LMFDB - Embedded newform 252.12.t.a.17.7

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			17.7
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3708.57 - 6423.43i) q^{5} +(-40837.0 + 17597.3i) q^{7} +O(q^{10})$	$q+(-3708.57 - 6423.43i) q^{5} +(-40837.0 + 17597.3i) q^{7} +(592973. + 342353. i) q^{11} +1.28250e6i q^{13} +(-2.64193e6 + 4.57596e6i) q^{17} +(-1.55286e7 + 8.96545e6i) q^{19} +(3.79566e6 - 2.19142e6i) q^{23} +(-3.09290e6 + 5.35706e6i) q^{25} -6.56439e7i q^{29} +(-1.57608e8 - 9.09951e7i) q^{31} +(2.64482e8 + 1.97053e8i) q^{35} +(1.92839e8 + 3.34006e8i) q^{37} +1.03774e9 q^{41} +9.00477e8 q^{43} +(1.08006e9 + 1.87071e9i) q^{47} +(1.35800e9 - 1.43724e9i) q^{49} +(1.80502e8 + 1.04213e8i) q^{53} -5.07856e9i q^{55} +(-1.71174e9 + 2.96482e9i) q^{59} +(-2.95447e9 + 1.70577e9i) q^{61} +(8.23804e9 - 4.75624e9i) q^{65} +(4.27788e9 - 7.40951e9i) q^{67} -2.58872e9i q^{71} +(-5.59445e9 - 3.22996e9i) q^{73} +(-3.02397e10 - 3.54597e9i) q^{77} +(6.48236e9 + 1.12278e10i) q^{79} -1.06453e10 q^{83} +3.91912e10 q^{85} +(-3.57621e10 - 6.19418e10i) q^{89} +(-2.25685e10 - 5.23735e10i) q^{91} +(1.15178e11 + 6.64979e10i) q^{95} +5.47518e10i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3708.57	−	6423.43i	−0.530727	−	0.919246i	−0.999357	−	0.0358518i	$-0.988586\pi$
$5$	−3708.57	−	6423.43i	−0.530727	−	0.919246i	0.468630	−	0.883395i	$-0.344748\pi$
$6$		0			0
$7$	−40837.0	+	17597.3i	−0.918364	+	0.395737i
$7$	−40837.0	+	17597.3i	−0.918364	+	0.395737i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	592973.	+	342353.i	1.11013	+	0.640935i	0.938864	−	0.344289i	$-0.111880\pi$
$11$	592973.	+	342353.i	1.11013	+	0.640935i	0.171269	+	0.985224i	$0.445213\pi$
$12$		0			0
$13$			1.28250e6i			0.958007i	0.877813	+	0.479004i	$0.159002\pi$
$13$			1.28250e6i			0.958007i	−0.877813	+	0.479004i	$0.840998\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.64193e6	+	4.57596e6i	−0.451287	+	0.781652i	−0.998466	−	0.0553635i	$-0.982368\pi$
$17$	−2.64193e6	+	4.57596e6i	−0.451287	+	0.781652i	0.547179	+	0.837015i	$0.315702\pi$
$18$		0			0
$19$	−1.55286e7	+	8.96545e6i	−1.43876	+	0.830667i	−0.997764	−	0.0668427i	$-0.978707\pi$
$19$	−1.55286e7	+	8.96545e6i	−1.43876	+	0.830667i	−0.440994	+	0.897510i	$0.645374\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.79566e6	−	2.19142e6i	0.122966	−	0.0709943i	−0.437256	−	0.899337i	$-0.644049\pi$
$23$	3.79566e6	−	2.19142e6i	0.122966	−	0.0709943i	0.560221	+	0.828343i	$0.310716\pi$
$24$		0			0
$25$	−3.09290e6	+	5.35706e6i	−0.0633426	+	0.109713i
$26$		0			0
$27$		0			0
$28$		0			0
$29$		−	6.56439e7i		−	0.594299i	−0.954831	−	0.297150i	$-0.903964\pi$
$29$		−	6.56439e7i		−	0.594299i	0.954831	−	0.297150i	$-0.0960361\pi$
$30$		0			0
$31$	−1.57608e8	−	9.09951e7i	−0.988756	−	0.570859i	−0.0838541	−	0.996478i	$-0.526723\pi$
$31$	−1.57608e8	−	9.09951e7i	−0.988756	−	0.570859i	−0.904902	+	0.425619i	$0.860056\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.64482e8	+	1.97053e8i	0.851180	+	0.634175i
$36$		0			0
$37$	1.92839e8	+	3.34006e8i	0.457177	+	0.791854i	0.998810	−	0.0487607i	$-0.0155272\pi$
$37$	1.92839e8	+	3.34006e8i	0.457177	+	0.791854i	−0.541633	+	0.840615i	$0.682194\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.03774e9			1.39887			0.699435	−	0.714696i	$-0.253435\pi$
$41$	1.03774e9			1.39887			0.699435	+	0.714696i	$0.253435\pi$
$42$		0			0
$43$	9.00477e8			0.934106			0.467053	−	0.884229i	$-0.345316\pi$
$43$	9.00477e8			0.934106			0.467053	+	0.884229i	$0.345316\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.08006e9	+	1.87071e9i	0.686922	+	1.18978i	0.972829	+	0.231527i	$0.0743721\pi$
$47$	1.08006e9	+	1.87071e9i	0.686922	+	1.18978i	−0.285906	+	0.958258i	$0.592295\pi$
$48$		0			0
$49$	1.35800e9	−	1.43724e9i	0.686785	−	0.726861i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.80502e8	+	1.04213e8i	0.0592878	+	0.0342298i	0.529351	−	0.848403i	$-0.322436\pi$
$53$	1.80502e8	+	1.04213e8i	0.0592878	+	0.0342298i	−0.470063	+	0.882633i	$0.655769\pi$
$54$		0			0
$55$		−	5.07856e9i		−	1.36065i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.71174e9	+	2.96482e9i	−0.311710	+	0.539898i	−0.978733	−	0.205139i	$-0.934235\pi$
$59$	−1.71174e9	+	2.96482e9i	−0.311710	+	0.539898i	0.667022	+	0.745038i	$0.267569\pi$
$60$		0			0
$61$	−2.95447e9	+	1.70577e9i	−0.447884	+	0.258586i	−0.706936	−	0.707277i	$-0.749923\pi$
$61$	−2.95447e9	+	1.70577e9i	−0.447884	+	0.258586i	0.259052	+	0.965863i	$0.416590\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	8.23804e9	−	4.75624e9i	0.880645	−	0.508440i
$66$		0			0
$67$	4.27788e9	−	7.40951e9i	0.387095	−	0.670468i	−0.604963	−	0.796254i	$-0.706812\pi$
$67$	4.27788e9	−	7.40951e9i	0.387095	−	0.670468i	0.992057	+	0.125786i	$0.0401453\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	2.58872e9i		−	0.170280i	−0.996369	−	0.0851400i	$-0.972866\pi$
$71$		−	2.58872e9i		−	0.170280i	0.996369	−	0.0851400i	$-0.0271338\pi$
$72$		0			0
$73$	−5.59445e9	−	3.22996e9i	−0.315851	−	0.182356i	0.333691	−	0.942683i	$-0.391706\pi$
$73$	−5.59445e9	−	3.22996e9i	−0.315851	−	0.182356i	−0.649542	+	0.760326i	$0.725039\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−3.02397e10	−	3.54597e9i	−1.27315	−	0.149292i
$78$		0			0
$79$	6.48236e9	+	1.12278e10i	0.237020	+	0.410530i	0.959858	−	0.280488i	$-0.0904961\pi$
$79$	6.48236e9	+	1.12278e10i	0.237020	+	0.410530i	−0.722838	+	0.691017i	$0.757163\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.06453e10			−0.296638			−0.148319	−	0.988940i	$-0.547386\pi$
$83$	−1.06453e10			−0.296638			−0.148319	+	0.988940i	$0.547386\pi$
$84$		0			0
$85$	3.91912e10			0.958041
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.57621e10	−	6.19418e10i	−0.678857	−	1.17581i	−0.975325	−	0.220772i	$-0.929142\pi$
$89$	−3.57621e10	−	6.19418e10i	−0.678857	−	1.17581i	0.296469	−	0.955043i	$-0.404191\pi$
$90$		0			0
$91$	−2.25685e10	−	5.23735e10i	−0.379119	−	0.879799i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.15178e11	+	6.64979e10i	1.52718	+	0.881715i
