LMFDB - Embedded newform 2156.2.i.e.1145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2156,2,Mod(177,2156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2156, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("2156.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2156 = 2^{2} \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2156.i (of order $3$, degree $2$, 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:	$17.2157466758$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 308)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1145.1
Root			$1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2156.1145
Dual form			2156.2.i.e.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 + 2.12132i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{11} -0.449490 q^{13} +4.89898 q^{15} +(0.224745 - 0.389270i) q^{17} +(2.44949 + 4.24264i) q^{19} +(0.449490 + 0.778539i) q^{23} +(0.500000 - 0.866025i) q^{25} +2.89898 q^{29} +(-3.22474 + 5.58542i) q^{31} +(1.22474 + 2.12132i) q^{33} +(-2.00000 - 3.46410i) q^{37} +(0.550510 - 0.953512i) q^{39} -9.34847 q^{41} +2.89898 q^{43} +(-3.00000 + 5.19615i) q^{45} +(3.22474 + 5.58542i) q^{47} +(0.550510 + 0.953512i) q^{51} +(-4.89898 + 8.48528i) q^{53} -2.00000 q^{55} -12.0000 q^{57} +(-3.67423 + 6.36396i) q^{59} +(-2.67423 - 4.63191i) q^{61} +(0.449490 + 0.778539i) q^{65} +(7.34847 - 12.7279i) q^{67} -2.20204 q^{69} -12.8990 q^{71} +(-6.22474 + 10.7816i) q^{73} +(1.22474 + 2.12132i) q^{75} +(5.44949 + 9.43879i) q^{79} +(4.50000 - 7.79423i) q^{81} -16.8990 q^{83} -0.898979 q^{85} +(-3.55051 + 6.14966i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-7.89898 - 13.6814i) q^{93} +(4.89898 - 8.48528i) q^{95} +5.10102 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5} - 6 q^{9} + 2 q^{11} + 8 q^{13} - 4 q^{17} - 8 q^{23} + 2 q^{25} - 8 q^{29} - 8 q^{31} - 8 q^{37} + 12 q^{39} - 8 q^{41} - 8 q^{43} - 12 q^{45} + 8 q^{47} + 12 q^{51} - 8 q^{55} - 48 q^{57}+ \cdots - 12 q^{99}+O(q^{100}) $ 4 * q - 4 * q^5 - 6 * q^9 + 2 * q^11 + 8 * q^13 - 4 * q^17 - 8 * q^23 + 2 * q^25 - 8 * q^29 - 8 * q^31 - 8 * q^37 + 12 * q^39 - 8 * q^41 - 8 * q^43 - 12 * q^45 + 8 * q^47 + 12 * q^51 - 8 * q^55 - 48 * q^57 + 4 * q^61 - 8 * q^65 - 48 * q^69 - 32 * q^71 - 20 * q^73 + 12 * q^79 + 18 * q^81 - 48 * q^83 + 16 * q^85 - 24 * q^87 - 12 * q^89 - 12 * q^93 + 40 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2156\mathbb{Z}\right)^\times$.

$n$	$981$	$1079$	$1277$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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			0
$2$		0			0
$3$	−1.22474	+	2.12132i	−0.707107	+	1.22474i	0.258819	+	0.965926i	$0.416667\pi$
$3$	−1.22474	+	2.12132i	−0.707107	+	1.22474i	−0.965926	+	0.258819i	$0.916667\pi$
$4$		0			0
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−0.449490			−0.124666			−0.0623330	−	0.998055i	$-0.519854\pi$
$13$	−0.449490			−0.124666			−0.0623330	+	0.998055i	$0.519854\pi$
$14$		0			0
$15$	4.89898			1.26491
$16$		0			0
$17$	0.224745	−	0.389270i	0.0545086	−	0.0944117i	−0.837484	−	0.546463i	$-0.815974\pi$
$17$	0.224745	−	0.389270i	0.0545086	−	0.0944117i	0.891992	+	0.452051i	$0.149307\pi$
$18$		0			0
$19$	2.44949	+	4.24264i	0.561951	+	0.973329i	0.997326	+	0.0730792i	$0.0232826\pi$
$19$	2.44949	+	4.24264i	0.561951	+	0.973329i	−0.435375	+	0.900249i	$0.643384\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	0.449490	+	0.778539i	0.0937251	+	0.162337i	0.909076	−	0.416631i	$-0.136789\pi$
$23$	0.449490	+	0.778539i	0.0937251	+	0.162337i	−0.815351	+	0.578967i	$0.803456\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.89898			0.538327			0.269163	−	0.963095i	$-0.413253\pi$
$29$	2.89898			0.538327			0.269163	+	0.963095i	$0.413253\pi$
$30$		0			0
$31$	−3.22474	+	5.58542i	−0.579181	+	1.00317i	0.416392	+	0.909185i	$0.363294\pi$
$31$	−3.22474	+	5.58542i	−0.579181	+	1.00317i	−0.995573	+	0.0939863i	$0.970039\pi$
$32$		0			0
$33$	1.22474	+	2.12132i	0.213201	+	0.369274i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	0.653476	−	0.756948i	$-0.273310\pi$
$37$	−2.00000	−	3.46410i	−0.328798	−	0.569495i	−0.982274	+	0.187453i	$0.939977\pi$
$38$		0			0
$39$	0.550510	−	0.953512i	0.0881522	−	0.152684i
$40$		0			0
$41$	−9.34847			−1.45999			−0.729993	−	0.683455i	$-0.760477\pi$
$41$	−9.34847			−1.45999			−0.729993	+	0.683455i	$0.760477\pi$
$42$		0			0
$43$	2.89898			0.442090			0.221045	−	0.975264i	$-0.429053\pi$
$43$	2.89898			0.442090			0.221045	+	0.975264i	$0.429053\pi$
$44$		0			0
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$		0			0
$47$	3.22474	+	5.58542i	0.470377	+	0.814718i	0.999426	−	0.0338739i	$-0.0107845\pi$
$47$	3.22474	+	5.58542i	0.470377	+	0.814718i	−0.529049	+	0.848591i	$0.677451\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	0.550510	+	0.953512i	0.0770869	+	0.133518i
$52$		0			0
$53$	−4.89898	+	8.48528i	−0.672927	+	1.16554i	0.304144	+	0.952626i	$0.401630\pi$
$53$	−4.89898	+	8.48528i	−0.672927	+	1.16554i	−0.977070	+	0.212917i	$0.931704\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−12.0000			−1.58944
$58$		0			0
$59$	−3.67423	+	6.36396i	−0.478345	+	0.828517i	−0.999692	−	0.0248275i	$-0.992096\pi$
$59$	−3.67423	+	6.36396i	−0.478345	+	0.828517i	0.521347	+	0.853345i	$0.325430\pi$
$60$		0			0
$61$	−2.67423	−	4.63191i	−0.342401	−	0.593055i	0.642477	−	0.766305i	$-0.277907\pi$
$61$	−2.67423	−	4.63191i	−0.342401	−	0.593055i	−0.984878	+	0.173249i	$0.944573\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.449490	+	0.778539i	0.0557523	+	0.0965659i
$66$		0			0
$67$	7.34847	−	12.7279i	0.897758	−	1.55496i	0.0674052	−	0.997726i	$-0.478528\pi$
$67$	7.34847	−	12.7279i	0.897758	−	1.55496i	0.830353	−	0.557237i	$-0.188139\pi$
$68$		0			0
$69$	−2.20204			−0.265095
$70$		0			0
$71$	−12.8990			−1.53083			−0.765414	−	0.643539i	$-0.777466\pi$
$71$	−12.8990			−1.53083			−0.765414	+	0.643539i	$0.777466\pi$
$72$		0			0
$73$	−6.22474	+	10.7816i	−0.728551	+	1.26189i	0.228944	+	0.973440i	$0.426473\pi$
