LMFDB - Embedded newform 252.12.t.a.17.16

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			17.16
Character	$\chi$	$=$	252.17
Dual form			252.12.t.a.89.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(11.5001 + 19.9187i) q^{5} +(-9655.86 + 43406.1i) q^{7} +O(q^{10})$	$q+(11.5001 + 19.9187i) q^{5} +(-9655.86 + 43406.1i) q^{7} +(-866549. - 500302. i) q^{11} +1.96677e6i q^{13} +(-5.15075e6 + 8.92136e6i) q^{17} +(86620.1 - 50010.1i) q^{19} +(-4.11110e7 + 2.37355e7i) q^{23} +(2.44138e7 - 4.22859e7i) q^{25} +1.43463e8i q^{29} +(1.35624e8 + 7.83028e7i) q^{31} +(-975635. + 306841. i) q^{35} +(-8.38300e7 - 1.45198e8i) q^{37} -1.37400e7 q^{41} -1.33366e9 q^{43} +(-7.44565e8 - 1.28962e9i) q^{47} +(-1.79086e9 - 8.38247e8i) q^{49} +(1.06369e9 + 6.14121e8i) q^{53} -2.30140e7i q^{55} +(-2.83274e9 + 4.90645e9i) q^{59} +(8.76775e9 - 5.06206e9i) q^{61} +(-3.91754e7 + 2.26179e7i) q^{65} +(-3.65304e9 + 6.32724e9i) q^{67} +2.66198e9i q^{71} +(1.27629e10 + 7.36864e9i) q^{73} +(3.00835e10 - 3.27827e10i) q^{77} +(2.02751e10 + 3.51175e10i) q^{79} -8.35523e9 q^{83} -2.36936e8 q^{85} +(-8.64117e9 - 1.49669e10i) q^{89} +(-8.53698e10 - 1.89908e10i) q^{91} +(1.99227e6 + 1.15024e6i) q^{95} -1.68607e11i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	11.5001	+	19.9187i	0.00164575	+	0.00285053i	0.866847	−	0.498574i	$-0.166143\pi$
$5$	11.5001	+	19.9187i	0.00164575	+	0.00285053i	−0.865201	+	0.501425i	$0.832809\pi$
$6$		0			0
$7$	−9655.86	+	43406.1i	−0.217146	+	0.976139i
$7$	−9655.86	+	43406.1i	−0.217146	+	0.976139i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−866549.	−	500302.i	−1.62231	−	0.936640i	−0.986301	−	0.164957i	$-0.947252\pi$
$11$	−866549.	−	500302.i	−1.62231	−	0.936640i	−0.636007	−	0.771683i	$-0.719415\pi$
$12$		0			0
$13$			1.96677e6i			1.46915i	0.678530	+	0.734573i	$0.262617\pi$
$13$			1.96677e6i			1.46915i	−0.678530	+	0.734573i	$0.737383\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.15075e6	+	8.92136e6i	−0.879835	+	1.52392i	−0.0283146	+	0.999599i	$0.509014\pi$
$17$	−5.15075e6	+	8.92136e6i	−0.879835	+	1.52392i	−0.851521	+	0.524321i	$0.824319\pi$
$18$		0			0
$19$	86620.1	−	50010.1i	0.00802553	−	0.00463354i	−0.495982	−	0.868333i	$-0.665192\pi$
$19$	86620.1	−	50010.1i	0.00802553	−	0.00463354i	0.504007	+	0.863699i	$0.331858\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.11110e7	+	2.37355e7i	−1.33185	+	0.768944i	−0.985583	−	0.169192i	$-0.945884\pi$
$23$	−4.11110e7	+	2.37355e7i	−1.33185	+	0.768944i	−0.346267	+	0.938136i	$0.612551\pi$
$24$		0			0
$25$	2.44138e7	−	4.22859e7i	0.499995	−	0.866016i
$26$		0			0
$27$		0			0
$28$		0			0
$29$			1.43463e8i			1.29882i	0.760437	+	0.649412i	$0.224985\pi$
$29$			1.43463e8i			1.29882i	−0.760437	+	0.649412i	$0.775015\pi$
$30$		0			0
$31$	1.35624e8	+	7.83028e7i	0.850841	+	0.491233i	0.860934	−	0.508716i	$-0.169880\pi$
$31$	1.35624e8	+	7.83028e7i	0.850841	+	0.491233i	−0.0100936	+	0.999949i	$0.503213\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−975635.	+	306841.i	−0.00313988	+	0.000987504i
$36$		0			0
$37$	−8.38300e7	−	1.45198e8i	−0.198742	−	0.344231i	0.749379	−	0.662142i	$-0.230352\pi$
$37$	−8.38300e7	−	1.45198e8i	−0.198742	−	0.344231i	−0.948121	+	0.317910i	$0.897019\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.37400e7			−0.0185215			−0.00926074	−	0.999957i	$-0.502948\pi$
$41$	−1.37400e7			−0.0185215			−0.00926074	+	0.999957i	$0.502948\pi$
$42$		0			0
$43$	−1.33366e9			−1.38346			−0.691731	−	0.722155i	$-0.743152\pi$
$43$	−1.33366e9			−1.38346			−0.691731	+	0.722155i	$0.743152\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.44565e8	−	1.28962e9i	−0.473548	−	0.820210i	0.525993	−	0.850489i	$-0.323694\pi$
$47$	−7.44565e8	−	1.28962e9i	−0.473548	−	0.820210i	−0.999541	+	0.0302790i	$0.990360\pi$
$48$		0			0
$49$	−1.79086e9	−	8.38247e8i	−0.905695	−	0.423929i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.06369e9	+	6.14121e8i	0.349379	+	0.201714i	0.664412	−	0.747367i	$-0.268682\pi$
$53$	1.06369e9	+	6.14121e8i	0.349379	+	0.201714i	−0.315032	+	0.949081i	$0.602015\pi$
$54$		0			0
$55$		−	2.30140e7i		−	0.00616591i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.83274e9	+	4.90645e9i	−0.515847	+	0.893472i	0.483984	+	0.875077i	$0.339189\pi$
$59$	−2.83274e9	+	4.90645e9i	−0.515847	+	0.893472i	−0.999831	+	0.0183957i	$0.994144\pi$
$60$		0			0
$61$	8.76775e9	−	5.06206e9i	1.32915	−	0.767385i	0.343982	−	0.938976i	$-0.388224\pi$
$61$	8.76775e9	−	5.06206e9i	1.32915	−	0.767385i	0.985168	+	0.171591i	$0.0548906\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.91754e7	+	2.26179e7i	−0.00418784	+	0.00241785i
$66$		0			0
$67$	−3.65304e9	+	6.32724e9i	−0.330554	+	0.572537i	−0.982621	−	0.185625i	$-0.940569\pi$
$67$	−3.65304e9	+	6.32724e9i	−0.330554	+	0.572537i	0.652066	+	0.758162i	$0.273902\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			2.66198e9i			0.175099i	0.996160	+	0.0875495i	$0.0279036\pi$
$71$			2.66198e9i			0.175099i	−0.996160	+	0.0875495i	$0.972096\pi$
$72$		0			0
$73$	1.27629e10	+	7.36864e9i	0.720564	+	0.416018i	0.814960	−	0.579517i	$-0.196759\pi$
$73$	1.27629e10	+	7.36864e9i	0.720564	+	0.416018i	−0.0943965	+	0.995535i	$0.530092\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.00835e10	−	3.27827e10i	1.26657	−	1.38021i
$78$		0			0
$79$	2.02751e10	+	3.51175e10i	0.741333	+	1.28403i	0.951888	+	0.306445i	$0.0991395\pi$
$79$	2.02751e10	+	3.51175e10i	0.741333	+	1.28403i	−0.210555	+	0.977582i	$0.567527\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−8.35523e9			−0.232825			−0.116412	−	0.993201i	$-0.537139\pi$
$83$	−8.35523e9			−0.232825			−0.116412	+	0.993201i	$0.537139\pi$
$84$		0			0
$85$	−2.36936e8			−0.00579197
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.64117e9	−	1.49669e10i	−0.164032	−	0.284111i	0.772279	−	0.635283i	$-0.219117\pi$
$89$	−8.64117e9	−	1.49669e10i	−0.164032	−	0.284111i	−0.936311	+	0.351172i	$0.885783\pi$
$90$		0			0
$91$	−8.53698e10	−	1.89908e10i	−1.43409	−	0.319019i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.99227e6	+	1.15024e6i	2.64161e−5	+	1.52513e-5i
