LMFDB - Embedded newform 27.10.c.a.19.1

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			19.1
Root			$0.500000 + 22.2094i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.10.c.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-19.9839 + 34.6131i) q^{2} +(-542.712 - 940.005i) q^{4} +(-1103.58 - 1911.45i) q^{5} +(-2172.76 + 3763.33i) q^{7} +22918.5 q^{8} +O(q^{10})$	\(q+(-19.9839 + 34.6131i) q^{2} +(-542.712 - 940.005i) q^{4} +(-1103.58 - 1911.45i) q^{5} +(-2172.76 + 3763.33i) q^{7} +22918.5 q^{8} +88215.0 q^{10} +(-4138.79 + 7168.59i) q^{11} +(34563.2 + 59865.3i) q^{13} +(-86840.4 - 150412. i) q^{14} +(-180132. + 311998. i) q^{16} +41893.6 q^{17} +12629.9 q^{19} +(-1.19785e6 + 2.07473e6i) q^{20} +(-165418. - 286513. i) q^{22} +(609041. + 1.05489e6i) q^{23} +(-1.45920e6 + 2.52740e6i) q^{25} -2.76283e6 q^{26} +4.71673e6 q^{28} +(3.21809e6 - 5.57389e6i) q^{29} +(369878. + 640648. i) q^{31} +(-1.33234e6 - 2.30769e6i) q^{32} +(-837198. + 1.45007e6i) q^{34} +9.59122e6 q^{35} +1.64142e7 q^{37} +(-252394. + 437160. i) q^{38} +(-2.52923e7 - 4.38075e7i) q^{40} +(1.18987e6 + 2.06092e6i) q^{41} +(-1.10625e7 + 1.91609e7i) q^{43} +8.98468e6 q^{44} -4.86841e7 q^{46} +(-1.70843e7 + 2.95908e7i) q^{47} +(1.07350e7 + 1.85936e7i) q^{49} +(-5.83209e7 - 1.01015e8i) q^{50} +(3.75158e7 - 6.49792e7i) q^{52} +1.05262e8 q^{53} +1.82699e7 q^{55} +(-4.97964e7 + 8.62498e7i) q^{56} +(1.28620e8 + 2.22776e8i) q^{58} +(4.43759e7 + 7.68614e7i) q^{59} +(5.94329e7 - 1.02941e8i) q^{61} -2.95664e7 q^{62} -7.79534e7 q^{64} +(7.62863e7 - 1.32132e8i) q^{65} +(-4.90722e7 - 8.49956e7i) q^{67} +(-2.27362e7 - 3.93802e7i) q^{68} +(-1.91670e8 + 3.31982e8i) q^{70} -3.15854e8 q^{71} +4.17458e6 q^{73} +(-3.28020e8 + 5.68147e8i) q^{74} +(-6.85439e6 - 1.18722e7i) q^{76} +(-1.79852e7 - 3.11513e7i) q^{77} +(2.33429e8 - 4.04312e8i) q^{79} +7.95157e8 q^{80} -9.51133e7 q^{82} +(5.59890e6 - 9.69757e6i) q^{83} +(-4.62328e7 - 8.00776e7i) q^{85} +(-4.42145e8 - 7.65817e8i) q^{86} +(-9.48548e7 + 1.64293e8i) q^{88} +7.22061e8 q^{89} -3.00391e8 q^{91} +(6.61068e8 - 1.14500e9i) q^{92} +(-6.82820e8 - 1.18268e9i) q^{94} +(-1.39380e7 - 2.41414e7i) q^{95} +(3.48673e8 - 6.03920e8i) q^{97} -8.58111e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−19.9839	+	34.6131i	−0.883172	+	1.52970i	−0.0353766	+	0.999374i	$0.511263\pi$
$2$	−19.9839	+	34.6131i	−0.883172	+	1.52970i	−0.847795	+	0.530324i	$0.822070\pi$
$3$		0			0
$3$		0			0
$4$	−542.712	−	940.005i	−1.05998	−	1.83595i
$5$	−1103.58	−	1911.45i	−0.789655	−	1.36772i	−0.926179	−	0.377085i	$-0.876926\pi$
$5$	−1103.58	−	1911.45i	−0.789655	−	1.36772i	0.136524	−	0.990637i	$-0.456407\pi$
$6$		0			0
$7$	−2172.76	+	3763.33i	−0.342035	+	0.592422i	−0.984811	−	0.173633i	$-0.944449\pi$
$7$	−2172.76	+	3763.33i	−0.342035	+	0.592422i	0.642775	+	0.766055i	$0.277783\pi$
$8$	22918.5			1.97825
$9$		0			0
$10$	88215.0			2.78960
$11$	−4138.79	+	7168.59i	−0.0852327	+	0.147627i	−0.905490	−	0.424367i	$-0.860497\pi$
$11$	−4138.79	+	7168.59i	−0.0852327	+	0.147627i	0.820258	+	0.571994i	$0.193830\pi$
$12$		0			0
$13$	34563.2	+	59865.3i	0.335637	+	0.581340i	0.983607	−	0.180326i	$-0.0577152\pi$
$13$	34563.2	+	59865.3i	0.335637	+	0.581340i	−0.647970	+	0.761666i	$0.724382\pi$
$14$	−86840.4	−	150412.i	−0.604151	−	1.04642i
$15$		0			0
$16$	−180132.	+	311998.i	−0.687149	+	1.19018i
$17$	41893.6			0.121654			0.0608272	−	0.998148i	$-0.480626\pi$
$17$	41893.6			0.121654			0.0608272	+	0.998148i	$0.480626\pi$
$18$		0			0
$19$	12629.9			0.0222335			0.0111168	−	0.999938i	$-0.496461\pi$
$19$	12629.9			0.0222335			0.0111168	+	0.999938i	$0.496461\pi$
$20$	−1.19785e6	+	2.07473e6i	−1.67404	+	2.89953i
$21$		0			0
$22$	−165418.	−	286513.i	−0.150550	−	0.260761i
$23$	609041.	+	1.05489e6i	0.453807	+	0.786017i	0.998619	−	0.0525412i	$-0.0167321\pi$
$23$	609041.	+	1.05489e6i	0.453807	+	0.786017i	−0.544811	+	0.838559i	$0.683399\pi$
$24$		0			0
$25$	−1.45920e6	+	2.52740e6i	−0.747109	+	1.29403i
$26$	−2.76283e6			−1.18570
$27$		0			0
$28$	4.71673e6			1.45021
$29$	3.21809e6	−	5.57389e6i	0.844903	−	1.46341i	−0.0408032	−	0.999167i	$-0.512992\pi$
$29$	3.21809e6	−	5.57389e6i	0.844903	−	1.46341i	0.885706	−	0.464247i	$-0.153675\pi$
$30$		0			0
$31$	369878.	+	640648.i	0.0719335	+	0.124592i	0.899749	−	0.436408i	$-0.143750\pi$
$31$	369878.	+	640648.i	0.0719335	+	0.124592i	−0.827815	+	0.561001i	$0.810416\pi$
$32$	−1.33234e6	−	2.30769e6i	−0.224616	−	0.389047i
$33$		0			0
$34$	−837198.	+	1.45007e6i	−0.107442	+	0.186095i
$35$	9.59122e6			1.08036
$36$		0			0
$37$	1.64142e7			1.43983			0.719916	−	0.694061i	$-0.244180\pi$
$37$	1.64142e7			1.43983			0.719916	+	0.694061i	$0.244180\pi$
$38$	−252394.	+	437160.i	−0.0196360	+	0.0340106i
$39$		0			0
$40$	−2.52923e7	−	4.38075e7i	−1.56213	−	2.70569i
$41$	1.18987e6	+	2.06092e6i	0.0657618	+	0.113903i	0.897032	−	0.441966i	$-0.145719\pi$
$41$	1.18987e6	+	2.06092e6i	0.0657618	+	0.113903i	−0.831270	+	0.555869i	$0.812386\pi$
$42$		0			0
$43$	−1.10625e7	+	1.91609e7i	−0.493453	+	0.854686i	−0.999972	−	0.00754294i	$-0.997599\pi$
$43$	−1.10625e7	+	1.91609e7i	−0.493453	+	0.854686i	0.506518	+	0.862229i	$0.330932\pi$
$44$	8.98468e6			0.361381
$45$		0			0
$46$	−4.86841e7			−1.60316
$47$	−1.70843e7	+	2.95908e7i	−0.510688	+	0.884538i	0.489235	+	0.872152i	$0.337276\pi$
$47$	−1.70843e7	+	2.95908e7i	−0.510688	+	0.884538i	−0.999923	+	0.0123862i	$0.996057\pi$
$48$		0			0
$49$	1.07350e7	+	1.85936e7i	0.266024	+	0.460767i
$50$	−5.83209e7	−	1.01015e8i	−1.31965	−	2.28570i
$51$		0			0
$52$	3.75158e7	−	6.49792e7i	0.711539	−	1.23242i
$53$	1.05262e8			1.83245			0.916223	−	0.400668i	$-0.131222\pi$
$53$	1.05262e8			1.83245			0.916223	+	0.400668i	$0.131222\pi$
$54$		0			0
$55$	1.82699e7			0.269218
$56$	−4.97964e7	+	8.62498e7i	−0.676630	+	1.17196i
$57$		0			0
$58$	1.28620e8	+	2.22776e8i	1.49239	+	2.58489i
$59$	4.43759e7	+	7.68614e7i	0.476775	+	0.825799i	0.999646	−	0.0266134i	$-0.00847231\pi$
$59$	4.43759e7	+	7.68614e7i	0.476775	+	0.825799i	−0.522871	+	0.852412i	$0.675139\pi$
$60$		0			0
$61$	5.94329e7	−	1.02941e8i	0.549595	−	0.951926i	−0.448707	−	0.893679i	$-0.648115\pi$
$61$	5.94329e7	−	1.02941e8i	0.549595	−	0.951926i	0.998302	−	0.0582475i	$-0.0185513\pi$
$62$	−2.95664e7			−0.254118
$63$		0			0
$64$	−7.79534e7			−0.580798
$65$	7.62863e7	−	1.32132e8i	0.530074	−	0.918116i
$66$		0			0
$67$	−4.90722e7	−	8.49956e7i	−0.297508	−	0.515299i	0.678057	−	0.735009i	$-0.262822\pi$
$67$	−4.90722e7	−	8.49956e7i	−0.297508	−	0.515299i	−0.975565	+	0.219710i	$0.929489\pi$
$68$	−2.27362e7	−	3.93802e7i	−0.128952	−	0.223351i
$69$		0			0
$70$	−1.91670e8	+	3.31982e8i	−0.954142	+	1.65262i
$71$	−3.15854e8			−1.47511			−0.737554	−	0.675288i	$-0.764019\pi$
$71$	−3.15854e8			−1.47511			−0.737554	+	0.675288i	$0.764019\pi$
$72$		0			0
$73$	4.17458e6			0.0172052			0.00860260	−	0.999963i	$-0.497262\pi$
$73$	4.17458e6			0.0172052			0.00860260	+	0.999963i	$0.497262\pi$
$74$	−3.28020e8	+	5.68147e8i	−1.27162	+	2.20251i
$75$		0			0
$76$	−6.85439e6	−	1.18722e7i	−0.0235672	−	0.0408196i
$77$	−1.79852e7	−	3.11513e7i	−0.0583051	−	0.100987i
$78$		0			0
$79$	2.33429e8	−	4.04312e8i	0.674270	−	1.16787i	−0.302412	−	0.953177i	$-0.597792\pi$
$79$	2.33429e8	−	4.04312e8i	0.674270	−	1.16787i	0.976682	−	0.214692i	$-0.0688748\pi$
$80$	7.95157e8			2.17044
$81$		0			0
$82$	−9.51133e7			−0.232316
$83$	5.59890e6	−	9.69757e6i	0.0129494	−	0.0224291i	−0.859478	−	0.511173i	$-0.829211\pi$
