LMFDB - Embedded newform 252.9.z.e.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,9,Mod(73,252)]

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, 0, 1]))

N = Newforms(chi, 9, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("252.73");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	252.z (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:	$102.659409735$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 10 x^{19} - 1751639 x^{18} + 15765036 x^{17} + 1288400424989 x^{16} - 10307560742020 x^{15} + \cdots + 51\!\cdots\!63 $ x^20 - 10x^19 - 1751639x^18 + 15765036x^17 + 1288400424989x^16 - 10307560742020x^15 - 516815190850700874x^14 + 3617886719518590784x^13 + 122992744079100130844521x^12 - 738003497470953185965030x^11 - 17716220051138913180459215577x^10 + 88587865373982244785457265884x^9 + 1507689855516745584812805692686751x^8 - 6031290957377412523625955897396396x^7 - 69448792452425943361067315312590506770x^6 + 208367487247705803791441930629487279968x^5 + 1331037342615679684155036722672299751825731x^4 - 2662421971413455508046552715438433455340210x^3 - 47007135303470257351659397734299414285784783x^2 + 48338381018096768126520835100261119832719644*x + 515596507492955532983572496163412311048918663
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 2^{36}\cdot 3^{26}\cdot 7^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.3
Root			$357.003 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.e.145.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-534.755 + 308.741i) q^{5} +(-750.736 - 2280.61i) q^{7} +O(q^{10})$	$q+(-534.755 + 308.741i) q^{5} +(-750.736 - 2280.61i) q^{7} +(10012.2 - 17341.6i) q^{11} -54961.3i q^{13} +(-82287.8 - 47508.9i) q^{17} +(50039.8 - 28890.5i) q^{19} +(210993. + 365450. i) q^{23} +(-4670.69 + 8089.87i) q^{25} +1.09995e6 q^{29} +(189251. + 109264. i) q^{31} +(1.10558e6 + 987786. i) q^{35} +(-770458. - 1.33447e6i) q^{37} -376213. i q^{41} +1.37356e6 q^{43} +(-5.15852e6 + 2.97827e6i) q^{47} +(-4.63759e6 + 3.42428e6i) q^{49} +(6.64313e6 - 1.15062e7i) q^{53} +1.23646e7i q^{55} +(-1.54090e7 - 8.89642e6i) q^{59} +(-2.14563e6 + 1.23878e6i) q^{61} +(1.69688e7 + 2.93908e7i) q^{65} +(1.01117e7 - 1.75139e7i) q^{67} -1.39469e7 q^{71} +(-1.95536e7 - 1.12893e7i) q^{73} +(-4.70659e7 - 9.81492e6i) q^{77} +(-3.41314e7 - 5.91174e7i) q^{79} -2.02081e7i q^{83} +5.86717e7 q^{85} +(8.57842e7 - 4.95275e7i) q^{89} +(-1.25345e8 + 4.12614e7i) q^{91} +(-1.78394e7 + 3.08987e7i) q^{95} +1.53229e8i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 7238 q^{7}+O(q^{10}) $ 20 * q - 7238 * q^7	$ 20 q - 7238 q^{7} - 107256 q^{19} + 1348832 q^{25} - 4734426 q^{31} + 6802748 q^{37} - 596128 q^{43} - 19249258 q^{49} + 32573772 q^{61} - 25999304 q^{67} - 52899612 q^{73} - 129945530 q^{79} - 83755728 q^{85} + 42306852 q^{91}+O(q^{100}) $ 20 * q - 7238 * q^7 - 107256 * q^19 + 1348832 * q^25 - 4734426 * q^31 + 6802748 * q^37 - 596128 * q^43 - 19249258 * q^49 + 32573772 * q^61 - 25999304 * q^67 - 52899612 * q^73 - 129945530 * q^79 - 83755728 * q^85 + 42306852 * 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
$5$	−534.755	+	308.741i	−0.855608	+	0.493985i	−0.862539	−	0.505991i	$-0.831127\pi$
$5$	−534.755	+	308.741i	−0.855608	+	0.493985i	0.00693126	+	0.999976i	$0.497794\pi$
$6$		0			0
$7$	−750.736	−	2280.61i	−0.312676	−	0.949860i
$7$	−750.736	−	2280.61i	−0.312676	−	0.949860i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	10012.2	−	17341.6i	0.683844	−	1.18445i	−0.289955	−	0.957040i	$-0.593640\pi$
$11$	10012.2	−	17341.6i	0.683844	−	1.18445i	0.973799	−	0.227412i	$-0.0730263\pi$
$12$		0			0
$13$		−	54961.3i		−	1.92435i	−0.272439	−	0.962173i	$-0.587830\pi$
$13$		−	54961.3i		−	1.92435i	0.272439	−	0.962173i	$-0.412170\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−82287.8	−	47508.9i	−0.985235	−	0.568826i	−0.0813884	−	0.996682i	$-0.525935\pi$
$17$	−82287.8	−	47508.9i	−0.985235	−	0.568826i	−0.903847	+	0.427857i	$0.859269\pi$
$18$		0			0
$19$	50039.8	−	28890.5i	0.383974	−	0.221687i	−0.295572	−	0.955320i	$-0.595510\pi$
$19$	50039.8	−	28890.5i	0.383974	−	0.221687i	0.679546	+	0.733633i	$0.262177\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	210993.	+	365450.i	0.753974	+	1.30592i	0.945883	+	0.324508i	$0.105199\pi$
$23$	210993.	+	365450.i	0.753974	+	1.30592i	−0.191909	+	0.981413i	$0.561468\pi$
$24$		0			0
$25$	−4670.69	+	8089.87i	−0.0119570	+	0.0207101i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.09995e6			1.55517			0.777587	−	0.628775i	$-0.216443\pi$
$29$	1.09995e6			1.55517			0.777587	+	0.628775i	$0.216443\pi$
$30$		0			0
$31$	189251.	+	109264.i	0.204924	+	0.118313i	0.598950	−	0.800786i	$-0.295585\pi$
$31$	189251.	+	109264.i	0.204924	+	0.118313i	−0.394026	+	0.919099i	$0.628918\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	1.10558e6	+	987786.i	0.736745	+	0.658250i
$36$		0			0
$37$	−770458.	−	1.33447e6i	−0.411095	−	0.712038i	0.583915	−	0.811815i	$-0.301520\pi$
$37$	−770458.	−	1.33447e6i	−0.411095	−	0.712038i	−0.995010	+	0.0997774i	$0.968187\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	376213.i		−	0.133137i	−0.997782	−	0.0665685i	$-0.978795\pi$
$41$		−	376213.i		−	0.133137i	0.997782	−	0.0665685i	$-0.0212051\pi$
$42$		0			0
$43$	1.37356e6			0.401768			0.200884	−	0.979615i	$-0.435619\pi$
$43$	1.37356e6			0.401768			0.200884	+	0.979615i	$0.435619\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.15852e6	+	2.97827e6i	−1.05714	+	0.610342i	−0.924641	−	0.380841i	$-0.875635\pi$
$47$	−5.15852e6	+	2.97827e6i	−1.05714	+	0.610342i	−0.132503	+	0.991183i	$0.542301\pi$
$48$		0			0
$49$	−4.63759e6	+	3.42428e6i	−0.804467	+	0.593997i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.64313e6	−	1.15062e7i	0.841917	−	1.45824i	−0.0463546	−	0.998925i	$-0.514760\pi$
$53$	6.64313e6	−	1.15062e7i	0.841917	−	1.45824i	0.888272	−	0.459318i	$-0.151906\pi$
$54$		0			0
$55$			1.23646e7i			1.35124i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.54090e7	−	8.89642e6i	−1.27165	−	0.734188i	−0.296352	−	0.955079i	$-0.595770\pi$
$59$	−1.54090e7	−	8.89642e6i	−1.27165	−	0.734188i	−0.975298	+	0.220891i	$0.929103\pi$
$60$		0			0
$61$	−2.14563e6	+	1.23878e6i	−0.154966	+	0.0894696i	−0.575478	−	0.817817i	$-0.695184\pi$
