LMFDB - Embedded newform 81.7.d.e.26.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,7,Mod(26,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("81.26");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	81.d (of order $6$, degree $2$, not 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:	$18.6343807732$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.58594980096.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 21x^{6} + 341x^{4} - 2100x^{2} + 10000 $ x^8 - 21x^6 + 341x^4 - 2100*x^2 + 10000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{16} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.4
Root			$3.20565 + 1.85078i$ of defining polynomial
Character	$\chi$	$=$	81.26
Dual form			81.7.d.e.53.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(12.2150 + 7.05234i) q^{2} +(67.4711 + 116.863i) q^{4} +(119.008 - 68.7094i) q^{5} +(257.384 - 445.803i) q^{7} +1000.62i q^{8} +1938.25 q^{10} +(1055.05 + 609.131i) q^{11} +(85.2313 + 147.625i) q^{13} +(6287.91 - 3630.33i) q^{14} +(-2738.55 + 4743.30i) q^{16} +1574.10i q^{17} -11289.1 q^{19} +(16059.2 + 9271.79i) q^{20} +(8591.60 + 14881.1i) q^{22} +(-9156.17 + 5286.32i) q^{23} +(1629.46 - 2822.30i) q^{25} +2404.32i q^{26} +69464.0 q^{28} +(-7504.48 - 4332.71i) q^{29} +(13104.5 + 22697.7i) q^{31} +(-11442.9 + 6606.58i) q^{32} +(-11101.1 + 19227.7i) q^{34} -70738.9i q^{35} +21866.9 q^{37} +(-137896. - 79614.3i) q^{38} +(68751.8 + 119082. i) q^{40} +(-33053.3 + 19083.3i) q^{41} +(-11947.5 + 20693.8i) q^{43} +164395. i q^{44} -149124. q^{46} +(-23121.8 - 13349.4i) q^{47} +(-73668.9 - 127598. i) q^{49} +(39807.7 - 22983.0i) q^{50} +(-11501.3 + 19920.8i) q^{52} -213997. i q^{53} +167412. q^{55} +(446078. + 257543. i) q^{56} +(-61111.5 - 105848. i) q^{58} +(141759. - 81844.5i) q^{59} +(-55538.9 + 96196.1i) q^{61} +369671. i q^{62} +164166. q^{64} +(20286.4 + 11712.4i) q^{65} +(190518. + 329986. i) q^{67} +(-183955. + 106206. i) q^{68} +(498875. - 864076. i) q^{70} -675048. i q^{71} -762939. q^{73} +(267105. + 154213. i) q^{74} +(-761685. - 1.31928e6i) q^{76} +(543105. - 313562. i) q^{77} +(-257854. + 446616. i) q^{79} +752655. i q^{80} -538328. q^{82} +(-782690. - 451887. i) q^{83} +(108155. + 187331. i) q^{85} +(-291879. + 168516. i) q^{86} +(-609507. + 1.05570e6i) q^{88} +644278. i q^{89} +87748.8 q^{91} +(-1.23555e6 - 713347. i) q^{92} +(-188289. - 326125. i) q^{94} +(-1.34349e6 + 775664. i) q^{95} +(308235. - 533878. i) q^{97} -2.07815e6i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 194 q^{4} + 676 q^{7} + 6516 q^{10} + 3448 q^{13} - 10498 q^{16} - 7328 q^{19} + 58014 q^{22} - 17392 q^{25} + 304684 q^{28} + 153244 q^{31} - 65988 q^{34} + 257920 q^{37} + 338058 q^{40} - 126008 q^{43}+ \cdots - 975212 q^{97}+O(q^{100}) $ 8 * q + 194 * q^4 + 676 * q^7 + 6516 * q^10 + 3448 * q^13 - 10498 * q^16 - 7328 * q^19 + 58014 * q^22 - 17392 * q^25 + 304684 * q^28 + 153244 * q^31 - 65988 * q^34 + 257920 * q^37 + 338058 * q^40 - 126008 * q^43 - 233136 * q^46 - 121872 * q^49 + 71884 * q^52 + 108360 * q^55 - 567036 * q^58 - 167696 * q^61 - 57988 * q^64 - 8 * q^67 + 2104830 * q^70 - 3763352 * q^73 - 3764384 * q^76 - 1188728 * q^79 - 2732688 * q^82 + 176472 * q^85 - 27342 * q^88 - 747472 * q^91 - 1381140 * q^94 - 975212 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	12.2150	+	7.05234i	1.52688	+	0.881543i	0.999491	+	0.0319175i	$0.0101614\pi$
$2$	12.2150	+	7.05234i	1.52688	+	0.881543i	0.527387	+	0.849625i	$0.323172\pi$
$3$		0			0
$3$		0			0
$4$	67.4711	+	116.863i	1.05424	+	1.82599i
$5$	119.008	−	68.7094i	0.952065	−	0.549675i	0.0583432	−	0.998297i	$-0.481418\pi$
$5$	119.008	−	68.7094i	0.952065	−	0.549675i	0.893722	+	0.448622i	$0.148085\pi$
$6$		0			0
$7$	257.384	−	445.803i	0.750392	−	1.29972i	−0.197241	−	0.980355i	$-0.563198\pi$
$7$	257.384	−	445.803i	0.750392	−	1.29972i	0.947633	−	0.319362i	$-0.103468\pi$
$8$			1000.62i			1.95433i
$9$		0			0
$10$	1938.25			1.93825
$11$	1055.05	+	609.131i	0.792672	+	0.457649i	0.840902	−	0.541187i	$-0.182025\pi$
$11$	1055.05	+	609.131i	0.792672	+	0.457649i	−0.0482305	+	0.998836i	$0.515358\pi$
$12$		0			0
$13$	85.2313	+	147.625i	0.0387944	+	0.0671939i	0.884771	−	0.466027i	$-0.154315\pi$
$13$	85.2313	+	147.625i	0.0387944	+	0.0671939i	−0.845976	+	0.533221i	$0.820982\pi$
$14$	6287.91	−	3630.33i	2.29151	−	1.32300i
$15$		0			0
$16$	−2738.55	+	4743.30i	−0.668590	+	1.15803i
$17$			1574.10i			0.320395i	0.987085	+	0.160197i	$0.0512131\pi$
$17$			1574.10i			0.320395i	−0.987085	+	0.160197i	$0.948787\pi$
$18$		0			0
$19$	−11289.1			−1.64588			−0.822938	−	0.568131i	$-0.807667\pi$
$19$	−11289.1			−1.64588			−0.822938	+	0.568131i	$0.807667\pi$
$20$	16059.2	+	9271.79i	2.00740	+	1.15897i
$21$		0			0
$22$	8591.60	+	14881.1i	0.806875	+	1.39755i
$23$	−9156.17	+	5286.32i	−0.752542	+	0.434480i	−0.826611	−	0.562773i	$-0.809735\pi$
$23$	−9156.17	+	5286.32i	−0.752542	+	0.434480i	0.0740699	+	0.997253i	$0.476401\pi$
$24$		0			0
$25$	1629.46	−	2822.30i	0.104285	−	0.180627i
$26$			2404.32i			0.136796i
$27$		0			0
$28$	69464.0			3.16436
$29$	−7504.48	−	4332.71i	−0.307699	−	0.177650i	0.338197	−	0.941075i	$-0.390183\pi$
$29$	−7504.48	−	4332.71i	−0.307699	−	0.177650i	−0.645896	+	0.763425i	$0.723516\pi$
$30$		0			0
$31$	13104.5	+	22697.7i	0.439883	+	0.761899i	0.997680	−	0.0680779i	$-0.0216867\pi$
$31$	13104.5	+	22697.7i	0.439883	+	0.761899i	−0.557797	+	0.829977i	$0.688353\pi$
$32$	−11442.9	+	6606.58i	−0.349211	+	0.201617i
$33$		0			0
$34$	−11101.1	+	19227.7i	−0.282442	+	0.489204i
$35$		−	70738.9i		−	1.64989i
$36$		0			0
$37$	21866.9			0.431701			0.215850	−	0.976426i	$-0.430748\pi$
$37$	21866.9			0.431701			0.215850	+	0.976426i	$0.430748\pi$
$38$	−137896.	−	79614.3i	−2.51305	−	1.45091i
$39$		0			0
$40$	68751.8	+	119082.i	1.07425	+	1.86065i
$41$	−33053.3	+	19083.3i	−0.479582	+	0.276887i	−0.720242	−	0.693723i	$-0.755969\pi$
$41$	−33053.3	+	19083.3i	−0.479582	+	0.276887i	0.240660	+	0.970609i	$0.422636\pi$
$42$		0			0
$43$	−11947.5	+	20693.8i	−0.150270	+	0.260276i	−0.931327	−	0.364185i	$-0.881348\pi$
$43$	−11947.5	+	20693.8i	−0.150270	+	0.260276i	0.781056	+	0.624460i	$0.214681\pi$
$44$			164395.i			1.92988i
$45$		0			0
$46$	−149124.			−1.53205
$47$	−23121.8	−	13349.4i	−0.222704	−	0.128578i	0.384498	−	0.923126i	$-0.374375\pi$
$47$	−23121.8	−	13349.4i	−0.222704	−	0.128578i	−0.607202	+	0.794548i	$0.707708\pi$
$48$		0			0
$49$	−73668.9	−	127598.i	−0.626175	−	1.08457i
$50$	39807.7	−	22983.0i	0.318461	−	0.183864i
$51$		0			0
$52$	−11501.3	+	19920.8i	−0.0817969	+	0.141676i
$53$		−	213997.i		−	1.43741i	−0.695315	−	0.718705i	$-0.744735\pi$
$53$		−	213997.i		−	1.43741i	0.695315	−	0.718705i	$-0.255265\pi$
$54$		0			0
$55$	167412.			1.00623
$56$	446078.	+	257543.i	2.54008	+	1.46651i
$57$		0			0
$58$	−61111.5	−	105848.i	−0.313213	−	0.542500i
$59$	141759.	−	81844.5i	0.690231	−	0.398505i	−0.113468	−	0.993542i	$-0.536196\pi$
$59$	141759.	−	81844.5i	0.690231	−	0.398505i	0.803698	+	0.595037i	$0.202863\pi$
$60$		0			0
$61$	−55538.9	+	96196.1i	−0.244685	+	0.423807i	−0.962043	−	0.272898i	$-0.912018\pi$
$61$	−55538.9	+	96196.1i	−0.244685	+	0.423807i	0.717358	+	0.696705i	$0.245351\pi$
$62$			369671.i			1.55110i
$63$		0			0
$64$	164166.			0.626245
$65$	20286.4	+	11712.4i	0.0738696	+	0.0426486i
$66$		0			0
$67$	190518.	+	329986.i	0.633447	+	1.09716i	0.986842	+	0.161689i	$0.0516941\pi$
$67$	190518.	+	329986.i	0.633447	+	1.09716i	−0.353394	+	0.935474i	$0.614973\pi$