$73$	−6.22474	+	10.7816i	−0.728551	+	1.26189i	−0.957495	+	0.288448i	$0.906861\pi$
$74$		0			0
$75$	1.22474	+	2.12132i	0.141421	+	0.244949i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	5.44949	+	9.43879i	0.613115	+	1.06195i	0.990712	+	0.135977i	$0.0434173\pi$
$79$	5.44949	+	9.43879i	0.613115	+	1.06195i	−0.377597	+	0.925970i	$0.623249\pi$
$80$		0			0
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		0			0
$83$	−16.8990			−1.85490			−0.927452	−	0.373942i	$-0.878006\pi$
$83$	−16.8990			−1.85490			−0.927452	+	0.373942i	$0.878006\pi$
$84$		0			0
$85$	−0.898979			−0.0975080
$86$		0			0
$87$	−3.55051	+	6.14966i	−0.380655	+	0.659313i
$88$		0			0
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	−7.89898	−	13.6814i	−0.819086	−	1.41870i
$94$		0			0
$95$	4.89898	−	8.48528i	0.502625	−	0.870572i
$96$		0			0
$97$	5.10102			0.517930			0.258965	−	0.965887i	$-0.416619\pi$
$97$	5.10102			0.517930			0.258965	+	0.965887i	$0.416619\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$		0			0
$101$	4.22474	−	7.31747i	0.420378	−	0.728116i	−0.575599	−	0.817732i	$-0.695231\pi$
$101$	4.22474	−	7.31747i	0.420378	−	0.728116i	0.995976	+	0.0896167i	$0.0285642\pi$
$102$		0			0
$103$	−7.22474	−	12.5136i	−0.711875	−	1.23300i	−0.964152	−	0.265349i	$-0.914513\pi$
$103$	−7.22474	−	12.5136i	−0.711875	−	1.23300i	0.252277	−	0.967655i	$-0.418821\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$		0			0
$109$	−7.44949	+	12.9029i	−0.713532	+	1.23587i	0.249991	+	0.968248i	$0.419572\pi$
$109$	−7.44949	+	12.9029i	−0.713532	+	1.23587i	−0.963523	+	0.267625i	$0.913761\pi$
$110$		0			0
$111$	9.79796			0.929981
$112$		0			0
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$		0			0
$115$	0.898979	−	1.55708i	0.0838303	−	0.145198i
$116$		0			0
$117$	0.674235	+	1.16781i	0.0623330	+	0.107964i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$		0			0
$123$	11.4495	−	19.8311i	1.03237	−	1.78811i
$124$		0			0
$125$	−12.0000			−1.07331
$126$		0			0
$127$	−1.79796			−0.159543			−0.0797715	−	0.996813i	$-0.525419\pi$
$127$	−1.79796			−0.159543			−0.0797715	+	0.996813i	$0.525419\pi$
$128$		0			0
$129$	−3.55051	+	6.14966i	−0.312605	+	0.541448i
$130$		0			0
$131$	−4.89898	−	8.48528i	−0.428026	−	0.741362i	0.568672	−	0.822564i	$-0.307457\pi$
$131$	−4.89898	−	8.48528i	−0.428026	−	0.741362i	−0.996698	+	0.0812020i	$0.974124\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.89898	+	8.48528i	−0.418548	+	0.724947i	−0.995794	−	0.0916241i	$-0.970794\pi$
$137$	−4.89898	+	8.48528i	−0.418548	+	0.724947i	0.577246	+	0.816571i	$0.304128\pi$
$138$		0			0
$139$	22.6969			1.92513			0.962565	−	0.271052i	$-0.0873717\pi$
$139$	22.6969			1.92513			0.962565	+	0.271052i	$0.0873717\pi$
$140$		0			0
$141$	−15.7980			−1.33043
$142$		0			0
$143$	−0.224745	+	0.389270i	−0.0187941	+	0.0325524i
$144$		0			0
$145$	−2.89898	−	5.02118i	−0.240747	−	0.416986i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.89898	−	10.2173i	−0.483263	−	0.837036i	0.516552	−	0.856256i	$-0.327215\pi$
$149$	−5.89898	−	10.2173i	−0.483263	−	0.837036i	−0.999815	+	0.0192193i	$0.993882\pi$
$150$		0			0
$151$	−4.34847	+	7.53177i	−0.353873	+	0.612927i	−0.986924	−	0.161183i	$-0.948469\pi$
$151$	−4.34847	+	7.53177i	−0.353873	+	0.612927i	0.633051	+	0.774110i	$0.281802\pi$
$152$		0			0
$153$	−1.34847			−0.109017
$154$		0			0
$155$	12.8990			1.03607
$156$		0			0
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$		0			0
$159$	−12.0000	−	20.7846i	−0.951662	−	1.64833i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−4.44949	−	7.70674i	−0.348511	−	0.603639i	0.637474	−	0.770472i	$-0.279979\pi$
$163$	−4.44949	−	7.70674i	−0.348511	−	0.603639i	−0.985985	+	0.166833i	$0.946646\pi$
$164$		0			0
$165$	2.44949	−	4.24264i	0.190693	−	0.330289i
$166$		0			0
$167$	13.7980			1.06772			0.533859	−	0.845573i	$-0.320741\pi$
$167$	13.7980			1.06772			0.533859	+	0.845573i	$0.320741\pi$
$168$		0			0
$169$	−12.7980			−0.984458
$170$		0			0
$171$	7.34847	−	12.7279i	0.561951	−	0.973329i
$172$		0			0
$173$	−5.12372	−	8.87455i	−0.389550	−	0.674720i	0.602839	−	0.797863i	$-0.294036\pi$
$173$	−5.12372	−	8.87455i	−0.389550	−	0.674720i	−0.992389	+	0.123143i	$0.960703\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−9.00000	−	15.5885i	−0.676481	−	1.17170i
$178$		0			0
$179$	7.79796	−	13.5065i	0.582847	−	1.00952i	−0.412293	−	0.911051i	$-0.635272\pi$
$179$	7.79796	−	13.5065i	0.582847	−	1.00952i	0.995140	−	0.0984691i	$-0.0313946\pi$
$180$		0			0
$181$	9.10102			0.676474			0.338237	−	0.941061i	$-0.390170\pi$
$181$	9.10102			0.676474			0.338237	+	0.941061i	$0.390170\pi$
$182$		0			0
$183$	13.1010			0.968455
$184$		0			0
$185$	−4.00000	+	6.92820i	−0.294086	+	0.509372i
$186$		0			0
$187$	−0.224745	−	0.389270i	−0.0164350	−	0.0284662i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.898979	+	1.55708i	0.0650479	+	0.112666i	0.896715	−	0.442608i	$-0.145947\pi$
$191$	0.898979	+	1.55708i	0.0650479	+	0.112666i	−0.831667	+	0.555274i	$0.812613\pi$
$192$		0			0
$193$	−10.7980	+	18.7026i	−0.777254	+	1.34624i	0.156265	+	0.987715i	$0.450055\pi$
$193$	−10.7980	+	18.7026i	−0.777254	+	1.34624i	−0.933519	+	0.358528i	$0.883279\pi$
$194$		0			0
$195$	−2.20204			−0.157691
$196$		0			0
$197$	−25.5959			−1.82363			−0.911817	−	0.410597i	$-0.865320\pi$
$197$	−25.5959			−1.82363			−0.911817	+	0.410597i	$0.865320\pi$
$198$		0			0
$199$	−13.0227	+	22.5560i	−0.923155	+	1.59895i	−0.128653	+	0.991690i	$0.541065\pi$
$199$	−13.0227	+	22.5560i	−0.923155	+	1.59895i	−0.794502	+	0.607262i	$0.792268\pi$
$200$		0			0
$201$	18.0000	+	31.1769i	1.26962	+	2.19905i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	9.34847	+	16.1920i	0.652925	+	1.13090i
$206$		0			0
$207$	1.34847	−	2.33562i	0.0937251	−	0.162337i
$208$		0			0
$209$	4.89898			0.338869
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$		0			0
$213$	15.7980	−	27.3629i	1.08246	−	1.87487i
$214$		0			0
$215$	−2.89898	−	5.02118i	−0.197709	−	0.342442i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−15.2474	−	26.4094i	−1.03033	−	1.78458i