$61$	−2.14563e6	+	1.23878e6i	−0.154966	+	0.0894696i	0.420512	+	0.907287i	$0.361851\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.69688e7	+	2.93908e7i	0.950599	+	1.64649i
$66$		0			0
$67$	1.01117e7	−	1.75139e7i	0.501791	−	0.869128i	−0.498207	−	0.867058i	$-0.666008\pi$
$67$	1.01117e7	−	1.75139e7i	0.501791	−	0.869128i	0.999998	−	0.00206964i	$-0.000658786\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.39469e7			−0.548836			−0.274418	−	0.961610i	$-0.588485\pi$
$71$	−1.39469e7			−0.548836			−0.274418	+	0.961610i	$0.588485\pi$
$72$		0			0
$73$	−1.95536e7	−	1.12893e7i	−0.688551	−	0.397535i	0.114518	−	0.993421i	$-0.463468\pi$
$73$	−1.95536e7	−	1.12893e7i	−0.688551	−	0.397535i	−0.803069	+	0.595886i	$0.796801\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.70659e7	−	9.81492e6i	−1.33888	−	0.279205i
$78$		0			0
$79$	−3.41314e7	−	5.91174e7i	−0.876286	−	1.51777i	−0.855386	−	0.517991i	$-0.826680\pi$
$79$	−3.41314e7	−	5.91174e7i	−0.876286	−	1.51777i	−0.0209000	−	0.999782i	$-0.506653\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	2.02081e7i		−	0.425807i	−0.977073	−	0.212904i	$-0.931708\pi$
$83$		−	2.02081e7i		−	0.425807i	0.977073	−	0.212904i	$-0.0682920\pi$
$84$		0			0
$85$	5.86717e7			1.12397
$86$		0			0
$87$		0			0
$88$		0			0
$89$	8.57842e7	−	4.95275e7i	1.36725	−	0.789381i	0.376672	−	0.926347i	$-0.377068\pi$
$89$	8.57842e7	−	4.95275e7i	1.36725	−	0.789381i	0.990576	+	0.136966i	$0.0437350\pi$
$90$		0			0
$91$	−1.25345e8	+	4.12614e7i	−1.82786	+	0.601698i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.78394e7	+	3.08987e7i	−0.219021	+	0.379355i
$96$		0			0
$97$			1.53229e8i			1.73083i	0.501054	+	0.865416i	$0.332946\pi$
$97$			1.53229e8i			1.73083i	−0.501054	+	0.865416i	$0.667054\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−200235.	−	115606.i	−0.00192422	−	0.00111095i	0.499038	−	0.866580i	$-0.333687\pi$
$101$	−200235.	−	115606.i	−0.00192422	−	0.00111095i	−0.500962	+	0.865469i	$0.667020\pi$
$102$		0			0
$103$	−5.48173e7	+	3.16488e7i	−0.487045	+	0.281195i	−0.723348	−	0.690484i	$-0.757398\pi$
$103$	−5.48173e7	+	3.16488e7i	−0.487045	+	0.281195i	0.236303	+	0.971679i	$0.424064\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.28012e7	+	1.43416e8i	0.631686	+	1.09411i	0.987207	+	0.159445i	$0.0509703\pi$
$107$	8.28012e7	+	1.43416e8i	0.631686	+	1.09411i	−0.355520	+	0.934669i	$0.615696\pi$
$108$		0			0
$109$	−5.08987e7	+	8.81591e7i	−0.360579	+	0.624541i	−0.988056	−	0.154094i	$-0.950754\pi$
$109$	−5.08987e7	+	8.81591e7i	−0.360579	+	0.624541i	0.627477	+	0.778635i	$0.284088\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.67939e7			0.532323			0.266161	−	0.963928i	$-0.414245\pi$
$113$	8.67939e7			0.532323			0.266161	+	0.963928i	$0.414245\pi$
$114$		0			0
$115$	−2.25659e8	−	1.30284e8i	−1.29021	−	0.744904i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−4.65730e7	+	2.23333e8i	−0.232245	+	1.11369i
$120$		0			0
$121$	−9.33071e7	−	1.61613e8i	−0.435284	−	0.753935i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	2.46972e8i		−	1.01160i
$126$		0			0
$127$	−3.20685e8			−1.23272			−0.616359	−	0.787465i	$-0.711393\pi$
$127$	−3.20685e8			−1.23272			−0.616359	+	0.787465i	$0.711393\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.24550e8	−	1.87379e8i	1.10204	−	0.636261i	0.165281	−	0.986246i	$-0.447147\pi$
$131$	3.24550e8	−	1.87379e8i	1.10204	−	0.636261i	0.936755	+	0.349985i	$0.113813\pi$
$132$		0			0
$133$	−1.03455e8	−	9.24324e7i	−0.330631	−	0.295405i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.06158e8	+	3.57076e8i	−0.585218	+	1.01363i	0.409630	+	0.912252i	$0.365658\pi$
$137$	−2.06158e8	+	3.57076e8i	−0.585218	+	1.01363i	−0.994848	+	0.101376i	$0.967676\pi$
$138$		0			0
$139$		−	1.48791e8i		−	0.398581i	−0.979940	−	0.199290i	$-0.936136\pi$
$139$		−	1.48791e8i		−	0.398581i	0.979940	−	0.199290i	$-0.0638637\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−9.53114e8	−	5.50281e8i	−2.27930	−	1.31595i
$144$		0			0
$145$	−5.88201e8	+	3.39598e8i	−1.33062	+	0.768234i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.14977e8	−	1.99146e8i	−0.233274	−	0.404043i	0.725495	−	0.688227i	$-0.241611\pi$
$149$	−1.14977e8	−	1.99146e8i	−0.233274	−	0.404043i	−0.958770	+	0.284184i	$0.908277\pi$
$150$		0			0
$151$	−2.26244e8	+	3.91866e8i	−0.435180	+	0.753754i	−0.997310	−	0.0732946i	$-0.976649\pi$
$151$	−2.26244e8	+	3.91866e8i	−0.435180	+	0.753754i	0.562130	+	0.827049i	$0.309982\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−1.34937e8			−0.233779
$156$		0			0
$157$	−5.79759e8	−	3.34724e8i	−0.954221	−	0.550920i	−0.0598315	−	0.998208i	$-0.519056\pi$
$157$	−5.79759e8	−	3.34724e8i	−0.954221	−	0.550920i	−0.894390	+	0.447289i	$0.852390\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.75051e8	−	7.55549e8i	1.00469	−	1.12450i
$162$		0			0
$163$	1.39051e8	+	2.40844e8i	0.196981	+	0.341182i	0.947548	−	0.319613i	$-0.103553\pi$
$163$	1.39051e8	+	2.40844e8i	0.196981	+	0.341182i	−0.750567	+	0.660794i	$0.770220\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			1.45736e9i			1.87370i	0.349726	+	0.936852i	$0.386275\pi$
$167$			1.45736e9i			1.87370i	−0.349726	+	0.936852i	$0.613725\pi$
$168$		0			0
$169$	−2.20501e9			−2.70311
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.14202e8	+	2.39140e8i	−0.462411	+	0.266973i	−0.713057	−	0.701106i	$-0.752690\pi$
$173$	−4.14202e8	+	2.39140e8i	−0.462411	+	0.266973i	0.250647	+	0.968079i	$0.419357\pi$
$174$		0			0
$175$	2.19563e7	+	4.57868e6i	0.0234103	+	0.00488189i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	1.13555e8	−	1.96683e8i	0.110610	−	0.191582i	−0.805407	−	0.592723i	$-0.798053\pi$
$179$	1.13555e8	−	1.96683e8i	0.110610	−	0.191582i	0.916016	+	0.401141i	$0.131386\pi$
$180$		0			0
$181$		−	1.37679e9i		−	1.28278i	−0.767214	−	0.641391i	$-0.778358\pi$
$181$		−	1.37679e9i		−	1.28278i	0.767214	−	0.641391i	$-0.221642\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.24013e8	+	4.75744e8i	0.703472	+	0.406150i
$186$		0			0
$187$	−1.64776e9	+	9.51333e8i	−1.34749	+	0.777976i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.38320e8	+	7.59193e8i	0.329350	+	0.570451i	0.982383	−	0.186878i	$-0.0598370\pi$
$191$	4.38320e8	+	7.59193e8i	0.329350	+	0.570451i	−0.653033	+	0.757330i	$0.726504\pi$
