LMFDB - Embedded newform 81.10.e.a.10.13

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			10.13
Character	$\chi$	$=$	81.10
Dual form			81.10.e.a.73.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.622466 + 3.53018i) q^{2} +(469.048 - 170.719i) q^{4} +(-22.7101 - 19.0560i) q^{5} +(10919.6 + 3974.40i) q^{7} +(1812.30 + 3139.00i) q^{8} +(53.1349 - 92.0324i) q^{10} +(57583.8 - 48318.5i) q^{11} +(-13317.6 + 75527.7i) q^{13} +(-7233.28 + 41021.9i) q^{14} +(185821. - 155922. i) q^{16} +(-271792. + 470757. i) q^{17} +(21415.8 + 37093.3i) q^{19} +(-13905.3 - 5061.13i) q^{20} +(206417. + 173204. i) q^{22} +(368370. - 134076. i) q^{23} +(-339004. - 1.92259e6i) q^{25} -274916. q^{26} +5.80031e6 q^{28} +(-354864. - 2.01253e6i) q^{29} +(-4.94332e6 + 1.79922e6i) q^{31} +(2.08773e6 + 1.75181e6i) q^{32} +(-1.83104e6 - 666444. i) q^{34} +(-172248. - 298342. i) q^{35} +(-962281. + 1.66672e6i) q^{37} +(-117615. + 98690.9i) q^{38} +(18659.3 - 105822. i) q^{40} +(388724. - 2.20457e6i) q^{41} +(-1.10450e7 + 9.26782e6i) q^{43} +(1.87606e7 - 3.24944e7i) q^{44} +(702609. + 1.21695e6i) q^{46} +(5.28349e7 + 1.92303e7i) q^{47} +(7.25284e7 + 6.08586e7i) q^{49} +(6.57606e6 - 2.39349e6i) q^{50} +(6.64747e6 + 3.76997e7i) q^{52} +8.13096e7 q^{53} -2.22849e6 q^{55} +(7.31393e6 + 4.14794e7i) q^{56} +(6.88371e6 - 2.50547e6i) q^{58} +(-1.05713e8 - 8.87036e7i) q^{59} +(4.28541e7 + 1.55976e7i) q^{61} +(-9.42863e6 - 1.63309e7i) q^{62} +(5.72138e7 - 9.90972e7i) q^{64} +(1.74170e6 - 1.46146e6i) q^{65} +(7.95651e6 - 4.51236e7i) q^{67} +(-4.71160e7 + 2.67208e8i) q^{68} +(945983. - 793774. i) q^{70} +(1.37584e7 - 2.38303e7i) q^{71} +(2.01252e8 + 3.48578e8i) q^{73} +(-6.48280e6 - 2.35955e6i) q^{74} +(1.63776e7 + 1.37424e7i) q^{76} +(8.20827e8 - 2.98757e8i) q^{77} +(1.82228e7 + 1.03347e8i) q^{79} -7.19127e6 q^{80} +8.02448e6 q^{82} +(-8.46228e7 - 4.79920e8i) q^{83} +(1.51432e7 - 5.51166e6i) q^{85} +(-3.95922e7 - 3.32218e7i) q^{86} +(2.56031e8 + 9.31878e7i) q^{88} +(3.04571e8 + 5.27532e8i) q^{89} +(-4.45599e8 + 7.71800e8i) q^{91} +(1.49894e8 - 1.25776e8i) q^{92} +(-3.49986e7 + 1.98487e8i) q^{94} +(220495. - 1.25049e6i) q^{95} +(3.34866e8 - 2.80986e8i) q^{97} +(-1.69695e8 + 2.93921e8i) 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 $

$2$	0.622466	+	3.53018i	0.0275094	+	0.156013i	0.995468	−	0.0950959i	$-0.0303158\pi$
$2$	0.622466	+	3.53018i	0.0275094	+	0.156013i	−0.967959	+	0.251109i	$0.919205\pi$
$3$		0			0
$3$		0			0
$4$	469.048	−	170.719i	0.916109	−	0.333436i
$5$	−22.7101	−	19.0560i	−0.0162500	−	0.0136354i	0.634626	−	0.772819i	$-0.281154\pi$
$5$	−22.7101	−	19.0560i	−0.0162500	−	0.0136354i	−0.650876	+	0.759184i	$0.725598\pi$
$6$		0			0
$7$	10919.6	+	3974.40i	1.71895	+	0.625648i	0.997748	−	0.0670731i	$-0.0213661\pi$
$7$	10919.6	+	3974.40i	1.71895	+	0.625648i	0.721206	+	0.692721i	$0.243588\pi$
$8$	1812.30	+	3139.00i	0.156432	+	0.270948i
$9$		0			0
$10$	53.1349	−	92.0324i	0.00168027	−	0.00291032i
$11$	57583.8	−	48318.5i	1.18586	−	0.995054i	0.185937	−	0.982562i	$-0.440468\pi$
$11$	57583.8	−	48318.5i	1.18586	−	0.995054i	0.999922	−	0.0124925i	$-0.00397659\pi$
$12$		0			0
$13$	−13317.6	+	75527.7i	−0.129324	+	0.733434i	0.849321	+	0.527877i	$0.177012\pi$
$13$	−13317.6	+	75527.7i	−0.129324	+	0.733434i	−0.978645	+	0.205557i	$0.934099\pi$
$14$	−7233.28	+	41021.9i	−0.0503221	+	0.285391i
$15$		0			0
$16$	185821.	−	155922.i	0.708851	−	0.594796i
$17$	−271792.	+	470757.i	−0.789253	+	1.36703i	0.137172	+	0.990547i	$0.456199\pi$
$17$	−271792.	+	470757.i	−0.789253	+	1.36703i	−0.926425	+	0.376479i	$0.877135\pi$
$18$		0			0
$19$	21415.8	+	37093.3i	0.0377002	+	0.0652986i	0.884260	−	0.466995i	$-0.154663\pi$
$19$	21415.8	+	37093.3i	0.0377002	+	0.0652986i	−0.846560	+	0.532294i	$0.821330\pi$
$20$	−13905.3	−	5061.13i	−0.0194333	−	0.00707315i
$21$		0			0
$22$	206417.	+	173204.i	0.187864	+	0.157637i
$23$	368370.	−	134076.i	0.274479	−	0.0999021i	−0.201113	−	0.979568i	$-0.564456\pi$
$23$	368370.	−	134076.i	0.274479	−	0.0999021i	0.475592	+	0.879666i	$0.342234\pi$
$24$		0			0
$25$	−339004.	−	1.92259e6i	−0.173570	−	0.984365i
$26$	−274916.			−0.117983
$27$		0			0
$28$	5.80031e6			1.78336
$29$	−354864.	−	2.01253e6i	−0.0931688	−	0.528387i	−0.995293	−	0.0969104i	$-0.969104\pi$
$29$	−354864.	−	2.01253e6i	−0.0931688	−	0.528387i	0.902124	−	0.431476i	$-0.142007\pi$
$30$		0			0
$31$	−4.94332e6	+	1.79922e6i	−0.961372	+	0.349911i	−0.774571	−	0.632487i	$-0.782034\pi$
$31$	−4.94332e6	+	1.79922e6i	−0.961372	+	0.349911i	−0.186801	+	0.982398i	$0.559812\pi$
$32$	2.08773e6	+	1.75181e6i	0.351964	+	0.295333i
$33$		0			0
$34$	−1.83104e6	−	666444.i	−0.234986	−	0.0855280i
$35$	−172248.	−	298342.i	−0.0194021	−	0.0336054i
$36$		0			0
$37$	−962281.	+	1.66672e6i	−0.0844100	+	0.146202i	−0.905140	−	0.425114i	$-0.860234\pi$
$37$	−962281.	+	1.66672e6i	−0.0844100	+	0.146202i	0.820730	+	0.571317i	$0.193567\pi$
$38$	−117615.	+	98690.9i	−0.00915035	+	0.00767805i
$39$		0			0
$40$	18659.3	−	105822.i	0.00115246	−	0.00653593i
$41$	388724.	−	2.20457e6i	0.0214840	−	0.121842i	−0.972180	−	0.234236i	$-0.924741\pi$
$41$	388724.	−	2.20457e6i	0.0214840	−	0.121842i	0.993664	+	0.112395i	$0.0358521\pi$
$42$		0			0
$43$	−1.10450e7	+	9.26782e6i	−0.492670	+	0.413399i	−0.854982	−	0.518658i	$-0.826432\pi$
$43$	−1.10450e7	+	9.26782e6i	−0.492670	+	0.413399i	0.362312	+	0.932057i	$0.381987\pi$
$44$	1.87606e7	−	3.24944e7i	0.754589	−	1.30699i
$45$		0			0
$46$	702609.	+	1.21695e6i	0.0231368	+	0.0400741i
$47$	5.28349e7	+	1.92303e7i	1.57936	+	0.574839i	0.975064	−	0.221923i	$-0.0712332\pi$
$47$	5.28349e7	+	1.92303e7i	1.57936	+	0.574839i	0.604293	+	0.796762i	$0.293455\pi$
$48$		0			0
$49$	7.25284e7	+	6.08586e7i	1.79732	+	1.50813i
$50$	6.57606e6	−	2.39349e6i	0.148799	−	0.0541585i
$51$		0			0
$52$	6.64747e6	+	3.76997e7i	0.126079	+	0.715027i
$53$	8.13096e7			1.41547			0.707735	−	0.706478i	$-0.249717\pi$
$53$	8.13096e7			1.41547			0.707735	+	0.706478i	$0.249717\pi$
$54$		0			0
$55$	−2.22849e6			−0.0328382
$56$	7.31393e6	+	4.14794e7i	0.0993813	+	0.563619i
$57$		0			0
$58$	6.88371e6	−	2.50547e6i	0.0798724	−	0.0290712i
$59$	−1.05713e8	−	8.87036e7i	−1.13578	−	0.953031i	−0.136486	−	0.990642i	$-0.543581\pi$
$59$	−1.05713e8	−	8.87036e7i	−1.13578	−	0.953031i	−0.999292	+	0.0376106i	$0.988025\pi$
$60$		0			0
$61$	4.28541e7	+	1.55976e7i	0.396285	+	0.144236i	0.532473	−	0.846447i	$-0.321263\pi$
$61$	4.28541e7	+	1.55976e7i	0.396285	+	0.144236i	−0.136188	+	0.990683i	$0.543485\pi$
$62$	−9.42863e6	−	1.63309e7i	−0.0810375	−	0.140361i
$63$		0			0
$64$	5.72138e7	−	9.90972e7i	0.426276	−	0.738332i
$65$	1.74170e6	−	1.46146e6i	0.0121022	−	0.0101549i
$66$		0			0
$67$	7.95651e6	−	4.51236e7i	0.0482376	−	0.273569i	−0.951143	−	0.308750i	$-0.900089\pi$
$67$	7.95651e6	−	4.51236e7i	0.0482376	−	0.273569i	0.999381	+	0.0351805i	$0.0112006\pi$
$68$	−4.71160e7	+	2.67208e8i	−0.267226	+	1.51551i
$69$		0			0
$70$	945983.	−	793774.i	0.00470915	−	0.00395144i
$71$	1.37584e7	−	2.38303e7i	0.0642549	−	0.111293i	−0.832108	−	0.554613i	$-0.812866\pi$
$71$	1.37584e7	−	2.38303e7i	0.0642549	−	0.111293i	0.896363	+	0.443320i	$0.146200\pi$
$72$		0			0
$73$	2.01252e8	+	3.48578e8i	0.829443	+	1.43664i	0.898476	+	0.439024i	$0.144676\pi$
$73$	2.01252e8	+	3.48578e8i	0.829443	+	1.43664i	−0.0690322	+	0.997614i	$0.521991\pi$
$74$	−6.48280e6	−	2.35955e6i	−0.0251316	−	0.00914716i
$75$		0			0
$76$	1.63776e7	+	1.37424e7i	0.0563104	+	0.0472500i
$77$	8.20827e8	−	2.98757e8i	2.66099	−	0.968521i
$78$		0			0
$79$	1.82228e7	+	1.03347e8i	0.0526373	+	0.298521i	0.999749	−	0.0223817i	$-0.00712492\pi$
$79$	1.82228e7	+	1.03347e8i	0.0526373	+	0.298521i	−0.947112	+	0.320903i	$0.896014\pi$
$80$	−7.19127e6			−0.0196291
$81$		0			0
$82$	8.02448e6			0.0195999
$83$	−8.46228e7	−	4.79920e8i	−0.195720	−	1.10998i	−0.911389	−	0.411545i	$-0.864989\pi$
$83$	−8.46228e7	−	4.79920e8i	−0.195720	−	1.10998i	0.715669	−	0.698440i	$-0.246122\pi$
$84$		0			0
$85$	1.51432e7	−	5.51166e6i	0.0314653	−	0.0114524i
$86$	−3.95922e7	−	3.32218e7i	−0.0780488	−	0.0654907i
$87$		0			0
$88$	2.56031e8	+	9.31878e7i	0.455115	+	0.165648i
$89$	3.04571e8	+	5.27532e8i	0.514557	+	0.891239i	0.999857	+	0.0168913i	$0.00537691\pi$
