LMFDB - Embedded newform 900.3.u.c.149.12

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			149.12
Character	$\chi$	$=$	900.149
Dual form			900.3.u.c.749.12

$q$-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	−0.915007	−	0.403438i	$-0.867815\pi$
$7$	−7.16186	+	4.13490i	−1.02312	+	0.590700i	−0.108115	+	0.994138i	$0.534482\pi$
$8$		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	0.978091	−	0.208179i	$-0.0667538\pi$
$13$	16.7290	+	9.65850i	1.28685	+	0.742962i	0.308757	+	0.951141i	$0.400087\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−7.87471			−0.463218			−0.231609	−	0.972809i	$-0.574399\pi$
$17$	−7.87471			−0.463218			−0.231609	+	0.972809i	$0.574399\pi$
$18$		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	−0.852580	−	0.522596i	$-0.824964\pi$
$23$	0.604705	−	1.04738i	0.0262915	−	0.0455383i	0.878872	+	0.477058i	$0.158297\pi$
$24$		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	$0.166950\pi$
$37$			37.0571i			1.00154i	−0.865579	+	0.500772i	$0.833050\pi$
$38$		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	0.268472	−	0.963287i	$-0.413481\pi$
$43$	53.1884	−	30.7083i	1.23694	−	0.714148i	0.968468	+	0.249140i	$0.0801479\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	46.0201	+	79.7091i	0.979151	+	1.69594i	0.665496	+	0.746402i	$0.268220\pi$
$47$	46.0201	+	79.7091i	0.979151	+	1.69594i	0.313655	+	0.949537i	$0.398446\pi$
$48$		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	$-0.663741\pi$
$53$	−52.1540			−0.984038			−0.492019	+	0.870584i	$0.663741\pi$
$54$		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	0.994429	−	0.105411i	$-0.0336159\pi$
$67$	93.8237	+	54.1692i	1.40035	+	0.808495i	0.405926	+	0.913906i	$0.366949\pi$
$68$		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	$0.151218\pi$
$73$			66.7798i			0.914792i	−0.889263	+	0.457396i	$0.848782\pi$
$74$		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	0.999874	−	0.0158947i	$-0.00505964\pi$
$83$	40.3522	+	69.8921i	0.486172	+	0.842074i	−0.513702	+	0.857969i	$0.671726\pi$
$84$		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	−0.850550	−	0.525895i	$-0.823731\pi$
$97$	−79.5774	+	45.9441i	−0.820386	+	0.473650i	0.0301635	+	0.999545i	$0.490397\pi$
$98$		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	−0.00208213	−	0.999998i	$-0.500663\pi$
$103$	−89.5221	−	51.6856i	−0.869147	−	0.501802i	−0.867065	+	0.498196i	$0.833996\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−21.9162			−0.204824			−0.102412	−	0.994742i	$-0.532656\pi$
$107$	−21.9162			−0.204824			−0.102412	+	0.994742i	$0.532656\pi$
$108$		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	$-0.656585\pi$
$113$	59.5708	−	103.180i	0.527175	−	0.913094i	0.999498	−	0.0316683i	$-0.0100820\pi$
$114$		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	$0.180085\pi$
$127$			136.157i			1.07211i	−0.844185	+	0.536053i	$0.819915\pi$
$128$		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	$-0.761361\pi$
$137$	−130.982	−	226.868i	−0.956075	−	1.65597i	−0.224186	−	0.974546i	$-0.571972\pi$
$138$		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	0.904248	−	0.427008i	$-0.140432\pi$
$157$	154.892	+	89.4268i	0.986572	+	0.569598i	0.0823242	+	0.996606i	$0.473766\pi$
$158$		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	$-0.995680\pi$
