LMFDB - Embedded newform 324.11.g.e.269.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,11,Mod(53,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("324.53");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	324.g (of order $6$, 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:	$205.855749866$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} - 862x^{6} + 2600x^{5} + 278207x^{4} - 560752x^{3} - 39833846x^{2} + 40114656x + 2136938124 $ x^8 - 4x^7 - 862x^6 + 2600x^5 + 278207x^4 - 560752x^3 - 39833846x^2 + 40114656*x + 2136938124
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{30} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.2
Root			$16.4302 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	324.269
Dual form			324.11.g.e.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2732.87 + 1577.82i) q^{5} +(6831.13 - 11831.9i) q^{7} +O(q^{10})$	$q+(-2732.87 + 1577.82i) q^{5} +(6831.13 - 11831.9i) q^{7} +(-54331.2 - 31368.1i) q^{11} +(-100189. - 173533. i) q^{13} +556674. i q^{17} -3.25649e6 q^{19} +(5.33186e6 - 3.07835e6i) q^{23} +(96223.2 - 166663. i) q^{25} +(-3.49254e7 - 2.01642e7i) q^{29} +(2.38921e7 + 4.13824e7i) q^{31} +4.31132e7i q^{35} -7.11048e7 q^{37} +(1.21209e8 - 6.99801e7i) q^{41} +(-1.08820e7 + 1.88481e7i) q^{43} +(-1.44771e8 - 8.35838e7i) q^{47} +(4.79091e7 + 8.29809e7i) q^{49} -7.91424e8i q^{53} +1.97973e8 q^{55} +(-2.48086e8 + 1.43232e8i) q^{59} +(-5.06541e8 + 8.77355e8i) q^{61} +(5.47608e8 + 3.16162e8i) q^{65} +(-4.63864e8 - 8.03436e8i) q^{67} -2.49137e9i q^{71} +9.45207e8 q^{73} +(-7.42287e8 + 4.28559e8i) q^{77} +(1.67985e9 - 2.90959e9i) q^{79} +(-4.44732e9 - 2.56766e9i) q^{83} +(-8.78332e8 - 1.52132e9i) q^{85} +3.50859e9i q^{89} -2.73763e9 q^{91} +(8.89954e9 - 5.13815e9i) q^{95} +(3.03475e9 - 5.25633e9i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 21584 q^{7}+O(q^{10}) $ 8 * q - 21584 * q^7	$ 8 q - 21584 q^{7} + 646912 q^{13} - 2877056 q^{19} + 48796580 q^{25} + 99886192 q^{31} - 487726352 q^{37} + 460449760 q^{43} - 439434108 q^{49} + 2261649600 q^{55} - 2750573000 q^{61} - 2190062816 q^{67} + 10099298944 q^{73} + 795481360 q^{79} + 8212243320 q^{85} - 62190452224 q^{91} - 632084096 q^{97}+O(q^{100}) $ 8 * q - 21584 * q^7 + 646912 * q^13 - 2877056 * q^19 + 48796580 * q^25 + 99886192 * q^31 - 487726352 * q^37 + 460449760 * q^43 - 439434108 * q^49 + 2261649600 * q^55 - 2750573000 * q^61 - 2190062816 * q^67 + 10099298944 * q^73 + 795481360 * q^79 + 8212243320 * q^85 - 62190452224 * q^91 - 632084096 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2732.87	+	1577.82i	−0.874517	+	0.504903i	−0.868847	−	0.495081i	$-0.835138\pi$
$5$	−2732.87	+	1577.82i	−0.874517	+	0.504903i	−0.00567031	+	0.999984i	$0.501805\pi$
$6$		0			0
$7$	6831.13	−	11831.9i	0.406445	−	0.703984i	−0.588043	−	0.808830i	$-0.700102\pi$
$7$	6831.13	−	11831.9i	0.406445	−	0.703984i	0.994489	+	0.104846i	$0.0334348\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−54331.2	−	31368.1i	−0.337354	−	0.194771i	0.321747	−	0.946826i	$-0.395730\pi$
$11$	−54331.2	−	31368.1i	−0.337354	−	0.194771i	−0.659101	+	0.752054i	$0.729063\pi$
$12$		0			0
$13$	−100189.	−	173533.i	−0.269839	−	0.467375i	0.698981	−	0.715140i	$-0.253637\pi$
$13$	−100189.	−	173533.i	−0.269839	−	0.467375i	−0.968820	+	0.247765i	$0.920304\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			556674.i			0.392064i	0.980598	+	0.196032i	$0.0628056\pi$
$17$			556674.i			0.392064i	−0.980598	+	0.196032i	$0.937194\pi$
$18$		0			0
$19$	−3.25649e6			−1.31517			−0.657584	−	0.753381i	$-0.728422\pi$
$19$	−3.25649e6			−1.31517			−0.657584	+	0.753381i	$0.728422\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	5.33186e6	−	3.07835e6i	0.828399	−	0.478277i	−0.0249049	−	0.999690i	$-0.507928\pi$
$23$	5.33186e6	−	3.07835e6i	0.828399	−	0.478277i	0.853304	+	0.521413i	$0.174595\pi$
$24$		0			0
$25$	96223.2	−	166663.i	0.00985326	−	0.0170663i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.49254e7	−	2.01642e7i	−1.70275	−	0.983083i	−0.942954	−	0.332922i	$-0.891965\pi$
$29$	−3.49254e7	−	2.01642e7i	−1.70275	−	0.983083i	−0.759796	−	0.650162i	$-0.774701\pi$
$30$		0			0
$31$	2.38921e7	+	4.13824e7i	0.834539	+	1.44546i	0.894405	+	0.447257i	$0.147599\pi$
$31$	2.38921e7	+	4.13824e7i	0.834539	+	1.44546i	−0.0598666	+	0.998206i	$0.519068\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			4.31132e7i			0.820861i
$36$		0			0
$37$	−7.11048e7			−1.02539			−0.512696	−	0.858570i	$-0.671353\pi$
$37$	−7.11048e7			−1.02539			−0.512696	+	0.858570i	$0.671353\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.21209e8	−	6.99801e7i	1.04620	−	0.604026i	0.124619	−	0.992205i	$-0.460229\pi$
$41$	1.21209e8	−	6.99801e7i	1.04620	−	0.604026i	0.921584	+	0.388179i	$0.126896\pi$
$42$		0			0
$43$	−1.08820e7	+	1.88481e7i	−0.0740227	+	0.128211i	−0.900661	−	0.434523i	$-0.856917\pi$
$43$	−1.08820e7	+	1.88481e7i	−0.0740227	+	0.128211i	0.826638	+	0.562734i	$0.190250\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.44771e8	−	8.35838e7i	−0.631238	−	0.364446i	0.149993	−	0.988687i	$-0.452075\pi$
$47$	−1.44771e8	−	8.35838e7i	−0.631238	−	0.364446i	−0.781232	+	0.624241i	$0.785408\pi$
$48$		0			0
$49$	4.79091e7	+	8.29809e7i	0.169604	+	0.293764i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	7.91424e8i		−	1.89247i	−0.323474	−	0.946237i	$-0.604851\pi$
$53$		−	7.91424e8i		−	1.89247i	0.323474	−	0.946237i	$-0.395149\pi$
$54$		0			0
$55$	1.97973e8			0.393363
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.48086e8	+	1.43232e8i	−0.347010	+	0.200346i	−0.663368	−	0.748294i	$-0.730873\pi$
$59$	−2.48086e8	+	1.43232e8i	−0.347010	+	0.200346i	0.316358	+	0.948640i	$0.397540\pi$
$60$		0			0
$61$	−5.06541e8	+	8.77355e8i	−0.599743	+	1.03879i	0.393115	+	0.919489i	$0.371397\pi$
$61$	−5.06541e8	+	8.77355e8i	−0.599743	+	1.03879i	−0.992859	+	0.119297i	$0.961936\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.47608e8	+	3.16162e8i	0.471958	+	0.272485i
$66$		0			0
$67$	−4.63864e8	−	8.03436e8i	−0.343571	−	0.595083i	0.641522	−	0.767105i	$-0.278303\pi$
$67$	−4.63864e8	−	8.03436e8i	−0.343571	−	0.595083i	−0.985093	+	0.172022i	$0.944970\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	2.49137e9i		−	1.38085i	−0.723405	−	0.690424i	$-0.757424\pi$
