LMFDB - Embedded newform 900.3.u.c.149.1

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			149.1
Character	$\chi$	$=$	900.149
Dual form			900.3.u.c.749.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.96464 + 0.459278i) q^{3} +(7.16186 - 4.13490i) q^{7} +(8.57813 - 2.72318i) q^{9} +O(q^{10})$	\(q+(-2.96464 + 0.459278i) q^{3} +(7.16186 - 4.13490i) q^{7} +(8.57813 - 2.72318i) q^{9} +(3.29604 - 1.90297i) q^{11} +(-16.7290 - 9.65850i) q^{13} +7.87471 q^{17} +12.3401 q^{19} +(-19.3332 + 15.5478i) q^{21} +(-0.604705 + 1.04738i) q^{23} +(-24.1803 + 12.0130i) q^{27} +(-10.7443 + 6.20324i) q^{29} +(-4.65731 + 8.06669i) q^{31} +(-8.89757 + 7.15541i) q^{33} -37.0571i q^{37} +(54.0314 + 20.9507i) q^{39} +(40.1391 + 23.1743i) q^{41} +(-53.1884 + 30.7083i) q^{43} +(-46.0201 - 79.7091i) q^{47} +(9.69479 - 16.7919i) q^{49} +(-23.3456 + 3.61668i) q^{51} +52.1540 q^{53} +(-36.5838 + 5.66752i) q^{57} +(54.4701 + 31.4484i) q^{59} +(11.6631 + 20.2011i) q^{61} +(50.1752 - 54.9727i) q^{63} +(-93.8237 - 54.1692i) q^{67} +(1.31169 - 3.38283i) q^{69} -134.509i q^{71} -66.7798i q^{73} +(15.7372 - 27.2576i) q^{77} +(-62.2089 - 107.749i) q^{79} +(66.1686 - 46.7196i) q^{81} +(-40.3522 - 69.8921i) q^{83} +(29.0040 - 23.3250i) q^{87} -176.513i q^{89} -159.748 q^{91} +(10.1024 - 26.0538i) q^{93} +(79.5774 - 45.9441i) q^{97} +(23.0917 - 25.2997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.96464	+	0.459278i	−0.988212	+	0.153093i
$3$	−2.96464	+	0.459278i	−0.988212	+	0.153093i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	7.16186	−	4.13490i	1.02312	−	0.590700i	0.108115	−	0.994138i	$-0.465518\pi$
$7$	7.16186	−	4.13490i	1.02312	−	0.590700i	0.915007	+	0.403438i	$0.132185\pi$
$8$		0			0
$9$	8.57813	−	2.72318i	0.953125	−	0.302576i
$10$		0			0
$11$	3.29604	−	1.90297i	0.299640	−	0.172997i	−0.342641	−	0.939466i	$-0.611321\pi$
$11$	3.29604	−	1.90297i	0.299640	−	0.172997i	0.642281	+	0.766469i	$0.277988\pi$
$12$		0			0
$13$	−16.7290	−	9.65850i	−1.28685	−	0.742962i	−0.308757	−	0.951141i	$-0.599913\pi$
$13$	−16.7290	−	9.65850i	−1.28685	−	0.742962i	−0.978091	+	0.208179i	$0.933246\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	7.87471			0.463218			0.231609	−	0.972809i	$-0.425601\pi$
$17$	7.87471			0.463218			0.231609	+	0.972809i	$0.425601\pi$
$18$		0			0
$19$	12.3401			0.649478			0.324739	−	0.945804i	$-0.394724\pi$
$19$	12.3401			0.649478			0.324739	+	0.945804i	$0.394724\pi$
$20$		0			0
$21$	−19.3332	+	15.5478i	−0.920630	+	0.740369i
$22$		0			0
$23$	−0.604705	+	1.04738i	−0.0262915	+	0.0455383i	−0.878872	−	0.477058i	$-0.841703\pi$
$23$	−0.604705	+	1.04738i	−0.0262915	+	0.0455383i	0.852580	+	0.522596i	$0.175036\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−24.1803	+	12.0130i	−0.895568	+	0.444925i
$28$		0			0
$29$	−10.7443	+	6.20324i	−0.370494	+	0.213905i	−0.673674	−	0.739028i	$-0.735285\pi$
$29$	−10.7443	+	6.20324i	−0.370494	+	0.213905i	0.303180	+	0.952933i	$0.401952\pi$
$30$		0			0
$31$	−4.65731	+	8.06669i	−0.150236	+	0.260216i	−0.931314	−	0.364217i	$-0.881337\pi$
$31$	−4.65731	+	8.06669i	−0.150236	+	0.260216i	0.781078	+	0.624433i	$0.214670\pi$
$32$		0			0
$33$	−8.89757	+	7.15541i	−0.269623	+	0.216831i
$34$		0			0
$35$		0			0
$36$		0			0
$37$		−	37.0571i		−	1.00154i	−0.865579	−	0.500772i	$-0.833050\pi$
$37$		−	37.0571i		−	1.00154i	0.865579	−	0.500772i	$-0.166950\pi$
$38$		0			0
$39$	54.0314	+	20.9507i	1.38542	+	0.537197i
$40$		0			0
$41$	40.1391	+	23.1743i	0.979002	+	0.565227i	0.901969	−	0.431802i	$-0.142122\pi$
$41$	40.1391	+	23.1743i	0.979002	+	0.565227i	0.0770331	+	0.997029i	$0.475455\pi$
$42$		0			0
$43$	−53.1884	+	30.7083i	−1.23694	+	0.714148i	−0.968468	−	0.249140i	$-0.919852\pi$
$43$	−53.1884	+	30.7083i	−1.23694	+	0.714148i	−0.268472	+	0.963287i	$0.586519\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−46.0201	−	79.7091i	−0.979151	−	1.69594i	−0.665496	−	0.746402i	$-0.731780\pi$
$47$	−46.0201	−	79.7091i	−0.979151	−	1.69594i	−0.313655	−	0.949537i	$-0.601554\pi$
$48$		0			0
$49$	9.69479	−	16.7919i	0.197853	−	0.342691i
$50$		0			0
$51$	−23.3456	+	3.61668i	−0.457758	+	0.0709152i
$52$		0			0
$53$	52.1540			0.984038			0.492019	−	0.870584i	$-0.336259\pi$
$53$	52.1540			0.984038			0.492019	+	0.870584i	$0.336259\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−36.5838	+	5.66752i	−0.641822	+	0.0994303i
$58$		0			0
$59$	54.4701	+	31.4484i	0.923223	+	0.533023i	0.884662	−	0.466233i	$-0.154389\pi$
$59$	54.4701	+	31.4484i	0.923223	+	0.533023i	0.0385610	+	0.999256i	$0.487723\pi$
$60$		0			0
$61$	11.6631	+	20.2011i	0.191199	+	0.331166i	0.945648	−	0.325193i	$-0.105429\pi$
$61$	11.6631	+	20.2011i	0.191199	+	0.331166i	−0.754449	+	0.656359i	$0.772096\pi$
$62$		0			0
$63$	50.1752	−	54.9727i	0.796432	−	0.872583i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−93.8237	−	54.1692i	−1.40035	−	0.808495i	−0.405926	−	0.913906i	$-0.633051\pi$
$67$	−93.8237	−	54.1692i	−1.40035	−	0.808495i	−0.994429	+	0.105411i	$0.966384\pi$
$68$		0			0
$69$	1.31169	−	3.38283i	0.0190100	−	0.0490265i
$70$		0			0
$71$		−	134.509i		−	1.89449i	−0.320510	−	0.947245i	$-0.603854\pi$
$71$		−	134.509i		−	1.89449i	0.320510	−	0.947245i	$-0.396146\pi$
$72$		0			0
$73$		−	66.7798i		−	0.914792i	−0.889263	−	0.457396i	$-0.848782\pi$
$73$		−	66.7798i		−	0.914792i	0.889263	−	0.457396i	$-0.151218\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	15.7372	−	27.2576i	0.204379	−	0.353995i
$78$		0			0
$79$	−62.2089	−	107.749i	−0.787455	−	1.36391i	−0.927521	−	0.373770i	$-0.878065\pi$
$79$	−62.2089	−	107.749i	−0.787455	−	1.36391i	0.140066	−	0.990142i	$-0.455268\pi$
$80$		0			0
$81$	66.1686	−	46.7196i	0.816896	−	0.576785i
$82$		0			0
$83$	−40.3522	−	69.8921i	−0.486172	−	0.842074i	0.513702	−	0.857969i	$-0.328274\pi$
$83$	−40.3522	−	69.8921i	−0.486172	−	0.842074i	−0.999874	+	0.0158947i	$0.994940\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	29.0040	−	23.3250i	0.333380	−	0.268103i
$88$		0			0
$89$		−	176.513i		−	1.98330i	−0.128976	−	0.991648i	$-0.541169\pi$
$89$		−	176.513i		−	1.98330i	0.128976	−	0.991648i	$-0.458831\pi$
$90$		0			0
$91$	−159.748			−1.75547
$92$		0			0
