LMFDB - Embedded newform 27.10.c.a.19.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,10,Mod(10,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("27.10");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	27.c (of order $3$, degree $2$, 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:	$13.9059675764$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 $ x^16 - 8x^15 + 1984x^14 - 13748x^13 + 1552498x^12 - 9136628x^11 + 609566956x^10 - 2964409064x^9 + 126210674407x^8 - 487156186164x^7 + 13162328064828x^6 - 37794288146040x^5 + 578928267028062x^4 - 1095428523832956x^3 + 5807598664427172x^2 - 5266103139591300*x + 1336504689748125
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{40}\cdot 17^{2} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			19.4
Root			$0.500000 + 3.55897i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.10.c.a.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.83216 + 6.63749i) q^{2} +(226.629 + 392.533i) q^{4} +(1105.48 + 1914.74i) q^{5} +(3116.58 - 5398.07i) q^{7} -7398.05 q^{8} +O(q^{10})$	\(q+(-3.83216 + 6.63749i) q^{2} +(226.629 + 392.533i) q^{4} +(1105.48 + 1914.74i) q^{5} +(3116.58 - 5398.07i) q^{7} -7398.05 q^{8} -16945.4 q^{10} +(9312.12 - 16129.1i) q^{11} +(84699.6 + 146704. i) q^{13} +(23886.4 + 41372.5i) q^{14} +(-87683.6 + 151872. i) q^{16} -433113. q^{17} +51200.2 q^{19} +(-501066. + 867871. i) q^{20} +(71371.1 + 123618. i) q^{22} +(152281. + 263759. i) q^{23} +(-1.46759e6 + 2.54194e6i) q^{25} -1.29833e6 q^{26} +2.82523e6 q^{28} +(-568995. + 985528. i) q^{29} +(389293. + 674275. i) q^{31} +(-2.56594e6 - 4.44433e6i) q^{32} +(1.65976e6 - 2.87479e6i) q^{34} +1.37812e7 q^{35} -6.32050e6 q^{37} +(-196207. + 339841. i) q^{38} +(-8.17836e6 - 1.41653e7i) q^{40} +(-1.23991e6 - 2.14759e6i) q^{41} +(1.56300e7 - 2.70719e7i) q^{43} +8.44159e6 q^{44} -2.33427e6 q^{46} +(5.07040e6 - 8.78219e6i) q^{47} +(750710. + 1.30027e6i) q^{49} +(-1.12481e7 - 1.94822e7i) q^{50} +(-3.83908e7 + 6.64948e7i) q^{52} +3.32278e7 q^{53} +4.11773e7 q^{55} +(-2.30566e7 + 3.99352e7i) q^{56} +(-4.36096e6 - 7.55340e6i) q^{58} +(-2.33603e7 - 4.04612e7i) q^{59} +(3.06902e7 - 5.31570e7i) q^{61} -5.96733e6 q^{62} -5.04557e7 q^{64} +(-1.87267e8 + 3.24355e8i) q^{65} +(1.37409e8 + 2.37999e8i) q^{67} +(-9.81560e7 - 1.70011e8i) q^{68} +(-5.28117e7 + 9.14726e7i) q^{70} +2.93935e8 q^{71} -1.55084e8 q^{73} +(2.42212e7 - 4.19523e7i) q^{74} +(1.16034e7 + 2.00978e7i) q^{76} +(-5.80439e7 - 1.00535e8i) q^{77} +(1.17883e8 - 2.04180e8i) q^{79} -3.87728e8 q^{80} +1.90061e7 q^{82} +(1.68070e8 - 2.91106e8i) q^{83} +(-4.78796e8 - 8.29299e8i) q^{85} +(1.19793e8 + 2.07488e8i) q^{86} +(-6.88915e7 + 1.19324e8i) q^{88} +1.03812e9 q^{89} +1.05589e9 q^{91} +(-6.90228e7 + 1.19551e8i) q^{92} +(3.88611e7 + 6.73095e7i) q^{94} +(5.66005e7 + 9.80350e7i) q^{95} +(1.34786e8 - 2.33457e8i) q^{97} -1.15074e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) $ 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + 1020 q^{10} - 99150 q^{11} + 32435 q^{13} - 394824 q^{14} - 328193 q^{16} + 831078 q^{17} - 170554 q^{19} - 1855164 q^{20} + 529359 q^{22} - 1064559 q^{23} - 2293229 q^{25} - 2436312 q^{26} + 1225724 q^{28} + 1309053 q^{29} - 2359819 q^{31} - 5760063 q^{32} + 981801 q^{34} + 31066554 q^{35} + 16391516 q^{37} - 39490203 q^{38} - 16760496 q^{40} - 54747318 q^{41} + 15249608 q^{43} + 332509926 q^{44} + 2390520 q^{46} - 156295545 q^{47} + 15239583 q^{49} - 315590163 q^{50} - 19773358 q^{52} + 525516228 q^{53} - 7579770 q^{55} - 470339790 q^{56} + 55408560 q^{58} - 307774074 q^{59} + 69192125 q^{61} + 914436924 q^{62} - 403588478 q^{64} - 482470359 q^{65} + 14328044 q^{67} - 915409575 q^{68} - 229271934 q^{70} + 1239601392 q^{71} + 598613198 q^{73} - 1022736000 q^{74} + 119954093 q^{76} - 717995541 q^{77} + 30257531 q^{79} + 2927826528 q^{80} - 202376022 q^{82} - 1176168291 q^{83} + 4818366 q^{85} - 1426944009 q^{86} + 911312427 q^{88} + 3317041296 q^{89} - 739230122 q^{91} + 76813998 q^{92} - 1954316784 q^{94} + 391400652 q^{95} - 267311278 q^{97} - 4827300318 q^{98}+O(q^{100}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8 + 1020 * q^10 - 99150 * q^11 + 32435 * q^13 - 394824 * q^14 - 328193 * q^16 + 831078 * q^17 - 170554 * q^19 - 1855164 * q^20 + 529359 * q^22 - 1064559 * q^23 - 2293229 * q^25 - 2436312 * q^26 + 1225724 * q^28 + 1309053 * q^29 - 2359819 * q^31 - 5760063 * q^32 + 981801 * q^34 + 31066554 * q^35 + 16391516 * q^37 - 39490203 * q^38 - 16760496 * q^40 - 54747318 * q^41 + 15249608 * q^43 + 332509926 * q^44 + 2390520 * q^46 - 156295545 * q^47 + 15239583 * q^49 - 315590163 * q^50 - 19773358 * q^52 + 525516228 * q^53 - 7579770 * q^55 - 470339790 * q^56 + 55408560 * q^58 - 307774074 * q^59 + 69192125 * q^61 + 914436924 * q^62 - 403588478 * q^64 - 482470359 * q^65 + 14328044 * q^67 - 915409575 * q^68 - 229271934 * q^70 + 1239601392 * q^71 + 598613198 * q^73 - 1022736000 * q^74 + 119954093 * q^76 - 717995541 * q^77 + 30257531 * q^79 + 2927826528 * q^80 - 202376022 * q^82 - 1176168291 * q^83 + 4818366 * q^85 - 1426944009 * q^86 + 911312427 * q^88 + 3317041296 * q^89 - 739230122 * q^91 + 76813998 * q^92 - 1954316784 * q^94 + 391400652 * q^95 - 267311278 * q^97 - 4827300318 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−3.83216	+	6.63749i	−0.169359	+	0.293339i	−0.938195	−	0.346108i	$-0.887503\pi$
$2$	−3.83216	+	6.63749i	−0.169359	+	0.293339i	0.768836	+	0.639447i	$0.220836\pi$
$3$		0			0
$3$		0			0
$4$	226.629	+	392.533i	0.442635	+	0.766666i
$5$	1105.48	+	1914.74i	0.791014	+	1.37008i	0.925340	+	0.379139i	$0.123780\pi$
$5$	1105.48	+	1914.74i	0.791014	+	1.37008i	−0.134326	+	0.990937i	$0.542887\pi$
$6$		0			0
$7$	3116.58	−	5398.07i	0.490610	−	0.849762i	−0.509331	−	0.860570i	$-0.670107\pi$
$7$	3116.58	−	5398.07i	0.490610	−	0.849762i	0.999942	+	0.0108087i	$0.00344058\pi$
$8$	−7398.05			−0.638575
$9$		0			0
$10$	−16945.4			−0.535862
$11$	9312.12	−	16129.1i	0.191770	−	0.332156i	−0.754067	−	0.656798i	$-0.771910\pi$
$11$	9312.12	−	16129.1i	0.191770	−	0.332156i	0.945837	+	0.324642i	$0.105244\pi$
$12$		0			0
$13$	84699.6	+	146704.i	0.822501	+	1.42461i	0.903814	+	0.427925i	$0.140755\pi$
$13$	84699.6	+	146704.i	0.822501	+	1.42461i	−0.0813133	+	0.996689i	$0.525911\pi$
$14$	23886.4	+	41372.5i	0.166179	+	0.287830i
$15$		0			0
$16$	−87683.6	+	151872.i	−0.334486	+	0.579347i
$17$	−433113.			−1.25771			−0.628856	−	0.777522i	$-0.716476\pi$
$17$	−433113.			−1.25771			−0.628856	+	0.777522i	$0.716476\pi$
$18$		0			0
$19$	51200.2			0.0901322			0.0450661	−	0.998984i	$-0.485650\pi$
$19$	51200.2			0.0901322			0.0450661	+	0.998984i	$0.485650\pi$
$20$	−501066.	+	867871.i	−0.700261	+	1.21289i
$21$		0			0
$22$	71371.1	+	123618.i	0.0649561	+	0.112507i
$23$	152281.	+	263759.i	0.113468	+	0.196532i	0.917166	−	0.398505i	$-0.130471\pi$
$23$	152281.	+	263759.i	0.113468	+	0.196532i	−0.803699	+	0.595037i	$0.797138\pi$
$24$		0			0
$25$	−1.46759e6	+	2.54194e6i	−0.751406	+	1.30147i
$26$	−1.29833e6			−0.557192
$27$		0			0
$28$	2.82523e6			0.868645
$29$	−568995.	+	985528.i	−0.149389	+	0.258749i	−0.931002	−	0.365015i	$-0.881064\pi$
$29$	−568995.	+	985528.i	−0.149389	+	0.258749i	0.781613	+	0.623764i	$0.214397\pi$
$30$		0			0
$31$	389293.	+	674275.i	0.0757092	+	0.131132i	0.901394	−	0.432999i	$-0.142545\pi$
$31$	389293.	+	674275.i	0.0757092	+	0.131132i	−0.825685	+	0.564131i	$0.809211\pi$
$32$	−2.56594e6	−	4.44433e6i	−0.432584	−	0.749258i
$33$		0			0
$34$	1.65976e6	−	2.87479e6i	0.213005	−	0.368935i
$35$	1.37812e7			1.55232
$36$		0			0
$37$	−6.32050e6			−0.554426			−0.277213	−	0.960808i	$-0.589411\pi$
$37$	−6.32050e6			−0.554426			−0.277213	+	0.960808i	$0.589411\pi$
$38$	−196207.	+	339841.i	−0.0152647	+	0.0264393i
$39$		0			0
$40$	−8.17836e6	−	1.41653e7i	−0.505122	−	0.874897i
$41$	−1.23991e6	−	2.14759e6i	−0.0685271	−	0.118692i	0.829726	−	0.558171i	$-0.188497\pi$
$41$	−1.23991e6	−	2.14759e6i	−0.0685271	−	0.118692i	−0.898253	+	0.439478i	$0.855163\pi$
$42$		0			0
$43$	1.56300e7	−	2.70719e7i	0.697189	−	1.20757i	−0.272249	−	0.962227i	$-0.587767\pi$
