LMFDB - Embedded newform 252.9.z.e.73.2

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			73.2
Root			$564.961 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.e.145.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-846.691 + 488.837i) q^{5} +(-1709.42 - 1686.02i) q^{7} +O(q^{10})$	$q+(-846.691 + 488.837i) q^{5} +(-1709.42 - 1686.02i) q^{7} +(-8638.29 + 14962.0i) q^{11} +45420.7i q^{13} +(112273. + 64821.0i) q^{17} +(136906. - 79042.6i) q^{19} +(176386. + 305510. i) q^{23} +(282611. - 489497. i) q^{25} -256521. q^{29} +(-152858. - 88252.6i) q^{31} +(2.27154e6 + 591913. i) q^{35} +(1.07120e6 + 1.85537e6i) q^{37} +4.55839e6i q^{41} -5.94536e6 q^{43} +(2.16783e6 - 1.25160e6i) q^{47} +(79443.6 + 5.76425e6i) q^{49} +(-811797. + 1.40607e6i) q^{53} -1.68909e7i q^{55} +(-9.69707e6 - 5.59861e6i) q^{59} +(-3.54943e6 + 2.04926e6i) q^{61} +(-2.22033e7 - 3.84573e7i) q^{65} +(510451. - 884128. i) q^{67} -9.23408e6 q^{71} +(2.42644e7 + 1.40090e7i) q^{73} +(3.99927e7 - 1.10119e7i) q^{77} +(934661. + 1.61888e6i) q^{79} +8.27975e6i q^{83} -1.26748e8 q^{85} +(-1.18525e7 + 6.84303e6i) q^{89} +(7.65804e7 - 7.76431e7i) q^{91} +(-7.72779e7 + 1.33849e8i) q^{95} -9.99327e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−846.691	+	488.837i	−1.35471	+	0.782140i	−0.988904	−	0.148553i	$-0.952538\pi$
$5$	−846.691	+	488.837i	−1.35471	+	0.782140i	−0.365801	+	0.930693i	$0.619205\pi$
$6$		0			0
$7$	−1709.42	−	1686.02i	−0.711962	−	0.702218i
$7$	−1709.42	−	1686.02i	−0.711962	−	0.702218i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−8638.29	+	14962.0i	−0.590007	+	1.02192i	0.404224	+	0.914660i	$0.367542\pi$
$11$	−8638.29	+	14962.0i	−0.590007	+	1.02192i	−0.994231	+	0.107262i	$0.965792\pi$
$12$		0			0
$13$			45420.7i			1.59030i	0.606410	+	0.795152i	$0.292609\pi$
$13$			45420.7i			1.59030i	−0.606410	+	0.795152i	$0.707391\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	112273.	+	64821.0i	1.34425	+	0.776104i	0.987428	−	0.158067i	$-0.0505263\pi$
$17$	112273.	+	64821.0i	1.34425	+	0.776104i	0.356824	+	0.934172i	$0.383860\pi$
$18$		0			0
$19$	136906.	−	79042.6i	1.05053	−	0.606522i	0.127730	−	0.991809i	$-0.459231\pi$
$19$	136906.	−	79042.6i	1.05053	−	0.606522i	0.922797	+	0.385287i	$0.125897\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	176386.	+	305510.i	0.630308	+	1.09173i	0.987489	+	0.157690i	$0.0504048\pi$
$23$	176386.	+	305510.i	0.630308	+	1.09173i	−0.357181	+	0.934035i	$0.616262\pi$
$24$		0			0
$25$	282611.	−	489497.i	0.723485	−	1.25311i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−256521.			−0.362686			−0.181343	−	0.983420i	$-0.558044\pi$
$29$	−256521.			−0.362686			−0.181343	+	0.983420i	$0.558044\pi$
$30$		0			0
$31$	−152858.	−	88252.6i	−0.165517	−	0.0955610i	0.414954	−	0.909843i	$-0.363798\pi$
$31$	−152858.	−	88252.6i	−0.165517	−	0.0955610i	−0.580470	+	0.814282i	$0.697131\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	2.27154e6	+	591913.i	1.51373	+	0.394444i
$36$		0			0
$37$	1.07120e6	+	1.85537e6i	0.571563	+	0.989976i	0.996406	+	0.0847087i	$0.0269960\pi$
$37$	1.07120e6	+	1.85537e6i	0.571563	+	0.989976i	−0.424843	+	0.905267i	$0.639671\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			4.55839e6i			1.61315i	0.591129	+	0.806577i	$0.298682\pi$
$41$			4.55839e6i			1.61315i	−0.591129	+	0.806577i	$0.701318\pi$
$42$		0			0
$43$	−5.94536e6			−1.73902			−0.869509	−	0.493917i	$-0.835565\pi$
$43$	−5.94536e6			−1.73902			−0.869509	+	0.493917i	$0.835565\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.16783e6	−	1.25160e6i	0.444256	−	0.256492i	−0.261145	−	0.965300i	$-0.584100\pi$
$47$	2.16783e6	−	1.25160e6i	0.444256	−	0.256492i	0.705401	+	0.708808i	$0.250767\pi$
$48$		0			0
$49$	79443.6	+	5.76425e6i	0.0137808	+	0.999905i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−811797.	+	1.40607e6i	−0.102883	+	0.178199i	−0.912871	−	0.408247i	$-0.866140\pi$
$53$	−811797.	+	1.40607e6i	−0.102883	+	0.178199i	0.809988	+	0.586446i	$0.199473\pi$
$54$		0			0
$55$		−	1.68909e7i		−	1.84587i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−9.69707e6	−	5.59861e6i	−0.800263	−	0.462032i	0.0433004	−	0.999062i	$-0.486213\pi$
$59$	−9.69707e6	−	5.59861e6i	−0.800263	−	0.462032i	−0.843563	+	0.537030i	$0.819546\pi$
$60$		0			0
$61$	−3.54943e6	+	2.04926e6i	−0.256354	+	0.148006i	−0.622670	−	0.782485i	$-0.713952\pi$
$61$	−3.54943e6	+	2.04926e6i	−0.256354	+	0.148006i	0.366316	+	0.930490i	$0.380619\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.22033e7	−	3.84573e7i	−1.24384	−	2.15440i
$66$		0			0
$67$	510451.	−	884128.i	0.0253312	−	0.0438749i	−0.853082	−	0.521777i	$-0.825269\pi$
$67$	510451.	−	884128.i	0.0253312	−	0.0438749i	0.878413	+	0.477902i	$0.158603\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.23408e6			−0.363379			−0.181690	−	0.983356i	$-0.558157\pi$
$71$	−9.23408e6			−0.363379			−0.181690	+	0.983356i	$0.558157\pi$
$72$		0			0
$73$	2.42644e7	+	1.40090e7i	0.854432	+	0.493306i	0.862144	−	0.506664i	$-0.169121\pi$
$73$	2.42644e7	+	1.40090e7i	0.854432	+	0.493306i	−0.00771188	+	0.999970i	$0.502455\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.99927e7	−	1.10119e7i	1.13767	−	0.313257i
$78$		0			0
$79$	934661.	+	1.61888e6i	0.0239964	+	0.0415629i	0.877774	−	0.479075i	$-0.159028\pi$
$79$	934661.	+	1.61888e6i	0.0239964	+	0.0415629i	−0.853778	+	0.520637i	$0.825694\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			8.27975e6i			0.174464i	0.996188	+	0.0872318i	$0.0278021\pi$
$83$			8.27975e6i			0.174464i	−0.996188	+	0.0872318i	$0.972198\pi$
$84$		0			0
$85$	−1.26748e8			−2.42809
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.18525e7	+	6.84303e6i	−0.188907	+	0.109066i	−0.591471	−	0.806326i	$-0.701453\pi$
$89$	−1.18525e7	+	6.84303e6i	−0.188907	+	0.109066i	0.402564	+	0.915392i	$0.368119\pi$
$90$		0			0
$91$	7.65804e7	−	7.76431e7i	1.11674	−	1.13224i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−7.72779e7	+	1.33849e8i	−0.948770	+	1.64332i
