LMFDB - Embedded newform 252.9.z.d.73.6

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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 $ x^12 - 3x^11 + 148097x^10 + 46071824x^9 + 21578502553x^8 + 3561445462121x^7 + 576413321817541x^6 + 47217566733462528x^5 + 5214056955297543333x^4 + 358752845334081085965x^3 + 30962072851910211245661x^2 + 1221542968331193193318500*x + 45396580558961892385326096
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{10}\cdot 7^{4} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			73.6
Root			$44.6586 - 77.3509i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.d.145.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(939.615 - 542.487i) q^{5} +(1451.57 - 1912.52i) q^{7} +O(q^{10})$	$q+(939.615 - 542.487i) q^{5} +(1451.57 - 1912.52i) q^{7} +(8435.48 - 14610.7i) q^{11} +9958.41i q^{13} +(91736.7 + 52964.2i) q^{17} +(147650. - 85245.9i) q^{19} +(105694. + 183067. i) q^{23} +(393272. - 681166. i) q^{25} +567529. q^{29} +(549248. + 317108. i) q^{31} +(326400. - 2.58449e6i) q^{35} +(-1.07740e6 - 1.86611e6i) q^{37} +5.45428e6i q^{41} +5.56726e6 q^{43} +(-2.76739e6 + 1.59775e6i) q^{47} +(-1.55068e6 - 5.55233e6i) q^{49} +(-4.38272e6 + 7.59109e6i) q^{53} -1.83046e7i q^{55} +(8.08566e6 + 4.66826e6i) q^{59} +(-2.13748e7 + 1.23407e7i) q^{61} +(5.40231e6 + 9.35707e6i) q^{65} +(-6.91779e6 + 1.19820e7i) q^{67} -1.19189e7 q^{71} +(-1.83300e7 - 1.05828e7i) q^{73} +(-1.56985e7 - 3.73415e7i) q^{77} +(-8.61190e6 - 1.49162e7i) q^{79} +6.82663e7i q^{83} +1.14930e8 q^{85} +(7.87155e7 - 4.54464e7i) q^{89} +(1.90457e7 + 1.44553e7i) q^{91} +(9.24895e7 - 1.60197e8i) q^{95} -3.95376e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) $ 12 * q - 285 * q^5 + 198 * q^7	$ 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) $ 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

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
$5$	939.615	−	542.487i	1.50338	−	0.867979i	0.503392	−	0.864058i	$-0.332085\pi$
$5$	939.615	−	542.487i	1.50338	−	0.867979i	0.999992	−	0.00392070i	$-0.00124800\pi$
$6$		0			0
$7$	1451.57	−	1912.52i	0.604570	−	0.796552i
$7$	1451.57	−	1912.52i	0.604570	−	0.796552i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	8435.48	−	14610.7i	0.576155	−	0.997929i	−0.419760	−	0.907635i	$-0.637886\pi$
$11$	8435.48	−	14610.7i	0.576155	−	0.997929i	0.995915	−	0.0902942i	$-0.0287807\pi$
$12$		0			0
$13$			9958.41i			0.348672i	0.984686	+	0.174336i	$0.0557778\pi$
$13$			9958.41i			0.348672i	−0.984686	+	0.174336i	$0.944222\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	91736.7	+	52964.2i	1.09837	+	0.634142i	0.935792	−	0.352554i	$-0.114687\pi$
$17$	91736.7	+	52964.2i	1.09837	+	0.634142i	0.162575	+	0.986696i	$0.448020\pi$
$18$		0			0
$19$	147650.	−	85245.9i	1.13297	−	0.654122i	0.188292	−	0.982113i	$-0.439705\pi$
$19$	147650.	−	85245.9i	1.13297	−	0.654122i	0.944681	+	0.327991i	$0.106372\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	105694.	+	183067.i	0.377692	+	0.654183i	0.990726	−	0.135874i	$-0.0433843\pi$
$23$	105694.	+	183067.i	0.377692	+	0.654183i	−0.613034	+	0.790057i	$0.710051\pi$
$24$		0			0
$25$	393272.	−	681166.i	1.00678	−	1.74379i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	567529.			0.802409			0.401205	−	0.915989i	$-0.368592\pi$
$29$	567529.			0.802409			0.401205	+	0.915989i	$0.368592\pi$
$30$		0			0
$31$	549248.	+	317108.i	0.594732	+	0.343369i	0.766967	−	0.641687i	$-0.221765\pi$
$31$	549248.	+	317108.i	0.594732	+	0.343369i	−0.172234	+	0.985056i	$0.555099\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	326400.	−	2.58449e6i	0.217510	−	1.72228i
$36$		0			0
$37$	−1.07740e6	−	1.86611e6i	−0.574870	−	0.995703i	−0.996056	−	0.0887291i	$-0.971719\pi$
$37$	−1.07740e6	−	1.86611e6i	−0.574870	−	0.995703i	0.421186	−	0.906974i	$-0.361614\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			5.45428e6i			1.93020i	0.261884	+	0.965099i	$0.415656\pi$
$41$			5.45428e6i			1.93020i	−0.261884	+	0.965099i	$0.584344\pi$
$42$		0			0
$43$	5.56726e6			1.62842			0.814212	−	0.580568i	$-0.197169\pi$
$43$	5.56726e6			1.62842			0.814212	+	0.580568i	$0.197169\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.76739e6	+	1.59775e6i	−0.567125	+	0.327430i	−0.756000	−	0.654572i	$-0.772849\pi$
$47$	−2.76739e6	+	1.59775e6i	−0.567125	+	0.327430i	0.188876	+	0.982001i	$0.439516\pi$
$48$		0			0
$49$	−1.55068e6	−	5.55233e6i	−0.268991	−	0.963143i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−4.38272e6	+	7.59109e6i	−0.555443	+	0.962056i	0.442425	+	0.896805i	$0.354118\pi$
$53$	−4.38272e6	+	7.59109e6i	−0.555443	+	0.962056i	−0.997869	+	0.0652510i	$0.979215\pi$
$54$		0			0
$55$		−	1.83046e7i		−	2.00036i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	8.08566e6	+	4.66826e6i	0.667279	+	0.385254i	0.795045	−	0.606551i	$-0.207447\pi$
$59$	8.08566e6	+	4.66826e6i	0.667279	+	0.385254i	−0.127766	+	0.991804i	$0.540781\pi$
$60$		0			0
$61$	−2.13748e7	+	1.23407e7i	−1.54377	+	0.891296i	−0.545174	+	0.838323i	$0.683536\pi$
$61$	−2.13748e7	+	1.23407e7i	−1.54377	+	0.891296i	−0.998596	+	0.0529726i	$0.983130\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.40231e6	+	9.35707e6i	0.302640	+	0.524187i
$66$		0			0
$67$	−6.91779e6	+	1.19820e7i	−0.343295	+	0.594605i	−0.985043	−	0.172311i	$-0.944877\pi$
$67$	−6.91779e6	+	1.19820e7i	−0.343295	+	0.594605i	0.641747	+	0.766916i	$0.278210\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.19189e7			−0.469031			−0.234515	−	0.972112i	$-0.575350\pi$
$71$	−1.19189e7			−0.469031			−0.234515	+	0.972112i	$0.575350\pi$
$72$		0			0
$73$	−1.83300e7	−	1.05828e7i	−0.645463	−	0.372658i	0.141253	−	0.989974i	$-0.454887\pi$
$73$	−1.83300e7	−	1.05828e7i	−0.645463	−	0.372658i	−0.786716	+	0.617315i	$0.788220\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.56985e7	−	3.73415e7i	−0.446577	−	1.06226i
$78$		0			0
$79$	−8.61190e6	−	1.49162e7i	−0.221101	−	0.382958i	0.734042	−	0.679104i	$-0.237632\pi$
