LMFDB - Embedded newform 1800.2.m.e.899.6

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:	$12$
Coefficient field:	12.0.426337261060096.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 $ x^12 - 4x^9 - 3x^8 + 4x^7 + 8x^6 + 8x^5 - 12x^4 - 32*x^3 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			899.6
Root			$1.19252 - 0.760198i$ of defining polynomial
Character	$\chi$	$=$	1800.899
Dual form			1800.2.m.e.899.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.305697 + 1.38078i) q^{2} +(-1.81310 - 0.844199i) q^{4} +1.41421 q^{7} +(1.71991 - 2.24542i) q^{8} +O(q^{10})$	\(q+(-0.305697 + 1.38078i) q^{2} +(-1.81310 - 0.844199i) q^{4} +1.41421 q^{7} +(1.71991 - 2.24542i) q^{8} -0.191427i q^{11} -2.63700 q^{13} +(-0.432320 + 1.95272i) q^{14} +(2.57466 + 3.06123i) q^{16} -6.20522 q^{17} +1.52311 q^{19} +(0.264318 + 0.0585185i) q^{22} +5.25240i q^{23} +(0.806122 - 3.64111i) q^{26} +(-2.56411 - 1.19388i) q^{28} +0.270718 q^{29} -6.20522i q^{31} +(-5.01395 + 2.61922i) q^{32} +(1.89692 - 8.56804i) q^{34} +7.61944 q^{37} +(-0.465611 + 2.10308i) q^{38} +9.22508i q^{41} +12.7755i q^{43} +(-0.161602 + 0.347076i) q^{44} +(-7.25240 - 1.60564i) q^{46} +3.79383i q^{47} -5.00000 q^{49} +(4.78114 + 2.22615i) q^{52} +8.77551i q^{53} +(2.43232 - 3.17550i) q^{56} +(-0.0827577 + 0.373802i) q^{58} +10.4479i q^{59} +0.382853i q^{61} +(8.56804 + 1.89692i) q^{62} +(-2.08382 - 7.72384i) q^{64} +1.72928i q^{67} +(11.2507 + 5.23844i) q^{68} -9.72928 q^{71} +5.45856i q^{73} +(-2.32924 + 10.5208i) q^{74} +(-2.76156 - 1.28581i) q^{76} -0.270718i q^{77} -14.3077i q^{79} +(-12.7378 - 2.82008i) q^{82} -15.2389 q^{83} +(-17.6402 - 3.90543i) q^{86} +(-0.429833 - 0.329237i) q^{88} -3.56822i q^{89} -3.72928 q^{91} +(4.43407 - 9.52311i) q^{92} +(-5.23844 - 1.15976i) q^{94} +7.31695i q^{97} +(1.52848 - 6.90389i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{4}+O(q^{10}) $ 12 * q - 4 * q^4	$ 12 q - 4 q^{4} - 12 q^{16} - 32 q^{19} + 40 q^{26} + 24 q^{29} + 8 q^{34} + 24 q^{44} - 16 q^{46} - 60 q^{49} + 24 q^{56} - 28 q^{64} - 96 q^{71} - 8 q^{74} - 8 q^{76} - 80 q^{86} - 24 q^{91} - 88 q^{94}+O(q^{100}) $ 12 * q - 4 * q^4 - 12 * q^16 - 32 * q^19 + 40 * q^26 + 24 * q^29 + 8 * q^34 + 24 * q^44 - 16 * q^46 - 60 * q^49 + 24 * q^56 - 28 * q^64 - 96 * q^71 - 8 * q^74 - 8 * q^76 - 80 * q^86 - 24 * q^91 - 88 * 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 $

$2$	−0.305697	+	1.38078i	−0.216160	+	0.976358i
$2$	−0.305697	+	1.38078i	−0.216160	+	0.976358i
$3$		0			0
$3$		0			0
$4$	−1.81310	−	0.844199i	−0.906550	−	0.422099i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	1.41421			0.534522			0.267261	−	0.963624i	$-0.413881\pi$
$7$	1.41421			0.534522			0.267261	+	0.963624i	$0.413881\pi$
$8$	1.71991	−	2.24542i	0.608080	−	0.793876i
$9$		0			0
$10$		0			0
$11$		−	0.191427i		−	0.0577173i	−0.999584	−	0.0288587i	$-0.990813\pi$
$11$		−	0.191427i		−	0.0577173i	0.999584	−	0.0288587i	$-0.00918727\pi$
$12$		0			0
$13$	−2.63700			−0.731372			−0.365686	−	0.930738i	$-0.619166\pi$
$13$	−2.63700			−0.731372			−0.365686	+	0.930738i	$0.619166\pi$
$14$	−0.432320	+	1.95272i	−0.115542	+	0.521885i
$15$		0			0
$16$	2.57466	+	3.06123i	0.643664	+	0.765308i
$17$	−6.20522			−1.50499			−0.752494	−	0.658599i	$-0.771149\pi$
$17$	−6.20522			−1.50499			−0.752494	+	0.658599i	$0.771149\pi$
$18$		0			0
$19$	1.52311			0.349426			0.174713	−	0.984619i	$-0.444100\pi$
$19$	1.52311			0.349426			0.174713	+	0.984619i	$0.444100\pi$
$20$		0			0
$21$		0			0
$22$	0.264318	+	0.0585185i	0.0563528	+	0.0124762i
$23$			5.25240i			1.09520i	0.836740	+	0.547600i	$0.184458\pi$
$23$			5.25240i			1.09520i	−0.836740	+	0.547600i	$0.815542\pi$
$24$		0			0
$25$		0			0
$26$	0.806122	−	3.64111i	0.158094	−	0.714081i
$27$		0			0
$28$	−2.56411	−	1.19388i	−0.484571	−	0.225622i
$29$	0.270718			0.0502711			0.0251356	−	0.999684i	$-0.491998\pi$
$29$	0.270718			0.0502711			0.0251356	+	0.999684i	$0.491998\pi$
$30$		0			0
$31$		−	6.20522i		−	1.11449i	−0.830348	−	0.557245i	$-0.811858\pi$
$31$		−	6.20522i		−	1.11449i	0.830348	−	0.557245i	$-0.188142\pi$
$32$	−5.01395	+	2.61922i	−0.886349	+	0.463017i
$33$		0			0
$34$	1.89692	−	8.56804i	0.325318	−	1.46941i
$35$		0			0
$36$		0			0
$37$	7.61944			1.25263			0.626314	−	0.779571i	$-0.284563\pi$
$37$	7.61944			1.25263			0.626314	+	0.779571i	$0.284563\pi$
$38$	−0.465611	+	2.10308i	−0.0755321	+	0.341165i
$39$		0			0
$40$		0			0
$41$			9.22508i			1.44071i	0.693603	+	0.720357i	$0.256022\pi$
$41$			9.22508i			1.44071i	−0.693603	+	0.720357i	$0.743978\pi$
$42$		0			0
$43$			12.7755i			1.94825i	0.226016	+	0.974124i	$0.427430\pi$
$43$			12.7755i			1.94825i	−0.226016	+	0.974124i	$0.572570\pi$
$44$	−0.161602	+	0.347076i	−0.0243625	+	0.0523236i
$45$		0			0
$46$	−7.25240	−	1.60564i	−1.06931	−	0.236739i
$47$			3.79383i			0.553387i	0.960958	+	0.276694i	$0.0892387\pi$
$47$			3.79383i			0.553387i	−0.960958	+	0.276694i	$0.910761\pi$
$48$		0			0
$49$	−5.00000			−0.714286
$50$		0			0
$51$		0			0
$52$	4.78114	+	2.22615i	0.663025	+	0.308712i
$53$			8.77551i			1.20541i	0.797964	+	0.602705i	$0.205910\pi$
$53$			8.77551i			1.20541i	−0.797964	+	0.602705i	$0.794090\pi$
$54$		0			0
$55$		0			0
$56$	2.43232	−	3.17550i	0.325032	−	0.424344i
$57$		0			0
$58$	−0.0827577	+	0.373802i	−0.0108666	+	0.0490826i
$59$			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	$0.00780245\pi$
$61$			0.382853i			0.0490194i	−0.999700	+	0.0245097i	$0.992198\pi$
$62$	8.56804	+	1.89692i	1.08814	+	0.240909i
$63$		0			0
$64$	−2.08382	−	7.72384i	−0.260477	−	0.965480i