$96$		0			0
$97$		−	9.99327e7i		−	1.12881i	−0.825498	−	0.564405i	$-0.809106\pi$
$97$		−	9.99327e7i		−	1.12881i	0.825498	−	0.564405i	$-0.190894\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.50506e8	+	8.68948e7i	1.44633	+	0.835042i	0.998261	−	0.0589546i	$-0.0187767\pi$
$101$	1.50506e8	+	8.68948e7i	1.44633	+	0.835042i	0.448074	+	0.893996i	$0.352110\pi$
$102$		0			0
$103$	−1.59117e8	+	9.18663e7i	−1.41374	+	0.816221i	−0.995738	−	0.0922275i	$-0.970601\pi$
$103$	−1.59117e8	+	9.18663e7i	−1.41374	+	0.816221i	−0.417998	+	0.908448i	$0.637268\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.42634e6	−	9.39870e6i	−0.0413973	−	0.0717023i	0.844584	−	0.535423i	$-0.179848\pi$
$107$	−5.42634e6	−	9.39870e6i	−0.0413973	−	0.0717023i	−0.885982	+	0.463720i	$0.846514\pi$
$108$		0			0
$109$	−8.53127e7	+	1.47766e8i	−0.604377	+	1.04681i	0.387773	+	0.921755i	$0.373245\pi$
$109$	−8.53127e7	+	1.47766e8i	−0.604377	+	1.04681i	−0.992150	+	0.125057i	$0.960089\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	2.75586e8			1.69022			0.845110	−	0.534593i	$-0.179535\pi$
$113$	2.75586e8			1.69022			0.845110	+	0.534593i	$0.179535\pi$
$114$		0			0
$115$	−2.98689e8	−	1.72448e8i	−1.70776	−	0.985978i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.26326e7	−	3.00102e8i	−0.412063	−	1.49651i
$120$		0			0
$121$	−4.20606e7	−	7.28511e7i	−0.196216	−	0.339856i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			1.70700e8i			0.699186i
$126$		0			0
$127$	−9.73594e7			−0.374251			−0.187126	−	0.982336i	$-0.559917\pi$
$127$	−9.73594e7			−0.374251			−0.187126	+	0.982336i	$0.559917\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.60282e8	+	2.08009e8i	−1.22337	+	0.706313i	−0.965635	−	0.259903i	$-0.916310\pi$
$131$	−3.60282e8	+	2.08009e8i	−1.22337	+	0.706313i	−0.257735	+	0.966216i	$0.582976\pi$
$132$		0			0
$133$	−3.67297e8	−	9.57094e7i	−1.17385	−	0.305878i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.06060e8	−	1.83701e8i	0.301071	−	0.521470i	−0.675308	−	0.737536i	$-0.735989\pi$
$137$	1.06060e8	−	1.83701e8i	0.301071	−	0.521470i	0.976379	+	0.216066i	$0.0693227\pi$
$138$		0			0
$139$		−	2.79705e8i		−	0.749273i	−0.927172	−	0.374637i	$-0.877767\pi$
$139$		−	2.79705e8i		−	0.749273i	0.927172	−	0.374637i	$-0.122233\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.79582e8	−	3.92357e8i	−1.62517	−	0.938290i
$144$		0			0
$145$	2.17194e8	−	1.25397e8i	0.491333	−	0.283671i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.31619e8	+	2.27971e8i	0.267039	+	0.462524i	0.968096	−	0.250581i	$-0.0806215\pi$
$149$	1.31619e8	+	2.27971e8i	0.267039	+	0.462524i	−0.701057	+	0.713105i	$0.747288\pi$
$150$		0			0
$151$	1.72737e7	−	2.99189e7i	0.0332259	−	0.0575490i	−0.848934	−	0.528498i	$-0.822755\pi$
$151$	1.72737e7	−	2.99189e7i	0.0332259	−	0.0575490i	0.882160	+	0.470949i	$0.156089\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.72565e8			0.298968
$156$		0			0
$157$	−9.30127e8	−	5.37009e8i	−1.53089	−	0.883859i	−0.999321	−	0.0368430i	$-0.988270\pi$
$157$	−9.30127e8	−	5.37009e8i	−1.53089	−	0.883859i	−0.531568	−	0.847016i	$-0.678397\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.13579e8	−	8.19636e8i	0.317873	−	1.21988i
$162$		0			0
$163$	−5.44879e8	−	9.43759e8i	−0.771880	−	1.33694i	−0.936531	−	0.350584i	$-0.885983\pi$
$163$	−5.44879e8	−	9.43759e8i	−0.771880	−	1.33694i	0.164651	−	0.986352i	$-0.447350\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	4.24896e8i		−	0.546282i	−0.961974	−	0.273141i	$-0.911937\pi$
$167$		−	4.24896e8i		−	0.546282i	0.961974	−	0.273141i	$-0.0880625\pi$
$168$		0			0
$169$	−1.24731e9			−1.52907
$170$		0			0
$171$		0			0
$172$		0			0
$173$	5.66736e8	−	3.27205e8i	0.632697	−	0.365288i	−0.149099	−	0.988822i	$-0.547637\pi$
$173$	5.66736e8	−	3.27205e8i	0.632697	−	0.365288i	0.781796	+	0.623534i	$0.214304\pi$
$174$		0			0
$175$	−1.30841e9	+	3.60267e8i	−1.39505	+	0.384125i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.01808e8	+	1.56198e9i	−0.878420	+	1.52147i	−0.0253447	+	0.999679i	$0.508068\pi$
$179$	−9.01808e8	+	1.56198e9i	−0.878420	+	1.52147i	−0.853075	+	0.521789i	$0.825265\pi$
$180$		0			0
$181$			1.31380e9i			1.22409i	0.790821	+	0.612047i	$0.209654\pi$
$181$			1.31380e9i			1.22409i	−0.790821	+	0.612047i	$0.790346\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.81395e9	−	1.04729e9i	−1.54860	−	0.894084i
$186$		0			0
$187$	−1.93970e9	+	1.11988e9i	−1.58624	+	0.915813i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.28526e9	+	2.22614e9i	0.965737	+	1.67271i	0.707622	+	0.706591i	$0.249768\pi$
$191$	1.28526e9	+	2.22614e9i	0.965737	+	1.67271i	0.258115	+	0.966114i	$0.416899\pi$
$192$		0			0
$193$	7.86723e8	−	1.36264e9i	0.567012	−	0.982094i	−0.429847	−	0.902902i	$-0.641433\pi$
$193$	7.86723e8	−	1.36264e9i	0.567012	−	0.982094i	0.996859	−	0.0791924i	$-0.0252341\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.46763e9			1.63838			0.819192	−	0.573519i	$-0.194422\pi$
$197$	2.46763e9			1.63838			0.819192	+	0.573519i	$0.194422\pi$
$198$		0			0
$199$	−8.44252e8	−	4.87429e8i	−0.538344	−	0.310813i	0.206063	−	0.978539i	$-0.433935\pi$
$199$	−8.44252e8	−	4.87429e8i	−0.538344	−	0.310813i	−0.744408	+	0.667726i	$0.767268\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.38502e8	+	4.32501e8i	0.258219	+	0.254685i
$204$		0			0
$205$	−2.22831e9	−	3.85955e9i	−1.26171	−	2.18535i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			2.73117e9i			1.43141i
$210$		0			0
$211$	1.66366e9			0.839335			0.419667	−	0.907678i	$-0.362147\pi$
$211$	1.66366e9			0.839335			0.419667	+	0.907678i	$0.362147\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.03388e9	−	2.90631e9i	2.35586	−	1.36016i
$216$		0			0
$217$	1.12503e8	+	4.08583e8i	0.0507369	+	0.184264i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.94422e9	+	5.09953e9i	−1.23424	+	2.13777i
$222$		0			0
$223$		−	2.09358e9i		−	0.846584i	−0.905993	−	0.423292i	$-0.860874\pi$