$96$		0			0
$97$		−	1.68607e11i		−	1.99357i	−0.0801314	−	0.996784i	$-0.525534\pi$
$97$		−	1.68607e11i		−	1.99357i	0.0801314	−	0.996784i	$-0.474466\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.09756e10	+	5.36513e10i	−0.293259	+	0.507940i	−0.974578	−	0.224046i	$-0.928073\pi$
$101$	−3.09756e10	+	5.36513e10i	−0.293259	+	0.507940i	0.681319	+	0.731987i	$0.261407\pi$
$102$		0			0
$103$	−8.28465e10	+	4.78315e10i	−0.704157	+	0.406545i	−0.808894	−	0.587955i	$-0.799933\pi$
$103$	−8.28465e10	+	4.78315e10i	−0.704157	+	0.406545i	0.104737	+	0.994500i	$0.466600\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.36618e10	+	1.36612e10i	−0.163094	+	0.0941622i	−0.579325	−	0.815096i	$-0.696684\pi$
$107$	−2.36618e10	+	1.36612e10i	−0.163094	+	0.0941622i	0.416232	+	0.909259i	$0.363351\pi$
$108$		0			0
$109$	6.56977e10	−	1.13792e11i	0.408983	−	0.708378i	−0.585793	−	0.810460i	$-0.699217\pi$
$109$	6.56977e10	−	1.13792e11i	0.408983	−	0.708378i	0.994776	+	0.102082i	$0.0325504\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$			2.71579e11i			1.38665i	0.720627	+	0.693323i	$0.243854\pi$
$113$			2.71579e11i			1.38665i	−0.720627	+	0.693323i	$0.756146\pi$
$114$		0			0
$115$	−9.45558e8	−	5.45918e8i	−0.00438379	−	0.00253098i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.37507e11	−	3.09718e11i	−1.29651	−	1.18975i
$120$		0			0
$121$	3.57949e11	+	6.19985e11i	1.25459	+	2.17301i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.24609e9			0.00658298
$126$		0			0
$127$	1.05482e10			0.0283307			0.0141653	−	0.999900i	$-0.495491\pi$
$127$	1.05482e10			0.0283307			0.0141653	+	0.999900i	$0.495491\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.42239e9	+	1.11239e10i	0.0145447	+	0.0251922i	0.873206	−	0.487351i	$-0.162037\pi$
$131$	6.42239e9	+	1.11239e10i	0.0145447	+	0.0251922i	−0.858661	+	0.512543i	$0.828703\pi$
$132$		0			0
$133$	1.33435e9	+	4.24273e9i	0.00278027	+	0.00884019i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.02534e11	+	3.47873e11i	1.06664	+	0.615826i	0.927262	−	0.374414i	$-0.122156\pi$
$137$	6.02534e11	+	3.47873e11i	1.06664	+	0.615826i	0.139379	+	0.990239i	$0.455489\pi$
$138$		0			0
$139$		−	7.97459e11i		−	1.30355i	−0.758413	−	0.651774i	$-0.774025\pi$
$139$		−	7.97459e11i		−	1.30355i	0.758413	−	0.651774i	$-0.225975\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.83979e11	−	1.70430e12i	1.37606	−	2.38341i
$144$		0			0
$145$	−2.85759e9	+	1.64983e9i	−0.00370233	+	0.00213754i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.29587e11	+	5.36697e11i	−1.03697	+	0.598694i	−0.918973	−	0.394320i	$-0.870980\pi$
$149$	−9.29587e11	+	5.36697e11i	−1.03697	+	0.598694i	−0.117995	+	0.993014i	$0.537647\pi$
$150$		0			0
$151$	4.57718e11	−	7.92791e11i	0.474487	−	0.821836i	−0.525086	−	0.851049i	$-0.675967\pi$
$151$	4.57718e11	−	7.92791e11i	0.474487	−	0.821836i	0.999573	+	0.0292131i	$0.00930014\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$			3.60194e9i			0.00323380i
$156$		0			0
$157$	−1.28544e12	−	7.42150e11i	−1.07549	−	0.620932i	−0.145810	−	0.989313i	$-0.546579\pi$
$157$	−1.28544e12	−	7.42150e11i	−1.07549	−	0.620932i	−0.929675	+	0.368381i	$0.879912\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.33302e11	−	2.01366e12i	−0.461390	−	1.46704i
$162$		0			0
$163$	1.35055e12	+	2.33922e12i	0.919343	+	1.59235i	0.800415	+	0.599447i	$0.204613\pi$
$163$	1.35055e12	+	2.33922e12i	0.919343	+	1.59235i	0.118929	+	0.992903i	$0.462054\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.89232e12			−1.72308			−0.861540	−	0.507690i	$-0.830500\pi$
$167$	−2.89232e12			−1.72308			−0.861540	+	0.507690i	$0.830500\pi$
$168$		0			0
$169$	−2.07602e12			−1.15839
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.79119e11	+	1.52268e12i	0.431315	+	0.747059i	0.996987	−	0.0775713i	$-0.0247165\pi$
$173$	8.79119e11	+	1.52268e12i	0.431315	+	0.747059i	−0.565672	+	0.824630i	$0.691383\pi$
$174$		0			0
$175$	1.59973e12	+	1.46802e12i	0.736780	+	0.676116i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.22049e11	+	3.01405e11i	0.212334	+	0.122591i	0.602396	−	0.798198i	$-0.294213\pi$
$179$	5.22049e11	+	3.01405e11i	0.212334	+	0.122591i	−0.390062	+	0.920789i	$0.627546\pi$
$180$		0			0
$181$		−	1.10745e12i		−	0.423733i	−0.977299	−	0.211867i	$-0.932046\pi$
$181$		−	1.10745e12i		−	0.423733i	0.977299	−	0.211867i	$-0.0679542\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.92810e9	−	3.33956e9i	0.000654161	−	0.00113304i
$186$		0			0
$187$	8.92675e12	−	5.15386e12i	2.85473	−	1.64818i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	9.83427e9	−	5.67782e9i	0.00279936	−	0.00161621i	−0.498600	−	0.866832i	$-0.666152\pi$
$191$	9.83427e9	−	5.67782e9i	0.00279936	−	0.00161621i	0.501399	+	0.865216i	$0.332819\pi$
$192$		0			0
$193$	3.19675e8	−	5.53693e8i	8.59297e−5	−	0.000148835i	−0.865982	−	0.500074i	$-0.833306\pi$
$193$	3.19675e8	−	5.53693e8i	8.59297e−5	−	0.000148835i	0.866068	+	0.499926i	$0.166639\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	3.84901e12i		−	0.924240i	−0.886817	−	0.462120i	$-0.847089\pi$
$197$		−	3.84901e12i		−	0.924240i	0.886817	−	0.462120i	$-0.152911\pi$
$198$		0			0
$199$	−2.47949e12	−	1.43153e12i	−0.563209	−	0.325169i	0.191223	−	0.981547i	$-0.438755\pi$
$199$	−2.47949e12	−	1.43153e12i	−0.563209	−	0.325169i	−0.754433	+	0.656377i	$0.772088\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−6.22716e12	−	1.38526e12i	−1.26783	−	0.282034i
$204$		0			0
$205$	−1.58011e8	−	2.73683e8i	−3.04818e−5	−	5.27960e-5i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.00081e11			−0.0173598
$210$		0			0
$211$	−4.29030e12			−0.706210			−0.353105	−	0.935584i	$-0.614874\pi$
$211$	−4.29030e12			−0.706210			−0.353105	+	0.935584i	$0.614874\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.53371e10	−	2.65647e10i	−0.00227684	−	0.00394360i
$216$		0			0
$217$	−4.70839e12	+	5.13085e12i	−0.664269	+	0.723870i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.75463e13	−	1.01303e13i	−2.23886	−	1.29261i