$93$	10.1024	−	26.0538i	0.108628	−	0.280148i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	79.5774	−	45.9441i	0.820386	−	0.473650i	−0.0301635	−	0.999545i	$-0.509603\pi$
$97$	79.5774	−	45.9441i	0.820386	−	0.473650i	0.850550	+	0.525895i	$0.176269\pi$
$98$		0			0
$99$	23.0917	−	25.2997i	0.233250	−	0.255552i
$100$		0			0
$101$	35.2716	−	20.3641i	0.349223	−	0.201624i	−0.315120	−	0.949052i	$-0.602045\pi$
$101$	35.2716	−	20.3641i	0.349223	−	0.201624i	0.664343	+	0.747428i	$0.268711\pi$
$102$		0			0
$103$	89.5221	+	51.6856i	0.869147	+	0.501802i	0.867065	−	0.498196i	$-0.166004\pi$
$103$	89.5221	+	51.6856i	0.869147	+	0.501802i	0.00208213	+	0.999998i	$0.499337\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	21.9162			0.204824			0.102412	−	0.994742i	$-0.467344\pi$
$107$	21.9162			0.204824			0.102412	+	0.994742i	$0.467344\pi$
$108$		0			0
$109$	80.9662			0.742810			0.371405	−	0.928471i	$-0.378876\pi$
$109$	80.9662			0.742810			0.371405	+	0.928471i	$0.378876\pi$
$110$		0			0
$111$	17.0195	+	109.861i	0.153329	+	0.989737i
$112$		0			0
$113$	−59.5708	+	103.180i	−0.527175	+	0.913094i	0.472324	+	0.881425i	$0.343415\pi$
$113$	−59.5708	+	103.180i	−0.527175	+	0.913094i	−0.999498	+	0.0316683i	$0.989918\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−169.805	−	37.2957i	−1.45133	−	0.318767i
$118$		0			0
$119$	56.3975	−	32.5611i	0.473929	−	0.273623i
$120$		0			0
$121$	−53.2574	+	92.2445i	−0.440144	+	0.762351i
$122$		0			0
$123$	−129.641	−	50.2684i	−1.05399	−	0.408686i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	136.157i		−	1.07211i	−0.844185	−	0.536053i	$-0.819915\pi$
$127$		−	136.157i		−	1.07211i	0.844185	−	0.536053i	$-0.180085\pi$
$128$		0			0
$129$	143.581	−	115.467i	1.11303	−	0.895095i
$130$		0			0
$131$	−162.827	−	94.0080i	−1.24295	−	0.717618i	−0.273257	−	0.961941i	$-0.588101\pi$
$131$	−162.827	−	94.0080i	−1.24295	−	0.717618i	−0.969694	+	0.244323i	$0.921434\pi$
$132$		0			0
$133$	88.3779	−	51.0250i	0.664495	−	0.383647i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	130.982	+	226.868i	0.956075	+	1.65597i	0.731889	+	0.681424i	$0.238639\pi$
$137$	130.982	+	226.868i	0.956075	+	1.65597i	0.224186	+	0.974546i	$0.428028\pi$
$138$		0			0
$139$	−41.3482	+	71.6171i	−0.297469	+	0.515231i	−0.975556	−	0.219750i	$-0.929476\pi$
$139$	−41.3482	+	71.6171i	−0.297469	+	0.515231i	0.678087	+	0.734981i	$0.262809\pi$
$140$		0			0
$141$	173.041	+	215.172i	1.22724	+	1.52605i
$142$		0			0
$143$	−73.5194			−0.514122
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−21.0294	+	54.2344i	−0.143057	+	0.368941i
$148$		0			0
$149$	17.5623	+	10.1396i	0.117868	+	0.0680510i	0.557775	−	0.829992i	$-0.311655\pi$
$149$	17.5623	+	10.1396i	0.117868	+	0.0680510i	−0.439907	+	0.898043i	$0.644989\pi$
$150$		0			0
$151$	−9.31435	−	16.1329i	−0.0616844	−	0.106841i	0.833534	−	0.552468i	$-0.186314\pi$
$151$	−9.31435	−	16.1329i	−0.0616844	−	0.106841i	−0.895218	+	0.445628i	$0.852981\pi$
$152$		0			0
$153$	67.5502	−	21.4443i	0.441505	−	0.140159i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−154.892	−	89.4268i	−0.986572	−	0.569598i	−0.0823242	−	0.996606i	$-0.526234\pi$
$157$	−154.892	−	89.4268i	−0.986572	−	0.569598i	−0.904248	+	0.427008i	$0.859568\pi$
$158$		0			0
$159$	−154.618	+	23.9532i	−0.972438	+	0.150649i
$160$		0			0
$161$			10.0016i			0.0621216i
$162$		0			0
$163$			4.42383i			0.0271401i	0.999908	+	0.0135700i	$0.00431961\pi$
$163$			4.42383i			0.0271401i	−0.999908	+	0.0135700i	$0.995680\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	8.06435	−	13.9679i	0.0482895	−	0.0836399i	−0.840870	−	0.541237i	$-0.817956\pi$
$167$	8.06435	−	13.9679i	0.0482895	−	0.0836399i	0.889160	+	0.457597i	$0.151290\pi$
$168$		0			0
$169$	102.073	+	176.796i	0.603984	+	1.04613i
$170$		0			0
$171$	105.855	−	33.6043i	0.619034	−	0.196516i
$172$		0			0
$173$	−104.274	−	180.607i	−0.602738	−	1.04397i	−0.992405	−	0.123017i	$-0.960743\pi$
$173$	−104.274	−	180.607i	−0.602738	−	1.04397i	0.389666	−	0.920956i	$-0.372590\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−175.928	−	68.2160i	−0.993942	−	0.385401i
$178$		0			0
$179$		−	15.0917i		−	0.0843110i	−0.999111	−	0.0421555i	$-0.986578\pi$
$179$		−	15.0917i		−	0.0843110i	0.999111	−	0.0421555i	$-0.0134225\pi$
$180$		0			0
$181$	−334.817			−1.84982			−0.924910	−	0.380187i	$-0.875860\pi$
$181$	−334.817			−1.84982			−0.924910	+	0.380187i	$0.875860\pi$
$182$		0			0
$183$	−43.8548	−	54.5323i	−0.239644	−	0.297991i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	25.9554	−	14.9853i	0.138799	−	0.0801355i
$188$		0			0
$189$	−123.504	+	186.018i	−0.653458	+	0.984225i
$190$		0			0
$191$	262.232	−	151.399i	1.37294	−	0.792667i	0.381643	−	0.924310i	$-0.375358\pi$
$191$	262.232	−	151.399i	1.37294	−	0.792667i	0.991297	+	0.131642i	$0.0420251\pi$
$192$		0			0
$193$	146.209	+	84.4137i	0.757559	+	0.437377i	0.828418	−	0.560110i	$-0.189241\pi$
$193$	146.209	+	84.4137i	0.757559	+	0.437377i	−0.0708599	+	0.997486i	$0.522574\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	327.080			1.66030			0.830152	−	0.557537i	$-0.188254\pi$
$197$	327.080			1.66030			0.830152	+	0.557537i	$0.188254\pi$
$198$		0			0
$199$	−165.715			−0.832736			−0.416368	−	0.909196i	$-0.636697\pi$
$199$	−165.715			−0.832736			−0.416368	+	0.909196i	$0.636697\pi$
$200$		0			0
$201$	303.032	+	117.501i	1.50762	+	0.584580i
$202$		0			0
$203$	−51.2996	+	88.8535i	−0.252707	+	0.437702i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−2.33503	+	10.6313i	−0.0112803	+	0.0513589i
$208$		0			0
$209$	40.6734	−	23.4828i	0.194610	−	0.112358i
$210$		0			0
$211$	94.4460	−	163.585i	0.447611	−	0.775285i	−0.550619	−	0.834757i	$-0.685608\pi$
$211$	94.4460	−	163.585i	0.447611	−	0.775285i	0.998230	+	0.0594715i	$0.0189415\pi$
$212$		0			0
$213$	61.7769	+	398.770i	0.290032	+	1.87216i
$214$		0			0
$215$		0			0
$216$		0			0
$217$			77.0300i			0.354977i
$218$		0			0
$219$	30.6705	+	197.978i	0.140048	+	0.904009i
$220$		0			0
$221$	−131.736	−	76.0579i	−0.596091	−	0.344153i
$222$		0			0
$223$	−249.229	+	143.892i	−1.11762	+	0.645256i	−0.940792	−	0.338986i	$-0.889916\pi$
