LMFDB - Embedded newform 252.9.z.e.145.4

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			145.4
Root			$286.330 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	252.145
Dual form			252.9.z.e.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-428.745 - 247.536i) q^{5} +(1933.79 + 1423.12i) q^{7} +O(q^{10})$	$q+(-428.745 - 247.536i) q^{5} +(1933.79 + 1423.12i) q^{7} +(1062.17 + 1839.73i) q^{11} -15639.3i q^{13} +(48991.8 - 28285.4i) q^{17} +(-140021. - 80841.3i) q^{19} +(-223626. + 387331. i) q^{23} +(-72764.3 - 126031. i) q^{25} +1.33434e6 q^{29} +(-467329. + 269813. i) q^{31} +(-476829. - 1.08884e6i) q^{35} +(531934. - 921336. i) q^{37} +4.94716e6i q^{41} +2.05532e6 q^{43} +(2.47316e6 + 1.42788e6i) q^{47} +(1.71427e6 + 5.50402e6i) q^{49} +(-6.97472e6 - 1.20806e7i) q^{53} -1.05170e6i q^{55} +(5.87945e6 - 3.39450e6i) q^{59} +(480161. + 277221. i) q^{61} +(-3.87130e6 + 6.70529e6i) q^{65} +(-1.71524e7 - 2.97088e7i) q^{67} -2.21608e7 q^{71} +(-1.19338e7 + 6.89001e6i) q^{73} +(-564145. + 5.06924e6i) q^{77} +(1.94917e7 - 3.37606e7i) q^{79} -6.23163e7i q^{83} -2.80066e7 q^{85} +(4.64932e7 + 2.68429e7i) q^{89} +(2.22566e7 - 3.02432e7i) q^{91} +(4.00223e7 + 6.93206e7i) q^{95} -2.92340e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

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
$5$	−428.745	−	247.536i	−0.685992	−	0.396058i	0.116117	−	0.993236i	$-0.462955\pi$
$5$	−428.745	−	247.536i	−0.685992	−	0.396058i	−0.802109	+	0.597178i	$0.796289\pi$
$6$		0			0
$7$	1933.79	+	1423.12i	0.805409	+	0.592719i
$7$	1933.79	+	1423.12i	0.805409	+	0.592719i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1062.17	+	1839.73i	0.0725475	+	0.125656i	0.900017	−	0.435854i	$-0.143554\pi$
$11$	1062.17	+	1839.73i	0.0725475	+	0.125656i	−0.827470	+	0.561510i	$0.810220\pi$
$12$		0			0
$13$		−	15639.3i		−	0.547577i	−0.961790	−	0.273788i	$-0.911723\pi$
$13$		−	15639.3i		−	0.547577i	0.961790	−	0.273788i	$-0.0882768\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	48991.8	−	28285.4i	0.586580	−	0.338662i	−0.177164	−	0.984181i	$-0.556692\pi$
$17$	48991.8	−	28285.4i	0.586580	−	0.338662i	0.763744	+	0.645519i	$0.223359\pi$
$18$		0			0
$19$	−140021.	−	80841.3i	−1.07443	−	0.620325i	−0.145044	−	0.989425i	$-0.546332\pi$
$19$	−140021.	−	80841.3i	−1.07443	−	0.620325i	−0.929390	+	0.369100i	$0.879666\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−223626.	+	387331.i	−0.799117	+	1.38411i	0.121075	+	0.992643i	$0.461366\pi$
$23$	−223626.	+	387331.i	−0.799117	+	1.38411i	−0.920192	+	0.391467i	$0.871968\pi$
$24$		0			0
$25$	−72764.3	−	126031.i	−0.186277	−	0.322641i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.33434e6			1.88658			0.943291	−	0.331966i	$-0.107712\pi$
$29$	1.33434e6			1.88658			0.943291	+	0.331966i	$0.107712\pi$
$30$		0			0
$31$	−467329.	+	269813.i	−0.506030	+	0.292156i	−0.731200	−	0.682163i	$-0.761039\pi$
$31$	−467329.	+	269813.i	−0.506030	+	0.292156i	0.225170	+	0.974319i	$0.427706\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−476829.	−	1.08884e6i	−0.317753	−	0.725589i
$36$		0			0
$37$	531934.	−	921336.i	0.283825	−	0.491599i	−0.688499	−	0.725238i	$-0.741730\pi$
$37$	531934.	−	921336.i	0.283825	−	0.491599i	0.972324	+	0.233638i	$0.0750632\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			4.94716e6i			1.75073i	0.483459	+	0.875367i	$0.339380\pi$
$41$			4.94716e6i			1.75073i	−0.483459	+	0.875367i	$0.660620\pi$
$42$		0			0
$43$	2.05532e6			0.601180			0.300590	−	0.953753i	$-0.402816\pi$
$43$	2.05532e6			0.601180			0.300590	+	0.953753i	$0.402816\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.47316e6	+	1.42788e6i	0.506828	+	0.292617i	0.731529	−	0.681811i	$-0.238807\pi$
$47$	2.47316e6	+	1.42788e6i	0.506828	+	0.292617i	−0.224701	+	0.974428i	$0.572141\pi$
$48$		0			0
$49$	1.71427e6	+	5.50402e6i	0.297368	+	0.954763i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−6.97472e6	−	1.20806e7i	−0.883941	−	1.53103i	−0.846923	−	0.531715i	$-0.821548\pi$
$53$	−6.97472e6	−	1.20806e7i	−0.883941	−	1.53103i	−0.0370175	−	0.999315i	$-0.511786\pi$
$54$		0			0
$55$		−	1.05170e6i		−	0.114932i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.87945e6	−	3.39450e6i	0.485209	−	0.280136i	−0.237376	−	0.971418i	$-0.576287\pi$
$59$	5.87945e6	−	3.39450e6i	0.485209	−	0.280136i	0.722585	+	0.691282i	$0.242954\pi$
$60$		0			0
$61$	480161.	+	277221.i	0.0346791	+	0.0200220i	0.517239	−	0.855841i	$-0.326960\pi$
$61$	480161.	+	277221.i	0.0346791	+	0.0200220i	−0.482560	+	0.875863i	$0.660293\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.87130e6	+	6.70529e6i	−0.216872	+	0.375633i
$66$		0			0
$67$	−1.71524e7	−	2.97088e7i	−0.851188	−	1.47430i	−0.880137	−	0.474720i	$-0.842549\pi$
$67$	−1.71524e7	−	2.97088e7i	−0.851188	−	1.47430i	0.0289486	−	0.999581i	$-0.490784\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.21608e7			−0.872071			−0.436036	−	0.899929i	$-0.643618\pi$
$71$	−2.21608e7			−0.872071			−0.436036	+	0.899929i	$0.643618\pi$
$72$		0			0
$73$	−1.19338e7	+	6.89001e6i	−0.420232	+	0.242621i	−0.695177	−	0.718839i	$-0.744674\pi$
$73$	−1.19338e7	+	6.89001e6i	−0.420232	+	0.242621i	0.274945	+	0.961460i	$0.411340\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−564145.	+	5.06924e6i	−0.0160483	+	0.144205i
$78$		0			0
$79$	1.94917e7	−	3.37606e7i	0.500428	−	0.866767i	−0.499572	−	0.866272i	$-0.666509\pi$
$79$	1.94917e7	−	3.37606e7i	0.500428	−	0.866767i	1.00000		0.000494391i	$-0.000157370\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	6.23163e7i		−	1.31307i	−0.754294	−	0.656537i	$-0.772021\pi$
$83$		−	6.23163e7i		−	1.31307i	0.754294	−	0.656537i	$-0.227979\pi$
$84$		0			0
$85$	−2.80066e7			−0.536519
$86$		0			0
$87$		0			0
$88$		0			0
$89$	4.64932e7	+	2.68429e7i	0.741019	+	0.427827i	0.822440	−	0.568852i	$-0.192612\pi$
$89$	4.64932e7	+	2.68429e7i	0.741019	+	0.427827i	−0.0814208	+	0.996680i	$0.525946\pi$
$90$		0			0
$91$	2.22566e7	−	3.02432e7i	0.324559	−	0.441023i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.00223e7	+	6.93206e7i	0.491369	+	0.851076i
