LMFDB - Embedded newform 81.10.e.a.10.19

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			10.19
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.45544 + 25.2681i) q^{2} +(-137.502 + 50.0467i) q^{4} +(84.0511 + 70.5273i) q^{5} +(7618.26 + 2772.82i) q^{7} +(4691.20 + 8125.40i) q^{8} +(-1407.60 + 2438.04i) q^{10} +(31769.4 - 26657.7i) q^{11} +(30545.4 - 173231. i) q^{13} +(-36121.1 + 204853. i) q^{14} +(-241803. + 202897. i) q^{16} +(157212. - 272299. i) q^{17} +(-320002. - 554259. i) q^{19} +(-15086.9 - 5491.17i) q^{20} +(815135. + 683979. i) q^{22} +(1.49889e6 - 545550. i) q^{23} +(-337066. - 1.91160e6i) q^{25} +4.51332e6 q^{26} -1.18630e6 q^{28} +(1.23208e6 + 6.98745e6i) q^{29} +(1.65256e6 - 601483. i) q^{31} +(-2.52424e6 - 2.11809e6i) q^{32} +(7.58092e6 + 2.75923e6i) q^{34} +(444764. + 770353. i) q^{35} +(6.47138e6 - 1.12088e7i) q^{37} +(1.25793e7 - 1.05553e7i) q^{38} +(-178761. + 1.01381e6i) q^{40} +(-1.43503e6 + 8.13844e6i) q^{41} +(-1.11765e7 + 9.37816e6i) q^{43} +(-3.03423e6 + 5.25544e6i) q^{44} +(2.04632e7 + 3.54433e7i) q^{46} +(8.39723e6 + 3.05634e6i) q^{47} +(1.94367e7 + 1.63093e7i) q^{49} +(4.68006e7 - 1.70340e7i) q^{50} +(4.46960e6 + 2.53484e7i) q^{52} -2.81172e7 q^{53} +4.55034e6 q^{55} +(1.32085e7 + 7.49093e7i) q^{56} +(-1.71070e8 + 6.22644e7i) q^{58} +(5.73824e6 + 4.81496e6i) q^{59} +(4.23338e7 + 1.54083e7i) q^{61} +(2.25612e7 + 3.90772e7i) q^{62} +(-3.85334e7 + 6.67418e7i) q^{64} +(1.47849e7 - 1.24060e7i) q^{65} +(-3.79484e7 + 2.15216e8i) q^{67} +(-7.98931e6 + 4.53096e7i) q^{68} +(-1.74837e7 + 1.46706e7i) q^{70} +(-1.08934e7 + 1.88680e7i) q^{71} +(-3.48700e7 - 6.03966e7i) q^{73} +(3.12057e8 + 1.13579e8i) q^{74} +(7.17397e7 + 6.01968e7i) q^{76} +(3.15944e8 - 1.14994e8i) q^{77} +(9.90613e7 + 5.61805e8i) q^{79} -3.46336e7 q^{80} -2.12036e8 q^{82} +(5.52959e7 + 3.13598e8i) q^{83} +(3.24183e7 - 1.17993e7i) q^{85} +(-2.86764e8 - 2.40624e8i) q^{86} +(3.65641e8 + 1.33082e8i) q^{88} +(-2.42736e8 - 4.20431e8i) q^{89} +(7.13042e8 - 1.23502e9i) q^{91} +(-1.78797e8 + 1.50029e8i) q^{92} +(-3.98145e7 + 2.25799e8i) q^{94} +(1.21939e7 - 6.91549e7i) q^{95} +(7.51254e8 - 6.30377e8i) q^{97} +(-3.25506e8 + 5.63793e8i) 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 $

$2$	4.45544	+	25.2681i	0.196905	+	1.11670i	0.909680	+	0.415310i	$0.136327\pi$
$2$	4.45544	+	25.2681i	0.196905	+	1.11670i	−0.712776	+	0.701392i	$0.752562\pi$
$3$		0			0
$3$		0			0
$4$	−137.502	+	50.0467i	−0.268559	+	0.0977474i
$5$	84.0511	+	70.5273i	0.0601421	+	0.0504652i	0.672363	−	0.740221i	$-0.265279\pi$
$5$	84.0511	+	70.5273i	0.0601421	+	0.0504652i	−0.612221	+	0.790687i	$0.709724\pi$
$6$		0			0
$7$	7618.26	+	2772.82i	1.19926	+	0.436496i	0.862967	−	0.505260i	$-0.168603\pi$
$7$	7618.26	+	2772.82i	1.19926	+	0.436496i	0.336296	+	0.941756i	$0.390826\pi$
$8$	4691.20	+	8125.40i	0.404929	+	0.701358i
$9$		0			0
$10$	−1407.60	+	2438.04i	−0.0445123	+	0.0770976i
$11$	31769.4	−	26657.7i	0.654247	−	0.548978i	−0.254109	−	0.967176i	$-0.581782\pi$
$11$	31769.4	−	26657.7i	0.654247	−	0.548978i	0.908356	+	0.418197i	$0.137338\pi$
$12$		0			0
$13$	30545.4	−	173231.i	0.296620	−	1.68221i	−0.363926	−	0.931428i	$-0.618564\pi$
$13$	30545.4	−	173231.i	0.296620	−	1.68221i	0.660545	−	0.750786i	$-0.270325\pi$
$14$	−36121.1	+	204853.i	−0.251296	+	1.42517i
$15$		0			0
$16$	−241803.	+	202897.i	−0.922406	+	0.773991i
$17$	157212.	−	272299.i	0.456526	−	0.790726i	−0.542249	−	0.840218i	$-0.682427\pi$
$17$	157212.	−	272299.i	0.456526	−	0.790726i	0.998775	+	0.0494922i	$0.0157603\pi$
$18$		0			0
$19$	−320002.	−	554259.i	−0.563328	−	0.975712i	−0.997203	−	0.0747394i	$-0.976188\pi$
$19$	−320002.	−	554259.i	−0.563328	−	0.975712i	0.433875	−	0.900973i	$-0.357146\pi$
$20$	−15086.9	−	5491.17i	−0.0210845	−	0.00767414i
$21$		0			0
$22$	815135.	+	683979.i	0.741869	+	0.622502i
$23$	1.49889e6	−	545550.i	1.11685	−	0.406499i	0.283346	−	0.959018i	$-0.408556\pi$
$23$	1.49889e6	−	545550.i	1.11685	−	0.406499i	0.833500	+	0.552519i	$0.186333\pi$
$24$		0			0
$25$	−337066.	−	1.91160e6i	−0.172578	−	0.978738i
$26$	4.51332e6			1.93694
$27$		0			0
$28$	−1.18630e6			−0.364739
$29$	1.23208e6	+	6.98745e6i	0.323479	+	1.83454i	0.520152	+	0.854074i	$0.325875\pi$
$29$	1.23208e6	+	6.98745e6i	0.323479	+	1.83454i	−0.196672	+	0.980469i	$0.563014\pi$
$30$		0			0
$31$	1.65256e6	−	601483.i	0.321388	−	0.116976i	−0.176288	−	0.984339i	$-0.556409\pi$
$31$	1.65256e6	−	601483.i	0.321388	−	0.116976i	0.497676	+	0.867363i	$0.334187\pi$
$32$	−2.52424e6	−	2.11809e6i	−0.425555	−	0.357083i
$33$		0			0
$34$	7.58092e6	+	2.75923e6i	0.972897	+	0.354106i
$35$	444764.	+	770353.i	0.0500983	+	0.0867728i
$36$		0			0
$37$	6.47138e6	−	1.12088e7i	0.567661	−	0.983218i	−0.429135	−	0.903240i	$-0.641182\pi$
$37$	6.47138e6	−	1.12088e7i	0.567661	−	0.983218i	0.996797	−	0.0799780i	$-0.0254850\pi$
$38$	1.25793e7	−	1.05553e7i	0.978658	−	0.821191i
$39$		0			0
$40$	−178761.	+	1.01381e6i	−0.0110409	+	0.0626159i
$41$	−1.43503e6	+	8.13844e6i	−0.0793108	+	0.449794i	0.919129	+	0.393957i	$0.128894\pi$
$41$	−1.43503e6	+	8.13844e6i	−0.0793108	+	0.449794i	−0.998440	+	0.0558374i	$0.982217\pi$
$42$		0			0
$43$	−1.11765e7	+	9.37816e6i	−0.498535	+	0.418321i	−0.857073	−	0.515194i	$-0.827720\pi$
$43$	−1.11765e7	+	9.37816e6i	−0.498535	+	0.418321i	0.358538	+	0.933515i	$0.383275\pi$
$44$	−3.03423e6	+	5.25544e6i	−0.122043	+	0.211384i
$45$		0			0
$46$	2.04632e7	+	3.54433e7i	0.673850	+	1.16714i
$47$	8.39723e6	+	3.05634e6i	0.251013	+	0.0913612i	0.464462	−	0.885593i	$-0.346248\pi$
$47$	8.39723e6	+	3.05634e6i	0.251013	+	0.0913612i	−0.213449	+	0.976954i	$0.568470\pi$
$48$		0			0
$49$	1.94367e7	+	1.63093e7i	0.481660	+	0.404160i
$50$	4.68006e7	−	1.70340e7i	1.05898	−	0.385436i
$51$		0			0
$52$	4.46960e6	+	2.53484e7i	0.0847722	+	0.480767i
$53$	−2.81172e7			−0.489475			−0.244738	−	0.969589i	$-0.578702\pi$
$53$	−2.81172e7			−0.489475			−0.244738	+	0.969589i	$0.578702\pi$
$54$		0			0
$55$	4.55034e6			0.0670521
$56$	1.32085e7	+	7.49093e7i	0.179477	+	1.01786i
$57$		0			0
$58$	−1.71070e8	+	6.22644e7i	−1.98494	+	0.722460i
$59$	5.73824e6	+	4.81496e6i	0.0616517	+	0.0517319i	0.673093	−	0.739558i	$-0.264965\pi$
$59$	5.73824e6	+	4.81496e6i	0.0616517	+	0.0517319i	−0.611441	+	0.791290i	$0.709410\pi$
$60$		0			0
$61$	4.23338e7	+	1.54083e7i	0.391474	+	0.142485i	0.530255	−	0.847838i	$-0.322096\pi$
$61$	4.23338e7	+	1.54083e7i	0.391474	+	0.142485i	−0.138781	+	0.990323i	$0.544318\pi$
$62$	2.25612e7	+	3.90772e7i	0.193910	+	0.335862i
$63$		0			0
$64$	−3.85334e7	+	6.67418e7i	−0.287096	+	0.497265i
$65$	1.47849e7	−	1.24060e7i	0.102733	−	0.0862029i
$66$		0			0
$67$	−3.79484e7	+	2.15216e8i	−0.230068	+	1.30478i	0.622688	+	0.782471i	$0.286041\pi$
$67$	−3.79484e7	+	2.15216e8i	−0.230068	+	1.30478i	−0.852756	+	0.522310i	$0.825070\pi$
$68$	−7.98931e6	+	4.53096e7i	−0.0453126	+	0.256981i
$69$		0			0
$70$	−1.74837e7	+	1.46706e7i	−0.0870348	+	0.0730309i
$71$	−1.08934e7	+	1.88680e7i	−0.0508747	+	0.0881176i	−0.890341	−	0.455294i	$-0.849534\pi$
$71$	−1.08934e7	+	1.88680e7i	−0.0508747	+	0.0881176i	0.839467	+	0.543411i	$0.182868\pi$
$72$		0			0
$73$	−3.48700e7	−	6.03966e7i	−0.143714	−	0.248920i	0.785178	−	0.619270i	$-0.212571\pi$
$73$	−3.48700e7	−	6.03966e7i	−0.143714	−	0.248920i	−0.928892	+	0.370350i	$0.879238\pi$
$74$	3.12057e8	+	1.13579e8i	1.20974	+	0.440308i
$75$		0			0
$76$	7.17397e7	+	6.01968e7i	0.246660	+	0.206972i
$77$	3.15944e8	−	1.14994e8i	1.02424	−	0.372793i
$78$		0			0
$79$	9.90613e7	+	5.61805e8i	0.286142	+	1.62279i	0.701176	+	0.712988i	$0.252659\pi$
$79$	9.90613e7	+	5.61805e8i	0.286142	+	1.62279i	−0.415034	+	0.909806i	$0.636230\pi$
$80$	−3.46336e7			−0.0945350
$81$		0			0
$82$	−2.12036e8			−0.517902
$83$	5.52959e7	+	3.13598e8i	0.127891	+	0.725308i	0.979548	+	0.201208i	$0.0644869\pi$
$83$	5.52959e7	+	3.13598e8i	0.127891	+	0.725308i	−0.851657	+	0.524099i	$0.824402\pi$
$84$		0			0
$85$	3.24183e7	−	1.17993e7i	0.0673605	−	0.0245172i
$86$	−2.86764e8	−	2.40624e8i	−0.565303	−	0.474346i
