LMFDB - Embedded newform 72.22.f.a.35.63

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,22,Mod(35,72)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

N = Newforms(chi, 22, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("72.35");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	72.f (of order $2$, degree $1$, 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:	$201.223687887$
Analytic rank:	$0$
Dimension:	$84$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			35.63
Character	$\chi$	$=$	72.35
Dual form			72.22.f.a.35.64

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1049.06 - 998.310i) q^{2} +(103905. - 2.09458e6i) q^{4} -2.17906e7 q^{5} +8.90529e8i q^{7} +(-1.98203e9 - 2.30107e9i) q^{8} +O(q^{10})$	\(q+(1049.06 - 998.310i) q^{2} +(103905. - 2.09458e6i) q^{4} -2.17906e7 q^{5} +8.90529e8i q^{7} +(-1.98203e9 - 2.30107e9i) q^{8} +(-2.28597e10 + 2.17538e10i) q^{10} -3.82633e10i q^{11} -4.83887e11i q^{13} +(8.89024e11 + 9.34219e11i) q^{14} +(-4.37645e12 - 4.35276e11i) q^{16} -2.21884e12i q^{17} +1.16847e13 q^{19} +(-2.26417e12 + 4.56422e13i) q^{20} +(-3.81986e13 - 4.01405e13i) q^{22} -8.76881e13 q^{23} -2.00507e12 q^{25} +(-4.83069e14 - 5.07627e14i) q^{26} +(1.86528e15 + 9.25308e13i) q^{28} -4.27624e15 q^{29} -2.49379e15i q^{31} +(-5.02571e15 + 3.91243e15i) q^{32} +(-2.21509e15 - 2.32770e15i) q^{34} -1.94052e16i q^{35} +5.91817e15i q^{37} +(1.22579e16 - 1.16649e16i) q^{38} +(4.31898e16 + 5.01418e16i) q^{40} -2.79351e16i q^{41} -5.17433e16 q^{43} +(-8.01454e16 - 3.97577e15i) q^{44} +(-9.19902e16 + 8.75400e16i) q^{46} -2.93354e17 q^{47} -2.34495e17 q^{49} +(-2.10344e15 + 2.00168e15i) q^{50} +(-1.01354e18 - 5.02785e16i) q^{52} +7.56626e17 q^{53} +8.33782e17i q^{55} +(2.04917e18 - 1.76506e18i) q^{56} +(-4.48604e18 + 4.26901e18i) q^{58} +4.55809e18i q^{59} +6.83311e18i q^{61} +(-2.48958e18 - 2.61614e18i) q^{62} +(-1.36646e18 + 9.12159e18i) q^{64} +1.05442e19i q^{65} +2.07614e18 q^{67} +(-4.64753e18 - 2.30550e17i) q^{68} +(-1.93724e19 - 2.03572e19i) q^{70} +1.22268e19 q^{71} +6.26851e19 q^{73} +(5.90817e18 + 6.20852e18i) q^{74} +(1.21410e18 - 2.44744e19i) q^{76} +3.40746e19 q^{77} -7.16868e19i q^{79} +(9.53657e19 + 9.48494e18i) q^{80} +(-2.78879e19 - 2.93057e19i) q^{82} +1.85258e20i q^{83} +4.83500e19i q^{85} +(-5.42819e19 + 5.16559e19i) q^{86} +(-8.80465e19 + 7.58392e19i) q^{88} -2.85566e20i q^{89} +4.30915e20 q^{91} +(-9.11128e18 + 1.83670e20i) q^{92} +(-3.07746e20 + 2.92858e20i) q^{94} -2.54616e20 q^{95} +9.52477e20 q^{97} +(-2.46000e20 + 2.34099e20i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 2424084 q^{4}+O(q^{10}) $ 84 * q + 2424084 * q^4	$ 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 80\!\cdots\!00 q^{25}+ \cdots - 16\!\cdots\!12 q^{97}+O(q^{100}) $ 84 * q + 2424084 * q^4 + 17057181612 * q^10 - 4099708064904 * q^16 + 92015527242864 * q^19 - 236011369239528 * q^22 + 8010864257812500 * q^25 - 3042238700022024 * q^28 + 74414158327329924 * q^34 + 75018327243317184 * q^40 + 707788847336454432 * q^43 - 162639476543943288 * q^46 - 5423745715136249124 * q^49 - 70566629446202808 * q^52 - 14491558288019904108 * q^58 - 28749968749508108064 * q^64 - 13653811098426494352 * q^67 + 140256684870035374392 * q^70 - 71781309378863778384 * q^73 + 376055720386305092400 * q^76 - 368362114062816367548 * q^82 - 592572120184082106720 * q^88 - 522206955652189957200 * q^91 - 528772551789914644488 * q^94 - 1686050813935078492512 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	1049.06	−	998.310i	0.724412	−	0.689367i
$2$	1049.06	−	998.310i	0.724412	−	0.689367i
$3$		0			0
$3$		0			0
$4$	103905.	−	2.09458e6i	0.0495460	−	0.998772i
$5$	−2.17906e7			−0.997895			−0.498948	−	0.866632i	$-0.666280\pi$
$5$	−2.17906e7			−0.997895			−0.498948	+	0.866632i	$0.666280\pi$
$6$		0			0
$7$			8.90529e8i			1.19157i	0.803145	+	0.595784i	$0.203158\pi$
$7$			8.90529e8i			1.19157i	−0.803145	+	0.595784i	$0.796842\pi$
$8$	−1.98203e9	−	2.30107e9i	−0.652629	−	0.757678i
$9$		0			0
$10$	−2.28597e10	+	2.17538e10i	−0.722888	+	0.687916i
$11$		−	3.82633e10i		−	0.444794i	−0.974956	−	0.222397i	$-0.928612\pi$
$11$		−	3.82633e10i		−	0.444794i	0.974956	−	0.222397i	$-0.0713882\pi$
$12$		0			0
$13$		−	4.83887e11i		−	0.973506i	−0.873540	−	0.486753i	$-0.838181\pi$
$13$		−	4.83887e11i		−	0.973506i	0.873540	−	0.486753i	$-0.161819\pi$
$14$	8.89024e11	+	9.34219e11i	0.821427	+	0.863186i
$15$		0			0
$16$	−4.37645e12	−	4.35276e11i	−0.995090	−	0.0989703i
$17$		−	2.21884e12i		−	0.266939i	−0.991053	−	0.133470i	$-0.957388\pi$
$17$		−	2.21884e12i		−	0.266939i	0.991053	−	0.133470i	$-0.0426119\pi$
$18$		0			0
$19$	1.16847e13			0.437223			0.218612	−	0.975812i	$-0.429847\pi$
$19$	1.16847e13			0.437223			0.218612	+	0.975812i	$0.429847\pi$
$20$	−2.26417e12	+	4.56422e13i	−0.0494417	+	0.996670i
$21$		0			0
$22$	−3.81986e13	−	4.01405e13i	−0.306627	−	0.322214i
$23$	−8.76881e13			−0.441366			−0.220683	−	0.975346i	$-0.570829\pi$
$23$	−8.76881e13			−0.441366			−0.220683	+	0.975346i	$0.570829\pi$
$24$		0			0
$25$	−2.00507e12			−0.00420493
$26$	−4.83069e14	−	5.07627e14i	−0.671103	−	0.705220i
$27$		0			0
$28$	1.86528e15	+	9.25308e13i	1.19010	+	0.0590374i
$29$	−4.27624e15			−1.88748			−0.943742	−	0.330683i	$-0.892721\pi$
$29$	−4.27624e15			−1.88748			−0.943742	+	0.330683i	$0.892721\pi$
$30$		0			0
$31$		−	2.49379e15i		−	0.546465i	−0.961948	−	0.273233i	$-0.911907\pi$
$31$		−	2.49379e15i		−	0.546465i	0.961948	−	0.273233i	$-0.0880929\pi$
$32$	−5.02571e15	+	3.91243e15i	−0.789082	+	0.614287i
$33$		0			0
$34$	−2.21509e15	−	2.32770e15i	−0.184019	−	0.193374i
$35$		−	1.94052e16i		−	1.18906i
$36$		0			0
$37$			5.91817e15i			0.202334i	0.994869	+	0.101167i	$0.0322577\pi$
$37$			5.91817e15i			0.202334i	−0.994869	+	0.101167i	$0.967742\pi$
$38$	1.22579e16	−	1.16649e16i	0.316730	−	0.301407i
$39$		0			0
$40$	4.31898e16	+	5.01418e16i	0.651255	+	0.756083i
$41$		−	2.79351e16i		−	0.325028i	−0.986706	−	0.162514i	$-0.948040\pi$
$41$		−	2.79351e16i		−	0.325028i	0.986706	−	0.162514i	$-0.0519602\pi$
$42$		0			0
$43$	−5.17433e16			−0.365120			−0.182560	−	0.983195i	$-0.558438\pi$
$43$	−5.17433e16			−0.365120			−0.182560	+	0.983195i	$0.558438\pi$
$44$	−8.01454e16	−	3.97577e15i	−0.444248	−	0.0220378i
$45$		0			0
$46$	−9.19902e16	+	8.75400e16i	−0.319731	+	0.304263i
$47$	−2.93354e17			−0.813513			−0.406756	−	0.913537i	$-0.633340\pi$
$47$	−2.93354e17			−0.813513			−0.406756	+	0.913537i	$0.633340\pi$
$48$		0			0
$49$	−2.34495e17			−0.419832
$50$	−2.10344e15	+	2.00168e15i	−0.00304610	+	0.00289874i
$51$		0			0
$52$	−1.01354e18	−	5.02785e16i	−0.972310	−	0.0482333i
$53$	7.56626e17			0.594271			0.297136	−	0.954835i	$-0.403969\pi$
$53$	7.56626e17			0.594271			0.297136	+	0.954835i	$0.403969\pi$
$54$		0			0
$55$			8.33782e17i			0.443858i
$56$	2.04917e18	−	1.76506e18i	0.902824	−	0.777651i
$57$		0			0
$58$	−4.48604e18	+	4.26901e18i	−1.36732	+	1.30117i
$59$			4.55809e18i			1.16101i	0.814256	+	0.580506i	$0.197145\pi$
$59$			4.55809e18i			1.16101i	−0.814256	+	0.580506i	$0.802855\pi$
$60$		0			0
$61$			6.83311e18i			1.22646i	0.789903	+	0.613232i	$0.210131\pi$
$61$			6.83311e18i			1.22646i	−0.789903	+	0.613232i	$0.789869\pi$
