LMFDB - Embedded newform 252.9.z.b.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:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 38255 x^{8} + 1483053595 x^{6} - 139470625170 x^{5} + 5194605060018 x^{4} + \cdots + 15\!\cdots\!00 $ x^10 - 38255x^8 + 1483053595x^6 - 139470625170x^5 + 5194605060018x^4 - 71600654137860x^3 + 119846615988780x^2 + 4263507454127400*x + 15758720495290800
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{8}\cdot 7^{3} $
Twist minimal:	no (minimal twist has level 84)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.4
Root			$38.0902 - 21.9914i$ of defining polynomial
Character	$\chi$	$=$	252.145
Dual form			252.9.z.b.73.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(374.307 + 216.106i) q^{5} +(83.7630 + 2399.54i) q^{7} +O(q^{10})$	$q+(374.307 + 216.106i) q^{5} +(83.7630 + 2399.54i) q^{7} +(-6902.31 - 11955.2i) q^{11} +3223.79i q^{13} +(21339.9 - 12320.6i) q^{17} +(29141.7 + 16825.0i) q^{19} +(112905. - 195558. i) q^{23} +(-101909. - 176511. i) q^{25} +908389. q^{29} +(925773. - 534495. i) q^{31} +(-487202. + 916265. i) q^{35} +(979412. - 1.69639e6i) q^{37} +2.90040e6i q^{41} -4.01000e6 q^{43} +(4.29428e6 + 2.47930e6i) q^{47} +(-5.75077e6 + 401985. i) q^{49} +(3.98900e6 + 6.90915e6i) q^{53} -5.96653e6i q^{55} +(-4.69735e6 + 2.71201e6i) q^{59} +(1.84448e6 + 1.06491e6i) q^{61} +(-696680. + 1.20669e6i) q^{65} +(-9.53767e6 - 1.65197e7i) q^{67} +2.08687e7 q^{71} +(-9.66235e6 + 5.57856e6i) q^{73} +(2.81087e7 - 1.75638e7i) q^{77} +(1.21508e7 - 2.10458e7i) q^{79} +3.92213e7i q^{83} +1.06502e7 q^{85} +(-1.02177e7 - 5.89920e6i) q^{89} +(-7.73560e6 + 270034. i) q^{91} +(7.27196e6 + 1.25954e7i) q^{95} +7.80671e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 1389 q^{5} + 1217 q^{7}+O(q^{10}) $ 10 * q - 1389 * q^5 + 1217 * q^7	$ 10 q - 1389 q^{5} + 1217 q^{7} + 879 q^{11} + 13674 q^{17} - 29268 q^{19} - 312732 q^{23} - 22052 q^{25} + 289794 q^{29} + 242787 q^{31} - 1209372 q^{35} + 1913308 q^{37} - 861848 q^{43} + 305448 q^{47} + 9821659 q^{49} + 10663233 q^{53} - 18410871 q^{59} - 13937808 q^{61} + 14966808 q^{65} - 20722822 q^{67} - 113032584 q^{71} + 43436322 q^{73} + 98823405 q^{77} - 42189637 q^{79} + 142602108 q^{85} - 67171914 q^{89} - 246091266 q^{91} + 140649894 q^{95}+O(q^{100}) $ 10 * q - 1389 * q^5 + 1217 * q^7 + 879 * q^11 + 13674 * q^17 - 29268 * q^19 - 312732 * q^23 - 22052 * q^25 + 289794 * q^29 + 242787 * q^31 - 1209372 * q^35 + 1913308 * q^37 - 861848 * q^43 + 305448 * q^47 + 9821659 * q^49 + 10663233 * q^53 - 18410871 * q^59 - 13937808 * q^61 + 14966808 * q^65 - 20722822 * q^67 - 113032584 * q^71 + 43436322 * q^73 + 98823405 * q^77 - 42189637 * q^79 + 142602108 * q^85 - 67171914 * q^89 - 246091266 * q^91 + 140649894 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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
$5$	374.307	+	216.106i	0.598891	+	0.345770i	0.768605	−	0.639724i	$-0.220951\pi$
$5$	374.307	+	216.106i	0.598891	+	0.345770i	−0.169714	+	0.985493i	$0.554284\pi$
$6$		0			0
$7$	83.7630	+	2399.54i	0.0348867	+	0.999391i
$7$	83.7630	+	2399.54i	0.0348867	+	0.999391i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−6902.31	−	11955.2i	−0.471437	−	0.816553i	0.528029	−	0.849226i	$-0.322931\pi$
$11$	−6902.31	−	11955.2i	−0.471437	−	0.816553i	−0.999466	+	0.0326733i	$0.989598\pi$
$12$		0			0
$13$			3223.79i			0.112874i	0.998406	+	0.0564369i	$0.0179740\pi$
$13$			3223.79i			0.112874i	−0.998406	+	0.0564369i	$0.982026\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	21339.9	−	12320.6i	0.255503	−	0.147515i	−0.366778	−	0.930308i	$-0.619539\pi$
$17$	21339.9	−	12320.6i	0.255503	−	0.147515i	0.622282	+	0.782794i	$0.286206\pi$
$18$		0			0
$19$	29141.7	+	16825.0i	0.223615	+	0.129104i	0.607623	−	0.794226i	$-0.292123\pi$
$19$	29141.7	+	16825.0i	0.223615	+	0.129104i	−0.384008	+	0.923330i	$0.625457\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	112905.	−	195558.i	0.403462	−	0.698817i	−0.590679	−	0.806907i	$-0.701140\pi$
$23$	112905.	−	195558.i	0.403462	−	0.698817i	0.994141	+	0.108090i	$0.0344734\pi$
$24$		0			0
$25$	−101909.	−	176511.i	−0.260887	−	0.451869i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	908389.			1.28434			0.642170	−	0.766562i	$-0.278034\pi$
$29$	908389.			1.28434			0.642170	+	0.766562i	$0.278034\pi$
$30$		0			0
$31$	925773.	−	534495.i	1.00244	−	0.578758i	0.0934693	−	0.995622i	$-0.470204\pi$
$31$	925773.	−	534495.i	1.00244	−	0.578758i	0.908969	+	0.416864i	$0.136871\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−487202.	+	916265.i	−0.324666	+	0.610589i
$36$		0			0
$37$	979412.	−	1.69639e6i	0.522587	−	0.905147i	−0.477067	−	0.878867i	$-0.658300\pi$
$37$	979412.	−	1.69639e6i	0.522587	−	0.905147i	0.999655	−	0.0262808i	$-0.00836640\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			2.90040e6i			1.02641i	0.858265	+	0.513207i	$0.171543\pi$
$41$			2.90040e6i			1.02641i	−0.858265	+	0.513207i	$0.828457\pi$
$42$		0			0
$43$	−4.01000e6			−1.17293			−0.586463	−	0.809976i	$-0.699480\pi$
$43$	−4.01000e6			−1.17293			−0.586463	+	0.809976i	$0.699480\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.29428e6	+	2.47930e6i	0.880033	+	0.508087i	0.870669	−	0.491869i	$-0.163686\pi$
$47$	4.29428e6	+	2.47930e6i	0.880033	+	0.508087i	0.00936356	+	0.999956i	$0.497019\pi$
$48$		0			0
$49$	−5.75077e6	+	401985.i	−0.997566	+	0.0697309i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.98900e6	+	6.90915e6i	0.505546	+	0.875631i	0.999979	+	0.00641571i	$0.00204220\pi$
$53$	3.98900e6	+	6.90915e6i	0.505546	+	0.875631i	−0.494434	+	0.869215i	$0.664624\pi$
$54$		0			0
$55$		−	5.96653e6i		−	0.652035i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.69735e6	+	2.71201e6i	−0.387654	+	0.223812i	−0.681143	−	0.732150i	$-0.738517\pi$
$59$	−4.69735e6	+	2.71201e6i	−0.387654	+	0.223812i	0.293489	+	0.955962i	$0.405184\pi$
$60$		0			0
$61$	1.84448e6	+	1.06491e6i	0.133216	+	0.0769120i	0.565127	−	0.825004i	$-0.308827\pi$
$61$	1.84448e6	+	1.06491e6i	0.133216	+	0.0769120i	−0.431911	+	0.901916i	$0.642161\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−696680.	+	1.20669e6i	−0.0390283	+	0.0675991i
$66$		0			0
$67$	−9.53767e6	−	1.65197e7i	−0.473307	−	0.819792i	0.526226	−	0.850345i	$-0.323607\pi$
