LMFDB - Embedded newform 252.9.z.e.73.1

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			73.1
Root			$590.770 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.e.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-885.405 + 511.189i) q^{5} +(765.093 + 2275.84i) q^{7} +O(q^{10})$	$q+(-885.405 + 511.189i) q^{5} +(765.093 + 2275.84i) q^{7} +(-89.3699 + 154.793i) q^{11} -19474.4i q^{13} +(-64245.6 - 37092.2i) q^{17} +(4266.93 - 2463.51i) q^{19} +(-96237.7 - 166689. i) q^{23} +(327315. - 566927. i) q^{25} -1.17929e6 q^{29} +(-950064. - 548520. i) q^{31} +(-1.84080e6 - 1.62393e6i) q^{35} +(1.46795e6 + 2.54256e6i) q^{37} +71941.4i q^{41} +634388. q^{43} +(-190090. + 109749. i) q^{47} +(-4.59407e6 + 3.48245e6i) q^{49} +(601096. - 1.04113e6i) q^{53} -182740. i q^{55} +(8.57841e6 + 4.95275e6i) q^{59} +(1.33423e7 - 7.70320e6i) q^{61} +(9.95511e6 + 1.72428e7i) q^{65} +(922496. - 1.59781e6i) q^{67} +3.59965e7 q^{71} +(1.11337e7 + 6.42804e6i) q^{73} +(-420661. - 84960.2i) q^{77} +(-2.23201e7 - 3.86596e7i) q^{79} -2.52746e7i q^{83} +7.58445e7 q^{85} +(-5.07125e7 + 2.92789e7i) q^{89} +(4.43206e7 - 1.48997e7i) q^{91} +(-2.51864e6 + 4.36241e6i) q^{95} +1.08177e8i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−885.405	+	511.189i	−1.41665	+	0.817902i	−0.996003	−	0.0893233i	$-0.971530\pi$
$5$	−885.405	+	511.189i	−1.41665	+	0.817902i	−0.420645	+	0.907225i	$0.638196\pi$
$6$		0			0
$7$	765.093	+	2275.84i	0.318656	+	0.947870i
$7$	765.093	+	2275.84i	0.318656	+	0.947870i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−89.3699	+	154.793i	−0.00610409	+	0.0105726i	−0.869061	−	0.494704i	$-0.835276\pi$
$11$	−89.3699	+	154.793i	−0.00610409	+	0.0105726i	0.862957	+	0.505277i	$0.168610\pi$
$12$		0			0
$13$		−	19474.4i		−	0.681854i	−0.940090	−	0.340927i	$-0.889259\pi$
$13$		−	19474.4i		−	0.681854i	0.940090	−	0.340927i	$-0.110741\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−64245.6	−	37092.2i	−0.769215	−	0.444107i	0.0633793	−	0.997990i	$-0.479812\pi$
$17$	−64245.6	−	37092.2i	−0.769215	−	0.444107i	−0.832595	+	0.553883i	$0.813146\pi$
$18$		0			0
$19$	4266.93	−	2463.51i	0.0327417	−	0.0189034i	−0.483540	−	0.875322i	$-0.660649\pi$
$19$	4266.93	−	2463.51i	0.0327417	−	0.0189034i	0.516281	+	0.856419i	$0.327316\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−96237.7	−	166689.i	−0.343902	−	0.595655i	0.641252	−	0.767330i	$-0.278415\pi$
$23$	−96237.7	−	166689.i	−0.343902	−	0.595655i	−0.985154	+	0.171675i	$0.945082\pi$
$24$		0			0
$25$	327315.	−	566927.i	0.837927	−	1.45133i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.17929e6			−1.66736			−0.833682	−	0.552245i	$-0.813771\pi$
$29$	−1.17929e6			−1.66736			−0.833682	+	0.552245i	$0.813771\pi$
$30$		0			0
$31$	−950064.	−	548520.i	−1.02874	−	0.593944i	−0.112118	−	0.993695i	$-0.535763\pi$
$31$	−950064.	−	548520.i	−1.02874	−	0.593944i	−0.916624	+	0.399751i	$0.869097\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.84080e6	−	1.62393e6i	−1.22669	−	1.08217i
$36$		0			0
$37$	1.46795e6	+	2.54256e6i	0.783256	+	1.35664i	0.930035	+	0.367470i	$0.119776\pi$
$37$	1.46795e6	+	2.54256e6i	0.783256	+	1.35664i	−0.146779	+	0.989169i	$0.546891\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			71941.4i			0.0254591i	0.999919	+	0.0127296i	$0.00405206\pi$
$41$			71941.4i			0.0254591i	−0.999919	+	0.0127296i	$0.995948\pi$
$42$		0			0
$43$	634388.			0.185559			0.0927793	−	0.995687i	$-0.470425\pi$
$43$	634388.			0.185559			0.0927793	+	0.995687i	$0.470425\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−190090.	+	109749.i	−0.0389554	+	0.0224909i	−0.519351	−	0.854561i	$-0.673826\pi$
$47$	−190090.	+	109749.i	−0.0389554	+	0.0224909i	0.480396	+	0.877052i	$0.340493\pi$
$48$		0			0
$49$	−4.59407e6	+	3.48245e6i	−0.796917	+	0.604089i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	601096.	−	1.04113e6i	0.0761798	−	0.131947i	−0.825419	−	0.564521i	$-0.809061\pi$
$53$	601096.	−	1.04113e6i	0.0761798	−	0.131947i	0.901599	+	0.432573i	$0.142394\pi$
$54$		0			0
$55$		−	182740.i		−	0.0199702i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.57841e6	+	4.95275e6i	0.707944	+	0.408732i	0.810299	−	0.586016i	$-0.199305\pi$
$59$	8.57841e6	+	4.95275e6i	0.707944	+	0.408732i	−0.102355	+	0.994748i	$0.532638\pi$
$60$		0			0
$61$	1.33423e7	−	7.70320e6i	0.963635	−	0.556355i	0.0663454	−	0.997797i	$-0.478866\pi$
$61$	1.33423e7	−	7.70320e6i	0.963635	−	0.556355i	0.897290	+	0.441442i	$0.145533\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9.95511e6	+	1.72428e7i	0.557690	+	0.965947i
$66$		0			0
$67$	922496.	−	1.59781e6i	0.0457789	−	0.0792913i	−0.842228	−	0.539121i	$-0.818756\pi$
$67$	922496.	−	1.59781e6i	0.0457789	−	0.0792913i	0.888007	+	0.459830i	$0.152090\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	3.59965e7			1.41654			0.708268	−	0.705944i	$-0.249477\pi$
$71$	3.59965e7			1.41654			0.708268	+	0.705944i	$0.249477\pi$
$72$		0			0
$73$	1.11337e7	+	6.42804e6i	0.392056	+	0.226354i	0.683051	−	0.730371i	$-0.260653\pi$
$73$	1.11337e7	+	6.42804e6i	0.392056	+	0.226354i	−0.290995	+	0.956725i	$0.593986\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−420661.	−	84960.2i	−0.0119665	−	0.00241687i
$78$		0			0
$79$	−2.23201e7	−	3.86596e7i	−0.573045	−	0.992542i	−0.996251	−	0.0865090i	$-0.972429\pi$
$79$	−2.23201e7	−	3.86596e7i	−0.573045	−	0.992542i	0.423207	−	0.906033i	$-0.360904\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	2.52746e7i		−	0.532564i	−0.963895	−	0.266282i	$-0.914205\pi$
$83$		−	2.52746e7i		−	0.532564i	0.963895	−	0.266282i	$-0.0857953\pi$
$84$		0			0
$85$	7.58445e7			1.45294
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.07125e7	+	2.92789e7i	−0.808267	+	0.466653i	−0.846354	−	0.532621i	$-0.821207\pi$
$89$	−5.07125e7	+	2.92789e7i	−0.808267	+	0.466653i	0.0380869	+	0.999274i	$0.487874\pi$
$90$		0			0
$91$	4.43206e7	−	1.48997e7i	0.646309	−	0.217277i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.51864e6	+	4.36241e6i	−0.0309223	+	0.0535589i
