LMFDB - Embedded newform 1800.2.b.d.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1800,2,Mod(251,1800)]

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, 0]))

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

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

chi := DirichletCharacter("1800.251");

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.b (of order $2$, degree $1$, 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:	$6$
Coefficient field:	6.0.2580992.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + x^{4} + 2x^{2} - 8x + 8 $ x^6 - 2x^5 + x^4 + 2x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.2
Root			$1.38078 - 0.305697i$ of defining polynomial
Character	$\chi$	$=$	1800.251
Dual form			1800.2.b.d.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38078 + 0.305697i) q^{2} +(1.81310 - 0.844199i) q^{4} -1.41421i q^{7} +(-2.24542 + 1.71991i) q^{8} +0.191427i q^{11} -2.63700i q^{13} +(0.432320 + 1.95272i) q^{14} +(2.57466 - 3.06123i) q^{16} +6.20522i q^{17} -1.52311 q^{19} +(-0.0585185 - 0.264318i) q^{22} +5.25240 q^{23} +(0.806122 + 3.64111i) q^{26} +(-1.19388 - 2.56411i) q^{28} -0.270718 q^{29} +6.20522i q^{31} +(-2.61922 + 5.01395i) q^{32} +(-1.89692 - 8.56804i) q^{34} -7.61944i q^{37} +(2.10308 - 0.465611i) q^{38} -9.22508i q^{41} +12.7755 q^{43} +(0.161602 + 0.347076i) q^{44} +(-7.25240 + 1.60564i) q^{46} -3.79383 q^{47} +5.00000 q^{49} +(-2.22615 - 4.78114i) q^{52} +8.77551 q^{53} +(2.43232 + 3.17550i) q^{56} +(0.373802 - 0.0827577i) q^{58} +10.4479i q^{59} -0.382853i q^{61} +(-1.89692 - 8.56804i) q^{62} +(2.08382 - 7.72384i) q^{64} -1.72928 q^{67} +(5.23844 + 11.2507i) q^{68} -9.72928 q^{71} +5.45856 q^{73} +(2.32924 + 10.5208i) q^{74} +(-2.76156 + 1.28581i) q^{76} +0.270718 q^{77} -14.3077i q^{79} +(2.82008 + 12.7378i) q^{82} -15.2389i q^{83} +(-17.6402 + 3.90543i) q^{86} +(-0.329237 - 0.429833i) q^{88} -3.56822i q^{89} -3.72928 q^{91} +(9.52311 - 4.43407i) q^{92} +(5.23844 - 1.15976i) q^{94} -7.31695 q^{97} +(-6.90389 + 1.52848i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 6 q^{16} + 16 q^{19} + 20 q^{22} - 4 q^{23} + 20 q^{26} + 8 q^{28} - 12 q^{29} - 22 q^{32} - 4 q^{34} + 20 q^{38} + 16 q^{43} - 12 q^{44} - 8 q^{46} - 8 q^{47} + 30 q^{49}+ \cdots - 10 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 6 * q^16 + 16 * q^19 + 20 * q^22 - 4 * q^23 + 20 * q^26 + 8 * q^28 - 12 * q^29 - 22 * q^32 - 4 * q^34 + 20 * q^38 + 16 * q^43 - 12 * q^44 - 8 * q^46 - 8 * q^47 + 30 * q^49 + 4 * q^52 - 8 * q^53 + 12 * q^56 + 20 * q^58 - 4 * q^62 + 14 * q^64 + 44 * q^68 - 48 * q^71 + 12 * q^73 + 4 * q^74 - 4 * q^76 + 12 * q^77 - 16 * q^82 - 40 * q^86 + 8 * q^88 - 12 * q^91 + 32 * q^92 + 44 * q^94 - 4 * q^97 - 10 * q^98

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 $

$2$	−1.38078	+	0.305697i	−0.976358	+	0.216160i
$2$	−1.38078	+	0.305697i	−0.976358	+	0.216160i
$3$		0			0
$3$		0			0
$4$	1.81310	−	0.844199i	0.906550	−	0.422099i
$5$		0			0
$5$		0			0
$6$		0			0
$7$		−	1.41421i		−	0.534522i	−0.963624	−	0.267261i	$-0.913881\pi$
$7$		−	1.41421i		−	0.534522i	0.963624	−	0.267261i	$-0.0861187\pi$
$8$	−2.24542	+	1.71991i	−0.793876	+	0.608080i
$9$		0			0
$10$		0			0
$11$			0.191427i			0.0577173i	0.999584	+	0.0288587i	$0.00918727\pi$
$11$			0.191427i			0.0577173i	−0.999584	+	0.0288587i	$0.990813\pi$
$12$		0			0
$13$		−	2.63700i		−	0.731372i	−0.930738	−	0.365686i	$-0.880834\pi$
$13$		−	2.63700i		−	0.731372i	0.930738	−	0.365686i	$-0.119166\pi$
$14$	0.432320	+	1.95272i	0.115542	+	0.521885i
$15$		0			0
$16$	2.57466	−	3.06123i	0.643664	−	0.765308i
$17$			6.20522i			1.50499i	0.658599	+	0.752494i	$0.271149\pi$
$17$			6.20522i			1.50499i	−0.658599	+	0.752494i	$0.728851\pi$
$18$		0			0
$19$	−1.52311			−0.349426			−0.174713	−	0.984619i	$-0.555900\pi$
$19$	−1.52311			−0.349426			−0.174713	+	0.984619i	$0.555900\pi$
$20$		0			0
$21$		0			0
$22$	−0.0585185	−	0.264318i	−0.0124762	−	0.0563528i
$23$	5.25240			1.09520			0.547600	−	0.836740i	$-0.315542\pi$
$23$	5.25240			1.09520			0.547600	+	0.836740i	$0.315542\pi$
$24$		0			0
$25$		0			0
$26$	0.806122	+	3.64111i	0.158094	+	0.714081i
$27$		0			0
$28$	−1.19388	−	2.56411i	−0.225622	−	0.484571i
$29$	−0.270718			−0.0502711			−0.0251356	−	0.999684i	$-0.508002\pi$
$29$	−0.270718			−0.0502711			−0.0251356	+	0.999684i	$0.508002\pi$
$30$		0			0
$31$			6.20522i			1.11449i	0.830348	+	0.557245i	$0.188142\pi$
$31$			6.20522i			1.11449i	−0.830348	+	0.557245i	$0.811858\pi$
$32$	−2.61922	+	5.01395i	−0.463017	+	0.886349i
$33$		0			0
$34$	−1.89692	−	8.56804i	−0.325318	−	1.46941i
$35$		0			0
$36$		0			0
$37$		−	7.61944i		−	1.25263i	−0.779571	−	0.626314i	$-0.784563\pi$
$37$		−	7.61944i		−	1.25263i	0.779571	−	0.626314i	$-0.215437\pi$
$38$	2.10308	−	0.465611i	0.341165	−	0.0755321i
$39$		0			0
$40$		0			0
$41$		−	9.22508i		−	1.44071i	−0.693603	−	0.720357i	$-0.743978\pi$
$41$		−	9.22508i		−	1.44071i	0.693603	−	0.720357i	$-0.256022\pi$
$42$		0			0
$43$	12.7755			1.94825			0.974124	−	0.226016i	$-0.0725702\pi$
$43$	12.7755			1.94825			0.974124	+	0.226016i	$0.0725702\pi$
$44$	0.161602	+	0.347076i	0.0243625	+	0.0523236i
$45$		0			0
$46$	−7.25240	+	1.60564i	−1.06931	+	0.236739i
$47$	−3.79383			−0.553387			−0.276694	−	0.960958i	$-0.589239\pi$
$47$	−3.79383			−0.553387			−0.276694	+	0.960958i	$0.589239\pi$
$48$		0			0
$49$	5.00000			0.714286
$50$		0			0
$51$		0			0
$52$	−2.22615	−	4.78114i	−0.308712	−	0.663025i
$53$	8.77551			1.20541			0.602705	−	0.797964i	$-0.294090\pi$
$53$	8.77551			1.20541			0.602705	+	0.797964i	$0.294090\pi$
$54$		0			0
$55$		0			0
$56$	2.43232	+	3.17550i	0.325032	+	0.424344i
$57$		0			0
$58$	0.373802	−	0.0827577i	0.0490826	−	0.0108666i
$59$			10.4479i			1.36020i	0.733121	+	0.680098i	$0.238063\pi$
$59$			10.4479i			1.36020i	−0.733121	+	0.680098i	$0.761937\pi$
$60$		0			0
$61$		−	0.382853i		−	0.0490194i	−0.999700	−	0.0245097i	$-0.992198\pi$
$61$		−	0.382853i		−	0.0490194i	0.999700	−	0.0245097i	$-0.00780245\pi$
$62$	−1.89692	−	8.56804i	−0.240909	−	1.08814i
$63$		0			0
$64$	2.08382	−	7.72384i	0.260477	−	0.965480i
$65$		0			0
$66$		0			0
$67$	−1.72928			−0.211265			−0.105633	−	0.994405i	$-0.533687\pi$
$67$	−1.72928			−0.211265			−0.105633	+	0.994405i	$0.533687\pi$
$68$	5.23844	+	11.2507i	0.635255	+	1.36435i
$69$		0			0
$70$		0			0
$71$	−9.72928			−1.15465			−0.577327	−	0.816513i	$-0.695904\pi$
