LMFDB - Embedded newform 1800.2.m.f.899.19

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			899.19
Character	$\chi$	$=$	1800.899
Dual form			1800.2.m.f.899.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.376495 + 1.36318i) q^{2} +(-1.71650 + 1.02646i) q^{4} -1.04148 q^{7} +(-2.04550 - 1.95344i) q^{8} +O(q^{10})$	\(q+(0.376495 + 1.36318i) q^{2} +(-1.71650 + 1.02646i) q^{4} -1.04148 q^{7} +(-2.04550 - 1.95344i) q^{8} +2.67678i q^{11} +0.761250 q^{13} +(-0.392112 - 1.41972i) q^{14} +(1.89277 - 3.52384i) q^{16} -2.17822 q^{17} -3.36812 q^{19} +(-3.64893 + 1.00779i) q^{22} -4.98346i q^{23} +(0.286607 + 1.03772i) q^{26} +(1.78771 - 1.06904i) q^{28} -7.88672 q^{29} -4.48369i q^{31} +(5.51623 + 1.25348i) q^{32} +(-0.820090 - 2.96931i) q^{34} +0.663622 q^{37} +(-1.26808 - 4.59134i) q^{38} +8.94600i q^{41} -2.41742i q^{43} +(-2.74760 - 4.59471i) q^{44} +(6.79333 - 1.87624i) q^{46} -7.27940i q^{47} -5.91532 q^{49} +(-1.30669 + 0.781391i) q^{52} -1.00363i q^{53} +(2.13035 + 2.03448i) q^{56} +(-2.96931 - 10.7510i) q^{58} +4.94677i q^{59} -12.4752i q^{61} +(6.11206 - 1.68808i) q^{62} +(0.368120 + 7.99153i) q^{64} -14.3639i q^{67} +(3.73893 - 2.23585i) q^{68} -4.44908 q^{71} -3.65577i q^{73} +(0.249850 + 0.904635i) q^{74} +(5.78139 - 3.45723i) q^{76} -2.78782i q^{77} -13.3396i q^{79} +(-12.1950 + 3.36812i) q^{82} +7.77520 q^{83} +(3.29537 - 0.910146i) q^{86} +(5.22894 - 5.47535i) q^{88} +6.69806i q^{89} -0.792829 q^{91} +(5.11531 + 8.55412i) q^{92} +(9.92311 - 2.74065i) q^{94} -13.3073i q^{97} +(-2.22708 - 8.06362i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.376495	+	1.36318i	0.266222	+	0.963912i
$2$	0.376495	+	1.36318i	0.266222	+	0.963912i
$3$		0			0
$3$		0			0
$4$	−1.71650	+	1.02646i	−0.858252	+	0.513229i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.04148			−0.393643			−0.196822	−	0.980439i	$-0.563062\pi$
$7$	−1.04148			−0.393643			−0.196822	+	0.980439i	$0.563062\pi$
$8$	−2.04550	−	1.95344i	−0.723193	−	0.690646i
$9$		0			0
$10$		0			0
$11$			2.67678i			0.807080i	0.914962	+	0.403540i	$0.132220\pi$
$11$			2.67678i			0.807080i	−0.914962	+	0.403540i	$0.867780\pi$
$12$		0			0
$13$	0.761250			0.211133			0.105566	−	0.994412i	$-0.466334\pi$
$13$	0.761250			0.211133			0.105566	+	0.994412i	$0.466334\pi$
$14$	−0.392112	−	1.41972i	−0.104796	−	0.379437i
$15$		0			0
$16$	1.89277	−	3.52384i	0.473193	−	0.880959i
$17$	−2.17822			−0.528297			−0.264148	−	0.964482i	$-0.585091\pi$
$17$	−2.17822			−0.528297			−0.264148	+	0.964482i	$0.585091\pi$
$18$		0			0
$19$	−3.36812			−0.772700			−0.386350	−	0.922352i	$-0.626264\pi$
$19$	−3.36812			−0.772700			−0.386350	+	0.922352i	$0.626264\pi$
$20$		0			0
$21$		0			0
$22$	−3.64893	+	1.00779i	−0.777954	+	0.214862i
$23$		−	4.98346i		−	1.03912i	−0.854433	−	0.519561i	$-0.826095\pi$
$23$		−	4.98346i		−	1.03912i	0.854433	−	0.519561i	$-0.173905\pi$
$24$		0			0
$25$		0			0
$26$	0.286607	+	1.03772i	0.0562082	+	0.203513i
$27$		0			0
$28$	1.78771	−	1.06904i	0.337845	−	0.202029i
$29$	−7.88672			−1.46453			−0.732263	−	0.681022i	$-0.761536\pi$
$29$	−7.88672			−1.46453			−0.732263	+	0.681022i	$0.761536\pi$
$30$		0			0
$31$		−	4.48369i		−	0.805294i	−0.915355	−	0.402647i	$-0.868090\pi$
$31$		−	4.48369i		−	0.805294i	0.915355	−	0.402647i	$-0.131910\pi$
$32$	5.51623	+	1.25348i	0.975141	+	0.221585i
$33$		0			0
$34$	−0.820090	−	2.96931i	−0.140644	−	0.509232i
$35$		0			0
$36$		0			0
$37$	0.663622			0.109099			0.0545494	−	0.998511i	$-0.482628\pi$
$37$	0.663622			0.109099			0.0545494	+	0.998511i	$0.482628\pi$
$38$	−1.26808	−	4.59134i	−0.205710	−	0.744814i
$39$		0			0
$40$		0			0
$41$			8.94600i			1.39713i	0.715546	+	0.698565i	$0.246178\pi$
$41$			8.94600i			1.39713i	−0.715546	+	0.698565i	$0.753822\pi$
$42$		0			0
$43$		−	2.41742i		−	0.368653i	−0.982865	−	0.184327i	$-0.940990\pi$
$43$		−	2.41742i		−	0.368653i	0.982865	−	0.184327i	$-0.0590104\pi$
$44$	−2.74760	−	4.59471i	−0.414217	−	0.692678i
$45$		0			0
$46$	6.79333	−	1.87624i	1.00162	−	0.276637i
$47$		−	7.27940i		−	1.06181i	−0.847432	−	0.530905i	$-0.821852\pi$
$47$		−	7.27940i		−	1.06181i	0.847432	−	0.530905i	$-0.178148\pi$
$48$		0			0
$49$	−5.91532			−0.845045
$50$		0			0
$51$		0			0
$52$	−1.30669	+	0.781391i	−0.181205	+	0.108359i
$53$		−	1.00363i		−	0.137859i	−0.997622	−	0.0689293i	$-0.978042\pi$
$53$		−	1.00363i		−	0.137859i	0.997622	−	0.0689293i	$-0.0219583\pi$
$54$		0			0
$55$		0			0
$56$	2.13035	+	2.03448i	0.284680	+	0.271868i
$57$		0			0
$58$	−2.96931	−	10.7510i	−0.389889	−	1.41167i
$59$			4.94677i			0.644015i	0.946737	+	0.322007i	$0.104358\pi$
$59$			4.94677i			0.644015i	−0.946737	+	0.322007i	$0.895642\pi$
$60$		0			0
$61$		−	12.4752i		−	1.59729i	−0.601804	−	0.798644i	$-0.705551\pi$
$61$		−	12.4752i		−	1.59729i	0.601804	−	0.798644i	$-0.294449\pi$
$62$	6.11206	−	1.68808i	0.776233	−	0.214387i
$63$		0			0
$64$	0.368120	+	7.99153i	0.0460150	+	0.998941i
$65$		0			0
$66$		0			0
$67$		−	14.3639i		−	1.75483i	−0.479731	−	0.877415i	$-0.659266\pi$
$67$		−	14.3639i		−	1.75483i	0.479731	−	0.877415i	$-0.340734\pi$
$68$	3.73893	−	2.23585i	0.453412	−	0.271137i
$69$		0			0
$70$		0			0
$71$	−4.44908			−0.528009			−0.264004	−	0.964521i	$-0.585043\pi$
$71$	−4.44908			−0.528009			−0.264004	+	0.964521i	$0.585043\pi$
$72$		0			0
$73$		−	3.65577i		−	0.427875i	−0.976847	−	0.213938i	$-0.931371\pi$
$73$		−	3.65577i		−	0.427875i	0.976847	−	0.213938i	$-0.0686289\pi$
$74$	0.249850	+	0.904635i	0.0290445	+	0.105162i
$75$		0			0
$76$	5.78139	−	3.45723i	0.663171	−	0.396572i
$77$		−	2.78782i		−	0.317702i
$78$		0			0
$79$		−	13.3396i		−	1.50083i	−0.660970	−	0.750413i	$-0.729855\pi$
$79$		−	13.3396i		−	1.50083i	0.660970	−	0.750413i	$-0.270145\pi$
$80$		0			0
$81$		0			0
$82$	−12.1950	+	3.36812i	−1.34671	+	0.371947i
$83$	7.77520			0.853439			0.426719	−	0.904384i	$-0.359669\pi$
$83$	7.77520			0.853439			0.426719	+	0.904384i	$0.359669\pi$
$84$		0			0
$85$		0			0
$86$	3.29537	−	0.910146i	0.355349	−	0.0981435i
$87$		0			0
$88$	5.22894	−	5.47535i	0.557407	−	0.583674i
$89$			6.69806i			0.709992i	0.934868	+	0.354996i	$0.115518\pi$
$89$			6.69806i			0.709992i	−0.934868	+	0.354996i	$0.884482\pi$
$90$		0			0
