LMFDB - Embedded newform 81.9.f.a.8.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(8,81)]

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([1]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, 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:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			8.14
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(7.66670 + 1.35185i) q^{2} +(-183.611 - 66.8288i) q^{4} +(24.0534 + 28.6657i) q^{5} +(-2598.90 + 945.921i) q^{7} +(-3043.29 - 1757.05i) q^{8} +(145.659 + 252.288i) q^{10} +(4786.80 - 5704.68i) q^{11} +(2684.14 + 15222.5i) q^{13} +(-21203.7 + 3738.78i) q^{14} +(17361.5 + 14568.0i) q^{16} +(124728. - 72011.7i) q^{17} +(-101393. + 175618. i) q^{19} +(-2500.76 - 6870.79i) q^{20} +(44410.8 - 37265.1i) q^{22} +(39698.1 - 109070. i) q^{23} +(67588.2 - 383312. i) q^{25} +120335. i q^{26} +540399. q^{28} +(609347. + 107444. i) q^{29} +(1.01617e6 + 369854. i) q^{31} +(691668. + 824298. i) q^{32} +(1.05360e6 - 383479. i) q^{34} +(-89627.8 - 51746.6i) q^{35} +(-978631. - 1.69504e6i) q^{37} +(-1.01476e6 + 1.20934e6i) q^{38} +(-22834.5 - 129501. i) q^{40} +(1.39463e6 - 245911. i) q^{41} +(2.04961e6 + 1.71982e6i) q^{43} +(-1.26014e6 + 727544. i) q^{44} +(451799. - 782539. i) q^{46} +(1.82238e6 + 5.00694e6i) q^{47} +(1.44340e6 - 1.21116e6i) q^{49} +(1.03636e6 - 2.84736e6i) q^{50} +(524465. - 2.97439e6i) q^{52} -3.45452e6i q^{53} +278668. q^{55} +(9.57122e6 + 1.68767e6i) q^{56} +(4.52643e6 + 1.64749e6i) q^{58} +(1.16111e7 + 1.38375e7i) q^{59} +(1.16719e7 - 4.24821e6i) q^{61} +(7.29065e6 + 4.20926e6i) q^{62} +(1.28751e6 + 2.23004e6i) q^{64} +(-371801. + 443096. i) q^{65} +(-1.92937e6 - 1.09420e7i) q^{67} +(-2.77138e7 + 4.88669e6i) q^{68} +(-617196. - 517889. i) q^{70} +(2.34487e7 - 1.35381e7i) q^{71} +(-1.28556e7 + 2.22665e7i) q^{73} +(-5.21144e6 - 1.43183e7i) q^{74} +(3.03531e7 - 2.54693e7i) q^{76} +(-7.04421e6 + 1.93538e7i) q^{77} +(-981583. + 5.56684e6i) q^{79} +848091. i q^{80} +1.10246e7 q^{82} +(-5.90784e6 - 1.04171e6i) q^{83} +(5.06440e6 + 1.84329e6i) q^{85} +(1.33888e7 + 1.59561e7i) q^{86} +(-2.45910e7 + 8.95039e6i) q^{88} +(-3.29258e7 - 1.90097e7i) q^{89} +(-2.13751e7 - 3.70227e7i) q^{91} +(-1.45780e7 + 1.73734e7i) q^{92} +(7.20300e6 + 4.08503e7i) q^{94} +(-7.47305e6 + 1.31770e6i) q^{95} +(9.92181e6 + 8.32538e6i) q^{97} +(1.27034e7 - 7.33433e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	7.66670	+	1.35185i	0.479169	+	0.0844904i	0.408015	−	0.912975i	$-0.366221\pi$
$2$	7.66670	+	1.35185i	0.479169	+	0.0844904i	0.0711532	+	0.997465i	$0.477332\pi$
$3$		0			0
$3$		0			0
$4$	−183.611	−	66.8288i	−0.717229	−	0.261050i
$5$	24.0534	+	28.6657i	0.0384854	+	0.0458652i	0.784944	−	0.619567i	$-0.212692\pi$
$5$	24.0534	+	28.6657i	0.0384854	+	0.0458652i	−0.746458	+	0.665432i	$0.768247\pi$
$6$		0			0
$7$	−2598.90	+	945.921i	−1.08242	+	0.393970i	−0.820809	−	0.571203i	$-0.806477\pi$
$7$	−2598.90	+	945.921i	−1.08242	+	0.393970i	−0.261614	+	0.965173i	$0.584255\pi$
$8$	−3043.29	−	1757.05i	−0.742991	−	0.428966i
$9$		0			0
$10$	145.659	+	252.288i	0.0145659	+	0.0252288i
$11$	4786.80	−	5704.68i	0.326945	−	0.389637i	−0.577385	−	0.816472i	$-0.695927\pi$
$11$	4786.80	−	5704.68i	0.326945	−	0.389637i	0.904330	+	0.426835i	$0.140371\pi$
$12$		0			0
$13$	2684.14	+	15222.5i	0.0939791	+	0.532982i	0.995055	+	0.0993213i	$0.0316672\pi$
$13$	2684.14	+	15222.5i	0.0939791	+	0.532982i	−0.901076	+	0.433661i	$0.857222\pi$
$14$	−21203.7	+	3738.78i	−0.551949	+	0.0973236i
$15$		0			0
$16$	17361.5	+	14568.0i	0.264916	+	0.222291i
$17$	124728.	−	72011.7i	1.49337	−	0.862198i	0.493400	−	0.869802i	$-0.335754\pi$
$17$	124728.	−	72011.7i	1.49337	−	0.862198i	0.999971	+	0.00760413i	$0.00242049\pi$
$18$		0			0
$19$	−101393.	+	175618.i	−0.778024	+	1.34758i	0.155054	+	0.987906i	$0.450445\pi$
$19$	−101393.	+	175618.i	−0.778024	+	1.34758i	−0.933079	+	0.359672i	$0.882889\pi$
$20$	−2500.76	−	6870.79i	−0.0156298	−	0.0429424i
$21$		0			0
$22$	44410.8	−	37265.1i	0.189582	−	0.159078i
$23$	39698.1	−	109070.i	0.141860	−	0.389756i	−0.848333	−	0.529462i	$-0.822394\pi$
$23$	39698.1	−	109070.i	0.141860	−	0.389756i	0.990193	+	0.139707i	$0.0446159\pi$
$24$		0			0
$25$	67588.2	−	383312.i	0.173026	−	0.981277i
$26$			120335.i			0.263329i
$27$		0			0
$28$	540399.			0.879190
$29$	609347.	+	107444.i	0.861534	+	0.151912i	0.586922	−	0.809643i	$-0.300340\pi$
$29$	609347.	+	107444.i	0.861534	+	0.151912i	0.274612	+	0.961555i	$0.411451\pi$
$30$		0			0
$31$	1.01617e6	+	369854.i	1.10032	+	0.400483i	0.827433	−	0.561564i	$-0.189800\pi$
$31$	1.01617e6	+	369854.i	1.10032	+	0.400483i	0.272884	+	0.962047i	$0.412022\pi$
$32$	691668.	+	824298.i	0.659626	+	0.786112i
$33$		0			0
$34$	1.05360e6	−	383479.i	0.788424	−	0.286963i
$35$	−89627.8	−	51746.6i	−0.0597270	−	0.0344834i
$36$		0			0
$37$	−978631.	−	1.69504e6i	−0.522170	−	0.904426i	−0.999667	−	0.0257923i	$-0.991789\pi$
$37$	−978631.	−	1.69504e6i	−0.522170	−	0.904426i	0.477497	−	0.878633i	$-0.341544\pi$
$38$	−1.01476e6	+	1.20934e6i	−0.486662	+	0.579982i
$39$		0			0
$40$	−22834.5	−	129501.i	−0.00891974	−	0.0505864i
$41$	1.39463e6	−	245911.i	0.493541	−	0.0870247i	0.0786625	−	0.996901i	$-0.474935\pi$
$41$	1.39463e6	−	245911.i	0.493541	−	0.0870247i	0.414879	+	0.909877i	$0.363824\pi$
$42$		0			0
$43$	2.04961e6	+	1.71982e6i	0.599510	+	0.503049i	0.891288	−	0.453437i	$-0.149802\pi$
$43$	2.04961e6	+	1.71982e6i	0.599510	+	0.503049i	−0.291778	+	0.956486i	$0.594247\pi$
$44$	−1.26014e6	+	727544.i	−0.336209	+	0.194110i
$45$		0			0
$46$	451799.	−	782539.i	0.100905	−	0.174773i
$47$	1.82238e6	+	5.00694e6i	0.373462	+	1.02608i	0.974013	+	0.226492i	$0.0727258\pi$
$47$	1.82238e6	+	5.00694e6i	0.373462	+	1.02608i	−0.600551	+	0.799587i	$0.705052\pi$
$48$		0			0
$49$	1.44340e6	−	1.21116e6i	0.250382	−	0.210095i
$50$	1.03636e6	−	2.84736e6i	0.165817	−	0.455578i
$51$		0			0
$52$	524465.	−	2.97439e6i	0.0717304	−	0.406803i
$53$		−	3.45452e6i		−	0.437809i	−0.975746	−	0.218905i	$-0.929752\pi$
$53$		−	3.45452e6i		−	0.437809i	0.975746	−	0.218905i	$-0.0702483\pi$
$54$		0			0
$55$	278668.			0.0304534
$56$	9.57122e6	+	1.68767e6i	0.973230	+	0.171607i
$57$		0			0
$58$	4.52643e6	+	1.64749e6i	0.399985	+	0.145583i
$59$	1.16111e7	+	1.38375e7i	0.958217	+	1.14196i	0.989801	+	0.142458i	$0.0455005\pi$
$59$	1.16111e7	+	1.38375e7i	0.958217	+	1.14196i	−0.0315836	+	0.999501i	$0.510055\pi$
$60$		0			0
$61$	1.16719e7	−	4.24821e6i	0.842987	−	0.306822i	0.115810	−	0.993271i	$-0.463054\pi$
$61$	1.16719e7	−	4.24821e6i	0.842987	−	0.306822i	0.727178	+	0.686449i	$0.240832\pi$
$62$	7.29065e6	+	4.20926e6i	0.493401	+	0.284865i
$63$		0			0
$64$	1.28751e6	+	2.23004e6i	0.0767418	+	0.132921i
$65$	−371801.	+	443096.i	−0.0208285	+	0.0248224i
$66$		0			0
$67$	−1.92937e6	−	1.09420e7i	−0.0957452	−	0.542998i	−0.994516	−	0.104580i	$-0.966650\pi$
$67$	−1.92937e6	−	1.09420e7i	−0.0957452	−	0.542998i	0.898771	−	0.438418i	$-0.144461\pi$
$68$	−2.77138e7	+	4.88669e6i	−1.29617	+	0.228549i
$69$		0			0
$70$	−617196.	−	517889.i	−0.0257058	−	0.0215697i
$71$	2.34487e7	−	1.35381e7i	0.922752	−	0.532751i	0.0382397	−	0.999269i	$-0.487825\pi$
$71$	2.34487e7	−	1.35381e7i	0.922752	−	0.532751i	0.884512	+	0.466518i	$0.154492\pi$
$72$		0			0
$73$	−1.28556e7	+	2.22665e7i	−0.452690	+	0.784082i	−0.998552	−	0.0537933i	$-0.982869\pi$
$73$	−1.28556e7	+	2.22665e7i	−0.452690	+	0.784082i	0.545862	+	0.837875i	$0.316202\pi$
$74$	−5.21144e6	−	1.43183e7i	−0.173792	−	0.477491i
$75$		0			0
$76$	3.03531e7	−	2.54693e7i	0.909807	−	0.763418i
$77$	−7.04421e6	+	1.93538e7i	−0.200387	+	0.550558i
$78$		0			0
$79$	−981583.	+	5.56684e6i	−0.0252011	+	0.142922i	−0.994812	−	0.101729i	$-0.967562\pi$
$79$	−981583.	+	5.56684e6i	−0.0252011	+	0.142922i	0.969611	+	0.244652i	$0.0786736\pi$
$80$			848091.i			0.0207054i
$81$		0			0
$82$	1.10246e7			0.243842
$83$	−5.90784e6	−	1.04171e6i	−0.124485	−	0.0219500i	0.111059	−	0.993814i	$-0.464576\pi$
$83$	−5.90784e6	−	1.04171e6i	−0.124485	−	0.0219500i	−0.235543	+	0.971864i	$0.575687\pi$
