LMFDB - Embedded newform 252.12.t.a.17.25

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			17.25
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.25

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4361.32 + 7554.02i) q^{5} +(-11789.7 + 42875.7i) q^{7} +O(q^{10})$	$q+(4361.32 + 7554.02i) q^{5} +(-11789.7 + 42875.7i) q^{7} +(129544. + 74792.0i) q^{11} -758692. i q^{13} +(1.25346e6 - 2.17106e6i) q^{17} +(1.04797e6 - 605046. i) q^{19} +(3.59059e6 - 2.07303e6i) q^{23} +(-1.36281e7 + 2.36046e7i) q^{25} +1.21781e7i q^{29} +(-2.04314e8 - 1.17961e8i) q^{31} +(-3.75303e8 + 9.79348e7i) q^{35} +(-218812. - 378994. i) q^{37} -1.80920e7 q^{41} -1.24280e9 q^{43} +(2.10792e8 + 3.65102e8i) q^{47} +(-1.69933e9 - 1.01099e9i) q^{49} +(-3.11198e9 - 1.79670e9i) q^{53} +1.30477e9i q^{55} +(2.77294e9 - 4.80288e9i) q^{59} +(-8.18507e9 + 4.72565e9i) q^{61} +(5.73118e9 - 3.30890e9i) q^{65} +(5.15115e8 - 8.92205e8i) q^{67} -1.70682e10i q^{71} +(2.47212e9 + 1.42728e9i) q^{73} +(-4.73405e9 + 4.67250e9i) q^{77} +(-3.67781e9 - 6.37015e9i) q^{79} -4.75432e9 q^{83} +2.18670e10 q^{85} +(2.27909e10 + 3.94750e10i) q^{89} +(3.25295e10 + 8.94477e9i) q^{91} +(9.14106e9 + 5.27760e9i) q^{95} +1.41563e10i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	4361.32	+	7554.02i	0.624141	+	1.08104i	0.988706	+	0.149866i	$0.0478842\pi$
$5$	4361.32	+	7554.02i	0.624141	+	1.08104i	−0.364566	+	0.931178i	$0.618782\pi$
$6$		0			0
$7$	−11789.7	+	42875.7i	−0.265134	+	0.964212i
$7$	−11789.7	+	42875.7i	−0.265134	+	0.964212i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	129544.	+	74792.0i	0.242525	+	0.140022i	0.616337	−	0.787483i	$-0.288616\pi$
$11$	129544.	+	74792.0i	0.242525	+	0.140022i	−0.373812	+	0.927505i	$0.621949\pi$
$12$		0			0
$13$		−	758692.i		−	0.566731i	−0.959012	−	0.283366i	$-0.908549\pi$
$13$		−	758692.i		−	0.566731i	0.959012	−	0.283366i	$-0.0914510\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.25346e6	−	2.17106e6i	0.214112	−	0.370854i	−0.738885	−	0.673831i	$-0.764647\pi$
$17$	1.25346e6	−	2.17106e6i	0.214112	−	0.370854i	0.952998	+	0.302978i	$0.0979808\pi$
$18$		0			0
$19$	1.04797e6	−	605046.i	0.0970967	−	0.0560588i	−0.450665	−	0.892693i	$-0.648813\pi$
$19$	1.04797e6	−	605046.i	0.0970967	−	0.0560588i	0.547762	+	0.836634i	$0.315480\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.59059e6	−	2.07303e6i	0.116322	−	0.0671587i	−0.440710	−	0.897650i	$-0.645273\pi$
$23$	3.59059e6	−	2.07303e6i	0.116322	−	0.0671587i	0.557032	+	0.830491i	$0.311940\pi$
$24$		0			0
$25$	−1.36281e7	+	2.36046e7i	−0.279104	+	0.483421i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			1.21781e7i			0.110253i	0.998479	+	0.0551263i	$0.0175561\pi$
$29$			1.21781e7i			0.110253i	−0.998479	+	0.0551263i	$0.982444\pi$
$30$		0			0
$31$	−2.04314e8	−	1.17961e8i	−1.28177	−	0.740029i	−0.304597	−	0.952481i	$-0.598522\pi$
$31$	−2.04314e8	−	1.17961e8i	−1.28177	−	0.740029i	−0.977172	+	0.212452i	$0.931855\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−3.75303e8	+	9.79348e7i	−1.20784	+	0.315183i
$36$		0			0
$37$	−218812.	−	378994.i	−0.000518755	−	0.000898510i	0.865766	−	0.500449i	$-0.166832\pi$
$37$	−218812.	−	378994.i	−0.000518755	−	0.000898510i	−0.866285	+	0.499551i	$0.833498\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.80920e7			−0.0243879			−0.0121940	−	0.999926i	$-0.503882\pi$
$41$	−1.80920e7			−0.0243879			−0.0121940	+	0.999926i	$0.503882\pi$
$42$		0			0
$43$	−1.24280e9			−1.28921			−0.644607	−	0.764514i	$-0.722979\pi$
$43$	−1.24280e9			−1.28921			−0.644607	+	0.764514i	$0.722979\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.10792e8	+	3.65102e8i	0.134065	+	0.232208i	0.925240	−	0.379382i	$-0.123864\pi$
$47$	2.10792e8	+	3.65102e8i	0.134065	+	0.232208i	−0.791175	+	0.611590i	$0.790530\pi$
$48$		0			0
$49$	−1.69933e9	−	1.01099e9i	−0.859408	−	0.511290i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−3.11198e9	−	1.79670e9i	−1.02216	−	0.590146i	−0.107433	−	0.994212i	$-0.534263\pi$
$53$	−3.11198e9	−	1.79670e9i	−1.02216	−	0.590146i	−0.914730	+	0.404067i	$0.867596\pi$
$54$		0			0
$55$			1.30477e9i			0.349573i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.77294e9	−	4.80288e9i	0.504958	−	0.874612i	−0.495026	−	0.868878i	$-0.664841\pi$
$59$	2.77294e9	−	4.80288e9i	0.504958	−	0.874612i	0.999984	−	0.00573396i	$-0.00182519\pi$
$60$		0			0
$61$	−8.18507e9	+	4.72565e9i	−1.24082	+	0.716387i	−0.969261	−	0.246035i	$-0.920872\pi$
$61$	−8.18507e9	+	4.72565e9i	−1.24082	+	0.716387i	−0.271558	+	0.962422i	$0.587539\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.73118e9	−	3.30890e9i	0.612661	−	0.353720i
$66$		0			0
$67$	5.15115e8	−	8.92205e8i	0.0466114	−	0.0807334i	−0.841778	−	0.539823i	$-0.818491\pi$
$67$	5.15115e8	−	8.92205e8i	0.0466114	−	0.0807334i	0.888390	+	0.459090i	$0.151824\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	1.70682e10i		−	1.12271i	−0.827576	−	0.561353i	$-0.810281\pi$
$71$		−	1.70682e10i		−	1.12271i	0.827576	−	0.561353i	$-0.189719\pi$
$72$		0			0
$73$	2.47212e9	+	1.42728e9i	0.139570	+	0.0805810i	0.568159	−	0.822919i	$-0.307656\pi$
$73$	2.47212e9	+	1.42728e9i	0.139570	+	0.0805810i	−0.428589	+	0.903500i	$0.640989\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.73405e9	+	4.67250e9i	−0.199312	+	0.196721i
$78$		0			0
$79$	−3.67781e9	−	6.37015e9i	−0.134474	−	0.232917i	0.790922	−	0.611917i	$-0.209601\pi$
$79$	−3.67781e9	−	6.37015e9i	−0.134474	−	0.232917i	−0.925397	+	0.379000i	$0.876268\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.75432e9			−0.132483			−0.0662414	−	0.997804i	$-0.521101\pi$
$83$	−4.75432e9			−0.132483			−0.0662414	+	0.997804i	$0.521101\pi$
$84$		0			0
$85$	2.18670e10			0.534545
$86$		0			0
$87$		0			0
$88$		0			0
$89$	2.27909e10	+	3.94750e10i	0.432630	+	0.749337i	0.997099	−	0.0761171i	$-0.0242523\pi$
$89$	2.27909e10	+	3.94750e10i	0.432630	+	0.749337i	−0.564469	+	0.825454i	$0.690919\pi$
$90$		0			0
$91$	3.25295e10	+	8.94477e9i	0.546449	+	0.150259i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	9.14106e9	+	5.27760e9i	0.121204	+	0.0699772i
