LMFDB - Embedded newform 81.10.e.a.10.1

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			10.1
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-7.14775 - 40.5369i) q^{2} +(-1111.03 + 404.381i) q^{4} +(610.019 + 511.867i) q^{5} +(4530.75 + 1649.06i) q^{7} +(13796.1 + 23895.6i) q^{8} +(16389.2 - 28387.0i) q^{10} +(-11267.0 + 9454.10i) q^{11} +(-12174.2 + 69043.0i) q^{13} +(34463.1 - 195450. i) q^{14} +(406315. - 340939. i) q^{16} +(313935. - 543751. i) q^{17} +(-179335. - 310617. i) q^{19} +(-884736. - 322018. i) q^{20} +(463773. + 389152. i) q^{22} +(-2.16249e6 + 787080. i) q^{23} +(-229041. - 1.29896e6i) q^{25} +2.88581e6 q^{26} -5.70063e6 q^{28} +(-38439.2 - 218000. i) q^{29} +(-8.47317e6 + 3.08398e6i) q^{31} +(-5.90275e6 - 4.95299e6i) q^{32} +(-2.42859e7 - 8.83935e6i) q^{34} +(1.91975e6 + 3.32510e6i) q^{35} +(4.94997e6 - 8.57361e6i) q^{37} +(-1.13096e7 + 9.48988e6i) q^{38} +(-3.81546e6 + 2.16386e7i) q^{40} +(6.02891e6 - 3.41916e7i) q^{41} +(745981. - 625952. i) q^{43} +(8.69483e6 - 1.50599e7i) q^{44} +(4.73627e7 + 8.20346e7i) q^{46} +(3.06202e7 + 1.11448e7i) q^{47} +(-1.31043e7 - 1.09958e7i) q^{49} +(-5.10185e7 + 1.85692e7i) q^{50} +(-1.43939e7 - 8.16316e7i) q^{52} +3.52475e7 q^{53} -1.17123e7 q^{55} +(2.31016e7 + 1.31016e8i) q^{56} +(-8.56228e6 + 3.11641e6i) q^{58} +(-7.09656e7 - 5.95472e7i) q^{59} +(-8.27266e7 - 3.01100e7i) q^{61} +(1.85579e8 + 3.21432e8i) q^{62} +(-2.28034e7 + 3.94967e7i) q^{64} +(-4.27673e7 + 3.58860e7i) q^{65} +(-3.89948e7 + 2.21151e8i) q^{67} +(-1.28908e8 + 7.31071e8i) q^{68} +(1.21067e8 - 1.01588e8i) q^{70} +(1.79802e7 - 3.11427e7i) q^{71} +(7.80253e7 + 1.35144e8i) q^{73} +(-3.82928e8 - 1.39375e8i) q^{74} +(3.24853e8 + 2.72584e8i) q^{76} +(-6.66382e7 + 2.42543e7i) q^{77} +(-1.32512e7 - 7.51515e7i) q^{79} +4.22375e8 q^{80} -1.42912e9 q^{82} +(-1.07463e8 - 6.09454e8i) q^{83} +(4.69834e8 - 1.71006e8i) q^{85} +(-3.07062e7 - 2.57656e7i) q^{86} +(-3.81352e8 - 1.38801e8i) q^{88} +(-1.99082e8 - 3.44820e8i) q^{89} +(-1.69014e8 + 2.92741e8i) q^{91} +(2.08430e9 - 1.74893e9i) q^{92} +(2.32911e8 - 1.32091e9i) q^{94} +(4.95968e7 - 2.81277e8i) q^{95} +(-6.56060e8 + 5.50500e8i) q^{97} +(-3.52071e8 + 6.09804e8i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

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

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 $

$2$	−7.14775	−	40.5369i	−0.315889	−	1.79149i	−0.567192	−	0.823586i	$-0.691970\pi$
$2$	−7.14775	−	40.5369i	−0.315889	−	1.79149i	0.251303	−	0.967909i	$-0.419141\pi$
$3$		0			0
$3$		0			0
$4$	−1111.03	+	404.381i	−2.16997	+	0.789806i
$5$	610.019	+	511.867i	0.436494	+	0.366262i	0.834396	−	0.551166i	$-0.185817\pi$
$5$	610.019	+	511.867i	0.436494	+	0.366262i	−0.397901	+	0.917428i	$0.630261\pi$
$6$		0			0
$7$	4530.75	+	1649.06i	0.713229	+	0.259594i	0.673049	−	0.739598i	$-0.264984\pi$
$7$	4530.75	+	1649.06i	0.713229	+	0.259594i	0.0401806	+	0.999192i	$0.487207\pi$
$8$	13796.1	+	23895.6i	1.19084	+	2.06259i
$9$		0			0
$10$	16389.2	−	28387.0i	0.518273	−	0.897675i
$11$	−11267.0	+	9454.10i	−0.232028	+	0.194694i	−0.751387	−	0.659862i	$-0.770615\pi$
$11$	−11267.0	+	9454.10i	−0.232028	+	0.194694i	0.519360	+	0.854556i	$0.326170\pi$
$12$		0			0
$13$	−12174.2	+	69043.0i	−0.118221	+	0.670463i	0.866884	+	0.498509i	$0.166119\pi$
$13$	−12174.2	+	69043.0i	−0.118221	+	0.670463i	−0.985105	+	0.171954i	$0.944992\pi$
$14$	34463.1	−	195450.i	0.239760	−	1.35975i
$15$		0			0
$16$	406315.	−	340939.i	1.54997	−	1.30058i
$17$	313935.	−	543751.i	0.911632	−	1.57899i	0.0998723	−	0.995000i	$-0.468157\pi$
$17$	313935.	−	543751.i	0.911632	−	1.57899i	0.811759	−	0.583992i	$-0.198510\pi$
$18$		0			0
$19$	−179335.	−	310617.i	−0.315699	−	0.546806i	0.663887	−	0.747833i	$-0.268906\pi$
$19$	−179335.	−	310617.i	−0.315699	−	0.546806i	−0.979586	+	0.201027i	$0.935572\pi$
$20$	−884736.	−	322018.i	−1.23646	−	0.450033i
$21$		0			0
$22$	463773.	+	389152.i	0.422088	+	0.354174i
$23$	−2.16249e6	+	787080.i	−1.61131	+	0.586467i	−0.981698	−	0.190445i	$-0.939007\pi$
$23$	−2.16249e6	+	787080.i	−1.61131	+	0.586467i	−0.629608	+	0.776913i	$0.716785\pi$
$24$		0			0
$25$	−229041.	−	1.29896e6i	−0.117269	−	0.665065i
$26$	2.88581e6			1.23848
$27$		0			0
$28$	−5.70063e6			−1.75272
$29$	−38439.2	−	218000.i	−0.0100921	−	0.0572354i	0.979346	−	0.202193i	$-0.0648067\pi$
$29$	−38439.2	−	218000.i	−0.0100921	−	0.0572354i	−0.989438	+	0.144957i	$0.953696\pi$
$30$		0			0
$31$	−8.47317e6	+	3.08398e6i	−1.64785	+	0.599769i	−0.988386	−	0.151966i	$-0.951440\pi$
$31$	−8.47317e6	+	3.08398e6i	−1.64785	+	0.599769i	−0.659466	+	0.751735i	$0.729217\pi$
$32$	−5.90275e6	−	4.95299e6i	−0.995129	−	0.835012i
$33$		0			0
$34$	−2.42859e7	−	8.83935e6i	−3.11673	−	1.13440i
$35$	1.91975e6	+	3.32510e6i	0.216241	+	0.374540i
$36$		0			0
$37$	4.94997e6	−	8.57361e6i	0.434205	−	0.752066i	−0.563025	−	0.826440i	$-0.690363\pi$
$37$	4.94997e6	−	8.57361e6i	0.434205	−	0.752066i	0.997230	+	0.0743741i	$0.0236959\pi$
$38$	−1.13096e7	+	9.48988e6i	−0.879875	+	0.738303i
$39$		0			0
$40$	−3.81546e6	+	2.16386e7i	−0.235655	+	1.33647i
$41$	6.02891e6	−	3.41916e7i	0.333205	−	1.88970i	−0.111078	−	0.993812i	$-0.535430\pi$
$41$	6.02891e6	−	3.41916e7i	0.333205	−	1.88970i	0.444283	−	0.895887i	$-0.353459\pi$
$42$		0			0
$43$	745981.	−	625952.i	0.0332751	−	0.0279211i	−0.625998	−	0.779824i	$-0.715308\pi$
$43$	745981.	−	625952.i	0.0332751	−	0.0279211i	0.659274	+	0.751903i	$0.270864\pi$
$44$	8.69483e6	−	1.50599e7i	0.349723	−	0.605738i
$45$		0			0
$46$	4.73627e7	+	8.20346e7i	1.55965	+	2.70139i
$47$	3.06202e7	+	1.11448e7i	0.915307	+	0.333145i	0.756370	−	0.654144i	$-0.226971\pi$
$47$	3.06202e7	+	1.11448e7i	0.915307	+	0.333145i	0.158937	+	0.987289i	$0.449193\pi$
$48$		0			0
$49$	−1.31043e7	−	1.09958e7i	−0.324738	−	0.272487i
$50$	−5.10185e7	+	1.85692e7i	−1.15442	+	0.420173i
$51$		0			0
$52$	−1.43939e7	−	8.16316e7i	−0.273000	−	1.54826i
$53$	3.52475e7			0.613602			0.306801	−	0.951774i	$-0.400741\pi$
$53$	3.52475e7			0.613602			0.306801	+	0.951774i	$0.400741\pi$
$54$		0			0
$55$	−1.17123e7			−0.172588
$56$	2.31016e7	+	1.31016e8i	0.313903	+	1.78023i
$57$		0			0
$58$	−8.56228e6	+	3.11641e6i	−0.0993489	+	0.0361601i
$59$	−7.09656e7	−	5.95472e7i	−0.762454	−	0.639775i	0.176310	−	0.984335i	$-0.443584\pi$
$59$	−7.09656e7	−	5.95472e7i	−0.762454	−	0.639775i	−0.938764	+	0.344559i	$0.888028\pi$
$60$		0			0
$61$	−8.27266e7	−	3.01100e7i	−0.764999	−	0.278437i	−0.0700959	−	0.997540i	$-0.522331\pi$
$61$	−8.27266e7	−	3.01100e7i	−0.764999	−	0.278437i	−0.694903	+	0.719103i	$0.744553\pi$
$62$	1.85579e8	+	3.21432e8i	1.59502	+	2.76266i
$63$		0			0
$64$	−2.28034e7	+	3.94967e7i	−0.169899	+	0.294273i
$65$	−4.27673e7	+	3.58860e7i	−0.297168	+	0.249353i
$66$		0			0
$67$	−3.89948e7	+	2.21151e8i	−0.236412	+	1.34076i	0.603206	+	0.797585i	$0.293890\pi$
$67$	−3.89948e7	+	2.21151e8i	−0.236412	+	1.34076i	−0.839619	+	0.543176i	$0.817222\pi$
$68$	−1.28908e8	+	7.31071e8i	−0.731119	+	4.14638i
$69$		0			0
$70$	1.21067e8	−	1.01588e8i	0.602678	−	0.505707i
$71$	1.79802e7	−	3.11427e7i	0.0839717	−	0.145443i	−0.820981	−	0.570956i	$-0.806573\pi$
$71$	1.79802e7	−	3.11427e7i	0.0839717	−	0.145443i	0.904953	+	0.425512i	$0.139906\pi$
$72$		0			0
$73$	7.80253e7	+	1.35144e8i	0.321575	+	0.556984i	0.980813	−	0.194950i	$-0.0624544\pi$
$73$	7.80253e7	+	1.35144e8i	0.321575	+	0.556984i	−0.659238	+	0.751934i	$0.729121\pi$
$74$	−3.82928e8	−	1.39375e8i	−1.48448	−	0.540307i
$75$		0			0
$76$	3.24853e8	+	2.72584e8i	1.11693	+	0.937215i
$77$	−6.66382e7	+	2.42543e7i	−0.216030	+	0.0786286i
$78$		0			0
$79$	−1.32512e7	−	7.51515e7i	−0.0382767	−	0.217078i	0.959670	−	0.281129i	$-0.0907090\pi$
$79$	−1.32512e7	−	7.51515e7i	−0.0382767	−	0.217078i	−0.997947	+	0.0640514i	$0.979598\pi$
$80$	4.22375e8			1.15291
$81$		0			0
$82$	−1.42912e9			−3.49064
$83$	−1.07463e8	−	6.09454e8i	−0.248547	−	1.40958i	−0.812109	−	0.583505i	$-0.801681\pi$
$83$	−1.07463e8	−	6.09454e8i	−0.248547	−	1.40958i	0.563562	−	0.826073i	$-0.309430\pi$