$65$		0			0
$66$		0			0
$67$			1.72928i			0.211265i	0.994405	+	0.105633i	$0.0336868\pi$
$67$			1.72928i			0.211265i	−0.994405	+	0.105633i	$0.966313\pi$
$68$	11.2507	+	5.23844i	1.36435	+	0.635255i
$69$		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
$73$			5.45856i			0.638877i	0.947607	+	0.319438i	$0.103494\pi$
$73$			5.45856i			0.638877i	−0.947607	+	0.319438i	$0.896506\pi$
$74$	−2.32924	+	10.5208i	−0.270768	+	1.22301i
$75$		0			0
$76$	−2.76156	−	1.28581i	−0.316772	−	0.147493i
$77$		−	0.270718i		−	0.0308512i
$78$		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
$82$	−12.7378	−	2.82008i	−1.40665	−	0.311425i
$83$	−15.2389			−1.67268			−0.836342	−	0.548208i	$-0.815310\pi$
$83$	−15.2389			−1.67268			−0.836342	+	0.548208i	$0.815310\pi$
$84$		0			0
$85$		0			0
$86$	−17.6402	−	3.90543i	−1.90219	−	0.421134i
$87$		0			0
$88$	−0.429833	−	0.329237i	−0.0458204	−	0.0350968i
$89$		−	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
$92$	4.43407	−	9.52311i	0.462283	−	0.992853i
$93$		0			0
$94$	−5.23844	−	1.15976i	−0.540304	−	0.119620i
$95$		0			0
$96$		0			0
$97$			7.31695i			0.742923i	0.928448	+	0.371462i	$0.121143\pi$
$97$			7.31695i			0.742923i	−0.928448	+	0.371462i	$0.878857\pi$
$98$	1.52848	−	6.90389i	0.154400	−	0.697399i
$99$		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
$103$	−2.08863			−0.205799			−0.102899	−	0.994692i	$-0.532812\pi$
$103$	−2.08863			−0.205799			−0.102899	+	0.994692i	$0.532812\pi$
$104$	−4.53540	+	5.92117i	−0.444733	+	0.580619i
$105$		0			0
$106$	−12.1170	−	2.68264i	−1.17691	−	0.260561i
$107$	2.82843			0.273434			0.136717	−	0.990610i	$-0.456345\pi$
$107$	2.82843			0.273434			0.136717	+	0.990610i	$0.456345\pi$
$108$		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
$112$	3.64111	+	4.32924i	0.344053	+	0.409074i
$113$	−5.82237			−0.547722			−0.273861	−	0.961769i	$-0.588301\pi$
$113$	−5.82237			−0.547722			−0.273861	+	0.961769i	$0.588301\pi$
$114$		0			0
$115$		0			0
$116$	−0.490839	−	0.228540i	−0.0455733	−	0.0212194i
$117$		0			0
$118$	−14.4262	−	3.19388i	−1.32804	−	0.294020i
$119$	−8.77551			−0.804450
$120$		0			0
$121$	10.9634			0.996669
$122$	−0.528636	−	0.117037i	−0.0478604	−	0.0105960i
$123$		0			0
$124$	−5.23844	+	11.2507i	−0.470426	+	1.01034i
$125$		0			0
$126$		0			0
$127$	−20.5388			−1.82252			−0.911261	−	0.411829i	$-0.864890\pi$
$127$	−20.5388			−1.82252			−0.911261	+	0.411829i	$0.864890\pi$
$128$	11.3019	−	0.516138i	0.998959	−	0.0456206i
$129$		0			0
$130$		0			0
$131$			13.5679i			1.18543i	0.805413	+	0.592715i	$0.201944\pi$
$131$			13.5679i			1.18543i	−0.805413	+	0.592715i	$0.798056\pi$
$132$		0			0
$133$	2.15401			0.186776
$134$	−2.38776	−	0.528636i	−0.206271	−	0.0456672i
$135$		0			0
$136$	−10.6724	+	13.9333i	−0.915153	+	1.19477i
$137$	−4.72563			−0.403738			−0.201869	−	0.979413i	$-0.564702\pi$
$137$	−4.72563			−0.403738			−0.201869	+	0.979413i	$0.564702\pi$
$138$		0			0
$139$	−15.7572			−1.33651			−0.668254	−	0.743934i	$-0.732958\pi$
$139$	−15.7572			−1.33651			−0.668254	+	0.743934i	$0.732958\pi$
$140$		0			0
$141$		0			0
$142$	2.97421	−	13.4340i	0.249590	−	1.12735i
$143$			0.504792i			0.0422129i
$144$		0			0
$145$		0			0
$146$	−7.53707	−	1.66866i	−0.623772	−	0.138100i
$147$		0			0
$148$	−13.8148	−	6.43232i	−1.13557	−	0.528733i
$149$	−7.72928			−0.633207			−0.316604	−	0.948558i	$-0.602543\pi$
$149$	−7.72928			−0.633207			−0.316604	+	0.948558i	$0.602543\pi$
$150$		0			0
$151$		−	22.2098i		−	1.80741i	−0.428158	−	0.903704i	$-0.640837\pi$
$151$		−	22.2098i		−	1.80741i	0.428158	−	0.903704i	$-0.359163\pi$
$152$	2.61962	−	3.42003i	0.212479	−	0.277401i
$153$		0			0
$154$	0.373802	+	0.0827577i	0.0301218	+	0.00666880i
$155$		0			0
$156$		0			0
$157$	8.00229			0.638652			0.319326	−	0.947645i	$-0.396543\pi$
$157$	8.00229			0.638652			0.319326	+	0.947645i	$0.396543\pi$
$158$	19.7557	+	4.37380i	1.57168	+	0.347961i
$159$		0			0
$160$		0			0
$161$			7.42801i			0.585409i
$162$		0			0
$163$			0.953771i			0.0747051i	0.999302	+	0.0373526i	$0.0118925\pi$
$163$			0.953771i			0.0747051i	−0.999302	+	0.0373526i	$0.988108\pi$
$164$	7.78780	−	16.7260i	0.608125	−	1.30608i
$165$		0			0
$166$	4.65847	−	21.0415i	0.361568	−	1.63314i
$167$			11.7572i			0.909799i	0.890543	+	0.454899i	$0.150325\pi$
$167$			11.7572i			0.909799i	−0.890543	+	0.454899i	$0.849675\pi$
$168$		0			0
$169$	−6.04623			−0.465095
$170$		0			0
$171$		0			0
$172$	10.7851	−	23.1633i	0.822354	−	1.76618i
$173$		−	3.22449i		−	0.245153i	−0.992459	−	0.122577i	$-0.960884\pi$
$173$		−	3.22449i		−	0.245153i	0.992459	−	0.122577i	$-0.0391157\pi$
$174$		0			0
$175$		0			0
$176$	0.586002	−	0.492858i	0.0441715	−	0.0371506i
$177$		0			0
$178$	4.92693	+	1.09079i	0.369289	+	0.0817585i
$179$		−	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	$0.353490\pi$
$181$			24.1070i			1.79186i	−0.444195	+	0.895930i	$0.646510\pi$
$182$	1.14003	−	5.14931i	0.0845046	−	0.381692i
$183$		0			0
$184$	11.7938	+	9.03365i	0.869453	+	0.665970i
$185$		0			0
$186$		0			0
$187$			1.18785i			0.0868639i
$188$	3.20275	−	6.87859i	0.233585	−	0.501673i
$189$		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
$193$			15.3169i			1.10254i	0.834328	+	0.551269i	$0.185856\pi$
$193$			15.3169i			1.10254i	−0.834328	+	0.551269i	$0.814144\pi$
$194$	−10.1031	−	2.23677i	−0.725359	−	0.160590i
$195$		0			0
$196$	9.06550	+	4.22099i	0.647535	+	0.301500i
$197$		−	17.0462i		−	1.21449i	−0.794513	−	0.607247i	$-0.792274\pi$
$197$		−	17.0462i		−	1.21449i	0.794513	−	0.607247i	$-0.207726\pi$
$198$		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
