LMFDB - Embedded newform 1800.2.m.f.899.3

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			899.3
Character	$\chi$	$=$	1800.899
Dual form			1800.2.m.f.899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35383 + 0.408843i) q^{2} +(1.66570 - 1.10700i) q^{4} -3.40004 q^{7} +(-1.80247 + 2.17970i) q^{8} +O(q^{10})$	\(q+(-1.35383 + 0.408843i) q^{2} +(1.66570 - 1.10700i) q^{4} -3.40004 q^{7} +(-1.80247 + 2.17970i) q^{8} -2.19073i q^{11} -6.77043 q^{13} +(4.60306 - 1.39008i) q^{14} +(1.54908 - 3.68787i) q^{16} +6.90203 q^{17} -1.49781 q^{19} +(0.895664 + 2.96587i) q^{22} -5.21543i q^{23} +(9.16599 - 2.76804i) q^{26} +(-5.66342 + 3.76386i) q^{28} +2.08435 q^{29} +2.76509i q^{31} +(-0.589430 + 5.62606i) q^{32} +(-9.34415 + 2.82184i) q^{34} +5.06297 q^{37} +(2.02778 - 0.612369i) q^{38} +1.10635i q^{41} +3.60035i q^{43} +(-2.42515 - 3.64909i) q^{44} +(2.13229 + 7.06079i) q^{46} +11.0705i q^{47} +4.56024 q^{49} +(-11.2775 + 7.49490i) q^{52} +1.22832i q^{53} +(6.12847 - 7.41106i) q^{56} +(-2.82184 + 0.852170i) q^{58} +11.5408i q^{59} +10.6228i q^{61} +(-1.13049 - 3.74345i) q^{62} +(-1.50219 - 7.85770i) q^{64} -10.8234i q^{67} +(11.4967 - 7.64058i) q^{68} +2.86369 q^{71} +12.7566i q^{73} +(-6.85438 + 2.06996i) q^{74} +(-2.49490 + 1.65808i) q^{76} +7.44856i q^{77} -11.4256i q^{79} +(-0.452325 - 1.49781i) q^{82} -8.71239 q^{83} +(-1.47198 - 4.87425i) q^{86} +(4.77514 + 3.94873i) q^{88} -1.40802i q^{89} +23.0197 q^{91} +(-5.77351 - 8.68731i) q^{92} +(-4.52611 - 14.9876i) q^{94} +8.19194i q^{97} +(-6.17378 + 1.86442i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.722122\pi$
$7$	−3.40004			−1.28509			−0.642546	+	0.766247i	$0.722122\pi$
$8$	−1.80247	+	2.17970i	−0.637270	+	0.770641i
$9$		0			0
$10$		0			0
$11$		−	2.19073i		−	0.660530i	−0.943888	−	0.330265i	$-0.892862\pi$
$11$		−	2.19073i		−	0.660530i	0.943888	−	0.330265i	$-0.107138\pi$
$12$		0			0
$13$	−6.77043			−1.87778			−0.938889	−	0.344219i	$-0.888144\pi$
$13$	−6.77043			−1.87778			−0.938889	+	0.344219i	$0.888144\pi$
$14$	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	$-0.184311\pi$
$17$	6.90203			1.67399			0.836994	+	0.547212i	$0.184311\pi$
$18$		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	$0.0798759\pi$
$31$			2.76509i			0.496625i	−0.968680	+	0.248312i	$0.920124\pi$
$32$	−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	$-0.363371\pi$
$37$	5.06297			0.832347			0.416173	+	0.909285i	$0.363371\pi$
$38$	2.02778	−	0.612369i	0.328949	−	0.0993394i
$39$		0			0
$40$		0			0
$41$			1.10635i			0.172783i	0.996261	+	0.0863917i	$0.0275336\pi$
$41$			1.10635i			0.172783i	−0.996261	+	0.0863917i	$0.972466\pi$
$42$		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	$0.270546\pi$
$59$			11.5408i			1.50249i	−0.660025	+	0.751243i	$0.729454\pi$
$60$		0			0
$61$			10.6228i			1.36011i	0.733162	+	0.680054i	$0.238044\pi$
$61$			10.6228i			1.36011i	−0.733162	+	0.680054i	$0.761956\pi$
$62$	−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	$-0.777797\pi$
$79$		−	11.4256i		−	1.28548i	0.766084	−	0.642740i	$-0.222203\pi$
$80$		0			0
$81$		0			0
$82$	−0.452325	−	1.49781i	−0.0499509	−	0.165406i
$83$	−8.71239			−0.956309			−0.478155	−	0.878276i	$-0.658694\pi$
