LMFDB - Embedded newform 252.9.z.d.73.4

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

Embedding invariants

Embedding label			73.4
Root			$-28.8366 + 49.9465i$ of defining polynomial
Character	$\chi$	$=$	252.73
Dual form			252.9.z.d.145.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(203.366 - 117.413i) q^{5} +(1130.34 + 2118.29i) q^{7} +O(q^{10})$	$q+(203.366 - 117.413i) q^{5} +(1130.34 + 2118.29i) q^{7} +(7474.44 - 12946.1i) q^{11} -39673.5i q^{13} +(-84679.4 - 48889.7i) q^{17} +(-177843. + 102678. i) q^{19} +(185312. + 320970. i) q^{23} +(-167741. + 290535. i) q^{25} -117048. q^{29} +(437915. + 252830. i) q^{31} +(478588. + 298070. i) q^{35} +(-986447. - 1.70858e6i) q^{37} -3.25966e6i q^{41} -4.13332e6 q^{43} +(4.79532e6 - 2.76858e6i) q^{47} +(-3.20947e6 + 4.78876e6i) q^{49} +(3.39093e6 - 5.87326e6i) q^{53} -3.51040e6i q^{55} +(1.91904e7 + 1.10796e7i) q^{59} +(-3.97144e6 + 2.29291e6i) q^{61} +(-4.65820e6 - 8.06823e6i) q^{65} +(-1.86385e7 + 3.22828e7i) q^{67} -4.19870e7 q^{71} +(1.08607e7 + 6.27044e6i) q^{73} +(3.58722e7 + 1.19951e6i) q^{77} +(-2.01064e7 - 3.48253e7i) q^{79} -5.31441e6i q^{83} -2.29612e7 q^{85} +(-6.45415e7 + 3.72630e7i) q^{89} +(8.40397e7 - 4.48445e7i) q^{91} +(-2.41115e7 + 4.17623e7i) q^{95} -3.76415e7i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) $ 12 * q - 285 * q^5 + 198 * q^7	$ 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) $ 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	203.366	−	117.413i	0.325386	−	0.187862i	−0.328405	−	0.944537i	$-0.606511\pi$
$5$	203.366	−	117.413i	0.325386	−	0.187862i	0.653791	+	0.756676i	$0.273178\pi$
$6$		0			0
$7$	1130.34	+	2118.29i	0.470778	+	0.882251i
$7$	1130.34	+	2118.29i	0.470778	+	0.882251i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	7474.44	−	12946.1i	0.510514	−	0.884237i	−0.489411	−	0.872053i	$-0.662788\pi$
$11$	7474.44	−	12946.1i	0.510514	−	0.884237i	0.999926	−	0.0121839i	$-0.00387834\pi$
$12$		0			0
$13$		−	39673.5i		−	1.38908i	−0.719455	−	0.694539i	$-0.755608\pi$
$13$		−	39673.5i		−	1.38908i	0.719455	−	0.694539i	$-0.244392\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−84679.4	−	48889.7i	−1.01387	−	0.585358i	−0.101547	−	0.994831i	$-0.532379\pi$
$17$	−84679.4	−	48889.7i	−1.01387	−	0.585358i	−0.912322	+	0.409473i	$0.865713\pi$
$18$		0			0
$19$	−177843.	+	102678.i	−1.36465	+	0.787882i	−0.990239	−	0.139380i	$-0.955489\pi$
$19$	−177843.	+	102678.i	−1.36465	+	0.787882i	−0.374413	+	0.927262i	$0.622156\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	185312.	+	320970.i	0.662205	+	1.14697i	0.980035	+	0.198825i	$0.0637124\pi$
$23$	185312.	+	320970.i	0.662205	+	1.14697i	−0.317830	+	0.948148i	$0.602954\pi$
$24$		0			0
$25$	−167741.	+	290535.i	−0.429416	+	0.743771i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−117048.			−0.165490			−0.0827448	−	0.996571i	$-0.526369\pi$
$29$	−117048.			−0.165490			−0.0827448	+	0.996571i	$0.526369\pi$
$30$		0			0
$31$	437915.	+	252830.i	0.474180	+	0.273768i	0.717988	−	0.696056i	$-0.245063\pi$
$31$	437915.	+	252830.i	0.474180	+	0.273768i	−0.243808	+	0.969823i	$0.578397\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	478588.	+	298070.i	0.318926	+	0.198631i
$36$		0			0
$37$	−986447.	−	1.70858e6i	−0.526341	−	0.911649i	−0.999529	−	0.0306877i	$-0.990230\pi$
$37$	−986447.	−	1.70858e6i	−0.526341	−	0.911649i	0.473188	−	0.880961i	$-0.343103\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	3.25966e6i		−	1.15355i	−0.816903	−	0.576776i	$-0.804311\pi$
$41$		−	3.25966e6i		−	1.15355i	0.816903	−	0.576776i	$-0.195689\pi$
$42$		0			0
$43$	−4.13332e6			−1.20900			−0.604498	−	0.796607i	$-0.706626\pi$
$43$	−4.13332e6			−1.20900			−0.604498	+	0.796607i	$0.706626\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.79532e6	−	2.76858e6i	0.982711	−	0.567369i	0.0796238	−	0.996825i	$-0.474628\pi$
$47$	4.79532e6	−	2.76858e6i	0.982711	−	0.567369i	0.903088	+	0.429456i	$0.141295\pi$
$48$		0			0
$49$	−3.20947e6	+	4.78876e6i	−0.556735	+	0.830690i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.39093e6	−	5.87326e6i	0.429749	−	0.744347i	−0.567102	−	0.823648i	$-0.691935\pi$
$53$	3.39093e6	−	5.87326e6i	0.429749	−	0.744347i	0.996851	+	0.0793006i	$0.0252687\pi$
$54$		0			0
$55$		−	3.51040e6i		−	0.383624i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.91904e7	+	1.10796e7i	1.58371	+	0.914355i	0.994312	+	0.106511i	$0.0339680\pi$
$59$	1.91904e7	+	1.10796e7i	1.58371	+	0.914355i	0.589397	+	0.807843i	$0.299365\pi$
$60$		0			0
$61$	−3.97144e6	+	2.29291e6i	−0.286833	+	0.165603i	−0.636513	−	0.771266i	$-0.719624\pi$
$61$	−3.97144e6	+	2.29291e6i	−0.286833	+	0.165603i	0.349680	+	0.936869i	$0.386290\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.65820e6	−	8.06823e6i	−0.260954	−	0.451986i
$66$		0			0
$67$	−1.86385e7	+	3.22828e7i	−0.924934	+	1.60203i	−0.133267	+	0.991080i	$0.542547\pi$
$67$	−1.86385e7	+	3.22828e7i	−0.924934	+	1.60203i	−0.791667	+	0.610952i	$0.790787\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.19870e7			−1.65227			−0.826135	−	0.563472i	$-0.809465\pi$
$71$	−4.19870e7			−1.65227			−0.826135	+	0.563472i	$0.809465\pi$
$72$		0			0
$73$	1.08607e7	+	6.27044e6i	0.382443	+	0.220804i	0.678881	−	0.734249i	$-0.262465\pi$
$73$	1.08607e7	+	6.27044e6i	0.382443	+	0.220804i	−0.296438	+	0.955052i	$0.595799\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.58722e7	+	1.19951e6i	1.02046	+	0.0341224i
$78$		0			0
$79$	−2.01064e7	−	3.48253e7i	−0.516209	−	0.894100i	−0.999823	−	0.0188184i	$-0.994010\pi$
$79$	−2.01064e7	−	3.48253e7i	−0.516209	−	0.894100i	0.483614	−	0.875281i	$-0.339324\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	5.31441e6i		−	0.111981i	−0.998431	−	0.0559903i	$-0.982168\pi$
$83$		−	5.31441e6i		−	0.111981i	0.998431	−	0.0559903i	$-0.0178316\pi$
$84$		0			0
$85$	−2.29612e7			−0.439865
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.45415e7	+	3.72630e7i	−1.02868	+	0.593907i	−0.916605	−	0.399793i	$-0.869082\pi$
$89$	−6.45415e7	+	3.72630e7i	−1.02868	+	0.593907i	−0.112072	+	0.993700i	$0.535749\pi$
