LMFDB - Embedded newform 81.10.e.a.19.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,10,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, 10, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 10 $
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:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			19.9
Character	$\chi$	$=$	81.19
Dual form			81.10.e.a.64.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-17.4636 + 6.35623i) q^{2} +(-127.639 + 107.102i) q^{4} +(-280.318 - 1589.76i) q^{5} +(610.601 + 512.355i) q^{7} +(6305.87 - 10922.1i) q^{8} +(15000.2 + 25981.2i) q^{10} +(4495.09 - 25492.9i) q^{11} +(106141. + 38632.3i) q^{13} +(-13919.9 - 5066.44i) q^{14} +(-25886.0 + 146807. i) q^{16} +(-64251.1 - 111286. i) q^{17} +(-175832. + 304550. i) q^{19} +(206046. + 172893. i) q^{20} +(83538.4 + 473770. i) q^{22} +(1965.39 - 1649.15i) q^{23} +(-613422. + 223267. i) q^{25} -2.09916e6 q^{26} -132811. q^{28} +(3.90737e6 - 1.42216e6i) q^{29} +(-4.10711e6 + 3.44627e6i) q^{31} +(640209. + 3.63081e6i) q^{32} +(1.82942e6 + 1.53506e6i) q^{34} +(643359. - 1.11433e6i) q^{35} +(1.52669e6 + 2.64430e6i) q^{37} +(1.13487e6 - 6.43617e6i) q^{38} +(-1.91312e7 - 6.96317e6i) q^{40} +(2.20476e7 + 8.02467e6i) q^{41} +(3.33783e6 - 1.89298e7i) q^{43} +(2.15659e6 + 3.73533e6i) q^{44} +(-23840.3 + 41292.6i) q^{46} +(-1.67023e7 - 1.40149e7i) q^{47} +(-6.89700e6 - 3.91149e7i) q^{49} +(9.29341e6 - 7.79810e6i) q^{50} +(-1.76854e7 + 6.43695e6i) q^{52} -8.11126e7 q^{53} -4.17877e7 q^{55} +(9.44636e6 - 3.43819e6i) q^{56} +(-5.91971e7 + 4.96722e7i) q^{58} +(-3.01060e7 - 1.70740e8i) q^{59} +(-7.48377e7 - 6.27963e7i) q^{61} +(4.98196e7 - 8.62901e7i) q^{62} +(-7.24209e7 - 1.25437e8i) q^{64} +(3.16628e7 - 1.79568e8i) q^{65} +(2.17705e8 + 7.92381e7i) q^{67} +(2.01199e7 + 7.32305e6i) q^{68} +(-4.15242e6 + 2.35496e7i) q^{70} +(-1.41531e8 - 2.45140e8i) q^{71} +(2.29279e8 - 3.97123e8i) q^{73} +(-4.34693e7 - 3.64750e7i) q^{74} +(-1.01749e7 - 5.77045e7i) q^{76} +(1.58061e7 - 1.32629e7i) q^{77} +(-5.29687e8 + 1.92790e8i) q^{79} +2.40644e8 q^{80} -4.36037e8 q^{82} +(-6.29101e7 + 2.28974e7i) q^{83} +(-1.58908e8 + 1.33339e8i) q^{85} +(6.20314e7 + 3.51798e8i) q^{86} +(-2.50091e8 - 2.09851e8i) q^{88} +(-2.71094e8 + 4.69549e8i) q^{89} +(4.50165e7 + 7.79709e7i) q^{91} +(-74232.5 + 420994. i) q^{92} +(3.80764e8 + 1.38587e8i) q^{94} +(5.33450e8 + 1.94160e8i) q^{95} +(1.23991e7 - 7.03187e7i) q^{97} +(3.69070e8 + 6.39247e8i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	−17.4636	+	6.35623i	−0.771789	+	0.280908i	−0.697745	−	0.716347i	$-0.745813\pi$
$2$	−17.4636	+	6.35623i	−0.771789	+	0.280908i	−0.0740446	+	0.997255i	$0.523591\pi$
$3$		0			0
$3$		0			0
$4$	−127.639	+	107.102i	−0.249295	+	0.209184i
$5$	−280.318	−	1589.76i	−0.200579	−	1.13754i	−0.904247	−	0.427010i	$-0.859567\pi$
$5$	−280.318	−	1589.76i	−0.200579	−	1.13754i	0.703668	−	0.710529i	$-0.251544\pi$
$6$		0			0
$7$	610.601	+	512.355i	0.0961205	+	0.0806547i	0.689582	−	0.724208i	$-0.257794\pi$
$7$	610.601	+	512.355i	0.0961205	+	0.0806547i	−0.593461	+	0.804863i	$0.702239\pi$
$8$	6305.87	−	10922.1i	0.544302	−	0.942760i
$9$		0			0
$10$	15000.2	+	25981.2i	0.474349	+	0.821597i
$11$	4495.09	−	25492.9i	0.0925702	−	0.524992i	−0.902895	−	0.429862i	$-0.858562\pi$
$11$	4495.09	−	25492.9i	0.0925702	−	0.524992i	0.995465	−	0.0951300i	$-0.0303267\pi$
$12$		0			0
$13$	106141.	+	38632.3i	1.03072	+	0.375150i	0.801354	−	0.598191i	$-0.204114\pi$
$13$	106141.	+	38632.3i	1.03072	+	0.375150i	0.229363	+	0.973341i	$0.426336\pi$
$14$	−13919.9	−	5066.44i	−0.0968414	−	0.0352474i
$15$		0			0
$16$	−25886.0	+	146807.i	−0.0987472	+	0.560023i
$17$	−64251.1	−	111286.i	−0.186578	−	0.323162i	0.757529	−	0.652801i	$-0.226406\pi$
$17$	−64251.1	−	111286.i	−0.186578	−	0.323162i	−0.944107	+	0.329639i	$0.893073\pi$
$18$		0			0
$19$	−175832.	+	304550.i	−0.309533	+	0.536127i	−0.978260	−	0.207381i	$-0.933506\pi$
$19$	−175832.	+	304550.i	−0.309533	+	0.536127i	0.668727	+	0.743508i	$0.266839\pi$
$20$	206046.	+	172893.i	0.287958	+	0.241625i
$21$		0			0
$22$	83538.4	+	473770.i	0.0760299	+	0.431187i
$23$	1965.39	−	1649.15i	0.00146444	−	0.00122881i	−0.642055	−	0.766659i	$-0.721918\pi$
$23$	1965.39	−	1649.15i	0.00146444	−	0.00122881i	0.643520	+	0.765430i	$0.277474\pi$
$24$		0			0
$25$	−613422.	+	223267.i	−0.314072	+	0.114313i
$26$	−2.09916e6			−0.900879
$27$		0			0
$28$	−132811.			−0.0408340
$29$	3.90737e6	−	1.42216e6i	1.02587	−	0.373387i	0.226364	−	0.974043i	$-0.427316\pi$
$29$	3.90737e6	−	1.42216e6i	1.02587	−	0.373387i	0.799508	+	0.600656i	$0.205094\pi$
$30$		0			0
$31$	−4.10711e6	+	3.44627e6i	−0.798746	+	0.670227i	−0.947893	−	0.318588i	$-0.896792\pi$
$31$	−4.10711e6	+	3.44627e6i	−0.798746	+	0.670227i	0.149147	+	0.988815i	$0.452347\pi$
$32$	640209.	+	3.63081e6i	0.107931	+	0.612108i
$33$		0			0
$34$	1.82942e6	+	1.53506e6i	0.234778	+	0.197002i
$35$	643359.	−	1.11433e6i	0.0724682	−	0.125519i
$36$		0			0
$37$	1.52669e6	+	2.64430e6i	0.133919	+	0.231955i	0.925184	−	0.379519i	$-0.123910\pi$
$37$	1.52669e6	+	2.64430e6i	0.133919	+	0.231955i	−0.791265	+	0.611474i	$0.790577\pi$
$38$	1.13487e6	−	6.43617e6i	0.0882917	−	0.500727i
$39$		0			0
$40$	−1.91312e7	−	6.96317e6i	−1.18160	−	0.430068i
$41$	2.20476e7	+	8.02467e6i	1.21852	+	0.443507i	0.869653	−	0.493664i	$-0.164343\pi$
$41$	2.20476e7	+	8.02467e6i	1.21852	+	0.443507i	0.348872	+	0.937171i	$0.386565\pi$
$42$		0			0
$43$	3.33783e6	−	1.89298e7i	0.148887	−	0.844379i	−0.815277	−	0.579071i	$-0.803415\pi$
$43$	3.33783e6	−	1.89298e7i	0.148887	−	0.844379i	0.964164	−	0.265308i	$-0.0854735\pi$
$44$	2.15659e6	+	3.73533e6i	0.0867424	+	0.150242i
$45$		0			0
$46$	−23840.3	+	41292.6i	−0.000785058	+	0.00135976i
$47$	−1.67023e7	−	1.40149e7i	−0.499270	−	0.418937i	0.358065	−	0.933697i	$-0.383437\pi$
$47$	−1.67023e7	−	1.40149e7i	−0.499270	−	0.418937i	−0.857335	+	0.514760i	$0.827881\pi$
$48$		0			0
$49$	−6.89700e6	−	3.91149e7i	−0.170914	−	0.969303i
$50$	9.29341e6	−	7.79810e6i	0.210286	−	0.176451i
$51$		0			0
$52$	−1.76854e7	+	6.43695e6i	−0.335428	+	0.122086i
$53$	−8.11126e7			−1.41204			−0.706020	−	0.708192i	$-0.749511\pi$
$53$	−8.11126e7			−1.41204			−0.706020	+	0.708192i	$0.749511\pi$
$54$		0			0
$55$	−4.17877e7			−0.615767
$56$	9.44636e6	−	3.43819e6i	0.128357	−	0.0467180i
$57$		0			0
$58$	−5.91971e7	+	4.96722e7i	−0.686869	+	0.576352i
$59$	−3.01060e7	−	1.70740e8i	−0.323459	−	1.83443i	−0.520291	−	0.853989i	$-0.674177\pi$
$59$	−3.01060e7	−	1.70740e8i	−0.323459	−	1.83443i	0.196832	−	0.980437i	$-0.436935\pi$
$60$		0			0
$61$	−7.48377e7	−	6.27963e7i	−0.692048	−	0.580697i	0.227451	−	0.973790i	$-0.426961\pi$
$61$	−7.48377e7	−	6.27963e7i	−0.692048	−	0.580697i	−0.919499	+	0.393092i	$0.871405\pi$
$62$	4.98196e7	−	8.62901e7i	0.428191	−	0.741649i
$63$		0			0
$64$	−7.24209e7	−	1.25437e8i	−0.539577	−	0.934576i
$65$	3.16628e7	−	1.79568e8i	0.220008	−	1.24773i
$66$		0			0
$67$	2.17705e8	+	7.92381e7i	1.31987	+	0.480394i	0.903417	−	0.428763i	$-0.141051\pi$
$67$	2.17705e8	+	7.92381e7i	1.31987	+	0.480394i	0.416454	+	0.909157i	$0.363273\pi$
$68$	2.01199e7	+	7.32305e6i	0.114113	+	0.0415338i
$69$		0			0
$70$	−4.15242e6	+	2.35496e7i	−0.0206709	+	0.117231i
$71$	−1.41531e8	−	2.45140e8i	−0.660983	−	1.14486i	−0.980358	−	0.197228i	$-0.936806\pi$
$71$	−1.41531e8	−	2.45140e8i	−0.660983	−	1.14486i	0.319375	−	0.947629i	$-0.396527\pi$
$72$		0			0
$73$	2.29279e8	−	3.97123e8i	0.944957	−	1.63671i	0.189119	−	0.981954i	$-0.439437\pi$
$73$	2.29279e8	−	3.97123e8i	0.944957	−	1.63671i	0.755837	−	0.654759i	$-0.227230\pi$
$74$	−4.34693e7	−	3.64750e7i	−0.168515	−	0.141401i
$75$		0			0
$76$	−1.01749e7	−	5.77045e7i	−0.0349838	−	0.198403i
$77$	1.58061e7	−	1.32629e7i	0.0512410	−	0.0429963i
$78$		0			0
$79$	−5.29687e8	+	1.92790e8i	−1.53002	+	0.556882i	−0.963627	−	0.267252i	$-0.913884\pi$
$79$	−5.29687e8	+	1.92790e8i	−1.53002	+	0.556882i	−0.566394	+	0.824134i	$0.691662\pi$
$80$	2.40644e8			0.656855
$81$		0			0
$82$	−4.36037e8			−1.06503
$83$	−6.29101e7	+	2.28974e7i	−0.145502	+	0.0529584i	−0.413745	−	0.910393i	$-0.635779\pi$