$96$		0			0
$97$		−	2.92340e7i		−	0.330218i	−0.986275	−	0.165109i	$-0.947202\pi$
$97$		−	2.92340e7i		−	0.330218i	0.986275	−	0.165109i	$-0.0527977\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.15074e8	+	6.64378e7i	−1.10583	+	0.638454i	−0.937747	−	0.347318i	$-0.887092\pi$
$101$	−1.15074e8	+	6.64378e7i	−1.10583	+	0.638454i	−0.168087	+	0.985772i	$0.553759\pi$
$102$		0			0
$103$	−8.24124e7	−	4.75808e7i	−0.732224	−	0.422750i	0.0870114	−	0.996207i	$-0.472268\pi$
$103$	−8.24124e7	−	4.75808e7i	−0.732224	−	0.422750i	−0.819235	+	0.573458i	$0.805602\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.88716e7	−	6.73275e7i	0.296549	−	0.513638i	−0.678795	−	0.734328i	$-0.737497\pi$
$107$	3.88716e7	−	6.73275e7i	0.296549	−	0.513638i	0.975344	+	0.220690i	$0.0708308\pi$
$108$		0			0
$109$	−1.53205e7	−	2.65360e7i	−0.108535	−	0.187987i	0.806642	−	0.591040i	$-0.201282\pi$
$109$	−1.53205e7	−	2.65360e7i	−0.108535	−	0.187987i	−0.915177	+	0.403053i	$0.867949\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.30284e8			0.799056			0.399528	−	0.916721i	$-0.369174\pi$
$113$	1.30284e8			0.799056			0.399528	+	0.916721i	$0.369174\pi$
$114$		0			0
$115$	1.91757e8	−	1.10711e8i	1.09638	−	0.632993i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.34993e8	+	1.50231e7i	0.673169	+	0.0749156i
$120$		0			0
$121$	1.04923e8	−	1.81732e8i	0.489474	−	0.847793i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			2.65435e8i			1.08722i
$126$		0			0
$127$	−2.78124e8			−1.06911			−0.534557	−	0.845132i	$-0.679522\pi$
$127$	−2.78124e8			−1.06911			−0.534557	+	0.845132i	$0.679522\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.16821e8	−	1.82917e8i	−1.07579	−	0.621110i	−0.146036	−	0.989279i	$-0.546651\pi$
$131$	−3.16821e8	−	1.82917e8i	−1.07579	−	0.621110i	−0.929759	+	0.368169i	$0.879985\pi$
$132$		0			0
$133$	−1.55725e8	−	3.55597e8i	−0.497681	−	1.13645i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.91348e8	−	3.31425e8i	−0.543178	−	0.940812i	−0.998719	−	0.0505971i	$-0.983888\pi$
$137$	−1.91348e8	−	3.31425e8i	−0.543178	−	0.940812i	0.455541	−	0.890215i	$-0.349446\pi$
$138$		0			0
$139$		−	5.95007e8i		−	1.59391i	−0.604040	−	0.796954i	$-0.706443\pi$
$139$		−	5.95007e8i		−	1.59391i	0.604040	−	0.796954i	$-0.293557\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.87722e7	−	1.66116e7i	0.0688063	−	0.0397253i
$144$		0			0
$145$	−5.72093e8	−	3.30298e8i	−1.29418	−	0.747196i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.12693e8	−	1.95190e8i	0.228639	−	0.396015i	−0.728766	−	0.684763i	$-0.759906\pi$
$149$	1.12693e8	−	1.95190e8i	0.228639	−	0.396015i	0.957405	+	0.288748i	$0.0932390\pi$
$150$		0			0
$151$	−4.57375e8	−	7.92196e8i	−0.879760	−	1.52379i	−0.851604	−	0.524185i	$-0.824370\pi$
$151$	−4.57375e8	−	7.92196e8i	−0.879760	−	1.52379i	−0.0281557	−	0.999604i	$-0.508963\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.67153e8			0.462843
$156$		0			0
$157$	1.82590e8	−	1.05418e8i	0.300523	−	0.173507i	−0.342155	−	0.939644i	$-0.611157\pi$
$157$	1.82590e8	−	1.05418e8i	0.300523	−	0.173507i	0.642678	+	0.766136i	$0.277823\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−9.83662e8	+	4.30770e8i	−1.46400	+	0.641124i
$162$		0			0
$163$	1.37742e8	−	2.38576e8i	0.195126	−	0.337969i	−0.751816	−	0.659373i	$-0.770822\pi$
$163$	1.37742e8	−	2.38576e8i	0.195126	−	0.337969i	0.946942	+	0.321405i	$0.104155\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	5.66593e8i		−	0.728460i	−0.931309	−	0.364230i	$-0.881332\pi$
$167$		−	5.66593e8i		−	0.728460i	0.931309	−	0.364230i	$-0.118668\pi$
$168$		0			0
$169$	5.71142e8			0.700160
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.27950e9	+	7.38720e8i	1.42842	+	0.824699i	0.996996	−	0.0774499i	$-0.0246778\pi$
$173$	1.27950e9	+	7.38720e8i	1.42842	+	0.824699i	0.431425	+	0.902149i	$0.358011\pi$
$174$		0			0
$175$	3.86470e7	−	3.47270e8i	0.0412063	−	0.370267i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.83010e8	−	6.63393e8i	−0.373077	−	0.646188i	0.616960	−	0.786994i	$-0.288364\pi$
$179$	−3.83010e8	−	6.63393e8i	−0.373077	−	0.646188i	−0.990037	+	0.140806i	$0.955031\pi$
$180$		0			0
$181$		−	1.84765e9i		−	1.72150i	−0.509030	−	0.860749i	$-0.669996\pi$
$181$		−	1.84765e9i		−	1.72150i	0.509030	−	0.860749i	$-0.330004\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.56128e8	+	2.63345e8i	−0.389403	+	0.224822i
$186$		0			0
$187$	1.04075e8	+	6.00878e7i	0.0851099	+	0.0491382i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−1.14741e8	+	1.98737e8i	−0.0862152	+	0.149329i	−0.905908	−	0.423474i	$-0.860811\pi$
$191$	−1.14741e8	+	1.98737e8i	−0.0862152	+	0.149329i	0.819693	+	0.572803i	$0.194144\pi$
$192$		0			0
$193$	−7.44633e8	−	1.28974e9i	−0.536677	−	0.929552i	−0.999080	−	0.0428820i	$-0.986346\pi$
$193$	−7.44633e8	−	1.28974e9i	−0.536677	−	0.929552i	0.462403	−	0.886670i	$-0.346987\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.44196e8			0.294924			0.147462	−	0.989068i	$-0.452890\pi$
$197$	4.44196e8			0.294924			0.147462	+	0.989068i	$0.452890\pi$
$198$		0			0
$199$	−1.25444e9	+	7.24251e8i	−0.799904	+	0.461825i	−0.843437	−	0.537227i	$-0.819472\pi$
$199$	−1.25444e9	+	7.24251e8i	−0.799904	+	0.461825i	0.0435338	+	0.999052i	$0.486138\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.58034e9	+	1.89893e9i	1.51947	+	1.11821i
$204$		0			0
$205$	1.22460e9	−	2.12107e9i	0.693392	−	1.20099i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	3.43469e8i		−	0.180012i
$210$		0			0
$211$	−1.24503e8			−0.0628129			−0.0314065	−	0.999507i	$-0.509999\pi$
$211$	−1.24503e8			−0.0628129			−0.0314065	+	0.999507i	$0.509999\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.81206e8	−	5.08765e8i	−0.412405	−	0.238102i
$216$		0			0
$217$	−1.28769e9	−	1.43304e8i	−0.580728	−	0.0646280i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.42365e8	−	7.66199e8i	−0.185444	−	0.321198i
$222$		0			0
$223$		−	1.07401e9i		−	0.434300i	−0.976138	−	0.217150i	$-0.930324\pi$