$163$		−	4.42383i		−	0.0271401i	0.999908	−	0.0135700i	$-0.00431961\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.06435	+	13.9679i	−0.0482895	+	0.0836399i	−0.889160	−	0.457597i	$-0.848710\pi$
$167$	−8.06435	+	13.9679i	−0.0482895	+	0.0836399i	0.840870	+	0.541237i	$0.182044\pi$
$168$		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	$0.0392571\pi$
$173$	104.274	+	180.607i	0.602738	+	1.04397i	−0.389666	+	0.920956i	$0.627410\pi$
$174$		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	0.0708599	−	0.997486i	$-0.477426\pi$
$193$	−146.209	−	84.4137i	−0.757559	−	0.437377i	−0.828418	+	0.560110i	$0.810759\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−327.080			−1.66030			−0.830152	−	0.557537i	$-0.811746\pi$
$197$	−327.080			−1.66030			−0.830152	+	0.557537i	$0.811746\pi$
$198$		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	0.176825	−	0.984242i	$-0.443417\pi$
$223$	249.229	−	143.892i	1.11762	−	0.645256i	0.940792	+	0.338986i	$0.110084\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−99.2817	−	171.961i	−0.437364	−	0.757537i	0.560121	−	0.828411i	$-0.310755\pi$
$227$	−99.2817	−	171.961i	−0.437364	−	0.757537i	−0.997485	+	0.0708736i	$0.977421\pi$
$228$		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	$-0.672459\pi$
$233$	−240.304			−1.03135			−0.515675	+	0.856784i	$0.672459\pi$
$234$		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	−0.913512	−	0.406812i	$-0.866641\pi$
$257$	−26.8428	+	46.4932i	−0.104447	+	0.180907i	0.809065	+	0.587719i	$0.199974\pi$
$258$		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	0.875682	−	0.482888i	$-0.160412\pi$
$263$	5.16722	+	8.94989i	0.0196472	+	0.0340300i	−0.856035	+	0.516918i	$0.827079\pi$
$264$		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	−0.583501	−	0.812112i	$-0.698318\pi$
$277$	−47.6279	+	27.4980i	−0.171942	+	0.0992708i	0.411559	+	0.911383i	$0.364984\pi$
$278$		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	0.822590	−	0.568635i	$-0.192528\pi$
$283$	209.825	+	121.143i	0.741433	+	0.428066i	−0.0811572	+	0.996701i	$0.525862\pi$
$284$		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	−0.955467	−	0.295098i	$-0.904648\pi$
$293$	−65.0963	+	112.750i	−0.222172	+	0.384812i	0.733296	+	0.679910i	$0.237981\pi$
$294$		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	$0.0610662\pi$
$307$			117.072i			0.381341i	−0.981654	+	0.190670i	$0.938934\pi$
$308$		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	−0.712992	−	0.701172i	$-0.752661\pi$
$313$	−144.686	+	83.5346i	−0.462256	+	0.266884i	0.250736	+	0.968055i	$0.419327\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−97.9549	−	169.663i	−0.309006	−	0.535214i	0.669139	−	0.743137i	$-0.266663\pi$
$317$	−97.9549	−	169.663i	−0.309006	−	0.535214i	−0.978145	+	0.207923i	$0.933330\pi$
$318$		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	−0.363700	−	0.931516i	$-0.618487\pi$
$337$	−455.714	−	263.107i	−1.35227	−	0.780732i	−0.988567	+	0.150784i	$0.951820\pi$
$338$		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	$-0.606082\pi$
$347$	227.219	−	393.556i	0.654811	−	1.13417i	0.981941	−	0.189186i	$-0.0605851\pi$
$348$		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	0.785676	−	0.618638i	$-0.212315\pi$
$353$	−50.4501	−	87.3821i	−0.142918	−	0.247541i	−0.928594	+	0.371097i	$0.878982\pi$
$354$		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	−0.831452	−	0.555596i	$-0.812490\pi$