$202$	−4.75390	+	21.4725i	−0.334483	+	1.51080i
$203$	0.382853			0.0268710
$204$		0			0
$205$		0			0
$206$	0.638488	−	2.88394i	0.0444856	−	0.200933i
$207$		0			0
$208$	−6.78937	−	8.07247i	−0.470758	−	0.559725i
$209$		−	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	$0.303186\pi$
$212$	7.40828	−	15.9109i	0.508803	−	1.09276i
$213$		0			0
$214$	−0.864641	+	3.90543i	−0.0591056	+	0.266970i
$215$		0			0
$216$		0			0
$217$		−	8.77551i		−	0.595720i
$218$	7.28223	+	1.61224i	0.493215	+	0.109195i
$219$		0			0
$220$		0			0
$221$	16.3632			1.10071
$222$		0			0
$223$	22.3099			1.49398			0.746992	−	0.664833i	$-0.231497\pi$
$223$	22.3099			1.49398			0.746992	+	0.664833i	$0.231497\pi$
$224$	−7.09079	+	3.70414i	−0.473774	+	0.247493i
$225$		0			0
$226$	1.77988	−	8.03940i	0.118396	−	0.534773i
$227$	−8.86813			−0.588599			−0.294299	−	0.955713i	$-0.595086\pi$
$227$	−8.86813			−0.588599			−0.294299	+	0.955713i	$0.595086\pi$
$228$		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
$232$	0.465611	−	0.607876i	0.0305689	−	0.0399090i
$233$	−15.0734			−0.987488			−0.493744	−	0.869607i	$-0.664372\pi$
$233$	−15.0734			−0.987488			−0.493744	+	0.869607i	$0.664372\pi$
$234$		0			0
$235$		0			0
$236$	8.82008	−	18.9430i	0.574138	−	1.23309i
$237$		0			0
$238$	2.68264	−	12.1170i	0.173890	−	0.785431i
$239$	−19.0462			−1.23200			−0.615999	−	0.787747i	$-0.711247\pi$
$239$	−19.0462			−1.23200			−0.615999	+	0.787747i	$0.711247\pi$
$240$		0			0
$241$	18.5048			1.19200			0.595999	−	0.802985i	$-0.296756\pi$
$241$	18.5048			1.19200			0.595999	+	0.802985i	$0.296756\pi$
$242$	−3.35146	+	15.1380i	−0.215440	+	0.973105i
$243$		0			0
$244$	0.323204	−	0.694151i	0.0206910	−	0.0444385i
$245$		0			0
$246$		0			0
$247$	−4.01645			−0.255561
$248$	−13.9333	−	10.6724i	−0.884767	−	0.677700i
$249$		0			0
$250$		0			0
$251$			16.8186i			1.06158i	0.847503	+	0.530790i	$0.178105\pi$
$251$			16.8186i			1.06158i	−0.847503	+	0.530790i	$0.821895\pi$
$252$		0			0
$253$	1.00545			0.0632120
$254$	6.27864	−	28.3595i	0.393957	−	1.77943i
$255$		0			0
$256$	−2.74229	+	15.7632i	−0.171393	+	0.985203i
$257$	9.79936			0.611267			0.305634	−	0.952149i	$-0.401132\pi$
$257$	9.79936			0.611267			0.305634	+	0.952149i	$0.401132\pi$
$258$		0			0
$259$	10.7755			0.669558
$260$		0			0
$261$		0			0
$262$	−18.7342	−	4.14765i	−1.15740	−	0.256243i
$263$			5.79383i			0.357263i	0.983916	+	0.178632i	$0.0571670\pi$
$263$			5.79383i			0.357263i	−0.983916	+	0.178632i	$0.942833\pi$
$264$		0			0
$265$		0			0
$266$	−0.658473	+	2.97421i	−0.0403736	+	0.182360i
$267$		0			0
$268$	1.45986	−	3.13536i	0.0891750	−	0.191523i
$269$	15.1878			0.926019			0.463010	−	0.886353i	$-0.346770\pi$
$269$	15.1878			0.926019			0.463010	+	0.886353i	$0.346770\pi$
$270$		0			0
$271$		−	10.1304i		−	0.615377i	−0.951487	−	0.307689i	$-0.900444\pi$
$271$		−	10.1304i		−	0.615377i	0.951487	−	0.307689i	$-0.0995555\pi$
$272$	−15.9763	−	18.9956i	−0.968706	−	1.15178i
$273$		0			0
$274$	1.44461	−	6.52505i	0.0872721	−	0.394193i
$275$		0			0
$276$		0			0
$277$	14.7559			0.886595			0.443298	−	0.896375i	$-0.353809\pi$
$277$	14.7559			0.886595			0.443298	+	0.896375i	$0.353809\pi$
$278$	4.81692	−	21.7572i	0.288900	−	1.30491i
$279$		0			0
$280$		0			0
$281$		−	21.5442i		−	1.28522i	−0.766193	−	0.642611i	$-0.777851\pi$
$281$		−	21.5442i		−	1.28522i	0.766193	−	0.642611i	$-0.222149\pi$
$282$		0			0
$283$		−	18.2707i		−	1.08608i	−0.839706	−	0.543041i	$-0.817273\pi$
$283$		−	18.2707i		−	1.08608i	0.839706	−	0.543041i	$-0.182727\pi$
$284$	17.6402	+	8.21345i	1.04675	+	0.487379i
$285$		0			0
$286$	−0.697006	−	0.154313i	−0.0412149	−	0.00912474i
$287$			13.0462i			0.770095i
$288$		0			0
$289$	21.5048			1.26499
$290$		0			0
$291$		0			0
$292$	4.60811	−	9.89692i	0.269669	−	0.579173i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		0			0
$295$		0			0
$296$	13.1047	−	17.1088i	0.761698	−	0.994431i
$297$		0			0
$298$	2.36282	−	10.6724i	0.136874	−	0.618237i
$299$		−	13.8506i		−	0.800999i
$300$		0			0
$301$			18.0673i			1.04138i
$302$	30.6668	+	6.78946i	1.76468	+	0.390690i
$303$		0			0
$304$	3.92150	+	4.66261i	0.224913	+	0.267419i
$305$		0			0
$306$		0			0
$307$			22.5048i			1.28442i	0.766530	+	0.642208i	$0.221982\pi$
$307$			22.5048i			1.28442i	−0.766530	+	0.642208i	$0.778018\pi$
$308$	−0.228540	+	0.490839i	−0.0130223	+	0.0279681i
$309$		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
$313$			2.23407i			0.126277i	0.998005	+	0.0631387i	$0.0201110\pi$
$313$			2.23407i			0.126277i	−0.998005	+	0.0631387i	$0.979889\pi$
$314$	−2.44627	+	11.0494i	−0.138051	+	0.623553i
$315$		0			0
$316$	−12.0785	+	25.9412i	−0.679469	+	1.45931i
$317$		−	16.5048i		−	0.927001i	−0.886097	−	0.463501i	$-0.846593\pi$
$317$		−	16.5048i		−	0.927001i	0.886097	−	0.463501i	$-0.153407\pi$
$318$		0			0
$319$		−	0.0518227i		−	0.00290151i
$320$		0			0
$321$		0			0
$322$	−10.2564	−	2.27072i	−0.571569	−	0.126542i
$323$	−9.45126			−0.525882
$324$		0			0
$325$		0			0
$326$	−1.31695	−	0.291565i	−0.0729389	−	0.0161483i
$327$		0			0
$328$	20.7142	+	15.8663i	1.14375	+	0.876070i
$329$			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	$0.616122\pi$
$332$	27.6296	+	12.8646i	1.51637	+	0.706039i
$333$		0			0
$334$	−16.2341	−	3.59413i	−0.888289	−	0.196662i
$335$		0			0
$336$		0			0
$337$		−	27.0096i		−	1.47131i	−0.677359	−	0.735653i	$-0.736875\pi$
$337$		−	27.0096i		−	1.47131i	0.677359	−	0.735653i	$-0.263125\pi$
$338$	1.84831	−	8.34850i	0.100535	−	0.454099i
$339$		0			0
$340$		0			0
$341$	−1.18785			−0.0643254
$342$		0			0