$84$		0			0
$85$	4.69834e8	−	1.71006e8i	0.976247	−	0.355325i
$86$	−3.07062e7	−	2.57656e7i	−0.0605318	−	0.0507922i
$87$		0			0
$88$	−3.81352e8	−	1.38801e8i	−0.677882	−	0.246729i
$89$	−1.99082e8	−	3.44820e8i	−0.336339	−	0.582556i	0.647402	−	0.762148i	$-0.275855\pi$
$89$	−1.99082e8	−	3.44820e8i	−0.336339	−	0.582556i	−0.983741	+	0.179593i	$0.942522\pi$
$90$		0			0
$91$	−1.69014e8	+	2.92741e8i	−0.258367	+	0.447504i
$92$	2.08430e9	−	1.74893e9i	3.03330	−	2.54524i
$93$		0			0
$94$	2.32911e8	−	1.32091e9i	0.307691	−	1.74500i
$95$	4.95968e7	−	2.81277e8i	0.0624737	−	0.354306i
$96$		0			0
$97$	−6.56060e8	+	5.50500e8i	−0.752438	+	0.631371i	−0.936147	−	0.351610i	$-0.885634\pi$
$97$	−6.56060e8	+	5.50500e8i	−0.752438	+	0.631371i	0.183708	+	0.982981i	$0.441190\pi$
$98$	−3.52071e8	+	6.09804e8i	−0.385578	+	0.667841i
$99$		0			0
$100$	7.79743e8	+	1.35055e9i	0.779743	+	1.35055i
$101$	−1.27420e9	−	4.63770e8i	−1.21840	−	0.443462i	−0.348791	−	0.937201i	$-0.613408\pi$
$101$	−1.27420e9	−	4.63770e8i	−1.21840	−	0.443462i	−0.869610	+	0.493739i	$0.835630\pi$
$102$		0			0
$103$	−1.56088e8	−	1.30973e8i	−0.136648	−	0.114661i	0.571902	−	0.820322i	$-0.306206\pi$
$103$	−1.56088e8	−	1.30973e8i	−0.136648	−	0.114661i	−0.708550	+	0.705661i	$0.750650\pi$
$104$	−1.81778e9	+	6.61618e8i	−1.52367	+	0.554572i
$105$		0			0
$106$	−2.51940e8	−	1.42882e9i	−0.193830	−	1.09926i
$107$	−5.27545e8			−0.389074			−0.194537	−	0.980895i	$-0.562320\pi$
$107$	−5.27545e8			−0.389074			−0.194537	+	0.980895i	$0.562320\pi$
$108$		0			0
$109$	−1.19433e9			−0.810411			−0.405205	−	0.914226i	$-0.632800\pi$
$109$	−1.19433e9			−0.810411			−0.405205	+	0.914226i	$0.632800\pi$
$110$	8.37165e7	+	4.74780e8i	0.0545185	+	0.309190i
$111$		0			0
$112$	2.40314e9	−	8.74672e8i	1.44311	−	0.525248i
$113$	−3.74659e8	−	3.14376e8i	−0.216164	−	0.181383i	0.528276	−	0.849073i	$-0.322839\pi$
$113$	−3.74659e8	−	3.14376e8i	−0.216164	−	0.181383i	−0.744440	+	0.667690i	$0.767283\pi$
$114$		0			0
$115$	−1.72204e9	−	6.26770e8i	−0.918126	−	0.334171i
$116$	1.30862e8	+	2.26659e8i	0.0671046	+	0.116229i
$117$		0			0
$118$	−1.90661e9	+	3.30235e9i	−0.905303	+	1.56803i
$119$	2.31904e9	−	1.94590e9i	1.06010	−	0.889529i
$120$		0			0
$121$	−3.71889e8	+	2.10909e9i	−0.157717	+	0.894459i
$122$	−6.29258e8	+	3.56870e9i	−0.257163	+	1.45845i
$123$		0			0
$124$	8.16681e9	−	6.85277e9i	3.10209	−	2.60297i
$125$	1.30283e9	−	2.25657e9i	0.477302	−	0.826712i
$126$		0			0
$127$	−9.80631e8	−	1.69850e9i	−0.334494	−	0.579361i	0.648893	−	0.760879i	$-0.275232\pi$
$127$	−9.80631e8	−	1.69850e9i	−0.334494	−	0.579361i	−0.983388	+	0.181518i	$0.941899\pi$
$128$	−1.94322e9	−	7.07274e8i	−0.639848	−	0.232886i
$129$		0			0
$130$	1.76040e9	+	1.47715e9i	0.540587	+	0.453606i
$131$	−2.66929e9	+	9.71542e8i	−0.791908	+	0.288231i	−0.706129	−	0.708083i	$-0.749560\pi$
$131$	−2.66929e9	+	9.71542e8i	−0.791908	+	0.288231i	−0.0857791	+	0.996314i	$0.527338\pi$
$132$		0			0
$133$	−3.00296e8	−	1.70306e9i	−0.0832178	−	0.471952i
$134$	9.24348e9			2.47665
$135$		0			0
$136$	1.73244e10			4.34242
$137$	1.07383e9	+	6.09000e9i	0.260432	+	1.47698i	0.781736	+	0.623610i	$0.214335\pi$
$137$	1.07383e9	+	6.09000e9i	0.260432	+	1.47698i	−0.521304	+	0.853371i	$0.674554\pi$
$138$		0			0
$139$	−3.79593e8	+	1.38160e8i	−0.0862484	+	0.0313919i	−0.384784	−	0.923007i	$-0.625724\pi$
$139$	−3.79593e8	+	1.38160e8i	−0.0862484	+	0.0313919i	0.298536	+	0.954399i	$0.403502\pi$
$140$	−3.47749e9	−	2.91796e9i	−0.765051	−	0.641954i
$141$		0			0
$142$	−1.39095e9	−	5.06263e8i	−0.287086	−	0.104491i
$143$	−5.15574e8	−	8.93000e8i	−0.103105	−	0.178583i
$144$		0			0
$145$	8.81381e7	−	1.52660e8i	0.0165580	−	0.0286793i
$146$	4.92060e9	−	4.12887e9i	0.896252	−	0.752045i
$147$		0			0
$148$	−2.03255e9	+	1.15272e10i	−0.348228	+	1.97490i
$149$	1.45367e9	−	8.24418e9i	0.241617	−	1.37028i	−0.586602	−	0.809876i	$-0.699535\pi$
$149$	1.45367e9	−	8.24418e9i	0.241617	−	1.37028i	0.828219	−	0.560404i	$-0.189354\pi$
$150$		0			0
$151$	−2.19866e9	+	1.84490e9i	−0.344161	+	0.288786i	−0.798440	−	0.602074i	$-0.794341\pi$
$151$	−2.19866e9	+	1.84490e9i	−0.344161	+	0.288786i	0.454279	+	0.890859i	$0.349897\pi$
$152$	4.94825e9	−	8.57062e9i	0.751892	−	1.30232i
$153$		0			0
$154$	1.45951e9	+	2.52794e9i	0.209104	+	0.362179i
$155$	−6.74738e9	−	2.45584e9i	−0.938950	−	0.341750i
$156$		0			0
$157$	−9.24618e9	−	7.75847e9i	−1.21455	−	1.01913i	−0.999092	−	0.0426115i	$-0.986432\pi$
$157$	−9.24618e9	−	7.75847e9i	−1.21455	−	1.01913i	−0.215455	−	0.976514i	$-0.569123\pi$
$158$	−2.95169e9	+	1.07433e9i	−0.376803	+	0.137145i
$159$		0			0
$160$	−1.06552e9	−	6.04284e9i	−0.128535	−	0.728956i
$161$	−1.10956e10			−1.30147
$162$		0			0
$163$	2.45692e9			0.272613			0.136306	−	0.990667i	$-0.456477\pi$
$163$	2.45692e9			0.272613			0.136306	+	0.990667i	$0.456477\pi$
$164$	7.12816e9	+	4.04258e10i	0.769449	+	4.36376i
$165$		0			0
$166$	−2.39372e10	+	8.71244e9i	−2.44674	+	0.890540i
$167$	−2.10568e9	−	1.76688e9i	−0.209492	−	0.175785i	0.532004	−	0.846742i	$-0.321439\pi$
$167$	−2.10568e9	−	1.76688e9i	−0.209492	−	0.175785i	−0.741496	+	0.670957i	$0.765884\pi$
$168$		0			0
$169$	5.34624e9	+	1.94587e9i	0.504148	+	0.183495i
$170$	−1.02903e10	−	1.78233e10i	−0.944948	−	1.63670i
$171$		0			0
$172$	−5.75681e8	+	9.97110e8i	−0.0501538	+	0.0868690i
$173$	8.22330e8	−	6.90017e8i	0.0697973	−	0.0585669i	−0.607222	−	0.794533i	$-0.707716\pi$
$173$	8.22330e8	−	6.90017e8i	0.0697973	−	0.0585669i	0.677019	+	0.735966i	$0.263272\pi$
$174$		0			0
$175$	1.10433e9	−	6.26295e9i	0.0890075	−	0.504786i
$176$	−1.35467e9	+	7.68269e9i	−0.106420	+	0.603540i
$177$		0			0
$178$	−1.25549e10	+	1.05349e10i	−0.937400	+	0.786572i
$179$	1.00514e9	−	1.74096e9i	0.0731793	−	0.126750i	−0.827114	−	0.562035i	$-0.810019\pi$
$179$	1.00514e9	−	1.74096e9i	0.0731793	−	0.126750i	0.900293	+	0.435284i	$0.143352\pi$
$180$		0			0
$181$	1.23846e9	+	2.14507e9i	0.0857683	+	0.148555i	0.905718	−	0.423880i	$-0.139332\pi$
$181$	1.23846e9	+	2.14507e9i	0.0857683	+	0.148555i	−0.819950	+	0.572435i	$0.805999\pi$
$182$	1.30749e10	+	4.75887e9i	0.883317	+	0.321501i
$183$		0			0
$184$	−4.86417e10	−	4.08152e10i	−3.12845	−	2.62508i
$185$	7.40812e9	−	2.69634e9i	0.464981	−	0.169239i
$186$		0			0
$187$	1.60359e9	+	9.09439e9i	0.0958970	+	0.543859i
$188$	−3.85266e10			−2.24931
$189$		0			0
$190$	−1.17566e10			−0.654472
$191$	−1.85354e9	−	1.05119e10i	−0.100775	−	0.571521i	−0.992824	−	0.119584i	$-0.961844\pi$
$191$	−1.85354e9	−	1.05119e10i	−0.100775	−	0.571521i	0.892049	−	0.451938i	$-0.149267\pi$
$192$		0			0
$193$	1.43013e10	−	5.20525e9i	0.741939	−	0.270044i	0.0567293	−	0.998390i	$-0.481933\pi$
$193$	1.43013e10	−	5.20525e9i	0.741939	−	0.270044i	0.685210	+	0.728346i	$0.259711\pi$
$194$	2.70049e10	+	2.26598e10i	1.36878	+	1.14855i
$195$		0			0
$196$	1.90058e10	+	6.91753e9i	0.919884	+	0.334810i
$197$	−7.06195e9	−	1.22317e10i	−0.334062	−	0.578612i	0.649242	−	0.760581i	$-0.275086\pi$
$197$	−7.06195e9	−	1.22317e10i	−0.334062	−	0.578612i	−0.983304	+	0.181970i	$0.941753\pi$
$198$		0			0
$199$	1.85850e10	−	3.21902e10i	0.840088	−	1.45507i	−0.0497323	−	0.998763i	$-0.515837\pi$
$199$	1.85850e10	−	3.21902e10i	0.840088	−	1.45507i	0.889820	−	0.456312i	$-0.150830\pi$
$200$	2.78795e10	−	2.33936e10i	1.23211	−	1.03386i
$201$		0			0
$202$	−9.69214e9	+	5.49669e10i	−0.409580	+	2.32284i
$203$	1.85336e8	−	1.05109e9i	0.00765997	−	0.0434418i
$204$		0			0
$205$	2.11793e10	−	1.77715e10i	0.837567	−	0.702802i
$206$	−4.19358e9	+	7.26349e9i	−0.162249	+	0.281024i
$207$		0			0
$208$	1.85929e10	+	3.22039e10i	0.688751	+	1.19295i
$209$	4.95716e9	+	1.80426e9i	0.179711	+	0.0654094i
$210$		0			0
$211$	1.26584e10	+	1.06217e10i	0.439651	+	0.368911i	0.835579	−	0.549371i	$-0.185133\pi$
$211$	1.26584e10	+	1.06217e10i	0.439651	+	0.368911i	−0.395928	+	0.918282i	$0.629577\pi$
$212$	−3.91609e10	+	1.42534e10i	−1.33150	+	0.484626i
$213$		0			0
$214$	3.77076e9	+	2.13850e10i	0.122904	+	0.697024i
$215$	7.75466e8			0.0247508
$216$		0			0
$217$	−4.34755e10			−1.33099