$223$		−	2.09358e9i		−	0.846584i	0.905993	−	0.423292i	$-0.139126\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.79354e9	−	2.19020e9i	−1.42870	−	0.824862i	−0.431684	−	0.902025i	$-0.642080\pi$
$227$	−3.79354e9	−	2.19020e9i	−1.42870	−	0.824862i	−0.997018	+	0.0771636i	$0.975414\pi$
$228$		0			0
$229$	−1.65087e8	+	9.53133e7i	−0.0600305	+	0.0346586i	−0.529715	−	0.848176i	$-0.677701\pi$
$229$	−1.65087e8	+	9.53133e7i	−0.0600305	+	0.0346586i	0.469684	+	0.882834i	$0.344368\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.14144e9	−	1.97703e9i	−0.387283	−	0.670794i	0.604800	−	0.796377i	$-0.293253\pi$
$233$	−1.14144e9	−	1.97703e9i	−0.387283	−	0.670794i	−0.992083	+	0.125583i	$0.959920\pi$
$234$		0			0
$235$	−1.22365e9	+	2.11943e9i	−0.401224	+	0.694941i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	5.49617e8			0.168449			0.0842246	−	0.996447i	$-0.473159\pi$
$239$	5.49617e8			0.168449			0.0842246	+	0.996447i	$0.473159\pi$
$240$		0			0
$241$	2.24621e9	+	1.29685e9i	0.665858	+	0.384433i	0.794505	−	0.607257i	$-0.207730\pi$
$241$	2.24621e9	+	1.29685e9i	0.665858	+	0.384433i	−0.128648	+	0.991690i	$0.541064\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.88505e9	−	4.84171e9i	−0.800734	−	1.34380i
$246$		0			0
$247$	3.59017e9	+	6.21836e9i	0.964555	+	1.67066i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	6.99854e9i		−	1.76325i	−0.471955	−	0.881623i	$-0.656451\pi$
$251$		−	6.99854e9i		−	1.76325i	0.471955	−	0.881623i	$-0.343549\pi$
$252$		0			0
$253$	−6.09469e9			−1.48754
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.10057e9	−	6.35413e8i	0.252281	−	0.145654i	−0.368527	−	0.929617i	$-0.620138\pi$
$257$	1.10057e9	−	6.35413e8i	0.252281	−	0.145654i	0.620808	+	0.783962i	$0.286805\pi$
$258$		0			0
$259$	1.29707e9	−	4.97769e9i	0.288247	−	1.10619i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.64995e9	+	2.85780e9i	−0.344865	+	0.597323i	−0.985329	−	0.170665i	$-0.945409\pi$
$263$	−1.64995e9	+	2.85780e9i	−0.344865	+	0.597323i	0.640464	+	0.767988i	$0.278742\pi$
$264$		0			0
$265$		−	1.58735e9i		−	0.321876i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.90593e9	−	4.56449e9i	−1.50988	−	0.871732i	−0.999934	−	0.0115288i	$-0.996330\pi$
$269$	−7.90593e9	−	4.56449e9i	−1.50988	−	0.871732i	−0.509951	−	0.860203i	$-0.670336\pi$
$270$		0			0
$271$	5.43925e9	−	3.14035e9i	1.00847	−	0.582239i	0.0977251	−	0.995213i	$-0.468843\pi$
$271$	5.43925e9	−	3.14035e9i	1.00847	−	0.582239i	0.910743	+	0.412974i	$0.135510\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	4.88256e9	+	8.45684e9i	0.853722	+	1.47869i
$276$		0			0
$277$	−2.10235e9	+	3.64138e9i	−0.357097	+	0.618510i	−0.987474	−	0.157779i	$-0.949567\pi$
$277$	−2.10235e9	+	3.64138e9i	−0.357097	+	0.618510i	0.630378	+	0.776288i	$0.282900\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.09860e9			0.817760			0.408880	−	0.912588i	$-0.365919\pi$
$281$	5.09860e9			0.817760			0.408880	+	0.912588i	$0.365919\pi$
$282$		0			0
$283$	−5.67916e9	−	3.27887e9i	−0.885398	−	0.511185i	−0.0129635	−	0.999916i	$-0.504127\pi$
$283$	−5.67916e9	−	3.27887e9i	−0.885398	−	0.511185i	−0.872434	+	0.488731i	$0.837460\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.68555e9	−	7.79220e9i	1.13278	−	1.14850i
$288$		0			0
$289$	4.91565e9	+	8.51415e9i	0.704676	+	1.22053i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			1.35034e10i			1.83220i	0.400950	+	0.916100i	$0.368680\pi$
$293$			1.35034e10i			1.83220i	−0.400950	+	0.916100i	$0.631320\pi$
$294$		0			0
$295$	1.09472e10			1.44549
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.38765e10	+	8.01158e9i	−1.73618	+	1.00238i
$300$		0			0
$301$	1.01631e10	+	1.00240e10i	1.23812	+	1.22117i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	2.00351e9	−	3.47019e9i	0.231522	−	0.401009i
$306$		0			0
$307$		−	2.59567e9i		−	0.292210i	−0.989269	−	0.146105i	$-0.953326\pi$
$307$		−	2.59567e9i		−	0.292210i	0.989269	−	0.146105i	$-0.0466738\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.71175e9	+	2.14298e9i	0.396769	+	0.229075i	0.685089	−	0.728459i	$-0.259763\pi$
$311$	3.71175e9	+	2.14298e9i	0.396769	+	0.229075i	−0.288320	+	0.957534i	$0.593097\pi$
$312$		0			0
$313$	−1.39801e9	+	8.07143e8i	−0.145658	+	0.0840956i	−0.571058	−	0.820910i	$-0.693467\pi$
$313$	−1.39801e9	+	8.07143e8i	−0.145658	+	0.0840956i	0.425400	+	0.905005i	$0.360133\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.98176e8	+	1.03607e9i	0.0592369	+	0.102601i	0.894123	−	0.447821i	$-0.147800\pi$
$317$	5.98176e8	+	1.03607e9i	0.0592369	+	0.102601i	−0.834886	+	0.550423i	$0.814467\pi$
$318$		0			0
$319$	2.21590e9	−	3.83805e9i	0.213987	−	0.370637i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.04945e10			1.88290
$324$		0			0
$325$	2.22333e10	+	1.28364e10i	1.99283	+	1.15056i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.81596e9	−	1.51551e9i	−0.496407	−	0.129352i
$330$		0			0
$331$	4.35888e9	+	7.54981e9i	0.363131	+	0.628961i	0.988474	−	0.151388i	$-0.0483744\pi$
$331$	4.35888e9	+	7.54981e9i	0.363131	+	0.628961i	−0.625343	+	0.780350i	$0.715041\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			9.98111e8i			0.0792500i
$336$		0			0
$337$	8.30127e9			0.643613			0.321807	−	0.946805i	$-0.395710\pi$
$337$	8.30127e9			0.643613			0.321807	+	0.946805i	$0.395710\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.64086e9	−	1.52470e9i	0.195312	−	0.112763i
$342$		0			0
$343$	9.58287e9	−	9.98748e9i	0.692340	−	0.721572i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.57983e9	+	4.46839e9i	−0.177940	+	0.308200i	−0.941175	−	0.337921i	$-0.890276\pi$
$347$	−2.57983e9	+	4.46839e9i	−0.177940	+	0.308200i	0.763235	+	0.646121i	$0.223610\pi$
$348$		0			0
$349$			2.71690e9i			0.183135i	0.995799	+	0.0915675i	$0.0291877\pi$
$349$			2.71690e9i			0.183135i	−0.995799	+	0.0915675i	$0.970812\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.59922e10	+	9.23311e9i	1.02994	+	0.594633i	0.916966	−	0.398965i	$-0.130631\pi$
