LMFDB - Embedded newform 81.8.e.a.10.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,8,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, 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:	$25.3031870642$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			10.16
Character	$\chi$	$=$	81.10
Dual form			81.8.e.a.73.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.26179 + 12.8272i) q^{2} +(-39.1414 + 14.2463i) q^{4} +(4.19097 + 3.51664i) q^{5} +(-1350.63 - 491.588i) q^{7} +(562.337 + 973.996i) q^{8} +(-35.6297 + 61.7124i) q^{10} +(916.360 - 768.917i) q^{11} +(294.159 - 1668.26i) q^{13} +(3250.88 - 18436.6i) q^{14} +(-15306.0 + 12843.3i) q^{16} +(10997.3 - 19047.8i) q^{17} +(-16743.5 - 29000.6i) q^{19} +(-214.139 - 77.9404i) q^{20} +(11935.7 + 10015.2i) q^{22} +(17635.4 - 6418.77i) q^{23} +(-13561.1 - 76908.6i) q^{25} +22064.4 q^{26} +59868.6 q^{28} +(-30705.1 - 174137. i) q^{29} +(199467. - 72600.2i) q^{31} +(-89084.5 - 74750.7i) q^{32} +(269204. + 97982.3i) q^{34} +(-3931.70 - 6809.90i) q^{35} +(-117016. + 202677. i) q^{37} +(334127. - 280366. i) q^{38} +(-1068.46 + 6059.53i) q^{40} +(-95223.1 + 540037. i) q^{41} +(379740. - 318640. i) q^{43} +(-24913.3 + 43151.2i) q^{44} +(122223. + 211696. i) q^{46} +(30204.4 + 10993.5i) q^{47} +(951661. + 798539. i) q^{49} +(955852. - 347902. i) q^{50} +(12252.7 + 69488.5i) q^{52} +1.06896e6 q^{53} +6544.45 q^{55} +(-280702. - 1.59194e6i) q^{56} +(2.16425e6 - 787722. i) q^{58} +(-2.28094e6 - 1.91394e6i) q^{59} +(-2.42205e6 - 881553. i) q^{61} +(1.38241e6 + 2.39441e6i) q^{62} +(-521406. + 903101. i) q^{64} +(7099.47 - 5957.16i) q^{65} +(-172140. + 976252. i) q^{67} +(-159087. + 902228. i) q^{68} +(78459.5 - 65835.3i) q^{70} +(-373502. + 646925. i) q^{71} +(-2.19519e6 - 3.80218e6i) q^{73} +(-2.86445e6 - 1.04258e6i) q^{74} +(1.06851e6 + 896589. i) q^{76} +(-1.61565e6 + 588048. i) q^{77} +(-631110. - 3.57920e6i) q^{79} -109313. q^{80} -7.14255e6 q^{82} +(-894305. - 5.07185e6i) q^{83} +(113074. - 41155.5i) q^{85} +(4.94615e6 + 4.15032e6i) q^{86} +(1.26423e6 + 460140. i) q^{88} +(2.30314e6 + 3.98916e6i) q^{89} +(-1.21739e6 + 2.10859e6i) q^{91} +(-598831. + 502479. i) q^{92} +(-72700.3 + 412304. i) q^{94} +(31813.2 - 180422. i) q^{95} +(-1.24500e7 + 1.04468e7i) q^{97} +(-8.09058e6 + 1.40133e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{2} - 6 q^{4} + 219 q^{5} - 6 q^{7} + 4611 q^{8} - 3 q^{10} - 9399 q^{11} - 6 q^{13} - 16647 q^{14} + 378 q^{16} + 58959 q^{17} - 3 q^{19} - 240243 q^{20} + 105762 q^{22} + 144084 q^{23} - 107997 q^{25}+ \cdots + 88493274 q^{98}+O(q^{100}) $ 120 * q + 6 * q^2 - 6 * q^4 + 219 * q^5 - 6 * q^7 + 4611 * q^8 - 3 * q^10 - 9399 * q^11 - 6 * q^13 - 16647 * q^14 + 378 * q^16 + 58959 * q^17 - 3 * q^19 - 240243 * q^20 + 105762 * q^22 + 144084 * q^23 - 107997 * q^25 - 443202 * q^26 - 12 * q^28 - 107886 * q^29 + 297975 * q^31 + 639576 * q^32 - 265806 * q^34 + 450672 * q^35 - 3 * q^37 + 145596 * q^38 + 283521 * q^40 - 227085 * q^41 - 1080969 * q^43 + 1205115 * q^44 - 3 * q^46 + 5184339 * q^47 + 976008 * q^49 - 2324559 * q^50 - 3366135 * q^52 - 5631750 * q^53 - 12 * q^55 - 5254923 * q^56 + 3884295 * q^58 + 12534492 * q^59 + 3865440 * q^61 + 9923646 * q^62 - 10223619 * q^64 - 17158395 * q^65 + 5567061 * q^67 - 19858455 * q^68 - 1020993 * q^70 + 18563877 * q^71 + 3770934 * q^73 + 36278085 * q^74 - 1156998 * q^76 - 8471751 * q^77 + 16415526 * q^79 - 101080590 * q^80 - 12 * q^82 - 3147699 * q^83 - 7672131 * q^85 + 70854834 * q^86 - 34323078 * q^88 + 54647613 * q^89 + 3315066 * q^91 - 73858515 * q^92 + 22126539 * q^94 - 32541447 * q^95 + 41250117 * q^97 + 88493274 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	2.26179	+	12.8272i	0.199916	+	1.13378i	0.905243	+	0.424895i	$0.139689\pi$
$2$	2.26179	+	12.8272i	0.199916	+	1.13378i	−0.705327	+	0.708882i	$0.749200\pi$
$3$		0			0
$3$		0			0
$4$	−39.1414	+	14.2463i	−0.305792	+	0.111299i
$5$	4.19097	+	3.51664i	0.0149941	+	0.0125815i	0.650254	−	0.759717i	$-0.274663\pi$
$5$	4.19097	+	3.51664i	0.0149941	+	0.0125815i	−0.635260	+	0.772299i	$0.719107\pi$
$6$		0			0
$7$	−1350.63	−	491.588i	−1.48830	−	0.541699i	−0.535302	−	0.844661i	$-0.679802\pi$
$7$	−1350.63	−	491.588i	−1.48830	−	0.541699i	−0.953003	+	0.302962i	$0.902025\pi$
$8$	562.337	+	973.996i	0.388313	+	0.672578i
$9$		0			0
$10$	−35.6297	+	61.7124i	−0.0112671	+	0.0195152i
$11$	916.360	−	768.917i	0.207583	−	0.174183i	−0.533069	−	0.846072i	$-0.678961\pi$
$11$	916.360	−	768.917i	0.207583	−	0.174183i	0.740652	+	0.671889i	$0.234517\pi$
$12$		0			0
$13$	294.159	−	1668.26i	0.0371347	−	0.210601i	−0.960595	−	0.277953i	$-0.910344\pi$
$13$	294.159	−	1668.26i	0.0371347	−	0.210601i	0.997729	+	0.0673520i	$0.0214551\pi$
$14$	3250.88	−	18436.6i	0.316630	−	1.79570i
$15$		0			0
$16$	−15306.0	+	12843.3i	−0.934207	+	0.783893i
$17$	10997.3	−	19047.8i	0.542892	−	0.940317i	−0.455844	−	0.890060i	$-0.650663\pi$
$17$	10997.3	−	19047.8i	0.542892	−	0.940317i	0.998736	−	0.0502573i	$-0.0160041\pi$
$18$		0			0
$19$	−16743.5	−	29000.6i	−0.560026	−	0.969994i	−0.997493	−	0.0707596i	$-0.977458\pi$
$19$	−16743.5	−	29000.6i	−0.560026	−	0.969994i	0.437467	−	0.899234i	$-0.355876\pi$
$20$	−214.139	−	77.9404i	−0.00598538	−	0.00217850i
$21$		0			0
$22$	11935.7	+	10015.2i	0.238983	+	0.200531i
$23$	17635.4	−	6418.77i	0.302231	−	0.110003i	−0.186453	−	0.982464i	$-0.559699\pi$
$23$	17635.4	−	6418.77i	0.302231	−	0.110003i	0.488684	+	0.872461i	$0.337477\pi$
$24$		0			0
$25$	−13561.1	−	76908.6i	−0.173582	−	0.984430i
$26$	22064.4			0.246199
$27$		0			0
$28$	59868.6			0.515402
$29$	−30705.1	−	174137.i	−0.233785	−	1.32586i	−0.845157	−	0.534519i	$-0.820493\pi$
$29$	−30705.1	−	174137.i	−0.233785	−	1.32586i	0.611371	−	0.791344i	$-0.290618\pi$
$30$		0			0
$31$	199467.	−	72600.2i	1.20256	−	0.437695i	0.338442	−	0.940987i	$-0.390100\pi$
$31$	199467.	−	72600.2i	1.20256	−	0.437695i	0.864116	+	0.503292i	$0.167878\pi$
$32$	−89084.5	−	74750.7i	−0.480593	−	0.403265i
$33$		0			0
$34$	269204.	+	97982.3i	1.17464	+	0.427535i
$35$	−3931.70	−	6809.90i	−0.0155004	−	0.0268474i
$36$		0			0
$37$	−117016.	+	202677.i	−0.379786	+	0.657808i	−0.991031	−	0.133633i	$-0.957336\pi$
$37$	−117016.	+	202677.i	−0.379786	+	0.657808i	0.611245	+	0.791441i	$0.290669\pi$
$38$	334127.	−	280366.i	0.987799	−	0.828862i
$39$		0			0
$40$	−1068.46	+	6059.53i	−0.00263966	+	0.0149702i
$41$	−95223.1	+	540037.i	−0.215774	+	1.22371i	0.663785	+	0.747924i	$0.268949\pi$
$41$	−95223.1	+	540037.i	−0.215774	+	1.22371i	−0.879559	+	0.475791i	$0.842162\pi$
$42$		0			0
$43$	379740.	−	318640.i	0.728361	−	0.611168i	−0.201323	−	0.979525i	$-0.564524\pi$
$43$	379740.	−	318640.i	0.728361	−	0.611168i	0.929684	+	0.368357i	$0.120080\pi$
$44$	−24913.3	+	43151.2i	−0.0440908	+	0.0763675i
$45$		0			0
$46$	122223.	+	211696.i	0.185139	+	0.320671i
$47$	30204.4	+	10993.5i	0.0424354	+	0.0154452i	0.363151	−	0.931730i	$-0.381701\pi$
$47$	30204.4	+	10993.5i	0.0424354	+	0.0154452i	−0.320715	+	0.947176i	$0.603923\pi$
$48$		0			0
$49$	951661.	+	798539.i	1.15557	+	0.969638i
$50$	955852.	−	347902.i	1.08142	−	0.393606i
$51$		0			0
$52$	12252.7	+	69488.5i	0.0120843	+	0.0685332i
$53$	1.06896e6			0.986267			0.493134	−	0.869954i	$-0.335851\pi$
$53$	1.06896e6			0.986267			0.493134	+	0.869954i	$0.335851\pi$
$54$		0			0
$55$	6544.45			0.00530400
$56$	−280702.	−	1.59194e6i	−0.213594	−	1.21135i
$57$		0			0
$58$	2.16425e6	−	787722.i	1.45650	−	0.530121i
$59$	−2.28094e6	−	1.91394e6i	−1.44588	−	1.21324i	−0.935520	−	0.353274i	$-0.885068\pi$
$59$	−2.28094e6	−	1.91394e6i	−1.44588	−	1.21324i	−0.510359	−	0.859962i	$-0.670487\pi$
$60$		0			0
$61$	−2.42205e6	−	881553.i	−1.36624	−	0.497272i	−0.448264	−	0.893901i	$-0.647958\pi$
$61$	−2.42205e6	−	881553.i	−1.36624	−	0.497272i	−0.917979	+	0.396629i	$0.870180\pi$
$62$	1.38241e6	+	2.39441e6i	0.736659	+	1.27593i
$63$		0			0
$64$	−521406.	+	903101.i	−0.248626	+	0.430632i
$65$	7099.47	−	5957.16i	0.00320649	−	0.00269056i
$66$		0			0
$67$	−172140.	+	976252.i	−0.0699228	+	0.396552i	0.929680	+	0.368368i	$0.120083\pi$
$67$	−172140.	+	976252.i	−0.0699228	+	0.396552i	−0.999603	+	0.0281836i	$0.991028\pi$
$68$	−159087.	+	902228.i	−0.0613556	+	0.347965i