$90$		0			0
$91$	8.40397e7	−	4.48445e7i	1.22552	−	0.653948i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.41115e7	+	4.17623e7i	−0.296026	+	0.512731i
$96$		0			0
$97$		−	3.76415e7i		−	0.425187i	−0.977141	−	0.212593i	$-0.931809\pi$
$97$		−	3.76415e7i		−	0.425187i	0.977141	−	0.212593i	$-0.0681909\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.57943e8	−	9.11884e7i	−1.51780	−	0.876303i	−0.999781	−	0.0209346i	$-0.993336\pi$
$101$	−1.57943e8	−	9.11884e7i	−1.51780	−	0.876303i	−0.518020	−	0.855368i	$-0.673331\pi$
$102$		0			0
$103$	−9.37340e7	+	5.41173e7i	−0.832814	+	0.480826i	−0.854815	−	0.518932i	$-0.826330\pi$
$103$	−9.37340e7	+	5.41173e7i	−0.832814	+	0.480826i	0.0220010	+	0.999758i	$0.492996\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.48762e6	+	1.64330e7i	0.0723806	+	0.125367i	0.899944	−	0.436005i	$-0.143607\pi$
$107$	9.48762e6	+	1.64330e7i	0.0723806	+	0.125367i	−0.827564	+	0.561372i	$0.810274\pi$
$108$		0			0
$109$	3.98197e7	−	6.89697e7i	0.282093	−	0.488599i	−0.689807	−	0.723993i	$-0.742305\pi$
$109$	3.98197e7	−	6.89697e7i	0.282093	−	0.488599i	0.971900	+	0.235394i	$0.0756381\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.14140e8			−1.31336			−0.656680	−	0.754169i	$-0.728040\pi$
$113$	−2.14140e8			−1.31336			−0.656680	+	0.754169i	$0.728040\pi$
$114$		0			0
$115$	7.53723e7	+	4.35162e7i	0.430944	+	0.248806i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.84586e6	−	2.34637e8i	0.0391249	−	1.17006i
$120$		0			0
$121$	−4.55511e6	−	7.88969e6i	−0.0212499	−	0.0368060i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			1.70509e8i			0.698406i
$126$		0			0
$127$	2.22002e8			0.853381			0.426690	−	0.904398i	$-0.359679\pi$
$127$	2.22002e8			0.853381			0.426690	+	0.904398i	$0.359679\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.38205e8	+	2.52998e8i	−1.48796	+	0.859075i	−0.999906	−	0.0137373i	$-0.995627\pi$
$131$	−4.38205e8	+	2.52998e8i	−1.48796	+	0.859075i	−0.488056	+	0.872812i	$0.662294\pi$
$132$		0			0
$133$	−4.18523e8	−	2.60661e8i	−1.33756	−	0.833048i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.73086e8	+	2.99795e8i	−0.491339	+	0.851023i	−0.999950	−	0.00997260i	$-0.996826\pi$
$137$	−1.73086e8	+	2.99795e8i	−0.491339	+	0.851023i	0.508612	+	0.860996i	$0.330159\pi$
$138$		0			0
$139$		−	1.04014e8i		−	0.278632i	−0.990248	−	0.139316i	$-0.955510\pi$
$139$		−	1.04014e8i		−	0.278632i	0.990248	−	0.139316i	$-0.0444904\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.13617e8	−	2.96537e8i	−1.22827	−	0.709144i
$144$		0			0
$145$	−2.38035e7	+	1.37430e7i	−0.0538480	+	0.0310891i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.71762e8	−	2.97501e8i	−0.348483	−	0.603591i	0.637497	−	0.770453i	$-0.279970\pi$
$149$	−1.71762e8	−	2.97501e8i	−0.348483	−	0.603591i	−0.985980	+	0.166862i	$0.946637\pi$
$150$		0			0
$151$	−4.21266e8	+	7.29654e8i	−0.810305	+	1.40349i	0.102346	+	0.994749i	$0.467365\pi$
$151$	−4.21266e8	+	7.29654e8i	−0.810305	+	1.40349i	−0.912651	+	0.408740i	$0.865968\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.18743e8			0.205722
$156$		0			0
$157$	−3.00370e8	−	1.73419e8i	−0.494377	−	0.285429i	0.232011	−	0.972713i	$-0.425469\pi$
$157$	−3.00370e8	−	1.73419e8i	−0.494377	−	0.285429i	−0.726388	+	0.687284i	$0.758803\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−4.70440e8	+	7.55349e8i	−0.700166	+	1.12420i
$162$		0			0
$163$	6.38287e7	+	1.10555e8i	0.0904203	+	0.156612i	0.907688	−	0.419646i	$-0.137846\pi$
$163$	6.38287e7	+	1.10555e8i	0.0904203	+	0.156612i	−0.817268	+	0.576258i	$0.804512\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	4.84232e8i		−	0.622569i	−0.950317	−	0.311284i	$-0.899241\pi$
$167$		−	4.84232e8i		−	0.622569i	0.950317	−	0.311284i	$-0.100759\pi$
$168$		0			0
$169$	−7.58252e8			−0.929537
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.57674e8	−	4.37444e8i	0.845860	−	0.488357i	−0.0133921	−	0.999910i	$-0.504263\pi$
$173$	7.57674e8	−	4.37444e8i	0.845860	−	0.488357i	0.859252	+	0.511553i	$0.170930\pi$
$174$		0			0
$175$	−8.05041e8	−	2.69192e7i	−0.858352	−	0.0287019i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.06371e8	−	1.05027e9i	0.590645	−	1.02303i	−0.403501	−	0.914979i	$-0.632207\pi$
$179$	6.06371e8	−	1.05027e9i	0.590645	−	1.02303i	0.994146	−	0.108048i	$-0.0344599\pi$
$180$		0			0
$181$			2.75613e8i			0.256794i	0.991723	+	0.128397i	$0.0409832\pi$
$181$			2.75613e8i			0.256794i	−0.991723	+	0.128397i	$0.959017\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.01220e8	−	2.31644e8i	−0.342528	−	0.197758i
$186$		0			0
$187$	−1.26586e9	+	7.30846e8i	−1.03519	+	0.597667i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.56485e8	−	1.65668e9i	−0.718695	−	1.24482i	−0.961517	−	0.274746i	$-0.911406\pi$
$191$	−9.56485e8	−	1.65668e9i	−0.718695	−	1.24482i	0.242821	−	0.970071i	$-0.421927\pi$
$192$		0			0
$193$	4.90016e8	−	8.48733e8i	0.353168	−	0.611705i	−0.633635	−	0.773632i	$-0.718438\pi$
$193$	4.90016e8	−	8.48733e8i	0.353168	−	0.611705i	0.986803	+	0.161928i	$0.0517711\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.49081e9			−0.989824			−0.494912	−	0.868943i	$-0.664800\pi$
$197$	−1.49081e9			−0.989824			−0.494912	+	0.868943i	$0.664800\pi$
$198$		0			0
$199$	−8.60781e8	−	4.96972e8i	−0.548884	−	0.316898i	0.199788	−	0.979839i	$-0.435975\pi$
$199$	−8.60781e8	−	4.96972e8i	−0.548884	−	0.316898i	−0.748672	+	0.662941i	$0.769308\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.32304e8	−	2.47940e8i	−0.0779090	−	0.146004i
$204$		0			0
$205$	−3.82728e8	−	6.62904e8i	−0.216708	−	0.375349i
$206$		0			0
$207$		0			0
$208$		0			0
$209$			3.06983e9i			1.60890i
$210$		0			0
$211$	−4.64537e8			−0.234364			−0.117182	−	0.993110i	$-0.537386\pi$
$211$	−4.64537e8			−0.234364			−0.117182	+	0.993110i	$0.537386\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−8.40576e8	+	4.85307e8i	−0.393390	+	0.227124i
$216$		0			0
$217$	−4.05745e7	+	1.21341e9i	−0.0182984	+	0.547229i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−1.93962e9	+	3.35952e9i	−0.813107	+	1.40834i
$222$		0			0