$218$	8.53677e9	+	4.84144e10i	0.256000	+	1.45185i
$219$		0			0
$220$	1.30127e10	−	4.73623e9i	0.374511	−	0.136311i
$221$	3.37203e10	+	2.82947e10i	0.950882	+	0.797885i
$222$		0			0
$223$	2.84518e10	+	1.03556e10i	0.770439	+	0.280417i	0.697180	−	0.716896i	$-0.254438\pi$
$223$	2.84518e10	+	1.03556e10i	0.770439	+	0.280417i	0.0732588	+	0.997313i	$0.476660\pi$
$224$	−1.85761e10	−	3.21748e10i	−0.492991	−	0.853885i
$225$		0			0
$226$	−1.00659e10	+	1.74346e10i	−0.256663	+	0.444553i
$227$	−3.81651e10	+	3.20243e10i	−0.954003	+	0.800503i	−0.979967	−	0.199160i	$-0.936179\pi$
$227$	−3.81651e10	+	3.20243e10i	−0.954003	+	0.800503i	0.0259645	+	0.999663i	$0.491734\pi$
$228$		0			0
$229$	−1.88665e9	+	1.06998e10i	−0.0453349	+	0.257107i	−0.999049	−	0.0436088i	$-0.986114\pi$
$229$	−1.88665e9	+	1.06998e10i	−0.0453349	+	0.257107i	0.953714	+	0.300716i	$0.0972256\pi$
$230$	−1.30986e10	+	7.42861e10i	−0.308639	+	1.75038i
$231$		0			0
$232$	4.67892e9	−	3.92608e9i	0.106035	−	0.0889741i
$233$	−6.88739e9	+	1.19293e10i	−0.153092	+	0.265164i	−0.932363	−	0.361524i	$-0.882256\pi$
$233$	−6.88739e9	+	1.19293e10i	−0.153092	+	0.265164i	0.779270	+	0.626688i	$0.215590\pi$
$234$		0			0
$235$	1.29742e10	+	2.24720e10i	0.277508	+	0.480658i
$236$	1.02924e11	+	3.74614e10i	2.15980	+	0.786104i
$237$		0			0
$238$	−9.54568e10	−	8.00978e10i	−1.92846	−	1.61817i
$239$	5.98955e10	−	2.18002e10i	1.18742	−	0.432185i	0.328602	−	0.944469i	$-0.393423\pi$
$239$	5.98955e10	−	2.18002e10i	1.18742	−	0.432185i	0.858816	+	0.512284i	$0.171200\pi$
$240$		0			0
$241$	−5.53987e9	−	3.14182e10i	−0.105785	−	0.599935i	−0.990904	−	0.134571i	$-0.957034\pi$
$241$	−5.53987e9	−	3.14182e10i	−0.105785	−	0.599935i	0.885119	−	0.465364i	$-0.154077\pi$
$242$	8.81540e10			1.65224
$243$		0			0
$244$	1.04087e11			1.87994
$245$	−2.36549e9	−	1.34153e10i	−0.0419443	−	0.237878i
$246$		0			0
$247$	2.36292e10	−	8.60031e9i	0.403936	−	0.147021i
$248$	−1.90591e11	−	1.59924e11i	−3.19940	−	2.68462i
$249$		0			0
$250$	−1.00787e11	−	3.66834e10i	−1.63182	−	0.593935i
$251$	−5.75801e9	−	9.97317e9i	−0.0915674	−	0.158599i	0.816603	−	0.577199i	$-0.195854\pi$
$251$	−5.75801e9	−	9.97317e9i	−0.0915674	−	0.158599i	−0.908171	+	0.418600i	$0.862521\pi$
$252$		0			0
$253$	1.69235e10	−	2.93124e10i	0.259686	−	0.449789i
$254$	−6.18427e10	+	5.18922e10i	−0.932259	+	0.782258i
$255$		0			0
$256$	−1.88359e10	+	1.06823e11i	−0.274098	+	1.55449i
$257$	1.22925e10	−	6.97140e10i	0.175768	−	0.996830i	−0.761486	−	0.648182i	$-0.775530\pi$
$257$	1.22925e10	−	6.97140e10i	0.175768	−	0.996830i	0.937254	−	0.348648i	$-0.113359\pi$
$258$		0			0
$259$	3.65655e10	−	3.06821e10i	0.504920	−	0.423678i
$260$	3.30040e10	−	5.71646e10i	0.447905	−	0.775795i
$261$		0			0
$262$	5.84627e10	+	1.01260e11i	0.766519	+	1.32765i
$263$	2.74165e10	+	9.97877e9i	0.353354	+	0.128610i	0.512598	−	0.858629i	$-0.328683\pi$
$263$	2.74165e10	+	9.97877e9i	0.353354	+	0.128610i	−0.159243	+	0.987239i	$0.550905\pi$
$264$		0			0
$265$	2.15016e10	+	1.80420e10i	0.267833	+	0.224739i
$266$	−6.68903e10	+	2.43461e10i	−0.819212	+	0.298169i
$267$		0			0
$268$	−4.61047e10	−	2.61473e11i	−0.545932	−	3.09614i
$269$	4.39248e10			0.511475			0.255738	−	0.966746i	$-0.417682\pi$
$269$	4.39248e10			0.511475			0.255738	+	0.966746i	$0.417682\pi$
$270$		0			0
$271$	1.35029e11			1.52078			0.760390	−	0.649467i	$-0.225008\pi$
$271$	1.35029e11			1.52078			0.760390	+	0.649467i	$0.225008\pi$
$272$	−5.78294e10	−	3.27967e11i	−0.640603	−	3.63304i
$273$		0			0
$274$	2.39194e11	−	8.70596e10i	2.56374	−	0.933124i
$275$	1.48611e10	+	1.24699e10i	0.156694	+	0.131482i
$276$		0			0
$277$	8.87735e10	+	3.23109e10i	0.905992	+	0.329754i	0.752651	−	0.658419i	$-0.228775\pi$
$277$	8.87735e10	+	3.23109e10i	0.905992	+	0.329754i	0.153341	+	0.988173i	$0.450997\pi$
$278$	8.31383e9	+	1.44000e10i	0.0834833	+	0.144597i
$279$		0			0
$280$	−5.29702e10	+	9.17470e10i	−0.515015	+	0.892033i
$281$	−3.60036e10	+	3.02106e10i	−0.344483	+	0.289056i	−0.798570	−	0.601902i	$-0.794410\pi$
$281$	−3.60036e10	+	3.02106e10i	−0.344483	+	0.289056i	0.454087	+	0.890957i	$0.349965\pi$
$282$		0			0
$283$	−2.69725e10	+	1.52969e11i	−0.249967	+	1.41763i	0.558702	+	0.829368i	$0.311299\pi$
$283$	−2.69725e10	+	1.52969e11i	−0.249967	+	1.41763i	−0.808669	+	0.588264i	$0.799812\pi$
$284$	−7.38302e9	+	4.18712e10i	−0.0673444	+	0.381929i
$285$		0			0
$286$	−3.25143e10	+	2.72827e10i	−0.287360	+	0.241124i
$287$	8.36995e10	−	1.44972e11i	0.728206	−	1.26129i
$288$		0			0
$289$	−1.37816e11	−	2.38705e11i	−1.16214	−	2.01289i
$290$	−6.81834e9	−	2.48167e9i	−0.0566093	−	0.0206041i
$291$		0			0
$292$	−1.41338e11	−	1.18596e11i	−1.13772	−	0.954659i
$293$	−1.65217e11	+	6.01339e10i	−1.30963	+	0.476667i	−0.900122	−	0.435638i	$-0.856523\pi$
$293$	−1.65217e11	+	6.01339e10i	−1.30963	+	0.476667i	−0.409510	+	0.912305i	$0.634300\pi$
$294$		0			0
$295$	−1.28101e10	−	7.26499e10i	−0.0984815	−	0.558516i
$296$	2.73162e11			2.06827
$297$		0			0
$298$	−3.44584e11			−2.53117
$299$	−2.80160e10	−	1.58887e11i	−0.202715	−	1.14965i
$300$		0			0
$301$	4.41209e9	−	1.60587e9i	0.0309809	−	0.0112761i
$302$	9.05018e10	+	7.59400e10i	0.626075	+	0.525339i
$303$		0			0
$304$	−1.78768e11	−	6.50661e10i	−1.20049	−	0.436942i
$305$	−3.50525e10	−	6.07127e10i	−0.231937	−	0.401726i
$306$		0			0
$307$	−1.29034e11	+	2.23494e11i	−0.829054	+	1.43596i	0.0697274	+	0.997566i	$0.477787\pi$
$307$	−1.29034e11	+	2.23494e11i	−0.829054	+	1.43596i	−0.898781	+	0.438397i	$0.855546\pi$
$308$	6.42288e10	−	5.38944e10i	0.406679	−	0.341244i
$309$		0			0
$310$	−5.13238e10	+	2.91071e11i	−0.315639	+	1.79008i
$311$	−1.72714e10	+	9.79512e10i	−0.104690	+	0.593729i	0.886653	+	0.462435i	$0.153024\pi$
$311$	−1.72714e10	+	9.79512e10i	−0.104690	+	0.593729i	−0.991344	+	0.131294i	$0.958087\pi$
$312$		0			0
$313$	1.92171e11	−	1.61251e11i	1.13172	−	0.949627i	0.132584	−	0.991172i	$-0.457672\pi$
$313$	1.92171e11	−	1.61251e11i	1.13172	−	0.949627i	0.999137	+	0.0415451i	$0.0132280\pi$
$314$	−2.48415e11	+	4.30267e11i	−1.44210	+	2.49778i
$315$		0			0
$316$	4.51123e10	+	7.81367e10i	0.254509	+	0.440822i
$317$	1.25214e9	+	4.55743e8i	0.00696446	+	0.00253486i	0.345500	−	0.938419i	$-0.387709\pi$
$317$	1.25214e9	+	4.55743e8i	0.00696446	+	0.00253486i	−0.338536	+	0.940954i	$0.609932\pi$
$318$		0			0
$319$	2.49408e9	+	2.09278e9i	0.0134851	+	0.0113153i
$320$	−3.41276e10	+	1.24214e10i	−0.181941	+	0.0662211i
$321$		0			0
$322$	7.93088e10	+	4.49782e11i	0.411121	+	2.33158i
$323$	−2.25198e11			−1.15120
$324$		0			0
$325$	9.24722e10			0.459765
$326$	−1.75614e10	−	9.95958e10i	−0.0861154	−	0.488385i
$327$		0			0
$328$	9.00206e11	−	3.27648e11i	4.29447	−	1.56306i
$329$	1.20354e11	+	1.00989e11i	0.566342	+	0.475217i
$330$		0			0
$331$	9.39293e10	+	3.41875e10i	0.430105	+	0.156546i	0.547996	−	0.836481i	$-0.315391\pi$
$331$	9.39293e10	+	3.41875e10i	0.430105	+	0.156546i	−0.117890	+	0.993027i	$0.537613\pi$
$332$	3.65846e11	+	6.33663e11i	1.65263	+	2.86245i
$333$		0			0
$334$	−5.65728e10	+	9.79869e10i	−0.248742	+	0.430833i
$335$	−1.36987e11	+	1.14946e11i	−0.594263	+	0.498645i
$336$		0			0
$337$	3.50356e10	−	1.98697e11i	0.147970	−	0.839182i	−0.816964	−	0.576689i	$-0.804344\pi$
$337$	3.50356e10	−	1.98697e11i	0.147970	−	0.839182i	0.964934	−	0.262493i	$-0.0845445\pi$
$338$	4.06660e10	−	2.30629e11i	0.169475	−	0.961143i
$339$		0			0
$340$	−4.52847e11	+	3.79984e11i	−1.83779	+	1.54209i
$341$	6.63105e10	−	1.14853e11i	0.265575	−	0.459990i
$342$		0			0
$343$	−1.38523e11	−	2.39928e11i	−0.540378	−	0.935962i
$344$	2.52492e10	+	9.18994e9i	0.0972151	+	0.0353834i
$345$		0			0
$346$	−3.38490e10	−	2.84026e10i	−0.126970	−	0.106541i
$347$	3.25761e11	−	1.18567e11i	1.20619	−	0.439018i	0.340811	−	0.940132i	$-0.389298\pi$
$347$	3.25761e11	−	1.18567e11i	1.20619	−	0.439018i	0.865381	+	0.501114i	$0.167076\pi$
$348$		0			0
$349$	3.72094e10	+	2.11025e11i	0.134257	+	0.761411i	0.975374	+	0.220557i	$0.0707876\pi$
$349$	3.72094e10	+	2.11025e11i	0.134257	+	0.761411i	−0.841117	+	0.540854i	$0.818101\pi$