$71$		−	2.49137e9i		−	1.38085i	0.723405	−	0.690424i	$-0.242576\pi$
$72$		0			0
$73$	9.45207e8			0.455945			0.227973	−	0.973668i	$-0.426790\pi$
$73$	9.45207e8			0.455945			0.227973	+	0.973668i	$0.426790\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.42287e8	+	4.28559e8i	−0.274232	+	0.158328i
$78$		0			0
$79$	1.67985e9	−	2.90959e9i	0.545928	−	0.945574i	−0.452620	−	0.891703i	$-0.649511\pi$
$79$	1.67985e9	−	2.90959e9i	0.545928	−	0.945574i	0.998548	−	0.0538711i	$-0.0171560\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.44732e9	−	2.56766e9i	−1.12904	−	0.651850i	−0.185344	−	0.982674i	$-0.559340\pi$
$83$	−4.44732e9	−	2.56766e9i	−1.12904	−	0.651850i	−0.943693	+	0.330824i	$0.892673\pi$
$84$		0			0
$85$	−8.78332e8	−	1.52132e9i	−0.197954	−	0.342866i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			3.50859e9i			0.628322i	0.949370	+	0.314161i	$0.101723\pi$
$89$			3.50859e9i			0.628322i	−0.949370	+	0.314161i	$0.898277\pi$
$90$		0			0
$91$	−2.73763e9			−0.438699
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.89954e9	−	5.13815e9i	1.15014	−	0.664032i
$96$		0			0
$97$	3.03475e9	−	5.25633e9i	0.353398	−	0.612103i	−0.633445	−	0.773788i	$-0.718360\pi$
$97$	3.03475e9	−	5.25633e9i	0.353398	−	0.612103i	0.986842	+	0.161685i	$0.0516929\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	5.89527e9	+	3.40364e9i	0.560915	+	0.323844i	0.753513	−	0.657433i	$-0.228358\pi$
$101$	5.89527e9	+	3.40364e9i	0.560915	+	0.323844i	−0.192598	+	0.981278i	$0.561691\pi$
$102$		0			0
$103$	8.72492e9	+	1.51120e10i	0.752619	+	1.30358i	0.946549	+	0.322560i	$0.104543\pi$
$103$	8.72492e9	+	1.51120e10i	0.752619	+	1.30358i	−0.193930	+	0.981015i	$0.562123\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			2.69087e10i			1.91855i	0.282473	+	0.959275i	$0.408845\pi$
$107$			2.69087e10i			1.91855i	−0.282473	+	0.959275i	$0.591155\pi$
$108$		0			0
$109$	4.93582e9			0.320794			0.160397	−	0.987053i	$-0.448723\pi$
$109$	4.93582e9			0.320794			0.160397	+	0.987053i	$0.448723\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.58231e10	+	9.13548e9i	−0.858816	+	0.495837i	−0.863615	−	0.504151i	$-0.831805\pi$
$113$	−1.58231e10	+	9.13548e9i	−0.858816	+	0.495837i	0.00479989	+	0.999988i	$0.498472\pi$
$114$		0			0
$115$	−9.71418e9	+	1.68254e10i	−0.482966	+	0.836522i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	6.58649e9	+	3.80271e9i	0.276007	+	0.159352i
$120$		0			0
$121$	−1.10008e10	−	1.90539e10i	−0.424128	−	0.734611i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	3.02095e10i		−	0.989905i
$126$		0			0
$127$	−2.34860e10			−0.710871			−0.355436	−	0.934701i	$-0.615667\pi$
$127$	−2.34860e10			−0.710871			−0.355436	+	0.934701i	$0.615667\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.70862e10	+	9.86470e9i	−0.442882	+	0.255698i	−0.704819	−	0.709387i	$-0.748972\pi$
$131$	−1.70862e10	+	9.86470e9i	−0.442882	+	0.255698i	0.261937	+	0.965085i	$0.415639\pi$
$132$		0			0
$133$	−2.22455e10	+	3.85303e10i	−0.534544	+	0.925857i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.22593e10	+	3.59454e10i	1.29003	+	0.744802i	0.978660	−	0.205485i	$-0.0658773\pi$
$137$	6.22593e10	+	3.59454e10i	1.29003	+	0.744802i	0.311374	+	0.950287i	$0.399211\pi$
$138$		0			0
$139$	1.20174e10	+	2.08148e10i	0.231600	+	0.401142i	0.958279	−	0.285834i	$-0.0922708\pi$
$139$	1.20174e10	+	2.08148e10i	0.231600	+	0.401142i	−0.726679	+	0.686977i	$0.758937\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			1.25710e10i			0.210228i
$144$		0			0
$145$	1.27262e11			1.98545
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.70874e10	+	9.86541e9i	−0.232672	+	0.134333i	−0.611804	−	0.791009i	$-0.709556\pi$
$149$	−1.70874e10	+	9.86541e9i	−0.232672	+	0.134333i	0.379132	+	0.925343i	$0.376223\pi$
$150$		0			0
$151$	2.06016e10	−	3.56831e10i	0.262432	−	0.454546i	−0.704455	−	0.709748i	$-0.748809\pi$
$151$	2.06016e10	−	3.56831e10i	0.262432	−	0.454546i	0.966888	+	0.255202i	$0.0821420\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.30588e11	−	7.53950e10i	−1.45964	−	0.842722i
$156$		0			0
$157$	4.15028e10	+	7.18849e10i	0.435090	+	0.753598i	0.997303	−	0.0733946i	$-0.0233833\pi$
$157$	4.15028e10	+	7.18849e10i	0.435090	+	0.753598i	−0.562213	+	0.826992i	$0.690050\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	8.41145e10i		−	0.777573i
$162$		0			0
$163$	−1.05593e11			−0.917696			−0.458848	−	0.888515i	$-0.651738\pi$
$163$	−1.05593e11			−0.917696			−0.458848	+	0.888515i	$0.651738\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.30416e11	−	7.52959e10i	1.00404	−	0.579681i	0.0945962	−	0.995516i	$-0.469844\pi$
$167$	1.30416e11	−	7.52959e10i	1.00404	−	0.579681i	0.909440	+	0.415835i	$0.136511\pi$
$168$		0			0
$169$	4.88534e10	−	8.46166e10i	0.354374	−	0.613793i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.11150e10	−	4.10583e10i	−0.458913	−	0.264954i	0.252674	−	0.967552i	$-0.418690\pi$
$173$	−7.11150e10	−	4.10583e10i	−0.458913	−	0.264954i	−0.711587	+	0.702598i	$0.752023\pi$
$174$		0			0
$175$	−1.31463e9	−	2.27700e9i	−0.00800962	−	0.0138731i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			1.13910e11i			0.619867i	0.950758	+	0.309933i	$0.100307\pi$
$179$			1.13910e11i			0.619867i	−0.950758	+	0.309933i	$0.899693\pi$
$180$		0			0
$181$	5.06895e10			0.260930			0.130465	−	0.991453i	$-0.458353\pi$
$181$	5.06895e10			0.260930			0.130465	+	0.991453i	$0.458353\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.94320e11	−	1.12191e11i	0.896723	−	0.517723i
$186$		0			0
$187$	1.74618e10	−	3.02448e10i	0.0763628	−	0.132264i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.30109e10	−	2.48324e10i	−0.169205	−	0.0976903i	0.413006	−	0.910728i	$-0.364479\pi$
$191$	−4.30109e10	−	2.48324e10i	−0.169205	−	0.0976903i	−0.582211	+	0.813038i	$0.697812\pi$
$192$		0			0
$193$	1.36173e11	+	2.35858e11i	0.508515	+	0.880775i	0.999951	+	0.00986088i	$0.00313887\pi$
$193$	1.36173e11	+	2.35858e11i	0.508515	+	0.880775i	−0.491436	+	0.870914i	$0.663528\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	2.60900e11i		−	0.879313i	−0.898166	−	0.439656i	$-0.855100\pi$
$197$		−	2.60900e11i		−	0.879313i	0.898166	−	0.439656i	$-0.144900\pi$
$198$		0			0
