LMFDB - Embedded newform 252.12.t.a.17.28

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			17.28
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5672.42 + 9824.92i) q^{5} +(44073.4 - 5904.51i) q^{7} +O(q^{10})$	$q+(5672.42 + 9824.92i) q^{5} +(44073.4 - 5904.51i) q^{7} +(-847547. - 489331. i) q^{11} +543547. i q^{13} +(1.36376e6 - 2.36209e6i) q^{17} +(-3.62466e6 + 2.09270e6i) q^{19} +(-6.66157e6 + 3.84606e6i) q^{23} +(-3.99387e7 + 6.91758e7i) q^{25} -2.06566e8i q^{29} +(4.21951e7 + 2.43613e7i) q^{31} +(3.08014e8 + 3.99525e8i) q^{35} +(-2.72501e8 - 4.71986e8i) q^{37} +1.42571e9 q^{41} +1.26115e9 q^{43} +(5.06475e8 + 8.77240e8i) q^{47} +(1.90760e9 - 5.20464e8i) q^{49} +(3.80559e9 + 2.19716e9i) q^{53} -1.11028e10i q^{55} +(3.96250e9 - 6.86325e9i) q^{59} +(-1.92948e9 + 1.11399e9i) q^{61} +(-5.34031e9 + 3.08323e9i) q^{65} +(-1.39621e9 + 2.41831e9i) q^{67} +1.07642e10i q^{71} +(-1.48643e9 - 8.58190e8i) q^{73} +(-4.02435e10 - 1.65621e10i) q^{77} +(-1.58790e10 - 2.75033e10i) q^{79} +3.27471e10 q^{83} +3.09432e10 q^{85} +(2.15264e10 + 3.72848e10i) q^{89} +(3.20938e9 + 2.39560e10i) q^{91} +(-4.11212e10 - 2.37414e10i) q^{95} +1.40456e11i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	5672.42	+	9824.92i	0.811771	+	1.40603i	0.911624	+	0.411026i	$0.134829\pi$
$5$	5672.42	+	9824.92i	0.811771	+	1.40603i	−0.0998528	+	0.995002i	$0.531837\pi$
$6$		0			0
$7$	44073.4	−	5904.51i	0.991145	−	0.132784i
$7$	44073.4	−	5904.51i	0.991145	−	0.132784i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−847547.	−	489331.i	−1.58673	−	0.916101i	−0.993841	−	0.110819i	$-0.964653\pi$
$11$	−847547.	−	489331.i	−1.58673	−	0.916101i	−0.592892	−	0.805282i	$-0.702014\pi$
$12$		0			0
$13$			543547.i			0.406021i	0.979177	+	0.203011i	$0.0650726\pi$
$13$			543547.i			0.406021i	−0.979177	+	0.203011i	$0.934927\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.36376e6	−	2.36209e6i	0.232953	−	0.403486i	−0.725723	−	0.687987i	$-0.758495\pi$
$17$	1.36376e6	−	2.36209e6i	0.232953	−	0.403486i	0.958676	+	0.284501i	$0.0918280\pi$
$18$		0			0
$19$	−3.62466e6	+	2.09270e6i	−0.335833	+	0.193893i	−0.658428	−	0.752644i	$-0.728778\pi$
$19$	−3.62466e6	+	2.09270e6i	−0.335833	+	0.193893i	0.322595	+	0.946537i	$0.395445\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.66157e6	+	3.84606e6i	−0.215811	+	0.124598i	−0.604009	−	0.796977i	$-0.706431\pi$
$23$	−6.66157e6	+	3.84606e6i	−0.215811	+	0.124598i	0.388198	+	0.921576i	$0.373098\pi$
$24$		0			0
$25$	−3.99387e7	+	6.91758e7i	−0.817944	+	1.41672i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	2.06566e8i		−	1.87012i	−0.354492	−	0.935059i	$-0.615346\pi$
$29$		−	2.06566e8i		−	1.87012i	0.354492	−	0.935059i	$-0.384654\pi$
$30$		0			0
$31$	4.21951e7	+	2.43613e7i	0.264711	+	0.152831i	0.626482	−	0.779436i	$-0.284494\pi$
$31$	4.21951e7	+	2.43613e7i	0.264711	+	0.152831i	−0.361771	+	0.932267i	$0.617828\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.08014e8	+	3.99525e8i	0.991280	+	1.28579i
$36$		0			0
$37$	−2.72501e8	−	4.71986e8i	−0.646039	−	1.11897i	−0.984060	−	0.177834i	$-0.943091\pi$
$37$	−2.72501e8	−	4.71986e8i	−0.646039	−	1.11897i	0.338021	−	0.941138i	$-0.390242\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.42571e9			1.92185			0.960926	−	0.276806i	$-0.0892760\pi$
$41$	1.42571e9			1.92185			0.960926	+	0.276806i	$0.0892760\pi$
$42$		0			0
$43$	1.26115e9			1.30824			0.654122	−	0.756389i	$-0.273038\pi$
$43$	1.26115e9			1.30824			0.654122	+	0.756389i	$0.273038\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.06475e8	+	8.77240e8i	0.322121	+	0.557931i	0.980926	−	0.194384i	$-0.0622707\pi$
$47$	5.06475e8	+	8.77240e8i	0.322121	+	0.557931i	−0.658804	+	0.752315i	$0.728937\pi$
$48$		0			0
$49$	1.90760e9	−	5.20464e8i	0.964737	−	0.263216i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.80559e9	+	2.19716e9i	1.24999	+	0.721680i	0.971106	−	0.238647i	$-0.0767038\pi$
$53$	3.80559e9	+	2.19716e9i	1.24999	+	0.721680i	0.278879	+	0.960326i	$0.410037\pi$
$54$		0			0
$55$		−	1.11028e10i		−	2.97466i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.96250e9	−	6.86325e9i	0.721577	−	1.24981i	−0.238790	−	0.971071i	$-0.576751\pi$
$59$	3.96250e9	−	6.86325e9i	0.721577	−	1.24981i	0.960367	−	0.278737i	$-0.0899159\pi$
$60$		0			0
$61$	−1.92948e9	+	1.11399e9i	−0.292501	+	0.168875i	−0.639069	−	0.769149i	$-0.720680\pi$
$61$	−1.92948e9	+	1.11399e9i	−0.292501	+	0.168875i	0.346568	+	0.938025i	$0.387347\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.34031e9	+	3.08323e9i	−0.570877	+	0.329596i
$66$		0			0
$67$	−1.39621e9	+	2.41831e9i	−0.126340	+	0.218827i	−0.922256	−	0.386580i	$-0.873656\pi$
$67$	−1.39621e9	+	2.41831e9i	−0.126340	+	0.218827i	0.795916	+	0.605407i	$0.206990\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.07642e10i			0.708042i	0.935237	+	0.354021i	$0.115186\pi$
$71$			1.07642e10i			0.708042i	−0.935237	+	0.354021i	$0.884814\pi$
$72$		0			0
$73$	−1.48643e9	−	8.58190e8i	−0.0839206	−	0.0484516i	0.457452	−	0.889234i	$-0.348762\pi$
$73$	−1.48643e9	−	8.58190e8i	−0.0839206	−	0.0484516i	−0.541373	+	0.840782i	$0.682095\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.02435e10	−	1.65621e10i	−1.69433	−	0.697296i
$78$		0			0
$79$	−1.58790e10	−	2.75033e10i	−0.580598	−	1.00562i	−0.995409	−	0.0957171i	$-0.969486\pi$
$79$	−1.58790e10	−	2.75033e10i	−0.580598	−	1.00562i	0.414811	−	0.909908i	$-0.363848\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.27471e10			0.912523			0.456261	−	0.889846i	$-0.349188\pi$
$83$	3.27471e10			0.912523			0.456261	+	0.889846i	$0.349188\pi$
$84$		0			0
$85$	3.09432e10			0.756417
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.15264e10	+	3.72848e10i	0.408626	+	0.707762i	0.994736	−	0.102470i	$-0.0326745\pi$
$89$	2.15264e10	+	3.72848e10i	0.408626	+	0.707762i	−0.586110	+	0.810232i	$0.699341\pi$
$90$		0			0
$91$	3.20938e9	+	2.39560e10i	0.0539130	+	0.402426i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.11212e10	−	2.37414e10i	−0.545238	−	0.314793i
