LMFDB - Embedded newform 27.10.c.a.19.6

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			19.6
Root			$0.500000 - 13.2694i$ of defining polynomial
Character	$\chi$	$=$	27.19
Dual form			27.10.c.a.10.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(10.7416 - 18.6050i) q^{2} +(25.2357 + 43.7094i) q^{4} +(-22.4201 - 38.8327i) q^{5} +(-4672.78 + 8093.49i) q^{7} +12083.7 q^{8} +O(q^{10})$	\(q+(10.7416 - 18.6050i) q^{2} +(25.2357 + 43.7094i) q^{4} +(-22.4201 - 38.8327i) q^{5} +(-4672.78 + 8093.49i) q^{7} +12083.7 q^{8} -963.310 q^{10} +(-27578.5 + 47767.3i) q^{11} +(39984.4 + 69255.0i) q^{13} +(100386. + 173874. i) q^{14} +(116878. - 202438. i) q^{16} -8591.55 q^{17} +643299. q^{19} +(1131.57 - 1959.94i) q^{20} +(592474. + 1.02620e6i) q^{22} +(266733. + 461996. i) q^{23} +(975557. - 1.68971e6i) q^{25} +1.71799e6 q^{26} -471682. q^{28} +(-2.64026e6 + 4.57306e6i) q^{29} +(1.67161e6 + 2.89532e6i) q^{31} +(582517. + 1.00895e6i) q^{32} +(-92287.1 + 159846. i) q^{34} +419056. q^{35} -2.03491e7 q^{37} +(6.91007e6 - 1.19686e7i) q^{38} +(-270917. - 469242. i) q^{40} +(-1.59074e7 - 2.75524e7i) q^{41} +(2.27763e6 - 3.94496e6i) q^{43} -2.78384e6 q^{44} +1.14606e7 q^{46} +(-9.00010e6 + 1.55886e7i) q^{47} +(-2.34929e7 - 4.06909e7i) q^{49} +(-2.09581e7 - 3.63005e7i) q^{50} +(-2.01806e6 + 3.49539e6i) q^{52} +6.95534e7 q^{53} +2.47324e6 q^{55} +(-5.64644e7 + 9.77992e7i) q^{56} +(5.67213e7 + 9.82441e7i) q^{58} +(3.24115e7 + 5.61383e7i) q^{59} +(-4.37764e7 + 7.58229e7i) q^{61} +7.18233e7 q^{62} +1.44711e8 q^{64} +(1.79290e6 - 3.10540e6i) q^{65} +(-8.37026e7 - 1.44977e8i) q^{67} +(-216813. - 375532. i) q^{68} +(4.50133e6 - 7.79654e6i) q^{70} +1.55996e8 q^{71} +3.05377e8 q^{73} +(-2.18582e8 + 3.78596e8i) q^{74} +(1.62341e7 + 2.81182e7i) q^{76} +(-2.57736e8 - 4.46412e8i) q^{77} +(1.79955e8 - 3.11692e8i) q^{79} -1.04816e7 q^{80} -6.83484e8 q^{82} +(2.31984e8 - 4.01807e8i) q^{83} +(192623. + 333633. i) q^{85} +(-4.89307e7 - 8.47505e7i) q^{86} +(-3.33250e8 + 5.77206e8i) q^{88} +2.70335e8 q^{89} -7.47352e8 q^{91} +(-1.34624e7 + 2.33175e7i) q^{92} +(1.93351e8 + 3.34894e8i) q^{94} +(-1.44228e7 - 2.49810e7i) q^{95} +(7.54926e7 - 1.30757e8i) q^{97} -1.00941e9 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10.7416	−	18.6050i	0.474717	−	0.822233i	−0.524864	−	0.851186i	$-0.675884\pi$
$2$	10.7416	−	18.6050i	0.474717	−	0.822233i	0.999581	+	0.0289528i	$0.00921724\pi$
$3$		0			0
$3$		0			0
$4$	25.2357	+	43.7094i	0.0492884	+	0.0853700i
$5$	−22.4201	−	38.8327i	−0.0160425	−	0.0277864i	0.857893	−	0.513829i	$-0.171773\pi$
$5$	−22.4201	−	38.8327i	−0.0160425	−	0.0277864i	−0.873935	+	0.486042i	$0.838440\pi$
$6$		0			0
$7$	−4672.78	+	8093.49i	−0.735587	+	1.27407i	0.218879	+	0.975752i	$0.429760\pi$
$7$	−4672.78	+	8093.49i	−0.735587	+	1.27407i	−0.954465	+	0.298321i	$0.903573\pi$
$8$	12083.7			1.04303
$9$		0			0
$10$	−963.310			−0.0304625
$11$	−27578.5	+	47767.3i	−0.567941	+	0.983702i	0.428829	+	0.903386i	$0.358926\pi$
$11$	−27578.5	+	47767.3i	−0.567941	+	0.983702i	−0.996769	+	0.0803165i	$0.974407\pi$
$12$		0			0
$13$	39984.4	+	69255.0i	0.388280	+	0.672521i	0.992218	−	0.124510i	$-0.0397359\pi$
$13$	39984.4	+	69255.0i	0.388280	+	0.672521i	−0.603938	+	0.797031i	$0.706403\pi$
$14$	100386.	+	173874.i	0.698390	+	1.20965i
$15$		0			0
$16$	116878.	−	202438.i	0.445853	−	0.772240i
$17$	−8591.55			−0.0249489			−0.0124745	−	0.999922i	$-0.503971\pi$
$17$	−8591.55			−0.0249489			−0.0124745	+	0.999922i	$0.503971\pi$
$18$		0			0
$19$	643299.			1.13246			0.566229	−	0.824248i	$-0.308402\pi$
$19$	643299.			1.13246			0.566229	+	0.824248i	$0.308402\pi$
$20$	1131.57	−	1959.94i	0.00158142	−	0.00273909i
$21$		0			0
$22$	592474.	+	1.02620e6i	0.539222	+	0.933960i
$23$	266733.	+	461996.i	0.198748	+	0.344241i	0.948123	−	0.317905i	$-0.102979\pi$
$23$	266733.	+	461996.i	0.198748	+	0.344241i	−0.749375	+	0.662146i	$0.769646\pi$
$24$		0			0
$25$	975557.	−	1.68971e6i	0.499485	−	0.865134i
$26$	1.71799e6			0.737292
$27$		0			0
$28$	−471682.			−0.145024
$29$	−2.64026e6	+	4.57306e6i	−0.693195	+	1.20065i	0.277590	+	0.960700i	$0.410464\pi$
$29$	−2.64026e6	+	4.57306e6i	−0.693195	+	1.20065i	−0.970785	+	0.239950i	$0.922869\pi$
$30$		0			0
$31$	1.67161e6	+	2.89532e6i	0.325094	+	0.563079i	0.981531	−	0.191302i	$-0.0612708\pi$
$31$	1.67161e6	+	2.89532e6i	0.325094	+	0.563079i	−0.656438	+	0.754380i	$0.727938\pi$
$32$	582517.	+	1.00895e6i	0.0982050	+	0.170096i
$33$		0			0
$34$	−92287.1	+	159846.i	−0.0118437	+	0.0205138i
$35$	419056.			0.0472026
$36$		0			0