$353$	1.59922e10	+	9.23311e9i	1.02994	+	0.594633i	0.112969	+	0.993598i	$0.463964\pi$
$354$		0			0
$355$	7.81841e9	−	4.51396e9i	0.492272	−	0.284213i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.07542e10	−	1.86269e10i	−0.647443	−	1.12140i	−0.983731	−	0.179646i	$-0.942505\pi$
$359$	−1.07542e10	−	1.86269e10i	−0.647443	−	1.12140i	0.336288	−	0.941759i	$-0.390828\pi$
$360$		0			0
$361$	4.00368e9	−	6.93457e9i	0.235738	−	0.408311i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.73926e10			−1.54334
$366$		0			0
$367$	2.48644e10	+	1.43555e10i	1.37061	+	0.791321i	0.991005	−	0.133828i	$-0.0427271\pi$
$367$	2.48644e10	+	1.43555e10i	1.37061	+	0.791321i	0.379603	+	0.925149i	$0.376060\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.75838e9	−	1.03486e9i	0.198383	−	0.0546245i
$372$		0			0
$373$	−1.10431e10	−	1.91272e10i	−0.570499	−	0.988134i	−0.996515	−	0.0834180i	$-0.973416\pi$
$373$	−1.10431e10	−	1.91272e10i	−0.570499	−	0.988134i	0.426015	−	0.904716i	$-0.359917\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	1.16514e10i		−	0.576781i
$378$		0			0
$379$	2.24567e10			1.08840			0.544202	−	0.838954i	$-0.316833\pi$
$379$	2.24567e10			1.08840			0.544202	+	0.838954i	$0.316833\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.35037e10	+	7.79638e9i	−0.627565	+	0.362325i	−0.779808	−	0.626018i	$-0.784683\pi$
$383$	−1.35037e10	+	7.79638e9i	−0.627565	+	0.362325i	0.152244	+	0.988343i	$0.451350\pi$
$384$		0			0
$385$	−2.84784e10	+	2.88736e10i	−1.29620	+	1.31419i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.98498e9	−	6.90218e9i	0.174031	−	0.301431i	−0.765794	−	0.643086i	$-0.777654\pi$
$389$	3.98498e9	−	6.90218e9i	0.174031	−	0.301431i	0.939826	+	0.341654i	$0.110987\pi$
$390$		0			0
$391$			4.57341e10i			1.95674i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.58274e9	−	9.13794e8i	−0.0650160	−	0.0375370i
$396$		0			0
$397$	−1.22794e10	+	7.08953e9i	−0.494329	+	0.285401i	−0.726369	−	0.687305i	$-0.758793\pi$
$397$	−1.22794e10	+	7.08953e9i	−0.494329	+	0.285401i	0.232040	+	0.972706i	$0.425460\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.45356e10	−	2.51763e10i	−0.562153	−	0.973678i	−0.997308	−	0.0733222i	$-0.976640\pi$
$401$	−1.45356e10	−	2.51763e10i	−0.562153	−	0.973678i	0.435155	−	0.900355i	$-0.356693\pi$
$402$		0			0
$403$	4.00850e9	−	6.94292e9i	0.151971	−	0.263222i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.70134e10			−1.34890
$408$		0			0
$409$	−2.44164e10	−	1.40968e10i	−0.872545	−	0.503764i	−0.00435165	−	0.999991i	$-0.501385\pi$
$409$	−2.44164e10	−	1.40968e10i	−0.872545	−	0.503764i	−0.868193	+	0.496227i	$0.834719\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.13699e9	+	2.59199e10i	0.245310	+	0.890908i
$414$		0			0
$415$	−4.04745e9	−	7.01039e9i	−0.136455	−	0.236347i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	2.81393e10i		−	0.912971i	−0.889731	−	0.456486i	$-0.849108\pi$
$419$		−	2.81393e10i		−	0.912971i	0.889731	−	0.456486i	$-0.150892\pi$
$420$		0			0
$421$	1.99214e10			0.634151			0.317075	−	0.948400i	$-0.397299\pi$
$421$	1.99214e10			0.634151			0.317075	+	0.948400i	$0.397299\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.34594e10	−	3.66383e10i	1.94509	−	1.12300i
$426$		0			0
$427$	9.52258e9	+	2.48137e9i	0.286446	+	0.0746414i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.27925e9	−	5.67983e9i	0.0950310	−	0.164599i	−0.814591	−	0.580036i	$-0.803038\pi$
$431$	3.27925e9	−	5.67983e9i	0.0950310	−	0.164599i	0.909622	+	0.415438i	$0.136372\pi$
$432$		0			0
$433$		−	2.63808e10i		−	0.750475i	−0.926929	−	0.375238i	$-0.877561\pi$
$433$		−	2.63808e10i		−	0.750475i	0.926929	−	0.375238i	$-0.122439\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	4.82965e10	+	2.78840e10i	1.32431	+	0.764592i
$438$		0			0
$439$	3.83188e10	−	2.21234e10i	1.03170	−	0.595653i	0.114229	−	0.993454i	$-0.463560\pi$
$439$	3.83188e10	−	2.21234e10i	1.03170	−	0.595653i	0.917471	+	0.397802i	$0.130227\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.70776e9	−	4.68997e9i	−0.0703064	−	0.121774i	0.828729	−	0.559650i	$-0.189064\pi$
$443$	−2.70776e9	−	4.68997e9i	−0.0703064	−	0.121774i	−0.899036	+	0.437876i	$0.855731\pi$
$444$		0			0
$445$	6.69026e9	−	1.15879e10i	0.170609	−	0.295504i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.89044e10			−0.465135			−0.232567	−	0.972580i	$-0.574713\pi$
$449$	−1.89044e10			−0.465135			−0.232567	+	0.972580i	$0.574713\pi$
$450$		0			0
$451$	−6.82024e10	−	3.93767e10i	−1.64852	−	0.951771i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.68851e10	+	1.03175e11i	−0.627287	+	2.40730i
$456$		0			0
$457$	1.87173e10	+	3.24193e10i	0.429120	+	0.743257i	0.996795	−	0.0799952i	$-0.0254905\pi$
$457$	1.87173e10	+	3.24193e10i	0.429120	+	0.743257i	−0.567676	+	0.823252i	$0.692157\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			5.85532e10i			1.29642i	0.761460	+	0.648212i	$0.224483\pi$
$461$			5.85532e10i			1.29642i	−0.761460	+	0.648212i	$0.775517\pi$
$462$		0			0
$463$	2.74489e10			0.597311			0.298655	−	0.954361i	$-0.403462\pi$
$463$	2.74489e10			0.597311			0.298655	+	0.954361i	$0.403462\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.98491e10	+	3.45539e10i	−1.25832	+	0.726490i	−0.972747	−	0.231868i	$-0.925516\pi$
$467$	−5.98491e10	+	3.45539e10i	−1.25832	+	0.726490i	−0.285570	+	0.958358i	$0.592183\pi$
$468$		0			0
$469$	−2.36324e9	+	6.50713e8i	−0.0488445	+	0.0134493i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	5.13577e10	−	8.89541e10i	1.02603	−	1.77714i
$474$		0			0
$475$		−	8.93533e10i		−	1.75524i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.09562e10	+	1.20991e10i	0.398081	+	0.229832i	0.685656	−	0.727926i	$-0.259516\pi$
$479$	2.09562e10	+	1.20991e10i	0.398081	+	0.229832i	−0.287575	+	0.957758i	$0.592849\pi$
$480$		0			0
$481$	−8.42724e10	+	4.86547e10i	−1.57436	+	0.908959i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.88508e10	+	8.46121e10i	0.882887	+	1.52920i
$486$		0			0