$62$	−2.48958e18	−	2.61614e18i	−0.376715	−	0.395866i
$63$		0			0
$64$	−1.36646e18	+	9.12159e18i	−0.148151	+	0.988965i
$65$			1.05442e19i			0.971457i
$66$		0			0
$67$	2.07614e18			0.139146			0.0695731	−	0.997577i	$-0.477836\pi$
$67$	2.07614e18			0.139146			0.0695731	+	0.997577i	$0.477836\pi$
$68$	−4.64753e18	−	2.30550e17i	−0.266612	−	0.0132258i
$69$		0			0
$70$	−1.93724e19	−	2.03572e19i	−0.819698	−	0.861369i
$71$	1.22268e19			0.445758			0.222879	−	0.974846i	$-0.428454\pi$
$71$	1.22268e19			0.445758			0.222879	+	0.974846i	$0.428454\pi$
$72$		0			0
$73$	6.26851e19			1.70716			0.853580	−	0.520961i	$-0.174426\pi$
$73$	6.26851e19			1.70716			0.853580	+	0.520961i	$0.174426\pi$
$74$	5.90817e18	+	6.20852e18i	0.139483	+	0.146573i
$75$		0			0
$76$	1.21410e18	−	2.44744e19i	0.0216626	−	0.436686i
$77$	3.40746e19			0.530002
$78$		0			0
$79$		−	7.16868e19i		−	0.851833i	−0.904762	−	0.425917i	$-0.859952\pi$
$79$		−	7.16868e19i		−	0.851833i	0.904762	−	0.425917i	$-0.140048\pi$
$80$	9.53657e19	+	9.48494e18i	0.992996	+	0.0987620i
$81$		0			0
$82$	−2.78879e19	−	2.93057e19i	−0.224063	−	0.235454i
$83$			1.85258e20i			1.31056i	0.755385	+	0.655282i	$0.227450\pi$
$83$			1.85258e20i			1.31056i	−0.755385	+	0.655282i	$0.772550\pi$
$84$		0			0
$85$			4.83500e19i			0.266378i
$86$	−5.42819e19	+	5.16559e19i	−0.264497	+	0.251701i
$87$		0			0
$88$	−8.80465e19	+	7.58392e19i	−0.337011	+	0.290286i
$89$		−	2.85566e20i		−	0.970758i	−0.874304	−	0.485379i	$-0.838682\pi$
$89$		−	2.85566e20i		−	0.970758i	0.874304	−	0.485379i	$-0.161318\pi$
$90$		0			0
$91$	4.30915e20			1.16000
$92$	−9.11128e18	+	1.83670e20i	−0.0218679	+	0.440824i
$93$		0			0
$94$	−3.07746e20	+	2.92858e20i	−0.589319	+	0.560809i
$95$	−2.54616e20			−0.436303
$96$		0			0
$97$	9.52477e20			1.31145			0.655724	−	0.755001i	$-0.272363\pi$
$97$	9.52477e20			1.31145			0.655724	+	0.755001i	$0.272363\pi$
$98$	−2.46000e20	+	2.34099e20i	−0.304131	+	0.289418i
$99$		0			0
$100$	−2.08337e17	+	4.19976e18i	−0.000208337	+	0.00419976i
$101$	−7.40415e20			−0.666962			−0.333481	−	0.942757i	$-0.608223\pi$
$101$	−7.40415e20			−0.666962			−0.333481	+	0.942757i	$0.608223\pi$
$102$		0			0
$103$		−	1.01409e21i		−	0.743508i	−0.928331	−	0.371754i	$-0.878756\pi$
$103$		−	1.01409e21i		−	0.743508i	0.928331	−	0.371754i	$-0.121244\pi$
$104$	−1.11346e21	+	9.59080e20i	−0.737604	+	0.635338i
$105$		0			0
$106$	7.93747e20	−	7.55348e20i	0.430497	−	0.409671i
$107$		−	1.84528e21i		−	0.906846i	−0.891295	−	0.453423i	$-0.850203\pi$
$107$		−	1.84528e21i		−	0.906846i	0.891295	−	0.453423i	$-0.149797\pi$
$108$		0			0
$109$			8.08113e20i			0.326960i	0.986547	+	0.163480i	$0.0522718\pi$
$109$			8.08113e20i			0.326960i	−0.986547	+	0.163480i	$0.947728\pi$
$110$	8.32373e20	+	8.74688e20i	0.305981	+	0.321536i
$111$		0			0
$112$	3.87626e20	−	3.89736e21i	0.117930	−	1.18572i
$113$		−	1.03198e21i		−	0.285988i	−0.989724	−	0.142994i	$-0.954327\pi$
$113$		−	1.03198e21i		−	0.285988i	0.989724	−	0.142994i	$-0.0456730\pi$
$114$		0			0
$115$	1.91078e21			0.440437
$116$	−4.44325e20	+	8.95691e21i	−0.0935172	+	1.88517i
$117$		0			0
$118$	4.55038e21	+	4.78171e21i	0.800363	+	0.841051i
$119$	1.97594e21			0.318076
$120$		0			0
$121$	5.93617e21			0.802158
$122$	6.82156e21	+	7.16834e21i	0.845484	+	0.888466i
$123$		0			0
$124$	−5.22344e21	−	2.59119e20i	−0.545794	−	0.0270752i
$125$	1.04343e22			1.00209
$126$		0			0
$127$			2.05105e21i			0.166739i	0.996519	+	0.0833693i	$0.0265681\pi$
$127$			2.05105e21i			0.166739i	−0.996519	+	0.0833693i	$0.973432\pi$
$128$	7.67268e21	+	1.09332e22i	0.574437	+	0.818549i
$129$		0			0
$130$	1.05264e22	+	1.10615e22i	0.669690	+	0.703735i
$131$			3.08968e22i			1.81370i	0.421457	+	0.906848i	$0.361519\pi$
$131$			3.08968e22i			1.81370i	−0.421457	+	0.906848i	$0.638481\pi$
$132$		0			0
$133$			1.04055e22i			0.520981i
$134$	2.17800e21	−	2.07263e21i	0.100799	−	0.0959227i
$135$		0			0
$136$	−5.10571e21	+	4.39782e21i	−0.202254	+	0.174212i
$137$			4.38025e22i			1.60669i	0.595511	+	0.803347i	$0.296949\pi$
$137$			4.38025e22i			1.60669i	−0.595511	+	0.803347i	$0.703051\pi$
$138$		0			0
$139$	−2.08156e22			−0.655744			−0.327872	−	0.944722i	$-0.606331\pi$
$139$	−2.08156e22			−0.655744			−0.327872	+	0.944722i	$0.606331\pi$
$140$	−4.06457e22	−	2.01631e21i	−1.18760	−	0.0589131i
$141$		0			0
$142$	1.28266e22	−	1.22061e22i	0.322913	−	0.307291i
$143$	−1.85151e22			−0.433010
$144$		0			0
$145$	9.31820e22			1.88351
$146$	6.57605e22	−	6.25792e22i	1.23669	−	1.17686i
$147$		0			0
$148$	1.23961e22	+	6.14931e20i	0.202086	+	0.0100249i
$149$	2.02470e21			0.0307543			0.0153772	−	0.999882i	$-0.495105\pi$
$149$	2.02470e21			0.0307543			0.0153772	+	0.999882i	$0.495105\pi$
$150$		0			0
$151$		−	1.22747e23i		−	1.62089i	−0.585817	−	0.810443i	$-0.699226\pi$
$151$		−	1.22747e23i		−	1.62089i	0.585817	−	0.810443i	$-0.300774\pi$
$152$	−2.31594e22	−	2.68872e22i	−0.285344	−	0.331274i
$153$		0			0
$154$	3.57463e22	−	3.40170e22i	0.383940	−	0.365366i
$155$			5.43414e22i			0.545315i
$156$		0			0
$157$			1.53066e23i			1.34256i	0.741206	+	0.671278i	$0.234254\pi$
$157$			1.53066e23i			1.34256i	−0.741206	+	0.671278i	$0.765746\pi$
$158$	−7.15656e22	−	7.52038e22i	−0.587226	−	0.617078i
$159$		0			0
$160$	1.09513e23	−	8.52543e22i	0.787422	−	0.612994i
$161$		−	7.80888e22i		−	0.525917i
$162$		0			0
$163$	−2.27169e23			−1.34394			−0.671968	−	0.740580i	$-0.734551\pi$
$163$	−2.27169e23			−1.34394			−0.671968	+	0.740580i	$0.734551\pi$
$164$	−5.85123e22	−	2.90261e21i	−0.324629	−	0.0161038i
$165$		0			0
$166$	1.84945e23	+	1.94347e23i	0.903459	+	0.949388i
$167$	−3.10645e22			−0.142476			−0.0712379	−	0.997459i	$-0.522695\pi$
$167$	−3.10645e22			−0.142476			−0.0712379	+	0.997459i	$0.522695\pi$
$168$		0			0
$169$	1.29181e22			0.0522863
$170$	4.82683e22	+	5.07221e22i	0.183632	+	0.192967i
$171$		0			0
$172$	−5.37641e21	+	1.08380e23i	−0.0180902	+	0.364671i
$173$	3.90989e22			0.123788			0.0618942	−	0.998083i	$-0.480286\pi$
$173$	3.90989e22			0.123788			0.0618942	+	0.998083i	$0.480286\pi$
$174$		0			0
$175$		−	1.78557e21i		−	0.00501045i
$176$	−1.66551e22	+	1.67458e23i	−0.0440214	+	0.442611i
$177$		0			0
$178$	−2.85083e23	−	2.99576e23i	−0.669208	−	0.703229i
$179$		−	6.34529e23i		−	1.40441i	−0.711974	−	0.702206i	$-0.752199\pi$
$179$		−	6.34529e23i		−	1.40441i	0.711974	−	0.702206i	$-0.247801\pi$
$180$		0			0
$181$			2.93863e23i			0.578789i	0.957210	+	0.289395i	$0.0934540\pi$
$181$			2.93863e23i			0.578789i	−0.957210	+	0.289395i	$0.906546\pi$
$182$	4.52056e23	−	4.30187e23i	0.840316	−	0.799664i
$183$		0			0
$184$	1.73801e23	+	2.01776e23i	0.288048	+	0.334413i
$185$		−	1.28961e23i		−	0.201908i
$186$		0			0
$187$	−8.49002e22			−0.118733
$188$	−3.04811e22	+	6.14452e23i	−0.0403063	+	0.812514i
$189$		0			0
$190$	−2.67108e23	+	2.54186e23i	−0.316063	+	0.300773i
$191$	1.68725e24			1.88942			0.944712	−	0.327902i	$-0.106342\pi$
$191$	1.68725e24			1.88942			0.944712	+	0.327902i	$0.106342\pi$
$192$		0			0
$193$	2.63739e23			0.264742			0.132371	−	0.991200i	$-0.457741\pi$
$193$	2.63739e23			0.264742			0.132371	+	0.991200i	$0.457741\pi$
$194$	9.99206e23	−	9.50867e23i	0.950029	−	0.904069i
$195$		0			0
$196$	−2.43654e22	+	4.91169e23i	−0.0208010	+	0.419316i