$199$	2.08123e11			0.666891			0.333445	−	0.942769i	$-0.391789\pi$
$199$	2.08123e11			0.666891			0.333445	+	0.942769i	$0.391789\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.77159e11	+	2.75488e11i	−1.38415	+	0.799139i
$204$		0			0
$205$	−2.20832e11	+	3.82493e11i	−0.609948	+	1.05646i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.76929e11	+	1.02150e11i	0.443677	+	0.256157i
$210$		0			0
$211$	2.04358e11	+	3.53959e11i	0.488629	+	0.846331i	0.999914	−	0.0130803i	$-0.00416372\pi$
$211$	2.04358e11	+	3.53959e11i	0.488629	+	0.846331i	−0.511285	+	0.859411i	$0.670830\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	6.86791e10i		−	0.149497i
$216$		0			0
$217$	6.52841e11			1.35678
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.66014e10	−	5.57729e10i	0.183241	−	0.105794i
$222$		0			0
$223$	−4.46714e11	+	7.73731e11i	−0.810038	+	1.40303i	0.102799	+	0.994702i	$0.467220\pi$
$223$	−4.46714e11	+	7.73731e11i	−0.810038	+	1.40303i	−0.912837	+	0.408325i	$0.866113\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.28123e11	+	3.62647e11i	1.04211	+	0.601665i	0.920431	−	0.390904i	$-0.127838\pi$
$227$	6.28123e11	+	3.62647e11i	1.04211	+	0.601665i	0.121683	+	0.992569i	$0.461171\pi$
$228$		0			0
$229$	3.36733e11	+	5.83238e11i	0.534697	+	0.926122i	0.999178	+	0.0405393i	$0.0129076\pi$
$229$	3.36733e11	+	5.83238e11i	0.534697	+	0.926122i	−0.464481	+	0.885583i	$0.653759\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			3.23198e11i			0.470640i	0.971918	+	0.235320i	$0.0756138\pi$
$233$			3.23198e11i			0.470640i	−0.971918	+	0.235320i	$0.924386\pi$
$234$		0			0
$235$	5.27521e11			0.736038
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.24161e11	+	5.33565e11i	−1.18511	+	0.684223i	−0.957191	−	0.289457i	$-0.906525\pi$
$239$	−9.24161e11	+	5.33565e11i	−1.18511	+	0.684223i	−0.227918	+	0.973680i	$0.573192\pi$
$240$		0			0
$241$	3.30867e11	−	5.73079e11i	0.406976	−	0.704903i	−0.587573	−	0.809171i	$-0.699917\pi$
$241$	3.30867e11	−	5.73079e11i	0.406976	−	0.704903i	0.994549	+	0.104268i	$0.0332499\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.61858e11	−	1.51184e11i	−0.296644	−	0.171267i
$246$		0			0
$247$	3.26265e11	+	5.65108e11i	0.354884	+	0.614677i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			1.09896e12i			1.10309i	0.834145	+	0.551546i	$0.185962\pi$
$251$			1.09896e12i			1.10309i	−0.834145	+	0.551546i	$0.814038\pi$
$252$		0			0
$253$	−3.86249e11			−0.372619
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.63037e12	−	9.41295e11i	1.45419	−	0.839577i	0.455474	−	0.890249i	$-0.349470\pi$
$257$	1.63037e12	−	9.41295e11i	1.45419	−	0.839577i	0.998715	+	0.0506726i	$0.0161365\pi$
$258$		0			0
$259$	−4.85726e11	+	8.41302e11i	−0.416766	+	0.721860i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.28331e11	−	1.31827e11i	−0.181462	−	0.104767i	0.406517	−	0.913643i	$-0.366743\pi$
$263$	−2.28331e11	−	1.31827e11i	−0.181462	−	0.104767i	−0.587979	+	0.808876i	$0.700076\pi$
$264$		0			0
$265$	1.24873e12	+	2.16286e12i	0.955515	+	1.65500i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			1.21572e12i			0.863123i	0.902084	+	0.431561i	$0.142037\pi$
$269$			1.21572e12i			0.863123i	−0.902084	+	0.431561i	$0.857963\pi$
$270$		0			0
$271$	1.65179e12			1.13008			0.565039	−	0.825064i	$-0.308861\pi$
$271$	1.65179e12			1.13008			0.565039	+	0.825064i	$0.308861\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.04558e10	+	6.03669e9i	−0.00664807	+	0.00383827i
$276$		0			0
$277$	4.11699e11	−	7.13084e11i	0.252453	−	0.437262i	−0.711747	−	0.702436i	$-0.752096\pi$
$277$	4.11699e11	−	7.13084e11i	0.252453	−	0.437262i	0.964201	+	0.265174i	$0.0854292\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.15938e11	−	2.40142e11i	−0.237409	−	0.137068i	0.376577	−	0.926386i	$-0.377101\pi$
$281$	−4.15938e11	−	2.40142e11i	−0.237409	−	0.137068i	−0.613985	+	0.789318i	$0.710435\pi$
$282$		0			0
$283$	1.44594e12	+	2.50443e12i	0.796557	+	1.37968i	0.921846	+	0.387557i	$0.126681\pi$
$283$	1.44594e12	+	2.50443e12i	0.796557	+	1.37968i	−0.125289	+	0.992120i	$0.539986\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	1.91217e12i		−	0.982014i
$288$		0			0
$289$	1.70611e12			0.846286
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.24590e12	−	7.19318e11i	0.576957	−	0.333106i	−0.182966	−	0.983119i	$-0.558570\pi$
$293$	1.24590e12	−	7.19318e11i	0.576957	−	0.333106i	0.759923	+	0.650013i	$0.225236\pi$
$294$		0			0
$295$	4.51990e11	−	7.82870e11i	0.202311	−	0.350412i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.06839e12	−	6.16837e11i	−0.447069	−	0.258116i
$300$		0			0
$301$	1.48672e11	+	2.57508e11i	0.0601724	+	0.104222i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	3.19692e12i		−	1.21125i
$306$		0			0
$307$	4.68857e12			1.71929			0.859644	−	0.510893i	$-0.170685\pi$
$307$	4.68857e12			1.71929			0.859644	+	0.510893i	$0.170685\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.48029e12	+	2.00935e12i	−1.19623	+	0.690643i	−0.959712	−	0.280985i	$-0.909339\pi$
$311$	−3.48029e12	+	2.00935e12i	−1.19623	+	0.690643i	−0.236516	+	0.971628i	$0.576006\pi$
$312$		0			0
$313$	−2.80726e12	+	4.86232e12i	−0.934461	+	1.61853i	−0.158870	+	0.987300i	$0.550785\pi$
$313$	−2.80726e12	+	4.86232e12i	−0.934461	+	1.61853i	−0.775591	+	0.631235i	$0.782548\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.93760e10	−	5.16012e10i	−0.0279206	−	0.0161200i	0.485975	−	0.873973i	$-0.338465\pi$
$317$	−8.93760e10	−	5.16012e10i	−0.0279206	−	0.0161200i	−0.513895	+	0.857853i	$0.671798\pi$
$318$		0			0
$319$	1.26503e12	+	2.19109e12i	0.382953	+	0.663294i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.81280e12i		−	0.515630i
$324$		0			0
$325$	−3.85622e10			−0.0106352
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.97790e12	+	1.14194e12i	−0.513128	+	0.296254i
$330$		0			0
$331$	−9.80379e11	+	1.69807e12i	−0.246748	+	0.427381i	−0.962622	−	0.270850i	$-0.912695\pi$
$331$	−9.80379e11	+	1.69807e12i	−0.246748	+	0.427381i	0.715873	+	0.698230i	$0.246029\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.53536e12	+	1.46379e12i	0.600917	+	0.346940i
$336$		0			0
$337$	3.76687e12	+	6.52441e12i	0.866624	+	1.50104i	0.865425	+	0.501038i	$0.167048\pi$
