LMFDB - Embedded newform 72.22.f.a.35.25

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			35.25
Character	$\chi$	$=$	72.35
Dual form			72.22.f.a.35.26

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-917.224 - 1120.65i) q^{2} +(-414552. + 2.05577e6i) q^{4} -3.53375e7 q^{5} +2.13540e8i q^{7} +(2.68403e9 - 1.42104e9i) q^{8} +O(q^{10})$	\(q+(-917.224 - 1120.65i) q^{2} +(-414552. + 2.05577e6i) q^{4} -3.53375e7 q^{5} +2.13540e8i q^{7} +(2.68403e9 - 1.42104e9i) q^{8} +(3.24124e10 + 3.96009e10i) q^{10} -6.53997e10i q^{11} -8.18805e11i q^{13} +(2.39303e11 - 1.95864e11i) q^{14} +(-4.05434e12 - 1.70445e12i) q^{16} +8.70488e12i q^{17} -6.82262e12 q^{19} +(1.46492e13 - 7.26458e13i) q^{20} +(-7.32900e13 + 5.99861e13i) q^{22} -3.72344e14 q^{23} +7.71900e14 q^{25} +(-9.17592e14 + 7.51027e14i) q^{26} +(-4.38990e14 - 8.85235e13i) q^{28} -2.96399e14 q^{29} +7.68194e15i q^{31} +(1.80865e15 + 6.10685e15i) q^{32} +(9.75511e15 - 7.98433e15i) q^{34} -7.54597e15i q^{35} -5.18267e16i q^{37} +(6.25787e15 + 7.64576e15i) q^{38} +(-9.48469e16 + 5.02158e16i) q^{40} -1.54716e17i q^{41} +2.16974e17 q^{43} +(1.34447e17 + 2.71116e16i) q^{44} +(3.41523e17 + 4.17266e17i) q^{46} +4.92590e17 q^{47} +5.12946e17 q^{49} +(-7.08005e17 - 8.65029e17i) q^{50} +(1.68327e18 + 3.39437e17i) q^{52} +1.02272e17 q^{53} +2.31106e18i q^{55} +(3.03448e17 + 5.73149e17i) q^{56} +(2.71864e17 + 3.32159e17i) q^{58} -2.54628e18i q^{59} -2.77810e18i q^{61} +(8.60875e18 - 7.04606e18i) q^{62} +(5.18469e18 - 7.62821e18i) q^{64} +2.89345e19i q^{65} +8.26367e18 q^{67} +(-1.78952e19 - 3.60863e18i) q^{68} +(-8.45638e18 + 6.92135e18i) q^{70} -2.50955e19 q^{71} +4.37897e19 q^{73} +(-5.80795e19 + 4.75367e19i) q^{74} +(2.82833e18 - 1.40257e19i) q^{76} +1.39655e19 q^{77} +7.98374e19i q^{79} +(1.43270e20 + 6.02309e19i) q^{80} +(-1.73382e20 + 1.41909e20i) q^{82} +3.14959e19i q^{83} -3.07609e20i q^{85} +(-1.99014e20 - 2.43152e20i) q^{86} +(-9.29352e19 - 1.75535e20i) q^{88} +1.80324e20i q^{89} +1.74848e20 q^{91} +(1.54356e20 - 7.65454e20i) q^{92} +(-4.51815e20 - 5.52020e20i) q^{94} +2.41094e20 q^{95} +1.12322e21 q^{97} +(-4.70487e20 - 5.74832e20i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−917.224	−	1120.65i	−0.633374	−	0.773846i
$2$	−917.224	−	1120.65i	−0.633374	−	0.773846i
$3$		0			0
$3$		0			0
$4$	−414552.	+	2.05577e6i	−0.197674	+	0.980268i
$5$	−3.53375e7			−1.61827			−0.809134	−	0.587624i	$-0.800063\pi$
$5$	−3.53375e7			−1.61827			−0.809134	+	0.587624i	$0.800063\pi$
$6$		0			0
$7$			2.13540e8i			0.285726i	0.989742	+	0.142863i	$0.0456309\pi$
$7$			2.13540e8i			0.285726i	−0.989742	+	0.142863i	$0.954369\pi$
$8$	2.68403e9	−	1.42104e9i	0.883777	−	0.467907i
$9$		0			0
$10$	3.24124e10	+	3.96009e10i	1.02497	+	1.25229i
$11$		−	6.53997e10i		−	0.760243i	−0.924937	−	0.380121i	$-0.875882\pi$
$11$		−	6.53997e10i		−	0.760243i	0.924937	−	0.380121i	$-0.124118\pi$
$12$		0			0
$13$		−	8.18805e11i		−	1.64731i	−0.567092	−	0.823654i	$-0.691932\pi$
$13$		−	8.18805e11i		−	1.64731i	0.567092	−	0.823654i	$-0.308068\pi$
$14$	2.39303e11	−	1.95864e11i	0.221108	−	0.180972i
$15$		0			0
$16$	−4.05434e12	−	1.70445e12i	−0.921850	−	0.387547i
$17$			8.70488e12i			1.04725i	0.851950	+	0.523624i	$0.175420\pi$
$17$			8.70488e12i			1.04725i	−0.851950	+	0.523624i	$0.824580\pi$
$18$		0			0
$19$	−6.82262e12			−0.255293			−0.127646	−	0.991820i	$-0.540742\pi$
$19$	−6.82262e12			−0.255293			−0.127646	+	0.991820i	$0.540742\pi$
$20$	1.46492e13	−	7.26458e13i	0.319889	−	1.58634i
$21$		0			0
$22$	−7.32900e13	+	5.99861e13i	−0.588310	+	0.481518i
$23$	−3.72344e14			−1.87414			−0.937070	−	0.349142i	$-0.886473\pi$
$23$	−3.72344e14			−1.87414			−0.937070	+	0.349142i	$0.886473\pi$
$24$		0			0
$25$	7.71900e14			1.61879
$26$	−9.17592e14	+	7.51027e14i	−1.27476	+	1.04336i
$27$		0			0
$28$	−4.38990e14	−	8.85235e13i	−0.280088	−	0.0564806i
$29$	−2.96399e14			−0.130827			−0.0654135	−	0.997858i	$-0.520837\pi$
$29$	−2.96399e14			−0.130827			−0.0654135	+	0.997858i	$0.520837\pi$
$30$		0			0
$31$			7.68194e15i			1.68334i	0.539989	+	0.841672i	$0.318428\pi$
$31$			7.68194e15i			1.68334i	−0.539989	+	0.841672i	$0.681572\pi$
$32$	1.80865e15	+	6.10685e15i	0.283975	+	0.958832i
$33$		0			0
$34$	9.75511e15	−	7.98433e15i	0.810408	−	0.663300i
$35$		−	7.54597e15i		−	0.462382i
$36$		0			0
$37$		−	5.18267e16i		−	1.77188i	−0.463797	−	0.885942i	$-0.653513\pi$
$37$		−	5.18267e16i		−	1.77188i	0.463797	−	0.885942i	$-0.346487\pi$
$38$	6.25787e15	+	7.64576e15i	0.161696	+	0.197557i
$39$		0			0
$40$	−9.48469e16	+	5.02158e16i	−1.43019	+	0.757200i
$41$		−	1.54716e17i		−	1.80013i	−0.435752	−	0.900067i	$-0.643517\pi$
$41$		−	1.54716e17i		−	1.80013i	0.435752	−	0.900067i	$-0.356483\pi$
$42$		0			0
$43$	2.16974e17			1.53105			0.765525	−	0.643406i	$-0.222479\pi$
$43$	2.16974e17			1.53105			0.765525	+	0.643406i	$0.222479\pi$
$44$	1.34447e17	+	2.71116e16i	0.745241	+	0.150280i
$45$		0			0
$46$	3.41523e17	+	4.17266e17i	1.18703	+	1.45029i
$47$	4.92590e17			1.36602			0.683011	−	0.730408i	$-0.260670\pi$
$47$	4.92590e17			1.36602			0.683011	+	0.730408i	$0.260670\pi$
$48$		0			0
$49$	5.12946e17			0.918360
$50$	−7.08005e17	−	8.65029e17i	−1.02530	−	1.25270i
$51$		0			0
$52$	1.68327e18	+	3.39437e17i	1.61480	+	0.325630i
$53$	1.02272e17			0.0803267			0.0401634	−	0.999193i	$-0.487212\pi$
$53$	1.02272e17			0.0803267			0.0401634	+	0.999193i	$0.487212\pi$
$54$		0			0
$55$			2.31106e18i			1.23028i
$56$	3.03448e17	+	5.73149e17i	0.133693	+	0.252518i
$57$		0			0
$58$	2.71864e17	+	3.32159e17i	0.0828625	+	0.101240i
$59$		−	2.54628e18i		−	0.648576i	−0.945958	−	0.324288i	$-0.894875\pi$
$59$		−	2.54628e18i		−	0.648576i	0.945958	−	0.324288i	$-0.105125\pi$
$60$		0			0
$61$		−	2.77810e18i		−	0.498636i	−0.968422	−	0.249318i	$-0.919793\pi$
$61$		−	2.77810e18i		−	0.498636i	0.968422	−	0.249318i	$-0.0802065\pi$
$62$	8.60875e18	−	7.04606e18i	1.30265	−	1.06619i
$63$		0			0
$64$	5.18469e18	−	7.62821e18i	0.562125	−	0.827052i
$65$			2.89345e19i			2.66579i
$66$		0			0
$67$	8.26367e18			0.553844			0.276922	−	0.960892i	$-0.410686\pi$
$67$	8.26367e18			0.553844			0.276922	+	0.960892i	$0.410686\pi$
$68$	−1.78952e19	−	3.60863e18i	−1.02658	−	0.207013i
$69$		0			0
$70$	−8.45638e18	+	6.92135e18i	−0.357812	+	0.292861i
$71$	−2.50955e19			−0.914920			−0.457460	−	0.889230i	$-0.651241\pi$
$71$	−2.50955e19			−0.914920			−0.457460	+	0.889230i	$0.651241\pi$
$72$		0			0
$73$	4.37897e19			1.19256			0.596282	−	0.802775i	$-0.296644\pi$
$73$	4.37897e19			1.19256			0.596282	+	0.802775i	$0.296644\pi$
$74$	−5.80795e19	+	4.75367e19i	−1.37116	+	1.12227i
$75$		0			0
$76$	2.82833e18	−	1.40257e19i	0.0504647	−	0.250255i
$77$	1.39655e19			0.217221
$78$		0			0
$79$			7.98374e19i			0.948684i	0.880341	+	0.474342i	$0.157314\pi$
$79$			7.98374e19i			0.948684i	−0.880341	+	0.474342i	$0.842686\pi$
$80$	1.43270e20	+	6.02309e19i	1.49180	+	0.627154i
$81$		0			0