$223$	−249.229	+	143.892i	−1.11762	+	0.645256i	−0.176825	+	0.984242i	$0.556583\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	99.2817	+	171.961i	0.437364	+	0.757537i	0.997485	−	0.0708736i	$-0.0225787\pi$
$227$	99.2817	+	171.961i	0.437364	+	0.757537i	−0.560121	+	0.828411i	$0.689245\pi$
$228$		0			0
$229$	−191.729	+	332.085i	−0.837245	+	1.45015i	0.0549441	+	0.998489i	$0.482502\pi$
$229$	−191.729	+	332.085i	−0.837245	+	1.45015i	−0.892189	+	0.451662i	$0.850831\pi$
$230$		0			0
$231$	−34.1362	+	88.0366i	−0.147776	+	0.381111i
$232$		0			0
$233$	240.304			1.03135			0.515675	−	0.856784i	$-0.327541\pi$
$233$	240.304			1.03135			0.515675	+	0.856784i	$0.327541\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	233.914	+	290.865i	0.986977	+	1.22728i
$238$		0			0
$239$	62.2301	+	35.9285i	0.260377	+	0.150329i	0.624506	−	0.781020i	$-0.285300\pi$
$239$	62.2301	+	35.9285i	0.260377	+	0.150329i	−0.364130	+	0.931348i	$0.618633\pi$
$240$		0			0
$241$	−85.1369	−	147.461i	−0.353265	−	0.611873i	0.633554	−	0.773698i	$-0.281595\pi$
$241$	−85.1369	−	147.461i	−0.353265	−	0.611873i	−0.986819	+	0.161825i	$0.948262\pi$
$242$		0			0
$243$	−174.708	+	168.896i	−0.718965	+	0.695047i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−206.437	−	119.187i	−0.835779	−	0.482537i
$248$		0			0
$249$	151.730	+	188.672i	0.609356	+	0.757718i
$250$		0			0
$251$		−	78.9688i		−	0.314617i	−0.987550	−	0.157308i	$-0.949718\pi$
$251$		−	78.9688i		−	0.314617i	0.987550	−	0.157308i	$-0.0502817\pi$
$252$		0			0
$253$			4.60295i			0.0181935i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	26.8428	−	46.4932i	0.104447	−	0.180907i	−0.809065	−	0.587719i	$-0.800026\pi$
$257$	26.8428	−	46.4932i	0.104447	−	0.180907i	0.913512	+	0.406812i	$0.133359\pi$
$258$		0			0
$259$	−153.227	−	265.398i	−0.591612	−	1.02470i
$260$		0			0
$261$	−75.2737	+	82.4710i	−0.288405	+	0.315981i
$262$		0			0
$263$	−5.16722	−	8.94989i	−0.0196472	−	0.0340300i	0.856035	−	0.516918i	$-0.172921\pi$
$263$	−5.16722	−	8.94989i	−0.0196472	−	0.0340300i	−0.875682	+	0.482888i	$0.839588\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	81.0686	+	523.298i	0.303628	+	1.95992i
$268$		0			0
$269$		−	30.2492i		−	0.112451i	−0.998418	−	0.0562254i	$-0.982093\pi$
$269$		−	30.2492i		−	0.112451i	0.998418	−	0.0562254i	$-0.0179065\pi$
$270$		0			0
$271$	−139.993			−0.516579			−0.258290	−	0.966068i	$-0.583159\pi$
$271$	−139.993			−0.516579			−0.258290	+	0.966068i	$0.583159\pi$
$272$		0			0
$273$	473.594	−	73.3686i	1.73478	−	0.268749i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	47.6279	−	27.4980i	0.171942	−	0.0992708i	−0.411559	−	0.911383i	$-0.635016\pi$
$277$	47.6279	−	27.4980i	0.171942	−	0.0992708i	0.583501	+	0.812112i	$0.301682\pi$
$278$		0			0
$279$	−17.9839	+	81.8798i	−0.0644584	+	0.293476i
$280$		0			0
$281$	427.134	−	246.606i	1.52005	−	0.877600i	0.520328	−	0.853967i	$-0.325810\pi$
$281$	427.134	−	246.606i	1.52005	−	0.877600i	0.999721	−	0.0236336i	$-0.00752352\pi$
$282$		0			0
$283$	−209.825	−	121.143i	−0.741433	−	0.428066i	0.0811572	−	0.996701i	$-0.474138\pi$
$283$	−209.825	−	121.143i	−0.741433	−	0.428066i	−0.822590	+	0.568635i	$0.807472\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	383.294			1.33552
$288$		0			0
$289$	−226.989			−0.785429
$290$		0			0
$291$	−214.817	+	172.756i	−0.738203	+	0.593662i
$292$		0			0
$293$	65.0963	−	112.750i	0.222172	−	0.384812i	−0.733296	−	0.679910i	$-0.762019\pi$
$293$	65.0963	−	112.750i	0.222172	−	0.384812i	0.955467	+	0.295098i	$0.0953522\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−56.8390	+	85.6098i	−0.191377	+	0.288248i
$298$		0			0
$299$	20.2322	−	11.6811i	0.0676664	−	0.0390672i
$300$		0			0
$301$	−253.952	+	439.857i	−0.843694	+	1.46132i
$302$		0			0
$303$	−95.2146	+	76.5714i	−0.314240	+	0.252711i
$304$		0			0
$305$		0			0
$306$		0			0
$307$		−	117.072i		−	0.381341i	−0.981654	−	0.190670i	$-0.938934\pi$
$307$		−	117.072i		−	0.381341i	0.981654	−	0.190670i	$-0.0610662\pi$
$308$		0			0
$309$	−289.138	−	112.113i	−0.935723	−	0.362827i
$310$		0			0
$311$	16.4771	+	9.51306i	0.0529810	+	0.0305886i	0.526257	−	0.850326i	$-0.323595\pi$
$311$	16.4771	+	9.51306i	0.0529810	+	0.0305886i	−0.473276	+	0.880914i	$0.656928\pi$
$312$		0			0
$313$	144.686	−	83.5346i	0.462256	−	0.266884i	−0.250736	−	0.968055i	$-0.580673\pi$
$313$	144.686	−	83.5346i	0.462256	−	0.266884i	0.712992	+	0.701172i	$0.247339\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	97.9549	+	169.663i	0.309006	+	0.535214i	0.978145	−	0.207923i	$-0.0666703\pi$
$317$	97.9549	+	169.663i	0.309006	+	0.535214i	−0.669139	+	0.743137i	$0.733337\pi$
$318$		0			0
$319$	−23.6092	+	40.8923i	−0.0740100	+	0.128189i
$320$		0			0
$321$	−64.9735	+	10.0656i	−0.202410	+	0.0313571i
$322$		0			0
$323$	97.1745			0.300850
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−240.035	+	37.1860i	−0.734053	+	0.113719i
$328$		0			0
$329$	−659.178	−	380.577i	−2.00358	−	1.15677i
$330$		0			0
$331$	40.9636	+	70.9510i	0.123757	+	0.214353i	0.921246	−	0.388980i	$-0.127172\pi$
$331$	40.9636	+	70.9510i	0.123757	+	0.214353i	−0.797489	+	0.603333i	$0.793839\pi$
$332$		0			0
$333$	−100.913	−	317.881i	−0.303043	−	0.954596i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	455.714	+	263.107i	1.35227	+	0.780732i	0.988567	−	0.150784i	$-0.0481799\pi$
$337$	455.714	+	263.107i	1.35227	+	0.780732i	0.363700	+	0.931516i	$0.381513\pi$
$338$		0			0
$339$	129.217	−	333.249i	0.381173	−	0.983036i
$340$		0			0
$341$			35.4509i			0.103962i
$342$		0			0
$343$			244.872i			0.713913i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−227.219	+	393.556i	−0.654811	+	1.13417i	0.327130	+	0.944979i	$0.393918\pi$
$347$	−227.219	+	393.556i	−0.654811	+	1.13417i	−0.981941	+	0.189186i	$0.939415\pi$
$348$		0			0
$349$	−102.845	−	178.134i	−0.294686	−	0.510411i	0.680226	−	0.733003i	$-0.261882\pi$
$349$	−102.845	−	178.134i	−0.294686	−	0.510411i	−0.974912	+	0.222591i	$0.928548\pi$
$350$		0			0
$351$	520.541	+	32.5803i	1.48302	+	0.0928213i
$352$		0			0
$353$	50.4501	+	87.3821i	0.142918	+	0.247541i	0.928594	−	0.371097i	$-0.121018\pi$
$353$	50.4501	+	87.3821i	0.142918	+	0.247541i	−0.785676	+	0.618638i	$0.787685\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−152.243	+	122.434i	−0.426452	+	0.342952i