$67$	−9.53767e6	−	1.65197e7i	−0.473307	−	0.819792i	−0.999533	+	0.0305527i	$0.990273\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.08687e7			0.821223			0.410612	−	0.911810i	$-0.365315\pi$
$71$	2.08687e7			0.821223			0.410612	+	0.911810i	$0.365315\pi$
$72$		0			0
$73$	−9.66235e6	+	5.57856e6i	−0.340245	+	0.196440i	−0.660380	−	0.750931i	$-0.729605\pi$
$73$	−9.66235e6	+	5.57856e6i	−0.340245	+	0.196440i	0.320136	+	0.947372i	$0.396272\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.81087e7	−	1.75638e7i	0.799609	−	0.499637i
$78$		0			0
$79$	1.21508e7	−	2.10458e7i	0.311958	−	0.540328i	−0.666828	−	0.745212i	$-0.732348\pi$
$79$	1.21508e7	−	2.10458e7i	0.311958	−	0.540328i	0.978786	+	0.204884i	$0.0656817\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			3.92213e7i			0.826436i	0.910632	+	0.413218i	$0.135595\pi$
$83$			3.92213e7i			0.826436i	−0.910632	+	0.413218i	$0.864405\pi$
$84$		0			0
$85$	1.06502e7			0.204025
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.02177e7	−	5.89920e6i	−0.162852	−	0.0940228i	0.416359	−	0.909200i	$-0.363306\pi$
$89$	−1.02177e7	−	5.89920e6i	−0.162852	−	0.0940228i	−0.579211	+	0.815178i	$0.696639\pi$
$90$		0			0
$91$	−7.73560e6	+	270034.i	−0.112805	+	0.00393779i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.27196e6	+	1.25954e7i	0.0892806	+	0.154638i
$96$		0			0
$97$			7.80671e7i			0.881822i	0.897551	+	0.440911i	$0.145345\pi$
$97$			7.80671e7i			0.881822i	−0.897551	+	0.440911i	$0.854655\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.07926e7	+	1.77781e7i	−0.295911	+	0.170844i	−0.640604	−	0.767871i	$-0.721316\pi$
$101$	−3.07926e7	+	1.77781e7i	−0.295911	+	0.170844i	0.344694	+	0.938715i	$0.387983\pi$
$102$		0			0
$103$	1.83451e8	+	1.05915e8i	1.62994	+	0.941044i	0.984110	+	0.177560i	$0.0568202\pi$
$103$	1.83451e8	+	1.05915e8i	1.62994	+	0.941044i	0.645826	+	0.763485i	$0.276513\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.59050e7	−	1.14151e8i	0.502786	−	0.870851i	−0.497209	−	0.867631i	$-0.665642\pi$
$107$	6.59050e7	−	1.14151e8i	0.502786	−	0.870851i	0.999995	−	0.00322029i	$-0.00102505\pi$
$108$		0			0
$109$	9.29656e7	+	1.61021e8i	0.658591	+	1.14071i	0.980980	+	0.194107i	$0.0621808\pi$
$109$	9.29656e7	+	1.61021e8i	0.658591	+	1.14071i	−0.322389	+	0.946607i	$0.604486\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.85733e7			0.297909			0.148955	−	0.988844i	$-0.452409\pi$
$113$	4.85733e7			0.297909			0.148955	+	0.988844i	$0.452409\pi$
$114$		0			0
$115$	8.45224e7	−	4.87990e7i	0.483260	−	0.279010i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	3.13512e7	+	5.01739e7i	0.156339	+	0.250201i
$120$		0			0
$121$	1.18956e7	−	2.06038e7i	0.0554940	−	0.0961184i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	2.56925e8i		−	1.05237i
$126$		0			0
$127$	1.32804e8			0.510502			0.255251	−	0.966875i	$-0.417842\pi$
$127$	1.32804e8			0.510502			0.255251	+	0.966875i	$0.417842\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.33780e8	+	1.34973e8i	0.793821	+	0.458313i	0.841306	−	0.540559i	$-0.181787\pi$
$131$	2.33780e8	+	1.34973e8i	0.793821	+	0.458313i	−0.0474851	+	0.998872i	$0.515121\pi$
$132$		0			0
$133$	−3.79312e7	+	7.13360e7i	−0.121224	+	0.227983i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.88322e8	+	4.99388e8i	0.818456	+	1.41761i	0.906820	+	0.421519i	$0.138503\pi$
$137$	2.88322e8	+	4.99388e8i	0.818456	+	1.41761i	−0.0883640	+	0.996088i	$0.528164\pi$
$138$		0			0
$139$			1.98197e8i			0.530930i	0.964120	+	0.265465i	$0.0855255\pi$
$139$			1.98197e8i			0.530930i	−0.964120	+	0.265465i	$0.914475\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.85409e7	−	2.22516e7i	0.0921674	−	0.0532129i
$144$		0			0
$145$	3.40016e8	+	1.96308e8i	0.769179	+	0.444086i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.00595e8	−	1.74236e8i	0.204095	−	0.353504i	−0.745749	−	0.666227i	$-0.767908\pi$
$149$	1.00595e8	−	1.74236e8i	0.204095	−	0.353504i	0.949844	+	0.312724i	$0.101241\pi$
$150$		0			0
$151$	−4.83143e8	−	8.36828e8i	−0.929326	−	1.60964i	−0.784452	−	0.620190i	$-0.787056\pi$
$151$	−4.83143e8	−	8.36828e8i	−0.929326	−	1.60964i	−0.144874	−	0.989450i	$-0.546278\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	4.62031e8			0.800468
$156$		0			0
$157$	−3.13710e8	+	1.81120e8i	−0.516332	+	0.298105i	−0.735433	−	0.677598i	$-0.763021\pi$
$157$	−3.13710e8	+	1.81120e8i	−0.516332	+	0.298105i	0.219100	+	0.975702i	$0.429688\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.78705e8	+	2.54540e8i	0.712467	+	0.378837i
$162$		0			0
$163$	−3.14898e7	+	5.45419e7i	−0.0446087	+	0.0772645i	−0.887468	−	0.460870i	$-0.847537\pi$
$163$	−3.14898e7	+	5.45419e7i	−0.0446087	+	0.0772645i	0.842859	+	0.538135i	$0.180871\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$			9.92784e8i			1.27641i	0.769868	+	0.638203i	$0.220322\pi$
$167$			9.92784e8i			1.27641i	−0.769868	+	0.638203i	$0.779678\pi$
$168$		0			0
$169$	8.05338e8			0.987260
$170$		0			0
$171$		0			0
$172$		0			0
$173$	1.20331e9	+	6.94731e8i	1.34336	+	0.775590i	0.987299	−	0.158872i	$-0.0507859\pi$
$173$	1.20331e9	+	6.94731e8i	1.34336	+	0.775590i	0.356062	+	0.934462i	$0.384119\pi$
$174$		0			0
$175$	4.15009e8	−	2.59319e8i	0.442492	−	0.276492i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.36947e8	+	7.56814e8i	0.425614	+	0.737186i	0.996478	−	0.0838594i	$-0.0267247\pi$
$179$	4.36947e8	+	7.56814e8i	0.425614	+	0.737186i	−0.570863	+	0.821045i	$0.693391\pi$
$180$		0			0
$181$			3.49705e8i			0.325827i	0.986640	+	0.162913i	$0.0520891\pi$
$181$			3.49705e8i			0.325827i	−0.986640	+	0.162913i	$0.947911\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	7.33201e8	−	4.23314e8i	0.625945	−	0.361390i
$186$		0			0
$187$	−2.94589e8	−	1.70081e8i	−0.240907	−	0.139088i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.50191e8	+	4.33344e8i	−0.187992	+	0.325611i	−0.944580	−	0.328280i	$-0.893531\pi$
$191$	−2.50191e8	+	4.33344e8i	−0.187992	+	0.325611i	0.756589	+	0.653891i	$0.226864\pi$
$192$		0			0
$193$	−2.34010e8	−	4.05317e8i	−0.168657	−	0.292123i	0.769291	−	0.638899i	$-0.220610\pi$
$193$	−2.34010e8	−	4.05317e8i	−0.168657	−	0.292123i	−0.937948	+	0.346776i	$0.887276\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.45218e9			1.62812			0.814062	−	0.580779i	$-0.197252\pi$