$96$		0			0
$97$			1.08177e8i			1.22193i	0.791657	+	0.610965i	$0.209219\pi$
$97$			1.08177e8i			1.22193i	−0.791657	+	0.610965i	$0.790781\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.42918e8	−	8.25135e7i	−1.37341	−	0.792938i	−0.382054	−	0.924140i	$-0.624783\pi$
$101$	−1.42918e8	−	8.25135e7i	−1.37341	−	0.792938i	−0.991356	+	0.131202i	$0.958116\pi$
$102$		0			0
$103$	−6.72330e6	+	3.88170e6i	−0.0597356	+	0.0344884i	−0.529570	−	0.848266i	$-0.677647\pi$
$103$	−6.72330e6	+	3.88170e6i	−0.0597356	+	0.0344884i	0.469835	+	0.882754i	$0.344314\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.40986e7	−	4.17400e7i	−0.183847	−	0.318432i	0.759340	−	0.650694i	$-0.225522\pi$
$107$	−2.40986e7	−	4.17400e7i	−0.183847	−	0.318432i	−0.943187	+	0.332261i	$0.892188\pi$
$108$		0			0
$109$	8.30456e7	−	1.43839e8i	0.588316	−	1.01899i	−0.406137	−	0.913812i	$-0.633125\pi$
$109$	8.30456e7	−	1.43839e8i	0.588316	−	1.01899i	0.994453	−	0.105181i	$-0.0335421\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.10120e8			−0.675389			−0.337694	−	0.941256i	$-0.609647\pi$
$113$	−1.10120e8			−0.675389			−0.337694	+	0.941256i	$0.609647\pi$
$114$		0			0
$115$	1.70419e8	+	9.83913e7i	0.974375	+	0.562555i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.52620e7	−	1.74592e8i	0.175841	−	0.870634i
$120$		0			0
$121$	1.07163e8	+	1.85613e8i	0.499925	+	0.865896i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			2.69913e8i			1.10557i
$126$		0			0
$127$	4.16647e8			1.60160			0.800798	−	0.598935i	$-0.204409\pi$
$127$	4.16647e8			1.60160			0.800798	+	0.598935i	$0.204409\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	4.35188e8	−	2.51256e8i	1.47772	−	0.853162i	0.478037	−	0.878340i	$-0.341348\pi$
$131$	4.35188e8	−	2.51256e8i	1.47772	−	0.853162i	0.999683	+	0.0251777i	$0.00801514\pi$
$132$		0			0
$133$	8.87114e6	+	7.82601e6i	0.0283513	+	0.0250112i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.63136e8	+	4.55764e8i	−0.746960	+	1.29377i	0.202313	+	0.979321i	$0.435154\pi$
$137$	−2.63136e8	+	4.55764e8i	−0.746960	+	1.29377i	−0.949273	+	0.314452i	$0.898179\pi$
$138$		0			0
$139$		−	4.75267e8i		−	1.27315i	−0.771216	−	0.636574i	$-0.780351\pi$
$139$		−	4.75267e8i		−	1.27315i	0.771216	−	0.636574i	$-0.219649\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.01451e6	+	1.74043e6i	0.00720896	+	0.00416210i
$144$		0			0
$145$	1.04415e9	−	6.02842e8i	2.36207	−	1.36374i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.89018e8	+	3.27389e8i	0.383494	+	0.664232i	0.991559	−	0.129656i	$-0.0413872\pi$
$149$	1.89018e8	+	3.27389e8i	0.383494	+	0.664232i	−0.608065	+	0.793887i	$0.708054\pi$
$150$		0			0
$151$	9.48044e7	−	1.64206e8i	0.182356	−	0.315850i	−0.760326	−	0.649541i	$-0.774961\pi$
$151$	9.48044e7	−	1.64206e8i	0.182356	−	0.315850i	0.942682	+	0.333691i	$0.108294\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.12159e9			1.94315
$156$		0			0
$157$	4.56334e8	+	2.63464e8i	0.751076	+	0.433634i	0.826083	−	0.563549i	$-0.190564\pi$
$157$	4.56334e8	+	2.63464e8i	0.751076	+	0.433634i	−0.0750066	+	0.997183i	$0.523898\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	3.05725e8	−	3.46554e8i	0.455017	−	0.515783i
$162$		0			0
$163$	3.83633e8	+	6.64472e8i	0.543457	+	0.941296i	0.998702	+	0.0509295i	$0.0162184\pi$
$163$	3.83633e8	+	6.64472e8i	0.543457	+	0.941296i	−0.455245	+	0.890366i	$0.650448\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	3.12292e8i		−	0.401508i	−0.979642	−	0.200754i	$-0.935661\pi$
$167$		−	3.12292e8i		−	0.401508i	0.979642	−	0.200754i	$-0.0643392\pi$
$168$		0			0
$169$	4.36477e8			0.535075
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−7.88275e7	+	4.55111e7i	−0.0880022	+	0.0508081i	−0.543355	−	0.839503i	$-0.682846\pi$
$173$	−7.88275e7	+	4.55111e7i	−0.0880022	+	0.0508081i	0.455353	+	0.890311i	$0.349513\pi$
$174$		0			0
$175$	1.54066e9	+	3.11165e8i	1.64269	+	0.331771i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−9.27225e8	+	1.60600e9i	−0.903177	+	1.56435i	−0.0798315	+	0.996808i	$0.525438\pi$
$179$	−9.27225e8	+	1.60600e9i	−0.903177	+	1.56435i	−0.823346	+	0.567540i	$0.807895\pi$
$180$		0			0
$181$			4.07233e8i			0.379428i	0.981839	+	0.189714i	$0.0607560\pi$
$181$			4.07233e8i			0.379428i	−0.981839	+	0.189714i	$0.939244\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.59946e9	−	1.50080e9i	−2.21920	−	1.28125i
$186$		0			0
$187$	1.14833e7	−	6.62986e6i	0.00939071	−	0.00542173i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.98416e7	+	1.03649e8i	0.0449645	+	0.0778808i	0.887632	−	0.460554i	$-0.152349\pi$
$191$	5.98416e7	+	1.03649e8i	0.0449645	+	0.0778808i	−0.842667	+	0.538435i	$0.819016\pi$
$192$		0			0
$193$	4.84829e8	−	8.39749e8i	0.349429	−	0.605230i	−0.636719	−	0.771096i	$-0.719709\pi$
$193$	4.84829e8	−	8.39749e8i	0.349429	−	0.605230i	0.986148	+	0.165867i	$0.0530421\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.18199e9			0.784784			0.392392	−	0.919798i	$-0.371648\pi$
$197$	1.18199e9			0.784784			0.392392	+	0.919798i	$0.371648\pi$
$198$		0			0
$199$	1.76730e9	+	1.02035e9i	1.12693	+	0.650633i	0.943161	−	0.332336i	$-0.107837\pi$
$199$	1.76730e9	+	1.02035e9i	1.12693	+	0.650633i	0.183769	+	0.982969i	$0.441170\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.02270e8	−	2.68388e9i	−0.531315	−	1.58044i
$204$		0			0
$205$	−3.67756e7	−	6.36973e7i	−0.0208231	−	0.0360666i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			880655.i			0.000461552i
$210$		0			0
$211$	2.10575e9			1.06237			0.531186	−	0.847255i	$-0.321746\pi$
$211$	2.10575e9			1.06237			0.531186	+	0.847255i	$0.321746\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−5.61690e8	+	3.24292e8i	−0.262871	+	0.151769i
$216$		0			0
$217$	5.21455e8	−	2.58186e9i	0.235168	−	1.16438i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.22350e8	+	1.25115e9i	−0.302816	+	0.524493i
$222$		0			0
$223$		−	1.37045e9i		−	0.554172i	−0.960845	−	0.277086i	$-0.910631\pi$