$96$		0			0
$97$			1.40456e11i			1.66071i	0.557232	+	0.830357i	$0.311863\pi$
$97$			1.40456e11i			1.66071i	−0.557232	+	0.830357i	$0.688137\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−8.20119e8	+	1.42049e9i	−0.00776442	+	0.0134484i	−0.869882	−	0.493261i	$-0.835805\pi$
$101$	−8.20119e8	+	1.42049e9i	−0.00776442	+	0.0134484i	0.862117	+	0.506709i	$0.169138\pi$
$102$		0			0
$103$	1.36046e10	−	7.85462e9i	0.115633	−	0.0667606i	−0.441068	−	0.897474i	$-0.645400\pi$
$103$	1.36046e10	−	7.85462e9i	0.115633	−	0.0667606i	0.556701	+	0.830713i	$0.312067\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.88120e10	+	1.08611e10i	−0.129665	+	0.0748623i	−0.563430	−	0.826164i	$-0.690518\pi$
$107$	−1.88120e10	+	1.08611e10i	−0.129665	+	0.0748623i	0.433764	+	0.901026i	$0.357185\pi$
$108$		0			0
$109$	−8.61218e10	+	1.49167e11i	−0.536127	+	0.928599i	0.462981	+	0.886368i	$0.346780\pi$
$109$	−8.61218e10	+	1.49167e11i	−0.536127	+	0.928599i	−0.999108	+	0.0422306i	$0.986554\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	2.12137e11i		−	1.08314i	−0.840655	−	0.541572i	$-0.817829\pi$
$113$		−	2.12137e11i		−	1.08314i	0.840655	−	0.541572i	$-0.182171\pi$
$114$		0			0
$115$	−7.55744e10	−	4.36329e10i	−0.350378	−	0.202291i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	4.61583e10	−	1.12158e11i	0.177314	−	0.430845i
$120$		0			0
$121$	3.36234e11	+	5.82375e11i	1.17848	+	2.04119i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.52248e11			−1.03239
$126$		0			0
$127$	−6.84011e11			−1.83714			−0.918570	−	0.395257i	$-0.870655\pi$
$127$	−6.84011e11			−1.83714			−0.918570	+	0.395257i	$0.870655\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.36654e11	+	4.09897e11i	0.535947	+	0.928287i	0.999117	+	0.0420178i	$0.0133786\pi$
$131$	2.36654e11	+	4.09897e11i	0.535947	+	0.928287i	−0.463170	+	0.886269i	$0.653288\pi$
$132$		0			0
$133$	−1.47395e11	+	1.13634e11i	−0.307113	+	0.236769i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.39932e11	+	3.11730e11i	0.955820	+	0.551843i	0.894884	−	0.446299i	$-0.147258\pi$
$137$	5.39932e11	+	3.11730e11i	0.955820	+	0.551843i	0.0609357	+	0.998142i	$0.480592\pi$
$138$		0			0
$139$		−	1.13335e12i		−	1.85260i	−0.376782	−	0.926302i	$-0.622969\pi$
$139$		−	1.13335e12i		−	1.85260i	0.376782	−	0.926302i	$-0.377031\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.65975e11	−	4.60681e11i	0.371956	−	0.644247i
$144$		0			0
$145$	2.02949e12	−	1.17173e12i	2.62944	−	1.51811i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.01409e11	−	2.31753e11i	0.447778	−	0.258525i	−0.259114	−	0.965847i	$-0.583430\pi$
$149$	4.01409e11	−	2.31753e11i	0.447778	−	0.258525i	0.706891	+	0.707322i	$0.250097\pi$
$150$		0			0
$151$	4.13906e11	−	7.16907e11i	0.429071	−	0.743172i	−0.567720	−	0.823222i	$-0.692174\pi$
$151$	4.13906e11	−	7.16907e11i	0.429071	−	0.743172i	0.996791	+	0.0800494i	$0.0255078\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			5.52751e11i			0.496255i
$156$		0			0
$157$	−1.53605e12	−	8.86839e11i	−1.28516	−	0.741987i	−0.307373	−	0.951589i	$-0.599450\pi$
$157$	−1.53605e12	−	8.86839e11i	−1.28516	−	0.741987i	−0.977787	+	0.209602i	$0.932783\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.70889e11	+	2.08842e11i	−0.197355	+	0.152151i
$162$		0			0
$163$	5.29329e11	+	9.16825e11i	0.360325	+	0.624101i	0.988014	−	0.154363i	$-0.0493326\pi$
$163$	5.29329e11	+	9.16825e11i	0.360325	+	0.624101i	−0.627690	+	0.778464i	$0.715999\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.70349e12			1.61059			0.805294	−	0.592875i	$-0.202007\pi$
$167$	2.70349e12			1.61059			0.805294	+	0.592875i	$0.202007\pi$
$168$		0			0
$169$	1.49672e12			0.835147
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.21278e11	+	3.83265e11i	0.108564	+	0.188038i	0.915189	−	0.403026i	$-0.132041\pi$
$173$	2.21278e11	+	3.83265e11i	0.108564	+	0.188038i	−0.806625	+	0.591064i	$0.798708\pi$
$174$		0			0
$175$	−1.35178e12	+	3.28463e12i	−0.622583	+	1.51278i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	2.47254e11	+	1.42752e11i	0.100566	+	0.0580618i	0.549439	−	0.835534i	$-0.314841\pi$
$179$	2.47254e11	+	1.42752e11i	0.100566	+	0.0580618i	−0.448874	+	0.893595i	$0.648175\pi$
$180$		0			0
$181$			2.08415e12i			0.797438i	0.917073	+	0.398719i	$0.130545\pi$
$181$			2.08415e12i			0.797438i	−0.917073	+	0.398719i	$0.869455\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.09148e12	−	5.35460e12i	1.04887	−	1.81670i
$186$		0			0
$187$	−2.31169e12	+	1.33466e12i	−0.739267	+	0.426816i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.09461e12	+	1.20932e12i	−0.596237	+	0.344237i	−0.767560	−	0.640978i	$-0.778529\pi$
$191$	−2.09461e12	+	1.20932e12i	−0.596237	+	0.344237i	0.171323	+	0.985215i	$0.445196\pi$
$192$		0			0
$193$	−1.97395e12	+	3.41897e12i	−0.530603	+	0.919032i	0.468759	+	0.883326i	$0.344701\pi$
$193$	−1.97395e12	+	3.41897e12i	−0.530603	+	0.919032i	−0.999362	+	0.0357058i	$0.988632\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			2.09391e12i			0.502799i	0.967883	+	0.251399i	$0.0808908\pi$
$197$			2.09391e12i			0.502799i	−0.967883	+	0.251399i	$0.919109\pi$
$198$		0			0
$199$	−1.52666e12	−	8.81418e11i	−0.346777	−	0.200212i	0.316488	−	0.948597i	$-0.397496\pi$
$199$	−1.52666e12	−	8.81418e11i	−0.346777	−	0.200212i	−0.663265	+	0.748385i	$0.730830\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.21967e12	−	9.10405e12i	−0.248321	−	1.85356i
$204$		0			0
$205$	8.08722e12	+	1.40075e13i	1.56010	+	2.70218i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.09609e12			0.710502
$210$		0			0
$211$	−7.46673e11			−0.122907			−0.0614536	−	0.998110i	$-0.519574\pi$
$211$	−7.46673e11			−0.122907			−0.0614536	+	0.998110i	$0.519574\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	7.15375e12	+	1.23907e13i	1.06199	+	1.83943i
$216$		0			0
$217$	2.00352e12	+	8.24545e11i	0.282661	+	0.116328i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.28391e12	+	7.41265e11i	0.163824	+	0.0945837i
$222$		0			0