$87$		0			0
$88$	3.65641e8	+	1.33082e8i	0.649954	+	0.236564i
$89$	−2.42736e8	−	4.20431e8i	−0.410090	−	0.710296i	0.584810	−	0.811171i	$-0.301169\pi$
$89$	−2.42736e8	−	4.20431e8i	−0.410090	−	0.710296i	−0.994899	+	0.100875i	$0.967836\pi$
$90$		0			0
$91$	7.13042e8	−	1.23502e9i	1.09001	−	1.88794i
$92$	−1.78797e8	+	1.50029e8i	−0.260205	+	0.218338i
$93$		0			0
$94$	−3.98145e7	+	2.25799e8i	−0.0525976	+	0.298296i
$95$	1.21939e7	−	6.91549e7i	0.0153598	−	0.0871098i
$96$		0			0
$97$	7.51254e8	−	6.30377e8i	0.861617	−	0.722982i	−0.100699	−	0.994917i	$-0.532108\pi$
$97$	7.51254e8	−	6.30377e8i	0.861617	−	0.722982i	0.962316	+	0.271935i	$0.0876635\pi$
$98$	−3.25506e8	+	5.63793e8i	−0.356486	+	0.617451i
$99$		0			0
$100$	1.42016e8	+	2.45980e8i	0.142016	+	0.245980i
$101$	1.40207e9	+	5.10313e8i	1.34068	+	0.487967i	0.910026	−	0.414551i	$-0.136061\pi$
$101$	1.40207e9	+	5.10313e8i	1.34068	+	0.487967i	0.430652	+	0.902518i	$0.358284\pi$
$102$		0			0
$103$	−1.11621e9	−	9.36610e8i	−0.977187	−	0.819957i	0.00647559	−	0.999979i	$-0.497939\pi$
$103$	−1.11621e9	−	9.36610e8i	−0.977187	−	0.819957i	−0.983663	+	0.180022i	$0.942383\pi$
$104$	1.55087e9	−	5.64470e8i	1.29994	−	0.473141i
$105$		0			0
$106$	−1.25275e8	−	7.10468e8i	−0.0963799	−	0.546598i
$107$	−1.81438e9			−1.33814			−0.669069	−	0.743200i	$-0.733307\pi$
$107$	−1.81438e9			−1.33814			−0.669069	+	0.743200i	$0.733307\pi$
$108$		0			0
$109$	1.13564e9			0.770588			0.385294	−	0.922794i	$-0.374100\pi$
$109$	1.13564e9			0.770588			0.385294	+	0.922794i	$0.374100\pi$
$110$	2.02738e7	+	1.14978e8i	0.0132029	+	0.0748772i
$111$		0			0
$112$	−2.40472e9	+	8.75245e8i	−1.44405	+	0.525592i
$113$	−7.35916e8	−	6.17507e8i	−0.424596	−	0.356278i	0.405312	−	0.914178i	$-0.367163\pi$
$113$	−7.35916e8	−	6.17507e8i	−0.424596	−	0.356278i	−0.829908	+	0.557900i	$0.811607\pi$
$114$		0			0
$115$	1.64459e8	+	5.98583e7i	0.0876835	+	0.0319142i
$116$	−5.19112e8	−	8.99128e8i	−0.266195	−	0.461063i
$117$		0			0
$118$	−9.60983e7	+	1.66447e8i	−0.0456296	+	0.0790328i
$119$	1.95272e9	−	1.63852e9i	0.892643	−	0.749017i
$120$		0			0
$121$	−1.10791e8	+	6.28329e8i	−0.0469863	+	0.266473i
$122$	−2.00721e8	+	1.13834e9i	−0.0820301	+	0.465216i
$123$		0			0
$124$	−1.97128e8	+	1.65410e8i	−0.0748775	+	0.0628297i
$125$	2.13638e8	−	3.70032e8i	0.0782679	−	0.135564i
$126$		0			0
$127$	−2.13572e9	−	3.69917e9i	−0.728496	−	1.26179i	−0.957519	−	0.288371i	$-0.906886\pi$
$127$	−2.13572e9	−	3.69917e9i	−0.728496	−	1.26179i	0.229023	−	0.973421i	$-0.426447\pi$
$128$	−3.44350e9	−	1.25333e9i	−1.13385	−	0.412687i
$129$		0			0
$130$	3.79349e8	+	3.18312e8i	0.116491	+	0.0977479i
$131$	−4.88204e9	+	1.77692e9i	−1.44837	+	0.527164i	−0.942136	−	0.335231i	$-0.891186\pi$
$131$	−4.88204e9	+	1.77692e9i	−1.44837	+	0.527164i	−0.506236	+	0.862395i	$0.668963\pi$
$132$		0			0
$133$	−9.00995e8	−	5.10980e9i	−0.249684	−	1.41603i
$134$	−5.60717e9			−1.50235
$135$		0			0
$136$	2.95005e9			0.739442
$137$	7.34198e8	+	4.16384e9i	0.178062	+	1.00984i	0.934550	+	0.355831i	$0.115802\pi$
$137$	7.34198e8	+	4.16384e9i	0.178062	+	1.00984i	−0.756488	+	0.654007i	$0.773087\pi$
$138$		0			0
$139$	−2.10427e9	+	7.65891e8i	−0.478118	+	0.174021i	−0.569826	−	0.821765i	$-0.692989\pi$
$139$	−2.10427e9	+	7.65891e8i	−0.478118	+	0.174021i	0.0917085	+	0.995786i	$0.470767\pi$
$140$	−9.97096e7	−	8.36663e7i	−0.0219362	−	0.0184066i
$141$		0			0
$142$	−5.25292e8	−	1.91191e8i	−0.108419	−	0.0394611i
$143$	−3.64754e9	−	6.31772e9i	−0.729437	−	1.26342i
$144$		0			0
$145$	−3.89248e8	+	6.74198e8i	−0.0731258	+	0.126658i
$146$	1.37074e9	−	1.15019e9i	0.249671	−	0.209499i
$147$		0			0
$148$	−3.28867e8	+	1.86510e9i	−0.0563434	+	0.319539i
$149$	4.85461e8	−	2.75319e9i	0.0806893	−	0.457612i	−0.917514	−	0.397702i	$-0.869808\pi$
$149$	4.85461e8	−	2.75319e9i	0.0806893	−	0.457612i	0.998204	−	0.0599096i	$-0.0190812\pi$
$150$		0			0
$151$	3.17698e8	−	2.66580e8i	0.0497299	−	0.0417284i	−0.617584	−	0.786505i	$-0.711888\pi$
$151$	3.17698e8	−	2.66580e8i	0.0497299	−	0.0417284i	0.667314	+	0.744777i	$0.267444\pi$
$152$	3.00238e9	−	5.20028e9i	0.456216	−	0.790189i
$153$		0			0
$154$	4.31336e9	+	7.47096e9i	0.617977	+	1.07037i
$155$	1.81321e8	+	6.59953e7i	0.0252322	+	0.00918375i
$156$		0			0
$157$	5.22920e9	+	4.38782e9i	0.686889	+	0.576368i	0.918010	−	0.396557i	$-0.129795\pi$
$157$	5.22920e9	+	4.38782e9i	0.686889	+	0.576368i	−0.231121	+	0.972925i	$0.574239\pi$
$158$	−1.37544e10	+	5.00618e9i	−1.75583	+	0.639071i
$159$		0			0
$160$	−6.27822e7	−	3.56056e8i	−0.00757350	−	0.0429515i
$161$	1.29316e10			1.51683
$162$		0			0
$163$	1.04810e10			1.16294			0.581471	−	0.813567i	$-0.302478\pi$
$163$	1.04810e10			1.16294			0.581471	+	0.813567i	$0.302478\pi$
$164$	−2.09983e8	−	1.19087e9i	−0.0226666	−	0.128549i
$165$		0			0
$166$	−7.67766e9	+	2.79444e9i	−0.784770	+	0.285633i
$167$	1.16520e10	+	9.77720e9i	1.15925	+	0.972726i	0.999895	−	0.0144960i	$-0.00461437\pi$
$167$	1.16520e10	+	9.77720e9i	1.15925	+	0.972726i	0.159354	+	0.987221i	$0.449059\pi$
$168$		0			0
$169$	−1.91111e10	−	6.95587e9i	−1.80217	−	0.655936i
$170$	4.42584e8	+	7.66578e8i	0.0406420	+	0.0703941i
$171$		0			0
$172$	1.06744e9	−	1.84886e9i	0.0929962	−	0.161074i
$173$	8.06085e9	−	6.76386e9i	0.684185	−	0.574099i	−0.233041	−	0.972467i	$-0.574868\pi$
$173$	8.06085e9	−	6.76386e9i	0.684185	−	0.574099i	0.917226	+	0.398368i	$0.130423\pi$
$174$		0			0
$175$	2.73266e9	−	1.54977e10i	0.220249	−	1.24909i
$176$	−2.27318e9	+	1.28918e10i	−0.178577	+	1.01276i
$177$		0			0
$178$	9.54198e9	−	8.00667e9i	0.712440	−	0.597808i
$179$	−2.51198e9	+	4.35088e9i	−0.182885	+	0.316766i	−0.942862	−	0.333184i	$-0.891877\pi$
$179$	−2.51198e9	+	4.35088e9i	−0.182885	+	0.316766i	0.759977	+	0.649950i	$0.225210\pi$
$180$		0			0
$181$	6.61938e9	+	1.14651e10i	0.458420	+	0.794007i	0.998878	−	0.0473645i	$-0.0150822\pi$
$181$	6.61938e9	+	1.14651e10i	0.458420	+	0.794007i	−0.540458	+	0.841371i	$0.681749\pi$
$182$	3.43836e10	+	1.25146e10i	2.32290	+	0.845466i
$183$		0			0
$184$	1.14644e10	+	9.61976e9i	0.737345	+	0.618706i
$185$	1.33445e9	−	4.85700e8i	0.0837586	−	0.0304856i
$186$		0			0
$187$	−2.26433e9	−	1.28417e10i	−0.135411	−	0.767953i
$188$	−1.30760e9			−0.0763420
$189$		0			0
$190$	1.80174e9			0.100300
$191$	−5.01304e9	−	2.84304e10i	−0.272553	−	1.54573i	−0.746628	−	0.665241i	$-0.768329\pi$
$191$	−5.01304e9	−	2.84304e10i	−0.272553	−	1.54573i	0.474075	−	0.880484i	$-0.342782\pi$
$192$		0			0
$193$	−1.84204e10	+	6.70447e9i	−0.955632	+	0.347822i	−0.772320	−	0.635233i	$-0.780904\pi$
$193$	−1.84204e10	+	6.70447e9i	−0.955632	+	0.347822i	−0.183312	+	0.983055i	$0.558682\pi$
$194$	1.92756e10	+	1.61741e10i	0.977012	+	0.819810i
$195$		0			0
$196$	−3.48881e9	−	1.26982e9i	−0.168860	−	0.0614598i
$197$	−2.21917e9	−	3.84371e9i	−0.104977	−	0.181825i	0.808752	−	0.588150i	$-0.200143\pi$
$197$	−2.21917e9	−	3.84371e9i	−0.104977	−	0.181825i	−0.913729	+	0.406325i	$0.866810\pi$
$198$		0			0
$199$	−1.35846e10	+	2.35292e10i	−0.614054	+	1.06357i	0.376495	+	0.926419i	$0.377129\pi$
$199$	−1.35846e10	+	2.35292e10i	−0.614054	+	1.06357i	−0.990550	+	0.137155i	$0.956204\pi$
$200$	1.39512e10	−	1.17065e10i	0.616564	−	0.517358i
$201$		0			0
$202$	−6.64777e9	+	3.77014e10i	−0.280928	+	1.59322i
$203$	−9.98867e9	+	5.66486e10i	−0.412834	+	2.34130i
$204$		0			0
$205$	−6.94597e8	+	5.82836e8i	−0.0274689	+	0.0230491i
$206$	1.86931e10	−	3.23774e10i	0.723235	−	1.25268i
$207$		0			0
$208$	2.77622e10	+	4.80855e10i	1.02841	+	1.78127i
$209$	−2.49415e10	−	9.07797e9i	−0.904200	−	0.329102i
$210$		0			0
$211$	−7.17083e8	−	6.01704e8i	−0.0249057	−	0.0208984i	0.630250	−	0.776392i	$-0.282952\pi$
$211$	−7.17083e8	−	6.01704e8i	−0.0249057	−	0.0208984i	−0.655156	+	0.755494i	$0.727397\pi$
$212$	3.86617e9	−	1.40717e9i	0.131453	−	0.0478449i
$213$		0			0
$214$	−8.08386e9	−	4.58459e10i	−0.263486	−	1.49430i
$215$	−1.60081e9			−0.0510936
$216$		0			0
$217$	1.42574e10			0.436489
$218$	5.05979e9	+	2.86955e10i	0.151732	+	0.860517i
$219$		0			0
$220$	−6.25682e8	+	2.27730e8i	−0.0180074	+	0.00655417i