$82$	−1.73382e20	+	1.41909e20i	−1.39303	+	1.14016i
$83$			3.14959e19i			0.222809i	0.993775	+	0.111405i	$0.0355350\pi$
$83$			3.14959e19i			0.222809i	−0.993775	+	0.111405i	$0.964465\pi$
$84$		0			0
$85$		−	3.07609e20i		−	1.69473i
$86$	−1.99014e20	−	2.43152e20i	−0.969728	−	1.18480i
$87$		0			0
$88$	−9.29352e19	−	1.75535e20i	−0.355723	−	0.671885i
$89$			1.80324e20i			0.612998i	0.951871	+	0.306499i	$0.0991576\pi$
$89$			1.80324e20i			0.612998i	−0.951871	+	0.306499i	$0.900842\pi$
$90$		0			0
$91$	1.74848e20			0.470680
$92$	1.54356e20	−	7.65454e20i	0.370468	−	1.83716i
$93$		0			0
$94$	−4.51815e20	−	5.52020e20i	−0.865204	−	1.05709i
$95$	2.41094e20			0.413132
$96$		0			0
$97$	1.12322e21			1.54655			0.773273	−	0.634073i	$-0.218618\pi$
$97$	1.12322e21			1.54655			0.773273	+	0.634073i	$0.218618\pi$
$98$	−4.70487e20	−	5.74832e20i	−0.581666	−	0.710669i
$99$		0			0
$100$	−3.19993e20	+	1.58685e21i	−0.319993	+	1.58685i
$101$	2.01971e20			0.181934			0.0909670	−	0.995854i	$-0.471004\pi$
$101$	2.01971e20			0.181934			0.0909670	+	0.995854i	$0.471004\pi$
$102$		0			0
$103$		−	8.68609e20i		−	0.636844i	−0.947949	−	0.318422i	$-0.896847\pi$
$103$		−	8.68609e20i		−	0.636844i	0.947949	−	0.318422i	$-0.103153\pi$
$104$	−1.16355e21	−	2.19770e21i	−0.770788	−	1.45585i
$105$		0			0
$106$	−9.38063e19	−	1.14611e20i	−0.0508769	−	0.0621605i
$107$		−	1.75197e21i		−	0.860988i	−0.902593	−	0.430494i	$-0.858339\pi$
$107$		−	1.75197e21i		−	0.860988i	0.902593	−	0.430494i	$-0.141661\pi$
$108$		0			0
$109$			7.60276e20i			0.307605i	0.988102	+	0.153802i	$0.0491519\pi$
$109$			7.60276e20i			0.307605i	−0.988102	+	0.153802i	$0.950848\pi$
$110$	2.58988e21	−	2.11976e21i	0.952044	−	0.779226i
$111$		0			0
$112$	3.63968e20	−	8.65765e20i	0.110732	−	0.263397i
$113$		−	7.96445e19i		−	0.0220715i	−0.999939	−	0.0110358i	$-0.996487\pi$
$113$		−	7.96445e19i		−	0.0220715i	0.999939	−	0.0110358i	$-0.00351286\pi$
$114$		0			0
$115$	1.31577e22			3.03286
$116$	1.22873e20	−	6.09328e20i	0.0258611	−	0.128245i
$117$		0			0
$118$	−2.85349e21	+	2.33551e21i	−0.501897	+	0.410791i
$119$	−1.85884e21			−0.299226
$120$		0			0
$121$	3.12314e21			0.422031
$122$	−3.11327e21	+	2.54814e21i	−0.385868	+	0.315824i
$123$		0			0
$124$	−1.57923e22	−	3.18456e21i	−1.65013	−	0.332753i
$125$	−1.04268e22			−1.00137
$126$		0			0
$127$		−	7.00667e21i		−	0.569604i	−0.958586	−	0.284802i	$-0.908072\pi$
$127$		−	7.00667e21i		−	0.569604i	0.958586	−	0.284802i	$-0.0919278\pi$
$128$	−1.33041e22	+	1.18657e21i	−0.996046	+	0.0888356i
$129$		0			0
$130$	3.24254e22	−	2.65394e22i	2.06291	−	1.68844i
$131$			4.45906e21i			0.261755i	0.991399	+	0.130877i	$0.0417794\pi$
$131$			4.45906e21i			0.261755i	−0.991399	+	0.130877i	$0.958221\pi$
$132$		0			0
$133$		−	1.45690e21i		−	0.0729439i
$134$	−7.57963e21	−	9.26066e21i	−0.350791	−	0.428590i
$135$		0			0
$136$	1.23699e22	+	2.33642e22i	0.490015	+	0.925533i
$137$		−	1.63994e22i		−	0.601537i	−0.953697	−	0.300768i	$-0.902757\pi$
$137$		−	1.63994e22i		−	0.601537i	0.953697	−	0.300768i	$-0.0972431\pi$
$138$		0			0
$139$	−4.51369e22			−1.42192			−0.710962	−	0.703230i	$-0.751740\pi$
$139$	−4.51369e22			−1.42192			−0.710962	+	0.703230i	$0.751740\pi$
$140$	1.55128e22	+	3.12820e21i	0.453258	+	0.0914008i
$141$		0			0
$142$	2.30182e22	+	2.81232e22i	0.579487	+	0.708007i
$143$	−5.35495e22			−1.25235
$144$		0			0
$145$	1.04740e22			0.211713
$146$	−4.01649e22	−	4.90728e22i	−0.755340	−	0.922860i
$147$		0			0
$148$	1.06544e23	+	2.14849e22i	1.73692	+	0.350255i
$149$	1.15065e23			1.74778			0.873888	−	0.486128i	$-0.161591\pi$
$149$	1.15065e23			1.74778			0.873888	+	0.486128i	$0.161591\pi$
$150$		0			0
$151$			8.80285e21i			0.116243i	0.998310	+	0.0581213i	$0.0185110\pi$
$151$			8.80285e21i			0.116243i	−0.998310	+	0.0581213i	$0.981489\pi$
$152$	−1.83121e22	+	9.69519e21i	−0.225622	+	0.119453i
$153$		0			0
$154$	−1.28095e22	−	1.56504e22i	−0.137582	−	0.168096i
$155$		−	2.71460e23i		−	2.72410i
$156$		0			0
$157$			7.83719e22i			0.687407i	0.939078	+	0.343704i	$0.111682\pi$
$157$			7.83719e22i			0.687407i	−0.939078	+	0.343704i	$0.888318\pi$
$158$	8.94696e22	−	7.32288e22i	0.734135	−	0.600872i
$159$		0			0
$160$	−6.39132e22	−	2.15801e23i	−0.459548	−	1.55165i
$161$		−	7.95104e22i		−	0.535491i
$162$		0			0
$163$	−7.75013e22			−0.458500			−0.229250	−	0.973368i	$-0.573627\pi$
$163$	−7.75013e22			−0.458500			−0.229250	+	0.973368i	$0.573627\pi$
$164$	3.18061e23	+	6.41378e22i	1.76461	+	0.355839i
$165$		0			0
$166$	3.52958e22	−	2.88888e22i	0.172420	−	0.141122i
$167$	−3.77628e23			−1.73198			−0.865988	−	0.500065i	$-0.833309\pi$
$167$	−3.77628e23			−1.73198			−0.865988	+	0.500065i	$0.833309\pi$
$168$		0			0
$169$	−4.23376e23			−1.71363
$170$	−3.44721e23	+	2.82146e23i	−1.31146	+	1.07340i
$171$		0			0
$172$	−8.99471e22	+	4.46049e23i	−0.302649	+	1.50084i
$173$	7.73712e22			0.244960			0.122480	−	0.992471i	$-0.460915\pi$
$173$	7.73712e22			0.244960			0.122480	+	0.992471i	$0.460915\pi$
$174$		0			0
$175$			1.64832e23i			0.462532i
$176$	−1.11470e23	+	2.65152e23i	−0.294629	+	0.700830i
$177$		0			0
$178$	2.02080e23	−	1.65398e23i	0.474366	−	0.388257i
$179$			6.75484e22i			0.149506i	0.997202	+	0.0747529i	$0.0238168\pi$
$179$			6.75484e22i			0.149506i	−0.997202	+	0.0747529i	$0.976183\pi$
$180$		0			0
$181$			1.73245e23i			0.341222i	0.985338	+	0.170611i	$0.0545741\pi$
$181$			1.73245e23i			0.341222i	−0.985338	+	0.170611i	$0.945426\pi$
$182$	−1.60375e23	−	1.95943e23i	−0.298116	−	0.364233i
$183$		0			0
$184$	−9.99383e23	+	5.29114e23i	−1.65632	+	0.876924i
$185$			1.83142e24i			2.86738i
$186$		0			0
$187$	5.69296e23			0.796162
$188$	−2.04204e23	+	1.01265e24i	−0.270027	+	1.33907i
$189$		0			0
$190$	−2.21137e23	−	2.70182e23i	−0.261667	−	0.319700i
$191$	4.74799e23			0.531691			0.265846	−	0.964016i	$-0.414349\pi$
$191$	4.74799e23			0.531691			0.265846	+	0.964016i	$0.414349\pi$
$192$		0			0
$193$	−6.43113e23			−0.645559			−0.322779	−	0.946474i	$-0.604617\pi$
$193$	−6.43113e23			−0.645559			−0.322779	+	0.946474i	$0.604617\pi$
$194$	−1.03025e24	−	1.25874e24i	−0.979543	−	1.19679i
$195$		0			0
$196$	−2.12643e23	+	1.05450e24i	−0.181536	+	0.900239i
$197$	3.01952e23			0.244367			0.122183	−	0.992508i	$-0.461010\pi$
$197$	3.01952e23			0.244367			0.122183	+	0.992508i	$0.461010\pi$
$198$		0			0
$199$		−	2.00282e24i		−	1.45775i	−0.684646	−	0.728876i	$-0.740043\pi$
$199$		−	2.00282e24i		−	1.45775i	0.684646	−	0.728876i	$-0.259957\pi$
$200$	2.07181e24	−	1.09690e24i	1.43065	−	0.757445i
$201$		0			0
$202$	−1.85252e23	−	2.26338e23i	−0.115232	−	0.140789i
$203$		−	6.32930e22i		−	0.0373807i
$204$		0			0
$205$			5.46727e24i			2.91310i
$206$	−9.73405e23	+	7.96709e23i	−0.492819	+	0.403361i
$207$		0			0
$208$	−1.39561e24	+	3.31971e24i	−0.638409	+	1.51857i
$209$			4.46197e23i			0.194084i
$210$		0			0
$211$	4.48208e24			1.76406			0.882031	−	0.471191i	$-0.156176\pi$
$211$	4.48208e24			1.76406			0.882031	+	0.471191i	$0.156176\pi$