$68$	−183955.	+	106206.i	−0.585038	+	0.337772i
$69$		0			0
$70$	498875.	−	864076.i	1.45445	−	2.51917i
$71$		−	675048.i		−	1.88608i	−0.332682	−	0.943039i	$-0.607953\pi$
$71$		−	675048.i		−	1.88608i	0.332682	−	0.943039i	$-0.392047\pi$
$72$		0			0
$73$	−762939.			−1.96120			−0.980599	−	0.196025i	$-0.937197\pi$
$73$	−762939.			−1.96120			−0.980599	+	0.196025i	$0.937197\pi$
$74$	267105.	+	154213.i	0.659154	+	0.380563i
$75$		0			0
$76$	−761685.	−	1.31928e6i	−1.73514	−	3.00535i
$77$	543105.	−	313562.i	1.18963	−	0.686832i
$78$		0			0
$79$	−257854.	+	446616.i	−0.522989	+	0.905843i	0.476653	+	0.879091i	$0.341850\pi$
$79$	−257854.	+	446616.i	−0.522989	+	0.905843i	−0.999642	+	0.0267519i	$0.991484\pi$
$80$			752655.i			1.47003i
$81$		0			0
$82$	−538328.			−0.976350
$83$	−782690.	−	451887.i	−1.36885	−	0.790306i	−0.378068	−	0.925778i	$-0.623412\pi$
$83$	−782690.	−	451887.i	−1.36885	−	0.790306i	−0.990781	+	0.135472i	$0.956745\pi$
$84$		0			0
$85$	108155.	+	187331.i	0.176113	+	0.305037i
$86$	−291879.	+	168516.i	−0.458889	+	0.264940i
$87$		0			0
$88$	−609507.	+	1.05570e6i	−0.894398	+	1.54914i
$89$			644278.i			0.913910i	0.889490	+	0.456955i	$0.151060\pi$
$89$			644278.i			0.913910i	−0.889490	+	0.456955i	$0.848940\pi$
$90$		0			0
$91$	87748.8			0.116444
$92$	−1.23555e6	−	713347.i	−1.58671	−	0.916089i
$93$		0			0
$94$	−188289.	−	326125.i	−0.226694	−	0.392646i
$95$	−1.34349e6	+	775664.i	−1.56698	+	0.904697i
$96$		0			0
$97$	308235.	−	533878.i	0.337728	−	0.584961i	−0.646277	−	0.763103i	$-0.723675\pi$
$97$	308235.	−	533878.i	0.337728	−	0.584961i	0.984005	+	0.178141i	$0.0570084\pi$
$98$		−	2.07815e6i		−	2.20800i
$99$		0			0
$100$	439765.			0.439765
$101$	−539557.	−	311514.i	−0.523689	−	0.302352i	0.214754	−	0.976668i	$-0.431105\pi$
$101$	−539557.	−	311514.i	−0.523689	−	0.302352i	−0.738443	+	0.674316i	$0.764438\pi$
$102$		0			0
$103$	375348.	+	650121.i	0.343496	+	0.594953i	0.985079	−	0.172101i	$-0.0550554\pi$
$103$	375348.	+	650121.i	0.343496	+	0.594953i	−0.641583	+	0.767053i	$0.721722\pi$
$104$	−147716.	+	85283.9i	−0.131319	+	0.0758171i
$105$		0			0
$106$	1.50918e6	−	2.61398e6i	1.26714	−	2.19475i
$107$			345428.i			0.281973i	0.990012	+	0.140986i	$0.0450273\pi$
$107$			345428.i			0.281973i	−0.990012	+	0.140986i	$0.954973\pi$
$108$		0			0
$109$	1.17208e6			0.905061			0.452530	−	0.891749i	$-0.350521\pi$
$109$	1.17208e6			0.905061			0.452530	+	0.891749i	$0.350521\pi$
$110$	2.04494e6	+	1.18065e6i	1.53639	+	0.887038i
$111$		0			0
$112$	1.40972e6	+	2.44170e6i	1.00341	+	1.73796i
$113$	2.12463e6	−	1.22665e6i	1.47247	−	0.850132i	0.472952	−	0.881088i	$-0.343189\pi$
$113$	2.12463e6	−	1.22665e6i	1.47247	−	0.850132i	0.999521	+	0.0309561i	$0.00985519\pi$
$114$		0			0
$115$	−726439.	+	1.25823e6i	−0.477646	+	0.827307i
$116$		−	1.16933e6i		−	0.749141i
$117$		0			0
$118$	2.30878e6			1.40520
$119$	701738.	+	405149.i	0.416422	+	0.240422i
$120$		0			0
$121$	−143699.	−	248894.i	−0.0811143	−	0.140494i
$122$	−1.35682e6	+	783358.i	−0.747208	+	0.431401i
$123$		0			0
$124$	−1.76836e6	+	3.06288e6i	−0.927480	+	1.60644i
$125$			1.69933e6i			0.870058i
$126$		0			0
$127$	−1.53816e6			−0.750913			−0.375456	−	0.926840i	$-0.622514\pi$
$127$	−1.53816e6			−0.750913			−0.375456	+	0.926840i	$0.622514\pi$
$128$	2.73764e6	+	1.58058e6i	1.30541	+	0.753679i
$129$		0			0
$130$	165199.	+	286134.i	0.0751932	+	0.130238i
$131$	−976209.	+	563615.i	−0.434239	+	0.250708i	−0.701151	−	0.713013i	$-0.747330\pi$
$131$	−976209.	+	563615.i	−0.434239	+	0.250708i	0.266912	+	0.963721i	$0.413997\pi$
$132$		0			0
$133$	−2.90563e6	+	5.03269e6i	−1.23505	+	2.13917i
$134$			5.37438e6i			2.23364i
$135$		0			0
$136$	−1.57507e6			−0.626157
$137$	2.77647e6	+	1.60300e6i	1.07977	+	0.623406i	0.930834	−	0.365441i	$-0.119082\pi$
$137$	2.77647e6	+	1.60300e6i	1.07977	+	0.623406i	0.148936	+	0.988847i	$0.452415\pi$
$138$		0			0
$139$	33342.8	+	57751.4i	0.0124153	+	0.0215039i	0.872166	−	0.489210i	$-0.162715\pi$
$139$	33342.8	+	57751.4i	0.0124153	+	0.0215039i	−0.859751	+	0.510713i	$0.829381\pi$
$140$	8.26678e6	−	4.77283e6i	3.01268	−	1.73937i
$141$		0			0
$142$	4.76067e6	−	8.24573e6i	1.66266	−	2.87981i
$143$			207668.i			0.0710169i
$144$		0			0
$145$	−1.19079e6			−0.390600
$146$	−9.31932e6	−	5.38051e6i	−2.99451	−	1.72888i
$147$		0			0
$148$	1.47539e6	+	2.55544e6i	0.455114	+	0.788281i
$149$	−1.41029e6	+	814231.i	−0.426333	+	0.246144i	−0.697783	−	0.716309i	$-0.745830\pi$
$149$	−1.41029e6	+	814231.i	−0.426333	+	0.246144i	0.271450	+	0.962453i	$0.412497\pi$
$150$		0			0
$151$	182810.	−	316636.i	0.0530968	−	0.0919664i	−0.838255	−	0.545278i	$-0.816424\pi$
$151$	182810.	−	316636.i	0.0530968	−	0.0919664i	0.891352	+	0.453311i	$0.149757\pi$
$152$		−	1.12960e7i		−	3.21658i
$153$		0			0
$154$	8.84538e6			2.42189
$155$	3.11910e6	+	1.80081e6i	0.837594	+	0.483585i
$156$		0			0
$157$	2.59463e6	+	4.49403e6i	0.670465	+	1.16128i	0.977772	+	0.209669i	$0.0672387\pi$
$157$	2.59463e6	+	4.49403e6i	0.670465	+	1.16128i	−0.307307	+	0.951610i	$0.599428\pi$
$158$	−6.29938e6	+	3.63695e6i	−1.59708	+	0.922074i
$159$		0			0
$160$	−907868.	+	1.57247e6i	−0.221648	+	0.383905i
$161$			5.44246e6i			1.30412i
$162$		0			0
$163$	−3.00726e6			−0.694397			−0.347199	−	0.937792i	$-0.612867\pi$
$163$	−3.00726e6			−0.694397			−0.347199	+	0.937792i	$0.612867\pi$
$164$	−4.46028e6	−	2.57514e6i	−1.01119	−	0.583808i
$165$		0			0
$166$	−6.37372e6	−	1.10396e7i	−1.39338	−	2.41340i
$167$	−4.14290e6	+	2.39191e6i	−0.889519	+	0.513564i	−0.873785	−	0.486312i	$-0.838342\pi$
$167$	−4.14290e6	+	2.39191e6i	−0.889519	+	0.513564i	−0.0157339	+	0.999876i	$0.505008\pi$
$168$		0			0
$169$	2.39888e6	−	4.15497e6i	0.496990	−	0.860812i
$170$			3.05100e6i			0.621005i
$171$		0			0
$172$	−3.22446e6			−0.633681
$173$	−3.06223e6	−	1.76798e6i	−0.591425	−	0.341459i	0.174236	−	0.984704i	$-0.444254\pi$
$173$	−3.06223e6	−	1.76798e6i	−0.591425	−	0.341459i	−0.765661	+	0.643245i	$0.777588\pi$
$174$		0			0
$175$	−838793.	−	1.45283e6i	−0.156509	−	0.271082i
$176$	−5.77858e6	+	3.33627e6i	−1.05995	+	0.611960i
$177$		0			0
$178$	−4.54367e6	+	7.86987e6i	−0.805651	+	1.39543i
$179$		−	8.57291e6i		−	1.49475i	−0.664401	−	0.747376i	$-0.731313\pi$
$179$		−	8.57291e6i		−	1.49475i	0.664401	−	0.747376i	$-0.268687\pi$
$180$		0			0
$181$	1.79208e6			0.302219			0.151110	−	0.988517i	$-0.451715\pi$
$181$	1.79208e6			0.302219			0.151110	+	0.988517i	$0.451715\pi$
$182$	1.07185e6	+	618835.i	0.177796	+	0.102650i
$183$		0			0
$184$	−5.28958e6	−	9.16182e6i	−0.849118	−	1.47071i
$185$	2.60234e6	−	1.50246e6i	0.411007	−	0.237295i
$186$		0			0
$187$	−958833.	+	1.66075e6i	−0.146628	+	0.253968i
$188$		−	3.60278e6i		−	0.542206i
$189$		0			0
$190$	−2.18810e7			−3.19012
$191$	8.75348e6	+	5.05382e6i	1.25626	+	0.725304i	0.972346	−	0.233545i	$-0.0750327\pi$
$191$	8.75348e6	+	5.05382e6i	1.25626	+	0.725304i	0.283917	+	0.958849i	$0.408366\pi$
$192$		0			0
$193$	3.82329e6	+	6.62213e6i	0.531820	+	0.921140i	0.999310	+	0.0371413i	$0.0118252\pi$
$193$	3.82329e6	+	6.62213e6i	0.531820	+	0.921140i	−0.467490	+	0.883999i	$0.654842\pi$
$194$	7.53019e6	−	4.34755e6i	1.03134	−	0.595443i
$195$		0			0
$196$	9.94104e6	−	1.72184e7i	1.32027	−	2.28678i
$197$			4.94403e6i			0.646669i	0.946285	+	0.323335i	$0.104804\pi$
$197$			4.94403e6i			0.646669i	−0.946285	+	0.323335i	$0.895196\pi$
$198$		0			0
$199$	−1.96814e6			−0.249745			−0.124872	−	0.992173i	$-0.539852\pi$
$199$	−1.96814e6			−0.249745			−0.124872	+	0.992173i	$0.539852\pi$
$200$	2.82404e6	+	1.63046e6i	0.353005	+	0.203808i