$96$		0			0
$97$			1.41563e10i			0.167381i	0.996492	+	0.0836906i	$0.0266707\pi$
$97$			1.41563e10i			0.167381i	−0.996492	+	0.0836906i	$0.973329\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.76121e10	+	3.05050e10i	−0.166741	+	0.288804i	−0.937272	−	0.348598i	$-0.886658\pi$
$101$	−1.76121e10	+	3.05050e10i	−0.166741	+	0.288804i	0.770531	+	0.637402i	$0.219991\pi$
$102$		0			0
$103$	1.21057e11	−	6.98921e10i	1.02893	−	0.594051i	0.112249	−	0.993680i	$-0.464194\pi$
$103$	1.21057e11	−	6.98921e10i	1.02893	−	0.594051i	0.916677	+	0.399629i	$0.130861\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.27927e11	+	7.38586e10i	−0.881761	+	0.509085i	−0.871239	−	0.490859i	$-0.836683\pi$
$107$	−1.27927e11	+	7.38586e10i	−0.881761	+	0.509085i	−0.0105227	+	0.999945i	$0.503350\pi$
$108$		0			0
$109$	5.79741e9	−	1.00414e10i	0.0360901	−	0.0625099i	−0.847416	−	0.530929i	$-0.821843\pi$
$109$	5.79741e9	−	1.00414e10i	0.0360901	−	0.0625099i	0.883506	+	0.468419i	$0.155176\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			1.26983e11i			0.648356i	0.945996	+	0.324178i	$0.105088\pi$
$113$			1.26983e11i			0.648356i	−0.945996	+	0.324178i	$0.894912\pi$
$114$		0			0
$115$	3.13194e10	+	1.80823e10i	0.145203	+	0.0838329i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.83078e10	+	7.93393e10i	0.300813	+	0.304775i
$120$		0			0
$121$	−1.31468e11	−	2.27710e11i	−0.460788	−	0.798108i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.88164e11			0.551482
$126$		0			0
$127$	3.07657e10			0.0826315			0.0413158	−	0.999146i	$-0.486845\pi$
$127$	3.07657e10			0.0826315			0.0413158	+	0.999146i	$0.486845\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.06847e11	−	5.31474e11i	−0.694911	−	1.20362i	−0.970211	−	0.242263i	$-0.922110\pi$
$131$	−3.06847e11	−	5.31474e11i	−0.694911	−	1.20362i	0.275299	−	0.961359i	$-0.411223\pi$
$132$		0			0
$133$	1.35865e10	+	5.20658e10i	0.0283090	+	0.108485i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−3.90038e11	−	2.25188e11i	−0.690468	−	0.398642i	0.113319	−	0.993559i	$-0.463852\pi$
$137$	−3.90038e11	−	2.25188e11i	−0.690468	−	0.398642i	−0.803787	+	0.594917i	$0.797185\pi$
$138$		0			0
$139$			3.33640e11i			0.545377i	0.962102	+	0.272689i	$0.0879129\pi$
$139$			3.33640e11i			0.545377i	−0.962102	+	0.272689i	$0.912087\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	5.67441e10	−	9.82837e10i	0.0793547	−	0.137446i
$144$		0			0
$145$	−9.19933e10	+	5.31123e10i	−0.119188	+	0.0688131i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	7.15151e11	−	4.12893e11i	0.797762	−	0.460588i	−0.0449259	−	0.998990i	$-0.514305\pi$
$149$	7.15151e11	−	4.12893e11i	0.797762	−	0.460588i	0.842688	+	0.538402i	$0.180972\pi$
$150$		0			0
$151$	−1.23376e11	+	2.13693e11i	−0.127896	+	0.221522i	−0.922861	−	0.385133i	$-0.874156\pi$
$151$	−1.23376e11	+	2.13693e11i	−0.127896	+	0.221522i	0.794965	+	0.606655i	$0.207489\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	2.05786e12i		−	1.84753i
$156$		0			0
$157$	−4.44101e11	−	2.56402e11i	−0.371564	−	0.214523i	0.302577	−	0.953125i	$-0.402153\pi$
$157$	−4.44101e11	−	2.56402e11i	−0.371564	−	0.214523i	−0.674142	+	0.738602i	$0.735486\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.65505e10	+	1.78390e11i	0.0339142	+	0.129965i
$162$		0			0
$163$	−1.05497e8	−	1.82727e8i	−7.18141e−5	−	0.000124386i	0.865989	−	0.500062i	$-0.166690\pi$
$163$	−1.05497e8	−	1.82727e8i	−7.18141e−5	−	0.000124386i	−0.866061	+	0.499938i	$0.833356\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.13896e12			−0.678530			−0.339265	−	0.940691i	$-0.610178\pi$
$167$	−1.13896e12			−0.678530			−0.339265	+	0.940691i	$0.610178\pi$
$168$		0			0
$169$	1.21655e12			0.678816
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.30172e11	+	3.98669e11i	0.112927	+	0.195595i	0.916949	−	0.399004i	$-0.130644\pi$
$173$	2.30172e11	+	3.98669e11i	0.112927	+	0.195595i	−0.804022	+	0.594599i	$0.797311\pi$
$174$		0			0
$175$	−8.51391e11	−	8.62606e11i	−0.392121	−	0.397286i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.49163e12	−	1.43854e12i	−1.01343	−	0.585102i	−0.101233	−	0.994863i	$-0.532279\pi$
$179$	−2.49163e12	−	1.43854e12i	−1.01343	−	0.585102i	−0.912193	+	0.409761i	$0.865612\pi$
$180$		0			0
$181$		−	1.60319e12i		−	0.613412i	−0.951804	−	0.306706i	$-0.900773\pi$
$181$		−	1.60319e12i		−	0.613412i	0.951804	−	0.306706i	$-0.0992269\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.90862e9	−	3.30582e9i	0.000647552	−	0.00112159i
$186$		0			0
$187$	3.24756e11	−	1.87498e11i	0.103855	−	0.0599608i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−3.07729e12	+	1.77667e12i	−0.875960	+	0.505736i	−0.869324	−	0.494242i	$-0.835446\pi$
$191$	−3.07729e12	+	1.77667e12i	−0.875960	+	0.505736i	−0.00663583	+	0.999978i	$0.502112\pi$
$192$		0			0
$193$	2.02411e12	−	3.50586e12i	0.544088	−	0.942389i	−0.454575	−	0.890708i	$-0.650209\pi$
$193$	2.02411e12	−	3.50586e12i	0.544088	−	0.942389i	0.998664	−	0.0516803i	$-0.0164577\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			2.20481e12i			0.529429i	0.964327	+	0.264714i	$0.0852777\pi$
$197$			2.20481e12i			0.529429i	−0.964327	+	0.264714i	$0.914722\pi$
$198$		0			0
$199$	2.47845e12	+	1.43094e12i	0.562975	+	0.325034i	0.754339	−	0.656486i	$-0.227958\pi$
$199$	2.47845e12	+	1.43094e12i	0.562975	+	0.325034i	−0.191364	+	0.981519i	$0.561291\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.22143e11	−	1.43576e11i	−0.106307	−	0.0292317i
$204$		0			0
$205$	−7.89049e10	−	1.36667e11i	−0.0152215	−	0.0263644i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.81010e11			0.0313978
$210$		0			0
$211$	9.13448e12			1.50359			0.751797	−	0.659395i	$-0.229187\pi$
$211$	9.13448e12			1.50359			0.751797	+	0.659395i	$0.229187\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.42025e12	−	9.38815e12i	−0.804652	−	1.39370i
$216$		0			0
$217$	7.46647e12	−	7.36940e12i	1.05338	−	1.03969i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.64716e12	−	9.50991e11i	−0.210174	−	0.121344i