$337$	3.76687e12	+	6.52441e12i	0.866624	+	1.50104i	0.00119922	+	0.999999i	$0.499618\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	2.99781e12i		−	0.650177i
$342$		0			0
$343$	5.16834e12			1.08863
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.06156e12	−	4.07700e12i	1.40363	−	0.810388i	0.408869	−	0.912593i	$-0.365923\pi$
$347$	7.06156e12	−	4.07700e12i	1.40363	−	0.810388i	0.994763	+	0.102205i	$0.0325898\pi$
$348$		0			0
$349$	−3.06943e12	+	5.31641e12i	−0.592831	+	1.02681i	0.401019	+	0.916070i	$0.368656\pi$
$349$	−3.06943e12	+	5.31641e12i	−0.592831	+	1.02681i	−0.993849	+	0.110743i	$0.964677\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.74041e12	+	1.00483e12i	0.317525	+	0.183323i	0.650289	−	0.759687i	$-0.274648\pi$
$353$	1.74041e12	+	1.00483e12i	0.317525	+	0.183323i	−0.332764	+	0.943010i	$0.607981\pi$
$354$		0			0
$355$	3.93093e12	+	6.80857e12i	0.697194	+	1.20758i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			6.41488e12i			1.07576i	0.843021	+	0.537881i	$0.180775\pi$
$359$			6.41488e12i			1.07576i	−0.843021	+	0.537881i	$0.819225\pi$
$360$		0			0
$361$	4.47364e12			0.729667
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.58312e12	+	1.49137e12i	−0.398732	+	0.230208i
$366$		0			0
$367$	1.08001e12	−	1.87063e12i	0.162217	−	0.280969i	−0.773446	−	0.633862i	$-0.781469\pi$
$367$	1.08001e12	−	1.87063e12i	0.162217	−	0.280969i	0.935664	+	0.352893i	$0.114802\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.36402e12	−	5.40632e12i	−1.33227	−	0.769187i
$372$		0			0
$373$	3.36900e12	+	5.83528e12i	0.466613	+	0.808198i	0.999273	−	0.0381319i	$-0.0121407\pi$
$373$	3.36900e12	+	5.83528e12i	0.466613	+	0.808198i	−0.532660	+	0.846330i	$0.678807\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			8.08094e12i			1.06110i
$378$		0			0
$379$	−1.21474e13			−1.55342			−0.776709	−	0.629859i	$-0.783113\pi$
$379$	−1.21474e13			−1.55342			−0.776709	+	0.629859i	$0.783113\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.99639e12	−	1.15262e12i	0.242243	−	0.139859i	−0.373964	−	0.927443i	$-0.622002\pi$
$383$	1.99639e12	−	1.15262e12i	0.242243	−	0.139859i	0.616207	+	0.787584i	$0.288668\pi$
$384$		0			0
$385$	1.35238e12	−	2.34239e12i	0.159880	−	0.276921i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.04959e12	+	4.07008e12i	0.791436	+	0.456936i	0.840468	−	0.541861i	$-0.182280\pi$
$389$	7.04959e12	+	4.07008e12i	0.791436	+	0.456936i	−0.0490317	+	0.998797i	$0.515614\pi$
$390$		0			0
$391$	1.71364e12	+	2.96811e12i	0.187515	+	0.324785i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			1.06020e13i			1.10256i
$396$		0			0
$397$	1.04376e13			1.05840			0.529198	−	0.848498i	$-0.322493\pi$
$397$	1.04376e13			1.05840			0.529198	+	0.848498i	$0.322493\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.43840e12	+	1.40781e12i	−0.235171	+	0.135776i	−0.612955	−	0.790118i	$-0.710019\pi$
$401$	−2.43840e12	+	1.40781e12i	−0.235171	+	0.135776i	0.377784	+	0.925894i	$0.376686\pi$
$402$		0			0
$403$	4.78748e12	−	8.29215e12i	0.450383	−	0.780085i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.86321e12	+	2.23043e12i	0.345920	+	0.199717i
$408$		0			0
$409$	−4.84652e12	−	8.39442e12i	−0.423461	−	0.733456i	0.572814	−	0.819685i	$-0.305852\pi$
$409$	−4.84652e12	−	8.39442e12i	−0.423461	−	0.733456i	−0.996275	+	0.0862290i	$0.972518\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			3.91375e12i			0.325719i
$414$		0			0
$415$	1.62052e13			1.31648
$416$		0			0
$417$		0			0
$418$		0			0
$419$	8.41292e11	−	4.85720e11i	0.0651443	−	0.0376111i	−0.467074	−	0.884218i	$-0.654692\pi$
$419$	8.41292e11	−	4.85720e11i	0.0651443	−	0.0376111i	0.532218	+	0.846607i	$0.321359\pi$
$420$		0			0
$421$	−5.59916e11	+	9.69802e11i	−0.0423362	+	0.0733285i	−0.886417	−	0.462887i	$-0.846813\pi$
$421$	−5.59916e11	+	9.69802e11i	−0.0423362	+	0.0733285i	0.844081	+	0.536216i	$0.180147\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	9.27773e10	+	5.35650e10i	0.00669109	+	0.00386310i
$426$		0			0
$427$	6.92049e12	+	1.19866e13i	0.487526	+	0.844419i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	2.25045e13i		−	1.51316i	−0.653904	−	0.756578i	$-0.726870\pi$
$431$		−	2.25045e13i		−	1.51316i	0.653904	−	0.756578i	$-0.273130\pi$
$432$		0			0
$433$	1.09000e12			0.0716125			0.0358062	−	0.999359i	$-0.488600\pi$
$433$	1.09000e12			0.0716125			0.0358062	+	0.999359i	$0.488600\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.73631e13	+	1.00246e13i	−1.08948	+	0.629014i
$438$		0			0
$439$	−9.41276e12	+	1.63034e13i	−0.577291	+	0.999897i	0.418498	+	0.908218i	$0.362557\pi$
$439$	−9.41276e12	+	1.63034e13i	−0.577291	+	0.999897i	−0.995789	+	0.0916791i	$0.970777\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	6.75300e12	+	3.89884e12i	0.395802	+	0.228516i	0.684671	−	0.728852i	$-0.259946\pi$
$443$	6.75300e12	+	3.89884e12i	0.395802	+	0.228516i	−0.288869	+	0.957369i	$0.593279\pi$
$444$		0			0
$445$	−5.53592e12	−	9.58850e12i	−0.317241	−	0.549478i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	2.97774e13i		−	1.63176i	−0.578224	−	0.815878i	$-0.696254\pi$
$449$		−	2.97774e13i		−	1.63176i	0.578224	−	0.815878i	$-0.303746\pi$
$450$		0			0
$451$	−8.78059e12			−0.470588
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.48156e12	−	4.31948e12i	0.383650	−	0.221500i
$456$		0			0
$457$	−8.36834e11	+	1.44944e12i	−0.0419815	+	0.0727141i	−0.886253	−	0.463202i	$-0.846700\pi$
$457$	−8.36834e11	+	1.44944e12i	−0.0419815	+	0.0727141i	0.844271	+	0.535916i	$0.180034\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−1.21318e13	−	7.00429e12i	−0.582667	−	0.336403i	0.179526	−	0.983753i	$-0.442544\pi$
$461$	−1.21318e13	−	7.00429e12i	−0.582667	−	0.336403i	−0.762192	+	0.647351i	$0.775877\pi$
$462$		0			0
$463$	−1.72886e13	−	2.99447e13i	−0.812557	−	1.40739i	−0.911069	−	0.412255i	$-0.864741\pi$
$463$	−1.72886e13	−	2.99447e13i	−0.812557	−	1.40739i	0.0985114	−	0.995136i	$-0.468592\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$			1.98869e13i			0.895330i	0.894201	+	0.447665i	$0.147744\pi$
$467$			1.98869e13i			0.895330i	−0.894201	+	0.447665i	$0.852256\pi$
$468$		0			0
$469$	−1.26749e13			−0.558571
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.18246e12	−	6.82694e11i	0.0499437	−	0.0288350i
$474$		0			0
