.12521i) q^{9} +O(q^{10})$	\(q+(-2.69243 - 1.32320i) q^{3} +(1.36039 + 2.35627i) q^{7} +(5.49831 + 7.12521i) q^{9} +(-2.77248 + 1.60069i) q^{11} +(3.99574 - 6.92082i) q^{13} -1.82475i q^{17} +15.4409 q^{19} +(-0.544949 - 8.14414i) q^{21} +(-28.0288 - 16.1825i) q^{23} +(-5.37572 - 26.4594i) q^{27} +(-25.5744 + 14.7654i) q^{29} +(-26.5013 + 45.9016i) q^{31} +(9.58274 - 0.641210i) q^{33} -30.0450 q^{37} +(-19.9158 + 13.3466i) q^{39} +(66.5294 + 38.4108i) q^{41} +(4.49000 + 7.77691i) q^{43} +(10.2573 - 5.92207i) q^{47} +(20.7987 - 36.0244i) q^{49} +(-2.41450 + 4.91300i) q^{51} +28.9838i q^{53} +(-41.5735 - 20.4313i) q^{57} +(-16.6328 - 9.60298i) q^{59} +(30.9820 + 53.6624i) q^{61} +(-9.30905 + 22.6485i) q^{63} +(2.59309 - 4.49136i) q^{67} +(54.0530 + 80.6577i) q^{69} +96.0332i q^{71} +127.394 q^{73} +(-7.54332 - 4.35514i) q^{77} +(24.2255 + 41.9598i) q^{79} +(-20.5373 + 78.3532i) q^{81} +(-83.1807 + 48.0244i) q^{83} +(88.3948 - 5.91477i) q^{87} +21.4877i q^{89} +21.7431 q^{91} +(132.090 - 88.5202i) q^{93} +(83.3867 + 144.430i) q^{97} +(-26.6492 - 10.9534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{9}+O(q^{10}) $ 24 * q - 2 * q^9	$ 24 q - 2 q^{9} - 18 q^{11} - 26 q^{21} - 36 q^{29} + 30 q^{31} - 6 q^{39} - 36 q^{41} - 108 q^{49} + 124 q^{51} + 306 q^{59} + 48 q^{61} + 268 q^{69} - 114 q^{79} - 14 q^{81} - 84 q^{91} - 418 q^{99}+O(q^{100}) $ 24 * q - 2 * q^9 - 18 * q^11 - 26 * q^21 - 36 * q^29 + 30 * q^31 - 6 * q^39 - 36 * q^41 - 108 * q^49 + 124 * q^51 + 306 * q^59 + 48 * q^61 + 268 * q^69 - 114 * q^79 - 14 * q^81 - 84 * q^91 - 418 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−2.69243	−	1.32320i	−0.897475	−	0.441065i
$3$	−2.69243	−	1.32320i	−0.897475	−	0.441065i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.36039	+	2.35627i	0.194342	+	0.336610i	0.946684	−	0.322162i	$-0.104410\pi$
$7$	1.36039	+	2.35627i	0.194342	+	0.336610i	−0.752343	+	0.658772i	$0.771076\pi$
$8$		0			0
$9$	5.49831	+	7.12521i	0.610923	+	0.791690i
$10$		0			0
$11$	−2.77248	+	1.60069i	−0.252044	+	0.145518i	−0.620700	−	0.784048i	$-0.713151\pi$
$11$	−2.77248	+	1.60069i	−0.252044	+	0.145518i	0.368656	+	0.929566i	$0.379818\pi$
$12$		0			0
$13$	3.99574	−	6.92082i	0.307364	−	0.532371i	−0.670421	−	0.741981i	$-0.733886\pi$
$13$	3.99574	−	6.92082i	0.307364	−	0.532371i	0.977785	+	0.209611i	$0.0672196\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	1.82475i		−	0.107338i	−0.998559	−	0.0536691i	$-0.982908\pi$
$17$		−	1.82475i		−	0.107338i	0.998559	−	0.0536691i	$-0.0170916\pi$
$18$		0			0
$19$	15.4409			0.812679			0.406340	−	0.913722i	$-0.366805\pi$
$19$	15.4409			0.812679			0.406340	+	0.913722i	$0.366805\pi$
$20$		0			0
$21$	−0.544949	−	8.14414i	−0.0259499	−	0.387816i
$22$		0			0
$23$	−28.0288	−	16.1825i	−1.21865	−	0.703585i	−0.254017	−	0.967200i	$-0.581752\pi$
$23$	−28.0288	−	16.1825i	−1.21865	−	0.703585i	−0.964628	+	0.263614i	$0.915085\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−5.37572	−	26.4594i	−0.199101	−	0.979979i
$28$		0			0
$29$	−25.5744	+	14.7654i	−0.881877	+	0.509152i	−0.871277	−	0.490792i	$-0.836708\pi$
$29$	−25.5744	+	14.7654i	−0.881877	+	0.509152i	−0.0106004	+	0.999944i	$0.503374\pi$
$30$		0			0
$31$	−26.5013	+	45.9016i	−0.854880	+	1.48070i	0.0218756	+	0.999761i	$0.493036\pi$
$31$	−26.5013	+	45.9016i	−0.854880	+	1.48070i	−0.876756	+	0.480935i	$0.840297\pi$
$32$		0			0
$33$	9.58274	−	0.641210i	0.290386	−	0.0194306i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−30.0450			−0.812028			−0.406014	−	0.913867i	$-0.633082\pi$
$37$	−30.0450			−0.812028			−0.406014	+	0.913867i	$0.633082\pi$
$38$		0			0
$39$	−19.9158	+	13.3466i	−0.510662	+	0.342222i
$40$		0			0
$41$	66.5294	+	38.4108i	1.62267	+	0.936848i	0.986203	+	0.165542i	$0.0529373\pi$
$41$	66.5294	+	38.4108i	1.62267	+	0.936848i	0.636465	+	0.771306i	$0.280396\pi$
$42$		0			0
$43$	4.49000	+	7.77691i	0.104419	+	0.180858i	0.913501	−	0.406838i	$-0.133368\pi$
$43$	4.49000	+	7.77691i	0.104419	+	0.180858i	−0.809082	+	0.587696i	$0.800035\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	10.2573	−	5.92207i	0.218241	−	0.126002i	−0.386894	−	0.922124i	$-0.626452\pi$
$47$	10.2573	−	5.92207i	0.218241	−	0.126002i	0.605136	+	0.796122i	$0.293119\pi$
$48$		0			0
$49$	20.7987	−	36.0244i	0.424463	−	0.735191i
$50$		0			0
$51$	−2.41450	+	4.91300i	−0.0473431	+	0.0963333i
$52$		0			0
$53$			28.9838i			0.546864i	0.961891	+	0.273432i	$0.0881589\pi$
$53$			28.9838i			0.546864i	−0.961891	+	0.273432i	$0.911841\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−41.5735	−	20.4313i	−0.729359	−	0.358445i
$58$		0			0
$59$	−16.6328	−	9.60298i	−0.281913	−	0.162762i	0.352376	−	0.935858i	$-0.385374\pi$
$59$	−16.6328	−	9.60298i	−0.281913	−	0.162762i	−0.634289	+	0.773096i	$0.718707\pi$
$60$		0			0
$61$	30.9820	+	53.6624i	0.507902	+	0.879712i	0.999958	+	0.00914834i	$0.00291205\pi$
$61$	30.9820	+	53.6624i	0.507902	+	0.879712i	−0.492056	+	0.870563i	$0.663755\pi$
$62$		0			0
$63$	−9.30905	+	22.6485i	−0.147763	+	0.359501i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.59309	−	4.49136i	0.0387028	−	0.0670352i	−0.846025	−	0.533143i	$-0.821011\pi$
$67$	2.59309	−	4.49136i	0.0387028	−	0.0670352i	0.884728	+	0.466108i	$0.154344\pi$
$68$		0			0
$69$	54.0530	+	80.6577i	0.783377	+	1.16895i
$70$		0			0
$71$			96.0332i			1.35258i	0.736635	+	0.676290i	$0.236413\pi$
$71$			96.0332i			1.35258i	−0.736635	+	0.676290i	$0.763587\pi$
$72$		0			0
$73$	127.394			1.74512			0.872561	−	0.488506i	$-0.162458\pi$
$73$	127.394			1.74512			0.872561	+	0.488506i	$0.162458\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.54332	−	4.35514i	−0.0979652	−	0.0565603i
$78$		0			0
$79$	24.2255	+	41.9598i	0.306652	+	0.531137i	0.977628	−	0.210342i	$-0.0674578\pi$
$79$	24.2255	+	41.9598i	0.306652	+	0.531137i	−0.670976	+	0.741479i	$0.734125\pi$
$80$		0			0
$81$	−20.5373	+	78.3532i	−0.253547	+	0.967323i
$82$		0			0
$83$	−83.1807	+	48.0244i	−1.00218	+	0.578608i	−0.908892	−	0.417032i	$-0.863070\pi$
$83$	−83.1807	+	48.0244i	−1.00218	+	0.578608i	−0.0932858	+	0.995639i	$0.529737\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	88.3948	−	5.91477i	1.01603	−	0.0679858i
$88$		0			0