$212$	−4.23971e22	+	2.10248e23i	−0.0158785	+	0.0787417i
$213$		0			0
$214$	−1.96334e24	+	1.60695e24i	−0.666272	+	0.545328i
$215$	−7.66732e24			−2.47765
$216$		0			0
$217$	−1.64040e24			−0.480976
$218$	8.52002e23	−	6.97343e23i	0.238039	−	0.194829i
$219$		0			0
$220$	−4.75101e24	−	9.58054e23i	−1.20600	−	0.243194i
$221$	7.12760e24			1.72514
$222$		0			0
$223$			2.96303e24i			0.652431i	0.945295	+	0.326216i	$0.105774\pi$
$223$			2.96303e24i			0.652431i	−0.945295	+	0.326216i	$0.894226\pi$
$224$	−1.30406e24	+	3.86220e23i	−0.273963	+	0.0811391i
$225$		0			0
$226$	−8.92535e22	+	7.30519e22i	−0.0170799	+	0.0139795i
$227$		−	5.76554e24i		−	1.05334i	−0.850070	−	0.526670i	$-0.823440\pi$
$227$		−	5.76554e24i		−	1.05334i	0.850070	−	0.526670i	$-0.176560\pi$
$228$		0			0
$229$		−	8.38661e23i		−	0.139738i	−0.997556	−	0.0698689i	$-0.977742\pi$
$229$		−	8.38661e23i		−	0.139738i	0.997556	−	0.0698689i	$-0.0222581\pi$
$230$	−1.20686e25	−	1.47451e25i	−1.92094	−	2.34697i
$231$		0			0
$232$	−7.95544e23	+	4.21193e23i	−0.115622	+	0.0612149i
$233$			2.39766e22i			0.00333082i	0.999999	+	0.00166541i	$0.000530116\pi$
$233$			2.39766e22i			0.00333082i	−0.999999	+	0.00166541i	$0.999470\pi$
$234$		0			0
$235$	−1.74069e25			−2.21059
$236$	5.23457e24	+	1.05557e24i	0.635778	+	0.128206i
$237$		0			0
$238$	1.70497e24	+	2.08311e24i	0.189522	+	0.231555i
$239$	−8.19979e24			−0.872217			−0.436109	−	0.899894i	$-0.643644\pi$
$239$	−8.19979e24			−0.872217			−0.436109	+	0.899894i	$0.643644\pi$
$240$		0			0
$241$	−1.04012e25			−1.01369			−0.506843	−	0.862038i	$-0.669188\pi$
$241$	−1.04012e25			−1.01369			−0.506843	+	0.862038i	$0.669188\pi$
$242$	−2.86461e24	−	3.49994e24i	−0.267304	−	0.326587i
$243$		0			0
$244$	5.71113e24	+	1.15167e24i	0.488797	+	0.0985674i
$245$	−1.81262e25			−1.48615
$246$		0			0
$247$			5.58639e24i			0.420546i
$248$	1.09163e25	+	2.06186e25i	0.787649	+	1.48770i
$249$		0			0
$250$	9.56370e24	+	1.16848e25i	0.634243	+	0.774907i
$251$		−	1.77459e25i		−	1.12856i	−0.825584	−	0.564279i	$-0.809154\pi$
$251$		−	1.77459e25i		−	1.12856i	0.825584	−	0.564279i	$-0.190846\pi$
$252$		0			0
$253$			2.43512e25i			1.42480i
$254$	−7.85201e24	+	6.42669e24i	−0.440785	+	0.360772i
$255$		0			0
$256$	1.35325e25	+	1.38208e25i	0.699615	+	0.714520i
$257$		−	1.65498e25i		−	0.821286i	−0.911796	−	0.410643i	$-0.865304\pi$
$257$		−	1.65498e25i		−	0.821286i	0.911796	−	0.410643i	$-0.134696\pi$
$258$		0			0
$259$	1.10671e25			0.506274
$260$	−5.94827e25	−	1.19949e25i	−2.61319	−	0.526957i
$261$		0			0
$262$	4.99704e24	−	4.08996e24i	0.202558	−	0.165789i
$263$	−2.04862e25			−0.797860			−0.398930	−	0.916981i	$-0.630618\pi$
$263$	−2.04862e25			−0.797860			−0.398930	+	0.916981i	$0.630618\pi$
$264$		0			0
$265$	−3.61403e24			−0.129990
$266$	−1.63268e24	+	1.33631e24i	−0.0564473	+	0.0462008i
$267$		0			0
$268$	−3.42572e24	+	1.69882e25i	−0.109480	+	0.542915i
$269$	−2.31211e25			−0.710573			−0.355287	−	0.934757i	$-0.615617\pi$
$269$	−2.31211e25			−0.710573			−0.355287	+	0.934757i	$0.615617\pi$
$270$		0			0
$271$			2.74156e25i			0.779507i	0.920919	+	0.389753i	$0.127440\pi$
$271$			2.74156e25i			0.779507i	−0.920919	+	0.389753i	$0.872560\pi$
$272$	1.48370e25	−	3.52925e25i	0.405857	−	0.965405i
$273$		0			0
$274$	−1.83780e25	+	1.50419e25i	−0.465497	+	0.380998i
$275$		−	5.04820e25i		−	1.23067i
$276$		0			0
$277$		−	7.77857e24i		−	0.175737i	−0.996132	−	0.0878683i	$-0.971995\pi$
$277$		−	7.77857e24i		−	0.175737i	0.996132	−	0.0878683i	$-0.0280055\pi$
$278$	4.14007e25	+	5.05826e25i	0.900611	+	1.10035i
$279$		0			0
$280$	−1.07231e25	−	2.02536e25i	−0.216352	−	0.408643i
$281$		−	7.03386e25i		−	1.36703i	−0.729937	−	0.683514i	$-0.760451\pi$
$281$		−	7.03386e25i		−	1.36703i	0.729937	−	0.683514i	$-0.239549\pi$
$282$		0			0
$283$	−2.21797e24			−0.0400128			−0.0200064	−	0.999800i	$-0.506369\pi$
$283$	−2.21797e24			−0.0400128			−0.0200064	+	0.999800i	$0.506369\pi$
$284$	1.04034e25	−	5.15906e25i	0.180856	−	0.896866i
$285$		0			0
$286$	4.91169e25	+	6.00102e25i	0.793209	+	0.969129i
$287$	3.30381e25			0.514346
$288$		0			0
$289$	−6.68303e24			−0.0967266
$290$	−9.60699e24	−	1.17376e25i	−0.134094	−	0.163833i
$291$		0			0
$292$	−1.81531e25	+	9.00215e25i	−0.235739	+	1.16903i
$293$	−9.29368e25			−1.16433			−0.582167	−	0.813069i	$-0.697795\pi$
$293$	−9.29368e25			−1.16433			−0.582167	+	0.813069i	$0.697795\pi$
$294$		0			0
$295$			8.99792e25i			1.04957i
$296$	−7.36475e25	−	1.39104e26i	−0.829078	−	1.56595i
$297$		0			0
$298$	−1.05540e26	−	1.28947e26i	−1.10700	−	1.35251i
$299$			3.04877e26i			3.08729i
$300$		0			0
$301$			4.63327e25i			0.437461i
$302$	9.86490e24	−	8.07418e24i	0.0899538	−	0.0736251i
$303$		0			0
$304$	2.76612e25	+	1.16288e25i	0.235342	+	0.0989378i
$305$			9.81709e25i			0.806928i
$306$		0			0
$307$	−1.70989e26			−1.31225			−0.656124	−	0.754653i	$-0.727805\pi$
$307$	−1.70989e26			−1.31225			−0.656124	+	0.754653i	$0.727805\pi$
$308$	−5.78941e24	+	2.87098e25i	−0.0429390	+	0.212935i
$309$		0			0
$310$	−3.04211e26	+	2.48990e26i	−2.10803	+	1.72538i
$311$	1.74628e26			1.16985			0.584925	−	0.811088i	$-0.301124\pi$
$311$	1.74628e26			1.16985			0.584925	+	0.811088i	$0.301124\pi$
$312$		0			0
$313$	1.23660e26			0.774484			0.387242	−	0.921978i	$-0.373428\pi$
$313$	1.23660e26			0.774484			0.387242	+	0.921978i	$0.373428\pi$
$314$	8.78273e25	−	7.18846e25i	0.531947	−	0.435386i
$315$		0			0
$316$	−1.64127e26	−	3.30968e25i	−0.929965	−	0.187530i
$317$	−1.91656e26			−1.05051			−0.525255	−	0.850945i	$-0.676030\pi$
$317$	−1.91656e26			−1.05051			−0.525255	+	0.850945i	$0.676030\pi$
$318$		0			0
$319$			1.93844e25i			0.0994602i
$320$	−1.83214e26	+	2.69562e26i	−0.909669	+	1.33839i
$321$		0			0
$322$	−8.91032e25	+	7.29288e25i	−0.414387	+	0.339166i
$323$		−	5.93901e25i		−	0.267355i
$324$		0			0
$325$		−	6.32035e26i		−	2.66665i
$326$	7.10861e25	+	8.68517e25i	0.290402	+	0.354808i
$327$		0			0
$328$	−2.19857e26	−	4.15263e26i	−0.842296	−	1.59092i
$329$			1.05188e26i			0.390309i
$330$		0			0
$331$	−1.96575e26			−0.684437			−0.342219	−	0.939620i	$-0.611178\pi$
$331$	−1.96575e26			−0.684437			−0.342219	+	0.939620i	$0.611178\pi$
$332$	−6.47483e25	−	1.30567e25i	−0.218413	−	0.0440436i
$333$		0			0
$334$	3.46370e26	+	4.23189e26i	1.09699	+	1.34028i
$335$	−2.92017e26			−0.896268
$336$		0			0
$337$	2.72863e26			0.786738			0.393369	−	0.919381i	$-0.371309\pi$
$337$	2.72863e26			0.786738			0.393369	+	0.919381i	$0.371309\pi$
$338$	3.88331e26	+	4.74456e26i	1.08537	+	1.32608i
$339$		0			0
$340$	6.32373e26	+	1.27520e26i	1.66129	+	0.335003i
$341$	5.02396e26			1.27975
$342$		0			0
$343$			2.28807e26i			0.548126i
$344$	5.82366e26	−	3.08328e26i	1.35311	−	0.716390i
$345$		0			0
$346$	−7.09667e25	−	8.67059e25i	−0.155151	−	0.189561i
$347$			2.09538e26i			0.444431i	0.974998	+	0.222215i	$0.0713289\pi$
$347$			2.09538e26i			0.444431i	−0.974998	+	0.222215i	$0.928671\pi$
$348$		0			0