$222$		0			0
$223$		−	9.58836e12i		−	1.16431i	−0.813079	−	0.582154i	$-0.802210\pi$
$223$		−	9.58836e12i		−	1.16431i	0.813079	−	0.582154i	$-0.197790\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.69186e12	−	9.85859e12i	0.626776	−	1.08561i	−0.361419	−	0.932403i	$-0.617708\pi$
$227$	5.69186e12	−	9.85859e12i	0.626776	−	1.08561i	0.988195	−	0.153204i	$-0.0489590\pi$
$228$		0			0
$229$	1.47341e13	−	8.50676e12i	1.54607	−	0.892625i	0.547636	−	0.836717i	$-0.315528\pi$
$229$	1.47341e13	−	8.50676e12i	1.54607	−	0.892625i	0.998436	−	0.0559079i	$-0.0178053\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.82646e12	−	3.94126e12i	0.651236	−	0.375991i	−0.137694	−	0.990475i	$-0.543969\pi$
$233$	6.82646e12	−	3.94126e12i	0.651236	−	0.375991i	0.788929	+	0.614484i	$0.210636\pi$
$234$		0			0
$235$	1.71251e10	−	2.96615e10i	0.00155869	−	0.00269973i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	1.33846e13i		−	1.11024i	−0.831770	−	0.555120i	$-0.812672\pi$
$239$		−	1.33846e13i		−	1.11024i	0.831770	−	0.555120i	$-0.187328\pi$
$240$		0			0
$241$	7.31664e12	+	4.22426e12i	0.579719	+	0.334701i	0.761022	−	0.648726i	$-0.224698\pi$
$241$	7.31664e12	+	4.22426e12i	0.579719	+	0.334701i	−0.181302	+	0.983427i	$0.558031\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.89817e9	−	4.53114e10i	−0.000282129	−	0.00327939i
$246$		0			0
$247$	9.83584e10	+	1.70362e11i	0.00680735	+	0.0117907i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	7.29725e12			0.462332			0.231166	−	0.972914i	$-0.425746\pi$
$251$	7.29725e12			0.462332			0.231166	+	0.972914i	$0.425746\pi$
$252$		0			0
$253$	4.74996e13			2.88089
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−1.17267e13	−	2.03112e13i	−0.652442	−	1.13006i	−0.982529	−	0.186112i	$-0.940411\pi$
$257$	−1.17267e13	−	2.03112e13i	−0.652442	−	1.13006i	0.330087	−	0.943951i	$-0.392922\pi$
$258$		0			0
$259$	7.11192e12	−	2.23672e12i	0.379174	−	0.119251i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.67295e13	−	9.65878e12i	−0.819835	−	0.473332i	0.0305248	−	0.999534i	$-0.490282\pi$
$263$	−1.67295e13	−	9.65878e12i	−0.819835	−	0.473332i	−0.850359	+	0.526202i	$0.823615\pi$
$264$		0			0
$265$			2.82497e10i			0.00132789i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.54103e12	+	1.30615e13i	−0.326433	+	0.565398i	−0.981801	−	0.189911i	$-0.939180\pi$
$269$	−7.54103e12	+	1.30615e13i	−0.326433	+	0.565398i	0.655369	+	0.755309i	$0.272513\pi$
$270$		0			0
$271$	−1.01891e13	+	5.88268e12i	−0.423453	+	0.244481i	−0.696553	−	0.717505i	$-0.745284\pi$
$271$	−1.01891e13	+	5.88268e12i	−0.423453	+	0.244481i	0.273101	+	0.961985i	$0.411951\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.23115e13	+	2.44286e13i	−1.62229	+	0.936630i
$276$		0			0
$277$	1.31657e13	−	2.28037e13i	0.485072	−	0.840169i	−0.514781	−	0.857322i	$-0.672127\pi$
$277$	1.31657e13	−	2.28037e13i	0.485072	−	0.840169i	0.999853	+	0.0171528i	$0.00546018\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	5.63734e13i		−	1.91950i	−0.280848	−	0.959752i	$-0.590616\pi$
$281$		−	5.63734e13i		−	1.91950i	0.280848	−	0.959752i	$-0.409384\pi$
$282$		0			0
$283$	3.45860e12	+	1.99683e12i	0.113260	+	0.0653905i	0.555560	−	0.831477i	$-0.312504\pi$
$283$	3.45860e12	+	1.99683e12i	0.113260	+	0.0653905i	−0.442300	+	0.896867i	$0.645837\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.32672e11	−	5.96400e11i	0.00402186	−	0.0180795i
$288$		0			0
$289$	−3.59245e13	−	6.22231e13i	−1.04822	−	1.81557i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−3.10431e13			−0.839833			−0.419916	−	0.907563i	$-0.637941\pi$
$293$	−3.10431e13			−0.839833			−0.419916	+	0.907563i	$0.637941\pi$
$294$		0			0
$295$	−1.30307e11			−0.00339583
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.66822e13	−	8.08559e13i	−1.12969	−	1.95668i
$300$		0			0
$301$	1.28776e13	−	5.78888e13i	0.300413	−	1.35045i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.01659e11	+	1.16428e11i	0.00437491	+	0.00252586i
$306$		0			0
$307$			4.63806e13i			0.970677i	0.874326	+	0.485339i	$0.161304\pi$
$307$			4.63806e13i			0.970677i	−0.874326	+	0.485339i	$0.838696\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.31858e13	−	2.28385e13i	0.256995	−	0.445129i	−0.708440	−	0.705771i	$-0.750601\pi$
$311$	1.31858e13	−	2.28385e13i	0.256995	−	0.445129i	0.965436	+	0.260642i	$0.0839342\pi$
$312$		0			0
$313$	−4.55233e13	+	2.62829e13i	−0.856524	+	0.494514i	−0.862847	−	0.505466i	$-0.831321\pi$
$313$	−4.55233e13	+	2.62829e13i	−0.856524	+	0.494514i	0.00632286	+	0.999980i	$0.497987\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.11310e11	−	1.79735e11i	0.00546219	−	0.00315360i	−0.497266	−	0.867598i	$-0.665663\pi$
$317$	3.11310e11	−	1.79735e11i	0.00546219	−	0.00315360i	0.502729	+	0.864444i	$0.332330\pi$
$318$		0			0
$319$	7.17747e13	−	1.24317e14i	1.21653	−	2.10709i
$320$		0			0
$321$		0			0
$322$		0			0
$323$			1.03036e12i			0.0163070i
$324$		0			0
$325$	8.31667e13	+	4.80163e13i	1.27230	+	0.734565i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.31670e13	−	1.98662e13i	0.903468	−	0.284144i
$330$		0			0
$331$	4.49845e13	+	7.79155e13i	0.622314	+	1.07788i	0.989054	+	0.147555i	$0.0471404\pi$
$331$	4.49845e13	+	7.79155e13i	0.622314	+	1.07788i	−0.366740	+	0.930323i	$0.619526\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−1.68040e11			−0.00217604
$336$		0			0
$337$	1.02721e14			1.28734			0.643671	−	0.765302i	$-0.277410\pi$
$337$	1.02721e14			1.28734			0.643671	+	0.765302i	$0.277410\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−7.83501e13	−	1.35706e14i	−0.920217	−	1.59386i
$342$		0			0
$343$	5.36773e13	−	6.96401e13i	0.610482	−	0.792030i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.82475e13	−	4.51762e13i	−0.834945	−	0.482056i	0.0205975	−	0.999788i	$-0.493443\pi$
$347$	−7.82475e13	−	4.51762e13i	−0.834945	−	0.482056i	−0.855543	+	0.517732i	$0.826776\pi$
$348$		0			0
$349$			5.58170e13i			0.577068i	0.957470	+	0.288534i	$0.0931678\pi$
