LMFDB - Embedded newform 252.12.t.a.17.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,12,Mod(17,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("252.17");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	252.t (of order $6$, degree $2$, 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:	$193.622481501$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.8
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2849.90 - 4936.17i) q^{5} +(36467.2 + 25445.4i) q^{7} +O(q^{10})$	$q+(-2849.90 - 4936.17i) q^{5} +(36467.2 + 25445.4i) q^{7} +(133135. + 76865.3i) q^{11} +872983. i q^{13} +(2.54209e6 - 4.40304e6i) q^{17} +(1.14169e7 - 6.59156e6i) q^{19} +(-2.59055e7 + 1.49566e7i) q^{23} +(8.17024e6 - 1.41513e7i) q^{25} -9.25814e7i q^{29} +(-5.18945e7 - 2.99613e7i) q^{31} +(2.16749e7 - 2.52525e8i) q^{35} +(2.61995e8 + 4.53788e8i) q^{37} -7.05097e7 q^{41} +1.13212e9 q^{43} +(4.08358e8 + 7.07297e8i) q^{47} +(6.82389e8 + 1.85585e9i) q^{49} +(-4.61363e9 - 2.66368e9i) q^{53} -8.76233e8i q^{55} +(-1.92083e9 + 3.32698e9i) q^{59} +(-2.27373e9 + 1.31274e9i) q^{61} +(4.30919e9 - 2.48791e9i) q^{65} +(-3.09864e9 + 5.36701e9i) q^{67} +1.93867e10i q^{71} +(1.53992e10 + 8.89073e9i) q^{73} +(2.89918e9 + 6.19073e9i) q^{77} +(-9.58975e9 - 1.66099e10i) q^{79} +6.37611e9 q^{83} -2.89788e10 q^{85} +(7.70667e9 + 1.33483e10i) q^{89} +(-2.22134e10 + 3.18353e10i) q^{91} +(-6.50741e10 - 3.75705e10i) q^{95} -8.96304e10i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 31278 q^{7}+O(q^{10}) $ 60 * q - 31278 * q^7	$ 60 q - 31278 q^{7} - 34858710 q^{19} - 323828862 q^{25} + 1186783866 q^{31} - 706751058 q^{37} + 1104997284 q^{43} + 7568925402 q^{49} - 5130550116 q^{61} - 22208949354 q^{67} + 54154878858 q^{73} - 61996342614 q^{79} + 107647163952 q^{85} - 2229336678 q^{91}+O(q^{100}) $ 60 * q - 31278 * q^7 - 34858710 * q^19 - 323828862 * q^25 + 1186783866 * q^31 - 706751058 * q^37 + 1104997284 * q^43 + 7568925402 * q^49 - 5130550116 * q^61 - 22208949354 * q^67 + 54154878858 * q^73 - 61996342614 * q^79 + 107647163952 * q^85 - 2229336678 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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
$5$	−2849.90	−	4936.17i	−0.407844	−	0.706407i	0.586804	−	0.809729i	$-0.300386\pi$
$5$	−2849.90	−	4936.17i	−0.407844	−	0.706407i	−0.994648	+	0.103323i	$0.967053\pi$
$6$		0			0
$7$	36467.2	+	25445.4i	0.820094	+	0.572229i
$7$	36467.2	+	25445.4i	0.820094	+	0.572229i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	133135.	+	76865.3i	0.249248	+	0.143903i	0.619420	−	0.785060i	$-0.287368\pi$
$11$	133135.	+	76865.3i	0.249248	+	0.143903i	−0.370172	+	0.928963i	$0.620701\pi$
$12$		0			0
$13$			872983.i			0.652105i	0.945352	+	0.326052i	$0.105719\pi$
$13$			872983.i			0.652105i	−0.945352	+	0.326052i	$0.894281\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.54209e6	−	4.40304e6i	0.434233	−	0.752113i	−0.563000	−	0.826457i	$-0.690353\pi$
$17$	2.54209e6	−	4.40304e6i	0.434233	−	0.752113i	0.997233	+	0.0743438i	$0.0236862\pi$
$18$		0			0
$19$	1.14169e7	−	6.59156e6i	1.05780	−	0.610722i	0.132978	−	0.991119i	$-0.457546\pi$
$19$	1.14169e7	−	6.59156e6i	1.05780	−	0.610722i	0.924823	+	0.380397i	$0.124213\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.59055e7	+	1.49566e7i	−0.839246	+	0.484539i	−0.857008	−	0.515303i	$-0.827679\pi$
$23$	−2.59055e7	+	1.49566e7i	−0.839246	+	0.484539i	0.0177619	+	0.999842i	$0.494346\pi$
$24$		0			0
$25$	8.17024e6	−	1.41513e7i	0.167327	−	0.289818i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	9.25814e7i		−	0.838175i	−0.907946	−	0.419088i	$-0.862350\pi$
$29$		−	9.25814e7i		−	0.838175i	0.907946	−	0.419088i	$-0.137650\pi$
$30$		0			0
$31$	−5.18945e7	−	2.99613e7i	−0.325561	−	0.187963i	0.328308	−	0.944571i	$-0.393522\pi$
$31$	−5.18945e7	−	2.99613e7i	−0.325561	−	0.187963i	−0.653869	+	0.756608i	$0.726855\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.16749e7	−	2.52525e8i	0.0697563	−	0.812700i
$36$		0			0
$37$	2.61995e8	+	4.53788e8i	0.621131	+	1.07583i	0.989276	+	0.146062i	$0.0466598\pi$
$37$	2.61995e8	+	4.53788e8i	0.621131	+	1.07583i	−0.368145	+	0.929769i	$0.620007\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.05097e7			−0.0950468			−0.0475234	−	0.998870i	$-0.515133\pi$
$41$	−7.05097e7			−0.0950468			−0.0475234	+	0.998870i	$0.515133\pi$
$42$		0			0
$43$	1.13212e9			1.17440			0.587200	−	0.809442i	$-0.300230\pi$
$43$	1.13212e9			1.17440			0.587200	+	0.809442i	$0.300230\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.08358e8	+	7.07297e8i	0.259719	+	0.449846i	0.966166	−	0.257919i	$-0.0830369\pi$
$47$	4.08358e8	+	7.07297e8i	0.259719	+	0.449846i	−0.706448	+	0.707765i	$0.749704\pi$
$48$		0			0
$49$	6.82389e8	+	1.85585e9i	0.345107	+	0.938563i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.61363e9	−	2.66368e9i	−1.51539	−	0.874912i	−0.999837	−	0.0180561i	$-0.994252\pi$
$53$	−4.61363e9	−	2.66368e9i	−1.51539	−	0.874912i	−0.515555	−	0.856856i	$-0.672414\pi$
$54$		0			0
$55$		−	8.76233e8i		−	0.234760i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.92083e9	+	3.32698e9i	−0.349787	+	0.605848i	−0.986211	−	0.165491i	$-0.947079\pi$
$59$	−1.92083e9	+	3.32698e9i	−0.349787	+	0.605848i	0.636425	+	0.771339i	$0.280413\pi$
$60$		0			0
$61$	−2.27373e9	+	1.31274e9i	−0.344686	+	0.199005i	−0.662342	−	0.749201i	$-0.730438\pi$
$61$	−2.27373e9	+	1.31274e9i	−0.344686	+	0.199005i	0.317656	+	0.948206i	$0.397104\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.30919e9	−	2.48791e9i	0.460651	−	0.265957i
$66$		0			0
$67$	−3.09864e9	+	5.36701e9i	−0.280388	+	0.485647i	−0.971480	−	0.237120i	$-0.923797\pi$
$67$	−3.09864e9	+	5.36701e9i	−0.280388	+	0.485647i	0.691092	+	0.722767i	$0.257130\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.93867e10i			1.27521i	0.770363	+	0.637605i	$0.220075\pi$
$71$			1.93867e10i			1.27521i	−0.770363	+	0.637605i	$0.779925\pi$
$72$		0			0
$73$	1.53992e10	+	8.89073e9i	0.869405	+	0.501951i	0.867151	−	0.498046i	$-0.165949\pi$
$73$	1.53992e10	+	8.89073e9i	0.869405	+	0.501951i	0.00225482	+	0.999997i	$0.499282\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.89918e9	+	6.19073e9i	0.122061	+	0.260641i
$78$		0			0