$89$	3.04571e8	+	5.27532e8i	0.514557	+	0.891239i	−0.485300	+	0.874347i	$0.661290\pi$
$90$		0			0
$91$	−4.45599e8	+	7.71800e8i	−0.681174	+	1.17983i
$92$	1.49894e8	−	1.25776e8i	0.218142	−	0.183043i
$93$		0			0
$94$	−3.49986e7	+	1.98487e8i	−0.0462355	+	0.262214i
$95$	220495.	−	1.25049e6i	0.000277743	−	0.00157516i
$96$		0			0
$97$	3.34866e8	−	2.80986e8i	0.384059	−	0.322264i	−0.430235	−	0.902717i	$-0.641569\pi$
$97$	3.34866e8	−	2.80986e8i	0.384059	−	0.322264i	0.814293	+	0.580453i	$0.197125\pi$
$98$	−1.69695e8	+	2.93921e8i	−0.185846	+	0.321894i
$99$		0			0
$100$	−4.87232e8	−	8.43911e8i	−0.487232	−	0.843911i
$101$	−4.87744e8	−	1.77524e8i	−0.466386	−	0.169751i	0.0981285	−	0.995174i	$-0.468714\pi$
$101$	−4.87744e8	−	1.77524e8i	−0.466386	−	0.169751i	−0.564515	+	0.825423i	$0.690937\pi$
$102$		0			0
$103$	−1.16009e9	−	9.73433e8i	−1.01561	−	0.852194i	−0.0265363	−	0.999648i	$-0.508448\pi$
$103$	−1.16009e9	−	9.73433e8i	−1.01561	−	0.852194i	−0.989069	+	0.147454i	$0.952892\pi$
$104$	−2.61217e8	+	9.50752e7i	−0.218953	+	0.0796925i
$105$		0			0
$106$	5.06125e7	+	2.87038e8i	0.0389387	+	0.220832i
$107$	5.26875e8			0.388580			0.194290	−	0.980944i	$-0.437760\pi$
$107$	5.26875e8			0.388580			0.194290	+	0.980944i	$0.437760\pi$
$108$		0			0
$109$	−1.23860e9			−0.840447			−0.420224	−	0.907421i	$-0.638048\pi$
$109$	−1.23860e9			−0.840447			−0.420224	+	0.907421i	$0.638048\pi$
$110$	−1.38716e6	−	7.86697e6i	−0.000903357	−	0.00512319i
$111$		0			0
$112$	2.64878e9	−	9.64078e8i	1.59061	−	0.578937i
$113$	−1.37971e9	−	1.15772e9i	−0.796042	−	0.667958i	0.151191	−	0.988505i	$-0.451689\pi$
$113$	−1.37971e9	−	1.15772e9i	−0.796042	−	0.667958i	−0.947233	+	0.320546i	$0.896134\pi$
$114$		0			0
$115$	−1.09207e7	−	3.97479e6i	−0.00582249	−	0.00211921i
$116$	−5.10027e8	−	8.83392e8i	−0.261536	−	0.452994i
$117$		0			0
$118$	2.47337e8	−	4.28400e8i	0.117441	−	0.203414i
$119$	−4.83883e9	+	4.06026e9i	−2.21197	+	1.85606i
$120$		0			0
$121$	5.71759e8	−	3.24260e9i	0.242481	−	1.37518i
$122$	−2.83871e7	+	1.60991e8i	−0.0116012	+	0.0657936i
$123$		0			0
$124$	−2.01149e9	+	1.68784e9i	−0.764049	+	0.641113i
$125$	−5.78891e7	+	1.00267e8i	−0.0212081	+	0.0367335i
$126$		0			0
$127$	−1.07400e9	−	1.86022e9i	−0.366342	−	0.634524i	0.622648	−	0.782502i	$-0.286057\pi$
$127$	−1.07400e9	−	1.86022e9i	−0.366342	−	0.634524i	−0.988991	+	0.147978i	$0.952723\pi$
$128$	1.69666e9	+	6.17535e8i	0.558664	+	0.203337i
$129$		0			0
$130$	6.24336e6	+	5.23880e6i	0.00191723	+	0.00160874i
$131$	−2.56218e9	+	9.32557e8i	−0.760131	+	0.276665i	−0.692863	−	0.721070i	$-0.743651\pi$
$131$	−2.56218e9	+	9.32557e8i	−0.760131	+	0.276665i	−0.0672688	+	0.997735i	$0.521429\pi$
$132$		0			0
$133$	8.64280e7	+	4.90157e8i	0.0239509	+	0.135832i
$134$	1.64247e8			0.0440074
$135$		0			0
$136$	−1.97028e9			−0.493858
$137$	−5.56084e8	−	3.15371e9i	−0.134865	−	0.764855i	−0.974954	−	0.222407i	$-0.928609\pi$
$137$	−5.56084e8	−	3.15371e9i	−0.134865	−	0.764855i	0.840089	−	0.542448i	$-0.182502\pi$
$138$		0			0
$139$	−4.61033e9	+	1.67802e9i	−1.04753	+	0.381268i	−0.807729	−	0.589554i	$-0.799303\pi$
$139$	−4.61033e9	+	1.67802e9i	−1.04753	+	0.381268i	−0.239798	+	0.970823i	$0.577081\pi$
$140$	−1.31725e8	−	1.10531e8i	−0.0289797	−	0.0243168i
$141$		0			0
$142$	9.26893e7	+	3.37362e7i	0.0191308	+	0.00696303i
$143$	2.88251e9	+	4.99266e9i	0.576446	+	0.998434i
$144$		0			0
$145$	−3.02919e7	+	5.24671e7i	−0.00569076	+	0.00985668i
$146$	−1.10527e9	+	9.27433e8i	−0.201317	+	0.168925i
$147$		0			0
$148$	−1.66814e8	+	9.46051e8i	−0.0285796	+	0.162083i
$149$	1.68982e9	−	9.58342e9i	0.280867	−	1.59288i	−0.438817	−	0.898576i	$-0.644602\pi$
$149$	1.68982e9	−	9.58342e9i	0.280867	−	1.59288i	0.719684	−	0.694301i	$-0.244287\pi$
$150$		0			0
$151$	2.57350e9	−	2.15942e9i	0.402836	−	0.338020i	−0.418753	−	0.908100i	$-0.637533\pi$
$151$	2.57350e9	−	2.15942e9i	0.402836	−	0.338020i	0.821589	+	0.570081i	$0.193088\pi$
$152$	−7.76239e7	+	1.34449e8i	−0.0117950	+	0.0204296i
$153$		0			0
$154$	1.56560e9	+	2.71170e9i	0.224304	+	0.388507i
$155$	1.46549e8	+	5.33396e7i	0.0203935	+	0.00742261i
$156$		0			0
$157$	3.38970e9	+	2.84429e9i	0.445259	+	0.373617i	0.837673	−	0.546172i	$-0.183916\pi$
$157$	3.38970e9	+	2.84429e9i	0.445259	+	0.373617i	−0.392414	+	0.919789i	$0.628360\pi$
$158$	−3.53489e8	+	1.28660e8i	−0.0451252	+	0.0164242i
$159$		0			0
$160$	−1.40299e7	−	7.95675e7i	−0.00169244	−	0.00959833i
$161$	4.55531e9			0.534320
$162$		0			0
$163$	−6.09961e9			−0.676796			−0.338398	−	0.941003i	$-0.609885\pi$
$163$	−6.09961e9			−0.676796			−0.338398	+	0.941003i	$0.609885\pi$
$164$	−1.94032e8	−	1.10041e9i	−0.0209448	−	0.118784i
$165$		0			0
$166$	1.64153e9	−	5.97467e8i	0.167788	−	0.0610699i
$167$	4.36900e9	+	3.66602e9i	0.434668	+	0.364730i	0.833710	−	0.552203i	$-0.186213\pi$
$167$	4.36900e9	+	3.66602e9i	0.434668	+	0.364730i	−0.399042	+	0.916933i	$0.630657\pi$
$168$		0			0
$169$	4.43790e9	+	1.61526e9i	0.418492	+	0.152319i
$170$	2.88833e7	+	5.00273e7i	0.00265232	+	0.00459396i
$171$		0			0
$172$	−3.59842e9	+	6.23264e9i	−0.313497	+	0.542993i
$173$	−1.45691e10	+	1.22249e10i	−1.23659	+	1.03762i	−0.238805	+	0.971067i	$0.576756\pi$
$173$	−1.45691e10	+	1.22249e10i	−1.23659	+	1.03762i	−0.997783	+	0.0665532i	$0.978800\pi$
$174$		0			0
$175$	3.93935e9	−	2.23412e10i	0.317507	−	1.80067i
$176$	3.16634e9	−	1.79572e10i	0.248743	−	1.41069i
$177$		0			0
$178$	−1.67270e9	+	1.40356e9i	−0.124890	+	0.104795i
$179$	−1.03647e9	+	1.79523e9i	−0.0754606	+	0.130702i	−0.901286	−	0.433224i	$-0.857376\pi$
$179$	−1.03647e9	+	1.79523e9i	−0.0754606	+	0.130702i	0.825826	+	0.563925i	$0.190709\pi$
$180$		0			0
$181$	−9.02008e9	−	1.56232e10i	−0.624679	−	1.08198i	−0.988603	−	0.150547i	$-0.951897\pi$
$181$	−9.02008e9	−	1.56232e10i	−0.624679	−	1.08198i	0.363924	−	0.931429i	$-0.381437\pi$
$182$	−3.00196e9	−	1.09263e9i	−0.202808	−	0.0738159i
$183$		0			0
$184$	1.08846e9	+	9.13328e8i	0.0700057	+	0.0587417i
$185$	5.36145e7	−	1.95141e7i	0.00336519	−	0.00122483i
$186$		0			0
$187$	7.09550e9	+	4.02406e10i	0.424322	+	2.40645i
$188$	2.80651e10			1.63854
$189$		0			0
$190$	4.55171e6			0.000253386
$191$	1.16527e9	+	6.60859e9i	0.0633545	+	0.359301i	0.999960	+	0.00891625i	$0.00283817\pi$
$191$	1.16527e9	+	6.60859e9i	0.0633545	+	0.359301i	−0.936606	+	0.350385i	$0.886051\pi$
$192$		0			0
$193$	3.04547e10	−	1.10846e10i	1.57996	−	0.575059i	0.604767	−	0.796403i	$-0.293266\pi$
$193$	3.04547e10	−	1.10846e10i	1.57996	−	0.575059i	0.975196	+	0.221343i	$0.0710442\pi$
$194$	1.20037e9	+	1.00723e9i	0.0608426	+	0.0510530i
$195$		0			0
$196$	4.44090e10	+	1.61636e10i	2.14941	+	0.782321i
$197$	1.20372e10	+	2.08491e10i	0.569414	+	0.986254i	0.996624	+	0.0821017i	$0.0261632\pi$
$197$	1.20372e10	+	2.08491e10i	0.569414	+	0.986254i	−0.427210	+	0.904153i	$0.640503\pi$
$198$		0			0
$199$	−1.19253e10	+	2.06552e10i	−0.539052	+	0.933665i	0.459904	+	0.887969i	$0.347884\pi$
$199$	−1.19253e10	+	2.06552e10i	−0.539052	+	0.933665i	−0.998955	+	0.0456960i	$0.985449\pi$
$200$	5.42063e9	−	4.54845e9i	0.239560	−	0.201015i
$201$		0			0
$202$	3.23088e8	−	1.83233e9i	0.0136534	−	0.0774322i
$203$	4.12364e9	−	2.33863e10i	0.170431	−	0.966563i
$204$		0			0
$205$	−5.08382e7	+	4.26583e7i	−0.00201047	+	0.00168698i
$206$	2.71427e9	−	4.70126e9i	0.105015	−	0.181891i
$207$		0			0
$208$	9.30177e9	+	1.61111e10i	0.344572	+	0.596817i
$209$	3.02550e9	+	1.10119e9i	0.109683	+	0.0399213i
$210$		0			0
$211$	−1.19856e10	−	1.00571e10i	−0.416281	−	0.349302i	0.410465	−	0.911876i	$-0.365366\pi$
$211$	−1.19856e10	−	1.00571e10i	−0.416281	−	0.349302i	−0.826746	+	0.562575i	$0.809811\pi$
$212$	3.81381e10	−	1.38811e10i	1.29672	−	0.471969i
$213$		0			0
$214$	3.27962e8	+	1.85996e9i	0.0106896	+	0.0606237i
$215$	4.27439e8			0.0136427
$216$		0			0
$217$	−6.11298e10			−1.87147
$218$	−7.70984e8	−	4.37246e9i	−0.0231202	−	0.131121i
$219$		0			0
$220$	−1.04527e9	+	3.80447e8i	−0.0300833	+	0.0109494i
$221$	−3.19356e10	−	2.67972e10i	−0.900554	−	0.755655i
$222$		0			0
$223$	−8.91449e9	−	3.24461e9i	−0.241393	−	0.0878598i	0.218491	−	0.975839i	$-0.429887\pi$
$223$	−8.91449e9	−	3.24461e9i	−0.241393	−	0.0878598i	−0.459884	+	0.887979i	$0.652109\pi$
$224$	1.58347e10	+	2.74265e10i	0.420236	+	0.727870i
$225$		0			0