$83$	−6.29101e7	+	2.28974e7i	−0.145502	+	0.0529584i	0.268243	+	0.963351i	$0.413557\pi$
$84$		0			0
$85$	−1.58908e8	+	1.33339e8i	−0.330187	+	0.277059i
$86$	6.20314e7	+	3.51798e8i	0.122284	+	0.693506i
$87$		0			0
$88$	−2.50091e8	−	2.09851e8i	−0.444555	−	0.373026i
$89$	−2.71094e8	+	4.69549e8i	−0.458000	+	0.793279i	−0.998855	−	0.0478365i	$-0.984767\pi$
$89$	−2.71094e8	+	4.69549e8i	−0.458000	+	0.793279i	0.540855	+	0.841116i	$0.318101\pi$
$90$		0			0
$91$	4.50165e7	+	7.79709e7i	0.0688154	+	0.119192i
$92$	−74232.5	+	420994.i	−0.000108031	+	0.000612675i
$93$		0			0
$94$	3.80764e8	+	1.38587e8i	0.503014	+	0.183082i
$95$	5.33450e8	+	1.94160e8i	0.671951	+	0.244570i
$96$		0			0
$97$	1.23991e7	−	7.03187e7i	0.0142206	−	0.0806488i	−0.976872	−	0.213827i	$-0.931407\pi$
$97$	1.23991e7	−	7.03187e7i	0.0142206	−	0.0806488i	0.991092	+	0.133178i	$0.0425182\pi$
$98$	3.69070e8	+	6.39247e8i	0.404195	+	0.700086i
$99$		0			0
$100$	5.43843e7	−	9.41964e7i	0.0543843	−	0.0941964i
$101$	−1.11072e8	−	9.32004e7i	−0.106208	−	0.0891192i	0.588137	−	0.808761i	$-0.299862\pi$
$101$	−1.11072e8	−	9.32004e7i	−0.106208	−	0.0891192i	−0.694345	+	0.719642i	$0.744306\pi$
$102$		0			0
$103$	2.46300e8	+	1.39683e9i	0.215624	+	1.22286i	0.879821	+	0.475305i	$0.157662\pi$
$103$	2.46300e8	+	1.39683e9i	0.215624	+	1.22286i	−0.664198	+	0.747557i	$0.731227\pi$
$104$	1.09126e9	−	9.15675e8i	0.914698	−	0.767523i
$105$		0			0
$106$	1.41652e9	−	5.15571e8i	1.08980	−	0.396654i
$107$	−2.27609e9			−1.67866			−0.839328	−	0.543625i	$-0.817051\pi$
$107$	−2.27609e9			−1.67866			−0.839328	+	0.543625i	$0.817051\pi$
$108$		0			0
$109$	−7.56560e8			−0.513362			−0.256681	−	0.966496i	$-0.582629\pi$
$109$	−7.56560e8			−0.513362			−0.256681	+	0.966496i	$0.582629\pi$
$110$	7.29763e8	−	2.65612e8i	0.475242	−	0.172974i
$111$		0			0
$112$	−9.10231e7	+	7.63774e7i	−0.0546601	+	0.0458653i
$113$	3.43870e8	+	1.95018e9i	0.198400	+	1.12518i	0.907493	+	0.420067i	$0.137993\pi$
$113$	3.43870e8	+	1.95018e9i	0.198400	+	1.12518i	−0.709093	+	0.705115i	$0.750895\pi$
$114$		0			0
$115$	−3.17269e6	−	2.66221e6i	−0.00169156	−	0.00141939i
$116$	−3.46416e8	+	6.00011e8i	−0.177639	+	0.307679i
$117$		0			0
$118$	1.61102e9	+	2.79037e9i	0.764948	+	1.32493i
$119$	1.77862e7	−	1.00871e8i	0.00813060	−	0.0461109i
$120$		0			0
$121$	1.58606e9	+	5.77280e8i	0.672645	+	0.244823i
$122$	1.70608e9	+	6.20964e8i	0.697238	+	0.253774i
$123$		0			0
$124$	1.55125e8	−	8.79759e8i	0.0589230	−	0.334169i
$125$	−1.04956e9	−	1.81788e9i	−0.384512	−	0.665995i
$126$		0			0
$127$	1.94110e9	−	3.36209e9i	0.662112	−	1.14681i	−0.317948	−	0.948108i	$-0.602994\pi$
$127$	1.94110e9	−	3.36209e9i	0.662112	−	1.14681i	0.980060	−	0.198703i	$-0.0636731\pi$
$128$	6.16009e8	+	5.16893e8i	0.202835	+	0.170198i
$129$		0			0
$130$	5.88433e8	+	3.33717e9i	0.180697	+	1.02479i
$131$	−8.75614e8	+	7.34727e8i	−0.259772	+	0.217974i	−0.763366	−	0.645966i	$-0.776455\pi$
$131$	−8.75614e8	+	7.34727e8i	−0.259772	+	0.217974i	0.503595	+	0.863940i	$0.332010\pi$
$132$		0			0
$133$	−2.63401e8	+	9.58701e7i	−0.0729936	+	0.0265675i
$134$	−4.30556e9			−1.15361
$135$		0			0
$136$	−1.62064e9			−0.406219
$137$	−2.92900e9	+	1.06607e9i	−0.710356	+	0.258549i	−0.671826	−	0.740709i	$-0.734490\pi$
$137$	−2.92900e9	+	1.06607e9i	−0.710356	+	0.258549i	−0.0385301	+	0.999257i	$0.512268\pi$
$138$		0			0
$139$	1.22616e9	−	1.02887e9i	0.278599	−	0.233772i	−0.492771	−	0.870159i	$-0.664016\pi$
$139$	1.22616e9	−	1.02887e9i	0.278599	−	0.233772i	0.771370	+	0.636387i	$0.219572\pi$
$140$	3.72292e7	+	2.11137e8i	0.00819045	+	0.0464503i
$141$		0			0
$142$	4.02981e9	+	3.38141e9i	0.831739	+	0.697912i
$143$	1.46196e9	−	2.53220e9i	0.292364	−	0.506390i
$144$		0			0
$145$	−3.35620e9	−	5.81312e9i	−0.630511	−	1.09208i
$146$	−1.47983e9	+	8.39256e9i	−0.269541	+	1.52864i
$147$		0			0
$148$	−4.78075e8	−	1.74005e8i	−0.0819065	−	0.0298115i
$149$	4.49393e8	+	1.63566e8i	0.0746945	+	0.0271866i	0.379097	−	0.925357i	$-0.376235\pi$
$149$	4.49393e8	+	1.63566e8i	0.0746945	+	0.0271866i	−0.304403	+	0.952543i	$0.598457\pi$
$150$		0			0
$151$	1.20387e9	−	6.82747e9i	0.188444	−	1.06872i	−0.733006	−	0.680222i	$-0.761883\pi$
$151$	1.20387e9	−	6.82747e9i	0.188444	−	1.06872i	0.921450	−	0.388497i	$-0.127006\pi$
$152$	2.21755e9	+	3.84091e9i	0.336959	+	0.583630i
$153$		0			0
$154$	−1.91730e8	+	3.32086e8i	−0.0274692	+	0.0475781i
$155$	6.63004e9	+	5.56327e9i	0.922622	+	0.774172i
$156$		0			0
$157$	1.25829e9	+	7.13614e9i	0.165285	+	0.937379i	0.948770	+	0.315968i	$0.102329\pi$
$157$	1.25829e9	+	7.13614e9i	0.165285	+	0.937379i	−0.783485	+	0.621411i	$0.786560\pi$
$158$	8.02482e9	−	6.73362e9i	1.02442	−	0.859591i
$159$		0			0
$160$	5.59265e9	−	2.03556e9i	0.674648	−	0.245552i
$161$	2.04502e6			0.000239873
$162$		0			0
$163$	−1.48150e10			−1.64383			−0.821915	−	0.569610i	$-0.807094\pi$
$163$	−1.48150e10			−1.64383			−0.821915	+	0.569610i	$0.807094\pi$
$164$	−3.67360e9	+	1.33708e9i	−0.396547	+	0.144331i
$165$		0			0
$166$	9.53096e8	−	7.99743e8i	0.0974205	−	0.0817455i
$167$	−3.07828e9	−	1.74578e10i	−0.306256	−	1.73686i	−0.617534	−	0.786544i	$-0.711868\pi$
$167$	−3.07828e9	−	1.74578e10i	−0.306256	−	1.73686i	0.311278	−	0.950319i	$-0.399243\pi$
$168$		0			0
$169$	1.65000e9	+	1.38451e9i	0.155594	+	0.130559i
$170$	1.92756e9	−	3.33864e9i	0.177006	−	0.306584i
$171$		0			0
$172$	1.60138e9	+	2.77367e9i	0.139513	+	0.241644i
$173$	−2.08583e9	+	1.18294e10i	−0.177040	+	1.00405i	0.758722	+	0.651414i	$0.225824\pi$
$173$	−2.08583e9	+	1.18294e10i	−0.177040	+	1.00405i	−0.935762	+	0.352631i	$0.885287\pi$
$174$		0			0
$175$	−4.88948e8	−	1.77962e8i	−0.0394086	−	0.0143436i
$176$	3.62617e9	+	1.31982e9i	0.284867	+	0.103683i
$177$		0			0
$178$	1.74972e9	−	9.92316e9i	0.130641	−	0.740900i
$179$	−1.07814e10	−	1.86739e10i	−0.784939	−	1.35955i	−0.929036	−	0.369990i	$-0.879361\pi$
$179$	−1.07814e10	−	1.86739e10i	−0.784939	−	1.35955i	0.144097	−	0.989564i	$-0.453972\pi$
$180$		0			0
$181$	−1.09960e10	+	1.90457e10i	−0.761522	+	1.31900i	0.180543	+	0.983567i	$0.442214\pi$
$181$	−1.09960e10	+	1.90457e10i	−0.761522	+	1.31900i	−0.942066	+	0.335428i	$0.891119\pi$
$182$	−1.28175e9	−	1.07552e9i	−0.0865929	−	0.0726601i
$183$		0			0
$184$	−5.61875e6	−	3.18655e7i	−0.000361376	−	0.00204946i
$185$	3.77585e9	−	3.16831e9i	0.236996	−	0.198864i
$186$		0			0
$187$	−3.12582e9	+	1.13771e9i	−0.186929	+	0.0680367i
$188$	3.63289e9			0.212100
$189$		0			0
$190$	−1.05501e10			−0.587307
$191$	−4.20187e9	+	1.52936e9i	−0.228451	+	0.0831493i	−0.453709	−	0.891150i	$-0.649900\pi$
$191$	−4.20187e9	+	1.52936e9i	−0.228451	+	0.0831493i	0.225259	+	0.974299i	$0.427677\pi$
$192$		0			0
$193$	−2.16606e10	+	1.81754e10i	−1.12373	+	0.942921i	−0.998787	−	0.0492430i	$-0.984319\pi$
$193$	−2.16606e10	+	1.81754e10i	−1.12373	+	0.942921i	−0.124943	+	0.992164i	$0.539875\pi$
$194$	2.30429e8	+	1.30683e9i	0.0116797	+	0.0662386i
$195$		0			0
$196$	5.06961e9	+	4.25391e9i	0.245370	+	0.205890i
$197$	8.39382e9	−	1.45385e10i	0.397065	−	0.687737i	−0.596297	−	0.802764i	$-0.703362\pi$
$197$	8.39382e9	−	1.45385e10i	0.397065	−	0.687737i	0.993362	+	0.115027i	$0.0366953\pi$
$198$		0			0
$199$	−1.43606e10	−	2.48733e10i	−0.649134	−	1.12433i	−0.983330	−	0.181830i	$-0.941798\pi$
$199$	−1.43606e10	−	2.48733e10i	−0.649134	−	1.12433i	0.334196	−	0.942504i	$-0.391535\pi$
$200$	−1.42961e9	+	8.10775e9i	−0.0631806	+	0.358315i
$201$		0			0
$202$	2.53212e9	+	9.21615e8i	0.107005	+	0.0389465i
$203$	3.11449e9	+	1.13358e9i	0.128723	+	0.0468512i
$204$		0			0
$205$	6.57697e9	−	3.72999e10i	0.260096	−	1.47508i
$206$	−1.31799e10	−	2.28282e10i	−0.509928	−	0.883221i
$207$		0			0
$208$	−8.41904e9	+	1.45822e10i	−0.311873	+	0.540180i
$209$	6.97349e9	+	5.85145e9i	0.252809	+	0.212132i
$210$		0			0
$211$	−1.83777e9	−	1.04225e10i	−0.0638294	−	0.361995i	−0.999947	−	0.0103071i	$-0.996719\pi$
$211$	−1.83777e9	−	1.04225e10i	−0.0638294	−	0.361995i	0.936117	−	0.351687i	$-0.114392\pi$
$212$	1.03532e10	−	8.68732e9i	0.352015	−	0.295376i
$213$		0			0
$214$	3.97487e10	−	1.44673e10i	1.29557	−	0.471548i