$192$		0			0
$193$	−1.10859e9	+	1.92013e9i	−0.798987	+	1.38389i	0.121289	+	0.992617i	$0.461297\pi$
$193$	−1.10859e9	+	1.92013e9i	−0.798987	+	1.38389i	−0.920276	+	0.391270i	$0.872036\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.18728e9			1.45224			0.726120	−	0.687568i	$-0.241322\pi$
$197$	2.18728e9			1.45224			0.726120	+	0.687568i	$0.241322\pi$
$198$		0			0
$199$	4.49294e8	+	2.59400e8i	0.286496	+	0.165408i	0.636360	−	0.771392i	$-0.280439\pi$
$199$	4.49294e8	+	2.59400e8i	0.286496	+	0.165408i	−0.349865	+	0.936800i	$0.613772\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−8.25769e8	−	2.50855e9i	−0.486266	−	1.47720i
$204$		0			0
$205$	1.16152e8	+	2.01182e8i	0.0657677	+	0.113913i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	1.15703e9i		−	0.606398i
$210$		0			0
$211$	−3.03664e9			−1.53201			−0.766007	−	0.642832i	$-0.777759\pi$
$211$	−3.03664e9			−1.53201			−0.766007	+	0.642832i	$0.777759\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−7.34520e8	+	4.24075e8i	−0.343755	+	0.198467i
$216$		0			0
$217$	1.07112e8	−	5.13637e8i	0.0483057	−	0.231642i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.61115e9	+	4.52264e9i	−1.09462	+	1.89593i
$222$		0			0
$223$		−	2.79756e8i		−	0.113125i	−0.998399	−	0.0565627i	$-0.981986\pi$
$223$		−	2.79756e8i		−	0.113125i	0.998399	−	0.0565627i	$-0.0180141\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.15376e8	−	4.13023e8i	−0.269421	−	0.155550i	0.359204	−	0.933259i	$-0.383048\pi$
$227$	−7.15376e8	−	4.13023e8i	−0.269421	−	0.155550i	−0.628624	+	0.777709i	$0.716382\pi$
$228$		0			0
$229$	5.66627e8	−	3.27142e8i	0.206042	−	0.118958i	−0.393429	−	0.919355i	$-0.628711\pi$
$229$	5.66627e8	−	3.27142e8i	0.206042	−	0.118958i	0.599471	+	0.800397i	$0.295378\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.62310e8	−	1.32036e9i	−0.258647	−	0.447990i	0.707232	−	0.706981i	$-0.249943\pi$
$233$	−7.62310e8	−	1.32036e9i	−0.258647	−	0.447990i	−0.965880	+	0.258991i	$0.916610\pi$
$234$		0			0
$235$	1.83903e9	−	3.18529e9i	0.603000	−	1.04443i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	5.51914e9			1.69153			0.845766	−	0.533554i	$-0.179144\pi$
$239$	5.51914e9			1.69153			0.845766	+	0.533554i	$0.179144\pi$
$240$		0			0
$241$	−3.81695e9	−	2.20372e9i	−1.13148	−	0.653262i	−0.187176	−	0.982326i	$-0.559933\pi$
$241$	−3.81695e9	−	2.20372e9i	−1.13148	−	0.653262i	−0.944308	+	0.329064i	$0.893267\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.42276e9	−	3.26296e9i	0.394882	−	0.905624i
$246$		0			0
$247$	−1.58786e9	−	2.75025e9i	−0.426603	−	0.738898i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	1.04730e8i		−	0.0263862i	−0.999913	−	0.0131931i	$-0.995800\pi$
$251$		−	1.04730e8i		−	0.0263862i	0.999913	−	0.0131931i	$-0.00419962\pi$
$252$		0			0
$253$	8.44997e9			2.06240
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−4.67321e9	+	2.69808e9i	−1.07123	+	0.618474i	−0.928517	−	0.371290i	$-0.878916\pi$
$257$	−4.67321e9	+	2.69808e9i	−1.07123	+	0.618474i	−0.142712	+	0.989764i	$0.545582\pi$
$258$		0			0
$259$	−2.46501e9	+	2.75895e9i	−0.547796	+	0.613120i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−8.70883e8	+	1.50841e9i	−0.182027	+	0.315281i	−0.942571	−	0.334006i	$-0.891599\pi$
$263$	−8.70883e8	+	1.50841e9i	−0.182027	+	0.315281i	0.760543	+	0.649287i	$0.224933\pi$
$264$		0			0
$265$			8.20402e9i			1.66358i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.49563e9	−	3.75025e9i	−1.24054	−	0.716228i	−0.271338	−	0.962484i	$-0.587466\pi$
$269$	−6.49563e9	−	3.75025e9i	−1.24054	−	0.716228i	−0.969205	+	0.246256i	$0.920800\pi$
$270$		0			0
$271$	1.43383e9	−	8.27820e8i	0.265839	−	0.153482i	−0.361156	−	0.932505i	$-0.617618\pi$
$271$	1.43383e9	−	8.27820e8i	0.265839	−	0.153482i	0.626995	+	0.779023i	$0.284284\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.35273e7	+	1.61994e8i	0.0163534	+	0.0283249i
$276$		0			0
$277$	−1.86228e9	+	3.22556e9i	−0.316320	+	0.547881i	−0.979717	−	0.200386i	$-0.935781\pi$
$277$	−1.86228e9	+	3.22556e9i	−0.316320	+	0.547881i	0.663398	+	0.748267i	$0.269114\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−4.25218e9			−0.682003			−0.341001	−	0.940063i	$-0.610766\pi$
$281$	−4.25218e9			−0.682003			−0.341001	+	0.940063i	$0.610766\pi$
$282$		0			0
$283$	6.99908e9	+	4.04092e9i	1.09118	+	0.629991i	0.933890	−	0.357561i	$-0.116392\pi$
$283$	6.99908e9	+	4.04092e9i	1.09118	+	0.629991i	0.157288	+	0.987553i	$0.449725\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.57997e8	+	2.82437e8i	−0.126461	+	0.0416288i
$288$		0			0
$289$	1.02631e9	+	1.77762e9i	0.147125	+	0.254829i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			4.36774e9i			0.592634i	0.955090	+	0.296317i	$0.0957585\pi$
$293$			4.36774e9i			0.592634i	−0.955090	+	0.296317i	$0.904241\pi$
$294$		0			0
$295$	1.09867e10			1.45071
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.00856e10	−	1.15964e10i	2.51304	−	1.45091i
$300$		0			0
$301$	−1.03118e9	−	3.13257e9i	−0.125623	−	0.381623i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	7.64925e8	−	1.32489e9i	0.0883933	−	0.153102i
$306$		0			0
$307$		−	2.92930e9i		−	0.329769i	−0.986313	−	0.164885i	$-0.947275\pi$
$307$		−	2.92930e9i		−	0.329769i	0.986313	−	0.164885i	$-0.0527252\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.82421e9	−	2.78526e9i	−0.515685	−	0.297731i	0.219482	−	0.975616i	$-0.429563\pi$
$311$	−4.82421e9	−	2.78526e9i	−0.515685	−	0.297731i	−0.735167	+	0.677886i	$0.762896\pi$
$312$		0			0
$313$	1.24818e10	−	7.20638e9i	1.30047	−	0.750827i	0.319985	−	0.947422i	$-0.396322\pi$
$313$	1.24818e10	−	7.20638e9i	1.30047	−	0.750827i	0.980485	+	0.196596i	$0.0629886\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.13011e9	+	1.40818e10i	0.805118	+	1.39451i	0.916211	+	0.400695i	$0.131231\pi$
$317$	8.13011e9	+	1.40818e10i	0.805118	+	1.39451i	−0.111093	+	0.993810i	$0.535435\pi$
$318$		0			0
$319$	1.10128e10	−	1.90748e10i	1.06350	−	1.84203i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.49023e9			−0.504406
$324$		0			0
$325$	4.44629e8	+	2.56707e8i	0.0398533	+	0.0230093i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.06650e10	+	9.52870e9i	0.910283	+	0.813299i
$330$		0			0