$79$	−9.58975e9	−	1.66099e10i	−0.350638	−	0.607322i	0.635724	−	0.771917i	$-0.280702\pi$
$79$	−9.58975e9	−	1.66099e10i	−0.350638	−	0.607322i	−0.986361	+	0.164595i	$0.947368\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.37611e9			0.177675			0.0888375	−	0.996046i	$-0.471685\pi$
$83$	6.37611e9			0.177675			0.0888375	+	0.996046i	$0.471685\pi$
$84$		0			0
$85$	−2.89788e10			−0.708397
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.70667e9	+	1.33483e10i	0.146292	+	0.253386i	0.929854	−	0.367928i	$-0.119933\pi$
$89$	7.70667e9	+	1.33483e10i	0.146292	+	0.253386i	−0.783562	+	0.621314i	$0.786599\pi$
$90$		0			0
$91$	−2.22134e10	+	3.18353e10i	−0.373153	+	0.534787i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.50741e10	−	3.75705e10i	−0.862836	−	0.498159i
$96$		0			0
$97$		−	8.96304e10i		−	1.05977i	−0.848070	−	0.529884i	$-0.822235\pi$
$97$		−	8.96304e10i		−	1.05977i	0.848070	−	0.529884i	$-0.177765\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	8.05219e10	−	1.39468e11i	0.762336	−	1.32041i	−0.179307	−	0.983793i	$-0.557386\pi$
$101$	8.05219e10	−	1.39468e11i	0.762336	−	1.32041i	0.941643	−	0.336612i	$-0.109281\pi$
$102$		0			0
$103$	1.18170e11	−	6.82254e10i	1.00439	−	0.579884i	0.0948453	−	0.995492i	$-0.469764\pi$
$103$	1.18170e11	−	6.82254e10i	1.00439	−	0.579884i	0.909544	+	0.415608i	$0.136431\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.15891e10	−	4.71055e10i	0.562369	−	0.324684i	−0.191727	−	0.981448i	$-0.561409\pi$
$107$	8.15891e10	−	4.71055e10i	0.562369	−	0.324684i	0.754096	+	0.656764i	$0.228075\pi$
$108$		0			0
$109$	−2.66869e10	+	4.62231e10i	−0.166132	+	0.287748i	−0.937057	−	0.349178i	$-0.886461\pi$
$109$	−2.66869e10	+	4.62231e10i	−0.166132	+	0.287748i	0.770925	+	0.636926i	$0.219794\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			1.44693e10i			0.0738784i	0.999318	+	0.0369392i	$0.0117608\pi$
$113$			1.44693e10i			0.0738784i	−0.999318	+	0.0369392i	$0.988239\pi$
$114$		0			0
$115$	1.47656e11	+	8.52493e10i	0.684563	+	0.395233i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.04740e11	−	9.58819e10i	0.786493	−	0.368322i
$120$		0			0
$121$	−1.30839e11	−	2.26620e11i	−0.458584	−	0.794290i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.71448e11			−1.08866
$126$		0			0
$127$	−3.32889e11			−0.894084			−0.447042	−	0.894513i	$-0.647523\pi$
$127$	−3.32889e11			−0.894084			−0.447042	+	0.894513i	$0.647523\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.71221e11	+	2.96564e11i	0.387762	+	0.671623i	0.992148	−	0.125068i	$-0.0399150\pi$
$131$	1.71221e11	+	2.96564e11i	0.387762	+	0.671623i	−0.604386	+	0.796691i	$0.706582\pi$
$132$		0			0
$133$	5.84068e11	+	5.01322e10i	1.21697	+	0.104456i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.26905e10	−	3.04209e10i	−0.0932758	−	0.0538528i	0.452637	−	0.891695i	$-0.350484\pi$
$137$	−5.26905e10	−	3.04209e10i	−0.0932758	−	0.0538528i	−0.545912	+	0.837842i	$0.683817\pi$
$138$		0			0
$139$			6.87829e11i			1.12434i	0.827021	+	0.562172i	$0.190034\pi$
$139$			6.87829e11i			1.12434i	−0.827021	+	0.562172i	$0.809966\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.71021e10	+	1.16224e11i	−0.0938400	+	0.162536i
$144$		0			0
$145$	−4.56997e11	+	2.63847e11i	−0.592092	+	0.341845i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.12825e11	−	2.96080e11i	0.572064	−	0.330281i	−0.185909	−	0.982567i	$-0.559523\pi$
$149$	5.12825e11	−	2.96080e11i	0.572064	−	0.330281i	0.757973	+	0.652285i	$0.226190\pi$
$150$		0			0
$151$	1.09955e11	−	1.90447e11i	0.113983	−	0.197424i	−0.803390	−	0.595454i	$-0.796972\pi$
$151$	1.09955e11	−	1.90447e11i	0.113983	−	0.197424i	0.917373	+	0.398029i	$0.130306\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			3.41547e11i			0.306638i
$156$		0			0
$157$	1.08826e11	+	6.28306e10i	0.0910507	+	0.0525682i	0.544834	−	0.838544i	$-0.316593\pi$
$157$	1.08826e11	+	6.28306e10i	0.0910507	+	0.0525682i	−0.453783	+	0.891112i	$0.649926\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.32528e12	−	1.13752e11i	−0.965528	−	0.0828740i
$162$		0			0
$163$	9.18894e11	+	1.59157e12i	0.625509	+	1.08341i	0.988442	+	0.151599i	$0.0484421\pi$
$163$	9.18894e11	+	1.59157e12i	0.625509	+	1.08341i	−0.362933	+	0.931815i	$0.618225\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	4.26372e11			0.254008			0.127004	−	0.991902i	$-0.459464\pi$
$167$	4.26372e11			0.254008			0.127004	+	0.991902i	$0.459464\pi$
$168$		0			0
$169$	1.03006e12			0.574760
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.15808e12	−	2.00585e12i	−0.568179	−	0.984114i	−0.996746	−	0.0806046i	$-0.974315\pi$
$173$	−1.15808e12	−	2.00585e12i	−0.568179	−	0.984114i	0.428567	−	0.903510i	$-0.359018\pi$
$174$		0			0
$175$	6.58031e11	−	3.08162e11i	0.303066	−	0.141929i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.29070e12	+	1.32254e12i	0.931702	+	0.537918i	0.887349	−	0.461098i	$-0.152544\pi$
$179$	2.29070e12	+	1.32254e12i	0.931702	+	0.537918i	0.0443522	+	0.999016i	$0.485878\pi$
$180$		0			0
$181$		−	1.35623e12i		−	0.518921i	−0.965754	−	0.259460i	$-0.916455\pi$
$181$		−	1.35623e12i		−	0.518921i	0.965754	−	0.259460i	$-0.0835447\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.49332e12	−	2.58650e12i	0.506649	−	0.877542i
$186$		0			0
$187$	6.76882e11	−	3.90798e11i	0.216463	−	0.124975i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.08925e12	−	2.36093e12i	1.16402	−	0.672047i	0.211756	−	0.977323i	$-0.432082\pi$
$191$	4.08925e12	−	2.36093e12i	1.16402	−	0.672047i	0.952264	+	0.305275i	$0.0987485\pi$
$192$		0			0
$193$	−6.82226e11	+	1.18165e12i	−0.183385	+	0.317631i	−0.943031	−	0.332705i	$-0.892039\pi$
$193$	−6.82226e11	+	1.18165e12i	−0.183385	+	0.317631i	0.759646	+	0.650336i	$0.225372\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	5.79290e12i		−	1.39102i	−0.718518	−	0.695508i	$-0.755179\pi$
$197$		−	5.79290e12i		−	1.39102i	0.718518	−	0.695508i	$-0.244821\pi$
$198$		0			0
$199$	2.36111e12	+	1.36319e12i	0.536321	+	0.309645i	0.743586	−	0.668640i	$-0.233123\pi$
$199$	2.36111e12	+	1.36319e12i	0.536321	+	0.309645i	−0.207266	+	0.978285i	$0.566457\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.35577e12	−	3.37619e12i	0.479628	−	0.687382i