$84$		0			0
$85$	5.06440e6	+	1.84329e6i	0.0970179	+	0.0353116i
$86$	1.33888e7	+	1.59561e7i	0.244764	+	0.291698i
$87$		0			0
$88$	−2.45910e7	+	8.95039e6i	−0.410058	+	0.149249i
$89$	−3.29258e7	−	1.90097e7i	−0.524779	−	0.302981i	0.214109	−	0.976810i	$-0.431315\pi$
$89$	−3.29258e7	−	1.90097e7i	−0.524779	−	0.302981i	−0.738888	+	0.673829i	$0.764649\pi$
$90$		0			0
$91$	−2.13751e7	−	3.70227e7i	−0.311704	−	0.539887i
$92$	−1.45780e7	+	1.73734e7i	−0.203491	+	0.242512i
$93$		0			0
$94$	7.20300e6	+	4.08503e7i	0.0922576	+	0.523219i
$95$	−7.47305e6	+	1.31770e6i	−0.0917495	+	0.0161779i
$96$		0			0
$97$	9.92181e6	+	8.32538e6i	0.112074	+	0.0940410i	0.697102	−	0.716972i	$-0.254472\pi$
$97$	9.92181e6	+	8.32538e6i	0.112074	+	0.0940410i	−0.585029	+	0.811013i	$0.698917\pi$
$98$	1.27034e7	−	7.33433e6i	0.137726	−	0.0795162i
$99$		0			0
$100$	−3.80261e7	+	6.58632e7i	−0.380261	+	0.658632i
$101$	−2.54486e7	−	6.99195e7i	−0.244556	−	0.671912i	−0.999863	−	0.0165413i	$-0.994735\pi$
$101$	−2.54486e7	−	6.99195e7i	−0.244556	−	0.671912i	0.755307	−	0.655371i	$-0.227488\pi$
$102$		0			0
$103$	−3.98778e7	+	3.34615e7i	−0.354309	+	0.297301i	−0.802518	−	0.596628i	$-0.796507\pi$
$103$	−3.98778e7	+	3.34615e7i	−0.354309	+	0.297301i	0.448209	+	0.893929i	$0.352062\pi$
$104$	1.85780e7	−	5.10426e7i	0.158806	−	0.436315i
$105$		0			0
$106$	4.66998e6	−	2.64848e7i	0.0369906	−	0.209784i
$107$		−	2.19636e8i		−	1.67559i	−0.545986	−	0.837795i	$-0.683845\pi$
$107$		−	2.19636e8i		−	1.67559i	0.545986	−	0.837795i	$-0.316155\pi$
$108$		0			0
$109$	−2.65997e8			−1.88439			−0.942194	−	0.335067i	$-0.891241\pi$
$109$	−2.65997e8			−1.88439			−0.942194	+	0.335067i	$0.891241\pi$
$110$	2.13646e6	+	376716.i	0.0145923	+	0.00257302i
$111$		0			0
$112$	−5.89010e7	−	2.14382e7i	−0.374326	−	0.136244i
$113$	7.63601e6	+	9.10024e6i	0.0468331	+	0.0558135i	0.788953	−	0.614454i	$-0.210624\pi$
$113$	7.63601e6	+	9.10024e6i	0.0468331	+	0.0558135i	−0.742119	+	0.670268i	$0.766179\pi$
$114$		0			0
$115$	4.08144e6	−	1.48552e6i	0.0233357	−	0.00849352i
$116$	−1.04702e8	−	6.04498e7i	−0.578260	−	0.333859i
$117$		0			0
$118$	7.03123e7	+	1.21785e8i	0.362663	+	0.628151i
$119$	−2.56037e8	+	3.05134e8i	−1.27678	+	1.52161i
$120$		0			0
$121$	2.75931e7	+	1.56488e8i	0.128724	+	0.730028i
$122$	9.52276e7	−	1.67912e7i	0.429857	−	0.0757953i
$123$		0			0
$124$	−1.61862e8	−	1.35818e8i	−0.684633	−	0.574476i
$125$	2.52726e7	−	1.45912e7i	0.103517	−	0.0597654i
$126$		0			0
$127$	−1.66357e7	+	2.88139e7i	−0.0639479	+	0.110761i	−0.896227	−	0.443596i	$-0.853702\pi$
$127$	−1.66357e7	+	2.88139e7i	−0.0639479	+	0.110761i	0.832279	+	0.554357i	$0.187036\pi$
$128$	−8.73591e7	−	2.40017e8i	−0.325438	−	0.894133i
$129$		0			0
$130$	−3.44948e6	+	2.89446e6i	−0.0120776	+	0.0101343i
$131$	−1.61936e8	+	4.44915e8i	−0.549867	+	1.51075i	0.284022	+	0.958818i	$0.408331\pi$
$131$	−1.61936e8	+	4.44915e8i	−0.549867	+	1.51075i	−0.833890	+	0.551931i	$0.813891\pi$
$132$		0			0
$133$	9.73893e7	−	5.52322e8i	0.311246	−	1.76517i
$134$		−	8.64974e7i		−	0.268277i
$135$		0			0
$136$	−5.06111e8			−1.47942
$137$	−2.76763e8	−	4.88007e7i	−0.785643	−	0.138530i	−0.233586	−	0.972336i	$-0.575046\pi$
$137$	−2.76763e8	−	4.88007e7i	−0.785643	−	0.138530i	−0.552057	+	0.833806i	$0.686157\pi$
$138$		0			0
$139$	6.76410e8	+	2.46193e8i	1.81197	+	0.659503i	0.996769	+	0.0803220i	$0.0255949\pi$
$139$	6.76410e8	+	2.46193e8i	1.81197	+	0.659503i	0.815199	+	0.579180i	$0.196627\pi$
$140$	1.29984e7	+	1.54909e7i	0.0338360	+	0.0403242i
$141$		0			0
$142$	1.98075e8	−	7.20935e7i	0.487166	−	0.177314i
$143$	9.96879e7	+	5.75548e7i	0.238396	+	0.137638i
$144$		0			0
$145$	1.15769e7	+	2.00518e7i	0.0261891	+	0.0453608i
$146$	−1.28661e8	+	1.53332e8i	−0.283162	+	0.337459i
$147$		0			0
$148$	6.64097e7	+	3.76628e8i	0.138415	+	0.784993i
$149$	8.91020e8	−	1.57111e8i	1.80777	−	0.318758i	0.834949	−	0.550327i	$-0.185497\pi$
$149$	8.91020e8	−	1.57111e8i	1.80777	−	0.318758i	0.972819	+	0.231569i	$0.0743859\pi$
$150$		0			0
$151$	−2.47852e8	−	2.07973e8i	−0.476744	−	0.400036i	0.372503	−	0.928031i	$-0.378500\pi$
$151$	−2.47852e8	−	2.07973e8i	−0.476744	−	0.400036i	−0.849247	+	0.527995i	$0.822944\pi$
$152$	6.17136e8	−	3.56304e8i	1.15613	−	0.667492i
$153$		0			0
$154$	−8.01692e7	+	1.38857e8i	−0.142536	+	0.246880i
$155$	1.38401e7	+	3.80254e7i	0.0239780	+	0.0658790i
$156$		0			0
$157$	5.95886e8	−	5.00008e8i	0.980764	−	0.822959i	−0.00344009	−	0.999994i	$-0.501095\pi$
$157$	5.95886e8	−	5.00008e8i	0.980764	−	0.822959i	0.984205	+	0.177035i	$0.0566506\pi$
$158$	−1.50510e7	+	4.13523e7i	−0.0241511	+	0.0663546i
$159$		0			0
$160$	−6.99213e6	+	3.96543e7i	−0.0106691	+	0.0605077i
$161$			3.21012e8i			0.477769i
$162$		0			0
$163$	1.09107e9			1.54561			0.772806	−	0.634642i	$-0.218852\pi$
$163$	1.09107e9			1.54561			0.772806	+	0.634642i	$0.218852\pi$
$164$	−2.72503e8	−	4.80496e7i	−0.376700	−	0.0664223i
$165$		0			0
$166$	−4.38854e7	−	1.59730e7i	−0.0577947	−	0.0210355i
$167$	8.88832e8	+	1.05927e9i	1.14276	+	1.36188i	0.922294	+	0.386488i	$0.126312\pi$
$167$	8.88832e8	+	1.05927e9i	1.14276	+	1.36188i	0.220462	+	0.975396i	$0.429243\pi$
$168$		0			0
$169$	5.42016e8	−	1.97278e8i	0.664455	−	0.241842i
$170$	3.63354e7	+	2.09782e7i	0.0435045	+	0.0251173i
$171$		0			0
$172$	−2.61396e8	−	4.52751e8i	−0.298665	−	0.517303i
$173$	−2.53987e7	+	3.02690e7i	−0.0283548	+	0.0337920i	−0.780035	−	0.625735i	$-0.784799\pi$
$173$	−2.53987e7	+	3.02690e7i	−0.0283548	+	0.0337920i	0.751681	+	0.659527i	$0.229243\pi$
$174$		0			0
$175$	1.86928e8	+	1.06012e9i	0.199307	+	1.13032i
$176$	1.66212e8	−	2.93077e7i	0.173225	−	0.0305443i
$177$		0			0
$178$	−2.26734e8	−	1.90252e8i	−0.225858	−	0.189518i
$179$	5.49026e8	−	3.16980e8i	0.534787	−	0.308759i	−0.208177	−	0.978091i	$-0.566753\pi$
$179$	5.49026e8	−	3.16980e8i	0.534787	−	0.308759i	0.742963	+	0.669332i	$0.233420\pi$
$180$		0			0
$181$	−4.29163e8	+	7.43332e8i	−0.399860	+	0.692578i	−0.993708	−	0.111999i	$-0.964275\pi$
$181$	−4.29163e8	+	7.43332e8i	−0.399860	+	0.692578i	0.593848	+	0.804577i	$0.297608\pi$
$182$	−1.13827e8	−	3.12738e8i	−0.103743	−	0.285033i
$183$		0			0
$184$	−3.12453e8	+	2.62179e8i	−0.272592	+	0.228732i
$185$	2.50501e7	−	6.88246e7i	0.0213857	−	0.0587567i
$186$		0			0
$187$	1.86243e8	−	1.05624e9i	0.152305	−	0.863764i
$188$		−	1.04111e9i		−	0.833425i
$189$		0			0
$190$	−5.90750e7			−0.0453304
$191$	−6.61152e8	−	1.16579e8i	−0.496784	−	0.0875965i	−0.0803582	−	0.996766i	$-0.525606\pi$
$191$	−6.61152e8	−	1.16579e8i	−0.496784	−	0.0875965i	−0.416426	+	0.909170i	$0.636718\pi$
$192$		0			0
$193$	−2.97918e7	−	1.08433e7i	−0.0214718	−	0.00781508i	0.331262	−	0.943539i	$-0.392526\pi$
$193$	−2.97918e7	−	1.08433e7i	−0.0214718	−	0.00781508i	−0.352734	+	0.935724i	$0.614748\pi$
$194$	6.48129e7	+	7.72410e7i	0.0457567	+	0.0545307i
$195$		0			0
$196$	−3.45964e8	+	1.25921e8i	−0.234426	+	0.0853242i
$197$	8.67018e8	+	5.00573e8i	0.575656	+	0.332355i	0.759405	−	0.650618i	$-0.225490\pi$
$197$	8.67018e8	+	5.00573e8i	0.575656	+	0.332355i	−0.183749	+	0.982973i	$0.558823\pi$
$198$		0			0
$199$	1.45511e8	+	2.52033e8i	0.0927865	+	0.160711i	0.908683	−	0.417488i	$-0.137089\pi$
$199$	1.45511e8	+	2.52033e8i	0.0927865	+	0.160711i	−0.815896	+	0.578198i	$0.803756\pi$
$200$	−8.79186e8	+	1.04777e9i	−0.549491	+	0.654858i
$201$		0			0
$202$	−1.00586e8	−	5.70454e8i	−0.0604135	−	0.342622i
$203$	−1.68526e9	+	2.97157e8i	−0.992392	+	0.174986i
$204$		0			0
$205$	4.05948e7	+	3.40631e7i	0.0229856	+	0.0192872i
$206$	−3.50966e8	+	2.02630e8i	−0.194893	+	0.112521i
$207$		0			0
$208$	−1.75161e8	+	3.03388e8i	−0.0935803	+	0.162086i
$209$	5.16496e8	+	1.41906e9i	0.270696	+	0.743731i
$210$		0			0
$211$	2.57792e9	−	2.16313e9i	1.30059	−	1.09132i	0.310543	−	0.950559i	$-0.399489\pi$
$211$	2.57792e9	−	2.16313e9i	1.30059	−	1.09132i	0.990043	−	0.140762i	$-0.0449553\pi$
$212$	−2.30862e8	+	6.34287e8i	−0.114290	+	0.314009i
$213$		0			0
$214$	2.96913e8	−	1.68388e9i	0.141571	−	0.802890i
$215$			1.00121e8i			0.0468567i