$222$		0			0
$223$			3.67632e12i			0.446413i	0.974771	+	0.223207i	$0.0716525\pi$
$223$			3.67632e12i			0.446413i	−0.974771	+	0.223207i	$0.928348\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.26632e12	−	5.65743e12i	0.359680	−	0.622984i	−0.628227	−	0.778030i	$-0.716219\pi$
$227$	3.26632e12	−	5.65743e12i	0.359680	−	0.622984i	0.987907	+	0.155046i	$0.0495525\pi$
$228$		0			0
$229$	1.09258e13	−	6.30799e12i	1.14645	−	0.661906i	0.198433	−	0.980114i	$-0.436415\pi$
$229$	1.09258e13	−	6.30799e12i	1.14645	−	0.661906i	0.948021	+	0.318209i	$0.103081\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.04795e12	+	6.05036e11i	−0.0999734	+	0.0577197i	−0.549153	−	0.835722i	$-0.685050\pi$
$233$	−1.04795e12	+	6.05036e11i	−0.0999734	+	0.0577197i	0.449180	+	0.893441i	$0.351716\pi$
$234$		0			0
$235$	−1.83866e12	+	3.18465e12i	−0.167351	+	0.289861i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	1.14841e13i		−	0.952600i	−0.879283	−	0.476300i	$-0.841978\pi$
$239$		−	1.14841e13i		−	0.952600i	0.879283	−	0.476300i	$-0.158022\pi$
$240$		0			0
$241$	−2.42289e12	−	1.39886e12i	−0.191973	−	0.110836i	0.400933	−	0.916107i	$-0.368686\pi$
$241$	−2.42289e12	−	1.39886e12i	−0.191973	−	0.110836i	−0.592906	+	0.805272i	$0.702019\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.25696e11	−	1.72460e13i	0.0163347	−	1.24817i
$246$		0			0
$247$	−4.59044e11	−	7.95087e11i	−0.0317703	−	0.0550277i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.95078e13			−1.23596			−0.617978	−	0.786196i	$-0.712048\pi$
$251$	−1.95078e13			−1.23596			−0.617978	+	0.786196i	$0.712048\pi$
$252$		0			0
$253$	6.20184e11			0.0376147
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.89978e12	−	1.71469e13i	−0.550799	−	0.954012i	−0.998217	−	0.0596872i	$-0.980990\pi$
$257$	−9.89978e12	−	1.71469e13i	−0.550799	−	0.954012i	0.447418	−	0.894325i	$-0.352344\pi$
$258$		0			0
$259$	1.88294e10	−	4.91350e9i	0.00100389	−	0.000261964i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.33556e13	−	1.92579e13i	−1.63460	−	0.943739i	−0.982648	−	0.185481i	$-0.940616\pi$
$263$	−3.33556e13	−	1.92579e13i	−1.63460	−	0.943739i	−0.651955	−	0.758257i	$-0.726051\pi$
$264$		0			0
$265$		−	3.13440e13i		−	1.47334i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.60727e13	−	2.78387e13i	0.695746	−	1.20507i	−0.274183	−	0.961678i	$-0.588407\pi$
$269$	1.60727e13	−	2.78387e13i	0.695746	−	1.20507i	0.969929	−	0.243389i	$-0.0782593\pi$
$270$		0			0
$271$	2.36313e12	−	1.36436e12i	0.0982104	−	0.0567018i	−0.450090	−	0.892983i	$-0.648608\pi$
$271$	2.36313e12	−	1.36436e12i	0.0982104	−	0.0567018i	0.548301	+	0.836281i	$0.315275\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−3.53087e12	+	2.03855e12i	−0.135379	+	0.0781611i
$276$		0			0
$277$	1.48020e12	−	2.56377e12i	0.0545356	−	0.0944585i	−0.837469	−	0.546485i	$-0.815965\pi$
$277$	1.48020e12	−	2.56377e12i	0.0545356	−	0.0944585i	0.892004	+	0.452027i	$0.149299\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	5.12287e12i		−	0.174433i	−0.996189	−	0.0872165i	$-0.972203\pi$
$281$		−	5.12287e12i		−	0.174433i	0.996189	−	0.0872165i	$-0.0277972\pi$
$282$		0			0
$283$	−3.18625e13	−	1.83958e13i	−1.04341	−	0.602412i	−0.122612	−	0.992455i	$-0.539127\pi$
$283$	−3.18625e13	−	1.83958e13i	−1.04341	−	0.602412i	−0.920797	+	0.390042i	$0.872460\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.13300e11	−	7.75708e11i	0.00646606	−	0.0235151i
$288$		0			0
$289$	1.39936e13	+	2.42377e13i	0.408312	+	0.707217i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.46585e13			−1.47872			−0.739360	−	0.673311i	$-0.764872\pi$
$293$	−5.46585e13			−1.47872			−0.739360	+	0.673311i	$0.764872\pi$
$294$		0			0
$295$	4.83747e13			1.26066
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.57279e12	−	2.72415e12i	−0.0380609	−	0.0659234i
$300$		0			0
$301$	1.46523e13	−	5.32860e13i	0.341814	−	1.24308i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.13953e13	−	4.12201e13i	−1.54889	−	0.894253i
$306$		0			0
$307$			1.04775e12i			0.0219278i	0.999940	+	0.0109639i	$0.00348999\pi$
$307$			1.04775e12i			0.0219278i	−0.999940	+	0.0109639i	$0.996510\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	9.68202e12	−	1.67698e13i	0.188705	−	0.326847i	−0.756114	−	0.654440i	$-0.772904\pi$
$311$	9.68202e12	−	1.67698e13i	0.188705	−	0.326847i	0.944819	+	0.327593i	$0.106238\pi$
$312$		0			0
$313$	8.01956e13	−	4.63009e13i	1.50889	−	0.871156i	0.508940	−	0.860802i	$-0.330038\pi$
$313$	8.01956e13	−	4.63009e13i	1.50889	−	0.871156i	0.999946	−	0.0103536i	$-0.00329571\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.88455e13	−	1.08804e13i	0.330659	−	0.190906i	−0.325474	−	0.945551i	$-0.605524\pi$
$317$	1.88455e13	−	1.08804e13i	0.330659	−	0.190906i	0.656134	+	0.754645i	$0.272191\pi$
$318$		0			0
$319$	−9.10821e11	+	1.57759e12i	−0.0154378	+	0.0267390i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	3.03361e12i		−	0.0480115i
$324$		0			0
$325$	1.79086e13	+	1.03395e13i	0.273970	+	0.158177i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.81392e13	+	4.73340e12i	−0.259442	+	0.0677011i
$330$		0			0
$331$	9.37734e12	+	1.62420e13i	0.129726	+	0.224691i	0.923570	−	0.383429i	$-0.125257\pi$
$331$	9.37734e12	+	1.62420e13i	0.129726	+	0.224691i	−0.793845	+	0.608121i	$0.791924\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	8.98631e12			0.116368
$336$		0			0
$337$	1.01150e14			1.26766			0.633830	−	0.773472i	$-0.281482\pi$
$337$	1.01150e14			1.26766			0.633830	+	0.773472i	$0.281482\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.76451e13	−	3.05622e13i	−0.207240	−	0.358951i
$342$		0			0
$343$	6.33815e13	−	6.09408e13i	0.720850	−	0.693092i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−4.56842e13	−	2.63758e13i	−0.487476	−	0.281445i	0.236051	−	0.971741i	$-0.424147\pi$
$347$	−4.56842e13	−	2.63758e13i	−0.487476	−	0.281445i	−0.723527	+	0.690296i	$0.757480\pi$
$348$		0			0
$349$			1.07224e13i			0.110854i	0.998463	+	0.0554272i	$0.0176521\pi$