$358$		0			0
$359$			430.783i			1.19995i	0.800018	+	0.599977i	$0.204823\pi$
$359$			430.783i			1.19995i	−0.800018	+	0.599977i	$0.795177\pi$
$360$		0			0
$361$	−208.722			−0.578178
$362$		0			0
$363$	115.523	−	297.931i	0.318245	−	0.820748i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	281.129	−	162.310i	0.766018	−	0.442261i	−0.0654344	−	0.997857i	$-0.520843\pi$
$367$	281.129	−	162.310i	0.766018	−	0.442261i	0.831452	+	0.555596i	$0.187510\pi$
$368$		0			0
$369$	407.426	+	89.4861i	1.10414	+	0.242510i
$370$		0			0
$371$	373.520	−	215.652i	1.00679	−	0.581271i
$372$		0			0
$373$	−118.210	−	68.2485i	−0.316917	−	0.182972i	0.333101	−	0.942891i	$-0.391905\pi$
$373$	−118.210	−	68.2485i	−0.316917	−	0.182972i	−0.650017	+	0.759919i	$0.725238\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	239.656			0.635693
$378$		0			0
$379$	26.1240			0.0689286			0.0344643	−	0.999406i	$-0.489027\pi$
$379$	26.1240			0.0689286			0.0344643	+	0.999406i	$0.489027\pi$
$380$		0			0
$381$	62.5341	+	403.657i	0.164131	+	1.05947i
$382$		0			0
$383$	−243.068	+	421.006i	−0.634642	+	1.09923i	0.351948	+	0.936019i	$0.385519\pi$
$383$	−243.068	+	421.006i	−0.634642	+	1.09923i	−0.986591	+	0.163213i	$0.947814\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−372.633	+	408.262i	−0.962875	+	1.05494i
$388$		0			0
$389$	−188.122	+	108.612i	−0.483605	+	0.279209i	−0.721918	−	0.691979i	$-0.756739\pi$
$389$	−188.122	+	108.612i	−0.483605	+	0.279209i	0.238313	+	0.971188i	$0.423406\pi$
$390$		0			0
$391$	−4.76188	+	8.24781i	−0.0121787	+	0.0210941i
$392$		0			0
$393$	525.897	+	203.917i	1.33816	+	0.518872i
$394$		0			0
$395$		0			0
$396$		0			0
$397$		−	506.995i		−	1.27707i	−0.769595	−	0.638533i	$-0.779542\pi$
$397$		−	506.995i		−	1.27707i	0.769595	−	0.638533i	$-0.220458\pi$
$398$		0			0
$399$	−238.574	+	191.861i	−0.597929	+	0.480853i
$400$		0			0
$401$	−433.469	−	250.263i	−1.08097	−	0.624098i	−0.149812	−	0.988715i	$-0.547867\pi$
$401$	−433.469	−	250.263i	−1.08097	−	0.624098i	−0.931158	+	0.364616i	$0.881200\pi$
$402$		0			0
$403$	155.824	−	89.9652i	0.386661	−	0.223239i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−70.5186	−	122.142i	−0.173264	−	0.300103i
$408$		0			0
$409$	221.644	−	383.899i	0.541917	−	0.938628i	−0.456877	−	0.889530i	$-0.651032\pi$
$409$	221.644	−	383.899i	0.541917	−	0.938628i	0.998794	−	0.0490978i	$-0.0156346\pi$
$410$		0			0
$411$	−492.510	−	612.423i	−1.19832	−	1.49008i
$412$		0			0
$413$	520.143			1.25943
$414$		0			0
$415$		0			0
$416$		0			0
$417$	89.6901	−	231.309i	0.215084	−	0.554698i
$418$		0			0
$419$	79.3438	+	45.8092i	0.189365	+	0.109330i	0.591685	−	0.806169i	$-0.298463\pi$
$419$	79.3438	+	45.8092i	0.189365	+	0.109330i	−0.402320	+	0.915499i	$0.631796\pi$
$420$		0			0
$421$	1.07420	+	1.86057i	0.00255155	+	0.00441941i	0.867298	−	0.497789i	$-0.165854\pi$
$421$	1.07420	+	1.86057i	0.00255155	+	0.00441941i	−0.864747	+	0.502208i	$0.832521\pi$
$422$		0			0
$423$	−611.829	−	558.434i	−1.44640	−	1.32017i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	167.059	+	96.4516i	0.391239	+	0.225882i
$428$		0			0
$429$	217.958	−	33.7658i	0.508061	−	0.0787082i
$430$		0			0
$431$		−	770.877i		−	1.78858i	−0.447491	−	0.894289i	$-0.647682\pi$
$431$		−	770.877i		−	1.78858i	0.447491	−	0.894289i	$-0.352318\pi$
$432$		0			0
$433$			304.898i			0.704153i	0.935971	+	0.352076i	$0.114524\pi$
$433$			304.898i			0.704153i	−0.935971	+	0.352076i	$0.885476\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−7.46211	+	12.9248i	−0.0170758	+	0.0295761i
$438$		0			0
$439$	183.954	+	318.618i	0.419031	+	0.725782i	0.995842	−	0.0910950i	$-0.0290367\pi$
$439$	183.954	+	318.618i	0.419031	+	0.725782i	−0.576812	+	0.816877i	$0.695703\pi$
$440$		0			0
$441$	37.4358	−	170.443i	0.0848885	−	0.386493i
$442$		0			0
$443$	90.4041	+	156.585i	0.204073	+	0.353464i	0.949837	−	0.312746i	$-0.101249\pi$
$443$	90.4041	+	156.585i	0.204073	+	0.353464i	−0.745764	+	0.666210i	$0.767915\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−56.7227	−	21.9942i	−0.126896	−	0.0492041i
$448$		0			0
$449$		−	284.309i		−	0.633205i	−0.948558	−	0.316603i	$-0.897458\pi$
$449$		−	284.309i		−	0.633205i	0.948558	−	0.316603i	$-0.102542\pi$
$450$		0			0
$451$	176.400			0.391131
$452$		0			0
$453$	35.0232	+	43.5504i	0.0773138	+	0.0961377i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−206.998	+	119.510i	−0.452949	+	0.261510i	−0.709075	−	0.705133i	$-0.750887\pi$
$457$	−206.998	+	119.510i	−0.452949	+	0.261510i	0.256126	+	0.966643i	$0.417554\pi$
$458$		0			0
$459$	−190.413	+	94.5987i	−0.414843	+	0.206097i
$460$		0			0
$461$	−35.0175	+	20.2174i	−0.0759599	+	0.0438555i	−0.537499	−	0.843264i	$-0.680631\pi$
$461$	−35.0175	+	20.2174i	−0.0759599	+	0.0438555i	0.461539	+	0.887120i	$0.347297\pi$
$462$		0			0
$463$	550.667	+	317.928i	1.18935	+	0.686669i	0.958158	−	0.286240i	$-0.0924053\pi$
$463$	550.667	+	317.928i	1.18935	+	0.686669i	0.231188	+	0.972909i	$0.425739\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	34.8159			0.0745522			0.0372761	−	0.999305i	$-0.488132\pi$
$467$	34.8159			0.0745522			0.0372761	+	0.999305i	$0.488132\pi$
$468$		0			0
$469$	−895.936			−1.91031
$470$		0			0
$471$	500.270	+	193.980i	1.06214	+	0.411846i
$472$		0			0
$473$	−116.874	+	202.432i	−0.247091	+	0.427975i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	447.384	−	142.025i	0.937912	−	0.297746i
$478$		0			0
$479$	24.1869	−	13.9643i	0.0504945	−	0.0291530i	−0.474540	−	0.880234i	$-0.657386\pi$
$479$	24.1869	−	13.9643i	0.0504945	−	0.0291530i	0.525035	+	0.851081i	$0.324052\pi$
$480$		0			0
$481$	−357.916	+	619.929i	−0.744108	+	1.28883i
$482$		0			0
$483$	−4.59350	−	29.6510i	−0.00951036	−	0.0613893i
$484$		0			0
$485$		0			0
$486$		0			0
$487$			236.451i			0.485527i	0.970086	+	0.242763i	$0.0780538\pi$
$487$			236.451i			0.485527i	−0.970086	+	0.242763i	$0.921946\pi$
$488$		0			0
$489$	−2.03177	−	13.1150i	−0.00415494	−	0.0268201i
$490$		0			0
$491$	59.4344	+	34.3145i	0.121048	+	0.0698869i	0.559301	−	0.828964i	$-0.311070\pi$
$491$	59.4344	+	34.3145i	0.121048	+	0.0698869i	−0.438254	+	0.898851i	$0.644403\pi$
$492$		0			0
