LMFDB - Embedded newform 81.10.e.a.19.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$41.7179027293$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			19.14
Character	$\chi$	$=$	81.19
Dual form			81.10.e.a.64.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.57613 - 1.66557i) q^{2} +(-374.048 + 313.863i) q^{4} +(-461.629 - 2618.03i) q^{5} +(5320.32 + 4464.28i) q^{7} +(-2435.60 + 4218.58i) q^{8} +(-6472.99 - 11211.5i) q^{10} +(5911.61 - 33526.4i) q^{11} +(115823. + 42156.3i) q^{13} +(31782.0 + 11567.7i) q^{14} +(39293.1 - 222842. i) q^{16} +(-54853.3 - 95008.6i) q^{17} +(-2962.69 + 5131.52i) q^{19} +(994374. + 834379. i) q^{20} +(-28788.4 - 163267. i) q^{22} +(-140728. + 118085. i) q^{23} +(-4.80563e6 + 1.74910e6i) q^{25} +600238. q^{26} -3.39123e6 q^{28} +(-5.64337e6 + 2.05402e6i) q^{29} +(6.88793e6 - 5.77966e6i) q^{31} +(-624438. - 3.54137e6i) q^{32} +(-409259. - 343409. i) q^{34} +(9.23159e6 - 1.59896e7i) q^{35} +(-2.83524e6 - 4.91077e6i) q^{37} +(-5010.70 + 28417.1i) q^{38} +(1.21687e7 + 4.42905e6i) q^{40} +(-3.13238e7 - 1.14009e7i) q^{41} +(-1.71312e6 + 9.71560e6i) q^{43} +(8.31149e6 + 1.43959e7i) q^{44} +(-447310. + 774764. i) q^{46} +(-2.21279e7 - 1.85675e7i) q^{47} +(1.36869e6 + 7.76222e6i) q^{49} +(-1.90779e7 + 1.60083e7i) q^{50} +(-5.65549e7 + 2.05843e7i) q^{52} +1.54382e7 q^{53} -9.05020e7 q^{55} +(-3.17911e7 + 1.15710e7i) q^{56} +(-2.24036e7 + 1.87989e7i) q^{58} +(1.95594e6 + 1.10927e7i) q^{59} +(-7.31062e7 - 6.13434e7i) q^{61} +(2.18936e7 - 3.79208e7i) q^{62} +(4.91718e7 + 8.51680e7i) q^{64} +(5.68989e7 - 3.22690e8i) q^{65} +(-2.31914e8 - 8.44099e7i) q^{67} +(5.03375e7 + 1.83213e7i) q^{68} +(1.56131e7 - 8.85462e7i) q^{70} +(-6.37879e7 - 1.10484e8i) q^{71} +(1.66241e7 - 2.87938e7i) q^{73} +(-2.11537e7 - 1.77500e7i) q^{74} +(-502411. - 2.84931e6i) q^{76} +(1.81123e8 - 1.51980e8i) q^{77} +(-7.97854e7 + 2.90395e7i) q^{79} -6.01546e8 q^{80} -1.62331e8 q^{82} +(-1.82136e8 + 6.62920e7i) q^{83} +(-2.23413e8 + 1.87466e8i) q^{85} +(8.34259e6 + 4.73132e7i) q^{86} +(1.27036e8 + 1.06596e8i) q^{88} +(-2.53280e8 + 4.38693e8i) q^{89} +(4.28020e8 + 7.41353e8i) q^{91} +(1.55765e7 - 8.83388e7i) q^{92} +(-1.32186e8 - 4.81117e7i) q^{94} +(1.48021e7 + 5.38753e6i) q^{95} +(-9.83028e7 + 5.57503e8i) q^{97} +(1.91919e7 + 3.32413e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) $ 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.57613	−	1.66557i	0.202238	−	0.0736087i	−0.238915	−	0.971040i	$-0.576792\pi$
$2$	4.57613	−	1.66557i	0.202238	−	0.0736087i	0.441153	+	0.897432i	$0.354570\pi$
$3$		0			0
$3$		0			0
$4$	−374.048	+	313.863i	−0.730562	+	0.613015i
$5$	−461.629	−	2618.03i	−0.330315	−	1.87331i	−0.469338	−	0.883018i	$-0.655508\pi$
$5$	−461.629	−	2618.03i	−0.330315	−	1.87331i	0.139024	−	0.990289i	$-0.455604\pi$
$6$		0			0
$7$	5320.32	+	4464.28i	0.837523	+	0.702765i	0.957005	−	0.290071i	$-0.0936791\pi$
$7$	5320.32	+	4464.28i	0.837523	+	0.702765i	−0.119482	+	0.992836i	$0.538124\pi$
$8$	−2435.60	+	4218.58i	−0.210233	+	0.364134i
$9$		0			0
$10$	−6472.99	−	11211.5i	−0.204694	−	0.354540i
$11$	5911.61	−	33526.4i	0.121741	−	0.690430i	−0.861449	−	0.507845i	$-0.830442\pi$
$11$	5911.61	−	33526.4i	0.121741	−	0.690430i	0.983190	−	0.182585i	$-0.0584466\pi$
$12$		0			0
$13$	115823.	+	42156.3i	1.12474	+	0.409371i	0.836379	−	0.548151i	$-0.184668\pi$
$13$	115823.	+	42156.3i	1.12474	+	0.409371i	0.288359	+	0.957522i	$0.406890\pi$
$14$	31782.0	+	11567.7i	0.221109	+	0.0804770i
$15$		0			0
$16$	39293.1	−	222842.i	0.149891	−	0.850076i
$17$	−54853.3	−	95008.6i	−0.159288	−	0.275894i	0.775324	−	0.631563i	$-0.217586\pi$
$17$	−54853.3	−	95008.6i	−0.159288	−	0.275894i	−0.934612	+	0.355669i	$0.884253\pi$
$18$		0			0
$19$	−2962.69	+	5131.52i	−0.00521548	+	0.00903348i	−0.868621	−	0.495476i	$-0.834993\pi$
$19$	−2962.69	+	5131.52i	−0.00521548	+	0.00903348i	0.863406	+	0.504510i	$0.168327\pi$
$20$	994374.	+	834379.i	1.38968	+	1.16608i
$21$		0			0
$22$	−28788.4	−	163267.i	−0.0262009	−	0.148593i
$23$	−140728.	+	118085.i	−0.104859	+	0.0879871i	−0.693710	−	0.720255i	$-0.744025\pi$
$23$	−140728.	+	118085.i	−0.104859	+	0.0879871i	0.588851	+	0.808242i	$0.299581\pi$
$24$		0			0
$25$	−4.80563e6	+	1.74910e6i	−2.46048	+	0.895542i
$26$	600238.			0.257598
$27$		0			0
$28$	−3.39123e6			−1.04267
$29$	−5.64337e6	+	2.05402e6i	−1.48166	+	0.539278i	−0.951238	−	0.308458i	$-0.900187\pi$
$29$	−5.64337e6	+	2.05402e6i	−1.48166	+	0.539278i	−0.530417	+	0.847737i	$0.677965\pi$
$30$		0			0
$31$	6.88793e6	−	5.77966e6i	1.33956	−	1.12402i	0.357817	−	0.933792i	$-0.383521\pi$
$31$	6.88793e6	−	5.77966e6i	1.33956	−	1.12402i	0.981740	−	0.190230i	$-0.0609235\pi$
$32$	−624438.	−	3.54137e6i	−0.105272	−	0.597030i
$33$		0			0
$34$	−409259.	−	343409.i	−0.0525223	−	0.0440714i
$35$	9.23159e6	−	1.59896e7i	1.03985	−	1.80107i
$36$		0			0
$37$	−2.83524e6	−	4.91077e6i	−0.248703	−	0.430767i	0.714463	−	0.699673i	$-0.246671\pi$
$37$	−2.83524e6	−	4.91077e6i	−0.248703	−	0.430767i	−0.963166	+	0.268907i	$0.913338\pi$
$38$	−5010.70	+	28417.1i	−0.000389827	+	0.00221082i
$39$		0			0
$40$	1.21687e7	+	4.42905e6i	0.751579	+	0.273552i
$41$	−3.13238e7	−	1.14009e7i	−1.73120	−	0.630105i	−0.732484	−	0.680785i	$-0.761639\pi$
$41$	−3.13238e7	−	1.14009e7i	−1.73120	−	0.630105i	−0.998715	+	0.0506797i	$0.983861\pi$
$42$		0			0
$43$	−1.71312e6	+	9.71560e6i	−0.0764153	+	0.433373i	0.922466	+	0.386079i	$0.126171\pi$
$43$	−1.71312e6	+	9.71560e6i	−0.0764153	+	0.433373i	−0.998881	+	0.0472937i	$0.984940\pi$
$44$	8.31149e6	+	1.43959e7i	0.334304	+	0.579032i
$45$		0			0
$46$	−447310.	+	774764.i	−0.0147299	+	0.0255129i
$47$	−2.21279e7	−	1.85675e7i	−0.661455	−	0.555027i	0.249068	−	0.968486i	$-0.419876\pi$
$47$	−2.21279e7	−	1.85675e7i	−0.661455	−	0.555027i	−0.910522	+	0.413460i	$0.864320\pi$
$48$		0			0
$49$	1.36869e6	+	7.76222e6i	0.0339174	+	0.192355i
$50$	−1.90779e7	+	1.60083e7i	−0.431683	+	0.362225i
$51$		0			0
$52$	−5.65549e7	+	2.05843e7i	−1.07264	+	0.390410i
$53$	1.54382e7			0.268755			0.134377	−	0.990930i	$-0.457097\pi$
$53$	1.54382e7			0.268755			0.134377	+	0.990930i	$0.457097\pi$
$54$		0			0
$55$	−9.05020e7			−1.33360
$56$	−3.17911e7	+	1.15710e7i	−0.431976	+	0.157226i
$57$		0			0
$58$	−2.24036e7	+	1.87989e7i	−0.259952	+	0.218125i
$59$	1.95594e6	+	1.10927e7i	0.0210146	+	0.119180i	0.993511	−	0.113740i	$-0.0362832\pi$
$59$	1.95594e6	+	1.10927e7i	0.0210146	+	0.119180i	−0.972496	+	0.232920i	$0.925172\pi$
$60$		0			0
$61$	−7.31062e7	−	6.13434e7i	−0.676037	−	0.567262i	0.238809	−	0.971067i	$-0.423243\pi$
$61$	−7.31062e7	−	6.13434e7i	−0.676037	−	0.567262i	−0.914845	+	0.403805i	$0.867688\pi$
$62$	2.18936e7	−	3.79208e7i	0.188172	−	0.325923i
$63$		0			0
$64$	4.91718e7	+	8.51680e7i	0.366358	+	0.634551i
$65$	5.68989e7	−	3.22690e8i	0.395361	−	2.24220i
$66$		0			0
$67$	−2.31914e8	−	8.44099e7i	−1.40602	−	0.511748i	−0.476059	−	0.879413i	$-0.657935\pi$
$67$	−2.31914e8	−	8.44099e7i	−1.40602	−	0.511748i	−0.929958	+	0.367665i	$0.880157\pi$
$68$	5.03375e7	+	1.83213e7i	0.285497	+	0.103912i
$69$		0			0
$70$	1.56131e7	−	8.85462e7i	0.0777227	−	0.440787i
$71$	−6.37879e7	−	1.10484e8i	−0.297904	−	0.515984i	0.677753	−	0.735290i	$-0.262954\pi$
$71$	−6.37879e7	−	1.10484e8i	−0.297904	−	0.515984i	−0.975656	+	0.219306i	$0.929621\pi$
$72$		0			0
$73$	1.66241e7	−	2.87938e7i	0.0685150	−	0.118671i	−0.829733	−	0.558161i	$-0.811507\pi$
$73$	1.66241e7	−	2.87938e7i	0.0685150	−	0.118671i	0.898248	+	0.439489i	$0.144841\pi$
$74$	−2.11537e7	−	1.77500e7i	−0.0820054	−	0.0688107i
$75$		0			0
$76$	−502411.	−	2.84931e6i	−0.00172742	−	0.00979669i
$77$	1.81123e8	−	1.51980e8i	0.587171	−	0.492695i
$78$		0			0
$79$	−7.97854e7	+	2.90395e7i	−0.230463	+	0.0838817i	−0.454670	−	0.890660i	$-0.650243\pi$
$79$	−7.97854e7	+	2.90395e7i	−0.230463	+	0.0838817i	0.224207	+	0.974541i	$0.428021\pi$
$80$	−6.01546e8			−1.64197
$81$		0			0
$82$	−1.62331e8			−0.396496
$83$	−1.82136e8	+	6.62920e7i	−0.421254	+	0.153324i	−0.543945	−	0.839121i	$-0.683070\pi$