$223$		−	6.58116e7i		−	0.0266123i	−0.999911	−	0.0133062i	$-0.995764\pi$
$223$		−	6.58116e7i		−	0.0266123i	0.999911	−	0.0133062i	$-0.00423561\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.98442e9	−	1.14570e9i	−0.747360	−	0.431489i	0.0773791	−	0.997002i	$-0.475345\pi$
$227$	−1.98442e9	−	1.14570e9i	−0.747360	−	0.431489i	−0.824739	+	0.565513i	$0.808678\pi$
$228$		0			0
$229$	2.77398e9	−	1.60156e9i	1.00870	−	0.582373i	0.0978887	−	0.995197i	$-0.468791\pi$
$229$	2.77398e9	−	1.60156e9i	1.00870	−	0.582373i	0.910811	+	0.412825i	$0.135458\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.43830e8	−	1.28835e9i	−0.252377	−	0.437130i	0.711803	−	0.702380i	$-0.247879\pi$
$233$	−7.43830e8	−	1.28835e9i	−0.252377	−	0.437130i	−0.964180	+	0.265249i	$0.914546\pi$
$234$		0			0
$235$	6.50137e8	−	1.12607e9i	0.213173	−	0.369227i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−9.50233e8			−0.291232			−0.145616	−	0.989341i	$-0.546516\pi$
$239$	−9.50233e8			−0.291232			−0.145616	+	0.989341i	$0.546516\pi$
$240$		0			0
$241$	−3.55088e9	−	2.05010e9i	−1.05261	−	0.607725i	−0.129232	−	0.991614i	$-0.541251\pi$
$241$	−3.55088e9	−	2.05010e9i	−1.05261	−	0.607725i	−0.923379	+	0.383889i	$0.874584\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−9.04318e7	+	1.35071e9i	−0.0250990	+	0.374884i
$246$		0			0
$247$	4.07358e9	+	7.05564e9i	1.09443	+	1.89561i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	4.77515e9i		−	1.20307i	−0.798845	−	0.601537i	$-0.794555\pi$
$251$		−	4.77515e9i		−	1.20307i	0.798845	−	0.601537i	$-0.205445\pi$
$252$		0			0
$253$	5.54042e9			1.35226
$254$		0			0
$255$		0			0
$256$		0			0
$257$	4.28158e9	−	2.47197e9i	0.981457	−	0.566645i	0.0787473	−	0.996895i	$-0.474908\pi$
$257$	4.28158e9	−	2.47197e9i	0.981457	−	0.566645i	0.902710	+	0.430250i	$0.141575\pi$
$258$		0			0
$259$	2.50423e9	−	4.02085e9i	0.556514	−	0.893550i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.41497e9	+	5.91490e9i	−0.713779	+	1.23630i	0.249650	+	0.968336i	$0.419685\pi$
$263$	−3.41497e9	+	5.91490e9i	−0.713779	+	1.23630i	−0.963429	+	0.267965i	$0.913649\pi$
$264$		0			0
$265$		−	1.59256e9i		−	0.322933i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	3.01169e9	+	1.73880e9i	0.575176	+	0.332078i	0.759214	−	0.650841i	$-0.225584\pi$
$269$	3.01169e9	+	1.73880e9i	0.575176	+	0.332078i	−0.184038	+	0.982919i	$0.558917\pi$
$270$		0			0
$271$	−5.59984e9	+	3.23307e9i	−1.03824	+	0.599429i	−0.919335	−	0.393477i	$-0.871272\pi$
$271$	−5.59984e9	+	3.23307e9i	−1.03824	+	0.599429i	−0.118907	+	0.992905i	$0.537939\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.50754e9	+	4.34318e9i	0.438446	+	0.759411i
$276$		0			0
$277$	2.15914e9	−	3.73973e9i	0.366742	−	0.635216i	−0.622312	−	0.782769i	$-0.713806\pi$
$277$	2.15914e9	−	3.73973e9i	0.366742	−	0.635216i	0.989054	+	0.147553i	$0.0471397\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−5.64214e9			−0.904938			−0.452469	−	0.891780i	$-0.649457\pi$
$281$	−5.64214e9			−0.904938			−0.452469	+	0.891780i	$0.649457\pi$
$282$		0			0
$283$	3.51708e9	+	2.03059e9i	0.548323	+	0.316574i	0.748445	−	0.663197i	$-0.230801\pi$
$283$	3.51708e9	+	2.03059e9i	0.548323	+	0.316574i	−0.200122	+	0.979771i	$0.564134\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	6.90489e9	−	3.68452e9i	1.01772	−	0.543067i
$288$		0			0
$289$	1.29252e9	+	2.23871e9i	0.185287	+	0.320927i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	8.43223e7i		−	0.0114412i	−0.999984	−	0.00572061i	$-0.998179\pi$
$293$		−	8.43223e7i		−	0.0114412i	0.999984	−	0.00572061i	$-0.00182094\pi$
$294$		0			0
$295$	5.20356e9			0.687088
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.27340e10	−	7.35197e9i	1.59323	−	0.919854i
$300$		0			0
$301$	−4.67205e9	−	8.75554e9i	−0.569169	−	1.06664i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−5.38438e8	+	9.32601e8i	−0.0622209	+	0.107770i
$306$		0			0
$307$		−	6.10423e9i		−	0.687191i	−0.939118	−	0.343596i	$-0.888355\pi$
$307$		−	6.10423e9i		−	0.687191i	0.939118	−	0.343596i	$-0.111645\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.74096e9	+	1.00514e9i	0.186100	+	0.107445i	0.590156	−	0.807289i	$-0.299066\pi$
$311$	1.74096e9	+	1.00514e9i	0.186100	+	0.107445i	−0.404055	+	0.914735i	$0.632400\pi$
$312$		0			0
$313$	−1.10102e10	+	6.35672e9i	−1.14714	+	0.662302i	−0.948189	−	0.317708i	$-0.897087\pi$
$313$	−1.10102e10	+	6.35672e9i	−1.14714	+	0.662302i	−0.198951	+	0.980009i	$0.563754\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.98773e9	−	5.17489e9i	−0.295872	−	0.512465i	0.679315	−	0.733846i	$-0.262277\pi$
$317$	−2.98773e9	−	5.17489e9i	−0.295872	−	0.512465i	−0.975187	+	0.221381i	$0.928943\pi$
$318$		0			0
$319$	−8.74866e8	+	1.51531e9i	−0.0844849	+	0.146332i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.00795e10			1.84477
$324$		0			0
$325$	1.15265e10	+	6.65485e9i	1.03316	+	0.596492i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	1.12850e10	+	7.02842e9i	0.963201	+	0.599894i
$330$		0			0
$331$	6.42439e9	+	1.11274e10i	0.535205	+	0.927002i	0.999153	+	0.0411400i	$0.0130990\pi$
$331$	6.42439e9	+	1.11274e10i	0.535205	+	0.927002i	−0.463948	+	0.885862i	$0.653568\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$			8.75362e9i			0.695038i
$336$		0			0
$337$	−9.70137e9			−0.752166			−0.376083	−	0.926586i	$-0.622729\pi$
$337$	−9.70137e9			−0.752166			−0.376083	+	0.926586i	$0.622729\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.54634e9	−	3.77953e9i	0.484151	−	0.279525i
$342$		0			0
$343$	−1.37718e10	−	1.38565e9i	−0.994976	−	0.100110i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.48892e8	−	1.12391e9i	0.0447563	−	0.0775203i	−0.842779	−	0.538259i	$-0.819082\pi$
$347$	6.48892e8	−	1.12391e9i	0.0447563	−	0.0775203i	0.887536	+	0.460739i	$0.152416\pi$
$348$		0			0
$349$			2.01643e10i			1.35919i	0.733587	+	0.679596i	$0.237845\pi$
$349$			2.01643e10i			1.35919i	−0.733587	+	0.679596i	$0.762155\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.27487e10	+	1.31340e10i	1.46507	+	0.845857i	0.999238	−	0.0390186i	$-0.0124232\pi$