$215$	−3.10294e10			−0.990378
$216$		0			0
$217$	−4.27352e9			−0.130833
$218$	1.32123e10	−	4.80887e9i	0.396208	−	0.144208i
$219$		0			0
$220$	5.33375e9	−	4.47555e9i	0.153508	−	0.128808i
$221$	−2.52046e9	−	1.42942e10i	−0.0710745	−	0.403084i
$222$		0			0
$223$	4.93800e9	+	4.14348e9i	0.133715	+	0.112200i	0.707192	−	0.707021i	$-0.249962\pi$
$223$	4.93800e9	+	4.14348e9i	0.133715	+	0.112200i	−0.573477	+	0.819221i	$0.694406\pi$
$224$	−1.46935e9	+	2.54499e9i	−0.0389950	+	0.0675413i
$225$		0			0
$226$	−1.84010e10	−	3.18715e10i	−0.469196	−	0.812671i
$227$	−5.28046e8	+	2.99470e9i	−0.0131994	+	0.0748578i	−0.990696	−	0.136094i	$-0.956545\pi$
$227$	−5.28046e8	+	2.99470e9i	−0.0131994	+	0.0748578i	0.977497	+	0.210952i	$0.0676562\pi$
$228$		0			0
$229$	1.65307e10	+	6.01668e9i	0.397220	+	0.144576i	0.532904	−	0.846176i	$-0.321101\pi$
$229$	1.65307e10	+	6.01668e9i	0.397220	+	0.144576i	−0.135684	+	0.990752i	$0.543323\pi$
$230$	7.23282e7	+	2.63253e7i	0.00170425	+	0.000620295i
$231$		0			0
$232$	9.10634e9	−	5.16446e10i	0.206371	−	1.17039i
$233$	−2.16335e9	−	3.74704e9i	−0.0480868	−	0.0832887i	0.840980	−	0.541066i	$-0.181979\pi$
$233$	−2.16335e9	−	3.74704e9i	−0.0480868	−	0.0832887i	−0.889067	+	0.457777i	$0.848646\pi$
$234$		0			0
$235$	−1.75983e10	+	3.04812e10i	−0.376415	+	0.651969i
$236$	2.21293e10	+	1.85687e10i	0.464369	+	0.389651i
$237$		0			0
$238$	3.30546e8	+	1.87462e9i	0.00667783	+	0.0378719i
$239$	5.29871e10	−	4.44615e10i	1.05046	−	0.881442i	0.0573191	−	0.998356i	$-0.481745\pi$
$239$	5.29871e10	−	4.44615e10i	1.05046	−	0.881442i	0.993142	+	0.116914i	$0.0373003\pi$
$240$		0			0
$241$	−3.12649e10	+	1.13795e10i	−0.597007	+	0.217293i	−0.622809	−	0.782374i	$-0.714008\pi$
$241$	−3.12649e10	+	1.13795e10i	−0.597007	+	0.217293i	0.0258013	+	0.999667i	$0.491786\pi$
$242$	−3.13677e10			−0.587913
$243$		0			0
$244$	1.62778e10			0.293997
$245$	−6.02499e10	+	2.19292e10i	−1.06834	+	0.388843i
$246$		0			0
$247$	−3.04285e10	+	2.55325e10i	−0.520169	+	0.436473i
$248$	1.17416e10	+	6.65900e10i	0.197104	+	1.11783i
$249$		0			0
$250$	2.98839e10	+	2.50756e10i	0.483846	+	0.405995i
$251$	−1.43058e10	+	2.47784e10i	−0.227500	+	0.394042i	−0.957067	−	0.289868i	$-0.906389\pi$
$251$	−1.43058e10	+	2.47784e10i	−0.227500	+	0.394042i	0.729566	+	0.683910i	$0.239722\pi$
$252$		0			0
$253$	−3.32072e7	−	5.75166e7i	−0.000509554	−	0.000882573i
$254$	−1.25284e10	+	7.10522e10i	−0.188862	+	1.07109i
$255$		0			0
$256$	5.56434e10	+	2.02525e10i	0.809718	+	0.294713i
$257$	−1.28810e10	−	4.68831e9i	−0.184184	−	0.0670374i	0.248282	−	0.968688i	$-0.420134\pi$
$257$	−1.28810e10	−	4.68831e9i	−0.184184	−	0.0670374i	−0.432466	+	0.901650i	$0.642356\pi$
$258$		0			0
$259$	−4.22624e8	+	2.39682e9i	−0.00583586	+	0.0330968i
$260$	1.51907e10	+	2.63111e10i	0.206157	+	0.357075i
$261$		0			0
$262$	1.06213e10	−	1.83966e10i	0.139258	−	0.241202i
$263$	−1.54430e10	−	1.29582e10i	−0.199036	−	0.167011i	0.537822	−	0.843058i	$-0.319247\pi$
$263$	−1.54430e10	−	1.29582e10i	−0.199036	−	0.167011i	−0.736858	+	0.676047i	$0.763692\pi$
$264$		0			0
$265$	2.27373e10	+	1.28950e11i	0.283226	+	1.60625i
$266$	3.99055e9	−	3.34847e9i	0.0488726	−	0.0410090i
$267$		0			0
$268$	−3.62742e10	+	1.32027e10i	−0.429528	+	0.156335i
$269$	1.53806e10			0.179096			0.0895481	−	0.995982i	$-0.471458\pi$
$269$	1.53806e10			0.179096			0.0895481	+	0.995982i	$0.471458\pi$
$270$		0			0
$271$	5.60281e10			0.631022			0.315511	−	0.948922i	$-0.397824\pi$
$271$	5.60281e10			0.631022			0.315511	+	0.948922i	$0.397824\pi$
$272$	1.80007e10	−	6.55174e9i	0.199402	−	0.0725766i
$273$		0			0
$274$	4.43746e10	−	3.72347e10i	0.475617	−	0.399090i
$275$	2.93435e9	+	1.66415e10i	0.0309396	+	0.175467i
$276$		0			0
$277$	1.30917e11	+	1.09852e11i	1.33609	+	1.12111i	0.982612	+	0.185670i	$0.0594456\pi$
$277$	1.30917e11	+	1.09852e11i	1.33609	+	1.12111i	0.353478	+	0.935443i	$0.384999\pi$
$278$	−1.48734e10	+	2.57615e10i	−0.149351	+	0.258684i
$279$		0			0
$280$	−8.11388e9	−	1.40537e10i	−0.0788892	−	0.136640i
$281$	9.07283e9	−	5.14545e10i	0.0868089	−	0.492318i	−0.910143	−	0.414295i	$-0.864028\pi$
$281$	9.07283e9	−	5.14545e10i	0.0868089	−	0.492318i	0.996952	−	0.0780227i	$-0.0248607\pi$
$282$		0			0
$283$	6.89819e10	+	2.51073e10i	0.639287	+	0.232681i	0.641268	−	0.767317i	$-0.278408\pi$
$283$	6.89819e10	+	2.51073e10i	0.639287	+	0.232681i	−0.00198143	+	0.999998i	$0.500631\pi$
$284$	4.43199e10	+	1.61311e10i	0.404265	+	0.147140i
$285$		0			0
$286$	−9.43593e9	+	5.35138e10i	−0.0833946	+	0.472954i
$287$	9.35081e9	+	1.61961e10i	0.0813543	+	0.140910i
$288$		0			0
$289$	5.10375e10	−	8.83996e10i	0.430377	−	0.745435i
$290$	9.55609e10	+	8.01851e10i	0.793395	+	0.665737i
$291$		0			0
$292$	1.32677e10	+	7.52448e10i	0.106800	+	0.605694i
$293$	1.75418e10	−	1.47193e10i	0.139050	−	0.116676i	−0.570610	−	0.821221i	$-0.693293\pi$
$293$	1.75418e10	−	1.47193e10i	0.139050	−	0.116676i	0.709660	+	0.704545i	$0.248849\pi$
$294$		0			0
$295$	−2.62996e11	+	9.57226e10i	−2.02185	+	0.735894i
$296$	3.85084e10			0.291570
$297$		0			0
$298$	−8.88769e9			−0.0652853
$299$	2.72319e8	−	9.91161e7i	0.00197042	−	0.000717173i
$300$		0			0
$301$	1.17368e10	−	9.84838e9i	0.0824142	−	0.0691537i
$302$	2.23731e10	+	1.26884e11i	0.154773	+	0.877761i
$303$		0			0
$304$	−4.01584e10	−	3.36969e10i	−0.269678	−	0.226287i
$305$	−7.88527e10	+	1.36577e11i	−0.521756	+	0.903708i
$306$		0			0
$307$	−2.68079e9	−	4.64326e9i	−0.0172242	−	0.0298333i	0.857285	−	0.514842i	$-0.172150\pi$
$307$	−2.68079e9	−	4.64326e9i	−0.0172242	−	0.0298333i	−0.874509	+	0.485009i	$0.838816\pi$
$308$	−5.96997e8	+	3.38574e9i	−0.00378002	+	0.0214375i
$309$		0			0
$310$	−1.51146e11	−	5.50126e10i	−0.929541	−	0.338325i
$311$	−6.13619e9	−	2.23339e9i	−0.0371944	−	0.0135376i	0.323356	−	0.946277i	$-0.395189\pi$
$311$	−6.13619e9	−	2.23339e9i	−0.0371944	−	0.0135376i	−0.360550	+	0.932740i	$0.617411\pi$
$312$		0			0
$313$	4.11967e10	−	2.33638e11i	0.242612	−	1.37592i	−0.583361	−	0.812213i	$-0.698263\pi$
$313$	4.11967e10	−	2.33638e11i	0.242612	−	1.37592i	0.825973	−	0.563709i	$-0.190626\pi$
$314$	−6.73333e10	−	1.16625e11i	−0.390883	−	0.677029i
$315$		0			0
$316$	4.69606e10	−	8.13381e10i	0.264936	−	0.458883i
$317$	−2.09537e11	−	1.75822e11i	−1.16545	−	0.977929i	−0.165485	−	0.986212i	$-0.552919\pi$
$317$	−2.09537e11	−	1.75822e11i	−1.16545	−	0.977929i	−0.999966	+	0.00828314i	$0.997363\pi$
$318$		0			0
$319$	−1.86912e10	−	1.06003e11i	−0.101060	−	0.573139i
$320$	−1.79113e11	+	1.50294e11i	−0.954889	+	0.801247i
$321$		0			0
$322$	−3.57134e7	+	1.29986e7i	−0.000185131	+	6.73822e-5i
$323$	4.51896e10			0.231008
$324$		0			0
$325$	−7.37347e10			−0.366604
$326$	2.58723e11	−	9.41674e10i	1.26869	−	0.461765i
$327$		0			0
$328$	2.26676e11	−	1.90204e11i	1.08137	−	0.907374i
$329$	−3.01783e9	−	1.71150e10i	−0.0142008	−	0.0805369i
$330$		0			0
$331$	−1.45802e11	−	1.22342e11i	−0.667631	−	0.560209i	0.244732	−	0.969591i	$-0.421300\pi$
$331$	−1.45802e11	−	1.22342e11i	−0.667631	−	0.560209i	−0.912363	+	0.409382i	$0.865744\pi$
$332$	5.57744e9	−	9.66041e9i	0.0251950	−	0.0436389i
$333$		0			0
$334$	1.64724e11	+	2.85310e11i	0.724264	+	1.25446i
$335$	6.49430e10	−	3.68310e11i	0.281729	−	1.59776i
$336$		0			0
$337$	−2.47427e11	−	9.00562e10i	−1.04499	−	0.380346i	−0.238221	−	0.971211i	$-0.576564\pi$
$337$	−2.47427e11	−	9.00562e10i	−1.04499	−	0.380346i	−0.806771	+	0.590865i	$0.798787\pi$
$338$	−3.76152e10	−	1.36908e10i	−0.156761	−	0.0570564i
$339$		0			0
$340$	6.00193e9	−	3.40386e10i	0.0243577	−	0.138139i
$341$	6.93938e10	+	1.20194e11i	0.277924	+	0.481378i
$342$		0			0
$343$	3.19120e10	−	5.52731e10i	0.124489	−	0.215621i
$344$	−1.85705e11	−	1.55825e11i	−0.715007	−	0.599962i
$345$		0			0
$346$	−3.87639e10	−	2.19841e11i	−0.145407	−	0.824644i
$347$	1.87218e11	−	1.57095e11i	0.693210	−	0.581673i	−0.226623	−	0.973983i	$-0.572768\pi$
$347$	1.87218e11	−	1.57095e11i	0.693210	−	0.581673i	0.919833	+	0.392310i	$0.128324\pi$
$348$		0			0
$349$	−1.11185e11	+	4.04679e10i	−0.401172	+	0.146015i	−0.534723	−	0.845027i	$-0.679584\pi$