$220$		0			0
$221$	−0.101021	+	0.174973i	−0.00679538	+	0.0117699i
$222$		0			0
$223$	−13.1464			−0.880350			−0.440175	−	0.897912i	$-0.645084\pi$
$223$	−13.1464			−0.880350			−0.440175	+	0.897912i	$0.645084\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$		0			0
$227$	−0.898979	+	1.55708i	−0.0596674	+	0.103347i	−0.894316	−	0.447436i	$-0.852337\pi$
$227$	−0.898979	+	1.55708i	−0.0596674	+	0.103347i	0.834649	+	0.550783i	$0.185671\pi$
$228$		0			0
$229$	2.55051	+	4.41761i	0.168542	+	0.291924i	0.937908	−	0.346885i	$-0.112761\pi$
$229$	2.55051	+	4.41761i	0.168542	+	0.291924i	−0.769365	+	0.638809i	$0.779427\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.550510	+	0.953512i	0.0360651	+	0.0624666i	0.883495	−	0.468441i	$-0.155184\pi$
$233$	0.550510	+	0.953512i	0.0360651	+	0.0624666i	−0.847429	+	0.530908i	$0.821851\pi$
$234$		0			0
$235$	6.44949	−	11.1708i	0.420718	−	0.728706i
$236$		0			0
$237$	−26.6969			−1.73415
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	0.674235	−	1.16781i	0.0434313	−	0.0752252i	−0.843493	−	0.537141i	$-0.819504\pi$
$241$	0.674235	−	1.16781i	0.0434313	−	0.0752252i	0.886924	+	0.461916i	$0.152838\pi$
$242$		0			0
$243$	11.0227	+	19.0919i	0.707107	+	1.22474i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−1.10102	−	1.90702i	−0.0700563	−	0.121341i
$248$		0			0
$249$	20.6969	−	35.8481i	1.31162	−	2.27178i
$250$		0			0
$251$	2.44949			0.154610			0.0773052	−	0.997007i	$-0.475368\pi$
$251$	2.44949			0.154610			0.0773052	+	0.997007i	$0.475368\pi$
$252$		0			0
$253$	0.898979			0.0565184
$254$		0			0
$255$	1.10102	−	1.90702i	0.0689486	−	0.119422i
$256$		0			0
$257$	1.89898	+	3.28913i	0.118455	+	0.205170i	0.919156	−	0.393895i	$-0.128873\pi$
$257$	1.89898	+	3.28913i	0.118455	+	0.205170i	−0.800701	+	0.599065i	$0.795539\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−4.34847	−	7.53177i	−0.269163	−	0.466205i
$262$		0			0
$263$	−9.79796	+	16.9706i	−0.604168	+	1.04645i	0.388014	+	0.921653i	$0.373161\pi$
$263$	−9.79796	+	16.9706i	−0.604168	+	1.04645i	−0.992182	+	0.124796i	$0.960172\pi$
$264$		0			0
$265$	19.5959			1.20377
$266$		0			0
$267$	14.6969			0.899438
$268$		0			0
$269$	6.55051	−	11.3458i	0.399392	−	0.691767i	−0.594259	−	0.804274i	$-0.702555\pi$
$269$	6.55051	−	11.3458i	0.399392	−	0.691767i	0.993651	+	0.112507i	$0.0358880\pi$
$270$		0			0
$271$	−0.651531	−	1.12848i	−0.0395777	−	0.0685505i	0.845558	−	0.533884i	$-0.179268\pi$
$271$	−0.651531	−	1.12848i	−0.0395777	−	0.0685505i	−0.885136	+	0.465333i	$0.845935\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$		0			0
$277$	−7.89898	+	13.6814i	−0.474604	+	0.822038i	−0.999577	−	0.0290810i	$-0.990742\pi$
$277$	−7.89898	+	13.6814i	−0.474604	+	0.822038i	0.524973	+	0.851119i	$0.324075\pi$
$278$		0			0
$279$	19.3485			1.15836
$280$		0			0
$281$	−5.10102			−0.304301			−0.152151	−	0.988357i	$-0.548620\pi$
$281$	−5.10102			−0.304301			−0.152151	+	0.988357i	$0.548620\pi$
$282$		0			0
$283$	12.0000	−	20.7846i	0.713326	−	1.23552i	−0.250276	−	0.968175i	$-0.580521\pi$
$283$	12.0000	−	20.7846i	0.713326	−	1.23552i	0.963602	−	0.267342i	$-0.0861454\pi$
$284$		0			0
$285$	12.0000	+	20.7846i	0.710819	+	1.23117i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	8.39898	+	14.5475i	0.494058	+	0.855733i
$290$		0			0
$291$	−6.24745	+	10.8209i	−0.366232	+	0.634332i
$292$		0			0
$293$	−10.6515			−0.622269			−0.311135	−	0.950366i	$-0.600709\pi$
$293$	−10.6515			−0.622269			−0.311135	+	0.950366i	$0.600709\pi$
$294$		0			0
$295$	14.6969			0.855689
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−0.202041	−	0.349945i	−0.0116843	−	0.0202379i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	10.3485	+	17.9241i	0.594504	+	1.02971i
$304$		0			0
$305$	−5.34847	+	9.26382i	−0.306252	+	0.530445i
$306$		0			0
$307$	−1.79796			−0.102615			−0.0513075	−	0.998683i	$-0.516339\pi$
$307$	−1.79796			−0.102615			−0.0513075	+	0.998683i	$0.516339\pi$
$308$		0			0
$309$	35.3939			2.01349
$310$		0			0
$311$	0.775255	−	1.34278i	0.0439607	−	0.0761421i	−0.843208	−	0.537588i	$-0.819336\pi$
$311$	0.775255	−	1.34278i	0.0439607	−	0.0761421i	0.887169	+	0.461446i	$0.152669\pi$
$312$		0			0
$313$	−2.79796	−	4.84621i	−0.158150	−	0.273924i	0.776052	−	0.630669i	$-0.217220\pi$
$313$	−2.79796	−	4.84621i	−0.158150	−	0.273924i	−0.934202	+	0.356746i	$0.883886\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.79796	+	11.7744i	0.381811	+	0.661317i	0.991321	−	0.131462i	$-0.0419670\pi$
$317$	6.79796	+	11.7744i	0.381811	+	0.661317i	−0.609510	+	0.792779i	$0.708634\pi$
$318$		0			0
$319$	1.44949	−	2.51059i	0.0811558	−	0.140566i
$320$		0			0
$321$	−9.79796			−0.546869
$322$		0			0
$323$	2.20204			0.122525
$324$		0			0
$325$	−0.224745	+	0.389270i	−0.0124666	+	0.0215928i
$326$		0			0
$327$	−18.2474	−	31.6055i	−1.00909	−	1.74779i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.851957	+	0.523612i	$0.175416\pi$
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.0274825	+	0.999622i	$0.491251\pi$
$332$		0			0
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$		0			0
$335$	−29.3939			−1.60596
$336$		0			0
$337$	20.6969			1.12743			0.563717	−	0.825968i	$-0.309371\pi$
$337$	20.6969			1.12743			0.563717	+	0.825968i	$0.309371\pi$
$338$		0			0
$339$	12.2474	−	21.2132i	0.665190	−	1.15214i
$340$		0			0
$341$	3.22474	+	5.58542i	0.174630	+	0.302468i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	2.20204	+	3.81405i	0.118554	+	0.205341i
$346$		0			0
$347$	−13.2474	+	22.9453i	−0.711160	+	1.23177i	0.253262	+	0.967398i	$0.418497\pi$
$347$	−13.2474	+	22.9453i	−0.711160	+	1.23177i	−0.964422	+	0.264368i	$0.914837\pi$
$348$		0			0
$349$	1.75255			0.0938119			0.0469060	−	0.998899i	$-0.485064\pi$
$349$	1.75255			0.0938119			0.0469060	+	0.998899i	$0.485064\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.7980	+	22.1667i	−0.681167	+	1.17982i	0.293459	+	0.955972i	$0.405194\pi$
$353$	−12.7980	+	22.1667i	−0.681167	+	1.17982i	−0.974625	+	0.223843i	$0.928140\pi$