$83$	−1.82136e8	+	6.62920e7i	−0.421254	+	0.153324i	0.122691	+	0.992445i	$0.460848\pi$
$84$		0			0
$85$	−2.23413e8	+	1.87466e8i	−0.464220	+	0.389527i
$86$	8.34259e6	+	4.73132e7i	0.0164459	+	0.0932693i
$87$		0			0
$88$	1.27036e8	+	1.06596e8i	0.225815	+	0.189482i
$89$	−2.53280e8	+	4.38693e8i	−0.427903	+	0.741150i	−0.996687	−	0.0813373i	$-0.974081\pi$
$89$	−2.53280e8	+	4.38693e8i	−0.427903	+	0.741150i	0.568783	+	0.822487i	$0.307414\pi$
$90$		0			0
$91$	4.28020e8	+	7.41353e8i	0.654302	+	1.13328i
$92$	1.55765e7	−	8.83388e7i	0.0226686	−	0.128560i
$93$		0			0
$94$	−1.32186e8	−	4.81117e7i	−0.174626	−	0.0635587i
$95$	1.48021e7	+	5.38753e6i	0.0186452	+	0.00678631i
$96$		0			0
$97$	−9.83028e7	+	5.57503e8i	−0.112744	+	0.639403i	0.875099	+	0.483945i	$0.160796\pi$
$97$	−9.83028e7	+	5.57503e8i	−0.112744	+	0.639403i	−0.987843	+	0.155458i	$0.950315\pi$
$98$	1.91919e7	+	3.32413e7i	0.0210184	+	0.0364049i
$99$		0			0
$100$	1.24855e9	−	2.16256e9i	1.24855	−	2.16256i
$101$	3.40147e8	+	2.85417e8i	0.325252	+	0.272919i	0.790762	−	0.612124i	$-0.209685\pi$
$101$	3.40147e8	+	2.85417e8i	0.325252	+	0.272919i	−0.465510	+	0.885043i	$0.654129\pi$
$102$		0			0
$103$	5.31317e6	+	3.01325e7i	0.00465143	+	0.0263795i	0.987045	−	0.160443i	$-0.0512922\pi$
$103$	5.31317e6	+	3.01325e7i	0.00465143	+	0.0263795i	−0.982394	+	0.186822i	$0.940181\pi$
$104$	−4.59940e8	+	3.85935e8i	−0.385523	+	0.323493i
$105$		0			0
$106$	7.06473e7	−	2.57135e7i	0.0543525	−	0.0197827i
$107$	1.43344e9			1.05719			0.528594	−	0.848875i	$-0.322719\pi$
$107$	1.43344e9			1.05719			0.528594	+	0.848875i	$0.322719\pi$
$108$		0			0
$109$	−1.59066e9			−1.07934			−0.539671	−	0.841876i	$-0.681451\pi$
$109$	−1.59066e9			−1.07934			−0.539671	+	0.841876i	$0.681451\pi$
$110$	−4.14149e8	+	1.50738e8i	−0.269705	+	0.0981646i
$111$		0			0
$112$	1.20388e9	−	1.01018e9i	0.722941	−	0.606619i
$113$	−1.50382e8	−	8.52859e8i	−0.0867647	−	0.492067i	−0.996962	−	0.0778917i	$-0.975181\pi$
$113$	−1.50382e8	−	8.52859e8i	−0.0867647	−	0.492067i	0.910197	−	0.414175i	$-0.135930\pi$
$114$		0			0
$115$	3.74113e8	+	3.13918e8i	0.199463	+	0.167370i
$116$	1.46621e9	−	2.53955e9i	0.751856	−	1.30225i
$117$		0			0
$118$	2.74263e7	+	4.75037e7i	0.0130226	+	0.0225558i
$119$	1.32308e8	−	7.50356e8i	0.0604818	−	0.343010i
$120$		0			0
$121$	1.12667e9	+	4.10076e8i	0.477820	+	0.173912i
$122$	−4.36716e8	−	1.58951e8i	−0.178476	−	0.0649599i
$123$		0			0
$124$	−7.62392e8	+	4.32374e9i	−0.289588	+	1.64234i
$125$	4.20151e9	+	7.27723e9i	1.53925	+	2.66607i
$126$		0			0
$127$	2.15089e9	−	3.72545e9i	0.733671	−	1.27076i	−0.221633	−	0.975130i	$-0.571139\pi$
$127$	2.15089e9	−	3.72545e9i	0.733671	−	1.27076i	0.955304	−	0.295625i	$-0.0955279\pi$
$128$	1.77727e9	+	1.49131e9i	0.585207	+	0.491047i
$129$		0			0
$130$	−2.77087e8	−	1.57144e9i	−0.0850885	−	0.482561i
$131$	−3.07746e9	+	2.58230e9i	−0.913002	+	0.766099i	−0.972688	−	0.232118i	$-0.925435\pi$
$131$	−3.07746e9	+	2.58230e9i	−0.913002	+	0.766099i	0.0596859	+	0.998217i	$0.480990\pi$
$132$		0			0
$133$	−3.86710e7	+	1.40751e7i	−0.0107165	+	0.00390049i
$134$	−1.20186e9			−0.322020
$135$		0			0
$136$	5.34402e8			0.133950
$137$	4.87686e8	−	1.77503e8i	0.118276	−	0.0430490i	−0.282204	−	0.959354i	$-0.591066\pi$
$137$	4.87686e8	−	1.77503e8i	0.118276	−	0.0430490i	0.400480	+	0.916305i	$0.368843\pi$
$138$		0			0
$139$	3.19369e8	−	2.67983e8i	0.0725649	−	0.0608892i	−0.605784	−	0.795629i	$-0.707140\pi$
$139$	3.19369e8	−	2.67983e8i	0.0725649	−	0.0608892i	0.678349	+	0.734740i	$0.262696\pi$
$140$	1.56549e9	+	8.87833e9i	0.344408	+	1.95324i
$141$		0			0
$142$	−4.75921e8	−	3.99345e8i	−0.0982284	−	0.0824234i
$143$	2.09805e9	−	3.63393e9i	0.419570	−	0.726716i
$144$		0			0
$145$	7.98261e9	+	1.38263e10i	1.49965	+	2.59746i
$146$	2.81158e7	−	1.59453e8i	0.00512110	−	0.0290432i
$147$		0			0
$148$	2.60183e9	+	9.46987e8i	0.445759	+	0.162243i
$149$	1.12972e9	+	4.11185e8i	0.187773	+	0.0683437i	0.434195	−	0.900819i	$-0.357033\pi$
$149$	1.12972e9	+	4.11185e8i	0.187773	+	0.0683437i	−0.246422	+	0.969163i	$0.579255\pi$
$150$		0			0
$151$	1.06844e9	−	6.05944e9i	0.167246	−	0.948497i	−0.779473	−	0.626436i	$-0.784513\pi$
$151$	1.06844e9	−	6.05944e9i	0.167246	−	0.948497i	0.946719	−	0.322061i	$-0.104376\pi$
$152$	−1.44318e7	−	2.49967e7i	−0.00219293	−	0.00379827i
$153$		0			0
$154$	5.75707e8	−	9.97154e8i	0.0824818	−	0.142863i
$155$	−1.83110e10	−	1.53647e10i	−2.54811	−	2.13812i
$156$		0			0
$157$	−1.96061e9	−	1.11192e10i	−0.257539	−	1.46058i	−0.789470	−	0.613789i	$-0.789645\pi$
$157$	−1.96061e9	−	1.11192e10i	−0.257539	−	1.46058i	0.531931	−	0.846787i	$-0.321466\pi$
$158$	−3.16741e8	+	2.65777e8i	−0.0404340	+	0.0339282i
$159$		0			0
$160$	−8.98313e9	+	3.26959e9i	−1.08365	+	0.394415i
$161$	−1.27588e9			−0.149656
$162$		0			0
$163$	1.13198e10			1.25602			0.628008	−	0.778207i	$-0.283871\pi$
$163$	1.13198e10			1.25602			0.628008	+	0.778207i	$0.283871\pi$
$164$	1.52949e10	−	5.56690e9i	1.65101	−	0.600919i
$165$		0			0
$166$	−7.23062e8	+	6.06721e8i	−0.0739076	+	0.0620158i
$167$	−3.33597e8	−	1.89192e9i	−0.0331893	−	0.188226i	0.963706	−	0.266966i	$-0.0860212\pi$
$167$	−3.33597e8	−	1.89192e9i	−0.0331893	−	0.188226i	−0.996895	+	0.0787406i	$0.974910\pi$
$168$		0			0
$169$	3.51441e9	+	2.94894e9i	0.331407	+	0.278084i
$170$	−7.10129e8	+	1.22998e9i	−0.0652105	+	0.112948i
$171$		0			0
$172$	−2.40858e9	−	4.17179e9i	−0.209838	−	0.363450i
$173$	1.31628e9	−	7.46502e9i	0.111723	−	0.633612i	−0.876598	−	0.481224i	$-0.840192\pi$
$173$	1.31628e9	−	7.46502e9i	0.111723	−	0.633612i	0.988321	−	0.152388i	$-0.0486965\pi$
$174$		0			0
$175$	−3.33760e10	−	1.21479e10i	−2.69006	−	0.979103i
$176$	−7.23882e9	−	2.63471e9i	−0.568670	−	0.206979i
$177$		0			0
$178$	−4.28364e8	+	2.42937e9i	−0.0319833	+	0.181386i
$179$	5.48042e9	+	9.49237e9i	0.399002	+	0.691092i	0.993603	−	0.112929i	$-0.0360233\pi$
$179$	5.48042e9	+	9.49237e9i	0.399002	+	0.691092i	−0.594601	+	0.804021i	$0.702690\pi$
$180$		0			0
$181$	−5.38037e9	+	9.31908e9i	−0.372614	+	0.645386i	−0.989967	−	0.141300i	$-0.954872\pi$
$181$	−5.38037e9	+	9.31908e9i	−0.372614	+	0.645386i	0.617353	+	0.786686i	$0.288205\pi$
$182$	3.19346e9	+	2.67963e9i	0.215744	+	0.181031i
$183$		0			0
$184$	−1.55394e8	−	8.81281e8i	−0.00999431	−	0.0566805i
$185$	−1.15477e10	+	9.68968e9i	−0.724808	+	0.608186i
$186$		0			0
$187$	−3.50957e9	+	1.27738e9i	−0.209878	+	0.0763893i
$188$	1.41046e10			0.823473
$189$		0			0
$190$	7.67097e7			0.00427031
$191$	−1.93056e10	+	7.02666e9i	−1.04962	+	0.382031i	−0.808520	−	0.588469i	$-0.799731\pi$
$191$	−1.93056e10	+	7.02666e9i	−1.04962	+	0.382031i	−0.241102	+	0.970500i	$0.577509\pi$
$192$		0			0
$193$	−1.51679e10	+	1.27274e10i	−0.786899	+	0.660286i	−0.944976	−	0.327140i	$-0.893915\pi$
$193$	−1.51679e10	+	1.27274e10i	−0.786899	+	0.660286i	0.158077	+	0.987427i	$0.449471\pi$
$194$	4.78716e8	+	2.71494e9i	0.0242645	+	0.137611i
$195$		0			0
$196$	−2.94823e9	−	2.47386e9i	−0.142695	−	0.119736i
$197$	7.81933e9	−	1.35435e10i	0.369889	−	0.640667i	−0.619659	−	0.784871i	$-0.712729\pi$
$197$	7.81933e9	−	1.35435e10i	0.369889	−	0.640667i	0.989548	+	0.144204i	$0.0460623\pi$
$198$		0			0
$199$	−1.86449e10	−	3.22939e10i	−0.842793	−	1.45976i	−0.887524	−	0.460761i	$-0.847577\pi$
$199$	−1.86449e10	−	3.22939e10i	−0.842793	−	1.45976i	0.0447318	−	0.998999i	$-0.485757\pi$
$200$	4.32584e9	−	2.45331e10i	0.191177	−	1.08422i
$201$		0			0
$202$	2.03194e9	+	7.39566e8i	0.0858677	+	0.0312533i
$203$	−3.91942e10	−	1.42655e10i	−1.61991	−	0.589597i
$204$		0			0
$205$	−1.53880e10	+	8.72695e10i	−0.608540	+	3.45120i
$206$	7.45016e7	+	1.29041e8i	0.00288246	+	0.00499257i
$207$		0			0
$208$	1.39453e10	−	2.41539e10i	0.516585	−	0.894752i
$209$	1.54527e8	+	1.29664e8i	0.00560205	+	0.00470068i
$210$		0			0
$211$	−3.65433e9	−	2.07247e10i	−0.126922	−	0.719810i	−0.980148	−	0.198268i	$-0.936468\pi$
$211$	−3.65433e9	−	2.07247e10i	−0.126922	−	0.719810i	0.853226	−	0.521541i	$-0.174643\pi$
$212$	−5.77464e9	+	4.84550e9i	−0.196342	+	0.164751i
$213$		0			0
$214$	6.55960e9	−	2.38750e9i	0.213804	−	0.0778183i
$215$	2.62265e10			0.837081