$216$		0			0
$217$	−2.99076e9			−1.34879
$218$	−2.03932e9	−	3.59587e8i	−0.902940	−	0.159213i
$219$		0			0
$220$	−5.11663e7	−	1.86230e7i	−0.0218420	−	0.00794985i
$221$	1.43098e9	+	1.70538e9i	0.599882	+	0.714911i
$222$		0			0
$223$	−3.84150e8	+	1.39819e8i	−0.155339	+	0.0565388i	−0.418519	−	0.908208i	$-0.637451\pi$
$223$	−3.84150e8	+	1.39819e8i	−0.155339	+	0.0565388i	0.263180	+	0.964747i	$0.415229\pi$
$224$	−2.57729e9	−	1.48800e9i	−1.02370	−	0.591032i
$225$		0			0
$226$	4.62409e7	+	8.00915e7i	0.0177252	+	0.0307010i
$227$	1.70797e9	−	2.03548e9i	0.643246	−	0.766591i	−0.341633	−	0.939833i	$-0.610980\pi$
$227$	1.70797e9	−	2.03548e9i	0.643246	−	0.766591i	0.984879	+	0.173243i	$0.0554245\pi$
$228$		0			0
$229$	7.47013e8	+	4.23652e9i	0.271635	+	1.54052i	0.749451	+	0.662060i	$0.230318\pi$
$229$	7.47013e8	+	4.23652e9i	0.271635	+	1.54052i	−0.477816	+	0.878460i	$0.658571\pi$
$230$	3.32993e7	−	5.87157e6i	0.0118994	−	0.00209818i
$231$		0			0
$232$	−1.66563e9	−	1.39763e9i	−0.574947	−	0.482438i
$233$	2.49677e9	−	1.44151e9i	0.847138	−	0.489095i	−0.0125463	−	0.999921i	$-0.503994\pi$
$233$	2.49677e9	−	1.44151e9i	0.847138	−	0.489095i	0.859684	+	0.510826i	$0.170660\pi$
$234$		0			0
$235$	−9.96932e7	+	1.72674e8i	−0.0326884	+	0.0566180i
$236$	−1.20717e9	−	3.31667e9i	−0.389153	−	1.06919i
$237$		0			0
$238$	−2.37546e9	+	1.99324e9i	−0.740353	+	0.621230i
$239$	6.28233e8	−	1.72606e9i	0.192544	−	0.529010i	−0.805426	−	0.592696i	$-0.798064\pi$
$239$	6.28233e8	−	1.72606e9i	0.192544	−	0.529010i	0.997970	+	0.0636865i	$0.0202858\pi$
$240$		0			0
$241$	−7.37356e8	+	4.18175e9i	−0.218579	+	1.23962i	0.656007	+	0.754755i	$0.272244\pi$
$241$	−7.37356e8	+	4.18175e9i	−0.218579	+	1.23962i	−0.874586	+	0.484870i	$0.838867\pi$
$242$			1.23705e9i			0.360682i
$243$		0			0
$244$	−2.42698e9			−0.684711
$245$	6.94374e7	+	1.22437e7i	0.0192721	+	0.00339819i
$246$		0			0
$247$	−2.94549e9	−	1.07207e9i	−0.791353	−	0.288029i
$248$	−2.44264e9	−	2.91102e9i	−0.645733	−	0.769554i
$249$		0			0
$250$	2.13483e8	−	7.77013e7i	0.0546516	−	0.0198915i
$251$	−6.55995e9	−	3.78739e9i	−1.65274	−	0.954212i	−0.975937	−	0.218052i	$-0.930030\pi$
$251$	−6.55995e9	−	3.78739e9i	−1.65274	−	0.954212i	−0.676807	−	0.736160i	$-0.736637\pi$
$252$		0			0
$253$	−4.32181e8	−	7.48559e8i	−0.105483	−	0.182702i
$254$	−1.66493e8	+	1.98419e8i	−0.0400001	+	0.0476703i
$255$		0			0
$256$	−4.59760e8	−	2.60743e9i	−0.107046	−	0.607089i
$257$	1.33863e8	−	2.36037e7i	0.0306852	−	0.00541062i	−0.158285	−	0.987394i	$-0.550596\pi$
$257$	1.33863e8	−	2.36037e7i	0.0306852	−	0.00541062i	0.188970	+	0.981983i	$0.439485\pi$
$258$		0			0
$259$	4.14673e9	+	3.47952e9i	0.921525	+	0.773251i
$260$	9.78782e7	−	5.65100e7i	0.0214187	−	0.0123661i
$261$		0			0
$262$	−1.84297e9	+	3.19212e9i	−0.391123	+	0.677445i
$263$	3.23234e9	+	8.88079e9i	0.675608	+	1.85622i	0.484899	+	0.874570i	$0.338856\pi$
$263$	3.23234e9	+	8.88079e9i	0.675608	+	1.85622i	0.190709	+	0.981647i	$0.438921\pi$
$264$		0			0
$265$	9.90265e7	−	8.30931e7i	0.0200802	−	0.0168493i
$266$	1.49331e9	−	4.10283e9i	0.298279	−	0.819515i
$267$		0			0
$268$	−3.76989e8	+	2.13801e9i	−0.0730784	+	0.414448i
$269$		−	1.18549e8i		−	0.0226407i	−0.999936	−	0.0113204i	$-0.996397\pi$
$269$		−	1.18549e8i		−	0.0226407i	0.999936	−	0.0113204i	$-0.00360346\pi$
$270$		0			0
$271$	3.58270e9			0.664252			0.332126	−	0.943235i	$-0.392234\pi$
$271$	3.58270e9			0.664252			0.332126	+	0.943235i	$0.392234\pi$
$272$	3.21453e9	+	5.66809e8i	0.587276	+	0.103553i
$273$		0			0
$274$	−2.05589e9	−	7.48281e8i	−0.364751	−	0.132759i
$275$	−1.86314e9	−	2.22040e9i	−0.325773	−	0.388241i
$276$		0			0
$277$	1.39013e9	−	5.05965e8i	0.236122	−	0.0859412i	−0.221249	−	0.975217i	$-0.571013\pi$
$277$	1.39013e9	−	5.05965e8i	0.236122	−	0.0859412i	0.457371	+	0.889276i	$0.348791\pi$
$278$	4.85301e9	+	2.80189e9i	0.812517	+	0.469107i
$279$		0			0
$280$	1.81842e8	+	3.14960e8i	0.0295844	+	0.0512417i
$281$	3.91017e9	−	4.65996e9i	0.627149	−	0.747407i	−0.355133	−	0.934816i	$-0.615565\pi$
$281$	3.91017e9	−	4.65996e9i	0.627149	−	0.747407i	0.982282	+	0.187409i	$0.0600090\pi$
$282$		0			0
$283$	−8.05969e8	−	4.57088e9i	−0.125653	−	0.712613i	−0.980918	−	0.194422i	$-0.937717\pi$
$283$	−8.05969e8	−	4.57088e9i	−0.125653	−	0.712613i	0.855265	−	0.518191i	$-0.173394\pi$
$284$	−5.21016e9	+	9.18691e8i	−0.800898	+	0.141220i
$285$		0			0
$286$	6.86472e8	+	5.76018e8i	0.102603	+	0.0860938i
$287$	−3.39189e9	+	1.95831e9i	−0.499935	+	0.288638i
$288$		0			0
$289$	6.88348e9	−	1.19225e10i	0.986772	−	1.70914i
$290$	6.16496e7	+	1.69381e8i	0.00871643	+	0.0239482i
$291$		0			0
$292$	3.84847e9	−	3.22925e9i	0.529366	−	0.444191i
$293$	−3.86218e9	+	1.06113e10i	−0.524037	+	1.43978i	0.341952	+	0.939717i	$0.388912\pi$
$293$	−3.86218e9	+	1.06113e10i	−0.524037	+	1.43978i	−0.865989	+	0.500063i	$0.833310\pi$
$294$		0			0
$295$	−1.17377e8	+	6.65679e8i	−0.0154987	+	0.0878976i
$296$			6.87800e9i			0.895974i
$297$		0			0
$298$	7.04357e9			0.893158
$299$	1.76687e9	+	3.11546e8i	0.221065	+	0.0389797i
$300$		0			0
$301$	−6.95353e9	−	2.53088e9i	−0.847109	−	0.308323i
$302$	−1.61906e9	−	1.92952e9i	−0.194642	−	0.231965i
$303$		0			0
$304$	−4.31874e9	+	1.57189e9i	−0.505665	+	0.184047i
$305$	4.02526e8	+	2.32399e8i	0.0465152	+	0.0268556i
$306$		0			0
$307$	1.60427e9	+	2.77868e9i	0.180603	+	0.312813i	0.942086	−	0.335372i	$-0.108862\pi$
$307$	1.60427e9	+	2.77868e9i	0.180603	+	0.312813i	−0.761483	+	0.648185i	$0.775529\pi$
$308$	2.58678e9	−	3.08281e9i	0.287446	−	0.342565i
$309$		0			0
$310$	5.47035e7	+	3.10239e8i	0.00592336	+	0.0335931i
$311$	5.93601e9	−	1.04668e9i	0.634531	−	0.111885i	0.152875	−	0.988245i	$-0.451147\pi$
$311$	5.93601e9	−	1.04668e9i	0.634531	−	0.111885i	0.481656	+	0.876361i	$0.340036\pi$
$312$		0			0
$313$	2.47074e9	+	2.07320e9i	0.257425	+	0.216005i	0.762362	−	0.647151i	$-0.224040\pi$
$313$	2.47074e9	+	2.07320e9i	0.257425	+	0.216005i	−0.504937	+	0.863156i	$0.668484\pi$
$314$	5.24441e9	−	3.02786e9i	0.539484	−	0.311471i
$315$		0			0
$316$	5.52254e8	−	9.56532e8i	0.0553848	−	0.0959292i
$317$	−1.44241e9	−	3.96300e9i	−0.142841	−	0.392452i	0.847556	−	0.530706i	$-0.178073\pi$
$317$	−1.44241e9	−	3.96300e9i	−0.142841	−	0.392452i	−0.990397	+	0.138254i	$0.955851\pi$
$318$		0			0
$319$	3.52975e9	−	2.96181e9i	0.340864	−	0.286019i
$320$	−3.29566e7	+	9.05476e7i	−0.00314299	+	0.00863529i
$321$		0			0
$322$	−4.33959e8	+	2.46110e9i	−0.0403669	+	0.228932i
$323$			2.92059e10i			2.68325i
$324$		0			0
$325$	6.01637e9			0.539264
$326$	8.36487e9	+	1.47495e9i	0.740609	+	0.130589i
$327$		0			0
$328$	−4.67634e9	−	1.70205e9i	−0.404028	−	0.147054i
$329$	−9.47233e9	−	1.12887e10i	−0.808488	−	0.963518i
$330$		0			0
$331$	−5.24937e9	+	1.91061e9i	−0.437316	+	0.159170i	−0.551290	−	0.834314i	$-0.685864\pi$
$331$	−5.24937e9	+	1.91061e9i	−0.437316	+	0.159170i	0.113974	+	0.993484i	$0.463642\pi$
$332$	1.01513e9	+	5.86083e8i	0.0835541	+	0.0482400i
$333$		0			0
$334$	5.38244e9	+	9.32265e9i	0.432507	+	0.749124i
$335$	2.67253e8	−	3.18500e8i	0.0212199	−	0.0252889i
$336$		0			0
$337$	−3.28023e8	−	1.86031e9i	−0.0254322	−	0.144233i	0.969448	−	0.245299i	$-0.0788860\pi$
$337$	−3.28023e8	−	1.86031e9i	−0.0254322	−	0.144233i	−0.994880	+	0.101065i	$0.967775\pi$
$338$	4.42217e9	−	7.79747e8i	0.338819	−	0.0597430i
$339$		0			0
$340$	−8.06692e8	−	6.76895e8i	−0.0603659	−	0.0506530i
$341$	6.97408e9	−	4.02649e9i	0.515786	−	0.297789i
$342$		0			0
$343$	5.36623e9	−	9.29458e9i	0.387697	−	0.671511i
$344$	−3.21574e9	−	8.83518e9i	−0.229640	−	0.630931i
$345$		0			0
$346$	−2.35643e8	+	1.97728e8i	−0.0164418	+	0.0137963i
$347$	4.26463e9	−	1.17170e10i	0.294146	−	0.808160i	−0.701303	−	0.712864i	$-0.747398\pi$
$347$	4.26463e9	−	1.17170e10i	0.294146	−	0.808160i	0.995449	−	0.0952965i	$-0.0303799\pi$
$348$		0			0
$349$	−2.62191e9	+	1.48696e10i	−0.176733	+	1.00230i	0.759392	+	0.650633i	$0.225496\pi$
$349$	−2.62191e9	+	1.48696e10i	−0.176733	+	1.00230i	−0.936125	+	0.351667i	$0.885615\pi$
$350$			8.38032e9i			0.558455i
$351$		0			0