$350$	−2.61774e11			−0.932438
$351$		0			0
$352$	1.13332e11			0.393469
$353$	3.27725e10	+	1.85862e11i	0.112337	+	0.637096i	0.988034	+	0.154235i	$0.0492912\pi$
$353$	3.27725e10	+	1.85862e11i	0.112337	+	0.637096i	−0.875697	+	0.482861i	$0.839598\pi$
$354$		0			0
$355$	2.69092e10	−	9.79414e9i	0.0899234	−	0.0327295i
$356$	3.60624e11	+	3.02599e11i	1.18995	+	0.998489i
$357$		0			0
$358$	−7.77574e10	−	2.83014e10i	−0.250189	−	0.0910614i
$359$	−2.94795e11	−	5.10600e11i	−0.936688	−	1.62239i	−0.771596	−	0.636113i	$-0.780541\pi$
$359$	−2.94795e11	−	5.10600e11i	−0.936688	−	1.62239i	−0.165093	−	0.986278i	$-0.552792\pi$
$360$		0			0
$361$	9.70220e10	−	1.68047e11i	0.300669	−	0.520773i
$362$	7.81022e10	−	6.55355e10i	0.239042	−	0.200580i
$363$		0			0
$364$	6.94004e10	−	3.93589e11i	0.207208	−	1.17513i
$365$	−2.15787e10	+	1.22379e11i	−0.0636366	+	0.360901i
$366$		0			0
$367$	1.05932e11	−	8.88876e10i	0.304811	−	0.255767i	−0.477532	−	0.878614i	$-0.658469\pi$
$367$	1.05932e11	−	8.88876e10i	0.304811	−	0.255767i	0.782343	+	0.622847i	$0.214024\pi$
$368$	−6.10304e11	+	1.05708e12i	−1.73473	+	3.00464i
$369$		0			0
$370$	−1.62252e11	−	2.81029e11i	−0.450074	−	0.779550i
$371$	1.59698e11	+	5.81252e10i	0.437639	+	0.159287i
$372$		0			0
$373$	−2.03146e11	−	1.70460e11i	−0.543399	−	0.455966i	0.329299	−	0.944226i	$-0.393188\pi$
$373$	−2.03146e11	−	1.70460e11i	−0.543399	−	0.455966i	−0.872699	+	0.488259i	$0.837632\pi$
$374$	3.57196e11	−	1.30009e11i	0.944028	−	0.343598i
$375$		0			0
$376$	1.56127e11	+	8.85443e11i	0.402841	+	2.28463i
$377$	1.55193e10			0.0395673
$378$		0			0
$379$	−7.58515e11			−1.88837			−0.944186	−	0.329413i	$-0.893149\pi$
$379$	−7.58515e11			−1.88837			−0.944186	+	0.329413i	$0.893149\pi$
$380$	5.86398e10	+	3.32563e11i	0.144267	+	0.818177i
$381$		0			0
$382$	−4.12873e11	+	1.50273e11i	−0.992044	+	0.361074i
$383$	−6.74536e10	−	5.66003e10i	−0.160181	−	0.134408i	0.559174	−	0.829050i	$-0.311118\pi$
$383$	−6.74536e10	−	5.66003e10i	−0.160181	−	0.134408i	−0.719355	+	0.694642i	$0.755563\pi$
$384$		0			0
$385$	−5.30655e10	−	1.93143e10i	−0.123095	−	0.0448028i
$386$	−3.13227e11	−	5.42525e11i	−0.718152	−	1.24388i
$387$		0			0
$388$	5.06289e11	−	8.76918e11i	1.13411	−	1.96434i
$389$	−4.64860e11	+	3.90064e11i	−1.02932	+	0.863700i	−0.990770	−	0.135557i	$-0.956718\pi$
$389$	−4.64860e11	+	3.90064e11i	−1.02932	+	0.863700i	−0.0385478	+	0.999257i	$0.512273\pi$
$390$		0			0
$391$	−2.50904e11	+	1.42295e12i	−0.542890	+	3.07888i
$392$	8.19632e10	−	4.64836e11i	0.175320	−	0.994289i
$393$		0			0
$394$	−4.45356e11	+	3.73698e11i	−0.931053	+	0.781247i
$395$	3.03840e10	−	5.26267e10i	0.0627998	−	0.108772i
$396$		0			0
$397$	−2.20373e10	−	3.81697e10i	−0.0445246	−	0.0771189i	0.842904	−	0.538064i	$-0.180844\pi$
$397$	−2.20373e10	−	3.81697e10i	−0.0445246	−	0.0771189i	−0.887429	+	0.460945i	$0.847511\pi$
$398$	−1.43773e12	−	5.23292e11i	−2.87213	−	1.04537i
$399$		0			0
$400$	−5.35927e11	−	4.49697e11i	−1.04673	−	0.878314i
$401$	5.04373e11	−	1.83577e11i	0.974096	−	0.354542i	0.194554	−	0.980892i	$-0.437674\pi$
$401$	5.04373e11	−	1.83577e11i	0.974096	−	0.354542i	0.779542	+	0.626350i	$0.215452\pi$
$402$		0			0
$403$	−1.09774e11	−	6.22558e11i	−0.207313	−	1.17573i
$404$	1.60321e12			2.99415
$405$		0			0
$406$	−4.39327e10			−0.0802455
$407$	2.52846e10	+	1.43396e11i	0.0456752	+	0.259037i
$408$		0			0
$409$	−1.01606e12	+	3.69816e11i	−1.79541	+	0.653477i	−0.796614	+	0.604489i	$0.793378\pi$
$409$	−1.01606e12	+	3.69816e11i	−1.79541	+	0.653477i	−0.998799	+	0.0489884i	$0.984400\pi$
$410$	−8.71788e11	−	7.31517e11i	−1.52364	−	1.27849i
$411$		0			0
$412$	2.26381e11	+	8.23960e10i	0.387082	+	0.140886i
$413$	−2.23331e11	−	3.86820e11i	−0.377723	−	0.654235i
$414$		0			0
$415$	2.46405e11	−	4.26785e11i	0.407786	−	0.706306i
$416$	4.13831e11	−	3.47245e11i	0.677490	−	0.568481i
$417$		0			0
$418$	3.77065e10	−	2.13844e11i	0.0604119	−	0.342613i
$419$	7.68804e10	−	4.36011e11i	0.121858	−	0.691089i	−0.861267	−	0.508153i	$-0.830329\pi$
$419$	7.68804e10	−	4.36011e11i	0.121858	−	0.691089i	0.983125	−	0.182936i	$-0.0585603\pi$
$420$		0			0
$421$	3.12954e11	−	2.62599e11i	0.485524	−	0.407403i	−0.366895	−	0.930262i	$-0.619579\pi$
$421$	3.12954e11	−	2.62599e11i	0.485524	−	0.407403i	0.852419	+	0.522859i	$0.175135\pi$
$422$	3.40090e11	−	5.89053e11i	0.522021	−	0.904167i
$423$		0			0
$424$	4.86279e11	+	8.42260e11i	0.730700	+	1.26561i
$425$	−7.78213e11	−	2.83246e11i	−1.15704	−	0.421128i
$426$		0			0
$427$	−3.25160e11	−	2.72842e11i	−0.473339	−	0.397179i
$428$	5.86116e11	−	2.13329e11i	0.844280	−	0.307293i
$429$		0			0
$430$	−5.54284e9	−	3.14350e10i	−0.00781851	−	0.0443410i
$431$	−5.82971e11			−0.813765			−0.406882	−	0.913481i	$-0.633384\pi$
$431$	−5.82971e11			−0.813765			−0.406882	+	0.913481i	$0.633384\pi$
$432$		0			0
$433$	−1.16880e11			−0.159788			−0.0798941	−	0.996803i	$-0.525458\pi$
$433$	−1.16880e11			−0.159788			−0.0798941	+	0.996803i	$0.525458\pi$
$434$	3.10752e11	+	1.76236e12i	0.420446	+	2.38447i
$435$		0			0
$436$	1.32693e12	−	4.82964e11i	1.75857	−	0.640067i
$437$	6.32289e11	+	5.30553e11i	0.829371	+	0.695925i
$438$		0			0
$439$	5.71311e11	+	2.07940e11i	0.734145	+	0.267207i	0.681918	−	0.731428i	$-0.261146\pi$
$439$	5.71311e11	+	2.07940e11i	0.734145	+	0.267207i	0.0522269	+	0.998635i	$0.483368\pi$
$440$	−1.61584e11	−	2.79872e11i	−0.205524	−	0.355978i
$441$		0			0
$442$	9.05956e11	−	1.56916e12i	1.12903	−	1.95554i
$443$	5.52540e11	−	4.63636e11i	0.681628	−	0.571954i	−0.234854	−	0.972031i	$-0.575461\pi$
$443$	5.52540e11	−	4.63636e11i	0.681628	−	0.571954i	0.916481	+	0.400077i	$0.131017\pi$
$444$		0			0
$445$	5.50582e10	−	3.12250e11i	0.0665582	−	0.377470i
$446$	2.16418e11	−	1.22737e12i	0.258992	−	1.46882i
$447$		0			0
$448$	−1.68449e11	+	1.41346e11i	−0.197568	+	0.165780i
$449$	−1.42233e11	+	2.46354e11i	−0.165155	+	0.286056i	−0.936710	−	0.350106i	$-0.886146\pi$
$449$	−1.42233e11	+	2.46354e11i	−0.165155	+	0.286056i	0.771556	+	0.636162i	$0.219479\pi$
$450$		0			0
$451$	2.55324e11	+	4.42233e11i	0.290601	+	0.503335i
$452$	5.43384e11	+	1.97776e11i	0.612328	+	0.222869i
$453$		0			0
$454$	1.57096e12	+	1.31819e12i	1.73546	+	1.45622i
$455$	−2.52946e11	+	9.20649e10i	−0.276679	+	0.100703i
$456$		0			0
$457$	2.06323e11	+	1.17011e12i	0.221271	+	1.25489i	0.869688	+	0.493603i	$0.164320\pi$
$457$	2.06323e11	+	1.17011e12i	0.221271	+	1.25489i	−0.648417	+	0.761285i	$0.724569\pi$
$458$	4.47220e11			0.474927
$459$		0			0
$460$	2.16668e12			2.25624
$461$	2.17478e11	+	1.23338e12i	0.224265	+	1.27187i	0.864085	+	0.503346i	$0.167898\pi$
$461$	2.17478e11	+	1.23338e12i	0.224265	+	1.27187i	−0.639820	+	0.768525i	$0.720991\pi$
$462$		0			0
$463$	1.83754e11	−	6.68811e10i	0.185833	−	0.0676377i	−0.247428	−	0.968906i	$-0.579585\pi$
$463$	1.83754e11	−	6.68811e10i	0.185833	−	0.0676377i	0.433261	+	0.901269i	$0.357363\pi$
$464$	−8.99430e10	−	7.54712e10i	−0.0900817	−	0.0755875i
$465$		0			0
$466$	5.32807e11	+	1.93926e11i	0.523399	+	0.190502i
$467$	−7.42753e10	−	1.28649e11i	−0.0722634	−	0.125164i	0.827630	−	0.561275i	$-0.189689\pi$
$467$	−7.42753e10	−	1.28649e11i	−0.0722634	−	0.125164i	−0.899893	+	0.436111i	$0.856356\pi$
$468$		0			0
$469$	−5.41366e11	+	9.37674e11i	−0.516670	+	0.894899i
$470$	8.18208e11	−	6.86558e11i	0.773434	−	0.648989i
$471$		0			0
$472$	4.43866e11	−	2.51729e12i	0.411635	−	2.33450i
$473$	−2.48712e9	+	1.41051e10i	−0.00228466	+	0.0129569i
$474$		0			0
$475$	−3.62402e11	+	3.04092e11i	−0.326640	+	0.274084i
$476$	−1.78963e12	+	3.09973e12i	−1.59783	+	2.76753i
$477$		0			0
$478$	−1.31183e12	−	2.27215e12i	−1.14935	−	1.99073i
$479$	−3.91658e11	−	1.42552e11i	−0.339936	−	0.123727i	0.166411	−	0.986057i	$-0.446782\pi$
$479$	−3.91658e11	−	1.42552e11i	−0.339936	−	0.123727i	−0.506347	+	0.862330i	$0.669004\pi$
$480$		0			0
$481$	5.31686e11	+	4.46138e11i	0.452900	+	0.380028i
$482$	−1.23400e12	+	4.49139e11i	−1.04136	+	0.379026i
$483$		0			0
$484$	−4.39695e11	−	2.49364e12i	−0.364207	−	2.06552i