$223$		−	2.85629e12i		−	0.346837i	−0.984848	−	0.173418i	$-0.944519\pi$
$223$		−	2.85629e12i		−	0.346837i	0.984848	−	0.173418i	$-0.0554813\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.41032e12	−	9.37096e12i	0.595773	−	1.03191i	−0.397664	−	0.917531i	$-0.630179\pi$
$227$	5.41032e12	−	9.37096e12i	0.595773	−	1.03191i	0.993437	−	0.114379i	$-0.0364877\pi$
$228$		0			0
$229$	5.99160e12	−	3.45925e12i	0.628706	−	0.362984i	−0.151545	−	0.988450i	$-0.548425\pi$
$229$	5.99160e12	−	3.45925e12i	0.628706	−	0.362984i	0.780251	+	0.625467i	$0.215091\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.92245e12	+	3.41933e12i	−0.564994	+	0.326199i	−0.755147	−	0.655555i	$-0.772435\pi$
$233$	−5.92245e12	+	3.41933e12i	−0.564994	+	0.326199i	0.190154	+	0.981754i	$0.439101\pi$
$234$		0			0
$235$	−5.74588e12	+	9.95215e12i	−0.522978	+	0.905824i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	2.13050e13i		−	1.76723i	−0.468214	−	0.883615i	$-0.655102\pi$
$239$		−	2.13050e13i		−	1.76723i	0.468214	−	0.883615i	$-0.344898\pi$
$240$		0			0
$241$	3.64493e12	+	2.10440e12i	0.288799	+	0.166738i	0.637400	−	0.770533i	$-0.280010\pi$
$241$	3.64493e12	+	2.10440e12i	0.288799	+	0.166738i	−0.348601	+	0.937271i	$0.613343\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.59342e13	+	1.57897e13i	1.15323	+	1.14278i
$246$		0			0
$247$	−1.13748e12	−	1.97017e12i	−0.0787247	−	0.136355i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.89516e13			1.20072			0.600359	−	0.799731i	$-0.295024\pi$
$251$	1.89516e13			1.20072			0.600359	+	0.799731i	$0.295024\pi$
$252$		0			0
$253$	7.52799e12			0.456579
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.62580e12	−	8.01212e12i	−0.257368	−	0.445774i	0.708168	−	0.706044i	$-0.249522\pi$
$257$	−4.62580e12	−	8.01212e12i	−0.257368	−	0.445774i	−0.965536	+	0.260270i	$0.916189\pi$
$258$		0			0
$259$	−1.47969e13	−	1.91930e13i	−0.788900	−	1.02328i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.80364e13	+	1.04133e13i	0.883881	+	0.510309i	0.871936	−	0.489620i	$-0.162864\pi$
$263$	1.80364e13	+	1.04133e13i	0.883881	+	0.510309i	0.0119447	+	0.999929i	$0.496198\pi$
$264$		0			0
$265$			4.98529e13i			2.34335i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.01605e13	−	1.75986e13i	0.439824	−	0.761798i	−0.557851	−	0.829941i	$-0.688374\pi$
$269$	1.01605e13	−	1.75986e13i	0.439824	−	0.761798i	0.997676	+	0.0681428i	$0.0217073\pi$
$270$		0			0
$271$	1.57379e13	−	9.08627e12i	0.654056	−	0.377619i	−0.135952	−	0.990715i	$-0.543409\pi$
$271$	1.57379e13	−	9.08627e12i	0.654056	−	0.377619i	0.790008	+	0.613096i	$0.210076\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.76997e13	−	3.90865e13i	2.59572	−	1.49864i
$276$		0			0
$277$	−5.33065e12	+	9.23296e12i	−0.196400	+	0.340175i	−0.947359	−	0.320175i	$-0.896258\pi$
$277$	−5.33065e12	+	9.23296e12i	−0.196400	+	0.340175i	0.750959	+	0.660349i	$0.229592\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			4.90036e13i			1.66857i	0.551336	+	0.834284i	$0.314118\pi$
$281$			4.90036e13i			1.66857i	−0.551336	+	0.834284i	$0.685882\pi$
$282$		0			0
$283$	−1.48641e13	−	8.58181e12i	−0.486759	−	0.281031i	0.236470	−	0.971639i	$-0.424010\pi$
$283$	−1.48641e13	−	8.58181e12i	−0.486759	−	0.281031i	−0.723229	+	0.690608i	$0.757343\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.28358e13	−	8.41812e12i	1.90483	−	0.255191i
$288$		0			0
$289$	1.34163e13	+	2.32377e13i	0.391466	+	0.678039i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.54391e13			0.958762			0.479381	−	0.877607i	$-0.340861\pi$
$293$	3.54391e13			0.958762			0.479381	+	0.877607i	$0.340861\pi$
$294$		0			0
$295$	8.99078e13			2.34302
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−2.09051e12	−	3.62087e12i	−0.0505896	−	0.0876238i
$300$		0			0
$301$	5.55830e13	−	7.44645e12i	1.29666	−	0.173713i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.18897e13	−	1.26380e13i	−0.474887	−	0.274176i
$306$		0			0
$307$			1.56473e13i			0.327476i	0.986504	+	0.163738i	$0.0523552\pi$
$307$			1.56473e13i			0.327476i	−0.986504	+	0.163738i	$0.947645\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.44573e13	−	2.50408e13i	0.281777	−	0.488052i	−0.690046	−	0.723766i	$-0.742410\pi$
$311$	1.44573e13	−	2.50408e13i	0.281777	−	0.488052i	0.971822	+	0.235714i	$0.0757428\pi$
$312$		0			0
$313$	−6.65691e13	+	3.84337e13i	−1.25250	+	0.723133i	−0.971606	−	0.236605i	$-0.923965\pi$
$313$	−6.65691e13	+	3.84337e13i	−1.25250	+	0.723133i	−0.280897	+	0.959738i	$0.590632\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	4.38346e13	−	2.53079e13i	0.769114	−	0.444048i	−0.0634444	−	0.997985i	$-0.520209\pi$
$317$	4.38346e13	−	2.53079e13i	0.769114	−	0.444048i	0.832558	+	0.553937i	$0.186875\pi$
$318$		0			0
$319$	−1.01079e14	+	1.75074e14i	−1.71322	+	2.96738i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.14157e13i			0.180672i
$324$		0			0
$325$	−3.76003e13	−	2.17085e13i	−0.575218	−	0.332102i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.75017e13	+	3.56725e13i	0.393353	+	0.510218i
$330$		0			0
$331$	1.48489e13	+	2.57190e13i	0.205418	+	0.355795i	0.950266	−	0.311440i	$-0.100811\pi$
$331$	1.48489e13	+	2.57190e13i	0.205418	+	0.355795i	−0.744848	+	0.667235i	$0.767478\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−3.16796e13			−0.410235
$336$		0			0
$337$	2.63741e13			0.330532			0.165266	−	0.986249i	$-0.447152\pi$
$337$	2.63741e13			0.330532			0.165266	+	0.986249i	$0.447152\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.38415e13	−	4.12947e13i	−0.280017	−	0.485004i
$342$		0			0
$343$	8.10013e13	−	3.42020e13i	0.921244	−	0.388986i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.45416e14	−	8.39559e13i	−1.55167	−	0.895858i	−0.998006	−	0.0631191i	$-0.979895\pi$
$347$	−1.45416e14	−	8.39559e13i	−1.55167	−	0.895858i	−0.553666	−	0.832739i	$-0.686771\pi$
$348$		0			0
$349$			1.42968e14i			1.47809i	0.673658	+	0.739043i	$0.264722\pi$