$349$			5.58170e13i			0.577068i	−0.957470	+	0.288534i	$0.906832\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−2.57547e13	+	4.46084e13i	−0.250089	+	0.433168i	−0.963550	−	0.267528i	$-0.913793\pi$
$353$	−2.57547e13	+	4.46084e13i	−0.250089	+	0.433168i	0.713461	+	0.700695i	$0.247127\pi$
$354$		0			0
$355$	−5.30231e10	+	3.06129e10i	−0.000499125	+	0.000288170i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.18975e14	−	6.86904e13i	1.05302	−	0.607963i	0.129528	−	0.991576i	$-0.458654\pi$
$359$	1.18975e14	−	6.86904e13i	1.05302	−	0.607963i	0.923494	+	0.383613i	$0.125320\pi$
$360$		0			0
$361$	−5.82401e13	+	1.00875e14i	−0.499957	+	0.865951i
$362$		0			0
$363$		0			0
$364$		0			0
$365$			3.38959e11i			0.00273865i
$366$		0			0
$367$	1.49247e13	+	8.61678e12i	0.117015	+	0.0675588i	0.557365	−	0.830267i	$-0.311812\pi$
$367$	1.49247e13	+	8.61678e12i	0.117015	+	0.0675588i	−0.440350	+	0.897826i	$0.645146\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.69274e13	+	4.02407e13i	−0.272768	+	0.297242i
$372$		0			0
$373$	−8.23892e13	−	1.42702e14i	−0.590842	−	1.02337i	−0.994119	−	0.108291i	$-0.965462\pi$
$373$	−8.23892e13	−	1.42702e14i	−0.590842	−	1.02337i	0.403277	−	0.915078i	$-0.367871\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.82158e14			−1.90816
$378$		0			0
$379$	−5.42928e13			−0.356637			−0.178319	−	0.983973i	$-0.557066\pi$
$379$	−5.42928e13			−0.356637			−0.178319	+	0.983973i	$0.557066\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	4.51958e13	+	7.82815e13i	0.280224	+	0.485362i	0.971440	−	0.237286i	$-0.0762580\pi$
$383$	4.51958e13	+	7.82815e13i	0.280224	+	0.485362i	−0.691216	+	0.722648i	$0.742925\pi$
$384$		0			0
$385$	9.98949e11	+	2.22220e11i	0.00601879	+	0.00133890i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.78815e13	+	1.03239e13i	0.101785	+	0.0587654i	0.550028	−	0.835146i	$-0.314617\pi$
$389$	1.78815e13	+	1.03239e13i	0.101785	+	0.0587654i	−0.448244	+	0.893911i	$0.647950\pi$
$390$		0			0
$391$		−	4.89022e14i		−	2.70618i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.66329e11	+	8.07705e11i	−0.00244010	+	0.00422638i
$396$		0			0
$397$	7.18023e12	−	4.14551e12i	0.0365419	−	0.0210974i	−0.481618	−	0.876381i	$-0.659951\pi$
$397$	7.18023e12	−	4.14551e12i	0.0365419	−	0.0210974i	0.518160	+	0.855284i	$0.326617\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	3.00472e14	−	1.73477e14i	1.44714	−	0.835505i	0.448826	−	0.893619i	$-0.351842\pi$
$401$	3.00472e14	−	1.73477e14i	1.44714	−	0.835505i	0.998310	+	0.0581144i	$0.0185088\pi$
$402$		0			0
$403$	−1.54003e14	+	2.66742e14i	−0.721693	+	1.25001i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			1.67761e14i			0.744599i
$408$		0			0
$409$	−2.28684e13	−	1.32031e13i	−0.0988000	−	0.0570422i	0.449786	−	0.893136i	$-0.351500\pi$
$409$	−2.28684e13	−	1.32031e13i	−0.0988000	−	0.0570422i	−0.548586	+	0.836094i	$0.684834\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.85617e14	−	1.70334e14i	−0.760139	−	0.697552i
$414$		0			0
$415$	−9.60856e10	−	1.66425e11i	−0.000383172	−	0.000663674i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	2.25764e14			0.854038			0.427019	−	0.904243i	$-0.359564\pi$
$419$	2.25764e14			0.854038			0.427019	+	0.904243i	$0.359564\pi$
$420$		0			0
$421$	−1.69685e14			−0.625304			−0.312652	−	0.949868i	$-0.601217\pi$
$421$	−1.69685e14			−0.625304			−0.312652	+	0.949868i	$0.601217\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.51499e14	+	4.35609e14i	0.879826	+	1.52390i
$426$		0			0
$427$	1.35064e14	+	4.29453e14i	0.460455	+	1.46407i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.70790e14	−	9.86056e13i	−0.553143	−	0.319357i	0.197246	−	0.980354i	$-0.436800\pi$
$431$	−1.70790e14	−	9.86056e13i	−0.553143	−	0.319357i	−0.750389	+	0.660997i	$0.770134\pi$
$432$		0			0
$433$			3.53250e14i			1.11532i	0.830070	+	0.557660i	$0.188301\pi$
$433$			3.53250e14i			1.11532i	−0.830070	+	0.557660i	$0.811699\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.37403e12	+	4.11194e12i	−0.00712587	+	0.0123424i
$438$		0			0
$439$	3.31130e14	−	1.91178e14i	0.969267	−	0.559607i	0.0702544	−	0.997529i	$-0.477619\pi$
$439$	3.31130e14	−	1.91178e14i	0.969267	−	0.559607i	0.899013	+	0.437922i	$0.144286\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−4.60058e14	+	2.65614e14i	−1.28113	+	0.739658i	−0.977054	−	0.212991i	$-0.931679\pi$
$443$	−4.60058e14	+	2.65614e14i	−1.28113	+	0.739658i	−0.304071	+	0.952649i	$0.598346\pi$
$444$		0			0
$445$	1.98748e11	−	3.44241e11i	0.000539911	−	0.000935154i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			3.99677e14i			1.03360i	0.856105	+	0.516802i	$0.172877\pi$
$449$			3.99677e14i			1.03360i	−0.856105	+	0.516802i	$0.827123\pi$
$450$		0			0
$451$	1.19064e13	+	6.87416e12i	0.0300475	+	0.0173480i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−6.03485e11	−	1.91885e12i	−0.00145079	−	0.00461294i
$456$		0			0
$457$	1.82167e14	+	3.15522e14i	0.427493	+	0.740440i	0.996650	−	0.0817890i	$-0.0260634\pi$
$457$	1.82167e14	+	3.15522e14i	0.427493	+	0.740440i	−0.569156	+	0.822229i	$0.692730\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.20414e14			0.269354			0.134677	−	0.990890i	$-0.457000\pi$
$461$	1.20414e14			0.269354			0.134677	+	0.990890i	$0.457000\pi$
$462$		0			0
$463$	−7.46137e14			−1.62976			−0.814879	−	0.579632i	$-0.803196\pi$
$463$	−7.46137e14			−1.62976			−0.814879	+	0.579632i	$0.803196\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.76208e14	+	3.05201e14i	0.367099	+	0.635833i	0.989111	−	0.147174i	$-0.0470179\pi$
$467$	1.76208e14	+	3.05201e14i	0.367099	+	0.635833i	−0.622012	+	0.783008i	$0.713685\pi$
$468$		0			0
$469$	−2.39368e14	−	2.19659e14i	−0.487097	−	0.446991i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.15568e15	+	6.67231e14i	2.24440	+	1.29581i
$474$		0			0
$475$		−	4.88375e12i		−	0.00926699i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.84464e14	−	6.65910e14i	0.696642	−	1.20662i	−0.272981	−	0.962019i	$-0.588010\pi$
$479$	3.84464e14	−	6.65910e14i	0.696642	−	1.20662i	0.969624	−	0.244601i	$-0.0786569\pi$
$480$		0			0