$43$	1.56300e7	−	2.70719e7i	0.697189	−	1.20757i	0.969437	−	0.245339i	$-0.0788993\pi$
$44$	8.44159e6			0.339537
$45$		0			0
$46$	−2.33427e6			−0.0768671
$47$	5.07040e6	−	8.78219e6i	0.151566	−	0.262520i	−0.780237	−	0.625484i	$-0.784902\pi$
$47$	5.07040e6	−	8.78219e6i	0.151566	−	0.262520i	0.931803	+	0.362964i	$0.118235\pi$
$48$		0			0
$49$	750710.	+	1.30027e6i	0.0186033	+	0.0322219i
$50$	−1.12481e7	−	1.94822e7i	−0.254515	−	0.440832i
$51$		0			0
$52$	−3.83908e7	+	6.64948e7i	−0.728135	+	1.26117i
$53$	3.32278e7			0.578442			0.289221	−	0.957262i	$-0.406604\pi$
$53$	3.32278e7			0.578442			0.289221	+	0.957262i	$0.406604\pi$
$54$		0			0
$55$	4.11773e7			0.606772
$56$	−2.30566e7	+	3.99352e7i	−0.313292	+	0.542637i
$57$		0			0
$58$	−4.36096e6	−	7.55340e6i	−0.0506007	−	0.0876429i
$59$	−2.33603e7	−	4.04612e7i	−0.250983	−	0.434715i	0.712814	−	0.701353i	$-0.247420\pi$
$59$	−2.33603e7	−	4.04612e7i	−0.250983	−	0.434715i	−0.963797	+	0.266639i	$0.914087\pi$
$60$		0			0
$61$	3.06902e7	−	5.31570e7i	0.283802	−	0.491560i	−0.688516	−	0.725221i	$-0.741737\pi$
$61$	3.06902e7	−	5.31570e7i	0.283802	−	0.491560i	0.972318	+	0.233662i	$0.0750708\pi$
$62$	−5.96733e6			−0.0512882
$63$		0			0
$64$	−5.04557e7			−0.375924
$65$	−1.87267e8	+	3.24355e8i	−1.30122	+	2.25378i
$66$		0			0
$67$	1.37409e8	+	2.37999e8i	0.833062	+	1.44291i	0.895599	+	0.444863i	$0.146748\pi$
$67$	1.37409e8	+	2.37999e8i	0.833062	+	1.44291i	−0.0625367	+	0.998043i	$0.519919\pi$
$68$	−9.81560e7	−	1.70011e8i	−0.556707	−	0.964245i
$69$		0			0
$70$	−5.28117e7	+	9.14726e7i	−0.262899	+	0.455355i
$71$	2.93935e8			1.37274			0.686372	−	0.727251i	$-0.259202\pi$
$71$	2.93935e8			1.37274			0.686372	+	0.727251i	$0.259202\pi$
$72$		0			0
$73$	−1.55084e8			−0.639168			−0.319584	−	0.947558i	$-0.603543\pi$
$73$	−1.55084e8			−0.639168			−0.319584	+	0.947558i	$0.603543\pi$
$74$	2.42212e7	−	4.19523e7i	0.0938971	−	0.162635i
$75$		0			0
$76$	1.16034e7	+	2.00978e7i	0.0398957	+	0.0691013i
$77$	−5.80439e7	−	1.00535e8i	−0.188169	−	0.325918i
$78$		0			0
$79$	1.17883e8	−	2.04180e8i	0.340511	−	0.589782i	−0.644017	−	0.765011i	$-0.722733\pi$
$79$	1.17883e8	−	2.04180e8i	0.340511	−	0.589782i	0.984528	+	0.175230i	$0.0560668\pi$
$80$	−3.87728e8			−1.05833
$81$		0			0
$82$	1.90061e7			0.0464228
$83$	1.68070e8	−	2.91106e8i	0.388722	−	0.673287i	−0.603556	−	0.797321i	$-0.706250\pi$
$83$	1.68070e8	−	2.91106e8i	0.388722	−	0.673287i	0.992278	+	0.124034i	$0.0395832\pi$
$84$		0			0
$85$	−4.78796e8	−	8.29299e8i	−0.994867	−	1.72316i
$86$	1.19793e8	+	2.07488e8i	0.236150	+	0.409025i
$87$		0			0
$88$	−6.88915e7	+	1.19324e8i	−0.122460	+	0.212107i
$89$	1.03812e9			1.75384			0.876922	−	0.480633i	$-0.159593\pi$
$89$	1.03812e9			1.75384			0.876922	+	0.480633i	$0.159593\pi$
$90$		0			0
$91$	1.05589e9			1.61411
$92$	−6.90228e7	+	1.19551e8i	−0.100449	+	0.173983i
$93$		0			0
$94$	3.88611e7	+	6.73095e7i	0.0513382	+	0.0889203i
$95$	5.66005e7	+	9.80350e7i	0.0712958	+	0.123488i
$96$		0			0
$97$	1.34786e8	−	2.33457e8i	0.154587	−	0.267753i	−0.778321	−	0.627866i	$-0.783929\pi$
$97$	1.34786e8	−	2.33457e8i	0.154587	−	0.267753i	0.932909	+	0.360113i	$0.117262\pi$
$98$	−1.15074e7			−0.0126026
$99$		0			0
$100$	−1.33039e9			−1.33039
$101$	4.90047e8	−	8.48786e8i	0.468588	−	0.811618i	−0.530767	−	0.847518i	$-0.678096\pi$
$101$	4.90047e8	−	8.48786e8i	0.468588	−	0.811618i	0.999355	+	0.0358992i	$0.0114295\pi$
$102$		0			0
$103$	8.36838e7	+	1.44945e8i	0.0732611	+	0.126892i	0.900329	−	0.435210i	$-0.143326\pi$
$103$	8.36838e7	+	1.44945e8i	0.0732611	+	0.126892i	−0.827068	+	0.562102i	$0.809993\pi$
$104$	−6.26612e8	−	1.08532e9i	−0.525229	−	0.909723i
$105$		0			0
$106$	−1.27334e8	+	2.20549e8i	−0.0979644	+	0.169679i
$107$	−1.91944e9			−1.41563			−0.707813	−	0.706400i	$-0.750318\pi$
$107$	−1.91944e9			−1.41563			−0.707813	+	0.706400i	$0.750318\pi$
$108$		0			0
$109$	2.60871e8			0.177013			0.0885066	−	0.996076i	$-0.471791\pi$
$109$	2.60871e8			0.177013			0.0885066	+	0.996076i	$0.471791\pi$
$110$	−1.57798e8	+	2.73314e8i	−0.102762	+	0.177990i
$111$		0			0
$112$	5.46545e8	+	9.46644e8i	0.328205	+	0.568468i
$113$	1.63303e9	+	2.82850e9i	0.942197	+	1.63193i	0.761268	+	0.648438i	$0.224577\pi$
$113$	1.63303e9	+	2.82850e9i	0.942197	+	1.63193i	0.180929	+	0.983496i	$0.442089\pi$
$114$		0			0
$115$	−3.36687e8	+	5.83159e8i	−0.179509	+	0.310918i
$116$	−5.15803e8			−0.264499
$117$		0			0
$118$	3.58081e8			0.170025
$119$	−1.34983e9	+	2.33797e9i	−0.617046	+	1.06876i
$120$		0			0
$121$	1.00554e9	+	1.74165e9i	0.426448	+	0.738630i
$122$	2.35220e8	+	4.07412e8i	0.0961290	+	0.166500i
$123$		0			0
$124$	−1.76450e8	+	3.05621e8i	−0.0670231	+	0.116087i
$125$	−2.17127e9			−0.795461
$126$		0			0
$127$	−1.25753e9			−0.428944			−0.214472	−	0.976730i	$-0.568803\pi$
$127$	−1.25753e9			−0.428944			−0.214472	+	0.976730i	$0.568803\pi$
$128$	1.50711e9	−	2.61040e9i	0.496251	−	0.859531i
$129$		0			0
$130$	−1.43527e9	−	2.48596e9i	−0.440747	−	0.763396i
$131$	−9.06758e8	−	1.57055e9i	−0.269011	−	0.465941i	0.699596	−	0.714539i	$-0.253364\pi$
$131$	−9.06758e8	−	1.57055e9i	−0.269011	−	0.465941i	−0.968607	+	0.248598i	$0.920030\pi$
$132$		0			0
$133$	1.59569e8	−	2.76382e8i	0.0442198	−	0.0765909i
$134$	−2.10629e9			−0.564347
$135$		0			0
$136$	3.20419e9			0.803144
$137$	3.25621e9	−	5.63992e9i	0.789714	−	1.36783i	−0.136428	−	0.990650i	$-0.543562\pi$
$137$	3.25621e9	−	5.63992e9i	0.789714	−	1.36783i	0.926142	−	0.377175i	$-0.123104\pi$
$138$		0			0
$139$	9.16659e8	+	1.58770e9i	0.208277	+	0.360746i	0.951172	−	0.308662i	$-0.0998811\pi$
$139$	9.16659e8	+	1.58770e9i	0.208277	+	0.360746i	−0.742895	+	0.669408i	$0.766548\pi$
$140$	3.12322e9	+	5.40957e9i	0.687110	+	1.19011i
$141$		0			0
$142$	−1.12641e9	+	1.95099e9i	−0.232487	+	0.402679i
$143$	3.15493e9			0.630925
$144$		0			0
$145$	−2.51604e9			−0.472674
$146$	5.94308e8	−	1.02937e9i	0.108249	−	0.187493i
$147$		0			0
$148$	−1.43241e9	−	2.48101e9i	−0.245408	−	0.425060i
$149$	−5.34302e8	−	9.25439e8i	−0.0888074	−	0.153819i	0.818200	−	0.574934i	$-0.194972\pi$
$149$	−5.34302e8	−	9.25439e8i	−0.0888074	−	0.153819i	−0.907007	+	0.421115i	$0.861639\pi$
$150$		0			0
$151$	4.03980e9	−	6.99713e9i	0.632358	−	1.09528i	−0.354710	−	0.934976i	$-0.615420\pi$
$151$	4.03980e9	−	6.99713e9i	0.632358	−	1.09528i	0.987068	−	0.160300i	$-0.0512463\pi$
$152$	−3.78781e8			−0.0575562
$153$		0			0
$154$	8.89733e8			0.127473
$155$	−8.60707e8	+	1.49079e9i	−0.119774	+	0.207455i
$156$		0			0
$157$	−3.62446e9	−	6.27775e9i	−0.476096	−	0.824623i	0.523528	−	0.852008i	$-0.324615\pi$
$157$	−3.62446e9	−	6.27775e9i	−0.476096	−	0.824623i	−0.999625	+	0.0273849i	$0.991282\pi$
$158$	9.03496e8	+	1.56490e9i	0.115337	+	0.199770i
$159$		0			0
$160$	5.67316e9	−	9.82619e9i	0.684360	−	1.18535i
$161$	1.89839e9			0.222673
$162$		0			0
$163$	−1.25726e10			−1.39502			−0.697511	−	0.716574i	$-0.745709\pi$
$163$	−1.25726e10			−1.39502			−0.697511	+	0.716574i	$0.745709\pi$
$164$	5.61999e8	−	9.73411e8i	0.0606650	−	0.105075i
$165$		0			0
$166$	1.28814e9	+	2.23113e9i	0.131667	+	0.228054i
$167$	−7.07474e9	−	1.22538e10i	−0.703860	−	1.21912i	−0.967101	−	0.254392i	$-0.918125\pi$
$167$	−7.07474e9	−	1.22538e10i	−0.703860	−	1.21912i	0.263241	−	0.964730i	$-0.415209\pi$
$168$		0			0
$169$	−9.04581e9	+	1.56678e10i	−0.853016	+	1.47747i
$170$	7.33929e9			0.673959
$171$		0			0
$172$	1.41688e10			1.23440
$173$	−6.14075e9	+	1.06361e10i	−0.521211	+	0.902764i	0.478484	+	0.878096i	$0.341186\pi$
$173$	−6.14075e9	+	1.06361e10i	−0.521211	+	0.902764i	−0.999696	+	0.0246683i	$0.992147\pi$
$174$		0			0
$175$	9.14771e9	+	1.58443e10i	0.737294	+	1.27703i
$176$	1.63304e9	+	2.82851e9i	0.128289	+	0.222203i
$177$		0			0
$178$	−3.97823e9	+	6.89049e9i	−0.297030	+	0.514470i
$179$	5.47007e8			0.0398249			0.0199124	−	0.999802i	$-0.493661\pi$
$179$	5.47007e8			0.0398249			0.0199124	+	0.999802i	$0.493661\pi$
$180$		0			0
$181$	8.46578e9			0.586291			0.293146	−	0.956068i	$-0.405298\pi$
$181$	8.46578e9			0.586291			0.293146	+	0.956068i	$0.405298\pi$
$182$	−4.04634e9	+	7.00847e9i	−0.273364	+	0.473481i
$183$		0			0
$184$	−1.12659e9	−	1.95130e9i	−0.0724576	−	0.125500i