$91$	−0.792829			−0.0831110
$92$	5.11531	+	8.55412i	0.533308	+	0.891829i
$93$		0			0
$94$	9.92311	−	2.74065i	1.02349	−	0.282677i
$95$		0			0
$96$		0			0
$97$		−	13.3073i		−	1.35115i	−0.737290	−	0.675577i	$-0.763895\pi$
$97$		−	13.3073i		−	1.35115i	0.737290	−	0.675577i	$-0.236105\pi$
$98$	−2.22708	−	8.06362i	−0.224969	−	0.814549i
$99$		0			0
$100$		0			0
$101$	3.94938			0.392978			0.196489	−	0.980506i	$-0.437046\pi$
$101$	3.94938			0.392978			0.196489	+	0.980506i	$0.437046\pi$
$102$		0			0
$103$	−17.3423			−1.70879			−0.854394	−	0.519626i	$-0.826071\pi$
$103$	−17.3423			−1.70879			−0.854394	+	0.519626i	$0.826071\pi$
$104$	−1.55714	−	1.48706i	−0.152690	−	0.145818i
$105$		0			0
$106$	1.36812	−	0.377860i	0.132884	−	0.0367010i
$107$	−6.13962			−0.593539			−0.296770	−	0.954949i	$-0.595909\pi$
$107$	−6.13962			−0.593539			−0.296770	+	0.954949i	$0.595909\pi$
$108$		0			0
$109$			17.6032i			1.68608i	0.537852	+	0.843039i	$0.319236\pi$
$109$			17.6032i			1.68608i	−0.537852	+	0.843039i	$0.680764\pi$
$110$		0			0
$111$		0			0
$112$	−1.97129	+	3.67001i	−0.186269	+	0.346784i
$113$	9.52648			0.896176			0.448088	−	0.893989i	$-0.352105\pi$
$113$	9.52648			0.896176			0.448088	+	0.893989i	$0.352105\pi$
$114$		0			0
$115$		0			0
$116$	13.5376	−	8.09538i	1.25693	−	0.751637i
$117$		0			0
$118$	−6.74332	+	1.86243i	−0.620773	+	0.171451i
$119$	2.26858			0.207961
$120$		0			0
$121$	3.83484			0.348622
$122$	17.0059	−	4.69685i	1.53964	−	0.425233i
$123$		0			0
$124$	4.60232	+	7.69627i	0.413300	+	0.691145i
$125$		0			0
$126$		0			0
$127$	−10.6531			−0.945313			−0.472657	−	0.881247i	$-0.656705\pi$
$127$	−10.6531			−0.945313			−0.472657	+	0.881247i	$0.656705\pi$
$128$	−10.7553	+	3.51058i	−0.950641	+	0.310294i
$129$		0			0
$130$		0			0
$131$			14.6249i			1.27778i	0.769297	+	0.638892i	$0.220607\pi$
$131$			14.6249i			1.27778i	−0.769297	+	0.638892i	$0.779393\pi$
$132$		0			0
$133$	3.50784			0.304168
$134$	19.5806	−	5.40793i	1.69150	−	0.467174i
$135$		0			0
$136$	4.45555	+	4.25504i	0.382060	+	0.364866i
$137$	−16.6613			−1.42347			−0.711736	−	0.702447i	$-0.752091\pi$
$137$	−16.6613			−1.42347			−0.711736	+	0.702447i	$0.752091\pi$
$138$		0			0
$139$	2.47401			0.209843			0.104921	−	0.994481i	$-0.466541\pi$
$139$	2.47401			0.209843			0.104921	+	0.994481i	$0.466541\pi$
$140$		0			0
$141$		0			0
$142$	−1.67506	−	6.06489i	−0.140568	−	0.508954i
$143$			2.03770i			0.170401i
$144$		0			0
$145$		0			0
$146$	4.98346	−	1.37638i	0.412434	−	0.113910i
$147$		0			0
$148$	−1.13911	+	0.681180i	−0.0936343	+	0.0559926i
$149$	−10.7674			−0.882096			−0.441048	−	0.897484i	$-0.645393\pi$
$149$	−10.7674			−0.882096			−0.441048	+	0.897484i	$0.645393\pi$
$150$		0			0
$151$			2.56398i			0.208654i	0.994543	+	0.104327i	$0.0332688\pi$
$151$			2.56398i			0.208654i	−0.994543	+	0.104327i	$0.966731\pi$
$152$	6.88948	+	6.57943i	0.558811	+	0.533662i
$153$		0			0
$154$	3.80029	−	1.04960i	0.306236	−	0.0845791i
$155$		0			0
$156$		0			0
$157$	21.6489			1.72777			0.863886	−	0.503688i	$-0.168024\pi$
$157$	21.6489			1.72777			0.863886	+	0.503688i	$0.168024\pi$
$158$	18.1843	−	5.02230i	1.44666	−	0.399552i
$159$		0			0
$160$		0			0
$161$			5.19018i			0.409044i
$162$		0			0
$163$		−	1.84213i		−	0.144287i	−0.997394	−	0.0721433i	$-0.977016\pi$
$163$		−	1.84213i		−	0.144287i	0.997394	−	0.0721433i	$-0.0229839\pi$
$164$	−9.18269	−	15.3558i	−0.717048	−	1.19909i
$165$		0			0
$166$	2.92732	+	10.5990i	0.227204	+	0.822640i
$167$		−	20.2225i		−	1.56487i	−0.622735	−	0.782433i	$-0.713979\pi$
$167$		−	20.2225i		−	1.56487i	0.622735	−	0.782433i	$-0.286021\pi$
$168$		0			0
$169$	−12.4205			−0.955423
$170$		0			0
$171$		0			0
$172$	2.48138	+	4.14951i	0.189203	+	0.316397i
$173$			21.7379i			1.65270i	0.563156	+	0.826351i	$0.309587\pi$
$173$			21.7379i			1.65270i	−0.563156	+	0.826351i	$0.690413\pi$
$174$		0			0
$175$		0			0
$176$	9.43254	+	5.06653i	0.711004	+	0.381904i
$177$		0			0
$178$	−9.13064	+	2.52178i	−0.684370	+	0.189015i
$179$			13.6156i			1.01768i	0.860862	+	0.508838i	$0.169925\pi$
$179$			13.6156i			1.01768i	−0.860862	+	0.508838i	$0.830075\pi$
$180$		0			0
$181$		−	6.88995i		−	0.512126i	−0.966660	−	0.256063i	$-0.917575\pi$
$181$		−	6.88995i		−	0.512126i	0.966660	−	0.256063i	$-0.0824254\pi$
$182$	−0.298496	−	1.08077i	−0.0221260	−	0.0801117i
$183$		0			0
$184$	−9.73490	+	10.1936i	−0.717666	+	0.751486i
$185$		0			0
$186$		0			0
$187$		−	5.83063i		−	0.426378i
$188$	7.47199	+	12.4951i	0.544951	+	0.911300i
$189$		0			0
$190$		0			0
$191$	−0.823063			−0.0595548			−0.0297774	−	0.999557i	$-0.509480\pi$
$191$	−0.823063			−0.0595548			−0.0297774	+	0.999557i	$0.509480\pi$
$192$		0			0
$193$			20.6473i			1.48623i	0.669165	+	0.743114i	$0.266652\pi$
$193$			20.6473i			1.48623i	−0.669165	+	0.743114i	$0.733348\pi$
$194$	18.1402	−	5.01013i	1.30239	−	0.359707i
$195$		0			0
$196$	10.1537	−	6.07182i	0.725261	−	0.433701i
$197$		−	7.67571i		−	0.546871i	−0.961890	−	0.273436i	$-0.911840\pi$
$197$		−	7.67571i		−	0.546871i	0.961890	−	0.273436i	$-0.0881601\pi$
$198$		0			0
$199$		−	19.7110i		−	1.39728i	−0.715475	−	0.698639i	$-0.753790\pi$
$199$		−	19.7110i		−	1.39728i	0.715475	−	0.698639i	$-0.246210\pi$
$200$		0			0
$201$		0			0
$202$	1.48692	+	5.38371i	0.104619	+	0.378796i
$203$	8.21387			0.576501
$204$		0			0
$205$		0			0
$206$	−6.52928	−	23.6406i	−0.454916	−	1.64712i
$207$		0			0
$208$	1.44087	−	2.68252i	0.0999065	−	0.185999i
$209$		−	9.01572i		−	0.623631i
$210$		0			0
$211$	−3.46672			−0.238659			−0.119329	−	0.992855i	$-0.538074\pi$
$211$	−3.46672			−0.238659			−0.119329	+	0.992855i	$0.538074\pi$
$212$	1.03018	+	1.72273i	0.0707530	+	0.118317i
$213$		0			0
$214$	−2.31153	−	8.36939i	−0.158013	−	0.572119i
$215$		0			0
$216$		0			0
$217$			4.66968i			0.316999i
$218$	−23.9963	+	6.62750i	−1.62523	+	0.448871i
$219$		0			0
$220$		0			0
$221$	−1.65817			−0.111541
$222$		0			0
$223$	−17.9866			−1.20447			−0.602235	−	0.798319i	$-0.705723\pi$
$223$	−17.9866			−1.20447			−0.602235	+	0.798319i	$0.705723\pi$
$224$	−5.74505	−	1.30547i	−0.383858	−	0.0872256i
$225$		0			0
$226$	3.58667	+	12.9863i	0.238582	+	0.863835i
$227$	−25.4518			−1.68929			−0.844647	−	0.535323i	$-0.820190\pi$