$89$			21.4877i			0.241435i	0.992687	+	0.120717i	$0.0385195\pi$
$89$			21.4877i			0.241435i	−0.992687	+	0.120717i	$0.961481\pi$
$90$		0			0
$91$	21.7431			0.238935
$92$		0			0
$93$	132.090	−	88.5202i	1.42032	−	0.951830i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	83.3867	+	144.430i	0.859657	+	1.48897i	0.872256	+	0.489049i	$0.162656\pi$
$97$	83.3867	+	144.430i	0.859657	+	1.48897i	−0.0125994	+	0.999921i	$0.504011\pi$
$98$		0			0
$99$	−26.6492	−	10.9534i	−0.269184	−	0.110641i
$100$		0			0
$101$	8.04463	−	4.64457i	0.0796498	−	0.0459858i	−0.459646	−	0.888102i	$-0.652024\pi$
$101$	8.04463	−	4.64457i	0.0796498	−	0.0459858i	0.539296	+	0.842116i	$0.318690\pi$
$102$		0			0
$103$	−74.4089	+	128.880i	−0.722416	+	1.25126i	0.237612	+	0.971360i	$0.423635\pi$
$103$	−74.4089	+	128.880i	−0.722416	+	1.25126i	−0.960029	+	0.279902i	$0.909698\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			128.718i			1.20297i	0.798884	+	0.601486i	$0.205424\pi$
$107$			128.718i			1.20297i	−0.798884	+	0.601486i	$0.794576\pi$
$108$		0			0
$109$	−51.9030			−0.476174			−0.238087	−	0.971244i	$-0.576520\pi$
$109$	−51.9030			−0.476174			−0.238087	+	0.971244i	$0.576520\pi$
$110$		0			0
$111$	80.8940	+	39.7555i	0.728775	+	0.358158i
$112$		0			0
$113$	−74.2232	−	42.8528i	−0.656842	−	0.379228i	0.134230	−	0.990950i	$-0.457144\pi$
$113$	−74.2232	−	42.8528i	−0.656842	−	0.379228i	−0.791073	+	0.611722i	$0.790477\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	71.2821	−	9.58230i	0.609248	−	0.0819000i
$118$		0			0
$119$	4.29959	−	2.48237i	0.0361310	−	0.0208603i
$120$		0			0
$121$	−55.3756	+	95.9133i	−0.457649	+	0.792672i
$122$		0			0
$123$	−128.300	−	191.449i	−1.04309	−	1.55650i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	44.5884			0.351090			0.175545	−	0.984471i	$-0.443831\pi$
$127$	44.5884			0.351090			0.175545	+	0.984471i	$0.443831\pi$
$128$		0			0
$129$	−1.79862	−	26.8799i	−0.0139428	−	0.208371i
$130$		0			0
$131$	−81.7238	−	47.1833i	−0.623846	−	0.360178i	0.154519	−	0.987990i	$-0.450617\pi$
$131$	−81.7238	−	47.1833i	−0.623846	−	0.360178i	−0.778365	+	0.627812i	$0.783951\pi$
$132$		0			0
$133$	21.0057	+	36.3829i	0.157937	+	0.273556i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−30.5615	+	17.6447i	−0.223077	+	0.128793i	−0.607374	−	0.794416i	$-0.707777\pi$
$137$	−30.5615	+	17.6447i	−0.223077	+	0.128793i	0.384297	+	0.923209i	$0.374444\pi$
$138$		0			0
$139$	−61.3817	+	106.316i	−0.441595	+	0.764864i	−0.997808	−	0.0661751i	$-0.978920\pi$
$139$	−61.3817	+	106.316i	−0.441595	+	0.764864i	0.556213	+	0.831040i	$0.312254\pi$
$140$		0			0
$141$	−35.4532	+	2.37228i	−0.251441	+	0.0168247i
$142$		0			0
$143$			25.5838i			0.178908i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−103.666	+	69.4722i	−0.705212	+	0.472600i
$148$		0			0
$149$	199.229	+	115.025i	1.33711	+	0.771978i	0.986377	−	0.164499i	$-0.0526007\pi$
$149$	199.229	+	115.025i	1.33711	+	0.771978i	0.350728	+	0.936477i	$0.385934\pi$
$150$		0			0
$151$	−56.8466	−	98.4612i	−0.376467	−	0.652061i	0.614078	−	0.789245i	$-0.289528\pi$
$151$	−56.8466	−	98.4612i	−0.376467	−	0.652061i	−0.990545	+	0.137185i	$0.956195\pi$
$152$		0			0
$153$	13.0017	−	10.0330i	0.0849785	−	0.0655753i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	81.9039	−	141.862i	0.521681	−	0.903578i	−0.478001	−	0.878359i	$-0.658638\pi$
$157$	81.9039	−	141.862i	0.521681	−	0.903578i	0.999682	−	0.0252188i	$-0.00802824\pi$
$158$		0			0
$159$	38.3512	−	78.0367i	0.241203	−	0.490797i
$160$		0			0
$161$		−	88.0579i		−	0.546944i
$162$		0			0
$163$	237.537			1.45728			0.728641	−	0.684896i	$-0.240152\pi$
$163$	237.537			1.45728			0.728641	+	0.684896i	$0.240152\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−195.400	−	112.814i	−1.17006	−	0.675535i	−0.216367	−	0.976312i	$-0.569421\pi$
$167$	−195.400	−	112.814i	−1.17006	−	0.675535i	−0.953694	+	0.300777i	$0.902754\pi$
$168$		0			0
$169$	52.5682	+	91.0508i	0.311054	+	0.538762i
$170$		0			0
$171$	84.8988	+	110.020i	0.496484	+	0.643390i
$172$		0			0
$173$	−173.349	+	100.083i	−1.00202	+	0.578516i	−0.908845	−	0.417134i	$-0.863035\pi$
$173$	−173.349	+	100.083i	−1.00202	+	0.578516i	−0.0931742	+	0.995650i	$0.529701\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	32.0761	+	47.8638i	0.181221	+	0.270417i
$178$		0			0
$179$		−	180.163i		−	1.00650i	−0.864141	−	0.503249i	$-0.832138\pi$
$179$		−	180.163i		−	1.00650i	0.864141	−	0.503249i	$-0.167862\pi$
$180$		0			0
$181$	264.087			1.45904			0.729522	−	0.683957i	$-0.239742\pi$
$181$	264.087			1.45904			0.729522	+	0.683957i	$0.239742\pi$
$182$		0			0
$183$	−12.4108	−	185.477i	−0.0678188	−	1.01354i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	2.92086	+	5.05908i	0.0156196	+	0.0270539i
$188$		0			0
$189$	55.0324	−	48.6618i	0.291177	−	0.257470i
$190$		0			0
$191$	−195.986	+	113.153i	−1.02611	+	0.592423i	−0.915867	−	0.401482i	$-0.868495\pi$
$191$	−195.986	+	113.153i	−1.02611	+	0.592423i	−0.110240	+	0.993905i	$0.535162\pi$
$192$		0			0
$193$	−108.682	+	188.243i	−0.563121	+	0.975353i	0.434101	+	0.900864i	$0.357066\pi$
$193$	−108.682	+	188.243i	−0.563121	+	0.975353i	−0.997222	+	0.0744893i	$0.976267\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	260.058i		−	1.32009i	−0.751225	−	0.660046i	$-0.770537\pi$
$197$		−	260.058i		−	1.32009i	0.751225	−	0.660046i	$-0.229463\pi$
$198$		0			0
$199$	−253.121			−1.27197			−0.635983	−	0.771703i	$-0.719405\pi$
$199$	−253.121			−1.27197			−0.635983	+	0.771703i	$0.719405\pi$
$200$		0			0
$201$	−12.9246	+	8.66148i	−0.0643017	+	0.0430919i
$202$		0			0
$203$	−69.5825	−	40.1735i	−0.342771	−	0.197899i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−38.8077	−	288.688i	−0.187477	−	1.39463i
$208$		0			0
$209$	−42.8097	+	24.7162i	−0.204831	+	0.118259i
$210$		0			0
$211$	147.164	−	254.895i	0.697459	−	1.20803i	−0.271886	−	0.962329i	$-0.587647\pi$
$211$	147.164	−	254.895i	0.697459	−	1.20803i	0.969345	−	0.245704i	$-0.0790192\pi$
$212$		0			0
$213$	127.071	−	258.562i	0.596576	−	1.21391i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−144.208			−0.664555
$218$		0			0
$219$	−342.998	−	168.567i	−1.56620	−	0.769713i
$220$		0			0
$221$	−12.6288	−	7.29121i	−0.0571437	−	0.0329919i
