LMFDB - Embedded newform 1800.2.m.f.899.32

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(899,1800)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1800, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1800.899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1800.m (of order $2$, degree $1$, 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:	$14.3730723638$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			899.32
Character	$\chi$	$=$	1800.899
Dual form			1800.2.m.f.899.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35383 + 0.408843i) q^{2} +(1.66570 + 1.10700i) q^{4} +3.40004 q^{7} +(1.80247 + 2.17970i) q^{8} +O(q^{10})$	\(q+(1.35383 + 0.408843i) q^{2} +(1.66570 + 1.10700i) q^{4} +3.40004 q^{7} +(1.80247 + 2.17970i) q^{8} +2.19073i q^{11} +6.77043 q^{13} +(4.60306 + 1.39008i) q^{14} +(1.54908 + 3.68787i) q^{16} -6.90203 q^{17} -1.49781 q^{19} +(-0.895664 + 2.96587i) q^{22} -5.21543i q^{23} +(9.16599 + 2.76804i) q^{26} +(5.66342 + 3.76386i) q^{28} +2.08435 q^{29} -2.76509i q^{31} +(0.589430 + 5.62606i) q^{32} +(-9.34415 - 2.82184i) q^{34} -5.06297 q^{37} +(-2.02778 - 0.612369i) q^{38} -1.10635i q^{41} +3.60035i q^{43} +(-2.42515 + 3.64909i) q^{44} +(2.13229 - 7.06079i) q^{46} +11.0705i q^{47} +4.56024 q^{49} +(11.2775 + 7.49490i) q^{52} +1.22832i q^{53} +(6.12847 + 7.41106i) q^{56} +(2.82184 + 0.852170i) q^{58} -11.5408i q^{59} -10.6228i q^{61} +(1.13049 - 3.74345i) q^{62} +(-1.50219 + 7.85770i) q^{64} -10.8234i q^{67} +(-11.4967 - 7.64058i) q^{68} +2.86369 q^{71} +12.7566i q^{73} +(-6.85438 - 2.06996i) q^{74} +(-2.49490 - 1.65808i) q^{76} +7.44856i q^{77} +11.4256i q^{79} +(0.452325 - 1.49781i) q^{82} +8.71239 q^{83} +(-1.47198 + 4.87425i) q^{86} +(-4.77514 + 3.94873i) q^{88} +1.40802i q^{89} +23.0197 q^{91} +(5.77351 - 8.68731i) q^{92} +(-4.52611 + 14.9876i) q^{94} +8.19194i q^{97} +(6.17378 + 1.86442i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4}+O(q^{10}) $ 32 * q + 8 * q^4	$ 32 q + 8 q^{4} - 16 q^{16} - 32 q^{19} - 24 q^{34} + 40 q^{46} + 64 q^{49} - 64 q^{64} + 72 q^{76} + 96 q^{91} + 40 q^{94}+O(q^{100}) $ 32 * q + 8 * q^4 - 16 * q^16 - 32 * q^19 - 24 * q^34 + 40 * q^46 + 64 * q^49 - 64 * q^64 + 72 * q^76 + 96 * q^91 + 40 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1001$	$1351$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

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 $

$2$	1.35383	+	0.408843i	0.957300	+	0.289096i
$2$	1.35383	+	0.408843i	0.957300	+	0.289096i
$3$		0			0
$3$		0			0
$4$	1.66570	+	1.10700i	0.832848	+	0.553502i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	3.40004			1.28509			0.642546	−	0.766247i	$-0.277878\pi$
$7$	3.40004			1.28509			0.642546	+	0.766247i	$0.277878\pi$
$8$	1.80247	+	2.17970i	0.637270	+	0.770641i
$9$		0			0
$10$		0			0
$11$			2.19073i			0.660530i	0.943888	+	0.330265i	$0.107138\pi$
$11$			2.19073i			0.660530i	−0.943888	+	0.330265i	$0.892862\pi$
$12$		0			0
$13$	6.77043			1.87778			0.938889	−	0.344219i	$-0.111856\pi$
$13$	6.77043			1.87778			0.938889	+	0.344219i	$0.111856\pi$
$14$	4.60306	+	1.39008i	1.23022	+	0.371515i
$15$		0			0
$16$	1.54908	+	3.68787i	0.387270	+	0.921966i
$17$	−6.90203			−1.67399			−0.836994	−	0.547212i	$-0.815689\pi$
$17$	−6.90203			−1.67399			−0.836994	+	0.547212i	$0.815689\pi$
$18$		0			0
$19$	−1.49781			−0.343621			−0.171811	−	0.985130i	$-0.554962\pi$
$19$	−1.49781			−0.343621			−0.171811	+	0.985130i	$0.554962\pi$
$20$		0			0
$21$		0			0
$22$	−0.895664	+	2.96587i	−0.190956	+	0.632326i
$23$		−	5.21543i		−	1.08749i	−0.839250	−	0.543746i	$-0.817005\pi$
$23$		−	5.21543i		−	1.08749i	0.839250	−	0.543746i	$-0.182995\pi$
$24$		0			0
$25$		0			0
$26$	9.16599	+	2.76804i	1.79760	+	0.542857i
$27$		0			0
$28$	5.66342	+	3.76386i	1.07029	+	0.711302i
$29$	2.08435			0.387053			0.193527	−	0.981095i	$-0.438007\pi$
$29$	2.08435			0.387053			0.193527	+	0.981095i	$0.438007\pi$
$30$		0			0
$31$		−	2.76509i		−	0.496625i	−0.968680	−	0.248312i	$-0.920124\pi$
$31$		−	2.76509i		−	0.496625i	0.968680	−	0.248312i	$-0.0798759\pi$
$32$	0.589430	+	5.62606i	0.104197	+	0.994557i
$33$		0			0
$34$	−9.34415	−	2.82184i	−1.60251	−	0.483942i
$35$		0			0
$36$		0			0
$37$	−5.06297			−0.832347			−0.416173	−	0.909285i	$-0.636629\pi$
$37$	−5.06297			−0.832347			−0.416173	+	0.909285i	$0.636629\pi$
$38$	−2.02778	−	0.612369i	−0.328949	−	0.0993394i
$39$		0			0
$40$		0			0
$41$		−	1.10635i		−	0.172783i	−0.996261	−	0.0863917i	$-0.972466\pi$
$41$		−	1.10635i		−	0.172783i	0.996261	−	0.0863917i	$-0.0275336\pi$
$42$		0			0
$43$			3.60035i			0.549048i	0.961580	+	0.274524i	$0.0885203\pi$
$43$			3.60035i			0.549048i	−0.961580	+	0.274524i	$0.911480\pi$
$44$	−2.42515	+	3.64909i	−0.365605	+	0.550121i
$45$		0			0
$46$	2.13229	−	7.06079i	0.314389	−	1.04106i
$47$			11.0705i			1.61480i	0.590001	+	0.807402i	$0.299127\pi$
$47$			11.0705i			1.61480i	−0.590001	+	0.807402i	$0.700873\pi$
$48$		0			0
$49$	4.56024			0.651463
$50$		0			0
$51$		0			0
$52$	11.2775	+	7.49490i	1.56390	+	1.03936i
$53$			1.22832i			0.168723i	0.996435	+	0.0843613i	$0.0268850\pi$
$53$			1.22832i			0.168723i	−0.996435	+	0.0843613i	$0.973115\pi$
$54$		0			0
$55$		0			0
$56$	6.12847	+	7.41106i	0.818951	+	0.990344i
$57$		0			0
$58$	2.82184	+	0.852170i	0.370526	+	0.111895i
$59$		−	11.5408i		−	1.50249i	−0.660025	−	0.751243i	$-0.729454\pi$
$59$		−	11.5408i		−	1.50249i	0.660025	−	0.751243i	$-0.270546\pi$
$60$		0			0
$61$		−	10.6228i		−	1.36011i	−0.733162	−	0.680054i	$-0.761956\pi$
$61$		−	10.6228i		−	1.36011i	0.733162	−	0.680054i	$-0.238044\pi$
$62$	1.13049	−	3.74345i	0.143572	−	0.475419i
$63$		0			0
$64$	−1.50219	+	7.85770i	−0.187774	+	0.982212i
$65$		0			0
$66$		0			0
$67$		−	10.8234i		−	1.32229i	−0.750260	−	0.661143i	$-0.770072\pi$
$67$		−	10.8234i		−	1.32229i	0.750260	−	0.661143i	$-0.229928\pi$
$68$	−11.4967	−	7.64058i	−1.39418	−	0.926556i
$69$		0			0
$70$		0			0
$71$	2.86369			0.339857			0.169929	−	0.985456i	$-0.445646\pi$
$71$	2.86369			0.339857			0.169929	+	0.985456i	$0.445646\pi$
$72$		0			0
$73$			12.7566i			1.49304i	0.665361	+	0.746521i	$0.268277\pi$
$73$			12.7566i			1.49304i	−0.665361	+	0.746521i	$0.731723\pi$
$74$	−6.85438	−	2.06996i	−0.796806	−	0.240628i
$75$		0			0
$76$	−2.49490	−	1.65808i	−0.286184	−	0.190195i