$226$	3.22812e9	−	5.59128e9i	0.0823118	−	0.142568i
$227$	−2.08597e10	+	1.75033e10i	−0.521424	+	0.437527i	−0.865128	−	0.501551i	$-0.832763\pi$
$227$	−2.08597e10	+	1.75033e10i	−0.521424	+	0.437527i	0.343704	+	0.939078i	$0.388318\pi$
$228$		0			0
$229$	−1.25825e9	+	7.13589e9i	−0.0302348	+	0.171470i	−0.996186	−	0.0872538i	$-0.972191\pi$
$229$	−1.25825e9	+	7.13589e9i	−0.0302348	+	0.171470i	0.965951	+	0.258724i	$0.0833020\pi$
$230$	7.23400e6	−	4.10260e7i	0.000170452	−	0.000966684i
$231$		0			0
$232$	5.67422e9	−	4.76124e9i	0.128591	−	0.107901i
$233$	−2.04232e10	+	3.53741e10i	−0.453966	+	0.786291i	−0.998628	−	0.0523639i	$-0.983324\pi$
$233$	−2.04232e10	+	3.53741e10i	−0.453966	+	0.786291i	0.544662	+	0.838655i	$0.316658\pi$
$234$		0			0
$235$	−8.33431e8	−	1.44354e9i	−0.0178264	−	0.0308763i
$236$	−6.47278e10	−	2.35590e10i	−1.35827	−	0.494371i
$237$		0			0
$238$	−1.73454e10	−	1.45545e10i	−0.350420	−	0.294037i
$239$	3.02635e10	−	1.10150e10i	0.599968	−	0.218370i	−0.0241401	−	0.999709i	$-0.507685\pi$
$239$	3.02635e10	−	1.10150e10i	0.599968	−	0.218370i	0.624108	+	0.781338i	$0.285463\pi$
$240$		0			0
$241$	−1.21126e9	−	6.86942e9i	−0.0231293	−	0.131173i	0.971057	−	0.238849i	$-0.0767701\pi$
$241$	−1.21126e9	−	6.86942e9i	−0.0231293	−	0.131173i	−0.994186	+	0.107676i	$0.965659\pi$
$242$	1.18029e10			0.221217
$243$		0			0
$244$	2.27634e10			0.411134
$245$	−4.87404e8	−	2.76421e9i	−0.00864255	−	0.0490143i
$246$		0			0
$247$	−3.08678e9	+	1.12349e9i	−0.0527678	+	0.0192059i
$248$	−1.46066e10	−	1.22564e10i	−0.245197	−	0.205745i
$249$		0			0
$250$	−3.89994e8	−	1.41946e8i	−0.00631434	−	0.00229823i
$251$	−3.09023e10	−	5.35243e10i	−0.491427	−	0.851176i	0.508525	−	0.861047i	$-0.330191\pi$
$251$	−3.09023e10	−	5.35243e10i	−0.491427	−	0.851176i	−0.999951	+	0.00987155i	$0.996858\pi$
$252$		0			0
$253$	1.47338e10	−	2.55197e10i	0.226085	−	0.391591i
$254$	5.89839e9	−	4.94933e9i	0.0889163	−	0.0746096i
$255$		0			0
$256$	9.04962e9	−	5.13229e10i	0.131689	−	0.746847i
$257$	−1.97508e10	+	1.12013e11i	−0.282414	+	1.60165i	0.431964	+	0.901891i	$0.357821\pi$
$257$	−1.97508e10	+	1.12013e11i	−0.282414	+	1.60165i	−0.714378	+	0.699760i	$0.753290\pi$
$258$		0			0
$259$	−1.71319e10	+	1.43754e10i	−0.236568	+	0.198504i
$260$	5.67441e8	−	9.82837e8i	0.00770089	−	0.0133383i
$261$		0			0
$262$	−4.88696e9	−	8.46447e9i	−0.0640742	−	0.110980i
$263$	−1.52797e10	−	5.56136e9i	−0.196931	−	0.0716770i	0.241672	−	0.970358i	$-0.422304\pi$
$263$	−1.52797e10	−	5.56136e9i	−0.196931	−	0.0716770i	−0.438603	+	0.898681i	$0.644526\pi$
$264$		0			0
$265$	−1.84655e9	−	1.54944e9i	−0.0230014	−	0.0193005i
$266$	−1.67654e9	+	6.10212e8i	−0.0205328	+	0.00747332i
$267$		0			0
$268$	−3.97149e9	−	2.25235e10i	−0.0470270	−	0.266703i
$269$	4.23295e10			0.492899			0.246450	−	0.969156i	$-0.420736\pi$
$269$	4.23295e10			0.492899			0.246450	+	0.969156i	$0.420736\pi$
$270$		0			0
$271$	−2.92982e10			−0.329974			−0.164987	−	0.986296i	$-0.552758\pi$
$271$	−2.92982e10			−0.329974			−0.164987	+	0.986296i	$0.552758\pi$
$272$	2.28969e10	+	1.29855e11i	0.253640	+	1.43846i
$273$		0			0
$274$	1.07870e10	−	3.92615e9i	0.115617	−	0.0420813i
$275$	−1.12418e11	−	9.43297e10i	−1.18533	−	0.994606i
$276$		0			0
$277$	−8.70542e10	−	3.16851e10i	−0.888445	−	0.323368i	−0.142832	−	0.989747i	$-0.545621\pi$
$277$	−8.70542e10	−	3.16851e10i	−0.888445	−	0.323368i	−0.745613	+	0.666379i	$0.767843\pi$
$278$	−8.79348e9	−	1.52308e10i	−0.0882997	−	0.152940i
$279$		0			0
$280$	6.24331e8	−	1.08137e9i	0.00607021	−	0.0105139i
$281$	−8.74599e10	+	7.33876e10i	−0.836817	+	0.702173i	−0.956845	−	0.290598i	$-0.906146\pi$
$281$	−8.74599e10	+	7.33876e10i	−0.836817	+	0.702173i	0.120028	+	0.992770i	$0.461701\pi$
$282$		0			0
$283$	1.45773e10	−	8.26721e10i	0.135095	−	0.766161i	−0.839699	−	0.543053i	$-0.817268\pi$
$283$	1.45773e10	−	8.26721e10i	0.135095	−	0.766161i	0.974794	−	0.223109i	$-0.0716204\pi$
$284$	2.38507e9	−	1.35264e10i	0.0217554	−	0.123381i
$285$		0			0
$286$	−1.58307e10	+	1.32835e10i	−0.139911	+	0.117400i
$287$	1.30065e10	−	2.25279e10i	0.113160	−	0.195999i
$288$		0			0
$289$	−8.84477e10	−	1.53196e11i	−0.745841	−	1.29183i
$290$	−2.04074e8	−	7.42768e7i	−0.00169432	−	0.000616683i
$291$		0			0
$292$	1.53906e11	+	1.29142e11i	1.23889	+	1.03955i
$293$	−1.38460e11	+	5.03954e10i	−1.09754	+	0.399472i	−0.826409	−	0.563070i	$-0.809620\pi$
$293$	−1.38460e11	+	5.03954e10i	−1.09754	+	0.399472i	−0.271132	+	0.962542i	$0.587398\pi$
$294$		0			0
$295$	7.10409e8	+	4.02893e9i	0.00546147	+	0.0309735i
$296$	−6.97578e9			−0.0528178
$297$		0			0
$298$	3.48831e10			0.256237
$299$	5.22063e9	+	2.96077e10i	0.0377749	+	0.214232i
$300$		0			0
$301$	−1.57440e11	+	5.73035e10i	−1.10552	+	0.402376i
$302$	9.22507e9	+	7.74075e9i	0.0638173	+	0.0535491i
$303$		0			0
$304$	9.76318e9	+	3.55351e9i	0.0655632	+	0.0238630i
$305$	−6.75991e8	−	1.17085e9i	−0.00447292	−	0.00774733i
$306$		0			0
$307$	−4.67883e10	+	8.10397e10i	−0.300618	+	0.520685i	−0.976276	−	0.216530i	$-0.930526\pi$
$307$	−4.67883e10	+	8.10397e10i	−0.300618	+	0.520685i	0.675658	+	0.737215i	$0.263860\pi$
$308$	3.34004e11	−	2.80262e11i	2.11482	−	1.77454i
$309$		0			0
$310$	−9.70763e7	+	5.50547e8i	−0.000597016	+	0.00338584i
$311$	2.03276e10	−	1.15284e11i	0.123215	−	0.698789i	−0.859137	−	0.511746i	$-0.828999\pi$
$311$	2.03276e10	−	1.15284e11i	0.123215	−	0.698789i	0.982352	−	0.187042i	$-0.0598902\pi$
$312$		0			0
$313$	2.13959e10	−	1.79533e10i	0.126003	−	0.105729i	−0.577608	−	0.816314i	$-0.696014\pi$
$313$	2.13959e10	−	1.79533e10i	0.126003	−	0.105729i	0.703612	+	0.710585i	$0.251570\pi$
$314$	−7.93090e9	+	1.37367e10i	−0.0460404	+	0.0797443i
$315$		0			0
$316$	2.61907e10	+	4.53636e10i	0.147759	+	0.255926i
$317$	−1.30469e11	−	4.74869e10i	−0.725673	−	0.264123i	−0.0473408	−	0.998879i	$-0.515075\pi$
$317$	−1.30469e11	−	4.74869e10i	−0.725673	−	0.264123i	−0.678332	+	0.734755i	$0.737297\pi$
$318$		0			0
$319$	−1.17677e11	−	9.87428e10i	−0.636259	−	0.533884i
$320$	−3.18773e9	+	1.16024e9i	−0.0169944	+	0.00618546i
$321$		0			0
$322$	2.83552e9	+	1.60811e10i	0.0146988	+	0.0833610i
$323$	−2.32826e10			−0.119020
$324$		0			0
$325$	1.49723e11			0.744413
$326$	−3.79680e9	−	2.15327e10i	−0.0186182	−	0.105589i
$327$		0			0
$328$	7.62462e9	−	2.77514e9i	0.0363736	−	0.0132389i
$329$	5.00505e11	+	4.19974e11i	2.35520	+	1.97624i
$330$		0			0
$331$	3.54098e10	+	1.28881e10i	0.162143	+	0.0590151i	0.421816	−	0.906681i	$-0.361393\pi$
$331$	3.54098e10	+	1.28881e10i	0.162143	+	0.0590151i	−0.259674	+	0.965696i	$0.583615\pi$
$332$	−1.21624e11	−	2.10659e11i	−0.549411	−	0.951607i
$333$		0			0
$334$	−1.02222e10	+	1.77053e10i	−0.0449452	+	0.0778474i
$335$	−1.04057e9	+	8.73141e8i	−0.00451408	+	0.00378776i
$336$		0			0
$337$	−3.22114e10	+	1.82680e11i	−0.136043	+	0.771537i	0.838085	+	0.545539i	$0.183675\pi$
$337$	−3.22114e10	+	1.82680e11i	−0.136043	+	0.771537i	−0.974128	+	0.225997i	$0.927436\pi$
$338$	−2.93973e9	+	1.66720e10i	−0.0122513	+	0.0694805i
$339$		0			0
$340$	6.16193e9	−	5.17047e9i	0.0250070	−	0.0209834i
$341$	−1.97720e11	+	3.42460e11i	−0.791872	+	1.37156i
$342$		0			0
$343$	3.15641e11	+	5.46706e11i	1.23132	+	2.13270i
$344$	−4.91085e10	−	1.78740e10i	−0.189079	−	0.0688192i
$345$		0			0
$346$	−5.22249e10	−	4.38219e10i	−0.195900	−	0.164380i
$347$	4.05791e10	−	1.47696e10i	0.150252	−	0.0546871i	−0.265800	−	0.964028i	$-0.585636\pi$
$347$	4.05791e10	−	1.47696e10i	0.150252	−	0.0546871i	0.416051	+	0.909341i	$0.363414\pi$
$348$		0			0
$349$	−5.70295e10	−	3.23430e11i	−0.205771	−	1.16699i	−0.896221	−	0.443608i	$-0.853698\pi$
$349$	−5.70295e10	−	3.23430e11i	−0.205771	−	1.16699i	0.690450	−	0.723380i	$-0.257413\pi$
$350$	8.13204e10			0.289663
$351$		0			0
$352$	2.04864e11			0.711252
$353$	−5.87912e10	−	3.33422e11i	−0.201524	−	1.14290i	−0.902817	−	0.430025i	$-0.858505\pi$
$353$	−5.87912e10	−	3.33422e11i	−0.201524	−	1.14290i	0.701293	−	0.712873i	$-0.252606\pi$
$354$		0			0
$355$	−7.66565e8	+	2.79007e8i	−0.00256166	+	0.000932368i
$356$	2.32918e11	+	1.95442e11i	0.768562	+	0.644900i
$357$		0			0
$358$	−6.98264e9	−	2.54147e9i	−0.0224671	−	0.00817734i
$359$	−1.46279e11	−	2.53362e11i	−0.464789	−	0.805038i	0.534403	−	0.845230i	$-0.320537\pi$