$349$			7.59154e26i			1.51587i	0.652328	+	0.757937i	$0.273792\pi$
$349$			7.59154e26i			1.51587i	−0.652328	+	0.757937i	$0.726208\pi$
$350$	1.84718e26	−	1.51188e26i	0.357928	−	0.292956i
$351$		0			0
$352$	3.99386e26	−	1.18285e26i	0.728945	−	0.215890i
$353$		−	6.92267e26i		−	1.22642i	−0.789920	−	0.613210i	$-0.789878\pi$
$353$		−	6.92267e26i		−	1.22642i	0.789920	−	0.613210i	$-0.210122\pi$
$354$		0			0
$355$	8.86811e26			1.48059
$356$	−3.70705e26	−	7.47538e25i	−0.600902	−	0.121174i
$357$		0			0
$358$	7.56980e25	−	6.19570e25i	0.115694	−	0.0946932i
$359$	3.97170e26			0.589502			0.294751	−	0.955574i	$-0.404763\pi$
$359$	3.97170e26			0.589502			0.294751	+	0.955574i	$0.404763\pi$
$360$		0			0
$361$	−6.67661e26			−0.934826
$362$	1.94147e26	−	1.58905e26i	0.264053	−	0.216121i
$363$		0			0
$364$	−7.24835e25	+	3.59447e26i	−0.0930410	+	0.461392i
$365$	−1.54742e27			−1.92989
$366$		0			0
$367$		−	1.64436e27i		−	1.93644i	−0.250107	−	0.968218i	$-0.580466\pi$
$367$		−	1.64436e27i		−	1.93644i	0.250107	−	0.968218i	$-0.419534\pi$
$368$	1.50961e27	+	6.34641e26i	1.72768	+	0.726317i
$369$		0			0
$370$	2.05238e27	−	1.67983e27i	2.21891	−	1.81613i
$371$			2.18392e25i			0.0229515i
$372$		0			0
$373$		−	1.16479e27i		−	1.15692i	−0.815710	−	0.578461i	$-0.803653\pi$
$373$		−	1.16479e27i		−	1.15692i	0.815710	−	0.578461i	$-0.196347\pi$
$374$	−5.22172e26	−	6.37981e26i	−0.504269	−	0.616106i
$375$		0			0
$376$	1.32213e27	−	6.99988e26i	1.20726	−	0.639172i
$377$			2.42693e26i			0.215512i
$378$		0			0
$379$	−1.73279e27			−1.45558			−0.727789	−	0.685801i	$-0.759452\pi$
$379$	−1.73279e27			−1.45558			−0.727789	+	0.685801i	$0.759452\pi$
$380$	−9.99461e25	+	4.95635e26i	−0.0816654	+	0.404980i
$381$		0			0
$382$	−4.35497e26	−	5.32083e26i	−0.336760	−	0.411447i
$383$	−7.52593e26			−0.566204			−0.283102	−	0.959090i	$-0.591364\pi$
$383$	−7.52593e26			−0.566204			−0.283102	+	0.959090i	$0.591364\pi$
$384$		0			0
$385$	−4.93504e26			−0.351522
$386$	5.89879e26	+	7.20704e26i	0.408880	+	0.499563i
$387$		0			0
$388$	−4.65635e26	+	2.30909e27i	−0.305712	+	1.51603i
$389$	1.70711e27			1.09091			0.545457	−	0.838139i	$-0.316356\pi$
$389$	1.70711e27			1.09091			0.545457	+	0.838139i	$0.316356\pi$
$390$		0			0
$391$		−	3.24121e27i		−	1.96269i
$392$	1.37676e27	−	7.28915e26i	0.811626	−	0.429708i
$393$		0			0
$394$	−2.76957e26	−	3.38381e26i	−0.154776	−	0.189102i
$395$		−	2.82125e27i		−	1.53523i
$396$		0			0
$397$		−	1.71591e27i		−	0.885509i	−0.896643	−	0.442755i	$-0.854001\pi$
$397$		−	1.71591e27i		−	0.885509i	0.896643	−	0.442755i	$-0.145999\pi$
$398$	−2.24445e27	+	1.83703e27i	−1.12807	+	0.923303i
$399$		0			0
$400$	−3.12955e27	−	1.31566e27i	−1.49228	−	0.627357i
$401$			2.31456e27i			1.07511i	0.843230	+	0.537554i	$0.180651\pi$
$401$			2.31456e27i			1.07511i	−0.843230	+	0.537554i	$0.819349\pi$
$402$		0			0
$403$	6.29001e27			2.77299
$404$	−8.37274e25	+	4.15205e26i	−0.0359636	+	0.178344i
$405$		0			0
$406$	−7.09292e25	+	5.80539e25i	−0.0289269	+	0.0236760i
$407$	−3.38945e27			−1.34706
$408$		0			0
$409$	−6.66680e26			−0.251665			−0.125833	−	0.992051i	$-0.540160\pi$
$409$	−6.66680e26			−0.251665			−0.125833	+	0.992051i	$0.540160\pi$
$410$	6.12689e27	−	5.01471e27i	2.25429	−	1.84508i
$411$		0			0
$412$	1.78566e27	+	3.60084e26i	0.624278	+	0.125887i
$413$	5.43734e26			0.185315
$414$		0			0
$415$		−	1.11298e27i		−	0.360566i
$416$	5.00032e27	−	1.48093e27i	1.57949	−	0.467795i
$417$		0			0
$418$	5.00030e26	−	4.09263e26i	0.150191	−	0.122928i
$419$			1.38995e27i			0.407147i	0.979060	+	0.203574i	$0.0652556\pi$
$419$			1.38995e27i			0.407147i	−0.979060	+	0.203574i	$0.934744\pi$
$420$		0			0
$421$		−	2.97738e26i		−	0.0829606i	−0.999139	−	0.0414803i	$-0.986793\pi$
$421$		−	2.97738e26i		−	0.0829606i	0.999139	−	0.0414803i	$-0.0132074\pi$
$422$	−4.11107e27	−	5.02284e27i	−1.11731	−	1.36511i
$423$		0			0
$424$	2.74501e26	−	1.45332e26i	0.0709910	−	0.0375855i
$425$			6.71930e27i			1.69528i
$426$		0			0
$427$	5.93235e26			0.142474
$428$	3.60165e27	+	7.26283e26i	0.843999	+	0.170195i
$429$		0			0
$430$	7.03265e27	+	8.59237e27i	1.56928	+	1.91732i
$431$	−5.00917e27			−1.09082			−0.545412	−	0.838168i	$-0.683627\pi$
$431$	−5.00917e27			−1.09082			−0.545412	+	0.838168i	$0.683627\pi$
$432$		0			0
$433$	7.26998e27			1.50803			0.754015	−	0.656857i	$-0.228114\pi$
$433$	7.26998e27			1.50803			0.754015	+	0.656857i	$0.228114\pi$
$434$	1.50462e27	+	1.83831e27i	0.304638	+	0.372201i
$435$		0			0
$436$	−1.56295e27	−	3.15174e26i	−0.301535	−	0.0608054i
$437$	2.54036e27			0.478454
$438$		0			0
$439$		−	1.76314e27i		−	0.316526i	−0.987397	−	0.158263i	$-0.949411\pi$
$439$		−	1.76314e27i		−	0.316526i	0.987397	−	0.158263i	$-0.0505893\pi$
$440$	3.28410e27	+	6.20296e27i	0.575656	+	1.08729i
$441$		0			0
$442$	−6.53760e27	−	7.98753e27i	−1.09266	−	1.33499i
$443$			4.04831e27i			0.660746i	0.943850	+	0.330373i	$0.107175\pi$
$443$			4.04831e27i			0.660746i	−0.943850	+	0.330373i	$0.892825\pi$
$444$		0			0
$445$		−	6.37220e27i		−	0.991995i
$446$	3.32051e27	−	2.71776e27i	0.504881	−	0.413233i
$447$		0			0
$448$	1.62893e27	+	1.10714e27i	0.236311	+	0.160614i
$449$			1.42377e27i			0.201769i	0.994898	+	0.100885i	$0.0321673\pi$
$449$			1.42377e27i			0.201769i	−0.994898	+	0.100885i	$0.967833\pi$
$450$		0			0
$451$	−1.01184e28			−1.36854
$452$	1.63731e26	+	3.30168e25i	0.0216360	+	0.00436296i
$453$		0			0
$454$	−6.46114e27	+	5.28829e27i	−0.815123	+	0.667159i
$455$	−6.17868e27			−0.761686
$456$		0			0
$457$	1.95280e26			0.0229899			0.0114949	−	0.999934i	$-0.496341\pi$
$457$	1.95280e26			0.0229899			0.0114949	+	0.999934i	$0.496341\pi$
$458$	−9.39844e26	+	7.69240e26i	−0.108135	+	0.0885063i
$459$		0			0
$460$	−5.45455e27	+	2.70492e28i	−0.599517	+	2.97302i
$461$	−1.11927e28			−1.20247			−0.601234	−	0.799073i	$-0.705324\pi$
$461$	−1.11927e28			−1.20247			−0.601234	+	0.799073i	$0.705324\pi$
$462$		0			0
$463$		−	7.60297e27i		−	0.780518i	−0.920705	−	0.390259i	$-0.872385\pi$
$463$		−	7.60297e27i		−	0.780518i	0.920705	−	0.390259i	$-0.127615\pi$
$464$	1.20170e27	+	5.05196e26i	0.120603	+	0.0507016i
$465$		0			0
$466$	2.68694e25	−	2.19919e25i	0.00257754	−	0.00210965i
$467$			1.29395e28i			1.21364i	0.794838	+	0.606821i	$0.207556\pi$
$467$			1.29395e28i			1.21364i	−0.794838	+	0.606821i	$0.792444\pi$
$468$		0			0
$469$			1.76463e27i			0.158248i
$470$	1.59660e28	+	1.95070e28i	1.40013	+	1.71066i
$471$		0			0
$472$	−3.61836e27	−	6.83431e27i	−0.303473	−	0.573196i
$473$		−	1.41900e28i		−	1.16397i
$474$		0			0
$475$	−5.26638e27			−0.413266
$476$	7.70587e26	−	3.82135e27i	0.0591492	−	0.293322i
$477$		0			0
$478$	7.52104e27	+	9.18908e27i	0.552440	+	0.674962i
$479$	−1.25655e28			−0.902937			−0.451468	−	0.892287i	$-0.649100\pi$
$479$	−1.25655e28			−0.902937			−0.451468	+	0.892287i	$0.649100\pi$
$480$		0			0
$481$	−4.24359e28			−2.91884
$482$	9.54021e27	+	1.16561e28i	0.642043	+	0.784437i
$483$		0			0
$484$	−1.29470e27	+	6.42045e27i	−0.0834245	+	0.413703i