$69$		0			0
$70$	78459.5	−	65835.3i	0.0273402	−	0.0229412i
$71$	−373502.	+	646925.i	−0.123848	+	0.214511i	−0.921282	−	0.388895i	$-0.872857\pi$
$71$	−373502.	+	646925.i	−0.123848	+	0.214511i	0.797434	+	0.603406i	$0.206190\pi$
$72$		0			0
$73$	−2.19519e6	−	3.80218e6i	−0.660454	−	1.14394i	−0.980497	−	0.196536i	$-0.937031\pi$
$73$	−2.19519e6	−	3.80218e6i	−0.660454	−	1.14394i	0.320043	−	0.947403i	$-0.396303\pi$
$74$	−2.86445e6	−	1.04258e6i	−0.821733	−	0.299086i
$75$		0			0
$76$	1.06851e6	+	896589.i	0.279211	+	0.234286i
$77$	−1.61565e6	+	588048.i	−0.403301	+	0.146790i
$78$		0			0
$79$	−631110.	−	3.57920e6i	−0.144016	−	0.816755i	−0.968152	−	0.250363i	$-0.919450\pi$
$79$	−631110.	−	3.57920e6i	−0.144016	−	0.816755i	0.824136	−	0.566392i	$-0.191661\pi$
$80$	−109313.			−0.0238701
$81$		0			0
$82$	−7.14255e6			−1.43056
$83$	−894305.	−	5.07185e6i	−0.171677	−	0.973629i	−0.941910	−	0.335866i	$-0.890971\pi$
$83$	−894305.	−	5.07185e6i	−0.171677	−	0.973629i	0.770233	−	0.637763i	$-0.220140\pi$
$84$		0			0
$85$	113074.	−	41155.5i	0.0199708	−	0.00726877i
$86$	4.94615e6	+	4.15032e6i	0.838539	+	0.703617i
$87$		0			0
$88$	1.26423e6	+	460140.i	0.197759	+	0.0719782i
$89$	2.30314e6	+	3.98916e6i	0.346303	+	0.599814i	0.985590	−	0.169155i	$-0.0541037\pi$
$89$	2.30314e6	+	3.98916e6i	0.346303	+	0.599814i	−0.639287	+	0.768968i	$0.720770\pi$
$90$		0			0
$91$	−1.21739e6	+	2.10859e6i	−0.169350	+	0.293323i
$92$	−598831.	+	502479.i	−0.0801764	+	0.0672760i
$93$		0			0
$94$	−72700.3	+	412304.i	−0.00902794	+	0.0512000i
$95$	31813.2	−	180422.i	0.00380693	−	0.0215902i
$96$		0			0
$97$	−1.24500e7	+	1.04468e7i	−1.38506	+	1.16221i	−0.417769	+	0.908553i	$0.637188\pi$
$97$	−1.24500e7	+	1.04468e7i	−1.38506	+	1.16221i	−0.967295	+	0.253654i	$0.918368\pi$
$98$	−8.09058e6	+	1.40133e7i	−0.868337	+	1.50400i
$99$		0			0
$100$	1.62646e6	+	2.81711e6i	0.162646	+	0.281711i
$101$	1.08384e6	+	394485.i	0.104674	+	0.0380983i	0.393826	−	0.919185i	$-0.371151\pi$
$101$	1.08384e6	+	394485.i	0.104674	+	0.0380983i	−0.289152	+	0.957283i	$0.593373\pi$
$102$		0			0
$103$	−3.37394e6	−	2.83107e6i	−0.304234	−	0.255282i	0.477870	−	0.878430i	$-0.341409\pi$
$103$	−3.37394e6	−	2.83107e6i	−0.304234	−	0.255282i	−0.782104	+	0.623148i	$0.785853\pi$
$104$	1.79029e6	−	651613.i	0.156066	−	0.0568032i
$105$		0			0
$106$	2.41775e6	+	1.37117e7i	0.197170	+	1.11821i
$107$	−9.03128e6			−0.712699			−0.356349	−	0.934353i	$-0.615979\pi$
$107$	−9.03128e6			−0.712699			−0.356349	+	0.934353i	$0.615979\pi$
$108$		0			0
$109$	−8.38933e6			−0.620489			−0.310245	−	0.950657i	$-0.600411\pi$
$109$	−8.38933e6			−0.620489			−0.310245	+	0.950657i	$0.600411\pi$
$110$	14802.1	+	83947.1i	0.00106035	+	0.00601355i
$111$		0			0
$112$	2.69864e7	−	9.82223e6i	1.81502	−	0.660613i
$113$	1.57643e7	+	1.32278e7i	1.02778	+	0.862407i	0.990585	−	0.136901i	$-0.0437141\pi$
$113$	1.57643e7	+	1.32278e7i	1.02778	+	0.862407i	0.0371923	+	0.999308i	$0.488159\pi$
$114$		0			0
$115$	96482.1	+	35116.6i	0.00591567	+	0.00215313i
$116$	3.68265e6	+	6.37853e6i	0.219057	+	0.379418i
$117$		0			0
$118$	1.93915e7	−	3.35870e7i	1.08649	−	1.88185i
$119$	−2.42169e7	+	2.03204e7i	−1.31736	+	1.10539i
$120$		0			0
$121$	−3.13543e6	+	1.77819e7i	−0.160897	+	0.912493i
$122$	5.82973e6	−	3.30620e7i	0.290662	−	1.64843i
$123$		0			0
$124$	−6.77314e6	+	5.68334e6i	−0.319017	+	0.267687i
$125$	427334.	−	740165.i	0.0195696	−	0.0338956i
$126$		0			0
$127$	−1.76865e7	−	3.06340e7i	−0.766178	−	1.32706i	−0.939621	−	0.342216i	$-0.888823\pi$
$127$	−1.76865e7	−	3.06340e7i	−0.766178	−	1.32706i	0.173443	−	0.984844i	$-0.444511\pi$
$128$	−2.67512e7	−	9.73664e6i	−1.12748	−	0.410369i
$129$		0			0
$130$	92471.4	+	77592.7i	0.00369152	+	0.00309756i
$131$	3.98270e7	−	1.44959e7i	1.54785	−	0.563371i	0.579937	−	0.814662i	$-0.303077\pi$
$131$	3.98270e7	−	1.44959e7i	1.54785	−	0.563371i	0.967912	+	0.251291i	$0.0808551\pi$
$132$		0			0
$133$	8.35787e6	+	4.73998e7i	0.308045	+	1.74701i
$134$	−1.29119e7			−0.463580
$135$		0			0
$136$	2.47367e7			0.843248
$137$	−3.03025e6	−	1.71854e7i	−0.100683	−	0.571001i	−0.992857	−	0.119310i	$-0.961932\pi$
$137$	−3.03025e6	−	1.71854e7i	−0.100683	−	0.571001i	0.892174	−	0.451692i	$-0.149179\pi$
$138$		0			0
$139$	1.91345e7	−	6.96439e6i	0.604318	−	0.219954i	−0.0216975	−	0.999765i	$-0.506907\pi$
$139$	1.91345e7	−	6.96439e6i	0.604318	−	0.219954i	0.626015	+	0.779811i	$0.284685\pi$
$140$	250908.	+	210537.i	0.00772798	+	0.00648455i
$141$		0			0
$142$	−9.14303e6	−	3.32779e6i	−0.267967	−	0.0975319i
$143$	−1.01320e6	−	1.75491e6i	−0.0289746	−	0.0501854i
$144$		0			0
$145$	483694.	−	837783.i	0.0131760	−	0.0228215i
$146$	4.38064e7	−	3.67579e7i	1.16494	−	0.977499i
$147$		0			0
$148$	1.69276e6	−	9.60011e6i	0.0429219	−	0.243422i
$149$	6.39632e6	−	3.62753e7i	0.158408	−	0.898379i	−0.797195	−	0.603722i	$-0.793684\pi$
$149$	6.39632e6	−	3.62753e7i	0.158408	−	0.898379i	0.955603	−	0.294657i	$-0.0952053\pi$
$150$		0			0
$151$	−361682.	+	303487.i	−0.00854885	+	0.00717333i	−0.647052	−	0.762446i	$-0.723998\pi$
$151$	−361682.	+	303487.i	−0.00854885	+	0.00717333i	0.638503	+	0.769619i	$0.279554\pi$
$152$	1.88310e7	−	3.26162e7i	0.434931	−	0.753322i
$153$		0			0
$154$	−1.11973e7	−	1.93943e7i	−0.247053	−	0.427908i
$155$	1.09127e6	+	397190.i	0.0235381	+	0.00856718i
$156$		0			0
$157$	−5.21288e7	−	4.37413e7i	−1.07505	−	0.902075i	−0.0795504	−	0.996831i	$-0.525348\pi$
$157$	−5.21288e7	−	4.37413e7i	−1.07505	−	0.902075i	−0.995501	+	0.0947560i	$0.969793\pi$
$158$	4.44838e7	−	1.61908e7i	0.897227	−	0.326564i
$159$		0			0
$160$	−110479.	−	626557.i	−0.00213235	−	0.0120932i
$161$	−2.69742e7			−0.509400
$162$		0			0
$163$	1.82610e7			0.330270			0.165135	−	0.986271i	$-0.447194\pi$
$163$	1.82610e7			0.330270			0.165135	+	0.986271i	$0.447194\pi$
$164$	−3.96636e6	−	2.24944e7i	−0.0702164	−	0.398217i
$165$		0			0
$166$	6.30351e7	−	2.29429e7i	1.06956	−	0.389287i
$167$	4.75246e7	+	3.98779e7i	0.789607	+	0.662559i	0.945648	−	0.325191i	$-0.105429\pi$
$167$	4.75246e7	+	3.98779e7i	0.789607	+	0.662559i	−0.156041	+	0.987751i	$0.549873\pi$
$168$		0			0
$169$	5.62678e7	+	2.04798e7i	0.896719	+	0.326379i
$170$	783659.	+	1.35734e6i	0.0122336	+	0.0211893i
$171$		0			0
$172$	−1.03241e7	+	1.78819e7i	−0.154704	+	0.267956i
$173$	−6.40510e7	+	5.37452e7i	−0.940513	+	0.789184i	−0.977674	−	0.210125i	$-0.932613\pi$
$173$	−6.40510e7	+	5.37452e7i	−0.940513	+	0.789184i	0.0371615	+	0.999309i	$0.488168\pi$
$174$		0			0
$175$	−1.94914e7	+	1.10541e8i	−0.274922	+	1.55916i
$176$	−4.15041e6	+	2.35382e7i	−0.0573848	+	0.325446i
$177$		0			0
$178$	−4.59606e7	+	3.85655e7i	−0.610824	+	0.512542i
$179$	−4.47798e7	+	7.75608e7i	−0.583574	+	1.01078i	0.411477	+	0.911420i	$0.365013\pi$
$179$	−4.47798e7	+	7.75608e7i	−0.583574	+	1.01078i	−0.995052	+	0.0993603i	$0.968320\pi$
$180$		0			0
$181$	−259263.	−	449056.i	−0.00324986	−	0.00562893i	0.864396	−	0.502812i	$-0.167701\pi$
$181$	−259263.	−	449056.i	−0.00324986	−	0.00562893i	−0.867646	+	0.497183i	$0.834368\pi$
$182$	−2.98008e7	−	1.08466e7i	−0.366419	−	0.133366i
$183$		0			0
$184$	1.61689e7	+	1.35673e7i	0.191345	+	0.160558i
$185$	−1.20315e6	+	437912.i	−0.0139708	+	0.00508494i
$186$		0			0
$187$	−4.56875e6	−	2.59107e7i	−0.0510918	−	0.289756i
$188$	−1.33886e6			−0.0146954
$189$		0			0
$190$	2.38626e6			0.0252395
$191$	1.50980e7	+	8.56249e7i	0.156784	+	0.889167i	0.957137	+	0.289637i	$0.0935346\pi$
$191$	1.50980e7	+	8.56249e7i	0.156784	+	0.889167i	−0.800352	+	0.599530i	$0.795354\pi$
$192$		0			0
$193$	1.21280e8	−	4.41423e7i	1.21433	−	0.441982i	0.346129	−	0.938187i	$-0.387496\pi$
$193$	1.21280e8	−	4.41423e7i	1.21433	−	0.441982i	0.868205	+	0.496205i	$0.165274\pi$
$194$	−1.62163e8	−	1.36071e8i	−1.59458	−	1.33801i
$195$		0			0
$196$	−4.86255e7	−	1.76982e7i	−0.461284	−	0.167894i
$197$	8.33198e7	+	1.44314e8i	0.776456	+	1.34486i	0.933973	+	0.357344i	$0.116318\pi$
$197$	8.33198e7	+	1.44314e8i	0.776456	+	1.34486i	−0.157517	+	0.987516i	$0.550349\pi$
$198$		0			0
$199$	1.96276e7	−	3.39961e7i	0.176556	−	0.305804i	−0.764143	−	0.645047i	$-0.776838\pi$
$199$	1.96276e7	−	3.39961e7i	0.176556	−	0.305804i	0.940699	+	0.339243i	$0.110171\pi$
$200$	6.72828e7	−	5.64570e7i	0.594702	−	0.499014i
$201$		0			0
