LMFDB - Embedded newform 9.15.d.a.5.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9,15,Mod(2,9)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9.2"); S:= CuspForms(chi, 15); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 15, names="a")

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	9.d (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$11.1896071337$
Analytic rank:	$0$
Dimension:	$26$
Relative dimension:	$13$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	9.5
Dual form			9.15.d.a.2.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(129.548 - 74.7948i) q^{2} +(1398.48 + 1681.44i) q^{3} +(2996.54 - 5190.15i) q^{4} +(31950.1 + 18446.4i) q^{5} +(306934. + 113228. i) q^{6} +(153772. + 266342. i) q^{7} +1.55438e6i q^{8} +(-871480. + 4.70290e6i) q^{9} +5.51879e6 q^{10} +(8.07458e6 - 4.66186e6i) q^{11} +(1.29175e7 - 2.21984e6i) q^{12} +(2.46419e7 - 4.26810e7i) q^{13} +(3.98420e7 + 2.30028e7i) q^{14} +(1.36651e7 + 7.95190e7i) q^{15} +(1.65355e8 + 2.86402e8i) q^{16} -1.60558e8i q^{17} +(2.38854e8 + 6.74436e8i) q^{18} +1.10366e9 q^{19} +(1.91479e8 - 1.10551e8i) q^{20} +(-2.32789e8 + 6.31032e8i) q^{21} +(6.97366e8 - 1.20787e9i) q^{22} +(-5.63572e9 - 3.25379e9i) q^{23} +(-2.61358e9 + 2.17376e9i) q^{24} +(-2.37122e9 - 4.10707e9i) q^{25} -7.37234e9i q^{26} +(-9.12638e9 + 5.11158e9i) q^{27} +1.84314e9 q^{28} +(5.84016e9 - 3.37182e9i) q^{29} +(7.71791e9 + 9.27948e9i) q^{30} +(-5.34495e9 + 9.25772e9i) q^{31} +(2.07879e10 + 1.20019e10i) q^{32} +(1.91308e10 + 7.05737e9i) q^{33} +(-1.20089e10 - 2.08000e10i) q^{34} +1.13462e10i q^{35} +(2.17974e10 + 1.86155e10i) q^{36} -1.45967e11 q^{37} +(1.42978e11 - 8.25481e10i) q^{38} +(1.06226e11 - 1.82547e10i) q^{39} +(-2.86727e10 + 4.96625e10i) q^{40} +(1.88610e11 + 1.08894e11i) q^{41} +(1.70405e10 + 9.91606e10i) q^{42} +(-7.02322e10 - 1.21646e11i) q^{43} -5.58777e10i q^{44} +(-1.14596e11 + 1.34183e11i) q^{45} -9.73465e11 q^{46} +(4.86126e11 - 2.80665e11i) q^{47} +(-2.50322e11 + 6.78561e11i) q^{48} +(2.91820e11 - 5.05446e11i) q^{49} +(-6.14375e11 - 3.54710e11i) q^{50} +(2.69968e11 - 2.24537e11i) q^{51} +(-1.47680e11 - 2.55790e11i) q^{52} -2.07734e12i q^{53} +(-7.99989e11 + 1.34480e12i) q^{54} +3.43979e11 q^{55} +(-4.13995e11 + 2.39020e11i) q^{56} +(1.54345e12 + 1.85573e12i) q^{57} +(5.04389e11 - 8.73628e11i) q^{58} +(1.90853e12 + 1.10189e12i) q^{59} +(4.53664e11 + 1.67357e11i) q^{60} +(2.01361e12 + 3.48768e12i) q^{61} +1.59910e12i q^{62} +(-1.38659e12 + 4.91066e11i) q^{63} -1.82762e12 q^{64} +(1.57462e12 - 9.09108e11i) q^{65} +(3.00621e12 - 5.16610e11i) q^{66} +(1.82254e12 - 3.15674e12i) q^{67} +(-8.33320e11 - 4.81118e11i) q^{68} +(-2.41041e12 - 1.40265e13i) q^{69} +(8.48638e11 + 1.46988e12i) q^{70} +4.60775e12i q^{71} +(-7.31008e12 - 1.35461e12i) q^{72} -1.45384e13 q^{73} +(-1.89097e13 + 1.09175e13i) q^{74} +(3.58967e12 - 9.73070e12i) q^{75} +(3.30716e12 - 5.72817e12i) q^{76} +(2.48330e12 + 1.43373e12i) q^{77} +(1.23961e13 - 1.03101e13i) q^{78} +(1.41356e13 + 2.44835e13i) q^{79} +1.22008e13i q^{80} +(-2.13578e13 - 8.19698e12i) q^{81} +3.25789e13 q^{82} +(3.75647e12 - 2.16880e12i) q^{83} +(2.57759e12 + 3.09912e12i) q^{84} +(2.96172e12 - 5.12985e12i) q^{85} +(-1.81969e13 - 1.05060e13i) q^{86} +(1.38368e13 + 5.10443e12i) q^{87} +(7.24628e12 + 1.25509e13i) q^{88} -1.98593e13i q^{89} +(-4.80951e12 + 2.59543e13i) q^{90} +1.51570e13 q^{91} +(-3.37753e13 + 1.95002e13i) q^{92} +(-2.30411e13 + 3.95955e12i) q^{93} +(4.19846e13 - 7.27195e13i) q^{94} +(3.52621e13 + 2.03586e13i) q^{95} +(8.89102e12 + 5.17379e13i) q^{96} +(8.91638e12 + 1.54436e13i) q^{97} -8.73064e13i q^{98} +(1.48875e13 + 4.20367e13i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q - 3 q^{2} - 2199 q^{3} + 98303 q^{4} - 107994 q^{5} + 24957 q^{6} - 146330 q^{7} - 5316525 q^{9} - 32772 q^{10} - 15978711 q^{11} - 53795046 q^{12} - 23281436 q^{13} - 349442850 q^{14} + 207365400 q^{15}+ \cdots - 195117933369168 q^{99}+O(q^{100}) $ 26 * q - 3 * q^2 - 2199 * q^3 + 98303 * q^4 - 107994 * q^5 + 24957 * q^6 - 146330 * q^7 - 5316525 * q^9 - 32772 * q^10 - 15978711 * q^11 - 53795046 * q^12 - 23281436 * q^13 - 349442850 * q^14 + 207365400 * q^15 - 671072257 * q^16 - 2272246668 * q^18 + 195706222 * q^19 + 2822935854 * q^20 + 1958992050 * q^21 - 204235521 * q^22 - 6101133672 * q^23 + 10931998527 * q^24 + 14614789727 * q^25 - 34016586282 * q^27 - 9052979204 * q^28 + 85191770166 * q^29 + 91857763818 * q^30 + 15357554728 * q^31 - 237242922057 * q^32 + 76352726421 * q^33 - 16566014943 * q^34 - 570464313633 * q^36 - 77721425444 * q^37 + 476314869819 * q^38 + 353897273784 * q^39 - 88855733850 * q^40 - 938882938233 * q^41 + 700091392140 * q^42 - 29709800063 * q^43 - 84148700094 * q^45 + 1553142786144 * q^46 - 1272741434580 * q^47 + 803069876301 * q^48 - 945184029255 * q^49 + 3573994524699 * q^50 - 1993755292875 * q^51 + 1825489374856 * q^52 + 6488294941323 * q^54 - 3772940931372 * q^55 - 7790759725422 * q^56 - 10739943123909 * q^57 + 3747043240302 * q^58 + 5874788534451 * q^59 + 1848130753878 * q^60 - 4867968901544 * q^61 + 5766639947244 * q^63 + 1211169309434 * q^64 - 22156719464856 * q^65 - 6375059860230 * q^66 - 8251061484125 * q^67 + 30687017243265 * q^68 + 23068377735552 * q^69 + 6871822387932 * q^70 - 46243200240621 * q^72 + 16120119648922 * q^73 + 8549243621166 * q^74 + 1090840096221 * q^75 + 14422972781521 * q^76 + 13919363311398 * q^77 + 109811947190436 * q^78 - 10740904544582 * q^79 - 140975607018501 * q^81 - 67076318933382 * q^82 - 11295125984532 * q^83 + 30827942753826 * q^84 + 10590724937466 * q^85 + 97019495740221 * q^86 + 151937485500582 * q^87 - 26136212294541 * q^88 - 392755154255226 * q^90 + 70870424994080 * q^91 - 474274297000284 * q^92 - 124466752375728 * q^93 - 46678164316620 * q^94 + 440317551118746 * q^95 + 823174447870656 * q^96 + 7621755375583 * q^97 - 195117933369168 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/9\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	129.548	−	74.7948i	1.01210	−	0.584335i	0.100292	−	0.994958i	$-0.468022\pi$
$2$	129.548	−	74.7948i	1.01210	−	0.584335i	0.911805	+	0.410623i	$0.134689\pi$
$3$	1398.48	+	1681.44i	0.639451	+	0.768832i
$3$	1398.48	+	1681.44i	0.639451	+	0.768832i
$4$	2996.54	−	5190.15i	0.182894	−	0.316782i
$5$	31950.1	+	18446.4i	0.408962	+	0.236114i	0.690344	−	0.723482i	$-0.257459\pi$
$5$	31950.1	+	18446.4i	0.408962	+	0.236114i	−0.281382	+	0.959596i	$0.590793\pi$
$6$	306934.	+	113228.i	1.09644	+	0.404479i
$7$	153772.	+	266342.i	0.186721	+	0.323410i	0.944155	−	0.329502i	$-0.106881\pi$
$7$	153772.	+	266342.i	0.186721	+	0.323410i	−0.757434	+	0.652911i	$0.773547\pi$
$8$			1.55438e6i			0.741184i
$9$	−871480.	+	4.70290e6i	−0.182205	+	0.983261i
$10$	5.51879e6			0.551879
$11$	8.07458e6	−	4.66186e6i	0.414354	−	0.239227i	−0.278305	−	0.960493i	$-0.589773\pi$
$11$	8.07458e6	−	4.66186e6i	0.414354	−	0.239227i	0.692659	+	0.721266i	$0.256439\pi$
$12$	1.29175e7	−	2.21984e6i	0.360504	−	0.0619517i
$13$	2.46419e7	−	4.26810e7i	0.392708	−	0.680191i	−0.600097	−	0.799927i	$-0.704872\pi$
$13$	2.46419e7	−	4.26810e7i	0.392708	−	0.680191i	0.992806	+	0.119736i	$0.0382049\pi$
$14$	3.98420e7	+	2.30028e7i	0.377959	+	0.218215i
$15$	1.36651e7	+	7.95190e7i	0.0799789	+	0.465406i
$16$	1.65355e8	+	2.86402e8i	0.615994	+	1.06693i
$17$		−	1.60558e8i		−	0.391281i	−0.980676	−	0.195641i	$-0.937321\pi$
$17$		−	1.60558e8i		−	0.391281i	0.980676	−	0.195641i	$-0.0626786\pi$
$18$	2.38854e8	+	6.74436e8i	0.390144	+	1.10162i
$19$	1.10366e9			1.23470			0.617348	−	0.786690i	$-0.288207\pi$
$19$	1.10366e9			1.23470			0.617348	+	0.786690i	$0.288207\pi$
$20$	1.91479e8	−	1.10551e8i	0.149593	−	0.0863678i
$21$	−2.32789e8	+	6.31032e8i	−0.129249	+	0.350361i
$22$	6.97366e8	−	1.20787e9i	0.279577	−	0.484242i
$23$	−5.63572e9	−	3.25379e9i	−1.65522	−	0.955639i	−0.974878	−	0.222741i	$-0.928500\pi$
$23$	−5.63572e9	−	3.25379e9i	−1.65522	−	0.955639i	−0.680338	−	0.732898i	$-0.738167\pi$
$24$	−2.61358e9	+	2.17376e9i	−0.569846	+	0.473951i
$25$	−2.37122e9	−	4.10707e9i	−0.388500	−	0.672902i
$26$		−	7.37234e9i		−	0.917892i
$27$	−9.12638e9	+	5.11158e9i	−0.872473	+	0.488662i
$28$	1.84314e9			0.136600
$29$	5.84016e9	−	3.37182e9i	0.338562	−	0.195469i	−0.321074	−	0.947054i	$-0.604044\pi$
$29$	5.84016e9	−	3.37182e9i	0.338562	−	0.195469i	0.659636	+	0.751585i	$0.270710\pi$
$30$	7.71791e9	+	9.27948e9i	0.352899	+	0.424302i
$31$	−5.34495e9	+	9.25772e9i	−0.194273	+	0.336490i	−0.946662	−	0.322229i	$-0.895568\pi$
$31$	−5.34495e9	+	9.25772e9i	−0.194273	+	0.336490i	0.752389	+	0.658719i	$0.228901\pi$
$32$	2.07879e10	+	1.20019e10i	0.605007	+	0.349301i
$33$	1.91308e10	+	7.05737e9i	0.448884	+	0.165594i
$34$	−1.20089e10	−	2.08000e10i	−0.228639	−	0.396015i
$35$			1.13462e10i			0.176350i
$36$	2.17974e10	+	1.86155e10i	0.278155	+	0.237552i
$37$	−1.45967e11			−1.53759			−0.768796	−	0.639494i	$-0.779144\pi$
$37$	−1.45967e11			−1.53759			−0.768796	+	0.639494i	$0.779144\pi$
$38$	1.42978e11	−	8.25481e10i	1.24963	−	0.721476i
$39$	1.06226e11	−	1.82547e10i	0.774070	−	0.133022i
$40$	−2.86727e10	+	4.96625e10i	−0.175004	+	0.303116i
$41$	1.88610e11	+	1.08894e11i	0.968453	+	0.559137i	0.898764	−	0.438432i	$-0.144466\pi$
$41$	1.88610e11	+	1.08894e11i	0.968453	+	0.559137i	0.0696888	+	0.997569i	$0.477799\pi$
$42$	1.70405e10	+	9.91606e10i	0.0739158	+	0.430124i
$43$	−7.02322e10	−	1.21646e11i	−0.258379	−	0.447525i	0.707429	−	0.706785i	$-0.249855\pi$
$43$	−7.02322e10	−	1.21646e11i	−0.258379	−	0.447525i	−0.965808	+	0.259259i	$0.916522\pi$
$44$		−	5.58777e10i		−	0.175013i
$45$	−1.14596e11	+	1.34183e11i	−0.306677	+	0.359095i
$46$	−9.73465e11			−2.23365
$47$	4.86126e11	−	2.80665e11i	0.959542	−	0.553992i	0.0635100	−	0.997981i	$-0.479771\pi$
$47$	4.86126e11	−	2.80665e11i	0.959542	−	0.553992i	0.896032	+	0.443989i	$0.146437\pi$
$48$	−2.50322e11	+	6.78561e11i	−0.426394	+	1.15585i
$49$	2.91820e11	−	5.05446e11i	0.430271	−	0.745251i
$50$	−6.14375e11	−	3.54710e11i	−0.786400	−	0.454028i
$51$	2.69968e11	−	2.24537e11i	0.300830	−	0.250205i
$52$	−1.47680e11	−	2.55790e11i	−0.143648	−	0.248806i
