LMFDB - Embedded newform 252.12.t.a.17.22

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			17.22
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2700.97 + 4678.22i) q^{5} +(4004.48 - 44286.5i) q^{7} +O(q^{10})$	$q+(2700.97 + 4678.22i) q^{5} +(4004.48 - 44286.5i) q^{7} +(340633. + 196665. i) q^{11} +2.36123e6i q^{13} +(-3.94565e6 + 6.83407e6i) q^{17} +(-5.92539e6 + 3.42102e6i) q^{19} +(-2.50366e7 + 1.44549e7i) q^{23} +(9.82359e6 - 1.70150e7i) q^{25} -4.75591e7i q^{29} +(-1.45313e8 - 8.38965e7i) q^{31} +(2.17998e8 - 1.00883e8i) q^{35} +(-2.07000e8 - 3.58534e8i) q^{37} +1.32518e9 q^{41} -1.71848e8 q^{43} +(-3.33734e7 - 5.78044e7i) q^{47} +(-1.94526e9 - 3.54689e8i) q^{49} +(-6.71761e8 - 3.87842e8i) q^{53} +2.12474e9i q^{55} +(-2.25190e9 + 3.90041e9i) q^{59} +(-5.99546e8 + 3.46148e8i) q^{61} +(-1.10463e10 + 6.37761e9i) q^{65} +(2.47653e8 - 4.28948e8i) q^{67} +1.34975e10i q^{71} +(-1.37824e10 - 7.95725e9i) q^{73} +(1.00736e10 - 1.42979e10i) q^{77} +(1.08540e10 + 1.87996e10i) q^{79} +2.48592e10 q^{83} -4.26283e10 q^{85} +(-1.70878e10 - 2.95969e10i) q^{89} +(1.04571e11 + 9.45550e9i) q^{91} +(-3.20086e10 - 1.84802e10i) q^{95} -7.99477e9i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2700.97	+	4678.22i	0.386531	+	0.669492i	0.991980	−	0.126392i	$-0.0403398\pi$
$5$	2700.97	+	4678.22i	0.386531	+	0.669492i	−0.605449	+	0.795884i	$0.707006\pi$
$6$		0			0
$7$	4004.48	−	44286.5i	0.0900548	−	0.995937i
$7$	4004.48	−	44286.5i	0.0900548	−	0.995937i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	340633.	+	196665.i	0.637716	+	0.368186i	0.783734	−	0.621096i	$-0.213312\pi$
$11$	340633.	+	196665.i	0.637716	+	0.368186i	−0.146018	+	0.989282i	$0.546646\pi$
$12$		0			0
$13$			2.36123e6i			1.76380i	0.471434	+	0.881901i	$0.343737\pi$
$13$			2.36123e6i			1.76380i	−0.471434	+	0.881901i	$0.656263\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.94565e6	+	6.83407e6i	−0.673984	+	1.16737i	0.302781	+	0.953060i	$0.402085\pi$
$17$	−3.94565e6	+	6.83407e6i	−0.673984	+	1.16737i	−0.976765	+	0.214314i	$0.931248\pi$
$18$		0			0
$19$	−5.92539e6	+	3.42102e6i	−0.549000	+	0.316965i	−0.748718	−	0.662888i	$-0.769330\pi$
$19$	−5.92539e6	+	3.42102e6i	−0.549000	+	0.316965i	0.199719	+	0.979853i	$0.435997\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.50366e7	+	1.44549e7i	−0.811096	+	0.468286i	−0.847336	−	0.531057i	$-0.821795\pi$
$23$	−2.50366e7	+	1.44549e7i	−0.811096	+	0.468286i	0.0362405	+	0.999343i	$0.488462\pi$
$24$		0			0
$25$	9.82359e6	−	1.70150e7i	0.201187	−	0.348466i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	4.75591e7i		−	0.430571i	−0.976551	−	0.215285i	$-0.930932\pi$
$29$		−	4.75591e7i		−	0.430571i	0.976551	−	0.215285i	$-0.0690682\pi$
$30$		0			0
$31$	−1.45313e8	−	8.38965e7i	−0.911622	−	0.526325i	−0.0306696	−	0.999530i	$-0.509764\pi$
$31$	−1.45313e8	−	8.38965e7i	−0.911622	−	0.526325i	−0.880953	+	0.473204i	$0.843097\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.17998e8	−	1.00883e8i	0.701581	−	0.324670i
$36$		0			0
$37$	−2.07000e8	−	3.58534e8i	−0.490750	−	0.850004i	0.509193	−	0.860652i	$-0.329944\pi$
$37$	−2.07000e8	−	3.58534e8i	−0.490750	−	0.850004i	−0.999943	+	0.0106482i	$0.996611\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.32518e9			1.78634			0.893170	−	0.449720i	$-0.148476\pi$
$41$	1.32518e9			1.78634			0.893170	+	0.449720i	$0.148476\pi$
$42$		0			0
$43$	−1.71848e8			−0.178266			−0.0891329	−	0.996020i	$-0.528410\pi$
$43$	−1.71848e8			−0.178266			−0.0891329	+	0.996020i	$0.528410\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.33734e7	−	5.78044e7i	−0.0212257	−	0.0367640i	0.855217	−	0.518269i	$-0.173424\pi$
$47$	−3.33734e7	−	5.78044e7i	−0.0212257	−	0.0367640i	−0.876443	+	0.481505i	$0.840090\pi$
$48$		0			0
$49$	−1.94526e9	−	3.54689e8i	−0.983780	−	0.179378i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.71761e8	−	3.87842e8i	−0.220647	−	0.127391i	0.385603	−	0.922665i	$-0.373993\pi$
$53$	−6.71761e8	−	3.87842e8i	−0.220647	−	0.127391i	−0.606250	+	0.795274i	$0.707327\pi$
$54$		0			0
$55$			2.12474e9i			0.569261i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.25190e9	+	3.90041e9i	−0.410075	+	0.710271i	−0.994898	−	0.100890i	$-0.967831\pi$
$59$	−2.25190e9	+	3.90041e9i	−0.410075	+	0.710271i	0.584822	+	0.811161i	$0.301164\pi$
$60$		0			0
$61$	−5.99546e8	+	3.46148e8i	−0.0908884	+	0.0524745i	−0.544755	−	0.838595i	$-0.683377\pi$
$61$	−5.99546e8	+	3.46148e8i	−0.0908884	+	0.0524745i	0.453867	+	0.891069i	$0.350044\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.10463e10	+	6.37761e9i	−1.18085	+	0.681765i
$66$		0			0
$67$	2.47653e8	−	4.28948e8i	0.0224095	−	0.0388144i	−0.854603	−	0.519282i	$-0.826200\pi$
$67$	2.47653e8	−	4.28948e8i	0.0224095	−	0.0388144i	0.877013	+	0.480467i	$0.159533\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.34975e10i			0.887836i	0.896067	+	0.443918i	$0.146412\pi$
$71$			1.34975e10i			0.887836i	−0.896067	+	0.443918i	$0.853588\pi$
$72$		0			0
$73$	−1.37824e10	−	7.95725e9i	−0.778122	−	0.449249i	0.0576420	−	0.998337i	$-0.481642\pi$
$73$	−1.37824e10	−	7.95725e9i	−0.778122	−	0.449249i	−0.835764	+	0.549088i	$0.814975\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.00736e10	−	1.42979e10i	0.424119	−	0.601968i
$78$		0			0
$79$	1.08540e10	+	1.87996e10i	0.396862	+	0.687385i	0.993337	−	0.115247i	$-0.0367658\pi$
$79$	1.08540e10	+	1.87996e10i	0.396862	+	0.687385i	−0.596475	+	0.802632i	$0.703432\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.48592e10			0.692721			0.346360	−	0.938102i	$-0.387417\pi$
$83$	2.48592e10			0.692721			0.346360	+	0.938102i	$0.387417\pi$
$84$		0			0
$85$	−4.26283e10			−1.04206
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.70878e10	−	2.95969e10i	−0.324370	−	0.561826i	0.657014	−	0.753878i	$-0.271819\pi$
$89$	−1.70878e10	−	2.95969e10i	−0.324370	−	0.561826i	−0.981385	+	0.192052i	$0.938486\pi$
$90$		0			0
$91$	1.04571e11	+	9.45550e9i	1.75664	+	0.158839i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.20086e10	−	1.84802e10i	−0.424411	−	0.245034i
