LMFDB - Embedded newform 72.22.f.a.35.40

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			35.40
Character	$\chi$	$=$	72.35
Dual form			72.22.f.a.35.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-259.127 + 1424.78i) q^{2} +(-1.96286e6 - 738399. i) q^{4} +3.78460e7 q^{5} -1.95935e8i q^{7} +(1.56069e9 - 2.60531e9i) q^{8} +O(q^{10})$	\(q+(-259.127 + 1424.78i) q^{2} +(-1.96286e6 - 738399. i) q^{4} +3.78460e7 q^{5} -1.95935e8i q^{7} +(1.56069e9 - 2.60531e9i) q^{8} +(-9.80691e9 + 5.39223e10i) q^{10} -4.29505e10i q^{11} -7.25729e10i q^{13} +(2.79165e11 + 5.07721e10i) q^{14} +(3.30758e12 + 2.89875e12i) q^{16} +8.33127e12i q^{17} -2.11393e13 q^{19} +(-7.42863e13 - 2.79454e13i) q^{20} +(6.11951e13 + 1.11296e13i) q^{22} -4.93376e13 q^{23} +9.55480e14 q^{25} +(1.03401e14 + 1.88056e13i) q^{26} +(-1.44678e14 + 3.84593e14i) q^{28} -2.69501e15 q^{29} -1.12089e15i q^{31} +(-4.98717e15 + 3.96144e15i) q^{32} +(-1.18702e16 - 2.15886e15i) q^{34} -7.41535e15i q^{35} -3.66628e16i q^{37} +(5.47775e15 - 3.01188e16i) q^{38} +(5.90658e16 - 9.86003e16i) q^{40} +8.22158e16i q^{41} -2.81191e17 q^{43} +(-3.17146e16 + 8.43057e16i) q^{44} +(1.27847e16 - 7.02954e16i) q^{46} -3.37533e17 q^{47} +5.20155e17 q^{49} +(-2.47591e17 + 1.36135e18i) q^{50} +(-5.35878e16 + 1.42450e17i) q^{52} -7.67842e17 q^{53} -1.62550e18i q^{55} +(-5.10471e17 - 3.05794e17i) q^{56} +(6.98351e17 - 3.83981e18i) q^{58} +5.94464e18i q^{59} -3.41895e18i q^{61} +(1.59703e18 + 2.90454e17i) q^{62} +(-4.35188e18 - 8.13214e18i) q^{64} -2.74659e18i q^{65} +5.71427e18 q^{67} +(6.15180e18 - 1.63531e19i) q^{68} +(1.05653e19 + 1.92152e18i) q^{70} +1.23772e19 q^{71} +3.13941e19 q^{73} +(5.22365e19 + 9.50032e18i) q^{74} +(4.14934e19 + 1.56092e19i) q^{76} -8.41551e18 q^{77} +8.71218e19i q^{79} +(1.25179e20 + 1.09706e20i) q^{80} +(-1.17140e20 - 2.13043e19i) q^{82} +4.57741e19i q^{83} +3.15305e20i q^{85} +(7.28643e19 - 4.00636e20i) q^{86} +(-1.11899e20 - 6.70323e19i) q^{88} +1.01044e20i q^{89} -1.42196e19 q^{91} +(9.68428e19 + 3.64309e19i) q^{92} +(8.74640e19 - 4.80912e20i) q^{94} -8.00035e20 q^{95} -2.74438e20 q^{97} +(-1.34786e20 + 7.41108e20i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−259.127	+	1424.78i	−0.178936	+	0.983861i
$2$	−259.127	+	1424.78i	−0.178936	+	0.983861i
$3$		0			0
$3$		0			0
$4$	−1.96286e6	−	738399.i	−0.935964	−	0.352096i
$5$	3.78460e7			1.73314			0.866572	−	0.499052i	$-0.166319\pi$
$5$	3.78460e7			1.73314			0.866572	+	0.499052i	$0.166319\pi$
$6$		0			0
$7$		−	1.95935e8i		−	0.262170i	−0.991371	−	0.131085i	$-0.958154\pi$
$7$		−	1.95935e8i		−	0.262170i	0.991371	−	0.131085i	$-0.0418461\pi$
$8$	1.56069e9	−	2.60531e9i	0.513891	−	0.857855i
$9$		0			0
$10$	−9.80691e9	+	5.39223e10i	−0.310122	+	1.70517i
$11$		−	4.29505e10i		−	0.499281i	−0.968339	−	0.249640i	$-0.919688\pi$
$11$		−	4.29505e10i		−	0.499281i	0.968339	−	0.249640i	$-0.0803124\pi$
$12$		0			0
$13$		−	7.25729e10i		−	0.146005i	−0.997332	−	0.0730027i	$-0.976742\pi$
$13$		−	7.25729e10i		−	0.146005i	0.997332	−	0.0730027i	$-0.0232582\pi$
$14$	2.79165e11	+	5.07721e10i	0.257939	+	0.0469116i
$15$		0			0
$16$	3.30758e12	+	2.89875e12i	0.752056	+	0.659099i
$17$			8.33127e12i			1.00230i	0.865361	+	0.501150i	$0.167089\pi$
$17$			8.33127e12i			1.00230i	−0.865361	+	0.501150i	$0.832911\pi$
$18$		0			0
$19$	−2.11393e13			−0.791001			−0.395500	−	0.918466i	$-0.629429\pi$
$19$	−2.11393e13			−0.791001			−0.395500	+	0.918466i	$0.629429\pi$
$20$	−7.42863e13	−	2.79454e13i	−1.62216	−	0.610233i
$21$		0			0
$22$	6.11951e13	+	1.11296e13i	0.491223	+	0.0893393i
$23$	−4.93376e13			−0.248334			−0.124167	−	0.992261i	$-0.539626\pi$
$23$	−4.93376e13			−0.248334			−0.124167	+	0.992261i	$0.539626\pi$
$24$		0			0
$25$	9.55480e14			2.00379
$26$	1.03401e14	+	1.88056e13i	0.143649	+	0.0261256i
$27$		0			0
$28$	−1.44678e14	+	3.84593e14i	−0.0923091	+	0.245382i
$29$	−2.69501e15			−1.18955			−0.594774	−	0.803893i	$-0.702758\pi$
$29$	−2.69501e15			−1.18955			−0.594774	+	0.803893i	$0.702758\pi$
$30$		0			0
$31$		−	1.12089e15i		−	0.245622i	−0.992430	−	0.122811i	$-0.960809\pi$
$31$		−	1.12089e15i		−	0.245622i	0.992430	−	0.122811i	$-0.0391908\pi$
$32$	−4.98717e15	+	3.96144e15i	−0.783031	+	0.621982i
$33$		0			0
$34$	−1.18702e16	−	2.15886e15i	−0.986123	−	0.179347i
$35$		−	7.41535e15i		−	0.454378i
$36$		0			0
$37$		−	3.66628e16i		−	1.25345i	−0.779240	−	0.626726i	$-0.784395\pi$
$37$		−	3.66628e16i		−	1.25345i	0.779240	−	0.626726i	$-0.215605\pi$
$38$	5.47775e15	−	3.01188e16i	0.141539	−	0.778234i
$39$		0			0
$40$	5.90658e16	−	9.86003e16i	0.890648	−	1.48679i
$41$			8.22158e16i			0.956587i	0.878200	+	0.478294i	$0.158745\pi$
$41$			8.22158e16i			0.956587i	−0.878200	+	0.478294i	$0.841255\pi$
$42$		0			0
$43$	−2.81191e17			−1.98419			−0.992094	−	0.125493i	$-0.959949\pi$
$43$	−2.81191e17			−1.98419			−0.992094	+	0.125493i	$0.959949\pi$
$44$	−3.17146e16	+	8.43057e16i	−0.175795	+	0.467309i
$45$		0			0
$46$	1.27847e16	−	7.02954e16i	0.0444359	−	0.244326i
$47$	−3.37533e17			−0.936029			−0.468014	−	0.883721i	$-0.655030\pi$
$47$	−3.37533e17			−0.936029			−0.468014	+	0.883721i	$0.655030\pi$
$48$		0			0
$49$	5.20155e17			0.931267
$50$	−2.47591e17	+	1.36135e18i	−0.358550	+	1.97145i
$51$		0			0
$52$	−5.35878e16	+	1.42450e17i	−0.0514080	+	0.136656i
$53$	−7.67842e17			−0.603080			−0.301540	−	0.953454i	$-0.597501\pi$
$53$	−7.67842e17			−0.603080			−0.301540	+	0.953454i	$0.597501\pi$
$54$		0			0
$55$		−	1.62550e18i		−	0.865325i
$56$	−5.10471e17	−	3.05794e17i	−0.224904	−	0.134727i
$57$		0			0
$58$	6.98351e17	−	3.83981e18i	0.212853	−	1.17035i
$59$			5.94464e18i			1.51419i	0.653306	+	0.757094i	$0.273381\pi$
$59$			5.94464e18i			1.51419i	−0.653306	+	0.757094i	$0.726619\pi$
$60$		0			0
$61$		−	3.41895e18i		−	0.613662i	−0.951764	−	0.306831i	$-0.900731\pi$
$61$		−	3.41895e18i		−	0.613662i	0.951764	−	0.306831i	$-0.0992686\pi$
$62$	1.59703e18	+	2.90454e17i	0.241657	+	0.0439506i
$63$		0			0
$64$	−4.35188e18	−	8.13214e18i	−0.471831	−	0.881689i
$65$		−	2.74659e18i		−	0.253048i
$66$		0			0
$67$	5.71427e18			0.382979			0.191490	−	0.981495i	$-0.438668\pi$
$67$	5.71427e18			0.382979			0.191490	+	0.981495i	$0.438668\pi$
$68$	6.15180e18	−	1.63531e19i	0.352906	−	0.938116i
$69$		0			0
$70$	1.05653e19	+	1.92152e18i	0.447045	+	0.0813046i
$71$	1.23772e19			0.451241			0.225620	−	0.974215i	$-0.427559\pi$
$71$	1.23772e19			0.451241			0.225620	+	0.974215i	$0.427559\pi$
$72$		0			0
$73$	3.13941e19			0.854983			0.427492	−	0.904019i	$-0.359397\pi$
$73$	3.13941e19			0.854983			0.427492	+	0.904019i	$0.359397\pi$
$74$	5.22365e19	+	9.50032e18i	1.23322	+	0.224288i
$75$		0			0
$76$	4.14934e19	+	1.56092e19i	0.740348	+	0.278508i
$77$	−8.41551e18			−0.130896
$78$		0			0
$79$			8.71218e19i			1.03524i	0.855610	+	0.517621i	$0.173182\pi$
$79$			8.71218e19i			1.03524i	−0.855610	+	0.517621i	$0.826818\pi$
$80$	1.25179e20	+	1.09706e20i	1.30342	+	1.14231i