$79$	−8.61190e6	−	1.49162e7i	−0.221101	−	0.382958i	−0.955143	+	0.296147i	$0.904298\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			6.82663e7i			1.43845i	0.694779	+	0.719223i	$0.255502\pi$
$83$			6.82663e7i			1.43845i	−0.694779	+	0.719223i	$0.744498\pi$
$84$		0			0
$85$	1.14930e8			2.20169
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.87155e7	−	4.54464e7i	1.25459	−	0.724335i	0.282569	−	0.959247i	$-0.408814\pi$
$89$	7.87155e7	−	4.54464e7i	1.25459	−	0.724335i	0.972017	+	0.234912i	$0.0754802\pi$
$90$		0			0
$91$	1.90457e7	+	1.44553e7i	0.277735	+	0.210796i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	9.24895e7	−	1.60197e8i	1.13553	−	1.96679i
$96$		0			0
$97$		−	3.95376e7i		−	0.446605i	−0.974749	−	0.223302i	$-0.928316\pi$
$97$		−	3.95376e7i		−	0.446605i	0.974749	−	0.223302i	$-0.0716837\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.01453e8	−	5.85738e7i	−0.974941	−	0.562882i	−0.0742019	−	0.997243i	$-0.523641\pi$
$101$	−1.01453e8	−	5.85738e7i	−0.974941	−	0.562882i	−0.900739	+	0.434361i	$0.856974\pi$
$102$		0			0
$103$	−4.22305e7	+	2.43818e7i	−0.375212	+	0.216629i	−0.675733	−	0.737146i	$-0.736173\pi$
$103$	−4.22305e7	+	2.43818e7i	−0.375212	+	0.216629i	0.300521	+	0.953775i	$0.402839\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.90508e7	−	1.02279e8i	−0.450496	−	0.780282i	0.547921	−	0.836530i	$-0.315420\pi$
$107$	−5.90508e7	−	1.02279e8i	−0.450496	−	0.780282i	−0.998417	+	0.0562482i	$0.982086\pi$
$108$		0			0
$109$	−7.54688e6	+	1.30716e7i	−0.0534640	+	0.0926024i	−0.891519	−	0.452984i	$-0.850360\pi$
$109$	−7.54688e6	+	1.30716e7i	−0.0534640	+	0.0926024i	0.838055	+	0.545586i	$0.183693\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.94293e7			0.425823			0.212911	−	0.977072i	$-0.431705\pi$
$113$	6.94293e7			0.425823			0.212911	+	0.977072i	$0.431705\pi$
$114$		0			0
$115$	1.98623e8	+	1.14675e8i	1.13563	+	0.655658i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.34458e8	−	9.85671e7i	1.16917	−	0.491523i
$120$		0			0
$121$	−3.51352e7	−	6.08560e7i	−0.163908	−	0.283898i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	4.29561e8i		−	1.75948i
$126$		0			0
$127$	−1.00139e8			−0.384934			−0.192467	−	0.981303i	$-0.561649\pi$
$127$	−1.00139e8			−0.384934			−0.192467	+	0.981303i	$0.561649\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.73342e6	−	3.88754e6i	0.0228639	−	0.0132005i	−0.488524	−	0.872550i	$-0.662465\pi$
$131$	6.73342e6	−	3.88754e6i	0.0228639	−	0.0132005i	0.511388	+	0.859350i	$0.329131\pi$
$132$		0			0
$133$	5.12902e7	−	4.06125e8i	0.163919	−	1.29793i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	5.53803e7	−	9.59215e7i	0.157207	−	0.272291i	−0.776653	−	0.629928i	$-0.783084\pi$
$137$	5.53803e7	−	9.59215e7i	0.157207	−	0.272291i	0.933861	+	0.357637i	$0.116418\pi$
$138$		0			0
$139$			3.31664e8i			0.888464i	0.895912	+	0.444232i	$0.146523\pi$
$139$			3.31664e8i			0.888464i	−0.895912	+	0.444232i	$0.853477\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.45499e8	+	8.40040e7i	0.347949	+	0.200889i
$144$		0			0
$145$	5.33258e8	−	3.07877e8i	1.20633	−	0.696474i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.47265e8	−	6.01481e8i	−0.704557	−	1.22033i	−0.966851	−	0.255341i	$-0.917812\pi$
$149$	−3.47265e8	−	6.01481e8i	−0.704557	−	1.22033i	0.262294	−	0.964988i	$-0.415521\pi$
$150$		0			0
$151$	−4.10896e8	+	7.11694e8i	−0.790359	+	1.36894i	0.135385	+	0.990793i	$0.456773\pi$
$151$	−4.10896e8	+	7.11694e8i	−0.790359	+	1.36894i	−0.925745	+	0.378150i	$0.876561\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	6.88109e8			1.19215
$156$		0			0
$157$	−4.16332e8	−	2.40369e8i	−0.685238	−	0.395622i	0.116588	−	0.993180i	$-0.462804\pi$
$157$	−4.16332e8	−	2.40369e8i	−0.685238	−	0.395622i	−0.801825	+	0.597558i	$0.796138\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.03542e8	+	6.35933e7i	0.749432	+	0.0946472i
$162$		0			0
$163$	−3.04664e8	−	5.27694e8i	−0.431590	−	0.747536i	0.565420	−	0.824803i	$-0.308714\pi$
$163$	−3.04664e8	−	5.27694e8i	−0.431590	−	0.747536i	−0.997010	+	0.0772671i	$0.975381\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			1.84576e8i			0.237307i	0.992936	+	0.118653i	$0.0378577\pi$
$167$			1.84576e8i			0.237307i	−0.992936	+	0.118653i	$0.962142\pi$
$168$		0			0
$169$	7.16561e8			0.878428
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.92420e8	−	1.68829e8i	0.326454	−	0.188478i	−0.327812	−	0.944743i	$-0.606311\pi$
$173$	2.92420e8	−	1.68829e8i	0.326454	−	0.188478i	0.654266	+	0.756265i	$0.272978\pi$
$174$		0			0
$175$	−7.31884e8	−	1.74090e9i	−0.780351	−	1.85619i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−2.92703e8	+	5.06977e8i	−0.285112	+	0.493828i	−0.972636	−	0.232333i	$-0.925364\pi$
$179$	−2.92703e8	+	5.06977e8i	−0.285112	+	0.493828i	0.687524	+	0.726161i	$0.258697\pi$
$180$		0			0
$181$		−	1.29407e9i		−	1.20571i	−0.797850	−	0.602856i	$-0.794029\pi$
$181$		−	1.29407e9i		−	1.20571i	0.797850	−	0.602856i	$-0.205971\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.02468e9	−	1.16895e9i	−1.72850	−	0.997950i
$186$		0			0
$187$	1.54769e9	−	8.93557e8i	1.26566	−	0.730728i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.80043e8	+	1.35107e9i	0.586118	+	1.01519i	0.994735	+	0.102480i	$0.0326777\pi$
$191$	7.80043e8	+	1.35107e9i	0.586118	+	1.01519i	−0.408617	+	0.912706i	$0.633989\pi$
$192$		0			0
$193$	8.76806e8	−	1.51867e9i	0.631937	−	1.09455i	−0.355218	−	0.934784i	$-0.615593\pi$
$193$	8.76806e8	−	1.51867e9i	0.631937	−	1.09455i	0.987155	−	0.159764i	$-0.0510734\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.78624e9			1.18598			0.592988	−	0.805212i	$-0.297948\pi$
$197$	1.78624e9			1.18598			0.592988	+	0.805212i	$0.297948\pi$
$198$		0			0
$199$	−2.60521e9	−	1.50412e9i	−1.66123	−	0.959114i	−0.972127	−	0.234454i	$-0.924670\pi$
$199$	−2.60521e9	−	1.50412e9i	−1.66123	−	0.959114i	−0.689107	−	0.724660i	$-0.741997\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	8.23809e8	−	1.08541e9i	0.485112	−	0.639161i
$204$		0			0
$205$	2.95888e9	+	5.12492e9i	1.67537	+	2.90183i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	2.87636e9i		−	1.50750i