$227$	−25.4518			−1.68929			−0.844647	+	0.535323i	$0.820190\pi$
$228$		0			0
$229$			16.8475i			1.11331i	0.830743	+	0.556656i	$0.187916\pi$
$229$			16.8475i			1.11331i	−0.830743	+	0.556656i	$0.812084\pi$
$230$		0			0
$231$		0			0
$232$	16.1323	+	15.4063i	1.05913	+	1.01147i
$233$	−1.06730			−0.0699213			−0.0349606	−	0.999389i	$-0.511131\pi$
$233$	−1.06730			−0.0699213			−0.0349606	+	0.999389i	$0.511131\pi$
$234$		0			0
$235$		0			0
$236$	−5.07765	−	8.49115i	−0.330527	−	0.552727i
$237$		0			0
$238$	0.854108	+	3.09248i	0.0553636	+	0.200456i
$239$	18.1544			1.17431			0.587154	−	0.809475i	$-0.300248\pi$
$239$	18.1544			1.17431			0.587154	+	0.809475i	$0.300248\pi$
$240$		0			0
$241$	−13.3073			−0.857200			−0.428600	−	0.903494i	$-0.640993\pi$
$241$	−13.3073			−0.857200			−0.428600	+	0.903494i	$0.640993\pi$
$242$	1.44380	+	5.22757i	0.0928108	+	0.336041i
$243$		0			0
$244$	12.8053	+	21.4138i	0.819774	+	1.37088i
$245$		0			0
$246$		0			0
$247$	−2.56398			−0.163142
$248$	−8.75863	+	9.17138i	−0.556174	+	0.582383i
$249$		0			0
$250$		0			0
$251$		−	11.4972i		−	0.725699i	−0.931848	−	0.362850i	$-0.881804\pi$
$251$		−	11.4972i		−	0.725699i	0.931848	−	0.362850i	$-0.118196\pi$
$252$		0			0
$253$	13.3396			0.838655
$254$	−4.01085	−	14.5221i	−0.251663	−	0.911198i
$255$		0			0
$256$	−8.83484	−	13.3396i	−0.552178	−	0.833727i
$257$	−7.36840			−0.459628			−0.229814	−	0.973235i	$-0.573812\pi$
$257$	−7.36840			−0.459628			−0.229814	+	0.973235i	$0.573812\pi$
$258$		0			0
$259$	−0.691151			−0.0429460
$260$		0			0
$261$		0			0
$262$	−19.9363	+	5.50619i	−1.23167	+	0.340174i
$263$		−	1.73421i		−	0.106936i	−0.998570	−	0.0534679i	$-0.982973\pi$
$263$		−	1.73421i		−	0.106936i	0.998570	−	0.0534679i	$-0.0170275\pi$
$264$		0			0
$265$		0			0
$266$	1.32068	+	4.78180i	0.0809762	+	0.293191i
$267$		0			0
$268$	14.7439	+	24.6557i	0.900630	+	1.50609i
$269$	−16.7849			−1.02339			−0.511696	−	0.859166i	$-0.670983\pi$
$269$	−16.7849			−1.02339			−0.511696	+	0.859166i	$0.670983\pi$
$270$		0			0
$271$			21.1430i			1.28435i	0.766559	+	0.642173i	$0.221967\pi$
$271$			21.1430i			1.28435i	−0.766559	+	0.642173i	$0.778033\pi$
$272$	−4.12288	+	7.67571i	−0.249986	+	0.465408i
$273$		0			0
$274$	−6.27289	−	22.7123i	−0.378959	−	1.37210i
$275$		0			0
$276$		0			0
$277$	27.2342			1.63634			0.818172	−	0.574974i	$-0.194988\pi$
$277$	27.2342			1.63634			0.818172	+	0.574974i	$0.194988\pi$
$278$	0.931451	+	3.37251i	0.0558647	+	0.202270i
$279$		0			0
$280$		0			0
$281$			4.70336i			0.280579i	0.990111	+	0.140289i	$0.0448033\pi$
$281$			4.70336i			0.280579i	−0.990111	+	0.140289i	$0.955197\pi$
$282$		0			0
$283$			11.6754i			0.694033i	0.937859	+	0.347016i	$0.112805\pi$
$283$			11.6754i			0.694033i	−0.937859	+	0.347016i	$0.887195\pi$
$284$	7.63687	−	4.56679i	0.453165	−	0.270989i
$285$		0			0
$286$	−2.77775	+	0.767183i	−0.164252	+	0.0453645i
$287$		−	9.31710i		−	0.549971i
$288$		0			0
$289$	−12.2553			−0.720902
$290$		0			0
$291$		0			0
$292$	3.75249	+	6.27514i	0.219598	+	0.367225i
$293$			13.9042i			0.812295i	0.913808	+	0.406147i	$0.133128\pi$
$293$			13.9042i			0.812295i	−0.913808	+	0.406147i	$0.866872\pi$
$294$		0			0
$295$		0			0
$296$	−1.35744	−	1.29635i	−0.0788995	−	0.0753487i
$297$		0			0
$298$	−4.05385	−	14.6778i	−0.234833	−	0.850262i
$299$		−	3.79366i		−	0.219393i
$300$		0			0
$301$			2.51770i			0.145118i
$302$	−3.49516	+	0.965325i	−0.201124	+	0.0555482i
$303$		0			0
$304$	−6.37508	+	11.8687i	−0.365636	+	0.680717i
$305$		0			0
$306$		0			0
$307$			0.679652i			0.0387898i	0.999812	+	0.0193949i	$0.00617398\pi$
$307$			0.679652i			0.0387898i	−0.999812	+	0.0193949i	$0.993826\pi$
$308$	2.86158	+	4.78530i	0.163054	+	0.272668i
$309$		0			0
$310$		0			0
$311$	−16.3078			−0.924731			−0.462365	−	0.886689i	$-0.652999\pi$
$311$	−16.3078			−0.924731			−0.462365	+	0.886689i	$0.652999\pi$
$312$		0			0
$313$			6.17907i			0.349262i	0.984634	+	0.174631i	$0.0558732\pi$
$313$			6.17907i			0.349262i	−0.984634	+	0.174631i	$0.944127\pi$
$314$	8.15070	+	29.5113i	0.459970	+	1.66542i
$315$		0			0
$316$	13.6926	+	22.8975i	0.770266	+	1.28809i
$317$			29.4787i			1.65569i	0.560957	+	0.827845i	$0.310433\pi$
$317$			29.4787i			1.65569i	−0.560957	+	0.827845i	$0.689567\pi$
$318$		0			0
$319$		−	21.1110i		−	1.18199i
$320$		0			0
$321$		0			0
$322$	−7.07514	+	1.95407i	−0.394282	+	0.108896i
$323$	7.33652			0.408215
$324$		0			0
$325$		0			0
$326$	2.51115	−	0.693551i	0.139080	−	0.0384123i
$327$		0			0
$328$	17.4755	−	18.2990i	0.964923	−	1.01039i
$329$			7.58136i			0.417974i
$330$		0			0
$331$	−18.3524			−1.00874			−0.504370	−	0.863488i	$-0.668275\pi$
$331$	−18.3524			−1.00874			−0.504370	+	0.863488i	$0.668275\pi$
$332$	−13.3462	+	7.98091i	−0.732465	+	0.438009i
$333$		0			0
$334$	27.5669	−	7.61367i	1.50839	−	0.416601i
$335$		0			0
$336$		0			0
$337$		−	5.39201i		−	0.293721i	−0.989157	−	0.146861i	$-0.953083\pi$
$337$		−	5.39201i		−	0.293721i	0.989157	−	0.146861i	$-0.0469169\pi$
$338$	−4.67625	−	16.9313i	−0.254354	−	0.920943i
$339$		0			0
$340$		0			0
$341$	12.0019			0.649937
$342$		0			0
$343$	13.4511			0.726289
$344$	−4.72229	+	4.94483i	−0.254609	+	0.266607i
$345$		0			0
$346$	−29.6326	+	8.18420i	−1.59306	+	0.439985i
$347$	21.9173			1.17658			0.588292	−	0.808649i	$-0.299801\pi$
$347$	21.9173			1.17658			0.588292	+	0.808649i	$0.299801\pi$
$348$		0			0
$349$			7.01567i			0.375540i	0.982213	+	0.187770i	$0.0601260\pi$
$349$			7.01567i			0.375540i	−0.982213	+	0.187770i	$0.939874\pi$
$350$		0			0
$351$		0			0
$352$	−3.35528	+	14.7657i	−0.178837	+	0.787017i
$353$	−21.5542			−1.14721			−0.573606	−	0.819131i	$-0.694456\pi$
$353$	−21.5542			−1.14721			−0.573606	+	0.819131i	$0.694456\pi$
$354$		0			0
$355$		0			0
$356$	−6.87527	−	11.4972i	−0.364389	−	0.609352i
$357$		0			0
$358$	−18.5604	+	5.12619i	−0.980950	+	0.270928i
$359$	30.1894			1.59334			0.796669	−	0.604416i	$-0.206594\pi$
$359$	30.1894			1.59334			0.796669	+	0.604416i	$0.206594\pi$
$360$		0			0
$361$	−7.65577			−0.402935
$362$	9.39222	−	2.59403i	0.493644	−	0.136339i
$363$		0			0
$364$	1.36089	−	0.813805i	0.0713302	−	0.0426550i
$365$		0			0
$366$		0			0