$493$	−84.6085	+	48.8487i	−0.171620	+	0.0990846i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−556.180	−	963.333i	−1.11908	−	1.93829i
$498$		0			0
$499$	148.403	−	257.042i	0.297402	−	0.515115i	−0.678139	−	0.734934i	$-0.737213\pi$
$499$	148.403	−	257.042i	0.297402	−	0.515115i	0.975541	+	0.219819i	$0.0705466\pi$
$500$		0			0
$501$	−17.4927	+	45.1134i	−0.0349156	+	0.0900467i
$502$		0			0
$503$	−854.175			−1.69816			−0.849081	−	0.528263i	$-0.822843\pi$
$503$	−854.175			−1.69816			−0.849081	+	0.528263i	$0.822843\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−383.809	−	477.256i	−0.757019	−	0.941334i
$508$		0			0
$509$	567.421	+	327.601i	1.11478	+	0.643616i	0.940062	−	0.341003i	$-0.110767\pi$
$509$	567.421	+	327.601i	1.11478	+	0.643616i	0.174714	+	0.984619i	$0.444100\pi$
$510$		0			0
$511$	−276.128	−	478.268i	−0.540368	−	0.935944i
$512$		0			0
$513$	−298.387	+	148.241i	−0.581651	+	0.288969i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−303.368	−	175.150i	−0.586786	−	0.338781i
$518$		0			0
$519$	392.083	+	487.545i	0.755458	+	0.939392i
$520$		0			0
$521$			886.683i			1.70189i	0.525258	+	0.850943i	$0.323969\pi$
$521$			886.683i			1.70189i	−0.525258	+	0.850943i	$0.676031\pi$
$522$		0			0
$523$		−	416.390i		−	0.796158i	−0.917351	−	0.398079i	$-0.869677\pi$
$523$		−	416.390i		−	0.796158i	0.917351	−	0.398079i	$-0.130323\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−36.6749	+	63.5229i	−0.0695919	+	0.120537i
$528$		0			0
$529$	263.769	+	456.861i	0.498618	+	0.863631i
$530$		0			0
$531$	552.891	+	121.436i	1.04123	+	0.228693i
$532$		0			0
$533$	−447.658	−	775.367i	−0.839884	−	1.45472i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6.93127	+	44.7413i	0.0129074	+	0.0833172i
$538$		0			0
$539$		−	73.7956i		−	0.136912i
$540$		0			0
$541$	932.175			1.72306			0.861529	−	0.507708i	$-0.169507\pi$
$541$	932.175			1.72306			0.861529	+	0.507708i	$0.169507\pi$
$542$		0			0
$543$	992.611	−	153.774i	1.82801	−	0.283194i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−554.443	+	320.108i	−1.01361	+	0.585206i	−0.912245	−	0.409644i	$-0.865653\pi$
$547$	−554.443	+	320.108i	−1.01361	+	0.585206i	−0.101361	+	0.994850i	$0.532320\pi$
$548$		0			0
$549$	155.059	+	141.527i	0.282439	+	0.257790i
$550$		0			0
$551$	−132.586	+	76.5485i	−0.240628	+	0.138927i
$552$		0			0
$553$	−891.063	−	514.455i	−1.61133	−	0.930299i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−255.289			−0.458328			−0.229164	−	0.973388i	$-0.573599\pi$
$557$	−255.289			−0.458328			−0.229164	+	0.973388i	$0.573599\pi$
$558$		0			0
$559$	1186.39			2.12234
$560$		0			0
$561$	−70.0658	+	56.3468i	−0.124894	+	0.100440i
$562$		0			0
$563$	−261.834	+	453.510i	−0.465070	+	0.805525i	−0.999205	−	0.0398747i	$-0.987304\pi$
$563$	−261.834	+	453.510i	−0.465070	+	0.805525i	0.534135	+	0.845399i	$0.320637\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	280.709	−	608.199i	0.495077	−	1.07266i
$568$		0			0
$569$	714.948	−	412.775i	1.25650	−	0.725440i	0.284107	−	0.958793i	$-0.408303\pi$
$569$	714.948	−	412.775i	1.25650	−	0.725440i	0.972392	+	0.233353i	$0.0749696\pi$
$570$		0			0
$571$	72.0237	−	124.749i	0.126136	−	0.218474i	−0.796040	−	0.605244i	$-0.793076\pi$
$571$	72.0237	−	124.749i	0.126136	−	0.218474i	0.922176	+	0.386769i	$0.126409\pi$
$572$		0			0
$573$	−707.887	+	569.281i	−1.23540	+	0.993510i
$574$		0			0
$575$		0			0
$576$		0			0
$577$		−	444.934i		−	0.771116i	−0.922684	−	0.385558i	$-0.874009\pi$
$577$		−	444.934i		−	0.771116i	0.922684	−	0.385558i	$-0.125991\pi$
$578$		0			0
$579$	−472.225	−	183.105i	−0.815587	−	0.316244i
$580$		0			0
$581$	−577.994	−	333.705i	−0.994826	−	0.574363i
$582$		0			0
$583$	171.902	−	99.2476i	0.294857	−	0.170236i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	36.0133	+	62.3769i	0.0613515	+	0.106264i	0.895070	−	0.445926i	$-0.147126\pi$
$587$	36.0133	+	62.3769i	0.0613515	+	0.106264i	−0.833718	+	0.552190i	$0.813792\pi$
$588$		0			0
$589$	−57.4716	+	99.5437i	−0.0975748	+	0.169005i
$590$		0			0
$591$	−969.673	+	150.221i	−1.64073	+	0.254180i
$592$		0			0
$593$	1018.32			1.71724			0.858619	−	0.512614i	$-0.171323\pi$
$593$	1018.32			1.71724			0.858619	+	0.512614i	$0.171323\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	491.283	−	76.1090i	0.822920	−	0.127486i
$598$		0			0
$599$	728.467	+	420.580i	1.21614	+	0.702138i	0.964090	−	0.265577i	$-0.0855625\pi$
$599$	728.467	+	420.580i	1.21614	+	0.702138i	0.252048	+	0.967715i	$0.418896\pi$
$600$		0			0
$601$	288.843	+	500.290i	0.480603	+	0.832429i	0.999752	−	0.0222543i	$-0.00708436\pi$
$601$	288.843	+	500.290i	0.480603	+	0.832429i	−0.519149	+	0.854684i	$0.673751\pi$
$602$		0			0
$603$	−952.344	−	209.171i	−1.57934	−	0.346884i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−246.130	−	142.103i	−0.405486	−	0.234108i	0.283362	−	0.959013i	$-0.408550\pi$
$607$	−246.130	−	142.103i	−0.405486	−	0.234108i	−0.688848	+	0.724905i	$0.741883\pi$
$608$		0			0
$609$	111.276	−	286.979i	0.182719	−	0.471230i
$610$		0			0
$611$			1777.94i			2.90989i
$612$		0			0
$613$			272.783i			0.444996i	0.974933	+	0.222498i	$0.0714211\pi$
$613$			272.783i			0.444996i	−0.974933	+	0.222498i	$0.928579\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	39.5342	−	68.4752i	0.0640748	−	0.110981i	−0.832208	−	0.554463i	$-0.812924\pi$
$617$	39.5342	−	68.4752i	0.0640748	−	0.110981i	0.896283	+	0.443482i	$0.146257\pi$
$618$		0			0
$619$	−171.368	−	296.818i	−0.276847	−	0.479513i	0.693753	−	0.720213i	$-0.255956\pi$
$619$	−171.368	−	296.818i	−0.276847	−	0.479513i	−0.970599	+	0.240701i	$0.922623\pi$
$620$		0			0
$621$	2.03981	−	32.5903i	0.00328471	−	0.0524804i
$622$		0			0
$623$	−729.865	−	1264.16i	−1.17153	−	2.02915i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−109.797	+	88.2984i	−0.175114	+	0.140827i
$628$		0			0
$629$		−	291.814i		−	0.463933i
$630$		0			0
$631$	−608.714			−0.964681			−0.482341	−	0.875984i	$-0.660213\pi$
$631$	−608.714			−0.964681			−0.482341	+	0.875984i	$0.660213\pi$
$632$		0			0
$633$	−204.867	+	528.347i	−0.323644	+	0.834672i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−324.368	+	187.274i	−0.509213	+	0.293994i
$638$		0			0