$352$	8.01323e9			0.521960
$353$	1.77537e10	+	3.13045e9i	1.14338	+	0.201608i	0.713083	−	0.701080i	$-0.247298\pi$
$353$	1.77537e10	+	3.13045e9i	1.14338	+	0.201608i	0.430295	+	0.902688i	$0.358409\pi$
$354$		0			0
$355$	9.52100e8	+	3.46536e8i	0.0599472	+	0.0218190i
$356$	4.77513e9	+	5.69077e9i	0.297293	+	0.354300i
$357$		0			0
$358$	4.63772e9	−	1.68799e9i	0.282340	−	0.102763i
$359$	−2.52845e10	−	1.45980e10i	−1.52222	−	0.878852i	−0.999655	−	0.0262509i	$-0.991643\pi$
$359$	−2.52845e10	−	1.45980e10i	−1.52222	−	0.878852i	−0.522562	−	0.852602i	$-0.675024\pi$
$360$		0			0
$361$	−1.20693e10	−	2.09046e10i	−0.710644	−	1.23087i
$362$	−4.29513e9	+	5.11874e9i	−0.250117	+	0.298077i
$363$		0			0
$364$	1.45051e9	+	8.22623e9i	0.0826255	+	0.468592i
$365$	−9.47507e8	+	1.67071e8i	−0.0533840	+	0.00941304i
$366$		0			0
$367$	6.35266e9	+	5.33051e9i	0.350180	+	0.293836i	0.800862	−	0.598849i	$-0.204375\pi$
$367$	6.35266e9	+	5.33051e9i	0.350180	+	0.293836i	−0.450682	+	0.892684i	$0.648819\pi$
$368$	2.27815e9	−	1.31529e9i	0.124220	−	0.0717184i
$369$		0			0
$370$	2.85092e8	−	4.93794e8i	0.0152117	−	0.0263475i
$371$	3.26771e9	+	8.97795e9i	0.172483	+	0.473894i
$372$		0			0
$373$	−2.11366e10	+	1.77357e10i	−1.09194	+	0.916248i	−0.996857	−	0.0792207i	$-0.974757\pi$
$373$	−2.11366e10	+	1.77357e10i	−1.09194	+	0.916248i	−0.0950853	+	0.995469i	$0.530312\pi$
$374$	2.85574e9	−	7.84608e9i	0.145960	−	0.401020i
$375$		0			0
$376$	3.25139e9	−	1.84396e10i	0.162674	−	0.922570i
$377$			9.56417e9i			0.473458i
$378$		0			0
$379$	2.32513e10			1.12691			0.563457	−	0.826145i	$-0.309471\pi$
$379$	2.32513e10			1.12691			0.563457	+	0.826145i	$0.309471\pi$
$380$	1.46019e9	+	2.57471e8i	0.0700286	+	0.0123479i
$381$		0			0
$382$	−4.91126e9	−	1.78755e9i	−0.230642	−	0.0839470i
$383$	−3.20145e9	−	3.81534e9i	−0.148782	−	0.177312i	0.686506	−	0.727124i	$-0.259144\pi$
$383$	−3.20145e9	−	3.81534e9i	−0.148782	−	0.177312i	−0.835288	+	0.549812i	$0.814699\pi$
$384$		0			0
$385$	−7.24228e8	+	2.63597e8i	−0.0329634	+	0.0119977i
$386$	−2.13746e8	−	1.23406e8i	−0.00962829	−	0.00555890i
$387$		0			0
$388$	−1.26537e9	−	2.19169e9i	−0.0558331	−	0.0967057i
$389$	−6.62163e9	+	7.89136e9i	−0.289179	+	0.344630i	−0.891002	−	0.453999i	$-0.849997\pi$
$389$	−6.62163e9	+	7.89136e9i	−0.289179	+	0.344630i	0.601823	+	0.798630i	$0.294441\pi$
$390$		0			0
$391$	−2.90283e9	−	1.64628e10i	−0.124198	−	0.704361i
$392$	−6.52075e9	+	1.14978e9i	−0.276155	+	0.0486936i
$393$		0			0
$394$	5.97047e9	+	5.00982e9i	0.247756	+	0.207892i
$395$	−1.83188e8	+	1.05764e8i	−0.00752503	+	0.00434458i
$396$		0			0
$397$	−1.12454e10	+	1.94777e10i	−0.452704	+	0.784107i	−0.998553	−	0.0537771i	$-0.982874\pi$
$397$	−1.12454e10	+	1.94777e10i	−0.452704	+	0.784107i	0.545849	+	0.837884i	$0.316207\pi$
$398$	7.74882e8	+	2.12897e9i	0.0308818	+	0.0848472i
$399$		0			0
$400$	6.75753e9	−	5.67024e9i	0.263966	−	0.221494i
$401$	1.26623e10	−	3.47894e10i	0.489705	−	1.34545i	−0.411242	−	0.911526i	$-0.634905\pi$
$401$	1.26623e10	−	3.47894e10i	0.489705	−	1.34545i	0.900947	−	0.433928i	$-0.142873\pi$
$402$		0			0
$403$	−2.90258e9	+	1.64613e10i	−0.110043	+	0.624086i
$404$			1.45386e10i			0.545756i
$405$		0			0
$406$	−1.33221e10			−0.490308
$407$	−1.43542e10	−	2.53103e9i	−0.523119	−	0.0922400i
$408$		0			0
$409$	−1.04727e10	−	3.81173e9i	−0.374251	−	0.136216i	0.148044	−	0.988981i	$-0.452702\pi$
$409$	−1.04727e10	−	3.81173e9i	−0.374251	−	0.136216i	−0.522296	+	0.852764i	$0.674924\pi$
$410$	2.65180e8	+	3.16029e8i	0.00938438	+	0.0111839i
$411$		0			0
$412$	9.55817e9	−	3.47889e9i	0.331731	−	0.120740i
$413$	−4.32652e10	−	2.49792e10i	−1.48709	−	0.858574i
$414$		0			0
$415$	−1.12242e8	−	1.94409e8i	−0.00378411	−	0.00655428i
$416$	−1.06913e10	+	1.27414e10i	−0.356992	+	0.425447i
$417$		0			0
$418$	2.04147e9	+	1.15777e10i	0.0668709	+	0.379244i
$419$	−2.88812e10	+	5.09254e9i	−0.937044	+	0.165226i	−0.621259	−	0.783605i	$-0.713379\pi$
$419$	−2.88812e10	+	5.09254e9i	−0.937044	+	0.165226i	−0.315784	+	0.948831i	$0.602268\pi$
$420$		0			0
$421$	−3.97225e10	−	3.33311e10i	−1.26447	−	1.06102i	−0.995191	−	0.0979530i	$-0.968771\pi$
$421$	−3.97225e10	−	3.33311e10i	−1.26447	−	1.06102i	−0.269278	−	0.963062i	$-0.586785\pi$
$422$	2.26883e10	−	1.30991e10i	0.715406	−	0.413040i
$423$		0			0
$424$	−6.06976e9	+	1.05131e10i	−0.187805	+	0.325288i
$425$	−1.91728e10	−	5.26768e10i	−0.587664	−	1.61459i
$426$		0			0
$427$	−2.63155e10	+	2.20813e10i	−0.791590	+	0.664223i
$428$	−1.46780e10	+	4.03274e10i	−0.437412	+	1.20178i
$429$		0			0
$430$	−1.35348e8	+	7.67598e8i	−0.00395894	+	0.0224523i
$431$		−	2.99834e9i		−	0.0868905i	−0.999056	−	0.0434452i	$-0.986167\pi$
$431$		−	2.99834e9i		−	0.0868905i	0.999056	−	0.0434452i	$-0.0138334\pi$
$432$		0			0
$433$	−6.72699e10			−1.91368			−0.956839	−	0.290617i	$-0.906139\pi$
$433$	−6.72699e10			−1.91368			−0.956839	+	0.290617i	$0.906139\pi$
$434$	−2.29293e10	−	4.04305e9i	−0.646296	−	0.113959i
$435$		0			0
$436$	4.88398e10	+	1.77762e10i	1.35154	+	0.491919i
$437$	1.51295e10	+	1.80306e10i	0.414856	+	0.494406i
$438$		0			0
$439$	−4.83773e10	+	1.76079e10i	−1.30252	+	0.474078i	−0.897816	−	0.440371i	$-0.854847\pi$
$439$	−4.83773e10	+	1.76079e10i	−1.30252	+	0.474078i	−0.404702	+	0.914449i	$0.632625\pi$
$440$	−8.48067e8	−	4.89631e8i	−0.0226266	−	0.0130635i
$441$		0			0
$442$	8.66551e9	+	1.50091e10i	0.227041	+	0.393247i
$443$	1.96213e10	−	2.33837e10i	0.509463	−	0.607154i	−0.448593	−	0.893736i	$-0.648075\pi$
$443$	1.96213e10	−	2.33837e10i	0.509463	−	0.607154i	0.958056	+	0.286582i	$0.0925191\pi$
$444$		0			0
$445$	−2.47050e8	−	1.40109e9i	−0.00630006	−	0.0357294i
$446$	−3.13417e9	+	5.52639e8i	−0.0792107	+	0.0139670i
$447$		0			0
$448$	−5.45556e9	−	4.57776e9i	−0.135434	−	0.113642i
$449$	4.45495e10	−	2.57207e10i	1.09612	−	0.632845i	0.160920	−	0.986967i	$-0.448554\pi$
$449$	4.45495e10	−	2.57207e10i	1.09612	−	0.632845i	0.935199	+	0.354123i	$0.115220\pi$
$450$		0			0
$451$	5.27297e9	−	9.13304e9i	0.127453	−	0.220754i
$452$	−7.93894e8	−	2.18121e9i	−0.0190199	−	0.0522568i
$453$		0			0
$454$	1.58462e10	−	1.32965e10i	0.372993	−	0.312978i
$455$	5.47140e8	−	1.50325e9i	0.0127659	−	0.0350741i
$456$		0			0
$457$	1.83947e9	−	1.04321e10i	0.0421723	−	0.239171i	−0.956434	−	0.291949i	$-0.905696\pi$
$457$	1.83947e9	−	1.04321e10i	0.0421723	−	0.239171i	0.998606	+	0.0527778i	$0.0168075\pi$
$458$			3.34900e10i			0.761120i
$459$		0			0
$460$	−8.48670e8			−0.0189543
$461$	1.61670e10	+	2.85068e9i	0.357953	+	0.0631168i	0.349733	−	0.936849i	$-0.386272\pi$
$461$	1.61670e10	+	2.85068e9i	0.357953	+	0.0631168i	0.00822026	+	0.999966i	$0.497383\pi$
$462$		0			0
$463$	2.17181e10	+	7.90475e9i	0.472605	+	0.172014i	0.567332	−	0.823489i	$-0.307976\pi$
$463$	2.17181e10	+	7.90475e9i	0.472605	+	0.172014i	−0.0947270	+	0.995503i	$0.530198\pi$
$464$	9.01393e9	+	1.07424e10i	0.194465	+	0.231755i
$465$		0			0
$466$	2.10906e10	−	7.67637e9i	0.447246	−	0.162784i
$467$	−3.17397e10	−	1.83249e10i	−0.667322	−	0.385278i	0.127739	−	0.991808i	$-0.459228\pi$
$467$	−3.17397e10	−	1.83249e10i	−0.667322	−	0.385278i	−0.795061	+	0.606529i	$0.792561\pi$
$468$		0			0
$469$	1.53645e10	+	2.66121e10i	0.317562	+	0.550033i
$470$	−9.97745e8	+	1.18907e9i	−0.0204469	+	0.0243677i
$471$		0			0
$472$	−1.10227e10	−	6.25128e10i	−0.222085	−	1.25951i
$473$	1.96221e10	−	3.45990e9i	0.392013	−	0.0691225i
$474$		0			0
$475$	6.04633e10	+	5.07348e10i	1.18773	+	0.996624i
$476$	6.74029e10	−	3.89151e10i	1.31296	−	0.758036i
$477$		0			0
$478$	7.14984e9	−	1.23839e10i	0.136957	−	0.237217i
$479$	3.04605e10	+	8.36895e10i	0.578622	+	1.58975i	0.790505	+	0.612456i	$0.209818\pi$
$479$	3.04605e10	+	8.36895e10i	0.578622	+	1.58975i	−0.211883	+	0.977295i	$0.567960\pi$
$480$		0			0
$481$	2.31759e10	−	1.94469e10i	0.432969	−	0.363304i
$482$	−1.13062e10	+	3.10634e10i	−0.209473	+	0.575521i
$483$		0			0
$484$	5.39153e9	−	3.05769e10i	0.0982495	−	0.557200i
$485$			4.84670e8i			0.00875949i
$486$		0			0
$487$	−2.06487e10			−0.367093			−0.183547	−	0.983011i	$-0.558758\pi$