$77$			7.44856i			0.848842i
$78$		0			0
$79$			11.4256i			1.28548i	0.766084	+	0.642740i	$0.222203\pi$
$79$			11.4256i			1.28548i	−0.766084	+	0.642740i	$0.777797\pi$
$80$		0			0
$81$		0			0
$82$	0.452325	−	1.49781i	0.0499509	−	0.165406i
$83$	8.71239			0.956309			0.478155	−	0.878276i	$-0.341306\pi$
$83$	8.71239			0.956309			0.478155	+	0.878276i	$0.341306\pi$
$84$		0			0
$85$		0			0
$86$	−1.47198	+	4.87425i	−0.158727	+	0.525604i
$87$		0			0
$88$	−4.77514	+	3.94873i	−0.509031	+	0.420936i
$89$			1.40802i			0.149250i	0.997212	+	0.0746250i	$0.0237760\pi$
$89$			1.40802i			0.149250i	−0.997212	+	0.0746250i	$0.976224\pi$
$90$		0			0
$91$	23.0197			2.41312
$92$	5.77351	−	8.68731i	0.601930	−	0.905715i
$93$		0			0
$94$	−4.52611	+	14.9876i	−0.466833	+	1.54585i
$95$		0			0
$96$		0			0
$97$			8.19194i			0.831766i	0.909418	+	0.415883i	$0.136527\pi$
$97$			8.19194i			0.831766i	−0.909418	+	0.415883i	$0.863473\pi$
$98$	6.17378	+	1.86442i	0.623646	+	0.188335i
$99$		0			0
$100$		0			0
$101$	10.8451			1.07912			0.539562	−	0.841946i	$-0.318590\pi$
$101$	10.8451			1.07912			0.539562	+	0.841946i	$0.318590\pi$
$102$		0			0
$103$	8.28038			0.815890			0.407945	−	0.913006i	$-0.366246\pi$
$103$	8.28038			0.815890			0.407945	+	0.913006i	$0.366246\pi$
$104$	12.2035	+	14.7575i	1.19665	+	1.44709i
$105$		0			0
$106$	−0.502189	+	1.66293i	−0.0487769	+	0.161518i
$107$	−15.1520			−1.46479			−0.732397	−	0.680877i	$-0.761599\pi$
$107$	−15.1520			−1.46479			−0.732397	+	0.680877i	$0.761599\pi$
$108$		0			0
$109$		−	9.65885i		−	0.925150i	−0.886580	−	0.462575i	$-0.846926\pi$
$109$		−	9.65885i		−	0.925150i	0.886580	−	0.462575i	$-0.153074\pi$
$110$		0			0
$111$		0			0
$112$	5.26693	+	12.5389i	0.497678	+	1.18481i
$113$	−4.23645			−0.398532			−0.199266	−	0.979945i	$-0.563856\pi$
$113$	−4.23645			−0.398532			−0.199266	+	0.979945i	$0.563856\pi$
$114$		0			0
$115$		0			0
$116$	3.47189	+	2.30738i	0.322356	+	0.214235i
$117$		0			0
$118$	4.71838	−	15.6243i	0.434362	−	1.43833i
$119$	−23.4671			−2.15123
$120$		0			0
$121$	6.20070			0.563700
$122$	4.34305	−	14.3814i	0.393201	−	1.30203i
$123$		0			0
$124$	3.06097	−	4.60579i	0.274883	−	0.413613i
$125$		0			0
$126$		0			0
$127$	−14.1165			−1.25264			−0.626319	−	0.779567i	$-0.715439\pi$
$127$	−14.1165			−1.25264			−0.626319	+	0.779567i	$0.715439\pi$
$128$	−5.24627	+	10.0238i	−0.463709	+	0.885988i
$129$		0			0
$130$		0			0
$131$		−	6.66667i		−	0.582470i	−0.956652	−	0.291235i	$-0.905934\pi$
$131$		−	6.66667i		−	0.582470i	0.956652	−	0.291235i	$-0.0940662\pi$
$132$		0			0
$133$	−5.09261			−0.441585
$134$	4.42506	−	14.6530i	0.382267	−	1.26582i
$135$		0			0
$136$	−12.4407	−	15.0444i	−1.06678	−	1.29004i
$137$	−17.2860			−1.47684			−0.738420	−	0.674341i	$-0.764428\pi$
$137$	−17.2860			−1.47684			−0.738420	+	0.674341i	$0.764428\pi$
$138$		0			0
$139$	−16.4150			−1.39230			−0.696150	−	0.717897i	$-0.745105\pi$
$139$	−16.4150			−1.39230			−0.696150	+	0.717897i	$0.745105\pi$
$140$		0			0
$141$		0			0
$142$	3.87694	+	1.17080i	0.325346	+	0.0982513i
$143$			14.8322i			1.24033i
$144$		0			0
$145$		0			0
$146$	−5.21543	+	17.2702i	−0.431632	+	1.42929i
$147$		0			0
$148$	−8.43336	−	5.60473i	−0.693218	−	0.460706i
$149$	−13.4642			−1.10303			−0.551515	−	0.834165i	$-0.685950\pi$
$149$	−13.4642			−1.10303			−0.551515	+	0.834165i	$0.685950\pi$
$150$		0			0
$151$		−	10.1408i		−	0.825248i	−0.910901	−	0.412624i	$-0.864612\pi$
$151$		−	10.1408i		−	0.825248i	0.910901	−	0.412624i	$-0.135388\pi$
$152$	−2.69976	−	3.26478i	−0.218980	−	0.264809i
$153$		0			0
$154$	−3.04529	+	10.0841i	−0.245397	+	0.812597i
$155$		0			0
$156$		0			0
$157$	14.4030			1.14948			0.574740	−	0.818336i	$-0.305103\pi$
$157$	14.4030			1.14948			0.574740	+	0.818336i	$0.305103\pi$
$158$	−4.67127	+	15.4683i	−0.371627	+	1.23059i
$159$		0			0
$160$		0			0
$161$		−	17.7326i		−	1.39753i
$162$		0			0
$163$		−	18.9172i		−	1.48171i	−0.671667	−	0.740853i	$-0.734422\pi$
$163$		−	18.9172i		−	1.48171i	0.671667	−	0.740853i	$-0.265578\pi$
$164$	1.22474	−	1.84285i	0.0956360	−	0.143902i
$165$		0			0
$166$	11.7951	+	3.56200i	0.915475	+	0.276465i
$167$		−	7.03238i		−	0.544182i	−0.962272	−	0.272091i	$-0.912285\pi$
$167$		−	7.03238i		−	0.544182i	0.962272	−	0.272091i	$-0.0877152\pi$
$168$		0			0
$169$	32.8387			2.52605
$170$		0			0
$171$		0			0
$172$	−3.98560	+	5.99709i	−0.303900	+	0.457273i
$173$		−	4.26166i		−	0.324008i	−0.986790	−	0.162004i	$-0.948204\pi$
$173$		−	4.26166i		−	0.324008i	0.986790	−	0.162004i	$-0.0517958\pi$
$174$		0			0
$175$		0			0
$176$	−8.07912	+	3.39362i	−0.608986	+	0.255804i
$177$		0			0
$178$	−0.575660	+	1.90622i	−0.0431475	+	0.142877i
$179$		−	16.7146i		−	1.24931i	−0.780902	−	0.624653i	$-0.785240\pi$
$179$		−	16.7146i		−	1.24931i	0.780902	−	0.624653i	$-0.214760\pi$
$180$		0			0
$181$			4.71446i			0.350423i	0.984531	+	0.175211i	$0.0560609\pi$
$181$			4.71446i			0.350423i	−0.984531	+	0.175211i	$0.943939\pi$
$182$	31.1647	+	9.41144i	2.31008	+	0.697622i
$183$		0			0
$184$	11.3681	−	9.40066i	0.838066	−	0.693026i
$185$		0			0
$186$		0			0
$187$		−	15.1205i		−	1.10572i
$188$	−12.2551	+	18.4401i	−0.893798	+	1.34489i
$189$		0			0
$190$		0			0
$191$	−11.4776			−0.830490			−0.415245	−	0.909710i	$-0.636304\pi$
$191$	−11.4776			−0.830490			−0.415245	+	0.909710i	$0.636304\pi$
$192$		0			0
$193$			16.8858i			1.21547i	0.794141	+	0.607733i	$0.207921\pi$
$193$			16.8858i			1.21547i	−0.794141	+	0.607733i	$0.792079\pi$
$194$	−3.34922	+	11.0905i	−0.240460	+	0.796250i
$195$		0			0
$196$	7.59597	+	5.04821i	0.542569	+	0.360586i
$197$			25.4537i			1.81350i	0.421664	+	0.906752i	$0.361446\pi$
$197$			25.4537i			1.81350i	−0.421664	+	0.906752i	$0.638554\pi$
$198$		0			0
$199$		−	21.8063i		−	1.54581i	−0.634521	−	0.772905i	$-0.718803\pi$
$199$		−	21.8063i		−	1.54581i	0.634521	−	0.772905i	$-0.281197\pi$
$200$		0			0
$201$		0			0
$202$	14.6824	+	4.43393i	1.03305	+	0.311970i
$203$	7.08685			0.497399
$204$		0			0
$205$		0			0
$206$	11.2102	+	3.38537i	0.781052	+	0.235870i
$207$		0			0
$208$	10.4879	+	24.9684i	0.727208	+	1.73125i
$209$		−	3.28130i		−	0.226972i
$210$		0			0
$211$	−7.70289			−0.530289			−0.265144	−	0.964209i	$-0.585420\pi$
$211$	−7.70289			−0.530289			−0.265144	+	0.964209i	$0.585420\pi$
$212$	−1.35975	+	2.04600i	−0.0933883	+	0.140520i