$37$	−2.03491e7			−1.78500			−0.892500	−	0.451048i	$-0.851050\pi$
$37$	−2.03491e7			−1.78500			−0.892500	+	0.451048i	$0.851050\pi$
$38$	6.91007e6	−	1.19686e7i	0.537596	−	0.931144i
$39$		0			0
$40$	−270917.	−	469242.i	−0.0167327	−	0.0289819i
$41$	−1.59074e7	−	2.75524e7i	−0.879168	−	1.52276i	−0.852256	−	0.523125i	$-0.824766\pi$
$41$	−1.59074e7	−	2.75524e7i	−0.879168	−	1.52276i	−0.0269120	−	0.999638i	$-0.508567\pi$
$42$		0			0
$43$	2.27763e6	−	3.94496e6i	0.101595	−	0.175968i	−0.810747	−	0.585397i	$-0.800939\pi$
$43$	2.27763e6	−	3.94496e6i	0.101595	−	0.175968i	0.912342	+	0.409429i	$0.134272\pi$
$44$	−2.78384e6			−0.111972
$45$		0			0
$46$	1.14606e7			0.377395
$47$	−9.00010e6	+	1.55886e7i	−0.269034	+	0.465980i	−0.968613	−	0.248575i	$-0.920038\pi$
$47$	−9.00010e6	+	1.55886e7i	−0.269034	+	0.465980i	0.699579	+	0.714555i	$0.253371\pi$
$48$		0			0
$49$	−2.34929e7	−	4.06909e7i	−0.582175	−	1.00836i
$50$	−2.09581e7	−	3.63005e7i	−0.474228	−	0.821387i
$51$		0			0
$52$	−2.01806e6	+	3.49539e6i	−0.0382754	+	0.0662950i
$53$	6.95534e7			1.21081			0.605406	−	0.795917i	$-0.293011\pi$
$53$	6.95534e7			1.21081			0.605406	+	0.795917i	$0.293011\pi$
$54$		0			0
$55$	2.47324e6			0.0364447
$56$	−5.64644e7	+	9.77992e7i	−0.767235	+	1.32889i
$57$		0			0
$58$	5.67213e7	+	9.82441e7i	0.658143	+	1.13994i
$59$	3.24115e7	+	5.61383e7i	0.348229	+	0.603150i	0.985935	−	0.167130i	$-0.0534499\pi$
$59$	3.24115e7	+	5.61383e7i	0.348229	+	0.603150i	−0.637706	+	0.770280i	$0.720117\pi$
$60$		0			0
$61$	−4.37764e7	+	7.58229e7i	−0.404814	+	0.701159i	−0.994300	−	0.106620i	$-0.965997\pi$
$61$	−4.37764e7	+	7.58229e7i	−0.404814	+	0.701159i	0.589486	+	0.807779i	$0.299330\pi$
$62$	7.18233e7			0.617309
$63$		0			0
$64$	1.44711e8			1.07818
$65$	1.79290e6	−	3.10540e6i	0.0124580	−	0.0215778i
$66$		0			0
$67$	−8.37026e7	−	1.44977e8i	−0.507461	−	0.878948i	−0.999963	−	0.00863632i	$-0.997251\pi$
$67$	−8.37026e7	−	1.44977e8i	−0.507461	−	0.878948i	0.492502	−	0.870311i	$-0.336082\pi$
$68$	−216813.	−	375532.i	−0.00122969	−	0.00212989i
$69$		0			0
$70$	4.50133e6	−	7.79654e6i	0.0224078	−	0.0388115i
$71$	1.55996e8			0.728537			0.364268	−	0.931294i	$-0.381319\pi$
$71$	1.55996e8			0.728537			0.364268	+	0.931294i	$0.381319\pi$
$72$		0			0
$73$	3.05377e8			1.25859			0.629294	−	0.777168i	$-0.283344\pi$
$73$	3.05377e8			1.25859			0.629294	+	0.777168i	$0.283344\pi$
$74$	−2.18582e8	+	3.78596e8i	−0.847369	+	1.46769i
$75$		0			0
$76$	1.62341e7	+	2.81182e7i	0.0558170	+	0.0966778i
$77$	−2.57736e8	−	4.46412e8i	−0.835539	−	1.44720i
$78$		0			0
$79$	1.79955e8	−	3.11692e8i	0.519808	−	0.900333i	−0.479927	−	0.877308i	$-0.659337\pi$
$79$	1.79955e8	−	3.11692e8i	0.519808	−	0.900333i	0.999735	−	0.0230250i	$-0.00732973\pi$
$80$	−1.04816e7			−0.0286104
$81$		0			0
$82$	−6.83484e8			−1.66942
$83$	2.31984e8	−	4.01807e8i	0.536545	−	0.929323i	−0.462542	−	0.886597i	$-0.653063\pi$
$83$	2.31984e8	−	4.01807e8i	0.536545	−	0.929323i	0.999087	−	0.0427255i	$-0.0136041\pi$
$84$		0			0
$85$	192623.	+	333633.i	0.000400242	+	0.000693240i
$86$	−4.89307e7	−	8.47505e7i	−0.0964581	−	0.167070i
$87$		0			0
$88$	−3.33250e8	+	5.77206e8i	−0.592377	+	1.02603i
$89$	2.70335e8			0.456717			0.228358	−	0.973577i	$-0.426664\pi$
$89$	2.70335e8			0.456717			0.228358	+	0.973577i	$0.426664\pi$
$90$		0			0
$91$	−7.47352e8			−1.14246
$92$	−1.34624e7	+	2.33175e7i	−0.0195919	+	0.0339342i
$93$		0			0
$94$	1.93351e8	+	3.34894e8i	0.255430	+	0.442417i
$95$	−1.44228e7	−	2.49810e7i	−0.0181674	−	0.0314669i
$96$		0			0
$97$	7.54926e7	−	1.30757e8i	0.0865828	−	0.149966i	−0.819482	−	0.573105i	$-0.805739\pi$
$97$	7.54926e7	−	1.30757e8i	0.0865828	−	0.149966i	0.906065	+	0.423139i	$0.139072\pi$
$98$	−1.00941e9			−1.10547
$99$		0			0
$100$	9.84753e7			0.0984753
$101$	1.56102e8	−	2.70377e8i	0.149267	−	0.258538i	−0.781690	−	0.623667i	$-0.785642\pi$
$101$	1.56102e8	−	2.70377e8i	0.149267	−	0.258538i	0.930957	+	0.365130i	$0.118975\pi$
$102$		0			0
$103$	−4.29318e8	−	7.43601e8i	−0.375848	−	0.650987i	0.614606	−	0.788834i	$-0.289315\pi$
$103$	−4.29318e8	−	7.43601e8i	−0.375848	−	0.650987i	−0.990454	+	0.137847i	$0.955982\pi$
$104$	4.83159e8	+	8.36856e8i	0.404986	+	0.701457i
$105$		0			0
$106$	7.47115e8	−	1.29404e9i	0.574793	−	0.995570i
$107$	2.37971e8			0.175508			0.0877542	−	0.996142i	$-0.472031\pi$
$107$	2.37971e8			0.175508			0.0877542	+	0.996142i	$0.472031\pi$
$108$		0			0
$109$	7.89834e8			0.535940			0.267970	−	0.963427i	$-0.413647\pi$
$109$	7.89834e8			0.535940			0.267970	+	0.963427i	$0.413647\pi$
$110$	2.65666e7	−	4.60147e7i	0.0173009	−	0.0299661i