$71$	−9.72928			−1.15465			−0.577327	+	0.816513i	$0.695904\pi$
$72$		0			0
$73$	5.45856			0.638877			0.319438	−	0.947607i	$-0.396506\pi$
$73$	5.45856			0.638877			0.319438	+	0.947607i	$0.396506\pi$
$74$	2.32924	+	10.5208i	0.270768	+	1.22301i
$75$		0			0
$76$	−2.76156	+	1.28581i	−0.316772	+	0.147493i
$77$	0.270718			0.0308512
$78$		0			0
$79$		−	14.3077i		−	1.60974i	−0.593454	−	0.804868i	$-0.702236\pi$
$79$		−	14.3077i		−	1.60974i	0.593454	−	0.804868i	$-0.297764\pi$
$80$		0			0
$81$		0			0
$82$	2.82008	+	12.7378i	0.311425	+	1.40665i
$83$		−	15.2389i		−	1.67268i	−0.548208	−	0.836342i	$-0.684690\pi$
$83$		−	15.2389i		−	1.67268i	0.548208	−	0.836342i	$-0.315310\pi$
$84$		0			0
$85$		0			0
$86$	−17.6402	+	3.90543i	−1.90219	+	0.421134i
$87$		0			0
$88$	−0.329237	−	0.429833i	−0.0350968	−	0.0458204i
$89$		−	3.56822i		−	0.378231i	−0.981955	−	0.189115i	$-0.939438\pi$
$89$		−	3.56822i		−	0.378231i	0.981955	−	0.189115i	$-0.0605620\pi$
$90$		0			0
$91$	−3.72928			−0.390935
$92$	9.52311	−	4.43407i	0.992853	−	0.462283i
$93$		0			0
$94$	5.23844	−	1.15976i	0.540304	−	0.119620i
$95$		0			0
$96$		0			0
$97$	−7.31695			−0.742923			−0.371462	−	0.928448i	$-0.621143\pi$
$97$	−7.31695			−0.742923			−0.371462	+	0.928448i	$0.621143\pi$
$98$	−6.90389	+	1.52848i	−0.697399	+	0.154400i
$99$		0			0
$100$		0			0
$101$	15.5510			1.54738			0.773692	−	0.633562i	$-0.218408\pi$
$101$	15.5510			1.54738			0.773692	+	0.633562i	$0.218408\pi$
$102$		0			0
$103$		−	2.08863i		−	0.205799i	−0.994692	−	0.102899i	$-0.967188\pi$
$103$		−	2.08863i		−	0.205799i	0.994692	−	0.102899i	$-0.0328120\pi$
$104$	4.53540	+	5.92117i	0.444733	+	0.580619i
$105$		0			0
$106$	−12.1170	+	2.68264i	−1.17691	+	0.260561i
$107$		−	2.82843i		−	0.273434i	−0.990610	−	0.136717i	$-0.956345\pi$
$107$		−	2.82843i		−	0.273434i	0.990610	−	0.136717i	$-0.0436552\pi$
$108$		0			0
$109$		−	5.27400i		−	0.505158i	−0.967576	−	0.252579i	$-0.918721\pi$
$109$		−	5.27400i		−	0.505158i	0.967576	−	0.252579i	$-0.0812787\pi$
$110$		0			0
$111$		0			0
$112$	−4.32924	−	3.64111i	−0.409074	−	0.344053i
$113$		−	5.82237i		−	0.547722i	−0.961769	−	0.273861i	$-0.911699\pi$
$113$		−	5.82237i		−	0.547722i	0.961769	−	0.273861i	$-0.0883009\pi$
$114$		0			0
$115$		0			0
$116$	−0.490839	+	0.228540i	−0.0455733	+	0.0212194i
$117$		0			0
$118$	−3.19388	−	14.4262i	−0.294020	−	1.32804i
$119$	8.77551			0.804450
$120$		0			0
$121$	10.9634			0.996669
$122$	0.117037	+	0.528636i	0.0105960	+	0.0478604i
$123$		0			0
$124$	5.23844	+	11.2507i	0.470426	+	1.01034i
$125$		0			0
$126$		0			0
$127$			20.5388i			1.82252i	0.411829	+	0.911261i	$0.364890\pi$
$127$			20.5388i			1.82252i	−0.411829	+	0.911261i	$0.635110\pi$
$128$	−0.516138	+	11.3019i	−0.0456206	+	0.998959i
$129$		0			0
$130$		0			0
$131$		−	13.5679i		−	1.18543i	−0.805413	−	0.592715i	$-0.798056\pi$
$131$		−	13.5679i		−	1.18543i	0.805413	−	0.592715i	$-0.201944\pi$
$132$		0			0
$133$			2.15401i			0.186776i
$134$	2.38776	−	0.528636i	0.206271	−	0.0456672i
$135$		0			0
$136$	−10.6724	−	13.9333i	−0.915153	−	1.19477i
$137$			4.72563i			0.403738i	0.979413	+	0.201869i	$0.0647015\pi$
$137$			4.72563i			0.403738i	−0.979413	+	0.201869i	$0.935298\pi$
$138$		0			0
$139$	15.7572			1.33651			0.668254	−	0.743934i	$-0.267042\pi$
$139$	15.7572			1.33651			0.668254	+	0.743934i	$0.267042\pi$
$140$		0			0
$141$		0			0
$142$	13.4340	−	2.97421i	1.12735	−	0.249590i
$143$	0.504792			0.0422129
$144$		0			0
$145$		0			0
$146$	−7.53707	+	1.66866i	−0.623772	+	0.138100i
$147$		0			0
$148$	−6.43232	−	13.8148i	−0.528733	−	1.13557i
$149$	7.72928			0.633207			0.316604	−	0.948558i	$-0.397457\pi$
$149$	7.72928			0.633207			0.316604	+	0.948558i	$0.397457\pi$
$150$		0			0
$151$			22.2098i			1.80741i	0.428158	+	0.903704i	$0.359163\pi$
$151$			22.2098i			1.80741i	−0.428158	+	0.903704i	$0.640837\pi$
$152$	3.42003	−	2.61962i	0.277401	−	0.212479i
$153$		0			0
$154$	−0.373802	+	0.0827577i	−0.0301218	+	0.00666880i
$155$		0			0
$156$		0			0
$157$		−	8.00229i		−	0.638652i	−0.947645	−	0.319326i	$-0.896543\pi$
$157$		−	8.00229i		−	0.638652i	0.947645	−	0.319326i	$-0.103457\pi$
$158$	4.37380	+	19.7557i	0.347961	+	1.57168i
$159$		0			0
$160$		0			0
$161$		−	7.42801i		−	0.585409i
$162$		0			0
$163$	0.953771			0.0747051			0.0373526	−	0.999302i	$-0.488108\pi$
$163$	0.953771			0.0747051			0.0373526	+	0.999302i	$0.488108\pi$
$164$	−7.78780	−	16.7260i	−0.608125	−	1.30608i
$165$		0			0
$166$	4.65847	+	21.0415i	0.361568	+	1.63314i
$167$	−11.7572			−0.909799			−0.454899	−	0.890543i	$-0.650325\pi$
$167$	−11.7572			−0.909799			−0.454899	+	0.890543i	$0.650325\pi$
$168$		0			0
$169$	6.04623			0.465095
$170$		0			0
$171$		0			0
$172$	23.1633	−	10.7851i	1.76618	−	0.822354i
$173$	−3.22449			−0.245153			−0.122577	−	0.992459i	$-0.539116\pi$
$173$	−3.22449			−0.245153			−0.122577	+	0.992459i	$0.539116\pi$
$174$		0			0
$175$		0			0
$176$	0.586002	+	0.492858i	0.0441715	+	0.0371506i
$177$		0			0
$178$	1.09079	+	4.92693i	0.0817585	+	0.369289i
$179$		−	12.6019i		−	0.941908i	−0.882158	−	0.470954i	$-0.843910\pi$
$179$		−	12.6019i		−	0.941908i	0.882158	−	0.470954i	$-0.156090\pi$
$180$		0			0
$181$		−	24.1070i		−	1.79186i	−0.444195	−	0.895930i	$-0.646510\pi$
$181$		−	24.1070i		−	1.79186i	0.444195	−	0.895930i	$-0.353490\pi$
$182$	5.14931	−	1.14003i	0.381692	−	0.0845046i
$183$		0			0
$184$	−11.7938	+	9.03365i	−0.869453	+	0.665970i
$185$		0			0
$186$		0			0
$187$	−1.18785			−0.0868639
$188$	−6.87859	+	3.20275i	−0.501673	+	0.233585i
$189$		0			0
$190$		0			0
$191$	10.9171			0.789936			0.394968	−	0.918695i	$-0.370756\pi$
$191$	10.9171			0.789936			0.394968	+	0.918695i	$0.370756\pi$
$192$		0			0
$193$	15.3169			1.10254			0.551269	−	0.834328i	$-0.314144\pi$
$193$	15.3169			1.10254			0.551269	+	0.834328i	$0.314144\pi$
$194$	10.1031	−	2.23677i	0.725359	−	0.160590i
$195$		0			0
$196$	9.06550	−	4.22099i	0.647535	−	0.301500i
$197$	17.0462			1.21449			0.607247	−	0.794513i	$-0.292274\pi$
$197$	17.0462			1.21449			0.607247	+	0.794513i	$0.292274\pi$
$198$		0			0
$199$			4.72563i			0.334991i	0.985873	+	0.167496i	$0.0535680\pi$
$199$			4.72563i			0.334991i	−0.985873	+	0.167496i	$0.946432\pi$
$200$		0			0
$201$		0			0
$202$	−21.4725	+	4.75390i	−1.51080	+	0.334483i
$203$			0.382853i			0.0268710i
$204$		0			0
$205$		0			0
$206$	0.638488	+	2.88394i	0.0444856	+	0.200933i
$207$		0			0
$208$	−8.07247	−	6.78937i	−0.559725	−	0.470758i