$213$		0			0
$214$	−20.5131	−	6.19477i	−1.40225	−	0.423466i
$215$		0			0
$216$		0			0
$217$		−	9.40140i		−	0.638209i
$218$	3.94895	−	13.0764i	0.267457	−	0.885646i
$219$		0			0
$220$		0			0
$221$	−46.7297			−3.14338
$222$		0			0
$223$	−14.7663			−0.988828			−0.494414	−	0.869227i	$-0.664617\pi$
$223$	−14.7663			−0.988828			−0.494414	+	0.869227i	$0.664617\pi$
$224$	2.00408	+	19.1288i	0.133903	+	1.27810i
$225$		0			0
$226$	−5.73542	−	1.73204i	−0.381514	−	0.115214i
$227$	17.0307			1.13037			0.565183	−	0.824965i	$-0.308806\pi$
$227$	17.0307			1.13037			0.565183	+	0.824965i	$0.308806\pi$
$228$		0			0
$229$		−	6.33299i		−	0.418496i	−0.977863	−	0.209248i	$-0.932898\pi$
$229$		−	6.33299i		−	0.418496i	0.977863	−	0.209248i	$-0.0671015\pi$
$230$		0			0
$231$		0			0
$232$	3.75698	+	4.54325i	0.246658	+	0.298279i
$233$	−7.04085			−0.461261			−0.230631	−	0.973041i	$-0.574079\pi$
$233$	−7.04085			−0.461261			−0.230631	+	0.973041i	$0.574079\pi$
$234$		0			0
$235$		0			0
$236$	12.7757	−	19.2235i	0.831630	−	1.25134i
$237$		0			0
$238$	−31.7704	−	9.59437i	−2.05937	−	0.621911i
$239$	25.0886			1.62285			0.811424	−	0.584458i	$-0.198693\pi$
$239$	25.0886			1.62285			0.811424	+	0.584458i	$0.198693\pi$
$240$		0			0
$241$	−8.19194			−0.527689			−0.263845	−	0.964565i	$-0.584991\pi$
$241$	−8.19194			−0.527689			−0.263845	+	0.964565i	$0.584991\pi$
$242$	8.39468	+	2.53511i	0.539630	+	0.162963i
$243$		0			0
$244$	11.7595	−	17.6943i	0.752823	−	1.13276i
$245$		0			0
$246$		0			0
$247$	−10.1408			−0.645245
$248$	6.02707	−	4.98400i	0.382719	−	0.316484i
$249$		0			0
$250$		0			0
$251$			2.34533i			0.148036i	0.997257	+	0.0740181i	$0.0235823\pi$
$251$			2.34533i			0.148036i	−0.997257	+	0.0740181i	$0.976418\pi$
$252$		0			0
$253$	11.4256			0.718321
$254$	−19.1113	−	5.77144i	−1.19915	−	0.362132i
$255$		0			0
$256$	−11.2007	+	11.4256i	−0.700044	+	0.714100i
$257$	−24.6347			−1.53667			−0.768334	−	0.640049i	$-0.778914\pi$
$257$	−24.6347			−1.53667			−0.768334	+	0.640049i	$0.778914\pi$
$258$		0			0
$259$	−17.2143			−1.06964
$260$		0			0
$261$		0			0
$262$	2.72562	−	9.02552i	0.168389	−	0.557599i
$263$		−	21.1154i		−	1.30203i	−0.759064	−	0.651016i	$-0.774343\pi$
$263$		−	21.1154i		−	1.30203i	0.759064	−	0.651016i	$-0.225657\pi$
$264$		0			0
$265$		0			0
$266$	−6.89451	−	2.08208i	−0.422730	−	0.127660i
$267$		0			0
$268$	11.9815	−	18.0284i	0.731888	−	1.10126i
$269$	7.81173			0.476289			0.238145	−	0.971230i	$-0.423461\pi$
$269$	7.81173			0.476289			0.238145	+	0.971230i	$0.423461\pi$
$270$		0			0
$271$		−	22.1272i		−	1.34413i	−0.740492	−	0.672066i	$-0.765407\pi$
$271$		−	22.1272i		−	1.34413i	0.740492	−	0.672066i	$-0.234593\pi$
$272$	−10.6918	−	25.4537i	−0.648285	−	1.54336i
$273$		0			0
$274$	−23.4022	−	7.06724i	−1.41378	−	0.426948i
$275$		0			0
$276$		0			0
$277$	−0.934293			−0.0561362			−0.0280681	−	0.999606i	$-0.508936\pi$
$277$	−0.934293			−0.0561362			−0.0280681	+	0.999606i	$0.508936\pi$
$278$	−22.2230	−	6.71114i	−1.33285	−	0.402507i
$279$		0			0
$280$		0			0
$281$		−	5.34899i		−	0.319094i	−0.987190	−	0.159547i	$-0.948997\pi$
$281$		−	5.34899i		−	0.319094i	0.987190	−	0.159547i	$-0.0510034\pi$
$282$		0			0
$283$		−	4.68975i		−	0.278777i	−0.990238	−	0.139388i	$-0.955486\pi$
$283$		−	4.68975i		−	0.278777i	0.990238	−	0.139388i	$-0.0445137\pi$
$284$	4.77003	+	3.17012i	0.283049	+	0.188112i
$285$		0			0
$286$	−6.06403	+	20.0802i	−0.358574	+	1.18737i
$287$		−	3.76164i		−	0.222043i
$288$		0			0
$289$	30.6380			1.80223
$290$		0			0
$291$		0			0
$292$	−14.1216	+	21.2485i	−0.826403	+	1.24348i
$293$			23.3603i			1.36472i	0.731015	+	0.682361i	$0.239047\pi$
$293$			23.3603i			1.36472i	−0.731015	+	0.682361i	$0.760953\pi$
$294$		0			0
$295$		0			0
$296$	−9.12586	−	11.0358i	−0.530430	−	0.641440i
$297$		0			0
$298$	−18.2282	−	5.50474i	−1.05593	−	0.318881i
$299$		−	35.3107i		−	2.04207i
$300$		0			0
$301$			12.2413i			0.705578i
$302$	4.14600	−	13.7289i	0.238576	−	0.790010i
$303$		0			0
$304$	−2.32023	−	5.52372i	−0.133074	−	0.316807i
$305$		0			0
$306$		0			0
$307$		−	17.0109i		−	0.970865i	−0.874274	−	0.485433i	$-0.838662\pi$
$307$		−	17.0109i		−	0.970865i	0.874274	−	0.485433i	$-0.161338\pi$
$308$	−8.24559	+	12.4070i	−0.469836	+	0.706956i
$309$		0			0
$310$		0			0
$311$	6.52043			0.369740			0.184870	−	0.982763i	$-0.440814\pi$
$311$	6.52043			0.369740			0.184870	+	0.982763i	$0.440814\pi$
$312$		0			0
$313$			0.555863i			0.0314192i	0.999877	+	0.0157096i	$0.00500073\pi$
$313$			0.555863i			0.0314192i	−0.999877	+	0.0157096i	$0.994999\pi$
$314$	19.4991	+	5.88854i	1.10040	+	0.332310i
$315$		0			0
$316$	−12.6482	+	19.0316i	−0.711517	+	1.07061i
$317$		−	23.7836i		−	1.33582i	−0.744242	−	0.667910i	$-0.767189\pi$
$317$		−	23.7836i		−	1.33582i	0.744242	−	0.667910i	$-0.232811\pi$
$318$		0			0
$319$			4.56624i			0.255660i
$320$		0			0
$321$		0			0
$322$	7.24986	−	24.0069i	0.404019	−	1.33785i
$323$	10.3379			0.575218
$324$		0			0
$325$		0			0
$326$	7.73414	−	25.6106i	0.428355	−	1.41844i
$327$		0			0
$328$	2.41152	−	1.99417i	0.133154	−	0.110110i
$329$			37.6402i			2.07517i
$330$		0			0
$331$	7.02670			0.386222			0.193111	−	0.981177i	$-0.438142\pi$
$331$	7.02670			0.386222			0.193111	+	0.981177i	$0.438142\pi$
$332$	14.5122	+	9.64466i	0.796460	+	0.529319i
$333$		0			0
$334$	2.87514	−	9.52063i	0.157321	−	0.520946i
$335$		0			0
$336$		0			0
$337$			10.7522i			0.585709i	0.956157	+	0.292854i	$0.0946051\pi$
$337$			10.7522i			0.585709i	−0.956157	+	0.292854i	$0.905395\pi$
$338$	44.4579	+	13.4259i	2.41819	+	0.730271i
$339$		0			0
$340$		0			0
$341$	6.05756			0.328035
$342$		0			0
$343$	−8.29527			−0.447902
$344$	−7.84768	+	6.48953i	−0.423119	+	0.349892i
$345$		0			0
$346$	1.74235	−	5.76956i	0.0936693	−	0.310173i
$347$	−5.42974			−0.291484			−0.145742	−	0.989323i	$-0.546557\pi$
$347$	−5.42974			−0.291484			−0.145742	+	0.989323i	$0.546557\pi$
$348$		0			0
$349$			10.1852i			0.545202i	0.962127	+	0.272601i	$0.0878839\pi$
$349$			10.1852i			0.545202i	−0.962127	+	0.272601i	$0.912116\pi$
$350$		0			0
$351$		0			0
$352$	−12.3252	+	1.29128i	−0.656935	+	0.0688255i
$353$	−3.31287			−0.176326			−0.0881631	−	0.996106i	$-0.528100\pi$
$353$	−3.31287			−0.176326			−0.0881631	+	0.996106i	$0.528100\pi$
$354$		0			0
$355$		0			0
$356$	−1.55869	+	2.34533i	−0.0826102	+	0.124302i