$354$		0			0
$355$	12.8990	+	22.3417i	0.684607	+	1.18577i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	12.3485	+	21.3882i	0.651727	+	1.12882i	0.982704	+	0.185186i	$0.0592887\pi$
$359$	12.3485	+	21.3882i	0.651727	+	1.12882i	−0.330976	+	0.943639i	$0.607378\pi$
$360$		0			0
$361$	−2.50000	+	4.33013i	−0.131579	+	0.227901i
$362$		0			0
$363$	2.44949			0.128565
$364$		0			0
$365$	24.8990			1.30327
$366$		0			0
$367$	−10.5732	+	18.3133i	−0.551917	+	0.955949i	0.446219	+	0.894924i	$0.352770\pi$
$367$	−10.5732	+	18.3133i	−0.551917	+	0.955949i	−0.998136	+	0.0610250i	$0.980563\pi$
$368$		0			0
$369$	14.0227	+	24.2880i	0.729993	+	1.26438i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−2.10102	−	3.63907i	−0.108787	−	0.188424i	0.806492	−	0.591245i	$-0.201363\pi$
$373$	−2.10102	−	3.63907i	−0.108787	−	0.188424i	−0.915279	+	0.402820i	$0.868030\pi$
$374$		0			0
$375$	14.6969	−	25.4558i	0.758947	−	1.31453i
$376$		0			0
$377$	−1.30306			−0.0671111
$378$		0			0
$379$	−3.10102			−0.159289			−0.0796444	−	0.996823i	$-0.525378\pi$
$379$	−3.10102			−0.159289			−0.0796444	+	0.996823i	$0.525378\pi$
$380$		0			0
$381$	2.20204	−	3.81405i	0.112814	−	0.195400i
$382$		0			0
$383$	−13.6742	−	23.6845i	−0.698721	−	1.21022i	−0.968910	−	0.247413i	$-0.920420\pi$
$383$	−13.6742	−	23.6845i	−0.698721	−	1.21022i	0.270189	−	0.962807i	$-0.412914\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−4.34847	−	7.53177i	−0.221045	−	0.382861i
$388$		0			0
$389$	6.79796	−	11.7744i	0.344670	−	0.596986i	−0.640624	−	0.767855i	$-0.721324\pi$
$389$	6.79796	−	11.7744i	0.344670	−	0.596986i	0.985294	+	0.170869i	$0.0546574\pi$
$390$		0			0
$391$	0.404082			0.0204353
$392$		0			0
$393$	24.0000			1.21064
$394$		0			0
$395$	10.8990	−	18.8776i	0.548387	−	0.949834i
$396$		0			0
$397$	12.7980	+	22.1667i	0.642311	+	1.11252i	0.984916	+	0.173036i	$0.0553576\pi$
$397$	12.7980	+	22.1667i	0.642311	+	1.11252i	−0.342604	+	0.939480i	$0.611309\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.8990	+	24.0737i	0.694082	+	1.20219i	0.970489	+	0.241145i	$0.0775228\pi$
$401$	13.8990	+	24.0737i	0.694082	+	1.20219i	−0.276407	+	0.961041i	$0.589144\pi$
$402$		0			0
$403$	1.44949	−	2.51059i	0.0722042	−	0.125061i
$404$		0			0
$405$	−18.0000			−0.894427
$406$		0			0
$407$	−4.00000			−0.198273
$408$		0			0
$409$	5.77526	−	10.0030i	0.285568	−	0.494618i	−0.687179	−	0.726488i	$-0.741151\pi$
$409$	5.77526	−	10.0030i	0.285568	−	0.494618i	0.972747	+	0.231870i	$0.0744844\pi$
$410$		0			0
$411$	−12.0000	−	20.7846i	−0.591916	−	1.02523i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	16.8990	+	29.2699i	0.829538	+	1.43680i
$416$		0			0
$417$	−27.7980	+	48.1475i	−1.36127	+	2.35779i
$418$		0			0
$419$	18.4495			0.901317			0.450658	−	0.892697i	$-0.351189\pi$
$419$	18.4495			0.901317			0.450658	+	0.892697i	$0.351189\pi$
$420$		0			0
$421$	−5.79796			−0.282575			−0.141288	−	0.989969i	$-0.545124\pi$
$421$	−5.79796			−0.282575			−0.141288	+	0.989969i	$0.545124\pi$
$422$		0			0
$423$	9.67423	−	16.7563i	0.470377	−	0.814718i
$424$		0			0
$425$	−0.224745	−	0.389270i	−0.0109017	−	0.0188823i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−0.550510	−	0.953512i	−0.0265789	−	0.0460360i
$430$		0			0
$431$	4.55051	−	7.88171i	0.219190	−	0.379649i	−0.735370	−	0.677665i	$-0.762992\pi$
$431$	4.55051	−	7.88171i	0.219190	−	0.379649i	0.954561	+	0.298017i	$0.0963251\pi$
$432$		0			0
$433$	21.1010			1.01405			0.507025	−	0.861931i	$-0.330745\pi$
$433$	21.1010			1.01405			0.507025	+	0.861931i	$0.330745\pi$
$434$		0			0
$435$	14.2020			0.680936
$436$		0			0
$437$	−2.20204	+	3.81405i	−0.105338	+	0.182451i
$438$		0			0
$439$	12.4495	+	21.5631i	0.594182	+	1.02915i	0.993662	+	0.112411i	$0.0358573\pi$
$439$	12.4495	+	21.5631i	0.594182	+	1.02915i	−0.399480	+	0.916742i	$0.630809\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	−0.996551	−	0.0829786i	$-0.973557\pi$
$443$	−12.0000	−	20.7846i	−0.570137	−	0.987507i	0.426414	−	0.904528i	$-0.359777\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$		0			0
$447$	28.8990			1.36687
$448$		0			0
$449$	19.5959			0.924789			0.462394	−	0.886674i	$-0.346990\pi$
$449$	19.5959			0.924789			0.462394	+	0.886674i	$0.346990\pi$
$450$		0			0
$451$	−4.67423	+	8.09601i	−0.220101	+	0.381226i
$452$		0			0
$453$	−10.6515	−	18.4490i	−0.500453	−	0.866809i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−9.69694	−	16.7956i	−0.453604	−	0.785665i	0.545003	−	0.838434i	$-0.316528\pi$
$457$	−9.69694	−	16.7956i	−0.453604	−	0.785665i	−0.998607	+	0.0527695i	$0.983195\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−37.3485			−1.73949			−0.869746	−	0.493500i	$-0.835717\pi$
$461$	−37.3485			−1.73949			−0.869746	+	0.493500i	$0.835717\pi$
$462$		0			0
$463$	−24.8990			−1.15715			−0.578577	−	0.815628i	$-0.696392\pi$
$463$	−24.8990			−1.15715			−0.578577	+	0.815628i	$0.696392\pi$
$464$		0			0
$465$	−15.7980	+	27.3629i	−0.732613	+	1.26892i
$466$		0			0
$467$	−3.67423	−	6.36396i	−0.170023	−	0.294489i	0.768404	−	0.639965i	$-0.221051\pi$
$467$	−3.67423	−	6.36396i	−0.170023	−	0.294489i	−0.938428	+	0.345476i	$0.887718\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−12.2474	−	21.2132i	−0.564333	−	0.977453i
$472$		0			0
$473$	1.44949	−	2.51059i	0.0666476	−	0.115437i
$474$		0			0
$475$	4.89898			0.224781
$476$		0			0
$477$	29.3939			1.34585
$478$		0			0
$479$	−0.449490	+	0.778539i	−0.0205377	+	0.0355724i	−0.876112	−	0.482108i	$-0.839871\pi$
$479$	−0.449490	+	0.778539i	−0.0205377	+	0.0355724i	0.855574	+	0.517681i	$0.173204\pi$
$480$		0			0
$481$	0.898979	+	1.55708i	0.0409899	+	0.0709967i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.10102	−	8.83523i	−0.231625	−	0.401187i
$486$		0			0
$487$	−18.4495	+	31.9555i	−0.836026	+	1.44804i	0.0571660	+	0.998365i	$0.481794\pi$
$487$	−18.4495	+	31.9555i	−0.836026	+	1.44804i	−0.893192	+	0.449675i	$0.851540\pi$
$488$		0			0
$489$	21.7980			0.985738
$490$		0			0
$491$	32.6969			1.47559			0.737796	−	0.675024i	$-0.235867\pi$