$197$	−1.46868e24			−1.18859			−0.594293	−	0.804249i	$-0.702568\pi$
$197$	−1.46868e24			−1.18859			−0.594293	+	0.804249i	$0.702568\pi$
$198$		0			0
$199$			5.49124e23i			0.399681i	0.979828	+	0.199840i	$0.0640424\pi$
$199$			5.49124e23i			0.399681i	−0.979828	+	0.199840i	$0.935958\pi$
$200$	3.97411e21	+	4.61379e21i	0.00274426	+	0.00318598i
$201$		0			0
$202$	−7.76741e23	+	7.39164e23i	−0.483155	+	0.459781i
$203$		−	3.80811e24i		−	2.24906i
$204$		0			0
$205$			6.08725e23i			0.324344i
$206$	−1.01238e24	−	1.06384e24i	−0.512550	−	0.538606i
$207$		0			0
$208$	−2.10624e23	+	2.11771e24i	−0.0963481	+	0.968726i
$209$		−	4.47093e23i		−	0.194474i
$210$		0			0
$211$	2.90217e24			1.14224			0.571120	−	0.820867i	$-0.306509\pi$
$211$	2.90217e24			1.14224			0.571120	+	0.820867i	$0.306509\pi$
$212$	7.86176e22	−	1.58481e24i	0.0294438	−	0.593541i
$213$		0			0
$214$	−1.84217e24	−	1.93582e24i	−0.625150	−	0.656931i
$215$	1.12752e24			0.364351
$216$		0			0
$217$	2.22079e24			0.651150
$218$	8.06748e23	+	8.47760e23i	0.225395	+	0.236853i
$219$		0			0
$220$	1.74642e24	+	8.66345e22i	0.443313	+	0.0219914i
$221$	−1.07367e24			−0.259867
$222$		0			0
$223$			4.06044e24i			0.894072i	0.894516	+	0.447036i	$0.147520\pi$
$223$			4.06044e24i			0.894072i	−0.894516	+	0.447036i	$0.852480\pi$
$224$	−3.48413e24	−	4.47554e24i	−0.731964	−	0.940245i
$225$		0			0
$226$	−1.03024e24	−	1.08261e24i	−0.197151	−	0.207173i
$227$		−	3.65333e24i		−	0.667448i	−0.942671	−	0.333724i	$-0.891695\pi$
$227$		−	3.65333e24i		−	0.667448i	0.942671	−	0.333724i	$-0.108305\pi$
$228$		0			0
$229$			3.39657e24i			0.565936i	0.959129	+	0.282968i	$0.0913190\pi$
$229$			3.39657e24i			0.565936i	−0.959129	+	0.282968i	$0.908681\pi$
$230$	2.00453e24	−	1.90755e24i	0.319058	−	0.303623i
$231$		0			0
$232$	8.47565e24	+	9.83992e24i	1.23183	+	1.43010i
$233$			9.47332e24i			1.31603i	0.753006	+	0.658014i	$0.228603\pi$
$233$			9.47332e24i			1.31603i	−0.753006	+	0.658014i	$0.771397\pi$
$234$		0			0
$235$	6.39237e24			0.811801
$236$	9.54726e24	+	4.73610e23i	1.15959	+	0.0575235i
$237$		0			0
$238$	2.07288e24	−	1.97260e24i	0.230418	−	0.219271i
$239$	1.09757e25			1.16749			0.583745	−	0.811937i	$-0.301587\pi$
$239$	1.09757e25			1.16749			0.583745	+	0.811937i	$0.301587\pi$
$240$		0			0
$241$	1.58378e25			1.54353			0.771767	−	0.635905i	$-0.219373\pi$
$241$	1.58378e25			1.54353			0.771767	+	0.635905i	$0.219373\pi$
$242$	6.22740e24	−	5.92614e24i	0.581093	−	0.552981i
$243$		0			0
$244$	1.43125e25	+	7.09997e23i	1.22496	+	0.0607664i
$245$	5.10981e24			0.418948
$246$		0			0
$247$		−	5.65405e24i		−	0.425639i
$248$	−5.73839e24	+	4.94278e24i	−0.414045	+	0.356639i
$249$		0			0
$250$	1.09462e25	−	1.04166e25i	0.725927	−	0.690809i
$251$			3.73948e24i			0.237814i	0.992905	+	0.118907i	$0.0379390\pi$
$251$			3.73948e24i			0.237814i	−0.992905	+	0.118907i	$0.962061\pi$
$252$		0			0
$253$			3.35524e24i			0.196317i
$254$	2.04758e24	+	2.15167e24i	0.114944	+	0.120788i
$255$		0			0
$256$	1.89639e25	+	3.80993e24i	0.980410	+	0.196969i
$257$		−	9.76300e24i		−	0.484491i	−0.970215	−	0.242245i	$-0.922116\pi$
$257$		−	9.76300e24i		−	0.484491i	0.970215	−	0.242245i	$-0.0778839\pi$
$258$		0			0
$259$	−5.27030e24			−0.241095
$260$	2.20856e25	+	1.09560e24i	0.970264	+	0.0481318i
$261$		0			0
$262$	3.08446e25	+	3.24126e25i	1.25030	+	1.31386i
$263$	−6.53732e24			−0.254603			−0.127302	−	0.991864i	$-0.540632\pi$
$263$	−6.53732e24			−0.254603			−0.127302	+	0.991864i	$0.540632\pi$
$264$		0			0
$265$	−1.64874e25			−0.593021
$266$	1.03879e25	+	1.09160e25i	0.359147	+	0.377405i
$267$		0			0
$268$	2.15722e23	−	4.34863e24i	0.00689413	−	0.138975i
$269$	1.70394e25			0.523666			0.261833	−	0.965113i	$-0.415673\pi$
$269$	1.70394e25			0.523666			0.261833	+	0.965113i	$0.415673\pi$
$270$		0			0
$271$			7.01430e25i			1.99437i	0.0749517	+	0.997187i	$0.476120\pi$
$271$			7.01430e25i			1.99437i	−0.0749517	+	0.997187i	$0.523880\pi$
$272$	−9.65809e23	+	9.71066e24i	−0.0264191	+	0.265629i
$273$		0			0
$274$	4.37285e25	+	4.59515e25i	1.10760	+	1.16391i
$275$			7.67204e22i			0.00187033i
$276$		0			0
$277$			6.79027e25i			1.53409i	0.641596	+	0.767043i	$0.278273\pi$
$277$			6.79027e25i			1.53409i	−0.641596	+	0.767043i	$0.721727\pi$
$278$	−2.18369e25	+	2.07805e25i	−0.475029	+	0.452048i
$279$		0			0
$280$	−4.46527e25	+	3.84617e25i	−0.900924	+	0.776014i
$281$		−	4.29933e25i		−	0.835573i	−0.908545	−	0.417787i	$-0.862806\pi$
$281$		−	4.29933e25i		−	0.835573i	0.908545	−	0.417787i	$-0.137194\pi$
$282$		0			0
$283$	4.56696e25			0.823890			0.411945	−	0.911209i	$-0.364850\pi$
$283$	4.56696e25			0.823890			0.411945	+	0.911209i	$0.364850\pi$
$284$	1.27043e24	−	2.56099e25i	0.0220855	−	0.445211i
$285$		0			0
$286$	−1.94235e25	+	1.84838e25i	−0.313678	+	0.298503i
$287$	2.48770e25			0.387292
$288$		0			0
$289$	6.41687e25			0.928743
$290$	9.77536e25	−	9.30246e25i	1.36444	−	1.29843i
$291$		0			0
$292$	6.51333e24	−	1.31299e26i	0.0845830	−	1.70506i
$293$	3.33271e25			0.417530			0.208765	−	0.977966i	$-0.433056\pi$
$293$	3.33271e25			0.417530			0.208765	+	0.977966i	$0.433056\pi$
$294$		0			0
$295$		−	9.93236e25i		−	1.15857i
$296$	1.36181e25	−	1.17300e25i	0.153304	−	0.132049i
$297$		0			0
$298$	2.12404e24	−	2.02128e24i	0.0222788	−	0.0212010i
$299$			4.24311e25i			0.429672i
$300$		0			0
$301$		−	4.60789e25i		−	0.435065i
$302$	−1.22539e26	−	1.28769e26i	−1.11739	−	1.17419i
$303$		0			0
$304$	−5.11373e25	−	5.08605e24i	−0.435076	−	0.0432721i
$305$		−	1.48898e26i		−	1.22388i
$306$		0			0
$307$	1.51387e26			1.16181			0.580904	−	0.813972i	$-0.302699\pi$
$307$	1.51387e26			1.16181			0.580904	+	0.813972i	$0.302699\pi$
$308$	3.54053e24	−	7.13718e25i	0.0262595	−	0.529351i
$309$		0			0
$310$	5.42495e25	+	5.70074e25i	0.375922	+	0.395033i
$311$	−2.67148e26			−1.78965			−0.894826	−	0.446415i	$-0.852700\pi$
$311$	−2.67148e26			−1.78965			−0.894826	+	0.446415i	$0.852700\pi$
$312$		0			0
$313$	1.80737e26			1.13196			0.565980	−	0.824419i	$-0.308498\pi$
$313$	1.80737e26			1.13196			0.565980	+	0.824419i	$0.308498\pi$
$314$	1.52807e26	+	1.60576e26i	0.925514	+	0.972564i
$315$		0			0
$316$	−1.50153e26	−	7.44865e24i	−0.850787	−	0.0422049i
$317$	1.21047e26			0.663486			0.331743	−	0.943370i	$-0.392363\pi$
$317$	1.21047e26			0.663486			0.331743	+	0.943370i	$0.392363\pi$
$318$		0			0
$319$			1.63623e26i			0.839542i
$320$	2.97760e25	−	1.98765e26i	0.147840	−	0.986883i
$321$		0			0
$322$	−7.79568e25	−	8.19199e25i	−0.362550	−	0.380981i
$323$		−	2.59264e25i		−	0.116712i
$324$		0			0
$325$			9.70225e23i			0.00409352i
$326$	−2.38314e26	+	2.26785e26i	−0.973564	+	0.926466i
$327$		0			0
$328$	−6.42807e25	+	5.53684e25i	−0.246266	+	0.212122i
$329$		−	2.61240e26i		−	0.969355i
$330$		0			0
$331$	−3.46911e26			−1.20788			−0.603941	−	0.797029i	$-0.706404\pi$
$331$	−3.46911e26			−1.20788			−0.603941	+	0.797029i	$0.706404\pi$
$332$	3.88038e26	+	1.92494e25i	1.30895	+	0.0649331i
$333$		0			0
$334$	−3.25885e25	+	3.10120e25i	−0.103211	+	0.0982182i
$335$	−4.52404e25			−0.138853
$336$		0			0
$337$	−6.49146e26			−1.87167			−0.935834	−	0.352442i	$-0.885351\pi$
$337$	−6.49146e26			−1.87167			−0.935834	+	0.352442i	$0.885351\pi$
$338$	1.35519e25	−	1.28963e25i	0.0378768	−	0.0360445i
$339$		0			0