$210$		0			0
$211$	3.33988e9			1.68501			0.842503	−	0.538692i	$-0.181081\pi$
$211$	3.33988e9			1.68501			0.842503	+	0.538692i	$0.181081\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	5.23108e9	−	3.02016e9i	2.44815	−	1.41344i
$216$		0			0
$217$	1.40375e9	−	5.90143e8i	0.633069	−	0.266145i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.27439e8	+	9.13552e8i	−0.221107	+	0.382969i
$222$		0			0
$223$		−	1.94513e9i		−	0.786556i	−0.919420	−	0.393278i	$-0.871341\pi$
$223$		−	1.94513e9i		−	0.786556i	0.919420	−	0.393278i	$-0.128659\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.17894e9	−	6.80660e8i	−0.444004	−	0.256346i	0.261290	−	0.965260i	$-0.415852\pi$
$227$	−1.17894e9	−	6.80660e8i	−0.444004	−	0.256346i	−0.705295	+	0.708914i	$0.749185\pi$
$228$		0			0
$229$	−3.23205e9	+	1.86603e9i	−1.17527	+	0.678541i	−0.954915	−	0.296880i	$-0.904054\pi$
$229$	−3.23205e9	+	1.86603e9i	−1.17527	+	0.678541i	−0.220352	+	0.975420i	$0.570721\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	1.72263e8	+	2.98368e8i	0.0584477	+	0.101234i	0.893769	−	0.448528i	$-0.148052\pi$
$233$	1.72263e8	+	2.98368e8i	0.0584477	+	0.101234i	−0.835321	+	0.549762i	$0.814718\pi$
$234$		0			0
$235$	−1.73352e9	+	3.00254e9i	−0.568404	+	0.984505i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.17982e9			−0.974565			−0.487283	−	0.873244i	$-0.662012\pi$
$239$	−3.17982e9			−0.974565			−0.487283	+	0.873244i	$0.662012\pi$
$240$		0			0
$241$	−4.09977e9	−	2.36701e9i	−1.21532	−	0.701667i	−0.251409	−	0.967881i	$-0.580894\pi$
$241$	−4.09977e9	−	2.36701e9i	−1.21532	−	0.701667i	−0.963914	+	0.266214i	$0.914227\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−4.46911e9	−	4.37583e9i	−1.24038	−	1.21449i
$246$		0			0
$247$	8.48913e8	+	1.47036e9i	0.228074	+	0.395035i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			7.03152e9i			1.77155i	0.464112	+	0.885776i	$0.346373\pi$
$251$			7.03152e9i			1.77155i	−0.464112	+	0.885776i	$0.653627\pi$
$252$		0			0
$253$	3.56631e9			0.870437
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.10931e9	−	6.40462e8i	0.254286	−	0.146812i	−0.367439	−	0.930047i	$-0.619765\pi$
$257$	1.10931e9	−	6.40462e8i	0.254286	−	0.146812i	0.621725	+	0.783236i	$0.286432\pi$
$258$		0			0
$259$	−5.13289e9	−	6.48243e8i	−1.14068	−	0.144058i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.37972e8	+	4.12179e8i	−0.0497396	+	0.0861516i	−0.889823	−	0.456305i	$-0.849172\pi$
$263$	−2.37972e8	+	4.12179e8i	−0.0497396	+	0.0861516i	0.840084	+	0.542457i	$0.182506\pi$
$264$		0			0
$265$			9.51027e9i			1.92845i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	4.95417e9	+	2.86029e9i	0.946154	+	0.546262i	0.891884	−	0.452264i	$-0.149384\pi$
$269$	4.95417e9	+	2.86029e9i	0.946154	+	0.546262i	0.0542696	+	0.998526i	$0.482717\pi$
$270$		0			0
$271$	−5.53293e9	+	3.19444e9i	−1.02584	+	0.592267i	−0.915789	−	0.401659i	$-0.868434\pi$
$271$	−5.53293e9	+	3.19444e9i	−1.02584	+	0.592267i	−0.110048	+	0.993926i	$0.535100\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−6.63487e9	−	1.14919e10i	−1.16012	−	2.00938i
$276$		0			0
$277$	−2.63656e9	+	4.56666e9i	−0.447836	+	0.775675i	−0.998245	−	0.0592204i	$-0.981139\pi$
$277$	−2.63656e9	+	4.56666e9i	−0.447836	+	0.775675i	0.550409	+	0.834895i	$0.314472\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−7.48748e9			−1.20091			−0.600455	−	0.799658i	$-0.705014\pi$
$281$	−7.48748e9			−1.20091			−0.600455	+	0.799658i	$0.705014\pi$
$282$		0			0
$283$	−3.62475e9	−	2.09275e9i	−0.565109	−	0.326266i	0.190085	−	0.981768i	$-0.439124\pi$
$283$	−3.62475e9	−	2.09275e9i	−0.565109	−	0.326266i	−0.755193	+	0.655502i	$0.772457\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.04314e10	+	7.91728e9i	1.53750	+	1.16694i
$288$		0			0
$289$	2.12254e9	+	3.67634e9i	0.304273	+	0.527017i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			1.12022e9i			0.151997i	0.997108	+	0.0759983i	$0.0242143\pi$
$293$			1.12022e9i			0.151997i	−0.997108	+	0.0759983i	$0.975786\pi$
$294$		0			0
$295$	1.01299e10			1.33757
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−1.82306e9	+	1.05254e9i	−0.228095	+	0.131691i
$300$		0			0
$301$	8.08127e9	−	1.06475e10i	0.984496	−	1.29712i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.33894e10	+	2.31911e10i	−1.54725	+	2.67992i
$306$		0			0
$307$		−	1.02340e10i		−	1.15210i	−0.817413	−	0.576051i	$-0.804593\pi$
$307$		−	1.02340e10i		−	1.15210i	0.817413	−	0.576051i	$-0.195407\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.99552e9	−	3.46151e9i	−0.640892	−	0.370019i	0.144066	−	0.989568i	$-0.453982\pi$
$311$	−5.99552e9	−	3.46151e9i	−0.640892	−	0.370019i	−0.784958	+	0.619549i	$0.787316\pi$
$312$		0			0
$313$	4.79188e8	−	2.76659e8i	0.0499262	−	0.0288249i	−0.474829	−	0.880078i	$-0.657490\pi$
$313$	4.79188e8	−	2.76659e8i	0.0499262	−	0.0288249i	0.524755	+	0.851253i	$0.324157\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.72093e8	+	1.16410e9i	0.0665568	+	0.115280i	0.897384	−	0.441251i	$-0.145465\pi$
$317$	6.72093e8	+	1.16410e9i	0.0665568	+	0.115280i	−0.830827	+	0.556531i	$0.812132\pi$
$318$		0			0
$319$	4.78738e9	−	8.29198e9i	0.462312	−	0.800747i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.80599e10			1.65923
$324$		0			0
$325$	6.78333e9	+	3.91636e9i	0.608009	+	0.351034i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−9.61326e8	+	7.61194e9i	−0.0820516	+	0.649698i
$330$		0			0
$331$	3.38567e8	+	5.86414e8i	0.0282054	+	0.0488532i	0.879784	−	0.475374i	$-0.157687\pi$
$331$	3.38567e8	+	5.86414e8i	0.0282054	+	0.0488532i	−0.851578	+	0.524228i	$0.824354\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			1.50112e10i			1.19189i
$336$		0			0
$337$	−1.73692e10			−1.34667			−0.673333	−	0.739340i	$-0.735138\pi$
$337$	−1.73692e10			−1.34667			−0.673333	+	0.739340i	$0.735138\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.26634e9	−	5.34992e9i	0.685316	−	0.395667i
$342$		0			0
$343$	−1.28699e10	−	5.09389e9i	−0.929817	−	0.368022i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.82405e9	+	1.52837e10i	−0.608626	+	1.05417i	0.382842	+	0.923814i	$0.374946\pi$
