LMFDB - Embedded newform 252.12.t.a.17.12

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			17.12
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1048.47 - 1816.01i) q^{5} +(-42450.8 - 13238.5i) q^{7} +O(q^{10})$	$q+(-1048.47 - 1816.01i) q^{5} +(-42450.8 - 13238.5i) q^{7} +(57588.1 + 33248.5i) q^{11} -772133. i q^{13} +(-5.64039e6 + 9.76943e6i) q^{17} +(-8.21619e6 + 4.74362e6i) q^{19} +(1.70645e7 - 9.85217e6i) q^{23} +(2.22155e7 - 3.84783e7i) q^{25} +3.03858e7i q^{29} +(2.13631e8 + 1.23340e8i) q^{31} +(2.04673e7 + 9.09713e7i) q^{35} +(1.45332e8 + 2.51722e8i) q^{37} -1.26091e9 q^{41} -1.27049e9 q^{43} +(1.24463e9 + 2.15576e9i) q^{47} +(1.62681e9 + 1.12397e9i) q^{49} +(4.41926e8 + 2.55146e8i) q^{53} -1.39441e8i q^{55} +(3.93266e9 - 6.81156e9i) q^{59} +(8.63663e9 - 4.98636e9i) q^{61} +(-1.40220e9 + 8.09562e8i) q^{65} +(-9.65546e9 + 1.67237e10i) q^{67} -3.06044e9i q^{71} +(-1.57956e10 - 9.11958e9i) q^{73} +(-2.00450e9 - 2.17381e9i) q^{77} +(-1.59752e10 - 2.76698e10i) q^{79} +1.76803e10 q^{83} +2.36552e10 q^{85} +(-1.13345e10 - 1.96319e10i) q^{89} +(-1.02219e10 + 3.27777e10i) q^{91} +(1.72289e10 + 9.94713e9i) q^{95} +1.30442e10i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1048.47	−	1816.01i	−0.150045	−	0.259886i	0.781198	−	0.624283i	$-0.214609\pi$
$5$	−1048.47	−	1816.01i	−0.150045	−	0.259886i	−0.931244	+	0.364396i	$0.881275\pi$
$6$		0			0
$7$	−42450.8	−	13238.5i	−0.954655	−	0.297715i
$7$	−42450.8	−	13238.5i	−0.954655	−	0.297715i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	57588.1	+	33248.5i	0.107813	+	0.0622461i	0.552937	−	0.833223i	$-0.313507\pi$
$11$	57588.1	+	33248.5i	0.107813	+	0.0622461i	−0.445124	+	0.895469i	$0.646840\pi$
$12$		0			0
$13$		−	772133.i		−	0.576772i	−0.957514	−	0.288386i	$-0.906881\pi$
$13$		−	772133.i		−	0.576772i	0.957514	−	0.288386i	$-0.0931186\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.64039e6	+	9.76943e6i	−0.963473	+	1.66878i	−0.249812	+	0.968294i	$0.580369\pi$
$17$	−5.64039e6	+	9.76943e6i	−0.963473	+	1.66878i	−0.713662	+	0.700490i	$0.752965\pi$
$18$		0			0
$19$	−8.21619e6	+	4.74362e6i	−0.761247	+	0.439506i	−0.829743	−	0.558145i	$-0.811513\pi$
$19$	−8.21619e6	+	4.74362e6i	−0.761247	+	0.439506i	0.0684961	+	0.997651i	$0.478180\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.70645e7	−	9.85217e6i	0.552827	−	0.319175i	−0.197434	−	0.980316i	$-0.563261\pi$
$23$	1.70645e7	−	9.85217e6i	0.552827	−	0.319175i	0.750262	+	0.661141i	$0.229928\pi$
$24$		0			0
$25$	2.22155e7	−	3.84783e7i	0.454973	−	0.788036i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			3.03858e7i			0.275095i	0.990495	+	0.137547i	$0.0439219\pi$
$29$			3.03858e7i			0.275095i	−0.990495	+	0.137547i	$0.956078\pi$
$30$		0			0
$31$	2.13631e8	+	1.23340e8i	1.34022	+	0.773775i	0.986839	−	0.161705i	$-0.0516995\pi$
$31$	2.13631e8	+	1.23340e8i	1.34022	+	0.773775i	0.353378	+	0.935480i	$0.385033\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.04673e7	+	9.09713e7i	0.0658696	+	0.292773i
$36$		0			0
$37$	1.45332e8	+	2.51722e8i	0.344549	+	0.596776i	0.985272	−	0.170996i	$-0.0546986\pi$
$37$	1.45332e8	+	2.51722e8i	0.344549	+	0.596776i	−0.640723	+	0.767772i	$0.721365\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.26091e9			−1.69970			−0.849852	−	0.527021i	$-0.823309\pi$
$41$	−1.26091e9			−1.69970			−0.849852	+	0.527021i	$0.823309\pi$
$42$		0			0
$43$	−1.27049e9			−1.31793			−0.658966	−	0.752172i	$-0.729006\pi$
$43$	−1.27049e9			−1.31793			−0.658966	+	0.752172i	$0.729006\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	1.24463e9	+	2.15576e9i	0.791591	+	1.37108i	0.924982	+	0.380012i	$0.124080\pi$
$47$	1.24463e9	+	2.15576e9i	0.791591	+	1.37108i	−0.133391	+	0.991063i	$0.542587\pi$
$48$		0			0
$49$	1.62681e9	+	1.12397e9i	0.822732	+	0.568430i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.41926e8	+	2.55146e8i	0.145155	+	0.0838054i	0.570819	−	0.821076i	$-0.306626\pi$
$53$	4.41926e8	+	2.55146e8i	0.145155	+	0.0838054i	−0.425663	+	0.904882i	$0.639959\pi$
$54$		0			0
$55$		−	1.39441e8i		−	0.0373590i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	3.93266e9	−	6.81156e9i	0.716143	−	1.24040i	−0.246374	−	0.969175i	$-0.579239\pi$
$59$	3.93266e9	−	6.81156e9i	0.716143	−	1.24040i	0.962517	−	0.271222i	$-0.0874276\pi$
$60$		0			0
$61$	8.63663e9	−	4.98636e9i	1.30927	−	0.755909i	0.327299	−	0.944921i	$-0.393862\pi$
$61$	8.63663e9	−	4.98636e9i	1.30927	−	0.755909i	0.981975	+	0.189011i	$0.0605283\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.40220e9	+	8.09562e8i	−0.149895	+	0.0865419i
$66$		0			0
$67$	−9.65546e9	+	1.67237e10i	−0.873698	+	1.51329i	−0.0155548	+	0.999879i	$0.504951\pi$
$67$	−9.65546e9	+	1.67237e10i	−0.873698	+	1.51329i	−0.858143	+	0.513410i	$0.828382\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.06044e9i		−	0.201309i	−0.994921	−	0.100655i	$-0.967906\pi$
$71$		−	3.06044e9i		−	0.201309i	0.994921	−	0.100655i	$-0.0320937\pi$
$72$		0			0
$73$	−1.57956e10	−	9.11958e9i	−0.891784	−	0.514872i	−0.0172583	−	0.999851i	$-0.505494\pi$
$73$	−1.57956e10	−	9.11958e9i	−0.891784	−	0.514872i	−0.874526	+	0.484979i	$0.838827\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−2.00450e9	−	2.17381e9i	−0.0843931	−	0.0915212i
$78$		0			0
$79$	−1.59752e10	−	2.76698e10i	−0.584112	−	1.01171i	−0.994985	−	0.100019i	$-0.968110\pi$
$79$	−1.59752e10	−	2.76698e10i	−0.584112	−	1.01171i	0.410873	−	0.911692i	$-0.365224\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.76803e10			0.492675			0.246338	−	0.969184i	$-0.420773\pi$
$83$	1.76803e10			0.492675			0.246338	+	0.969184i	$0.420773\pi$
$84$		0			0
$85$	2.36552e10			0.578259
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.13345e10	−	1.96319e10i	−0.215158	−	0.372664i	0.738164	−	0.674622i	$-0.235693\pi$
$89$	−1.13345e10	−	1.96319e10i	−0.215158	−	0.372664i	−0.953321	+	0.301957i	$0.902360\pi$
$90$		0			0
$91$	−1.02219e10	+	3.27777e10i	−0.171713	+	0.550618i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.72289e10	+	9.94713e9i	0.228443	+	0.131892i