$197$	2.45218e9			1.62812			0.814062	+	0.580779i	$0.197252\pi$
$198$		0			0
$199$	8.11486e8	−	4.68511e8i	0.517450	−	0.298750i	−0.218441	−	0.975850i	$-0.570097\pi$
$199$	8.11486e8	−	4.68511e8i	0.517450	−	0.298750i	0.735891	+	0.677100i	$0.236764\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	7.60894e7	+	2.17971e9i	0.0448064	+	1.28356i
$204$		0			0
$205$	−6.26794e8	+	1.08564e9i	−0.354903	+	0.614709i
$206$		0			0
$207$		0			0
$208$		0			0
$209$		−	4.64525e8i		−	0.243458i
$210$		0			0
$211$	1.15290e9			0.581648			0.290824	−	0.956777i	$-0.406071\pi$
$211$	1.15290e9			0.581648			0.290824	+	0.956777i	$0.406071\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.50097e9	−	8.66586e8i	−0.702455	−	0.405563i
$216$		0			0
$217$	1.36009e9	+	2.17666e9i	0.613377	+	0.981637i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.97190e7	+	6.87953e7i	0.0166506	+	0.0288396i
$222$		0			0
$223$		−	4.36603e9i		−	1.76550i	−0.469844	−	0.882749i	$-0.655690\pi$
$223$		−	4.36603e9i		−	1.76550i	0.469844	−	0.882749i	$-0.344310\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.97909e7	+	1.14263e7i	−0.00745352	+	0.00430329i	−0.503722	−	0.863866i	$-0.668036\pi$
$227$	−1.97909e7	+	1.14263e7i	−0.00745352	+	0.00430329i	0.496269	+	0.868169i	$0.334703\pi$
$228$		0			0
$229$	2.21311e9	+	1.27774e9i	0.804749	+	0.464622i	0.845129	−	0.534563i	$-0.179524\pi$
$229$	2.21311e9	+	1.27774e9i	0.804749	+	0.464622i	−0.0403802	+	0.999184i	$0.512857\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.38427e9	−	4.12968e9i	0.808970	−	1.40118i	−0.104608	−	0.994513i	$-0.533359\pi$
$233$	2.38427e9	−	4.12968e9i	0.808970	−	1.40118i	0.913578	−	0.406663i	$-0.133308\pi$
$234$		0			0
$235$	1.07159e9	+	1.85604e9i	0.351362	+	0.608577i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.03549e9			0.317360			0.158680	−	0.987330i	$-0.449276\pi$
$239$	1.03549e9			0.317360			0.158680	+	0.987330i	$0.449276\pi$
$240$		0			0
$241$	−3.22795e9	+	1.86366e9i	−0.956884	+	0.552457i	−0.895213	−	0.445639i	$-0.852976\pi$
$241$	−3.22795e9	+	1.86366e9i	−0.956884	+	0.552457i	−0.0616712	+	0.998097i	$0.519643\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.23942e9	−	1.09231e9i	−0.621544	−	0.303167i
$246$		0			0
$247$	−5.42401e7	+	9.39467e7i	−0.0145725	+	0.0252402i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			6.14337e8i			0.154779i	0.997001	+	0.0773894i	$0.0246585\pi$
$251$			6.14337e8i			0.154779i	−0.997001	+	0.0773894i	$0.975342\pi$
$252$		0			0
$253$	−3.11723e9			−0.760828
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.99301e9	−	3.46007e9i	−1.37377	−	0.793144i	−0.382365	−	0.924011i	$-0.624890\pi$
$257$	−5.99301e9	−	3.46007e9i	−1.37377	−	0.793144i	−0.991400	+	0.130868i	$0.958224\pi$
$258$		0			0
$259$	4.15260e9	+	2.20804e9i	0.922828	+	0.490691i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.64705e9	−	2.85277e9i	−0.344257	−	0.596271i	0.640961	−	0.767573i	$-0.278536\pi$
$263$	−1.64705e9	−	2.85277e9i	−0.344257	−	0.596271i	−0.985219	+	0.171302i	$0.945203\pi$
$264$		0			0
$265$			3.44819e9i			0.699210i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.32809e8	+	4.23087e8i	−0.139953	+	0.0808018i	−0.568341	−	0.822793i	$-0.692415\pi$
$269$	−7.32809e8	+	4.23087e8i	−0.139953	+	0.0808018i	0.428389	+	0.903595i	$0.359081\pi$
$270$		0			0
$271$	5.00561e9	+	2.88999e9i	0.928067	+	0.535820i	0.886200	−	0.463303i	$-0.153336\pi$
$271$	5.00561e9	+	2.88999e9i	0.928067	+	0.535820i	0.0418675	+	0.999123i	$0.486669\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.40681e9	+	2.43667e9i	−0.245983	+	0.426055i
$276$		0			0
$277$	−4.52504e9	−	7.83759e9i	−0.768604	−	1.33126i	−0.938320	−	0.345769i	$-0.887618\pi$
$277$	−4.52504e9	−	7.83759e9i	−0.768604	−	1.33126i	0.169715	−	0.985493i	$-0.445715\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−3.48332e9			−0.558687			−0.279343	−	0.960191i	$-0.590117\pi$
$281$	−3.48332e9			−0.558687			−0.279343	+	0.960191i	$0.590117\pi$
$282$		0			0
$283$	−5.09155e9	+	2.93961e9i	−0.793788	+	0.458294i	−0.841294	−	0.540577i	$-0.818206\pi$
$283$	−5.09155e9	+	2.93961e9i	−0.793788	+	0.458294i	0.0475064	+	0.998871i	$0.484873\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−6.95962e9	+	2.42946e8i	−1.02579	+	0.0358082i
$288$		0			0
$289$	−3.18428e9	+	5.51534e9i	−0.456479	+	0.790644i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			5.84504e9i			0.793080i	0.918017	+	0.396540i	$0.129789\pi$
$293$			5.84504e9i			0.793080i	−0.918017	+	0.396540i	$0.870211\pi$
$294$		0			0
$295$	−2.34433e9			−0.309550
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.30436e8	+	3.63983e8i	0.0788781	+	0.0455403i
$300$		0			0
$301$	−3.35890e8	−	9.62215e9i	−0.0409195	−	1.17221i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.60268e8	+	7.97207e8i	0.0531877	+	0.0921238i
$306$		0			0
$307$		−	9.48408e9i		−	1.06768i	−0.845585	−	0.533841i	$-0.820748\pi$
$307$		−	9.48408e9i		−	1.06768i	0.845585	−	0.533841i	$-0.179252\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	3.11264e9	−	1.79708e9i	0.332726	−	0.192099i	−0.324325	−	0.945946i	$-0.605137\pi$
$311$	3.11264e9	−	1.79708e9i	0.332726	−	0.192099i	0.657051	+	0.753846i	$0.271804\pi$
$312$		0			0
$313$	7.72906e8	+	4.46237e8i	0.0805284	+	0.0464931i	0.539724	−	0.841842i	$-0.318529\pi$
$313$	7.72906e8	+	4.46237e8i	0.0805284	+	0.0464931i	−0.459195	+	0.888335i	$0.651862\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	6.15360e9	−	1.06583e10i	0.609386	−	1.05549i	−0.381956	−	0.924180i	$-0.624750\pi$
$317$	6.15360e9	−	1.06583e10i	0.609386	−	1.05549i	0.991342	−	0.131306i	$-0.0419172\pi$
$318$		0			0
$319$	−6.26998e9	−	1.08599e10i	−0.605486	−	1.04873i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	8.29174e8			0.0761791
$324$		0			0
$325$	5.69035e8	−	3.28532e8i	0.0510041	−	0.0294472i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−5.58948e9	+	1.05120e10i	−0.477076	+	0.897223i
$330$		0			0
$331$	7.20962e8	−	1.24874e9i	0.0600621	−	0.104031i	−0.834431	−	0.551113i	$-0.814203\pi$
$331$	7.20962e8	−	1.24874e9i	0.0600621	−	0.104031i	0.894493	+	0.447082i	$0.147537\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$		−	8.24460e9i		−	0.654621i
$336$		0			0
$337$	−2.10452e9			−0.163168			−0.0815838	−	0.996666i	$-0.525998\pi$