$347$	−8.82405e9	+	1.52837e10i	−0.608626	+	1.05417i	−0.991467	+	0.130356i	$0.958388\pi$
$348$		0			0
$349$			9.49559e9i			0.640059i	0.947408	+	0.320030i	$0.103693\pi$
$349$			9.49559e9i			0.640059i	−0.947408	+	0.320030i	$0.896307\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.12231e9	−	3.53472e9i	−0.394290	−	0.227644i	0.289727	−	0.957109i	$-0.406435\pi$
$353$	−6.12231e9	−	3.53472e9i	−0.394290	−	0.227644i	−0.684017	+	0.729466i	$0.739769\pi$
$354$		0			0
$355$	−1.11991e10	+	6.46583e9i	−0.705134	+	0.407109i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.55145e9	+	1.13474e10i	0.394421	+	0.683157i	0.993027	−	0.117887i	$-0.0376119\pi$
$359$	6.55145e9	+	1.13474e10i	0.394421	+	0.683157i	−0.598606	+	0.801043i	$0.704279\pi$
$360$		0			0
$361$	6.04193e9	−	1.04649e10i	0.355752	−	0.616180i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.29642e10			−1.29384
$366$		0			0
$367$	2.12630e10	+	1.22762e10i	1.17209	+	0.676707i	0.954172	−	0.299260i	$-0.0967399\pi$
$367$	2.12630e10	+	1.22762e10i	1.17209	+	0.676707i	0.217919	+	0.975967i	$0.430073\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.15629e9	+	1.94011e10i	0.430524	+	1.02407i
$372$		0			0
$373$	5.64618e9	+	9.77947e9i	0.291689	+	0.505219i	0.974209	−	0.225647i	$-0.0724496\pi$
$373$	5.64618e9	+	9.77947e9i	0.291689	+	0.505219i	−0.682521	+	0.730866i	$0.739116\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			5.65168e9i			0.279777i
$378$		0			0
$379$	−3.52545e9			−0.170867			−0.0854335	−	0.996344i	$-0.527228\pi$
$379$	−3.52545e9			−0.170867			−0.0854335	+	0.996344i	$0.527228\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.74394e10	+	1.58422e10i	−1.27521	+	0.736240i	−0.975963	−	0.217937i	$-0.930067\pi$
$383$	−2.74394e10	+	1.58422e10i	−1.27521	+	0.736240i	−0.299243	+	0.954177i	$0.596734\pi$
$384$		0			0
$385$	−3.50079e10	−	2.65704e10i	−1.59339	−	1.20936i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.01146e9	+	3.48396e9i	−0.0878443	+	0.152151i	−0.906600	−	0.421992i	$-0.861331\pi$
$389$	−2.01146e9	+	3.48396e9i	−0.0878443	+	0.152151i	0.818755	+	0.574143i	$0.194664\pi$
$390$		0			0
$391$			2.23920e10i			0.958043i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.61837e10	−	9.34368e9i	−0.664799	−	0.383822i
$396$		0			0
$397$	−3.37145e10	+	1.94651e10i	−1.35724	+	0.783600i	−0.989250	−	0.146232i	$-0.953286\pi$
$397$	−3.37145e10	+	1.94651e10i	−1.35724	+	0.783600i	−0.367985	+	0.929832i	$0.619952\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.03692e10	−	3.52804e10i	−0.787764	−	1.36445i	−0.927334	−	0.374234i	$-0.877906\pi$
$401$	−2.03692e10	−	3.52804e10i	−0.787764	−	1.36445i	0.139571	−	0.990212i	$-0.455428\pi$
$402$		0			0
$403$	−3.15790e9	+	5.46963e9i	−0.119723	+	0.207366i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−3.63535e10			−1.32486
$408$		0			0
$409$	−1.08712e10	−	6.27648e9i	−0.388493	−	0.224297i	0.293014	−	0.956108i	$-0.405342\pi$
$409$	−1.08712e10	−	6.27648e9i	−0.388493	−	0.224297i	−0.681507	+	0.731812i	$0.738675\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	2.06651e10	−	8.68769e9i	0.710291	−	0.298610i
$414$		0			0
$415$	3.70336e10	+	6.41440e10i	1.24854	+	2.16254i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			1.94158e9i			0.0629941i	0.999504	+	0.0314970i	$0.0100275\pi$
$419$			1.94158e9i			0.0629941i	−0.999504	+	0.0314970i	$0.989973\pi$
$420$		0			0
$421$	1.38803e9			0.0441846			0.0220923	−	0.999756i	$-0.492967\pi$
$421$	1.38803e9			0.0441846			0.0220923	+	0.999756i	$0.492967\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	7.21549e10	−	4.16586e10i	2.21162	−	1.27688i
$426$		0			0
$427$	−7.42511e9	+	5.87932e10i	−0.223353	+	1.76854i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.62135e10	−	2.80826e10i	0.469860	−	0.813821i	−0.529546	−	0.848281i	$-0.677638\pi$
$431$	1.62135e10	−	2.80826e10i	0.469860	−	0.813821i	0.999406	+	0.0344602i	$0.0109712\pi$
$432$		0			0
$433$		−	4.65333e10i		−	1.32377i	−0.749606	−	0.661884i	$-0.769757\pi$
$433$		−	4.65333e10i		−	1.32377i	0.749606	−	0.661884i	$-0.230243\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.12114e10	+	1.80199e10i	0.855831	+	0.494114i
$438$		0			0
$439$	−4.44106e10	+	2.56404e10i	−1.19572	+	0.690347i	−0.959597	−	0.281377i	$-0.909209\pi$
$439$	−4.44106e10	+	2.56404e10i	−1.19572	+	0.690347i	−0.236119	+	0.971724i	$0.575876\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.09215e10	−	3.62371e10i	−0.543223	−	0.940891i	−0.998716	−	0.0506512i	$-0.983870\pi$
$443$	−2.09215e10	−	3.62371e10i	−0.543223	−	0.940891i	0.455493	−	0.890239i	$-0.349463\pi$
$444$		0			0
$445$	4.93082e10	−	8.54042e10i	1.25742	−	2.17791i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.89337e10			−0.711900			−0.355950	−	0.934505i	$-0.615843\pi$
$449$	−2.89337e10			−0.711900			−0.355950	+	0.934505i	$0.615843\pi$
$450$		0			0
$451$	7.96907e10	+	4.60095e10i	1.92620	+	1.11209i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.57374e10	+	3.25043e9i	0.600509	+	0.0758394i
$456$		0			0
$457$	−3.38299e10	−	5.85951e10i	−0.775597	−	1.34337i	−0.934458	−	0.356072i	$-0.884116\pi$
$457$	−3.38299e10	−	5.85951e10i	−0.775597	−	1.34337i	0.158862	−	0.987301i	$-0.449218\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			2.13195e10i			0.472035i	0.971749	+	0.236017i	$0.0758422\pi$
$461$			2.13195e10i			0.472035i	−0.971749	+	0.236017i	$0.924158\pi$
$462$		0			0
$463$	5.73662e10			1.24834			0.624168	−	0.781290i	$-0.285438\pi$
$463$	5.73662e10			1.24834			0.624168	+	0.781290i	$0.285438\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.40331e10	−	8.10202e9i	0.295044	−	0.170343i	−0.345171	−	0.938540i	$-0.612179\pi$
$467$	1.40331e10	−	8.10202e9i	0.295044	−	0.170343i	0.640214	+	0.768196i	$0.278846\pi$
$468$		0			0
$469$	1.28741e10	+	3.06231e10i	0.266088	+	0.632933i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.69625e10	−	8.13414e10i	0.938224	−	1.62505i
$474$		0			0