$185$	−6.98716e9	−	1.21021e10i	−0.438559	−	0.759606i
$186$		0			0
$187$	−4.03320e9	+	6.98571e9i	−0.241192	+	0.417757i
$188$	4.59640e9			0.268354
$189$		0			0
$190$	−8.67609e8			−0.0482984
$191$	−1.45905e10	+	2.52716e10i	−0.793271	+	1.37399i	0.130661	+	0.991427i	$0.458290\pi$
$191$	−1.45905e10	+	2.52716e10i	−0.793271	+	1.37399i	−0.923932	+	0.382558i	$0.875043\pi$
$192$		0			0
$193$	−1.06260e10	−	1.84048e10i	−0.551268	−	0.954824i	−0.998183	−	0.0602479i	$-0.980811\pi$
$193$	−1.06260e10	−	1.84048e10i	−0.551268	−	0.954824i	0.446915	−	0.894576i	$-0.352522\pi$
$194$	1.03305e9	+	1.78929e9i	0.0523615	+	0.0906928i
$195$		0			0
$196$	−3.40266e8	+	5.89357e8i	−0.0164689	+	0.0285251i
$197$	−1.91891e10			−0.907728			−0.453864	−	0.891071i	$-0.649955\pi$
$197$	−1.91891e10			−0.907728			−0.453864	+	0.891071i	$0.649955\pi$
$198$		0			0
$199$	6.01109e9			0.271716			0.135858	−	0.990728i	$-0.456621\pi$
$199$	6.01109e9			0.271716			0.135858	+	0.990728i	$0.456621\pi$
$200$	1.08573e10	−	1.88054e10i	0.479829	−	0.831088i
$201$		0			0
$202$	3.75587e9	+	6.50536e9i	0.158719	+	0.274910i
$203$	3.54663e9	+	6.14295e9i	0.146583	+	0.253889i
$204$		0			0
$205$	2.74138e9	−	4.74821e9i	0.108412	−	0.187775i
$206$	−1.28276e9			−0.0496298
$207$		0			0
$208$	−2.97071e10			−1.10046
$209$	4.76782e8	−	8.25811e8i	0.0172847	−	0.0299380i
$210$		0			0
$211$	6.05024e9	+	1.04793e10i	0.210137	+	0.363967i	0.951757	−	0.306852i	$-0.0992758\pi$
$211$	6.05024e9	+	1.04793e10i	0.210137	+	0.363967i	−0.741621	+	0.670820i	$0.765942\pi$
$212$	7.53038e9	+	1.30430e10i	0.256039	+	0.443472i
$213$		0			0
$214$	7.35562e9	−	1.27403e10i	0.239749	−	0.415258i
$215$	6.91142e10			2.20594
$216$		0			0
$217$	4.85304e9			0.148575
$218$	−9.99697e8	+	1.73153e9i	−0.0299788	+	0.0519248i
$219$		0			0
$220$	9.33197e9	+	1.61634e10i	0.268579	+	0.465192i
$221$	−3.66845e10	−	6.35395e10i	−1.03447	−	1.79175i
$222$		0			0
$223$	2.63189e10	−	4.55857e10i	0.712682	−	1.23440i	−0.251165	−	0.967944i	$-0.580814\pi$
$223$	2.63189e10	−	4.55857e10i	0.712682	−	1.23440i	0.963847	−	0.266457i	$-0.0858530\pi$
$224$	−3.19877e10			−0.848921
$225$		0			0
$226$	−2.50322e10			−0.638279
$227$	6.19793e9	−	1.07351e10i	0.154928	−	0.268343i	−0.778105	−	0.628135i	$-0.783819\pi$
$227$	6.19793e9	−	1.07351e10i	0.154928	−	0.268343i	0.933033	+	0.359791i	$0.117152\pi$
$228$		0			0
$229$	−2.20676e10	−	3.82222e10i	−0.530268	−	0.918451i	−0.999376	−	0.0353106i	$-0.988758\pi$
$229$	−2.20676e10	−	3.82222e10i	−0.530268	−	0.918451i	0.469108	−	0.883141i	$-0.344575\pi$
$230$	−2.58047e9	−	4.46951e9i	−0.0608029	−	0.105314i
$231$		0			0
$232$	4.20945e9	−	7.29099e9i	0.0953959	−	0.165231i
$233$	5.44229e10			1.20971			0.604853	−	0.796337i	$-0.293232\pi$
$233$	5.44229e10			1.20971			0.604853	+	0.796337i	$0.293232\pi$
$234$		0			0
$235$	2.24208e10			0.479563
$236$	1.05882e10	−	1.83393e10i	0.222187	−	0.384840i
$237$		0			0
$238$	−1.03455e10	−	1.79190e10i	−0.209005	−	0.362007i
$239$	4.21933e10	+	7.30809e10i	0.836474	+	1.44882i	0.892825	+	0.450405i	$0.148720\pi$
$239$	4.21933e10	+	7.30809e10i	0.836474	+	1.44882i	−0.0563504	+	0.998411i	$0.517946\pi$
$240$		0			0
$241$	−3.24645e10	+	5.62302e10i	−0.619916	+	1.07373i	0.369585	+	0.929197i	$0.379500\pi$
$241$	−3.24645e10	+	5.62302e10i	−0.619916	+	1.07373i	−0.989501	+	0.144528i	$0.953833\pi$
$242$	−1.54136e10			−0.288892
$243$		0			0
$244$	2.78212e10			0.502483
$245$	−1.65978e9	+	2.87483e9i	−0.0294309	+	0.0509759i
$246$		0			0
$247$	4.33663e9	+	7.51127e9i	0.0741338	+	0.128404i
$248$	−2.88001e9	−	4.98832e9i	−0.0483460	−	0.0837378i
$249$		0			0
$250$	8.32065e9	−	1.44118e10i	0.134719	−	0.233339i
$251$	−4.84990e10			−0.771260			−0.385630	−	0.922654i	$-0.626016\pi$
$251$	−4.84990e10			−0.771260			−0.385630	+	0.922654i	$0.626016\pi$
$252$		0			0
$253$	5.67225e9			0.0870389
$254$	4.81904e9	−	8.34682e9i	0.0726455	−	0.125826i
$255$		0			0
$256$	−1.36567e9	−	2.36541e9i	−0.0198731	−	0.0344213i
$257$	1.82031e10	+	3.15287e10i	0.260284	+	0.450824i	0.966317	−	0.257354i	$-0.0828506\pi$
$257$	1.82031e10	+	3.15287e10i	0.260284	+	0.450824i	−0.706034	+	0.708178i	$0.749517\pi$
$258$		0			0
$259$	−1.96983e10	+	3.41185e10i	−0.272007	+	0.471130i
$260$	−1.69760e11			−2.30386
$261$		0			0
$262$	1.38994e10			0.182238
$263$	−1.36692e10	+	2.36758e10i	−0.176174	+	0.305143i	−0.940567	−	0.339608i	$-0.889706\pi$
$263$	−1.36692e10	+	2.36758e10i	−0.176174	+	0.305143i	0.764393	+	0.644751i	$0.223039\pi$
$264$		0			0
$265$	3.67325e10	+	6.36225e10i	0.457556	+	0.792509i
$266$	1.22299e9	+	2.11828e9i	0.0149780	+	0.0259427i
$267$		0			0
$268$	−6.22816e10	+	1.07875e11i	−0.737485	+	1.27736i
$269$	−1.34342e9			−0.0156432			−0.00782159	−	0.999969i	$-0.502490\pi$
$269$	−1.34342e9			−0.0156432			−0.00782159	+	0.999969i	$0.502490\pi$
$270$		0			0
$271$	−1.98471e10			−0.223530			−0.111765	−	0.993735i	$-0.535650\pi$
$271$	−1.98471e10			−0.223530			−0.111765	+	0.993735i	$0.535650\pi$
$272$	3.79769e10	−	6.57780e10i	0.420688	−	0.728652i
$273$		0			0
$274$	2.49566e10	+	4.32262e10i	0.267491	+	0.463307i
$275$	2.73327e10	+	4.73417e10i	0.288195	+	0.499168i
$276$		0			0
$277$	6.66879e10	−	1.15507e11i	0.680594	−	1.17882i	−0.294206	−	0.955742i	$-0.595055\pi$
$277$	6.66879e10	−	1.15507e11i	0.680594	−	1.17882i	0.974800	−	0.223081i	$-0.0716113\pi$
$278$	−1.40511e10			−0.141094
$279$		0			0
$280$	−1.01954e11			−0.991272
$281$	3.21667e9	−	5.57144e9i	0.0307772	−	0.0533076i	−0.850227	−	0.526417i	$-0.823535\pi$
$281$	3.21667e9	−	5.57144e9i	0.0307772	−	0.0533076i	0.881004	+	0.473109i	$0.156868\pi$
$282$		0			0
$283$	1.92398e10	+	3.33244e10i	0.178305	+	0.308833i	0.941300	−	0.337571i	$-0.109605\pi$
$283$	1.92398e10	+	3.33244e10i	0.178305	+	0.308833i	−0.762995	+	0.646404i	$0.776272\pi$
$284$	6.66143e10	+	1.15379e11i	0.607624	+	1.05244i
$285$		0			0
$286$	−1.20902e10	+	2.09408e10i	−0.106853	+	0.185075i
$287$	−1.54571e10			−0.134480
$288$		0			0
$289$	6.89991e10			0.581839
$290$	9.64187e9	−	1.67002e10i	0.0800516	−	0.138653i
$291$		0			0
$292$	−3.51466e10	−	6.08757e10i	−0.282918	−	0.490028i
$293$	−9.29644e10	−	1.61019e11i	−0.736906	−	1.27636i	−0.953882	−	0.300182i	$-0.902953\pi$
$293$	−9.29644e10	−	1.61019e11i	−0.736906	−	1.27636i	0.216976	−	0.976177i	$-0.430381\pi$
$294$		0			0
$295$	5.16484e10	−	8.94576e10i	0.397061	−	0.687730i
$296$	4.67594e10			0.354043
$297$		0			0
$298$	8.19013e9			0.0601613
$299$	−2.57964e10	+	4.46806e10i	−0.186654	+	0.323295i
$300$		0			0
$301$	−9.74240e10	−	1.68743e11i	−0.684096	−	1.18489i
$302$	3.09623e10	+	5.36283e10i	0.214191	+	0.370990i
$303$		0			0
$304$	−4.48941e9	+	7.77589e9i	−0.0301480	+	0.0522179i
$305$	1.35709e11			0.897966
$306$		0			0
$307$	1.44816e11			0.930450			0.465225	−	0.885192i	$-0.345973\pi$
$307$	1.44816e11			0.930450			0.465225	+	0.885192i	$0.345973\pi$
$308$	2.63089e10	−	4.55683e10i	0.166580	−	0.288526i
$309$		0			0
$310$	−6.59673e9	−	1.14259e10i	−0.0405697	−	0.0702687i
$311$	8.64353e9	+	1.49710e10i	0.0523925	+	0.0907465i	0.891032	−	0.453940i	$-0.149982\pi$
$311$	8.64353e9	+	1.49710e10i	0.0523925	+	0.0907465i	−0.838640	+	0.544687i	$0.816649\pi$
$312$		0			0
$313$	−3.03029e10	+	5.24862e10i	−0.178457	+	0.309097i	−0.941352	−	0.337425i	$-0.890444\pi$
$313$	−3.03029e10	+	5.24862e10i	−0.178457	+	0.309097i	0.762895	+	0.646522i	$0.223777\pi$
$314$	5.55580e10			0.322525
$315$		0			0
$316$	1.06863e11			0.602887
$317$	1.23929e11	−	2.14652e11i	0.689298	−	1.19390i	−0.282768	−	0.959188i	$-0.591253\pi$
$317$	1.23929e11	−	2.14652e11i	0.689298	−	1.19390i	0.972065	−	0.234710i	$-0.0754140\pi$
$318$		0			0
$319$	1.05971e10	+	1.83547e10i	0.0572966	+	0.0992407i
$320$	−5.57776e10	−	9.66096e10i	−0.297361	−	0.515045i
$321$		0			0
$322$	−7.27492e9	+	1.26005e10i	−0.0377118	+	0.0653187i
$323$	−2.21755e10			−0.113360
$324$		0			0
$325$	−4.97217e11			−2.47213
$326$	4.81803e10	−	8.34507e10i	0.236260	−	0.409214i
$327$		0			0
$328$	9.17290e9	+	1.58879e10i	0.0437597	+	0.0757941i
$329$	−3.16046e10	−	5.47407e10i	−0.148720	−	0.257590i
$330$		0			0
$331$	−1.52348e10	+	2.63875e10i	−0.0697607	+	0.120829i	−0.898796	−	0.438367i	$-0.855557\pi$