$337$	−2.10452e9			−0.163168			−0.0815838	+	0.996666i	$0.525998\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.27799e10	−	7.37850e9i	−0.945173	−	0.545696i
$342$		0			0
$343$	−1.44628e9	−	1.37655e10i	−0.104490	−	0.994526i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	3.19525e9	+	5.53434e9i	0.220388	+	0.381723i	0.954926	−	0.296845i	$-0.0959344\pi$
$347$	3.19525e9	+	5.53434e9i	0.220388	+	0.381723i	−0.734538	+	0.678567i	$0.762601\pi$
$348$		0			0
$349$			1.17252e9i			0.0790346i	0.999219	+	0.0395173i	$0.0125820\pi$
$349$			1.17252e9i			0.0790346i	−0.999219	+	0.0395173i	$0.987418\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−1.60024e10	+	9.23900e9i	−1.03059	+	0.595013i	−0.917154	−	0.398532i	$-0.869520\pi$
$353$	−1.60024e10	+	9.23900e9i	−1.03059	+	0.595013i	−0.113438	+	0.993545i	$0.536186\pi$
$354$		0			0
$355$	7.81128e9	+	4.50985e9i	0.491823	+	0.283954i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	1.23847e10	−	2.14508e10i	0.745600	−	1.29142i	−0.204314	−	0.978905i	$-0.565496\pi$
$359$	1.23847e10	−	2.14508e10i	0.745600	−	1.29142i	0.949914	−	0.312512i	$-0.101170\pi$
$360$		0			0
$361$	−7.92562e9	−	1.37276e10i	−0.466664	−	0.808286i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.82224e9			−0.271693
$366$		0			0
$367$	−2.07383e10	+	1.19733e10i	−1.14316	+	0.660006i	−0.947212	−	0.320607i	$-0.896113\pi$
$367$	−2.07383e10	+	1.19733e10i	−1.14316	+	0.660006i	−0.195952	+	0.980613i	$0.562780\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.62446e10	+	1.01505e10i	−0.857461	+	0.535786i
$372$		0			0
$373$	−1.13190e10	+	1.96050e10i	−0.584751	+	1.01282i	0.410155	+	0.912016i	$0.365475\pi$
$373$	−1.13190e10	+	1.96050e10i	−0.584751	+	1.01282i	−0.994906	+	0.100803i	$0.967859\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			2.92845e9i			0.144968i
$378$		0			0
$379$	−3.53911e10			−1.71529			−0.857644	−	0.514245i	$-0.828072\pi$
$379$	−3.53911e10			−1.71529			−0.857644	+	0.514245i	$0.828072\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.67174e10	−	2.11988e10i	−1.70639	−	0.985183i	−0.938947	−	0.344061i	$-0.888197\pi$
$383$	−3.67174e10	−	2.11988e10i	−1.70639	−	0.985183i	−0.767439	−	0.641122i	$-0.778469\pi$
$384$		0			0
$385$	1.43169e10	−	4.99774e8i	0.651638	−	0.0227473i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.82067e10	+	3.15350e10i	0.795121	+	1.37719i	0.922762	+	0.385370i	$0.125926\pi$
$389$	1.82067e10	+	3.15350e10i	0.795121	+	1.37719i	−0.127641	+	0.991820i	$0.540741\pi$
$390$		0			0
$391$		−	5.56424e9i		−	0.238067i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.09626e9	−	5.25173e9i	0.373658	−	0.215732i
$396$		0			0
$397$	9.66830e9	+	5.58199e9i	0.389214	+	0.224713i	0.681819	−	0.731521i	$-0.261189\pi$
$397$	9.66830e9	+	5.58199e9i	0.389214	+	0.224713i	−0.292606	+	0.956233i	$0.594522\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.55936e9	+	1.13611e10i	−0.253679	+	0.439384i	−0.964536	−	0.263952i	$-0.914974\pi$
$401$	−6.55936e9	+	1.13611e10i	−0.253679	+	0.439384i	0.710857	+	0.703336i	$0.248307\pi$
$402$		0			0
$403$	1.72310e9	+	2.98449e9i	0.0653266	+	0.113149i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.70408e10			−0.985468
$408$		0			0
$409$	2.95703e10	−	1.70724e10i	1.05673	−	0.610102i	0.132202	−	0.991223i	$-0.457795\pi$
$409$	2.95703e10	−	1.70724e10i	1.05673	−	0.610102i	0.924525	+	0.381121i	$0.124462\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−6.90104e9	−	1.10443e10i	−0.237200	−	0.379610i
$414$		0			0
$415$	−8.47596e9	+	1.46808e10i	−0.285757	+	0.494945i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	3.49852e10i		−	1.13509i	−0.823344	−	0.567543i	$-0.807894\pi$
$419$		−	3.49852e10i		−	1.13509i	0.823344	−	0.567543i	$-0.192106\pi$
$420$		0			0
$421$	1.41410e10			0.450146			0.225073	−	0.974342i	$-0.427738\pi$
$421$	1.41410e10			0.450146			0.225073	+	0.974342i	$0.427738\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.34944e9	−	2.51115e9i	−0.133315	−	0.0769693i
$426$		0			0
$427$	−2.40080e9	+	4.51510e9i	−0.0722178	+	0.135818i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.04983e9	−	1.22107e10i	−0.204301	−	0.353859i	0.745609	−	0.666384i	$-0.232159\pi$
$431$	−7.04983e9	−	1.22107e10i	−0.204301	−	0.353859i	−0.949910	+	0.312525i	$0.898825\pi$
$432$		0			0
$433$			1.05233e10i			0.299365i	0.988734	+	0.149683i	$0.0478252\pi$
$433$			1.05233e10i			0.299365i	−0.988734	+	0.149683i	$0.952175\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	6.58050e9	−	3.79926e9i	0.180440	−	0.104177i
$438$		0			0
$439$	5.71624e10	+	3.30027e10i	1.53905	+	0.888571i	0.998895	+	0.0470049i	$0.0149676\pi$
$439$	5.71624e10	+	3.30027e10i	1.53905	+	0.888571i	0.540155	+	0.841566i	$0.318366\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.33675e10	−	5.77942e10i	0.866380	−	1.50061i	0.000709897	−	1.00000i	$-0.499774\pi$
$443$	3.33675e10	−	5.77942e10i	0.866380	−	1.50061i	0.865670	−	0.500615i	$-0.166893\pi$
$444$		0			0
$445$	−2.54971e9	−	4.41622e9i	−0.0650205	−	0.112619i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	4.05035e10			0.996569			0.498285	−	0.867014i	$-0.333963\pi$
$449$	4.05035e10			0.996569			0.498285	+	0.867014i	$0.333963\pi$
$450$		0			0
$451$	3.46747e10	−	2.00195e10i	0.838121	−	0.483889i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−2.95384e9	−	1.57064e9i	−0.0689195	−	0.0366463i
$456$		0			0
$457$	−3.16521e10	+	5.48230e10i	−0.725667	+	1.25689i	0.233032	+	0.972469i	$0.425135\pi$
$457$	−3.16521e10	+	5.48230e10i	−0.725667	+	1.25689i	−0.958699	+	0.284423i	$0.908198\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			4.09845e10i			0.907436i	0.891145	+	0.453718i	$0.149903\pi$
$461$			4.09845e10i			0.907436i	−0.891145	+	0.453718i	$0.850097\pi$
$462$		0			0
$463$	−1.54289e10			−0.335745			−0.167873	−	0.985809i	$-0.553690\pi$
$463$	−1.54289e10			−0.335745			−0.167873	+	0.985809i	$0.553690\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−2.98997e10	−	1.72626e10i	−0.628636	−	0.362943i	0.151588	−	0.988444i	$-0.451561\pi$
$467$	−2.98997e10	−	1.72626e10i	−0.628636	−	0.362943i	−0.780224	+	0.625501i	$0.784895\pi$
$468$		0			0
$469$	3.88408e10	−	2.42697e10i	0.802781	−	0.501619i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	2.76783e10	+	4.79402e10i	0.552961	+	0.957757i
$474$		0			0