$96$		0			0
$97$			1.30442e10i			0.154232i	0.997022	+	0.0771159i	$0.0245711\pi$
$97$			1.30442e10i			0.154232i	−0.997022	+	0.0771159i	$0.975429\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.07713e10	−	5.32974e10i	0.291325	−	0.504590i	−0.682798	−	0.730607i	$-0.739237\pi$
$101$	3.07713e10	−	5.32974e10i	0.291325	−	0.504590i	0.974123	+	0.226017i	$0.0725705\pi$
$102$		0			0
$103$	1.78348e11	−	1.02969e11i	1.51588	−	0.875193i	0.516052	−	0.856557i	$-0.327401\pi$
$103$	1.78348e11	−	1.02969e11i	1.51588	−	0.875193i	0.999826	−	0.0186353i	$-0.00593214\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.40407e11	+	1.38799e11i	−1.65705	+	0.956700i	−0.682987	+	0.730430i	$0.739320\pi$
$107$	−2.40407e11	+	1.38799e11i	−1.65705	+	0.956700i	−0.974065	+	0.226269i	$0.927347\pi$
$108$		0			0
$109$	−8.19588e10	+	1.41957e11i	−0.510211	+	0.883712i	0.489719	+	0.871880i	$0.337099\pi$
$109$	−8.19588e10	+	1.41957e11i	−0.510211	+	0.883712i	−0.999930	+	0.0118313i	$0.996234\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			3.46222e11i			1.76776i	0.467713	+	0.883880i	$0.345078\pi$
$113$			3.46222e11i			1.76776i	−0.467713	+	0.883880i	$0.654922\pi$
$114$		0			0
$115$	−3.57833e10	−	2.06595e10i	−0.165898	−	0.0957815i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.68772e11	−	3.40050e11i	1.41661	−	1.30627i
$120$		0			0
$121$	−1.40445e11	−	2.43258e11i	−0.492251	−	0.852603i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.95559e11			−0.573157
$126$		0			0
$127$	−3.04105e11			−0.816776			−0.408388	−	0.912809i	$-0.633909\pi$
$127$	−3.04105e11			−0.816776			−0.408388	+	0.912809i	$0.633909\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.21193e11	−	5.56322e11i	−0.727401	−	1.25990i	−0.957978	−	0.286841i	$-0.907395\pi$
$131$	−3.21193e11	−	5.56322e11i	−0.727401	−	1.25990i	0.230577	−	0.973054i	$-0.425939\pi$
$132$		0			0
$133$	4.11582e11	−	9.26001e10i	0.857576	−	0.192942i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.27220e11	+	3.04390e11i	0.933315	+	0.538850i	0.887859	−	0.460116i	$-0.152192\pi$
$137$	5.27220e11	+	3.04390e11i	0.933315	+	0.538850i	0.0454568	+	0.998966i	$0.485526\pi$
$138$		0			0
$139$			4.58370e11i			0.749263i	0.927174	+	0.374632i	$0.122231\pi$
$139$			4.58370e11i			0.749263i	−0.927174	+	0.374632i	$0.877769\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.56723e10	−	4.44657e10i	0.0359018	−	0.0621837i
$144$		0			0
$145$	5.51810e10	−	3.18588e10i	0.0714933	−	0.0412767i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.47619e12	−	8.52278e11i	1.64671	−	0.950729i	0.668345	−	0.743852i	$-0.267003\pi$
$149$	1.47619e12	−	8.52278e11i	1.64671	−	0.950729i	0.978367	−	0.206878i	$-0.0663302\pi$
$150$		0			0
$151$	−2.09736e10	+	3.63273e10i	−0.0217420	+	0.0376582i	−0.876692	−	0.481053i	$-0.840255\pi$
$151$	−2.09736e10	+	3.63273e10i	−0.0217420	+	0.0376582i	0.854950	+	0.518711i	$0.173588\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	5.17275e11i		−	0.464406i
$156$		0			0
$157$	−1.14619e12	−	6.61753e11i	−0.958977	−	0.553666i	−0.0631190	−	0.998006i	$-0.520105\pi$
$157$	−1.14619e12	−	6.61753e11i	−0.958977	−	0.553666i	−0.895858	+	0.444340i	$0.853438\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−8.54828e11	+	1.92324e11i	−0.622782	+	0.140117i
$162$		0			0
$163$	−7.01412e11	−	1.21488e12i	−0.477465	−	0.826993i	0.522202	−	0.852822i	$-0.325111\pi$
$163$	−7.01412e11	−	1.21488e12i	−0.477465	−	0.826993i	−0.999666	+	0.0258290i	$0.991777\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	1.10537e12			0.658514			0.329257	−	0.944240i	$-0.393202\pi$
$167$	1.10537e12			0.658514			0.329257	+	0.944240i	$0.393202\pi$
$168$		0			0
$169$	1.19597e12			0.667335
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.84012e11	+	1.35795e12i	0.384653	+	0.666239i	0.991721	−	0.128411i	$-0.0409877\pi$
$173$	7.84012e11	+	1.35795e12i	0.384653	+	0.666239i	−0.607068	+	0.794650i	$0.707654\pi$
$174$		0			0
$175$	−1.45246e12	+	1.33933e12i	−0.668952	+	0.616850i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.38517e12	−	7.99729e11i	−0.563393	−	0.325275i	0.191113	−	0.981568i	$-0.438790\pi$
$179$	−1.38517e12	−	7.99729e11i	−0.563393	−	0.325275i	−0.754506	+	0.656293i	$0.772124\pi$
$180$		0			0
$181$		−	6.07709e11i		−	0.232522i	−0.993219	−	0.116261i	$-0.962909\pi$
$181$		−	6.07709e11i		−	0.232522i	0.993219	−	0.116261i	$-0.0370908\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.04753e11	−	5.27848e11i	0.103396	−	0.179087i
$186$		0			0
$187$	−6.49638e11	+	3.75069e11i	−0.207751	+	0.119945i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.57938e12	−	1.48921e12i	0.734230	−	0.423908i	−0.0857374	−	0.996318i	$-0.527325\pi$
$191$	2.57938e12	−	1.48921e12i	0.734230	−	0.423908i	0.819968	+	0.572410i	$0.193991\pi$
$192$		0			0
$193$	2.40213e12	−	4.16062e12i	0.645701	−	1.11839i	−0.338438	−	0.940989i	$-0.609898\pi$
$193$	2.40213e12	−	4.16062e12i	0.645701	−	1.11839i	0.984139	−	0.177399i	$-0.0567682\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	2.82870e12i		−	0.679239i	−0.940563	−	0.339620i	$-0.889702\pi$
$197$		−	2.82870e12i		−	0.679239i	0.940563	−	0.339620i	$-0.110298\pi$
$198$		0			0
$199$	1.38714e12	+	8.00866e11i	0.315086	+	0.181915i	0.649200	−	0.760618i	$-0.275104\pi$
$199$	1.38714e12	+	8.00866e11i	0.315086	+	0.181915i	−0.334114	+	0.942533i	$0.608437\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.02263e11	−	1.28990e12i	0.0818997	−	0.262620i
$204$		0			0
$205$	1.32203e12	+	2.28983e12i	0.255033	+	0.441730i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.30873e11			−0.109430
$210$		0			0
$211$	−5.39333e12			−0.887776			−0.443888	−	0.896082i	$-0.646401\pi$
$211$	−5.39333e12			−0.887776			−0.443888	+	0.896082i	$0.646401\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	1.33207e12	+	2.30722e12i	0.197750	+	0.342513i
$216$		0			0
$217$	−7.43597e12	−	8.06404e12i	−1.04908	−	1.13769i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.54331e12	+	4.35513e12i	0.962508	+	0.555704i