$475$	−3.13350e11	+	5.42737e11i	−0.0129587	+	0.0224451i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.80373e13	+	1.04138e13i	0.715310	+	0.412984i	0.813024	−	0.582230i	$-0.197820\pi$
$479$	1.80373e13	+	1.04138e13i	0.715310	+	0.412984i	−0.0977142	+	0.995215i	$0.531153\pi$
$480$		0			0
$481$	7.12395e12	+	1.23390e13i	0.276691	+	0.479243i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			1.91531e13i			0.713726i
$486$		0			0
$487$	−1.83888e13			−0.671286			−0.335643	−	0.941989i	$-0.608954\pi$
$487$	−1.83888e13			−0.671286			−0.335643	+	0.941989i	$0.608954\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	2.08218e13	−	1.20215e13i	0.729642	−	0.421259i	−0.0886489	−	0.996063i	$-0.528255\pi$
$491$	2.08218e13	−	1.20215e13i	0.729642	−	0.421259i	0.818291	+	0.574804i	$0.194922\pi$
$492$		0			0
$493$	1.12249e13	−	1.94421e13i	0.385431	−	0.667587i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.94775e13	−	1.70188e13i	−0.972095	−	0.561240i
$498$		0			0
$499$	−6.00146e11	−	1.03948e12i	−0.0193979	−	0.0335981i	0.856164	−	0.516705i	$-0.172842\pi$
$499$	−6.00146e11	−	1.03948e12i	−0.0193979	−	0.0335981i	−0.875561	+	0.483107i	$0.839508\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	6.28291e13i		−	1.95128i	−0.219367	−	0.975642i	$-0.570399\pi$
$503$		−	6.28291e13i		−	1.95128i	0.219367	−	0.975642i	$-0.429601\pi$
$504$		0			0
$505$	−2.14813e13			−0.654039
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.95511e13	−	1.70614e13i	0.864939	−	0.499373i	−0.000724328	−	1.00000i	$-0.500231\pi$
$509$	2.95511e13	−	1.70614e13i	0.864939	−	0.499373i	0.865663	+	0.500627i	$0.166897\pi$
$510$		0			0
$511$	6.45683e12	−	1.11836e13i	0.185317	−	0.320978i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.76881e13	−	2.75327e13i	−1.31636	−	0.759999i
$516$		0			0
$517$	5.24374e12	+	9.08242e12i	0.141967	+	0.245895i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			6.35549e13i			1.65562i	0.561009	+	0.827810i	$0.310413\pi$
$521$			6.35549e13i			1.65562i	−0.561009	+	0.827810i	$0.689587\pi$
$522$		0			0
$523$	−2.68002e13			−0.684903			−0.342451	−	0.939536i	$-0.611257\pi$
$523$	−2.68002e13			−0.684903			−0.342451	+	0.939536i	$0.611257\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.30365e13	+	1.33001e13i	−0.566714	+	0.327192i
$528$		0			0
$529$	−1.76074e12	+	3.04970e12i	−0.0425028	+	0.0736171i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.42877e13	−	1.40225e13i	−0.564613	−	0.325980i
$534$		0			0
$535$	−4.24570e13	−	7.35378e13i	−0.968681	−	1.67781i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	6.01127e12i		−	0.132136i
$540$		0			0
$541$	−2.13159e13			−0.459958			−0.229979	−	0.973196i	$-0.573866\pi$
$541$	−2.13159e13			−0.459958			−0.229979	+	0.973196i	$0.573866\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.34889e13	+	7.78784e12i	−0.280540	+	0.161970i
$546$		0			0
$547$	2.23883e13	−	3.87777e13i	0.457177	−	0.791854i	−0.541633	−	0.840615i	$-0.682194\pi$
$547$	2.23883e13	−	3.87777e13i	0.457177	−	0.791854i	0.998810	+	0.0487606i	$0.0155272\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.13734e14	+	6.56643e13i	2.23940	+	1.29292i
$552$		0			0
$553$	−2.29505e13	−	3.97515e13i	−0.443779	−	0.768649i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			2.37300e13i			0.442611i	0.975205	+	0.221305i	$0.0710317\pi$
$557$			2.37300e13i			0.442611i	−0.975205	+	0.221305i	$0.928968\pi$
$558$		0			0
$559$	4.36103e12			0.0798969
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.10684e12	−	3.52579e12i	0.107963	−	0.0623324i	−0.445046	−	0.895508i	$-0.646813\pi$
$563$	6.10684e12	−	3.52579e12i	0.107963	−	0.0623324i	0.553009	+	0.833175i	$0.313479\pi$
$564$		0			0
$565$	2.88283e13	−	4.99321e13i	0.500699	−	0.867236i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.57428e13	+	3.79566e13i	1.10227	+	0.636395i	0.936816	−	0.349823i	$-0.113758\pi$
$569$	6.57428e13	+	3.79566e13i	1.10227	+	0.636395i	0.165452	+	0.986218i	$0.447092\pi$
$570$		0			0
$571$	−5.27631e13	−	9.13883e13i	−0.869260	−	1.50560i	−0.862754	−	0.505623i	$-0.831263\pi$
$571$	−5.27631e13	−	9.13883e13i	−0.869260	−	1.50560i	−0.00650539	−	0.999979i	$-0.502071\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	1.18484e12i		−	0.0188503i
$576$		0			0
$577$	−5.22466e13			−0.816919			−0.408459	−	0.912777i	$-0.633934\pi$
$577$	−5.22466e13			−0.816919			−0.408459	+	0.912777i	$0.633934\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−6.07604e13	+	3.50801e13i	−0.917783	+	0.529883i
$582$		0			0
$583$	−2.48255e13	+	4.29990e13i	−0.368600	+	0.638434i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.16181e13	−	4.71223e13i	−1.17111	−	0.676138i	−0.217166	−	0.976135i	$-0.569681\pi$
$587$	−8.16181e13	−	4.71223e13i	−1.17111	−	0.676138i	−0.953940	+	0.299996i	$0.903015\pi$
$588$		0			0
$589$	−7.78044e13	−	1.34761e14i	−1.09756	−	1.90103i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	2.00339e13i		−	0.273208i	−0.990626	−	0.136604i	$-0.956381\pi$
$593$		−	2.00339e13i		−	0.273208i	0.990626	−	0.136604i	$-0.0436188\pi$
$594$		0			0
$595$	−2.40000e13			−0.321830
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.10587e14	+	6.38473e13i	−1.43407	+	0.827959i	−0.997428	−	0.0716784i	$-0.977164\pi$
$599$	−1.10587e14	+	6.38473e13i	−1.43407	+	0.827959i	−0.436639	+	0.899637i	$0.643831\pi$
$600$		0			0
$601$	−4.20803e12	+	7.28852e12i	−0.0536669	+	0.0929538i	−0.891611	−	0.452803i	$-0.850424\pi$
$601$	−4.20803e12	+	7.28852e12i	−0.0536669	+	0.0929538i	0.837944	+	0.545756i	$0.183758\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.01274e13	+	3.47146e13i	0.741814	+	0.428287i
$606$		0			0
$607$	−1.64882e13	−	2.85585e13i	−0.200092	−	0.346570i	0.748466	−	0.663174i	$-0.230791\pi$
$607$	−1.64882e13	−	2.85585e13i	−0.200092	−	0.346570i	−0.948558	+	0.316603i	$0.897458\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			3.34968e13i			0.393367i
$612$		0			0
$613$	−4.25352e13			−0.491412			−0.245706	−	0.969344i	$-0.579020\pi$
$613$	−4.25352e13			−0.491412			−0.245706	+	0.969344i	$0.579020\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.38495e14	−	7.99601e13i	1.54885	−	0.894226i	0.550615	−	0.834759i	$-0.314393\pi$
$617$	1.38495e14	−	7.99601e13i	1.54885	−	0.894226i	0.998230	−	0.0594674i	$-0.0189402\pi$