$485$	−3.96919e28			−2.50273
$486$		0			0
$487$			4.72266e27i			0.285189i	0.989781	+	0.142594i	$0.0455445\pi$
$487$			4.72266e27i			0.285189i	−0.989781	+	0.142594i	$0.954456\pi$
$488$	−3.94777e27	−	7.45650e27i	−0.233316	−	0.440684i
$489$		0			0
$490$	1.66258e28	+	2.03131e28i	0.941292	+	1.15005i
$491$		−	2.29570e28i		−	1.27221i	−0.771601	−	0.636107i	$-0.780544\pi$
$491$		−	2.29570e28i		−	1.27221i	0.771601	−	0.636107i	$-0.219456\pi$
$492$		0			0
$493$		−	2.58012e27i		−	0.137008i
$494$	6.26038e27	−	5.12397e27i	0.325438	−	0.266363i
$495$		0			0
$496$	1.30935e28	−	3.11452e28i	0.652374	−	1.55179i
$497$		−	5.35890e27i		−	0.261417i
$498$		0			0
$499$	−1.92349e28			−0.899566			−0.449783	−	0.893138i	$-0.648499\pi$
$499$	−1.92349e28			−0.899566			−0.449783	+	0.893138i	$0.648499\pi$
$500$	4.32245e27	−	2.14351e28i	0.197945	−	0.981612i
$501$		0			0
$502$	−1.98869e28	+	1.62770e28i	−0.873329	+	0.714799i
$503$	1.25571e28			0.540038			0.270019	−	0.962855i	$-0.412970\pi$
$503$	1.25571e28			0.540038			0.270019	+	0.962855i	$0.412970\pi$
$504$		0			0
$505$	−7.13713e27			−0.294418
$506$	2.72891e28	−	2.23355e28i	1.10258	−	0.902432i
$507$		0			0
$508$	1.44041e28	+	2.90463e27i	0.558364	+	0.112596i
$509$	−3.17220e28			−1.20455			−0.602274	−	0.798289i	$-0.705739\pi$
$509$	−3.17220e28			−1.20455			−0.602274	+	0.798289i	$0.705739\pi$
$510$		0			0
$511$			9.35086e27i			0.340747i
$512$	3.07592e27	−	2.78420e28i	0.109810	−	0.993953i
$513$		0			0
$514$	−1.85465e28	+	1.51799e28i	−0.635549	+	0.520182i
$515$			3.06944e28i			1.03058i
$516$		0			0
$517$		−	3.22152e28i		−	1.03851i
$518$	−1.01510e28	−	1.24023e28i	−0.320661	−	0.391778i
$519$		0			0
$520$	4.11169e28	+	7.76611e28i	1.24734	+	2.35596i
$521$		−	2.03282e28i		−	0.604371i	−0.953249	−	0.302185i	$-0.902284\pi$
$521$		−	2.03282e28i		−	0.604371i	0.953249	−	0.302185i	$-0.0977162\pi$
$522$		0			0
$523$	−1.28427e28			−0.366765			−0.183383	−	0.983042i	$-0.558705\pi$
$523$	−1.28427e28			−0.366765			−0.183383	+	0.983042i	$0.558705\pi$
$524$	−9.16681e27	−	1.84851e27i	−0.256590	−	0.0517421i
$525$		0			0
$526$	1.87905e28	+	2.29579e28i	0.505344	+	0.617420i
$527$	−6.68704e28			−1.76288
$528$		0			0
$529$	9.91684e28			2.51240
$530$	3.31488e27	+	4.05006e27i	0.0823325	+	0.100592i
$531$		0			0
$532$	2.99506e27	+	6.03963e26i	0.0715045	+	0.0144191i
$533$	−1.26682e29			−2.96538
$534$		0			0
$535$			6.19102e28i			1.39331i
$536$	2.21800e28	−	1.17430e28i	0.489475	−	0.259148i
$537$		0			0
$538$	2.12072e28	+	2.59106e28i	0.450059	+	0.549874i
$539$		−	3.35465e28i		−	0.698177i
$540$		0			0
$541$		−	5.54209e28i		−	1.10944i	−0.832038	−	0.554718i	$-0.812826\pi$
$541$		−	5.54209e28i		−	1.10944i	0.832038	−	0.554718i	$-0.187174\pi$
$542$	3.07232e28	−	2.51462e28i	0.603218	−	0.493720i
$543$		0			0
$544$	−5.31594e28	+	1.57441e28i	−1.00413	+	0.297392i
$545$		−	2.68662e28i		−	0.497787i
$546$		0			0
$547$	4.99558e28			0.890675			0.445337	−	0.895363i	$-0.353084\pi$
$547$	4.99558e28			0.890675			0.445337	+	0.895363i	$0.353084\pi$
$548$	3.37134e28	+	6.79841e27i	0.589667	+	0.118908i
$549$		0			0
$550$	−5.65726e28	+	4.63033e28i	−0.952352	+	0.779478i
$551$	2.02222e27			0.0333992
$552$		0			0
$553$	−1.70485e28			−0.271064
$554$	−8.71704e27	+	7.13469e27i	−0.135993	+	0.111307i
$555$		0			0
$556$	1.87116e28	−	9.27912e28i	0.281077	−	1.39387i
$557$	9.55294e28			1.40818			0.704089	−	0.710111i	$-0.251355\pi$
$557$	9.55294e28			1.40818			0.704089	+	0.710111i	$0.251355\pi$
$558$		0			0
$559$		−	1.77659e29i		−	2.52211i
$560$	−1.28617e28	+	3.05939e28i	−0.179195	+	0.426247i
$561$		0			0
$562$	−7.88249e28	+	6.45163e28i	−1.05787	+	0.865841i
$563$			1.16802e29i			1.53855i	0.638917	+	0.769276i	$0.279383\pi$
$563$			1.16802e29i			1.53855i	−0.638917	+	0.769276i	$0.720617\pi$
$564$		0			0
$565$			2.81444e27i			0.0357176i
$566$	2.03438e27	+	2.48557e27i	0.0253431	+	0.0309637i
$567$		0			0
$568$	−6.73571e28	+	3.56616e28i	−0.808585	+	0.428098i
$569$			6.35273e28i			0.748655i	0.927297	+	0.374327i	$0.122126\pi$
$569$			6.35273e28i			0.748655i	−0.927297	+	0.374327i	$0.877874\pi$
$570$		0			0
$571$	−2.25081e28			−0.255658			−0.127829	−	0.991796i	$-0.540801\pi$
$571$	−2.25081e28			−0.255658			−0.127829	+	0.991796i	$0.540801\pi$
$572$	2.21991e28	−	1.10086e29i	0.247558	−	1.22764i
$573$		0			0
$574$	−3.03033e28	−	3.70241e28i	−0.325773	−	0.398024i
$575$	−2.87412e29			−3.03384
$576$		0			0
$577$	−5.30213e28			−0.539640			−0.269820	−	0.962911i	$-0.586964\pi$
$577$	−5.30213e28			−0.539640			−0.269820	+	0.962911i	$0.586964\pi$
$578$	6.12984e27	+	7.48933e27i	0.0612642	+	0.0748515i
$579$		0			0
$580$	−4.34201e27	+	2.15321e28i	−0.0418502	+	0.207536i
$581$	−6.72564e27			−0.0636625
$582$		0			0
$583$		−	6.68855e27i		−	0.0610678i
$584$	1.17533e29	−	6.22267e28i	1.05396	−	0.558010i
$585$		0			0
$586$	8.52438e28	+	1.04149e29i	0.737459	+	0.901015i
$587$			7.08909e28i			0.602408i	0.953560	+	0.301204i	$0.0973884\pi$
$587$			7.08909e28i			0.602408i	−0.953560	+	0.301204i	$0.902612\pi$
$588$		0			0
$589$		−	5.24110e28i		−	0.429746i
$590$	1.00835e29	−	8.25311e28i	0.812204	−	0.664770i
$591$		0			0
$592$	−8.83359e28	+	2.10123e29i	−0.686688	+	1.63341i
$593$			1.34080e29i			1.02397i	0.858993	+	0.511987i	$0.171090\pi$
$593$			1.34080e29i			1.02397i	−0.858993	+	0.511987i	$0.828910\pi$
$594$		0			0
$595$	6.56868e28			0.484228
$596$	−4.77002e28	+	2.36546e29i	−0.345490	+	1.71329i
$597$		0			0
$598$	3.41660e29	−	2.79640e29i	2.38908	−	1.95541i
$599$	2.42398e29			1.66551			0.832754	−	0.553642i	$-0.186763\pi$
$599$	2.42398e29			1.66551			0.832754	+	0.553642i	$0.186763\pi$
$600$		0			0
$601$	−2.29994e29			−1.52593			−0.762965	−	0.646439i	$-0.776257\pi$
$601$	−2.29994e29			−1.52593			−0.762965	+	0.646439i	$0.776257\pi$
$602$	5.19227e28	−	4.24975e28i	0.338527	−	0.277077i
$603$		0			0
$604$	−1.80966e28	−	3.64924e27i	−0.113949	−	0.0229781i
$605$	−1.10364e29			−0.682959
$606$		0			0
$607$		−	1.44418e29i		−	0.863256i	−0.902052	−	0.431628i	$-0.857939\pi$
$607$		−	1.44418e29i		−	0.863256i	0.902052	−	0.431628i	$-0.142061\pi$
$608$	−1.23397e28	−	4.16647e28i	−0.0724968	−	0.244783i
$609$		0			0
$610$	1.10015e29	−	9.00447e28i	0.624437	−	0.511087i
$611$		−	4.03335e29i		−	2.25026i
$612$		0			0
$613$			1.80810e29i			0.974736i	0.873197	+	0.487368i	$0.162043\pi$
$613$			1.80810e29i			0.974736i	−0.873197	+	0.487368i	$0.837957\pi$
$614$	1.56835e29	+	1.91619e29i	0.831144	+	1.01548i
$615$		0			0
$616$	3.74837e28	−	1.98454e28i	0.191975	−	0.101639i
$617$		−	5.57508e28i		−	0.280709i	−0.990101	−	0.140355i	$-0.955176\pi$
$617$		−	5.57508e28i		−	0.280709i	0.990101	−	0.140355i	$-0.0448243\pi$
$618$		0			0
$619$	−7.64671e28			−0.372154			−0.186077	−	0.982535i	$-0.559577\pi$
$619$	−7.64671e28			−0.372154			−0.186077	+	0.982535i	$0.559577\pi$
$620$	5.58060e29	+	1.12534e29i	2.67035	+	0.538484i
$621$		0			0
$622$	−1.60173e29	−	1.95697e29i	−0.740952	−	0.905283i