$111$		0			0
$112$	1.09229e9	+	1.89190e9i	0.655927	+	1.13610i
$113$	−2.63143e7	−	4.55777e7i	−0.0151823	−	0.0262966i	0.858334	−	0.513091i	$-0.171500\pi$
$113$	−2.63143e7	−	4.55777e7i	−0.0151823	−	0.0262966i	−0.873517	+	0.486794i	$0.838166\pi$
$114$		0			0
$115$	1.19604e7	−	2.07159e7i	0.00637681	−	0.0110450i
$116$	−2.66515e8			−0.136666
$117$		0			0
$118$	1.39260e9			0.661240
$119$	4.01464e7	−	6.95356e7i	0.0183521	−	0.0317867i
$120$		0			0
$121$	−3.42170e8	−	5.92656e8i	−0.145114	−	0.251344i
$122$	9.40458e8	+	1.62892e9i	0.384344	+	0.665703i
$123$		0			0
$124$	−8.43686e7	+	1.46131e8i	−0.0320467	+	0.0555065i
$125$	−1.75067e8			−0.0641369
$126$		0			0
$127$	1.15652e9			0.394489			0.197244	−	0.980354i	$-0.436801\pi$
$127$	1.15652e9			0.394489			0.197244	+	0.980354i	$0.436801\pi$
$128$	1.25618e9	−	2.17578e9i	0.413627	−	0.716423i
$129$		0			0
$130$	−3.85174e7	−	6.67140e7i	−0.0118280	−	0.0204867i
$131$	2.97421e9	+	5.15149e9i	0.882371	+	1.52831i	0.848697	+	0.528879i	$0.177388\pi$
$131$	2.97421e9	+	5.15149e9i	0.882371	+	1.52831i	0.0336741	+	0.999433i	$0.489279\pi$
$132$		0			0
$133$	−3.00599e9	+	5.20653e9i	−0.833020	+	1.44283i
$134$	−3.59640e9			−0.963600
$135$		0			0
$136$	−1.03818e8			−0.0260223
$137$	−7.47351e8	+	1.29445e9i	−0.181252	+	0.313937i	−0.942307	−	0.334750i	$-0.891348\pi$
$137$	−7.47351e8	+	1.29445e9i	−0.181252	+	0.313937i	0.761055	+	0.648687i	$0.224682\pi$
$138$		0			0
$139$	−2.56437e9	−	4.44162e9i	−0.582658	−	1.00919i	−0.995163	−	0.0982382i	$-0.968679\pi$
$139$	−2.56437e9	−	4.44162e9i	−0.582658	−	1.00919i	0.412505	−	0.910955i	$-0.364654\pi$
$140$	1.05751e7	+	1.83167e7i	0.00232654	+	0.00402968i
$141$		0			0
$142$	1.67565e9	−	2.90231e9i	0.345849	−	0.599027i
$143$	−4.41083e9			−0.882081
$144$		0			0
$145$	2.36779e8			0.0444823
$146$	3.28024e9	−	5.68154e9i	0.597472	−	1.03485i
$147$		0			0
$148$	−5.13523e8	−	8.89449e8i	−0.0879797	−	0.152385i
$149$	−5.20851e9	−	9.02140e9i	−0.865715	−	1.49946i	−0.866335	−	0.499463i	$-0.833531\pi$
$149$	−5.20851e9	−	9.02140e9i	−0.865715	−	1.49946i	0.000619610	−	1.00000i	$-0.499803\pi$
$150$		0			0
$151$	−4.59960e8	+	7.96674e8i	−0.0719985	+	0.124705i	−0.899777	−	0.436350i	$-0.856271\pi$
$151$	−4.59960e8	+	7.96674e8i	−0.0719985	+	0.124705i	0.827779	+	0.561055i	$0.189604\pi$
$152$	7.77343e9			1.18118
$153$		0			0
$154$	−1.10740e10			−1.58658
$155$	7.49554e7	−	1.29827e8i	0.0104306	−	0.0180664i
$156$		0			0
$157$	2.67288e9	+	4.62957e9i	0.351100	+	0.608123i	0.986443	−	0.164107i	$-0.0524743\pi$
$157$	2.67288e9	+	4.62957e9i	0.351100	+	0.608123i	−0.635342	+	0.772231i	$0.719141\pi$
$158$	−3.86602e9	−	6.69614e9i	−0.493523	−	0.854806i
$159$		0			0
$160$	2.61201e7	−	4.52414e7i	0.00315091	−	0.00545753i
$161$	−4.98554e9			−0.584785
$162$		0			0
$163$	6.82475e9			0.757256			0.378628	−	0.925549i	$-0.376396\pi$
$163$	6.82475e9			0.757256			0.378628	+	0.925549i	$0.376396\pi$
$164$	8.02867e8	−	1.39061e9i	0.0866655	−	0.150109i
$165$		0			0
$166$	−4.98376e9	−	8.63212e9i	−0.509413	−	0.882330i
$167$	2.90778e9	+	5.03642e9i	0.289293	+	0.501069i	0.973641	−	0.228086i	$-0.0732466\pi$
$167$	2.90778e9	+	5.03642e9i	0.289293	+	0.501069i	−0.684348	+	0.729155i	$0.739913\pi$
$168$		0			0
$169$	2.10475e9	−	3.64553e9i	0.198477	−	0.343772i
$170$	8.27633e6			0.000760007
$171$		0			0
$172$	2.29909e8			0.0200299
$173$	−6.15871e9	+	1.06672e10i	−0.522736	+	0.905405i	0.476914	+	0.878950i	$0.341755\pi$
$173$	−6.15871e9	+	1.06672e10i	−0.522736	+	0.905405i	−0.999650	+	0.0264553i	$0.991578\pi$
$174$		0			0
$175$	9.11712e9	+	1.57913e10i	0.734829	+	1.27276i
$176$	6.44662e9	+	1.11659e10i	0.506436	+	0.877173i
$177$		0			0
$178$	2.90383e9	−	5.02958e9i	0.216811	−	0.375528i
$179$	1.65764e10			1.20684			0.603422	−	0.797422i	$-0.293804\pi$
$179$	1.65764e10			1.20684			0.603422	+	0.797422i	$0.293804\pi$
$180$		0			0
$181$	−1.06374e9			−0.0736685			−0.0368343	−	0.999321i	$-0.511727\pi$
$181$	−1.06374e9			−0.0736685			−0.0368343	+	0.999321i	$0.511727\pi$
$182$	−8.02777e9	+	1.39045e10i	−0.542342	+	0.939365i
$183$		0			0
$184$	3.22312e9	+	5.58262e9i	0.207299	+	0.359052i
$185$	4.56229e8	+	7.90211e8i	0.0286358	+	0.0495987i
$186$		0			0
$187$	2.36942e8	−	4.10395e8i	0.0141695	−	0.0245423i
$188$	−9.08493e8			−0.0530410
$189$		0			0
$190$	−6.19696e8			−0.0344975
$191$	−6.49586e9	+	1.12512e10i	−0.353172	+	0.611712i	−0.986803	−	0.161923i	$-0.948230\pi$
$191$	−6.49586e9	+	1.12512e10i	−0.353172	+	0.611712i	0.633631	+	0.773635i	$0.281564\pi$
$192$		0			0
$193$	5.59579e9	+	9.69218e9i	0.290304	+	0.502821i	0.973882	−	0.227057i	$-0.0729102\pi$