$223$		−	1.37045e9i		−	0.554172i	0.960845	−	0.277086i	$-0.0893687\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.28035e9	−	1.89391e9i	−1.23543	−	0.713274i	−0.267270	−	0.963622i	$-0.586122\pi$
$227$	−3.28035e9	−	1.89391e9i	−1.23543	−	0.713274i	−0.968156	+	0.250348i	$0.919455\pi$
$228$		0			0
$229$	1.41344e7	−	8.16050e6i	0.00513967	−	0.00296739i	−0.497428	−	0.867505i	$-0.665722\pi$
$229$	1.41344e7	−	8.16050e6i	0.00513967	−	0.00296739i	0.502568	+	0.864538i	$0.332389\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.88764e9	+	5.00154e9i	0.979760	+	1.69699i	0.663237	+	0.748409i	$0.269182\pi$
$233$	2.88764e9	+	5.00154e9i	0.979760	+	1.69699i	0.316523	+	0.948585i	$0.397485\pi$
$234$		0			0
$235$	1.12204e8	−	1.94344e8i	0.0367907	−	0.0637234i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	4.29837e9			1.31738			0.658692	−	0.752413i	$-0.271110\pi$
$239$	4.29837e9			1.31738			0.658692	+	0.752413i	$0.271110\pi$
$240$		0			0
$241$	6.66397e8	+	3.84744e8i	0.197544	+	0.114052i	0.595510	−	0.803348i	$-0.296950\pi$
$241$	6.66397e8	+	3.84744e8i	0.197544	+	0.114052i	−0.397965	+	0.917401i	$0.630284\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.28742e9	−	5.43182e9i	0.634865	−	1.50758i
$246$		0			0
$247$	−4.79755e7	−	8.30960e7i	−0.0128894	−	0.0223250i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			7.09715e9i			1.78809i	0.447979	+	0.894044i	$0.352144\pi$
$251$			7.09715e9i			1.78809i	−0.447979	+	0.894044i	$0.647856\pi$
$252$		0			0
$253$	3.44030e7			0.00839682
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.26184e9	−	3.61527e9i	1.43539	−	0.828721i	0.437863	−	0.899042i	$-0.355735\pi$
$257$	6.26184e9	−	3.61527e9i	1.43539	−	0.828721i	0.997524	+	0.0703204i	$0.0224022\pi$
$258$		0			0
$259$	−4.66334e9	+	5.28610e9i	−1.03633	+	1.17473i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.10490e9	+	5.37785e9i	−0.648971	+	1.12405i	0.334398	+	0.942432i	$0.391467\pi$
$263$	−3.10490e9	+	5.37785e9i	−0.648971	+	1.12405i	−0.983369	+	0.181619i	$0.941866\pi$
$264$		0			0
$265$			1.22909e9i			0.249231i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.16864e9	−	6.74713e8i	−0.223188	−	0.128858i	0.384238	−	0.923234i	$-0.374464\pi$
$269$	−1.16864e9	−	6.74713e8i	−0.223188	−	0.128858i	−0.607426	+	0.794377i	$0.707798\pi$
$270$		0			0
$271$	9.80116e8	−	5.65870e8i	0.181719	−	0.104916i	−0.406381	−	0.913704i	$-0.633209\pi$
$271$	9.80116e8	−	5.65870e8i	0.181719	−	0.104916i	0.588100	+	0.808788i	$0.299876\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	5.85043e7	+	1.01332e8i	0.0102296	+	0.0177181i
$276$		0			0
$277$	−1.79327e9	+	3.10604e9i	−0.304599	+	0.527580i	−0.977172	−	0.212450i	$-0.931856\pi$
$277$	−1.79327e9	+	3.10604e9i	−0.304599	+	0.527580i	0.672573	+	0.740030i	$0.265189\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.75399e9			0.922877			0.461439	−	0.887172i	$-0.347333\pi$
$281$	5.75399e9			0.922877			0.461439	+	0.887172i	$0.347333\pi$
$282$		0			0
$283$	−9.95966e9	−	5.75021e9i	−1.55274	−	0.896475i	−0.997917	−	0.0645064i	$-0.979453\pi$
$283$	−9.95966e9	−	5.75021e9i	−1.55274	−	0.896475i	−0.554823	−	0.831969i	$-0.687214\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.63727e8	+	5.50419e7i	−0.0241320	+	0.00811270i
$288$		0			0
$289$	−7.36211e8	−	1.27515e9i	−0.105538	−	0.182798i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	1.07373e10i		−	1.45688i	−0.685108	−	0.728442i	$-0.740245\pi$
$293$		−	1.07373e10i		−	1.45688i	0.685108	−	0.728442i	$-0.259755\pi$
$294$		0			0
$295$	−1.01272e10			−1.33721
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.24617e9	+	1.87418e9i	−0.406150	+	0.234491i
$300$		0			0
$301$	4.85366e8	+	1.44376e9i	0.0591293	+	0.175886i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.87558e9	+	1.36409e10i	−0.910088	+	1.57632i
$306$		0			0
$307$			8.74603e9i			0.984595i	0.870427	+	0.492297i	$0.163843\pi$
$307$			8.74603e9i			0.984595i	−0.870427	+	0.492297i	$0.836157\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.53768e10	−	8.87781e9i	−1.64371	−	0.948996i	−0.979499	−	0.201449i	$-0.935435\pi$
$311$	−1.53768e10	−	8.87781e9i	−1.64371	−	0.948996i	−0.664210	−	0.747546i	$-0.731232\pi$
$312$		0			0
$313$	−6.41291e9	+	3.70250e9i	−0.668156	+	0.385760i	−0.795378	−	0.606114i	$-0.792727\pi$
$313$	−6.41291e9	+	3.70250e9i	−0.668156	+	0.385760i	0.127222	+	0.991874i	$0.459394\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−5.94697e9	−	1.03005e10i	−0.588924	−	1.02005i	−0.994374	−	0.105928i	$-0.966219\pi$
$317$	−5.94697e9	−	1.03005e10i	−0.588924	−	1.02005i	0.405450	−	0.914117i	$-0.367115\pi$
$318$		0			0
$319$	1.05393e8	−	1.82547e8i	0.0101777	−	0.0176283i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−3.65509e8			−0.0335805
$324$		0			0
$325$	−1.10406e10	−	6.37428e9i	−0.989597	−	0.571344i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−3.95206e8	−	3.48646e8i	−0.0337319	−	0.0297578i
$330$		0			0
$331$	−6.62889e9	−	1.14816e10i	−0.552241	−	0.956510i	−0.998112	−	0.0614129i	$-0.980439\pi$
$331$	−6.62889e9	−	1.14816e10i	−0.552241	−	0.956510i	0.445871	−	0.895097i	$-0.352894\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			1.88628e9i			0.149771i
$336$		0			0
$337$	−5.54131e8			−0.0429628			−0.0214814	−	0.999769i	$-0.506838\pi$
$337$	−5.54131e8			−0.0429628			−0.0214814	+	0.999769i	$0.506838\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	1.69814e8	−	9.80424e7i	0.0125591	−	0.00725097i
$342$		0			0
$343$	−1.14404e10	−	7.79095e9i	−0.826540	−	0.562878i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.46399e9	−	1.29280e10i	0.514818	−	0.891690i	−0.485035	−	0.874495i	$-0.661193\pi$
$347$	7.46399e9	−	1.29280e10i	0.514818	−	0.891690i	0.999852	−	0.0171952i	$-0.00547366\pi$
$348$		0			0
$349$		−	1.96683e10i		−	1.32576i	−0.748724	−	0.662882i	$-0.769333\pi$
$349$		−	1.96683e10i		−	1.32576i	0.748724	−	0.662882i	$-0.230667\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.25411e10	+	7.24064e9i	0.807679	+	0.466313i	0.846149	−	0.532946i	$-0.178915\pi$