$331$	−2.42352e9	−	4.19767e9i	−0.201899	−	0.349700i	0.747241	−	0.664553i	$-0.231378\pi$
$331$	−2.42352e9	−	4.19767e9i	−0.201899	−	0.349700i	−0.949140	+	0.314853i	$0.898045\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			1.24875e10i			0.991510i
$336$		0			0
$337$	1.83740e10			1.42457			0.712284	−	0.701891i	$-0.247661\pi$
$337$	1.83740e10			1.42457			0.712284	+	0.701891i	$0.247661\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	3.78962e9	−	2.18794e9i	0.280271	−	0.161815i
$342$		0			0
$343$	1.12911e10	+	8.00583e9i	0.815752	+	0.578402i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.52534e9	+	2.64197e9i	−0.105208	+	0.182226i	−0.913823	−	0.406112i	$-0.866884\pi$
$347$	−1.52534e9	+	2.64197e9i	−0.105208	+	0.182226i	0.808615	+	0.588338i	$0.200218\pi$
$348$		0			0
$349$			1.05312e8i			0.00709863i	0.999994	+	0.00354932i	$0.00112978\pi$
$349$			1.05312e8i			0.00709863i	−0.999994	+	0.00354932i	$0.998870\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.12157e10	−	6.47541e9i	−0.722319	−	0.417031i	0.0932863	−	0.995639i	$-0.470263\pi$
$353$	−1.12157e10	−	6.47541e9i	−0.722319	−	0.417031i	−0.815606	+	0.578608i	$0.803596\pi$
$354$		0			0
$355$	7.45815e9	−	4.30596e9i	0.469589	−	0.271117i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−3.07794e9	−	5.33115e9i	−0.185303	−	0.320954i	0.758376	−	0.651818i	$-0.225993\pi$
$359$	−3.07794e9	−	5.33115e9i	−0.185303	−	0.320954i	−0.943679	+	0.330864i	$0.892660\pi$
$360$		0			0
$361$	−6.82246e9	+	1.18168e10i	−0.401709	+	0.695781i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.39419e10			0.785506
$366$		0			0
$367$	2.46136e10	+	1.42107e10i	1.35679	+	0.783341i	0.989189	−	0.146644i	$-0.0468473\pi$
$367$	2.46136e10	+	1.42107e10i	1.35679	+	0.783341i	0.367597	+	0.929985i	$0.380181\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−3.12285e10	−	6.51227e9i	−1.64837	−	0.343745i
$372$		0			0
$373$	1.55292e10	+	2.68973e10i	0.802256	+	1.38955i	0.918128	+	0.396285i	$0.129701\pi$
$373$	1.55292e10	+	2.68973e10i	0.802256	+	1.38955i	−0.115871	+	0.993264i	$0.536966\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	6.04544e10i		−	2.99269i
$378$		0			0
$379$	−2.09851e10			−1.01708			−0.508538	−	0.861040i	$-0.669814\pi$
$379$	−2.09851e10			−1.01708			−0.508538	+	0.861040i	$0.669814\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.52677e10	+	1.45883e10i	−1.17428	+	0.677968i	−0.954683	−	0.297623i	$-0.903806\pi$
$383$	−2.52677e10	+	1.45883e10i	−1.17428	+	0.677968i	−0.219592	+	0.975592i	$0.570473\pi$
$384$		0			0
$385$	2.81990e10	−	9.28258e9i	1.28348	−	0.422499i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.52716e9	−	2.64512e9i	0.0666940	−	0.115517i	−0.830750	−	0.556645i	$-0.812088\pi$
$389$	1.52716e9	−	2.64512e9i	0.0666940	−	0.115517i	0.897444	+	0.441128i	$0.145422\pi$
$390$		0			0
$391$		−	4.00961e10i		−	1.71552i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.65039e10	+	2.10755e10i	1.49951	+	0.865745i
$396$		0			0
$397$	−2.03949e10	+	1.17750e10i	−0.821029	+	0.474022i	−0.850771	−	0.525536i	$-0.823865\pi$
$397$	−2.03949e10	+	1.17750e10i	−0.821029	+	0.474022i	0.0297420	+	0.999558i	$0.490531\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.64589e9	−	6.31487e9i	−0.141002	−	0.244223i	0.786872	−	0.617116i	$-0.211699\pi$
$401$	−3.64589e9	−	6.31487e9i	−0.141002	−	0.244223i	−0.927874	+	0.372893i	$0.878366\pi$
$402$		0			0
$403$	6.00530e9	−	1.04015e10i	0.227674	−	0.394344i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.08558e10			−1.12450
$408$		0			0
$409$	−5.53566e9	−	3.19602e9i	−0.197823	−	0.114213i	0.397817	−	0.917465i	$-0.369768\pi$
$409$	−5.53566e9	−	3.19602e9i	−0.197823	−	0.114213i	−0.595640	+	0.803252i	$0.703101\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−8.72116e9	+	4.18209e10i	−0.299760	+	1.43745i
$414$		0			0
$415$	6.23906e9	+	1.08064e10i	0.210342	+	0.364324i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			2.79463e10i			0.906710i	0.891330	+	0.453355i	$0.149773\pi$
$419$			2.79463e10i			0.906710i	−0.891330	+	0.453355i	$0.850227\pi$
$420$		0			0
$421$	−1.37743e10			−0.438471			−0.219236	−	0.975672i	$-0.570356\pi$
$421$	−1.37743e10			−0.438471			−0.219236	+	0.975672i	$0.570356\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.68681e8	−	4.43798e8i	0.0235608	−	0.0136028i
$426$		0			0
$427$	4.43598e9	+	3.96336e9i	0.133438	+	0.119221i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	2.39670e10	−	4.15121e10i	0.694553	−	1.20300i	−0.275778	−	0.961221i	$-0.588936\pi$
$431$	2.39670e10	−	4.15121e10i	0.694553	−	1.20300i	0.970331	−	0.241780i	$-0.0777311\pi$
$432$		0			0
$433$		−	1.89618e10i		−	0.539421i	−0.962941	−	0.269710i	$-0.913072\pi$
$433$		−	1.89618e10i		−	0.539421i	0.962941	−	0.269710i	$-0.0869280\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.11161e10	+	1.21914e10i	0.579012	+	0.334293i
$438$		0			0
$439$	1.80396e10	−	1.04152e10i	0.485701	−	0.280420i	−0.237088	−	0.971488i	$-0.576193\pi$
$439$	1.80396e10	−	1.04152e10i	0.485701	−	0.280420i	0.722789	+	0.691068i	$0.242860\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.13390e9	+	3.69603e9i	0.0554064	+	0.0959667i	0.892398	−	0.451249i	$-0.149021\pi$
$443$	2.13390e9	+	3.69603e9i	0.0554064	+	0.0959667i	−0.836992	+	0.547215i	$0.815688\pi$
$444$		0			0
$445$	−3.05823e10	+	5.29702e10i	−0.779885	+	1.35080i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.76647e10			0.434631			0.217315	−	0.976101i	$-0.430270\pi$
$449$	1.76647e10			0.434631			0.217315	+	0.976101i	$0.430270\pi$
$450$		0			0
$451$	−6.52413e9	−	3.76671e9i	−0.157694	−	0.0910449i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	5.42900e10	−	6.07640e10i	1.26670	−	1.41775i
$456$		0			0
$457$	−9.32670e9	−	1.61543e10i	−0.213827	−	0.370360i	0.739082	−	0.673616i	$-0.235260\pi$
$457$	−9.32670e9	−	1.61543e10i	−0.213827	−	0.370360i	−0.952909	+	0.303256i	$0.901926\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			5.34641e10i			1.18375i	0.806031	+	0.591873i	$0.201611\pi$
$461$			5.34641e10i			1.18375i	−0.806031	+	0.591873i	$0.798389\pi$
$462$		0			0
$463$	9.51355e9			0.207023			0.103511	−	0.994628i	$-0.466992\pi$
$463$	9.51355e9			0.207023			0.103511	+	0.994628i	$0.466992\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.06656e10	+	2.92518e10i	−1.06524	+	0.615014i	−0.926876	−	0.375368i	$-0.877516\pi$