$359$	−1.46279e11	−	2.53362e11i	−0.464789	−	0.805038i	−0.999192	+	0.0401915i	$0.987203\pi$
$360$		0			0
$361$	1.60427e11	−	2.77867e11i	0.497157	−	0.861102i
$362$	4.95381e10	−	4.15674e10i	0.151618	−	0.127223i
$363$		0			0
$364$	−7.72460e10	+	4.38084e11i	−0.230632	+	1.30798i
$365$	2.07207e9	−	1.17513e10i	0.00611064	−	0.0346551i
$366$		0			0
$367$	1.89419e11	−	1.58942e11i	0.545038	−	0.457341i	−0.328218	−	0.944602i	$-0.606448\pi$
$367$	1.89419e11	−	1.58942e11i	0.545038	−	0.457341i	0.873257	+	0.487260i	$0.162004\pi$
$368$	4.75455e10	−	8.23512e10i	0.135143	−	0.234075i
$369$		0			0
$370$	1.02261e8	+	1.77122e8i	0.000283664	+	0.000491320i
$371$	8.87866e11	+	3.23157e11i	2.43313	+	0.885586i
$372$		0			0
$373$	3.71295e11	+	3.11553e11i	0.993183	+	0.833379i	0.986025	−	0.166595i	$-0.0532773\pi$
$373$	3.71295e11	+	3.11553e11i	0.993183	+	0.833379i	0.00715718	+	0.999974i	$0.497722\pi$
$374$	−1.37640e11	+	5.00968e10i	−0.363766	+	0.132400i
$375$		0			0
$376$	3.53888e10	+	2.00700e11i	0.0913106	+	0.517848i
$377$	1.56728e11			0.399586
$378$		0			0
$379$	−5.20198e9			−0.0129507			−0.00647533	−	0.999979i	$-0.502061\pi$
$379$	−5.20198e9			−0.0129507			−0.00647533	+	0.999979i	$0.502061\pi$
$380$	−1.10060e8	−	6.24183e8i	−0.000270772	−	0.00153563i
$381$		0			0
$382$	−2.26042e10	+	8.22725e9i	−0.0543130	+	0.0197683i
$383$	−4.72458e11	−	3.96439e11i	−1.12194	−	0.941417i	−0.123237	−	0.992377i	$-0.539327\pi$
$383$	−4.72458e11	−	3.96439e11i	−1.12194	−	0.941417i	−0.998701	+	0.0509601i	$0.983772\pi$
$384$		0			0
$385$	−2.43342e10	−	8.85691e9i	−0.0564473	−	0.0205451i
$386$	5.80877e10	+	1.00611e11i	0.133181	+	0.230676i
$387$		0			0
$388$	1.09098e11	−	1.88964e11i	0.244385	−	0.423288i
$389$	2.01555e11	−	1.69124e11i	0.446293	−	0.374484i	−0.391765	−	0.920065i	$-0.628135\pi$
$389$	2.01555e11	−	1.69124e11i	0.446293	−	0.374484i	0.838058	+	0.545581i	$0.183691\pi$
$390$		0			0
$391$	−3.70028e10	+	2.09854e11i	−0.0800644	+	0.454068i
$392$	−5.95917e10	+	3.37961e11i	−0.127467	+	0.722902i
$393$		0			0
$394$	−6.61082e10	+	5.54714e10i	−0.138205	+	0.115967i
$395$	1.55553e9	−	2.69426e9i	0.00321509	−	0.00556869i
$396$		0			0
$397$	−3.27148e11	−	5.66638e11i	−0.660979	−	1.14485i	−0.980359	−	0.197222i	$-0.936808\pi$
$397$	−3.27148e11	−	5.66638e11i	−0.660979	−	1.14485i	0.319380	−	0.947627i	$-0.396525\pi$
$398$	−8.03397e10	−	2.92413e10i	−0.160493	−	0.0584147i
$399$		0			0
$400$	−3.62768e11	−	3.04399e11i	−0.708532	−	0.594529i
$401$	−3.44274e11	+	1.25305e11i	−0.664896	+	0.242002i	−0.652349	−	0.757919i	$-0.726216\pi$
$401$	−3.44274e11	+	1.25305e11i	−0.664896	+	0.242002i	−0.0125474	+	0.999921i	$0.503994\pi$
$402$		0			0
$403$	−7.00581e10	−	3.97319e11i	−0.132308	−	0.750355i
$404$	−2.59082e11			−0.483862
$405$		0			0
$406$	8.51248e10			0.155485
$407$	2.51217e10	+	1.42472e11i	0.0453809	+	0.257368i
$408$		0			0
$409$	−8.00148e10	+	2.91230e10i	−0.141389	+	0.0514614i	−0.411745	−	0.911299i	$-0.635081\pi$
$409$	−8.00148e10	+	2.91230e10i	−0.141389	+	0.0514614i	0.270356	+	0.962760i	$0.412858\pi$
$410$	−1.82236e8	−	1.52915e8i	−0.000318499	−	0.000267252i
$411$		0			0
$412$	−7.10323e11	−	2.58536e11i	−1.21456	−	0.442063i
$413$	−8.01795e11	−	1.38875e12i	−1.35609	−	2.34881i
$414$		0			0
$415$	−7.22357e9	+	1.25116e10i	−0.0119546	+	0.0207060i
$416$	−1.60114e11	+	1.34351e11i	−0.262125	+	0.219949i
$417$		0			0
$418$	−2.00413e9	+	1.13660e10i	−0.00321095	+	0.0182102i
$419$	−1.06895e11	+	6.06234e11i	−0.169432	+	0.960897i	0.774944	+	0.632030i	$0.217778\pi$
$419$	−1.06895e11	+	6.06234e11i	−0.169432	+	0.960897i	−0.944376	+	0.328867i	$0.893333\pi$
$420$		0			0
$421$	−7.60634e11	+	6.38248e11i	−1.18007	+	0.990193i	−0.180088	+	0.983651i	$0.557638\pi$
$421$	−7.60634e11	+	6.38248e11i	−1.18007	+	0.990193i	−0.999979	+	0.00654286i	$0.997917\pi$
$422$	2.80427e10	−	4.85713e10i	0.0430441	−	0.0745545i
$423$		0			0
$424$	1.47358e11	+	2.55231e11i	0.221425	+	0.383519i
$425$	9.97210e11	+	3.62955e11i	1.48264	+	0.539638i
$426$		0			0
$427$	4.05957e11	+	3.40638e11i	0.590955	+	0.495870i
$428$	2.47130e11	−	8.99478e10i	0.355982	−	0.129567i
$429$		0			0
$430$	2.66066e8	+	1.50894e9i	0.000375303	+	0.00212845i
$431$	7.59519e11			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$431$	7.59519e11			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$432$		0			0
$433$	8.25974e11			1.12920			0.564600	−	0.825365i	$-0.309030\pi$
$433$	8.25974e11			1.12920			0.564600	+	0.825365i	$0.309030\pi$
$434$	−3.80512e10	−	2.15799e11i	−0.0514831	−	0.291975i
$435$		0			0
$436$	−5.80961e11	+	2.11452e11i	−0.769941	+	0.280236i
$437$	1.28622e10	+	1.07927e10i	0.0168714	+	0.0141568i
$438$		0			0
$439$	−2.46572e11	−	8.97449e10i	−0.316850	−	0.115324i	0.178700	−	0.983904i	$-0.442811\pi$
$439$	−2.46572e11	−	8.97449e10i	−0.316850	−	0.115324i	−0.495549	+	0.868580i	$0.665033\pi$
$440$	−4.03870e9	−	6.99524e9i	−0.00513694	−	0.00889745i
$441$		0			0
$442$	7.47199e10	−	1.29419e11i	0.0931186	−	0.161286i
$443$	−5.74601e11	+	4.82148e11i	−0.708842	+	0.594789i	−0.924274	−	0.381730i	$-0.875329\pi$
$443$	−5.74601e11	+	4.82148e11i	−0.708842	+	0.594789i	0.215432	+	0.976519i	$0.430884\pi$
$444$		0			0
$445$	3.13584e9	−	1.77842e10i	0.00379082	−	0.0214988i
$446$	5.90508e9	−	3.34894e10i	0.00706674	−	0.0400775i
$447$		0			0
$448$	1.01860e12	−	8.54708e11i	1.19468	−	1.00246i
$449$	−5.55725e11	+	9.62545e11i	−0.645285	+	1.11767i	0.338950	+	0.940804i	$0.389928\pi$
$449$	−5.55725e11	+	9.62545e11i	−0.645285	+	1.11767i	−0.984236	+	0.176863i	$0.943405\pi$
$450$		0			0
$451$	−8.41371e10	−	1.45730e11i	−0.0957620	−	0.165865i
$452$	−8.44797e11	−	3.07481e11i	−0.951983	−	0.346494i
$453$		0			0
$454$	−7.47743e10	−	6.27431e10i	−0.0826040	−	0.0693130i
$455$	2.48270e10	−	9.03630e9i	0.0271565	−	0.00988415i
$456$		0			0
$457$	−1.02191e11	−	5.79554e11i	−0.109595	−	0.621543i	−0.989285	−	0.145996i	$-0.953361\pi$
$457$	−1.02191e11	−	5.79554e11i	−0.109595	−	0.621543i	0.879690	−	0.475547i	$-0.157750\pi$
$458$	−2.59742e10			−0.0275834
$459$		0			0
$460$	−5.80089e9			−0.00604066
$461$	−1.48156e11	−	8.40233e11i	−0.152779	−	0.866455i	−0.960788	−	0.277284i	$-0.910566\pi$
$461$	−1.48156e11	−	8.40233e11i	−0.152779	−	0.866455i	0.808009	−	0.589171i	$-0.200545\pi$
$462$		0			0
$463$	−8.60570e11	+	3.13222e11i	−0.870306	+	0.316765i	−0.738291	−	0.674482i	$-0.764367\pi$
$463$	−8.60570e11	+	3.13222e11i	−0.870306	+	0.316765i	−0.132015	+	0.991248i	$0.542145\pi$
$464$	−3.79740e11	−	3.18640e11i	−0.380325	−	0.319131i
$465$		0			0
$466$	−1.37590e11	−	5.00785e10i	−0.135160	−	0.0491943i
$467$	−3.97890e11	−	6.89166e11i	−0.387113	−	0.670499i	0.604947	−	0.796266i	$-0.293194\pi$
$467$	−3.97890e11	−	6.89166e11i	−0.387113	−	0.670499i	−0.992060	+	0.125767i	$0.959861\pi$
$468$		0			0
$469$	2.66221e11	−	4.61108e11i	0.254076	−	0.440073i
$470$	4.57719e9	−	3.84072e9i	0.00432672	−	0.00363055i
$471$		0			0
$472$	8.68570e10	−	4.92591e11i	0.0805501	−	0.456822i
$473$	−1.88203e11	+	1.06735e12i	−0.172883	+	0.980466i
$474$		0			0
$475$	6.40550e10	−	5.37485e10i	0.0577340	−	0.0484446i
$476$	−1.57648e12	+	2.73054e12i	−1.40752	+	2.43790i
$477$		0			0
$478$	5.77229e10	+	9.99790e10i	0.0505734	+	0.0875958i
$479$	−6.95990e11	−	2.53320e11i	−0.604078	−	0.219866i	0.0218320	−	0.999762i	$-0.493050\pi$
$479$	−6.95990e11	−	2.53320e11i	−0.604078	−	0.219866i	−0.625910	+	0.779895i	$0.715272\pi$
$480$		0			0
$481$	−1.13068e11	−	9.48755e10i	−0.0963136	−	0.0808167i
$482$	2.34963e10	−	8.55195e9i	0.0198284	−	0.00721695i
$483$		0			0
$484$	−2.85394e11	−	1.61855e12i	−0.236396	−	1.34067i
$485$	−1.29593e10			−0.0106351
$486$		0			0
$487$	−1.92211e12			−1.54845			−0.774226	−	0.632910i	$-0.781860\pi$
$487$	−1.92211e12			−1.54845			−0.774226	+	0.632910i	$0.781860\pi$
$488$	2.87037e10	+	1.62787e11i	0.0229112	+	0.129936i
$489$		0			0
$490$	9.45475e9	−	3.44125e9i	0.00740914	−	0.00269671i
$491$	−4.47515e11	−	3.75510e11i	−0.347489	−	0.291578i	0.452292	−	0.891870i	$-0.350606\pi$
$491$	−4.47515e11	−	3.75510e11i	−0.347489	−	0.291578i	−0.799781	+	0.600292i	$0.795051\pi$
$492$		0			0
$493$	1.04386e12	+	3.79935e11i	0.795852	+	0.289667i
$494$	−5.88755e9	−	1.01975e10i	−0.00444798	−	0.00770413i
$495$		0			0
$496$	−6.38034e11	+	1.10511e12i	−0.473344	+	0.819855i
$497$	2.44947e11	−	2.05535e11i	0.180081	−	0.151106i