$202$	−2.60874e6	+	1.47949e7i	−0.0222690	+	0.126294i
$203$	−4.41326e7	+	2.50288e8i	−0.370274	+	2.09993i
$204$		0			0
$205$	−2.29819e6	+	1.92841e6i	−0.0186315	+	0.0156337i
$206$	2.86837e7	−	4.96816e7i	0.228612	−	0.395968i
$207$		0			0
$208$	1.69235e7	+	2.93124e7i	0.130397	+	0.225855i
$209$	−3.76421e7	−	1.37006e7i	−0.285208	−	0.103807i
$210$		0			0
$211$	−3.49432e7	−	2.93209e7i	−0.256079	−	0.214876i	0.505705	−	0.862706i	$-0.331232\pi$
$211$	−3.49432e7	−	2.93209e7i	−0.256079	−	0.214876i	−0.761785	+	0.647830i	$0.775677\pi$
$212$	−4.18404e7	+	1.52287e7i	−0.301592	+	0.109771i
$213$		0			0
$214$	−2.04268e7	−	1.15846e8i	−0.142480	−	0.808042i
$215$	2.71202e6			0.0186105
$216$		0			0
$217$	−3.05095e8			−2.02687
$218$	−1.89749e7	−	1.07612e8i	−0.124045	−	0.703497i
$219$		0			0
$220$	−256159.	+	93234.1i	−0.00162192	+	0.000590331i
$221$	−2.85417e7	−	2.39493e7i	−0.177872	−	0.149252i
$222$		0			0
$223$	−1.59536e8	−	5.80664e7i	−0.963367	−	0.350637i	−0.188015	−	0.982166i	$-0.560205\pi$
$223$	−1.59536e8	−	5.80664e7i	−0.963367	−	0.350637i	−0.775352	+	0.631529i	$0.782428\pi$
$224$	8.35732e7	+	1.44753e8i	0.496820	+	0.860518i
$225$		0			0
$226$	−1.34020e8	+	2.32130e8i	−0.772309	+	1.33768i
$227$	−6.25650e6	+	5.24983e6i	−0.0355011	+	0.0297889i	−0.660366	−	0.750944i	$-0.729599\pi$
$227$	−6.25650e6	+	5.24983e6i	−0.0355011	+	0.0297889i	0.624864	+	0.780733i	$0.285154\pi$
$228$		0			0
$229$	−5.52307e7	+	3.13229e8i	−0.303918	+	1.72360i	0.324637	+	0.945839i	$0.394758\pi$
$229$	−5.52307e7	+	3.13229e8i	−0.303918	+	1.72360i	−0.628555	+	0.777766i	$0.716353\pi$
$230$	−232227.	+	1.31702e6i	−0.00125853	+	0.00713750i
$231$		0			0
$232$	1.52342e8	−	1.27830e8i	0.800964	−	0.672088i
$233$	1.76173e8	−	3.05140e8i	0.912417	−	1.58035i	0.101778	−	0.994807i	$-0.467547\pi$
$233$	1.76173e8	−	3.05140e8i	0.912417	−	1.58035i	0.810640	−	0.585546i	$-0.199120\pi$
$234$		0			0
$235$	87925.7	+	152292.i	0.000441955	+	0.000765489i
$236$	1.16546e8	+	4.24191e7i	0.577170	+	0.210073i
$237$		0			0
$238$	−3.15427e8	−	2.64675e8i	−1.51663	−	1.27260i
$239$	−2.38903e8	+	8.69535e7i	−1.13195	+	0.411997i	−0.839001	−	0.544130i	$-0.816860\pi$
$239$	−2.38903e8	+	8.69535e7i	−1.13195	+	0.411997i	−0.292952	+	0.956127i	$0.594638\pi$
$240$		0			0
$241$	−1.75072e7	−	9.92884e7i	−0.0805671	−	0.456918i	−0.998225	−	0.0595482i	$-0.981034\pi$
$241$	−1.75072e7	−	9.92884e7i	−0.0805671	−	0.456918i	0.917658	−	0.397370i	$-0.130077\pi$
$242$	−2.35184e8			−1.06673
$243$		0			0
$244$	1.07361e8			0.473132
$245$	1.18021e6	+	6.69331e6i	0.00512718	+	0.0290777i
$246$		0			0
$247$	−5.33056e7	+	1.94017e7i	−0.225078	+	0.0819218i
$248$	1.82880e8	+	1.53455e8i	0.761353	+	0.638851i
$249$		0			0
$250$	1.04608e7	+	3.80742e6i	0.0423423	+	0.0154113i
$251$	−1.35795e8	−	2.35204e8i	−0.542033	−	0.938828i	−0.998787	−	0.0492355i	$-0.984321\pi$
$251$	−1.35795e8	−	2.35204e8i	−0.542033	−	0.938828i	0.456754	−	0.889593i	$-0.349012\pi$
$252$		0			0
$253$	1.12249e7	−	1.94421e7i	0.0435773	−	0.0754781i
$254$	3.52946e8	−	2.96157e8i	1.35142	−	1.13398i
$255$		0			0
$256$	4.12101e7	−	2.33714e8i	0.153519	−	0.870652i
$257$	5.37242e7	−	3.04685e8i	0.197426	−	1.11966i	−0.711495	−	0.702691i	$-0.751982\pi$
$257$	5.37242e7	−	3.04685e8i	0.197426	−	1.11966i	0.908921	−	0.416968i	$-0.136907\pi$
$258$		0			0
$259$	2.57678e8	−	2.16218e8i	0.921570	−	0.773289i
$260$	−193016.	+	334313.i	−0.000681060	+	0.00117963i
$261$		0			0
$262$	2.76022e8	+	4.78084e8i	0.948176	+	1.64229i
$263$	2.20619e8	+	8.02987e7i	0.747821	+	0.272185i	0.687689	−	0.726006i	$-0.258625\pi$
$263$	2.20619e8	+	8.02987e7i	0.747821	+	0.272185i	0.0601325	+	0.998190i	$0.480848\pi$
$264$		0			0
$265$	4.47997e6	+	3.75914e6i	0.0147882	+	0.0124087i
$266$	−5.89104e8	+	2.14416e8i	−1.91914	+	0.698510i
$267$		0			0
$268$	−7.17019e6	−	4.06642e7i	−0.0227541	−	0.129045i
$269$	7.71837e7			0.241764			0.120882	−	0.992667i	$-0.461428\pi$
$269$	7.71837e7			0.241764			0.120882	+	0.992667i	$0.461428\pi$
$270$		0			0
$271$	4.05282e8			1.23699			0.618493	−	0.785790i	$-0.287743\pi$
$271$	4.05282e8			1.23699			0.618493	+	0.785790i	$0.287743\pi$
$272$	7.63122e7	+	4.32788e8i	0.229934	+	1.30402i
$273$		0			0
$274$	2.13587e8	−	7.77393e7i	0.627260	−	0.228304i
$275$	−7.15632e7	−	6.00486e7i	−0.207503	−	0.174116i
$276$		0			0
$277$	2.46614e8	+	8.97600e7i	0.697169	+	0.253749i	0.666202	−	0.745772i	$-0.267919\pi$
$277$	2.46614e8	+	8.97600e7i	0.697169	+	0.253749i	0.0309672	+	0.999520i	$0.490141\pi$
$278$	1.32612e8	+	2.29691e8i	0.370191	+	0.641189i
$279$		0			0
$280$	4.42188e6	−	7.65892e6i	0.0120380	−	0.0208504i
$281$	−5.19869e8	+	4.36222e8i	−1.39773	+	1.17283i	−0.435627	+	0.900127i	$0.643473\pi$
$281$	−5.19869e8	+	4.36222e8i	−1.39773	+	1.17283i	−0.962098	+	0.272704i	$0.912082\pi$
$282$		0			0
$283$	−5.38308e7	+	3.05290e8i	−0.141182	+	0.800681i	0.829172	+	0.558993i	$0.188812\pi$
$283$	−5.38308e7	+	3.05290e8i	−0.141182	+	0.800681i	−0.970354	+	0.241688i	$0.922299\pi$
$284$	5.40310e6	−	3.06425e7i	0.0139968	−	0.0793799i
$285$		0			0
$286$	2.02189e7	−	1.69657e7i	0.0511066	−	0.0428836i
$287$	3.94086e8	−	6.82577e8i	0.984022	−	1.70438i
$288$		0			0
$289$	−3.67105e7	−	6.35845e7i	−0.0894639	−	0.154956i
$290$	1.18404e7	+	4.30957e6i	0.0285085	+	0.0103763i
$291$		0			0
$292$	1.40090e8	+	1.17549e8i	0.329281	+	0.276299i
$293$	5.20570e8	−	1.89472e8i	1.20904	−	0.440056i	0.342673	−	0.939455i	$-0.388668\pi$
$293$	5.20570e8	−	1.89472e8i	1.20904	−	0.440056i	0.866372	+	0.499399i	$0.166446\pi$
$294$		0			0
$295$	−2.82873e6	−	1.60425e7i	−0.00641525	−	0.0363827i
$296$	−2.63209e8			−0.589902
$297$		0			0
$298$	4.79779e8			1.05023
$299$	−5.52054e6	−	3.13085e7i	−0.0119435	−	0.0677351i
$300$		0			0
$301$	−6.69526e8	+	2.43688e8i	−1.41509	+	0.515051i
$302$	−4.71094e6	−	3.95295e6i	−0.00984201	−	0.00825843i
$303$		0			0
$304$	6.28740e8	+	2.28843e8i	1.28355	+	0.467175i
$305$	−7.05062e6	−	1.22120e7i	−0.0142291	−	0.0246456i
$306$		0			0
$307$	3.39921e8	−	5.88760e8i	0.670491	−	1.16132i	−0.307274	−	0.951621i	$-0.599417\pi$
$307$	3.39921e8	−	5.88760e8i	0.670491	−	1.16132i	0.977765	−	0.209704i	$-0.0672500\pi$
$308$	5.48612e7	−	4.60340e7i	0.106989	−	0.0897742i
$309$		0			0
$310$	−2.62663e6	+	1.48963e7i	−0.00500764	+	0.0283997i
$311$	4.98335e7	−	2.82620e8i	0.0939420	−	0.532772i	−0.901124	−	0.433561i	$-0.857257\pi$
$311$	4.98335e7	−	2.82620e8i	0.0939420	−	0.532772i	0.995066	−	0.0992110i	$-0.0316319\pi$
$312$		0			0
$313$	−3.27990e8	+	2.75216e8i	−0.604581	+	0.507304i	−0.892915	−	0.450226i	$-0.851343\pi$
$313$	−3.27990e8	+	2.75216e8i	−0.604581	+	0.507304i	0.288333	+	0.957530i	$0.406899\pi$
$314$	4.43175e8	−	7.67601e8i	0.807833	−	1.39921i
$315$		0			0
$316$	7.56929e7	+	1.31104e8i	0.134943	+	0.233728i
$317$	4.08692e8	+	1.48752e8i	0.720591	+	0.262274i	0.676176	−	0.736740i	$-0.263636\pi$
$317$	4.08692e8	+	1.48752e8i	0.720591	+	0.262274i	0.0444141	+	0.999013i	$0.485858\pi$
$318$		0			0
$319$	−1.62034e8	−	1.35963e8i	−0.279472	−	0.234505i
$320$	−5.36108e6	+	1.95127e6i	−0.00914592	+	0.00332884i
$321$		0			0
$322$	−6.10100e7	−	3.46005e8i	−0.101837	−	0.577546i
$323$	−7.36531e8			−1.21614
$324$		0			0
$325$	−1.32292e8			−0.213768
$326$	4.13026e7	+	2.34238e8i	0.0660261	+	0.374452i
$327$		0			0
$328$	−5.79541e8	+	2.10936e8i	−0.906830	+	0.330059i
$329$	−3.53906e7	−	2.96963e7i	−0.0547901	−	0.0459744i
$330$		0			0
$331$	−1.55840e8	−	5.67211e7i	−0.236201	−	0.0859700i	0.221208	−	0.975227i	$-0.429000\pi$
$331$	−1.55840e8	−	5.67211e7i	−0.236201	−	0.0859700i	−0.457409	+	0.889257i	$0.651222\pi$
$332$	1.07259e8	+	1.85779e8i	0.160861	+	0.278620i
$333$		0			0
$334$	−4.04032e8	+	6.99805e8i	−0.593340	+	1.02769i
$335$	−4.15456e6	+	3.48609e6i	−0.00603766	+	0.00506619i
$336$		0			0
$337$	1.94766e8	−	1.10457e9i	0.277210	−	1.57213i	−0.454644	−	0.890673i	$-0.650234\pi$
$337$	1.94766e8	−	1.10457e9i	0.277210	−	1.57213i	0.731854	−	0.681462i	$-0.238655\pi$
$338$	−1.35433e8	+	7.68080e8i	−0.190773	+	1.08193i
$339$		0			0
$340$	−3.83954e6	+	3.22176e6i	−0.00529790	+	0.00444546i
$341$	1.26960e8	−	2.19902e8i	0.173392	−	0.300323i
$342$		0			0
$343$	−3.00945e8	−	5.21252e8i	−0.402678	−	0.697459i
$344$	5.23896e8	+	1.90682e8i	0.693890	+	0.252555i
$345$		0			0
$346$	−8.34271e8	−	7.00037e8i	−1.08278	−	0.908562i
