LMFDB - Embedded newform 252.12.t.a.17.13

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			17.13
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-687.929 - 1191.53i) q^{5} +(-37416.0 - 24028.5i) q^{7} +O(q^{10})$	$q+(-687.929 - 1191.53i) q^{5} +(-37416.0 - 24028.5i) q^{7} +(564901. + 326146. i) q^{11} -958271. i q^{13} +(3.39128e6 - 5.87387e6i) q^{17} +(1.15218e7 - 6.65210e6i) q^{19} +(-3.61706e7 + 2.08831e7i) q^{23} +(2.34676e7 - 4.06470e7i) q^{25} +1.22721e8i q^{29} +(-8.30740e7 - 4.79628e7i) q^{31} +(-2.89115e6 + 6.11121e7i) q^{35} +(1.74553e8 + 3.02335e8i) q^{37} +1.06829e8 q^{41} +8.40500e8 q^{43} +(2.37526e8 + 4.11408e8i) q^{47} +(8.22584e8 + 1.79810e9i) q^{49} +(1.78880e9 + 1.03276e9i) q^{53} -8.97461e8i q^{55} +(-8.22276e8 + 1.42422e9i) q^{59} +(-7.13105e9 + 4.11711e9i) q^{61} +(-1.14181e9 + 6.59222e8i) q^{65} +(8.67691e9 - 1.50289e10i) q^{67} -1.85284e10i q^{71} +(-1.63890e10 - 9.46221e9i) q^{73} +(-1.32995e10 - 2.57768e10i) q^{77} +(1.50852e10 + 2.61283e10i) q^{79} +7.61917e9 q^{83} -9.33184e9 q^{85} +(2.98941e10 + 5.17781e10i) q^{89} +(-2.30259e10 + 3.58546e10i) q^{91} +(-1.58523e10 - 9.15234e9i) q^{95} -1.23513e9i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−687.929	−	1191.53i	−0.0984484	−	0.170518i	0.812594	−	0.582830i	$-0.198055\pi$
$5$	−687.929	−	1191.53i	−0.0984484	−	0.170518i	−0.911043	+	0.412312i	$0.864721\pi$
$6$		0			0
$7$	−37416.0	−	24028.5i	−0.841430	−	0.540366i
$7$	−37416.0	−	24028.5i	−0.841430	−	0.540366i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	564901.	+	326146.i	1.05758	+	0.610594i	0.924762	−	0.380547i	$-0.124264\pi$
$11$	564901.	+	326146.i	1.05758	+	0.610594i	0.132817	+	0.991141i	$0.457598\pi$
$12$		0			0
$13$		−	958271.i		−	0.715813i	−0.933757	−	0.357907i	$-0.883491\pi$
$13$		−	958271.i		−	0.715813i	0.933757	−	0.357907i	$-0.116509\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.39128e6	−	5.87387e6i	0.579288	−	1.00336i	−0.416273	−	0.909240i	$-0.636664\pi$
$17$	3.39128e6	−	5.87387e6i	0.579288	−	1.00336i	0.995561	−	0.0941169i	$-0.0300028\pi$
$18$		0			0
$19$	1.15218e7	−	6.65210e6i	1.06752	−	0.616331i	0.140014	−	0.990150i	$-0.455285\pi$
$19$	1.15218e7	−	6.65210e6i	1.06752	−	0.616331i	0.927502	+	0.373819i	$0.121952\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.61706e7	+	2.08831e7i	−1.17180	+	0.676538i	−0.954103	−	0.299479i	$-0.903187\pi$
$23$	−3.61706e7	+	2.08831e7i	−1.17180	+	0.676538i	−0.217695	+	0.976017i	$0.569854\pi$
$24$		0			0
$25$	2.34676e7	−	4.06470e7i	0.480616	−	0.832451i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			1.22721e8i			1.11104i	0.831504	+	0.555519i	$0.187481\pi$
$29$			1.22721e8i			1.11104i	−0.831504	+	0.555519i	$0.812519\pi$
$30$		0			0
$31$	−8.30740e7	−	4.79628e7i	−0.521166	−	0.300895i	0.216246	−	0.976339i	$-0.430619\pi$
$31$	−8.30740e7	−	4.79628e7i	−0.521166	−	0.300895i	−0.737411	+	0.675444i	$0.763952\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.89115e6	+	6.11121e7i	−0.00930457	+	0.196677i
$36$		0			0
$37$	1.74553e8	+	3.02335e8i	0.413826	+	0.716767i	0.995304	−	0.0967943i	$-0.0308589\pi$
$37$	1.74553e8	+	3.02335e8i	0.413826	+	0.716767i	−0.581479	+	0.813562i	$0.697526\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.06829e8			0.144005			0.0720027	−	0.997404i	$-0.477061\pi$
$41$	1.06829e8			0.144005			0.0720027	+	0.997404i	$0.477061\pi$
$42$		0			0
$43$	8.40500e8			0.871889			0.435945	−	0.899973i	$-0.356414\pi$
$43$	8.40500e8			0.871889			0.435945	+	0.899973i	$0.356414\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.37526e8	+	4.11408e8i	0.151068	+	0.261658i	0.931621	−	0.363433i	$-0.118395\pi$
$47$	2.37526e8	+	4.11408e8i	0.151068	+	0.261658i	−0.780552	+	0.625091i	$0.785062\pi$
$48$		0			0
$49$	8.22584e8	+	1.79810e9i	0.416008	+	0.909361i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.78880e9	+	1.03276e9i	0.587549	+	0.339222i	0.764128	−	0.645065i	$-0.223170\pi$
$53$	1.78880e9	+	1.03276e9i	0.587549	+	0.339222i	−0.176579	+	0.984287i	$0.556503\pi$
$54$		0			0
$55$		−	8.97461e8i		−	0.240448i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−8.22276e8	+	1.42422e9i	−0.149738	+	0.259354i	−0.931131	−	0.364686i	$-0.881176\pi$
$59$	−8.22276e8	+	1.42422e9i	−0.149738	+	0.259354i	0.781393	+	0.624040i	$0.214510\pi$
$60$		0			0
$61$	−7.13105e9	+	4.11711e9i	−1.08103	+	0.624135i	−0.931175	−	0.364572i	$-0.881215\pi$
$61$	−7.13105e9	+	4.11711e9i	−1.08103	+	0.624135i	−0.149859	+	0.988707i	$0.547882\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.14181e9	+	6.59222e8i	−0.122059	+	0.0704707i
$66$		0			0
$67$	8.67691e9	−	1.50289e10i	0.785152	−	1.35992i	−0.143756	−	0.989613i	$-0.545918\pi$
$67$	8.67691e9	−	1.50289e10i	0.785152	−	1.35992i	0.928908	−	0.370310i	$-0.120749\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.85284e10i		−	1.21876i	−0.792880	−	0.609378i	$-0.791419\pi$
$71$		−	1.85284e10i		−	1.21876i	0.792880	−	0.609378i	$-0.208581\pi$
$72$		0			0
$73$	−1.63890e10	−	9.46221e9i	−0.925289	−	0.534216i	−0.0399707	−	0.999201i	$-0.512726\pi$
$73$	−1.63890e10	−	9.46221e9i	−0.925289	−	0.534216i	−0.885319	+	0.464985i	$0.846060\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.32995e10	−	2.57768e10i	−0.559934	−	1.08525i
$78$		0			0
$79$	1.50852e10	+	2.61283e10i	0.551571	+	0.955349i	0.998161	+	0.0606106i	$0.0193048\pi$
$79$	1.50852e10	+	2.61283e10i	0.551571	+	0.955349i	−0.446590	+	0.894739i	$0.647362\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.61917e9			0.212314			0.106157	−	0.994349i	$-0.466145\pi$
$83$	7.61917e9			0.212314			0.106157	+	0.994349i	$0.466145\pi$
$84$		0			0
$85$	−9.33184e9			−0.228120
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.98941e10	+	5.17781e10i	0.567467	+	0.982881i	0.996816	+	0.0797423i	$0.0254097\pi$
$89$	2.98941e10	+	5.17781e10i	0.567467	+	0.982881i	−0.429349	+	0.903139i	$0.641257\pi$
$90$		0			0
$91$	−2.30259e10	+	3.58546e10i	−0.386801	+	0.602307i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.58523e10	−	9.15234e9i	−0.210190	−	0.121353i