$96$		0			0
$97$			5.47518e10i			0.647372i	0.946164	+	0.323686i	$0.104922\pi$
$97$			5.47518e10i			0.647372i	−0.946164	+	0.323686i	$0.895078\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.54524e10	+	9.60464e10i	−0.524992	+	0.909313i	0.474584	+	0.880210i	$0.342598\pi$
$101$	−5.54524e10	+	9.60464e10i	−0.524992	+	0.909313i	−0.999576	+	0.0291030i	$0.990735\pi$
$102$		0			0
$103$	−1.00144e11	+	5.78184e10i	−0.851181	+	0.491430i	−0.861049	−	0.508522i	$-0.830192\pi$
$103$	−1.00144e11	+	5.78184e10i	−0.851181	+	0.491430i	0.00986790	+	0.999951i	$0.496859\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−8.81059e8	+	5.08680e8i	−0.00607287	+	0.00350618i	−0.503033	−	0.864267i	$-0.667783\pi$
$107$	−8.81059e8	+	5.08680e8i	−0.00607287	+	0.00350618i	0.496960	+	0.867773i	$0.334449\pi$
$108$		0			0
$109$	−1.28634e11	+	2.22801e11i	−0.800777	+	1.38699i	0.118328	+	0.992975i	$0.462246\pi$
$109$	−1.28634e11	+	2.22801e11i	−0.800777	+	1.38699i	−0.919105	+	0.394012i	$0.871087\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	2.19512e10i		−	0.112080i	−0.998429	−	0.0560398i	$-0.982153\pi$
$113$		−	2.19512e10i		−	0.112080i	0.998429	−	0.0560398i	$-0.0178474\pi$
$114$		0			0
$115$	−2.81529e10	−	1.62541e10i	−0.130522	−	0.0753572i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.73642e10	−	2.33360e11i	0.105117	−	0.896432i
$120$		0			0
$121$	9.17551e10	+	1.58925e11i	0.321596	+	0.557021i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.16284e11			−0.926984
$126$		0			0
$127$	−1.13943e11			−0.306032			−0.153016	−	0.988224i	$-0.548899\pi$
$127$	−1.13943e11			−0.306032			−0.153016	+	0.988224i	$0.548899\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.23610e11	−	3.87304e11i	−0.506407	−	0.877122i	−0.999973	−	0.00741384i	$-0.997640\pi$
$131$	−2.23610e11	−	3.87304e11i	−0.506407	−	0.877122i	0.493566	−	0.869709i	$-0.335693\pi$
$132$		0			0
$133$	4.76375e11	−	6.39383e11i	0.992578	−	1.33222i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.51078e11	+	1.44960e11i	0.444473	+	0.256617i	0.705493	−	0.708717i	$-0.250726\pi$
$137$	2.51078e11	+	1.44960e11i	0.444473	+	0.256617i	−0.261020	+	0.965333i	$0.584059\pi$
$138$		0			0
$139$		−	7.09226e11i		−	1.15932i	−0.814858	−	0.579660i	$-0.803185\pi$
$139$		−	7.09226e11i		−	1.15932i	0.814858	−	0.579660i	$-0.196815\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.39067e11	+	7.60487e11i	−0.614021	+	1.06351i
$144$		0			0
$145$	−4.21659e11	+	2.43445e11i	−0.546308	+	0.315411i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	8.26243e11	−	4.77031e11i	0.921686	−	0.532136i	0.0375137	−	0.999296i	$-0.488056\pi$
$149$	8.26243e11	−	4.77031e11i	0.921686	−	0.532136i	0.884173	+	0.467160i	$0.154723\pi$
$150$		0			0
$151$	8.11547e11	−	1.40564e12i	0.841280	−	1.45714i	−0.0475338	−	0.998870i	$-0.515136\pi$
$151$	8.11547e11	−	1.40564e12i	0.841280	−	1.45714i	0.888813	−	0.458269i	$-0.151530\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			1.34985e12i			1.21188i
$156$		0			0
$157$	1.41994e12	+	8.19804e11i	1.18802	+	0.685901i	0.957855	−	0.287251i	$-0.0927415\pi$
$157$	1.41994e12	+	8.19804e11i	1.18802	+	0.685901i	0.230161	+	0.973153i	$0.426075\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.16440e11	+	1.56285e11i	−0.0848322	+	0.113861i
$162$		0			0
$163$	−1.14562e12	−	1.98428e12i	−0.779848	−	1.35074i	−0.932029	−	0.362384i	$-0.881963\pi$
$163$	−1.14562e12	−	1.98428e12i	−0.779848	−	1.35074i	0.152181	−	0.988353i	$-0.451370\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.86532e12			−1.11125			−0.555627	−	0.831432i	$-0.687522\pi$
$167$	−1.86532e12			−1.11125			−0.555627	+	0.831432i	$0.687522\pi$
$168$		0			0
$169$	1.47356e11			0.0822223
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.94388e10	−	1.72233e11i	−0.0487868	−	0.0845012i	0.840601	−	0.541655i	$-0.182202\pi$
$173$	−9.94388e10	−	1.72233e11i	−0.0487868	−	0.0845012i	−0.889388	+	0.457154i	$0.848869\pi$
$174$		0			0
$175$	3.20351e10	−	2.73193e11i	0.0147543	−	0.125823i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.68481e12	−	2.12743e12i	−1.49873	−	0.865293i	−0.498733	−	0.866756i	$-0.666201\pi$
$179$	−3.68481e12	−	2.12743e12i	−1.49873	−	0.865293i	−0.999999	+	0.00146240i	$0.999535\pi$
$180$		0			0
$181$			9.54235e10i			0.0365110i	0.999833	+	0.0182555i	$0.00581122\pi$
$181$			9.54235e10i			0.0365110i	−0.999833	+	0.0182555i	$0.994189\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.43031e12	−	2.47737e12i	0.485273	−	0.840517i
$186$		0			0
$187$	−3.13319e12	+	1.80895e12i	−1.00198	+	0.578491i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.27138e12	−	7.34031e11i	0.361903	−	0.208945i	−0.308012	−	0.951382i	$-0.599664\pi$
$191$	1.27138e12	−	7.34031e11i	0.361903	−	0.208945i	0.669915	+	0.742438i	$0.266331\pi$
$192$		0			0
$193$	−1.33602e12	+	2.31406e12i	−0.359128	+	0.622027i	−0.987815	−	0.155631i	$-0.950259\pi$
$193$	−1.33602e12	+	2.31406e12i	−0.359128	+	0.622027i	0.628688	+	0.777658i	$0.283592\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			4.10444e12i			0.985575i	0.870150	+	0.492787i	$0.164022\pi$
$197$			4.10444e12i			0.985575i	−0.870150	+	0.492787i	$0.835978\pi$
$198$		0			0
$199$	3.09012e12	+	1.78408e12i	0.701912	+	0.405249i	0.808059	−	0.589101i	$-0.200518\pi$
$199$	3.09012e12	+	1.78408e12i	0.701912	+	0.405249i	−0.106147	+	0.994350i	$0.533851\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.15515e12	+	2.68070e12i	0.235186	+	0.545783i
$204$		0			0
$205$	−3.84853e12	−	6.66585e12i	−0.742418	−	1.28591i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.22774e13			−2.12962
$210$		0			0
$211$	−5.93732e12			−0.977320			−0.488660	−	0.872474i	$-0.662514\pi$
$211$	−5.93732e12			−0.977320			−0.488660	+	0.872474i	$0.662514\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−3.33948e12	−	5.78415e12i	−0.495755	−	0.858673i
$216$		0			0
$217$	8.03751e12	+	9.42494e11i	1.13395	+	0.132969i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.86867e12	−	3.38828e12i	−0.748828	−	0.432336i
$222$		0			0