$193$	5.59579e9	+	9.69218e9i	0.290304	+	0.502821i	−0.683577	+	0.729878i	$0.739577\pi$
$194$	−1.62182e9	−	2.80908e9i	−0.0822045	−	0.142382i
$195$		0			0
$196$	1.18572e9	−	2.05372e9i	0.0573890	−	0.0994006i
$197$	3.23317e10			1.52943			0.764716	−	0.644368i	$-0.222879\pi$
$197$	3.23317e10			1.52943			0.764716	+	0.644368i	$0.222879\pi$
$198$		0			0
$199$	7.46055e9			0.337234			0.168617	−	0.985682i	$-0.446070\pi$
$199$	7.46055e9			0.337234			0.168617	+	0.985682i	$0.446070\pi$
$200$	1.17883e10	−	2.04180e10i	0.520976	−	0.902356i
$201$		0			0
$202$	−3.35358e9	−	5.80857e9i	−0.141719	−	0.245464i
$203$	−2.46747e10	−	4.27378e10i	−1.01981	−	1.76636i
$204$		0			0
$205$	−7.13289e8	+	1.23545e9i	−0.0282081	+	0.0488578i
$206$	−1.84463e10			−0.713684
$207$		0			0
$208$	1.86931e10			0.692464
$209$	−1.77412e10	+	3.07287e10i	−0.643169	+	1.11400i
$210$		0			0
$211$	−1.84818e10	−	3.20113e10i	−0.641907	−	1.11182i	−0.985007	−	0.172516i	$-0.944810\pi$
$211$	−1.84818e10	−	3.20113e10i	−0.641907	−	1.11182i	0.343100	−	0.939299i	$-0.388523\pi$
$212$	1.75522e9	+	3.04014e9i	0.0596790	+	0.103367i
$213$		0			0
$214$	2.55620e9	−	4.42746e9i	0.0833167	−	0.144309i
$215$	−2.04258e8			−0.00651937
$216$		0			0
$217$	−3.12443e10			−0.956538
$218$	8.48408e9	−	1.46949e10i	0.254420	−	0.440668i
$219$		0			0
$220$	6.24139e7	+	1.08104e8i	0.00179630	+	0.00311129i
$221$	−3.43528e8	−	5.95008e8i	−0.00968717	−	0.0167787i
$222$		0			0
$223$	−8.77631e9	+	1.52010e10i	−0.237651	+	0.411624i	−0.960040	−	0.279863i	$-0.909711\pi$
$223$	−8.77631e9	+	1.52010e10i	−0.237651	+	0.411624i	0.722389	+	0.691487i	$0.243044\pi$
$224$	−1.08879e10			−0.288953
$225$		0			0
$226$	−1.13063e9			−0.0288292
$227$	1.76110e10	−	3.05031e10i	0.440217	−	0.762479i	−0.557488	−	0.830185i	$-0.688235\pi$
$227$	1.76110e10	−	3.05031e10i	0.440217	−	0.762479i	0.997705	+	0.0677064i	$0.0215681\pi$
$228$		0			0
$229$	−1.79995e10	−	3.11760e10i	−0.432514	−	0.749136i	0.564575	−	0.825382i	$-0.309040\pi$
$229$	−1.79995e10	−	3.11760e10i	−0.432514	−	0.749136i	−0.997089	+	0.0762454i	$0.975707\pi$
$230$	−2.56947e8	−	4.45045e8i	−0.00605436	−	0.0104865i
$231$		0			0
$232$	−3.19041e10	+	5.52595e10i	−0.723020	+	1.25231i
$233$	−1.22534e10			−0.272367			−0.136184	−	0.990684i	$-0.543484\pi$
$233$	−1.22534e10			−0.272367			−0.136184	+	0.990684i	$0.543484\pi$
$234$		0			0
$235$	8.07131e8			0.0172639
$236$	−1.63585e9	+	2.83337e9i	−0.0343273	+	0.0594565i
$237$		0			0
$238$	−8.62474e8	−	1.49385e9i	−0.0174241	−	0.0301794i
$239$	6.28307e9	+	1.08826e10i	0.124561	+	0.215745i	0.921561	−	0.388233i	$-0.126915\pi$
$239$	6.28307e9	+	1.08826e10i	0.124561	+	0.215745i	−0.797000	+	0.603979i	$0.793581\pi$
$240$		0			0
$241$	−5.74525e9	+	9.95107e9i	−0.109707	+	0.190017i	−0.915651	−	0.401973i	$-0.868324\pi$
$241$	−5.74525e9	+	9.95107e9i	−0.109707	+	0.190017i	0.805945	+	0.591991i	$0.201658\pi$
$242$	−1.47018e10			−0.275551
$243$		0			0
$244$	−4.41890e9			−0.0798105
$245$	−1.05342e9	+	1.82458e9i	−0.0186791	+	0.0323531i
$246$		0			0
$247$	2.57219e10	+	4.45517e10i	0.439711	+	0.761601i
$248$	2.01993e10	+	3.49862e10i	0.339081	+	0.587305i
$249$		0			0
$250$	−1.88050e9	+	3.25712e9i	−0.0304469	+	0.0527355i
$251$	4.00421e10			0.636774			0.318387	−	0.947961i	$-0.396859\pi$
$251$	4.00421e10			0.636774			0.318387	+	0.947961i	$0.396859\pi$
$252$		0			0
$253$	−2.94244e10			−0.451508
$254$	1.24228e10	−	2.15170e10i	0.187270	−	0.324362i
$255$		0			0
$256$	1.00592e10	+	1.74231e10i	0.146381	+	0.253539i
$257$	−2.20727e10	−	3.82311e10i	−0.315615	−	0.546661i	0.663953	−	0.747774i	$-0.268877\pi$
$257$	−2.20727e10	−	3.82311e10i	−0.315615	−	0.546661i	−0.979568	+	0.201113i	$0.935544\pi$
$258$		0			0
$259$	9.50869e10	−	1.64695e11i	1.31302	−	2.27422i
$260$	1.80980e8			0.00245613
$261$		0			0
$262$	1.27791e11			1.67551
$263$	−1.36277e10	+	2.36038e10i	−0.175639	+	0.304215i	−0.940382	−	0.340120i	$-0.889532\pi$
$263$	−1.36277e10	+	2.36038e10i	−0.175639	+	0.304215i	0.764743	+	0.644335i	$0.222866\pi$
$264$		0			0
$265$	−1.55939e9	−	2.70094e9i	−0.0194244	−	0.0336441i
$266$	6.45784e10	+	1.11853e11i	0.790897	+	1.36987i
$267$		0			0
$268$	4.22458e9	−	7.31719e9i	0.0500238	−	0.0866438i
$269$	−1.37243e11			−1.59810			−0.799051	−	0.601263i	$-0.794664\pi$
$269$	−1.37243e11			−1.59810			−0.799051	+	0.601263i	$0.794664\pi$
$270$		0			0
$271$	9.04089e9			0.101824			0.0509119	−	0.998703i	$-0.483787\pi$
$271$	9.04089e9			0.101824			0.0509119	+	0.998703i	$0.483787\pi$
$272$	−1.00416e9	+	1.73926e9i	−0.0111235	+	0.0192665i
$273$		0			0