$223$		−	1.07401e9i		−	0.434300i	0.976138	−	0.217150i	$-0.0696761\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−3.61590e9	+	2.08764e9i	−1.36180	+	0.786234i	−0.989863	−	0.142025i	$-0.954639\pi$
$227$	−3.61590e9	+	2.08764e9i	−1.36180	+	0.786234i	−0.371935	+	0.928259i	$0.621305\pi$
$228$		0			0
$229$	−2.27312e9	−	1.31238e9i	−0.826571	−	0.477221i	0.0261064	−	0.999659i	$-0.491689\pi$
$229$	−2.27312e9	−	1.31238e9i	−0.826571	−	0.477221i	−0.852677	+	0.522438i	$0.825022\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.84691e8	−	1.18592e9i	0.232312	−	0.402376i	−0.726176	−	0.687509i	$-0.758704\pi$
$233$	6.84691e8	−	1.18592e9i	0.232312	−	0.402376i	0.958488	+	0.285133i	$0.0920377\pi$
$234$		0			0
$235$	−7.06903e8	−	1.22439e9i	−0.231786	−	0.401466i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.37306e9			0.727307			0.363653	−	0.931534i	$-0.381529\pi$
$239$	2.37306e9			0.727307			0.363653	+	0.931534i	$0.381529\pi$
$240$		0			0
$241$	2.85917e9	−	1.65074e9i	0.847564	−	0.489341i	−0.0122645	−	0.999925i	$-0.503904\pi$
$241$	2.85917e9	−	1.65074e9i	0.847564	−	0.489341i	0.859828	+	0.510584i	$0.170571\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	6.27458e8	−	2.78416e9i	0.174149	−	0.772735i
$246$		0			0
$247$	−1.26430e9	+	2.18984e9i	−0.339675	+	0.588335i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	3.12960e7i		−	0.00788487i	−0.999992	−	0.00394244i	$-0.998745\pi$
$251$		−	3.12960e7i		−	0.00788487i	0.999992	−	0.00394244i	$-0.00125492\pi$
$252$		0			0
$253$	−9.50112e8			−0.231896
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.40586e8	−	3.69842e8i	−0.146840	−	0.0847782i	0.424780	−	0.905297i	$-0.360352\pi$
$257$	−6.40586e8	−	3.69842e8i	−0.146840	−	0.0847782i	−0.571620	+	0.820518i	$0.693685\pi$
$258$		0			0
$259$	2.33982e9	−	1.02466e9i	0.519975	−	0.227710i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.59579e9	−	4.49604e9i	−0.542558	−	0.939738i	−0.998756	−	0.0498601i	$-0.984122\pi$
$263$	−2.59579e9	−	4.49604e9i	−0.542558	−	0.939738i	0.456198	−	0.889878i	$-0.349211\pi$
$264$		0			0
$265$			6.90598e9i			1.40037i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−3.76648e9	+	2.17458e9i	−0.719328	+	0.415304i	−0.814505	−	0.580156i	$-0.802992\pi$
$269$	−3.76648e9	+	2.17458e9i	−0.719328	+	0.415304i	0.0951772	+	0.995460i	$0.469658\pi$
$270$		0			0
$271$	3.75508e9	+	2.16799e9i	0.696212	+	0.401958i	0.805935	−	0.592004i	$-0.201663\pi$
$271$	3.75508e9	+	2.16799e9i	0.696212	+	0.401958i	−0.109723	+	0.993962i	$0.534996\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.54576e8	−	2.67733e8i	0.0270278	−	0.0468136i
$276$		0			0
$277$	5.19364e9	+	8.99565e9i	0.882171	+	1.52797i	0.848922	+	0.528518i	$0.177252\pi$
$277$	5.19364e9	+	8.99565e9i	0.882171	+	1.52797i	0.0332491	+	0.999447i	$0.489415\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.25066e9			0.842149			0.421074	−	0.907026i	$-0.361653\pi$
$281$	5.25066e9			0.842149			0.421074	+	0.907026i	$0.361653\pi$
$282$		0			0
$283$	−4.61734e8	+	2.66582e8i	−0.0719857	+	0.0415610i	−0.535561	−	0.844497i	$-0.679900\pi$
$283$	−4.61734e8	+	2.66582e8i	−0.0719857	+	0.0415610i	0.463575	+	0.886058i	$0.346566\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.04039e9	+	9.56675e9i	−1.03769	+	1.41006i
$288$		0			0
$289$	−1.88775e9	+	3.26968e9i	−0.270616	+	0.468720i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	4.02293e9i		−	0.545849i	−0.962036	−	0.272924i	$-0.912009\pi$
$293$		−	4.02293e9i		−	0.545849i	0.962036	−	0.272924i	$-0.0879908\pi$
$294$		0			0
$295$	−3.36105e9			−0.443799
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.05760e9	+	3.49736e9i	0.757907	+	0.437578i
$300$		0			0
$301$	3.97454e9	+	2.92496e9i	0.484196	+	0.356331i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.37245e8	−	2.37714e8i	−0.0158597	−	0.0274699i
$306$		0			0
$307$			7.66029e9i			0.862366i	0.902265	+	0.431183i	$0.141904\pi$
$307$			7.66029e9i			0.862366i	−0.902265	+	0.431183i	$0.858096\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.30940e10	−	7.55982e9i	1.39969	−	0.808109i	0.405326	−	0.914172i	$-0.367158\pi$
$311$	1.30940e10	−	7.55982e9i	1.39969	−	0.808109i	0.994359	+	0.106063i	$0.0338246\pi$
$312$		0			0
$313$	2.40149e9	+	1.38650e9i	0.250209	+	0.144458i	0.619860	−	0.784712i	$-0.287189\pi$
$313$	2.40149e9	+	1.38650e9i	0.250209	+	0.144458i	−0.369651	+	0.929171i	$0.620523\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.98768e9	−	3.44277e9i	0.196839	−	0.340934i	−0.750663	−	0.660685i	$-0.770266\pi$
$317$	1.98768e9	−	3.44277e9i	0.196839	−	0.340934i	0.947502	+	0.319751i	$0.103599\pi$
$318$		0			0
$319$	1.41730e9	+	2.45483e9i	0.136867	+	0.237061i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−9.14652e9			−0.840322
$324$		0			0
$325$	−1.97105e9	+	1.13799e9i	−0.176670	+	0.102001i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.75052e9	+	6.28081e9i	0.234764	+	0.536083i
$330$		0			0
$331$	−4.95902e9	+	8.58927e9i	−0.413127	+	0.715557i	−0.995230	−	0.0975583i	$-0.968897\pi$
$331$	−4.95902e9	+	8.58927e9i	−0.413127	+	0.715557i	0.582103	+	0.813115i	$0.302230\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			1.69833e10i			1.34848i
$336$		0			0
$337$	7.98626e9			0.619189			0.309595	−	0.950869i	$-0.399807\pi$
$337$	7.98626e9			0.619189			0.309595	+	0.950869i	$0.399807\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−9.92765e8	−	5.73173e8i	−0.0734224	−	0.0423905i
$342$		0			0
$343$	−4.51784e9	+	1.30832e10i	−0.326403	+	0.945231i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.76637e9	+	3.05945e9i	0.121833	+	0.211021i	0.920491	−	0.390765i	$-0.127789\pi$
$347$	1.76637e9	+	3.05945e9i	0.121833	+	0.211021i	−0.798658	+	0.601786i	$0.794456\pi$
$348$		0			0
$349$			1.17888e10i			0.794638i	0.917680	+	0.397319i	$0.130059\pi$
$349$			1.17888e10i			0.794638i	−0.917680	+	0.397319i	$0.869941\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.39483e10	+	8.05305e9i	−0.898301	+	0.518634i	−0.876649	−	0.481131i	$-0.840226\pi$
$353$	−1.39483e10	+	8.05305e9i	−0.898301	+	0.518634i	−0.0216525	+	0.999766i	$0.506893\pi$