$216$		0			0
$217$	6.24480e10			1.91183
$218$	−7.27908e9	+	2.64937e9i	−0.218284	+	0.0794489i
$219$		0			0
$220$	3.38521e10	−	2.84053e10i	0.974279	−	0.817517i
$221$	−2.34808e9	−	1.33166e10i	−0.0662138	−	0.375517i
$222$		0			0
$223$	−1.02797e10	−	8.62566e9i	−0.278360	−	0.233572i	0.492909	−	0.870081i	$-0.335933\pi$
$223$	−1.02797e10	−	8.62566e9i	−0.278360	−	0.233572i	−0.771269	+	0.636509i	$0.780378\pi$
$224$	1.24874e10	−	2.16289e10i	0.331403	−	0.574007i
$225$		0			0
$226$	−2.10867e9	−	3.65232e9i	−0.0537675	−	0.0931281i
$227$	−1.41125e9	+	8.00361e9i	−0.0352767	+	0.200064i	−0.997353	−	0.0727179i	$-0.976833\pi$
$227$	−1.41125e9	+	8.00361e9i	−0.0352767	+	0.200064i	0.962076	+	0.272782i	$0.0879438\pi$
$228$		0			0
$229$	−5.36739e9	−	1.95357e9i	−0.128974	−	0.0469428i	0.276727	−	0.960949i	$-0.410750\pi$
$229$	−5.36739e9	−	1.95357e9i	−0.128974	−	0.0469428i	−0.405701	+	0.914006i	$0.632973\pi$
$230$	2.23485e9	+	8.13417e8i	0.0526590	+	0.0191663i
$231$		0			0
$232$	5.07994e9	−	2.88098e10i	0.115123	−	0.652896i
$233$	−1.01771e10	−	1.76273e10i	−0.226216	−	0.391817i	0.730468	−	0.682947i	$-0.239302\pi$
$233$	−1.01771e10	−	1.76273e10i	−0.226216	−	0.391817i	−0.956684	+	0.291130i	$0.905969\pi$
$234$		0			0
$235$	−3.83954e10	+	6.65028e10i	−0.821247	+	1.42244i
$236$	−4.21320e9	−	3.53529e9i	−0.0884113	−	0.0741859i
$237$		0			0
$238$	−6.44316e8	−	3.65410e9i	−0.0130167	−	0.0738216i
$239$	−1.79775e10	+	1.50849e10i	−0.356400	+	0.299055i	−0.803354	−	0.595502i	$-0.796953\pi$
$239$	−1.79775e10	+	1.50849e10i	−0.356400	+	0.299055i	0.446954	+	0.894557i	$0.352509\pi$
$240$		0			0
$241$	−6.83027e10	+	2.48602e10i	−1.30425	+	0.474709i	−0.898379	−	0.439221i	$-0.855254\pi$
$241$	−6.83027e10	+	2.48602e10i	−1.30425	+	0.474709i	−0.405872	+	0.913930i	$0.633032\pi$
$242$	5.83881e9			0.109435
$243$		0			0
$244$	4.65987e10			0.841627
$245$	1.96899e10	−	7.16653e9i	0.349137	−	0.127075i
$246$		0			0
$247$	−5.59475e8	+	4.69455e8i	−0.00956410	+	0.00802523i
$248$	7.60573e9	+	4.31343e10i	0.127676	+	0.724085i
$249$		0			0
$250$	3.13474e10	+	2.63036e10i	0.507542	+	0.425878i
$251$	−3.76413e10	+	6.51966e10i	−0.598594	+	1.03680i	0.394435	+	0.918924i	$0.370940\pi$
$251$	−3.76413e10	+	6.51966e10i	−0.598594	+	1.03680i	−0.993029	+	0.117871i	$0.962393\pi$
$252$		0			0
$253$	3.12703e9	+	5.41618e9i	0.0479833	+	0.0831095i
$254$	3.63773e9	−	2.06306e10i	0.0548376	−	0.311000i
$255$		0			0
$256$	−3.66984e10	−	1.33571e10i	−0.534032	−	0.194372i
$257$	5.03767e10	+	1.83356e10i	0.720328	+	0.262178i	0.676065	−	0.736842i	$-0.263684\pi$
$257$	5.03767e10	+	1.83356e10i	0.720328	+	0.262178i	0.0442631	+	0.999020i	$0.485906\pi$
$258$		0			0
$259$	6.83869e9	−	3.87842e10i	0.0944331	−	0.535557i
$260$	7.99976e10	+	1.38560e11i	1.08567	+	1.88043i
$261$		0			0
$262$	−9.78185e9	+	1.69427e10i	−0.128252	+	0.222139i
$263$	−2.87859e10	−	2.41542e10i	−0.371004	−	0.311309i	0.438155	−	0.898900i	$-0.355632\pi$
$263$	−2.87859e10	−	2.41542e10i	−0.371004	−	0.311309i	−0.809158	+	0.587590i	$0.800077\pi$
$264$		0			0
$265$	−7.12673e9	−	4.04177e10i	−0.0887737	−	0.503460i
$266$	−1.53520e8	+	1.28819e8i	−0.00188017	+	0.00157765i
$267$		0			0
$268$	1.13240e11	−	4.12161e10i	1.34089	−	0.488045i
$269$	7.79017e10			0.907114			0.453557	−	0.891227i	$-0.350155\pi$
$269$	7.79017e10			0.907114			0.453557	+	0.891227i	$0.350155\pi$
$270$		0			0
$271$	7.78122e10			0.876367			0.438183	−	0.898886i	$-0.355622\pi$
$271$	7.78122e10			0.876367			0.438183	+	0.898886i	$0.355622\pi$
$272$	−2.33273e10	+	8.49044e9i	−0.258407	+	0.0940525i
$273$		0			0
$274$	1.93607e9	−	1.62455e9i	0.0207512	−	0.0174123i
$275$	3.02322e10	+	1.71455e11i	0.318767	+	1.80781i
$276$		0			0
$277$	−5.20155e10	−	4.36462e10i	−0.530852	−	0.445438i	0.337543	−	0.941310i	$-0.390404\pi$
$277$	−5.20155e10	−	4.36462e10i	−0.530852	−	0.445438i	−0.868396	+	0.495872i	$0.834848\pi$
$278$	1.01513e9	−	1.75826e9i	0.0101934	−	0.0176555i
$279$		0			0
$280$	4.49689e10	+	7.78884e10i	0.437221	+	0.757289i
$281$	3.21660e10	−	1.82423e11i	0.307765	−	1.74542i	−0.302431	−	0.953171i	$-0.597798\pi$
$281$	3.21660e10	−	1.82423e11i	0.307765	−	1.74542i	0.610196	−	0.792250i	$-0.291091\pi$
$282$		0			0
$283$	1.22078e11	+	4.44327e10i	1.13135	+	0.411779i	0.838783	−	0.544465i	$-0.183267\pi$
$283$	1.22078e11	+	4.44327e10i	1.13135	+	0.411779i	0.292570	+	0.956244i	$0.405490\pi$
$284$	5.85366e10	+	2.13056e10i	0.533943	+	0.194339i
$285$		0			0
$286$	3.54837e9	−	2.01238e10i	0.0313604	−	0.177854i
$287$	−1.15756e11	−	2.00495e11i	−1.00710	−	1.74435i
$288$		0			0
$289$	5.32762e10	−	9.22770e10i	0.449255	−	0.778132i
$290$	5.95582e10	+	4.99752e10i	0.494482	+	0.414919i
$291$		0			0
$292$	2.81911e9	+	1.59880e10i	0.0226929	+	0.128698i
$293$	3.81018e9	−	3.19712e9i	0.0302024	−	0.0253428i	−0.627561	−	0.778567i	$-0.715947\pi$
$293$	3.81018e9	−	3.19712e9i	0.0302024	−	0.0253428i	0.657764	+	0.753224i	$0.271502\pi$
$294$		0			0
$295$	2.81380e10	−	1.02414e10i	0.216319	−	0.0787335i
$296$	2.76220e10			0.209143
$297$		0			0
$298$	5.85461e9			0.0430055
$299$	−2.12776e10	+	7.74443e9i	−0.153958	+	0.0560362i
$300$		0			0
$301$	−5.24875e10	+	4.40422e10i	−0.368559	+	0.309257i
$302$	−5.20311e9	−	2.95083e10i	−0.0359942	−	0.204133i
$303$		0			0
$304$	1.02711e9	+	8.61845e8i	0.00689739	+	0.00578760i
$305$	−1.26851e11	+	2.19712e11i	−0.839351	+	1.45380i
$306$		0			0
$307$	−4.94616e10	−	8.56700e10i	−0.317794	−	0.550435i	0.662234	−	0.749297i	$-0.269609\pi$
$307$	−4.94616e10	−	8.56700e10i	−0.317794	−	0.550435i	−0.980027	+	0.198862i	$0.936275\pi$
$308$	−2.00476e10	+	1.13696e11i	−0.126936	+	0.719889i
$309$		0			0
$310$	−1.09384e11	−	3.98127e10i	−0.672710	−	0.244846i
$311$	−2.77134e11	−	1.00869e11i	−1.67984	−	0.611413i	−0.686554	−	0.727079i	$-0.740877\pi$
$311$	−2.77134e11	−	1.00869e11i	−1.67984	−	0.611413i	−0.993288	+	0.115666i	$0.963100\pi$
$312$		0			0
$313$	−2.98680e10	+	1.69390e11i	−0.175896	+	0.997556i	0.761209	+	0.648507i	$0.224606\pi$
$313$	−2.98680e10	+	1.69390e11i	−0.175896	+	0.997556i	−0.937105	+	0.349049i	$0.886505\pi$
$314$	−2.74918e10	−	4.76172e10i	−0.159595	−	0.276427i
$315$		0			0
$316$	2.07291e10	−	3.59039e10i	0.116947	−	0.202558i
$317$	3.21208e10	+	2.69525e10i	0.178657	+	0.149911i	0.727731	−	0.685863i	$-0.240575\pi$
$317$	3.21208e10	+	2.69525e10i	0.178657	+	0.149911i	−0.549074	+	0.835774i	$0.685019\pi$
$318$		0			0
$319$	3.55024e10	+	2.01344e11i	0.191955	+	1.08863i
$320$	2.00273e11	−	1.68049e11i	1.06770	−	0.895903i
$321$		0			0
$322$	−5.83860e9	+	2.12508e9i	−0.0302661	+	0.0110160i
$323$	6.50052e8			0.00332305
$324$		0			0
$325$	−6.30340e11			−3.13401
$326$	5.18009e10	−	1.88540e10i	0.254014	−	0.0924536i
$327$		0			0
$328$	1.24388e11	−	1.04374e11i	0.593398	−	0.497920i
$329$	−3.48370e10	−	1.97570e11i	−0.163930	−	0.929694i
$330$		0			0
$331$	−5.75995e9	−	4.83317e9i	−0.0263750	−	0.0221313i	0.629505	−	0.776997i	$-0.283258\pi$
$331$	−5.75995e9	−	4.83317e9i	−0.0263750	−	0.0221313i	−0.655880	+	0.754865i	$0.727702\pi$
$332$	4.73208e10	−	8.19621e10i	0.213762	−	0.370247i
$333$		0			0
$334$	−4.67772e9	−	8.10204e9i	−0.0205672	−	0.0356234i
$335$	−1.13929e11	+	6.46124e11i	−0.494234	+	2.80294i
$336$		0			0
$337$	4.35666e11	+	1.58569e11i	1.84001	+	0.669707i	0.989651	+	0.143498i	$0.0458351\pi$
$337$	4.35666e11	+	1.58569e11i	1.84001	+	0.669707i	0.850355	+	0.526209i	$0.176387\pi$
$338$	2.09941e10	+	7.64121e9i	0.0874926	+	0.0318447i
$339$		0			0
$340$	2.47285e10	−	1.40243e11i	0.100356	−	0.569147i
$341$	−1.53052e11	−	2.65095e11i	−0.612979	−	1.06171i
$342$		0			0
$343$	1.12761e11	−	1.95307e11i	0.439880	−	0.761895i
$344$	−3.68136e10	−	3.08903e10i	−0.141741	−	0.118935i
$345$		0			0
$346$	−6.41006e9	−	3.63533e10i	−0.0240447	−	0.136364i
$347$	3.47880e11	−	2.91906e11i	1.28809	−	1.08084i	0.296019	−	0.955182i	$-0.404341\pi$
$347$	3.47880e11	−	2.91906e11i	1.28809	−	1.08084i	0.992074	−	0.125656i	$-0.0401035\pi$
$348$		0			0
$349$	−9.52669e10	+	3.46743e10i	−0.343738	+	0.125110i	−0.508120	−	0.861286i	$-0.669659\pi$
$349$	−9.52669e10	+	3.46743e10i	−0.343738	+	0.125110i	0.164382	+	0.986397i	$0.447437\pi$