$223$		−	6.16342e12i		−	0.748420i	−0.927344	−	0.374210i	$-0.877914\pi$
$223$		−	6.16342e12i		−	0.748420i	0.927344	−	0.374210i	$-0.122086\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.50127e12	+	1.29926e13i	−0.826024	+	1.43071i	0.0751110	+	0.997175i	$0.476069\pi$
$227$	−7.50127e12	+	1.29926e13i	−0.826024	+	1.43071i	−0.901135	+	0.433540i	$0.857264\pi$
$228$		0			0
$229$	5.43988e12	−	3.14071e12i	0.570813	−	0.329559i	−0.186661	−	0.982424i	$-0.559767\pi$
$229$	5.43988e12	−	3.14071e12i	0.570813	−	0.329559i	0.757474	+	0.652865i	$0.226433\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.49668e13	+	8.64111e12i	−1.42782	+	0.824350i	−0.996948	−	0.0780645i	$-0.975126\pi$
$233$	−1.49668e13	+	8.64111e12i	−1.42782	+	0.824350i	−0.430868	+	0.902415i	$0.641793\pi$
$234$		0			0
$235$	8.01092e12	−	1.38753e13i	0.729137	−	1.26290i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	2.10905e13i		−	1.74944i	−0.484627	−	0.874721i	$-0.661045\pi$
$239$		−	2.10905e13i		−	1.74944i	0.484627	−	0.874721i	$-0.338955\pi$
$240$		0			0
$241$	−1.54257e12	−	8.90601e11i	−0.122222	−	0.0705651i	0.437642	−	0.899149i	$-0.355814\pi$
$241$	−1.54257e12	−	8.90601e11i	−0.122222	−	0.0705651i	−0.559865	+	0.828584i	$0.689147\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.42682e13	−	3.39290e12i	−1.03266	−	0.245560i
$246$		0			0
$247$	−1.14982e13	−	1.99154e13i	−0.795785	−	1.37834i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	8.65530e12			0.548374			0.274187	−	0.961676i	$-0.411591\pi$
$251$	8.65530e12			0.548374			0.274187	+	0.961676i	$0.411591\pi$
$252$		0			0
$253$	3.00096e12			0.182011
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.04736e12	−	1.39384e13i	−0.447735	−	0.775500i	0.550503	−	0.834833i	$-0.314436\pi$
$257$	−8.04736e12	−	1.39384e13i	−0.447735	−	0.775500i	−0.998238	+	0.0593329i	$0.981103\pi$
$258$		0			0
$259$	−1.37526e13	−	1.02464e13i	−0.733221	−	0.546289i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.53409e12	−	2.04041e12i	−0.173189	−	0.0999908i	0.410900	−	0.911681i	$-0.365215\pi$
$263$	−3.53409e12	−	2.04041e12i	−0.173189	−	0.0999908i	−0.584089	+	0.811690i	$0.698548\pi$
$264$		0			0
$265$		−	1.54592e12i		−	0.0726668i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.94564e13	+	3.36995e13i	−0.842220	+	1.45877i	0.0457942	+	0.998951i	$0.485418\pi$
$269$	−1.94564e13	+	3.36995e13i	−0.842220	+	1.45877i	−0.888014	+	0.459817i	$0.847915\pi$
$270$		0			0
$271$	2.12446e13	−	1.22656e13i	0.882912	−	0.509749i	0.0112943	−	0.999936i	$-0.496405\pi$
$271$	2.12446e13	−	1.22656e13i	0.882912	−	0.509749i	0.871617	+	0.490187i	$0.163072\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.66801e12	+	2.11773e12i	−0.140637	+	0.0811970i
$276$		0			0
$277$	2.11531e13	−	3.66382e13i	0.779354	−	1.34988i	−0.152960	−	0.988232i	$-0.548880\pi$
$277$	2.11531e13	−	3.66382e13i	0.779354	−	1.34988i	0.932314	−	0.361649i	$-0.117786\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	4.84994e12i		−	0.165140i	−0.996585	−	0.0825698i	$-0.973687\pi$
$281$		−	4.84994e12i		−	0.165140i	0.996585	−	0.0825698i	$-0.0263127\pi$
$282$		0			0
$283$	−2.11198e13	−	1.21935e13i	−0.691614	−	0.399303i	0.112602	−	0.993640i	$-0.464081\pi$
$283$	−2.11198e13	−	1.21935e13i	−0.691614	−	0.399303i	−0.804216	+	0.594337i	$0.797415\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.23782e13	+	1.82614e13i	−1.28467	+	0.553584i
$288$		0			0
$289$	3.17633e12	+	5.50156e12i	0.0926802	+	0.160527i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−2.73198e13			−0.739105			−0.369552	−	0.929210i	$-0.620489\pi$
$293$	−2.73198e13			−0.739105			−0.369552	+	0.929210i	$0.620489\pi$
$294$		0			0
$295$	2.53924e13			0.661733
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.81050e12	+	4.86793e12i	0.0680130	+	0.117802i
$300$		0			0
$301$	−3.67728e13	+	1.58459e13i	−0.857849	+	0.369660i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.19137e13	+	1.26519e13i	0.475409	+	0.274477i
$306$		0			0
$307$		−	7.05159e13i		−	1.47579i	−0.674913	−	0.737897i	$-0.735819\pi$
$307$		−	7.05159e13i		−	1.47579i	0.674913	−	0.737897i	$-0.264181\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−6.50781e12	+	1.12719e13i	−0.126839	+	0.219691i	−0.922450	−	0.386116i	$-0.873816\pi$
$311$	−6.50781e12	+	1.12719e13i	−0.126839	+	0.219691i	0.795611	+	0.605807i	$0.207150\pi$
$312$		0			0
$313$	−7.36075e12	+	4.24973e12i	−0.138493	+	0.0799590i	−0.567646	−	0.823273i	$-0.692146\pi$
$313$	−7.36075e12	+	4.24973e12i	−0.138493	+	0.0799590i	0.429153	+	0.903232i	$0.358812\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.67969e13	+	5.01122e13i	−1.52292	+	0.879261i	−0.523292	+	0.852153i	$0.675296\pi$
$317$	−8.67969e13	+	5.01122e13i	−1.52292	+	0.879261i	−0.999633	+	0.0271074i	$0.991370\pi$
$318$		0			0
$319$	2.24734e13	−	3.89250e13i	0.380908	−	0.659751i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	9.47444e13i		−	1.49948i
$324$		0			0
$325$	−6.87043e12	−	3.96664e12i	−0.105105	−	0.0606827i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−7.70257e13	−	5.73882e13i	−1.10169	−	0.820815i
$330$		0			0
$331$	2.48027e13	+	4.29596e13i	0.343119	+	0.594300i	0.985010	−	0.172496i	$-0.0551831\pi$
$331$	2.48027e13	+	4.29596e13i	0.343119	+	0.594300i	−0.641891	+	0.766796i	$0.721850\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−6.34593e13			−0.821767
$336$		0			0
$337$	−1.03446e14			−1.29643			−0.648215	−	0.761457i	$-0.724484\pi$
$337$	−1.03446e14			−1.29643			−0.648215	+	0.761457i	$0.724484\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.23049e13	−	1.07915e14i	−0.731767	−	1.26746i
$342$		0			0
$343$	−3.01651e13	+	8.25897e13i	−0.343073	+	0.939309i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.16652e14	−	6.73488e13i	−1.24474	−	0.718651i	−0.274684	−	0.961534i	$-0.588573\pi$
$347$	−1.16652e14	−	6.73488e13i	−1.24474	−	0.718651i	−0.970055	+	0.242884i	$0.921907\pi$
$348$		0			0
$349$		−	1.08904e14i		−	1.12591i	−0.826487	−	0.562956i	$-0.809664\pi$