$498$		0			0
$499$	1.93241e11	−	1.09592e12i	0.139523	−	0.791276i	−0.832079	−	0.554657i	$-0.812850\pi$
$499$	1.93241e11	−	1.09592e12i	0.139523	−	0.791276i	0.971603	−	0.236619i	$-0.0760393\pi$
$500$	−1.00353e10	+	5.69128e10i	−0.00718065	+	0.0407235i
$501$		0			0
$502$	1.69715e11	−	1.42408e11i	0.119276	−	0.100084i
$503$	8.76388e11	−	1.51795e12i	0.610436	−	1.05731i	−0.380730	−	0.924686i	$-0.624327\pi$
$503$	8.76388e11	−	1.51795e12i	0.610436	−	1.05731i	0.991167	−	0.132621i	$-0.0423393\pi$
$504$		0			0
$505$	7.69379e9	+	1.33260e10i	0.00526416	+	0.00911780i
$506$	9.92603e10	+	3.61278e10i	0.0673129	+	0.0244999i
$507$		0			0
$508$	−8.21333e11	−	6.89180e11i	−0.547183	−	0.459141i
$509$	2.12923e12	−	7.74978e11i	1.40603	−	0.511752i	0.476065	−	0.879410i	$-0.342063\pi$
$509$	2.12923e12	−	7.74978e11i	1.40603	−	0.511752i	0.929961	+	0.367659i	$0.119841\pi$
$510$		0			0
$511$	8.12193e11	+	4.60618e12i	0.526945	+	2.98845i
$512$	1.11125e12			0.714659
$513$		0			0
$514$	−4.07719e11			−0.257648
$515$	7.79603e9	+	4.42135e10i	0.00488361	+	0.0276963i
$516$		0			0
$517$	3.97162e12	−	1.44555e12i	2.44489	−	0.889868i
$518$	−6.14116e10	−	5.15305e10i	−0.0374772	−	0.0314471i
$519$		0			0
$520$	7.74401e9	+	2.81859e9i	0.00464463	+	0.00169051i
$521$	1.02983e11	+	1.78372e11i	0.0612346	+	0.106062i	0.895018	−	0.446031i	$-0.147163\pi$
$521$	1.02983e11	+	1.78372e11i	0.0612346	+	0.106062i	−0.833783	+	0.552092i	$0.813830\pi$
$522$		0			0
$523$	−4.36557e11	+	7.56139e11i	−0.255143	+	0.441920i	−0.964934	−	0.262492i	$-0.915456\pi$
$523$	−4.36557e11	+	7.56139e11i	−0.255143	+	0.441920i	0.709792	+	0.704412i	$0.248789\pi$
$524$	−1.04258e12	+	8.74828e11i	−0.604113	+	0.506911i
$525$		0			0
$526$	1.01215e10	−	5.74018e10i	0.00576512	−	0.0326956i
$527$	4.96558e11	−	2.81612e12i	0.280429	−	1.59039i
$528$		0			0
$529$	−1.26204e12	+	1.05898e12i	−0.700686	+	0.587946i
$530$	4.32038e9	−	7.48312e9i	0.00237838	−	0.00411947i
$531$		0			0
$532$	1.24218e11	+	2.15152e11i	0.0672331	+	0.116451i
$533$	1.61329e11	+	5.87189e10i	0.0865844	+	0.0315141i
$534$		0			0
$535$	−1.19654e10	−	1.00401e10i	−0.00631443	−	0.00529843i
$536$	1.56063e11	−	5.68022e10i	0.0816691	−	0.0297251i
$537$		0			0
$538$	2.63487e10	+	1.49431e11i	0.0135593	+	0.0768988i
$539$	7.11706e12			3.63204
$540$		0			0
$541$	2.76531e11			0.138789			0.0693947	−	0.997589i	$-0.477893\pi$
$541$	2.76531e11			0.138789			0.0693947	+	0.997589i	$0.477893\pi$
$542$	−1.82371e10	−	1.03428e11i	−0.00907737	−	0.0514803i
$543$		0			0
$544$	−1.39210e12	+	5.06684e11i	−0.681517	+	0.248052i
$545$	2.81286e10	+	2.36027e10i	0.0136573	+	0.0114598i
$546$		0			0
$547$	2.99487e12	+	1.09004e12i	1.43032	+	0.520596i	0.937025	−	0.349264i	$-0.113568\pi$
$547$	2.99487e12	+	1.09004e12i	1.43032	+	0.520596i	0.493300	+	0.869859i	$0.335790\pi$
$548$	−7.99229e11	−	1.38431e12i	−0.378581	−	0.655722i
$549$		0			0
$550$	2.63024e11	−	4.55572e11i	0.122564	−	0.212288i
$551$	6.70517e10	−	5.62631e10i	0.0309904	−	0.0260041i
$552$		0			0
$553$	−2.11756e11	+	1.20093e12i	−0.0962879	+	0.546076i
$554$	5.76659e10	−	3.27040e11i	0.0260091	−	0.147505i
$555$		0			0
$556$	−1.87599e12	+	1.57414e12i	−0.832520	+	0.698567i
$557$	−1.33084e12	+	2.30508e12i	−0.585837	+	1.01470i	0.408934	+	0.912564i	$0.365901\pi$
$557$	−1.33084e12	+	2.30508e12i	−0.585837	+	1.01470i	−0.994771	+	0.102135i	$0.967433\pi$
$558$		0			0
$559$	−5.52885e11	−	9.57625e11i	−0.239487	−	0.414803i
$560$	−7.85255e10	−	2.85809e10i	−0.0337415	−	0.0122809i
$561$		0			0
$562$	−3.13512e11	−	2.63068e11i	−0.132569	−	0.111238i
$563$	−2.66557e12	+	9.70188e11i	−1.11816	+	0.406975i	−0.833979	−	0.551797i	$-0.813942\pi$
$563$	−2.66557e12	+	9.70188e11i	−1.11816	+	0.406975i	−0.284177	+	0.958772i	$0.591720\pi$
$564$		0			0
$565$	9.27192e9	+	5.25837e10i	0.00382782	+	0.0217087i
$566$	3.00921e11			0.123248
$567$		0			0
$568$	9.97378e10			0.0402061
$569$	7.81924e11	+	4.43451e12i	0.312722	+	1.77354i	0.584716	+	0.811238i	$0.301206\pi$
$569$	7.81924e11	+	4.43451e12i	0.312722	+	1.77354i	−0.271993	+	0.962299i	$0.587683\pi$
$570$		0			0
$571$	4.16858e12	−	1.51724e12i	1.64107	−	0.597299i	0.653841	−	0.756632i	$-0.273157\pi$
$571$	4.16858e12	−	1.51724e12i	1.64107	−	0.597299i	0.987225	+	0.159333i	$0.0509344\pi$
$572$	2.20438e12	+	1.84969e12i	0.861002	+	0.722467i
$573$		0			0
$574$	8.76238e10	+	3.18925e10i	0.0336914	+	0.0122627i
$575$	−3.82651e11	−	6.62771e11i	−0.145981	−	0.252847i
$576$		0			0
$577$	−1.86336e12	+	3.22743e12i	−0.699850	+	1.21218i	0.268668	+	0.963233i	$0.413416\pi$
$577$	−1.86336e12	+	3.22743e12i	−0.699850	+	1.21218i	−0.968518	+	0.248943i	$0.919917\pi$
$578$	4.85753e11	−	4.07595e11i	0.181026	−	0.151899i
$579$		0			0
$580$	−5.25119e9	+	2.97810e10i	−0.00192678	+	0.0109273i
$581$	9.83347e11	−	5.57684e12i	0.358026	−	2.03046i
$582$		0			0
$583$	4.68212e12	−	3.92876e12i	1.67855	−	1.40847i
$584$	−7.29459e11	+	1.26346e12i	−0.259503	+	0.449473i
$585$		0			0
$586$	−2.64092e11	−	4.57420e11i	−0.0925157	−	0.160242i
$587$	−2.98032e12	−	1.08475e12i	−1.03608	−	0.377101i	−0.232685	−	0.972552i	$-0.574751\pi$
$587$	−2.98032e12	−	1.08475e12i	−1.03608	−	0.377101i	−0.803391	+	0.595451i	$0.796973\pi$
$588$		0			0
$589$	−1.72604e11	−	1.44832e11i	−0.0590926	−	0.0495846i
$590$	−1.37806e10	+	5.01574e9i	−0.00468204	+	0.00170412i
$591$		0			0
$592$	8.10668e10	+	4.59753e11i	0.0271266	+	0.153843i
$593$	2.54616e12			0.845550			0.422775	−	0.906235i	$-0.361056\pi$
$593$	2.54616e12			0.845550			0.422775	+	0.906235i	$0.361056\pi$
$594$		0			0
$595$	1.87262e11			0.0612526
$596$	−8.43472e11	−	4.78357e12i	−0.273818	−	1.55290i
$597$		0			0
$598$	−1.01271e11	+	3.68595e10i	−0.0323839	+	0.0117868i
$599$	3.10165e11	+	2.60259e11i	0.0984401	+	0.0826010i	0.690679	−	0.723161i	$-0.257312\pi$
$599$	3.10165e11	+	2.60259e11i	0.0984401	+	0.0826010i	−0.592239	+	0.805762i	$0.701756\pi$
$600$		0			0
$601$	−2.37822e12	−	8.65600e11i	−0.743560	−	0.270634i	−0.0576668	−	0.998336i	$-0.518366\pi$
$601$	−2.37822e12	−	8.65600e11i	−0.743560	−	0.270634i	−0.685893	+	0.727702i	$0.740588\pi$
$602$	−3.00293e11	−	5.20122e11i	−0.0931881	−	0.161407i
$603$		0			0
$604$	8.38440e11	−	1.45222e12i	0.256334	−	0.443983i
$605$	−7.47758e10	+	6.27443e10i	−0.0226914	+	0.0190404i
$606$		0			0
$607$	1.43864e11	−	8.15892e11i	0.0430133	−	0.243940i	−0.955719	−	0.294281i	$-0.904920\pi$
$607$	1.43864e11	−	8.15892e11i	0.0430133	−	0.243940i	0.998732	+	0.0503410i	$0.0160308\pi$
$608$	−2.02700e10	+	1.14957e11i	−0.00601573	+	0.0341169i
$609$		0			0
$610$	3.71253e9	−	3.11518e9i	0.00108564	−	0.000910960i
$611$	−2.15605e12	+	3.73440e12i	−0.625856	+	1.08401i
$612$		0			0
$613$	4.90481e11	+	8.49538e11i	0.140297	+	0.243002i	0.927609	−	0.373554i	$-0.121861\pi$
$613$	4.90481e11	+	8.49538e11i	0.140297	+	0.243002i	−0.787311	+	0.616556i	$0.788527\pi$
$614$	−3.15209e11	−	1.14727e11i	−0.0895037	−	0.0325767i
$615$		0			0
$616$	2.42539e12	+	2.03514e12i	0.678684	+	0.569483i
$617$	−2.43456e12	+	8.86107e11i	−0.676296	+	0.246152i	−0.657256	−	0.753667i	$-0.728283\pi$
$617$	−2.43456e12	+	8.86107e11i	−0.676296	+	0.246152i	−0.0190397	+	0.999819i	$0.506061\pi$
$618$		0			0
$619$	2.32520e10	+	1.31869e11i	0.00636579	+	0.0361022i	0.987825	−	0.155568i	$-0.0497208\pi$
$619$	2.32520e10	+	1.31869e11i	0.00636579	+	0.0361022i	−0.981459	+	0.191670i	$0.938610\pi$
$620$	7.78447e10			0.0211576
$621$		0			0
$622$	4.19625e11			0.112410
$623$	1.22916e12	+	6.97091e12i	0.326898	+	1.85393i
$624$		0			0
$625$	−3.57980e12	+	1.30294e12i	−0.938424	+	0.341558i
$626$	7.66966e10	+	6.43561e10i	0.0199614	+	0.0167496i
$627$		0			0
$628$	2.07551e12	+	7.55423e11i	0.532483	+	0.193808i
$629$	−5.23080e11	−	9.06001e11i	−0.133242	−	0.230782i
$630$		0			0
$631$	2.14081e12	−	3.70799e12i	0.537584	−	0.931122i	−0.461450	−	0.887166i	$-0.652670\pi$
$631$	2.14081e12	−	3.70799e12i	0.537584	−	0.931122i	0.999033	−	0.0439561i	$-0.0139962\pi$
$632$	−2.91380e11	+	2.44497e11i	−0.0726496	+	0.0609602i
$633$		0			0
$634$	8.64246e10	−	4.90138e11i	0.0212440	−	0.120481i
$635$	−1.10578e10	+	6.27119e10i	−0.00269890	+	0.0153062i
$636$		0			0
$637$	−5.56241e12	+	4.66742e12i	−1.33855	+	1.12318i
$638$	2.75330e11	−	4.76885e11i	0.0657900	−	0.113952i
$639$		0			0