$349$	−1.11185e11	+	4.04679e10i	−0.401172	+	0.146015i	0.133551	+	0.991042i	$0.457362\pi$
$350$	9.66996e9			0.0344444
$351$		0			0
$352$	9.54377e10			0.331343
$353$	−8.80596e10	+	3.20511e10i	−0.301850	+	0.109864i	−0.488505	−	0.872561i	$-0.662458\pi$
$353$	−8.80596e10	+	3.20511e10i	−0.301850	+	0.109864i	0.186655	+	0.982425i	$0.440235\pi$
$354$		0			0
$355$	−3.50039e11	+	2.93718e11i	−1.16974	+	0.981528i
$356$	−1.56874e10	−	8.89676e10i	−0.0517638	−	0.293567i
$357$		0			0
$358$	3.06977e11	+	2.57584e11i	0.987717	+	0.828793i
$359$	8.91130e10	−	1.54348e11i	0.283150	−	0.490430i	−0.689009	−	0.724753i	$-0.741954\pi$
$359$	8.91130e10	−	1.54348e11i	0.283150	−	0.490430i	0.972159	+	0.234323i	$0.0752874\pi$
$360$		0			0
$361$	9.95100e10	+	1.72356e11i	0.308379	+	0.534128i
$362$	7.09716e10	−	4.02500e11i	0.217218	−	1.23190i
$363$		0			0
$364$	−1.40967e10	−	5.13078e9i	−0.0420883	−	0.0153189i
$365$	−6.95602e11	−	2.53178e11i	−2.05136	−	0.746636i
$366$		0			0
$367$	−2.64512e10	+	1.50012e11i	−0.0761111	+	0.431647i	0.922812	+	0.385251i	$0.125885\pi$
$367$	−2.64512e10	+	1.50012e11i	−0.0761111	+	0.431647i	−0.998923	+	0.0463968i	$0.985226\pi$
$368$	1.91231e8	+	3.31222e8i	0.000543554	+	0.000941464i
$369$		0			0
$370$	−4.58014e10	+	7.93303e10i	−0.127049	+	0.220055i
$371$	−4.95274e10	−	4.15585e10i	−0.135726	−	0.113888i
$372$		0			0
$373$	−1.18121e11	−	6.69899e11i	−0.315965	−	1.79193i	−0.566758	−	0.823884i	$-0.691802\pi$
$373$	−1.18121e11	−	6.69899e11i	−0.315965	−	1.79193i	0.250793	−	0.968041i	$-0.419309\pi$
$374$	4.73566e10	−	3.97369e10i	0.125158	−	0.105020i
$375$		0			0
$376$	−2.58394e11	+	9.40478e10i	−0.666711	+	0.242663i
$377$	4.69674e11			1.19746
$378$		0			0
$379$	−1.34945e11			−0.335954			−0.167977	−	0.985791i	$-0.553723\pi$
$379$	−1.34945e11			−0.335954			−0.167977	+	0.985791i	$0.553723\pi$
$380$	−8.88841e10	+	3.23512e10i	−0.218674	+	0.0795910i
$381$		0			0
$382$	6.36589e10	−	5.34161e10i	0.152959	−	0.128347i
$383$	6.63858e10	+	3.76492e11i	0.157645	+	0.894050i	0.956328	+	0.292297i	$0.0944196\pi$
$383$	6.63858e10	+	3.76492e11i	0.157645	+	0.894050i	−0.798683	+	0.601753i	$0.794469\pi$
$384$		0			0
$385$	−2.55156e10	−	2.14101e10i	−0.0591878	−	0.0496645i
$386$	2.62744e11	−	4.55087e11i	0.602408	−	1.04340i
$387$		0			0
$388$	5.94867e9	+	1.03034e10i	0.0133253	+	0.0230801i
$389$	−7.26294e10	+	4.11902e11i	−0.160820	+	0.912054i	0.792451	+	0.609936i	$0.208805\pi$
$389$	−7.26294e10	+	4.11902e11i	−0.160820	+	0.912054i	−0.953270	+	0.302118i	$0.902306\pi$
$390$		0			0
$391$	−3.09806e8	−	1.12760e8i	−0.000670339	−	0.000243984i
$392$	−4.70708e11	−	1.71324e11i	−1.00685	−	0.366463i
$393$		0			0
$394$	−5.41761e10	+	3.07248e11i	−0.113260	+	0.642327i
$395$	4.54971e11	+	7.88033e11i	0.940365	+	1.62876i
$396$		0			0
$397$	2.77084e11	−	4.79923e11i	0.559827	−	0.969649i	−0.437683	−	0.899129i	$-0.644201\pi$
$397$	2.77084e11	−	4.79923e11i	0.559827	−	0.969649i	0.997510	−	0.0705199i	$-0.0224658\pi$
$398$	4.08889e11	+	3.43099e11i	0.816830	+	0.685401i
$399$		0			0
$400$	−1.68981e10	−	9.58339e10i	−0.0330041	−	0.187176i
$401$	−7.45020e10	+	6.25146e10i	−0.143886	+	0.120735i	−0.711890	−	0.702291i	$-0.752160\pi$
$401$	−7.45020e10	+	6.25146e10i	−0.143886	+	0.120735i	0.568004	+	0.823026i	$0.307716\pi$
$402$		0			0
$403$	−5.69071e11	+	2.07125e11i	−1.07472	+	0.391165i
$404$	2.41591e10			0.0451195
$405$		0			0
$406$	−6.15956e10			−0.112508
$407$	7.42736e10	−	2.70334e10i	0.134171	−	0.0488344i
$408$		0			0
$409$	2.35442e11	−	1.97559e11i	0.416033	−	0.349093i	−0.410618	−	0.911807i	$-0.634687\pi$
$409$	2.35442e11	−	1.97559e11i	0.416033	−	0.349093i	0.826652	+	0.562714i	$0.190243\pi$
$410$	1.22229e11	+	6.93195e11i	0.213622	+	1.21151i
$411$		0			0
$412$	−1.81041e11	−	1.51912e11i	−0.309556	−	0.259749i
$413$	6.90965e10	−	1.19679e11i	0.116864	−	0.202414i
$414$		0			0
$415$	5.40362e10	+	9.35935e10i	0.0894270	+	0.154892i
$416$	−7.23136e10	+	4.10111e11i	−0.118386	+	0.671400i
$417$		0			0
$418$	−1.58975e11	−	5.78623e10i	−0.254705	−	0.0927049i
$419$	−7.46444e11	−	2.71683e11i	−1.18313	−	0.430626i	−0.325827	−	0.945430i	$-0.605643\pi$
$419$	−7.46444e11	−	2.71683e11i	−1.18313	−	0.430626i	−0.857308	+	0.514804i	$0.827865\pi$
$420$		0			0
$421$	−6.14953e10	+	3.48757e11i	−0.0954053	+	0.541070i	0.899217	+	0.437503i	$0.144137\pi$
$421$	−6.14953e10	+	3.48757e11i	−0.0954053	+	0.541070i	−0.994622	+	0.103568i	$0.966974\pi$
$422$	9.83421e10	+	1.70334e11i	0.150950	+	0.261453i
$423$		0			0
$424$	−5.11486e11	+	8.85920e11i	−0.768577	+	1.33121i
$425$	6.42596e10	+	5.39202e10i	0.0955405	+	0.0801680i
$426$		0			0
$427$	−1.35220e10	−	7.66869e10i	−0.0196841	−	0.111634i
$428$	2.90518e11	−	2.43773e11i	0.418481	−	0.351147i
$429$		0			0
$430$	5.41886e11	−	1.97230e11i	0.764363	−	0.278205i
$431$	4.28096e11			0.597576			0.298788	−	0.954319i	$-0.403418\pi$
$431$	4.28096e11			0.597576			0.298788	+	0.954319i	$0.403418\pi$
$432$		0			0
$433$	1.26300e12			1.72666			0.863330	−	0.504639i	$-0.168375\pi$
$433$	1.26300e12			1.72666			0.863330	+	0.504639i	$0.168375\pi$
$434$	7.46310e10	−	2.71635e10i	0.100975	−	0.0367520i
$435$		0			0
$436$	9.65667e10	−	8.10291e10i	0.127979	−	0.107387i
$437$	1.56672e8	+	8.88533e8i	0.000205507	+	0.00116549i
$438$		0			0
$439$	6.80449e11	+	5.70965e11i	0.874390	+	0.733701i	0.965018	−	0.262184i	$-0.0844428\pi$
$439$	6.80449e11	+	5.70965e11i	0.874390	+	0.733701i	−0.0906275	+	0.995885i	$0.528887\pi$
$440$	−2.63508e11	+	4.56409e11i	−0.335163	+	0.580520i
$441$		0			0
$442$	1.34874e11	+	2.33608e11i	0.168084	+	0.291130i
$443$	4.14262e9	−	2.34940e10i	0.00511044	−	0.0289827i	−0.982146	−	0.188121i	$-0.939760\pi$
$443$	4.14262e9	−	2.34940e10i	0.00511044	−	0.0289827i	0.987256	+	0.159138i	$0.0508715\pi$
$444$		0			0
$445$	8.22463e11	+	2.99352e11i	0.994252	+	0.361878i
$446$	−1.12572e11	−	4.09729e10i	−0.134718	−	0.0490332i
$447$		0			0
$448$	2.00478e10	−	1.13697e11i	0.0235134	−	0.133351i
$449$	−2.17348e11	−	3.76458e11i	−0.252375	−	0.437127i	0.711804	−	0.702378i	$-0.247878\pi$
$449$	−2.17348e11	−	3.76458e11i	−0.252375	−	0.437127i	−0.964179	+	0.265251i	$0.914545\pi$
$450$		0			0
$451$	3.03679e11	−	5.25987e11i	0.345637	−	0.598660i
$452$	−2.52760e11	−	2.12091e11i	−0.284830	−	0.239001i
$453$		0			0
$454$	−9.81341e9	−	5.56546e10i	−0.0108410	−	0.0614823i
$455$	1.11336e11	−	9.34221e10i	0.121782	−	0.102188i
$456$		0			0
$457$	1.03488e12	−	3.76664e11i	1.10985	−	0.403954i	0.278914	−	0.960316i	$-0.410026\pi$
$457$	1.03488e12	−	3.76664e11i	1.10985	−	0.403954i	0.830940	+	0.556362i	$0.187803\pi$
$458$	−3.26929e11			−0.347183
$459$		0			0
$460$	6.90087e8			0.000718611
$461$	6.56893e10	−	2.39090e10i	0.0677393	−	0.0246551i	−0.307928	−	0.951410i	$-0.599636\pi$
$461$	6.56893e10	−	2.39090e10i	0.0677393	−	0.0246551i	0.375668	+	0.926754i	$0.377413\pi$
$462$		0			0
$463$	−4.84959e11	+	4.06929e11i	−0.490445	+	0.411532i	−0.854186	−	0.519968i	$-0.825944\pi$
$463$	−4.84959e11	+	4.06929e11i	−0.490445	+	0.411532i	0.363741	+	0.931500i	$0.381499\pi$
$464$	1.07637e11	+	6.10441e11i	0.107803	+	0.611383i
$465$		0			0
$466$	6.15969e10	+	5.16860e10i	0.0605094	+	0.0507734i
$467$	−5.33198e11	+	9.23527e11i	−0.518756	+	0.898511i	0.481007	+	0.876717i	$0.340271\pi$
$467$	−5.33198e11	+	9.23527e11i	−0.518756	+	0.898511i	−0.999762	+	0.0217944i	$0.993062\pi$
$468$		0			0
$469$	9.23327e10	+	1.59925e11i	0.0881207	+	0.152629i
$470$	1.13585e11	−	6.44171e11i	0.107369	−	0.608921i
$471$		0			0
$472$	−2.05468e12	−	7.47842e11i	−1.90548	−	0.693539i
$473$	−4.67571e11	−	1.70182e11i	−0.429509	−	0.156329i
$474$		0			0
$475$	3.98632e10	−	2.26075e11i	0.0359294	−	0.203766i
$476$	8.53324e9	+	1.47800e10i	0.00761873	+	0.0131960i
$477$		0			0
$478$	−6.42739e11	+	1.11326e12i	−0.563130	+	0.975370i
$479$	−5.72842e11	−	4.80671e11i	−0.497193	−	0.417194i	0.359403	−	0.933182i	$-0.382980\pi$
$479$	−5.72842e11	−	4.80671e11i	−0.497193	−	0.417194i	−0.856596	+	0.515988i	$0.827425\pi$
$480$		0			0
$481$	5.98893e10	+	3.39649e11i	0.0510148	+	0.289319i
$482$	4.73666e11	−	3.97453e11i	0.399724	−	0.335409i
$483$		0			0