$340$	1.01273e26	+	5.02383e24i	0.266050	+	0.0131979i
$341$	−9.54208e25			−0.243065
$342$		0			0
$343$			2.88576e26i			0.691309i
$344$	1.02557e26	+	1.19065e26i	0.238288	+	0.276643i
$345$		0			0
$346$	4.10171e25	−	3.90328e25i	0.0896739	−	0.0853357i
$347$		−	1.79370e26i		−	0.380443i	−0.981741	−	0.190221i	$-0.939079\pi$
$347$		−	1.79370e26i		−	0.380443i	0.981741	−	0.190221i	$-0.0609206\pi$
$348$		0			0
$349$			6.75439e25i			0.134871i	0.997724	+	0.0674356i	$0.0214817\pi$
$349$			6.75439e25i			0.134871i	−0.997724	+	0.0674356i	$0.978518\pi$
$350$	−1.78255e24	−	1.87317e24i	−0.00345404	−	0.00362963i
$351$		0			0
$352$	1.49702e26	+	1.92300e26i	0.273232	+	0.350979i
$353$			5.51274e26i			0.976637i	0.872666	+	0.488318i	$0.162389\pi$
$353$			5.51274e26i			0.976637i	−0.872666	+	0.488318i	$0.837611\pi$
$354$		0			0
$355$	−2.66429e26			−0.444820
$356$	−5.98139e26	−	2.96718e25i	−0.969566	−	0.0480972i
$357$		0			0
$358$	−6.33457e26	−	6.65659e26i	−0.968155	−	1.01737i
$359$	−2.43646e25			−0.0361633			−0.0180817	−	0.999837i	$-0.505756\pi$
$359$	−2.43646e25			−0.0361633			−0.0180817	+	0.999837i	$0.505756\pi$
$360$		0			0
$361$	−5.77678e26			−0.808836
$362$	2.93367e26	+	3.08281e26i	0.398998	+	0.419282i
$363$		0			0
$364$	4.47744e25	−	9.02585e26i	0.0574732	−	1.15857i
$365$	−1.36595e27			−1.70357
$366$		0			0
$367$		−	1.16093e26i		−	0.136714i	−0.997661	−	0.0683570i	$-0.978224\pi$
$367$		−	1.16093e26i		−	0.136714i	0.997661	−	0.0683570i	$-0.0217757\pi$
$368$	3.83763e26	+	3.81685e25i	0.439199	+	0.0436821i
$369$		0			0
$370$	−1.28743e26	−	1.35288e26i	−0.139189	−	0.146265i
$371$			6.73797e26i			0.708114i
$372$		0			0
$373$		−	8.30996e26i		−	0.825384i	−0.910871	−	0.412692i	$-0.864589\pi$
$373$		−	8.30996e26i		−	0.825384i	0.910871	−	0.412692i	$-0.135411\pi$
$374$	−8.90655e25	+	8.47568e25i	−0.0860117	+	0.0818507i
$375$		0			0
$376$	5.81437e26	+	6.75027e26i	0.530922	+	0.616381i
$377$			2.06922e27i			1.83748i
$378$		0			0
$379$	1.09303e27			0.918162			0.459081	−	0.888394i	$-0.348179\pi$
$379$	1.09303e27			0.918162			0.459081	+	0.888394i	$0.348179\pi$
$380$	−2.64560e25	+	5.33313e26i	−0.0216171	+	0.435767i
$381$		0			0
$382$	1.77003e27	−	1.68440e27i	1.36872	−	1.30251i
$383$	−7.09173e26			−0.533537			−0.266769	−	0.963761i	$-0.585956\pi$
$383$	−7.09173e26			−0.533537			−0.266769	+	0.963761i	$0.585956\pi$
$384$		0			0
$385$	−7.42507e26			−0.528887
$386$	2.76678e26	−	2.63293e26i	0.191782	−	0.182504i
$387$		0			0
$388$	9.89676e25	−	1.99504e27i	0.0649770	−	1.30984i
$389$	−1.42899e27			−0.913187			−0.456593	−	0.889675i	$-0.650931\pi$
$389$	−1.42899e27			−0.913187			−0.456593	+	0.889675i	$0.650931\pi$
$390$		0			0
$391$			1.94566e26i			0.117818i
$392$	4.64778e26	+	5.39590e26i	0.273994	+	0.318097i
$393$		0			0
$394$	−1.54073e27	+	1.46619e27i	−0.861026	+	0.819372i
$395$			1.56210e27i			0.850040i
$396$		0			0
$397$		−	4.26565e26i		−	0.220133i	−0.993924	−	0.110066i	$-0.964894\pi$
$397$		−	4.26565e26i		−	0.220133i	0.993924	−	0.110066i	$-0.0351063\pi$
$398$	5.48196e26	+	5.76065e26i	0.275527	+	0.289534i
$399$		0			0
$400$	8.77508e24	+	8.72757e23i	0.00418428	+	0.000416163i
$401$			1.44569e27i			0.671520i	0.941947	+	0.335760i	$0.108993\pi$
$401$			1.44569e27i			0.671520i	−0.941947	+	0.335760i	$0.891007\pi$
$402$		0			0
$403$	−1.20671e27			−0.531987
$404$	−7.69332e25	+	1.55086e27i	−0.0330453	+	0.666143i
$405$		0			0
$406$	−3.80168e27	−	3.99494e27i	−1.55043	−	1.62925i
$407$	2.26449e26			0.0899972
$408$		0			0
$409$	3.52483e27			1.33059			0.665294	−	0.746581i	$-0.268306\pi$
$409$	3.52483e27			1.33059			0.665294	+	0.746581i	$0.268306\pi$
$410$	6.07696e26	+	6.38589e26i	0.223592	+	0.234958i
$411$		0			0
$412$	−2.12409e27	−	1.05369e26i	−0.742595	−	0.0368378i
$413$	−4.05911e27			−1.38342
$414$		0			0
$415$		−	4.03690e27i		−	1.30780i
$416$	1.89317e27	+	2.43187e27i	0.598012	+	0.768176i
$417$		0			0
$418$	−4.46338e26	−	4.69028e26i	−0.134064	−	0.140880i
$419$		−	2.28742e27i		−	0.670037i	−0.942212	−	0.335018i	$-0.891257\pi$
$419$		−	2.28742e27i		−	0.670037i	0.942212	−	0.335018i	$-0.108743\pi$
$420$		0			0
$421$			6.39946e27i			1.78312i	0.452899	+	0.891562i	$0.350390\pi$
$421$			6.39946e27i			1.78312i	−0.452899	+	0.891562i	$0.649610\pi$
$422$	3.04455e27	−	2.89727e27i	0.827452	−	0.787422i
$423$		0			0
$424$	−1.49966e27	−	1.74105e27i	−0.387839	−	0.450266i
$425$			4.44892e24i			0.00112246i
$426$		0			0
$427$	−6.08508e27			−1.46141
$428$	−3.86509e27	−	1.91735e26i	−0.905733	−	0.0449306i
$429$		0			0
$430$	1.18284e27	−	1.12561e27i	0.263940	−	0.251172i
$431$	−7.58568e27			−1.65190			−0.825949	−	0.563745i	$-0.809360\pi$
$431$	−7.58568e27			−1.65190			−0.825949	+	0.563745i	$0.809360\pi$
$432$		0			0
$433$	3.38867e27			0.702921			0.351460	−	0.936203i	$-0.385685\pi$
$433$	3.38867e27			0.702921			0.351460	+	0.936203i	$0.385685\pi$
$434$	2.32975e27	−	2.21704e27i	0.471701	−	0.448881i
$435$		0			0
$436$	1.69265e27	+	8.39674e25i	0.326558	+	0.0161995i
$437$	−1.02461e27			−0.192975
$438$		0			0
$439$			7.72632e27i			1.38706i	0.720428	+	0.693530i	$0.243945\pi$
$439$			7.72632e27i			1.38706i	−0.720428	+	0.693530i	$0.756055\pi$
$440$	1.91859e27	−	1.65258e27i	0.336302	−	0.289675i
$441$		0			0
$442$	−1.12634e27	+	1.07185e27i	−0.188251	+	0.179144i
$443$		−	2.46574e27i		−	0.402447i	−0.979545	−	0.201223i	$-0.935508\pi$
$443$		−	2.46574e27i		−	0.402447i	0.979545	−	0.201223i	$-0.0644917\pi$
$444$		0			0
$445$			6.22266e27i			0.968715i
$446$	4.05358e27	+	4.25965e27i	0.616344	+	0.647676i
$447$		0			0
$448$	−8.12304e27	−	1.21687e27i	−1.17842	−	0.176532i
$449$		−	1.18937e28i		−	1.68551i	−0.538295	−	0.842756i	$-0.680931\pi$
$449$		−	1.18937e28i		−	1.68551i	0.538295	−	0.842756i	$-0.319069\pi$
$450$		0			0
$451$	−1.06889e27			−0.144570
$452$	−2.16156e27	−	1.07228e26i	−0.285637	−	0.0141696i
$453$		0			0
$454$	−3.64716e27	−	3.83256e27i	−0.460117	−	0.483507i
$455$	−9.38992e27			−1.15756
$456$		0			0
$457$	−9.14169e27			−1.07623			−0.538117	−	0.842870i	$-0.680864\pi$
$457$	−9.14169e27			−1.07623			−0.538117	+	0.842870i	$0.680864\pi$
$458$	3.39083e27	+	3.56320e27i	0.390138	+	0.409971i
$459$		0			0
$460$	1.98541e26	−	4.00228e27i	0.0218219	−	0.439896i
$461$	−2.04911e27			−0.220143			−0.110072	−	0.993924i	$-0.535108\pi$
$461$	−2.04911e27			−0.220143			−0.110072	+	0.993924i	$0.535108\pi$
$462$		0			0
$463$		−	3.88888e26i		−	0.0399231i	−0.999801	−	0.0199616i	$-0.993646\pi$
$463$		−	3.88888e26i		−	0.0399231i	0.999801	−	0.0199616i	$-0.00635438\pi$
$464$	1.87148e28	+	1.86134e27i	1.87822	+	0.186805i
$465$		0			0
$466$	9.45731e27	+	9.93809e27i	0.907226	+	0.953346i
$467$		−	1.67480e27i		−	0.157086i	−0.996911	−	0.0785428i	$-0.974973\pi$
$467$		−	1.67480e27i		−	0.157086i	0.996911	−	0.0785428i	$-0.0250267\pi$
$468$		0			0
$469$			1.84886e27i			0.165802i
$470$	6.70599e27	−	6.38157e27i	0.588078	−	0.559629i
$471$		0			0
$472$	1.04885e28	−	9.03428e27i	0.879673	−	0.757709i
$473$			1.97987e27i			0.162403i
$474$		0			0
$475$	−2.34285e25			−0.00183849
$476$	2.05311e26	−	4.13876e27i	0.0157594	−	0.317686i
$477$		0			0
$478$	1.15141e28	−	1.09571e28i	0.845744	−	0.804829i
$479$	4.04070e27			0.290358			0.145179	−	0.989405i	$-0.453624\pi$
$479$	4.04070e27			0.290358			0.145179	+	0.989405i	$0.453624\pi$