$96$		0			0
$97$		−	1.23513e9i		−	0.0146039i	−0.999973	−	0.00730193i	$-0.997676\pi$
$97$		−	1.23513e9i		−	0.0146039i	0.999973	−	0.00730193i	$-0.00232430\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.52663e10	+	1.30365e11i	−0.712579	+	1.23422i	0.251308	+	0.967907i	$0.419139\pi$
$101$	−7.52663e10	+	1.30365e11i	−0.712579	+	1.23422i	−0.963886	+	0.266315i	$0.914194\pi$
$102$		0			0
$103$	−2.51969e10	+	1.45474e10i	−0.214162	+	0.123646i	−0.603244	−	0.797557i	$-0.706126\pi$
$103$	−2.51969e10	+	1.45474e10i	−0.214162	+	0.123646i	0.389082	+	0.921203i	$0.372792\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.37689e11	−	1.37230e11i	1.63832	−	0.945884i	0.656906	−	0.753973i	$-0.271865\pi$
$107$	2.37689e11	−	1.37230e11i	1.63832	−	0.945884i	0.981412	−	0.191911i	$-0.0614685\pi$
$108$		0			0
$109$	1.53376e11	−	2.65655e11i	0.954797	−	1.65376i	0.219965	−	0.975508i	$-0.429406\pi$
$109$	1.53376e11	−	2.65655e11i	0.954797	−	1.65376i	0.734832	−	0.678249i	$-0.237261\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			2.65809e10i			0.135718i	0.997695	+	0.0678591i	$0.0216168\pi$
$113$			2.65809e10i			0.135718i	−0.997695	+	0.0678591i	$0.978383\pi$
$114$		0			0
$115$	4.97656e10	+	2.87322e10i	0.230723	+	0.133208i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.68029e11	+	1.38289e11i	−1.02961	+	0.531226i
$120$		0			0
$121$	7.00865e10	+	1.21393e11i	0.245649	+	0.425477i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−1.31757e11			−0.386160
$126$		0			0
$127$	−1.03443e11			−0.277832			−0.138916	−	0.990304i	$-0.544362\pi$
$127$	−1.03443e11			−0.277832			−0.138916	+	0.990304i	$0.544362\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.11221e11	−	3.65845e11i	−0.478349	−	0.828524i	0.521343	−	0.853347i	$-0.325431\pi$
$131$	−2.11221e11	−	3.65845e11i	−0.478349	−	0.828524i	−0.999692	+	0.0248229i	$0.992098\pi$
$132$		0			0
$133$	−5.90938e11	−	2.79567e10i	−1.23128	−	0.0582507i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.60518e11	+	9.26751e10i	0.284158	+	0.164059i	0.635304	−	0.772262i	$-0.280875\pi$
$137$	1.60518e11	+	9.26751e10i	0.284158	+	0.164059i	−0.351146	+	0.936321i	$0.614208\pi$
$138$		0			0
$139$		−	4.74274e9i		−	0.00775261i	−0.999992	−	0.00387630i	$-0.998766\pi$
$139$		−	4.74274e9i		−	0.00775261i	0.999992	−	0.00387630i	$-0.00123387\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.12536e11	−	5.41328e11i	0.437071	−	0.757029i
$144$		0			0
$145$	1.46225e11	−	8.44232e10i	0.189452	−	0.109380i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.41484e12	−	8.16858e11i	1.57828	−	0.911218i	0.583175	−	0.812346i	$-0.301810\pi$
$149$	1.41484e12	−	8.16858e11i	1.57828	−	0.911218i	0.995100	−	0.0988715i	$-0.0315233\pi$
$150$		0			0
$151$	−2.37409e11	+	4.11204e11i	−0.246107	+	0.426270i	−0.962442	−	0.271486i	$-0.912485\pi$
$151$	−2.37409e11	+	4.11204e11i	−0.246107	+	0.426270i	0.716335	+	0.697756i	$0.245818\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			1.31980e11i			0.118491i
$156$		0			0
$157$	−8.19831e11	−	4.73329e11i	−0.685924	−	0.396018i	0.116159	−	0.993231i	$-0.462942\pi$
$157$	−8.19831e11	−	4.73329e11i	−0.685924	−	0.396018i	−0.802083	+	0.597212i	$0.796275\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.85515e12	+	8.77652e10i	1.35156	+	0.0639411i
$162$		0			0
$163$	1.80802e11	+	3.13158e11i	0.123075	+	0.213173i	0.920979	−	0.389612i	$-0.127391\pi$
$163$	1.80802e11	+	3.13158e11i	0.123075	+	0.213173i	−0.797904	+	0.602785i	$0.794058\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.51123e12			−1.49605			−0.748024	−	0.663672i	$-0.768997\pi$
$167$	−2.51123e12			−1.49605			−0.748024	+	0.663672i	$0.768997\pi$
$168$		0			0
$169$	8.73877e11			0.487611
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.16641e11	−	1.58767e12i	−0.449723	−	0.778944i	0.548644	−	0.836056i	$-0.315144\pi$
$173$	−9.16641e11	−	1.58767e12i	−0.449723	−	0.778944i	−0.998368	+	0.0571120i	$0.981811\pi$
$174$		0			0
$175$	−1.85475e12	+	9.56957e11i	−0.854233	+	0.440741i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.92845e11	+	2.84544e11i	0.200456	+	0.115733i	0.596868	−	0.802339i	$-0.296412\pi$
$179$	4.92845e11	+	2.84544e11i	0.200456	+	0.115733i	−0.396412	+	0.918073i	$0.629745\pi$
$180$		0			0
$181$		−	2.89239e12i		−	1.10669i	−0.832953	−	0.553343i	$-0.813352\pi$
$181$		−	2.89239e12i		−	1.10669i	0.832953	−	0.553343i	$-0.186648\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.40160e11	−	4.15969e11i	0.0814810	−	0.141129i
$186$		0			0
$187$	3.83148e12	−	2.21211e12i	1.22529	−	0.707419i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.46021e11	−	2.57510e11i	0.126961	−	0.0733012i	−0.435174	−	0.900346i	$-0.643313\pi$
$191$	4.46021e11	−	2.57510e11i	0.126961	−	0.0733012i	0.562136	+	0.827045i	$0.309980\pi$
$192$		0			0
$193$	−6.23579e11	+	1.08007e12i	−0.167620	+	0.290327i	−0.937583	−	0.347762i	$-0.886942\pi$
$193$	−6.23579e11	+	1.08007e12i	−0.167620	+	0.290327i	0.769962	+	0.638089i	$0.220275\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			1.91243e12i			0.459221i	0.973283	+	0.229610i	$0.0737452\pi$
$197$			1.91243e12i			0.459221i	−0.973283	+	0.229610i	$0.926255\pi$
$198$		0			0
$199$	−7.44492e12	−	4.29832e12i	−1.69109	−	0.976354i	−0.953636	−	0.300962i	$-0.902692\pi$
$199$	−7.44492e12	−	4.29832e12i	−1.69109	−	0.976354i	−0.737459	−	0.675392i	$-0.763974\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.94880e12	−	4.59172e12i	0.600368	−	0.934861i
$204$		0			0
$205$	−7.34909e10	−	1.27290e11i	−0.0141771	−	0.0245555i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.67822e12			1.50531
$210$		0			0
$211$	−5.71280e12			−0.940363			−0.470181	−	0.882570i	$-0.655812\pi$
$211$	−5.71280e12			−0.940363			−0.470181	+	0.882570i	$0.655812\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.78205e11	−	1.00148e12i	−0.0858361	−	0.148672i
$216$		0			0
$217$	1.95582e12	+	3.79072e12i	0.275931	+	0.534802i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.62876e12	−	3.24977e12i	−0.718216	−	0.414662i
$222$		0			0