$485$	−6.81992e11			−0.559682
$486$		0			0
$487$	8.13106e11			0.655038			0.327519	−	0.944845i	$-0.393787\pi$
$487$	8.13106e11			0.655038			0.327519	+	0.944845i	$0.393787\pi$
$488$	−4.21810e11	−	2.39220e12i	−0.336688	−	1.90945i
$489$		0			0
$490$	−5.26908e11	+	1.91779e11i	−0.412908	+	0.150286i
$491$	7.40724e11	+	6.21541e11i	0.575161	+	0.482618i	0.883354	−	0.468706i	$-0.155280\pi$
$491$	7.40724e11	+	6.21541e11i	0.575161	+	0.482618i	−0.308193	+	0.951324i	$0.599724\pi$
$492$		0			0
$493$	−1.30605e11	−	4.75363e10i	−0.0995746	−	0.0362422i
$494$	−5.17525e11	−	8.96380e11i	−0.390985	−	0.677206i
$495$		0			0
$496$	−2.39133e12	+	4.14190e12i	−1.77407	+	3.07278i
$497$	1.32820e11	−	1.11449e11i	0.0976472	−	0.0819358i
$498$		0			0
$499$	8.23566e10	−	4.67068e11i	0.0594629	−	0.337231i	−0.940534	−	0.339699i	$-0.889675\pi$
$499$	8.23566e10	−	4.67068e11i	0.0594629	−	0.337231i	0.999997	+	0.00246860i	$0.000785780\pi$
$500$	−5.34967e11	+	3.03395e12i	−0.382792	+	2.17092i
$501$		0			0
$502$	−3.63125e11	+	3.04698e11i	−0.255205	+	0.214142i
$503$	3.26449e11	−	5.65427e11i	0.227384	−	0.393840i	−0.729648	−	0.683823i	$-0.760316\pi$
$503$	3.26449e11	−	5.65427e11i	0.227384	−	0.393840i	0.957032	+	0.289982i	$0.0936495\pi$
$504$		0			0
$505$	−5.39896e11	−	9.35127e11i	−0.369402	−	0.639823i
$506$	−1.30920e12	−	4.76509e11i	−0.887825	−	0.323142i
$507$		0			0
$508$	1.77635e12	+	1.49053e12i	1.18343	+	0.993013i
$509$	2.59505e12	−	9.44520e11i	1.71362	−	0.623708i	0.716367	−	0.697724i	$-0.245804\pi$
$509$	2.59505e12	−	9.44520e11i	1.71362	−	0.623708i	0.997257	+	0.0740162i	$0.0235816\pi$
$510$		0			0
$511$	1.30653e11	+	7.40971e11i	0.0847668	+	0.480737i
$512$	3.40614e12			2.19052
$513$		0			0
$514$	−2.91385e12			−1.84134
$515$	−2.81757e10	−	1.59793e11i	−0.0176499	−	0.100098i
$516$		0			0
$517$	−4.50360e11	+	1.63918e11i	−0.277238	+	0.100906i
$518$	−1.50512e12	−	1.26294e12i	−0.918515	−	0.770726i
$519$		0			0
$520$	−1.44754e12	−	5.26862e11i	−0.868193	−	0.315996i
$521$	8.13033e11	+	1.40821e12i	0.483436	+	0.837335i	0.999819	−	0.0190225i	$-0.00605542\pi$
$521$	8.13033e11	+	1.40821e12i	0.483436	+	0.837335i	−0.516384	+	0.856357i	$0.672722\pi$
$522$		0			0
$523$	−1.51821e12	+	2.62962e12i	−0.887310	+	1.53687i	−0.0442670	+	0.999020i	$0.514095\pi$
$523$	−1.51821e12	+	2.62962e12i	−0.887310	+	1.53687i	−0.843043	+	0.537846i	$0.819238\pi$
$524$	2.57278e12	−	2.15882e12i	1.49077	−	1.25091i
$525$		0			0
$526$	2.08543e11	−	1.18270e12i	0.118784	−	0.673659i
$527$	−9.83104e11	+	5.57546e12i	−0.555203	+	3.14871i
$528$		0			0
$529$	2.67709e12	−	2.24634e12i	1.48632	−	1.24717i
$530$	5.77679e11	−	1.00057e12i	0.318013	−	0.550815i
$531$		0			0
$532$	1.02232e12	+	1.77071e12i	0.553331	+	0.958397i
$533$	2.28730e12	+	8.32508e11i	1.22758	+	0.446803i
$534$		0			0
$535$	−3.21812e11	−	2.70032e11i	−0.169828	−	0.142503i
$536$	−5.82251e12	+	2.11922e12i	−3.04697	+	1.10901i
$537$		0			0
$538$	−3.13963e11	−	1.78058e12i	−0.161569	−	0.916305i
$539$	2.51602e11			0.128400
$540$		0			0
$541$	−1.58146e12			−0.793726			−0.396863	−	0.917878i	$-0.629901\pi$
$541$	−1.58146e12			−0.793726			−0.396863	+	0.917878i	$0.629901\pi$
$542$	−9.65155e11	−	5.47367e12i	−0.480397	−	2.72447i
$543$		0			0
$544$	−4.54627e12	+	1.65471e12i	−2.22567	+	0.810077i
$545$	−7.28564e11	−	6.11338e11i	−0.353739	−	0.296823i
$546$		0			0
$547$	1.15222e12	+	4.19374e11i	0.550292	+	0.200290i	0.602176	−	0.798363i	$-0.294300\pi$
$547$	1.15222e12	+	4.19374e11i	0.550292	+	0.200290i	−0.0518842	+	0.998653i	$0.516523\pi$
$548$	−3.65573e12	−	6.33192e12i	−1.73166	−	2.99932i
$549$		0			0
$550$	3.99268e11	−	6.91552e11i	0.186051	−	0.322250i
$551$	−6.08209e10	+	5.10348e10i	−0.0281106	+	0.0235876i
$552$		0			0
$553$	6.38912e10	−	3.62345e11i	0.0290521	−	0.164763i
$554$	6.75253e11	−	3.82955e12i	0.304560	−	1.72725i
$555$		0			0
$556$	3.65868e11	−	3.07000e11i	0.162363	−	0.136239i
$557$	1.21100e11	−	2.09751e11i	0.0533083	−	0.0923327i	−0.838140	−	0.545455i	$-0.816357\pi$
$557$	1.21100e11	−	2.09751e11i	0.0533083	−	0.0923327i	0.891448	+	0.453123i	$0.149690\pi$
$558$		0			0
$559$	3.41360e10	+	5.91252e10i	0.0147863	+	0.0256106i
$560$	1.91368e12	+	6.96522e11i	0.822286	+	0.299288i
$561$		0			0
$562$	1.48199e12	+	1.24354e12i	0.626660	+	0.525830i
$563$	−1.16668e12	+	4.24637e11i	−0.489401	+	0.178127i	−0.574921	−	0.818209i	$-0.694967\pi$
$563$	−1.16668e12	+	4.24637e11i	−0.489401	+	0.178127i	0.0855200	+	0.996336i	$0.472745\pi$
$564$		0			0
$565$	−6.76304e10	−	3.83551e11i	−0.0279205	−	0.158345i
$566$	6.39367e12			2.61864
$567$		0			0
$568$	9.92231e11			0.399986
$569$	−1.46981e11	−	8.33569e11i	−0.0587835	−	0.333378i	0.941207	−	0.337832i	$-0.109693\pi$
$569$	−1.46981e11	−	8.33569e11i	−0.0587835	−	0.333378i	−0.999990	+	0.00445380i	$0.998582\pi$
$570$		0			0
$571$	−2.22536e12	+	8.09964e11i	−0.876068	+	0.318862i	−0.740622	−	0.671922i	$-0.765469\pi$
$571$	−2.22536e12	+	8.09964e11i	−0.876068	+	0.318862i	−0.135446	+	0.990785i	$0.543247\pi$
$572$	9.33929e11	+	7.83659e11i	0.364780	+	0.306087i
$573$		0			0
$574$	−6.47497e12	−	2.35670e12i	−2.48963	−	0.906150i
$575$	1.51768e12	+	2.62870e12i	0.578995	+	1.00285i
$576$		0			0
$577$	1.15852e12	−	2.00661e12i	0.435122	−	0.753653i	−0.562184	−	0.827012i	$-0.690039\pi$
$577$	1.15852e12	−	2.00661e12i	0.435122	−	0.753653i	0.997306	+	0.0733595i	$0.0233720\pi$
$578$	−8.69127e12	+	7.29284e12i	−3.23898	+	2.71783i
$579$		0			0
$580$	−3.61912e10	+	2.05250e11i	−0.0132793	+	0.0753109i
$581$	5.18136e11	−	2.93850e12i	0.188648	−	1.06987i
$582$		0			0
$583$	−3.97132e11	+	3.33233e11i	−0.142372	+	0.119465i
$584$	−2.15289e12	+	3.72892e12i	−0.765887	+	1.32656i
$585$		0			0
$586$	3.61857e12	+	6.26754e12i	1.26764	+	2.19562i
$587$	3.32608e12	+	1.21060e12i	1.15628	+	0.420850i	0.847766	−	0.530370i	$-0.177947\pi$
$587$	3.32608e12	+	1.21060e12i	1.15628	+	0.420850i	0.308511	+	0.951221i	$0.400169\pi$
$588$		0			0
$589$	2.47747e12	+	2.07884e12i	0.848182	+	0.711709i
$590$	−2.85344e12	+	1.03857e12i	−0.969469	+	0.352858i
$591$		0			0
$592$	−9.11827e11	−	5.17123e12i	−0.305116	−	1.73040i
$593$	−3.05373e12			−1.01411			−0.507055	−	0.861914i	$-0.669266\pi$
$593$	−3.05373e12			−1.01411			−0.507055	+	0.861914i	$0.669266\pi$
$594$		0			0
$595$	2.41070e12			0.788528
$596$	1.71872e12	+	9.74734e12i	0.557952	+	3.16430i
$597$		0			0
$598$	−6.24052e12	+	2.27136e12i	−1.99556	+	0.726325i
$599$	3.81742e12	+	3.20319e12i	1.21157	+	1.01663i	0.999222	+	0.0394356i	$0.0125560\pi$
$599$	3.81742e12	+	3.20319e12i	1.21157	+	1.01663i	0.212350	+	0.977194i	$0.431888\pi$
$600$		0			0
$601$	−1.37297e12	−	4.99720e11i	−0.429265	−	0.156240i	0.118347	−	0.992972i	$-0.462241\pi$
$601$	−1.37297e12	−	4.99720e11i	−0.429265	−	0.156240i	−0.547612	+	0.836733i	$0.684463\pi$
$602$	−9.66334e10	−	1.67374e11i	−0.0299877	−	0.0519402i
$603$		0			0
$604$	1.69673e12	−	2.93882e12i	0.518736	−	0.898478i
$605$	−1.30643e12	+	1.09623e12i	−0.396449	+	0.332660i
$606$		0			0
$607$	4.76637e11	−	2.70314e12i	0.142508	−	0.808201i	−0.826827	−	0.562457i	$-0.809856\pi$
$607$	4.76637e11	−	2.70314e12i	0.142508	−	0.808201i	0.969335	−	0.245745i	$-0.0790325\pi$
$608$	−4.79915e11	+	2.72173e12i	−0.142429	+	0.807755i
$609$		0			0
$610$	−2.21056e12	+	1.85488e12i	−0.646424	+	0.542414i
$611$	−1.14225e12	+	1.97843e12i	−0.331569	+	0.574295i
$612$		0			0
$613$	2.20008e12	+	3.81065e12i	0.629312	+	1.09000i	0.987690	+	0.156424i	$0.0499966\pi$
$613$	2.20008e12	+	3.81065e12i	0.629312	+	1.09000i	−0.358378	+	0.933577i	$0.616670\pi$
$614$	9.98206e12	+	3.63317e12i	2.83441	+	1.03164i
$615$		0			0
$616$	−1.49892e12	−	1.25774e12i	−0.419436	−	0.351948i
$617$	−5.67443e12	+	2.06532e12i	−1.57630	+	0.573727i	−0.974395	−	0.224841i	$-0.927814\pi$
$617$	−5.67443e12	+	2.06532e12i	−1.57630	+	0.573727i	−0.601905	+	0.798568i	$0.705592\pi$
$618$		0			0
$619$	−7.79984e11	−	4.42351e12i	−0.213539	−	1.21104i	−0.883423	−	0.468575i	$-0.844767\pi$
$619$	−7.79984e11	−	4.42351e12i	−0.213539	−	1.21104i	0.669884	−	0.742466i	$-0.266344\pi$
$620$	8.48961e12			2.30741