$222$		0			0
$223$	216.144	+	374.373i	0.969256	+	1.67880i	0.697717	+	0.716374i	$0.254199\pi$
$223$	216.144	+	374.373i	0.969256	+	1.67880i	0.271540	+	0.962427i	$0.412467\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−353.826	+	204.281i	−1.55870	+	0.899918i	−0.561322	+	0.827598i	$0.689707\pi$
$227$	−353.826	+	204.281i	−1.55870	+	0.899918i	−0.997381	+	0.0723201i	$0.976960\pi$
$228$		0			0
$229$	115.657	−	200.323i	0.505051	−	0.874774i	−0.494932	−	0.868932i	$-0.664807\pi$
$229$	115.657	−	200.323i	0.505051	−	0.874774i	0.999983	−	0.00584253i	$-0.00185974\pi$
$230$		0			0
$231$	14.5471	+	21.7072i	0.0629746	+	0.0939705i
$232$		0			0
$233$			136.907i			0.587584i	0.955869	+	0.293792i	$0.0949173\pi$
$233$			136.907i			0.587584i	−0.955869	+	0.293792i	$0.905083\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−9.70432	−	145.029i	−0.0409465	−	0.611936i
$238$		0			0
$239$	28.1897	+	16.2753i	0.117948	+	0.0680976i	0.557814	−	0.829966i	$-0.311640\pi$
$239$	28.1897	+	16.2753i	0.117948	+	0.0680976i	−0.439865	+	0.898064i	$0.644974\pi$
$240$		0			0
$241$	−105.816	−	183.279i	−0.439071	−	0.760493i	0.558547	−	0.829473i	$-0.311359\pi$
$241$	−105.816	−	183.279i	−0.439071	−	0.760493i	−0.997618	+	0.0689800i	$0.978026\pi$
$242$		0			0
$243$	158.972	−	183.785i	0.654205	−	0.756318i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	61.6978	−	106.864i	0.249789	−	0.432647i
$248$		0			0
$249$	287.504	−	19.2377i	1.15463	−	0.0772600i
$250$		0			0
$251$		−	314.643i		−	1.25356i	−0.779197	−	0.626779i	$-0.784373\pi$
$251$		−	314.643i		−	1.25356i	0.779197	−	0.626779i	$-0.215627\pi$
$252$		0			0
$253$	103.613			0.409536
$254$		0			0
$255$		0			0
$256$		0			0
$257$	27.0876	+	15.6391i	0.105399	+	0.0608524i	0.551773	−	0.833994i	$-0.313951\pi$
$257$	27.0876	+	15.6391i	0.105399	+	0.0608524i	−0.446374	+	0.894847i	$0.647285\pi$
$258$		0			0
$259$	−40.8730	−	70.7941i	−0.157811	−	0.273336i
$260$		0			0
$261$	−245.823	−	101.039i	−0.941850	−	0.387121i
$262$		0			0
$263$	−259.919	+	150.065i	−0.988287	+	0.570588i	−0.904762	−	0.425918i	$-0.859951\pi$
$263$	−259.919	+	150.065i	−0.988287	+	0.570588i	−0.0835251	+	0.996506i	$0.526618\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	28.4324	−	57.8540i	0.106489	−	0.216682i
$268$		0			0
$269$		−	4.75658i		−	0.0176824i	−0.999961	−	0.00884122i	$-0.997186\pi$
$269$		−	4.75658i		−	0.0176824i	0.999961	−	0.00884122i	$-0.00281429\pi$
$270$		0			0
$271$	−331.919			−1.22479			−0.612396	−	0.790551i	$-0.709794\pi$
$271$	−331.919			−1.22479			−0.612396	+	0.790551i	$0.709794\pi$
$272$		0			0
$273$	−58.5416	−	28.7703i	−0.214438	−	0.105386i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	159.572	+	276.386i	0.576071	+	0.997785i	0.995924	+	0.0901929i	$0.0287484\pi$
$277$	159.572	+	276.386i	0.576071	+	0.997785i	−0.419853	+	0.907592i	$0.637918\pi$
$278$		0			0
$279$	−472.771	+	63.5536i	−1.69452	+	0.227791i
$280$		0			0
$281$	193.228	−	111.560i	0.687643	−	0.397011i	−0.115085	−	0.993356i	$-0.536714\pi$
$281$	193.228	−	111.560i	0.687643	−	0.397011i	0.802729	+	0.596345i	$0.203381\pi$
$282$		0			0
$283$	95.6888	−	165.738i	0.338123	−	0.585646i	−0.645957	−	0.763374i	$-0.723541\pi$
$283$	95.6888	−	165.738i	0.338123	−	0.585646i	0.984080	+	0.177728i	$0.0568747\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			209.015i			0.728274i
$288$		0			0
$289$	285.670			0.988479
$290$		0			0
$291$	−33.4033	−	499.204i	−0.114788	−	1.71548i
$292$		0			0
$293$	−327.768	−	189.237i	−1.11866	−	0.645861i	−0.177604	−	0.984102i	$-0.556835\pi$
$293$	−327.768	−	189.237i	−1.11866	−	0.645861i	−0.941059	+	0.338241i	$0.890168\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	57.2576	+	64.7534i	0.192786	+	0.218025i
$298$		0			0
$299$	−223.992	+	129.322i	−0.749136	+	0.432514i
$300$		0			0
$301$	−12.2163	+	21.1593i	−0.0405858	+	0.0702966i
$302$		0			0
$303$	−27.8052	+	1.86053i	−0.0917664	+	0.00614037i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	346.416			1.12839			0.564196	−	0.825641i	$-0.309186\pi$
$307$	346.416			1.12839			0.564196	+	0.825641i	$0.309186\pi$
$308$		0			0
$309$	370.874	−	248.542i	1.20024	−	0.804344i
$310$		0			0
$311$	67.4633	+	38.9499i	0.216924	+	0.125241i	0.604525	−	0.796586i	$-0.293363\pi$
$311$	67.4633	+	38.9499i	0.216924	+	0.125241i	−0.387601	+	0.921827i	$0.626696\pi$
$312$		0			0
$313$	18.2088	+	31.5386i	0.0581752	+	0.100762i	0.893646	−	0.448772i	$-0.148138\pi$
$313$	18.2088	+	31.5386i	0.0581752	+	0.100762i	−0.835471	+	0.549534i	$0.814805\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	207.221	−	119.639i	0.653693	−	0.377410i	−0.136177	−	0.990685i	$-0.543482\pi$
$317$	207.221	−	119.639i	0.653693	−	0.377410i	0.789869	+	0.613275i	$0.210148\pi$
$318$		0			0
$319$	47.2698	−	81.8737i	0.148181	−	0.256657i
$320$		0			0
$321$	170.319	−	346.563i	0.530589	−	1.07964i
$322$		0			0
$323$		−	28.1758i		−	0.0872315i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	139.745	+	68.6778i	0.427354	+	0.210024i
$328$		0			0
$329$	27.9080	+	16.1127i	0.0848266	+	0.0489747i
$330$		0			0
$331$	−24.5386	−	42.5021i	−0.0741348	−	0.128405i	0.826575	−	0.562827i	$-0.190286\pi$
$331$	−24.5386	−	42.5021i	−0.0741348	−	0.128405i	−0.900710	+	0.434422i	$0.856953\pi$
$332$		0			0
$333$	−165.197	−	214.077i	−0.496087	−	0.642875i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−276.158	+	478.319i	−0.819459	+	1.41934i	0.0866225	+	0.996241i	$0.472393\pi$
$337$	−276.158	+	478.319i	−0.819459	+	1.41934i	−0.906081	+	0.423103i	$0.860941\pi$
$338$		0			0
$339$	143.138	+	213.590i	0.422235	+	0.630058i
$340$		0			0
$341$		−	169.682i		−	0.497601i
$342$		0			0
$343$	246.496			0.718646
$344$		0			0
$345$		0			0
$346$		0			0
$347$	347.063	+	200.377i	1.00018	+	0.577455i	0.908302	−	0.418315i	$-0.137379\pi$
$347$	347.063	+	200.377i	1.00018	+	0.577455i	0.0918794	+	0.995770i	$0.470713\pi$
$348$		0			0
$349$	−51.5180	−	89.2318i	−0.147616	−	0.255678i	0.782730	−	0.622362i	$-0.213827\pi$
$349$	−51.5180	−	89.2318i	−0.147616	−	0.255678i	−0.930346	+	0.366683i	$0.880493\pi$
$350$		0			0
$351$	−204.601	−	68.5205i	−0.582909	−	0.195215i
$352$		0			0
$353$	−413.578	+	238.779i	−1.17161	+	0.676428i	−0.954058	−	0.299621i	$-0.903140\pi$