$640$	−2.67636e10	−	4.63559e10i	−0.00630572	−	0.0109218i
$641$	−6.11925e12	−	2.22722e12i	−1.43165	−	0.521078i	−0.494246	−	0.869322i	$-0.664556\pi$
$641$	−6.11925e12	−	2.22722e12i	−1.43165	−	0.521078i	−0.937404	+	0.348244i	$0.886778\pi$
$642$		0			0
$643$	−2.80734e12	−	2.35563e12i	−0.647657	−	0.543449i	0.258702	−	0.965957i	$-0.416705\pi$
$643$	−2.80734e12	−	2.35563e12i	−0.647657	−	0.543449i	−0.906359	+	0.422509i	$0.861150\pi$
$644$	2.13666e12	−	7.77680e11i	0.489495	−	0.178162i
$645$		0			0
$646$	−1.44926e10	−	8.21916e10i	−0.00327416	−	0.0185687i
$647$	5.92408e12			1.32908			0.664541	−	0.747252i	$-0.268627\pi$
$647$	5.92408e12			1.32908			0.664541	+	0.747252i	$0.268627\pi$
$648$		0			0
$649$	−1.03734e13			−2.29519
$650$	9.31976e10	+	5.28550e11i	0.0204783	+	0.116138i
$651$		0			0
$652$	−2.86101e12	+	1.04132e12i	−0.620019	+	0.225668i
$653$	−5.49403e12	−	4.61004e12i	−1.18245	−	0.992192i	−0.999960	−	0.00898382i	$-0.997140\pi$
$653$	−5.49403e12	−	4.61004e12i	−1.18245	−	0.992192i	−0.182489	−	0.983208i	$-0.558415\pi$
$654$		0			0
$655$	7.59581e10	+	2.76465e10i	0.0161246	+	0.00586886i
$656$	−2.71508e11	−	4.70265e11i	−0.0572420	−	0.0991461i
$657$		0			0
$658$	−1.17103e12	+	2.02829e12i	−0.243530	+	0.421807i
$659$	8.27124e11	−	6.94040e11i	0.170839	−	0.143351i	−0.553360	−	0.832942i	$-0.686654\pi$
$659$	8.27124e11	−	6.94040e11i	0.170839	−	0.143351i	0.724198	+	0.689592i	$0.242210\pi$
$660$		0			0
$661$	1.60591e12	−	9.10759e12i	0.327202	−	1.85565i	−0.166525	−	0.986037i	$-0.553255\pi$
$661$	1.60591e12	−	9.10759e12i	0.327202	−	1.85565i	0.493727	−	0.869617i	$-0.335634\pi$
$662$	−2.34560e10	+	1.33025e11i	−0.00474670	+	0.0269199i
$663$		0			0
$664$	1.35311e12	−	1.13539e12i	0.270132	−	0.226667i
$665$	7.37766e9	−	1.27785e10i	0.00146292	−	0.00253386i
$666$		0			0
$667$	−4.00553e11	−	6.93778e11i	−0.0783598	−	0.135723i
$668$	2.67513e12	+	9.73667e11i	0.519817	+	0.189198i
$669$		0			0
$670$	−3.73006e9	−	3.12989e9i	−0.000715121	−	0.000600058i
$671$	3.22135e12	−	1.17248e12i	0.613461	−	0.223282i
$672$		0			0
$673$	1.25090e12	+	7.09420e12i	0.235047	+	1.33302i	0.842515	+	0.538673i	$0.181074\pi$
$673$	1.25090e12	+	7.09420e12i	0.235047	+	1.33302i	−0.607468	+	0.794344i	$0.707815\pi$
$674$	−6.64944e11			−0.124113
$675$		0			0
$676$	2.35734e12			0.434173
$677$	7.57017e11	+	4.29326e12i	0.138502	+	0.785485i	0.972357	+	0.233501i	$0.0750181\pi$
$677$	7.57017e11	+	4.29326e12i	0.138502	+	0.785485i	−0.833854	+	0.551984i	$0.813871\pi$
$678$		0			0
$679$	4.77334e12	−	1.73735e12i	0.861803	−	0.313671i
$680$	4.47452e10	+	3.75456e10i	0.00802520	+	0.00673394i
$681$		0			0
$682$	−1.33202e12	−	4.84815e11i	−0.235766	−	0.0858118i
$683$	−4.68906e12	−	8.12170e12i	−0.824504	−	1.42808i	−0.902297	−	0.431114i	$-0.858121\pi$
$683$	−4.68906e12	−	8.12170e12i	−0.824504	−	1.42808i	0.0777931	−	0.996970i	$-0.475213\pi$
$684$		0			0
$685$	−4.74684e10	+	8.22177e10i	−0.00823753	+	0.0142678i
$686$	−1.73350e12	+	1.45458e12i	−0.298857	+	0.250771i
$687$		0			0
$688$	−6.07325e11	+	3.44431e12i	−0.103341	+	0.586077i
$689$	−1.08285e12	+	6.14113e12i	−0.183055	+	1.03815i
$690$		0			0
$691$	2.10441e12	−	1.76581e12i	0.351139	−	0.294641i	−0.450108	−	0.892974i	$-0.648615\pi$
$691$	2.10441e12	−	1.76581e12i	0.351139	−	0.294641i	0.801247	+	0.598333i	$0.204170\pi$
$692$	−4.74657e12	+	8.22130e12i	−0.786869	+	1.36290i
$693$		0			0
$694$	7.73983e10	+	1.34058e11i	0.0126653	+	0.0219369i
$695$	1.36677e11	+	4.97464e10i	0.0222210	+	0.00808780i
$696$		0			0
$697$	9.32163e11	+	7.82178e11i	0.149604	+	0.125533i
$698$	1.10627e12	−	4.02649e11i	0.176405	−	0.0642062i
$699$		0			0
$700$	−1.96633e12	−	1.11516e13i	−0.309538	−	1.75548i
$701$	1.46058e12			0.228452			0.114226	−	0.993455i	$-0.463561\pi$
$701$	1.46058e12			0.228452			0.114226	+	0.993455i	$0.463561\pi$
$702$		0			0
$703$	−8.24321e10			−0.0127291
$704$	−1.49364e12	−	8.47088e12i	−0.229177	−	1.29973i
$705$		0			0
$706$	1.14044e12	−	4.15087e11i	0.172764	−	0.0628808i
$707$	−4.62040e12	−	3.87697e12i	−0.695492	−	0.583587i
$708$		0			0
$709$	3.43983e12	+	1.25200e12i	0.511245	+	0.186078i	0.584745	−	0.811217i	$-0.301195\pi$
$709$	3.43983e12	+	1.25200e12i	0.511245	+	0.186078i	−0.0735000	+	0.997295i	$0.523417\pi$
$710$	−1.46210e9	−	2.53244e9i	−0.000215931	−	0.000374004i
$711$		0			0
$712$	−1.10395e12	+	1.91210e12i	−0.160987	+	0.278837i
$713$	−1.57974e12	+	1.32556e12i	−0.228919	+	0.192086i
$714$		0			0
$715$	2.96781e10	−	1.68313e11i	0.00424677	−	0.0240846i
$716$	−1.79676e11	+	1.01899e12i	−0.0255495	+	0.144898i
$717$		0			0
$718$	8.03360e11	−	6.74099e11i	0.112811	−	0.0946594i
$719$	−4.57492e12	+	7.92399e12i	−0.638415	+	1.10577i	0.347365	+	0.937730i	$0.387076\pi$
$719$	−4.57492e12	+	7.92399e12i	−0.638415	+	1.10577i	−0.985781	+	0.168038i	$0.946257\pi$
$720$		0			0
$721$	−8.79889e12	−	1.52401e13i	−1.21260	−	2.10029i
$722$	1.08078e12	+	3.93372e11i	0.148020	+	0.0538748i
$723$		0			0
$724$	−6.89804e12	−	5.78814e12i	−0.933044	−	0.782917i
$725$	−3.74897e12	+	1.36451e12i	−0.503954	+	0.183424i
$726$		0			0
$727$	−3.51895e11	−	1.99570e12i	−0.0467206	−	0.264966i	0.952496	−	0.304553i	$-0.0985069\pi$
$727$	−3.51895e11	−	1.99570e12i	−0.0467206	−	0.264966i	−0.999216	+	0.0395869i	$0.987396\pi$
$728$	−3.23024e12			−0.426230
$729$		0			0
$730$	4.27740e10			0.00557477
$731$	−1.36096e12	−	7.71841e12i	−0.176286	−	0.999769i
$732$		0			0
$733$	−6.70847e12	+	2.44168e12i	−0.858332	+	0.312407i	−0.733433	−	0.679762i	$-0.762083\pi$
$733$	−6.70847e12	+	2.44168e12i	−0.858332	+	0.312407i	−0.124899	+	0.992169i	$0.539861\pi$
$734$	6.79000e11	+	5.69748e11i	0.0863450	+	0.0724521i
$735$		0			0
$736$	1.00393e12	+	3.65401e11i	0.126111	+	0.0459007i
$737$	−1.72214e12	−	2.98283e12i	−0.215013	−	0.372414i
$738$		0			0
$739$	6.03293e11	−	1.04493e12i	0.0744095	−	0.128881i	−0.826420	−	0.563054i	$-0.809626\pi$
$739$	6.03293e11	−	1.04493e12i	0.0744095	−	0.128881i	0.900829	+	0.434173i	$0.142959\pi$
$740$	2.18163e10	−	1.83061e10i	0.00267448	−	0.00224415i
$741$		0			0
$742$	−5.88135e11	+	3.33548e12i	−0.0712294	+	0.403962i
$743$	−2.17919e12	+	1.23588e13i	−0.262329	+	1.48774i	0.514207	+	0.857666i	$0.328086\pi$
$743$	−2.17919e12	+	1.23588e13i	−0.262329	+	1.48774i	−0.776536	+	0.630073i	$0.783025\pi$
$744$		0			0
$745$	−2.20998e11	+	1.85439e11i	−0.0262836	+	0.0220545i
$746$	−8.68721e11	+	1.50467e12i	−0.102696	+	0.177875i
$747$		0			0
$748$	1.01980e13	+	1.76634e13i	1.19112	+	2.06309i
$749$	5.75324e12	+	2.09401e12i	0.667951	+	0.243114i
$750$		0			0
$751$	6.41449e12	+	5.38239e12i	0.735838	+	0.617441i	0.931716	−	0.363187i	$-0.118311\pi$
$751$	6.41449e12	+	5.38239e12i	0.735838	+	0.617441i	−0.195878	+	0.980628i	$0.562756\pi$
$752$	1.28163e13	−	4.66474e12i	1.46144	−	0.531921i
$753$		0			0
$754$	9.75577e10	+	5.53277e11i	0.0109924	+	0.0623407i
$755$	−9.95945e10			−0.0111551
$756$		0			0
$757$	1.61554e13			1.78808			0.894041	−	0.447986i	$-0.147859\pi$
$757$	1.61554e13			1.78808			0.894041	+	0.447986i	$0.147859\pi$
$758$	−3.23805e9	−	1.83639e10i	−0.000356264	−	0.00202048i
$759$		0			0
$760$	4.32490e9	−	1.57413e9i	0.000470235	−	0.000171151i
$761$	6.12432e12	+	5.13892e12i	0.661953	+	0.555444i	0.910671	−	0.413131i	$-0.135565\pi$
$761$	6.12432e12	+	5.13892e12i	0.661953	+	0.555444i	−0.248719	+	0.968576i	$0.580009\pi$
$762$		0			0
$763$	−1.35249e13	−	4.92267e12i	−1.44469	−	0.525824i
$764$	1.67478e12	+	2.90081e12i	0.177844	+	0.308035i
$765$		0			0
$766$	1.10541e12	−	1.91463e12i	0.116010	−	0.200935i
$767$	8.10742e12	−	6.80293e12i	0.845869	−	0.709769i
$768$		0			0
$769$	−3.19080e12	+	1.80959e13i	−0.329026	+	1.86600i	0.150696	+	0.988580i	$0.451849\pi$
$769$	−3.19080e12	+	1.80959e13i	−0.329026	+	1.86600i	−0.479722	+	0.877421i	$0.659262\pi$
$770$	1.61193e10	−	9.14170e10i	0.00165249	−	0.00937171i
$771$		0			0
$772$	1.23924e13	−	1.03984e13i	1.25567	−	1.05363i
$773$	7.62566e12	−	1.32080e13i	0.768192	−	1.33055i	−0.170350	−	0.985384i	$-0.554490\pi$
$773$	7.62566e12	−	1.32080e13i	0.768192	−	1.33055i	0.938542	−	0.345164i	$-0.112177\pi$
$774$		0			0
$775$	5.13497e12	+	8.89403e12i	0.511305	+	0.885607i
$776$	1.48889e12	+	5.41913e11i	0.147396	+	0.0536478i
$777$		0			0
$778$	7.22501e11	+	6.06250e11i	0.0707017	+	0.0593258i
$779$	9.00994e10	−	3.27935e10i	0.00876604	−	0.00319058i