$480$		0			0
$481$	2.86373e27			0.196974
$482$	1.66148e28	−	1.58111e28i	1.11816	−	1.06406i
$483$		0			0
$484$	6.16801e26	−	1.24338e28i	0.0397437	−	0.801173i
$485$	−2.07551e28			−1.30869
$486$		0			0
$487$			2.41848e28i			1.46046i	0.683202	+	0.730229i	$0.260587\pi$
$487$			2.41848e28i			1.46046i	−0.683202	+	0.730229i	$0.739413\pi$
$488$	1.57234e28	−	1.35434e28i	0.929265	−	0.800426i
$489$		0			0
$490$	5.36050e27	−	5.10117e27i	0.303491	−	0.288809i
$491$			5.39692e27i			0.299082i	0.988756	+	0.149541i	$0.0477796\pi$
$491$			5.39692e27i			0.299082i	−0.988756	+	0.149541i	$0.952220\pi$
$492$		0			0
$493$			9.48830e27i			0.503844i
$494$	−5.64450e27	−	5.93144e27i	−0.293422	−	0.308338i
$495$		0			0
$496$	−1.08549e27	+	1.09140e28i	−0.0540838	+	0.543782i
$497$			1.08883e28i			0.531151i
$498$		0			0
$499$	3.31297e28			1.54939			0.774696	−	0.632333i	$-0.217903\pi$
$499$	3.31297e28			1.54939			0.774696	+	0.632333i	$0.217903\pi$
$500$	1.08418e27	−	2.18554e28i	0.0496496	−	1.00086i
$501$		0			0
$502$	3.73316e27	+	3.92294e27i	0.163941	+	0.172275i
$503$	−3.77927e28			−1.62534			−0.812670	−	0.582724i	$-0.801987\pi$
$503$	−3.77927e28			−1.62534			−0.812670	+	0.582724i	$0.801987\pi$
$504$		0			0
$505$	1.61341e28			0.665558
$506$	3.34957e27	+	3.51985e27i	0.135334	+	0.142214i
$507$		0			0
$508$	4.29607e27	+	2.13115e26i	0.166534	+	0.00826123i
$509$	−8.98207e27			−0.341067			−0.170533	−	0.985352i	$-0.554549\pi$
$509$	−8.98207e27			−0.341067			−0.170533	+	0.985352i	$0.554549\pi$
$510$		0			0
$511$			5.58229e28i			2.03420i
$512$	2.36978e28	−	1.49350e28i	0.846005	−	0.533176i
$513$		0			0
$514$	−9.74651e27	−	1.02420e28i	−0.333992	−	0.350971i
$515$			2.20977e28i			0.741943i
$516$		0			0
$517$			1.12247e28i			0.361846i
$518$	−5.52887e27	+	5.26140e27i	−0.174652	+	0.166203i
$519$		0			0
$520$	2.42629e28	−	2.08990e28i	0.736051	−	0.634001i
$521$		−	2.09029e28i		−	0.621456i	−0.950499	−	0.310728i	$-0.899427\pi$
$521$		−	2.09029e28i		−	0.621456i	0.950499	−	0.310728i	$-0.100573\pi$
$522$		0			0
$523$	4.50442e28			1.28639			0.643193	−	0.765704i	$-0.277609\pi$
$523$	4.50442e28			1.28639			0.643193	+	0.765704i	$0.277609\pi$
$524$	6.47157e28	+	3.21034e27i	1.81147	+	0.0898614i
$525$		0			0
$526$	−6.85804e27	+	6.52627e27i	−0.184438	+	0.175515i
$527$	−5.53333e27			−0.145873
$528$		0			0
$529$	−3.17824e28			−0.805196
$530$	−1.72963e28	+	1.64595e28i	−0.429591	+	0.408809i
$531$		0			0
$532$	2.17952e28	+	1.08119e27i	0.520341	+	0.0258125i
$533$	−1.35174e28			−0.316416
$534$		0			0
$535$			4.02099e28i			0.904938i
$536$	−4.11498e27	−	4.77734e27i	−0.0908107	−	0.105428i
$537$		0			0
$538$	1.78753e28	−	1.70106e28i	0.379350	−	0.360998i
$539$			8.97257e27i			0.186739i
$540$		0			0
$541$			4.97434e28i			0.995783i	0.867239	+	0.497891i	$0.165892\pi$
$541$			4.97434e28i			0.995783i	−0.867239	+	0.497891i	$0.834108\pi$
$542$	7.00245e28	+	7.35843e28i	1.37486	+	1.44475i
$543$		0			0
$544$	8.68106e27	+	1.11513e28i	0.163978	+	0.210637i
$545$		−	1.76093e28i		−	0.326271i
$546$		0			0
$547$	−3.86434e27			−0.0688983			−0.0344491	−	0.999406i	$-0.510968\pi$
$547$	−3.86434e27			−0.0688983			−0.0344491	+	0.999406i	$0.510968\pi$
$548$	9.17477e28	+	4.55132e27i	1.60472	+	0.0796052i
$549$		0			0
$550$	7.65908e25	+	8.04844e25i	0.00128934	+	0.00135489i
$551$	−4.99664e28			−0.825251
$552$		0			0
$553$	6.38391e28			1.01502
$554$	6.77880e28	+	7.12341e28i	1.05755	+	1.11131i
$555$		0			0
$556$	−2.16286e27	+	4.36000e28i	−0.0324895	+	0.654939i
$557$	−1.38397e28			−0.204008			−0.102004	−	0.994784i	$-0.532525\pi$
$557$	−1.38397e28			−0.204008			−0.102004	+	0.994784i	$0.532525\pi$
$558$		0			0
$559$			2.50379e28i			0.355446i
$560$	−8.44661e27	+	8.49259e28i	−0.117682	+	1.18322i
$561$		0			0
$562$	−4.29207e28	−	4.51026e28i	−0.576017	−	0.605299i
$563$		−	8.76099e28i		−	1.15402i	−0.816736	−	0.577012i	$-0.804219\pi$
$563$		−	8.76099e28i		−	1.15402i	0.816736	−	0.577012i	$-0.195781\pi$
$564$		0			0
$565$			2.24875e28i			0.285386i
$566$	4.79102e28	−	4.55924e28i	0.596836	−	0.567963i
$567$		0			0
$568$	−2.42339e28	−	2.81346e28i	−0.290915	−	0.337741i
$569$			5.46180e27i			0.0643661i	0.999482	+	0.0321830i	$0.0102459\pi$
$569$			5.46180e27i			0.0643661i	−0.999482	+	0.0321830i	$0.989754\pi$
$570$		0			0
$571$	−2.60392e28			−0.295766			−0.147883	−	0.989005i	$-0.547246\pi$
$571$	−2.60392e28			−0.295766			−0.147883	+	0.989005i	$0.547246\pi$
$572$	−1.92382e27	+	3.87813e28i	−0.0214539	+	0.432478i
$573$		0			0
$574$	2.60975e28	−	2.48350e28i	0.280559	−	0.266987i
$575$	1.75820e26			0.00185591
$576$		0			0
$577$	8.12378e28			0.826822			0.413411	−	0.910544i	$-0.364337\pi$
$577$	8.12378e28			0.826822			0.413411	+	0.910544i	$0.364337\pi$
$578$	6.73168e28	−	6.40602e28i	0.672793	−	0.640245i
$579$		0			0
$580$	9.68212e27	−	1.95177e29i	0.0933204	−	1.88120i
$581$	−1.64978e29			−1.56162
$582$		0			0
$583$		−	2.89510e28i		−	0.264328i
$584$	−1.24244e29	−	1.44243e29i	−1.11414	−	1.29348i
$585$		0			0
$586$	3.49622e28	−	3.32708e28i	0.302464	−	0.287831i
$587$			7.63529e27i			0.0648822i	0.999474	+	0.0324411i	$0.0103281\pi$
$587$			7.63529e27i			0.0648822i	−0.999474	+	0.0324411i	$0.989672\pi$
$588$		0			0
$589$		−	2.91391e28i		−	0.238927i
$590$	−9.91558e28	−	1.04197e29i	−0.798679	−	0.839281i
$591$		0			0
$592$	2.57604e27	−	2.59006e28i	0.0200251	−	0.201341i
$593$			3.47952e28i			0.265733i	0.991134	+	0.132866i	$0.0424181\pi$
$593$			3.47952e28i			0.265733i	−0.991134	+	0.132866i	$0.957582\pi$
$594$		0			0
$595$	−4.30571e28			−0.317407
$596$	2.10378e26	−	4.24090e27i	0.00152375	−	0.0307165i
$597$		0			0
$598$	4.23594e28	+	4.45128e28i	0.296202	+	0.311260i
$599$	−2.41191e29			−1.65722			−0.828610	−	0.559826i	$-0.810868\pi$
$599$	−2.41191e29			−1.65722			−0.828610	+	0.559826i	$0.810868\pi$
$600$		0			0
$601$	−5.20539e28			−0.345360			−0.172680	−	0.984978i	$-0.555243\pi$
$601$	−5.20539e28			−0.345360			−0.172680	+	0.984978i	$0.555243\pi$
$602$	−4.60010e28	−	4.83395e28i	−0.299919	−	0.315166i
$603$		0			0
$604$	−2.57103e29	−	1.27541e28i	−1.61890	−	0.0803084i
$605$	−1.29353e29			−0.800470
$606$		0			0
$607$			1.89256e27i			0.0113128i	0.999984	+	0.00565638i	$0.00180049\pi$
$607$			1.89256e27i			0.0113128i	−0.999984	+	0.00565638i	$0.998200\pi$
$608$	−5.87236e28	+	4.57154e28i	−0.345005	+	0.268581i
$609$		0			0
$610$	−1.48646e29	−	1.56203e29i	−0.843705	−	0.886596i
$611$			1.41950e29i			0.791960i
$612$		0			0
$613$			1.05961e29i			0.571230i	0.958344	+	0.285615i	$0.0921978\pi$
$613$			1.05961e29i			0.571230i	−0.958344	+	0.285615i	$0.907802\pi$
$614$	1.58814e29	−	1.51131e29i	0.841628	−	0.800912i
$615$		0			0
$616$	−6.75369e28	−	7.84079e28i	−0.345895	−	0.401571i
$617$		−	6.70216e28i		−	0.337459i	−0.985662	−	0.168729i	$-0.946034\pi$
$617$		−	6.70216e28i		−	0.337459i	0.985662	−	0.168729i	$-0.0539664\pi$
$618$		0			0
$619$	−3.87251e29			−1.88469			−0.942346	−	0.334639i	$-0.891386\pi$
$619$	−3.87251e29			−1.88469			−0.942346	+	0.334639i	$0.891386\pi$
$620$	1.13822e29	+	5.64636e27i	0.544646	+	0.0270182i
$621$		0			0
$622$	−2.80255e29	+	2.66697e29i	−1.29645	+	1.23373i
$623$	2.54304e29			1.15672
$624$		0			0
$625$	−2.26414e29			−0.995777
$626$	1.89604e29	−	1.80431e29i	0.820006	−	0.780336i