$350$	−1.72966e11			−0.616104
$351$		0			0
$352$	−1.22421e11			−0.425023
$353$	1.08927e11	−	3.96463e10i	0.373380	−	0.135899i	−0.148512	−	0.988911i	$-0.547449\pi$
$353$	1.08927e11	−	3.96463e10i	0.373380	−	0.135899i	0.521892	+	0.853011i	$0.325226\pi$
$354$		0			0
$355$	−2.59803e11	+	2.18001e11i	−0.868195	+	0.728502i
$356$	−4.29511e10	−	2.43588e11i	−0.141726	−	0.803767i
$357$		0			0
$358$	4.08893e10	+	3.43102e10i	0.131564	+	0.110395i
$359$	1.58363e11	−	2.74293e11i	0.503187	−	0.871545i	−0.496806	−	0.867861i	$-0.665494\pi$
$359$	1.58363e11	−	2.74293e11i	0.503187	−	0.871545i	0.999993	−	0.00368385i	$-0.00117261\pi$
$360$		0			0
$361$	1.61326e11	+	2.79425e11i	0.499946	+	0.865931i
$362$	−9.09966e9	+	5.16067e10i	−0.0278507	+	0.157949i
$363$		0			0
$364$	−3.92784e11	−	1.42962e11i	−1.17273	−	0.426838i
$365$	−8.30571e10	−	3.02303e10i	−0.244940	−	0.0891507i
$366$		0			0
$367$	2.87711e10	−	1.63169e11i	0.0827865	−	0.469505i	−0.915026	−	0.403395i	$-0.867830\pi$
$367$	2.87711e10	−	1.63169e11i	0.0827865	−	0.469505i	0.997812	−	0.0661102i	$-0.0210589\pi$
$368$	2.07847e10	+	3.60001e10i	0.0590783	+	0.102327i
$369$		0			0
$370$	−3.67049e10	+	6.35748e10i	−0.101816	+	0.176351i
$371$	8.21363e10	+	6.89206e10i	0.225088	+	0.188871i
$372$		0			0
$373$	−1.73575e10	−	9.84392e10i	−0.0464298	−	0.263317i	0.952753	−	0.303748i	$-0.0982380\pi$
$373$	−1.73575e10	−	9.84392e10i	−0.0464298	−	0.263317i	−0.999182	+	0.0404311i	$0.987127\pi$
$374$	−1.39327e10	+	1.16909e10i	−0.0368224	+	0.0308977i
$375$		0			0
$376$	1.32223e11	−	4.81254e10i	0.341164	−	0.124174i
$377$	−7.40224e11			−1.88724
$378$		0			0
$379$	−5.62976e11			−1.40156			−0.700782	−	0.713375i	$-0.747166\pi$
$379$	−5.62976e11			−1.40156			−0.700782	+	0.713375i	$0.747166\pi$
$380$	−7.22765e9	+	2.63065e9i	−0.0177816	+	0.00647198i
$381$		0			0
$382$	−7.66414e10	+	6.43098e10i	−0.184153	+	0.154523i
$383$	9.50765e10	+	5.39206e11i	0.225776	+	1.28044i	0.861195	+	0.508274i	$0.169716\pi$
$383$	9.50765e10	+	5.39206e11i	0.225776	+	1.28044i	−0.635419	+	0.772168i	$0.719172\pi$
$384$		0			0
$385$	−4.81499e11	−	4.04026e11i	−1.11692	−	0.937208i
$386$	−4.82120e10	+	8.35056e10i	−0.110538	+	0.191458i
$387$		0			0
$388$	−1.38210e11	−	2.39387e11i	−0.309597	−	0.536237i
$389$	6.15454e10	−	3.49041e11i	0.136277	−	0.772865i	−0.837685	−	0.546154i	$-0.816091\pi$
$389$	6.15454e10	−	3.49041e11i	0.136277	−	0.772865i	0.973962	−	0.226711i	$-0.0727974\pi$
$390$		0			0
$391$	1.89385e10	+	6.89304e9i	0.0409779	+	0.0149147i
$392$	−3.60792e10	−	1.31317e10i	−0.0771737	−	0.0280889i
$393$		0			0
$394$	1.32246e10	−	7.50004e10i	0.0276471	−	0.156794i
$395$	1.12857e11	+	1.95475e11i	0.233262	+	0.404021i
$396$		0			0
$397$	−1.77909e11	+	3.08147e11i	−0.359451	+	0.622587i	−0.987869	−	0.155288i	$-0.950369\pi$
$397$	−1.77909e11	+	3.08147e11i	−0.359451	+	0.622587i	0.628418	+	0.777876i	$0.283703\pi$
$398$	−1.39109e11	−	1.16726e11i	−0.277896	−	0.233182i
$399$		0			0
$400$	2.00947e11	+	1.13962e12i	0.392474	+	2.22583i
$401$	5.80297e11	−	4.86927e11i	1.12073	−	0.940404i	0.122089	−	0.992519i	$-0.461041\pi$
$401$	5.80297e11	−	4.86927e11i	1.12073	−	0.940404i	0.998641	+	0.0521151i	$0.0165963\pi$
$402$		0			0
$403$	1.04143e12	−	3.79051e11i	1.96679	−	0.715854i
$404$	−2.16813e11			−0.404921
$405$		0			0
$406$	−2.03118e11			−0.371006
$407$	−1.81401e11	+	6.60247e10i	−0.327692	+	0.119270i
$408$		0			0
$409$	9.82358e10	−	8.24296e10i	0.173586	−	0.145656i	−0.551856	−	0.833940i	$-0.686080\pi$
$409$	9.82358e10	−	8.24296e10i	0.173586	−	0.145656i	0.725442	+	0.688284i	$0.241636\pi$
$410$	7.49365e10	+	4.24986e11i	0.130968	+	0.742758i
$411$		0			0
$412$	−1.14449e10	−	9.60338e9i	−0.0195692	−	0.0164205i
$413$	−3.91145e10	+	6.77484e10i	−0.0661550	+	0.114584i
$414$		0			0
$415$	2.57633e11	+	4.46234e11i	0.426369	+	0.738492i
$416$	7.69662e10	−	4.36497e11i	0.126003	−	0.714598i
$417$		0			0
$418$	9.23101e8	+	3.35981e8i	0.00147896	+	0.000538297i
$419$	−3.30308e11	−	1.20222e11i	−0.523547	−	0.190555i	0.0667078	−	0.997773i	$-0.478750\pi$
$419$	−3.30308e11	−	1.20222e11i	−0.523547	−	0.190555i	−0.590255	+	0.807217i	$0.700973\pi$
$420$		0			0
$421$	2.00477e11	−	1.13696e12i	0.311024	−	1.76391i	−0.282671	−	0.959217i	$-0.591221\pi$
$421$	2.00477e11	−	1.13696e12i	0.311024	−	1.76391i	0.593696	−	0.804690i	$-0.297668\pi$
$422$	−5.12412e10	−	8.87524e10i	−0.0786527	−	0.136230i
$423$		0			0
$424$	−3.76014e10	+	6.51275e10i	−0.0565012	+	0.0978629i
$425$	4.29784e11	+	3.60632e11i	0.638999	+	0.536184i
$426$		0			0
$427$	−1.15094e11	−	6.52733e11i	−0.167544	−	0.950189i
$428$	−5.36175e11	+	4.49904e11i	−0.772342	+	0.648072i
$429$		0			0
$430$	1.20016e11	−	4.36822e10i	0.169290	−	0.0616165i
$431$	−2.90675e10			−0.0405751			−0.0202875	−	0.999794i	$-0.506458\pi$
$431$	−2.90675e10			−0.0405751			−0.0202875	+	0.999794i	$0.506458\pi$
$432$		0			0
$433$	1.37177e12			1.87537			0.937683	−	0.347492i	$-0.112967\pi$
$433$	1.37177e12			1.87537			0.937683	+	0.347492i	$0.112967\pi$
$434$	2.85770e11	−	1.04012e11i	0.386645	−	0.140727i
$435$		0			0
$436$	5.94984e11	−	4.99251e11i	0.788527	−	0.661653i
$437$	−1.89022e8	−	1.07200e9i	−0.000247940	−	0.00140614i
$438$		0			0
$439$	5.68569e11	+	4.77086e11i	0.730623	+	0.613065i	0.930301	−	0.366796i	$-0.119545\pi$
$439$	5.68569e11	+	4.77086e11i	0.730623	+	0.613065i	−0.199679	+	0.979861i	$0.563990\pi$
$440$	2.20427e11	−	3.81790e11i	0.280367	−	0.485610i
$441$		0			0
$442$	−3.29250e10	−	5.70277e10i	−0.0410323	−	0.0710699i
$443$	−2.04805e11	+	1.16150e12i	−0.252652	+	1.43286i	0.549376	+	0.835575i	$0.314865\pi$
$443$	−2.04805e11	+	1.16150e12i	−0.252652	+	1.43286i	−0.802028	+	0.597286i	$0.796246\pi$
$444$		0			0
$445$	1.26543e12	+	4.60580e11i	1.52974	+	0.556781i
$446$	−6.14077e10	−	2.23506e10i	−0.0734880	−	0.0267474i
$447$		0			0
$448$	−1.18604e11	+	6.72637e11i	−0.139107	+	0.788915i
$449$	3.97840e11	+	6.89078e11i	0.461955	+	0.800129i	0.999058	−	0.0433871i	$-0.0138149\pi$
$449$	3.97840e11	+	6.89078e11i	0.461955	+	0.800129i	−0.537104	+	0.843516i	$0.680482\pi$
$450$		0			0
$451$	−5.67406e11	+	9.82776e11i	−0.645802	+	1.11856i
$452$	3.23931e11	+	2.71811e11i	0.365031	+	0.306298i
$453$		0			0
$454$	6.87254e9	+	3.89761e10i	0.00759217	+	0.0430573i
$455$	1.74330e12	−	1.46280e12i	1.90686	−	1.60005i
$456$		0			0
$457$	−1.14029e12	+	4.15032e11i	−1.22291	+	0.445101i	−0.871162	−	0.490995i	$-0.836633\pi$
$457$	−1.14029e12	+	4.15032e11i	−1.22291	+	0.445101i	−0.351743	+	0.936096i	$0.614411\pi$
$458$	−2.78157e10			−0.0295389
$459$		0			0
$460$	−2.38464e11			−0.248320
$461$	−1.31219e12	+	4.77599e11i	−1.35314	+	0.492503i	−0.913927	−	0.405879i	$-0.866965\pi$
$461$	−1.31219e12	+	4.77599e11i	−1.35314	+	0.492503i	−0.439214	+	0.898382i	$0.644743\pi$
$462$		0			0
$463$	−1.37393e11	+	1.15286e11i	−0.138947	+	0.116591i	−0.709612	−	0.704592i	$-0.751130\pi$
$463$	−1.37393e11	+	1.15286e11i	−0.138947	+	0.116591i	0.570665	+	0.821183i	$0.306685\pi$
$464$	2.35977e11	+	1.33829e12i	0.236340	+	1.34035i
$465$		0			0
$466$	−7.59313e10	−	6.37140e10i	−0.0745907	−	0.0625890i
$467$	1.49304e11	−	2.58602e11i	0.145260	−	0.251597i	−0.784210	−	0.620495i	$-0.786932\pi$
$467$	1.49304e11	−	2.58602e11i	0.145260	−	0.251597i	0.929470	+	0.368898i	$0.120265\pi$
$468$		0			0
$469$	−8.57028e11	−	1.48442e12i	−0.817932	−	1.41670i
$470$	−6.49369e10	+	3.68276e11i	−0.0613835	+	0.348123i
$471$		0			0
$472$	−5.15592e10	−	1.87660e10i	−0.0478153	−	0.0174034i
$473$	3.15602e11	+	1.14870e11i	0.289911	+	0.105519i
$474$		0			0
$475$	5.26199e9	−	2.98422e10i	0.00474273	−	0.0268974i
$476$	1.86020e11	+	3.22196e11i	0.166084	+	0.287666i
$477$		0			0
$478$	−5.71422e10	+	9.89732e10i	−0.0500647	+	0.0867145i
$479$	1.31141e12	+	1.10041e12i	1.13823	+	0.955088i	0.999379	−	0.0352250i	$-0.0112148\pi$
$479$	1.31141e12	+	1.10041e12i	1.13823	+	0.955088i	0.138851	+	0.990313i	$0.455659\pi$
$480$		0			0
$481$	−1.21367e11	−	6.88306e11i	−0.103383	−	0.586312i
$482$	−2.71156e11	+	2.27526e11i	−0.228827	+	0.192008i
$483$		0			0