$53$		−	2.07734e12i		−	1.76838i	−0.467128	−	0.884190i	$-0.654711\pi$
$53$		−	2.07734e12i		−	1.76838i	0.467128	−	0.884190i	$-0.345289\pi$
$54$	−7.99989e11	+	1.34480e12i	−0.597486	+	1.00439i
$55$	3.43979e11			0.225940
$56$	−4.13995e11	+	2.39020e11i	−0.239706	+	0.138394i
$57$	1.54345e12	+	1.85573e12i	0.789528	+	0.949274i
$58$	5.04389e11	−	8.73628e11i	0.228439	−	0.395668i
$59$	1.90853e12	+	1.10189e12i	0.766895	+	0.442767i	0.831766	−	0.555127i	$-0.187330\pi$
$59$	1.90853e12	+	1.10189e12i	0.766895	+	0.442767i	−0.0648709	+	0.997894i	$0.520664\pi$
$60$	4.53664e11	+	1.67357e11i	0.162060	+	0.0597842i
$61$	2.01361e12	+	3.48768e12i	0.640718	+	1.10976i	0.985273	+	0.170990i	$0.0546965\pi$
$61$	2.01361e12	+	3.48768e12i	0.640718	+	1.10976i	−0.344555	+	0.938766i	$0.611970\pi$
$62$			1.59910e12i			0.454081i
$63$	−1.38659e12	+	4.91066e11i	−0.352017	+	0.124668i
$64$	−1.82762e12			−0.415553
$65$	1.57462e12	−	9.09108e11i	0.321205	−	0.185448i
$66$	3.00621e12	−	5.16610e11i	0.551077	−	0.0947012i
$67$	1.82254e12	−	3.15674e12i	0.300714	−	0.520852i	−0.675584	−	0.737283i	$-0.736108\pi$
$67$	1.82254e12	−	3.15674e12i	0.300714	−	0.520852i	0.976298	+	0.216431i	$0.0694416\pi$
$68$	−8.33320e11	−	4.81118e11i	−0.123951	−	0.0715630i
$69$	−2.41041e12	−	1.40265e13i	−0.323703	−	1.88367i
$70$	8.48638e11	+	1.46988e12i	0.103047	+	0.178483i
$71$			4.60775e12i			0.506618i	0.967385	+	0.253309i	$0.0815189\pi$
$71$			4.60775e12i			0.506618i	−0.967385	+	0.253309i	$0.918481\pi$
$72$	−7.31008e12	−	1.35461e12i	−0.728777	−	0.135047i
$73$	−1.45384e13			−1.31601			−0.658003	−	0.753016i	$-0.728598\pi$
$73$	−1.45384e13			−1.31601			−0.658003	+	0.753016i	$0.728598\pi$
$74$	−1.89097e13	+	1.09175e13i	−1.55619	+	0.898469i
$75$	3.58967e12	−	9.73070e12i	0.268922	−	0.728979i
$76$	3.30716e12	−	5.72817e12i	0.225819	−	0.391130i
$77$	2.48330e12	+	1.43373e12i	0.154737	+	0.0893373i
$78$	1.23961e13	−	1.03101e13i	0.705705	−	0.586947i
$79$	1.41356e13	+	2.44835e13i	0.736077	+	1.27492i	0.954249	+	0.299013i	$0.0966575\pi$
$79$	1.41356e13	+	2.44835e13i	0.736077	+	1.27492i	−0.218171	+	0.975910i	$0.570009\pi$
$80$			1.22008e13i			0.581779i
$81$	−2.13578e13	−	8.19698e12i	−0.933603	−	0.358310i
$82$	3.25789e13			1.30689
$83$	3.75647e12	−	2.16880e12i	0.138431	−	0.0799231i	−0.429185	−	0.903217i	$-0.641199\pi$
$83$	3.75647e12	−	2.16880e12i	0.138431	−	0.0799231i	0.567616	+	0.823293i	$0.307866\pi$
$84$	2.57759e12	+	3.09912e12i	0.0873492	+	0.105023i
$85$	2.96172e12	−	5.12985e12i	0.0923871	−	0.160019i
$86$	−1.81969e13	−	1.05060e13i	−0.523009	−	0.301959i
$87$	1.38368e13	+	5.10443e12i	0.366777	+	0.135305i
$88$	7.24628e12	+	1.25509e13i	0.177311	+	0.307112i
$89$		−	1.98593e13i		−	0.448986i	−0.974476	−	0.224493i	$-0.927927\pi$
$89$		−	1.98593e13i		−	0.448986i	0.974476	−	0.224493i	$-0.0720726\pi$
$90$	−4.80951e12	+	2.59543e13i	−0.100555	+	0.542641i
$91$	1.51570e13			0.293307
$92$	−3.37753e13	+	1.95002e13i	−0.605458	+	0.349562i
$93$	−2.30411e13	+	3.95955e12i	−0.382932	+	0.0658059i
$94$	4.19846e13	−	7.27195e13i	0.647433	−	1.12139i
$95$	3.52621e13	+	2.03586e13i	0.504944	+	0.291529i
$96$	8.89102e12	+	5.17379e13i	0.118319	+	0.688509i
$97$	8.91638e12	+	1.54436e13i	0.110354	+	0.191138i	0.915913	−	0.401377i	$-0.131468\pi$
$97$	8.91638e12	+	1.54436e13i	0.110354	+	0.191138i	−0.805559	+	0.592515i	$0.798135\pi$
$98$		−	8.73064e13i		−	1.00569i
$99$	1.48875e13	+	4.20367e13i	0.159725	+	0.451006i
$100$	−2.84218e13			−0.284218
$101$	−1.16665e12	+	6.73563e11i	−0.0108815	+	0.00628245i	−0.505431	−	0.862867i	$-0.668666\pi$
$101$	−1.16665e12	+	6.73563e11i	−0.0108815	+	0.00628245i	0.494549	+	0.869150i	$0.335333\pi$
$102$	1.81797e13	−	4.92806e13i	0.158265	−	0.429017i
$103$	−1.12147e14	+	1.94245e14i	−0.911859	+	1.57939i	−0.100423	+	0.994945i	$0.532020\pi$
$103$	−1.12147e14	+	1.94245e14i	−0.911859	+	1.57939i	−0.811436	+	0.584441i	$0.801314\pi$
$104$	6.63422e13	+	3.83027e13i	0.504146	+	0.291069i
$105$	−1.90779e13	+	1.58674e13i	−0.135583	+	0.112767i
$106$	−1.55374e14	−	2.69116e14i	−1.03333	−	1.78977i
$107$		−	1.28823e14i		−	0.802244i	−0.916025	−	0.401122i	$-0.868620\pi$
$107$		−	1.28823e14i		−	0.802244i	0.916025	−	0.401122i	$-0.131380\pi$
$108$	−8.17652e11	+	6.26843e13i	−0.00477092	+	0.365757i
$109$	−2.51082e14			−1.37351			−0.686753	−	0.726891i	$-0.740965\pi$
$109$	−2.51082e14			−1.37351			−0.686753	+	0.726891i	$0.740965\pi$
$110$	4.45619e13	−	2.57278e13i	0.228673	−	0.132024i
$111$	−2.04131e14	−	2.45433e14i	−0.983215	−	1.18215i
$112$	−5.08539e13	+	8.80816e13i	−0.230037	+	0.398436i
$113$	2.29159e14	+	1.32305e14i	0.974063	+	0.562376i	0.900473	−	0.434913i	$-0.143221\pi$
$113$	2.29159e14	+	1.32305e14i	0.974063	+	0.562376i	0.0735906	+	0.997289i	$0.476554\pi$
$114$	3.38750e14	+	1.24966e14i	1.35377	+	0.499409i
$115$	−1.20041e14	−	2.07918e14i	−0.451280	−	0.781640i
$116$		−	4.04151e13i		−	0.143001i
$117$	1.79250e14	+	1.53084e14i	0.597251	+	0.510069i
$118$	3.29664e14			1.03490
$119$	4.27633e13	−	2.46894e13i	0.126544	−	0.0730603i
$120$	−1.23602e14	+	2.12408e13i	−0.344952	+	0.0592791i
$121$	−1.46409e14	+	2.53588e14i	−0.385541	+	0.667776i
$122$	5.21721e14	+	3.01215e14i	1.29694	+	0.748787i
$123$	8.06691e13	+	4.69423e14i	0.189396	+	1.10212i
$124$	3.20327e13	+	5.54822e13i	0.0710626	+	0.123084i
$125$		−	4.00138e14i		−	0.839150i
$126$	−1.42901e14	+	1.67327e14i	−0.283428	+	0.331872i
$127$	3.84344e14			0.721264			0.360632	−	0.932708i	$-0.382561\pi$
$127$	3.84344e14			0.721264			0.360632	+	0.932708i	$0.382561\pi$
$128$	−5.77354e14	+	3.33335e14i	−1.02559	+	0.592123i
$129$	1.06321e14	−	2.88210e14i	0.178851	−	0.484820i
$130$	1.35993e14	−	2.35547e14i	0.216727	−	0.375383i
$131$	−6.99904e14	−	4.04090e14i	−1.05716	−	0.610350i	−0.132512	−	0.991181i	$-0.542304\pi$
$131$	−6.99904e14	−	4.04090e14i	−1.05716	−	0.610350i	−0.924644	+	0.380832i	$0.875638\pi$
$132$	9.39548e13	−	7.81439e13i	0.134556	−	0.111912i
$133$	1.69713e14	+	2.93951e14i	0.230543	+	0.399313i
$134$		−	5.45267e14i		−	0.702871i
$135$	−3.85879e14	−	5.03340e12i	−0.472188	−	0.00615921i
$136$	2.49567e14			0.290012
$137$	−7.42632e14	+	4.28759e14i	−0.819841	+	0.473335i	−0.850362	−	0.526199i	$-0.823617\pi$
$137$	−7.42632e14	+	4.28759e14i	−0.819841	+	0.473335i	0.0305207	+	0.999534i	$0.490283\pi$
$138$	−1.36137e15	−	1.63682e15i	−1.42831	−	1.71730i
$139$	4.71586e14	−	8.16811e14i	0.470389	−	0.814738i	−0.529038	−	0.848598i	$-0.677447\pi$
$139$	4.71586e14	−	8.16811e14i	0.470389	−	0.814738i	0.999427	+	0.0338608i	$0.0107803\pi$
$140$	5.88885e13	+	3.39993e13i	0.0558643	+	0.0322533i
$141$	1.15176e15	+	4.24885e14i	1.03951	+	0.383476i
$142$	3.44636e14	+	5.96927e14i	0.296034	+	0.512746i
$143$		−	4.59508e14i		−	0.375786i
$144$	−1.49103e15	+	5.28052e14i	−1.16131	+	0.411282i
$145$	2.48792e14			0.184612
$146$	−1.88343e15	+	1.08740e15i	−1.33193	+	0.768987i
$147$	1.25798e15	−	2.16181e14i	0.848110	−	0.145746i
$148$	−4.37394e14	+	7.57589e14i	−0.281217	+	0.487081i
$149$	1.26645e15	+	7.31183e14i	0.776753	+	0.448458i	0.835278	−	0.549827i	$-0.185307\pi$
$149$	1.26645e15	+	7.31183e14i	0.776753	+	0.448458i	−0.0585254	+	0.998286i	$0.518640\pi$
$150$	−2.62770e14	−	1.52909e15i	−0.153793	−	0.894938i
$151$	2.17909e14	+	3.77430e14i	0.121741	+	0.210862i	0.920454	−	0.390850i	$-0.127819\pi$
$151$	2.17909e14	+	3.77430e14i	0.121741	+	0.210862i	−0.798713	+	0.601712i	$0.794486\pi$
$152$			1.71550e15i			0.915138i
$153$	7.55089e14	+	1.39923e14i	0.384732	+	0.0712934i
$154$	4.28943e14			0.208812
$155$	−3.41544e14	+	1.97190e14i	−0.158900	+	0.0917411i
$156$	2.23566e14	−	6.06032e14i	0.0994339	−	0.269540i
$157$	2.39012e14	−	4.13981e14i	0.101653	−	0.176069i	−0.810713	−	0.585444i	$-0.800920\pi$
$157$	2.39012e14	−	4.13981e14i	0.101653	−	0.176069i	0.912366	+	0.409376i	$0.134253\pi$
$158$	3.66248e15	+	2.11453e15i	1.48996	+	0.860231i
$159$	3.49291e15	−	2.90511e15i	1.35959	−	1.13079i
$160$	4.42784e14	+	7.66924e14i	0.164950	+	0.285701i
$161$		−	2.00137e15i		−	0.713750i
$162$	−3.37997e15	+	5.35550e14i	−1.15427	+	0.182892i
$163$	−3.72556e15			−1.21865			−0.609325	−	0.792921i	$-0.708559\pi$
$163$	−3.72556e15			−1.21865			−0.609325	+	0.792921i	$0.708559\pi$
$164$	1.13036e15	−	6.52611e14i	0.354249	−	0.204526i
$165$	4.81047e14	+	5.78378e14i	0.144477	+	0.173710i
$166$	3.24430e14	−	5.61929e14i	0.0934037	−	0.161780i
$167$	−2.33686e15	−	1.34919e15i	−0.645086	−	0.372441i	0.141485	−	0.989940i	$-0.454812\pi$
$167$	−2.33686e15	−	1.34919e15i	−0.645086	−	0.372441i	−0.786571	+	0.617500i	$0.788146\pi$
$168$	−9.80860e14	−	3.61841e14i	−0.259682	−	0.0957972i
$169$	7.54246e14	+	1.30639e15i	0.191560	+	0.331792i
$170$		−	8.86085e14i		−	0.215940i
$171$	−9.61819e14	+	5.19041e15i	−0.224968	+	1.21403i
$172$	−8.41813e14			−0.189024
$173$	−2.06128e15	+	1.19008e15i	−0.444441	+	0.256598i	−0.705480	−	0.708730i	$-0.749268\pi$
$173$	−2.06128e15	+	1.19008e15i	−0.444441	+	0.256598i	0.261039	+	0.965328i	$0.415935\pi$
$174$	2.17433e15	−	3.73652e14i	0.450277	−	0.0773790i
$175$	7.29256e14	−	1.26311e15i	0.145082	−	0.251289i
$176$	2.67034e15	+	1.54172e15i	0.510478	+	0.294725i
$177$	8.16284e14	+	4.75005e15i	0.149978	+	0.872741i
$178$	−1.48537e15	−	2.57274e15i	−0.262358	−	0.454418i
$179$		−	9.72633e15i		−	1.65188i	−0.563761	−	0.825938i	$-0.690646\pi$
$179$		−	9.72633e15i		−	1.65188i	0.563761	−	0.825938i	$-0.309354\pi$
$180$	3.53039e14	+	9.96853e14i	0.0576654	+	0.162826i
$181$	−7.95145e15			−1.24939			−0.624693	−	0.780871i	$-0.714776\pi$
$181$	−7.95145e15			−1.24939			−0.624693	+	0.780871i	$0.714776\pi$
$182$	1.96356e15	−	1.13366e15i	0.296855	−	0.171389i
$183$	−3.04831e15	+	8.26320e15i	−0.443508	+	1.20224i
$184$	5.05760e15	−	8.76003e15i	0.708305	−	1.22682i
$185$	−4.66365e15	−	2.69256e15i	−0.628817	−	0.363047i
$186$	−2.68878e15	+	2.23631e15i	−0.349112	+	0.290363i
$187$	−7.48499e14	−	1.29644e15i	−0.0936052	−	0.162129i
$188$		−	3.36409e15i		−	0.405287i
$189$	−2.76481e15	−	1.64472e15i	−0.320947	−	0.190923i
$190$	6.09087e15			0.681403
$191$	5.81012e15	−	3.35448e15i	0.626544	−	0.361736i	−0.152868	−	0.988247i	$-0.548851\pi$
$191$	5.81012e15	−	3.35448e15i	0.626544	−	0.361736i	0.779413	+	0.626511i	$0.215518\pi$
$192$	−2.55589e15	−	3.07303e15i	−0.265726	−	0.319490i