$331$	−1.52348e10	+	2.63875e10i	−0.0697607	+	0.120829i	0.829035	+	0.559196i	$0.188890\pi$
$332$	1.52358e11			0.688248
$333$		0			0
$334$	1.08446e11			0.476821
$335$	−3.03804e11	+	5.26203e11i	−1.31793	+	2.28272i
$336$		0			0
$337$	−2.66771e10	−	4.62062e10i	−0.112669	−	0.195149i	0.804177	−	0.594391i	$-0.202607\pi$
$337$	−2.66771e10	−	4.62062e10i	−0.112669	−	0.195149i	−0.916846	+	0.399242i	$0.869273\pi$
$338$	−6.93299e10	−	1.20083e11i	−0.288932	−	0.500445i
$339$		0			0
$340$	2.17018e11	−	3.75886e11i	0.880726	−	1.52546i
$341$	1.45006e10			0.0580751
$342$		0			0
$343$	2.60889e11			1.01773
$344$	−1.15631e11	+	2.00279e11i	−0.445207	+	0.771122i
$345$		0			0
$346$	−4.70646e10	−	8.15184e10i	−0.176544	−	0.305783i
$347$	−6.25615e10	−	1.08360e11i	−0.231646	−	0.401222i	0.726647	−	0.687011i	$-0.241078\pi$
$347$	−6.25615e10	−	1.08360e11i	−0.231646	−	0.401222i	−0.958293	+	0.285789i	$0.907744\pi$
$348$		0			0
$349$	−1.27508e11	+	2.20851e11i	−0.460070	+	0.796865i	−0.998964	−	0.0455090i	$-0.985509\pi$
$349$	−1.27508e11	+	2.20851e11i	−0.460070	+	0.796865i	0.538894	+	0.842374i	$0.318842\pi$
$350$	−1.40222e11			−0.499470
$351$		0			0
$352$	−9.55772e10			−0.331827
$353$	1.66531e10	−	2.88441e10i	0.0570834	−	0.0988713i	−0.836072	−	0.548620i	$-0.815153\pi$
$353$	1.66531e10	−	2.88441e10i	0.0570834	−	0.0988713i	0.893155	+	0.449749i	$0.148487\pi$
$354$		0			0
$355$	3.24938e11	+	5.62810e11i	1.08586	+	1.88076i
$356$	2.35267e11	+	4.07495e11i	0.776313	+	1.34461i
$357$		0			0
$358$	−2.09622e9	+	3.63076e9i	−0.00674471	+	0.0116822i
$359$	8.10854e10			0.257643			0.128821	−	0.991668i	$-0.458881\pi$
$359$	8.10854e10			0.257643			0.128821	+	0.991668i	$0.458881\pi$
$360$		0			0
$361$	−3.20066e11			−0.991876
$362$	−3.24422e10	+	5.61916e10i	−0.0992938	+	0.171982i
$363$		0			0
$364$	2.39296e11	+	4.14472e11i	0.714461	+	1.23748i
$365$	−1.71442e11	−	2.96946e11i	−0.505590	−	0.875708i
$366$		0			0
$367$	−2.35647e11	+	4.08152e11i	−0.678054	+	1.17442i	0.297512	+	0.954718i	$0.403843\pi$
$367$	−2.35647e11	+	4.08152e11i	−0.678054	+	1.17442i	−0.975566	+	0.219706i	$0.929490\pi$
$368$	−5.34103e10			−0.151813
$369$		0			0
$370$	1.07104e11			0.297096
$371$	1.03557e11	−	1.79366e11i	0.283790	−	0.491538i
$372$		0			0
$373$	−2.53168e11	−	4.38500e11i	−0.677204	−	1.17295i	−0.975819	−	0.218578i	$-0.929858\pi$
$373$	−2.53168e11	−	4.38500e11i	−0.677204	−	1.17295i	0.298616	−	0.954373i	$-0.403475\pi$
$374$	−3.09117e10	−	5.35407e10i	−0.0816961	−	0.141502i
$375$		0			0
$376$	−3.75110e10	+	6.49710e10i	−0.0967863	+	0.167639i
$377$	−1.92775e11			−0.491489
$378$		0			0
$379$	3.43255e11			0.854557			0.427278	−	0.904120i	$-0.359472\pi$
$379$	3.43255e11			0.854557			0.427278	+	0.904120i	$0.359472\pi$
$380$	−2.56546e10	+	4.44351e10i	−0.0631161	+	0.109320i
$381$		0			0
$382$	−1.11827e11	−	1.93689e11i	−0.268695	−	0.465394i
$383$	−2.19794e11	−	3.80695e11i	−0.521942	−	0.904030i	−0.999674	−	0.0255246i	$-0.991874\pi$
$383$	−2.19794e11	−	3.80695e11i	−0.521942	−	0.904030i	0.477732	−	0.878506i	$-0.341459\pi$
$384$		0			0
$385$	1.28332e11	−	2.22278e11i	0.297689	−	0.515612i
$386$	1.62882e11			0.373449
$387$		0			0
$388$	1.22186e11			0.273703
$389$	−2.52265e11	+	4.36935e11i	−0.558577	+	0.967484i	0.439038	+	0.898468i	$0.355319\pi$
$389$	−2.52265e11	+	4.36935e11i	−0.558577	+	0.967484i	−0.997616	+	0.0690158i	$0.978014\pi$
$390$		0			0
$391$	−6.59551e10	−	1.14238e11i	−0.142709	−	0.247180i
$392$	−5.55379e9	−	9.61945e9i	−0.0118796	−	0.0205761i
$393$		0			0
$394$	7.35356e10	−	1.27367e11i	0.153732	−	0.266272i
$395$	5.21269e11			1.07739
$396$		0			0
$397$	−2.62244e11			−0.529844			−0.264922	−	0.964270i	$-0.585346\pi$
$397$	−2.62244e11			−0.529844			−0.264922	+	0.964270i	$0.585346\pi$
$398$	−2.30355e10	+	3.98986e10i	−0.0460175	+	0.0797047i
$399$		0			0
$400$	−2.57367e11	−	4.45773e11i	−0.502670	−	0.870650i
$401$	1.23763e11	+	2.14363e11i	0.239023	+	0.414000i	0.960434	−	0.278507i	$-0.0898395\pi$
$401$	1.23763e11	+	2.14363e11i	0.239023	+	0.414000i	−0.721411	+	0.692507i	$0.756506\pi$
$402$		0			0
$403$	−6.59459e10	+	1.14222e11i	−0.124542	+	0.215713i
$404$	4.44235e11			0.829654
$405$		0			0
$406$	−5.43651e10			−0.0993008
$407$	−5.88573e10	+	1.01944e11i	−0.106323	+	0.184156i
$408$		0			0
$409$	−7.78721e10	−	1.34878e11i	−0.137603	−	0.238335i	0.788986	−	0.614411i	$-0.210606\pi$
$409$	−7.78721e10	−	1.34878e11i	−0.137603	−	0.238335i	−0.926589	+	0.376076i	$0.877273\pi$
$410$	2.10108e10	+	3.63918e10i	0.0367210	+	0.0636027i
$411$		0			0
$412$	−3.79304e10	+	6.56973e10i	−0.0648559	+	0.112334i
$413$	−2.91216e11			−0.492538
$414$		0			0
$415$	7.43190e11			1.22994
$416$	4.34668e11	−	7.52866e11i	0.711602	−	1.23253i
$417$		0			0
$418$	3.65421e9	+	6.32928e9i	0.00585464	+	0.0101405i
$419$	4.60177e11	+	7.97051e11i	0.729394	+	1.26335i	0.957140	+	0.289627i	$0.0935312\pi$
$419$	4.60177e11	+	7.97051e11i	0.729394	+	1.26335i	−0.227746	+	0.973721i	$0.573135\pi$
$420$		0			0
$421$	4.28419e11	−	7.42043e11i	0.664660	−	1.15122i	−0.314718	−	0.949185i	$-0.601910\pi$
$421$	4.28419e11	−	7.42043e11i	0.664660	−	1.15122i	0.979377	−	0.202039i	$-0.0647567\pi$
$422$	−9.27419e10			−0.142354
$423$		0			0
$424$	−2.45821e11			−0.369379
$425$	6.35632e11	−	1.10095e12i	0.945052	−	1.63688i
$426$		0			0
$427$	−1.91297e11	−	3.31336e11i	−0.278472	−	0.482328i
$428$	−4.35002e11	−	7.53446e11i	−0.626606	−	1.08531i
$429$		0			0
$430$	−2.64857e11	+	4.58745e11i	−0.373597	+	0.647088i
$431$	−5.94731e11			−0.830181			−0.415090	−	0.909780i	$-0.636250\pi$
$431$	−5.94731e11			−0.830181			−0.415090	+	0.909780i	$0.636250\pi$
$432$		0			0
$433$	−1.28268e12			−1.75357			−0.876787	−	0.480880i	$-0.840317\pi$
$433$	−1.28268e12			−1.75357			−0.876787	+	0.480880i	$0.840317\pi$
$434$	−1.85976e10	+	3.22120e10i	−0.0251625	+	0.0435827i
$435$		0			0
$436$	5.91209e10	+	1.02400e11i	0.0783522	+	0.135710i
$437$	7.79683e9	+	1.35045e10i	0.0102271	+	0.0177138i
$438$		0			0
$439$	4.00633e11	−	6.93916e11i	0.514821	−	0.891696i	−0.485031	−	0.874497i	$-0.661192\pi$
$439$	4.00633e11	−	6.93916e11i	0.514821	−	0.891696i	0.999852	−	0.0171991i	$-0.00547493\pi$
$440$	−3.04631e11			−0.387470
$441$		0			0
$442$	5.62324e11			0.700787
$443$	3.57521e11	−	6.19245e11i	0.441047	−	0.763916i	−0.556720	−	0.830700i	$-0.687941\pi$
$443$	3.57521e11	−	6.19245e11i	0.441047	−	0.763916i	0.997767	+	0.0667840i	$0.0212739\pi$
$444$		0			0
$445$	1.14761e12	+	1.98772e12i	1.38731	+	2.40290i
$446$	2.01716e11	+	3.49383e11i	0.241398	+	0.418114i
$447$		0			0
$448$	−1.57249e11	+	2.72363e11i	−0.184432	+	0.319446i
$449$	−8.30808e11			−0.964700			−0.482350	−	0.875979i	$-0.660217\pi$
$449$	−8.30808e11			−0.964700			−0.482350	+	0.875979i	$0.660217\pi$
$450$		0			0
$451$	−4.61847e10			−0.0525659
$452$	−7.40185e11	+	1.28204e12i	−0.834099	+	1.44470i
$453$		0			0
$454$	4.75029e10	+	8.22774e10i	0.0524770	+	0.0908928i
$455$	1.16726e12	+	2.02176e12i	1.27678	+	2.21145i
$456$		0			0
$457$	−2.80720e11	+	4.86221e11i	−0.301058	+	0.521447i	−0.976376	−	0.216079i	$-0.930673\pi$
$457$	−2.80720e11	+	4.86221e11i	−0.301058	+	0.521447i	0.675318	+	0.737527i	$0.264006\pi$
$458$	3.38266e11			0.359223
$459$		0			0
$460$	−3.05212e11			−0.317827
$461$	2.67794e11	−	4.63834e11i	0.276151	−	0.478308i	−0.694274	−	0.719711i	$-0.744274\pi$
$461$	2.67794e11	−	4.63834e11i	0.276151	−	0.478308i	0.970425	+	0.241403i	$0.0776075\pi$
$462$		0			0
$463$	−6.33673e11	−	1.09755e12i	−0.640841	−	1.10997i	−0.985245	−	0.171148i	$-0.945252\pi$
$463$	−6.33673e11	−	1.09755e12i	−0.640841	−	1.10997i	0.344404	−	0.938822i	$-0.388081\pi$
$464$	−9.97831e10	−	1.72829e11i	−0.0999369	−	0.173096i
$465$		0			0
$466$	−2.08557e11	+	3.61231e11i	−0.204875	+	0.354853i
$467$	−9.53957e11			−0.928117			−0.464059	−	0.885804i	$-0.653607\pi$
$467$	−9.53957e11			−0.928117			−0.464059	+	0.885804i	$0.653607\pi$
$468$		0			0
$469$	1.71298e12			1.63483
$470$	−8.59201e10	+	1.48818e11i	−0.0812184	+	0.140674i
$471$		0			0
$472$	1.72820e11	+	2.99333e11i	0.160271	+	0.277598i
$473$	−2.91096e11	−	5.04194e11i	−0.267400	−	0.463151i
$474$		0			0
$475$	−7.51408e10	+	1.30148e11i	−0.0677258	+	0.117305i
$476$	−1.22364e12			−1.09251
$477$		0			0