$83$	5.59890e6	−	9.69757e6i	0.0129494	−	0.0224291i	0.872428	+	0.488744i	$0.162545\pi$
$84$		0			0
$85$	−4.62328e7	−	8.00776e7i	−0.0960650	−	0.166389i
$86$	−4.42145e8	−	7.65817e8i	−0.871608	−	1.50967i
$87$		0			0
$88$	−9.48548e7	+	1.64293e8i	−0.168611	+	0.292044i
$89$	7.22061e8			1.21988			0.609942	−	0.792446i	$-0.291193\pi$
$89$	7.22061e8			1.21988			0.609942	+	0.792446i	$0.291193\pi$
$90$		0			0
$91$	−3.00391e8			−0.459198
$92$	6.61068e8	−	1.14500e9i	0.962057	−	1.66633i
$93$		0			0
$94$	−6.82820e8	−	1.18268e9i	−0.902051	−	1.56240i
$95$	−1.39380e7	−	2.41414e7i	−0.0175568	−	0.0304093i
$96$		0			0
$97$	3.48673e8	−	6.03920e8i	0.399895	−	0.692638i	−0.593818	−	0.804600i	$-0.702380\pi$
$97$	3.48673e8	−	6.03920e8i	0.399895	−	0.692638i	0.993713	+	0.111962i	$0.0357133\pi$
$98$	−8.58111e8			−0.939779
$99$		0			0
$100$	3.16770e9			3.16770
$101$	−1.55558e8	+	2.69434e8i	−0.148746	+	0.257636i	−0.930764	−	0.365620i	$-0.880857\pi$
$101$	−1.55558e8	+	2.69434e8i	−0.148746	+	0.257636i	0.782018	+	0.623256i	$0.214190\pi$
$102$		0			0
$103$	3.89849e8	+	6.75238e8i	0.341294	+	0.591139i	0.984673	−	0.174409i	$-0.0558014\pi$
$103$	3.89849e8	+	6.75238e8i	0.341294	+	0.591139i	−0.643379	+	0.765548i	$0.722468\pi$
$104$	7.92137e8	+	1.37202e9i	0.663973	+	1.15003i
$105$		0			0
$106$	−2.10355e9	+	3.64346e9i	−1.61836	+	2.80309i
$107$	4.21203e8			0.310645			0.155322	−	0.987864i	$-0.450358\pi$
$107$	4.21203e8			0.310645			0.155322	+	0.987864i	$0.450358\pi$
$108$		0			0
$109$	−1.81817e9			−1.23371			−0.616857	−	0.787076i	$-0.711594\pi$
$109$	−1.81817e9			−1.23371			−0.616857	+	0.787076i	$0.711594\pi$
$110$	−3.65103e8	+	6.32377e8i	−0.237765	+	0.411822i
$111$		0			0
$112$	−7.82767e8	−	1.35579e9i	−0.470058	−	0.814164i
$113$	1.11921e8	+	1.93852e8i	0.0645739	+	0.111845i	0.896505	−	0.443034i	$-0.146098\pi$
$113$	1.11921e8	+	1.93852e8i	0.0645739	+	0.111845i	−0.831931	+	0.554879i	$0.812764\pi$
$114$		0			0
$115$	1.34425e9	−	2.32830e9i	0.716702	−	1.24136i
$116$	−6.98597e9			−3.58233
$117$		0			0
$118$	−3.54722e9			−1.68430
$119$	−9.10248e7	+	1.57660e8i	−0.0416101	+	0.0720708i
$120$		0			0
$121$	1.14471e9	+	1.98270e9i	0.485471	+	0.840860i
$122$	2.37540e9	+	4.11432e9i	0.970773	+	1.68143i
$123$		0			0
$124$	4.01475e8	−	6.95374e8i	0.152497	−	0.264132i
$125$	2.13050e9			0.780524
$126$		0			0
$127$	4.30949e9			1.46997			0.734986	−	0.678082i	$-0.237189\pi$
$127$	4.30949e9			1.46997			0.734986	+	0.678082i	$0.237189\pi$
$128$	2.23997e9	−	3.87975e9i	0.737561	−	1.27749i
$129$		0			0
$130$	3.04900e9	+	5.28102e9i	0.936293	+	1.62171i
$131$	1.36090e8	+	2.35714e8i	0.0403742	+	0.0699303i	0.885506	−	0.464627i	$-0.153812\pi$
$131$	1.36090e8	+	2.35714e8i	0.0403742	+	0.0699303i	−0.845132	+	0.534557i	$0.820478\pi$
$132$		0			0
$133$	−2.74417e7	+	4.75305e7i	−0.00760465	+	0.0131716i
$134$	3.92261e9			1.05100
$135$		0			0
$136$	9.60139e8			0.240663
$137$	−9.94174e7	+	1.72196e8i	−0.0241113	+	0.0417619i	−0.877829	−	0.478974i	$-0.841009\pi$
$137$	−9.94174e7	+	1.72196e8i	−0.0241113	+	0.0417619i	0.853718	+	0.520736i	$0.174342\pi$
$138$		0			0
$139$	2.80165e9	+	4.85260e9i	0.636572	+	1.10257i	0.986180	+	0.165678i	$0.0529814\pi$
$139$	2.80165e9	+	4.85260e9i	0.636572	+	1.10257i	−0.349608	+	0.936896i	$0.613685\pi$
$140$	−5.20527e9	−	9.01580e9i	−1.14516	−	1.98348i
$141$		0			0
$142$	6.31199e9	−	1.09327e10i	1.30277	−	2.25647i
$143$	−5.72200e8			−0.114429
$144$		0			0
$145$	−1.42056e10			−2.66873
$146$	−8.34243e7	+	1.44495e8i	−0.0151951	+	0.0263188i
$147$		0			0
$148$	−8.90818e9	−	1.54294e10i	−1.52620	−	2.64346i
$149$	5.23469e8	+	9.06676e8i	0.0870068	+	0.150700i	0.906245	−	0.422754i	$-0.138936\pi$
$149$	5.23469e8	+	9.06676e8i	0.0870068	+	0.150700i	−0.819238	+	0.573454i	$0.805603\pi$
$150$		0			0
$151$	−4.14232e9	+	7.17471e9i	−0.648406	+	1.12307i	0.335097	+	0.942184i	$0.391231\pi$
$151$	−4.14232e9	+	7.17471e9i	−0.648406	+	1.12307i	−0.983504	+	0.180889i	$0.942103\pi$
$152$	2.89458e8			0.0439834
$153$		0			0
$154$	1.43766e9			0.205974
$155$	8.16377e8	−	1.41401e9i	0.113605	−	0.196770i
$156$		0			0
$157$	−2.01799e8	−	3.49526e8i	−0.0265076	−	0.0459125i	0.852467	−	0.522781i	$-0.175105\pi$
$157$	−2.01799e8	−	3.49526e8i	−0.0265076	−	0.0459125i	−0.878975	+	0.476868i	$0.841772\pi$
$158$	9.32966e9	+	1.61594e10i	1.19099	+	2.06286i
$159$		0			0
$160$	−2.94069e9	+	5.09342e9i	−0.354739	+	0.614426i
$161$	−5.29320e9			−0.620872
$162$		0			0
$163$	4.57840e9			0.508007			0.254004	−	0.967203i	$-0.418253\pi$
$163$	4.57840e9			0.508007			0.254004	+	0.967203i	$0.418253\pi$
$164$	1.29152e9	−	2.23697e9i	0.139413	−	0.241470i
$165$		0			0
$166$	2.23775e8	+	3.87590e8i	0.0228732	+	0.0396175i
$167$	−4.24681e9	−	7.35569e9i	−0.422511	−	0.731811i	0.573673	−	0.819084i	$-0.305518\pi$
$167$	−4.24681e9	−	7.35569e9i	−0.422511	−	0.731811i	−0.996184	+	0.0872731i	$0.972185\pi$
$168$		0			0
$169$	2.91301e9	−	5.04549e9i	0.274696	−	0.475787i
$170$	3.69565e9			0.339368
$171$		0			0
$172$	2.40151e10			2.09221
$173$	−3.53574e9	+	6.12409e9i	−0.300105	+	0.519797i	−0.976160	−	0.217054i	$-0.930355\pi$
$173$	−3.53574e9	+	6.12409e9i	−0.300105	+	0.519797i	0.676054	+	0.736852i	$0.263688\pi$
$174$		0			0
$175$	−6.34097e9	−	1.09829e10i	−0.511075	−	0.885208i
$176$	−1.49106e9	−	2.58259e9i	−0.117135	−	0.202884i
$177$		0			0
$178$	−1.44296e10	+	2.49928e10i	−1.07737	+	1.86606i
$179$	−1.24682e10			−0.907749			−0.453874	−	0.891066i	$-0.649958\pi$
$179$	−1.24682e10			−0.907749			−0.453874	+	0.891066i	$0.649958\pi$
$180$		0			0
$181$	5.38680e9			0.373059			0.186530	−	0.982449i	$-0.440276\pi$
$181$	5.38680e9			0.373059			0.186530	+	0.982449i	$0.440276\pi$
$182$	6.00297e9	−	1.03975e10i	0.405551	−	0.702435i
$183$		0			0
$184$	1.39583e10	+	2.41765e10i	0.897744	+	1.55494i
$185$	−1.81143e10	−	3.13749e10i	−1.13697	−	1.96929i
$186$		0			0
$187$	−1.73389e8	+	3.00318e8i	−0.0103689	+	0.0179595i
$188$	3.70873e10			2.16529
$189$		0			0
$190$	1.11415e9			0.0620227
$191$	−1.35610e10	+	2.34884e10i	−0.737296	+	1.27703i	0.216413	+	0.976302i	$0.430564\pi$
$191$	−1.35610e10	+	2.34884e10i	−0.737296	+	1.27703i	−0.953709	+	0.300732i	$0.902769\pi$
$192$		0			0
$193$	3.76358e9	+	6.51871e9i	0.195251	+	0.338185i	0.946983	−	0.321284i	$-0.104115\pi$
$193$	3.76358e9	+	6.51871e9i	0.195251	+	0.338185i	−0.751732	+	0.659469i	$0.770781\pi$
$194$	1.39357e10	+	2.41373e10i	0.706351	+	1.22344i
$195$		0			0
$196$	1.16521e10	−	2.01820e10i	0.563963	−	0.976812i
$197$	7.91081e9			0.374217			0.187108	−	0.982339i	$-0.440088\pi$
$197$	7.91081e9			0.374217			0.187108	+	0.982339i	$0.440088\pi$
$198$		0			0
$199$	−1.98001e10			−0.895010			−0.447505	−	0.894282i	$-0.647687\pi$
$199$	−1.98001e10			−0.895010			−0.447505	+	0.894282i	$0.647687\pi$
$200$	−3.34426e10	+	5.79243e10i	−1.47797	+	2.55992i
$201$		0			0
$202$	−6.21730e9	−	1.07687e10i	−0.262737	−	0.455074i
$203$	1.39843e10	+	2.42214e10i	0.577973	+	1.00108i
$204$		0			0
$205$	2.62623e9	−	4.54877e9i	0.103858	−	0.179888i
$206$	−3.11628e10			−1.20569
$207$		0			0
$208$	−2.49038e10			−0.922530
$209$	−5.22725e7	+	9.05386e7i	−0.00189502	+	0.00328228i
$210$		0			0
$211$	−1.38998e10	−	2.40751e10i	−0.482766	−	0.836176i	0.517038	−	0.855963i	$-0.327035\pi$
$211$	−1.38998e10	−	2.40751e10i	−0.482766	−	0.836176i	−0.999804	+	0.0197866i	$0.993701\pi$
$212$	−5.71271e10	−	9.89470e10i	−1.94236	−	3.36427i
$213$		0			0
$214$	−8.41727e9	+	1.45791e10i	−0.274353	+	0.475193i
$215$	4.88333e10			1.55863
$216$		0			0