$347$	5.89105e8	−	2.14417e8i	0.756902	−	0.275490i	0.0653951	−	0.997859i	$-0.479169\pi$
$347$	5.89105e8	−	2.14417e8i	0.756902	−	0.275490i	0.691507	+	0.722370i	$0.256947\pi$
$348$		0			0
$349$	2.00694e8	+	1.13819e9i	0.252723	+	1.43326i	0.801850	+	0.597525i	$0.203849\pi$
$349$	2.00694e8	+	1.13819e9i	0.252723	+	1.43326i	−0.549127	+	0.835739i	$0.685040\pi$
$350$	−1.46202e9			−1.82270
$351$		0			0
$352$	−1.39111e8			−0.170005
$353$	−4.37131e7	−	2.47909e8i	−0.0528932	−	0.299972i	0.946873	−	0.321609i	$-0.104223\pi$
$353$	−4.37131e7	−	2.47909e8i	−0.0528932	−	0.299972i	−0.999766	+	0.0216364i	$0.993112\pi$
$354$		0			0
$355$	−3.84034e6	+	1.39777e6i	−0.00455586	+	0.00165820i
$356$	−1.46979e8	−	1.23330e8i	−0.172655	−	0.144875i
$357$		0			0
$358$	−1.09617e9	−	3.98974e8i	−1.26267	−	0.459573i
$359$	6.01731e7	+	1.04223e8i	0.0686391	+	0.118886i	0.898302	−	0.439378i	$-0.144801\pi$
$359$	6.01731e7	+	1.04223e8i	0.0686391	+	0.118886i	−0.829663	+	0.558264i	$0.811468\pi$
$360$		0			0
$361$	−1.13753e8	+	1.97026e8i	−0.127259	+	0.220419i
$362$	5.17375e6	−	4.34129e6i	0.00573225	−	0.00480993i
$363$		0			0
$364$	1.76109e7	−	9.98762e7i	0.0191393	−	0.108544i
$365$	4.17094e6	−	2.36546e7i	0.00448961	−	0.0254618i
$366$		0			0
$367$	8.72383e8	−	7.32016e8i	0.921247	−	0.773018i	−0.0529784	−	0.998596i	$-0.516871\pi$
$367$	8.72383e8	−	7.32016e8i	0.921247	−	0.773018i	0.974225	+	0.225578i	$0.0724270\pi$
$368$	−1.87490e8	+	3.24743e8i	−0.196115	+	0.339682i
$369$		0			0
$370$	−8.33847e6	−	1.44427e7i	−0.00855816	−	0.0148232i
$371$	−1.44376e9	−	5.25486e8i	−1.46787	−	0.534260i
$372$		0			0
$373$	1.37048e9	+	1.14997e9i	1.36738	+	1.14737i	0.973624	+	0.228159i	$0.0732705\pi$
$373$	1.37048e9	+	1.14997e9i	1.36738	+	1.14737i	0.393760	+	0.919213i	$0.371174\pi$
$374$	3.22028e8	−	1.17209e8i	0.318305	−	0.115854i
$375$		0			0
$376$	6.27743e6	+	3.56011e7i	0.00609010	+	0.0345387i
$377$	−2.99538e8			−0.287910
$378$		0			0
$379$	5.19397e8			0.490074			0.245037	−	0.969514i	$-0.421200\pi$
$379$	5.19397e8			0.490074			0.245037	+	0.969514i	$0.421200\pi$
$380$	1.32513e6	+	7.51516e6i	0.00123884	+	0.00702580i
$381$		0			0
$382$	−1.06418e9	+	3.87330e8i	−0.976774	+	0.355517i
$383$	−5.09232e7	−	4.27297e7i	−0.0463149	−	0.0388628i	0.619336	−	0.785126i	$-0.287402\pi$
$383$	−5.09232e7	−	4.27297e7i	−0.0463149	−	0.0388628i	−0.665651	+	0.746263i	$0.731846\pi$
$384$		0			0
$385$	−8.83910e6	−	3.21717e6i	−0.00789397	−	0.00287317i
$386$	8.40532e8	+	1.45584e9i	0.743873	+	1.28843i
$387$		0			0
$388$	3.38483e8	−	5.86270e8i	0.294189	−	0.509550i
$389$	−7.52754e8	+	6.31636e8i	−0.648380	+	0.544055i	−0.906579	−	0.422036i	$-0.861315\pi$
$389$	−7.52754e8	+	6.31636e8i	−0.648380	+	0.544055i	0.258199	+	0.966092i	$0.416871\pi$
$390$		0			0
$391$	7.16779e7	−	4.06505e8i	0.0606410	−	0.343912i
$392$	−2.42619e8	+	1.37596e9i	−0.203434	+	1.15373i
$393$		0			0
$394$	−1.66270e9	+	1.39517e9i	−1.36955	+	1.14919i
$395$	9.94182e6	−	1.72197e7i	0.00811663	−	0.0140584i
$396$		0			0
$397$	−6.10031e8	−	1.05660e9i	−0.489311	−	0.847512i	0.510613	−	0.859811i	$-0.329418\pi$
$397$	−6.10031e8	−	1.05660e9i	−0.489311	−	0.847512i	−0.999924	+	0.0122987i	$0.996085\pi$
$398$	4.80469e8	+	1.74876e8i	0.382010	+	0.139040i
$399$		0			0
$400$	1.19533e9	+	1.00300e9i	0.933849	+	0.783592i
$401$	−4.95883e8	+	1.80487e8i	−0.384038	+	0.139778i	−0.526822	−	0.849975i	$-0.676617\pi$
$401$	−4.95883e8	+	1.80487e8i	−0.384038	+	0.139778i	0.142784	+	0.989754i	$0.454394\pi$
$402$		0			0
$403$	−6.24407e7	−	3.54119e8i	−0.0475226	−	0.269514i
$404$	−4.80429e7			−0.0362489
$405$		0			0
$406$	−3.31032e9			−2.45488
$407$	4.86135e7	+	2.75701e8i	0.0357418	+	0.202702i
$408$		0			0
$409$	1.27025e9	−	4.62333e8i	0.918031	−	0.334136i	0.160576	−	0.987023i	$-0.448665\pi$
$409$	1.27025e9	−	4.62333e8i	0.918031	−	0.334136i	0.757455	+	0.652888i	$0.226443\pi$
$410$	−2.99342e7	−	2.51178e7i	−0.0214499	−	0.0179986i
$411$		0			0
$412$	1.72393e8	+	6.27459e7i	0.121445	+	0.0442023i
$413$	2.13983e9	+	3.70629e9i	1.49470	+	2.58890i
$414$		0			0
$415$	1.40879e7	−	2.44010e7i	0.00967560	−	0.0167586i
$416$	−1.50908e8	+	1.26627e8i	−0.102775	+	0.0862383i
$417$		0			0
$418$	9.06024e7	−	5.13832e8i	0.0606768	−	0.344115i
$419$	1.78253e8	−	1.01093e9i	0.118383	−	0.671383i	−0.866637	−	0.498940i	$-0.833723\pi$
$419$	1.78253e8	−	1.01093e9i	0.118383	−	0.671383i	0.985020	−	0.172443i	$-0.0551660\pi$
$420$		0			0
$421$	−5.03941e8	+	4.22857e8i	−0.329149	+	0.276189i	−0.792353	−	0.610063i	$-0.791144\pi$
$421$	−5.03941e8	+	4.22857e8i	−0.329149	+	0.276189i	0.463204	+	0.886252i	$0.346700\pi$
$422$	2.97071e8	−	5.14542e8i	0.192427	−	0.333294i
$423$		0			0
$424$	6.01114e8	+	1.04116e9i	0.382980	+	0.663341i
$425$	−1.61408e9	−	5.87476e8i	−1.01991	−	0.371218i
$426$		0			0
$427$	2.83792e9	+	2.38130e9i	1.76401	+	1.48018i
$428$	3.53497e8	−	1.28662e8i	0.217937	−	0.0793228i
$429$		0			0
$430$	6.13401e6	+	3.47877e7i	0.00372053	+	0.0211002i
$431$	1.08232e9			0.651154			0.325577	−	0.945516i	$-0.394441\pi$
$431$	1.08232e9			0.651154			0.325577	+	0.945516i	$0.394441\pi$
$432$		0			0
$433$	6.42005e8			0.380041			0.190021	−	0.981780i	$-0.439144\pi$
$433$	6.42005e8			0.380041			0.190021	+	0.981780i	$0.439144\pi$
$434$	−6.90060e8	−	3.91353e9i	−0.405203	−	2.29802i
$435$		0			0
$436$	3.28370e8	−	1.19517e8i	0.189741	−	0.0690599i
$437$	−4.81426e8	−	4.03965e8i	−0.275959	−	0.231557i
$438$		0			0
$439$	−1.30664e9	−	4.75580e8i	−0.737109	−	0.268286i	−0.0539382	−	0.998544i	$-0.517177\pi$
$439$	−1.30664e9	−	4.75580e8i	−0.737109	−	0.268286i	−0.683171	+	0.730258i	$0.739400\pi$
$440$	3.68018e6	+	6.37427e6i	0.00205961	+	0.00356735i
$441$		0			0
$442$	2.42648e8	−	4.20279e8i	0.133659	−	0.231505i
$443$	2.46316e9	−	2.06684e9i	1.34611	−	1.12952i	0.366094	−	0.930578i	$-0.380695\pi$
$443$	2.46316e9	−	2.06684e9i	1.34611	−	1.12952i	0.980012	−	0.198939i	$-0.0637496\pi$
$444$		0			0
$445$	−4.37604e6	+	2.48178e7i	−0.00235408	+	0.0133507i
$446$	3.83994e8	−	2.17774e9i	0.204952	−	1.16234i
$447$		0			0
$448$	1.14818e9	−	9.63435e8i	0.603304	−	0.506232i
$449$	4.51576e8	−	7.82152e8i	0.235433	−	0.407783i	−0.723965	−	0.689837i	$-0.757682\pi$
$449$	4.51576e8	−	7.82152e8i	0.235433	−	0.407783i	0.959399	+	0.282054i	$0.0910157\pi$
$450$		0			0
$451$	3.27985e8	+	5.68087e8i	0.168359	+	0.291606i
$452$	−8.05481e8	−	2.93171e8i	−0.410271	−	0.149326i
$453$		0			0
$454$	−8.14916e7	−	6.83796e7i	−0.0408712	−	0.0342950i
$455$	−1.25172e7	+	4.55589e6i	−0.00622970	+	0.00226743i
$456$		0			0
$457$	−2.39224e8	−	1.35671e9i	−0.117246	−	0.664935i	−0.985614	−	0.169014i	$-0.945942\pi$
$457$	−2.39224e8	−	1.35671e9i	−0.117246	−	0.664935i	0.868368	−	0.495921i	$-0.165169\pi$
$458$	−4.14278e9			−2.01494
$459$		0			0
$460$	−4.27672e6			−0.00204861
$461$	2.98676e8	+	1.69387e9i	0.141986	+	0.805245i	0.969738	+	0.244150i	$0.0785088\pi$
$461$	2.98676e8	+	1.69387e9i	0.141986	+	0.805245i	−0.827751	+	0.561095i	$0.810380\pi$
$462$		0			0
$463$	7.08753e8	−	2.57965e8i	0.331865	−	0.120789i	−0.170713	−	0.985321i	$-0.554607\pi$
$463$	7.08753e8	−	2.57965e8i	0.331865	−	0.120789i	0.502578	+	0.864532i	$0.332385\pi$
$464$	2.70647e9	+	2.27100e9i	1.25774	+	1.05537i
$465$		0			0
$466$	4.31257e9	+	1.56965e9i	1.97417	+	0.718541i
$467$	7.19037e8	+	1.24541e9i	0.326695	+	0.565852i	0.981854	−	0.189639i	$-0.0607318\pi$
$467$	7.19037e8	+	1.24541e9i	0.326695	+	0.565852i	−0.655159	+	0.755491i	$0.727398\pi$
$468$		0			0
$469$	7.12409e8	−	1.23393e9i	0.318878	−	0.552313i
$470$	−1.75461e6	+	1.47229e6i	−0.000779540	+	0.000654112i
$471$		0			0
$472$	5.81509e8	−	3.29790e9i	0.254542	−	1.44358i
$473$	1.02971e8	−	5.83977e8i	0.0447405	−	0.253736i
$474$		0			0
$475$	−2.00334e9	+	1.68100e9i	−0.857681	+	0.719680i
$476$	6.58391e8	−	1.14037e9i	0.279808	−	0.484641i
$477$		0			0
$478$	−1.65572e9	−	2.86779e9i	−0.693408	−	1.20102i
$479$	−7.34515e8	−	2.67342e8i	−0.305370	−	0.111146i	0.184790	−	0.982778i	$-0.440839\pi$
$479$	−7.34515e8	−	2.67342e8i	−0.305370	−	0.111146i	−0.490160	+	0.871632i	$0.663062\pi$
$480$		0			0
$481$	3.03696e8	+	2.54832e8i	0.124432	+	0.104411i
$482$	1.23400e9	−	4.49138e8i	0.501937	−	0.182690i
$483$		0			0
$484$	−1.30601e8	−	7.40676e8i	−0.0523586	−	0.296941i
$485$	−8.89156e7			−0.0353901