$367$	3.71691			0.194021			0.0970105	−	0.995283i	$-0.469072\pi$
$367$	3.71691			0.194021			0.0970105	+	0.995283i	$0.469072\pi$
$368$	−17.5609	−	9.43254i	−0.915424	−	0.491705i
$369$		0			0
$370$		0			0
$371$			1.04526i			0.0542671i
$372$		0			0
$373$	21.1055			1.09280			0.546400	−	0.837524i	$-0.315998\pi$
$373$	21.1055			1.09280			0.546400	+	0.837524i	$0.315998\pi$
$374$	7.94818	−	2.19520i	0.410991	−	0.113511i
$375$		0			0
$376$	−14.2199	+	14.8900i	−0.733335	+	0.767893i
$377$	−6.00377			−0.309210
$378$		0			0
$379$	18.4625			0.948355			0.474178	−	0.880429i	$-0.342745\pi$
$379$	18.4625			0.948355			0.474178	+	0.880429i	$0.342745\pi$
$380$		0			0
$381$		0			0
$382$	−0.309879	−	1.12198i	−0.0158548	−	0.0574055i
$383$		−	22.7946i		−	1.16475i	−0.812921	−	0.582375i	$-0.802124\pi$
$383$		−	22.7946i		−	1.16475i	0.812921	−	0.582375i	$-0.197876\pi$
$384$		0			0
$385$		0			0
$386$	−28.1460	+	7.77361i	−1.43259	+	0.395666i
$387$		0			0
$388$	13.6594	+	22.8421i	0.693451	+	1.15963i
$389$	−29.6897			−1.50533			−0.752665	−	0.658404i	$-0.771232\pi$
$389$	−29.6897			−1.50533			−0.752665	+	0.658404i	$0.771232\pi$
$390$		0			0
$391$			10.8551i			0.548965i
$392$	12.0998	+	11.5552i	0.611130	+	0.583627i
$393$		0			0
$394$	10.4633	−	2.88986i	0.527136	−	0.145589i
$395$		0			0
$396$		0			0
$397$	−11.2511			−0.564678			−0.282339	−	0.959315i	$-0.591110\pi$
$397$	−11.2511			−0.564678			−0.282339	+	0.959315i	$0.591110\pi$
$398$	26.8696	−	7.42109i	1.34685	−	0.371986i
$399$		0			0
$400$		0			0
$401$		−	17.1280i		−	0.855331i	−0.903937	−	0.427666i	$-0.859336\pi$
$401$		−	17.1280i		−	0.855331i	0.903937	−	0.427666i	$-0.140664\pi$
$402$		0			0
$403$		−	3.41321i		−	0.170024i
$404$	−6.77913	+	4.05387i	−0.337274	+	0.201688i
$405$		0			0
$406$	3.09248	+	11.1970i	0.153477	+	0.555696i
$407$			1.77637i			0.0880515i
$408$		0			0
$409$	22.2892			1.10213			0.551065	−	0.834462i	$-0.314222\pi$
$409$	22.2892			1.10213			0.551065	+	0.834462i	$0.314222\pi$
$410$		0			0
$411$		0			0
$412$	29.7681	−	17.8011i	1.46657	−	0.876999i
$413$		−	5.15197i		−	0.253512i
$414$		0			0
$415$		0			0
$416$	4.19923	+	0.954209i	0.205884	+	0.0467840i
$417$		0			0
$418$	12.2900	−	3.39437i	0.601125	−	0.166024i
$419$			29.9477i			1.46304i	0.681820	+	0.731520i	$0.261189\pi$
$419$			29.9477i			1.46304i	−0.681820	+	0.731520i	$0.738811\pi$
$420$		0			0
$421$			0.457304i			0.0222877i	0.999938	+	0.0111438i	$0.00354726\pi$
$421$			0.457304i			0.0222877i	−0.999938	+	0.0111438i	$0.996453\pi$
$422$	−1.30520	−	4.72575i	−0.0635362	−	0.230046i
$423$		0			0
$424$	−1.96053	+	2.05291i	−0.0952116	+	0.0996984i
$425$		0			0
$426$		0			0
$427$			12.9927i			0.628761i
$428$	10.5387	−	6.30206i	0.509406	−	0.304621i
$429$		0			0
$430$		0			0
$431$	−37.5538			−1.80890			−0.904452	−	0.426576i	$-0.859720\pi$
$431$	−37.5538			−1.80890			−0.904452	+	0.426576i	$0.859720\pi$
$432$		0			0
$433$		−	11.5530i		−	0.555200i	−0.960697	−	0.277600i	$-0.910461\pi$
$433$		−	11.5530i		−	0.555200i	0.960697	−	0.277600i	$-0.0895389\pi$
$434$	−6.36560	+	1.75811i	−0.305559	+	0.0843920i
$435$		0			0
$436$	−18.0689	−	30.2159i	−0.865344	−	1.44708i
$437$			16.7849i			0.802930i
$438$		0			0
$439$		−	31.9187i		−	1.52339i	−0.647933	−	0.761697i	$-0.724366\pi$
$439$		−	31.9187i		−	1.52339i	0.647933	−	0.761697i	$-0.275634\pi$
$440$		0			0
$441$		0			0
$442$	−0.624293	−	2.26038i	−0.0296946	−	0.107516i
$443$	−29.7160			−1.41185			−0.705925	−	0.708287i	$-0.749468\pi$
$443$	−29.7160			−1.41185			−0.705925	+	0.708287i	$0.749468\pi$
$444$		0			0
$445$		0			0
$446$	−6.77185	−	24.5189i	−0.320656	−	1.16100i
$447$		0			0
$448$	−0.383391	−	8.32303i	−0.0181135	−	0.393226i
$449$			4.98651i			0.235328i	0.993053	+	0.117664i	$0.0375405\pi$
$449$			4.98651i			0.235328i	−0.993053	+	0.117664i	$0.962459\pi$
$450$		0			0
$451$	−23.9465			−1.12760
$452$	−16.3522	+	9.77853i	−0.769145	+	0.459943i
$453$		0			0
$454$	−9.58246	−	34.6953i	−0.449727	−	1.62833i
$455$		0			0
$456$		0			0
$457$			28.7278i			1.34383i	0.740628	+	0.671915i	$0.234528\pi$
$457$			28.7278i			1.34383i	−0.740628	+	0.671915i	$0.765472\pi$
$458$	−22.9661	+	6.34298i	−1.07313	+	0.296388i
$459$		0			0
$460$		0			0
$461$	−21.1683			−0.985908			−0.492954	−	0.870055i	$-0.664083\pi$
$461$	−21.1683			−0.985908			−0.492954	+	0.870055i	$0.664083\pi$
$462$		0			0
$463$	−12.4206			−0.577236			−0.288618	−	0.957444i	$-0.593196\pi$
$463$	−12.4206			−0.577236			−0.288618	+	0.957444i	$0.593196\pi$
$464$	−14.9277	+	27.7915i	−0.693003	+	1.29019i
$465$		0			0
$466$	−0.401833	−	1.45492i	−0.0186146	−	0.0673979i
$467$	−3.23928			−0.149896			−0.0749479	−	0.997187i	$-0.523879\pi$
$467$	−3.23928			−0.149896			−0.0749479	+	0.997187i	$0.523879\pi$
$468$		0			0
$469$			14.9598i			0.690777i
$470$		0			0
$471$		0			0
$472$	9.66323	−	10.1186i	0.444786	−	0.465747i
$473$	6.47091			0.297533
$474$		0			0
$475$		0			0
$476$	−3.89403	+	2.32860i	−0.178483	+	0.106731i
$477$		0			0
$478$	6.83502	+	24.7476i	0.312627	+	1.13193i
$479$	−14.2397			−0.650627			−0.325313	−	0.945606i	$-0.605470\pi$
$479$	−14.2397			−0.650627			−0.325313	+	0.945606i	$0.605470\pi$
$480$		0			0
$481$	0.505183			0.0230343
$482$	−5.01013	−	18.1402i	−0.228205	−	0.826265i
$483$		0			0
$484$	−6.58252	+	3.93630i	−0.299205	+	0.178923i
$485$		0			0
$486$		0			0
$487$	−28.2812			−1.28154			−0.640772	−	0.767732i	$-0.721385\pi$
$487$	−28.2812			−1.28154			−0.640772	+	0.767732i	$0.721385\pi$
$488$	−24.3696	+	25.5180i	−1.10316	+	1.15515i
$489$		0			0
$490$		0			0
$491$		−	24.8493i		−	1.12143i	−0.828008	−	0.560716i	$-0.810526\pi$
$491$		−	24.8493i		−	1.12143i	0.828008	−	0.560716i	$-0.189474\pi$
$492$		0			0
$493$	17.1790			0.773705
$494$	−0.965325	−	3.49516i	−0.0434320	−	0.157255i
$495$		0			0
$496$	−15.7998	−	8.48659i	−0.709431	−	0.381059i
$497$	4.63364			0.207847
$498$		0			0
$499$	9.57416			0.428598			0.214299	−	0.976768i	$-0.431253\pi$
$499$	9.57416			0.428598			0.214299	+	0.976768i	$0.431253\pi$
$500$		0			0
$501$		0			0
$502$	15.6728	−	4.32865i	0.699510	−	0.193197i
$503$		−	4.30319i		−	0.191870i	−0.995388	−	0.0959350i	$-0.969416\pi$
$503$		−	4.30319i		−	0.191870i	0.995388	−	0.0959350i	$-0.0305841\pi$
$504$		0			0
$505$		0			0