$274$	1.60555e10	+	2.78090e10i	0.172086	+	0.298062i
$275$	5.38088e10	+	9.31995e10i	0.567356	+	0.982690i
$276$		0			0
$277$	−2.06072e10	+	3.56927e10i	−0.210310	+	0.364267i	−0.951811	−	0.306684i	$-0.900781\pi$
$277$	−2.06072e10	+	3.56927e10i	−0.210310	+	0.364267i	0.741502	+	0.670951i	$0.234114\pi$
$278$	−1.10182e11			−1.10639
$279$		0			0
$280$	5.06374e9			0.0492335
$281$	7.23643e10	−	1.25339e11i	0.692383	−	1.19924i	−0.278673	−	0.960386i	$-0.589894\pi$
$281$	7.23643e10	−	1.25339e11i	0.692383	−	1.19924i	0.971055	−	0.238856i	$-0.0767723\pi$
$282$		0			0
$283$	1.80193e10	+	3.12103e10i	0.166993	+	0.289240i	0.937361	−	0.348359i	$-0.113261\pi$
$283$	1.80193e10	+	3.12103e10i	0.166993	+	0.289240i	−0.770368	+	0.637599i	$0.779928\pi$
$284$	3.93667e9	+	6.81851e9i	0.0359084	+	0.0621952i
$285$		0			0
$286$	−4.73794e10	+	8.20636e10i	−0.418738	+	0.725276i
$287$	2.97327e11			2.58682
$288$		0			0
$289$	−1.18514e11			−0.999378
$290$	2.54339e9	−	4.40528e9i	0.0211165	−	0.0365748i
$291$		0			0
$292$	7.70639e9	+	1.33479e10i	0.0620337	+	0.107446i
$293$	−1.96451e10	−	3.40262e10i	−0.155722	−	0.269718i	0.777600	−	0.628759i	$-0.216437\pi$
$293$	−1.96451e10	−	3.40262e10i	−0.155722	−	0.269718i	−0.933322	+	0.359042i	$0.883104\pi$
$294$		0			0
$295$	1.45333e9	−	2.51725e9i	0.0111729	−	0.0193520i
$296$	−2.45893e11			−1.86180
$297$		0			0
$298$	−2.23791e11			−1.64388
$299$	−2.13303e10	+	3.69452e10i	−0.154340	+	0.267324i
$300$		0			0
$301$	2.12857e10	+	3.68679e10i	0.149464	+	0.258880i
$302$	9.88142e9	+	1.71151e10i	0.0683578	+	0.118399i
$303$		0			0
$304$	7.51873e10	−	1.30228e11i	0.504909	−	0.874529i
$305$	3.92588e9			0.0259769
$306$		0			0
$307$	6.02560e10			0.387148			0.193574	−	0.981086i	$-0.437992\pi$
$307$	6.02560e10			0.387148			0.193574	+	0.981086i	$0.437992\pi$
$308$	1.30083e10	−	2.25310e10i	0.0823648	−	0.142660i
$309$		0			0
$310$	−1.61028e9	−	2.78909e9i	−0.00990318	−	0.0171528i
$311$	−1.40942e11	−	2.44119e11i	−0.854319	−	1.47972i	−0.877276	−	0.479987i	$-0.840641\pi$
$311$	−1.40942e11	−	2.44119e11i	−0.854319	−	1.47972i	0.0229572	−	0.999736i	$-0.492692\pi$
$312$		0			0
$313$	−7.42999e10	+	1.28691e11i	−0.437561	+	0.757878i	−0.997501	−	0.0706552i	$-0.977491\pi$
$313$	−7.42999e10	+	1.28691e11i	−0.437561	+	0.757878i	0.559940	+	0.828533i	$0.310824\pi$
$314$	1.14844e11			0.666692
$315$		0			0
$316$	1.81652e10			0.102482
$317$	−7.01595e10	+	1.21520e11i	−0.390229	+	0.675897i	−0.992480	−	0.122411i	$-0.960938\pi$
$317$	−7.01595e10	+	1.21520e11i	−0.390229	+	0.675897i	0.602250	+	0.798307i	$0.294271\pi$
$318$		0			0
$319$	−1.45629e11	−	2.52236e11i	−0.787388	−	1.36380i
$320$	−3.24444e9	−	5.61953e9i	−0.0172968	−	0.0299589i
$321$		0			0
$322$	−5.35528e10	+	9.27561e10i	−0.277607	+	0.480829i
$323$	−5.52694e9			−0.0282536
$324$		0			0
$325$	1.56028e11			0.775761
$326$	7.33088e10	−	1.26975e11i	0.359482	−	0.622641i
$327$		0			0
$328$	−1.92220e11	−	3.32935e11i	−0.916994	−	1.58828i
$329$	−8.41109e10	−	1.45684e11i	−0.395795	−	0.685538i
$330$		0			0
$331$	5.96051e10	−	1.03239e11i	0.272934	−	0.472735i	−0.696678	−	0.717384i	$-0.745339\pi$
$331$	5.96051e10	−	1.03239e11i	0.272934	−	0.472735i	0.969612	+	0.244649i	$0.0786727\pi$
$332$	2.34170e10			0.105782
$333$		0			0
$334$	1.24937e11			0.549328
$335$	−3.75323e9	+	6.50079e9i	−0.0162819	+	0.0282010i
$336$		0			0
$337$	1.75620e11	+	3.04183e11i	0.741720	+	1.28470i	0.951711	+	0.306994i	$0.0993232\pi$
$337$	1.75620e11	+	3.04183e11i	0.741720	+	1.28470i	−0.209991	+	0.977703i	$0.567343\pi$
$338$	−4.52167e10	−	7.83177e10i	−0.188440	−	0.326388i
$339$		0			0
$340$	−9.72194e6	+	1.68389e7i	−3.94546e−5	+	6.83374e-5i
$341$	−1.84402e11			−0.738536
$342$		0			0
$343$	6.19811e10			0.241789
$344$	2.75221e10	−	4.76697e10i	0.105967	−	0.183540i
$345$		0			0
$346$	1.32309e11	+	2.29166e11i	0.496303	+	0.859622i
$347$	1.78653e11	+	3.09436e11i	0.661496	+	1.14574i	0.980223	+	0.197898i	$0.0634114\pi$
$347$	1.78653e11	+	3.09436e11i	0.661496	+	1.14574i	−0.318727	+	0.947847i	$0.603255\pi$
$348$		0			0
$349$	−2.15106e11	+	3.72574e11i	−0.776136	+	1.34431i	0.158017	+	0.987436i	$0.449490\pi$
$349$	−2.15106e11	+	3.72574e11i	−0.776136	+	1.34431i	−0.934154	+	0.356871i	$0.883843\pi$
$350$	3.91730e11			1.39534
$351$		0			0
$352$	−6.42597e10			−0.223099
$353$	−2.59498e11	+	4.49464e11i	−0.889505	+	1.54067i	−0.0490434	+	0.998797i	$0.515617\pi$
$353$	−2.59498e11	+	4.49464e11i	−0.889505	+	1.54067i	−0.840462	+	0.541871i	$0.817716\pi$
$354$		0			0
$355$	−3.49744e9	−	6.05775e9i	−0.0116875	−	0.0202434i
$356$	6.82207e9	+	1.18162e10i	0.0225108	+	0.0389899i