$221$	−4.23686e10	−	3.55515e10i	−1.19476	−	1.00252i
$222$		0			0
$223$	−6.71686e8	−	2.44474e8i	−0.0181884	−	0.00662003i	0.332910	−	0.942959i	$-0.391969\pi$
$223$	−6.71686e8	−	2.44474e8i	−0.0181884	−	0.00662003i	−0.351098	+	0.936339i	$0.614192\pi$
$224$	−1.33573e10	−	2.31354e10i	−0.354488	−	0.613990i
$225$		0			0
$226$	1.23244e10	−	2.13465e10i	0.314251	−	0.544299i
$227$	−1.07172e10	+	8.99283e9i	−0.267896	+	0.224792i	−0.766833	−	0.641847i	$-0.778168\pi$
$227$	−1.07172e10	+	8.99283e9i	−0.267896	+	0.224792i	0.498937	+	0.866638i	$0.333724\pi$
$228$		0			0
$229$	5.82085e9	−	3.30117e10i	0.139871	−	0.793246i	−0.831473	−	0.555566i	$-0.812502\pi$
$229$	5.82085e9	−	3.30117e10i	0.139871	−	0.793246i	0.971343	−	0.237681i	$-0.0763871\pi$
$230$	−7.79764e8	+	4.42226e9i	−0.0183733	+	0.104200i
$231$		0			0
$232$	−5.09959e10	+	4.27907e10i	−1.15569	+	0.969735i
$233$	−1.55624e10	+	2.69549e10i	−0.345920	+	0.599151i	−0.985520	−	0.169557i	$-0.945766\pi$
$233$	−1.55624e10	+	2.69549e10i	−0.345920	+	0.599151i	0.639600	+	0.768708i	$0.279100\pi$
$234$		0			0
$235$	4.90241e8	+	8.49122e8i	0.0104859	+	0.0181621i
$236$	−1.02999e9	−	3.74887e8i	−0.0216138	−	0.00786677i
$237$		0			0
$238$	5.01026e10	+	4.20411e10i	1.01219	+	0.849332i
$239$	−7.84743e10	+	2.85623e10i	−1.55574	+	0.566243i	−0.969755	−	0.244080i	$-0.921514\pi$
$239$	−7.84743e10	+	2.85623e10i	−1.55574	+	0.566243i	−0.585984	+	0.810322i	$0.699292\pi$
$240$		0			0
$241$	2.59293e9	+	1.47053e10i	0.0495125	+	0.280799i	0.999505	−	0.0314747i	$-0.0100204\pi$
$241$	2.59293e9	+	1.47053e10i	0.0495125	+	0.280799i	−0.949992	+	0.312274i	$0.898909\pi$
$242$	−1.63703e10			−0.306822
$243$		0			0
$244$	−6.59212e9			−0.119061
$245$	4.83424e8	+	2.74163e9i	0.00857197	+	0.0486141i
$246$		0			0
$247$	−1.05790e11	+	3.85043e10i	−1.80845	+	0.658222i
$248$	1.26398e10	+	1.06060e10i	0.212181	+	0.178041i
$249$		0			0
$250$	1.03019e10	+	3.74957e9i	0.166796	+	0.0607088i
$251$	−3.13522e10	−	5.43035e10i	−0.498581	−	0.863568i	0.501418	−	0.865205i	$-0.332812\pi$
$251$	−3.13522e10	−	5.43035e10i	−0.498581	−	0.863568i	−0.999999	+	0.00163777i	$0.999479\pi$
$252$		0			0
$253$	3.30756e10	−	5.72886e10i	0.507534	−	0.879075i
$254$	8.39554e10	−	7.04469e10i	1.26560	−	1.06197i
$255$		0			0
$256$	9.47510e9	−	5.37360e10i	0.137881	−	0.781962i
$257$	5.29759e9	−	3.00441e10i	0.0757493	−	0.429596i	−0.923223	−	0.384265i	$-0.874455\pi$
$257$	5.29759e9	−	3.00441e10i	0.0757493	−	0.429596i	0.998972	−	0.0453306i	$-0.0144341\pi$
$258$		0			0
$259$	8.03806e10	−	6.74473e10i	1.10995	−	0.931356i
$260$	−1.41208e9	+	2.44579e9i	−0.0191636	+	0.0331924i
$261$		0			0
$262$	−6.66509e10	−	1.15443e11i	−0.873876	−	1.51360i
$263$	8.34502e10	+	3.03734e10i	1.07554	+	0.391464i	0.818246	−	0.574869i	$-0.194947\pi$
$263$	8.34502e10	+	3.03734e10i	1.07554	+	0.391464i	0.257294	+	0.966333i	$0.417169\pi$
$264$		0			0
$265$	−2.36328e9	−	1.98303e9i	−0.0294381	−	0.0247015i
$266$	1.25100e11	−	4.55328e10i	1.53212	−	0.557644i
$267$		0			0
$268$	−5.55286e9	−	3.14918e10i	−0.0657521	−	0.372899i
$269$	−7.05924e10			−0.822002			−0.411001	−	0.911635i	$-0.634821\pi$
$269$	−7.05924e10			−0.822002			−0.411001	+	0.911635i	$0.634821\pi$
$270$		0			0
$271$	7.22203e10			0.813388			0.406694	−	0.913564i	$-0.366682\pi$
$271$	7.22203e10			0.813388			0.406694	+	0.913564i	$0.366682\pi$
$272$	1.72343e10	+	9.77406e10i	0.190912	+	1.08272i
$273$		0			0
$274$	−1.01941e11	+	3.71035e10i	−1.09263	+	0.397684i
$275$	−6.16671e10	−	5.17449e10i	−0.650214	−	0.545595i
$276$		0			0
$277$	−7.82591e10	−	2.84840e10i	−0.798685	−	0.290698i	−0.0897438	−	0.995965i	$-0.528605\pi$
$277$	−7.82591e10	−	2.84840e10i	−0.798685	−	0.290698i	−0.708942	+	0.705267i	$0.750827\pi$
$278$	−2.87281e10	−	4.97584e10i	−0.288473	−	0.499649i
$279$		0			0
$280$	−4.17295e9	+	7.22777e9i	−0.0405726	+	0.0702737i
$281$	−1.36797e11	+	1.14786e11i	−1.30888	+	1.09828i	−0.320339	+	0.947303i	$0.603797\pi$
$281$	−1.36797e11	+	1.14786e11i	−1.30888	+	1.09828i	−0.988538	+	0.150975i	$0.951759\pi$
$282$		0			0
$283$	2.15209e10	−	1.22051e11i	0.199444	−	1.13110i	−0.706502	−	0.707711i	$-0.749728\pi$
$283$	2.15209e10	−	1.22051e11i	0.199444	−	1.13110i	0.905946	−	0.423393i	$-0.139161\pi$
$284$	5.53590e8	−	3.13957e9i	0.00504959	−	0.0286376i
$285$		0			0
$286$	1.43385e11	−	1.20315e11i	1.26724	−	1.06334i
$287$	−3.34988e10	+	5.80217e10i	−0.291448	+	0.504803i
$288$		0			0
$289$	9.86278e9	+	1.70828e10i	0.0831685	+	0.144052i
$290$	−1.87700e10	−	6.83171e9i	−0.155838	−	0.0567203i
$291$		0			0
$292$	7.81734e9	+	6.55953e9i	0.0629269	+	0.0528019i
$293$	4.87408e10	−	1.77402e10i	0.386357	−	0.140622i	−0.141537	−	0.989933i	$-0.545204\pi$
$293$	4.87408e10	−	1.77402e10i	0.386357	−	0.140622i	0.527893	+	0.849311i	$0.322982\pi$
$294$		0			0
$295$	1.42720e8	+	8.09405e8i	0.00109720	+	0.00622253i
$296$	1.21434e11			0.919451
$297$		0			0
$298$	7.17307e10			0.526904
$299$	−4.87223e10	−	2.76318e11i	−0.352539	−	1.99935i
$300$		0			0
$301$	−1.11149e11	+	4.04549e10i	−0.780471	+	0.284068i
$302$	8.15145e9	+	6.83988e9i	0.0563902	+	0.0473170i
$303$		0			0
$304$	1.89835e11	+	6.90943e10i	1.27481	+	0.463993i
$305$	2.47150e9	+	4.28077e9i	0.0163535	+	0.0283252i
$306$		0			0
$307$	8.07586e10	−	1.39878e11i	0.518879	−	0.898725i	−0.480880	−	0.876786i	$-0.659683\pi$
$307$	8.07586e10	−	1.39878e11i	0.518879	−	0.898725i	0.999759	−	0.0219384i	$-0.00698376\pi$
$308$	−3.76879e10	+	3.16239e10i	−0.238629	+	0.200234i
$309$		0			0
$310$	−8.59710e8	+	4.87566e9i	−0.00528718	+	0.0299851i
$311$	3.73002e9	−	2.11540e10i	0.0226094	−	0.128224i	−0.971414	−	0.237392i	$-0.923707\pi$
$311$	3.73002e9	−	2.11540e10i	0.0226094	−	0.128224i	0.994023	+	0.109168i	$0.0348185\pi$
$312$		0			0
$313$	−2.30702e11	+	1.93582e11i	−1.35863	+	1.14003i	−0.382230	+	0.924067i	$0.624844\pi$
$313$	−2.30702e11	+	1.93582e11i	−1.35863	+	1.14003i	−0.976402	+	0.215961i	$0.930712\pi$
$314$	−8.75733e10	+	1.51681e11i	−0.508380	+	0.880540i
$315$		0			0
$316$	−4.17376e10	−	7.22916e10i	−0.235470	−	0.407846i
$317$	8.99911e10	+	3.27541e10i	0.500533	+	0.182179i	0.579934	−	0.814664i	$-0.303078\pi$
$317$	8.99911e10	+	3.27541e10i	0.500533	+	0.182179i	−0.0794005	+	0.996843i	$0.525301\pi$
$318$		0			0
$319$	2.25412e11	+	1.89143e11i	1.21876	+	1.02266i
$320$	−7.94589e9	+	2.89207e9i	−0.0423611	+	0.0154182i
$321$		0			0
$322$	5.76161e10	+	3.26757e11i	0.298671	+	1.69384i
$323$	−2.01232e11			−1.02869
$324$		0			0
$325$	−3.41444e11			−1.69764
$326$	4.66974e10	+	2.64834e11i	0.228989	+	1.29866i
$327$		0			0
$328$	−7.28600e10	+	2.65189e10i	−0.347582	+	0.126509i
$329$	5.54976e10	+	4.65680e10i	0.261152	+	0.219132i
$330$		0			0
$331$	1.45754e11	+	5.30501e10i	0.667413	+	0.242919i	0.653434	−	0.756984i	$-0.273328\pi$
$331$	1.45754e11	+	5.30501e10i	0.667413	+	0.242919i	0.0139795	+	0.999902i	$0.495550\pi$
$332$	−2.32978e10	−	4.03531e10i	−0.105243	−	0.182287i
$333$		0			0
$334$	−1.95136e11	+	3.37986e11i	−0.857983	+	1.48607i
$335$	−1.83682e10	+	1.54127e10i	−0.0796828	+	0.0668618i
$336$		0			0
$337$	7.19624e10	−	4.08119e11i	0.303928	−	1.72366i	−0.324578	−	0.945859i	$-0.605222\pi$
$337$	7.19624e10	−	4.08119e11i	0.303928	−	1.72366i	0.628506	−	0.777804i	$-0.283667\pi$
$338$	9.06131e10	−	5.13892e11i	0.377629	−	2.14164i
$339$		0			0
$340$	−3.86707e9	+	3.24486e9i	−0.0156938	+	0.0131686i
$341$	3.64667e10	−	6.31622e10i	0.146050	−	0.252966i
$342$		0			0
$343$	−6.07260e10	−	1.05181e11i	−0.236893	−	0.410310i
$344$	−1.28632e11	−	4.68183e10i	−0.495264	−	0.180261i
$345$		0			0
$346$	2.06824e11	+	1.73546e11i	0.775817	+	0.650987i
$347$	−1.52587e11	+	5.55372e10i	−0.564983	+	0.205637i	−0.608691	−	0.793407i	$-0.708305\pi$
$347$	−1.52587e11	+	5.55372e10i	−0.564983	+	0.205637i	0.0437078	+	0.999044i	$0.486083\pi$
$348$		0			0
$349$	2.39737e10	+	1.35962e11i	0.0865009	+	0.490571i	0.997023	+	0.0771097i	$0.0245692\pi$
$349$	2.39737e10	+	1.35962e11i	0.0865009	+	0.490571i	−0.910522	+	0.413461i	$0.864320\pi$
$350$	4.03771e11			1.43823
$351$		0			0
$352$	−1.36657e11			−0.474449