$475$		−	6.85845e9i		−	0.134726i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	5.19585e10	−	2.99983e10i	0.986994	−	0.569842i	0.0826199	−	0.996581i	$-0.473671\pi$
$479$	5.19585e10	−	2.99983e10i	0.986994	−	0.569842i	0.904375	+	0.426740i	$0.140338\pi$
$480$		0			0
$481$	5.46881e9	+	3.15742e9i	0.102167	+	0.0589864i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.68708e10	+	2.92210e10i	−0.304907	+	0.528115i
$486$		0			0
$487$	7.27140e8	+	1.25944e9i	0.0129271	+	0.0223904i	0.872417	−	0.488763i	$-0.162552\pi$
$487$	7.27140e8	+	1.25944e9i	0.0129271	+	0.0223904i	−0.859489	+	0.511153i	$0.829218\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.42504e10			1.10548			0.552739	−	0.833355i	$-0.313583\pi$
$491$	6.42504e10			1.10548			0.552739	+	0.833355i	$0.313583\pi$
$492$		0			0
$493$	1.93849e10	−	1.11919e10i	0.328153	−	0.189459i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.74802e9	+	5.00752e10i	0.0286498	+	0.820724i
$498$		0			0
$499$	−1.47773e10	+	2.55951e10i	−0.238338	+	0.412813i	−0.960238	−	0.279184i	$-0.909936\pi$
$499$	−1.47773e10	+	2.55951e10i	−0.238338	+	0.412813i	0.721900	+	0.691998i	$0.243269\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			3.65527e10i			0.571015i	0.958376	+	0.285508i	$0.0921622\pi$
$503$			3.65527e10i			0.571015i	−0.958376	+	0.285508i	$0.907838\pi$
$504$		0			0
$505$	−1.53678e10			−0.236291
$506$		0			0
$507$		0			0
$508$		0			0
$509$	6.42278e10	+	3.70819e10i	0.956867	+	0.552447i	0.895207	−	0.445650i	$-0.147027\pi$
$509$	6.42278e10	+	3.70819e10i	0.956867	+	0.552447i	0.0616596	+	0.998097i	$0.480361\pi$
$510$		0			0
$511$	−1.41953e10	−	2.27179e10i	−0.208191	−	0.333184i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	4.57779e10	+	7.92897e10i	0.650769	+	1.12717i
$516$		0			0
$517$		−	6.84517e10i		−	0.958125i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−1.33656e10	+	7.71665e9i	−0.181401	+	0.104732i	−0.587951	−	0.808897i	$-0.700065\pi$
$521$	−1.33656e10	+	7.71665e9i	−0.181401	+	0.104732i	0.406550	+	0.913629i	$0.366732\pi$
$522$		0			0
$523$	−3.44919e10	−	1.99139e10i	−0.461010	−	0.266164i	0.251459	−	0.967868i	$-0.419090\pi$
$523$	−3.44919e10	−	1.99139e10i	−0.461010	−	0.266164i	−0.712469	+	0.701704i	$0.752423\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.31706e10	−	2.28121e10i	0.170751	−	0.295749i
$528$		0			0
$529$	1.36603e10	+	2.36603e10i	0.174437	+	0.302133i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.35027e9			−0.115855
$534$		0			0
$535$	4.93374e10	−	2.84850e10i	0.602228	−	0.347697i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.44994e10	+	6.59767e10i	0.527229	+	0.781692i
$540$		0			0
$541$	3.80963e9	−	6.59847e9i	0.0444727	−	0.0770290i	−0.842932	−	0.538020i	$-0.819173\pi$
$541$	3.80963e9	−	6.59847e9i	0.0444727	−	0.0770290i	0.887405	+	0.460991i	$0.152506\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$			8.03617e10i			0.910884i
$546$		0			0
$547$	−9.03887e10			−1.00964			−0.504818	−	0.863226i	$-0.668441\pi$
$547$	−9.03887e10			−1.00964			−0.504818	+	0.863226i	$0.668441\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.64720e10	+	1.52836e10i	0.287197	+	0.165814i
$552$		0			0
$553$	5.15180e10	+	2.73935e10i	0.550882	+	0.292918i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.86872e10	+	8.43287e10i	0.505817	+	0.876101i	0.999977	+	0.00673046i	$0.00214239\pi$
$557$	4.86872e10	+	8.43287e10i	0.505817	+	0.876101i	−0.494160	+	0.869371i	$0.664524\pi$
$558$		0			0
$559$		−	1.29274e10i		−	0.132393i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.63982e11	−	9.46751e10i	1.63216	−	0.942329i	0.648736	−	0.761014i	$-0.275298\pi$
$563$	1.63982e11	−	9.46751e10i	1.63216	−	0.942329i	0.983425	−	0.181315i	$-0.0580353\pi$
$564$		0			0
$565$	1.81813e10	+	1.04970e10i	0.178415	+	0.103008i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.52884e9	+	9.57622e9i	−0.0527454	+	0.0913577i	−0.891193	−	0.453625i	$-0.850131\pi$
$569$	−5.52884e9	+	9.57622e9i	−0.0527454	+	0.0913577i	0.838447	+	0.544983i	$0.183464\pi$
$570$		0			0
$571$	2.80453e9	+	4.85758e9i	0.0263824	+	0.0456957i	0.878915	−	0.476978i	$-0.158268\pi$
$571$	2.80453e9	+	4.85758e9i	0.0263824	+	0.0456957i	−0.852533	+	0.522674i	$0.824935\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−4.60242e10			−0.421031
$576$		0			0
$577$	−1.30662e11	+	7.54375e10i	−1.17881	+	0.680587i	−0.955739	−	0.294215i	$-0.904942\pi$
$577$	−1.30662e11	+	7.54375e10i	−1.17881	+	0.680587i	−0.223072	+	0.974802i	$0.571609\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−9.41130e10	+	3.28529e9i	−0.825933	+	0.0288316i
$582$		0			0
$583$	5.50666e10	−	9.53782e10i	0.476666	−	0.825610i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	2.18697e11i		−	1.84201i	−0.389556	−	0.921003i	$-0.627371\pi$
$587$		−	2.18697e11i		−	1.84201i	0.389556	−	0.921003i	$-0.372629\pi$
$588$		0			0
$589$	3.59715e10			0.298880
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.98077e11	+	1.14360e11i	1.60183	+	0.924816i	0.991121	+	0.132960i	$0.0424483\pi$
$593$	1.98077e11	+	1.14360e11i	1.60183	+	0.924816i	0.610708	+	0.791856i	$0.290885\pi$
$594$		0			0
$595$	8.92094e8	+	2.55556e10i	0.00711775	+	0.203901i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.69028e10	−	1.50520e11i	−0.675036	−	1.16920i	−0.976458	−	0.215705i	$-0.930795\pi$
$599$	−8.69028e10	−	1.50520e11i	−0.675036	−	1.16920i	0.301423	−	0.953491i	$-0.402538\pi$
$600$		0			0
$601$			3.36846e10i			0.258187i	0.991632	+	0.129093i	$0.0412067\pi$
$601$			3.36846e10i			0.258187i	−0.991632	+	0.129093i	$0.958793\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.90523e9	−	5.14144e9i	0.0664697	−	0.0383763i
$606$		0			0
$607$	9.20478e10	+	5.31438e10i	0.678045	+	0.391470i	0.799118	−	0.601174i	$-0.205300\pi$
$607$	9.20478e10	+	5.31438e10i	0.678045	+	0.391470i	−0.121073	+	0.992644i	$0.538633\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−7.99275e9	+	1.38438e10i	−0.0573497	+	0.0993326i
$612$		0			0
$613$	5.34031e10	+	9.24969e10i	0.378203	+	0.655066i	0.990801	−	0.135328i	$-0.0432089\pi$
$613$	5.34031e10	+	9.24969e10i	0.378203	+	0.655066i	−0.612598	+	0.790395i	$0.709876\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.04431e11			−0.720593			−0.360297	−	0.932838i	$-0.617325\pi$
$617$	−1.04431e11			−0.720593			−0.360297	+	0.932838i	$0.617325\pi$
$618$		0			0