$639$	−366.292	−	1153.83i	−0.573227	−	1.80569i
$640$		0			0
$641$	145.345	−	83.9152i	0.226748	−	0.130913i	−0.382323	−	0.924029i	$-0.624876\pi$
$641$	145.345	−	83.9152i	0.226748	−	0.130913i	0.609071	+	0.793116i	$0.291542\pi$
$642$		0			0
$643$	184.409	+	106.469i	0.286795	+	0.165581i	0.636496	−	0.771280i	$-0.280383\pi$
$643$	184.409	+	106.469i	0.286795	+	0.165581i	−0.349700	+	0.936862i	$0.613717\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−242.229			−0.374388			−0.187194	−	0.982323i	$-0.559939\pi$
$647$	−242.229			−0.374388			−0.187194	+	0.982323i	$0.559939\pi$
$648$		0			0
$649$	239.381			0.368846
$650$		0			0
$651$	−35.3782	−	228.366i	−0.0543443	−	0.350792i
$652$		0			0
$653$	160.909	−	278.702i	0.246414	−	0.426802i	−0.716114	−	0.697983i	$-0.754081\pi$
$653$	160.909	−	278.702i	0.246414	−	0.426802i	0.962528	+	0.271181i	$0.0874142\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−181.854	−	572.846i	−0.276794	−	0.871912i
$658$		0			0
$659$	−411.471	+	237.563i	−0.624387	+	0.360490i	−0.778575	−	0.627551i	$-0.784057\pi$
$659$	−411.471	+	237.563i	−0.624387	+	0.360490i	0.154188	+	0.988042i	$0.450724\pi$
$660$		0			0
$661$	579.528	−	1003.77i	0.876745	−	1.51857i	0.0218529	−	0.999761i	$-0.493043\pi$
$661$	579.528	−	1003.77i	0.876745	−	1.51857i	0.854892	−	0.518806i	$-0.173623\pi$
$662$		0			0
$663$	425.481	+	164.980i	0.641751	+	0.248839i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		−	15.0045i		−	0.0224956i
$668$		0			0
$669$	672.785	−	541.053i	1.00566	−	0.808749i
$670$		0			0
$671$	76.8842	+	44.3891i	0.114582	+	0.0661537i
$672$		0			0
$673$	126.200	−	72.8616i	0.187518	−	0.108264i	−0.403302	−	0.915067i	$-0.632138\pi$
$673$	126.200	−	72.8616i	0.187518	−	0.108264i	0.590820	+	0.806803i	$0.298804\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	197.288	+	341.713i	0.291415	+	0.504745i	0.974145	−	0.225926i	$-0.0725407\pi$
$677$	197.288	+	341.713i	0.291415	+	0.504745i	−0.682730	+	0.730671i	$0.739207\pi$
$678$		0			0
$679$	379.948	−	658.089i	0.559570	−	0.969204i
$680$		0			0
$681$	−373.312	−	464.204i	−0.548182	−	0.681650i
$682$		0			0
$683$	510.506			0.747447			0.373723	−	0.927540i	$-0.378081\pi$
$683$	510.506			0.747447			0.373723	+	0.927540i	$0.378081\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	415.888	−	1072.57i	0.605368	−	1.56123i
$688$		0			0
$689$	−872.486	−	503.730i	−1.26631	−	0.731103i
$690$		0			0
$691$	−420.136	−	727.697i	−0.608011	−	1.05311i	−0.991568	−	0.129589i	$-0.958634\pi$
$691$	−420.136	−	727.697i	−0.608011	−	1.05311i	0.383556	−	0.923517i	$-0.374699\pi$
$692$		0			0
$693$	60.7682	−	276.674i	0.0876886	−	0.399242i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	316.083	+	182.491i	0.453491	+	0.261823i
$698$		0			0
$699$	−712.415	+	110.366i	−1.01919	+	0.157892i
$700$		0			0
$701$			596.790i			0.851340i	0.904878	+	0.425670i	$0.139962\pi$
$701$			596.790i			0.851340i	−0.904878	+	0.425670i	$0.860038\pi$
$702$		0			0
$703$		−	457.288i		−	0.650480i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	168.407	−	291.689i	0.238199	−	0.412573i
$708$		0			0
$709$	660.644	+	1144.27i	0.931797	+	1.61392i	0.780248	+	0.625470i	$0.215093\pi$
$709$	660.644	+	1144.27i	0.931797	+	1.61392i	0.151549	+	0.988450i	$0.451574\pi$
$710$		0			0
$711$	−827.057	−	754.879i	−1.16323	−	1.06171i
$712$		0			0
$713$	−5.63260	−	9.75594i	−0.00789986	−	0.0136830i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−200.991	−	77.9342i	−0.280322	−	0.108695i
$718$		0			0
$719$		−	833.256i		−	1.15891i	−0.815004	−	0.579455i	$-0.803266\pi$
$719$		−	833.256i		−	1.15891i	0.815004	−	0.579455i	$-0.196734\pi$
$720$		0			0
$721$	854.859			1.18566
$722$		0			0
$723$	320.126	+	398.068i	0.442774	+	0.550578i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	237.094	−	136.886i	0.326126	−	0.188289i	−0.327994	−	0.944680i	$-0.606372\pi$
$727$	237.094	−	136.886i	0.326126	−	0.188289i	0.654120	+	0.756391i	$0.273039\pi$
$728$		0			0
$729$	440.376	−	580.956i	0.604083	−	0.796922i
$730$		0			0
$731$	−418.843	+	241.819i	−0.572973	+	0.330806i
$732$		0			0
$733$	−465.925	−	269.002i	−0.635642	−	0.366988i	0.147292	−	0.989093i	$-0.452944\pi$
$733$	−465.925	−	269.002i	−0.635642	−	0.366988i	−0.782934	+	0.622105i	$0.786278\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−412.329			−0.559470
$738$		0			0
$739$	51.4149			0.0695736			0.0347868	−	0.999395i	$-0.488925\pi$
$739$	51.4149			0.0695736			0.0347868	+	0.999395i	$0.488925\pi$
$740$		0			0
$741$	666.752	+	258.533i	0.899800	+	0.348897i
$742$		0			0
$743$	−416.955	+	722.188i	−0.561178	+	0.971989i	0.436216	+	0.899842i	$0.356318\pi$
$743$	−416.955	+	722.188i	−0.561178	+	0.971989i	−0.997394	+	0.0721467i	$0.977015\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−536.476	−	489.657i	−0.718174	−	0.655498i
$748$		0			0
$749$	156.961	−	90.6212i	0.209560	−	0.120990i
$750$		0			0
$751$	492.855	−	853.650i	0.656265	−	1.13668i	−0.325310	−	0.945607i	$-0.605469\pi$
$751$	492.855	−	853.650i	0.656265	−	1.13668i	0.981575	−	0.191077i	$-0.0611979\pi$
$752$		0			0
$753$	36.2686	+	234.114i	0.0481655	+	0.310908i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			414.403i			0.547428i	0.961811	+	0.273714i	$0.0882522\pi$
$757$			414.403i			0.547428i	−0.961811	+	0.273714i	$0.911748\pi$
$758$		0			0
$759$	−2.11403	−	13.6461i	−0.00278528	−	0.0179790i
$760$		0			0
$761$	−401.140	−	231.598i	−0.527122	−	0.304334i	0.212721	−	0.977113i	$-0.431767\pi$
$761$	−401.140	−	231.598i	−0.527122	−	0.304334i	−0.739844	+	0.672779i	$0.765101\pi$
$762$		0			0
$763$	579.869	−	334.787i	0.759985	−	0.438778i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−607.488	−	1052.20i	−0.792031	−	1.37184i
$768$		0			0
$769$	−105.504	+	182.738i	−0.137196	+	0.237630i	−0.926434	−	0.376457i	$-0.877142\pi$
$769$	−105.504	+	182.738i	−0.137196	+	0.237630i	0.789238	+	0.614087i	$0.210476\pi$
$770$		0			0
$771$	−58.2260	+	150.164i	−0.0755201	+	0.194765i
$772$		0			0
$773$	1401.96			1.81367			0.906833	−	0.421490i	$-0.138493\pi$
$773$	1401.96			1.81367			0.906833	+	0.421490i	$0.138493\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	576.155	+	716.433i	0.741512	+	0.922051i
$778$		0			0