$349$			1.07224e13i			0.110854i	−0.998463	+	0.0554272i	$0.982348\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.45945e13	−	1.29202e14i	0.724346	−	1.25460i	−0.234897	−	0.972020i	$-0.575475\pi$
$353$	7.45945e13	−	1.29202e14i	0.724346	−	1.25460i	0.959243	−	0.282584i	$-0.0911915\pi$
$354$		0			0
$355$	1.28933e14	−	7.44397e13i	1.21369	−	0.700727i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.11240e14	+	6.42243e13i	−0.984556	+	0.568434i	−0.903643	−	0.428287i	$-0.859117\pi$
$359$	−1.11240e14	+	6.42243e13i	−0.984556	+	0.568434i	−0.0809137	+	0.996721i	$0.525784\pi$
$360$		0			0
$361$	−5.75130e13	+	9.96154e13i	−0.493715	+	0.855139i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			2.48992e13i			0.201175i
$366$		0			0
$367$	−1.42221e14	−	8.21115e13i	−1.11507	−	0.643784i	−0.174930	−	0.984581i	$-0.555970\pi$
$367$	−1.42221e14	−	8.21115e13i	−1.11507	−	0.643784i	−0.940137	+	0.340796i	$0.889303\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.13724e14	−	1.12246e14i	0.840035	−	0.829113i
$372$		0			0
$373$	1.69749e13	+	2.94014e13i	0.121733	+	0.210848i	0.920451	−	0.390857i	$-0.127821\pi$
$373$	1.69749e13	+	2.94014e13i	0.121733	+	0.210848i	−0.798718	+	0.601705i	$0.794488\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	9.23939e12			0.0624836
$378$		0			0
$379$	1.20118e14			0.789029			0.394514	−	0.918890i	$-0.370913\pi$
$379$	1.20118e14			0.789029			0.394514	+	0.918890i	$0.370913\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−8.98322e12	−	1.55594e13i	−0.0556979	−	0.0964716i	0.836832	−	0.547460i	$-0.184405\pi$
$383$	−8.98322e12	−	1.55594e13i	−0.0556979	−	0.0964716i	−0.892530	+	0.450988i	$0.851072\pi$
$384$		0			0
$385$	−5.59428e13	−	1.53828e13i	−0.337062	−	0.0926836i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.18473e14	−	6.84001e13i	−0.674365	−	0.389345i	0.123364	−	0.992362i	$-0.460632\pi$
$389$	−1.18473e14	−	6.84001e13i	−0.674365	−	0.389345i	−0.797728	+	0.603017i	$0.793965\pi$
$390$		0			0
$391$		−	1.03938e13i		−	0.0575180i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.20802e13	−	5.55645e13i	0.167862	−	0.290746i
$396$		0			0
$397$	−2.14689e14	+	1.23951e14i	−1.09260	+	0.630814i	−0.934268	−	0.356571i	$-0.883946\pi$
$397$	−2.14689e14	+	1.23951e14i	−1.09260	+	0.630814i	−0.158334	+	0.987386i	$0.550612\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.54656e14	+	1.47025e14i	−1.22648	+	0.708106i	−0.966291	−	0.257452i	$-0.917117\pi$
$401$	−2.54656e14	+	1.47025e14i	−1.22648	+	0.708106i	−0.260185	+	0.965559i	$0.583784\pi$
$402$		0			0
$403$	−8.94960e13	+	1.55012e14i	−0.419398	+	0.726418i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	6.54616e10i		−	0.000290548i
$408$		0			0
$409$	−3.62842e14	−	2.09487e14i	−1.56761	−	0.905062i	−0.996447	−	0.0842275i	$-0.973158\pi$
$409$	−3.62842e14	−	2.09487e14i	−1.56761	−	0.905062i	−0.571166	−	0.820834i	$-0.693509\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.73235e14	+	1.75517e14i	0.709430	+	0.718775i
$414$		0			0
$415$	−2.07351e13	−	3.59143e13i	−0.0826879	−	0.143220i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.06174e14			−0.401642			−0.200821	−	0.979628i	$-0.564361\pi$
$419$	−1.06174e14			−0.401642			−0.200821	+	0.979628i	$0.564361\pi$
$420$		0			0
$421$	4.81356e13			0.177384			0.0886920	−	0.996059i	$-0.471731\pi$
$421$	4.81356e13			0.177384			0.0886920	+	0.996059i	$0.471731\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	3.41646e13	+	5.91748e13i	0.119519	+	0.207013i
$426$		0			0
$427$	−1.06116e14	−	4.06655e14i	−0.361766	−	1.38635i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.77322e12	−	5.64257e12i	−0.0316528	−	0.0182748i	0.484090	−	0.875018i	$-0.339151\pi$
$431$	−9.77322e12	−	5.64257e12i	−0.0316528	−	0.0182748i	−0.515743	+	0.856743i	$0.672484\pi$
$432$		0			0
$433$			3.38151e14i			1.06765i	0.845596	+	0.533823i	$0.179245\pi$
$433$			3.38151e14i			1.06765i	−0.845596	+	0.533823i	$0.820755\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.50855e12	−	4.34494e12i	0.00752967	−	0.0130418i
$438$		0			0
$439$	2.42476e13	−	1.39994e13i	0.0709764	−	0.0409782i	−0.464092	−	0.885787i	$-0.653619\pi$
$439$	2.42476e13	−	1.39994e13i	0.0709764	−	0.0409782i	0.535068	+	0.844809i	$0.320286\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.61881e14	−	2.66667e14i	1.28620	−	0.742590i	0.308228	−	0.951312i	$-0.400264\pi$
$443$	4.61881e14	−	2.66667e14i	1.28620	−	0.742590i	0.977975	+	0.208723i	$0.0669306\pi$
$444$		0			0
$445$	−1.98797e14	+	3.44326e14i	−0.540044	+	0.935384i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			3.36282e14i			0.869658i	0.900513	+	0.434829i	$0.143191\pi$
$449$			3.36282e14i			0.869658i	−0.900513	+	0.434829i	$0.856809\pi$
$450$		0			0
$451$	−2.34370e12	−	1.35314e12i	−0.00591468	−	0.00341484i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	7.43023e13	+	2.84739e14i	0.178624	+	0.684518i
$456$		0			0
$457$	2.37740e14	+	4.11777e14i	0.557908	+	0.966324i	0.997671	+	0.0682107i	$0.0217290\pi$
$457$	2.37740e14	+	4.11777e14i	0.557908	+	0.966324i	−0.439763	+	0.898114i	$0.644938\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.07480e14			1.35887			0.679434	−	0.733737i	$-0.262225\pi$
$461$	6.07480e14			1.35887			0.679434	+	0.733737i	$0.262225\pi$
$462$		0			0
$463$	4.18543e14			0.914208			0.457104	−	0.889413i	$-0.348887\pi$
$463$	4.18543e14			0.914208			0.457104	+	0.889413i	$0.348887\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.70252e14	+	4.68091e14i	0.563024	+	0.975186i	0.997231	+	0.0743726i	$0.0236954\pi$
$467$	2.70252e14	+	4.68091e14i	0.563024	+	0.975186i	−0.434207	+	0.900813i	$0.642971\pi$
$468$		0			0
$469$	3.21809e13	+	3.26048e13i	0.0654858	+	0.0663484i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.60997e14	−	9.29516e13i	−0.312666	−	0.180518i
$474$		0			0
$475$			3.29825e13i			0.0625848i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.10665e14	−	1.91678e14i	0.200524	−	0.347317i	−0.748174	−	0.663503i	$-0.769069\pi$
$479$	1.10665e14	−	1.91678e14i	0.200524	−	0.347317i	0.948697	+	0.316186i	$0.102402\pi$