$349$			1.42968e14i			1.47809i	−0.673658	+	0.739043i	$0.735278\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.09139e13	−	8.81855e13i	0.494397	−	0.856321i	−0.505582	−	0.862778i	$-0.668722\pi$
$353$	5.09139e13	−	8.81855e13i	0.494397	−	0.856321i	0.999979	+	0.00645776i	$0.00205558\pi$
$354$		0			0
$355$	−1.05757e14	+	6.10588e13i	−0.995527	+	0.574768i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.71458e13	+	5.03136e13i	−0.771306	+	0.445314i	−0.833340	−	0.552760i	$-0.813575\pi$
$359$	−8.71458e13	+	5.03136e13i	−0.771306	+	0.445314i	0.0620341	+	0.998074i	$0.480241\pi$
$360$		0			0
$361$	−4.94863e13	+	8.57129e13i	−0.424811	+	0.735794i
$362$		0			0
$363$		0			0
$364$		0			0
$365$		−	1.94721e13i		−	0.157326i
$366$		0			0
$367$	6.89985e13	+	3.98363e13i	0.540974	+	0.312331i	0.745474	−	0.666535i	$-0.232223\pi$
$367$	6.89985e13	+	3.98363e13i	0.540974	+	0.312331i	−0.204500	+	0.978867i	$0.565557\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.80699e14	+	7.43661e13i	1.33474	+	0.549311i
$372$		0			0
$373$	−6.01347e13	−	1.04156e14i	−0.431247	−	0.746943i	0.565734	−	0.824588i	$-0.308593\pi$
$373$	−6.01347e13	−	1.04156e14i	−0.431247	−	0.746943i	−0.996981	+	0.0776456i	$0.975260\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.12278e14			0.759307
$378$		0			0
$379$	2.62304e14			1.72301			0.861507	−	0.507746i	$-0.169521\pi$
$379$	2.62304e14			1.72301			0.861507	+	0.507746i	$0.169521\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.87691e13	+	1.71073e14i	0.612390	+	1.06069i	0.990836	+	0.135067i	$0.0431249\pi$
$383$	9.87691e13	+	1.71073e14i	0.612390	+	1.06069i	−0.378447	+	0.925623i	$0.623542\pi$
$384$		0			0
$385$	−6.55564e13	−	4.89337e14i	−0.394986	−	2.94831i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.53876e14	+	8.88402e13i	0.875885	+	0.505693i	0.869300	−	0.494286i	$-0.164570\pi$
$389$	1.53876e14	+	8.88402e13i	0.875885	+	0.505693i	0.00658588	+	0.999978i	$0.497904\pi$
$390$		0			0
$391$			2.09803e13i			0.116102i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.80145e14	−	3.12021e14i	0.942624	−	1.63267i
$396$		0			0
$397$	2.68208e14	−	1.54850e14i	1.36497	−	0.788068i	0.374692	−	0.927149i	$-0.377748\pi$
$397$	2.68208e14	−	1.54850e14i	1.36497	−	0.788068i	0.990281	+	0.139082i	$0.0444150\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	9.59794e13	−	5.54137e13i	0.462257	−	0.266884i	−0.250736	−	0.968056i	$-0.580672\pi$
$401$	9.59794e13	−	5.54137e13i	0.462257	−	0.266884i	0.712993	+	0.701171i	$0.247339\pi$
$402$		0			0
$403$	−1.32415e13	+	2.29350e13i	−0.0620527	+	0.107478i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			5.33373e14i			2.36735i
$408$		0			0
$409$	−2.30479e14	−	1.33067e14i	−0.995758	−	0.574901i	−0.0887675	−	0.996052i	$-0.528293\pi$
$409$	−2.30479e14	−	1.33067e14i	−0.995758	−	0.574901i	−0.906990	+	0.421151i	$0.861626\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.34117e14	−	3.25883e14i	0.549234	−	1.33456i
$414$		0			0
$415$	1.85756e14	+	3.21738e14i	0.740759	+	1.28303i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.72173e14			−1.40789			−0.703943	−	0.710256i	$-0.748579\pi$
$419$	−3.72173e14			−1.40789			−0.703943	+	0.710256i	$0.748579\pi$
$420$		0			0
$421$	−1.24304e14			−0.458072			−0.229036	−	0.973418i	$-0.573557\pi$
$421$	−1.24304e14			−0.458072			−0.229036	+	0.973418i	$0.573557\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	1.08933e14	+	1.88678e14i	0.381084	+	0.660057i
$426$		0			0
$427$	−7.84614e13	+	6.04899e13i	−0.267487	+	0.206219i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−2.92157e14	−	1.68677e14i	−0.946219	−	0.546300i	−0.0543148	−	0.998524i	$-0.517297\pi$
$431$	−2.92157e14	−	1.68677e14i	−0.946219	−	0.546300i	−0.891904	+	0.452224i	$0.850631\pi$
$432$		0			0
$433$		−	2.58068e14i		−	0.814798i	−0.913250	−	0.407399i	$-0.866436\pi$
$433$		−	2.58068e14i		−	0.814798i	0.913250	−	0.407399i	$-0.133564\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	1.60973e13	−	2.78813e13i	0.0483176	−	0.0836885i
$438$		0			0
$439$	3.05591e14	−	1.76433e14i	0.894511	−	0.516446i	0.0190955	−	0.999818i	$-0.493921\pi$
$439$	3.05591e14	−	1.76433e14i	0.894511	−	0.516446i	0.875415	+	0.483372i	$0.160588\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.52628e14	+	2.03590e14i	−0.981966	+	0.566938i	−0.902863	−	0.429928i	$-0.858539\pi$
$443$	−3.52628e14	+	2.03590e14i	−0.981966	+	0.566938i	−0.0791030	+	0.996866i	$0.525206\pi$
$444$		0			0
$445$	−2.44214e14	+	4.22990e14i	−0.663422	+	1.14908i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	1.36007e14i		−	0.351727i	−0.984415	−	0.175863i	$-0.943728\pi$
$449$		−	1.36007e14i		−	0.351727i	0.984415	−	0.175863i	$-0.0562717\pi$
$450$		0			0
$451$	−1.20836e15	−	6.97644e14i	−3.04947	−	1.76061i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.17160e14	+	1.67420e14i	−0.522057	+	0.402481i
$456$		0			0
$457$	2.52312e14	+	4.37017e14i	0.592105	+	1.02556i	0.993949	+	0.109847i	$0.0350361\pi$
$457$	2.52312e14	+	4.37017e14i	0.592105	+	1.02556i	−0.401844	+	0.915708i	$0.631631\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.90106e14			−0.648935			−0.324467	−	0.945897i	$-0.605185\pi$
$461$	−2.90106e14			−0.648935			−0.324467	+	0.945897i	$0.605185\pi$
$462$		0			0
$463$	4.79704e14			1.04780			0.523900	−	0.851780i	$-0.324477\pi$
$463$	4.79704e14			1.04780			0.523900	+	0.851780i	$0.324477\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.24029e14	−	3.88029e14i	−0.466725	−	0.808391i	0.532553	−	0.846397i	$-0.321233\pi$
$467$	−2.24029e14	−	3.88029e14i	−0.466725	−	0.808391i	−0.999278	+	0.0380055i	$0.987900\pi$
$468$		0			0
$469$	−4.72568e13	+	1.14827e14i	−0.0961643	+	0.233665i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.06888e15	−	6.17118e14i	−2.07583	−	1.19848i
$474$		0			0
$475$		−	3.34319e14i		−	0.634374i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−2.89637e14	+	5.01666e14i	−0.524818	+	0.909011i	0.474765	+	0.880113i	$0.342533\pi$
$479$	−2.89637e14	+	5.01666e14i	−0.524818	+	0.909011i	−0.999582	+	0.0288983i	$0.990800\pi$
$480$		0			0