$353$	1.25411e10	+	7.24064e9i	0.807679	+	0.466313i	−0.0384705	+	0.999260i	$0.512249\pi$
$354$		0			0
$355$	−3.18715e10	+	1.84010e10i	−2.00673	+	1.15859i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.20020e9	+	1.07391e10i	0.373274	+	0.646530i	0.990067	−	0.140595i	$-0.0449017\pi$
$359$	6.20020e9	+	1.07391e10i	0.373274	+	0.646530i	−0.616793	+	0.787126i	$0.711568\pi$
$360$		0			0
$361$	−8.47964e9	+	1.46872e10i	−0.499285	+	0.864788i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.31438e10			−0.740540
$366$		0			0
$367$	2.27624e10	+	1.31419e10i	1.25474	+	0.724423i	0.972047	−	0.234788i	$-0.0754395\pi$
$367$	2.27624e10	+	1.31419e10i	1.25474	+	0.724423i	0.282691	+	0.959211i	$0.408773\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	2.82933e9	+	5.71436e8i	0.149344	+	0.0301628i
$372$		0			0
$373$	−2.39767e9	−	4.15288e9i	−0.123866	−	0.214543i	0.797423	−	0.603421i	$-0.206196\pi$
$373$	−2.39767e9	−	4.15288e9i	−0.123866	−	0.214543i	−0.921289	+	0.388878i	$0.872863\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			2.29661e10i			1.13690i
$378$		0			0
$379$	−2.55248e10			−1.23710			−0.618551	−	0.785744i	$-0.712280\pi$
$379$	−2.55248e10			−1.23710			−0.618551	+	0.785744i	$0.712280\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.05386e10	−	6.08448e9i	0.489767	−	0.282767i	−0.234711	−	0.972065i	$-0.575414\pi$
$383$	1.05386e10	−	6.08448e9i	0.489767	−	0.282767i	0.724478	+	0.689298i	$0.242081\pi$
$384$		0			0
$385$	4.15886e8	−	1.39813e8i	0.0189291	−	0.00636361i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.13562e10	−	1.96696e10i	0.495948	−	0.859008i	−0.504041	−	0.863680i	$-0.668154\pi$
$389$	1.13562e10	−	1.96696e10i	0.495948	−	0.859008i	0.999989	+	0.00467229i	$0.00148724\pi$
$390$		0			0
$391$			1.42787e10i			0.610916i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	3.95247e10	+	2.28196e10i	1.62360	+	0.937388i
$396$		0			0
$397$	5.08354e8	−	2.93498e8i	0.0204646	−	0.0118153i	−0.489733	−	0.871873i	$-0.662906\pi$
$397$	5.08354e8	−	2.93498e8i	0.0204646	−	0.0118153i	0.510197	+	0.860057i	$0.329572\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	5.10243e9	+	8.83767e9i	0.197333	+	0.341791i	0.947663	−	0.319273i	$-0.103439\pi$
$401$	5.10243e9	+	8.83767e9i	0.197333	+	0.341791i	−0.750330	+	0.661064i	$0.770105\pi$
$402$		0			0
$403$	−1.06821e10	+	1.85020e10i	−0.404983	+	0.701452i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.24762e8			−0.0191243
$408$		0			0
$409$	−4.17938e10	−	2.41297e10i	−1.49355	−	0.862299i	−0.493573	−	0.869704i	$-0.664309\pi$
$409$	−4.17938e10	−	2.41297e10i	−1.49355	−	0.862299i	−0.999973	+	0.00740547i	$0.997643\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.70837e9	+	2.33124e10i	−0.161834	+	0.801284i
$414$		0			0
$415$	1.29201e10	+	2.23783e10i	0.435585	+	0.754456i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	2.77178e10i		−	0.899296i	−0.893206	−	0.449648i	$-0.851549\pi$
$419$		−	2.77178e10i		−	0.899296i	0.893206	−	0.449648i	$-0.148451\pi$
$420$		0			0
$421$	1.48421e10			0.472461			0.236231	−	0.971697i	$-0.424088\pi$
$421$	1.48421e10			0.472461			0.236231	+	0.971697i	$0.424088\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.20572e10	+	2.42817e10i	−1.28909	+	0.744258i
$426$		0			0
$427$	2.77394e10	+	2.44713e10i	0.834421	+	0.736116i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	3.21503e10	−	5.56860e10i	0.931700	−	1.61375i	0.151285	−	0.988490i	$-0.451659\pi$
$431$	3.21503e10	−	5.56860e10i	0.931700	−	1.61375i	0.780415	−	0.625262i	$-0.215008\pi$
$432$		0			0
$433$		−	3.96724e10i		−	1.12859i	−0.825573	−	0.564296i	$-0.809148\pi$
$433$		−	3.96724e10i		−	1.12859i	0.825573	−	0.564296i	$-0.190852\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−8.21279e8	−	4.74165e8i	−0.0225198	−	0.0130018i
$438$		0			0
$439$	3.43439e10	−	1.98284e10i	0.924679	−	0.533864i	0.0395542	−	0.999217i	$-0.487406\pi$
$439$	3.43439e10	−	1.98284e10i	0.924679	−	0.533864i	0.885125	+	0.465354i	$0.154073\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.44772e10	−	2.50752e10i	−0.375897	−	0.651072i	0.614564	−	0.788867i	$-0.289332\pi$
$443$	−1.44772e10	−	2.50752e10i	−0.375897	−	0.651072i	−0.990461	+	0.137795i	$0.955999\pi$
$444$		0			0
$445$	2.99340e10	−	5.18473e10i	0.763353	−	1.32217i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.19948e10			−1.52535			−0.762675	−	0.646782i	$-0.776115\pi$
$449$	−6.19948e10			−1.52535			−0.762675	+	0.646782i	$0.776115\pi$
$450$		0			0
$451$	−1.11360e7	−	6.42940e6i	−0.000269169	−	0.000155405i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.16251e10	+	3.58485e10i	−0.737882	+	0.836422i
$456$		0			0
$457$	−2.46381e9	−	4.26744e9i	−0.0564861	−	0.0978368i	0.836400	−	0.548120i	$-0.184656\pi$
$457$	−2.46381e9	−	4.26744e9i	−0.0564861	−	0.0978368i	−0.892886	+	0.450283i	$0.851323\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	3.17242e10i		−	0.702404i	−0.936300	−	0.351202i	$-0.885773\pi$
$461$		−	3.17242e10i		−	0.702404i	0.936300	−	0.351202i	$-0.114227\pi$
$462$		0			0
$463$	4.40978e9			0.0959606			0.0479803	−	0.998848i	$-0.484722\pi$
$463$	4.40978e9			0.0959606			0.0479803	+	0.998848i	$0.484722\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−3.65266e10	+	2.10887e10i	−0.767966	+	0.443386i	−0.832149	−	0.554553i	$-0.812889\pi$
$467$	−3.65266e10	+	2.10887e10i	−0.767966	+	0.443386i	0.0641824	+	0.997938i	$0.479556\pi$
$468$		0			0
$469$	4.34215e9	+	8.76978e8i	0.0897456	+	0.0181258i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−5.66952e7	+	9.81990e7i	−0.00113267	+	0.00196183i
$474$		0			0
$475$		−	3.22538e9i		−	0.0633587i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	4.82676e10	+	2.78673e10i	0.916882	+	0.529362i	0.882639	−	0.470052i	$-0.155765\pi$
$479$	4.82676e10	+	2.78673e10i	0.916882	+	0.529362i	0.0342429	+	0.999414i	$0.489098\pi$
$480$		0			0
$481$	4.95149e10	−	2.85875e10i	0.925030	−	0.534066i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−5.52987e10	−	9.57802e10i	−0.999420	−	1.73105i