$475$		−	1.34099e11i		−	2.63422i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	8.47162e10	+	4.89109e10i	1.60925	+	0.929103i	0.989537	+	0.144276i	$0.0460854\pi$
$479$	8.47162e10	+	4.89109e10i	1.60925	+	0.929103i	0.619716	+	0.784826i	$0.287248\pi$
$480$		0			0
$481$	1.85835e10	−	1.07292e10i	0.347173	−	0.200441i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−2.14486e10	−	3.71501e10i	−0.387644	−	0.671418i
$486$		0			0
$487$	2.47120e10	−	4.28025e10i	0.439332	−	0.760945i	−0.558306	−	0.829635i	$-0.688548\pi$
$487$	2.47120e10	−	4.28025e10i	0.439332	−	0.760945i	0.997638	+	0.0686896i	$0.0218818\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−4.36304e10			−0.750695			−0.375348	−	0.926884i	$-0.622477\pi$
$491$	−4.36304e10			−0.750695			−0.375348	+	0.926884i	$0.622477\pi$
$492$		0			0
$493$	5.20632e10	+	3.00587e10i	0.881340	+	0.508842i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−1.73011e10	+	2.27951e10i	−0.283562	+	0.373608i
$498$		0			0
$499$	1.70928e10	+	2.96057e10i	0.275684	+	0.477499i	0.970308	−	0.241874i	$-0.0777622\pi$
$499$	1.70928e10	+	2.96057e10i	0.275684	+	0.477499i	−0.694623	+	0.719374i	$0.744429\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	1.10624e10i		−	0.172813i	−0.996260	−	0.0864063i	$-0.972462\pi$
$503$		−	1.10624e10i		−	0.172813i	0.996260	−	0.0864063i	$-0.0275383\pi$
$504$		0			0
$505$	−1.27102e11			−1.95428
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.58080e10	−	5.53148e10i	1.42735	−	0.824081i	0.430440	−	0.902619i	$-0.358358\pi$
$509$	9.58080e10	−	5.53148e10i	1.42735	−	0.824081i	0.996911	+	0.0785379i	$0.0250252\pi$
$510$		0			0
$511$	−4.68473e10	+	1.96948e10i	−0.687069	+	0.288847i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.64536e10	+	4.58189e10i	−0.376059	+	0.651353i
$516$		0			0
$517$			5.39112e10i			0.754600i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.11862e11	−	6.45834e10i	−1.51820	−	0.876536i	−0.999771	−	0.0214183i	$-0.993182\pi$
$521$	−1.11862e11	−	6.45834e10i	−1.51820	−	0.876536i	−0.518434	−	0.855118i	$-0.673485\pi$
$522$		0			0
$523$	4.41818e10	−	2.55084e10i	0.590523	−	0.340939i	−0.174781	−	0.984607i	$-0.555922\pi$
$523$	4.41818e10	−	2.55084e10i	0.590523	−	0.340939i	0.765304	+	0.643669i	$0.222588\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.35908e10	+	5.81810e10i	0.435490	+	0.754290i
$528$		0			0
$529$	1.68131e10	−	2.91212e10i	0.214697	−	0.371866i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−5.43159e10			−0.673005
$534$		0			0
$535$	−1.10970e11	−	6.40686e10i	−1.35454	−	0.782042i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−9.42040e10	−	2.41801e10i	−1.11613	−	0.286485i
$540$		0			0
$541$	−5.42593e10	−	9.39799e10i	−0.633410	−	1.09710i	−0.986850	−	0.161641i	$-0.948321\pi$
$541$	−5.42593e10	−	9.39799e10i	−0.633410	−	1.09710i	0.353439	−	0.935457i	$-0.385012\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			1.63763e10i			0.185623i
$546$		0			0
$547$	−6.18018e10			−0.690322			−0.345161	−	0.938544i	$-0.612176\pi$
$547$	−6.18018e10			−0.690322			−0.345161	+	0.938544i	$0.612176\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	8.37957e10	−	4.83795e10i	0.909108	−	0.524874i
$552$		0			0
$553$	−4.10284e10	−	5.18156e9i	−0.438717	−	0.0554064i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.68485e10	+	4.65029e10i	−0.278932	+	0.483125i	−0.971120	−	0.238593i	$-0.923314\pi$
$557$	−2.68485e10	+	4.65029e10i	−0.278932	+	0.483125i	0.692188	+	0.721718i	$0.256647\pi$
$558$		0			0
$559$			5.54410e10i			0.567785i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.24343e11	+	7.17894e10i	1.23762	+	0.714540i	0.968607	−	0.248596i	$-0.0799693\pi$
$563$	1.24343e11	+	7.17894e10i	1.23762	+	0.714540i	0.269013	+	0.963137i	$0.413303\pi$
$564$		0			0
$565$	6.52368e10	−	3.76645e10i	0.640175	−	0.369605i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.80492e10	−	8.32237e10i	−0.458392	−	0.793958i	0.540484	−	0.841354i	$-0.318241\pi$
$569$	−4.80492e10	−	8.32237e10i	−0.458392	−	0.793958i	−0.998876	+	0.0473959i	$0.984908\pi$
$570$		0			0
$571$	1.02075e11	−	1.76799e11i	0.960231	−	1.66317i	0.238316	−	0.971188i	$-0.423405\pi$
$571$	1.02075e11	−	1.76799e11i	0.960231	−	1.66317i	0.721915	−	0.691981i	$-0.243262\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	1.66266e11			1.52101
$576$		0			0
$577$	−1.23039e10	−	7.10368e9i	−0.111005	−	0.0640885i	0.443470	−	0.896289i	$-0.353747\pi$
$577$	−1.23039e10	−	7.10368e9i	−0.111005	−	0.0640885i	−0.554474	+	0.832201i	$0.687081\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.30561e11	+	9.90934e10i	1.14580	+	0.869641i
$582$		0			0
$583$	7.39406e10	+	1.28069e11i	0.640043	+	1.10859i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	6.63318e10i		−	0.558688i	−0.960191	−	0.279344i	$-0.909883\pi$
$587$		−	6.63318e10i		−	0.558688i	0.960191	−	0.279344i	$-0.0901170\pi$
$588$		0			0
$589$	1.08129e11			0.898421
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.13541e10	+	5.27433e10i	−0.738770	+	0.426529i	−0.821622	−	0.570033i	$-0.806930\pi$
$593$	−9.13541e10	+	5.27433e10i	−0.738770	+	0.426529i	0.0828520	+	0.996562i	$0.473597\pi$
$594$		0			0
$595$	1.66829e11	−	2.19805e11i	1.33107	−	1.75376i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.35115e10	−	1.27326e11i	0.571016	−	0.989028i	−0.425446	−	0.904984i	$-0.639883\pi$
$599$	7.35115e10	−	1.27326e11i	0.571016	−	0.989028i	0.996462	−	0.0840447i	$-0.0267839\pi$
$600$		0			0
$601$			1.86033e11i			1.42591i	0.701210	+	0.712954i	$0.252643\pi$
$601$			1.86033e11i			1.42591i	−0.701210	+	0.712954i	$0.747357\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.60272e10	−	3.81208e10i	−0.492834	−	0.284538i
$606$		0			0
$607$	−5.85799e10	+	3.38211e10i	−0.431513	+	0.249134i	−0.699991	−	0.714152i	$-0.746813\pi$
$607$	−5.85799e10	+	3.38211e10i	−0.431513	+	0.249134i	0.268478	+	0.963286i	$0.413479\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.59111e10	−	2.75588e10i	−0.114165	−	0.197740i
$612$		0			0
$613$	−1.19635e11	+	2.07214e11i	−0.847261	+	1.46750i	0.0363824	+	0.999338i	$0.488417\pi$