$478$	−6.46765e11			−0.566658
$479$	−6.43441e11	+	1.11447e12i	−0.558469	+	0.967297i	0.439155	+	0.898411i	$0.355278\pi$
$479$	−6.43441e11	+	1.11447e12i	−0.558469	+	0.967297i	−0.997625	+	0.0688858i	$0.978056\pi$
$480$		0			0
$481$	−5.35344e11	−	9.27243e11i	−0.456016	−	0.789843i
$482$	−2.48819e11	−	4.30966e11i	−0.209977	−	0.363690i
$483$		0			0
$484$	−4.55770e11	+	7.89418e11i	−0.377522	+	0.653887i
$485$	5.96012e11			0.489122
$486$		0			0
$487$	−1.22356e12			−0.985704			−0.492852	−	0.870113i	$-0.664046\pi$
$487$	−1.22356e12			−0.985704			−0.492852	+	0.870113i	$0.664046\pi$
$488$	−2.27048e11	+	3.93258e11i	−0.181229	+	0.313898i
$489$		0			0
$490$	−1.27211e10	−	2.20336e10i	−0.00996880	−	0.0172665i
$491$	−5.85291e11	−	1.01375e12i	−0.454470	−	0.787165i	0.544188	−	0.838963i	$-0.316838\pi$
$491$	−5.85291e11	−	1.01375e12i	−0.454470	−	0.787165i	−0.998658	+	0.0517987i	$0.983505\pi$
$492$		0			0
$493$	2.46439e11	−	4.26845e11i	0.187888	−	0.325431i
$494$	−6.64747e10			−0.0502210
$495$		0			0
$496$	−1.36538e11			−0.101295
$497$	9.16072e11	−	1.58668e12i	0.673482	−	1.16650i
$498$		0			0
$499$	1.10884e12	+	1.92057e12i	0.800602	+	1.38668i	0.919221	+	0.393743i	$0.128820\pi$
$499$	1.10884e12	+	1.92057e12i	0.800602	+	1.38668i	−0.118619	+	0.992940i	$0.537847\pi$
$500$	−4.92073e11	−	8.52296e11i	−0.352099	−	0.609853i
$501$		0			0
$502$	1.85856e11	−	3.21912e11i	0.130620	−	0.226240i
$503$	2.31868e12			1.61505			0.807524	−	0.589834i	$-0.200807\pi$
$503$	2.31868e12			1.61505			0.807524	+	0.589834i	$0.200807\pi$
$504$		0			0
$505$	2.16694e12			1.48264
$506$	−2.17370e10	+	3.76495e10i	−0.0147408	+	0.0255319i
$507$		0			0
$508$	−2.84992e11	−	4.93621e11i	−0.189866	−	0.328857i
$509$	1.26661e12	+	2.19383e12i	0.836396	+	1.44868i	0.892889	+	0.450277i	$0.148675\pi$
$509$	1.26661e12	+	2.19383e12i	0.836396	+	1.44868i	−0.0564927	+	0.998403i	$0.517992\pi$
$510$		0			0
$511$	−4.83332e11	+	8.37155e11i	−0.313582	+	0.543140i
$512$	1.56422e12			1.00596
$513$		0			0
$514$	−2.79029e11			−0.176326
$515$	−1.85021e11	+	3.20465e11i	−0.115901	+	0.200747i
$516$		0			0
$517$	−9.44323e10	−	1.63562e11i	−0.0581317	−	0.100687i
$518$	−1.50974e11	−	2.61495e11i	−0.0921338	−	0.159580i
$519$		0			0
$520$	1.38541e12	−	2.39960e12i	0.830926	−	1.43921i
$521$	−9.44125e11			−0.561384			−0.280692	−	0.959798i	$-0.590564\pi$
$521$	−9.44125e11			−0.561384			−0.280692	+	0.959798i	$0.590564\pi$
$522$		0			0
$523$	−1.67874e12			−0.981128			−0.490564	−	0.871405i	$-0.663209\pi$
$523$	−1.67874e12			−0.981128			−0.490564	+	0.871405i	$0.663209\pi$
$524$	4.10995e11	−	7.11865e11i	0.238148	−	0.412484i
$525$		0			0
$526$	−1.04765e11	−	1.81459e11i	−0.0596735	−	0.103358i
$527$	−1.68608e11	−	2.92037e11i	−0.0952204	−	0.164927i
$528$		0			0
$529$	8.54197e11	−	1.47951e12i	0.474250	−	0.821425i
$530$	−5.63059e11			−0.309965
$531$		0			0
$532$	1.44652e11			0.0782929
$533$	2.10040e11	−	3.63799e11i	0.112727	−	0.195249i
$534$		0			0
$535$	−2.12190e12	−	3.67524e12i	−1.11978	−	1.93952i
$536$	−1.01656e12	−	1.76073e12i	−0.531973	−	0.921404i
$537$		0			0
$538$	5.14818e9	−	8.91691e9i	0.00264932	−	0.00458875i
$539$	2.79628e10			0.0142703
$540$		0			0
$541$	−1.34365e12			−0.674372			−0.337186	−	0.941438i	$-0.609475\pi$
$541$	−1.34365e12			−0.674372			−0.337186	+	0.941438i	$0.609475\pi$
$542$	7.60574e10	−	1.31735e11i	0.0378569	−	0.0655700i
$543$		0			0
$544$	1.11134e12	+	1.92490e12i	0.544066	+	0.942351i
$545$	2.88386e11	+	4.99499e11i	0.140020	+	0.242522i
$546$		0			0
$547$	3.04392e11	−	5.27222e11i	0.145375	−	0.251797i	−0.784138	−	0.620587i	$-0.786894\pi$
$547$	3.04392e11	−	5.27222e11i	0.145375	−	0.251797i	0.929513	+	0.368790i	$0.120228\pi$
$548$	2.95181e12			1.39822
$549$		0			0
$550$	−4.18974e11			−0.195234
$551$	−2.91326e10	+	5.04592e10i	−0.0134647	+	0.0233216i
$552$		0			0
$553$	−7.34785e11	−	1.27268e12i	−0.334116	−	0.578706i
$554$	5.11117e11	+	8.85281e11i	0.230529	+	0.399289i
$555$		0			0
$556$	−4.15483e11	+	7.19638e11i	−0.184381	+	0.319358i
$557$	6.12226e11			0.269503			0.134751	−	0.990879i	$-0.456976\pi$
$557$	6.12226e11			0.269503			0.134751	+	0.990879i	$0.456976\pi$
$558$		0			0
$559$	5.29541e12			2.29375
$560$	−1.20838e12	+	2.09298e12i	−0.519229	+	0.899331i
$561$		0			0
$562$	2.46536e10	+	4.27013e10i	0.0104248	+	0.0180563i
$563$	−2.12194e12	−	3.67531e12i	−0.890114	−	1.54172i	−0.839737	−	0.542993i	$-0.817291\pi$
$563$	−2.12194e12	−	3.67531e12i	−0.890114	−	1.54172i	−0.0503772	−	0.998730i	$-0.516042\pi$
$564$		0			0
$565$	−3.61055e12	+	6.25366e12i	−1.49058	+	2.58176i
$566$	−2.94921e11			−0.120790
$567$		0			0
$568$	−2.17455e12			−0.876600
$569$	−2.05395e12	+	3.55754e12i	−0.821456	+	1.42280i	0.0831427	+	0.996538i	$0.473504\pi$
$569$	−2.05395e12	+	3.55754e12i	−0.821456	+	1.42280i	−0.904598	+	0.426265i	$0.859829\pi$
$570$		0			0
$571$	1.90871e12	+	3.30597e12i	0.751409	+	1.30148i	0.947140	+	0.320821i	$0.103959\pi$
$571$	1.90871e12	+	3.30597e12i	0.751409	+	1.30148i	−0.195731	+	0.980658i	$0.562708\pi$
$572$	7.15000e11	+	1.23842e12i	0.279270	+	0.483709i
$573$		0			0
$574$	5.92340e10	−	1.02596e11i	0.0227755	−	0.0394483i
$575$	−8.93946e11			−0.341041
$576$		0			0
$577$	1.58536e12			0.595440			0.297720	−	0.954653i	$-0.403774\pi$
$577$	1.58536e12			0.595440			0.297720	+	0.954653i	$0.403774\pi$
$578$	−2.64415e11	+	4.57981e11i	−0.0985398	+	0.170676i
$579$		0			0
$580$	−5.70208e11	−	9.87629e11i	−0.209222	−	0.362383i
$581$	−1.04761e12	−	1.81451e12i	−0.381422	−	0.660643i
$582$		0			0
$583$	3.09421e11	−	5.35933e11i	0.110928	−	0.192133i
$584$	1.14732e12			0.408157
$585$		0			0
$586$	1.42502e12			0.499207
$587$	7.16024e11	−	1.24019e12i	0.248918	−	0.431139i	−0.714308	−	0.699832i	$-0.753258\pi$
$587$	7.16024e11	−	1.24019e12i	0.248918	−	0.431139i	0.963226	+	0.268693i	$0.0865917\pi$
$588$		0			0
$589$	1.99318e10	+	3.45230e10i	0.00682384	+	0.0118192i
$590$	3.95850e11	+	6.85632e11i	0.134492	+	0.232947i
$591$		0			0
$592$	5.54204e11	−	9.59910e11i	0.185448	−	0.321205i
$593$	−4.74549e12			−1.57592			−0.787961	−	0.615725i	$-0.788863\pi$
$593$	−4.74549e12			−1.57592			−0.787961	+	0.615725i	$0.788863\pi$
$594$		0			0
$595$	−5.96881e12			−1.95237
$596$	2.42177e11	−	4.19463e11i	0.0786185	−	0.136171i
$597$		0			0
$598$	−1.97712e11	−	3.42446e11i	−0.0632232	−	0.109506i
$599$	7.86184e10	+	1.36171e11i	0.0249519	+	0.0432179i	0.878232	−	0.478235i	$-0.158723\pi$
$599$	7.86184e10	+	1.36171e11i	0.0249519	+	0.0432179i	−0.853280	+	0.521453i	$0.825390\pi$
$600$		0			0
$601$	1.65008e12	−	2.85803e12i	0.515906	−	0.893576i	−0.483923	−	0.875110i	$-0.660789\pi$
$601$	1.65008e12	−	2.85803e12i	0.515906	−	0.893576i	0.999830	−	0.0184653i	$-0.00587803\pi$
$602$	1.49338e12			0.463431
$603$		0			0
$604$	3.66214e12			1.11962
$605$	−2.22321e12	+	3.85070e12i	−0.674653	+	1.16853i
$606$		0			0
$607$	1.95171e12	+	3.38046e12i	0.583534	+	1.01071i	0.995056	+	0.0993113i	$0.0316640\pi$
$607$	1.95171e12	+	3.38046e12i	0.583534	+	1.01071i	−0.411522	+	0.911400i	$0.635003\pi$
$608$	−1.31376e11	−	2.27550e11i	−0.0389898	−	0.0675323i
$609$		0			0
$610$	−5.20059e11	+	9.00768e11i	−0.152079	+	0.263408i
$611$	1.71784e12			0.498653
$612$		0			0
$613$	−2.67659e12			−0.765615			−0.382807	−	0.923828i	$-0.625043\pi$
$613$	−2.67659e12			−0.765615			−0.382807	+	0.923828i	$0.625043\pi$
$614$	−5.54957e11	+	9.61214e11i	−0.157580	+	0.272937i
$615$		0			0
$616$	4.29411e11	+	7.43762e11i	0.120160	+	0.208123i
$617$	1.82429e12	+	3.15976e12i	0.506769	+	0.877750i	0.999969	+	0.00783384i	$0.00249362\pi$
$617$	1.82429e12	+	3.15976e12i	0.506769	+	0.877750i	−0.493200	+	0.869916i	$0.664173\pi$
$618$		0			0
$619$	−4.83256e11	+	8.37024e11i	−0.132303	+	0.229155i	−0.924564	−	0.381027i	$-0.875571\pi$
$619$	−4.83256e11	+	8.37024e11i	−0.132303	+	0.229155i	0.792261	+	0.610182i	$0.208904\pi$
$620$	−7.80245e11			−0.212065
$621$		0			0
$622$	−1.32493e11			−0.0354926
$623$	3.23537e12	−	5.60382e12i	0.860454	−	1.49035i
$624$		0			0
$625$	4.66099e11	+	8.07307e11i	0.122185	+	0.211631i
$626$	−2.32251e11	−	4.02271e11i	−0.0604468	−	0.104697i
$627$		0			0
$628$	1.64282e12	−	2.84544e12i	0.421474	−	0.730014i
$629$	2.73749e12			0.697308