$353$	2.27487e10	+	1.31340e10i	1.46507	+	0.845857i	0.465828	+	0.884875i	$0.345756\pi$
$354$		0			0
$355$	−8.53872e9	+	4.92983e9i	−0.537625	+	0.310398i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.13441e10	−	1.96486e10i	−0.682958	−	1.18292i	−0.974074	−	0.226230i	$-0.927360\pi$
$359$	−1.13441e10	−	1.96486e10i	−0.682958	−	1.18292i	0.291116	−	0.956688i	$-0.405973\pi$
$360$		0			0
$361$	1.25936e10	−	2.18128e10i	0.741517	−	1.28435i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.94493e9			0.165922
$366$		0			0
$367$	9.38693e8	+	5.41955e8i	0.0517439	+	0.0298744i	0.525649	−	0.850702i	$-0.323823\pi$
$367$	9.38693e8	+	5.41955e8i	0.0517439	+	0.0298744i	−0.473905	+	0.880576i	$0.657156\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.62741e10	+	5.44179e8i	0.859018	+	0.0287241i
$372$		0			0
$373$	1.91674e9	+	3.31989e9i	0.0990211	+	0.171510i	0.911280	−	0.411788i	$-0.135096\pi$
$373$	1.91674e9	+	3.31989e9i	0.0990211	+	0.171510i	−0.812259	+	0.583297i	$0.801762\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			4.64369e9i			0.229878i
$378$		0			0
$379$	3.26734e10			1.58357			0.791785	−	0.610800i	$-0.209152\pi$
$379$	3.26734e10			1.58357			0.791785	+	0.610800i	$0.209152\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.54251e10	−	8.90569e9i	0.716858	−	0.413878i	−0.0967371	−	0.995310i	$-0.530841\pi$
$383$	1.54251e10	−	8.90569e9i	0.716858	−	0.413878i	0.813595	+	0.581432i	$0.197507\pi$
$384$		0			0
$385$	7.43603e9	−	3.96794e9i	0.338453	−	0.180602i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.92749e9	−	1.19988e10i	0.302536	−	0.524008i	−0.674173	−	0.738573i	$-0.735500\pi$
$389$	6.92749e9	−	1.19988e10i	0.302536	−	0.524008i	0.976710	+	0.214565i	$0.0688333\pi$
$390$		0			0
$391$		−	3.62394e10i		−	1.55051i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.17791e9	−	4.72152e9i	−0.335934	−	0.193951i
$396$		0			0
$397$	−1.66863e10	+	9.63385e9i	−0.671735	+	0.387827i	−0.796734	−	0.604330i	$-0.793441\pi$
$397$	−1.66863e10	+	9.63385e9i	−0.671735	+	0.387827i	0.124998	+	0.992157i	$0.460107\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−9.58138e9	−	1.65954e10i	−0.370553	−	0.641817i	0.619097	−	0.785314i	$-0.287499\pi$
$401$	−9.58138e9	−	1.65954e10i	−0.370553	−	0.641817i	−0.989651	+	0.143497i	$0.954165\pi$
$402$		0			0
$403$	1.00306e10	−	1.73736e10i	0.380285	−	0.658672i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−2.94926e10			−1.07482
$408$		0			0
$409$	3.45544e10	+	1.99500e10i	1.23484	+	0.712935i	0.968035	−	0.250815i	$-0.0806987\pi$
$409$	3.45544e10	+	1.99500e10i	1.23484	+	0.712935i	0.266805	+	0.963751i	$0.414032\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.77806e9	+	5.31744e10i	−0.0611148	+	1.82769i
$414$		0			0
$415$	−6.23984e8	−	1.08077e9i	−0.0210369	−	0.0364369i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			5.17883e10i			1.68026i	0.542387	+	0.840129i	$0.317521\pi$
$419$			5.17883e10i			1.68026i	−0.542387	+	0.840129i	$0.682479\pi$
$420$		0			0
$421$	5.78196e9			0.184055			0.0920273	−	0.995756i	$-0.470665\pi$
$421$	5.78196e9			0.184055			0.0920273	+	0.995756i	$0.470665\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	2.84083e10	−	1.64016e10i	0.870743	−	0.502724i
$426$		0			0
$427$	−9.34612e9	−	5.82088e9i	−0.281138	−	0.175096i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.29999e10	+	2.25165e10i	−0.376730	+	0.652516i	−0.990584	−	0.136903i	$-0.956285\pi$
$431$	−1.29999e10	+	2.25165e10i	−0.376730	+	0.652516i	0.613854	+	0.789420i	$0.289618\pi$
$432$		0			0
$433$			3.85244e10i			1.09593i	0.836500	+	0.547967i	$0.184598\pi$
$433$			3.85244e10i			1.09593i	−0.836500	+	0.547967i	$0.815402\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−6.59128e10	−	3.80548e10i	−1.80736	−	1.04348i
$438$		0			0
$439$	5.36255e10	−	3.09607e10i	1.44382	−	0.833591i	0.445720	−	0.895172i	$-0.352948\pi$
$439$	5.36255e10	−	3.09607e10i	1.44382	−	0.833591i	0.998102	+	0.0615814i	$0.0196144\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.82777e9	−	1.18260e10i	−0.177282	−	0.307061i	0.763667	−	0.645611i	$-0.223397\pi$
$443$	−6.82777e9	−	1.18260e10i	−0.177282	−	0.307061i	−0.940949	+	0.338550i	$0.890064\pi$
$444$		0			0
$445$	−8.75037e9	+	1.51561e10i	−0.223144	+	0.386498i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−6.45335e10			−1.58782			−0.793908	−	0.608038i	$-0.791957\pi$
$449$	−6.45335e10			−1.58782			−0.793908	+	0.608038i	$0.791957\pi$
$450$		0			0
$451$	−4.21999e10	−	2.43641e10i	−1.02001	−	0.588904i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	1.18255e10	−	1.89872e10i	0.275914	−	0.443013i
$456$		0			0
$457$	2.13781e10	+	3.70279e10i	0.490122	+	0.848916i	0.999935	−	0.0113692i	$-0.00361901\pi$
$457$	2.13781e10	+	3.70279e10i	0.490122	+	0.848916i	−0.509814	+	0.860285i	$0.670286\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			3.19885e10i			0.708256i	0.935197	+	0.354128i	$0.115222\pi$
$461$			3.19885e10i			0.708256i	−0.935197	+	0.354128i	$0.884778\pi$
$462$		0			0
$463$	−6.84419e9			−0.148935			−0.0744677	−	0.997223i	$-0.523726\pi$
$463$	−6.84419e9			−0.148935			−0.0744677	+	0.997223i	$0.523726\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.83350e10	−	1.05857e10i	0.385490	−	0.222563i	−0.294714	−	0.955585i	$-0.595224\pi$
$467$	1.83350e10	−	1.05857e10i	0.385490	−	0.222563i	0.680204	+	0.733023i	$0.261891\pi$
$468$		0			0
$469$	−8.94519e10	−	2.99112e9i	−1.84883	−	0.0618219i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.08942e10	+	5.35104e10i	−0.617210	+	1.06904i
$474$		0			0
$475$		−	6.88928e10i		−	1.35332i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−9.99972e9	−	5.77334e9i	−0.189953	−	0.109669i	0.402008	−	0.915636i	$-0.368313\pi$
$479$	−9.99972e9	−	5.77334e9i	−0.189953	−	0.109669i	−0.591960	+	0.805967i	$0.701646\pi$
$480$		0			0
$481$	−6.77852e10	+	3.91358e10i	−1.26635	+	0.731128i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.41961e9	−	7.65500e9i	−0.0798762	−	0.138350i
$486$		0			0
$487$	3.40949e10	−	5.90541e10i	0.606141	−	1.04987i	−0.385729	−	0.922612i	$-0.626050\pi$