$627$		0			0
$628$	3.20609e29	+	1.59044e28i	1.34091	+	0.0665183i
$629$	1.31315e28			0.0540110
$630$		0			0
$631$		−	2.06072e28i		−	0.0819804i	−0.999160	−	0.0409902i	$-0.986949\pi$
$631$		−	2.06072e28i		−	0.0819804i	0.999160	−	0.0409902i	$-0.0130512\pi$
$632$	−1.64956e29	+	1.42086e29i	−0.645415	+	0.555931i
$633$		0			0
$634$	1.26986e29	−	1.20842e29i	0.480637	−	0.457385i
$635$		−	4.46936e28i		−	0.166388i
$636$		0			0
$637$			1.13469e29i			0.408709i
$638$	1.63347e29	+	1.71651e29i	0.578753	+	0.608174i
$639$		0			0
$640$	−1.67193e29	−	2.38243e29i	−0.573228	−	0.816826i
$641$			4.33253e29i			1.46128i	0.682765	+	0.730638i	$0.260777\pi$
$641$			4.33253e29i			1.46128i	−0.682765	+	0.730638i	$0.739223\pi$
$642$		0			0
$643$	−4.99623e29			−1.63090			−0.815450	−	0.578827i	$-0.803511\pi$
$643$	−4.99623e29			−1.63090			−0.815450	+	0.578827i	$0.803511\pi$
$644$	−1.63563e29	−	8.11385e27i	−0.525271	−	0.0260571i
$645$		0			0
$646$	−2.58826e28	−	2.71984e28i	−0.0804575	−	0.0845477i
$647$	−1.37434e29			−0.420338			−0.210169	−	0.977665i	$-0.567401\pi$
$647$	−1.37434e29			−0.420338			−0.210169	+	0.977665i	$0.567401\pi$
$648$		0			0
$649$	1.74407e29			0.516411
$650$	9.68585e26	+	1.01782e27i	0.00282194	+	0.00296540i
$651$		0			0
$652$	−2.36041e28	+	4.75822e29i	−0.0665867	+	1.34229i
$653$	−3.21253e29			−0.891782			−0.445891	−	0.895087i	$-0.647113\pi$
$653$	−3.21253e29			−0.891782			−0.445891	+	0.895087i	$0.647113\pi$
$654$		0			0
$655$		−	6.73261e29i		−	1.80988i
$656$	−1.21595e28	+	1.22257e29i	−0.0321681	+	0.323432i
$657$		0			0
$658$	−2.60799e29	−	2.74057e29i	−0.668241	−	0.702213i
$659$			2.28016e29i			0.575001i	0.957781	+	0.287500i	$0.0928242\pi$
$659$			2.28016e29i			0.575001i	−0.957781	+	0.287500i	$0.907176\pi$
$660$		0			0
$661$		−	2.40304e29i		−	0.587010i	−0.955958	−	0.293505i	$-0.905178\pi$
$661$		−	2.40304e29i		−	0.587010i	0.955958	−	0.293505i	$-0.0948217\pi$
$662$	−3.63931e29	+	3.46325e29i	−0.875004	+	0.832674i
$663$		0			0
$664$	4.26292e29	−	3.67188e29i	0.992985	−	0.855311i
$665$		−	2.26743e29i		−	0.519884i
$666$		0			0
$667$	3.74976e29			0.833070
$668$	−3.22777e27	+	6.50670e28i	−0.00705911	+	0.142301i
$669$		0			0
$670$	−4.74599e28	+	4.51640e28i	−0.100587	+	0.0957209i
$671$	2.61457e29			0.545524
$672$		0			0
$673$	−1.70562e27			−0.00344925			−0.00172462	−	0.999999i	$-0.500549\pi$
$673$	−1.70562e27			−0.00344925			−0.00172462	+	0.999999i	$0.500549\pi$
$674$	−6.80994e29	+	6.48049e29i	−1.35586	+	1.29027i
$675$		0			0
$676$	1.34226e27	−	2.70579e28i	0.00259058	−	0.0522221i
$677$	1.25887e29			0.239221			0.119610	−	0.992821i	$-0.461835\pi$
$677$	1.25887e29			0.239221			0.119610	+	0.992821i	$0.461835\pi$
$678$		0			0
$679$			8.48208e29i			1.56268i
$680$	1.11257e29	−	9.58313e28i	0.201828	−	0.173846i
$681$		0			0
$682$	−1.00102e29	+	9.52595e28i	−0.176079	+	0.167561i
$683$			3.09146e29i			0.535483i	0.963491	+	0.267741i	$0.0862773\pi$
$683$			3.09146e29i			0.535483i	−0.963491	+	0.267741i	$0.913723\pi$
$684$		0			0
$685$		−	9.54485e29i		−	1.60331i
$686$	2.88089e29	+	3.02734e29i	0.476566	+	0.500793i
$687$		0			0
$688$	2.26452e29	+	2.25226e28i	0.363327	+	0.0361360i
$689$		−	3.66121e29i		−	0.578527i
$690$		0			0
$691$	4.68187e29			0.717629			0.358815	−	0.933409i	$-0.383181\pi$
$691$	4.68187e29			0.717629			0.358815	+	0.933409i	$0.383181\pi$
$692$	4.06259e27	−	8.18956e28i	0.00613322	−	0.123636i
$693$		0			0
$694$	−1.79066e29	−	1.88170e29i	−0.262265	−	0.275597i
$695$	4.53586e29			0.654364
$696$		0			0
$697$	−6.19837e28			−0.0867627
$698$	6.74298e28	+	7.08577e28i	0.0929757	+	0.0977023i
$699$		0			0
$700$	−3.74001e27	−	1.85530e26i	−0.00500430	−	0.000248248i
$701$	6.27256e29			0.826810			0.413405	−	0.910547i	$-0.364339\pi$
$701$	6.27256e29			0.826810			0.413405	+	0.910547i	$0.364339\pi$
$702$		0			0
$703$			6.91518e28i			0.0884652i
$704$	3.49022e29	+	5.22851e28i	0.439886	+	0.0658969i
$705$		0			0
$706$	5.50342e29	+	5.78320e29i	0.673261	+	0.707487i
$707$		−	6.59361e29i		−	0.794730i
$708$		0			0
$709$		−	9.31186e29i		−	1.08956i	−0.838579	−	0.544780i	$-0.816613\pi$
$709$		−	9.31186e29i		−	1.08956i	0.838579	−	0.544780i	$-0.183387\pi$
$710$	−2.79501e29	+	2.65979e29i	−0.322233	+	0.306644i
$711$		0			0
$712$	−6.57106e29	+	5.66001e29i	−0.735522	+	0.633544i
$713$			2.18676e29i			0.241191i
$714$		0			0
$715$	4.03456e29			0.432099
$716$	−1.32907e30	−	6.59310e28i	−1.40269	−	0.0695830i
$717$		0			0
$718$	−2.55600e28	+	2.43235e28i	−0.0261971	+	0.0249298i
$719$	3.28458e28			0.0331762			0.0165881	−	0.999862i	$-0.494720\pi$
$719$	3.28458e28			0.0331762			0.0165881	+	0.999862i	$0.494720\pi$
$720$		0			0
$721$	9.03076e29			0.885940
$722$	−6.06020e29	+	5.76702e29i	−0.585931	+	0.557585i
$723$		0			0
$724$	6.15519e29	+	3.05340e28i	0.578078	+	0.0286767i
$725$	8.57414e27			0.00793673
$726$		0			0
$727$			1.05506e30i			0.948781i	0.880314	+	0.474391i	$0.157332\pi$
$727$			1.05506e30i			0.948781i	−0.880314	+	0.474391i	$0.842668\pi$
$728$	−8.54088e29	−	9.91565e29i	−0.757048	−	0.878904i
$729$		0			0
$730$	−1.43296e30	+	1.36364e30i	−1.23408	+	1.17438i
$731$			1.14810e29i			0.0974648i
$732$		0			0
$733$		−	9.48676e29i		−	0.782576i	−0.920268	−	0.391288i	$-0.872030\pi$
$733$		−	9.48676e29i		−	0.782576i	0.920268	−	0.391288i	$-0.127970\pi$
$734$	−1.15897e29	−	1.21789e29i	−0.0942461	−	0.0990372i
$735$		0			0
$736$	4.40695e29	−	3.43074e29i	0.348274	−	0.271125i
$737$		−	7.94399e28i		−	0.0618914i
$738$		0			0
$739$	8.58334e29			0.649965			0.324982	−	0.945720i	$-0.394642\pi$
$739$	8.58334e29			0.649965			0.324982	+	0.945720i	$0.394642\pi$
$740$	−2.70118e29	−	1.33997e28i	−0.201661	−	0.0100038i
$741$		0			0
$742$	6.72659e29	+	7.06854e29i	0.488151	+	0.512966i
$743$	2.01870e30			1.44441			0.722204	−	0.691680i	$-0.243129\pi$
$743$	2.01870e30			1.44441			0.722204	+	0.691680i	$0.243129\pi$
$744$		0			0
$745$	−4.41196e28			−0.0306896
$746$	−8.29592e29	−	8.71765e29i	−0.568993	−	0.597918i
$747$		0			0
$748$	−8.82160e27	+	1.77830e29i	−0.00588275	+	0.118587i
$749$	1.64328e30			1.08057
$750$		0			0
$751$		−	5.78878e29i		−	0.370141i	−0.982725	−	0.185071i	$-0.940749\pi$
$751$		−	5.78878e29i		−	0.370141i	0.982725	−	0.185071i	$-0.0592514\pi$
$752$	1.28385e30	+	1.27690e29i	0.809519	+	0.0805136i
$753$		0			0
$754$	2.06572e30	+	2.17073e30i	1.26670	+	1.33109i
$755$			2.67473e30i			1.61747i
$756$		0			0
$757$		−	2.07003e29i		−	0.121750i	−0.998145	−	0.0608752i	$-0.980611\pi$
$757$		−	2.07003e29i		−	0.121750i	0.998145	−	0.0608752i	$-0.0193892\pi$
$758$	1.14665e30	−	1.09118e30i	0.665128	−	0.632951i
$759$		0			0
$760$	5.04658e29	+	5.85889e29i	0.284744	+	0.330577i
$761$		−	2.06637e30i		−	1.14992i	−0.818181	−	0.574961i	$-0.805017\pi$
$761$		−	2.06637e30i		−	1.14992i	0.818181	−	0.574961i	$-0.194983\pi$
$762$		0			0
$763$	−7.19648e29			−0.389594
$764$	1.75315e29	−	3.53408e30i	0.0936134	−	1.88710i
$765$		0			0
$766$	−7.43965e29	+	7.07974e29i	−0.386501	+	0.367803i
$767$	2.20560e30			1.13025
$768$		0			0
$769$	5.98274e28			0.0298314			0.0149157	−	0.999889i	$-0.495252\pi$
$769$	5.98274e28			0.0298314			0.0149157	+	0.999889i	$0.495252\pi$
$770$	−7.78935e29	+	7.41252e29i	−0.383132	+	0.364597i
$771$		0			0