$491$	32.6969			1.47559			0.737796	+	0.675024i	$0.235867\pi$
$492$		0			0
$493$	0.651531	−	1.12848i	0.0293435	−	0.0508244i
$494$		0			0
$495$	3.00000	+	5.19615i	0.134840	+	0.233550i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	21.3485	+	36.9766i	0.955689	+	1.65530i	0.732784	+	0.680461i	$0.238221\pi$
$499$	21.3485	+	36.9766i	0.955689	+	1.65530i	0.222905	+	0.974840i	$0.428446\pi$
$500$		0			0
$501$	−16.8990	+	29.2699i	−0.754991	+	1.30768i
$502$		0			0
$503$	−24.4949			−1.09217			−0.546087	−	0.837729i	$-0.683883\pi$
$503$	−24.4949			−1.09217			−0.546087	+	0.837729i	$0.683883\pi$
$504$		0			0
$505$	−16.8990			−0.751995
$506$		0			0
$507$	15.6742	−	27.1486i	0.696117	−	1.20571i
$508$		0			0
$509$	12.3485	+	21.3882i	0.547336	+	0.948014i	0.998456	+	0.0555507i	$0.0176915\pi$
$509$	12.3485	+	21.3882i	0.547336	+	0.948014i	−0.451120	+	0.892464i	$0.648975\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−14.4495	+	25.0273i	−0.636721	+	1.10283i
$516$		0			0
$517$	6.44949			0.283648
$518$		0			0
$519$	25.1010			1.10181
$520$		0			0
$521$	4.55051	−	7.88171i	0.199361	−	0.345304i	−0.748960	−	0.662615i	$-0.769447\pi$
$521$	4.55051	−	7.88171i	0.199361	−	0.345304i	0.948322	+	0.317311i	$0.102780\pi$
$522$		0			0
$523$	−12.6969	−	21.9917i	−0.555198	−	0.961632i	−0.997888	−	0.0649569i	$-0.979309\pi$
$523$	−12.6969	−	21.9917i	−0.555198	−	0.961632i	0.442690	−	0.896675i	$-0.354024\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.44949	+	2.51059i	0.0631408	+	0.109363i
$528$		0			0
$529$	11.0959	−	19.2187i	0.482431	−	0.835595i
$530$		0			0
$531$	22.0454			0.956689
$532$		0			0
$533$	4.20204			0.182011
$534$		0			0
$535$	4.00000	−	6.92820i	0.172935	−	0.299532i
$536$		0			0
$537$	19.1010	+	33.0839i	0.824270	+	1.42768i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	8.79796	+	15.2385i	0.378254	+	0.655155i	0.990808	−	0.135274i	$-0.0431913\pi$
$541$	8.79796	+	15.2385i	0.378254	+	0.655155i	−0.612554	+	0.790428i	$0.709858\pi$
$542$		0			0
$543$	−11.1464	+	19.3062i	−0.478339	+	0.828507i
$544$		0			0
$545$	29.7980			1.27640
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$		0			0
$549$	−8.02270	+	13.8957i	−0.342401	+	0.593055i
$550$		0			0
$551$	7.10102	+	12.2993i	0.302514	+	0.523969i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−9.79796	−	16.9706i	−0.415900	−	0.720360i
$556$		0			0
$557$	21.8990	−	37.9301i	0.927890	−	1.60715i	0.141043	−	0.990004i	$-0.454955\pi$
$557$	21.8990	−	37.9301i	0.927890	−	1.60715i	0.786847	−	0.617148i	$-0.211712\pi$
$558$		0			0
$559$	−1.30306			−0.0551136
$560$		0			0
$561$	1.10102			0.0464851
$562$		0			0
$563$	13.1464	−	22.7703i	0.554056	−	0.959653i	−0.443920	−	0.896066i	$-0.646413\pi$
$563$	13.1464	−	22.7703i	0.554056	−	0.959653i	0.997976	−	0.0635867i	$-0.0202540\pi$
$564$		0			0
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.34847	+	7.53177i	0.182297	+	0.315748i	0.942662	−	0.333748i	$-0.108313\pi$
$569$	4.34847	+	7.53177i	0.182297	+	0.315748i	−0.760365	+	0.649496i	$0.774980\pi$
$570$		0			0
$571$	5.10102	−	8.83523i	0.213471	−	0.369743i	−0.739327	−	0.673346i	$-0.764856\pi$
$571$	5.10102	−	8.83523i	0.213471	−	0.369743i	0.952799	+	0.303603i	$0.0981898\pi$
$572$		0			0
$573$	−4.40408			−0.183983
$574$		0			0
$575$	0.898979			0.0374900
$576$		0			0
$577$	11.2474	−	19.4812i	0.468237	−	0.811011i	−0.531104	−	0.847307i	$-0.678223\pi$
$577$	11.2474	−	19.4812i	0.468237	−	0.811011i	0.999341	+	0.0362958i	$0.0115559\pi$
$578$		0			0
$579$	−26.4495	−	45.8119i	−1.09920	−	1.90388i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	4.89898	+	8.48528i	0.202895	+	0.351424i
$584$		0			0
$585$	1.34847	−	2.33562i	0.0557523	−	0.0965659i
$586$		0			0
$587$	21.5505			0.889485			0.444742	−	0.895659i	$-0.353295\pi$
$587$	21.5505			0.889485			0.444742	+	0.895659i	$0.353295\pi$
$588$		0			0
$589$	−31.5959			−1.30189
$590$		0			0
$591$	31.3485	−	54.2971i	1.28950	−	2.23349i
$592$		0			0
$593$	0.426786	+	0.739215i	0.0175260	+	0.0303559i	0.874655	−	0.484745i	$-0.161088\pi$
$593$	0.426786	+	0.739215i	0.0175260	+	0.0303559i	−0.857129	+	0.515101i	$0.827754\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−31.8990	−	55.2507i	−1.30554	−	2.26126i
$598$		0			0
$599$	3.55051	−	6.14966i	0.145070	−	0.251268i	−0.784329	−	0.620345i	$-0.786993\pi$
$599$	3.55051	−	6.14966i	0.145070	−	0.251268i	0.929399	+	0.369076i	$0.120326\pi$
$600$		0			0
$601$	6.65153			0.271322			0.135661	−	0.990755i	$-0.456684\pi$
$601$	6.65153			0.271322			0.135661	+	0.990755i	$0.456684\pi$
$602$		0			0
$603$	−44.0908			−1.79552
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	−7.79796	−	13.5065i	−0.316509	−	0.548210i	0.663248	−	0.748400i	$-0.269178\pi$
$607$	−7.79796	−	13.5065i	−0.316509	−	0.548210i	−0.979757	+	0.200190i	$0.935844\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.44949	−	2.51059i	−0.0586401	−	0.101568i
$612$		0			0
$613$	8.34847	−	14.4600i	0.337191	−	0.584033i	−0.646712	−	0.762734i	$-0.723856\pi$
$613$	8.34847	−	14.4600i	0.337191	−	0.584033i	0.983903	+	0.178702i	$0.0571897\pi$
$614$		0			0
$615$	−45.7980			−1.84675
$616$		0			0
$617$	−29.3939			−1.18335			−0.591676	−	0.806176i	$-0.701534\pi$
$617$	−29.3939			−1.18335			−0.591676	+	0.806176i	$0.701534\pi$
$618$		0			0
$619$	−2.77526	+	4.80688i	−0.111547	+	0.193205i	−0.916394	−	0.400277i	$-0.868914\pi$
$619$	−2.77526	+	4.80688i	−0.111547	+	0.193205i	0.804847	+	0.593482i	$0.202247\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$		0			0
$627$	−6.00000	+	10.3923i	−0.239617	+	0.415029i
$628$		0			0
$629$	−1.79796			−0.0716893
$630$		0			0
$631$	−2.20204			−0.0876619			−0.0438309	−	0.999039i	$-0.513956\pi$
$631$	−2.20204			−0.0876619			−0.0438309	+	0.999039i	$0.513956\pi$
$632$		0			0
$633$	24.4949	−	42.4264i	0.973585	−	1.68630i
$634$		0			0
$635$	1.79796	+	3.11416i	0.0713498	+	0.123582i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	19.3485	+	33.5125i	0.765414	+	1.32574i
$640$		0			0
$641$	3.79796	−	6.57826i	0.150010	−	0.259826i	−0.781221	−	0.624255i	$-0.785403\pi$