$357$		0			0
$358$	1.78057e11	−	3.08404e11i	0.572908	−	0.992307i
$359$	4.22565e11			1.34267			0.671334	−	0.741155i	$-0.265721\pi$
$359$	4.22565e11			1.34267			0.671334	+	0.741155i	$0.265721\pi$
$360$		0			0
$361$	9.11460e10			0.282459
$362$	−1.14263e10	+	1.97909e10i	−0.0349717	+	0.0605727i
$363$		0			0
$364$	−1.88599e10	−	3.26663e10i	−0.0563098	−	0.0975314i
$365$	−6.84657e9	−	1.18586e10i	−0.0201909	−	0.0349716i
$366$		0			0
$367$	9.37397e10	−	1.62362e11i	0.269728	−	0.467183i	−0.699064	−	0.715060i	$-0.746400\pi$
$367$	9.37397e10	−	1.62362e11i	0.269728	−	0.467183i	0.968792	+	0.247877i	$0.0797329\pi$
$368$	1.24701e11			0.354449
$369$		0			0
$370$	1.96025e10			0.0543756
$371$	−3.25007e11	+	5.62929e11i	−0.890657	+	1.54266i
$372$		0			0
$373$	−1.77249e10	−	3.07005e10i	−0.0474127	−	0.0821212i	0.841345	−	0.540498i	$-0.181764\pi$
$373$	−1.77249e10	−	3.07005e10i	−0.0474127	−	0.0821212i	−0.888758	+	0.458377i	$0.848431\pi$
$374$	−5.09027e9	−	8.81661e9i	−0.0134530	−	0.0233013i
$375$		0			0
$376$	−1.08754e11	+	1.88368e11i	−0.280609	+	0.486029i
$377$	−4.22277e11			−1.07662
$378$		0			0
$379$	2.58921e11			0.644602			0.322301	−	0.946637i	$-0.395544\pi$
$379$	2.58921e11			0.644602			0.322301	+	0.946637i	$0.395544\pi$
$380$	7.27938e8	−	1.26082e9i	0.00179089	−	0.00310191i
$381$		0			0
$382$	1.39552e11	+	2.41711e11i	0.335313	+	0.580779i
$383$	5.85055e10	+	1.01334e11i	0.138932	+	0.240637i	0.927093	−	0.374832i	$-0.122300\pi$
$383$	5.85055e10	+	1.01334e11i	0.138932	+	0.240637i	−0.788161	+	0.615470i	$0.788966\pi$
$384$		0			0
$385$	−1.15569e10	+	2.00172e10i	−0.0268083	+	0.0464333i
$386$	2.40431e11			0.551249
$387$		0			0
$388$	7.62042e9			0.0170701
$389$	2.08184e11	−	3.60585e11i	0.460971	−	0.798425i	−0.538039	−	0.842920i	$-0.680835\pi$
$389$	2.08184e11	−	3.60585e11i	0.460971	−	0.798425i	0.999010	+	0.0444950i	$0.0141679\pi$
$390$		0			0
$391$	−2.29165e9	−	3.96926e9i	−0.00495854	−	0.00858844i
$392$	−2.83881e11	−	4.91696e11i	−0.607224	−	1.05174i
$393$		0			0
$394$	3.47294e11	−	6.01531e11i	0.726047	−	1.25755i
$395$	−1.61384e10			−0.0333560
$396$		0			0
$397$	−4.63043e11			−0.935544			−0.467772	−	0.883849i	$-0.654943\pi$
$397$	−4.63043e11			−0.935544			−0.467772	+	0.883849i	$0.654943\pi$
$398$	8.01383e10	−	1.38804e11i	0.160091	−	0.277285i
$399$		0			0
$400$	−2.28042e11	−	3.94980e11i	−0.445394	−	0.771445i
$401$	−3.17986e11	−	5.50767e11i	−0.614127	−	1.06370i	−0.990537	−	0.137245i	$-0.956175\pi$
$401$	−3.17986e11	−	5.50767e11i	−0.614127	−	1.06370i	0.376411	−	0.926453i	$-0.377158\pi$
$402$		0			0
$403$	−1.33677e11	+	2.31535e11i	−0.252455	+	0.437265i
$404$	1.57574e10			0.0294285
$405$		0			0
$406$	−1.06018e12			−1.93648
$407$	5.61198e11	−	9.72023e11i	1.01377	−	1.75591i
$408$		0			0
$409$	6.14694e10	+	1.06468e11i	0.108619	+	0.188133i	0.915211	−	0.402975i	$-0.132024\pi$
$409$	6.14694e10	+	1.06468e11i	0.108619	+	0.188133i	−0.806592	+	0.591108i	$0.798691\pi$
$410$	1.53238e10	+	2.65415e10i	0.0267817	+	0.0463872i
$411$		0			0
$412$	2.16683e10	−	3.75305e10i	0.0370498	−	0.0641722i
$413$	−6.05806e11			−1.02461
$414$		0			0
$415$	−2.08043e10			−0.0344300
$416$	−4.65832e10	+	8.06844e10i	−0.0762622	+	0.132090i
$417$		0			0
$418$	3.81138e11	+	6.60151e11i	0.610646	+	1.05767i
$419$	4.29042e11	+	7.43123e11i	0.680044	+	1.17787i	0.974967	+	0.222350i	$0.0713726\pi$
$419$	4.29042e11	+	7.43123e11i	0.680044	+	1.17787i	−0.294923	+	0.955521i	$0.595294\pi$
$420$		0			0
$421$	−1.32546e11	+	2.29576e11i	−0.205635	+	0.356170i	−0.950335	−	0.311229i	$-0.899259\pi$
$421$	−1.32546e11	+	2.29576e11i	−0.205635	+	0.356170i	0.744700	+	0.667400i	$0.232593\pi$
$422$	−7.94095e11			−1.21890
$423$		0			0
$424$	8.40462e11			1.26291
$425$	−8.38155e9	+	1.45173e10i	−0.0124616	+	0.0215841i
$426$		0			0
$427$	−4.09115e11	−	7.08607e11i	−0.595552	−	1.03153i
$428$	6.00537e9	+	1.04016e10i	0.00865053	+	0.0149831i
$429$		0			0
$430$	−2.19406e9	+	3.80022e9i	−0.00309485	+	0.00536045i
$431$	2.69116e11			0.375658			0.187829	−	0.982202i	$-0.439855\pi$
$431$	2.69116e11			0.375658			0.187829	+	0.982202i	$0.439855\pi$
$432$		0			0
$433$	−1.07088e12			−1.46401			−0.732006	−	0.681298i	$-0.761416\pi$
$433$	−1.07088e12			−1.46401			−0.732006	+	0.681298i	$0.761416\pi$
$434$	−3.35614e11	+	5.81301e11i	−0.454085	+	0.786497i
$435$		0			0
$436$	1.99320e10	+	3.45232e10i	0.0264156	+	0.0457532i
$437$	1.71589e11	+	2.97201e11i	0.225073	+	0.389838i
$438$		0			0
$439$	2.56418e11	−	4.44129e11i	0.329502	−	0.570714i	−0.652911	−	0.757434i	$-0.726453\pi$