$779$	495.319	+	285.973i	0.635840	+	0.367102i
$780$		0			0
$781$	−255.966	−	443.347i	−0.327742	−	0.567665i
$782$		0			0
$783$	185.282	−	279.068i	0.236631	−	0.356409i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−339.881	−	196.231i	−0.431870	−	0.249340i	0.268273	−	0.963343i	$-0.413547\pi$
$787$	−339.881	−	196.231i	−0.431870	−	0.249340i	−0.700143	+	0.714003i	$0.746880\pi$
$788$		0			0
$789$	19.4294	+	24.1600i	0.0246254	+	0.0306210i
$790$		0			0
$791$			985.276i			1.24561i
$792$		0			0
$793$		−	450.593i		−	0.568213i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−542.129	+	938.996i	−0.680213	+	1.17816i	0.294703	+	0.955589i	$0.404779\pi$
$797$	−542.129	+	938.996i	−0.680213	+	1.17816i	−0.974916	+	0.222574i	$0.928554\pi$
$798$		0			0
$799$	−362.395	−	627.686i	−0.453560	−	0.785589i
$800$		0			0
$801$	−480.678	−	1514.15i	−0.600097	−	1.89033i
$802$		0			0
$803$	−127.080	−	220.109i	−0.158257	−	0.274109i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	13.8928	+	89.6780i	0.0172154	+	0.111125i
$808$		0			0
$809$			1256.56i			1.55323i	0.629975	+	0.776616i	$0.283065\pi$
$809$			1256.56i			1.55323i	−0.629975	+	0.776616i	$0.716935\pi$
$810$		0			0
$811$	1478.32			1.82284			0.911418	−	0.411482i	$-0.134989\pi$
$811$	1478.32			1.82284			0.911418	+	0.411482i	$0.134989\pi$
$812$		0			0
$813$	415.028	−	64.2957i	0.510490	−	0.0790845i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−656.349	+	378.943i	−0.803365	+	0.463823i
$818$		0			0
$819$	−1370.34	+	435.022i	−1.67318	+	0.531163i
$820$		0			0
$821$	757.934	−	437.593i	0.923184	−	0.533001i	0.0385346	−	0.999257i	$-0.487731\pi$
$821$	757.934	−	437.593i	0.923184	−	0.533001i	0.884649	+	0.466257i	$0.154398\pi$
$822$		0			0
$823$	419.225	+	242.040i	0.509387	+	0.294095i	0.732582	−	0.680679i	$-0.238315\pi$
$823$	419.225	+	242.040i	0.509387	+	0.294095i	−0.223195	+	0.974774i	$0.571649\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−262.221			−0.317075			−0.158537	−	0.987353i	$-0.550678\pi$
$827$	−262.221			−0.317075			−0.158537	+	0.987353i	$0.550678\pi$
$828$		0			0
$829$	−441.413			−0.532465			−0.266232	−	0.963909i	$-0.585779\pi$
$829$	−441.413			−0.532465			−0.266232	+	0.963909i	$0.585779\pi$
$830$		0			0
$831$	−128.570	+	103.396i	−0.154718	+	0.124424i
$832$		0			0
$833$	76.3436	−	132.231i	0.0916490	−	0.158741i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	15.7101	−	251.003i	0.0187696	−	0.299885i
$838$		0			0
$839$	−632.454	+	365.147i	−0.753818	+	0.435217i	−0.827072	−	0.562096i	$-0.809995\pi$
$839$	−632.454	+	365.147i	−0.753818	+	0.435217i	0.0732535	+	0.997313i	$0.476662\pi$
$840$		0			0
$841$	−343.540	+	595.028i	−0.408489	+	0.707524i
$842$		0			0
$843$	−1153.03	+	927.269i	−1.36778	+	1.09996i
$844$		0			0
$845$		0			0
$846$		0			0
$847$			880.856i			1.03997i
$848$		0			0
$849$	677.694	+	262.776i	0.798226	+	0.309512i
$850$		0			0
$851$	38.8129	+	22.4086i	0.0456086	+	0.0263321i
$852$		0			0
$853$	−513.830	+	296.660i	−0.602380	+	0.347784i	−0.769977	−	0.638071i	$-0.779733\pi$
$853$	−513.830	+	296.660i	−0.602380	+	0.347784i	0.167597	+	0.985856i	$0.446399\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−706.162	−	1223.11i	−0.823993	−	1.42720i	−0.902686	−	0.430299i	$-0.858408\pi$
$857$	−706.162	−	1223.11i	−0.823993	−	1.42720i	0.0786932	−	0.996899i	$-0.474925\pi$
$858$		0			0
$859$	350.028	−	606.266i	0.407483	−	0.705781i	−0.587124	−	0.809497i	$-0.699740\pi$
$859$	350.028	−	606.266i	0.407483	−	0.705781i	0.994607	+	0.103716i	$0.0330732\pi$
$860$		0			0
$861$	−1136.33	+	176.038i	−1.31977	+	0.204458i
$862$		0			0
$863$	1185.65			1.37387			0.686935	−	0.726719i	$-0.258956\pi$
$863$	1185.65			1.37387			0.686935	+	0.726719i	$0.258956\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	672.940	−	104.251i	0.776170	−	0.120243i
$868$		0			0
$869$	−410.087	−	236.764i	−0.471906	−	0.272455i
$870$		0			0
$871$	1046.39	+	1812.39i	1.20136	+	2.08082i
$872$		0			0
$873$	557.511	−	610.818i	0.638616	−	0.699677i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	1293.84	+	747.001i	1.47531	+	0.851769i	0.999612	−	0.0278418i	$-0.00886347\pi$
$877$	1293.84	+	747.001i	1.47531	+	0.851769i	0.475694	+	0.879611i	$0.342197\pi$
$878$		0			0
$879$	−141.203	+	364.160i	−0.160641	+	0.414289i
$880$		0			0
$881$		−	89.7969i		−	0.101926i	−0.998701	−	0.0509630i	$-0.983771\pi$
$881$		−	89.7969i		−	0.101926i	0.998701	−	0.0509630i	$-0.0162291\pi$
$882$		0			0
$883$			709.600i			0.803624i	0.915722	+	0.401812i	$0.131620\pi$
$883$			709.600i			0.803624i	−0.915722	+	0.401812i	$0.868380\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	339.575	−	588.161i	0.382835	−	0.663090i	−0.608631	−	0.793453i	$-0.708281\pi$
$887$	339.575	−	588.161i	0.382835	−	0.663090i	0.991466	+	0.130363i	$0.0416144\pi$
$888$		0			0
$889$	−562.997	−	975.140i	−0.633293	−	1.09689i
$890$		0			0
$891$	129.188	−	279.907i	0.144992	−	0.314149i
$892$		0			0
$893$	−567.892	−	983.617i	−0.635937	−	1.10147i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−54.6164	+	43.9224i	−0.0608878	+	0.0489659i
$898$		0			0
$899$		−	115.562i		−	0.128545i
$900$		0			0
$901$	410.698			0.455824
$902$		0			0
$903$	550.858	−	1420.65i	0.610031	−	1.57326i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	218.198	−	125.977i	0.240571	−	0.138894i	−0.374868	−	0.927078i	$-0.622312\pi$
$907$	218.198	−	125.977i	0.240571	−	0.138894i	0.615439	+	0.788184i	$0.288979\pi$
$908$		0			0
$909$	247.109	−	270.736i	0.271847	−	0.297840i
$910$		0			0
$911$	−815.790	+	470.997i	−0.895488	+	0.517011i	−0.875734	−	0.482794i	$-0.839622\pi$
$911$	−815.790	+	470.997i	−0.895488	+	0.517011i	−0.0197547	+	0.999805i	$0.506289\pi$
$912$		0			0
$913$	−266.005	−	153.578i	−0.291353	−	0.168213i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1554.85			−1.69559
$918$		0			0
$919$	795.449			0.865560			0.432780	−	0.901500i	$-0.357533\pi$
$919$	795.449			0.865560			0.432780	+	0.901500i	$0.357533\pi$
$920$		0			0
$921$	53.7684	+	347.075i	0.0583805	+	0.376846i
$922$		0			0
$923$	−1299.15	+	2250.20i	−1.40753	+	2.43792i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	908.681	+	199.581i	0.980239	+	0.215298i
$928$		0			0