$343$	−16.9706			−0.916324
$344$	28.6864	+	21.9727i	1.54667	+	1.18469i
$345$		0			0
$346$	4.45231	+	0.985716i	0.239357	+	0.0529924i
$347$	−5.07372			−0.272372			−0.136186	−	0.990683i	$-0.543484\pi$
$347$	−5.07372			−0.272372			−0.136186	+	0.990683i	$0.543484\pi$
$348$		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
$352$	0.501389	+	0.959804i	0.0267241	+	0.0511577i
$353$	−14.3077			−0.761519			−0.380760	−	0.924674i	$-0.624337\pi$
$353$	−14.3077			−0.761519			−0.380760	+	0.924674i	$0.624337\pi$
$354$		0			0
$355$		0			0
$356$	−3.01229	+	6.46954i	−0.159651	+	0.342885i
$357$		0			0
$358$	17.4004	+	3.85235i	0.919640	+	0.203603i
$359$	31.8217			1.67949			0.839744	−	0.542983i	$-0.182705\pi$
$359$	31.8217			1.67949			0.839744	+	0.542983i	$0.182705\pi$
$360$		0			0
$361$	−16.6801			−0.877901
$362$	−33.2864	−	7.36943i	−1.74950	−	0.387329i
$363$		0			0
$364$	6.76156	+	3.14826i	0.354402	+	0.165013i
$365$		0			0
$366$		0			0
$367$	−22.9844			−1.19977			−0.599887	−	0.800085i	$-0.704788\pi$
$367$	−22.9844			−1.19977			−0.599887	+	0.800085i	$0.704788\pi$
$368$	−16.0788	+	13.5231i	−0.838166	+	0.704941i
$369$		0			0
$370$		0			0
$371$			12.4104i			0.644318i
$372$		0			0
$373$	14.2423			0.737437			0.368718	−	0.929541i	$-0.379797\pi$
$373$	14.2423			0.737437			0.368718	+	0.929541i	$0.379797\pi$
$374$	−1.64015	−	0.363120i	−0.0848102	−	0.0187765i
$375$		0			0
$376$	8.51875	+	6.52505i	0.439321	+	0.336504i
$377$	−0.713884			−0.0367669
$378$		0			0
$379$	8.71096			0.447452			0.223726	−	0.974652i	$-0.428178\pi$
$379$	8.71096			0.447452			0.223726	+	0.974652i	$0.428178\pi$
$380$		0			0
$381$		0			0
$382$	−3.33733	+	15.0741i	−0.170753	+	0.771260i
$383$		−	18.7110i		−	0.956085i	−0.878337	−	0.478043i	$-0.841346\pi$
$383$		−	18.7110i		−	0.956085i	0.878337	−	0.478043i	$-0.158654\pi$
$384$		0			0
$385$		0			0
$386$	−21.1493	−	4.68234i	−1.07647	−	0.238325i
$387$		0			0
$388$	6.17696	−	13.2663i	0.313588	−	0.673497i
$389$	27.0096			1.36944			0.684720	−	0.728806i	$-0.259924\pi$
$389$	27.0096			1.36944			0.684720	+	0.728806i	$0.259924\pi$
$390$		0			0
$391$		−	32.5923i		−	1.64826i
$392$	−8.59955	+	11.2271i	−0.434343	+	0.567054i
$393$		0			0
$394$	23.5371	+	5.21098i	1.18578	+	0.262525i
$395$		0			0
$396$		0			0
$397$	25.3952			1.27455			0.637274	−	0.770638i	$-0.280062\pi$
$397$	25.3952			1.27455			0.637274	+	0.770638i	$0.280062\pi$
$398$	−6.52505	−	1.44461i	−0.327071	−	0.0724118i
$399$		0			0
$400$		0			0
$401$		−	6.01380i		−	0.300315i	−0.988662	−	0.150157i	$-0.952022\pi$
$401$		−	6.01380i		−	0.300315i	0.988662	−	0.150157i	$-0.0479780\pi$
$402$		0			0
$403$			16.3632i			0.815108i
$404$	−28.1955	−	13.1282i	−1.40278	−	0.653150i
$405$		0			0
$406$	−0.117037	+	0.528636i	−0.00580845	+	0.0262358i
$407$		−	1.45856i		−	0.0722983i
$408$		0			0
$409$	19.5510			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$409$	19.5510			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$410$		0			0
$411$		0			0
$412$	3.78690	+	1.76322i	0.186567	+	0.0868676i
$413$			14.7755i			0.727055i
$414$		0			0
$415$		0			0
$416$	13.2218	−	6.90689i	0.648251	−	0.338638i
$417$		0			0
$418$	0.402586	+	0.0891304i	0.0196911	+	0.00435951i
$419$			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	$0.0334778\pi$
$421$			4.30802i			0.209960i	−0.994474	+	0.104980i	$0.966522\pi$
$422$	−5.14795	+	23.2524i	−0.250598	+	1.13191i
$423$		0			0
$424$	19.7047	+	15.0931i	0.956945	+	0.732985i
$425$		0			0
$426$		0			0
$427$			0.541436i			0.0262019i
$428$	−5.12822	−	2.38776i	−0.247882	−	0.115417i
$429$		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
$433$		−	9.45856i		−	0.454550i	−0.973831	−	0.227275i	$-0.927018\pi$
$433$		−	9.45856i		−	0.454550i	0.973831	−	0.227275i	$-0.0729816\pi$
$434$	12.1170	+	2.68264i	0.581636	+	0.128771i
$435$		0			0
$436$	−4.45231	+	9.56229i	−0.213227	+	0.457950i
$437$			8.00000i			0.382692i
$438$		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
$442$	−5.00217	+	22.5939i	−0.237929	+	1.07468i
$443$	25.0730			1.19125			0.595627	−	0.803261i	$-0.296904\pi$
$443$	25.0730			1.19125			0.595627	+	0.803261i	$0.296904\pi$
$444$		0			0
$445$		0			0
$446$	−6.82008	+	30.8051i	−0.322940	+	1.45866i
$447$		0			0
$448$	−2.94696	−	10.9232i	−0.139231	−	0.516071i
$449$			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
$452$	10.5565	+	4.91524i	0.496538	+	0.231193i
$453$		0			0
$454$	2.71096	−	12.2449i	0.127232	−	0.574683i
$455$		0			0
$456$		0			0
$457$			28.8680i			1.35039i	0.737641	+	0.675193i	$0.235940\pi$
$457$			28.8680i			1.35039i	−0.737641	+	0.675193i	$0.764060\pi$
$458$	−29.3810	−	6.50479i	−1.37288	−	0.303949i
$459$		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
$463$	16.6136			0.772100			0.386050	−	0.922478i	$-0.373839\pi$
$463$	16.6136			0.772100			0.386050	+	0.922478i	$0.373839\pi$
$464$	0.697006	+	0.828731i	0.0323577	+	0.0384729i
$465$		0			0
$466$	4.60788	−	20.8130i	0.213456	−	0.964142i
$467$	−1.47959			−0.0684673			−0.0342336	−	0.999414i	$-0.510899\pi$
$467$	−1.47959			−0.0684673			−0.0342336	+	0.999414i	$0.510899\pi$
$468$		0			0
$469$			2.44557i			0.112926i
$470$		0			0
$471$		0			0
$472$	23.4598	+	17.9694i	1.07983	+	0.827108i
$473$	2.44557			0.112448
$474$		0			0
$475$		0			0
$476$	15.9109	+	7.40828i	0.729274	+	0.339558i
$477$		0			0
$478$	5.82237	−	26.2986i	0.266309	−	1.20287i
$479$	−2.81215			−0.128491			−0.0642453	−	0.997934i	$-0.520464\pi$
$479$	−2.81215			−0.128491			−0.0642453	+	0.997934i	$0.520464\pi$
$480$		0			0
$481$	−20.0925			−0.916137
$482$	−5.65685	+	25.5510i	−0.257663	+	1.16382i