$223$			1.51135e12i			0.183522i	0.995781	+	0.0917612i	$0.0292496\pi$
$223$			1.51135e12i			0.183522i	−0.995781	+	0.0917612i	$0.970750\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.47158e12	−	1.12091e13i	0.712636	−	1.23432i	−0.251228	−	0.967928i	$-0.580834\pi$
$227$	6.47158e12	−	1.12091e13i	0.712636	−	1.23432i	0.963864	−	0.266395i	$-0.0858324\pi$
$228$		0			0
$229$	2.79574e12	−	1.61412e12i	0.293360	−	0.169372i	−0.346096	−	0.938199i	$-0.612493\pi$
$229$	2.79574e12	−	1.61412e12i	0.293360	−	0.169372i	0.639456	+	0.768828i	$0.279160\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.02714e13	−	5.93020e12i	0.979879	−	0.565733i	0.0776454	−	0.996981i	$-0.475260\pi$
$233$	1.02714e13	−	5.93020e12i	0.979879	−	0.565733i	0.902234	+	0.431248i	$0.141926\pi$
$234$		0			0
$235$	3.26803e11	−	5.66039e11i	0.0297449	−	0.0515196i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	1.86751e13i		−	1.54908i	−0.632525	−	0.774540i	$-0.717981\pi$
$239$		−	1.86751e13i		−	1.54908i	0.632525	−	0.774540i	$-0.282019\pi$
$240$		0			0
$241$	−1.91859e13	−	1.10770e13i	−1.52016	−	0.877665i	−0.999718	−	0.0237679i	$-0.992434\pi$
$241$	−1.91859e13	−	1.10770e13i	−1.52016	−	0.877665i	−0.520442	−	0.853897i	$-0.674233\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.57661e12	−	2.21710e12i	0.114107	−	0.160462i
$246$		0			0
$247$	−6.37451e12	−	1.10410e13i	−0.441178	−	0.764142i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.05662e13			0.669445			0.334723	−	0.942317i	$-0.391357\pi$
$251$	1.05662e13			0.669445			0.334723	+	0.942317i	$0.391357\pi$
$252$		0			0
$253$	−2.72438e13			−1.65236
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.48985e13	−	2.58050e13i	−0.828916	−	1.43572i	−0.898889	−	0.438175i	$-0.855625\pi$
$257$	−1.48985e13	−	2.58050e13i	−0.828916	−	1.43572i	0.0699737	−	0.997549i	$-0.477708\pi$
$258$		0			0
$259$	7.33591e11	−	1.55064e13i	0.0391116	−	0.826727i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	1.76356e13	+	1.01819e13i	0.864241	+	0.498970i	0.865430	−	0.501030i	$-0.167045\pi$
$263$	1.76356e13	+	1.01819e13i	0.864241	+	0.498970i	−0.00118942	+	0.999999i	$0.500379\pi$
$264$		0			0
$265$		−	2.84187e12i		−	0.133583i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−2.72728e12	+	4.72378e12i	−0.118057	+	0.204481i	−0.918998	−	0.394263i	$-0.871000\pi$
$269$	−2.72728e12	+	4.72378e12i	−0.118057	+	0.204481i	0.800941	+	0.598744i	$0.204333\pi$
$270$		0			0
$271$	−2.00549e13	+	1.15787e13i	−0.833467	+	0.481202i	−0.855038	−	0.518565i	$-0.826466\pi$
$271$	−2.00549e13	+	1.15787e13i	−0.833467	+	0.481202i	0.0215712	+	0.999767i	$0.493133\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.65137e13	−	1.53077e13i	1.01658	−	0.586922i
$276$		0			0
$277$	1.13902e13	−	1.97284e13i	0.419656	−	0.726865i	−0.576249	−	0.817274i	$-0.695484\pi$
$277$	1.13902e13	−	1.97284e13i	0.419656	−	0.726865i	0.995905	+	0.0904090i	$0.0288174\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	4.53731e13i		−	1.54495i	−0.635047	−	0.772474i	$-0.719019\pi$
$281$		−	4.53731e13i		−	1.54495i	0.635047	−	0.772474i	$-0.280981\pi$
$282$		0			0
$283$	4.14142e13	+	2.39105e13i	1.35620	+	0.783002i	0.989109	−	0.147183i	$-0.0470207\pi$
$283$	4.14142e13	+	2.39105e13i	1.35620	+	0.783002i	0.367090	+	0.930185i	$0.380354\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.99712e12	−	2.56695e12i	−0.121170	−	0.0778157i
$288$		0			0
$289$	−5.86563e12	−	1.01596e13i	−0.171150	−	0.296440i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.60478e13			1.24577			0.622883	−	0.782315i	$-0.285961\pi$
$293$	4.60478e13			1.24577			0.622883	+	0.782315i	$0.285961\pi$
$294$		0			0
$295$	2.26267e12			0.0589658
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.00117e13	+	3.46612e13i	0.484275	+	0.838789i
$300$		0			0
$301$	−3.14481e13	−	2.01960e13i	−0.733634	−	0.471140i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	9.81131e12	+	5.66456e12i	0.212852	+	0.122890i
$306$		0			0
$307$		−	7.85523e13i		−	1.64398i	−0.569498	−	0.821992i	$-0.692863\pi$
$307$		−	7.85523e13i		−	1.64398i	0.569498	−	0.821992i	$-0.307137\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.93199e13	−	6.81040e13i	0.766355	−	1.32737i	−0.173172	−	0.984892i	$-0.555402\pi$
$311$	3.93199e13	−	6.81040e13i	0.766355	−	1.32737i	0.939527	−	0.342474i	$-0.111265\pi$
$312$		0			0
$313$	−8.79722e13	+	5.07908e13i	−1.65520	+	0.955633i	−0.680321	+	0.732914i	$0.738160\pi$
$313$	−8.79722e13	+	5.07908e13i	−1.65520	+	0.955633i	−0.974883	+	0.222719i	$0.928507\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	7.38157e12	−	4.26175e12i	0.129516	−	0.0747760i	−0.433842	−	0.900989i	$-0.642842\pi$
$317$	7.38157e12	−	4.26175e12i	0.129516	−	0.0747760i	0.563358	+	0.826213i	$0.309509\pi$
$318$		0			0
$319$	−4.00249e13	+	6.93252e13i	−0.678393	+	1.17501i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	9.02365e13i		−	1.42813i
$324$		0			0
$325$	−3.89509e13	−	2.24883e13i	−0.595880	−	0.344031i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	9.98249e11	−	2.11006e13i	0.0142778	−	0.301799i
$330$		0			0
$331$	−6.20486e13	−	1.07471e14i	−0.858377	−	1.48675i	−0.873477	−	0.486866i	$-0.838140\pi$
$331$	−6.20486e13	−	1.07471e14i	−0.858377	−	1.48675i	0.0150998	−	0.999886i	$-0.495193\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.38764e13			−0.309188
$336$		0			0
$337$	6.08209e13			0.762234			0.381117	−	0.924527i	$-0.375539\pi$
$337$	6.08209e13			0.762234			0.381117	+	0.924527i	$0.375539\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.12857e13	−	5.41885e13i	−0.367449	−	0.636441i
$342$		0			0
$343$	1.24280e13	−	8.70433e13i	0.141346	−	0.989960i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.66613e13	−	2.11664e13i	−0.391197	−	0.225858i	0.291482	−	0.956576i	$-0.405852\pi$
$347$	−3.66613e13	−	2.11664e13i	−0.391197	−	0.225858i	−0.682679	+	0.730719i	$0.739185\pi$
$348$		0			0
$349$			1.28531e13i			0.132882i	0.997790	+	0.0664412i	$0.0211645\pi$