$487$	−2.06487e10			−0.367093			−0.183547	+	0.983011i	$0.558758\pi$
$488$	−4.29852e10	−	7.57945e9i	−0.757948	−	0.133647i
$489$		0			0
$490$	5.15804e8	+	1.87737e8i	0.00894748	+	0.00325662i
$491$	1.51222e10	+	1.80220e10i	0.260190	+	0.310082i	0.880286	−	0.474444i	$-0.157351\pi$
$491$	1.51222e10	+	1.80220e10i	0.260190	+	0.310082i	−0.620096	+	0.784526i	$0.712906\pi$
$492$		0			0
$493$	8.37397e10	−	3.04788e10i	1.41757	−	0.515953i
$494$	−2.11329e10	−	1.22011e10i	−0.354856	−	0.204876i
$495$		0			0
$496$	1.22541e10	+	2.12248e10i	0.202468	+	0.350684i
$497$	−4.81347e10	+	5.73647e10i	−0.788919	+	0.940198i
$498$		0			0
$499$	4.39743e9	+	2.49391e10i	0.0709246	+	0.402233i	0.999515	+	0.0311280i	$0.00990996\pi$
$499$	4.39743e9	+	2.49391e10i	0.0709246	+	0.402233i	−0.928591	+	0.371105i	$0.878979\pi$
$500$	−5.61543e9	+	9.90152e8i	−0.0898469	+	0.0158424i
$501$		0			0
$502$	−4.51732e10	−	3.79048e10i	−0.711322	−	0.596870i
$503$	8.07649e10	−	4.66296e10i	1.26168	−	0.728434i	0.288284	−	0.957545i	$-0.406915\pi$
$503$	8.07649e10	−	4.66296e10i	1.26168	−	0.728434i	0.973400	+	0.229111i	$0.0735819\pi$
$504$		0			0
$505$	1.39217e9	−	2.41130e9i	0.0214055	−	0.0370754i
$506$	−2.30146e9	−	6.32322e9i	−0.0351077	−	0.0964575i
$507$		0			0
$508$	4.98009e9	−	4.17879e9i	0.0747795	−	0.0627474i
$509$	−2.18961e10	+	6.01590e10i	−0.326208	+	0.896250i	0.662854	+	0.748749i	$0.269345\pi$
$509$	−2.18961e10	+	6.01590e10i	−0.326208	+	0.896250i	−0.989062	+	0.147501i	$0.952877\pi$
$510$		0			0
$511$	1.23480e10	−	7.00288e10i	0.181097	−	1.02705i
$512$			4.47759e10i			0.651575i
$513$		0			0
$514$	1.05820e9			0.0151605
$515$	−1.91839e9	−	3.38265e8i	−0.0272715	−	0.00480870i
$516$		0			0
$517$	3.72863e10	+	1.35711e10i	0.521900	+	0.189956i
$518$	2.70880e10	+	3.22822e10i	0.376234	+	0.448378i
$519$		0			0
$520$	1.91004e9	−	6.95197e8i	0.0261233	−	0.00950812i
$521$	−9.62836e10	−	5.55894e10i	−1.30678	−	0.754468i	−0.325220	−	0.945638i	$-0.605438\pi$
$521$	−9.62836e10	−	5.55894e10i	−1.30678	−	0.754468i	−0.981557	+	0.191170i	$0.938772\pi$
$522$		0			0
$523$	−3.92357e10	−	6.79583e10i	−0.524415	−	0.908313i	−0.999596	−	0.0284250i	$-0.990951\pi$
$523$	−3.92357e10	−	6.79583e10i	−0.524415	−	0.908313i	0.475181	−	0.879888i	$-0.342383\pi$
$524$	5.94663e10	−	7.08692e10i	0.788761	−	0.940009i
$525$		0			0
$526$	1.27759e10	+	7.24560e10i	0.166898	+	0.946523i
$527$	1.53378e11	−	2.70447e10i	1.98848	−	0.350622i
$528$		0			0
$529$	4.96694e10	+	4.16776e10i	0.634259	+	0.532206i
$530$	8.71535e8	−	5.03181e8i	0.0110454	−	0.00637706i
$531$		0			0
$532$	−5.47927e10	+	9.49037e10i	−0.684031	+	1.18478i
$533$	7.48676e9	+	2.05697e10i	0.0927651	+	0.254870i
$534$		0			0
$535$	6.29601e9	−	5.28298e9i	0.0768512	−	0.0644858i
$536$	−1.33540e10	+	3.66898e10i	−0.161790	+	0.444514i
$537$		0			0
$538$	1.60261e8	−	9.08883e8i	0.00191292	−	0.0108487i
$539$		−	1.40317e10i		−	0.166248i
$540$		0			0
$541$	5.30837e10			0.619687			0.309844	−	0.950788i	$-0.399723\pi$
$541$	5.30837e10			0.619687			0.309844	+	0.950788i	$0.399723\pi$
$542$	2.74675e10	+	4.84326e9i	0.318289	+	0.0561229i
$543$		0			0
$544$	1.45629e11	+	5.30047e10i	1.66285	+	0.605228i
$545$	−6.39813e9	−	7.62499e9i	−0.0725215	−	0.0864278i
$546$		0			0
$547$	2.28786e10	−	8.32712e9i	0.255552	−	0.0930134i	−0.211067	−	0.977472i	$-0.567694\pi$
$547$	2.28786e10	−	8.32712e9i	0.255552	−	0.0930134i	0.466620	+	0.884458i	$0.345472\pi$
$548$	4.75553e10	+	2.74560e10i	0.527323	+	0.304450i
$549$		0			0
$550$	−1.12825e10	−	1.95418e10i	−0.123297	−	0.213557i
$551$	−8.06525e10	+	9.61180e10i	−0.875007	+	1.04279i
$552$		0			0
$553$	−2.71475e9	−	1.53961e10i	−0.0290288	−	0.164631i
$554$	1.13417e10	−	1.99984e9i	0.120403	−	0.0212303i
$555$		0			0
$556$	−1.07743e11	−	9.04073e10i	−1.12743	−	0.946028i
$557$	5.15104e10	−	2.97396e10i	0.535149	−	0.308968i	−0.207962	−	0.978137i	$-0.566683\pi$
$557$	5.15104e10	−	2.97396e10i	0.535149	−	0.308968i	0.743111	+	0.669169i	$0.233350\pi$
$558$		0			0
$559$	−2.06786e10	+	3.58164e10i	−0.211775	+	0.366804i
$560$	−8.02227e8	−	2.20410e9i	−0.00815728	−	0.0224119i
$561$		0			0
$562$	3.62776e10	−	3.04406e10i	0.363659	−	0.305146i
$563$	8.78895e9	−	2.41474e10i	0.0874789	−	0.240346i	−0.888237	−	0.459385i	$-0.848070\pi$
$563$	8.78895e9	−	2.41474e10i	0.0874789	−	0.240346i	0.975716	+	0.219039i	$0.0702921\pi$
$564$		0			0
$565$	−7.71931e7	+	4.37784e8i	−0.000757503	+	0.00429601i
$566$		−	3.61331e10i		−	0.352078i
$567$		0			0
$568$	−9.51482e10			−0.914128
$569$	−1.36983e11	−	2.41538e10i	−1.30683	−	0.230429i	−0.523493	−	0.852030i	$-0.675371\pi$
$569$	−1.36983e11	−	2.41538e10i	−1.30683	−	0.230429i	−0.783334	+	0.621601i	$0.786483\pi$
$570$		0			0
$571$	−3.21798e10	−	1.17125e10i	−0.302719	−	0.110181i	0.186195	−	0.982513i	$-0.440384\pi$
$571$	−3.21798e10	−	1.17125e10i	−0.302719	−	0.110181i	−0.488913	+	0.872332i	$0.662607\pi$
$572$	−1.44574e10	−	1.72297e10i	−0.135054	−	0.160951i
$573$		0			0
$574$	−2.86519e10	+	1.04284e10i	−0.263940	+	0.0960664i
$575$	−3.91245e10	−	2.25886e10i	−0.357913	−	0.206641i
$576$		0			0
$577$	−4.06482e10	−	7.04048e10i	−0.366723	−	0.635183i	0.622328	−	0.782756i	$-0.286187\pi$
$577$	−4.06482e10	−	7.04048e10i	−0.366723	−	0.635183i	−0.989051	+	0.147574i	$0.952854\pi$
$578$	6.88910e10	−	8.21011e10i	0.617236	−	0.735593i
$579$		0			0
$580$	−7.85604e8	−	4.45538e9i	−0.00694212	−	0.0393707i
$581$	1.63392e10	−	2.88105e9i	0.143393	−	0.0252840i
$582$		0			0
$583$	−1.97070e10	−	1.65361e10i	−0.170587	−	0.143139i
$584$	7.82466e10	−	4.51757e10i	0.672689	−	0.388377i
$585$		0			0
$586$	−4.39549e10	+	7.61322e10i	−0.372750	+	0.645621i
$587$	−1.12180e10	−	3.08212e10i	−0.0944850	−	0.259595i	0.883443	−	0.468539i	$-0.155220\pi$
$587$	−1.12180e10	−	3.08212e10i	−0.0944850	−	0.259595i	−0.977928	+	0.208944i	$0.932997\pi$
$588$		0			0
$589$	−1.67985e11	+	1.40956e11i	−1.39576	+	1.17118i
$590$	−1.79979e9	+	4.94489e9i	−0.0148530	+	0.0408083i
$591$		0			0
$592$	7.70288e9	−	4.36852e10i	0.0627142	−	0.355670i
$593$			1.79096e11i			1.44833i	0.689628	+	0.724164i	$0.257774\pi$
$593$			1.79096e11i			1.44833i	−0.689628	+	0.724164i	$0.742226\pi$
$594$		0			0
$595$	−1.49054e10			−0.118926
$596$	−1.74100e11	−	3.06986e10i	−1.37979	−	0.243295i
$597$		0			0
$598$	1.31249e10	+	4.77706e9i	0.102634	+	0.0373557i
$599$	3.31382e10	+	3.94926e10i	0.257408	+	0.306767i	0.879235	−	0.476387i	$-0.158054\pi$
$599$	3.31382e10	+	3.94926e10i	0.257408	+	0.306767i	−0.621828	+	0.783154i	$0.713610\pi$
$600$		0			0
$601$	−1.52122e10	+	5.53680e9i	−0.116599	+	0.0424386i	−0.399661	−	0.916663i	$-0.630872\pi$
$601$	−1.52122e10	+	5.53680e9i	−0.116599	+	0.0424386i	0.283062	+	0.959102i	$0.408650\pi$
$602$	−4.98893e10	−	2.88036e10i	−0.379858	−	0.219311i
$603$		0			0
$604$	3.16097e10	+	5.47497e10i	0.237505	+	0.411371i
$605$	−3.82214e9	+	4.55504e9i	−0.0285289	+	0.0339994i
$606$		0			0
$607$	6.49937e9	+	3.68597e10i	0.0478758	+	0.271517i	0.999343	−	0.0362316i	$-0.0115354\pi$
$607$	6.49937e9	+	3.68597e10i	0.0478758	+	0.271517i	−0.951468	+	0.307749i	$0.900424\pi$
$608$	−2.14892e11	+	3.78912e10i	−1.57255	+	0.277283i
$609$		0			0
$610$	2.77188e9	+	2.32588e9i	0.0200196	+	0.0167984i
$611$	−7.13266e10	+	4.11804e10i	−0.511784	+	0.295479i
$612$		0			0
$613$	1.05930e11	−	1.83475e11i	0.750197	−	1.29938i	−0.197530	−	0.980297i	$-0.563292\pi$
$613$	1.05930e11	−	1.83475e11i	0.750197	−	1.29938i	0.947727	−	0.319083i	$-0.103375\pi$
$614$	8.54311e9	+	2.34720e10i	0.0601094	+	0.165149i
$615$		0			0
$616$	5.54431e10	−	4.65223e10i	0.385057	−	0.323101i
$617$	5.33383e10	−	1.46546e11i	0.368043	−	1.01119i	−0.608062	−	0.793889i	$-0.708053\pi$
$617$	5.33383e10	−	1.46546e11i	0.368043	−	1.01119i	0.976105	−	0.217300i	$-0.0697249\pi$
$618$		0			0
$619$	7.73618e9	−	4.38741e10i	0.0526944	−	0.298845i	−0.947059	−	0.321060i	$-0.895961\pi$
$619$	7.73618e9	−	4.38741e10i	0.0526944	−	0.298845i	0.999753	+	0.0222154i	$0.00707198\pi$
$620$		−	7.90678e9i		−	0.0535098i
$621$		0			0
$622$	4.69245e10			0.313501
$623$	1.03552e11	+	1.82591e10i	0.687397	+	0.121207i