$480$		0			0
$481$	−2.87540e11	+	1.66011e11i	−0.000509213	+	0.000293994i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.06937e14	+	6.17403e13i	−0.180946	+	0.104469i
$486$		0			0
$487$	−9.31654e13	+	1.61367e14i	−0.154115	+	0.266935i	−0.932737	−	0.360559i	$-0.882586\pi$
$487$	−9.31654e13	+	1.61367e14i	−0.154115	+	0.266935i	0.778621	+	0.627494i	$0.215919\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			1.18455e15i			1.87329i	0.350285	+	0.936643i	$0.386085\pi$
$491$			1.18455e15i			1.87329i	−0.350285	+	0.936643i	$0.613915\pi$
$492$		0			0
$493$	2.64393e13	+	1.52647e13i	0.0408876	+	0.0236064i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.31810e14	+	2.01229e14i	1.08253	+	0.297667i
$498$		0			0
$499$	1.66515e14	+	2.88412e14i	0.240935	+	0.417312i	0.960981	−	0.276615i	$-0.0892125\pi$
$499$	1.66515e14	+	2.88412e14i	0.240935	+	0.417312i	−0.720046	+	0.693927i	$0.755879\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−3.41377e14			−0.472726			−0.236363	−	0.971665i	$-0.575956\pi$
$503$	−3.41377e14			−0.472726			−0.236363	+	0.971665i	$0.575956\pi$
$504$		0			0
$505$	−3.07247e14			−0.416280
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.81432e14	+	8.33865e14i	0.624579	+	1.08180i	0.988622	+	0.150420i	$0.0480626\pi$
$509$	4.81432e14	+	8.33865e14i	0.624579	+	1.08180i	−0.364043	+	0.931382i	$0.618604\pi$
$510$		0			0
$511$	−9.03411e13	+	8.91666e13i	−0.114702	+	0.113211i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.05593e15	+	6.09644e14i	1.28439	+	0.741543i
$516$		0			0
$517$			6.30622e13i			0.0750881i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.50775e14	+	4.34355e14i	−0.286205	+	0.495722i	−0.972901	−	0.231223i	$-0.925727\pi$
$521$	−2.50775e14	+	4.34355e14i	−0.286205	+	0.495722i	0.686696	+	0.726945i	$0.259060\pi$
$522$		0			0
$523$	−4.66928e14	+	2.69581e14i	−0.521784	+	0.301252i	−0.737664	−	0.675168i	$-0.764071\pi$
$523$	−4.66928e14	+	2.69581e14i	−0.521784	+	0.301252i	0.215880	+	0.976420i	$0.430738\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−5.12200e14	+	2.95719e14i	−0.548885	+	0.316899i
$528$		0			0
$529$	−4.67810e14	+	8.10271e14i	−0.490979	+	0.850401i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			1.37263e13i			0.0138214i
$534$		0			0
$535$	−1.11586e15	−	6.44242e14i	−1.10069	−	0.635482i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.44524e14	−	2.58063e14i	−0.136836	−	0.244336i
$540$		0			0
$541$	−6.13329e14	−	1.06232e15i	−0.568995	−	0.985529i	−0.996666	−	0.0815938i	$-0.973999\pi$
$541$	−6.13329e14	−	1.06232e15i	−0.568995	−	0.985529i	0.427670	−	0.903935i	$-0.359334\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.01137e14			0.0901012
$546$		0			0
$547$	−1.40996e15			−1.23105			−0.615526	−	0.788116i	$-0.711056\pi$
$547$	−1.40996e15			−1.23105			−0.615526	+	0.788116i	$0.711056\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.36828e12	+	1.27622e13i	0.00618063	+	0.0107052i
$552$		0			0
$553$	3.16485e14	−	8.25863e13i	0.260235	−	0.0679079i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	6.76579e14	+	3.90623e14i	0.534706	+	0.308713i	0.742931	−	0.669368i	$-0.233435\pi$
$557$	6.76579e14	+	3.90623e14i	0.534706	+	0.308713i	−0.208225	+	0.978081i	$0.566768\pi$
$558$		0			0
$559$			9.42903e14i			0.730638i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−3.28044e14	+	5.68189e14i	−0.244420	+	0.423347i	−0.961968	−	0.273161i	$-0.911931\pi$
$563$	−3.28044e14	+	5.68189e14i	−0.244420	+	0.423347i	0.717549	+	0.696508i	$0.245264\pi$
$564$		0			0
$565$	−9.59231e14	+	5.53812e14i	−0.700901	+	0.404665i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.05239e15	−	6.07597e14i	0.739705	−	0.427069i	−0.0822571	−	0.996611i	$-0.526213\pi$
$569$	1.05239e15	−	6.07597e14i	0.739705	−	0.427069i	0.821962	+	0.569542i	$0.192880\pi$
$570$		0			0
$571$	−1.30837e15	+	2.26617e15i	−0.902054	+	1.56240i	−0.0772312	+	0.997013i	$0.524608\pi$
$571$	−1.30837e15	+	2.26617e15i	−0.902054	+	1.56240i	−0.824823	+	0.565391i	$0.808725\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			1.13006e14i			0.0749769i
$576$		0			0
$577$	3.89004e14	+	2.24592e14i	0.253214	+	0.146193i	0.621235	−	0.783624i	$-0.286631\pi$
$577$	3.89004e14	+	2.24592e14i	0.253214	+	0.146193i	−0.368021	+	0.929817i	$0.619965\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.60522e13	−	2.03845e14i	0.0351256	−	0.127741i
$582$		0			0
$583$	−2.68758e14	−	4.65503e14i	−0.165266	−	0.286250i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.21840e14			0.545942			0.272971	−	0.962022i	$-0.411994\pi$
$587$	9.21840e14			0.545942			0.272971	+	0.962022i	$0.411994\pi$
$588$		0			0
$589$	−2.85487e14			−0.165941
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.62814e14	+	4.55206e14i	0.147179	+	0.254922i	0.930184	−	0.367094i	$-0.119647\pi$
$593$	2.62814e14	+	4.55206e14i	0.147179	+	0.254922i	−0.783005	+	0.622016i	$0.786314\pi$
$594$		0			0
$595$	−2.57806e14	+	9.37562e14i	−0.141726	+	0.515415i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.93376e14	−	2.84851e14i	−0.261415	−	0.150928i	0.363565	−	0.931569i	$-0.381559\pi$
$599$	−4.93376e14	−	2.84851e14i	−0.261415	−	0.150928i	−0.624980	+	0.780641i	$0.714893\pi$
$600$		0			0
$601$		−	1.24420e15i		−	0.647261i	−0.946184	−	0.323630i	$-0.895097\pi$
$601$		−	1.24420e15i		−	0.647261i	0.946184	−	0.323630i	$-0.104903\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.14675e15	−	1.98623e15i	0.575193	−	0.996263i
$606$		0			0
$607$	−2.92017e13	+	1.68596e13i	−0.0143837	+	0.00830442i	−0.507175	−	0.861843i	$-0.669310\pi$
$607$	−2.92017e13	+	1.68596e13i	−0.0143837	+	0.00830442i	0.492791	+	0.870148i	$0.335977\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.77000e14	−	1.59926e14i	0.131599	−	0.0759789i
$612$		0			0
$613$	2.09978e15	−	3.63693e15i	0.979811	−	1.69708i	0.316763	−	0.948505i	$-0.397404\pi$
$613$	2.09978e15	−	3.63693e15i	0.979811	−	1.69708i	0.663048	−	0.748577i	$-0.269263\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			8.19256e14i			0.368851i	0.982846	+	0.184426i	$0.0590425\pi$