$353$	−7.95863e8	−	4.51356e9i	−0.00272805	−	0.0154715i	0.983413	−	0.181379i	$-0.0580559\pi$
$353$	−7.95863e8	−	4.51356e9i	−0.00272805	−	0.0154715i	−0.986141	+	0.165907i	$0.946945\pi$
$354$		0			0
$355$	−2.24631e9	+	8.17590e8i	−0.00750658	+	0.00273217i
$356$	5.44178e10	+	4.56620e10i	0.179563	+	0.150671i
$357$		0			0
$358$	−1.21130e11	−	4.40878e10i	−0.389744	−	0.141855i
$359$	2.89687e11	+	5.01752e11i	0.920457	+	1.59428i	0.798710	+	0.601717i	$0.205516\pi$
$359$	2.89687e11	+	5.01752e11i	0.920457	+	1.59428i	0.121747	+	0.992561i	$0.461150\pi$
$360$		0			0
$361$	−4.34584e10	+	7.52721e10i	−0.134676	+	0.233266i
$362$	−2.60209e11	+	2.18341e11i	−0.796404	+	0.668262i
$363$		0			0
$364$	−3.62359e10	+	2.05504e11i	−0.108189	+	0.613569i
$365$	1.32874e9	−	7.53568e9i	0.00391853	−	0.0222231i
$366$		0			0
$367$	−3.33676e11	+	2.79987e11i	−0.960124	+	0.805640i	−0.980973	−	0.194143i	$-0.937807\pi$
$367$	−3.33676e11	+	2.79987e11i	−0.960124	+	0.805640i	0.0208492	+	0.999783i	$0.493363\pi$
$368$	−2.51745e11	+	4.36035e11i	−0.715560	+	1.23939i
$369$		0			0
$370$	1.82183e10	+	3.15550e10i	0.0505358	+	0.0875306i
$371$	−2.14204e11	−	7.79639e10i	−0.587010	−	0.213654i
$372$		0			0
$373$	−3.48663e11	−	2.92563e11i	−0.932645	−	0.782582i	0.0436452	−	0.999047i	$-0.486103\pi$
$373$	−3.48663e11	−	2.92563e11i	−0.932645	−	0.782582i	−0.976290	+	0.216465i	$0.930547\pi$
$374$	3.14396e11	−	1.14431e11i	0.830911	−	0.302427i
$375$		0			0
$376$	1.45591e10	+	8.25688e10i	0.0375655	+	0.213045i
$377$	1.24808e12			3.18204
$378$		0			0
$379$	4.85580e11			1.20888			0.604441	−	0.796650i	$-0.293396\pi$
$379$	4.85580e11			1.20888			0.604441	+	0.796650i	$0.293396\pi$
$380$	1.78429e9	+	1.01192e10i	0.00438975	+	0.0248955i
$381$		0			0
$382$	6.96046e11	−	2.53340e11i	1.67245	−	0.608721i
$383$	3.47490e11	+	2.91579e11i	0.825178	+	0.692407i	0.954179	−	0.299238i	$-0.0967324\pi$
$383$	3.47490e11	+	2.91579e11i	0.825178	+	0.692407i	−0.129001	+	0.991645i	$0.541177\pi$
$384$		0			0
$385$	3.46657e10	+	1.26173e10i	0.0804131	+	0.0292680i
$386$	−2.51480e11	−	4.35576e11i	−0.576582	−	0.998669i
$387$		0			0
$388$	−7.17508e10	+	1.24276e11i	−0.160725	+	0.278384i
$389$	5.71115e11	−	4.79222e11i	1.26459	−	1.06112i	0.269413	−	0.963025i	$-0.413170\pi$
$389$	5.71115e11	−	4.79222e11i	1.26459	−	1.06112i	0.995177	−	0.0980930i	$-0.0312743\pi$
$390$		0			0
$391$	8.70900e10	−	4.93912e11i	0.188440	−	1.06870i
$392$	−4.13383e10	+	2.34441e11i	−0.0884230	+	0.501472i
$393$		0			0
$394$	8.72359e10	−	7.31996e10i	0.182374	−	0.153030i
$395$	−3.12963e10	+	5.42068e10i	−0.0646854	+	0.112038i
$396$		0			0
$397$	2.50177e11	+	4.33320e11i	0.505464	+	0.875490i	0.999980	+	0.00632111i	$0.00201209\pi$
$397$	2.50177e11	+	4.33320e11i	0.505464	+	0.875490i	−0.494516	+	0.869169i	$0.664655\pi$
$398$	−6.55062e11	−	2.38423e11i	−1.30860	−	0.476293i
$399$		0			0
$400$	4.69361e11	+	3.93841e11i	0.916721	+	0.769220i
$401$	−1.79203e11	+	6.52246e10i	−0.346096	+	0.125968i	−0.509219	−	0.860637i	$-0.670065\pi$
$401$	−1.79203e11	+	6.52246e10i	−0.346096	+	0.125968i	0.163123	+	0.986606i	$0.447843\pi$
$402$		0			0
$403$	−5.37176e10	−	3.04648e11i	−0.101448	−	0.575341i
$404$	−2.18327e11			−0.407748
$405$		0			0
$406$	−1.47590e12			−2.69582
$407$	−9.32078e10	−	5.28608e11i	−0.168375	−	0.954901i
$408$		0			0
$409$	2.51318e11	−	9.14721e10i	0.444087	−	0.161634i	−0.110291	−	0.993899i	$-0.535178\pi$
$409$	2.51318e11	−	9.14721e10i	0.444087	−	0.161634i	0.554378	+	0.832265i	$0.312956\pi$
$410$	−1.78219e10	−	1.49543e10i	−0.0311477	−	0.0261360i
$411$		0			0
$412$	2.00355e11	+	7.29233e10i	0.342581	+	0.124689i
$413$	3.03644e10	+	5.25927e10i	0.0513558	+	0.0889509i
$414$		0			0
$415$	−1.74696e10	+	3.02582e10i	−0.0289111	+	0.0500756i
$416$	−4.44024e11	+	3.72580e11i	−0.726919	+	0.609957i
$417$		0			0
$418$	1.18257e11	−	6.70671e11i	0.189468	−	1.07452i
$419$	−1.50100e10	+	8.51262e10i	−0.0237913	+	0.134927i	−0.994390	−	0.105777i	$-0.966267\pi$
$419$	−1.50100e10	+	8.51262e10i	−0.0237913	+	0.134927i	0.970599	+	0.240704i	$0.0773783\pi$
$420$		0			0
$421$	6.46541e11	−	5.42512e11i	1.00306	−	0.841667i	0.0156538	−	0.999877i	$-0.495017\pi$
$421$	6.46541e11	−	5.42512e11i	1.00306	−	0.841667i	0.987405	+	0.158211i	$0.0505726\pi$
$422$	1.20090e10	−	2.08002e10i	0.0184332	−	0.0319272i
$423$		0			0
$424$	−1.31903e11	−	2.28463e11i	−0.198203	−	0.343297i
$425$	−5.73517e11	−	2.08743e11i	−0.852699	−	0.310357i
$426$		0			0
$427$	2.79786e11	+	2.34768e11i	0.407287	+	0.341754i
$428$	2.49481e11	−	9.08036e10i	0.359369	−	0.130800i
$429$		0			0
$430$	−7.13231e9	−	4.04494e10i	−0.0100606	−	0.0570563i
$431$	3.08273e11			0.430317			0.215158	−	0.976579i	$-0.430973\pi$
$431$	3.08273e11			0.430317			0.215158	+	0.976579i	$0.430973\pi$
$432$		0			0
$433$	2.72266e11			0.372218			0.186109	−	0.982529i	$-0.440412\pi$
$433$	2.72266e11			0.372218			0.186109	+	0.982529i	$0.440412\pi$
$434$	6.35232e10	+	3.60258e11i	0.0859466	+	0.487428i
$435$		0			0
$436$	−1.56153e11	+	5.68351e10i	−0.206948	+	0.0753230i
$437$	−7.82022e11	−	6.56195e11i	−1.02578	−	0.860729i
$438$		0			0
$439$	−8.24438e11	−	3.00071e11i	−1.05942	−	0.385597i	−0.247209	−	0.968962i	$-0.579513\pi$
$439$	−8.24438e11	−	3.00071e11i	−1.05942	−	0.385597i	−0.812210	+	0.583366i	$0.801736\pi$
$440$	2.13466e10	+	3.69734e10i	0.0271513	+	0.0470275i
$441$		0			0
$442$	7.09547e11	−	1.22897e12i	0.884262	−	1.53159i
$443$	−4.11776e11	+	3.45521e11i	−0.507978	+	0.426244i	−0.860417	−	0.509591i	$-0.829797\pi$
$443$	−4.11776e11	+	3.45521e11i	−0.507978	+	0.426244i	0.352439	+	0.935835i	$0.385352\pi$
$444$		0			0
$445$	9.24961e9	−	5.24572e10i	0.0111816	−	0.0634139i
$446$	3.18472e9	−	1.80615e10i	0.00381122	−	0.0216145i
$447$		0			0
$448$	−4.78620e11	+	4.01610e11i	−0.561358	+	0.471035i
$449$	−3.65447e11	+	6.32972e11i	−0.424341	+	0.734981i	−0.996359	−	0.0852606i	$-0.972828\pi$
$449$	−3.65447e11	+	6.32972e11i	−0.424341	+	0.734981i	0.572017	+	0.820242i	$0.306161\pi$
$450$		0			0
$451$	1.71362e11	+	2.96808e11i	0.195038	+	0.337816i
$452$	1.32094e11	+	4.80784e10i	0.148854	+	0.0541785i
$453$		0			0
$454$	−2.74982e11	−	2.30737e11i	−0.303775	−	0.254898i
$455$	1.47035e11	−	5.35163e10i	0.160831	−	0.0585376i
$456$		0			0
$457$	1.02347e11	+	5.80440e11i	0.109762	+	0.622493i	0.989211	+	0.146499i	$0.0468005\pi$
$457$	1.02347e11	+	5.80440e11i	0.109762	+	0.622493i	−0.879449	+	0.475994i	$0.842088\pi$
$458$	8.60076e11			0.913361
$459$		0			0
$460$	−2.56092e10			−0.0266677
$461$	−1.13979e11	−	6.46408e11i	−0.117536	−	0.666580i	−0.985463	−	0.169889i	$-0.945659\pi$
$461$	−1.13979e11	−	6.46408e11i	−0.117536	−	0.666580i	0.867927	−	0.496691i	$-0.165452\pi$
$462$		0			0
$463$	3.47506e11	−	1.26482e11i	0.351437	−	0.127913i	−0.160269	−	0.987073i	$-0.551236\pi$
$463$	3.47506e11	−	1.26482e11i	0.351437	−	0.127913i	0.511706	+	0.859161i	$0.329014\pi$
$464$	−1.71565e12	−	1.43960e12i	−1.71830	−	1.44182i
$465$		0			0
$466$	−7.50436e11	−	2.73136e11i	−0.737186	−	0.268314i
$467$	−4.78730e11	−	8.29185e11i	−0.465763	−	0.806725i	0.533473	−	0.845817i	$-0.320887\pi$
$467$	−4.78730e11	−	8.29185e11i	−0.465763	−	0.806725i	−0.999236	+	0.0390926i	$0.987553\pi$
$468$		0			0
$469$	−8.85855e11	+	1.53435e12i	−0.845444	+	1.46435i
$470$	−1.92714e10	+	1.61707e10i	−0.0182169	+	0.0152858i
$471$		0			0
$472$	−1.22042e10	+	6.92135e10i	−0.0113180	+	0.0641877i
$473$	−1.05069e11	+	5.95877e11i	−0.0965161	+	0.547370i
$474$		0			0
$475$	−9.51659e11	+	7.98536e11i	−0.857748	+	0.719736i
$476$	−1.86500e11	+	3.23027e11i	−0.166513	+	0.288409i
$477$		0			0
$478$	−1.07135e12	−	1.85564e12i	−0.938657	−	1.62580i
$479$	1.47698e11	+	5.37578e10i	0.128193	+	0.0466586i	0.405320	−	0.914175i	$-0.367160\pi$
$479$	1.47698e11	+	5.37578e10i	0.128193	+	0.0466586i	−0.277127	+	0.960833i	$0.589382\pi$
$480$		0			0
$481$	−1.74404e12	−	1.46342e12i	−1.48560	−	1.24657i
$482$	−3.60021e11	+	1.31037e11i	−0.303820	+	0.110581i
$483$		0			0
$484$	−1.62117e10	−	9.19413e10i	−0.0134284	−	0.0761564i
$485$	1.07603e11			0.0883049
$486$		0			0