$349$		−	1.08904e14i		−	1.12591i	0.826487	−	0.562956i	$-0.190336\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.45907e13	+	5.99128e13i	−0.335891	+	0.581780i	−0.983656	−	0.180060i	$-0.942371\pi$
$353$	−3.45907e13	+	5.99128e13i	−0.335891	+	0.581780i	0.647765	+	0.761840i	$0.275704\pi$
$354$		0			0
$355$	−1.66284e13	+	9.60043e12i	−0.156529	+	0.0903722i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.14142e14	+	6.58999e13i	−1.01024	+	0.583264i	−0.911263	−	0.411826i	$-0.864891\pi$
$359$	−1.14142e14	+	6.58999e13i	−1.01024	+	0.583264i	−0.0989798	+	0.995089i	$0.531558\pi$
$360$		0			0
$361$	1.02513e14	−	1.77558e14i	0.880016	−	1.52423i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			4.79141e13i			0.387126i
$366$		0			0
$367$	1.94935e14	+	1.12546e14i	1.52836	+	0.882399i	0.999431	+	0.0337337i	$0.0107398\pi$
$367$	1.94935e14	+	1.12546e14i	1.52836	+	0.882399i	0.528930	+	0.848666i	$0.322594\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.20504e12	−	1.07940e12i	−0.0679938	−	0.00797308i
$372$		0			0
$373$	−1.08019e14	−	1.87095e14i	−0.774644	−	1.34172i	−0.934995	−	0.354662i	$-0.884596\pi$
$373$	−1.08019e14	−	1.87095e14i	−0.774644	−	1.34172i	0.160351	−	0.987060i	$-0.448737\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8.41883e13			0.569343
$378$		0			0
$379$	−2.90455e14			−1.90794			−0.953968	−	0.299908i	$-0.903044\pi$
$379$	−2.90455e14			−1.90794			−0.953968	+	0.299908i	$0.903044\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.11329e14	+	1.92828e14i	0.690264	+	1.19557i	0.971751	+	0.236008i	$0.0758390\pi$
$383$	1.11329e14	+	1.92828e14i	0.690264	+	1.19557i	−0.281487	+	0.959565i	$0.590828\pi$
$384$		0			0
$385$	8.93688e13	+	2.07393e14i	0.538458	+	1.24957i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.33479e14	+	1.34799e14i	1.32900	+	0.767298i	0.985145	−	0.171725i	$-0.0549340\pi$
$389$	2.33479e14	+	1.34799e14i	1.32900	+	0.767298i	0.343854	+	0.939023i	$0.388267\pi$
$390$		0			0
$391$			2.31584e13i			0.128155i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	4.80806e13	−	8.32780e13i	0.251585	−	0.435759i
$396$		0			0
$397$	2.22861e14	−	1.28669e14i	1.13419	−	0.654826i	0.189206	−	0.981937i	$-0.439409\pi$
$397$	2.22861e14	−	1.28669e14i	1.13419	−	0.654826i	0.944986	+	0.327112i	$0.106075\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.21544e14	−	1.85643e14i	1.54863	−	0.894099i	0.550378	−	0.834916i	$-0.314484\pi$
$401$	3.21544e14	−	1.85643e14i	1.54863	−	0.894099i	0.998247	−	0.0591836i	$-0.0188497\pi$
$402$		0			0
$403$	1.16701e14	−	2.02132e14i	0.546887	−	0.947236i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			2.64075e14i			1.17208i
$408$		0			0
$409$	1.15045e13	+	6.64212e12i	0.0497037	+	0.0286965i	0.524646	−	0.851321i	$-0.324198\pi$
$409$	1.15045e13	+	6.64212e12i	0.0497037	+	0.0286965i	−0.474942	+	0.880017i	$0.657531\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.77296e13	−	1.51196e14i	0.0726060	−	0.619178i
$414$		0			0
$415$	3.94787e13	+	6.83790e13i	0.157434	+	0.272683i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.72777e14			−1.03188			−0.515942	−	0.856624i	$-0.672558\pi$
$419$	−2.72777e14			−1.03188			−0.515942	+	0.856624i	$0.672558\pi$
$420$		0			0
$421$	2.13799e13			0.0787870			0.0393935	−	0.999224i	$-0.487457\pi$
$421$	2.13799e13			0.0787870			0.0393935	+	0.999224i	$0.487457\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.63425e13	−	2.83060e13i	−0.0571714	−	0.0990237i
$426$		0			0
$427$	9.06350e13	−	1.21649e14i	0.308989	−	0.414720i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.70833e13	+	5.02776e13i	0.282040	+	0.162836i	0.634346	−	0.773049i	$-0.281269\pi$
$431$	8.70833e13	+	5.02776e13i	0.282040	+	0.162836i	−0.352307	+	0.935885i	$0.614603\pi$
$432$		0			0
$433$			1.35879e14i			0.429012i	0.976723	+	0.214506i	$0.0688142\pi$
$433$			1.35879e14i			0.429012i	−0.976723	+	0.214506i	$0.931186\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.92942e13	+	6.80595e13i	−0.117945	+	0.204287i
$438$		0			0
$439$	−5.38438e14	+	3.10868e14i	−1.57609	+	0.909956i	−0.580693	+	0.814122i	$0.697218\pi$
$439$	−5.38438e14	+	3.10868e14i	−1.57609	+	0.909956i	−0.995397	+	0.0958339i	$0.969448\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.71968e14	−	2.72491e14i	1.31429	−	0.758807i	0.331488	−	0.943459i	$-0.392449\pi$
$443$	4.71968e14	−	2.72491e14i	1.31429	−	0.758807i	0.982804	+	0.184653i	$0.0591161\pi$
$444$		0			0
$445$	−2.65252e14	+	4.59431e14i	−0.720575	+	1.24807i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	4.96256e14i		−	1.28337i	−0.766970	−	0.641683i	$-0.778236\pi$
$449$		−	4.96256e14i		−	1.28337i	0.766970	−	0.641683i	$-0.221764\pi$
$450$		0			0
$451$	6.15351e14	+	3.55273e14i	1.55293	+	0.896585i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.52720e14	+	3.39198e14i	−0.607544	+	0.815437i
$456$		0			0
$457$	−1.82758e14	−	3.16546e14i	−0.428881	−	0.742844i	0.567893	−	0.823103i	$-0.307759\pi$
$457$	−1.82758e14	−	3.16546e14i	−0.428881	−	0.742844i	−0.996774	+	0.0802582i	$0.974426\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	3.06373e14			0.685324			0.342662	−	0.939459i	$-0.388671\pi$
$461$	3.06373e14			0.685324			0.342662	+	0.939459i	$0.388671\pi$
$462$		0			0
$463$	−2.89529e14			−0.632407			−0.316203	−	0.948691i	$-0.602408\pi$
$463$	−2.89529e14			−0.632407			−0.316203	+	0.948691i	$0.602408\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−1.25276e13	−	2.16984e13i	−0.0260990	−	0.0452048i	0.852681	−	0.522432i	$-0.174975\pi$
$467$	−1.25276e13	−	2.16984e13i	−0.0260990	−	0.0452048i	−0.878780	+	0.477227i	$0.841642\pi$
$468$		0			0
$469$	−4.43087e13	+	3.77861e14i	−0.0901651	+	0.768921i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.33958e14	+	3.08281e14i	1.03698	+	0.598701i
$474$		0			0
$475$		−	1.10917e14i		−	0.210466i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.19771e14	+	7.27064e14i	−0.760619	+	1.31743i	0.181914	+	0.983315i	$0.441771\pi$
$479$	−4.19771e14	+	7.27064e14i	−0.760619	+	1.31743i	−0.942532	+	0.334115i	$0.891562\pi$
$480$		0			0