$484$	−2.64271e11	+	9.61870e10i	−0.218900	+	0.0796732i
$485$	−1.15266e11			−0.0945936
$486$		0			0
$487$	6.87914e11			0.554184			0.277092	−	0.960843i	$-0.410629\pi$
$487$	6.87914e11			0.554184			0.277092	+	0.960843i	$0.410629\pi$
$488$	−1.15778e12	+	4.21399e11i	−0.924141	+	0.336360i
$489$		0			0
$490$	9.12793e11	−	7.65924e11i	0.715303	−	0.600210i
$491$	3.57819e11	+	2.02929e12i	0.277841	+	1.57572i	0.729789	+	0.683672i	$0.239618\pi$
$491$	3.57819e11	+	2.02929e12i	0.277841	+	1.57572i	−0.451948	+	0.892045i	$0.649271\pi$
$492$		0			0
$493$	−4.09320e11	−	3.43460e11i	−0.312070	−	0.261858i
$494$	3.69100e11	−	6.39300e11i	0.278852	−	0.482985i
$495$		0			0
$496$	−3.99619e11	−	6.92161e11i	−0.296469	−	0.513499i
$497$	3.91793e10	−	2.22197e11i	0.0288040	−	0.163356i
$498$		0			0
$499$	2.01988e12	+	7.35175e11i	1.45839	+	0.530809i	0.944920	−	0.327300i	$-0.106139\pi$
$499$	2.01988e12	+	7.35175e11i	1.45839	+	0.530809i	0.513466	+	0.858110i	$0.328361\pi$
$500$	3.28663e11	+	1.19624e11i	0.235172	+	0.0855957i
$501$		0			0
$502$	9.23340e10	−	5.23652e11i	0.0648925	−	0.368024i
$503$	7.52953e10	+	1.30415e11i	0.0524460	+	0.0908391i	0.891057	−	0.453892i	$-0.149965\pi$
$503$	7.52953e10	+	1.30415e11i	0.0524460	+	0.0908391i	−0.838611	+	0.544731i	$0.816632\pi$
$504$		0			0
$505$	−1.17031e11	+	2.02703e11i	−0.0800735	+	0.138691i
$506$	9.45506e8	+	7.93373e8i	0.000641190	+	0.000538022i
$507$		0			0
$508$	1.12326e11	+	6.37030e11i	0.0748328	+	0.424398i
$509$	1.00277e12	−	8.41426e11i	0.662174	−	0.555630i	−0.248563	−	0.968616i	$-0.579958\pi$
$509$	1.00277e12	−	8.41426e11i	0.662174	−	0.555630i	0.910738	+	0.412985i	$0.135514\pi$
$510$		0			0
$511$	3.43466e11	−	1.25011e11i	0.222838	−	0.0811065i
$512$	−1.51218e12			−0.972501
$513$		0			0
$514$	2.54749e11			0.160982
$515$	2.15159e12	−	7.83114e11i	1.34780	−	0.490561i
$516$		0			0
$517$	−4.32358e11	+	3.62792e11i	−0.266156	+	0.223332i
$518$	−7.85420e9	−	4.45434e10i	−0.00479312	−	0.0271831i
$519$		0			0
$520$	−1.76160e12	−	1.47816e12i	−1.05656	−	0.886556i
$521$	5.73452e10	−	9.93248e10i	0.0340979	−	0.0590593i	−0.848473	−	0.529239i	$-0.822478\pi$
$521$	5.73452e10	−	9.93248e10i	0.0340979	−	0.0590593i	0.882571	+	0.470180i	$0.155811\pi$
$522$		0			0
$523$	−1.53405e12	−	2.65706e12i	−0.896566	−	1.55290i	−0.831854	−	0.554995i	$-0.812720\pi$
$523$	−1.53405e12	−	2.65706e12i	−0.896566	−	1.55290i	−0.0647127	−	0.997904i	$-0.520613\pi$
$524$	3.30719e10	−	1.87560e11i	0.0191632	−	0.108680i
$525$		0			0
$526$	3.52056e11	+	1.28138e11i	0.200529	+	0.0729865i
$527$	6.47409e11	+	2.35638e11i	0.365621	+	0.133075i
$528$		0			0
$529$	−3.12766e11	+	1.77378e12i	−0.173648	+	0.984804i
$530$	−1.21671e12	−	2.10740e12i	−0.669800	−	1.16013i
$531$		0			0
$532$	2.33524e10	−	4.04475e10i	0.0126395	−	0.0218922i
$533$	2.03015e12	+	1.70350e12i	1.08957	+	0.914259i
$534$		0			0
$535$	6.38027e11	+	3.61843e12i	0.336703	+	1.90954i
$536$	2.23826e12	−	1.87813e12i	1.17130	−	0.982841i
$537$		0			0
$538$	−2.68600e11	+	9.77623e10i	−0.138225	+	0.0503096i
$539$	−1.02815e12			−0.524698
$540$		0			0
$541$	−2.16618e12			−1.08719			−0.543597	−	0.839346i	$-0.682938\pi$
$541$	−2.16618e12			−1.08719			−0.543597	+	0.839346i	$0.682938\pi$
$542$	−9.78453e11	+	3.56128e11i	−0.487016	+	0.177259i
$543$		0			0
$544$	3.62924e11	−	3.04530e11i	0.177673	−	0.149085i
$545$	2.12077e11	+	1.20275e12i	0.102970	+	0.583970i
$546$		0			0
$547$	−2.55652e12	−	2.14518e12i	−1.22098	−	1.02452i	−0.998773	−	0.0495193i	$-0.984231\pi$
$547$	−2.55652e12	−	2.14518e12i	−1.22098	−	1.02452i	−0.222202	−	0.975001i	$-0.571324\pi$
$548$	2.59677e11	−	4.49773e11i	0.123004	−	0.213050i
$549$		0			0
$550$	−1.57022e11	−	2.71970e11i	−0.0731691	−	0.126733i
$551$	−2.53920e11	+	1.44005e12i	−0.117358	+	0.665573i
$552$		0			0
$553$	−4.22204e11	−	1.53670e11i	−0.191982	−	0.0698756i
$554$	−2.98452e12	−	1.08628e12i	−1.34611	−	0.489944i
$555$		0			0
$556$	−4.63118e10	+	2.62648e11i	−0.0205521	+	0.116557i
$557$	1.36006e12	+	2.35570e12i	0.598702	+	1.03698i	0.993013	+	0.118006i	$0.0376501\pi$
$557$	1.36006e12	+	2.35570e12i	0.598702	+	1.03698i	−0.394311	+	0.918977i	$0.629017\pi$
$558$		0			0
$559$	1.08558e12	−	1.88028e12i	0.470229	−	0.814460i
$560$	1.46937e11	+	1.23295e11i	0.0631372	+	0.0529784i
$561$		0			0
$562$	1.68613e11	+	9.56250e11i	0.0712979	+	0.404351i
$563$	2.02498e12	−	1.69916e12i	0.849441	−	0.712766i	−0.110225	−	0.993907i	$-0.535157\pi$
$563$	2.02498e12	−	1.69916e12i	0.849441	−	0.712766i	0.959667	+	0.281141i	$0.0907128\pi$
$564$		0			0
$565$	3.00393e12	−	1.09334e12i	1.24014	−	0.451376i
$566$	−1.36426e12			−0.558757
$567$		0			0
$568$	−3.56992e12			−1.43910
$569$	−1.25065e12	+	4.55200e11i	−0.500186	+	0.182053i	−0.579778	−	0.814775i	$-0.696861\pi$
$569$	−1.25065e12	+	4.55200e11i	−0.500186	+	0.182053i	0.0795917	+	0.996828i	$0.474638\pi$
$570$		0			0
$571$	−1.49100e12	+	1.25110e12i	−0.586969	+	0.492526i	−0.887227	−	0.461332i	$-0.847372\pi$
$571$	−1.49100e12	+	1.25110e12i	−0.586969	+	0.492526i	0.300258	+	0.953858i	$0.402927\pi$
$572$	8.45994e10	+	4.79787e11i	0.0330434	+	0.187399i
$573$		0			0
$574$	−2.66245e11	−	2.23406e11i	−0.102371	−	0.0858996i
$575$	−8.37409e8	+	1.45043e9i	−0.000319471	+	0.000553341i
$576$		0			0
$577$	−8.98161e11	−	1.55566e12i	−0.337336	−	0.584283i	0.646595	−	0.762834i	$-0.276193\pi$
$577$	−8.98161e11	−	1.55566e12i	−0.337336	−	0.584283i	−0.983931	+	0.178550i	$0.942859\pi$
$578$	−3.29411e11	+	1.86818e12i	−0.122762	+	0.696216i
$579$		0			0
$580$	1.05098e12	+	3.82525e11i	0.385628	+	0.140357i
$581$	−5.01446e10	−	1.82511e10i	−0.0182571	−	0.00664504i
$582$		0			0
$583$	−3.64609e11	+	2.06780e12i	−0.130713	+	0.741310i
$584$	−2.89161e12	−	5.00842e12i	−1.02868	−	1.78173i
$585$		0			0
$586$	−2.12783e11	+	3.68552e11i	−0.0745416	+	0.129110i
$587$	−3.44036e12	−	2.88680e12i	−1.19600	−	1.00357i	−0.999735	−	0.0230158i	$-0.992673\pi$
$587$	−3.44036e12	−	2.88680e12i	−1.19600	−	1.00357i	−0.196268	−	0.980550i	$-0.562882\pi$
$588$		0			0
$589$	−3.27401e11	−	1.85679e12i	−0.112089	−	0.635687i
$590$	3.98442e12	−	3.34332e12i	1.35373	−	1.13591i
$591$		0			0
$592$	−4.27721e11	+	1.55678e11i	−0.143124	+	0.0520929i
$593$	2.68424e12			0.891407			0.445703	−	0.895181i	$-0.352954\pi$
$593$	2.68424e12			0.891407			0.445703	+	0.895181i	$0.352954\pi$
$594$		0			0
$595$	−1.65346e11			−0.0540838
$596$	−7.48784e10	+	2.72535e10i	−0.0243080	+	0.00884738i
$597$		0			0
$598$	−4.12567e9	+	3.46185e9i	−0.00131929	+	0.00110701i
$599$	−8.87977e10	−	5.03597e11i	−0.0281826	−	0.159832i	0.967469	−	0.252991i	$-0.0814144\pi$
$599$	−8.87977e10	−	5.03597e11i	−0.0281826	−	0.159832i	−0.995651	+	0.0931597i	$0.970303\pi$
$600$		0			0
$601$	2.07245e12	+	1.73900e12i	0.647962	+	0.543705i	0.906452	−	0.422309i	$-0.138780\pi$
$601$	2.07245e12	+	1.73900e12i	0.647962	+	0.543705i	−0.258490	+	0.966014i	$0.583225\pi$
$602$	−1.42369e11	+	2.46590e11i	−0.0441805	+	0.0765229i
$603$		0			0
$604$	5.77575e11	+	1.00039e12i	0.176580	+	0.305846i
$605$	4.73135e11	−	2.68328e12i	0.143577	−	0.814267i
$606$		0			0
$607$	−4.72762e10	−	1.72071e10i	−0.0141349	−	0.00514470i	0.334943	−	0.942238i	$-0.391283\pi$
$607$	−4.72762e10	−	1.72071e10i	−0.0141349	−	0.00514470i	−0.349078	+	0.937094i	$0.613505\pi$
$608$	−1.21833e12	−	4.43436e11i	−0.361576	−	0.131603i
$609$		0			0
$610$	5.08938e11	−	2.88633e12i	0.148827	−	0.844038i
$611$	−1.23137e12	−	2.13280e12i	−0.357441	−	0.619107i
$612$		0			0
$613$	6.02886e9	−	1.04423e10i	0.00172450	−	0.00298692i	−0.865162	−	0.501493i	$-0.832784\pi$
$613$	6.02886e9	−	1.04423e10i	0.00172450	−	0.00298692i	0.866886	+	0.498506i	$0.166118\pi$
$614$	7.63299e10	+	6.40484e10i	0.0216739	+	0.0181866i
$615$		0			0
$616$	−4.51874e10	−	2.56270e11i	−0.0126446	−	0.0717109i
$617$	3.43937e12	−	2.88597e12i	0.955422	−	0.801694i	−0.0247802	−	0.999693i	$-0.507889\pi$
$617$	3.43937e12	−	2.88597e12i	0.955422	−	0.801694i	0.980202	+	0.197999i	$0.0634441\pi$
$618$		0			0
$619$	6.52254e12	−	2.37401e12i	1.78570	−	0.649942i	0.786214	−	0.617954i	$-0.212038\pi$
$619$	6.52254e12	−	2.37401e12i	1.78570	−	0.649942i	0.999488	−	0.0319882i	$-0.0101839\pi$