$353$	−413.578	+	238.779i	−1.17161	+	0.676428i	−0.217550	+	0.976049i	$0.569806\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−14.8610	+	0.994394i	−0.0416274	+	0.00278542i
$358$		0			0
$359$		−	585.178i		−	1.63002i	−0.579445	−	0.815012i	$-0.696731\pi$
$359$		−	585.178i		−	1.63002i	0.579445	−	0.815012i	$-0.303269\pi$
$360$		0			0
$361$	−122.578			−0.339552
$362$		0			0
$363$	276.007	−	184.967i	0.760349	−	0.509550i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	18.9727	+	32.8618i	0.0516968	+	0.0895416i	0.890716	−	0.454561i	$-0.150204\pi$
$367$	18.9727	+	32.8618i	0.0516968	+	0.0895416i	−0.839019	+	0.544102i	$0.816870\pi$
$368$		0			0
$369$	92.1141	+	685.230i	0.249632	+	1.85699i
$370$		0			0
$371$	−68.2936	+	39.4293i	−0.184080	+	0.106278i
$372$		0			0
$373$	−57.1561	+	98.9972i	−0.153233	+	0.265408i	−0.932414	−	0.361391i	$-0.882302\pi$
$373$	−57.1561	+	98.9972i	−0.153233	+	0.265408i	0.779181	+	0.626799i	$0.215635\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			235.995i			0.625981i
$378$		0			0
$379$	157.951			0.416757			0.208378	−	0.978048i	$-0.433181\pi$
$379$	157.951			0.416757			0.208378	+	0.978048i	$0.433181\pi$
$380$		0			0
$381$	−120.051	−	58.9992i	−0.315094	−	0.154854i
$382$		0			0
$383$	−56.8675	−	32.8325i	−0.148479	−	0.0857245i	0.423920	−	0.905700i	$-0.360654\pi$
$383$	−56.8675	−	32.8325i	−0.148479	−	0.0857245i	−0.572399	+	0.819975i	$0.693987\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−30.7247	+	74.7520i	−0.0793921	+	0.193158i
$388$		0			0
$389$	−380.293	+	219.562i	−0.977616	+	0.564427i	−0.901550	−	0.432676i	$-0.857569\pi$
$389$	−380.293	+	219.562i	−0.977616	+	0.564427i	−0.0760665	+	0.997103i	$0.524236\pi$
$390$		0			0
$391$	−29.5289	+	51.1456i	−0.0755215	+	0.130807i
$392$		0			0
$393$	157.603	+	235.174i	0.401024	+	0.598407i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−108.265			−0.272707			−0.136353	−	0.990660i	$-0.543538\pi$
$397$	−108.265			−0.272707			−0.136353	+	0.990660i	$0.543538\pi$
$398$		0			0
$399$	−8.41451	−	125.753i	−0.0210890	−	0.315170i
$400$		0			0
$401$	84.9001	+	49.0171i	0.211721	+	0.122237i	0.602111	−	0.798412i	$-0.294326\pi$
$401$	84.9001	+	49.0171i	0.211721	+	0.122237i	−0.390390	+	0.920650i	$0.627660\pi$
$402$		0			0
$403$	211.784	+	366.821i	0.525519	+	0.910226i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	83.2994	−	48.0929i	0.204667	−	0.118164i
$408$		0			0
$409$	30.2529	−	52.3996i	0.0739681	−	0.128116i	−0.826669	−	0.562689i	$-0.809767\pi$
$409$	30.2529	−	52.3996i	0.0739681	−	0.128116i	0.900637	+	0.434572i	$0.143100\pi$
$410$		0			0
$411$	105.632	−	7.06816i	0.257012	−	0.0171975i
$412$		0			0
$413$		−	52.2552i		−	0.126526i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	305.943	−	205.028i	0.733675	−	0.491675i
$418$		0			0
$419$	−12.1092	−	6.99127i	−0.0289003	−	0.0166856i	0.485480	−	0.874248i	$-0.338645\pi$
$419$	−12.1092	−	6.99127i	−0.0289003	−	0.0166856i	−0.514381	+	0.857562i	$0.671978\pi$
$420$		0			0
$421$	115.320	+	199.740i	0.273919	+	0.474442i	0.969862	−	0.243656i	$-0.0783466\pi$
$421$	115.320	+	199.740i	0.273919	+	0.474442i	−0.695943	+	0.718097i	$0.745013\pi$
$422$		0			0
$423$	98.5940	+	40.5243i	0.233083	+	0.0958021i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−84.2953	+	146.004i	−0.197413	+	0.341929i
$428$		0			0
$429$	33.8524	−	68.8825i	0.0789100	−	0.160565i
$430$		0			0
$431$		−	153.008i		−	0.355008i	−0.984120	−	0.177504i	$-0.943198\pi$
$431$		−	153.008i		−	0.355008i	0.984120	−	0.177504i	$-0.0568023\pi$
$432$		0			0
$433$	301.530			0.696374			0.348187	−	0.937425i	$-0.386797\pi$
$433$	301.530			0.696374			0.348187	+	0.937425i	$0.386797\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−432.791	−	249.872i	−0.990368	−	0.571789i
$438$		0			0
$439$	−244.893	−	424.167i	−0.557842	−	0.966211i	−0.997676	−	0.0681318i	$-0.978296\pi$
$439$	−244.893	−	424.167i	−0.557842	−	0.966211i	0.439834	−	0.898079i	$-0.355037\pi$
$440$		0			0
$441$	371.039	−	49.8780i	0.841357	−	0.113102i
$442$		0			0
$443$	86.6072	−	50.0027i	0.195502	−	0.112873i	−0.399054	−	0.916927i	$-0.630661\pi$
$443$	86.6072	−	50.0027i	0.195502	−	0.112873i	0.594556	+	0.804055i	$0.297328\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−384.208	−	573.314i	−0.859526	−	1.28258i
$448$		0			0
$449$		−	561.661i		−	1.25092i	−0.780258	−	0.625458i	$-0.784912\pi$
$449$		−	561.661i		−	1.25092i	0.780258	−	0.625458i	$-0.215088\pi$
$450$		0			0
$451$	−245.935			−0.545311
$452$		0			0
$453$	22.7717	+	340.318i	0.0502687	+	0.751255i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−297.031	−	514.473i	−0.649958	−	1.12576i	−0.983132	−	0.182896i	$-0.941453\pi$
$457$	−297.031	−	514.473i	−0.649958	−	1.12576i	0.333174	−	0.942865i	$-0.391880\pi$
$458$		0			0
$459$	−48.2818	+	9.80934i	−0.105189	+	0.0213711i
$460$		0			0
$461$	115.530	−	66.7015i	0.250608	−	0.144689i	−0.369435	−	0.929257i	$-0.620449\pi$
$461$	115.530	−	66.7015i	0.250608	−	0.144689i	0.620043	+	0.784568i	$0.287115\pi$
$462$		0			0
$463$	242.017	−	419.185i	0.522714	−	0.905368i	−0.476936	−	0.878938i	$-0.658253\pi$
$463$	242.017	−	419.185i	0.522714	−	0.905368i	0.999651	−	0.0264298i	$-0.00841385\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	150.725i		−	0.322751i	−0.986893	−	0.161376i	$-0.948407\pi$
$467$		−	150.725i		−	0.322751i	0.986893	−	0.161376i	$-0.0515931\pi$
$468$		0			0
$469$	14.1104			0.0300862
$470$		0			0
$471$	−408.231	+	273.577i	−0.866733	+	0.580843i
$472$		0			0
$473$	−24.8969	−	14.3742i	−0.0526362	−	0.0303895i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−206.516	+	159.362i	−0.432947	+	0.334092i
$478$		0			0
$479$	−589.607	+	340.410i	−1.23091	+	0.710667i	−0.967220	−	0.253940i	$-0.918274\pi$
$479$	−589.607	+	340.410i	−1.23091	+	0.710667i	−0.263692	+	0.964607i	$0.584940\pi$
$480$		0			0
$481$	−120.052	+	207.936i	−0.249589	+	0.432300i
$482$		0			0
$483$	−116.518	+	237.089i	−0.241238	+	0.490868i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	684.297			1.40513			0.702564	−	0.711621i	$-0.252038\pi$
$487$	684.297			1.40513			0.702564	+	0.711621i	$0.252038\pi$
$488$		0			0
$489$	−639.550	−	314.308i	−1.30787	−	0.642756i
$490$		0			0