$354$		0			0
$355$	9.50133e9	+	5.48560e9i	0.598234	+	0.345391i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.78100e9	−	8.28093e9i	0.287833	−	0.498541i	−0.685459	−	0.728111i	$-0.740399\pi$
$359$	4.78100e9	−	8.28093e9i	0.287833	−	0.498541i	0.973292	+	0.229570i	$0.0737318\pi$
$360$		0			0
$361$	4.57886e9	+	7.93082e9i	0.269605	+	0.466970i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	6.82210e9			0.384368
$366$		0			0
$367$	−2.48860e10	+	1.43680e10i	−1.37180	+	0.792010i	−0.991155	−	0.132710i	$-0.957632\pi$
$367$	−2.48860e10	+	1.43680e10i	−1.37180	+	0.792010i	−0.380647	+	0.924720i	$0.624299\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.70445e9	−	3.32871e10i	0.195537	−	1.75703i
$372$		0			0
$373$	2.48457e9	−	4.30341e9i	0.128356	−	0.222319i	−0.794684	−	0.607024i	$-0.792363\pi$
$373$	2.48457e9	−	4.30341e9i	0.128356	−	0.222319i	0.923040	+	0.384704i	$0.125697\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	2.08683e10i		−	1.03305i
$378$		0			0
$379$	3.03220e10			1.46961			0.734804	−	0.678280i	$-0.237274\pi$
$379$	3.03220e10			1.46961			0.734804	+	0.678280i	$0.237274\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.45211e10	−	8.38379e9i	−0.674848	−	0.389624i	0.123063	−	0.992399i	$-0.460728\pi$
$383$	−1.45211e10	−	8.38379e9i	−0.674848	−	0.389624i	−0.797911	+	0.602775i	$0.794062\pi$
$384$		0			0
$385$	1.49669e9	−	2.03376e9i	0.0681224	−	0.0925674i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.83553e9	+	6.64334e9i	0.167505	+	0.290127i	0.937542	−	0.347872i	$-0.113096\pi$
$389$	3.83553e9	+	6.64334e9i	0.167505	+	0.290127i	−0.770037	+	0.637999i	$0.779762\pi$
$390$		0			0
$391$			2.53014e10i			1.08252i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−1.67140e10	+	9.64980e9i	−0.686579	+	0.396397i
$396$		0			0
$397$	1.70191e10	+	9.82597e9i	0.685132	+	0.395561i	0.801786	−	0.597612i	$-0.203884\pi$
$397$	1.70191e10	+	9.82597e9i	0.685132	+	0.395561i	−0.116654	+	0.993173i	$0.537217\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.16330e10	+	3.74694e10i	−0.836639	+	1.44910i	0.0560491	+	0.998428i	$0.482150\pi$
$401$	−2.16330e10	+	3.74694e10i	−0.836639	+	1.44910i	−0.892689	+	0.450674i	$0.851184\pi$
$402$		0			0
$403$	4.21969e9	+	7.30872e9i	0.159978	+	0.277090i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.26001e9			0.0823632
$408$		0			0
$409$	1.76795e10	−	1.02073e10i	0.631796	−	0.364768i	−0.149651	−	0.988739i	$-0.547815\pi$
$409$	1.76795e10	−	1.02073e10i	0.631796	−	0.364768i	0.781447	+	0.623971i	$0.214482\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.62004e10	+	1.80291e9i	0.556834	+	0.0619688i
$414$		0			0
$415$	−1.54255e10	+	2.67178e10i	−0.520053	+	0.900758i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	1.55195e10i		−	0.503524i	−0.967789	−	0.251762i	$-0.918990\pi$
$419$		−	1.55195e10i		−	0.503524i	0.967789	−	0.251762i	$-0.0810101\pi$
$420$		0			0
$421$	−2.58425e9			−0.0822633			−0.0411317	−	0.999154i	$-0.513096\pi$
$421$	−2.58425e9			−0.0822633			−0.0411317	+	0.999154i	$0.513096\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−7.12971e9	−	4.11634e9i	−0.218532	−	0.126170i
$426$		0			0
$427$	5.34011e8	+	1.21941e9i	0.0160635	+	0.0366809i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.10297e10	+	1.91041e10i	0.319637	+	0.553627i	0.980412	−	0.196957i	$-0.0631058\pi$
$431$	1.10297e10	+	1.91041e10i	0.319637	+	0.553627i	−0.660776	+	0.750583i	$0.729773\pi$
$432$		0			0
$433$		−	6.09726e10i		−	1.73453i	−0.497843	−	0.867267i	$-0.665874\pi$
$433$		−	6.09726e10i		−	1.73453i	0.497843	−	0.867267i	$-0.334126\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.26247e10	−	3.61564e10i	1.71720	−	0.991424i
$438$		0			0
$439$	−5.10681e10	−	2.94842e10i	−1.37497	−	0.793836i	−0.383417	−	0.923575i	$-0.625253\pi$
$439$	−5.10681e10	−	2.94842e10i	−1.37497	−	0.793836i	−0.991548	+	0.129739i	$0.958586\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	1.02703e10	−	1.77888e10i	0.266668	−	0.461882i	−0.701332	−	0.712835i	$-0.747411\pi$
$443$	1.02703e10	−	1.77888e10i	0.266668	−	0.461882i	0.967999	+	0.250953i	$0.0807441\pi$
$444$		0			0
$445$	−1.32891e10	−	2.30175e10i	−0.338889	−	0.586972i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.11616e10			−1.50485			−0.752425	−	0.658678i	$-0.771116\pi$
$449$	−6.11616e10			−1.50485			−0.752425	+	0.658678i	$0.771116\pi$
$450$		0			0
$451$	−9.10143e9	+	5.25471e9i	−0.219990	+	0.127011i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.70287e10	+	7.45729e9i	−0.397316	+	0.173994i
$456$		0			0
$457$	6.93723e9	−	1.20156e10i	0.159045	−	0.275475i	−0.775479	−	0.631373i	$-0.782492\pi$
$457$	6.93723e9	−	1.20156e10i	0.159045	−	0.275475i	0.934525	+	0.355898i	$0.115825\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			7.22295e10i			1.59923i	0.600513	+	0.799615i	$0.294963\pi$
$461$			7.22295e10i			1.59923i	−0.600513	+	0.799615i	$0.705037\pi$
$462$		0			0
$463$	−5.19540e10			−1.13056			−0.565281	−	0.824898i	$-0.691232\pi$
$463$	−5.19540e10			−1.13056			−0.565281	+	0.824898i	$0.691232\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	5.77578e10	+	3.33465e10i	1.21435	+	0.701104i	0.963703	−	0.266975i	$-0.0860242\pi$
$467$	5.77578e10	+	3.33465e10i	1.21435	+	0.701104i	0.250644	+	0.968079i	$0.419358\pi$
$468$		0			0
$469$	9.11008e9	−	8.18604e10i	0.188291	−	1.69193i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.18309e9	+	3.78122e9i	0.0436141	+	0.0755419i
$474$		0			0
$475$			2.35295e10i			0.462208i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	3.78886e10	−	2.18750e10i	0.719724	−	0.415533i	−0.0949269	−	0.995484i	$-0.530262\pi$
$479$	3.78886e10	−	2.18750e10i	0.719724	−	0.415533i	0.814651	+	0.579951i	$0.196928\pi$
$480$		0			0
$481$	−1.44091e10	−	8.31909e9i	−0.269188	−	0.155416i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.23647e9	+	1.25339e10i	−0.130786	+	0.226527i
$486$		0			0
$487$	−2.08822e9	−	3.61691e9i	−0.0371245	−	0.0643016i	0.846866	−	0.531806i	$-0.178486\pi$