$439$	2.56418e11	−	4.44129e11i	0.329502	−	0.570714i	0.982413	+	0.186721i	$0.0597859\pi$
$440$	2.98859e10			0.0380128
$441$		0			0
$442$	−1.47602e10			−0.0183946
$443$	1.15112e11	−	1.99381e11i	0.142006	−	0.245961i	−0.786246	−	0.617913i	$-0.787978\pi$
$443$	1.15112e11	−	1.99381e11i	0.142006	−	0.245961i	0.928252	+	0.371953i	$0.121312\pi$
$444$		0			0
$445$	−6.06092e9	−	1.04978e10i	−0.00732687	−	0.0126905i
$446$	1.88543e11	+	3.26567e11i	0.225634	+	0.390809i
$447$		0			0
$448$	−6.76204e11	+	1.17122e12i	−0.793098	+	1.37369i
$449$	1.09130e12			1.26717			0.633586	−	0.773672i	$-0.281582\pi$
$449$	1.09130e12			1.26717			0.633586	+	0.773672i	$0.281582\pi$
$450$		0			0
$451$	1.75481e12			1.99726
$452$	1.32812e9	−	2.30037e9i	0.00149663	−	0.00259223i
$453$		0			0
$454$	−3.78340e11	−	6.55305e11i	−0.417957	−	0.723922i
$455$	1.67557e10	+	2.90217e10i	0.0183278	+	0.0317447i
$456$		0			0
$457$	4.57932e10	−	7.93162e10i	0.0491109	−	0.0850626i	−0.840425	−	0.541928i	$-0.817695\pi$
$457$	4.57932e10	−	7.93162e10i	0.0491109	−	0.0850626i	0.889536	+	0.456865i	$0.151028\pi$
$458$	−7.73373e11			−0.821286
$459$		0			0
$460$	1.20731e9			0.00125721
$461$	2.32909e11	−	4.03410e11i	0.240177	−	0.415999i	−0.720587	−	0.693364i	$-0.756128\pi$
$461$	2.32909e11	−	4.03410e11i	0.240177	−	0.415999i	0.960765	+	0.277365i	$0.0894611\pi$
$462$		0			0
$463$	5.34865e11	+	9.26413e11i	0.540916	+	0.936893i	0.998852	+	0.0479083i	$0.0152555\pi$
$463$	5.34865e11	+	9.26413e11i	0.540916	+	0.936893i	−0.457936	+	0.888985i	$0.651411\pi$
$464$	6.17175e11	+	1.06898e12i	0.618126	+	1.07063i
$465$		0			0
$466$	−1.31621e11	+	2.27975e11i	−0.129297	+	0.223950i
$467$	−1.30619e12			−1.27081			−0.635406	−	0.772178i	$-0.719167\pi$
$467$	−1.30619e12			−1.27081			−0.635406	+	0.772178i	$0.719167\pi$
$468$		0			0
$469$	1.56449e12			1.49313
$470$	8.66988e9	−	1.50167e10i	0.00819545	−	0.0141949i
$471$		0			0
$472$	3.91650e11	+	6.78358e11i	0.363211	+	0.629100i
$473$	1.25627e11	+	2.17592e11i	0.115400	+	0.199879i
$474$		0			0
$475$	6.27575e11	−	1.08699e12i	0.565646	−	0.979727i
$476$	4.05248e9			0.00361818
$477$		0			0
$478$	2.69961e11			0.236524
$479$	1.06821e12	−	1.85019e12i	0.927139	−	1.60585i	0.139055	−	0.990285i	$-0.455593\pi$
$479$	1.06821e12	−	1.85019e12i	0.927139	−	1.60585i	0.788084	−	0.615568i	$-0.211073\pi$
$480$		0			0
$481$	−8.13647e11	−	1.40928e12i	−0.693080	−	1.20045i
$482$	1.23427e11	+	2.13781e11i	0.104159	+	0.180409i
$483$		0			0
$484$	1.72698e10	−	2.99121e10i	0.0143048	−	0.0247767i
$485$	−6.77019e9			−0.00555601
$486$		0			0
$487$	−1.44314e12			−1.16259			−0.581297	−	0.813692i	$-0.697454\pi$
$487$	−1.44314e12			−1.16259			−0.581297	+	0.813692i	$0.697454\pi$
$488$	−5.28980e11	+	9.16221e11i	−0.422231	+	0.731326i
$489$		0			0
$490$	2.26309e10	+	3.91979e10i	0.0177345	+	0.0307171i
$491$	−3.86766e11	−	6.69898e11i	−0.300318	−	0.520166i	0.675890	−	0.737002i	$-0.263759\pi$
$491$	−3.86766e11	−	6.69898e11i	−0.300318	−	0.520166i	−0.976208	+	0.216837i	$0.930426\pi$
$492$		0			0
$493$	2.26839e10	−	3.92897e10i	0.0172945	−	0.0299549i
$494$	1.10518e12			0.834952
$495$		0			0
$496$	7.81498e11			0.579776
$497$	−7.28936e11	+	1.26255e12i	−0.535902	+	0.928210i
$498$		0			0
$499$	2.59942e11	+	4.50233e11i	0.187683	+	0.325076i	0.944477	−	0.328577i	$-0.106569\pi$
$499$	2.59942e11	+	4.50233e11i	0.187683	+	0.325076i	−0.756794	+	0.653653i	$0.773236\pi$
$500$	−4.41792e9	−	7.65206e9i	−0.00316120	−	0.00547537i
$501$		0			0
$502$	4.30117e11	−	7.44984e11i	0.302287	−	0.523577i
$503$	−1.32324e12			−0.921683			−0.460842	−	0.887482i	$-0.652452\pi$
$503$	−1.32324e12			−0.921683			−0.460842	+	0.887482i	$0.652452\pi$
$504$		0			0
$505$	−1.39993e10			−0.00957844
$506$	−3.16065e11	+	5.47441e11i	−0.214338	+	0.371245i
$507$		0			0
$508$	2.91854e10	+	5.05506e10i	0.0194437	+	0.0336775i
$509$	8.27751e11	+	1.43371e12i	0.546600	+	0.946739i	0.998504	+	0.0546727i	$0.0174115\pi$
$509$	8.27751e11	+	1.43371e12i	0.546600	+	0.946739i	−0.451904	+	0.892066i	$0.649255\pi$
$510$		0			0
$511$	−1.42696e12	+	2.47156e12i	−0.925800	+	1.60353i
$512$	1.71854e12			1.10521
$513$		0			0
$514$	−9.48387e11			−0.599310
$515$	−1.92507e10	+	3.33432e10i	−0.0120591	+	0.0208869i
$516$		0			0
$517$	−4.96418e11	−	8.59821e11i	−0.305591	−	0.529298i
$518$	−2.04277e12	−	3.53819e12i	−1.24663	−	2.15922i
$519$		0			0
$520$	2.16649e10	−	3.75247e10i	0.0129940	−	0.0225062i
$521$	−3.36913e11			−0.200331			−0.100165	−	0.994971i	$-0.531937\pi$
$521$	−3.36913e11			−0.200331			−0.100165	+	0.994971i	$0.531937\pi$
$522$		0			0
$523$	−2.63804e12			−1.54179			−0.770893	−	0.636964i	$-0.780190\pi$