$491$	557.013	+	321.592i	1.13445	+	0.654973i	0.945049	−	0.326927i	$-0.106013\pi$
$491$	557.013	+	321.592i	1.13445	+	0.654973i	0.189397	+	0.981901i	$0.439347\pi$
$492$		0			0
$493$	26.9432	+	46.6669i	0.0546514	+	0.0946591i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−226.280	+	130.643i	−0.455291	+	0.262863i
$498$		0			0
$499$	−167.805	+	290.647i	−0.336283	+	0.582459i	−0.983730	−	0.179651i	$-0.942503\pi$
$499$	−167.805	+	290.647i	−0.336283	+	0.582459i	0.647448	+	0.762110i	$0.275836\pi$
$500$		0			0
$501$	376.825	+	562.297i	0.752146	+	1.12235i
$502$		0			0
$503$			402.227i			0.799655i	0.916590	+	0.399828i	$0.130930\pi$
$503$			402.227i			0.799655i	−0.916590	+	0.399828i	$0.869070\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−21.0579	−	314.705i	−0.0415343	−	0.620721i
$508$		0			0
$509$	825.062	+	476.350i	1.62095	+	0.935854i	0.986667	+	0.162749i	$0.0520362\pi$
$509$	825.062	+	476.350i	1.62095	+	0.935854i	0.634279	+	0.773104i	$0.281297\pi$
$510$		0			0
$511$	173.306	+	300.174i	0.339150	+	0.587425i
$512$		0			0
$513$	−83.0061	−	408.558i	−0.161805	−	0.796409i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−18.9589	+	32.8377i	−0.0366709	+	0.0635159i
$518$		0			0
$519$	599.160	−	40.0916i	1.15445	−	0.0772478i
$520$		0			0
$521$			581.220i			1.11558i	0.829980	+	0.557792i	$0.188352\pi$
$521$			581.220i			1.11558i	−0.829980	+	0.557792i	$0.811648\pi$
$522$		0			0
$523$	−873.203			−1.66960			−0.834802	−	0.550550i	$-0.814418\pi$
$523$	−873.203			−1.66960			−0.834802	+	0.550550i	$0.814418\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	83.7588	+	48.3582i	0.158935	+	0.0917613i
$528$		0			0
$529$	259.244	+	449.024i	0.490064	+	0.848817i
$530$		0			0
$531$	−23.0292	−	171.313i	−0.0433695	−	0.322623i
$532$		0			0
$533$	531.668	−	306.958i	0.997500	−	0.575907i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−238.391	+	485.076i	−0.443932	+	0.903307i
$538$		0			0
$539$			133.169i			0.247067i
$540$		0			0
$541$	285.224			0.527216			0.263608	−	0.964630i	$-0.415087\pi$
$541$	285.224			0.527216			0.263608	+	0.964630i	$0.415087\pi$
$542$		0			0
$543$	−711.035	−	349.439i	−1.30946	−	0.643534i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−124.431	−	215.520i	−0.227479	−	0.394004i	0.729582	−	0.683894i	$-0.239715\pi$
$547$	−124.431	−	215.520i	−0.227479	−	0.394004i	−0.957060	+	0.289889i	$0.906382\pi$
$548$		0			0
$549$	−212.008	+	515.806i	−0.386170	+	0.939537i
$550$		0			0
$551$	−394.893	+	227.991i	−0.716684	+	0.413777i
$552$		0			0
$553$	−65.9124	+	114.164i	−0.119191	+	0.206444i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	865.154i		−	1.55324i	−0.629971	−	0.776619i	$-0.716933\pi$
$557$		−	865.154i		−	1.55324i	0.629971	−	0.776619i	$-0.283067\pi$
$558$		0			0
$559$	71.7635			0.128378
$560$		0			0
$561$	−1.17005	−	17.4861i	−0.00208564	−	0.0311695i
$562$		0			0
$563$	−51.7396	−	29.8719i	−0.0918998	−	0.0530584i	0.453346	−	0.891335i	$-0.350230\pi$
$563$	−51.7396	−	29.8719i	−0.0918998	−	0.0530584i	−0.545246	+	0.838276i	$0.683564\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−212.560	+	58.1997i	−0.374885	+	0.102645i
$568$		0			0
$569$	539.984	−	311.760i	0.949006	−	0.547909i	0.0562337	−	0.998418i	$-0.482091\pi$
$569$	539.984	−	311.760i	0.949006	−	0.547909i	0.892772	+	0.450509i	$0.148757\pi$
$570$		0			0
$571$	173.203	−	299.996i	0.303332	−	0.525387i	−0.673556	−	0.739136i	$-0.735234\pi$
$571$	173.203	−	299.996i	0.303332	−	0.525387i	0.976889	+	0.213749i	$0.0685675\pi$
$572$		0			0
$573$	677.402	−	45.3270i	1.18220	−	0.0791047i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−772.123			−1.33817			−0.669084	−	0.743187i	$-0.733313\pi$
$577$	−772.123			−1.33817			−0.669084	+	0.743187i	$0.733313\pi$
$578$		0			0
$579$	541.701	−	363.023i	0.935581	−	0.626982i
$580$		0			0
$581$	−226.317	−	130.664i	−0.389530	−	0.224895i
$582$		0			0
$583$	−46.3942	−	80.3571i	−0.0795784	−	0.137834i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−333.912	+	192.784i	−0.568845	+	0.328423i	−0.756688	−	0.653776i	$-0.773184\pi$
$587$	−333.912	+	192.784i	−0.568845	+	0.328423i	0.187843	+	0.982199i	$0.439850\pi$
$588$		0			0
$589$	−409.204	+	708.762i	−0.694744	+	1.20333i
$590$		0			0
$591$	−344.108	+	700.187i	−0.582247	+	1.18475i
$592$		0			0
$593$		−	685.677i		−	1.15628i	−0.815936	−	0.578142i	$-0.803778\pi$
$593$		−	685.677i		−	1.15628i	0.815936	−	0.578142i	$-0.196222\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	681.509	+	334.929i	1.14156	+	0.561020i
$598$		0			0
$599$	628.802	+	363.039i	1.04975	+	0.606075i	0.922580	−	0.385806i	$-0.126076\pi$
$599$	628.802	+	363.039i	1.04975	+	0.606075i	0.127173	+	0.991881i	$0.459410\pi$
$600$		0			0
$601$	53.1719	+	92.0964i	0.0884723	+	0.153239i	0.906866	−	0.421420i	$-0.138468\pi$
$601$	53.1719	+	92.0964i	0.0884723	+	0.153239i	−0.818393	+	0.574659i	$0.805135\pi$
$602$		0			0
$603$	46.2594	−	6.21856i	0.0767155	−	0.0103127i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	124.449	−	215.552i	0.205023	−	0.355111i	−0.745117	−	0.666934i	$-0.767606\pi$
$607$	124.449	−	215.552i	0.205023	−	0.355111i	0.950140	+	0.311823i	$0.100940\pi$
$608$		0			0
$609$	134.188	+	200.235i	0.220342	+	0.328794i
$610$		0			0
$611$		−	94.6522i		−	0.154914i
$612$		0			0
$613$	−1125.21			−1.83558			−0.917791	−	0.397064i	$-0.870029\pi$
$613$	−1125.21			−1.83558			−0.917791	+	0.397064i	$0.870029\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	214.708	+	123.962i	0.347987	+	0.200911i	0.663798	−	0.747912i	$-0.268943\pi$
$617$	214.708	+	123.962i	0.347987	+	0.200911i	−0.315811	+	0.948822i	$0.602277\pi$
$618$		0			0
$619$	−173.326	−	300.209i	−0.280009	−	0.484990i	0.691378	−	0.722494i	$-0.257004\pi$
$619$	−173.326	−	300.209i	−0.280009	−	0.484990i	−0.971387	+	0.237504i	$0.923671\pi$
$620$		0			0
$621$	−277.503	+	828.620i	−0.446865	+	1.33433i
$622$		0			0
$623$	−50.6307	+	29.2317i	−0.0812693	+	0.0469208i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	147.966	−	9.90086i	0.235991	−	0.0157909i
$628$		0			0
$629$			54.8246i			0.0871616i
$630$		0			0
$631$	380.005			0.602226			0.301113	−	0.953588i	$-0.402642\pi$
$631$	380.005			0.602226			0.301113	+	0.953588i	$0.402642\pi$
$632$		0			0