$620$	−1.44209e12			−0.391949
$621$		0			0
$622$	1.21356e11			0.0325091
$623$	−4.06106e11	+	1.47811e11i	−0.108005	+	0.0393106i
$624$		0			0
$625$	−3.57248e12	+	2.99767e12i	−0.936504	+	0.785821i
$626$	7.65614e11	+	4.34201e12i	0.199262	+	1.13007i
$627$		0			0
$628$	−9.24903e11	−	7.76086e11i	−0.237289	−	0.199109i
$629$	1.96183e11	−	3.39799e11i	0.0499727	−	0.0865553i
$630$		0			0
$631$	2.17006e12	+	3.75865e12i	0.544928	+	0.943843i	0.998611	+	0.0526798i	$0.0167763\pi$
$631$	2.17006e12	+	3.75865e12i	0.544928	+	0.943843i	−0.453684	+	0.891163i	$0.649890\pi$
$632$	−1.23447e12	+	7.00100e12i	−0.307788	+	1.74555i
$633$		0			0
$634$	4.77684e12	+	1.73863e12i	1.17419	+	0.427370i
$635$	−5.88904e12	−	2.14343e12i	−1.43735	−	0.523152i
$636$		0			0
$637$	7.79039e11	−	4.41815e12i	0.187470	−	1.06319i
$638$	1.00019e12	+	1.73239e12i	0.238996	+	0.413954i
$639$		0			0
$640$	6.49057e11	−	1.12420e12i	0.152923	−	0.264871i
$641$	6.22809e12	+	5.22599e12i	1.45712	+	1.22267i	0.927174	+	0.374631i	$0.122231\pi$
$641$	6.22809e12	+	5.22599e12i	1.45712	+	1.22267i	0.529942	+	0.848034i	$0.322214\pi$
$642$		0			0
$643$	−7.54498e11	−	4.27897e12i	−0.174064	−	0.987165i	−0.939219	−	0.343319i	$-0.888449\pi$
$643$	−7.54498e11	−	4.27897e12i	−0.174064	−	0.987165i	0.765155	−	0.643846i	$-0.222662\pi$
$644$	−2.61025e8	+	2.19026e8i	−5.97991e−5	+	5.01774e-5i
$645$		0			0
$646$	−7.89173e11	+	2.87235e11i	−0.178290	+	0.0648921i
$647$	−5.86334e12			−1.31545			−0.657727	−	0.753256i	$-0.728482\pi$
$647$	−5.86334e12			−1.31545			−0.657727	+	0.753256i	$0.728482\pi$
$648$		0			0
$649$	−4.48798e12			−0.993002
$650$	1.28767e12	−	4.68675e11i	0.282941	−	0.102982i
$651$		0			0
$652$	1.89097e12	−	1.58671e12i	0.409799	−	0.343862i
$653$	1.16333e12	+	6.59756e12i	0.250376	+	1.41995i	0.807669	+	0.589636i	$0.200729\pi$
$653$	1.16333e12	+	6.59756e12i	0.250376	+	1.41995i	−0.557293	+	0.830316i	$0.688160\pi$
$654$		0			0
$655$	1.41349e12	+	1.18606e12i	0.300059	+	0.251780i
$656$	−1.74880e12	+	3.02901e12i	−0.368700	+	0.638607i
$657$		0			0
$658$	1.61489e11	+	2.79707e11i	0.0335835	+	0.0581684i
$659$	4.47489e10	−	2.53783e11i	0.00924267	−	0.0524178i	−0.979838	−	0.199796i	$-0.935972\pi$
$659$	4.47489e10	−	2.53783e11i	0.00924267	−	0.0524178i	0.989080	+	0.147378i	$0.0470833\pi$
$660$		0			0
$661$	−4.08951e12	−	1.48846e12i	−0.833229	−	0.303271i	−0.110046	−	0.993927i	$-0.535100\pi$
$661$	−4.08951e12	−	1.48846e12i	−0.833229	−	0.303271i	−0.723184	+	0.690656i	$0.757322\pi$
$662$	3.32386e12	+	1.20978e12i	0.672638	+	0.244820i
$663$		0			0
$664$	−1.46616e11	+	8.31499e11i	−0.0292701	+	0.165999i
$665$	2.26246e11	+	3.91870e11i	0.0448626	+	0.0777042i
$666$		0			0
$667$	5.33411e9	−	9.23895e9i	0.00104351	−	0.00180741i
$668$	2.26268e12	+	1.89861e12i	0.439671	+	0.368928i
$669$		0			0
$670$	1.20693e12	+	6.84481e12i	0.231390	+	1.31228i
$671$	−1.93726e12	+	1.62556e12i	−0.368924	+	0.309564i
$672$		0			0
$673$	4.63098e12	−	1.68554e12i	0.870173	−	0.316717i	0.131936	−	0.991258i	$-0.457881\pi$
$673$	4.63098e12	−	1.68554e12i	0.870173	−	0.316717i	0.738237	+	0.674541i	$0.235659\pi$
$674$	4.89339e12			0.913356
$675$		0			0
$676$	−3.58889e11			−0.0660998
$677$	−8.07971e11	+	2.94078e11i	−0.147825	+	0.0538038i	−0.414873	−	0.909879i	$-0.636174\pi$
$677$	−8.07971e11	+	2.94078e11i	−0.147825	+	0.0538038i	0.267048	+	0.963683i	$0.413952\pi$
$678$		0			0
$679$	4.35990e10	−	3.65839e10i	0.00787160	−	0.00660505i
$680$	4.54293e11	+	2.57642e12i	0.0814790	+	0.462091i
$681$		0			0
$682$	−1.97584e12	−	1.65793e12i	−0.349722	−	0.293451i
$683$	−2.19930e12	+	3.80931e12i	−0.386716	+	0.669812i	−0.992006	−	0.126194i	$-0.959724\pi$
$683$	−2.19930e12	+	3.80931e12i	−0.386716	+	0.669812i	0.605290	+	0.796005i	$0.293057\pi$
$684$		0			0
$685$	2.51584e12	+	4.35756e12i	0.436592	+	0.756199i
$686$	−2.05969e11	+	1.16811e12i	−0.0355094	+	0.201384i
$687$		0			0
$688$	2.69261e12	+	9.80031e11i	0.458169	+	0.166760i
$689$	−8.60940e12	−	3.13356e12i	−1.45541	−	0.529727i
$690$		0			0
$691$	−1.08407e12	+	6.14808e12i	−0.180887	+	1.02586i	0.750240	+	0.661166i	$0.229938\pi$
$691$	−1.08407e12	+	6.14808e12i	−0.180887	+	1.02586i	−0.931127	+	0.364695i	$0.881173\pi$
$692$	−1.00071e12	−	1.73329e12i	−0.165895	−	0.287338i
$693$		0			0
$694$	−2.27097e12	+	3.93344e12i	−0.371616	+	0.643657i
$695$	−1.97937e12	−	1.66088e12i	−0.321806	−	0.270027i
$696$		0			0
$697$	−5.23548e11	−	2.96919e12i	−0.0840251	−	0.476530i
$698$	1.68446e12	−	1.41343e12i	0.268603	−	0.225385i
$699$		0			0
$700$	8.14691e10	−	2.96523e10i	0.0128248	−	0.00466785i
$701$	1.23156e13			1.92630			0.963150	−	0.268965i	$-0.0866815\pi$
$701$	1.23156e13			1.92630			0.963150	+	0.268965i	$0.0866815\pi$
$702$		0			0
$703$	−1.07376e12			−0.165810
$704$	−3.52329e12	+	1.28237e12i	−0.540593	+	0.196760i
$705$		0			0
$706$	1.33411e12	−	1.11945e12i	0.202102	−	0.169584i
$707$	−2.00689e10	−	1.13816e11i	−0.00302090	−	0.0171324i
$708$		0			0
$709$	6.51478e12	+	5.46655e12i	0.968259	+	0.812466i	0.982277	−	0.187436i	$-0.0600178\pi$
$709$	6.51478e12	+	5.46655e12i	0.968259	+	0.812466i	−0.0140180	+	0.999902i	$0.504462\pi$
$710$	4.24601e12	−	7.35430e12i	0.627073	−	1.08612i
$711$		0			0
$712$	3.41897e12	+	5.92184e12i	0.498581	+	0.863568i
$713$	−2.38862e9	+	1.35465e10i	−0.000346133	+	0.00196302i
$714$		0			0
$715$	−4.43540e12	−	1.61435e12i	−0.634681	−	0.231005i
$716$	3.37614e12	+	1.22881e12i	0.480078	+	0.174734i
$717$		0			0
$718$	−5.75161e11	+	3.26190e12i	−0.0807661	+	0.458047i
$719$	3.51879e12	+	6.09472e12i	0.491036	+	0.850499i	0.999947	−	0.0103202i	$-0.00328507\pi$
$719$	3.51879e12	+	6.09472e12i	0.491036	+	0.850499i	−0.508911	+	0.860819i	$0.669952\pi$
$720$		0			0
$721$	−5.65284e11	+	9.79101e11i	−0.0779037	+	0.134933i
$722$	−2.83334e12	−	2.37745e12i	−0.388044	−	0.325608i
$723$		0			0
$724$	−6.36307e11	−	3.60868e12i	−0.0860683	−	0.488117i
$725$	−2.07934e12	+	1.74477e12i	−0.279515	+	0.234541i
$726$		0			0
$727$	−6.18464e12	+	2.25102e12i	−0.821125	+	0.298865i	−0.718211	−	0.695825i	$-0.755039\pi$
$727$	−6.18464e12	+	2.25102e12i	−0.821125	+	0.298865i	−0.102914	+	0.994690i	$0.532817\pi$
$728$	1.13547e12			0.149826
$729$		0			0
$730$	1.37570e13			1.79296
$731$	−2.32108e12	+	8.44804e11i	−0.300650	+	0.109428i
$732$		0			0
$733$	3.20204e12	−	2.68683e12i	0.409693	−	0.343773i	−0.414533	−	0.910034i	$-0.636055\pi$
$733$	3.20204e12	−	2.68683e12i	0.409693	−	0.343773i	0.824226	+	0.566261i	$0.191611\pi$
$734$	−4.91579e11	−	2.78788e12i	−0.0625116	−	0.354521i
$735$		0			0
$736$	7.24602e9	+	6.08013e9i	0.000910226	+	0.000763770i
$737$	2.99861e12	−	5.19375e12i	0.374384	−	0.648451i
$738$		0			0
$739$	−3.48679e12	−	6.03931e12i	−0.430057	−	0.744881i	0.566820	−	0.823841i	$-0.308173\pi$
$739$	−3.48679e12	−	6.03931e12i	−0.430057	−	0.744881i	−0.996878	+	0.0789601i	$0.974840\pi$
$740$	−1.42614e11	+	8.08802e11i	−0.0174831	+	0.0991515i
$741$		0			0
$742$	1.12908e12	+	4.10952e11i	0.136744	+	0.0497707i
$743$	−9.07412e12	−	3.30271e12i	−1.09233	−	0.397577i	−0.267848	−	0.963461i	$-0.586313\pi$
$743$	−9.07412e12	−	3.30271e12i	−1.09233	−	0.397577i	−0.824484	+	0.565885i	$0.808535\pi$
$744$		0			0
$745$	1.34058e11	−	7.60278e11i	0.0159437	−	0.0904210i
$746$	6.32086e12	+	1.09480e13i	0.747225	+	1.29423i
$747$		0			0
$748$	2.77127e11	−	4.79998e11i	0.0323684	−	0.0560638i
$749$	−1.38978e12	−	1.16616e12i	−0.161353	−	0.135392i
$750$		0			0
$751$	8.52907e11	+	4.83708e12i	0.0978413	+	0.554885i	0.993840	+	0.110828i	$0.0353503\pi$
$751$	8.52907e11	+	4.83708e12i	0.0978413	+	0.554885i	−0.895998	+	0.444057i	$0.853539\pi$
$752$	2.48983e12	−	2.08922e12i	0.283916	−	0.238234i
$753$		0			0
$754$	−8.20220e12	+	2.98536e12i	−0.924186	+	0.336376i
$755$	−1.11915e13			−1.25351
$756$		0			0
$757$	−4.59607e12			−0.508692			−0.254346	−	0.967113i	$-0.581860\pi$
$757$	−4.59607e12			−0.508692			−0.254346	+	0.967113i	$0.581860\pi$
$758$	2.35662e12	−	8.57740e11i	0.259286	−	0.0943723i
$759$		0			0
$760$	5.48450e12	−	4.60205e12i	0.596316	−	0.500368i
$761$	−1.02595e12	−	5.81848e12i	−0.110891	−	0.628895i	−0.988703	−	0.149889i	$-0.952108\pi$