$487$	3.40949e10	−	5.90541e10i	0.606141	−	1.04987i	0.991870	−	0.127255i	$-0.0406165\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	3.71885e10			0.639857			0.319929	−	0.947442i	$-0.396341\pi$
$491$	3.71885e10			0.639857			0.319929	+	0.947442i	$0.396341\pi$
$492$		0			0
$493$	9.91152e9	+	5.72242e9i	0.167785	+	0.0968706i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.74595e10	−	8.89404e10i	−0.777853	−	1.45772i
$498$		0			0
$499$	2.66255e10	+	4.61166e10i	0.429432	+	0.743799i	0.996823	−	0.0796501i	$-0.0253803\pi$
$499$	2.66255e10	+	4.61166e10i	0.429432	+	0.743799i	−0.567390	+	0.823449i	$0.692047\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	9.10881e10i		−	1.42295i	−0.702711	−	0.711475i	$-0.748027\pi$
$503$		−	9.10881e10i		−	1.42295i	0.702711	−	0.711475i	$-0.251973\pi$
$504$		0			0
$505$	−4.28270e10			−0.658494
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.02031e9	+	2.89848e9i	−0.0747927	+	0.0431816i	−0.536930	−	0.843627i	$-0.680416\pi$
$509$	−5.02031e9	+	2.89848e9i	−0.0747927	+	0.0431816i	0.462137	+	0.886808i	$0.347083\pi$
$510$		0			0
$511$	−1.00629e9	+	3.00938e10i	−0.0147584	+	0.441361i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.27082e10	+	2.20113e10i	−0.180657	+	0.312907i
$516$		0			0
$517$		−	8.27743e10i		−	1.15860i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	6.38767e10	+	3.68792e10i	0.866945	+	0.500531i	0.866332	−	0.499469i	$-0.166471\pi$
$521$	6.38767e10	+	3.68792e10i	0.866945	+	0.500531i	0.000613137		1.00000i	$0.499805\pi$
$522$		0			0
$523$	−8.49467e10	+	4.90440e10i	−1.13538	+	0.655510i	−0.945281	−	0.326256i	$-0.894213\pi$
$523$	−8.49467e10	+	4.90440e10i	−1.13538	+	0.655510i	−0.190095	+	0.981766i	$0.560880\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−2.47216e10	−	4.28190e10i	−0.320504	−	0.555129i
$528$		0			0
$529$	−2.95256e10	+	5.11398e10i	−0.377030	+	0.653035i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.29322e11			−1.60237
$534$		0			0
$535$	3.85892e9	+	2.22795e9i	0.0471032	+	0.0271950i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	3.80069e10	+	7.73435e10i	0.450305	+	0.916365i
$540$		0			0
$541$	1.61177e10	+	2.79168e10i	0.188155	+	0.325894i	0.944635	−	0.328123i	$-0.106416\pi$
$541$	1.61177e10	+	2.79168e10i	0.188155	+	0.325894i	−0.756480	+	0.654017i	$0.773083\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$		−	1.87015e10i		−	0.211978i
$546$		0			0
$547$	−9.97958e10			−1.11471			−0.557356	−	0.830273i	$-0.688184\pi$
$547$	−9.97958e10			−1.11471			−0.557356	+	0.830273i	$0.688184\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.08161e10	−	1.20182e10i	0.225836	−	0.130386i
$552$		0			0
$553$	5.10428e10	−	8.19554e10i	0.545801	−	0.876349i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	3.01561e10	−	5.22319e10i	0.313295	−	0.542644i	−0.665778	−	0.746150i	$-0.731900\pi$
$557$	3.01561e10	−	5.22319e10i	0.313295	−	0.542644i	0.979074	+	0.203506i	$0.0652337\pi$
$558$		0			0
$559$			1.63983e11i			1.67939i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.10263e8	+	6.36604e7i	0.00109748	+	0.000633630i	0.500549	−	0.865708i	$-0.333132\pi$
$563$	1.10263e8	+	6.36604e7i	0.00109748	+	0.000633630i	−0.499451	+	0.866342i	$0.666465\pi$
$564$		0			0
$565$	−4.35488e10	+	2.51429e10i	−0.427349	+	0.246730i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.12713e10	+	8.88046e10i	0.489132	+	0.847201i	0.999922	−	0.0125047i	$-0.00398046\pi$
$569$	5.12713e10	+	8.88046e10i	0.489132	+	0.847201i	−0.510790	+	0.859705i	$0.670647\pi$
$570$		0			0
$571$	3.04428e10	−	5.27285e10i	0.286378	−	0.496022i	−0.686564	−	0.727069i	$-0.740882\pi$
$571$	3.04428e10	−	5.27285e10i	0.286378	−	0.496022i	0.972943	+	0.231047i	$0.0742152\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.24337e11			−1.13745
$576$		0			0
$577$	−2.41312e10	−	1.39322e10i	−0.217709	−	0.125694i	0.387180	−	0.922004i	$-0.373449\pi$
$577$	−2.41312e10	−	1.39322e10i	−0.217709	−	0.125694i	−0.604889	+	0.796310i	$0.706783\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.12574e10	−	6.00709e9i	0.0987951	−	0.0527181i
$582$		0			0
$583$	−5.06906e10	−	8.77986e10i	−0.438786	−	0.760000i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	4.01355e9i		−	0.0338047i	−0.999857	−	0.0169023i	$-0.994620\pi$
$587$		−	4.01355e9i		−	0.0338047i	0.999857	−	0.0169023i	$-0.00538043\pi$
$588$		0			0
$589$	−1.03840e11			−0.862787
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.32222e11	+	7.63384e10i	−1.06926	+	0.617340i	−0.927980	−	0.372630i	$-0.878456\pi$
$593$	−1.32222e11	+	7.63384e10i	−1.06926	+	0.617340i	−0.141283	+	0.989969i	$0.545123\pi$
$594$		0			0
$595$	−2.59540e10	−	4.86384e10i	−0.207079	−	0.388071i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	5.45784e10	−	9.45325e10i	0.423949	−	0.734301i	−0.572373	−	0.819993i	$-0.693977\pi$
$599$	5.45784e10	−	9.45325e10i	0.423949	−	0.734301i	0.996322	+	0.0856928i	$0.0273104\pi$
$600$		0			0
$601$			1.79228e11i			1.37375i	0.726776	+	0.686875i	$0.241018\pi$
$601$			1.79228e11i			1.37375i	−0.726776	+	0.686875i	$0.758982\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.85271e9	−	1.06966e9i	−0.0138289	−	0.00798409i
$606$		0			0
$607$	3.96127e10	−	2.28704e10i	0.291796	−	0.168469i	−0.346955	−	0.937882i	$-0.612784\pi$
$607$	3.96127e10	−	2.28704e10i	0.291796	−	0.168469i	0.638752	+	0.769413i	$0.279451\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.09839e11	−	1.90247e11i	−0.788119	−	1.36506i
$612$		0			0
$613$	6.70156e10	−	1.16074e11i	0.474607	−	0.822044i	−0.524970	−	0.851121i	$-0.675924\pi$
$613$	6.70156e10	−	1.16074e11i	0.474607	−	0.822044i	0.999577	+	0.0290771i	$0.00925685\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.21594e11			−0.839015			−0.419508	−	0.907752i	$-0.637797\pi$
$617$	−1.21594e11			−0.839015			−0.419508	+	0.907752i	$0.637797\pi$
$618$		0			0
$619$	−3.51231e10	−	2.02783e10i	−0.239238	−	0.138124i	0.375589	−	0.926787i	$-0.377441\pi$
$619$	−3.51231e10	−	2.02783e10i	−0.239238	−	0.138124i	−0.614826	+	0.788662i	$0.710774\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.51888e11	−	9.45974e10i	−1.00825	−	0.627953i