$633$	−733.504	+	491.559i	−1.15877	+	0.776555i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−166.212	−	287.888i	−0.260929	−	0.451943i
$638$		0			0
$639$	−684.257	+	528.020i	−1.07082	+	0.826322i
$640$		0			0
$641$	−947.308	+	546.929i	−1.47786	+	0.853243i	−0.999687	−	0.0250231i	$-0.992034\pi$
$641$	−947.308	+	546.929i	−1.47786	+	0.853243i	−0.478173	+	0.878266i	$0.658701\pi$
$642$		0			0
$643$	416.678	−	721.708i	0.648022	−	1.12241i	−0.335573	−	0.942014i	$-0.608930\pi$
$643$	416.678	−	721.708i	0.648022	−	1.12241i	0.983595	−	0.180393i	$-0.0577368\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			801.328i			1.23853i	0.785183	+	0.619264i	$0.212569\pi$
$647$			801.328i			1.23853i	−0.785183	+	0.619264i	$0.787431\pi$
$648$		0			0
$649$	61.4857			0.0947392
$650$		0			0
$651$	388.271	+	190.816i	0.596422	+	0.293112i
$652$		0			0
$653$	799.139	+	461.383i	1.22380	+	0.706559i	0.965725	−	0.259567i	$-0.0835799\pi$
$653$	799.139	+	461.383i	1.22380	+	0.706559i	0.258071	+	0.966126i	$0.416913\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	700.450	+	907.708i	1.06613	+	1.38160i
$658$		0			0
$659$	−707.274	+	408.345i	−1.07325	+	0.619643i	−0.929068	−	0.369908i	$-0.879389\pi$
$659$	−707.274	+	408.345i	−1.07325	+	0.619643i	−0.144185	+	0.989551i	$0.546056\pi$
$660$		0			0
$661$	327.247	−	566.808i	0.495078	−	0.857501i	−0.504906	−	0.863174i	$-0.668473\pi$
$661$	327.247	−	566.808i	0.495078	−	0.857501i	0.999984	+	0.00567397i	$0.00180609\pi$
$662$		0			0
$663$	24.3543	+	36.3414i	0.0367334	+	0.0548135i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	955.763			1.43293
$668$		0			0
$669$	−86.5836	−	1293.97i	−0.129422	−	1.93419i
$670$		0			0
$671$	−171.794	−	99.1854i	−0.256027	−	0.147817i
$672$		0			0
$673$	−237.017	−	410.526i	−0.352180	−	0.609994i	0.634451	−	0.772963i	$-0.281226\pi$
$673$	−237.017	−	410.526i	−0.352180	−	0.609994i	−0.986631	+	0.162969i	$0.947893\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	815.479	−	470.817i	1.20455	−	0.695446i	0.242984	−	0.970030i	$-0.421874\pi$
$677$	815.479	−	470.817i	1.20455	−	0.695446i	0.961563	+	0.274584i	$0.0885403\pi$
$678$		0			0
$679$	−226.877	+	392.963i	−0.334134	+	0.578737i
$680$		0			0
$681$	1222.95	−	81.8315i	1.79582	−	0.120164i
$682$		0			0
$683$			388.521i			0.568845i	0.958699	+	0.284422i	$0.0918018\pi$
$683$			388.521i			0.568845i	−0.958699	+	0.284422i	$0.908198\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−576.464	+	386.319i	−0.839104	+	0.562328i
$688$		0			0
$689$	200.592	+	115.812i	0.291134	+	0.168087i
$690$		0			0
$691$	465.511	+	806.289i	0.673678	+	1.16684i	0.976853	+	0.213909i	$0.0686198\pi$
$691$	465.511	+	806.289i	0.673678	+	1.16684i	−0.303176	+	0.952935i	$0.598047\pi$
$692$		0			0
$693$	−10.4442	−	77.6937i	−0.0150710	−	0.112112i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	70.0899	−	121.399i	0.100559	−	0.174174i
$698$		0			0
$699$	181.155	−	368.612i	0.259163	−	0.527342i
$700$		0			0
$701$		−	213.622i		−	0.304739i	−0.988324	−	0.152370i	$-0.951310\pi$
$701$		−	213.622i		−	0.304739i	0.988324	−	0.152370i	$-0.0486904\pi$
$702$		0			0
$703$	−463.923			−0.659919
$704$		0			0
$705$		0			0
$706$		0			0
$707$	21.8877	+	12.6369i	0.0309585	+	0.0178739i
$708$		0			0
$709$	236.600	+	409.804i	0.333710	+	0.578002i	0.983236	−	0.182337i	$-0.0583661\pi$
$709$	236.600	+	409.804i	0.333710	+	0.578002i	−0.649526	+	0.760339i	$0.725033\pi$
$710$		0			0
$711$	−165.773	+	403.320i	−0.233155	+	0.567257i
$712$		0			0
$713$	1485.60	−	857.712i	2.08359	−	1.20296i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−54.3632	−	81.1205i	−0.0758203	−	0.113139i
$718$		0			0
$719$		−	113.785i		−	0.158254i	−0.996865	−	0.0791272i	$-0.974787\pi$
$719$		−	113.785i		−	0.158254i	0.996865	−	0.0791272i	$-0.0252133\pi$
$720$		0			0
$721$	−404.901			−0.561582
$722$		0			0
$723$	42.3880	+	633.480i	0.0586280	+	0.876182i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	0.376667	+	0.652407i	0.000518112	+	0.000897396i	0.866284	−	0.499551i	$-0.166502\pi$
$727$	0.376667	+	0.652407i	0.000518112	+	0.000897396i	−0.865766	+	0.500449i	$0.833168\pi$
$728$		0			0
$729$	−671.203	+	284.477i	−0.920718	+	0.390229i
$730$		0			0
$731$	14.1909	−	8.19312i	0.0194130	−	0.0112081i
$732$		0			0
$733$	−301.475	+	522.169i	−0.411289	+	0.712373i	−0.995031	−	0.0995662i	$-0.968254\pi$
$733$	−301.475	+	522.169i	−0.411289	+	0.712373i	0.583742	+	0.811939i	$0.301588\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			16.6029i			0.0225277i
$738$		0			0
$739$	362.775			0.490900			0.245450	−	0.969409i	$-0.421064\pi$
$739$	362.775			0.490900			0.245450	+	0.969409i	$0.421064\pi$
$740$		0			0
$741$	−307.518	+	206.084i	−0.415005	+	0.278116i
$742$		0			0
$743$	951.039	+	549.083i	1.28000	+	0.739008i	0.976848	−	0.213935i	$-0.0686279\pi$
$743$	951.039	+	549.083i	1.28000	+	0.739008i	0.303151	+	0.952942i	$0.401961\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−799.537	−	328.627i	−1.07033	−	0.439930i
$748$		0			0
$749$	−303.294	+	175.107i	−0.404932	+	0.233787i
$750$		0			0
$751$	−510.640	+	884.454i	−0.679946	+	1.17770i	0.295051	+	0.955482i	$0.404664\pi$
$751$	−510.640	+	884.454i	−0.679946	+	1.17770i	−0.974997	+	0.222220i	$0.928670\pi$
$752$		0			0
$753$	−416.334	+	847.153i	−0.552901	+	1.12504i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−314.598			−0.415585			−0.207793	−	0.978173i	$-0.566628\pi$
$757$	−314.598			−0.415585			−0.207793	+	0.978173i	$0.566628\pi$
$758$		0			0
$759$	−278.969	−	137.100i	−0.367549	−	0.180632i
$760$		0			0
$761$	740.520	+	427.540i	0.973089	+	0.561813i	0.900176	−	0.435525i	$-0.143437\pi$
$761$	740.520	+	427.540i	0.973089	+	0.561813i	0.0729122	+	0.997338i	$0.476771\pi$
$762$		0			0
$763$	−70.6084	−	122.297i	−0.0925404	−	0.160285i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−132.921	+	76.7419i	−0.173300	+	0.100055i
$768$		0			0
$769$	214.504	−	371.532i	0.278939	−	0.483136i	−0.692182	−	0.721723i	$-0.743351\pi$
$769$	214.504	−	371.532i	0.278939	−	0.483136i	0.971121	+	0.238586i	$0.0766840\pi$
$770$		0			0
$771$	−52.2379	−	77.9493i	−0.0677535	−	0.101102i
$772$		0			0
$773$		−	153.265i		−	0.198273i	−0.995074	−	0.0991366i	$-0.968392\pi$