$619$	−1.91873e10	+	1.10778e10i	−0.130693	+	0.0754554i	−0.563921	−	0.825829i	$-0.690708\pi$
$619$	−1.91873e10	+	1.10778e10i	−0.130693	+	0.0754554i	0.433228	+	0.901284i	$0.357374\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.32995e10	−	2.50119e10i	0.0882842	−	0.166033i
$624$		0			0
$625$	1.57150e10	−	2.72192e10i	0.102990	−	0.178384i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	4.82677e10i		−	0.308357i
$630$		0			0
$631$	2.53563e11			1.59944			0.799722	−	0.600371i	$-0.204980\pi$
$631$	2.53563e11			1.59944			0.799722	+	0.600371i	$0.204980\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.97095e10	+	2.86998e10i	0.305735	+	0.176516i
$636$		0			0
$637$	−1.29591e9	−	1.85393e10i	−0.00787079	−	0.112599i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.44352e10	−	7.69641e10i	−0.263206	−	0.455886i	0.703886	−	0.710313i	$-0.251446\pi$
$641$	−4.44352e10	−	7.69641e10i	−0.263206	−	0.455886i	−0.967092	+	0.254427i	$0.918113\pi$
$642$		0			0
$643$			1.06138e10i			0.0620909i	0.999518	+	0.0310455i	$0.00988367\pi$
$643$			1.06138e10i			0.0620909i	−0.999518	+	0.0310455i	$0.990116\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.13261e11	+	1.23126e11i	−1.21701	+	0.702642i	−0.964278	−	0.264894i	$-0.914663\pi$
$647$	−2.13261e11	+	1.23126e11i	−1.21701	+	0.702642i	−0.252734	+	0.967536i	$0.581330\pi$
$648$		0			0
$649$	6.48451e10	+	3.74383e10i	0.365509	+	0.211027i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.72691e10	−	6.45521e10i	0.204973	−	0.355024i	−0.745151	−	0.666896i	$-0.767623\pi$
$653$	3.72691e10	−	6.45521e10i	0.204973	−	0.355024i	0.950124	+	0.311872i	$0.100956\pi$
$654$		0			0
$655$	5.83370e10	+	1.01043e11i	0.316941	+	0.548958i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.29564e11			−0.686975			−0.343488	−	0.939157i	$-0.611608\pi$
$659$	−1.29564e11			−0.686975			−0.343488	+	0.939157i	$0.611608\pi$
$660$		0			0
$661$	−2.62586e10	+	1.51604e10i	−0.137552	+	0.0794155i	−0.567197	−	0.823582i	$-0.691972\pi$
$661$	−2.62586e10	+	1.51604e10i	−0.137552	+	0.0794155i	0.429645	+	0.902998i	$0.358639\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.96140e10	+	1.85044e10i	−0.151430	+	0.0946211i
$666$		0			0
$667$	1.02562e11	−	1.77642e11i	0.518183	−	0.897519i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	2.94014e10i		−	0.145037i
$672$		0			0
$673$	−2.10696e11			−1.02706			−0.513530	−	0.858071i	$-0.671663\pi$
$673$	−2.10696e11			−1.02706			−0.513530	+	0.858071i	$0.671663\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.82781e10	−	2.20999e10i	−0.182220	−	0.105205i	0.406115	−	0.913822i	$-0.366883\pi$
$677$	−3.82781e10	−	2.20999e10i	−0.182220	−	0.105205i	−0.588335	+	0.808617i	$0.700216\pi$
$678$		0			0
$679$	−1.87325e11	+	6.53913e9i	−0.881285	+	0.0307639i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.69506e10	−	1.15962e11i	−0.307660	−	0.532883i	0.670190	−	0.742190i	$-0.266213\pi$
$683$	−6.69506e10	−	1.15962e11i	−0.307660	−	0.532883i	−0.977850	+	0.209307i	$0.932879\pi$
$684$		0			0
$685$			2.49232e11i			1.13199i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.22736e10	+	1.28597e10i	−0.0988358	+	0.0570629i
$690$		0			0
$691$	−3.36307e11	−	1.94167e11i	−1.47511	−	0.851653i	−0.475501	−	0.879715i	$-0.657733\pi$
$691$	−3.36307e11	−	1.94167e11i	−1.47511	−	0.851653i	−0.999606	+	0.0280622i	$0.991066\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−4.28315e10	+	7.41864e10i	−0.183580	+	0.317969i
$696$		0			0
$697$	3.57346e10	+	6.18942e10i	0.151411	+	0.262252i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.53431e11			−0.635392			−0.317696	−	0.948193i	$-0.602909\pi$
$701$	−1.53431e11			−0.635392			−0.317696	+	0.948193i	$0.602909\pi$
$702$		0			0
$703$	5.70835e10	−	3.29572e10i	0.233716	−	0.134936i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.52386e10	−	7.23989e10i	−0.181064	−	0.289771i
$708$		0			0
$709$	−5.25372e10	+	9.09971e10i	−0.207913	+	0.360116i	−0.951057	−	0.309016i	$-0.900000\pi$
$709$	−5.25372e10	+	9.09971e10i	−0.207913	+	0.360116i	0.743144	+	0.669132i	$0.233334\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$		−	2.41389e11i		−	0.934028i
$714$		0			0
$715$	1.92348e10			0.0735976
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.52234e11	−	8.78923e10i	−0.569634	−	0.328878i	0.187369	−	0.982290i	$-0.440004\pi$
$719$	−1.52234e11	−	8.78923e10i	−0.569634	−	0.328878i	−0.757003	+	0.653411i	$0.773337\pi$
$720$		0			0
$721$	−2.38782e11	+	4.49069e11i	−0.883608	+	1.66177i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.25729e10	−	1.60341e11i	−0.335067	−	0.580353i
$726$		0			0
$727$		−	3.71190e11i		−	1.32880i	−0.747379	−	0.664398i	$-0.768688\pi$
$727$		−	3.71190e11i		−	1.32880i	0.747379	−	0.664398i	$-0.231312\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.55730e10	+	4.94056e10i	−0.299686	+	0.173024i
$732$		0			0
$733$	3.30816e10	+	1.90996e10i	0.114596	+	0.0661621i	0.556203	−	0.831047i	$-0.312258\pi$
$733$	3.30816e10	+	1.90996e10i	0.114596	+	0.0661621i	−0.441606	+	0.897209i	$0.645591\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−1.31664e11	+	2.28049e11i	−0.446269	+	0.772961i
$738$		0			0
$739$	−1.92789e11	−	3.33920e11i	−0.646404	−	1.11960i	−0.983975	−	0.178305i	$-0.942939\pi$
$739$	−1.92789e11	−	3.33920e11i	−0.646404	−	1.11960i	0.337571	−	0.941300i	$-0.390395\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−5.07236e11			−1.66439			−0.832194	−	0.554485i	$-0.812915\pi$
$743$	−5.07236e11			−1.66439			−0.832194	+	0.554485i	$0.812915\pi$
$744$		0			0
$745$	7.53071e10	−	4.34786e10i	0.244462	−	0.141140i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	2.79430e11	+	1.48580e11i	0.887862	+	0.472099i
$750$		0			0
$751$	3.14299e11	−	5.44382e11i	0.988060	−	1.71137i	0.360600	−	0.932721i	$-0.382572\pi$
$751$	3.14299e11	−	5.44382e11i	0.988060	−	1.71137i	0.627460	−	0.778649i	$-0.284095\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$		−	4.17641e11i		−	1.28533i
$756$		0			0
$757$	−3.39756e11			−1.03463			−0.517314	−	0.855796i	$-0.673068\pi$
$757$	−3.39756e11			−1.03463			−0.517314	+	0.855796i	$0.673068\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.74796e11	+	3.31859e11i	1.71386	+	0.989497i	0.929205	+	0.369564i	$0.120493\pi$
$761$	5.74796e11	+	3.31859e11i	1.71386	+	0.989497i	0.784655	+	0.619933i	$0.212840\pi$