$484$	−5.50138e11	+	2.00234e11i	−0.455688	+	0.165857i
$485$	1.50494e12			1.23504
$486$		0			0
$487$	1.41982e12			1.14380			0.571902	−	0.820322i	$-0.306206\pi$
$487$	1.41982e12			1.14380			0.571902	+	0.820322i	$0.306206\pi$
$488$	4.36840e11	−	1.58997e11i	0.348685	−	0.126911i
$489$		0			0
$490$	7.81670e10	−	6.55899e10i	0.0612550	−	0.0513990i
$491$	7.41242e10	+	4.20379e11i	0.0575564	+	0.326418i	0.999968	−	0.00803776i	$-0.00255853\pi$
$491$	7.41242e10	+	4.20379e11i	0.0575564	+	0.326418i	−0.942411	+	0.334456i	$0.891447\pi$
$492$		0			0
$493$	5.04706e11	+	4.23499e11i	0.384793	+	0.322880i
$494$	−1.77832e9	+	3.08013e9i	−0.00134350	+	0.00232701i
$495$		0			0
$496$	−1.01730e12	−	1.76202e12i	−0.754716	−	1.30721i
$497$	1.53859e11	−	8.72576e11i	0.113115	−	0.641505i
$498$		0			0
$499$	−8.04147e11	−	2.92686e11i	−0.580608	−	0.211324i	0.0349857	−	0.999388i	$-0.488861\pi$
$499$	−8.04147e11	−	2.92686e11i	−0.580608	−	0.211324i	−0.615594	+	0.788064i	$0.711084\pi$
$500$	−3.85562e12	−	1.40333e12i	−2.75886	−	1.00414i
$501$		0			0
$502$	−6.36615e10	+	3.61042e11i	−0.0447414	+	0.253741i
$503$	−4.28703e11	−	7.42535e11i	−0.298607	−	0.517203i	0.677210	−	0.735790i	$-0.263189\pi$
$503$	−4.28703e11	−	7.42535e11i	−0.298607	−	0.517203i	−0.975818	+	0.218586i	$0.929855\pi$
$504$		0			0
$505$	5.90208e11	−	1.02227e12i	0.403826	−	0.699447i
$506$	2.33307e10	+	1.95768e10i	0.0158216	+	0.0132759i
$507$		0			0
$508$	3.64747e11	+	2.06858e12i	0.242999	+	1.37812i
$509$	1.01419e12	−	8.51009e11i	0.669716	−	0.561959i	−0.243265	−	0.969960i	$-0.578219\pi$
$509$	1.01419e12	−	8.51009e11i	0.669716	−	0.561959i	0.912981	+	0.408001i	$0.133774\pi$
$510$		0			0
$511$	2.16989e11	−	7.89776e10i	0.140781	−	0.0512401i
$512$	−1.37806e12			−0.886242
$513$		0			0
$514$	2.61069e11			0.164976
$515$	7.64349e10	−	2.78200e10i	0.0478806	−	0.0174271i
$516$		0			0
$517$	−7.53314e11	+	6.32105e11i	−0.463734	+	0.389119i
$518$	−3.33032e10	−	1.88872e11i	−0.0203236	−	0.115261i
$519$		0			0
$520$	1.22271e12	+	1.02598e12i	0.733345	+	0.615350i
$521$	−3.88475e11	+	6.72858e11i	−0.230990	+	0.400086i	−0.958100	−	0.286435i	$-0.907530\pi$
$521$	−3.88475e11	+	6.72858e11i	−0.230990	+	0.400086i	0.727110	+	0.686521i	$0.240863\pi$
$522$		0			0
$523$	5.46297e11	+	9.46213e11i	0.319279	+	0.553008i	0.980338	−	0.197326i	$-0.0632258\pi$
$523$	5.46297e11	+	9.46213e11i	0.319279	+	0.553008i	−0.661059	+	0.750334i	$0.729893\pi$
$524$	3.40629e11	−	1.93180e12i	0.197375	−	1.11937i
$525$		0			0
$526$	−1.71958e11	−	6.25877e10i	−0.0979462	−	0.0356495i
$527$	−9.26943e11	−	3.37380e11i	−0.523486	−	0.190533i
$528$		0			0
$529$	−3.06907e11	+	1.74055e12i	−0.170395	+	0.966355i
$530$	−9.99316e10	−	1.73087e11i	−0.0550125	−	0.0952844i
$531$		0			0
$532$	1.00471e10	−	1.74022e10i	0.00543801	−	0.00941892i
$533$	−3.14741e12	−	2.64099e12i	−1.68920	−	1.41741i
$534$		0			0
$535$	−6.61717e11	−	3.75278e12i	−0.349205	−	1.98044i
$536$	9.20940e11	−	7.72761e11i	0.481937	−	0.404393i
$537$		0			0
$538$	3.56488e11	−	1.29751e11i	0.183453	−	0.0667714i
$539$	2.68331e11			0.136937
$540$		0			0
$541$	1.46916e12			0.737362			0.368681	−	0.929556i	$-0.379810\pi$
$541$	1.46916e12			0.737362			0.368681	+	0.929556i	$0.379810\pi$
$542$	3.56078e11	−	1.29602e11i	0.177235	−	0.0645082i
$543$		0			0
$544$	−3.02208e11	+	2.53582e11i	−0.147949	+	0.124144i
$545$	7.34296e11	+	4.16440e12i	0.356523	+	2.02194i
$546$		0			0
$547$	−1.73121e12	−	1.45266e12i	−0.826813	−	0.693778i	0.127744	−	0.991807i	$-0.459226\pi$
$547$	−1.73121e12	−	1.45266e12i	−0.826813	−	0.693778i	−0.954557	+	0.298029i	$0.903671\pi$
$548$	−1.26706e11	+	2.19461e11i	−0.0600185	+	0.103955i
$549$		0			0
$550$	4.23918e11	+	7.34248e11i	0.197538	+	0.342145i
$551$	6.17928e9	−	3.50445e10i	0.00285599	−	0.0161971i
$552$		0			0
$553$	−5.54124e11	−	2.01685e11i	−0.251967	−	0.0917086i
$554$	−3.10725e11	−	1.13095e11i	−0.140147	−	0.0510092i
$555$		0			0
$556$	−3.53495e10	+	2.00477e11i	−0.0156872	+	0.0889667i
$557$	9.48819e11	+	1.64340e12i	0.417672	+	0.723429i	0.995705	−	0.0925847i	$-0.0295129\pi$
$557$	9.48819e11	+	1.64340e12i	0.417672	+	0.723429i	−0.578033	+	0.816013i	$0.696180\pi$
$558$		0			0
$559$	−6.07994e11	+	1.05308e12i	−0.263358	+	0.456149i
$560$	−3.20042e12	−	2.68547e12i	−1.37518	−	1.15392i
$561$		0			0
$562$	−1.56643e11	−	8.88364e11i	−0.0662364	−	0.375645i
$563$	−1.28665e12	+	1.07963e12i	−0.539727	+	0.452884i	−0.871444	−	0.490494i	$-0.836816\pi$
$563$	−1.28665e12	+	1.07963e12i	−0.539727	+	0.452884i	0.331718	+	0.943379i	$0.392372\pi$
$564$		0			0
$565$	−2.16339e12	+	7.87409e11i	−0.893133	+	0.325074i
$566$	6.32650e11			0.259113
$567$		0			0
$568$	6.21447e11			0.250517
$569$	3.70092e12	−	1.34702e12i	1.48015	−	0.538729i	0.529311	−	0.848428i	$-0.322450\pi$
$569$	3.70092e12	−	1.34702e12i	1.48015	−	0.538729i	0.950835	+	0.309699i	$0.100228\pi$
$570$		0			0
$571$	−1.53572e12	+	1.28862e12i	−0.604574	+	0.507298i	−0.892912	−	0.450231i	$-0.851342\pi$
$571$	−1.53572e12	+	1.28862e12i	−0.604574	+	0.507298i	0.288338	+	0.957529i	$0.406897\pi$
$572$	3.55787e11	+	2.01777e12i	0.138966	+	0.788114i
$573$		0			0
$574$	−8.63651e11	−	7.24690e11i	−0.332074	−	0.278643i
$575$	4.69744e11	−	8.13620e11i	0.179207	−	0.310396i
$576$		0			0
$577$	1.02872e12	+	1.78180e12i	0.386373	+	0.669217i	0.991959	−	0.126563i	$-0.0403945\pi$
$577$	1.02872e12	+	1.78180e12i	0.386373	+	0.669217i	−0.605586	+	0.795780i	$0.707061\pi$
$578$	9.01043e10	−	5.11007e11i	0.0335792	−	0.190437i
$579$		0			0
$580$	−7.32545e12	−	2.66624e12i	−2.68787	−	0.978304i
$581$	−1.26497e12	−	4.60410e11i	−0.460560	−	0.167630i
$582$		0			0
$583$	9.12648e10	−	5.17589e11i	0.0327186	−	0.185556i
$584$	8.09794e10	+	1.40260e11i	0.0288082	+	0.0498973i
$585$		0			0
$586$	1.21108e10	−	2.09766e10i	0.00424263	−	0.00734845i
$587$	−8.72183e11	−	7.31849e11i	−0.303205	−	0.254419i	0.478472	−	0.878103i	$-0.341191\pi$
$587$	−8.72183e11	−	7.31849e11i	−0.303205	−	0.254419i	−0.781677	+	0.623684i	$0.785635\pi$
$588$		0			0
$589$	9.25168e9	+	5.24689e10i	0.00316739	+	0.0179632i
$590$	1.11705e11	−	9.37318e10i	0.0379524	−	0.0318458i
$591$		0			0
$592$	−1.20573e12	+	4.38851e11i	−0.403463	+	0.146848i
$593$	−4.18935e11			−0.139124			−0.0695618	−	0.997578i	$-0.522160\pi$
$593$	−4.18935e11			−0.139124			−0.0695618	+	0.997578i	$0.522160\pi$
$594$		0			0
$595$	−2.02553e12			−0.662540
$596$	−5.51626e11	+	2.00775e11i	−0.179076	+	0.0651782i
$597$		0			0
$598$	−8.44703e10	+	7.08790e10i	−0.0270115	+	0.0226653i
$599$	2.68444e11	+	1.52242e12i	0.0851987	+	0.483186i	0.997314	+	0.0732510i	$0.0233374\pi$
$599$	2.68444e11	+	1.52242e12i	0.0851987	+	0.483186i	−0.912115	+	0.409935i	$0.865551\pi$
$600$		0			0
$601$	−2.68519e12	−	2.25315e12i	−0.839538	−	0.704456i	0.117922	−	0.993023i	$-0.462377\pi$
$601$	−2.68519e12	−	2.25315e12i	−0.839538	−	0.704456i	−0.957460	+	0.288567i	$0.906821\pi$
$602$	−1.66834e11	+	2.88965e11i	−0.0517726	+	0.0896728i
$603$		0			0
$604$	1.50219e12	+	2.60186e12i	0.459259	+	0.795460i
$605$	5.53484e11	−	3.13896e12i	0.167960	−	0.952549i
$606$		0			0
$607$	4.98286e12	+	1.81361e12i	1.48981	+	0.542245i	0.953398	−	0.301714i	$-0.0975588\pi$
$607$	4.98286e12	+	1.81361e12i	1.48981	+	0.542245i	0.536408	+	0.843959i	$0.319781\pi$
$608$	2.00226e10	+	7.28763e9i	0.00594230	+	0.00216282i
$609$		0			0
$610$	−2.14539e11	+	1.21671e12i	−0.0627367	+	0.355797i
$611$	−1.78019e12	−	3.08339e12i	−0.516752	−	0.895040i
$612$		0			0
$613$	1.90893e12	−	3.30636e12i	0.546031	−	0.945753i	−0.452511	−	0.891759i	$-0.649472\pi$
$613$	1.90893e12	−	3.30636e12i	0.546031	−	0.945753i	0.998541	−	0.0539938i	$-0.0171951\pi$
$614$	−3.69032e11	−	3.09655e11i	−0.104787	−	0.0879266i
$615$		0			0
$616$	1.99998e11	+	1.13424e12i	0.0559645	+	0.317390i
$617$	2.96152e12	−	2.48501e12i	0.822681	−	0.690312i	−0.130917	−	0.991393i	$-0.541792\pi$
$617$	2.96152e12	−	2.48501e12i	0.822681	−	0.690312i	0.953598	+	0.301082i	$0.0973477\pi$
$618$		0			0
$619$	−2.79994e12	+	1.01910e12i	−0.766552	+	0.279002i	−0.695553	−	0.718474i	$-0.744841\pi$
$619$	−2.79994e12	+	1.01910e12i	−0.766552	+	0.279002i	−0.0709983	+	0.997476i	$0.522618\pi$