$613$	−1.19635e11	+	2.07214e11i	−0.847261	+	1.46750i	−0.883643	+	0.468161i	$0.844917\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	3.40881e10			0.235214			0.117607	−	0.993060i	$-0.462478\pi$
$617$	3.40881e10			0.235214			0.117607	+	0.993060i	$0.462478\pi$
$618$		0			0
$619$	8.42286e10	+	4.86294e10i	0.573716	+	0.331235i	0.758632	−	0.651519i	$-0.225868\pi$
$619$	8.42286e10	+	4.86294e10i	0.573716	+	0.331235i	−0.184916	+	0.982754i	$0.559201\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.73439e10	−	2.16514e11i	0.181513	−	1.43725i
$624$		0			0
$625$	−7.94095e10	−	1.37541e11i	−0.520418	−	0.901391i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	2.28254e11i		−	1.45820i
$630$		0			0
$631$	−1.63168e11			−1.02924			−0.514621	−	0.857418i	$-0.672067\pi$
$631$	−1.63168e11			−1.02924			−0.514621	+	0.857418i	$0.672067\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−9.40916e10	+	5.43238e10i	−0.578704	+	0.334115i
$636$		0			0
$637$	5.52923e10	−	1.54423e10i	0.335820	−	0.0937895i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.04255e10	−	3.53779e10i	0.120987	−	0.209556i	−0.799170	−	0.601105i	$-0.794727\pi$
$641$	2.04255e10	−	3.53779e10i	0.120987	−	0.209556i	0.920157	+	0.391549i	$0.128061\pi$
$642$		0			0
$643$			1.66499e11i			0.974022i	0.873396	+	0.487011i	$0.161913\pi$
$643$			1.66499e11i			0.974022i	−0.873396	+	0.487011i	$0.838087\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	4.33764e10	+	2.50434e10i	0.247535	+	0.142914i	0.618635	−	0.785678i	$-0.287686\pi$
$647$	4.33764e10	+	2.50434e10i	0.247535	+	0.142914i	−0.371100	+	0.928593i	$0.621019\pi$
$648$		0			0
$649$	1.36413e11	−	7.87580e10i	0.768912	−	0.443931i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.99393e10	+	5.18564e10i	0.164660	+	0.285200i	0.936535	−	0.350575i	$-0.114014\pi$
$653$	2.99393e10	+	5.18564e10i	0.164660	+	0.285200i	−0.771874	+	0.635775i	$0.780681\pi$
$654$		0			0
$655$	4.21788e9	−	7.30558e9i	0.0229155	−	0.0396908i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	5.62292e10			0.298140			0.149070	−	0.988827i	$-0.452372\pi$
$659$	5.62292e10			0.298140			0.149070	+	0.988827i	$0.452372\pi$
$660$		0			0
$661$	1.99084e11	+	1.14941e11i	1.04287	+	0.602102i	0.920645	−	0.390400i	$-0.127663\pi$
$661$	1.99084e11	+	1.14941e11i	1.04287	+	0.602102i	0.122226	+	0.992502i	$0.460997\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.72124e11	−	4.09425e11i	−0.880147	−	2.09357i
$666$		0			0
$667$	5.99843e10	+	1.03896e11i	0.303064	+	0.524922i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			4.16400e11i			2.05410i
$672$		0			0
$673$	9.84906e10			0.480103			0.240052	−	0.970760i	$-0.422836\pi$
$673$	9.84906e10			0.480103			0.240052	+	0.970760i	$0.422836\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.28763e11	+	7.43413e10i	−0.612965	+	0.353896i	−0.774125	−	0.633033i	$-0.781810\pi$
$677$	−1.28763e11	+	7.43413e10i	−0.612965	+	0.353896i	0.161160	+	0.986928i	$0.448477\pi$
$678$		0			0
$679$	−7.56165e10	−	5.73917e10i	−0.355744	−	0.270004i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.76448e11	+	3.05616e11i	−0.810836	+	1.40441i	0.101444	+	0.994841i	$0.467654\pi$
$683$	−1.76448e11	+	3.05616e11i	−0.810836	+	1.40441i	−0.912280	+	0.409568i	$0.865680\pi$
$684$		0			0
$685$		−	1.20172e11i		−	0.545811i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.55951e10	−	4.36449e10i	−0.335442	−	0.193667i
$690$		0			0
$691$	−2.91147e11	+	1.68094e11i	−1.27703	+	0.737291i	−0.976300	−	0.216420i	$-0.930562\pi$
$691$	−2.91147e11	+	1.68094e11i	−1.27703	+	0.737291i	−0.300725	+	0.953711i	$0.597229\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.79924e11	+	3.11637e11i	0.771168	+	1.33570i
$696$		0			0
$697$	−2.88882e11	+	5.00358e11i	−1.22402	+	2.12007i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−4.11369e11			−1.70357			−0.851784	−	0.523893i	$-0.824479\pi$
$701$	−4.11369e11			−1.70357			−0.851784	+	0.523893i	$0.824479\pi$
$702$		0			0
$703$	−3.18156e11	−	1.83687e11i	−1.30262	−	0.752070i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.59290e11	+	1.09007e11i	−1.03778	+	0.436290i
$708$		0			0
$709$	−6.95122e10	−	1.20399e11i	−0.275091	−	0.476472i	0.695067	−	0.718945i	$-0.255375\pi$
$709$	−6.95122e10	−	1.20399e11i	−0.275091	−	0.476472i	−0.970158	+	0.242473i	$0.922041\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			1.34066e11i			0.518751i
$714$		0			0
$715$	1.82284e11			0.697469
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.01094e11	−	5.83667e10i	0.378277	−	0.218398i	−0.298791	−	0.954318i	$-0.596583\pi$
$719$	1.01094e11	−	5.83667e10i	0.378277	−	0.218398i	0.677068	+	0.735920i	$0.263250\pi$
$720$		0			0
$721$	−1.46699e10	+	1.16159e11i	−0.0542857	+	0.429843i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.23193e11	−	3.86581e11i	0.807846	−	1.39923i
$726$		0			0
$727$			2.43338e11i			0.871109i	0.900162	+	0.435555i	$0.143448\pi$
$727$			2.43338e11i			0.871109i	−0.900162	+	0.435555i	$0.856552\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.10722e11	+	2.94865e11i	1.78861	+	1.03265i
$732$		0			0
$733$	4.20029e11	−	2.42504e11i	1.45500	−	0.840046i	0.456243	−	0.889855i	$-0.349195\pi$
$733$	4.20029e11	−	2.42504e11i	1.45500	−	0.840046i	0.998759	+	0.0498097i	$0.0158615\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.16710e11	+	2.02147e11i	0.395582	+	0.685169i
$738$		0			0
$739$	−1.98657e11	+	3.44083e11i	−0.666078	+	1.15368i	0.312913	+	0.949782i	$0.398695\pi$
$739$	−1.98657e11	+	3.44083e11i	−0.666078	+	1.15368i	−0.978992	+	0.203900i	$0.934638\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−2.20639e11			−0.723980			−0.361990	−	0.932182i	$-0.617903\pi$
$743$	−2.20639e11			−0.723980			−0.361990	+	0.932182i	$0.617903\pi$
$744$		0			0
$745$	−6.52591e11	−	3.76774e11i	−2.11844	−	1.22308i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.81327e11	−	3.55294e10i	−0.893892	−	0.112891i
$750$		0			0
$751$	2.44854e8	+	4.24099e8i	0.000769745	+	0.00133324i	0.866410	−	0.499333i	$-0.166422\pi$