$780$		0			0
$781$	−3.59182e11	−	2.03702e12i	−0.0345450	−	0.195915i
$782$	−7.63853e11			−0.0730432
$783$		0			0
$784$	2.29665e13			2.17106
$785$	−2.27794e10	−	1.29188e11i	−0.00214106	−	0.0121425i
$786$		0			0
$787$	−1.32688e12	+	4.82945e11i	−0.123295	+	0.0448757i	−0.402931	−	0.915230i	$-0.632009\pi$
$787$	−1.32688e12	+	4.82945e11i	−0.123295	+	0.0448757i	0.279636	+	0.960106i	$0.409786\pi$
$788$	9.20538e12	+	7.72423e12i	0.850499	+	0.713653i
$789$		0			0
$790$	1.04795e10	+	3.81423e9i	0.000957236	+	0.000348405i
$791$	−1.04646e13	−	1.81253e13i	−0.950452	−	1.64623i
$792$		0			0
$793$	−1.74876e12	+	3.02895e12i	−0.157037	+	0.271996i
$794$	1.79669e12	−	1.50760e12i	0.160429	−	0.134616i
$795$		0			0
$796$	−2.06729e12	+	1.17242e13i	−0.182512	+	1.03508i
$797$	2.31063e11	−	1.31042e12i	0.0202847	−	0.115040i	−0.972984	−	0.230872i	$-0.925842\pi$
$797$	2.31063e11	−	1.31042e12i	0.0202847	−	0.115040i	0.993269	+	0.115832i	$0.0369533\pi$
$798$		0			0
$799$	−2.34129e13	+	1.96458e13i	−2.03233	+	1.70533i
$800$	2.66026e12	−	4.60770e12i	0.229625	−	0.397722i
$801$		0			0
$802$	−6.56649e11	−	1.13735e12i	−0.0560465	−	0.0970754i
$803$	2.84316e13	+	1.03483e13i	2.41314	+	0.878310i
$804$		0			0
$805$	−1.03451e11	−	8.68060e10i	−0.00868270	−	0.00728565i
$806$	1.35900e12	−	4.94635e11i	0.113426	−	0.0412836i
$807$		0			0
$808$	−3.26691e11	−	1.85276e12i	−0.0269641	−	0.152921i
$809$	9.82761e12			0.806639			0.403320	−	0.915059i	$-0.367856\pi$
$809$	9.82761e12			0.806639			0.403320	+	0.915059i	$0.367856\pi$
$810$		0			0
$811$	−1.63992e13			−1.33116			−0.665579	−	0.746327i	$-0.731815\pi$
$811$	−1.63992e13			−1.33116			−0.665579	+	0.746327i	$0.731815\pi$
$812$	−2.05832e12	−	1.16733e13i	−0.166154	−	0.942305i
$813$		0			0
$814$	−4.87314e11	+	1.77368e11i	−0.0389045	+	0.0141601i
$815$	1.38523e11	+	1.16234e11i	0.0109979	+	0.00922836i
$816$		0			0
$817$	−5.80310e11	−	2.11216e11i	−0.0455681	−	0.0165854i
$818$	−1.52616e11	−	2.64338e11i	−0.0119182	−	0.0206429i
$819$		0			0
$820$	−1.65629e10	+	2.86879e10i	−0.00127931	+	0.00221583i
$821$	−9.31885e12	+	7.81944e12i	−0.715843	+	0.600664i	−0.926232	−	0.376954i	$-0.876972\pi$
$821$	−9.31885e12	+	7.81944e12i	−0.715843	+	0.600664i	0.210389	+	0.977618i	$0.432527\pi$
$822$		0			0
$823$	1.11253e12	−	6.30950e12i	0.0845307	−	0.479397i	−0.912926	−	0.408125i	$-0.866183\pi$
$823$	1.11253e12	−	6.30950e12i	0.0845307	−	0.479397i	0.997457	−	0.0712727i	$-0.0227060\pi$
$824$	9.53169e11	−	5.40569e12i	0.0720273	−	0.408487i
$825$		0			0
$826$	4.40344e12	−	3.69493e12i	0.329141	−	0.276182i
$827$	−2.52386e12	+	4.37145e12i	−0.187625	+	0.324975i	−0.944458	−	0.328633i	$-0.893412\pi$
$827$	−2.52386e12	+	4.37145e12i	−0.187625	+	0.324975i	0.756833	+	0.653608i	$0.226746\pi$
$828$		0			0
$829$	−2.92131e12	−	5.05985e12i	−0.214824	−	0.372085i	0.738394	−	0.674369i	$-0.235584\pi$
$829$	−2.92131e12	−	5.05985e12i	−0.214824	−	0.372085i	−0.953218	+	0.302284i	$0.902251\pi$
$830$	−4.86645e10	−	1.77124e10i	−0.00355927	−	0.00129547i
$831$		0			0
$832$	6.72263e12	+	5.64096e12i	0.486390	+	0.408129i
$833$	−4.83622e13	+	1.76024e13i	−3.48020	+	1.26669i
$834$		0			0
$835$	−2.93604e10	−	1.66511e11i	−0.00209013	−	0.0118537i
$836$	1.60710e12			0.113793
$837$		0			0
$838$	−2.20665e12			−0.154574
$839$	1.43832e12	+	8.15714e12i	0.100214	+	0.568341i	0.993024	+	0.117909i	$0.0376190\pi$
$839$	1.43832e12	+	8.15714e12i	0.100214	+	0.568341i	−0.892811	+	0.450432i	$0.851270\pi$
$840$		0			0
$841$	9.70790e12	−	3.53339e12i	0.669180	−	0.243562i
$842$	−2.72660e12	−	2.28789e12i	−0.186946	−	0.156867i
$843$		0			0
$844$	−7.33874e12	−	2.67108e12i	−0.497829	−	0.181195i
$845$	−7.00045e10	−	1.21251e11i	−0.00472357	−	0.00818147i
$846$		0			0
$847$	1.91307e13	−	3.31354e13i	1.27719	−	2.21216i
$848$	1.51090e13	−	1.26780e13i	1.00336	−	0.841916i
$849$		0			0
$850$	−6.60566e11	+	3.74626e12i	−0.0434042	+	0.246157i
$851$	−1.31009e11	+	7.42988e11i	−0.00856283	+	0.0485622i
$852$		0			0
$853$	8.53576e12	−	7.16235e12i	0.552041	−	0.463218i	−0.323590	−	0.946197i	$-0.604890\pi$
$853$	8.53576e12	−	7.16235e12i	0.552041	−	0.463218i	0.875632	+	0.482980i	$0.160445\pi$
$854$	−9.49819e11	+	1.64514e12i	−0.0611055	+	0.105838i
$855$		0			0
$856$	9.54857e11	+	1.65386e12i	0.0607864	+	0.105285i
$857$	8.44946e12	+	3.07535e12i	0.535076	+	0.194752i	0.595403	−	0.803427i	$-0.296992\pi$
$857$	8.44946e12	+	3.07535e12i	0.535076	+	0.194752i	−0.0603275	+	0.998179i	$0.519215\pi$
$858$		0			0
$859$	2.09794e13	+	1.76038e13i	1.31469	+	1.10316i	0.987402	+	0.158231i	$0.0505792\pi$
$859$	2.09794e13	+	1.76038e13i	1.31469	+	1.10316i	0.327288	+	0.944925i	$0.393865\pi$
$860$	2.00490e11	−	7.29722e10i	0.0124982	−	0.00454899i
$861$		0			0
$862$	4.72775e11	+	2.68124e12i	0.0291657	+	0.165407i
$863$	−1.22058e13			−0.749061			−0.374530	−	0.927215i	$-0.622196\pi$
$863$	−1.22058e13			−0.749061			−0.374530	+	0.927215i	$0.622196\pi$
$864$		0			0
$865$	5.63824e11			0.0342429
$866$	5.14141e11	+	2.91584e12i	0.0310636	+	0.176170i
$867$		0			0
$868$	−2.86728e13	+	1.04360e13i	−1.71448	+	0.624018i
$869$	6.04290e12	+	5.07059e12i	0.359465	+	0.301627i
$870$		0			0
$871$	3.30212e12	+	1.20187e12i	0.194407	+	0.0707582i
$872$	−2.24471e12	−	3.88796e12i	−0.131473	−	0.227718i
$873$		0			0
$874$	−3.00939e10	+	5.21241e10i	−0.00174452	+	0.00302160i
$875$	−1.03062e12	+	8.64797e11i	−0.0594380	+	0.0498744i
$876$		0			0
$877$	4.30409e12	−	2.44097e13i	0.245687	−	1.39336i	−0.573203	−	0.819413i	$-0.694300\pi$
$877$	4.30409e12	−	2.44097e13i	0.245687	−	1.39336i	0.818891	−	0.573949i	$-0.194589\pi$
$878$	1.63333e11	−	9.26306e11i	0.00927573	−	0.0526053i
$879$		0			0
$880$	−4.14100e11	+	3.47472e11i	−0.0232774	+	0.0195320i
$881$	7.24461e12	−	1.25480e13i	0.405157	−	0.701753i	−0.589183	−	0.808000i	$-0.700550\pi$
$881$	7.24461e12	−	1.25480e13i	0.405157	−	0.701753i	0.994340	+	0.106247i	$0.0338835\pi$
$882$		0			0
$883$	7.09123e12	+	1.22824e13i	0.392553	+	0.679922i	0.992786	−	0.119904i	$-0.0382586\pi$
$883$	7.09123e12	+	1.22824e13i	0.392553	+	0.679922i	−0.600232	+	0.799826i	$0.704925\pi$
$884$	−1.95541e13	−	7.11712e12i	−1.07697	−	0.391985i
$885$		0			0
$886$	−2.05974e12	−	1.72832e12i	−0.112295	−	0.0942266i
$887$	1.98639e13	−	7.22986e12i	1.07748	−	0.392170i	0.258509	−	0.966009i	$-0.416769\pi$
$887$	1.98639e13	−	7.22986e12i	1.07748	−	0.392170i	0.818968	+	0.573839i	$0.194547\pi$
$888$		0			0
$889$	−4.33435e12	−	2.45813e13i	−0.232737	−	1.31992i
$890$	6.47334e10			0.00345838
$891$		0			0
$892$	−4.73524e12			−0.250438
$893$	4.18186e11	+	2.37165e12i	0.0220059	+	0.124801i
$894$		0			0
$895$	5.77483e10	−	2.10187e10i	0.00300840	−	0.00109497i
$896$	1.60725e13	+	1.34864e13i	0.833100	+	0.699054i
$897$		0			0
$898$	−3.74388e12	−	1.36266e12i	−0.192122	−	0.0699268i
$899$	5.37520e12	+	9.31012e12i	0.274458	+	0.475375i
$900$		0			0
$901$	−2.20993e13	+	3.82771e13i	−1.11716	+	1.93498i
$902$	4.62080e11	−	3.87731e11i	0.0232428	−	0.0195030i
$903$		0			0
$904$	1.13362e12	−	6.42906e12i	0.0564558	−	0.320177i
$905$	−9.28699e10	+	5.26692e11i	−0.00460210	+	0.0260998i
$906$		0			0
$907$	−7.35009e11	+	6.16746e11i	−0.0360629	+	0.0302603i	−0.660641	−	0.750702i	$-0.729715\pi$
$907$	−7.35009e11	+	6.16746e11i	−0.0360629	+	0.0302603i	0.624578	+	0.780962i	$0.285271\pi$
$908$	−6.79602e12	+	1.17711e13i	−0.331794	+	0.574684i
$909$		0			0
$910$	4.73537e10	+	8.20191e10i	0.00228912	+	0.00396487i
$911$	−2.51220e13	−	9.14364e12i	−1.20843	−	0.439832i	−0.342270	−	0.939602i	$-0.611196\pi$
$911$	−2.51220e13	−	9.14364e12i	−1.20843	−	0.439832i	−0.866158	+	0.499770i	$0.833418\pi$
$912$		0			0
$913$	−2.80619e13	−	2.35467e13i	−1.33659	−	1.12153i
$914$	1.98232e12	−	7.21506e11i	0.0939541	−	0.0341965i
$915$		0			0
$916$	6.28056e11	+	3.56188e12i	0.0294760	+	0.167167i
$917$	−3.16842e13			−1.47973
$918$		0			0
$919$	2.56915e13			1.18815			0.594073	−	0.804411i	$-0.297519\pi$
$919$	2.56915e13			1.18815			0.594073	+	0.804411i	$0.297519\pi$
$920$	−7.31466e9	−	4.14835e10i	−0.000336627	−	0.00190911i
$921$		0			0
$922$	2.87395e12	−	1.04603e12i	0.130976	−	0.0476712i
$923$	1.61662e12	+	1.35650e12i	0.0733161	+	0.0615196i
$924$		0			0
$925$	3.53063e12	+	1.28504e12i	0.158568	+	0.0577139i
$926$	−1.64140e12	−	2.84300e12i	−0.0733612	−	0.127065i