$222$		0			0
$223$		−	1.46183e13i		−	1.77509i	−0.460722	−	0.887544i	$-0.652410\pi$
$223$		−	1.46183e13i		−	1.77509i	0.460722	−	0.887544i	$-0.347590\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.03682e12	−	1.04561e13i	0.664762	−	1.15140i	−0.314587	−	0.949228i	$-0.601866\pi$
$227$	6.03682e12	−	1.04561e13i	0.664762	−	1.15140i	0.979350	−	0.202174i	$-0.0648005\pi$
$228$		0			0
$229$	−1.03341e13	+	5.96637e12i	−1.08437	+	0.626059i	−0.932071	−	0.362276i	$-0.882000\pi$
$229$	−1.03341e13	+	5.96637e12i	−1.08437	+	0.626059i	−0.152295	+	0.988335i	$0.548666\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.36301e13	−	7.86937e12i	1.30030	−	0.750727i	0.319843	−	0.947471i	$-0.396370\pi$
$233$	1.36301e13	−	7.86937e12i	1.30030	−	0.750727i	0.980455	+	0.196743i	$0.0630365\pi$
$234$		0			0
$235$	2.60992e12	−	4.52051e12i	0.237549	−	0.411447i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	1.86034e13i		−	1.54314i	−0.636146	−	0.771569i	$-0.719472\pi$
$239$		−	1.86034e13i		−	1.54314i	0.636146	−	0.771569i	$-0.280528\pi$
$240$		0			0
$241$	−1.29531e13	−	7.47847e12i	−1.02631	−	0.592542i	−0.110386	−	0.993889i	$-0.535209\pi$
$241$	−1.29531e13	−	7.47847e12i	−1.02631	−	0.592542i	−0.915926	+	0.401347i	$0.868542\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.35475e11	−	4.13276e12i	0.0242799	−	0.299107i
$246$		0			0
$247$	3.66271e12	+	6.34400e12i	0.253495	+	0.439066i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	2.54629e13			1.61325			0.806625	−	0.591063i	$-0.201292\pi$
$251$	2.54629e13			1.61325			0.806625	+	0.591063i	$0.201292\pi$
$252$		0			0
$253$	1.31028e12			0.0794696
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7.95558e12	−	1.37795e13i	−0.442629	−	0.766655i	0.555255	−	0.831680i	$-0.312621\pi$
$257$	−7.95558e12	−	1.37795e13i	−0.442629	−	0.766655i	−0.997884	+	0.0650250i	$0.979287\pi$
$258$		0			0
$259$	−2.83702e12	−	1.26098e13i	−0.151256	−	0.672293i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.04404e11	+	4.64423e11i	0.0394201	+	0.0227592i	0.519581	−	0.854421i	$-0.326088\pi$
$263$	8.04404e11	+	4.64423e11i	0.0394201	+	0.0227592i	−0.480160	+	0.877181i	$0.659422\pi$
$264$		0			0
$265$		−	1.07006e12i		−	0.0502985i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.50521e13	−	2.60711e13i	0.651569	−	1.12855i	−0.331173	−	0.943570i	$-0.607444\pi$
$269$	1.50521e13	−	2.60711e13i	0.651569	−	1.12855i	0.982742	−	0.184981i	$-0.0592223\pi$
$270$		0			0
$271$	1.33119e13	−	7.68565e12i	0.553236	−	0.319411i	−0.197190	−	0.980365i	$-0.563182\pi$
$271$	1.33119e13	−	7.68565e12i	0.553236	−	0.319411i	0.750426	+	0.660954i	$0.229848\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.55869e12	−	1.47726e12i	0.0981044	−	0.0566406i
$276$		0			0
$277$	−1.53361e13	+	2.65629e13i	−0.565036	+	0.978671i	0.432011	+	0.901869i	$0.357804\pi$
$277$	−1.53361e13	+	2.65629e13i	−0.565036	+	0.978671i	−0.997046	+	0.0768021i	$0.975529\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			1.11154e13i			0.378479i	0.981931	+	0.189240i	$0.0606023\pi$
$281$			1.11154e13i			0.378479i	−0.981931	+	0.189240i	$0.939398\pi$
$282$		0			0
$283$	−2.78685e13	−	1.60899e13i	−0.912616	−	0.526899i	−0.0313440	−	0.999509i	$-0.509979\pi$
$283$	−2.78685e13	−	1.60899e13i	−0.912616	−	0.526899i	−0.881272	+	0.472610i	$0.843312\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	5.35267e13	+	1.66926e13i	1.62263	+	0.506027i
$288$		0			0
$289$	−4.64920e13	−	8.05264e13i	−1.35656	−	2.34963i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.68720e13			0.997527			0.498764	−	0.866738i	$-0.333788\pi$
$293$	3.68720e13			0.997527			0.498764	+	0.866738i	$0.333788\pi$
$294$		0			0
$295$	−1.64932e13			−0.429816
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.60719e12	−	1.31760e13i	−0.184091	−	0.318855i
$300$		0			0
$301$	5.39331e13	+	1.68193e13i	1.25817	+	0.392368i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.81106e13	−	1.04561e13i	−0.392901	−	0.226842i
$306$		0			0
$307$			1.22500e13i			0.256375i	0.991750	+	0.128187i	$0.0409159\pi$
$307$			1.22500e13i			0.256375i	−0.991750	+	0.128187i	$0.959084\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.16235e12	+	8.94146e12i	−0.100616	+	0.174271i	−0.911938	−	0.410327i	$-0.865415\pi$
$311$	−5.16235e12	+	8.94146e12i	−0.100616	+	0.174271i	0.811323	+	0.584598i	$0.198748\pi$
$312$		0			0
$313$	2.96455e13	−	1.71158e13i	0.557782	−	0.322036i	−0.194473	−	0.980908i	$-0.562300\pi$
$313$	2.96455e13	−	1.71158e13i	0.557782	−	0.322036i	0.752255	+	0.658872i	$0.228966\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.32765e13	−	3.65327e13i	1.11024	−	0.640996i	0.171347	−	0.985211i	$-0.445188\pi$
$317$	6.32765e13	−	3.65327e13i	1.11024	−	0.640996i	0.938891	+	0.344214i	$0.111855\pi$
$318$		0			0
$319$	−1.01028e12	+	1.74986e12i	−0.0171236	+	0.0296589i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.07023e14i		−	1.69381i
$324$		0			0
$325$	−2.97104e13	−	1.71533e13i	−0.454517	−	0.262415i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.42963e13	−	1.07990e14i	−0.347507	−	1.54457i
$330$		0			0
$331$	−1.62644e13	−	2.81708e13i	−0.225001	−	0.389713i	0.731319	−	0.682036i	$-0.238905\pi$
$331$	−1.62644e13	−	2.81708e13i	−0.225001	−	0.389713i	−0.956320	+	0.292323i	$0.905572\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	4.04940e13			0.524378
$336$		0			0
$337$	−1.22765e14			−1.53855			−0.769273	−	0.638920i	$-0.779382\pi$
$337$	−1.22765e14			−1.53855			−0.769273	+	0.638920i	$0.779382\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	8.20174e12	+	1.42058e13i	0.0963290	+	0.166847i
$342$		0			0
$343$	−5.41796e13	−	6.92500e13i	−0.616195	−	0.787593i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.46832e14	+	8.47733e13i	1.56678	+	0.904580i	0.996541	+	0.0831006i	$0.0264823\pi$
$347$	1.46832e14	+	8.47733e13i	1.56678	+	0.904580i	0.570238	+	0.821480i	$0.306851\pi$
$348$		0			0
$349$		−	1.41054e14i		−	1.45829i	−0.684358	−	0.729146i	$-0.739917\pi$