$96$		0			0
$97$		−	7.99477e9i		−	0.0945282i	−0.998882	−	0.0472641i	$-0.984950\pi$
$97$		−	7.99477e9i		−	0.0945282i	0.998882	−	0.0472641i	$-0.0150502\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.95490e10	−	5.11804e10i	0.279753	−	0.484547i	−0.691570	−	0.722309i	$-0.743081\pi$
$101$	2.95490e10	−	5.11804e10i	0.279753	−	0.484547i	0.971323	+	0.237762i	$0.0764140\pi$
$102$		0			0
$103$	1.40418e11	−	8.10706e10i	1.19349	−	0.689063i	0.234395	−	0.972141i	$-0.424689\pi$
$103$	1.40418e11	−	8.10706e10i	1.19349	−	0.689063i	0.959097	+	0.283079i	$0.0913558\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−9.58732e10	+	5.53524e10i	−0.660825	+	0.381528i	−0.792591	−	0.609753i	$-0.791269\pi$
$107$	−9.58732e10	+	5.53524e10i	−0.660825	+	0.381528i	0.131766	+	0.991281i	$0.457935\pi$
$108$		0			0
$109$	−7.87065e10	+	1.36324e11i	−0.489965	+	0.848644i	−0.999933	−	0.0115492i	$-0.996324\pi$
$109$	−7.87065e10	+	1.36324e11i	−0.489965	+	0.848644i	0.509969	+	0.860193i	$0.329657\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	2.42059e11i		−	1.23592i	−0.786211	−	0.617958i	$-0.787960\pi$
$113$		−	2.42059e11i		−	1.23592i	0.786211	−	0.617958i	$-0.212040\pi$
$114$		0			0
$115$	−1.35246e11	−	7.80844e10i	−0.627028	−	0.362015i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.86856e11	+	2.02106e11i	1.10194	+	0.776373i
$120$		0			0
$121$	−6.53017e10	−	1.13106e11i	−0.228879	−	0.396429i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.69899e11			1.08412
$126$		0			0
$127$	−2.71254e11			−0.728543			−0.364271	−	0.931293i	$-0.618682\pi$
$127$	−2.71254e11			−0.728543			−0.364271	+	0.931293i	$0.618682\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.23359e11	−	3.86870e11i	−0.505839	−	0.876138i	−0.999977	−	0.00675504i	$-0.997850\pi$
$131$	−2.23359e11	−	3.86870e11i	−0.505839	−	0.876138i	0.494139	−	0.869383i	$-0.335484\pi$
$132$		0			0
$133$	1.27777e11	+	2.76114e11i	0.266237	+	0.575313i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.71042e11	−	2.71956e11i	−0.833866	−	0.481433i	0.0213084	−	0.999773i	$-0.493217\pi$
$137$	−4.71042e11	−	2.71956e11i	−0.833866	−	0.481433i	−0.855175	+	0.518340i	$0.826550\pi$
$138$		0			0
$139$		−	4.89521e11i		−	0.800184i	−0.916475	−	0.400092i	$-0.868978\pi$
$139$		−	4.89521e11i		−	0.800184i	0.916475	−	0.400092i	$-0.131022\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.64371e11	+	8.04314e11i	−0.649407	+	1.12481i
$144$		0			0
$145$	2.22492e11	−	1.28456e11i	0.288264	−	0.166429i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.02931e12	+	5.94275e11i	−1.14822	+	0.662923i	−0.948452	−	0.316921i	$-0.897351\pi$
$149$	−1.02931e12	+	5.94275e11i	−1.14822	+	0.662923i	−0.199764	+	0.979844i	$0.564018\pi$
$150$		0			0
$151$	−7.46820e11	+	1.29353e12i	−0.774181	+	1.34092i	0.161072	+	0.986943i	$0.448505\pi$
$151$	−7.46820e11	+	1.29353e12i	−0.774181	+	1.34092i	−0.935253	+	0.353979i	$0.884828\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	9.06407e11i		−	0.813765i
$156$		0			0
$157$	4.97874e11	+	2.87447e11i	0.416554	+	0.240497i	0.693602	−	0.720359i	$-0.256023\pi$
$157$	4.97874e11	+	2.87447e11i	0.416554	+	0.240497i	−0.277048	+	0.960856i	$0.589356\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.39897e11	+	1.16667e12i	0.393341	+	0.849972i
$162$		0			0
$163$	9.55478e11	+	1.65494e12i	0.650413	+	1.12655i	0.983023	+	0.183483i	$0.0587373\pi$
$163$	9.55478e11	+	1.65494e12i	0.650413	+	1.12655i	−0.332610	+	0.943064i	$0.607929\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	7.78403e11			0.463728			0.231864	−	0.972748i	$-0.425517\pi$
$167$	7.78403e11			0.463728			0.231864	+	0.972748i	$0.425517\pi$
$168$		0			0
$169$	−3.78325e12			−2.11100
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−1.70124e12	−	2.94663e12i	−0.834664	−	1.44568i	−0.894304	−	0.447460i	$-0.852329\pi$
$173$	−1.70124e12	−	2.94663e12i	−0.834664	−	1.44568i	0.0596400	−	0.998220i	$-0.481005\pi$
$174$		0			0
$175$	−7.14194e11	−	5.03188e11i	−0.328932	−	0.231751i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.35774e10	+	1.93859e10i	0.0136570	+	0.00788488i	0.506813	−	0.862056i	$-0.330823\pi$
$179$	3.35774e10	+	1.93859e10i	0.0136570	+	0.00788488i	−0.493156	+	0.869941i	$0.664157\pi$
$180$		0			0
$181$		−	4.20245e12i		−	1.60794i	−0.594669	−	0.803971i	$-0.702717\pi$
$181$		−	4.20245e12i		−	1.60794i	0.594669	−	0.803971i	$-0.297283\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.11820e12	−	1.93678e12i	0.379381	−	0.657106i
$186$		0			0
$187$	−2.68804e12	+	1.55194e12i	−0.859621	+	0.496303i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.50011e12	−	1.44344e12i	0.711666	−	0.410881i	−0.100011	−	0.994986i	$-0.531888\pi$
$191$	2.50011e12	−	1.44344e12i	0.711666	−	0.410881i	0.811678	+	0.584106i	$0.198555\pi$
$192$		0			0
$193$	2.17096e12	−	3.76022e12i	0.583563	−	1.01076i	−0.411490	−	0.911414i	$-0.634992\pi$
$193$	2.17096e12	−	3.76022e12i	0.583563	−	1.01076i	0.995053	−	0.0993460i	$-0.0316751\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	7.21480e12i		−	1.73245i	−0.499657	−	0.866223i	$-0.666541\pi$
$197$		−	7.21480e12i		−	1.73245i	0.499657	−	0.866223i	$-0.333459\pi$
$198$		0			0
$199$	−1.38871e12	−	8.01772e11i	−0.315442	−	0.182121i	0.333917	−	0.942602i	$-0.391629\pi$
$199$	−1.38871e12	−	8.01772e11i	−0.315442	−	0.182121i	−0.649359	+	0.760482i	$0.724963\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.10622e12	−	1.90449e11i	−0.428821	−	0.0387750i
$204$		0			0
$205$	3.57927e12	+	6.19948e12i	0.690476	+	1.19594i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−2.69118e12			−0.466808
$210$		0			0
$211$	8.39437e11			0.138177			0.0690883	−	0.997611i	$-0.477991\pi$
$211$	8.39437e11			0.138177			0.0690883	+	0.997611i	$0.477991\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.64156e11	−	8.03942e11i	−0.0689053	−	0.119347i
$216$		0			0
$217$	−4.29738e12	+	6.09944e12i	−0.606283	+	0.860520i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.61368e13	−	9.31659e12i	−2.05902	−	1.18877i