$357$		0			0
$358$	6.83364	−	22.6287i	0.361169	−	1.19596i
$359$	−17.4632			−0.921675			−0.460837	−	0.887485i	$-0.652451\pi$
$359$	−17.4632			−0.921675			−0.460837	+	0.887485i	$0.652451\pi$
$360$		0			0
$361$	−16.7566			−0.881924
$362$	−1.92747	+	6.38256i	−0.101306	+	0.335460i
$363$		0			0
$364$	38.3438	+	25.4829i	2.00976	+	1.33567i
$365$		0			0
$366$		0			0
$367$	−12.9801			−0.677555			−0.338777	−	0.940867i	$-0.610013\pi$
$367$	−12.9801			−0.677555			−0.338777	+	0.940867i	$0.610013\pi$
$368$	19.2338	−	8.07912i	1.00263	−	0.421153i
$369$		0			0
$370$		0			0
$371$			4.17633i			0.216824i
$372$		0			0
$373$	1.12168			0.0580782			0.0290391	−	0.999578i	$-0.490755\pi$
$373$	1.12168			0.0580782			0.0290391	+	0.999578i	$0.490755\pi$
$374$	6.18190	−	20.4705i	0.319658	−	1.05851i
$375$		0			0
$376$	−24.1305	+	19.9543i	−1.24443	+	1.02907i
$377$	14.1119			0.726801
$378$		0			0
$379$	−0.618293			−0.0317596			−0.0158798	−	0.999874i	$-0.505055\pi$
$379$	−0.618293			−0.0317596			−0.0158798	+	0.999874i	$0.505055\pi$
$380$		0			0
$381$		0			0
$382$	−15.5387	−	4.69253i	−0.795028	−	0.240091i
$383$		−	24.2163i		−	1.23740i	−0.785629	−	0.618698i	$-0.787661\pi$
$383$		−	24.2163i		−	1.23740i	0.785629	−	0.618698i	$-0.212339\pi$
$384$		0			0
$385$		0			0
$386$	−6.90364	+	22.8605i	−0.351386	+	1.16357i
$387$		0			0
$388$	−9.06852	+	13.6453i	−0.460384	+	0.692734i
$389$	3.75448			0.190360			0.0951798	−	0.995460i	$-0.469657\pi$
$389$	3.75448			0.190360			0.0951798	+	0.995460i	$0.469657\pi$
$390$		0			0
$391$			35.9970i			1.82045i
$392$	8.21971	+	9.93996i	0.415158	+	0.502044i
$393$		0			0
$394$	−10.4066	+	34.4600i	−0.524276	+	1.73607i
$395$		0			0
$396$		0			0
$397$	−14.7811			−0.741842			−0.370921	−	0.928664i	$-0.620958\pi$
$397$	−14.7811			−0.741842			−0.370921	+	0.928664i	$0.620958\pi$
$398$	8.91537	−	29.5220i	0.446887	−	1.47981i
$399$		0			0
$400$		0			0
$401$		−	6.10353i		−	0.304796i	−0.988319	−	0.152398i	$-0.951300\pi$
$401$		−	6.10353i		−	0.304796i	0.988319	−	0.152398i	$-0.0486996\pi$
$402$		0			0
$403$		−	18.7208i		−	0.932551i
$404$	18.0646	+	12.0055i	0.898747	+	0.597298i
$405$		0			0
$406$	9.59437	+	2.89741i	0.476161	+	0.143796i
$407$		−	11.0916i		−	0.549790i
$408$		0			0
$409$	−1.77408			−0.0877224			−0.0438612	−	0.999038i	$-0.513966\pi$
$409$	−1.77408			−0.0877224			−0.0438612	+	0.999038i	$0.513966\pi$
$410$		0			0
$411$		0			0
$412$	13.7926	+	9.16642i	0.679512	+	0.451597i
$413$		−	39.2392i		−	1.93083i
$414$		0			0
$415$		0			0
$416$	3.99069	+	38.0908i	0.195660	+	1.86756i
$417$		0			0
$418$	1.34154	−	4.44231i	0.0656167	−	0.217281i
$419$			12.0019i			0.586333i	0.956061	+	0.293166i	$0.0947090\pi$
$419$			12.0019i			0.586333i	−0.956061	+	0.293166i	$0.905291\pi$
$420$		0			0
$421$			35.6189i			1.73596i	0.496601	+	0.867979i	$0.334581\pi$
$421$			35.6189i			1.73596i	−0.496601	+	0.867979i	$0.665419\pi$
$422$	−10.4284	−	3.14927i	−0.507646	−	0.153304i
$423$		0			0
$424$	−2.67737	+	2.21401i	−0.130024	+	0.107522i
$425$		0			0
$426$		0			0
$427$		−	36.1179i		−	1.74787i
$428$	−25.2385	−	16.7733i	−1.21995	−	0.810767i
$429$		0			0
$430$		0			0
$431$	−6.57864			−0.316882			−0.158441	−	0.987368i	$-0.550647\pi$
$431$	−6.57864			−0.316882			−0.158441	+	0.987368i	$0.550647\pi$
$432$		0			0
$433$		−	8.76970i		−	0.421445i	−0.977546	−	0.210722i	$-0.932418\pi$
$433$		−	8.76970i		−	0.421445i	0.977546	−	0.210722i	$-0.0675816\pi$
$434$	3.84369	−	12.7279i	0.184503	−	0.610957i
$435$		0			0
$436$	10.6924	−	16.0887i	0.512073	−	0.770509i
$437$			7.81173i			0.373686i
$438$		0			0
$439$			23.4120i			1.11739i	0.829372	+	0.558696i	$0.188698\pi$
$439$			23.4120i			1.11739i	−0.829372	+	0.558696i	$0.811302\pi$
$440$		0			0
$441$		0			0
$442$	−63.2639	−	19.1051i	−3.00916	−	0.908737i
$443$	39.6702			1.88479			0.942393	−	0.334507i	$-0.108570\pi$
$443$	39.6702			1.88479			0.942393	+	0.334507i	$0.108570\pi$
$444$		0			0
$445$		0			0
$446$	−19.9911	−	6.03712i	−0.946605	−	0.285866i
$447$		0			0
$448$	−5.10750	+	26.7165i	−0.241307	+	1.26223i
$449$			31.6995i			1.49599i	0.663702	+	0.747997i	$0.268984\pi$
$449$			31.6995i			1.49599i	−0.663702	+	0.747997i	$0.731016\pi$
$450$		0			0
$451$	2.42372			0.114129
$452$	−7.05663	−	4.68977i	−0.331916	−	0.220588i
$453$		0			0
$454$	23.0566	+	6.96287i	1.08210	+	0.326784i
$455$		0			0
$456$		0			0
$457$			21.6467i			1.01259i	0.862360	+	0.506296i	$0.168986\pi$
$457$			21.6467i			1.01259i	−0.862360	+	0.506296i	$0.831014\pi$
$458$	2.58920	−	8.57377i	0.120985	−	0.400626i
$459$		0			0
$460$		0			0
$461$	28.2684			1.31659			0.658294	−	0.752761i	$-0.271278\pi$
$461$	28.2684			1.31659			0.658294	+	0.752761i	$0.271278\pi$
$462$		0			0
$463$	−1.99390			−0.0926644			−0.0463322	−	0.998926i	$-0.514753\pi$
$463$	−1.99390			−0.0926644			−0.0463322	+	0.998926i	$0.514753\pi$
$464$	3.22882	+	7.68679i	0.149894	+	0.356850i
$465$		0			0
$466$	−9.53209	−	2.87860i	−0.441566	−	0.133349i
$467$	27.1759			1.25755			0.628775	−	0.777588i	$-0.283557\pi$
$467$	27.1759			1.25755			0.628775	+	0.777588i	$0.283557\pi$
$468$		0			0
$469$		−	36.7998i		−	1.69926i
$470$		0			0
$471$		0			0
$472$	25.1555	−	20.8020i	1.15788	−	0.957490i
$473$	−7.88740			−0.362663
$474$		0			0
$475$		0			0
$476$	−39.0891	−	25.9782i	−1.79165	−	1.19071i
$477$		0			0
$478$	33.9656	+	10.2573i	1.55355	+	0.469158i
$479$	−25.6006			−1.16972			−0.584860	−	0.811134i	$-0.698851\pi$
$479$	−25.6006			−1.16972			−0.584860	+	0.811134i	$0.698851\pi$
$480$		0			0
$481$	−34.2784			−1.56296
$482$	−11.0905	−	3.34922i	−0.505157	−	0.152553i
$483$		0			0
$484$	10.3285	+	6.86421i	0.469476	+	0.312009i
$485$		0			0
$486$		0			0
$487$	0.889762			0.0403190			0.0201595	−	0.999797i	$-0.493583\pi$
$487$	0.889762			0.0403190			0.0201595	+	0.999797i	$0.493583\pi$
$488$	23.1545	−	19.1473i	1.04815	−	0.866757i
$489$		0			0
$490$		0			0
$491$		−	22.9051i		−	1.03369i	−0.856079	−	0.516845i	$-0.827106\pi$
$491$		−	22.9051i		−	1.03369i	0.856079	−	0.516845i	$-0.172894\pi$
$492$		0			0
$493$	−14.3862			−0.647923
$494$	−13.7289	−	4.14600i	−0.617693	−	0.186537i
$495$		0			0
$496$	10.1973	−	4.28334i	0.457871	−	0.192328i
$497$	9.73665			0.436748
$498$		0			0
$499$	−38.2427			−1.71198			−0.855990	−	0.516993i	$-0.827051\pi$
$499$	−38.2427			−1.71198			−0.855990	+	0.516993i	$0.827051\pi$