$483$		0			0
$484$	−19.8776	−	9.25525i	−0.903530	−	0.420693i
$485$		0			0
$486$		0			0
$487$	16.9447			0.767835			0.383918	−	0.923367i	$-0.374575\pi$
$487$	16.9447			0.767835			0.383918	+	0.923367i	$0.374575\pi$
$488$	0.859666	+	0.658473i	0.0389153	+	0.0298077i
$489$		0			0
$490$		0			0
$491$		−	26.0696i		−	1.17650i	−0.808678	−	0.588252i	$-0.799816\pi$
$491$		−	26.0696i		−	1.17650i	0.808678	−	0.588252i	$-0.200184\pi$
$492$		0			0
$493$	−1.67987			−0.0756574
$494$	1.22782	−	5.54583i	0.0552421	−	0.249519i
$495$		0			0
$496$	18.9956	−	15.9763i	0.852929	−	0.717358i
$497$	−13.7593			−0.617188
$498$		0			0
$499$	−22.5327			−1.00870			−0.504351	−	0.863499i	$-0.668268\pi$
$499$	−22.5327			−1.00870			−0.504351	+	0.863499i	$0.668268\pi$
$500$		0			0
$501$		0			0
$502$	−23.2228	−	5.14139i	−1.03648	−	0.229472i
$503$		−	8.80342i		−	0.392525i	−0.980551	−	0.196262i	$-0.937120\pi$
$503$		−	8.80342i		−	0.392525i	0.980551	−	0.196262i	$-0.0628805\pi$
$504$		0			0
$505$		0			0
$506$	−0.307362	+	1.38830i	−0.0136639	+	0.0617176i
$507$		0			0
$508$	37.2389	+	17.3388i	1.65221	+	0.769286i
$509$	20.6339			0.914581			0.457291	−	0.889317i	$-0.348820\pi$
$509$	20.6339			0.914581			0.457291	+	0.889317i	$0.348820\pi$
$510$		0			0
$511$			7.71957i			0.341494i
$512$	−20.9272	−	8.60527i	−0.924862	−	0.380303i
$513$		0			0
$514$	−2.99563	+	13.5307i	−0.132132	+	0.596815i
$515$		0			0
$516$		0			0
$517$	0.726241			0.0319400
$518$	−3.29404	+	14.8786i	−0.144732	+	0.653728i
$519$		0			0
$520$		0			0
$521$			8.55066i			0.374611i	0.982302	+	0.187306i	$0.0599755\pi$
$521$			8.55066i			0.374611i	−0.982302	+	0.187306i	$0.940025\pi$
$522$		0			0
$523$		−	33.0096i		−	1.44341i	−0.692202	−	0.721704i	$-0.743359\pi$
$523$		−	33.0096i		−	1.44341i	0.692202	−	0.721704i	$-0.256641\pi$
$524$	11.4540	−	24.5999i	0.500369	−	1.07465i
$525$		0			0
$526$	−8.00000	−	1.77116i	−0.348817	−	0.0772261i
$527$			38.5048i			1.67730i
$528$		0			0
$529$	−4.58767			−0.199464
$530$		0			0
$531$		0			0
$532$	−3.90543	−	1.81841i	−0.169322	−	0.0788382i
$533$		−	24.3265i		−	1.05370i
$534$		0			0
$535$		0			0
$536$	3.88296	+	2.97421i	0.167718	+	0.128466i
$537$		0			0
$538$	−4.64287	+	20.9711i	−0.200169	+	0.904126i
$539$			0.957133i			0.0412267i
$540$		0			0
$541$			27.6493i			1.18874i	0.804193	+	0.594369i	$0.202598\pi$
$541$			27.6493i			1.18874i	−0.804193	+	0.594369i	$0.797402\pi$
$542$	13.9878	+	3.09683i	0.600828	+	0.133020i
$543$		0			0
$544$	31.1127	−	16.2529i	1.33394	−	0.696835i
$545$		0			0
$546$		0			0
$547$		−	9.85838i		−	0.421514i	−0.977538	−	0.210757i	$-0.932407\pi$
$547$		−	9.85838i		−	0.421514i	0.977538	−	0.210757i	$-0.0675929\pi$
$548$	8.56804	+	3.98937i	0.366008	+	0.170418i
$549$		0			0
$550$		0			0
$551$	0.412335			0.0175661
$552$		0			0
$553$		−	20.2341i		−	0.860440i
$554$	−4.51082	+	20.3746i	−0.191647	+	0.865634i
$555$		0			0
$556$	28.5693	+	13.3022i	1.21161	+	0.564139i
$557$			2.68305i			0.113685i	0.998383	+	0.0568423i	$0.0181032\pi$
$557$			2.68305i			0.113685i	−0.998383	+	0.0568423i	$0.981897\pi$
$558$		0			0
$559$		−	33.6890i		−	1.42489i
$560$		0			0
$561$		0			0
$562$	29.7478	+	6.58600i	1.25484	+	0.277814i
$563$	−12.0794			−0.509087			−0.254543	−	0.967061i	$-0.581925\pi$
$563$	−12.0794			−0.509087			−0.254543	+	0.967061i	$0.581925\pi$
$564$		0			0
$565$		0			0
$566$	25.2278	+	5.58530i	1.06040	+	0.234768i
$567$		0			0
$568$	−16.7335	+	21.8463i	−0.702122	+	0.916651i
$569$		−	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	$0.492601\pi$
$572$	0.426145	−	0.915238i	0.0178180	−	0.0382680i
$573$		0			0
$574$	−18.0140	−	3.98819i	−0.751888	−	0.166464i
$575$		0			0
$576$		0			0
$577$			14.7755i			0.615113i	0.951530	+	0.307556i	$0.0995112\pi$
$577$			14.7755i			0.615113i	−0.951530	+	0.307556i	$0.900489\pi$
$578$	−6.57394	+	29.6934i	−0.273440	+	1.23508i
$579$		0			0
$580$		0			0
$581$	−21.5510			−0.894087
$582$		0			0
$583$	1.67987			0.0695730
$584$	12.2568	+	9.38824i	0.507189	+	0.388488i
$585$		0			0
$586$	−8.28467	−	1.83418i	−0.342237	−	0.0757693i
$587$	13.5590			0.559640			0.279820	−	0.960052i	$-0.409725\pi$
$587$	13.5590			0.559640			0.279820	+	0.960052i	$0.409725\pi$
$588$		0			0
$589$		−	9.45126i		−	0.389433i
$590$		0			0
$591$		0			0
$592$	19.6174	+	23.3249i	0.806271	+	0.958646i
$593$	31.9921			1.31376			0.656879	−	0.753996i	$-0.271876\pi$
$593$	31.9921			1.31376			0.656879	+	0.753996i	$0.271876\pi$
$594$		0			0
$595$		0			0
$596$	14.0140	+	6.52505i	0.574034	+	0.267277i
$597$		0			0
$598$	19.1246	+	4.23407i	0.782062	+	0.173144i
$599$	−3.82174			−0.156152			−0.0780760	−	0.996947i	$-0.524878\pi$
$599$	−3.82174			−0.156152			−0.0780760	+	0.996947i	$0.524878\pi$
$600$		0			0
$601$	31.6435			1.29076			0.645382	−	0.763860i	$-0.276698\pi$
$601$	31.6435			1.29076			0.645382	+	0.763860i	$0.276698\pi$
$602$	−24.9469	−	5.52311i	−1.01676	−	0.225105i
$603$		0			0
$604$	−18.7495	+	40.2686i	−0.762906	+	1.63850i
$605$		0			0
$606$		0			0
$607$	−34.7204			−1.40926			−0.704629	−	0.709576i	$-0.748886\pi$
$607$	−34.7204			−1.40926			−0.704629	+	0.709576i	$0.748886\pi$
$608$	−7.63682	+	3.98937i	−0.309714	+	0.161790i
$609$		0			0
$610$		0			0
$611$		−	10.0043i		−	0.404732i
$612$		0			0
$613$	−26.3612			−1.06472			−0.532359	−	0.846519i	$-0.678694\pi$
$613$	−26.3612			−1.06472			−0.532359	+	0.846519i	$0.678694\pi$
$614$	−31.0741	−	6.87964i	−1.25405	−	0.277640i
$615$		0			0
$616$	−0.607876	−	0.465611i	−0.0244920	−	0.0187600i
$617$	7.88509			0.317442			0.158721	−	0.987323i	$-0.449263\pi$