$486$		0			0
$487$	−1.30429e10	+	2.25910e10i	−0.231877	+	0.401623i	−0.958361	−	0.285561i	$-0.907820\pi$
$487$	−1.30429e10	+	2.25910e10i	−0.231877	+	0.401623i	0.726483	+	0.687184i	$0.241153\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.26082e10			−0.561049			−0.280525	−	0.959847i	$-0.590508\pi$
$491$	−3.26082e10			−0.561049			−0.280525	+	0.959847i	$0.590508\pi$
$492$		0			0
$493$	7.57645e10	+	4.37427e10i	1.28256	+	0.740487i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.75407e10	+	8.19223e10i	0.451387	+	1.34269i
$498$		0			0
$499$	2.19192e10	+	3.79653e10i	0.353528	+	0.612328i	0.986865	−	0.161548i	$-0.0516487\pi$
$499$	2.19192e10	+	3.79653e10i	0.353528	+	0.612328i	−0.633337	+	0.773876i	$0.718315\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	6.00135e10i		−	0.937513i	−0.883327	−	0.468756i	$-0.844702\pi$
$503$		−	6.00135e10i		−	0.937513i	0.883327	−	0.468756i	$-0.155298\pi$
$504$		0			0
$505$	1.68720e11			2.59418
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.52781e10	−	3.76883e10i	0.972514	−	0.561481i	0.0725126	−	0.997367i	$-0.476898\pi$
$509$	6.52781e10	−	3.76883e10i	0.972514	−	0.561481i	0.900002	+	0.435886i	$0.143565\pi$
$510$		0			0
$511$	−6.11087e9	+	3.02565e10i	−0.0896230	+	0.443747i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.96856e9	−	6.87375e9i	0.0564162	−	0.0977158i
$516$		0			0
$517$		−	3.92329e7i		−	0.000549146i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.51950e10	+	4.91874e10i	1.15628	+	0.667579i	0.950410	−	0.311000i	$-0.100664\pi$
$521$	8.51950e10	+	4.91874e10i	1.15628	+	0.667579i	0.205871	+	0.978579i	$0.433997\pi$
$522$		0			0
$523$	−9.50672e10	+	5.48871e10i	−1.27064	+	0.733607i	−0.975109	−	0.221725i	$-0.928831\pi$
$523$	−9.50672e10	+	5.48871e10i	−1.27064	+	0.733607i	−0.295535	+	0.955332i	$0.595498\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.06917e10	+	7.04800e10i	0.527549	+	0.913742i
$528$		0			0
$529$	2.06321e10	−	3.57358e10i	0.263463	−	0.456332i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.40102e9			0.0173594
$534$		0			0
$535$	4.26740e10	+	2.46378e10i	0.520893	+	0.300737i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.28489e8	−	1.02236e9i	−0.00152233	−	0.0121129i
$540$		0			0
$541$	−3.52106e10	−	6.09865e10i	−0.411040	−	0.711942i	0.583964	−	0.811780i	$-0.301501\pi$
$541$	−3.52106e10	−	6.09865e10i	−0.411040	−	0.711942i	−0.995004	+	0.0998378i	$0.968168\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			1.69808e11i			1.92474i
$546$		0			0
$547$	1.51267e11			1.68965			0.844823	−	0.535046i	$-0.179706\pi$
$547$	1.51267e11			1.68965			0.844823	+	0.535046i	$0.179706\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.03196e9	+	2.90521e9i	−0.0545923	+	0.0315189i
$552$		0			0
$553$	7.09060e10	−	8.03752e10i	0.758198	−	0.859451i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.44814e10	−	1.29006e11i	0.773797	−	1.34026i	−0.161671	−	0.986845i	$-0.551688\pi$
$557$	7.44814e10	−	1.29006e11i	0.773797	−	1.34026i	0.935468	−	0.353411i	$-0.114978\pi$
$558$		0			0
$559$		−	1.23543e10i		−	0.126524i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	6.90339e10	+	3.98568e10i	0.687115	+	0.396706i	0.802530	−	0.596612i	$-0.203487\pi$
$563$	6.90339e10	+	3.98568e10i	0.687115	+	0.396706i	−0.115416	+	0.993317i	$0.536820\pi$
$564$		0			0
$565$	9.75011e10	−	5.62923e10i	0.956788	−	0.552402i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.97355e9	−	1.55427e10i	−0.0856082	−	0.148278i	0.820042	−	0.572303i	$-0.193950\pi$
$569$	−8.97355e9	−	1.55427e10i	−0.0856082	−	0.148278i	−0.905650	+	0.424026i	$0.860617\pi$
$570$		0			0
$571$	7.55428e9	−	1.30844e10i	0.0710639	−	0.123086i	−0.828304	−	0.560279i	$-0.810694\pi$
$571$	7.55428e9	−	1.30844e10i	0.0710639	−	0.123086i	0.899368	+	0.437193i	$0.144027\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.26000e11			−1.15266
$576$		0			0
$577$	4.29450e10	+	2.47943e10i	0.387444	+	0.223691i	0.681052	−	0.732235i	$-0.261523\pi$
$577$	4.29450e10	+	2.47943e10i	0.387444	+	0.223691i	−0.293608	+	0.955926i	$0.594856\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	5.75209e10	−	1.93374e10i	0.504802	−	0.169705i
$582$		0			0
$583$	1.07440e8	+	1.86091e8i	0.000930017	+	0.00161084i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			8.84088e9i			0.0744634i	0.999307	+	0.0372317i	$0.0118540\pi$
$587$			8.84088e9i			0.0744634i	−0.999307	+	0.0372317i	$0.988146\pi$
$588$		0			0
$589$	−5.40514e9			−0.0449103
$590$		0			0
$591$		0			0
$592$		0			0
$593$	9.92824e10	−	5.73207e10i	0.802885	−	0.463546i	−0.0415939	−	0.999135i	$-0.513244\pi$
$593$	9.92824e10	−	5.73207e10i	0.802885	−	0.463546i	0.844479	+	0.535589i	$0.179910\pi$
$594$		0			0
$595$	5.80281e10	+	1.72610e11i	0.462989	+	1.37720i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−4.15055e10	+	7.18897e10i	−0.322403	+	0.558418i	−0.980983	−	0.194092i	$-0.937824\pi$
$599$	−4.15055e10	+	7.18897e10i	−0.322403	+	0.558418i	0.658581	+	0.752510i	$0.271157\pi$
$600$		0			0
$601$		−	6.02491e10i		−	0.461799i	−0.972978	−	0.230899i	$-0.925833\pi$
$601$		−	6.02491e10i		−	0.461799i	0.972978	−	0.230899i	$-0.0741668\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.89766e11	−	1.09562e11i	−1.41644	−	0.817780i
$606$		0			0
$607$	−2.83559e10	+	1.63713e10i	−0.208876	+	0.120595i	−0.600789	−	0.799408i	$-0.705147\pi$
$607$	−2.83559e10	+	1.63713e10i	−0.208876	+	0.120595i	0.391913	+	0.920002i	$0.371813\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.13729e9	+	3.70190e9i	0.0153355	+	0.0265619i
$612$		0			0
$613$	8.89776e10	−	1.54114e11i	0.630143	−	1.09144i	−0.357379	−	0.933959i	$-0.616330\pi$
$613$	8.89776e10	−	1.54114e11i	0.630143	−	1.09144i	0.987522	−	0.157480i	$-0.0503370\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.06150e11			0.732452			0.366226	−	0.930526i	$-0.380650\pi$
$617$	1.06150e11			0.732452			0.366226	+	0.930526i	$0.380650\pi$
$618$		0			0