$617$			8.19256e14i			0.368851i	−0.982846	+	0.184426i	$0.940958\pi$
$618$		0			0
$619$	1.65913e15	+	9.57899e14i	0.733807	+	0.423664i	0.819813	−	0.572631i	$-0.194077\pi$
$619$	1.65913e15	+	9.57899e14i	0.733807	+	0.423664i	−0.0860065	+	0.996295i	$0.527411\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.96122e15	+	5.11777e14i	−0.837225	+	0.218473i
$624$		0			0
$625$	1.48608e15	+	2.57396e15i	0.623306	+	1.07960i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.09709e12			−0.000444287
$630$		0			0
$631$	−9.71505e14			−0.386619			−0.193310	−	0.981138i	$-0.561922\pi$
$631$	−9.71505e14			−0.386619			−0.193310	+	0.981138i	$0.561922\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.34179e14	+	2.32405e14i	0.0515737	+	0.0893283i
$636$		0			0
$637$	−7.67028e14	+	1.28927e15i	−0.289764	+	0.487053i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.18343e15	+	1.26060e15i	0.796928	+	0.460107i	0.842396	−	0.538859i	$-0.181144\pi$
$641$	2.18343e15	+	1.26060e15i	0.796928	+	0.460107i	−0.0454676	+	0.998966i	$0.514478\pi$
$642$		0			0
$643$			6.00427e14i			0.215427i	0.994182	+	0.107713i	$0.0343529\pi$
$643$			6.00427e14i			0.215427i	−0.994182	+	0.107713i	$0.965647\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.00235e15	+	3.46817e15i	−0.694330	+	1.20262i	0.276076	+	0.961136i	$0.410966\pi$
$647$	−2.00235e15	+	3.46817e15i	−0.694330	+	1.20262i	−0.970406	+	0.241480i	$0.922367\pi$
$648$		0			0
$649$	7.18434e14	−	4.14788e14i	0.244929	−	0.141410i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.92307e14	−	3.41968e14i	0.195220	−	0.112710i	−0.399204	−	0.916862i	$-0.630713\pi$
$653$	5.92307e14	−	3.41968e14i	0.195220	−	0.112710i	0.594424	+	0.804152i	$0.297380\pi$
$654$		0			0
$655$	2.67651e15	−	4.63585e15i	0.867445	−	1.50246i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	4.90887e15i		−	1.53855i	−0.638918	−	0.769275i	$-0.720618\pi$
$659$		−	4.90887e15i		−	1.53855i	0.638918	−	0.769275i	$-0.279382\pi$
$660$		0			0
$661$	2.41300e15	+	1.39315e15i	0.743789	+	0.429427i	0.823445	−	0.567396i	$-0.192049\pi$
$661$	2.41300e15	+	1.39315e15i	0.743789	+	0.429427i	−0.0796563	+	0.996822i	$0.525382\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−3.34051e14	+	3.29708e14i	−0.0996080	+	0.0983130i
$666$		0			0
$667$	2.52454e13	+	4.37264e13i	0.00740442	+	0.0128248i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.41376e15			−0.401239
$672$		0			0
$673$	1.87136e15			0.522487			0.261244	−	0.965273i	$-0.415867\pi$
$673$	1.87136e15			0.522487			0.261244	+	0.965273i	$0.415867\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−4.95397e14	−	8.58052e14i	−0.133880	−	0.231887i	0.791289	−	0.611442i	$-0.209410\pi$
$677$	−4.95397e14	−	8.58052e14i	−0.133880	−	0.231887i	−0.925169	+	0.379555i	$0.876077\pi$
$678$		0			0
$679$	−6.06964e14	−	1.66899e14i	−0.161391	−	0.0443783i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.26169e15	−	7.28436e14i	−0.324817	−	0.187533i	0.328721	−	0.944427i	$-0.393382\pi$
$683$	−1.26169e15	−	7.28436e14i	−0.324817	−	0.187533i	−0.653537	+	0.756894i	$0.726716\pi$
$684$		0			0
$685$		−	3.92847e15i		−	0.995235i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.36314e15	+	2.36104e15i	−0.334454	+	0.579291i
$690$		0			0
$691$	1.88905e15	−	1.09064e15i	0.456157	−	0.263362i	−0.254270	−	0.967133i	$-0.581835\pi$
$691$	1.88905e15	−	1.09064e15i	0.456157	−	0.263362i	0.710427	+	0.703771i	$0.248502\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−2.52033e15	+	1.45511e15i	−0.589577	+	0.340392i
$696$		0			0
$697$	−2.26776e13	+	3.92788e13i	−0.00522176	+	0.00904436i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	2.14692e15i		−	0.479035i	−0.970892	−	0.239517i	$-0.923011\pi$
$701$		−	2.14692e15i		−	0.479035i	0.970892	−	0.239517i	$-0.0769892\pi$
$702$		0			0
$703$	−4.58618e11	−	2.64783e11i	−0.000100739	−	5.81615e-5i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.10028e15	−	1.11478e15i	−0.234260	−	0.237345i
$708$		0			0
$709$	−3.09704e15	−	5.36424e15i	−0.649222	−	1.12449i	−0.983309	−	0.181943i	$-0.941761\pi$
$709$	−3.09704e15	−	5.36424e15i	−0.649222	−	1.12449i	0.334087	−	0.942542i	$-0.391572\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.78145e14			−0.198798
$714$		0			0
$715$	9.89916e14			0.198114
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.67289e15	−	6.36163e15i	−0.712851	−	1.23469i	−0.963783	−	0.266689i	$-0.914070\pi$
$719$	−3.67289e15	−	6.36163e15i	−0.712851	−	1.23469i	0.250931	−	0.968005i	$-0.419263\pi$
$720$		0			0
$721$	1.56945e15	+	6.01441e15i	0.299988	+	1.14961i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.87458e14	−	1.65964e14i	−0.0532985	−	0.0307719i
$726$		0			0
$727$		−	2.14052e15i		−	0.390914i	−0.980712	−	0.195457i	$-0.937381\pi$
$727$		−	2.14052e15i		−	0.390914i	0.980712	−	0.195457i	$-0.0626190\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.55780e15	+	2.69819e15i	−0.276037	+	0.478110i
$732$		0			0
$733$	−2.84473e15	+	1.64240e15i	−0.496557	+	0.286687i	−0.727291	−	0.686330i	$-0.759221\pi$
$733$	−2.84473e15	+	1.64240e15i	−0.496557	+	0.286687i	0.230734	+	0.973017i	$0.425887\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.33460e14	−	7.70529e13i	0.0226089	−	0.0130532i
$738$		0			0
$739$	3.86396e15	−	6.69258e15i	0.644894	−	1.11699i	−0.339432	−	0.940631i	$-0.610235\pi$
$739$	3.86396e15	−	6.69258e15i	0.644894	−	1.11699i	0.984326	−	0.176359i	$-0.0564319\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	1.03354e16i		−	1.67451i	−0.546811	−	0.837256i	$-0.684158\pi$
$743$		−	1.03354e16i		−	1.67451i	0.546811	−	0.837256i	$-0.315842\pi$
$744$		0			0
$745$	6.23800e15	+	3.60151e15i	0.995832	+	0.574944i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.65852e15	−	6.35573e15i	−0.257081	−	0.985180i
$750$		0			0
$751$	−3.37318e15	−	5.84251e15i	−0.515252	−	0.892442i	−0.999843	−	0.0177015i	$-0.994365\pi$
$751$	−3.37318e15	−	5.84251e15i	−0.515252	−	0.892442i	0.484592	−	0.874740i	$-0.338968\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.15232e15			−0.319300