$193$	−7.23820e15	+	1.25369e16i	−0.725653	+	1.25687i	0.233051	+	0.972464i	$0.425129\pi$
$193$	−7.23820e15	+	1.25369e16i	−0.725653	+	1.25687i	−0.958705	+	0.284404i	$0.908204\pi$
$194$	2.31021e15	+	1.33380e15i	0.223377	+	0.128967i
$195$	3.73068e15	+	1.37626e15i	0.347973	+	0.128368i
$196$	−1.74890e15	−	3.02918e15i	−0.157388	−	0.272604i
$197$			8.61721e15i			0.748347i	0.927359	+	0.374174i	$0.122074\pi$
$197$			8.61721e15i			0.748347i	−0.927359	+	0.374174i	$0.877926\pi$
$198$	5.07278e15	+	4.33229e15i	0.425196	+	0.363129i
$199$	−2.20192e15			−0.178168			−0.0890842	−	0.996024i	$-0.528394\pi$
$199$	−2.20192e15			−0.178168			−0.0890842	+	0.996024i	$0.528394\pi$
$200$	6.38393e15	−	3.68576e15i	0.498744	−	0.287950i
$201$	7.85663e15	−	1.35014e15i	0.592740	−	0.101861i
$202$	−1.00758e14	+	1.74518e14i	−0.00734210	+	0.0127169i
$203$	1.79611e15	+	1.03699e15i	0.126433	+	0.0729962i
$204$	−3.56413e14	−	2.07401e15i	−0.0242405	−	0.141058i
$205$	4.01742e15	+	6.95837e15i	0.264040	+	0.457331i
$206$			3.35521e16i			2.13132i
$207$	2.02137e16	−	2.36687e16i	1.24123	−	1.45339i
$208$	1.62986e16			0.967623
$209$	8.91160e15	−	5.14511e15i	0.511601	−	0.295373i
$210$	−1.28471e15	+	3.48253e15i	−0.0713297	+	0.193357i
$211$	−9.35311e15	+	1.62001e16i	−0.502318	+	0.870040i	0.497678	+	0.867362i	$0.334186\pi$
$211$	−9.35311e15	+	1.62001e16i	−0.502318	+	0.870040i	−0.999996	+	0.00267859i	$0.999147\pi$
$212$	−1.07817e16	−	6.22481e15i	−0.560191	−	0.323426i
$213$	−7.74763e15	+	6.44384e15i	−0.389504	+	0.323957i
$214$	−9.63528e15	−	1.66888e16i	−0.468779	−	0.811949i
$215$		−	5.18213e15i		−	0.244028i
$216$	−7.94531e15	−	1.41858e16i	−0.362188	−	0.646663i
$217$	−3.28762e15			−0.145099
$218$	−3.25273e16	+	1.87797e16i	−1.39012	+	0.802587i
$219$	−2.03317e16	−	2.44454e16i	−0.841521	−	1.01179i
$220$	1.03074e15	−	1.78530e15i	0.0413230	−	0.0715736i
$221$	−6.85276e15	−	3.95645e15i	−0.266146	−	0.153659i
$222$	−4.48020e16	−	1.65275e16i	−1.68588	−	0.621924i
$223$	−4.64056e15	−	8.03769e15i	−0.169214	−	0.293087i	0.768930	−	0.639333i	$-0.220790\pi$
$223$	−4.64056e15	−	8.03769e15i	−0.169214	−	0.293087i	−0.938144	+	0.346246i	$0.887456\pi$
$224$			7.38224e15i			0.260887i
$225$	2.13816e16	−	7.57238e15i	0.732425	−	0.259391i
$226$	3.95829e16			1.31446
$227$	1.03337e16	−	5.96619e15i	0.332718	−	0.192095i	−0.324329	−	0.945944i	$-0.605139\pi$
$227$	1.03337e16	−	5.96619e15i	0.332718	−	0.192095i	0.657047	+	0.753849i	$0.271805\pi$
$228$	1.42565e16	−	2.44995e15i	0.445113	−	0.0764915i
$229$	−8.37085e14	+	1.44987e15i	−0.0253467	+	0.0439018i	−0.878421	−	0.477888i	$-0.841402\pi$
$229$	−8.37085e14	+	1.44987e15i	−0.0253467	+	0.0439018i	0.853074	+	0.521790i	$0.174736\pi$
$230$	−3.11023e16	−	1.79569e16i	−0.913479	−	0.527397i
$231$	1.06211e15	+	6.18055e15i	0.0302612	+	0.176093i
$232$	5.24107e15	+	9.07780e15i	0.144879	+	0.250937i
$233$			8.13317e15i			0.218157i	0.994033	+	0.109078i	$0.0347899\pi$
$233$			8.13317e15i			0.218157i	−0.994033	+	0.109078i	$0.965210\pi$
$234$	3.46714e16	+	6.42485e15i	0.902527	+	0.167244i
$235$	2.07091e16			0.523221
$236$	1.14380e16	−	6.60372e15i	0.280521	−	0.161959i
$237$	−2.13992e16	+	5.80077e16i	−0.509516	+	1.38117i
$238$	3.69328e15	−	6.39694e15i	0.0853833	−	0.147888i
$239$	−2.32813e16	−	1.34415e16i	−0.522664	−	0.301760i	0.215360	−	0.976535i	$-0.430907\pi$
$239$	−2.32813e16	−	1.34415e16i	−0.522664	−	0.301760i	−0.738024	+	0.674775i	$0.764241\pi$
$240$	−2.05148e16	+	1.70626e16i	−0.447290	+	0.372019i
$241$	4.02326e16	+	6.96849e16i	0.852037	+	1.47577i	0.879367	+	0.476145i	$0.157966\pi$
$241$	4.02326e16	+	6.96849e16i	0.852037	+	1.47577i	−0.0273297	+	0.999626i	$0.508700\pi$
$242$			4.38026e16i			0.901139i
$243$	−1.60858e16	−	4.73751e16i	−0.321513	−	0.946905i
$244$	2.41354e16			0.468734
$245$	1.86474e16	−	1.07661e16i	0.351929	−	0.203186i
$246$	4.55609e16	+	5.47793e16i	0.835693	+	1.00478i
$247$	2.71963e16	−	4.71053e16i	0.484876	−	0.839829i
$248$	−1.43900e16	−	8.30806e15i	−0.249401	−	0.143992i
$249$	8.90003e15	+	3.28324e15i	0.149967	+	0.0553232i
$250$	−2.99282e16	−	5.18372e16i	−0.490344	−	0.849301i
$251$		−	3.03882e16i		−	0.484159i	−0.970256	−	0.242080i	$-0.922170\pi$
$251$		−	3.03882e16i		−	0.484159i	0.970256	−	0.242080i	$-0.0778295\pi$
$252$	−1.60626e15	+	8.66811e15i	−0.0248893	+	0.134314i
$253$	−6.06748e16			−0.914460
$254$	4.97912e16	−	2.87470e16i	0.729989	−	0.421460i
$255$	1.27674e16	−	2.19405e15i	0.182105	−	0.0312942i
$256$	−3.48917e16	+	6.04342e16i	−0.484219	+	0.838693i
$257$	2.70003e16	+	1.55886e16i	0.364617	+	0.210511i	0.671104	−	0.741363i	$-0.265820\pi$
$257$	2.70003e16	+	1.55886e16i	0.364617	+	0.210511i	−0.306487	+	0.951875i	$0.599154\pi$
$258$	−7.78287e15	−	4.52894e16i	−0.102283	−	0.595194i
$259$	−2.24456e16	−	3.88770e16i	−0.287100	−	0.497272i
$260$		−	1.08967e16i		−	0.135669i
$261$	1.07678e16	+	3.04042e16i	0.130509	+	0.368511i
$262$	−1.20895e17			−1.42659
$263$	7.00721e16	−	4.04561e16i	0.805109	−	0.464830i	−0.0401454	−	0.999194i	$-0.512782\pi$
$263$	7.00721e16	−	4.04561e16i	0.805109	−	0.464830i	0.845255	+	0.534364i	$0.179449\pi$
$264$	−1.09698e16	+	2.97364e16i	−0.122736	+	0.332706i
$265$	3.83194e16	−	6.63711e16i	0.417539	−	0.723200i
$266$	4.39720e16	+	2.53873e16i	0.466665	+	0.269429i
$267$	3.33920e16	−	2.77728e16i	0.345195	−	0.287105i
$268$	−1.09226e16	−	1.89185e16i	−0.109998	−	0.190522i
$269$			1.11604e17i			1.09500i	0.836805	+	0.547501i	$0.184421\pi$
$269$			1.11604e17i			1.09500i	−0.836805	+	0.547501i	$0.815579\pi$
$270$	−5.03665e16	+	2.82097e16i	−0.481499	+	0.269682i
$271$	−2.03175e17			−1.89272			−0.946360	−	0.323115i	$-0.895270\pi$
$271$	−2.03175e17			−1.89272			−0.946360	+	0.323115i	$0.895270\pi$
$272$	4.59842e16	−	2.65490e16i	0.417471	−	0.241027i
$273$	2.11967e16	+	2.54854e16i	0.187555	+	0.225504i
$274$	−6.41379e16	+	1.11090e17i	−0.553173	+	0.958123i
$275$	−3.82932e16	−	2.21086e16i	−0.321953	−	0.185880i
$276$	−8.00223e16	−	2.95204e16i	−0.655915	−	0.241968i
$277$	4.89924e16	+	8.48574e16i	0.391535	+	0.678158i	0.992652	−	0.121002i	$-0.0386109\pi$
$277$	4.89924e16	+	8.48574e16i	0.391535	+	0.678158i	−0.601117	+	0.799161i	$0.705278\pi$
$278$		−	1.41089e17i		−	1.09946i
$279$	−3.88802e16	−	3.32047e16i	−0.295460	−	0.252331i
$280$	−1.76363e16			−0.130707
$281$	−5.09960e16	+	2.94426e16i	−0.368631	+	0.212829i	−0.672860	−	0.739770i	$-0.734935\pi$
$281$	−5.09960e16	+	2.94426e16i	−0.368631	+	0.212829i	0.304229	+	0.952599i	$0.401601\pi$
$282$	1.80988e17	−	3.11023e16i	1.27616	−	0.219305i
$283$	1.30701e17	−	2.26381e17i	0.899028	−	1.55716i	0.0702902	−	0.997527i	$-0.477607\pi$
$283$	1.30701e17	−	2.26381e17i	0.899028	−	1.55716i	0.828738	−	0.559636i	$-0.189059\pi$
$284$	2.39149e16	+	1.38073e16i	0.160487	+	0.0926574i
$285$	1.50817e16	+	8.77620e16i	0.0987497	+	0.574636i
$286$	−3.43688e16	−	5.95285e16i	−0.219585	−	0.380332i
$287$			6.69798e16i			0.417609i
$288$	−7.45600e16	+	8.73040e16i	−0.453689	+	0.531235i
$289$	1.42599e17			0.846899
$290$	3.22306e16	−	1.86083e16i	0.186845	−	0.107875i
$291$	−1.34981e16	+	3.65899e16i	−0.0763872	+	0.207067i
$292$	−4.35649e16	+	7.54567e16i	−0.240690	+	0.416886i
$293$	−4.72349e16	−	2.72711e16i	−0.254795	−	0.147106i	0.367163	−	0.930157i	$-0.380329\pi$
$293$	−4.72349e16	−	2.72711e16i	−0.254795	−	0.147106i	−0.621958	+	0.783051i	$0.713662\pi$
$294$	1.46800e17	−	1.22096e17i	0.773205	−	0.643089i
$295$	4.06519e16	+	7.04112e16i	0.209087	+	0.362149i
$296$		−	2.26887e17i		−	1.13964i
$297$	−4.98622e16	+	8.38197e16i	−0.244611	+	0.411198i
$298$	2.18755e17			1.04820
$299$	−2.77749e17	+	1.60359e17i	−1.30003	+	0.750575i
$300$	−3.97472e16	−	4.77893e16i	−0.181743	−	0.218515i
$301$	2.15996e16	−	3.74115e16i	0.0964893	−	0.167124i
$302$	5.64596e16	+	3.25970e16i	0.246428	+	0.142275i
$303$	−2.76408e15	−	1.01968e15i	−0.0117883	−	0.00434874i
$304$	1.82495e17	+	3.16091e17i	0.760565	+	1.31734i
$305$			1.48576e17i			0.605130i
$306$	1.08286e17	−	3.83499e16i	0.431045	−	0.152656i
$307$	2.69380e17			1.04809			0.524043	−	0.851692i	$-0.324423\pi$
$307$	2.69380e17			1.04809			0.524043	+	0.851692i	$0.324423\pi$
$308$	1.48826e16	−	8.59246e15i	0.0566009	−	0.0326785i
$309$	−4.83445e17	+	8.30788e16i	−1.79737	+	0.308874i
$310$	−2.94976e16	+	5.10914e16i	−0.107215	+	0.185702i
$311$	1.15333e17	+	6.65875e16i	0.409855	+	0.236630i	0.690727	−	0.723115i	$-0.257290\pi$
$311$	1.15333e17	+	6.65875e16i	0.409855	+	0.236630i	−0.280872	+	0.959745i	$0.590624\pi$
$312$	2.83747e16	+	1.65116e17i	0.0985937	+	0.573728i
$313$	−1.05131e17	−	1.82092e17i	−0.357206	−	0.618699i	0.630287	−	0.776362i	$-0.282937\pi$
$313$	−1.05131e17	−	1.82092e17i	−0.357206	−	0.618699i	−0.987493	+	0.157663i	$0.949604\pi$
$314$		−	7.15074e16i		−	0.237598i
$315$	−5.33601e16	−	9.88799e15i	−0.173398	−	0.0321317i
$316$	1.69431e17			0.538497
$317$	−3.44228e17	+	1.98740e17i	−1.07012	+	0.617833i	−0.928214	−	0.372047i	$-0.878656\pi$
$317$	−3.44228e17	+	1.98740e17i	−1.07012	+	0.617833i	−0.141904	+	0.989880i	$0.545323\pi$
$318$	2.35213e17	−	6.37604e17i	0.715273	−	1.93893i
$319$	3.14379e16	−	5.44520e16i	0.0935231	−	0.161987i
$320$	−5.83927e16	−	3.37130e16i	−0.169945	−	0.0981179i
$321$	2.16607e17	−	1.80156e17i	0.616790	−	0.512995i
$322$	−1.49692e17	−	2.59274e17i	−0.417069	−	0.722385i
$323$		−	1.77201e17i		−	0.483114i
$324$	−1.06543e17	+	8.62879e16i	−0.284256	+	0.230216i
$325$	−2.33725e17			−0.610269
$326$	−4.82641e17	+	2.78653e17i	−1.23339	+	0.712099i
$327$	−3.51133e17	−	4.22179e17i	−0.878290	−	1.05600i
$328$	−1.69263e17	+	2.93171e17i	−0.414423	+	0.717802i
$329$	1.49506e17	+	8.63171e16i	0.358333	+	0.206883i
$330$	1.05579e17	+	3.89481e16i	0.247730	+	0.0913879i
$331$	4.50209e15	+	7.79784e15i	0.0103423	+	0.0179134i	0.871150	−	0.491017i	$-0.163375\pi$
$331$	4.50209e15	+	7.79784e15i	0.0103423	+	0.0179134i	−0.860808	+	0.508930i	$0.830041\pi$
$332$		−	2.59955e16i		−	0.0584698i
$333$	1.27207e17	−	6.86467e17i	0.280157	−	1.51185i
$334$	−4.03649e17			−0.870520
$335$	1.16461e17	−	6.72388e16i	0.245961	−	0.142006i
$336$	−2.19222e17	+	3.76727e16i	−0.453428	+	0.0779205i
$337$	−3.10938e16	+	5.38560e16i	−0.0629889	+	0.109100i	−0.895800	−	0.444457i	$-0.853397\pi$
$337$	−3.10938e16	+	5.38560e16i	−0.0629889	+	0.109100i	0.832811	+	0.553557i	$0.186730\pi$