$619$	−2.07518e11	−	1.19811e11i	−1.41349	−	0.816080i	−0.417777	−	0.908550i	$-0.637191\pi$
$619$	−2.07518e11	−	1.19811e11i	−1.41349	−	0.816080i	−0.995716	+	0.0924692i	$0.970524\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.05434e11	−	9.30123e10i	−0.699885	−	0.617430i
$624$		0			0
$625$	−1.01192e10	−	1.75269e10i	−0.0663169	−	0.114864i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	2.17798e11i		−	1.39140i
$630$		0			0
$631$	3.78175e10			0.238548			0.119274	−	0.992861i	$-0.461943\pi$
$631$	3.78175e10			0.238548			0.119274	+	0.992861i	$0.461943\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.68901e11	+	2.12985e11i	−2.26890	+	1.30995i
$636$		0			0
$637$	6.78188e10	+	8.94669e10i	0.411901	+	0.543381i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.03428e11	+	1.79142e11i	−0.612638	+	1.06112i	0.378155	+	0.925742i	$0.376558\pi$
$641$	−1.03428e11	+	1.79142e11i	−0.612638	+	1.06112i	−0.990794	+	0.135379i	$0.956775\pi$
$642$		0			0
$643$		−	7.87609e10i		−	0.460752i	−0.973102	−	0.230376i	$-0.926004\pi$
$643$		−	7.87609e10i		−	0.460752i	0.973102	−	0.230376i	$-0.0739955\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.92434e11	−	1.11102e11i	−1.09816	−	0.634022i	−0.162421	−	0.986721i	$-0.551930\pi$
$647$	−1.92434e11	−	1.11102e11i	−1.09816	−	0.634022i	−0.935737	+	0.352700i	$0.885264\pi$
$648$		0			0
$649$	−1.53330e9	+	8.85254e8i	−0.00864270	+	0.00498987i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−3.38559e10	−	5.86402e10i	−0.186201	−	0.322510i	0.757780	−	0.652511i	$-0.226284\pi$
$653$	−3.38559e10	−	5.86402e10i	−0.186201	−	0.322510i	−0.943981	+	0.330001i	$0.892951\pi$
$654$		0			0
$655$	−2.56879e11	+	4.44927e11i	−1.39561	+	2.41726i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.67964e11			1.42080			0.710402	−	0.703796i	$-0.248513\pi$
$659$	2.67964e11			1.42080			0.710402	+	0.703796i	$0.248513\pi$
$660$		0			0
$661$	−7.26106e10	−	4.19218e10i	−0.380360	−	0.219601i	0.297615	−	0.954686i	$-0.403809\pi$
$661$	−7.26106e10	−	4.19218e10i	−0.380360	−	0.219601i	−0.677975	+	0.735085i	$0.737142\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.18551e10	−	2.39436e9i	−0.0606205	−	0.0122434i
$666$		0			0
$667$	1.13493e11	+	1.96575e11i	0.573409	+	0.993173i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			2.75374e9i			0.0135842i
$672$		0			0
$673$	−8.88652e10			−0.433183			−0.216592	−	0.976262i	$-0.569494\pi$
$673$	−8.88652e10			−0.433183			−0.216592	+	0.976262i	$0.569494\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.38108e11	−	1.37471e11i	1.13349	−	0.654422i	0.188681	−	0.982038i	$-0.439579\pi$
$677$	2.38108e11	−	1.37471e11i	1.13349	−	0.654422i	0.944811	+	0.327616i	$0.106245\pi$
$678$		0			0
$679$	−2.46192e11	+	8.27652e10i	−1.15823	+	0.389375i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	4.99131e10	−	8.64521e10i	0.229368	−	0.397276i	−0.728253	−	0.685308i	$-0.759668\pi$
$683$	4.99131e10	−	8.64521e10i	0.229368	−	0.397276i	0.957621	+	0.288032i	$0.0930009\pi$
$684$		0			0
$685$		−	5.38048e11i		−	2.44376i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.02754e10	−	1.17060e10i	−0.0899688	−	0.0519435i
$690$		0			0
$691$	−3.80607e11	+	2.19744e11i	−1.66942	+	0.963838i	−0.701463	+	0.712706i	$0.747469\pi$
$691$	−3.80607e11	+	2.19744e11i	−1.66942	+	0.963838i	−0.967953	+	0.251132i	$0.919197\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.42951e11	+	4.20804e11i	1.04131	+	1.80360i
$696$		0			0
$697$	2.66847e9	−	4.62192e9i	0.0113066	−	0.0195836i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.37767e11			0.570524			0.285262	−	0.958450i	$-0.407919\pi$
$701$	1.37767e11			0.570524			0.285262	+	0.958450i	$0.407919\pi$
$702$		0			0
$703$	1.25273e10	+	7.23261e9i	0.0512902	+	0.0296124i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	7.84421e10	−	3.88388e11i	0.313958	−	1.55449i
$708$		0			0
$709$	−8.01965e10	−	1.38904e11i	−0.317373	−	0.549707i	0.662566	−	0.749004i	$-0.269468\pi$
$709$	−8.01965e10	−	1.38904e11i	−0.317373	−	0.549707i	−0.979939	+	0.199297i	$0.936134\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			2.11153e11i			0.817033i
$714$		0			0
$715$	−3.55875e9			−0.0136167
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.30536e11	−	7.53649e10i	0.488443	−	0.282003i	−0.235485	−	0.971878i	$-0.575668\pi$
$719$	1.30536e11	−	7.53649e10i	0.488443	−	0.282003i	0.723928	+	0.689875i	$0.242335\pi$
$720$		0			0
$721$	−1.39781e10	−	1.23313e10i	−0.0517256	−	0.0456317i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.86001e11	+	6.68574e11i	−1.39713	+	2.41990i
$726$		0			0
$727$			2.37942e11i			0.851793i	0.904772	+	0.425896i	$0.140041\pi$
$727$			2.37942e11i			0.851793i	−0.904772	+	0.425896i	$0.859959\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−4.07567e10	−	2.35309e10i	−0.142735	−	0.0824078i
$732$		0			0
$733$	−4.06304e11	+	2.34580e11i	−1.40746	+	0.812597i	−0.995143	−	0.0984440i	$-0.968613\pi$
$733$	−4.06304e11	+	2.34580e11i	−1.40746	+	0.812597i	−0.412316	+	0.911041i	$0.635280\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.64887e8	+	2.85592e8i	0.000558877	+	0.000968003i
$738$		0			0
$739$	−3.62346e10	+	6.27601e10i	−0.121491	+	0.210429i	−0.920356	−	0.391082i	$-0.872101\pi$
$739$	−3.62346e10	+	6.27601e10i	−0.121491	+	0.210429i	0.798865	+	0.601511i	$0.205434\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	4.93093e11			1.61798			0.808990	−	0.587822i	$-0.200015\pi$
$743$	4.93093e11			1.61798			0.808990	+	0.587822i	$0.200015\pi$
$744$		0			0
$745$	−3.34716e11	−	1.93248e11i	−1.08655	−	0.627322i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	7.65557e10	−	8.67794e10i	0.243249	−	0.275733i
$750$		0			0
$751$	−2.51634e11	−	4.35842e11i	−0.791059	−	1.37015i	−0.925312	−	0.379207i	$-0.876197\pi$
$751$	−2.51634e11	−	4.35842e11i	−0.791059	−	1.37015i	0.134253	−	0.990947i	$-0.457137\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			1.93852e11i			0.596598i
$756$		0			0
$757$	9.55961e10			0.291110			0.145555	−	0.989350i	$-0.453503\pi$