$487$	−4.83887e10	+	8.38117e10i	−0.860257	+	1.49001i	0.0114238	+	0.999935i	$0.496364\pi$
$487$	−4.83887e10	+	8.38117e10i	−0.860257	+	1.49001i	−0.871681	+	0.490074i	$0.836970\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.08126e10			0.186039			0.0930197	−	0.995664i	$-0.470348\pi$
$491$	1.08126e10			0.186039			0.0930197	+	0.995664i	$0.470348\pi$
$492$		0			0
$493$	−2.88004e10	−	1.66279e10i	−0.487541	−	0.281482i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.57849e10	+	1.55689e10i	0.258712	+	0.255171i
$498$		0			0
$499$	−3.54346e10	−	6.13745e10i	−0.571512	−	0.989888i	−0.996411	−	0.0846472i	$-0.973024\pi$
$499$	−3.54346e10	−	6.13745e10i	−0.571512	−	0.989888i	0.424899	−	0.905241i	$-0.360310\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	4.35358e10i		−	0.680102i	−0.940407	−	0.340051i	$-0.889556\pi$
$503$		−	4.35358e10i		−	0.680102i	0.940407	−	0.340051i	$-0.110444\pi$
$504$		0			0
$505$	−1.69910e11			−2.61248
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.52593e10	+	8.80998e9i	−0.227334	+	0.131251i	−0.609342	−	0.792908i	$-0.708566\pi$
$509$	−1.52593e10	+	8.80998e9i	−0.227334	+	0.131251i	0.382008	+	0.924159i	$0.375233\pi$
$510$		0			0
$511$	−1.78584e10	−	6.48577e10i	−0.261915	−	0.951213i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	8.98154e10	−	1.55565e11i	1.27680	−	2.21148i
$516$		0			0
$517$			4.32466e10i			0.605327i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−4.48331e10	−	2.58844e10i	−0.608482	−	0.351307i	0.163889	−	0.986479i	$-0.447596\pi$
$521$	−4.48331e10	−	2.58844e10i	−0.608482	−	0.351307i	−0.772371	+	0.635172i	$0.780929\pi$
$522$		0			0
$523$	−5.20242e9	+	3.00362e9i	−0.0695342	+	0.0401456i	−0.534364	−	0.845254i	$-0.679449\pi$
$523$	−5.20242e9	+	3.00362e9i	−0.0695342	+	0.0401456i	0.464830	+	0.885400i	$0.346116\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.14412e10	−	1.98168e10i	−0.148331	−	0.256916i
$528$		0			0
$529$	−2.30686e10	+	3.99560e10i	−0.294577	+	0.510222i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.07045e11			−2.56541
$534$		0			0
$535$	9.18888e9	+	5.30520e9i	0.112162	+	0.0647570i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.69307e10	−	4.86046e10i	−1.02996	−	0.575868i
$540$		0			0
$541$	−3.09965e10	−	5.36876e10i	−0.361846	−	0.626736i	0.626418	−	0.779487i	$-0.284520\pi$
$541$	−3.09965e10	−	5.36876e10i	−0.361846	−	0.626736i	−0.988265	+	0.152751i	$0.951187\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	1.66816e11i		−	1.89083i
$546$		0			0
$547$	−5.84834e9			−0.0653256			−0.0326628	−	0.999466i	$-0.510399\pi$
$547$	−5.84834e9			−0.0653256			−0.0326628	+	0.999466i	$0.510399\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−3.51192e10	+	2.02761e10i	−0.381012	+	0.219977i
$552$		0			0
$553$	1.13174e9	−	4.34321e9i	0.0121017	−	0.0464419i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.74617e10	+	1.51488e11i	−0.908652	+	1.57383i	−0.0927123	+	0.995693i	$0.529554\pi$
$557$	−8.74617e10	+	1.51488e11i	−0.908652	+	1.57383i	−0.815939	+	0.578138i	$0.803780\pi$
$558$		0			0
$559$		−	2.70042e11i		−	2.76557i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.43101e11	+	8.26195e10i	1.42433	+	0.822335i	0.996665	−	0.0816034i	$-0.0260041\pi$
$563$	1.43101e11	+	8.26195e10i	1.42433	+	0.822335i	0.427662	+	0.903939i	$0.359337\pi$
$564$		0			0
$565$	−2.33336e11	+	1.34717e11i	−2.28975	+	1.32199i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.91033e10	−	1.19690e11i	−0.659249	−	1.14185i	−0.980810	−	0.194964i	$-0.937541\pi$
$569$	−6.91033e10	−	1.19690e11i	−0.659249	−	1.14185i	0.321561	−	0.946889i	$-0.395792\pi$
$570$		0			0
$571$	7.43962e10	−	1.28858e11i	0.699852	−	1.21218i	−0.268665	−	0.963234i	$-0.586583\pi$
$571$	7.43962e10	−	1.28858e11i	0.699852	−	1.21218i	0.968517	−	0.248946i	$-0.0800841\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.99395e11			1.82407
$576$		0			0
$577$	−3.66087e10	−	2.11360e10i	−0.330279	−	0.190687i	0.325686	−	0.945478i	$-0.394405\pi$
$577$	−3.66087e10	−	2.11360e10i	−0.330279	−	0.190687i	−0.655965	+	0.754791i	$0.727738\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.39599e10	−	1.41536e10i	0.122511	−	0.124211i
$582$		0			0
$583$	−1.40251e10	−	2.42921e10i	−0.121403	−	0.210277i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			1.07791e11i			0.907883i	0.891032	+	0.453941i	$0.149982\pi$
$587$			1.07791e11i			0.907883i	−0.891032	+	0.453941i	$0.850018\pi$
$588$		0			0
$589$	−2.79029e10			−0.231840
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.22934e10	+	1.28711e10i	−0.180284	+	0.104087i	−0.587426	−	0.809278i	$-0.699859\pi$
$593$	−2.22934e10	+	1.28711e10i	−0.180284	+	0.104087i	0.407142	+	0.913365i	$0.366525\pi$
$594$		0			0
$595$	2.16665e11	+	2.13700e11i	1.72871	+	1.70505i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.96137e10	−	3.39720e10i	0.152354	−	0.263884i	−0.779739	−	0.626105i	$-0.784648\pi$
$599$	1.96137e10	−	3.39720e10i	0.152354	−	0.263884i	0.932092	+	0.362221i	$0.117981\pi$
$600$		0			0
$601$		−	5.18453e10i		−	0.397385i	−0.980062	−	0.198692i	$-0.936331\pi$
$601$		−	5.18453e10i		−	0.397385i	0.980062	−	0.198692i	$-0.0636695\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.12246e10	+	4.11216e10i	0.531629	+	0.306936i
$606$		0			0
$607$	4.65711e10	−	2.68879e10i	0.343054	−	0.198062i	−0.318568	−	0.947900i	$-0.603202\pi$
$607$	4.65711e10	−	2.68879e10i	0.343054	−	0.198062i	0.661622	+	0.749838i	$0.269869\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	5.68484e10	+	9.84643e10i	0.407900	+	0.706503i
$612$		0			0
$613$	−1.07592e11	+	1.86355e11i	−0.761972	+	1.31977i	0.179860	+	0.983692i	$0.442435\pi$
$613$	−1.07592e11	+	1.86355e11i	−0.761972	+	1.31977i	−0.941833	+	0.336083i	$0.890898\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.50538e10			0.103874			0.0519368	−	0.998650i	$-0.483461\pi$
$617$	1.50538e10			0.103874			0.0519368	+	0.998650i	$0.483461\pi$
$618$		0			0