$222$		0			0
$223$			1.43605e13i			1.74378i	0.489701	+	0.871890i	$0.337106\pi$
$223$			1.43605e13i			1.74378i	−0.489701	+	0.871890i	$0.662894\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	1.38982e11	−	2.40724e11i	0.0153044	−	0.0265080i	−0.858272	−	0.513195i	$-0.828462\pi$
$227$	1.38982e11	−	2.40724e11i	0.0153044	−	0.0265080i	0.873576	+	0.486687i	$0.161795\pi$
$228$		0			0
$229$	−2.97705e12	+	1.71880e12i	−0.312385	+	0.180356i	−0.647993	−	0.761646i	$-0.724392\pi$
$229$	−2.97705e12	+	1.71880e12i	−0.312385	+	0.180356i	0.335608	+	0.942002i	$0.391058\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.31378e12	−	3.06791e12i	0.506927	−	0.292675i	−0.224642	−	0.974441i	$-0.572121\pi$
$233$	5.31378e12	−	3.06791e12i	0.506927	−	0.292675i	0.731570	+	0.681767i	$0.238788\pi$
$234$		0			0
$235$	1.80281e11	−	3.12256e11i	0.0164088	−	0.0284209i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	2.81277e12i		−	0.233317i	−0.993172	−	0.116658i	$-0.962782\pi$
$239$		−	2.81277e12i		−	0.233317i	0.993172	−	0.116658i	$-0.0372183\pi$
$240$		0			0
$241$	−7.88784e12	−	4.55405e12i	−0.624977	−	0.360831i	0.153827	−	0.988098i	$-0.450840\pi$
$241$	−7.88784e12	−	4.55405e12i	−0.624977	−	0.360831i	−0.778804	+	0.627267i	$0.784174\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.59477e12	−	1.00583e13i	−0.260170	−	0.727968i
$246$		0			0
$247$	−8.07783e12	−	1.39912e13i	−0.559064	−	0.968327i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−2.15275e13			−1.36392			−0.681958	−	0.731391i	$-0.738871\pi$
$251$	−2.15275e13			−1.36392			−0.681958	+	0.731391i	$0.738871\pi$
$252$		0			0
$253$	−1.13711e13			−0.689665
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.04237e12	−	7.00158e12i	−0.224907	−	0.389551i	0.731384	−	0.681965i	$-0.238875\pi$
$257$	−4.04237e12	−	7.00158e12i	−0.224907	−	0.389551i	−0.956292	+	0.292415i	$0.905541\pi$
$258$		0			0
$259$	−1.67071e13	+	7.73154e12i	−0.890745	+	0.412209i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.02297e13	−	5.90609e12i	−0.501308	−	0.289430i	0.227946	−	0.973674i	$-0.426799\pi$
$263$	−1.02297e13	−	5.90609e12i	−0.501308	−	0.289430i	−0.729253	+	0.684244i	$0.760132\pi$
$264$		0			0
$265$		−	4.19019e12i		−	0.196962i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.75322e13	−	3.03667e13i	0.758927	−	1.31450i	−0.184471	−	0.982838i	$-0.559057\pi$
$269$	1.75322e13	−	3.03667e13i	0.758927	−	1.31450i	0.943398	−	0.331662i	$-0.107609\pi$
$270$		0			0
$271$	−3.65747e13	+	2.11164e13i	−1.52002	+	0.877585i	−0.520301	+	0.853983i	$0.674180\pi$
$271$	−3.65747e13	+	2.11164e13i	−1.52002	+	0.877585i	−0.999721	+	0.0236019i	$0.992487\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.69248e12	−	3.86391e12i	0.256601	−	0.148148i
$276$		0			0
$277$	−1.50774e13	+	2.61148e13i	−0.555505	+	0.962162i	0.442359	+	0.896838i	$0.354142\pi$
$277$	−1.50774e13	+	2.61148e13i	−0.555505	+	0.962162i	−0.997864	+	0.0653245i	$0.979192\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			3.28392e13i			1.11817i	0.829110	+	0.559085i	$0.188847\pi$
$281$			3.28392e13i			1.11817i	−0.829110	+	0.559085i	$0.811153\pi$
$282$		0			0
$283$	1.05883e12	+	6.11313e11i	0.0346736	+	0.0200188i	0.517237	−	0.855842i	$-0.326961\pi$
$283$	1.05883e12	+	6.11313e11i	0.0346736	+	0.0200188i	−0.482563	+	0.875861i	$0.660294\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.30666e12	−	5.86876e13i	0.160868	−	1.77908i
$288$		0			0
$289$	−1.40004e13	−	2.42494e13i	−0.408509	−	0.707559i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.60561e13			−1.51653			−0.758265	−	0.651946i	$-0.773953\pi$
$293$	−5.60561e13			−1.51653			−0.758265	+	0.651946i	$0.773953\pi$
$294$		0			0
$295$	−2.43293e13			−0.634028
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.41313e13	−	5.91172e13i	−0.825965	−	1.43061i
$300$		0			0
$301$	−6.88162e11	+	7.61054e12i	−0.0160537	+	0.177541i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.23871e12	−	1.86987e12i	−0.0702624	−	0.0405660i
$306$		0			0
$307$			7.45597e13i			1.56043i	0.625514	+	0.780213i	$0.284889\pi$
$307$			7.45597e13i			1.56043i	−0.625514	+	0.780213i	$0.715111\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.62262e13	−	8.00661e13i	0.900961	−	1.56051i	0.0747115	−	0.997205i	$-0.476196\pi$
$311$	4.62262e13	−	8.00661e13i	0.900961	−	1.56051i	0.826249	−	0.563305i	$-0.190470\pi$
$312$		0			0
$313$	1.45348e13	−	8.39167e12i	0.273474	−	0.157890i	−0.356992	−	0.934108i	$-0.616198\pi$
$313$	1.45348e13	−	8.39167e12i	0.273474	−	0.157890i	0.630465	+	0.776218i	$0.282864\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.78507e13	+	1.60796e13i	−0.488664	+	0.282130i	−0.724020	−	0.689779i	$-0.757708\pi$
$317$	−2.78507e13	+	1.60796e13i	−0.488664	+	0.282130i	0.235356	+	0.971909i	$0.424374\pi$
$318$		0			0
$319$	9.35320e12	−	1.62002e13i	0.158530	−	0.274582i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	5.39927e13i		−	0.854518i
$324$		0			0
$325$	4.01762e13	+	2.31958e13i	0.614626	+	0.354854i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.69360e12	+	1.24651e12i	−0.0385261	+	0.0178287i
$330$		0			0
$331$	−5.76964e13	−	9.99331e13i	−0.798169	−	1.38247i	−0.920808	−	0.390017i	$-0.872469\pi$
$331$	−5.76964e13	−	9.99331e13i	−0.798169	−	1.38247i	0.122639	−	0.992451i	$-0.460864\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.67561e12			0.0346479
$336$		0			0
$337$	−4.19794e13			−0.526105			−0.263052	−	0.964782i	$-0.584729\pi$
$337$	−4.19794e13			−0.526105			−0.263052	+	0.964782i	$0.584729\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.29990e13	−	5.71559e13i	−0.387571	−	0.671293i
$342$		0			0
$343$	−2.34976e13	+	8.47281e13i	−0.267243	+	0.963629i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.70933e13	−	4.45099e13i	−0.822630	−	0.474946i	0.0286923	−	0.999588i	$-0.490866\pi$
$347$	−7.70933e13	−	4.45099e13i	−0.822630	−	0.474946i	−0.851323	+	0.524642i	$0.824199\pi$
$348$		0			0
$349$			4.61283e12i			0.0476901i	0.999716	+	0.0238450i	$0.00759083\pi$