$349$		−	1.41054e14i		−	1.45829i	0.684358	−	0.729146i	$-0.260083\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.42962e13	−	7.67232e13i	0.430136	−	0.745017i	−0.566749	−	0.823890i	$-0.691799\pi$
$353$	4.42962e13	−	7.67232e13i	0.430136	−	0.745017i	0.996885	+	0.0788738i	$0.0251324\pi$
$354$		0			0
$355$	−5.55780e12	+	3.20880e12i	−0.0523175	+	0.0302055i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.18843e13	+	1.84084e13i	−0.282200	+	0.162928i	−0.634419	−	0.772989i	$-0.718761\pi$
$359$	−3.18843e13	+	1.84084e13i	−0.282200	+	0.162928i	0.352219	+	0.935918i	$0.385427\pi$
$360$		0			0
$361$	−1.32413e13	+	2.29345e13i	−0.113668	+	0.196879i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			3.82466e13i			0.309017i
$366$		0			0
$367$	−1.38598e14	−	8.00196e13i	−1.08666	−	0.627384i	−0.153975	−	0.988075i	$-0.549208\pi$
$367$	−1.38598e14	−	8.00196e13i	−1.08666	−	0.627384i	−0.932685	+	0.360691i	$0.882541\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.53824e13	−	1.66816e13i	−0.113623	−	0.123220i
$372$		0			0
$373$	6.12728e13	+	1.06128e14i	0.439409	+	0.761079i	0.997644	−	0.0686041i	$-0.0218545\pi$
$373$	6.12728e13	+	1.06128e14i	0.439409	+	0.761079i	−0.558235	+	0.829683i	$0.688521\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.34619e13			0.158667
$378$		0			0
$379$	2.51479e14			1.65191			0.825953	−	0.563738i	$-0.190637\pi$
$379$	2.51479e14			1.65191			0.825953	+	0.563738i	$0.190637\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.41979e13	−	1.63156e14i	−0.584047	−	1.01160i	−0.994993	−	0.0999397i	$-0.968135\pi$
$383$	−9.41979e13	−	1.63156e14i	−0.584047	−	1.01160i	0.410946	−	0.911660i	$-0.365198\pi$
$384$		0			0
$385$	−1.84599e12	+	5.91937e12i	−0.0111223	+	0.0356649i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.03753e13	+	4.64047e13i	0.457509	+	0.264143i	0.710996	−	0.703196i	$-0.248244\pi$
$389$	8.03753e13	+	4.64047e13i	0.457509	+	0.264143i	−0.253487	+	0.967339i	$0.581578\pi$
$390$		0			0
$391$			2.22280e14i			1.23007i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.34991e13	+	5.80221e13i	−0.175287	+	0.303605i
$396$		0			0
$397$	−1.14124e14	+	6.58895e13i	−0.580803	+	0.335327i	−0.761453	−	0.648221i	$-0.775513\pi$
$397$	−1.14124e14	+	6.58895e13i	−0.580803	+	0.335327i	0.180649	+	0.983548i	$0.442180\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	8.84269e13	−	5.10533e13i	0.425883	−	0.245884i	−0.271708	−	0.962380i	$-0.587589\pi$
$401$	8.84269e13	−	5.10533e13i	0.425883	−	0.245884i	0.697591	+	0.716496i	$0.254255\pi$
$402$		0			0
$403$	9.52349e13	−	1.64952e14i	0.446291	−	0.772999i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			1.93282e13i			0.0857873i
$408$		0			0
$409$	3.15978e14	+	1.82430e14i	1.36514	+	0.788167i	0.990303	−	0.138922i	$-0.0443637\pi$
$409$	3.15978e14	+	1.82430e14i	1.36514	+	0.788167i	0.374842	+	0.927089i	$0.377697\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.57119e14	+	2.37093e14i	−1.05295	+	0.970944i
$414$		0			0
$415$	−1.85374e13	−	3.21077e13i	−0.0739237	−	0.128040i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.19521e13			−0.347844			−0.173922	−	0.984759i	$-0.555644\pi$
$419$	−9.19521e13			−0.347844			−0.173922	+	0.984759i	$0.555644\pi$
$420$		0			0
$421$	4.99113e13			0.183928			0.0919639	−	0.995762i	$-0.470686\pi$
$421$	4.99113e13			0.183928			0.0919639	+	0.995762i	$0.470686\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.50608e14	+	4.34065e14i	0.876708	+	1.51850i
$426$		0			0
$427$	−4.32644e14	+	9.73387e13i	−1.47495	+	0.331843i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3.55599e14	−	2.05305e14i	−1.15169	−	0.664929i	−0.202392	−	0.979305i	$-0.564872\pi$
$431$	−3.55599e14	−	2.05305e14i	−1.15169	−	0.664929i	−0.949299	+	0.314375i	$0.898205\pi$
$432$		0			0
$433$		−	1.52804e14i		−	0.482450i	−0.970469	−	0.241225i	$-0.922451\pi$
$433$		−	1.52804e14i		−	0.482450i	0.970469	−	0.241225i	$-0.0775492\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−9.34699e13	+	1.61895e14i	−0.280559	+	0.485942i
$438$		0			0
$439$	−6.37932e13	+	3.68310e13i	−0.186732	+	0.107810i	−0.590452	−	0.807073i	$-0.701050\pi$
$439$	−6.37932e13	+	3.68310e13i	−0.186732	+	0.107810i	0.403720	+	0.914883i	$0.367717\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.21839e14	−	7.03439e13i	0.339286	−	0.195887i	−0.320670	−	0.947191i	$-0.603908\pi$
$443$	1.21839e14	−	7.03439e13i	0.339286	−	0.195887i	0.659956	+	0.751304i	$0.270575\pi$
$444$		0			0
$445$	−2.37679e13	+	4.11672e13i	−0.0645669	+	0.111833i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	1.42002e14i		−	0.367230i	−0.982998	−	0.183615i	$-0.941220\pi$
$449$		−	1.42002e14i		−	0.367230i	0.982998	−	0.183615i	$-0.0587800\pi$
$450$		0			0
$451$	−7.26135e13	−	4.19234e13i	−0.183251	−	0.105800i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.02420e13	−	1.58034e13i	0.168863	−	0.0379917i
$456$		0			0
$457$	3.09816e14	+	5.36616e14i	0.727050	+	1.25929i	0.958125	+	0.286351i	$0.0924425\pi$
$457$	3.09816e14	+	5.36616e14i	0.727050	+	1.25929i	−0.231075	+	0.972936i	$0.574224\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.18830e14			−1.60795			−0.803973	−	0.594666i	$-0.797284\pi$
$461$	−7.18830e14			−1.60795			−0.803973	+	0.594666i	$0.797284\pi$
$462$		0			0
$463$	3.27192e14			0.714673			0.357336	−	0.933976i	$-0.383685\pi$
$463$	3.27192e14			0.714673			0.357336	+	0.933976i	$0.383685\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.41187e13	+	9.37363e13i	0.112747	+	0.195283i	0.916877	−	0.399170i	$-0.130702\pi$
$467$	5.41187e13	+	9.37363e13i	0.112747	+	0.195283i	−0.804130	+	0.594453i	$0.797368\pi$
$468$		0			0
$469$	6.31279e14	−	5.82112e14i	1.28461	−	1.18456i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−7.31648e13	−	4.22417e13i	−0.142091	−	0.0820362i
$474$		0			0
$475$			4.21527e14i			0.799854i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.61201e14	+	2.79208e14i	−0.292093	+	0.505920i	−0.974304	−	0.225235i	$-0.927685\pi$
$479$	−1.61201e14	+	2.79208e14i	−0.292093	+	0.505920i	0.682211	+	0.731155i	$0.261018\pi$
$480$		0			0