$217$	−3.21463e9			−0.0984151
$218$	3.63340e10	−	6.29324e10i	1.08958	−	1.88721i
$219$		0			0
$220$	−9.91528e9	−	1.71738e10i	−0.285366	−	0.494269i
$221$	1.44798e9	+	2.50798e9i	0.0408317	+	0.0707226i
$222$		0			0
$223$	−1.53014e10	+	2.65028e10i	−0.414343	+	0.717662i	−0.995359	−	0.0962293i	$-0.969322\pi$
$223$	−1.53014e10	+	2.65028e10i	−0.414343	+	0.717662i	0.581017	+	0.813892i	$0.302655\pi$
$224$	1.15795e10			0.307307
$225$		0			0
$226$	−8.94644e9			−0.228119
$227$	5.88893e9	−	1.01999e10i	0.147204	−	0.254965i	−0.782989	−	0.622036i	$-0.786306\pi$
$227$	5.88893e9	−	1.01999e10i	0.147204	−	0.254965i	0.930193	+	0.367071i	$0.119639\pi$
$228$		0			0
$229$	3.97514e10	+	6.88514e10i	0.955196	+	1.65445i	0.733920	+	0.679236i	$0.237689\pi$
$229$	3.97514e10	+	6.88514e10i	0.955196	+	1.65445i	0.221276	+	0.975211i	$0.428978\pi$
$230$	5.37266e10	+	9.30572e10i	1.26594	+	2.19268i
$231$		0			0
$232$	7.37536e10	−	1.27745e11i	1.67143	−	2.89500i
$233$	−2.44585e10			−0.543661			−0.271831	−	0.962345i	$-0.587629\pi$
$233$	−2.44585e10			−0.543661			−0.271831	+	0.962345i	$0.587629\pi$
$234$		0			0
$235$	7.54151e10			1.61307
$236$	4.81667e10	−	8.34272e10i	1.01075	−	1.75067i
$237$		0			0
$238$	−3.63806e9	−	6.30131e9i	−0.0734977	−	0.127302i
$239$	1.03475e10	+	1.79225e10i	0.205138	+	0.355310i	0.950177	−	0.311712i	$-0.100902\pi$
$239$	1.03475e10	+	1.79225e10i	0.205138	+	0.355310i	−0.745039	+	0.667021i	$0.767569\pi$
$240$		0			0
$241$	2.56371e10	−	4.44048e10i	0.489545	−	0.847917i	−0.510383	−	0.859947i	$-0.670496\pi$
$241$	2.56371e10	−	4.44048e10i	0.489545	−	0.847917i	0.999928	+	0.0120307i	$0.00382958\pi$
$242$	−9.15034e10			−1.71502
$243$		0			0
$244$	−1.29020e11			−2.33025
$245$	2.36938e10	−	4.10389e10i	0.420134	−	0.727694i
$246$		0			0
$247$	4.36530e8	+	7.56092e8i	0.00746239	+	0.0129252i
$248$	8.47705e9	+	1.46827e10i	0.142302	+	0.246475i
$249$		0			0
$250$	−4.25757e10	+	7.37432e10i	−0.689337	+	1.19397i
$251$	1.02820e11			1.63510			0.817552	−	0.575855i	$-0.195331\pi$
$251$	1.02820e11			1.63510			0.817552	+	0.575855i	$0.195331\pi$
$252$		0			0
$253$	−1.00828e10			−0.154717
$254$	−8.61204e10	+	1.49165e11i	−1.29824	+	2.24861i
$255$		0			0
$256$	6.95707e10	+	1.20500e11i	1.01239	+	1.75351i
$257$	−2.90942e10	−	5.03927e10i	−0.416014	−	0.720557i	0.579520	−	0.814958i	$-0.303240\pi$
$257$	−2.90942e10	−	5.03927e10i	−0.416014	−	0.720557i	−0.995534	+	0.0944005i	$0.969907\pi$
$258$		0			0
$259$	−3.56641e10	+	6.17721e10i	−0.492473	+	0.852988i
$260$	−1.65606e11			−2.24748
$261$		0			0
$262$	−1.08784e10			−0.142630
$263$	−2.83424e10	+	4.90905e10i	−0.365289	+	0.632699i	−0.988822	−	0.149098i	$-0.952363\pi$
$263$	−2.83424e10	+	4.90905e10i	−0.365289	+	0.632699i	0.623534	+	0.781796i	$0.285696\pi$
$264$		0			0
$265$	−1.16165e11	−	2.01204e11i	−1.44700	−	2.50628i
$266$	−1.09678e9	−	1.89969e9i	−0.0134324	−	0.0232656i
$267$		0			0
$268$	−5.32641e10	+	9.22562e10i	−0.630708	+	1.09242i
$269$	1.24479e11			1.44947			0.724737	−	0.689026i	$-0.241961\pi$
$269$	1.24479e11			1.44947			0.724737	+	0.689026i	$0.241961\pi$
$270$		0			0
$271$	1.72085e11			1.93812			0.969062	−	0.246816i	$-0.0793842\pi$
$271$	1.72085e11			1.93812			0.969062	+	0.246816i	$0.0793842\pi$
$272$	−7.54638e9	+	1.30707e10i	−0.0835947	+	0.144790i
$273$		0			0
$274$	−3.97349e9	−	6.88229e9i	−0.0425888	−	0.0737659i
$275$	−1.20786e10	−	2.09208e10i	−0.127356	−	0.220588i
$276$		0			0
$277$	−6.70133e10	+	1.16070e11i	−0.683915	+	1.18458i	0.289862	+	0.957068i	$0.406391\pi$
$277$	−6.70133e10	+	1.16070e11i	−0.683915	+	1.18458i	−0.973777	+	0.227507i	$0.926943\pi$
$278$	−2.23951e11			−2.24881
$279$		0			0
$280$	2.19816e11			2.13722
$281$	−6.28091e10	+	1.08789e11i	−0.600958	+	1.04089i	0.391718	+	0.920085i	$0.371881\pi$
$281$	−6.28091e10	+	1.08789e11i	−0.600958	+	1.04089i	−0.992676	+	0.120805i	$0.961453\pi$
$282$		0			0
$283$	6.31516e9	+	1.09382e10i	0.0585256	+	0.101369i	0.893804	−	0.448458i	$-0.148027\pi$
$283$	6.31516e9	+	1.09382e10i	0.0585256	+	0.101369i	−0.835278	+	0.549828i	$0.814693\pi$
$284$	1.71418e11	+	2.96904e11i	1.56359	+	2.70822i
$285$		0			0
$286$	1.14348e10	−	1.98056e10i	0.101060	−	0.175042i
$287$	−1.03412e10			−0.0899714
$288$		0			0
$289$	−1.16833e11			−0.985200
$290$	2.83883e11	−	4.91700e11i	2.35694	−	4.08234i
$291$		0			0
$292$	−2.26559e9	−	3.92412e9i	−0.0182372	−	0.0315878i
$293$	−4.11968e10	−	7.13550e10i	−0.326557	−	0.565614i	0.655269	−	0.755396i	$-0.272555\pi$
$293$	−4.11968e10	−	7.13550e10i	−0.326557	−	0.565614i	−0.981826	+	0.189782i	$0.939222\pi$
$294$		0			0
$295$	9.79444e10	−	1.69645e11i	0.752975	−	1.30419i
$296$	3.76188e11			2.84835
$297$		0			0
$298$	−4.18438e10			−0.307368
$299$	−4.21009e10	+	7.29209e10i	−0.304629	+	0.527633i
$300$		0			0
$301$	−4.80724e10	−	8.32639e10i	−0.337557	−	0.584665i
$302$	−1.65559e11	−	2.86757e11i	−1.14531	−	1.98373i
$303$		0			0
$304$	−2.27505e9	+	3.94050e9i	−0.0152777	+	0.0264618i
$305$	−2.62355e11			−1.73596
$306$		0			0
$307$	1.60599e11			1.03186			0.515931	−	0.856630i	$-0.327446\pi$
$307$	1.60599e11			1.03186			0.515931	+	0.856630i	$0.327446\pi$
$308$	−1.95216e10	+	3.38123e10i	−0.123605	+	0.214090i
$309$		0			0
$310$	3.26288e10	+	5.65147e10i	0.200666	+	0.347563i
$311$	5.20453e10	+	9.01450e10i	0.315471	+	0.546412i	0.979538	−	0.201262i	$-0.0645042\pi$
$311$	5.20453e10	+	9.01450e10i	0.315471	+	0.546412i	−0.664067	+	0.747674i	$0.731171\pi$
$312$		0			0
$313$	1.73815e10	−	3.01056e10i	0.102362	−	0.177296i	−0.810296	−	0.586021i	$-0.800693\pi$
$313$	1.73815e10	−	3.01056e10i	0.102362	−	0.177296i	0.912657	+	0.408726i	$0.134027\pi$
$314$	1.61309e10			0.0936431
$315$		0			0
$316$	−5.06740e11			−2.85886
$317$	8.40884e10	−	1.45645e11i	0.467702	−	0.810084i	−0.531617	−	0.846985i	$-0.678415\pi$
$317$	8.40884e10	−	1.45645e11i	0.467702	−	0.810084i	0.999319	+	0.0369011i	$0.0117487\pi$
$318$		0			0
$319$	2.66380e10	+	4.61383e10i	0.144027	+	0.249462i
$320$	8.60276e10	+	1.49004e11i	0.458630	+	0.794371i
$321$		0			0
$322$	1.05779e11	−	1.83214e11i	0.548337	−	0.949747i
$323$	5.29112e8			0.00270481
$324$		0			0
$325$	−2.01738e11			−1.00303
$326$	−9.14943e10	+	1.58473e11i	−0.448657	+	0.777097i
$327$		0			0
$328$	2.72701e10	+	4.72332e10i	0.130093	+	0.225328i
$329$	−7.42400e10	−	1.28588e11i	−0.349347	−	0.605086i
$330$		0			0
$331$	4.45717e10	−	7.72005e10i	0.204096	−	0.353504i	−0.745749	−	0.666227i	$-0.767908\pi$
$331$	4.45717e10	−	7.72005e10i	0.204096	−	0.353504i	0.949844	+	0.312723i	$0.101241\pi$
$332$	−1.21543e10			−0.0549048
$333$		0			0
$334$	3.39471e11			1.49260
$335$	−1.08310e11	+	1.87598e11i	−0.469858	+	0.813817i
$336$		0			0
$337$	1.01221e10	+	1.75320e10i	0.0427500	+	0.0740451i	0.886609	−	0.462520i	$-0.153055\pi$
$337$	1.01221e10	+	1.75320e10i	0.0427500	+	0.0740451i	−0.843859	+	0.536565i	$0.819721\pi$
$338$	1.16427e11	+	2.01657e11i	0.485207	+	0.840404i
$339$		0			0
$340$	−5.01822e10	+	8.69181e10i	−0.203655	+	0.352740i
$341$	−6.12339e9			−0.0245243
$342$		0			0
$343$	−2.68656e11			−1.04803
$344$	−2.53536e11	+	4.39138e11i	−0.976174	+	1.69078i
$345$		0			0
$346$	−1.41316e11	−	2.44766e11i	−0.530089	−	0.918140i
$347$	−1.30566e11	−	2.26148e11i	−0.483447	−	0.837354i	0.516373	−	0.856364i	$-0.327282\pi$
$347$	−1.30566e11	−	2.26148e11i	−0.483447	−	0.837354i	−0.999819	+	0.0190098i	$0.993949\pi$
$348$		0			0
$349$	−1.81998e11	+	3.15230e11i	−0.656678	+	1.13740i	0.324793	+	0.945785i	$0.394705\pi$
$349$	−1.81998e11	+	3.15230e11i	−0.656678	+	1.13740i	−0.981470	+	0.191614i	$0.938628\pi$