$487$	9.94903e11			0.801494			0.400747	−	0.916189i	$-0.368751\pi$
$487$	9.94903e11			0.801494			0.400747	+	0.916189i	$0.368751\pi$
$488$	7.33983e10	+	4.16262e11i	0.0585864	+	0.332260i
$489$		0			0
$490$	−6.71219e10	+	2.44304e10i	−0.0525996	+	0.0191447i
$491$	9.69176e11	+	8.13235e11i	0.752551	+	0.631465i	0.936176	−	0.351531i	$-0.114339\pi$
$491$	9.69176e11	+	8.13235e11i	0.752551	+	0.631465i	−0.183625	+	0.982996i	$0.558783\pi$
$492$		0			0
$493$	2.09637e12	+	7.63018e11i	1.59830	+	0.581733i
$494$	−1.44427e12	−	2.50155e12i	−1.09113	−	1.88989i
$495$		0			0
$496$	−2.77556e11	+	4.80740e11i	−0.205912	+	0.356651i
$497$	−1.35306e11	+	1.13536e11i	−0.0994752	+	0.0834696i
$498$		0			0
$499$	−3.10039e11	+	1.75832e12i	−0.223853	+	1.26954i	0.641012	+	0.767531i	$0.278515\pi$
$499$	−3.10039e11	+	1.75832e12i	−0.223853	+	1.26954i	−0.864865	+	0.502005i	$0.832596\pi$
$500$	−1.08568e10	+	6.15721e10i	−0.00776851	+	0.0440574i
$501$		0			0
$502$	1.23246e12	−	1.03416e12i	0.866175	−	0.726807i
$503$	−1.40784e12	+	2.43845e12i	−0.980614	+	1.69847i	−0.320608	+	0.947212i	$0.603887\pi$
$503$	−1.40784e12	+	2.43845e12i	−0.980614	+	1.69847i	−0.660006	+	0.751260i	$0.729446\pi$
$504$		0			0
$505$	8.18548e10	+	1.41777e11i	0.0560058	+	0.0970049i
$506$	1.59494e12	+	5.80511e11i	1.08160	+	0.393670i
$507$		0			0
$508$	4.78797e11	+	4.01758e11i	0.318981	+	0.267657i
$509$	1.73547e12	−	6.31658e11i	1.14600	−	0.417111i	0.301926	−	0.953331i	$-0.402370\pi$
$509$	1.73547e12	−	6.31658e11i	1.14600	−	0.417111i	0.844078	+	0.536220i	$0.180148\pi$
$510$		0			0
$511$	−9.81798e10	−	5.56805e11i	−0.0636983	−	0.361251i
$512$	−4.76200e11			−0.306249
$513$		0			0
$514$	7.82760e11			0.494646
$515$	−2.77620e10	−	1.57446e11i	−0.0173908	−	0.0986279i
$516$		0			0
$517$	3.48250e11	−	1.26753e11i	0.214380	−	0.0780278i
$518$	2.06239e12	+	1.73055e12i	1.25860	+	1.05609i
$519$		0			0
$520$	1.70163e11	+	6.19341e10i	0.102058	+	0.0371463i
$521$	−5.70725e11	−	9.88524e11i	−0.339357	−	0.587784i	0.644955	−	0.764221i	$-0.276876\pi$
$521$	−5.70725e11	−	9.88524e11i	−0.339357	−	0.587784i	−0.984312	+	0.176437i	$0.943543\pi$
$522$		0			0
$523$	7.74685e11	−	1.34179e12i	0.452760	−	0.784203i	−0.545797	−	0.837918i	$-0.683773\pi$
$523$	7.74685e11	−	1.34179e12i	0.452760	−	0.784203i	0.998556	+	0.0537149i	$0.0171062\pi$
$524$	5.82361e11	−	4.88659e11i	0.337444	−	0.283149i
$525$		0			0
$526$	−3.95669e11	+	2.24395e12i	−0.225370	+	1.27814i
$527$	9.60190e10	−	5.44551e11i	0.0542262	−	0.307532i
$528$		0			0
$529$	5.69273e11	−	4.77676e11i	0.316060	−	0.265206i
$530$	3.95779e10	−	6.85509e10i	0.0217877	−	0.0377374i
$531$		0			0
$532$	3.79617e11	+	6.57516e11i	0.205468	+	0.355880i
$533$	1.36600e12	+	4.97183e11i	0.733125	+	0.266836i
$534$		0			0
$535$	−1.52501e11	−	1.27963e11i	−0.0804784	−	0.0675294i
$536$	−1.92674e12	+	7.01275e11i	−1.00828	+	0.366984i
$537$		0			0
$538$	−3.14520e11	−	1.78373e12i	−0.161856	−	0.917931i
$539$	1.05226e12			0.537000
$540$		0			0
$541$	1.67071e12			0.838519			0.419260	−	0.907866i	$-0.362290\pi$
$541$	1.67071e12			0.838519			0.419260	+	0.907866i	$0.362290\pi$
$542$	3.21774e11	+	1.82487e12i	0.160160	+	0.908312i
$543$		0			0
$544$	−9.73595e11	+	3.54360e11i	−0.476632	+	0.173480i
$545$	9.54520e10	+	8.00937e10i	0.0463448	+	0.0388879i
$546$		0			0
$547$	2.00767e12	+	7.30731e11i	0.958845	+	0.348991i	0.773581	−	0.633698i	$-0.218464\pi$
$547$	2.00767e12	+	7.30731e11i	0.958845	+	0.348991i	0.185264	+	0.982689i	$0.440686\pi$
$548$	−3.09340e11	−	5.35793e11i	−0.146529	−	0.253796i
$549$		0			0
$550$	1.03274e12	−	1.78876e12i	0.481236	−	0.833526i
$551$	3.47859e12	−	2.91889e12i	1.60776	−	1.34907i
$552$		0			0
$553$	−8.03108e11	+	4.55465e12i	−0.365183	+	2.07106i
$554$	3.71056e11	−	2.10437e12i	0.167358	−	0.949133i
$555$		0			0
$556$	2.51011e11	−	2.10623e11i	0.111393	−	0.0934695i
$557$	−1.17338e12	+	2.03235e12i	−0.516523	+	0.894644i	0.483293	+	0.875459i	$0.339441\pi$
$557$	−1.17338e12	+	2.03235e12i	−0.516523	+	0.894644i	−0.999816	+	0.0191856i	$0.993893\pi$
$558$		0			0
$559$	1.28320e12	+	2.22257e12i	0.555830	+	0.962725i
$560$	−2.63848e11	−	9.60327e10i	−0.113372	−	0.0412642i
$561$		0			0
$562$	−3.50993e12	−	2.94518e12i	−1.48417	−	1.24537i
$563$	−3.50589e11	+	1.27604e11i	−0.147065	+	0.0535274i	−0.414504	−	0.910047i	$-0.636045\pi$
$563$	−3.50589e11	+	1.27604e11i	−0.147065	+	0.0535274i	0.267439	+	0.963575i	$0.413823\pi$
$564$		0			0
$565$	−1.83035e10	−	1.03804e11i	−0.00755642	−	0.0428546i
$566$	3.17988e12			1.30238
$567$		0			0
$568$	−2.04413e11			−0.0824026
$569$	5.56861e11	+	3.15812e12i	0.222711	+	1.26306i	0.867013	+	0.498285i	$0.166037\pi$
$569$	5.56861e11	+	3.15812e12i	0.222711	+	1.26306i	−0.644302	+	0.764771i	$0.722852\pi$
$570$		0			0
$571$	−2.33936e12	+	8.51457e11i	−0.920947	+	0.335197i	−0.758615	−	0.651539i	$-0.774124\pi$
$571$	−2.33936e12	+	8.51457e11i	−0.920947	+	0.335197i	−0.162332	+	0.986736i	$0.551901\pi$
$572$	8.17725e11	+	6.86153e11i	0.319393	+	0.268002i
$573$		0			0
$574$	−1.61535e12	−	5.87938e11i	−0.621101	−	0.226062i
$575$	−1.54810e12	−	2.68138e12i	−0.590599	−	1.02295i
$576$		0			0
$577$	−3.04673e11	+	5.27710e11i	−0.114431	+	0.198200i	−0.917552	−	0.397616i	$-0.869838\pi$
$577$	−3.04673e11	+	5.27710e11i	−0.114431	+	0.198200i	0.803121	+	0.595816i	$0.203171\pi$
$578$	−3.87707e11	+	3.25325e11i	−0.144487	+	0.121239i
$579$		0			0
$580$	1.97811e10	−	1.12184e11i	0.00725813	−	0.0411629i
$581$	−4.48294e11	+	2.54240e12i	−0.163219	+	0.925659i
$582$		0			0
$583$	−8.93266e11	+	7.49539e11i	−0.320238	+	0.268711i
$584$	3.27164e11	−	5.66665e11i	0.116388	−	0.201590i
$585$		0			0
$586$	6.65423e11	+	1.15255e12i	0.233109	+	0.403756i
$587$	3.13886e12	+	1.14245e12i	1.09119	+	0.397161i	0.824062	−	0.566500i	$-0.191703\pi$
$587$	3.13886e12	+	1.14245e12i	1.09119	+	0.397161i	0.267129	+	0.963661i	$0.413925\pi$
$588$		0			0
$589$	−8.62200e11	−	7.23472e11i	−0.295182	−	0.247687i
$590$	−1.98162e10	+	7.21252e9i	−0.00673266	+	0.00245049i
$591$		0			0
$592$	7.09423e11	+	4.02334e12i	0.237387	+	1.34629i
$593$	−9.26282e11			−0.307608			−0.153804	−	0.988101i	$-0.549152\pi$
$593$	−9.26282e11			−0.307608			−0.153804	+	0.988101i	$0.549152\pi$
$594$		0			0
$595$	2.79689e11			0.0914847
$596$	7.10359e10	+	4.02865e11i	0.0230606	+	0.130783i
$597$		0			0
$598$	6.76495e12	−	2.46224e12i	2.16326	−	0.787363i
$599$	2.59758e12	+	2.17963e12i	0.824420	+	0.691771i	0.954003	−	0.299798i	$-0.0969193\pi$
$599$	2.59758e12	+	2.17963e12i	0.824420	+	0.691771i	−0.129583	+	0.991569i	$0.541364\pi$
$600$		0			0
$601$	−5.41711e12	−	1.97167e12i	−1.69368	−	0.616451i	−0.698603	−	0.715510i	$-0.746194\pi$
$601$	−5.41711e12	−	1.97167e12i	−1.69368	−	0.616451i	−0.995082	+	0.0990591i	$0.968417\pi$
$602$	−1.51744e12	−	2.62828e12i	−0.470898	−	0.815619i
$603$		0			0
$604$	−3.03427e10	+	5.25550e10i	−0.00927657	+	0.0160675i
$605$	−5.36264e10	+	4.49979e10i	−0.0162735	+	0.0136551i
$606$		0			0
$607$	−7.66200e11	+	4.34533e12i	−0.229083	+	1.29919i	0.625641	+	0.780111i	$0.284838\pi$
$607$	−7.66200e11	+	4.34533e12i	−0.229083	+	1.29919i	−0.854724	+	0.519083i	$0.826274\pi$
$608$	−3.66210e11	+	2.07688e12i	−0.108683	+	0.616375i
$609$		0			0
$610$	−9.71551e10	+	8.15228e10i	−0.0284107	+	0.0238394i
$611$	7.85950e11	−	1.36131e12i	0.228144	−	0.395158i
$612$		0			0
$613$	−8.72696e11	−	1.51155e12i	−0.249627	−	0.432366i	0.713796	−	0.700354i	$-0.246975\pi$
$613$	−8.72696e11	−	1.51155e12i	−0.249627	−	0.432366i	−0.963422	+	0.267988i	$0.913641\pi$
$614$	3.89426e12	+	1.41740e12i	1.10578	+	0.402470i
$615$		0			0
$616$	2.41653e12	+	2.02771e12i	0.676207	+	0.567405i
$617$	−4.60148e12	+	1.67480e12i	−1.27824	+	0.465243i	−0.889851	−	0.456251i	$-0.849192\pi$
$617$	−4.60148e12	+	1.67480e12i	−1.27824	+	0.465243i	−0.388393	+	0.921494i	$0.626970\pi$
$618$		0			0
$619$	−2.29876e11	−	1.30369e12i	−0.0629340	−	0.356916i	−0.999970	−	0.00768481i	$-0.997554\pi$
$619$	−2.29876e11	−	1.30369e12i	−0.0629340	−	0.356916i	0.937037	−	0.349231i	$-0.113557\pi$
$620$	−2.82348e10			−0.00767400
$621$		0			0
$622$	5.51140e11			0.147640