$506$	5.02230	+	18.1843i	0.223268	+	0.808389i
$507$		0			0
$508$	18.2861	−	10.9350i	0.811317	−	0.485162i
$509$	20.3575			0.902330			0.451165	−	0.892441i	$-0.351009\pi$
$509$	20.3575			0.902330			0.451165	+	0.892441i	$0.351009\pi$
$510$		0			0
$511$			3.80741i			0.168430i
$512$	14.8580	−	17.0657i	0.656637	−	0.754207i
$513$		0			0
$514$	−2.77416	−	10.0444i	−0.122363	−	0.443041i
$515$		0			0
$516$		0			0
$517$	19.4854			0.856965
$518$	−0.260214	−	0.942161i	−0.0114332	−	0.0413962i
$519$		0			0
$520$		0			0
$521$		−	4.03301i		−	0.176689i	−0.996090	−	0.0883447i	$-0.971842\pi$
$521$		−	4.03301i		−	0.176689i	0.996090	−	0.0883447i	$-0.0281577\pi$
$522$		0			0
$523$		−	32.7163i		−	1.43058i	−0.698825	−	0.715292i	$-0.746294\pi$
$523$		−	32.7163i		−	1.43058i	0.698825	−	0.715292i	$-0.253706\pi$
$524$	−15.0118	−	25.1037i	−0.655795	−	1.09666i
$525$		0			0
$526$	2.36403	−	0.652919i	0.103077	−	0.0284686i
$527$			9.76648i			0.425435i
$528$		0			0
$529$	−1.83484			−0.0797757
$530$		0			0
$531$		0			0
$532$	−6.02121	+	3.60064i	−0.261053	+	0.156108i
$533$			6.81015i			0.294980i
$534$		0			0
$535$		0			0
$536$	−28.0591	+	29.3813i	−1.21197	+	1.26908i
$537$		0			0
$538$	−6.31942	−	22.8808i	−0.272449	−	0.986460i
$539$		−	15.8340i		−	0.682019i
$540$		0			0
$541$		−	3.20942i		−	0.137984i	−0.997617	−	0.0689919i	$-0.978022\pi$
$541$		−	3.20942i		−	0.137984i	0.997617	−	0.0689919i	$-0.0219783\pi$
$542$	−28.8217	+	7.96023i	−1.23800	+	0.341921i
$543$		0			0
$544$	−12.0156	−	2.73035i	−0.515164	−	0.117063i
$545$		0			0
$546$		0			0
$547$		−	14.7898i		−	0.632364i	−0.948699	−	0.316182i	$-0.897599\pi$
$547$		−	14.7898i		−	0.632364i	0.948699	−	0.316182i	$-0.102401\pi$
$548$	28.5992	−	17.1021i	1.22170	−	0.730567i
$549$		0			0
$550$		0			0
$551$	26.5634			1.13164
$552$		0			0
$553$			13.8930i			0.590790i
$554$	10.2535	+	37.1250i	0.435630	+	1.57729i
$555$		0			0
$556$	−4.24664	+	2.53946i	−0.180098	+	0.107697i
$557$		−	0.138067i		−	0.00585009i	−0.999996	−	0.00292504i	$-0.999069\pi$
$557$		−	0.138067i		−	0.00585009i	0.999996	−	0.00292504i	$-0.000931071\pi$
$558$		0			0
$559$		−	1.84026i		−	0.0778348i
$560$		0			0
$561$		0			0
$562$	−6.41151	+	1.77079i	−0.270453	+	0.0746962i
$563$	−4.06536			−0.171335			−0.0856673	−	0.996324i	$-0.527302\pi$
$563$	−4.06536			−0.171335			−0.0856673	+	0.996324i	$0.527302\pi$
$564$		0			0
$565$		0			0
$566$	−15.9157	+	4.39574i	−0.668987	+	0.184767i
$567$		0			0
$568$	9.10059	+	8.69103i	0.381852	+	0.364667i
$569$		−	25.1962i		−	1.05628i	−0.849158	−	0.528139i	$-0.822890\pi$
$569$		−	25.1962i		−	1.05628i	0.849158	−	0.528139i	$-0.177110\pi$
$570$		0			0
$571$	38.8322			1.62508			0.812538	−	0.582908i	$-0.198085\pi$
$571$	38.8322			1.62508			0.812538	+	0.582908i	$0.198085\pi$
$572$	−2.09161	−	3.49772i	−0.0874547	−	0.146247i
$573$		0			0
$574$	12.7009	−	3.50784i	0.530123	−	0.146414i
$575$		0			0
$576$		0			0
$577$			37.2003i			1.54867i	0.632777	+	0.774334i	$0.281915\pi$
$577$			37.2003i			1.54867i	−0.632777	+	0.774334i	$0.718085\pi$
$578$	−4.61407	−	16.7062i	−0.191920	−	0.694886i
$579$		0			0
$580$		0			0
$581$	−8.09773			−0.335950
$582$		0			0
$583$	2.68649			0.111263
$584$	−7.14133	+	7.47786i	−0.295510	+	0.309436i
$585$		0			0
$586$	−18.9540	+	5.23487i	−0.782981	+	0.216251i
$587$	36.6223			1.51156			0.755781	−	0.654824i	$-0.227257\pi$
$587$	36.6223			1.51156			0.755781	+	0.654824i	$0.227257\pi$
$588$		0			0
$589$			15.1016i			0.622251i
$590$		0			0
$591$		0			0
$592$	1.25608	−	2.33850i	0.0516248	−	0.0961116i
$593$	−9.80367			−0.402589			−0.201294	−	0.979531i	$-0.564515\pi$
$593$	−9.80367			−0.402589			−0.201294	+	0.979531i	$0.564515\pi$
$594$		0			0
$595$		0			0
$596$	18.4822	−	11.0522i	0.757060	−	0.452717i
$597$		0			0
$598$	5.17143	−	1.42829i	0.211475	−	0.0584072i
$599$	9.54489			0.389994			0.194997	−	0.980804i	$-0.437530\pi$
$599$	9.54489			0.389994			0.194997	+	0.980804i	$0.437530\pi$
$600$		0			0
$601$	14.8167			0.604386			0.302193	−	0.953247i	$-0.402281\pi$
$601$	14.8167			0.604386			0.302193	+	0.953247i	$0.402281\pi$
$602$	−3.43207	+	0.947900i	−0.139881	+	0.0386335i
$603$		0			0
$604$	−2.63182	−	4.40109i	−0.107087	−	0.179078i
$605$		0			0
$606$		0			0
$607$	−14.4606			−0.586936			−0.293468	−	0.955969i	$-0.594809\pi$
$607$	−14.4606			−0.586936			−0.293468	+	0.955969i	$0.594809\pi$
$608$	−18.5793	−	4.22186i	−0.753491	−	0.171219i
$609$		0			0
$610$		0			0
$611$		−	5.54144i		−	0.224183i
$612$		0			0
$613$	32.6016			1.31677			0.658384	−	0.752683i	$-0.271240\pi$
$613$	32.6016			1.31677			0.658384	+	0.752683i	$0.271240\pi$
$614$	−0.926487	+	0.255885i	−0.0373900	+	0.0103267i
$615$		0			0
$616$	−5.44585	+	5.70248i	−0.219419	+	0.229759i
$617$	19.6531			0.791205			0.395603	−	0.918422i	$-0.370536\pi$
$617$	19.6531			0.791205			0.395603	+	0.918422i	$0.370536\pi$
$618$		0			0
$619$	−0.939202			−0.0377497			−0.0188748	−	0.999822i	$-0.506008\pi$
$619$	−0.939202			−0.0377497			−0.0188748	+	0.999822i	$0.506008\pi$
$620$		0			0
$621$		0			0
$622$	−6.13980	−	22.2304i	−0.246184	−	0.891359i
$623$		−	6.97590i		−	0.279484i
$624$		0			0
$625$		0			0
$626$	−8.42317	+	2.32639i	−0.336658	+	0.0929812i
$627$		0			0
$628$	−37.1604	+	22.2217i	−1.48286	+	0.886742i
$629$	−1.44552			−0.0576366
$630$		0			0
$631$			2.56398i			0.102071i	0.998697	+	0.0510353i	$0.0162521\pi$
$631$			2.56398i			0.102071i	−0.998697	+	0.0510353i	$0.983748\pi$
$632$	−26.0582	+	27.2862i	−1.03654	+	1.08539i
$633$		0			0
$634$	−40.1847	+	11.0986i	−1.59594	+	0.440781i
$635$		0			0
$636$		0			0
$637$	−4.50304			−0.178417
$638$	28.7781	−	7.94818i	1.13933	−	0.314672i
$639$		0			0
$640$		0			0
$641$			7.81493i			0.308671i	0.988018	+	0.154336i	$0.0493237\pi$
$641$			7.81493i			0.308671i	−0.988018	+	0.154336i	$0.950676\pi$
$642$		0			0
$643$			41.2496i			1.62673i	0.581757	+	0.813363i	$0.302366\pi$
$643$			41.2496i			1.62673i	−0.581757	+	0.813363i	$0.697634\pi$
$644$	−5.32750	−	8.90896i	−0.209933	−	0.351062i
$645$		0			0
$646$	2.76216	+	10.0010i	0.108676	+	0.393483i
$647$			25.6101i			1.00684i	0.864043	+	0.503418i	$0.167925\pi$
$647$			25.6101i			1.00684i	−0.864043	+	0.503418i	$0.832075\pi$
$648$		0			0
$649$	−13.2414			−0.519771