$350$	5.06869e11			1.80547
$351$		0			0
$352$	2.20572e10			0.0765787
$353$	1.43068e11	−	2.47801e11i	0.490406	−	0.849408i	−0.509533	−	0.860451i	$-0.670182\pi$
$353$	1.43068e11	−	2.47801e11i	0.490406	−	0.849408i	0.999939	+	0.0110432i	$0.00351522\pi$
$354$		0			0
$355$	3.48569e11	+	6.03739e11i	1.16483	+	2.01754i
$356$	−3.91871e11	−	6.78741e11i	−1.29306	−	2.23964i
$357$		0			0
$358$	2.49163e11	−	4.31564e11i	0.801698	−	1.38858i
$359$	3.55452e11			1.12942			0.564710	−	0.825290i	$-0.308988\pi$
$359$	3.55452e11			1.12942			0.564710	+	0.825290i	$0.308988\pi$
$360$		0			0
$361$	−3.22528e11			−0.999506
$362$	−1.07649e11	+	1.86454e11i	−0.329475	+	0.570668i
$363$		0			0
$364$	1.63026e11	+	2.82369e11i	0.486743	+	0.843063i
$365$	−4.60696e9	−	7.97950e9i	−0.0135862	−	0.0235319i
$366$		0			0
$367$	9.17091e10	−	1.58845e11i	0.263885	−	0.457063i	−0.703386	−	0.710808i	$-0.748329\pi$
$367$	9.17091e10	−	1.58845e11i	0.263885	−	0.457063i	0.967271	+	0.253746i	$0.0816626\pi$
$368$	−4.38831e11			−1.24733
$369$		0			0
$370$	1.44798e12			4.01656
$371$	−2.28710e11	+	3.96137e11i	−0.626761	+	1.08558i
$372$		0			0
$373$	1.83383e11	+	3.17628e11i	0.490533	+	0.849628i	0.999941	−	0.0108971i	$-0.00346872\pi$
$373$	1.83383e11	+	3.17628e11i	0.490533	+	0.849628i	−0.509407	+	0.860525i	$0.670135\pi$
$374$	−6.92997e9	−	1.20031e10i	−0.0183151	−	0.0317227i
$375$		0			0
$376$	−3.91545e11	+	6.78177e11i	−1.01027	+	1.74984i
$377$	4.44910e11			1.13432
$378$		0			0
$379$	9.56611e10			0.238154			0.119077	−	0.992885i	$-0.462006\pi$
$379$	9.56611e10			0.238154			0.119077	+	0.992885i	$0.462006\pi$
$380$	−1.51287e10	+	2.62037e10i	−0.0372199	+	0.0644667i
$381$		0			0
$382$	−5.42003e11	−	9.38778e11i	−1.30232	−	2.25568i
$383$	3.57222e11	+	6.18726e11i	0.848288	+	1.46928i	0.882735	+	0.469872i	$0.155700\pi$
$383$	3.57222e11	+	6.18726e11i	0.848288	+	1.46928i	−0.0344462	+	0.999407i	$0.510967\pi$
$384$		0			0
$385$	−3.96961e10	+	6.87556e10i	−0.0920819	+	0.159490i
$386$	−3.00844e11			−0.689761
$387$		0			0
$388$	−7.56916e11			−1.69553
$389$	1.95115e11	−	3.37949e11i	0.432034	−	0.748305i	−0.565014	−	0.825081i	$-0.691129\pi$
$389$	1.95115e11	−	3.37949e11i	0.432034	−	0.748305i	0.997048	+	0.0767763i	$0.0244627\pi$
$390$		0			0
$391$	2.55150e10	+	4.41932e10i	0.0552077	+	0.0956225i
$392$	2.46031e11	+	4.26137e11i	0.526262	+	0.911512i
$393$		0			0
$394$	−1.58089e11	+	2.73818e11i	−0.330498	+	0.572439i
$395$	−1.03043e12			−2.12976
$396$		0			0
$397$	−3.19066e10			−0.0644649			−0.0322325	−	0.999480i	$-0.510262\pi$
$397$	−3.19066e10			−0.0644649			−0.0322325	+	0.999480i	$0.510262\pi$
$398$	3.95682e11	−	6.85342e11i	0.790447	−	1.36909i
$399$		0			0
$400$	−5.25696e11	−	9.10533e11i	−1.02675	−	1.77838i
$401$	−2.91662e11	−	5.05173e11i	−0.563287	−	0.975642i	−0.997207	−	0.0746901i	$-0.976203\pi$
$401$	−2.91662e11	−	5.05173e11i	−0.563287	−	0.975642i	0.433920	−	0.900951i	$-0.357130\pi$
$402$		0			0
$403$	−2.55684e10	+	4.42857e10i	−0.0482870	+	0.0836356i
$404$	3.37692e11			0.630674
$405$		0			0
$406$	−1.11784e12			−2.04180
$407$	−6.79349e10	+	1.17667e11i	−0.122721	+	0.212559i
$408$		0			0
$409$	−2.98447e11	−	5.16926e11i	−0.527367	−	0.913426i	−0.999491	−	0.0318943i	$-0.989846\pi$
$409$	−2.98447e11	−	5.16926e11i	−0.527367	−	0.913426i	0.472124	−	0.881532i	$-0.343487\pi$
$410$	1.04965e11	+	1.81804e11i	0.183449	+	0.317744i
$411$		0			0
$412$	4.23151e11	−	7.32920e11i	0.723533	−	1.25320i
$413$	−3.85673e11			−0.652295
$414$		0			0
$415$	−2.47152e10			−0.0409023
$416$	9.21003e10	−	1.59522e11i	0.150779	−	0.261157i
$417$		0			0
$418$	−2.08921e9	−	3.61863e9i	−0.00334726	−	0.00579763i
$419$	1.56398e11	+	2.70889e11i	0.247895	+	0.429366i	0.962941	−	0.269711i	$-0.0869280\pi$
$419$	1.56398e11	+	2.70889e11i	0.247895	+	0.429366i	−0.715047	+	0.699076i	$0.753595\pi$
$420$		0			0
$421$	3.03250e11	−	5.25245e11i	0.470470	−	0.814878i	−0.528960	−	0.848647i	$-0.677418\pi$
$421$	3.03250e11	−	5.25245e11i	0.470470	−	0.814878i	0.999430	+	0.0337688i	$0.0107510\pi$
$422$	1.11109e12			1.70546
$423$		0			0
$424$	2.41245e12			3.62504
$425$	−6.11311e10	+	1.05882e11i	−0.0908891	+	0.157425i
$426$		0			0
$427$	2.58267e11	+	4.47331e11i	0.375961	+	0.651184i
$428$	−2.28592e11	−	3.95933e11i	−0.329279	−	0.570327i
$429$		0			0
$430$	−9.75880e11	+	1.69027e12i	−1.37654	+	2.38424i
$431$	4.53090e11			0.632466			0.316233	−	0.948682i	$-0.397582\pi$
$431$	4.53090e11			0.632466			0.316233	+	0.948682i	$0.397582\pi$
$432$		0			0
$433$	1.62218e11			0.221771			0.110885	−	0.993833i	$-0.464631\pi$
$433$	1.62218e11			0.221771			0.110885	+	0.993833i	$0.464631\pi$
$434$	6.42407e10	−	1.11268e11i	0.0869174	−	0.150545i
$435$		0			0
$436$	9.86740e11	+	1.70908e12i	1.30772	+	2.26503i
$437$	7.69213e9	+	1.33232e10i	0.0100897	+	0.0174759i
$438$		0			0
$439$	5.71922e11	−	9.90598e11i	0.734931	−	1.27294i	−0.219823	−	0.975540i	$-0.570548\pi$
$439$	5.71922e11	−	9.90598e11i	0.734931	−	1.27294i	0.954754	−	0.297398i	$-0.0961187\pi$
$440$	4.18718e11			0.532579
$441$		0			0
$442$	−1.15745e11			−0.144246
$443$	6.63980e11	−	1.15005e12i	0.819103	−	1.41873i	−0.0872411	−	0.996187i	$-0.527805\pi$
$443$	6.63980e11	−	1.15005e12i	0.819103	−	1.41873i	0.906344	−	0.422541i	$-0.138862\pi$
$444$		0			0
$445$	−7.96849e11	−	1.38018e12i	−0.963288	−	1.66846i
$446$	−6.11563e11	−	1.05926e12i	−0.731871	−	1.26764i
$447$		0			0
$448$	1.69374e11	−	2.93365e11i	0.198653	−	0.344078i
$449$	−5.29567e11			−0.614911			−0.307456	−	0.951562i	$-0.599478\pi$
$449$	−5.29567e11			−0.614911			−0.307456	+	0.951562i	$0.599478\pi$
$450$		0			0
$451$	−1.96986e10			−0.0224202
$452$	1.21481e11	−	2.10412e11i	0.136895	−	0.237109i
$453$		0			0
$454$	2.35367e11	+	4.07668e11i	0.260013	+	0.450356i
$455$	3.31504e11	+	5.74182e11i	0.362608	+	0.628055i
$456$		0			0
$457$	−5.32572e11	+	9.22441e11i	−0.571157	+	0.989272i	0.425291	+	0.905057i	$0.360172\pi$
$457$	−5.32572e11	+	9.22441e11i	−0.571157	+	0.989272i	−0.996448	+	0.0842156i	$0.973162\pi$
$458$	−3.17755e12			−3.37441
$459$		0			0
$460$	−2.91816e12			−3.03877
$461$	−4.10593e11	+	7.11169e11i	−0.423407	+	0.733362i	−0.996270	−	0.0862888i	$-0.972499\pi$
$461$	−4.10593e11	+	7.11169e11i	−0.423407	+	0.733362i	0.572863	+	0.819651i	$0.305833\pi$
$462$		0			0
$463$	−1.91618e11	−	3.31892e11i	−0.193786	−	0.335647i	0.752716	−	0.658345i	$-0.228743\pi$
$463$	−1.91618e11	−	3.31892e11i	−0.193786	−	0.335647i	−0.946502	+	0.322699i	$0.895410\pi$
$464$	1.15936e12	+	2.00807e12i	1.16115	+	2.01117i
$465$		0			0
$466$	4.88776e11	−	8.46586e11i	0.480146	−	0.831638i
$467$	9.49206e11			0.923495			0.461748	−	0.887011i	$-0.347223\pi$
$467$	9.49206e11			0.923495			0.461748	+	0.887011i	$0.347223\pi$
$468$		0			0
$469$	4.26489e11			0.407033
$470$	−1.50709e12	+	2.61035e12i	−1.42462	+	2.46751i
$471$		0			0
$472$	1.01703e12	+	1.76155e12i	0.943180	+	1.63363i
$473$	−9.15709e10	−	1.58605e11i	−0.0841167	−	0.145694i
$474$		0			0
$475$	−1.84295e10	+	3.19208e10i	−0.0166109	+	0.0287709i
$476$	1.97601e11			0.176424
$477$		0			0
$478$	−8.27136e11			−0.724689
$479$	−2.45674e11	+	4.25521e11i	−0.213231	+	0.369327i	−0.952724	−	0.303838i	$-0.901732\pi$
$479$	−2.45674e11	+	4.25521e11i	−0.213231	+	0.369327i	0.739493	+	0.673164i	$0.235065\pi$
$480$		0			0
$481$	5.67328e11	+	9.82641e11i	0.483261	+	0.837032i
$482$	1.02466e12	+	1.77476e12i	0.864704	+	1.49771i
$483$		0			0
$484$	1.24250e12	−	2.15207e12i	1.02918	−	1.78260i
$485$	−1.53915e12			−1.26312
