LMFDB - Embedded newform 108.7.g.a.89.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,7,Mod(17,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("108.17");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	108.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:	$24.8458410309$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 59 x^{10} + 602 x^{9} + 26655 x^{8} + 692184 x^{7} - 4209870 x^{6} + \cdots + 166668145981081 $ x^12 - 2x^11 + 59x^10 + 602x^9 + 26655x^8 + 692184x^7 - 4209870x^6 - 34154736x^5 + 2261179815x^4 - 21421205158x^3 + 1095551670899x^2 - 17316244703642*x + 166668145981081
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{24} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.3
Root			$-16.7265 - 5.11172i$ of defining polynomial
Character	$\chi$	$=$	108.89
Dual form			108.7.g.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-51.3356 + 29.6386i) q^{5} +(76.8738 - 133.149i) q^{7} +O(q^{10})$	$q+(-51.3356 + 29.6386i) q^{5} +(76.8738 - 133.149i) q^{7} +(587.230 + 339.038i) q^{11} +(-826.070 - 1430.80i) q^{13} +6420.23i q^{17} +2857.79 q^{19} +(-6075.95 + 3507.95i) q^{23} +(-6055.60 + 10488.6i) q^{25} +(-8027.87 - 4634.89i) q^{29} +(26119.0 + 45239.4i) q^{31} +9113.74i q^{35} +58462.5 q^{37} +(-102770. + 59334.4i) q^{41} +(-44827.4 + 77643.4i) q^{43} +(58769.9 + 33930.8i) q^{47} +(47005.3 + 81415.6i) q^{49} +221631. i q^{53} -40194.5 q^{55} +(-145784. + 84168.7i) q^{59} +(106190. - 183926. i) q^{61} +(84813.7 + 48967.2i) q^{65} +(54371.1 + 94173.5i) q^{67} -408102. i q^{71} +39555.6 q^{73} +(90285.3 - 52126.2i) q^{77} +(-209166. + 362286. i) q^{79} +(22035.7 + 12722.3i) q^{83} +(-190287. - 329586. i) q^{85} -1.26291e6i q^{89} -254013. q^{91} +(-146706. + 84700.9i) q^{95} +(435032. - 753498. i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 216 q^{5} - 120 q^{7}+O(q^{10}) $ 12 * q + 216 * q^5 - 120 * q^7	$ 12 q + 216 q^{5} - 120 q^{7} + 2214 q^{11} - 840 q^{13} - 12900 q^{19} + 8208 q^{23} + 24078 q^{25} + 29268 q^{29} + 3120 q^{31} + 12768 q^{37} + 16578 q^{41} + 71430 q^{43} + 329508 q^{47} - 238914 q^{49} + 5400 q^{55} - 428058 q^{59} - 93576 q^{61} + 1426464 q^{65} + 104334 q^{67} + 221820 q^{73} - 3461184 q^{77} + 123468 q^{79} + 2901420 q^{83} + 377568 q^{85} + 91488 q^{91} - 7249716 q^{95} - 1033482 q^{97}+O(q^{100}) $ 12 * q + 216 * q^5 - 120 * q^7 + 2214 * q^11 - 840 * q^13 - 12900 * q^19 + 8208 * q^23 + 24078 * q^25 + 29268 * q^29 + 3120 * q^31 + 12768 * q^37 + 16578 * q^41 + 71430 * q^43 + 329508 * q^47 - 238914 * q^49 + 5400 * q^55 - 428058 * q^59 - 93576 * q^61 + 1426464 * q^65 + 104334 * q^67 + 221820 * q^73 - 3461184 * q^77 + 123468 * q^79 + 2901420 * q^83 + 377568 * q^85 + 91488 * q^91 - 7249716 * q^95 - 1033482 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−51.3356	+	29.6386i	−0.410685	+	0.237109i	−0.691084	−	0.722774i	$-0.742867\pi$
$5$	−51.3356	+	29.6386i	−0.410685	+	0.237109i	0.280399	+	0.959884i	$0.409533\pi$
$6$		0			0
$7$	76.8738	−	133.149i	0.224122	−	0.388190i	−0.731934	−	0.681376i	$-0.761382\pi$
$7$	76.8738	−	133.149i	0.224122	−	0.388190i	0.956056	+	0.293185i	$0.0947153\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	587.230	+	339.038i	0.441195	+	0.254724i	0.704104	−	0.710097i	$-0.251349\pi$
$11$	587.230	+	339.038i	0.441195	+	0.254724i	−0.262909	+	0.964821i	$0.584682\pi$
$12$		0			0
$13$	−826.070	−	1430.80i	−0.375999	−	0.651250i	0.614477	−	0.788935i	$-0.289367\pi$
$13$	−826.070	−	1430.80i	−0.375999	−	0.651250i	−0.990476	+	0.137685i	$0.956034\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			6420.23i			1.30678i	0.757020	+	0.653392i	$0.226655\pi$
$17$			6420.23i			1.30678i	−0.757020	+	0.653392i	$0.773345\pi$
$18$		0			0
$19$	2857.79			0.416648			0.208324	−	0.978060i	$-0.433199\pi$
$19$	2857.79			0.416648			0.208324	+	0.978060i	$0.433199\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6075.95	+	3507.95i	−0.499379	+	0.288317i	−0.728457	−	0.685091i	$-0.759762\pi$
$23$	−6075.95	+	3507.95i	−0.499379	+	0.288317i	0.229078	+	0.973408i	$0.426429\pi$
$24$		0			0
$25$	−6055.60	+	10488.6i	−0.387559	+	0.671271i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−8027.87	−	4634.89i	−0.329160	−	0.190040i	0.326308	−	0.945263i	$-0.394195\pi$
$29$	−8027.87	−	4634.89i	−0.329160	−	0.190040i	−0.655468	+	0.755223i	$0.727529\pi$
$30$		0			0
$31$	26119.0	+	45239.4i	0.876740	+	1.51856i	0.854897	+	0.518797i	$0.173620\pi$
$31$	26119.0	+	45239.4i	0.876740	+	1.51856i	0.0218431	+	0.999761i	$0.493047\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			9113.74i			0.212565i
$36$		0			0
$37$	58462.5			1.15418			0.577088	−	0.816682i	$-0.304189\pi$
$37$	58462.5			1.15418			0.577088	+	0.816682i	$0.304189\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−102770.	+	59334.4i	−1.49113	+	0.860904i	−0.999948	−	0.0101531i	$-0.996768\pi$
$41$	−102770.	+	59334.4i	−1.49113	+	0.860904i	−0.491181	+	0.871057i	$0.663435\pi$
$42$		0			0
$43$	−44827.4	+	77643.4i	−0.563817	+	0.976560i	0.433341	+	0.901230i	$0.357334\pi$
$43$	−44827.4	+	77643.4i	−0.563817	+	0.976560i	−0.997159	+	0.0753303i	$0.975999\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	58769.9	+	33930.8i	0.566058	+	0.326814i	0.755573	−	0.655064i	$-0.227358\pi$
$47$	58769.9	+	33930.8i	0.566058	+	0.326814i	−0.189515	+	0.981878i	$0.560692\pi$
$48$		0			0
$49$	47005.3	+	81415.6i	0.399539	+	0.692021i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			221631.i			1.48869i	0.667797	+	0.744343i	$0.267237\pi$
$53$			221631.i			1.48869i	−0.667797	+	0.744343i	$0.732763\pi$
$54$		0			0
$55$	−40194.5			−0.241590
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−145784.	+	84168.7i	−0.709831	+	0.409821i	−0.810999	−	0.585048i	$-0.801076\pi$
$59$	−145784.	+	84168.7i	−0.709831	+	0.409821i	0.101167	+	0.994869i	$0.467742\pi$
$60$		0			0
$61$	106190.	−	183926.i	0.467836	−	0.810316i	−0.531488	−	0.847066i	$-0.678367\pi$
$61$	106190.	−	183926.i	0.467836	−	0.810316i	0.999324	+	0.0367498i	$0.0117005\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	84813.7	+	48967.2i	0.308834	+	0.178306i
$66$		0			0
$67$	54371.1	+	94173.5i	0.180777	+	0.313115i	0.942145	−	0.335204i	$-0.108805\pi$