$650$		0			0
$651$		0			0
$652$	1.89087	+	3.16202i	0.0740521	+	0.123834i
$653$		−	10.3906i		−	0.406615i	−0.979115	−	0.203307i	$-0.934831\pi$
$653$		−	10.3906i		−	0.406615i	0.979115	−	0.203307i	$-0.0651691\pi$
$654$		0			0
$655$		0			0
$656$	31.5242	+	16.9327i	1.23081	+	0.661112i
$657$		0			0
$658$	−10.3347	+	2.85434i	−0.402890	+	0.111274i
$659$		−	38.7919i		−	1.51112i	−0.655081	−	0.755559i	$-0.727365\pi$
$659$		−	38.7919i		−	1.51112i	0.655081	−	0.755559i	$-0.272635\pi$
$660$		0			0
$661$			7.45594i			0.290002i	0.989431	+	0.145001i	$0.0463186\pi$
$661$			7.45594i			0.290002i	−0.989431	+	0.145001i	$0.953681\pi$
$662$	−6.90958	−	25.0176i	−0.268549	−	0.972336i
$663$		0			0
$664$	−15.9041	−	15.1884i	−0.617201	−	0.589424i
$665$		0			0
$666$		0			0
$667$			39.3031i			1.52182i
$668$	20.7576	+	34.7120i	0.803134	+	1.34305i
$669$		0			0
$670$		0			0
$671$	33.3934			1.28914
$672$		0			0
$673$		−	21.3878i		−	0.824439i	−0.911085	−	0.412219i	$-0.864754\pi$
$673$		−	21.3878i		−	0.824439i	0.911085	−	0.412219i	$-0.135246\pi$
$674$	7.35026	−	2.03006i	0.283121	−	0.0781950i
$675$		0			0
$676$	21.3198	−	12.7491i	0.819994	−	0.490350i
$677$			19.4998i			0.749437i	0.927139	+	0.374718i	$0.122261\pi$
$677$			19.4998i			0.749437i	−0.927139	+	0.374718i	$0.877739\pi$
$678$		0			0
$679$			13.8593i			0.531873i
$680$		0			0
$681$		0			0
$682$	4.51863	+	16.3607i	0.173027	+	0.626482i
$683$	4.37992			0.167593			0.0837965	−	0.996483i	$-0.473295\pi$
$683$	4.37992			0.167593			0.0837965	+	0.996483i	$0.473295\pi$
$684$		0			0
$685$		0			0
$686$	5.06425	+	18.3362i	0.193354	+	0.700079i
$687$		0			0
$688$	−8.51859	−	4.57562i	−0.324768	−	0.174444i
$689$		−	0.764011i		−	0.0291065i
$690$		0			0
$691$	−10.3754			−0.394699			−0.197350	−	0.980333i	$-0.563233\pi$
$691$	−10.3754			−0.394699			−0.197350	+	0.980333i	$0.563233\pi$
$692$	−22.3130	−	37.3132i	−0.848214	−	1.41843i
$693$		0			0
$694$	8.25176	+	29.8772i	0.313232	+	1.13412i
$695$		0			0
$696$		0			0
$697$		−	19.4864i		−	0.738100i
$698$	−9.56361	+	2.64136i	−0.361988	+	0.0999770i
$699$		0			0
$700$		0			0
$701$	45.6169			1.72293			0.861463	−	0.507821i	$-0.169549\pi$
$701$	45.6169			1.72293			0.861463	+	0.507821i	$0.169549\pi$
$702$		0			0
$703$	−2.23516			−0.0843006
$704$	−21.3916	+	0.985377i	−0.806225	+	0.0371378i
$705$		0			0
$706$	−8.11502	−	29.3821i	−0.305413	−	1.10581i
$707$	−4.11321			−0.154693
$708$		0			0
$709$			18.7992i			0.706018i	0.935620	+	0.353009i	$0.114841\pi$
$709$			18.7992i			0.706018i	−0.935620	+	0.353009i	$0.885159\pi$
$710$		0			0
$711$		0			0
$712$	13.0843	−	13.7009i	0.490354	−	0.513461i
$713$	−22.3443			−0.836800
$714$		0			0
$715$		0			0
$716$	−13.9758	−	23.3712i	−0.522301	−	0.873423i
$717$		0			0
$718$	11.3662	+	41.1535i	0.424181	+	1.53584i
$719$	31.7473			1.18397			0.591987	−	0.805947i	$-0.298344\pi$
$719$	31.7473			1.18397			0.591987	+	0.805947i	$0.298344\pi$
$720$		0			0
$721$	18.0617			0.672652
$722$	−2.88235	−	10.4362i	−0.107270	−	0.388394i
$723$		0			0
$724$	7.07224	+	11.8266i	0.262838	+	0.439533i
$725$		0			0
$726$		0			0
$727$	−2.04221			−0.0757415			−0.0378707	−	0.999283i	$-0.512058\pi$
$727$	−2.04221			−0.0757415			−0.0378707	+	0.999283i	$0.512058\pi$
$728$	1.62173	+	1.54875i	0.0601053	+	0.0574003i
$729$		0			0
$730$		0			0
$731$			5.26568i			0.194758i
$732$		0			0
$733$	−44.2124			−1.63302			−0.816512	−	0.577329i	$-0.804095\pi$
$733$	−44.2124			−1.63302			−0.816512	+	0.577329i	$0.804095\pi$
$734$	1.39940	+	5.06680i	0.0516526	+	0.187019i
$735$		0			0
$736$	6.24664	−	27.4899i	0.230254	−	1.01329i
$737$	38.4490			1.41629
$738$		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
$742$	−1.42487	+	0.393534i	−0.0523087	+	0.0144471i
$743$			0.230881i			0.00847019i	0.999991	+	0.00423509i	$0.00134808\pi$
$743$			0.230881i			0.00847019i	−0.999991	+	0.00423509i	$0.998652\pi$
$744$		0			0
$745$		0			0
$746$	7.94610	+	28.7705i	0.290927	+	1.05336i
$747$		0			0
$748$	5.98489	+	10.0083i	0.218829	+	0.365940i
$749$	6.39430			0.233643
$750$		0			0
$751$			11.8602i			0.432784i	0.976307	+	0.216392i	$0.0694290\pi$
$751$			11.8602i			0.432784i	−0.976307	+	0.216392i	$0.930571\pi$
$752$	−25.6514	−	13.7782i	−0.935410	−	0.502440i
$753$		0			0
$754$	−2.26038	−	8.18420i	−0.0823184	−	0.298051i
$755$		0			0
$756$		0			0
$757$	−19.1644			−0.696541			−0.348271	−	0.937394i	$-0.613231\pi$
$757$	−19.1644			−0.696541			−0.348271	+	0.937394i	$0.613231\pi$
$758$	6.95103	+	25.1677i	0.252473	+	0.914131i
$759$		0			0
$760$		0			0
$761$		−	39.4466i		−	1.42994i	−0.699156	−	0.714970i	$-0.746441\pi$
$761$		−	39.4466i		−	1.42994i	0.699156	−	0.714970i	$-0.253559\pi$
$762$		0			0
$763$		−	18.3334i		−	0.663713i
$764$	1.41279	−	0.844839i	0.0511130	−	0.0305652i
$765$		0			0
$766$	31.0731	−	8.58204i	1.12272	−	0.310082i
$767$			3.76573i			0.135973i
$768$		0			0
$769$	15.4822			0.558302			0.279151	−	0.960247i	$-0.409947\pi$
$769$	15.4822			0.558302			0.279151	+	0.960247i	$0.409947\pi$
$770$		0			0
$771$		0			0
$772$	−21.1936	−	35.4412i	−0.762775	−	1.27556i
$773$		−	21.3689i		−	0.768587i	−0.923211	−	0.384294i	$-0.874445\pi$
$773$		−	21.3689i		−	0.768587i	0.923211	−	0.384294i	$-0.125555\pi$
$774$		0			0
$775$		0			0
$776$	−25.9951	+	27.2201i	−0.933170	+	0.977144i
$777$		0			0
$778$	−11.1780	−	40.4724i	−0.400751	−	1.45100i
$779$		−	30.1312i		−	1.07956i
$780$		0			0
$781$		−	11.9092i		−	0.426145i
$782$	−14.7974	+	4.08688i	−0.529154	+	0.146147i
$783$		0			0
$784$	−11.1963	+	20.8446i	−0.399869	+	0.744450i
$785$		0			0
$786$		0			0
$787$		−	21.0913i		−	0.751824i	−0.926655	−	0.375912i	$-0.877329\pi$
$787$		−	21.0913i		−	0.751824i	0.926655	−	0.375912i	$-0.122671\pi$
$788$	7.87878	+	13.1754i	0.280670	+	0.469353i
$789$		0			0
$790$		0			0
$791$	−9.92166			−0.352774
$792$		0			0
$793$		−	9.49676i		−	0.337240i
$794$	−4.23599	−	15.3373i	−0.150330	−	0.544300i
$795$		0			0
$796$	20.2325	+	33.8340i	0.717123	+	1.19922i
$797$		−	16.1346i		−	0.571515i	−0.958302	−	0.285758i	$-0.907755\pi$
$797$		−	16.1346i		−	0.571515i	0.958302	−	0.285758i	$-0.0922453\pi$
$798$		0			0
$799$			15.8562i			0.560951i
$800$		0			0
$801$		0			0
$802$	23.3485	−	6.44859i	0.824464	−	0.227708i