$83$	−8.71239			−0.956309			−0.478155	+	0.878276i	$0.658694\pi$
$84$		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	$-0.976224\pi$
$89$		−	1.40802i		−	0.149250i	0.997212	−	0.0746250i	$-0.0237760\pi$
$90$		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	$-0.633754\pi$
$103$	−8.28038			−0.815890			−0.407945	+	0.913006i	$0.633754\pi$
$104$	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	$-0.238401\pi$
$107$	15.1520			1.46479			0.732397	+	0.680877i	$0.238401\pi$
$108$		0			0
$109$			9.65885i			0.925150i	0.886580	+	0.462575i	$0.153074\pi$
$109$			9.65885i			0.925150i	−0.886580	+	0.462575i	$0.846926\pi$
$110$		0			0
$111$		0			0
$112$	−5.26693	+	12.5389i	−0.497678	+	1.18481i
$113$	4.23645			0.398532			0.199266	−	0.979945i	$-0.436144\pi$
$113$	4.23645			0.398532			0.199266	+	0.979945i	$0.436144\pi$
$114$		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	$-0.284561\pi$
$127$	14.1165			1.25264			0.626319	+	0.779567i	$0.284561\pi$
$128$	5.24627	+	10.0238i	0.463709	+	0.885988i
$129$		0			0
$130$		0			0
$131$			6.66667i			0.582470i	0.956652	+	0.291235i	$0.0940662\pi$
$131$			6.66667i			0.582470i	−0.956652	+	0.291235i	$0.905934\pi$
$132$		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	$-0.235572\pi$
$137$	17.2860			1.47684			0.738420	+	0.674341i	$0.235572\pi$
$138$		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	$0.135388\pi$
$151$			10.1408i			0.825248i	−0.910901	+	0.412624i	$0.864612\pi$
$152$	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	$-0.694897\pi$
$157$	−14.4030			−1.14948			−0.574740	+	0.818336i	$0.694897\pi$
$158$	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	$0.214760\pi$
$179$			16.7146i			1.24931i	−0.780902	+	0.624653i	$0.785240\pi$
$180$		0			0
$181$		−	4.71446i		−	0.350423i	−0.984531	−	0.175211i	$-0.943939\pi$
$181$		−	4.71446i		−	0.350423i	0.984531	−	0.175211i	$-0.0560609\pi$
$182$	−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	$0.281197\pi$
$199$			21.8063i			1.54581i	−0.634521	+	0.772905i	$0.718803\pi$
$200$		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	$-0.335383\pi$
$223$	14.7663			0.988828			0.494414	+	0.869227i	$0.335383\pi$
$224$	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	$-0.691194\pi$
$227$	−17.0307			−1.13037			−0.565183	+	0.824965i	$0.691194\pi$
$228$		0			0
$229$			6.33299i			0.418496i	0.977863	+	0.209248i	$0.0671015\pi$
$229$			6.33299i			0.418496i	−0.977863	+	0.209248i	$0.932898\pi$
$230$		0			0
$231$		0			0
$232$	−3.75698	+	4.54325i	−0.246658	+	0.298279i
$233$	7.04085			0.461261			0.230631	−	0.973041i	$-0.425921\pi$
$233$	7.04085			0.461261			0.230631	+	0.973041i	$0.425921\pi$
$234$		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	$-0.976418\pi$
$251$		−	2.34533i		−	0.148036i	0.997257	−	0.0740181i	$-0.0235823\pi$
$252$		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	$-0.221086\pi$
$257$	24.6347			1.53667			0.768334	+	0.640049i	$0.221086\pi$
$258$		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	$0.234593\pi$
$271$			22.1272i			1.34413i	−0.740492	+	0.672066i	$0.765407\pi$
$272$	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	$-0.491064\pi$