$67$	54371.1	+	94173.5i	0.180777	+	0.313115i	−0.761368	+	0.648320i	$0.775472\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	408102.i		−	1.14023i	−0.821564	−	0.570117i	$-0.806898\pi$
$71$		−	408102.i		−	1.14023i	0.821564	−	0.570117i	$-0.193102\pi$
$72$		0			0
$73$	39555.6			0.101681			0.0508404	−	0.998707i	$-0.483810\pi$
$73$	39555.6			0.101681			0.0508404	+	0.998707i	$0.483810\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	90285.3	−	52126.2i	0.197763	−	0.114178i
$78$		0			0
$79$	−209166.	+	362286.i	−0.424238	+	0.734803i	−0.996349	−	0.0853740i	$-0.972791\pi$
$79$	−209166.	+	362286.i	−0.424238	+	0.734803i	0.572111	+	0.820177i	$0.306125\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	22035.7	+	12722.3i	0.0385383	+	0.0222501i	0.519145	−	0.854686i	$-0.326250\pi$
$83$	22035.7	+	12722.3i	0.0385383	+	0.0222501i	−0.480607	+	0.876936i	$0.659584\pi$
$84$		0			0
$85$	−190287.	−	329586.i	−0.309850	−	0.536677i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	1.26291e6i		−	1.79145i	−0.444611	−	0.895724i	$-0.646658\pi$
$89$		−	1.26291e6i		−	1.79145i	0.444611	−	0.895724i	$-0.353342\pi$
$90$		0			0
$91$	−254013.			−0.337079
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−146706.	+	84700.9i	−0.171111	+	0.0987910i
$96$		0			0
$97$	435032.	−	753498.i	0.476658	−	0.825595i	−0.522985	−	0.852342i	$-0.675182\pi$
$97$	435032.	−	753498.i	0.476658	−	0.825595i	0.999642	+	0.0267470i	$0.00851484\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.23317e6	+	711969.i	1.19690	+	0.691030i	0.959863	−	0.280471i	$-0.0904905\pi$
$101$	1.23317e6	+	711969.i	1.19690	+	0.691030i	0.237037	+	0.971501i	$0.423824\pi$
$102$		0			0
$103$	−812565.	−	1.40740e6i	−0.743612	−	1.28797i	−0.950840	−	0.309681i	$-0.899778\pi$
$103$	−812565.	−	1.40740e6i	−0.743612	−	1.28797i	0.207228	−	0.978293i	$-0.433556\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1.10780e6i		−	0.904292i	−0.891944	−	0.452146i	$-0.850659\pi$
$107$		−	1.10780e6i		−	0.904292i	0.891944	−	0.452146i	$-0.149341\pi$
$108$		0			0
$109$	−513511.			−0.396525			−0.198262	−	0.980149i	$-0.563530\pi$
$109$	−513511.			−0.396525			−0.198262	+	0.980149i	$0.563530\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	424592.	−	245138.i	0.294264	−	0.169893i	−0.345599	−	0.938382i	$-0.612324\pi$
$113$	424592.	−	245138.i	0.294264	−	0.169893i	0.639863	+	0.768489i	$0.278991\pi$
$114$		0			0
$115$	207942.	−	360166.i	0.136725	−	0.236815i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	854849.	+	493547.i	0.507281	+	0.292879i
$120$		0			0
$121$	−655887.	−	1.13603e6i	−0.370231	−	0.641260i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	1.64413e6i		−	0.841793i
$126$		0			0
$127$	−114175.			−0.0557389			−0.0278694	−	0.999612i	$-0.508872\pi$
$127$	−114175.			−0.0557389			−0.0278694	+	0.999612i	$0.508872\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.84454e6	+	2.21965e6i	−1.71014	+	0.987348i	−0.775782	+	0.631001i	$0.782645\pi$
$131$	−3.84454e6	+	2.21965e6i	−1.71014	+	0.987348i	−0.934354	+	0.356347i	$0.884022\pi$
$132$		0			0
$133$	219689.	−	380512.i	0.0933799	−	0.161739i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.46358e6	+	1.42235e6i	0.958085	+	0.553151i	0.895583	−	0.444894i	$-0.146759\pi$
$137$	2.46358e6	+	1.42235e6i	0.958085	+	0.553151i	0.0625020	+	0.998045i	$0.480092\pi$
$138$		0			0
$139$	2.02940e6	+	3.51502e6i	0.755654	+	1.30883i	0.945049	+	0.326929i	$0.106014\pi$
$139$	2.02940e6	+	3.51502e6i	0.755654	+	1.30883i	−0.189395	+	0.981901i	$0.560653\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	1.12028e6i		−	0.383104i
$144$		0			0
$145$	549488.			0.180241
$146$		0			0
$147$		0			0
$148$		0			0
$149$	506083.	−	292187.i	0.152990	−	0.0883289i	−0.421551	−	0.906805i	$-0.638514\pi$
$149$	506083.	−	292187.i	0.152990	−	0.0883289i	0.574541	+	0.818476i	$0.305181\pi$
$150$		0			0
$151$	−2.13100e6	+	3.69100e6i	−0.618946	+	1.07205i	0.370733	+	0.928740i	$0.379107\pi$
$151$	−2.13100e6	+	3.69100e6i	−0.618946	+	1.07205i	−0.989678	+	0.143306i	$0.954227\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−2.68167e6	−	1.54826e6i	−0.720128	−	0.415766i
$156$		0			0
$157$	2.14089e6	+	3.70813e6i	0.553217	+	0.958201i	0.998040	+	0.0625818i	$0.0199334\pi$
$157$	2.14089e6	+	3.70813e6i	0.553217	+	0.958201i	−0.444822	+	0.895619i	$0.646733\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			1.07868e6i			0.258472i
$162$		0			0
$163$	1.85229e6			0.427707			0.213853	−	0.976866i	$-0.431399\pi$
$163$	1.85229e6			0.427707			0.213853	+	0.976866i	$0.431399\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.77994e6	+	4.49175e6i	−1.67042	+	0.964420i	−0.703023	+	0.711167i	$0.748167\pi$
$167$	−7.77994e6	+	4.49175e6i	−1.67042	+	0.964420i	−0.967400	+	0.253253i	$0.918500\pi$
$168$		0			0
$169$	1.04862e6	−	1.81626e6i	0.217249	−	0.376287i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.75707e6	+	2.74649e6i	0.918757	+	0.530445i	0.883238	−	0.468924i	$-0.155358\pi$
$173$	4.75707e6	+	2.74649e6i	0.918757	+	0.530445i	0.0355189	+	0.999369i	$0.488692\pi$
$174$		0			0
$175$	931034.	+	1.61260e6i	0.173721	+	0.300893i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			2.48807e6i			0.433814i	0.976192	+	0.216907i	$0.0695969\pi$
$179$			2.48807e6i			0.433814i	−0.976192	+	0.216907i	$0.930403\pi$
$180$		0			0
$181$	5.06731e6			0.854558			0.427279	−	0.904120i	$-0.359472\pi$
$181$	5.06731e6			0.854558			0.427279	+	0.904120i	$0.359472\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−3.00121e6	+	1.73275e6i	−0.474003	+	0.273666i
$186$		0			0
$187$	−2.17670e6	+	3.77015e6i	−0.332869	+	0.576546i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.69888e6	+	2.71290e6i	0.674364	+	0.389344i	0.797728	−	0.603017i	$-0.206035\pi$
$191$	4.69888e6	+	2.71290e6i	0.674364	+	0.389344i	−0.123364	+	0.992361i	$0.539368\pi$
$192$		0			0
$193$	−2.81775e6	−	4.88049e6i	−0.391950	−	0.678877i	0.600757	−	0.799432i	$-0.294866\pi$
$193$	−2.81775e6	−	4.88049e6i	−0.391950	−	0.678877i	−0.992707	+	0.120555i	$0.961533\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			1.52261e6i			0.199154i	0.995030	+	0.0995771i	$0.0317490\pi$