$486$		0			0
$487$	−9.45953e8			−0.371123			−0.185562	−	0.982633i	$-0.559410\pi$
$487$	−9.45953e8			−0.371123			−0.185562	+	0.982633i	$0.559410\pi$
$488$	−5.03377e8	−	2.85479e9i	−0.196076	−	1.11200i
$489$		0			0
$490$	−8.31872e7	+	3.02777e7i	−0.0319426	+	0.0116262i
$491$	−1.96294e9	−	1.64710e9i	−0.748379	−	0.627964i	0.186695	−	0.982418i	$-0.440222\pi$
$491$	−1.96294e9	−	1.64710e9i	−0.748379	−	0.627964i	−0.935074	+	0.354454i	$0.884667\pi$
$492$		0			0
$493$	−3.65461e9	−	1.33017e9i	−1.37365	−	0.499968i
$494$	−3.69435e8	−	6.39881e8i	−0.137878	−	0.238811i
$495$		0			0
$496$	−2.12063e9	+	3.67304e9i	−0.780332	+	1.35158i
$497$	8.22482e8	−	6.90144e8i	0.300524	−	0.252169i
$498$		0			0
$499$	2.82535e8	−	1.60234e9i	0.101794	−	0.577300i	−0.890659	−	0.454672i	$-0.849757\pi$
$499$	2.82535e8	−	1.60234e9i	0.101794	−	0.577300i	0.992453	−	0.122629i	$-0.0391324\pi$
$500$	−6.18184e6	+	3.50590e7i	−0.00221168	+	0.0125431i
$501$		0			0
$502$	2.70987e9	−	2.27385e9i	0.956061	−	0.802231i
$503$	2.16263e8	−	3.74579e8i	0.0757695	−	0.131237i	−0.825651	−	0.564181i	$-0.809192\pi$
$503$	2.16263e8	−	3.74579e8i	0.0757695	−	0.131237i	0.901421	+	0.432944i	$0.142525\pi$
$504$		0			0
$505$	3.15508e6	+	5.46475e6i	0.00109016	+	0.00188821i
$506$	2.74776e8	+	1.00010e8i	0.0942871	+	0.0343177i
$507$		0			0
$508$	1.12870e9	+	9.47088e8i	0.381992	+	0.320529i
$509$	−7.08016e8	+	2.57697e8i	−0.237975	+	0.0866157i	−0.458254	−	0.888821i	$-0.651525\pi$
$509$	−7.08016e8	+	2.57697e8i	−0.237975	+	0.0866157i	0.220280	+	0.975437i	$0.429303\pi$
$510$		0			0
$511$	1.09578e9	+	6.21446e9i	0.363286	+	2.06030i
$512$	−5.52800e8			−0.182022
$513$		0			0
$514$	4.02978e9			1.30891
$515$	−4.18422e6	−	2.37299e7i	−0.00134986	−	0.00765545i
$516$		0			0
$517$	3.61312e7	−	1.31507e7i	0.0114992	−	0.00418535i
$518$	3.35629e9	+	2.81626e9i	1.06097	+	0.890263i
$519$		0			0
$520$	9.79455e6	+	3.56493e6i	0.00305473	+	0.00111183i
$521$	3.91735e8	+	6.78505e8i	0.121356	+	0.210194i	0.920303	−	0.391207i	$-0.127942\pi$
$521$	3.91735e8	+	6.78505e8i	0.121356	+	0.210194i	−0.798947	+	0.601402i	$0.794609\pi$
$522$		0			0
$523$	1.77238e9	−	3.06985e9i	0.541752	−	0.938341i	−0.457052	−	0.889440i	$-0.651095\pi$
$523$	1.77238e9	−	3.06985e9i	0.541752	−	0.938341i	0.998804	−	0.0489013i	$-0.0155720\pi$
$524$	−1.35237e9	+	1.13477e9i	−0.410617	+	0.344548i
$525$		0			0
$526$	−5.31017e8	+	3.01155e9i	−0.159096	+	0.902276i
$527$	8.10721e8	−	4.59783e9i	0.241287	−	1.36841i
$528$		0			0
$529$	−2.33844e9	+	1.96218e9i	−0.686802	+	0.576295i
$530$	−3.80866e7	+	6.59679e7i	−0.0111124	+	0.0192472i
$531$		0			0
$532$	−1.00241e9	−	1.73622e9i	−0.288639	−	0.499937i
$533$	8.72909e8	+	3.17713e8i	0.249703	+	0.0908845i
$534$		0			0
$535$	−3.78498e7	−	3.17598e7i	−0.0106863	−	0.00896684i
$536$	−1.04767e9	+	3.81319e8i	−0.293864	+	0.106958i
$537$		0			0
$538$	1.74573e8	+	9.90052e8i	0.0483325	+	0.274107i
$539$	1.48607e9			0.408771
$540$		0			0
$541$	3.13979e8			0.0852532			0.0426266	−	0.999091i	$-0.486427\pi$
$541$	3.13979e8			0.0852532			0.0426266	+	0.999091i	$0.486427\pi$
$542$	9.16661e8	+	5.19864e9i	0.247293	+	1.40247i
$543$		0			0
$544$	−2.40352e9	+	8.74812e8i	−0.640107	+	0.232980i
$545$	−3.51594e7	−	2.95023e7i	−0.00930367	−	0.00780670i
$546$		0			0
$547$	−2.93207e9	−	1.06718e9i	−0.765981	−	0.278794i	−0.0706667	−	0.997500i	$-0.522513\pi$
$547$	−2.93207e9	−	1.06718e9i	−0.765981	−	0.278794i	−0.695314	+	0.718706i	$0.744735\pi$
$548$	3.63436e8	+	6.29489e8i	0.0943400	+	0.163402i
$549$		0			0
$550$	6.08397e8	−	1.05377e9i	0.155926	−	0.270071i
$551$	−4.53597e9	+	3.80613e9i	−1.15515	+	0.969288i
$552$		0			0
$553$	−9.07098e8	+	5.14441e9i	−0.228095	+	1.29359i
$554$	−5.93585e8	+	3.36639e9i	−0.148320	+	0.841162i
$555$		0			0
$556$	−6.49733e8	+	5.45191e8i	−0.160315	+	0.134520i
$557$	−1.12588e9	+	1.95008e9i	−0.276057	+	0.478144i	−0.970401	−	0.241499i	$-0.922361\pi$
$557$	−1.12588e9	+	1.95008e9i	−0.276057	+	0.478144i	0.694345	+	0.719643i	$0.255694\pi$
$558$		0			0
$559$	−4.19869e8	−	7.27234e8i	−0.101665	−	0.176089i
$560$	1.47640e8	+	5.37367e7i	0.0355261	+	0.0129304i
$561$		0			0
$562$	−6.77135e9	−	5.68184e9i	−1.60916	−	1.35024i
$563$	2.27725e9	−	8.28852e8i	0.537814	−	0.195748i	−0.0588103	−	0.998269i	$-0.518731\pi$
$563$	2.27725e9	−	8.28852e8i	0.537814	−	0.195748i	0.596624	+	0.802521i	$0.296508\pi$
$564$		0			0
$565$	1.95502e7	+	1.10875e8i	0.00456017	+	0.0258620i
$566$	−4.03777e9			−0.936018
$567$		0			0
$568$	−8.40136e8			−0.192367
$569$	1.25702e9	+	7.12891e9i	0.286055	+	1.62230i	0.701494	+	0.712676i	$0.252517\pi$
$569$	1.25702e9	+	7.12891e9i	0.286055	+	1.62230i	−0.415439	+	0.909621i	$0.636372\pi$
$570$		0			0
$571$	−1.70919e8	+	6.22094e7i	−0.0384206	+	0.0139839i	−0.361159	−	0.932504i	$-0.617619\pi$
$571$	−1.70919e8	+	6.22094e7i	−0.0384206	+	0.0139839i	0.322738	+	0.946488i	$0.395397\pi$
$572$	6.46588e7	+	5.42551e7i	0.0144458	+	0.0121215i
$573$		0			0
$574$	9.64691e9	+	3.51119e9i	2.12910	+	0.774930i
$575$	−7.32814e8	−	1.26927e9i	−0.160752	−	0.278430i
$576$		0			0
$577$	−4.95492e8	+	8.58216e8i	−0.107379	+	0.185987i	−0.914708	−	0.404116i	$-0.867579\pi$
$577$	−4.95492e8	+	8.58216e8i	−0.107379	+	0.185987i	0.807328	+	0.590102i	$0.200913\pi$
$578$	7.32581e8	−	6.14708e8i	0.157800	−	0.132410i
$579$		0			0
$580$	−6.99715e6	+	3.96828e7i	−0.00148910	+	0.00844509i
$581$	−1.28539e9	+	7.28981e9i	−0.271906	+	1.54205i
$582$		0			0
$583$	9.79549e8	−	8.21939e8i	0.204732	−	0.171791i
$584$	2.46887e9	−	4.27622e9i	0.512925	−	0.888413i
$585$		0			0
$586$	3.60782e9	+	6.24892e9i	0.740633	+	1.28281i
$587$	−8.44657e8	−	3.07430e8i	−0.172364	−	0.0627354i	0.254397	−	0.967100i	$-0.418123\pi$
$587$	−8.44657e8	−	3.07430e8i	−0.172364	−	0.0627354i	−0.426761	+	0.904365i	$0.640345\pi$
$588$		0			0
$589$	−5.44523e9	−	4.56909e9i	−1.09803	−	0.921353i
$590$	1.99383e8	−	7.25694e7i	0.0399674	−	0.0145469i
$591$		0			0
$592$	−8.11996e8	−	4.60506e9i	−0.160853	−	0.912240i
$593$	−4.20907e9			−0.828885			−0.414443	−	0.910075i	$-0.636023\pi$
$593$	−4.20907e9			−0.828885			−0.414443	+	0.910075i	$0.636023\pi$
$594$		0			0
$595$	−1.72952e8			−0.0336601
$596$	2.66428e8	+	1.51099e9i	0.0515488	+	0.292348i
$597$		0			0
$598$	3.89115e8	−	1.41626e8i	0.0744088	−	0.0270826i
$599$	−6.20645e9	−	5.20783e9i	−1.17991	−	0.990064i	−0.999980	−	0.00638485i	$-0.997968\pi$
$599$	−6.20645e9	−	5.20783e9i	−1.17991	−	0.990064i	−0.179932	−	0.983679i	$-0.557588\pi$
$600$		0			0
$601$	−6.70007e9	−	2.43863e9i	−1.25898	−	0.458231i	−0.375554	−	0.926801i	$-0.622547\pi$
$601$	−6.70007e9	−	2.43863e9i	−1.25898	−	0.458231i	−0.883427	+	0.468569i	$0.844770\pi$
$602$	−4.64016e9	−	8.03699e9i	−0.866852	−	1.50143i
$603$		0			0
$604$	9.83315e6	−	1.70315e7i	0.00181578	−	0.00314503i
$605$	−7.56731e7	+	6.34973e7i	−0.0138931	+	0.0116577i
$606$		0			0
$607$	6.83671e8	−	3.87729e9i	0.124076	−	0.703668i	−0.857777	−	0.514022i	$-0.828155\pi$
$607$	6.83671e8	−	3.87729e9i	0.124076	−	0.703668i	0.981853	−	0.189646i	$-0.0607340\pi$
$608$	−6.76230e8	+	3.83509e9i	−0.122020	+	0.692011i
$609$		0			0
$610$	1.40700e8	−	1.18061e8i	0.0250980	−	0.0210597i
$611$	2.72249e7	−	4.71549e7i	0.00482861	−	0.00836339i
$612$		0			0
$613$	2.59844e9	+	4.50064e9i	0.455619	+	0.789155i	0.998724	−	0.0505100i	$-0.0160847\pi$
$613$	2.59844e9	+	4.50064e9i	0.455619	+	0.789155i	−0.543105	+	0.839665i	$0.682751\pi$
$614$	8.32098e9	+	3.02859e9i	1.45073	+	0.528021i
$615$		0			0
$616$	−1.48130e9	−	1.24296e9i	−0.255334	−	0.214251i
$617$	−6.65865e8	+	2.42355e8i	−0.114127	+	0.0415388i	−0.398452	−	0.917189i	$-0.630453\pi$
$617$	−6.65865e8	+	2.42355e8i	−0.114127	+	0.0415388i	0.284326	+	0.958728i	$0.408230\pi$
$618$		0			0
$619$	−7.83048e8	−	4.44089e9i	−0.132700	−	0.752579i	−0.976434	−	0.215817i	$-0.930758\pi$
$619$	−7.83048e8	−	4.44089e9i	−0.132700	−	0.752579i	0.843734	−	0.536762i	$-0.180353\pi$
$620$	−4.83724e7			−0.00815129
$621$		0			0
$622$	3.73794e9			0.622825
$623$	−1.14966e9	−	6.52006e9i	−0.190486	−	1.08030i
$624$		0			0
$625$	−5.72884e9	+	2.08513e9i	−0.938613	+	0.341627i
$626$	−4.27210e9	−	3.58472e9i	−0.696035	−	0.584043i
$627$		0			0
$628$	2.66354e9	+	9.69450e8i	0.429142	+	0.156195i
$629$	2.57371e9	+	4.45779e9i	0.412365	+	0.714238i
$630$		0			0