$349$			1.28531e13i			0.132882i	−0.997790	+	0.0664412i	$0.978836\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	6.56535e13	−	1.13715e14i	0.637525	−	1.10423i	−0.348449	−	0.937328i	$-0.613292\pi$
$353$	6.56535e13	−	1.13715e14i	0.637525	−	1.10423i	0.985974	−	0.166898i	$-0.0533751\pi$
$354$		0			0
$355$	−2.20771e13	+	1.27462e13i	−0.207819	+	0.119985i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.75761e13	−	2.16946e13i	0.332577	−	0.192014i	−0.324407	−	0.945917i	$-0.605165\pi$
$359$	3.75761e13	−	2.16946e13i	0.332577	−	0.192014i	0.656985	+	0.753904i	$0.271832\pi$
$360$		0			0
$361$	3.02556e13	−	5.24043e13i	0.259727	−	0.449860i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			2.60373e13i			0.210371i
$366$		0			0
$367$	−8.69021e13	−	5.01729e13i	−0.681344	−	0.393374i	0.119017	−	0.992892i	$-0.462026\pi$
$367$	−8.69021e13	−	5.01729e13i	−0.681344	−	0.393374i	−0.800361	+	0.599518i	$0.795359\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.21139e13	−	8.16241e13i	−0.311077	−	0.602923i
$372$		0			0
$373$	4.48316e13	+	7.76506e13i	0.321504	+	0.556861i	0.980798	−	0.195024i	$-0.0624784\pi$
$373$	4.48316e13	+	7.76506e13i	0.321504	+	0.556861i	−0.659295	+	0.751884i	$0.729145\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.17600e14			0.795297
$378$		0			0
$379$	−1.22298e14			−0.803350			−0.401675	−	0.915782i	$-0.631572\pi$
$379$	−1.22298e14			−0.803350			−0.401675	+	0.915782i	$0.631572\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.26365e14	+	2.18870e14i	0.783490	+	1.35704i	0.929897	+	0.367820i	$0.119896\pi$
$383$	1.26365e14	+	2.18870e14i	0.783490	+	1.35704i	−0.146407	+	0.989224i	$0.546771\pi$
$384$		0			0
$385$	−2.15647e13	+	3.35794e13i	−0.129930	+	0.202320i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.11577e13	+	4.10829e13i	0.405041	+	0.233851i	0.688657	−	0.725087i	$-0.258201\pi$
$389$	7.11577e13	+	4.10829e13i	0.405041	+	0.233851i	−0.283616	+	0.958938i	$0.591534\pi$
$390$		0			0
$391$			2.83282e14i			1.56764i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.07551e13	−	3.59488e13i	0.108603	−	0.188105i
$396$		0			0
$397$	2.69223e14	−	1.55436e14i	1.37014	−	0.791049i	0.379192	−	0.925318i	$-0.376202\pi$
$397$	2.69223e14	−	1.55436e14i	1.37014	−	0.791049i	0.990945	+	0.134269i	$0.0428687\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.14185e14	+	6.59248e13i	−0.549940	+	0.317508i	−0.749098	−	0.662459i	$-0.769513\pi$
$401$	−1.14185e14	+	6.59248e13i	−0.549940	+	0.317508i	0.199158	+	0.979967i	$0.436179\pi$
$402$		0			0
$403$	−4.59613e13	+	7.96074e13i	−0.215385	+	0.373057i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			2.27719e14i			1.01072i
$408$		0			0
$409$	−1.19627e14	−	6.90669e13i	−0.516835	−	0.298395i	0.218804	−	0.975769i	$-0.429785\pi$
$409$	−1.19627e14	−	6.90669e13i	−0.516835	−	0.298395i	−0.735639	+	0.677374i	$0.763118\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	6.49883e13	−	3.35306e13i	0.266140	−	0.137315i
$414$		0			0
$415$	−5.24144e12	−	9.07845e12i	−0.0209019	−	0.0362032i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−2.40638e14			−0.910304			−0.455152	−	0.890414i	$-0.650415\pi$
$419$	−2.40638e14			−0.910304			−0.455152	+	0.890414i	$0.650415\pi$
$420$		0			0
$421$	2.13681e14			0.787435			0.393718	−	0.919231i	$-0.371189\pi$
$421$	2.13681e14			0.787435			0.393718	+	0.919231i	$0.371189\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.59170e14	−	2.75691e14i	−0.556830	−	0.964458i
$426$		0			0
$427$	3.65743e14	+	1.73029e13i	1.24688	+	0.0589884i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.50631e14	−	8.69669e13i	−0.487854	−	0.281663i	0.235830	−	0.971794i	$-0.424219\pi$
$431$	−1.50631e14	−	8.69669e13i	−0.487854	−	0.281663i	−0.723684	+	0.690132i	$0.757553\pi$
$432$		0			0
$433$			9.74550e13i			0.307695i	0.988095	+	0.153848i	$0.0491665\pi$
$433$			9.74550e13i			0.307695i	−0.988095	+	0.153848i	$0.950834\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.77833e14	+	4.81221e14i	−0.833942	+	1.44443i
$438$		0			0
$439$	−3.04290e13	+	1.75682e13i	−0.0890702	+	0.0514247i	−0.543874	−	0.839167i	$-0.683043\pi$
$439$	−3.04290e13	+	1.75682e13i	−0.0890702	+	0.0514247i	0.454803	+	0.890592i	$0.349710\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.61202e13	−	5.54950e13i	0.267667	−	0.154537i	−0.360160	−	0.932890i	$-0.617278\pi$
$443$	9.61202e13	−	5.54950e13i	0.267667	−	0.154537i	0.627827	+	0.778353i	$0.283945\pi$
$444$		0			0
$445$	4.11300e13	−	7.12393e13i	0.111732	−	0.193526i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			3.75387e14i			0.970787i	0.874296	+	0.485393i	$0.161324\pi$
$449$			3.75387e14i			0.970787i	−0.874296	+	0.485393i	$0.838676\pi$
$450$		0			0
$451$	6.03480e13	+	3.48419e13i	0.152297	+	0.0879288i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.85620e13	+	2.77050e12i	0.140784	+	0.00666034i
$456$		0			0
$457$	−2.06746e13	−	3.58095e13i	−0.0485175	−	0.0840348i	0.840747	−	0.541429i	$-0.182116\pi$
$457$	−2.06746e13	−	3.58095e13i	−0.0485175	−	0.0840348i	−0.889264	+	0.457394i	$0.848783\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.90892e13			0.0427005			0.0213502	−	0.999772i	$-0.493203\pi$
$461$	1.90892e13			0.0427005			0.0213502	+	0.999772i	$0.493203\pi$
$462$		0			0
$463$	9.22284e13			0.201451			0.100725	−	0.994914i	$-0.467884\pi$
$463$	9.22284e13			0.201451			0.100725	+	0.994914i	$0.467884\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.34685e14	−	4.06486e14i	−0.488925	−	0.846844i	0.510993	−	0.859585i	$-0.329278\pi$
$467$	−2.34685e14	−	4.06486e14i	−0.488925	−	0.846844i	−0.999919	+	0.0127410i	$0.995944\pi$
$468$		0			0
$469$	−6.85777e14	+	3.53826e14i	−1.39551	+	0.720010i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.74800e14	+	2.74126e14i	0.922092	+	0.532370i
$474$		0			0
$475$		−	6.24434e14i		−	1.18487i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−3.96685e14	+	6.87079e14i	−0.718788	+	1.24498i	0.242693	+	0.970103i	$0.421969\pi$
$479$	−3.96685e14	+	6.87079e14i	−0.718788	+	1.24498i	−0.961480	+	0.274874i	$0.911364\pi$
$480$		0			0