$349$			4.61283e12i			0.0476901i	−0.999716	+	0.0238450i	$0.992409\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.43037e13	−	2.47748e13i	0.138895	−	0.240574i	−0.788183	−	0.615441i	$-0.788978\pi$
$353$	1.43037e13	−	2.47748e13i	0.138895	−	0.240574i	0.927079	+	0.374867i	$0.122311\pi$
$354$		0			0
$355$	−6.31443e13	+	3.64564e13i	−0.594399	+	0.343176i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.50462e14	+	8.68692e13i	−1.33170	+	0.768859i	−0.985561	−	0.169323i	$-0.945842\pi$
$359$	−1.50462e14	+	8.68692e13i	−1.33170	+	0.768859i	−0.346142	+	0.938182i	$0.612508\pi$
$360$		0			0
$361$	−3.48383e13	+	6.03417e13i	−0.299066	+	0.517998i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	8.59692e13i		−	0.694596i
$366$		0			0
$367$	1.40860e14	+	8.13257e13i	1.10440	+	0.637624i	0.937372	−	0.348329i	$-0.113251\pi$
$367$	1.40860e14	+	8.13257e13i	1.10440	+	0.637624i	0.167025	+	0.985953i	$0.446584\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.98662e13	+	2.81968e13i	−0.146743	+	0.208278i
$372$		0			0
$373$	3.59376e13	+	6.22457e13i	0.257721	+	0.446386i	0.965631	−	0.259917i	$-0.0836951\pi$
$373$	3.59376e13	+	6.22457e13i	0.257721	+	0.446386i	−0.707910	+	0.706303i	$0.750362\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.12298e14			0.759442
$378$		0			0
$379$	−1.59423e14			−1.04721			−0.523606	−	0.851960i	$-0.675414\pi$
$379$	−1.59423e14			−1.04721			−0.523606	+	0.851960i	$0.675414\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.04799e14	+	1.81517e14i	0.649776	+	1.12545i	0.983176	+	0.182660i	$0.0584707\pi$
$383$	1.04799e14	+	1.81517e14i	0.649776	+	1.12545i	−0.333400	+	0.942785i	$0.608196\pi$
$384$		0			0
$385$	9.40973e13	+	8.50849e12i	0.566948	+	0.0512647i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.32253e14	−	1.34091e14i	−1.32202	−	0.763268i	−0.337969	−	0.941157i	$-0.609740\pi$
$389$	−2.32253e14	−	1.34091e14i	−1.32202	−	0.763268i	−0.984051	+	0.177889i	$0.943073\pi$
$390$		0			0
$391$		−	2.28136e14i		−	1.26247i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−5.86325e13	+	1.01554e14i	−0.306799	+	0.531392i
$396$		0			0
$397$	−2.02107e14	+	1.16687e14i	−1.02857	+	0.593846i	−0.916575	−	0.399863i	$-0.869058\pi$
$397$	−2.02107e14	+	1.16687e14i	−1.02857	+	0.593846i	−0.111996	+	0.993709i	$0.535724\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	2.69993e14	−	1.55880e14i	1.30034	−	0.750753i	0.319880	−	0.947458i	$-0.396357\pi$
$401$	2.69993e14	−	1.55880e14i	1.30034	−	0.750753i	0.980463	+	0.196705i	$0.0630241\pi$
$402$		0			0
$403$	1.98099e14	−	3.43117e14i	0.928334	−	1.60792i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	1.62838e14i		−	0.722749i
$408$		0			0
$409$	−1.03199e14	−	5.95817e13i	−0.445857	−	0.257415i	0.260222	−	0.965549i	$-0.416204\pi$
$409$	−1.03199e14	−	5.95817e13i	−0.445857	−	0.257415i	−0.706079	+	0.708133i	$0.749538\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.63718e14	+	1.15348e14i	0.670456	+	0.472372i
$414$		0			0
$415$	6.71440e13	+	1.16297e14i	0.267758	+	0.463771i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.45115e14			0.927241			0.463620	−	0.886034i	$-0.346550\pi$
$419$	2.45115e14			0.927241			0.463620	+	0.886034i	$0.346550\pi$
$420$		0			0
$421$	−4.58067e14			−1.68802			−0.844009	−	0.536329i	$-0.819811\pi$
$421$	−4.58067e14			−1.68802			−0.844009	+	0.536329i	$0.819811\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.75209e13	+	1.34270e14i	0.271194	+	0.469721i
$426$		0			0
$427$	1.29288e13	+	2.79379e13i	0.0440763	+	0.0952447i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.16894e14	+	6.74886e13i	0.378587	+	0.218577i	0.677203	−	0.735796i	$-0.263192\pi$
$431$	1.16894e14	+	6.74886e13i	0.378587	+	0.218577i	−0.298616	+	0.954373i	$0.596525\pi$
$432$		0			0
$433$		−	2.84613e14i		−	0.898610i	−0.893378	−	0.449305i	$-0.851672\pi$
$433$		−	2.84613e14i		−	0.898610i	0.893378	−	0.449305i	$-0.148328\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.89010e13	−	1.71302e14i	0.296861	−	0.514178i
$438$		0			0
$439$	−8.05389e13	+	4.64991e13i	−0.235749	+	0.136110i	−0.613222	−	0.789911i	$-0.710127\pi$
$439$	−8.05389e13	+	4.64991e13i	−0.235749	+	0.136110i	0.377472	+	0.926021i	$0.376793\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.75581e14	+	2.74577e14i	−1.32435	+	0.764616i	−0.984420	−	0.175833i	$-0.943738\pi$
$443$	−4.75581e14	+	2.74577e14i	−1.32435	+	0.764616i	−0.339934	+	0.940449i	$0.610405\pi$
$444$		0			0
$445$	9.23072e13	−	1.59881e14i	0.250759	−	0.434327i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			7.15312e14i			1.84987i	0.380129	+	0.924934i	$0.375880\pi$
$449$			7.15312e14i			1.84987i	−0.380129	+	0.924934i	$0.624120\pi$
$450$		0			0
$451$	4.51401e14	+	2.60616e14i	1.13918	+	0.657705i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.38207e14	+	5.14743e14i	0.572653	+	1.23745i
$456$		0			0
$457$	2.63739e14	+	4.56810e14i	0.618922	+	1.07200i	0.989683	+	0.143276i	$0.0457637\pi$
$457$	2.63739e14	+	4.56810e14i	0.618922	+	1.07200i	−0.370761	+	0.928728i	$0.620903\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−3.01854e14			−0.675215			−0.337607	−	0.941287i	$-0.609618\pi$
$461$	−3.01854e14			−0.675215			−0.337607	+	0.941287i	$0.609618\pi$
$462$		0			0
$463$	8.27040e14			1.80647			0.903236	−	0.429144i	$-0.141185\pi$
$463$	8.27040e14			1.80647			0.903236	+	0.429144i	$0.141185\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.81459e14	−	3.14297e14i	−0.378039	−	0.654783i	0.612738	−	0.790286i	$-0.290068\pi$
$467$	−1.81459e14	−	3.14297e14i	−0.378039	−	0.654783i	−0.990777	+	0.135503i	$0.956735\pi$
$468$		0			0
$469$	−1.80049e13	−	1.26854e13i	−0.0366386	−	0.0258139i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.85372e13	−	3.37965e13i	−0.113683	−	0.0656349i
$474$		0			0
$475$			1.34427e14i			0.255077i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.87101e14	+	4.97273e14i	−0.520222	+	0.901052i	0.479501	+	0.877541i	$0.340818\pi$
$479$	−2.87101e14	+	4.97273e14i	−0.520222	+	0.901052i	−0.999724	+	0.0235104i	$0.992516\pi$
$480$		0			0