$467$	−5.06656e10	+	2.92518e10i	−1.06524	+	0.615014i	−0.138360	+	0.990382i	$0.544183\pi$
$468$		0			0
$469$	−4.75336e10	−	9.91246e9i	−0.982448	−	0.204876i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.37523e10	−	2.38197e10i	0.274746	−	0.475874i
$474$		0			0
$475$			5.39754e8i			0.0106028i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.27318e10	+	3.62182e10i	1.19164	+	0.687995i	0.958679	−	0.284491i	$-0.0918246\pi$
$479$	6.27318e10	+	3.62182e10i	1.19164	+	0.687995i	0.232963	+	0.972486i	$0.425158\pi$
$480$		0			0
$481$	−7.33443e10	+	4.23454e10i	−1.37021	+	0.791089i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.73082e10	−	8.19401e10i	−0.855006	−	1.48091i
$486$		0			0
$487$	2.05514e10	−	3.55961e10i	0.365364	−	0.632829i	−0.623471	−	0.781847i	$-0.714278\pi$
$487$	2.05514e10	−	3.55961e10i	0.365364	−	0.632829i	0.988834	+	0.149018i	$0.0476112\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.94153e10			−1.19434			−0.597171	−	0.802114i	$-0.703709\pi$
$491$	−6.94153e10			−1.19434			−0.597171	+	0.802114i	$0.703709\pi$
$492$		0			0
$493$	−9.05121e10	−	5.22572e10i	−1.53221	−	0.884623i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.04704e10	+	3.18074e10i	0.171608	+	0.521318i
$498$		0			0
$499$	−4.72460e10	−	8.18325e10i	−0.762014	−	1.31985i	−0.941811	−	0.336143i	$-0.890877\pi$
$499$	−4.72460e10	−	8.18325e10i	−0.762014	−	1.31985i	0.179797	−	0.983704i	$-0.442456\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			1.86742e10i			0.291722i	0.989305	+	0.145861i	$0.0465952\pi$
$503$			1.86742e10i			0.291722i	−0.989305	+	0.145861i	$0.953405\pi$
$504$		0			0
$505$	1.42769e8			0.00219517
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.20450e10	+	6.95417e9i	−0.179446	+	0.103603i	−0.587033	−	0.809563i	$-0.699704\pi$
$509$	−1.20450e10	+	6.95417e9i	−0.179446	+	0.103603i	0.407586	+	0.913167i	$0.366371\pi$
$510$		0			0
$511$	−1.10669e10	+	5.30696e10i	−0.162309	+	0.778327i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	1.95426e10	−	3.38487e10i	0.277813	−	0.481186i
$516$		0			0
$517$			1.19276e11i			1.66951i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	2.08781e10	+	1.20540e10i	0.283361	+	0.163598i	0.634944	−	0.772558i	$-0.281023\pi$
$521$	2.08781e10	+	1.20540e10i	0.283361	+	0.163598i	−0.351583	+	0.936157i	$0.614357\pi$
$522$		0			0
$523$	−6.64362e10	+	3.83570e10i	−0.887970	+	0.512670i	−0.873278	−	0.487222i	$-0.838010\pi$
$523$	−6.64362e10	+	3.83570e10i	−0.887970	+	0.512670i	−0.0146920	+	0.999892i	$0.504677\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.03820e10	−	1.79822e10i	−0.134599	−	0.233132i
$528$		0			0
$529$	−4.98804e10	+	8.63953e10i	−0.636953	+	1.10323i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.06772e10			−0.256202
$534$		0			0
$535$	−8.85567e10	−	5.11282e10i	−1.08095	−	0.624088i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.29500e10	+	1.14707e11i	0.153432	+	1.35905i
$540$		0			0
$541$	1.11688e10	+	1.93448e10i	0.130381	+	0.225827i	0.923824	−	0.382818i	$-0.125046\pi$
$541$	1.11688e10	+	1.93448e10i	0.130381	+	0.225827i	−0.793442	+	0.608646i	$0.791713\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	6.28580e10i		−	0.712483i
$546$		0			0
$547$	2.84774e10			0.318091			0.159045	−	0.987271i	$-0.449158\pi$
$547$	2.84774e10			0.318091			0.159045	+	0.987271i	$0.449158\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.50411e10	−	3.17780e10i	0.597146	−	0.344763i
$552$		0			0
$553$	−1.09200e11	+	1.22222e11i	−1.16768	+	1.30692i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.68470e10	+	8.11414e10i	−0.486700	+	0.842989i	−0.999883	−	0.0152903i	$-0.995133\pi$
$557$	−4.68470e10	+	8.11414e10i	−0.486700	+	0.842989i	0.513183	+	0.858279i	$0.328466\pi$
$558$		0			0
$559$		−	7.54928e10i		−	0.773140i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−1.08714e11	−	6.27658e10i	−1.08206	−	0.624726i	−0.150606	−	0.988594i	$-0.548123\pi$
$563$	−1.08714e11	−	6.27658e10i	−1.08206	−	0.624726i	−0.931450	+	0.363868i	$0.881456\pi$
$564$		0			0
$565$	−4.64134e10	+	2.67968e10i	−0.455460	+	0.262960i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.82494e10	−	1.00891e11i	−0.555702	−	0.962504i	−0.997849	−	0.0655615i	$-0.979116\pi$
$569$	−5.82494e10	−	1.00891e11i	−0.555702	−	0.962504i	0.442146	−	0.896943i	$-0.354217\pi$
$570$		0			0
$571$	2.72065e10	−	4.71230e10i	0.255934	−	0.443290i	−0.709215	−	0.704992i	$-0.750950\pi$
$571$	2.72065e10	−	4.71230e10i	0.255934	−	0.443290i	0.965149	+	0.261702i	$0.0842837\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.94192e9			−0.0360609
$576$		0			0
$577$	3.45186e10	+	1.99293e10i	0.311422	+	0.179800i	0.647563	−	0.762012i	$-0.275788\pi$
$577$	3.45186e10	+	1.99293e10i	0.311422	+	0.179800i	−0.336141	+	0.941812i	$0.609122\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−4.60868e10	+	1.51709e10i	−0.404457	+	0.133140i
$582$		0			0
$583$	−1.33024e11	−	2.30405e11i	−1.15148	−	1.99442i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	1.67244e11i		−	1.40863i	−0.709887	−	0.704315i	$-0.751254\pi$
$587$		−	1.67244e11i		−	1.40863i	0.709887	−	0.704315i	$-0.248746\pi$
$588$		0			0
$589$	1.26268e10			0.104914
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.76644e10	+	1.01985e10i	−0.142850	+	0.0824745i	−0.569722	−	0.821838i	$-0.692949\pi$
$593$	−1.76644e10	+	1.01985e10i	−0.142850	+	0.0824745i	0.426872	+	0.904312i	$0.359616\pi$
$594$		0			0
$595$	−4.40470e10	−	1.33808e11i	−0.351438	−	1.06761i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.56266e9	−	6.17071e9i	0.0276737	−	0.0479323i	−0.851857	−	0.523775i	$-0.824523\pi$
$599$	3.56266e9	−	6.17071e9i	0.0276737	−	0.0479323i	0.879531	+	0.475842i	$0.157857\pi$
$600$		0			0
$601$		−	1.24623e10i		−	0.0955217i	−0.998859	−	0.0477608i	$-0.984791\pi$
$601$		−	1.24623e10i		−	0.0955217i	0.998859	−	0.0477608i	$-0.0152085\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.97928e10	+	5.76154e10i	0.744865	+	0.430048i
$606$		0			0
$607$	2.63526e10	−	1.52147e10i	0.194119	−	0.112075i	−0.399790	−	0.916607i	$-0.630917\pi$
$607$	2.63526e10	−	1.52147e10i	0.194119	−	0.112075i	0.593909	+	0.804532i	$0.297584\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.63690e11	+	2.83519e11i	1.17451	+	2.03431i