$481$	2.56546e14	−	1.48117e14i	0.454327	−	0.262306i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.37997e15	+	7.96724e14i	−2.33501	+	1.34812i
$486$		0			0
$487$	1.68706e14	−	2.92207e14i	0.279075	−	0.483372i	−0.692080	−	0.721821i	$-0.743306\pi$
$487$	1.68706e14	−	2.92207e14i	0.279075	−	0.483372i	0.971155	+	0.238449i	$0.0766389\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			4.14831e13i			0.0656029i	0.999462	+	0.0328015i	$0.0104429\pi$
$491$			4.14831e13i			0.0656029i	−0.999462	+	0.0328015i	$0.989557\pi$
$492$		0			0
$493$	−4.87928e14	−	2.81705e14i	−0.754566	−	0.435649i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.35571e13	+	4.74413e14i	0.0940164	+	0.701772i
$498$		0			0
$499$	8.76955e13	+	1.51893e14i	0.126889	+	0.219778i	0.922470	−	0.386069i	$-0.126167\pi$
$499$	8.76955e13	+	1.51893e14i	0.126889	+	0.219778i	−0.795581	+	0.605848i	$0.792834\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	3.43959e14			0.476303			0.238151	−	0.971228i	$-0.423459\pi$
$503$	3.43959e14			0.476303			0.238151	+	0.971228i	$0.423459\pi$
$504$		0			0
$505$	−1.86082e13			−0.0252117
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.89589e13	+	6.74788e13i	0.0505428	+	0.0875426i	0.890190	−	0.455590i	$-0.150572\pi$
$509$	3.89589e13	+	6.74788e13i	0.0505428	+	0.0875426i	−0.839647	+	0.543132i	$0.817238\pi$
$510$		0			0
$511$	−7.05792e13	−	2.90467e13i	−0.0896111	−	0.0368793i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.54342e14	+	8.91094e13i	0.187735	+	0.108389i
$516$		0			0
$517$		−	9.91336e14i		−	1.18038i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.66979e14	−	4.62422e14i	0.304699	−	0.527753i	−0.672496	−	0.740101i	$-0.734778\pi$
$521$	2.66979e14	−	4.62422e14i	0.304699	−	0.527753i	0.977194	+	0.212348i	$0.0681109\pi$
$522$		0			0
$523$	1.02363e13	−	5.90991e12i	0.0114388	−	0.00660422i	−0.494270	−	0.869309i	$-0.664564\pi$
$523$	1.02363e13	−	5.90991e12i	0.0114388	−	0.00660422i	0.505709	+	0.862704i	$0.331231\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.15088e14	−	6.64458e13i	0.123330	−	0.0712048i
$528$		0			0
$529$	−4.46821e14	+	7.73916e14i	−0.468950	+	0.812246i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			7.74940e14i			0.780312i
$534$		0			0
$535$	−2.13419e14	−	1.23218e14i	−0.210517	−	0.121542i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.87146e15	−	4.92331e14i	−1.77191	−	0.466143i
$540$		0			0
$541$	−1.79508e14	−	3.10916e14i	−0.166532	−	0.288442i	0.770666	−	0.637239i	$-0.219924\pi$
$541$	−1.79508e14	−	3.10916e14i	−0.166532	−	0.288442i	−0.937198	+	0.348797i	$0.886590\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−1.95408e15			−1.74085
$546$		0			0
$547$	−3.40103e14			−0.296948			−0.148474	−	0.988916i	$-0.547436\pi$
$547$	−3.40103e14			−0.296948			−0.148474	+	0.988916i	$0.547436\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.32280e14	+	7.48731e14i	0.362603	+	0.628047i
$552$		0			0
$553$	−8.62237e14	−	1.11841e15i	−0.708987	−	0.919626i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.07690e14	+	3.50850e14i	0.480263	+	0.277280i	0.720526	−	0.693428i	$-0.243900\pi$
$557$	6.07690e14	+	3.50850e14i	0.480263	+	0.277280i	−0.240263	+	0.970708i	$0.577234\pi$
$558$		0			0
$559$			6.85492e14i			0.531175i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.10708e15	−	1.91752e15i	0.824865	−	1.42871i	−0.0771566	−	0.997019i	$-0.524584\pi$
$563$	1.10708e15	−	1.91752e15i	0.824865	−	1.42871i	0.902022	−	0.431690i	$-0.142083\pi$
$564$		0			0
$565$	2.08423e15	−	1.20333e15i	1.52293	−	0.879264i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.79631e14	+	3.92385e14i	−0.477700	+	0.275800i	−0.719458	−	0.694536i	$-0.755610\pi$
$569$	−6.79631e14	+	3.92385e14i	−0.477700	+	0.275800i	0.241757	+	0.970337i	$0.422276\pi$
$570$		0			0
$571$	1.09475e15	−	1.89616e15i	0.754771	−	1.30730i	−0.190717	−	0.981645i	$-0.561081\pi$
$571$	1.09475e15	−	1.89616e15i	0.754771	−	1.30730i	0.945488	−	0.325657i	$-0.105585\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	6.14425e14i		−	0.407658i
$576$		0			0
$577$	−1.88068e14	−	1.08581e14i	−0.122419	−	0.0706784i	0.437540	−	0.899199i	$-0.355850\pi$
$577$	−1.88068e14	−	1.08581e14i	−0.122419	−	0.0706784i	−0.559959	+	0.828520i	$0.689183\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.44328e15	−	1.93356e14i	0.904442	−	0.121168i
$582$		0			0
$583$	−2.15028e15	−	3.72439e15i	−1.32226	−	2.29023i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.10662e15			0.655375			0.327688	−	0.944786i	$-0.393731\pi$
$587$	1.10662e15			0.655375			0.327688	+	0.944786i	$0.393731\pi$
$588$		0			0
$589$	−2.03924e14			−0.118532
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.36066e15	+	2.35673e15i	0.761989	+	1.31980i	0.941824	+	0.336107i	$0.109110\pi$
$593$	1.36066e15	+	2.35673e15i	0.761989	+	1.31980i	−0.179835	+	0.983697i	$0.557556\pi$
$594$		0			0
$595$	1.36377e15	−	1.82704e14i	0.749718	−	0.100440i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.69493e15	−	9.78570e14i	−0.898060	−	0.518495i	−0.0214895	−	0.999769i	$-0.506841\pi$
$599$	−1.69493e15	−	9.78570e14i	−0.898060	−	0.518495i	−0.876570	+	0.481274i	$0.840174\pi$
$600$		0			0
$601$			1.19830e15i			0.623382i	0.950184	+	0.311691i	$0.100895\pi$
$601$			1.19830e15i			0.623382i	−0.950184	+	0.311691i	$0.899105\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.81453e15	+	6.60695e15i	−1.91331	+	3.31396i
$606$		0			0
$607$	−2.20039e15	+	1.27039e15i	−1.08383	+	0.625749i	−0.931927	−	0.362646i	$-0.881873\pi$
$607$	−2.20039e15	+	1.27039e15i	−1.08383	+	0.625749i	−0.151903	+	0.988395i	$0.548540\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.76821e14	+	2.75293e14i	−0.226532	+	0.130788i
$612$		0			0
$613$	1.64809e15	−	2.85457e15i	0.769038	−	1.33201i	−0.169047	−	0.985608i	$-0.554069\pi$
$613$	1.64809e15	−	2.85457e15i	0.769038	−	1.33201i	0.938085	−	0.346405i	$-0.112598\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	3.62412e15i		−	1.63168i	−0.578281	−	0.815838i	$-0.696276\pi$