$619$	−4.10121e10	−	2.36784e10i	−0.279351	−	0.161283i	0.353779	−	0.935329i	$-0.384897\pi$
$619$	−4.10121e10	−	2.36784e10i	−0.279351	−	0.161283i	−0.633129	+	0.774046i	$0.718230\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.17984e10	+	8.28594e9i	0.211083	+	0.0550034i
$624$		0			0
$625$	2.69506e10	+	4.66799e10i	0.176624	+	0.305921i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			2.77745e11i			1.77437i
$630$		0			0
$631$	1.35034e11			0.851777			0.425889	−	0.904776i	$-0.359962\pi$
$631$	1.35034e11			0.851777			0.425889	+	0.904776i	$0.359962\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	8.24333e10	−	4.75929e10i	0.507000	−	0.292717i
$636$		0			0
$637$	−2.61816e11	+	3.60838e9i	−1.59015	+	0.0219157i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.20204e11	+	2.08199e11i	−0.712011	+	1.23324i	0.252090	+	0.967704i	$0.418882\pi$
$641$	−1.20204e11	+	2.08199e11i	−0.712011	+	1.23324i	−0.964101	+	0.265535i	$0.914451\pi$
$642$		0			0
$643$			9.50845e10i			0.556245i	0.960546	+	0.278122i	$0.0897121\pi$
$643$			9.50845e10i			0.556245i	−0.960546	+	0.278122i	$0.910288\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.92646e11	−	1.11224e11i	−1.09937	−	0.634721i	−0.163314	−	0.986574i	$-0.552218\pi$
$647$	−1.92646e11	−	1.11224e11i	−1.09937	−	0.634721i	−0.936055	+	0.351853i	$0.885552\pi$
$648$		0			0
$649$	1.67532e11	−	9.67247e10i	0.944320	−	0.545204i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.76435e11	−	3.05594e11i	−0.970356	−	1.68071i	−0.694479	−	0.719513i	$-0.744365\pi$
$653$	−1.76435e11	−	3.05594e11i	−0.970356	−	1.68071i	−0.275877	−	0.961193i	$-0.588968\pi$
$654$		0			0
$655$	2.03365e11	−	3.52239e11i	1.10487	−	1.91369i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.07537e11			1.10041			0.550204	−	0.835030i	$-0.314550\pi$
$659$	2.07537e11			1.10041			0.550204	+	0.835030i	$0.314550\pi$
$660$		0			0
$661$	−1.63702e11	−	9.45132e10i	−0.857526	−	0.495093i	0.00565708	−	0.999984i	$-0.498199\pi$
$661$	−1.63702e11	−	9.45132e10i	−0.857526	−	0.495093i	−0.863183	+	0.504891i	$0.831533\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	3.57774e11	−	9.85124e10i	1.82946	−	0.503738i
$666$		0			0
$667$	−4.52467e10	−	7.83696e10i	−0.228604	−	0.395954i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	7.08085e10i		−	0.349298i
$672$		0			0
$673$	3.90179e11			1.90197			0.950986	−	0.309234i	$-0.100073\pi$
$673$	3.90179e11			1.90197			0.950986	+	0.309234i	$0.100073\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	4.65394e10	−	2.68695e10i	0.221547	−	0.127910i	−0.385119	−	0.922867i	$-0.625840\pi$
$677$	4.65394e10	−	2.68695e10i	0.221547	−	0.127910i	0.606666	+	0.794957i	$0.292506\pi$
$678$		0			0
$679$	−1.68489e11	+	1.70827e11i	−0.792670	+	0.803670i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.61542e11	+	2.79798e11i	−0.742337	+	1.28577i	0.209091	+	0.977896i	$0.432949\pi$
$683$	−1.61542e11	+	2.79798e11i	−0.742337	+	1.28577i	−0.951428	+	0.307870i	$0.900384\pi$
$684$		0			0
$685$			2.07384e11i			0.941917i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.38649e10	−	3.68724e10i	−0.283390	−	0.163616i
$690$		0			0
$691$	−9.47002e10	+	5.46752e10i	−0.415373	+	0.239816i	−0.693096	−	0.720845i	$-0.743754\pi$
$691$	−9.47002e10	+	5.46752e10i	−0.415373	+	0.239816i	0.277722	+	0.960661i	$0.410420\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.36730e11	+	2.36823e11i	0.586036	+	1.01504i
$696$		0			0
$697$	−2.95479e11	+	5.11785e11i	−1.25198	+	2.16849i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	2.81449e10			0.116554			0.0582770	−	0.998300i	$-0.481439\pi$
$701$	2.81449e10			0.116554			0.0582770	+	0.998300i	$0.481439\pi$
$702$		0			0
$703$	2.93307e11	+	1.69341e11i	1.20088	+	0.693331i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.10772e11	−	4.02297e11i	−0.443355	−	1.61016i
$708$		0			0
$709$	7.57586e10	+	1.31218e11i	0.299811	+	0.519287i	0.976092	−	0.217356i	$-0.0697432\pi$
$709$	7.57586e10	+	1.31218e11i	0.299811	+	0.519287i	−0.676282	+	0.736643i	$0.736410\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	6.22661e10i		−	0.240932i
$714$		0			0
$715$	7.67195e11			2.93550
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.01296e10	+	4.62629e10i	−0.299832	+	0.173108i	−0.642367	−	0.766397i	$-0.722048\pi$
$719$	−8.01296e10	+	4.62629e10i	−0.299832	+	0.173108i	0.342536	+	0.939505i	$0.388714\pi$
$720$		0			0
$721$	4.26887e11	+	1.11237e11i	1.57969	+	0.411632i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−7.24957e10	+	1.25566e11i	−0.262398	+	0.454487i
$726$		0			0
$727$		−	2.82131e11i		−	1.00998i	−0.863125	−	0.504990i	$-0.831496\pi$
$727$		−	2.82131e11i		−	1.00998i	0.863125	−	0.504990i	$-0.168504\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.67505e11	−	3.85384e11i	−2.33768	−	1.34966i
$732$		0			0
$733$	−3.23590e10	+	1.86825e10i	−0.112093	+	0.0647171i	−0.554998	−	0.831851i	$-0.687281\pi$
$733$	−3.23590e10	+	1.86825e10i	−0.112093	+	0.0647171i	0.442905	+	0.896568i	$0.353948\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	8.81885e9	+	1.52747e10i	0.0298911	+	0.0517729i
$738$		0			0
$739$	7.09130e10	−	1.22825e11i	0.237765	−	0.411821i	−0.722307	−	0.691572i	$-0.756918\pi$
$739$	7.09130e10	−	1.22825e11i	0.237765	−	0.411821i	0.960073	+	0.279751i	$0.0902518\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.41839e11			−0.793544			−0.396772	−	0.917917i	$-0.629870\pi$
$743$	−2.41839e11			−0.793544			−0.396772	+	0.917917i	$0.629870\pi$
$744$		0			0
$745$	−2.22882e11	−	1.28681e11i	−0.723518	−	0.417723i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.57054e9	+	2.52153e10i	−0.0208773	+	0.0801192i
$750$		0			0
$751$	5.13187e10	+	8.88866e10i	0.161330	+	0.279432i	0.935346	−	0.353734i	$-0.115088\pi$
$751$	5.13187e10	+	8.88866e10i	0.161330	+	0.279432i	−0.774016	+	0.633166i	$0.781755\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			3.37761e10i			0.103949i
$756$		0			0
$757$	4.93451e11			1.50266			0.751330	−	0.659927i	$-0.229413\pi$