$486$		0			0
$487$	−4.36740e11			−0.351838			−0.175919	−	0.984405i	$-0.556290\pi$
$487$	−4.36740e11			−0.351838			−0.175919	+	0.984405i	$0.556290\pi$
$488$	1.36211e12	−	2.35925e12i	1.08724	−	1.88315i
$489$		0			0
$490$	9.46990e11	+	1.64024e12i	0.742101	+	1.28536i
$491$	−9.21516e9	−	1.59611e10i	−0.00715544	−	0.0123936i	0.862426	−	0.506184i	$-0.168944\pi$
$491$	−9.21516e9	−	1.59611e10i	−0.00715544	−	0.0123936i	−0.869581	+	0.493790i	$0.835611\pi$
$492$		0			0
$493$	1.34817e11	−	2.33510e11i	0.102786	−	0.178031i
$494$	−3.48943e10			−0.0263623
$495$		0			0
$496$	−2.66507e11			−0.197716
$497$	6.86275e11	−	1.18866e12i	0.504538	−	0.873886i
$498$		0			0
$499$	−8.42550e10	−	1.45934e11i	−0.0608336	−	0.105367i	0.834005	−	0.551757i	$-0.186043\pi$
$499$	−8.42550e10	−	1.45934e11i	−0.0608336	−	0.105367i	−0.894838	+	0.446391i	$0.852709\pi$
$500$	−1.15625e12	−	2.00268e12i	−0.827343	−	1.43300i
$501$		0			0
$502$	−2.05474e12	+	3.55892e12i	−1.44408	+	2.50122i
$503$	1.21652e12			0.847348			0.423674	−	0.905815i	$-0.360740\pi$
$503$	1.21652e12			0.847348			0.423674	+	0.905815i	$0.360740\pi$
$504$		0			0
$505$	6.86680e11			0.469833
$506$	2.01493e11	−	3.48996e11i	0.136642	−	0.236670i
$507$		0			0
$508$	−2.33881e12	−	4.05094e12i	−1.55815	−	2.69879i
$509$	4.37914e11	+	7.58490e11i	0.289174	+	0.500864i	0.973613	−	0.228206i	$-0.0732860\pi$
$509$	4.37914e11	+	7.58490e11i	0.289174	+	0.500864i	−0.684439	+	0.729070i	$0.739953\pi$
$510$		0			0
$511$	−9.07036e9	+	1.57103e10i	−0.00588478	+	0.0101927i
$512$	−3.26744e12			−2.10132
$513$		0			0
$514$	2.32566e12			1.46965
$515$	8.60456e11	−	1.49035e12i	0.539009	−	0.933591i
$516$		0			0
$517$	−1.41416e11	−	2.44940e11i	−0.0870547	−	0.150783i
$518$	−1.42542e12	−	2.46889e12i	−0.869877	−	1.50667i
$519$		0			0
$520$	1.74837e12	−	3.02826e12i	1.04862	−	1.81626i
$521$	1.84603e12			1.09766			0.548830	−	0.835934i	$-0.315073\pi$
$521$	1.84603e12			1.09766			0.548830	+	0.835934i	$0.315073\pi$
$522$		0			0
$523$	2.49101e12			1.45585			0.727926	−	0.685656i	$-0.240484\pi$
$523$	2.49101e12			1.45585			0.727926	+	0.685656i	$0.240484\pi$
$524$	1.47715e11	−	2.55850e11i	0.0855921	−	0.148250i
$525$		0			0
$526$	−1.13278e12	−	1.96204e12i	−0.645225	−	1.11756i
$527$	1.54955e10	+	2.68391e10i	0.00875103	+	0.0151572i
$528$		0			0
$529$	1.58714e11	−	2.74900e11i	0.0881177	−	0.152624i
$530$	9.28571e12			5.11180
$531$		0			0
$532$	5.95718e10			0.0322432
$533$	−8.22518e10	+	1.42464e11i	−0.0441442	+	0.0764599i
$534$		0			0
$535$	−4.64829e11	−	8.05108e11i	−0.245302	−	0.424876i
$536$	−1.12466e12	−	1.94797e12i	−0.588545	−	1.01939i
$537$		0			0
$538$	−2.48757e12	+	4.30860e12i	−1.28013	+	2.21726i
$539$	−1.77720e11			−0.0906958
$540$		0			0
$541$	−3.86244e10			−0.0193854			−0.00969269	−	0.999953i	$-0.503085\pi$
$541$	−3.86244e10			−0.0193854			−0.00969269	+	0.999953i	$0.503085\pi$
$542$	−3.43893e12	+	5.95641e12i	−1.71170	+	2.96475i
$543$		0			0
$544$	−5.58167e10	−	9.66774e10i	−0.0273256	−	0.0473293i
$545$	2.00648e12	+	3.47533e12i	0.974208	+	1.68738i
$546$		0			0
$547$	−2.07167e12	+	3.58823e12i	−0.989411	+	1.71371i	−0.369010	+	0.929425i	$0.620303\pi$
$547$	−2.07167e12	+	3.58823e12i	−0.989411	+	1.71371i	−0.620401	+	0.784285i	$0.713030\pi$
$548$	2.15820e11			0.102230
$549$		0			0
$550$	9.65512e11			0.449910
$551$	4.06441e10	−	7.03976e10i	0.0187852	−	0.0325369i
$552$		0			0
$553$	1.01437e12	+	1.75694e12i	0.461248	+	0.798905i
$554$	−2.67837e12	−	4.63908e12i	−1.20803	−	2.09237i
$555$		0			0
$556$	3.04098e12	−	5.26713e12i	1.34951	−	2.33742i
$557$	−3.76741e12			−1.65842			−0.829210	−	0.558937i	$-0.811209\pi$
$557$	−3.76741e12			−1.65842			−0.829210	+	0.558937i	$0.811209\pi$
$558$		0			0
$559$	−1.52943e12			−0.662484
$560$	−1.72769e12	+	2.99244e12i	−0.742367	+	1.28582i
$561$		0			0
$562$	−2.51034e12	−	4.34804e12i	−1.06150	−	1.83857i
$563$	−6.56959e11	−	1.13789e12i	−0.275582	−	0.477322i	0.694700	−	0.719300i	$-0.255537\pi$
$563$	−6.56959e11	−	1.13789e12i	−0.275582	−	0.477322i	−0.970282	+	0.241978i	$0.922204\pi$
$564$		0			0
$565$	2.47026e11	−	4.27861e11i	0.101982	−	0.176638i
$566$	−5.04806e11			−0.206753
$567$		0			0
$568$	−7.23889e12			−2.91813
$569$	1.80021e11	−	3.11806e11i	0.0719978	−	0.124704i	−0.827779	−	0.561054i	$-0.810396\pi$
$569$	1.80021e11	−	3.11806e11i	0.0719978	−	0.124704i	0.899777	+	0.436351i	$0.143729\pi$
$570$		0			0
$571$	−1.06470e12	−	1.84412e12i	−0.419147	−	0.725984i	0.576707	−	0.816951i	$-0.304337\pi$
$571$	−1.06470e12	−	1.84412e12i	−0.419147	−	0.725984i	−0.995854	+	0.0909672i	$0.971004\pi$
$572$	3.10540e11	+	5.37871e11i	0.121293	+	0.210085i
$573$		0			0
$574$	2.06658e11	−	3.57943e11i	0.0794602	−	0.137629i
$575$	−3.55485e12			−1.35617
$576$		0			0
$577$	9.24466e11			0.347216			0.173608	−	0.984815i	$-0.444457\pi$
$577$	9.24466e11			0.347216			0.173608	+	0.984815i	$0.444457\pi$
$578$	2.33477e12	−	4.04395e12i	0.870101	−	1.50706i
$579$		0			0
$580$	7.70955e12	+	1.33533e13i	2.82881	+	4.89964i
$581$	2.43301e10	+	4.21410e10i	0.00885832	+	0.0153431i
$582$		0			0
$583$	−4.35658e11	+	7.54583e11i	−0.156184	+	0.270519i
$584$	9.56750e10			0.0340362
$585$		0			0
$586$	3.29309e12			1.15362
$587$	−1.67810e12	+	2.90655e12i	−0.583373	+	1.01043i	0.411704	+	0.911318i	$0.364934\pi$
$587$	−1.67810e12	+	2.90655e12i	−0.583373	+	1.01043i	−0.995076	+	0.0991132i	$0.968399\pi$
$588$		0			0
$589$	4.67152e9	+	8.09131e9i	0.00159934	+	0.00277013i
$590$	3.91462e12	+	6.78032e12i	1.33001	+	2.30365i
$591$		0			0
$592$	−2.95672e12	+	5.12119e12i	−0.989379	+	1.71365i
$593$	2.23226e12			0.741308			0.370654	−	0.928771i	$-0.379134\pi$
$593$	2.23226e12			0.741308			0.370654	+	0.928771i	$0.379134\pi$
$594$		0			0
$595$	4.01811e11			0.131430
$596$	5.68186e11	−	9.84127e11i	0.184452	−	0.319480i
$597$		0			0
$598$	−1.68268e12	−	2.91449e12i	−0.538079	−	0.931980i
$599$	−9.21454e11	−	1.59601e12i	−0.292451	−	0.506540i	0.681938	−	0.731410i	$-0.261137\pi$
$599$	−9.21454e11	−	1.59601e12i	−0.292451	−	0.506540i	−0.974389	+	0.224870i	$0.927804\pi$
$600$		0			0
$601$	1.67573e11	−	2.90245e11i	0.0523925	−	0.0907464i	−0.838640	−	0.544687i	$-0.816649\pi$
$601$	1.67573e11	−	2.90245e11i	0.0523925	−	0.0907464i	0.891032	+	0.453940i	$0.149982\pi$
$602$	3.84270e12			1.19248
$603$		0			0
$604$	8.99234e12			2.74920
$605$	2.52656e12	−	4.37613e12i	0.766709	−	1.32798i
$606$		0			0
$607$	−1.50886e10	−	2.61342e10i	−0.00451128	−	0.00781376i	0.863761	−	0.503902i	$-0.168103\pi$
$607$	−1.50886e10	−	2.61342e10i	−0.00451128	−	0.00781376i	−0.868272	+	0.496088i	$0.834769\pi$
$608$	−1.68274e10	−	2.91458e10i	−0.00499401	−	0.00864989i
$609$		0			0
$610$	5.24287e12	−	9.08092e12i	1.53315	−	2.65550i
$611$	−2.36195e12			−0.685623
$612$		0			0
$613$	−6.97355e11			−0.199472			−0.0997360	−	0.995014i	$-0.531800\pi$
$613$	−6.97355e11			−0.199472			−0.0997360	+	0.995014i	$0.531800\pi$
$614$	−3.20940e12	+	5.55885e12i	−0.911310	+	1.57844i
$615$		0			0
$616$	−4.12193e11	−	7.13940e11i	−0.115342	−	0.199778i
$617$	−5.30375e11	−	9.18636e11i	−0.147333	−	0.255188i	0.782908	−	0.622138i	$-0.213736\pi$
$617$	−5.30375e11	−	9.18636e11i	−0.147333	−	0.255188i	−0.930241	+	0.366949i	$0.880402\pi$
$618$		0			0
$619$	−3.84166e10	+	6.65395e10i	−0.0105175	+	0.0182168i	−0.871236	−	0.490864i	$-0.836681\pi$
$619$	−3.84166e10	+	6.65395e10i	−0.0105175	+	0.0182168i	0.860719	+	0.509081i	$0.170015\pi$
$620$	−1.77223e12			−0.481679
$621$		0			0
$622$	−4.16027e12			−1.11446