$481$	1.94363e14	−	1.12215e14i	0.344204	−	0.198726i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.36885e13	−	1.36765e13i	0.0400827	−	0.0231418i
$486$		0			0
$487$	−3.87215e14	+	6.70676e14i	−0.640535	+	1.10944i	0.344778	+	0.938684i	$0.387954\pi$
$487$	−3.87215e14	+	6.70676e14i	−0.640535	+	1.10944i	−0.985313	+	0.170755i	$0.945379\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			7.94482e14i			1.25642i	0.778043	+	0.628212i	$0.216213\pi$
$491$			7.94482e14i			1.25642i	−0.778043	+	0.628212i	$0.783787\pi$
$492$		0			0
$493$	−2.96852e14	−	1.71388e14i	−0.459074	−	0.265046i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.05157e13	+	1.29918e14i	−0.0599326	+	0.192181i
$498$		0			0
$499$	−7.47295e13	−	1.29435e14i	−0.108128	−	0.187284i	0.806884	−	0.590710i	$-0.201152\pi$
$499$	−7.47295e13	−	1.29435e14i	−0.108128	−	0.187284i	−0.915012	+	0.403427i	$0.867819\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−3.62961e13			−0.0502616			−0.0251308	−	0.999684i	$-0.508000\pi$
$503$	−3.62961e13			−0.0502616			−0.0251308	+	0.999684i	$0.508000\pi$
$504$		0			0
$505$	−1.29052e14			−0.174848
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.97989e14	−	6.89338e14i	−0.516326	−	0.894302i	−0.999820	−	0.0189549i	$-0.993966\pi$
$509$	−3.97989e14	−	6.89338e14i	−0.516326	−	0.894302i	0.483495	−	0.875347i	$-0.339367\pi$
$510$		0			0
$511$	5.49805e14	+	5.96243e14i	0.698061	+	0.757022i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−3.73987e14	−	2.15922e14i	−0.454901	−	0.262637i
$516$		0			0
$517$			1.65528e14i			0.197094i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.23203e14	+	1.07942e15i	−0.711250	+	1.23192i	0.253139	+	0.967430i	$0.418537\pi$
$521$	−6.23203e14	+	1.07942e15i	−0.711250	+	1.23192i	−0.964388	+	0.264490i	$0.914796\pi$
$522$		0			0
$523$	4.13510e14	−	2.38740e14i	0.462090	−	0.266788i	−0.250833	−	0.968031i	$-0.580704\pi$
$523$	4.13510e14	−	2.38740e14i	0.462090	−	0.266788i	0.712923	+	0.701243i	$0.247371\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.40992e15	+	1.39137e15i	−2.58253	+	1.49102i
$528$		0			0
$529$	−2.82274e14	+	4.88914e14i	−0.296255	+	0.513128i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			9.73592e14i			0.980341i
$534$		0			0
$535$	5.04121e14	+	2.91054e14i	0.497266	+	0.287097i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.63145e13	+	1.18816e14i	0.0533190	+	0.112496i
$540$		0			0
$541$	3.85919e14	+	6.68432e14i	0.358023	+	0.620115i	0.987631	−	0.156799i	$-0.0501175\pi$
$541$	3.85919e14	+	6.68432e14i	0.358023	+	0.620115i	−0.629607	+	0.776914i	$0.716784\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.43727e14			0.306220
$546$		0			0
$547$	1.08412e15			0.946562			0.473281	−	0.880912i	$-0.343070\pi$
$547$	1.08412e15			0.946562			0.473281	+	0.880912i	$0.343070\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.44139e14	−	2.49656e14i	−0.120906	−	0.209415i
$552$		0			0
$553$	3.11851e14	+	1.38609e15i	0.256424	+	1.13973i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.14372e15	+	6.60326e14i	0.903889	+	0.521861i	0.878460	−	0.477816i	$-0.158571\pi$
$557$	1.14372e15	+	6.60326e14i	0.903889	+	0.521861i	0.0254294	+	0.999677i	$0.491905\pi$
$558$		0			0
$559$			9.80984e14i			0.760146i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.98701e13	−	1.55660e14i	0.0669605	−	0.115979i	−0.830601	−	0.556867i	$-0.812003\pi$
$563$	8.98701e13	−	1.55660e14i	0.0669605	−	0.115979i	0.897562	+	0.440888i	$0.145337\pi$
$564$		0			0
$565$	6.28743e14	−	3.63005e14i	0.459417	−	0.265244i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.60016e15	+	9.23855e14i	−1.12473	+	0.649361i	−0.942603	−	0.333915i	$-0.891630\pi$
$569$	−1.60016e15	+	9.23855e14i	−1.12473	+	0.649361i	−0.182123	+	0.983276i	$0.558297\pi$
$570$		0			0
$571$	7.78146e14	−	1.34779e15i	0.536491	−	0.929230i	−0.462599	−	0.886568i	$-0.653083\pi$
$571$	7.78146e14	−	1.34779e15i	0.536491	−	0.929230i	0.999090	−	0.0426618i	$-0.0135838\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	8.75482e14i		−	0.580864i
$576$		0			0
$577$	1.30170e15	+	7.51539e14i	0.847316	+	0.489198i	0.859744	−	0.510725i	$-0.170623\pi$
$577$	1.30170e15	+	7.51539e14i	0.847316	+	0.489198i	−0.0124283	+	0.999923i	$0.503956\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.50543e14	−	2.34061e14i	−0.470335	−	0.146677i
$582$		0			0
$583$	1.69665e13	+	2.93868e13i	0.0104331	+	0.0180707i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.09470e15			0.648313			0.324157	−	0.946003i	$-0.394919\pi$
$587$	1.09470e15			0.648313			0.324157	+	0.946003i	$0.394919\pi$
$588$		0			0
$589$	−2.34031e15			−1.36032
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.58176e14	+	2.73969e14i	0.0885809	+	0.153427i	0.906912	−	0.421321i	$-0.138433\pi$
$593$	1.58176e14	+	2.73969e14i	0.0885809	+	0.153427i	−0.818331	+	0.574748i	$0.805100\pi$
$594$		0			0
$595$	−1.00418e15	−	3.13160e14i	−0.552038	−	0.172156i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.26264e14	−	2.46104e14i	−0.225856	−	0.130398i	0.382803	−	0.923830i	$-0.374959\pi$
$599$	−4.26264e14	−	2.46104e14i	−0.225856	−	0.130398i	−0.608659	+	0.793432i	$0.708292\pi$
$600$		0			0
$601$		−	5.10312e14i		−	0.265476i	−0.991151	−	0.132738i	$-0.957623\pi$
$601$		−	5.10312e14i		−	0.265476i	0.991151	−	0.132738i	$-0.0423770\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.94506e14	+	5.10099e14i	−0.147720	+	0.255859i
$606$		0			0
$607$	−3.19445e14	+	1.84432e14i	−0.157347	+	0.0908443i	−0.576606	−	0.817022i	$-0.695623\pi$
$607$	−3.19445e14	+	1.84432e14i	−0.157347	+	0.0908443i	0.419259	+	0.907867i	$0.362290\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.66453e15	−	9.61017e14i	0.790797	−	0.456567i
$612$		0			0
$613$	−1.16623e15	+	2.01997e15i	−0.544192	+	0.942569i	0.454465	+	0.890765i	$0.349831\pi$
$613$	−1.16623e15	+	2.01997e15i	−0.544192	+	0.942569i	−0.998657	+	0.0518043i	$0.983503\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	7.54002e14i		−	0.339472i	−0.985490	−	0.169736i	$-0.945708\pi$