$641$	3.79796	−	6.57826i	0.150010	−	0.259826i	0.931231	+	0.364429i	$0.118736\pi$
$642$		0			0
$643$	4.24745			0.167503			0.0837515	−	0.996487i	$-0.473310\pi$
$643$	4.24745			0.167503			0.0837515	+	0.996487i	$0.473310\pi$
$644$		0			0
$645$	14.2020			0.559205
$646$		0			0
$647$	−0.123724	+	0.214297i	−0.00486411	+	0.00842488i	−0.868447	−	0.495782i	$-0.834882\pi$
$647$	−0.123724	+	0.214297i	−0.00486411	+	0.00842488i	0.863583	+	0.504207i	$0.168215\pi$
$648$		0			0
$649$	3.67423	+	6.36396i	0.144226	+	0.249807i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.69694	−	13.3315i	−0.301204	−	0.521701i	0.675205	−	0.737631i	$-0.264055\pi$
$653$	−7.69694	−	13.3315i	−0.301204	−	0.521701i	−0.976409	+	0.215929i	$0.930722\pi$
$654$		0			0
$655$	−9.79796	+	16.9706i	−0.382838	+	0.663095i
$656$		0			0
$657$	37.3485			1.45710
$658$		0			0
$659$	5.10102			0.198708			0.0993538	−	0.995052i	$-0.468322\pi$
$659$	5.10102			0.198708			0.0993538	+	0.995052i	$0.468322\pi$
$660$		0			0
$661$	14.7980	−	25.6308i	0.575574	−	0.996923i	−0.420405	−	0.907337i	$-0.638112\pi$
$661$	14.7980	−	25.6308i	0.575574	−	0.996923i	0.995979	−	0.0895867i	$-0.0285546\pi$
$662$		0			0
$663$	−0.247449	−	0.428594i	−0.00961011	−	0.0166452i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	1.30306	+	2.25697i	0.0504547	+	0.0873902i
$668$		0			0
$669$	16.1010	−	27.8878i	0.622501	−	1.07820i
$670$		0			0
$671$	−5.34847			−0.206475
$672$		0			0
$673$	7.30306			0.281512			0.140756	−	0.990044i	$-0.455047\pi$
$673$	7.30306			0.281512			0.140756	+	0.990044i	$0.455047\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.4722	−	25.0666i	−0.556212	−	0.963387i	−0.997808	−	0.0661730i	$-0.978921\pi$
$677$	−14.4722	−	25.0666i	−0.556212	−	0.963387i	0.441597	−	0.897214i	$-0.354412\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−2.20204	−	3.81405i	−0.0843824	−	0.146155i
$682$		0			0
$683$	13.1010	−	22.6916i	0.501297	−	0.868271i	−0.498702	−	0.866773i	$-0.666190\pi$
$683$	13.1010	−	22.6916i	0.501297	−	0.868271i	0.999999	−	0.00149785i	$-0.000476782\pi$
$684$		0			0
$685$	19.5959			0.748722
$686$		0			0
$687$	−12.4949			−0.476710
$688$		0			0
$689$	2.20204	−	3.81405i	0.0838911	−	0.145304i
$690$		0			0
$691$	20.5732	+	35.6339i	0.782642	+	1.35558i	0.930398	+	0.366552i	$0.119462\pi$
$691$	20.5732	+	35.6339i	0.782642	+	1.35558i	−0.147756	+	0.989024i	$0.547205\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−22.6969	−	39.3123i	−0.860944	−	1.49120i
$696$		0			0
$697$	−2.10102	+	3.63907i	−0.0795818	+	0.137840i
$698$		0			0
$699$	−2.69694			−0.102008
$700$		0			0
$701$	−20.6969			−0.781713			−0.390856	−	0.920452i	$-0.627821\pi$
$701$	−20.6969			−0.781713			−0.390856	+	0.920452i	$0.627821\pi$
$702$		0			0
$703$	9.79796	−	16.9706i	0.369537	−	0.640057i
$704$		0			0
$705$	15.7980	+	27.3629i	0.594986	+	1.03055i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−1.89898	−	3.28913i	−0.0713177	−	0.123526i	0.828161	−	0.560490i	$-0.189387\pi$
$709$	−1.89898	−	3.28913i	−0.0713177	−	0.123526i	−0.899479	+	0.436964i	$0.856054\pi$
$710$		0			0
$711$	16.3485	−	28.3164i	0.613115	−	1.06195i
$712$		0			0
$713$	−5.79796			−0.217135
$714$		0			0
$715$	0.898979			0.0336199
$716$		0			0
$717$	−19.5959	+	33.9411i	−0.731823	+	1.26755i
$718$		0			0
$719$	−22.5732	−	39.0980i	−0.841839	−	1.45811i	−0.888338	−	0.459189i	$-0.848140\pi$
$719$	−22.5732	−	39.0980i	−0.841839	−	1.45811i	0.0464996	−	0.998918i	$-0.485193\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	1.65153	+	2.86054i	0.0614211	+	0.106384i
$724$		0			0
$725$	1.44949	−	2.51059i	0.0538327	−	0.0932410i
$726$		0			0
$727$	−1.55051			−0.0575052			−0.0287526	−	0.999587i	$-0.509154\pi$
$727$	−1.55051			−0.0575052			−0.0287526	+	0.999587i	$0.509154\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	0.651531	−	1.12848i	0.0240977	−	0.0417385i
$732$		0			0
$733$	−22.6742	−	39.2729i	−0.837492	−	1.45058i	−0.891985	−	0.452064i	$-0.850688\pi$
$733$	−22.6742	−	39.2729i	−0.837492	−	1.45058i	0.0544933	−	0.998514i	$-0.482646\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.34847	−	12.7279i	−0.270684	−	0.468839i
$738$		0			0
$739$	20.6969	−	35.8481i	0.761349	−	1.31870i	−0.180806	−	0.983519i	$-0.557871\pi$
$739$	20.6969	−	35.8481i	0.761349	−	1.31870i	0.942155	−	0.335177i	$-0.108796\pi$
$740$		0			0
$741$	5.39388			0.198149
$742$		0			0
$743$	−19.5959			−0.718905			−0.359452	−	0.933163i	$-0.617036\pi$
$743$	−19.5959			−0.718905			−0.359452	+	0.933163i	$0.617036\pi$
$744$		0			0
$745$	−11.7980	+	20.4347i	−0.432244	+	0.748668i
$746$		0			0
$747$	25.3485	+	43.9048i	0.927452	+	1.60639i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	6.44949	+	11.1708i	0.235345	+	0.407630i	0.959373	−	0.282141i	$-0.0910446\pi$
$751$	6.44949	+	11.1708i	0.235345	+	0.407630i	−0.724028	+	0.689771i	$0.757711\pi$
$752$		0			0
$753$	−3.00000	+	5.19615i	−0.109326	+	0.189358i
$754$		0			0
$755$	17.3939			0.633028
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$		0			0
$759$	−1.10102	+	1.90702i	−0.0399645	+	0.0692206i
$760$		0			0
$761$	−24.9217	−	43.1656i	−0.903410	−	1.56475i	−0.823037	−	0.567988i	$-0.807722\pi$
$761$	−24.9217	−	43.1656i	−0.903410	−	1.56475i	−0.0803733	−	0.996765i	$-0.525611\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	1.34847	+	2.33562i	0.0487540	+	0.0844444i
$766$		0			0
$767$	1.65153	−	2.86054i	0.0596333	−	0.103288i
$768$		0			0
$769$	39.1464			1.41166			0.705828	−	0.708383i	$-0.250575\pi$
$769$	39.1464			1.41166			0.705828	+	0.708383i	$0.250575\pi$
$770$		0			0
$771$	−9.30306			−0.335042
$772$		0			0
$773$	−1.65153	+	2.86054i	−0.0594014	+	0.102886i	−0.894197	−	0.447674i	$-0.852253\pi$
$773$	−1.65153	+	2.86054i	−0.0594014	+	0.102886i	0.834795	+	0.550560i	$0.185586\pi$
$774$		0			0
$775$	3.22474	+	5.58542i	0.115836	+	0.200634i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−22.8990	−	39.6622i	−0.820441	−	1.42105i
$780$		0			0
$781$	−6.44949	+	11.1708i	−0.230781	+	0.399724i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	20.0000			0.713831