$617$	7.88509			0.317442			0.158721	+	0.987323i	$0.449263\pi$
$618$		0			0
$619$	38.9325			1.56483			0.782415	−	0.622757i	$-0.213988\pi$
$619$	38.9325			1.56483			0.782415	+	0.622757i	$0.213988\pi$
$620$		0			0
$621$		0			0
$622$	9.49073	−	42.8680i	0.380544	−	1.71885i
$623$		−	5.04623i		−	0.202173i
$624$		0			0
$625$		0			0
$626$	−3.08476	−	0.682949i	−0.123292	−	0.0272961i
$627$		0			0
$628$	−14.5089	−	6.75552i	−0.578970	−	0.269575i
$629$	−47.2803			−1.88519
$630$		0			0
$631$		−	0.800468i		−	0.0318661i	−0.999873	−	0.0159331i	$-0.994928\pi$
$631$		−	0.800468i		−	0.0318661i	0.999873	−	0.0159331i	$-0.00507186\pi$
$632$	−32.1267	−	24.6079i	−1.27793	−	0.978849i
$633$		0			0
$634$	22.7895	+	5.04546i	0.905085	+	0.200381i
$635$		0			0
$636$		0			0
$637$	13.1850			0.522409
$638$	0.0715557	+	0.0158420i	0.00283292	+	0.000627192i
$639$		0			0
$640$		0			0
$641$		−	22.8931i		−	0.904222i	−0.891962	−	0.452111i	$-0.850671\pi$
$641$		−	22.8931i		−	0.904222i	0.891962	−	0.452111i	$-0.149329\pi$
$642$		0			0
$643$			12.9538i			0.510847i	0.966829	+	0.255423i	$0.0822149\pi$
$643$			12.9538i			0.510847i	−0.966829	+	0.255423i	$0.917785\pi$
$644$	6.27072	−	13.4677i	0.247101	−	0.530702i
$645$		0			0
$646$	2.88922	−	13.0501i	0.113675	−	0.513449i
$647$		−	15.6647i		−	0.615844i	−0.951412	−	0.307922i	$-0.900366\pi$
$647$		−	15.6647i		−	0.615844i	0.951412	−	0.307922i	$-0.0996336\pi$
$648$		0			0
$649$	2.00000			0.0785069
$650$		0			0
$651$		0			0
$652$	0.805173	−	1.72928i	0.0315330	−	0.0677239i
$653$		−	41.5144i		−	1.62458i	−0.583252	−	0.812292i	$-0.698220\pi$
$653$		−	41.5144i		−	1.62458i	0.583252	−	0.812292i	$-0.301780\pi$
$654$		0			0
$655$		0			0
$656$	−28.2401	+	23.7514i	−1.10259	+	0.927336i
$657$		0			0
$658$	−7.40828	−	1.64015i	−0.288805	−	0.0639398i
$659$			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	$0.125814\pi$
$661$			19.7990i			0.770091i	−0.922897	+	0.385046i	$0.874186\pi$
$662$	3.96846	−	17.9248i	0.154238	−	0.696668i
$663$		0			0
$664$	−26.2095	+	34.2177i	−1.01713	+	1.32790i
$665$		0			0
$666$		0			0
$667$			1.42192i			0.0550569i
$668$	9.92541	−	21.3169i	0.384025	−	0.824777i
$669$		0			0
$670$		0			0
$671$	0.0732884			0.00282927
$672$		0			0
$673$		−	34.1849i		−	1.31773i	−0.752260	−	0.658866i	$-0.771036\pi$
$673$		−	34.1849i		−	1.31773i	0.752260	−	0.658866i	$-0.228964\pi$
$674$	37.2943	+	8.25674i	1.43652	+	0.318038i
$675$		0			0
$676$	10.9624	+	5.10422i	0.421631	+	0.196316i
$677$		−	17.0462i		−	0.655140i	−0.944827	−	0.327570i	$-0.893770\pi$
$677$		−	17.0462i		−	0.655140i	0.944827	−	0.327570i	$-0.106230\pi$
$678$		0			0
$679$			10.3477i			0.397109i
$680$		0			0
$681$		0			0
$682$	0.363120	−	1.64015i	0.0139046	−	0.0628046i
$683$	28.6671			1.09692			0.548459	−	0.836178i	$-0.315215\pi$
$683$	28.6671			1.09692			0.548459	+	0.836178i	$0.315215\pi$
$684$		0			0
$685$		0			0
$686$	5.18785	−	23.4326i	0.198073	−	0.894660i
$687$		0			0
$688$	−39.1088	+	32.8925i	−1.49101	+	1.25402i
$689$		−	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	$0.672199\pi$
$692$	−2.72211	+	5.84632i	−0.103479	+	0.222244i
$693$		0			0
$694$	1.55102	−	7.00569i	0.0588760	−	0.265932i
$695$		0			0
$696$		0			0
$697$		−	57.2437i		−	2.16826i
$698$	−27.7951	−	6.15368i	−1.05206	−	0.232920i
$699$		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
$703$	11.6053			0.437701
$704$	−1.47855	+	0.398898i	−0.0557249	+	0.0150340i
$705$		0			0
$706$	4.37380	−	19.7557i	0.164610	−	0.743516i
$707$	21.9925			0.827112
$708$		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
$712$	−8.01216	−	6.13702i	−0.300268	−	0.229995i
$713$	32.5923			1.22059
$714$		0			0
$715$		0			0
$716$	−10.6385	+	22.8484i	−0.397579	+	0.853886i
$717$		0			0
$718$	−9.72780	+	43.9388i	−0.363038	+	1.63978i
$719$	−10.1416			−0.378218			−0.189109	−	0.981956i	$-0.560560\pi$
$719$	−10.1416			−0.378218			−0.189109	+	0.981956i	$0.560560\pi$
$720$		0			0
$721$	−2.95377			−0.110004
$722$	5.09906	−	23.0316i	0.189767	−	0.857146i
$723$		0			0
$724$	20.3511	−	43.7084i	0.756343	−	1.62441i
$725$		0			0
$726$		0			0
$727$	−4.86524			−0.180442			−0.0902208	−	0.995922i	$-0.528757\pi$
$727$	−4.86524			−0.180442			−0.0902208	+	0.995922i	$0.528757\pi$
$728$	−6.41403	+	8.37380i	−0.237720	+	0.310354i
$729$		0			0
$730$		0			0
$731$		−	79.2749i		−	2.93209i
$732$		0			0
$733$	−9.09903			−0.336080			−0.168040	−	0.985780i	$-0.553744\pi$
$733$	−9.09903			−0.336080			−0.168040	+	0.985780i	$0.553744\pi$
$734$	7.02624	−	31.7363i	0.259343	−	1.17141i
$735$		0			0
$736$	−13.7572	−	26.3352i	−0.507097	−	0.970730i
$737$	0.331031			0.0121937
$738$		0			0
$739$	−12.5693			−0.462371			−0.231185	−	0.972910i	$-0.574260\pi$
$739$	−12.5693			−0.462371			−0.231185	+	0.972910i	$0.574260\pi$
$740$		0			0
$741$		0			0
$742$	−17.1361	−	3.79383i	−0.629085	−	0.139276i
$743$			23.6647i			0.868175i	0.900871	+	0.434087i	$0.142929\pi$
$743$			23.6647i			0.868175i	−0.900871	+	0.434087i	$0.857071\pi$
$744$		0			0
$745$		0			0
$746$	−4.35382	+	19.6654i	−0.159405	+	0.720002i
$747$		0			0
$748$	1.00278	−	2.15368i	0.0366652	−	0.0787464i
$749$	4.00000			0.146157
$750$		0			0
$751$			31.2782i			1.14136i	0.821173	+	0.570679i	$0.193320\pi$
$751$			31.2782i			1.14136i	−0.821173	+	0.570679i	$0.806680\pi$
$752$	−11.6138	+	9.76781i	−0.423512	+	0.356196i
$753$		0			0
$754$	0.218232	−	0.985716i	0.00794754	−	0.0358977i
$755$		0			0
$756$		0			0
$757$	−39.1150			−1.42166			−0.710829	−	0.703365i	$-0.751680\pi$
$757$	−39.1150			−1.42166			−0.710829	+	0.703365i	$0.751680\pi$
$758$	−2.66291	+	12.0279i	−0.0967213	+	0.436873i
$759$		0			0