$773$		−	153.265i		−	0.198273i	0.995074	−	0.0991366i	$-0.0316081\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	16.3730	+	244.691i	0.0210721	+	0.314918i
$778$		0			0
$779$	1027.27	+	593.097i	1.31871	+	0.761357i
$780$		0			0
$781$	−153.720	−	266.250i	−0.196824	−	0.340910i
$782$		0			0
$783$	528.166	+	597.311i	0.674541	+	0.762849i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−188.838	+	327.078i	−0.239947	+	0.415601i	−0.960699	−	0.277593i	$-0.910463\pi$
$787$	−188.838	+	327.078i	−0.239947	+	0.415601i	0.720752	+	0.693193i	$0.243797\pi$
$788$		0			0
$789$	898.378	−	60.1132i	1.13863	−	0.0761891i
$790$		0			0
$791$		−	233.186i		−	0.294799i
$792$		0			0
$793$	495.184			0.624444
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−517.022	−	298.503i	−0.648711	−	0.374533i	0.139251	−	0.990257i	$-0.455530\pi$
$797$	−517.022	−	298.503i	−0.648711	−	0.374533i	−0.787962	+	0.615724i	$0.788864\pi$
$798$		0			0
$799$	−10.8063	−	18.7170i	−0.0135248	−	0.0234256i
$800$		0			0
$801$	−153.104	+	118.146i	−0.191142	+	0.147498i
$802$		0			0
$803$	−353.197	+	203.919i	−0.439847	+	0.253946i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−6.29389	+	12.8067i	−0.00779911	+	0.0158696i
$808$		0			0
$809$		−	1144.94i		−	1.41526i	−0.706585	−	0.707628i	$-0.749765\pi$
$809$		−	1144.94i		−	1.41526i	0.706585	−	0.707628i	$-0.250235\pi$
$810$		0			0
$811$	227.892			0.281001			0.140501	−	0.990081i	$-0.455129\pi$
$811$	227.892			0.281001			0.140501	+	0.990081i	$0.455129\pi$
$812$		0			0
$813$	893.666	+	439.194i	1.09922	+	0.540213i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	69.3297	+	120.083i	0.0848589	+	0.146980i
$818$		0			0
$819$	119.550	+	154.924i	0.145971	+	0.189162i
$820$		0			0
$821$	9.97405	−	5.75852i	0.0121487	−	0.00701403i	−0.493913	−	0.869511i	$-0.664434\pi$
$821$	9.97405	−	5.75852i	0.0121487	−	0.00701403i	0.506062	+	0.862497i	$0.331101\pi$
$822$		0			0
$823$	44.1399	−	76.4526i	0.0536330	−	0.0928950i	−0.837962	−	0.545728i	$-0.816253\pi$
$823$	44.1399	−	76.4526i	0.0536330	−	0.0928950i	0.891595	+	0.452833i	$0.149587\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			149.980i			0.181355i	0.995880	+	0.0906773i	$0.0289032\pi$
$827$			149.980i			0.181355i	−0.995880	+	0.0906773i	$0.971097\pi$
$828$		0			0
$829$	−1074.30			−1.29589			−0.647947	−	0.761685i	$-0.724372\pi$
$829$	−1074.30			−1.29589			−0.647947	+	0.761685i	$0.724372\pi$
$830$		0			0
$831$	−63.9217	−	955.295i	−0.0769214	−	1.14957i
$832$		0			0
$833$	−65.7354	−	37.9523i	−0.0789140	−	0.0455610i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	1356.99	+	454.455i	1.62126	+	0.542957i
$838$		0			0
$839$	−714.738	+	412.654i	−0.851893	+	0.491840i	−0.861289	−	0.508115i	$-0.830342\pi$
$839$	−714.738	+	412.654i	−0.851893	+	0.491840i	0.00939630	+	0.999956i	$0.497009\pi$
$840$		0			0
$841$	15.5348	−	26.9071i	0.0184718	−	0.0319941i
$842$		0			0
$843$	−667.867	+	44.6890i	−0.792251	+	0.0530119i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−301.330			−0.355761
$848$		0			0
$849$	−476.939	+	319.622i	−0.561765	+	0.376468i
$850$		0			0
$851$	842.128	+	486.203i	0.989575	+	0.571331i
$852$		0			0
$853$	−493.807	−	855.298i	−0.578906	−	1.00269i	−0.995605	−	0.0936499i	$-0.970147\pi$
$853$	−493.807	−	855.298i	−0.578906	−	1.00269i	0.416699	−	0.909044i	$-0.363187\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	760.254	−	438.933i	0.887111	−	0.512174i	0.0141144	−	0.999900i	$-0.495507\pi$
$857$	760.254	−	438.933i	0.887111	−	0.512174i	0.872996	+	0.487727i	$0.162174\pi$
$858$		0			0
$859$	506.900	−	877.977i	0.590105	−	1.02209i	−0.404113	−	0.914709i	$-0.632420\pi$
$859$	506.900	−	877.977i	0.590105	−	1.02209i	0.994218	−	0.107383i	$-0.0342470\pi$
$860$		0			0
$861$	276.567	−	562.756i	0.321216	−	0.653608i
$862$		0			0
$863$		−	1206.16i		−	1.39764i	−0.715300	−	0.698818i	$-0.753710\pi$
$863$		−	1206.16i		−	1.39764i	0.715300	−	0.698818i	$-0.246290\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−769.146	−	377.998i	−0.887135	−	0.435984i
$868$		0			0
$869$	−134.330	−	77.5553i	−0.154580	−	0.0892466i
$870$		0			0
$871$	−20.7226	−	35.8926i	−0.0237917	−	0.0412084i
$872$		0			0
$873$	−570.609	+	1388.27i	−0.653619	+	1.59023i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	90.5257	−	156.795i	0.103222	−	0.178786i	−0.809788	−	0.586722i	$-0.800418\pi$
$877$	90.5257	−	156.795i	0.103222	−	0.178786i	0.913010	+	0.407936i	$0.133751\pi$
$878$		0			0
$879$	632.094	+	943.209i	0.719106	+	1.07305i
$880$		0			0
$881$			442.390i			0.502146i	0.967968	+	0.251073i	$0.0807834\pi$
$881$			442.390i			0.502146i	−0.967968	+	0.251073i	$0.919217\pi$
$882$		0			0
$883$	−177.122			−0.200591			−0.100296	−	0.994958i	$-0.531979\pi$
$883$	−177.122			−0.200591			−0.100296	+	0.994958i	$0.531979\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	834.177	+	481.612i	0.940447	+	0.542968i	0.890101	−	0.455764i	$-0.150634\pi$
$887$	834.177	+	481.612i	0.940447	+	0.542968i	0.0503469	+	0.998732i	$0.483967\pi$
$888$		0			0
$889$	60.6577	+	105.062i	0.0682314	+	0.118180i
$890$		0			0
$891$	−68.4802	−	250.107i	−0.0768577	−	0.280703i
$892$		0			0
$893$	158.383	−	91.4422i	0.177360	−	0.102399i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	774.199	−	51.8040i	0.863098	−	0.0577525i
$898$		0			0
$899$		−	1565.21i		−	1.74106i
$900$		0			0
$901$	52.8881			0.0586994
$902$		0			0
$903$	60.8894	−	40.8052i	0.0674301	−	0.0451885i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−415.179	−	719.111i	−0.457750	−	0.792846i	0.541092	−	0.840963i	$-0.318011\pi$
$907$	−415.179	−	719.111i	−0.457750	−	0.792846i	−0.998842	+	0.0481178i	$0.984678\pi$
$908$		0			0
$909$	77.3254	+	31.7824i	0.0850664	+	0.0349642i
$910$		0			0
$911$	508.041	−	293.318i	0.557674	−	0.321973i	−0.194537	−	0.980895i	$-0.562320\pi$
$911$	508.041	−	293.318i	0.557674	−	0.321973i	0.752212	+	0.658922i	$0.228987\pi$
$912$		0			0
$913$	153.745	−	266.294i	0.168395	−	0.291669i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	256.751i		−	0.279990i
$918$		0			0
$919$	−34.9078			−0.0379846			−0.0189923	−	0.999820i	$-0.506046\pi$
$919$	−34.9078			−0.0379846			−0.0189923	+	0.999820i	$0.506046\pi$
$920$		0			0
$921$	−932.700	−	458.377i	−1.01270	−	0.497695i