$481$	2.89718e14	−	1.67269e14i	0.513072	−	0.296222i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.47169e12	+	8.49681e11i	−0.00249021	+	0.00143773i
$486$		0			0
$487$	−2.26602e14	+	3.92486e14i	−0.374847	+	0.649255i	−0.990304	−	0.138916i	$-0.955638\pi$
$487$	−2.26602e14	+	3.92486e14i	−0.374847	+	0.649255i	0.615457	+	0.788171i	$0.288972\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	2.82034e14i		−	0.446019i	−0.974816	−	0.223009i	$-0.928412\pi$
$491$		−	2.82034e14i		−	0.446019i	0.974816	−	0.223009i	$-0.0715881\pi$
$492$		0			0
$493$	7.20846e14	+	4.16181e14i	1.11477	+	0.643612i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.45210e14	+	6.93258e14i	−0.658575	+	1.02550i
$498$		0			0
$499$	6.12112e14	+	1.06021e15i	0.885683	+	1.53405i	0.844929	+	0.534878i	$0.179643\pi$
$499$	6.12112e14	+	1.06021e15i	0.885683	+	1.53405i	0.0407536	+	0.999169i	$0.487024\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−9.47420e14			−1.31195			−0.655977	−	0.754781i	$-0.727743\pi$
$503$	−9.47420e14			−1.31195			−0.655977	+	0.754781i	$0.727743\pi$
$504$		0			0
$505$	2.07111e14			0.280609
$506$		0			0
$507$		0			0
$508$		0			0
$509$	2.27215e14	+	3.93548e14i	0.294774	+	0.510563i	0.974932	−	0.222502i	$-0.0714224\pi$
$509$	2.27215e14	+	3.93548e14i	0.294774	+	0.510563i	−0.680158	+	0.733065i	$0.738089\pi$
$510$		0			0
$511$	3.85848e14	+	7.47843e14i	0.489894	+	0.949501i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.46673e13	+	2.00152e13i	0.0421678	+	0.0243456i
$516$		0			0
$517$			3.09873e14i			0.368966i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.12355e14	+	8.87425e14i	−0.584741	+	1.01280i	0.410166	+	0.912011i	$0.365471\pi$
$521$	−5.12355e14	+	8.87425e14i	−0.584741	+	1.01280i	−0.994908	+	0.100791i	$0.967863\pi$
$522$		0			0
$523$	3.75779e14	−	2.16956e14i	0.419927	−	0.242445i	−0.275119	−	0.961410i	$-0.588717\pi$
$523$	3.75779e14	−	2.16956e14i	0.419927	−	0.242445i	0.695046	+	0.718965i	$0.255384\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.63454e14	+	3.25311e14i	−0.603810	+	0.348610i
$528$		0			0
$529$	3.95804e14	−	6.85553e14i	0.415407	−	0.719507i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	1.02371e14i		−	0.103081i
$534$		0			0
$535$	−3.27026e14	−	1.88809e14i	−0.322580	−	0.186241i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.21765e14	+	1.28403e15i	−0.115288	+	1.21573i
$540$		0			0
$541$	4.52135e14	+	7.83122e14i	0.419453	+	0.726514i	0.995885	−	0.0906312i	$-0.0288885\pi$
$541$	4.52135e14	+	7.83122e14i	0.419453	+	0.726514i	−0.576431	+	0.817146i	$0.695555\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−4.22047e14			−0.375993
$546$		0			0
$547$	7.69201e14			0.671598			0.335799	−	0.941934i	$-0.390994\pi$
$547$	7.69201e14			0.671598			0.335799	+	0.941934i	$0.390994\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.16351e14	+	1.41396e15i	0.684767	+	1.18605i
$552$		0			0
$553$	6.33983e13	−	1.34009e15i	0.0521302	−	1.10191i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−5.66553e14	−	3.27099e14i	−0.447751	−	0.258509i	0.259129	−	0.965843i	$-0.416565\pi$
$557$	−5.66553e14	−	3.27099e14i	−0.447751	−	0.258509i	−0.706880	+	0.707334i	$0.749898\pi$
$558$		0			0
$559$		−	8.05427e14i		−	0.624110i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	4.23280e14	−	7.33142e14i	0.315378	−	0.546250i	−0.664140	−	0.747608i	$-0.731202\pi$
$563$	4.23280e14	−	7.33142e14i	0.315378	−	0.546250i	0.979518	+	0.201358i	$0.0645354\pi$
$564$		0			0
$565$	3.16719e13	−	1.82858e13i	0.0231423	−	0.0133612i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.42172e15	+	8.20833e14i	−0.999305	+	0.576949i	−0.908043	−	0.418878i	$-0.862424\pi$
$569$	−1.42172e15	+	8.20833e14i	−0.999305	+	0.576949i	−0.0912624	+	0.995827i	$0.529090\pi$
$570$		0			0
$571$	−1.03897e14	+	1.79955e14i	−0.0716314	+	0.124069i	−0.899616	−	0.436681i	$-0.856154\pi$
$571$	−1.03897e14	+	1.79955e14i	−0.0716314	+	0.124069i	0.827985	+	0.560750i	$0.189487\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			1.96030e15i			1.30062i
$576$		0			0
$577$	1.92573e15	+	1.11182e15i	1.25351	+	0.723716i	0.971805	−	0.235784i	$-0.0757659\pi$
$577$	1.92573e15	+	1.11182e15i	1.25351	+	0.723716i	0.281707	+	0.959500i	$0.409099\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.85079e14	−	1.83077e14i	−0.178647	−	0.114727i
$582$		0			0
$583$	6.73663e14	+	1.16682e15i	0.414253	+	0.717508i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.77025e15			1.04839			0.524196	−	0.851597i	$-0.324366\pi$
$587$	1.77025e15			1.04839			0.524196	+	0.851597i	$0.324366\pi$
$588$		0			0
$589$	−1.27621e15			−0.741803
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.59556e14	−	4.49564e14i	−0.145355	−	0.251762i	0.784150	−	0.620571i	$-0.213099\pi$
$593$	−2.59556e14	−	4.49564e14i	−0.145355	−	0.251762i	−0.929505	+	0.368809i	$0.879766\pi$
$594$		0			0
$595$	3.49160e14	+	2.24231e14i	0.191947	+	0.123268i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.20861e15	−	1.27514e15i	−1.17023	−	0.675633i	−0.216496	−	0.976284i	$-0.569463\pi$
$599$	−2.20861e15	−	1.27514e15i	−1.17023	−	0.675633i	−0.953734	+	0.300651i	$0.902796\pi$
$600$		0			0
$601$			3.60662e15i			1.87625i	0.346299	+	0.938124i	$0.387438\pi$
$601$			3.60662e15i			1.87625i	−0.346299	+	0.938124i	$0.612562\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.64291e13	−	1.67020e14i	0.0483675	−	0.0837750i
$606$		0			0
$607$	−1.27072e15	+	7.33650e14i	−0.625909	+	0.361369i	−0.779166	−	0.626817i	$-0.784357\pi$
$607$	−1.27072e15	+	7.33650e14i	−0.625909	+	0.361369i	0.153257	+	0.988186i	$0.451024\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.94240e14	−	2.27615e14i	0.187298	−	0.108137i
$612$		0			0
$613$	−1.02717e14	+	1.77911e14i	−0.0479302	+	0.0830176i	−0.888995	−	0.457917i	$-0.848596\pi$
$613$	−1.02717e14	+	1.77911e14i	−0.0479302	+	0.0830176i	0.841065	+	0.540934i	$0.181929\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	4.94211e14i		−	0.222507i	−0.993792	−	0.111254i	$-0.964513\pi$
$617$		−	4.94211e14i		−	0.222507i	0.993792	−	0.111254i	$-0.0354866\pi$