$201$		0			0
$202$	−4.39380e6	−	7.61029e6i	−0.533073	−	0.923309i
$203$	−3.86307e6	+	2.23034e6i	−0.461790	+	0.266615i
$204$		0			0
$205$	−2.62241e6	+	4.54214e6i	−0.304396	+	0.527229i
$206$			1.05883e7i			1.21123i
$207$		0			0
$208$	−933639.			−0.103750
$209$	−1.19105e7	−	6.87652e6i	−1.30464	−	0.753234i
$210$		0			0
$211$	−4.14983e6	−	7.18771e6i	−0.441756	−	0.765144i	0.556064	−	0.831140i	$-0.312311\pi$
$211$	−4.14983e6	−	7.18771e6i	−0.441756	−	0.765144i	−0.997820	+	0.0659953i	$0.978978\pi$
$212$	2.50085e7	−	1.44386e7i	2.62470	−	1.51537i
$213$		0			0
$214$	−2.43608e6	+	4.21941e6i	−0.248571	+	0.430537i
$215$			3.28363e6i			0.330399i
$216$		0			0
$217$	1.34916e7			1.32034
$218$	1.43170e7	+	8.26591e6i	1.38192	+	0.797850i
$219$		0			0
$220$	1.12955e7	+	1.95643e7i	1.06081	+	1.83737i
$221$	−232376.	+	134163.i	−0.0215286	+	0.0124295i
$222$		0			0
$223$	−4.68890e6	+	8.12141e6i	−0.422821	+	0.732347i	−0.996214	−	0.0869334i	$-0.972293\pi$
$223$	−4.68890e6	+	8.12141e6i	−0.422821	+	0.732347i	0.573394	+	0.819280i	$0.305627\pi$
$224$			6.80172e6i			0.605167i
$225$		0			0
$226$	3.46031e7			2.99771
$227$	3.17328e6	+	1.83209e6i	0.271288	+	0.156628i	0.629473	−	0.777022i	$-0.283271\pi$
$227$	3.17328e6	+	1.83209e6i	0.271288	+	0.156628i	−0.358185	+	0.933651i	$0.616604\pi$
$228$		0			0
$229$	−2.49452e6	−	4.32063e6i	−0.207721	−	0.359783i	0.743275	−	0.668986i	$-0.233271\pi$
$229$	−2.49452e6	−	4.32063e6i	−0.207721	−	0.359783i	−0.950996	+	0.309202i	$0.899938\pi$
$230$	−1.77469e7	+	1.02462e7i	−1.45861	+	0.842130i
$231$		0			0
$232$	4.33539e6	−	7.50911e6i	0.347187	−	0.601346i
$233$		−	5.00370e6i		−	0.395570i	−0.980245	−	0.197785i	$-0.936625\pi$
$233$		−	5.00370e6i		−	0.395570i	0.980245	−	0.197785i	$-0.0633749\pi$
$234$		0			0
$235$	−3.66890e6			−0.282705
$236$	1.91293e7	+	1.10443e7i	1.45533	+	0.840236i
$237$		0			0
$238$	5.71449e6	+	9.89780e6i	0.423884	+	0.734189i
$239$	1.63810e7	−	9.45757e6i	1.19990	−	0.692765i	0.239370	−	0.970928i	$-0.423059\pi$
$239$	1.63810e7	−	9.45757e6i	1.19990	−	0.692765i	0.960534	+	0.278163i	$0.0897256\pi$
$240$		0			0
$241$	7.62573e6	−	1.32081e7i	0.544791	−	0.943606i	−0.453829	−	0.891089i	$-0.649942\pi$
$241$	7.62573e6	−	1.32081e7i	0.544791	−	0.943606i	0.998620	−	0.0525173i	$-0.0167245\pi$
$242$		−	4.05366e6i		−	0.286023i
$243$		0			0
$244$	−1.49891e7			−1.03182
$245$	−1.75344e7	−	1.01235e7i	−1.19232	−	0.688386i
$246$		0			0
$247$	−962181.	−	1.66655e6i	−0.0638508	−	0.110593i
$248$	−2.27118e7	+	1.31126e7i	−1.48900	+	0.859676i
$249$		0			0
$250$	−1.19843e7	+	2.07574e7i	−0.766994	+	1.32847i
$251$		−	1.44796e7i		−	0.915661i	−0.889040	−	0.457830i	$-0.848627\pi$
$251$		−	1.44796e7i		−	0.915661i	0.889040	−	0.457830i	$-0.151373\pi$
$252$		0			0
$253$	−1.28802e7			−0.795358
$254$	−1.87886e7	−	1.08476e7i	−1.14655	−	0.661962i
$255$		0			0
$256$	1.70402e7	+	2.95146e7i	1.01568	+	1.75921i
$257$	1.03463e7	−	5.97342e6i	0.609515	−	0.351904i	−0.163261	−	0.986583i	$-0.552201\pi$
$257$	1.03463e7	−	5.97342e6i	0.609515	−	0.351904i	0.772776	+	0.634679i	$0.218868\pi$
$258$		0			0
$259$	5.62821e6	−	9.74834e6i	0.323945	−	0.561089i
$260$			3.16099e6i			0.179847i
$261$		0			0
$262$	−1.58992e7			−0.884040
$263$	−1.31116e7	−	7.56999e6i	−0.720757	−	0.416129i	0.0942745	−	0.995546i	$-0.469947\pi$
$263$	−1.31116e7	−	7.56999e6i	−0.720757	−	0.416129i	−0.815031	+	0.579417i	$0.803280\pi$
$264$		0			0
$265$	−1.47036e7	−	2.54674e7i	−0.790109	−	1.36851i
$266$	−7.09846e7	+	4.09830e7i	−3.77154	+	2.17750i
$267$		0			0
$268$	−2.57089e7	+	4.45290e7i	−1.33561	+	2.31334i
$269$		−	3.37864e7i		−	1.73574i	−0.496789	−	0.867871i	$-0.665488\pi$
$269$		−	3.37864e7i		−	1.73574i	0.496789	−	0.867871i	$-0.334512\pi$
$270$		0			0
$271$	−292052.			−0.0146741			−0.00733707	−	0.999973i	$-0.502335\pi$
$271$	−292052.			−0.0146741			−0.00733707	+	0.999973i	$0.502335\pi$
$272$	−7.46643e6	−	4.31074e6i	−0.371028	−	0.214213i
$273$		0			0
$274$	2.26098e7	+	3.91612e7i	1.09912	+	1.90373i
$275$	3.43830e6	−	1.98510e6i	0.165328	−	0.0954521i
$276$		0			0
$277$	5.92330e6	−	1.02595e7i	0.278692	−	0.482708i	−0.692368	−	0.721545i	$-0.743433\pi$
$277$	5.92330e6	−	1.02595e7i	0.278692	−	0.482708i	0.971060	+	0.238836i	$0.0767659\pi$
$278$			940578.i			0.0437785i
$279$		0			0
$280$	7.07825e7			3.22442
$281$	−2.31829e6	−	1.33847e6i	−0.104484	−	0.0603238i	0.446847	−	0.894610i	$-0.352547\pi$
$281$	−2.31829e6	−	1.33847e6i	−0.104484	−	0.0603238i	−0.551331	+	0.834286i	$0.685880\pi$
$282$		0			0
$283$	1.55551e7	+	2.69422e7i	0.686298	+	1.18870i	0.973027	+	0.230691i	$0.0740987\pi$
$283$	1.55551e7	+	2.69422e7i	0.686298	+	1.18870i	−0.286729	+	0.958012i	$0.592568\pi$
$284$	7.88884e7	−	4.55462e7i	3.44396	−	1.98837i
$285$		0			0
$286$	−1.46455e6	+	2.53667e6i	−0.0626044	+	0.108434i
$287$			1.96470e7i			0.831094i
$288$		0			0
$289$	2.16598e7			0.897347
$290$	−1.45455e7	−	8.39787e6i	−0.596397	−	0.344330i
$291$		0			0
$292$	−5.14763e7	−	8.91596e7i	−2.06756	−	3.58113i
$293$	2.03856e6	−	1.17696e6i	0.0810438	−	0.0467906i	−0.458930	−	0.888472i	$-0.651767\pi$
$293$	2.03856e6	−	1.17696e6i	0.0810438	−	0.0467906i	0.539974	+	0.841682i	$0.318434\pi$
$294$		0			0
$295$	1.12470e7	−	1.94803e7i	0.438096	−	0.758805i
$296$			2.18804e7i			0.843686i
$297$		0			0
$298$	−2.29689e7			−0.867945
$299$	−1.56078e6	−	901120.i	−0.0583888	−	0.0337108i
$300$		0			0
$301$	6.15022e6	+	1.06525e7i	0.225523	+	0.390618i
$302$	4.46605e6	−	2.57848e6i	0.162145	−	0.0936143i
$303$		0			0
$304$	3.09156e7	−	5.35474e7i	1.10042	−	1.90598i
$305$			1.52642e7i			0.537989i
$306$		0			0
$307$	3.99249e6			0.137984			0.0689920	−	0.997617i	$-0.478022\pi$
$307$	3.99249e6			0.137984			0.0689920	+	0.997617i	$0.478022\pi$
$308$	7.32877e7	+	4.23127e7i	2.50830	+	1.44817i
$309$		0			0
$310$	2.53999e7	+	4.39939e7i	0.852602	+	1.47675i
$311$	−2.61007e7	+	1.50692e7i	−0.867703	+	0.500969i	−0.866584	−	0.499031i	$-0.833689\pi$
$311$	−2.61007e7	+	1.50692e7i	−0.867703	+	0.500969i	−0.00111874	+	0.999999i	$0.500356\pi$
$312$		0			0
$313$	1.89456e7	−	3.28147e7i	0.617838	−	1.07013i	−0.372041	−	0.928216i	$-0.621342\pi$
$313$	1.89456e7	−	3.28147e7i	0.617838	−	1.07013i	0.989879	−	0.141911i	$-0.0453246\pi$
$314$			7.31928e7i			2.36417i
$315$		0			0
$316$	−6.95907e7			−2.20541
$317$	3.00895e7	+	1.73722e7i	0.944577	+	0.545352i	0.891392	−	0.453233i	$-0.149729\pi$
$317$	3.00895e7	+	1.73722e7i	0.944577	+	0.545352i	0.0531849	+	0.998585i	$0.483063\pi$
$318$		0			0
$319$	−5.27838e6	−	9.14242e6i	−0.162603	−	0.281637i
$320$	1.95371e7	−	1.12798e7i	0.596226	−	0.344231i
$321$		0			0
$322$	−3.83821e7	+	6.64798e7i	−1.14964	+	1.99123i
$323$		−	1.77701e7i		−	0.527330i
$324$		0			0
$325$	555522.			0.0161827
$326$	−3.67337e7	−	2.12082e7i	−1.06026	−	0.612141i
$327$		0			0
$328$	−1.90951e7	−	3.30737e7i	−0.541128	−	0.937262i
$329$	−1.19024e7	+	6.87183e6i	−0.334230	+	0.192968i
$330$		0			0
$331$	−1.83106e7	+	3.17150e7i	−0.504917	+	0.874541i	0.495067	+	0.868855i	$0.335143\pi$
$331$	−1.83106e7	+	3.17150e7i	−0.504917	+	0.874541i	−0.999984	+	0.00568670i	$0.998190\pi$
$332$		−	1.21957e8i		−	3.33267i
$333$		0			0
$334$	−6.74742e7			−1.81092
$335$	4.53463e7	+	2.61807e7i	1.20617	+	0.696380i
$336$		0			0
$337$	−2.26572e7	−	3.92434e7i	−0.591992	−	1.02536i	−0.993964	−	0.109709i	$-0.965008\pi$
$337$	−2.26572e7	−	3.92434e7i	−0.591992	−	1.02536i	0.401971	−	0.915652i	$-0.368325\pi$
$338$	5.86046e7	−	3.38354e7i	1.51769	−	0.876236i
$339$		0			0
$340$	−1.45947e7	+	2.52788e7i	−0.371329	+	0.643161i
$341$			3.19296e7i			0.805248i