$277$	0.934293			0.0561362			0.0280681	+	0.999606i	$0.491064\pi$
$278$	22.2230	−	6.71114i	1.33285	−	0.402507i
$279$		0			0
$280$		0			0
$281$			5.34899i			0.319094i	0.987190	+	0.159547i	$0.0510034\pi$
$281$			5.34899i			0.319094i	−0.987190	+	0.159547i	$0.948997\pi$
$282$		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	$-0.453443\pi$
$347$	5.42974			0.291484			0.145742	+	0.989323i	$0.453443\pi$
$348$		0			0
$349$		−	10.1852i		−	0.545202i	−0.962127	−	0.272601i	$-0.912116\pi$
$349$		−	10.1852i		−	0.545202i	0.962127	−	0.272601i	$-0.0878839\pi$
$350$		0			0
$351$		0			0
$352$	12.3252	+	1.29128i	0.656935	+	0.0688255i
$353$	3.31287			0.176326			0.0881631	−	0.996106i	$-0.471900\pi$
$353$	3.31287			0.176326			0.0881631	+	0.996106i	$0.471900\pi$
$354$		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	$-0.389987\pi$
$367$	12.9801			0.677555			0.338777	+	0.940867i	$0.389987\pi$
$368$	−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	$-0.509245\pi$
$373$	−1.12168			−0.0580782			−0.0290391	+	0.999578i	$0.509245\pi$
$374$	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	$-0.379042\pi$
$397$	14.7811			0.741842			0.370921	+	0.928664i	$0.379042\pi$
$398$	−8.91537	−	29.5220i	−0.446887	−	1.47981i
$399$		0			0
$400$		0			0
$401$			6.10353i			0.304796i	0.988319	+	0.152398i	$0.0486996\pi$
$401$			6.10353i			0.304796i	−0.988319	+	0.152398i	$0.951300\pi$
$402$		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	$-0.905291\pi$
$419$		−	12.0019i		−	0.586333i	0.956061	−	0.293166i	$-0.0947090\pi$
$420$		0			0
$421$		−	35.6189i		−	1.73596i	−0.496601	−	0.867979i	$-0.665419\pi$
$421$		−	35.6189i		−	1.73596i	0.496601	−	0.867979i	$-0.334581\pi$
$422$	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	$-0.811302\pi$
$439$		−	23.4120i		−	1.11739i	0.829372	−	0.558696i	$-0.188698\pi$
$440$		0			0
$441$		0			0
$442$	63.2639	−	19.1051i	3.00916	−	0.908737i
$443$	−39.6702			−1.88479			−0.942393	−	0.334507i	$-0.891430\pi$
$443$	−39.6702			−1.88479			−0.942393	+	0.334507i	$0.891430\pi$
$444$		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	$-0.731016\pi$
$449$		−	31.6995i		−	1.49599i	0.663702	−	0.747997i	$-0.268984\pi$
$450$		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	$-0.485247\pi$
$463$	1.99390			0.0926644			0.0463322	+	0.998926i	$0.485247\pi$
$464$	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	$-0.716443\pi$
$467$	−27.1759			−1.25755			−0.628775	+	0.777588i	$0.716443\pi$
$468$		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	$-0.506417\pi$
$487$	−0.889762			−0.0403190			−0.0201595	+	0.999797i	$0.506417\pi$
$488$	−23.1545	−	19.1473i	−1.04815	−	0.866757i
$489$		0			0
$490$		0			0
$491$			22.9051i			1.03369i	0.856079	+	0.516845i	$0.172894\pi$
$491$			22.9051i			1.03369i	−0.856079	+	0.516845i	$0.827106\pi$
$492$		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	$0.149755\pi$
$521$			20.6937i			0.906607i	−0.891356	+	0.453304i	$0.850245\pi$
$522$		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	$0.395563\pi$
$541$			44.0374i			1.89331i	−0.322243	+	0.946657i	$0.604437\pi$
$542$	−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	$-0.337274\pi$