$204$		0			0
$205$	2.00945e11	+	3.48048e11i	0.0387643	+	0.0671417i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.02665e12			0.351540
$210$		0			0
$211$	6.54196e12			1.07685			0.538424	−	0.842674i	$-0.319020\pi$
$211$	6.54196e12			1.07685			0.538424	+	0.842674i	$0.319020\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.22642e12	−	5.58833e12i	−0.478972	−	0.829603i
$216$		0			0
$217$	−1.13007e12	−	2.41308e12i	−0.159433	−	0.340443i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.84377e12	+	2.21920e12i	0.490456	+	0.283165i
$222$		0			0
$223$			8.69623e10i			0.0105598i	0.999986	+	0.00527988i	$0.00168065\pi$
$223$			8.69623e10i			0.0105598i	−0.999986	+	0.00527988i	$0.998319\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.55495e12	+	4.42530e12i	−0.281346	+	0.487305i	−0.971716	−	0.236151i	$-0.924114\pi$
$227$	−2.55495e12	+	4.42530e12i	−0.281346	+	0.487305i	0.690371	+	0.723456i	$0.257447\pi$
$228$		0			0
$229$	−5.20429e12	+	3.00470e12i	−0.546092	+	0.315287i	−0.747544	−	0.664212i	$-0.768767\pi$
$229$	−5.20429e12	+	3.00470e12i	−0.546092	+	0.315287i	0.201452	+	0.979498i	$0.435434\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.97110e12	−	4.02477e12i	0.665034	−	0.383957i	−0.129159	−	0.991624i	$-0.541228\pi$
$233$	6.97110e12	−	4.02477e12i	0.665034	−	0.383957i	0.794192	+	0.607667i	$0.207894\pi$
$234$		0			0
$235$	2.32756e12	−	4.03145e12i	0.211849	−	0.366934i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	7.06549e12i		−	0.586076i	−0.956101	−	0.293038i	$-0.905334\pi$
$239$		−	7.06549e12i		−	0.586076i	0.956101	−	0.293038i	$-0.0946662\pi$
$240$		0			0
$241$	1.72689e13	+	9.97019e12i	1.36827	+	0.789968i	0.990706	−	0.136017i	$-0.0434303\pi$
$241$	1.72689e13	+	9.97019e12i	1.36827	+	0.789968i	0.377559	+	0.925986i	$0.376764\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	7.21603e12	−	8.65736e12i	0.522257	−	0.626573i
$246$		0			0
$247$	5.75432e12	+	9.96678e12i	0.398255	+	0.689797i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.26862e13			1.43733			0.718665	−	0.695356i	$-0.244753\pi$
$251$	2.26862e13			1.43733			0.718665	+	0.695356i	$0.244753\pi$
$252$		0			0
$253$	−4.59856e12			−0.278907
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.67068e11	−	2.89370e11i	−0.00929523	−	0.0160998i	0.861340	−	0.508028i	$-0.169625\pi$
$257$	−1.67068e11	−	2.89370e11i	−0.00929523	−	0.0160998i	−0.870636	+	0.491928i	$0.836292\pi$
$258$		0			0
$259$	−1.99261e12	+	2.32150e13i	−0.106236	+	1.23771i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.74412e13	−	1.00697e13i	−0.854712	−	0.493468i	0.00752588	−	0.999972i	$-0.497604\pi$
$263$	−1.74412e13	−	1.00697e13i	−0.854712	−	0.493468i	−0.862238	+	0.506503i	$0.830938\pi$
$264$		0			0
$265$			3.03648e13i			1.42731i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.86815e13	−	3.23573e13i	0.808675	−	1.40067i	−0.105106	−	0.994461i	$-0.533518\pi$
$269$	1.86815e13	−	3.23573e13i	0.808675	−	1.40067i	0.913782	−	0.406206i	$-0.133148\pi$
$270$		0			0
$271$	3.36600e13	−	1.94336e13i	1.39889	−	0.807648i	0.404611	−	0.914489i	$-0.367407\pi$
$271$	3.36600e13	−	1.94336e13i	1.39889	−	0.807648i	0.994276	+	0.106841i	$0.0340736\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.17548e12	−	1.25602e12i	0.0834116	−	0.0481577i
$276$		0			0
$277$	1.29575e13	−	2.24430e13i	0.477399	−	0.826880i	−0.522265	−	0.852783i	$-0.674913\pi$
$277$	1.29575e13	−	2.24430e13i	0.477399	−	0.826880i	0.999664	+	0.0259032i	$0.00824617\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	4.82067e13i		−	1.64143i	−0.571336	−	0.820716i	$-0.693575\pi$
$281$		−	4.82067e13i		−	1.64143i	0.571336	−	0.820716i	$-0.306425\pi$
$282$		0			0
$283$	4.11760e13	+	2.37730e13i	1.34840	+	0.778498i	0.988023	−	0.154309i	$-0.0493151\pi$
$283$	4.11760e13	+	2.37730e13i	1.34840	+	0.778498i	0.360376	+	0.932807i	$0.382648\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−2.57129e12	−	1.79415e12i	−0.0779473	−	0.0543886i
$288$		0			0
$289$	4.21146e12	+	7.29447e12i	0.122884	+	0.212841i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.80581e12			0.265284			0.132642	−	0.991164i	$-0.457654\pi$
$293$	9.80581e12			0.265284			0.132642	+	0.991164i	$0.457654\pi$
$294$		0			0
$295$	2.18967e13			0.570633
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.30568e13	−	2.26151e13i	−0.315970	−	0.547276i
$300$		0			0
$301$	4.12853e13	+	2.88072e13i	0.963117	+	0.672026i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.29598e13	+	7.48233e12i	0.281157	+	0.162326i
$306$		0			0
$307$		−	1.94451e12i		−	0.0406958i	−0.999793	−	0.0203479i	$-0.993523\pi$
$307$		−	1.94451e12i		−	0.0406958i	0.999793	−	0.0203479i	$-0.00647739\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.67797e13	−	8.10248e13i	0.911749	−	1.57919i	0.100155	−	0.994972i	$-0.468066\pi$
$311$	4.67797e13	−	8.10248e13i	0.911749	−	1.57919i	0.811593	−	0.584223i	$-0.198601\pi$
$312$		0			0
$313$	−4.50336e13	+	2.60001e13i	−0.847310	+	0.489195i	−0.859742	−	0.510728i	$-0.829376\pi$
$313$	−4.50336e13	+	2.60001e13i	−0.847310	+	0.489195i	0.0124321	+	0.999923i	$0.496043\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.84784e13	−	5.10830e13i	1.55243	−	0.896294i	0.554484	−	0.832195i	$-0.312916\pi$
$317$	8.84784e13	−	5.10830e13i	1.55243	−	0.896294i	0.997944	−	0.0640995i	$-0.0204175\pi$
$318$		0			0
$319$	7.11630e12	−	1.23258e13i	0.120616	−	0.208913i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	6.70255e13i		−	1.06078i
$324$		0			0
$325$	1.23538e13	+	7.13248e12i	0.188992	+	0.109114i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.10578e12	+	3.61840e13i	−0.0444214	+	0.517534i
$330$		0			0
$331$	−2.92977e13	−	5.07451e13i	−0.405303	−	0.702005i	0.589054	−	0.808094i	$-0.299501\pi$
$331$	−2.92977e13	−	5.07451e13i	−0.405303	−	0.702005i	−0.994357	+	0.106089i	$0.966167\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.53232e13			0.457419
$336$		0			0
$337$	2.17354e12			0.0272397			0.0136198	−	0.999907i	$-0.495665\pi$
$337$	2.17354e12			0.0272397			0.0136198	+	0.999907i	$0.495665\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.60597e12	−	7.97778e12i	−0.0540969	−	0.0936986i
$342$		0			0