$630$		0			0
$631$	−4.92249e12			−1.23610			−0.618049	−	0.786139i	$-0.712077\pi$
$631$	−4.92249e12			−1.23610			−0.618049	+	0.786139i	$0.712077\pi$
$632$	−8.72106e11	+	1.51053e12i	−0.217442	+	0.376620i
$633$		0			0
$634$	9.49832e11	+	1.64516e12i	0.233478	+	0.404395i
$635$	−1.39016e12	−	2.40784e12i	−0.339300	−	0.587686i
$636$		0			0
$637$	−1.27170e11	+	2.20265e11i	−0.0306025	+	0.0530050i
$638$	−1.62439e11			−0.0388148
$639$		0			0
$640$	6.66431e12			1.57016
$641$	2.40584e12	−	4.16704e12i	0.562866	−	0.974913i	−0.434378	−	0.900731i	$-0.643032\pi$
$641$	2.40584e12	−	4.16704e12i	0.562866	−	0.974913i	0.997245	−	0.0741828i	$-0.0236348\pi$
$642$		0			0
$643$	−2.66650e12	−	4.61852e12i	−0.615167	−	1.06550i	−0.990355	−	0.138551i	$-0.955755\pi$
$643$	−2.66650e12	−	4.61852e12i	−0.615167	−	1.06550i	0.375189	−	0.926948i	$-0.377578\pi$
$644$	4.30230e11	+	7.45180e11i	0.0985630	+	0.170716i
$645$		0			0
$646$	8.49799e10	−	1.47189e11i	0.0191986	−	0.0332530i
$647$	−6.50961e12			−1.46045			−0.730223	−	0.683209i	$-0.760584\pi$
$647$	−6.50961e12			−1.46045			−0.730223	+	0.683209i	$0.760584\pi$
$648$		0			0
$649$	−8.70134e11			−0.192524
$650$	1.90541e12	−	3.30028e12i	0.418677	−	0.725170i
$651$		0			0
$652$	−2.84932e12	−	4.93517e12i	−0.617486	−	1.06952i
$653$	2.67842e12	+	4.63916e12i	0.576460	+	0.998458i	0.995881	+	0.0906665i	$0.0288997\pi$
$653$	2.67842e12	+	4.63916e12i	0.576460	+	0.998458i	−0.419421	+	0.907792i	$0.637767\pi$
$654$		0			0
$655$	2.00480e12	−	3.47241e12i	0.425583	−	0.737132i
$656$	4.34879e11			0.0916856
$657$		0			0
$658$	4.84455e11			0.100748
$659$	6.53510e11	−	1.13191e12i	0.134980	−	0.233791i	−0.790610	−	0.612320i	$-0.790236\pi$
$659$	6.53510e11	−	1.13191e12i	0.134980	−	0.233791i	0.925590	+	0.378529i	$0.123570\pi$
$660$		0			0
$661$	−6.08403e10	−	1.05379e11i	−0.0123961	−	0.0214707i	0.859761	−	0.510697i	$-0.170613\pi$
$661$	−6.08403e10	−	1.05379e11i	−0.0123961	−	0.0214707i	−0.872157	+	0.489226i	$0.837279\pi$
$662$	−1.16764e11	−	2.02242e11i	−0.0236292	−	0.0409270i
$663$		0			0
$664$	−1.24339e12	+	2.15362e12i	−0.248228	+	0.429944i
$665$	7.05599e11			0.139914
$666$		0			0
$667$	−3.46590e11			−0.0678030
$668$	3.20668e12	−	5.55414e12i	0.623106	−	1.07925i
$669$		0			0
$670$	−2.32845e12	−	4.03299e12i	−0.446406	−	0.773198i
$671$	−5.71582e11	−	9.90009e11i	−0.108850	−	0.188533i
$672$		0			0
$673$	−1.64753e12	+	2.85361e12i	−0.309575	+	0.536200i	−0.978269	−	0.207337i	$-0.933520\pi$
$673$	−1.64753e12	+	2.85361e12i	−0.309575	+	0.536200i	0.668694	+	0.743538i	$0.266854\pi$
$674$	4.08924e11			0.0763261
$675$		0			0
$676$	−8.20017e12			−1.51030
$677$	5.84161e11	−	1.01180e12i	0.106877	−	0.185116i	−0.807627	−	0.589694i	$-0.799248\pi$
$677$	5.84161e11	−	1.01180e12i	0.106877	−	0.185116i	0.914503	+	0.404578i	$0.132582\pi$
$678$		0			0
$679$	−8.40145e11	−	1.45517e12i	−0.151684	−	0.262725i
$680$	3.54215e12	+	6.13519e12i	0.635298	+	1.10037i
$681$		0			0
$682$	−5.55685e10	+	9.62474e10i	−0.00983555	+	0.0170357i
$683$	−7.05520e11			−0.124055			−0.0620277	−	0.998074i	$-0.519757\pi$
$683$	−7.05520e11			−0.124055			−0.0620277	+	0.998074i	$0.519757\pi$
$684$		0			0
$685$	1.43986e13			2.49870
$686$	−9.99767e11	+	1.73165e12i	−0.172362	+	0.298539i
$687$		0			0
$688$	2.74099e12	+	4.74753e12i	0.466400	+	0.807829i
$689$	2.81438e12	+	4.87465e12i	0.475769	+	0.824056i
$690$		0			0
$691$	2.84563e12	−	4.92877e12i	0.474817	−	0.822408i	−0.524767	−	0.851246i	$-0.675847\pi$
$691$	2.84563e12	−	4.92877e12i	0.474817	−	0.822408i	0.999584	+	0.0288384i	$0.00918082\pi$
$692$	−5.56669e12			−0.922825
$693$		0			0
$694$	9.58982e11			0.156925
$695$	−2.02669e12	+	3.51033e12i	−0.329500	+	0.570711i
$696$		0			0
$697$	5.37021e11	+	9.30147e11i	0.0861874	+	0.149281i
$698$	−9.77264e11	−	1.69267e12i	−0.155834	−	0.269913i
$699$		0			0
$700$	−4.14627e12	+	7.18155e12i	−0.652705	+	1.13052i
$701$	3.75961e12			0.588046			0.294023	−	0.955798i	$-0.405006\pi$
$701$	3.75961e12			0.588046			0.294023	+	0.955798i	$0.405006\pi$
$702$		0			0
$703$	−3.23611e11			−0.0499717
$704$	−4.69850e11	+	8.13804e11i	−0.0720912	+	0.124866i
$705$		0			0
$706$	1.27635e11	+	2.21070e11i	0.0193352	+	0.0334895i
$707$	−3.05454e12	−	5.29061e12i	−0.459788	−	0.796376i
$708$		0			0
$709$	1.85253e12	−	3.20868e12i	0.275333	−	0.476890i	−0.694886	−	0.719120i	$-0.744545\pi$
$709$	1.85253e12	−	3.20868e12i	0.275333	−	0.476890i	0.970219	+	0.242229i	$0.0778787\pi$
$710$	−4.98086e12			−0.735600
$711$		0			0
$712$	−7.68003e12			−1.11996
$713$	−1.18564e11	+	2.05359e11i	−0.0171811	+	0.0297585i
$714$		0			0
$715$	3.48770e12	+	6.04087e12i	0.499071	+	0.864416i
$716$	1.23968e11	+	2.14718e11i	0.0176279	+	0.0305324i
$717$		0			0
$718$	−3.10732e11	+	5.38204e11i	−0.0436341	+	0.0755765i
$719$	1.23468e11			0.0172296			0.00861478	−	0.999963i	$-0.497258\pi$
$719$	1.23468e11			0.0172296			0.00861478	+	0.999963i	$0.497258\pi$
$720$		0			0
$721$	1.04323e12			0.143771
$722$	1.22654e12	−	2.12444e12i	0.167983	−	0.290956i
$723$		0			0
$724$	1.91859e12	+	3.32310e12i	0.259513	+	0.449490i
$725$	−1.67010e12	−	2.89270e12i	−0.224503	−	0.388850i
$726$		0			0
$727$	−5.89947e12	+	1.02182e13i	−0.783264	+	1.35665i	0.146766	+	0.989171i	$0.453113\pi$
$727$	−5.89947e12	+	1.02182e13i	−0.783264	+	1.35665i	−0.930031	+	0.367482i	$0.880220\pi$
$728$	−7.81153e12			−1.03073
$729$		0			0
$730$	2.62797e12			0.342505
$731$	−6.76955e12	+	1.17252e13i	−0.876862	+	1.51877i
$732$		0			0
$733$	3.53411e12	+	6.12126e12i	0.452181	+	0.783200i	0.998521	−	0.0543633i	$-0.0173129\pi$
$733$	3.53411e12	+	6.12126e12i	0.452181	+	0.783200i	−0.546341	+	0.837563i	$0.683980\pi$
$734$	−1.80607e12	−	3.12821e12i	−0.229669	−	0.397799i
$735$		0			0
$736$	7.81489e11	−	1.35358e12i	0.0981686	−	0.170033i
$737$	5.11826e12			0.639026
$738$		0			0
$739$	−4.61726e12			−0.569488			−0.284744	−	0.958604i	$-0.591909\pi$
$739$	−4.61726e12			−0.569488			−0.284744	+	0.958604i	$0.591909\pi$
$740$	3.16699e12	−	5.48538e12i	0.388243	−	0.672456i
$741$		0			0
$742$	7.93693e11	+	1.37472e12i	0.0961247	+	0.166493i
$743$	−7.55678e11	−	1.30887e12i	−0.0909677	−	0.157561i	0.816951	−	0.576707i	$-0.195663\pi$
$743$	−7.55678e11	−	1.30887e12i	−0.0909677	−	0.157561i	−0.907919	+	0.419147i	$0.862329\pi$
$744$		0			0
$745$	1.18132e12	−	2.04610e12i	0.140496	−	0.243346i
$746$	3.88072e12			0.458763
$747$		0			0
$748$	−3.65616e12			−0.427040
$749$	−5.98209e12	+	1.03613e13i	−0.694521	+	1.20294i
$750$		0			0
$751$	−7.49028e12	−	1.29735e13i	−0.859247	−	1.48826i	−0.872648	−	0.488350i	$-0.837599\pi$
$751$	−7.49028e12	−	1.29735e13i	−0.859247	−	1.48826i	0.0134003	−	0.999910i	$-0.495734\pi$
$752$	8.89182e11	+	1.54011e12i	0.101394	+	0.175619i
$753$		0			0
$754$	7.38743e11	−	1.27954e12i	0.0832382	−	0.144173i
$755$	1.78636e13			2.00082
$756$		0			0
$757$	3.27715e12			0.362714			0.181357	−	0.983417i	$-0.441951\pi$
$757$	3.27715e12			0.362714			0.181357	+	0.983417i	$0.441951\pi$
$758$	−1.31541e12	+	2.27836e12i	−0.144727	+	0.250674i
$759$		0			0
$760$	−4.18733e11	−	7.25267e11i	−0.0455278	−	0.0788564i
$761$	2.91809e12	+	5.05428e12i	0.315404	+	0.546296i	0.979523	−	0.201331i	$-0.0645265\pi$
$761$	2.91809e12	+	5.05428e12i	0.315404	+	0.546296i	−0.664119	+	0.747627i	$0.731193\pi$
$762$		0			0
$763$	8.13023e11	−	1.40820e12i	0.0868445	−	0.150419i
$764$	−1.32266e13			−1.40452
$765$		0			0
$766$	3.36915e12			0.353583
$767$	3.95721e12	−	6.85409e12i	0.412867	−	0.715106i
$768$		0			0
$769$	7.88296e11	+	1.36537e12i	0.0812870	+	0.140793i	0.903803	−	0.427949i	$-0.140764\pi$
$769$	7.88296e11	+	1.36537e12i	0.0812870	+	0.140793i	−0.822516	+	0.568742i	$0.807430\pi$
$770$	9.83578e11	+	1.70361e12i	0.100833	+	0.174647i
$771$		0			0
$772$	4.81633e12	−	8.34213e12i	0.488021	−	0.845277i
$773$	−1.49007e13			−1.50106			−0.750529	−	0.660837i	$-0.770201\pi$
$773$	−1.49007e13			−1.50106			−0.750529	+	0.660837i	$0.770201\pi$
$774$		0			0
$775$	−2.28529e12			−0.227553
$776$	−9.97157e11	+	1.72713e12i	−0.0987156	+	0.170980i
$777$		0			0
$778$	−1.93344e12	−	3.34881e12i	−0.189200	−	0.327705i
$779$	−6.34835e10	−	1.09957e11i	−0.00617650	−	0.0106980i
$780$		0			0