$481$	8.46582e14	−	4.88774e14i	1.49924	−	0.865586i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.74013e13	−	2.15936e13i	0.0632859	−	0.0365381i
$486$		0			0
$487$	3.04344e14	−	5.27139e14i	0.503449	−	0.871998i	−0.496544	−	0.868012i	$-0.665398\pi$
$487$	3.04344e14	−	5.27139e14i	0.503449	−	0.871998i	0.999992	−	0.00398663i	$-0.00126899\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	2.23677e14i		−	0.353730i	−0.984235	−	0.176865i	$-0.943404\pi$
$491$		−	2.23677e14i		−	0.353730i	0.984235	−	0.176865i	$-0.0565957\pi$
$492$		0			0
$493$	3.25022e14	+	1.87652e14i	0.502637	+	0.290198i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	5.97757e14	+	5.40505e13i	0.884229	+	0.0799539i
$498$		0			0
$499$	−3.07164e14	−	5.32023e14i	−0.444444	−	0.769800i	0.553569	−	0.832803i	$-0.313265\pi$
$499$	−3.07164e14	−	5.32023e14i	−0.444444	−	0.769800i	−0.998013	+	0.0630035i	$0.979932\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	5.47466e14			0.758112			0.379056	−	0.925374i	$-0.376249\pi$
$503$	5.47466e14			0.758112			0.379056	+	0.925374i	$0.376249\pi$
$504$		0			0
$505$	3.19244e14			0.432534
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.35621e14	+	1.10093e15i	0.824614	+	1.42827i	0.902214	+	0.431289i	$0.141941\pi$
$509$	6.35621e14	+	1.10093e15i	0.824614	+	1.42827i	−0.0776001	+	0.996985i	$0.524726\pi$
$510$		0			0
$511$	−4.07590e14	+	5.78507e14i	−0.517498	+	0.734504i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.58532e14	+	4.37939e14i	0.922644	+	0.532689i
$516$		0			0
$517$		−	2.62535e13i		−	0.0312600i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.23767e14	−	1.08040e15i	0.711893	−	1.23304i	−0.252253	−	0.967661i	$-0.581171\pi$
$521$	6.23767e14	−	1.08040e15i	0.711893	−	1.23304i	0.964146	−	0.265374i	$-0.0854953\pi$
$522$		0			0
$523$	8.95535e14	−	5.17038e14i	1.00075	−	0.577780i	0.0922764	−	0.995733i	$-0.470586\pi$
$523$	8.95535e14	−	5.17038e14i	1.00075	−	0.577780i	0.908469	+	0.417953i	$0.137252\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.14671e15	−	6.62053e14i	1.22884	−	0.709470i
$528$		0			0
$529$	−5.85175e13	+	1.01355e14i	−0.0614157	+	0.106375i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			3.12906e15i			3.15075i
$534$		0			0
$535$	−5.17901e14	−	2.99010e14i	−0.510859	−	0.294945i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−5.92864e14	−	5.03382e14i	−0.561328	−	0.476606i
$540$		0			0
$541$	−6.22170e14	−	1.07763e15i	−0.577197	−	0.999734i	−0.995799	−	0.0915645i	$-0.970813\pi$
$541$	−6.22170e14	−	1.07763e15i	−0.577197	−	0.999734i	0.418602	−	0.908170i	$-0.362520\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−8.50336e14			−0.757547
$546$		0			0
$547$	−2.78552e14			−0.243207			−0.121603	−	0.992579i	$-0.538804\pi$
$547$	−2.78552e14			−0.243207			−0.121603	+	0.992579i	$0.538804\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.62701e14	+	2.81806e14i	0.136476	+	0.236383i
$552$		0			0
$553$	8.76033e14	−	4.05401e14i	0.720332	−	0.333347i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.78466e14	+	5.07183e14i	0.694259	+	0.400831i	0.805206	−	0.592996i	$-0.202055\pi$
$557$	8.78466e14	+	5.07183e14i	0.694259	+	0.400831i	−0.110947	+	0.993826i	$0.535388\pi$
$558$		0			0
$559$		−	4.05773e14i		−	0.314426i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.14888e15	+	1.98992e15i	−0.856012	+	1.48266i	0.0196912	+	0.999806i	$0.493732\pi$
$563$	−1.14888e15	+	1.98992e15i	−0.856012	+	1.48266i	−0.875703	+	0.482850i	$0.839602\pi$
$564$		0			0
$565$	1.13240e15	−	6.53793e14i	0.827436	−	0.477720i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.53352e14	+	3.19478e14i	−0.388941	+	0.224555i	−0.681701	−	0.731631i	$-0.738760\pi$
$569$	−5.53352e14	+	3.19478e14i	−0.388941	+	0.224555i	0.292760	+	0.956186i	$0.405426\pi$
$570$		0			0
$571$	−4.06657e14	+	7.04350e14i	−0.280369	+	0.485613i	−0.971475	−	0.237140i	$-0.923790\pi$
$571$	−4.06657e14	+	7.04350e14i	−0.280369	+	0.485613i	0.691107	+	0.722752i	$0.257123\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			5.67995e14i			0.376853i
$576$		0			0
$577$	−1.83403e14	−	1.05888e14i	−0.119382	−	0.0689253i	0.439120	−	0.898429i	$-0.355290\pi$
$577$	−1.83403e14	−	1.05888e14i	−0.119382	−	0.0689253i	−0.558502	+	0.829503i	$0.688624\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	9.95483e13	−	1.10093e15i	0.0623828	−	0.689906i
$582$		0			0
$583$	−1.52550e14	−	2.64224e14i	−0.0938067	−	0.162478i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−1.12299e15			−0.665066			−0.332533	−	0.943092i	$-0.607903\pi$
$587$	−1.12299e15			−0.665066			−0.332533	+	0.943092i	$0.607903\pi$
$588$		0			0
$589$	1.14805e15			0.667307
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.64461e14	+	1.15088e15i	0.372108	+	0.644510i	0.989890	−	0.141840i	$-0.0453019\pi$
$593$	6.64461e14	+	1.15088e15i	0.372108	+	0.644510i	−0.617782	+	0.786350i	$0.711969\pi$
$594$		0			0
$595$	−1.70704e14	+	1.88786e15i	−0.0938429	+	1.03783i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	2.42460e15	+	1.39984e15i	1.28467	+	0.741705i	0.977698	−	0.210014i	$-0.0673509\pi$
$599$	2.42460e15	+	1.39984e15i	1.28467	+	0.741705i	0.306972	+	0.951719i	$0.400684\pi$
$600$		0			0
$601$			1.11706e15i			0.581121i	0.956857	+	0.290560i	$0.0938417\pi$
$601$			1.11706e15i			0.581121i	−0.956857	+	0.290560i	$0.906158\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	3.52756e14	−	6.10991e14i	0.176938	−	0.306465i
$606$		0			0
$607$	−1.84629e15	+	1.06595e15i	−0.909413	+	0.525050i	−0.880242	−	0.474525i	$-0.842620\pi$
$607$	−1.84629e15	+	1.06595e15i	−0.909413	+	0.525050i	−0.0291707	+	0.999574i	$0.509287\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.36490e14	−	7.88023e13i	0.0648445	−	0.0374380i
$612$		0			0
$613$	9.32483e14	−	1.61511e15i	0.435119	−	0.753649i	−0.562186	−	0.827011i	$-0.690040\pi$
$613$	9.32483e14	−	1.61511e15i	0.435119	−	0.753649i	0.997305	+	0.0733621i	$0.0233729\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	1.84138e15i		−	0.829038i	−0.910041	−	0.414519i	$-0.863950\pi$