$762$		0			0
$763$	−3.78589e11	+	2.36562e11i	−1.11704	+	0.697986i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.74296e9	−	1.51432e10i	−0.0252625	−	0.0437560i
$768$		0			0
$769$		−	3.99685e11i		−	1.14291i	−0.820633	−	0.571456i	$-0.806379\pi$
$769$		−	3.99685e11i		−	1.14291i	0.820633	−	0.571456i	$-0.193621\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.18869e10	−	4.72774e10i	0.229349	−	0.132415i	−0.380923	−	0.924607i	$-0.624394\pi$
$773$	8.18869e10	−	4.72774e10i	0.229349	−	0.132415i	0.610272	+	0.792192i	$0.291060\pi$
$774$		0			0
$775$	−1.88689e11	−	1.08940e11i	−0.523045	−	0.301980i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.87991e10	+	8.45226e10i	−0.132514	+	0.229521i
$780$		0			0
$781$	−1.44042e11	−	2.49488e11i	−0.387155	−	0.670573i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.56565e11			−0.412302
$786$		0			0
$787$	−2.38365e10	+	1.37620e10i	−0.0621362	+	0.0358743i	−0.530746	−	0.847531i	$-0.678088\pi$
$787$	−2.38365e10	+	1.37620e10i	−0.0621362	+	0.0358743i	0.468610	+	0.883405i	$0.344755\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.06864e9	+	1.16554e11i	0.0103931	+	0.297728i
$792$		0			0
$793$	−3.43305e9	+	5.94622e9i	−0.00868135	+	0.0150365i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	1.49359e11i		−	0.370167i	−0.982723	−	0.185084i	$-0.940744\pi$
$797$		−	1.49359e11i		−	0.370167i	0.982723	−	0.185084i	$-0.0592556\pi$
$798$		0			0
$799$	1.22186e11			0.299802
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.33385e11	+	7.70099e10i	0.320808	+	0.185219i
$804$		0			0
$805$	1.24175e11	+	1.98727e11i	0.295700	+	0.473232i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	3.45374e9	+	5.98206e9i	0.00806298	+	0.0139655i	0.870029	−	0.493001i	$-0.164100\pi$
$809$	3.45374e9	+	5.98206e9i	0.00806298	+	0.0139655i	−0.861966	+	0.506966i	$0.830767\pi$
$810$		0			0
$811$		−	3.74372e11i		−	0.865406i	−0.901537	−	0.432703i	$-0.857560\pi$
$811$		−	3.74372e11i		−	0.865406i	0.901537	−	0.432703i	$-0.142440\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.35737e10	+	1.36103e10i	−0.0534315	+	0.0308487i
$816$		0			0
$817$	−1.16858e11	−	6.74682e10i	−0.262284	−	0.151430i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.25087e11	+	7.36272e11i	−0.935632	+	1.62056i	−0.162128	+	0.986770i	$0.551836\pi$
$821$	−4.25087e11	+	7.36272e11i	−0.935632	+	1.62056i	−0.773504	+	0.633792i	$0.781498\pi$
$822$		0			0
$823$	1.48472e11	+	2.57161e11i	0.323627	+	0.560539i	0.981234	−	0.192823i	$-0.0617642\pi$
$823$	1.48472e11	+	2.57161e11i	0.323627	+	0.560539i	−0.657606	+	0.753362i	$0.728431\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.43560e11			−0.734482			−0.367241	−	0.930126i	$-0.619698\pi$
$827$	−3.43560e11			−0.734482			−0.367241	+	0.930126i	$0.619698\pi$
$828$		0			0
$829$	1.65330e11	−	9.54533e10i	0.350053	−	0.202103i	−0.314656	−	0.949206i	$-0.601889\pi$
$829$	1.65330e11	−	9.54533e10i	0.350053	−	0.202103i	0.664708	+	0.747103i	$0.268556\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.17768e11	+	7.94312e10i	−0.244595	+	0.164972i
$834$		0			0
$835$	−2.14547e11	+	3.71606e11i	−0.441343	+	0.764428i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	3.92637e11i		−	0.792399i	−0.918164	−	0.396199i	$-0.870329\pi$
$839$		−	3.92637e11i		−	0.792399i	0.918164	−	0.396199i	$-0.129671\pi$
$840$		0			0
$841$	3.24924e11			0.649529
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.01443e11	+	1.74038e11i	0.591261	+	0.341364i
$846$		0			0
$847$	5.04361e10	+	2.68182e10i	0.0979959	+	0.0521070i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.21162e11	−	3.83063e11i	−0.421688	−	0.730386i
$852$		0			0
$853$			8.40881e11i			1.58832i	0.607707	+	0.794161i	$0.292089\pi$
$853$			8.40881e11i			1.58832i	−0.607707	+	0.794161i	$0.707911\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.17115e11	+	3.56292e11i	−1.14404	+	0.660514i	−0.947429	−	0.319966i	$-0.896328\pi$
$857$	−6.17115e11	+	3.56292e11i	−1.14404	+	0.660514i	−0.196615	+	0.980481i	$0.562995\pi$
$858$		0			0
$859$	−4.48728e11	−	2.59073e11i	−0.824158	−	0.475828i	0.0276900	−	0.999617i	$-0.491185\pi$
$859$	−4.48728e11	−	2.59073e11i	−0.824158	−	0.475828i	−0.851848	+	0.523789i	$0.824518\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.65673e11	−	6.33365e11i	0.659250	−	1.14185i	−0.321560	−	0.946889i	$-0.604207\pi$
$863$	3.65673e11	−	6.33365e11i	0.659250	−	1.14185i	0.980810	−	0.194965i	$-0.0624594\pi$
$864$		0			0
$865$	3.00271e11	+	5.20085e11i	0.536351	+	0.928987i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−3.35475e11			−0.588275
$870$		0			0
$871$	5.32561e10	−	3.07474e10i	0.0925330	−	0.0534240i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.16502e11	−	2.15208e10i	1.05173	−	0.0367136i
$876$		0			0
$877$	3.40974e11	−	5.90584e11i	0.576398	−	0.998351i	−0.419490	−	0.907760i	$-0.637791\pi$
$877$	3.40974e11	−	5.90584e11i	0.576398	−	0.998351i	0.995888	−	0.0905912i	$-0.0288757\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1.12611e12i		−	1.86929i	−0.355580	−	0.934646i	$-0.615717\pi$
$881$		−	1.12611e12i		−	1.86929i	0.355580	−	0.934646i	$-0.384283\pi$
$882$		0			0
$883$	−2.79315e10			−0.0459464			−0.0229732	−	0.999736i	$-0.507313\pi$
$883$	−2.79315e10			−0.0459464			−0.0229732	+	0.999736i	$0.507313\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	3.70745e11	+	2.14050e11i	0.598937	+	0.345796i	0.768623	−	0.639702i	$-0.220942\pi$
$887$	3.70745e11	+	2.14050e11i	0.598937	+	0.345796i	−0.169687	+	0.985498i	$0.554276\pi$
$888$		0			0
$889$	1.11241e10	+	3.18669e11i	0.0178097	+	0.510191i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.34284e10	+	1.44502e11i	0.131192	+	0.227232i
$894$		0			0
$895$			3.77707e11i			0.588658i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	8.40962e11	−	4.85530e11i	1.28747	−	0.743322i
$900$		0			0
$901$	1.70250e11	+	9.82937e10i	0.258337	+	0.149151i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−7.55733e10	+	1.30897e11i	−0.112661	+	0.195135i
$906$		0			0
$907$	3.94184e11	+	6.82746e11i	0.582465	+	1.00886i	0.995186	+	0.0980011i	$0.0312449\pi$
$907$	3.94184e11	+	6.82746e11i	0.582465	+	1.00886i	−0.412722	+	0.910857i	$0.635422\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−8.76508e11			−1.27257			−0.636286	−	0.771453i	$-0.719530\pi$