$500$		0			0
$501$		0			0
$502$	−0.958873	+	3.17518i	−0.0427966	+	0.141715i
$503$			18.7426i			0.835692i	0.908518	+	0.417846i	$0.137215\pi$
$503$			18.7426i			0.835692i	−0.908518	+	0.417846i	$0.862785\pi$
$504$		0			0
$505$		0			0
$506$	15.4683	+	4.67127i	0.687649	+	0.207663i
$507$		0			0
$508$	−23.5138	−	15.6271i	−1.04326	−	0.693338i
$509$	33.2746			1.47487			0.737435	−	0.675418i	$-0.236037\pi$
$509$	33.2746			1.47487			0.737435	+	0.675418i	$0.236037\pi$
$510$		0			0
$511$			43.3728i			1.91870i
$512$	−19.8351	+	10.8890i	−0.876595	+	0.481229i
$513$		0			0
$514$	−33.3511	−	10.0717i	−1.47105	−	0.444244i
$515$		0			0
$516$		0			0
$517$	−24.2526			−1.06663
$518$	−23.3051	−	7.03793i	−1.02397	−	0.309229i
$519$		0			0
$520$		0			0
$521$		−	20.6937i		−	0.906607i	−0.891356	−	0.453304i	$-0.850245\pi$
$521$		−	20.6937i		−	0.906607i	0.891356	−	0.453304i	$-0.149755\pi$
$522$		0			0
$523$		−	17.8501i		−	0.780529i	−0.920703	−	0.390265i	$-0.872384\pi$
$523$		−	17.8501i		−	0.780529i	0.920703	−	0.390265i	$-0.127616\pi$
$524$	7.38004	−	11.1046i	0.322399	−	0.485109i
$525$		0			0
$526$	8.63288	−	28.5866i	0.376411	−	1.24643i
$527$			19.0847i			0.831343i
$528$		0			0
$529$	−4.20070			−0.182639
$530$		0			0
$531$		0			0
$532$	−8.48274	−	5.63754i	−0.367773	−	0.244419i
$533$		−	7.49048i		−	0.324449i
$534$		0			0
$535$		0			0
$536$	23.5917	−	19.5088i	1.01901	−	0.842653i
$537$		0			0
$538$	10.5757	+	3.19377i	0.455952	+	0.137693i
$539$			9.99026i			0.430311i
$540$		0			0
$541$		−	44.0374i		−	1.89331i	−0.322243	−	0.946657i	$-0.604437\pi$
$541$		−	44.0374i		−	1.89331i	0.322243	−	0.946657i	$-0.395563\pi$
$542$	9.04654	−	29.9564i	0.388582	−	1.28674i
$543$		0			0
$544$	−4.06826	−	38.8312i	−0.174425	−	1.66488i
$545$		0			0
$546$		0			0
$547$			37.4193i			1.59994i	0.600043	+	0.799968i	$0.295150\pi$
$547$			37.4193i			1.59994i	−0.600043	+	0.799968i	$0.704850\pi$
$548$	−28.7931	−	19.1356i	−1.22998	−	0.817434i
$549$		0			0
$550$		0			0
$551$	−3.12196			−0.133000
$552$		0			0
$553$			38.8474i			1.65196i
$554$	−1.26487	−	0.381979i	−0.0537392	−	0.0162287i
$555$		0			0
$556$	−27.3423	−	18.1714i	−1.15957	−	0.770641i
$557$		−	16.7349i		−	0.709082i	−0.935040	−	0.354541i	$-0.884637\pi$
$557$		−	16.7349i		−	0.709082i	0.935040	−	0.354541i	$-0.115363\pi$
$558$		0			0
$559$			24.3759i			1.03099i
$560$		0			0
$561$		0			0
$562$	2.18690	−	7.24161i	0.0922487	−	0.305469i
$563$	−23.2171			−0.978482			−0.489241	−	0.872149i	$-0.662726\pi$
$563$	−23.2171			−0.978482			−0.489241	+	0.872149i	$0.662726\pi$
$564$		0			0
$565$		0			0
$566$	1.91737	−	6.34912i	0.0805932	−	0.266873i
$567$		0			0
$568$	5.16172	+	6.24199i	0.216581	+	0.261908i
$569$		−	31.3601i		−	1.31468i	−0.753592	−	0.657342i	$-0.771681\pi$
$569$		−	31.3601i		−	1.31468i	0.753592	−	0.657342i	$-0.228319\pi$
$570$		0			0
$571$	−17.1533			−0.717844			−0.358922	−	0.933368i	$-0.616856\pi$
$571$	−17.1533			−0.717844			−0.358922	+	0.933368i	$0.616856\pi$
$572$	−16.4193	+	24.7059i	−0.686525	+	1.03301i
$573$		0			0
$574$	1.53792	−	5.09261i	0.0641915	−	0.212561i
$575$		0			0
$576$		0			0
$577$			20.6555i			0.859900i	0.902853	+	0.429950i	$0.141469\pi$
$577$			20.6555i			0.859900i	−0.902853	+	0.429950i	$0.858531\pi$
$578$	41.4785	+	12.5261i	1.72528	+	0.521018i
$579$		0			0
$580$		0			0
$581$	29.6224			1.22895
$582$		0			0
$583$	−2.69091			−0.111446
$584$	−27.8055	+	22.9933i	−1.15060	+	0.951471i
$585$		0			0
$586$	−9.55068	+	31.6258i	−0.394535	+	1.30645i
$587$	29.5429			1.21936			0.609682	−	0.792646i	$-0.291297\pi$
$587$	29.5429			1.21936			0.609682	+	0.792646i	$0.291297\pi$
$588$		0			0
$589$			4.14158i			0.170651i
$590$		0			0
$591$		0			0
$592$	−7.84294	−	18.6715i	−0.322343	−	0.767395i
$593$	8.30386			0.340999			0.170499	−	0.985358i	$-0.445462\pi$
$593$	8.30386			0.340999			0.170499	+	0.985358i	$0.445462\pi$
$594$		0			0
$595$		0			0
$596$	−22.4273	−	14.9049i	−0.918656	−	0.610530i
$597$		0			0
$598$	14.4365	−	47.8046i	0.590353	−	1.95487i
$599$	44.6453			1.82416			0.912079	−	0.410014i	$-0.134476\pi$
$599$	44.6453			1.82416			0.912079	+	0.410014i	$0.134476\pi$
$600$		0			0
$601$	−1.76532			−0.0720089			−0.0360044	−	0.999352i	$-0.511463\pi$
$601$	−1.76532			−0.0720089			−0.0360044	+	0.999352i	$0.511463\pi$
$602$	−5.00477	+	16.5726i	−0.203979	+	0.675450i
$603$		0			0
$604$	11.2259	−	16.8915i	0.456777	−	0.687306i
$605$		0			0
$606$		0			0
$607$	29.2563			1.18747			0.593737	−	0.804659i	$-0.297652\pi$
$607$	29.2563			1.18747			0.593737	+	0.804659i	$0.297652\pi$
$608$	−0.882854	−	8.42678i	−0.0358045	−	0.341751i
$609$		0			0
$610$		0			0
$611$			74.9523i			3.03225i
$612$		0			0
$613$	−9.76069			−0.394230			−0.197115	−	0.980380i	$-0.563157\pi$
$613$	−9.76069			−0.394230			−0.197115	+	0.980380i	$0.563157\pi$
$614$	6.95480	−	23.0299i	0.280673	−	0.929410i
$615$		0			0
$616$	−16.2356	+	13.4258i	−0.654152	+	0.540942i
$617$	−7.65657			−0.308242			−0.154121	−	0.988052i	$-0.549255\pi$
$617$	−7.65657			−0.308242			−0.154121	+	0.988052i	$0.549255\pi$
$618$		0			0
$619$	2.30587			0.0926806			0.0463403	−	0.998926i	$-0.485244\pi$
$619$	2.30587			0.0926806			0.0463403	+	0.998926i	$0.485244\pi$
$620$		0			0
$621$		0			0
$622$	8.82754	+	2.66583i	0.353952	+	0.106890i
$623$			4.78732i			0.191800i
$624$		0			0
$625$		0			0
$626$	−0.227261	+	0.752542i	−0.00908316	+	0.0300776i
$627$		0			0
$628$	23.9909	+	15.9441i	0.957342	+	0.636240i
$629$	34.9447			1.39334
$630$		0			0
$631$		−	10.1408i		−	0.403700i	−0.979416	−	0.201850i	$-0.935305\pi$
$631$		−	10.1408i		−	0.403700i	0.979416	−	0.201850i	$-0.0646953\pi$
$632$	−24.9044	+	20.5943i	−0.990643	+	0.819198i
$633$		0			0
$634$	9.72376	−	32.1989i	0.386180	−	1.27878i
$635$		0			0
$636$		0			0
$637$	30.8748			1.22330
$638$	−1.86687	+	6.18190i	−0.0739103	+	0.244744i
$639$		0			0
$640$		0			0
$641$			34.5280i			1.36377i	0.731458	+	0.681886i	$0.238840\pi$
$641$			34.5280i			1.36377i	−0.731458	+	0.681886i	$0.761160\pi$
$642$		0			0
$643$			13.5530i			0.534477i	0.963630	+	0.267238i	$0.0861111\pi$
$643$			13.5530i			0.534477i	−0.963630	+	0.267238i	$0.913889\pi$
$644$	19.6301	−	29.5372i	0.773535	−	1.16393i
$645$		0			0
$646$	13.9958	+	4.22659i	0.550656	+	0.166293i
$647$			2.73596i			0.107562i	0.998553	+	0.0537808i	$0.0171272\pi$