$338$	1.95423e17	+	1.12827e17i	0.387756	+	0.223871i
$339$	9.80116e16	+	5.70341e17i	0.190493	+	1.10850i
$340$	−1.77498e16	−	3.07435e16i	−0.0337941	−	0.0585331i
$341$			9.96697e16i			0.185901i
$342$	2.63614e17	+	7.44349e17i	0.481710	+	1.36017i
$343$	3.88079e17			0.694803
$344$	1.89083e17	−	1.09167e17i	0.331699	−	0.191506i
$345$	1.81725e17	−	4.92610e17i	0.312378	−	0.846779i
$346$	−1.78024e17	+	3.08346e17i	−0.299878	+	0.519404i
$347$	8.66876e17	+	5.00491e17i	1.43104	+	0.826209i	0.997200	−	0.0747825i	$-0.0238262\pi$
$347$	8.66876e17	+	5.00491e17i	1.43104	+	0.826209i	0.433836	+	0.900992i	$0.357160\pi$
$348$	6.79554e16	−	5.65197e16i	0.109943	−	0.0914419i
$349$	1.50217e17	+	2.60184e17i	0.238200	+	0.412574i	0.960198	−	0.279321i	$-0.0901093\pi$
$349$	1.50217e17	+	2.60184e17i	0.238200	+	0.412574i	−0.721998	+	0.691895i	$0.756776\pi$
$350$		−	2.18178e17i		−	0.339106i
$351$	−6.72392e15	+	5.15481e17i	−0.0102441	+	0.785350i
$352$	2.23805e17			0.334249
$353$	9.01012e17	−	5.20199e17i	1.31919	−	0.761635i	0.335592	−	0.942007i	$-0.391064\pi$
$353$	9.01012e17	−	5.20199e17i	1.31919	−	0.761635i	0.983598	+	0.180372i	$0.0577303\pi$
$354$	4.61028e17	+	5.54308e17i	0.661766	+	0.795661i
$355$	−8.49965e16	+	1.47218e17i	−0.119620	+	0.207187i
$356$	−1.03073e17	−	5.95090e16i	−0.142231	−	0.0821169i
$357$	1.01317e17	+	3.73761e16i	0.137090	+	0.0505727i
$358$	−7.27479e17	−	1.26003e18i	−0.965249	−	1.67186i
$359$			8.63108e15i			0.0112306i	0.999984	+	0.00561531i	$0.00178742\pi$
$359$			8.63108e15i			0.0112306i	−0.999984	+	0.00561531i	$0.998213\pi$
$360$	−2.08570e17	−	1.78125e17i	−0.266155	−	0.227304i
$361$	4.19060e17			0.524476
$362$	−1.03010e18	+	5.94728e17i	−1.26450	+	0.730059i
$363$	−6.31142e17	+	1.08460e17i	−0.759942	+	0.130594i
$364$	4.54184e16	−	7.86669e16i	0.0536441	−	0.0929143i
$365$	−4.64505e17	−	2.68182e17i	−0.538196	−	0.310727i
$366$	2.23141e17	+	1.29848e18i	0.253637	+	1.47594i
$367$	−1.35662e17	−	2.34973e17i	−0.151285	−	0.262033i	0.780415	−	0.625262i	$-0.215008\pi$
$367$	−1.35662e17	−	2.34973e17i	−0.151285	−	0.262033i	−0.931700	+	0.363228i	$0.881674\pi$
$368$		−	2.15211e18i		−	2.35467i
$369$	−6.76490e17	+	7.92117e17i	−0.726234	+	0.850364i
$370$	−8.05558e17			−0.848565
$371$	5.53281e17	−	3.19437e17i	0.571911	−	0.330193i
$372$	−4.84927e16	+	1.31452e17i	−0.0491899	+	0.133341i
$373$	2.65636e17	−	4.60096e17i	0.264439	−	0.458022i	−0.702977	−	0.711212i	$-0.748147\pi$
$373$	2.65636e17	−	4.60096e17i	0.264439	−	0.458022i	0.967417	+	0.253190i	$0.0814799\pi$
$374$	−1.93934e17	−	1.11968e17i	−0.189475	−	0.109393i
$375$	6.72806e17	−	5.59585e17i	0.645165	−	0.536595i
$376$	4.36259e17	+	7.55623e17i	0.410610	+	0.711197i
$377$		−	3.32351e17i		−	0.307049i
$378$	−4.81193e17	−	6.27667e15i	−0.436392	−	0.00569229i
$379$	−8.22885e17			−0.732597			−0.366298	−	0.930497i	$-0.619375\pi$
$379$	−8.22885e17			−0.732597			−0.366298	+	0.930497i	$0.619375\pi$
$380$	2.11328e17	−	1.22010e17i	0.184702	−	0.106638i
$381$	5.37497e17	+	6.46250e17i	0.461213	+	0.554531i
$382$	5.01795e17	−	8.69135e17i	0.422749	−	0.732223i
$383$	−1.14603e18	−	6.61659e17i	−0.947989	−	0.547322i	−0.0555336	−	0.998457i	$-0.517686\pi$
$383$	−1.14603e18	−	6.61659e17i	−0.947989	−	0.547322i	−0.892456	+	0.451135i	$0.851019\pi$
$384$	−1.36790e18	−	5.04621e17i	−1.11106	−	0.409870i
$385$	5.28944e16	+	9.16158e16i	0.0421876	+	0.0730711i
$386$			2.16552e18i			1.69610i
$387$	6.33294e17	−	2.24283e17i	0.487112	−	0.172512i
$388$	1.06873e17			0.0807320
$389$	6.27576e17	−	3.62331e17i	0.465607	−	0.268818i	−0.248792	−	0.968557i	$-0.580034\pi$
$389$	6.27576e17	−	3.62331e17i	0.465607	−	0.268818i	0.714399	+	0.699739i	$0.246700\pi$
$390$	5.86241e17	−	1.00744e17i	0.427193	−	0.0734120i
$391$	−5.22421e17	+	9.04860e17i	−0.373924	+	0.647655i
$392$	7.85653e17	+	4.53597e17i	0.552368	+	0.318910i
$393$	−2.99350e17	−	1.74195e18i	−0.206744	−	1.20306i
$394$	6.44523e17	+	1.11635e18i	0.437285	+	0.757400i
$395$			1.04300e18i			0.695193i
$396$	2.62788e17	+	4.86964e16i	0.172083	+	0.0318882i
$397$	−1.88478e18			−1.21262			−0.606312	−	0.795227i	$-0.707352\pi$
$397$	−1.88478e18			−1.21262			−0.606312	+	0.795227i	$0.707352\pi$
$398$	−2.85256e17	+	1.64692e17i	−0.180324	+	0.104110i
$399$	−2.56920e17	+	6.96445e17i	−0.159583	+	0.432590i
$400$	7.84183e17	−	1.35824e18i	0.478627	−	0.829007i
$401$	4.19505e17	+	2.42201e17i	0.251609	+	0.145267i	0.620501	−	0.784206i	$-0.286929\pi$
$401$	4.19505e17	+	2.42201e17i	0.251609	+	0.145267i	−0.368892	+	0.929472i	$0.620263\pi$
$402$	9.16831e17	−	7.62545e17i	0.540390	−	0.449452i
$403$	2.63419e17	+	4.56255e17i	0.152585	+	0.264285i
$404$			8.07343e15i			0.00459609i
$405$	−5.31181e17	−	6.55870e17i	−0.297206	−	0.366972i
$406$	3.10245e17			0.170617
$407$	−1.17862e18	+	6.80476e17i	−0.637107	+	0.367834i
$408$	3.49015e17	+	4.19631e17i	0.185448	+	0.222970i
$409$	−1.19864e17	+	2.07611e17i	−0.0626076	+	0.108440i	−0.895630	−	0.444799i	$-0.853275\pi$
$409$	−1.19864e17	+	2.07611e17i	−0.0626076	+	0.108440i	0.833023	+	0.553239i	$0.186608\pi$
$410$	1.04090e18	+	6.00964e17i	0.534469	+	0.308576i
$411$	−1.75949e18	−	6.49077e17i	−0.888163	−	0.327645i
$412$	6.72106e17	+	1.16412e18i	0.333547	+	0.577721i
$413$			6.77763e17i			0.330695i
$414$	8.48356e17	−	4.57812e18i	0.406982	−	2.19626i
$415$	1.60026e17			0.0754839
$416$	1.02450e18	−	5.91498e17i	0.475182	−	0.274347i
$417$	2.03292e18	−	3.49352e17i	0.927187	−	0.159335i
$418$	7.69656e17	−	1.33308e18i	0.345193	−	0.597893i
$419$	−1.28482e18	−	7.41793e17i	−0.566689	−	0.327178i	0.189137	−	0.981951i	$-0.439431\pi$
$419$	−1.28482e18	−	7.41793e17i	−0.566689	−	0.327178i	−0.755826	+	0.654772i	$0.772764\pi$
$420$	2.51868e16	+	1.46565e17i	0.0109251	+	0.0635747i
$421$	6.07915e17	+	1.05294e18i	0.259339	+	0.449189i	0.966065	−	0.258299i	$-0.0831619\pi$
$421$	6.07915e17	+	1.05294e18i	0.259339	+	0.449189i	−0.706726	+	0.707488i	$0.749829\pi$
$422$			2.79826e18i			1.17409i
$423$	8.96292e17	+	2.53080e18i	0.369885	+	1.04442i
$424$	3.22896e18			1.31069
$425$	−6.59422e17	+	3.80718e17i	−0.263294	+	0.152013i
$426$	−5.21728e17	+	1.41427e18i	−0.204916	+	0.555477i
$427$	−6.19276e17	+	1.07262e18i	−0.239270	+	0.414429i
$428$	−6.68610e17	−	3.86022e17i	−0.254136	−	0.146726i
$429$	7.72633e17	−	6.42612e17i	0.288916	−	0.240297i
$430$	−3.87597e17	−	6.71337e17i	−0.142594	−	0.246980i
$431$			2.13220e18i			0.771770i	0.922547	+	0.385885i	$0.126104\pi$
$431$			2.13220e18i			0.771770i	−0.922547	+	0.385885i	$0.873896\pi$
$432$	−2.97306e18	−	1.76859e18i	−1.05881	−	0.629857i
$433$	1.46090e18			0.511925			0.255962	−	0.966687i	$-0.417608\pi$
$433$	1.46090e18			0.511925			0.255962	+	0.966687i	$0.417608\pi$
$434$	−4.25907e17	+	2.45897e17i	−0.146854	+	0.0847863i
$435$	3.47930e17	+	4.18327e17i	0.118050	+	0.141936i
$436$	−7.52377e17	+	1.30316e18i	−0.251206	+	0.435102i
$437$	−6.21992e18	−	3.59107e18i	−2.04369	−	1.17992i
$438$	−4.46233e18	−	1.64616e18i	−1.44292	−	0.532297i
$439$	−9.07022e16	−	1.57101e17i	−0.0288647	−	0.0499951i	0.851232	−	0.524789i	$-0.175856\pi$
$439$	−9.07022e16	−	1.57101e17i	−0.0288647	−	0.0499951i	−0.880097	+	0.474794i	$0.842523\pi$
$440$			5.34672e17i			0.167463i
$441$	2.12275e18	+	1.81289e18i	0.654378	+	0.558857i
$442$	−1.18369e18			−0.359154
$443$	2.55792e18	−	1.47681e18i	0.763942	−	0.441062i	−0.0667673	−	0.997769i	$-0.521269\pi$
$443$	2.55792e18	−	1.47681e18i	0.763942	−	0.441062i	0.830709	+	0.556706i	$0.187935\pi$
$444$	−1.88552e18	+	3.24022e17i	−0.554308	+	0.0952564i
$445$	3.66332e17	−	6.34506e17i	0.106012	−	0.183618i
$446$	−1.20236e18	−	6.94180e17i	−0.342522	−	0.197755i
$447$	5.41662e17	+	3.15199e18i	0.151906	+	0.883960i
$448$	−2.81038e17	−	4.86772e17i	−0.0775923	−	0.134394i
$449$		−	6.59664e18i		−	1.79307i	−0.442969	−	0.896537i	$-0.646075\pi$
$449$		−	6.59664e18i		−	1.79307i	0.442969	−	0.896537i	$-0.353925\pi$
$450$	2.20358e18	−	2.58023e18i	0.589714	−	0.690510i
$451$	2.03060e18			0.535043
$452$	1.37336e18	−	7.92912e17i	0.356301	−	0.205710i
$453$	−3.29882e17	+	8.94228e17i	−0.0842697	+	0.228434i
$454$	8.92480e17	−	1.54582e18i	0.224496	−	0.388838i
$455$	4.84267e17	+	2.79592e17i	0.119951	+	0.0692539i
$456$	−2.88451e18	+	2.39910e18i	−0.703587	+	0.585186i
$457$	−2.96363e18	−	5.13316e18i	−0.711886	−	1.23302i	−0.964148	−	0.265364i	$-0.914508\pi$
$457$	−2.96363e18	−	5.13316e18i	−0.711886	−	1.23302i	0.252262	−	0.967659i	$-0.418826\pi$
$458$			2.50439e17i			0.0592438i
$459$	8.20704e17	+	1.46531e18i	0.191204	+	0.341383i
$460$	−1.43883e18			−0.330146
$461$	8.24105e17	−	4.75797e17i	0.186241	−	0.107526i	−0.403980	−	0.914768i	$-0.632374\pi$
$461$	8.24105e17	−	4.75797e17i	0.186241	−	0.107526i	0.590222	+	0.807241i	$0.299040\pi$
$462$	5.99868e17	+	7.21240e17i	0.133525	+	0.160541i
$463$	−9.26244e17	+	1.60430e18i	−0.203076	+	0.351738i	−0.949518	−	0.313713i	$-0.898427\pi$
$463$	−9.26244e17	+	1.60430e18i	−0.203076	+	0.351738i	0.746442	+	0.665450i	$0.231760\pi$
$464$	1.93139e18	+	1.11509e18i	0.417105	+	0.240815i
$465$	−8.09205e17	−	2.98517e17i	−0.172142	−	0.0635036i
$466$	6.08319e17	+	1.05364e18i	0.127476	+	0.220796i
$467$			7.47533e18i			1.54316i	0.636130	+	0.771582i	$0.280534\pi$
$467$			7.47533e18i			1.54316i	−0.636130	+	0.771582i	$0.719466\pi$
$468$	1.33166e18	−	4.71611e17i	0.270814	−	0.0959098i
$469$	1.12103e18			0.224598
$470$	2.68283e18	−	1.54893e18i	0.529551	−	0.305736i
$471$	1.03034e18	−	1.77060e17i	0.200370	−	0.0344330i
$472$	−1.71276e18	+	2.96658e18i	−0.328172	+	0.568410i
$473$	−1.13419e18	−	6.54825e17i	−0.214120	−	0.123623i
$474$	1.56645e18	+	9.11536e18i	0.291386	+	1.69561i
$475$	−2.61702e18	−	4.53281e18i	−0.479680	−	0.830830i
$476$		−	2.95931e17i		−	0.0534492i
$477$	9.76951e18	+	1.81036e18i	1.73878	+	0.322207i
$478$	−4.02141e18			−0.705315
$479$	9.05226e18	−	5.22633e18i	1.56462	−	0.903333i	0.567840	−	0.823139i	$-0.307779\pi$
$479$	9.05226e18	−	5.22633e18i	1.56462	−	0.903333i	0.996779	−	0.0801943i	$-0.0255541\pi$
$480$	−6.70309e17	+	1.81704e18i	−0.114179	+	0.309511i
$481$	−3.59689e18	+	6.22999e18i	−0.603825	+	1.04586i
$482$	1.04241e19	+	6.01838e18i	1.72469	+	0.995750i
$483$	3.36517e18	−	2.79887e18i	0.548754	−	0.456408i
$484$	8.77440e17	+	1.51977e18i	0.141026	+	0.244265i