$781$	2.73716e12	−	4.74090e12i	0.263251	−	0.455965i
$782$	1.01100e12			0.0966766
$783$		0			0
$784$	−2.63300e11			−0.0248902
$785$	8.01350e12	−	1.38798e13i	0.753198	−	1.30458i
$786$		0			0
$787$	−4.94718e12	−	8.56877e12i	−0.459697	−	0.796219i	0.539248	−	0.842147i	$-0.318709\pi$
$787$	−4.94718e12	−	8.56877e12i	−0.459697	−	0.796219i	−0.998945	+	0.0459287i	$0.985375\pi$
$788$	−4.34880e12	−	7.53234e12i	−0.401792	−	0.695925i
$789$		0			0
$790$	−1.99758e12	+	3.45992e12i	−0.182466	+	0.316041i
$791$	2.03579e13			1.84901
$792$		0			0
$793$	1.03978e13			0.933710
$794$	1.00496e12	−	1.74064e12i	0.0897339	−	0.155424i
$795$		0			0
$796$	1.36229e12	+	2.35955e12i	0.120271	+	0.208315i
$797$	1.27503e11	+	2.20842e11i	0.0111933	+	0.0193874i	0.871568	−	0.490275i	$-0.163104\pi$
$797$	1.27503e11	+	2.20842e11i	0.0111933	+	0.0193874i	−0.860374	+	0.509662i	$0.829770\pi$
$798$		0			0
$799$	−2.19606e12	+	3.80368e12i	−0.190626	+	0.330174i
$800$	1.50630e13			1.30018
$801$		0			0
$802$	−1.89711e12			−0.161923
$803$	−1.44416e12	+	2.50136e12i	−0.122573	+	0.212303i
$804$		0			0
$805$	2.09862e12	+	3.63492e12i	0.176138	+	0.305079i
$806$	−5.05430e11	−	8.75431e11i	−0.0421846	−	0.0730658i
$807$		0			0
$808$	−3.62539e12	+	6.27936e12i	−0.299229	+	0.518279i
$809$	1.62301e13			1.33215			0.666075	−	0.745885i	$-0.267973\pi$
$809$	1.62301e13			1.33215			0.666075	+	0.745885i	$0.267973\pi$
$810$		0			0
$811$	−4.16753e12			−0.338287			−0.169143	−	0.985591i	$-0.554100\pi$
$811$	−4.16753e12			−0.338287			−0.169143	+	0.985591i	$0.554100\pi$
$812$	−1.60754e12	+	2.78434e12i	−0.129766	+	0.224761i
$813$		0			0
$814$	−4.51101e11	−	7.81330e11i	−0.0360134	−	0.0623770i
$815$	−1.38987e13	−	2.40733e13i	−1.10348	−	1.91129i
$816$		0			0
$817$	8.00257e11	−	1.38609e12i	0.0628392	−	0.108841i
$818$	1.19367e12			0.0932171
$819$		0			0
$820$	2.48510e12			0.191947
$821$	−1.10895e12	+	1.92075e12i	−0.0851855	+	0.147546i	−0.905470	−	0.424410i	$-0.860482\pi$
$821$	−1.10895e12	+	1.92075e12i	−0.0851855	+	0.147546i	0.820285	+	0.571955i	$0.193815\pi$
$822$		0			0
$823$	2.36686e11	+	4.09953e11i	0.0179835	+	0.0311483i	0.874877	−	0.484345i	$-0.160942\pi$
$823$	2.36686e11	+	4.09953e11i	0.0179835	+	0.0311483i	−0.856894	+	0.515493i	$0.827609\pi$
$824$	−6.19096e11	−	1.07231e12i	−0.0467828	−	0.0810301i
$825$		0			0
$826$	1.11599e12	−	1.93295e12i	0.0834159	−	0.144481i
$827$	3.43656e12			0.255475			0.127738	−	0.991808i	$-0.459228\pi$
$827$	3.43656e12			0.255475			0.127738	+	0.991808i	$0.459228\pi$
$828$		0			0
$829$	−1.73227e13			−1.27386			−0.636929	−	0.770922i	$-0.719796\pi$
$829$	−1.73227e13			−1.27386			−0.636929	+	0.770922i	$0.719796\pi$
$830$	−2.84802e12	+	4.93292e12i	−0.208301	+	0.360788i
$831$		0			0
$832$	−4.27358e12	−	7.40206e12i	−0.309198	−	0.535547i
$833$	−3.25143e11	−	5.63163e11i	−0.0233976	−	0.0405258i
$834$		0			0
$835$	1.56419e13	−	2.70926e13i	1.11353	−	1.92868i
$836$	4.32211e11			0.0306032
$837$		0			0
$838$	−7.05389e12			−0.494118
$839$	−1.22497e13	+	2.12171e13i	−0.853486	+	1.47828i	0.0245567	+	0.999698i	$0.492183\pi$
$839$	−1.22497e13	+	2.12171e13i	−0.853486	+	1.47828i	−0.878043	+	0.478583i	$0.841151\pi$
$840$		0			0
$841$	6.60606e12	+	1.14420e13i	0.455366	+	0.788717i
$842$	3.28354e12	+	5.68726e12i	0.225132	+	0.389941i
$843$		0			0
$844$	−2.74232e12	+	4.74984e12i	−0.186028	+	0.322209i
$845$	−3.99997e13			−2.69899
$846$		0			0
$847$	1.25354e13			0.836879
$848$	−2.91353e12	+	5.04638e12i	−0.193481	+	0.335119i
$849$		0			0
$850$	4.87169e12	+	8.43801e12i	0.320106	+	0.554440i
$851$	−9.62495e11	−	1.66709e12i	−0.0629094	−	0.108962i
$852$		0			0
$853$	−1.92703e12	+	3.33772e12i	−0.124629	+	0.215863i	−0.921588	−	0.388170i	$-0.873107\pi$
$853$	−1.92703e12	+	3.33772e12i	−0.124629	+	0.215863i	0.796959	+	0.604033i	$0.206441\pi$
$854$	2.93232e12			0.188647
$855$		0			0
$856$	1.42001e13			0.903984
$857$	−1.88200e12	+	3.25971e12i	−0.119181	+	0.206427i	−0.919443	−	0.393223i	$-0.871360\pi$
$857$	−1.88200e12	+	3.25971e12i	−0.119181	+	0.206427i	0.800263	+	0.599650i	$0.204693\pi$
$858$		0			0
$859$	1.17704e12	+	2.03869e12i	0.0737599	+	0.127756i	0.900546	−	0.434760i	$-0.143167\pi$
$859$	1.17704e12	+	2.03869e12i	0.0737599	+	0.127756i	−0.826786	+	0.562516i	$0.809833\pi$
$860$	1.56633e13	+	2.71296e13i	0.976428	+	1.69122i
$861$		0			0
$862$	2.27910e12	−	3.94752e12i	0.140599	−	0.243524i
$863$	1.83375e13			1.12536			0.562680	−	0.826675i	$-0.309770\pi$
$863$	1.83375e13			1.12536			0.562680	+	0.826675i	$0.309770\pi$
$864$		0			0
$865$	−2.71538e13			−1.64914
$866$	4.91545e12	−	8.51380e12i	0.296984	−	0.514391i
$867$		0			0
$868$	1.09984e12	+	1.90498e12i	0.0657644	+	0.113907i
$869$	−2.19549e12	−	3.80270e12i	−0.130600	−	0.226205i
$870$		0			0
$871$	−2.32769e13	+	4.03168e13i	−1.37039	+	2.37358i
$872$	−1.92993e12			−0.113036
$873$		0			0
$874$	−1.19515e11			−0.00692820
$875$	−6.76693e12	+	1.17207e13i	−0.390261	+	0.675952i
$876$		0			0
$877$	−5.75313e11	−	9.96472e11i	−0.0328402	−	0.0568809i	0.849138	−	0.528171i	$-0.177122\pi$
$877$	−5.75313e11	−	9.96472e11i	−0.0328402	−	0.0568809i	−0.881978	+	0.471290i	$0.843789\pi$
$878$	3.07058e12	+	5.31840e12i	0.174379	+	0.302034i
$879$		0			0
$880$	−3.61057e12	+	6.25370e12i	−0.202957	+	0.351532i
$881$	−2.37153e13			−1.32628			−0.663142	−	0.748494i	$-0.730777\pi$
$881$	−2.37153e13			−1.32628			−0.663142	+	0.748494i	$0.730777\pi$
$882$		0			0
$883$	2.59683e13			1.43754			0.718771	−	0.695247i	$-0.244705\pi$
$883$	2.59683e13			1.43754			0.718771	+	0.695247i	$0.244705\pi$
$884$	1.66276e13	−	2.87998e13i	0.915785	−	1.58619i
$885$		0			0
$886$	2.74016e12	+	4.74609e12i	0.149391	+	0.258752i
$887$	−7.91049e12	−	1.37014e13i	−0.429089	−	0.743204i	0.567704	−	0.823233i	$-0.307832\pi$
$887$	−7.91049e12	−	1.37014e13i	−0.429089	−	0.743204i	−0.996793	+	0.0800293i	$0.974499\pi$
$888$		0			0
$889$	−3.91918e12	+	6.78821e12i	−0.210444	+	0.364500i
$890$	−1.75913e13			−0.939818
$891$		0			0
$892$	2.38585e13			1.26183
$893$	2.59605e11	−	4.49649e11i	0.0136610	−	0.0236615i
$894$		0			0
$895$	6.04703e11	+	1.04738e12i	0.0315020	+	0.0545631i
$896$	−9.39407e12	−	1.62710e13i	−0.486931	−	0.843389i
$897$		0			0
$898$	3.18379e12	−	5.51449e12i	0.163381	−	0.282984i
$899$	−8.86023e11			−0.0452404
$900$		0			0
$901$	−1.43914e13			−0.727513
$902$	1.76987e11	−	3.06551e11i	0.00890251	−	0.0154196i
$903$		0			0
$904$	−1.20813e13	−	2.09253e13i	−0.601664	−	1.04211i
$905$	9.35871e12	+	1.62098e13i	0.463765	+	0.803264i
$906$		0			0
$907$	−7.76777e12	+	1.34542e13i	−0.381122	+	0.660122i	−0.991223	−	0.132202i	$-0.957795\pi$
$907$	−7.76777e12	+	1.34542e13i	−0.381122	+	0.660122i	0.610101	+	0.792323i	$0.291129\pi$
$908$	5.61852e12			0.274306
$909$		0			0
$910$	−1.78925e13			−0.864939
$911$	2.56238e12	−	4.43818e12i	0.123257	−	0.213487i	−0.797793	−	0.602931i	$-0.793999\pi$
$911$	2.56238e12	−	4.43818e12i	0.123257	−	0.213487i	0.921050	+	0.389444i	$0.127333\pi$
$912$		0			0
$913$	−3.13018e12	−	5.42163e12i	−0.149091	−	0.258233i
$914$	−2.15152e12	−	3.72655e12i	−0.101974	−	0.176624i
$915$		0			0
$916$	1.00023e13	−	1.73245e13i	0.469430	−	0.813077i
$917$	−1.13039e13			−0.527919
$918$		0			0
$919$	2.60261e13			1.20362			0.601810	−	0.798639i	$-0.294446\pi$
$919$	2.60261e13			1.20362			0.601810	+	0.798639i	$0.294446\pi$
$920$	2.49082e12	−	4.31423e12i	0.114630	−	0.198545i
$921$		0			0
$922$	2.05246e12	+	3.55497e12i	0.0935375	+	0.162012i
$923$	2.48962e13	+	4.31215e13i	1.12908	+	1.95563i
$924$		0			0
$925$	9.27590e12	−	1.60663e13i	0.416599	−	0.721570i
$926$	9.71334e12			0.434129
$927$		0			0
$928$	5.84002e12			0.258493
$929$	2.01836e13	−	3.49590e13i	0.889052	−	1.53988i	0.0480546	−	0.998845i	$-0.484698\pi$
$929$	2.01836e13	−	3.49590e13i	0.889052	−	1.53988i	0.840998	−	0.541039i	$-0.181969\pi$
$930$		0			0
$931$	3.84365e10	+	6.65740e10i	0.00167676	+	0.00290423i
$932$	1.23338e13	+	2.13628e13i	0.535458	+	0.927440i
$933$		0			0
$934$	3.65572e12	−	6.33188e12i	0.157185	−	0.272253i
$935$	−1.78344e13			−0.763144
$936$		0			0
$937$	−1.54039e12			−0.0652835			−0.0326418	−	0.999467i	$-0.510392\pi$
$937$	−1.54039e12			−0.0652835			−0.0326418	+	0.999467i	$0.510392\pi$