$81$		0			0
$82$	−1.17140e20	−	2.13043e19i	−0.941148	−	0.171168i
$83$			4.57741e19i			0.323817i	0.986806	+	0.161909i	$0.0517650\pi$
$83$			4.57741e19i			0.323817i	−0.986806	+	0.161909i	$0.948235\pi$
$84$		0			0
$85$			3.15305e20i			1.73713i
$86$	7.28643e19	−	4.00636e20i	0.355043	−	1.95217i
$87$		0			0
$88$	−1.11899e20	−	6.70323e19i	−0.428311	−	0.256576i
$89$			1.01044e20i			0.343492i	0.985141	+	0.171746i	$0.0549409\pi$
$89$			1.01044e20i			0.343492i	−0.985141	+	0.171746i	$0.945059\pi$
$90$		0			0
$91$	−1.42196e19			−0.0382782
$92$	9.68428e19	+	3.64309e19i	0.232432	+	0.0874375i
$93$		0			0
$94$	8.74640e19	−	4.80912e20i	0.167489	−	0.920922i
$95$	−8.00035e20			−1.37092
$96$		0			0
$97$	−2.74438e20			−0.377869			−0.188935	−	0.981990i	$-0.560503\pi$
$97$	−2.74438e20			−0.377869			−0.188935	+	0.981990i	$0.560503\pi$
$98$	−1.34786e20	+	7.41108e20i	−0.166637	+	0.916237i
$99$		0			0
$100$	−1.87547e21	−	7.05526e20i	−1.87547	−	0.705526i
$101$	−1.25842e21			−1.13357			−0.566787	−	0.823864i	$-0.691814\pi$
$101$	−1.25842e21			−1.13357			−0.566787	+	0.823864i	$0.691814\pi$
$102$		0			0
$103$			2.56504e21i			1.88063i	0.340302	+	0.940316i	$0.389471\pi$
$103$			2.56504e21i			1.88063i	−0.340302	+	0.940316i	$0.610529\pi$
$104$	−1.89075e20	−	1.13264e20i	−0.125252	−	0.0750309i
$105$		0			0
$106$	1.98969e20	−	1.09401e21i	0.107913	−	0.593347i
$107$			2.51950e21i			1.23818i	0.785319	+	0.619091i	$0.212499\pi$
$107$			2.51950e21i			1.23818i	−0.785319	+	0.619091i	$0.787501\pi$
$108$		0			0
$109$			3.17445e21i			1.28437i	0.766549	+	0.642185i	$0.221972\pi$
$109$			3.17445e21i			1.28437i	−0.766549	+	0.642185i	$0.778028\pi$
$110$	2.31599e21	+	4.21212e20i	0.851359	+	0.154838i
$111$		0			0
$112$	5.67966e20	−	6.48071e20i	0.172796	−	0.197167i
$113$			2.40322e21i			0.665993i	0.942928	+	0.332997i	$0.108060\pi$
$113$			2.40322e21i			0.665993i	−0.942928	+	0.332997i	$0.891940\pi$
$114$		0			0
$115$	−1.86723e21			−0.430398
$116$	5.28993e21	+	1.99000e21i	1.11337	+	0.418835i
$117$		0			0
$118$	−8.46982e21	−	1.54042e21i	−1.48975	−	0.270943i
$119$	1.63239e21			0.262773
$120$		0			0
$121$	5.55551e21			0.750719
$122$	4.87126e21	+	8.85942e20i	0.603758	+	0.109806i
$123$		0			0
$124$	−8.27667e20	+	2.20016e21i	−0.0864825	+	0.229893i
$125$	1.81147e22			1.73971
$126$		0			0
$127$			5.45808e21i			0.443712i	0.975079	+	0.221856i	$0.0712115\pi$
$127$			5.45808e21i			0.443712i	−0.975079	+	0.221856i	$0.928789\pi$
$128$	1.27142e22	−	4.09322e21i	0.951887	−	0.306450i
$129$		0			0
$130$	3.91329e21	+	7.11716e20i	0.248964	+	0.0452795i
$131$			8.89056e21i			0.521892i	0.965353	+	0.260946i	$0.0840345\pi$
$131$			8.89056e21i			0.521892i	−0.965353	+	0.260946i	$0.915966\pi$
$132$		0			0
$133$			4.14192e21i			0.207377i
$134$	−1.48072e21	+	8.14159e21i	−0.0685288	+	0.376798i
$135$		0			0
$136$	2.17055e22	+	1.30025e22i	0.859828	+	0.515073i
$137$			8.22596e21i			0.301732i	0.988554	+	0.150866i	$0.0482061\pi$
$137$			8.22596e21i			0.301732i	−0.988554	+	0.150866i	$0.951794\pi$
$138$		0			0
$139$	2.78728e21			0.0878063			0.0439032	−	0.999036i	$-0.486021\pi$
$139$	2.78728e21			0.0878063			0.0439032	+	0.999036i	$0.486021\pi$
$140$	−5.47549e21	+	1.45553e22i	−0.159985	+	0.425281i
$141$		0			0
$142$	−3.20726e21	+	1.76348e22i	−0.0807432	+	0.443958i
$143$	−3.11704e21			−0.0728977
$144$		0			0
$145$	−1.01995e23			−2.06166
$146$	−8.13505e21	+	4.47297e22i	−0.152987	+	0.841184i
$147$		0			0
$148$	−2.70718e22	+	7.19639e22i	−0.441336	+	1.17319i
$149$	6.80198e22			1.03319			0.516594	−	0.856230i	$-0.327200\pi$
$149$	6.80198e22			1.03319			0.516594	+	0.856230i	$0.327200\pi$
$150$		0			0
$151$		−	1.09369e23i		−	1.44422i	−0.691776	−	0.722112i	$-0.743172\pi$
$151$		−	1.09369e23i		−	1.44422i	0.691776	−	0.722112i	$-0.256828\pi$
$152$	−3.29918e22	+	5.50742e22i	−0.406488	+	0.678564i
$153$		0			0
$154$	2.18069e21	−	1.19903e22i	0.0234221	−	0.128784i
$155$		−	4.24213e22i		−	0.425698i
$156$		0			0
$157$		−	4.50076e22i		−	0.394766i	−0.980326	−	0.197383i	$-0.936756\pi$
$157$		−	4.50076e22i		−	0.394766i	0.980326	−	0.197383i	$-0.0632442\pi$
$158$	−1.24130e23	−	2.25756e22i	−1.01853	−	0.185242i
$159$		0			0
$160$	−1.88744e23	+	1.49924e23i	−1.35711	+	1.07798i
$161$			9.66697e21i			0.0651057i
$162$		0			0
$163$	−2.34394e23			−1.38668			−0.693341	−	0.720610i	$-0.743862\pi$
$163$	−2.34394e23			−1.38668			−0.693341	+	0.720610i	$0.743862\pi$
$164$	6.07081e22	−	1.61378e23i	0.336811	−	0.895331i
$165$		0			0
$166$	−6.52182e22	−	1.18613e22i	−0.318591	−	0.0579426i
$167$	−3.10268e23			−1.42303			−0.711515	−	0.702671i	$-0.751991\pi$
$167$	−3.10268e23			−1.42303			−0.711515	+	0.702671i	$0.751991\pi$
$168$		0			0
$169$	2.41798e23			0.978682
$170$	−4.49241e23	−	8.17040e22i	−1.70909	−	0.310835i
$171$		0			0
$172$	5.51939e23	+	2.07631e23i	1.85713	+	0.698626i
$173$	4.74103e23			1.50103			0.750514	−	0.660855i	$-0.229806\pi$
$173$	4.74103e23			1.50103			0.750514	+	0.660855i	$0.229806\pi$
$174$		0			0
$175$		−	1.87212e23i		−	0.525332i
$176$	1.24503e23	−	1.42062e23i	0.329075	−	0.375487i
$177$		0			0
$178$	−1.43966e23	−	2.61833e22i	−0.337949	−	0.0614632i
$179$		−	2.18179e22i		−	0.0482899i	−0.999708	−	0.0241449i	$-0.992314\pi$
$179$		−	2.18179e22i		−	0.0482899i	0.999708	−	0.0241449i	$-0.00768632\pi$
$180$		0			0
$181$			7.13447e23i			1.40520i	0.711587	+	0.702598i	$0.247977\pi$
$181$			7.13447e23i			1.40520i	−0.711587	+	0.702598i	$0.752023\pi$
$182$	3.68468e21	−	2.02598e22i	0.00684936	−	0.0376605i
$183$		0			0
$184$	−7.70007e22	+	1.28540e23i	−0.127617	+	0.213035i
$185$		−	1.38754e24i		−	2.17241i
$186$		0			0
$187$	3.57832e23			0.500429
$188$	6.62530e23	+	2.49234e23i	0.876089	+	0.329572i
$189$		0			0
$190$	2.07311e23	−	1.13988e24i	0.245307	−	1.34879i
$191$	−1.30572e24			−1.46217			−0.731087	−	0.682284i	$-0.760987\pi$
$191$	−1.30572e24			−1.46217			−0.731087	+	0.682284i	$0.760987\pi$
$192$		0			0
$193$	−6.19588e22			−0.0621944			−0.0310972	−	0.999516i	$-0.509900\pi$
$193$	−6.19588e22			−0.0621944			−0.0310972	+	0.999516i	$0.509900\pi$
$194$	7.11144e22	−	3.91015e23i	0.0676145	−	0.371771i
$195$		0			0
$196$	−1.02099e24	−	3.84082e23i	−0.871632	−	0.327896i
$197$	3.16504e23			0.256144			0.128072	−	0.991765i	$-0.459121\pi$
$197$	3.16504e23			0.256144			0.128072	+	0.991765i	$0.459121\pi$
$198$		0			0
$199$		−	7.59165e23i		−	0.552559i	−0.961077	−	0.276280i	$-0.910898\pi$
$199$		−	7.59165e23i		−	0.552559i	0.961077	−	0.276280i	$-0.0891016\pi$
$200$	1.49121e24	−	2.48932e24i	1.02973	−	1.71896i
$201$		0			0
$202$	3.26090e23	−	1.79297e24i	0.202837	−	1.11528i
$203$			5.28048e23i			0.311864i
$204$		0			0
$205$			3.11153e24i			1.65790i
$206$	−3.65463e24	−	6.64672e23i	−1.85028	−	0.336513i
$207$		0			0
$208$	2.10370e23	−	2.40040e23i	0.0962320	−	0.109804i
$209$			9.07941e23i			0.394931i
$210$		0			0
$211$	−1.24637e24			−0.490547			−0.245274	−	0.969454i	$-0.578878\pi$
$211$	−1.24637e24			−0.490547			−0.245274	+	0.969454i	$0.578878\pi$