$481$	−4.28363e14	+	2.47315e14i	−0.758602	+	0.437979i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.51695e14	−	2.03051e14i	0.595095	−	0.343578i
$486$		0			0
$487$	7.79582e13	−	1.35028e14i	0.128959	−	0.223364i	−0.794314	−	0.607507i	$-0.792170\pi$
$487$	7.79582e13	−	1.35028e14i	0.128959	−	0.223364i	0.923274	+	0.384143i	$0.125503\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	9.68840e14i		−	1.53216i	−0.642746	−	0.766080i	$-0.722205\pi$
$491$		−	9.68840e14i		−	1.53216i	0.642746	−	0.766080i	$-0.277795\pi$
$492$		0			0
$493$	3.00384e14	+	1.73427e14i	0.464535	+	0.268200i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	4.55544e13	+	1.05715e14i	0.0673861	+	0.156379i
$498$		0			0
$499$	2.87626e14	+	4.98183e14i	0.416175	+	0.720836i	0.995551	−	0.0942246i	$-0.0300372\pi$
$499$	2.87626e14	+	4.98183e14i	0.416175	+	0.720836i	−0.579376	+	0.815060i	$0.696704\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.23881e14			1.27936			0.639679	−	0.768642i	$-0.279067\pi$
$503$	9.23881e14			1.27936			0.639679	+	0.768642i	$0.279067\pi$
$504$		0			0
$505$	8.22596e14			1.11451
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.85201e14	−	8.40392e14i	−0.629468	−	1.09027i	−0.987659	−	0.156622i	$-0.949940\pi$
$509$	−4.85201e14	−	8.40392e14i	−0.629468	−	1.09027i	0.358191	−	0.933648i	$-0.383394\pi$
$510$		0			0
$511$	2.85299e14	+	3.34547e13i	0.362231	+	0.0424759i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.42785e14	+	4.28847e14i	0.903490	+	0.521630i
$516$		0			0
$517$			1.47904e15i			1.76109i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−8.32798e13	+	1.44245e14i	−0.0950457	+	0.164624i	−0.909628	−	0.415424i	$-0.863633\pi$
$521$	−8.32798e13	+	1.44245e14i	−0.0950457	+	0.164624i	0.814582	+	0.580048i	$0.196966\pi$
$522$		0			0
$523$	−5.47897e14	+	3.16329e14i	−0.612265	+	0.353492i	−0.773852	−	0.633367i	$-0.781672\pi$
$523$	−5.47897e14	+	3.16329e14i	−0.612265	+	0.353492i	0.161586	+	0.986859i	$0.448339\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.32780e14	−	4.80806e14i	0.892426	−	0.515242i
$528$		0			0
$529$	−4.66800e14	+	8.08522e14i	−0.489920	+	0.848566i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			1.33090e15i			1.34013i
$534$		0			0
$535$	6.53494e12	+	3.77295e12i	0.00644608	+	0.00372165i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.29730e15	−	3.87330e14i	1.22829	−	0.366727i
$540$		0			0
$541$	−1.18115e14	−	2.04582e14i	−0.109577	−	0.189794i	0.806022	−	0.591886i	$-0.201616\pi$
$541$	−1.18115e14	−	2.04582e14i	−0.109577	−	0.189794i	−0.915599	+	0.402092i	$0.868283\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.90820e15			1.69998
$546$		0			0
$547$	−9.59665e14			−0.837895			−0.418947	−	0.908011i	$-0.637601\pi$
$547$	−9.59665e14			−0.837895			−0.418947	+	0.908011i	$0.637601\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.88527e14	+	1.01936e15i	0.493665	+	0.855053i
$552$		0			0
$553$	−4.62299e14	−	3.44437e14i	−0.380132	−	0.283218i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.05991e15	+	6.11940e14i	0.837657	+	0.483621i	0.856467	−	0.516202i	$-0.172654\pi$
$557$	1.05991e15	+	6.11940e14i	0.837657	+	0.483621i	−0.0188102	+	0.999823i	$0.505988\pi$
$558$		0			0
$559$			1.15486e15i			0.894880i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.55877e14	−	1.13601e15i	0.488682	−	0.846422i	−0.511233	−	0.859442i	$-0.670811\pi$
$563$	6.55877e14	−	1.13601e15i	0.488682	−	0.846422i	0.999915	+	0.0130201i	$0.00414455\pi$
$564$		0			0
$565$	−1.41002e14	+	8.14075e13i	−0.103029	+	0.0594837i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−7.66345e14	+	4.42449e14i	−0.538650	+	0.310990i	−0.744532	−	0.667587i	$-0.767327\pi$
$569$	−7.66345e14	+	4.42449e14i	−0.538650	+	0.310990i	0.205882	+	0.978577i	$0.433994\pi$
$570$		0			0
$571$	6.37463e14	−	1.10412e15i	0.439497	−	0.761232i	−0.558153	−	0.829738i	$-0.688490\pi$
$571$	6.37463e14	−	1.10412e15i	0.439497	−	0.761232i	0.997651	+	0.0685061i	$0.0218232\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			2.71114e13i			0.0179878i
$576$		0			0
$577$	−9.92131e12	−	5.72807e12i	−0.00645806	−	0.00372856i	0.496767	−	0.867884i	$-0.334520\pi$
$577$	−9.92131e12	−	5.72807e12i	−0.00645806	−	0.00372856i	−0.503226	+	0.864155i	$0.667854\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	4.34721e14	−	1.87328e14i	0.272422	−	0.117391i
$582$		0			0
$583$	7.13552e13	+	1.23591e14i	0.0438782	+	0.0759993i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.62960e13			−0.0511071			−0.0255535	−	0.999673i	$-0.508135\pi$
$587$	−8.62960e13			−0.0511071			−0.0255535	+	0.999673i	$0.508135\pi$
$588$		0			0
$589$	3.26325e15			1.89677
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.61410e14	+	9.72390e14i	0.314398	+	0.544553i	0.979309	−	0.202369i	$-0.0648642\pi$
$593$	5.61410e14	+	9.72390e14i	0.314398	+	0.544553i	−0.664912	+	0.746922i	$0.731531\pi$
$594$		0			0
$595$	−1.60045e15	+	6.89658e14i	−0.879830	+	0.379132i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.51564e15	−	8.75054e14i	−0.803060	−	0.463647i	0.0414802	−	0.999139i	$-0.486793\pi$
$599$	−1.51564e15	−	8.75054e14i	−0.803060	−	0.463647i	−0.844540	+	0.535493i	$0.820126\pi$
$600$		0			0
$601$		−	2.25638e15i		−	1.17382i	−0.809651	−	0.586911i	$-0.800344\pi$
$601$		−	2.25638e15i		−	1.17382i	0.809651	−	0.586911i	$-0.199656\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	6.80560e14	−	1.17877e15i	0.341360	−	0.591252i
$606$		0			0
$607$	2.44645e15	−	1.41246e15i	1.20503	−	0.695724i	0.243360	−	0.969936i	$-0.421750\pi$
$607$	2.44645e15	−	1.41246e15i	1.20503	−	0.695724i	0.961669	+	0.274212i	$0.0884169\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.39918e15	+	1.38517e15i	−1.13982	+	0.658077i
$612$		0			0
$613$	3.78318e14	−	6.55267e14i	0.176533	−	0.305763i	−0.764158	−	0.645029i	$-0.776845\pi$
$613$	3.78318e14	−	6.55267e14i	0.176533	−	0.305763i	0.940691	+	0.339266i	$0.110179\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	1.73997e15i		−	0.783383i	−0.920097	−	0.391691i	$-0.871890\pi$