$631$	−2.12321e9	+	3.67750e9i	−0.336426	+	0.582707i	−0.983758	−	0.179501i	$-0.942552\pi$
$631$	−2.12321e9	+	3.67750e9i	−0.336426	+	0.582707i	0.647332	+	0.762208i	$0.275885\pi$
$632$	3.13123e9	−	2.62742e9i	0.493408	−	0.414018i
$633$		0			0
$634$	−9.83698e8	+	5.57883e9i	−0.153303	+	0.869422i
$635$	3.36050e7	−	1.90583e8i	0.00520830	−	0.0295377i
$636$		0			0
$637$	1.61211e9	−	1.35272e9i	0.247119	−	0.207357i
$638$	1.37754e9	−	2.38596e9i	0.210006	−	0.363740i
$639$		0			0
$640$	−7.78733e7	−	1.34880e8i	−0.0117424	−	0.0203385i
$641$	4.56402e9	+	1.66117e9i	0.684455	+	0.249121i	0.660759	−	0.750598i	$-0.270235\pi$
$641$	4.56402e9	+	1.66117e9i	0.684455	+	0.249121i	0.0236956	+	0.999719i	$0.492457\pi$
$642$		0			0
$643$	−5.39412e9	−	4.52620e9i	−0.800170	−	0.671422i	0.148070	−	0.988977i	$-0.452694\pi$
$643$	−5.39412e9	−	4.52620e9i	−0.800170	−	0.671422i	−0.948240	+	0.317555i	$0.897138\pi$
$644$	1.05581e9	−	3.84283e8i	0.155770	−	0.0566957i
$645$		0			0
$646$	−1.66587e9	−	9.44764e9i	−0.243124	−	1.37883i
$647$	1.11556e10			1.61930			0.809652	−	0.586911i	$-0.199656\pi$
$647$	1.11556e10			1.61930			0.809652	+	0.586911i	$0.199656\pi$
$648$		0			0
$649$	−3.56182e9			−0.511464
$650$	−2.99217e8	−	1.69694e9i	−0.0427356	−	0.242366i
$651$		0			0
$652$	−7.14762e8	+	2.60152e8i	−0.100994	+	0.0367587i
$653$	4.70902e8	+	3.95134e8i	0.0661812	+	0.0555326i	0.675278	−	0.737563i	$-0.264024\pi$
$653$	4.70902e8	+	3.95134e8i	0.0661812	+	0.0555326i	−0.609097	+	0.793096i	$0.708468\pi$
$654$		0			0
$655$	2.17891e8	+	7.93057e7i	0.0302966	+	0.0110271i
$656$	−5.47837e9	−	9.48881e9i	−0.757683	−	1.31235i
$657$		0			0
$658$	3.00875e8	−	5.21130e8i	0.0411713	−	0.0713108i
$659$	−2.91625e9	+	2.44702e9i	−0.396940	+	0.333072i	−0.819310	−	0.573351i	$-0.805643\pi$
$659$	−2.91625e9	+	2.44702e9i	−0.396940	+	0.333072i	0.422369	+	0.906424i	$0.361199\pi$
$660$		0			0
$661$	−1.46070e9	+	8.28405e9i	−0.196724	+	1.11568i	0.713219	+	0.700941i	$0.247236\pi$
$661$	−1.46070e9	+	8.28405e9i	−0.196724	+	1.11568i	−0.909943	+	0.414734i	$0.863875\pi$
$662$	3.75098e8	−	2.12729e9i	0.0502507	−	0.284986i
$663$		0			0
$664$	4.43707e9	−	3.72314e9i	0.588176	−	0.493539i
$665$	−1.31661e8	+	2.28043e8i	−0.0173612	+	0.0300705i
$666$		0			0
$667$	−1.65924e9	−	2.87389e9i	−0.216506	−	0.374999i
$668$	−2.42829e9	−	8.83826e8i	−0.315198	−	0.114723i
$669$		0			0
$670$	−5.41136e7	−	4.54067e7i	−0.00695096	−	0.00583255i
$671$	−2.89731e9	+	1.05453e9i	−0.370225	+	0.134751i
$672$		0			0
$673$	1.71287e9	+	9.71417e9i	0.216607	+	1.22844i	0.878097	+	0.478483i	$0.158813\pi$
$673$	1.71287e9	+	9.71417e9i	0.216607	+	1.22844i	−0.661490	+	0.749954i	$0.730076\pi$
$674$	1.46091e10			1.83787
$675$		0			0
$676$	−2.49416e9			−0.310535
$677$	4.98796e7	+	2.82881e8i	0.00617821	+	0.0350384i	0.987741	−	0.156102i	$-0.0498927\pi$
$677$	4.98796e7	+	2.82881e8i	0.00617821	+	0.0350384i	−0.981563	+	0.191140i	$0.938782\pi$
$678$		0			0
$679$	2.19509e10	−	7.98947e9i	2.69096	−	0.979431i
$680$	1.03671e8	+	8.69901e7i	0.0126437	+	0.0106093i
$681$		0			0
$682$	3.10789e9	+	1.13118e9i	0.375163	+	0.136548i
$683$	1.41357e8	+	2.44837e8i	0.0169763	+	0.0294039i	0.874389	−	0.485226i	$-0.161263\pi$
$683$	1.41357e8	+	2.44837e8i	0.0169763	+	0.0294039i	−0.857412	+	0.514630i	$0.827929\pi$
$684$		0			0
$685$	4.77352e7	−	8.26798e7i	0.00567442	−	0.00982839i
$686$	6.00554e9	−	5.03925e9i	0.710261	−	0.595980i
$687$		0			0
$688$	−1.71993e9	+	9.75423e9i	−0.201350	+	1.14191i
$689$	3.14443e8	−	1.78329e9i	0.0366247	−	0.207709i
$690$		0			0
$691$	9.68251e9	−	8.12459e9i	1.11639	−	0.936760i	0.117971	−	0.993017i	$-0.462361\pi$
$691$	9.68251e9	−	8.12459e9i	1.11639	−	0.936760i	0.998416	+	0.0562566i	$0.0179165\pi$
$692$	1.74137e9	−	3.01615e9i	0.199766	−	0.346004i
$693$		0			0
$694$	4.08280e9	+	7.07162e9i	0.463661	+	0.803084i
$695$	1.04683e8	+	3.81017e7i	0.0118285	+	0.00430524i
$696$		0			0
$697$	9.23934e9	+	7.75272e9i	1.03354	+	0.867241i
$698$	−1.41459e10	+	5.14869e9i	−1.57448	+	0.573063i
$699$		0			0
$700$	−8.11882e8	−	4.60441e9i	−0.0894643	−	0.507378i
$701$	4.40806e9			0.483320			0.241660	−	0.970361i	$-0.422308\pi$
$701$	4.40806e9			0.483320			0.241660	+	0.970361i	$0.422308\pi$
$702$		0			0
$703$	7.83701e9			0.850760
$704$	2.16615e8	+	1.22848e9i	0.0233983	+	0.132698i
$705$		0			0
$706$	3.08112e9	−	1.12143e9i	0.329527	−	0.119938i
$707$	−1.26994e9	−	1.06560e9i	−0.135149	−	0.113404i
$708$		0			0
$709$	−8.70335e9	−	3.16776e9i	−0.917117	−	0.333803i	−0.160026	−	0.987113i	$-0.551158\pi$
$709$	−8.70335e9	−	3.16776e9i	−0.917117	−	0.333803i	−0.757091	+	0.653310i	$0.773380\pi$
$710$	−2.66155e7	−	4.60995e7i	−0.00279081	−	0.00483383i
$711$		0			0
$712$	−2.59028e9	+	4.48650e9i	−0.268947	+	0.465831i
$713$	3.05169e9	−	2.56067e9i	0.315302	−	0.264570i
$714$		0			0
$715$	1.92510e6	−	1.09178e7i	0.000196962	−	0.00111703i
$716$	6.47787e8	−	3.67378e9i	0.0659533	−	0.374040i
$717$		0			0
$718$	−1.20079e9	+	1.00758e9i	−0.121069	+	0.101589i
$719$	−5.66535e9	+	9.81267e9i	−0.568428	+	0.984546i	0.428294	+	0.903639i	$0.359115\pi$
$719$	−5.66535e9	+	9.81267e9i	−0.568428	+	0.984546i	−0.996722	+	0.0809064i	$0.974219\pi$
$720$		0			0
$721$	3.16521e9	+	5.48231e9i	0.314506	+	0.544741i
$722$	−2.78458e9	−	1.01351e9i	−0.275347	−	0.100218i
$723$		0			0
$724$	1.65453e7	+	1.38831e7i	0.00162028	+	0.00135957i
$725$	−1.29763e10	+	4.72297e9i	−1.26464	+	0.460291i
$726$		0			0
$727$	3.48347e8	+	1.97558e9i	0.0336234	+	0.190688i	0.996993	−	0.0774885i	$-0.0246901\pi$
$727$	3.48347e8	+	1.97558e9i	0.0336234	+	0.190688i	−0.963370	+	0.268176i	$0.913579\pi$
$728$	−2.73834e9			−0.263043
$729$		0			0
$730$	3.12856e8			0.0297656
$731$	−1.89329e9	−	1.07374e10i	−0.179270	−	1.01669i
$732$		0			0
$733$	1.65008e9	−	6.00581e8i	0.154754	−	0.0563258i	−0.263482	−	0.964664i	$-0.584871\pi$
$733$	1.65008e9	−	6.00581e8i	0.154754	−	0.0563258i	0.418236	+	0.908339i	$0.362649\pi$
$734$	1.13629e10	+	9.53459e9i	1.06060	+	0.889950i
$735$		0			0
$736$	−2.05085e9	−	7.46448e8i	−0.189610	−	0.0690124i
$737$	5.92915e8	+	1.02696e9i	0.0545577	+	0.0944967i
$738$		0			0
$739$	−1.41722e9	+	2.45470e9i	−0.129176	+	0.223740i	−0.923358	−	0.383941i	$-0.874567\pi$
$739$	−1.41722e9	+	2.45470e9i	−0.129176	+	0.223740i	0.794181	+	0.607681i	$0.207900\pi$
$740$	4.08545e7	−	3.42810e7i	0.00370620	−	0.00310987i
$741$		0			0
$742$	3.47505e9	−	1.97080e10i	0.312282	−	1.77104i
$743$	7.93434e8	−	4.49979e9i	0.0709660	−	0.402468i	−0.928546	−	0.371218i	$-0.878940\pi$
$743$	7.93434e8	−	4.49979e9i	0.0709660	−	0.402468i	0.999512	−	0.0312497i	$-0.00994871\pi$
$744$		0			0
$745$	1.54374e8	−	1.29535e8i	0.0136782	−	0.0114773i
$746$	−1.16512e10	+	2.01804e10i	−1.02750	+	1.77969i
$747$		0			0
$748$	5.47958e8	+	9.49090e8i	0.0478731	+	0.0829186i
$749$	1.21979e10	+	4.43967e9i	1.06071	+	0.386068i
$750$		0			0
$751$	−3.66565e9	−	3.07584e9i	−0.315799	−	0.264987i	0.471085	−	0.882088i	$-0.343863\pi$
$751$	−3.66565e9	−	3.07584e9i	−0.315799	−	0.264987i	−0.786884	+	0.617101i	$0.788307\pi$
$752$	−6.03504e8	+	2.19657e8i	−0.0517508	+	0.0188358i
$753$		0			0
$754$	−6.77490e8	−	3.84224e9i	−0.0575577	−	0.326426i
$755$	−2.58306e6			−0.000218434
$756$		0			0
$757$	1.49204e9			0.125010			0.0625052	−	0.998045i	$-0.480091\pi$
$757$	1.49204e9			0.125010			0.0625052	+	0.998045i	$0.480091\pi$
$758$	1.17476e9	+	6.66242e9i	0.0979734	+	0.555635i
$759$		0			0
$760$	1.93620e8	−	7.04718e7i	0.0159993	−	0.00582328i
$761$	4.84834e9	+	4.06824e9i	0.398792	+	0.334626i	0.820027	−	0.572326i	$-0.193959\pi$
$761$	4.84834e9	+	4.06824e9i	0.398792	+	0.334626i	−0.421234	+	0.906952i	$0.638403\pi$
$762$		0			0
$763$	1.13308e10	+	4.12409e9i	0.923477	+	0.336118i
$764$	−1.81079e9	−	3.13638e9i	−0.146907	−	0.254450i
$765$		0			0
$766$	4.32926e8	−	7.49849e8i	0.0348027	−	0.0602800i
$767$	−3.86389e9	+	3.24219e9i	−0.309201	+	0.259451i
$768$		0			0
$769$	−2.81854e9	+	1.59847e10i	−0.223502	+	1.26754i	0.642026	+	0.766683i	$0.278094\pi$
$769$	−2.81854e9	+	1.59847e10i	−0.223502	+	1.26754i	−0.865528	+	0.500861i	$0.833017\pi$
$770$	2.12752e7	−	1.20658e8i	0.00167941	−	0.00952439i
$771$		0			0
$772$	−4.11820e9	+	3.45558e9i	−0.322141	+	0.270309i
$773$	7.59410e9	−	1.31534e10i	0.591355	−	1.02426i	−0.402695	−	0.915334i	$-0.631927\pi$