$623$	−1.56887e12	+	2.71735e12i	−0.417243	+	0.722687i
$624$		0			0
$625$	4.98828e11	+	8.63996e11i	0.130765	+	0.226491i
$626$	6.94699e11	+	1.20325e12i	0.180806	+	0.313165i
$627$		0			0
$628$	−2.19038e11	+	3.79384e11i	−0.0561953	+	0.0973331i
$629$	6.87650e11			0.175162
$630$		0			0
$631$	−7.39558e12			−1.85712			−0.928560	−	0.371183i	$-0.878952\pi$
$631$	−7.39558e12			−1.85712			−0.928560	+	0.371183i	$0.878952\pi$
$632$	5.34985e12	−	9.26621e12i	1.33387	−	2.31034i
$633$		0			0
$634$	3.36083e12	+	5.82112e12i	0.826123	+	1.43089i
$635$	−4.75585e12	−	8.23737e12i	−1.16077	−	2.01051i
$636$		0			0
$637$	−7.42075e11	+	1.28531e12i	−0.178575	+	0.309301i
$638$	−2.12932e12			−0.508801
$639$		0			0
$640$	−9.88792e12			−2.32967
$641$	−1.18942e12	+	2.06014e12i	−0.278275	+	0.481987i	−0.970956	−	0.239257i	$-0.923096\pi$
$641$	−1.18942e12	+	2.06014e12i	−0.278275	+	0.481987i	0.692681	+	0.721244i	$0.256429\pi$
$642$		0			0
$643$	−3.16832e12	−	5.48768e12i	−0.730936	−	1.26602i	−0.956484	−	0.291785i	$-0.905751\pi$
$643$	−3.16832e12	−	5.48768e12i	−0.730936	−	1.26602i	0.225548	−	0.974232i	$-0.427583\pi$
$644$	2.87268e12	+	4.97564e12i	0.658115	+	1.13989i
$645$		0			0
$646$	−1.05737e10	+	1.83142e10i	−0.00238881	+	0.00413754i
$647$	−1.61691e11			−0.0362759			−0.0181379	−	0.999835i	$-0.505774\pi$
$647$	−1.61691e11			−0.0362759			−0.0181379	+	0.999835i	$0.505774\pi$
$648$		0			0
$649$	−7.34651e11			−0.162547
$650$	4.03152e12	−	6.98280e12i	0.885847	−	1.53433i
$651$		0			0
$652$	−2.48475e12	−	4.30372e12i	−0.538479	−	0.932674i
$653$	1.08212e12	+	1.87428e12i	0.232897	+	0.403390i	0.958660	−	0.284556i	$-0.0918461\pi$
$653$	1.08212e12	+	1.87428e12i	0.232897	+	0.403390i	−0.725762	+	0.687946i	$0.758513\pi$
$654$		0			0
$655$	3.00371e11	−	5.20257e11i	0.0637634	−	0.110442i
$656$	−8.57338e11			−0.180753
$657$		0			0
$658$	5.93442e12			1.23413
$659$	−1.01477e12	+	1.75764e12i	−0.209597	+	0.363032i	−0.951588	−	0.307378i	$-0.900548\pi$
$659$	−1.01477e12	+	1.75764e12i	−0.209597	+	0.363032i	0.741991	+	0.670410i	$0.233882\pi$
$660$		0			0
$661$	2.20704e12	+	3.82270e12i	0.449680	+	0.778868i	0.998365	−	0.0571607i	$-0.0182047\pi$
$661$	2.20704e12	+	3.82270e12i	0.449680	+	0.778868i	−0.548685	+	0.836029i	$0.684871\pi$
$662$	1.78143e12	+	3.08553e12i	0.360503	+	0.624409i
$663$		0			0
$664$	1.28318e11	−	2.22254e11i	0.0256172	−	0.0443703i
$665$	1.21136e11			0.0240202
$666$		0			0
$667$	7.83979e12			1.53369
$668$	−4.60959e12	+	7.98404e12i	−0.895711	+	1.55142i
$669$		0			0
$670$	−4.32890e12	−	7.49788e12i	−0.829930	−	1.43748i
$671$	4.91961e11	+	8.52101e11i	0.0936869	+	0.162271i
$672$		0			0
$673$	3.63786e12	−	6.30096e12i	0.683563	−	1.18397i	−0.290323	−	0.956929i	$-0.593763\pi$
$673$	3.63786e12	−	6.30096e12i	0.683563	−	1.18397i	0.973886	−	0.227037i	$-0.0729039\pi$
$674$	−8.09115e11			−0.151022
$675$		0			0
$676$	−6.32371e12			−1.16469
$677$	−2.66342e12	+	4.61318e12i	−0.487294	+	0.844018i	−0.999893	−	0.0146098i	$-0.995349\pi$
$677$	−2.66342e12	+	4.61318e12i	−0.487294	+	0.844018i	0.512599	+	0.858628i	$0.328683\pi$
$678$		0			0
$679$	1.51517e12	+	2.62434e12i	0.273556	+	0.473813i
$680$	−1.05959e12	−	1.83526e12i	−0.190040	−	0.329160i
$681$		0			0
$682$	1.22369e11	−	2.11950e11i	0.0216592	−	0.0375148i
$683$	4.26484e12			0.749910			0.374955	−	0.927043i	$-0.377658\pi$
$683$	4.26484e12			0.749910			0.374955	+	0.927043i	$0.377658\pi$
$684$		0			0
$685$	4.38859e11			0.0761583
$686$	5.36879e12	−	9.29902e12i	0.925589	−	1.60317i
$687$		0			0
$688$	−3.98543e12	−	6.90296e12i	−0.678152	−	1.17459i
$689$	3.63821e12	+	6.30156e12i	0.615036	+	1.06527i
$690$		0			0
$691$	−3.04089e12	+	5.26698e12i	−0.507400	+	0.878842i	0.492564	+	0.870276i	$0.336060\pi$
$691$	−3.04089e12	+	5.26698e12i	−0.507400	+	0.878842i	−0.999963	+	0.00856561i	$0.997273\pi$
$692$	7.67556e12			1.27243
$693$		0			0
$694$	1.04369e13			1.70787
$695$	6.18367e12	−	1.07104e13i	1.00534	−	1.74131i
$696$		0			0
$697$	4.98482e10	+	8.63396e10i	0.00800022	+	0.0138568i
$698$	−7.27406e12	−	1.25990e13i	−1.15992	−	2.00904i
$699$		0			0
$700$	−6.88264e12	+	1.19211e13i	−1.08346	+	1.87661i
$701$	−1.02189e12			−0.159835			−0.0799174	−	0.996801i	$-0.525466\pi$
$701$	−1.02189e12			−0.159835			−0.0799174	+	0.996801i	$0.525466\pi$
$702$		0			0
$703$	2.07310e11			0.0320126
$704$	3.22633e11	−	5.58817e11i	0.0495030	−	0.0857417i
$705$		0			0
$706$	5.71810e12	+	9.90404e12i	0.866225	+	1.50035i
$707$	−6.75980e11	−	1.17083e12i	−0.101753	−	0.176241i
$708$		0			0
$709$	9.54547e11	−	1.65332e12i	0.141870	−	0.245725i	−0.786331	−	0.617805i	$-0.788022\pi$
$709$	9.54547e11	−	1.65332e12i	0.141870	−	0.245725i	0.928201	+	0.372080i	$0.121355\pi$
$710$	−2.78630e13			−4.11496
$711$		0			0
$712$	1.65485e13			2.41324
$713$	−4.50542e11	+	7.80362e11i	−0.0652879	+	0.113082i
$714$		0			0
$715$	6.31466e11	+	1.09373e12i	0.0903593	+	0.156507i
$716$	6.76665e12	+	1.17202e13i	0.962199	+	1.66658i
$717$		0			0
$718$	−7.10330e12	+	1.23033e13i	−0.997471	+	1.72767i
$719$	4.88529e12			0.681726			0.340863	−	0.940113i	$-0.389281\pi$
$719$	4.88529e12			0.681726			0.340863	+	0.940113i	$0.389281\pi$
$720$		0			0
$721$	−3.38819e12			−0.466938
$722$	6.44537e12	−	1.11637e13i	0.882735	−	1.52894i
$723$		0			0
$724$	−2.92348e12	−	5.06362e12i	−0.395437	−	0.684917i
$725$	9.39165e12	+	1.62668e13i	1.26247	+	2.18666i
$726$		0			0
$727$	5.08696e12	−	8.81087e12i	0.675388	−	1.16981i	−0.300967	−	0.953635i	$-0.597309\pi$
$727$	5.08696e12	−	8.81087e12i	0.675388	−	1.16981i	0.976355	−	0.216172i	$-0.0693573\pi$
$728$	−6.88450e12			−0.908408
$729$		0			0
$730$	3.68260e11			0.0479957
$731$	−4.63449e11	+	8.02718e11i	−0.0600308	+	0.103976i
$732$		0			0
$733$	6.27206e12	+	1.08635e13i	0.802495	+	1.38996i	0.917969	+	0.396651i	$0.129828\pi$
$733$	6.27206e12	+	1.08635e13i	0.802495	+	1.38996i	−0.115475	+	0.993310i	$0.536839\pi$
$734$	3.66541e12	+	6.34868e12i	0.466112	+	0.807330i
$735$		0			0
$736$	1.62291e12	−	2.81095e12i	0.203865	−	0.353105i
$737$	8.12398e11			0.101430
$738$		0			0
$739$	−9.22997e12			−1.13841			−0.569207	−	0.822194i	$-0.692750\pi$
$739$	−9.22997e12			−1.13841			−0.569207	+	0.822194i	$0.692750\pi$
$740$	−1.96617e13	+	3.40551e13i	−2.41034	+	4.17483i
$741$		0			0
$742$	−9.14102e12	−	1.58327e13i	−1.10708	−	1.91751i
$743$	−5.91953e12	−	1.02529e13i	−0.712587	−	1.23424i	−0.963883	−	0.266326i	$-0.914190\pi$
$743$	−5.91953e12	−	1.02529e13i	−0.712587	−	1.23424i	0.251296	−	0.967910i	$-0.419143\pi$
$744$		0			0
$745$	1.15538e12	−	2.00117e12i	0.137411	−	0.238002i
$746$	−1.46588e13			−1.73290
$747$		0			0
$748$	3.76401e11			0.0439636
$749$	−9.15173e11	+	1.58513e12i	−0.106251	+	0.184033i
$750$		0			0
$751$	3.65219e12	+	6.32577e12i	0.418960	+	0.725661i	0.995835	−	0.0911718i	$-0.0290612\pi$
$751$	3.65219e12	+	6.32577e12i	0.418960	+	0.725661i	−0.576875	+	0.816833i	$0.695728\pi$
$752$	−6.15484e12	−	1.06605e13i	−0.701838	−	1.21562i
$753$		0			0
$754$	−8.89103e12	+	1.53997e13i	−1.00180	+	1.73517i
$755$	1.82855e13			2.04807
$756$		0			0
$757$	4.96772e12			0.549827			0.274913	−	0.961469i	$-0.411351\pi$
$757$	4.96772e12			0.549827			0.274913	+	0.961469i	$0.411351\pi$
$758$	−1.91168e12	+	3.31113e12i	−0.210331	+	0.364304i
$759$		0			0
$760$	−3.19439e11	−	5.53284e11i	−0.0347317	−	0.0601571i
$761$	−7.26962e12	−	1.25914e13i	−0.785744	−	1.36095i	−0.928554	−	0.371198i	$-0.878947\pi$
$761$	−7.26962e12	−	1.25914e13i	−0.785744	−	1.36095i	0.142810	−	0.989750i	$-0.454386\pi$
$762$		0			0