$760$		0			0
$761$			2.76305i			0.100160i	0.998745	+	0.0500802i	$0.0159477\pi$
$761$			2.76305i			0.100160i	−0.998745	+	0.0500802i	$0.984052\pi$
$762$		0			0
$763$		−	7.45856i		−	0.270018i
$764$	−19.7938	−	9.21623i	−0.716116	−	0.333431i
$765$		0			0
$766$	25.8357	+	5.71988i	0.933482	+	0.206668i
$767$		−	27.5510i		−	0.994810i
$768$		0			0
$769$	−46.5606			−1.67902			−0.839509	−	0.543345i	$-0.817157\pi$
$769$	−46.5606			−1.67902			−0.839509	+	0.543345i	$0.817157\pi$
$770$		0			0
$771$		0			0
$772$	12.9306	−	27.7711i	0.465381	−	0.999505i
$773$			29.5877i			1.06419i	0.846683	+	0.532097i	$0.178596\pi$
$773$			29.5877i			1.06419i	−0.846683	+	0.532097i	$0.821404\pi$
$774$		0			0
$775$		0			0
$776$	16.4296	+	12.5845i	0.589789	+	0.451757i
$777$		0			0
$778$	−8.25674	+	37.2943i	−0.296019	+	1.33706i
$779$			14.0508i			0.503424i
$780$		0			0
$781$			1.86244i			0.0666435i
$782$	45.0027	+	9.96336i	1.60929	+	0.356289i
$783$		0			0
$784$	−12.8733	−	15.3062i	−0.459760	−	0.546649i
$785$		0			0
$786$		0			0
$787$		−	35.9267i		−	1.28065i	−0.768105	−	0.640324i	$-0.778800\pi$
$787$		−	35.9267i		−	1.28065i	0.768105	−	0.640324i	$-0.221200\pi$
$788$	−14.3904	+	30.9065i	−0.512637	+	1.10100i
$789$		0			0
$790$		0			0
$791$	−8.23407			−0.292770
$792$		0			0
$793$		−	1.00958i		−	0.0358514i
$794$	−7.76322	+	35.0651i	−0.275506	+	1.24441i
$795$		0			0
$796$	3.98937	−	8.56804i	0.141400	−	0.303686i
$797$		−	9.31695i		−	0.330023i	−0.986292	−	0.165012i	$-0.947234\pi$
$797$		−	9.31695i		−	0.330023i	0.986292	−	0.165012i	$-0.0527662\pi$
$798$		0			0
$799$		−	23.5416i		−	0.832841i
$800$		0			0
$801$		0			0
$802$	8.30372	+	1.83840i	0.293215	+	0.0649161i
$803$	1.04491			0.0368742
$804$		0			0
$805$		0			0
$806$	−22.5939	−	5.00217i	−0.795837	−	0.176194i
$807$		0			0
$808$	26.7464	−	34.9186i	0.940934	−	1.22843i
$809$			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	$0.649601\pi$
$812$	−0.694151	−	0.323204i	−0.0243599	−	0.0113423i
$813$		0			0
$814$	2.01395	+	0.445878i	0.0705890	+	0.0156280i
$815$		0			0
$816$		0			0
$817$			19.4586i			0.680769i
$818$	−5.97668	+	26.9956i	−0.208970	+	0.943880i
$819$		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
$823$	−33.5718			−1.17024			−0.585120	−	0.810947i	$-0.698953\pi$
$823$	−33.5718			−1.17024			−0.585120	+	0.810947i	$0.698953\pi$
$824$	−3.59226	+	4.68985i	−0.125142	+	0.163379i
$825$		0			0
$826$	−20.4017	−	4.51683i	−0.709866	−	0.157160i
$827$	53.4362			1.85816			0.929079	−	0.369881i	$-0.120601\pi$
$827$	53.4362			1.85816			0.929079	+	0.369881i	$0.120601\pi$
$828$		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
$832$	5.49503	+	20.3678i	0.190506	+	0.706125i
$833$	31.0261			1.07499
$834$		0			0
$835$		0			0
$836$	−0.246139	+	0.528636i	−0.00851288	+	0.0182833i
$837$		0			0
$838$	−2.70989	−	0.599955i	−0.0936117	−	0.0207251i
$839$	−24.9046			−0.859803			−0.429901	−	0.902876i	$-0.641452\pi$
$839$	−24.9046			−0.859803			−0.429901	+	0.902876i	$0.641452\pi$
$840$		0			0
$841$	−28.9267			−0.997473
$842$	−5.94842	−	1.31695i	−0.204996	−	0.0453850i
$843$		0			0
$844$	−30.5327	−	14.2164i	−1.05098	−	0.489347i
$845$		0			0
$846$		0			0
$847$	15.5045			0.532742
$848$	−26.8639	+	22.5939i	−0.922509	+	0.775878i
$849$		0			0
$850$		0			0
$851$			40.0203i			1.37188i
$852$		0			0
$853$	17.5448			0.600724			0.300362	−	0.953825i	$-0.402893\pi$
$853$	17.5448			0.600724			0.300362	+	0.953825i	$0.402893\pi$
$854$	−0.747604	−	0.165515i	−0.0255825	−	0.00566382i
$855$		0			0
$856$	4.86464	−	6.35101i	0.166270	−	0.217073i
$857$	−7.30196			−0.249430			−0.124715	−	0.992193i	$-0.539802\pi$
$857$	−7.30196			−0.249430			−0.124715	+	0.992193i	$0.539802\pi$
$858$		0			0
$859$	−15.2890			−0.521655			−0.260828	−	0.965385i	$-0.583995\pi$
$859$	−15.2890			−0.521655			−0.260828	+	0.965385i	$0.583995\pi$
$860$		0			0
$861$		0			0
$862$	3.61387	−	16.3232i	0.123089	−	0.555971i
$863$		−	41.9787i		−	1.42897i	−0.699649	−	0.714487i	$-0.746660\pi$
$863$		−	41.9787i		−	1.42897i	0.699649	−	0.714487i	$-0.253340\pi$
$864$		0			0
$865$		0			0
$866$	13.0602	+	2.89145i	0.443803	+	0.0982555i
$867$		0			0
$868$	−7.40828	+	15.9109i	−0.251453	+	0.540050i
$869$	−2.73887			−0.0929097
$870$		0			0
$871$		−	4.56012i		−	0.154514i
$872$	−11.8423	−	9.07081i	−0.401032	−	0.307176i
$873$		0			0
$874$	−11.0462	−	2.44557i	−0.373644	−	0.0827228i
$875$		0			0
$876$		0			0
$877$	−38.4800			−1.29938			−0.649689	−	0.760200i	$-0.725101\pi$
$877$	−38.4800			−1.29938			−0.649689	+	0.760200i	$0.725101\pi$
$878$	−22.1468	−	4.90317i	−0.747418	−	0.165474i
$879$		0			0
$880$		0			0
$881$		−	7.11053i		−	0.239560i	−0.992800	−	0.119780i	$-0.961781\pi$
$881$		−	7.11053i		−	0.239560i	0.992800	−	0.119780i	$-0.0382189\pi$
$882$		0			0
$883$			26.5048i			0.891957i	0.895044	+	0.445979i	$0.147144\pi$
$883$			26.5048i			0.891957i	−0.895044	+	0.445979i	$0.852856\pi$
$884$	−29.6681	−	13.8138i	−0.997845	−	0.464608i
$885$		0			0
$886$	−7.66473	+	34.6202i	−0.257502	+	1.16309i
$887$		−	39.3449i		−	1.32107i	−0.750795	−	0.660535i	$-0.770329\pi$
$887$		−	39.3449i		−	1.32107i	0.750795	−	0.660535i	$-0.229671\pi$
$888$		0			0
$889$	−29.0462			−0.974179
$890$		0			0
$891$		0			0
$892$	−40.4501	−	18.8340i	−1.35437	−	0.630610i
$893$			5.77844i			0.193368i
$894$		0			0
$895$		0			0
$896$	15.9833	−	0.729929i	0.533966	−	0.0243852i
$897$		0			0
$898$	−5.85815	−	1.29696i	−0.195489	−	0.0432802i
$899$		−	1.67987i		−	0.0560267i
$900$		0			0
$901$		−	54.4540i		−	1.81413i
$902$	−0.539838	+	2.43835i	−0.0179746	+	0.0811883i
$903$		0			0
$904$	−10.0140	+	13.0737i	−0.333059	+	0.434824i