$612$		0			0
$613$	1.49181e10	−	2.58389e10i	0.105650	−	0.182992i	−0.808353	−	0.588698i	$-0.799641\pi$
$613$	1.49181e10	−	2.58389e10i	0.105650	−	0.182992i	0.914004	+	0.405706i	$0.132974\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.31729e11			0.908951			0.454476	−	0.890759i	$-0.349827\pi$
$617$	1.31729e11			0.908951			0.454476	+	0.890759i	$0.349827\pi$
$618$		0			0
$619$	−9.67672e10	−	5.58686e10i	−0.659121	−	0.380544i	0.132821	−	0.991140i	$-0.457597\pi$
$619$	−9.67672e10	−	5.58686e10i	−0.659121	−	0.380544i	−0.791942	+	0.610596i	$0.790930\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.77354e11	−	1.58459e11i	−1.17731	−	1.05187i
$624$		0			0
$625$	7.44258e10	+	1.28909e11i	0.487757	+	0.844820i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1.46414e11i			0.935366i
$630$		0			0
$631$	1.70388e11			1.07479			0.537394	−	0.843331i	$-0.319409\pi$
$631$	1.70388e11			1.07479			0.537394	+	0.843331i	$0.319409\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.71488e11	−	9.90086e10i	1.05472	−	0.608945i
$636$		0			0
$637$	1.88203e11	+	2.54888e11i	1.14306	+	1.54807i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.05906e10	+	5.29845e10i	−0.181199	+	0.313846i	−0.942289	−	0.334800i	$-0.891331\pi$
$641$	−3.05906e10	+	5.29845e10i	−0.181199	+	0.313846i	0.761090	+	0.648646i	$0.224665\pi$
$642$		0			0
$643$		−	2.91845e11i		−	1.70730i	−0.520851	−	0.853648i	$-0.674385\pi$
$643$		−	2.91845e11i		−	1.70730i	0.520851	−	0.853648i	$-0.325615\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.80122e10	+	2.19463e10i	0.216923	+	0.125241i	0.604525	−	0.796586i	$-0.293363\pi$
$647$	3.80122e10	+	2.19463e10i	0.216923	+	0.125241i	−0.387602	+	0.921827i	$0.626696\pi$
$648$		0			0
$649$	−3.08556e11	+	1.78145e11i	−1.73922	+	1.00414i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.29185e11	+	2.23754e11i	0.710490	+	1.23060i	0.964674	+	0.263448i	$0.0848598\pi$
$653$	1.29185e11	+	2.23754e11i	0.710490	+	1.23060i	−0.254184	+	0.967156i	$0.581807\pi$
$654$		0			0
$655$	−1.15703e11	+	2.00404e11i	−0.628607	+	1.08878i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.43842e10			0.129291			0.0646453	−	0.997908i	$-0.479408\pi$
$659$	2.43842e10			0.129291			0.0646453	+	0.997908i	$0.479408\pi$
$660$		0			0
$661$	1.99492e11	+	1.15177e11i	1.04501	+	0.603335i	0.921247	−	0.388977i	$-0.127171\pi$
$661$	1.99492e11	+	1.15177e11i	1.04501	+	0.603335i	0.123760	+	0.992312i	$0.460505\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	8.38606e10	+	1.74879e10i	0.428816	+	0.0894236i
$666$		0			0
$667$	2.32081e11	+	4.01975e11i	1.17256	+	2.03093i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			4.96115e10i			0.244733i
$672$		0			0
$673$	−2.55818e11			−1.24701			−0.623505	−	0.781819i	$-0.714292\pi$
$673$	−2.55818e11			−1.24701			−0.623505	+	0.781819i	$0.714292\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.09308e11	−	6.31087e10i	0.520350	−	0.300424i	−0.216728	−	0.976232i	$-0.569538\pi$
$677$	1.09308e11	−	6.31087e10i	0.520350	−	0.300424i	0.737078	+	0.675808i	$0.236205\pi$
$678$		0			0
$679$	3.49457e11	−	1.15035e11i	1.64405	−	0.541190i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.14943e11	−	1.99087e11i	0.528201	−	0.914871i	−0.471258	−	0.881995i	$-0.656200\pi$
$683$	1.14943e11	−	1.99087e11i	0.528201	−	0.914871i	0.999459	−	0.0328759i	$-0.0104666\pi$
$684$		0			0
$685$		−	2.54597e11i		−	1.15636i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.32397e11	−	3.65115e11i	−2.80616	−	1.62014i
$690$		0			0
$691$	3.36193e11	−	1.94101e11i	1.47461	−	0.851364i	0.475016	−	0.879977i	$-0.342442\pi$
$691$	3.36193e11	−	1.94101e11i	1.47461	−	0.851364i	0.999591	+	0.0286128i	$0.00910899\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	4.59377e10	+	7.95665e10i	0.196893	+	0.341029i
$696$		0			0
$697$	−1.78735e10	+	3.09578e10i	−0.0757317	+	0.131171i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.95053e11			−1.22188			−0.610938	−	0.791678i	$-0.709208\pi$
$701$	−2.95053e11			−1.22188			−0.610938	+	0.791678i	$0.709208\pi$
$702$		0			0
$703$	−7.71072e10	−	4.45179e10i	−0.315699	−	0.182269i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.13328e8	+	5.43447e8i	−0.000453587	+	0.00217510i
$708$		0			0
$709$	−1.30909e11	−	2.26742e11i	−0.518067	−	0.897318i	−0.999780	−	0.0209890i	$-0.993318\pi$
$709$	−1.30909e11	−	2.26742e11i	−0.518067	−	0.897318i	0.481713	−	0.876329i	$-0.340015\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			9.22158e10i			0.356818i
$714$		0			0
$715$	6.79576e11			2.60024
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.38996e11	+	1.95719e11i	−1.26847	+	0.732349i	−0.974698	−	0.223527i	$-0.928243\pi$
$719$	−3.38996e11	+	1.95719e11i	−1.26847	+	0.732349i	−0.293769	+	0.955877i	$0.594909\pi$
$720$		0			0
$721$	1.13332e11	+	1.01257e11i	0.419384	+	0.374701i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.13750e9	+	8.89841e9i	−0.0185952	+	0.0322078i
$726$		0			0
$727$		−	4.07684e11i		−	1.45944i	−0.683747	−	0.729719i	$-0.739651\pi$
$727$		−	4.07684e11i		−	1.45944i	0.683747	−	0.729719i	$-0.260349\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−1.13028e11	−	6.52565e10i	−0.395835	−	0.228536i
$732$		0			0
$733$	−1.12013e11	+	6.46709e10i	−0.388020	+	0.224023i	−0.681302	−	0.732003i	$-0.738586\pi$
$733$	−1.12013e11	+	6.46709e10i	−0.388020	+	0.224023i	0.293282	+	0.956026i	$0.405252\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.02479e11	−	3.50704e11i	−0.686294	−	1.18870i
$738$		0			0
$739$	1.78609e11	−	3.09359e11i	0.598859	−	1.03725i	−0.394130	−	0.919055i	$-0.628954\pi$
$739$	1.78609e11	−	3.09359e11i	0.598859	−	1.03725i	0.992990	−	0.118200i	$-0.0377125\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	5.59095e11			1.83455			0.917277	−	0.398249i	$-0.130382\pi$
$743$	5.59095e11			1.83455			0.917277	+	0.398249i	$0.130382\pi$
$744$		0			0
$745$	1.22969e11	+	7.09964e10i	0.399183	+	0.230468i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.64914e11	−	2.96505e11i	0.841741	−	0.942117i
$750$		0			0
$751$	9.22661e10	+	1.59810e11i	0.290056	+	0.502392i	0.973823	−	0.227309i	$-0.0729926\pi$
$751$	9.22661e10	+	1.59810e11i	0.290056	+	0.502392i	−0.683766	+	0.729701i	$0.739659\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	2.79403e11i		−	0.859890i