$485$			6.57901e17i			0.104224i
$486$	−5.62731e18	−	4.93424e18i	−0.878712	−	0.770489i
$487$	−2.32289e18			−0.357540			−0.178770	−	0.983891i	$-0.557212\pi$
$487$	−2.32289e18			−0.357540			−0.178770	+	0.983891i	$0.557212\pi$
$488$	−5.42116e18	+	3.12991e18i	−0.822533	+	0.474890i
$489$	−5.21013e18	−	6.26430e18i	−0.779267	−	0.936937i
$490$	1.61049e18	−	2.78945e18i	0.237457	−	0.411288i
$491$	7.15665e17	+	4.13190e17i	0.104025	+	0.0600591i	0.551110	−	0.834433i	$-0.314204\pi$
$491$	7.15665e17	+	4.13190e17i	0.104025	+	0.0600591i	−0.447085	+	0.894492i	$0.647538\pi$
$492$	2.67810e18	+	9.87957e17i	0.383770	+	0.141574i
$493$	−5.41372e17	−	9.37684e17i	−0.0764834	−	0.132473i
$494$		−	8.13656e18i		−	1.13332i
$495$	−2.99771e17	+	1.61770e18i	−0.0411673	+	0.222158i
$496$	−3.53525e18			−0.478683
$497$	−1.22724e18	+	7.08545e17i	−0.163845	+	0.0945960i
$498$	1.39856e18	−	2.40338e17i	0.184109	−	0.0316386i
$499$	−1.87636e18	+	3.24996e18i	−0.243564	+	0.421865i	−0.961727	−	0.274010i	$-0.911650\pi$
$499$	−1.87636e18	+	3.24996e18i	−0.243564	+	0.421865i	0.718163	+	0.695875i	$0.244983\pi$
$500$	−2.07678e18	−	1.19903e18i	−0.265827	−	0.153476i
$501$	−9.99481e17	−	5.81609e18i	−0.126157	−	0.734120i
$502$	−2.27288e18	−	3.93674e18i	−0.282911	−	0.490016i
$503$		−	7.53136e18i		−	0.924480i	−0.886755	−	0.462240i	$-0.847046\pi$
$503$		−	7.53136e18i		−	0.924480i	0.886755	−	0.462240i	$-0.152954\pi$
$504$	−7.63300e17	−	2.15528e18i	−0.0924021	−	0.260910i
$505$	−4.96993e16			−0.00593350
$506$	−7.86032e18	+	4.53816e18i	−0.925522	+	0.534351i
$507$	−1.14182e18	+	3.09518e18i	−0.132599	+	0.359443i
$508$	1.15170e18	−	1.99481e18i	0.131915	−	0.228483i
$509$	−4.04899e17	−	2.33769e17i	−0.0457428	−	0.0264096i	0.476954	−	0.878928i	$-0.341741\pi$
$509$	−4.04899e17	−	2.33769e17i	−0.0457428	−	0.0264096i	−0.522697	+	0.852519i	$0.675074\pi$
$510$	1.48989e18	−	1.23917e18i	0.166021	−	0.138083i
$511$	−2.23561e18	−	3.87219e18i	−0.245725	−	0.425609i
$512$		−	4.83866e17i		−	0.0524608i
$513$	−1.00724e19	+	5.64145e18i	−1.07724	+	0.603349i
$514$	4.66379e18			0.492037
$515$	−7.16623e18	+	4.13743e18i	−0.745831	+	0.430606i
$516$	−1.17726e18	−	1.41545e18i	−0.120871	−	0.145328i
$517$	2.61684e18	−	4.53251e18i	0.265060	−	0.459097i
$518$	−5.81560e18	−	3.35764e18i	−0.581147	−	0.335525i
$519$	−4.88370e18	−	1.80160e18i	−0.481479	−	0.177618i
$520$	1.41310e18	+	2.44755e18i	0.137451	+	0.238072i
$521$			1.30139e19i			1.24894i	0.781048	+	0.624471i	$0.214685\pi$
$521$			1.30139e19i			1.24894i	−0.781048	+	0.624471i	$0.785315\pi$
$522$	3.66902e18	+	3.13344e18i	0.347422	+	0.296707i
$523$	1.02060e19			0.953549			0.476775	−	0.879026i	$-0.341806\pi$
$523$	1.02060e19			0.953549			0.476775	+	0.879026i	$0.341806\pi$
$524$	−4.19457e18	+	2.42174e18i	−0.386695	+	0.223259i
$525$	3.14368e18	−	5.40234e17i	0.285972	−	0.0491436i
$526$	6.05182e18	−	1.04821e19i	0.543233	−	0.940906i
$527$	1.48640e18	+	8.58174e17i	0.131662	+	0.0760153i
$528$	1.14211e18	+	6.64606e18i	0.0998321	+	0.580934i
$529$	1.53778e19	+	2.66352e19i	1.32649	+	2.29755i
$530$		−	1.14644e19i		−	0.975931i
$531$	−6.84535e18	+	8.01538e18i	−0.575087	+	0.673383i
$532$	2.03420e18			0.168660
$533$	9.29542e18	−	5.36671e18i	0.760639	−	0.439155i
$534$	2.24863e18	−	6.09547e18i	0.181606	−	0.492287i
$535$	2.37632e18	−	4.11590e18i	0.189421	−	0.328087i
$536$	4.90675e18	+	2.83292e18i	0.386047	+	0.222885i
$537$	1.63542e19	−	1.36021e19i	1.27002	−	1.05629i
$538$	8.34743e18	+	1.44582e19i	0.639848	+	1.10825i
$539$		−	5.44169e18i		−	0.411730i
$540$	−1.18243e18	+	1.98769e18i	−0.0883115	+	0.148454i
$541$	9.12458e18			0.672717			0.336358	−	0.941734i	$-0.390805\pi$
$541$	9.12458e18			0.672717			0.336358	+	0.941734i	$0.390805\pi$
$542$	−2.63211e19	+	1.51965e19i	−1.91562	+	1.10598i
$543$	−1.11199e19	−	1.33699e19i	−0.798921	−	0.960567i
$544$	1.92700e18	−	3.33766e18i	0.136675	−	0.236728i
$545$	−8.02211e18	−	4.63157e18i	−0.561712	−	0.324304i
$546$	4.65218e18	+	1.71620e18i	0.321594	+	0.118637i
$547$	−7.61351e18	−	1.31870e19i	−0.519605	−	0.899983i	−0.999740	−	0.0227881i	$-0.992746\pi$
$547$	−7.61351e18	−	1.31870e19i	−0.519605	−	0.899983i	0.480135	−	0.877195i	$-0.340588\pi$
$548$			5.13916e18i			0.346281i
$549$	−1.81570e19	+	6.43038e18i	−1.20792	+	0.427790i
$550$	−6.61443e18			−0.434464
$551$	6.44556e18	−	3.72134e18i	0.418022	−	0.241345i
$552$	2.18024e19	−	3.74668e18i	1.39614	−	0.239924i
$553$	−4.34732e18	+	7.52978e18i	−0.274882	+	0.476109i
$554$	1.26938e19	+	7.32876e18i	0.792543	+	0.457575i
$555$	−1.99465e18	−	1.16071e19i	−0.122975	−	0.715605i
$556$	−2.82625e18	−	4.89521e18i	−0.172063	−	0.298021i
$557$			1.48868e19i			0.894986i	0.894287	+	0.447493i	$0.147683\pi$
$557$			1.48868e19i			0.894986i	−0.894287	+	0.447493i	$0.852317\pi$
$558$	−7.52041e18	−	1.39358e18i	−0.446480	−	0.0827358i
$559$	−6.92261e18			−0.405870
$560$	−3.24958e18	+	1.87615e18i	−0.188153	+	0.108630i
$561$	1.13312e18	−	3.07159e18i	0.0647939	−	0.175640i
$562$	−4.40431e18	+	7.62848e18i	−0.248727	+	0.430808i
$563$	2.24592e19	+	1.29669e19i	1.25267	+	0.723229i	0.971639	−	0.236470i	$-0.0759905\pi$
$563$	2.24592e19	+	1.29669e19i	1.25267	+	0.723229i	0.281030	+	0.959699i	$0.409324\pi$
$564$	5.65650e18	−	4.70461e18i	0.311598	−	0.259161i
$565$	4.88110e18	+	8.45431e18i	0.265570	+	0.459980i
$566$		−	3.91030e19i		−	2.10133i
$567$	−1.10105e18	−	6.94895e18i	−0.0584421	−	0.368840i
$568$	−7.16217e18			−0.375497
$569$	−2.14534e19	+	1.23861e19i	−1.11099	+	0.641430i	−0.939085	−	0.343684i	$-0.888325\pi$
$569$	−2.14534e19	+	1.23861e19i	−1.11099	+	0.641430i	−0.171904	+	0.985114i	$0.554992\pi$
$570$	8.51795e18	+	1.02414e19i	0.435724	+	0.523884i
$571$	9.73630e18	−	1.68638e19i	0.491973	−	0.852122i	−0.507984	−	0.861366i	$-0.669609\pi$
$571$	9.73630e18	−	1.68638e19i	0.491973	−	0.852122i	0.999957	+	0.00924399i	$0.00294250\pi$
$572$	−2.38492e18	−	1.37693e18i	−0.119042	−	0.0687290i
$573$	1.37657e19	+	5.07818e18i	0.678758	+	0.250395i
$574$	5.00974e18	+	8.67712e18i	0.244024	+	0.422661i
$575$			3.08617e19i			1.48506i
$576$	1.59274e18	−	8.59512e18i	0.0757157	−	0.408597i
$577$	−3.59726e19			−1.68943			−0.844716	−	0.535215i	$-0.820231\pi$
$577$	−3.59726e19			−1.68943			−0.844716	+	0.535215i	$0.820231\pi$
$578$	1.84735e19	−	1.06657e19i	0.857144	−	0.494872i
$579$	−3.12025e19	+	5.36207e18i	−1.43034	+	0.245800i
$580$	7.45514e17	−	1.29127e18i	0.0337645	−	0.0584818i
$581$	1.15528e18	+	6.67003e17i	0.0516958	+	0.0298466i
$582$	9.88080e17	+	5.74975e18i	0.0436849	+	0.254207i
$583$	−9.68425e18	−	1.67736e19i	−0.423045	−	0.732735i
$584$		−	2.25982e19i		−	0.975402i
$585$	2.90320e18	+	8.19756e18i	0.123818	+	0.349618i
$586$	−8.15895e18			−0.343836
$587$	1.86467e19	−	1.07657e19i	0.776487	−	0.448305i	−0.0586968	−	0.998276i	$-0.518695\pi$
$587$	1.86467e19	−	1.07657e19i	0.776487	−	0.448305i	0.835184	+	0.549971i	$0.185361\pi$
$588$	2.64757e18	−	7.17690e18i	0.108945	−	0.295322i
$589$	−5.89901e18	+	1.02174e19i	−0.239868	+	0.415463i
$590$	1.05328e19	+	6.08111e18i	0.423233	+	0.244354i
$591$	−1.44893e19	+	1.20510e19i	−0.575353	+	0.478531i
$592$	−2.41362e19	−	4.18052e19i	−0.947147	−	1.64051i
$593$		−	3.06383e18i		−	0.118818i	−0.998234	−	0.0594090i	$-0.981078\pi$
$593$		−	3.06383e18i		−	0.118818i	0.998234	−	0.0594090i	$-0.0189216\pi$
$594$	−1.90287e17	+	1.45882e19i	−0.00729298	+	0.559107i
$595$	1.82172e18			0.0690023
$596$	7.58990e18	−	4.38203e18i	0.284127	−	0.164041i
$597$	−3.07934e18	−	3.70239e18i	−0.113930	−	0.136982i
$598$	−2.39880e19	+	4.15484e19i	−0.877174	+	1.51931i
$599$	−3.56687e19	−	2.05933e19i	−1.28914	−	0.744284i	−0.310638	−	0.950528i	$-0.600543\pi$
$599$	−3.56687e19	−	2.05933e19i	−1.28914	−	0.744284i	−0.978501	+	0.206244i	$0.933876\pi$
$600$	1.51252e19	+	5.57970e18i	0.540308	+	0.199320i
$601$	4.81655e17	+	8.34251e17i	0.0170065	+	0.0294561i	0.874403	−	0.485200i	$-0.161253\pi$
$601$	4.81655e17	+	8.34251e17i	0.0170065	+	0.0294561i	−0.857397	+	0.514656i	$0.827920\pi$
$602$		−	6.46214e18i		−	0.225528i
$603$	1.32575e19	+	1.13223e19i	0.457342	+	0.390582i
$604$	2.61189e18			0.0890629
$605$	−9.35558e18	+	5.40144e18i	−0.315343	+	0.182063i
$606$	−4.34349e17	+	7.46418e16i	−0.0144721	+	0.00248699i
$607$	2.72777e19	−	4.72464e19i	0.898435	−	1.55614i	0.0689407	−	0.997621i	$-0.478038\pi$
$607$	2.72777e19	−	4.72464e19i	0.898435	−	1.55614i	0.829495	−	0.558515i	$-0.188629\pi$
$608$	2.29428e19	+	1.32460e19i	0.747000	+	0.431281i
$609$	7.68201e17	+	4.47025e18i	0.0247260	+	0.143883i
$610$	1.11127e19	+	1.92477e19i	0.353599	+	0.612451i
$611$		−	2.76644e19i		−	0.870229i
$612$	2.98887e18	−	3.49974e18i	0.0929496	−	0.108837i
$613$	5.06895e19			1.55846			0.779228	−	0.626741i	$-0.215611\pi$
$613$	5.06895e19			1.55846			0.779228	+	0.626741i	$0.215611\pi$
$614$	3.48978e19	−	2.01482e19i	1.06077	−	0.612433i
$615$	−6.08178e18	+	1.64862e19i	−0.182770	+	0.495443i
$616$	−2.22856e18	+	3.85997e18i	−0.0662154	+	0.114688i
$617$	4.13254e18	+	2.38592e18i	0.121401	+	0.0700907i	0.559471	−	0.828850i	$-0.311004\pi$
$617$	4.13254e18	+	2.38592e18i	0.121401	+	0.0700907i	−0.438070	+	0.898941i	$0.644338\pi$
$618$	−5.64157e19	+	4.69219e19i	−1.63863	+	1.36288i
$619$	3.09682e18	+	5.36384e18i	0.0889367	+	0.154043i	0.907062	−	0.420997i	$-0.138320\pi$
$619$	3.09682e18	+	5.36384e18i	0.0889367	+	0.154043i	−0.818125	+	0.575040i	$0.804986\pi$
$620$			2.36355e18i			0.0671156i
$621$	6.80657e19	+	8.87847e17i	1.91112	+	0.0249285i
$622$	1.99216e19			0.553084
$623$	5.28935e18	−	3.05381e18i	0.145206	−	0.0838350i
$624$	2.27932e19	+	2.74050e19i	0.618747	+	0.743939i
$625$	−7.09165e18	+	1.22831e19i	−0.190365	+	0.329722i
$626$	−2.72390e19	−	1.57265e19i	−0.723055	−	0.417456i
$627$	2.11139e19	+	7.78894e18i	0.554236	+	0.204459i
$628$	−1.43242e18	−	2.48102e18i	−0.0371836	−	0.0644039i
$629$			2.34361e19i			0.601631i
$630$	−7.65229e18	+	2.71009e18i	−0.194271	+	0.0688017i
$631$	1.51766e19			0.381038			0.190519	−	0.981684i	$-0.438983\pi$
$631$	1.51766e19			0.381038			0.190519	+	0.981684i	$0.438983\pi$
$632$	−3.80566e19	+	2.19720e19i	−0.944953	+	0.545569i
$633$	−4.03195e19	+	6.92880e18i	−0.990122	+	0.170150i
$634$	−2.97295e19	+	5.14930e19i	−0.722042	+	1.25061i