$761$	−1.02595e12	−	5.81848e12i	−0.110891	−	0.628895i	0.877812	−	0.479006i	$-0.159003\pi$
$762$		0			0
$763$	−4.61956e11	−	3.87627e11i	−0.0493447	−	0.0414051i
$764$	3.72526e11	−	6.45235e11i	0.0395582	−	0.0685169i
$765$		0			0
$766$	−3.55241e12	−	6.15295e12i	−0.372815	−	0.645734i
$767$	3.40057e12	−	1.92856e13i	0.354791	−	2.01212i
$768$		0			0
$769$	−1.45061e13	−	5.27977e12i	−1.49583	−	0.544436i	−0.540849	−	0.841119i	$-0.681897\pi$
$769$	−1.45061e13	−	5.27977e12i	−1.49583	−	0.544436i	−0.954976	+	0.296684i	$0.904119\pi$
$770$	5.81682e11	+	2.11715e11i	0.0596317	+	0.0217042i
$771$		0			0
$772$	8.18118e11	−	4.63978e12i	0.0828969	−	0.470132i
$773$	−5.05669e11	−	8.75844e11i	−0.0509400	−	0.0882306i	0.839431	−	0.543466i	$-0.182888\pi$
$773$	−5.05669e11	−	8.75844e11i	−0.0509400	−	0.0882306i	−0.890371	+	0.455236i	$0.849555\pi$
$774$		0			0
$775$	1.74995e12	−	3.03100e12i	0.174248	−	0.301807i
$776$	−6.89841e11	−	5.78845e11i	−0.0682922	−	0.0573039i
$777$		0			0
$778$	−1.34977e12	−	7.65494e12i	−0.132085	−	0.749089i
$779$	−6.32059e12	+	5.30361e12i	−0.614949	+	0.516004i
$780$		0			0
$781$	−6.88552e12	+	2.50613e12i	−0.662228	+	0.241031i
$782$	6.12706e9			0.000585898
$783$		0			0
$784$	5.92086e12			0.559709
$785$	1.09920e13	−	4.00077e12i	1.03315	−	0.376037i
$786$		0			0
$787$	−1.50781e12	+	1.26520e12i	−0.140107	+	0.117564i	−0.710148	−	0.704053i	$-0.751372\pi$
$787$	−1.50781e12	+	1.26520e12i	−0.140107	+	0.117564i	0.570041	+	0.821616i	$0.306927\pi$
$788$	4.85725e11	+	2.75468e12i	0.0448768	+	0.254509i
$789$		0			0
$790$	−1.29543e13	−	1.08700e13i	−1.18330	−	0.992903i
$791$	−7.89219e11	+	1.36697e12i	−0.0716809	+	0.124155i
$792$		0			0
$793$	−5.51741e12	−	9.55643e12i	−0.495457	−	0.858156i
$794$	−1.78838e12	+	1.01424e13i	−0.159686	+	0.905625i
$795$		0			0
$796$	4.49696e12	+	1.63676e12i	0.397018	+	0.144503i
$797$	−1.89101e13	−	6.88272e12i	−1.66009	−	0.604223i	−0.669713	−	0.742620i	$-0.733583\pi$
$797$	−1.89101e13	−	6.88272e12i	−1.66009	−	0.604223i	−0.990377	+	0.138396i	$0.955805\pi$
$798$		0			0
$799$	−4.86522e11	+	2.75920e12i	−0.0422320	+	0.239510i
$800$	−1.20336e12	−	2.08428e12i	−0.103870	−	0.179908i
$801$		0			0
$802$	9.03715e11	−	1.56528e12i	0.0771342	−	0.133600i
$803$	−9.09321e12	−	7.63011e12i	−0.771786	−	0.647606i
$804$		0			0
$805$	−5.73255e8	−	3.25109e9i	−4.81134e−5	−	0.000272865i
$806$	8.62150e12	−	7.23429e12i	0.719573	−	0.603794i
$807$		0			0
$808$	−1.71835e12	+	6.25428e11i	−0.141827	+	0.0516209i
$809$	1.35819e12			0.111479			0.0557395	−	0.998445i	$-0.482248\pi$
$809$	1.35819e12			0.111479			0.0557395	+	0.998445i	$0.482248\pi$
$810$		0			0
$811$	6.18683e12			0.502197			0.251099	−	0.967962i	$-0.419208\pi$
$811$	6.18683e12			0.502197			0.251099	+	0.967962i	$0.419208\pi$
$812$	−5.18940e11	+	1.88879e11i	−0.0418905	+	0.0152469i
$813$		0			0
$814$	−1.12525e12	+	9.44200e11i	−0.0898340	+	0.0753797i
$815$	4.15290e12	+	2.35523e13i	0.329718	+	1.86992i
$816$		0			0
$817$	5.17816e12	+	4.34500e12i	0.406609	+	0.341185i
$818$	−2.85593e12	+	4.94661e12i	−0.223027	+	0.386294i
$819$		0			0
$820$	3.15541e12	+	5.46533e12i	0.243721	+	0.422138i
$821$	4.48393e12	−	2.54296e13i	0.344441	−	1.95342i	0.0461901	−	0.998933i	$-0.485292\pi$
$821$	4.48393e12	−	2.54296e13i	0.344441	−	1.95342i	0.298251	−	0.954488i	$-0.403597\pi$
$822$		0			0
$823$	−6.41370e12	−	2.33440e12i	−0.487315	−	0.177368i	0.0866652	−	0.996237i	$-0.472379\pi$
$823$	−6.41370e12	−	2.33440e12i	−0.487315	−	0.177368i	−0.573980	+	0.818869i	$0.694601\pi$
$824$	1.68095e13	+	6.11815e12i	1.27023	+	0.462326i
$825$		0			0
$826$	−4.45969e11	+	2.52921e12i	−0.0333345	+	0.189049i
$827$	−6.35461e12	−	1.10065e13i	−0.472404	−	0.818229i	0.527097	−	0.849805i	$-0.323281\pi$
$827$	−6.35461e12	−	1.10065e13i	−0.472404	−	0.818229i	−0.999501	+	0.0315767i	$0.989947\pi$
$828$		0			0
$829$	8.41727e12	−	1.45791e13i	0.618979	−	1.07210i	−0.370694	−	0.928755i	$-0.620880\pi$
$829$	8.41727e12	−	1.45791e13i	0.618979	−	1.07210i	0.989672	−	0.143347i	$-0.0457866\pi$
$830$	−1.53857e12	−	1.29101e12i	−0.112529	−	0.0944232i
$831$		0			0
$832$	−2.84094e12	−	1.61118e13i	−0.205545	−	1.16570i
$833$	−3.90980e12	+	3.28071e12i	−0.281353	+	0.236084i
$834$		0			0
$835$	−2.68908e13	+	9.78746e12i	−1.91432	+	0.696756i
$836$	−1.51679e12			−0.107398
$837$		0			0
$838$	1.47625e13			1.03410
$839$	2.09727e13	−	7.63342e12i	1.46125	−	0.531852i	0.515541	−	0.856865i	$-0.327591\pi$
$839$	2.09727e13	−	7.63342e12i	1.46125	−	0.531852i	0.945709	+	0.325013i	$0.105369\pi$
$840$		0			0
$841$	2.13183e12	−	1.78882e12i	0.146951	−	0.123306i
$842$	−1.14285e12	−	6.48143e12i	−0.0783584	−	0.444392i
$843$		0			0
$844$	1.35085e12	+	1.13349e12i	0.0916357	+	0.0768915i
$845$	1.73852e12	−	3.01121e12i	0.117307	−	0.203182i
$846$		0			0
$847$	6.72679e11	+	1.16511e12i	0.0449089	+	0.0777845i
$848$	2.09968e12	−	1.19079e13i	0.139435	−	0.790775i
$849$		0			0
$850$	−1.46493e12	−	5.33192e11i	−0.0962570	−	0.0350347i
$851$	7.36140e9	+	2.67933e9i	0.000481146	+	0.000175123i
$852$		0			0
$853$	1.19454e12	−	6.77458e12i	0.0772556	−	0.438139i	−0.921505	−	0.388367i	$-0.873039\pi$
$853$	1.19454e12	−	6.77458e12i	0.0772556	−	0.438139i	0.998761	−	0.0497720i	$-0.0158495\pi$
$854$	7.23582e11	+	1.25328e12i	0.0465508	+	0.0806284i
$855$		0			0
$856$	−1.43527e13	+	2.48596e13i	−0.913697	+	1.58257i
$857$	−9.37934e12	−	7.87020e12i	−0.593962	−	0.498393i	0.295537	−	0.955331i	$-0.404502\pi$
$857$	−9.37934e12	−	7.87020e12i	−0.593962	−	0.498393i	−0.889498	+	0.456938i	$0.848946\pi$
$858$		0			0
$859$	7.76449e11	+	4.40346e12i	0.0486568	+	0.275946i	0.999423	−	0.0339623i	$-0.0108126\pi$
$859$	7.76449e11	+	4.40346e12i	0.0486568	+	0.275946i	−0.950766	+	0.309909i	$0.899702\pi$
$860$	3.96057e12	−	3.32331e12i	0.246896	−	0.207171i
$861$		0			0
$862$	−7.47609e12	+	2.72107e12i	−0.461203	+	0.167864i
$863$	1.77022e13			1.08637			0.543185	−	0.839613i	$-0.317218\pi$
$863$	1.77022e13			1.08637			0.543185	+	0.839613i	$0.317218\pi$
$864$		0			0
$865$	1.93905e13			1.17765
$866$	−2.20565e13	+	8.02790e12i	−1.33262	+	0.485033i
$867$		0			0
$868$	5.45469e11	−	4.57702e11i	0.0326160	−	0.0273681i
$869$	2.53380e12	+	1.43699e13i	0.150724	+	0.854799i
$870$		0			0
$871$	2.00463e13	+	1.68209e13i	1.18019	+	0.990299i
$872$	−4.77077e12	+	8.26322e12i	−0.279424	+	0.483977i
$873$		0			0
$874$	−8.38378e9	−	1.45211e10i	−0.000486002	−	0.000841781i
$875$	2.90542e11	−	1.64775e12i	0.0167561	−	0.0950285i
$876$		0			0
$877$	1.81090e12	+	6.59112e11i	0.103370	+	0.0376237i	0.393187	−	0.919458i	$-0.371372\pi$
$877$	1.81090e12	+	6.59112e11i	0.103370	+	0.0376237i	−0.289817	+	0.957082i	$0.593595\pi$
$878$	−1.55123e13	−	5.64601e12i	−0.880948	−	0.320639i
$879$		0			0
$880$	1.08172e12	−	6.13471e12i	0.0608052	−	0.344844i
$881$	1.42842e13	+	2.47410e13i	0.798850	+	1.38365i	0.920365	+	0.391059i	$0.127891\pi$
$881$	1.42842e13	+	2.47410e13i	0.798850	+	1.38365i	−0.121515	+	0.992590i	$0.538775\pi$
$882$		0			0
$883$	−1.57308e11	+	2.72466e11i	−0.00870821	+	0.0150831i	−0.870347	−	0.492440i	$-0.836105\pi$
$883$	−1.57308e11	+	2.72466e11i	−0.00870821	+	0.0150831i	0.861638	+	0.507523i	$0.169439\pi$
$884$	1.85265e12	+	1.55456e12i	0.102037	+	0.0856192i
$885$		0			0
$886$	7.69880e10	+	4.36621e11i	0.00419731	+	0.0238041i
$887$	−6.42115e12	+	5.38798e12i	−0.348302	+	0.292260i	−0.800108	−	0.599856i	$-0.795224\pi$
$887$	−6.42115e12	+	5.38798e12i	−0.348302	+	0.292260i	0.451806	+	0.892116i	$0.350780\pi$
$888$		0			0
$889$	2.90782e12	−	1.05836e12i	0.156138	−	0.0568297i
$890$	−1.62659e13			−0.869007
$891$		0			0
$892$	−1.07406e12			−0.0568049
$893$	7.20503e12	−	2.62242e12i	0.379144	−	0.137997i
$894$		0			0
$895$	−2.66648e13	+	2.23744e13i	−1.38910	+	1.16560i
$896$	1.11303e11	+	6.31230e11i	0.00576926	+	0.0327191i
$897$		0			0
$898$	6.18853e12	+	5.19279e12i	0.317573	+	0.266476i
$899$	−1.11468e13	+	1.93068e13i	−0.569157	+	0.985809i
$900$		0			0
$901$	5.21157e12	+	9.02671e12i	0.263456	+	0.456318i
$902$	−1.96003e12	+	1.11159e13i	−0.0985900	+	0.559132i
$903$		0			0
$904$	2.34685e13	+	8.54184e12i	1.16877	+	0.425396i