$757$	4.93451e11			1.50266			0.751330	+	0.659927i	$0.229413\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.40157e11	−	1.96390e11i	1.01424	−	0.585572i	0.101810	−	0.994804i	$-0.467537\pi$
$761$	3.40157e11	−	1.96390e11i	1.01424	−	0.585572i	0.912430	+	0.409232i	$0.134203\pi$
$762$		0			0
$763$	3.94973e11	−	1.08755e11i	1.16538	−	0.320886i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	2.54293e11	−	4.40448e11i	0.734771	−	1.27266i
$768$		0			0
$769$		−	1.64508e11i		−	0.470414i	−0.971945	−	0.235207i	$-0.924423\pi$
$769$		−	1.64508e11i		−	0.470414i	0.971945	−	0.235207i	$-0.0755768\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.29267e11	−	2.47838e11i	−1.20229	−	0.694143i	−0.241227	−	0.970469i	$-0.577550\pi$
$773$	−4.29267e11	−	2.47838e11i	−1.20229	−	0.694143i	−0.961064	+	0.276325i	$0.910883\pi$
$774$		0			0
$775$	−8.63988e10	+	4.98824e10i	−0.239498	+	0.138274i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.60307e11	+	6.24069e11i	0.978414	+	1.69466i
$780$		0			0
$781$	7.97666e10	−	1.38160e11i	0.214396	−	0.371345i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	1.05004e12			2.76520
$786$		0			0
$787$	5.53284e11	+	3.19439e11i	1.44228	+	0.832700i	0.998002	−	0.0631899i	$-0.0201274\pi$
$787$	5.53284e11	+	3.19439e11i	1.44228	+	0.832700i	0.444277	+	0.895890i	$0.353461\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−4.71092e11	−	4.64644e11i	−1.20337	−	1.18690i
$792$		0			0
$793$	−9.30790e10	−	1.61218e11i	−0.235374	−	0.407680i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			4.06022e10i			0.100627i	0.998733	+	0.0503137i	$0.0160221\pi$
$797$			4.06022e10i			0.100627i	−0.998733	+	0.0503137i	$0.983978\pi$
$798$		0			0
$799$	3.24519e11			0.796257
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.19205e11	+	2.42028e11i	−1.00824	+	0.582108i
$804$		0			0
$805$	2.19834e11	+	7.98384e11i	0.523493	+	1.90120i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.06565e11	+	5.30986e11i	−0.715696	+	1.23962i	0.246994	+	0.969017i	$0.420557\pi$
$809$	−3.06565e11	+	5.30986e11i	−0.715696	+	1.23962i	−0.962690	+	0.270605i	$0.912776\pi$
$810$		0			0
$811$		−	2.56559e11i		−	0.593067i	−0.955023	−	0.296533i	$-0.904169\pi$
$811$		−	2.56559e11i		−	0.593067i	0.955023	−	0.296533i	$-0.0958306\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	9.22689e11	+	5.32715e11i	2.09134	+	1.20744i
$816$		0			0
$817$	−8.13954e11	+	4.69936e11i	−1.82689	+	1.05475i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	2.02568e11	+	3.50858e11i	0.445859	+	0.772251i	0.998112	−	0.0614260i	$-0.0195648\pi$
$821$	2.02568e11	+	3.50858e11i	0.445859	+	0.772251i	−0.552252	+	0.833677i	$0.686231\pi$
$822$		0			0
$823$	−1.02225e11	+	1.77059e11i	−0.222821	+	0.385938i	−0.955664	−	0.294461i	$-0.904860\pi$
$823$	−1.02225e11	+	1.77059e11i	−0.222821	+	0.385938i	0.732842	+	0.680399i	$0.238193\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.08149e10			−0.108635			−0.0543174	−	0.998524i	$-0.517298\pi$
$827$	−5.08149e10			−0.108635			−0.0543174	+	0.998524i	$0.517298\pi$
$828$		0			0
$829$	−3.06253e11	−	1.76815e11i	−0.648428	−	0.374370i	0.139426	−	0.990233i	$-0.455474\pi$
$829$	−3.06253e11	−	1.76815e11i	−0.648428	−	0.374370i	−0.787854	+	0.615862i	$0.788808\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−3.64725e11	+	6.52321e11i	−0.757506	+	1.35482i
$834$		0			0
$835$	2.07705e11	+	3.59756e11i	0.427269	+	0.740051i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	6.60899e10i		−	0.133379i	−0.997774	−	0.0666895i	$-0.978756\pi$
$839$		−	6.60899e10i		−	0.133379i	0.997774	−	0.0666895i	$-0.0212437\pi$
$840$		0			0
$841$	−4.34443e11			−0.868459
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.05609e12	−	6.09731e11i	2.07144	−	1.19595i
$846$		0			0
$847$	−5.09294e10	+	1.95448e11i	−0.0989544	+	0.379750i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−3.77890e11	+	6.54524e11i	−0.720521	+	1.24798i
$852$		0			0
$853$		−	8.64257e11i		−	1.63248i	−0.577716	−	0.816238i	$-0.696056\pi$
$853$		−	8.64257e11i		−	1.63248i	0.577716	−	0.816238i	$-0.303944\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.11573e11	−	3.53092e11i	−1.13377	−	0.654582i	−0.188890	−	0.981998i	$-0.560489\pi$
$857$	−6.11573e11	−	3.53092e11i	−1.13377	−	0.654582i	−0.944880	+	0.327416i	$0.893822\pi$
$858$		0			0
$859$	3.43234e11	−	1.98166e11i	0.630401	−	0.363962i	−0.150506	−	0.988609i	$-0.548090\pi$
$859$	3.43234e11	−	1.98166e11i	0.630401	−	0.363962i	0.780908	+	0.624647i	$0.214757\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.59916e11	+	4.50188e11i	0.468586	+	0.811616i	0.999355	−	0.0359010i	$-0.0114301\pi$
$863$	2.59916e11	+	4.50188e11i	0.468586	+	0.811616i	−0.530769	+	0.847517i	$0.678097\pi$
$864$		0			0
$865$	−3.19900e11	+	5.54083e11i	−0.571413	+	0.989716i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.22955e10			−0.0566321
$870$		0			0
$871$	4.01577e10	+	2.31851e10i	0.0697744	+	0.0402843i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.87804e11	−	2.91798e11i	0.490981	−	0.497794i
$876$		0			0
$877$	1.86776e11	+	3.23505e11i	0.315735	+	0.546868i	0.979593	−	0.200990i	$-0.0644157\pi$
$877$	1.86776e11	+	3.23505e11i	0.315735	+	0.546868i	−0.663859	+	0.747858i	$0.731082\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	4.57361e11i		−	0.759198i	−0.925151	−	0.379599i	$-0.876062\pi$
$881$		−	4.57361e11i		−	0.759198i	0.925151	−	0.379599i	$-0.123938\pi$
$882$		0			0
$883$	−5.90083e11			−0.970668			−0.485334	−	0.874329i	$-0.661302\pi$
$883$	−5.90083e11			−0.970668			−0.485334	+	0.874329i	$0.661302\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.11693e11	+	3.53161e11i	−0.988187	+	0.570530i	−0.904732	−	0.425981i	$-0.859929\pi$
$887$	−6.11693e11	+	3.53161e11i	−0.988187	+	0.570530i	−0.0834554	+	0.996512i	$0.526596\pi$
$888$		0			0
$889$	1.66428e11	+	1.64150e11i	0.266453	+	0.262806i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.97859e11	−	3.42702e11i	0.311136	−	0.538903i
$894$		0			0