$635$	1.22798e19	+	7.08977e18i	0.294969	+	0.170301i
$636$	−4.61135e18	−	2.68340e19i	−0.109554	−	0.637508i
$637$	−1.43820e19	−	2.49103e19i	−0.337942	−	0.585332i
$638$		−	9.40557e18i		−	0.218595i
$639$	−2.16698e19	−	4.01556e18i	−0.498137	−	0.0923082i
$640$	−2.45954e19			−0.559234
$641$	2.33683e19	−	1.34917e19i	0.525559	−	0.303431i	−0.213647	−	0.976911i	$-0.568534\pi$
$641$	2.33683e19	−	1.34917e19i	0.525559	−	0.303431i	0.739206	+	0.673479i	$0.235201\pi$
$642$	1.45864e19	−	3.95400e19i	0.324491	−	0.879613i
$643$	2.51225e19	−	4.35134e19i	0.552823	−	0.957517i	−0.445247	−	0.895408i	$-0.646884\pi$
$643$	2.51225e19	−	4.35134e19i	0.552823	−	0.957517i	0.998069	−	0.0621091i	$-0.0197827\pi$
$644$	−1.03874e19	−	5.99718e18i	−0.226103	−	0.130541i
$645$	8.71341e18	−	7.24710e18i	0.187616	−	0.156044i
$646$	−1.32538e19	−	2.29562e19i	−0.282300	−	0.488958i
$647$			5.18661e19i			1.09283i	0.837514	+	0.546416i	$0.184008\pi$
$647$			5.18661e19i			1.09283i	−0.837514	+	0.546416i	$0.815992\pi$
$648$	1.27412e19	−	3.31981e19i	0.265573	−	0.691971i
$649$	2.05475e19			0.423688
$650$	−3.02787e19	+	1.74814e19i	−0.617652	+	0.356601i
$651$	−4.59767e18	−	5.52793e18i	−0.0927836	−	0.111557i
$652$	−1.11638e19	+	1.93363e19i	−0.222884	+	0.386046i
$653$	−7.72909e19	−	4.46239e19i	−1.52664	−	0.881405i	−0.999500	−	0.0316266i	$-0.989931\pi$
$653$	−7.72909e19	−	4.46239e19i	−1.52664	−	0.881405i	−0.527139	−	0.849779i	$-0.676735\pi$
$654$	−7.70656e19	−	2.84296e19i	−1.50597	−	0.555555i
$655$	−1.49080e19	−	2.58214e19i	−0.288224	−	0.499219i
$656$			7.20246e19i			1.37770i
$657$	1.26700e19	−	6.83729e19i	0.239783	−	1.29398i
$658$	2.58243e19			0.483557
$659$	7.75359e19	−	4.47654e19i	1.43650	−	0.829362i	0.438893	−	0.898539i	$-0.355371\pi$
$659$	7.75359e19	−	4.47654e19i	1.43650	−	0.829362i	0.997604	+	0.0691771i	$0.0220374\pi$
$660$	4.44334e18	−	7.63577e17i	0.0814521	−	0.0139973i
$661$	−2.12752e19	+	3.68497e19i	−0.385890	+	0.668381i	−0.991892	−	0.127082i	$-0.959439\pi$
$661$	−2.12752e19	+	3.68497e19i	−0.385890	+	0.668381i	0.606002	+	0.795463i	$0.292772\pi$
$662$	1.16648e18	+	6.73466e17i	0.0209349	+	0.0120867i
$663$	−2.93094e18	−	1.70555e19i	−0.0520490	−	0.302879i
$664$	3.37113e18	+	5.83896e18i	0.0592377	+	0.102603i
$665$			1.25224e19i			0.217738i
$666$	−3.48647e19	−	9.84452e19i	−0.599883	−	1.69385i
$667$	−4.38847e19			−0.747192
$668$	−1.40050e19	+	8.08578e18i	−0.235965	+	0.136234i
$669$	7.02512e18	−	1.90433e19i	0.117131	−	0.317512i
$670$	1.00582e19	−	1.74214e19i	0.165958	−	0.287447i
$671$	3.25181e19	+	1.87744e19i	0.530968	+	0.306554i
$672$	−1.24128e19	+	1.03239e19i	−0.200578	+	0.166824i
$673$	5.79961e19	+	1.00452e20i	0.927456	+	1.60640i	0.787563	+	0.616235i	$0.211343\pi$
$673$	5.79961e19	+	1.00452e20i	0.927456	+	1.60640i	0.139894	+	0.990167i	$0.455324\pi$
$674$			9.30261e18i			0.147226i
$675$	4.26342e19	+	2.53620e19i	0.667778	+	0.397244i
$676$	9.04050e18			0.140141
$677$	−8.24552e19	+	4.76055e19i	−1.26502	+	0.730360i	−0.974041	−	0.226370i	$-0.927314\pi$
$677$	−8.24552e19	+	4.76055e19i	−1.26502	+	0.730360i	−0.290979	+	0.956730i	$0.593981\pi$
$678$	5.53558e19	+	6.65560e19i	0.840534	+	1.01060i
$679$	−2.74219e18	+	4.74961e18i	−0.0412106	+	0.0713788i
$680$	7.97371e18	+	4.60362e18i	0.118604	+	0.0684758i
$681$	2.44833e19	+	9.03193e18i	0.360446	+	0.132969i
$682$	7.45478e18	+	1.29121e19i	0.108629	+	0.188150i
$683$			1.09770e20i			1.58321i	0.611034	+	0.791604i	$0.290754\pi$
$683$			1.09770e20i			1.58321i	−0.611034	+	0.791604i	$0.709246\pi$
$684$	2.40569e19	+	2.05452e19i	0.343437	+	0.293304i
$685$	−3.16362e19			−0.447045
$686$	5.02751e19	−	2.90263e19i	0.703208	−	0.405997i
$687$	−3.60852e18	+	6.20114e17i	−0.0499610	+	0.00858568i
$688$	2.32264e19	−	4.02293e19i	0.318319	−	0.551345i
$689$	−8.86627e19	−	5.11894e19i	−1.20284	−	0.694457i
$690$	−1.33025e19	−	7.74090e19i	−0.178645	−	1.03956i
$691$	2.89603e19	+	5.01608e19i	0.384997	+	0.666834i	0.991769	−	0.128042i	$-0.0408692\pi$
$691$	2.89603e19	+	5.01608e19i	0.384997	+	0.666834i	−0.606772	+	0.794876i	$0.707536\pi$
$692$			1.42645e19i			0.187721i
$693$	−8.90685e18	+	1.04292e19i	−0.116036	+	0.135869i
$694$	1.49737e20			1.93113
$695$	3.01345e19	−	1.73981e19i	0.384742	−	0.222131i
$696$	−7.93421e18	+	2.15076e19i	−0.100286	+	0.271849i
$697$	1.74838e19	−	3.02829e19i	0.218780	−	0.378938i
$698$	3.89208e19	+	2.24709e19i	0.482163	+	0.278377i
$699$	−1.36754e19	+	1.13741e19i	−0.167726	+	0.139500i
$700$	−4.37048e18	−	7.56990e18i	−0.0530693	−	0.0919187i
$701$		−	1.25085e20i		−	1.50376i	−0.659300	−	0.751880i	$-0.729147\pi$
$701$		−	1.25085e20i		−	1.50376i	0.659300	−	0.751880i	$-0.270853\pi$
$702$	3.76843e19	+	6.72827e19i	0.448539	+	0.800836i
$703$	−1.61098e20			−1.89846
$704$	−1.47573e19	+	8.52011e18i	−0.172186	+	0.0994115i
$705$	2.89612e19	+	3.48210e19i	0.334574	+	0.402269i
$706$	7.78165e19	−	1.34782e20i	0.890099	−	1.54170i
$707$	−3.58796e17	−	2.07151e17i	−0.00406361	−	0.00234612i
$708$	2.70995e19	+	9.99706e18i	0.303899	+	0.112109i
$709$	3.32061e19	+	5.75147e19i	0.368718	+	0.638638i	0.989365	−	0.145451i	$-0.0464634\pi$
$709$	3.32061e19	+	5.75147e19i	0.368718	+	0.638638i	−0.620647	+	0.784090i	$0.713130\pi$
$710$			2.54292e19i			0.279592i
$711$	−1.27463e20	+	4.51413e19i	−1.38770	+	0.491459i
$712$	3.08687e19			0.332781
$713$	6.02453e19	−	3.47826e19i	0.643127	−	0.371309i
$714$	1.59210e19	−	2.73599e18i	0.168300	−	0.0289219i
$715$	8.47627e18	−	1.46813e19i	0.0887284	−	0.153682i
$716$	−5.04811e19	−	2.91453e19i	−0.523284	−	0.302118i
$717$	−9.95747e18	−	5.79436e19i	−0.102215	−	0.594801i
$718$	6.45560e17	+	1.11814e18i	0.00656244	+	0.0113665i
$719$		−	1.18331e20i		−	1.19123i	−0.803269	−	0.595616i	$-0.796908\pi$
$719$		−	1.18331e20i		−	1.19123i	0.803269	−	0.595616i	$-0.203092\pi$
$720$	−5.73792e19	−	1.06328e19i	−0.572041	−	0.106003i
$721$	−6.89806e19			−0.681052
$722$	5.42886e19	−	3.13435e19i	0.530821	−	0.306470i
$723$	−6.09062e19	+	1.65101e20i	−0.589784	+	1.59876i
$724$	−2.38268e19	+	4.12693e19i	−0.228505	+	0.395783i
$725$	−2.76966e19	−	1.59906e19i	−0.263063	−	0.151880i
$726$	−7.36512e19	+	6.12570e19i	−0.692825	+	0.576234i
$727$	−4.80326e19	−	8.31949e19i	−0.447502	−	0.775097i	0.550721	−	0.834690i	$-0.314353\pi$
$727$	−4.80326e19	−	8.31949e19i	−0.447502	−	0.775097i	−0.998223	+	0.0595931i	$0.981020\pi$
$728$			2.35596e19i			0.217394i
$729$	5.71625e19	−	9.33004e19i	0.522419	−	0.852689i
$730$	−8.02345e19			−0.726275
$731$	−1.95312e19	+	1.12763e19i	−0.175108	+	0.101099i
$732$	3.37529e19	+	4.05822e19i	0.299732	+	0.360378i
$733$	−8.00772e19	+	1.38698e20i	−0.704338	+	1.21995i	0.262592	+	0.964907i	$0.415423\pi$
$733$	−8.00772e19	+	1.38698e20i	−0.704338	+	1.21995i	−0.966930	+	0.255042i	$0.917911\pi$
$734$	−3.51496e19	−	2.02936e19i	−0.306230	−	0.176802i
$735$	4.41804e19	+	1.62982e19i	0.381257	+	0.140646i
$736$	−7.81031e19	−	1.35279e20i	−0.667611	−	1.15634i
$737$		−	3.39858e19i		−	0.287756i
$738$	−2.83919e19	+	1.53216e20i	−0.238122	+	1.28502i
$739$	−1.28317e19			−0.106604			−0.0533021	−	0.998578i	$-0.516975\pi$
$739$	−1.28317e19			−0.106604			−0.0533021	+	0.998578i	$0.516975\pi$
$740$	−2.79496e19	+	1.61367e19i	−0.230014	+	0.132798i
$741$	1.17238e20	−	2.01470e19i	0.955742	−	0.164242i
$742$	4.77845e19	−	8.27651e19i	0.385886	−	0.668375i
$743$	1.35176e20	+	7.80438e19i	1.08138	+	0.624333i	0.931268	−	0.364336i	$-0.118704\pi$
$743$	1.35176e20	+	7.80438e19i	1.08138	+	0.624333i	0.150110	+	0.988669i	$0.452037\pi$
$744$	−6.15463e18	−	3.58145e19i	−0.0487743	−	0.283823i
$745$	2.69754e19	+	4.67228e19i	0.211775	+	0.366805i
$746$		−	7.94729e19i		−	0.618084i
$747$	6.92596e18	+	1.95564e19i	0.0533625	+	0.150676i
$748$	−8.97161e18			−0.0684793
$749$	3.43109e19	−	1.98094e19i	0.259453	−	0.149795i
$750$	4.53069e19	−	1.22816e20i	0.339419	−	0.920079i
$751$	−3.43695e19	+	5.95297e19i	−0.255090	+	0.441829i	−0.964920	−	0.262544i	$-0.915438\pi$
$751$	−3.43695e19	+	5.95297e19i	−0.255090	+	0.441829i	0.709830	+	0.704373i	$0.248772\pi$
$752$	1.60766e20	+	9.28185e19i	1.18214	+	0.682511i
$753$	5.10957e19	−	4.24972e19i	0.372237	−	0.309596i
$754$	−2.48582e19	−	4.30556e19i	−0.179420	−	0.310764i
$755$			1.60786e19i			0.114979i
$756$	−1.68212e19	+	9.42135e18i	−0.119180	+	0.0667514i
$757$	−1.73606e19			−0.121869			−0.0609347	−	0.998142i	$-0.519408\pi$
$757$	−1.73606e19			−0.121869			−0.0609347	+	0.998142i	$0.519408\pi$
$758$	−1.06604e20	+	6.15476e19i	−0.741459	+	0.428082i
$759$	−8.48524e19	−	1.02021e20i	−0.584752	−	0.703066i
$760$	−3.16449e19	+	5.48106e19i	−0.216077	+	0.374256i
$761$	−2.81760e19	−	1.62674e19i	−0.190628	−	0.110059i	0.401648	−	0.915794i	$-0.368437\pi$
$761$	−2.81760e19	−	1.62674e19i	−0.190628	−	0.110059i	−0.592277	+	0.805735i	$0.701771\pi$
$762$	1.17968e20	+	4.35186e19i	0.790824	+	0.291736i
$763$	−3.86096e19	−	6.68737e19i	−0.256462	−	0.444205i
$764$		−	4.02072e19i		−	0.264637i
$765$	2.15441e19	+	1.83992e19i	0.140507	+	0.119997i
$766$	−1.97955e20			−1.27928
$767$	9.40597e19	−	5.43054e19i	0.602332	−	0.347756i
$768$	−1.50411e20	+	2.58478e19i	−0.954448	+	0.164019i
$769$	−4.90393e18	+	8.49386e18i	−0.0308361	+	0.0534098i	−0.881032	−	0.473057i	$-0.843150\pi$
$769$	−4.90393e18	+	8.49386e18i	−0.0308361	+	0.0534098i	0.850196	+	0.526467i	$0.176484\pi$
$770$	1.37048e19	+	7.91246e18i	0.0853959	+	0.0493034i
$771$	1.15481e19	+	6.71996e19i	0.0713065	+	0.414941i
$772$	4.33790e19	+	7.51347e19i	0.265435	+	0.459748i
$773$		−	3.51963e19i		−	0.213422i	−0.994290	−	0.106711i	$-0.965968\pi$
$773$		−	3.51963e19i		−	0.213422i	0.994290	−	0.106711i	$-0.0340320\pi$
$774$	6.52670e19	−	7.64227e19i	0.392200	−	0.459236i
$775$	5.06961e19			0.301900
$776$	−2.40052e19	+	1.38594e19i	−0.141668	+	0.0817923i
$777$	3.39794e19	−	9.21095e19i	0.198732	−	0.538713i
$778$	5.42010e19	−	9.38790e19i	0.314160	−	0.544141i
$779$	2.08162e20	+	1.20182e20i	1.19575	+	0.690364i
$780$	1.83221e19	−	1.52388e19i	0.104307	−	0.0867539i
$781$	2.14807e19	+	3.72056e19i	0.121197	+	0.209919i
$782$			1.56298e20i			0.873987i
$783$	−3.60642e19	+	6.06249e19i	−0.199868	+	0.335984i
$784$	1.93015e20			1.06018
$785$	1.52729e19	−	8.81783e18i	0.0831447	−	0.0480036i
$786$	−1.69070e20	−	2.03278e20i	−0.912237	−	1.09681i