$905$		0			0
$906$		0			0
$907$		−	22.1974i		−	0.737054i	−0.929617	−	0.368527i	$-0.879862\pi$
$907$		−	22.1974i		−	0.737054i	0.929617	−	0.368527i	$-0.120138\pi$
$908$	16.0788	+	7.48647i	0.533594	+	0.248447i
$909$		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
$913$			2.91713i			0.0965428i
$914$	−39.8603	−	8.82484i	−1.31846	−	0.291900i
$915$		0			0
$916$	17.9634	−	38.5802i	0.593526	−	1.27472i
$917$			19.1878i			0.633638i
$918$		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
$922$	−11.2310	+	50.7282i	−0.369872	+	1.67065i
$923$	25.6561			0.844481
$924$		0			0
$925$		0			0
$926$	−5.07873	+	22.9397i	−0.166897	+	0.753846i
$927$		0			0
$928$	−1.35737	+	0.709071i	−0.0445578	+	0.0232764i
$929$			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
$932$	27.3295	+	12.7249i	0.895207	+	0.416818i
$933$		0			0
$934$	0.452306	−	2.04299i	0.0147999	−	0.0668486i
$935$		0			0
$936$		0			0
$937$			35.0096i			1.14371i	0.820354	+	0.571857i	$0.193777\pi$
$937$			35.0096i			1.14371i	−0.820354	+	0.571857i	$0.806223\pi$
$938$	−3.37680	−	0.747604i	−0.110256	−	0.0244101i
$939$		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
$943$	−48.4538			−1.57787
$944$	−31.9833	+	26.8997i	−1.04097	+	0.875509i
$945$		0			0
$946$	−0.747604	+	3.37680i	−0.0243067	+	0.109789i
$947$	−20.7650			−0.674771			−0.337385	−	0.941367i	$-0.609543\pi$
$947$	−20.7650			−0.674771			−0.337385	+	0.941367i	$0.609543\pi$
$948$		0			0
$949$		−	14.3942i		−	0.467257i
$950$		0			0
$951$		0			0
$952$	−15.0931	+	19.7047i	−0.489170	+	0.638633i
$953$	38.4147			1.24437			0.622186	−	0.782869i	$-0.286245\pi$
$953$	38.4147			1.24437			0.622186	+	0.782869i	$0.286245\pi$
$954$		0			0
$955$		0			0
$956$	34.5327	+	16.0788i	1.11687	+	0.520026i
$957$		0			0
$958$	0.859666	−	3.88296i	0.0277746	−	0.125453i
$959$	−6.68305			−0.215807
$960$		0			0
$961$	−7.50479			−0.242090
$962$	6.14220	−	27.7432i	0.198032	−	0.894478i
$963$		0			0
$964$	−33.5510	−	15.6217i	−1.08061	−	0.503142i
$965$		0			0
$966$		0			0
$967$	−16.6013			−0.533861			−0.266930	−	0.963716i	$-0.586009\pi$
$967$	−16.6013			−0.533861			−0.266930	+	0.963716i	$0.586009\pi$
$968$	18.8560	−	24.6173i	0.606054	−	0.791231i
$969$		0			0
$970$		0			0
$971$		−	10.3171i		−	0.331092i	−0.986202	−	0.165546i	$-0.947061\pi$
$971$		−	10.3171i		−	0.331092i	0.986202	−	0.165546i	$-0.0529386\pi$
$972$		0			0
$973$	−22.2840			−0.714393
$974$	−5.17992	+	23.3968i	−0.165975	+	0.749682i
$975$		0			0
$976$	−1.17200	+	0.985716i	−0.0375149	+	0.0315520i
$977$	32.0439			1.02518			0.512588	−	0.858635i	$-0.328687\pi$
$977$	32.0439			1.02518			0.512588	+	0.858635i	$0.328687\pi$
$978$		0			0
$979$	−0.683053			−0.0218305
$980$		0			0
$981$		0			0
$982$	35.9963	+	7.96939i	1.14869	+	0.254313i
$983$			24.8034i			0.791106i	0.918443	+	0.395553i	$0.129447\pi$
$983$			24.8034i			0.791106i	−0.918443	+	0.395553i	$0.870553\pi$
$984$		0			0
$985$		0			0
$986$	0.513530	−	2.31952i	0.0163541	−	0.0738687i
$987$		0			0
$988$	7.28223	+	3.39069i	0.231679	+	0.107872i
$989$	−67.1020			−2.13372
$990$		0			0
$991$			15.7872i			0.501498i	0.968052	+	0.250749i	$0.0806769\pi$
$991$			15.7872i			0.501498i	−0.968052	+	0.250749i	$0.919323\pi$
$992$	16.2529	+	31.1127i	0.516029	+	0.987828i
$993$		0			0
$994$	4.20617	−	18.9985i	0.133412	−	0.602597i
$995$		0			0
$996$		0			0
$997$	51.3823			1.62729			0.813647	−	0.581359i	$-0.197479\pi$
$997$	51.3823			1.62729			0.813647	+	0.581359i	$0.197479\pi$
$998$	6.88817	−	31.1127i	0.218041	−	0.984854i
$999$		0			0

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.305697 + 1.38078i) q^{2} +(-1.81310 - 0.844199i) q^{4} +1.41421 q^{7} +(1.71991 - 2.24542i) q^{8} +O(q^{10})\)	\(q+(-0.305697 + 1.38078i) q^{2} +(-1.81310 - 0.844199i) q^{4} +1.41421 q^{7} +(1.71991 - 2.24542i) q^{8} -0.191427i q^{11} -2.63700 q^{13} +(-0.432320 + 1.95272i) q^{14} +(2.57466 + 3.06123i) q^{16} -6.20522 q^{17} +1.52311 q^{19} +(0.264318 + 0.0585185i) q^{22} +5.25240i q^{23} +(0.806122 - 3.64111i) q^{26} +(-2.56411 - 1.19388i) q^{28} +0.270718 q^{29} -6.20522i q^{31} +(-5.01395 + 2.61922i) q^{32} +(1.89692 - 8.56804i) q^{34} +7.61944 q^{37} +(-0.465611 + 2.10308i) q^{38} +9.22508i q^{41} +12.7755i q^{43} +(-0.161602 + 0.347076i) q^{44} +(-7.25240 - 1.60564i) q^{46} +3.79383i q^{47} -5.00000 q^{49} +(4.78114 + 2.22615i) q^{52} +8.77551i q^{53} +(2.43232 - 3.17550i) q^{56} +(-0.0827577 + 0.373802i) q^{58} +10.4479i q^{59} +0.382853i q^{61} +(8.56804 + 1.89692i) q^{62} +(-2.08382 - 7.72384i) q^{64} +1.72928i q^{67} +(11.2507 + 5.23844i) q^{68} -9.72928 q^{71} +5.45856i q^{73} +(-2.32924 + 10.5208i) q^{74} +(-2.76156 - 1.28581i) q^{76} -0.270718i q^{77} -14.3077i q^{79} +(-12.7378 - 2.82008i) q^{82} -15.2389 q^{83} +(-17.6402 - 3.90543i) q^{86} +(-0.429833 - 0.329237i) q^{88} -3.56822i q^{89} -3.72928 q^{91} +(4.43407 - 9.52311i) q^{92} +(-5.23844 - 1.15976i) q^{94} +7.31695i q^{97} +(1.52848 - 6.90389i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{4}+O(q^{10}) \) 12 * q - 4 * q^4	\( 12 q - 4 q^{4} - 12 q^{16} - 32 q^{19} + 40 q^{26} + 24 q^{29} + 8 q^{34} + 24 q^{44} - 16 q^{46} - 60 q^{49} + 24 q^{56} - 28 q^{64} - 96 q^{71} - 8 q^{74} - 8 q^{76} - 80 q^{86} - 24 q^{91} - 88 q^{94}+O(q^{100}) \) 12 * q - 4 * q^4 - 12 * q^16 - 32 * q^19 + 40 * q^26 + 24 * q^29 + 8 * q^34 + 24 * q^44 - 16 * q^46 - 60 * q^49 + 24 * q^56 - 28 * q^64 - 96 * q^71 - 8 * q^74 - 8 * q^76 - 80 * q^86 - 24 * q^91 - 88 * q^94

Introduction

L-functions

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