$623$	−6.83446e11	−	3.87601e12i	−0.181764	−	1.03083i
$624$		0			0
$625$	−3.51849e12	+	1.28063e12i	−0.922352	+	0.335709i
$626$	−5.91932e12	−	4.96690e12i	−1.54059	−	1.29271i
$627$		0			0
$628$	−9.38621e11	−	3.41630e11i	−0.240809	−	0.0876471i
$629$	−2.03476e12	−	3.52430e12i	−0.518304	−	0.897729i
$630$		0			0
$631$	5.92182e10	−	1.02569e11i	0.0148704	−	0.0257563i	−0.858494	−	0.512823i	$-0.828600\pi$
$631$	5.92182e10	−	1.02569e11i	0.0148704	−	0.0257563i	0.873365	+	0.487067i	$0.161933\pi$
$632$	−4.10017e12	+	3.44045e12i	−1.02229	+	0.857805i
$633$		0			0
$634$	−4.26683e11	+	2.41984e12i	−0.104883	+	0.594818i
$635$	8.13830e10	−	4.61546e11i	0.0198633	−	0.112650i
$636$		0			0
$637$	3.41899e12	−	2.86887e12i	0.822754	−	0.690373i
$638$	−3.77497e12	+	6.53843e12i	−0.902028	+	1.56236i
$639$		0			0
$640$	−2.01036e11	−	3.48204e11i	−0.0473657	−	0.0820397i
$641$	−5.47166e12	−	1.99152e12i	−1.28014	−	0.465933i	−0.389662	−	0.920958i	$-0.627408\pi$
$641$	−5.47166e12	−	1.99152e12i	−1.28014	−	0.465933i	−0.890479	+	0.455025i	$0.849630\pi$
$642$		0			0
$643$	−1.95249e12	−	1.63833e12i	−0.450442	−	0.377965i	0.389158	−	0.921171i	$-0.372766\pi$
$643$	−1.95249e12	−	1.63833e12i	−0.450442	−	0.377965i	−0.839600	+	0.543206i	$0.817210\pi$
$644$	−1.77812e12	+	6.47184e11i	−0.407358	+	0.148266i
$645$		0			0
$646$	−8.96579e11	−	5.08475e12i	−0.202555	−	1.14874i
$647$	4.00707e12			0.898995			0.449497	−	0.893282i	$-0.351603\pi$
$647$	4.00707e12			0.898995			0.449497	+	0.893282i	$0.351603\pi$
$648$		0			0
$649$	3.10656e11			0.0687351
$650$	−1.52129e12	−	8.62764e12i	−0.334272	−	1.89575i
$651$		0			0
$652$	−1.44116e12	+	5.24538e11i	−0.312318	+	0.113674i
$653$	1.65621e11	+	1.38973e11i	0.0356457	+	0.0299103i	0.660436	−	0.750882i	$-0.270371\pi$
$653$	1.65621e11	+	1.38973e11i	0.0356457	+	0.0299103i	−0.624791	+	0.780792i	$0.714816\pi$
$654$		0			0
$655$	−5.35661e11	−	1.94965e11i	−0.113712	−	0.0413876i
$656$	−1.30427e12	−	2.25906e12i	−0.274980	−	0.476279i
$657$		0			0
$658$	−9.29418e11	+	1.60980e12i	−0.193283	+	0.334777i
$659$	2.27434e10	−	1.90839e10i	0.00469754	−	0.00394170i	−0.640436	−	0.768012i	$-0.721246\pi$
$659$	2.27434e10	−	1.90839e10i	0.00469754	−	0.00394170i	0.645133	+	0.764070i	$0.276802\pi$
$660$		0			0
$661$	1.41760e12	−	8.03962e12i	0.288833	−	1.63806i	−0.402428	−	0.915451i	$-0.631834\pi$
$661$	1.41760e12	−	8.03962e12i	0.288833	−	1.63806i	0.691262	−	0.722604i	$-0.257055\pi$
$662$	−6.91076e11	+	3.91929e12i	−0.139851	+	0.793133i
$663$		0			0
$664$	−2.28871e12	+	1.92045e12i	−0.456913	+	0.383396i
$665$	2.84650e11	−	4.93029e11i	0.0564436	−	0.0977631i
$666$		0			0
$667$	5.65875e12	+	9.80124e12i	1.10702	+	1.91741i
$668$	−2.09149e12	−	7.61241e11i	−0.406408	−	0.147920i
$669$		0			0
$670$	−4.71289e11	−	3.95458e11i	−0.0903546	−	0.0758165i
$671$	1.75567e12	−	6.39011e11i	0.334342	−	0.121691i
$672$		0			0
$673$	−1.65813e12	−	9.40374e12i	−0.311567	−	1.76699i	−0.590855	−	0.806778i	$-0.701209\pi$
$673$	−1.65813e12	−	9.40374e12i	−0.311567	−	1.76699i	0.279288	−	0.960207i	$-0.409902\pi$
$674$	1.06330e13			1.98466
$675$		0			0
$676$	2.97593e12			0.548104
$677$	−6.00860e11	−	3.40765e12i	−0.109932	−	0.623456i	−0.989135	−	0.147009i	$-0.953035\pi$
$677$	−6.00860e11	−	3.40765e12i	−0.109932	−	0.623456i	0.879203	−	0.476447i	$-0.158076\pi$
$678$		0			0
$679$	7.47117e12	−	2.71928e12i	1.34888	−	0.490954i
$680$	2.47955e11	+	2.08059e11i	0.0444716	+	0.0373161i
$681$		0			0
$682$	1.75846e12	+	6.40028e11i	0.311246	+	0.113284i
$683$	−2.39728e12	−	4.15221e12i	−0.421527	−	0.730106i	0.574562	−	0.818461i	$-0.305172\pi$
$683$	−2.39728e12	−	4.15221e12i	−0.421527	−	0.730106i	−0.996089	+	0.0883547i	$0.971839\pi$
$684$		0			0
$685$	−2.31954e11	+	4.01757e11i	−0.0402527	+	0.0697197i
$686$	2.38715e12	−	2.00306e12i	0.411549	−	0.345330i
$687$		0			0
$688$	7.99702e11	−	4.53534e12i	0.136076	−	0.771723i
$689$	−8.58850e11	+	4.87078e12i	−0.145188	+	0.823402i
$690$		0			0
$691$	5.59946e12	−	4.69850e12i	0.934318	−	0.783986i	−0.0422697	−	0.999106i	$-0.513459\pi$
$691$	5.59946e12	−	4.69850e12i	0.934318	−	0.783986i	0.976588	+	0.215121i	$0.0690144\pi$
$692$	−7.69875e11	+	1.33346e12i	−0.127627	+	0.221057i
$693$		0			0
$694$	−2.08316e12	−	3.60814e12i	−0.340883	−	0.590427i
$695$	−2.30882e11	−	8.40343e10i	−0.0375370	−	0.0136623i
$696$		0			0
$697$	1.99048e12	+	1.67021e12i	0.319456	+	0.268056i
$698$	−3.32867e12	+	1.21154e12i	−0.530789	+	0.193191i
$699$		0			0
$700$	3.99861e11	+	2.26772e12i	0.0629459	+	0.356984i
$701$	−7.93236e12			−1.24071			−0.620356	−	0.784320i	$-0.713012\pi$
$701$	−7.93236e12			−1.24071			−0.620356	+	0.784320i	$0.713012\pi$
$702$		0			0
$703$	−8.28341e12			−1.27912
$704$	5.54999e11	+	3.14756e12i	0.0851560	+	0.482944i
$705$		0			0
$706$	1.10503e11	−	4.02199e10i	0.0167399	−	0.00609283i
$707$	9.26635e12	+	7.77539e12i	1.39483	+	1.17040i
$708$		0			0
$709$	1.99947e12	+	7.27748e11i	0.297172	+	0.108162i	0.486303	−	0.873790i	$-0.338345\pi$
$709$	1.99947e12	+	7.27748e11i	0.297172	+	0.108162i	−0.189132	+	0.981952i	$0.560567\pi$
$710$	−3.06672e10	−	5.31172e10i	−0.00452910	−	0.00784464i
$711$		0			0
$712$	2.27744e12	−	3.94465e12i	0.332114	−	0.575239i
$713$	2.14886e12	−	1.80311e12i	0.311391	−	0.261288i
$714$		0			0
$715$	1.38992e11	−	7.88262e11i	0.0198890	−	0.112796i
$716$	1.27656e11	−	7.23971e11i	0.0181523	−	0.102947i
$717$		0			0
$718$	−1.13876e13	+	9.55535e12i	−1.59909	+	1.34180i
$719$	−4.05230e12	+	7.01879e12i	−0.565486	+	0.979450i	0.431519	+	0.902104i	$0.357978\pi$
$719$	−4.05230e12	+	7.01879e12i	−0.565486	+	0.979450i	−0.997004	+	0.0773458i	$0.975355\pi$
$720$		0			0
$721$	−5.90651e12	−	1.02304e13i	−0.813996	−	1.40988i
$722$	−2.09561e12	−	7.62739e11i	−0.287007	−	0.104462i
$723$		0			0
$724$	−1.48397e12	−	1.24520e12i	−0.200725	−	0.168428i
$725$	1.29419e13	−	4.71047e12i	1.73971	−	0.633203i
$726$		0			0
$727$	−1.43195e12	−	8.12097e12i	−0.190117	−	1.07821i	−0.919202	−	0.393786i	$-0.871165\pi$
$727$	−1.43195e12	−	8.12097e12i	−0.190117	−	1.07821i	0.729085	−	0.684423i	$-0.239946\pi$
$728$	1.33801e13			1.76550
$729$		0			0
$730$	1.96332e11			0.0255882
$731$	7.96591e11	+	4.51769e12i	0.103183	+	0.585179i
$732$		0			0
$733$	6.65271e12	−	2.42139e12i	0.851198	−	0.309811i	0.120669	−	0.992693i	$-0.461496\pi$
$733$	6.65271e12	−	2.42139e12i	0.851198	−	0.309811i	0.730529	+	0.682882i	$0.239274\pi$
$734$	−8.56141e12	−	7.18388e12i	−1.08871	−	0.913538i
$735$		0			0
$736$	−4.93908e12	−	1.79768e12i	−0.620434	−	0.225820i
$737$	4.53156e12	+	7.84889e12i	0.565775	+	0.979951i
$738$		0			0
$739$	−3.08807e12	+	5.34870e12i	−0.380879	+	0.659702i	−0.991188	−	0.132461i	$-0.957712\pi$
$739$	−3.08807e12	+	5.34870e12i	−0.380879	+	0.659702i	0.610309	+	0.792164i	$0.291045\pi$
$740$	−1.59182e11	+	1.33570e11i	−0.0195142	+	0.0163744i
$741$		0			0
$742$	1.01562e12	−	5.75989e12i	0.123003	−	0.697584i
$743$	1.71216e12	−	9.71014e12i	0.206108	−	1.16890i	−0.689579	−	0.724210i	$-0.742204\pi$
$743$	1.71216e12	−	9.71014e12i	0.206108	−	1.16890i	0.895687	−	0.444685i	$-0.146684\pi$
$744$		0			0
$745$	2.34978e11	−	1.97170e11i	0.0279463	−	0.0234497i
$746$	5.83906e12	−	1.01135e13i	0.690269	−	1.19558i
$747$		0			0
$748$	9.54034e11	+	1.65243e12i	0.111431	+	0.193004i
$749$	−1.38224e13	−	5.03095e12i	−1.60478	−	0.584092i
$750$		0			0
$751$	−4.50268e12	−	3.77820e12i	−0.516526	−	0.433416i	0.346893	−	0.937905i	$-0.387237\pi$
$751$	−4.50268e12	−	3.77820e12i	−0.516526	−	0.433416i	−0.863419	+	0.504488i	$0.831681\pi$
$752$	−2.65060e12	+	9.64740e11i	−0.302248	+	0.110009i
$753$		0			0
$754$	5.56075e12	+	3.15366e13i	0.626559	+	3.55340i
$755$	4.55040e10			0.00509669
$756$		0			0
$757$	6.21771e12			0.688175			0.344088	−	0.938938i	$-0.388188\pi$
$757$	6.21771e12			0.688175			0.344088	+	0.938938i	$0.388188\pi$
$758$	2.16347e12	+	1.22697e13i	0.238035	+	1.34996i
$759$		0			0
$760$	6.19115e11	−	2.25340e11i	0.0673148	−	0.0245006i
$761$	−1.07483e13	−	9.01886e12i	−1.16173	−	0.974811i	−0.161807	−	0.986822i	$-0.551732\pi$