$487$	−2.08822e9	−	3.61691e9i	−0.0371245	−	0.0643016i	−0.883991	+	0.467505i	$0.845153\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.01240e10			−0.518307			−0.259153	−	0.965836i	$-0.583443\pi$
$491$	−3.01240e10			−0.518307			−0.259153	+	0.965836i	$0.583443\pi$
$492$		0			0
$493$	6.53719e10	−	3.77425e10i	1.10663	−	0.638915i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.28543e10	−	3.15374e10i	−0.702374	−	0.516893i
$498$		0			0
$499$	3.25369e10	−	5.63555e10i	0.524776	−	0.908938i	−0.474808	−	0.880089i	$-0.657483\pi$
$499$	3.25369e10	−	5.63555e10i	0.524776	−	0.908938i	0.999584	−	0.0288486i	$-0.00918408\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	4.63371e10i		−	0.723864i	−0.932204	−	0.361932i	$-0.882117\pi$
$503$		−	4.63371e10i		−	0.723864i	0.932204	−	0.361932i	$-0.117883\pi$
$504$		0			0
$505$	6.57830e10			1.01146
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−3.46633e10	−	2.00129e10i	−0.516415	−	0.298152i	0.219052	−	0.975713i	$-0.429704\pi$
$509$	−3.46633e10	−	2.00129e10i	−0.516415	−	0.298152i	−0.735466	+	0.677561i	$0.763037\pi$
$510$		0			0
$511$	−3.28828e10	−	3.65946e9i	−0.482265	−	0.0536702i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	2.35559e10	+	4.08001e10i	0.334866	+	0.580006i
$516$		0			0
$517$			6.06659e9i			0.0849146i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.05814e10	−	2.34297e10i	0.550777	−	0.317992i	−0.198658	−	0.980069i	$-0.563658\pi$
$521$	4.05814e10	−	2.34297e10i	0.550777	−	0.317992i	0.749436	+	0.662077i	$0.230325\pi$
$522$		0			0
$523$	−7.50830e10	−	4.33492e10i	−1.00354	−	0.579395i	−0.0942468	−	0.995549i	$-0.530044\pi$
$523$	−7.50830e10	−	4.33492e10i	−1.00354	−	0.579395i	−0.909294	+	0.416154i	$0.863378\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.52635e10	+	2.64372e10i	−0.197885	+	0.342746i
$528$		0			0
$529$	−6.08613e10	−	1.05415e11i	−0.777175	−	1.34611i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.73702e10			0.958661
$534$		0			0
$535$	−3.33320e10	+	1.92442e10i	−0.406861	+	0.234901i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−8.30506e9	+	8.99999e9i	−0.0983984	+	0.106632i
$540$		0			0
$541$	3.33406e10	−	5.77477e10i	0.389211	−	0.674133i	−0.603133	−	0.797641i	$-0.706081\pi$
$541$	3.33406e10	−	5.77477e10i	0.389211	−	0.674133i	0.992344	+	0.123508i	$0.0394145\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			1.51695e10i			0.171944i
$546$		0			0
$547$	−3.37378e10			−0.376849			−0.188425	−	0.982088i	$-0.560338\pi$
$547$	−3.37378e10			−0.376849			−0.188425	+	0.982088i	$0.560338\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.86837e11	−	1.07870e11i	−2.02701	−	1.17029i
$552$		0			0
$553$	8.57382e10	−	3.75469e10i	0.916799	−	0.401489i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.38794e10	−	4.13604e10i	−0.248087	−	0.429699i	0.714908	−	0.699218i	$-0.246468\pi$
$557$	−2.38794e10	−	4.13604e10i	−0.248087	−	0.429699i	−0.962995	+	0.269520i	$0.913135\pi$
$558$		0			0
$559$		−	3.21438e10i		−	0.329192i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.30170e10	+	5.37034e10i	−0.925825	+	0.534525i	−0.885489	−	0.464661i	$-0.846176\pi$
$563$	−9.30170e10	+	5.37034e10i	−0.925825	+	0.534525i	−0.0403360	+	0.999186i	$0.512843\pi$
$564$		0			0
$565$	−5.58586e10	−	3.22500e10i	−0.548146	−	0.316472i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.54714e10	−	2.67973e10i	0.147598	−	0.255648i	−0.782741	−	0.622348i	$-0.786179\pi$
$569$	1.54714e10	−	2.67973e10i	0.147598	−	0.255648i	0.930339	+	0.366700i	$0.119512\pi$
$570$		0			0
$571$	−5.37493e10	−	9.30965e10i	−0.505625	−	0.875768i	−0.999979	−	0.00650703i	$-0.997929\pi$
$571$	−5.37493e10	−	9.30965e10i	−0.505625	−	0.875768i	0.494354	−	0.869261i	$-0.335405\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	6.50878e10			0.595427
$576$		0			0
$577$	−5.22110e10	+	3.01440e10i	−0.471041	+	0.271955i	−0.716675	−	0.697407i	$-0.754337\pi$
$577$	−5.22110e10	+	3.01440e10i	−0.471041	+	0.271955i	0.245635	+	0.969363i	$0.421004\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.86834e10	−	1.20506e11i	0.778284	−	1.05756i
$582$		0			0
$583$	1.48167e10	−	2.56632e10i	0.128255	−	0.222145i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			2.16561e10i			0.182401i	0.995833	+	0.0912005i	$0.0290704\pi$
$587$			2.16561e10i			0.182401i	−0.995833	+	0.0912005i	$0.970930\pi$
$588$		0			0
$589$	8.72480e10			0.724927
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.44121e11	+	8.32084e10i	1.16549	+	0.672897i	0.952614	−	0.304182i	$-0.0983831\pi$
$593$	1.44121e11	+	8.32084e10i	1.16549	+	0.672897i	0.212878	+	0.977079i	$0.431716\pi$
$594$		0			0
$595$	−5.41589e10	−	3.98568e10i	−0.432118	−	0.318005i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	8.40903e10	+	1.45649e11i	0.653189	+	1.13136i	0.982345	+	0.187080i	$0.0599024\pi$
$599$	8.40903e10	+	1.45649e11i	0.653189	+	1.13136i	−0.329156	+	0.944276i	$0.606764\pi$
$600$		0			0
$601$		−	7.87638e10i		−	0.603710i	−0.953354	−	0.301855i	$-0.902394\pi$
$601$		−	7.87638e10i		−	0.603710i	0.953354	−	0.301855i	$-0.0976059\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−8.99705e10	+	5.19445e10i	−0.671550	+	0.387720i
$606$		0			0
$607$	−2.54048e10	−	1.46674e10i	−0.187137	−	0.108044i	0.403504	−	0.914978i	$-0.367792\pi$
$607$	−2.54048e10	−	1.46674e10i	−0.187137	−	0.108044i	−0.590642	+	0.806934i	$0.701125\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.23311e10	−	3.86785e10i	0.160230	−	0.277527i
$612$		0			0
$613$	−5.10346e10	−	8.83945e10i	−0.361429	−	0.626013i	0.626767	−	0.779206i	$-0.284378\pi$
$613$	−5.10346e10	−	8.83945e10i	−0.361429	−	0.626013i	−0.988196	+	0.153193i	$0.951044\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−2.49461e11			−1.72132			−0.860661	−	0.509179i	$-0.829949\pi$
$617$	−2.49461e11			−1.72132			−0.860661	+	0.509179i	$0.829949\pi$
$618$		0			0
$619$	−1.46061e11	+	8.43281e10i	−0.994879	+	0.574394i	−0.906729	−	0.421713i	$-0.861429\pi$
$619$	−1.46061e11	+	8.43281e10i	−0.994879	+	0.574394i	−0.0881501	+	0.996107i	$0.528096\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	5.17074e10	+	1.18074e11i	0.343242	+	0.783792i