$787$	−6.45585e19	+	1.11819e20i	−0.345248	+	0.597986i	−0.985399	−	0.170263i	$-0.945538\pi$
$787$	−6.45585e19	+	1.11819e20i	−0.345248	+	0.597986i	0.640151	+	0.768249i	$0.278872\pi$
$788$	4.47247e19	+	2.58218e19i	0.237063	+	0.136868i
$789$	1.66019e20	+	6.12446e19i	0.872204	+	0.321758i
$790$	7.80112e19	+	1.35119e20i	0.406226	+	0.703603i
$791$			8.13793e19i			0.420028i
$792$	−6.53408e19	+	2.31407e19i	−0.334278	+	0.118386i
$793$	1.98477e20			1.00646
$794$	−2.44170e20	+	1.40972e20i	−1.22729	+	0.708578i
$795$	1.65188e20	−	2.83871e19i	0.823015	−	0.141433i
$796$	−6.59814e18	+	1.14283e19i	−0.0325859	+	0.0564405i
$797$	−2.14420e20	−	1.23795e20i	−1.04968	−	0.606032i	−0.127119	−	0.991887i	$-0.540573\pi$
$797$	−2.14420e20	−	1.23795e20i	−1.04968	−	0.606032i	−0.922559	+	0.385855i	$0.873906\pi$
$798$	1.88069e19	+	1.09440e20i	0.0912636	+	0.531073i
$799$	−4.50630e19	−	7.80514e19i	−0.216767	−	0.375451i
$800$		−	1.13836e20i		−	0.542814i
$801$	9.33962e19	+	1.73069e19i	0.441470	+	0.0818074i
$802$	7.24616e19			0.339537
$803$	−1.17392e20	+	6.77762e19i	−0.545291	+	0.314824i
$804$	1.65352e19	−	4.48229e19i	0.0761409	−	0.206399i
$805$	3.69181e19	−	6.39440e19i	0.168527	−	0.291897i
$806$	6.82511e19	+	3.94048e19i	0.308862	+	0.178321i
$807$	−1.87655e20	+	1.56076e20i	−0.841872	+	0.700200i
$808$	−1.04697e18	−	1.81341e18i	−0.00465645	−	0.00806520i
$809$		−	2.39808e20i		−	1.05736i	−0.848821	−	0.528681i	$-0.822687\pi$
$809$		−	2.39808e20i		−	1.05736i	0.848821	−	0.528681i	$-0.177313\pi$
$810$	−1.17869e20	−	4.52374e19i	−0.515236	−	0.197744i
$811$	3.42865e20			1.48586			0.742928	−	0.669371i	$-0.233436\pi$
$811$	3.42865e20			1.48586			0.742928	+	0.669371i	$0.233436\pi$
$812$	1.07642e19	−	6.21473e18i	0.0462478	−	0.0267012i
$813$	−2.84137e20	−	3.41626e20i	−1.21030	−	1.45518i
$814$	−1.01792e20	+	1.76309e20i	−0.429876	+	0.744568i
$815$	−1.19032e20	−	6.87233e19i	−0.498381	−	0.287740i
$816$	1.08948e20	+	4.01912e19i	0.452261	+	0.166840i
$817$	−7.75125e19	−	1.34256e20i	−0.319020	−	0.552558i
$818$			3.58610e19i			0.146335i
$819$	−1.32090e19	+	7.12817e19i	−0.0534420	+	0.288397i
$820$	4.81534e19			0.193166
$821$	−4.15721e20	+	2.40017e20i	−1.65348	+	0.954639i	−0.677860	+	0.735191i	$0.737092\pi$
$821$	−4.15721e20	+	2.40017e20i	−1.65348	+	0.954639i	−0.975624	+	0.219448i	$0.929574\pi$
$822$	−2.76486e20	+	4.75135e19i	−1.09036	+	0.187376i
$823$	1.74191e20	−	3.01708e20i	0.681126	−	1.17974i	−0.293512	−	0.955955i	$-0.594824\pi$
$823$	1.74191e20	−	3.01708e20i	0.681126	−	1.17974i	0.974638	−	0.223789i	$-0.0718427\pi$
$824$	−3.01929e20	−	1.74319e20i	−1.17062	−	0.675855i
$825$	−1.63781e19	−	9.53059e19i	−0.0629630	−	0.366389i
$826$	5.06932e19	+	8.78032e19i	0.193237	+	0.334695i
$827$		−	1.57173e20i		−	0.594073i	−0.954866	−	0.297036i	$-0.904002\pi$
$827$		−	1.57173e20i		−	0.594073i	0.954866	−	0.297036i	$-0.0959983\pi$
$828$	−6.22730e19	−	1.75836e20i	−0.233393	−	0.659015i
$829$	1.90105e20			0.706498			0.353249	−	0.935529i	$-0.385077\pi$
$829$	1.90105e20			0.706498			0.353249	+	0.935529i	$0.385077\pi$
$830$	2.07311e19	−	1.19691e19i	0.0763971	−	0.0441079i
$831$	−7.41673e19	+	2.01049e20i	−0.271022	+	0.734674i
$832$	−4.50360e19	+	7.80046e19i	−0.163191	+	0.282655i
$833$	−8.11534e19	−	4.68539e19i	−0.291603	−	0.168357i
$834$	2.37232e20	−	1.97310e20i	0.845299	−	0.703050i
$835$	−4.97754e19	−	8.62135e19i	−0.175877	−	0.304628i
$836$		−	6.16701e19i		−	0.216088i
$837$	1.45845e18	−	1.11811e20i	0.00506774	−	0.388512i
$838$	−2.21929e20			−0.764727
$839$	−2.96222e20	+	1.71024e20i	−1.01224	+	0.584418i	−0.911847	−	0.410530i	$-0.865344\pi$
$839$	−2.96222e20	+	1.71024e20i	−1.01224	+	0.584418i	−0.100394	+	0.994948i	$0.532010\pi$
$840$	−2.46639e19	−	2.96542e19i	−0.0835810	−	0.100492i
$841$	−1.26041e20	+	2.18309e20i	−0.423584	+	0.733668i
$842$	1.57509e20	+	9.09378e19i	0.524953	+	0.303082i
$843$	−1.20823e20	−	4.45717e19i	−0.399352	−	0.147322i
$844$	5.60538e19	+	9.70881e19i	0.183742	+	0.318250i
$845$			5.56525e19i			0.180921i
$846$	3.05404e20	+	2.60823e20i	0.984651	+	0.840918i
$847$	−9.00547e19			−0.287954
$848$	5.94954e20	−	3.43497e20i	1.88674	−	1.08931i
$849$	5.63427e20	−	9.68235e19i	1.77208	−	0.304528i
$850$	−5.69514e19	+	9.86428e19i	−0.177653	+	0.307704i
$851$	8.22627e20	+	4.74944e20i	2.54505	+	1.46938i
$852$	1.02285e19	+	5.95206e19i	0.0313858	+	0.182638i
$853$	−8.44903e19	−	1.46341e20i	−0.257136	−	0.445373i	0.708337	−	0.705874i	$-0.249446\pi$
$853$	−8.44903e19	−	1.46341e20i	−0.257136	−	0.445373i	−0.965474	+	0.260501i	$0.916112\pi$
$854$			1.85275e20i			0.559256i
$855$	−1.26475e20	+	1.48092e20i	−0.378653	+	0.443373i
$856$	2.00239e20			0.594610
$857$	−1.22693e20	+	7.08368e19i	−0.361372	+	0.208638i	−0.669682	−	0.742648i	$-0.733570\pi$
$857$	−1.22693e20	+	7.08368e19i	−0.361372	+	0.208638i	0.308311	+	0.951286i	$0.400236\pi$
$858$	5.20293e19	−	1.41038e20i	0.151998	−	0.412027i
$859$	6.81490e19	−	1.18038e20i	0.197473	−	0.342033i	−0.750236	−	0.661171i	$-0.770060\pi$
$859$	6.81490e19	−	1.18038e20i	0.197473	−	0.342033i	0.947708	+	0.319138i	$0.103393\pi$
$860$	−2.68960e19	−	1.55284e19i	−0.0773035	−	0.0446312i
$861$	−1.12622e20	+	9.36698e19i	−0.321071	+	0.267041i
$862$	1.59478e20	+	2.76224e20i	0.450972	+	0.781106i
$863$			1.58254e20i			0.443894i	0.975059	+	0.221947i	$0.0712411\pi$
$863$			1.58254e20i			0.443894i	−0.975059	+	0.221947i	$0.928759\pi$
$864$	−2.51067e20	−	3.27490e18i	−0.698542	−	0.00911176i
$865$	−8.78108e19			−0.242346
$866$	1.89258e20	−	1.09268e20i	0.518117	−	0.299135i
$867$	1.99422e20	+	2.39771e20i	0.541550	+	0.651123i
$868$	−9.85149e18	+	1.70633e19i	−0.0265377	+	0.0459647i
$869$	2.28278e20	+	1.31796e20i	0.609993	+	0.352180i
$870$	7.63626e19	+	2.81703e19i	0.202416	+	0.0746718i
$871$	−8.98217e19	−	1.55576e20i	−0.236186	−	0.409086i
$872$		−	3.90276e20i		−	1.01802i
$873$	−8.04003e19	+	2.84741e19i	−0.208045	+	0.0736800i
$874$	−1.07438e21			−2.75788
$875$	1.06573e20	−	6.15302e19i	0.271389	−	0.156687i
$876$	−1.87800e20	+	3.22730e19i	−0.474425	+	0.0815287i
$877$	−5.70271e19	+	9.87739e19i	−0.142917	+	0.247540i	−0.928594	−	0.371097i	$-0.878982\pi$
$877$	−5.70271e19	+	9.87739e19i	−0.142917	+	0.247540i	0.785677	+	0.618637i	$0.212315\pi$
$878$	−2.35007e19	−	1.35681e19i	−0.0584277	−	0.0337332i
$879$	−2.02025e19	−	1.17561e20i	−0.0498291	−	0.289961i
$880$	5.68784e19	+	9.85163e19i	0.139177	+	0.241062i
$881$			3.33760e20i			0.810219i	0.914268	+	0.405109i	$0.132767\pi$
$881$			3.33760e20i			0.810219i	−0.914268	+	0.405109i	$0.867233\pi$
$882$	4.10594e20	+	7.60858e19i	0.988854	+	0.183241i
$883$	−1.77256e20			−0.423522			−0.211761	−	0.977322i	$-0.567920\pi$
$883$	−1.77256e20			−0.423522			−0.211761	+	0.977322i	$0.567920\pi$
$884$	−4.10691e19	+	2.37113e19i	−0.0973530	+	0.0562068i
$885$	−6.15410e19	+	1.66822e20i	−0.144731	+	0.392330i
$886$	2.20916e20	−	3.82638e20i	0.515456	−	0.892796i
$887$	−4.30804e20	−	2.48725e20i	−0.997274	−	0.575777i	−0.0898337	−	0.995957i	$-0.528634\pi$
$887$	−4.30804e20	−	2.48725e20i	−0.997274	−	0.575777i	−0.907441	+	0.420180i	$0.861967\pi$
$888$	3.81496e20	−	3.17297e20i	0.876191	−	0.728743i
$889$	5.91016e19	+	1.02367e20i	0.134675	+	0.233264i
$890$		−	1.09599e20i		−	0.247786i
$891$	−2.10669e20	+	3.33801e19i	−0.472559	+	0.0748762i
$892$	−5.56225e19			−0.123793
$893$	5.36518e20	−	3.09759e20i	1.18474	−	0.684012i
$894$	3.05924e20	+	3.67822e20i	0.670272	+	0.805889i
$895$	1.79416e20	−	3.10757e20i	0.390031	−	0.675554i
$896$	−1.77562e20	−	1.02516e20i	−0.382996	−	0.221123i
$897$	−6.58059e20	−	2.42759e20i	−1.40837	−	0.519552i
$898$	−4.93394e20	−	8.54584e20i	−1.04776	−	1.81477i
$899$			7.20888e19i			0.151897i
$900$	2.47690e19	−	1.33665e20i	0.0517858	−	0.279460i
$901$	−3.33533e20			−0.691934
$902$	2.63061e20	−	1.51878e20i	0.541515	−	0.312644i
$903$	9.31116e19	−	1.60010e19i	0.190191	−	0.0326838i
$904$	−2.05651e20	+	3.56199e20i	−0.416824	+	0.721960i
$905$	−2.54050e20	−	1.46676e20i	−0.510951	−	0.294998i
$906$	2.41479e19	+	1.40519e20i	0.0481928	+	0.280439i
$907$	2.38047e20	+	4.12310e20i	0.471425	+	0.816532i	0.999466	−	0.0326871i	$-0.0104065\pi$
$907$	2.38047e20	+	4.12310e20i	0.471425	+	0.816532i	−0.528041	+	0.849219i	$0.677073\pi$
$908$		−	7.15116e19i		−	0.140532i
$909$	−2.15099e18	−	6.07362e18i	−0.00419462	−	0.0118441i
$910$	8.36480e19			0.161870
$911$	1.04981e20	−	6.06106e19i	0.201595	−	0.116391i	−0.395804	−	0.918335i	$-0.629534\pi$
$911$	1.04981e20	−	6.06106e19i	0.201595	−	0.116391i	0.597399	+	0.801944i	$0.296201\pi$
$912$	−2.76271e20	+	7.48901e20i	−0.526467	+	1.42712i
$913$	2.02213e19	−	3.50243e19i	0.0382396	−	0.0662329i
$914$	−7.67868e20	−	4.43329e20i	−1.44100	−	0.831960i
$915$	−2.49820e20	+	2.07780e20i	−0.465243	+	0.386951i
$916$	5.01671e18	+	8.68920e18i	0.00927152	+	0.0160587i
$917$		−	2.48551e20i		−	0.455859i
$918$	2.15919e20	+	1.28444e20i	0.392999	+	0.233785i
$919$	−5.15778e19			−0.0931653			−0.0465826	−	0.998914i	$-0.514833\pi$
$919$	−5.15778e19			−0.0931653			−0.0465826	+	0.998914i	$0.514833\pi$
$920$	3.23182e20	−	1.86589e20i	0.579339	−	0.334481i
$921$	3.76723e20	+	4.52945e20i	0.670200	+	0.805802i
$922$	7.11743e19	−	1.23278e20i	0.125663	−	0.217654i
$923$	1.96663e20	+	1.13544e20i	0.344597	+	0.198953i
$924$	3.52606e19	+	1.30077e19i	0.0613178	+	0.0226202i
$925$	3.46118e20	+	5.99495e20i	0.597355	+	1.03465i
$926$			2.77113e20i			0.474657i
$927$	−8.15780e20	−	6.96698e20i	−1.38680	−	1.18437i
$928$	1.61873e20			0.273110
$929$	−8.76394e20	+	5.05986e20i	−1.46754	+	0.847283i	−0.999339	−	0.0363405i	$-0.988430\pi$
$929$	−8.76394e20	+	5.05986e20i	−1.46754	+	0.847283i	−0.468198	+	0.883624i	$0.655097\pi$
$930$	−1.27159e20	+	2.18519e19i	−0.211332	+	0.0363169i
$931$	3.22070e20	−	5.57841e20i	0.531254	−	0.920159i
$932$	4.22124e19	+	2.43713e19i	0.0691081	+	0.0398996i
$933$	4.93281e19	+	2.87046e20i	0.0801536	+	0.466423i
$934$	5.59116e20	+	9.68417e20i	0.901724	+	1.56183i
$935$		−	5.52285e19i		−	0.0884060i
$936$	−2.37950e20	+	2.78621e20i	−0.378055	+	0.442673i
$937$	8.95113e20			1.41156			0.705782	−	0.708429i	$-0.250596\pi$
$937$	8.95113e20			1.41156			0.705782	+	0.708429i	$0.250596\pi$
$938$	1.45227e20	−	8.38471e19i	0.227315	−	0.131241i
$939$	1.59152e20	−	4.31422e20i	0.247260	−	0.670259i