$209$		−	0.291565i		−	0.0201680i
$210$		0			0
$211$	16.8401			1.15932			0.579659	−	0.814859i	$-0.303186\pi$
$211$	16.8401			1.15932			0.579659	+	0.814859i	$0.303186\pi$
$212$	15.9109	−	7.40828i	1.09276	−	0.508803i
$213$		0			0
$214$	0.864641	+	3.90543i	0.0591056	+	0.266970i
$215$		0			0
$216$		0			0
$217$	8.77551			0.595720
$218$	1.61224	+	7.28223i	0.109195	+	0.493215i
$219$		0			0
$220$		0			0
$221$	16.3632			1.10071
$222$		0			0
$223$			22.3099i			1.49398i	0.664833	+	0.746992i	$0.268503\pi$
$223$			22.3099i			1.49398i	−0.664833	+	0.746992i	$0.731497\pi$
$224$	7.09079	+	3.70414i	0.473774	+	0.247493i
$225$		0			0
$226$	1.77988	+	8.03940i	0.118396	+	0.534773i
$227$			8.86813i			0.588599i	0.955713	+	0.294299i	$0.0950863\pi$
$227$			8.86813i			0.588599i	−0.955713	+	0.294299i	$0.904914\pi$
$228$		0			0
$229$			21.2786i			1.40613i	0.711126	+	0.703064i	$0.248185\pi$
$229$			21.2786i			1.40613i	−0.711126	+	0.703064i	$0.751815\pi$
$230$		0			0
$231$		0			0
$232$	0.607876	−	0.465611i	0.0399090	−	0.0305689i
$233$		−	15.0734i		−	0.987488i	−0.869607	−	0.493744i	$-0.835628\pi$
$233$		−	15.0734i		−	0.987488i	0.869607	−	0.493744i	$-0.164372\pi$
$234$		0			0
$235$		0			0
$236$	8.82008	+	18.9430i	0.574138	+	1.23309i
$237$		0			0
$238$	−12.1170	+	2.68264i	−0.785431	+	0.173890i
$239$	19.0462			1.23200			0.615999	−	0.787747i	$-0.288753\pi$
$239$	19.0462			1.23200			0.615999	+	0.787747i	$0.288753\pi$
$240$		0			0
$241$	18.5048			1.19200			0.595999	−	0.802985i	$-0.296756\pi$
$241$	18.5048			1.19200			0.595999	+	0.802985i	$0.296756\pi$
$242$	−15.1380	+	3.35146i	−0.973105	+	0.215440i
$243$		0			0
$244$	−0.323204	−	0.694151i	−0.0206910	−	0.0444385i
$245$		0			0
$246$		0			0
$247$			4.01645i			0.255561i
$248$	−10.6724	−	13.9333i	−0.677700	−	0.884767i
$249$		0			0
$250$		0			0
$251$		−	16.8186i		−	1.06158i	−0.847503	−	0.530790i	$-0.821895\pi$
$251$		−	16.8186i		−	1.06158i	0.847503	−	0.530790i	$-0.178105\pi$
$252$		0			0
$253$			1.00545i			0.0632120i
$254$	−6.27864	−	28.3595i	−0.393957	−	1.77943i
$255$		0			0
$256$	−2.74229	−	15.7632i	−0.171393	−	0.985203i
$257$		−	9.79936i		−	0.611267i	−0.952149	−	0.305634i	$-0.901132\pi$
$257$		−	9.79936i		−	0.611267i	0.952149	−	0.305634i	$-0.0988682\pi$
$258$		0			0
$259$	−10.7755			−0.669558
$260$		0			0
$261$		0			0
$262$	4.14765	+	18.7342i	0.256243	+	1.15740i
$263$	5.79383			0.357263			0.178632	−	0.983916i	$-0.442833\pi$
$263$	5.79383			0.357263			0.178632	+	0.983916i	$0.442833\pi$
$264$		0			0
$265$		0			0
$266$	−0.658473	−	2.97421i	−0.0403736	−	0.182360i
$267$		0			0
$268$	−3.13536	+	1.45986i	−0.191523	+	0.0891750i
$269$	−15.1878			−0.926019			−0.463010	−	0.886353i	$-0.653230\pi$
$269$	−15.1878			−0.926019			−0.463010	+	0.886353i	$0.653230\pi$
$270$		0			0
$271$			10.1304i			0.615377i	0.951487	+	0.307689i	$0.0995555\pi$
$271$			10.1304i			0.615377i	−0.951487	+	0.307689i	$0.900444\pi$
$272$	18.9956	+	15.9763i	1.15178	+	0.968706i
$273$		0			0
$274$	−1.44461	−	6.52505i	−0.0872721	−	0.394193i
$275$		0			0
$276$		0			0
$277$		−	14.7559i		−	0.886595i	−0.896375	−	0.443298i	$-0.853809\pi$
$277$		−	14.7559i		−	0.886595i	0.896375	−	0.443298i	$-0.146191\pi$
$278$	−21.7572	+	4.81692i	−1.30491	+	0.288900i
$279$		0			0
$280$		0			0
$281$			21.5442i			1.28522i	0.766193	+	0.642611i	$0.222149\pi$
$281$			21.5442i			1.28522i	−0.766193	+	0.642611i	$0.777851\pi$
$282$		0			0
$283$	−18.2707			−1.08608			−0.543041	−	0.839706i	$-0.682727\pi$
$283$	−18.2707			−1.08608			−0.543041	+	0.839706i	$0.682727\pi$
$284$	−17.6402	+	8.21345i	−1.04675	+	0.487379i
$285$		0			0
$286$	−0.697006	+	0.154313i	−0.0412149	+	0.00912474i
$287$	−13.0462			−0.770095
$288$		0			0
$289$	−21.5048			−1.26499
$290$		0			0
$291$		0			0
$292$	9.89692	−	4.60811i	0.579173	−	0.269669i
$293$	6.00000			0.350524			0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000			0.350524			0.175262	+	0.984522i	$0.443923\pi$
$294$		0			0
$295$		0			0
$296$	13.1047	+	17.1088i	0.761698	+	0.994431i
$297$		0			0
$298$	−10.6724	+	2.36282i	−0.618237	+	0.136874i
$299$		−	13.8506i		−	0.800999i
$300$		0			0
$301$		−	18.0673i		−	1.04138i
$302$	−6.78946	−	30.6668i	−0.390690	−	1.76468i
$303$		0			0
$304$	−3.92150	+	4.66261i	−0.224913	+	0.267419i
$305$		0			0
$306$		0			0
$307$	−22.5048			−1.28442			−0.642208	−	0.766530i	$-0.721982\pi$
$307$	−22.5048			−1.28442			−0.642208	+	0.766530i	$0.721982\pi$
$308$	0.490839	−	0.228540i	0.0279681	−	0.0130223i
$309$		0			0
$310$		0			0
$311$	−31.0462			−1.76047			−0.880235	−	0.474538i	$-0.842615\pi$
$311$	−31.0462			−1.76047			−0.880235	+	0.474538i	$0.842615\pi$
$312$		0			0
$313$	2.23407			0.126277			0.0631387	−	0.998005i	$-0.479889\pi$
$313$	2.23407			0.126277			0.0631387	+	0.998005i	$0.479889\pi$
$314$	2.44627	+	11.0494i	0.138051	+	0.623553i
$315$		0			0
$316$	−12.0785	−	25.9412i	−0.679469	−	1.45931i
$317$	16.5048			0.927001			0.463501	−	0.886097i	$-0.346593\pi$
$317$	16.5048			0.927001			0.463501	+	0.886097i	$0.346593\pi$
$318$		0			0
$319$		−	0.0518227i		−	0.00290151i
$320$		0			0
$321$		0			0
$322$	2.27072	+	10.2564i	0.126542	+	0.571569i
$323$		−	9.45126i		−	0.525882i
$324$		0			0
$325$		0			0
$326$	−1.31695	+	0.291565i	−0.0729389	+	0.0161483i
$327$		0			0
$328$	15.8663	+	20.7142i	0.876070	+	1.14375i
$329$			5.36529i			0.295798i
$330$		0			0
$331$	−12.9817			−0.713538			−0.356769	−	0.934193i	$-0.616122\pi$
$331$	−12.9817			−0.713538			−0.356769	+	0.934193i	$0.616122\pi$
$332$	−12.8646	−	27.6296i	−0.706039	−	1.51637i
$333$		0			0
$334$	16.2341	−	3.59413i	0.888289	−	0.196662i
$335$		0			0
$336$		0			0
$337$	27.0096			1.47131			0.735653	−	0.677359i	$-0.236875\pi$
$337$	27.0096			1.47131			0.735653	+	0.677359i	$0.236875\pi$
$338$	−8.34850	+	1.84831i	−0.454099	+	0.100535i
$339$		0			0
$340$		0			0
$341$	−1.18785			−0.0643254
$342$		0			0
$343$		−	16.9706i		−	0.916324i
$344$	−28.6864	+	21.9727i	−1.54667	+	1.18469i
$345$		0			0
$346$	4.45231	−	0.985716i	0.239357	−	0.0529924i
$347$			5.07372i			0.272372i	0.990683	+	0.136186i	$0.0434844\pi$
$347$			5.07372i			0.272372i	−0.990683	+	0.136186i	$0.956516\pi$
$348$		0			0
$349$			20.1300i			1.07754i	0.842454	+	0.538768i	$0.181110\pi$
$349$			20.1300i			1.07754i	−0.842454	+	0.538768i	$0.818890\pi$
$350$		0			0
$351$		0			0
$352$	−0.959804	−	0.501389i	−0.0511577	−	0.0267241i
$353$		−	14.3077i		−	0.761519i	−0.924674	−	0.380760i	$-0.875663\pi$