$624$		0			0
$625$	−4.55036e10	−	7.88146e10i	−0.298212	−	0.516519i
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1.92908e11i			1.23239i
$630$		0			0
$631$	2.35096e11			1.48296			0.741478	−	0.670978i	$-0.234125\pi$
$631$	2.35096e11			1.48296			0.741478	+	0.670978i	$0.234125\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	4.51478e10	−	2.60661e10i	0.277678	−	0.160317i
$636$		0			0
$637$	1.89987e11	+	1.27331e11i	1.15389	+	0.773349i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.51414e11	+	2.62257e11i	−0.896881	+	1.55344i	−0.0654207	+	0.997858i	$0.520839\pi$
$641$	−1.51414e11	+	2.62257e11i	−0.896881	+	1.55344i	−0.831460	+	0.555585i	$0.812494\pi$
$642$		0			0
$643$		−	1.17949e11i		−	0.690001i	−0.938603	−	0.345000i	$-0.887879\pi$
$643$		−	1.17949e11i		−	0.690001i	0.938603	−	0.345000i	$-0.112121\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.55386e11	+	8.97120e10i	0.886735	+	0.511957i	0.872873	−	0.487947i	$-0.162254\pi$
$647$	1.55386e11	+	8.97120e10i	0.886735	+	0.511957i	0.0138619	+	0.999904i	$0.495587\pi$
$648$		0			0
$649$	2.86875e11	−	1.65627e11i	1.61701	−	0.933582i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	1.14200e11	+	1.97801e11i	0.628079	+	1.08786i	0.987937	+	0.154858i	$0.0494918\pi$
$653$	1.14200e11	+	1.97801e11i	0.628079	+	1.08786i	−0.359858	+	0.933007i	$0.617175\pi$
$654$		0			0
$655$	−5.94106e10	+	1.02902e11i	−0.322774	+	0.559061i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	2.80179e11			1.48557			0.742785	−	0.669530i	$-0.233504\pi$
$659$	2.80179e11			1.48557			0.742785	+	0.669530i	$0.233504\pi$
$660$		0			0
$661$	−8.31508e9	−	4.80071e9i	−0.0435573	−	0.0251478i	0.478063	−	0.878325i	$-0.341339\pi$
$661$	−8.31508e9	−	4.80071e9i	−0.0435573	−	0.0251478i	−0.521621	+	0.853178i	$0.674672\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.15719e11	−	3.86943e9i	−0.591720	−	0.0197861i
$666$		0			0
$667$	−2.16903e10	−	3.75688e10i	−0.109588	−	0.189812i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			6.85530e10i			0.338171i
$672$		0			0
$673$	−1.19348e11			−0.581776			−0.290888	−	0.956757i	$-0.593951\pi$
$673$	−1.19348e11			−0.581776			−0.290888	+	0.956757i	$0.593951\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	8.44704e10	−	4.87690e10i	0.402115	−	0.232161i	−0.285281	−	0.958444i	$-0.592087\pi$
$677$	8.44704e10	−	4.87690e10i	0.402115	−	0.232161i	0.687396	+	0.726283i	$0.258754\pi$
$678$		0			0
$679$	7.97354e10	−	4.25476e10i	0.375121	−	0.200169i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.69347e11	−	2.93317e11i	0.778204	−	1.34789i	−0.154772	−	0.987950i	$-0.549464\pi$
$683$	1.69347e11	−	2.93317e11i	0.778204	−	1.34789i	0.932976	−	0.359939i	$-0.117203\pi$
$684$		0			0
$685$			8.12907e10i			0.369214i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.33012e11	−	1.34530e11i	−1.03396	−	0.596955i
$690$		0			0
$691$	2.57158e11	−	1.48470e11i	1.12794	−	0.651219i	0.184527	−	0.982827i	$-0.440925\pi$
$691$	2.57158e11	−	1.48470e11i	1.12794	−	0.651219i	0.943417	+	0.331608i	$0.107591\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.22126e10	−	2.11529e10i	−0.0523443	−	0.0906630i
$696$		0			0
$697$	−1.59364e11	+	2.76026e11i	−0.675240	+	1.16955i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.94718e11			0.806370			0.403185	−	0.915118i	$-0.367903\pi$
$701$	1.94718e11			0.806370			0.403185	+	0.915118i	$0.367903\pi$
$702$		0			0
$703$	3.50865e11	+	2.02572e11i	1.43654	+	0.829389i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	1.46340e10	−	4.37642e11i	0.0585714	−	1.75163i
$708$		0			0
$709$	−2.00882e11	−	3.47938e11i	−0.794979	−	1.37694i	−0.922852	−	0.385154i	$-0.874148\pi$
$709$	−2.00882e11	−	3.47938e11i	−0.794979	−	1.37694i	0.127873	−	0.991791i	$-0.459185\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			1.87410e11i			0.725161i
$714$		0			0
$715$	−1.39270e11			−0.532884
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.54791e11	−	8.93684e10i	0.579201	−	0.334402i	−0.181615	−	0.983370i	$-0.558132\pi$
$719$	1.54791e11	−	8.93684e10i	0.579201	−	0.334402i	0.760816	+	0.648968i	$0.224799\pi$
$720$		0			0
$721$	−2.20587e11	−	1.37384e11i	−0.816280	−	0.508389i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.96337e10	−	3.40065e10i	0.0710639	−	0.123086i
$726$		0			0
$727$			1.97437e11i			0.706790i	0.935474	+	0.353395i	$0.114973\pi$
$727$			1.97437e11i			0.706790i	−0.935474	+	0.353395i	$0.885027\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	3.50006e11	+	2.02076e11i	1.22576	+	0.707695i
$732$		0			0
$733$	1.01144e11	−	5.83958e10i	0.350370	−	0.202286i	−0.314478	−	0.949265i	$-0.601830\pi$
$733$	1.01144e11	−	5.83958e10i	0.350370	−	0.202286i	0.664848	+	0.746979i	$0.268496\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.78624e11	+	4.82591e11i	0.944384	+	1.63572i
$738$		0			0
$739$	−8.45542e10	+	1.46452e11i	−0.283503	+	0.491042i	−0.972245	−	0.233965i	$-0.924830\pi$
$739$	−8.45542e10	+	1.46452e11i	−0.283503	+	0.491042i	0.688742	+	0.725006i	$0.258163\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	1.84466e11			0.605287			0.302644	−	0.953104i	$-0.402131\pi$
$743$	1.84466e11			0.605287			0.302644	+	0.953104i	$0.402131\pi$
$744$		0			0
$745$	−6.98611e10	−	4.03343e10i	−0.226783	−	0.130933i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.40856e10	+	3.86724e10i	−0.0765298	+	0.122878i
$750$		0			0
$751$	1.50650e11	+	2.60933e11i	0.473596	+	0.820293i	0.999543	−	0.0302244i	$-0.00962218\pi$
$751$	1.50650e11	+	2.60933e11i	0.473596	+	0.820293i	−0.525947	+	0.850518i	$0.676289\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			1.97849e11i			0.608900i
$756$		0			0
$757$	4.94329e11			1.50533			0.752666	−	0.658403i	$-0.228768\pi$
$757$	4.94329e11			1.50533			0.752666	+	0.658403i	$0.228768\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	5.78956e10	−	3.34260e10i	0.172626	−	0.0996658i	−0.411197	−	0.911546i	$-0.634889\pi$
$761$	5.78956e10	−	3.34260e10i	0.172626	−	0.0996658i	0.583824	+	0.811881i	$0.301556\pi$
$762$		0			0