$367$	−281.129	+	162.310i	−0.766018	+	0.442261i	0.0654344	+	0.997857i	$0.479157\pi$
$368$		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	0.650017	−	0.759919i	$-0.274762\pi$
$373$	118.210	+	68.2485i	0.316917	+	0.182972i	−0.333101	+	0.942891i	$0.608095\pi$
$374$		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	$-0.614481\pi$
$383$	243.068	−	421.006i	0.634642	−	1.09923i	0.986591	−	0.163213i	$-0.0521859\pi$
$384$		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	$0.220458\pi$
$397$			506.995i			1.27707i	−0.769595	+	0.638533i	$0.779542\pi$
$398$		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	$-0.885476\pi$
$433$		−	304.898i		−	0.704153i	0.935971	−	0.352076i	$-0.114524\pi$
$434$		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	0.745764	−	0.666210i	$-0.232085\pi$
$443$	−90.4041	−	156.585i	−0.204073	−	0.353464i	−0.949837	+	0.312746i	$0.898751\pi$
$444$		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	−0.256126	−	0.966643i	$-0.582446\pi$
$457$	206.998	−	119.510i	0.452949	−	0.261510i	0.709075	+	0.705133i	$0.249113\pi$
$458$		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	−0.231188	−	0.972909i	$-0.574261\pi$
$463$	−550.667	−	317.928i	−1.18935	−	0.686669i	−0.958158	+	0.286240i	$0.907595\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−34.8159			−0.0745522			−0.0372761	−	0.999305i	$-0.511868\pi$
$467$	−34.8159			−0.0745522			−0.0372761	+	0.999305i	$0.511868\pi$
$468$		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	$-0.921946\pi$
$487$		−	236.451i		−	0.485527i	0.970086	−	0.242763i	$-0.0780538\pi$
$488$		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	$-0.177157\pi$
$503$	854.175			1.69816			0.849081	+	0.528263i	$0.177157\pi$
$504$		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	$0.130323\pi$
$523$			416.390i			0.796158i	−0.917351	+	0.398079i	$0.869677\pi$
$524$		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	0.101361	−	0.994850i	$-0.467680\pi$
$547$	554.443	−	320.108i	1.01361	−	0.585206i	0.912245	+	0.409644i	$0.134347\pi$
$548$		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	$-0.426401\pi$
$557$	255.289			0.458328			0.229164	+	0.973388i	$0.426401\pi$
$558$		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	−0.534135	−	0.845399i	$-0.679363\pi$
$563$	261.834	−	453.510i	0.465070	−	0.805525i	0.999205	+	0.0398747i	$0.0126959\pi$
$564$		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	$0.125991\pi$
$577$			444.934i			0.771116i	−0.922684	+	0.385558i	$0.874009\pi$
$578$		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	0.833718	−	0.552190i	$-0.186208\pi$
$587$	−36.0133	−	62.3769i	−0.0613515	−	0.106264i	−0.895070	+	0.445926i	$0.852874\pi$
$588$		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	$-0.828677\pi$
$593$	−1018.32			−1.71724			−0.858619	+	0.512614i	$0.828677\pi$
$594$		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	0.688848	−	0.724905i	$-0.258117\pi$
$607$	246.130	+	142.103i	0.405486	+	0.234108i	−0.283362	+	0.959013i	$0.591450\pi$
$608$		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	$-0.928579\pi$
$613$		−	272.783i		−	0.444996i	0.974933	−	0.222498i	$-0.0714211\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−39.5342	+	68.4752i	−0.0640748	+	0.110981i	−0.896283	−	0.443482i	$-0.853743\pi$
$617$	−39.5342	+	68.4752i	−0.0640748	+	0.110981i	0.832208	+	0.554463i	$0.187076\pi$