$761$	−1.07483e13	−	9.01886e12i	−1.16173	−	0.974811i	−0.999928	+	0.0120113i	$0.996177\pi$
$762$		0			0
$763$	8.65162e12	+	3.14893e12i	0.924138	+	0.336359i
$764$	2.11215e12	+	3.65835e12i	0.224287	+	0.388477i
$765$		0			0
$766$	−5.81941e12	+	1.00795e13i	−0.610730	+	1.05782i
$767$	1.00938e12	−	8.46969e11i	0.105311	−	0.0883666i
$768$		0			0
$769$	−1.49740e12	+	8.49215e12i	−0.154407	+	0.875687i	0.804918	+	0.593386i	$0.202209\pi$
$769$	−1.49740e12	+	8.49215e12i	−0.154407	+	0.875687i	−0.959326	+	0.282302i	$0.908902\pi$
$770$	−1.64363e11	+	9.32151e11i	−0.0168499	+	0.0955605i
$771$		0			0
$772$	2.19730e12	−	1.84376e12i	0.222645	−	0.186821i
$773$	−7.40789e12	+	1.28308e13i	−0.746254	+	1.29255i	0.203353	+	0.979106i	$0.434816\pi$
$773$	−7.40789e12	+	1.28308e13i	−0.746254	+	1.29255i	−0.949607	+	0.313444i	$0.898517\pi$
$774$		0			0
$775$	−1.70682e12	−	2.95629e12i	−0.169953	−	0.294367i
$776$	8.64635e12	+	3.14701e12i	0.855963	+	0.311545i
$777$		0			0
$778$	1.46536e13	+	1.22958e13i	1.43396	+	1.20323i
$779$	4.97001e12	−	1.80894e12i	0.483547	−	0.175997i
$780$		0			0
$781$	1.56899e11	+	8.89818e11i	0.0150900	+	0.0855798i
$782$	1.28682e13			1.23052
$783$		0			0
$784$	−8.00897e12			−0.757102
$785$	1.30059e11	+	7.37602e11i	0.0122244	+	0.0693280i
$786$		0			0
$787$	−1.74504e13	+	6.35144e12i	−1.62151	+	0.590182i	−0.983669	−	0.179985i	$-0.942395\pi$
$787$	−1.74504e13	+	6.35144e12i	−1.62151	+	0.590182i	−0.637842	+	0.770167i	$0.720173\pi$
$788$	4.97506e11	+	4.17457e11i	0.0459653	+	0.0385694i
$789$		0			0
$790$	−1.50914e12	−	5.49282e11i	−0.137850	−	0.0501734i
$791$	−3.89417e12	−	6.74489e12i	−0.353688	−	0.612606i
$792$		0			0
$793$	3.96229e12	−	6.86289e12i	0.355809	−	0.616280i
$794$	−9.83450e12	+	8.25213e12i	−0.878133	+	0.736841i
$795$		0			0
$796$	6.90350e11	−	3.91517e12i	0.0609482	−	0.345654i
$797$	−2.09532e11	+	1.18832e12i	−0.0183945	+	0.104320i	−0.992623	−	0.121244i	$-0.961312\pi$
$797$	−2.09532e11	+	1.18832e12i	−0.0183945	+	0.104320i	0.974228	+	0.225565i	$0.0724227\pi$
$798$		0			0
$799$	2.15238e12	−	1.80606e12i	0.186835	−	0.156773i
$800$	−3.19810e12	+	5.53927e12i	−0.276050	+	0.478132i
$801$		0			0
$802$	−2.44653e12	−	4.23752e12i	−0.208817	−	0.361682i
$803$	−2.71783e12	−	9.89210e11i	−0.230676	−	0.0839592i
$804$		0			0
$805$	1.08692e12	+	9.12031e11i	0.0912252	+	0.0765470i
$806$	7.45853e12	−	2.71468e12i	0.622509	−	0.226575i
$807$		0			0
$808$	2.43091e12	+	1.37864e13i	0.200640	+	1.13789i
$809$	−1.87071e13			−1.53546			−0.767728	−	0.640776i	$-0.778613\pi$
$809$	−1.87071e13			−1.53546			−0.767728	+	0.640776i	$0.778613\pi$
$810$		0			0
$811$	−9.61711e12			−0.780640			−0.390320	−	0.920679i	$-0.627636\pi$
$811$	−9.61711e12			−0.780640			−0.390320	+	0.920679i	$0.627636\pi$
$812$	−1.46161e12	−	8.28920e12i	−0.117986	−	0.669130i
$813$		0			0
$814$	1.29416e13	−	4.71036e12i	1.03319	−	0.376049i
$815$	8.80938e11	+	7.39195e11i	0.0699417	+	0.0586881i
$816$		0			0
$817$	8.77441e12	+	3.19363e12i	0.688999	+	0.250775i
$818$	3.43106e12	+	5.94276e12i	0.267940	+	0.464086i
$819$		0			0
$820$	6.63395e10	−	1.14903e11i	0.00512401	−	0.00887505i
$821$	−9.35657e12	+	7.85109e12i	−0.718741	+	0.603095i	−0.927037	−	0.374971i	$-0.877653\pi$
$821$	−9.35657e12	+	7.85109e12i	−0.718741	+	0.603095i	0.208296	+	0.978066i	$0.433208\pi$
$822$		0			0
$823$	3.95125e11	−	2.24087e12i	0.0300217	−	0.170262i	−0.966110	−	0.258129i	$-0.916894\pi$
$823$	3.95125e11	−	2.24087e12i	0.0300217	−	0.170262i	0.996132	+	0.0878674i	$0.0280052\pi$
$824$	2.37397e12	−	1.34635e13i	0.179392	−	1.01738i
$825$		0			0
$826$	−1.19363e12	+	1.00157e12i	−0.0892194	+	0.0748640i
$827$	−1.37363e12	+	2.37919e12i	−0.102116	+	0.176870i	−0.912556	−	0.408951i	$-0.865895\pi$
$827$	−1.37363e12	+	2.37919e12i	−0.102116	+	0.176870i	0.810440	+	0.585821i	$0.199228\pi$
$828$		0			0
$829$	3.33612e12	+	5.77834e12i	0.245328	+	0.424920i	0.962224	−	0.272260i	$-0.0877711\pi$
$829$	3.33612e12	+	5.77834e12i	0.245328	+	0.424920i	−0.716896	+	0.697180i	$0.754438\pi$
$830$	−8.42400e11	−	3.06609e11i	−0.0616122	−	0.0224250i
$831$		0			0
$832$	1.03848e13	+	8.71384e12i	0.751348	+	0.630456i
$833$	7.49669e12	−	2.72857e12i	0.539470	−	0.196351i
$834$		0			0
$835$	2.89805e11	+	1.64357e12i	0.0206309	+	0.117003i
$836$	3.88383e12			0.275000
$837$		0			0
$838$	−2.21785e12			−0.155358
$839$	8.27842e11	+	4.69492e12i	0.0576791	+	0.327114i	0.999971	−	0.00767939i	$-0.00244445\pi$
$839$	8.27842e11	+	4.69492e12i	0.0576791	+	0.327114i	−0.942291	+	0.334794i	$0.891333\pi$
$840$		0			0
$841$	−3.36742e13	+	1.22564e13i	−2.32122	+	0.844854i
$842$	1.65889e13	+	1.39197e13i	1.13740	+	0.954390i
$843$		0			0
$844$	1.28714e11	+	4.68480e10i	0.00873140	+	0.00317797i
$845$	−1.11573e12	−	1.93250e12i	−0.0752842	−	0.130396i
$846$		0			0
$847$	−2.58628e12	+	4.47957e12i	−0.172663	+	0.299062i
$848$	6.79883e12	−	5.70490e12i	0.451495	−	0.378849i
$849$		0			0
$850$	2.71926e12	−	1.54217e13i	0.178676	−	1.01332i
$851$	3.58493e12	−	2.03311e13i	0.234313	−	1.32886i
$852$		0			0
$853$	−7.06963e12	+	5.93212e12i	−0.457221	+	0.383654i	−0.842107	−	0.539310i	$-0.818685\pi$
$853$	−7.06963e12	+	5.93212e12i	−0.457221	+	0.383654i	0.384886	+	0.922964i	$0.374241\pi$
$854$	−4.68557e12	+	8.11564e12i	−0.301441	+	0.522111i
$855$		0			0
$856$	−8.51162e12	−	1.47426e13i	−0.541851	−	0.938514i
$857$	1.26198e13	+	4.59322e12i	0.799167	+	0.290873i	0.709141	−	0.705067i	$-0.249083\pi$
$857$	1.26198e13	+	4.59322e12i	0.799167	+	0.290873i	0.0900256	+	0.995939i	$0.471305\pi$
$858$		0			0
$859$	2.32944e12	+	1.95463e12i	0.145976	+	0.122488i	0.712851	−	0.701315i	$-0.247403\pi$
$859$	2.32944e12	+	1.95463e12i	0.145976	+	0.122488i	−0.566875	+	0.823804i	$0.691848\pi$
$860$	2.20115e11	−	8.01151e10i	0.0137216	−	0.00499426i
$861$		0			0
$862$	1.37349e12	+	7.78947e12i	0.0847313	+	0.480535i
$863$	1.01909e13			0.625411			0.312706	−	0.949850i	$-0.398765\pi$
$863$	1.01909e13			0.625411			0.312706	+	0.949850i	$0.398765\pi$
$864$		0			0
$865$	1.15456e12			0.0701203
$866$	1.21306e12	+	6.87963e12i	0.0732915	+	0.415657i
$867$		0			0
$868$	−1.96043e12	+	7.13537e11i	−0.117223	+	0.0426656i
$869$	1.81235e13	+	1.52074e13i	1.07809	+	0.904622i
$870$		0			0
$871$	3.61230e13	+	1.31477e13i	2.12668	+	0.774048i
$872$	5.32753e12	+	9.22754e12i	0.312034	+	0.540458i
$873$		0			0
$874$	1.30965e13	−	2.26838e13i	0.759197	−	1.31497i
$875$	2.65358e12	−	2.22662e12i	0.153037	−	0.128413i
$876$		0			0
$877$	4.27796e12	−	2.42615e13i	0.244196	−	1.38490i	−0.578156	−	0.815926i	$-0.696228\pi$
$877$	4.27796e12	−	2.42615e13i	0.244196	−	1.38490i	0.822352	−	0.568979i	$-0.192661\pi$
$878$	3.90898e12	−	2.21689e13i	0.221992	−	1.25898i
$879$		0			0
$880$	−1.10029e12	+	9.23251e11i	−0.0618493	+	0.0518977i
$881$	5.70136e12	−	9.87504e12i	0.318850	−	0.552265i	−0.661398	−	0.750035i	$-0.730037\pi$
$881$	5.70136e12	−	9.87504e12i	0.318850	−	0.552265i	0.980248	+	0.197770i	$0.0633700\pi$
$882$		0			0
$883$	−2.15512e12	−	3.73277e12i	−0.119302	−	0.206637i	0.800189	−	0.599748i	$-0.204732\pi$
$883$	−2.15512e12	−	3.73277e12i	−0.119302	−	0.206637i	−0.919491	+	0.393110i	$0.871399\pi$
$884$	7.60501e12	+	2.76800e12i	0.418856	+	0.152451i
$885$		0			0
$886$	−1.05653e13	−	8.86535e12i	−0.576011	−	0.483330i
$887$	−1.26345e13	+	4.59860e12i	−0.685335	+	0.249442i	−0.661137	−	0.750266i	$-0.729926\pi$
$887$	−1.26345e13	+	4.59860e12i	−0.685335	+	0.249442i	−0.0241987	+	0.999707i	$0.507703\pi$
$888$		0			0
$889$	−6.01332e12	−	3.41032e13i	−0.322891	−	1.83121i
$890$	1.36670e12			0.0730161
$891$		0			0
$892$	1.04593e11			0.00553174
$893$	−9.93123e11	−	5.63228e12i	−0.0522602	−	0.296382i
$894$		0			0
$895$	−5.17990e11	+	1.88533e11i	−0.0269847	+	0.00982163i
$896$	−2.27582e13	−	1.90964e13i	−1.17965	−	0.989841i
$897$		0			0
$898$	−1.76222e13	−	6.41396e12i	−0.904309	−	0.329142i
$899$	6.23892e12	+	1.08061e13i	0.318559	+	0.551761i
$900$		0			0
$901$	−4.42036e12	+	7.65629e12i	−0.223458	+	0.387041i
$902$	−6.73626e12	+	5.65240e12i	−0.338836	+	0.284317i
$903$		0			0
$904$	1.56516e12	−	8.87646e12i	0.0779472	−	0.442061i