$212$	1.50716e24	+	5.66974e23i	0.564461	+	0.212342i
$213$		0			0
$214$	−3.58974e24	−	6.52870e23i	−1.21820	−	0.221555i
$215$	−1.06420e25			−3.43888
$216$		0			0
$217$	−2.19622e23			−0.0643946
$218$	−4.52290e24	−	8.22586e23i	−1.26364	−	0.229820i
$219$		0			0
$220$	−1.20027e24	+	3.19063e24i	−0.304678	+	0.809913i
$221$	6.04624e23			0.146341
$222$		0			0
$223$		−	1.89311e24i		−	0.416844i	−0.978039	−	0.208422i	$-0.933167\pi$
$223$		−	1.89311e24i		−	0.416844i	0.978039	−	0.208422i	$-0.0668328\pi$
$224$	7.76185e23	+	9.77161e23i	0.163065	+	0.205287i
$225$		0			0
$226$	−3.42407e24	−	6.22739e23i	−0.655245	−	0.119170i
$227$		−	8.26162e24i		−	1.50936i	−0.656091	−	0.754682i	$-0.727791\pi$
$227$		−	8.26162e24i		−	1.50936i	0.656091	−	0.754682i	$-0.272209\pi$
$228$		0			0
$229$			9.70169e24i			1.61650i	0.588842	+	0.808248i	$0.299584\pi$
$229$			9.70169e24i			1.61650i	−0.588842	+	0.808248i	$0.700416\pi$
$230$	4.83850e23	−	2.66040e24i	0.0770138	−	0.423452i
$231$		0			0
$232$	−4.20607e24	+	7.02133e24i	−0.611298	+	1.02046i
$233$		−	3.50445e24i		−	0.486836i	−0.969921	−	0.243418i	$-0.921731\pi$
$233$		−	3.50445e24i		−	0.486836i	0.969921	−	0.243418i	$-0.0782687\pi$
$234$		0			0
$235$	−1.27743e25			−1.62227
$236$	4.38952e24	−	1.16685e25i	0.533140	−	1.41722i
$237$		0			0
$238$	−4.22996e23	+	2.32580e24i	−0.0470195	+	0.258532i
$239$	9.98687e24			1.06231			0.531155	−	0.847275i	$-0.321758\pi$
$239$	9.98687e24			1.06231			0.531155	+	0.847275i	$0.321758\pi$
$240$		0			0
$241$	−1.51000e25			−1.47163			−0.735816	−	0.677181i	$-0.763201\pi$
$241$	−1.51000e25			−1.47163			−0.735816	+	0.677181i	$0.763201\pi$
$242$	−1.43958e24	+	7.91539e24i	−0.134331	+	0.738603i
$243$		0			0
$244$	−2.52455e24	+	6.71091e24i	−0.216068	+	0.574365i
$245$	1.96858e25			1.61402
$246$		0			0
$247$			1.53414e24i			0.115490i
$248$	−2.92027e24	−	1.74937e24i	−0.210708	−	0.126223i
$249$		0			0
$250$	−4.69401e24	+	2.58095e25i	−0.311296	+	1.71163i
$251$			1.58827e25i			1.01006i	0.863100	+	0.505032i	$0.168519\pi$
$251$			1.58827e25i			1.01006i	−0.863100	+	0.505032i	$0.831481\pi$
$252$		0			0
$253$			2.11907e24i			0.123988i
$254$	−7.77658e24	−	1.41434e24i	−0.436551	−	0.0793961i
$255$		0			0
$256$	2.53734e24	+	1.91757e25i	0.131178	+	0.991359i
$257$		−	2.46582e25i		−	1.22367i	−0.790986	−	0.611834i	$-0.790432\pi$
$257$		−	2.46582e25i		−	1.22367i	0.790986	−	0.611834i	$-0.209568\pi$
$258$		0			0
$259$	−7.18353e24			−0.328617
$260$	−2.02808e24	+	5.39117e24i	−0.0890974	+	0.236844i
$261$		0			0
$262$	−1.26671e25	−	2.30379e24i	−0.513469	−	0.0933853i
$263$	4.80092e24			0.186977			0.0934887	−	0.995620i	$-0.470198\pi$
$263$	4.80092e24			0.186977			0.0934887	+	0.995620i	$0.470198\pi$
$264$		0			0
$265$	−2.90597e25			−1.04522
$266$	−5.90134e24	−	1.07328e24i	−0.204030	−	0.0371071i
$267$		0			0
$268$	−1.12163e25	−	4.21941e24i	−0.358455	−	0.134846i
$269$	−1.56180e25			−0.479983			−0.239991	−	0.970775i	$-0.577145\pi$
$269$	−1.56180e25			−0.479983			−0.239991	+	0.970775i	$0.577145\pi$
$270$		0			0
$271$		−	5.66547e24i		−	0.161086i	−0.996751	−	0.0805431i	$-0.974335\pi$
$271$		−	5.66547e24i		−	0.161086i	0.996751	−	0.0805431i	$-0.0256655\pi$
$272$	−2.41502e25	+	2.75563e25i	−0.660614	+	0.753786i
$273$		0			0
$274$	−1.17202e25	−	2.13157e24i	−0.296862	−	0.0539907i
$275$		−	4.10383e25i		−	1.00045i
$276$		0			0
$277$		−	4.26837e25i		−	0.964327i	−0.876081	−	0.482163i	$-0.839851\pi$
$277$		−	4.26837e25i		−	0.964327i	0.876081	−	0.482163i	$-0.160149\pi$
$278$	−7.22261e23	+	3.97127e24i	−0.0157117	+	0.0863892i
$279$		0			0
$280$	−1.93193e25	−	1.15731e25i	−0.389791	−	0.233501i
$281$			6.49029e25i			1.26138i	0.776033	+	0.630692i	$0.217229\pi$
$281$			6.49029e25i			1.26138i	−0.776033	+	0.630692i	$0.782771\pi$
$282$		0			0
$283$	−9.38019e25			−1.69221			−0.846105	−	0.533016i	$-0.821058\pi$
$283$	−9.38019e25			−1.69221			−0.846105	+	0.533016i	$0.821058\pi$
$284$	−2.42946e25	−	9.13929e24i	−0.422345	−	0.158880i
$285$		0			0
$286$	8.07709e23	−	4.44110e24i	0.0130440	−	0.0717212i
$287$	1.61090e25			0.250788
$288$		0			0
$289$	−3.18100e23			−0.00460401
$290$	2.64298e25	−	1.45321e26i	0.368905	−	2.02838i
$291$		0			0
$292$	−6.16221e25	−	2.31814e25i	−0.800233	−	0.301036i
$293$	−1.39035e26			−1.74186			−0.870931	−	0.491406i	$-0.836483\pi$
$293$	−1.39035e26			−1.74186			−0.870931	+	0.491406i	$0.836483\pi$
$294$		0			0
$295$			2.24981e26i			2.62430i
$296$	−9.55178e25	−	5.72192e25i	−1.07528	−	0.644138i
$297$		0			0
$298$	−1.76258e25	+	9.69134e25i	−0.184875	+	1.01651i
$299$			3.58057e24i			0.0362581i
$300$		0			0
$301$			5.50952e25i			0.520195i
$302$	1.55826e26	+	2.83404e25i	1.42091	+	0.258424i
$303$		0			0
$304$	−6.99197e25	−	6.12773e25i	−0.594877	−	0.521348i
$305$		−	1.29393e26i		−	1.06356i
$306$		0			0
$307$	2.14727e26			1.64791			0.823955	−	0.566656i	$-0.191763\pi$
$307$	2.14727e26			1.64791			0.823955	+	0.566656i	$0.191763\pi$
$308$	1.65184e25	+	6.21401e24i	0.122514	+	0.0460881i
$309$		0			0
$310$	6.04411e25	+	1.09925e25i	0.418827	+	0.0761726i
$311$	4.37691e25			0.293214			0.146607	−	0.989195i	$-0.453165\pi$
$311$	4.37691e25			0.293214			0.146607	+	0.989195i	$0.453165\pi$
$312$		0			0
$313$	−1.13089e26			−0.708282			−0.354141	−	0.935192i	$-0.615227\pi$
$313$	−1.13089e26			−0.708282			−0.354141	+	0.935192i	$0.615227\pi$
$314$	6.41260e25	+	1.16627e25i	0.388394	+	0.0706378i
$315$		0			0
$316$	6.43307e25	−	1.71008e26i	0.364505	−	0.968950i
$317$	−2.83814e26			−1.55565			−0.777824	−	0.628482i	$-0.783676\pi$
$317$	−2.83814e26			−1.55565			−0.777824	+	0.628482i	$0.783676\pi$
$318$		0			0
$319$			1.15752e26i			0.593918i
$320$	−1.64701e26	−	3.07769e26i	−0.817751	−	1.52809i
$321$		0			0
$322$	−1.37733e25	−	2.50497e24i	−0.0640549	−	0.0116498i
$323$		−	1.76117e26i		−	0.792819i
$324$		0			0
$325$		−	6.93419e25i		−	0.292564i
$326$	6.07378e25	−	3.33961e26i	0.248127	−	1.36430i
$327$		0			0
$328$	2.14197e26	+	1.28313e26i	0.820613	+	0.491582i
$329$			6.61346e25i			0.245399i
$330$		0			0
$331$	−2.20653e26			−0.768274			−0.384137	−	0.923276i	$-0.625501\pi$
$331$	−2.20653e26			−0.768274			−0.384137	+	0.923276i	$0.625501\pi$
$332$	3.37996e25	−	8.98481e25i	0.114015	−	0.303081i
$333$		0			0
$334$	8.03989e25	−	4.42064e26i	0.254631	−	1.40006i
$335$	2.16262e26			0.663758
$336$		0			0
$337$	2.72539e26			0.785804			0.392902	−	0.919580i	$-0.371471\pi$
$337$	2.72539e26			0.785804			0.392902	+	0.919580i	$0.371471\pi$
$338$	−6.26563e25	+	3.44509e26i	−0.175122	+	0.962887i
$339$		0			0
$340$	2.32821e26	−	6.18899e26i	0.611637	−	1.62589i
$341$	−4.81429e25			−0.122634
$342$		0			0
$343$		−	2.11355e26i		−	0.506320i
$344$	−4.38852e26	+	7.32589e26i	−1.01966	+	1.70215i
$345$		0			0
$346$	−1.22853e26	+	6.75494e26i	−0.268588	+	1.47680i
$347$			5.72140e26i			1.21351i	0.794889	+	0.606755i	$0.207529\pi$
$347$			5.72140e26i			1.21351i	−0.794889	+	0.606755i	$0.792471\pi$
$348$		0			0