$342$		0			0
$343$	−1.52829e7			−0.378724
$344$	−2.07065e7	−	1.19549e7i	−0.508665	−	0.293678i
$345$		0			0
$346$	−2.49368e7	−	4.31918e7i	−0.602022	−	1.04273i
$347$	2.53109e7	−	1.46133e7i	0.605787	−	0.349751i	−0.165528	−	0.986205i	$-0.552933\pi$
$347$	2.53109e7	−	1.46133e7i	0.605787	−	0.349751i	0.771315	+	0.636454i	$0.219599\pi$
$348$		0			0
$349$	4.80635e6	−	8.32484e6i	0.113068	−	0.195839i	−0.803938	−	0.594713i	$-0.797266\pi$
$349$	4.80635e6	−	8.32484e6i	0.113068	−	0.195839i	0.917006	+	0.398874i	$0.130599\pi$
$350$		−	2.36618e7i		−	0.551879i
$351$		0			0
$352$	−1.60971e7			−0.369079
$353$	2.60926e7	+	1.50646e7i	0.593189	+	0.342478i	0.766357	−	0.642415i	$-0.222067\pi$
$353$	2.60926e7	+	1.50646e7i	0.593189	+	0.342478i	−0.173169	+	0.984892i	$0.555401\pi$
$354$		0			0
$355$	−4.63821e7	−	8.03362e7i	−1.03673	−	1.79567i
$356$	−7.52925e7	+	4.34702e7i	−1.66879	+	0.963477i
$357$		0			0
$358$	6.04591e7	−	1.04718e8i	1.31769	−	2.28230i
$359$			3.63910e7i			0.786521i	0.919427	+	0.393260i	$0.128653\pi$
$359$			3.63910e7i			0.786521i	−0.919427	+	0.393260i	$0.871347\pi$
$360$		0			0
$361$	8.03970e7			1.70891
$362$	2.18903e7	+	1.26384e7i	0.461452	+	0.266419i
$363$		0			0
$364$	5.92051e6	+	1.02546e7i	0.122759	+	0.212626i
$365$	−9.07960e7	+	5.24211e7i	−1.86719	+	1.07802i
$366$		0			0
$367$	−2.52979e7	+	4.38173e7i	−0.511784	+	0.886436i	0.488123	+	0.872775i	$0.337682\pi$
$367$	−2.52979e7	+	4.38173e7i	−0.511784	+	0.886436i	−0.999907	+	0.0136607i	$0.995652\pi$
$368$		−	5.79073e7i		−	1.16196i
$369$		0			0
$370$	4.23836e7			0.836743
$371$	−9.54007e7	−	5.50796e7i	−1.86823	−	1.07862i
$372$		0			0
$373$	4.72498e7	+	8.18391e7i	0.910487	+	1.57701i	0.813378	+	0.581736i	$0.197626\pi$
$373$	4.72498e7	+	8.18391e7i	0.910487	+	1.57701i	0.0971089	+	0.995274i	$0.469040\pi$
$374$	−2.34243e7	+	1.35240e7i	−0.447767	+	0.258519i
$375$		0			0
$376$	1.33576e7	−	2.31360e7i	0.251284	−	0.435237i
$377$		−	1.47713e6i		−	0.0275673i
$378$		0			0
$379$	−5.62274e7			−1.03283			−0.516417	−	0.856337i	$-0.672734\pi$
$379$	−5.62274e7			−1.03283			−0.516417	+	0.856337i	$0.672734\pi$
$380$	−1.81293e8	−	1.04670e8i	−3.30393	−	1.90753i
$381$		0			0
$382$	7.12826e7	+	1.23465e8i	1.27877	+	2.21490i
$383$	−1.83955e7	+	1.06206e7i	−0.327427	+	0.189040i	−0.654698	−	0.755890i	$-0.727204\pi$
$383$	−1.83955e7	+	1.06206e7i	−0.327427	+	0.189040i	0.327271	+	0.944930i	$0.393871\pi$
$384$		0			0
$385$	4.30892e7	−	7.46328e7i	0.755069	−	1.30782i
$386$			1.07853e8i			1.87529i
$387$		0			0
$388$	8.31877e7			1.42418
$389$	8.33267e7	+	4.81087e7i	1.41558	+	0.817288i	0.995907	−	0.0903860i	$-0.0288101\pi$
$389$	8.33267e7	+	4.81087e7i	1.41558	+	0.817288i	0.419677	+	0.907674i	$0.362143\pi$
$390$		0			0
$391$	−8.32119e6	−	1.44127e7i	−0.139205	−	0.241110i
$392$	1.27677e8	−	7.37144e7i	2.11960	−	1.22375i
$393$		0			0
$394$	−3.48670e7	+	6.03914e7i	−0.570067	+	0.987384i
$395$			7.08679e7i			1.14990i
$396$		0			0
$397$	2.71686e7			0.434206			0.217103	−	0.976149i	$-0.430339\pi$
$397$	2.71686e7			0.434206			0.217103	+	0.976149i	$0.430339\pi$
$398$	−2.40409e7	−	1.38800e7i	−0.381330	−	0.220161i
$399$		0			0
$400$	8.92468e6	+	1.54580e7i	0.139448	+	0.241531i
$401$	1.33304e7	−	7.69630e6i	0.206733	−	0.119357i	−0.393059	−	0.919513i	$-0.628583\pi$
$401$	1.33304e7	−	7.69630e6i	0.206733	−	0.119357i	0.599792	+	0.800156i	$0.295250\pi$
$402$		0			0
$403$	−2.23384e6	+	3.86912e6i	−0.0341300	+	0.0591148i
$404$		−	8.40727e7i		−	1.27500i
$405$		0			0
$406$	−6.29166e7			−0.940129
$407$	2.30706e7	+	1.33198e7i	0.342197	+	0.197568i
$408$		0			0
$409$	1.63204e7	+	2.82678e7i	0.238540	+	0.413164i	0.960296	−	0.278985i	$-0.0899978\pi$
$409$	1.63204e7	+	2.82678e7i	0.238540	+	0.413164i	−0.721755	+	0.692148i	$0.756664\pi$
$410$	−6.40655e7	+	3.69882e7i	−0.929549	+	0.536675i
$411$		0			0
$412$	−5.06502e7	+	8.77288e7i	−0.724252	+	1.25444i
$413$		−	8.42620e7i		−	1.19614i
$414$		0			0
$415$	−1.24195e8			−1.73765
$416$	−1.95059e6	−	1.12618e6i	−0.0270948	−	0.0156432i
$417$		0			0
$418$	−9.69911e7	−	1.67994e8i	−1.32802	−	2.30019i
$419$	7.67514e7	−	4.43125e7i	1.04338	−	0.602398i	0.122595	−	0.992457i	$-0.460878\pi$
$419$	7.67514e7	−	4.43125e7i	1.04338	−	0.602398i	0.920790	+	0.390058i	$0.127545\pi$
$420$		0			0
$421$	−4.75587e7	+	8.23740e7i	−0.637358	+	1.10394i	0.348652	+	0.937252i	$0.386639\pi$
$421$	−4.75587e7	+	8.23740e7i	−0.637358	+	1.10394i	−0.986010	+	0.166684i	$0.946694\pi$
$422$		−	1.17064e8i		−	1.55771i
$423$		0			0
$424$	2.14130e8			2.80918
$425$	4.44258e6	+	2.56493e6i	0.0578720	+	0.0334124i
$426$		0			0
$427$	2.85897e7	+	4.95188e7i	0.367219	+	0.636043i
$428$	−4.03679e7	+	2.33064e7i	−0.514879	+	0.297266i
$429$		0			0
$430$	−2.31573e7	+	4.01096e7i	−0.291261	+	0.504479i
$431$			8.05617e7i			1.00623i	0.864220	+	0.503115i	$0.167813\pi$
$431$			8.05617e7i			1.00623i	−0.864220	+	0.503115i	$0.832187\pi$
$432$		0			0
$433$	3.50511e7			0.431755			0.215878	−	0.976420i	$-0.430739\pi$
$433$	3.50511e7			0.431755			0.215878	+	0.976420i	$0.430739\pi$
$434$	1.64800e8	+	9.51475e7i	2.01599	+	1.16393i
$435$		0			0
$436$	7.90815e7	+	1.36973e8i	0.954147	+	1.65263i
$437$	1.03365e8	−	5.96776e7i	1.23859	−	0.715100i
$438$		0			0
$439$	2.31531e7	−	4.01023e7i	0.273663	−	0.473998i	−0.696134	−	0.717912i	$-0.745098\pi$
$439$	2.31531e7	−	4.01023e7i	0.273663	−	0.473998i	0.969797	+	0.243914i	$0.0784315\pi$
$440$			1.67515e8i			1.96651i
$441$		0			0
$442$	−3.78464e6			−0.0438286
$443$	−1.03092e8	−	5.95204e7i	−1.18581	−	0.684628i	−0.228458	−	0.973554i	$-0.573369\pi$
$443$	−1.03092e8	−	5.95204e7i	−1.18581	−	0.684628i	−0.957351	+	0.288926i	$0.906702\pi$
$444$		0			0
$445$	4.42680e7	+	7.66744e7i	0.502354	+	0.870102i
$446$	−1.14550e8	+	6.61354e7i	−1.29119	+	0.745469i
$447$		0			0
$448$	4.22538e7	−	7.31858e7i	0.469929	−	0.813941i
$449$			9.75546e7i			1.07773i	0.842393	+	0.538864i	$0.181146\pi$
$449$			9.75546e7i			1.07773i	−0.842393	+	0.538864i	$0.818854\pi$
$450$		0			0
$451$	−4.64970e7			−0.506868
$452$	2.86702e8	+	1.65527e8i	3.10467	+	1.79248i
$453$		0			0
$454$	2.58411e7	+	4.47581e7i	0.276149	+	0.478304i
$455$	1.04428e7	−	6.02917e6i	0.110862	−	0.0640063i
$456$		0			0
$457$	4.06870e6	−	7.04719e6i	0.0426292	−	0.0738359i	−0.843924	−	0.536463i	$-0.819760\pi$
$457$	4.06870e6	−	7.04719e6i	0.0426292	−	0.0738359i	0.886553	+	0.462628i	$0.153093\pi$
$458$		−	7.03688e7i		−	0.732460i
$459$		0			0
$460$	−1.96055e8			−2.01420
$461$	1.34509e8	+	7.76590e7i	1.37293	+	0.792664i	0.991297	−	0.131648i	$-0.0420269\pi$
$461$	1.34509e8	+	7.76590e7i	1.37293	+	0.792664i	0.381638	+	0.924312i	$0.375360\pi$
$462$		0			0
$463$	−3.81492e7	−	6.60764e7i	−0.384364	−	0.665738i	0.607317	−	0.794460i	$-0.292246\pi$
$463$	−3.81492e7	−	6.60764e7i	−0.384364	−	0.665738i	−0.991681	+	0.128722i	$0.958913\pi$
$464$	4.11027e7	−	2.37307e7i	0.411449	−	0.237550i
$465$		0			0
$466$	3.52878e7	−	6.11203e7i	0.348712	−	0.603987i
$467$		−	1.85842e8i		−	1.82470i	−0.409408	−	0.912352i	$-0.634265\pi$
$467$		−	1.85842e8i		−	1.82470i	0.409408	−	0.912352i	$-0.365735\pi$
$468$		0			0
$469$	1.96145e8			1.90133
$470$	−4.48157e7	−	2.58744e7i	−0.431655	−	0.249216i
$471$		0			0
$472$	8.18950e7	+	1.41846e8i	0.778810	+	1.34894i
$473$	−2.52104e7	+	1.45552e7i	−0.238230	+	0.137542i
$474$		0			0
$475$	−1.83950e7	+	3.18611e7i	−0.171640	+	0.297290i
$476$			1.09343e8i			1.01384i
$477$		0			0
$478$	2.66792e8			2.44281
$479$	−1.07230e8	−	6.19095e7i	−0.975689	−	0.563314i	−0.0747229	−	0.997204i	$-0.523807\pi$