$353$		−	14.3077i		−	0.761519i	0.924674	−	0.380760i	$-0.124337\pi$
$354$		0			0
$355$		0			0
$356$	−3.01229	−	6.46954i	−0.159651	−	0.342885i
$357$		0			0
$358$	3.85235	+	17.4004i	0.203603	+	0.919640i
$359$	−31.8217			−1.67949			−0.839744	−	0.542983i	$-0.817295\pi$
$359$	−31.8217			−1.67949			−0.839744	+	0.542983i	$0.817295\pi$
$360$		0			0
$361$	−16.6801			−0.877901
$362$	7.36943	+	33.2864i	0.387329	+	1.74950i
$363$		0			0
$364$	−6.76156	+	3.14826i	−0.354402	+	0.165013i
$365$		0			0
$366$		0			0
$367$			22.9844i			1.19977i	0.800085	+	0.599887i	$0.204788\pi$
$367$			22.9844i			1.19977i	−0.800085	+	0.599887i	$0.795212\pi$
$368$	13.5231	−	16.0788i	0.704941	−	0.838166i
$369$		0			0
$370$		0			0
$371$		−	12.4104i		−	0.644318i
$372$		0			0
$373$			14.2423i			0.737437i	0.929541	+	0.368718i	$0.120203\pi$
$373$			14.2423i			0.737437i	−0.929541	+	0.368718i	$0.879797\pi$
$374$	1.64015	−	0.363120i	0.0848102	−	0.0187765i
$375$		0			0
$376$	8.51875	−	6.52505i	0.439321	−	0.336504i
$377$			0.713884i			0.0367669i
$378$		0			0
$379$	−8.71096			−0.447452			−0.223726	−	0.974652i	$-0.571822\pi$
$379$	−8.71096			−0.447452			−0.223726	+	0.974652i	$0.571822\pi$
$380$		0			0
$381$		0			0
$382$	−15.0741	+	3.33733i	−0.771260	+	0.170753i
$383$	−18.7110			−0.956085			−0.478043	−	0.878337i	$-0.658654\pi$
$383$	−18.7110			−0.956085			−0.478043	+	0.878337i	$0.658654\pi$
$384$		0			0
$385$		0			0
$386$	−21.1493	+	4.68234i	−1.07647	+	0.238325i
$387$		0			0
$388$	−13.2663	+	6.17696i	−0.673497	+	0.313588i
$389$	−27.0096			−1.36944			−0.684720	−	0.728806i	$-0.740076\pi$
$389$	−27.0096			−1.36944			−0.684720	+	0.728806i	$0.740076\pi$
$390$		0			0
$391$			32.5923i			1.64826i
$392$	−11.2271	+	8.59955i	−0.567054	+	0.434343i
$393$		0			0
$394$	−23.5371	+	5.21098i	−1.18578	+	0.262525i
$395$		0			0
$396$		0			0
$397$		−	25.3952i		−	1.27455i	−0.770638	−	0.637274i	$-0.780062\pi$
$397$		−	25.3952i		−	1.27455i	0.770638	−	0.637274i	$-0.219938\pi$
$398$	−1.44461	−	6.52505i	−0.0724118	−	0.327071i
$399$		0			0
$400$		0			0
$401$			6.01380i			0.300315i	0.988662	+	0.150157i	$0.0479780\pi$
$401$			6.01380i			0.300315i	−0.988662	+	0.150157i	$0.952022\pi$
$402$		0			0
$403$	16.3632			0.815108
$404$	28.1955	−	13.1282i	1.40278	−	0.653150i
$405$		0			0
$406$	−0.117037	−	0.528636i	−0.00580845	−	0.0262358i
$407$	1.45856			0.0722983
$408$		0			0
$409$	−19.5510			−0.966736			−0.483368	−	0.875417i	$-0.660587\pi$
$409$	−19.5510			−0.966736			−0.483368	+	0.875417i	$0.660587\pi$
$410$		0			0
$411$		0			0
$412$	−1.76322	−	3.78690i	−0.0868676	−	0.186567i
$413$	14.7755			0.727055
$414$		0			0
$415$		0			0
$416$	13.2218	+	6.90689i	0.648251	+	0.338638i
$417$		0			0
$418$	0.0891304	+	0.402586i	0.00435951	+	0.0196911i
$419$			1.96258i			0.0958784i	0.998850	+	0.0479392i	$0.0152654\pi$
$419$			1.96258i			0.0958784i	−0.998850	+	0.0479392i	$0.984735\pi$
$420$		0			0
$421$		−	4.30802i		−	0.209960i	−0.994474	−	0.104980i	$-0.966522\pi$
$421$		−	4.30802i		−	0.209960i	0.994474	−	0.104980i	$-0.0334778\pi$
$422$	−23.2524	+	5.14795i	−1.13191	+	0.250598i
$423$		0			0
$424$	−19.7047	+	15.0931i	−0.956945	+	0.732985i
$425$		0			0
$426$		0			0
$427$	−0.541436			−0.0262019
$428$	−2.38776	−	5.12822i	−0.115417	−	0.247882i
$429$		0			0
$430$		0			0
$431$	−11.8217			−0.569433			−0.284717	−	0.958612i	$-0.591899\pi$
$431$	−11.8217			−0.569433			−0.284717	+	0.958612i	$0.591899\pi$
$432$		0			0
$433$	−9.45856			−0.454550			−0.227275	−	0.973831i	$-0.572982\pi$
$433$	−9.45856			−0.454550			−0.227275	+	0.973831i	$0.572982\pi$
$434$	−12.1170	+	2.68264i	−0.581636	+	0.128771i
$435$		0			0
$436$	−4.45231	−	9.56229i	−0.213227	−	0.457950i
$437$	−8.00000			−0.382692
$438$		0			0
$439$			16.0393i			0.765516i	0.923849	+	0.382758i	$0.125026\pi$
$439$			16.0393i			0.765516i	−0.923849	+	0.382758i	$0.874974\pi$
$440$		0			0
$441$		0			0
$442$	−22.5939	+	5.00217i	−1.07468	+	0.237929i
$443$			25.0730i			1.19125i	0.803261	+	0.595627i	$0.203096\pi$
$443$			25.0730i			1.19125i	−0.803261	+	0.595627i	$0.796904\pi$
$444$		0			0
$445$		0			0
$446$	−6.82008	−	30.8051i	−0.322940	−	1.45866i
$447$		0			0
$448$	−10.9232	−	2.94696i	−0.516071	−	0.139231i
$449$			4.24264i			0.200223i	0.994976	+	0.100111i	$0.0319199\pi$
$449$			4.24264i			0.200223i	−0.994976	+	0.100111i	$0.968080\pi$
$450$		0			0
$451$	1.76593			0.0831542
$452$	−4.91524	−	10.5565i	−0.231193	−	0.496538i
$453$		0			0
$454$	−2.71096	−	12.2449i	−0.127232	−	0.574683i
$455$		0			0
$456$		0			0
$457$	−28.8680			−1.35039			−0.675193	−	0.737641i	$-0.735940\pi$
$457$	−28.8680			−1.35039			−0.675193	+	0.737641i	$0.735940\pi$
$458$	−6.50479	−	29.3810i	−0.303949	−	1.37288i
$459$		0			0
$460$		0			0
$461$	36.7389			1.71110			0.855550	−	0.517721i	$-0.173219\pi$
$461$	36.7389			1.71110			0.855550	+	0.517721i	$0.173219\pi$
$462$		0			0
$463$			16.6136i			0.772100i	0.922478	+	0.386050i	$0.126161\pi$
$463$			16.6136i			0.772100i	−0.922478	+	0.386050i	$0.873839\pi$
$464$	−0.697006	+	0.828731i	−0.0323577	+	0.0384729i
$465$		0			0
$466$	4.60788	+	20.8130i	0.213456	+	0.964142i
$467$			1.47959i			0.0684673i	0.999414	+	0.0342336i	$0.0108990\pi$
$467$			1.47959i			0.0684673i	−0.999414	+	0.0342336i	$0.989101\pi$
$468$		0			0
$469$			2.44557i			0.112926i
$470$		0			0
$471$		0			0
$472$	−17.9694	−	23.4598i	−0.827108	−	1.07983i
$473$			2.44557i			0.112448i
$474$		0			0
$475$		0			0
$476$	15.9109	−	7.40828i	0.729274	−	0.339558i
$477$		0			0
$478$	−26.2986	+	5.82237i	−1.20287	+	0.266309i
$479$	2.81215			0.128491			0.0642453	−	0.997934i	$-0.479536\pi$
$479$	2.81215			0.128491			0.0642453	+	0.997934i	$0.479536\pi$
$480$		0			0
$481$	−20.0925			−0.916137
$482$	−25.5510	+	5.65685i	−1.16382	+	0.257663i
$483$		0			0
$484$	19.8776	−	9.25525i	0.903530	−	0.420693i
$485$		0			0
$486$		0			0
$487$		−	16.9447i		−	0.767835i	−0.923367	−	0.383918i	$-0.874575\pi$
$487$		−	16.9447i		−	0.767835i	0.923367	−	0.383918i	$-0.125425\pi$
$488$	0.658473	+	0.859666i	0.0298077	+	0.0389153i
$489$		0			0
$490$		0			0
$491$			26.0696i			1.17650i	0.808678	+	0.588252i	$0.200184\pi$
$491$			26.0696i			1.17650i	−0.808678	+	0.588252i	$0.799816\pi$
$492$		0			0
$493$		−	1.67987i		−	0.0756574i
$494$	−1.22782	−	5.54583i	−0.0552421	−	0.249519i
$495$		0			0
$496$	18.9956	+	15.9763i	0.852929	+	0.717358i
$497$			13.7593i			0.617188i
$498$		0			0