$349$		−	7.41558e26i		−	1.48074i	−0.672201	−	0.740369i	$-0.734651\pi$
$349$		−	7.41558e26i		−	1.48074i	0.672201	−	0.740369i	$-0.265349\pi$
$350$	2.66736e26	+	4.85117e25i	0.516854	+	0.0940009i
$351$		0			0
$352$	1.70146e26	+	2.14201e26i	0.310544	+	0.390952i
$353$			9.38011e26i			1.66178i	0.556437	+	0.830890i	$0.312168\pi$
$353$			9.38011e26i			1.66178i	−0.556437	+	0.830890i	$0.687832\pi$
$354$		0			0
$355$	4.68426e26			0.782065
$356$	7.46111e25	−	1.98336e26i	0.120942	−	0.321497i
$357$		0			0
$358$	3.10858e25	+	5.65361e24i	0.0475105	+	0.00864080i
$359$	7.59204e26			1.12685			0.563426	−	0.826167i	$-0.309483\pi$
$359$	7.59204e26			1.12685			0.563426	+	0.826167i	$0.309483\pi$
$360$		0			0
$361$	−2.67341e26			−0.374318
$362$	−1.01651e27	−	1.84874e26i	−1.38252	−	0.251440i
$363$		0			0
$364$	2.79110e25	+	1.04997e25i	0.0358270	+	0.0134776i
$365$	1.18814e27			1.48181
$366$		0			0
$367$		−	1.11452e27i		−	1.31249i	−0.754550	−	0.656243i	$-0.772145\pi$
$367$		−	1.11452e27i		−	1.31249i	0.754550	−	0.656243i	$-0.227855\pi$
$368$	−1.63188e26	−	1.43017e26i	−0.186761	−	0.163677i
$369$		0			0
$370$	1.97694e27	+	3.59549e26i	2.13735	+	0.388723i
$371$			1.50447e26i			0.158109i
$372$		0			0
$373$			3.41272e26i			0.338967i	0.985533	+	0.169483i	$0.0542099\pi$
$373$			3.41272e26i			0.338967i	−0.985533	+	0.169483i	$0.945790\pi$
$374$	−9.27239e25	+	5.09833e26i	−0.0895447	+	0.492352i
$375$		0			0
$376$	−5.26784e26	+	8.79378e26i	−0.481017	+	0.802977i
$377$			1.95585e26i			0.173680i
$378$		0			0
$379$	−1.04480e27			−0.877653			−0.438827	−	0.898572i	$-0.644606\pi$
$379$	−1.04480e27			−0.877653			−0.438827	+	0.898572i	$0.644606\pi$
$380$	1.57036e27	+	5.90746e26i	1.28313	+	0.482695i
$381$		0			0
$382$	3.38347e26	−	1.86036e27i	0.261636	−	1.43858i
$383$	−2.90390e26			−0.218471			−0.109236	−	0.994016i	$-0.534840\pi$
$383$	−2.90390e26			−0.218471			−0.109236	+	0.994016i	$0.534840\pi$
$384$		0			0
$385$	−3.18493e26			−0.226862
$386$	1.60552e25	−	8.82778e25i	0.0111288	−	0.0611906i
$387$		0			0
$388$	5.38684e26	+	2.02645e26i	0.353672	+	0.133046i
$389$	2.84822e27			1.82013			0.910066	−	0.414463i	$-0.136031\pi$
$389$	2.84822e27			1.82013			0.910066	+	0.414463i	$0.136031\pi$
$390$		0			0
$391$		−	4.11045e26i		−	0.248905i
$392$	8.11800e26	−	1.35516e27i	0.478570	−	0.798892i
$393$		0			0
$394$	−8.20147e25	+	4.50949e26i	−0.0458333	+	0.252010i
$395$			3.29721e27i			1.79422i
$396$		0			0
$397$			3.12625e27i			1.61333i	0.591008	+	0.806666i	$0.298730\pi$
$397$			3.12625e27i			1.61333i	−0.591008	+	0.806666i	$0.701270\pi$
$398$	1.08164e27	+	1.96720e26i	0.543641	+	0.0988728i
$399$		0			0
$400$	3.16032e27	+	2.76969e27i	1.50696	+	1.32069i
$401$			6.48755e26i			0.301346i	0.988584	+	0.150673i	$0.0481440\pi$
$401$			6.48755e26i			0.301346i	−0.988584	+	0.150673i	$0.951856\pi$
$402$		0			0
$403$	−8.13465e25			−0.0358621
$404$	2.47009e27	+	9.29214e26i	1.06098	+	0.399127i
$405$		0			0
$406$	−7.52353e26	−	1.36831e26i	−0.306830	−	0.0558036i
$407$	−1.57468e27			−0.625824
$408$		0			0
$409$	1.74848e27			0.660032			0.330016	−	0.943975i	$-0.392946\pi$
$409$	1.74848e27			0.660032			0.330016	+	0.943975i	$0.392946\pi$
$410$	−4.43326e27	−	8.06283e26i	−1.63115	−	0.296659i
$411$		0			0
$412$	1.89403e27	−	5.03482e27i	0.662164	−	1.76020i
$413$	1.16476e27			0.396974
$414$		0			0
$415$			1.73237e27i			0.561222i
$416$	2.87493e26	+	3.61933e26i	0.0908128	+	0.114327i
$417$		0			0
$418$	−1.29362e27	−	2.35272e26i	−0.388557	−	0.0706675i
$419$			5.85095e27i			1.71388i	0.515420	+	0.856938i	$0.327636\pi$
$419$			5.85095e27i			1.71388i	−0.515420	+	0.856938i	$0.672364\pi$
$420$		0			0
$421$			2.66479e25i			0.00742507i	0.999993	+	0.00371253i	$0.00118174\pi$
$421$			2.66479e25i			0.00742507i	−0.999993	+	0.00371253i	$0.998818\pi$
$422$	3.22968e26	−	1.77581e27i	0.0877766	−	0.482630i
$423$		0			0
$424$	−1.19836e27	+	2.00046e27i	−0.309918	+	0.517355i
$425$			7.96036e27i			2.00839i
$426$		0			0
$427$	−6.69892e26			−0.160884
$428$	1.86040e27	−	4.94542e27i	0.435959	−	1.15889i
$429$		0			0
$430$	2.75762e27	−	1.51625e28i	0.615340	−	3.38338i
$431$	−4.80020e27			−1.04532			−0.522658	−	0.852542i	$-0.675060\pi$
$431$	−4.80020e27			−1.04532			−0.522658	+	0.852542i	$0.675060\pi$
$432$		0			0
$433$	1.17718e27			0.244186			0.122093	−	0.992519i	$-0.461039\pi$
$433$	1.17718e27			0.244186			0.122093	+	0.992519i	$0.461039\pi$
$434$	5.69101e25	−	3.12914e26i	0.0115225	−	0.0633553i
$435$		0			0
$436$	2.34401e27	−	6.23100e27i	0.452222	−	1.20212i
$437$	1.04296e27			0.196432
$438$		0			0
$439$		−	7.39983e27i		−	1.32845i	−0.747534	−	0.664223i	$-0.768762\pi$
$439$		−	7.39983e27i		−	1.32845i	0.747534	−	0.664223i	$-0.231238\pi$
$440$	−4.23493e27	−	2.53690e27i	−0.742324	−	0.444683i
$441$		0			0
$442$	−1.56674e26	+	8.61458e26i	−0.0261857	+	0.143979i
$443$		−	3.55775e27i		−	0.580679i	−0.956924	−	0.290339i	$-0.906232\pi$
$443$		−	3.55775e27i		−	0.580679i	0.956924	−	0.290339i	$-0.0937682\pi$
$444$		0			0
$445$			3.82412e27i			0.595322i
$446$	2.69726e27	+	4.90555e26i	0.410117	+	0.0745885i
$447$		0			0
$448$	−1.59337e27	+	8.52685e26i	−0.231152	+	0.123700i
$449$		−	2.97281e27i		−	0.421289i	−0.977563	−	0.210644i	$-0.932444\pi$
$449$		−	2.97281e27i		−	0.421289i	0.977563	−	0.210644i	$-0.0675562\pi$
$450$		0			0
$451$	3.53121e27			0.477605
$452$	1.77454e27	−	4.71718e27i	0.234494	−	0.623346i
$453$		0			0
$454$	1.17710e28	+	2.14081e27i	1.48500	+	0.270080i
$455$	−5.38153e26			−0.0663417
$456$		0			0
$457$	−1.35008e28			−1.58943			−0.794713	−	0.606985i	$-0.792379\pi$
$457$	−1.35008e28			−1.58943			−0.794713	+	0.606985i	$0.792379\pi$
$458$	−1.38228e28	−	2.51397e27i	−1.59041	−	0.289250i
$459$		0			0
$460$	3.66511e27	+	1.37876e27i	0.402837	+	0.151542i
$461$	6.25593e27			0.672098			0.336049	−	0.941845i	$-0.390909\pi$
$461$	6.25593e27			0.672098			0.336049	+	0.941845i	$0.390909\pi$
$462$		0			0
$463$			1.34533e28i			1.38111i	0.723278	+	0.690557i	$0.242634\pi$
$463$			1.34533e28i			1.38111i	−0.723278	+	0.690557i	$0.757366\pi$
$464$	−8.91397e27	−	7.81216e27i	−0.894607	−	0.784029i
$465$		0			0
$466$	4.99308e27	+	9.08098e26i	0.478979	+	0.0871125i
$467$			8.93909e27i			0.838428i	0.907887	+	0.419214i	$0.137694\pi$
$467$			8.93909e27i			0.838428i	−0.907887	+	0.419214i	$0.862306\pi$
$468$		0			0
$469$		−	1.11963e27i		−	0.100406i
$470$	3.31016e27	−	1.82006e28i	0.290283	−	1.59609i
$471$		0			0
$472$	1.54876e28	+	9.27774e27i	1.29895	+	0.778128i
$473$			1.20773e28i			0.990667i
$474$		0			0
$475$	−2.01981e28			−1.58500
$476$	−3.20415e27	−	1.20535e27i	−0.245946	−	0.0925213i
$477$		0			0
$478$	−2.58787e27	+	1.42291e28i	−0.190086	+	1.04517i
$479$	2.23495e28			1.60600			0.803000	−	0.595980i	$-0.203236\pi$
$479$	2.23495e28			1.60600			0.803000	+	0.595980i	$0.203236\pi$
$480$		0			0
$481$	−2.66072e27			−0.183011
$482$	3.91283e27	−	2.15143e28i	0.263328	−	1.44788i
$483$		0			0
$484$	−1.09047e28	−	4.10218e27i	−0.702646	−	0.264325i