$773$	7.59410e9	−	1.31534e10i	0.591355	−	1.02426i	0.994050	−	0.108923i	$-0.0347401\pi$
$774$		0			0
$775$	−8.28858e9	−	1.43562e10i	−0.639623	−	1.10786i
$776$	−1.71763e10	−	6.25166e9i	−1.31951	−	0.480263i
$777$		0			0
$778$	−9.80470e9	−	8.22712e9i	−0.746459	−	0.626353i
$779$	1.72558e10	−	6.28058e9i	1.30783	−	0.476013i
$780$		0			0
$781$	1.55169e8	+	8.80008e8i	0.0116554	+	0.0661010i
$782$	5.37646e9			0.402043
$783$		0			0
$784$	−2.48220e10			−1.83963
$785$	−6.46480e7	−	3.66637e8i	−0.00476992	−	0.0270516i
$786$		0			0
$787$	−5.51581e9	+	2.00759e9i	−0.403365	+	0.146813i	−0.535732	−	0.844388i	$-0.679964\pi$
$787$	−5.51581e9	+	2.00759e9i	−0.403365	+	0.146813i	0.132367	+	0.991201i	$0.457742\pi$
$788$	−5.31719e9	−	4.46165e9i	−0.387116	−	0.324829i
$789$		0			0
$790$	2.43368e8	+	8.85786e7i	0.0175618	+	0.00639196i
$791$	−1.47890e10	−	2.56153e10i	−1.06248	−	1.84027i
$792$		0			0
$793$	−2.18312e9	+	3.78128e9i	−0.155461	+	0.269267i
$794$	1.21735e10	−	1.02148e10i	0.863069	−	0.724201i
$795$		0			0
$796$	−2.83935e8	+	1.61027e9i	−0.0199537	+	0.113163i
$797$	−1.30162e9	+	7.38183e9i	−0.0910707	+	0.516488i	0.904810	+	0.425815i	$0.140013\pi$
$797$	−1.30162e9	+	7.38183e9i	−0.0910707	+	0.516488i	−0.995881	+	0.0906724i	$0.971098\pi$
$798$		0			0
$799$	5.41569e8	−	4.54430e8i	0.0375612	−	0.0315176i
$800$	−4.54090e9	+	7.86506e9i	−0.313564	+	0.543109i
$801$		0			0
$802$	−3.43673e9	−	5.95258e9i	−0.235253	−	0.407470i
$803$	−4.93515e9	−	1.79625e9i	−0.336353	−	0.122423i
$804$		0			0
$805$	−1.13048e8	−	9.48588e7i	−0.00763798	−	0.00640903i
$806$	4.40113e9	−	1.60188e9i	0.296068	−	0.107760i
$807$		0			0
$808$	2.25256e8	+	1.27749e9i	0.0150223	+	0.0851957i
$809$	9.98418e9			0.662968			0.331484	−	0.943461i	$-0.392451\pi$
$809$	9.98418e9			0.662968			0.331484	+	0.943461i	$0.392451\pi$
$810$		0			0
$811$	6.54182e9			0.430651			0.215326	−	0.976542i	$-0.430919\pi$
$811$	6.54182e9			0.430651			0.215326	+	0.976542i	$0.430919\pi$
$812$	−1.83827e9	−	1.04254e10i	−0.120493	−	0.683352i
$813$		0			0
$814$	−3.42652e9	+	1.24715e9i	−0.222673	+	0.0810465i
$815$	7.65315e7	+	6.42176e7i	0.00495209	+	0.00415530i
$816$		0			0
$817$	−1.55989e10	−	5.67754e9i	−1.00073	−	0.364236i
$818$	8.80348e9	+	1.52481e10i	0.562364	+	0.974043i
$819$		0			0
$820$	6.24817e7	−	1.08222e8i	0.00395735	−	0.00685433i
$821$	−1.60378e10	+	1.34573e10i	−1.01145	+	0.848705i	−0.988529	−	0.151032i	$-0.951740\pi$
$821$	−1.60378e10	+	1.34573e10i	−1.01145	+	0.848705i	−0.0229187	+	0.999737i	$0.507296\pi$
$822$		0			0
$823$	−1.40791e9	+	7.98467e9i	−0.0880393	+	0.499296i	0.908620	+	0.417624i	$0.137137\pi$
$823$	−1.40791e9	+	7.98467e9i	−0.0880393	+	0.499296i	−0.996659	+	0.0816717i	$0.973974\pi$
$824$	8.60163e8	−	4.87822e9i	0.0535593	−	0.303750i
$825$		0			0
$826$	−4.27016e10	+	3.58309e10i	−2.63642	+	2.21222i
$827$	−1.11812e10	+	1.93665e10i	−0.687417	+	1.19064i	0.285253	+	0.958452i	$0.407922\pi$
$827$	−1.11812e10	+	1.93665e10i	−0.687417	+	1.19064i	−0.972671	+	0.232189i	$0.925411\pi$
$828$		0			0
$829$	−1.13780e10	−	1.97073e10i	−0.693627	−	1.20140i	−0.970641	−	0.240531i	$-0.922678\pi$
$829$	−1.13780e10	−	1.97073e10i	−0.693627	−	1.20140i	0.277015	−	0.960866i	$-0.410655\pi$
$830$	3.44860e8	+	1.25519e8i	0.0209349	+	0.00761966i
$831$		0			0
$832$	1.35323e9	+	1.13549e9i	0.0814591	+	0.0683523i
$833$	2.56761e10	−	9.34534e9i	1.53912	−	0.560193i
$834$		0			0
$835$	5.89381e7	+	3.34254e8i	0.00350343	+	0.0198689i
$836$	1.66855e9			0.0987680
$837$		0			0
$838$	1.33705e10			0.784865
$839$	3.62950e9	+	2.05839e10i	0.212168	+	1.20326i	0.885754	+	0.464155i	$0.153642\pi$
$839$	3.62950e9	+	2.05839e10i	0.212168	+	1.20326i	−0.673586	+	0.739109i	$0.735247\pi$
$840$		0			0
$841$	−1.31714e10	+	4.79399e9i	−0.763564	+	0.277915i
$842$	−6.56389e9	−	5.50775e9i	−0.378938	−	0.317967i
$843$		0			0
$844$	1.78544e9	+	6.49847e8i	0.102223	+	0.0372060i
$845$	1.63797e8	+	2.83704e8i	0.00933913	+	0.0161758i
$846$		0			0
$847$	1.29762e10	−	2.24754e10i	0.733760	−	1.27091i
$848$	−1.63615e10	+	1.37289e10i	−0.921378	+	0.773128i
$849$		0			0
$850$	3.88499e9	−	2.20329e10i	0.216982	−	1.23057i
$851$	−7.62684e8	+	4.32540e9i	−0.0424220	+	0.240587i
$852$		0			0
$853$	4.46060e9	−	3.74289e9i	0.246077	−	0.206483i	−0.511404	−	0.859341i	$-0.670874\pi$
$853$	4.46060e9	−	3.74289e9i	0.246077	−	0.206483i	0.757481	+	0.652857i	$0.226430\pi$
$854$	−2.41267e10	+	4.17886e10i	−1.32555	+	2.29591i
$855$		0			0
$856$	−5.07862e9	−	8.79643e9i	−0.276750	−	0.479345i
$857$	−2.44791e10	−	8.90966e9i	−1.32850	−	0.483535i	−0.422329	−	0.906443i	$-0.638787\pi$
$857$	−2.44791e10	−	8.90966e9i	−1.32850	−	0.483535i	−0.906173	+	0.422907i	$0.861010\pi$
$858$		0			0
$859$	1.13629e10	+	9.53458e9i	0.611663	+	0.513246i	0.895170	−	0.445724i	$-0.147054\pi$
$859$	1.13629e10	+	9.53458e9i	0.611663	+	0.513246i	−0.283508	+	0.958970i	$0.591498\pi$
$860$	−1.06152e8	+	3.86363e7i	−0.00569095	+	0.00207134i
$861$		0			0
$862$	2.44797e9	+	1.38831e10i	0.130176	+	0.738264i
$863$	2.11355e10			1.11937			0.559687	−	0.828704i	$-0.310921\pi$
$863$	2.11355e10			1.11937			0.559687	+	0.828704i	$0.310921\pi$
$864$		0			0
$865$	−4.57439e8			−0.0240313
$866$	1.45208e9	+	8.23515e9i	0.0759762	+	0.430882i
$867$		0			0
$868$	1.19418e10	−	4.34648e9i	0.619801	−	0.225589i
$869$	−3.33043e9	−	2.79457e9i	−0.172160	−	0.144459i
$870$		0			0
$871$	1.57800e9	+	5.74346e8i	0.0809178	+	0.0294517i
$872$	−4.71763e9	−	8.17117e9i	−0.240944	−	0.417327i
$873$		0			0
$874$	4.09286e9	−	7.08905e9i	0.207366	−	0.359168i
$875$	−9.41024e8	+	7.89613e8i	−0.0474868	+	0.0398461i
$876$		0			0
$877$	5.26742e9	−	2.98730e10i	0.263693	−	1.49548i	−0.509037	−	0.860745i	$-0.669998\pi$
$877$	5.26742e9	−	2.98730e10i	0.263693	−	1.49548i	0.772730	−	0.634734i	$-0.218890\pi$
$878$	3.14502e9	−	1.78363e10i	0.156817	−	0.889352i
$879$		0			0
$880$	−1.00170e8	+	8.40523e7i	−0.00495503	+	0.00415777i
$881$	3.82992e9	−	6.63362e9i	0.188701	−	0.326840i	−0.756116	−	0.654437i	$-0.772906\pi$
$881$	3.82992e9	−	6.63362e9i	0.188701	−	0.326840i	0.944817	+	0.327598i	$0.106239\pi$
$882$		0			0
$883$	8.33122e9	+	1.44301e10i	0.407236	+	0.705353i	0.994579	−	0.103985i	$-0.0331594\pi$
$883$	8.33122e9	+	1.44301e10i	0.407236	+	0.705353i	−0.587343	+	0.809338i	$0.699826\pi$
$884$	1.45835e9	+	5.30796e8i	0.0710034	+	0.0258431i
$885$		0			0
$886$	3.20829e10	+	2.69207e10i	1.54973	+	1.30038i
$887$	8.74648e9	−	3.18346e9i	0.420824	−	0.153168i	−0.122924	−	0.992416i	$-0.539227\pi$
$887$	8.74648e9	−	3.18346e9i	0.420824	−	0.153168i	0.543748	+	0.839249i	$0.317005\pi$
$888$		0			0
$889$	8.82861e9	+	5.00695e10i	0.421440	+	2.39011i
$890$	−3.28241e8			−0.0156073
$891$		0			0
$892$	7.07169e9			0.333615
$893$	−1.86909e8	−	1.06002e9i	−0.00878317	−	0.0498118i
$894$		0			0
$895$	−4.60425e8	+	1.67581e8i	−0.0214673	+	0.00781347i
$896$	3.13445e10	+	2.63011e10i	1.45574	+	1.22151i
$897$		0			0
$898$	1.10542e10	+	4.02340e9i	0.509402	+	0.185407i
$899$	−1.87671e10	−	3.25055e10i	−0.861465	−	1.49210i
$900$		0			0
$901$	1.17556e10	−	2.03613e10i	0.535437	−	0.927404i
$902$	−6.54514e9	+	5.49203e9i	−0.296959	+	0.249178i
$903$		0			0
$904$	−4.01899e9	+	2.27928e10i	−0.180937	+	1.02614i
$905$	492608.	−	2.79372e6i	2.20918e−5	−	0.000125289i
$906$		0			0
$907$	2.37992e10	−	1.99699e10i	1.05910	−	0.888689i	0.0650781	−	0.997880i	$-0.479270\pi$
$907$	2.37992e10	−	1.99699e10i	1.05910	−	0.888689i	0.994021	+	0.109191i	$0.0348259\pi$
$908$	1.70097e8	−	2.94617e8i	0.00754045	−	0.0130604i
$909$		0			0
$910$	−8.67506e7	−	1.50256e8i	−0.00381617	−	0.00660980i
$911$	1.55761e9	+	5.66923e8i	0.0682565	+	0.0248433i	0.375923	−	0.926651i	$-0.377326\pi$
$911$	1.55761e9	+	5.66923e8i	0.0682565	+	0.0248433i	−0.307666	+	0.951494i	$0.599548\pi$
$912$		0			0
$913$	−4.71934e9	−	3.96000e9i	−0.205227	−	0.172206i
$914$	1.68617e10	−	6.13716e9i	0.730449	−	0.265862i
$915$		0			0
$916$	−2.30054e9	−	1.30470e10i	−0.0989000	−	0.560890i
$917$	−6.09174e10			−2.60885
$918$		0			0
$919$	−1.73662e10			−0.738075			−0.369037	−	0.929415i	$-0.620313\pi$
$919$	−1.73662e10			−0.738075			−0.369037	+	0.929415i	$0.620313\pi$
$920$	2.00520e7	+	1.13721e8i	0.000848986	+	0.00481484i
$921$		0			0
$922$	−2.10522e10	+	7.66236e9i	−0.884583	+	0.321962i
$923$	9.69367e8	+	8.13396e8i	0.0405772	+	0.0340483i