$343$	−2.23379e13	+	8.50412e13i	−0.254053	+	0.967190i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.23887e14	+	7.15263e13i	1.32195	+	0.763227i	0.984039	−	0.177951i	$-0.0569470\pi$
$347$	1.23887e14	+	7.15263e13i	1.32195	+	0.763227i	0.337909	+	0.941179i	$0.390280\pi$
$348$		0			0
$349$		−	4.98428e13i		−	0.515303i	−0.966238	−	0.257651i	$-0.917051\pi$
$349$		−	4.98428e13i		−	0.515303i	0.966238	−	0.257651i	$-0.0829486\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.00410e13	+	1.21315e14i	−0.680129	+	1.17802i	0.294812	+	0.955555i	$0.404743\pi$
$353$	−7.00410e13	+	1.21315e14i	−0.680129	+	1.17802i	−0.974941	+	0.222463i	$0.928590\pi$
$354$		0			0
$355$	9.56958e13	−	5.52500e13i	0.900817	−	0.520087i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	8.50065e12	−	4.90785e12i	0.0752372	−	0.0434382i	−0.461909	−	0.886927i	$-0.652836\pi$
$359$	8.50065e12	−	4.90785e12i	0.0752372	−	0.0434382i	0.537147	+	0.843489i	$0.319502\pi$
$360$		0			0
$361$	2.86523e13	−	4.96272e13i	0.245963	−	0.426020i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	1.01351e14i		−	0.818872i
$366$		0			0
$367$	3.54160e13	+	2.04475e13i	0.277675	+	0.160316i	0.632370	−	0.774666i	$-0.282082\pi$
$367$	3.54160e13	+	2.04475e13i	0.277675	+	0.160316i	−0.354695	+	0.934982i	$0.615415\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.00468e14	−	2.14533e14i	−0.742113	−	1.58466i
$372$		0			0
$373$	9.23359e13	+	1.59931e14i	0.662174	+	1.14692i	0.980043	+	0.198785i	$0.0636994\pi$
$373$	9.23359e13	+	1.59931e14i	0.662174	+	1.14692i	−0.317869	+	0.948135i	$0.602967\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.08220e13			0.546578
$378$		0			0
$379$	−1.66452e14			−1.09339			−0.546694	−	0.837332i	$-0.684114\pi$
$379$	−1.66452e14			−1.09339			−0.546694	+	0.837332i	$0.684114\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.11630e13	−	5.39759e13i	−0.193217	−	0.334662i	0.753097	−	0.657909i	$-0.228559\pi$
$383$	−3.11630e13	−	5.39759e13i	−0.193217	−	0.334662i	−0.946315	+	0.323247i	$0.895226\pi$
$384$		0			0
$385$	2.22961e13	−	3.19538e13i	0.134337	−	0.192526i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.71934e13	−	2.72471e13i	−0.268632	−	0.155095i	0.359634	−	0.933094i	$-0.382902\pi$
$389$	−4.71934e13	−	2.72471e13i	−0.268632	−	0.155095i	−0.628266	+	0.777999i	$0.716235\pi$
$390$		0			0
$391$			1.52084e14i			0.841610i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.46596e13	+	9.46732e13i	−0.286011	+	0.495385i
$396$		0			0
$397$	−1.71183e13	+	9.88324e12i	−0.0871189	+	0.0502981i	−0.542927	−	0.839780i	$-0.682684\pi$
$397$	−1.71183e13	+	9.88324e12i	−0.0871189	+	0.0502981i	0.455808	+	0.890078i	$0.349350\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.38031e14	−	7.96925e13i	0.664789	−	0.383816i	−0.129310	−	0.991604i	$-0.541276\pi$
$401$	1.38031e14	−	7.96925e13i	0.664789	−	0.383816i	0.794099	+	0.607788i	$0.207943\pi$
$402$		0			0
$403$	2.61557e13	−	4.53030e13i	0.122571	−	0.212300i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			8.05533e13i			0.357531i
$408$		0			0
$409$	3.19760e14	+	1.84614e14i	1.38149	+	0.797601i	0.992335	−	0.123573i	$-0.0394353\pi$
$409$	3.19760e14	+	1.84614e14i	1.38149	+	0.797601i	0.389150	+	0.921174i	$0.372769\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.54704e14	+	7.24493e13i	−0.633542	+	0.296694i
$414$		0			0
$415$	−1.81713e13	−	3.14736e13i	−0.0724637	−	0.125511i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.89820e14			−0.718066			−0.359033	−	0.933325i	$-0.616893\pi$
$419$	−1.89820e14			−0.718066			−0.359033	+	0.933325i	$0.616893\pi$
$420$		0			0
$421$	6.67182e13			0.245863			0.122931	−	0.992415i	$-0.460770\pi$
$421$	6.67182e13			0.245863			0.122931	+	0.992415i	$0.460770\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.15390e13	−	7.19477e13i	−0.145317	−	0.251697i
$426$		0			0
$427$	−1.16320e14	−	9.98404e12i	−0.396551	−	0.0340371i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.67952e14	+	1.54702e14i	0.867824	+	0.501039i	0.866625	−	0.498961i	$-0.166285\pi$
$431$	2.67952e14	+	1.54702e14i	0.867824	+	0.501039i	0.00119961	+	0.999999i	$0.499618\pi$
$432$		0			0
$433$		−	4.65238e14i		−	1.46890i	−0.678664	−	0.734449i	$-0.737441\pi$
$433$		−	4.65238e14i		−	1.46890i	0.678664	−	0.734449i	$-0.262559\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.97174e14	+	3.41516e14i	−0.591837	+	1.02509i
$438$		0			0
$439$	−4.04324e14	+	2.33437e14i	−1.18352	+	0.683304i	−0.956826	−	0.290663i	$-0.906124\pi$
$439$	−4.04324e14	+	2.33437e14i	−1.18352	+	0.683304i	−0.226692	+	0.973967i	$0.572791\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.53897e14	+	1.46587e14i	−0.707028	+	0.408203i	−0.809960	−	0.586486i	$-0.800511\pi$
$443$	−2.53897e14	+	1.46587e14i	−0.707028	+	0.408203i	0.102932	+	0.994688i	$0.467178\pi$
$444$		0			0
$445$	4.39264e13	−	7.60828e13i	0.119329	−	0.206684i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			1.25518e14i			0.324601i	0.986741	+	0.162300i	$0.0518913\pi$
$449$			1.25518e14i			0.324601i	−0.986741	+	0.162300i	$0.948109\pi$
$450$		0			0
$451$	−9.38729e12	−	5.41975e12i	−0.0236902	−	0.0136776i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.20450e14	+	1.89218e13i	0.529965	+	0.0454884i
$456$		0			0
$457$	−2.31197e14	−	4.00446e14i	−0.542555	−	0.939733i	−0.998756	−	0.0498565i	$-0.984124\pi$
$457$	−2.31197e14	−	4.00446e14i	−0.542555	−	0.939733i	0.456201	−	0.889877i	$-0.349210\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.90953e14			−0.650831			−0.325415	−	0.945571i	$-0.605504\pi$
$461$	−2.90953e14			−0.650831			−0.325415	+	0.945571i	$0.605504\pi$
$462$		0			0
$463$	−5.16608e14			−1.12841			−0.564203	−	0.825636i	$-0.690817\pi$
$463$	−5.16608e14			−1.12841			−0.564203	+	0.825636i	$0.690817\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.28000e14	+	2.21702e14i	0.266665	+	0.461878i	0.967999	−	0.250956i	$-0.0807449\pi$
$467$	1.28000e14	+	2.21702e14i	0.266665	+	0.461878i	−0.701333	+	0.712833i	$0.747412\pi$
$468$		0			0
$469$	−2.49564e14	+	1.16874e14i	−0.507846	+	0.237829i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.50724e14	+	8.70208e13i	0.292717	+	0.169000i
$474$		0			0
$475$		−	2.15419e14i		−	0.408760i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.73224e13	−	3.00032e13i	0.0313879	−	0.0543654i	−0.849905	−	0.526936i	$-0.823341\pi$