$927$		0			0
$928$	2.78472e12	−	4.82327e12i	0.123258	−	0.213489i
$929$	−1.68836e13	+	1.41670e13i	−0.743694	+	0.624034i	−0.933827	−	0.357725i	$-0.883553\pi$
$929$	−1.68836e13	+	1.41670e13i	−0.743694	+	0.624034i	0.190133	+	0.981758i	$0.439108\pi$
$930$		0			0
$931$	−7.04189e11	+	3.99365e12i	−0.0307196	+	0.174219i
$932$	−3.54043e12	+	2.00788e13i	−0.153704	+	0.871698i
$933$		0			0
$934$	2.18521e12	−	1.83361e12i	0.0939576	−	0.0788398i
$935$	6.05686e11	−	1.04908e12i	0.0259176	−	0.0448906i
$936$		0			0
$937$	−1.20291e13	−	2.08351e13i	−0.509808	−	0.883013i	−0.999935	−	0.0113620i	$-0.996383\pi$
$937$	−1.20291e13	−	2.08351e13i	−0.509808	−	0.883013i	0.490128	−	0.871651i	$-0.336950\pi$
$938$	1.79351e12	+	6.52783e11i	0.0756467	+	0.0275332i
$939$		0			0
$940$	−6.37360e11	−	5.34809e11i	−0.0266262	−	0.0223421i
$941$	3.23085e11	−	1.17593e11i	0.0134327	−	0.00488910i	−0.335295	−	0.942113i	$-0.608836\pi$
$941$	3.23085e11	−	1.17593e11i	0.0134327	−	0.00488910i	0.348728	+	0.937224i	$0.386614\pi$
$942$		0			0
$943$	−1.52384e11	−	8.64214e11i	−0.00627534	−	0.0355892i
$944$	−3.34745e13			−1.37196
$945$		0			0
$946$	−3.88509e12			−0.157722
$947$	−6.08982e12	−	3.45371e13i	−0.246054	−	1.39544i	−0.818033	−	0.575172i	$-0.804935\pi$
$947$	−6.08982e12	−	3.45371e13i	−0.246054	−	1.39544i	0.571979	−	0.820268i	$-0.306176\pi$
$948$		0			0
$949$	−2.90075e13	+	1.05579e13i	−1.16095	+	0.422550i
$950$	2.29614e11	+	1.92669e11i	0.00914623	+	0.00767460i
$951$		0			0
$952$	−2.15146e13	−	7.83067e12i	−0.848920	−	0.308981i
$953$	2.44675e13	+	4.23790e13i	0.960887	+	1.66430i	0.720281	+	0.693682i	$0.244013\pi$
$953$	2.44675e13	+	4.23790e13i	0.960887	+	1.66430i	0.240605	+	0.970623i	$0.422654\pi$
$954$		0			0
$955$	9.94700e10	−	1.72287e11i	0.00386970	−	0.00670251i
$956$	1.23145e13	−	1.03331e13i	0.476823	−	0.400102i
$957$		0			0
$958$	4.61034e11	−	2.61465e12i	0.0176843	−	0.100293i
$959$	6.46189e12	−	3.66472e13i	0.246704	−	1.39913i
$960$		0			0
$961$	9.45324e11	−	7.93221e11i	0.0357541	−	0.0300012i
$962$	2.64546e11	−	4.58208e11i	0.00995896	−	0.0172494i
$963$		0			0
$964$	−1.74088e12	−	3.01530e12i	−0.0649267	−	0.112456i
$965$	−9.02858e11	−	3.28613e11i	−0.0335156	−	0.0121987i
$966$		0			0
$967$	−1.04522e13	−	8.77040e12i	−0.384403	−	0.322552i	0.430025	−	0.902817i	$-0.358505\pi$
$967$	−1.04522e13	−	8.77040e12i	−0.384403	−	0.322552i	−0.814428	+	0.580265i	$0.802949\pi$
$968$	1.12147e13	−	4.08183e12i	0.410535	−	0.149423i
$969$		0			0
$970$	−8.06672e9	−	4.57486e10i	−0.000292566	−	0.00165922i
$971$	2.94353e13			1.06263			0.531315	−	0.847174i	$-0.321698\pi$
$971$	2.94353e13			1.06263			0.531315	+	0.847174i	$0.321698\pi$
$972$		0			0
$973$	−5.70119e13			−2.03919
$974$	−1.19645e12	−	6.78539e12i	−0.0425969	−	0.241579i
$975$		0			0
$976$	1.03952e13	−	3.78354e12i	0.366698	−	0.133467i
$977$	−3.50342e13	−	2.93971e13i	−1.23017	−	1.03224i	−0.998228	−	0.0595087i	$-0.981047\pi$
$977$	−3.50342e13	−	2.93971e13i	−1.23017	−	1.03224i	−0.231945	−	0.972729i	$-0.574509\pi$
$978$		0			0
$979$	4.30279e13	+	1.56609e13i	1.49702	+	0.544872i
$980$	−7.00520e11	−	1.21334e12i	−0.0242607	−	0.0420207i
$981$		0			0
$982$	1.04705e12	−	1.81355e12i	0.0359308	−	0.0622340i
$983$	−4.62893e12	+	3.88414e12i	−0.158121	+	0.132679i	−0.718416	−	0.695614i	$-0.755132\pi$
$983$	−4.62893e12	+	3.88414e12i	−0.158121	+	0.132679i	0.560294	+	0.828293i	$0.310688\pi$
$984$		0			0
$985$	1.23934e11	−	7.02866e11i	0.00419496	−	0.0237908i
$986$	−6.91470e11	+	3.92152e12i	−0.0232985	+	0.132132i
$987$		0			0
$988$	−1.25604e12	+	1.05395e12i	−0.0419371	+	0.0351894i
$989$	−2.82604e12	+	4.89485e12i	−0.0939280	+	0.162688i
$990$		0			0
$991$	−9.22065e12	−	1.59706e13i	−0.303690	−	0.526006i	0.673279	−	0.739389i	$-0.264885\pi$
$991$	−9.22065e12	−	1.59706e13i	−0.303690	−	0.526006i	−0.976969	+	0.213382i	$0.931552\pi$
$992$	−1.34722e13	−	4.90348e12i	−0.441709	−	0.160769i
$993$		0			0
$994$	8.78046e11	+	7.36768e11i	0.0285285	+	0.0239382i
$995$	6.64431e11	−	2.41833e11i	0.0214905	−	0.00782189i
$996$		0			0
$997$	8.36094e12	+	4.74173e13i	0.267995	+	1.51988i	0.760368	+	0.649492i	$0.225019\pi$
$997$	8.36094e12	+	4.74173e13i	0.267995	+	1.51988i	−0.492373	+	0.870384i	$0.663870\pi$
$998$	3.98909e12			0.127288
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.10.e.a.10.13		156
3.2	odd	2		27.10.e.a.13.14	✓	156
27.2	odd	18		27.10.e.a.25.14	yes	156
27.25	even	9	inner	81.10.e.a.73.13		156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.10.e.a.13.14	✓	156	3.2	odd	2
27.10.e.a.25.14	yes	156	27.2	odd	18
81.10.e.a.10.13		156	1.1	even	1	trivial
81.10.e.a.73.13		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+(0.622466 + 3.53018i) q^{2} +(469.048 - 170.719i) q^{4} +(-22.7101 - 19.0560i) q^{5} +(10919.6 + 3974.40i) q^{7} +(1812.30 + 3139.00i) q^{8} +(53.1349 - 92.0324i) q^{10} +(57583.8 - 48318.5i) q^{11} +(-13317.6 + 75527.7i) q^{13} +(-7233.28 + 41021.9i) q^{14} +(185821. - 155922. i) q^{16} +(-271792. + 470757. i) q^{17} +(21415.8 + 37093.3i) q^{19} +(-13905.3 - 5061.13i) q^{20} +(206417. + 173204. i) q^{22} +(368370. - 134076. i) q^{23} +(-339004. - 1.92259e6i) q^{25} -274916. q^{26} +5.80031e6 q^{28} +(-354864. - 2.01253e6i) q^{29} +(-4.94332e6 + 1.79922e6i) q^{31} +(2.08773e6 + 1.75181e6i) q^{32} +(-1.83104e6 - 666444. i) q^{34} +(-172248. - 298342. i) q^{35} +(-962281. + 1.66672e6i) q^{37} +(-117615. + 98690.9i) q^{38} +(18659.3 - 105822. i) q^{40} +(388724. - 2.20457e6i) q^{41} +(-1.10450e7 + 9.26782e6i) q^{43} +(1.87606e7 - 3.24944e7i) q^{44} +(702609. + 1.21695e6i) q^{46} +(5.28349e7 + 1.92303e7i) q^{47} +(7.25284e7 + 6.08586e7i) q^{49} +(6.57606e6 - 2.39349e6i) q^{50} +(6.64747e6 + 3.76997e7i) q^{52} +8.13096e7 q^{53} -2.22849e6 q^{55} +(7.31393e6 + 4.14794e7i) q^{56} +(6.88371e6 - 2.50547e6i) q^{58} +(-1.05713e8 - 8.87036e7i) q^{59} +(4.28541e7 + 1.55976e7i) q^{61} +(-9.42863e6 - 1.63309e7i) q^{62} +(5.72138e7 - 9.90972e7i) q^{64} +(1.74170e6 - 1.46146e6i) q^{65} +(7.95651e6 - 4.51236e7i) q^{67} +(-4.71160e7 + 2.67208e8i) q^{68} +(945983. - 793774. i) q^{70} +(1.37584e7 - 2.38303e7i) q^{71} +(2.01252e8 + 3.48578e8i) q^{73} +(-6.48280e6 - 2.35955e6i) q^{74} +(1.63776e7 + 1.37424e7i) q^{76} +(8.20827e8 - 2.98757e8i) q^{77} +(1.82228e7 + 1.03347e8i) q^{79} -7.19127e6 q^{80} +8.02448e6 q^{82} +(-8.46228e7 - 4.79920e8i) q^{83} +(1.51432e7 - 5.51166e6i) q^{85} +(-3.95922e7 - 3.32218e7i) q^{86} +(2.56031e8 + 9.31878e7i) q^{88} +(3.04571e8 + 5.27532e8i) q^{89} +(-4.45599e8 + 7.71800e8i) q^{91} +(1.49894e8 - 1.25776e8i) q^{92} +(-3.49986e7 + 1.98487e8i) q^{94} +(220495. - 1.25049e6i) q^{95} +(3.34866e8 - 2.80986e8i) q^{97} +(-1.69695e8 + 2.93921e8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q + 6 q^{2} - 6 q^{4} - 2382 q^{5} - 6 q^{7} - 36861 q^{8} - 3 q^{10} + 121767 q^{11} - 6 q^{13} + 720417 q^{14} + 1530 q^{16} - 1002249 q^{17} - 3 q^{19} + 8448573 q^{20} - 1585014 q^{22} - 9316482 q^{23}+ \cdots - 6901039926 q^{98}+O(q^{100}) \) 156 * q + 6 * q^2 - 6 * q^4 - 2382 * q^5 - 6 * q^7 - 36861 * q^8 - 3 * q^10 + 121767 * q^11 - 6 * q^13 + 720417 * q^14 + 1530 * q^16 - 1002249 * q^17 - 3 * q^19 + 8448573 * q^20 - 1585014 * q^22 - 9316482 * q^23 + 2192178 * q^25 + 33129678 * q^26 - 12 * q^28 - 19657236 * q^29 - 4633692 * q^31 + 37550952 * q^32 + 14341770 * q^34 - 34449663 * q^35 - 3 * q^37 + 92022060 * q^38 + 6645801 * q^40 + 33127221 * q^41 + 2356203 * q^43 - 1001541 * q^44 - 3 * q^46 + 33488952 * q^47 - 93214644 * q^49 + 72027753 * q^50 + 160531713 * q^52 - 4841352 * q^53 - 12 * q^55 + 91770981 * q^56 - 320682489 * q^58 - 538090854 * q^59 + 36683436 * q^61 + 55862958 * q^62 - 956301315 * q^64 + 852347310 * q^65 - 109026897 * q^67 + 508886217 * q^68 - 815297649 * q^70 - 940878639 * q^71 - 221849931 * q^73 - 838884579 * q^74 + 908401146 * q^76 + 967811358 * q^77 - 1228059150 * q^79 + 2497115154 * q^80 - 12 * q^82 + 297703284 * q^83 + 1535949369 * q^85 - 2930201574 * q^86 + 2837227002 * q^88 - 1774997208 * q^89 + 551343507 * q^91 + 6896645517 * q^92 + 414852915 * q^94 + 9000269169 * q^95 + 3371772333 * q^97 - 6901039926 * q^98

Introduction

L-functions

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