$924$		0			0
$925$	1.71745e10	+	6.25100e9i	0.713490	+	0.259689i
$926$	4.91202e9	+	8.50787e9i	0.203293	+	0.352113i
$927$		0			0
$928$	−1.02815e10	+	1.78081e10i	−0.422319	+	0.731477i
$929$	2.23840e10	−	1.87824e10i	0.915971	−	0.768591i	−0.0572745	−	0.998358i	$-0.518241\pi$
$929$	2.23840e10	−	1.87824e10i	0.915971	−	0.768591i	0.973246	+	0.229768i	$0.0737966\pi$
$930$		0			0
$931$	7.22395e9	−	4.09691e10i	0.293394	−	1.66392i
$932$	−2.54853e9	+	1.44534e10i	−0.103118	+	0.584810i
$933$		0			0
$934$	−1.43488e10	+	1.20401e10i	−0.576239	+	0.483522i
$935$	7.19710e7	−	1.24657e8i	0.00287950	−	0.00498744i
$936$		0			0
$937$	8.77877e9	+	1.52053e10i	0.348614	+	0.603817i	0.986004	−	0.166725i	$-0.0533191\pi$
$937$	8.77877e9	+	1.52053e10i	0.348614	+	0.603817i	−0.637389	+	0.770542i	$0.719986\pi$
$938$	1.74392e10	+	6.34735e9i	0.689949	+	0.251121i
$939$		0			0
$940$	−5.61112e6	−	4.70829e6i	−0.000220345	−	0.000184891i
$941$	3.24494e10	−	1.18106e10i	1.26953	−	0.462072i	0.382575	−	0.923925i	$-0.375037\pi$
$941$	3.24494e10	−	1.18106e10i	1.26953	−	0.462072i	0.886956	+	0.461853i	$0.152815\pi$
$942$		0			0
$943$	1.78707e9	+	1.01350e10i	0.0693987	+	0.393580i
$944$	5.94934e10			2.30180
$945$		0			0
$946$	7.72370e9			0.296624
$947$	−8.33813e9	−	4.72879e10i	−0.319039	−	1.80936i	−0.548621	−	0.836071i	$-0.684847\pi$
$947$	−8.33813e9	−	4.72879e10i	−0.319039	−	1.80936i	0.229582	−	0.973289i	$-0.426264\pi$
$948$		0			0
$949$	−6.98875e9	+	2.54370e9i	−0.265441	+	0.0966126i
$950$	−2.60937e10	−	2.18952e10i	−0.987421	−	0.828544i
$951$		0			0
$952$	−3.34100e10	−	1.21602e10i	−1.25501	−	0.456786i
$953$	8.01373e9	+	1.38802e10i	0.299923	+	0.519482i	0.976118	−	0.217241i	$-0.0697057\pi$
$953$	8.01373e9	+	1.38802e10i	0.299923	+	0.519482i	−0.676195	+	0.736723i	$0.736372\pi$
$954$		0			0
$955$	−2.37837e8	+	4.11946e8i	−0.00883624	+	0.0153048i
$956$	8.11222e9	−	6.80696e9i	0.300287	−	0.251971i
$957$		0			0
$958$	1.76794e9	−	1.00265e10i	0.0649661	−	0.368441i
$959$	−4.35539e9	+	2.47007e10i	−0.159464	+	0.904364i
$960$		0			0
$961$	1.34406e10	−	1.12780e10i	0.488525	−	0.409921i
$962$	−2.58189e9	+	4.47196e9i	−0.0935027	+	0.161951i
$963$		0			0
$964$	2.09975e9	+	3.63687e9i	0.0754914	+	0.130755i
$965$	6.63513e8	+	2.41499e8i	0.0237686	+	0.00865107i
$966$		0			0
$967$	1.43456e10	+	1.20374e10i	0.510182	+	0.428093i	0.861193	−	0.508278i	$-0.169718\pi$
$967$	1.43456e10	+	1.20374e10i	0.510182	+	0.428093i	−0.351011	+	0.936371i	$0.614162\pi$
$968$	−1.90827e10	+	6.94553e9i	−0.676201	+	0.246117i
$969$		0			0
$970$	−2.01108e8	−	1.14054e9i	−0.00707503	−	0.0401245i
$971$	2.06237e9			0.0722934			0.0361467	−	0.999346i	$-0.488492\pi$
$971$	2.06237e9			0.0722934			0.0361467	+	0.999346i	$0.488492\pi$
$972$		0			0
$973$	−2.92672e10			−1.01856
$974$	−2.13954e9	−	1.21340e10i	−0.0741933	−	0.420771i
$975$		0			0
$976$	4.83940e10	−	1.76140e10i	1.66616	−	0.606433i
$977$	−1.51585e10	−	1.27195e10i	−0.520028	−	0.436355i	0.344614	−	0.938745i	$-0.388010\pi$
$977$	−1.51585e10	−	1.27195e10i	−0.520028	−	0.436355i	−0.864641	+	0.502390i	$0.832454\pi$
$978$		0			0
$979$	5.17784e9	+	1.88458e9i	0.176364	+	0.0641911i
$980$	−1.41550e8	−	2.45172e8i	−0.00480417	−	0.00832106i
$981$		0			0
$982$	1.66880e10	−	2.89044e10i	0.562359	−	0.974034i
$983$	3.17068e10	−	2.66052e10i	1.06467	−	0.893364i	0.0701111	−	0.997539i	$-0.477665\pi$
$983$	3.17068e10	−	2.66052e10i	1.06467	−	0.893364i	0.994559	+	0.104175i	$0.0332202\pi$
$984$		0			0
$985$	−1.58310e8	+	8.97823e8i	−0.00527816	+	0.0299339i
$986$	8.79643e9	−	4.98870e10i	0.292238	−	1.65737i
$987$		0			0
$988$	1.81005e9	−	1.51881e9i	0.0597093	−	0.0501021i
$989$	4.65160e9	−	8.05681e9i	0.152903	−	0.264835i
$990$		0			0
$991$	−6.74755e9	−	1.16871e10i	−0.220236	−	0.381460i	0.734644	−	0.678453i	$-0.237349\pi$
$991$	−6.74755e9	−	1.16871e10i	−0.220236	−	0.381460i	−0.954880	+	0.296993i	$0.904016\pi$
$992$	−2.31964e10	−	8.44279e9i	−0.754448	−	0.274597i
$993$		0			0
$994$	1.07129e10	+	8.98920e9i	0.345983	+	0.290315i
$995$	2.01811e8	−	7.34532e7i	0.00649478	−	0.00236391i
$996$		0			0
$997$	−8.62945e9	−	4.89400e10i	−0.275772	−	1.56398i	−0.736499	−	0.676439i	$-0.763522\pi$
$997$	−8.62945e9	−	4.89400e10i	−0.275772	−	1.56398i	0.460727	−	0.887542i	$-0.347589\pi$
$998$	2.11926e10			0.674880
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.8.e.a.10.16		120
3.2	odd	2		27.8.e.a.13.5	✓	120
27.2	odd	18		27.8.e.a.25.5	yes	120
27.25	even	9	inner	81.8.e.a.73.16		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.8.e.a.13.5	✓	120	3.2	odd	2
27.8.e.a.25.5	yes	120	27.2	odd	18
81.8.e.a.10.16		120	1.1	even	1	trivial
81.8.e.a.73.16		120	27.25	even	9	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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.26179 + 12.8272i) q^{2} +(-39.1414 + 14.2463i) q^{4} +(4.19097 + 3.51664i) q^{5} +(-1350.63 - 491.588i) q^{7} +(562.337 + 973.996i) q^{8} +(-35.6297 + 61.7124i) q^{10} +(916.360 - 768.917i) q^{11} +(294.159 - 1668.26i) q^{13} +(3250.88 - 18436.6i) q^{14} +(-15306.0 + 12843.3i) q^{16} +(10997.3 - 19047.8i) q^{17} +(-16743.5 - 29000.6i) q^{19} +(-214.139 - 77.9404i) q^{20} +(11935.7 + 10015.2i) q^{22} +(17635.4 - 6418.77i) q^{23} +(-13561.1 - 76908.6i) q^{25} +22064.4 q^{26} +59868.6 q^{28} +(-30705.1 - 174137. i) q^{29} +(199467. - 72600.2i) q^{31} +(-89084.5 - 74750.7i) q^{32} +(269204. + 97982.3i) q^{34} +(-3931.70 - 6809.90i) q^{35} +(-117016. + 202677. i) q^{37} +(334127. - 280366. i) q^{38} +(-1068.46 + 6059.53i) q^{40} +(-95223.1 + 540037. i) q^{41} +(379740. - 318640. i) q^{43} +(-24913.3 + 43151.2i) q^{44} +(122223. + 211696. i) q^{46} +(30204.4 + 10993.5i) q^{47} +(951661. + 798539. i) q^{49} +(955852. - 347902. i) q^{50} +(12252.7 + 69488.5i) q^{52} +1.06896e6 q^{53} +6544.45 q^{55} +(-280702. - 1.59194e6i) q^{56} +(2.16425e6 - 787722. i) q^{58} +(-2.28094e6 - 1.91394e6i) q^{59} +(-2.42205e6 - 881553. i) q^{61} +(1.38241e6 + 2.39441e6i) q^{62} +(-521406. + 903101. i) q^{64} +(7099.47 - 5957.16i) q^{65} +(-172140. + 976252. i) q^{67} +(-159087. + 902228. i) q^{68} +(78459.5 - 65835.3i) q^{70} +(-373502. + 646925. i) q^{71} +(-2.19519e6 - 3.80218e6i) q^{73} +(-2.86445e6 - 1.04258e6i) q^{74} +(1.06851e6 + 896589. i) q^{76} +(-1.61565e6 + 588048. i) q^{77} +(-631110. - 3.57920e6i) q^{79} -109313. q^{80} -7.14255e6 q^{82} +(-894305. - 5.07185e6i) q^{83} +(113074. - 41155.5i) q^{85} +(4.94615e6 + 4.15032e6i) q^{86} +(1.26423e6 + 460140. i) q^{88} +(2.30314e6 + 3.98916e6i) q^{89} +(-1.21739e6 + 2.10859e6i) q^{91} +(-598831. + 502479. i) q^{92} +(-72700.3 + 412304. i) q^{94} +(31813.2 - 180422. i) q^{95} +(-1.24500e7 + 1.04468e7i) q^{97} +(-8.09058e6 + 1.40133e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{2} - 6 q^{4} + 219 q^{5} - 6 q^{7} + 4611 q^{8} - 3 q^{10} - 9399 q^{11} - 6 q^{13} - 16647 q^{14} + 378 q^{16} + 58959 q^{17} - 3 q^{19} - 240243 q^{20} + 105762 q^{22} + 144084 q^{23} - 107997 q^{25}+ \cdots + 88493274 q^{98}+O(q^{100}) \) 120 * q + 6 * q^2 - 6 * q^4 + 219 * q^5 - 6 * q^7 + 4611 * q^8 - 3 * q^10 - 9399 * q^11 - 6 * q^13 - 16647 * q^14 + 378 * q^16 + 58959 * q^17 - 3 * q^19 - 240243 * q^20 + 105762 * q^22 + 144084 * q^23 - 107997 * q^25 - 443202 * q^26 - 12 * q^28 - 107886 * q^29 + 297975 * q^31 + 639576 * q^32 - 265806 * q^34 + 450672 * q^35 - 3 * q^37 + 145596 * q^38 + 283521 * q^40 - 227085 * q^41 - 1080969 * q^43 + 1205115 * q^44 - 3 * q^46 + 5184339 * q^47 + 976008 * q^49 - 2324559 * q^50 - 3366135 * q^52 - 5631750 * q^53 - 12 * q^55 - 5254923 * q^56 + 3884295 * q^58 + 12534492 * q^59 + 3865440 * q^61 + 9923646 * q^62 - 10223619 * q^64 - 17158395 * q^65 + 5567061 * q^67 - 19858455 * q^68 - 1020993 * q^70 + 18563877 * q^71 + 3770934 * q^73 + 36278085 * q^74 - 1156998 * q^76 - 8471751 * q^77 + 16415526 * q^79 - 101080590 * q^80 - 12 * q^82 - 3147699 * q^83 - 7672131 * q^85 + 70854834 * q^86 - 34323078 * q^88 + 54647613 * q^89 + 3315066 * q^91 - 73858515 * q^92 + 22126539 * q^94 - 32541447 * q^95 + 41250117 * q^97 + 88493274 * q^98

Introduction

L-functions

Modular forms

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Database

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