$624$		0			0
$625$	−1.41846e11	−	5.16276e10i	−0.929599	−	0.338346i
$626$	1.61398e10	+	1.92347e10i	0.105100	+	0.125253i
$627$		0			0
$628$	−1.42826e11	+	5.19844e10i	−0.918266	+	0.334221i
$629$	−2.44125e11	−	1.40946e11i	−1.55959	−	0.900429i
$630$		0			0
$631$	9.52325e10	+	1.64948e11i	0.600714	+	1.04047i	0.992713	+	0.120502i	$0.0384503\pi$
$631$	9.52325e10	+	1.64948e11i	0.600714	+	1.04047i	−0.391999	+	0.919966i	$0.628216\pi$
$632$	1.27684e10	−	1.52168e10i	0.0800330	−	0.0953796i
$633$		0			0
$634$	−5.70119e9	−	3.23330e10i	−0.0352865	−	0.200120i
$635$	−1.22612e9	+	2.16198e8i	−0.00754114	+	0.00132971i
$636$		0			0
$637$	2.23111e10	+	1.87213e10i	0.135508	+	0.113704i
$638$	3.10655e10	−	1.79357e10i	0.187497	−	0.108252i
$639$		0			0
$640$	4.77898e9	−	8.27744e9i	0.0284850	−	0.0493374i
$641$	1.00079e10	+	2.74965e10i	0.0592804	+	0.162871i	0.965797	−	0.259298i	$-0.0834911\pi$
$641$	1.00079e10	+	2.74965e10i	0.0592804	+	0.162871i	−0.906517	+	0.422169i	$0.861269\pi$
$642$		0			0
$643$	−8.94608e10	+	7.50665e10i	−0.523346	+	0.439139i	−0.865796	−	0.500397i	$-0.833188\pi$
$643$	−8.94608e10	+	7.50665e10i	−0.523346	+	0.439139i	0.342450	+	0.939536i	$0.388743\pi$
$644$	2.14528e10	−	5.89412e10i	0.124721	−	0.342670i
$645$		0			0
$646$	−3.94819e10	+	2.23913e11i	−0.226708	+	1.28573i
$647$			2.25850e11i			1.28885i	0.764667	+	0.644425i	$0.222903\pi$
$647$			2.25850e11i			1.28885i	−0.764667	+	0.644425i	$0.777097\pi$
$648$		0			0
$649$	1.34518e11			0.758234
$650$	4.61257e10	+	8.13321e9i	0.258398	+	0.0455626i
$651$		0			0
$652$	−2.00331e11	−	7.29146e10i	−1.10856	−	0.403482i
$653$	−1.81964e11	−	2.16856e11i	−1.00077	−	1.19267i	−0.981227	−	0.192858i	$-0.938224\pi$
$653$	−1.81964e11	−	2.16856e11i	−1.00077	−	1.19267i	−0.0195398	−	0.999809i	$-0.506220\pi$
$654$		0			0
$655$	−1.66489e10	+	6.05972e9i	−0.0904526	+	0.0329221i
$656$	2.77953e10	+	1.60476e10i	0.150092	+	0.0866554i
$657$		0			0
$658$	−5.73610e10	−	9.93521e10i	−0.305994	−	0.529997i
$659$	−3.52316e10	+	4.19873e10i	−0.186806	+	0.222626i	−0.851317	−	0.524652i	$-0.824195\pi$
$659$	−3.52316e10	+	4.19873e10i	−0.186806	+	0.222626i	0.664511	+	0.747278i	$0.268640\pi$
$660$		0			0
$661$	−1.81789e10	−	1.03098e11i	−0.0952276	−	0.540063i	−0.994677	−	0.103038i	$-0.967144\pi$
$661$	−1.81789e10	−	1.03098e11i	−0.0952276	−	0.540063i	0.899450	−	0.437024i	$-0.143968\pi$
$662$	−4.28282e10	+	7.55176e9i	−0.222996	+	0.0393202i
$663$		0			0
$664$	1.61490e10	+	1.35506e10i	0.0830753	+	0.0697085i
$665$	1.81753e10	−	1.04935e10i	0.0929381	−	0.0536578i
$666$		0			0
$667$	3.59088e10	−	6.21959e10i	0.181425	−	0.314238i
$668$	−9.24093e10	−	2.53892e11i	−0.464098	−	1.27510i
$669$		0			0
$670$	2.47951e9	−	2.08056e9i	0.0123046	−	0.0103248i
$671$	3.16361e10	−	8.69196e10i	0.156061	−	0.428773i
$672$		0			0
$673$	−3.36410e10	+	1.90788e11i	−0.163987	+	0.930015i	0.786116	+	0.618079i	$0.212089\pi$
$673$	−3.36410e10	+	1.90788e11i	−0.163987	+	0.930015i	−0.950103	+	0.311936i	$0.899022\pi$
$674$		−	1.47059e10i		−	0.0712609i
$675$		0			0
$676$	−1.12704e11			−0.539699
$677$	3.16004e11	+	5.57200e10i	1.50431	+	0.265250i	0.864245	−	0.503071i	$-0.167796\pi$
$677$	3.16004e11	+	5.57200e10i	1.50431	+	0.265250i	0.640065	+	0.768321i	$0.278908\pi$
$678$		0			0
$679$	−3.36609e10	−	1.22516e10i	−0.158360	−	0.0576385i
$680$	−1.21737e10	−	1.45080e10i	−0.0569360	−	0.0678536i
$681$		0			0
$682$	5.89114e10	−	2.14420e10i	0.272309	−	0.0991123i
$683$	3.37083e11	+	1.94615e11i	1.54901	+	0.894321i	0.998218	+	0.0596780i	$0.0190074\pi$
$683$	3.37083e11	+	1.94615e11i	1.54901	+	0.894321i	0.550792	+	0.834643i	$0.314326\pi$
$684$		0			0
$685$	−5.25818e9	−	9.10743e9i	−0.0238821	−	0.0413650i
$686$	5.37061e10	−	6.40044e10i	0.242509	−	0.289010i
$687$		0			0
$688$	1.05298e10	+	5.97175e10i	0.0469966	+	0.266531i
$689$	5.25865e10	−	9.27242e9i	0.233344	−	0.0411449i
$690$		0			0
$691$	2.64622e11	+	2.22045e11i	1.16069	+	0.973930i	0.999915	−	0.0130614i	$-0.00415771\pi$
$691$	2.64622e11	+	2.22045e11i	1.16069	+	0.973930i	0.160770	+	0.986992i	$0.448602\pi$
$692$	6.68630e9	−	3.86034e9i	0.0291583	−	0.0168345i
$693$		0			0
$694$	4.85352e10	−	8.40654e10i	0.209227	−	0.362392i
$695$	9.21265e9	+	2.53116e10i	0.0394862	+	0.108487i
$696$		0			0
$697$	1.56241e11	−	1.31102e11i	0.662008	−	0.555491i
$698$	−4.02028e10	+	1.10456e11i	−0.169369	+	0.465339i
$699$		0			0
$700$	3.65246e10	−	2.07141e11i	0.152122	−	0.862729i
$701$			7.99935e9i			0.0331271i	0.999863	+	0.0165635i	$0.00527258\pi$
$701$			7.99935e9i			0.0331271i	−0.999863	+	0.0165635i	$0.994727\pi$
$702$		0			0
$703$	3.96905e11			1.62505
$704$	1.88847e10	+	3.32989e9i	0.0768812	+	0.0135562i
$705$		0			0
$706$	1.31880e11	+	4.80005e10i	0.530837	+	0.193209i
$707$	1.32277e11	+	1.57641e11i	0.529426	+	0.630945i
$708$		0			0
$709$	−2.58748e11	+	9.41764e10i	−1.02398	+	0.372698i	−0.798786	−	0.601616i	$-0.794524\pi$
$709$	−2.58748e11	+	9.41764e10i	−1.02398	+	0.372698i	−0.225194	+	0.974314i	$0.572302\pi$
$710$	6.83100e9	+	3.94388e9i	0.0268813	+	0.0155199i
$711$		0			0
$712$	6.68018e10	+	1.15704e11i	0.259937	+	0.450224i
$713$	8.06798e10	−	9.61504e10i	0.312181	−	0.372043i
$714$		0			0
$715$	7.47982e8	+	4.24201e9i	0.00286198	+	0.0162311i
$716$	−1.21990e11	+	2.15102e10i	−0.464166	+	0.0818450i
$717$		0			0
$718$	−1.74114e11	−	1.46099e11i	−0.655144	−	0.549731i
$719$	−2.56982e11	+	1.48369e11i	−0.961585	+	0.555172i	−0.896661	−	0.442719i	$-0.854014\pi$
$719$	−2.56982e11	+	1.48369e11i	−0.961585	+	0.555172i	−0.0649248	+	0.997890i	$0.520681\pi$
$720$		0			0
$721$	7.19864e10	−	1.24684e11i	0.266385	−	0.461392i
$722$	−6.42717e10	−	1.76585e11i	−0.236522	−	0.649838i
$723$		0			0
$724$	1.28475e11	−	1.07803e11i	0.467588	−	0.392353i
$725$	8.23692e10	−	2.26308e11i	0.298135	−	0.819119i
$726$		0			0
$727$	−4.88255e10	+	2.76903e11i	−0.174787	+	0.991267i	0.763602	+	0.645687i	$0.223429\pi$
$727$	−4.88255e10	+	2.76903e11i	−0.174787	+	0.991267i	−0.938389	+	0.345580i	$0.887682\pi$
$728$			1.50228e11i			0.534841i
$729$		0			0
$730$	−7.49011e9			−0.0263752
$731$	3.79490e11	+	6.69144e10i	1.32902	+	0.234342i
$732$		0			0
$733$	−3.89034e11	−	1.41597e11i	−1.34763	−	0.490498i	−0.435424	−	0.900225i	$-0.643402\pi$
$733$	−3.89034e11	−	1.41597e11i	−1.34763	−	0.490498i	−0.912208	+	0.409728i	$0.865624\pi$
$734$	4.14979e10	+	4.94552e10i	0.142969	+	0.170384i
$735$		0			0
$736$	1.17364e11	−	4.27169e10i	0.399966	−	0.145576i
$737$	−7.16562e10	−	4.13708e10i	−0.242876	−	0.140224i
$738$		0			0
$739$	−7.10244e10	−	1.23018e11i	−0.238139	−	0.412468i	0.722042	−	0.691850i	$-0.243204\pi$
$739$	−7.10244e10	−	1.23018e11i	−0.238139	−	0.412468i	−0.960180	+	0.279382i	$0.909871\pi$
$740$	−9.19893e9	+	1.09629e10i	−0.0306768	+	0.0365592i
$741$		0			0
$742$	1.29157e10	+	7.32487e10i	0.0426092	+	0.241649i
$743$	−1.74447e11	+	3.07596e10i	−0.572410	+	0.100931i	−0.452358	−	0.891836i	$-0.649417\pi$
$743$	−1.74447e11	+	3.07596e10i	−0.572410	+	0.100931i	−0.120052	+	0.992768i	$0.538306\pi$
$744$		0			0
$745$	2.59358e10	+	2.17627e10i	0.0841926	+	0.0706460i
$746$	−1.86024e11	+	1.07401e11i	−0.600639	+	0.346779i
$747$		0			0
$748$	−1.04783e11	+	1.81490e11i	−0.334723	+	0.579757i
$749$	2.07758e11	+	5.70810e11i	0.660131	+	1.81370i
$750$		0			0
$751$	1.35565e11	−	1.13753e11i	0.426175	−	0.357603i	−0.404331	−	0.914613i	$-0.632496\pi$
$751$	1.35565e11	−	1.13753e11i	0.426175	−	0.357603i	0.830506	+	0.557009i	$0.188051\pi$
$752$	−4.13021e10	+	1.13476e11i	−0.129152	+	0.354841i
$753$		0			0
$754$	−1.29293e10	+	7.33256e10i	−0.0400027	+	0.226866i
$755$		−	1.21073e10i		−	0.0372615i
$756$		0			0
$757$	−2.71823e11			−0.827755			−0.413878	−	0.910333i	$-0.635826\pi$
$757$	−2.71823e11			−0.827755			−0.413878	+	0.910333i	$0.635826\pi$
$758$	1.78261e11	+	3.14322e10i	0.539982	+	0.0952134i
$759$		0			0
$760$	2.50579e10	+	9.12035e9i	0.0751088	+	0.0273374i
$761$	−2.67176e11	−	3.18408e11i	−0.796634	−	0.949391i	0.202922	−	0.979195i	$-0.434956\pi$
$761$	−2.67176e11	−	3.18408e11i	−0.796634	−	0.949391i	−0.999556	+	0.0298038i	$0.990512\pi$