$624$		0			0
$625$	3.72811e10	−	6.45728e10i	0.244325	−	0.423184i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	6.01839e10i		−	0.384483i
$630$		0			0
$631$	8.03011e10			0.506529			0.253265	−	0.967397i	$-0.418496\pi$
$631$	8.03011e10			0.506529			0.253265	+	0.967397i	$0.418496\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.19244e11	+	6.88458e10i	0.733404	+	0.423431i
$636$		0			0
$637$	8.60792e10	−	2.68100e10i	0.522806	−	0.162832i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.51587e10	−	7.82172e10i	−0.267491	−	0.463308i	0.700722	−	0.713434i	$-0.252861\pi$
$641$	−4.51587e10	−	7.82172e10i	−0.267491	−	0.463308i	−0.968213	+	0.250126i	$0.919528\pi$
$642$		0			0
$643$			2.94542e11i			1.72307i	0.507696	+	0.861536i	$0.330497\pi$
$643$			2.94542e11i			1.72307i	−0.507696	+	0.861536i	$0.669503\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.46833e11	−	8.47741e10i	0.837928	−	0.483778i	−0.0186314	−	0.999826i	$-0.505931\pi$
$647$	1.46833e11	−	8.47741e10i	0.837928	−	0.483778i	0.856559	+	0.516048i	$0.172598\pi$
$648$		0			0
$649$	1.24899e10	+	7.21107e9i	0.0704015	+	0.0406463i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.31238e10	−	7.46926e10i	0.237172	−	0.410795i	−0.722729	−	0.691131i	$-0.757113\pi$
$653$	4.31238e10	−	7.46926e10i	0.237172	−	0.410795i	0.959902	+	0.280337i	$0.0904461\pi$
$654$		0			0
$655$	9.05571e10	+	1.56849e11i	0.491991	+	0.852153i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7.84405e10			0.415909			0.207955	−	0.978138i	$-0.433319\pi$
$659$	7.84405e10			0.415909			0.207955	+	0.978138i	$0.433319\pi$
$660$		0			0
$661$	1.79270e11	−	1.03502e11i	0.939080	−	0.542178i	0.0494080	−	0.998779i	$-0.484267\pi$
$661$	1.79270e11	−	1.03502e11i	0.939080	−	0.542178i	0.889672	+	0.456601i	$0.150933\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.12569e10	+	1.91008e11i	−0.108696	+	0.976708i
$666$		0			0
$667$	−2.98394e11	+	5.16833e11i	−1.50760	+	2.61124i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			1.17782e9i			0.00581018i
$672$		0			0
$673$	3.74989e11			1.82792			0.913961	−	0.405801i	$-0.133008\pi$
$673$	3.74989e11			1.82792			0.913961	+	0.405801i	$0.133008\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	1.82953e11	+	1.05628e11i	0.870932	+	0.502833i	0.867658	−	0.497162i	$-0.165625\pi$
$677$	1.82953e11	+	1.05628e11i	0.870932	+	0.502833i	0.00327401	+	0.999995i	$0.498958\pi$
$678$		0			0
$679$	4.16034e10	−	5.65323e10i	0.195727	−	0.265961i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.80288e11	−	3.12268e11i	−0.828484	−	1.43498i	−0.899227	−	0.437482i	$-0.855870\pi$
$683$	−1.80288e11	−	3.12268e11i	−0.828484	−	1.43498i	0.0707428	−	0.997495i	$-0.477463\pi$
$684$		0			0
$685$			1.89462e11i			0.860519i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.88932e11	+	1.09080e11i	−0.838356	+	0.484025i
$690$		0			0
$691$	−1.19035e11	−	6.87249e10i	−0.522110	−	0.301441i	0.215687	−	0.976462i	$-0.430801\pi$
$691$	−1.19035e11	−	6.87249e10i	−0.522110	−	0.301441i	−0.737798	+	0.675022i	$0.764134\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.47286e11	+	2.55106e11i	−0.631279	+	1.09341i
$696$		0			0
$697$	1.39932e11	+	2.42370e11i	0.592908	+	1.02695i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	3.01153e11			1.24714			0.623570	−	0.781767i	$-0.285682\pi$
$701$	3.01153e11			1.24714			0.623570	+	0.781767i	$0.285682\pi$
$702$		0			0
$703$	−1.48964e11	+	8.60044e10i	−0.609902	+	0.352127i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.17077e11	−	3.52868e10i	−1.26907	−	0.141232i
$708$		0			0
$709$	1.24726e11	−	2.16031e11i	0.493595	−	0.854931i	−0.506378	−	0.862312i	$-0.669016\pi$
$709$	1.24726e11	−	2.16031e11i	0.493595	−	0.854931i	0.999973	+	0.00738024i	$0.00234922\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	2.41348e11i		−	0.933868i
$714$		0			0
$715$	−1.64479e10			−0.0629341
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−2.58304e11	−	1.49132e11i	−0.966531	−	0.558027i	−0.0683543	−	0.997661i	$-0.521775\pi$
$719$	−2.58304e11	−	1.49132e11i	−0.966531	−	0.558027i	−0.898177	+	0.439634i	$0.855108\pi$
$720$		0			0
$721$	−9.16550e10	−	2.09294e11i	−0.339168	−	0.774489i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.70926e10	−	1.68169e11i	−0.351426	−	0.608688i
$726$		0			0
$727$			5.07469e11i			1.81665i	0.418263	+	0.908326i	$0.362639\pi$
$727$			5.07469e11i			1.81665i	−0.418263	+	0.908326i	$0.637361\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.00694e11	−	5.81354e10i	0.352640	−	0.203597i
$732$		0			0
$733$	7.01877e9	+	4.05229e9i	0.0243134	+	0.0140373i	0.512107	−	0.858921i	$-0.328865\pi$
$733$	7.01877e9	+	4.05229e9i	0.0243134	+	0.0140373i	−0.487794	+	0.872959i	$0.662198\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.64375e10	−	6.31116e10i	0.123503	−	0.213914i
$738$		0			0
$739$	1.21836e11	+	2.11026e11i	0.408506	+	0.707553i	0.994723	−	0.102601i	$-0.0327166\pi$
$739$	1.21836e11	+	2.11026e11i	0.408506	+	0.707553i	−0.586217	+	0.810154i	$0.699383\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.89064e11			0.620376			0.310188	−	0.950675i	$-0.399608\pi$
$743$	1.89064e11			0.620376			0.310188	+	0.950675i	$0.399608\pi$
$744$		0			0
$745$	−9.66329e10	+	5.57910e10i	−0.313689	+	0.181109i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.70984e11	−	7.48783e10i	0.543287	−	0.237919i
$750$		0			0
$751$	−2.32130e11	+	4.02061e11i	−0.729746	+	1.26396i	0.227245	+	0.973838i	$0.427028\pi$
$751$	−2.32130e11	+	4.02061e11i	−0.729746	+	1.26396i	−0.956991	+	0.290119i	$0.906305\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			4.52867e11i			1.39374i
$756$		0			0
$757$	2.81923e11			0.858513			0.429257	−	0.903183i	$-0.358776\pi$
$757$	2.81923e11			0.858513			0.429257	+	0.903183i	$0.358776\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.54973e9	−	1.47209e9i	−0.00760248	−	0.00438929i	0.496194	−	0.868212i	$-0.334730\pi$
$761$	−2.54973e9	−	1.47209e9i	−0.00760248	−	0.00438929i	−0.503796	+	0.863822i	$0.668064\pi$
$762$		0			0