$756$		0			0
$757$	−7.60627e15			−1.11210			−0.556051	−	0.831148i	$-0.687684\pi$
$757$	−7.60627e15			−1.11210			−0.556051	+	0.831148i	$0.687684\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.49720e15	−	9.52143e15i	−0.780775	−	1.35234i	−0.931491	−	0.363765i	$-0.881491\pi$
$761$	−5.49720e15	−	9.52143e15i	−0.780775	−	1.35234i	0.150716	−	0.988577i	$-0.451842\pi$
$762$		0			0
$763$	3.62183e14	+	3.66954e14i	0.0507041	+	0.0513720i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−3.64390e15	−	2.10381e15i	−0.495670	−	0.286175i
$768$		0			0
$769$			4.11565e15i			0.551879i	0.961175	+	0.275939i	$0.0889889\pi$
$769$			4.11565e15i			0.551879i	−0.961175	+	0.275939i	$0.911011\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	5.14748e15	−	8.91570e15i	0.670822	−	1.16190i	−0.306849	−	0.951758i	$-0.599275\pi$
$773$	5.14748e15	−	8.91570e15i	0.670822	−	1.16190i	0.977671	−	0.210140i	$-0.0673920\pi$
$774$		0			0
$775$	5.56883e15	−	3.21517e15i	0.715492	−	0.413090i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.89599e13	+	1.09465e13i	−0.00236799	+	0.00136716i
$780$		0			0
$781$	1.27656e15	−	2.21107e15i	0.157203	−	0.272284i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	4.47300e15i		−	0.535570i
$786$		0			0
$787$	4.89636e15	+	2.82691e15i	0.578112	+	0.333773i	0.760383	−	0.649475i	$-0.225011\pi$
$787$	4.89636e15	+	2.82691e15i	0.578112	+	0.333773i	−0.182271	+	0.983248i	$0.558345\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−5.44448e15	−	1.49709e15i	−0.625152	−	0.171901i
$792$		0			0
$793$	3.58531e15	+	6.20995e15i	0.405999	+	0.703210i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.62595e15			0.619691			0.309845	−	0.950787i	$-0.399723\pi$
$797$	5.62595e15			0.619691			0.309845	+	0.950787i	$0.399723\pi$
$798$		0			0
$799$	1.05688e15			0.114820
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.13498e14	+	3.69789e14i	0.0225662	+	0.0390858i
$804$		0			0
$805$	−1.14454e15	+	1.12966e15i	−0.119331	+	0.117779i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.32730e14	−	7.66317e13i	−0.0134664	−	0.00777484i	0.493252	−	0.869887i	$-0.335808\pi$
$809$	−1.32730e14	−	7.66317e13i	−0.0134664	−	0.00777484i	−0.506718	+	0.862112i	$0.669141\pi$
$810$		0			0
$811$		−	1.04981e16i		−	1.05075i	−0.850872	−	0.525373i	$-0.823926\pi$
$811$		−	1.04981e16i		−	1.05075i	0.850872	−	0.525373i	$-0.176074\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.20215e11	−	1.59386e12i	8.96442e−5	−	0.000155268i
$816$		0			0
$817$	−1.30242e15	+	7.51952e14i	−0.125178	+	0.0722718i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.79542e15	−	1.61394e15i	0.261553	−	0.151008i	−0.363490	−	0.931598i	$-0.618415\pi$
$821$	2.79542e15	−	1.61394e15i	0.261553	−	0.151008i	0.625043	+	0.780591i	$0.285082\pi$
$822$		0			0
$823$	6.19056e15	−	1.07224e16i	0.571519	−	0.989900i	−0.424891	−	0.905245i	$-0.639688\pi$
$823$	6.19056e15	−	1.07224e16i	0.571519	−	0.989900i	0.996410	−	0.0846558i	$-0.0269791\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	3.75450e15i		−	0.337498i	−0.985659	−	0.168749i	$-0.946027\pi$
$827$		−	3.75450e15i		−	0.337498i	0.985659	−	0.168749i	$-0.0539727\pi$
$828$		0			0
$829$	2.87886e15	+	1.66211e15i	0.255370	+	0.147438i	0.622221	−	0.782842i	$-0.286231\pi$
$829$	2.87886e15	+	1.66211e15i	0.255370	+	0.147438i	−0.366850	+	0.930280i	$0.619564\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.32496e15	+	2.42211e15i	−0.373624	+	0.209241i
$834$		0			0
$835$	−4.96738e15	−	8.60376e15i	−0.423498	−	0.733521i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−1.91147e16			−1.58736			−0.793682	−	0.608333i	$-0.791839\pi$
$839$	−1.91147e16			−1.58736			−0.793682	+	0.608333i	$0.791839\pi$
$840$		0			0
$841$	1.20522e16			0.987844
$842$		0			0
$843$		0			0
$844$		0			0
$845$	5.30575e15	+	9.18982e15i	0.423677	+	0.733830i
$846$		0			0
$847$	1.13132e16	−	2.95216e15i	0.891715	−	0.232692i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.57133e12	−	9.07208e11i	−0.000120685	−	6.96778e-5i
$852$		0			0
$853$			5.29718e15i			0.401629i	0.979629	+	0.200815i	$0.0643589\pi$
$853$			5.29718e15i			0.401629i	−0.979629	+	0.200815i	$0.935641\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.25534e16	+	2.17431e16i	−0.927614	+	1.60667i	−0.140310	+	0.990108i	$0.544810\pi$
$857$	−1.25534e16	+	2.17431e16i	−0.927614	+	1.60667i	−0.787303	+	0.616566i	$0.788523\pi$
$858$		0			0
$859$	7.61482e14	−	4.39642e14i	0.0555517	−	0.0320728i	−0.471967	−	0.881616i	$-0.656456\pi$
$859$	7.61482e14	−	4.39642e14i	0.0555517	−	0.0320728i	0.527519	+	0.849543i	$0.323122\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.45284e15	−	1.99350e15i	0.245537	−	0.141761i	−0.372182	−	0.928160i	$-0.621390\pi$
$863$	3.45284e15	−	1.99350e15i	0.245537	−	0.141761i	0.617719	+	0.786399i	$0.288057\pi$
$864$		0			0
$865$	−2.00770e15	+	3.47744e15i	−0.140965	+	0.244158i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	1.10028e15i		−	0.0753174i
$870$		0			0
$871$	−6.76909e14	−	3.90813e14i	−0.0457541	−	0.0264162i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.21840e15	+	8.06767e15i	−0.146216	+	0.531745i
$876$		0			0
$877$	1.86320e15	+	3.22716e15i	0.121272	+	0.210050i	0.920270	−	0.391285i	$-0.127969\pi$
$877$	1.86320e15	+	3.22716e15i	0.121272	+	0.210050i	−0.798997	+	0.601335i	$0.794636\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−3.00287e15			−0.190620			−0.0953102	−	0.995448i	$-0.530384\pi$
$881$	−3.00287e15			−0.190620			−0.0953102	+	0.995448i	$0.530384\pi$
$882$		0			0
$883$	2.31492e15			0.145129			0.0725643	−	0.997364i	$-0.476882\pi$
$883$	2.31492e15			0.145129			0.0725643	+	0.997364i	$0.476882\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	6.01448e15	+	1.04174e16i	0.367805	+	0.637057i	0.989222	−	0.146423i	$-0.0467760\pi$
$887$	6.01448e15	+	1.04174e16i	0.367805	+	0.637057i	−0.621417	+	0.783480i	$0.713443\pi$
$888$		0			0
$889$	−3.62719e14	+	1.31910e15i	−0.0219084	+	0.0796743i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	4.41808e14	+	2.55078e14i	0.0260346	+	0.0150311i