$485$	−1.03864e28			−0.654902
$486$		0			0
$487$			1.17302e28i			0.708356i	0.935178	+	0.354178i	$0.115239\pi$
$487$			1.17302e28i			0.708356i	−0.935178	+	0.354178i	$0.884761\pi$
$488$	−8.90741e27	−	5.33591e27i	−0.526433	−	0.315356i
$489$		0			0
$490$	−5.10112e27	+	2.80480e28i	−0.288806	+	1.58797i
$491$		−	2.40743e28i		−	1.33413i	−0.744999	−	0.667066i	$-0.767550\pi$
$491$		−	2.40743e28i		−	1.33413i	0.744999	−	0.667066i	$-0.232450\pi$
$492$		0			0
$493$		−	2.24529e28i		−	1.19228i
$494$	−2.18581e27	−	3.97536e26i	−0.113626	−	0.0206654i
$495$		0			0
$496$	3.24919e27	−	3.70744e27i	0.161889	−	0.184721i
$497$		−	2.42512e27i		−	0.118302i
$498$		0			0
$499$	−3.82590e28			−1.78928			−0.894639	−	0.446790i	$-0.852567\pi$
$499$	−3.82590e28			−1.78928			−0.894639	+	0.446790i	$0.852567\pi$
$500$	−3.55566e28	−	1.33759e28i	−1.62830	−	0.612544i
$501$		0			0
$502$	−2.26293e28	−	4.11563e27i	−0.993763	−	0.180737i
$503$	3.01329e28			1.29592			0.647958	−	0.761676i	$-0.275623\pi$
$503$	3.01329e28			1.29592			0.647958	+	0.761676i	$0.275623\pi$
$504$		0			0
$505$	−4.76260e28			−1.96465
$506$	−3.01922e27	−	5.49110e26i	−0.121987	−	0.0221860i
$507$		0			0
$508$	4.03025e27	−	1.07134e28i	0.156229	−	0.415298i
$509$	−3.10299e28			−1.17827			−0.589133	−	0.808036i	$-0.700531\pi$
$509$	−3.10299e28			−1.17827			−0.589133	+	0.808036i	$0.700531\pi$
$510$		0			0
$511$		−	6.15120e27i		−	0.224151i
$512$	−2.79787e28	−	1.35377e27i	−0.998831	−	0.0483294i
$513$		0			0
$514$	3.51326e28	+	6.38961e27i	1.20392	+	0.218958i
$515$			9.70766e28i			3.25941i
$516$		0			0
$517$			1.44972e28i			0.467341i
$518$	1.86145e27	−	1.02350e28i	0.0588015	−	0.323314i
$519$		0			0
$520$	−7.15571e27	−	4.28657e27i	−0.217079	−	0.130039i
$521$			2.57504e28i			0.765574i	0.923837	+	0.382787i	$0.125036\pi$
$521$			2.57504e28i			0.765574i	−0.923837	+	0.382787i	$0.874964\pi$
$522$		0			0
$523$	−2.30325e28			−0.657769			−0.328885	−	0.944370i	$-0.606673\pi$
$523$	−2.30325e28			−0.657769			−0.328885	+	0.944370i	$0.606673\pi$
$524$	6.56479e27	−	1.74509e28i	0.183756	−	0.488472i
$525$		0			0
$526$	−1.24405e27	+	6.84027e27i	−0.0334570	+	0.183960i
$527$	9.33847e27			0.246186
$528$		0			0
$529$	−3.70374e28			−0.938330
$530$	7.53016e27	−	4.14038e28i	0.187028	−	1.02836i
$531$		0			0
$532$	3.05839e27	−	8.13001e27i	0.0730165	−	0.194097i
$533$	5.96663e27			0.139667
$534$		0			0
$535$			9.53528e28i			2.14595i
$536$	8.91819e27	−	1.48874e28i	0.196810	−	0.328541i
$537$		0			0
$538$	4.04704e27	−	2.22522e28i	0.0858862	−	0.472236i
$539$		−	2.23409e28i		−	0.464964i
$540$		0			0
$541$			3.45501e28i			0.691638i	0.938301	+	0.345819i	$0.112399\pi$
$541$			3.45501e28i			0.691638i	−0.938301	+	0.345819i	$0.887601\pi$
$542$	8.07206e27	+	1.46808e27i	0.158486	+	0.0288241i
$543$		0			0
$544$	−3.30038e28	−	4.15494e28i	−0.623412	−	0.784832i
$545$			1.20140e29i			2.22600i
$546$		0			0
$547$	−1.91688e28			−0.341765			−0.170882	−	0.985291i	$-0.554662\pi$
$547$	−1.91688e28			−0.341765			−0.170882	+	0.985291i	$0.554662\pi$
$548$	6.07405e27	−	1.61464e28i	0.106239	−	0.282410i
$549$		0			0
$550$	5.84707e28	+	1.06341e28i	0.984305	+	0.179017i
$551$	5.69706e28			0.940933
$552$		0			0
$553$	1.70702e28			0.271410
$554$	6.08149e28	+	1.10605e28i	0.948763	+	0.172553i
$555$		0			0
$556$	−5.47104e27	−	2.05813e27i	−0.0821835	−	0.0309163i
$557$	2.74067e28			0.403996			0.201998	−	0.979386i	$-0.435257\pi$
$557$	2.74067e28			0.403996			0.201998	+	0.979386i	$0.435257\pi$
$558$		0			0
$559$			2.04069e28i			0.289702i
$560$	2.14952e28	−	2.45269e28i	0.299480	−	0.341718i
$561$		0			0
$562$	−9.24725e28	−	1.68181e28i	−1.24103	−	0.225707i
$563$		−	4.85224e28i		−	0.639152i	−0.947561	−	0.319576i	$-0.896460\pi$
$563$		−	4.85224e28i		−	0.639152i	0.947561	−	0.319576i	$-0.103540\pi$
$564$		0			0
$565$			9.09522e28i			1.15426i
$566$	2.43066e28	−	1.33647e29i	0.302797	−	1.66490i
$567$		0			0
$568$	1.93169e28	−	3.22463e28i	0.231889	−	0.387099i
$569$			4.11641e27i			0.0485110i	0.999706	+	0.0242555i	$0.00772152\pi$
$569$			4.11641e27i			0.0485110i	−0.999706	+	0.0242555i	$0.992278\pi$
$570$		0			0
$571$	−6.59699e28			−0.749319			−0.374659	−	0.927163i	$-0.622240\pi$
$571$	−6.59699e28			−0.749319			−0.374659	+	0.927163i	$0.622240\pi$
$572$	6.11831e27	+	2.30162e27i	0.0682296	+	0.0256670i
$573$		0			0
$574$	−4.17427e27	+	2.29518e28i	−0.0448751	+	0.246741i
$575$	−4.71411e28			−0.497608
$576$		0			0
$577$	−5.42260e28			−0.551902			−0.275951	−	0.961172i	$-0.588993\pi$
$577$	−5.42260e28			−0.551902			−0.275951	+	0.961172i	$0.588993\pi$
$578$	8.24284e25	−	4.53223e26i	0.000823824	−	0.00452971i
$579$		0			0
$580$	2.00202e29	+	7.53133e28i	1.92964	+	0.725902i
$581$	8.96876e27			0.0848951
$582$		0			0
$583$			3.29792e28i			0.301106i
$584$	4.89964e28	−	8.17912e28i	0.439369	−	0.733452i
$585$		0			0
$586$	3.60277e28	−	1.98094e29i	0.311682	−	1.71375i
$587$			2.02520e29i			1.72094i	0.509497	+	0.860472i	$0.329831\pi$
$587$			2.02520e29i			1.72094i	−0.509497	+	0.860472i	$0.670169\pi$
$588$		0			0
$589$			2.36949e28i			0.194287i
$590$	−3.20549e29	−	5.82986e28i	−2.58195	−	0.469583i
$591$		0			0
$592$	1.06276e29	−	1.21265e29i	0.826148	−	0.942666i
$593$			4.50663e28i			0.344174i	0.985082	+	0.172087i	$0.0550510\pi$
$593$			4.50663e28i			0.344174i	−0.985082	+	0.172087i	$0.944949\pi$
$594$		0			0
$595$	6.17793e28			0.455423
$596$	−1.33513e29	−	5.02258e28i	−0.967027	−	0.363782i
$597$		0			0
$598$	−5.10154e27	−	9.27824e26i	−0.0356729	−	0.00648788i
$599$	−2.69377e29			−1.85088			−0.925441	−	0.378892i	$-0.876305\pi$
$599$	−2.69377e29			−1.85088			−0.925441	+	0.378892i	$0.876305\pi$
$600$		0			0
$601$	2.98583e28			0.198099			0.0990496	−	0.995082i	$-0.468420\pi$
$601$	2.98583e28			0.198099			0.0990496	+	0.995082i	$0.468420\pi$
$602$	−7.84987e28	−	1.42767e28i	−0.511799	−	0.0930816i
$603$		0			0
$604$	−8.07577e28	+	2.14675e29i	−0.508506	+	1.35174i
$605$	2.10254e29			1.30110
$606$		0			0
$607$		−	3.14282e29i		−	1.87862i	−0.343073	−	0.939309i	$-0.611468\pi$
$607$		−	3.14282e29i		−	1.87862i	0.343073	−	0.939309i	$-0.388532\pi$
$608$	1.05425e29	−	8.37418e28i	0.619378	−	0.491988i
$609$		0			0
$610$	1.84357e29	+	3.35293e28i	1.04640	+	0.190310i
$611$			2.44958e28i			0.136665i
$612$		0			0
$613$		−	2.30644e29i		−	1.24339i	−0.783259	−	0.621695i	$-0.786444\pi$
$613$		−	2.30644e29i		−	1.24339i	0.783259	−	0.621695i	$-0.213556\pi$
$614$	−5.56415e28	+	3.05939e29i	−0.294870	+	1.62131i
$615$		0			0
$616$	−1.31340e28	+	2.19250e28i	−0.0672665	+	0.112290i
$617$		−	1.40297e29i		−	0.706408i	−0.935546	−	0.353204i	$-0.885092\pi$
$617$		−	1.40297e29i		−	0.706408i	0.935546	−	0.353204i	$-0.114908\pi$
$618$		0			0
$619$	−7.97068e28			−0.387921			−0.193961	−	0.981009i	$-0.562133\pi$
$619$	−7.97068e28			−0.387921			−0.193961	+	0.981009i	$0.562133\pi$
$620$	−3.13239e28	+	8.32670e28i	−0.149887	+	0.398438i
$621$		0			0
$622$	−1.13418e28	+	6.23615e28i	−0.0524665	+	0.288481i