$895$		−	1.76335e12i		−	2.74819i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.92113e10	+	2.26386e10i	0.0600305	+	0.0346587i
$900$		0			0
$901$	−1.82286e11	+	1.05243e11i	−0.276602	+	0.159696i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.42235e11	−	1.11238e12i	−0.957413	−	1.65829i
$906$		0			0
$907$	3.42244e11	−	5.92785e11i	0.505717	−	0.875927i	−0.494262	−	0.869313i	$-0.664561\pi$
$907$	3.42244e11	−	5.92785e11i	0.505717	−	0.875927i	0.999978	−	0.00661355i	$-0.00210517\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.89093e11			−1.29084			−0.645422	−	0.763827i	$-0.723318\pi$
$911$	−8.89093e11			−1.29084			−0.645422	+	0.763827i	$0.723318\pi$
$912$		0			0
$913$	−1.23881e11	−	7.15228e10i	−0.178288	−	0.102935i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	9.66583e11	+	2.51870e11i	1.36698	+	0.356204i
$918$		0			0
$919$	−3.07140e11	−	5.31983e11i	−0.430601	−	0.745822i	0.566324	−	0.824182i	$-0.308365\pi$
$919$	−3.07140e11	−	5.31983e11i	−0.430601	−	0.745822i	−0.996925	+	0.0783601i	$0.975032\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	4.19418e11i		−	0.577884i
$924$		0			0
$925$	1.21093e12			1.65407
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.20333e11	+	1.27209e11i	−0.295813	+	0.170787i	−0.640560	−	0.767908i	$-0.721298\pi$
$929$	−2.20333e11	+	1.27209e11i	−0.295813	+	0.170787i	0.344748	+	0.938695i	$0.387964\pi$
$930$		0			0
$931$	4.66498e11	+	7.82880e11i	0.620942	+	1.04207i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.09488e12	−	1.89639e12i	1.43259	−	2.48132i
$936$		0			0
$937$		−	8.86048e11i		−	1.14947i	−0.818338	−	0.574737i	$-0.805104\pi$
$937$		−	8.86048e11i		−	1.14947i	0.818338	−	0.574737i	$-0.194896\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.08049e11	−	1.77852e11i	−0.392882	−	0.226830i	0.290526	−	0.956867i	$-0.406170\pi$
$941$	−3.08049e11	−	1.77852e11i	−0.392882	−	0.226830i	−0.683408	+	0.730037i	$0.739503\pi$
$942$		0			0
$943$	−1.39263e12	+	8.04036e11i	−1.76112	+	1.01678i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.89968e11	−	6.75445e11i	−0.484875	−	0.839828i	0.514974	−	0.857206i	$-0.327801\pi$
$947$	−3.89968e11	−	6.75445e11i	−0.484875	−	0.839828i	−0.999849	+	0.0173780i	$0.994468\pi$
$948$		0			0
$949$	−6.36300e11	+	1.10210e12i	−0.784508	+	1.35881i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.36658e12			−1.65678			−0.828389	−	0.560154i	$-0.810742\pi$
$953$	−1.36658e12			−1.65678			−0.828389	+	0.560154i	$0.810742\pi$
$954$		0			0
$955$	−2.17644e12	−	1.25657e12i	−2.61658	−	1.51068i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.91025e11	+	1.35203e11i	−0.580536	+	0.159850i
$960$		0			0
$961$	−4.10868e11	−	7.11645e11i	−0.481736	−	0.834392i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			1.53832e12i			1.77393i
$966$		0			0
$967$	1.53907e12			1.76016			0.880082	−	0.474823i	$-0.157488\pi$
$967$	1.53907e12			1.76016			0.880082	+	0.474823i	$0.157488\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.98525e9	−	3.45559e9i	0.00673295	−	0.00388727i	−0.496630	−	0.867962i	$-0.665429\pi$
$971$	5.98525e9	−	3.45559e9i	0.00673295	−	0.00388727i	0.503363	+	0.864075i	$0.332096\pi$
$972$		0			0
$973$	−4.71589e11	+	4.78133e11i	−0.526153	+	0.533454i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−7.22091e11	+	1.25070e12i	−0.792526	+	1.37270i	0.131872	+	0.991267i	$0.457901\pi$
$977$	−7.22091e11	+	1.25070e12i	−0.792526	+	1.37270i	−0.924398	+	0.381429i	$0.875432\pi$
$978$		0			0
$979$		−	2.36448e11i		−	0.257398i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.20611e12	+	6.96348e11i	1.29173	+	0.745783i	0.978961	−	0.204045i	$-0.0654090\pi$
$983$	1.20611e12	+	6.96348e11i	1.29173	+	0.745783i	0.312772	+	0.949828i	$0.398742\pi$
$984$		0			0
$985$	−2.08932e12	+	1.20627e12i	−2.21953	+	1.28145i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−1.04868e12	−	1.81636e12i	−1.09612	−	1.89853i
$990$		0			0
$991$	−3.13321e11	+	5.42688e11i	−0.324859	+	0.562673i	−0.981484	−	0.191545i	$-0.938650\pi$
$991$	−3.13321e11	+	5.42688e11i	−0.324859	+	0.562673i	0.656625	+	0.754218i	$0.271984\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.53094e11			0.972397
$996$		0			0
$997$	−1.26032e12	−	7.27645e11i	−1.27556	−	0.736443i	−0.299528	−	0.954088i	$-0.596829\pi$
$997$	−1.26032e12	−	7.27645e11i	−1.27556	−	0.736443i	−0.976028	+	0.217645i	$0.930163\pi$
$998$		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.73.2	✓	20
3.2	odd	2	inner	252.9.z.e.73.9	yes	20
7.5	odd	6	inner	252.9.z.e.145.2	yes	20
21.5	even	6	inner	252.9.z.e.145.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.9.z.e.73.2	✓	20	1.1	even	1	trivial
252.9.z.e.73.9	yes	20	3.2	odd	2	inner
252.9.z.e.145.2	yes	20	7.5	odd	6	inner
252.9.z.e.145.9	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)

\(f(q)\)	\(=\)	\(q+(-846.691 + 488.837i) q^{5} +(-1709.42 - 1686.02i) q^{7} +O(q^{10})\)	\(q+(-846.691 + 488.837i) q^{5} +(-1709.42 - 1686.02i) q^{7} +(-8638.29 + 14962.0i) q^{11} +45420.7i q^{13} +(112273. + 64821.0i) q^{17} +(136906. - 79042.6i) q^{19} +(176386. + 305510. i) q^{23} +(282611. - 489497. i) q^{25} -256521. q^{29} +(-152858. - 88252.6i) q^{31} +(2.27154e6 + 591913. i) q^{35} +(1.07120e6 + 1.85537e6i) q^{37} +4.55839e6i q^{41} -5.94536e6 q^{43} +(2.16783e6 - 1.25160e6i) q^{47} +(79443.6 + 5.76425e6i) q^{49} +(-811797. + 1.40607e6i) q^{53} -1.68909e7i q^{55} +(-9.69707e6 - 5.59861e6i) q^{59} +(-3.54943e6 + 2.04926e6i) q^{61} +(-2.22033e7 - 3.84573e7i) q^{65} +(510451. - 884128. i) q^{67} -9.23408e6 q^{71} +(2.42644e7 + 1.40090e7i) q^{73} +(3.99927e7 - 1.10119e7i) q^{77} +(934661. + 1.61888e6i) q^{79} +8.27975e6i q^{83} -1.26748e8 q^{85} +(-1.18525e7 + 6.84303e6i) q^{89} +(7.65804e7 - 7.76431e7i) q^{91} +(-7.72779e7 + 1.33849e8i) q^{95} -9.99327e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 7238 q^{7}+O(q^{10}) \) 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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