$803$	9.78569			0.345329
$804$		0			0
$805$		0			0
$806$	4.65281	−	1.28505i	0.163888	−	0.0452641i
$807$		0			0
$808$	−8.07845	−	7.71489i	−0.284199	−	0.271409i
$809$		−	32.1159i		−	1.12913i	−0.825387	−	0.564567i	$-0.809043\pi$
$809$		−	32.1159i		−	1.12913i	0.825387	−	0.564567i	$-0.190957\pi$
$810$		0			0
$811$	36.7393			1.29009			0.645046	−	0.764144i	$-0.276838\pi$
$811$	36.7393			1.29009			0.645046	+	0.764144i	$0.276838\pi$
$812$	−14.0991	+	8.43119i	−0.494783	+	0.295877i
$813$		0			0
$814$	−2.42151	+	0.668794i	−0.0848739	+	0.0234412i
$815$		0			0
$816$		0			0
$817$			8.14216i			0.284858i
$818$	8.39176	+	30.3841i	0.293411	+	1.06236i
$819$		0			0
$820$		0			0
$821$	27.6548			0.965159			0.482579	−	0.875852i	$-0.339700\pi$
$821$	27.6548			0.965159			0.482579	+	0.875852i	$0.339700\pi$
$822$		0			0
$823$	−30.9997			−1.08058			−0.540290	−	0.841479i	$-0.681686\pi$
$823$	−30.9997			−1.08058			−0.540290	+	0.841479i	$0.681686\pi$
$824$	35.4736	+	33.8772i	1.23578	+	1.18017i
$825$		0			0
$826$	7.02305	−	1.93969i	0.244363	−	0.0674904i
$827$	52.9459			1.84111			0.920555	−	0.390612i	$-0.127737\pi$
$827$	52.9459			1.84111			0.920555	+	0.390612i	$0.127737\pi$
$828$		0			0
$829$		−	10.6962i		−	0.371494i	−0.982598	−	0.185747i	$-0.940529\pi$
$829$		−	10.6962i		−	0.371494i	0.982598	−	0.185747i	$-0.0594705\pi$
$830$		0			0
$831$		0			0
$832$	0.280232	+	6.08355i	0.00971528	+	0.210909i
$833$	12.8849			0.446435
$834$		0			0
$835$		0			0
$836$	9.25425	+	15.4755i	0.320065	+	0.535232i
$837$		0			0
$838$	−40.8240	+	11.2751i	−1.41024	+	0.389493i
$839$	−35.9077			−1.23967			−0.619836	−	0.784732i	$-0.712801\pi$
$839$	−35.9077			−1.23967			−0.619836	+	0.784732i	$0.712801\pi$
$840$		0			0
$841$	33.2003			1.14484
$842$	−0.623387	+	0.172173i	−0.0214833	+	0.00593346i
$843$		0			0
$844$	5.95064	−	3.55844i	0.204829	−	0.122487i
$845$		0			0
$846$		0			0
$847$	−3.99392			−0.137233
$848$	−3.53661	−	1.89963i	−0.121448	−	0.0652337i
$849$		0			0
$850$		0			0
$851$		−	3.30713i		−	0.113367i
$852$		0			0
$853$	−27.8867			−0.954824			−0.477412	−	0.878680i	$-0.658425\pi$
$853$	−27.8867			−0.954824			−0.477412	+	0.878680i	$0.658425\pi$
$854$	−17.7114	+	4.89168i	−0.606071	+	0.167390i
$855$		0			0
$856$	12.5586	+	11.9934i	0.429243	+	0.409926i
$857$	12.2792			0.419451			0.209725	−	0.977760i	$-0.432743\pi$
$857$	12.2792			0.419451			0.209725	+	0.977760i	$0.432743\pi$
$858$		0			0
$859$	54.1322			1.84697			0.923484	−	0.383638i	$-0.125329\pi$
$859$	54.1322			1.84697			0.923484	+	0.383638i	$0.125329\pi$
$860$		0			0
$861$		0			0
$862$	−14.1388	−	51.1925i	−0.481570	−	1.74362i
$863$			26.7638i			0.911052i	0.890223	+	0.455526i	$0.150549\pi$
$863$			26.7638i			0.911052i	−0.890223	+	0.455526i	$0.849451\pi$
$864$		0			0
$865$		0			0
$866$	15.7487	−	4.34962i	0.535163	−	0.147806i
$867$		0			0
$868$	−4.79323	−	8.01553i	−0.162693	−	0.272065i
$869$	35.7073			1.21129
$870$		0			0
$871$		−	10.9345i		−	0.370502i
$872$	34.3868	−	36.0073i	1.16448	−	1.21936i
$873$		0			0
$874$	−22.8808	+	6.31942i	−0.773953	+	0.213757i
$875$		0			0
$876$		0			0
$877$	−21.0134			−0.709572			−0.354786	−	0.934948i	$-0.615446\pi$
$877$	−21.0134			−0.709572			−0.354786	+	0.934948i	$0.615446\pi$
$878$	43.5108	−	12.0172i	1.46842	−	0.405561i
$879$		0			0
$880$		0			0
$881$			22.0846i			0.744049i	0.928223	+	0.372025i	$0.121336\pi$
$881$			22.0846i			0.744049i	−0.928223	+	0.372025i	$0.878664\pi$
$882$		0			0
$883$		−	35.7683i		−	1.20370i	−0.798609	−	0.601850i	$-0.794431\pi$
$883$		−	35.7683i		−	1.20370i	0.798609	−	0.601850i	$-0.205569\pi$
$884$	2.84626	−	1.70205i	0.0957301	−	0.0572460i
$885$		0			0
$886$	−11.1879	−	40.5082i	−0.375865	−	1.36090i
$887$		−	26.9214i		−	0.903934i	−0.892035	−	0.451967i	$-0.850723\pi$
$887$		−	26.9214i		−	0.903934i	0.892035	−	0.451967i	$-0.149277\pi$
$888$		0			0
$889$	11.0951			0.372116
$890$		0			0
$891$		0			0
$892$	30.8740	−	18.4624i	1.03374	−	0.618169i
$893$			24.5179i			0.820460i
$894$		0			0
$895$		0			0
$896$	11.2014	−	3.65620i	0.374213	−	0.122145i
$897$		0			0
$898$	−6.79749	+	1.87739i	−0.226835	+	0.0626494i
$899$			35.3616i			1.17938i
$900$		0			0
$901$			2.18612i			0.0728303i
$902$	−9.01572	−	32.6433i	−0.300191	−	1.08690i
$903$		0			0
$904$	−19.4864	−	18.6094i	−0.648108	−	0.618941i
$905$		0			0
$906$		0			0
$907$			37.7320i			1.25287i	0.779473	+	0.626436i	$0.215487\pi$
$907$			37.7320i			1.25287i	−0.779473	+	0.626436i	$0.784513\pi$
$908$	43.6881	−	26.1252i	1.44984	−	0.866994i
$909$		0			0
$910$		0			0
$911$	46.3639			1.53610			0.768052	−	0.640387i	$-0.221226\pi$
$911$	46.3639			1.53610			0.768052	+	0.640387i	$0.221226\pi$
$912$		0			0
$913$			20.8125i			0.688793i
$914$	−39.1611	+	10.8159i	−1.29533	+	0.357757i
$915$		0			0
$916$	−17.2932	−	28.9187i	−0.571383	−	0.955502i
$917$		−	15.2316i		−	0.502991i
$918$		0			0
$919$			35.3178i			1.16503i	0.812821	+	0.582513i	$0.197931\pi$
$919$			35.3178i			1.16503i	−0.812821	+	0.582513i	$0.802069\pi$
$920$		0			0
$921$		0			0
$922$	−7.96976	−	28.8562i	−0.262470	−	0.950328i
$923$	−3.38687			−0.111480
$924$		0			0
$925$		0			0
$926$	−4.67631	−	16.9315i	−0.153673	−	0.556405i
$927$		0			0
$928$	−43.5049	−	9.88581i	−1.42812	−	0.324518i
$929$		−	18.4028i		−	0.603775i	−0.953344	−	0.301888i	$-0.902383\pi$
$929$		−	18.4028i		−	0.603775i	0.953344	−	0.301888i	$-0.0976167\pi$
$930$		0			0
$931$	19.9235			0.652966
$932$	1.83203	−	1.09554i	0.0600101	−	0.0358856i
$933$		0			0
$934$	−1.21957	−	4.41571i	−0.0399056	−	0.144486i
$935$		0			0
$936$		0			0
$937$		−	22.3732i		−	0.730901i	−0.930831	−	0.365451i	$-0.880915\pi$
$937$		−	22.3732i		−	0.730901i	0.930831	−	0.365451i	$-0.119085\pi$
$938$	−20.3928	+	5.63227i	−0.665848	+	0.183900i
$939$		0			0
$940$		0			0
$941$	−4.31410			−0.140636			−0.0703179	−	0.997525i	$-0.522401\pi$
$941$	−4.31410			−0.140636			−0.0703179	+	0.997525i	$0.522401\pi$
$942$		0			0
$943$	44.5820			1.45179
$944$	17.4316	+	9.36310i	0.567350	+	0.304743i
$945$		0			0
$946$	2.43626	+	8.82099i	0.0792097	+	0.286795i
$947$	−21.7379			−0.706386			−0.353193	−	0.935551i	$-0.614904\pi$
$947$	−21.7379			−0.706386			−0.353193	+	0.935551i	$0.614904\pi$
$948$		0			0