$621$		0			0
$622$	4.09409e12			1.09673
$623$	−3.33363e11	−	1.89059e12i	−0.0886585	−	0.502808i
$624$		0			0
$625$	−4.70983e11	+	1.71424e11i	−0.123465	+	0.0449377i
$626$	−7.91021e12	−	6.63745e12i	−2.05875	−	1.72750i
$627$		0			0
$628$	1.34101e13	+	4.88089e12i	3.44044	+	1.25222i
$629$	−3.10794e12	−	5.38311e12i	−0.791671	−	1.37121i
$630$		0			0
$631$	3.92801e11	−	6.80352e11i	0.0986372	−	0.170845i	−0.812484	−	0.582984i	$-0.801885\pi$
$631$	3.92801e11	−	6.80352e11i	0.0986372	−	0.170845i	0.911121	+	0.412139i	$0.135218\pi$
$632$	1.61297e12	−	1.35345e12i	0.402162	−	0.337454i
$633$		0			0
$634$	9.52440e9	−	5.40156e10i	0.00234119	−	0.0132775i
$635$	2.71203e11	−	1.53807e12i	0.0661932	−	0.375400i
$636$		0			0
$637$	9.18720e11	−	7.70898e11i	0.221083	−	0.185511i
$638$	6.70079e10	−	1.16061e11i	0.0160115	−	0.0277328i
$639$		0			0
$640$	−8.23371e11	−	1.42612e12i	−0.193993	−	0.336005i
$641$	−5.14577e12	−	1.87291e12i	−1.20390	−	0.438182i	−0.339314	−	0.940673i	$-0.610195\pi$
$641$	−5.14577e12	−	1.87291e12i	−1.20390	−	0.438182i	−0.864582	+	0.502491i	$0.832417\pi$
$642$		0			0
$643$	1.99073e12	+	1.67042e12i	0.459265	+	0.385369i	0.842861	−	0.538132i	$-0.180870\pi$
$643$	1.99073e12	+	1.67042e12i	0.459265	+	0.385369i	−0.383595	+	0.923501i	$0.625314\pi$
$644$	1.23275e13	−	4.48686e12i	2.82416	−	1.02791i
$645$		0			0
$646$	1.60966e12	+	9.12881e12i	0.363652	+	2.06238i
$647$	3.38270e12			0.758917			0.379459	−	0.925209i	$-0.376110\pi$
$647$	3.38270e12			0.758917			0.379459	+	0.925209i	$0.376110\pi$
$648$		0			0
$649$	1.36253e12			0.301471
$650$	−6.60968e11	−	3.74854e12i	−0.145235	−	0.823667i
$651$		0			0
$652$	−2.72970e12	+	9.93530e11i	−0.591563	+	0.215311i
$653$	−2.24365e10	−	1.88264e10i	−0.00482886	−	0.00405190i	0.640370	−	0.768067i	$-0.278781\pi$
$653$	−2.24365e10	−	1.88264e10i	−0.00482886	−	0.00405190i	−0.645199	+	0.764015i	$0.723225\pi$
$654$		0			0
$655$	−2.12562e12	−	7.73661e11i	−0.451231	−	0.164235i
$656$	−9.20762e12	−	1.59481e13i	−1.94124	−	3.36233i
$657$		0			0
$658$	3.23352e12	−	5.60061e12i	0.672448	−	1.16471i
$659$	2.47399e12	−	2.07592e12i	0.510991	−	0.428772i	−0.350487	−	0.936568i	$-0.613984\pi$
$659$	2.47399e12	−	2.07592e12i	0.510991	−	0.428772i	0.861478	+	0.507795i	$0.169539\pi$
$660$		0			0
$661$	7.10451e11	−	4.02917e12i	0.144753	−	0.820935i	−0.822812	−	0.568313i	$-0.807596\pi$
$661$	7.10451e11	−	4.02917e12i	0.144753	−	0.820935i	0.967565	−	0.252622i	$-0.0812928\pi$
$662$	7.14470e11	−	4.05196e12i	0.144585	−	0.819982i
$663$		0			0
$664$	1.30807e13	−	1.09760e13i	2.61141	−	2.19123i
$665$	6.88554e11	−	1.19261e12i	0.136534	−	0.236484i
$666$		0			0
$667$	2.54708e11	+	4.41166e11i	0.0498282	+	0.0863051i
$668$	3.05396e12	+	1.11155e12i	0.593429	+	0.215991i
$669$		0			0
$670$	5.63870e12	+	4.73143e12i	1.08104	+	0.907101i
$671$	1.21674e12	−	4.42857e11i	0.231711	−	0.0843359i
$672$		0			0
$673$	1.44153e12	+	8.17531e12i	0.270867	+	1.53616i	0.751793	+	0.659399i	$0.229189\pi$
$673$	1.44153e12	+	8.17531e12i	0.270867	+	1.53616i	−0.480926	+	0.876761i	$0.659700\pi$
$674$	−8.30497e12			−1.55013
$675$		0			0
$676$	−6.72669e12			−1.23891
$677$	−9.57817e11	−	5.43205e12i	−0.175240	−	0.993836i	−0.937866	−	0.346997i	$-0.887202\pi$
$677$	−9.57817e11	−	5.43205e12i	−0.175240	−	0.993836i	0.762626	−	0.646839i	$-0.223910\pi$
$678$		0			0
$679$	−3.88025e12	+	1.41230e12i	−0.700561	+	0.254983i
$680$	1.05682e13	+	8.86776e12i	1.89544	+	1.59046i
$681$		0			0
$682$	−5.12976e12	−	1.86708e12i	−0.907962	−	0.330471i
$683$	1.71604e12	+	2.97227e12i	0.301741	+	0.522631i	0.976530	−	0.215379i	$-0.0690988\pi$
$683$	1.71604e12	+	2.97227e12i	0.301741	+	0.522631i	−0.674789	+	0.738010i	$0.735766\pi$
$684$		0			0
$685$	−2.46221e12	+	4.26468e12i	−0.427285	+	0.740080i
$686$	−8.73582e12	+	7.33023e12i	−1.50607	+	1.26374i
$687$		0			0
$688$	8.96918e10	−	5.08668e11i	0.0152618	−	0.0865538i
$689$	−4.29108e11	+	2.43359e12i	−0.0725404	+	0.411397i
$690$		0			0
$691$	−1.96927e12	+	1.65242e12i	−0.328590	+	0.275720i	−0.792125	−	0.610359i	$-0.791025\pi$
$691$	−1.96927e12	+	1.65242e12i	−0.328590	+	0.275720i	0.463535	+	0.886079i	$0.346581\pi$
$692$	−6.34601e11	+	1.09916e12i	−0.105202	+	0.182215i
$693$		0			0
$694$	−7.13481e12	−	1.23579e13i	−1.16752	−	2.02221i
$695$	−3.02278e11	−	1.10020e11i	−0.0491446	−	0.0178872i
$696$		0			0
$697$	−1.66991e13	−	1.40122e13i	−2.68006	−	2.24884i
$698$	8.28833e12	−	3.01670e12i	1.32165	−	0.481042i
$699$		0			0
$700$	1.30568e12	+	7.40487e12i	0.205539	+	1.16567i
$701$	−7.21141e12			−1.12795			−0.563974	−	0.825793i	$-0.690728\pi$
$701$	−7.21141e12			−1.12795			−0.563974	+	0.825793i	$0.690728\pi$
$702$		0			0
$703$	−3.55081e12			−0.548312
$704$	−1.16480e11	−	6.60593e11i	−0.0178721	−	0.101358i
$705$		0			0
$706$	7.30002e12	−	2.65699e12i	1.10587	−	0.402503i
$707$	−5.00829e12	−	4.20245e12i	−0.753879	−	0.632580i
$708$		0			0
$709$	−3.71627e12	−	1.35261e12i	−0.552331	−	0.201032i	0.0507508	−	0.998711i	$-0.483839\pi$
$709$	−3.71627e12	−	1.35261e12i	−0.552331	−	0.201032i	−0.603082	+	0.797679i	$0.706061\pi$
$710$	−5.89364e11	−	1.02081e12i	−0.0870404	−	0.150758i
$711$		0			0
$712$	5.49313e12	−	9.51437e12i	0.801050	−	1.38746i
$713$	1.58958e13	−	1.33381e13i	2.30345	−	1.93282i
$714$		0			0
$715$	1.42587e11	−	8.08652e11i	0.0204034	−	0.115714i
$716$	−4.12730e11	+	2.34071e12i	−0.0586891	+	0.332842i
$717$		0			0
$718$	−1.85910e13	+	1.55997e13i	−2.61062	+	2.19057i
$719$	−4.77880e12	+	8.27713e12i	−0.666867	+	1.15505i	0.311909	+	0.950112i	$0.399032\pi$
$719$	−4.77880e12	+	8.27713e12i	−0.666867	+	1.15505i	−0.978776	+	0.204935i	$0.934302\pi$
$720$		0			0
$721$	−4.91213e11	−	8.50806e11i	−0.0676957	−	0.117252i
$722$	−7.50560e12	−	2.73181e12i	−1.02794	−	0.374140i
$723$		0			0
$724$	−2.24338e12	−	1.88242e12i	−0.303445	−	0.254620i
$725$	−2.74368e11	+	9.98617e10i	−0.0368818	+	0.0134239i
$726$		0			0
$727$	2.15322e11	+	1.22115e12i	0.0285880	+	0.162131i	0.995760	−	0.0919936i	$-0.0293239\pi$
$727$	2.15322e11	+	1.22115e12i	0.0285880	+	0.162131i	−0.967172	+	0.254124i	$0.918213\pi$
$728$	−9.32697e12			−1.23069
$729$		0			0
$730$	5.11509e12			0.666654
$731$	−1.06173e11	−	6.02136e11i	−0.0137526	−	0.0779949i
$732$		0			0
$733$	6.07778e12	−	2.21213e12i	0.777637	−	0.283037i	0.0774499	−	0.996996i	$-0.475322\pi$
$733$	6.07778e12	−	2.21213e12i	0.777637	−	0.283037i	0.700187	+	0.713960i	$0.253100\pi$
$734$	−4.36040e12	−	3.65881e12i	−0.554491	−	0.465273i
$735$		0			0
$736$	1.66630e13	+	6.06484e12i	2.09316	+	0.761849i
$737$	−1.65143e12	−	2.86035e12i	−0.206184	−	0.357122i
$738$		0			0
$739$	−6.23321e12	+	1.07962e13i	−0.768798	+	1.33160i	0.169418	+	0.985544i	$0.445811\pi$
$739$	−6.23321e12	+	1.07962e13i	−0.768798	+	1.33160i	−0.938215	+	0.346052i	$0.887522\pi$
$740$	−7.14027e12	+	5.99140e12i	−0.875331	+	0.734490i
$741$		0			0
$742$	1.21474e12	−	6.88911e12i	0.147117	−	0.834344i
$743$	6.92503e11	−	3.92738e12i	0.0833627	−	0.472773i	−0.914335	−	0.404958i	$-0.867286\pi$
$743$	6.92503e11	−	3.92738e12i	0.0833627	−	0.472773i	0.997698	−	0.0678152i	$-0.0216028\pi$
$744$		0			0
$745$	5.10669e12	−	4.28502e12i	0.607346	−	0.509624i
$746$	−5.45788e12	+	9.45333e12i	−0.645207	+	1.11753i
$747$		0			0
$748$	−5.45922e12	−	9.45565e12i	−0.637637	−	1.10442i
$749$	−2.39017e12	−	8.69952e11i	−0.277499	−	0.101001i
$750$		0			0
$751$	9.84947e11	+	8.26468e11i	0.112988	+	0.0948083i	0.697531	−	0.716554i	$-0.254282\pi$
$751$	9.84947e11	+	8.26468e11i	0.112988	+	0.0948083i	−0.584543	+	0.811363i	$0.698726\pi$
$752$	1.62411e13	−	5.91129e12i	1.85198	−	0.674065i
$753$		0			0
$754$	−1.10928e11	−	6.29105e11i	−0.0124989	−	0.0708847i
$755$	−2.28557e12			−0.255996
$756$		0			0
$757$	1.42968e13			1.58237			0.791183	−	0.611580i	$-0.209466\pi$
$757$	1.42968e13			1.58237			0.791183	+	0.611580i	$0.209466\pi$
$758$	5.42167e12	+	3.07478e13i	0.596516	+	3.38301i
$759$		0			0
$760$	7.40554e12	−	2.69540e12i	0.805185	−	0.293063i
$761$	−7.85692e11	−	6.59273e11i	−0.0849222	−	0.0712582i	0.599338	−	0.800496i	$-0.295430\pi$