$617$		−	7.54002e14i		−	0.339472i	0.985490	−	0.169736i	$-0.0542915\pi$
$618$		0			0
$619$	−4.92526e14	−	2.84360e14i	−0.217836	−	0.125768i	0.387112	−	0.922033i	$-0.373473\pi$
$619$	−4.92526e14	−	2.84360e14i	−0.217836	−	0.125768i	−0.604948	+	0.796265i	$0.706806\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.21261e14	+	9.83443e14i	0.0944539	+	0.419822i
$624$		0			0
$625$	−8.79700e14	−	1.52369e15i	−0.368973	−	0.639080i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−3.27891e15			−1.32785
$630$		0			0
$631$	4.84312e14			0.192736			0.0963682	−	0.995346i	$-0.469277\pi$
$631$	4.84312e14			0.192736			0.0963682	+	0.995346i	$0.469277\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.18846e14	+	5.52258e14i	0.122553	+	0.212269i
$636$		0			0
$637$	8.67855e14	−	1.25611e15i	0.327854	−	0.474528i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−9.47887e14	−	5.47263e14i	−0.345969	−	0.199745i	0.316939	−	0.948446i	$-0.397345\pi$
$641$	−9.47887e14	−	5.47263e14i	−0.345969	−	0.199745i	−0.662909	+	0.748700i	$0.730678\pi$
$642$		0			0
$643$		−	1.95571e15i		−	0.701690i	−0.936434	−	0.350845i	$-0.885894\pi$
$643$		−	1.95571e15i		−	0.701690i	0.936434	−	0.350845i	$-0.114106\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.34586e14	−	7.52725e14i	0.150696	−	0.261014i	−0.780787	−	0.624797i	$-0.785182\pi$
$647$	4.34586e14	−	7.52725e14i	0.150696	−	0.261014i	0.931484	+	0.363783i	$0.118515\pi$
$648$		0			0
$649$	4.52948e14	−	2.61510e14i	0.154420	−	0.0891543i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.06655e15	−	2.92517e15i	1.66990	−	0.964115i	0.702206	−	0.711974i	$-0.252199\pi$
$653$	5.06655e15	−	2.92517e15i	1.66990	−	0.964115i	0.967690	−	0.252141i	$-0.0811347\pi$
$654$		0			0
$655$	−6.73525e14	+	1.16658e15i	−0.218286	+	0.378083i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	8.17530e14i		−	0.256232i	−0.991759	−	0.128116i	$-0.959107\pi$
$659$		−	8.17530e14i		−	0.256232i	0.991759	−	0.128116i	$-0.0408930\pi$
$660$		0			0
$661$	1.59955e15	+	9.23503e14i	0.493050	+	0.284662i	0.725839	−	0.687865i	$-0.241452\pi$
$661$	1.59955e15	+	9.23503e14i	0.493050	+	0.284662i	−0.232789	+	0.972527i	$0.574785\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.99696e14	−	6.50349e14i	−0.178818	−	0.193922i
$666$		0			0
$667$	2.99366e14	+	5.18518e14i	0.0878033	+	0.152080i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.63156e14			0.188210
$672$		0			0
$673$	1.11805e15			0.312161			0.156081	−	0.987744i	$-0.450114\pi$
$673$	1.11805e15			0.312161			0.156081	+	0.987744i	$0.450114\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.35311e15	+	2.34366e15i	0.365676	+	0.633369i	0.988884	−	0.148686i	$-0.0475045\pi$
$677$	1.35311e15	+	2.34366e15i	0.365676	+	0.633369i	−0.623208	+	0.782056i	$0.714171\pi$
$678$		0			0
$679$	1.72686e14	−	5.53738e14i	0.0459171	−	0.147238i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−8.74662e14	−	5.04986e14i	−0.225178	−	0.130007i	0.383167	−	0.923679i	$-0.374833\pi$
$683$	−8.74662e14	−	5.04986e14i	−0.225178	−	0.130007i	−0.608346	+	0.793672i	$0.708167\pi$
$684$		0			0
$685$		−	1.27658e15i		−	0.323408i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	1.97007e14	−	3.41226e14i	0.0483366	−	0.0837214i
$690$		0			0
$691$	−6.81035e15	+	3.93196e15i	−1.64452	+	0.949466i	−0.665326	+	0.746553i	$0.731707\pi$
$691$	−6.81035e15	+	3.93196e15i	−1.64452	+	0.949466i	−0.979197	+	0.202913i	$0.934959\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	8.32404e14	−	4.80589e14i	0.194723	−	0.112424i
$696$		0			0
$697$	7.11203e15	−	1.23184e16i	1.63762	−	2.83644i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			4.11591e15i			0.918367i	0.888341	+	0.459184i	$0.151858\pi$
$701$			4.11591e15i			0.918367i	−0.888341	+	0.459184i	$0.848142\pi$
$702$		0			0
$703$	−2.38815e15	−	1.37880e15i	−0.524574	−	0.302863i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.01184e15	+	1.85515e15i	−0.428339	+	0.394978i
$708$		0			0
$709$	6.25666e14	+	1.08369e15i	0.131156	+	0.227169i	0.924123	−	0.382096i	$-0.124798\pi$
$709$	6.25666e14	+	1.08369e15i	0.131156	+	0.227169i	−0.792966	+	0.609265i	$0.791464\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.86067e15			0.987878
$714$		0			0
$715$	−1.07667e14			−0.0215476
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.46207e15	−	2.53238e15i	−0.283766	−	0.491496i	0.688543	−	0.725195i	$-0.258250\pi$
$719$	−1.46207e15	−	2.53238e15i	−0.283766	−	0.491496i	−0.972309	+	0.233699i	$0.924917\pi$
$720$		0			0
$721$	−8.93419e15	+	2.01007e15i	−1.70770	+	0.384208i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.16920e15	+	6.75035e14i	0.216784	+	0.125161i
$726$		0			0
$727$		−	6.52980e14i		−	0.119251i	−0.998221	−	0.0596253i	$-0.981009\pi$
$727$		−	6.52980e14i		−	0.119251i	0.998221	−	0.0596253i	$-0.0189906\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.16603e15	−	1.24119e16i	1.26979	−	2.19935i
$732$		0			0
$733$	−4.50215e15	+	2.59932e15i	−0.785865	+	0.453719i	−0.838505	−	0.544894i	$-0.816570\pi$
$733$	−4.50215e15	+	2.59932e15i	−0.785865	+	0.453719i	0.0526400	+	0.998614i	$0.483236\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.11208e15	+	6.42059e14i	−0.188393	+	0.108769i
$738$		0			0
$739$	−2.08974e15	+	3.61953e15i	−0.348777	+	0.604099i	−0.986032	−	0.166554i	$-0.946736\pi$
$739$	−2.08974e15	+	3.61953e15i	−0.348777	+	0.604099i	0.637256	+	0.770652i	$0.280069\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	4.93833e15i		−	0.800095i	−0.916494	−	0.400048i	$-0.868994\pi$
$743$		−	4.93833e15i		−	0.800095i	0.916494	−	0.400048i	$-0.131006\pi$
$744$		0			0
$745$	−3.09549e15	−	1.78718e15i	−0.494163	−	0.285305i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.20430e16	−	2.70949e15i	1.86674	−	0.419989i
$750$		0			0
$751$	−2.87515e15	−	4.97990e15i	−0.439178	−	0.760678i	0.558448	−	0.829539i	$-0.311397\pi$
$751$	−2.87515e15	−	4.97990e15i	−0.439178	−	0.760678i	−0.997626	+	0.0688608i	$0.978064\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.79610e13			0.0130491