$949$		−	2.78295i		−	0.0903385i
$950$		0			0
$951$		0			0
$952$	−4.64038	−	4.43154i	−0.150396	−	0.143627i
$953$	47.7240			1.54593			0.772966	−	0.634448i	$-0.218773\pi$
$953$	47.7240			1.54593			0.772966	+	0.634448i	$0.218773\pi$
$954$		0			0
$955$		0			0
$956$	−31.1620	+	18.6347i	−1.00785	+	0.602689i
$957$		0			0
$958$	−5.36115	−	19.4112i	−0.173211	−	0.627147i
$959$	17.3525			0.560340
$960$		0			0
$961$	10.8965			0.351501
$962$	0.190198	+	0.688653i	0.00613225	+	0.0222031i
$963$		0			0
$964$	22.8421	−	13.6594i	0.735693	−	0.439940i
$965$		0			0
$966$		0			0
$967$	22.6722			0.729089			0.364545	−	0.931186i	$-0.381225\pi$
$967$	22.6722			0.729089			0.364545	+	0.931186i	$0.381225\pi$
$968$	−7.84416	−	7.49114i	−0.252121	−	0.240774i
$969$		0			0
$970$		0			0
$971$		−	32.9474i		−	1.05733i	−0.848830	−	0.528667i	$-0.822692\pi$
$971$		−	32.9474i		−	1.05733i	0.848830	−	0.528667i	$-0.177308\pi$
$972$		0			0
$973$	−2.57664			−0.0826031
$974$	−10.6477	−	38.5523i	−0.341175	−	1.23529i
$975$		0			0
$976$	−43.9606	−	23.6127i	−1.40714	−	0.755825i
$977$	7.60198			0.243209			0.121604	−	0.992579i	$-0.461196\pi$
$977$	7.60198			0.243209			0.121604	+	0.992579i	$0.461196\pi$
$978$		0			0
$979$	−17.9292			−0.573021
$980$		0			0
$981$		0			0
$982$	33.8739	−	9.35561i	1.08096	−	0.298550i
$983$		−	12.4057i		−	0.395679i	−0.980234	−	0.197839i	$-0.936608\pi$
$983$		−	12.4057i		−	0.395679i	0.980234	−	0.197839i	$-0.0633925\pi$
$984$		0			0
$985$		0			0
$986$	6.46781	+	23.4181i	0.205977	+	0.745783i
$987$		0			0
$988$	4.40109	−	2.63182i	0.140017	−	0.0837293i
$989$	−12.0471			−0.383076
$990$		0			0
$991$		−	42.0500i		−	1.33576i	−0.744268	−	0.667882i	$-0.767201\pi$
$991$		−	42.0500i		−	1.33576i	0.744268	−	0.667882i	$-0.232799\pi$
$992$	5.62020	−	24.7331i	0.178441	−	0.785276i
$993$		0			0
$994$	1.74454	+	6.31647i	0.0553334	+	0.200346i
$995$		0			0
$996$		0			0
$997$	−52.7506			−1.67063			−0.835314	−	0.549773i	$-0.814714\pi$
$997$	−52.7506			−1.67063			−0.835314	+	0.549773i	$0.814714\pi$
$998$	3.60462	+	13.0513i	0.114102	+	0.413131i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.m.f.899.19		32
3.2	odd	2	inner	1800.2.m.f.899.13		32
4.3	odd	2		7200.2.m.f.3599.19		32
5.2	odd	4		1800.2.b.h.251.2	yes	16
5.3	odd	4		1800.2.b.i.251.15	yes	16
5.4	even	2	inner	1800.2.m.f.899.14		32
8.3	odd	2	inner	1800.2.m.f.899.18		32
8.5	even	2		7200.2.m.f.3599.16		32
12.11	even	2		7200.2.m.f.3599.17		32
15.2	even	4		1800.2.b.h.251.15	yes	16
15.8	even	4		1800.2.b.i.251.2	yes	16
15.14	odd	2	inner	1800.2.m.f.899.20		32
20.3	even	4		7200.2.b.h.4751.7		16
20.7	even	4		7200.2.b.g.4751.9		16
20.19	odd	2		7200.2.m.f.3599.15		32
24.5	odd	2		7200.2.m.f.3599.14		32
24.11	even	2	inner	1800.2.m.f.899.16		32
40.3	even	4		1800.2.b.i.251.1	yes	16
40.13	odd	4		7200.2.b.h.4751.9		16
40.19	odd	2	inner	1800.2.m.f.899.15		32
40.27	even	4		1800.2.b.h.251.16	yes	16
40.29	even	2		7200.2.m.f.3599.20		32
40.37	odd	4		7200.2.b.g.4751.7		16
60.23	odd	4		7200.2.b.h.4751.8		16
60.47	odd	4		7200.2.b.g.4751.10		16
60.59	even	2		7200.2.m.f.3599.13		32
120.29	odd	2		7200.2.m.f.3599.18		32
120.53	even	4		7200.2.b.h.4751.10		16
120.59	even	2	inner	1800.2.m.f.899.17		32
120.77	even	4		7200.2.b.g.4751.8		16
120.83	odd	4		1800.2.b.i.251.16	yes	16
120.107	odd	4		1800.2.b.h.251.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1800.2.b.h.251.1	✓	16	120.107	odd	4
1800.2.b.h.251.2	yes	16	5.2	odd	4
1800.2.b.h.251.15	yes	16	15.2	even	4
1800.2.b.h.251.16	yes	16	40.27	even	4
1800.2.b.i.251.1	yes	16	40.3	even	4
1800.2.b.i.251.2	yes	16	15.8	even	4
1800.2.b.i.251.15	yes	16	5.3	odd	4
1800.2.b.i.251.16	yes	16	120.83	odd	4
1800.2.m.f.899.13		32	3.2	odd	2	inner
1800.2.m.f.899.14		32	5.4	even	2	inner
1800.2.m.f.899.15		32	40.19	odd	2	inner
1800.2.m.f.899.16		32	24.11	even	2	inner
1800.2.m.f.899.17		32	120.59	even	2	inner
1800.2.m.f.899.18		32	8.3	odd	2	inner
1800.2.m.f.899.19		32	1.1	even	1	trivial
1800.2.m.f.899.20		32	15.14	odd	2	inner
7200.2.b.g.4751.7		16	40.37	odd	4
7200.2.b.g.4751.8		16	120.77	even	4
7200.2.b.g.4751.9		16	20.7	even	4
7200.2.b.g.4751.10		16	60.47	odd	4
7200.2.b.h.4751.7		16	20.3	even	4
7200.2.b.h.4751.8		16	60.23	odd	4
7200.2.b.h.4751.9		16	40.13	odd	4
7200.2.b.h.4751.10		16	120.53	even	4
7200.2.m.f.3599.13		32	60.59	even	2
7200.2.m.f.3599.14		32	24.5	odd	2
7200.2.m.f.3599.15		32	20.19	odd	2
7200.2.m.f.3599.16		32	8.5	even	2
7200.2.m.f.3599.17		32	12.11	even	2
7200.2.m.f.3599.18		32	120.29	odd	2
7200.2.m.f.3599.19		32	4.3	odd	2
7200.2.m.f.3599.20		32	40.29	even	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)

\(f(q)\)	\(=\)	\(q+(0.376495 + 1.36318i) q^{2} +(-1.71650 + 1.02646i) q^{4} -1.04148 q^{7} +(-2.04550 - 1.95344i) q^{8} +O(q^{10})\)	\(q+(0.376495 + 1.36318i) q^{2} +(-1.71650 + 1.02646i) q^{4} -1.04148 q^{7} +(-2.04550 - 1.95344i) q^{8} +2.67678i q^{11} +0.761250 q^{13} +(-0.392112 - 1.41972i) q^{14} +(1.89277 - 3.52384i) q^{16} -2.17822 q^{17} -3.36812 q^{19} +(-3.64893 + 1.00779i) q^{22} -4.98346i q^{23} +(0.286607 + 1.03772i) q^{26} +(1.78771 - 1.06904i) q^{28} -7.88672 q^{29} -4.48369i q^{31} +(5.51623 + 1.25348i) q^{32} +(-0.820090 - 2.96931i) q^{34} +0.663622 q^{37} +(-1.26808 - 4.59134i) q^{38} +8.94600i q^{41} -2.41742i q^{43} +(-2.74760 - 4.59471i) q^{44} +(6.79333 - 1.87624i) q^{46} -7.27940i q^{47} -5.91532 q^{49} +(-1.30669 + 0.781391i) q^{52} -1.00363i q^{53} +(2.13035 + 2.03448i) q^{56} +(-2.96931 - 10.7510i) q^{58} +4.94677i q^{59} -12.4752i q^{61} +(6.11206 - 1.68808i) q^{62} +(0.368120 + 7.99153i) q^{64} -14.3639i q^{67} +(3.73893 - 2.23585i) q^{68} -4.44908 q^{71} -3.65577i q^{73} +(0.249850 + 0.904635i) q^{74} +(5.78139 - 3.45723i) q^{76} -2.78782i q^{77} -13.3396i q^{79} +(-12.1950 + 3.36812i) q^{82} +7.77520 q^{83} +(3.29537 - 0.910146i) q^{86} +(5.22894 - 5.47535i) q^{88} +6.69806i q^{89} -0.792829 q^{91} +(5.11531 + 8.55412i) q^{92} +(9.92311 - 2.74065i) q^{94} -13.3073i q^{97} +(-2.22708 - 8.06362i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4}+O(q^{10}) \) 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

Introduction

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