$763$	8.13713e9	−	7.31178e10i	0.0240089	−	0.215737i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.30878e10	−	9.19508e10i	−0.153396	−	0.265689i
$768$		0			0
$769$			3.03649e11i			0.868293i	0.900842	+	0.434146i	$0.142950\pi$
$769$			3.03649e11i			0.868293i	−0.900842	+	0.434146i	$0.857050\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−4.73971e11	+	2.73647e11i	−1.32750	+	0.766431i	−0.984912	−	0.173056i	$-0.944636\pi$
$773$	−4.73971e11	+	2.73647e11i	−1.32750	+	0.766431i	−0.342585	+	0.939487i	$0.611302\pi$
$774$		0			0
$775$	6.80098e10	+	3.92654e10i	0.188523	+	0.108844i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.99935e11	−	6.92707e11i	1.08602	−	1.88105i
$780$		0			0
$781$	−2.35385e10	−	4.07699e10i	−0.0632666	−	0.109581i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.04379e11			−0.274875
$786$		0			0
$787$	−3.54149e11	+	2.04468e11i	−0.923182	+	0.532999i	−0.884649	−	0.466258i	$-0.845602\pi$
$787$	−3.54149e11	+	2.04468e11i	−0.923182	+	0.532999i	−0.0385331	+	0.999257i	$0.512268\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.51942e11	+	1.85410e11i	0.643567	+	0.473616i
$792$		0			0
$793$	4.33556e9	−	7.50940e9i	0.0109636	−	0.0189895i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			2.43730e11i			0.604055i	0.953299	+	0.302027i	$0.0976634\pi$
$797$			2.43730e11i			0.604055i	−0.953299	+	0.302027i	$0.902337\pi$
$798$		0			0
$799$	1.61553e11			0.396394
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.53515e10	−	1.46367e10i	−0.0609736	−	0.0352031i
$804$		0			0
$805$	5.28371e11	+	5.88013e10i	1.25822	+	0.140024i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.88172e11	+	3.25924e11i	0.439300	+	0.760890i	0.997636	−	0.0687249i	$-0.0218931\pi$
$809$	1.88172e11	+	3.25924e11i	0.439300	+	0.760890i	−0.558335	+	0.829615i	$0.688560\pi$
$810$		0			0
$811$			6.15386e11i			1.42254i	0.702920	+	0.711269i	$0.251879\pi$
$811$			6.15386e11i			1.42254i	−0.702920	+	0.711269i	$0.748121\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−1.18112e11	+	6.81922e10i	−0.267710	+	0.154563i
$816$		0			0
$817$	−2.87788e11	−	1.66154e11i	−0.645928	−	0.372927i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.08388e11	+	5.34144e11i	−0.678774	+	1.17567i	0.296576	+	0.955009i	$0.404155\pi$
$821$	−3.08388e11	+	5.34144e11i	−0.678774	+	1.17567i	−0.975350	+	0.220662i	$0.929178\pi$
$822$		0			0
$823$	−3.77630e10	−	6.54074e10i	−0.0823127	−	0.142570i	0.821930	−	0.569588i	$-0.192897\pi$
$823$	−3.77630e10	−	6.54074e10i	−0.0823127	−	0.142570i	−0.904243	+	0.427018i	$0.859564\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.93362e11			0.413380			0.206690	−	0.978406i	$-0.433731\pi$
$827$	1.93362e11			0.413380			0.206690	+	0.978406i	$0.433731\pi$
$828$		0			0
$829$	−1.02147e11	+	5.89748e10i	−0.216276	+	0.124867i	−0.604225	−	0.796814i	$-0.706517\pi$
$829$	−1.02147e11	+	5.89748e10i	−0.216276	+	0.124867i	0.387949	+	0.921681i	$0.373184\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	2.39669e11	+	2.21163e11i	0.497773	+	0.459338i
$834$		0			0
$835$	−1.40252e11	+	2.42924e11i	−0.288512	+	0.499718i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	7.17469e11i		−	1.44796i	−0.689823	−	0.723978i	$-0.742312\pi$
$839$		−	7.17469e11i		−	1.44796i	0.689823	−	0.723978i	$-0.257688\pi$
$840$		0			0
$841$	1.28023e12			2.55920
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.44874e11	−	1.41378e11i	−0.480304	−	0.277304i
$846$		0			0
$847$	4.61525e11	−	2.02113e11i	0.896730	−	0.392700i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.37908e11	+	4.12069e11i	0.453618	+	0.785690i
$852$		0			0
$853$			6.84954e11i			1.29379i	0.762577	+	0.646897i	$0.223934\pi$
$853$			6.84954e11i			1.29379i	−0.762577	+	0.646897i	$0.776066\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.95605e11	−	2.86137e11i	0.918781	−	0.530458i	0.0355351	−	0.999368i	$-0.488686\pi$
$857$	4.95605e11	−	2.86137e11i	0.918781	−	0.530458i	0.883246	+	0.468910i	$0.155353\pi$
$858$		0			0
$859$	−1.20619e11	−	6.96395e10i	−0.221536	−	0.127904i	0.385126	−	0.922864i	$-0.374158\pi$
$859$	−1.20619e11	−	6.96395e10i	−0.221536	−	0.127904i	−0.606661	+	0.794961i	$0.707491\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.25312e11	−	3.90251e11i	0.406200	−	0.703560i	−0.588260	−	0.808672i	$-0.700187\pi$
$863$	2.25312e11	−	3.90251e11i	0.406200	−	0.703560i	0.994460	+	0.105112i	$0.0335201\pi$
$864$		0			0
$865$	−3.65720e11	−	6.33445e11i	−0.653257	−	1.13147i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	8.28140e10			0.145219
$870$		0			0
$871$	−4.64626e11	+	2.68252e11i	−0.807293	+	0.466091i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.77745e11	+	5.13294e11i	−0.644416	+	0.875658i
$876$		0			0
$877$	1.71149e11	−	2.96439e11i	0.289319	−	0.501114i	−0.684329	−	0.729174i	$-0.739905\pi$
$877$	1.71149e11	−	2.96439e11i	0.289319	−	0.501114i	0.973647	+	0.228059i	$0.0732380\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	6.49186e11i		−	1.07762i	−0.842427	−	0.538810i	$-0.818874\pi$
$881$		−	6.49186e11i		−	1.07762i	0.842427	−	0.538810i	$-0.181126\pi$
$882$		0			0
$883$	1.09905e11			0.180790			0.0903951	−	0.995906i	$-0.471187\pi$
$883$	1.09905e11			0.180790			0.0903951	+	0.995906i	$0.471187\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.02639e11	+	1.74729e11i	0.488912	+	0.282274i	0.724123	−	0.689671i	$-0.242245\pi$
$887$	3.02639e11	+	1.74729e11i	0.488912	+	0.282274i	−0.235211	+	0.971944i	$0.575578\pi$
$888$		0			0
$889$	−5.37833e11	−	3.95804e11i	−0.861074	−	0.633684i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.30863e11	−	3.99867e11i	−0.363035	−	0.628795i
$894$		0			0
$895$			3.79235e11i			0.591040i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−6.23578e11	+	3.60023e11i	−0.954667	+	0.551177i
$900$		0			0
$901$	−6.83408e11	−	3.94566e11i	−1.03700	−	0.598715i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.57361e11	+	7.92172e11i	−0.681812	+	1.18093i
$906$		0			0
$907$	−5.29895e11	−	9.17805e11i	−0.782998	−	1.35619i	−0.930188	−	0.367084i	$-0.880356\pi$