$479$	1.73224e13	−	3.00032e13i	0.0313879	−	0.0543654i	0.881293	+	0.472571i	$0.156674\pi$
$480$		0			0
$481$	−3.96149e14	+	2.28717e14i	−0.701554	+	0.405042i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.42431e14	+	2.55437e14i	−0.748627	+	0.432220i
$486$		0			0
$487$	4.41113e14	−	7.64031e14i	0.729694	−	1.26387i	−0.227318	−	0.973820i	$-0.572996\pi$
$487$	4.41113e14	−	7.64031e14i	0.729694	−	1.26387i	0.957013	−	0.290047i	$-0.0936708\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			6.88661e14i			1.08907i	0.838737	+	0.544537i	$0.183295\pi$
$491$			6.88661e14i			1.08907i	−0.838737	+	0.544537i	$0.816705\pi$
$492$		0			0
$493$	−4.07639e14	−	2.35351e14i	−0.630402	−	0.363963i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.93301e14	+	7.06978e14i	−0.729713	+	1.04579i
$498$		0			0
$499$	−4.80566e14	−	8.32364e14i	−0.695344	−	1.20437i	−0.970065	−	0.242847i	$-0.921919\pi$
$499$	−4.80566e14	−	8.32364e14i	−0.695344	−	1.20437i	0.274720	−	0.961524i	$-0.411415\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−3.86641e13			−0.0535407			−0.0267703	−	0.999642i	$-0.508522\pi$
$503$	−3.86641e13			−0.0535407			−0.0267703	+	0.999642i	$0.508522\pi$
$504$		0			0
$505$	−9.17917e14			−1.24366
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.52933e14	+	6.11298e14i	0.457873	+	0.793059i	0.998848	−	0.0479794i	$-0.0152782\pi$
$509$	3.52933e14	+	6.11298e14i	0.457873	+	0.793059i	−0.540976	+	0.841038i	$0.681945\pi$
$510$		0			0
$511$	3.35338e14	+	7.16059e14i	0.425762	+	0.909147i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.73544e14	−	3.88871e14i	−0.819268	−	0.473005i
$516$		0			0
$517$			1.25554e14i			0.149497i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.87301e14	+	3.24415e14i	−0.213763	+	0.370249i	−0.952889	−	0.303318i	$-0.901906\pi$
$521$	−1.87301e14	+	3.24415e14i	−0.213763	+	0.370249i	0.739126	+	0.673567i	$0.235239\pi$
$522$		0			0
$523$	3.25109e14	−	1.87702e14i	0.363303	−	0.209753i	−0.307225	−	0.951637i	$-0.599401\pi$
$523$	3.25109e14	−	1.87702e14i	0.363303	−	0.209753i	0.670529	+	0.741883i	$0.266067\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.63842e14	+	1.52329e14i	−0.282738	+	0.163239i
$528$		0			0
$529$	−2.90075e13	+	5.02425e13i	−0.0304442	+	0.0527309i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	6.15537e13i		−	0.0619805i
$534$		0			0
$535$	−4.65041e14	−	2.68492e14i	−0.458718	−	0.264841i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.18006e13	+	2.99530e14i	−0.0490452	+	0.283597i
$540$		0			0
$541$	−3.78872e13	−	6.56225e13i	−0.0351485	−	0.0608791i	0.847916	−	0.530131i	$-0.177857\pi$
$541$	−3.78872e13	−	6.56225e13i	−0.0351485	−	0.0608791i	−0.883065	+	0.469252i	$0.844524\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.04220e14			0.271023
$546$		0			0
$547$	6.63208e14			0.579055			0.289527	−	0.957170i	$-0.406502\pi$
$547$	6.63208e14			0.579055			0.289527	+	0.957170i	$0.406502\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−6.10256e14	−	1.05699e15i	−0.511892	−	0.886623i
$552$		0			0
$553$	7.29350e13	−	8.49734e14i	0.0599719	−	0.698706i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.01165e14	−	1.16143e14i	−0.158983	−	0.0917887i	0.418398	−	0.908264i	$-0.362592\pi$
$557$	−2.01165e14	−	1.16143e14i	−0.158983	−	0.0917887i	−0.577381	+	0.816475i	$0.695925\pi$
$558$		0			0
$559$			9.88321e14i			0.765831i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.11056e15	+	1.92354e15i	−0.827455	+	1.43319i	0.0725730	+	0.997363i	$0.476879\pi$
$563$	−1.11056e15	+	1.92354e15i	−0.827455	+	1.43319i	−0.900028	+	0.435831i	$0.856454\pi$
$564$		0			0
$565$	7.14231e13	−	4.12362e13i	0.0521882	−	0.0301309i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.66622e14	+	3.27139e14i	−0.398268	+	0.229940i	−0.685737	−	0.727850i	$-0.740520\pi$
$569$	−5.66622e14	+	3.27139e14i	−0.398268	+	0.229940i	0.287468	+	0.957790i	$0.407186\pi$
$570$		0			0
$571$	−3.67377e14	+	6.36315e14i	−0.253287	+	0.438706i	−0.964429	−	0.264343i	$-0.914845\pi$
$571$	−3.67377e14	+	6.36315e14i	−0.253287	+	0.438706i	0.711142	+	0.703049i	$0.248178\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			4.88795e14i			0.324305i
$576$		0			0
$577$	−3.46732e14	−	2.00186e14i	−0.225698	−	0.130307i	0.382888	−	0.923795i	$-0.374930\pi$
$577$	−3.46732e14	−	2.00186e14i	−0.225698	−	0.130307i	−0.608586	+	0.793488i	$0.708263\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.32519e14	+	1.62243e14i	0.145710	+	0.101671i
$582$		0			0
$583$	−4.09489e14	−	7.09256e14i	−0.251806	−	0.436140i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.18081e15			−1.29154			−0.645772	−	0.763531i	$-0.723464\pi$
$587$	−2.18081e15			−1.29154			−0.645772	+	0.763531i	$0.723464\pi$
$588$		0			0
$589$	−7.89968e14			−0.459172
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.89781e14	+	1.71435e15i	0.554291	+	0.960061i	0.997958	+	0.0638692i	$0.0203440\pi$
$593$	9.89781e14	+	1.71435e15i	0.554291	+	0.960061i	−0.443667	+	0.896192i	$0.646323\pi$
$594$		0			0
$595$	−1.05678e15	−	7.37378e14i	−0.580952	−	0.405366i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.26603e14	+	7.30944e13i	0.0670807	+	0.0387290i	0.533165	−	0.846011i	$-0.321002\pi$
$599$	1.26603e14	+	7.30944e13i	0.0670807	+	0.0387290i	−0.466085	+	0.884740i	$0.654336\pi$
$600$		0			0
$601$		−	2.83106e14i		−	0.147278i	−0.997285	−	0.0736391i	$-0.976539\pi$
$601$		−	2.83106e14i		−	0.147278i	0.997285	−	0.0736391i	$-0.0234613\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−7.45757e14	+	1.29169e15i	−0.374061	+	0.647893i
$606$		0			0
$607$	1.04870e15	−	6.05465e14i	0.516550	−	0.298230i	−0.218972	−	0.975731i	$-0.570270\pi$
$607$	1.04870e15	−	6.05465e14i	0.516550	−	0.298230i	0.735522	+	0.677501i	$0.236937\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−6.17458e14	+	3.56490e14i	−0.293346	+	0.169364i
$612$		0			0
$613$	−1.65605e15	+	2.86837e15i	−0.772755	+	1.33845i	0.163292	+	0.986578i	$0.447789\pi$
$613$	−1.65605e15	+	2.86837e15i	−0.772755	+	1.33845i	−0.936048	+	0.351873i	$0.885545\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	1.35461e15i		−	0.609884i	−0.952371	−	0.304942i	$-0.901363\pi$