$940$	6.20555e19	−	1.07483e20i	0.0956941	−	0.165747i
$941$	3.26128e20	+	1.88290e20i	0.499184	+	0.288204i	0.728377	−	0.685177i	$-0.240275\pi$
$941$	3.26128e20	+	1.88290e20i	0.499184	+	0.288204i	−0.229192	+	0.973381i	$0.573609\pi$
$942$	1.20235e20	−	1.00002e20i	0.182673	−	0.151933i
$943$	−7.08637e20	−	1.22740e21i	−1.06867	−	1.85098i
$944$			7.28812e20i			1.09097i
$945$	−5.79970e19	−	1.03550e20i	−0.0861753	−	0.153860i
$946$	−1.95910e20			−0.288948
$947$	8.26331e20	−	4.77082e20i	1.20977	−	0.698463i	0.247064	−	0.968999i	$-0.420534\pi$
$947$	8.26331e20	−	4.77082e20i	1.20977	−	0.698463i	0.962710	+	0.270536i	$0.0872010\pi$
$948$	2.36946e20	+	2.84887e20i	0.344342	+	0.414014i
$949$	−3.58254e20	+	6.20514e20i	−0.516806	+	0.895134i
$950$	−6.78062e20	−	3.91479e20i	−0.970966	−	0.560587i
$951$	−8.15565e20	−	3.00863e20i	−1.15930	−	0.427667i
$952$	3.83766e19	+	6.64702e19i	0.0541511	+	0.0937925i
$953$		−	6.86670e19i		−	0.0961829i	−0.998843	−	0.0480915i	$-0.984686\pi$
$953$		−	6.86670e19i		−	0.0961829i	0.998843	−	0.0480915i	$-0.0153139\pi$
$954$	1.40103e21	−	4.96180e20i	1.94809	−	0.689923i
$955$	2.47512e20			0.341644
$956$	−1.39527e20	+	8.05557e19i	−0.191184	+	0.110380i
$957$	1.35523e20	−	2.32893e19i	0.184344	−	0.0316790i
$958$	7.81805e20	−	1.35413e21i	1.05570	−	1.82852i
$959$	−2.28393e20	−	1.31863e20i	−0.306162	−	0.176763i
$960$	−2.49747e19	−	1.45331e20i	−0.0332354	−	0.193401i
$961$	3.21335e20	+	5.56569e20i	0.424516	+	0.735284i
$962$			1.07611e21i			1.41134i
$963$	6.05841e20	+	1.12267e20i	0.788814	+	0.146173i
$964$	4.82233e20			0.623330
$965$	−4.62523e20	+	2.67038e20i	−0.593529	+	0.342674i
$966$	2.26612e20	−	6.14288e20i	0.288697	−	0.782586i
$967$	−6.39879e20	+	1.10830e21i	−0.809305	+	1.40176i	0.104040	+	0.994573i	$0.466823\pi$
$967$	−6.39879e20	+	1.10830e21i	−0.809305	+	1.40176i	−0.913346	+	0.407185i	$0.866510\pi$
$968$	−3.94171e20	−	2.27575e20i	−0.494945	−	0.285757i
$969$	2.97953e20	−	2.47813e20i	0.371433	−	0.308928i
$970$	4.92076e19	+	8.52300e19i	0.0609018	+	0.105485i
$971$			4.07978e20i			0.501306i	0.968077	+	0.250653i	$0.0806453\pi$
$971$			4.07978e20i			0.501306i	−0.968077	+	0.250653i	$0.919355\pi$
$972$	−2.94086e20	−	5.84735e19i	−0.358765	−	0.0713338i
$973$	2.90068e20			0.351325
$974$	−3.00926e20	+	1.73740e20i	−0.361866	+	0.208923i
$975$	−3.26859e20	−	3.92993e20i	−0.390237	−	0.469194i
$976$	−6.65919e20	+	1.15341e21i	−0.789356	+	1.36720i
$977$	1.01319e21	+	5.84967e20i	1.19242	+	0.688446i	0.958855	−	0.283895i	$-0.0916267\pi$
$977$	1.01319e21	+	5.84967e20i	1.19242	+	0.688446i	0.233568	+	0.972341i	$0.424960\pi$
$978$	−1.14350e21	−	4.21839e20i	−1.33618	−	0.492919i
$979$	−9.25811e19	−	1.60355e20i	−0.107410	−	0.186039i
$980$		−	1.29043e20i		−	0.148646i
$981$	2.18813e20	−	1.18082e21i	0.250260	−	1.35051i
$982$	1.23618e20			0.140378
$983$	7.26339e19	−	4.19352e19i	0.0818964	−	0.0472829i	−0.458493	−	0.888698i	$-0.651610\pi$
$983$	7.26339e19	−	4.19352e19i	0.0818964	−	0.0472829i	0.540389	+	0.841415i	$0.318277\pi$
$984$	−7.29659e20	+	1.25390e20i	−0.816872	+	0.140377i
$985$	−1.58957e20	+	2.75321e20i	−0.176695	+	0.306045i
$986$	−1.40268e20	−	8.09837e19i	−0.154817	−	0.0893838i
$987$	6.39439e19	+	3.72097e20i	0.0700776	+	0.407789i
$988$	−1.62989e20	−	2.82305e20i	−0.177362	−	0.307200i
$989$			9.14082e20i			0.987668i
$990$	8.21607e19	+	2.31992e20i	0.0881491	+	0.248901i
$991$	−2.99221e20			−0.318769			−0.159385	−	0.987217i	$-0.550951\pi$
$991$	−2.99221e20			−0.318769			−0.159385	+	0.987217i	$0.550951\pi$
$992$	−2.22220e20	+	1.28299e20i	−0.235073	+	0.135719i
$993$	−6.81549e18	+	1.84751e19i	−0.00715900	+	0.0194063i
$994$	−1.05991e20	+	1.83582e20i	−0.110551	+	0.191481i
$995$	−7.03517e19	−	4.06176e19i	−0.0728640	−	0.0420681i
$996$	4.37098e19	−	3.63542e19i	0.0449535	−	0.0373886i
$997$	−1.61651e19	−	2.79988e19i	−0.0165087	−	0.0285939i	0.857653	−	0.514229i	$-0.171922\pi$
$997$	−1.61651e19	−	2.79988e19i	−0.0165087	−	0.0285939i	−0.874162	+	0.485635i	$0.838588\pi$
$998$			5.61369e20i			0.569292i
$999$	1.33215e21	−	7.46119e20i	1.34151	−	0.751363i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.15.d.a.5.11	yes	26
3.2	odd	2		27.15.d.a.17.3		26
9.2	odd	6	inner	9.15.d.a.2.11	✓	26
9.4	even	3		81.15.b.a.80.21		26
9.5	odd	6		81.15.b.a.80.6		26
9.7	even	3		27.15.d.a.8.3		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.15.d.a.2.11	✓	26	9.2	odd	6	inner
9.15.d.a.5.11	yes	26	1.1	even	1	trivial
27.15.d.a.8.3		26	9.7	even	3
27.15.d.a.17.3		26	3.2	odd	2
81.15.b.a.80.6		26	9.5	odd	6
81.15.b.a.80.21		26	9.4	even	3

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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	9.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(129.548 - 74.7948i) q^{2} +(1398.48 + 1681.44i) q^{3} +(2996.54 - 5190.15i) q^{4} +(31950.1 + 18446.4i) q^{5} +(306934. + 113228. i) q^{6} +(153772. + 266342. i) q^{7} +1.55438e6i q^{8} +(-871480. + 4.70290e6i) q^{9} +5.51879e6 q^{10} +(8.07458e6 - 4.66186e6i) q^{11} +(1.29175e7 - 2.21984e6i) q^{12} +(2.46419e7 - 4.26810e7i) q^{13} +(3.98420e7 + 2.30028e7i) q^{14} +(1.36651e7 + 7.95190e7i) q^{15} +(1.65355e8 + 2.86402e8i) q^{16} -1.60558e8i q^{17} +(2.38854e8 + 6.74436e8i) q^{18} +1.10366e9 q^{19} +(1.91479e8 - 1.10551e8i) q^{20} +(-2.32789e8 + 6.31032e8i) q^{21} +(6.97366e8 - 1.20787e9i) q^{22} +(-5.63572e9 - 3.25379e9i) q^{23} +(-2.61358e9 + 2.17376e9i) q^{24} +(-2.37122e9 - 4.10707e9i) q^{25} -7.37234e9i q^{26} +(-9.12638e9 + 5.11158e9i) q^{27} +1.84314e9 q^{28} +(5.84016e9 - 3.37182e9i) q^{29} +(7.71791e9 + 9.27948e9i) q^{30} +(-5.34495e9 + 9.25772e9i) q^{31} +(2.07879e10 + 1.20019e10i) q^{32} +(1.91308e10 + 7.05737e9i) q^{33} +(-1.20089e10 - 2.08000e10i) q^{34} +1.13462e10i q^{35} +(2.17974e10 + 1.86155e10i) q^{36} -1.45967e11 q^{37} +(1.42978e11 - 8.25481e10i) q^{38} +(1.06226e11 - 1.82547e10i) q^{39} +(-2.86727e10 + 4.96625e10i) q^{40} +(1.88610e11 + 1.08894e11i) q^{41} +(1.70405e10 + 9.91606e10i) q^{42} +(-7.02322e10 - 1.21646e11i) q^{43} -5.58777e10i q^{44} +(-1.14596e11 + 1.34183e11i) q^{45} -9.73465e11 q^{46} +(4.86126e11 - 2.80665e11i) q^{47} +(-2.50322e11 + 6.78561e11i) q^{48} +(2.91820e11 - 5.05446e11i) q^{49} +(-6.14375e11 - 3.54710e11i) q^{50} +(2.69968e11 - 2.24537e11i) q^{51} +(-1.47680e11 - 2.55790e11i) q^{52} -2.07734e12i q^{53} +(-7.99989e11 + 1.34480e12i) q^{54} +3.43979e11 q^{55} +(-4.13995e11 + 2.39020e11i) q^{56} +(1.54345e12 + 1.85573e12i) q^{57} +(5.04389e11 - 8.73628e11i) q^{58} +(1.90853e12 + 1.10189e12i) q^{59} +(4.53664e11 + 1.67357e11i) q^{60} +(2.01361e12 + 3.48768e12i) q^{61} +1.59910e12i q^{62} +(-1.38659e12 + 4.91066e11i) q^{63} -1.82762e12 q^{64} +(1.57462e12 - 9.09108e11i) q^{65} +(3.00621e12 - 5.16610e11i) q^{66} +(1.82254e12 - 3.15674e12i) q^{67} +(-8.33320e11 - 4.81118e11i) q^{68} +(-2.41041e12 - 1.40265e13i) q^{69} +(8.48638e11 + 1.46988e12i) q^{70} +4.60775e12i q^{71} +(-7.31008e12 - 1.35461e12i) q^{72} -1.45384e13 q^{73} +(-1.89097e13 + 1.09175e13i) q^{74} +(3.58967e12 - 9.73070e12i) q^{75} +(3.30716e12 - 5.72817e12i) q^{76} +(2.48330e12 + 1.43373e12i) q^{77} +(1.23961e13 - 1.03101e13i) q^{78} +(1.41356e13 + 2.44835e13i) q^{79} +1.22008e13i q^{80} +(-2.13578e13 - 8.19698e12i) q^{81} +3.25789e13 q^{82} +(3.75647e12 - 2.16880e12i) q^{83} +(2.57759e12 + 3.09912e12i) q^{84} +(2.96172e12 - 5.12985e12i) q^{85} +(-1.81969e13 - 1.05060e13i) q^{86} +(1.38368e13 + 5.10443e12i) q^{87} +(7.24628e12 + 1.25509e13i) q^{88} -1.98593e13i q^{89} +(-4.80951e12 + 2.59543e13i) q^{90} +1.51570e13 q^{91} +(-3.37753e13 + 1.95002e13i) q^{92} +(-2.30411e13 + 3.95955e12i) q^{93} +(4.19846e13 - 7.27195e13i) q^{94} +(3.52621e13 + 2.03586e13i) q^{95} +(8.89102e12 + 5.17379e13i) q^{96} +(8.91638e12 + 1.54436e13i) q^{97} -8.73064e13i q^{98} +(1.48875e13 + 4.20367e13i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q - 3 q^{2} - 2199 q^{3} + 98303 q^{4} - 107994 q^{5} + 24957 q^{6} - 146330 q^{7} - 5316525 q^{9} - 32772 q^{10} - 15978711 q^{11} - 53795046 q^{12} - 23281436 q^{13} - 349442850 q^{14} + 207365400 q^{15}+ \cdots - 195117933369168 q^{99}+O(q^{100}) \) 26 * q - 3 * q^2 - 2199 * q^3 + 98303 * q^4 - 107994 * q^5 + 24957 * q^6 - 146330 * q^7 - 5316525 * q^9 - 32772 * q^10 - 15978711 * q^11 - 53795046 * q^12 - 23281436 * q^13 - 349442850 * q^14 + 207365400 * q^15 - 671072257 * q^16 - 2272246668 * q^18 + 195706222 * q^19 + 2822935854 * q^20 + 1958992050 * q^21 - 204235521 * q^22 - 6101133672 * q^23 + 10931998527 * q^24 + 14614789727 * q^25 - 34016586282 * q^27 - 9052979204 * q^28 + 85191770166 * q^29 + 91857763818 * q^30 + 15357554728 * q^31 - 237242922057 * q^32 + 76352726421 * q^33 - 16566014943 * q^34 - 570464313633 * q^36 - 77721425444 * q^37 + 476314869819 * q^38 + 353897273784 * q^39 - 88855733850 * q^40 - 938882938233 * q^41 + 700091392140 * q^42 - 29709800063 * q^43 - 84148700094 * q^45 + 1553142786144 * q^46 - 1272741434580 * q^47 + 803069876301 * q^48 - 945184029255 * q^49 + 3573994524699 * q^50 - 1993755292875 * q^51 + 1825489374856 * q^52 + 6488294941323 * q^54 - 3772940931372 * q^55 - 7790759725422 * q^56 - 10739943123909 * q^57 + 3747043240302 * q^58 + 5874788534451 * q^59 + 1848130753878 * q^60 - 4867968901544 * q^61 + 5766639947244 * q^63 + 1211169309434 * q^64 - 22156719464856 * q^65 - 6375059860230 * q^66 - 8251061484125 * q^67 + 30687017243265 * q^68 + 23068377735552 * q^69 + 6871822387932 * q^70 - 46243200240621 * q^72 + 16120119648922 * q^73 + 8549243621166 * q^74 + 1090840096221 * q^75 + 14422972781521 * q^76 + 13919363311398 * q^77 + 109811947190436 * q^78 - 10740904544582 * q^79 - 140975607018501 * q^81 - 67076318933382 * q^82 - 11295125984532 * q^83 + 30827942753826 * q^84 + 10590724937466 * q^85 + 97019495740221 * q^86 + 151937485500582 * q^87 - 26136212294541 * q^88 - 392755154255226 * q^90 + 70870424994080 * q^91 - 474274297000284 * q^92 - 124466752375728 * q^93 - 46678164316620 * q^94 + 440317551118746 * q^95 + 823174447870656 * q^96 + 7621755375583 * q^97 - 195117933369168 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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