$907$	−5.29895e11	−	9.17805e11i	−0.782998	−	1.35619i	0.147190	−	0.989108i	$-0.452977\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.66809e11			−1.11330			−0.556652	−	0.830746i	$-0.687914\pi$
$911$	−7.66809e11			−1.11330			−0.556652	+	0.830746i	$0.687914\pi$
$912$		0			0
$913$	1.14645e11	−	6.61904e10i	0.164996	−	0.0952603i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.52353e11	−	8.04597e11i	−0.498311	−	1.13789i
$918$		0			0
$919$	3.25499e11	−	5.63780e11i	0.456339	−	0.790402i	−0.542425	−	0.840104i	$-0.682494\pi$
$919$	3.25499e11	−	5.63780e11i	0.456339	−	0.790402i	0.998764	+	0.0497021i	$0.0158272\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			3.46580e11i			0.477526i
$924$		0			0
$925$	−1.54823e11			−0.211480
$926$		0			0
$927$		0			0
$928$		0			0
$929$	9.11519e11	+	5.26266e11i	1.22378	+	0.706549i	0.965722	−	0.259580i	$-0.0835842\pi$
$929$	9.11519e11	+	5.26266e11i	1.22378	+	0.706549i	0.258058	+	0.966130i	$0.416918\pi$
$930$		0			0
$931$	2.04918e11	−	9.09264e11i	0.272760	−	1.21029i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−2.97478e10	−	5.15247e10i	−0.0389232	−	0.0674169i
$936$		0			0
$937$		−	3.22936e11i		−	0.418946i	−0.977814	−	0.209473i	$-0.932825\pi$
$937$		−	3.22936e11i		−	0.418946i	0.977814	−	0.209473i	$-0.0671748\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	9.73086e11	−	5.61812e11i	1.24106	−	0.716526i	0.271750	−	0.962368i	$-0.412398\pi$
$941$	9.73086e11	−	5.61812e11i	1.24106	−	0.716526i	0.969310	+	0.245841i	$0.0790642\pi$
$942$		0			0
$943$	−1.91619e12	−	1.10631e12i	−2.42321	−	1.39904i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.59737e11	−	6.23083e11i	0.447286	−	0.774723i	−0.550922	−	0.834557i	$-0.685724\pi$
$947$	3.59737e11	−	6.23083e11i	0.447286	−	0.774723i	0.998208	+	0.0598341i	$0.0190572\pi$
$948$		0			0
$949$	1.07755e11	+	1.86637e11i	0.132854	+	0.230109i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−4.43394e11			−0.537549			−0.268775	−	0.963203i	$-0.586619\pi$
$953$	−4.43394e11			−0.537549			−0.268775	+	0.963203i	$0.586619\pi$
$954$		0			0
$955$	9.83890e10	−	5.68049e10i	0.118286	−	0.0682924i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.01630e11	−	9.13216e11i	0.120156	−	1.07969i
$960$		0			0
$961$	−2.80848e11	+	4.86443e11i	−0.329289	+	0.570346i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			7.37294e11i			0.850220i
$966$		0			0
$967$	1.62631e12			1.85993			0.929965	−	0.367647i	$-0.119837\pi$
$967$	1.62631e12			1.85993			0.929965	+	0.367647i	$0.119837\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−1.05556e12	−	6.09425e11i	−1.18742	−	0.685557i	−0.229700	−	0.973261i	$-0.573775\pi$
$971$	−1.05556e12	−	6.09425e11i	−1.18742	−	0.685557i	−0.957719	+	0.287704i	$0.907108\pi$
$972$		0			0
$973$	8.46766e11	−	1.15062e12i	0.944739	−	1.28375i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−6.03817e11	−	1.04584e12i	−0.662715	−	1.14786i	−0.979899	−	0.199493i	$-0.936071\pi$
$977$	−6.03817e11	−	1.04584e12i	−0.662715	−	1.14786i	0.317184	−	0.948364i	$-0.397263\pi$
$978$		0			0
$979$			1.14047e11i			0.124151i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.14970e11	−	1.81848e11i	0.337330	−	0.194758i	−0.321760	−	0.946821i	$-0.604275\pi$
$983$	3.14970e11	−	1.81848e11i	0.337330	−	0.194758i	0.659091	+	0.752063i	$0.270941\pi$
$984$		0			0
$985$	−1.90447e11	−	1.09955e11i	−0.202316	−	0.116807i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.59621e11	+	7.96087e11i	−0.480413	+	0.832100i
$990$		0			0
$991$	−2.17673e11	−	3.77021e11i	−0.225689	−	0.390905i	0.730837	−	0.682552i	$-0.239130\pi$
$991$	−2.17673e11	−	3.77021e11i	−0.225689	−	0.390905i	−0.956526	+	0.291647i	$0.905797\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.17113e11			0.731637
$996$		0			0
$997$	−1.88123e11	+	1.08613e11i	−0.190397	+	0.109926i	−0.592169	−	0.805814i	$-0.701728\pi$
$997$	−1.88123e11	+	1.08613e11i	−0.190397	+	0.109926i	0.401771	+	0.915740i	$0.368395\pi$
$998$		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.145.4	yes	20
3.2	odd	2	inner	252.9.z.e.145.7	yes	20
7.3	odd	6	inner	252.9.z.e.73.4	✓	20
21.17	even	6	inner	252.9.z.e.73.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.9.z.e.73.4	✓	20	7.3	odd	6	inner
252.9.z.e.73.7	yes	20	21.17	even	6	inner
252.9.z.e.145.4	yes	20	1.1	even	1	trivial
252.9.z.e.145.7	yes	20	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-428.745 - 247.536i) q^{5} +(1933.79 + 1423.12i) q^{7} +O(q^{10})\)	\(q+(-428.745 - 247.536i) q^{5} +(1933.79 + 1423.12i) q^{7} +(1062.17 + 1839.73i) q^{11} -15639.3i q^{13} +(48991.8 - 28285.4i) q^{17} +(-140021. - 80841.3i) q^{19} +(-223626. + 387331. i) q^{23} +(-72764.3 - 126031. i) q^{25} +1.33434e6 q^{29} +(-467329. + 269813. i) q^{31} +(-476829. - 1.08884e6i) q^{35} +(531934. - 921336. i) q^{37} +4.94716e6i q^{41} +2.05532e6 q^{43} +(2.47316e6 + 1.42788e6i) q^{47} +(1.71427e6 + 5.50402e6i) q^{49} +(-6.97472e6 - 1.20806e7i) q^{53} -1.05170e6i q^{55} +(5.87945e6 - 3.39450e6i) q^{59} +(480161. + 277221. i) q^{61} +(-3.87130e6 + 6.70529e6i) q^{65} +(-1.71524e7 - 2.97088e7i) q^{67} -2.21608e7 q^{71} +(-1.19338e7 + 6.89001e6i) q^{73} +(-564145. + 5.06924e6i) q^{77} +(1.94917e7 - 3.37606e7i) q^{79} -6.23163e7i q^{83} -2.80066e7 q^{85} +(4.64932e7 + 2.68429e7i) q^{89} +(2.22566e7 - 3.02432e7i) q^{91} +(4.00223e7 + 6.93206e7i) q^{95} -2.92340e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 7238 q^{7}+O(q^{10}) \) 20 * q - 7238 * q^7	\( 20 q - 7238 q^{7} - 107256 q^{19} + 1348832 q^{25} - 4734426 q^{31} + 6802748 q^{37} - 596128 q^{43} - 19249258 q^{49} + 32573772 q^{61} - 25999304 q^{67} - 52899612 q^{73} - 129945530 q^{79} - 83755728 q^{85} + 42306852 q^{91}+O(q^{100}) \) 20 * q - 7238 * q^7 - 107256 * q^19 + 1348832 * q^25 - 4734426 * q^31 + 6802748 * q^37 - 596128 * q^43 - 19249258 * q^49 + 32573772 * q^61 - 25999304 * q^67 - 52899612 * q^73 - 129945530 * q^79 - 83755728 * q^85 + 42306852 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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