$499$	22.5327			1.00870			0.504351	−	0.863499i	$-0.331732\pi$
$499$	22.5327			1.00870			0.504351	+	0.863499i	$0.331732\pi$
$500$		0			0
$501$		0			0
$502$	5.14139	+	23.2228i	0.229472	+	1.03648i
$503$	−8.80342			−0.392525			−0.196262	−	0.980551i	$-0.562880\pi$
$503$	−8.80342			−0.392525			−0.196262	+	0.980551i	$0.562880\pi$
$504$		0			0
$505$		0			0
$506$	−0.307362	−	1.38830i	−0.0136639	−	0.0617176i
$507$		0			0
$508$	17.3388	+	37.2389i	0.769286	+	1.65221i
$509$	−20.6339			−0.914581			−0.457291	−	0.889317i	$-0.651180\pi$
$509$	−20.6339			−0.914581			−0.457291	+	0.889317i	$0.651180\pi$
$510$		0			0
$511$		−	7.71957i		−	0.341494i
$512$	8.60527	+	20.9272i	0.380303	+	0.924862i
$513$		0			0
$514$	2.99563	+	13.5307i	0.132132	+	0.596815i
$515$		0			0
$516$		0			0
$517$		−	0.726241i		−	0.0319400i
$518$	14.8786	−	3.29404i	0.653728	−	0.144732i
$519$		0			0
$520$		0			0
$521$		−	8.55066i		−	0.374611i	−0.982302	−	0.187306i	$-0.940025\pi$
$521$		−	8.55066i		−	0.374611i	0.982302	−	0.187306i	$-0.0599755\pi$
$522$		0			0
$523$	−33.0096			−1.44341			−0.721704	−	0.692202i	$-0.756641\pi$
$523$	−33.0096			−1.44341			−0.721704	+	0.692202i	$0.756641\pi$
$524$	−11.4540	−	24.5999i	−0.500369	−	1.07465i
$525$		0			0
$526$	−8.00000	+	1.77116i	−0.348817	+	0.0772261i
$527$	−38.5048			−1.67730
$528$		0			0
$529$	4.58767			0.199464
$530$		0			0
$531$		0			0
$532$	1.81841	+	3.90543i	0.0788382	+	0.169322i
$533$	−24.3265			−1.05370
$534$		0			0
$535$		0			0
$536$	3.88296	−	2.97421i	0.167718	−	0.128466i
$537$		0			0
$538$	20.9711	−	4.64287i	0.904126	−	0.200169i
$539$			0.957133i			0.0412267i
$540$		0			0
$541$		−	27.6493i		−	1.18874i	−0.804193	−	0.594369i	$-0.797402\pi$
$541$		−	27.6493i		−	1.18874i	0.804193	−	0.594369i	$-0.202598\pi$
$542$	−3.09683	−	13.9878i	−0.133020	−	0.600828i
$543$		0			0
$544$	−31.1127	−	16.2529i	−1.33394	−	0.696835i
$545$		0			0
$546$		0			0
$547$	9.85838			0.421514			0.210757	−	0.977538i	$-0.432407\pi$
$547$	9.85838			0.421514			0.210757	+	0.977538i	$0.432407\pi$
$548$	3.98937	+	8.56804i	0.170418	+	0.366008i
$549$		0			0
$550$		0			0
$551$	0.412335			0.0175661
$552$		0			0
$553$	−20.2341			−0.860440
$554$	4.51082	+	20.3746i	0.191647	+	0.865634i
$555$		0			0
$556$	28.5693	−	13.3022i	1.21161	−	0.564139i
$557$	−2.68305			−0.113685			−0.0568423	−	0.998383i	$-0.518103\pi$
$557$	−2.68305			−0.113685			−0.0568423	+	0.998383i	$0.518103\pi$
$558$		0			0
$559$		−	33.6890i		−	1.42489i
$560$		0			0
$561$		0			0
$562$	−6.58600	−	29.7478i	−0.277814	−	1.25484i
$563$		−	12.0794i		−	0.509087i	−0.967061	−	0.254543i	$-0.918075\pi$
$563$		−	12.0794i		−	0.509087i	0.967061	−	0.254543i	$-0.0819251\pi$
$564$		0			0
$565$		0			0
$566$	25.2278	−	5.58530i	1.06040	−	0.234768i
$567$		0			0
$568$	21.8463	−	16.7335i	0.916651	−	0.702122i
$569$		−	15.8479i		−	0.664379i	−0.943213	−	0.332190i	$-0.892213\pi$
$569$		−	15.8479i		−	0.664379i	0.943213	−	0.332190i	$-0.107787\pi$
$570$		0			0
$571$	1.11078			0.0464847			0.0232423	−	0.999730i	$-0.492601\pi$
$571$	1.11078			0.0464847			0.0232423	+	0.999730i	$0.492601\pi$
$572$	0.915238	−	0.426145i	0.0382680	−	0.0178180i
$573$		0			0
$574$	18.0140	−	3.98819i	0.751888	−	0.166464i
$575$		0			0
$576$		0			0
$577$	−14.7755			−0.615113			−0.307556	−	0.951530i	$-0.599511\pi$
$577$	−14.7755			−0.615113			−0.307556	+	0.951530i	$0.599511\pi$
$578$	29.6934	−	6.57394i	1.23508	−	0.273440i
$579$		0			0
$580$		0			0
$581$	−21.5510			−0.894087
$582$		0			0
$583$			1.67987i			0.0695730i
$584$	−12.2568	+	9.38824i	−0.507189	+	0.388488i
$585$		0			0
$586$	−8.28467	+	1.83418i	−0.342237	+	0.0757693i
$587$		−	13.5590i		−	0.559640i	−0.960052	−	0.279820i	$-0.909725\pi$
$587$		−	13.5590i		−	0.559640i	0.960052	−	0.279820i	$-0.0902748\pi$
$588$		0			0
$589$		−	9.45126i		−	0.389433i
$590$		0			0
$591$		0			0
$592$	−23.3249	−	19.6174i	−0.958646	−	0.806271i
$593$			31.9921i			1.31376i	0.753996	+	0.656879i	$0.228124\pi$
$593$			31.9921i			1.31376i	−0.753996	+	0.656879i	$0.771876\pi$
$594$		0			0
$595$		0			0
$596$	14.0140	−	6.52505i	0.574034	−	0.267277i
$597$		0			0
$598$	4.23407	+	19.1246i	0.173144	+	0.782062i
$599$	3.82174			0.156152			0.0780760	−	0.996947i	$-0.475122\pi$
$599$	3.82174			0.156152			0.0780760	+	0.996947i	$0.475122\pi$
$600$		0			0
$601$	31.6435			1.29076			0.645382	−	0.763860i	$-0.276698\pi$
$601$	31.6435			1.29076			0.645382	+	0.763860i	$0.276698\pi$
$602$	5.52311	+	24.9469i	0.225105	+	1.01676i
$603$		0			0
$604$	18.7495	+	40.2686i	0.762906	+	1.63850i
$605$		0			0
$606$		0			0
$607$			34.7204i			1.40926i	0.709576	+	0.704629i	$0.248886\pi$
$607$			34.7204i			1.40926i	−0.709576	+	0.704629i	$0.751114\pi$
$608$	3.98937	−	7.63682i	0.161790	−	0.309714i
$609$		0			0
$610$		0			0
$611$			10.0043i			0.404732i
$612$		0			0
$613$		−	26.3612i		−	1.06472i	−0.846519	−	0.532359i	$-0.821306\pi$
$613$		−	26.3612i		−	1.06472i	0.846519	−	0.532359i	$-0.178694\pi$
$614$	31.0741	−	6.87964i	1.25405	−	0.277640i
$615$		0			0
$616$	−0.607876	+	0.465611i	−0.0244920	+	0.0187600i
$617$		−	7.88509i		−	0.317442i	−0.987323	−	0.158721i	$-0.949263\pi$
$617$		−	7.88509i		−	0.317442i	0.987323	−	0.158721i	$-0.0507370\pi$
$618$		0			0
$619$	−38.9325			−1.56483			−0.782415	−	0.622757i	$-0.786012\pi$
$619$	−38.9325			−1.56483			−0.782415	+	0.622757i	$0.786012\pi$
$620$		0			0
$621$		0			0
$622$	42.8680	−	9.49073i	1.71885	−	0.380544i
$623$	−5.04623			−0.202173
$624$		0			0
$625$		0			0
$626$	−3.08476	+	0.682949i	−0.123292	+	0.0272961i
$627$		0			0
$628$	−6.75552	−	14.5089i	−0.269575	−	0.578970i
$629$	47.2803			1.88519
$630$		0			0
$631$			0.800468i			0.0318661i	0.999873	+	0.0159331i	$0.00507186\pi$
$631$			0.800468i			0.0318661i	−0.999873	+	0.0159331i	$0.994928\pi$
$632$	24.6079	+	32.1267i	0.978849	+	1.27793i
$633$		0			0
$634$	−22.7895	+	5.04546i	−0.905085	+	0.200381i
$635$		0			0
$636$		0			0
$637$		−	13.1850i		−	0.522409i
$638$	0.0158420	+	0.0715557i	0.000627192	+	0.00283292i
$639$		0			0
$640$		0			0
$641$			22.8931i			0.904222i	0.891962	+	0.452111i	$0.149329\pi$
$641$			22.8931i			0.904222i	−0.891962	+	0.452111i	$0.850671\pi$
$642$		0			0
$643$	12.9538			0.510847			0.255423	−	0.966829i	$-0.417785\pi$
$643$	12.9538			0.510847			0.255423	+	0.966829i	$0.417785\pi$
$644$	−6.27072	−	13.4677i	−0.247101	−	0.530702i
$645$		0			0
$646$	2.88922	+	13.0501i	0.113675	+	0.513449i
$647$	15.6647			0.615844			0.307922	−	0.951412i	$-0.400366\pi$