$623$	1.97981e28			0.0900534
$624$		0			0
$625$	2.29960e29			1.01137
$626$	2.93045e28	−	1.61128e29i	0.126737	−	0.696851i
$627$		0			0
$628$	−3.32336e28	+	8.83435e28i	−0.138996	+	0.369486i
$629$	3.05448e29			1.25633
$630$		0			0
$631$		−	4.65832e29i		−	1.85319i	−0.376055	−	0.926597i	$-0.622720\pi$
$631$		−	4.65832e29i		−	1.85319i	0.376055	−	0.926597i	$-0.377280\pi$
$632$	2.26979e29	+	1.35970e29i	0.888088	+	0.532002i
$633$		0			0
$634$	7.35438e28	−	4.04373e29i	0.278361	−	1.53054i
$635$			2.06566e29i			0.769017i
$636$		0			0
$637$		−	3.77492e28i		−	0.135970i
$638$	−1.64922e29	−	2.99945e28i	−0.584333	−	0.106273i
$639$		0			0
$640$	4.81182e29	−	1.54912e29i	1.64976	−	0.531122i
$641$			3.16773e29i			1.06841i	0.845355	+	0.534205i	$0.179389\pi$
$641$			3.16773e29i			1.06841i	−0.845355	+	0.534205i	$0.820611\pi$
$642$		0			0
$643$	−5.21978e28			−0.170387			−0.0851937	−	0.996364i	$-0.527151\pi$
$643$	−5.21978e28			−0.170387			−0.0851937	+	0.996364i	$0.527151\pi$
$644$	7.13809e27	−	1.89749e28i	0.0229235	−	0.0609366i
$645$		0			0
$646$	2.50928e29	+	4.56366e28i	0.780024	+	0.141864i
$647$	2.60421e29			0.796491			0.398246	−	0.917279i	$-0.369619\pi$
$647$	2.60421e29			0.796491			0.398246	+	0.917279i	$0.369619\pi$
$648$		0			0
$649$	2.55325e29			0.756005
$650$	9.87971e28	+	1.79684e28i	0.287842	+	0.0523502i
$651$		0			0
$652$	4.60082e29	+	1.73076e29i	1.29788	+	0.488245i
$653$	1.54820e29			0.429773			0.214886	−	0.976639i	$-0.431062\pi$
$653$	1.54820e29			0.429773			0.214886	+	0.976639i	$0.431062\pi$
$654$		0			0
$655$			3.36472e29i			0.904514i
$656$	−2.38323e29	+	2.71935e29i	−0.630485	+	0.719407i
$657$		0			0
$658$	−9.42275e28	−	1.71373e28i	−0.241438	−	0.0439106i
$659$		−	6.62583e29i		−	1.67087i	−0.549587	−	0.835436i	$-0.685215\pi$
$659$		−	6.62583e29i		−	1.67087i	0.549587	−	0.835436i	$-0.314785\pi$
$660$		0			0
$661$			4.87707e28i			0.119136i	0.998224	+	0.0595681i	$0.0189723\pi$
$661$			4.87707e28i			0.119136i	−0.998224	+	0.0595681i	$0.981028\pi$
$662$	5.71772e28	−	3.14383e29i	0.137472	−	0.755875i
$663$		0			0
$664$	1.19256e29	+	7.14391e28i	0.277788	+	0.166407i
$665$			1.56755e29i			0.359413i
$666$		0			0
$667$	1.32966e29			0.295405
$668$	6.09012e29	+	2.29102e29i	1.33190	+	0.501044i
$669$		0			0
$670$	−5.60393e28	+	3.08126e29i	−0.118770	+	0.653045i
$671$	−1.46845e29			−0.306390
$672$		0			0
$673$	5.68302e29			1.14927			0.574633	−	0.818411i	$-0.305145\pi$
$673$	5.68302e29			1.14927			0.574633	+	0.818411i	$0.305145\pi$
$674$	−7.06221e28	+	3.88308e29i	−0.140609	+	0.773121i
$675$		0			0
$676$	−4.74615e29	−	1.78543e29i	−0.916011	−	0.344590i
$677$	1.00086e29			0.190193			0.0950965	−	0.995468i	$-0.469684\pi$
$677$	1.00086e29			0.190193			0.0950965	+	0.995468i	$0.469684\pi$
$678$		0			0
$679$			5.37721e28i			0.0990660i
$680$	8.21466e29	+	4.92093e29i	1.49020	+	0.892695i
$681$		0			0
$682$	1.24751e28	−	6.85932e28i	0.0219437	−	0.120655i
$683$			3.67784e29i			0.637052i	0.947914	+	0.318526i	$0.103188\pi$
$683$			3.67784e29i			0.637052i	−0.947914	+	0.318526i	$0.896812\pi$
$684$		0			0
$685$			3.11319e29i			0.522944i
$686$	3.01136e29	+	5.47679e28i	0.498148	+	0.0905989i
$687$		0			0
$688$	−9.30062e29	−	8.15102e29i	−1.49222	−	1.30778i
$689$			5.57245e28i			0.0880530i
$690$		0			0
$691$	3.53882e29			0.542424			0.271212	−	0.962520i	$-0.412576\pi$
$691$	3.53882e29			0.542424			0.271212	+	0.962520i	$0.412576\pi$
$692$	−9.30597e29	−	3.50078e29i	−1.40491	−	0.528506i
$693$		0			0
$694$	−8.15176e29	−	1.48257e29i	−1.19392	−	0.217141i
$695$	1.05487e29			0.152181
$696$		0			0
$697$	−6.84961e29			−0.958787
$698$	1.05656e30	+	1.92158e29i	1.45684	+	0.264957i
$699$		0			0
$700$	−1.38237e29	+	3.67471e29i	−0.184968	+	0.491692i
$701$	−1.09765e30			−1.44685			−0.723427	−	0.690401i	$-0.757434\pi$
$701$	−1.09765e30			−1.44685			−0.723427	+	0.690401i	$0.757434\pi$
$702$		0			0
$703$			7.75024e29i			0.991481i
$704$	−3.49279e29	+	1.86915e29i	−0.440210	+	0.235576i
$705$		0			0
$706$	−1.33646e30	−	2.43064e29i	−1.63496	−	0.297352i
$707$			2.46568e29i			0.297189i
$708$		0			0
$709$			2.46312e29i			0.288204i	0.989563	+	0.144102i	$0.0460294\pi$
$709$			2.46312e29i			0.288204i	−0.989563	+	0.144102i	$0.953971\pi$
$710$	−1.21382e29	+	6.67405e29i	−0.139940	+	0.769443i
$711$		0			0
$712$	2.63252e29	+	1.57699e29i	0.294667	+	0.176518i
$713$			5.53022e28i			0.0609962i
$714$		0			0
$715$	−1.17967e29			−0.126342
$716$	−1.61103e28	+	4.28254e28i	−0.0170027	+	0.0451976i
$717$		0			0
$718$	−1.96730e29	+	1.08170e30i	−0.201634	+	1.10867i
$719$	2.45012e29			0.247477			0.123738	−	0.992315i	$-0.460512\pi$
$719$	2.45012e29			0.247477			0.123738	+	0.992315i	$0.460512\pi$
$720$		0			0
$721$	5.02582e29			0.493045
$722$	6.92754e28	−	3.80903e29i	0.0669790	−	0.368277i
$723$		0			0
$724$	5.26809e29	−	1.40040e30i	0.494764	−	1.31521i
$725$	−2.57503e30			−2.38360
$726$		0			0
$727$			1.15274e30i			1.03663i	0.855191	+	0.518313i	$0.173440\pi$
$727$			1.15274e30i			1.03663i	−0.855191	+	0.518313i	$0.826560\pi$
$728$	−2.21923e28	+	3.70463e28i	−0.0196709	+	0.0328372i
$729$		0			0
$730$	−3.07879e29	+	1.69284e30i	−0.265149	+	1.45789i
$731$		−	2.34268e30i		−	1.98875i
$732$		0			0
$733$		−	1.43262e30i		−	1.18179i	−0.806750	−	0.590893i	$-0.798776\pi$
$733$		−	1.43262e30i		−	1.18179i	0.806750	−	0.590893i	$-0.201224\pi$
$734$	1.58795e30	+	2.88803e29i	1.29130	+	0.234851i
$735$		0			0
$736$	2.46055e29	−	1.95448e29i	0.194453	−	0.154459i
$737$		−	2.45430e29i		−	0.191214i
$738$		0			0
$739$	−1.91369e30			−1.44912			−0.724561	−	0.689211i	$-0.757957\pi$
$739$	−1.91369e30			−1.44912			−0.724561	+	0.689211i	$0.757957\pi$
$740$	−1.02456e30	+	2.72354e30i	−0.764898	+	2.03330i
$741$		0			0
$742$	−2.14354e29	−	3.89849e28i	−0.155558	−	0.0282915i
$743$	2.10955e29			0.150941			0.0754706	−	0.997148i	$-0.475954\pi$
$743$	2.10955e29			0.150941			0.0754706	+	0.997148i	$0.475954\pi$
$744$		0			0
$745$	2.57428e30			1.79066
$746$	−4.86238e29	−	8.84327e28i	−0.333496	−	0.0606534i
$747$		0			0
$748$	−7.02373e29	−	2.64223e29i	−0.468383	−	0.176199i
$749$	4.93658e29			0.324614
$750$		0			0
$751$		−	6.19010e28i		−	0.0395802i	−0.999804	−	0.0197901i	$-0.993700\pi$
$751$		−	6.19010e28i		−	0.0395802i	0.999804	−	0.0197901i	$-0.00629980\pi$
$752$	−1.11642e30	−	9.78424e29i	−0.703946	−	0.616935i
$753$		0			0
$754$	−2.78666e29	−	5.06813e28i	−0.170877	−	0.0310777i
$755$		−	4.13916e30i		−	2.50305i
$756$		0			0
$757$		−	2.13188e30i		−	1.25388i	−0.779068	−	0.626939i	$-0.784307\pi$
$757$		−	2.13188e30i		−	1.25388i	0.779068	−	0.626939i	$-0.215693\pi$
$758$	2.70737e29	−	1.48862e30i	0.157044	−	0.863489i
$759$		0			0
$760$	−1.24861e30	+	2.08434e30i	−0.704503	+	1.17605i
$761$		−	2.00907e30i		−	1.11804i	−0.829154	−	0.559020i	$-0.811178\pi$
$761$		−	2.00907e30i		−	1.11804i	0.829154	−	0.559020i	$-0.188822\pi$
$762$		0			0
$763$	6.21986e29			0.336723
$764$	2.56294e30	+	9.64142e29i	1.36854	+	0.514826i