$618$		0			0
$619$	3.70288e13	−	6.41358e13i	0.407462	−	0.705745i	−0.587143	−	0.809483i	$-0.699747\pi$
$619$	3.70288e13	−	6.41358e13i	0.407462	−	0.705745i	0.994605	+	0.103739i	$0.0330806\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	4.15131e13	+	2.39676e13i	0.442329	+	0.255379i
$624$		0			0
$625$	4.86049e13	+	8.41861e13i	0.509659	+	0.882755i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	3.95822e13i		−	0.402019i
$630$		0			0
$631$	−9.16626e12			−0.0916316			−0.0458158	−	0.998950i	$-0.514589\pi$
$631$	−9.16626e12			−0.0916316			−0.0458158	+	0.998950i	$0.514589\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.41842e13	−	3.70567e13i	0.621669	−	0.358921i
$636$		0			0
$637$	9.59996e12	−	1.66276e13i	0.0915319	−	0.158538i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−6.39172e13	−	3.69026e13i	−0.590646	−	0.341010i	0.174707	−	0.984620i	$-0.444102\pi$
$641$	−6.39172e13	−	3.69026e13i	−0.590646	−	0.341010i	−0.765353	+	0.643611i	$0.777436\pi$
$642$		0			0
$643$	3.37575e13	+	5.84697e13i	0.307125	+	0.531956i	0.977732	−	0.209857i	$-0.0672997\pi$
$643$	3.37575e13	+	5.84697e13i	0.307125	+	0.531956i	−0.670607	+	0.741813i	$0.733966\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1.48268e14i			1.30775i	0.756601	+	0.653877i	$0.226859\pi$
$647$			1.48268e14i			1.30775i	−0.756601	+	0.653877i	$0.773141\pi$
$648$		0			0
$649$	1.79717e13			0.156087
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.15469e13	−	1.82136e13i	0.265699	−	0.153402i	−0.361232	−	0.932476i	$-0.617644\pi$
$653$	3.15469e13	−	1.82136e13i	0.265699	−	0.153402i	0.626932	+	0.779074i	$0.284311\pi$
$654$		0			0
$655$	3.11294e13	−	5.39178e13i	0.258205	−	0.447224i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.23906e14	−	7.15369e13i	−0.996928	−	0.575577i	−0.0895900	−	0.995979i	$-0.528556\pi$
$659$	−1.23906e14	−	7.15369e13i	−0.996928	−	0.575577i	−0.907338	+	0.420402i	$0.861889\pi$
$660$		0			0
$661$	−7.69524e13	−	1.33285e14i	−0.609838	−	1.05627i	−0.991267	−	0.131872i	$-0.957901\pi$
$661$	−7.69524e13	−	1.33285e14i	−0.609838	−	1.05627i	0.381429	−	0.924398i	$-0.375432\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	1.40397e14i		−	1.07957i
$666$		0			0
$667$	−2.48290e14			−1.88074
$668$		0			0
$669$		0			0
$670$		0			0
$671$	5.50420e13	−	3.17785e13i	0.404652	−	0.233626i
$672$		0			0
$673$	−9.77230e13	+	1.69261e14i	−0.707817	+	1.22598i	0.257848	+	0.966186i	$0.416987\pi$
$673$	−9.77230e13	+	1.69261e14i	−0.707817	+	1.22598i	−0.965665	+	0.259790i	$0.916347\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.55234e14	−	8.96247e13i	−1.09155	−	0.630208i	−0.157564	−	0.987509i	$-0.550364\pi$
$677$	−1.55234e14	−	8.96247e13i	−1.09155	−	0.630208i	−0.933990	+	0.357300i	$0.883697\pi$
$678$		0			0
$679$	−4.14615e13	−	7.18134e13i	−0.287274	−	0.497572i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			2.50626e13i			0.168625i	0.996439	+	0.0843127i	$0.0268695\pi$
$683$			2.50626e13i			0.168625i	−0.996439	+	0.0843127i	$0.973131\pi$
$684$		0			0
$685$	−2.26862e14			−1.50421
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.37338e14	+	7.92923e13i	−0.884495	+	0.510664i
$690$		0			0
$691$	1.48611e14	−	2.57402e14i	0.943324	−	1.63389i	0.184252	−	0.982879i	$-0.441014\pi$
$691$	1.48611e14	−	2.57402e14i	0.943324	−	1.63389i	0.759072	−	0.651007i	$-0.225653\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.56841e13	−	3.79227e13i	−0.405076	−	0.233870i
$696$		0			0
$697$	3.89561e13	+	6.74740e13i	0.236817	+	0.410178i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	2.01709e14i		−	1.19161i	−0.803129	−	0.595805i	$-0.796833\pi$
$701$		−	2.01709e14i		−	1.19161i	0.803129	−	0.595805i	$-0.203167\pi$
$702$		0			0
$703$	2.31552e14			1.34856
$704$		0			0
$705$		0			0
$706$		0			0
$707$	8.05427e13	−	4.65013e13i	0.455962	−	0.263250i
$708$		0			0
$709$	−1.27057e14	+	2.20069e14i	−0.709197	+	1.22837i	0.255958	+	0.966688i	$0.417609\pi$
$709$	−1.27057e14	+	2.20069e14i	−0.709197	+	1.22837i	−0.965155	+	0.261677i	$0.915724\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	2.54779e14	+	1.47097e14i	1.38266	+	0.798281i
$714$		0			0
$715$	−1.98348e13	−	3.43549e13i	−0.106145	−	0.183848i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	1.42854e14i		−	0.743445i	−0.928344	−	0.371723i	$-0.878767\pi$
$719$		−	1.42854e14i		−	0.743445i	0.928344	−	0.371723i	$-0.121233\pi$
$720$		0			0
$721$	2.38404e14			1.22359
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−6.72126e12	+	3.88052e12i	−0.0335553	+	0.0193731i
$726$		0			0
$727$	−8.46696e12	+	1.46652e13i	−0.0416923	+	0.0722131i	−0.886119	−	0.463459i	$-0.846608\pi$
$727$	−8.46696e12	+	1.46652e13i	−0.0416923	+	0.0722131i	0.844426	+	0.535672i	$0.179942\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.04923e13	−	6.05771e12i	−0.0502669	−	0.0290216i
$732$		0			0
$733$	1.43417e13	+	2.48405e13i	0.0677766	+	0.117392i	0.897922	−	0.440154i	$-0.145076\pi$
$733$	1.43417e13	+	2.48405e13i	0.0677766	+	0.117392i	−0.830146	+	0.557546i	$0.811743\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			5.82022e13i			0.267671i
$738$		0			0
$739$	3.36378e14			1.52618			0.763089	−	0.646294i	$-0.223682\pi$
$739$	3.36378e14			1.52618			0.763089	+	0.646294i	$0.223682\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.15836e14	+	6.68777e13i	−0.511562	+	0.295350i	−0.733475	−	0.679716i	$-0.762103\pi$
$743$	−1.15836e14	+	6.68777e13i	−0.511562	+	0.295350i	0.221914	+	0.975066i	$0.428770\pi$
$744$		0			0
$745$	3.11317e13	−	5.39217e13i	0.135650	−	0.234953i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.18379e14	+	1.83816e14i	1.35063	+	0.779786i
$750$		0			0
$751$	−3.76480e12	−	6.52083e12i	−0.0157595	−	0.0272963i	0.858038	−	0.513586i	$-0.171683\pi$
$751$	−3.76480e12	−	6.52083e12i	−0.0157595	−	0.0272963i	−0.873798	+	0.486290i	$0.838350\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			1.30023e14i			0.530011i
$756$		0			0
$757$	−1.62040e14			−0.651844			−0.325922	−	0.945397i	$-0.605675\pi$
$757$	−1.62040e14			−0.651844			−0.325922	+	0.945397i	$0.605675\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.13047e13	+	1.23003e13i	−0.0834743	+	0.0481939i	−0.541156	−	0.840922i	$-0.682013\pi$