$647$	15.6647			0.615844			0.307922	+	0.951412i	$0.400366\pi$
$648$		0			0
$649$	−2.00000			−0.0785069
$650$		0			0
$651$		0			0
$652$	1.72928	−	0.805173i	0.0677239	−	0.0315330i
$653$	−41.5144			−1.62458			−0.812292	−	0.583252i	$-0.801780\pi$
$653$	−41.5144			−1.62458			−0.812292	+	0.583252i	$0.801780\pi$
$654$		0			0
$655$		0			0
$656$	−28.2401	−	23.7514i	−1.10259	−	0.927336i
$657$		0			0
$658$	−1.64015	−	7.40828i	−0.0639398	−	0.288805i
$659$			34.8859i			1.35896i	0.733693	+	0.679481i	$0.237795\pi$
$659$			34.8859i			1.35896i	−0.733693	+	0.679481i	$0.762205\pi$
$660$		0			0
$661$		−	19.7990i		−	0.770091i	−0.922897	−	0.385046i	$-0.874186\pi$
$661$		−	19.7990i		−	0.770091i	0.922897	−	0.385046i	$-0.125814\pi$
$662$	17.9248	−	3.96846i	0.696668	−	0.154238i
$663$		0			0
$664$	26.2095	+	34.2177i	1.01713	+	1.32790i
$665$		0			0
$666$		0			0
$667$	−1.42192			−0.0550569
$668$	−21.3169	+	9.92541i	−0.824777	+	0.384025i
$669$		0			0
$670$		0			0
$671$	0.0732884			0.00282927
$672$		0			0
$673$	−34.1849			−1.31773			−0.658866	−	0.752260i	$-0.728964\pi$
$673$	−34.1849			−1.31773			−0.658866	+	0.752260i	$0.728964\pi$
$674$	−37.2943	+	8.25674i	−1.43652	+	0.318038i
$675$		0			0
$676$	10.9624	−	5.10422i	0.421631	−	0.196316i
$677$	17.0462			0.655140			0.327570	−	0.944827i	$-0.393770\pi$
$677$	17.0462			0.655140			0.327570	+	0.944827i	$0.393770\pi$
$678$		0			0
$679$			10.3477i			0.397109i
$680$		0			0
$681$		0			0
$682$	1.64015	−	0.363120i	0.0628046	−	0.0139046i
$683$			28.6671i			1.09692i	0.836178	+	0.548459i	$0.184785\pi$
$683$			28.6671i			1.09692i	−0.836178	+	0.548459i	$0.815215\pi$
$684$		0			0
$685$		0			0
$686$	5.18785	+	23.4326i	0.198073	+	0.894660i
$687$		0			0
$688$	32.8925	−	39.1088i	1.25402	−	1.49101i
$689$		−	23.1410i		−	0.881603i
$690$		0			0
$691$	−27.0741			−1.02995			−0.514974	−	0.857206i	$-0.672199\pi$
$691$	−27.0741			−1.02995			−0.514974	+	0.857206i	$0.672199\pi$
$692$	−5.84632	+	2.72211i	−0.222244	+	0.103479i
$693$		0			0
$694$	−1.55102	−	7.00569i	−0.0588760	−	0.265932i
$695$		0			0
$696$		0			0
$697$	57.2437			2.16826
$698$	−6.15368	−	27.7951i	−0.232920	−	1.05206i
$699$		0			0
$700$		0			0
$701$	−23.5510			−0.889510			−0.444755	−	0.895652i	$-0.646709\pi$
$701$	−23.5510			−0.889510			−0.444755	+	0.895652i	$0.646709\pi$
$702$		0			0
$703$			11.6053i			0.437701i
$704$	1.47855	+	0.398898i	0.0557249	+	0.0150340i
$705$		0			0
$706$	4.37380	+	19.7557i	0.164610	+	0.743516i
$707$		−	21.9925i		−	0.827112i
$708$		0			0
$709$		−	7.85033i		−	0.294825i	−0.989075	−	0.147413i	$-0.952905\pi$
$709$		−	7.85033i		−	0.294825i	0.989075	−	0.147413i	$-0.0470945\pi$
$710$		0			0
$711$		0			0
$712$	6.13702	+	8.01216i	0.229995	+	0.300268i
$713$			32.5923i			1.22059i
$714$		0			0
$715$		0			0
$716$	−10.6385	−	22.8484i	−0.397579	−	0.853886i
$717$		0			0
$718$	43.9388	−	9.72780i	1.63978	−	0.363038i
$719$	10.1416			0.378218			0.189109	−	0.981956i	$-0.439440\pi$
$719$	10.1416			0.378218			0.189109	+	0.981956i	$0.439440\pi$
$720$		0			0
$721$	−2.95377			−0.110004
$722$	23.0316	−	5.09906i	0.857146	−	0.189767i
$723$		0			0
$724$	−20.3511	−	43.7084i	−0.756343	−	1.62441i
$725$		0			0
$726$		0			0
$727$			4.86524i			0.180442i	0.995922	+	0.0902208i	$0.0287573\pi$
$727$			4.86524i			0.180442i	−0.995922	+	0.0902208i	$0.971243\pi$
$728$	8.37380	−	6.41403i	0.310354	−	0.237720i
$729$		0			0
$730$		0			0
$731$			79.2749i			2.93209i
$732$		0			0
$733$		−	9.09903i		−	0.336080i	−0.985780	−	0.168040i	$-0.946256\pi$
$733$		−	9.09903i		−	0.336080i	0.985780	−	0.168040i	$-0.0537438\pi$
$734$	−7.02624	−	31.7363i	−0.259343	−	1.17141i
$735$		0			0
$736$	−13.7572	+	26.3352i	−0.507097	+	0.970730i
$737$		−	0.331031i		−	0.0121937i
$738$		0			0
$739$	12.5693			0.462371			0.231185	−	0.972910i	$-0.425740\pi$
$739$	12.5693			0.462371			0.231185	+	0.972910i	$0.425740\pi$
$740$		0			0
$741$		0			0
$742$	3.79383	+	17.1361i	0.139276	+	0.629085i
$743$	23.6647			0.868175			0.434087	−	0.900871i	$-0.357071\pi$
$743$	23.6647			0.868175			0.434087	+	0.900871i	$0.357071\pi$
$744$		0			0
$745$		0			0
$746$	−4.35382	−	19.6654i	−0.159405	−	0.720002i
$747$		0			0
$748$	−2.15368	+	1.00278i	−0.0787464	+	0.0366652i
$749$	−4.00000			−0.146157
$750$		0			0
$751$		−	31.2782i		−	1.14136i	−0.821173	−	0.570679i	$-0.806680\pi$
$751$		−	31.2782i		−	1.14136i	0.821173	−	0.570679i	$-0.193320\pi$
$752$	−9.76781	+	11.6138i	−0.356196	+	0.423512i
$753$		0			0
$754$	−0.218232	−	0.985716i	−0.00794754	−	0.0358977i
$755$		0			0
$756$		0			0
$757$			39.1150i			1.42166i	0.703365	+	0.710829i	$0.251680\pi$
$757$			39.1150i			1.42166i	−0.703365	+	0.710829i	$0.748320\pi$
$758$	12.0279	−	2.66291i	0.436873	−	0.0967213i
$759$		0			0
$760$		0			0
$761$		−	2.76305i		−	0.100160i	−0.998745	−	0.0500802i	$-0.984052\pi$
$761$		−	2.76305i		−	0.100160i	0.998745	−	0.0500802i	$-0.0159477\pi$
$762$		0			0
$763$	−7.45856			−0.270018
$764$	19.7938	−	9.21623i	0.716116	−	0.333431i
$765$		0			0
$766$	25.8357	−	5.71988i	0.933482	−	0.206668i
$767$	27.5510			0.994810
$768$		0			0
$769$	46.5606			1.67902			0.839509	−	0.543345i	$-0.182843\pi$
$769$	46.5606			1.67902			0.839509	+	0.543345i	$0.182843\pi$
$770$		0			0
$771$		0			0
$772$	27.7711	−	12.9306i	0.999505	−	0.465381i
$773$	29.5877			1.06419			0.532097	−	0.846683i	$-0.321404\pi$
$773$	29.5877			1.06419			0.532097	+	0.846683i	$0.321404\pi$
$774$		0			0
$775$		0			0
$776$	16.4296	−	12.5845i	0.589789	−	0.451757i
$777$		0			0
$778$	37.2943	−	8.25674i	1.33706	−	0.296019i
$779$			14.0508i			0.503424i
$780$		0			0
$781$		−	1.86244i		−	0.0666435i
$782$	−9.96336	−	45.0027i	−0.356289	−	1.60929i
$783$		0			0
$784$	12.8733	−	15.3062i	0.459760	−	0.546649i
$785$		0			0
$786$		0			0
$787$	35.9267			1.28065			0.640324	−	0.768105i	$-0.278800\pi$
$787$	35.9267			1.28065			0.640324	+	0.768105i	$0.278800\pi$
$788$	30.9065	−	14.3904i	1.10100	−	0.512637i
$789$		0			0
$790$		0			0
$791$	−8.23407			−0.292770
$792$		0			0
$793$	−1.00958			−0.0358514
$794$	7.76322	+	35.0651i	0.275506	+	1.24441i
$795$		0			0
$796$	3.98937	+	8.56804i	0.141400	+	0.303686i
$797$	9.31695			0.330023			0.165012	−	0.986292i	$-0.447234\pi$
$797$	9.31695			0.330023			0.165012	+	0.986292i	$0.447234\pi$
$798$		0			0
$799$		−	23.5416i		−	0.832841i
$800$		0			0
$801$		0			0
$802$	−1.83840	−	8.30372i	−0.0649161	−	0.293215i
$803$			1.04491i			0.0368742i
$804$		0			0