$617$		−	1.35461e15i		−	0.609884i	0.952371	−	0.304942i	$-0.0986371\pi$
$618$		0			0
$619$	−1.03342e14	−	5.96643e13i	−0.0457063	−	0.0263886i	0.476973	−	0.878918i	$-0.341734\pi$
$619$	−1.03342e14	−	5.96643e13i	−0.0457063	−	0.0263886i	−0.522679	+	0.852530i	$0.675067\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−5.86132e13	+	6.82876e14i	−0.0250214	+	0.291513i
$624$		0			0
$625$	6.59650e14	+	1.14255e15i	0.276677	+	0.479219i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.66406e15			1.07886
$630$		0			0
$631$	1.95916e15			0.779668			0.389834	−	0.920885i	$-0.372532\pi$
$631$	1.95916e15			0.779668			0.389834	+	0.920885i	$0.372532\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.48698e14	+	1.64319e15i	0.364647	+	0.631587i
$636$		0			0
$637$	−1.62012e15	+	5.95714e14i	−0.612041	+	0.225046i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.32687e15	+	1.34342e15i	0.849283	+	0.490333i	0.860409	−	0.509605i	$-0.170208\pi$
$641$	2.32687e15	+	1.34342e15i	0.849283	+	0.490333i	−0.0111262	+	0.999938i	$0.503542\pi$
$642$		0			0
$643$		−	3.35250e15i		−	1.20284i	−0.798933	−	0.601420i	$-0.794602\pi$
$643$		−	3.35250e15i		−	1.20284i	0.798933	−	0.601420i	$-0.205398\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.37869e15	−	4.12001e15i	0.824829	−	1.42865i	−0.0772207	−	0.997014i	$-0.524605\pi$
$647$	2.37869e15	−	4.12001e15i	0.824829	−	1.42865i	0.902050	−	0.431632i	$-0.142062\pi$
$648$		0			0
$649$	−5.11458e14	+	2.95291e14i	−0.174367	+	0.100671i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.82187e14	−	2.78391e14i	0.158925	−	0.0917556i	−0.418428	−	0.908250i	$-0.637419\pi$
$653$	4.82187e14	−	2.78391e14i	0.158925	−	0.0917556i	0.577353	+	0.816494i	$0.304085\pi$
$654$		0			0
$655$	9.75925e14	−	1.69035e15i	0.316293	−	0.547835i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	1.30428e15i		−	0.408792i	−0.978888	−	0.204396i	$-0.934477\pi$
$659$		−	1.30428e15i		−	0.408792i	0.978888	−	0.204396i	$-0.0655230\pi$
$660$		0			0
$661$	−4.28977e15	−	2.47670e15i	−1.32229	−	0.763422i	−0.338193	−	0.941077i	$-0.609816\pi$
$661$	−4.28977e15	−	2.47670e15i	−1.32229	−	0.763422i	−0.984093	+	0.177654i	$0.943149\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.41707e15	−	3.02593e15i	−0.422545	−	0.902277i
$666$		0			0
$667$	1.38470e15	+	2.39837e15i	0.406128	+	0.703435i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.03616e14			−0.114550
$672$		0			0
$673$	3.70381e15			1.03411			0.517054	−	0.855953i	$-0.327029\pi$
$673$	3.70381e15			1.03411			0.517054	+	0.855953i	$0.327029\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.56735e15	−	4.44677e15i	−0.693820	−	1.20173i	−0.970577	−	0.240791i	$-0.922593\pi$
$677$	−2.56735e15	−	4.44677e15i	−0.693820	−	1.20173i	0.276757	−	0.960940i	$-0.410740\pi$
$678$		0			0
$679$	2.28068e15	−	3.26857e15i	0.606431	−	0.869109i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.74431e15	−	2.16178e15i	−0.963957	−	0.556541i	−0.0665683	−	0.997782i	$-0.521205\pi$
$683$	−3.74431e15	−	2.16178e15i	−0.963957	−	0.556541i	−0.897389	+	0.441241i	$0.854538\pi$
$684$		0			0
$685$			3.46785e14i			0.0878542i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	2.32535e15	−	4.02762e15i	0.570534	−	0.988194i
$690$		0			0
$691$	−6.16161e14	+	3.55741e14i	−0.148787	+	0.0859022i	−0.572545	−	0.819873i	$-0.694044\pi$
$691$	−6.16161e14	+	3.55741e14i	−0.148787	+	0.0859022i	0.423758	+	0.905775i	$0.360711\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.39524e15	−	1.96024e15i	0.794243	−	0.458557i
$696$		0			0
$697$	−1.79242e14	+	3.10457e14i	−0.0412724	+	0.0714860i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			6.52005e15i			1.45480i	0.686216	+	0.727398i	$0.259270\pi$
$701$			6.52005e15i			1.45480i	−0.686216	+	0.727398i	$0.740730\pi$
$702$		0			0
$703$	5.98235e15	+	3.45391e15i	1.31407	+	0.758676i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.48523e15	−	3.03710e15i	1.38076	−	0.646625i
$708$		0			0
$709$	1.75077e15	+	3.03243e15i	0.367008	+	0.635676i	0.989096	−	0.147271i	$-0.0470488\pi$
$709$	1.75077e15	+	3.03243e15i	0.367008	+	0.635676i	−0.622088	+	0.782947i	$0.713716\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.79247e15			0.364301
$714$		0			0
$715$	7.64936e14			0.153088
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−9.42662e14	−	1.63274e15i	−0.182956	−	0.316890i	0.759930	−	0.650005i	$-0.225233\pi$
$719$	−9.42662e14	−	1.63274e15i	−0.182956	−	0.316890i	−0.942886	+	0.333116i	$0.891900\pi$
$720$		0			0
$721$	6.04535e15	+	5.18890e14i	1.15552	+	0.0991816i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.31014e15	−	7.56412e14i	−0.242918	−	0.140249i
$726$		0			0
$727$			7.88315e15i			1.43966i	0.694149	+	0.719831i	$0.255781\pi$
$727$			7.88315e15i			1.43966i	−0.694149	+	0.719831i	$0.744219\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.87795e15	−	4.98476e15i	0.509963	−	0.883281i
$732$		0			0
$733$	8.67659e14	−	5.00943e14i	0.151453	−	0.0874413i	−0.422358	−	0.906429i	$-0.638798\pi$
$733$	8.67659e14	−	5.00943e14i	0.151453	−	0.0874413i	0.573811	+	0.818988i	$0.305464\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−8.25073e14	+	4.76356e14i	−0.139772	+	0.0806976i
$738$		0			0
$739$	−6.36246e14	+	1.10201e15i	−0.106189	+	0.183925i	−0.914223	−	0.405210i	$-0.867198\pi$
$739$	−6.36246e14	+	1.10201e15i	−0.106189	+	0.183925i	0.808034	+	0.589136i	$0.200532\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	4.74829e15i		−	0.769306i	−0.923061	−	0.384653i	$-0.874321\pi$
$743$		−	4.74829e15i		−	0.769306i	0.923061	−	0.384653i	$-0.125679\pi$
$744$		0			0
$745$	−2.92300e15	−	1.68759e15i	−0.466626	−	0.269407i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.17395e15	+	3.58262e14i	0.646989	+	0.0555329i
$750$		0			0
$751$	3.90104e15	+	6.75680e15i	0.595883	+	1.03210i	0.993422	+	0.114514i	$0.0365310\pi$
$751$	3.90104e15	+	6.75680e15i	0.595883	+	1.03210i	−0.397539	+	0.917585i	$0.630136\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.25344e15			−0.185949
$756$		0			0
$757$	2.92599e15			0.427804			0.213902	−	0.976855i	$-0.431383\pi$
$757$	2.92599e15			0.427804			0.213902	+	0.976855i	$0.431383\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.57437e15	+	4.45893e15i	0.365641	+	0.633309i	0.988879	−	0.148724i	$-0.0475165\pi$