$617$		−	1.73997e15i		−	0.783383i	0.920097	−	0.391691i	$-0.128110\pi$
$618$		0			0
$619$	9.64215e13	+	5.56690e13i	0.0426457	+	0.0246215i	0.521171	−	0.853452i	$-0.325495\pi$
$619$	9.64215e13	+	5.56690e13i	0.0426457	+	0.0246215i	−0.478526	+	0.878074i	$0.658829\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.55043e15	+	1.90020e15i	1.08875	+	0.811177i
$624$		0			0
$625$	1.32398e15	+	2.29320e15i	0.555318	+	0.961839i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.03787e15			−0.825272
$630$		0			0
$631$	−3.78252e15			−1.50529			−0.752644	−	0.658428i	$-0.771222\pi$
$631$	−3.78252e15			−1.50529			−0.752644	+	0.658428i	$0.771222\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.22564e14	+	7.31903e14i	0.162419	+	0.281318i
$636$		0			0
$637$	1.84326e15	+	1.74163e15i	0.696338	+	0.657945i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.37457e15	−	1.94831e15i	−1.23168	−	0.711113i	−0.264303	−	0.964440i	$-0.585142\pi$
$641$	−3.37457e15	−	1.94831e15i	−1.23168	−	0.711113i	−0.967381	+	0.253327i	$0.918475\pi$
$642$		0			0
$643$			3.34968e14i			0.120183i	0.998193	+	0.0600914i	$0.0191392\pi$
$643$			3.34968e14i			0.120183i	−0.998193	+	0.0600914i	$0.980861\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.80607e15	−	3.12820e15i	0.626269	−	1.08473i	−0.362025	−	0.932168i	$-0.617914\pi$
$647$	1.80607e15	−	3.12820e15i	0.626269	−	1.08473i	0.988294	−	0.152561i	$-0.0487522\pi$
$648$		0			0
$649$	−2.03003e15	+	1.17204e15i	−0.692080	+	0.399572i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.64319e15	−	9.48699e14i	0.541585	−	0.312684i	−0.204136	−	0.978942i	$-0.565439\pi$
$653$	1.64319e15	−	9.48699e14i	0.541585	−	0.312684i	0.745721	+	0.666258i	$0.232105\pi$
$654$		0			0
$655$	−1.65855e15	+	2.87269e15i	−0.537528	+	0.931025i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			1.98648e15i			0.622607i	0.950311	+	0.311303i	$0.100766\pi$
$659$			1.98648e15i			0.622607i	−0.950311	+	0.311303i	$0.899234\pi$
$660$		0			0
$661$	−3.77196e15	−	2.17774e15i	−1.16268	−	0.671271i	−0.210732	−	0.977544i	$-0.567585\pi$
$661$	−3.77196e15	−	2.17774e15i	−1.16268	−	0.671271i	−0.951944	+	0.306272i	$0.900918\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.87370e15	−	6.88761e14i	−1.75143	−	0.205376i
$666$		0			0
$667$	−1.43854e14	−	2.49162e14i	−0.0421919	−	0.0730785i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−2.33589e15			−0.662948
$672$		0			0
$673$	−1.38507e15			−0.386714			−0.193357	−	0.981129i	$-0.561937\pi$
$673$	−1.38507e15			−0.386714			−0.193357	+	0.981129i	$0.561937\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.18970e14	+	1.24529e15i	0.194300	+	0.336538i	0.946671	−	0.322202i	$-0.104423\pi$
$677$	7.18970e14	+	1.24529e15i	0.194300	+	0.336538i	−0.752371	+	0.658740i	$0.771090\pi$
$678$		0			0
$679$	−9.63484e14	−	2.23590e15i	−0.256189	−	0.594524i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.44912e15	−	8.36649e14i	−0.373070	−	0.215392i	0.301729	−	0.953394i	$-0.402436\pi$
$683$	−1.44912e15	−	8.36649e14i	−0.373070	−	0.215392i	−0.674799	+	0.738002i	$0.735770\pi$
$684$		0			0
$685$		−	2.15038e15i		−	0.544774i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.33653e14	+	2.31494e14i	−0.0327924	+	0.0567981i
$690$		0			0
$691$	4.42974e15	−	2.55751e15i	1.06967	−	0.617573i	0.141578	−	0.989927i	$-0.454782\pi$
$691$	4.42974e15	−	2.55751e15i	1.06967	−	0.617573i	0.928091	+	0.372354i	$0.121449\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.55566e15	+	2.63021e15i	−1.06570	+	0.615283i
$696$		0			0
$697$	−2.74164e15	+	4.74866e15i	−0.631292	+	1.09343i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			3.05862e15i			0.682459i	0.939980	+	0.341230i	$0.110843\pi$
$701$			3.05862e15i			0.682459i	−0.939980	+	0.341230i	$0.889157\pi$
$702$		0			0
$703$	−5.98903e15	−	3.45777e15i	−1.31553	−	0.759524i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.74356e14	−	4.89806e15i	0.122285	−	1.04284i
$708$		0			0
$709$	3.09928e15	+	5.36811e15i	0.649691	+	1.12530i	0.983197	+	0.182549i	$0.0584350\pi$
$709$	3.09928e15	+	5.36811e15i	0.649691	+	1.12530i	−0.333506	+	0.942748i	$0.608232\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.97635e14			−0.162111
$714$		0			0
$715$	6.51325e15			1.30351
$716$		0			0
$717$		0			0
$718$		0			0
$719$	6.79367e14	+	1.17670e15i	0.131855	+	0.228379i	0.924392	−	0.381445i	$-0.124573\pi$
$719$	6.79367e14	+	1.17670e15i	0.131855	+	0.228379i	−0.792537	+	0.609824i	$0.791240\pi$
$720$		0			0
$721$	3.07215e15	−	4.12340e15i	0.587217	−	0.788155i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.51658e14	+	2.03030e14i	0.0652021	+	0.0376445i
$726$		0			0
$727$		−	2.87547e15i		−	0.525133i	−0.964914	−	0.262567i	$-0.915431\pi$
$727$		−	2.87547e15i		−	0.525133i	0.964914	−	0.262567i	$-0.0845689\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−2.37900e15	+	4.12055e15i	−0.421550	+	0.730146i
$732$		0			0
$733$	7.40032e15	−	4.27258e15i	1.29175	−	0.745792i	0.312786	−	0.949824i	$-0.398738\pi$
$733$	7.40032e15	−	4.27258e15i	1.29175	−	0.745792i	0.978964	+	0.204031i	$0.0654044\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.07333e15	−	2.92909e15i	0.859453	−	0.496206i
$738$		0			0
$739$	8.08292e14	−	1.40000e15i	0.134904	−	0.233660i	−0.790657	−	0.612259i	$-0.790261\pi$
$739$	8.08292e14	−	1.40000e15i	0.134904	−	0.233660i	0.925561	+	0.378599i	$0.123594\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			6.23896e15i			1.01082i	0.862879	+	0.505410i	$0.168659\pi$
$743$			6.23896e15i			1.01082i	−0.862879	+	0.505410i	$0.831341\pi$
$744$		0			0
$745$	−6.12836e15	−	3.53821e15i	−0.978328	−	0.564838i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.70285e13	−	3.62772e13i	0.00418959	−	0.00562321i
$750$		0			0
$751$	−6.26639e15	−	1.08537e16i	−0.957190	−	1.65790i	−0.729276	−	0.684220i	$-0.760143\pi$
$751$	−6.26639e15	−	1.08537e16i	−0.957190	−	1.65790i	−0.227914	−	0.973681i	$-0.573191\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−1.20387e16			−1.78596
$756$		0			0
$757$	1.16592e16			1.70468			0.852339	−	0.522989i	$-0.175183\pi$