$805$		0			0
$806$	−22.5939	+	5.00217i	−0.795837	+	0.176194i
$807$		0			0
$808$	−34.9186	+	26.7464i	−1.22843	+	0.940934i
$809$			34.9207i			1.22775i	0.789405	+	0.613873i	$0.210389\pi$
$809$			34.9207i			1.22775i	−0.789405	+	0.613873i	$0.789611\pi$
$810$		0			0
$811$	−25.7938			−0.905744			−0.452872	−	0.891576i	$-0.649601\pi$
$811$	−25.7938			−0.905744			−0.452872	+	0.891576i	$0.649601\pi$
$812$	0.323204	+	0.694151i	0.0113423	+	0.0243599i
$813$		0			0
$814$	−2.01395	+	0.445878i	−0.0705890	+	0.0156280i
$815$		0			0
$816$		0			0
$817$	−19.4586			−0.680769
$818$	26.9956	−	5.97668i	0.943880	−	0.208970i
$819$		0			0
$820$		0			0
$821$	31.1878			1.08846			0.544232	−	0.838935i	$-0.316821\pi$
$821$	31.1878			1.08846			0.544232	+	0.838935i	$0.316821\pi$
$822$		0			0
$823$		−	33.5718i		−	1.17024i	−0.810947	−	0.585120i	$-0.801047\pi$
$823$		−	33.5718i		−	1.17024i	0.810947	−	0.585120i	$-0.198953\pi$
$824$	3.59226	+	4.68985i	0.125142	+	0.163379i
$825$		0			0
$826$	−20.4017	+	4.51683i	−0.709866	+	0.157160i
$827$		−	53.4362i		−	1.85816i	−0.369881	−	0.929079i	$-0.620601\pi$
$827$		−	53.4362i		−	1.85816i	0.369881	−	0.929079i	$-0.379399\pi$
$828$		0			0
$829$			0.634952i			0.0220528i	0.999939	+	0.0110264i	$0.00350988\pi$
$829$			0.634952i			0.0220528i	−0.999939	+	0.0110264i	$0.996490\pi$
$830$		0			0
$831$		0			0
$832$	−20.3678	−	5.49503i	−0.706125	−	0.190506i
$833$			31.0261i			1.07499i
$834$		0			0
$835$		0			0
$836$	−0.246139	−	0.528636i	−0.00851288	−	0.0182833i
$837$		0			0
$838$	−0.599955	−	2.70989i	−0.0207251	−	0.0936117i
$839$	24.9046			0.859803			0.429901	−	0.902876i	$-0.358548\pi$
$839$	24.9046			0.859803			0.429901	+	0.902876i	$0.358548\pi$
$840$		0			0
$841$	−28.9267			−0.997473
$842$	1.31695	+	5.94842i	0.0453850	+	0.204996i
$843$		0			0
$844$	30.5327	−	14.2164i	1.05098	−	0.489347i
$845$		0			0
$846$		0			0
$847$		−	15.5045i		−	0.532742i
$848$	22.5939	−	26.8639i	0.775878	−	0.922509i
$849$		0			0
$850$		0			0
$851$		−	40.0203i		−	1.37188i
$852$		0			0
$853$			17.5448i			0.600724i	0.953825	+	0.300362i	$0.0971075\pi$
$853$			17.5448i			0.600724i	−0.953825	+	0.300362i	$0.902893\pi$
$854$	0.747604	−	0.165515i	0.0255825	−	0.00566382i
$855$		0			0
$856$	4.86464	+	6.35101i	0.166270	+	0.217073i
$857$			7.30196i			0.249430i	0.992193	+	0.124715i	$0.0398017\pi$
$857$			7.30196i			0.249430i	−0.992193	+	0.124715i	$0.960198\pi$
$858$		0			0
$859$	15.2890			0.521655			0.260828	−	0.965385i	$-0.416005\pi$
$859$	15.2890			0.521655			0.260828	+	0.965385i	$0.416005\pi$
$860$		0			0
$861$		0			0
$862$	16.3232	−	3.61387i	0.555971	−	0.123089i
$863$	−41.9787			−1.42897			−0.714487	−	0.699649i	$-0.753340\pi$
$863$	−41.9787			−1.42897			−0.714487	+	0.699649i	$0.753340\pi$
$864$		0			0
$865$		0			0
$866$	13.0602	−	2.89145i	0.443803	−	0.0982555i
$867$		0			0
$868$	15.9109	−	7.40828i	0.540050	−	0.251453i
$869$	2.73887			0.0929097
$870$		0			0
$871$			4.56012i			0.154514i
$872$	9.07081	+	11.8423i	0.307176	+	0.401032i
$873$		0			0
$874$	11.0462	−	2.44557i	0.373644	−	0.0827228i
$875$		0			0
$876$		0			0
$877$			38.4800i			1.29938i	0.760200	+	0.649689i	$0.225101\pi$
$877$			38.4800i			1.29938i	−0.760200	+	0.649689i	$0.774899\pi$
$878$	−4.90317	−	22.1468i	−0.165474	−	0.747418i
$879$		0			0
$880$		0			0
$881$			7.11053i			0.239560i	0.992800	+	0.119780i	$0.0382189\pi$
$881$			7.11053i			0.239560i	−0.992800	+	0.119780i	$0.961781\pi$
$882$		0			0
$883$	26.5048			0.891957			0.445979	−	0.895044i	$-0.352856\pi$
$883$	26.5048			0.891957			0.445979	+	0.895044i	$0.352856\pi$
$884$	29.6681	−	13.8138i	0.997845	−	0.464608i
$885$		0			0
$886$	−7.66473	−	34.6202i	−0.257502	−	1.16309i
$887$	39.3449			1.32107			0.660535	−	0.750795i	$-0.270329\pi$
$887$	39.3449			1.32107			0.660535	+	0.750795i	$0.270329\pi$
$888$		0			0
$889$	29.0462			0.974179
$890$		0			0
$891$		0			0
$892$	18.8340	+	40.4501i	0.630610	+	1.35437i
$893$	5.77844			0.193368
$894$		0			0
$895$		0			0
$896$	15.9833	+	0.729929i	0.533966	+	0.0243852i
$897$		0			0
$898$	−1.29696	−	5.85815i	−0.0432802	−	0.195489i
$899$		−	1.67987i		−	0.0560267i
$900$		0			0
$901$			54.4540i			1.81413i
$902$	−2.43835	+	0.539838i	−0.0811883	+	0.0179746i
$903$		0			0
$904$	10.0140	+	13.0737i	0.333059	+	0.434824i
$905$		0			0
$906$		0			0
$907$	22.1974			0.737054			0.368527	−	0.929617i	$-0.379862\pi$
$907$	22.1974			0.737054			0.368527	+	0.929617i	$0.379862\pi$
$908$	7.48647	+	16.0788i	0.248447	+	0.533594i
$909$		0			0
$910$		0			0
$911$	−20.9538			−0.694229			−0.347115	−	0.937823i	$-0.612839\pi$
$911$	−20.9538			−0.694229			−0.347115	+	0.937823i	$0.612839\pi$
$912$		0			0
$913$	2.91713			0.0965428
$914$	39.8603	−	8.82484i	1.31846	−	0.291900i
$915$		0			0
$916$	17.9634	+	38.5802i	0.593526	+	1.27472i
$917$	−19.1878			−0.633638
$918$		0			0
$919$		−	7.88509i		−	0.260105i	−0.991507	−	0.130053i	$-0.958485\pi$
$919$		−	7.88509i		−	0.260105i	0.991507	−	0.130053i	$-0.0415146\pi$
$920$		0			0
$921$		0			0
$922$	−50.7282	+	11.2310i	−1.67065	+	0.369872i
$923$			25.6561i			0.844481i
$924$		0			0
$925$		0			0
$926$	−5.07873	−	22.9397i	−0.166897	−	0.753846i
$927$		0			0
$928$	0.709071	−	1.35737i	0.0232764	−	0.0445578i
$929$			6.35718i			0.208572i	0.994547	+	0.104286i	$0.0332558\pi$
$929$			6.35718i			0.208572i	−0.994547	+	0.104286i	$0.966744\pi$
$930$		0			0
$931$	−7.61557			−0.249590
$932$	−12.7249	−	27.3295i	−0.416818	−	0.895207i
$933$		0			0
$934$	−0.452306	−	2.04299i	−0.0147999	−	0.0668486i
$935$		0			0
$936$		0			0
$937$	−35.0096			−1.14371			−0.571857	−	0.820354i	$-0.693777\pi$
$937$	−35.0096			−1.14371			−0.571857	+	0.820354i	$0.693777\pi$
$938$	−0.747604	−	3.37680i	−0.0244101	−	0.110256i
$939$		0			0
$940$		0			0
$941$	−28.5606			−0.931049			−0.465525	−	0.885035i	$-0.654134\pi$
$941$	−28.5606			−0.931049			−0.465525	+	0.885035i	$0.654134\pi$
$942$		0			0
$943$		−	48.4538i		−	1.57787i
$944$	31.9833	+	26.8997i	1.04097	+	0.875509i
$945$		0			0
$946$	−0.747604	−	3.37680i	−0.0243067	−	0.109789i
$947$			20.7650i			0.674771i	0.941367	+	0.337385i	$0.109543\pi$
$947$			20.7650i			0.674771i	−0.941367	+	0.337385i	$0.890457\pi$
$948$		0			0
$949$		−	14.3942i		−	0.467257i
$950$		0			0
$951$		0			0
$952$	−19.7047	+	15.0931i	−0.638633	+	0.489170i
$953$			38.4147i			1.24437i	0.782869	+	0.622186i	$0.213755\pi$
$953$			38.4147i			1.24437i	−0.782869	+	0.622186i	$0.786245\pi$
$954$		0			0