$479$	−1.07230e8	−	6.19095e7i	−0.975689	−	0.563314i	−0.900966	+	0.433890i	$0.857141\pi$
$480$		0			0
$481$	1.86375e6	+	3.22811e6i	0.0167476	+	0.0290076i
$482$	1.86297e8	−	1.07559e8i	1.66366	−	0.960514i
$483$		0			0
$484$	1.93911e7	−	3.35863e7i	0.171027	−	0.296228i
$485$		−	8.47145e7i		−	0.742561i
$486$		0			0
$487$	−6.09360e7			−0.527578			−0.263789	−	0.964580i	$-0.584972\pi$
$487$	−6.09360e7			−0.527578			−0.263789	+	0.964580i	$0.584972\pi$
$488$	−9.62555e7	−	5.55731e7i	−0.828259	−	0.478196i
$489$		0			0
$490$	−1.42789e8	−	2.47317e8i	−1.21368	−	2.10216i
$491$	−5.61243e7	+	3.24034e7i	−0.474140	+	0.273745i	−0.717971	−	0.696073i	$-0.754929\pi$
$491$	−5.61243e7	+	3.24034e7i	−0.474140	+	0.273745i	0.243831	+	0.969818i	$0.421596\pi$
$492$		0			0
$493$	6.82012e6	−	1.18128e7i	0.0569182	−	0.0985852i
$494$		−	2.71425e7i		−	0.225149i
$495$		0			0
$496$	−1.43550e8			−1.17641
$497$	−3.00938e8	−	1.73747e8i	−2.45137	−	1.41530i
$498$		0			0
$499$	−1.43548e7	−	2.48633e7i	−0.115530	−	0.200104i	0.802461	−	0.596704i	$-0.203523\pi$
$499$	−1.43548e7	−	2.48633e7i	−0.115530	−	0.200104i	−0.917992	+	0.396600i	$0.870190\pi$
$500$	−1.98590e8	+	1.14656e8i	−1.58872	+	0.917246i
$501$		0			0
$502$	1.02115e8	−	1.76868e8i	0.807194	−	1.39810i
$503$			1.12463e8i			0.883702i	0.897088	+	0.441851i	$0.145678\pi$
$503$			1.12463e8i			0.883702i	−0.897088	+	0.441851i	$0.854322\pi$
$504$		0			0
$505$	−8.56156e7			−0.664781
$506$	−1.57332e8	−	9.08359e7i	−1.21441	−	0.701142i
$507$		0			0
$508$	−1.03781e8	−	1.79754e8i	−0.791639	−	1.37116i
$509$	−4.86521e7	+	2.80893e7i	−0.368934	+	0.213004i	−0.672993	−	0.739649i	$-0.734991\pi$
$509$	−4.86521e7	+	2.80893e7i	−0.368934	+	0.213004i	0.304059	+	0.952653i	$0.401658\pi$
$510$		0			0
$511$	−1.96369e8	+	3.40120e8i	−1.47167	+	2.54900i
$512$			2.78380e8i			2.07410i
$513$		0			0
$514$	1.68506e8			1.24087
$515$	8.93388e7	+	5.15798e7i	0.654061	+	0.377623i
$516$		0			0
$517$	−1.62630e7	−	2.81684e7i	−0.117687	−	0.203840i
$518$	1.37497e8	−	7.93841e7i	0.989247	−	0.571142i
$519$		0			0
$520$	−1.17196e7	+	2.02990e7i	−0.0833495	+	0.144366i
$521$		−	1.68861e8i		−	1.19403i	−0.802230	−	0.597015i	$-0.796353\pi$
$521$		−	1.68861e8i		−	1.19403i	0.802230	−	0.597015i	$-0.203647\pi$
$522$		0			0
$523$	−2.39748e8			−1.67591			−0.837955	−	0.545739i	$-0.816249\pi$
$523$	−2.39748e8			−1.67591			−0.837955	+	0.545739i	$0.816249\pi$
$524$	−1.31732e8	−	7.60554e7i	−0.915581	−	0.528611i
$525$		0			0
$526$	−1.06772e8	−	1.84935e8i	−0.733671	−	1.27076i
$527$	−3.57285e7	+	2.06279e7i	−0.244109	+	0.140936i
$528$		0			0
$529$	−1.81276e7	+	3.13979e7i	−0.122454	+	0.212097i
$530$		−	4.14780e8i		−	2.78606i
$531$		0			0
$532$	−7.84183e8			−5.20814
$533$	−5.63435e6	−	3.25299e6i	−0.0372102	−	0.0214833i
$534$		0			0
$535$	2.37342e7	+	4.11088e7i	0.154993	+	0.268456i
$536$	−3.30190e8	+	1.90635e8i	−2.14422	+	1.23797i
$537$		0			0
$538$	2.38273e8	−	4.12702e8i	1.53013	−	2.65027i
$539$		−	1.79496e8i		−	1.14627i
$540$		0			0
$541$	1.85322e8			1.17040			0.585200	−	0.810889i	$-0.301016\pi$
$541$	1.85322e8			1.17040			0.585200	+	0.810889i	$0.301016\pi$
$542$	−3.56742e6	−	2.05965e6i	−0.0224056	−	0.0129359i
$543$		0			0
$544$	−1.03994e7	−	1.80123e7i	−0.0645970	−	0.111885i
$545$	1.39487e8	−	8.05329e7i	0.861676	−	0.497489i
$546$		0			0
$547$	−1.26423e8	+	2.18971e8i	−0.772438	+	1.33790i	0.163785	+	0.986496i	$0.447630\pi$
$547$	−1.26423e8	+	2.18971e8i	−0.772438	+	1.33790i	−0.936223	+	0.351406i	$0.885704\pi$
$548$			4.32624e8i			2.62887i
$549$		0			0
$550$	5.59986e7			0.336580
$551$	8.47185e7	+	4.89122e7i	0.506435	+	0.292390i
$552$		0			0
$553$	1.32735e8	+	2.29904e8i	0.784893	+	1.35947i
$554$	1.44706e8	−	8.35463e7i	0.851056	−	0.491358i
$555$		0			0
$556$	−4.49934e6	+	7.79309e6i	−0.0261773	+	0.0453404i
$557$		−	1.01472e8i		−	0.587194i	−0.955929	−	0.293597i	$-0.905148\pi$
$557$		−	1.01472e8i		−	0.587194i	0.955929	−	0.293597i	$-0.0948524\pi$
$558$		0			0
$559$	−4.07322e6			−0.0233186
$560$	3.35536e8	+	1.93722e8i	1.91062	+	1.10310i
$561$		0			0
$562$	−1.88787e7	−	3.26988e7i	−0.106356	−	0.184214i
$563$	1.00331e8	−	5.79262e7i	0.562225	−	0.324601i	−0.191813	−	0.981431i	$-0.561437\pi$
$563$	1.00331e8	−	5.79262e7i	0.562225	−	0.324601i	0.754038	+	0.656831i	$0.228103\pi$
$564$		0			0
$565$	1.68565e8	−	2.91963e8i	0.934593	−	1.61876i
$566$			4.38799e8i			2.42000i
$567$		0			0
$568$	6.75465e8			3.68602
$569$	6.32337e7	+	3.65080e7i	0.343251	+	0.198176i	0.661709	−	0.749761i	$-0.269832\pi$
$569$	6.32337e7	+	3.65080e7i	0.343251	+	0.198176i	−0.318458	+	0.947937i	$0.603165\pi$
$570$		0			0
$571$	4.87571e7	+	8.44498e7i	0.261897	+	0.453618i	0.966746	−	0.255739i	$-0.0823187\pi$
$571$	4.87571e7	+	8.44498e7i	0.261897	+	0.453618i	−0.704849	+	0.709357i	$0.748985\pi$
$572$	−2.42688e7	+	1.40116e7i	−0.129676	+	0.0748686i
$573$		0			0
$574$	−1.38557e8	+	2.39988e8i	−0.732645	+	1.26898i
$575$			3.44553e7i			0.181239i
$576$		0			0
$577$	8.90080e7			0.463342			0.231671	−	0.972794i	$-0.425581\pi$
$577$	8.90080e7			0.463342			0.231671	+	0.972794i	$0.425581\pi$
$578$	2.64575e8	+	1.52752e8i	1.37014	+	0.791050i
$579$		0			0
$580$	−8.03440e7	−	1.39160e8i	−0.411784	−	0.713231i
$581$	−4.02905e8	+	2.32617e8i	−2.05435	+	1.18608i
$582$		0			0
$583$	1.30353e8	−	2.25777e8i	0.657830	−	1.13940i
$584$		−	7.63410e8i		−	3.83283i
$585$		0			0
$586$	3.32013e7			0.164992
$587$	1.09392e8	+	6.31572e7i	0.540841	+	0.312255i	0.745420	−	0.666596i	$-0.232249\pi$
$587$	1.09392e8	+	6.31572e7i	0.540841	+	0.312255i	−0.204579	+	0.978850i	$0.565582\pi$
$588$		0			0
$589$	−1.47938e8	−	2.56236e8i	−0.723992	−	1.25399i
$590$	2.74764e8	−	1.58635e8i	1.33784	−	0.772401i
$591$		0			0
$592$	−5.98836e7	+	1.03721e8i	−0.288631	+	0.499923i
$593$			1.59275e8i			0.763805i	0.924203	+	0.381902i	$0.124731\pi$
$593$			1.59275e8i			0.763805i	−0.924203	+	0.381902i	$0.875269\pi$
$594$		0			0
$595$	1.11350e8			0.528615
$596$	−1.90308e8	−	1.09874e8i	−0.898912	−	0.518987i
$597$		0			0
$598$	−1.27100e7	−	2.20144e7i	−0.0594350	−	0.102944i
$599$	1.23461e8	−	7.12804e7i	0.574448	−	0.331658i	−0.184476	−	0.982837i	$-0.559059\pi$
$599$	1.23461e8	−	7.12804e7i	0.574448	−	0.331658i	0.758924	+	0.651179i	$0.225725\pi$
$600$		0			0
$601$	5.92447e7	−	1.02615e8i	0.272914	−	0.472701i	−0.696693	−	0.717370i	$-0.745346\pi$
$601$	5.92447e7	−	1.02615e8i	0.272914	−	0.472701i	0.969607	+	0.244669i	$0.0786792\pi$
$602$			1.73494e8i			0.795234i
$603$		0			0
$604$	4.93375e7			0.223906
$605$	−3.42027e7	−	1.97469e7i	−0.154452	−	0.0891730i
$606$		0			0
$607$	4.03021e7	+	6.98052e7i	0.180203	+	0.312120i	0.941949	−	0.335755i	$-0.108991\pi$
$607$	4.03021e7	+	6.98052e7i	0.180203	+	0.312120i	−0.761747	+	0.647875i	$0.775658\pi$
$608$	1.29180e8	−	7.45821e7i	0.574757	−	0.331836i
$609$		0			0
$610$	−1.07648e8	+	1.86452e8i	−0.474260	+	0.821443i
$611$		−	4.55113e6i		−	0.0199524i
$612$		0			0
$613$	−2.49459e8			−1.08297			−0.541486	−	0.840710i	$-0.682138\pi$
$613$	−2.49459e8			−1.08297			−0.541486	+	0.840710i	$0.682138\pi$
$614$	4.87683e7	+	2.81564e7i	0.210685	+	0.121639i
$615$		0			0
$616$	3.13755e8	+	5.43440e8i	1.34230	+	2.32493i
$617$	2.98160e8	−	1.72143e8i	1.26939	−	0.732880i	0.294514	−	0.955647i	$-0.404842\pi$
$617$	2.98160e8	−	1.72143e8i	1.26939	−	0.732880i	0.974872	+	0.222767i	$0.0715088\pi$
$618$		0			0
$619$	−2.29719e7	+	3.97886e7i	−0.0968558	+	0.167759i	−0.910382	−	0.413770i	$-0.864212\pi$
$619$	−2.29719e7	+	3.97886e7i	−0.0968558	+	0.167759i	0.813526	+	0.581529i	$0.197545\pi$
$620$			4.86011e8i			2.03925i
$621$		0			0
$622$	−4.25094e8			−1.76650