$618$		0			0
$619$	−2.80686e15	−	1.62054e15i	−1.24143	−	0.716739i	−0.272044	−	0.962285i	$-0.587699\pi$
$619$	−2.80686e15	−	1.62054e15i	−1.24143	−	0.716739i	−0.969385	+	0.245546i	$0.921033\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.25635e14	−	2.65564e15i	0.0536325	−	1.13367i
$624$		0			0
$625$	−1.05524e15	−	1.82773e15i	−0.442599	−	0.766604i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	2.36783e15			0.958898
$630$		0			0
$631$	1.84985e15			0.736163			0.368081	−	0.929794i	$-0.380015\pi$
$631$	1.84985e15			0.736163			0.368081	+	0.929794i	$0.380015\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.11616e13	+	1.23256e14i	0.0273521	+	0.0473752i
$636$		0			0
$637$	1.72307e15	−	7.88259e14i	0.650933	−	0.297784i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.51978e14	+	3.76419e14i	0.237965	+	0.137389i	0.614241	−	0.789118i	$-0.289462\pi$
$641$	6.51978e14	+	3.76419e14i	0.237965	+	0.137389i	−0.376276	+	0.926508i	$0.622796\pi$
$642$		0			0
$643$		−	2.52913e15i		−	0.907426i	−0.891148	−	0.453713i	$-0.850099\pi$
$643$		−	2.52913e15i		−	0.907426i	0.891148	−	0.453713i	$-0.149901\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.68551e14	−	8.11555e14i	0.162474	−	0.281413i	−0.773281	−	0.634063i	$-0.781386\pi$
$647$	4.68551e14	−	8.11555e14i	0.162474	−	0.281413i	0.935755	+	0.352650i	$0.114719\pi$
$648$		0			0
$649$	−9.29010e14	+	5.36364e14i	−0.316719	+	0.182858i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.20051e15	+	6.93115e14i	−0.395679	+	0.228446i	−0.684618	−	0.728902i	$-0.740031\pi$
$653$	−1.20051e15	+	6.93115e14i	−0.395679	+	0.228446i	0.288939	+	0.957348i	$0.406698\pi$
$654$		0			0
$655$	−2.90610e14	+	5.03351e14i	−0.0941853	+	0.163134i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	4.97875e14i		−	0.156045i	−0.996952	−	0.0780226i	$-0.975139\pi$
$659$		−	4.97875e14i		−	0.156045i	0.996952	−	0.0780226i	$-0.0248606\pi$
$660$		0			0
$661$	5.35762e14	+	3.09322e14i	0.165144	+	0.0953462i	0.580294	−	0.814407i	$-0.302938\pi$
$661$	5.35762e14	+	3.09322e14i	0.165144	+	0.0953462i	−0.415150	+	0.909753i	$0.636271\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.73212e14	+	7.23352e14i	0.111285	+	0.215690i
$666$		0			0
$667$	−2.56279e15	−	4.43889e15i	−0.751660	−	1.30191i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−5.37112e15			−1.52437
$672$		0			0
$673$	2.92317e14			0.0816152			0.0408076	−	0.999167i	$-0.487007\pi$
$673$	2.92317e14			0.0816152			0.0408076	+	0.999167i	$0.487007\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.73738e14	+	1.16695e15i	0.182076	+	0.315365i	0.942587	−	0.333960i	$-0.108385\pi$
$677$	6.73738e14	+	1.16695e15i	0.182076	+	0.315365i	−0.760511	+	0.649325i	$0.775052\pi$
$678$		0			0
$679$	−2.96783e13	+	4.62135e13i	−0.00789143	+	0.0122881i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	2.19590e15	+	1.26780e15i	0.565324	+	0.326390i	0.755280	−	0.655403i	$-0.227501\pi$
$683$	2.19590e15	+	1.26780e15i	0.565324	+	0.326390i	−0.189955	+	0.981793i	$0.560834\pi$
$684$		0			0
$685$		−	2.55015e14i		−	0.0646053i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.89667e14	−	1.71415e15i	0.242819	−	0.420576i
$690$		0			0
$691$	−2.24103e15	+	1.29386e15i	−0.541152	+	0.312434i	−0.745546	−	0.666455i	$-0.767811\pi$
$691$	−2.24103e15	+	1.29386e15i	−0.541152	+	0.312434i	0.204394	+	0.978889i	$0.434478\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−5.65111e12	+	3.26267e12i	−0.00132196	+	0.000763232i
$696$		0			0
$697$	3.62288e14	−	6.27501e14i	0.0834206	−	0.144489i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			2.21801e15i			0.494896i	0.968901	+	0.247448i	$0.0795920\pi$
$701$			2.21801e15i			0.494896i	−0.968901	+	0.247448i	$0.920408\pi$
$702$		0			0
$703$	4.02232e15	+	2.32229e15i	0.883531	+	0.510107i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.94864e15	−	3.06919e15i	1.26652	−	0.653458i
$708$		0			0
$709$	−4.00498e15	−	6.93683e15i	−0.839549	−	1.45414i	−0.890273	−	0.455428i	$-0.849486\pi$
$709$	−4.00498e15	−	6.93683e15i	−0.839549	−	1.45414i	0.0507240	−	0.998713i	$-0.483847\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	4.00645e15			0.814268
$714$		0			0
$715$	−8.60011e14			−0.172116
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4.21035e15	−	7.29253e15i	−0.817163	−	1.41537i	−0.907764	−	0.419481i	$-0.862212\pi$
$719$	−4.21035e15	−	7.29253e15i	−0.817163	−	1.41537i	0.0906006	−	0.995887i	$-0.471121\pi$
$720$		0			0
$721$	1.29232e15	+	6.11383e13i	0.247016	+	0.0116861i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	4.98824e15	+	2.87996e15i	0.924886	+	0.533983i
$726$		0			0
$727$			3.12551e15i			0.570797i	0.958409	+	0.285398i	$0.0921259\pi$
$727$			3.12551e15i			0.570797i	−0.958409	+	0.285398i	$0.907874\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.85037e15	−	4.93699e15i	0.505075	−	0.874816i
$732$		0			0
$733$	2.59297e15	−	1.49705e15i	0.452612	−	0.261316i	−0.256321	−	0.966592i	$-0.582510\pi$
$733$	2.59297e15	−	1.49705e15i	0.452612	−	0.261316i	0.708933	+	0.705276i	$0.249177\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	9.80320e15	−	5.65988e15i	1.66072	−	0.958818i
$738$		0			0
$739$	−2.68245e15	+	4.64614e15i	−0.447701	+	0.775440i	−0.998236	−	0.0593716i	$-0.981090\pi$
$739$	−2.68245e15	+	4.64614e15i	−0.447701	+	0.775440i	0.550535	+	0.834812i	$0.314424\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	1.19194e16i		−	1.93115i	−0.260119	−	0.965576i	$-0.583762\pi$
$743$		−	1.19194e16i		−	1.93115i	0.260119	−	0.965576i	$-0.416238\pi$
$744$		0			0
$745$	−1.94662e15	−	1.12388e15i	−0.310757	−	0.179416i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.21908e16	−	5.76734e14i	−1.88965	−	0.0893975i
$750$		0			0
$751$	−4.91321e14	−	8.50992e14i	−0.0750491	−	0.129989i	0.826059	−	0.563584i	$-0.190578\pi$
$751$	−4.91321e14	−	8.50992e14i	−0.0750491	−	0.129989i	−0.901108	+	0.433596i	$0.857245\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.53282e14			0.0969153
$756$		0			0