$955$		0			0
$956$	34.5327	−	16.0788i	1.11687	−	0.520026i
$957$		0			0
$958$	−3.88296	+	0.859666i	−0.125453	+	0.0277746i
$959$	6.68305			0.215807
$960$		0			0
$961$	−7.50479			−0.242090
$962$	27.7432	−	6.14220i	0.894478	−	0.198032i
$963$		0			0
$964$	33.5510	−	15.6217i	1.08061	−	0.503142i
$965$		0			0
$966$		0			0
$967$			16.6013i			0.533861i	0.963716	+	0.266930i	$0.0860094\pi$
$967$			16.6013i			0.533861i	−0.963716	+	0.266930i	$0.913991\pi$
$968$	−24.6173	+	18.8560i	−0.791231	+	0.606054i
$969$		0			0
$970$		0			0
$971$			10.3171i			0.331092i	0.986202	+	0.165546i	$0.0529386\pi$
$971$			10.3171i			0.331092i	−0.986202	+	0.165546i	$0.947061\pi$
$972$		0			0
$973$		−	22.2840i		−	0.714393i
$974$	5.17992	+	23.3968i	0.165975	+	0.749682i
$975$		0			0
$976$	−1.17200	−	0.985716i	−0.0375149	−	0.0315520i
$977$		−	32.0439i		−	1.02518i	−0.858635	−	0.512588i	$-0.828687\pi$
$977$		−	32.0439i		−	1.02518i	0.858635	−	0.512588i	$-0.171313\pi$
$978$		0			0
$979$	0.683053			0.0218305
$980$		0			0
$981$		0			0
$982$	−7.96939	−	35.9963i	−0.254313	−	1.14869i
$983$	24.8034			0.791106			0.395553	−	0.918443i	$-0.370553\pi$
$983$	24.8034			0.791106			0.395553	+	0.918443i	$0.370553\pi$
$984$		0			0
$985$		0			0
$986$	0.513530	+	2.31952i	0.0163541	+	0.0738687i
$987$		0			0
$988$	3.39069	+	7.28223i	0.107872	+	0.231679i
$989$	67.1020			2.13372
$990$		0			0
$991$		−	15.7872i		−	0.501498i	−0.968052	−	0.250749i	$-0.919323\pi$
$991$		−	15.7872i		−	0.501498i	0.968052	−	0.250749i	$-0.0806769\pi$
$992$	−31.1127	−	16.2529i	−0.987828	−	0.516029i
$993$		0			0
$994$	−4.20617	−	18.9985i	−0.133412	−	0.602597i
$995$		0			0
$996$		0			0
$997$		−	51.3823i		−	1.62729i	−0.581359	−	0.813647i	$-0.697479\pi$
$997$		−	51.3823i		−	1.62729i	0.581359	−	0.813647i	$-0.302521\pi$
$998$	−31.1127	+	6.88817i	−0.984854	+	0.218041i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1800.2.b.d.251.2		6
3.2	odd	2		1800.2.b.e.251.5		6
4.3	odd	2		7200.2.b.e.4751.5		6
5.2	odd	4		1800.2.m.e.899.5		12
5.3	odd	4		1800.2.m.e.899.8		12
5.4	even	2		360.2.b.d.251.5	yes	6
8.3	odd	2		1800.2.b.e.251.6		6
8.5	even	2		7200.2.b.d.4751.2		6
12.11	even	2		7200.2.b.d.4751.5		6
15.2	even	4		1800.2.m.d.899.8		12
15.8	even	4		1800.2.m.d.899.5		12
15.14	odd	2		360.2.b.c.251.2	yes	6
20.3	even	4		7200.2.m.e.3599.9		12
20.7	even	4		7200.2.m.e.3599.3		12
20.19	odd	2		1440.2.b.d.431.2		6
24.5	odd	2		7200.2.b.e.4751.2		6
24.11	even	2	inner	1800.2.b.d.251.1		6
40.3	even	4		1800.2.m.d.899.7		12
40.13	odd	4		7200.2.m.d.3599.3		12
40.19	odd	2		360.2.b.c.251.1	✓	6
40.27	even	4		1800.2.m.d.899.6		12
40.29	even	2		1440.2.b.c.431.5		6
40.37	odd	4		7200.2.m.d.3599.9		12
60.23	odd	4		7200.2.m.d.3599.10		12
60.47	odd	4		7200.2.m.d.3599.4		12
60.59	even	2		1440.2.b.c.431.2		6
120.29	odd	2		1440.2.b.d.431.5		6
120.53	even	4		7200.2.m.e.3599.4		12
120.59	even	2		360.2.b.d.251.6	yes	6
120.77	even	4		7200.2.m.e.3599.10		12
120.83	odd	4		1800.2.m.e.899.6		12
120.107	odd	4		1800.2.m.e.899.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.b.c.251.1	✓	6	40.19	odd	2
360.2.b.c.251.2	yes	6	15.14	odd	2
360.2.b.d.251.5	yes	6	5.4	even	2
360.2.b.d.251.6	yes	6	120.59	even	2
1440.2.b.c.431.2		6	60.59	even	2
1440.2.b.c.431.5		6	40.29	even	2
1440.2.b.d.431.2		6	20.19	odd	2
1440.2.b.d.431.5		6	120.29	odd	2
1800.2.b.d.251.1		6	24.11	even	2	inner
1800.2.b.d.251.2		6	1.1	even	1	trivial
1800.2.b.e.251.5		6	3.2	odd	2
1800.2.b.e.251.6		6	8.3	odd	2
1800.2.m.d.899.5		12	15.8	even	4
1800.2.m.d.899.6		12	40.27	even	4
1800.2.m.d.899.7		12	40.3	even	4
1800.2.m.d.899.8		12	15.2	even	4
1800.2.m.e.899.5		12	5.2	odd	4
1800.2.m.e.899.6		12	120.83	odd	4
1800.2.m.e.899.7		12	120.107	odd	4
1800.2.m.e.899.8		12	5.3	odd	4
7200.2.b.d.4751.2		6	8.5	even	2
7200.2.b.d.4751.5		6	12.11	even	2
7200.2.b.e.4751.2		6	24.5	odd	2
7200.2.b.e.4751.5		6	4.3	odd	2
7200.2.m.d.3599.3		12	40.13	odd	4
7200.2.m.d.3599.4		12	60.47	odd	4
7200.2.m.d.3599.9		12	40.37	odd	4
7200.2.m.d.3599.10		12	60.23	odd	4
7200.2.m.e.3599.3		12	20.7	even	4
7200.2.m.e.3599.4		12	120.53	even	4
7200.2.m.e.3599.9		12	20.3	even	4
7200.2.m.e.3599.10		12	120.77	even	4

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.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38078 + 0.305697i) q^{2} +(1.81310 - 0.844199i) q^{4} -1.41421i q^{7} +(-2.24542 + 1.71991i) q^{8} +0.191427i q^{11} -2.63700i q^{13} +(0.432320 + 1.95272i) q^{14} +(2.57466 - 3.06123i) q^{16} +6.20522i q^{17} -1.52311 q^{19} +(-0.0585185 - 0.264318i) q^{22} +5.25240 q^{23} +(0.806122 + 3.64111i) q^{26} +(-1.19388 - 2.56411i) q^{28} -0.270718 q^{29} +6.20522i q^{31} +(-2.61922 + 5.01395i) q^{32} +(-1.89692 - 8.56804i) q^{34} -7.61944i q^{37} +(2.10308 - 0.465611i) q^{38} -9.22508i q^{41} +12.7755 q^{43} +(0.161602 + 0.347076i) q^{44} +(-7.25240 + 1.60564i) q^{46} -3.79383 q^{47} +5.00000 q^{49} +(-2.22615 - 4.78114i) q^{52} +8.77551 q^{53} +(2.43232 + 3.17550i) q^{56} +(0.373802 - 0.0827577i) q^{58} +10.4479i q^{59} -0.382853i q^{61} +(-1.89692 - 8.56804i) q^{62} +(2.08382 - 7.72384i) q^{64} -1.72928 q^{67} +(5.23844 + 11.2507i) q^{68} -9.72928 q^{71} +5.45856 q^{73} +(2.32924 + 10.5208i) q^{74} +(-2.76156 + 1.28581i) q^{76} +0.270718 q^{77} -14.3077i q^{79} +(2.82008 + 12.7378i) q^{82} -15.2389i q^{83} +(-17.6402 + 3.90543i) q^{86} +(-0.329237 - 0.429833i) q^{88} -3.56822i q^{89} -3.72928 q^{91} +(9.52311 - 4.43407i) q^{92} +(5.23844 - 1.15976i) q^{94} -7.31695 q^{97} +(-6.90389 + 1.52848i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} + 2 q^{4} - 2 q^{8} - 6 q^{16} + 16 q^{19} + 20 q^{22} - 4 q^{23} + 20 q^{26} + 8 q^{28} - 12 q^{29} - 22 q^{32} - 4 q^{34} + 20 q^{38} + 16 q^{43} - 12 q^{44} - 8 q^{46} - 8 q^{47} + 30 q^{49}+ \cdots - 10 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 + 2 * q^4 - 2 * q^8 - 6 * q^16 + 16 * q^19 + 20 * q^22 - 4 * q^23 + 20 * q^26 + 8 * q^28 - 12 * q^29 - 22 * q^32 - 4 * q^34 + 20 * q^38 + 16 * q^43 - 12 * q^44 - 8 * q^46 - 8 * q^47 + 30 * q^49 + 4 * q^52 - 8 * q^53 + 12 * q^56 + 20 * q^58 - 4 * q^62 + 14 * q^64 + 44 * q^68 - 48 * q^71 + 12 * q^73 + 4 * q^74 - 4 * q^76 + 12 * q^77 - 16 * q^82 - 40 * q^86 + 8 * q^88 - 12 * q^91 + 32 * q^92 + 44 * q^94 - 4 * q^97 - 10 * q^98

Introduction

L-functions

Modular forms

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Database

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