$623$	−3.85065e28			−0.175150
$624$		0			0
$625$	3.85595e26			0.00169587
$626$	−1.13424e29	−	1.38579e29i	−0.490538	−	0.599331i
$627$		0			0
$628$	−1.61115e29	−	3.24892e28i	−0.673843	−	0.135882i
$629$	4.51145e29			1.85560
$630$		0			0
$631$		−	1.93905e28i		−	0.0771404i	−0.999256	−	0.0385702i	$-0.987720\pi$
$631$		−	1.93905e28i		−	0.0771404i	0.999256	−	0.0385702i	$-0.0122803\pi$
$632$	1.13452e29	+	2.14286e29i	0.443897	+	0.838426i
$633$		0			0
$634$	1.75792e29	+	2.14779e29i	0.665366	+	0.812932i
$635$			2.47598e29i			0.921771i
$636$		0			0
$637$		−	4.20003e29i		−	1.51282i
$638$	2.17231e28	−	1.77798e28i	0.0769669	−	0.0629956i
$639$		0			0
$640$	4.70132e29	−	4.19302e28i	1.61187	−	0.143760i
$641$			2.85959e29i			0.964482i	0.876038	+	0.482241i	$0.160177\pi$
$641$			2.85959e29i			0.964482i	−0.876038	+	0.482241i	$0.839823\pi$
$642$		0			0
$643$	3.08405e29			1.00671			0.503357	−	0.864079i	$-0.332098\pi$
$643$	3.08405e29			1.00671			0.503357	+	0.864079i	$0.332098\pi$
$644$	1.63455e29	+	3.29612e28i	0.524925	+	0.105853i
$645$		0			0
$646$	−6.65554e28	+	5.44740e28i	−0.206891	+	0.169336i
$647$	−4.46851e29			−1.36668			−0.683341	−	0.730099i	$-0.739474\pi$
$647$	−4.46851e29			−1.36668			−0.683341	+	0.730099i	$0.739474\pi$
$648$		0			0
$649$	−1.66526e29			−0.493075
$650$	−7.08289e29	+	5.79718e29i	−2.06358	+	1.68899i
$651$		0			0
$652$	3.21283e28	−	1.59325e29i	0.0906334	−	0.449453i
$653$	1.04025e29			0.288769			0.144385	−	0.989522i	$-0.453880\pi$
$653$	1.04025e29			0.288769			0.144385	+	0.989522i	$0.453880\pi$
$654$		0			0
$655$		−	1.57572e29i		−	0.423590i
$656$	−2.63705e29	+	6.27271e29i	−0.697636	+	1.65945i
$657$		0			0
$658$	1.17878e29	−	9.64807e28i	0.302039	−	0.247211i
$659$			1.22900e29i			0.309924i	0.987920	+	0.154962i	$0.0495255\pi$
$659$			1.22900e29i			0.309924i	−0.987920	+	0.154962i	$0.950474\pi$
$660$		0			0
$661$		−	3.76637e29i		−	0.920043i	−0.887908	−	0.460022i	$-0.847842\pi$
$661$		−	3.76637e29i		−	0.920043i	0.887908	−	0.460022i	$-0.152158\pi$
$662$	1.80303e29	+	2.20291e29i	0.433505	+	0.529649i
$663$		0			0
$664$	4.47567e28	+	8.45360e28i	0.104254	+	0.196914i
$665$			5.14833e28i			0.118043i
$666$		0			0
$667$	1.10362e29			0.245188
$668$	1.56547e29	−	7.76318e29i	0.342366	−	1.69780i
$669$		0			0
$670$	2.67845e29	+	3.27248e29i	0.567673	+	0.693573i
$671$	−1.81687e29			−0.379085
$672$		0			0
$673$	8.72274e28			0.176398			0.0881992	−	0.996103i	$-0.471889\pi$
$673$	8.72274e28			0.176398			0.0881992	+	0.996103i	$0.471889\pi$
$674$	−2.50276e29	−	3.05783e29i	−0.498300	−	0.608814i
$675$		0			0
$676$	1.75512e29	−	8.70365e29i	0.338739	−	1.67981i
$677$	5.63852e29			1.07148			0.535740	−	0.844383i	$-0.320033\pi$
$677$	5.63852e29			1.07148			0.535740	+	0.844383i	$0.320033\pi$
$678$		0			0
$679$			2.39853e29i			0.441889i
$680$	−4.37123e29	−	8.25631e29i	−0.792975	−	1.49776i
$681$		0			0
$682$	−4.60810e29	−	5.63009e29i	−0.810561	−	0.990329i
$683$		−	4.52405e28i		−	0.0783628i	−0.999232	−	0.0391814i	$-0.987525\pi$
$683$		−	4.52405e28i		−	0.0783628i	0.999232	−	0.0391814i	$-0.0124750\pi$
$684$		0			0
$685$			5.79514e29i			0.973448i
$686$	2.56412e29	−	2.09867e29i	0.424165	−	0.347169i
$687$		0			0
$688$	−8.79687e29	−	3.69821e29i	−1.41140	−	0.593353i
$689$		−	8.37408e28i		−	0.132323i
$690$		0			0
$691$	−5.03910e28			−0.0772384			−0.0386192	−	0.999254i	$-0.512296\pi$
$691$	−5.03910e28			−0.0772384			−0.0386192	+	0.999254i	$0.512296\pi$
$692$	−3.20744e28	+	1.59057e29i	−0.0484222	+	0.240126i
$693$		0			0
$694$	2.34819e29	−	1.92194e29i	0.343921	−	0.281491i
$695$	1.59503e30			2.30106
$696$		0			0
$697$	1.34678e30			1.88518
$698$	8.50745e29	−	6.96314e29i	1.17305	−	0.960115i
$699$		0			0
$700$	−3.38856e29	−	6.83313e28i	−0.453405	−	0.0914304i
$701$	−6.61949e29			−0.872540			−0.436270	−	0.899816i	$-0.643701\pi$
$701$	−6.61949e29			−0.872540			−0.436270	+	0.899816i	$0.643701\pi$
$702$		0			0
$703$			3.53594e29i			0.452349i
$704$	−4.98882e29	−	3.39077e29i	−0.628760	−	0.427352i
$705$		0			0
$706$	−7.75787e29	+	6.34964e29i	−0.949059	+	0.776783i
$707$			4.31289e28i			0.0519833i
$708$		0			0
$709$		−	8.70415e29i		−	1.01845i	−0.860633	−	0.509227i	$-0.829932\pi$
$709$		−	8.70415e29i		−	1.01845i	0.860633	−	0.509227i	$-0.170068\pi$
$710$	−8.13405e29	−	9.93803e29i	−0.937765	−	1.14574i
$711$		0			0
$712$	2.56247e29	+	4.83996e29i	0.286826	+	0.541754i
$713$		−	2.86032e30i		−	3.15482i
$714$		0			0
$715$	1.89231e30			2.02665
$716$	−1.38864e29	−	2.80023e28i	−0.146556	−	0.0295534i
$717$		0			0
$718$	−3.64294e29	−	4.45088e29i	−0.373375	−	0.456183i
$719$	2.97307e29			0.300297			0.150149	−	0.988663i	$-0.452025\pi$
$719$	2.97307e29			0.300297			0.150149	+	0.988663i	$0.452025\pi$
$720$		0			0
$721$	1.85483e29			0.181963
$722$	6.12395e29	+	7.48213e29i	0.592095	+	0.723411i
$723$		0			0
$724$	−3.56153e29	−	7.18192e28i	−0.334489	−	0.0674506i
$725$	−2.28790e29			−0.211782
$726$		0			0
$727$			1.46339e30i			1.31598i	0.753028	+	0.657988i	$0.228592\pi$
$727$			1.46339e30i			1.31598i	−0.753028	+	0.657988i	$0.771408\pi$
$728$	4.69297e29	−	2.48465e29i	0.415976	−	0.220234i
$729$		0			0
$730$	1.41933e30	+	1.73411e30i	1.22234	+	1.49344i
$731$			1.88873e30i			1.60339i
$732$		0			0
$733$			1.55879e30i			1.28587i	0.765921	+	0.642935i	$0.222284\pi$
$733$			1.55879e30i			1.28587i	−0.765921	+	0.642935i	$0.777716\pi$
$734$	−1.84275e30	+	1.50825e30i	−1.49850	+	1.22649i
$735$		0			0
$736$	−6.73440e29	−	2.27385e30i	−0.532209	−	1.79698i
$737$		−	5.40441e29i		−	0.421056i
$738$		0			0
$739$	−1.25721e30			−0.952013			−0.476006	−	0.879442i	$-0.657916\pi$
$739$	−1.25721e30			−0.952013			−0.476006	+	0.879442i	$0.657916\pi$
$740$	−3.76499e30	−	7.59221e29i	−2.81080	−	0.566807i
$741$		0			0
$742$	2.44740e28	−	2.00314e28i	0.0177609	−	0.0145369i
$743$	1.92148e30			1.37484			0.687420	−	0.726260i	$-0.258743\pi$
$743$	1.92148e30			1.37484			0.687420	+	0.726260i	$0.258743\pi$
$744$		0			0
$745$	−4.06609e30			−2.82837
$746$	−1.30532e30	+	1.06837e30i	−0.895280	+	0.732765i
$747$		0			0
$748$	−2.36003e29	+	1.17034e30i	−0.157380	+	0.780452i
$749$	3.74116e29			0.246007
$750$		0			0
$751$			1.11985e30i			0.716043i	0.933713	+	0.358022i	$0.116549\pi$
$751$			1.11985e30i			0.716043i	−0.933713	+	0.358022i	$0.883451\pi$
$752$	−1.99713e30	−	8.39594e29i	−1.25927	−	0.529398i
$753$		0			0
$754$	2.71973e29	−	2.22603e29i	0.166773	−	0.136500i
$755$		−	3.11070e29i		−	0.188112i
$756$		0			0
$757$		−	7.30706e29i		−	0.429770i	−0.976639	−	0.214885i	$-0.931062\pi$
$757$		−	7.30706e29i		−	0.429770i	0.976639	−	0.214885i	$-0.0689377\pi$
$758$	1.58936e30	+	1.94185e30i	0.921926	+	1.12639i
$759$		0			0
$760$	6.47105e29	−	3.42603e29i	0.365117	−	0.193308i
$761$			2.46791e30i			1.37338i	0.726951	+	0.686689i	$0.240937\pi$
$761$			2.46791e30i			1.37338i	−0.726951	+	0.686689i	$0.759063\pi$
$762$		0			0
$763$	−1.62349e29			−0.0878908
$764$	−1.96829e29	+	9.76078e29i	−0.105101	+	0.521200i