$757$	9.55961e10			0.291110			0.145555	+	0.989350i	$0.453503\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.96935e11	−	2.29171e11i	1.18354	−	0.683314i	0.226705	−	0.973963i	$-0.427205\pi$
$761$	3.96935e11	−	2.29171e11i	1.18354	−	0.683314i	0.956830	+	0.290649i	$0.0938712\pi$
$762$		0			0
$763$	3.90892e11	+	7.89479e10i	1.15334	+	0.232939i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.64520e10	−	1.67060e11i	0.278695	−	0.482715i
$768$		0			0
$769$		−	6.23757e11i		−	1.78365i	−0.452379	−	0.891826i	$-0.649425\pi$
$769$		−	6.23757e11i		−	1.78365i	0.452379	−	0.891826i	$-0.350575\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−2.37168e11	−	1.36929e11i	−0.664259	−	0.383510i	0.129639	−	0.991561i	$-0.458618\pi$
$773$	−2.37168e11	−	1.36929e11i	−0.664259	−	0.383510i	−0.793898	+	0.608051i	$0.791951\pi$
$774$		0			0
$775$	−6.21941e11	+	3.59078e11i	−1.72402	+	0.995364i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	1.77228e8	+	3.06969e8i	0.000481264	+	0.000833574i
$780$		0			0
$781$	−3.21701e9	+	5.57202e9i	−0.00864666	+	0.0149764i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.38720e11			−1.41868
$786$		0			0
$787$	−3.25601e11	−	1.87986e11i	−0.848764	−	0.490034i	0.0114696	−	0.999934i	$-0.496349\pi$
$787$	−3.25601e11	−	1.87986e11i	−0.848764	−	0.490034i	−0.860234	+	0.509900i	$0.829682\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−8.42522e10	−	2.50616e11i	−0.215216	−	0.640181i
$792$		0			0
$793$	−1.50016e11	−	2.59835e11i	−0.379353	−	0.657059i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			1.47010e11i			0.364345i	0.983267	+	0.182172i	$0.0583129\pi$
$797$			1.47010e11i			0.364345i	−0.983267	+	0.182172i	$0.941687\pi$
$798$		0			0
$799$	1.62833e10			0.0399535
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−1.99004e9	+	1.14895e9i	−0.00478629	+	0.00276336i
$804$		0			0
$805$	−9.35365e10	+	4.63124e11i	−0.222740	+	1.10284i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−3.59804e11	+	6.23198e11i	−0.839985	+	1.45490i	0.0499213	+	0.998753i	$0.484103\pi$
$809$	−3.59804e11	+	6.23198e11i	−0.839985	+	1.45490i	−0.889906	+	0.456143i	$0.849230\pi$
$810$		0			0
$811$			4.46899e11i			1.03306i	0.856269	+	0.516531i	$0.172777\pi$
$811$			4.46899e11i			1.03306i	−0.856269	+	0.516531i	$0.827223\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−6.79341e11	−	3.92218e11i	−1.53978	−	0.888990i
$816$		0			0
$817$	2.70689e9	−	1.56282e9i	0.00607550	−	0.00350769i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.82753e11	−	4.89743e11i	−0.622350	−	1.07794i	−0.989047	−	0.147602i	$-0.952845\pi$
$821$	−2.82753e11	−	4.89743e11i	−0.622350	−	1.07794i	0.366696	−	0.930341i	$-0.380489\pi$
$822$		0			0
$823$	−4.08180e11	+	7.06988e11i	−0.889718	+	1.54104i	−0.0495086	+	0.998774i	$0.515766\pi$
$823$	−4.08180e11	+	7.06988e11i	−0.889718	+	1.54104i	−0.840209	+	0.542263i	$0.817568\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.58275e11			0.338369			0.169185	−	0.985584i	$-0.445887\pi$
$827$	1.58275e11			0.338369			0.169185	+	0.985584i	$0.445887\pi$
$828$		0			0
$829$	−2.94240e11	−	1.69880e11i	−0.622994	−	0.359686i	0.155040	−	0.987908i	$-0.450449\pi$
$829$	−2.94240e11	−	1.69880e11i	−0.622994	−	0.359686i	−0.778034	+	0.628223i	$0.783783\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	4.24321e11	−	5.33281e10i	0.881281	−	0.110758i
$834$		0			0
$835$	1.59640e11	+	2.76504e11i	0.328394	+	0.568796i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	2.17796e11i		−	0.439543i	−0.975551	−	0.219772i	$-0.929469\pi$
$839$		−	2.17796e11i		−	0.439543i	0.975551	−	0.219772i	$-0.0705312\pi$
$840$		0			0
$841$	8.90489e11			1.78010
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.86459e11	+	2.23122e11i	−0.758013	+	0.437639i
$846$		0			0
$847$	−3.40434e11	+	3.85897e11i	−0.661453	+	0.749788i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.82544e11	−	4.89381e11i	0.538726	−	0.933101i
$852$		0			0
$853$		−	3.85581e11i		−	0.728315i	−0.931337	−	0.364158i	$-0.881357\pi$
$853$		−	3.85581e11i		−	0.728315i	0.931337	−	0.364158i	$-0.118643\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−4.52464e11	−	2.61230e11i	−0.838804	−	0.484284i	0.0180535	−	0.999837i	$-0.494253\pi$
$857$	−4.52464e11	−	2.61230e11i	−0.838804	−	0.484284i	−0.856857	+	0.515553i	$0.827586\pi$
$858$		0			0
$859$	1.75889e10	−	1.01550e10i	0.0323047	−	0.0186512i	−0.483761	−	0.875200i	$-0.660729\pi$
$859$	1.75889e10	−	1.01550e10i	0.0323047	−	0.0186512i	0.516065	+	0.856549i	$0.327396\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.35353e11	+	5.80848e11i	0.604587	+	1.04718i	0.992117	+	0.125319i	$0.0399953\pi$
$863$	3.35353e11	+	5.80848e11i	0.604587	+	1.04718i	−0.387529	+	0.921857i	$0.626671\pi$
$864$		0			0
$865$	4.65295e10	−	8.05915e10i	0.0831121	−	0.143954i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	7.97899e9			0.0139917
$870$		0			0
$871$	−3.11164e10	−	1.79651e10i	−0.0540651	−	0.0312145i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−6.14279e11	+	2.06509e11i	−1.04793	+	0.352295i
$876$		0			0
$877$	−2.78980e11	−	4.83207e11i	−0.471601	−	0.816837i	0.527871	−	0.849324i	$-0.322990\pi$
$877$	−2.78980e11	−	4.83207e11i	−0.471601	−	0.816837i	−0.999472	+	0.0324877i	$0.989657\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1.26303e11i		−	0.209658i	−0.994490	−	0.104829i	$-0.966571\pi$
$881$		−	1.26303e11i		−	0.209658i	0.994490	−	0.104829i	$-0.0334295\pi$
$882$		0			0
$883$	3.53162e11			0.580939			0.290470	−	0.956884i	$-0.406188\pi$
$883$	3.53162e11			0.580939			0.290470	+	0.956884i	$0.406188\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.53648e11	+	2.04179e11i	−0.571317	+	0.329850i	−0.757675	−	0.652632i	$-0.773665\pi$
$887$	−3.53648e11	+	2.04179e11i	−0.571317	+	0.329850i	0.186358	+	0.982482i	$0.440332\pi$
$888$		0			0
$889$	3.18773e11	+	9.48220e11i	0.510358	+	1.51811i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.40733e8	+	9.36578e8i	−0.000850310	+	0.00147278i