$929$	−1414.36	+	816.581i	−1.52245	+	0.878989i	−0.522806	+	0.852452i	$0.675115\pi$
$929$	−1414.36	+	816.581i	−1.52245	+	0.878989i	−0.999648	+	0.0265372i	$0.991552\pi$
$930$		0			0
$931$	119.634	−	207.213i	0.128501	−	0.222570i
$932$		0			0
$933$	−53.2177	−	20.6352i	−0.0570394	−	0.0221170i
$934$		0			0
$935$		0			0
$936$		0			0
$937$			1336.80i			1.42668i	0.700817	+	0.713341i	$0.252819\pi$
$937$			1336.80i			1.42668i	−0.700817	+	0.713341i	$0.747181\pi$
$938$		0			0
$939$	−390.576	+	314.101i	−0.415949	+	0.334506i
$940$		0			0
$941$	−702.449	−	405.559i	−0.746492	−	0.430987i	0.0779329	−	0.996959i	$-0.475168\pi$
$941$	−702.449	−	405.559i	−0.746492	−	0.430987i	−0.824425	+	0.565971i	$0.808501\pi$
$942$		0			0
$943$	−48.5446	+	28.0272i	−0.0514789	+	0.0297214i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	261.881	+	453.592i	0.276538	+	0.478978i	0.970522	−	0.241013i	$-0.0774795\pi$
$947$	261.881	+	453.592i	0.276538	+	0.478978i	−0.693984	+	0.719990i	$0.744146\pi$
$948$		0			0
$949$	−644.993	+	1117.16i	−0.679656	+	1.17720i
$950$		0			0
$951$	−368.323	−	458.000i	−0.387301	−	0.481598i
$952$		0			0
$953$	−784.182			−0.822856			−0.411428	−	0.911442i	$-0.634970\pi$
$953$	−784.182			−0.822856			−0.411428	+	0.911442i	$0.634970\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	51.2117	−	132.074i	0.0535128	−	0.138008i
$958$		0			0
$959$	1876.15	+	1083.20i	1.95636	+	1.12951i
$960$		0			0
$961$	437.119	+	757.112i	0.454858	+	0.787838i
$962$		0			0
$963$	188.000	−	59.6818i	0.195223	−	0.0619748i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	964.960	+	557.120i	0.997890	+	0.576132i	0.907623	−	0.419785i	$-0.137895\pi$
$967$	964.960	+	557.120i	0.997890	+	0.576132i	0.0902669	+	0.995918i	$0.471228\pi$
$968$		0			0
$969$	−288.087	+	44.6301i	−0.297303	+	0.0460579i
$970$		0			0
$971$			1241.22i			1.27829i	0.769088	+	0.639143i	$0.220711\pi$
$971$			1241.22i			1.27829i	−0.769088	+	0.639143i	$0.779289\pi$
$972$		0			0
$973$			683.882i			0.702859i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−476.629	+	825.547i	−0.487850	+	0.844981i	−0.999902	−	0.0139732i	$-0.995552\pi$
$977$	−476.629	+	825.547i	−0.487850	+	0.844981i	0.512052	+	0.858954i	$0.328885\pi$
$978$		0			0
$979$	−335.900	−	581.795i	−0.343105	−	0.594275i
$980$		0			0
$981$	694.539	−	220.486i	0.707991	−	0.224756i
$982$		0			0
$983$	428.230	+	741.717i	0.435636	+	0.754544i	0.997347	−	0.0727894i	$-0.0231901\pi$
$983$	428.230	+	741.717i	0.435636	+	0.754544i	−0.561711	+	0.827333i	$0.689857\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	2129.01	+	825.526i	2.15706	+	0.836399i
$988$		0			0
$989$		−	74.2780i		−	0.0751041i
$990$		0			0
$991$	−995.644			−1.00469			−0.502343	−	0.864668i	$-0.667529\pi$
$991$	−995.644			−1.00469			−0.502343	+	0.864668i	$0.667529\pi$
$992$		0			0
$993$	−154.028	−	191.530i	−0.155114	−	0.192880i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	1199.31	−	692.421i	1.20292	−	0.694504i	0.241714	−	0.970348i	$-0.422290\pi$
$997$	1199.31	−	692.421i	1.20292	−	0.694504i	0.961203	+	0.275843i	$0.0889571\pi$
$998$		0			0
$999$	445.166	+	896.053i	0.445612	+	0.896950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.3.u.c.149.1		24
3.2	odd	2		2700.3.u.c.449.11		24
5.2	odd	4		180.3.o.b.41.3	✓	12
5.3	odd	4		900.3.p.c.401.4		12
5.4	even	2	inner	900.3.u.c.149.12		24
9.2	odd	6	inner	900.3.u.c.749.12		24
9.7	even	3		2700.3.u.c.2249.2		24
15.2	even	4		540.3.o.b.341.6		12
15.8	even	4		2700.3.p.c.2501.1		12
15.14	odd	2		2700.3.u.c.449.2		24
20.7	even	4		720.3.bs.b.401.4		12
45.2	even	12		180.3.o.b.101.3	yes	12
45.7	odd	12		540.3.o.b.521.6		12
45.22	odd	12		1620.3.g.b.161.7		12
45.29	odd	6	inner	900.3.u.c.749.1		24
45.32	even	12		1620.3.g.b.161.1		12
45.34	even	6		2700.3.u.c.2249.11		24
45.38	even	12		900.3.p.c.101.4		12
45.43	odd	12		2700.3.p.c.1601.1		12
60.47	odd	4		2160.3.bs.b.881.4		12
180.7	even	12		2160.3.bs.b.1601.4		12
180.47	odd	12		720.3.bs.b.641.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.3.o.b.41.3	✓	12	5.2	odd	4
180.3.o.b.101.3	yes	12	45.2	even	12
540.3.o.b.341.6		12	15.2	even	4
540.3.o.b.521.6		12	45.7	odd	12
720.3.bs.b.401.4		12	20.7	even	4
720.3.bs.b.641.4		12	180.47	odd	12
900.3.p.c.101.4		12	45.38	even	12
900.3.p.c.401.4		12	5.3	odd	4
900.3.u.c.149.1		24	1.1	even	1	trivial
900.3.u.c.149.12		24	5.4	even	2	inner
900.3.u.c.749.1		24	45.29	odd	6	inner
900.3.u.c.749.12		24	9.2	odd	6	inner
1620.3.g.b.161.1		12	45.32	even	12
1620.3.g.b.161.7		12	45.22	odd	12
2160.3.bs.b.881.4		12	60.47	odd	4
2160.3.bs.b.1601.4		12	180.7	even	12
2700.3.p.c.1601.1		12	45.43	odd	12
2700.3.p.c.2501.1		12	15.8	even	4
2700.3.u.c.449.2		24	15.14	odd	2
2700.3.u.c.449.11		24	3.2	odd	2
2700.3.u.c.2249.2		24	9.7	even	3
2700.3.u.c.2249.11		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)

\(f(q)\)	\(=\)	\(q+(-2.96464 + 0.459278i) q^{3} +(7.16186 - 4.13490i) q^{7} +(8.57813 - 2.72318i) q^{9} +O(q^{10})\)	\(q+(-2.96464 + 0.459278i) q^{3} +(7.16186 - 4.13490i) q^{7} +(8.57813 - 2.72318i) q^{9} +(3.29604 - 1.90297i) q^{11} +(-16.7290 - 9.65850i) q^{13} +7.87471 q^{17} +12.3401 q^{19} +(-19.3332 + 15.5478i) q^{21} +(-0.604705 + 1.04738i) q^{23} +(-24.1803 + 12.0130i) q^{27} +(-10.7443 + 6.20324i) q^{29} +(-4.65731 + 8.06669i) q^{31} +(-8.89757 + 7.15541i) q^{33} -37.0571i q^{37} +(54.0314 + 20.9507i) q^{39} +(40.1391 + 23.1743i) q^{41} +(-53.1884 + 30.7083i) q^{43} +(-46.0201 - 79.7091i) q^{47} +(9.69479 - 16.7919i) q^{49} +(-23.3456 + 3.61668i) q^{51} +52.1540 q^{53} +(-36.5838 + 5.66752i) q^{57} +(54.4701 + 31.4484i) q^{59} +(11.6631 + 20.2011i) q^{61} +(50.1752 - 54.9727i) q^{63} +(-93.8237 - 54.1692i) q^{67} +(1.31169 - 3.38283i) q^{69} -134.509i q^{71} -66.7798i q^{73} +(15.7372 - 27.2576i) q^{77} +(-62.2089 - 107.749i) q^{79} +(66.1686 - 46.7196i) q^{81} +(-40.3522 - 69.8921i) q^{83} +(29.0040 - 23.3250i) q^{87} -176.513i q^{89} -159.748 q^{91} +(10.1024 - 26.0538i) q^{93} +(79.5774 - 45.9441i) q^{97} +(23.0917 - 25.2997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 52 q^{9}+O(q^{10}) \) 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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