$762$		0			0
$763$	6.91298e11	−	2.51612e11i	2.03970	−	0.742392i
$764$	1.13604e11	+	6.55891e10i	0.333441	+	0.192512i
$765$		0			0
$766$	−1.93868e10	−	3.35789e10i	−0.0563107	−	0.0975330i
$767$	−1.79476e11	+	2.13891e11i	−0.518591	+	0.618033i
$768$		0			0
$769$	−5.30732e10	−	3.00993e11i	−0.151765	−	0.860699i	−0.961684	−	0.274159i	$-0.911601\pi$
$769$	−5.30732e10	−	3.00993e11i	−0.151765	−	0.860699i	0.809920	−	0.586540i	$-0.199511\pi$
$770$	−5.90878e9	+	1.04188e9i	−0.0168087	+	0.00296383i
$771$		0			0
$772$	4.74544e9	+	3.98190e9i	0.0133600	+	0.0112104i
$773$	−1.31306e11	+	7.58097e10i	−0.367763	+	0.212328i	−0.672481	−	0.740115i	$-0.734771\pi$
$773$	−1.31306e11	+	7.58097e10i	−0.367763	+	0.212328i	0.304718	+	0.952443i	$0.401438\pi$
$774$		0			0
$775$	2.10450e11	−	3.64510e11i	0.583368	−	1.01042i
$776$	−1.55669e10	−	4.27696e10i	−0.0429294	−	0.117947i
$777$		0			0
$778$	−6.14340e10	+	5.15492e10i	−0.167683	+	0.140703i
$779$	−9.82193e10	+	2.69855e11i	−0.266715	+	0.732793i
$780$		0			0
$781$	3.50135e10	−	1.98571e11i	0.0941090	−	0.533718i
$782$		−	1.30139e11i		−	0.348001i
$783$		0			0
$784$	4.27038e10			0.113032
$785$	2.86662e10	+	5.05462e9i	0.0754903	+	0.0133110i
$786$		0			0
$787$	−1.69477e11	−	6.16845e10i	−0.441786	−	0.160797i	0.111543	−	0.993760i	$-0.464421\pi$
$787$	−1.69477e11	−	6.16845e10i	−0.441786	−	0.160797i	−0.553329	+	0.832963i	$0.686643\pi$
$788$	−1.25741e11	−	1.49852e11i	−0.326116	−	0.388650i
$789$		0			0
$790$	−1.54742e9	+	5.63215e8i	−0.00397283	+	0.00144599i
$791$	−2.84533e10	−	1.64275e10i	−0.0726820	−	0.0419630i
$792$		0			0
$793$	9.59973e10	+	1.66272e11i	0.242754	+	0.420462i
$794$	−1.12546e11	+	1.34127e11i	−0.283171	+	0.337470i
$795$		0			0
$796$	−9.87436e9	−	5.60003e10i	−0.0245956	−	0.139488i
$797$	5.56877e11	−	9.81924e10i	1.38015	−	0.243357i	0.566187	−	0.824277i	$-0.308418\pi$
$797$	5.56877e11	−	9.81924e10i	1.38015	−	0.243357i	0.813961	+	0.580919i	$0.197307\pi$
$798$		0			0
$799$	5.87859e11	+	4.93272e11i	1.44240	+	1.21032i
$800$	3.62711e11	−	2.09412e11i	0.885526	−	0.511259i
$801$		0			0
$802$	1.44108e11	−	2.49602e11i	0.348329	−	0.603324i
$803$	6.54864e10	+	1.79922e11i	0.157503	+	0.432736i
$804$		0			0
$805$	−9.20204e9	+	7.72143e9i	−0.0219129	+	0.0183871i
$806$	−4.45063e10	+	1.22280e11i	−0.105459	+	0.289745i
$807$		0			0
$808$	−4.54041e10	+	2.57500e11i	−0.106525	+	0.604131i
$809$		−	5.05250e10i		−	0.117954i	−0.998259	−	0.0589769i	$-0.981216\pi$
$809$		−	5.05250e10i		−	0.117954i	0.998259	−	0.0589769i	$-0.0187838\pi$
$810$		0			0
$811$	3.28251e11			0.758791			0.379396	−	0.925235i	$-0.376132\pi$
$811$	3.28251e11			0.758791			0.379396	+	0.925235i	$0.376132\pi$
$812$	3.29291e11	+	5.80628e10i	0.757452	+	0.133559i
$813$		0			0
$814$	−1.06628e11	−	3.88092e10i	−0.242869	−	0.0883970i
$815$	2.62439e10	+	3.12762e10i	0.0594836	+	0.0708898i
$816$		0			0
$817$	−5.09847e11	+	1.85569e11i	−1.14433	+	0.416503i
$818$	−7.51378e10	−	4.33808e10i	−0.167821	−	0.0968913i
$819$		0			0
$820$	−5.17724e9	−	8.96724e9i	−0.0114510	−	0.0198337i
$821$	4.35639e11	−	5.19174e11i	0.958857	−	1.14272i	−0.0308373	−	0.999524i	$-0.509817\pi$
$821$	4.35639e11	−	5.19174e11i	0.958857	−	1.14272i	0.989694	−	0.143197i	$-0.0457382\pi$
$822$		0			0
$823$	1.04516e11	+	5.92737e11i	0.227815	+	1.29200i	0.857231	+	0.514933i	$0.172183\pi$
$823$	1.04516e11	+	5.92737e11i	0.227815	+	1.29200i	−0.629416	+	0.777069i	$0.716706\pi$
$824$	1.80153e11	−	3.17658e10i	0.390780	−	0.0689051i
$825$		0			0
$826$	−2.97933e11	−	2.49995e11i	−0.640027	−	0.537047i
$827$	−3.13017e11	+	1.80720e11i	−0.669184	+	0.386353i	−0.795767	−	0.605603i	$-0.792932\pi$
$827$	−3.13017e11	+	1.80720e11i	−0.669184	+	0.386353i	0.126584	+	0.991956i	$0.459599\pi$
$828$		0			0
$829$	−1.85216e11	+	3.20803e11i	−0.392157	+	0.679235i	−0.992734	−	0.120332i	$-0.961604\pi$
$829$	−1.85216e11	+	3.20803e11i	−0.392157	+	0.679235i	0.600577	+	0.799567i	$0.294938\pi$
$830$	−5.97716e8	−	1.64221e9i	−0.00125946	−	0.00346032i
$831$		0			0
$832$	−3.04909e10	+	2.55849e10i	−0.0636322	+	0.0533938i
$833$	9.28149e10	−	2.55007e11i	0.192769	−	0.529629i
$834$		0			0
$835$	−8.98527e9	+	5.09580e10i	−0.0184835	+	0.104825i
$836$		−	2.95071e11i		−	0.604090i
$837$		0			0
$838$	−2.28308e11			−0.462962
$839$	−4.93790e11	−	8.70685e10i	−0.996539	−	0.175717i	−0.348488	−	0.937313i	$-0.613305\pi$
$839$	−4.93790e11	−	8.70685e10i	−0.996539	−	0.175717i	−0.648051	+	0.761597i	$0.724416\pi$
$840$		0			0
$841$	−1.10319e11	−	4.01528e10i	−0.220529	−	0.0802660i
$842$	−2.59482e11	−	3.09238e11i	−0.516248	−	0.615241i
$843$		0			0
$844$	−6.17892e11	+	2.24894e11i	−1.21771	+	0.443209i
$845$	1.86925e10	+	1.07921e10i	0.0366640	+	0.0211679i
$846$		0			0
$847$	−2.19737e11	−	3.80595e11i	−0.426942	−	0.739486i
$848$	5.03256e10	−	5.99758e10i	0.0973209	−	0.115982i
$849$		0			0
$850$	−7.57810e10	−	4.29775e11i	−0.145173	−	0.823315i
$851$	−2.23727e11	+	3.94491e10i	−0.426580	+	0.0752176i
$852$		0			0
$853$	−1.25556e11	−	1.05354e11i	−0.237160	−	0.199001i	0.516460	−	0.856312i	$-0.327250\pi$
$853$	−1.25556e11	−	1.05354e11i	−0.237160	−	0.199001i	−0.753620	+	0.657310i	$0.771694\pi$
$854$	−2.31604e11	+	1.33716e11i	−0.435425	+	0.251393i
$855$		0			0
$856$	−3.85910e11	+	6.68415e11i	−0.718771	+	1.24495i
$857$	−2.24707e11	−	6.17377e11i	−0.416575	−	1.14453i	−0.953630	−	0.300982i	$-0.902685\pi$
$857$	−2.24707e11	−	6.17377e11i	−0.416575	−	1.14453i	0.537055	−	0.843547i	$-0.319537\pi$
$858$		0			0
$859$	−2.05655e11	+	1.72565e11i	−0.377717	+	0.316943i	−0.811806	−	0.583928i	$-0.801515\pi$
$859$	−2.05655e11	+	1.72565e11i	−0.377717	+	0.316943i	0.434088	+	0.900870i	$0.357071\pi$
$860$	6.69097e9	−	1.83833e10i	0.0122319	−	0.0336070i
$861$		0			0
$862$	4.05330e9	−	2.29874e10i	0.00734141	−	0.0416352i
$863$		−	7.75412e11i		−	1.39794i	−0.715150	−	0.698971i	$-0.753642\pi$
$863$		−	7.75412e11i		−	1.39794i	0.715150	−	0.698971i	$-0.246358\pi$
$864$		0			0
$865$	−1.47861e9			−0.00264112
$866$	−5.15738e11	−	9.09385e10i	−0.916975	−	0.161687i
$867$		0			0
$868$	5.49136e11	+	1.99869e11i	0.967388	+	0.352101i
$869$	2.70584e10	+	3.22469e10i	0.0474485	+	0.0565469i
$870$		0			0
$871$	1.61386e11	−	5.87398e10i	0.280410	−	0.102061i
$872$	8.09506e11	+	4.67368e11i	1.40008	+	0.808339i
$873$		0			0
$874$	9.16184e10	+	1.58688e11i	0.157014	+	0.271955i
$875$	−5.18789e10	+	6.18268e10i	−0.0885031	+	0.105474i
$876$		0			0
$877$	5.75848e10	+	3.26579e11i	0.0973440	+	0.552065i	0.994004	+	0.109345i	$0.0348754\pi$
$877$	5.75848e10	+	3.26579e11i	0.0973440	+	0.552065i	−0.896660	+	0.442720i	$0.854014\pi$
$878$	−3.94698e11	+	6.95958e10i	−0.664181	+	0.117113i
$879$		0			0
$880$	4.83809e9	+	4.05964e9i	0.00806758	+	0.00676950i
$881$	−3.43576e11	+	1.98364e11i	−0.570320	+	0.329275i	−0.757277	−	0.653094i	$-0.773471\pi$
$881$	−3.43576e11	+	1.98364e11i	−0.570320	+	0.329275i	0.186957	+	0.982368i	$0.440138\pi$
$882$		0			0
$883$	−2.25631e11	+	3.90804e11i	−0.371155	+	0.642860i	−0.989744	−	0.142856i	$-0.954372\pi$
$883$	−2.25631e11	+	3.90804e11i	−0.371155	+	0.642860i	0.618588	+	0.785715i	$0.287705\pi$
$884$	−1.48775e11	−	4.08757e11i	−0.243625	−	0.669354i
$885$		0			0
$886$	1.82042e11	−	1.52751e11i	0.295417	−	0.247885i
$887$	−1.74390e11	+	4.79133e11i	−0.281726	+	0.774037i	0.715431	+	0.698684i	$0.246231\pi$
$887$	−1.74390e11	+	4.79133e11i	−0.281726	+	0.774037i	−0.997157	+	0.0753529i	$0.975992\pi$
$888$		0			0
$889$	1.59788e10	−	9.06204e10i	0.0255822	−	0.145084i
$890$		−	1.10757e10i		−	0.0176527i
$891$		0			0
$892$	7.98779e10			0.126173
$893$	−1.06408e12	−	1.87627e11i	−1.67328	−	0.295045i
$894$		0			0
$895$	2.22924e10	+	8.11377e9i	0.0347428	+	0.0126453i
$896$	4.54074e11	+	5.41145e11i	0.704523	+	0.839617i
$897$		0			0
$898$	3.76318e11	−	1.36969e11i	0.578695	−	0.210628i
$899$	5.79459e11	+	3.34551e11i	0.887123	+	0.512181i
$900$		0			0
$901$	−2.48766e11	−	4.30875e11i	−0.377478	−	0.653812i
$902$	5.27727e10	−	6.28921e10i	0.0797229	−	0.0950101i
$903$		0			0
$904$	−7.24907e9	−	4.11115e10i	−0.0108545	−	0.0615587i