$761$	−7.85692e11	−	6.59273e11i	−0.0849222	−	0.0712582i	−0.684260	+	0.729238i	$0.739875\pi$
$762$		0			0
$763$	−5.41121e12	−	1.96952e12i	−0.578009	−	0.210378i
$764$	6.31015e12	+	1.09295e13i	0.670069	+	1.16059i
$765$		0			0
$766$	−1.81226e12	+	3.13892e12i	−0.190191	+	0.329421i
$767$	4.97527e12	−	4.17474e12i	0.519083	−	0.435563i
$768$		0			0
$769$	−7.73705e11	+	4.38790e12i	−0.0797824	+	0.452468i	0.918579	+	0.395238i	$0.129338\pi$
$769$	−7.73705e11	+	4.38790e12i	−0.0797824	+	0.452468i	−0.998361	+	0.0572301i	$0.981773\pi$
$770$	−4.03641e11	+	2.28916e12i	−0.0413797	+	0.234676i
$771$		0			0
$772$	−1.37842e13	+	1.15664e13i	−1.39671	+	1.17198i
$773$	5.03971e12	−	8.72904e12i	0.507690	−	0.879344i	−0.492271	−	0.870442i	$-0.663833\pi$
$773$	5.03971e12	−	8.72904e12i	0.507690	−	0.879344i	0.999960	−	0.00890202i	$-0.00283364\pi$
$774$		0			0
$775$	5.94666e12	+	1.02999e13i	0.592127	+	1.02559i
$776$	−2.22056e13	−	8.08219e12i	−2.19829	−	0.800113i
$777$		0			0
$778$	1.91347e13	+	1.60559e13i	1.87246	+	1.57118i
$779$	−1.17017e13	+	4.25906e12i	−1.13849	+	0.414377i
$780$		0			0
$781$	9.18434e10	+	5.20870e11i	0.00883321	+	0.0500956i
$782$	5.94752e13			5.68729
$783$		0			0
$784$	−9.07340e12			−0.857725
$785$	−1.66905e12	−	9.46563e12i	−0.156875	−	0.889684i
$786$		0			0
$787$	6.00349e12	−	2.18509e12i	0.557850	−	0.203041i	−0.0476808	−	0.998863i	$-0.515183\pi$
$787$	6.00349e12	−	2.18509e12i	0.557850	−	0.203041i	0.605531	+	0.795822i	$0.292961\pi$
$788$	1.27923e13	+	1.07340e13i	1.18190	+	0.991728i
$789$		0			0
$790$	−2.35050e12	−	8.55512e11i	−0.214703	−	0.0781455i
$791$	−1.17906e12	−	2.04220e12i	−0.107088	−	0.185483i
$792$		0			0
$793$	3.08601e12	−	5.34513e12i	0.277120	−	0.479986i
$794$	−1.38976e12	+	1.16615e12i	−0.124093	+	0.104127i
$795$		0			0
$796$	−7.63137e12	+	4.32796e13i	−0.673742	+	3.82098i
$797$	7.92225e11	−	4.49293e12i	0.0695483	−	0.394428i	−0.930085	−	0.367345i	$-0.880267\pi$
$797$	7.92225e11	−	4.49293e12i	0.0695483	−	0.394428i	0.999633	−	0.0270832i	$-0.00862191\pi$
$798$		0			0
$799$	1.56727e13	−	1.31510e13i	1.36046	−	1.14156i
$800$	−5.08175e12	+	8.80185e12i	−0.438640	+	0.759747i
$801$		0			0
$802$	−1.10468e13	−	1.91335e13i	−0.942866	−	1.63309i
$803$	−2.15677e12	−	7.85000e11i	−0.183056	−	0.0666269i
$804$		0			0
$805$	−6.76854e12	−	5.67948e12i	−0.568086	−	0.476681i
$806$	−2.44519e13	+	8.89977e12i	−2.04082	+	0.742799i
$807$		0			0
$808$	−6.49693e12	−	3.68459e13i	−0.536238	−	3.04115i
$809$	−3.65686e12			−0.300151			−0.150076	−	0.988675i	$-0.547952\pi$
$809$	−3.65686e12			−0.300151			−0.150076	+	0.988675i	$0.547952\pi$
$810$		0			0
$811$	−3.09618e12			−0.251323			−0.125662	−	0.992073i	$-0.540105\pi$
$811$	−3.09618e12			−0.251323			−0.125662	+	0.992073i	$0.540105\pi$
$812$	2.19128e11	+	1.24274e12i	0.0176887	+	0.100318i
$813$		0			0
$814$	5.63210e12	−	2.04992e12i	0.449635	−	0.163654i
$815$	1.49877e12	+	1.25761e12i	0.118994	+	0.0998478i
$816$		0			0
$817$	−3.28211e11	−	1.19459e11i	−0.0257724	−	0.00938037i
$818$	2.22537e13	+	3.85446e13i	1.73785	+	3.01005i
$819$		0			0
$820$	−1.63443e13	+	2.83092e13i	−1.26242	+	2.18658i
$821$	8.97341e11	−	7.52958e11i	0.0689308	−	0.0578398i	−0.607671	−	0.794189i	$-0.707896\pi$
$821$	8.97341e11	−	7.52958e11i	0.0689308	−	0.0578398i	0.676602	+	0.736349i	$0.263452\pi$
$822$		0			0
$823$	2.93059e12	−	1.66202e13i	0.222667	−	1.26281i	−0.644429	−	0.764664i	$-0.722905\pi$
$823$	2.93059e12	−	1.66202e13i	0.222667	−	1.26281i	0.867096	−	0.498142i	$-0.165984\pi$
$824$	9.76278e11	−	5.53674e12i	0.0737736	−	0.418391i
$825$		0			0
$826$	−1.40842e13	+	1.18180e13i	−1.05274	+	0.883354i
$827$	−2.26487e12	+	3.92288e12i	−0.168372	+	0.291629i	−0.937848	−	0.347047i	$-0.887184\pi$
$827$	−2.26487e12	+	3.92288e12i	−0.168372	+	0.291629i	0.769476	+	0.638676i	$0.220518\pi$
$828$		0			0
$829$	1.26865e13	+	2.19737e13i	0.932926	+	1.61588i	0.778291	+	0.627904i	$0.216087\pi$
$829$	1.26865e13	+	2.19737e13i	0.932926	+	1.61588i	0.154635	+	0.987972i	$0.450580\pi$
$830$	−1.90618e13	−	6.93792e12i	−1.39416	−	0.507432i
$831$		0			0
$832$	−2.44936e12	−	2.05526e12i	−0.177214	−	0.148700i
$833$	−1.00929e13	+	3.67352e12i	−0.726296	+	0.264350i
$834$		0			0
$835$	−3.80100e11	−	2.15566e12i	−0.0270588	−	0.153458i
$836$	−6.23714e12			−0.441629
$837$		0			0
$838$	−1.82240e13			−1.27658
$839$	−4.69997e11	−	2.66548e12i	−0.0327466	−	0.185715i	0.964047	−	0.265732i	$-0.0856137\pi$
$839$	−4.69997e11	−	2.66548e12i	−0.0327466	−	0.185715i	−0.996794	+	0.0800170i	$0.974503\pi$
$840$		0			0
$841$	1.35862e13	−	4.94498e12i	0.936519	−	0.340865i
$842$	−1.28819e13	−	1.08092e13i	−0.883232	−	0.741120i
$843$		0			0
$844$	−1.83590e13	−	6.68213e12i	−1.24540	−	0.453288i
$845$	2.26528e12	+	3.92358e12i	0.152850	+	0.264745i
$846$		0			0
$847$	−5.16295e12	+	8.94249e12i	−0.344685	+	0.597012i
$848$	1.43216e13	−	1.20172e13i	0.951064	−	0.798037i
$849$		0			0
$850$	−5.91945e12	+	3.35709e13i	−0.388952	+	2.20586i
$851$	−3.95613e12	+	2.24363e13i	−0.258576	+	1.46646i
$852$		0			0
$853$	4.30098e12	−	3.60895e12i	0.278161	−	0.233405i	−0.493024	−	0.870016i	$-0.664109\pi$
$853$	4.30098e12	−	3.60895e12i	0.278161	−	0.233405i	0.771185	+	0.636611i	$0.219664\pi$
$854$	−8.73600e12	+	1.51312e13i	−0.562021	+	0.973448i
$855$		0			0
$856$	−7.27808e12	−	1.26060e13i	−0.463324	−	0.802501i
$857$	7.89606e12	+	2.87393e12i	0.500030	+	0.181996i	0.579708	−	0.814825i	$-0.303167\pi$
$857$	7.89606e12	+	2.87393e12i	0.500030	+	0.181996i	−0.0796772	+	0.996821i	$0.525389\pi$
$858$		0			0
$859$	−9.99505e12	−	8.38684e12i	−0.626348	−	0.525568i	0.273444	−	0.961888i	$-0.411837\pi$
$859$	−9.99505e12	−	8.38684e12i	−0.626348	−	0.525568i	−0.899792	+	0.436320i	$0.856282\pi$
$860$	−8.61564e11	+	3.13584e11i	−0.0537087	+	0.0195484i
$861$		0			0
$862$	4.16693e12	+	2.36318e13i	0.257059	+	1.45786i
$863$	6.93129e12			0.425368			0.212684	−	0.977121i	$-0.431779\pi$
$863$	6.93129e12			0.425368			0.212684	+	0.977121i	$0.431779\pi$
$864$		0			0
$865$	8.54834e11			0.0519170
$866$	8.35429e11	+	4.73795e12i	0.0504753	+	0.286260i
$867$		0			0
$868$	4.83024e13	−	1.75806e13i	2.88822	−	1.05123i
$869$	8.59790e11	+	7.21450e11i	0.0511450	+	0.0429158i
$870$		0			0
$871$	−1.47942e13	−	5.38464e12i	−0.870982	−	0.317011i
$872$	−1.64771e13	−	2.85392e13i	−0.965067	−	1.67155i
$873$		0			0
$874$	1.69875e13	−	2.94233e13i	0.984757	−	1.70565i
$875$	9.62403e12	−	8.07552e12i	0.555036	−	0.465730i
$876$		0			0
$877$	1.47539e12	−	8.36735e12i	0.0842187	−	0.477628i	−0.913304	−	0.407279i	$-0.866478\pi$
$877$	1.47539e12	−	8.36735e12i	0.0842187	−	0.477628i	0.997522	−	0.0703488i	$-0.0224112\pi$
$878$	4.34566e12	−	2.46455e13i	0.246792	−	1.39963i
$879$		0			0
$880$	−4.75888e12	+	3.99318e12i	−0.267506	+	0.224464i
$881$	−8.66150e12	+	1.50022e13i	−0.484397	+	0.839000i	−0.999839	−	0.0179240i	$-0.994294\pi$
$881$	−8.66150e12	+	1.50022e13i	−0.484397	+	0.839000i	0.515442	+	0.856924i	$0.327628\pi$
$882$		0			0
$883$	6.59120e12	+	1.14163e13i	0.364873	+	0.631978i	0.988756	−	0.149540i	$-0.0477791\pi$
$883$	6.59120e12	+	1.14163e13i	0.364873	+	0.631978i	−0.623883	+	0.781518i	$0.714446\pi$
$884$	−4.89060e13	−	1.78003e13i	−2.69356	−	0.980377i
$885$		0			0
$886$	−2.27438e13	−	1.90843e13i	−1.23997	−	1.04046i
$887$	2.56149e13	−	9.32307e12i	1.38943	−	0.505712i	0.464408	−	0.885622i	$-0.346267\pi$
$887$	2.56149e13	−	9.32307e12i	1.38943	−	0.505712i	0.925023	+	0.379910i	$0.124045\pi$
$888$		0			0
$889$	−1.64206e12	−	9.31261e12i	−0.0881723	−	0.500050i
$890$	−1.30512e13			−0.697261
$891$		0			0
$892$	−3.57983e13			−1.89331
$893$	−2.02949e12	−	1.15098e13i	−0.106796	−	0.605669i
$894$		0			0
$895$	1.50429e12	−	5.47518e11i	0.0783662	−	0.0285230i
$896$	−7.63791e12	−	6.40897e12i	−0.395903	−	0.332202i
$897$		0			0
$898$	1.10031e13	+	4.00479e12i	0.564638	+	0.205512i
$899$	9.98009e11	+	1.72860e12i	0.0509584	+	0.0882625i
$900$		0			0
$901$	1.10654e13	−	1.91658e13i	0.559379	−	0.968872i
$902$	1.61018e13	−	1.35110e13i	0.809924	−	0.679607i
$903$		0			0
$904$	2.34337e12	−	1.32899e13i	0.116703	−	0.661856i