$786$		0			0
$787$	−5.34847	+	9.26382i	−0.190652	+	0.330220i	−0.945467	−	0.325719i	$-0.894394\pi$
$787$	−5.34847	+	9.26382i	−0.190652	+	0.330220i	0.754814	+	0.655939i	$0.227727\pi$
$788$		0			0
$789$	−24.0000	−	41.5692i	−0.854423	−	1.47990i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	1.20204	+	2.08200i	0.0426857	+	0.0739339i
$794$		0			0
$795$	−24.0000	+	41.5692i	−0.851192	+	1.47431i
$796$		0			0
$797$	−31.7980			−1.12634			−0.563171	−	0.826341i	$-0.690419\pi$
$797$	−31.7980			−1.12634			−0.563171	+	0.826341i	$0.690419\pi$
$798$		0			0
$799$	2.89898			0.102559
$800$		0			0
$801$	−9.00000	+	15.5885i	−0.317999	+	0.550791i
$802$		0			0
$803$	6.22474	+	10.7816i	0.219666	+	0.380473i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	16.0454	+	27.7915i	0.564825	+	0.978306i
$808$		0			0
$809$	12.7980	−	22.1667i	0.449952	−	0.779340i	−0.548430	−	0.836196i	$-0.684774\pi$
$809$	12.7980	−	22.1667i	0.449952	−	0.779340i	0.998382	+	0.0568562i	$0.0181077\pi$
$810$		0			0
$811$	−23.5959			−0.828565			−0.414282	−	0.910148i	$-0.635967\pi$
$811$	−23.5959			−0.828565			−0.414282	+	0.910148i	$0.635967\pi$
$812$		0			0
$813$	3.19184			0.111943
$814$		0			0
$815$	−8.89898	+	15.4135i	−0.311718	+	0.539911i
$816$		0			0
$817$	7.10102	+	12.2993i	0.248433	+	0.430299i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.89898	+	13.6814i	0.275676	+	0.477485i	0.970306	−	0.241883i	$-0.0777649\pi$
$821$	7.89898	+	13.6814i	0.275676	+	0.477485i	−0.694629	+	0.719368i	$0.744432\pi$
$822$		0			0
$823$	−17.5959	+	30.4770i	−0.613355	+	1.06236i	0.377316	+	0.926085i	$0.376847\pi$
$823$	−17.5959	+	30.4770i	−0.613355	+	1.06236i	−0.990671	+	0.136278i	$0.956486\pi$
$824$		0			0
$825$	2.44949			0.0852803
$826$		0			0
$827$	52.6969			1.83245			0.916226	−	0.400662i	$-0.131220\pi$
$827$	52.6969			1.83245			0.916226	+	0.400662i	$0.131220\pi$
$828$		0			0
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	−0.718481	−	0.695546i	$-0.755162\pi$
$829$	7.00000	−	12.1244i	0.243120	−	0.421096i	0.961601	+	0.274450i	$0.0884958\pi$
$830$		0			0
$831$	−19.3485	−	33.5125i	−0.671191	−	1.16254i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−13.7980	−	23.8988i	−0.477498	−	0.827051i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.55051			0.329720			0.164860	−	0.986317i	$-0.447283\pi$
$839$	9.55051			0.329720			0.164860	+	0.986317i	$0.447283\pi$
$840$		0			0
$841$	−20.5959			−0.710204
$842$		0			0
$843$	6.24745	−	10.8209i	0.215174	−	0.372692i
$844$		0			0
$845$	12.7980	+	22.1667i	0.440263	+	0.762558i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	29.3939	+	50.9117i	1.00880	+	1.74728i
$850$		0			0
$851$	1.79796	−	3.11416i	0.0616332	−	0.106752i
$852$		0			0
$853$	43.1464			1.47731			0.738653	−	0.674086i	$-0.235462\pi$
$853$	43.1464			1.47731			0.738653	+	0.674086i	$0.235462\pi$
$854$		0			0
$855$	−29.3939			−1.00525
$856$		0			0
$857$	−4.42679	+	7.66742i	−0.151216	+	0.261914i	−0.931675	−	0.363293i	$-0.881652\pi$
$857$	−4.42679	+	7.66742i	−0.151216	+	0.261914i	0.780459	+	0.625207i	$0.214986\pi$
$858$		0			0
$859$	−11.9217	−	20.6490i	−0.406763	−	0.704533i	0.587762	−	0.809034i	$-0.300009\pi$
$859$	−11.9217	−	20.6490i	−0.406763	−	0.704533i	−0.994525	+	0.104500i	$0.966676\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	0.998629	+	0.0523446i	$0.0166694\pi$
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	−0.453983	+	0.891010i	$0.649997\pi$
$864$		0			0
$865$	−10.2474	+	17.7491i	−0.348424	+	0.603488i
$866$		0			0
$867$	−41.1464			−1.39741
$868$		0			0
$869$	10.8990			0.369723
$870$		0			0
$871$	−3.30306	+	5.72107i	−0.111920	+	0.193851i
$872$		0			0
$873$	−7.65153	−	13.2528i	−0.258965	−	0.448541i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−18.3485	−	31.7805i	−0.619584	−	1.07315i	−0.989562	−	0.144110i	$-0.953968\pi$
$877$	−18.3485	−	31.7805i	−0.619584	−	1.07315i	0.369978	−	0.929041i	$-0.379365\pi$
$878$		0			0
$879$	13.0454	−	22.5953i	0.440011	−	0.762121i
$880$		0			0
$881$	−20.6969			−0.697298			−0.348649	−	0.937253i	$-0.613359\pi$
$881$	−20.6969			−0.697298			−0.348649	+	0.937253i	$0.613359\pi$
$882$		0			0
$883$	−29.7980			−1.00278			−0.501391	−	0.865221i	$-0.667178\pi$
$883$	−29.7980			−1.00278			−0.501391	+	0.865221i	$0.667178\pi$
$884$		0			0
$885$	−18.0000	+	31.1769i	−0.605063	+	1.04800i
$886$		0			0
$887$	15.1464	+	26.2344i	0.508567	+	0.880864i	0.999951	+	0.00992106i	$0.00315802\pi$
$887$	15.1464	+	26.2344i	0.508567	+	0.880864i	−0.491383	+	0.870943i	$0.663509\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−4.50000	−	7.79423i	−0.150756	−	0.261116i
$892$		0			0
$893$	−15.7980	+	27.3629i	−0.528659	+	0.915663i
$894$		0			0
$895$	−31.1918			−1.04263
$896$		0			0
$897$	0.989795			0.0330483
$898$		0			0
$899$	−9.34847	+	16.1920i	−0.311789	+	0.540034i
$900$		0			0
$901$	2.20204	+	3.81405i	0.0733606	+	0.127064i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.10102	−	15.7634i	−0.302528	−	0.523994i
$906$		0			0
$907$	−1.55051	+	2.68556i	−0.0514838	+	0.0891726i	−0.890619	−	0.454751i	$-0.849728\pi$
$907$	−1.55051	+	2.68556i	−0.0514838	+	0.0891726i	0.839135	+	0.543923i	$0.183062\pi$
$908$		0			0
$909$	−25.3485			−0.840756
$910$		0			0
$911$	36.4949			1.20913			0.604565	−	0.796556i	$-0.293347\pi$
$911$	36.4949			1.20913			0.604565	+	0.796556i	$0.293347\pi$
$912$		0			0
$913$	−8.44949	+	14.6349i	−0.279637	+	0.484346i
$914$		0			0
$915$	−13.1010	−	22.6916i	−0.433106	−	0.750162i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−2.20204	−	3.81405i	−0.0726386	−	0.125814i	0.827418	−	0.561586i	$-0.189809\pi$
$919$	−2.20204	−	3.81405i	−0.0726386	−	0.125814i	−0.900057	+	0.435772i	$0.856475\pi$
$920$		0			0
$921$	2.20204	−	3.81405i	0.0725597	−	0.125677i
$922$		0			0
$923$	5.79796			0.190842
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	−21.6742	+	37.5409i	−0.711875	+	1.23300i
$928$		0			0
$929$	26.1464	+	45.2869i	0.857836	+	1.48582i	0.873988	+	0.485947i	$0.161525\pi$