$763$	3.95044e12	−	6.84236e12i	0.421973	−	0.730879i
$764$	2.94389e13			3.12609
$765$		0			0
$766$	−2.85547e13			−2.99674
$767$	−3.06755e12	+	5.31316e12i	−0.320046	+	0.554337i
$768$		0			0
$769$	−6.05017e12	−	1.04792e13i	−0.623877	−	1.08059i	−0.988757	−	0.149532i	$-0.952223\pi$
$769$	−6.05017e12	−	1.04792e13i	−0.623877	−	1.08059i	0.364880	−	0.931054i	$-0.381110\pi$
$770$	−1.58656e12	−	2.74801e12i	−0.162648	−	0.281715i
$771$		0			0
$772$	4.08508e12	−	7.07557e12i	0.413926	−	0.716941i
$773$	7.51240e12			0.756782			0.378391	−	0.925646i	$-0.376477\pi$
$773$	7.51240e12			0.756782			0.378391	+	0.925646i	$0.376477\pi$
$774$		0			0
$775$	−2.15890e12			−0.214969
$776$	7.99106e12	−	1.38409e13i	0.791091	−	1.37021i
$777$		0			0
$778$	7.79832e12	+	1.35071e13i	0.763120	+	1.32176i
$779$	1.50280e10	+	2.60292e10i	0.00146212	+	0.00253246i
$780$		0			0
$781$	1.30725e12	−	2.26423e12i	0.125727	−	0.217766i
$782$	−2.03955e12			−0.195031
$783$		0			0
$784$	−7.73489e12			−0.731192
$785$	−4.45401e11	+	7.71458e11i	−0.0418637	+	0.0725101i
$786$		0			0
$787$	−3.04156e12	−	5.26813e12i	−0.282624	−	0.489520i	0.689406	−	0.724375i	$-0.257872\pi$
$787$	−3.04156e12	−	5.26813e12i	−0.282624	−	0.489520i	−0.972030	+	0.234856i	$0.924538\pi$
$788$	−4.29329e12	−	7.43620e12i	−0.396664	−	0.687042i
$789$		0			0
$790$	2.05920e13	−	3.56663e13i	1.88094	−	3.25789i
$791$	−9.72707e11			−0.0883462
$792$		0			0
$793$	8.21678e12			0.737857
$794$	6.37618e11	−	1.10439e12i	0.0569336	−	0.0986118i
$795$		0			0
$796$	1.07457e13	+	1.86122e13i	0.948696	+	1.64319i
$797$	−3.72388e12	−	6.44995e12i	−0.326914	−	0.566231i	0.654984	−	0.755643i	$-0.272675\pi$
$797$	−3.72388e12	−	6.44995e12i	−0.326914	−	0.566231i	−0.981898	+	0.189412i	$0.939342\pi$
$798$		0			0
$799$	−7.15722e11	+	1.23967e12i	−0.0621275	+	0.107608i
$800$	7.77661e12			0.671252
$801$		0			0
$802$	2.33141e13			1.98992
$803$	−1.72777e10	+	2.99259e10i	−0.00146645	+	0.00253996i
$804$		0			0
$805$	5.84145e12	+	1.01177e13i	0.490275	+	0.849181i
$806$	−1.02191e12	−	1.77000e12i	−0.0852915	−	0.147729i
$807$		0			0
$808$	−3.56515e12	+	6.17502e12i	−0.294257	+	0.509668i
$809$	−7.32627e12			−0.601333			−0.300666	−	0.953729i	$-0.597209\pi$
$809$	−7.32627e12			−0.601333			−0.300666	+	0.953729i	$0.597209\pi$
$810$		0			0
$811$	−1.94054e13			−1.57517			−0.787586	−	0.616205i	$-0.788669\pi$
$811$	−1.94054e13			−1.57517			−0.787586	+	0.616205i	$0.788669\pi$
$812$	1.51788e13	−	2.62905e13i	1.22528	−	2.12225i
$813$		0			0
$814$	−2.71521e12	−	4.70288e12i	−0.216767	−	0.375452i
$815$	−5.05262e12	−	8.75139e12i	−0.401150	−	0.694812i
$816$		0			0
$817$	−1.39718e11	+	2.41999e11i	−0.0109712	+	0.0190027i
$818$	2.38566e13			1.86302
$819$		0			0
$820$	−5.70115e12			−0.440352
$821$	−2.58219e12	+	4.47249e12i	−0.198356	+	0.343562i	−0.947995	−	0.318284i	$-0.896893\pi$
$821$	−2.58219e12	+	4.47249e12i	−0.198356	+	0.343562i	0.749640	+	0.661846i	$0.230227\pi$
$822$		0			0
$823$	1.05680e12	+	1.83043e12i	0.0802957	+	0.139076i	0.903377	−	0.428847i	$-0.141080\pi$
$823$	1.05680e12	+	1.83043e12i	0.0802957	+	0.139076i	−0.823081	+	0.567924i	$0.807747\pi$
$824$	8.93475e12	+	1.54754e13i	0.675165	+	1.16942i
$825$		0			0
$826$	7.70725e12	−	1.33493e13i	0.576089	−	0.997815i
$827$	−1.74289e13			−1.29567			−0.647835	−	0.761781i	$-0.724325\pi$
$827$	−1.74289e13			−1.29567			−0.647835	+	0.761781i	$0.724325\pi$
$828$		0			0
$829$	1.70846e13			1.25635			0.628173	−	0.778074i	$-0.283803\pi$
$829$	1.70846e13			1.25635			0.628173	+	0.778074i	$0.283803\pi$
$830$	4.93906e11	−	8.55471e11i	0.0361238	−	0.0625682i
$831$		0			0
$832$	−2.69432e12	−	4.66671e12i	−0.194937	−	0.337641i
$833$	4.49729e11	+	7.78954e11i	0.0323630	+	0.0560544i
$834$		0			0
$835$	−9.37335e12	+	1.62351e13i	−0.667276	+	1.15576i
$836$	1.13476e11			0.00803478
$837$		0			0
$838$	−1.25017e13			−0.875734
$839$	−1.15781e13	+	2.00539e13i	−0.806696	+	1.39724i	0.108444	+	0.994103i	$0.465413\pi$
$839$	−1.15781e13	+	2.00539e13i	−0.806696	+	1.39724i	−0.915140	+	0.403136i	$0.867920\pi$
$840$		0			0
$841$	−1.34586e13	−	2.33109e13i	−0.927721	−	1.60686i
$842$	1.21203e13	+	2.09929e13i	0.831012	+	1.43935i
$843$		0			0
$844$	−1.50872e13	+	2.61317e13i	−1.02345	+	1.77267i
$845$	−1.28589e13			−0.867660
$846$		0			0
$847$	−9.94876e12			−0.664192
$848$	−1.89611e13	+	3.28416e13i	−1.25916	+	2.18094i
$849$		0			0
$850$	−2.44327e12	−	4.23188e12i	−0.160541	−	0.278066i
$851$	9.99693e12	+	1.73152e13i	0.653406	+	1.13173i
$852$		0			0
$853$	−3.95259e12	+	6.84609e12i	−0.255630	+	0.442764i	−0.965066	−	0.262006i	$-0.915616\pi$
$853$	−3.95259e12	+	6.84609e12i	−0.255630	+	0.442764i	0.709437	+	0.704769i	$0.248949\pi$
$854$	−2.06447e13			−1.32815
$855$		0			0
$856$	9.65333e12			0.614533
$857$	1.35356e13	−	2.34444e13i	0.857164	−	1.48465i	−0.0174588	−	0.999848i	$-0.505558\pi$
$857$	1.35356e13	−	2.34444e13i	0.857164	−	1.48465i	0.874623	−	0.484804i	$-0.161109\pi$
$858$		0			0
$859$	−1.35523e13	−	2.34733e13i	−0.849268	−	1.47098i	−0.881863	−	0.471506i	$-0.843710\pi$
$859$	−1.35523e13	−	2.34733e13i	−0.849268	−	1.47098i	0.0325947	−	0.999469i	$-0.489623\pi$
$860$	−2.65024e13	−	4.59036e13i	−1.65212	−	2.86156i
$861$		0			0
$862$	−9.05451e12	+	1.56829e13i	−0.558576	+	0.967482i
$863$	1.94364e13			1.19280			0.596399	−	0.802688i	$-0.296598\pi$
$863$	1.94364e13			1.19280			0.596399	+	0.802688i	$0.296598\pi$
$864$		0			0
$865$	1.56079e13			0.947918
$866$	−3.24175e12	+	5.61487e12i	−0.195861	+	0.339242i
$867$		0			0
$868$	1.74462e12	+	3.02176e12i	0.104318	+	0.180685i
$869$	1.93223e12	+	3.34672e12i	0.114940	+	0.199081i
$870$		0			0
$871$	3.39219e12	−	5.87545e12i	0.199709	−	0.345907i
$872$	−4.16696e13			−2.44059
$873$		0			0
$874$	−6.14874e11			−0.0356439
$875$	−4.62906e12	+	8.01777e12i	−0.266967	+	0.462400i
$876$		0			0
$877$	−2.86815e12	−	4.96778e12i	−0.163721	−	0.283572i	0.772480	−	0.635040i	$-0.219016\pi$
$877$	−2.86815e12	−	4.96778e12i	−0.163721	−	0.283572i	−0.936200	+	0.351467i	$0.885683\pi$
$878$	2.28585e13	+	3.95920e13i	1.29814	+	2.24844i
$879$		0			0
$880$	−3.29099e12	+	5.70016e12i	−0.184993	+	0.320417i
$881$	−1.87555e13			−1.04891			−0.524453	−	0.851439i	$-0.675730\pi$
$881$	−1.87555e13			−1.04891			−0.524453	+	0.851439i	$0.675730\pi$
$882$		0			0
$883$	1.44505e13			0.799947			0.399973	−	0.916527i	$-0.369019\pi$
$883$	1.44505e13			0.799947			0.399973	+	0.916527i	$0.369019\pi$
$884$	1.57167e12	−	2.72222e12i	0.0865619	−	0.149930i
$885$		0			0
$886$	2.65378e13	+	4.59649e13i	1.44682	+	2.50596i
$887$	−8.24167e12	−	1.42750e13i	−0.447053	−	0.774318i	0.551140	−	0.834413i	$-0.314193\pi$
$887$	−8.24167e12	−	1.42750e13i	−0.447053	−	0.774318i	−0.998193	+	0.0600948i	$0.980860\pi$
$888$		0			0
$889$	−9.36349e12	+	1.62180e13i	−0.502782	+	0.870844i
$890$	6.36966e13			3.40299
$891$		0			0
$892$	3.32170e13			1.75679
$893$	−2.15772e11	+	3.73729e11i	−0.0113544	+	0.0196664i
$894$		0			0
$895$	1.37596e13	+	2.38324e13i	0.716808	+	1.24155i
$896$	9.73385e12	+	1.68595e13i	0.504543	+	0.873895i
$897$		0			0
$898$	1.05828e13	−	1.83300e13i	0.543072	−	0.940629i
$899$	4.76120e12			0.243107
$900$		0			0
$901$	4.40982e12			0.222925
$902$	3.93654e11	−	6.81829e11i	0.0198009	−	0.0342962i
$903$		0			0
$904$	2.56505e12	+	4.44280e12i	0.127743	+	0.221258i
$905$	−5.94475e12	−	1.02966e13i	−0.294588	−	0.510241i
$906$		0			0
$907$	−4.83281e11	+	8.37067e11i	−0.0237119	+	0.0410702i	−0.877638	−	0.479324i	$-0.840882\pi$
$907$	−4.83281e11	+	8.37067e11i	−0.0237119	+	0.0410702i	0.853926	+	0.520395i	$0.174215\pi$