$481$	2.85570e14	−	1.64874e14i	0.505726	−	0.291981i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	3.35843e12	−	1.93899e12i	0.00568273	−	0.00328092i
$486$		0			0
$487$	−1.79826e14	+	3.11469e14i	−0.297471	+	0.515234i	−0.975557	−	0.219748i	$-0.929476\pi$
$487$	−1.79826e14	+	3.11469e14i	−0.297471	+	0.515234i	0.678086	+	0.734983i	$0.262810\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	4.76622e14i		−	0.753748i	−0.926265	−	0.376874i	$-0.876999\pi$
$491$		−	4.76622e14i		−	0.753748i	0.926265	−	0.376874i	$-0.123001\pi$
$492$		0			0
$493$	−1.27988e15	−	7.38941e14i	−1.97930	−	1.14275i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.15546e14	−	2.57037e13i	−0.170921	−	0.0380221i
$498$		0			0
$499$	2.50175e14	+	4.33315e14i	0.361985	+	0.626976i	0.988287	−	0.152604i	$-0.0487659\pi$
$499$	2.50175e14	+	4.33315e14i	0.361985	+	0.626976i	−0.626303	+	0.779580i	$0.715433\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8.03031e14			1.11201			0.556004	−	0.831179i	$-0.312334\pi$
$503$	8.03031e14			1.11201			0.556004	+	0.831179i	$0.312334\pi$
$504$		0			0
$505$	−1.42488e12			−0.00193053
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.95221e14	+	1.03095e15i	0.772201	+	1.33749i	0.936354	+	0.351057i	$0.114178\pi$
$509$	5.95221e14	+	1.03095e15i	0.772201	+	1.33749i	−0.164153	+	0.986435i	$0.552489\pi$
$510$		0			0
$511$	−4.43081e14	+	4.82836e14i	−0.562559	+	0.613034i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.90548e12	−	1.10013e12i	−0.00231774	−	0.00133815i
$516$		0			0
$517$			1.49003e15i			1.77418i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.01620e14	+	6.95627e14i	−0.458362	+	0.793906i	−0.998875	−	0.0474299i	$-0.984897\pi$
$521$	−4.01620e14	+	6.95627e14i	−0.458362	+	0.793906i	0.540513	+	0.841336i	$0.318230\pi$
$522$		0			0
$523$	−1.49100e15	+	8.60830e14i	−1.66617	+	0.961963i	−0.696494	+	0.717563i	$0.745258\pi$
$523$	−1.49100e15	+	8.60830e14i	−1.66617	+	0.961963i	−0.969675	+	0.244400i	$0.921409\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.39713e15	+	8.06636e14i	−1.49720	+	0.864409i
$528$		0			0
$529$	6.50340e14	−	1.12642e15i	0.682550	−	1.18221i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		−	2.70234e13i		−	0.0272108i
$534$		0			0
$535$	−5.44224e11	−	3.14208e11i	−0.000536824	−	0.000309936i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.13249e15	+	1.62235e15i	1.07225	+	1.53605i
$540$		0			0
$541$	6.42661e14	+	1.11312e15i	0.596207	+	1.03266i	0.993375	+	0.114914i	$0.0366594\pi$
$541$	6.42661e14	+	1.11312e15i	0.596207	+	1.03266i	−0.397169	+	0.917746i	$0.630007\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	3.02211e12			0.00269234
$546$		0			0
$547$	8.03623e14			0.701652			0.350826	−	0.936441i	$-0.385901\pi$
$547$	8.03623e14			0.701652			0.350826	+	0.936441i	$0.385901\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.17459e12	+	1.24268e13i	0.00601816	+	0.0104238i
$552$		0			0
$553$	−1.72009e15	+	5.40973e14i	−1.41437	+	0.444823i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	1.02951e15	+	5.94389e14i	0.813632	+	0.469751i	0.848216	−	0.529651i	$-0.177677\pi$
$557$	1.02951e15	+	5.94389e14i	0.813632	+	0.469751i	−0.0345834	+	0.999402i	$0.511010\pi$
$558$		0			0
$559$		−	2.62299e15i		−	2.03251i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.27949e14	+	1.26085e15i	−0.542382	+	0.939433i	0.456385	+	0.889782i	$0.349144\pi$
$563$	−7.27949e14	+	1.26085e15i	−0.542382	+	0.939433i	−0.998767	+	0.0496502i	$0.984189\pi$
$564$		0			0
$565$	−5.40950e12	+	3.12318e12i	−0.00395267	+	0.00228208i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.21721e13	−	1.28010e13i	0.0155843	−	0.00899763i	−0.492188	−	0.870489i	$-0.663803\pi$
$569$	2.21721e13	−	1.28010e13i	0.0155843	−	0.00899763i	0.507772	+	0.861492i	$0.330469\pi$
$570$		0			0
$571$	9.61684e13	−	1.66569e14i	0.0663031	−	0.114840i	−0.830968	−	0.556320i	$-0.812213\pi$
$571$	9.61684e13	−	1.66569e14i	0.0663031	−	0.114840i	0.897271	+	0.441480i	$0.145546\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			2.31789e15i			1.53787i
$576$		0			0
$577$	1.64456e14	+	9.49486e13i	0.107049	+	0.0618047i	0.552569	−	0.833467i	$-0.313648\pi$
$577$	1.64456e14	+	9.49486e13i	0.107049	+	0.0618047i	−0.445520	+	0.895272i	$0.646981\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.06770e13	−	3.62668e14i	0.0505569	−	0.227269i
$582$		0			0
$583$	−6.14492e14	−	1.06433e15i	−0.377867	−	0.654485i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.42436e15			1.43578			0.717889	−	0.696158i	$-0.245109\pi$
$587$	2.42436e15			1.43578			0.717889	+	0.696158i	$0.245109\pi$
$588$		0			0
$589$	1.56637e13			0.00910460
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.22737e15	−	2.12586e15i	−0.687344	−	1.19051i	−0.972694	−	0.232091i	$-0.925443\pi$
$593$	−1.22737e15	−	2.12586e15i	−0.687344	−	1.19051i	0.285350	−	0.958423i	$-0.407890\pi$
$594$		0			0
$595$	2.28782e12	−	1.02845e13i	0.00125770	−	0.00565377i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.15668e15	−	6.67811e14i	−0.612868	−	0.353839i	0.161219	−	0.986919i	$-0.448457\pi$
$599$	−1.15668e15	−	6.67811e14i	−0.612868	−	0.353839i	−0.774087	+	0.633079i	$0.781791\pi$
$600$		0			0
$601$			2.83665e15i			1.47569i	0.674968	+	0.737847i	$0.264157\pi$
$601$			2.83665e15i			1.47569i	−0.674968	+	0.737847i	$0.735843\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.23286e12	+	1.42597e13i	−0.00412949	+	0.00715248i
$606$		0			0
$607$	−2.80681e15	+	1.62051e15i	−1.38253	+	0.798206i	−0.992459	−	0.122578i	$-0.960884\pi$
$607$	−2.80681e15	+	1.62051e15i	−1.38253	+	0.798206i	−0.390074	+	0.920783i	$0.627551\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.53639e15	−	1.46439e15i	1.20501	−	0.695712i
$612$		0			0
$613$	−2.04479e15	+	3.54169e15i	−0.954151	+	1.65264i	−0.217852	+	0.975982i	$0.569905\pi$
$613$	−2.04479e15	+	3.54169e15i	−0.954151	+	1.65264i	−0.736299	+	0.676656i	$0.763428\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	3.38686e15i		−	1.52486i	−0.647072	−	0.762429i	$-0.724007\pi$