$647$			2.73596i			0.107562i	−0.998553	+	0.0537808i	$0.982873\pi$
$648$		0			0
$649$	25.2828			0.992438
$650$		0			0
$651$		0			0
$652$	20.9414	−	31.5102i	0.820128	−	1.23404i
$653$			43.7055i			1.71033i	0.518359	+	0.855163i	$0.326543\pi$
$653$			43.7055i			1.71033i	−0.518359	+	0.855163i	$0.673457\pi$
$654$		0			0
$655$		0			0
$656$	4.08008	−	1.71383i	0.159300	−	0.0669138i
$657$		0			0
$658$	−15.3889	+	50.9584i	−0.599923	+	1.98656i
$659$			23.6812i			0.922488i	0.887273	+	0.461244i	$0.152597\pi$
$659$			23.6812i			0.922488i	−0.887273	+	0.461244i	$0.847403\pi$
$660$		0			0
$661$			12.1819i			0.473821i	0.971531	+	0.236911i	$0.0761348\pi$
$661$			12.1819i			0.473821i	−0.971531	+	0.236911i	$0.923865\pi$
$662$	9.51294	+	2.87282i	0.369731	+	0.111655i
$663$		0			0
$664$	15.7038	+	18.9904i	0.609427	+	0.736971i
$665$		0			0
$666$		0			0
$667$		−	10.8708i		−	0.420918i
$668$	7.78488	−	11.7138i	0.301206	−	0.453221i
$669$		0			0
$670$		0			0
$671$	23.2717			0.898393
$672$		0			0
$673$			3.43100i			0.132255i	0.997811	+	0.0661277i	$0.0210645\pi$
$673$			3.43100i			0.132255i	−0.997811	+	0.0661277i	$0.978936\pi$
$674$	−4.39595	+	14.5566i	−0.169326	+	0.560699i
$675$		0			0
$676$	54.6992	+	36.3526i	2.10382	+	1.39818i
$677$		−	10.4400i		−	0.401241i	−0.979669	−	0.200621i	$-0.935704\pi$
$677$		−	10.4400i		−	0.401241i	0.979669	−	0.200621i	$-0.0642958\pi$
$678$		0			0
$679$			27.8529i			1.06890i
$680$		0			0
$681$		0			0
$682$	8.20089	+	2.47659i	0.314028	+	0.0948336i
$683$	−29.1488			−1.11535			−0.557673	−	0.830061i	$-0.688306\pi$
$683$	−29.1488			−1.11535			−0.557673	+	0.830061i	$0.688306\pi$
$684$		0			0
$685$		0			0
$686$	−11.2304	−	3.39146i	−0.428777	−	0.129487i
$687$		0			0
$688$	−13.2776	+	5.57723i	−0.506204	+	0.212630i
$689$			8.31624i			0.316824i
$690$		0			0
$691$	14.6200			0.556173			0.278086	−	0.960556i	$-0.410300\pi$
$691$	14.6200			0.556173			0.278086	+	0.960556i	$0.410300\pi$
$692$	4.71768	−	7.09863i	0.179339	−	0.269850i
$693$		0			0
$694$	−7.35093	−	2.21991i	−0.279038	−	0.0842667i
$695$		0			0
$696$		0			0
$697$			7.63608i			0.289237i
$698$	−4.16415	+	13.7890i	−0.157616	+	0.521922i
$699$		0			0
$700$		0			0
$701$	−34.4008			−1.29930			−0.649651	−	0.760233i	$-0.725085\pi$
$701$	−34.4008			−1.29930			−0.649651	+	0.760233i	$0.725085\pi$
$702$		0			0
$703$	7.58337			0.286012
$704$	−17.2141	−	3.29089i	−0.648781	−	0.124030i
$705$		0			0
$706$	−4.48505	−	1.35444i	−0.168797	−	0.0509751i
$707$	36.8736			1.38678
$708$		0			0
$709$		−	10.9880i		−	0.412664i	−0.978482	−	0.206332i	$-0.933847\pi$
$709$		−	10.9880i		−	0.412664i	0.978482	−	0.206332i	$-0.0661527\pi$
$710$		0			0
$711$		0			0
$712$	−3.06907	+	2.53792i	−0.115018	+	0.0951126i
$713$	−14.4211			−0.540075
$714$		0			0
$715$		0			0
$716$	18.5031	−	27.8414i	0.691494	−	1.04048i
$717$		0			0
$718$	−23.6422	−	7.13972i	−0.882319	−	0.266452i
$719$	0.316476			0.0118025			0.00590127	−	0.999983i	$-0.498122\pi$
$719$	0.316476			0.0118025			0.00590127	+	0.999983i	$0.498122\pi$
$720$		0			0
$721$	28.1536			1.04849
$722$	−22.6855	−	6.85080i	−0.844266	−	0.254960i
$723$		0			0
$724$	−5.21893	+	7.85285i	−0.193960	+	0.291849i
$725$		0			0
$726$		0			0
$727$	25.7376			0.954556			0.477278	−	0.878752i	$-0.341623\pi$
$727$	25.7376			0.954556			0.477278	+	0.878752i	$0.341623\pi$
$728$	41.4924	+	50.1760i	1.53781	+	1.85965i
$729$		0			0
$730$		0			0
$731$		−	24.8497i		−	0.919100i
$732$		0			0
$733$	42.4319			1.56726			0.783628	−	0.621230i	$-0.213367\pi$
$733$	42.4319			1.56726			0.783628	+	0.621230i	$0.213367\pi$
$734$	−17.5728	−	5.30681i	−0.648623	−	0.195878i
$735$		0			0
$736$	29.3423	−	3.07413i	1.08157	−	0.113314i
$737$	23.7111			0.873409
$738$		0			0
$739$	−20.0000			−0.735712			−0.367856	−	0.929883i	$-0.619908\pi$
$739$	−20.0000			−0.735712			−0.367856	+	0.929883i	$0.619908\pi$
$740$		0			0
$741$		0			0
$742$	−1.70746	+	5.65402i	−0.0626829	+	0.207566i
$743$			8.63496i			0.316786i	0.987376	+	0.158393i	$0.0506313\pi$
$743$			8.63496i			0.316786i	−0.987376	+	0.158393i	$0.949369\pi$
$744$		0			0
$745$		0			0
$746$	1.51855	+	0.458589i	0.0555982	+	0.0167901i
$747$		0			0
$748$	16.7384	−	25.1861i	0.612018	−	0.920896i
$749$	−51.5172			−1.88240
$750$		0			0
$751$		−	22.3348i		−	0.815009i	−0.913203	−	0.407505i	$-0.866399\pi$
$751$		−	22.3348i		−	0.815009i	0.913203	−	0.407505i	$-0.133601\pi$
$752$	−40.8267	+	17.1492i	−1.48880	+	0.625365i
$753$		0			0
$754$	19.1051	+	5.76956i	0.695766	+	0.210115i
$755$		0			0
$756$		0			0
$757$	33.0197			1.20012			0.600060	−	0.799955i	$-0.295143\pi$
$757$	33.0197			1.20012			0.600060	+	0.799955i	$0.295143\pi$
$758$	−0.837062	−	0.252785i	−0.0304035	−	0.00918156i
$759$		0			0
$760$		0			0
$761$			35.1396i			1.27381i	0.770943	+	0.636905i	$0.219785\pi$
$761$			35.1396i			1.27381i	−0.770943	+	0.636905i	$0.780215\pi$
$762$		0			0
$763$		−	32.8404i		−	1.18890i
$764$	−19.1182	−	12.7058i	−0.691671	−	0.459678i
$765$		0			0
$766$	9.90066	−	32.7847i	0.357725	−	1.18456i
$767$		−	78.1363i		−	2.82134i
$768$		0			0
$769$	−19.6851			−0.709863			−0.354931	−	0.934892i	$-0.615496\pi$
$769$	−19.6851			−0.709863			−0.354931	+	0.934892i	$0.615496\pi$
$770$		0			0
$771$		0			0
$772$	−18.6927	+	28.1266i	−0.672764	+	1.01230i
$773$			29.6316i			1.06577i	0.846187	+	0.532887i	$0.178893\pi$
$773$			29.6316i			1.06577i	−0.846187	+	0.532887i	$0.821107\pi$
$774$		0			0
$775$		0			0
$776$	−17.8560	+	14.7657i	−0.640992	+	0.530059i
$777$		0			0
$778$	5.08292	+	1.53499i	0.182231	+	0.0550321i
$779$			1.65711i			0.0593720i
$780$		0			0
$781$			6.27357i			0.224486i
$782$	−14.7171	+	48.7338i	−0.526283	+	1.74272i
$783$		0			0
$784$	7.06418	+	16.8176i	0.252292	+	0.600627i
$785$		0			0
$786$		0			0
$787$			50.3229i			1.79382i	0.442214	+	0.896909i	$0.354193\pi$
$787$			50.3229i			1.79382i	−0.442214	+	0.896909i	$0.645807\pi$
$788$	−28.1774	+	42.3982i	−1.00378	+	1.51037i
$789$		0			0
$790$		0			0
$791$	−14.4041			−0.512150
$792$		0			0
$793$		−	71.9208i		−	2.55398i
$794$	−20.0111	−	6.04315i	−0.710166	−	0.214463i
$795$		0			0
$796$	24.1397	−	36.3227i	0.855610	−	1.28742i
$797$		−	24.6672i		−	0.873759i	−0.899520	−	0.436879i	$-0.856084\pi$
$797$		−	24.6672i		−	0.873759i	0.899520	−	0.436879i	$-0.143916\pi$
$798$		0			0
$799$		−	76.4092i		−	2.70316i
$800$		0			0