$905$	3.33605e13	+	1.21422e13i	1.65316	+	0.601699i
$906$		0			0
$907$	−1.54084e12	+	8.73856e12i	−0.0756007	+	0.428753i	0.923391	+	0.383860i	$0.125406\pi$
$907$	−1.54084e12	+	8.73856e12i	−0.0756007	+	0.428753i	−0.998992	+	0.0448924i	$0.985705\pi$
$908$	−2.53339e11	−	4.38796e11i	−0.0123685	−	0.0214228i
$909$		0			0
$910$	−1.35052e12	+	2.33916e12i	−0.0652850	+	0.113077i
$911$	1.14696e13	+	9.62414e12i	0.551716	+	0.462945i	0.875522	−	0.483179i	$-0.160518\pi$
$911$	1.14696e13	+	9.62414e12i	0.551716	+	0.462945i	−0.323805	+	0.946124i	$0.604962\pi$
$912$		0			0
$913$	3.00935e11	+	1.70669e12i	0.0143336	+	0.0812898i
$914$	−1.56785e13	+	1.31558e13i	−0.743099	+	0.623534i
$915$		0			0
$916$	−2.75436e12	+	1.00251e12i	−0.129268	+	0.0470497i
$917$	−9.11092e11			−0.0425501
$918$		0			0
$919$	−3.61739e13			−1.67292			−0.836461	−	0.548027i	$-0.815379\pi$
$919$	−3.61739e13			−1.67292			−0.836461	+	0.548027i	$0.815379\pi$
$920$	−4.90835e10	+	1.78649e10i	−0.00225886	+	0.000822159i
$921$		0			0
$922$	−9.95201e11	+	8.35073e11i	−0.0453546	+	0.0380570i
$923$	−5.55203e12	−	3.14871e13i	−0.251793	−	1.42799i
$924$		0			0
$925$	−1.52689e12	−	1.28121e12i	−0.0685757	−	0.0575418i
$926$	5.88259e12	−	1.01889e13i	0.262917	−	0.455386i
$927$		0			0
$928$	7.66513e12	+	1.32764e13i	0.339277	+	0.587644i
$929$	−3.46775e12	+	1.96666e13i	−0.152748	+	0.866280i	0.808067	+	0.589091i	$0.200514\pi$
$929$	−3.46775e12	+	1.96666e13i	−0.152748	+	0.866280i	−0.960815	+	0.277189i	$0.910597\pi$
$930$		0			0
$931$	1.31251e13	+	4.77716e12i	0.572573	+	0.208399i
$932$	6.77444e11	+	2.46569e11i	0.0294104	+	0.0107045i
$933$		0			0
$934$	3.44141e12	−	1.95172e13i	0.147971	−	0.839184i
$935$	2.68490e12	+	4.65039e12i	0.114889	+	0.198993i
$936$		0			0
$937$	1.43376e13	−	2.48334e13i	0.607642	−	1.05247i	−0.383986	−	0.923339i	$-0.625449\pi$
$937$	1.43376e13	−	2.48334e13i	0.607642	−	1.05247i	0.991628	−	0.129127i	$-0.0412176\pi$
$938$	−2.62898e12	−	2.20598e12i	−0.110885	−	0.0930440i
$939$		0			0
$940$	−1.01836e12	−	5.77542e12i	−0.0425429	−	0.241273i
$941$	−2.00326e13	+	1.68093e13i	−0.832881	+	0.698870i	−0.955951	−	0.293528i	$-0.905171\pi$
$941$	−2.00326e13	+	1.68093e13i	−0.832881	+	0.698870i	0.123069	+	0.992398i	$0.460726\pi$
$942$		0			0
$943$	5.65660e10	−	2.05883e10i	0.00232945	−	0.000847850i
$944$	2.58450e13			1.05926
$945$		0			0
$946$	9.24719e12			0.375405
$947$	−1.42502e13	+	5.18665e12i	−0.575766	+	0.209562i	−0.613458	−	0.789728i	$-0.710222\pi$
$947$	−1.42502e13	+	5.18665e12i	−0.575766	+	0.209562i	0.0376913	+	0.999289i	$0.488000\pi$
$948$		0			0
$949$	3.96778e13	−	3.32936e13i	1.58800	−	1.33249i
$950$	7.40832e11	+	4.20147e12i	0.0295096	+	0.167357i
$951$		0			0
$952$	−9.89562e11	−	8.30341e11i	−0.0390460	−	0.0327635i
$953$	4.99811e12	−	8.65697e12i	0.196285	−	0.339976i	−0.751036	−	0.660261i	$-0.770446\pi$
$953$	4.99811e12	−	8.65697e12i	0.196285	−	0.339976i	0.947321	+	0.320286i	$0.103779\pi$
$954$		0			0
$955$	3.60917e12	+	6.25126e12i	0.140408	+	0.243194i
$956$	−2.00132e12	+	1.13501e13i	−0.0774919	+	0.439478i
$957$		0			0
$958$	1.30591e13	+	4.75314e12i	0.500921	+	0.182320i
$959$	−2.33465e12	−	8.49744e11i	−0.0891330	−	0.0324417i
$960$		0			0
$961$	4.00352e11	−	2.27051e12i	0.0151421	−	0.0858752i
$962$	−3.20477e12	−	5.55082e12i	−0.120645	−	0.208963i
$963$		0			0
$964$	2.77186e12	−	4.80099e12i	0.103377	−	0.179054i
$965$	3.49663e13	+	2.93402e13i	1.29801	+	1.08916i
$966$		0			0
$967$	2.08182e12	+	1.18066e13i	0.0765638	+	0.434215i	0.998860	+	0.0477315i	$0.0151992\pi$
$967$	2.08182e12	+	1.18066e13i	0.0765638	+	0.434215i	−0.922296	+	0.386483i	$0.873690\pi$
$968$	1.63066e13	−	1.36829e13i	0.596932	−	0.500885i
$969$		0			0
$970$	2.01295e12	−	7.32654e11i	0.0730063	−	0.0265721i
$971$	1.18164e13			0.426577			0.213289	−	0.976989i	$-0.431583\pi$
$971$	1.18164e13			0.426577			0.213289	+	0.976989i	$0.431583\pi$
$972$		0			0
$973$	1.27584e12			0.0456339
$974$	−1.20135e13	+	4.37254e12i	−0.427713	+	0.155675i
$975$		0			0
$976$	1.11562e13	−	9.36113e12i	0.393542	−	0.330221i
$977$	−7.51419e12	−	4.26151e13i	−0.263850	−	1.49637i	−0.772291	−	0.635269i	$-0.780889\pi$
$977$	−7.51419e12	−	4.26151e13i	−0.263850	−	1.49637i	0.508441	−	0.861097i	$-0.330222\pi$
$978$		0			0
$979$	1.07516e13	+	9.02166e12i	0.374068	+	0.313880i
$980$	5.34159e12	−	9.25190e12i	0.184992	−	0.320416i
$981$		0			0
$982$	−1.91475e13	−	3.31644e13i	−0.657067	−	1.13807i
$983$	−5.72807e12	+	3.24855e13i	−0.195667	+	1.10968i	0.715799	+	0.698306i	$0.246063\pi$
$983$	−5.72807e12	+	3.24855e13i	−0.195667	+	1.10968i	−0.911466	+	0.411375i	$0.865049\pi$
$984$		0			0
$985$	−2.54657e13	−	9.26876e12i	−0.861971	−	0.313732i
$986$	9.33130e12	+	3.39632e12i	0.314410	+	0.114436i
$987$		0			0
$988$	1.14928e12	−	6.51790e12i	0.0383725	−	0.217621i
$989$	−2.46580e10	−	4.27089e10i	−0.000819548	−	0.00141950i
$990$		0			0
$991$	1.35439e12	−	2.34588e12i	0.0446080	−	0.0772634i	−0.842859	−	0.538134i	$-0.819129\pi$
$991$	1.35439e12	−	2.34588e12i	0.0446080	−	0.0772634i	0.887467	+	0.460871i	$0.152463\pi$
$992$	−1.51422e13	−	1.27058e13i	−0.496461	−	0.416580i
$993$		0			0
$994$	7.28122e11	+	4.12939e12i	0.0236573	+	0.134167i
$995$	−3.55171e13	+	2.98024e13i	−1.14877	+	0.963934i
$996$		0			0
$997$	3.57905e13	−	1.30267e13i	1.14720	−	0.417547i	0.302692	−	0.953088i	$-0.402115\pi$
$997$	3.57905e13	−	1.30267e13i	1.14720	−	0.417547i	0.844509	+	0.535541i	$0.179892\pi$
$998$	−3.99473e13			−1.27468
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.19.9		156
3.2	odd	2		27.10.e.a.7.18	yes	156
27.4	even	9	inner	81.10.e.a.64.9		156
27.23	odd	18		27.10.e.a.4.18	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.18	✓	156	27.23	odd	18
27.10.e.a.7.18	yes	156	3.2	odd	2
81.10.e.a.19.9		156	1.1	even	1	trivial
81.10.e.a.64.9		156	27.4	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:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-17.4636 + 6.35623i) q^{2} +(-127.639 + 107.102i) q^{4} +(-280.318 - 1589.76i) q^{5} +(610.601 + 512.355i) q^{7} +(6305.87 - 10922.1i) q^{8} +(15000.2 + 25981.2i) q^{10} +(4495.09 - 25492.9i) q^{11} +(106141. + 38632.3i) q^{13} +(-13919.9 - 5066.44i) q^{14} +(-25886.0 + 146807. i) q^{16} +(-64251.1 - 111286. i) q^{17} +(-175832. + 304550. i) q^{19} +(206046. + 172893. i) q^{20} +(83538.4 + 473770. i) q^{22} +(1965.39 - 1649.15i) q^{23} +(-613422. + 223267. i) q^{25} -2.09916e6 q^{26} -132811. q^{28} +(3.90737e6 - 1.42216e6i) q^{29} +(-4.10711e6 + 3.44627e6i) q^{31} +(640209. + 3.63081e6i) q^{32} +(1.82942e6 + 1.53506e6i) q^{34} +(643359. - 1.11433e6i) q^{35} +(1.52669e6 + 2.64430e6i) q^{37} +(1.13487e6 - 6.43617e6i) q^{38} +(-1.91312e7 - 6.96317e6i) q^{40} +(2.20476e7 + 8.02467e6i) q^{41} +(3.33783e6 - 1.89298e7i) q^{43} +(2.15659e6 + 3.73533e6i) q^{44} +(-23840.3 + 41292.6i) q^{46} +(-1.67023e7 - 1.40149e7i) q^{47} +(-6.89700e6 - 3.91149e7i) q^{49} +(9.29341e6 - 7.79810e6i) q^{50} +(-1.76854e7 + 6.43695e6i) q^{52} -8.11126e7 q^{53} -4.17877e7 q^{55} +(9.44636e6 - 3.43819e6i) q^{56} +(-5.91971e7 + 4.96722e7i) q^{58} +(-3.01060e7 - 1.70740e8i) q^{59} +(-7.48377e7 - 6.27963e7i) q^{61} +(4.98196e7 - 8.62901e7i) q^{62} +(-7.24209e7 - 1.25437e8i) q^{64} +(3.16628e7 - 1.79568e8i) q^{65} +(2.17705e8 + 7.92381e7i) q^{67} +(2.01199e7 + 7.32305e6i) q^{68} +(-4.15242e6 + 2.35496e7i) q^{70} +(-1.41531e8 - 2.45140e8i) q^{71} +(2.29279e8 - 3.97123e8i) q^{73} +(-4.34693e7 - 3.64750e7i) q^{74} +(-1.01749e7 - 5.77045e7i) q^{76} +(1.58061e7 - 1.32629e7i) q^{77} +(-5.29687e8 + 1.92790e8i) q^{79} +2.40644e8 q^{80} -4.36037e8 q^{82} +(-6.29101e7 + 2.28974e7i) q^{83} +(-1.58908e8 + 1.33339e8i) q^{85} +(6.20314e7 + 3.51798e8i) q^{86} +(-2.50091e8 - 2.09851e8i) q^{88} +(-2.71094e8 + 4.69549e8i) q^{89} +(4.50165e7 + 7.79709e7i) q^{91} +(-74232.5 + 420994. i) q^{92} +(3.80764e8 + 1.38587e8i) q^{94} +(5.33450e8 + 1.94160e8i) q^{95} +(1.23991e7 - 7.03187e7i) q^{97} +(3.69070e8 + 6.39247e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

L-functions

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