$905$	−2.52236e11	+	1.43050e12i	−0.0124994	+	0.0708875i
$906$		0			0
$907$	−5.73636e11	+	4.81338e11i	−0.0281451	+	0.0236166i	−0.656752	−	0.754107i	$-0.728070\pi$
$907$	−5.73636e11	+	4.81338e11i	−0.0281451	+	0.0236166i	0.628607	+	0.777723i	$0.283626\pi$
$908$	1.02358e12	−	1.77290e12i	0.0499731	−	0.0865559i
$909$		0			0
$910$	2.00736e12	+	3.47685e12i	0.0970373	+	0.168074i
$911$	−1.65663e12	−	6.02965e11i	−0.0796881	−	0.0290041i	0.301869	−	0.953350i	$-0.402390\pi$
$911$	−1.65663e12	−	6.02965e11i	−0.0796881	−	0.0290041i	−0.381557	+	0.924345i	$0.624612\pi$
$912$		0			0
$913$	1.01165e13	+	8.48877e12i	0.481851	+	0.404321i
$914$	−1.42106e13	+	5.17223e12i	−0.673526	+	0.245143i
$915$		0			0
$916$	8.51746e11	+	4.83049e12i	0.0399742	+	0.226705i
$917$	−4.21197e13			−1.96708
$918$		0			0
$919$	1.56722e12			0.0724786			0.0362393	−	0.999343i	$-0.488462\pi$
$919$	1.56722e12			0.0724786			0.0362393	+	0.999343i	$0.488462\pi$
$920$	2.85139e11	+	1.61710e12i	0.0131223	+	0.0744205i
$921$		0			0
$922$	1.58256e13	−	5.76006e12i	0.721228	−	0.262505i
$923$	2.93578e12	+	2.46341e12i	0.133142	+	0.111720i
$924$		0			0
$925$	−2.36079e13	−	8.59258e12i	−1.06028	−	0.385910i
$926$	4.74424e12	+	8.21727e12i	0.212040	+	0.367264i
$927$		0			0
$928$	1.16900e13	−	2.02477e13i	0.517427	−	0.896209i
$929$	−7.09152e12	+	5.95049e12i	−0.312369	+	0.262109i	−0.785471	−	0.618899i	$-0.787579\pi$
$929$	−7.09152e12	+	5.95049e12i	−0.312369	+	0.262109i	0.473101	+	0.881008i	$0.343135\pi$
$930$		0			0
$931$	2.81982e12	−	1.59920e13i	0.123012	−	0.697636i
$932$	7.90863e11	−	4.48520e12i	0.0343344	−	0.194720i
$933$		0			0
$934$	1.88189e13	−	1.57910e13i	0.809160	−	0.678966i
$935$	7.15368e11	−	1.23905e12i	0.0306110	−	0.0530198i
$936$		0			0
$937$	−9.20172e11	−	1.59378e12i	−0.0389979	−	0.0675463i	0.845868	−	0.533393i	$-0.179083\pi$
$937$	−9.20172e11	−	1.59378e12i	−0.0389979	−	0.0675463i	−0.884866	+	0.465847i	$0.845750\pi$
$938$	−4.27169e13	−	1.55477e13i	−1.80172	−	0.655771i
$939$		0			0
$940$	−1.09905e11	−	9.22212e10i	−0.00459136	−	0.00385261i
$941$	2.42935e12	−	8.84212e11i	0.101004	−	0.0367623i	−0.291024	−	0.956716i	$-0.593996\pi$
$941$	2.42935e12	−	8.84212e11i	0.101004	−	0.0367623i	0.392028	+	0.919953i	$0.371774\pi$
$942$		0			0
$943$	2.28898e12	+	1.29815e13i	0.0942627	+	0.534590i
$944$	−2.36447e12			−0.0969079
$945$		0			0
$946$	−1.55248e13			−0.630254
$947$	−3.03655e12	−	1.72212e13i	−0.122689	−	0.695805i	−0.982654	−	0.185451i	$-0.940625\pi$
$947$	−3.03655e12	−	1.72212e13i	−0.122689	−	0.695805i	0.859964	−	0.510354i	$-0.170486\pi$
$948$		0			0
$949$	−1.15277e13	+	4.19574e12i	−0.461365	+	0.167923i
$950$	−2.44175e13	−	2.04887e13i	−0.972626	−	0.816130i
$951$		0			0
$952$	2.24742e13	+	8.17996e12i	0.886786	+	0.322764i
$953$	−1.39218e13	−	2.41133e13i	−0.546737	−	0.946977i	−0.998495	−	0.0548362i	$-0.982536\pi$
$953$	−1.39218e13	−	2.41133e13i	−0.546737	−	0.946977i	0.451758	−	0.892140i	$-0.350797\pi$
$954$		0			0
$955$	1.58376e12	−	2.74316e12i	0.0616134	−	0.106718i
$956$	9.36093e12	−	7.85475e12i	0.362459	−	0.304139i
$957$		0			0
$958$	−7.00294e11	+	3.97157e12i	−0.0268618	+	0.152341i
$959$	−5.95228e12	+	3.37570e13i	−0.227248	+	1.28879i
$960$		0			0
$961$	−1.78847e13	+	1.50071e13i	−0.676437	+	0.567598i
$962$	2.92074e13	−	5.05887e13i	1.09952	−	1.90443i
$963$		0			0
$964$	−1.09248e12	−	1.89224e12i	−0.0407444	−	0.0705714i
$965$	−2.02110e12	−	7.35621e11i	−0.0750266	−	0.0273074i
$966$		0			0
$967$	4.08649e13	+	3.42897e13i	1.50291	+	1.26109i	0.876315	+	0.481738i	$0.159994\pi$
$967$	4.08649e13	+	3.42897e13i	1.50291	+	1.26109i	0.626590	+	0.779349i	$0.284450\pi$
$968$	−5.62517e12	+	2.04739e12i	−0.205919	+	0.0749484i
$969$		0			0
$970$	4.79417e11	+	2.71891e12i	0.0173876	+	0.0986102i
$971$	1.17481e13			0.424112			0.212056	−	0.977257i	$-0.431984\pi$
$971$	1.17481e13			0.424112			0.212056	+	0.977257i	$0.431984\pi$
$972$		0			0
$973$	−1.81545e13			−0.649348
$974$	4.43274e12	+	2.51393e13i	0.157818	+	0.895030i
$975$		0			0
$976$	−1.33627e13	+	4.86364e12i	−0.471380	+	0.171568i
$977$	−1.06736e12	−	8.95623e11i	−0.0374788	−	0.0314485i	0.623856	−	0.781539i	$-0.285565\pi$
$977$	−1.06736e12	−	8.95623e11i	−0.0374788	−	0.0314485i	−0.661335	+	0.750091i	$0.730010\pi$
$978$		0			0
$979$	−1.89193e13	−	6.88605e12i	−0.658237	−	0.239579i
$980$	−2.03681e11	−	3.52787e11i	−0.00705398	−	0.0122178i
$981$		0			0
$982$	−1.62308e13	+	2.81125e13i	−0.556978	+	0.964714i
$983$	1.17540e13	−	9.86282e12i	0.401510	−	0.336907i	−0.419567	−	0.907724i	$-0.637818\pi$
$983$	1.17540e13	−	9.86282e12i	0.401510	−	0.336907i	0.821077	+	0.570817i	$0.193374\pi$
$984$		0			0
$985$	8.45630e10	−	4.79580e11i	0.00286231	−	0.0162330i
$986$	−9.93971e12	+	5.63709e13i	−0.334910	+	1.89937i
$987$		0			0
$988$	1.26193e13	−	1.05888e13i	0.421336	−	0.353543i
$989$	−1.16360e13	+	2.01541e13i	−0.386740	+	0.669854i
$990$		0			0
$991$	2.02579e13	+	3.50877e13i	0.667211	+	1.15564i	0.978681	+	0.205387i	$0.0658453\pi$
$991$	2.02579e13	+	3.50877e13i	0.667211	+	1.15564i	−0.311470	+	0.950256i	$0.600821\pi$
$992$	−5.44546e12	−	1.98199e12i	−0.178539	−	0.0649827i
$993$		0			0
$994$	−3.47168e12	−	2.91308e12i	−0.112798	−	0.0946486i
$995$	−2.80124e12	+	1.01957e12i	−0.0906039	+	0.0329771i
$996$		0			0
$997$	−7.28464e12	−	4.13133e13i	−0.233496	−	1.32422i	−0.845757	−	0.533568i	$-0.820851\pi$
$997$	−7.28464e12	−	4.13133e13i	−0.233496	−	1.32422i	0.612261	−	0.790656i	$-0.290260\pi$
$998$	−4.58107e13			−1.46177
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.19		156
3.2	odd	2		27.10.e.a.13.8	✓	156
27.2	odd	18		27.10.e.a.25.8	yes	156
27.25	even	9	inner	81.10.e.a.73.19		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.8	✓	156	3.2	odd	2
27.10.e.a.25.8	yes	156	27.2	odd	18
81.10.e.a.10.19		156	1.1	even	1	trivial
81.10.e.a.73.19		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+(4.45544 + 25.2681i) q^{2} +(-137.502 + 50.0467i) q^{4} +(84.0511 + 70.5273i) q^{5} +(7618.26 + 2772.82i) q^{7} +(4691.20 + 8125.40i) q^{8} +(-1407.60 + 2438.04i) q^{10} +(31769.4 - 26657.7i) q^{11} +(30545.4 - 173231. i) q^{13} +(-36121.1 + 204853. i) q^{14} +(-241803. + 202897. i) q^{16} +(157212. - 272299. i) q^{17} +(-320002. - 554259. i) q^{19} +(-15086.9 - 5491.17i) q^{20} +(815135. + 683979. i) q^{22} +(1.49889e6 - 545550. i) q^{23} +(-337066. - 1.91160e6i) q^{25} +4.51332e6 q^{26} -1.18630e6 q^{28} +(1.23208e6 + 6.98745e6i) q^{29} +(1.65256e6 - 601483. i) q^{31} +(-2.52424e6 - 2.11809e6i) q^{32} +(7.58092e6 + 2.75923e6i) q^{34} +(444764. + 770353. i) q^{35} +(6.47138e6 - 1.12088e7i) q^{37} +(1.25793e7 - 1.05553e7i) q^{38} +(-178761. + 1.01381e6i) q^{40} +(-1.43503e6 + 8.13844e6i) q^{41} +(-1.11765e7 + 9.37816e6i) q^{43} +(-3.03423e6 + 5.25544e6i) q^{44} +(2.04632e7 + 3.54433e7i) q^{46} +(8.39723e6 + 3.05634e6i) q^{47} +(1.94367e7 + 1.63093e7i) q^{49} +(4.68006e7 - 1.70340e7i) q^{50} +(4.46960e6 + 2.53484e7i) q^{52} -2.81172e7 q^{53} +4.55034e6 q^{55} +(1.32085e7 + 7.49093e7i) q^{56} +(-1.71070e8 + 6.22644e7i) q^{58} +(5.73824e6 + 4.81496e6i) q^{59} +(4.23338e7 + 1.54083e7i) q^{61} +(2.25612e7 + 3.90772e7i) q^{62} +(-3.85334e7 + 6.67418e7i) q^{64} +(1.47849e7 - 1.24060e7i) q^{65} +(-3.79484e7 + 2.15216e8i) q^{67} +(-7.98931e6 + 4.53096e7i) q^{68} +(-1.74837e7 + 1.46706e7i) q^{70} +(-1.08934e7 + 1.88680e7i) q^{71} +(-3.48700e7 - 6.03966e7i) q^{73} +(3.12057e8 + 1.13579e8i) q^{74} +(7.17397e7 + 6.01968e7i) q^{76} +(3.15944e8 - 1.14994e8i) q^{77} +(9.90613e7 + 5.61805e8i) q^{79} -3.46336e7 q^{80} -2.12036e8 q^{82} +(5.52959e7 + 3.13598e8i) q^{83} +(3.24183e7 - 1.17993e7i) q^{85} +(-2.86764e8 - 2.40624e8i) q^{86} +(3.65641e8 + 1.33082e8i) q^{88} +(-2.42736e8 - 4.20431e8i) q^{89} +(7.13042e8 - 1.23502e9i) q^{91} +(-1.78797e8 + 1.50029e8i) q^{92} +(-3.98145e7 + 2.25799e8i) q^{94} +(1.21939e7 - 6.91549e7i) q^{95} +(7.51254e8 - 6.30377e8i) q^{97} +(-3.25506e8 + 5.63793e8i) 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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