$617$		−	1.84138e15i		−	0.829038i	0.910041	−	0.414519i	$-0.136050\pi$
$618$		0			0
$619$	3.70065e14	+	2.13657e14i	0.163674	+	0.0944971i	0.579599	−	0.814902i	$-0.303209\pi$
$619$	3.70065e14	+	2.13657e14i	0.163674	+	0.0944971i	−0.415926	+	0.909399i	$0.636542\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.37917e15	+	6.38238e14i	−0.588754	+	0.272457i
$624$		0			0
$625$	5.19420e14	+	8.99662e14i	0.217860	+	0.377345i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	3.26700e15			1.32303
$630$		0			0
$631$	1.90101e15			0.756524			0.378262	−	0.925699i	$-0.376522\pi$
$631$	1.90101e15			0.756524			0.378262	+	0.925699i	$0.376522\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−7.32648e14	−	1.26898e15i	−0.281605	−	0.487753i
$636$		0			0
$637$	8.37501e14	−	4.59320e15i	0.316387	−	1.73519i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.82632e15	−	1.63178e15i	−1.03158	−	0.595582i	−0.114142	−	0.993464i	$-0.536412\pi$
$641$	−2.82632e15	−	1.63178e15i	−1.03158	−	0.595582i	−0.917436	+	0.397882i	$0.869745\pi$
$642$		0			0
$643$			2.88521e15i			1.03518i	0.855628	+	0.517592i	$0.173171\pi$
$643$			2.88521e15i			1.03518i	−0.855628	+	0.517592i	$0.826829\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−6.53543e14	+	1.13197e15i	−0.226621	+	0.392520i	−0.956805	−	0.290732i	$-0.906101\pi$
$647$	−6.53543e14	+	1.13197e15i	−0.226621	+	0.392520i	0.730183	+	0.683251i	$0.239435\pi$
$648$		0			0
$649$	−1.53415e15	+	8.85740e14i	−0.523023	+	0.301968i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.43899e15	+	8.30799e14i	−0.474279	+	0.273825i	−0.718029	−	0.696013i	$-0.754956\pi$
$653$	−1.43899e15	+	8.30799e14i	−0.474279	+	0.273825i	0.243750	+	0.969838i	$0.421622\pi$
$654$		0			0
$655$	1.20657e15	−	2.08985e15i	0.391045	−	0.677310i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	3.70468e15i		−	1.16113i	−0.814213	−	0.580566i	$-0.802831\pi$
$659$		−	3.70468e15i		−	1.16113i	0.814213	−	0.580566i	$-0.197169\pi$
$660$		0			0
$661$	−1.81563e15	−	1.04825e15i	−0.559654	−	0.323116i	0.193353	−	0.981129i	$-0.438064\pi$
$661$	−1.81563e15	−	1.04825e15i	−0.559654	−	0.323116i	−0.753006	+	0.658013i	$0.771397\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−9.46599e14	+	1.34354e15i	−0.282259	+	0.400620i
$666$		0			0
$667$	6.87461e14	+	1.19072e15i	0.201630	+	0.349234i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.72301e14			−0.0772814
$672$		0			0
$673$	7.70894e14			0.215235			0.107617	−	0.994192i	$-0.465678\pi$
$673$	7.70894e14			0.215235			0.107617	+	0.994192i	$0.465678\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.62878e15	−	2.82114e15i	−0.440176	−	0.762407i	0.557527	−	0.830159i	$-0.311750\pi$
$677$	−1.62878e15	−	2.82114e15i	−0.440176	−	0.762407i	−0.997702	+	0.0677526i	$0.978417\pi$
$678$		0			0
$679$	−3.54060e14	−	3.20149e13i	−0.0941441	−	0.00851272i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.96071e15	−	1.13201e15i	−0.504776	−	0.291432i	0.225908	−	0.974149i	$-0.427465\pi$
$683$	−1.96071e15	−	1.13201e15i	−0.504776	−	0.291432i	−0.730684	+	0.682716i	$0.760799\pi$
$684$		0			0
$685$		−	2.93818e15i		−	0.744355i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.15784e14	−	1.58618e15i	0.224692	−	0.389178i
$690$		0			0
$691$	−4.07062e15	+	2.35017e15i	−0.982949	+	0.567506i	−0.903159	−	0.429306i	$-0.858758\pi$
$691$	−4.07062e15	+	2.35017e15i	−0.982949	+	0.567506i	−0.0797900	+	0.996812i	$0.525425\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.29009e15	−	1.32218e15i	0.535717	−	0.309296i
$696$		0			0
$697$	−5.22870e15	+	9.05638e15i	−1.20396	+	2.08533i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	4.94415e15i		−	1.10317i	−0.834118	−	0.551586i	$-0.814023\pi$
$701$		−	4.94415e15i		−	1.10317i	0.834118	−	0.551586i	$-0.185977\pi$
$702$		0			0
$703$	2.45311e15	+	1.41630e15i	0.538843	+	0.311101i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.14827e15	−	1.51357e15i	−0.457385	−	0.322253i
$708$		0			0
$709$	1.39341e15	+	2.41346e15i	0.292096	+	0.505925i	0.974305	−	0.225232i	$-0.0723139\pi$
$709$	1.39341e15	+	2.41346e15i	0.292096	+	0.505925i	−0.682209	+	0.731157i	$0.738981\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.85086e15			0.985884
$714$		0			0
$715$	−5.01701e15			−1.00406
$716$		0			0
$717$		0			0
$718$		0			0
$719$	3.58865e13	+	6.21573e13i	0.00696502	+	0.0120638i	0.869487	−	0.493956i	$-0.164450\pi$
$719$	3.58865e13	+	6.21573e13i	0.00696502	+	0.0120638i	−0.862522	+	0.506020i	$0.831116\pi$
$720$		0			0
$721$	−3.02803e15	−	6.54328e15i	−0.578783	−	1.25070i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−8.09216e14	−	4.67201e14i	−0.150039	−	0.0866253i
$726$		0			0
$727$		−	8.98933e15i		−	1.64168i	−0.571160	−	0.820839i	$-0.693506\pi$
$727$		−	8.98933e15i		−	1.64168i	0.571160	−	0.820839i	$-0.306494\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.78052e14	−	1.17442e15i	0.120148	−	0.208103i
$732$		0			0
$733$	1.18189e15	−	6.82366e14i	0.206303	−	0.119109i	−0.393289	−	0.919415i	$-0.628663\pi$
$733$	1.18189e15	−	6.82366e14i	0.206303	−	0.119109i	0.599592	+	0.800306i	$0.295329\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.68718e14	−	9.74093e13i	0.0285818	−	0.0165017i
$738$		0			0
$739$	−4.91302e15	+	8.50959e15i	−0.819981	+	1.42025i	0.0857143	+	0.996320i	$0.472683\pi$
$739$	−4.91302e15	+	8.50959e15i	−0.819981	+	1.42025i	−0.905695	+	0.423929i	$0.860651\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	8.69770e15i		−	1.40918i	−0.709615	−	0.704589i	$-0.751131\pi$
$743$		−	8.69770e15i		−	1.40918i	0.709615	−	0.704589i	$-0.248869\pi$
$744$		0			0
$745$	−5.56030e15	−	3.21024e15i	−0.887643	−	0.512481i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.06744e15	+	4.46754e15i	0.320467	+	0.692498i
$750$		0			0
$751$	1.22886e15	+	2.12846e15i	0.187709	+	0.325121i	0.944486	−	0.328552i	$-0.106561\pi$
$751$	1.22886e15	+	2.12846e15i	0.187709	+	0.325121i	−0.756777	+	0.653673i	$0.773227\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.06855e15			−1.19698