$617$		−	3.62412e15i		−	1.63168i	0.578281	−	0.815838i	$-0.303724\pi$
$618$		0			0
$619$	3.51621e15	+	2.03008e15i	1.55516	+	0.897874i	0.997708	+	0.0676667i	$0.0215555\pi$
$619$	3.51621e15	+	2.03008e15i	1.55516	+	0.897874i	0.557455	+	0.830207i	$0.311778\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.16889e15	+	1.51617e15i	0.498987	+	0.647236i
$624$		0			0
$625$	−4.79695e13	−	8.30856e13i	−0.0201199	−	0.0348486i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.48650e15			−0.601986
$630$		0			0
$631$	−5.32672e14			−0.211982			−0.105991	−	0.994367i	$-0.533801\pi$
$631$	−5.32672e14			−0.211982			−0.105991	+	0.994367i	$0.533801\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.88000e15	−	6.72035e15i	−1.49134	−	2.58307i
$636$		0			0
$637$	2.82896e14	+	1.03687e15i	0.106871	+	0.391704i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	1.38194e15	+	7.97865e14i	0.504395	+	0.291213i	0.730527	−	0.682884i	$-0.239275\pi$
$641$	1.38194e15	+	7.97865e14i	0.504395	+	0.291213i	−0.226132	+	0.974097i	$0.572608\pi$
$642$		0			0
$643$		−	3.55194e15i		−	1.27440i	−0.770699	−	0.637199i	$-0.780093\pi$
$643$		−	3.55194e15i		−	1.27440i	0.770699	−	0.637199i	$-0.219907\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	2.56072e14	−	4.43530e14i	0.0887951	−	0.153798i	−0.818207	−	0.574924i	$-0.805032\pi$
$647$	2.56072e14	−	4.43530e14i	0.0887951	−	0.153798i	0.907002	+	0.421126i	$0.138365\pi$
$648$		0			0
$649$	−6.71680e15	+	3.87795e15i	−2.28990	+	1.32207i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.78209e15	−	1.60624e15i	0.916958	−	0.529406i	0.0342946	−	0.999412i	$-0.489082\pi$
$653$	2.78209e15	−	1.60624e15i	0.916958	−	0.529406i	0.882663	+	0.470006i	$0.155748\pi$
$654$		0			0
$655$	−2.68480e15	+	4.65021e15i	−0.870132	+	1.50711i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			4.02221e15i			1.26065i	0.776331	+	0.630325i	$0.217078\pi$
$659$			4.02221e15i			1.26065i	−0.776331	+	0.630325i	$0.782922\pi$
$660$		0			0
$661$	5.34624e15	+	3.08665e15i	1.64794	+	0.951437i	0.977890	+	0.209118i	$0.0670593\pi$
$661$	5.34624e15	+	3.08665e15i	1.64794	+	0.951437i	0.670047	+	0.742319i	$0.266274\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.95253e15	−	8.03561e14i	−0.582210	−	0.239607i
$666$		0			0
$667$	7.94463e14	+	1.37605e15i	0.233014	+	0.403592i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.18044e15			0.618828
$672$		0			0
$673$	−4.94961e15			−1.38194			−0.690968	−	0.722885i	$-0.742816\pi$
$673$	−4.94961e15			−1.38194			−0.690968	+	0.722885i	$0.742816\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.41504e15	−	4.18298e15i	−0.652661	−	1.13044i	−0.982475	−	0.186396i	$-0.940319\pi$
$677$	−2.41504e15	−	4.18298e15i	−0.652661	−	1.13044i	0.329814	−	0.944046i	$-0.393014\pi$
$678$		0			0
$679$	8.29322e14	+	6.19036e15i	0.220516	+	1.64601i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.34390e15	+	7.75903e14i	0.345982	+	0.199753i	0.662914	−	0.748695i	$-0.269319\pi$
$683$	1.34390e15	+	7.75903e14i	0.345982	+	0.199753i	−0.316932	+	0.948448i	$0.602653\pi$
$684$		0			0
$685$			7.07305e15i			1.79188i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.19426e15	+	2.06852e15i	−0.293017	+	0.507521i
$690$		0			0
$691$	−1.97697e15	+	1.14141e15i	−0.477388	+	0.275620i	−0.719327	−	0.694671i	$-0.755550\pi$
$691$	−1.97697e15	+	1.14141e15i	−0.477388	+	0.275620i	0.241939	+	0.970291i	$0.422216\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.11351e16	−	6.42884e15i	2.60481	−	1.50389i
$696$		0			0
$697$	1.94432e15	−	3.36766e15i	0.447700	−	0.775440i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	1.12463e15i		−	0.250934i	−0.992098	−	0.125467i	$-0.959957\pi$
$701$		−	1.12463e15i		−	0.250934i	0.992098	−	0.125467i	$-0.0400428\pi$
$702$		0			0
$703$	1.97545e15	+	1.14053e15i	0.433922	+	0.250525i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.77581e13	+	6.74481e13i	−0.00590994	+	0.0143603i
$708$		0			0
$709$	5.98608e14	+	1.03682e15i	0.125484	+	0.217345i	0.921922	−	0.387376i	$-0.126618\pi$
$709$	5.98608e14	+	1.03682e15i	0.125484	+	0.217345i	−0.796438	+	0.604720i	$0.793285\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.74780e14			−0.0761701
$714$		0			0
$715$	6.03488e15			1.20777
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.78353e15	+	3.08916e15i	0.346155	+	0.599558i	0.985563	−	0.169310i	$-0.0541538\pi$
$719$	1.78353e15	+	3.08916e15i	0.346155	+	0.599558i	−0.639408	+	0.768868i	$0.720820\pi$
$720$		0			0
$721$	5.53223e14	−	4.26508e14i	0.105744	−	0.0815236i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.42893e16	+	8.24995e15i	2.64943	+	1.52965i
$726$		0			0
$727$		−	8.83850e15i		−	1.61413i	−0.590461	−	0.807066i	$-0.701054\pi$
$727$		−	8.83850e15i		−	1.61413i	0.590461	−	0.807066i	$-0.298946\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.71990e15	−	2.97895e15i	0.304759	−	0.527858i
$732$		0			0
$733$	5.22741e15	−	3.01805e15i	0.912462	−	0.526810i	0.0312393	−	0.999512i	$-0.490055\pi$
$733$	5.22741e15	−	3.01805e15i	0.912462	−	0.526810i	0.881222	+	0.472702i	$0.156721\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.36671e15	−	1.36642e15i	0.400935	−	0.231480i
$738$		0			0
$739$	3.32223e15	−	5.75428e15i	0.554480	−	0.960387i	−0.443464	−	0.896292i	$-0.646251\pi$
$739$	3.32223e15	−	5.75428e15i	0.554480	−	0.960387i	0.997944	−	0.0640948i	$-0.0204160\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	2.88145e15i		−	0.466845i	−0.972375	−	0.233422i	$-0.925008\pi$
$743$		−	2.88145e15i		−	0.466845i	0.972375	−	0.233422i	$-0.0749925\pi$
$744$		0			0
$745$	4.55392e15	+	2.62921e15i	0.726986	+	0.419725i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−7.64978e14	+	5.89761e14i	−0.118577	+	0.0914169i
$750$		0			0
$751$	−3.28179e15	−	5.68423e15i	−0.501292	−	0.868264i	−0.999999	−	0.00149285i	$-0.999525\pi$
$751$	−3.28179e15	−	5.68423e15i	−0.501292	−	0.868264i	0.498707	−	0.866771i	$-0.333809\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	9.39140e15			1.39323
$756$		0			0