$929$	26.1464	+	45.2869i	0.857836	+	1.48582i	−0.0161519	+	0.999870i	$0.505142\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	1.89898	+	3.28913i	0.0621698	+	0.107681i
$934$		0			0
$935$	−0.449490	+	0.778539i	−0.0146999	+	0.0254610i
$936$		0			0
$937$	32.9444			1.07625			0.538123	−	0.842866i	$-0.319134\pi$
$937$	32.9444			1.07625			0.538123	+	0.842866i	$0.319134\pi$
$938$		0			0
$939$	13.7071			0.447316
$940$		0			0
$941$	−21.7753	+	37.7158i	−0.709853	+	1.22950i	0.255058	+	0.966926i	$0.417905\pi$
$941$	−21.7753	+	37.7158i	−0.709853	+	1.22950i	−0.964911	+	0.262576i	$0.915428\pi$
$942$		0			0
$943$	−4.20204	−	7.27815i	−0.136837	−	0.237009i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−0.202041	−	0.349945i	−0.00656545	−	0.0113717i	0.862724	−	0.505675i	$-0.168757\pi$
$947$	−0.202041	−	0.349945i	−0.00656545	−	0.0113717i	−0.869289	+	0.494303i	$0.835423\pi$
$948$		0			0
$949$	2.79796	−	4.84621i	0.0908256	−	0.157315i
$950$		0			0
$951$	−33.3031			−1.07993
$952$		0			0
$953$	−43.7980			−1.41876			−0.709378	−	0.704829i	$-0.751024\pi$
$953$	−43.7980			−1.41876			−0.709378	+	0.704829i	$0.751024\pi$
$954$		0			0
$955$	1.79796	−	3.11416i	0.0581806	−	0.100772i
$956$		0			0
$957$	3.55051	+	6.14966i	0.114772	+	0.198790i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−5.29796	−	9.17633i	−0.170902	−	0.296011i
$962$		0			0
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$		0			0
$965$	43.1918			1.39039
$966$		0			0
$967$	−38.8990			−1.25091			−0.625453	−	0.780262i	$-0.715086\pi$
$967$	−38.8990			−1.25091			−0.625453	+	0.780262i	$0.715086\pi$
$968$		0			0
$969$	−2.69694	+	4.67123i	−0.0866381	+	0.150062i
$970$		0			0
$971$	19.0227	+	32.9483i	0.610468	+	1.05736i	0.991162	+	0.132660i	$0.0423518\pi$
$971$	19.0227	+	32.9483i	0.610468	+	1.05736i	−0.380694	+	0.924701i	$0.624315\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	−0.550510	−	0.953512i	−0.0176304	−	0.0305368i
$976$		0			0
$977$	−2.10102	+	3.63907i	−0.0672176	+	0.116424i	−0.897676	−	0.440657i	$-0.854746\pi$
$977$	−2.10102	+	3.63907i	−0.0672176	+	0.116424i	0.830458	+	0.557081i	$0.188079\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$		0			0
$981$	44.6969			1.42706
$982$		0			0
$983$	−9.67423	+	16.7563i	−0.308560	+	0.534442i	−0.978048	−	0.208381i	$-0.933180\pi$
$983$	−9.67423	+	16.7563i	−0.308560	+	0.534442i	0.669487	+	0.742823i	$0.266514\pi$
$984$		0			0
$985$	25.5959	+	44.3334i	0.815554	+	1.41258i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	1.30306	+	2.25697i	0.0414349	+	0.0717674i
$990$		0			0
$991$	−30.0454	+	52.0402i	−0.954424	+	1.65311i	−0.218743	+	0.975783i	$0.570196\pi$
$991$	−30.0454	+	52.0402i	−0.954424	+	1.65311i	−0.735681	+	0.677328i	$0.763138\pi$
$992$		0			0
$993$	−78.3837			−2.48743
$994$		0			0
$995$	52.0908			1.65139
$996$		0			0
$997$	10.4722	−	18.1384i	0.331658	−	0.574448i	−0.651179	−	0.758924i	$-0.725725\pi$
$997$	10.4722	−	18.1384i	0.331658	−	0.574448i	0.982837	+	0.184476i	$0.0590588\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2156.2.i.e.1145.1		4
7.2	even	3	inner	2156.2.i.e.177.1		4
7.3	odd	6		2156.2.a.c.1.1		2
7.4	even	3		308.2.a.b.1.2	✓	2
7.5	odd	6		2156.2.i.i.177.2		4
7.6	odd	2		2156.2.i.i.1145.2		4
21.11	odd	6		2772.2.a.n.1.1		2
28.3	even	6		8624.2.a.bj.1.2		2
28.11	odd	6		1232.2.a.n.1.1		2
35.4	even	6		7700.2.a.s.1.1		2
35.18	odd	12		7700.2.e.j.1849.4		4
35.32	odd	12		7700.2.e.j.1849.1		4
56.11	odd	6		4928.2.a.bq.1.2		2
56.53	even	6		4928.2.a.bp.1.1		2
77.32	odd	6		3388.2.a.h.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.2.a.b.1.2	✓	2	7.4	even	3
1232.2.a.n.1.1		2	28.11	odd	6
2156.2.a.c.1.1		2	7.3	odd	6
2156.2.i.e.177.1		4	7.2	even	3	inner
2156.2.i.e.1145.1		4	1.1	even	1	trivial
2156.2.i.i.177.2		4	7.5	odd	6
2156.2.i.i.1145.2		4	7.6	odd	2
2772.2.a.n.1.1		2	21.11	odd	6
3388.2.a.h.1.2		2	77.32	odd	6
4928.2.a.bp.1.1		2	56.53	even	6
4928.2.a.bq.1.2		2	56.11	odd	6
7700.2.a.s.1.1		2	35.4	even	6
7700.2.e.j.1849.1		4	35.32	odd	12
7700.2.e.j.1849.4		4	35.18	odd	12
8624.2.a.bj.1.2		2	28.3	even	6

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:	\( N \)	\(=\)	\( 2156 = 2^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2156.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 + 2.12132i) q^{3} +(-1.00000 - 1.73205i) q^{5} +(-1.50000 - 2.59808i) q^{9} +(0.500000 - 0.866025i) q^{11} -0.449490 q^{13} +4.89898 q^{15} +(0.224745 - 0.389270i) q^{17} +(2.44949 + 4.24264i) q^{19} +(0.449490 + 0.778539i) q^{23} +(0.500000 - 0.866025i) q^{25} +2.89898 q^{29} +(-3.22474 + 5.58542i) q^{31} +(1.22474 + 2.12132i) q^{33} +(-2.00000 - 3.46410i) q^{37} +(0.550510 - 0.953512i) q^{39} -9.34847 q^{41} +2.89898 q^{43} +(-3.00000 + 5.19615i) q^{45} +(3.22474 + 5.58542i) q^{47} +(0.550510 + 0.953512i) q^{51} +(-4.89898 + 8.48528i) q^{53} -2.00000 q^{55} -12.0000 q^{57} +(-3.67423 + 6.36396i) q^{59} +(-2.67423 - 4.63191i) q^{61} +(0.449490 + 0.778539i) q^{65} +(7.34847 - 12.7279i) q^{67} -2.20204 q^{69} -12.8990 q^{71} +(-6.22474 + 10.7816i) q^{73} +(1.22474 + 2.12132i) q^{75} +(5.44949 + 9.43879i) q^{79} +(4.50000 - 7.79423i) q^{81} -16.8990 q^{83} -0.898979 q^{85} +(-3.55051 + 6.14966i) q^{87} +(-3.00000 - 5.19615i) q^{89} +(-7.89898 - 13.6814i) q^{93} +(4.89898 - 8.48528i) q^{95} +5.10102 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5} - 6 q^{9} + 2 q^{11} + 8 q^{13} - 4 q^{17} - 8 q^{23} + 2 q^{25} - 8 q^{29} - 8 q^{31} - 8 q^{37} + 12 q^{39} - 8 q^{41} - 8 q^{43} - 12 q^{45} + 8 q^{47} + 12 q^{51} - 8 q^{55} - 48 q^{57}+ \cdots - 12 q^{99}+O(q^{100}) \) 4 * q - 4 * q^5 - 6 * q^9 + 2 * q^11 + 8 * q^13 - 4 * q^17 - 8 * q^23 + 2 * q^25 - 8 * q^29 - 8 * q^31 - 8 * q^37 + 12 * q^39 - 8 * q^41 - 8 * q^43 - 12 * q^45 + 8 * q^47 + 12 * q^51 - 8 * q^55 - 48 * q^57 + 4 * q^61 - 8 * q^65 - 48 * q^69 - 32 * q^71 - 20 * q^73 + 12 * q^79 + 18 * q^81 - 48 * q^83 + 16 * q^85 - 24 * q^87 - 12 * q^89 - 12 * q^93 + 40 * q^97 - 12 * q^99

Introduction

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