$197$			1.52261e6i			0.199154i	−0.995030	+	0.0995771i	$0.968251\pi$
$198$		0			0
$199$	−9.65115e6			−1.22467			−0.612336	−	0.790597i	$-0.709770\pi$
$199$	−9.65115e6			−1.22467			−0.612336	+	0.790597i	$0.709770\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.23427e6	+	712604.i	−0.147544	+	0.0851844i
$204$		0			0
$205$	3.51718e6	−	6.09194e6i	0.408257	−	0.707121i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.67818e6	+	968897.i	0.183823	+	0.106130i
$210$		0			0
$211$	1.73941e6	+	3.01275e6i	0.185163	+	0.320712i	0.943631	−	0.330998i	$-0.107385\pi$
$211$	1.73941e6	+	3.01275e6i	0.185163	+	0.320712i	−0.758468	+	0.651710i	$0.774052\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	5.31450e6i		−	0.534745i
$216$		0			0
$217$	8.03146e6			0.785987
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.18603e6	−	5.30356e6i	0.851042	−	0.491350i
$222$		0			0
$223$	−4.00207e6	+	6.93179e6i	−0.360886	+	0.625073i	−0.988107	−	0.153769i	$-0.950859\pi$
$223$	−4.00207e6	+	6.93179e6i	−0.360886	+	0.625073i	0.627221	+	0.778841i	$0.284192\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.70106e7	−	9.82108e6i	−1.45426	−	0.839618i	−0.455542	−	0.890214i	$-0.650555\pi$
$227$	−1.70106e7	−	9.82108e6i	−1.45426	−	0.839618i	−0.998719	+	0.0505959i	$0.983888\pi$
$228$		0			0
$229$	−5.27389e6	−	9.13465e6i	−0.439162	−	0.760651i	0.558463	−	0.829529i	$-0.311391\pi$
$229$	−5.27389e6	−	9.13465e6i	−0.439162	−	0.760651i	−0.997625	+	0.0688783i	$0.978058\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	5.28004e6i		−	0.417416i	−0.977978	−	0.208708i	$-0.933074\pi$
$233$		−	5.28004e6i		−	0.417416i	0.977978	−	0.208708i	$-0.0669259\pi$
$234$		0			0
$235$	−4.02265e6			−0.309962
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.74830e7	−	1.00938e7i	1.28063	−	0.739371i	0.303665	−	0.952779i	$-0.401790\pi$
$239$	1.74830e7	−	1.00938e7i	1.28063	−	0.739371i	0.976963	+	0.213407i	$0.0684562\pi$
$240$		0			0
$241$	3.20399e6	−	5.54946e6i	0.228897	−	0.396461i	−0.728585	−	0.684956i	$-0.759822\pi$
$241$	3.20399e6	−	5.54946e6i	0.228897	−	0.396461i	0.957481	+	0.288495i	$0.0931549\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.82610e6	−	2.78635e6i	−0.328169	−	0.189469i
$246$		0			0
$247$	−2.36073e6	−	4.08891e6i	−0.156659	−	0.271342i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	1.55033e7i		−	0.980400i	−0.871610	−	0.490200i	$-0.836924\pi$
$251$		−	1.55033e7i		−	0.980400i	0.871610	−	0.490200i	$-0.163076\pi$
$252$		0			0
$253$	−4.75731e6			−0.293765
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.88422e7	−	1.08786e7i	1.11002	−	0.640873i	0.171189	−	0.985238i	$-0.445239\pi$
$257$	1.88422e7	−	1.08786e7i	1.11002	−	0.640873i	0.938836	+	0.344365i	$0.111906\pi$
$258$		0			0
$259$	4.49423e6	−	7.78424e6i	0.258676	−	0.448040i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	6.28543e6	+	3.62890e6i	0.345516	+	0.199484i	0.662708	−	0.748878i	$-0.269407\pi$
$263$	6.28543e6	+	3.62890e6i	0.345516	+	0.199484i	−0.317193	+	0.948361i	$0.602740\pi$
$264$		0			0
$265$	−6.56885e6	−	1.13776e7i	−0.352981	−	0.611381i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			2.87490e7i			1.47695i	0.674280	+	0.738476i	$0.264454\pi$
$269$			2.87490e7i			1.47695i	−0.674280	+	0.738476i	$0.735546\pi$
$270$		0			0
$271$	−1.61888e7			−0.813405			−0.406703	−	0.913561i	$-0.633321\pi$
$271$	−1.61888e7			−0.813405			−0.406703	+	0.913561i	$0.633321\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−7.11207e6	+	4.10615e6i	−0.341978	+	0.197441i
$276$		0			0
$277$	7.67531e6	−	1.32940e7i	0.361124	−	0.625485i	−0.627022	−	0.779002i	$-0.715726\pi$
$277$	7.67531e6	−	1.32940e7i	0.361124	−	0.625485i	0.988146	+	0.153516i	$0.0490597\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−1.63531e7	−	9.44146e6i	−0.737023	−	0.425520i	0.0839630	−	0.996469i	$-0.473242\pi$
$281$	−1.63531e7	−	9.44146e6i	−0.737023	−	0.425520i	−0.820986	+	0.570948i	$0.806576\pi$
$282$		0			0
$283$	−105962.	−	183532.i	−0.00467511	−	0.00809752i	0.863678	−	0.504043i	$-0.168155\pi$
$283$	−105962.	−	183532.i	−0.00467511	−	0.00809752i	−0.868353	+	0.495946i	$0.834821\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			1.82450e7i			0.771790i
$288$		0			0
$289$	−1.70818e7			−0.707683
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.29442e7	−	7.47332e6i	0.514602	−	0.297106i	−0.220121	−	0.975473i	$-0.570645\pi$
$293$	1.29442e7	−	7.47332e6i	0.514602	−	0.297106i	0.734723	+	0.678367i	$0.237312\pi$
$294$		0			0
$295$	4.98929e6	−	8.64171e6i	0.194345	−	0.336615i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.00383e7	+	5.79562e6i	0.375532	+	0.216814i
$300$		0			0
$301$	6.89211e6	+	1.19375e7i	0.252728	+	0.437737i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			1.25893e7i			0.443713i
$306$		0			0
$307$	4.02227e7			1.39013			0.695066	−	0.718946i	$-0.255375\pi$
$307$	4.02227e7			1.39013			0.695066	+	0.718946i	$0.255375\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−481733.	+	278128.i	−0.0160149	+	0.00924622i	−0.507986	−	0.861365i	$-0.669610\pi$
$311$	−481733.	+	278128.i	−0.0160149	+	0.00924622i	0.491971	+	0.870611i	$0.336277\pi$
$312$		0			0
$313$	−2.50885e7	+	4.34546e7i	−0.818166	+	1.41711i	0.0888653	+	0.996044i	$0.471676\pi$
$313$	−2.50885e7	+	4.34546e7i	−0.818166	+	1.41711i	−0.907032	+	0.421062i	$0.861657\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.04985e7	−	2.33818e7i	−1.27134	−	0.734008i	−0.296100	−	0.955157i	$-0.595686\pi$
$317$	−4.04985e7	−	2.33818e7i	−1.27134	−	0.734008i	−0.975240	+	0.221149i	$0.929019\pi$
$318$		0			0
$319$	−3.14281e6	−	5.44350e6i	−0.0968157	−	0.167690i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.83476e7i			0.544469i
$324$		0			0
$325$	2.00094e7			0.582887
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.03572e6	−	5.21678e6i	0.253732	−	0.146492i
$330$		0			0
$331$	−1.72379e6	+	2.98570e6i	−0.0475337	+	0.0823307i	−0.888813	−	0.458269i	$-0.848469\pi$
$331$	−1.72379e6	+	2.98570e6i	−0.0475337	+	0.0823307i	0.841280	+	0.540600i	$0.181803\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.58235e6	−	3.22297e6i	−0.148485	−	0.0857279i
$336$		0			0
$337$	3.53568e7	+	6.12397e7i	0.923810	+	1.60009i	0.793463	+	0.608618i	$0.208276\pi$