$757$	−1.16075e16			−1.69711			−0.848555	−	0.529107i	$-0.822527\pi$
$757$	−1.16075e16			−1.69711			−0.848555	+	0.529107i	$0.822527\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.24131e15	+	5.61412e15i	0.460368	+	0.797381i	0.998979	−	0.0451735i	$-0.0143841\pi$
$761$	3.24131e15	+	5.61412e15i	0.460368	+	0.797381i	−0.538611	+	0.842555i	$0.681051\pi$
$762$		0			0
$763$	−1.21220e16	+	6.25433e15i	−1.69703	+	0.875580i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.36479e15	+	7.87963e14i	0.185649	+	0.107184i
$768$		0			0
$769$		−	9.67609e15i		−	1.29749i	−0.761005	−	0.648746i	$-0.775294\pi$
$769$		−	9.67609e15i		−	1.29749i	0.761005	−	0.648746i	$-0.224706\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.63625e15	−	8.03023e15i	0.604199	−	1.04650i	−0.387979	−	0.921668i	$-0.626827\pi$
$773$	4.63625e15	−	8.03023e15i	0.604199	−	1.04650i	0.992178	−	0.124835i	$-0.0398401\pi$
$774$		0			0
$775$	−3.89909e15	+	2.25114e15i	−0.500961	+	0.289230i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.23086e15	−	7.10638e14i	0.153728	−	0.0887549i
$780$		0			0
$781$	6.04296e15	−	1.04667e16i	0.744165	−	1.28893i
$782$		0			0
$783$		0			0
$784$		0			0
$785$			1.30247e15i			0.155949i
$786$		0			0
$787$	−8.81384e15	−	5.08867e15i	−1.04065	−	0.600819i	−0.120632	−	0.992697i	$-0.538492\pi$
$787$	−8.81384e15	−	5.08867e15i	−1.04065	−	0.600819i	−0.920017	+	0.391879i	$0.871825\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	6.38700e14	−	9.94550e14i	0.0733375	−	0.114197i
$792$		0			0
$793$	3.94531e15	+	6.83347e15i	0.446764	+	0.773818i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.72832e15			0.851264			0.425632	−	0.904896i	$-0.360052\pi$
$797$	7.72832e15			0.851264			0.425632	+	0.904896i	$0.360052\pi$
$798$		0			0
$799$	3.22208e15			0.350049
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−6.17212e15	−	1.06904e16i	−0.652378	−	1.12995i
$804$		0			0
$805$	−1.17164e15	−	2.27084e15i	−0.122156	−	0.236760i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−9.77174e15	−	5.64171e15i	−0.991414	−	0.572393i	−0.0857171	−	0.996320i	$-0.527318\pi$
$809$	−9.77174e15	−	5.64171e15i	−0.991414	−	0.572393i	−0.905697	+	0.423927i	$0.860651\pi$
$810$		0			0
$811$		−	9.33685e15i		−	0.934514i	−0.884122	−	0.467257i	$-0.845242\pi$
$811$		−	9.33685e15i		−	0.934514i	0.884122	−	0.467257i	$-0.154758\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.48758e14	−	4.30861e14i	0.0242331	−	0.0419730i
$816$		0			0
$817$	9.68405e15	−	5.59109e15i	0.930756	−	0.537372i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.36096e16	−	7.85753e15i	1.27338	−	0.735188i	0.297760	−	0.954641i	$-0.403760\pi$
$821$	1.36096e16	−	7.85753e15i	1.27338	−	0.735188i	0.975623	+	0.219453i	$0.0704271\pi$
$822$		0			0
$823$	1.56983e15	−	2.71903e15i	0.144929	−	0.251024i	−0.784418	−	0.620233i	$-0.787038\pi$
$823$	1.56983e15	−	2.71903e15i	0.144929	−	0.251024i	0.929346	+	0.369209i	$0.120371\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	5.54624e14i		−	0.0498561i	−0.999689	−	0.0249280i	$-0.992064\pi$
$827$		−	5.54624e14i		−	0.0498561i	0.999689	−	0.0249280i	$-0.00793567\pi$
$828$		0			0
$829$	−2.02517e15	−	1.16923e15i	−0.179644	−	0.103717i	0.407482	−	0.913213i	$-0.366407\pi$
$829$	−2.02517e15	−	1.16923e15i	−0.179644	−	0.103717i	−0.587125	+	0.809496i	$0.699740\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.33514e16	+	1.26612e15i	1.15340	+	0.109377i
$834$		0			0
$835$	1.72755e15	+	2.99220e15i	0.147283	+	0.255102i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	6.54198e15			0.543274			0.271637	−	0.962400i	$-0.412435\pi$
$839$	6.54198e15			0.543274			0.271637	+	0.962400i	$0.412435\pi$
$840$		0			0
$841$	−2.85989e15			−0.234408
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−6.01166e14	−	1.04125e15i	−0.0480045	−	0.0831463i
$846$		0			0
$847$	2.94552e14	−	6.22613e15i	0.0232168	−	0.490749i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.26274e16	−	7.29042e15i	−0.969841	−	0.559938i
$852$		0			0
$853$			9.30818e15i			0.705741i	0.935672	+	0.352870i	$0.114794\pi$
$853$			9.30818e15i			0.705741i	−0.935672	+	0.352870i	$0.885206\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−8.21644e15	+	1.42313e16i	−0.607141	+	1.05160i	0.384569	+	0.923096i	$0.374350\pi$
$857$	−8.21644e15	+	1.42313e16i	−0.607141	+	1.05160i	−0.991709	+	0.128502i	$0.958983\pi$
$858$		0			0
$859$	−1.78140e16	+	1.02849e16i	−1.29957	+	0.750308i	−0.980330	−	0.197366i	$-0.936761\pi$
$859$	−1.78140e16	+	1.02849e16i	−1.29957	+	0.750308i	−0.319241	+	0.947673i	$0.603428\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.03332e16	+	5.96590e15i	−0.734814	+	0.424245i	−0.820181	−	0.572104i	$-0.806127\pi$
$863$	−1.03332e16	+	5.96590e15i	−0.734814	+	0.424245i	0.0853666	+	0.996350i	$0.472794\pi$
$864$		0			0
$865$	−1.26117e15	+	2.18441e15i	−0.0885491	+	0.153372i
$866$		0			0
$867$		0			0
$868$		0			0
$869$			1.96799e16i			1.34714i
$870$		0			0
$871$	−1.44017e16	−	8.31483e15i	−0.973451	−	0.562022i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	4.92980e15	+	3.16592e15i	0.324927	+	0.208668i
$876$		0			0
$877$	1.48735e16	+	2.57617e16i	0.968089	+	1.67678i	0.701076	+	0.713087i	$0.252703\pi$
$877$	1.48735e16	+	2.57617e16i	0.968089	+	1.67678i	0.267013	+	0.963693i	$0.413963\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−9.36837e13			−0.00594698			−0.00297349	−	0.999996i	$-0.500946\pi$
$881$	−9.36837e13			−0.00594698			−0.00297349	+	0.999996i	$0.500946\pi$
$882$		0			0
$883$	3.12659e15			0.196014			0.0980069	−	0.995186i	$-0.468753\pi$
$883$	3.12659e15			0.196014			0.0980069	+	0.995186i	$0.468753\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	7.64417e15	+	1.32401e16i	0.467466	+	0.809676i	0.999309	−	0.0371677i	$-0.0118336\pi$
$887$	7.64417e15	+	1.32401e16i	0.467466	+	0.809676i	−0.531843	+	0.846843i	$0.678500\pi$
$888$		0			0
$889$	3.87043e15	+	2.48559e15i	0.233776	+	0.150131i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	5.47345e15	+	3.16010e15i	0.322536	+	0.186216i
$894$		0			0