$765$		0			0
$766$	7.52479e28	−	4.13743e29i	0.0390924	−	0.214945i
$767$	4.31420e29			0.221080
$768$		0			0
$769$	4.18607e28			0.0208727			0.0104364	−	0.999946i	$-0.496678\pi$
$769$	4.18607e28			0.0208727			0.0104364	+	0.999946i	$0.496678\pi$
$770$	8.25301e28	−	4.53783e29i	0.0405938	−	0.223201i
$771$		0			0
$772$	1.21616e29	+	4.57503e28i	0.0582117	+	0.0218984i
$773$	2.08036e30			0.982323			0.491162	−	0.871068i	$-0.336572\pi$
$773$	2.08036e30			0.982323			0.491162	+	0.871068i	$0.336572\pi$
$774$		0			0
$775$		−	1.07099e30i		−	0.492173i
$776$	−4.28313e29	+	7.14996e29i	−0.194184	+	0.324157i
$777$		0			0
$778$	−7.38051e29	+	4.05810e30i	−0.325687	+	1.79076i
$779$		−	1.73798e30i		−	0.756661i
$780$		0			0
$781$		−	5.31605e29i		−	0.225296i
$782$	5.85650e29	+	1.06513e29i	0.244888	+	0.0445381i
$783$		0			0
$784$	1.72045e30	+	1.50780e30i	0.700365	+	0.613797i
$785$		−	1.70336e30i		−	0.684185i
$786$		0			0
$787$	−1.95469e29			−0.0764440			−0.0382220	−	0.999269i	$-0.512169\pi$
$787$	−1.95469e29			−0.0764440			−0.0382220	+	0.999269i	$0.512169\pi$
$788$	−6.21252e29	−	2.33706e29i	−0.239741	−	0.0901873i
$789$		0			0
$790$	−4.69780e30	−	8.54396e29i	−1.76527	−	0.321051i
$791$	4.70875e29			0.174603
$792$		0			0
$793$	−2.48123e29			−0.0895980
$794$	−4.45423e30	−	8.10097e29i	−1.58729	−	0.288683i
$795$		0			0
$796$	−5.60567e29	+	1.49013e30i	−0.194554	+	0.517175i
$797$	−3.72135e30			−1.27464			−0.637321	−	0.770599i	$-0.719957\pi$
$797$	−3.72135e30			−1.27464			−0.637321	+	0.770599i	$0.719957\pi$
$798$		0			0
$799$		−	2.81208e30i		−	0.938181i
$800$	−4.76514e30	+	3.78507e30i	−1.56903	+	1.24632i
$801$		0			0
$802$	−9.24335e29	−	1.68110e29i	−0.296482	−	0.0539216i
$803$		−	1.34839e30i		−	0.426877i
$804$		0			0
$805$			3.65856e29i			0.112837i
$806$	2.10791e28	−	1.15901e29i	0.00641702	−	0.0352833i
$807$		0			0
$808$	−1.96400e30	+	3.27856e30i	−0.582534	+	0.972442i
$809$		−	4.06551e30i		−	1.19030i	−0.803615	−	0.595149i	$-0.797093\pi$
$809$		−	4.06551e30i		−	1.19030i	0.803615	−	0.595149i	$-0.202907\pi$
$810$		0			0
$811$	3.84580e29			0.109715			0.0548577	−	0.998494i	$-0.482529\pi$
$811$	3.84580e29			0.109715			0.0548577	+	0.998494i	$0.482529\pi$
$812$	3.89910e29	−	1.03648e30i	0.109806	−	0.291893i
$813$		0			0
$814$	4.08043e29	−	2.24358e30i	0.111982	−	0.615724i
$815$	−8.87087e30			−2.40332
$816$		0			0
$817$	5.94417e30			1.56949
$818$	−4.53077e29	+	2.49120e30i	−0.118103	+	0.649379i
$819$		0			0
$820$	2.29756e30	−	6.10750e30i	0.583741	−	1.55174i
$821$	−8.22175e29			−0.206234			−0.103117	−	0.994669i	$-0.532882\pi$
$821$	−8.22175e29			−0.206234			−0.103117	+	0.994669i	$0.532882\pi$
$822$		0			0
$823$			3.29641e30i			0.806015i	0.915197	+	0.403007i	$0.132035\pi$
$823$			3.29641e30i			0.806015i	−0.915197	+	0.403007i	$0.867965\pi$
$824$	6.68273e30	+	4.00323e30i	1.61331	+	0.966441i
$825$		0			0
$826$	−3.01822e29	+	1.65954e30i	−0.0710330	+	0.390567i
$827$		−	6.69806e30i		−	1.55647i	−0.627972	−	0.778236i	$-0.716115\pi$
$827$		−	6.69806e30i		−	1.55647i	0.627972	−	0.778236i	$-0.283885\pi$
$828$		0			0
$829$			1.89371e30i			0.429033i	0.976720	+	0.214517i	$0.0688176\pi$
$829$			1.89371e30i			0.429033i	−0.976720	+	0.214517i	$0.931182\pi$
$830$	−2.46824e30	−	4.48903e29i	−0.552164	−	0.100423i
$831$		0			0
$832$	−5.90173e29	+	3.15828e29i	−0.128731	+	0.0688899i
$833$			4.33355e30i			0.933408i
$834$		0			0
$835$	−1.17424e31			−2.46632
$836$	6.70423e29	−	1.78216e30i	0.139054	−	0.369641i
$837$		0			0
$838$	−8.33634e30	−	1.51614e30i	−1.68622	−	0.306674i
$839$	−7.86642e30			−1.57136			−0.785681	−	0.618631i	$-0.787687\pi$
$839$	−7.86642e30			−1.57136			−0.785681	+	0.618631i	$0.787687\pi$
$840$		0			0
$841$	2.13025e30			0.415023
$842$	−3.79674e28	−	6.90518e27i	−0.00730523	−	0.00132861i
$843$		0			0
$844$	2.44645e30	+	9.20319e29i	0.459135	+	0.172720i
$845$	9.15107e30			1.69620
$846$		0			0
$847$		−	1.08852e30i		−	0.196816i
$848$	−2.53970e30	−	2.22578e30i	−0.453550	−	0.397489i
$849$		0			0
$850$	−1.13418e31	−	2.06274e30i	−1.97598	−	0.359374i
$851$			1.80886e30i			0.311274i
$852$		0			0
$853$			3.63026e30i			0.609498i	0.952433	+	0.304749i	$0.0985726\pi$
$853$			3.63026e30i			0.609498i	−0.952433	+	0.304749i	$0.901427\pi$
$854$	1.73587e29	−	9.54450e29i	0.0287879	−	0.158287i
$855$		0			0
$856$	6.56407e30	+	3.93215e30i	1.06218	+	0.636291i
$857$			5.21740e30i			0.833980i	0.908911	+	0.416990i	$0.136915\pi$
$857$			5.21740e30i			0.833980i	−0.908911	+	0.416990i	$0.863085\pi$
$858$		0			0
$859$	1.26493e30			0.197305			0.0986527	−	0.995122i	$-0.468547\pi$
$859$	1.26493e30			0.197305			0.0986527	+	0.995122i	$0.468547\pi$
$860$	2.08886e31	+	7.85801e30i	3.21867	+	1.21082i
$861$		0			0
$862$	1.24386e30	−	6.83924e30i	0.187045	−	1.02845i
$863$	7.02820e30			1.04407			0.522037	−	0.852923i	$-0.325172\pi$
$863$	7.02820e30			1.04407			0.522037	+	0.852923i	$0.325172\pi$
$864$		0			0
$865$	1.79429e31			2.60150
$866$	−3.05039e29	+	1.67723e30i	−0.0436936	+	0.240245i
$867$		0			0
$868$	4.31088e29	+	1.62169e29i	0.0602710	+	0.0226731i
$869$	3.74192e30			0.516877
$870$		0			0
$871$		−	4.14701e29i		−	0.0559170i
$872$	8.27042e30	+	4.95433e30i	1.10180	+	0.660027i
$873$		0			0
$874$	−2.70259e29	+	1.48599e30i	−0.0351488	+	0.193262i
$875$		−	3.54930e30i		−	0.456099i
$876$		0			0
$877$			1.12477e31i			1.41114i	0.708642	+	0.705568i	$0.249308\pi$
$877$			1.12477e31i			1.41114i	−0.708642	+	0.705568i	$0.750692\pi$
$878$	1.05431e31	+	1.91750e30i	1.30701	+	0.237707i
$879$		0			0
$880$	4.71192e30	−	5.37648e30i	0.570335	−	0.650773i
$881$			4.83584e30i			0.578396i	0.957269	+	0.289198i	$0.0933886\pi$
$881$			4.83584e30i			0.578396i	−0.957269	+	0.289198i	$0.906611\pi$
$882$		0			0
$883$	8.05086e30			0.940275			0.470137	−	0.882593i	$-0.344204\pi$
$883$	8.05086e30			0.940275			0.470137	+	0.882593i	$0.344204\pi$
$884$	−1.18679e30	−	4.46454e29i	−0.136970	−	0.0515262i
$885$		0			0
$886$	5.06902e30	+	9.21909e29i	0.571307	+	0.103904i
$887$	−9.61739e30			−1.07117			−0.535586	−	0.844481i	$-0.679909\pi$
$887$	−9.61739e30			−1.07117			−0.535586	+	0.844481i	$0.679909\pi$
$888$		0			0
$889$	1.06943e30			0.116328
$890$	−5.44854e30	−	9.90934e29i	−0.585714	−	0.106525i
$891$		0			0
$892$	−1.39787e30	+	3.71590e30i	−0.146769	+	0.390151i
$893$	7.13520e30			0.740399
$894$		0			0
$895$		−	8.25719e29i		−	0.0836933i
$896$	−8.02005e29	−	2.49116e30i	−0.0803421	−	0.249556i
$897$		0			0
$898$	4.23560e30	+	7.70335e29i	0.414490	+	0.0753838i
$899$			3.02082e30i			0.292179i
$900$		0			0
$901$		−	6.39709e30i		−	0.604467i
$902$	−9.15031e29	+	5.03120e30i	−0.0854608	+	0.469897i
$903$		0			0
$904$	6.26113e30	+	3.75068e30i	0.571326	+	0.342248i
$905$			2.70011e31i			2.43541i
$906$		0			0
$907$	−1.37019e31			−1.20755			−0.603775	−	0.797155i	$-0.706338\pi$
$907$	−1.37019e31			−1.20755			−0.603775	+	0.797155i	$0.706338\pi$
$908$	−6.10038e30	+	1.62164e31i	−0.531441	+	1.41271i
$909$		0			0