$617$		−	3.38686e15i		−	1.52486i	0.647072	−	0.762429i	$-0.275993\pi$
$618$		0			0
$619$	1.63749e15	+	9.45404e14i	0.724235	+	0.418137i	0.816309	−	0.577615i	$-0.196016\pi$
$619$	1.63749e15	+	9.45404e14i	0.724235	+	0.418137i	−0.0920746	+	0.995752i	$0.529350\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	7.33095e14	−	2.30561e14i	0.312951	−	0.0984241i
$624$		0			0
$625$	−1.19205e15	−	2.06470e15i	−0.499984	−	0.865997i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.72715e15			0.699441
$630$		0			0
$631$	2.26763e15			0.902426			0.451213	−	0.892416i	$-0.350992\pi$
$631$	2.26763e15			0.902426			0.451213	+	0.892416i	$0.350992\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.21305e11	+	2.10106e11i	4.66253e−5	+	8.07575e-5i
$636$		0			0
$637$	1.64864e15	−	3.52220e15i	0.622814	−	1.33060i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.95266e14	−	3.43677e14i	−0.217266	−	0.125439i	0.387418	−	0.921904i	$-0.373367\pi$
$641$	−5.95266e14	−	3.43677e14i	−0.217266	−	0.125439i	−0.604684	+	0.796466i	$0.706700\pi$
$642$		0			0
$643$			2.84301e14i			0.102004i	0.998699	+	0.0510021i	$0.0162415\pi$
$643$			2.84301e14i			0.102004i	−0.998699	+	0.0510021i	$0.983758\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.12791e14	+	7.14975e14i	−0.143139	+	0.247923i	−0.928677	−	0.370890i	$-0.879053\pi$
$647$	−4.12791e14	+	7.14975e14i	−0.143139	+	0.247923i	0.785538	+	0.618813i	$0.212386\pi$
$648$		0			0
$649$	4.90941e15	−	2.83445e15i	1.67372	−	0.966325i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.68583e14	−	5.01477e14i	0.286279	−	0.165283i	−0.349984	−	0.936756i	$-0.613813\pi$
$653$	8.68583e14	−	5.01477e14i	0.286279	−	0.165283i	0.636262	+	0.771473i	$0.280480\pi$
$654$		0			0
$655$	−1.47716e11	+	2.55851e11i	−4.78740e−5	+	8.29202e-5i
$656$		0			0
$657$		0			0
$658$		0			0
$659$			5.00574e15i			1.56891i	0.620184	+	0.784456i	$0.287058\pi$
$659$			5.00574e15i			1.56891i	−0.620184	+	0.784456i	$0.712942\pi$
$660$		0			0
$661$	3.10059e15	+	1.79013e15i	0.955732	+	0.551792i	0.894857	−	0.446353i	$-0.147277\pi$
$661$	3.10059e15	+	1.79013e15i	0.955732	+	0.551792i	0.0608753	+	0.998145i	$0.480611\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.91645e10	+	7.53702e10i	−2.06236e−5	+	2.24740e-5i
$666$		0			0
$667$	−3.40515e15	−	5.89790e15i	−0.998722	−	1.72984i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.01302e16			−2.87506
$672$		0			0
$673$	−3.91527e15			−1.09315			−0.546574	−	0.837411i	$-0.684068\pi$
$673$	−3.91527e15			−1.09315			−0.546574	+	0.837411i	$0.684068\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.98069e15	+	3.43066e15i	0.535278	+	0.927129i	0.999150	+	0.0412263i	$0.0131265\pi$
$677$	1.98069e15	+	3.43066e15i	0.535278	+	0.927129i	−0.463872	+	0.885902i	$0.653540\pi$
$678$		0			0
$679$	7.31858e15	+	1.62805e15i	1.94600	+	0.432895i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.91517e15	−	2.26042e15i	−1.00794	−	0.581937i	−0.0973548	−	0.995250i	$-0.531038\pi$
$683$	−3.91517e15	−	2.26042e15i	−1.00794	−	0.581937i	−0.910589	+	0.413313i	$0.864371\pi$
$684$		0			0
$685$			1.60022e13i			0.00405399i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.20783e15	+	2.09203e15i	−0.296348	+	0.513289i
$690$		0			0
$691$	−4.19526e15	+	2.42213e15i	−1.01305	+	0.584883i	−0.912082	−	0.410007i	$-0.865526\pi$
$691$	−4.19526e15	+	2.42213e15i	−1.01305	+	0.584883i	−0.100964	+	0.994890i	$0.532193\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.58843e13	−	9.17082e12i	0.00371580	−	0.00214532i
$696$		0			0
$697$	7.07713e13	−	1.22580e14i	0.0162959	−	0.0282253i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	6.60368e15i		−	1.47345i	−0.676190	−	0.736727i	$-0.736370\pi$
$701$		−	6.60368e15i		−	1.47345i	0.676190	−	0.736727i	$-0.263630\pi$
$702$		0			0
$703$	−1.45227e13	−	8.38470e12i	−0.00319002	−	0.00184176i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.02970e15	−	1.86258e15i	−0.432140	−	0.396559i
$708$		0			0
$709$	1.15278e15	+	1.99667e15i	0.241652	+	0.418554i	0.961185	−	0.275904i	$-0.0889773\pi$
$709$	1.15278e15	+	1.99667e15i	0.241652	+	0.418554i	−0.719533	+	0.694459i	$0.755644\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−7.43421e15			−1.51092
$714$		0			0
$715$	4.52632e13			0.00905863
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−4.41440e15	−	7.64597e15i	−0.856768	−	1.48397i	−0.874995	−	0.484132i	$-0.839136\pi$
$719$	−4.41440e15	−	7.64597e15i	−0.856768	−	1.48397i	0.0182271	−	0.999834i	$-0.494198\pi$
$720$		0			0
$721$	−1.27622e15	−	4.05790e15i	−0.243940	−	0.775635i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	6.06646e15	+	3.50247e15i	1.12480	+	0.649405i
$726$		0			0
$727$		−	4.62928e15i		−	0.845424i	−0.906264	−	0.422712i	$-0.861078\pi$
$727$		−	4.62928e15i		−	0.845424i	0.906264	−	0.422712i	$-0.138922\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	6.86933e15	−	1.18980e16i	1.21722	−	2.10829i
$732$		0			0
$733$	2.19085e15	−	1.26489e15i	0.382420	−	0.220790i	−0.296451	−	0.955048i	$-0.595803\pi$
$733$	2.19085e15	−	1.26489e15i	0.382420	−	0.220790i	0.678870	+	0.734258i	$0.262470\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.33107e15	−	3.65524e15i	1.07252	−	0.619220i
$738$		0			0
$739$	3.96520e15	−	6.86792e15i	0.661790	−	1.14625i	−0.318355	−	0.947972i	$-0.603130\pi$
$739$	3.96520e15	−	6.86792e15i	0.661790	−	1.14625i	0.980145	−	0.198282i	$-0.0635363\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	3.64254e15i		−	0.590155i	−0.955473	−	0.295078i	$-0.904654\pi$
$743$		−	3.64254e15i		−	0.590155i	0.955473	−	0.295078i	$-0.0953455\pi$
$744$		0			0
$745$	−2.13806e13	−	1.23441e13i	−0.00341319	−	0.00197061i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−3.64503e14	−	1.15898e15i	−0.0565003	−	0.179649i
$750$		0			0
$751$	7.52341e14	+	1.30309e15i	0.114920	+	0.199047i	0.917748	−	0.397164i	$-0.130006\pi$
$751$	7.52341e14	+	1.30309e15i	0.114920	+	0.199047i	−0.802828	+	0.596211i	$0.796672\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	2.10551e13			0.00312356
$756$		0			0
$757$	1.87442e15			0.274056			0.137028	−	0.990567i	$-0.456245\pi$