$757$	1.16592e16			1.70468			0.852339	+	0.522989i	$0.175183\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−3.81718e15	−	6.61155e15i	−0.542160	−	0.939048i	−0.998780	−	0.0493862i	$-0.984273\pi$
$761$	−3.81718e15	−	6.61155e15i	−0.542160	−	0.939048i	0.456620	−	0.889662i	$-0.349060\pi$
$762$		0			0
$763$	1.33235e15	−	1.13622e16i	0.186523	−	1.59066i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.80238e15	−	2.19530e15i	−0.517226	−	0.298621i
$768$		0			0
$769$		−	5.39616e15i		−	0.723586i	−0.932258	−	0.361793i	$-0.882165\pi$
$769$		−	5.39616e15i		−	0.723586i	0.932258	−	0.361793i	$-0.117835\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.29007e14	−	1.08947e15i	0.0819725	−	0.141981i	−0.822125	−	0.569308i	$-0.807211\pi$
$773$	6.29007e14	−	1.08947e15i	0.0819725	−	0.141981i	0.904097	+	0.427327i	$0.140545\pi$
$774$		0			0
$775$	9.74933e14	−	5.62878e14i	0.125261	−	0.0723194i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.61147e16	+	9.30380e15i	−2.01263	+	1.16200i
$780$		0			0
$781$	8.86255e14	−	1.53504e15i	0.109138	−	0.189033i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	1.21612e16i		−	1.45611i
$786$		0			0
$787$	−1.44981e15	−	8.37049e14i	−0.171179	−	0.0988302i	0.411963	−	0.911201i	$-0.364843\pi$
$787$	−1.44981e15	−	8.37049e14i	−0.171179	−	0.0988302i	−0.583142	+	0.812371i	$0.698177\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	3.86281e14	+	8.96421e14i	0.0443540	+	0.102930i
$792$		0			0
$793$	−2.18764e15	−	3.78911e15i	−0.247727	−	0.429076i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.99900e15			−0.330336			−0.165168	−	0.986265i	$-0.552817\pi$
$797$	−2.99900e15			−0.330336			−0.165168	+	0.986265i	$0.552817\pi$
$798$		0			0
$799$	−1.14137e16			−1.24000
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.21157e15	−	3.83055e15i	−0.233757	−	0.404879i
$804$		0			0
$805$	1.43571e15	+	1.68354e14i	0.149689	+	0.0175528i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.66778e15	−	2.69494e15i	−0.473580	−	0.273421i	0.244157	−	0.969736i	$-0.421489\pi$
$809$	−4.66778e15	−	2.69494e15i	−0.473580	−	0.273421i	−0.717737	+	0.696314i	$0.754822\pi$
$810$		0			0
$811$			3.75137e15i			0.375470i	0.982220	+	0.187735i	$0.0601147\pi$
$811$			3.75137e15i			0.375470i	−0.982220	+	0.187735i	$0.939885\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−8.49725e15	+	1.47177e16i	−0.827773	+	1.43375i
$816$		0			0
$817$	−1.39832e16	+	8.07318e15i	−1.34395	+	0.775931i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	6.36234e15	−	3.67330e15i	0.595291	−	0.343692i	−0.171896	−	0.985115i	$-0.554989\pi$
$821$	6.36234e15	−	3.67330e15i	0.595291	−	0.343692i	0.767187	+	0.641424i	$0.221656\pi$
$822$		0			0
$823$	−1.99376e13	+	3.45330e13i	−0.00184066	+	0.00318812i	−0.866944	−	0.498405i	$-0.833919\pi$
$823$	−1.99376e13	+	3.45330e13i	−0.00184066	+	0.00318812i	0.865104	+	0.501593i	$0.167253\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	3.79012e14i		−	0.0340701i	−0.999855	−	0.0170350i	$-0.994577\pi$
$827$		−	3.79012e14i		−	0.0340701i	0.999855	−	0.0170350i	$-0.00542268\pi$
$828$		0			0
$829$	9.12243e15	+	5.26684e15i	0.809209	+	0.467197i	0.846681	−	0.532101i	$-0.178597\pi$
$829$	9.12243e15	+	5.26684e15i	0.809209	+	0.467197i	−0.0374720	+	0.999298i	$0.511930\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.98902e15	+	1.00112e16i	0.258215	+	0.864849i
$834$		0			0
$835$	6.91768e15	+	1.19818e16i	0.589773	+	1.02152i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.19261e16			−0.990390			−0.495195	−	0.868782i	$-0.664903\pi$
$839$	−1.19261e16			−0.990390			−0.495195	+	0.868782i	$0.664903\pi$
$840$		0			0
$841$	7.89139e15			0.646808
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−5.46478e14	−	9.46528e14i	−0.0436376	−	0.0755825i
$846$		0			0
$847$	−6.54365e15	−	4.87536e15i	−0.515776	−	0.384281i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.46390e15	+	8.45183e14i	0.112434	+	0.0649139i
$852$		0			0
$853$		−	1.28743e16i		−	0.976120i	−0.872810	−	0.488060i	$-0.837705\pi$
$853$		−	1.28743e16i		−	0.976120i	0.872810	−	0.488060i	$-0.162295\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.28404e16	−	2.22402e16i	0.948819	−	1.64340i	0.200900	−	0.979612i	$-0.435613\pi$
$857$	1.28404e16	−	2.22402e16i	0.948819	−	1.64340i	0.747919	−	0.663790i	$-0.231053\pi$
$858$		0			0
$859$	−1.49876e16	+	8.65312e15i	−1.09338	+	0.631263i	−0.934474	−	0.356031i	$-0.884130\pi$
$859$	−1.49876e16	+	8.65312e15i	−1.09338	+	0.631263i	−0.158906	+	0.987294i	$0.550797\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.52368e15	+	2.61175e15i	−0.321686	+	0.185726i	−0.652144	−	0.758095i	$-0.726130\pi$
$863$	−4.52368e15	+	2.61175e15i	−0.321686	+	0.185726i	0.330458	+	0.943821i	$0.392797\pi$
$864$		0			0
$865$	−7.37551e14	+	1.27748e15i	−0.0517849	+	0.0896942i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			8.87702e15i			0.607657i
$870$		0			0
$871$	9.50269e15	+	5.48638e15i	0.642313	+	0.370840i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.29161e16	−	5.56574e15i	0.851308	−	0.366842i
$876$		0			0
$877$	−7.44288e15	−	1.28914e16i	−0.484444	−	0.839081i	0.515397	−	0.856952i	$-0.327645\pi$
$877$	−7.44288e15	−	1.28914e16i	−0.484444	−	0.839081i	−0.999840	+	0.0178707i	$0.994311\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.69063e16			1.07320			0.536601	−	0.843836i	$-0.319708\pi$
$881$	1.69063e16			1.07320			0.536601	+	0.843836i	$0.319708\pi$
$882$		0			0
$883$	1.19826e16			0.751223			0.375611	−	0.926777i	$-0.377433\pi$
$883$	1.19826e16			0.751223			0.375611	+	0.926777i	$0.377433\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.07440e15	+	1.86091e15i	0.0657029	+	0.113801i	0.897006	−	0.442019i	$-0.145738\pi$
$887$	1.07440e15	+	1.86091e15i	0.0657029	+	0.113801i	−0.831303	+	0.555820i	$0.812404\pi$
$888$		0			0
$889$	4.65308e15	−	2.00508e15i	0.281048	−	0.121108i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.35435e16	−	1.93663e16i	−1.97663	−	1.14121i
$894$		0			0