$620$	1.16716e13			3.17226
$621$		0			0
$622$	−1.43621e12			−0.384734
$623$	−3.30598e12	+	1.20328e12i	−0.879233	+	0.320015i
$624$		0			0
$625$	9.46092e12	−	7.93865e12i	2.48012	−	2.08107i
$626$	1.45451e11	+	8.24896e11i	0.0378559	+	0.214691i
$627$		0			0
$628$	4.22327e12	+	3.54374e12i	1.08350	+	0.909167i
$629$	−3.11044e11	+	5.38744e11i	−0.0792307	+	0.137232i
$630$		0			0
$631$	2.17173e12	+	3.76155e12i	0.545349	+	0.944572i	0.998585	+	0.0531818i	$0.0169363\pi$
$631$	2.17173e12	+	3.76155e12i	0.545349	+	0.944572i	−0.453236	+	0.891391i	$0.649730\pi$
$632$	7.18197e10	−	4.07310e11i	0.0179068	−	0.101554i
$633$		0			0
$634$	1.91880e11	+	6.98387e10i	0.0471660	+	0.0171670i
$635$	−1.07462e13	−	3.91131e12i	−2.62286	−	0.954642i
$636$		0			0
$637$	−1.68700e11	+	9.56747e11i	−0.0405965	+	0.230234i
$638$	4.97817e11	+	8.62245e11i	0.118953	+	0.206033i
$639$		0			0
$640$	3.08385e12	−	5.34138e12i	0.726579	−	1.25847i
$641$	5.42976e12	+	4.55611e12i	1.27034	+	1.06594i	0.994500	+	0.104736i	$0.0333998\pi$
$641$	5.42976e12	+	4.55611e12i	1.27034	+	1.06594i	0.275838	+	0.961204i	$0.411045\pi$
$642$		0			0
$643$	−8.39702e11	−	4.76219e12i	−0.193721	−	1.09864i	−0.914229	−	0.405198i	$-0.867203\pi$
$643$	−8.39702e11	−	4.76219e12i	−0.193721	−	1.09864i	0.720508	−	0.693446i	$-0.243908\pi$
$644$	4.77241e11	−	4.00453e11i	0.109333	−	0.0917413i
$645$		0			0
$646$	2.97472e9	−	1.08271e9i	0.000672047	−	0.000244605i
$647$	1.79486e12			0.402681			0.201341	−	0.979521i	$-0.435470\pi$
$647$	1.79486e12			0.402681			0.201341	+	0.979521i	$0.435470\pi$
$648$		0			0
$649$	3.83460e11			0.0848435
$650$	−2.88452e12	+	1.04988e12i	−0.633816	+	0.230690i
$651$		0			0
$652$	−4.23415e12	+	3.55288e12i	−0.917598	+	0.769956i
$653$	1.27859e12	+	7.25124e12i	0.275183	+	1.56064i	0.738380	+	0.674385i	$0.235591\pi$
$653$	1.27859e12	+	7.25124e12i	0.275183	+	1.56064i	−0.463197	+	0.886255i	$0.653298\pi$
$654$		0			0
$655$	8.18116e12	+	6.86481e12i	1.73672	+	1.45728i
$656$	−3.77142e12	+	6.53229e12i	−0.795129	+	1.37720i
$657$		0			0
$658$	−4.88487e11	−	8.46084e11i	−0.101587	−	0.175953i
$659$	−1.31090e12	+	7.43447e12i	−0.270760	+	1.53556i	0.481356	+	0.876525i	$0.340144\pi$
$659$	−1.31090e12	+	7.43447e12i	−0.270760	+	1.53556i	−0.752116	+	0.659031i	$0.770967\pi$
$660$		0			0
$661$	3.45147e12	+	1.25623e12i	0.703230	+	0.255955i	0.668790	−	0.743452i	$-0.266813\pi$
$661$	3.45147e12	+	1.25623e12i	0.703230	+	0.255955i	0.0344409	+	0.999407i	$0.489035\pi$
$662$	−3.44083e10	−	1.25236e10i	−0.00696309	−	0.00253436i
$663$		0			0
$664$	1.63952e11	−	9.29815e11i	0.0327310	−	0.185627i
$665$	5.47006e10	+	9.47442e10i	0.0108466	+	0.0187869i
$666$		0			0
$667$	5.51632e11	−	9.55454e11i	0.107915	−	0.186915i
$668$	7.18586e11	+	6.02965e11i	0.139632	+	0.117165i
$669$		0			0
$670$	5.54813e11	+	3.14650e12i	0.106368	+	0.603242i
$671$	−2.48880e12	+	2.08835e12i	−0.473957	+	0.397697i
$672$		0			0
$673$	−5.33640e12	+	1.94229e12i	−1.00272	+	0.364961i	−0.790634	−	0.612289i	$-0.790249\pi$
$673$	−5.33640e12	+	1.94229e12i	−1.00272	+	0.364961i	−0.212089	+	0.977250i	$0.568027\pi$
$674$	2.25777e12			0.421416
$675$		0			0
$676$	−2.24012e12			−0.412583
$677$	3.38188e12	−	1.23091e12i	0.618742	−	0.225204i	−0.0135819	−	0.999908i	$-0.504323\pi$
$677$	3.38188e12	−	1.23091e12i	0.618742	−	0.225204i	0.632324	+	0.774704i	$0.282101\pi$
$678$		0			0
$679$	−3.01185e12	+	2.52724e12i	−0.543775	+	0.456282i
$680$	−2.46696e11	−	1.39908e12i	−0.0442457	−	0.250930i
$681$		0			0
$682$	−1.14192e12	−	9.58187e11i	−0.202119	−	0.169598i
$683$	4.82520e12	−	8.35750e12i	0.848443	−	1.46955i	−0.0341547	−	0.999417i	$-0.510874\pi$
$683$	4.82520e12	−	8.35750e12i	0.848443	−	1.46955i	0.882597	−	0.470129i	$-0.155793\pi$
$684$		0			0
$685$	−6.89837e11	−	1.19483e12i	−0.119712	−	0.207348i
$686$	1.90709e11	−	1.08156e12i	0.0328785	−	0.186463i
$687$		0			0
$688$	2.09773e12	+	7.63512e11i	0.356946	+	0.129918i
$689$	1.78811e12	+	6.50819e11i	0.302279	+	0.110021i
$690$		0			0
$691$	−9.70005e10	+	5.50117e11i	−0.0161854	+	0.0917918i	−0.991830	−	0.127564i	$-0.959284\pi$
$691$	−9.70005e10	+	5.50117e11i	−0.0161854	+	0.0917918i	0.975645	+	0.219355i	$0.0703954\pi$
$692$	1.85064e12	+	3.20541e12i	0.306793	+	0.531381i
$693$		0			0
$694$	1.10575e12	−	1.91522e12i	0.180942	−	0.313402i
$695$	−8.49016e11	−	7.12409e11i	−0.138033	−	0.115824i
$696$		0			0
$697$	6.35025e11	+	3.60141e12i	0.101916	+	0.577996i
$698$	−3.78201e11	+	3.17348e11i	−0.0603078	+	0.0506042i
$699$		0			0
$700$	1.62970e13	−	5.93161e12i	2.56546	−	0.933752i
$701$	−1.09556e13			−1.71358			−0.856790	−	0.515665i	$-0.827545\pi$
$701$	−1.09556e13			−1.71358			−0.856790	+	0.515665i	$0.827545\pi$
$702$		0			0
$703$	3.35996e10			0.00518843
$704$	3.14606e12	−	1.14507e12i	0.482714	−	0.175694i
$705$		0			0
$706$	4.32432e11	−	3.62853e11i	0.0655083	−	0.0549680i
$707$	5.35509e11	+	3.03702e12i	0.0806082	+	0.457152i
$708$		0			0
$709$	−6.60607e12	−	5.54315e12i	−0.981828	−	0.823851i	0.00253622	−	0.999997i	$-0.499193\pi$
$709$	−6.60607e12	−	5.54315e12i	−0.981828	−	0.823851i	−0.984364	+	0.176145i	$0.943637\pi$
$710$	−8.25797e11	+	1.43032e12i	−0.121958	+	0.211238i
$711$		0			0
$712$	−1.23378e12	−	2.13696e12i	−0.179919	−	0.311629i
$713$	−2.86835e11	+	1.62672e12i	−0.0415651	+	0.235727i
$714$		0			0
$715$	−1.04823e13	−	3.81523e12i	−1.49995	−	0.545938i
$716$	−5.02925e12	−	1.83050e12i	−0.715145	−	0.260292i
$717$		0			0
$718$	2.67835e11	−	1.51897e12i	0.0376103	−	0.213299i
$719$	2.35039e11	+	4.07099e11i	0.0327989	+	0.0568094i	0.881959	−	0.471326i	$-0.156225\pi$
$719$	2.35039e11	+	4.07099e11i	0.0327989	+	0.0568094i	−0.849160	+	0.528136i	$0.822891\pi$
$720$		0			0
$721$	−1.06252e11	+	1.84034e11i	−0.0146429	+	0.0253623i
$722$	1.20365e12	+	1.00999e12i	0.164848	+	0.138324i
$723$		0			0
$724$	−9.12401e11	−	5.17449e12i	−0.123413	−	0.699912i
$725$	2.35272e13	−	1.97417e13i	3.16264	−	2.65377i
$726$		0			0
$727$	5.70754e12	−	2.07737e12i	0.757782	−	0.275810i	0.0659051	−	0.997826i	$-0.479007\pi$
$727$	5.70754e12	−	2.07737e12i	0.757782	−	0.275810i	0.691876	+	0.722016i	$0.256784\pi$
$728$	−4.16995e12			−0.550224
$729$		0			0
$730$	−4.30431e11			−0.0560984
$731$	1.01704e12	−	3.70171e11i	0.131737	−	0.0479484i
$732$		0			0
$733$	−2.95176e12	+	2.47682e12i	−0.377670	+	0.316903i	−0.811787	−	0.583954i	$-0.801505\pi$
$733$	−2.95176e12	+	2.47682e12i	−0.377670	+	0.316903i	0.434117	+	0.900857i	$0.357061\pi$
$734$	−1.40110e11	−	7.94603e11i	−0.0178171	−	0.101046i
$735$		0			0
$736$	5.06058e11	+	4.24633e11i	0.0635696	+	0.0533413i
$737$	−4.20094e12	+	7.27625e12i	−0.524497	+	0.908456i
$738$		0			0
$739$	2.14964e12	+	3.72329e12i	0.265135	+	0.459227i	0.967599	−	0.252492i	$-0.0812502\pi$
$739$	2.14964e12	+	3.72329e12i	0.265135	+	0.459227i	−0.702464	+	0.711719i	$0.747917\pi$
$740$	1.27816e12	−	7.24881e12i	0.156690	−	0.888636i
$741$		0			0
$742$	4.90659e11	+	1.78585e11i	0.0594240	+	0.0216286i
$743$	9.27719e12	+	3.37662e12i	1.11678	+	0.406474i	0.833475	−	0.552557i	$-0.186348\pi$
$743$	9.27719e12	+	3.37662e12i	1.11678	+	0.406474i	0.283303	+	0.959031i	$0.408570\pi$
$744$		0			0
$745$	5.54981e11	−	3.14745e12i	0.0660047	−	0.374331i
$746$	−2.43388e11	−	4.21560e11i	−0.0287723	−	0.0498350i
$747$		0			0
$748$	9.11824e11	−	1.57933e12i	0.106501	−	0.184465i
$749$	7.62636e12	+	6.39927e12i	0.885419	+	0.742955i
$750$		0			0
$751$	1.33876e12	+	7.59249e12i	0.153576	+	0.870972i	0.960076	+	0.279739i	$0.0902478\pi$
$751$	1.33876e12	+	7.59249e12i	0.153576	+	0.870972i	−0.806500	+	0.591234i	$0.798641\pi$
$752$	−5.00711e12	+	4.20146e12i	−0.570961	+	0.479093i
$753$		0			0
$754$	−3.38736e12	+	1.23290e12i	−0.381672	+	0.138917i
$755$	−1.63570e13			−1.83207
$756$		0			0
$757$	8.97916e11			0.0993812			0.0496906	−	0.998765i	$-0.484176\pi$
$757$	8.97916e11			0.0993812			0.0496906	+	0.998765i	$0.484176\pi$
$758$	−2.57625e12	+	9.37678e11i	−0.283450	+	0.103167i
$759$		0			0
$760$	−5.87798e10	+	4.93221e10i	−0.00639097	+	0.00536266i
$761$	1.06405e12	+	6.03456e12i	0.115009	+	0.652250i	0.986746	+	0.162275i	$0.0518831\pi$