$757$	−8.36197e15			−1.22259			−0.611296	−	0.791402i	$-0.709351\pi$
$757$	−8.36197e15			−1.22259			−0.611296	+	0.791402i	$0.709351\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.00249e15	+	8.66456e15i	0.710510	+	1.23064i	0.964666	+	0.263476i	$0.0848691\pi$
$761$	5.00249e15	+	8.66456e15i	0.710510	+	1.23064i	−0.254156	+	0.967163i	$0.581798\pi$
$762$		0			0
$763$	−2.91492e15	+	7.08282e15i	−0.408077	+	0.991565i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.73050e15	+	2.15380e15i	0.507449	+	0.292976i
$768$		0			0
$769$			8.89426e15i			1.19266i	0.802741	+	0.596328i	$0.203374\pi$
$769$			8.89426e15i			1.19266i	−0.802741	+	0.596328i	$0.796626\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.51479e14	−	1.47480e15i	0.110965	−	0.192197i	−0.805195	−	0.593011i	$-0.797939\pi$
$773$	8.51479e14	−	1.47480e15i	0.110965	−	0.192197i	0.916160	+	0.400813i	$0.131272\pi$
$774$		0			0
$775$	−3.37043e15	+	1.94592e15i	−0.433038	+	0.250014i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.16772e15	+	2.98358e15i	−0.645420	+	0.372634i
$780$		0			0
$781$	5.26724e15	−	9.12312e15i	0.648638	−	1.12347i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	2.01221e16i		−	2.40929i
$786$		0			0
$787$	8.60191e15	+	4.96631e15i	1.01563	+	0.586372i	0.912834	−	0.408331i	$-0.133889\pi$
$787$	8.60191e15	+	4.96631e15i	1.01563	+	0.586372i	0.102792	+	0.994703i	$0.467222\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.25257e15	−	9.34962e15i	−0.143824	−	1.07355i
$792$		0			0
$793$	−6.05505e14	−	1.04877e15i	−0.0685670	−	0.118762i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.37303e15			0.591832			0.295916	−	0.955214i	$-0.404375\pi$
$797$	5.37303e15			0.591832			0.295916	+	0.955214i	$0.404375\pi$
$798$		0			0
$799$	2.76283e15			0.300156
$800$		0			0
$801$		0			0
$802$		0			0
$803$	8.39879e14	+	1.45471e15i	0.0887731	+	0.153759i
$804$		0			0
$805$	−3.58845e15	−	1.47682e15i	−0.374136	−	0.153975i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−7.30338e14	−	4.21661e14i	−0.0740981	−	0.0427805i	0.462493	−	0.886623i	$-0.346955\pi$
$809$	−7.30338e14	−	4.21661e14i	−0.0740981	−	0.0427805i	−0.536591	+	0.843842i	$0.680288\pi$
$810$		0			0
$811$			4.57944e15i			0.458350i	0.973385	+	0.229175i	$0.0736029\pi$
$811$			4.57944e15i			0.458350i	−0.973385	+	0.229175i	$0.926397\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.00516e15	+	1.04012e16i	−0.585002	+	1.01325i
$816$		0			0
$817$	−4.57123e15	+	2.63920e15i	−0.439351	+	0.253659i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.43417e15	+	1.40537e15i	−0.227752	+	0.131493i	−0.609535	−	0.792759i	$-0.708644\pi$
$821$	−2.43417e15	+	1.40537e15i	−0.227752	+	0.131493i	0.381782	+	0.924252i	$0.375310\pi$
$822$		0			0
$823$	−6.89192e15	+	1.19372e16i	−0.636269	+	1.10205i	0.349975	+	0.936759i	$0.386190\pi$
$823$	−6.89192e15	+	1.19372e16i	−0.636269	+	1.10205i	−0.986245	+	0.165292i	$0.947143\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1.13698e16i		−	1.02205i	−0.859566	−	0.511025i	$-0.829266\pi$
$827$		−	1.13698e16i		−	1.02205i	0.859566	−	0.511025i	$-0.170734\pi$
$828$		0			0
$829$	−3.30996e15	−	1.91100e15i	−0.293611	−	0.169516i	0.345958	−	0.938250i	$-0.387554\pi$
$829$	−3.30996e15	−	1.91100e15i	−0.293611	−	0.169516i	−0.639569	+	0.768734i	$0.720887\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.37212e15	−	5.21572e15i	0.118534	−	0.450574i
$834$		0			0
$835$	1.53353e16	+	2.65616e16i	1.30743	+	2.26453i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−6.96283e13			−0.00578223			−0.00289111	−	0.999996i	$-0.500920\pi$
$839$	−6.96283e13			−0.00578223			−0.00289111	+	0.999996i	$0.500920\pi$
$840$		0			0
$841$	−3.04688e16			−2.49734
$842$		0			0
$843$		0			0
$844$		0			0
$845$	8.49001e15	+	1.47051e16i	0.677948	+	1.17424i
$846$		0			0
$847$	1.82576e16	+	2.36819e16i	1.43908	+	1.86663i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.63057e15	+	2.09611e15i	0.278845	+	0.160991i
$852$		0			0
$853$		−	1.16787e16i		−	0.885473i	−0.896652	−	0.442736i	$-0.854008\pi$
$853$		−	1.16787e16i		−	0.885473i	0.896652	−	0.442736i	$-0.145992\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.16335e16	−	2.01497e16i	0.859635	−	1.48893i	−0.0126426	−	0.999920i	$-0.504024\pi$
$857$	1.16335e16	−	2.01497e16i	0.859635	−	1.48893i	0.872278	−	0.489011i	$-0.162642\pi$
$858$		0			0
$859$	1.76931e16	−	1.02151e16i	1.29075	−	0.745216i	0.311964	−	0.950094i	$-0.399013\pi$
$859$	1.76931e16	−	1.02151e16i	1.29075	−	0.745216i	0.978787	+	0.204878i	$0.0656799\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.09068e15	−	4.09381e15i	0.504230	−	0.291117i	−0.226229	−	0.974074i	$-0.572640\pi$
$863$	7.09068e15	−	4.09381e15i	0.504230	−	0.291117i	0.730459	+	0.682957i	$0.239306\pi$
$864$		0			0
$865$	−2.51037e15	+	4.34809e15i	−0.176258	+	0.305288i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			3.10804e16i			2.12754i
$870$		0			0
$871$	−1.31446e15	−	7.58906e14i	−0.0888483	−	0.0512966i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−1.55248e16	+	2.07985e15i	−1.02325	+	0.137084i
$876$		0			0
$877$	2.34742e15	+	4.06585e15i	0.152789	+	0.264639i	0.932252	−	0.361810i	$-0.117841\pi$
$877$	2.34742e15	+	4.06585e15i	0.152789	+	0.264639i	−0.779462	+	0.626449i	$0.784508\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	4.52584e15			0.287297			0.143649	−	0.989629i	$-0.454116\pi$
$881$	4.52584e15			0.287297			0.143649	+	0.989629i	$0.454116\pi$
$882$		0			0
$883$	1.57228e16			0.985706			0.492853	−	0.870113i	$-0.335954\pi$
$883$	1.57228e16			0.985706			0.492853	+	0.870113i	$0.335954\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.58308e15	−	4.47403e15i	−0.157964	−	0.273602i	0.776170	−	0.630523i	$-0.217160\pi$
$887$	−2.58308e15	−	4.47403e15i	−0.157964	−	0.273602i	−0.934134	+	0.356922i	$0.883826\pi$
$888$		0			0
$889$	−3.01467e16	+	4.03875e15i	−1.82087	+	0.243942i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.67160e15	−	2.11980e15i	−0.216358	−	0.124914i
$894$		0			0