$905$	−3.16310e10	+	5.57740e9i	−0.0471540	+	0.00831452i
$906$		0			0
$907$	−8.86132e11	−	7.43553e11i	−1.30939	−	1.09871i	−0.988440	−	0.151614i	$-0.951553\pi$
$907$	−8.86132e11	−	7.43553e11i	−1.30939	−	1.09871i	−0.320952	−	0.947096i	$-0.604003\pi$
$908$	−4.49630e11	+	2.59594e11i	−0.661473	+	0.381901i
$909$		0			0
$910$	6.22692e9	−	1.07853e10i	0.00908046	−	0.0157278i
$911$	1.13732e11	+	3.12476e11i	0.165124	+	0.453673i	0.994465	−	0.105069i	$-0.0335063\pi$
$911$	1.13732e11	+	3.12476e11i	0.165124	+	0.453673i	−0.829341	+	0.558742i	$0.811284\pi$
$912$		0			0
$913$	−3.42223e10	+	2.87159e10i	−0.0492522	+	0.0413275i
$914$	2.82053e10	−	7.74933e10i	0.0404153	−	0.111040i
$915$		0			0
$916$	1.45962e11	−	8.27792e11i	0.207328	−	1.17582i
$917$		−	1.30947e12i		−	1.85190i
$918$		0			0
$919$	−1.61529e11			−0.226459			−0.113229	−	0.993569i	$-0.536120\pi$
$919$	−1.61529e11			−0.226459			−0.113229	+	0.993569i	$0.536120\pi$
$920$	−1.50311e10	−	2.65039e9i	−0.0209817	−	0.00369964i
$921$		0			0
$922$	1.20094e11	+	4.37107e10i	0.166187	+	0.0604872i
$923$	2.69023e11	+	3.20609e11i	0.370666	+	0.441742i
$924$		0			0
$925$	−7.15872e11	+	2.60556e11i	−0.977842	+	0.355905i
$926$	1.55820e11	+	8.99629e10i	0.211924	+	0.122354i
$927$		0			0
$928$	3.32899e11	+	5.76599e11i	0.448871	+	0.777467i
$929$	−4.01736e11	+	4.78770e11i	−0.539359	+	0.642783i	−0.965044	−	0.262088i	$-0.915589\pi$
$929$	−4.01736e11	+	4.78770e11i	−0.539359	+	0.642783i	0.425685	+	0.904872i	$0.360033\pi$
$930$		0			0
$931$	6.63500e10	+	3.76290e11i	0.0883166	+	0.500868i
$932$	−5.54767e11	+	9.78203e10i	−0.735270	+	0.129648i
$933$		0			0
$934$	−2.18566e11	−	1.83399e11i	−0.287207	−	0.240996i
$935$	3.47576e10	−	2.00673e10i	0.0454782	−	0.0262569i
$936$		0			0
$937$	−2.07728e10	+	3.59796e10i	−0.0269487	+	0.0466765i	−0.879185	−	0.476480i	$-0.841912\pi$
$937$	−2.07728e10	+	3.59796e10i	−0.0269487	+	0.0466765i	0.852237	+	0.523157i	$0.175246\pi$
$938$	8.18197e10	+	2.24798e11i	0.105693	+	0.290389i
$939$		0			0
$940$	2.98443e10	−	2.50423e10i	0.0382252	−	0.0320747i
$941$	1.12104e11	−	3.08003e11i	0.142976	−	0.392822i	−0.847449	−	0.530877i	$-0.821863\pi$
$941$	1.12104e11	−	3.08003e11i	0.142976	−	0.392822i	0.990425	+	0.138055i	$0.0440850\pi$
$942$		0			0
$943$	2.85428e10	−	1.61874e11i	0.0360952	−	0.204706i
$944$			4.09391e11i			0.515526i
$945$		0			0
$946$	1.55114e11			0.193681
$947$	−1.83765e11	−	3.24028e10i	−0.228488	−	0.0402886i	0.0582317	−	0.998303i	$-0.481454\pi$
$947$	−1.83765e11	−	3.24028e10i	−0.228488	−	0.0402886i	−0.286720	+	0.958014i	$0.592565\pi$
$948$		0			0
$949$	−3.73458e11	−	1.35928e11i	−0.460445	−	0.167588i
$950$	3.94969e11	+	4.70705e11i	0.484918	+	0.577902i
$951$		0			0
$952$	1.31533e12	−	4.78741e11i	1.60135	−	0.582845i
$953$	−2.43325e11	−	1.40483e11i	−0.294995	−	0.170315i	0.345197	−	0.938530i	$-0.387812\pi$
$953$	−2.43325e11	−	1.40483e11i	−0.294995	−	0.170315i	−0.640192	+	0.768215i	$0.721145\pi$
$954$		0			0
$955$	−1.25611e10	−	2.17565e10i	−0.0151013	−	0.0261563i
$956$	−2.30701e11	+	2.74938e11i	−0.276196	+	0.329157i
$957$		0			0
$958$	1.20396e11	+	6.82800e11i	0.142939	+	0.810647i
$959$	7.65439e11	−	1.34968e11i	0.904974	−	0.159571i
$960$		0			0
$961$	2.42449e11	+	2.03439e11i	0.284268	+	0.238529i
$962$	2.03972e11	−	1.17763e11i	0.238161	−	0.137502i
$963$		0			0
$964$	4.14848e11	−	7.18537e11i	0.480375	−	0.832034i
$965$	−4.05762e8	−	1.11482e9i	−0.000467910	−	0.00128557i
$966$		0			0
$967$	3.59916e11	−	3.02005e11i	0.411619	−	0.345389i	−0.413345	−	0.910574i	$-0.635640\pi$
$967$	3.59916e11	−	3.02005e11i	0.411619	−	0.345389i	0.824964	+	0.565185i	$0.191195\pi$
$968$	1.90983e11	−	5.24721e11i	0.217517	−	0.597622i
$969$		0			0
$970$	−6.55198e8	+	3.71582e9i	−0.000740092	+	0.00419727i
$971$		−	1.13211e12i		−	1.27354i	−0.771056	−	0.636768i	$-0.780271\pi$
$971$		−	1.13211e12i		−	1.27354i	0.771056	−	0.636768i	$-0.219729\pi$
$972$		0			0
$973$	−1.99080e12			−2.22114
$974$	−1.58307e11	−	2.79138e10i	−0.175899	−	0.0310158i
$975$		0			0
$976$	2.64529e11	+	9.62808e10i	0.291524	+	0.106106i
$977$	1.01318e11	+	1.20746e11i	0.111201	+	0.132524i	0.818774	−	0.574117i	$-0.194654\pi$
$977$	1.01318e11	+	1.20746e11i	0.111201	+	0.132524i	−0.707573	+	0.706640i	$0.750210\pi$
$978$		0			0
$979$	−2.66053e11	+	9.68355e10i	−0.289626	+	0.105415i
$980$	−1.19312e10	−	6.88849e9i	−0.0129354	−	0.00746827i
$981$		0			0
$982$	9.15746e10	+	1.58612e11i	0.0984757	+	0.170565i
$983$	−2.32916e11	+	2.77578e11i	−0.249451	+	0.297284i	−0.876210	−	0.481929i	$-0.839936\pi$
$983$	−2.32916e11	+	2.77578e11i	−0.249451	+	0.297284i	0.626760	+	0.779213i	$0.284381\pi$
$984$		0			0
$985$	6.50544e9	+	3.68942e10i	0.00691085	+	0.0391934i
$986$	6.83210e11	−	1.20468e11i	0.722847	−	0.127457i
$987$		0			0
$988$	4.69178e11	+	3.93687e11i	0.492391	+	0.413165i
$989$	2.68946e11	−	1.55276e11i	0.281113	−	0.162300i
$990$		0			0
$991$	2.02286e11	−	3.50370e11i	0.209735	−	0.363272i	−0.741896	−	0.670515i	$-0.766073\pi$
$991$	2.02286e11	−	3.50370e11i	0.209735	−	0.363272i	0.951631	+	0.307243i	$0.0994064\pi$
$992$	3.97980e11	+	1.09344e12i	0.410974	+	1.12914i
$993$		0			0
$994$	−4.46582e11	+	3.74727e11i	−0.457463	+	0.383857i
$995$	−3.72467e9	+	1.02334e10i	−0.00380010	+	0.0104407i
$996$		0			0
$997$	2.68798e11	−	1.52443e12i	0.272048	−	1.54286i	−0.476137	−	0.879371i	$-0.657963\pi$
$997$	2.68798e11	−	1.52443e12i	0.272048	−	1.54286i	0.748185	−	0.663490i	$-0.230926\pi$
$998$			1.97145e11i			0.198730i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.14		138
3.2	odd	2		27.9.f.a.2.10	✓	138
27.13	even	9		27.9.f.a.14.10	yes	138
27.14	odd	18	inner	81.9.f.a.71.14		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.10	✓	138	3.2	odd	2
27.9.f.a.14.10	yes	138	27.13	even	9
81.9.f.a.8.14		138	1.1	even	1	trivial
81.9.f.a.71.14		138	27.14	odd	18	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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(7.66670 + 1.35185i) q^{2} +(-183.611 - 66.8288i) q^{4} +(24.0534 + 28.6657i) q^{5} +(-2598.90 + 945.921i) q^{7} +(-3043.29 - 1757.05i) q^{8} +(145.659 + 252.288i) q^{10} +(4786.80 - 5704.68i) q^{11} +(2684.14 + 15222.5i) q^{13} +(-21203.7 + 3738.78i) q^{14} +(17361.5 + 14568.0i) q^{16} +(124728. - 72011.7i) q^{17} +(-101393. + 175618. i) q^{19} +(-2500.76 - 6870.79i) q^{20} +(44410.8 - 37265.1i) q^{22} +(39698.1 - 109070. i) q^{23} +(67588.2 - 383312. i) q^{25} +120335. i q^{26} +540399. q^{28} +(609347. + 107444. i) q^{29} +(1.01617e6 + 369854. i) q^{31} +(691668. + 824298. i) q^{32} +(1.05360e6 - 383479. i) q^{34} +(-89627.8 - 51746.6i) q^{35} +(-978631. - 1.69504e6i) q^{37} +(-1.01476e6 + 1.20934e6i) q^{38} +(-22834.5 - 129501. i) q^{40} +(1.39463e6 - 245911. i) q^{41} +(2.04961e6 + 1.71982e6i) q^{43} +(-1.26014e6 + 727544. i) q^{44} +(451799. - 782539. i) q^{46} +(1.82238e6 + 5.00694e6i) q^{47} +(1.44340e6 - 1.21116e6i) q^{49} +(1.03636e6 - 2.84736e6i) q^{50} +(524465. - 2.97439e6i) q^{52} -3.45452e6i q^{53} +278668. q^{55} +(9.57122e6 + 1.68767e6i) q^{56} +(4.52643e6 + 1.64749e6i) q^{58} +(1.16111e7 + 1.38375e7i) q^{59} +(1.16719e7 - 4.24821e6i) q^{61} +(7.29065e6 + 4.20926e6i) q^{62} +(1.28751e6 + 2.23004e6i) q^{64} +(-371801. + 443096. i) q^{65} +(-1.92937e6 - 1.09420e7i) q^{67} +(-2.77138e7 + 4.88669e6i) q^{68} +(-617196. - 517889. i) q^{70} +(2.34487e7 - 1.35381e7i) q^{71} +(-1.28556e7 + 2.22665e7i) q^{73} +(-5.21144e6 - 1.43183e7i) q^{74} +(3.03531e7 - 2.54693e7i) q^{76} +(-7.04421e6 + 1.93538e7i) q^{77} +(-981583. + 5.56684e6i) q^{79} +848091. i q^{80} +1.10246e7 q^{82} +(-5.90784e6 - 1.04171e6i) q^{83} +(5.06440e6 + 1.84329e6i) q^{85} +(1.33888e7 + 1.59561e7i) q^{86} +(-2.45910e7 + 8.95039e6i) q^{88} +(-3.29258e7 - 1.90097e7i) q^{89} +(-2.13751e7 - 3.70227e7i) q^{91} +(-1.45780e7 + 1.73734e7i) q^{92} +(7.20300e6 + 4.08503e7i) q^{94} +(-7.47305e6 + 1.31770e6i) q^{95} +(9.92181e6 + 8.32538e6i) q^{97} +(1.27034e7 - 7.33433e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

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