$911$	−8.76508e11			−1.27257			−0.636286	+	0.771453i	$0.719530\pi$
$912$		0			0
$913$	4.68897e11	−	2.70718e11i	0.674829	−	0.389613i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−3.04291e11	+	5.72270e11i	−0.430340	+	0.809327i
$918$		0			0
$919$	6.03038e10	−	1.04449e11i	0.0845440	−	0.146434i	−0.820653	−	0.571427i	$-0.806390\pi$
$919$	6.03038e10	−	1.04449e11i	0.0845440	−	0.146434i	0.905197	+	0.424993i	$0.139723\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			6.72761e10i			0.0926946i
$924$		0			0
$925$	−3.99243e11			−0.545344
$926$		0			0
$927$		0			0
$928$		0			0
$929$	4.76098e11	+	2.74876e11i	0.639196	+	0.369040i	0.784305	−	0.620376i	$-0.213020\pi$
$929$	4.76098e11	+	2.74876e11i	0.639196	+	0.369040i	−0.145109	+	0.989416i	$0.546353\pi$
$930$		0			0
$931$	−1.74351e11	−	8.50420e10i	−0.232073	−	0.113197i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.35111e10	−	1.27325e11i	−0.0961848	−	0.166597i
$936$		0			0
$937$		−	7.46093e11i		−	0.967909i	−0.875093	−	0.483955i	$-0.839200\pi$
$937$		−	7.46093e11i		−	0.967909i	0.875093	−	0.483955i	$-0.160800\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.72272e11	−	4.45871e11i	0.984945	−	0.568658i	0.0811853	−	0.996699i	$-0.474129\pi$
$941$	7.72272e11	−	4.45871e11i	0.984945	−	0.568658i	0.903759	+	0.428041i	$0.140796\pi$
$942$		0			0
$943$	5.67195e11	+	3.27470e11i	0.717275	+	0.414119i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.89215e11	−	1.02055e12i	0.732611	−	1.26892i	−0.223152	−	0.974784i	$-0.571635\pi$
$947$	5.89215e11	−	1.02055e12i	0.732611	−	1.26892i	0.955764	−	0.294136i	$-0.0950319\pi$
$948$		0			0
$949$	−1.79841e10	−	3.11494e10i	−0.0221730	−	0.0384047i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.62724e11			−0.803454			−0.401727	−	0.915759i	$-0.631590\pi$
$953$	−6.62724e11			−0.803454			−0.401727	+	0.915759i	$0.631590\pi$
$954$		0			0
$955$	−1.87296e11	+	1.08136e11i	−0.225173	+	0.130004i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.17415e12	+	7.33669e11i	−1.38819	+	0.867413i
$960$		0			0
$961$	1.44924e11	−	2.51016e11i	0.169921	−	0.294312i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	2.02284e11i		−	0.233266i
$966$		0			0
$967$	7.71443e11			0.882263			0.441131	−	0.897443i	$-0.354577\pi$
$967$	7.71443e11			0.882263			0.441131	+	0.897443i	$0.354577\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.42118e12	+	8.20516e11i	1.59871	+	0.923018i	0.991735	+	0.128301i	$0.0409523\pi$
$971$	1.42118e12	+	8.20516e11i	1.59871	+	0.923018i	0.606979	+	0.794718i	$0.292381\pi$
$972$		0			0
$973$	−4.75581e11	+	1.66015e10i	−0.530607	+	0.0185224i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.74522e11	+	9.95102e11i	0.630563	+	1.09217i	0.987437	+	0.158015i	$0.0505093\pi$
$977$	5.74522e11	+	9.95102e11i	0.630563	+	1.09217i	−0.356874	+	0.934153i	$0.616157\pi$
$978$		0			0
$979$			1.62873e11i			0.177303i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.51092e11	−	5.49113e11i	1.01861	−	0.588096i	0.104910	−	0.994482i	$-0.466544\pi$
$983$	9.51092e11	−	5.49113e11i	1.01861	−	0.588096i	0.913701	+	0.406386i	$0.133211\pi$
$984$		0			0
$985$	9.17867e11	+	5.29931e11i	0.975068	+	0.562956i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.52750e11	+	7.84187e11i	−0.473231	+	0.819661i
$990$		0			0
$991$	5.20799e11	+	9.02050e11i	0.539977	+	0.935267i	0.998905	+	0.0467938i	$0.0149004\pi$
$991$	5.20799e11	+	9.02050e11i	0.539977	+	0.935267i	−0.458928	+	0.888474i	$0.651766\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	4.04993e11			0.413195
$996$		0			0
$997$	−5.42668e11	+	3.13310e11i	−0.549229	+	0.317098i	−0.748811	−	0.662783i	$-0.769375\pi$
$997$	−5.42668e11	+	3.13310e11i	−0.549229	+	0.317098i	0.199582	+	0.979881i	$0.436042\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.b.145.4		10
3.2	odd	2		84.9.m.a.61.2	✓	10
7.3	odd	6	inner	252.9.z.b.73.4		10
21.17	even	6		84.9.m.a.73.2	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.m.a.61.2	✓	10	3.2	odd	2
84.9.m.a.73.2	yes	10	21.17	even	6
252.9.z.b.73.4		10	7.3	odd	6	inner
252.9.z.b.145.4		10	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(374.307 + 216.106i) q^{5} +(83.7630 + 2399.54i) q^{7} +O(q^{10})\)	\(q+(374.307 + 216.106i) q^{5} +(83.7630 + 2399.54i) q^{7} +(-6902.31 - 11955.2i) q^{11} +3223.79i q^{13} +(21339.9 - 12320.6i) q^{17} +(29141.7 + 16825.0i) q^{19} +(112905. - 195558. i) q^{23} +(-101909. - 176511. i) q^{25} +908389. q^{29} +(925773. - 534495. i) q^{31} +(-487202. + 916265. i) q^{35} +(979412. - 1.69639e6i) q^{37} +2.90040e6i q^{41} -4.01000e6 q^{43} +(4.29428e6 + 2.47930e6i) q^{47} +(-5.75077e6 + 401985. i) q^{49} +(3.98900e6 + 6.90915e6i) q^{53} -5.96653e6i q^{55} +(-4.69735e6 + 2.71201e6i) q^{59} +(1.84448e6 + 1.06491e6i) q^{61} +(-696680. + 1.20669e6i) q^{65} +(-9.53767e6 - 1.65197e7i) q^{67} +2.08687e7 q^{71} +(-9.66235e6 + 5.57856e6i) q^{73} +(2.81087e7 - 1.75638e7i) q^{77} +(1.21508e7 - 2.10458e7i) q^{79} +3.92213e7i q^{83} +1.06502e7 q^{85} +(-1.02177e7 - 5.89920e6i) q^{89} +(-7.73560e6 + 270034. i) q^{91} +(7.27196e6 + 1.25954e7i) q^{95} +7.80671e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 1389 q^{5} + 1217 q^{7}+O(q^{10}) \) 10 * q - 1389 * q^5 + 1217 * q^7	\( 10 q - 1389 q^{5} + 1217 q^{7} + 879 q^{11} + 13674 q^{17} - 29268 q^{19} - 312732 q^{23} - 22052 q^{25} + 289794 q^{29} + 242787 q^{31} - 1209372 q^{35} + 1913308 q^{37} - 861848 q^{43} + 305448 q^{47} + 9821659 q^{49} + 10663233 q^{53} - 18410871 q^{59} - 13937808 q^{61} + 14966808 q^{65} - 20722822 q^{67} - 113032584 q^{71} + 43436322 q^{73} + 98823405 q^{77} - 42189637 q^{79} + 142602108 q^{85} - 67171914 q^{89} - 246091266 q^{91} + 140649894 q^{95}+O(q^{100}) \) 10 * q - 1389 * q^5 + 1217 * q^7 + 879 * q^11 + 13674 * q^17 - 29268 * q^19 - 312732 * q^23 - 22052 * q^25 + 289794 * q^29 + 242787 * q^31 - 1209372 * q^35 + 1913308 * q^37 - 861848 * q^43 + 305448 * q^47 + 9821659 * q^49 + 10663233 * q^53 - 18410871 * q^59 - 13937808 * q^61 + 14966808 * q^65 - 20722822 * q^67 - 113032584 * q^71 + 43436322 * q^73 + 98823405 * q^77 - 42189637 * q^79 + 142602108 * q^85 - 67171914 * q^89 - 246091266 * q^91 + 140649894 * q^95

Introduction

L-functions

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