$761$	−2.13047e13	+	1.23003e13i	−0.0834743	+	0.0481939i	0.457682	+	0.889116i	$0.348680\pi$
$762$		0			0
$763$	3.37172e13	−	5.83999e13i	0.130385	−	0.225834i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.97111e13	+	2.87007e13i	0.187274	+	0.108123i
$768$		0			0
$769$	−2.94173e12	−	5.09523e12i	−0.0109388	−	0.0189466i	0.860504	−	0.509443i	$-0.170149\pi$
$769$	−2.94173e12	−	5.09523e12i	−0.0109388	−	0.0189466i	−0.871443	+	0.490497i	$0.836815\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			1.52416e13i			0.0552247i	0.999619	+	0.0276124i	$0.00879041\pi$
$773$			1.52416e13i			0.0552247i	−0.999619	+	0.0276124i	$0.991210\pi$
$774$		0			0
$775$	9.19591e12			0.0328917
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−3.94716e14	+	2.27889e14i	−1.37593	+	0.794395i
$780$		0			0
$781$	−7.81496e13	+	1.35359e14i	−0.268950	+	0.465835i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.26843e14	−	1.30968e14i	−0.760987	−	0.439356i
$786$		0			0
$787$	1.52888e14	+	2.64809e14i	0.506406	+	0.877121i	0.999973	+	0.00741282i	$0.00235959\pi$
$787$	1.52888e14	+	2.64809e14i	0.506406	+	0.877121i	−0.493567	+	0.869708i	$0.664307\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			2.49623e14i			0.806123i
$792$		0			0
$793$	2.03000e14			0.647337
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.57428e14	−	2.64096e14i	1.42243	−	0.821240i	0.425924	−	0.904759i	$-0.359949\pi$
$797$	4.57428e14	−	2.64096e14i	1.42243	−	0.821240i	0.996506	+	0.0835187i	$0.0266158\pi$
$798$		0			0
$799$	4.65290e13	−	8.05905e13i	0.142886	−	0.247486i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.13542e13	−	2.96494e13i	−0.153815	−	0.0888051i
$804$		0			0
$805$	1.32718e14	+	2.29874e14i	0.392599	+	0.680001i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			1.65656e14i			0.478042i	0.971014	+	0.239021i	$0.0768264\pi$
$809$			1.65656e14i			0.478042i	−0.971014	+	0.239021i	$0.923174\pi$
$810$		0			0
$811$	1.08318e14			0.308742			0.154371	−	0.988013i	$-0.450665\pi$
$811$	1.08318e14			0.308742			0.154371	+	0.988013i	$0.450665\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.88573e14	−	1.66607e14i	0.802540	−	0.463347i
$816$		0			0
$817$	3.54370e13	−	6.13786e13i	0.0973523	−	0.168619i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.04040e14	−	1.17802e14i	−0.547015	−	0.315819i	0.200902	−	0.979611i	$-0.435613\pi$
$821$	−2.04040e14	−	1.17802e14i	−0.547015	−	0.315819i	−0.747917	+	0.663792i	$0.768946\pi$
$822$		0			0
$823$	2.63142e14	+	4.55776e14i	0.696933	+	1.20712i	0.969525	+	0.244994i	$0.0787860\pi$
$823$	2.63142e14	+	4.55776e14i	0.696933	+	1.20712i	−0.272591	+	0.962130i	$0.587881\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			3.77432e14i			0.975689i	0.872931	+	0.487845i	$0.162217\pi$
$827$			3.77432e14i			0.975689i	−0.872931	+	0.487845i	$0.837783\pi$
$828$		0			0
$829$	4.96486e13			0.126804			0.0634022	−	0.997988i	$-0.479805\pi$
$829$	4.96486e13			0.126804			0.0634022	+	0.997988i	$0.479805\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.61934e13	+	2.66697e13i	−0.115174	+	0.0664958i
$834$		0			0
$835$	−2.37607e14	+	4.11547e14i	−0.585364	+	1.01388i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	4.56175e14	+	2.63373e14i	1.09729	+	0.633520i	0.935508	−	0.353306i	$-0.114943\pi$
$839$	4.56175e14	+	2.63373e14i	1.09729	+	0.633520i	0.161782	+	0.986827i	$0.448276\pi$
$840$		0			0
$841$	6.02834e14	+	1.04414e15i	1.43291	+	2.48187i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			3.08328e14i			0.715697i
$846$		0			0
$847$	−3.00591e14			−0.689540
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.79121e14	+	2.18886e14i	−0.849435	+	0.490421i
$852$		0			0
$853$	−1.85931e14	+	3.22041e14i	−0.411724	+	0.713126i	−0.995078	−	0.0990913i	$-0.968406\pi$
$853$	−1.85931e14	+	3.22041e14i	−0.411724	+	0.713126i	0.583355	+	0.812217i	$0.301740\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.76643e14	−	2.75190e14i	−1.03107	−	0.595290i	−0.113780	−	0.993506i	$-0.536296\pi$
$857$	−4.76643e14	−	2.75190e14i	−1.03107	−	0.595290i	−0.917291	+	0.398216i	$0.869629\pi$
$858$		0			0
$859$	−2.45171e14	−	4.24648e14i	−0.524207	−	0.907953i	−0.999603	−	0.0281808i	$-0.991029\pi$
$859$	−2.45171e14	−	4.24648e14i	−0.524207	−	0.907953i	0.475396	−	0.879772i	$-0.342305\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	5.36959e14i		−	1.12173i	−0.827908	−	0.560863i	$-0.810469\pi$
$863$		−	5.36959e14i		−	1.12173i	0.827908	−	0.560863i	$-0.189531\pi$
$864$		0			0
$865$	2.59130e14			0.535103
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.82537e14	+	1.05388e14i	−0.368342	+	0.212662i
$870$		0			0
$871$	−9.29485e13	+	1.60992e14i	−0.185418	+	0.321153i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.57435e14	−	2.06365e14i	−0.696877	−	0.402342i
$876$		0			0
$877$	4.65452e14	+	8.06187e14i	0.897175	+	1.55395i	0.831089	+	0.556139i	$0.187718\pi$
$877$	4.65452e14	+	8.06187e14i	0.897175	+	1.55395i	0.0660858	+	0.997814i	$0.478949\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			1.41915e14i			0.267392i	0.991022	+	0.133696i	$0.0426846\pi$
$881$			1.41915e14i			0.267392i	−0.991022	+	0.133696i	$0.957315\pi$
$882$		0			0
$883$	9.56307e14			1.78153			0.890766	−	0.454462i	$-0.150168\pi$
$883$	9.56307e14			1.78153			0.890766	+	0.454462i	$0.150168\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.51363e14	−	4.33800e14i	1.36846	−	0.790080i	0.377728	−	0.925917i	$-0.376706\pi$
$887$	7.51363e14	−	4.33800e14i	1.36846	−	0.790080i	0.990731	+	0.135837i	$0.0433723\pi$
$888$		0			0
$889$	−1.60436e14	+	2.77883e14i	−0.288930	+	0.500442i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.71446e14	+	2.72190e14i	0.830185	+	0.479307i
$894$		0			0
$895$	−1.79730e14	−	3.11302e14i	−0.312972	−	0.542084i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	1.92706e15i		−	3.28169i
$900$		0			0
$901$	4.40566e14			0.741970
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.38527e14	+	7.99789e13i	−0.228188	+	0.131744i
$906$		0			0
$907$	9.75283e13	−	1.68924e14i	0.158889	−	0.275204i	−0.775579	−	0.631250i	$-0.782542\pi$
$907$	9.75283e13	−	1.68924e14i	0.158889	−	0.275204i	0.934468	+	0.356046i	$0.115875\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.64479e14	+	3.83637e14i	1.05898	+	0.611404i	0.925151	−	0.379599i	$-0.123938\pi$