$910$	1.39450e29	−	7.66752e29i	0.0118709	−	0.0652710i
$911$	1.28803e31			1.08389			0.541944	−	0.840415i	$-0.317688\pi$
$911$	1.28803e31			1.08389			0.541944	+	0.840415i	$0.317688\pi$
$912$		0			0
$913$	1.96602e30			0.161676
$914$	3.49843e30	−	1.92358e31i	0.284406	−	1.56377i
$915$		0			0
$916$	7.16372e30	−	1.90430e31i	0.569162	−	1.51298i
$917$	1.74197e30			0.136824
$918$		0			0
$919$		−	9.67929e30i		−	0.743072i	−0.928419	−	0.371536i	$-0.878831\pi$
$919$		−	9.67929e30i		−	0.743072i	0.928419	−	0.371536i	$-0.121169\pi$
$920$	−2.91416e30	+	4.86471e30i	−0.221178	+	0.369219i
$921$		0			0
$922$	−1.62108e30	+	8.91334e30i	−0.120263	+	0.661250i
$923$		−	8.98246e29i		−	0.0658836i
$924$		0			0
$925$		−	3.50306e31i		−	2.51165i
$926$	−1.91681e31	−	3.48612e30i	−1.35882	−	0.247131i
$927$		0			0
$928$	1.34405e31	−	1.06761e31i	0.931453	−	0.739877i
$929$		−	9.88469e30i		−	0.677326i	−0.940908	−	0.338663i	$-0.890025\pi$
$929$		−	9.88469e30i		−	0.677326i	0.940908	−	0.338663i	$-0.109975\pi$
$930$		0			0
$931$	−1.09957e31			−0.736633
$932$	−2.58768e30	+	6.87874e30i	−0.171413	+	0.455661i
$933$		0			0
$934$	−1.27363e31	−	2.31636e30i	−0.824897	−	0.150025i
$935$	1.35425e31			0.867315
$936$		0			0
$937$	2.43053e31			1.52207			0.761037	−	0.648708i	$-0.224690\pi$
$937$	2.43053e31			1.52207			0.761037	+	0.648708i	$0.224690\pi$
$938$	1.59522e30	+	2.90125e29i	0.0987851	+	0.0179662i
$939$		0			0
$940$	2.50741e31	+	9.43252e30i	1.51839	+	0.571196i
$941$	−1.38163e31			−0.827369			−0.413685	−	0.910420i	$-0.635758\pi$
$941$	−1.38163e31			−0.827369			−0.413685	+	0.910420i	$0.635758\pi$
$942$		0			0
$943$		−	4.05633e30i		−	0.237553i
$944$	−1.72320e31	+	1.96624e31i	−0.997999	+	1.13875i
$945$		0			0
$946$	−1.72075e31	−	3.12956e30i	−0.974679	−	0.177266i
$947$		−	1.10253e31i		−	0.617610i	−0.951125	−	0.308805i	$-0.900071\pi$
$947$		−	1.10253e31i		−	0.617610i	0.951125	−	0.308805i	$-0.0999291\pi$
$948$		0			0
$949$		−	2.27836e30i		−	0.124832i
$950$	5.23388e30	−	2.87779e31i	0.283613	−	1.55942i
$951$		0			0
$952$	2.54765e30	−	4.25287e30i	0.135037	−	0.225421i
$953$			1.87594e31i			0.983428i	0.870757	+	0.491714i	$0.163629\pi$
$953$			1.87594e31i			0.983428i	−0.870757	+	0.491714i	$0.836371\pi$
$954$		0			0
$955$	−4.94162e31			−2.53416
$956$	−1.96028e31	−	7.37430e30i	−0.994284	−	0.374035i
$957$		0			0
$958$	−5.79137e30	+	3.18432e31i	−0.287371	+	1.58008i
$959$	1.61175e30			0.0791049
$960$		0			0
$961$	1.95691e31			0.939670
$962$	6.89466e29	−	3.79095e30i	0.0327472	−	0.180057i
$963$		0			0
$964$	2.96393e31	+	1.11499e31i	1.37739	+	0.518156i
$965$	−2.34489e30			−0.107792
$966$		0			0
$967$			2.75038e31i			1.23713i	0.785734	+	0.618565i	$0.212286\pi$
$967$			2.75038e31i			1.23713i	−0.785734	+	0.618565i	$0.787714\pi$
$968$	8.67041e30	−	1.44738e31i	0.385788	−	0.644008i
$969$		0			0
$970$	2.69139e30	−	1.47983e31i	0.117186	−	0.644332i
$971$		−	7.56252e30i		−	0.325735i	−0.986648	−	0.162868i	$-0.947926\pi$
$971$		−	7.56252e30i		−	0.325735i	0.986648	−	0.162868i	$-0.0520743\pi$
$972$		0			0
$973$		−	5.46127e29i		−	0.0230202i
$974$	−1.67130e31	−	3.03962e30i	−0.696924	−	0.126751i
$975$		0			0
$976$	9.91066e30	−	1.13084e31i	0.404464	−	0.461508i
$977$			4.33329e31i			1.74954i	0.484536	+	0.874772i	$0.338989\pi$
$977$			4.33329e31i			1.74954i	−0.484536	+	0.874772i	$0.661011\pi$
$978$		0			0
$979$	4.33991e30			0.171499
$980$	−3.86404e31	−	1.45360e31i	−1.51066	−	0.568290i
$981$		0			0
$982$	3.43007e31	+	6.23831e30i	1.31260	+	0.238724i
$983$	2.71383e31			1.02747			0.513737	−	0.857948i	$-0.328261\pi$
$983$	2.71383e31			1.02747			0.513737	+	0.857948i	$0.328261\pi$
$984$		0			0
$985$	1.19784e31			0.443934
$986$	3.19905e31	+	5.81815e30i	1.17304	+	0.213342i
$987$		0			0
$988$	1.13281e30	−	3.01129e30i	0.0406637	−	0.108095i
$989$	1.38733e31			0.492741
$990$		0			0
$991$			3.84606e31i			1.33734i	0.743558	+	0.668672i	$0.233137\pi$
$991$			3.84606e31i			1.33734i	−0.743558	+	0.668672i	$0.766863\pi$
$992$	4.44035e30	+	5.59008e30i	0.152772	+	0.192329i
$993$		0			0
$994$	3.45527e30	+	6.28414e29i	0.116392	+	0.0211684i
$995$		−	2.87313e31i		−	0.957664i
$996$		0			0
$997$		−	3.68948e31i		−	1.20411i	−0.798455	−	0.602055i	$-0.794349\pi$
$997$		−	3.68948e31i		−	1.20411i	0.798455	−	0.602055i	$-0.205651\pi$
$998$	9.91394e30	−	5.45107e31i	0.320166	−	1.76040i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.22.f.a.35.40	yes	84
3.2	odd	2	inner	72.22.f.a.35.45	yes	84
8.3	odd	2	inner	72.22.f.a.35.46	yes	84
24.11	even	2	inner	72.22.f.a.35.39	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.22.f.a.35.39	✓	84	24.11	even	2	inner
72.22.f.a.35.40	yes	84	1.1	even	1	trivial
72.22.f.a.35.45	yes	84	3.2	odd	2	inner
72.22.f.a.35.46	yes	84	8.3	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)

\(f(q)\)	\(=\)	\(q+(-259.127 + 1424.78i) q^{2} +(-1.96286e6 - 738399. i) q^{4} +3.78460e7 q^{5} -1.95935e8i q^{7} +(1.56069e9 - 2.60531e9i) q^{8} +O(q^{10})\)	\(q+(-259.127 + 1424.78i) q^{2} +(-1.96286e6 - 738399. i) q^{4} +3.78460e7 q^{5} -1.95935e8i q^{7} +(1.56069e9 - 2.60531e9i) q^{8} +(-9.80691e9 + 5.39223e10i) q^{10} -4.29505e10i q^{11} -7.25729e10i q^{13} +(2.79165e11 + 5.07721e10i) q^{14} +(3.30758e12 + 2.89875e12i) q^{16} +8.33127e12i q^{17} -2.11393e13 q^{19} +(-7.42863e13 - 2.79454e13i) q^{20} +(6.11951e13 + 1.11296e13i) q^{22} -4.93376e13 q^{23} +9.55480e14 q^{25} +(1.03401e14 + 1.88056e13i) q^{26} +(-1.44678e14 + 3.84593e14i) q^{28} -2.69501e15 q^{29} -1.12089e15i q^{31} +(-4.98717e15 + 3.96144e15i) q^{32} +(-1.18702e16 - 2.15886e15i) q^{34} -7.41535e15i q^{35} -3.66628e16i q^{37} +(5.47775e15 - 3.01188e16i) q^{38} +(5.90658e16 - 9.86003e16i) q^{40} +8.22158e16i q^{41} -2.81191e17 q^{43} +(-3.17146e16 + 8.43057e16i) q^{44} +(1.27847e16 - 7.02954e16i) q^{46} -3.37533e17 q^{47} +5.20155e17 q^{49} +(-2.47591e17 + 1.36135e18i) q^{50} +(-5.35878e16 + 1.42450e17i) q^{52} -7.67842e17 q^{53} -1.62550e18i q^{55} +(-5.10471e17 - 3.05794e17i) q^{56} +(6.98351e17 - 3.83981e18i) q^{58} +5.94464e18i q^{59} -3.41895e18i q^{61} +(1.59703e18 + 2.90454e17i) q^{62} +(-4.35188e18 - 8.13214e18i) q^{64} -2.74659e18i q^{65} +5.71427e18 q^{67} +(6.15180e18 - 1.63531e19i) q^{68} +(1.05653e19 + 1.92152e18i) q^{70} +1.23772e19 q^{71} +3.13941e19 q^{73} +(5.22365e19 + 9.50032e18i) q^{74} +(4.14934e19 + 1.56092e19i) q^{76} -8.41551e18 q^{77} +8.71218e19i q^{79} +(1.25179e20 + 1.09706e20i) q^{80} +(-1.17140e20 - 2.13043e19i) q^{82} +4.57741e19i q^{83} +3.15305e20i q^{85} +(7.28643e19 - 4.00636e20i) q^{86} +(-1.11899e20 - 6.70323e19i) q^{88} +1.01044e20i q^{89} -1.42196e19 q^{91} +(9.68428e19 + 3.64309e19i) q^{92} +(8.74640e19 - 4.80912e20i) q^{94} -8.00035e20 q^{95} -2.74438e20 q^{97} +(-1.34786e20 + 7.41108e20i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 2424084 q^{4}+O(q^{10}) \) 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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