$756$		0			0
$757$	−4.16763e15			−0.609343			−0.304672	−	0.952457i	$-0.598547\pi$
$757$	−4.16763e15			−0.609343			−0.304672	+	0.952457i	$0.598547\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.25729e15	−	5.64179e15i	−0.462637	−	0.801311i	0.536454	−	0.843929i	$-0.319763\pi$
$761$	−3.25729e15	−	5.64179e15i	−0.462637	−	0.801311i	−0.999091	+	0.0426182i	$0.986430\pi$
$762$		0			0
$763$	5.72211e15	+	4.03154e15i	0.801072	+	0.564398i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.20977e15	−	5.31726e15i	−1.25278	−	0.723292i
$768$		0			0
$769$			8.34475e15i			1.11897i	0.828841	+	0.559485i	$0.189001\pi$
$769$			8.34475e15i			1.11897i	−0.828841	+	0.559485i	$0.810999\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.00958e15	−	1.74864e15i	0.131569	−	0.227884i	−0.792713	−	0.609596i	$-0.791332\pi$
$773$	1.00958e15	−	1.74864e15i	0.131569	−	0.227884i	0.924282	+	0.381711i	$0.124665\pi$
$774$		0			0
$775$	−2.85499e15	+	1.64833e15i	−0.366813	+	0.211780i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−7.85221e15	+	4.53348e15i	−0.980700	+	0.566207i
$780$		0			0
$781$	−2.65449e15	+	4.59770e15i	−0.326889	+	0.566188i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			3.10555e15i			0.371839i
$786$		0			0
$787$	−8.41249e15	−	4.85695e15i	−0.993261	−	0.573460i	−0.0870138	−	0.996207i	$-0.527732\pi$
$787$	−8.41249e15	−	4.85695e15i	−0.993261	−	0.573460i	−0.906248	+	0.422747i	$0.861066\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.07199e16	−	9.69319e14i	−1.23089	−	0.111300i
$792$		0			0
$793$	−8.17336e14	−	1.41567e15i	−0.0925546	−	0.160309i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.76310e15			0.304352			0.152176	−	0.988353i	$-0.451372\pi$
$797$	2.76310e15			0.304352			0.152176	+	0.988353i	$0.451372\pi$
$798$		0			0
$799$	5.26719e14			0.0572232
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.12982e15	−	5.42101e15i	−0.330814	−	0.572987i
$804$		0			0
$805$	−3.99967e15	+	5.67689e15i	−0.417011	+	0.591879i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	5.30508e15	+	3.06289e15i	0.538239	+	0.310753i	0.744365	−	0.667773i	$-0.232752\pi$
$809$	5.30508e15	+	3.06289e15i	0.538239	+	0.310753i	−0.206126	+	0.978526i	$0.566086\pi$
$810$		0			0
$811$			6.61829e15i			0.662416i	0.943558	+	0.331208i	$0.107456\pi$
$811$			6.61829e15i			0.662416i	−0.943558	+	0.331208i	$0.892544\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.16144e15	+	8.93987e15i	−0.502810	+	0.870892i
$816$		0			0
$817$	1.01827e15	−	5.87896e14i	0.0978678	−	0.0565040i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.62451e15	−	2.09261e15i	0.339126	−	0.195795i	−0.320759	−	0.947161i	$-0.603938\pi$
$821$	3.62451e15	−	2.09261e15i	0.339126	−	0.195795i	0.659886	+	0.751366i	$0.270605\pi$
$822$		0			0
$823$	6.57169e14	−	1.13825e15i	0.0606705	−	0.105084i	−0.834095	−	0.551621i	$-0.814009\pi$
$823$	6.57169e14	−	1.13825e15i	0.0606705	−	0.105084i	0.894765	+	0.446537i	$0.147343\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	6.09328e15i		−	0.547735i	−0.961767	−	0.273868i	$-0.911697\pi$
$827$		−	6.09328e15i		−	0.547735i	0.961767	−	0.273868i	$-0.0883030\pi$
$828$		0			0
$829$	−9.63913e15	−	5.56515e15i	−0.855043	−	0.493659i	0.00730638	−	0.999973i	$-0.497674\pi$
$829$	−9.63913e15	−	5.56515e15i	−0.855043	−	0.493659i	−0.862349	+	0.506314i	$0.831008\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.00993e16	−	1.18945e16i	0.872453	−	1.02754i
$834$		0			0
$835$	2.10244e15	+	3.64154e15i	0.179246	+	0.310462i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−4.85748e15			−0.403386			−0.201693	−	0.979449i	$-0.564644\pi$
$839$	−4.85748e15			−0.403386			−0.201693	+	0.979449i	$0.564644\pi$
$840$		0			0
$841$	9.93864e15			0.814609
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.02184e16	−	1.76989e16i	−0.815967	−	1.41330i
$846$		0			0
$847$	−5.27056e15	+	2.43905e15i	−0.415430	+	0.192248i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.03651e16	+	5.98432e15i	0.796091	+	0.459623i
$852$		0			0
$853$			3.57207e15i			0.270832i	0.990789	+	0.135416i	$0.0432371\pi$
$853$			3.57207e15i			0.270832i	−0.990789	+	0.135416i	$0.956763\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	8.97203e15	−	1.55400e16i	0.662973	−	1.14830i	−0.316857	−	0.948473i	$-0.602628\pi$
$857$	8.97203e15	−	1.55400e16i	0.662973	−	1.14830i	0.979831	−	0.199830i	$-0.0640391\pi$
$858$		0			0
$859$	1.29801e16	−	7.49404e15i	0.946923	−	0.546706i	0.0547990	−	0.998497i	$-0.482548\pi$
$859$	1.29801e16	−	7.49404e15i	0.946923	−	0.546706i	0.892124	+	0.451791i	$0.149215\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	9.90372e15	−	5.71792e15i	0.704270	−	0.406610i	−0.104666	−	0.994507i	$-0.533377\pi$
$863$	9.90372e15	−	5.71792e15i	0.704270	−	0.406610i	0.808936	+	0.587897i	$0.200044\pi$
$864$		0			0
$865$	9.18999e15	−	1.59175e16i	0.645247	−	1.11760i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			8.53838e15i			0.584476i
$870$		0			0
$871$	1.01284e15	+	5.84766e14i	0.0684610	+	0.0395260i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.48125e15	−	1.63815e16i	0.0976305	−	1.07972i
$876$		0			0
$877$	−1.35712e16	−	2.35061e16i	−0.883328	−	1.52997i	−0.847619	−	0.530606i	$-0.821964\pi$
$877$	−1.35712e16	−	2.35061e16i	−0.883328	−	1.52997i	−0.0357088	−	0.999362i	$-0.511369\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.01673e16			0.645415			0.322708	−	0.946499i	$-0.395407\pi$
$881$	1.01673e16			0.645415			0.322708	+	0.946499i	$0.395407\pi$
$882$		0			0
$883$	5.68150e15			0.356188			0.178094	−	0.984013i	$-0.443007\pi$
$883$	5.68150e15			0.356188			0.178094	+	0.984013i	$0.443007\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.16448e15	−	5.48105e15i	−0.193519	−	0.335184i	0.752895	−	0.658140i	$-0.228657\pi$
$887$	−3.16448e15	−	5.48105e15i	−0.193519	−	0.335184i	−0.946414	+	0.322956i	$0.895323\pi$
$888$		0			0
$889$	−1.08623e15	+	1.20129e16i	−0.0656088	+	0.725582i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.95501e14	+	2.28343e14i	0.0233058	+	0.0134556i