$623$	2.87221e8	+	1.65827e8i	1.18782	+	0.685791i
$624$		0			0
$625$	1.42220e8	+	2.46333e8i	0.582534	+	1.00898i
$626$	4.62841e8	−	2.67221e8i	1.88673	−	1.08930i
$627$		0			0
$628$	−3.50125e8	+	6.06434e8i	−1.41366	+	2.44852i
$629$			3.44207e7i			0.138315i
$630$		0			0
$631$	−2.71320e8			−1.07993			−0.539963	−	0.841689i	$-0.681562\pi$
$631$	−2.71320e8			−1.07993			−0.539963	+	0.841689i	$0.681562\pi$
$632$	−4.46892e8	−	2.58013e8i	−1.77032	−	1.02209i
$633$		0			0
$634$	2.45029e8	+	4.24403e8i	0.961502	+	1.66537i
$635$	−1.83053e8	+	1.05686e8i	−0.714918	+	0.412758i
$636$		0			0
$637$	1.25578e7	−	2.17507e7i	0.0485842	−	0.0841503i
$638$		−	1.48900e8i		−	0.573366i
$639$		0			0
$640$	4.34402e8			1.65711
$641$	−2.71512e8	−	1.56757e8i	−1.03089	−	0.595187i	−0.113654	−	0.993520i	$-0.536255\pi$
$641$	−2.71512e8	−	1.56757e8i	−1.03089	−	0.595187i	−0.917241	+	0.398333i	$0.869589\pi$
$642$		0			0
$643$	−2.97289e7	−	5.14920e7i	−0.111827	−	0.193690i	0.804680	−	0.593709i	$-0.202337\pi$
$643$	−2.97289e7	−	5.14920e7i	−0.111827	−	0.193690i	−0.916507	+	0.400019i	$0.869004\pi$
$644$	−6.36024e8	+	3.67209e8i	−2.38131	+	1.37485i
$645$		0			0
$646$	1.25321e8	−	2.17062e8i	0.464864	−	0.805168i
$647$		−	2.04779e8i		−	0.756089i	−0.925787	−	0.378045i	$-0.876597\pi$
$647$		−	2.04779e8i		−	0.756089i	0.925787	−	0.378045i	$-0.123403\pi$
$648$		0			0
$649$	1.99416e8			0.729502
$650$	6.78572e6	+	3.91774e6i	0.0247090	+	0.0142658i
$651$		0			0
$652$	−2.02903e8	−	3.51438e8i	−0.732058	−	1.26796i
$653$	2.94479e7	−	1.70017e7i	0.105758	−	0.0610596i	−0.446188	−	0.894939i	$-0.647219\pi$
$653$	2.94479e7	−	1.70017e7i	0.105758	−	0.0610596i	0.551946	+	0.833880i	$0.313885\pi$
$654$		0			0
$655$	−7.74512e7	+	1.34149e8i	−0.275616	+	0.477381i
$656$		−	2.09042e8i		−	0.740495i
$657$		0			0
$658$	−1.93850e8			−0.680438
$659$	2.10570e8	+	1.21573e8i	0.735766	+	0.424795i	0.820528	−	0.571606i	$-0.193680\pi$
$659$	2.10570e8	+	1.21573e8i	0.735766	+	0.424795i	−0.0847616	+	0.996401i	$0.527013\pi$
$660$		0			0
$661$	−2.25986e8	−	3.91420e8i	−0.782488	−	1.35531i	−0.930488	−	0.366322i	$-0.880617\pi$
$661$	−2.25986e8	−	3.91420e8i	−0.782488	−	1.35531i	0.148000	−	0.988987i	$-0.452717\pi$
$662$	−4.47330e8	+	2.58266e8i	−1.54189	+	0.890212i
$663$		0			0
$664$	4.52165e8	−	7.83174e8i	1.54452	−	2.67518i
$665$			7.98575e8i			2.71551i
$666$		0			0
$667$	9.16164e7			0.308742
$668$	−5.59052e8	−	3.22769e8i	−1.87553	−	1.08284i
$669$		0			0
$670$	3.69270e8	+	6.39595e8i	1.22778	+	2.12657i
$671$	−1.17192e8	+	6.76609e7i	−0.387910	+	0.223960i
$672$		0			0
$673$	−1.58780e8	+	2.75015e8i	−0.520896	+	0.902217i	0.478809	+	0.877919i	$0.341069\pi$
$673$	−1.58780e8	+	2.75015e8i	−0.520896	+	0.902217i	−0.999705	+	0.0242985i	$0.992265\pi$
$674$		−	6.39145e8i		−	2.08747i
$675$		0			0
$676$	6.47419e8			2.09578
$677$	−5.80706e7	−	3.35271e7i	−0.187150	−	0.108051i	0.403498	−	0.914981i	$-0.367794\pi$
$677$	−5.80706e7	−	3.35271e7i	−0.187150	−	0.108051i	−0.590648	+	0.806930i	$0.701128\pi$
$678$		0			0
$679$	−1.58670e8	−	2.74824e8i	−0.506856	−	0.877900i
$680$	−1.87446e8	+	1.08222e8i	−0.596142	+	0.344183i
$681$		0			0
$682$	−2.25178e8	+	3.90020e8i	−0.709861	+	1.22951i
$683$			1.51437e8i			0.475303i	0.971350	+	0.237652i	$0.0763777\pi$
$683$			1.51437e8i			0.475303i	−0.971350	+	0.237652i	$0.923622\pi$
$684$		0			0
$685$	4.40563e8			1.37068
$686$	−1.86681e8	−	1.07780e8i	−0.578265	−	0.333861i
$687$		0			0
$688$	−6.54378e7	−	1.13342e8i	−0.200939	−	0.348036i
$689$	3.15914e7	−	1.82393e7i	0.0965852	−	0.0557635i
$690$		0			0
$691$	−4.73402e7	+	8.19956e7i	−0.143482	+	0.248517i	−0.928805	−	0.370568i	$-0.879163\pi$
$691$	−4.73402e7	+	8.19956e7i	−0.143482	+	0.248517i	0.785324	+	0.619085i	$0.212496\pi$
$692$		−	4.77150e8i		−	1.43991i
$693$		0			0
$694$	4.12231e8			1.23328
$695$	7.93612e6	+	4.58192e6i	0.0236403	+	0.0136488i
$696$		0			0
$697$	−3.00390e7	−	5.20292e7i	−0.0887131	−	0.153656i
$698$	1.17419e8	−	6.77921e7i	0.345281	−	0.199348i
$699$		0			0
$700$	1.13189e8	−	1.96048e8i	0.329996	−	0.571569i
$701$		−	7.92713e6i		−	0.0230124i	−0.999934	−	0.0115062i	$-0.996337\pi$
$701$		−	7.92713e6i		−	0.0230124i	0.999934	−	0.0115062i	$-0.00366262\pi$
$702$		0			0
$703$	−2.46857e8			−0.710526
$704$	1.73203e8	+	9.99988e7i	0.496407	+	0.286600i
$705$		0			0
$706$	2.12481e8	+	3.68028e8i	0.603817	+	1.04584i
$707$	−2.77747e8	+	1.60357e8i	−0.785944	+	0.453765i
$708$		0			0
$709$	3.32737e8	−	5.76317e8i	0.933603	−	1.61705i	0.156496	−	0.987679i	$-0.449980\pi$
$709$	3.32737e8	−	5.76317e8i	0.933603	−	1.61705i	0.777107	−	0.629369i	$-0.216687\pi$
$710$		−	1.30841e9i		−	3.65569i
$711$		0			0
$712$	−6.44676e8			−1.78608
$713$	−2.39975e8	−	1.38550e8i	−0.662060	−	0.382241i
$714$		0			0
$715$	1.42687e7	+	2.47142e7i	0.0390362	+	0.0676127i
$716$	1.00186e9	−	5.78424e8i	2.72940	−	1.57582i
$717$		0			0
$718$	−2.56642e8	+	4.44516e8i	−0.693352	+	1.20092i
$719$			4.90198e8i			1.31882i	0.751784	+	0.659409i	$0.229194\pi$
$719$			4.90198e8i			1.31882i	−0.751784	+	0.659409i	$0.770806\pi$
$720$		0			0
$721$	3.86434e8			1.03103
$722$	9.82051e8	+	5.66987e8i	2.60929	+	1.50647i
$723$		0			0
$724$	1.20914e8	+	2.09429e8i	0.318610	+	0.551849i
$725$	−2.44564e7	+	1.41199e7i	−0.0641769	+	0.0370526i
$726$		0			0
$727$	1.04654e8	−	1.81265e8i	0.272365	−	0.471750i	−0.697102	−	0.716972i	$-0.745528\pi$
$727$	1.04654e8	−	1.81265e8i	0.272365	−	0.471750i	0.969467	+	0.245222i	$0.0788609\pi$
$728$			8.78030e7i			0.227570i
$729$		0			0
$730$	−1.47877e9			−3.80129
$731$	−3.25740e7	−	1.88066e7i	−0.0833910	−	0.0481458i
$732$		0			0
$733$	1.83336e8	+	3.17547e8i	0.465517	+	0.806299i	0.999225	−	0.0393698i	$-0.0125350\pi$
$733$	1.83336e8	+	3.17547e8i	0.465517	+	0.806299i	−0.533708	+	0.845669i	$0.679202\pi$
$734$	−6.18029e8	+	3.56819e8i	−1.56286	+	0.902319i
$735$		0			0
$736$	6.98490e7	−	1.20982e8i	0.175197	−	0.303450i
$737$			4.64201e8i			1.15959i
$738$		0			0
$739$	−6.11387e8			−1.51490			−0.757449	−	0.652895i	$-0.773554\pi$
$739$	−6.11387e8			−1.51490			−0.757449	+	0.652895i	$0.773554\pi$
$740$	3.51166e8	+	2.02746e8i	0.866597	+	0.500330i
$741$		0			0
$742$	−7.76880e8	−	1.34560e9i	−1.90170	−	3.29384i
$743$	−1.81962e8	+	1.05056e8i	−0.443623	+	0.256126i	−0.705133	−	0.709075i	$-0.749113\pi$
$743$	−1.81962e8	+	1.05056e8i	−0.443623	+	0.256126i	0.261510	+	0.965201i	$0.415779\pi$
$744$		0			0
$745$	−1.11891e8	+	1.93800e8i	−0.270598	+	0.468690i
$746$			1.33289e9i			3.21053i
$747$		0			0
$748$	−2.58774e8			−0.618324
$749$	1.53993e8	+	8.89079e7i	0.366484	+	0.211590i
$750$		0			0
$751$	−2.52848e8	−	4.37946e8i	−0.596953	−	1.03395i	−0.993268	−	0.115839i	$-0.963044\pi$
$751$	−2.52848e8	−	4.37946e8i	−0.596953	−	1.03395i	0.396315	−	0.918115i	$-0.370289\pi$
$752$	1.26640e8	−	7.31157e7i	0.297795	−	0.171932i
$753$		0			0
$754$	1.04172e7	−	1.80432e7i	0.0243018	−	0.0420919i
$755$		−	5.02430e7i		−	0.116744i
$756$		0			0
$757$	4.19839e8			0.967822			0.483911	−	0.875117i	$-0.339216\pi$
$757$	4.19839e8			0.967822			0.483911	+	0.875117i	$0.339216\pi$
$758$	−6.86819e8	−	3.96535e8i	−1.57701	−	0.910487i
$759$		0			0
$760$	−7.76143e8	−	1.34432e9i	−1.76808	−	3.06240i
$761$	6.34065e8	−	3.66078e8i	1.43873	−	0.830653i	0.440971	−	0.897521i	$-0.354634\pi$
$761$	6.34065e8	−	3.66078e8i	1.43873	−	0.830653i	0.997762	+	0.0668687i	$0.0213009\pi$
$762$		0			0
$763$	3.01675e8	−	5.22516e8i	0.679150	−	1.17632i
$764$			1.36395e9i			3.05856i
$765$		0			0
$766$	−2.99601e8			−0.666588
$767$	2.41646e7	+	1.39514e7i	0.0535542	+	0.0309195i
$768$		0			0