$337$	3.53568e7	+	6.12397e7i	0.923810	+	1.60009i	0.130347	+	0.991468i	$0.458391\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			3.54213e7i			0.893307i
$342$		0			0
$343$	3.25422e7			0.806425
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.19802e7	+	1.84638e7i	−0.765408	+	0.441908i	−0.831234	−	0.555923i	$-0.812365\pi$
$347$	−3.19802e7	+	1.84638e7i	−0.765408	+	0.441908i	0.0658262	+	0.997831i	$0.479032\pi$
$348$		0			0
$349$	−2.02452e7	+	3.50657e7i	−0.476261	+	0.824909i	−0.999630	−	0.0271976i	$-0.991342\pi$
$349$	−2.02452e7	+	3.50657e7i	−0.476261	+	0.824909i	0.523369	+	0.852106i	$0.324675\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.74286e7	−	2.16094e7i	−0.850901	−	0.491268i	0.0100535	−	0.999949i	$-0.496800\pi$
$353$	−3.74286e7	−	2.16094e7i	−0.850901	−	0.491268i	−0.860955	+	0.508681i	$0.830133\pi$
$354$		0			0
$355$	1.20956e7	+	2.09502e7i	0.270360	+	0.468277i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			3.23781e7i			0.699791i	0.936789	+	0.349896i	$0.113783\pi$
$359$			3.23781e7i			0.699791i	−0.936789	+	0.349896i	$0.886217\pi$
$360$		0			0
$361$	−3.88789e7			−0.826405
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.03061e6	+	1.17237e6i	−0.0417588	+	0.0241095i
$366$		0			0
$367$	9.80140e6	−	1.69765e7i	0.198285	−	0.343440i	−0.749687	−	0.661792i	$-0.769796\pi$
$367$	9.80140e6	−	1.69765e7i	0.198285	−	0.343440i	0.947972	+	0.318352i	$0.103130\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.95100e7	+	1.70376e7i	0.577894	+	0.333647i
$372$		0			0
$373$	−905558.	−	1.56847e6i	−0.0174498	−	0.0302239i	0.857169	−	0.515036i	$-0.172221\pi$
$373$	−905558.	−	1.56847e6i	−0.0174498	−	0.0302239i	−0.874618	+	0.484812i	$0.838888\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			1.53150e7i			0.285820i
$378$		0			0
$379$	−1.03932e7			−0.190912			−0.0954559	−	0.995434i	$-0.530431\pi$
$379$	−1.03932e7			−0.190912			−0.0954559	+	0.995434i	$0.530431\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.77788e7	−	1.02646e7i	0.316450	−	0.182703i	−0.333359	−	0.942800i	$-0.608182\pi$
$383$	1.77788e7	−	1.02646e7i	0.316450	−	0.182703i	0.649809	+	0.760097i	$0.274849\pi$
$384$		0			0
$385$	−3.08990e6	+	5.35187e6i	−0.0541455	+	0.0937828i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.02842e7	+	1.17111e7i	0.344595	+	0.198952i	0.662302	−	0.749237i	$-0.269579\pi$
$389$	2.02842e7	+	1.17111e7i	0.344595	+	0.198952i	−0.317707	+	0.948189i	$0.602913\pi$
$390$		0			0
$391$	−2.25218e7	−	3.90090e7i	−0.376768	−	0.652581i
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	2.47976e7i		−	0.402363i
$396$		0			0
$397$	2.83340e7			0.452831			0.226415	−	0.974031i	$-0.427299\pi$
$397$	2.83340e7			0.452831			0.226415	+	0.974031i	$0.427299\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.35430e7	+	1.35925e7i	−0.365113	+	0.210798i	−0.671322	−	0.741166i	$-0.734273\pi$
$401$	−2.35430e7	+	1.35925e7i	−0.365113	+	0.210798i	0.306208	+	0.951965i	$0.400940\pi$
$402$		0			0
$403$	4.31522e7	−	7.47418e7i	0.659307	−	1.14195i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.43309e7	+	1.98210e7i	0.509216	+	0.293996i
$408$		0			0
$409$	−3.49859e7	−	6.05973e7i	−0.511355	−	0.885693i	−0.999913	−	0.0131620i	$-0.995810\pi$
$409$	−3.49859e7	−	6.05973e7i	−0.511355	−	0.885693i	0.488558	−	0.872531i	$-0.337523\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			2.58815e7i			0.367400i
$414$		0			0
$415$	−1.50829e6			−0.0211028
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.73935e7	−	3.31362e7i	0.780227	−	0.450464i	−0.0562839	−	0.998415i	$-0.517925\pi$
$419$	5.73935e7	−	3.31362e7i	0.780227	−	0.450464i	0.836511	+	0.547951i	$0.184592\pi$
$420$		0			0
$421$	1.27092e6	−	2.20129e6i	0.0170322	−	0.0295006i	−0.857384	−	0.514678i	$-0.827912\pi$
$421$	1.27092e6	−	2.20129e6i	0.0170322	−	0.0295006i	0.874416	+	0.485177i	$0.161245\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.73393e7	−	3.88783e7i	−0.877206	−	0.506455i
$426$		0			0
$427$	−1.63264e7	−	2.82782e7i	−0.209705	−	0.363219i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	1.56169e8i		−	1.95057i	−0.220946	−	0.975286i	$-0.570914\pi$
$431$		−	1.56169e8i		−	1.95057i	0.220946	−	0.975286i	$-0.429086\pi$
$432$		0			0
$433$	−8.12049e7			−1.00027			−0.500136	−	0.865947i	$-0.666717\pi$
$433$	−8.12049e7			−1.00027			−0.500136	+	0.865947i	$0.666717\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.73638e7	+	1.00250e7i	−0.208065	+	0.120127i
$438$		0			0
$439$	−1.01429e7	+	1.75680e7i	−0.119886	+	0.207649i	−0.919722	−	0.392569i	$-0.871586\pi$
$439$	−1.01429e7	+	1.75680e7i	−0.119886	+	0.207649i	0.799836	+	0.600218i	$0.204920\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.20858e8	+	6.97776e7i	1.39016	+	0.802611i	0.993333	−	0.115281i	$-0.0367769\pi$
$443$	1.20858e8	+	6.97776e7i	1.39016	+	0.802611i	0.396830	+	0.917892i	$0.370110\pi$
$444$		0			0
$445$	3.74311e7	+	6.48325e7i	0.424769	+	0.735721i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	1.19418e8i		−	1.31926i	−0.751588	−	0.659632i	$-0.770712\pi$
$449$		−	1.19418e8i		−	1.31926i	0.751588	−	0.659632i	$-0.229288\pi$
$450$		0			0
$451$	−8.04663e7			−0.877172
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.30399e7	−	7.52859e6i	0.138433	−	0.0799244i
$456$		0			0
$457$	1.62162e7	−	2.80872e7i	0.169902	−	0.294279i	−0.768483	−	0.639870i	$-0.778988\pi$
$457$	1.62162e7	−	2.80872e7i	0.169902	−	0.294279i	0.938385	+	0.345591i	$0.112321\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.14592e7	−	1.81630e7i	−0.321104	−	0.185389i	0.330781	−	0.943708i	$-0.392688\pi$
$461$	−3.14592e7	−	1.81630e7i	−0.321104	−	0.185389i	−0.651884	+	0.758318i	$0.726021\pi$
$462$		0			0
$463$	−2.22272e7	−	3.84986e7i	−0.223945	−	0.387884i	0.732057	−	0.681243i	$-0.238560\pi$
$463$	−2.22272e7	−	3.84986e7i	−0.223945	−	0.387884i	−0.956002	+	0.293359i	$0.905227\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	1.52522e8i		−	1.49755i	−0.662822	−	0.748777i	$-0.730641\pi$
$467$		−	1.52522e8i		−	1.49755i	0.662822	−	0.748777i	$-0.269359\pi$
$468$		0			0
$469$	1.67189e7			0.162065
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.26480e7	+	3.03964e7i	−0.497507	+	0.287236i
$474$		0			0