$751$	2.44854e8	+	4.24099e8i	0.000769745	+	0.00133324i	−0.865640	+	0.500666i	$0.833088\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			8.91624e11i			2.74406i
$756$		0			0
$757$	−6.35724e10			−0.193591			−0.0967955	−	0.995304i	$-0.530859\pi$
$757$	−6.35724e10			−0.193591			−0.0967955	+	0.995304i	$0.530859\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.15892e10	+	2.97850e10i	−0.153823	+	0.0888095i	−0.574936	−	0.818199i	$-0.694973\pi$
$761$	−5.15892e10	+	2.97850e10i	−0.153823	+	0.0888095i	0.421113	+	0.907008i	$0.361640\pi$
$762$		0			0
$763$	1.40449e10	+	3.34079e10i	0.0414399	+	0.0985715i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.64884e10	+	8.05203e10i	−0.134327	+	0.232661i
$768$		0			0
$769$		−	3.28466e11i		−	0.939259i	−0.882864	−	0.469629i	$-0.844388\pi$
$769$		−	3.28466e11i		−	0.939259i	0.882864	−	0.469629i	$-0.155612\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.19975e11	−	2.42473e11i	−1.17627	−	0.679117i	−0.221118	−	0.975247i	$-0.570970\pi$
$773$	−4.19975e11	−	2.42473e11i	−1.17627	−	0.679117i	−0.955148	+	0.296130i	$0.904304\pi$
$774$		0			0
$775$	4.32007e11	−	2.49420e11i	1.19752	−	0.691391i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	4.64955e11	+	8.05325e11i	1.26259	+	2.18686i
$780$		0			0
$781$	−1.00541e11	+	1.74143e11i	−0.270234	+	0.468060i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−5.21589e11			−1.37357
$786$		0			0
$787$	2.48776e11	+	1.43631e11i	0.648500	+	0.374412i	0.787881	−	0.615827i	$-0.211178\pi$
$787$	2.48776e11	+	1.43631e11i	0.648500	+	0.374412i	−0.139381	+	0.990239i	$0.544511\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.00782e11	−	1.32785e11i	0.257440	−	0.339190i
$792$		0			0
$793$	−1.22894e11	−	2.12859e11i	−0.310769	−	0.538269i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			2.39071e11i			0.592506i	0.955109	+	0.296253i	$0.0957372\pi$
$797$			2.39071e11i			0.592506i	−0.955109	+	0.296253i	$0.904263\pi$
$798$		0			0
$799$	−3.38495e11			−0.830548
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.09245e11	+	1.78543e11i	−0.743773	+	0.429418i
$804$		0			0
$805$	5.07634e11	−	2.13412e11i	1.20884	−	0.508200i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.36214e10	+	9.28750e10i	−0.125183	+	0.216823i	−0.921804	−	0.387656i	$-0.873285\pi$
$809$	−5.36214e10	+	9.28750e10i	−0.125183	+	0.216823i	0.796622	+	0.604478i	$0.206618\pi$
$810$		0			0
$811$			1.36934e11i			0.316540i	0.987396	+	0.158270i	$0.0505916\pi$
$811$			1.36934e11i			0.316540i	−0.987396	+	0.158270i	$0.949408\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−5.72535e11	−	3.30553e11i	−1.29769	−	0.749222i
$816$		0			0
$817$	8.22006e11	−	4.74586e11i	1.84496	−	1.06519i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.88762e11	+	3.26945e11i	0.415472	+	0.719619i	0.995478	−	0.0949936i	$-0.0302831\pi$
$821$	1.88762e11	+	3.26945e11i	0.415472	+	0.719619i	−0.580006	+	0.814612i	$0.696950\pi$
$822$		0			0
$823$	−3.58340e11	+	6.20662e11i	−0.781080	+	1.35287i	0.150233	+	0.988651i	$0.451998\pi$
$823$	−3.58340e11	+	6.20662e11i	−0.781080	+	1.35287i	−0.931313	+	0.364220i	$0.881336\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	4.45077e11			0.951510			0.475755	−	0.879578i	$-0.342175\pi$
$827$	4.45077e11			0.951510			0.475755	+	0.879578i	$0.342175\pi$
$828$		0			0
$829$	−3.52361e11	−	2.03436e11i	−0.746053	−	0.430734i	0.0782131	−	0.996937i	$-0.475079\pi$
$829$	−3.52361e11	−	2.03436e11i	−0.746053	−	0.430734i	−0.824266	+	0.566203i	$0.808412\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	1.51820e11	−	5.91483e11i	0.315319	−	1.22846i
$834$		0			0
$835$	1.00130e11	+	1.73431e11i	0.205977	+	0.356763i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	2.89090e11i		−	0.583424i	−0.956506	−	0.291712i	$-0.905775\pi$
$839$		−	2.89090e11i		−	0.583424i	0.956506	−	0.291712i	$-0.0942249\pi$
$840$		0			0
$841$	−1.78158e11			−0.356140
$842$		0			0
$843$		0			0
$844$		0			0
$845$	6.73291e11	−	3.88725e11i	1.32061	−	0.762457i
$846$		0			0
$847$	−1.67390e11	−	2.11400e10i	−0.325233	−	0.0410743i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.27749e11	−	3.94472e11i	0.434248	−	0.752139i
$852$		0			0
$853$			8.33755e11i			1.57486i	0.616404	+	0.787430i	$0.288589\pi$
$853$			8.33755e11i			1.57486i	−0.616404	+	0.787430i	$0.711411\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	5.63733e11	+	3.25471e11i	1.04508	+	0.603378i	0.921268	−	0.388927i	$-0.127154\pi$
$857$	5.63733e11	+	3.25471e11i	1.04508	+	0.603378i	0.123813	+	0.992306i	$0.460488\pi$
$858$		0			0
$859$	7.76570e11	−	4.48353e11i	1.42629	−	0.823469i	0.429464	−	0.903084i	$-0.358702\pi$
$859$	7.76570e11	−	4.48353e11i	1.42629	−	0.823469i	0.996826	+	0.0796151i	$0.0253691\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−4.04187e9	−	7.00073e9i	−0.00728684	−	0.0126212i	0.862359	−	0.506297i	$-0.168986\pi$
$863$	−4.04187e9	−	7.00073e9i	−0.00728684	−	0.0126212i	−0.869646	+	0.493676i	$0.835653\pi$
$864$		0			0
$865$	1.83175e11	−	3.17268e11i	0.327191	−	0.566711i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.90582e11			−0.509553
$870$		0			0
$871$	−1.19321e11	−	6.88901e10i	−0.207322	−	0.119697i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−8.21545e11	−	6.23539e11i	−1.40152	−	1.06373i
$876$		0			0
$877$	−2.91022e11	−	5.04065e11i	−0.491957	−	0.852095i	0.508000	−	0.861357i	$-0.330385\pi$
$877$	−2.91022e11	−	5.04065e11i	−0.491957	−	0.852095i	−0.999957	+	0.00926195i	$0.997052\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			3.79168e11i			0.629403i	0.949191	+	0.314701i	$0.101904\pi$
$881$			3.79168e11i			0.629403i	−0.949191	+	0.314701i	$0.898096\pi$
$882$		0			0
$883$	2.21424e11			0.364235			0.182118	−	0.983277i	$-0.441705\pi$
$883$	2.21424e11			0.364235			0.182118	+	0.983277i	$0.441705\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.45661e11	+	1.41832e11i	−0.396863	+	0.229129i	−0.685130	−	0.728421i	$-0.740255\pi$
$887$	−2.45661e11	+	1.41832e11i	−0.396863	+	0.229129i	0.288266	+	0.957550i	$0.406921\pi$
$888$		0			0
$889$	−1.45358e11	+	1.91517e11i	−0.232719	+	0.306620i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.72403e11	+	4.71817e11i	−0.428358	+	0.741938i