$765$		0			0
$766$	6.90297e29	+	8.43392e29i	0.358619	+	0.438155i
$767$	−2.08491e30			−1.06840
$768$		0			0
$769$	1.09882e30			0.547896			0.273948	−	0.961744i	$-0.411670\pi$
$769$	1.09882e30			0.547896			0.273948	+	0.961744i	$0.411670\pi$
$770$	4.52654e29	+	5.53044e29i	0.222645	+	0.272024i
$771$		0			0
$772$	2.66604e29	−	1.32209e30i	0.127610	−	0.632821i
$773$	2.58219e30			1.21928			0.609641	−	0.792678i	$-0.291314\pi$
$773$	2.58219e30			1.21928			0.609641	+	0.792678i	$0.291314\pi$
$774$		0			0
$775$			5.92969e30i			2.72498i
$776$	3.01477e30	−	1.59614e30i	1.36680	−	0.723641i
$777$		0			0
$778$	−1.56580e30	−	1.91307e30i	−0.690956	−	0.844198i
$779$			1.05557e30i			0.459561i
$780$		0			0
$781$			1.64124e30i			0.695561i
$782$	−3.63226e30	+	2.97292e30i	−1.51882	+	1.24312i
$783$		0			0
$784$	−2.07966e30	−	8.74291e29i	−0.846591	−	0.355908i
$785$		−	2.76947e30i		−	1.11241i
$786$		0			0
$787$	−3.72973e30			−1.45862			−0.729310	−	0.684183i	$-0.760159\pi$
$787$	−3.72973e30			−1.45862			−0.729310	+	0.684183i	$0.760159\pi$
$788$	−1.25175e29	+	6.20743e29i	−0.0483049	+	0.239545i
$789$		0			0
$790$	−3.16163e30	+	2.58772e30i	−1.18803	+	0.972373i
$791$	1.70073e28			0.00630641
$792$		0			0
$793$	−2.27472e30			−0.821408
$794$	−1.92293e30	+	1.57387e30i	−0.685248	+	0.560859i
$795$		0			0
$796$	4.11733e30	+	8.30271e29i	1.42899	+	0.288159i
$797$	2.62142e30			0.897893			0.448946	−	0.893559i	$-0.351799\pi$
$797$	2.62142e30			0.897893			0.448946	+	0.893559i	$0.351799\pi$
$798$		0			0
$799$			4.28794e30i			1.43056i
$800$	1.39610e30	+	4.71388e30i	0.459696	+	1.55215i
$801$		0			0
$802$	2.59380e30	−	2.12297e30i	0.831967	−	0.680945i
$803$		−	2.86383e30i		−	0.906638i
$804$		0			0
$805$			2.80970e30i			0.866568i
$806$	−5.76934e30	−	7.04888e30i	−1.75634	−	2.14586i
$807$		0			0
$808$	5.42096e29	−	2.87007e29i	0.160789	−	0.0851283i
$809$		−	4.45244e30i		−	1.30358i	−0.758398	−	0.651792i	$-0.774018\pi$
$809$		−	4.45244e30i		−	1.30358i	0.758398	−	0.651792i	$-0.225982\pi$
$810$		0			0
$811$	1.88510e30			0.537793			0.268896	−	0.963169i	$-0.413341\pi$
$811$	1.88510e30			0.537793			0.268896	+	0.963169i	$0.413341\pi$
$812$	1.30116e29	+	2.62383e28i	0.0366431	+	0.00738919i
$813$		0			0
$814$	3.10888e30	+	3.79838e30i	0.853194	+	1.04242i
$815$	2.73870e30			0.741976
$816$		0			0
$817$	−1.48033e30			−0.390866
$818$	6.11495e29	+	7.47114e29i	0.159398	+	0.194750i
$819$		0			0
$820$	−1.12395e31	−	2.26647e30i	−2.85562	−	0.575844i
$821$	−1.84759e29			−0.0463449			−0.0231724	−	0.999731i	$-0.507377\pi$
$821$	−1.84759e29			−0.0463449			−0.0231724	+	0.999731i	$0.507377\pi$
$822$		0			0
$823$		−	1.84600e30i		−	0.451372i	−0.974200	−	0.225686i	$-0.927538\pi$
$823$		−	1.84600e30i		−	0.451372i	0.974200	−	0.225686i	$-0.0724623\pi$
$824$	−1.23432e30	−	2.33137e30i	−0.297984	−	0.562829i
$825$		0			0
$826$	−4.98726e29	−	6.09334e29i	−0.117374	−	0.143405i
$827$		−	8.49465e30i		−	1.97396i	−0.160851	−	0.986979i	$-0.551424\pi$
$827$		−	8.49465e30i		−	1.97396i	0.160851	−	0.986979i	$-0.448576\pi$
$828$		0			0
$829$		−	5.13084e30i		−	1.16243i	−0.813751	−	0.581214i	$-0.802578\pi$
$829$		−	5.13084e30i		−	1.16243i	0.813751	−	0.581214i	$-0.197422\pi$
$830$	−1.24726e30	+	1.02086e30i	−0.279022	+	0.228373i
$831$		0			0
$832$	−6.24601e30	−	4.24525e30i	−1.36241	−	0.925994i
$833$			4.46514e30i			0.961750i
$834$		0			0
$835$	1.33444e31			2.80280
$836$	−9.17279e29	−	1.84972e29i	−0.190255	−	0.0383654i
$837$		0			0
$838$	1.55764e30	−	1.27489e30i	0.315069	−	0.257877i
$839$	−3.74608e30			−0.748302			−0.374151	−	0.927368i	$-0.622066\pi$
$839$	−3.74608e30			−0.748302			−0.374151	+	0.927368i	$0.622066\pi$
$840$		0			0
$841$	−5.04499e30			−0.982884
$842$	−3.33659e29	+	2.73092e29i	−0.0641987	+	0.0525451i
$843$		0			0
$844$	−1.85806e30	+	9.21413e30i	−0.348709	+	1.72925i
$845$	1.49611e31			2.77311
$846$		0			0
$847$			6.66915e29i			0.120585i
$848$	−4.14645e29	−	1.74317e29i	−0.0740492	−	0.0311304i
$849$		0			0
$850$	7.52997e30	−	6.16310e30i	1.31188	−	1.07374i
$851$			1.92973e31i			3.32076i
$852$		0			0
$853$			4.21181e30i			0.707137i	0.935409	+	0.353569i	$0.115032\pi$
$853$			4.21181e30i			0.707137i	−0.935409	+	0.353569i	$0.884968\pi$
$854$	−5.44130e29	−	6.64808e29i	−0.0902391	−	0.110253i
$855$		0			0
$856$	−2.48961e30	−	4.70235e30i	−0.402863	−	0.760922i
$857$		−	4.95103e29i		−	0.0791402i	−0.999217	−	0.0395701i	$-0.987401\pi$
$857$		−	4.95103e29i		−	0.0791402i	0.999217	−	0.0395701i	$-0.0125988\pi$
$858$		0			0
$859$	6.65451e30			1.03798			0.518989	−	0.854781i	$-0.326309\pi$
$859$	6.65451e30			1.03798			0.518989	+	0.854781i	$0.326309\pi$
$860$	3.17850e30	−	1.57623e31i	0.489767	−	2.42876i
$861$		0			0
$862$	4.59453e30	+	5.61352e30i	0.690900	+	0.844129i
$863$	−5.33488e30			−0.792522			−0.396261	−	0.918138i	$-0.629693\pi$
$863$	−5.33488e30			−0.792522			−0.396261	+	0.918138i	$0.629693\pi$
$864$		0			0
$865$	−2.73410e30			−0.396411
$866$	−6.66820e30	−	8.14709e30i	−0.955148	−	1.16698i
$867$		0			0
$868$	6.80032e29	−	3.37229e30i	0.0950763	−	0.471485i
$869$	5.22134e30			0.721230
$870$		0			0
$871$		−	6.76633e30i		−	0.912352i
$872$	1.08038e30	+	2.04061e30i	0.143931	+	0.271854i
$873$		0			0
$874$	−2.33008e30	−	2.84685e30i	−0.303041	−	0.370250i
$875$		−	2.22654e30i		−	0.286118i
$876$		0			0
$877$		−	3.26171e30i		−	0.409214i	−0.978844	−	0.204607i	$-0.934408\pi$
$877$		−	3.26171e30i		−	0.409214i	0.978844	−	0.204607i	$-0.0655916\pi$
$878$	−1.97586e30	+	1.61719e30i	−0.244942	+	0.200479i
$879$		0			0
$880$	3.93908e30	−	9.36982e30i	0.476790	−	1.13413i
$881$		−	5.69874e29i		−	0.0681603i	−0.999419	−	0.0340802i	$-0.989150\pi$
$881$		−	5.69874e29i		−	0.0681603i	0.999419	−	0.0340802i	$-0.0108502\pi$
$882$		0			0
$883$	1.05180e31			1.22842			0.614211	−	0.789142i	$-0.289474\pi$
$883$	1.05180e31			1.22842			0.614211	+	0.789142i	$0.289474\pi$
$884$	−2.95476e30	+	1.46527e31i	−0.341015	+	1.69110i
$885$		0			0
$886$	4.53673e30	−	3.71321e30i	0.511316	−	0.418500i
$887$	−1.02411e31			−1.14064			−0.570319	−	0.821423i	$-0.693181\pi$
$887$	−1.02411e31			−1.14064			−0.570319	+	0.821423i	$0.693181\pi$
$888$		0			0
$889$	1.49621e30			0.162751
$890$	−7.14100e30	+	5.84474e30i	−0.767651	+	0.628304i
$891$		0			0
$892$	−6.09131e30	−	1.22833e30i	−0.639557	−	0.128969i
$893$	−3.36075e30			−0.348736
$894$		0			0
$895$		−	2.38699e30i		−	0.241941i
$896$	−2.53379e29	−	2.84095e30i	−0.0253827	−	0.284597i
$897$		0			0
$898$	1.59555e30	−	1.30592e30i	0.156138	−	0.127795i
$899$		−	2.27692e30i		−	0.220227i
$900$		0			0
$901$			8.90266e29i			0.0841220i
$902$	9.28082e30	+	1.13391e31i	0.866797	+	1.05904i
$903$		0			0
$904$	−1.13178e29	−	2.13768e29i	−0.0103274	−	0.0195063i
$905$		−	6.12205e30i		−	0.552188i
$906$		0			0
$907$	1.14790e31			1.01165			0.505823	−	0.862637i	$-0.331189\pi$
$907$	1.14790e31			1.01165			0.505823	+	0.862637i	$0.331189\pi$
$908$	1.18526e31	+	2.39012e30i	1.03256	+	0.208218i
$909$		0			0