$475$	−1.73056e7	+	2.99742e7i	−0.161475	+	0.279684i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	9.57151e7	+	5.52612e7i	0.870912	+	0.502821i	0.867651	−	0.497174i	$-0.165629\pi$
$479$	9.57151e7	+	5.52612e7i	0.870912	+	0.502821i	0.00326048	+	0.999995i	$0.498962\pi$
$480$		0			0
$481$	−4.82941e7	−	8.36478e7i	−0.433969	−	0.751656i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			5.15751e7i			0.452079i
$486$		0			0
$487$	1.83933e8			1.59247			0.796237	−	0.604985i	$-0.206821\pi$
$487$	1.83933e8			1.59247			0.796237	+	0.604985i	$0.206821\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.92505e6	+	3.99818e6i	−0.0585031	+	0.0337768i	−0.528966	−	0.848643i	$-0.677420\pi$
$491$	−6.92505e6	+	3.99818e6i	−0.0585031	+	0.0337768i	0.470463	+	0.882420i	$0.344087\pi$
$492$		0			0
$493$	2.97571e7	−	5.15408e7i	0.248342	−	0.430140i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.43385e7	−	3.13724e7i	−0.442628	−	0.255551i
$498$		0			0
$499$	−2.06168e7	−	3.57094e7i	−0.165928	−	0.287396i	0.771056	−	0.636767i	$-0.219729\pi$
$499$	−2.06168e7	−	3.57094e7i	−0.165928	−	0.287396i	−0.936984	+	0.349371i	$0.886395\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	4.69138e7i		−	0.368635i	−0.982867	−	0.184317i	$-0.940993\pi$
$503$		−	4.69138e7i		−	0.368635i	0.982867	−	0.184317i	$-0.0590075\pi$
$504$		0			0
$505$	−8.44072e7			−0.655398
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.78164e7	−	2.76068e7i	0.362596	−	0.209345i	−0.307623	−	0.951508i	$-0.599534\pi$
$509$	4.78164e7	−	2.76068e7i	0.362596	−	0.209345i	0.670219	+	0.742163i	$0.266200\pi$
$510$		0			0
$511$	3.04079e6	−	5.26680e6i	0.0227889	−	0.0394715i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.34271e7	+	4.81666e7i	0.610781	+	0.352634i
$516$		0			0
$517$	2.30076e7	+	3.98504e7i	0.166495	+	0.288377i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			5.59371e7i			0.395537i	0.980249	+	0.197768i	$0.0633694\pi$
$521$			5.59371e7i			0.395537i	−0.980249	+	0.197768i	$0.936631\pi$
$522$		0			0
$523$	−1.43384e8			−1.00230			−0.501149	−	0.865361i	$-0.667089\pi$
$523$	−1.43384e8			−1.00230			−0.501149	+	0.865361i	$0.667089\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.90447e8	+	1.67690e8i	−1.98443	+	1.14571i
$528$		0			0
$529$	−4.94065e7	+	8.55746e7i	−0.333747	+	0.578067i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.69791e8	+	9.80287e7i	1.12133	+	0.647398i
$534$		0			0
$535$	3.28336e7	+	5.68694e7i	0.214416	+	0.371379i
$536$		0			0
$537$		0			0
$538$		0			0
$539$			6.37463e7i			0.407088i
$540$		0			0
$541$	1.75550e8			1.10868			0.554342	−	0.832289i	$-0.312970\pi$
$541$	1.75550e8			1.10868			0.554342	+	0.832289i	$0.312970\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.63614e7	−	1.52198e7i	0.162847	−	0.0940197i
$546$		0			0
$547$	3.37262e6	−	5.84155e6i	0.0206066	−	0.0356916i	−0.855538	−	0.517740i	$-0.826774\pi$
$547$	3.37262e6	−	5.84155e6i	0.0206066	−	0.0356916i	0.876145	+	0.482048i	$0.160107\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.29419e7	−	1.32455e7i	−0.137144	−	0.0791799i
$552$		0			0
$553$	3.21588e7	+	5.57007e7i	0.190162	+	0.329371i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			2.14625e8i			1.24198i	0.783819	+	0.620990i	$0.213269\pi$
$557$			2.14625e8i			1.24198i	−0.783819	+	0.620990i	$0.786731\pi$
$558$		0			0
$559$	1.48122e8			0.847979
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.19704e8	+	1.26846e8i	−1.23115	+	0.710807i	−0.967270	−	0.253748i	$-0.918337\pi$
$563$	−2.19704e8	+	1.26846e8i	−1.23115	+	0.710807i	−0.263883	+	0.964555i	$0.585003\pi$
$564$		0			0
$565$	−1.45311e7	+	2.51687e7i	−0.0805664	+	0.139545i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.51808e7	−	5.49527e7i	−0.516669	−	0.298299i	0.218901	−	0.975747i	$-0.429753\pi$
$569$	−9.51808e7	−	5.49527e7i	−0.516669	−	0.298299i	−0.735571	+	0.677448i	$0.763086\pi$
$570$		0			0
$571$	6.39080e7	+	1.10692e8i	0.343279	+	0.594576i	0.985040	−	0.172329i	$-0.0551291\pi$
$571$	6.39080e7	+	1.10692e8i	0.343279	+	0.594576i	−0.641761	+	0.766905i	$0.721796\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	8.49710e7i		−	0.446958i
$576$		0			0
$577$	−5.97876e7			−0.311232			−0.155616	−	0.987818i	$-0.549736\pi$
$577$	−5.97876e7			−0.311232			−0.155616	+	0.987818i	$0.549736\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.38793e6	−	1.95602e6i	0.0172745	−	0.00997346i
$582$		0			0
$583$	−7.51413e7	+	1.30149e8i	−0.379204	+	0.656801i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.16069e8	+	6.70127e7i	0.573857	+	0.331316i	0.758688	−	0.651454i	$-0.225841\pi$
$587$	1.16069e8	+	6.70127e7i	0.573857	+	0.331316i	−0.184831	+	0.982770i	$0.559174\pi$
$588$		0			0
$589$	7.46425e7	+	1.29285e8i	0.365292	+	0.632704i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	2.75560e8i		−	1.32146i	−0.750626	−	0.660728i	$-0.770248\pi$
$593$		−	2.75560e8i		−	1.32146i	0.750626	−	0.660728i	$-0.229752\pi$
$594$		0			0
$595$	−5.85123e7			−0.277777
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.55365e8	+	1.47435e8i	−1.18817	+	0.685993i	−0.957891	−	0.287131i	$-0.907299\pi$
$599$	−2.55365e8	+	1.47435e8i	−1.18817	+	0.685993i	−0.230283	+	0.973124i	$0.573965\pi$
$600$		0			0
$601$	−6.77957e7	+	1.17426e8i	−0.312305	+	0.540928i	−0.978861	−	0.204527i	$-0.934434\pi$
$601$	−6.77957e7	+	1.17426e8i	−0.312305	+	0.540928i	0.666556	+	0.745455i	$0.267768\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.73408e7	+	3.88792e7i	0.304097	+	0.175570i
$606$		0			0
$607$	1.69952e8	+	2.94366e8i	0.759908	+	1.31620i	0.942897	+	0.333084i	$0.108089\pi$
$607$	1.69952e8	+	2.94366e8i	0.759908	+	1.31620i	−0.182989	+	0.983115i	$0.558577\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	1.12117e8i		−	0.491527i
$612$		0			0
$613$	3.34467e8			1.45202			0.726008	−	0.687686i	$-0.241373\pi$
$613$	3.34467e8			1.45202			0.726008	+	0.687686i	$0.241373\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	2.98933e8	−	1.72589e8i	1.27268	−	0.734780i	0.297186	−	0.954820i	$-0.403952\pi$
$617$	2.98933e8	−	1.72589e8i	1.27268	−	0.734780i	0.975491	+	0.220039i	$0.0706186\pi$
$618$		0			0
$619$	5.73101e7	−	9.92640e7i	0.241635	−	0.418523i	−0.719545	−	0.694445i	$-0.755650\pi$