$938$	−6.56440e12	+	1.13699e13i	−0.276874	+	0.479560i
$939$		0			0
$940$	5.08121e12	+	8.80091e12i	0.212271	+	0.367665i
$941$	−2.77277e12	−	4.80258e12i	−0.115282	−	0.199674i	0.802611	−	0.596503i	$-0.203444\pi$
$941$	−2.77277e12	−	4.80258e12i	−0.115282	−	0.199674i	−0.917892	+	0.396829i	$0.870110\pi$
$942$		0			0
$943$	3.77630e11	−	6.54075e11i	0.0155512	−	0.0269355i
$944$	8.19325e12			0.335801
$945$		0			0
$946$	4.46211e12			0.181147
$947$	8.80699e12	−	1.52542e13i	0.355838	−	0.616330i	−0.631423	−	0.775439i	$-0.717529\pi$
$947$	8.80699e12	−	1.52542e13i	0.355838	−	0.616330i	0.987261	+	0.159109i	$0.0508621\pi$
$948$		0			0
$949$	−1.31356e13	−	2.27515e13i	−0.525716	−	0.910567i
$950$	−5.75903e11	−	9.97493e11i	−0.0229400	−	0.0397332i
$951$		0			0
$952$	9.98610e12	−	1.72964e13i	0.394031	−	0.682481i
$953$	4.21531e13			1.65543			0.827717	−	0.561146i	$-0.189639\pi$
$953$	4.21531e13			1.65543			0.827717	+	0.561146i	$0.189639\pi$
$954$		0			0
$955$	−6.45180e13			−2.50995
$956$	−1.91244e13	+	3.31245e13i	−0.740505	+	1.28259i
$957$		0			0
$958$	−4.93154e12	−	8.54168e12i	−0.189164	−	0.327641i
$959$	−2.02965e13	−	3.51545e13i	−0.774884	−	1.34214i
$960$		0			0
$961$	1.29167e13	−	2.23724e13i	0.488536	−	0.846170i
$962$	8.20609e12			0.308922
$963$		0			0
$964$	−2.94296e13			−1.09759
$965$	2.34936e13	−	4.06921e13i	0.872121	−	1.51056i
$966$		0			0
$967$	1.62577e13	+	2.81592e13i	0.597918	+	1.03562i	0.993128	+	0.117033i	$0.0373383\pi$
$967$	1.62577e13	+	2.81592e13i	0.597918	+	1.03562i	−0.395210	+	0.918591i	$0.629328\pi$
$968$	−7.43905e12	−	1.28848e13i	−0.272319	−	0.471671i
$969$		0			0
$970$	−2.28401e12	+	3.95603e12i	−0.0828373	+	0.143478i
$971$	−4.38405e13			−1.58266			−0.791332	−	0.611386i	$-0.790612\pi$
$971$	−4.38405e13			−1.58266			−0.791332	+	0.611386i	$0.790612\pi$
$972$		0			0
$973$	1.14274e13			0.408731
$974$	4.68889e12	−	8.12140e12i	0.166938	−	0.289145i
$975$		0			0
$976$	5.38206e12	+	9.32200e12i	0.189856	+	0.328840i
$977$	6.56481e12	+	1.13706e13i	0.230514	+	0.399261i	0.957959	−	0.286904i	$-0.0926260\pi$
$977$	6.56481e12	+	1.13706e13i	0.230514	+	0.399261i	−0.727446	+	0.686165i	$0.759293\pi$
$978$		0			0
$979$	9.66707e12	−	1.67438e13i	0.336335	−	0.582550i
$980$	−1.50462e12			−0.0521087
$981$		0			0
$982$	8.97171e12			0.307874
$983$	−9.26273e12	+	1.60435e13i	−0.316408	+	0.548035i	−0.979736	−	0.200294i	$-0.935810\pi$
$983$	−9.26273e12	+	1.60435e13i	−0.316408	+	0.548035i	0.663328	+	0.748329i	$0.269144\pi$
$984$		0			0
$985$	−2.12130e13	−	3.67421e13i	−0.718025	−	1.24366i
$986$	1.88879e12	+	3.27148e12i	0.0636410	+	0.110230i
$987$		0			0
$988$	−1.96562e12	+	3.40455e12i	−0.0656285	+	0.113672i
$989$	9.52062e12			0.316433
$990$		0			0
$991$	3.95986e13			1.30421			0.652106	−	0.758127i	$-0.273885\pi$
$991$	3.95986e13			1.30421			0.652106	+	0.758127i	$0.273885\pi$
$992$	1.99780e12	−	3.46029e12i	0.0655012	−	0.113451i
$993$		0			0
$994$	7.02107e12	+	1.21608e13i	0.228121	+	0.395116i
$995$	6.64512e12	+	1.15097e13i	0.214931	+	0.372271i
$996$		0			0
$997$	−2.39753e13	+	4.15264e13i	−0.768485	+	1.33105i	0.169900	+	0.985461i	$0.445656\pi$
$997$	−2.39753e13	+	4.15264e13i	−0.768485	+	1.33105i	−0.938385	+	0.345593i	$0.887678\pi$
$998$	−1.69970e13			−0.542357
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.c.a.19.4		16
3.2	odd	2		9.10.c.a.7.5	yes	16
9.2	odd	6		81.10.a.c.1.4		8
9.4	even	3	inner	27.10.c.a.10.4		16
9.5	odd	6		9.10.c.a.4.5	✓	16
9.7	even	3		81.10.a.d.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.5	✓	16	9.5	odd	6
9.10.c.a.7.5	yes	16	3.2	odd	2
27.10.c.a.10.4		16	9.4	even	3	inner
27.10.c.a.19.4		16	1.1	even	1	trivial
81.10.a.c.1.4		8	9.2	odd	6
81.10.a.d.1.5		8	9.7	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.83216 + 6.63749i) q^{2} +(226.629 + 392.533i) q^{4} +(1105.48 + 1914.74i) q^{5} +(3116.58 - 5398.07i) q^{7} -7398.05 q^{8} +O(q^{10})\)	\(q+(-3.83216 + 6.63749i) q^{2} +(226.629 + 392.533i) q^{4} +(1105.48 + 1914.74i) q^{5} +(3116.58 - 5398.07i) q^{7} -7398.05 q^{8} -16945.4 q^{10} +(9312.12 - 16129.1i) q^{11} +(84699.6 + 146704. i) q^{13} +(23886.4 + 41372.5i) q^{14} +(-87683.6 + 151872. i) q^{16} -433113. q^{17} +51200.2 q^{19} +(-501066. + 867871. i) q^{20} +(71371.1 + 123618. i) q^{22} +(152281. + 263759. i) q^{23} +(-1.46759e6 + 2.54194e6i) q^{25} -1.29833e6 q^{26} +2.82523e6 q^{28} +(-568995. + 985528. i) q^{29} +(389293. + 674275. i) q^{31} +(-2.56594e6 - 4.44433e6i) q^{32} +(1.65976e6 - 2.87479e6i) q^{34} +1.37812e7 q^{35} -6.32050e6 q^{37} +(-196207. + 339841. i) q^{38} +(-8.17836e6 - 1.41653e7i) q^{40} +(-1.23991e6 - 2.14759e6i) q^{41} +(1.56300e7 - 2.70719e7i) q^{43} +8.44159e6 q^{44} -2.33427e6 q^{46} +(5.07040e6 - 8.78219e6i) q^{47} +(750710. + 1.30027e6i) q^{49} +(-1.12481e7 - 1.94822e7i) q^{50} +(-3.83908e7 + 6.64948e7i) q^{52} +3.32278e7 q^{53} +4.11773e7 q^{55} +(-2.30566e7 + 3.99352e7i) q^{56} +(-4.36096e6 - 7.55340e6i) q^{58} +(-2.33603e7 - 4.04612e7i) q^{59} +(3.06902e7 - 5.31570e7i) q^{61} -5.96733e6 q^{62} -5.04557e7 q^{64} +(-1.87267e8 + 3.24355e8i) q^{65} +(1.37409e8 + 2.37999e8i) q^{67} +(-9.81560e7 - 1.70011e8i) q^{68} +(-5.28117e7 + 9.14726e7i) q^{70} +2.93935e8 q^{71} -1.55084e8 q^{73} +(2.42212e7 - 4.19523e7i) q^{74} +(1.16034e7 + 2.00978e7i) q^{76} +(-5.80439e7 - 1.00535e8i) q^{77} +(1.17883e8 - 2.04180e8i) q^{79} -3.87728e8 q^{80} +1.90061e7 q^{82} +(1.68070e8 - 2.91106e8i) q^{83} +(-4.78796e8 - 8.29299e8i) q^{85} +(1.19793e8 + 2.07488e8i) q^{86} +(-6.88915e7 + 1.19324e8i) q^{88} +1.03812e9 q^{89} +1.05589e9 q^{91} +(-6.90228e7 + 1.19551e8i) q^{92} +(3.88611e7 + 6.73095e7i) q^{94} +(5.66005e7 + 9.80350e7i) q^{95} +(1.34786e8 - 2.33457e8i) q^{97} -1.15074e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8} + 1020 q^{10} - 99150 q^{11} + 32435 q^{13} - 394824 q^{14} - 328193 q^{16} + 831078 q^{17} - 170554 q^{19} - 1855164 q^{20} + 529359 q^{22} - 1064559 q^{23} - 2293229 q^{25} - 2436312 q^{26} + 1225724 q^{28} + 1309053 q^{29} - 2359819 q^{31} - 5760063 q^{32} + 981801 q^{34} + 31066554 q^{35} + 16391516 q^{37} - 39490203 q^{38} - 16760496 q^{40} - 54747318 q^{41} + 15249608 q^{43} + 332509926 q^{44} + 2390520 q^{46} - 156295545 q^{47} + 15239583 q^{49} - 315590163 q^{50} - 19773358 q^{52} + 525516228 q^{53} - 7579770 q^{55} - 470339790 q^{56} + 55408560 q^{58} - 307774074 q^{59} + 69192125 q^{61} + 914436924 q^{62} - 403588478 q^{64} - 482470359 q^{65} + 14328044 q^{67} - 915409575 q^{68} - 229271934 q^{70} + 1239601392 q^{71} + 598613198 q^{73} - 1022736000 q^{74} + 119954093 q^{76} - 717995541 q^{77} + 30257531 q^{79} + 2927826528 q^{80} - 202376022 q^{82} - 1176168291 q^{83} + 4818366 q^{85} - 1426944009 q^{86} + 911312427 q^{88} + 3317041296 q^{89} - 739230122 q^{91} + 76813998 q^{92} - 1954316784 q^{94} + 391400652 q^{95} - 267311278 q^{97} - 4827300318 q^{98}+O(q^{100}) \) 16 * q - 15 * q^2 - 1793 * q^4 - 453 * q^5 - 343 * q^7 + 14478 * q^8 + 1020 * q^10 - 99150 * q^11 + 32435 * q^13 - 394824 * q^14 - 328193 * q^16 + 831078 * q^17 - 170554 * q^19 - 1855164 * q^20 + 529359 * q^22 - 1064559 * q^23 - 2293229 * q^25 - 2436312 * q^26 + 1225724 * q^28 + 1309053 * q^29 - 2359819 * q^31 - 5760063 * q^32 + 981801 * q^34 + 31066554 * q^35 + 16391516 * q^37 - 39490203 * q^38 - 16760496 * q^40 - 54747318 * q^41 + 15249608 * q^43 + 332509926 * q^44 + 2390520 * q^46 - 156295545 * q^47 + 15239583 * q^49 - 315590163 * q^50 - 19773358 * q^52 + 525516228 * q^53 - 7579770 * q^55 - 470339790 * q^56 + 55408560 * q^58 - 307774074 * q^59 + 69192125 * q^61 + 914436924 * q^62 - 403588478 * q^64 - 482470359 * q^65 + 14328044 * q^67 - 915409575 * q^68 - 229271934 * q^70 + 1239601392 * q^71 + 598613198 * q^73 - 1022736000 * q^74 + 119954093 * q^76 - 717995541 * q^77 + 30257531 * q^79 + 2927826528 * q^80 - 202376022 * q^82 - 1176168291 * q^83 + 4818366 * q^85 - 1426944009 * q^86 + 911312427 * q^88 + 3317041296 * q^89 - 739230122 * q^91 + 76813998 * q^92 - 1954316784 * q^94 + 391400652 * q^95 - 267311278 * q^97 - 4827300318 * q^98

Introduction

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