$801$		0			0
$802$	2.49539	−	8.26313i	0.0881152	−	0.291781i
$803$	−27.9462			−0.986200
$804$		0			0
$805$		0			0
$806$	7.65388	−	25.3448i	0.269596	−	0.892731i
$807$		0			0
$808$	19.5479	+	23.6390i	0.687694	+	0.831617i
$809$			36.3064i			1.27646i	0.769844	+	0.638232i	$0.220334\pi$
$809$			36.3064i			1.27646i	−0.769844	+	0.638232i	$0.779666\pi$
$810$		0			0
$811$	−13.4434			−0.472062			−0.236031	−	0.971746i	$-0.575847\pi$
$811$	−13.4434			−0.472062			−0.236031	+	0.971746i	$0.575847\pi$
$812$	11.8045	+	7.84518i	0.414258	+	0.275312i
$813$		0			0
$814$	4.53472	−	15.0161i	0.158942	−	0.526314i
$815$		0			0
$816$		0			0
$817$		−	5.39264i		−	0.188665i
$818$	−2.40179	−	0.725318i	−0.0839767	−	0.0253602i
$819$		0			0
$820$		0			0
$821$	−20.2429			−0.706482			−0.353241	−	0.935532i	$-0.614920\pi$
$821$	−20.2429			−0.706482			−0.353241	+	0.935532i	$0.614920\pi$
$822$		0			0
$823$	−13.9803			−0.487322			−0.243661	−	0.969861i	$-0.578348\pi$
$823$	−13.9803			−0.487322			−0.243661	+	0.969861i	$0.578348\pi$
$824$	14.9252	+	18.0487i	0.519942	+	0.628758i
$825$		0			0
$826$	16.0427	−	53.1231i	0.558196	−	1.84839i
$827$	−56.4232			−1.96203			−0.981014	−	0.193939i	$-0.937874\pi$
$827$	−56.4232			−1.96203			−0.981014	+	0.193939i	$0.937874\pi$
$828$		0			0
$829$			38.5666i			1.33947i	0.742599	+	0.669737i	$0.233593\pi$
$829$			38.5666i			1.33947i	−0.742599	+	0.669737i	$0.766407\pi$
$830$		0			0
$831$		0			0
$832$	−10.1705	+	53.2000i	−0.352597	+	1.84438i
$833$	−31.4749			−1.09054
$834$		0			0
$835$		0			0
$836$	3.63241	−	5.46565i	0.125630	−	0.189033i
$837$		0			0
$838$	−4.90691	+	16.2485i	−0.169506	+	0.561297i
$839$	16.3765			0.565381			0.282691	−	0.959211i	$-0.408773\pi$
$839$	16.3765			0.565381			0.282691	+	0.959211i	$0.408773\pi$
$840$		0			0
$841$	−24.6555			−0.850190
$842$	−14.5625	+	48.2218i	−0.501858	+	1.66183i
$843$		0			0
$844$	−12.8307	−	8.52714i	−0.441650	−	0.293516i
$845$		0			0
$846$		0			0
$847$	21.0826			0.724407
$848$	−4.52987	+	1.90276i	−0.155556	+	0.0653412i
$849$		0			0
$850$		0			0
$851$			26.4055i			0.905170i
$852$		0			0
$853$	12.8864			0.441222			0.220611	−	0.975362i	$-0.429195\pi$
$853$	12.8864			0.441222			0.220611	+	0.975362i	$0.429195\pi$
$854$	14.7665	−	48.8973i	0.505300	−	1.67323i
$855$		0			0
$856$	−27.3110	−	33.0267i	−0.933470	−	1.12883i
$857$	30.3039			1.03516			0.517581	−	0.855634i	$-0.326833\pi$
$857$	30.3039			1.03516			0.517581	+	0.855634i	$0.326833\pi$
$858$		0			0
$859$	16.1565			0.551252			0.275626	−	0.961265i	$-0.411115\pi$
$859$	16.1565			0.551252			0.275626	+	0.961265i	$0.411115\pi$
$860$		0			0
$861$		0			0
$862$	−8.90634	−	2.68963i	−0.303351	−	0.0916092i
$863$		−	5.53190i		−	0.188308i	−0.995558	−	0.0941541i	$-0.969985\pi$
$863$		−	5.53190i		−	0.188308i	0.995558	−	0.0941541i	$-0.0300146\pi$
$864$		0			0
$865$		0			0
$866$	3.58543	−	11.8727i	0.121838	−	0.403449i
$867$		0			0
$868$	10.4074	−	15.6599i	0.353250	−	0.531530i
$869$	−25.0304			−0.849098
$870$		0			0
$871$		−	73.2789i		−	2.48296i
$872$	21.0534	−	17.4098i	0.712958	−	0.589571i
$873$		0			0
$874$	−3.19377	+	10.5757i	−0.108031	+	0.357729i
$875$		0			0
$876$		0			0
$877$	7.26715			0.245394			0.122697	−	0.992444i	$-0.460846\pi$
$877$	7.26715			0.245394			0.122697	+	0.992444i	$0.460846\pi$
$878$	−9.57182	+	31.6958i	−0.323033	+	1.06968i
$879$		0			0
$880$		0			0
$881$		−	8.51685i		−	0.286940i	−0.989655	−	0.143470i	$-0.954174\pi$
$881$		−	8.51685i		−	0.286940i	0.989655	−	0.143470i	$-0.0458260\pi$
$882$		0			0
$883$			22.9799i			0.773334i	0.922219	+	0.386667i	$0.126374\pi$
$883$			22.9799i			0.773334i	−0.922219	+	0.386667i	$0.873626\pi$
$884$	−77.8374	−	51.7300i	−2.61795	−	1.73987i
$885$		0			0
$886$	53.7065	+	16.2189i	1.80431	+	0.544883i
$887$			33.4214i			1.12218i	0.827754	+	0.561091i	$0.189618\pi$
$887$			33.4214i			1.12218i	−0.827754	+	0.561091i	$0.810382\pi$
$888$		0			0
$889$	−47.9966			−1.60976
$890$		0			0
$891$		0			0
$892$	−24.5962	−	16.3464i	−0.823543	−	0.547319i
$893$		−	16.5816i		−	0.554881i
$894$		0			0
$895$		0			0
$896$	−17.8375	+	34.0813i	−0.595909	+	1.13858i
$897$		0			0
$898$	−12.9601	+	42.9157i	−0.432485	+	1.43212i
$899$		−	5.76340i		−	0.192220i
$900$		0			0
$901$		−	8.47789i		−	0.282439i
$902$	3.28130	+	0.990921i	0.109255	+	0.0329941i
$903$		0			0
$904$	−7.63608	−	9.23419i	−0.253972	−	0.307125i
$905$		0			0
$906$		0			0
$907$		−	10.6744i		−	0.354439i	−0.984171	−	0.177219i	$-0.943290\pi$
$907$		−	10.6744i		−	0.354439i	0.984171	−	0.177219i	$-0.0567102\pi$
$908$	28.3679	+	18.8531i	0.941423	+	0.625660i
$909$		0			0
$910$		0			0
$911$	44.9218			1.48833			0.744164	−	0.667997i	$-0.232848\pi$
$911$	44.9218			1.48833			0.744164	+	0.667997i	$0.232848\pi$
$912$		0			0
$913$			19.0865i			0.631671i
$914$	−8.85012	+	29.3059i	−0.292736	+	0.969355i
$915$		0			0
$916$	7.01065	−	10.5488i	0.231638	−	0.348543i
$917$		−	22.6669i		−	0.748528i
$918$		0			0
$919$			0.403164i			0.0132991i	0.999978	+	0.00664957i	$0.00211664\pi$
$919$			0.403164i			0.0132991i	−0.999978	+	0.00664957i	$0.997883\pi$
$920$		0			0
$921$		0			0
$922$	38.2705	+	11.5573i	1.26037	+	0.380620i
$923$	19.3884			0.638177
$924$		0			0
$925$		0			0
$926$	−2.69940	−	0.815192i	−0.0887077	−	0.0267889i
$927$		0			0
$928$	1.22858	+	11.7267i	0.0403300	+	0.384947i
$929$			1.25756i			0.0412591i	0.999787	+	0.0206296i	$0.00656706\pi$
$929$			1.25756i			0.0412591i	−0.999787	+	0.0206296i	$0.993433\pi$
$930$		0			0
$931$	−6.83038			−0.223857
$932$	−11.7279	−	7.79425i	−0.384160	−	0.255309i
$933$		0			0
$934$	36.7914	+	11.1107i	1.20385	+	0.363552i
$935$		0			0
$936$		0			0
$937$			50.6667i			1.65521i	0.561311	+	0.827605i	$0.310297\pi$
$937$			50.6667i			1.65521i	−0.561311	+	0.827605i	$0.689703\pi$
$938$	15.0454	−	49.8206i	0.491248	−	1.62670i
$939$		0			0
$940$		0			0
$941$	43.1707			1.40732			0.703662	−	0.710535i	$-0.251547\pi$
$941$	43.1707			1.40732			0.703662	+	0.710535i	$0.251547\pi$
$942$		0			0
$943$	−5.77011			−0.187901
$944$	42.5610	−	17.8777i	1.38524	−	0.581868i
$945$		0			0
$946$	−10.6782	−	3.22471i	−0.347177	−	0.104844i
$947$	27.5139			0.894083			0.447042	−	0.894513i	$-0.352478\pi$
$947$	27.5139			0.894083			0.447042	+	0.894513i	$0.352478\pi$
$948$		0			0
$949$			86.3674i			2.80360i
$950$		0			0
$951$		0			0