$756$		0			0
$757$	7.14565e15			1.04475			0.522377	−	0.852714i	$-0.325045\pi$
$757$	7.14565e15			1.04475			0.522377	+	0.852714i	$0.325045\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−8.32592e14	−	1.44209e15i	−0.118254	−	0.204822i	0.800822	−	0.598903i	$-0.204396\pi$
$761$	−8.32592e14	−	1.44209e15i	−0.118254	−	0.204822i	−0.919076	+	0.394081i	$0.871063\pi$
$762$		0			0
$763$	5.35851e15	−	4.94117e15i	0.750170	−	0.691742i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.25943e15	−	3.03653e15i	−0.715425	−	0.413051i
$768$		0			0
$769$			4.62560e15i			0.620259i	0.950694	+	0.310130i	$0.100372\pi$
$769$			4.62560e15i			0.620259i	−0.950694	+	0.310130i	$0.899628\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.22827e15	−	2.12743e15i	0.160069	−	0.277247i	−0.774824	−	0.632177i	$-0.782162\pi$
$773$	1.22827e15	−	2.12743e15i	0.160069	−	0.277247i	0.934893	+	0.354929i	$0.115495\pi$
$774$		0			0
$775$	9.49183e15	−	5.48011e15i	1.21952	−	0.704093i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.03599e16	−	5.98129e15i	1.29390	−	0.747031i
$780$		0			0
$781$	1.01755e14	−	1.76245e14i	0.0125307	−	0.0217038i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			2.77532e15i			0.332300i
$786$		0			0
$787$	−8.27422e15	−	4.77712e15i	−0.976936	−	0.564034i	−0.0755923	−	0.997139i	$-0.524085\pi$
$787$	−8.27422e15	−	4.77712e15i	−0.976936	−	0.564034i	−0.901344	+	0.433105i	$0.857418\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.58347e15	−	1.46974e16i	0.526288	−	1.68760i
$792$		0			0
$793$	−3.85014e15	−	6.66863e15i	−0.435987	−	0.755152i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.58450e16			1.74530			0.872652	−	0.488342i	$-0.162398\pi$
$797$	1.58450e16			1.74530			0.872652	+	0.488342i	$0.162398\pi$
$798$		0			0
$799$	−2.80807e16			−3.05071
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.06425e14	−	1.05036e15i	−0.0640975	−	0.111020i
$804$		0			0
$805$	1.24553e15	+	1.35073e15i	0.129860	+	0.140829i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.36530e16	+	7.88256e15i	1.38520	+	0.799743i	0.992769	−	0.120040i	$-0.0383023\pi$
$809$	1.36530e16	+	7.88256e15i	1.38520	+	0.799743i	0.392427	+	0.919783i	$0.371636\pi$
$810$		0			0
$811$		−	1.29509e16i		−	1.29624i	−0.761538	−	0.648121i	$-0.775555\pi$
$811$		−	1.29509e16i		−	1.29624i	0.761538	−	0.648121i	$-0.224445\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.47082e15	+	2.54754e15i	−0.143283	+	0.248173i
$816$		0			0
$817$	1.04386e16	−	6.02670e15i	1.00327	−	0.579240i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.02863e16	+	5.93879e15i	−0.962435	+	0.555662i	−0.896922	−	0.442190i	$-0.854202\pi$
$821$	−1.02863e16	+	5.93879e15i	−0.962435	+	0.555662i	−0.0655134	+	0.997852i	$0.520869\pi$
$822$		0			0
$823$	−7.84543e15	+	1.35887e16i	−0.724299	+	1.25452i	0.234963	+	0.972004i	$0.424503\pi$
$823$	−7.84543e15	+	1.35887e16i	−0.724299	+	1.25452i	−0.959262	+	0.282518i	$0.908830\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	5.23605e15i		−	0.470678i	−0.971913	−	0.235339i	$-0.924380\pi$
$827$		−	5.23605e15i		−	0.470678i	0.971913	−	0.235339i	$-0.0756200\pi$
$828$		0			0
$829$	3.06522e14	+	1.76970e14i	0.0271901	+	0.0156982i	0.513533	−	0.858070i	$-0.328336\pi$
$829$	3.06522e14	+	1.76970e14i	0.0271901	+	0.0156982i	−0.486343	+	0.873768i	$0.661670\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.01564e16	+	9.55338e15i	−1.74127	+	0.825296i
$834$		0			0
$835$	−1.15895e15	−	2.00736e15i	−0.0988071	−	0.171139i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.26223e16			−1.04821			−0.524103	−	0.851655i	$-0.675599\pi$
$839$	−1.26223e16			−1.04821			−0.524103	+	0.851655i	$0.675599\pi$
$840$		0			0
$841$	1.12772e16			0.924323
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.25394e15	−	2.17190e15i	−0.100131	−	0.173431i
$846$		0			0
$847$	2.74162e15	+	1.21858e16i	0.216097	+	0.960492i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.96001e15	+	2.86367e15i	0.380952	+	0.219943i
$852$		0			0
$853$		−	7.36171e15i		−	0.558160i	−0.960268	−	0.279080i	$-0.909970\pi$
$853$		−	7.36171e15i		−	0.558160i	0.960268	−	0.279080i	$-0.0900295\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	3.25662e15	−	5.64063e15i	0.240643	−	0.416805i	−0.720255	−	0.693710i	$-0.755975\pi$
$857$	3.25662e15	−	5.64063e15i	0.240643	−	0.416805i	0.960898	+	0.276904i	$0.0893085\pi$
$858$		0			0
$859$	−2.45827e15	+	1.41928e15i	−0.179336	+	0.103540i	−0.586981	−	0.809601i	$-0.699683\pi$
$859$	−2.45827e15	+	1.41928e15i	−0.179336	+	0.103540i	0.407645	+	0.913141i	$0.366350\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.63694e15	−	3.25449e15i	0.400852	−	0.231432i	−0.286000	−	0.958230i	$-0.592326\pi$
$863$	5.63694e15	−	3.25449e15i	0.400852	−	0.231432i	0.686851	+	0.726798i	$0.258992\pi$
$864$		0			0
$865$	1.64403e15	−	2.84755e15i	0.115431	−	0.199932i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	2.12460e15i		−	0.145435i
$870$		0			0
$871$	1.29130e16	+	7.45530e15i	0.872822	+	0.503924i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	8.30165e15	+	2.58892e15i	0.547167	+	0.170637i
$876$		0			0
$877$	−3.18177e15	−	5.51099e15i	−0.207096	−	0.358700i	0.743703	−	0.668510i	$-0.233068\pi$
$877$	−3.18177e15	−	5.51099e15i	−0.207096	−	0.358700i	−0.950798	+	0.309810i	$0.899734\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.60136e16			1.01653			0.508265	−	0.861201i	$-0.330287\pi$
$881$	1.60136e16			1.01653			0.508265	+	0.861201i	$0.330287\pi$
$882$		0			0
$883$	−6.13799e15			−0.384806			−0.192403	−	0.981316i	$-0.561628\pi$
$883$	−6.13799e15			−0.384806			−0.192403	+	0.981316i	$0.561628\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.55053e15	−	9.61380e15i	−0.339433	−	0.587916i	0.644893	−	0.764273i	$-0.276902\pi$
$887$	−5.55053e15	−	9.61380e15i	−0.339433	−	0.587916i	−0.984326	+	0.176357i	$0.943569\pi$
$888$		0			0
$889$	1.29095e16	+	4.02590e15i	0.779739	+	0.243166i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.04522e16	−	1.18081e16i	−1.20519	−	0.695818i