$894$		0			0
$895$			2.09443e14i			0.0121910i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.99004e15	+	6.91095e15i	−0.226620	+	0.392518i
$900$		0			0
$901$	5.30107e15	−	3.06058e15i	0.297425	−	0.171718i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.96600e16	−	1.13507e16i	1.07650	−	0.621520i
$906$		0			0
$907$	−8.38089e15	+	1.45161e16i	−0.453367	+	0.785255i	−0.998593	−	0.0530343i	$-0.983111\pi$
$907$	−8.38089e15	+	1.45161e16i	−0.453367	+	0.785255i	0.545225	+	0.838290i	$0.316444\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			3.45702e16i			1.82537i	0.408663	+	0.912685i	$0.365995\pi$
$911$			3.45702e16i			1.82537i	−0.408663	+	0.912685i	$0.634005\pi$
$912$		0			0
$913$	8.46789e15	+	4.88894e15i	0.441759	+	0.255050i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.80275e16	+	8.34258e15i	−0.918131	+	0.424883i
$918$		0			0
$919$	1.22072e16	+	2.11435e16i	0.614300	+	1.06400i	0.990507	+	0.137463i	$0.0438947\pi$
$919$	1.22072e16	+	2.11435e16i	0.614300	+	1.06400i	−0.376207	+	0.926536i	$0.622772\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.18707e16			−1.56597
$924$		0			0
$925$	−8.13392e15			−0.394930
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.85208e16	+	3.20790e16i	0.878159	+	1.52102i	0.853359	+	0.521323i	$0.174561\pi$
$929$	1.85208e16	+	3.20790e16i	0.878159	+	1.52102i	0.0247998	+	0.999692i	$0.492105\pi$
$930$		0			0
$931$	1.27398e16	−	4.55310e15i	0.596951	−	0.213346i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.45206e16	−	8.38350e15i	−0.664541	−	0.383673i
$936$		0			0
$937$		−	7.23185e15i		−	0.327101i	−0.986535	−	0.163551i	$-0.947705\pi$
$937$		−	7.23185e15i		−	0.327101i	0.986535	−	0.163551i	$-0.0522947\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.75183e16	+	3.03425e16i	−0.774013	+	1.34063i	0.161334	+	0.986900i	$0.448420\pi$
$941$	−1.75183e16	+	3.03425e16i	−0.774013	+	1.34063i	−0.935347	+	0.353731i	$0.884913\pi$
$942$		0			0
$943$	−3.31780e16	+	1.91553e16i	−1.44889	+	0.836518i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.49218e15	+	2.01621e15i	−0.148995	+	0.0860223i	−0.572644	−	0.819804i	$-0.694082\pi$
$947$	−3.49218e15	+	2.01621e15i	−0.148995	+	0.0860223i	0.423649	+	0.905826i	$0.360749\pi$
$948$		0			0
$949$	1.87889e16	−	3.25433e16i	0.792387	−	1.37245i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			3.25006e16i			1.33931i	0.742673	+	0.669654i	$0.233558\pi$
$953$			3.25006e16i			1.33931i	−0.742673	+	0.669654i	$0.766442\pi$
$954$		0			0
$955$	1.35055e16	+	7.79739e15i	0.550163	+	0.317637i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.39303e16	+	1.97717e16i	−0.554570	+	0.787123i
$960$		0			0
$961$	1.37300e15	+	2.37810e15i	0.0540370	+	0.0935948i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.34548e16			0.902261
$966$		0			0
$967$	3.04765e15			0.115910			0.0579548	−	0.998319i	$-0.481542\pi$
$967$	3.04765e15			0.115910			0.0579548	+	0.998319i	$0.481542\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.08078e16	+	1.87197e16i	0.401821	+	0.695974i	0.993946	−	0.109872i	$-0.0350441\pi$
$971$	1.08078e16	+	1.87197e16i	0.401821	+	0.695974i	−0.592125	+	0.805846i	$0.701711\pi$
$972$		0			0
$973$	−2.16792e16	−	1.96028e15i	−0.796933	−	0.0720604i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.84288e16	+	1.64134e16i	1.02174	+	0.589900i	0.914606	−	0.404345i	$-0.132501\pi$
$977$	2.84288e16	+	1.64134e16i	1.02174	+	0.589900i	0.107130	+	0.994245i	$0.465834\pi$
$978$		0			0
$979$		−	1.34423e16i		−	0.477714i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.47053e16	−	4.27909e16i	0.858512	−	1.48699i	−0.0148358	−	0.999890i	$-0.504723\pi$
$983$	2.47053e16	−	4.27909e16i	0.858512	−	1.48699i	0.873348	−	0.487097i	$-0.161944\pi$
$984$		0			0
$985$	3.37524e16	−	1.94869e16i	1.15986	−	0.669645i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	4.30249e15	−	2.48404e15i	0.144591	−	0.0834794i
$990$		0			0
$991$	−3.07374e15	+	5.32387e15i	−0.102155	+	0.176938i	−0.912572	−	0.408915i	$-0.865907\pi$
$991$	−3.07374e15	+	5.32387e15i	−0.102155	+	0.176938i	0.810417	+	0.585853i	$0.199241\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	8.66225e15i		−	0.281581i
$996$		0			0
$997$	1.48816e16	+	8.59188e15i	0.478438	+	0.276226i	0.719765	−	0.694218i	$-0.244249\pi$
$997$	1.48816e16	+	8.59188e15i	0.478438	+	0.276226i	−0.241328	+	0.970444i	$0.577583\pi$
$998$		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.17.22	yes	60
3.2	odd	2	inner	252.12.t.a.17.9	✓	60
7.5	odd	6	inner	252.12.t.a.89.9	yes	60
21.5	even	6	inner	252.12.t.a.89.22	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.9	✓	60	3.2	odd	2	inner
252.12.t.a.17.22	yes	60	1.1	even	1	trivial
252.12.t.a.89.9	yes	60	7.5	odd	6	inner
252.12.t.a.89.22	yes	60	21.5	even	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)

\(f(q)\)	\(=\)	\(q+(2700.97 + 4678.22i) q^{5} +(4004.48 - 44286.5i) q^{7} +O(q^{10})\)	\(q+(2700.97 + 4678.22i) q^{5} +(4004.48 - 44286.5i) q^{7} +(340633. + 196665. i) q^{11} +2.36123e6i q^{13} +(-3.94565e6 + 6.83407e6i) q^{17} +(-5.92539e6 + 3.42102e6i) q^{19} +(-2.50366e7 + 1.44549e7i) q^{23} +(9.82359e6 - 1.70150e7i) q^{25} -4.75591e7i q^{29} +(-1.45313e8 - 8.38965e7i) q^{31} +(2.17998e8 - 1.00883e8i) q^{35} +(-2.07000e8 - 3.58534e8i) q^{37} +1.32518e9 q^{41} -1.71848e8 q^{43} +(-3.33734e7 - 5.78044e7i) q^{47} +(-1.94526e9 - 3.54689e8i) q^{49} +(-6.71761e8 - 3.87842e8i) q^{53} +2.12474e9i q^{55} +(-2.25190e9 + 3.90041e9i) q^{59} +(-5.99546e8 + 3.46148e8i) q^{61} +(-1.10463e10 + 6.37761e9i) q^{65} +(2.47653e8 - 4.28948e8i) q^{67} +1.34975e10i q^{71} +(-1.37824e10 - 7.95725e9i) q^{73} +(1.00736e10 - 1.42979e10i) q^{77} +(1.08540e10 + 1.87996e10i) q^{79} +2.48592e10 q^{83} -4.26283e10 q^{85} +(-1.70878e10 - 2.95969e10i) q^{89} +(1.04571e11 + 9.45550e9i) q^{91} +(-3.20086e10 - 1.84802e10i) q^{95} -7.99477e9i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 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

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