$619$	5.73101e7	−	9.92640e7i	0.241635	−	0.418523i	0.961180	+	0.275922i	$0.0889831\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.68156e8	−	9.70851e7i	−0.695423	−	0.401503i
$624$		0			0
$625$	−4.58891e7	−	7.94822e7i	−0.187962	−	0.325559i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			3.75342e8i			1.50826i
$630$		0			0
$631$	−3.72217e8			−1.48152			−0.740760	−	0.671769i	$-0.765535\pi$
$631$	−3.72217e8			−1.48152			−0.740760	+	0.671769i	$0.765535\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.86122e6	−	3.38398e6i	0.0228911	−	0.0132162i
$636$		0			0
$637$	7.76594e7	−	1.34510e8i	0.300452	−	0.520399i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.33506e8	−	1.92550e8i	−1.26628	−	0.731087i	−0.291997	−	0.956419i	$-0.594320\pi$
$641$	−3.33506e8	−	1.92550e8i	−1.26628	−	0.731087i	−0.974282	+	0.225332i	$0.927653\pi$
$642$		0			0
$643$	−1.12238e8	−	1.94403e8i	−0.422191	−	0.731256i	0.573963	−	0.818881i	$-0.305405\pi$
$643$	−1.12238e8	−	1.94403e8i	−0.422191	−	0.731256i	−0.996153	+	0.0876258i	$0.972072\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			1.62221e8i			0.598955i	0.954103	+	0.299477i	$0.0968123\pi$
$647$			1.62221e8i			0.598955i	−0.954103	+	0.299477i	$0.903188\pi$
$648$		0			0
$649$	−1.14145e8			−0.417565
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.40053e8	−	1.38595e8i	0.862119	−	0.497745i	−0.00260213	−	0.999997i	$-0.500828\pi$
$653$	2.40053e8	−	1.38595e8i	0.862119	−	0.497745i	0.864721	+	0.502252i	$0.167495\pi$
$654$		0			0
$655$	1.31575e8	−	2.27894e8i	0.468218	−	0.810978i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	3.40540e7	+	1.96611e7i	0.118990	+	0.0686992i	0.558314	−	0.829630i	$-0.311448\pi$
$659$	3.40540e7	+	1.96611e7i	0.118990	+	0.0686992i	−0.439323	+	0.898329i	$0.644782\pi$
$660$		0			0
$661$	−1.39609e8	−	2.41810e8i	−0.483404	−	0.837280i	0.516415	−	0.856339i	$-0.327266\pi$
$661$	−1.39609e8	−	2.41810e8i	−0.483404	−	0.837280i	−0.999818	+	0.0190590i	$0.993933\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			2.60451e7i			0.0885649i
$666$		0			0
$667$	6.50359e7			0.219167
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.24716e8	−	7.20047e7i	0.412814	−	0.238338i
$672$		0			0
$673$	6.34740e7	−	1.09940e8i	0.208234	−	0.360671i	−0.742925	−	0.669375i	$-0.766562\pi$
$673$	6.34740e7	−	1.09940e8i	0.208234	−	0.360671i	0.951158	+	0.308704i	$0.0998952\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.77884e8	+	2.75907e8i	1.54013	+	0.889193i	0.998830	+	0.0483627i	$0.0154003\pi$
$677$	4.77884e8	+	2.75907e8i	1.54013	+	0.889193i	0.541298	+	0.840831i	$0.317933\pi$
$678$		0			0
$679$	−6.68852e7	−	1.15849e8i	−0.213659	−	0.370068i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	1.16196e7i		−	0.0364695i	−0.999834	−	0.0182347i	$-0.994195\pi$
$683$		−	1.16196e7i		−	0.0364695i	0.999834	−	0.0182347i	$-0.00580462\pi$
$684$		0			0
$685$	−1.68626e8			−0.524628
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.17109e8	−	1.83083e8i	0.969506	−	0.559745i
$690$		0			0
$691$	−3.27200e8	+	5.66727e8i	−0.991698	+	1.71767i	−0.384486	+	0.923131i	$0.625621\pi$
$691$	−3.27200e8	+	5.66727e8i	−0.991698	+	1.71767i	−0.607212	+	0.794540i	$0.707712\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.08361e8	−	1.20297e8i	−0.620671	−	0.358345i
$696$		0			0
$697$	−3.80940e8	−	6.59808e8i	−1.12502	−	1.94858i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	8.65379e7i		−	0.251219i	−0.992080	−	0.125609i	$-0.959911\pi$
$701$		−	8.65379e7i		−	0.251219i	0.992080	−	0.125609i	$-0.0400886\pi$
$702$		0			0
$703$	1.67073e8			0.480885
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.89596e8	−	1.09464e8i	0.536503	−	0.309750i
$708$		0			0
$709$	3.39991e8	−	5.88881e8i	0.953957	−	1.65230i	0.217218	−	0.976123i	$-0.430302\pi$
$709$	3.39991e8	−	5.88881e8i	0.953957	−	1.65230i	0.736738	−	0.676178i	$-0.236365\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.17395e8	−	1.83248e8i	−0.875652	−	0.505558i
$714$		0			0
$715$	3.32034e7	+	5.75100e7i	0.0908375	+	0.157335i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	1.62934e8i		−	0.438354i	−0.975685	−	0.219177i	$-0.929663\pi$
$719$		−	1.62934e8i		−	0.438354i	0.975685	−	0.219177i	$-0.0703372\pi$
$720$		0			0
$721$	−2.49860e8			−0.666639
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9.72272e7	−	5.61341e7i	0.255137	−	0.147304i
$726$		0			0
$727$	−7.67295e7	+	1.32899e8i	−0.199691	+	0.345875i	−0.948428	−	0.316992i	$-0.897327\pi$
$727$	−7.67295e7	+	1.32899e8i	−0.199691	+	0.345875i	0.748737	+	0.662867i	$0.230661\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.98488e8	−	2.87802e8i	−1.27615	−	0.736787i
$732$		0			0
$733$	1.74756e8	+	3.02686e8i	0.443732	+	0.768566i	0.997963	−	0.0637970i	$-0.0203210\pi$
$733$	1.74756e8	+	3.02686e8i	0.443732	+	0.768566i	−0.554231	+	0.832363i	$0.686988\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$			7.37354e7i			0.184193i
$738$		0			0
$739$	5.10104e7			0.126394			0.0631968	−	0.998001i	$-0.479870\pi$
$739$	5.10104e7			0.126394			0.0631968	+	0.998001i	$0.479870\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.04849e8	−	2.33740e8i	0.987021	−	0.569857i	0.0826387	−	0.996580i	$-0.473665\pi$
$743$	4.04849e8	−	2.33740e8i	0.987021	−	0.569857i	0.904383	+	0.426723i	$0.140332\pi$
$744$		0			0
$745$	−1.73201e7	+	2.99993e7i	−0.0418872	+	0.0725507i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.47502e8	−	8.51605e7i	−0.351038	−	0.202672i
$750$		0			0
$751$	−1.38607e8	−	2.40074e8i	−0.327239	−	0.566795i	0.654724	−	0.755868i	$-0.272785\pi$
$751$	−1.38607e8	−	2.40074e8i	−0.327239	−	0.566795i	−0.981963	+	0.189073i	$0.939452\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	2.52640e8i		−	0.587031i
$756$		0			0
$757$	6.09490e8			1.40501			0.702504	−	0.711680i	$-0.252065\pi$
$757$	6.09490e8			1.40501			0.702504	+	0.711680i	$0.252065\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.53043e8	−	1.46095e8i	0.574171	−	0.331498i	−0.184643	−	0.982806i	$-0.559113\pi$
$761$	2.53043e8	−	1.46095e8i	0.574171	−	0.331498i	0.758813	+	0.651308i	$0.225779\pi$
$762$		0			0
$763$	−3.94756e7	+	6.83737e7i	−0.0888699	+	0.153927i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.40856e8	+	1.39058e8i	0.533792	+	0.308185i