$769$	1.26647e8	+	2.19359e8i	0.278494	+	0.482366i	0.971011	−	0.239036i	$-0.0768314\pi$
$769$	1.26647e8	+	2.19359e8i	0.278494	+	0.482366i	−0.692517	+	0.721402i	$0.743498\pi$
$770$	1.05267e9	−	6.07760e8i	2.30580	−	1.33125i
$771$		0			0
$772$	−5.15923e8	+	8.93604e8i	−1.12133	+	1.94220i
$773$		−	7.82197e8i		−	1.69347i	−0.532014	−	0.846735i	$-0.678565\pi$
$773$		−	7.82197e8i		−	1.69347i	0.532014	−	0.846735i	$-0.321435\pi$
$774$		0			0
$775$	8.54131e7			0.183493
$776$	5.34208e8	+	3.08425e8i	1.14321	+	0.660031i
$777$		0			0
$778$	6.78558e8	+	1.17530e9i	1.44095	+	2.49580i
$779$	3.73140e8	−	2.15433e8i	0.789332	−	0.455721i
$780$		0			0
$781$	4.11193e8	−	7.12207e8i	0.863162	−	1.49504i
$782$		−	2.34736e8i		−	0.490861i
$783$		0			0
$784$	8.06983e8			1.67462
$785$	6.17564e8	+	3.56550e8i	1.27665	+	0.737076i
$786$		0			0
$787$	−3.40918e8	−	5.90488e8i	−0.699401	−	1.21140i	−0.968674	−	0.248334i	$-0.920117\pi$
$787$	−3.40918e8	−	5.90488e8i	−0.699401	−	1.21140i	0.269274	−	0.963064i	$-0.413216\pi$
$788$	−5.77775e8	+	3.33579e8i	−1.18081	+	0.681742i
$789$		0			0
$790$	−4.99785e8	+	8.65653e8i	−1.01368	+	1.75575i
$791$		−	1.26289e9i		−	2.55173i
$792$		0			0
$793$	−1.89346e7			−0.0379696
$794$	3.31865e8	+	1.91602e8i	0.662980	+	0.382771i
$795$		0			0
$796$	−1.32793e8	−	2.30003e8i	−0.263290	−	0.456032i
$797$	−4.40332e7	+	2.54226e7i	−0.0869772	+	0.0502163i	−0.542858	−	0.839825i	$-0.682658\pi$
$797$	−4.40332e7	+	2.54226e7i	−0.0869772	+	0.0502163i	0.455881	+	0.890041i	$0.349324\pi$
$798$		0			0
$799$	2.10132e7	−	3.63960e7i	0.0411957	−	0.0713531i
$800$			4.30605e7i			0.0841026i
$801$		0			0
$802$	2.17108e8			0.420874
$803$	−8.04936e8	−	4.64730e8i	−1.55459	−	0.897541i
$804$		0			0
$805$	3.73948e8	+	6.47697e8i	0.716843	+	1.24161i
$806$	−5.45727e7	+	3.15075e7i	−0.104225	+	0.0601741i
$807$		0			0
$808$	3.11706e8	−	5.39890e8i	0.590896	−	1.02346i
$809$		−	1.02851e7i		−	0.0194251i	−0.999953	−	0.00971257i	$-0.996908\pi$
$809$		−	1.02851e7i		−	0.0194251i	0.999953	−	0.00971257i	$-0.00309166\pi$
$810$		0			0
$811$	4.84952e8			0.909152			0.454576	−	0.890708i	$-0.349791\pi$
$811$	4.84952e8			0.909152			0.454576	+	0.890708i	$0.349791\pi$
$812$	−5.21291e8	−	3.00968e8i	−0.973671	−	0.562149i
$813$		0			0
$814$	1.87872e8	+	3.25404e8i	0.348329	+	0.603323i
$815$	−3.57888e8	+	2.06627e8i	−0.661111	+	0.381693i
$816$		0			0
$817$	1.34877e8	−	2.33613e8i	0.247326	−	0.428382i
$818$			4.60389e8i			0.841133i
$819$		0			0
$820$	−7.07746e8			−1.28362
$821$	4.29688e8	+	2.48080e8i	0.776468	+	0.448294i	0.835177	−	0.549981i	$-0.185365\pi$
$821$	4.29688e8	+	2.48080e8i	0.776468	+	0.448294i	−0.0587089	+	0.998275i	$0.518698\pi$
$822$		0			0
$823$	1.60742e8	+	2.78412e8i	0.288356	+	0.499447i	0.973417	−	0.229038i	$-0.0735581\pi$
$823$	1.60742e8	+	2.78412e8i	0.288356	+	0.499447i	−0.685062	+	0.728485i	$0.740225\pi$
$824$	−6.50522e8	+	3.75579e8i	−1.16273	+	0.671305i
$825$		0			0
$826$	5.94245e8	−	1.02926e9i	1.05445	−	1.82636i
$827$			7.54902e8i			1.33467i	0.744757	+	0.667336i	$0.232565\pi$
$827$			7.54902e8i			1.33467i	−0.744757	+	0.667336i	$0.767435\pi$
$828$		0			0
$829$	−5.82262e8			−1.02201			−0.511004	−	0.859578i	$-0.670726\pi$
$829$	−5.82262e8			−1.02201			−0.511004	+	0.859578i	$0.670726\pi$
$830$	−1.51705e9	−	8.75868e8i	−2.65317	−	1.53181i
$831$		0			0
$832$	1.39921e7	+	2.42350e7i	0.0242948	+	0.0420798i
$833$	2.00852e8	−	1.15962e8i	0.347490	−	0.200623i
$834$		0			0
$835$	−3.28693e8	+	5.69312e8i	−0.564587	+	0.977893i
$836$		−	1.85586e9i		−	3.17634i
$837$		0			0
$838$	1.25003e9			2.12416
$839$	−5.75163e8	−	3.32071e8i	−0.973879	−	0.562270i	−0.0734627	−	0.997298i	$-0.523405\pi$
$839$	−5.75163e8	−	3.32071e8i	−0.973879	−	0.562270i	−0.900417	+	0.435028i	$0.856738\pi$
$840$		0			0
$841$	−2.59867e8	−	4.50103e8i	−0.436881	−	0.756700i
$842$	−1.16186e9	+	6.70800e8i	−1.94633	+	1.12372i
$843$		0			0
$844$	5.59987e8	−	9.69926e8i	0.931431	−	1.61329i
$845$		−	6.59301e8i		−	1.09273i
$846$		0			0
$847$	−1.47943e8			−0.243470
$848$	1.01505e9	+	5.86042e8i	1.66457	+	0.961039i
$849$		0			0
$850$	3.61775e7	+	6.26612e7i	0.0589090	+	0.102033i
$851$	−2.00217e8	+	1.15596e8i	−0.324873	+	0.187565i
$852$		0			0
$853$	−3.93890e8	+	6.82237e8i	−0.634640	+	1.09923i	0.351951	+	0.936018i	$0.385518\pi$
$853$	−3.93890e8	+	6.82237e8i	−0.634640	+	1.09923i	−0.986591	+	0.163211i	$0.947815\pi$
$854$			8.06497e8i			1.29488i
$855$		0			0
$856$	−3.45642e8			−0.551067
$857$	−8.35866e8	−	4.82588e8i	−1.32799	−	0.766715i	−0.343000	−	0.939335i	$-0.611443\pi$
$857$	−8.35866e8	−	4.82588e8i	−1.32799	−	0.766715i	−0.984988	+	0.172621i	$0.944776\pi$
$858$		0			0
$859$	2.97728e8	+	5.15681e8i	0.469722	+	0.813582i	0.999401	−	0.0346161i	$-0.0110208\pi$
$859$	2.97728e8	+	5.15681e8i	0.469722	+	0.813582i	−0.529679	+	0.848198i	$0.677688\pi$
$860$	−3.83736e8	+	2.21550e8i	−0.603306	+	0.348319i
$861$		0			0
$862$	−5.68149e8	+	9.84063e8i	−0.887034	+	1.53639i
$863$		−	9.85551e8i		−	1.53337i	−0.642024	−	0.766684i	$-0.721905\pi$
$863$		−	9.85551e8i		−	1.53337i	0.642024	−	0.766684i	$-0.278095\pi$
$864$		0			0
$865$	−4.85907e8			−0.750766
$866$	4.28150e8	+	2.47192e8i	0.659237	+	0.380611i
$867$		0			0
$868$	9.10294e8	+	1.57668e9i	1.39195	+	2.41092i
$869$	−5.44096e8	+	3.14134e8i	−0.829117	+	0.478691i
$870$		0			0
$871$	−3.24761e7	+	5.62503e7i	−0.0491484	+	0.0851276i
$872$			1.17280e9i			1.76879i
$873$		0			0
$874$	1.68347e9			2.52157
$875$	7.57567e8	+	4.37382e8i	1.13083	+	0.652884i
$876$		0			0
$877$	−1.84340e8	−	3.19286e8i	−0.273288	−	0.473349i	0.696413	−	0.717641i	$-0.254778\pi$
$877$	−1.84340e8	−	3.19286e8i	−0.273288	−	0.473349i	−0.969702	+	0.244291i	$0.921445\pi$
$878$	5.65631e8	−	3.26567e8i	0.835698	−	0.482491i
$879$		0			0
$880$	−4.58466e8	+	7.94086e8i	−0.672758	+	1.16525i
$881$		−	7.29792e8i		−	1.06726i	−0.845717	−	0.533632i	$-0.820827\pi$
$881$		−	7.29792e8i		−	1.06726i	0.845717	−	0.533632i	$-0.179173\pi$
$882$		0			0
$883$	−7.12900e7			−0.103549			−0.0517746	−	0.998659i	$-0.516488\pi$
$883$	−7.12900e7			−0.103549			−0.0517746	+	0.998659i	$0.516488\pi$
$884$	−3.13574e7	−	1.81042e7i	−0.0453924	−	0.0262073i
$885$		0			0
$886$	−8.39516e8	−	1.45408e9i	−1.20706	−	2.09068i
$887$	2.73062e8	−	1.57653e8i	0.391283	−	0.225907i	−0.291433	−	0.956591i	$-0.594132\pi$
$887$	2.73062e8	−	1.57653e8i	0.391283	−	0.225907i	0.682716	+	0.730684i	$0.260799\pi$
$888$		0			0
$889$	−3.95897e8	+	6.85715e8i	−0.563479	+	0.975974i
$890$			1.24877e9i			1.77139i
$891$		0			0
$892$	−1.26546e9			−1.78301
$893$	2.61023e8	+	1.50702e8i	0.366543	+	0.211624i
$894$		0			0
$895$	−5.89039e8	−	1.02025e9i	−0.821628	−	1.42310i
$896$	1.40925e9	−	8.13632e8i	1.95914	−	1.13111i
$897$		0			0
$898$	−6.87989e8	+	1.19163e9i	−0.950063	+	1.64556i
$899$		−	2.27113e8i		−	0.312581i
$900$		0			0
$901$	3.36853e8			0.460539
$902$	−5.67961e8	−	3.27913e8i	−0.773925	−	0.446826i
$903$		0			0
$904$	1.22741e9	+	2.12594e9i	1.66144	+	2.87770i
$905$	2.13272e8	−	1.23133e8i	0.287732	−	0.166122i
$906$		0			0
$907$	2.85210e8	−	4.93997e8i	0.382245	−	0.662068i	−0.609137	−	0.793065i	$-0.708484\pi$
$907$	2.85210e8	−	4.93997e8i	0.382245	−	0.662068i	0.991383	+	0.130996i	$0.0418176\pi$
$908$			4.94454e8i			0.660493i
$909$		0			0
$910$	1.70079e8			0.225697
$911$	−2.97529e8	−	1.71779e8i	−0.393527	−	0.227203i	0.290160	−	0.956978i	$-0.406291\pi$
$911$	−2.97529e8	−	1.71779e8i	−0.393527	−	0.227203i	−0.683687	+	0.729775i	$0.739625\pi$
$912$		0			0
$913$	−5.50516e8	−	9.53522e8i	−0.723366	−	1.25291i
$914$	9.93984e7	−	5.73877e7i	0.130179	−	0.0751589i