$894$		0			0
$895$			6.35151e11i			0.989885i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.11714e11	+	1.79968e11i	0.477219	+	0.275522i
$900$		0			0
$901$	−8.04112e11	+	4.64254e11i	−1.22016	+	0.704461i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.02016e11	−	1.21593e12i	−1.04653	−	1.81265i
$906$		0			0
$907$	3.30665e11	−	5.72728e11i	0.488606	−	0.846290i	−0.511308	−	0.859397i	$-0.670839\pi$
$907$	3.30665e11	−	5.72728e11i	0.488606	−	0.846290i	0.999914	+	0.0131074i	$0.00417235\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	9.94922e11			1.44449			0.722247	−	0.691635i	$-0.243110\pi$
$911$	9.94922e11			1.44449			0.722247	+	0.691635i	$0.243110\pi$
$912$		0			0
$913$	9.97417e11	+	5.75859e11i	1.43547	+	0.828768i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.33903e9	−	1.85209e10i	0.00330795	−	0.0261929i
$918$		0			0
$919$	3.13835e11	+	5.43578e11i	0.439986	+	0.762079i	0.997688	−	0.0679630i	$-0.0216500\pi$
$919$	3.13835e11	+	5.43578e11i	0.439986	+	0.762079i	−0.557702	+	0.830042i	$0.688317\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		−	1.18693e11i		−	0.163538i
$924$		0			0
$925$	−1.69484e12			−2.31506
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−2.80765e11	+	1.62100e11i	−0.376947	+	0.217631i	−0.676489	−	0.736453i	$-0.736499\pi$
$929$	−2.80765e11	+	1.62100e11i	−0.376947	+	0.217631i	0.299542	+	0.954083i	$0.403166\pi$
$930$		0			0
$931$	−7.02271e11	−	6.87613e11i	−0.934772	−	0.915262i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	9.69486e11	−	1.67920e12i	1.26851	−	2.19713i
$936$		0			0
$937$			1.21189e12i			1.57219i	0.618108	+	0.786093i	$0.287899\pi$
$937$			1.21189e12i			1.57219i	−0.618108	+	0.786093i	$0.712101\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	1.35199e11	+	7.80573e10i	0.172431	+	0.0995531i	0.583732	−	0.811947i	$-0.301592\pi$
$941$	1.35199e11	+	7.80573e10i	0.172431	+	0.0995531i	−0.411301	+	0.911500i	$0.634925\pi$
$942$		0			0
$943$	−9.98499e11	+	5.76484e11i	−1.26270	+	0.729022i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.78356e10	−	3.08921e10i	−0.0221762	−	0.0384103i	0.854724	−	0.519082i	$-0.173726\pi$
$947$	−1.78356e10	−	3.08921e10i	−0.0221762	−	0.0384103i	−0.876901	+	0.480672i	$0.840393\pi$
$948$		0			0
$949$	1.05388e11	−	1.82538e11i	0.129935	−	0.225055i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.75336e11			0.212569			0.106284	−	0.994336i	$-0.466105\pi$
$953$	1.75336e11			0.212569			0.106284	+	0.994336i	$0.466105\pi$
$954$		0			0
$955$	1.46588e12	+	8.46326e11i	1.76232	+	1.01748i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.03063e11	−	2.45153e11i	−0.121851	−	0.289843i
$960$		0			0
$961$	−2.25330e11	−	3.90283e11i	−0.264196	−	0.457600i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	1.90262e12i		−	2.19403i
$966$		0			0
$967$	−6.32296e11			−0.723127			−0.361563	−	0.932348i	$-0.617757\pi$
$967$	−6.32296e11			−0.723127			−0.361563	+	0.932348i	$0.617757\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.20551e11	−	2.42805e11i	0.473088	−	0.273137i	−0.244444	−	0.969664i	$-0.578605\pi$
$971$	4.20551e11	−	2.42805e11i	0.473088	−	0.273137i	0.717531	+	0.696526i	$0.245272\pi$
$972$		0			0
$973$	6.34316e11	+	4.81435e11i	0.707708	+	0.537138i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	3.84268e11	−	6.65572e11i	0.421751	−	0.730495i	−0.574360	−	0.818603i	$-0.694749\pi$
$977$	3.84268e11	−	6.65572e11i	0.421751	−	0.730495i	0.996111	+	0.0881084i	$0.0280822\pi$
$978$		0			0
$979$		−	1.53345e12i		−	1.66932i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.58883e10	+	5.53611e10i	0.102695	+	0.0592913i	0.550468	−	0.834856i	$-0.314449\pi$
$983$	9.58883e10	+	5.53611e10i	0.102695	+	0.0592913i	−0.447773	+	0.894147i	$0.647783\pi$
$984$		0			0
$985$	1.67838e12	−	9.69014e11i	1.78298	−	1.02940i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.88425e11	+	1.01918e12i	0.615043	+	1.06529i
$990$		0			0
$991$	5.66493e11	−	9.81195e11i	0.587354	−	1.01733i	−0.407223	−	0.913329i	$-0.633503\pi$
$991$	5.66493e11	−	9.81195e11i	0.587354	−	1.01733i	0.994577	−	0.103999i	$-0.0331638\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−3.26386e12			−3.32996
$996$		0			0
$997$	−1.13793e12	−	6.56982e11i	−1.15168	−	0.664925i	−0.202387	−	0.979306i	$-0.564870\pi$
$997$	−1.13793e12	−	6.56982e11i	−1.15168	−	0.664925i	−0.949297	+	0.314380i	$0.898203\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.d.73.6		12
3.2	odd	2		84.9.m.b.73.1	yes	12
7.5	odd	6	inner	252.9.z.d.145.6		12
21.5	even	6		84.9.m.b.61.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.m.b.61.1	✓	12	21.5	even	6
84.9.m.b.73.1	yes	12	3.2	odd	2
252.9.z.d.73.6		12	1.1	even	1	trivial
252.9.z.d.145.6		12	7.5	odd	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)

\(f(q)\)	\(=\)	\(q+(939.615 - 542.487i) q^{5} +(1451.57 - 1912.52i) q^{7} +O(q^{10})\)	\(q+(939.615 - 542.487i) q^{5} +(1451.57 - 1912.52i) q^{7} +(8435.48 - 14610.7i) q^{11} +9958.41i q^{13} +(91736.7 + 52964.2i) q^{17} +(147650. - 85245.9i) q^{19} +(105694. + 183067. i) q^{23} +(393272. - 681166. i) q^{25} +567529. q^{29} +(549248. + 317108. i) q^{31} +(326400. - 2.58449e6i) q^{35} +(-1.07740e6 - 1.86611e6i) q^{37} +5.45428e6i q^{41} +5.56726e6 q^{43} +(-2.76739e6 + 1.59775e6i) q^{47} +(-1.55068e6 - 5.55233e6i) q^{49} +(-4.38272e6 + 7.59109e6i) q^{53} -1.83046e7i q^{55} +(8.08566e6 + 4.66826e6i) q^{59} +(-2.13748e7 + 1.23407e7i) q^{61} +(5.40231e6 + 9.35707e6i) q^{65} +(-6.91779e6 + 1.19820e7i) q^{67} -1.19189e7 q^{71} +(-1.83300e7 - 1.05828e7i) q^{73} +(-1.56985e7 - 3.73415e7i) q^{77} +(-8.61190e6 - 1.49162e7i) q^{79} +6.82663e7i q^{83} +1.14930e8 q^{85} +(7.87155e7 - 4.54464e7i) q^{89} +(1.90457e7 + 1.44553e7i) q^{91} +(9.24895e7 - 1.60197e8i) q^{95} -3.95376e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) 12 * q - 285 * q^5 + 198 * q^7	\( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Introduction

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