$908$	−1.27840e13			−0.624136
$909$		0			0
$910$	−2.64990e13			−1.28098
$911$	8.89072e8	−	1.53992e9i	4.27666e−5	−	7.40739e-5i	−0.866004	−	0.500037i	$-0.833320\pi$
$911$	8.89072e8	−	1.53992e9i	4.27666e−5	−	7.40739e-5i	0.866047	+	0.499963i	$0.166653\pi$
$912$		0			0
$913$	4.63453e10	+	8.02724e10i	0.00220743	+	0.00382338i
$914$	−2.12857e13	−	3.68679e13i	−1.00886	−	1.74739i
$915$		0			0
$916$	4.31471e13	−	7.47329e13i	2.02498	−	3.50738i
$917$	−1.18276e12			−0.0552376
$918$		0			0
$919$	1.23275e13			0.570105			0.285052	−	0.958512i	$-0.407989\pi$
$919$	1.23275e13			0.570105			0.285052	+	0.958512i	$0.407989\pi$
$920$	3.08081e13	−	5.33612e13i	1.41782	−	2.45573i
$921$		0			0
$922$	−1.64105e13	−	2.84238e13i	−0.747882	−	1.29537i
$923$	−1.09169e13	−	1.89087e13i	−0.495100	−	0.857539i
$924$		0			0
$925$	−2.39516e13	+	4.14853e13i	−1.07571	+	1.86319i
$926$	1.53171e13			0.684584
$927$		0			0
$928$	−1.71504e13			−0.759116
$929$	9.55300e12	−	1.65463e13i	0.420794	−	0.728836i	−0.575224	−	0.817996i	$-0.695085\pi$
$929$	9.55300e12	−	1.65463e13i	0.420794	−	0.728836i	0.996017	+	0.0891604i	$0.0284184\pi$
$930$		0			0
$931$	1.35582e11	+	2.34835e11i	0.00591465	+	0.0102445i
$932$	1.32739e13	+	2.29911e13i	0.576272	+	0.998133i
$933$		0			0
$934$	−1.89688e13	+	3.28550e13i	−0.815605	+	1.41267i
$935$	7.65392e11			0.0327515
$936$		0			0
$937$	−4.13512e13			−1.75251			−0.876253	−	0.481851i	$-0.839965\pi$
$937$	−4.13512e13			−1.75251			−0.876253	+	0.481851i	$0.839965\pi$
$938$	−8.52290e12	+	1.47621e13i	−0.359480	+	0.622638i
$939$		0			0
$940$	−4.09287e13	−	7.08906e13i	−1.70983	−	2.96151i
$941$	2.10949e13	+	3.65375e13i	0.877051	+	1.51910i	0.854562	+	0.519349i	$0.173826\pi$
$941$	2.10949e13	+	3.65375e13i	0.877051	+	1.51910i	0.0224885	+	0.999747i	$0.492841\pi$
$942$		0			0
$943$	−1.44937e12	+	2.51037e12i	−0.0596864	+	0.103380i
$944$	−3.19741e13			−1.31046
$945$		0			0
$946$	7.31977e12			0.297158
$947$	−1.80301e13	+	3.12290e13i	−0.728489	+	1.26178i	0.229033	+	0.973419i	$0.426444\pi$
$947$	−1.80301e13	+	3.12290e13i	−0.728489	+	1.26178i	−0.957522	+	0.288361i	$0.906890\pi$
$948$		0			0
$949$	1.44287e11	+	2.49912e11i	0.00577470	+	0.0100021i
$950$	−7.36587e11	−	1.27581e12i	−0.0293405	−	0.0508192i
$951$		0			0
$952$	−2.08615e12	+	3.61332e12i	−0.0823151	+	0.142574i
$953$	1.37784e13			0.541104			0.270552	−	0.962705i	$-0.412794\pi$
$953$	1.37784e13			0.541104			0.270552	+	0.962705i	$0.412794\pi$
$954$		0			0
$955$	5.98624e13			2.32884
$956$	1.12315e13	−	1.94535e13i	0.434886	−	0.753245i
$957$		0			0
$958$	−9.81906e12	−	1.70071e13i	−0.376639	−	0.652358i
$959$	−4.32020e11	−	7.48281e11i	−0.0164938	−	0.0285681i
$960$		0			0
$961$	1.29462e13	−	2.24235e13i	0.489651	−	0.848101i
$962$	−4.53497e13			−1.70721
$963$		0			0
$964$	−5.56543e13			−2.07564
$965$	8.30679e12	−	1.43878e13i	0.308362	−	0.534098i
$966$		0			0
$967$	2.30760e13	+	3.99688e13i	0.848674	+	1.46995i	0.882392	+	0.470516i	$0.155932\pi$
$967$	2.30760e13	+	3.99688e13i	0.848674	+	1.46995i	−0.0337170	+	0.999431i	$0.510734\pi$
$968$	2.62351e13	+	4.54406e13i	0.960382	+	1.66343i
$969$		0			0
$970$	3.07582e13	−	5.32748e13i	1.11555	−	1.93218i
$971$	2.79369e13			1.00854			0.504268	−	0.863547i	$-0.331763\pi$
$971$	2.79369e13			1.00854			0.504268	+	0.863547i	$0.331763\pi$
$972$		0			0
$973$	−2.43493e13			−0.870919
$974$	8.72776e12	−	1.51169e13i	0.310733	−	0.538205i
$975$		0			0
$976$	2.14115e13	+	3.70859e13i	0.755307	+	1.30823i
$977$	3.24140e12	+	5.61427e12i	0.113817	+	0.197137i	0.917306	−	0.398182i	$-0.130359\pi$
$977$	3.24140e12	+	5.61427e12i	0.113817	+	0.197137i	−0.803489	+	0.595319i	$0.797026\pi$
$978$		0			0
$979$	−2.98846e12	+	5.17616e12i	−0.103974	+	0.180088i
$980$	−5.14357e13			−1.78134
$981$		0			0
$982$	7.36619e11			0.0252779
$983$	1.05088e13	−	1.82018e13i	0.358974	−	0.621761i	−0.628816	−	0.777554i	$-0.716460\pi$
$983$	1.05088e13	−	1.82018e13i	0.358974	−	0.621761i	0.987790	+	0.155793i	$0.0497933\pi$
$984$		0			0
$985$	−8.73019e12	−	1.51211e13i	−0.295502	−	0.511824i
$986$	5.38835e12	+	9.33290e12i	0.181556	+	0.314464i
$987$		0			0
$988$	4.73820e11	−	8.20681e11i	0.0158200	−	0.0274011i
$989$	−2.69501e13			−0.895731
$990$		0			0
$991$	−3.89754e13			−1.28369			−0.641844	−	0.766835i	$-0.721830\pi$
$991$	−3.89754e13			−1.28369			−0.641844	+	0.766835i	$0.721830\pi$
$992$	9.85610e11	−	1.70713e12i	0.0323149	−	0.0559710i
$993$		0			0
$994$	2.74289e13	+	4.75082e13i	0.891188	+	1.54358i
$995$	2.18509e13	+	3.78468e13i	0.706749	+	1.22412i
$996$		0			0
$997$	−1.31809e13	+	2.28300e13i	−0.422490	+	0.731774i	−0.996182	−	0.0872966i	$-0.972177\pi$
$997$	−1.31809e13	+	2.28300e13i	−0.422490	+	0.731774i	0.573692	+	0.819071i	$0.305511\pi$
$998$	6.73497e12			0.214906
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.c.a.19.1		16
3.2	odd	2		9.10.c.a.7.8	yes	16
9.2	odd	6		81.10.a.c.1.1		8
9.4	even	3	inner	27.10.c.a.10.1		16
9.5	odd	6		9.10.c.a.4.8	✓	16
9.7	even	3		81.10.a.d.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.8	✓	16	9.5	odd	6
9.10.c.a.7.8	yes	16	3.2	odd	2
27.10.c.a.10.1		16	9.4	even	3	inner
27.10.c.a.19.1		16	1.1	even	1	trivial
81.10.a.c.1.1		8	9.2	odd	6
81.10.a.d.1.8		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)

\(f(q)\)	\(=\)	\(q+(-19.9839 + 34.6131i) q^{2} +(-542.712 - 940.005i) q^{4} +(-1103.58 - 1911.45i) q^{5} +(-2172.76 + 3763.33i) q^{7} +22918.5 q^{8} +O(q^{10})\)	\(q+(-19.9839 + 34.6131i) q^{2} +(-542.712 - 940.005i) q^{4} +(-1103.58 - 1911.45i) q^{5} +(-2172.76 + 3763.33i) q^{7} +22918.5 q^{8} +88215.0 q^{10} +(-4138.79 + 7168.59i) q^{11} +(34563.2 + 59865.3i) q^{13} +(-86840.4 - 150412. i) q^{14} +(-180132. + 311998. i) q^{16} +41893.6 q^{17} +12629.9 q^{19} +(-1.19785e6 + 2.07473e6i) q^{20} +(-165418. - 286513. i) q^{22} +(609041. + 1.05489e6i) q^{23} +(-1.45920e6 + 2.52740e6i) q^{25} -2.76283e6 q^{26} +4.71673e6 q^{28} +(3.21809e6 - 5.57389e6i) q^{29} +(369878. + 640648. i) q^{31} +(-1.33234e6 - 2.30769e6i) q^{32} +(-837198. + 1.45007e6i) q^{34} +9.59122e6 q^{35} +1.64142e7 q^{37} +(-252394. + 437160. i) q^{38} +(-2.52923e7 - 4.38075e7i) q^{40} +(1.18987e6 + 2.06092e6i) q^{41} +(-1.10625e7 + 1.91609e7i) q^{43} +8.98468e6 q^{44} -4.86841e7 q^{46} +(-1.70843e7 + 2.95908e7i) q^{47} +(1.07350e7 + 1.85936e7i) q^{49} +(-5.83209e7 - 1.01015e8i) q^{50} +(3.75158e7 - 6.49792e7i) q^{52} +1.05262e8 q^{53} +1.82699e7 q^{55} +(-4.97964e7 + 8.62498e7i) q^{56} +(1.28620e8 + 2.22776e8i) q^{58} +(4.43759e7 + 7.68614e7i) q^{59} +(5.94329e7 - 1.02941e8i) q^{61} -2.95664e7 q^{62} -7.79534e7 q^{64} +(7.62863e7 - 1.32132e8i) q^{65} +(-4.90722e7 - 8.49956e7i) q^{67} +(-2.27362e7 - 3.93802e7i) q^{68} +(-1.91670e8 + 3.31982e8i) q^{70} -3.15854e8 q^{71} +4.17458e6 q^{73} +(-3.28020e8 + 5.68147e8i) q^{74} +(-6.85439e6 - 1.18722e7i) q^{76} +(-1.79852e7 - 3.11513e7i) q^{77} +(2.33429e8 - 4.04312e8i) q^{79} +7.95157e8 q^{80} -9.51133e7 q^{82} +(5.59890e6 - 9.69757e6i) q^{83} +(-4.62328e7 - 8.00776e7i) q^{85} +(-4.42145e8 - 7.65817e8i) q^{86} +(-9.48548e7 + 1.64293e8i) q^{88} +7.22061e8 q^{89} -3.00391e8 q^{91} +(6.61068e8 - 1.14500e9i) q^{92} +(-6.82820e8 - 1.18268e9i) q^{94} +(-1.39380e7 - 2.41414e7i) q^{95} +(3.48673e8 - 6.03920e8i) q^{97} -8.58111e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) \) 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

L-functions

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