$911$	6.64479e14	+	3.83637e14i	1.05898	+	0.611404i	0.133833	+	0.991004i	$0.457272\pi$
$912$		0			0
$913$	1.61086e14	+	2.79008e14i	0.253923	+	0.439808i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			2.69548e14i			0.415709i
$918$		0			0
$919$	5.50077e14			0.839162			0.419581	−	0.907718i	$-0.362177\pi$
$919$	5.50077e14			0.839162			0.419581	+	0.907718i	$0.362177\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−4.32335e14	+	2.49609e14i	−0.645374	+	0.372607i
$924$		0			0
$925$	−6.84193e12	+	1.18506e13i	−0.0101035	+	0.0174997i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−7.94912e13	−	4.58942e13i	−0.114879	−	0.0663254i	0.441460	−	0.897281i	$-0.354461\pi$
$929$	−7.94912e13	−	4.58942e13i	−0.114879	−	0.0663254i	−0.556338	+	0.830956i	$0.687794\pi$
$930$		0			0
$931$	−1.56015e14	−	2.70226e14i	−0.223058	−	0.386348i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			1.10207e14i			0.154223i
$936$		0			0
$937$	−1.24541e14			−0.172431			−0.0862154	−	0.996277i	$-0.527477\pi$
$937$	−1.24541e14			−0.172431			−0.0862154	+	0.996277i	$0.527477\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.16147e14	+	3.55733e14i	−0.835096	+	0.482143i	−0.855594	−	0.517647i	$-0.826808\pi$
$941$	−6.16147e14	+	3.55733e14i	−0.835096	+	0.482143i	0.0204983	+	0.999790i	$0.493475\pi$
$942$		0			0
$943$	4.30847e14	−	7.46249e14i	0.577783	−	1.00075i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.62532e14	−	2.09308e14i	−0.475988	−	0.274812i	0.242755	−	0.970088i	$-0.421949\pi$
$947$	−3.62532e14	−	2.09308e14i	−0.475988	−	0.274812i	−0.718743	+	0.695276i	$0.755282\pi$
$948$		0			0
$949$	−9.46997e13	−	1.64025e14i	−0.123032	−	0.213097i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1.44086e14i		−	0.183298i	−0.995791	−	0.0916488i	$-0.970786\pi$
$953$		−	1.44086e14i		−	0.183298i	0.995791	−	0.0916488i	$-0.0292137\pi$
$954$		0			0
$955$	1.56724e14			0.197296
$956$		0			0
$957$		0			0
$958$		0			0
$959$	8.50602e14	−	4.91095e14i	1.04866	−	0.605442i
$960$		0			0
$961$	−7.31854e14	+	1.26761e15i	−0.892910	+	1.54657i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−7.44284e14	−	4.29713e14i	−0.889411	−	0.513502i
$966$		0			0
$967$	5.48488e14	+	9.50009e14i	0.648686	+	1.12356i	0.983437	+	0.181251i	$0.0580146\pi$
$967$	5.48488e14	+	9.50009e14i	0.648686	+	1.12356i	−0.334751	+	0.942307i	$0.608652\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	7.77841e13i		−	0.0901145i	−0.998984	−	0.0450572i	$-0.985653\pi$
$971$		−	7.77841e13i		−	0.0901145i	0.998984	−	0.0450572i	$-0.0143470\pi$
$972$		0			0
$973$	3.28370e14			0.376530
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.46316e14	−	8.44755e13i	0.164369	−	0.0948982i	−0.415559	−	0.909566i	$-0.636414\pi$
$977$	1.46316e14	−	8.44755e13i	0.164369	−	0.0948982i	0.579928	+	0.814668i	$0.303081\pi$
$978$		0			0
$979$	1.10058e14	−	1.90626e14i	0.122379	−	0.211967i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−4.59733e14	−	2.65427e14i	−0.500885	−	0.289186i	0.228194	−	0.973616i	$-0.426718\pi$
$983$	−4.59733e14	−	2.65427e14i	−0.500885	−	0.289186i	−0.729079	+	0.684429i	$0.760051\pi$
$984$		0			0
$985$	4.11654e14	+	7.13005e14i	0.443967	+	0.768974i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			1.33994e14i			0.141613i
$990$		0			0
$991$	−9.48887e13			−0.0992765			−0.0496382	−	0.998767i	$-0.515807\pi$
$991$	−9.48887e13			−0.0992765			−0.0496382	+	0.998767i	$0.515807\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−5.68772e14	+	3.28381e14i	−0.583207	+	0.336715i
$996$		0			0
$997$	3.68680e14	−	6.38572e14i	0.374260	−	0.648238i	−0.615956	−	0.787781i	$-0.711230\pi$
$997$	3.68680e14	−	6.38572e14i	0.374260	−	0.648238i	0.990216	+	0.139543i	$0.0445634\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.11.g.e.269.2		8
3.2	odd	2	inner	324.11.g.e.269.3		8
9.2	odd	6		36.11.c.a.17.3	yes	4
9.4	even	3	inner	324.11.g.e.53.3		8
9.5	odd	6	inner	324.11.g.e.53.2		8
9.7	even	3		36.11.c.a.17.2	✓	4
36.7	odd	6		144.11.e.b.17.2		4
36.11	even	6		144.11.e.b.17.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.11.c.a.17.2	✓	4	9.7	even	3
36.11.c.a.17.3	yes	4	9.2	odd	6
144.11.e.b.17.2		4	36.7	odd	6
144.11.e.b.17.3		4	36.11	even	6
324.11.g.e.53.2		8	9.5	odd	6	inner
324.11.g.e.53.3		8	9.4	even	3	inner
324.11.g.e.269.2		8	1.1	even	1	trivial
324.11.g.e.269.3		8	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	324.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2732.87 + 1577.82i) q^{5} +(6831.13 - 11831.9i) q^{7} +O(q^{10})\)	\(q+(-2732.87 + 1577.82i) q^{5} +(6831.13 - 11831.9i) q^{7} +(-54331.2 - 31368.1i) q^{11} +(-100189. - 173533. i) q^{13} +556674. i q^{17} -3.25649e6 q^{19} +(5.33186e6 - 3.07835e6i) q^{23} +(96223.2 - 166663. i) q^{25} +(-3.49254e7 - 2.01642e7i) q^{29} +(2.38921e7 + 4.13824e7i) q^{31} +4.31132e7i q^{35} -7.11048e7 q^{37} +(1.21209e8 - 6.99801e7i) q^{41} +(-1.08820e7 + 1.88481e7i) q^{43} +(-1.44771e8 - 8.35838e7i) q^{47} +(4.79091e7 + 8.29809e7i) q^{49} -7.91424e8i q^{53} +1.97973e8 q^{55} +(-2.48086e8 + 1.43232e8i) q^{59} +(-5.06541e8 + 8.77355e8i) q^{61} +(5.47608e8 + 3.16162e8i) q^{65} +(-4.63864e8 - 8.03436e8i) q^{67} -2.49137e9i q^{71} +9.45207e8 q^{73} +(-7.42287e8 + 4.28559e8i) q^{77} +(1.67985e9 - 2.90959e9i) q^{79} +(-4.44732e9 - 2.56766e9i) q^{83} +(-8.78332e8 - 1.52132e9i) q^{85} +3.50859e9i q^{89} -2.73763e9 q^{91} +(8.89954e9 - 5.13815e9i) q^{95} +(3.03475e9 - 5.25633e9i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 21584 q^{7}+O(q^{10}) \) 8 * q - 21584 * q^7	\( 8 q - 21584 q^{7} + 646912 q^{13} - 2877056 q^{19} + 48796580 q^{25} + 99886192 q^{31} - 487726352 q^{37} + 460449760 q^{43} - 439434108 q^{49} + 2261649600 q^{55} - 2750573000 q^{61} - 2190062816 q^{67} + 10099298944 q^{73} + 795481360 q^{79} + 8212243320 q^{85} - 62190452224 q^{91} - 632084096 q^{97}+O(q^{100}) \) 8 * q - 21584 * q^7 + 646912 * q^13 - 2877056 * q^19 + 48796580 * q^25 + 99886192 * q^31 - 487726352 * q^37 + 460449760 * q^43 - 439434108 * q^49 + 2261649600 * q^55 - 2750573000 * q^61 - 2190062816 * q^67 + 10099298944 * q^73 + 795481360 * q^79 + 8212243320 * q^85 - 62190452224 * q^91 - 632084096 * q^97

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