$618$		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	0.349700	−	0.936862i	$-0.386283\pi$
$643$	−184.409	−	106.469i	−0.286795	−	0.165581i	−0.636496	+	0.771280i	$0.719617\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	242.229			0.374388			0.187194	−	0.982323i	$-0.440061\pi$
$647$	242.229			0.374388			0.187194	+	0.982323i	$0.440061\pi$
$648$		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	−0.962528	−	0.271181i	$-0.912586\pi$
$653$	−160.909	+	278.702i	−0.246414	+	0.426802i	0.716114	+	0.697983i	$0.245919\pi$
$654$		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	−0.590820	−	0.806803i	$-0.701196\pi$
$673$	−126.200	+	72.8616i	−0.187518	+	0.108264i	0.403302	+	0.915067i	$0.367862\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−197.288	−	341.713i	−0.291415	−	0.504745i	0.682730	−	0.730671i	$-0.260793\pi$
$677$	−197.288	−	341.713i	−0.291415	−	0.504745i	−0.974145	+	0.225926i	$0.927459\pi$
$678$		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	$-0.621919\pi$
$683$	−510.506			−0.747447			−0.373723	+	0.927540i	$0.621919\pi$
$684$		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	−0.654120	−	0.756391i	$-0.726961\pi$
$727$	−237.094	+	136.886i	−0.326126	+	0.188289i	0.327994	+	0.944680i	$0.393628\pi$
$728$		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	0.782934	−	0.622105i	$-0.213722\pi$
$733$	465.925	+	269.002i	0.635642	+	0.366988i	−0.147292	+	0.989093i	$0.547056\pi$
$734$		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	$-0.643682\pi$
$743$	416.955	−	722.188i	0.561178	−	0.971989i	0.997394	−	0.0721467i	$-0.0229850\pi$
$744$		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	$-0.911748\pi$
$757$		−	414.403i		−	0.547428i	0.961811	−	0.273714i	$-0.0882522\pi$
$758$		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	$-0.861507\pi$
$773$	−1401.96			−1.81367			−0.906833	+	0.421490i	$0.861507\pi$
$774$		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	0.700143	−	0.714003i	$-0.253120\pi$
$787$	339.881	+	196.231i	0.431870	+	0.249340i	−0.268273	+	0.963343i	$0.586453\pi$
$788$		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	$-0.595221\pi$
$797$	542.129	−	938.996i	0.680213	−	1.17816i	0.974916	−	0.222574i	$-0.0714459\pi$
$798$		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	0.223195	−	0.974774i	$-0.428351\pi$
$823$	−419.225	−	242.040i	−0.509387	−	0.294095i	−0.732582	+	0.680679i	$0.761685\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	262.221			0.317075			0.158537	−	0.987353i	$-0.449322\pi$
$827$	262.221			0.317075			0.158537	+	0.987353i	$0.449322\pi$
$828$		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	−0.167597	−	0.985856i	$-0.553601\pi$
$853$	513.830	−	296.660i	0.602380	−	0.347784i	0.769977	+	0.638071i	$0.220267\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	706.162	+	1223.11i	0.823993	+	1.42720i	0.902686	+	0.430299i	$0.141592\pi$
$857$	706.162	+	1223.11i	0.823993	+	1.42720i	−0.0786932	+	0.996899i	$0.525075\pi$
$858$		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	$-0.741044\pi$
$863$	−1185.65			−1.37387			−0.686935	+	0.726719i	$0.741044\pi$
$864$		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	−0.475694	−	0.879611i	$-0.657803\pi$
$877$	−1293.84	−	747.001i	−1.47531	−	0.851769i	−0.999612	+	0.0278418i	$0.991137\pi$
$878$		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	$-0.868380\pi$