$756$		0			0
$757$	4.72832e11			1.43987			0.719935	−	0.694041i	$-0.244171\pi$
$757$	4.72832e11			1.43987			0.719935	+	0.694041i	$0.244171\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.50188e11	−	8.67112e10i	0.447813	−	0.258545i	−0.259093	−	0.965852i	$-0.583424\pi$
$761$	1.50188e11	−	8.67112e10i	0.447813	−	0.258545i	0.706906	+	0.707307i	$0.250090\pi$
$762$		0			0
$763$	2.39268e11	+	4.98960e10i	0.705971	+	0.147220i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.88958e11	+	8.46900e11i	−1.41283	+	2.44710i
$768$		0			0
$769$			1.96725e9i			0.00562542i	0.999996	+	0.00281271i	$0.000895314\pi$
$769$			1.96725e9i			0.00562542i	−0.999996	+	0.00281271i	$0.999105\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.82266e11	+	2.20701e11i	1.07065	+	0.618141i	0.928359	−	0.371684i	$-0.121220\pi$
$773$	3.82266e11	+	2.20701e11i	1.07065	+	0.618141i	0.142292	+	0.989825i	$0.454553\pi$
$774$		0			0
$775$	−1.76787e9	+	1.02068e9i	−0.00490052	+	0.00282932i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.08690e10	−	1.88257e10i	−0.0295148	−	0.0511211i
$780$		0			0
$781$	−1.39638e11	+	2.41860e11i	−0.375318	+	0.650070i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	4.13372e11			1.08859
$786$		0			0
$787$	9.79181e10	+	5.65331e10i	0.255249	+	0.147368i	0.622165	−	0.782886i	$-0.286253\pi$
$787$	9.79181e10	+	5.65331e10i	0.255249	+	0.147368i	−0.366916	+	0.930254i	$0.619586\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−6.51593e10	−	1.97943e11i	−0.166445	−	0.505632i
$792$		0			0
$793$	6.80850e10	+	1.17927e11i	0.172170	+	0.298208i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			4.98251e11i			1.23485i	0.786629	+	0.617426i	$0.211825\pi$
$797$			4.98251e11i			1.23485i	−0.786629	+	0.617426i	$0.788175\pi$
$798$		0			0
$799$	5.65978e11			1.38871
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.91548e11	+	2.26060e11i	−0.941723	+	0.543704i
$804$		0			0
$805$	−1.27718e11	+	6.12449e11i	−0.304136	+	1.45843i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−2.12731e11	+	3.68460e11i	−0.496634	+	0.860195i	−0.999992	−	0.00388285i	$-0.998764\pi$
$809$	−2.12731e11	+	3.68460e11i	−0.496634	+	0.860195i	0.503359	+	0.864077i	$0.332097\pi$
$810$		0			0
$811$		−	4.55952e11i		−	1.05399i	−0.849869	−	0.526994i	$-0.823319\pi$
$811$		−	4.55952e11i		−	1.05399i	0.849869	−	0.526994i	$-0.176681\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.48717e11	−	8.58617e10i	−0.337077	−	0.194612i
$816$		0			0
$817$	6.87329e10	−	3.96830e10i	0.154268	−	0.0890668i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.14025e11	−	3.70703e11i	−0.471078	−	0.815931i	0.528375	−	0.849011i	$-0.322802\pi$
$821$	−2.14025e11	−	3.70703e11i	−0.471078	−	0.815931i	−0.999453	+	0.0330806i	$0.989468\pi$
$822$		0			0
$823$	3.99516e10	−	6.91983e10i	0.0870834	−	0.150833i	−0.819194	−	0.573517i	$-0.805579\pi$
$823$	3.99516e10	−	6.91983e10i	0.0870834	−	0.150833i	0.906277	+	0.422684i	$0.138912\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.92333e11			0.411180			0.205590	−	0.978638i	$-0.434089\pi$
$827$	1.92333e11			0.411180			0.205590	+	0.978638i	$0.434089\pi$
$828$		0			0
$829$	4.70459e10	+	2.71620e10i	0.0996102	+	0.0575100i	0.548978	−	0.835837i	$-0.315017\pi$
$829$	4.70459e10	+	2.71620e10i	0.0996102	+	0.0575100i	−0.449367	+	0.893347i	$0.648351\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.44301e11	−	6.14494e10i	1.13047	−	0.127625i
$834$		0			0
$835$	−4.49947e11	−	7.79330e11i	−0.925582	−	1.60316i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	1.14519e11i		−	0.231116i	−0.993301	−	0.115558i	$-0.963134\pi$
$839$		−	1.14519e11i		−	0.231116i	0.993301	−	0.115558i	$-0.0368655\pi$
$840$		0			0
$841$	7.09634e11			1.41857
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.17914e12	−	6.80776e11i	2.31280	−	1.33530i
$846$		0			0
$847$	−2.98527e11	+	3.34126e11i	−0.580029	+	0.649197i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.25122e11	−	5.63128e11i	0.619910	−	1.07372i
$852$		0			0
$853$			2.52816e11i			0.477538i	0.971076	+	0.238769i	$0.0767439\pi$
$853$			2.52816e11i			0.477538i	−0.971076	+	0.238769i	$0.923256\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.35338e11	+	3.66813e11i	1.17783	+	0.680019i	0.955511	−	0.294955i	$-0.0953048\pi$
$857$	6.35338e11	+	3.66813e11i	1.17783	+	0.680019i	0.222317	+	0.974975i	$0.428638\pi$
$858$		0			0
$859$	−6.41286e11	+	3.70246e11i	−1.17782	+	0.680015i	−0.955509	−	0.294961i	$-0.904693\pi$
$859$	−6.41286e11	+	3.70246e11i	−1.17782	+	0.680015i	−0.222311	+	0.974976i	$0.571360\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.45339e11	−	2.51735e11i	−0.262024	−	0.453838i	0.704756	−	0.709450i	$-0.251056\pi$
$863$	−1.45339e11	−	2.51735e11i	−0.262024	−	0.453838i	−0.966780	+	0.255612i	$0.917723\pi$
$864$		0			0
$865$	1.47664e11	−	2.55762e11i	0.263761	−	0.456848i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.36692e12			−2.39697
$870$		0			0
$871$	−9.62586e11	−	5.55749e11i	−1.67250	−	0.965620i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.63247e11	+	1.85411e11i	−0.960875	+	0.316302i
$876$		0			0
$877$	3.36290e10	+	5.82471e10i	0.0568480	+	0.0984636i	0.893049	−	0.449960i	$-0.148562\pi$
$877$	3.36290e10	+	5.82471e10i	0.0568480	+	0.0984636i	−0.836201	+	0.548423i	$0.815228\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	4.59947e10i		−	0.0763491i	−0.999271	−	0.0381746i	$-0.987846\pi$
$881$		−	4.59947e10i		−	0.0763491i	0.999271	−	0.0381746i	$-0.0121543\pi$
$882$		0			0
$883$	1.12554e12			1.85147			0.925736	−	0.378170i	$-0.123446\pi$
$883$	1.12554e12			1.85147			0.925736	+	0.378170i	$0.123446\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−9.90077e11	+	5.71621e11i	−1.59946	+	0.923451i	−0.607874	+	0.794033i	$0.707977\pi$
$887$	−9.90077e11	+	5.71621e11i	−1.59946	+	0.923451i	−0.991590	+	0.129418i	$0.958689\pi$
$888$		0			0
$889$	2.40750e11	+	7.31358e11i	0.385442	+	1.17091i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−1.72088e11	+	2.98065e11i	−0.270610	+	0.468711i
$894$		0			0
$895$			1.40236e11i			0.218558i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	2.08166e11	+	1.20185e11i	0.318692	+	0.183997i
$900$		0			0