$761$	2.57437e15	+	4.45893e15i	0.365641	+	0.633309i	−0.623238	+	0.782032i	$0.714183\pi$
$762$		0			0
$763$	−2.14936e15	+	1.00657e15i	−0.300902	+	0.140915i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−2.90439e15	−	1.67685e15i	−0.395076	−	0.228097i
$768$		0			0
$769$			1.54998e15i			0.207841i	0.994586	+	0.103921i	$0.0331388\pi$
$769$			1.54998e15i			0.207841i	−0.994586	+	0.103921i	$0.966861\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.38611e15	−	5.86492e15i	0.441280	−	0.764319i	−0.556505	−	0.830844i	$-0.687858\pi$
$773$	3.38611e15	−	5.86492e15i	0.441280	−	0.764319i	0.997785	+	0.0665250i	$0.0211912\pi$
$774$		0			0
$775$	−8.47982e14	+	4.89582e14i	−0.108950	+	0.0629023i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−8.05004e14	+	4.64769e14i	−0.100541	+	0.0580472i
$780$		0			0
$781$	−1.49016e15	+	2.58104e15i	−0.183507	+	0.317844i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	7.16242e14i		−	0.0857584i
$786$		0			0
$787$	2.15145e15	+	1.24214e15i	0.254021	+	0.146659i	0.621604	−	0.783332i	$-0.286481\pi$
$787$	2.15145e15	+	1.24214e15i	0.254021	+	0.146659i	−0.367583	+	0.929991i	$0.619815\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.68178e14	+	5.27657e14i	−0.0422754	+	0.0605872i
$792$		0			0
$793$	−1.14600e15	−	1.98492e15i	−0.129772	−	0.224772i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.27131e16			−1.40033			−0.700167	−	0.713979i	$-0.746891\pi$
$797$	−1.27131e16			−1.40033			−0.700167	+	0.713979i	$0.746891\pi$
$798$		0			0
$799$	4.15234e15			0.451113
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.36678e15	+	2.36733e15i	0.144465	+	0.250221i
$804$		0			0
$805$	3.21540e15	+	6.86597e15i	0.335242	+	0.715855i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.31833e15	+	4.22524e15i	0.742498	+	0.428681i	0.822977	−	0.568075i	$-0.192312\pi$
$809$	7.31833e15	+	4.22524e15i	0.742498	+	0.428681i	−0.0804790	+	0.996756i	$0.525645\pi$
$810$		0			0
$811$		−	1.02868e16i		−	1.02960i	−0.857312	−	0.514798i	$-0.827867\pi$
$811$		−	1.02868e16i		−	1.02960i	0.857312	−	0.514798i	$-0.172133\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.23751e15	−	9.07163e15i	0.510221	−	0.883728i
$816$		0			0
$817$	1.29253e16	−	7.46244e15i	1.24228	−	0.717232i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.17644e16	−	6.79217e15i	1.10073	−	0.635508i	0.164319	−	0.986407i	$-0.447457\pi$
$821$	1.17644e16	−	6.79217e15i	1.10073	−	0.635508i	0.936413	+	0.350899i	$0.114124\pi$
$822$		0			0
$823$	−3.46844e15	+	6.00752e15i	−0.320210	+	0.554621i	−0.980531	−	0.196363i	$-0.937087\pi$
$823$	−3.46844e15	+	6.00752e15i	−0.320210	+	0.554621i	0.660321	+	0.750984i	$0.270420\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1.61280e16i		−	1.44978i	−0.688867	−	0.724888i	$-0.741892\pi$
$827$		−	1.61280e16i		−	1.44978i	0.688867	−	0.724888i	$-0.258108\pi$
$828$		0			0
$829$	3.81844e15	+	2.20458e15i	0.338716	+	0.195558i	0.659704	−	0.751525i	$-0.270682\pi$
$829$	3.81844e15	+	2.20458e15i	0.338716	+	0.195558i	−0.320988	+	0.947083i	$0.604015\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	9.90606e15	+	1.71315e15i	0.855763	+	0.147995i
$834$		0			0
$835$	−1.21512e15	−	2.10464e15i	−0.103596	−	0.179433i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	1.65887e16			1.37760			0.688798	−	0.724954i	$-0.258139\pi$
$839$	1.65887e16			1.37760			0.688798	+	0.724954i	$0.258139\pi$
$840$		0			0
$841$	3.62920e15			0.297463
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.93557e15	−	5.08455e15i	−0.234412	−	0.406014i
$846$		0			0
$847$	9.95100e14	−	1.15935e16i	0.0784347	−	0.913807i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.35742e16	−	7.83708e15i	−1.04256	−	0.601924i
$852$		0			0
$853$			1.79970e16i			1.36452i	0.731110	+	0.682259i	$0.239002\pi$
$853$			1.79970e16i			1.36452i	−0.731110	+	0.682259i	$0.760998\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−9.01615e15	+	1.56164e16i	−0.666233	+	1.15395i	0.312716	+	0.949847i	$0.398761\pi$
$857$	−9.01615e15	+	1.56164e16i	−0.666233	+	1.15395i	−0.978949	+	0.204104i	$0.934572\pi$
$858$		0			0
$859$	3.49169e15	−	2.01593e15i	0.254726	−	0.147066i	−0.367200	−	0.930142i	$-0.619684\pi$
$859$	3.49169e15	−	2.01593e15i	0.254726	−	0.147066i	0.621926	+	0.783076i	$0.286350\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.29132e15	−	4.78699e15i	0.589609	−	0.340411i	−0.175334	−	0.984509i	$-0.556100\pi$
$863$	8.29132e15	−	4.78699e15i	0.589609	−	0.340411i	0.764943	+	0.644098i	$0.222767\pi$
$864$		0			0
$865$	−6.60082e15	+	1.14329e16i	−0.463457	+	0.802730i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	2.94848e15i		−	0.201832i
$870$		0			0
$871$	−4.68530e15	−	2.70506e15i	−0.316693	−	0.182843i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.35457e16	−	9.45163e15i	−0.892804	−	0.622964i
$876$		0			0
$877$	−7.78228e15	−	1.34793e16i	−0.506535	−	0.877344i	−0.999971	−	0.00756191i	$-0.997593\pi$
$877$	−7.78228e15	−	1.34793e16i	−0.506535	−	0.877344i	0.493437	−	0.869782i	$-0.335740\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.32955e16			0.843991			0.421995	−	0.906598i	$-0.361330\pi$
$881$	1.32955e16			0.843991			0.421995	+	0.906598i	$0.361330\pi$
$882$		0			0
$883$	9.53057e15			0.597496			0.298748	−	0.954332i	$-0.403431\pi$
$883$	9.53057e15			0.597496			0.298748	+	0.954332i	$0.403431\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.89529e15	−	1.19430e16i	−0.421670	−	0.730354i	0.574433	−	0.818552i	$-0.305223\pi$
$887$	−6.89529e15	−	1.19430e16i	−0.421670	−	0.730354i	−0.996103	+	0.0881977i	$0.971889\pi$
$888$		0			0
$889$	−1.21395e16	−	8.47049e15i	−0.733233	−	0.511621i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.32439e15	+	5.38344e15i	0.549461	+	0.317232i
$894$		0			0
$895$		−	1.50764e16i		−	0.877547i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−2.77386e15	+	4.80447e15i	−0.157546	+	0.272877i
$900$		0			0
$901$	−2.34565e16	+	1.35426e16i	−1.31607	+	0.759831i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.69458e15	+	3.86512e15i	−0.366569	+	0.211639i
$906$		0			0
$907$	1.04310e16	−	1.80670e16i	0.564267	−	0.977338i	−0.432851	−	0.901466i	$-0.642492\pi$