$883$		−	709.600i		−	0.803624i	0.915722	−	0.401812i	$-0.131620\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−339.575	+	588.161i	−0.382835	+	0.663090i	−0.991466	−	0.130363i	$-0.958386\pi$
$887$	−339.575	+	588.161i	−0.382835	+	0.663090i	0.608631	+	0.793453i	$0.291719\pi$
$888$		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	−0.615439	−	0.788184i	$-0.711021\pi$
$907$	−218.198	+	125.977i	−0.240571	+	0.138894i	0.374868	+	0.927078i	$0.377688\pi$
$908$		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	$-0.747181\pi$
$937$		−	1336.80i		−	1.42668i	0.700817	−	0.713341i	$-0.252819\pi$
$938$		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	0.693984	−	0.719990i	$-0.255854\pi$
$947$	−261.881	−	453.592i	−0.276538	−	0.478978i	−0.970522	+	0.241013i	$0.922520\pi$
$948$		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	$-0.365030\pi$
$953$	784.182			0.822856			0.411428	+	0.911442i	$0.365030\pi$
$954$		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	−0.0902669	−	0.995918i	$-0.528772\pi$
$967$	−964.960	−	557.120i	−0.997890	−	0.576132i	−0.907623	+	0.419785i	$0.862105\pi$
$968$		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	−0.512052	−	0.858954i	$-0.671115\pi$
$977$	476.629	−	825.547i	0.487850	−	0.844981i	0.999902	+	0.0139732i	$0.00444795\pi$
$978$		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	0.561711	−	0.827333i	$-0.310143\pi$
$983$	−428.230	−	741.717i	−0.435636	−	0.754544i	−0.997347	+	0.0727894i	$0.976810\pi$
$984$		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	−0.961203	−	0.275843i	$-0.911043\pi$
$997$	−1199.31	+	692.421i	−1.20292	+	0.694504i	−0.241714	+	0.970348i	$0.577710\pi$
$998$		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.149.12		24
3.2	odd	2		2700.3.u.c.449.2		24
5.2	odd	4		900.3.p.c.401.4		12
5.3	odd	4		180.3.o.b.41.3	✓	12
5.4	even	2	inner	900.3.u.c.149.1		24
9.2	odd	6	inner	900.3.u.c.749.1		24
9.7	even	3		2700.3.u.c.2249.11		24
15.2	even	4		2700.3.p.c.2501.1		12
15.8	even	4		540.3.o.b.341.6		12
15.14	odd	2		2700.3.u.c.449.11		24
20.3	even	4		720.3.bs.b.401.4		12
45.2	even	12		900.3.p.c.101.4		12
45.7	odd	12		2700.3.p.c.1601.1		12
45.13	odd	12		1620.3.g.b.161.7		12
45.23	even	12		1620.3.g.b.161.1		12
45.29	odd	6	inner	900.3.u.c.749.12		24
45.34	even	6		2700.3.u.c.2249.2		24
45.38	even	12		180.3.o.b.101.3	yes	12
45.43	odd	12		540.3.o.b.521.6		12
60.23	odd	4		2160.3.bs.b.881.4		12
180.43	even	12		2160.3.bs.b.1601.4		12
180.83	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	5.3	odd	4
180.3.o.b.101.3	yes	12	45.38	even	12
540.3.o.b.341.6		12	15.8	even	4
540.3.o.b.521.6		12	45.43	odd	12
720.3.bs.b.401.4		12	20.3	even	4
720.3.bs.b.641.4		12	180.83	odd	12
900.3.p.c.101.4		12	45.2	even	12
900.3.p.c.401.4		12	5.2	odd	4
900.3.u.c.149.1		24	5.4	even	2	inner
900.3.u.c.149.12		24	1.1	even	1	trivial
900.3.u.c.749.1		24	9.2	odd	6	inner
900.3.u.c.749.12		24	45.29	odd	6	inner
1620.3.g.b.161.1		12	45.23	even	12
1620.3.g.b.161.7		12	45.13	odd	12
2160.3.bs.b.881.4		12	60.23	odd	4
2160.3.bs.b.1601.4		12	180.43	even	12
2700.3.p.c.1601.1		12	45.7	odd	12
2700.3.p.c.2501.1		12	15.2	even	4
2700.3.u.c.449.2		24	3.2	odd	2
2700.3.u.c.449.11		24	15.14	odd	2
2700.3.u.c.2249.2		24	45.34	even	6
2700.3.u.c.2249.11		24	9.7	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	900.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

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