$763$	1.91107e11	+	6.39031e9i	0.563870	+	0.0188549i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.39565e11	−	7.61348e11i	1.27011	−	2.19989i
$768$		0			0
$769$			1.20153e11i			0.343581i	0.985134	+	0.171790i	$0.0549552\pi$
$769$			1.20153e11i			0.343581i	−0.985134	+	0.171790i	$0.945045\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	3.05856e11	+	1.76586e11i	0.856640	+	0.494582i	0.862886	−	0.505399i	$-0.168655\pi$
$773$	3.05856e11	+	1.76586e11i	0.856640	+	0.494582i	−0.00624545	+	0.999980i	$0.501988\pi$
$774$		0			0
$775$	−1.46912e11	+	8.48198e10i	−0.407241	+	0.235120i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	3.34694e11	+	5.79707e11i	0.908862	+	1.57420i
$780$		0			0
$781$	−3.13829e11	+	5.43568e11i	−0.843508	+	1.46100i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.14468e10			−0.214484
$786$		0			0
$787$	−4.79863e11	−	2.77049e11i	−1.25089	−	0.722201i	−0.279602	−	0.960116i	$-0.590203\pi$
$787$	−4.79863e11	−	2.77049e11i	−1.25089	−	0.722201i	−0.971286	+	0.237915i	$0.923536\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−2.42051e11	−	4.53610e11i	−0.618302	−	1.15871i
$792$		0			0
$793$	9.09678e10	+	1.57561e11i	0.230036	+	0.398433i
$794$		0			0
$795$		0			0
$796$		0			0
$797$			4.84023e11i			1.19959i	0.800154	+	0.599795i	$0.204751\pi$
$797$			4.84023e11i			1.19959i	−0.800154	+	0.599795i	$0.795249\pi$
$798$		0			0
$799$	−5.41419e11			−1.32845
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.62356e11	−	9.37360e10i	0.390486	−	0.225447i
$804$		0			0
$805$	−6.98353e9	+	2.08848e11i	−0.0166300	+	0.497333i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	1.05691e11	−	1.83062e11i	0.246743	−	0.427371i	−0.715877	−	0.698226i	$-0.753973\pi$
$809$	1.05691e11	−	1.83062e11i	0.246743	−	0.427371i	0.962620	+	0.270855i	$0.0873064\pi$
$810$		0			0
$811$		−	1.05159e11i		−	0.243089i	−0.992586	−	0.121544i	$-0.961215\pi$
$811$		−	1.05159e11i		−	0.243089i	0.992586	−	0.121544i	$-0.0387847\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	2.59612e10	+	1.49887e10i	0.0588429	+	0.0339730i
$816$		0			0
$817$	7.35080e11	−	4.24399e11i	1.64986	−	0.952546i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−5.78260e10	−	1.00158e11i	−0.127277	−	0.220450i	0.795344	−	0.606159i	$-0.207290\pi$
$821$	−5.78260e10	−	1.00158e11i	−0.127277	−	0.220450i	−0.922621	+	0.385708i	$0.873957\pi$
$822$		0			0
$823$	4.35537e11	−	7.54373e11i	0.949349	−	1.64432i	0.202550	−	0.979272i	$-0.435077\pi$
$823$	4.35537e11	−	7.54373e11i	0.949349	−	1.64432i	0.746799	−	0.665049i	$-0.231590\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−5.49297e11			−1.17432			−0.587159	−	0.809472i	$-0.699754\pi$
$827$	−5.49297e11			−1.17432			−0.587159	+	0.809472i	$0.699754\pi$
$828$		0			0
$829$	−3.02301e11	−	1.74533e11i	−0.640060	−	0.369539i	0.144577	−	0.989493i	$-0.453818\pi$
$829$	−3.02301e11	−	1.74533e11i	−0.640060	−	0.369539i	−0.784638	+	0.619954i	$0.787151\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	5.05897e11	−	2.48600e11i	1.05071	−	0.516322i
$834$		0			0
$835$	−5.68553e10	−	9.84763e10i	−0.116957	−	0.202575i
$836$		0			0
$837$		0			0
$838$		0			0
$839$		−	7.74760e11i		−	1.56358i	−0.623543	−	0.781789i	$-0.714307\pi$
$839$		−	7.74760e11i		−	1.56358i	0.623543	−	0.781789i	$-0.285693\pi$
$840$		0			0
$841$	−4.86546e11			−0.972613
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.54203e11	+	8.90290e10i	−0.302458	+	0.174624i
$846$		0			0
$847$	1.15638e10	−	1.85671e10i	0.0224681	−	0.0360752i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	3.65601e11	−	6.33240e11i	0.697091	−	1.20740i
$852$		0			0
$853$			4.31150e11i			0.814390i	0.913341	+	0.407195i	$0.133493\pi$
$853$			4.31150e11i			0.814390i	−0.913341	+	0.407195i	$0.866507\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.55977e11	+	1.47788e11i	0.474545	+	0.273979i	0.718140	−	0.695898i	$-0.244994\pi$
$857$	2.55977e11	+	1.47788e11i	0.474545	+	0.273979i	−0.243596	+	0.969877i	$0.578327\pi$
$858$		0			0
$859$	8.08069e11	−	4.66539e11i	1.48414	−	0.856870i	0.484305	−	0.874899i	$-0.339072\pi$
$859$	8.08069e11	−	4.66539e11i	1.48414	−	0.856870i	0.999837	+	0.0180286i	$0.00573900\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	3.21149e11	+	5.56246e11i	0.578980	+	1.00282i	0.995597	+	0.0937400i	$0.0298822\pi$
$863$	3.21149e11	+	5.56246e11i	0.578980	+	1.00282i	−0.416617	+	0.909082i	$0.636784\pi$
$864$		0			0
$865$	1.02724e11	−	1.77922e11i	0.183487	−	0.317809i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−6.01136e11			−1.05413
$870$		0			0
$871$	1.28077e12	+	7.39452e11i	2.22535	+	1.28481i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−3.61187e11	+	1.92733e11i	−0.616170	+	0.328795i
$876$		0			0
$877$	−2.91337e11	−	5.04610e11i	−0.492490	−	0.853017i	0.507473	−	0.861668i	$-0.330580\pi$
$877$	−2.91337e11	−	5.04610e11i	−0.492490	−	0.853017i	−0.999963	+	0.00865063i	$0.997246\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	1.79255e11i		−	0.297554i	−0.988871	−	0.148777i	$-0.952466\pi$
$881$		−	1.79255e11i		−	0.297554i	0.988871	−	0.148777i	$-0.0475337\pi$
$882$		0			0
$883$	−1.09789e12			−1.80599			−0.902993	−	0.429655i	$-0.858635\pi$
$883$	−1.09789e12			−1.80599			−0.902993	+	0.429655i	$0.858635\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.05091e11	+	2.91615e11i	−0.815972	+	0.471102i	−0.849026	−	0.528352i	$-0.822810\pi$
$887$	−5.05091e11	+	2.91615e11i	−0.815972	+	0.471102i	0.0330533	+	0.999454i	$0.489477\pi$
$888$		0			0
$889$	2.50938e11	+	4.70265e11i	0.401753	+	0.752896i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−5.68542e11	+	9.84744e11i	−0.894040	+	1.54852i
$894$		0			0
$895$		−	2.84784e11i		−	0.443838i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−5.12569e10	−	2.95932e10i	−0.0784718	−	0.0453057i
$900$		0			0
$901$	−5.74283e11	+	3.31562e11i	−0.871419	+	0.503114i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	3.23607e10	+	5.60503e10i	0.0482418	+	0.0835572i
$906$		0			0
$907$	−4.66059e11	+	8.07237e11i	−0.688671	+	1.19281i	0.283598	+	0.958943i	$0.408472\pi$