$563$	23.2171			0.978482			0.489241	+	0.872149i	$0.337274\pi$
$564$		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	$0.228319\pi$
$569$			31.3601i			1.31468i	−0.753592	+	0.657342i	$0.771681\pi$
$570$		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	$-0.708703\pi$
$587$	−29.5429			−1.21936			−0.609682	+	0.792646i	$0.708703\pi$
$588$		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	$-0.554538\pi$
$593$	−8.30386			−0.340999			−0.170499	+	0.985358i	$0.554538\pi$
$594$		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	$-0.702348\pi$
$607$	−29.2563			−1.18747			−0.593737	+	0.804659i	$0.702348\pi$
$608$	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	$-0.436843\pi$
$613$	9.76069			0.394230			0.197115	+	0.980380i	$0.436843\pi$
$614$	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	$-0.450745\pi$
$617$	7.65657			0.308242			0.154121	+	0.988052i	$0.450745\pi$
$618$		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	$0.0646953\pi$
$631$			10.1408i			0.403700i	−0.979416	+	0.201850i	$0.935305\pi$
$632$	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	$-0.761160\pi$
$641$		−	34.5280i		−	1.36377i	0.731458	−	0.681886i	$-0.238840\pi$
$642$		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	$-0.847403\pi$
$659$		−	23.6812i		−	0.922488i	0.887273	−	0.461244i	$-0.152597\pi$
$660$		0			0
$661$		−	12.1819i		−	0.473821i	−0.971531	−	0.236911i	$-0.923865\pi$
$661$		−	12.1819i		−	0.473821i	0.971531	−	0.236911i	$-0.0761348\pi$
$662$	−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	$-0.311694\pi$
$683$	29.1488			1.11535			0.557673	+	0.830061i	$0.311694\pi$
$684$		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	$0.0661527\pi$
$709$			10.9880i			0.412664i	−0.978482	+	0.206332i	$0.933847\pi$
$710$		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	$-0.658377\pi$
$727$	−25.7376			−0.954556			−0.477278	+	0.878752i	$0.658377\pi$
$728$	−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	$-0.786633\pi$
$733$	−42.4319			−1.56726			−0.783628	+	0.621230i	$0.786633\pi$
$734$	−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	$0.133601\pi$
$751$			22.3348i			0.815009i	−0.913203	+	0.407505i	$0.866399\pi$
$752$	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	$-0.704857\pi$
$757$	−33.0197			−1.20012			−0.600060	+	0.799955i	$0.704857\pi$
$758$	0.837062	−	0.252785i	0.0304035	−	0.00918156i
$759$		0			0
$760$		0			0
$761$		−	35.1396i		−	1.27381i	−0.770943	−	0.636905i	$-0.780215\pi$
$761$		−	35.1396i		−	1.27381i	0.770943	−	0.636905i	$-0.219785\pi$
$762$		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	$-0.779666\pi$
$809$		−	36.3064i		−	1.27646i	0.769844	−	0.638232i	$-0.220334\pi$
$810$		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	$-0.421652\pi$
$823$	13.9803			0.487322			0.243661	+	0.969861i	$0.421652\pi$
$824$	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	$-0.0621262\pi$
$827$	56.4232			1.96203			0.981014	+	0.193939i	$0.0621262\pi$
$828$		0			0
$829$		−	38.5666i		−	1.33947i	−0.742599	−	0.669737i	$-0.766407\pi$
$829$		−	38.5666i		−	1.33947i	0.742599	−	0.669737i	$-0.233593\pi$
$830$		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	$-0.570805\pi$