$761$	1.06405e12	+	6.03456e12i	0.115009	+	0.652250i	−0.871736	+	0.489975i	$0.837006\pi$
$762$		0			0
$763$	−8.46284e12	−	7.10116e12i	−0.903973	−	0.758524i
$764$	5.01580e12	−	8.68763e12i	0.532624	−	0.922531i
$765$		0			0
$766$	1.33317e12	+	2.30912e12i	0.139912	+	0.242335i
$767$	−2.41082e11	+	1.36725e12i	−0.0251528	+	0.142649i
$768$		0			0
$769$	2.97226e12	+	1.08182e12i	0.306492	+	0.111554i	0.490687	−	0.871336i	$-0.336746\pi$
$769$	2.97226e12	+	1.08182e12i	0.306492	+	0.111554i	−0.184196	+	0.982890i	$0.558968\pi$
$770$	−2.87634e12	−	1.04690e12i	−0.294871	−	0.107324i
$771$		0			0
$772$	1.67887e12	−	9.52133e12i	0.170113	−	0.964761i
$773$	−7.46155e12	−	1.29238e13i	−0.751660	−	1.30191i	−0.947018	−	0.321181i	$-0.895920\pi$
$773$	−7.46155e12	−	1.29238e13i	−0.751660	−	1.30191i	0.195358	−	0.980732i	$-0.437413\pi$
$774$		0			0
$775$	−2.29916e13	+	3.98226e13i	−2.28935	+	3.96526i
$776$	−2.11245e12	−	1.77255e12i	−0.209126	−	0.175478i
$777$		0			0
$778$	−2.99715e11	−	1.69977e12i	−0.0293292	−	0.166334i
$779$	1.51307e11	−	1.26961e11i	0.0147211	−	0.0123524i
$780$		0			0
$781$	−4.08122e12	+	1.48544e12i	−0.392518	+	0.142865i
$782$	9.81457e10			0.00938515
$783$		0			0
$784$	1.78353e12			0.168600
$785$	−2.82052e13	+	1.02659e13i	−2.65104	+	0.964899i
$786$		0			0
$787$	−2.59224e12	+	2.17515e12i	−0.240874	+	0.202117i	−0.755231	−	0.655459i	$-0.772475\pi$
$787$	−2.59224e12	+	2.17515e12i	−0.240874	+	0.202117i	0.514357	+	0.857576i	$0.328031\pi$
$788$	1.32600e12	+	7.52011e12i	0.122511	+	0.694795i
$789$		0			0
$790$	8.42028e11	+	7.06545e11i	0.0769138	+	0.0645384i
$791$	3.00732e12	−	5.20883e12i	0.273140	−	0.473092i
$792$		0			0
$793$	−5.88141e12	−	1.01869e13i	−0.528143	−	0.914771i
$794$	−3.00891e11	+	1.70644e12i	−0.0268669	+	0.152370i
$795$		0			0
$796$	1.71099e13	+	6.22751e12i	1.51057	+	0.549801i
$797$	−9.10535e12	−	3.31408e12i	−0.799345	−	0.290938i	−0.0901298	−	0.995930i	$-0.528728\pi$
$797$	−9.10535e12	−	3.31408e12i	−0.799345	−	0.290938i	−0.709215	+	0.704992i	$0.750950\pi$
$798$		0			0
$799$	−5.50287e11	+	3.12083e12i	−0.0477671	+	0.270901i
$800$	9.19503e12	+	1.59263e13i	0.793685	+	1.37470i
$801$		0			0
$802$	1.84450e12	−	3.19477e12i	0.157432	−	0.272681i
$803$	−8.67078e11	−	7.27564e11i	−0.0735932	−	0.0617521i
$804$		0			0
$805$	5.88984e11	+	3.34029e12i	0.0494336	+	0.280352i
$806$	4.13439e12	−	3.46917e12i	0.345068	−	0.289546i
$807$		0			0
$808$	−2.03252e12	+	7.39777e11i	−0.167758	+	0.0610590i
$809$	−9.47854e12			−0.777988			−0.388994	−	0.921240i	$-0.627177\pi$
$809$	−9.47854e12			−0.777988			−0.388994	+	0.921240i	$0.627177\pi$
$810$		0			0
$811$	−1.64633e12			−0.133636			−0.0668180	−	0.997765i	$-0.521285\pi$
$811$	−1.64633e12			−0.133636			−0.0668180	+	0.997765i	$0.521285\pi$
$812$	1.91379e13	−	6.96564e12i	1.54487	−	0.562288i
$813$		0			0
$814$	−7.20147e11	+	6.04275e11i	−0.0574925	+	0.0482419i
$815$	−5.22555e12	−	2.96356e13i	−0.414880	−	2.35290i
$816$		0			0
$817$	−4.47804e10	−	3.75752e10i	−0.00351632	−	0.00295054i
$818$	3.12247e11	−	5.40828e11i	0.0243842	−	0.0422347i
$819$		0			0
$820$	−2.16349e13	−	3.74727e13i	−1.67106	−	2.89436i
$821$	−3.35744e11	+	1.90410e12i	−0.0257907	+	0.146267i	−0.994984	−	0.100035i	$-0.968104\pi$
$821$	−3.35744e11	+	1.90410e12i	−0.0257907	+	0.146267i	0.969193	+	0.246302i	$0.0792155\pi$
$822$		0			0
$823$	7.37472e12	+	2.68418e12i	0.560333	+	0.203945i	0.606632	−	0.794983i	$-0.292520\pi$
$823$	7.37472e12	+	2.68418e12i	0.560333	+	0.203945i	−0.0462984	+	0.998928i	$0.514743\pi$
$824$	−1.40057e11	−	5.09766e10i	−0.0105836	−	0.00385211i
$825$		0			0
$826$	−6.61532e10	+	3.75173e11i	−0.00494471	+	0.0280428i
$827$	−5.40014e12	−	9.35331e12i	−0.401449	−	0.695329i	0.592452	−	0.805605i	$-0.298160\pi$
$827$	−5.40014e12	−	9.35331e12i	−0.401449	−	0.695329i	−0.993901	+	0.110276i	$0.964827\pi$
$828$		0			0
$829$	5.65271e12	−	9.79077e12i	0.415682	−	0.719982i	−0.579818	−	0.814746i	$-0.696876\pi$
$829$	5.65271e12	−	9.79077e12i	0.415682	−	0.719982i	0.995500	+	0.0947641i	$0.0302097\pi$
$830$	1.92220e12	+	1.61292e12i	0.140588	+	0.117967i
$831$		0			0
$832$	2.10488e12	+	1.19374e13i	0.152290	+	0.863681i
$833$	6.62401e11	−	5.55821e11i	0.0476671	−	0.0399974i
$834$		0			0
$835$	−4.79910e12	+	1.74673e12i	−0.341642	+	0.124347i
$836$	−9.84973e10			−0.00697423
$837$		0			0
$838$	−1.71177e12			−0.119908
$839$	1.33072e13	−	4.84341e12i	0.927164	−	0.337460i	0.166079	−	0.986112i	$-0.446889\pi$
$839$	1.33072e13	−	4.84341e12i	0.927164	−	0.337460i	0.761085	+	0.648652i	$0.224667\pi$
$840$		0			0
$841$	1.65155e13	−	1.38581e13i	1.13844	−	0.955262i
$842$	−9.76284e11	−	5.53678e12i	−0.0669378	−	0.379623i
$843$		0			0
$844$	7.87163e12	+	6.60508e12i	0.533978	+	0.448061i
$845$	6.09805e12	−	1.05621e13i	0.411468	−	0.712683i
$846$		0			0
$847$	4.16357e12	+	7.21152e12i	0.277965	+	0.481450i
$848$	6.06616e11	−	3.44029e12i	0.0402840	−	0.228462i
$849$		0			0
$850$	2.56741e12	+	9.34460e11i	0.168698	+	0.0614010i
$851$	9.78885e11	+	3.56285e11i	0.0639806	+	0.0232871i
$852$		0			0
$853$	1.79900e12	−	1.02027e13i	0.116349	−	0.659846i	−0.869725	−	0.493537i	$-0.835704\pi$
$853$	1.79900e12	−	1.02027e13i	0.116349	−	0.659846i	0.986074	−	0.166309i	$-0.0531850\pi$
$854$	−1.61386e12	−	2.79529e12i	−0.103826	−	0.179832i
$855$		0			0
$856$	−3.49129e12	+	6.04709e12i	−0.222256	+	0.384959i
$857$	−1.76054e13	−	1.47727e13i	−1.11489	−	0.935503i	−0.116554	−	0.993184i	$-0.537185\pi$
$857$	−1.76054e13	−	1.47727e13i	−1.11489	−	0.935503i	−0.998335	+	0.0576815i	$0.981629\pi$
$858$		0			0
$859$	5.53751e11	+	3.14048e12i	0.0347012	+	0.196800i	0.997230	−	0.0743789i	$-0.0236974\pi$
$859$	5.53751e11	+	3.14048e12i	0.0347012	+	0.196800i	−0.962529	+	0.271179i	$0.912586\pi$
$860$	−9.80998e12	+	8.23155e12i	−0.611540	+	0.513143i
$861$		0			0
$862$	−1.33016e11	+	4.84140e10i	−0.00820583	+	0.00298668i
$863$	1.49235e13			0.915844			0.457922	−	0.888992i	$-0.348594\pi$
$863$	1.49235e13			0.915844			0.457922	+	0.888992i	$0.348594\pi$
$864$		0			0
$865$	−2.01513e13			−1.22385
$866$	6.27740e12	−	2.28479e12i	0.379271	−	0.138043i
$867$		0			0
$868$	−2.33585e13	+	1.96001e13i	−1.39671	+	1.17198i
$869$	5.01930e11	+	2.84659e12i	0.0298576	+	0.169331i
$870$		0			0
$871$	−2.33027e13	−	1.95533e13i	−1.37191	−	1.15117i
$872$	3.87422e12	−	6.71035e12i	0.226913	−	0.393026i
$873$		0			0
$874$	−2.65048e9	−	4.59077e9i	−0.000153647	−	0.000266124i
$875$	−1.01342e13	+	5.74739e13i	−0.584458	+	3.31462i
$876$		0			0
$877$	−1.51021e13	−	5.49673e12i	−0.862066	−	0.313766i	−0.127116	−	0.991888i	$-0.540572\pi$
$877$	−1.51021e13	−	5.49673e12i	−0.862066	−	0.313766i	−0.734950	+	0.678121i	$0.762794\pi$
$878$	3.39647e12	+	1.23621e12i	0.192887	+	0.0702050i
$879$		0			0
$880$	−3.55610e12	+	2.01677e13i	−0.199895	+	1.13366i
$881$	1.97579e11	+	3.42217e11i	0.0110497	+	0.0191386i	0.871497	−	0.490400i	$-0.163149\pi$
$881$	1.97579e11	+	3.42217e11i	0.0110497	+	0.0191386i	−0.860448	+	0.509539i	$0.829816\pi$
$882$		0			0
$883$	−1.51712e12	+	2.62772e12i	−0.0839839	+	0.145464i	−0.904958	−	0.425501i	$-0.860098\pi$
$883$	−1.51712e12	+	2.62772e12i	−0.0839839	+	0.145464i	0.820974	+	0.570966i	$0.193431\pi$
$884$	5.05790e12	+	4.24408e12i	0.278571	+	0.233748i
$885$		0			0
$886$	9.97360e11	+	5.65631e12i	0.0543751	+	0.308377i
$887$	1.15421e13	−	9.68498e12i	0.626079	−	0.525343i	−0.273629	−	0.961835i	$-0.588224\pi$
$887$	1.15421e13	−	9.68498e12i	0.626079	−	0.525343i	0.899708	+	0.436493i	$0.143780\pi$
$888$		0			0
$889$	2.80749e13	−	1.02184e13i	1.50751	−	0.548688i
$890$	6.55791e12			0.350357
$891$		0			0
$892$	6.55237e12			0.346542
$893$	1.60838e11	−	5.85402e10i	0.00846363	−	0.00308051i
$894$		0			0
$895$	2.23213e13	−	1.87298e13i	1.16283	−	0.975732i
$896$	2.79804e12	+	1.58685e13i	0.145033	+	0.822525i
$897$		0			0
$898$	2.96828e12	+	2.49068e12i	0.152321	+	0.127813i
$899$	−2.69996e13	+	4.67647e13i	−1.37860	+	2.38781i
$900$		0			0
$901$	−8.46838e11	−	1.46677e12i	−0.0428093	−	0.0741480i
$902$	−9.59636e11	+	5.44237e12i	−0.0482700	+	0.273753i
$903$		0			0