$922$		0			0
$923$	664.628	+	383.723i	0.720074	+	0.415735i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1327.42	+	178.442i	−1.43195	+	0.192494i
$928$		0			0
$929$	−1415.66	+	817.330i	−1.52385	+	0.879796i	−0.524250	+	0.851565i	$0.675654\pi$
$929$	−1415.66	+	817.330i	−1.52385	+	0.879796i	−0.999601	+	0.0282314i	$0.991012\pi$
$930$		0			0
$931$	321.150	−	556.249i	0.344952	−	0.597475i
$932$		0			0
$933$	−130.101	−	194.137i	−0.139444	−	0.208078i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1714.52			−1.82980			−0.914898	−	0.403684i	$-0.867730\pi$
$937$	−1714.52			−1.82980			−0.914898	+	0.403684i	$0.867730\pi$
$938$		0			0
$939$	−7.29414	−	109.009i	−0.00776799	−	0.116091i
$940$		0			0
$941$	−899.820	−	519.511i	−0.956238	−	0.552084i	−0.0612251	−	0.998124i	$-0.519501\pi$
$941$	−899.820	−	519.511i	−0.956238	−	0.552084i	−0.895013	+	0.446040i	$0.852834\pi$
$942$		0			0
$943$	−1243.16	−	2153.22i	−1.31830	−	2.28337i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	708.957	−	409.316i	0.748634	−	0.432224i	−0.0765658	−	0.997065i	$-0.524396\pi$
$947$	708.957	−	409.316i	0.748634	−	0.432224i	0.825200	+	0.564840i	$0.191062\pi$
$948$		0			0
$949$	509.032	−	881.670i	0.536388	−	0.929051i
$950$		0			0
$951$	−716.231	+	47.9252i	−0.753135	+	0.0503946i
$952$		0			0
$953$			0.226778i			0.000237962i	1.00000		0.000118981i	$3.78728e-5\pi$
$953$			0.226778i			0.000237962i	−1.00000		0.000118981i	$0.999962\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−235.605	+	157.892i	−0.246192	+	0.164986i
$958$		0			0
$959$	−83.1513	−	48.0074i	−0.0867062	−	0.0500599i
$960$		0			0
$961$	−924.137	−	1600.65i	−0.961641	−	1.66561i
$962$		0			0
$963$	−917.143	+	707.731i	−0.952381	+	0.734923i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	83.4831	−	144.597i	0.0863321	−	0.149532i	−0.819626	−	0.572899i	$-0.805819\pi$
$967$	83.4831	−	144.597i	0.0863321	−	0.149532i	0.905958	+	0.423367i	$0.139152\pi$
$968$		0			0
$969$	−37.2821	+	75.8611i	−0.0384748	+	0.0782881i
$970$		0			0
$971$		−	1818.76i		−	1.87308i	−0.350557	−	0.936542i	$-0.614008\pi$
$971$		−	1818.76i		−	1.87308i	0.350557	−	0.936542i	$-0.385992\pi$
$972$		0			0
$973$	−334.012			−0.343281
$974$		0			0
$975$		0			0
$976$		0			0
$977$	747.609	+	431.632i	0.765209	+	0.441794i	0.831163	−	0.556029i	$-0.187676\pi$
$977$	747.609	+	431.632i	0.765209	+	0.441794i	−0.0659538	+	0.997823i	$0.521009\pi$
$978$		0			0
$979$	−34.3952	−	59.5743i	−0.0351330	−	0.0608522i
$980$		0			0
$981$	−285.378	−	369.820i	−0.290906	−	0.376982i
$982$		0			0
$983$	1158.47	−	668.841i	1.17850	−	0.680408i	0.222833	−	0.974857i	$-0.428469\pi$
$983$	1158.47	−	668.841i	1.17850	−	0.680408i	0.955667	+	0.294449i	$0.0951361\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−53.8199	−	80.3099i	−0.0545288	−	0.0813676i
$988$		0			0
$989$		−	290.637i		−	0.293870i
$990$		0			0
$991$	−738.550			−0.745257			−0.372629	−	0.927981i	$-0.621543\pi$
$991$	−738.550			−0.745257			−0.372629	+	0.927981i	$0.621543\pi$
$992$		0			0
$993$	9.82974	+	146.903i	0.00989903	+	0.147939i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	256.908	+	444.977i	0.257681	+	0.446316i	0.965620	−	0.259957i	$-0.0837084\pi$
$997$	256.908	+	444.977i	0.257681	+	0.446316i	−0.707939	+	0.706273i	$0.750375\pi$
$998$		0			0
$999$	161.514	+	794.975i	0.161676	+	0.795771i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.p.f.401.2		24
3.2	odd	2		2700.3.p.f.2501.9		24
5.2	odd	4		180.3.t.a.149.5	yes	24
5.3	odd	4		180.3.t.a.149.8	yes	24
5.4	even	2	inner	900.3.p.f.401.11		24
9.2	odd	6	inner	900.3.p.f.101.2		24
9.7	even	3		2700.3.p.f.1601.9		24
15.2	even	4		540.3.t.a.449.6		24
15.8	even	4		540.3.t.a.449.2		24
15.14	odd	2		2700.3.p.f.2501.4		24
45.2	even	12		180.3.t.a.29.8	yes	24
45.7	odd	12		540.3.t.a.89.2		24
45.13	odd	12		1620.3.b.b.809.5		24
45.22	odd	12		1620.3.b.b.809.19		24
45.23	even	12		1620.3.b.b.809.20		24
45.29	odd	6	inner	900.3.p.f.101.11		24
45.32	even	12		1620.3.b.b.809.6		24
45.34	even	6		2700.3.p.f.1601.4		24
45.38	even	12		180.3.t.a.29.5	✓	24
45.43	odd	12		540.3.t.a.89.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.t.a.29.5	✓	24	45.38	even	12
180.3.t.a.29.8	yes	24	45.2	even	12
180.3.t.a.149.5	yes	24	5.2	odd	4
180.3.t.a.149.8	yes	24	5.3	odd	4
540.3.t.a.89.2		24	45.7	odd	12
540.3.t.a.89.6		24	45.43	odd	12
540.3.t.a.449.2		24	15.8	even	4
540.3.t.a.449.6		24	15.2	even	4
900.3.p.f.101.2		24	9.2	odd	6	inner
900.3.p.f.101.11		24	45.29	odd	6	inner
900.3.p.f.401.2		24	1.1	even	1	trivial
900.3.p.f.401.11		24	5.4	even	2	inner
1620.3.b.b.809.5		24	45.13	odd	12
1620.3.b.b.809.6		24	45.32	even	12
1620.3.b.b.809.19		24	45.22	odd	12
1620.3.b.b.809.20		24	45.23	even	12
2700.3.p.f.1601.4		24	45.34	even	6
2700.3.p.f.1601.9		24	9.7	even	3
2700.3.p.f.2501.4		24	15.14	odd	2
2700.3.p.f.2501.9		24	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.69243 - 1.32320i) q^{3} +(1.36039 + 2.35627i) q^{7} +(5.49831 + 7.12521i) q^{9} +O(q^{10})\)	\(q+(-2.69243 - 1.32320i) q^{3} +(1.36039 + 2.35627i) q^{7} +(5.49831 + 7.12521i) q^{9} +(-2.77248 + 1.60069i) q^{11} +(3.99574 - 6.92082i) q^{13} -1.82475i q^{17} +15.4409 q^{19} +(-0.544949 - 8.14414i) q^{21} +(-28.0288 - 16.1825i) q^{23} +(-5.37572 - 26.4594i) q^{27} +(-25.5744 + 14.7654i) q^{29} +(-26.5013 + 45.9016i) q^{31} +(9.58274 - 0.641210i) q^{33} -30.0450 q^{37} +(-19.9158 + 13.3466i) q^{39} +(66.5294 + 38.4108i) q^{41} +(4.49000 + 7.77691i) q^{43} +(10.2573 - 5.92207i) q^{47} +(20.7987 - 36.0244i) q^{49} +(-2.41450 + 4.91300i) q^{51} +28.9838i q^{53} +(-41.5735 - 20.4313i) q^{57} +(-16.6328 - 9.60298i) q^{59} +(30.9820 + 53.6624i) q^{61} +(-9.30905 + 22.6485i) q^{63} +(2.59309 - 4.49136i) q^{67} +(54.0530 + 80.6577i) q^{69} +96.0332i q^{71} +127.394 q^{73} +(-7.54332 - 4.35514i) q^{77} +(24.2255 + 41.9598i) q^{79} +(-20.5373 + 78.3532i) q^{81} +(-83.1807 + 48.0244i) q^{83} +(88.3948 - 5.91477i) q^{87} +21.4877i q^{89} +21.7431 q^{91} +(132.090 - 88.5202i) q^{93} +(83.3867 + 144.430i) q^{97} +(-26.6492 - 10.9534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{9}+O(q^{10}) \) 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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