$905$	−3.42507e11	+	1.94246e12i	−0.0169727	+	0.0962571i
$906$		0			0
$907$	9.62927e10	−	8.07992e10i	0.00472455	−	0.00396437i	−0.640422	−	0.768023i	$-0.721241\pi$
$907$	9.62927e10	−	8.07992e10i	0.00472455	−	0.00396437i	0.645147	+	0.764059i	$0.276796\pi$
$908$	2.94524e13	−	5.10130e13i	1.43792	−	2.49055i
$909$		0			0
$910$	5.54002e12	+	9.59560e12i	0.267809	+	0.463859i
$911$	2.64073e13	+	9.61148e12i	1.27026	+	0.462336i	0.887198	−	0.461388i	$-0.152648\pi$
$911$	2.64073e13	+	9.61148e12i	1.27026	+	0.462336i	0.383059	+	0.923724i	$0.374871\pi$
$912$		0			0
$913$	6.97262e12	+	5.85072e12i	0.332107	+	0.278670i
$914$	4.59580e13	−	1.67273e13i	2.17823	−	0.792810i
$915$		0			0
$916$	−2.23065e12	−	1.26506e13i	−0.104689	−	0.593721i
$917$	−1.36960e13			−0.639635
$918$		0			0
$919$	−3.22440e12			−0.149118			−0.0745589	−	0.997217i	$-0.523755\pi$
$919$	−3.22440e12			−0.149118			−0.0745589	+	0.997217i	$0.523755\pi$
$920$	−8.78041e12	−	4.97962e13i	−0.404082	−	2.29166i
$921$		0			0
$922$	4.84429e13	−	1.76318e13i	2.20771	−	0.803539i
$923$	1.93129e12	+	1.62055e12i	0.0875871	+	0.0734943i
$924$		0			0
$925$	−1.22705e13	−	4.46609e12i	−0.551092	−	0.200581i
$926$	−4.02458e12	−	6.97078e12i	−0.179875	−	0.311553i
$927$		0			0
$928$	−8.52854e11	+	1.47719e12i	−0.0377493	+	0.0653837i
$929$	1.64090e12	−	1.37688e12i	0.0722787	−	0.0606490i	−0.605933	−	0.795516i	$-0.707200\pi$
$929$	1.64090e12	−	1.37688e12i	0.0722787	−	0.0606490i	0.678211	+	0.734867i	$0.262755\pi$
$930$		0			0
$931$	−1.06543e12	+	6.04236e12i	−0.0464785	+	0.263592i
$932$	2.82809e12	−	1.60389e13i	0.122778	−	0.696311i
$933$		0			0
$934$	−4.68411e12	+	3.93044e12i	−0.201403	+	0.168997i
$935$	−3.67690e12	+	6.36857e12i	−0.157336	+	0.272515i
$936$		0			0
$937$	−1.17509e13	−	2.03532e13i	−0.498017	−	0.862591i	0.501980	−	0.864879i	$-0.332605\pi$
$937$	−1.17509e13	−	2.03532e13i	−0.498017	−	0.862591i	−0.999997	+	0.00228788i	$0.999272\pi$
$938$	4.18799e13	+	1.52430e13i	1.76642	+	0.642923i
$939$		0			0
$940$	−2.35019e13	−	1.97205e13i	−0.981812	−	0.823838i
$941$	−2.17577e13	+	7.91915e12i	−0.904606	+	0.329250i	−0.752097	−	0.659053i	$-0.770957\pi$
$941$	−2.17577e13	+	7.91915e12i	−0.904606	+	0.329250i	−0.152509	+	0.988302i	$0.548735\pi$
$942$		0			0
$943$	1.38741e13	+	7.86842e13i	0.571352	+	3.24030i
$944$	−4.91364e13			−2.01386
$945$		0			0
$946$	5.89556e11			0.0239340
$947$	3.55631e12	+	2.01689e13i	0.143690	+	0.814904i	0.968410	+	0.249363i	$0.0802214\pi$
$947$	3.55631e12	+	2.01689e13i	0.143690	+	0.814904i	−0.824720	+	0.565541i	$0.808668\pi$
$948$		0			0
$949$	−1.02806e13	+	3.74184e12i	−0.411454	+	0.149757i
$950$	1.49173e13	+	1.25171e13i	0.594202	+	0.498594i
$951$		0			0
$952$	7.84924e13	+	2.85689e13i	3.09714	+	1.12727i
$953$	8.68246e12	+	1.50385e13i	0.340977	+	0.590589i	0.984614	−	0.174741i	$-0.0559090\pi$
$953$	8.68246e12	+	1.50385e13i	0.340977	+	0.590589i	−0.643638	+	0.765330i	$0.722576\pi$
$954$		0			0
$955$	4.25002e12	−	7.36124e12i	0.165339	−	0.286376i
$956$	−5.77299e13	+	4.84412e13i	−2.23532	+	1.87566i
$957$		0			0
$958$	−2.97914e12	+	1.68955e13i	−0.114274	+	0.648078i
$959$	−5.17751e12	+	2.93631e13i	−0.197668	+	1.12103i
$960$		0			0
$961$	4.20297e13	−	3.52671e13i	1.58965	−	1.33387i
$962$	1.42847e13	−	2.47418e13i	0.537753	−	0.931415i
$963$		0			0
$964$	1.88599e13	+	3.26662e13i	0.703383	+	1.21829i
$965$	1.13885e13	+	4.14506e12i	0.422759	+	0.153872i
$966$		0			0
$967$	1.09647e12	+	9.20050e11i	0.0403254	+	0.0338370i	0.662728	−	0.748861i	$-0.269399\pi$
$967$	1.09647e12	+	9.20050e11i	0.0403254	+	0.0338370i	−0.622402	+	0.782698i	$0.713843\pi$
$968$	−5.55286e13	+	2.02107e13i	−2.03272	+	0.739849i
$969$		0			0
$970$	4.87471e12	+	2.76458e13i	0.176797	+	1.00267i
$971$	6.08099e12			0.219527			0.109763	−	0.993958i	$-0.464991\pi$
$971$	6.08099e12			0.219527			0.109763	+	0.993958i	$0.464991\pi$
$972$		0			0
$973$	−1.94768e12			−0.0696641
$974$	−5.81187e12	−	3.29608e13i	−0.206919	−	1.17350i
$975$		0			0
$976$	−4.38787e13	+	1.59706e13i	−1.54785	+	0.563373i
$977$	2.77256e13	+	2.32645e13i	0.973544	+	0.816900i	0.983103	−	0.183054i	$-0.0585983\pi$
$977$	2.77256e13	+	2.32645e13i	0.973544	+	0.816900i	−0.00955887	+	0.999954i	$0.503043\pi$
$978$		0			0
$979$	5.50301e12	+	2.00293e12i	0.191460	+	0.0696858i
$980$	8.05302e12	+	1.39482e13i	0.278896	+	0.483061i
$981$		0			0
$982$	1.99008e13	−	3.44693e13i	0.682920	−	1.18285i
$983$	−8.25505e12	+	6.92681e12i	−0.281987	+	0.236615i	−0.772800	−	0.634650i	$-0.781144\pi$
$983$	−8.25505e12	+	6.92681e12i	−0.281987	+	0.236615i	0.490813	+	0.871265i	$0.336700\pi$
$984$		0			0
$985$	1.95305e12	−	1.10763e13i	0.0661076	−	0.374915i
$986$	−9.93443e11	+	5.63410e12i	−0.0334732	+	0.189836i
$987$		0			0
$988$	−2.27748e13	+	1.91104e13i	−0.760412	+	0.638061i
$989$	−1.12050e12	+	1.94076e12i	−0.0372416	+	0.0645043i
$990$		0			0
$991$	1.32194e13	+	2.28967e13i	0.435393	+	0.754122i	0.997328	−	0.0730591i	$-0.0232762\pi$
$991$	1.32194e13	+	2.28967e13i	0.435393	+	0.754122i	−0.561935	+	0.827181i	$0.689943\pi$
$992$	6.52899e13	+	2.37636e13i	2.14064	+	0.779129i
$993$		0			0
$994$	−5.46717e12	−	4.58750e12i	−0.177633	−	0.149052i
$995$	2.78143e13	−	1.01236e13i	0.899632	−	0.327439i
$996$		0			0
$997$	−8.72942e12	−	4.95070e13i	−0.279806	−	1.58686i	−0.723269	−	0.690567i	$-0.757361\pi$
$997$	−8.72942e12	−	4.95070e13i	−0.279806	−	1.58686i	0.443462	−	0.896293i	$-0.353750\pi$
$998$	−1.95221e13			−0.622931
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.1		156
3.2	odd	2		27.10.e.a.13.26	✓	156
27.2	odd	18		27.10.e.a.25.26	yes	156
27.25	even	9	inner	81.10.e.a.73.1		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.26	✓	156	3.2	odd	2
27.10.e.a.25.26	yes	156	27.2	odd	18
81.10.e.a.10.1		156	1.1	even	1	trivial
81.10.e.a.73.1		156	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.14775 - 40.5369i) q^{2} +(-1111.03 + 404.381i) q^{4} +(610.019 + 511.867i) q^{5} +(4530.75 + 1649.06i) q^{7} +(13796.1 + 23895.6i) q^{8} +(16389.2 - 28387.0i) q^{10} +(-11267.0 + 9454.10i) q^{11} +(-12174.2 + 69043.0i) q^{13} +(34463.1 - 195450. i) q^{14} +(406315. - 340939. i) q^{16} +(313935. - 543751. i) q^{17} +(-179335. - 310617. i) q^{19} +(-884736. - 322018. i) q^{20} +(463773. + 389152. i) q^{22} +(-2.16249e6 + 787080. i) q^{23} +(-229041. - 1.29896e6i) q^{25} +2.88581e6 q^{26} -5.70063e6 q^{28} +(-38439.2 - 218000. i) q^{29} +(-8.47317e6 + 3.08398e6i) q^{31} +(-5.90275e6 - 4.95299e6i) q^{32} +(-2.42859e7 - 8.83935e6i) q^{34} +(1.91975e6 + 3.32510e6i) q^{35} +(4.94997e6 - 8.57361e6i) q^{37} +(-1.13096e7 + 9.48988e6i) q^{38} +(-3.81546e6 + 2.16386e7i) q^{40} +(6.02891e6 - 3.41916e7i) q^{41} +(745981. - 625952. i) q^{43} +(8.69483e6 - 1.50599e7i) q^{44} +(4.73627e7 + 8.20346e7i) q^{46} +(3.06202e7 + 1.11448e7i) q^{47} +(-1.31043e7 - 1.09958e7i) q^{49} +(-5.10185e7 + 1.85692e7i) q^{50} +(-1.43939e7 - 8.16316e7i) q^{52} +3.52475e7 q^{53} -1.17123e7 q^{55} +(2.31016e7 + 1.31016e8i) q^{56} +(-8.56228e6 + 3.11641e6i) q^{58} +(-7.09656e7 - 5.95472e7i) q^{59} +(-8.27266e7 - 3.01100e7i) q^{61} +(1.85579e8 + 3.21432e8i) q^{62} +(-2.28034e7 + 3.94967e7i) q^{64} +(-4.27673e7 + 3.58860e7i) q^{65} +(-3.89948e7 + 2.21151e8i) q^{67} +(-1.28908e8 + 7.31071e8i) q^{68} +(1.21067e8 - 1.01588e8i) q^{70} +(1.79802e7 - 3.11427e7i) q^{71} +(7.80253e7 + 1.35144e8i) q^{73} +(-3.82928e8 - 1.39375e8i) q^{74} +(3.24853e8 + 2.72584e8i) q^{76} +(-6.66382e7 + 2.42543e7i) q^{77} +(-1.32512e7 - 7.51515e7i) q^{79} +4.22375e8 q^{80} -1.42912e9 q^{82} +(-1.07463e8 - 6.09454e8i) q^{83} +(4.69834e8 - 1.71006e8i) q^{85} +(-3.07062e7 - 2.57656e7i) q^{86} +(-3.81352e8 - 1.38801e8i) q^{88} +(-1.99082e8 - 3.44820e8i) q^{89} +(-1.69014e8 + 2.92741e8i) q^{91} +(2.08430e9 - 1.74893e9i) q^{92} +(2.32911e8 - 1.32091e9i) q^{94} +(4.95968e7 - 2.81277e8i) q^{95} +(-6.56060e8 + 5.50500e8i) q^{97} +(-3.52071e8 + 6.09804e8i) 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

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