$904$	3.96413e12	+	1.44282e12i	0.197419	+	0.0718548i
$905$	2.68813e13	+	9.78401e12i	1.33209	+	0.484840i
$906$		0			0
$907$	−2.62360e10	+	1.48791e11i	−0.00128725	+	0.00730038i	−0.985445	−	0.169997i	$-0.945624\pi$
$907$	−2.62360e10	+	1.48791e11i	−0.00128725	+	0.00730038i	0.984157	+	0.177297i	$0.0567354\pi$
$908$	−1.98417e12	−	3.43667e12i	−0.0968705	−	0.167785i
$909$		0			0
$910$	5.54114e12	−	9.59754e12i	0.267863	−	0.463953i
$911$	1.55070e13	+	1.30120e13i	0.745927	+	0.625907i	0.934422	−	0.356167i	$-0.115917\pi$
$911$	1.55070e13	+	1.30120e13i	0.745927	+	0.625907i	−0.188495	+	0.982074i	$0.560361\pi$
$912$		0			0
$913$	1.14582e12	+	6.49825e12i	0.0545753	+	0.309512i
$914$	−4.52685e12	+	3.79848e12i	−0.214555	+	0.180033i
$915$		0			0
$916$	2.62082e12	−	9.53899e11i	0.123000	−	0.0447685i
$917$	−2.79012e13			−1.30305
$918$		0			0
$919$	2.75145e13			1.27245			0.636226	−	0.771503i	$-0.280495\pi$
$919$	2.75145e13			1.27245			0.636226	+	0.771503i	$0.280495\pi$
$920$	−2.23548e12	+	8.13649e11i	−0.102879	+	0.0374448i
$921$		0			0
$922$	−5.20928e12	+	4.37110e12i	−0.237404	+	0.199206i
$923$	−2.73054e12	−	1.54857e13i	−0.123835	−	0.702300i
$924$		0			0
$925$	2.22145e13	+	1.86402e13i	0.997699	+	0.837169i
$926$	−4.36710e11	+	7.56404e11i	−0.0195184	+	0.0338068i
$927$		0			0
$928$	1.07980e13	+	1.87026e13i	0.477943	+	0.827821i
$929$	6.36048e12	−	3.60721e13i	0.280168	−	1.58891i	−0.441882	−	0.897073i	$-0.645689\pi$
$929$	6.36048e12	−	3.60721e13i	0.280168	−	1.58891i	0.722051	−	0.691840i	$-0.243200\pi$
$930$		0			0
$931$	−4.38870e10	−	1.59736e10i	−0.00191453	−	0.000696832i
$932$	9.33929e12	+	3.39922e12i	0.405455	+	0.147573i
$933$		0			0
$934$	2.52513e11	−	1.43207e12i	0.0108573	−	0.0615750i
$935$	4.96433e12	+	8.59847e12i	0.212426	+	0.367933i
$936$		0			0
$937$	−3.87556e12	+	6.71267e12i	−0.164251	+	0.284490i	−0.936389	−	0.350964i	$-0.885854\pi$
$937$	−3.87556e12	+	6.71267e12i	−0.164251	+	0.284490i	0.772138	+	0.635454i	$0.219187\pi$
$938$	−6.39428e12	−	5.36544e12i	−0.269699	−	0.226304i
$939$		0			0
$940$	−6.51108e12	−	3.69261e13i	−0.272005	−	1.54262i
$941$	1.41631e13	−	1.18843e13i	0.588852	−	0.494105i	−0.298989	−	0.954257i	$-0.596649\pi$
$941$	1.41631e13	−	1.18843e13i	0.588852	−	0.494105i	0.887840	+	0.460151i	$0.152205\pi$
$942$		0			0
$943$	5.75441e12	−	2.09443e12i	0.236973	−	0.0862510i
$944$	2.54877e12			0.104462
$945$		0			0
$946$	1.63556e12			0.0663981
$947$	−1.74549e13	+	6.35307e12i	−0.705250	+	0.256690i	−0.669651	−	0.742676i	$-0.733556\pi$
$947$	−1.74549e13	+	6.35307e12i	−0.705250	+	0.256690i	−0.0355992	+	0.999366i	$0.511334\pi$
$948$		0			0
$949$	3.13930e12	−	2.63419e12i	0.125642	−	0.105426i
$950$	−2.56249e10	−	1.45326e11i	−0.00102072	−	0.00578878i
$951$		0			0
$952$	2.84319e12	+	2.38572e12i	0.112186	+	0.0941355i
$953$	1.15888e13	−	2.00724e13i	0.455114	−	0.788281i	−0.543580	−	0.839357i	$-0.682932\pi$
$953$	1.15888e13	−	2.00724e13i	0.455114	−	0.788281i	0.998695	+	0.0510757i	$0.0162650\pi$
$954$		0			0
$955$	2.73080e13	+	4.72988e13i	1.06237	+	1.84007i
$956$	1.98984e12	−	1.12849e13i	0.0770473	−	0.436957i
$957$		0			0
$958$	7.83401e12	+	2.85135e12i	0.300496	+	0.109372i
$959$	3.38707e12	+	1.23279e12i	0.129312	+	0.0470658i
$960$		0			0
$961$	9.44793e12	−	5.35819e13i	0.357340	−	2.02657i
$962$	−1.70181e12	−	2.94763e12i	−0.0640655	−	0.110965i
$963$		0			0
$964$	1.77458e13	−	3.07366e13i	0.661834	−	1.14633i
$965$	4.03227e13	+	3.38347e13i	1.49684	+	1.25600i
$966$		0			0
$967$	4.54504e12	+	2.57762e13i	0.167155	+	0.947981i	0.946815	+	0.321778i	$0.104281\pi$
$967$	4.54504e12	+	2.57762e13i	0.167155	+	0.947981i	−0.779660	+	0.626203i	$0.784608\pi$
$968$	−4.47407e12	+	3.75419e12i	−0.163781	+	0.137428i
$969$		0			0
$970$	6.88678e12	−	2.50658e12i	0.249772	−	0.0909096i
$971$	−2.00568e13			−0.724060			−0.362030	−	0.932166i	$-0.617916\pi$
$971$	−2.00568e13			−0.724060			−0.362030	+	0.932166i	$0.617916\pi$
$972$		0			0
$973$	2.89550e12			0.103566
$974$	6.49726e12	−	2.36481e12i	0.231321	−	0.0841940i
$975$		0			0
$976$	−1.65425e13	+	1.38808e13i	−0.583548	+	0.489655i
$977$	1.72171e12	+	9.76430e12i	0.0604553	+	0.342859i	1.00000		0.000432585i	$0.000137696\pi$
$977$	1.72171e12	+	9.76430e12i	0.0604553	+	0.342859i	−0.939545	+	0.342427i	$0.888751\pi$
$978$		0			0
$979$	1.32105e13	+	1.10849e13i	0.459619	+	0.385666i
$980$	−5.11565e12	+	8.86056e12i	−0.177167	+	0.306863i
$981$		0			0
$982$	1.03937e12	+	1.80025e12i	0.0356673	+	0.0617776i
$983$	6.11838e12	−	3.46991e13i	0.209000	−	1.18530i	−0.682020	−	0.731333i	$-0.738899\pi$
$983$	6.11838e12	−	3.46991e13i	0.209000	−	1.18530i	0.891020	−	0.453964i	$-0.149990\pi$
$984$		0			0
$985$	−3.90668e13	−	1.42192e13i	−1.32235	−	0.481295i
$986$	3.01497e12	+	1.09736e12i	0.101587	+	0.0369745i
$987$		0			0
$988$	6.19256e10	−	3.51197e11i	0.00206759	−	0.0117259i
$989$	−9.06181e11	−	1.56955e12i	−0.0301184	−	0.0521666i
$990$		0			0
$991$	2.12032e13	−	3.67250e13i	0.698345	−	1.20957i	−0.270696	−	0.962665i	$-0.587254\pi$
$991$	2.12032e13	−	3.67250e13i	0.698345	−	1.20957i	0.969040	−	0.246903i	$-0.0794130\pi$
$992$	−2.47690e13	−	2.07836e13i	−0.812093	−	0.681427i
$993$		0			0
$994$	−7.49264e11	−	4.24928e12i	−0.0243442	−	0.138063i
$995$	−7.59392e13	+	6.37206e13i	−2.45619	+	2.06099i
$996$		0			0
$997$	−3.70869e13	+	1.34985e13i	−1.18875	+	0.432671i	−0.859286	−	0.511495i	$-0.829092\pi$
$997$	−3.70869e13	+	1.34985e13i	−1.18875	+	0.432671i	−0.329469	+	0.944167i	$0.606870\pi$
$998$	−4.16737e12			−0.132976
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.19.14		156
3.2	odd	2		27.10.e.a.7.13	yes	156
27.4	even	9	inner	81.10.e.a.64.14		156
27.23	odd	18		27.10.e.a.4.13	✓	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.4.13	✓	156	27.23	odd	18
27.10.e.a.7.13	yes	156	3.2	odd	2
81.10.e.a.19.14		156	1.1	even	1	trivial
81.10.e.a.64.14		156	27.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(4.57613 - 1.66557i) q^{2} +(-374.048 + 313.863i) q^{4} +(-461.629 - 2618.03i) q^{5} +(5320.32 + 4464.28i) q^{7} +(-2435.60 + 4218.58i) q^{8} +(-6472.99 - 11211.5i) q^{10} +(5911.61 - 33526.4i) q^{11} +(115823. + 42156.3i) q^{13} +(31782.0 + 11567.7i) q^{14} +(39293.1 - 222842. i) q^{16} +(-54853.3 - 95008.6i) q^{17} +(-2962.69 + 5131.52i) q^{19} +(994374. + 834379. i) q^{20} +(-28788.4 - 163267. i) q^{22} +(-140728. + 118085. i) q^{23} +(-4.80563e6 + 1.74910e6i) q^{25} +600238. q^{26} -3.39123e6 q^{28} +(-5.64337e6 + 2.05402e6i) q^{29} +(6.88793e6 - 5.77966e6i) q^{31} +(-624438. - 3.54137e6i) q^{32} +(-409259. - 343409. i) q^{34} +(9.23159e6 - 1.59896e7i) q^{35} +(-2.83524e6 - 4.91077e6i) q^{37} +(-5010.70 + 28417.1i) q^{38} +(1.21687e7 + 4.42905e6i) q^{40} +(-3.13238e7 - 1.14009e7i) q^{41} +(-1.71312e6 + 9.71560e6i) q^{43} +(8.31149e6 + 1.43959e7i) q^{44} +(-447310. + 774764. i) q^{46} +(-2.21279e7 - 1.85675e7i) q^{47} +(1.36869e6 + 7.76222e6i) q^{49} +(-1.90779e7 + 1.60083e7i) q^{50} +(-5.65549e7 + 2.05843e7i) q^{52} +1.54382e7 q^{53} -9.05020e7 q^{55} +(-3.17911e7 + 1.15710e7i) q^{56} +(-2.24036e7 + 1.87989e7i) q^{58} +(1.95594e6 + 1.10927e7i) q^{59} +(-7.31062e7 - 6.13434e7i) q^{61} +(2.18936e7 - 3.79208e7i) q^{62} +(4.91718e7 + 8.51680e7i) q^{64} +(5.68989e7 - 3.22690e8i) q^{65} +(-2.31914e8 - 8.44099e7i) q^{67} +(5.03375e7 + 1.83213e7i) q^{68} +(1.56131e7 - 8.85462e7i) q^{70} +(-6.37879e7 - 1.10484e8i) q^{71} +(1.66241e7 - 2.87938e7i) q^{73} +(-2.11537e7 - 1.77500e7i) q^{74} +(-502411. - 2.84931e6i) q^{76} +(1.81123e8 - 1.51980e8i) q^{77} +(-7.97854e7 + 2.90395e7i) q^{79} -6.01546e8 q^{80} -1.62331e8 q^{82} +(-1.82136e8 + 6.62920e7i) q^{83} +(-2.23413e8 + 1.87466e8i) q^{85} +(8.34259e6 + 4.73132e7i) q^{86} +(1.27036e8 + 1.06596e8i) q^{88} +(-2.53280e8 + 4.38693e8i) q^{89} +(4.28020e8 + 7.41353e8i) q^{91} +(1.55765e7 - 8.83388e7i) q^{92} +(-1.32186e8 - 4.81117e7i) q^{94} +(1.48021e7 + 5.38753e6i) q^{95} +(-9.83028e7 + 5.57503e8i) q^{97} +(1.91919e7 + 3.32413e7i) 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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