$895$		−	7.82985e14i		−	0.0455750i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	5.88603e15	−	1.01949e16i	0.334306	−	0.579035i
$900$		0			0
$901$	1.21326e16	−	7.00478e15i	0.680721	−	0.393014i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−3.44636e15	+	1.98976e15i	−0.188710	+	0.108952i
$906$		0			0
$907$	2.95377e15	−	5.11608e15i	0.159785	−	0.276756i	−0.775006	−	0.631954i	$-0.782253\pi$
$907$	2.95377e15	−	5.11608e15i	0.159785	−	0.276756i	0.934791	+	0.355198i	$0.115587\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	2.88921e16i		−	1.52555i	−0.646661	−	0.762777i	$-0.723835\pi$
$911$		−	2.88921e16i		−	1.52555i	0.646661	−	0.762777i	$-0.276165\pi$
$912$		0			0
$913$	4.30408e15	+	2.48496e15i	0.224538	+	0.129637i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−8.87695e14	+	1.87638e16i	−0.0452098	+	0.955628i
$918$		0			0
$919$	−9.24352e15	−	1.60102e16i	−0.465160	−	0.805680i	0.534049	−	0.845454i	$-0.320670\pi$
$919$	−9.24352e15	−	1.60102e16i	−0.465160	−	0.805680i	−0.999209	+	0.0397732i	$0.987336\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.77552e16			−0.872402
$924$		0			0
$925$	1.63853e16			0.795565
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−9.78558e15	−	1.69491e16i	−0.463981	−	0.803639i	0.535174	−	0.844742i	$-0.320246\pi$
$929$	−9.78558e15	−	1.69491e16i	−0.463981	−	0.803639i	−0.999155	+	0.0411033i	$0.986913\pi$
$930$		0			0
$931$	2.14388e16	+	1.52454e16i	1.00456	+	0.714358i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−5.27157e15	−	3.04354e15i	−0.241255	−	0.139289i
$936$		0			0
$937$		−	3.15352e16i		−	1.42636i	−0.700983	−	0.713178i	$-0.747255\pi$
$937$		−	3.15352e16i		−	1.42636i	0.700983	−	0.713178i	$-0.252745\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.65782e15	+	2.87144e15i	−0.0732480	+	0.126869i	−0.900323	−	0.435222i	$-0.856670\pi$
$941$	−1.65782e15	+	2.87144e15i	−0.0732480	+	0.126869i	0.827075	+	0.562091i	$0.190003\pi$
$942$		0			0
$943$	−3.86408e15	+	2.23093e15i	−0.168745	+	0.0974251i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.47751e15	−	2.00774e15i	0.148369	−	0.0856610i	−0.423978	−	0.905673i	$-0.639366\pi$
$947$	3.47751e15	−	2.00774e15i	0.148369	−	0.0856610i	0.572347	+	0.820012i	$0.306033\pi$
$948$		0			0
$949$	−9.06736e15	+	1.57051e16i	−0.382399	+	0.662335i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			3.64480e16i			1.50198i	0.660316	+	0.750988i	$0.270422\pi$
$953$			3.64480e16i			1.50198i	−0.660316	+	0.750988i	$0.729578\pi$
$954$		0			0
$955$	−6.13661e14	−	3.54297e14i	−0.0249983	−	0.0144328i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.77909e15	−	7.32454e15i	−0.150447	−	0.291594i
$960$		0			0
$961$	−8.10338e15	−	1.40355e16i	−0.318924	−	0.552393i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.71591e15			0.0660078
$966$		0			0
$967$	−3.22479e15			−0.122647			−0.0613234	−	0.998118i	$-0.519532\pi$
$967$	−3.22479e15			−0.122647			−0.0613234	+	0.998118i	$0.519532\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−8.32757e15	−	1.44238e16i	−0.309608	−	0.536257i	0.668669	−	0.743561i	$-0.266865\pi$
$971$	−8.32757e15	−	1.44238e16i	−0.309608	−	0.536257i	−0.978277	+	0.207304i	$0.933531\pi$
$972$		0			0
$973$	−1.13961e14	+	1.77454e14i	−0.00418925	+	0.00652328i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.60469e15	+	3.23587e15i	0.201433	+	0.116298i	0.597324	−	0.802000i	$-0.296231\pi$
$977$	5.60469e15	+	3.23587e15i	0.201433	+	0.116298i	−0.395891	+	0.918298i	$0.629564\pi$
$978$		0			0
$979$			3.89993e16i			1.38597i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.77474e16	+	3.07394e16i	−0.616723	+	1.06820i	0.373357	+	0.927688i	$0.378207\pi$
$983$	−1.77474e16	+	3.07394e16i	−0.616723	+	1.06820i	−0.990080	+	0.140508i	$0.955127\pi$
$984$		0			0
$985$	2.27872e15	−	1.31562e15i	0.0783052	−	0.0452096i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.04014e16	+	1.75523e16i	−1.02168	+	0.589866i
$990$		0			0
$991$	−2.36984e16	+	4.10468e16i	−0.787615	+	1.36419i	0.139810	+	0.990178i	$0.455351\pi$
$991$	−2.36984e16	+	4.10468e16i	−0.787615	+	1.36419i	−0.927424	+	0.374011i	$0.877982\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			1.18278e16i			0.384482i
$996$		0			0
$997$	3.52052e16	+	2.03257e16i	1.13184	+	0.653466i	0.944396	−	0.328810i	$-0.106648\pi$
$997$	3.52052e16	+	2.03257e16i	1.13184	+	0.653466i	0.187440	+	0.982276i	$0.439981\pi$
$998$		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.17.13	✓	60
3.2	odd	2	inner	252.12.t.a.17.18	yes	60
7.5	odd	6	inner	252.12.t.a.89.18	yes	60
21.5	even	6	inner	252.12.t.a.89.13	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.13	✓	60	1.1	even	1	trivial
252.12.t.a.17.18	yes	60	3.2	odd	2	inner
252.12.t.a.89.13	yes	60	21.5	even	6	inner
252.12.t.a.89.18	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)

\(f(q)\)	\(=\)	\(q+(-687.929 - 1191.53i) q^{5} +(-37416.0 - 24028.5i) q^{7} +O(q^{10})\)	\(q+(-687.929 - 1191.53i) q^{5} +(-37416.0 - 24028.5i) q^{7} +(564901. + 326146. i) q^{11} -958271. i q^{13} +(3.39128e6 - 5.87387e6i) q^{17} +(1.15218e7 - 6.65210e6i) q^{19} +(-3.61706e7 + 2.08831e7i) q^{23} +(2.34676e7 - 4.06470e7i) q^{25} +1.22721e8i q^{29} +(-8.30740e7 - 4.79628e7i) q^{31} +(-2.89115e6 + 6.11121e7i) q^{35} +(1.74553e8 + 3.02335e8i) q^{37} +1.06829e8 q^{41} +8.40500e8 q^{43} +(2.37526e8 + 4.11408e8i) q^{47} +(8.22584e8 + 1.79810e9i) q^{49} +(1.78880e9 + 1.03276e9i) q^{53} -8.97461e8i q^{55} +(-8.22276e8 + 1.42422e9i) q^{59} +(-7.13105e9 + 4.11711e9i) q^{61} +(-1.14181e9 + 6.59222e8i) q^{65} +(8.67691e9 - 1.50289e10i) q^{67} -1.85284e10i q^{71} +(-1.63890e10 - 9.46221e9i) q^{73} +(-1.32995e10 - 2.57768e10i) q^{77} +(1.50852e10 + 2.61283e10i) q^{79} +7.61917e9 q^{83} -9.33184e9 q^{85} +(2.98941e10 + 5.17781e10i) q^{89} +(-2.30259e10 + 3.58546e10i) q^{91} +(-1.58523e10 - 9.15234e9i) q^{95} -1.23513e9i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 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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