$901$	−1.09330e12	+	6.31216e11i	−1.65897	+	0.957808i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	4.25071e11	+	7.36244e11i	0.633676	+	1.09756i
$906$		0			0
$907$	2.51450e9	−	4.35525e9i	0.00371555	−	0.00643552i	−0.864162	−	0.503214i	$-0.832151\pi$
$907$	2.51450e9	−	4.35525e9i	0.00371555	−	0.00643552i	0.867877	+	0.496779i	$0.165484\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.16880e12			1.69695			0.848473	−	0.529239i	$-0.177523\pi$
$911$	1.16880e12			1.69695			0.848473	+	0.529239i	$0.177523\pi$
$912$		0			0
$913$	−3.50440e11	−	2.02327e11i	−0.504348	−	0.291185i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.70990e11	−	5.99500e11i	−0.948940	−	0.847836i
$918$		0			0
$919$	−4.25808e11	−	7.37520e11i	−0.596968	−	1.03398i	−0.993266	−	0.115857i	$-0.963038\pi$
$919$	−4.25808e11	−	7.37520e11i	−0.596968	−	1.03398i	0.396297	−	0.918122i	$-0.370295\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			7.66537e11i			1.05615i
$924$		0			0
$925$	1.43943e10			0.0196618
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−3.58747e11	+	2.07123e11i	−0.481643	+	0.278077i	−0.721101	−	0.692830i	$-0.756364\pi$
$929$	−3.58747e11	+	2.07123e11i	−0.481643	+	0.278077i	0.239458	+	0.970907i	$0.423030\pi$
$930$		0			0
$931$	−1.33135e11	+	3.05333e11i	−0.177213	+	0.406420i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	5.87431e11	−	1.01746e12i	0.768617	−	1.33128i
$936$		0			0
$937$		−	1.30071e12i		−	1.68741i	−0.536808	−	0.843705i	$-0.680370\pi$
$937$		−	1.30071e12i		−	1.68741i	0.536808	−	0.843705i	$-0.319630\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−7.76943e11	−	4.48568e11i	−0.990902	−	0.572098i	−0.0853583	−	0.996350i	$-0.527204\pi$
$941$	−7.76943e11	−	4.48568e11i	−0.990902	−	0.572098i	−0.905544	+	0.424253i	$0.860537\pi$
$942$		0			0
$943$	1.37487e11	−	7.93783e10i	0.173866	−	0.100382i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.01806e11	−	1.76333e11i	−0.126582	−	0.219247i	0.795768	−	0.605602i	$-0.207067\pi$
$947$	−1.01806e11	−	1.76333e11i	−0.126582	−	0.219247i	−0.922350	+	0.386355i	$0.873734\pi$
$948$		0			0
$949$	−6.20474e11	+	1.07469e12i	−0.764995	+	1.32501i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−9.36718e11			−1.13563			−0.567815	−	0.823156i	$-0.692211\pi$
$953$	−9.36718e11			−1.13563			−0.567815	+	0.823156i	$0.692211\pi$
$954$		0			0
$955$	−4.68788e11	−	2.70655e11i	−0.563589	−	0.325388i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	9.69122e11	+	2.02097e11i	1.14579	+	0.238938i
$960$		0			0
$961$	−4.02568e11	−	6.97269e11i	−0.472004	−	0.817535i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	1.36906e12i		−	1.57875i
$966$		0			0
$967$	−6.50527e11			−0.743976			−0.371988	−	0.928237i	$-0.621324\pi$
$967$	−6.50527e11			−0.743976			−0.371988	+	0.928237i	$0.621324\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−4.75548e11	+	2.74558e11i	−0.534955	+	0.308856i	−0.743032	−	0.669256i	$-0.766613\pi$
$971$	−4.75548e11	+	2.74558e11i	−0.534955	+	0.308856i	0.208077	+	0.978112i	$0.433280\pi$
$972$		0			0
$973$	−3.39334e11	+	1.11702e11i	−0.378596	+	0.124627i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	4.65868e11	−	8.06907e11i	0.511310	−	0.885616i	−0.488604	−	0.872506i	$-0.662494\pi$
$977$	4.65868e11	−	8.06907e11i	0.511310	−	0.885616i	0.999914	−	0.0131097i	$-0.00417308\pi$
$978$		0			0
$979$		−	1.98351e12i		−	2.15925i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.03641e11	−	3.48512e11i	−0.646494	−	0.373254i	0.140618	−	0.990064i	$-0.455091\pi$
$983$	−6.03641e11	−	3.48512e11i	−0.646494	−	0.373254i	−0.787112	+	0.616810i	$0.788425\pi$
$984$		0			0
$985$	−1.16966e12	+	6.75301e11i	−1.24255	+	0.717386i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	2.89812e11	+	5.01969e11i	0.302922	+	0.524677i
$990$		0			0
$991$	−7.15650e11	+	1.23954e12i	−0.742004	+	1.28519i	0.209577	+	0.977792i	$0.432791\pi$
$991$	−7.15650e11	+	1.23954e12i	−0.742004	+	1.28519i	−0.951581	+	0.307397i	$0.900542\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.20349e11			−0.326837
$996$		0			0
$997$	−1.42004e12	−	8.19863e11i	−1.43721	−	0.829776i	−0.439558	−	0.898214i	$-0.644865\pi$
$997$	−1.42004e12	−	8.19863e11i	−1.43721	−	0.829776i	−0.997655	+	0.0684384i	$0.978198\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.e.73.3	✓	20
3.2	odd	2	inner	252.9.z.e.73.8	yes	20
7.5	odd	6	inner	252.9.z.e.145.3	yes	20
21.5	even	6	inner	252.9.z.e.145.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.9.z.e.73.3	✓	20	1.1	even	1	trivial
252.9.z.e.73.8	yes	20	3.2	odd	2	inner
252.9.z.e.145.3	yes	20	7.5	odd	6	inner
252.9.z.e.145.8	yes	20	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-534.755 + 308.741i) q^{5} +(-750.736 - 2280.61i) q^{7} +O(q^{10})\)	\(q+(-534.755 + 308.741i) q^{5} +(-750.736 - 2280.61i) q^{7} +(10012.2 - 17341.6i) q^{11} -54961.3i q^{13} +(-82287.8 - 47508.9i) q^{17} +(50039.8 - 28890.5i) q^{19} +(210993. + 365450. i) q^{23} +(-4670.69 + 8089.87i) q^{25} +1.09995e6 q^{29} +(189251. + 109264. i) q^{31} +(1.10558e6 + 987786. i) q^{35} +(-770458. - 1.33447e6i) q^{37} -376213. i q^{41} +1.37356e6 q^{43} +(-5.15852e6 + 2.97827e6i) q^{47} +(-4.63759e6 + 3.42428e6i) q^{49} +(6.64313e6 - 1.15062e7i) q^{53} +1.23646e7i q^{55} +(-1.54090e7 - 8.89642e6i) q^{59} +(-2.14563e6 + 1.23878e6i) q^{61} +(1.69688e7 + 2.93908e7i) q^{65} +(1.01117e7 - 1.75139e7i) q^{67} -1.39469e7 q^{71} +(-1.95536e7 - 1.12893e7i) q^{73} +(-4.70659e7 - 9.81492e6i) q^{77} +(-3.41314e7 - 5.91174e7i) q^{79} -2.02081e7i q^{83} +5.86717e7 q^{85} +(8.57842e7 - 4.95275e7i) q^{89} +(-1.25345e8 + 4.12614e7i) q^{91} +(-1.78394e7 + 3.08987e7i) q^{95} +1.53229e8i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 7238 q^{7}+O(q^{10}) \) 20 * q - 7238 * q^7	\( 20 q - 7238 q^{7} - 107256 q^{19} + 1348832 q^{25} - 4734426 q^{31} + 6802748 q^{37} - 596128 q^{43} - 19249258 q^{49} + 32573772 q^{61} - 25999304 q^{67} - 52899612 q^{73} - 129945530 q^{79} - 83755728 q^{85} + 42306852 q^{91}+O(q^{100}) \) 20 * q - 7238 * q^7 - 107256 * q^19 + 1348832 * q^25 - 4734426 * q^31 + 6802748 * q^37 - 596128 * q^43 - 19249258 * q^49 + 32573772 * q^61 - 25999304 * q^67 - 52899612 * q^73 - 129945530 * q^79 - 83755728 * q^85 + 42306852 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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