$772$	2.74039e28	−	5.52421e29i	0.0131169	−	0.264416i
$773$	2.71660e30			1.28275			0.641373	−	0.767229i	$-0.278365\pi$
$773$	2.71660e30			1.28275			0.641373	+	0.767229i	$0.278365\pi$
$774$		0			0
$775$			5.00022e27i			0.00229785i
$776$	−1.88784e30	−	2.19171e30i	−0.855889	−	0.993655i
$777$		0			0
$778$	−1.49910e30	+	1.42658e30i	−0.661524	+	0.629521i
$779$		−	3.26412e29i		−	0.142110i
$780$		0			0
$781$		−	4.67837e29i		−	0.198271i
$782$	1.94237e29	+	2.04112e29i	0.0812198	+	0.0853487i
$783$		0			0
$784$	1.02626e30	+	1.02070e29i	0.417771	+	0.0415509i
$785$		−	3.33541e30i		−	1.33973i
$786$		0			0
$787$	−4.56931e30			−1.78696			−0.893482	−	0.449098i	$-0.851745\pi$
$787$	−4.56931e30			−1.78696			−0.893482	+	0.449098i	$0.851745\pi$
$788$	−1.52603e29	+	3.07625e30i	−0.0588896	+	1.18713i
$789$		0			0
$790$	1.55946e30	+	1.63874e30i	0.585990	+	0.615780i
$791$	9.19008e29			0.340774
$792$		0			0
$793$	3.30645e30			1.19397
$794$	−4.25844e29	−	4.47492e29i	−0.151752	−	0.159467i
$795$		0			0
$796$	1.15018e30	+	5.70570e28i	0.399190	+	0.0198026i
$797$	2.55125e30			0.873858			0.436929	−	0.899496i	$-0.356066\pi$
$797$	2.55125e30			0.873858			0.436929	+	0.899496i	$0.356066\pi$
$798$		0			0
$799$			6.50906e29i			0.217159i
$800$	1.00769e28	−	7.84467e27i	0.00331803	−	0.00258303i
$801$		0			0
$802$	1.44325e30	+	1.51662e30i	0.462924	+	0.486458i
$803$		−	2.39854e30i		−	0.759335i
$804$		0			0
$805$			1.70161e30i			0.524810i
$806$	−1.26592e30	+	1.20467e30i	−0.385378	+	0.366735i
$807$		0			0
$808$	1.46753e30	+	1.70375e30i	0.435278	+	0.505342i
$809$		−	4.19734e30i		−	1.22889i	−0.788958	−	0.614447i	$-0.789379\pi$
$809$		−	4.19734e30i		−	1.22889i	0.788958	−	0.614447i	$-0.210621\pi$
$810$		0			0
$811$	−5.24263e30			−1.49565			−0.747826	−	0.663895i	$-0.768902\pi$
$811$	−5.24263e30			−1.49565			−0.747826	+	0.663895i	$0.768902\pi$
$812$	−7.97639e30	−	3.95684e29i	−2.24630	−	0.111432i
$813$		0			0
$814$	2.37559e29	−	2.26066e29i	0.0651950	−	0.0620411i
$815$	4.95015e30			1.34111
$816$		0			0
$817$	−6.04602e29			−0.159639
$818$	3.69777e30	−	3.51888e30i	0.963895	−	0.917264i
$819$		0			0
$820$	1.27502e30	+	6.32498e28i	0.323945	+	0.0160699i
$821$	−5.54721e30			−1.39146			−0.695731	−	0.718302i	$-0.744920\pi$
$821$	−5.54721e30			−1.39146			−0.695731	+	0.718302i	$0.744920\pi$
$822$		0			0
$823$		−	4.17017e30i		−	1.01966i	−0.860275	−	0.509830i	$-0.829708\pi$
$823$		−	4.17017e30i		−	1.01966i	0.860275	−	0.509830i	$-0.170292\pi$
$824$	−2.33349e30	+	2.00996e30i	−0.563340	+	0.485235i
$825$		0			0
$826$	−4.25825e30	+	4.05225e30i	−1.00217	+	0.953686i
$827$		−	3.48635e29i		−	0.0810145i	−0.999179	−	0.0405072i	$-0.987103\pi$
$827$		−	3.48635e29i		−	0.0810145i	0.999179	−	0.0405072i	$-0.0128974\pi$
$828$		0			0
$829$		−	5.23470e30i		−	1.18596i	−0.805218	−	0.592979i	$-0.797952\pi$
$829$		−	5.23470e30i		−	1.18596i	0.805218	−	0.592979i	$-0.202048\pi$
$830$	−4.03008e30	−	4.23495e30i	−0.901558	−	0.947390i
$831$		0			0
$832$	4.41382e30	+	6.61210e29i	0.962763	+	0.144226i
$833$			5.20308e29i			0.112070i
$834$		0			0
$835$	6.76915e29			0.142176
$836$	−9.36471e29	−	4.64555e28i	−0.194235	−	0.00963542i
$837$		0			0
$838$	−2.28356e30	−	2.39964e30i	−0.461901	−	0.485383i
$839$	5.25097e29			0.104891			0.0524456	−	0.998624i	$-0.483298\pi$
$839$	5.25097e29			0.104891			0.0524456	+	0.998624i	$0.483298\pi$
$840$		0			0
$841$	1.31534e31			2.56259
$842$	6.38865e30	+	6.71342e30i	1.22923	+	1.29172i
$843$		0			0
$844$	3.01551e29	−	6.07882e30i	0.0565934	−	1.14084i
$845$	−2.81493e29			−0.0521763
$846$		0			0
$847$			5.28633e30i			0.955825i
$848$	−3.31134e30	−	3.29341e29i	−0.591354	−	0.0588152i
$849$		0			0
$850$	4.44141e27	+	4.66719e27i	0.000773788	+	0.000813124i
$851$		−	5.18954e29i		−	0.0893034i
$852$		0			0
$853$		−	6.95090e30i		−	1.16701i	−0.812108	−	0.583507i	$-0.801680\pi$
$853$		−	6.95090e30i		−	1.16701i	0.812108	−	0.583507i	$-0.198320\pi$
$854$	−6.38362e30	+	6.07479e30i	−1.05867	+	1.00745i
$855$		0			0
$856$	−4.24613e30	+	3.65742e30i	−0.687097	+	0.591834i
$857$			6.73384e30i			1.07638i	0.842825	+	0.538188i	$0.180891\pi$
$857$			6.73384e30i			1.07638i	−0.842825	+	0.538188i	$0.819109\pi$
$858$		0			0
$859$	9.35510e30			1.45922			0.729609	−	0.683865i	$-0.239702\pi$
$859$	9.35510e30			1.45922			0.729609	+	0.683865i	$0.239702\pi$
$860$	1.17155e29	−	2.36168e30i	0.0180521	−	0.363904i
$861$		0			0
$862$	−7.95784e30	+	7.57286e30i	−1.19665	+	1.13876i
$863$	7.54466e30			1.12080			0.560398	−	0.828224i	$-0.310648\pi$
$863$	7.54466e30			1.12080			0.560398	+	0.828224i	$0.310648\pi$
$864$		0			0
$865$	−8.51990e29			−0.123528
$866$	3.55492e30	−	3.38294e30i	0.509204	−	0.484570i
$867$		0			0
$868$	2.30753e29	−	4.65162e30i	0.0322619	−	0.650350i
$869$	−2.74297e30			−0.378891
$870$		0			0
$871$		−	1.00462e30i		−	0.135460i
$872$	1.85952e30	−	1.60171e30i	0.247730	−	0.213383i
$873$		0			0
$874$	−1.07487e30	+	1.02287e30i	−0.139794	+	0.133031i
$875$			9.29202e30i			1.19406i
$876$		0			0
$877$		−	1.20577e31i		−	1.51276i	−0.654133	−	0.756379i	$-0.726967\pi$
$877$		−	1.20577e31i		−	1.51276i	0.654133	−	0.756379i	$-0.273033\pi$
$878$	7.71326e30	+	8.10538e30i	0.956193	+	1.00480i
$879$		0			0
$880$	3.62925e29	−	3.64901e30i	0.0439288	−	0.441679i
$881$			1.45171e31i			1.73634i	0.496270	+	0.868168i	$0.334703\pi$
$881$			1.45171e31i			1.73634i	−0.496270	+	0.868168i	$0.665297\pi$
$882$		0			0
$883$	−8.69439e30			−1.01543			−0.507717	−	0.861524i	$-0.669510\pi$
$883$	−8.69439e30			−1.01543			−0.507717	+	0.861524i	$0.669510\pi$
$884$	−1.11560e29	+	2.24888e30i	−0.0128754	+	0.259548i
$885$		0			0
$886$	−2.46157e30	−	2.58671e30i	−0.277434	−	0.291537i
$887$	1.42864e31			1.59120			0.795600	−	0.605822i	$-0.207156\pi$
$887$	1.42864e31			1.59120			0.795600	+	0.605822i	$0.207156\pi$
$888$		0			0
$889$	−1.82652e30			−0.198680
$890$	6.21214e30	+	6.52795e30i	0.667800	+	0.701749i
$891$		0			0
$892$	8.50491e30	+	4.21902e29i	0.892974	+	0.0442977i
$893$	−3.42774e30			−0.355687
$894$		0			0
$895$			1.38268e31i			1.40146i
$896$	−9.73637e30	+	6.83274e30i	−0.975356	+	0.684480i
$897$		0			0
$898$	−1.18736e31	−	1.24773e31i	−1.16194	−	1.22101i
$899$			1.06641e31i			1.03144i
$900$		0			0
$901$		−	1.67883e30i		−	0.158634i
$902$	−1.12133e30	+	1.06708e30i	−0.104729	+	0.0996621i
$903$		0			0
$904$	−2.37466e30	+	2.04542e30i	−0.216687	+	0.186644i
$905$		−	6.40347e30i		−	0.577571i
$906$		0			0
$907$	−2.08707e31			−1.83934			−0.919668	−	0.392698i	$-0.871542\pi$
$907$	−2.08707e31			−1.83934			−0.919668	+	0.392698i	$0.871542\pi$
$908$	−7.65218e30	−	3.79601e29i	−0.666628	−	0.0330694i
$909$		0			0
$910$	−9.85059e30	+	9.37405e30i	−0.838548	+	0.797981i
$911$	−9.37384e30			−0.788814			−0.394407	−	0.918936i	$-0.629050\pi$
$911$	−9.37384e30			−0.788814			−0.394407	+	0.918936i	$0.629050\pi$
$912$		0			0
$913$	7.08860e30			0.582931
$914$	−9.59019e30	+	9.12625e30i	−0.779637	+	0.741920i
$915$		0			0
$916$	7.11437e30	+	3.52922e29i	0.565241	+	0.0280399i
$917$	−2.75145e31			−2.16114
$918$		0			0
$919$			6.69026e30i			0.513606i	0.966464	+	0.256803i	$0.0826692\pi$
$919$			6.69026e30i			0.513606i	−0.966464	+	0.256803i	$0.917331\pi$
$920$	−3.78723e30	−	4.39684e30i	−0.287442	−	0.333709i
$921$		0			0
$922$	−2.14964e30	+	2.04565e30i	−0.159474	+	0.151760i