$894$		0			0
$895$		−	1.89595e12i		−	2.95484i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.12041e12	+	6.46867e11i	1.71529	+	0.990321i
$900$		0			0
$901$	−7.72355e10	+	4.45920e10i	−0.117197	+	0.0676640i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−2.08173e11	−	3.60566e11i	−0.310335	−	0.537515i
$906$		0			0
$907$	3.15150e11	−	5.45855e11i	0.465680	−	0.806581i	−0.533552	−	0.845767i	$-0.679143\pi$
$907$	3.15150e11	−	5.45855e11i	0.465680	−	0.806581i	0.999232	+	0.0391859i	$0.0124765\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.47406e11			1.37551			0.687753	−	0.725945i	$-0.258597\pi$
$911$	9.47406e11			1.37551			0.687753	+	0.725945i	$0.258597\pi$
$912$		0			0
$913$	3.91234e9	+	2.25879e9i	0.00563058	+	0.00325082i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	9.04778e11	+	7.98184e11i	1.27957	+	1.12882i
$918$		0			0
$919$	3.99492e11	+	6.91941e11i	0.560075	+	0.970079i	0.997489	+	0.0708185i	$0.0225611\pi$
$919$	3.99492e11	+	6.91941e11i	0.560075	+	0.970079i	−0.437414	+	0.899260i	$0.644106\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	7.01012e11i		−	0.965871i
$924$		0			0
$925$	1.92193e12			2.62525
$926$		0			0
$927$		0			0
$928$		0			0
$929$	7.54944e11	−	4.35867e11i	1.01357	−	0.585182i	0.101332	−	0.994853i	$-0.467690\pi$
$929$	7.54944e11	−	4.35867e11i	1.01357	−	0.585182i	0.912234	+	0.409670i	$0.134356\pi$
$930$		0			0
$931$	−1.10235e10	+	2.61769e10i	−0.0146730	+	0.0348433i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.77822e9	+	1.17402e10i	−0.00886889	+	0.0153614i
$936$		0			0
$937$		−	2.93757e11i		−	0.381092i	−0.981678	−	0.190546i	$-0.938974\pi$
$937$		−	2.93757e11i		−	0.381092i	0.981678	−	0.190546i	$-0.0610258\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.62309e11	+	5.55589e11i	1.22731	+	0.708590i	0.966467	−	0.256790i	$-0.0826648\pi$
$941$	9.62309e11	+	5.55589e11i	1.22731	+	0.708590i	0.260847	+	0.965380i	$0.415998\pi$
$942$		0			0
$943$	1.19918e10	−	6.92348e9i	0.0151649	−	0.00875543i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	2.58116e11	+	4.47070e11i	0.320933	+	0.555873i	0.980681	−	0.195614i	$-0.0626701\pi$
$947$	2.58116e11	+	4.47070e11i	0.320933	+	0.555873i	−0.659748	+	0.751487i	$0.729337\pi$
$948$		0			0
$949$	1.25183e11	−	2.16823e11i	0.154340	−	0.267325i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.18648e11			−0.750018			−0.375009	−	0.927021i	$-0.622360\pi$
$953$	−6.18648e11			−0.750018			−0.375009	+	0.927021i	$0.622360\pi$
$954$		0			0
$955$	−1.05968e11	−	6.11807e10i	−0.127398	−	0.0735531i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.23857e12	−	2.50152e11i	−1.46435	−	0.295753i
$960$		0			0
$961$	1.75303e11	+	3.03633e11i	0.205539	+	0.356004i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			9.91357e11i			1.14320i
$966$		0			0
$967$	1.14154e12			1.30552			0.652760	−	0.757565i	$-0.273611\pi$
$967$	1.14154e12			1.30552			0.652760	+	0.757565i	$0.273611\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.03500e12	+	5.97555e11i	−1.16429	+	0.672204i	−0.952329	−	0.305074i	$-0.901319\pi$
$971$	−1.03500e12	+	5.97555e11i	−1.16429	+	0.672204i	−0.211963	+	0.977278i	$0.567986\pi$
$972$		0			0
$973$	1.08163e12	−	3.63623e11i	1.20678	−	0.405696i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	8.55277e11	−	1.48138e12i	0.938703	−	1.62588i	0.170810	−	0.985304i	$-0.445362\pi$
$977$	8.55277e11	−	1.48138e12i	0.938703	−	1.62588i	0.767893	−	0.640578i	$-0.221305\pi$
$978$		0			0
$979$		−	1.04666e10i		−	0.0113940i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.38729e11	+	5.41975e11i	1.00537	+	0.580451i	0.909833	−	0.414975i	$-0.136210\pi$
$983$	9.38729e11	+	5.41975e11i	1.00537	+	0.580451i	0.0955378	+	0.995426i	$0.469543\pi$
$984$		0			0
$985$	−1.04654e12	+	6.04222e11i	−1.11176	+	0.641877i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−6.10521e10	−	1.05745e11i	−0.0638139	−	0.110529i
$990$		0			0
$991$	−1.24842e11	+	2.16233e11i	−0.129439	+	0.224196i	−0.923460	−	0.383696i	$-0.874651\pi$
$991$	−1.24842e11	+	2.16233e11i	−0.129439	+	0.224196i	0.794020	+	0.607891i	$0.207984\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.08636e12			−2.12862
$996$		0			0
$997$	7.78246e11	+	4.49320e11i	0.787655	+	0.454753i	0.839136	−	0.543921i	$-0.183061\pi$
$997$	7.78246e11	+	4.49320e11i	0.787655	+	0.454753i	−0.0514813	+	0.998674i	$0.516394\pi$
$998$		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.73.1	✓	20
3.2	odd	2	inner	252.9.z.e.73.10	yes	20
7.5	odd	6	inner	252.9.z.e.145.1	yes	20
21.5	even	6	inner	252.9.z.e.145.10	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.9.z.e.73.1	✓	20	1.1	even	1	trivial
252.9.z.e.73.10	yes	20	3.2	odd	2	inner
252.9.z.e.145.1	yes	20	7.5	odd	6	inner
252.9.z.e.145.10	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)

\(f(q)\)	\(=\)	\(q+(-885.405 + 511.189i) q^{5} +(765.093 + 2275.84i) q^{7} +O(q^{10})\)	\(q+(-885.405 + 511.189i) q^{5} +(765.093 + 2275.84i) q^{7} +(-89.3699 + 154.793i) q^{11} -19474.4i q^{13} +(-64245.6 - 37092.2i) q^{17} +(4266.93 - 2463.51i) q^{19} +(-96237.7 - 166689. i) q^{23} +(327315. - 566927. i) q^{25} -1.17929e6 q^{29} +(-950064. - 548520. i) q^{31} +(-1.84080e6 - 1.62393e6i) q^{35} +(1.46795e6 + 2.54256e6i) q^{37} +71941.4i q^{41} +634388. q^{43} +(-190090. + 109749. i) q^{47} +(-4.59407e6 + 3.48245e6i) q^{49} +(601096. - 1.04113e6i) q^{53} -182740. i q^{55} +(8.57841e6 + 4.95275e6i) q^{59} +(1.33423e7 - 7.70320e6i) q^{61} +(9.95511e6 + 1.72428e7i) q^{65} +(922496. - 1.59781e6i) q^{67} +3.59965e7 q^{71} +(1.11337e7 + 6.42804e6i) q^{73} +(-420661. - 84960.2i) q^{77} +(-2.23201e7 - 3.86596e7i) q^{79} -2.52746e7i q^{83} +7.58445e7 q^{85} +(-5.07125e7 + 2.92789e7i) q^{89} +(4.43206e7 - 1.48997e7i) q^{91} +(-2.51864e6 + 4.36241e6i) q^{95} +1.08177e8i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 7238 q^{7}+O(q^{10}) \) 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

Related objects

Downloads

Learn more