$907$	1.04310e16	−	1.80670e16i	0.564267	−	0.977338i	0.997117	−	0.0758729i	$-0.0241743\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	5.77957e15i		−	0.305172i	−0.988290	−	0.152586i	$-0.951240\pi$
$911$		−	5.77957e15i		−	0.305172i	0.988290	−	0.152586i	$-0.0487601\pi$
$912$		0			0
$913$	8.48882e14	+	4.90102e14i	0.0442851	+	0.0255680i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.30222e15	+	1.51716e16i	−0.0663215	+	0.772683i
$918$		0			0
$919$	4.77641e15	+	8.27298e15i	0.240362	+	0.416319i	0.960817	−	0.277182i	$-0.0894005\pi$
$919$	4.77641e15	+	8.27298e15i	0.240362	+	0.416319i	−0.720455	+	0.693501i	$0.756067\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.69242e16			−0.831571
$924$		0			0
$925$	8.56224e15			0.415727
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.87598e16	+	3.24929e16i	0.889491	+	1.54064i	0.840478	+	0.541846i	$0.182274\pi$
$929$	1.87598e16	+	3.24929e16i	0.889491	+	1.54064i	0.0490130	+	0.998798i	$0.484392\pi$
$930$		0			0
$931$	2.00237e16	+	1.66900e16i	0.938256	+	0.782049i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−3.85809e15	−	2.22747e15i	−0.176566	−	0.101941i
$936$		0			0
$937$		−	4.80995e15i		−	0.217557i	−0.994066	−	0.108778i	$-0.965306\pi$
$937$		−	4.80995e15i		−	0.217557i	0.994066	−	0.108778i	$-0.0346939\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.14390e16	+	1.98129e16i	−0.505410	+	0.875395i	0.494571	+	0.869137i	$0.335325\pi$
$941$	−1.14390e16	+	1.98129e16i	−0.505410	+	0.875395i	−0.999980	+	0.00625784i	$0.998008\pi$
$942$		0			0
$943$	1.82659e15	−	1.05458e15i	0.0797677	−	0.0460539i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.73239e16	+	1.57755e16i	−1.16578	+	0.673065i	−0.952683	−	0.303965i	$-0.901689\pi$
$947$	−2.73239e16	+	1.57755e16i	−1.16578	+	0.673065i	−0.213100	+	0.977030i	$0.568356\pi$
$948$		0			0
$949$	−7.76145e15	+	1.34432e16i	−0.327325	+	0.566943i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			2.41318e16i			0.994442i	0.867624	+	0.497221i	$0.165646\pi$
$953$			2.41318e16i			0.994442i	−0.867624	+	0.497221i	$0.834354\pi$
$954$		0			0
$955$	−2.33079e16	−	1.34568e16i	−0.949477	−	0.548181i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.14740e15	−	2.45009e15i	−0.0456787	−	0.0975395i
$960$		0			0
$961$	−1.09089e16	−	1.88947e16i	−0.429340	−	0.743639i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.77709e15			0.299169
$966$		0			0
$967$	−1.82896e16			−0.695600			−0.347800	−	0.937569i	$-0.613071\pi$
$967$	−1.82896e16			−0.695600			−0.347800	+	0.937569i	$0.613071\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.20241e15	−	1.59390e16i	−0.342134	−	0.592593i	0.642695	−	0.766122i	$-0.277816\pi$
$971$	−9.20241e15	−	1.59390e16i	−0.342134	−	0.592593i	−0.984829	+	0.173529i	$0.944483\pi$
$972$		0			0
$973$	−1.75021e16	+	2.50832e16i	−0.643382	+	0.922067i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.90797e16	+	1.10157e16i	0.685728	+	0.395905i	0.802010	−	0.597311i	$-0.203764\pi$
$977$	1.90797e16	+	1.10157e16i	0.685728	+	0.395905i	−0.116282	+	0.993216i	$0.537098\pi$
$978$		0			0
$979$			2.36950e15i			0.0842078i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.78583e16	+	3.09315e16i	−0.620578	+	1.07487i	0.368800	+	0.929509i	$0.379769\pi$
$983$	−1.78583e16	+	3.09315e16i	−0.620578	+	1.07487i	−0.989378	+	0.145364i	$0.953565\pi$
$984$		0			0
$985$	−2.85947e16	+	1.65092e16i	−0.982623	+	0.567317i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.93281e16	+	1.69326e16i	−0.985610	+	0.569042i
$990$		0			0
$991$	2.02189e16	−	3.50201e16i	0.671973	−	1.16389i	−0.305370	−	0.952234i	$-0.598780\pi$
$991$	2.02189e16	−	3.50201e16i	0.671973	−	1.16389i	0.977344	−	0.211658i	$-0.0678864\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	1.55398e16i		−	0.505147i
$996$		0			0
$997$	−1.11670e15	−	6.44727e14i	−0.0359016	−	0.0207278i	0.481942	−	0.876203i	$-0.339932\pi$
$997$	−1.11670e15	−	6.44727e14i	−0.0359016	−	0.0207278i	−0.517843	+	0.855475i	$0.673265\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.12.t.a.17.8	✓	60
3.2	odd	2	inner	252.12.t.a.17.23	yes	60
7.5	odd	6	inner	252.12.t.a.89.23	yes	60
21.5	even	6	inner	252.12.t.a.89.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.8	✓	60	1.1	even	1	trivial
252.12.t.a.17.23	yes	60	3.2	odd	2	inner
252.12.t.a.89.8	yes	60	21.5	even	6	inner
252.12.t.a.89.23	yes	60	7.5	odd	6	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	252.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2849.90 - 4936.17i) q^{5} +(36467.2 + 25445.4i) q^{7} +O(q^{10})\)	\(q+(-2849.90 - 4936.17i) q^{5} +(36467.2 + 25445.4i) q^{7} +(133135. + 76865.3i) q^{11} +872983. i q^{13} +(2.54209e6 - 4.40304e6i) q^{17} +(1.14169e7 - 6.59156e6i) q^{19} +(-2.59055e7 + 1.49566e7i) q^{23} +(8.17024e6 - 1.41513e7i) q^{25} -9.25814e7i q^{29} +(-5.18945e7 - 2.99613e7i) q^{31} +(2.16749e7 - 2.52525e8i) q^{35} +(2.61995e8 + 4.53788e8i) q^{37} -7.05097e7 q^{41} +1.13212e9 q^{43} +(4.08358e8 + 7.07297e8i) q^{47} +(6.82389e8 + 1.85585e9i) q^{49} +(-4.61363e9 - 2.66368e9i) q^{53} -8.76233e8i q^{55} +(-1.92083e9 + 3.32698e9i) q^{59} +(-2.27373e9 + 1.31274e9i) q^{61} +(4.30919e9 - 2.48791e9i) q^{65} +(-3.09864e9 + 5.36701e9i) q^{67} +1.93867e10i q^{71} +(1.53992e10 + 8.89073e9i) q^{73} +(2.89918e9 + 6.19073e9i) q^{77} +(-9.58975e9 - 1.66099e10i) q^{79} +6.37611e9 q^{83} -2.89788e10 q^{85} +(7.70667e9 + 1.33483e10i) q^{89} +(-2.22134e10 + 3.18353e10i) q^{91} +(-6.50741e10 - 3.75705e10i) q^{95} -8.96304e10i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 60 * q - 31278 * q^7	\( 60 q - 31278 q^{7} - 34858710 q^{19} - 323828862 q^{25} + 1186783866 q^{31} - 706751058 q^{37} + 1104997284 q^{43} + 7568925402 q^{49} - 5130550116 q^{61} - 22208949354 q^{67} + 54154878858 q^{73} - 61996342614 q^{79} + 107647163952 q^{85} - 2229336678 q^{91}+O(q^{100}) \) 60 * q - 31278 * q^7 - 34858710 * q^19 - 323828862 * q^25 + 1186783866 * q^31 - 706751058 * q^37 + 1104997284 * q^43 + 7568925402 * q^49 - 5130550116 * q^61 - 22208949354 * q^67 + 54154878858 * q^73 - 61996342614 * q^79 + 107647163952 * q^85 - 2229336678 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more