$923$		−	5.91638e30i		−	0.433948i
$924$		0			0
$925$		−	1.18663e28i		−	0.000850801i
$926$	−3.88231e29	−	4.07967e29i	−0.0275217	−	0.0289208i
$927$		0			0
$928$	2.14911e31	−	1.67305e31i	1.48938	−	1.15946i
$929$		−	2.81215e31i		−	1.92696i	−0.267772	−	0.963482i	$-0.586287\pi$
$929$		−	2.81215e31i		−	1.92696i	0.267772	−	0.963482i	$-0.413713\pi$
$930$		0			0
$931$	−2.74000e30			−0.183560
$932$	1.98426e31	+	9.84330e29i	1.31441	+	0.0652039i
$933$		0			0
$934$	−1.67197e30	−	1.75697e30i	−0.108290	−	0.113795i
$935$	1.85003e30			0.118483
$936$		0			0
$937$	−2.22088e31			−1.39078			−0.695390	−	0.718632i	$-0.744769\pi$
$937$	−2.22088e31			−1.39078			−0.695390	+	0.718632i	$0.744769\pi$
$938$	1.84574e30	+	1.93957e30i	0.114298	+	0.120109i
$939$		0			0
$940$	6.64202e29	−	1.33893e31i	0.0402215	−	0.810804i
$941$	−9.54987e30			−0.571882			−0.285941	−	0.958247i	$-0.592306\pi$
$941$	−9.54987e30			−0.571882			−0.285941	+	0.958247i	$0.592306\pi$
$942$		0			0
$943$			2.44958e30i			0.143456i
$944$	1.98403e30	−	1.99483e31i	0.114906	−	1.15531i
$945$		0			0
$946$	1.97652e30	+	2.07700e30i	0.111955	+	0.117647i
$947$			1.93975e31i			1.08660i	0.839538	+	0.543300i	$0.182825\pi$
$947$			1.93975e31i			1.08660i	−0.839538	+	0.543300i	$0.817175\pi$
$948$		0			0
$949$		−	3.03325e31i		−	1.66193i
$950$	−2.45779e28	+	2.33889e28i	−0.00133183	+	0.00126740i
$951$		0			0
$952$	−3.91639e30	−	4.54678e30i	−0.207586	−	0.240999i
$953$		−	4.38799e30i		−	0.230033i	−0.993364	−	0.115017i	$-0.963308\pi$
$953$		−	4.38799e30i		−	0.230033i	0.993364	−	0.115017i	$-0.0366921\pi$
$954$		0			0
$955$	−3.67663e31			−1.88545
$956$	1.14043e30	−	2.29894e31i	0.0578445	−	1.16606i
$957$		0			0
$958$	4.23894e30	−	4.03387e30i	0.210339	−	0.200163i
$959$	−3.90074e31			−1.91448
$960$		0			0
$961$	1.46065e31			0.701376
$962$	3.00422e30	−	2.85889e30i	0.142690	−	0.135787i
$963$		0			0
$964$	1.64564e30	−	3.31735e31i	0.0764760	−	1.54164i
$965$	−5.74704e30			−0.264184
$966$		0			0
$967$			2.39748e31i			1.07839i	0.842180	+	0.539197i	$0.181272\pi$
$967$			2.39748e31i			1.07839i	−0.842180	+	0.539197i	$0.818728\pi$
$968$	−1.17657e31	−	1.36595e31i	−0.523511	−	0.607777i
$969$		0			0
$970$	−2.17733e31	+	2.07200e31i	−0.948030	+	0.902167i
$971$			2.98705e31i			1.28659i	0.765617	+	0.643296i	$0.222434\pi$
$971$			2.98705e31i			1.28659i	−0.765617	+	0.643296i	$0.777566\pi$
$972$		0			0
$973$		−	1.85369e31i		−	0.781363i
$974$	2.41440e31	+	2.53714e31i	1.00679	+	1.05797i
$975$		0			0
$976$	2.97429e30	−	2.99048e31i	0.121383	−	1.22044i
$977$		−	3.07943e31i		−	1.24330i	−0.783294	−	0.621652i	$-0.786462\pi$
$977$		−	3.07943e31i		−	1.24330i	0.783294	−	0.621652i	$-0.213538\pi$
$978$		0			0
$979$	−1.09267e31			−0.431788
$980$	5.30937e29	−	1.07029e31i	0.0207572	−	0.418434i
$981$		0			0
$982$	5.38780e30	+	5.66170e30i	0.206177	+	0.216659i
$983$	7.30276e30			0.276487			0.138244	−	0.990398i	$-0.455854\pi$
$983$	7.30276e30			0.276487			0.138244	+	0.990398i	$0.455854\pi$
$984$		0			0
$985$	3.20034e31			1.18608
$986$	9.47227e30	+	9.95381e30i	0.347333	+	0.364991i
$987$		0			0
$988$	−1.18428e31	−	5.87487e29i	−0.425116	−	0.0210887i
$989$	4.53727e30			0.161151
$990$		0			0
$991$			2.01010e31i			0.698948i	0.936946	+	0.349474i	$0.113640\pi$
$991$			2.01010e31i			0.698948i	−0.936946	+	0.349474i	$0.886360\pi$
$992$	9.75679e30	+	1.25331e31i	0.335687	+	0.431206i
$993$		0			0
$994$	1.08699e31	+	1.14225e31i	0.366158	+	0.384772i
$995$		−	1.19658e31i		−	0.398840i
$996$		0			0
$997$			5.00709e31i			1.63413i	0.576546	+	0.817065i	$0.304400\pi$
$997$			5.00709e31i			1.63413i	−0.576546	+	0.817065i	$0.695600\pi$
$998$	3.47550e31	−	3.30737e31i	1.12240	−	1.06810i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.22.f.a.35.63	yes	84
3.2	odd	2	inner	72.22.f.a.35.22	yes	84
8.3	odd	2	inner	72.22.f.a.35.21	✓	84
24.11	even	2	inner	72.22.f.a.35.64	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.22.f.a.35.21	✓	84	8.3	odd	2	inner
72.22.f.a.35.22	yes	84	3.2	odd	2	inner
72.22.f.a.35.63	yes	84	1.1	even	1	trivial
72.22.f.a.35.64	yes	84	24.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	72.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1049.06 - 998.310i) q^{2} +(103905. - 2.09458e6i) q^{4} -2.17906e7 q^{5} +8.90529e8i q^{7} +(-1.98203e9 - 2.30107e9i) q^{8} +O(q^{10})\)	\(q+(1049.06 - 998.310i) q^{2} +(103905. - 2.09458e6i) q^{4} -2.17906e7 q^{5} +8.90529e8i q^{7} +(-1.98203e9 - 2.30107e9i) q^{8} +(-2.28597e10 + 2.17538e10i) q^{10} -3.82633e10i q^{11} -4.83887e11i q^{13} +(8.89024e11 + 9.34219e11i) q^{14} +(-4.37645e12 - 4.35276e11i) q^{16} -2.21884e12i q^{17} +1.16847e13 q^{19} +(-2.26417e12 + 4.56422e13i) q^{20} +(-3.81986e13 - 4.01405e13i) q^{22} -8.76881e13 q^{23} -2.00507e12 q^{25} +(-4.83069e14 - 5.07627e14i) q^{26} +(1.86528e15 + 9.25308e13i) q^{28} -4.27624e15 q^{29} -2.49379e15i q^{31} +(-5.02571e15 + 3.91243e15i) q^{32} +(-2.21509e15 - 2.32770e15i) q^{34} -1.94052e16i q^{35} +5.91817e15i q^{37} +(1.22579e16 - 1.16649e16i) q^{38} +(4.31898e16 + 5.01418e16i) q^{40} -2.79351e16i q^{41} -5.17433e16 q^{43} +(-8.01454e16 - 3.97577e15i) q^{44} +(-9.19902e16 + 8.75400e16i) q^{46} -2.93354e17 q^{47} -2.34495e17 q^{49} +(-2.10344e15 + 2.00168e15i) q^{50} +(-1.01354e18 - 5.02785e16i) q^{52} +7.56626e17 q^{53} +8.33782e17i q^{55} +(2.04917e18 - 1.76506e18i) q^{56} +(-4.48604e18 + 4.26901e18i) q^{58} +4.55809e18i q^{59} +6.83311e18i q^{61} +(-2.48958e18 - 2.61614e18i) q^{62} +(-1.36646e18 + 9.12159e18i) q^{64} +1.05442e19i q^{65} +2.07614e18 q^{67} +(-4.64753e18 - 2.30550e17i) q^{68} +(-1.93724e19 - 2.03572e19i) q^{70} +1.22268e19 q^{71} +6.26851e19 q^{73} +(5.90817e18 + 6.20852e18i) q^{74} +(1.21410e18 - 2.44744e19i) q^{76} +3.40746e19 q^{77} -7.16868e19i q^{79} +(9.53657e19 + 9.48494e18i) q^{80} +(-2.78879e19 - 2.93057e19i) q^{82} +1.85258e20i q^{83} +4.83500e19i q^{85} +(-5.42819e19 + 5.16559e19i) q^{86} +(-8.80465e19 + 7.58392e19i) q^{88} -2.85566e20i q^{89} +4.30915e20 q^{91} +(-9.11128e18 + 1.83670e20i) q^{92} +(-3.07746e20 + 2.92858e20i) q^{94} -2.54616e20 q^{95} +9.52477e20 q^{97} +(-2.46000e20 + 2.34099e20i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2424084 q^{4}+O(q^{10}) \) 84 * q + 2424084 * q^4	\( 84 q + 2424084 q^{4} + 17057181612 q^{10} - 4099708064904 q^{16} + 92015527242864 q^{19} - 236011369239528 q^{22} + 80\!\cdots\!00 q^{25}+ \cdots - 16\!\cdots\!12 q^{97}+O(q^{100}) \) 84 * q + 2424084 * q^4 + 17057181612 * q^10 - 4099708064904 * q^16 + 92015527242864 * q^19 - 236011369239528 * q^22 + 8010864257812500 * q^25 - 3042238700022024 * q^28 + 74414158327329924 * q^34 + 75018327243317184 * q^40 + 707788847336454432 * q^43 - 162639476543943288 * q^46 - 5423745715136249124 * q^49 - 70566629446202808 * q^52 - 14491558288019904108 * q^58 - 28749968749508108064 * q^64 - 13653811098426494352 * q^67 + 140256684870035374392 * q^70 - 71781309378863778384 * q^73 + 376055720386305092400 * q^76 - 368362114062816367548 * q^82 - 592572120184082106720 * q^88 - 522206955652189957200 * q^91 - 528772551789914644488 * q^94 - 1686050813935078492512 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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