$915$		0			0
$916$	3.36616e8	−	5.83036e8i	0.437974	−	0.758593i
$917$			5.80262e8i			0.752517i
$918$		0			0
$919$	7.92851e8			1.02152			0.510758	−	0.859725i	$-0.329365\pi$
$919$	7.92851e8			1.02152			0.510758	+	0.859725i	$0.329365\pi$
$920$	−1.25901e9	−	7.26888e8i	−1.61683	−	0.933477i
$921$		0			0
$922$	1.09536e9	+	1.89721e9i	1.39753	+	2.42060i
$923$	9.96539e7	−	5.75352e7i	0.126733	−	0.0731693i
$924$		0			0
$925$	3.56312e7	−	6.17151e7i	0.0450200	−	0.0779769i
$926$		−	1.07617e9i		−	1.35533i
$927$		0			0
$928$	1.14498e8			0.143269
$929$	−1.57986e8	−	9.12134e7i	−0.197048	−	0.113766i	0.398230	−	0.917286i	$-0.369625\pi$
$929$	−1.57986e8	−	9.12134e7i	−0.197048	−	0.113766i	−0.595278	+	0.803520i	$0.702958\pi$
$930$		0			0
$931$	8.31653e8	+	1.44047e9i	1.03061	+	1.78506i
$932$	5.84750e8	−	3.37605e8i	0.722308	−	0.417025i
$933$		0			0
$934$	1.31062e9	−	2.27006e9i	1.60855	−	2.78610i
$935$			2.63523e8i			0.322392i
$936$		0			0
$937$	−3.34488e8			−0.406594			−0.203297	−	0.979117i	$-0.565166\pi$
$937$	−3.34488e8			−0.406594			−0.203297	+	0.979117i	$0.565166\pi$
$938$	2.39591e9	+	1.38328e9i	2.90310	+	1.67611i
$939$		0			0
$940$	−2.47545e8	−	4.28760e8i	−0.298037	−	0.516216i
$941$	−2.52152e8	+	1.45580e8i	−0.302618	+	0.174716i	−0.643618	−	0.765347i	$-0.722567\pi$
$941$	−2.52152e8	+	1.45580e8i	−0.302618	+	0.174716i	0.341001	+	0.940063i	$0.389234\pi$
$942$		0			0
$943$	2.01761e8	−	3.49460e8i	0.240604	−	0.416738i
$944$			8.96540e8i			1.06575i
$945$		0			0
$946$	−4.10594e8			−0.484997
$947$	−1.46907e8	−	8.48169e7i	−0.172979	−	0.0998694i	0.411011	−	0.911630i	$-0.365176\pi$
$947$	−1.46907e8	−	8.48169e7i	−0.172979	−	0.0998694i	−0.583990	+	0.811761i	$0.698509\pi$
$948$		0			0
$949$	−6.50263e7	−	1.12629e8i	−0.0760835	−	0.131780i
$950$	−4.49391e8	+	2.59456e8i	−0.524148	+	0.302617i
$951$		0			0
$952$	−4.05399e8	+	7.02171e8i	−0.469863	+	0.813827i
$953$			5.17958e8i			0.598434i	0.954185	+	0.299217i	$0.0967254\pi$
$953$			5.17958e8i			0.598434i	−0.954185	+	0.299217i	$0.903275\pi$
$954$		0			0
$955$	1.38898e9			1.59473
$956$	2.21049e9	+	1.27623e9i	2.52996	+	1.46068i
$957$		0			0
$958$	−8.73214e8	−	1.51245e9i	−0.993171	−	1.72022i
$959$	1.42924e9	−	8.25172e8i	1.62050	−	0.935597i
$960$		0			0
$961$	1.00294e8	−	1.73713e8i	0.113006	−	0.195733i
$962$			5.25751e7i			0.0590548i
$963$		0			0
$964$	2.05806e9			2.29735
$965$	9.10004e8	+	5.25391e8i	1.01266	+	0.584657i
$966$		0			0
$967$	6.87108e8	+	1.19011e9i	0.759881	+	1.31615i	0.942911	+	0.333046i	$0.108076\pi$
$967$	6.87108e8	+	1.19011e9i	0.759881	+	1.31615i	−0.183029	+	0.983107i	$0.558590\pi$
$968$	2.49048e8	−	1.43788e8i	0.274572	−	0.158524i
$969$		0			0
$970$	5.97436e8	−	1.03479e9i	0.654600	−	1.13380i
$971$			7.45510e8i			0.814321i	0.913357	+	0.407160i	$0.133481\pi$
$971$			7.45510e8i			0.814321i	−0.913357	+	0.407160i	$0.866519\pi$
$972$		0			0
$973$	3.43276e7			0.0372653
$974$	−7.44334e8	−	4.29742e8i	−0.805547	−	0.465083i
$975$		0			0
$976$	−3.04191e8	−	5.26875e8i	−0.327188	−	0.566707i
$977$	−8.48899e8	+	4.90112e8i	−0.910274	+	0.525547i	−0.880519	−	0.474010i	$-0.842806\pi$
$977$	−8.48899e8	+	4.90112e8i	−0.910274	+	0.525547i	−0.0297550	+	0.999557i	$0.509473\pi$
$978$		0			0
$979$	−3.92450e8	+	6.79743e8i	−0.418250	+	0.724431i
$980$		−	2.73217e9i		−	2.90288i
$981$		0			0
$982$	−9.14080e8			−0.965272
$983$	−8.77524e8	−	5.06639e8i	−0.923844	−	0.533381i	−0.0389845	−	0.999240i	$-0.512412\pi$
$983$	−8.77524e8	−	5.06639e8i	−0.923844	−	0.533381i	−0.884859	+	0.465858i	$0.845746\pi$
$984$		0			0
$985$	3.39701e8	+	5.88379e8i	0.355458	+	0.615671i
$986$	1.66616e8	−	9.61957e7i	0.173814	−	0.100352i
$987$		0			0
$988$	1.29839e8	−	2.24887e8i	0.134627	−	0.233182i
$989$		−	2.52634e8i		−	0.261158i
$990$		0			0
$991$	−1.85231e9			−1.90324			−0.951620	−	0.307279i	$-0.900582\pi$
$991$	−1.85231e9			−1.90324			−0.951620	+	0.307279i	$0.900582\pi$
$992$	−2.99909e8	−	1.73153e8i	−0.307224	−	0.177376i
$993$		0			0
$994$	−2.45064e9	−	4.24464e9i	−2.49529	−	4.32197i
$995$	−2.34225e8	+	1.35230e8i	−0.237773	+	0.137279i
$996$		0			0
$997$	−6.28324e8	+	1.08829e9i	−0.634013	+	1.09814i	0.352710	+	0.935733i	$0.385260\pi$
$997$	−6.28324e8	+	1.08829e9i	−0.634013	+	1.09814i	−0.986723	+	0.162410i	$0.948073\pi$
$998$		−	4.04941e8i		−	0.407380i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.7.d.e.26.4		8
3.2	odd	2	inner	81.7.d.e.26.1		8
9.2	odd	6		27.7.b.c.26.4	yes	4
9.4	even	3	inner	81.7.d.e.53.1		8
9.5	odd	6	inner	81.7.d.e.53.4		8
9.7	even	3		27.7.b.c.26.1	✓	4
36.7	odd	6		432.7.e.j.161.4		4
36.11	even	6		432.7.e.j.161.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.b.c.26.1	✓	4	9.7	even	3
27.7.b.c.26.4	yes	4	9.2	odd	6
81.7.d.e.26.1		8	3.2	odd	2	inner
81.7.d.e.26.4		8	1.1	even	1	trivial
81.7.d.e.53.1		8	9.4	even	3	inner
81.7.d.e.53.4		8	9.5	odd	6	inner
432.7.e.j.161.1		4	36.11	even	6
432.7.e.j.161.4		4	36.7	odd	6

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.2150 + 7.05234i) q^{2} +(67.4711 + 116.863i) q^{4} +(119.008 - 68.7094i) q^{5} +(257.384 - 445.803i) q^{7} +1000.62i q^{8} +1938.25 q^{10} +(1055.05 + 609.131i) q^{11} +(85.2313 + 147.625i) q^{13} +(6287.91 - 3630.33i) q^{14} +(-2738.55 + 4743.30i) q^{16} +1574.10i q^{17} -11289.1 q^{19} +(16059.2 + 9271.79i) q^{20} +(8591.60 + 14881.1i) q^{22} +(-9156.17 + 5286.32i) q^{23} +(1629.46 - 2822.30i) q^{25} +2404.32i q^{26} +69464.0 q^{28} +(-7504.48 - 4332.71i) q^{29} +(13104.5 + 22697.7i) q^{31} +(-11442.9 + 6606.58i) q^{32} +(-11101.1 + 19227.7i) q^{34} -70738.9i q^{35} +21866.9 q^{37} +(-137896. - 79614.3i) q^{38} +(68751.8 + 119082. i) q^{40} +(-33053.3 + 19083.3i) q^{41} +(-11947.5 + 20693.8i) q^{43} +164395. i q^{44} -149124. q^{46} +(-23121.8 - 13349.4i) q^{47} +(-73668.9 - 127598. i) q^{49} +(39807.7 - 22983.0i) q^{50} +(-11501.3 + 19920.8i) q^{52} -213997. i q^{53} +167412. q^{55} +(446078. + 257543. i) q^{56} +(-61111.5 - 105848. i) q^{58} +(141759. - 81844.5i) q^{59} +(-55538.9 + 96196.1i) q^{61} +369671. i q^{62} +164166. q^{64} +(20286.4 + 11712.4i) q^{65} +(190518. + 329986. i) q^{67} +(-183955. + 106206. i) q^{68} +(498875. - 864076. i) q^{70} -675048. i q^{71} -762939. q^{73} +(267105. + 154213. i) q^{74} +(-761685. - 1.31928e6i) q^{76} +(543105. - 313562. i) q^{77} +(-257854. + 446616. i) q^{79} +752655. i q^{80} -538328. q^{82} +(-782690. - 451887. i) q^{83} +(108155. + 187331. i) q^{85} +(-291879. + 168516. i) q^{86} +(-609507. + 1.05570e6i) q^{88} +644278. i q^{89} +87748.8 q^{91} +(-1.23555e6 - 713347. i) q^{92} +(-188289. - 326125. i) q^{94} +(-1.34349e6 + 775664. i) q^{95} +(308235. - 533878. i) q^{97} -2.07815e6i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 194 q^{4} + 676 q^{7} + 6516 q^{10} + 3448 q^{13} - 10498 q^{16} - 7328 q^{19} + 58014 q^{22} - 17392 q^{25} + 304684 q^{28} + 153244 q^{31} - 65988 q^{34} + 257920 q^{37} + 338058 q^{40} - 126008 q^{43}+ \cdots - 975212 q^{97}+O(q^{100}) \) 8 * q + 194 * q^4 + 676 * q^7 + 6516 * q^10 + 3448 * q^13 - 10498 * q^16 - 7328 * q^19 + 58014 * q^22 - 17392 * q^25 + 304684 * q^28 + 153244 * q^31 - 65988 * q^34 + 257920 * q^37 + 338058 * q^40 - 126008 * q^43 - 233136 * q^46 - 121872 * q^49 + 71884 * q^52 + 108360 * q^55 - 567036 * q^58 - 167696 * q^61 - 57988 * q^64 - 8 * q^67 + 2104830 * q^70 - 3763352 * q^73 - 3764384 * q^76 - 1188728 * q^79 - 2732688 * q^82 + 176472 * q^85 - 27342 * q^88 - 747472 * q^91 - 1381140 * q^94 - 975212 * q^97

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