$757$	1.87442e15			0.274056			0.137028	+	0.990567i	$0.456245\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	9.27224e14	+	1.60600e15i	0.131695	+	0.228102i	0.924330	−	0.381594i	$-0.124625\pi$
$761$	9.27224e14	+	1.60600e15i	0.131695	+	0.228102i	−0.792635	+	0.609696i	$0.791291\pi$
$762$		0			0
$763$	4.30489e15	+	3.95044e15i	0.602667	+	0.553045i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−9.64985e15	−	5.57134e15i	−1.31264	−	0.757854i
$768$		0			0
$769$			1.42059e14i			0.0190491i	0.999955	+	0.00952457i	$0.00303181\pi$
$769$			1.42059e14i			0.0190491i	−0.999955	+	0.00952457i	$0.996968\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.10209e15	+	3.64093e15i	−0.273946	+	0.474488i	−0.969869	−	0.243628i	$-0.921662\pi$
$773$	−2.10209e15	+	3.64093e15i	−0.273946	+	0.474488i	0.695923	+	0.718117i	$0.254996\pi$
$774$		0			0
$775$	6.62221e15	−	3.82334e15i	0.850832	−	0.491228i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.19016e12	+	6.87140e11i	−0.000148645	+	8.58201e-5i
$780$		0			0
$781$	1.33179e15	−	2.30674e15i	0.164005	−	0.284065i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		−	3.41391e13i		−	0.00408760i
$786$		0			0
$787$	−7.77943e15	−	4.49146e15i	−0.918516	−	0.530306i	−0.0353548	−	0.999375i	$-0.511256\pi$
$787$	−7.77943e15	−	4.49146e15i	−0.918516	−	0.530306i	−0.883161	+	0.469069i	$0.844589\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.17882e16	−	2.62233e15i	−1.35356	−	0.301104i
$792$		0			0
$793$	9.95591e15	+	1.72441e16i	1.12740	+	1.95272i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	3.92579e15			0.432420			0.216210	−	0.976347i	$-0.430630\pi$
$797$	3.92579e15			0.432420			0.216210	+	0.976347i	$0.430630\pi$
$798$		0			0
$799$	1.53403e16			1.66658
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.37310e15	−	1.27706e16i	−0.779317	−	1.34982i
$804$		0			0
$805$	3.28264e13	−	3.57717e13i	0.00342252	−	0.00372960i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−4.18413e15	−	2.41571e15i	−0.424510	−	0.245091i	0.272495	−	0.962157i	$-0.412151\pi$
$809$	−4.18413e15	−	2.41571e15i	−0.424510	−	0.245091i	−0.697005	+	0.717066i	$0.745485\pi$
$810$		0			0
$811$		−	1.36416e16i		−	1.36538i	−0.730710	−	0.682688i	$-0.760811\pi$
$811$		−	1.36416e16i		−	1.36538i	0.730710	−	0.682688i	$-0.239189\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−3.10627e13	+	5.38022e13i	−0.00302603	+	0.00524123i
$816$		0			0
$817$	−1.15521e14	+	6.66963e13i	−0.0111030	+	0.00641033i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−1.53119e16	+	8.84031e15i	−1.43265	+	0.827142i	−0.997322	−	0.0731290i	$-0.976702\pi$
$821$	−1.53119e16	+	8.84031e15i	−1.43265	+	0.827142i	−0.435330	+	0.900271i	$0.643368\pi$
$822$		0			0
$823$	2.63669e15	−	4.56689e15i	0.243423	−	0.421620i	−0.718264	−	0.695770i	$-0.755063\pi$
$823$	2.63669e15	−	4.56689e15i	0.243423	−	0.421620i	0.961687	+	0.274150i	$0.0883965\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			1.09486e16i			0.984187i	0.870542	+	0.492093i	$0.163768\pi$
$827$			1.09486e16i			0.984187i	−0.870542	+	0.492093i	$0.836232\pi$
$828$		0			0
$829$	5.55065e15	+	3.20467e15i	0.492372	+	0.284271i	0.725558	−	0.688161i	$-0.241582\pi$
$829$	5.55065e15	+	3.20467e15i	0.492372	+	0.284271i	−0.233186	+	0.972432i	$0.574915\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.67026e16	−	1.16593e16i	1.44290	−	1.00722i
$834$		0			0
$835$	−3.32618e13	−	5.76111e13i	−0.00283577	−	0.00491169i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	2.54319e15			0.211197			0.105599	−	0.994409i	$-0.466324\pi$
$839$	2.54319e15			0.211197			0.105599	+	0.994409i	$0.466324\pi$
$840$		0			0
$841$	−8.38105e15			−0.686942
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.38743e13	−	4.13516e13i	−0.00190642	−	0.00330202i
$846$		0			0
$847$	−3.03675e16	+	9.55068e15i	−2.39359	+	0.752793i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.89267e15	+	3.97949e15i	0.529389	+	0.305643i
$852$		0			0
$853$		−	7.26976e15i		−	0.551189i	−0.961274	−	0.275595i	$-0.911125\pi$
$853$		−	7.26976e15i		−	0.551189i	0.961274	−	0.275595i	$-0.0888747\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.15105e15	−	7.18983e15i	0.306735	−	0.531281i	−0.670911	−	0.741538i	$-0.734097\pi$
$857$	4.15105e15	−	7.18983e15i	0.306735	−	0.531281i	0.977646	+	0.210257i	$0.0674301\pi$
$858$		0			0
$859$	1.49473e16	−	8.62980e15i	1.09043	−	0.629562i	0.156741	−	0.987640i	$-0.449901\pi$
$859$	1.49473e16	−	8.62980e15i	1.09043	−	0.629562i	0.933692	+	0.358078i	$0.116568\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−2.34715e16	+	1.35513e16i	−1.66910	+	0.963655i	−0.700975	+	0.713186i	$0.747252\pi$
$863$	−2.34715e16	+	1.35513e16i	−1.66910	+	0.963655i	−0.968124	+	0.250470i	$0.919415\pi$
$864$		0			0
$865$	−2.02198e13	+	3.50218e13i	−0.00141968	+	0.00245895i
$866$		0			0
$867$		0			0
$868$		0			0
$869$		−	4.05747e16i		−	2.77745i
$870$		0			0
$871$	−1.24442e16	−	7.18468e15i	−0.841140	−	0.485632i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.16879e13	+	9.74941e13i	−0.00142947	+	0.00642590i
$876$		0			0
$877$	−1.95332e15	−	3.38325e15i	−0.127138	−	0.220210i	0.795429	−	0.606047i	$-0.207246\pi$
$877$	−1.95332e15	−	3.38325e15i	−0.127138	−	0.220210i	−0.922567	+	0.385838i	$0.873912\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.75839e16			1.11622			0.558108	−	0.829768i	$-0.311527\pi$
$881$	1.75839e16			1.11622			0.558108	+	0.829768i	$0.311527\pi$
$882$		0			0
$883$	1.16134e16			0.728072			0.364036	−	0.931385i	$-0.381399\pi$
$883$	1.16134e16			0.728072			0.364036	+	0.931385i	$0.381399\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.07215e16	+	1.85702e16i	0.655657	+	1.13563i	0.981729	+	0.190286i	$0.0609416\pi$
$887$	1.07215e16	+	1.85702e16i	0.655657	+	1.13563i	−0.326072	+	0.945345i	$0.605725\pi$
$888$		0			0
$889$	−1.01852e14	+	4.57856e14i	−0.00615189	+	0.0276547i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.28989e14	−	7.44716e13i	−0.00760096	−	0.00438841i
$894$		0			0