$894$		0			0
$895$		−	2.50958e16i		−	1.46074i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.43653e15	−	2.48815e15i	0.0815902	−	0.141318i
$900$		0			0
$901$	−7.80150e15	+	4.50420e15i	−0.437715	+	0.252715i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.21105e16	−	6.99201e15i	0.663125	−	0.382856i
$906$		0			0
$907$	−1.02771e16	+	1.78004e16i	−0.555942	+	0.962919i	0.441888	+	0.897070i	$0.354309\pi$
$907$	−1.02771e16	+	1.78004e16i	−0.555942	+	0.962919i	−0.997830	+	0.0658489i	$0.979024\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			1.81600e16i			0.958880i	0.877575	+	0.479440i	$0.159160\pi$
$911$			1.81600e16i			0.958880i	−0.877575	+	0.479440i	$0.840840\pi$
$912$		0			0
$913$	−6.15892e14	−	3.55585e14i	−0.0321303	−	0.0185505i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.64050e16	−	6.89034e15i	1.34479	−	0.350921i
$918$		0			0
$919$	8.00670e14	+	1.38680e15i	0.0402919	+	0.0697877i	0.885468	−	0.464700i	$-0.153838\pi$
$919$	8.00670e14	+	1.38680e15i	0.0402919	+	0.0697877i	−0.845176	+	0.534488i	$0.820505\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.29495e16			−0.636272
$924$		0			0
$925$	1.19280e13			0.000579145
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.71978e15	−	6.44285e15i	−0.176373	−	0.305486i	0.764263	−	0.644905i	$-0.223103\pi$
$929$	−3.71978e15	−	6.44285e15i	−0.176373	−	0.305486i	−0.940635	+	0.339419i	$0.889770\pi$
$930$		0			0
$931$	−2.39254e15	−	3.13109e13i	−0.112108	−	0.00146714i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.83272e15	+	1.63547e15i	0.129640	+	0.0748479i
$936$		0			0
$937$			3.19110e16i			1.44335i	0.692231	+	0.721676i	$0.256628\pi$
$937$			3.19110e16i			1.44335i	−0.692231	+	0.721676i	$0.743372\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.07737e16	−	3.59811e16i	0.917849	−	1.58976i	0.115173	−	0.993345i	$-0.463258\pi$
$941$	2.07737e16	−	3.59811e16i	0.917849	−	1.58976i	0.802676	−	0.596415i	$-0.203409\pi$
$942$		0			0
$943$	−6.49609e13	+	3.75052e13i	−0.00283686	+	0.00163786i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.78203e16	+	1.02886e16i	−0.760309	+	0.438965i	−0.829407	−	0.558645i	$-0.811321\pi$
$947$	−1.78203e16	+	1.02886e16i	−0.760309	+	0.438965i	0.0690975	+	0.997610i	$0.477988\pi$
$948$		0			0
$949$	1.08286e15	−	1.87557e15i	0.0456677	−	0.0790988i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	3.03758e15i		−	0.125175i	−0.998039	−	0.0625874i	$-0.980065\pi$
$953$		−	3.03758e15i		−	0.125175i	0.998039	−	0.0625874i	$-0.0199352\pi$
$954$		0			0
$955$	−2.68420e16	−	1.54973e16i	−1.09344	−	0.631301i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.42536e16	−	1.40682e16i	0.567441	−	0.560064i
$960$		0			0
$961$	1.51253e16	+	2.61978e16i	0.595287	+	1.03107i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.53112e16			1.35835
$966$		0			0
$967$	−3.93382e16			−1.49613			−0.748064	−	0.663626i	$-0.769017\pi$
$967$	−3.93382e16			−1.49613			−0.748064	+	0.663626i	$0.769017\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.27097e15	−	2.20139e15i	−0.0472531	−	0.0818447i	0.841431	−	0.540364i	$-0.181713\pi$
$971$	−1.27097e15	−	2.20139e15i	−0.0472531	−	0.0818447i	−0.888685	+	0.458519i	$0.848380\pi$
$972$		0			0
$973$	−1.43051e16	−	3.93353e15i	−0.525859	−	0.144598i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.12678e16	+	1.80525e16i	1.12377	+	0.648808i	0.942360	−	0.334600i	$-0.108601\pi$
$977$	3.12678e16	+	1.80525e16i	1.12377	+	0.648808i	0.181408	+	0.983408i	$0.441934\pi$
$978$		0			0
$979$			6.81831e15i			0.242310i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−1.43033e16	+	2.47740e16i	−0.497039	+	0.860898i	−0.999994	−	0.00341521i	$-0.998913\pi$
$983$	−1.43033e16	+	2.47740e16i	−0.497039	+	0.860898i	0.502955	+	0.864313i	$0.332246\pi$
$984$		0			0
$985$	−1.66552e16	+	9.61589e15i	−0.572336	+	0.330438i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.46239e15	+	2.57636e15i	−0.149964	+	0.0865819i
$990$		0			0
$991$	−2.88818e16	+	5.00247e16i	−0.959884	+	1.66257i	−0.237110	+	0.971483i	$0.576200\pi$
$991$	−2.88818e16	+	5.00247e16i	−0.959884	+	1.66257i	−0.722774	+	0.691085i	$0.757133\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$			2.49631e16i			0.811467i
$996$		0			0
$997$	−3.37257e16	−	1.94715e16i	−1.08427	−	0.626004i	−0.152225	−	0.988346i	$-0.548644\pi$
$997$	−3.37257e16	−	1.94715e16i	−1.08427	−	0.626004i	−0.932045	+	0.362342i	$0.881977\pi$
$998$		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.17.25	yes	60
3.2	odd	2	inner	252.12.t.a.17.6	✓	60
7.5	odd	6	inner	252.12.t.a.89.6	yes	60
21.5	even	6	inner	252.12.t.a.89.25	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.6	✓	60	3.2	odd	2	inner
252.12.t.a.17.25	yes	60	1.1	even	1	trivial
252.12.t.a.89.6	yes	60	7.5	odd	6	inner
252.12.t.a.89.25	yes	60	21.5	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4361.32 + 7554.02i) q^{5} +(-11789.7 + 42875.7i) q^{7} +O(q^{10})\)	\(q+(4361.32 + 7554.02i) q^{5} +(-11789.7 + 42875.7i) q^{7} +(129544. + 74792.0i) q^{11} -758692. i q^{13} +(1.25346e6 - 2.17106e6i) q^{17} +(1.04797e6 - 605046. i) q^{19} +(3.59059e6 - 2.07303e6i) q^{23} +(-1.36281e7 + 2.36046e7i) q^{25} +1.21781e7i q^{29} +(-2.04314e8 - 1.17961e8i) q^{31} +(-3.75303e8 + 9.79348e7i) q^{35} +(-218812. - 378994. i) q^{37} -1.80920e7 q^{41} -1.24280e9 q^{43} +(2.10792e8 + 3.65102e8i) q^{47} +(-1.69933e9 - 1.01099e9i) q^{49} +(-3.11198e9 - 1.79670e9i) q^{53} +1.30477e9i q^{55} +(2.77294e9 - 4.80288e9i) q^{59} +(-8.18507e9 + 4.72565e9i) q^{61} +(5.73118e9 - 3.30890e9i) q^{65} +(5.15115e8 - 8.92205e8i) q^{67} -1.70682e10i q^{71} +(2.47212e9 + 1.42728e9i) q^{73} +(-4.73405e9 + 4.67250e9i) q^{77} +(-3.67781e9 - 6.37015e9i) q^{79} -4.75432e9 q^{83} +2.18670e10 q^{85} +(2.27909e10 + 3.94750e10i) q^{89} +(3.25295e10 + 8.94477e9i) q^{91} +(9.14106e9 + 5.27760e9i) q^{95} +1.41563e10i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 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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