$853$	−12.8864			−0.441222			−0.220611	+	0.975362i	$0.570805\pi$
$854$	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	$-0.673167\pi$
$857$	−30.3039			−1.03516			−0.517581	+	0.855634i	$0.673167\pi$
$858$		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	$-0.539154\pi$
$877$	−7.26715			−0.245394			−0.122697	+	0.992444i	$0.539154\pi$
$878$	9.57182	+	31.6958i	0.323033	+	1.06968i
$879$		0			0
$880$		0			0
$881$			8.51685i			0.286940i	0.989655	+	0.143470i	$0.0458260\pi$
$881$			8.51685i			0.286940i	−0.989655	+	0.143470i	$0.954174\pi$
$882$		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	$-0.997883\pi$
$919$		−	0.403164i		−	0.0132991i	0.999978	−	0.00664957i	$-0.00211664\pi$
$920$		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	$-0.993433\pi$
$929$		−	1.25756i		−	0.0412591i	0.999787	−	0.0206296i	$-0.00656706\pi$
$930$		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	$-0.647522\pi$
$947$	−27.5139			−0.894083			−0.447042	+	0.894513i	$0.647522\pi$
$948$		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	$-0.483082\pi$
$953$	3.27995			0.106248			0.0531240	+	0.998588i	$0.483082\pi$
$954$		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	$-0.290041\pi$
$967$	38.1123			1.22561			0.612804	+	0.790235i	$0.290041\pi$
$968$	−11.1766	+	13.5157i	−0.359229	+	0.434410i
$969$		0			0
$970$		0			0
$971$			9.30893i			0.298738i	0.988782	+	0.149369i	$0.0477242\pi$
$971$			9.30893i			0.298738i	−0.988782	+	0.149369i	$0.952276\pi$
$972$		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	$-0.646388\pi$
$977$	−27.7469			−0.887703			−0.443851	+	0.896100i	$0.646388\pi$
$978$		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	$-0.991657\pi$
$991$		−	1.65002i		−	0.0524148i	0.999657	−	0.0262074i	$-0.00834302\pi$
$992$	−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	$-0.712372\pi$
$997$	−39.0762			−1.23756			−0.618778	+	0.785566i	$0.712372\pi$
$998$	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.899.3		32
3.2	odd	2	inner	1800.2.m.f.899.29		32
4.3	odd	2		7200.2.m.f.3599.25		32
5.2	odd	4		1800.2.b.i.251.7	yes	16
5.3	odd	4		1800.2.b.h.251.10	yes	16
5.4	even	2	inner	1800.2.m.f.899.30		32
8.3	odd	2	inner	1800.2.m.f.899.2		32
8.5	even	2		7200.2.m.f.3599.7		32
12.11	even	2		7200.2.m.f.3599.26		32
15.2	even	4		1800.2.b.i.251.10	yes	16
15.8	even	4		1800.2.b.h.251.7	✓	16
15.14	odd	2	inner	1800.2.m.f.899.4		32
20.3	even	4		7200.2.b.g.4751.4		16
20.7	even	4		7200.2.b.h.4751.14		16
20.19	odd	2		7200.2.m.f.3599.5		32
24.5	odd	2		7200.2.m.f.3599.8		32
24.11	even	2	inner	1800.2.m.f.899.32		32
40.3	even	4		1800.2.b.h.251.8	yes	16
40.13	odd	4		7200.2.b.g.4751.14		16
40.19	odd	2	inner	1800.2.m.f.899.31		32
40.27	even	4		1800.2.b.i.251.9	yes	16
40.29	even	2		7200.2.m.f.3599.27		32
40.37	odd	4		7200.2.b.h.4751.4		16
60.23	odd	4		7200.2.b.g.4751.3		16
60.47	odd	4		7200.2.b.h.4751.13		16
60.59	even	2		7200.2.m.f.3599.6		32
120.29	odd	2		7200.2.m.f.3599.28		32
120.53	even	4		7200.2.b.g.4751.13		16
120.59	even	2	inner	1800.2.m.f.899.1		32
120.77	even	4		7200.2.b.h.4751.3		16
120.83	odd	4		1800.2.b.h.251.9	yes	16
120.107	odd	4		1800.2.b.i.251.8	yes	16

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