$952$	−42.2989	−	51.1513i	−1.37091	−	1.65782i
$953$	−3.27995			−0.106248			−0.0531240	−	0.998588i	$-0.516918\pi$
$953$	−3.27995			−0.106248			−0.0531240	+	0.998588i	$0.516918\pi$
$954$		0			0
$955$		0			0
$956$	41.7900	+	27.7732i	1.35158	+	0.898250i
$957$		0			0
$958$	−34.6587	−	10.4666i	−1.11977	−	0.338161i
$959$	−58.7729			−1.89788
$960$		0			0
$961$	23.3543			0.753364
$962$	−46.4071	−	14.0145i	−1.49622	−	0.451845i
$963$		0			0
$964$	−13.6453	−	9.06852i	−0.439485	−	0.292077i
$965$		0			0
$966$		0			0
$967$	−38.1123			−1.22561			−0.612804	−	0.790235i	$-0.709959\pi$
$967$	−38.1123			−1.22561			−0.612804	+	0.790235i	$0.709959\pi$
$968$	11.1766	+	13.5157i	0.359229	+	0.434410i
$969$		0			0
$970$		0			0
$971$		−	9.30893i		−	0.298738i	−0.988782	−	0.149369i	$-0.952276\pi$
$971$		−	9.30893i		−	0.298738i	0.988782	−	0.149369i	$-0.0477242\pi$
$972$		0			0
$973$	−55.8115			−1.78923
$974$	1.20458	+	0.363773i	0.0385974	+	0.0116560i
$975$		0			0
$976$	39.1754	−	16.4556i	1.25397	−	0.526729i
$977$	27.7469			0.887703			0.443851	−	0.896100i	$-0.353612\pi$
$977$	27.7469			0.887703			0.443851	+	0.896100i	$0.353612\pi$
$978$		0			0
$979$	−3.08460			−0.0985841
$980$		0			0
$981$		0			0
$982$	9.36457	−	31.0095i	0.298835	−	0.989552i
$983$			41.2907i			1.31697i	0.752594	+	0.658485i	$0.228802\pi$
$983$			41.2907i			1.31697i	−0.752594	+	0.658485i	$0.771198\pi$
$984$		0			0
$985$		0			0
$986$	−19.4764	−	5.88170i	−0.620256	−	0.187312i
$987$		0			0
$988$	−16.8915	−	11.2259i	−0.537391	−	0.357145i
$989$	18.7774			0.597086
$990$		0			0
$991$			1.65002i			0.0524148i	0.999657	+	0.0262074i	$0.00834302\pi$
$991$			1.65002i			0.0524148i	−0.999657	+	0.0262074i	$0.991657\pi$
$992$	15.5566	−	1.62983i	0.493921	−	0.0517470i
$993$		0			0
$994$	13.1817	+	3.98076i	0.418099	+	0.126262i
$995$		0			0
$996$		0			0
$997$	39.0762			1.23756			0.618778	−	0.785566i	$-0.287628\pi$
$997$	39.0762			1.23756			0.618778	+	0.785566i	$0.287628\pi$
$998$	−51.7740	−	15.6353i	−1.63888	−	0.494925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.m.f.899.32		32
3.2	odd	2	inner	1800.2.m.f.899.2		32
4.3	odd	2		7200.2.m.f.3599.8		32
5.2	odd	4		1800.2.b.i.251.8	yes	16
5.3	odd	4		1800.2.b.h.251.9	yes	16
5.4	even	2	inner	1800.2.m.f.899.1		32
8.3	odd	2	inner	1800.2.m.f.899.29		32
8.5	even	2		7200.2.m.f.3599.26		32
12.11	even	2		7200.2.m.f.3599.7		32
15.2	even	4		1800.2.b.i.251.9	yes	16
15.8	even	4		1800.2.b.h.251.8	yes	16
15.14	odd	2	inner	1800.2.m.f.899.31		32
20.3	even	4		7200.2.b.g.4751.13		16
20.7	even	4		7200.2.b.h.4751.3		16
20.19	odd	2		7200.2.m.f.3599.28		32
24.5	odd	2		7200.2.m.f.3599.25		32
24.11	even	2	inner	1800.2.m.f.899.3		32
40.3	even	4		1800.2.b.h.251.7	✓	16
40.13	odd	4		7200.2.b.g.4751.3		16
40.19	odd	2	inner	1800.2.m.f.899.4		32
40.27	even	4		1800.2.b.i.251.10	yes	16
40.29	even	2		7200.2.m.f.3599.6		32
40.37	odd	4		7200.2.b.h.4751.13		16
60.23	odd	4		7200.2.b.g.4751.14		16
60.47	odd	4		7200.2.b.h.4751.4		16
60.59	even	2		7200.2.m.f.3599.27		32
120.29	odd	2		7200.2.m.f.3599.5		32
120.53	even	4		7200.2.b.g.4751.4		16
120.59	even	2	inner	1800.2.m.f.899.30		32
120.77	even	4		7200.2.b.h.4751.14		16
120.83	odd	4		1800.2.b.h.251.10	yes	16
120.107	odd	4		1800.2.b.i.251.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1800.2.b.h.251.7	✓	16	40.3	even	4
1800.2.b.h.251.8	yes	16	15.8	even	4
1800.2.b.h.251.9	yes	16	5.3	odd	4
1800.2.b.h.251.10	yes	16	120.83	odd	4
1800.2.b.i.251.7	yes	16	120.107	odd	4
1800.2.b.i.251.8	yes	16	5.2	odd	4
1800.2.b.i.251.9	yes	16	15.2	even	4
1800.2.b.i.251.10	yes	16	40.27	even	4
1800.2.m.f.899.1		32	5.4	even	2	inner
1800.2.m.f.899.2		32	3.2	odd	2	inner
1800.2.m.f.899.3		32	24.11	even	2	inner
1800.2.m.f.899.4		32	40.19	odd	2	inner
1800.2.m.f.899.29		32	8.3	odd	2	inner
1800.2.m.f.899.30		32	120.59	even	2	inner
1800.2.m.f.899.31		32	15.14	odd	2	inner
1800.2.m.f.899.32		32	1.1	even	1	trivial
7200.2.b.g.4751.3		16	40.13	odd	4
7200.2.b.g.4751.4		16	120.53	even	4
7200.2.b.g.4751.13		16	20.3	even	4
7200.2.b.g.4751.14		16	60.23	odd	4
7200.2.b.h.4751.3		16	20.7	even	4
7200.2.b.h.4751.4		16	60.47	odd	4
7200.2.b.h.4751.13		16	40.37	odd	4
7200.2.b.h.4751.14		16	120.77	even	4
7200.2.m.f.3599.5		32	120.29	odd	2
7200.2.m.f.3599.6		32	40.29	even	2
7200.2.m.f.3599.7		32	12.11	even	2
7200.2.m.f.3599.8		32	4.3	odd	2
7200.2.m.f.3599.25		32	24.5	odd	2
7200.2.m.f.3599.26		32	8.5	even	2
7200.2.m.f.3599.27		32	60.59	even	2
7200.2.m.f.3599.28		32	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1800.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.35383 + 0.408843i) q^{2} +(1.66570 + 1.10700i) q^{4} +3.40004 q^{7} +(1.80247 + 2.17970i) q^{8} +O(q^{10})\)	\(q+(1.35383 + 0.408843i) q^{2} +(1.66570 + 1.10700i) q^{4} +3.40004 q^{7} +(1.80247 + 2.17970i) q^{8} +2.19073i q^{11} +6.77043 q^{13} +(4.60306 + 1.39008i) q^{14} +(1.54908 + 3.68787i) q^{16} -6.90203 q^{17} -1.49781 q^{19} +(-0.895664 + 2.96587i) q^{22} -5.21543i q^{23} +(9.16599 + 2.76804i) q^{26} +(5.66342 + 3.76386i) q^{28} +2.08435 q^{29} -2.76509i q^{31} +(0.589430 + 5.62606i) q^{32} +(-9.34415 - 2.82184i) q^{34} -5.06297 q^{37} +(-2.02778 - 0.612369i) q^{38} -1.10635i q^{41} +3.60035i q^{43} +(-2.42515 + 3.64909i) q^{44} +(2.13229 - 7.06079i) q^{46} +11.0705i q^{47} +4.56024 q^{49} +(11.2775 + 7.49490i) q^{52} +1.22832i q^{53} +(6.12847 + 7.41106i) q^{56} +(2.82184 + 0.852170i) q^{58} -11.5408i q^{59} -10.6228i q^{61} +(1.13049 - 3.74345i) q^{62} +(-1.50219 + 7.85770i) q^{64} -10.8234i q^{67} +(-11.4967 - 7.64058i) q^{68} +2.86369 q^{71} +12.7566i q^{73} +(-6.85438 - 2.06996i) q^{74} +(-2.49490 - 1.65808i) q^{76} +7.44856i q^{77} +11.4256i q^{79} +(0.452325 - 1.49781i) q^{82} +8.71239 q^{83} +(-1.47198 + 4.87425i) q^{86} +(-4.77514 + 3.94873i) q^{88} +1.40802i q^{89} +23.0197 q^{91} +(5.77351 - 8.68731i) q^{92} +(-4.52611 + 14.9876i) q^{94} +8.19194i q^{97} +(6.17378 + 1.86442i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 32 * q + 8 * q^4	\( 32 q + 8 q^{4} - 16 q^{16} - 32 q^{19} - 24 q^{34} + 40 q^{46} + 64 q^{49} - 64 q^{64} + 72 q^{76} + 96 q^{91} + 40 q^{94}+O(q^{100}) \) 32 * q + 8 * q^4 - 16 * q^16 - 32 * q^19 - 24 * q^34 + 40 * q^46 + 64 * q^49 - 64 * q^64 + 72 * q^76 + 96 * q^91 + 40 * q^94

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