$895$			1.38647e13i			0.000807020i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.12335e16	+	1.94570e16i	−0.638025	+	1.10509i
$900$		0			0
$901$	−1.09576e16	+	6.32637e15i	−0.614793	+	0.354951i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.20590e13	−	1.27358e13i	0.00120786	−	0.000697361i
$906$		0			0
$907$	3.24276e15	−	5.61662e15i	0.175418	−	0.303833i	−0.764888	−	0.644164i	$-0.777206\pi$
$907$	3.24276e15	−	5.61662e15i	0.175418	−	0.303833i	0.940306	+	0.340330i	$0.110539\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	1.22553e15i		−	0.0647100i	−0.999476	−	0.0323550i	$-0.989699\pi$
$911$		−	1.22553e15i		−	0.0647100i	0.999476	−	0.0323550i	$-0.0103007\pi$
$912$		0			0
$913$	7.24022e15	+	4.18014e15i	0.377713	+	0.218073i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−5.44860e14	+	1.71360e14i	−0.0277494	+	0.00872728i
$918$		0			0
$919$	−1.10755e15	−	1.91833e15i	−0.0557350	−	0.0965359i	0.836812	−	0.547491i	$-0.184417\pi$
$919$	−1.10755e15	−	1.91833e15i	−0.0557350	−	0.0965359i	−0.892547	+	0.450955i	$0.851084\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−5.23550e15			−0.257246
$924$		0			0
$925$	−8.18643e15			−0.397480
$926$		0			0
$927$		0			0
$928$		0			0
$929$	1.29966e16	+	2.25109e16i	0.616233	+	1.06735i	0.990167	+	0.139892i	$0.0446754\pi$
$929$	1.29966e16	+	2.25109e16i	0.616233	+	1.06735i	−0.373934	+	0.927455i	$0.621991\pi$
$930$		0			0
$931$	−1.97045e14	+	1.69519e13i	−0.00923298	+	0.000794320i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.05316e14	+	1.18539e14i	0.00939636	+	0.00542499i
$936$		0			0
$937$			3.40600e16i			1.54056i	0.637709	+	0.770278i	$0.279882\pi$
$937$			3.40600e16i			1.54056i	−0.637709	+	0.770278i	$0.720118\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.84571e15	+	3.19687e15i	−0.0815495	+	0.141248i	−0.903916	−	0.427711i	$-0.859320\pi$
$941$	−1.84571e15	+	3.19687e15i	−0.0815495	+	0.141248i	0.822366	+	0.568959i	$0.192654\pi$
$942$		0			0
$943$	5.64866e14	−	3.26125e14i	0.0246678	−	0.0142420i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.90002e14	+	5.13843e14i	−0.0379723	+	0.0219233i	−0.518866	−	0.854856i	$-0.673646\pi$
$947$	−8.90002e14	+	5.13843e14i	−0.0379723	+	0.0219233i	0.480894	+	0.876779i	$0.340312\pi$
$948$		0			0
$949$	−1.44924e16	+	2.51016e16i	−0.611191	+	1.05861i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			1.38369e15i			0.0570199i	0.999594	+	0.0285099i	$0.00907623\pi$
$953$			1.38369e15i			0.0570199i	−0.999594	+	0.0285099i	$0.990924\pi$
$954$		0			0
$955$	2.26189e11	+	1.30590e11i	9.21411e−6	+	5.31977e-6i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.09178e16	+	2.27946e16i	−0.832748	+	0.907466i
$960$		0			0
$961$	−4.41596e14	−	7.64867e14i	−0.0173799	−	0.0301028i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.47051e10			5.65677e−7
$966$		0			0
$967$	4.83732e15			0.183975			0.0919876	−	0.995760i	$-0.470678\pi$
$967$	4.83732e15			0.183975			0.0919876	+	0.995760i	$0.470678\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.06237e16	+	1.84009e16i	0.394977	+	0.684120i	0.993098	−	0.117286i	$-0.0374193\pi$
$971$	1.06237e16	+	1.84009e16i	0.394977	+	0.684120i	−0.598121	+	0.801405i	$0.704086\pi$
$972$		0			0
$973$	3.46146e16	+	7.70015e15i	1.27244	+	0.283060i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.61786e16	+	1.51142e16i	0.940863	+	0.543207i	0.890231	−	0.455510i	$-0.150543\pi$
$977$	2.61786e16	+	1.51142e16i	0.940863	+	0.543207i	0.0506320	+	0.998717i	$0.483876\pi$
$978$		0			0
$979$			1.72928e16i			0.614554i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.62691e16	−	2.81790e16i	0.565353	−	0.979221i	−0.431663	−	0.902035i	$-0.642073\pi$
$983$	1.62691e16	−	2.81790e16i	0.565353	−	0.979221i	0.997017	−	0.0771860i	$-0.0245935\pi$
$984$		0			0
$985$	7.66672e13	−	4.42638e13i	0.00263457	−	0.00152107i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.48280e16	−	3.16549e16i	1.84256	−	1.06380i
$990$		0			0
$991$	−6.82053e15	+	1.18135e16i	−0.226680	+	0.392621i	−0.956822	−	0.290674i	$-0.906120\pi$
$991$	−6.82053e15	+	1.18135e16i	−0.226680	+	0.392621i	0.730142	+	0.683295i	$0.239454\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		−	6.58508e13i		−	0.00214059i
$996$		0			0
$997$	−6.41149e15	−	3.70168e15i	−0.206127	−	0.119008i	0.393383	−	0.919375i	$-0.371305\pi$
$997$	−6.41149e15	−	3.70168e15i	−0.206127	−	0.119008i	−0.599510	+	0.800367i	$0.704638\pi$
$998$		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.17.16	yes	60
3.2	odd	2	inner	252.12.t.a.17.15	✓	60
7.5	odd	6	inner	252.12.t.a.89.15	yes	60
21.5	even	6	inner	252.12.t.a.89.16	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.12.t.a.17.15	✓	60	3.2	odd	2	inner
252.12.t.a.17.16	yes	60	1.1	even	1	trivial
252.12.t.a.89.15	yes	60	7.5	odd	6	inner
252.12.t.a.89.16	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)

\(f(q)\)	\(=\)	\(q+(11.5001 + 19.9187i) q^{5} +(-9655.86 + 43406.1i) q^{7} +O(q^{10})\)	\(q+(11.5001 + 19.9187i) q^{5} +(-9655.86 + 43406.1i) q^{7} +(-866549. - 500302. i) q^{11} +1.96677e6i q^{13} +(-5.15075e6 + 8.92136e6i) q^{17} +(86620.1 - 50010.1i) q^{19} +(-4.11110e7 + 2.37355e7i) q^{23} +(2.44138e7 - 4.22859e7i) q^{25} +1.43463e8i q^{29} +(1.35624e8 + 7.83028e7i) q^{31} +(-975635. + 306841. i) q^{35} +(-8.38300e7 - 1.45198e8i) q^{37} -1.37400e7 q^{41} -1.33366e9 q^{43} +(-7.44565e8 - 1.28962e9i) q^{47} +(-1.79086e9 - 8.38247e8i) q^{49} +(1.06369e9 + 6.14121e8i) q^{53} -2.30140e7i q^{55} +(-2.83274e9 + 4.90645e9i) q^{59} +(8.76775e9 - 5.06206e9i) q^{61} +(-3.91754e7 + 2.26179e7i) q^{65} +(-3.65304e9 + 6.32724e9i) q^{67} +2.66198e9i q^{71} +(1.27629e10 + 7.36864e9i) q^{73} +(3.00835e10 - 3.27827e10i) q^{77} +(2.02751e10 + 3.51175e10i) q^{79} -8.35523e9 q^{83} -2.36936e8 q^{85} +(-8.64117e9 - 1.49669e10i) q^{89} +(-8.53698e10 - 1.89908e10i) q^{91} +(1.99227e6 + 1.15024e6i) q^{95} -1.68607e11i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 31278 q^{7}+O(q^{10}) \) 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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