$910$	5.66723e30	+	6.92412e30i	0.482432	+	0.589427i
$911$	1.85075e31			1.55742			0.778709	−	0.627385i	$-0.215875\pi$
$911$	1.85075e31			1.55742			0.778709	+	0.627385i	$0.215875\pi$
$912$		0			0
$913$	2.05982e30			0.169389
$914$	−1.79115e29	−	2.18840e29i	−0.0145612	−	0.0177906i
$915$		0			0
$916$	1.72409e30	+	3.47669e29i	0.136980	+	0.0276225i
$917$	−9.52189e29			−0.0747903
$918$		0			0
$919$		−	4.36965e30i		−	0.335454i	−0.985833	−	0.167727i	$-0.946357\pi$
$919$		−	4.36965e30i		−	0.335454i	0.985833	−	0.167727i	$-0.0536428\pi$
$920$	3.53157e31	−	1.86975e31i	2.68037	−	1.41910i
$921$		0			0
$922$	1.02662e31	+	1.25430e31i	0.761612	+	0.930524i
$923$			2.05483e31i			1.50716i
$924$		0			0
$925$		−	4.00050e31i		−	2.86831i
$926$	−8.52025e30	+	6.97363e30i	−0.604000	+	0.494360i
$927$		0			0
$928$	−5.36082e29	−	1.81006e30i	−0.0371516	−	0.125441i
$929$		−	2.00462e31i		−	1.37362i	−0.726838	−	0.686809i	$-0.759011\pi$
$929$		−	2.00462e31i		−	1.37362i	0.726838	−	0.686809i	$-0.240989\pi$
$930$		0			0
$931$	−3.49964e30			−0.234451
$932$	−4.92904e28	−	9.93956e27i	−0.00326509	−	0.000658416i
$933$		0			0
$934$	1.45006e31	−	1.18684e31i	0.939172	−	0.768690i
$935$	−2.01175e31			−1.28840
$936$		0			0
$937$	−2.03419e31			−1.27387			−0.636935	−	0.770918i	$-0.719798\pi$
$937$	−2.03419e31			−1.27387			−0.636935	+	0.770918i	$0.719798\pi$
$938$	1.97752e30	−	1.61856e30i	0.122459	−	0.100230i
$939$		0			0
$940$	7.21606e30	−	3.57846e31i	0.436976	−	2.16697i
$941$	5.39585e30			0.323124			0.161562	−	0.986863i	$-0.448347\pi$
$941$	5.39585e30			0.323124			0.161562	+	0.986863i	$0.448347\pi$
$942$		0			0
$943$			5.76076e31i			3.37370i
$944$	−4.34001e30	+	1.03235e31i	−0.251353	+	0.597889i
$945$		0			0
$946$	−1.59020e31	+	1.30154e31i	−0.900733	+	0.737228i
$947$		−	2.34321e31i		−	1.31261i	−0.754496	−	0.656305i	$-0.772118\pi$
$947$		−	2.34321e31i		−	1.31261i	0.754496	−	0.656305i	$-0.227882\pi$
$948$		0			0
$949$		−	3.58552e31i		−	1.96452i
$950$	4.83045e30	+	5.90176e30i	0.261752	+	0.319804i
$951$		0			0
$952$	−4.98919e30	+	2.64148e30i	−0.264449	+	0.140010i
$953$		−	1.39365e31i		−	0.730600i	−0.930890	−	0.365300i	$-0.880966\pi$
$953$		−	1.39365e31i		−	0.730600i	0.930890	−	0.365300i	$-0.119034\pi$
$954$		0			0
$955$	−1.67782e31			−0.860419
$956$	3.39924e30	−	1.68569e31i	0.172415	−	0.855007i
$957$		0			0
$958$	1.15254e31	+	1.40815e31i	0.571897	+	0.698733i
$959$	3.50193e30			0.171875
$960$		0			0
$961$	−3.81867e31			−1.83365
$962$	3.89232e31	+	4.75557e31i	1.84872	+	2.25873i
$963$		0			0
$964$	4.31183e30	−	2.13824e31i	0.200379	−	0.993684i
$965$	2.27260e31			1.04469
$966$		0			0
$967$		−	1.13822e31i		−	0.511974i	−0.966680	−	0.255987i	$-0.917600\pi$
$967$		−	1.13822e31i		−	0.511974i	0.966680	−	0.255987i	$-0.0824005\pi$
$968$	8.38260e30	−	4.43809e30i	0.372982	−	0.197471i
$969$		0			0
$970$	3.64064e31	+	4.44806e31i	1.58516	+	1.93672i
$971$			4.03311e31i			1.73716i	0.495553	+	0.868578i	$0.334965\pi$
$971$			4.03311e31i			1.73716i	−0.495553	+	0.868578i	$0.665035\pi$
$972$		0			0
$973$		−	9.63855e30i		−	0.406281i
$974$	5.29244e30	−	4.33174e30i	0.220692	−	0.180631i
$975$		0			0
$976$	−4.73512e30	+	1.12633e31i	−0.193245	+	0.459668i
$977$			2.88792e31i			1.16598i	0.812479	+	0.582991i	$0.198118\pi$
$977$			2.88792e31i			1.16598i	−0.812479	+	0.582991i	$0.801882\pi$
$978$		0			0
$979$	1.17931e31			0.466027
$980$	7.51427e30	−	3.72634e31i	0.293774	−	1.45683i
$981$		0			0
$982$	−2.57267e31	+	2.10567e31i	−0.984497	+	0.805787i
$983$	−2.28124e31			−0.863694			−0.431847	−	0.901947i	$-0.642138\pi$
$983$	−2.28124e31			−0.863694			−0.431847	+	0.901947i	$0.642138\pi$
$984$		0			0
$985$	−1.06702e31			−0.395451
$986$	−2.89140e30	+	2.36654e30i	−0.106023	+	0.0867775i
$987$		0			0
$988$	−1.14843e31	−	2.31585e30i	−0.412248	−	0.0831310i
$989$	−8.07890e31			−2.86940
$990$		0			0
$991$		−	1.64480e31i		−	0.571927i	−0.958241	−	0.285963i	$-0.907686\pi$
$991$		−	1.64480e31i		−	0.571927i	0.958241	−	0.285963i	$-0.0923136\pi$
$992$	−4.69124e31	+	1.38939e31i	−1.61404	+	0.478028i
$993$		0			0
$994$	−6.00544e30	+	4.91531e30i	−0.202296	+	0.165575i
$995$			7.07744e31i			2.35903i
$996$		0			0
$997$		−	1.69141e31i		−	0.552013i	−0.961156	−	0.276006i	$-0.910989\pi$
$997$		−	1.69141e31i		−	0.552013i	0.961156	−	0.276006i	$-0.0890111\pi$
$998$	1.76427e31	+	2.15555e31i	0.569762	+	0.696125i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.22.f.a.35.25	✓	84
3.2	odd	2	inner	72.22.f.a.35.60	yes	84
8.3	odd	2	inner	72.22.f.a.35.59	yes	84
24.11	even	2	inner	72.22.f.a.35.26	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.22.f.a.35.25	✓	84	1.1	even	1	trivial
72.22.f.a.35.26	yes	84	24.11	even	2	inner
72.22.f.a.35.59	yes	84	8.3	odd	2	inner
72.22.f.a.35.60	yes	84	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-917.224 - 1120.65i) q^{2} +(-414552. + 2.05577e6i) q^{4} -3.53375e7 q^{5} +2.13540e8i q^{7} +(2.68403e9 - 1.42104e9i) q^{8} +O(q^{10})\)	\(q+(-917.224 - 1120.65i) q^{2} +(-414552. + 2.05577e6i) q^{4} -3.53375e7 q^{5} +2.13540e8i q^{7} +(2.68403e9 - 1.42104e9i) q^{8} +(3.24124e10 + 3.96009e10i) q^{10} -6.53997e10i q^{11} -8.18805e11i q^{13} +(2.39303e11 - 1.95864e11i) q^{14} +(-4.05434e12 - 1.70445e12i) q^{16} +8.70488e12i q^{17} -6.82262e12 q^{19} +(1.46492e13 - 7.26458e13i) q^{20} +(-7.32900e13 + 5.99861e13i) q^{22} -3.72344e14 q^{23} +7.71900e14 q^{25} +(-9.17592e14 + 7.51027e14i) q^{26} +(-4.38990e14 - 8.85235e13i) q^{28} -2.96399e14 q^{29} +7.68194e15i q^{31} +(1.80865e15 + 6.10685e15i) q^{32} +(9.75511e15 - 7.98433e15i) q^{34} -7.54597e15i q^{35} -5.18267e16i q^{37} +(6.25787e15 + 7.64576e15i) q^{38} +(-9.48469e16 + 5.02158e16i) q^{40} -1.54716e17i q^{41} +2.16974e17 q^{43} +(1.34447e17 + 2.71116e16i) q^{44} +(3.41523e17 + 4.17266e17i) q^{46} +4.92590e17 q^{47} +5.12946e17 q^{49} +(-7.08005e17 - 8.65029e17i) q^{50} +(1.68327e18 + 3.39437e17i) q^{52} +1.02272e17 q^{53} +2.31106e18i q^{55} +(3.03448e17 + 5.73149e17i) q^{56} +(2.71864e17 + 3.32159e17i) q^{58} -2.54628e18i q^{59} -2.77810e18i q^{61} +(8.60875e18 - 7.04606e18i) q^{62} +(5.18469e18 - 7.62821e18i) q^{64} +2.89345e19i q^{65} +8.26367e18 q^{67} +(-1.78952e19 - 3.60863e18i) q^{68} +(-8.45638e18 + 6.92135e18i) q^{70} -2.50955e19 q^{71} +4.37897e19 q^{73} +(-5.80795e19 + 4.75367e19i) q^{74} +(2.82833e18 - 1.40257e19i) q^{76} +1.39655e19 q^{77} +7.98374e19i q^{79} +(1.43270e20 + 6.02309e19i) q^{80} +(-1.73382e20 + 1.41909e20i) q^{82} +3.14959e19i q^{83} -3.07609e20i q^{85} +(-1.99014e20 - 2.43152e20i) q^{86} +(-9.29352e19 - 1.75535e20i) q^{88} +1.80324e20i q^{89} +1.74848e20 q^{91} +(1.54356e20 - 7.65454e20i) q^{92} +(-4.51815e20 - 5.52020e20i) q^{94} +2.41094e20 q^{95} +1.12322e21 q^{97} +(-4.70487e20 - 5.74832e20i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2424084 q^{4}+O(q^{10}) \) 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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