$894$		0			0
$895$			3.35398e15i			0.195224i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.74779e15	+	6.49136e15i	−0.212861	+	0.368687i
$900$		0			0
$901$	−4.98527e15	+	2.87825e15i	−0.279706	+	0.161488i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.10361e15	+	6.37167e14i	−0.0604292	+	0.0348888i
$906$		0			0
$907$	5.93958e15	−	1.02876e16i	0.321303	−	0.556514i	−0.659454	−	0.751745i	$-0.729212\pi$
$907$	5.93958e15	−	1.02876e16i	0.321303	−	0.556514i	0.980757	+	0.195231i	$0.0625457\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			1.87902e16i			0.992157i	0.868278	+	0.496079i	$0.165227\pi$
$911$			1.87902e16i			0.992157i	−0.868278	+	0.496079i	$0.834773\pi$
$912$		0			0
$913$	1.01818e15	+	5.87844e14i	0.0531170	+	0.0306671i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	6.27000e15	+	2.78684e16i	0.319327	+	1.41932i
$918$		0			0
$919$	−5.53626e15	−	9.58908e15i	−0.278600	−	0.482549i	0.692437	−	0.721478i	$-0.256537\pi$
$919$	−5.53626e15	−	9.58908e15i	−0.278600	−	0.482549i	−0.971037	+	0.238929i	$0.923204\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.36307e15			−0.116109
$924$		0			0
$925$	1.29144e16			0.627041
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.00823e15	−	3.47836e15i	−0.0952199	−	0.164926i	0.814480	−	0.580191i	$-0.197022\pi$
$929$	−2.00823e15	−	3.47836e15i	−0.0952199	−	0.164926i	−0.909700	+	0.415265i	$0.863689\pi$
$930$		0			0
$931$	−1.86979e16	−	1.51779e15i	−0.876131	−	0.0711196i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.36226e15	+	7.86500e14i	0.0623441	+	0.0359944i
$936$		0			0
$937$			1.16203e16i			0.525594i	0.964851	+	0.262797i	$0.0846450\pi$
$937$			1.16203e16i			0.525594i	−0.964851	+	0.262797i	$0.915355\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.63937e16	+	2.83947e16i	−0.724325	+	1.25457i	0.234926	+	0.972013i	$0.424515\pi$
$941$	−1.63937e16	+	2.83947e16i	−0.724325	+	1.25457i	−0.959251	+	0.282554i	$0.908818\pi$
$942$		0			0
$943$	−2.15168e16	+	1.24227e16i	−0.939643	+	0.542503i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.14555e15	+	2.39343e15i	−0.176871	+	0.102117i	−0.585822	−	0.810440i	$-0.699228\pi$
$947$	−4.14555e15	+	2.39343e15i	−0.176871	+	0.102117i	0.408951	+	0.912557i	$0.365895\pi$
$948$		0			0
$949$	−7.04153e15	+	1.21963e16i	−0.296963	+	0.514356i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1.85035e16i		−	0.762504i	−0.924471	−	0.381252i	$-0.875493\pi$
$953$		−	1.85035e16i		−	0.762504i	0.924471	−	0.381252i	$-0.124507\pi$
$954$		0			0
$955$	−5.40884e15	−	3.12279e15i	−0.220336	−	0.127211i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.83512e16	−	1.99012e16i	−0.730571	−	0.792277i
$960$		0			0
$961$	1.77213e16	+	3.06942e16i	0.697455	+	1.20803i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.00743e16			−0.387538
$966$		0			0
$967$	2.99142e16			1.13771			0.568856	−	0.822437i	$-0.307386\pi$
$967$	2.99142e16			1.13771			0.568856	+	0.822437i	$0.307386\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−5.45816e15	−	9.45381e15i	−0.202927	−	0.351480i	0.746543	−	0.665337i	$-0.231712\pi$
$971$	−5.45816e15	−	9.45381e15i	−0.202927	−	0.351480i	−0.949470	+	0.313857i	$0.898379\pi$
$972$		0			0
$973$	6.06814e15	−	1.94581e16i	0.223067	−	0.715288i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.31507e16	+	1.33661e16i	0.832039	+	0.480378i	0.854550	−	0.519369i	$-0.173833\pi$
$977$	2.31507e16	+	1.33661e16i	0.832039	+	0.480378i	−0.0225113	+	0.999747i	$0.507166\pi$
$978$		0			0
$979$		−	1.50742e15i		−	0.0535710i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.22694e16	−	2.12512e16i	0.426362	−	0.738481i	−0.570184	−	0.821517i	$-0.693128\pi$
$983$	1.22694e16	−	2.12512e16i	0.426362	−	0.738481i	0.996547	+	0.0830355i	$0.0264615\pi$
$984$		0			0
$985$	−5.13695e15	+	2.96582e15i	−0.176525	+	0.101917i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.16801e16	+	1.25170e16i	−0.728589	+	0.420651i
$990$		0			0
$991$	1.15713e16	−	2.00420e16i	0.384570	−	0.666096i	−0.607139	−	0.794596i	$-0.707683\pi$
$991$	1.15713e16	−	2.00420e16i	0.384570	−	0.666096i	0.991709	+	0.128500i	$0.0410163\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	3.35875e15i		−	0.109182i
$996$		0			0
$997$	1.16538e16	+	6.72830e15i	0.374664	+	0.216313i	0.675494	−	0.737365i	$-0.263930\pi$
$997$	1.16538e16	+	6.72830e15i	0.374664	+	0.216313i	−0.300830	+	0.953678i	$0.597264\pi$
$998$		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.17.12	✓	60
3.2	odd	2	inner	252.12.t.a.17.19	yes	60
7.5	odd	6	inner	252.12.t.a.89.19	yes	60
21.5	even	6	inner	252.12.t.a.89.12	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.12	✓	60	1.1	even	1	trivial
252.12.t.a.17.19	yes	60	3.2	odd	2	inner
252.12.t.a.89.12	yes	60	21.5	even	6	inner
252.12.t.a.89.19	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)

\(f(q)\)	\(=\)	\(q+(-1048.47 - 1816.01i) q^{5} +(-42450.8 - 13238.5i) q^{7} +O(q^{10})\)	\(q+(-1048.47 - 1816.01i) q^{5} +(-42450.8 - 13238.5i) q^{7} +(57588.1 + 33248.5i) q^{11} -772133. i q^{13} +(-5.64039e6 + 9.76943e6i) q^{17} +(-8.21619e6 + 4.74362e6i) q^{19} +(1.70645e7 - 9.85217e6i) q^{23} +(2.22155e7 - 3.84783e7i) q^{25} +3.03858e7i q^{29} +(2.13631e8 + 1.23340e8i) q^{31} +(2.04673e7 + 9.09713e7i) q^{35} +(1.45332e8 + 2.51722e8i) q^{37} -1.26091e9 q^{41} -1.27049e9 q^{43} +(1.24463e9 + 2.15576e9i) q^{47} +(1.62681e9 + 1.12397e9i) q^{49} +(4.41926e8 + 2.55146e8i) q^{53} -1.39441e8i q^{55} +(3.93266e9 - 6.81156e9i) q^{59} +(8.63663e9 - 4.98636e9i) q^{61} +(-1.40220e9 + 8.09562e8i) q^{65} +(-9.65546e9 + 1.67237e10i) q^{67} -3.06044e9i q^{71} +(-1.57956e10 - 9.11958e9i) q^{73} +(-2.00450e9 - 2.17381e9i) q^{77} +(-1.59752e10 - 2.76698e10i) q^{79} +1.76803e10 q^{83} +2.36552e10 q^{85} +(-1.13345e10 - 1.96319e10i) q^{89} +(-1.02219e10 + 3.27777e10i) q^{91} +(1.72289e10 + 9.94713e9i) q^{95} +1.30442e10i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 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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