$895$			3.15589e16i			1.83694i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.97327e15	+	1.03460e16i	−0.339261	+	0.587617i
$900$		0			0
$901$	−9.53749e14	+	5.50647e14i	−0.0535116	+	0.0308949i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.12946e14	−	3.53885e14i	0.0335626	−	0.0193774i
$906$		0			0
$907$	5.62178e15	−	9.73720e15i	0.304112	−	0.526737i	−0.672951	−	0.739687i	$-0.734974\pi$
$907$	5.62178e15	−	9.73720e15i	0.304112	−	0.526737i	0.977063	+	0.212949i	$0.0683070\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			1.52527e16i			0.805370i	0.915339	+	0.402685i	$0.131923\pi$
$911$			1.52527e16i			0.805370i	−0.915339	+	0.402685i	$0.868077\pi$
$912$		0			0
$913$	−6.31234e15	−	3.64443e15i	−0.329307	−	0.190126i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.59471e16	+	1.18814e16i	0.812175	+	0.605114i
$918$		0			0
$919$	−9.85000e15	−	1.70607e16i	−0.495680	−	0.858542i	0.504308	−	0.863524i	$-0.331748\pi$
$919$	−9.85000e15	−	1.70607e16i	−0.495680	−	0.858542i	−0.999988	+	0.00498157i	$0.998414\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.32003e15			0.163129
$924$		0			0
$925$	−2.38572e15			−0.115835
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−1.64228e15	−	2.84451e15i	−0.0778683	−	0.134872i	0.824462	−	0.565918i	$-0.191478\pi$
$929$	−1.64228e15	−	2.84451e15i	−0.0778683	−	0.134872i	−0.902330	+	0.431046i	$0.858145\pi$
$930$		0			0
$931$	−8.20231e15	+	3.44934e16i	−0.384338	+	1.61627i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.32393e16	+	1.34172e16i	1.06355	+	0.614042i
$936$		0			0
$937$			1.06450e16i			0.481479i	0.970590	+	0.240740i	$0.0773900\pi$
$937$			1.06450e16i			0.481479i	−0.970590	+	0.240740i	$0.922610\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.94878e15	+	3.37539e15i	−0.0861033	+	0.149135i	−0.905861	−	0.423575i	$-0.860775\pi$
$941$	−1.94878e15	+	3.37539e15i	−0.0861033	+	0.149135i	0.819757	+	0.572711i	$0.194108\pi$
$942$		0			0
$943$	3.93891e15	−	2.27413e15i	0.172013	−	0.0993117i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.07975e16	−	6.23396e15i	0.460680	−	0.265974i	−0.251650	−	0.967818i	$-0.580973\pi$
$947$	1.07975e16	−	6.23396e15i	0.460680	−	0.265974i	0.712330	+	0.701844i	$0.247640\pi$
$948$		0			0
$949$	4.14242e15	−	7.17488e15i	0.174699	−	0.302587i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	4.46284e16i		−	1.83908i	−0.392996	−	0.919540i	$-0.628561\pi$
$953$		−	4.46284e16i		−	1.83908i	0.392996	−	0.919540i	$-0.371439\pi$
$954$		0			0
$955$	−9.43000e15	−	5.44441e15i	−0.384143	−	0.221785i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.28042e16	−	1.50144e15i	−0.509741	−	0.0597731i
$960$		0			0
$961$	3.85598e15	+	6.67875e15i	0.151759	+	0.262855i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.98189e16			0.762395
$966$		0			0
$967$	−1.44745e16			−0.550500			−0.275250	−	0.961373i	$-0.588761\pi$
$967$	−1.44745e16			−0.550500			−0.275250	+	0.961373i	$0.588761\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	9.85866e15	+	1.70757e16i	0.366532	+	0.634853i	0.989021	−	0.147776i	$-0.0472116\pi$
$971$	9.85866e15	+	1.70757e16i	0.366532	+	0.634853i	−0.622488	+	0.782629i	$0.713878\pi$
$972$		0			0
$973$	1.24805e16	+	2.89627e16i	0.458786	+	1.06468i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.61996e16	+	2.66734e16i	1.66042	+	0.958645i	0.972513	+	0.232847i	$0.0748040\pi$
$977$	4.61996e16	+	2.66734e16i	1.66042	+	0.958645i	0.687908	+	0.725798i	$0.258529\pi$
$978$		0			0
$979$		−	4.89730e16i		−	1.74041i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.00064e15	+	1.73317e15i	−0.0347724	+	0.0602276i	−0.882888	−	0.469584i	$-0.844404\pi$
$983$	−1.00064e15	+	1.73317e15i	−0.0347724	+	0.0602276i	0.848115	+	0.529811i	$0.177737\pi$
$984$		0			0
$985$	2.63646e16	−	1.52216e16i	0.905986	−	0.523071i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	3.41790e15	−	1.97333e15i	0.114863	−	0.0663162i
$990$		0			0
$991$	2.15996e15	−	3.74116e15i	0.0717861	−	0.124337i	−0.827898	−	0.560879i	$-0.810463\pi$
$991$	2.15996e15	−	3.74116e15i	0.0717861	−	0.124337i	0.899684	+	0.436541i	$0.143797\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	2.64655e16i		−	0.860307i
$996$		0			0
$997$	5.11903e16	+	2.95548e16i	1.64575	+	0.950176i	0.978734	+	0.205135i	$0.0657634\pi$
$997$	5.11903e16	+	2.95548e16i	1.64575	+	0.950176i	0.667019	+	0.745041i	$0.267570\pi$
$998$		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.17.7	✓	60
3.2	odd	2	inner	252.12.t.a.17.24	yes	60
7.5	odd	6	inner	252.12.t.a.89.24	yes	60
21.5	even	6	inner	252.12.t.a.89.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.7	✓	60	1.1	even	1	trivial
252.12.t.a.17.24	yes	60	3.2	odd	2	inner
252.12.t.a.89.7	yes	60	21.5	even	6	inner
252.12.t.a.89.24	yes	60	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	252.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3708.57 - 6423.43i) q^{5} +(-40837.0 + 17597.3i) q^{7} +O(q^{10})\)	\(q+(-3708.57 - 6423.43i) q^{5} +(-40837.0 + 17597.3i) q^{7} +(592973. + 342353. i) q^{11} +1.28250e6i q^{13} +(-2.64193e6 + 4.57596e6i) q^{17} +(-1.55286e7 + 8.96545e6i) q^{19} +(3.79566e6 - 2.19142e6i) q^{23} +(-3.09290e6 + 5.35706e6i) q^{25} -6.56439e7i q^{29} +(-1.57608e8 - 9.09951e7i) q^{31} +(2.64482e8 + 1.97053e8i) q^{35} +(1.92839e8 + 3.34006e8i) q^{37} +1.03774e9 q^{41} +9.00477e8 q^{43} +(1.08006e9 + 1.87071e9i) q^{47} +(1.35800e9 - 1.43724e9i) q^{49} +(1.80502e8 + 1.04213e8i) q^{53} -5.07856e9i q^{55} +(-1.71174e9 + 2.96482e9i) q^{59} +(-2.95447e9 + 1.70577e9i) q^{61} +(8.23804e9 - 4.75624e9i) q^{65} +(4.27788e9 - 7.40951e9i) q^{67} -2.58872e9i q^{71} +(-5.59445e9 - 3.22996e9i) q^{73} +(-3.02397e10 - 3.54597e9i) q^{77} +(6.48236e9 + 1.12278e10i) q^{79} -1.06453e10 q^{83} +3.91912e10 q^{85} +(-3.57621e10 - 6.19418e10i) q^{89} +(-2.25685e10 - 5.23735e10i) q^{91} +(1.15178e11 + 6.64979e10i) q^{95} +5.47518e10i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 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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