$895$			3.23900e15i			0.188531i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.03221e15	−	8.71605e15i	0.285812	−	0.495041i
$900$		0			0
$901$	1.03798e16	−	5.99278e15i	0.582375	−	0.336234i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.04766e16	+	1.18222e16i	−1.12122	+	0.647337i
$906$		0			0
$907$	9.06519e14	−	1.57014e15i	0.0490384	−	0.0849371i	−0.840464	−	0.541867i	$-0.817718\pi$
$907$	9.06519e14	−	1.57014e15i	0.0490384	−	0.0849371i	0.889503	+	0.456930i	$0.151051\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	2.87731e16i		−	1.51927i	−0.650349	−	0.759636i	$-0.725377\pi$
$911$		−	2.87731e16i		−	1.51927i	0.650349	−	0.759636i	$-0.274623\pi$
$912$		0			0
$913$	−2.77547e16	−	1.60242e16i	−1.44793	−	0.835963i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.28504e16	+	1.66682e16i	0.654463	+	0.848902i
$918$		0			0
$919$	−8.20224e15	−	1.42067e16i	−0.412759	−	0.714920i	0.582431	−	0.812880i	$-0.302102\pi$
$919$	−8.20224e15	−	1.42067e16i	−0.412759	−	0.714920i	−0.995190	+	0.0979599i	$0.968768\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.85082e15			−0.287480
$924$		0			0
$925$	4.35333e16			2.11369
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.45876e16	−	2.52665e16i	−0.691669	−	1.19801i	−0.971291	−	0.237895i	$-0.923543\pi$
$929$	−1.45876e16	−	2.52665e16i	−0.691669	−	1.19801i	0.279622	−	0.960110i	$-0.409791\pi$
$930$		0			0
$931$	−5.82523e15	+	5.87854e15i	−0.272954	+	0.275452i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.62258e16	−	1.51415e16i	−1.20023	−	0.692954i
$936$		0			0
$937$		−	1.37760e16i		−	0.623097i	−0.950230	−	0.311549i	$-0.899152\pi$
$937$		−	1.37760e16i		−	0.623097i	0.950230	−	0.311549i	$-0.100848\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.73411e16	+	3.00357e16i	−0.766186	+	1.32707i	0.173431	+	0.984846i	$0.444515\pi$
$941$	−1.73411e16	+	3.00357e16i	−0.766186	+	1.32707i	−0.939617	+	0.342228i	$0.888819\pi$
$942$		0			0
$943$	−9.49746e15	+	5.48336e15i	−0.414756	+	0.239460i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.76166e15	+	2.74915e15i	−0.203158	+	0.117293i	−0.598128	−	0.801401i	$-0.704088\pi$
$947$	−4.76166e15	+	2.74915e15i	−0.203158	+	0.117293i	0.394970	+	0.918694i	$0.370755\pi$
$948$		0			0
$949$	4.66467e14	−	8.07944e14i	0.0196724	−	0.0340735i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			4.41474e16i			1.81926i	0.415424	+	0.909628i	$0.363633\pi$
$953$			4.41474e16i			1.81926i	−0.415424	+	0.909628i	$0.636367\pi$
$954$		0			0
$955$	−2.37630e16	−	1.37196e16i	−0.968015	−	0.558884i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.56372e16	+	1.05510e16i	1.02063	+	0.420039i
$960$		0			0
$961$	−1.15173e16	−	1.99485e16i	−0.453285	−	0.785113i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−4.47882e16			−1.72291
$966$		0			0
$967$	2.42858e16			0.923650			0.461825	−	0.886971i	$-0.347195\pi$
$967$	2.42858e16			0.923650			0.461825	+	0.886971i	$0.347195\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.46681e14	−	6.00469e14i	−0.0128891	−	0.0223246i	0.859509	−	0.511121i	$-0.170770\pi$
$971$	−3.46681e14	−	6.00469e14i	−0.0128891	−	0.0223246i	−0.872398	+	0.488796i	$0.837436\pi$
$972$		0			0
$973$	−6.69188e15	−	4.99506e16i	−0.245996	−	1.83620i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−4.01586e15	−	2.31856e15i	−0.144330	−	0.0833292i	0.426096	−	0.904678i	$-0.359889\pi$
$977$	−4.01586e15	−	2.31856e15i	−0.144330	−	0.0833292i	−0.570426	+	0.821349i	$0.693222\pi$
$978$		0			0
$979$		−	4.21342e16i		−	1.49737i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.44098e16	−	2.49586e16i	0.500743	−	0.867312i	−0.499257	−	0.866454i	$-0.666394\pi$
$983$	1.44098e16	−	2.49586e16i	0.500743	−	0.867312i	1.00000		0.000857784i	$-0.000273041\pi$
$984$		0			0
$985$	−2.05725e16	+	1.18776e16i	−0.706949	+	0.408157i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.40121e15	+	4.85044e15i	−0.282333	+	0.163005i
$990$		0			0
$991$	1.43458e16	−	2.48476e16i	0.476781	−	0.825809i	−0.522865	−	0.852415i	$-0.675137\pi$
$991$	1.43458e16	−	2.48476e16i	0.476781	−	0.825809i	0.999646	+	0.0266068i	$0.00847022\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	1.99991e16i		−	0.650105i
$996$		0			0
$997$	−6.30602e14	−	3.64079e14i	−0.0202737	−	0.0117050i	0.489829	−	0.871819i	$-0.337059\pi$
$997$	−6.30602e14	−	3.64079e14i	−0.0202737	−	0.0117050i	−0.510103	+	0.860114i	$0.670393\pi$
$998$		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.17.28	yes	60
3.2	odd	2	inner	252.12.t.a.17.3	✓	60
7.5	odd	6	inner	252.12.t.a.89.3	yes	60
21.5	even	6	inner	252.12.t.a.89.28	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.3	✓	60	3.2	odd	2	inner
252.12.t.a.17.28	yes	60	1.1	even	1	trivial
252.12.t.a.89.3	yes	60	7.5	odd	6	inner
252.12.t.a.89.28	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)

\(f(q)\)	\(=\)	\(q+(5672.42 + 9824.92i) q^{5} +(44073.4 - 5904.51i) q^{7} +O(q^{10})\)	\(q+(5672.42 + 9824.92i) q^{5} +(44073.4 - 5904.51i) q^{7} +(-847547. - 489331. i) q^{11} +543547. i q^{13} +(1.36376e6 - 2.36209e6i) q^{17} +(-3.62466e6 + 2.09270e6i) q^{19} +(-6.66157e6 + 3.84606e6i) q^{23} +(-3.99387e7 + 6.91758e7i) q^{25} -2.06566e8i q^{29} +(4.21951e7 + 2.43613e7i) q^{31} +(3.08014e8 + 3.99525e8i) q^{35} +(-2.72501e8 - 4.71986e8i) q^{37} +1.42571e9 q^{41} +1.26115e9 q^{43} +(5.06475e8 + 8.77240e8i) q^{47} +(1.90760e9 - 5.20464e8i) q^{49} +(3.80559e9 + 2.19716e9i) q^{53} -1.11028e10i q^{55} +(3.96250e9 - 6.86325e9i) q^{59} +(-1.92948e9 + 1.11399e9i) q^{61} +(-5.34031e9 + 3.08323e9i) q^{65} +(-1.39621e9 + 2.41831e9i) q^{67} +1.07642e10i q^{71} +(-1.48643e9 - 8.58190e8i) q^{73} +(-4.02435e10 - 1.65621e10i) q^{77} +(-1.58790e10 - 2.75033e10i) q^{79} +3.27471e10 q^{83} +3.09432e10 q^{85} +(2.15264e10 + 3.72848e10i) q^{89} +(3.20938e9 + 2.39560e10i) q^{91} +(-4.11212e10 - 2.37414e10i) q^{95} +1.40456e11i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 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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