$768$		0			0
$769$	3.28242e8	+	5.68532e8i	0.721797	+	1.25019i	0.960279	+	0.279042i	$0.0900168\pi$
$769$	3.28242e8	+	5.68532e8i	0.721797	+	1.25019i	−0.238482	+	0.971147i	$0.576650\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			4.93327e8i			1.06806i	0.845465	+	0.534031i	$0.179323\pi$
$773$			4.93327e8i			1.06806i	−0.845465	+	0.534031i	$0.820677\pi$
$774$		0			0
$775$	−6.32664e8			−1.35915
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.93695e8	+	1.69565e8i	−0.621276	+	0.358694i
$780$		0			0
$781$	1.38362e8	−	2.39650e8i	0.290445	−	0.503065i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−2.19808e8	−	1.26906e8i	−0.454396	−	0.262346i
$786$		0			0
$787$	7.12144e7	+	1.23347e8i	0.146098	+	0.253049i	0.929782	−	0.368111i	$-0.119995\pi$
$787$	7.12144e7	+	1.23347e8i	0.146098	+	0.253049i	−0.783684	+	0.621160i	$0.786662\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	7.53789e7i		−	0.152307i
$792$		0			0
$793$	−3.50881e8			−0.703624
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.39457e7	−	3.11455e7i	0.106557	−	0.0615207i	−0.445774	−	0.895145i	$-0.647072\pi$
$797$	5.39457e7	−	3.11455e7i	0.106557	−	0.0615207i	0.552331	+	0.833625i	$0.313738\pi$
$798$		0			0
$799$	−2.17843e8	+	3.77316e8i	−0.427075	+	0.739716i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.32282e7	+	1.34108e7i	0.0448611	+	0.0259006i
$804$		0			0
$805$	−3.19705e7	−	5.53746e7i	−0.0612861	−	0.106151i
$806$		0			0
$807$		0			0
$808$		0			0
$809$			6.87496e8i			1.29845i	0.760597	+	0.649224i	$0.224906\pi$
$809$			6.87496e8i			1.29845i	−0.760597	+	0.649224i	$0.775094\pi$
$810$		0			0
$811$	1.75961e8			0.329879			0.164939	−	0.986304i	$-0.447257\pi$
$811$	1.75961e8			0.329879			0.164939	+	0.986304i	$0.447257\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.50885e7	+	5.48994e7i	−0.175653	+	0.101413i
$816$		0			0
$817$	−1.28107e8	+	2.21888e8i	−0.234913	+	0.406882i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.05686e8	−	1.18753e8i	−0.371686	−	0.214593i	0.302509	−	0.953147i	$-0.402176\pi$
$821$	−2.05686e8	−	1.18753e8i	−0.371686	−	0.214593i	−0.674195	+	0.738554i	$0.735509\pi$
$822$		0			0
$823$	1.78908e8	+	3.09878e8i	0.320945	+	0.555892i	0.980683	−	0.195603i	$-0.0626663\pi$
$823$	1.78908e8	+	3.09878e8i	0.320945	+	0.555892i	−0.659739	+	0.751495i	$0.729333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			8.43721e8i			1.49170i	0.666113	+	0.745851i	$0.267957\pi$
$827$			8.43721e8i			1.49170i	−0.666113	+	0.745851i	$0.732043\pi$
$828$		0			0
$829$	1.00864e9			1.77040			0.885199	−	0.465212i	$-0.154022\pi$
$829$	1.00864e9			1.77040			0.885199	+	0.465212i	$0.154022\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.22707e8	+	3.01785e8i	−0.904322	+	0.522111i
$834$		0			0
$835$	2.66259e8	−	4.61173e8i	0.457345	−	0.792145i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.25987e8	+	7.27385e7i	0.213324	+	0.123162i	0.602855	−	0.797851i	$-0.294030\pi$
$839$	1.25987e8	+	7.27385e7i	0.213324	+	0.123162i	−0.389531	+	0.921013i	$0.627363\pi$
$840$		0			0
$841$	−2.54447e8	−	4.40715e8i	−0.427769	−	0.740918i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			1.24319e8i			0.206047i
$846$		0			0
$847$	−2.01682e8			−0.331908
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.55215e8	+	2.05083e8i	−0.576371	+	0.332768i
$852$		0			0
$853$	−2.57698e8	+	4.46345e8i	−0.415206	+	0.719157i	−0.995450	−	0.0952852i	$-0.969624\pi$
$853$	−2.57698e8	+	4.46345e8i	−0.415206	+	0.719157i	0.580244	+	0.814442i	$0.302957\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.77473e8	+	2.17934e8i	0.599714	+	0.346245i	0.768929	−	0.639334i	$-0.220790\pi$
$857$	3.77473e8	+	2.17934e8i	0.599714	+	0.346245i	−0.169215	+	0.985579i	$0.554123\pi$
$858$		0			0
$859$	1.45729e8	+	2.52410e8i	0.229915	+	0.398224i	0.957783	−	0.287493i	$-0.0928220\pi$
$859$	1.45729e8	+	2.52410e8i	0.229915	+	0.398224i	−0.727868	+	0.685717i	$0.759489\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			9.92214e8i			1.54374i	0.635783	+	0.771868i	$0.280677\pi$
$863$			9.92214e8i			1.54374i	−0.635783	+	0.771868i	$0.719323\pi$
$864$		0			0
$865$	−3.25609e8			−0.503093
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.45657e8	+	1.41830e8i	−0.374344	+	0.216127i
$870$		0			0
$871$	8.98287e7	−	1.55588e8i	0.135944	−	0.235462i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.18914e8	−	1.26390e8i	−0.326776	−	0.188664i
$876$		0			0
$877$	5.93503e8	+	1.02798e9i	0.879881	+	1.52400i	0.851471	+	0.524402i	$0.175711\pi$
$877$	5.93503e8	+	1.02798e9i	0.879881	+	1.52400i	0.0284101	+	0.999596i	$0.490956\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1.23545e9i		−	1.80675i	−0.428847	−	0.903377i	$-0.641080\pi$
$881$		−	1.23545e9i		−	1.80675i	0.428847	−	0.903377i	$-0.358920\pi$
$882$		0			0
$883$	8.66631e8			1.25879			0.629394	−	0.777087i	$-0.283303\pi$
$883$	8.66631e8			1.25879			0.629394	+	0.777087i	$0.283303\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.04112e8	−	4.06519e8i	1.00895	−	0.582519i	0.0980680	−	0.995180i	$-0.468734\pi$
$887$	7.04112e8	−	4.06519e8i	1.00895	−	0.582519i	0.910885	+	0.412660i	$0.135400\pi$
$888$		0			0
$889$	−8.77703e6	+	1.52023e7i	−0.0124923	+	0.0216373i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.67952e8	+	9.69670e7i	0.235847	+	0.136166i
$894$		0			0
$895$	−7.37431e7	−	1.27727e8i	−0.102861	−	0.178161i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	4.84235e8i		−	0.666464i
$900$		0			0
$901$	−1.42292e9			−1.94539
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.60133e8	+	1.50188e8i	−0.350954	+	0.202623i
$906$		0			0
$907$	−1.06694e7	+	1.84799e7i	−0.0142994	+	0.0247672i	−0.873087	−	0.487565i	$-0.837885\pi$
$907$	−1.06694e7	+	1.84799e7i	−0.0142994	+	0.0247672i	0.858787	+	0.512332i	$0.171218\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.96531e8	−	1.13467e8i	−0.259942	−	0.150078i	0.364366	−	0.931256i	$-0.381286\pi$
$911$	−1.96531e8	−	1.13467e8i	−0.259942	−	0.150078i	−0.624308	+	0.781178i	$0.714619\pi$
$912$		0			0
$913$	8.62668e6	+	1.49419e7i	0.0113353	+	0.0196332i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			6.82531e8i			0.885145i