$907$	−4.66059e11	+	8.07237e11i	−0.688671	+	1.19281i	−0.972268	+	0.233869i	$0.924861\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−7.47091e11			−1.08468			−0.542338	−	0.840160i	$-0.682461\pi$
$911$	−7.47091e11			−1.08468			−0.542338	+	0.840160i	$0.682461\pi$
$912$		0			0
$913$	−6.88010e10	−	3.97223e10i	−0.0990174	−	0.0571677i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.03124e12	−	6.42270e11i	−1.45842	−	0.908322i
$918$		0			0
$919$	3.60674e11	+	6.24705e11i	0.505653	+	0.875817i	0.999979	+	0.00653993i	$0.00208174\pi$
$919$	3.60674e11	+	6.24705e11i	0.505653	+	0.875817i	−0.494326	+	0.869277i	$0.664585\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			1.66577e12i			2.29513i
$924$		0			0
$925$	6.61869e11			0.904077
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−5.66284e10	+	3.26944e10i	−0.0760276	+	0.0438945i	−0.537532	−	0.843243i	$-0.680643\pi$
$929$	−5.66284e10	+	3.26944e10i	−0.0760276	+	0.0438945i	0.461504	+	0.887138i	$0.347310\pi$
$930$		0			0
$931$	7.90822e10	−	1.18119e12i	0.105264	−	1.57224i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−1.71622e11	+	2.97258e11i	−0.224557	+	0.388945i
$936$		0			0
$937$			1.46812e11i			0.190460i	0.995455	+	0.0952301i	$0.0303587\pi$
$937$			1.46812e11i			0.190460i	−0.995455	+	0.0952301i	$0.969641\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−2.76414e11	−	1.59588e11i	−0.352535	−	0.203536i	0.313266	−	0.949665i	$-0.398577\pi$
$941$	−2.76414e11	−	1.59588e11i	−0.352535	−	0.203536i	−0.665801	+	0.746129i	$0.731910\pi$
$942$		0			0
$943$	1.04625e12	−	6.04054e11i	1.32309	−	0.763887i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1.63248e11	+	2.82754e11i	0.202977	+	0.351567i	0.949486	−	0.313808i	$-0.101605\pi$
$947$	1.63248e11	+	2.82754e11i	0.202977	+	0.351567i	−0.746509	+	0.665375i	$0.768272\pi$
$948$		0			0
$949$	2.48770e11	−	4.30882e11i	0.306714	−	0.531243i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.37626e12			−1.66851			−0.834254	−	0.551380i	$-0.814102\pi$
$953$	−1.37626e12			−1.66851			−0.834254	+	0.551380i	$0.814102\pi$
$954$		0			0
$955$	−3.89033e11	−	2.24608e11i	−0.467706	−	0.270030i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−8.30697e11	−	2.77771e10i	−0.982128	−	0.0328407i
$960$		0			0
$961$	−2.98599e11	−	5.17189e11i	−0.350103	−	0.606395i
$962$		0			0
$963$		0			0
$964$		0			0
$965$		−	2.30138e11i		−	0.265387i
$966$		0			0
$967$	−4.03059e11			−0.460959			−0.230480	−	0.973077i	$-0.574029\pi$
$967$	−4.03059e11			−0.460959			−0.230480	+	0.973077i	$0.574029\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.41001e12	−	8.14067e11i	1.58615	−	0.915764i	0.592216	−	0.805779i	$-0.298253\pi$
$971$	1.41001e12	−	8.14067e11i	1.58615	−	0.915764i	0.993933	−	0.109985i	$-0.0350802\pi$
$972$		0			0
$973$	2.20331e11	−	1.17571e11i	0.245824	−	0.131174i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	5.36831e11	−	9.29819e11i	0.589196	−	1.02052i	−0.405143	−	0.914254i	$-0.632778\pi$
$977$	5.36831e11	−	9.29819e11i	0.589196	−	1.02052i	0.994338	−	0.106263i	$-0.0338886\pi$
$978$		0			0
$979$			1.11408e12i			1.21279i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.63659e9	−	3.83164e9i	−0.00710773	−	0.00410365i	0.496442	−	0.868070i	$-0.334640\pi$
$983$	−6.63659e9	−	3.83164e9i	−0.00710773	−	0.00410365i	−0.503550	+	0.863966i	$0.667973\pi$
$984$		0			0
$985$	−3.03180e11	+	1.75041e11i	−0.322074	+	0.185950i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.65953e11	−	1.32667e12i	−0.800602	−	1.38668i
$990$		0			0
$991$	−1.26964e11	+	2.19908e11i	−0.131639	+	0.228006i	−0.924309	−	0.381646i	$-0.875357\pi$
$991$	−1.26964e11	+	2.19908e11i	−0.131639	+	0.228006i	0.792669	+	0.609652i	$0.208691\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−2.33405e11			−0.238132
$996$		0			0
$997$	−3.46237e11	−	1.99900e11i	−0.350423	−	0.202317i	0.314449	−	0.949275i	$-0.398180\pi$
$997$	−3.46237e11	−	1.99900e11i	−0.350423	−	0.202317i	−0.664872	+	0.746958i	$0.731514\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.9.z.d.73.4		12
3.2	odd	2		84.9.m.b.73.3	yes	12
7.5	odd	6	inner	252.9.z.d.145.4		12
21.5	even	6		84.9.m.b.61.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
84.9.m.b.61.3	✓	12	21.5	even	6
84.9.m.b.73.3	yes	12	3.2	odd	2
252.9.z.d.73.4		12	1.1	even	1	trivial
252.9.z.d.145.4		12	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	252.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(203.366 - 117.413i) q^{5} +(1130.34 + 2118.29i) q^{7} +O(q^{10})\)	\(q+(203.366 - 117.413i) q^{5} +(1130.34 + 2118.29i) q^{7} +(7474.44 - 12946.1i) q^{11} -39673.5i q^{13} +(-84679.4 - 48889.7i) q^{17} +(-177843. + 102678. i) q^{19} +(185312. + 320970. i) q^{23} +(-167741. + 290535. i) q^{25} -117048. q^{29} +(437915. + 252830. i) q^{31} +(478588. + 298070. i) q^{35} +(-986447. - 1.70858e6i) q^{37} -3.25966e6i q^{41} -4.13332e6 q^{43} +(4.79532e6 - 2.76858e6i) q^{47} +(-3.20947e6 + 4.78876e6i) q^{49} +(3.39093e6 - 5.87326e6i) q^{53} -3.51040e6i q^{55} +(1.91904e7 + 1.10796e7i) q^{59} +(-3.97144e6 + 2.29291e6i) q^{61} +(-4.65820e6 - 8.06823e6i) q^{65} +(-1.86385e7 + 3.22828e7i) q^{67} -4.19870e7 q^{71} +(1.08607e7 + 6.27044e6i) q^{73} +(3.58722e7 + 1.19951e6i) q^{77} +(-2.01064e7 - 3.48253e7i) q^{79} -5.31441e6i q^{83} -2.29612e7 q^{85} +(-6.45415e7 + 3.72630e7i) q^{89} +(8.40397e7 - 4.48445e7i) q^{91} +(-2.41115e7 + 4.17623e7i) q^{95} -3.76415e7i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) 12 * q - 285 * q^5 + 198 * q^7	\( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) 12 * q - 285 * q^5 + 198 * q^7 + 17919 * q^11 + 205782 * q^17 + 74313 * q^19 + 62832 * q^23 + 878679 * q^25 + 575454 * q^29 + 1442952 * q^31 + 3989514 * q^35 - 2058621 * q^37 + 7721322 * q^43 - 12088194 * q^47 - 16964694 * q^49 + 5506743 * q^53 - 7511901 * q^59 - 37215576 * q^61 - 5047122 * q^65 - 36824553 * q^67 + 30011556 * q^71 + 95080185 * q^73 + 38333727 * q^77 + 8514456 * q^79 + 20121540 * q^85 - 83038554 * q^89 - 198538635 * q^91 + 221605224 * q^95

Introduction

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