$918$		0			0
$919$	1.26885e9			1.63479			0.817396	−	0.576077i	$-0.195417\pi$
$919$	1.26885e9			1.63479			0.817396	+	0.576077i	$0.195417\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.83911e8	+	3.37121e8i	−0.742577	+	0.428727i
$924$		0			0
$925$	−3.54025e8	+	6.13190e8i	−0.447311	+	0.774765i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−4.83075e8	−	2.78903e8i	−0.602514	−	0.347862i	0.167516	−	0.985869i	$-0.446425\pi$
$929$	−4.83075e8	−	2.78903e8i	−0.602514	−	0.347862i	−0.770030	+	0.638008i	$0.779759\pi$
$930$		0			0
$931$	1.34331e8	+	2.32669e8i	0.166467	+	0.288329i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	2.58058e8i		−	0.315705i
$936$		0			0
$937$	−1.39223e8			−0.169236			−0.0846182	−	0.996413i	$-0.526967\pi$
$937$	−1.39223e8			−0.169236			−0.0846182	+	0.996413i	$0.526967\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.52077e8	+	2.03272e8i	−0.422541	+	0.243954i	−0.696164	−	0.717883i	$-0.745111\pi$
$941$	−3.52077e8	+	2.03272e8i	−0.422541	+	0.243954i	0.273623	+	0.961837i	$0.411778\pi$
$942$		0			0
$943$	4.16284e8	−	7.21025e8i	0.496426	−	0.859835i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	8.67192e8	+	5.00674e8i	1.02109	+	0.589529i	0.914420	−	0.404766i	$-0.132647\pi$
$947$	8.67192e8	+	5.00674e8i	1.02109	+	0.589529i	0.106673	+	0.994294i	$0.465980\pi$
$948$		0			0
$949$	−3.26757e7	−	5.65959e7i	−0.0382319	−	0.0662196i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1.33438e9i		−	1.54170i	−0.637017	−	0.770849i	$-0.719832\pi$
$953$		−	1.33438e9i		−	1.54170i	0.637017	−	0.770849i	$-0.280168\pi$
$954$		0			0
$955$	−3.21627e8			−0.369268
$956$		0			0
$957$		0			0
$958$		0			0
$959$	3.78769e8	−	2.18682e8i	0.429456	−	0.247946i
$960$		0			0
$961$	−9.20650e8	+	1.59461e9i	−1.03735	+	1.79674i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.89302e8	+	1.67029e8i	0.321936	+	0.185870i
$966$		0			0
$967$	−8.04831e8	−	1.39401e9i	−0.890072	−	1.54165i	−0.839787	−	0.542915i	$-0.817320\pi$
$967$	−8.04831e8	−	1.39401e9i	−0.890072	−	1.54165i	−0.0502847	−	0.998735i	$-0.516013\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	1.52289e9i		−	1.66345i	−0.555185	−	0.831727i	$-0.687352\pi$
$971$		−	1.52289e9i		−	1.66345i	0.555185	−	0.831727i	$-0.312648\pi$
$972$		0			0
$973$	6.24030e8			0.677434
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.10021e8	+	6.35204e7i	−0.117975	+	0.0681129i	−0.557826	−	0.829958i	$-0.688364\pi$
$977$	−1.10021e8	+	6.35204e7i	−0.117975	+	0.0681129i	0.439851	+	0.898071i	$0.355031\pi$
$978$		0			0
$979$	4.28176e8	−	7.41622e8i	0.456325	−	0.790377i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	7.66278e8	+	4.42411e8i	0.806726	+	0.465763i	0.845818	−	0.533472i	$-0.179113\pi$
$983$	7.66278e8	+	4.42411e8i	0.806726	+	0.465763i	−0.0390918	+	0.999236i	$0.512446\pi$
$984$		0			0
$985$	−4.51280e7	−	7.81641e7i	−0.0472213	−	0.0817897i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	6.29009e8i		−	0.650232i
$990$		0			0
$991$	−1.07134e9			−1.10079			−0.550396	−	0.834904i	$-0.685523\pi$
$991$	−1.07134e9			−1.10079			−0.550396	+	0.834904i	$0.685523\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.95448e8	−	2.86047e8i	0.502955	−	0.290381i
$996$		0			0
$997$	7.94263e8	−	1.37570e9i	0.801455	−	1.38816i	−0.117204	−	0.993108i	$-0.537393\pi$
$997$	7.94263e8	−	1.37570e9i	0.801455	−	1.38816i	0.918659	−	0.395052i	$-0.129274\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.7.g.a.89.3		12
3.2	odd	2		36.7.g.a.29.4	yes	12
4.3	odd	2		432.7.q.c.305.3		12
9.2	odd	6		324.7.c.b.161.8		12
9.4	even	3		36.7.g.a.5.4	✓	12
9.5	odd	6	inner	108.7.g.a.17.3		12
9.7	even	3		324.7.c.b.161.5		12
12.11	even	2		144.7.q.b.65.3		12
36.23	even	6		432.7.q.c.17.3		12
36.31	odd	6		144.7.q.b.113.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.7.g.a.5.4	✓	12	9.4	even	3
36.7.g.a.29.4	yes	12	3.2	odd	2
108.7.g.a.17.3		12	9.5	odd	6	inner
108.7.g.a.89.3		12	1.1	even	1	trivial
144.7.q.b.65.3		12	12.11	even	2
144.7.q.b.113.3		12	36.31	odd	6
324.7.c.b.161.5		12	9.7	even	3
324.7.c.b.161.8		12	9.2	odd	6
432.7.q.c.17.3		12	36.23	even	6
432.7.q.c.305.3		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	108.g (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-51.3356 + 29.6386i) q^{5} +(76.8738 - 133.149i) q^{7} +O(q^{10})\)	\(q+(-51.3356 + 29.6386i) q^{5} +(76.8738 - 133.149i) q^{7} +(587.230 + 339.038i) q^{11} +(-826.070 - 1430.80i) q^{13} +6420.23i q^{17} +2857.79 q^{19} +(-6075.95 + 3507.95i) q^{23} +(-6055.60 + 10488.6i) q^{25} +(-8027.87 - 4634.89i) q^{29} +(26119.0 + 45239.4i) q^{31} +9113.74i q^{35} +58462.5 q^{37} +(-102770. + 59334.4i) q^{41} +(-44827.4 + 77643.4i) q^{43} +(58769.9 + 33930.8i) q^{47} +(47005.3 + 81415.6i) q^{49} +221631. i q^{53} -40194.5 q^{55} +(-145784. + 84168.7i) q^{59} +(106190. - 183926. i) q^{61} +(84813.7 + 48967.2i) q^{65} +(54371.1 + 94173.5i) q^{67} -408102. i q^{71} +39555.6 q^{73} +(90285.3 - 52126.2i) q^{77} +(-209166. + 362286. i) q^{79} +(22035.7 + 12722.3i) q^{83} +(-190287. - 329586. i) q^{85} -1.26291e6i q^{89} -254013. q^{91} +(-146706. + 84700.9i) q^{95} +(435032. - 753498. i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 216 q^{5} - 120 q^{7}+O(q^{10}) \) 12 * q + 216 * q^5 - 120 * q^7	\( 12 q + 216 q^{5} - 120 q^{7} + 2214 q^{11} - 840 q^{13} - 12900 q^{19} + 8208 q^{23} + 24078 q^{25} + 29268 q^{29} + 3120 q^{31} + 12768 q^{37} + 16578 q^{41} + 71430 q^{43} + 329508 q^{47} - 238914 q^{49} + 5400 q^{55} - 428058 q^{59} - 93576 q^{61} + 1426464 q^{65} + 104334 q^{67} + 221820 q^{73} - 3461184 q^{77} + 123468 q^{79} + 2901420 q^{83} + 377568 q^{85} + 91488 q^{91} - 7249716 q^{95} - 1033482 q^{97}+O(q^{100}) \) 12 * q + 216 * q^5 - 120 * q^7 + 2214 * q^11 - 840 * q^13 - 12900 * q^19 + 8208 * q^23 + 24078 * q^25 + 29268 * q^29 + 3120 * q^31 + 12768 * q^37 + 16578 * q^41 + 71430 * q^43 + 329508 * q^47 - 238914 * q^49 + 5400 * q^55 - 428058 * q^59 - 93576 * q^61 + 1426464 * q^65 + 104334 * q^67 + 221820 * q^73 - 3461184 * q^77 + 123468 * q^79 + 2901420 * q^83 + 377568 * q^85 + 91488 * q^91 - 7249716 * q^95 - 1033482 * q^97

Introduction

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