$523$	−2.63804e12			−1.54179			−0.770893	+	0.636964i	$0.780190\pi$
$524$	−1.50112e11	+	2.60002e11i	−0.0869813	+	0.150656i
$525$		0			0
$526$	2.92766e11	+	5.07086e11i	0.166757	+	0.288832i
$527$	−1.43618e10	−	2.48753e10i	−0.00811073	−	0.0140482i
$528$		0			0
$529$	7.58283e11	−	1.31338e12i	0.420999	−	0.729191i
$530$	−6.70014e10			−0.0368844
$531$		0			0
$532$	−3.03433e11			−0.164233
$533$	1.27209e12	−	2.20333e12i	0.682727	−	1.18252i
$534$		0			0
$535$	−5.33533e9	−	9.24107e9i	−0.00281559	−	0.00487675i
$536$	−1.01144e12	−	1.75186e12i	−0.529294	−	0.916764i
$537$		0			0
$538$	−1.47421e12	+	2.55341e12i	−0.758646	+	1.31401i
$539$	2.59159e12			1.32256
$540$		0			0
$541$	−2.84689e12			−1.42884			−0.714419	−	0.699718i	$-0.753309\pi$
$541$	−2.84689e12			−1.42884			−0.714419	+	0.699718i	$0.753309\pi$
$542$	9.71137e10	−	1.68206e11i	0.0483375	−	0.0837229i
$543$		0			0
$544$	−5.00473e9	−	8.66844e9i	−0.00245011	−	0.00424371i
$545$	−1.77081e10	−	3.06714e10i	−0.00859781	−	0.0148918i
$546$		0			0
$547$	1.98785e12	−	3.44306e12i	0.949381	−	1.64438i	0.202649	−	0.979251i	$-0.435045\pi$
$547$	1.98785e12	−	3.44306e12i	0.949381	−	1.64438i	0.746732	−	0.665125i	$-0.231622\pi$
$548$	−7.54396e10			−0.0357344
$549$		0			0
$550$	2.31197e12			1.07733
$551$	−1.69848e12	+	2.94185e12i	−0.785014	+	1.35968i
$552$		0			0
$553$	1.68178e12	+	2.91293e12i	0.764727	+	1.32455i
$554$	4.42709e11	+	7.66794e11i	0.199675	+	0.345848i
$555$		0			0
$556$	1.29427e11	−	2.24174e11i	0.0574366	−	0.0994831i
$557$	−3.04474e12			−1.34030			−0.670151	−	0.742225i	$-0.733771\pi$
$557$	−3.04474e12			−1.34030			−0.670151	+	0.742225i	$0.733771\pi$
$558$		0			0
$559$	3.64278e11			0.157790
$560$	4.89782e10	−	8.48328e10i	0.0210454	−	0.0364517i
$561$		0			0
$562$	−1.55462e12	−	2.69268e12i	−0.657371	−	1.13860i
$563$	−1.20598e12	−	2.08882e12i	−0.505886	−	0.876220i	−0.999977	−	0.00680972i	$-0.997832\pi$
$563$	−1.20598e12	−	2.08882e12i	−0.505886	−	0.876220i	0.494091	−	0.869410i	$-0.335501\pi$
$564$		0			0
$565$	−1.17994e9	+	2.04371e9i	−0.000487125	+	0.000843725i
$566$	7.74224e11			0.317097
$567$		0			0
$568$	1.88501e12			0.759882
$569$	7.15985e11	−	1.24012e12i	0.286351	−	0.495974i	−0.686585	−	0.727050i	$-0.740891\pi$
$569$	7.15985e11	−	1.24012e12i	0.286351	−	0.495974i	0.972936	+	0.231075i	$0.0742243\pi$
$570$		0			0
$571$	−1.08784e10	−	1.88419e10i	−0.00428254	−	0.00741758i	0.863876	−	0.503704i	$-0.168030\pi$
$571$	−1.08784e10	−	1.88419e10i	−0.00428254	−	0.00741758i	−0.868159	+	0.496287i	$0.834697\pi$
$572$	−1.11310e11	−	1.92795e11i	−0.0434763	−	0.0753032i
$573$		0			0
$574$	3.19377e12	−	5.53177e12i	1.22800	−	2.12697i
$575$	1.04085e12			0.397086
$576$		0			0
$577$	2.44386e12			0.917879			0.458940	−	0.888467i	$-0.348229\pi$
$577$	2.44386e12			0.917879			0.458940	+	0.888467i	$0.348229\pi$
$578$	−1.27303e12	+	2.20496e12i	−0.474421	+	0.821721i
$579$		0			0
$580$	5.97527e9	+	1.03495e10i	0.00219246	+	0.00379745i
$581$	2.16802e12	+	3.75511e12i	0.789350	+	1.36719i
$582$		0			0
$583$	−1.91818e12	+	3.32238e12i	−0.687670	+	1.19108i
$584$	3.69008e12			1.31274
$585$		0			0
$586$	−8.44078e11			−0.295694
$587$	−2.07376e12	+	3.59186e12i	−0.720919	+	1.24867i	0.239712	+	0.970844i	$0.422947\pi$
$587$	−2.07376e12	+	3.59186e12i	−0.720919	+	1.24867i	−0.960632	+	0.277825i	$0.910386\pi$
$588$		0			0
$589$	1.07535e12	+	1.86256e12i	0.368155	+	0.637662i
$590$	−3.12223e10	−	5.40786e10i	−0.0106079	−	0.0183735i
$591$		0			0
$592$	−2.37836e12	+	4.11944e12i	−0.795847	+	1.37845i
$593$	1.12036e12			0.372059			0.186029	−	0.982544i	$-0.440438\pi$
$593$	1.12036e12			0.372059			0.186029	+	0.982544i	$0.440438\pi$
$594$		0			0
$595$	−3.60034e9			−0.00117765
$596$	2.62880e11	−	4.55322e11i	0.0853394	−	0.147812i
$597$		0			0
$598$	4.58244e11	+	7.93703e11i	0.146535	+	0.253806i
$599$	4.84352e10	+	8.38922e10i	0.0153724	+	0.0266257i	0.873609	−	0.486628i	$-0.161773\pi$
$599$	4.84352e10	+	8.38922e10i	0.0153724	+	0.0266257i	−0.858237	+	0.513254i	$0.828440\pi$
$600$		0			0
$601$	−4.21998e11	+	7.30923e11i	−0.131940	+	0.228526i	−0.924424	−	0.381366i	$-0.875454\pi$
$601$	−4.21998e11	+	7.30923e11i	−0.131940	+	0.228526i	0.792484	+	0.609892i	$0.208787\pi$
$602$	9.14569e11			0.283813
$603$		0			0
$604$	−4.64295e10			−0.0141948
$605$	−1.53430e10	+	2.65748e10i	−0.00465597	+	0.00806437i
$606$		0			0
$607$	1.56121e12	+	2.70409e12i	0.466779	+	0.808485i	0.999280	−	0.0379447i	$-0.0120811\pi$
$607$	1.56121e12	+	2.70409e12i	0.466779	+	0.808485i	−0.532501	+	0.846429i	$0.678748\pi$
$608$	3.74733e11	+	6.49056e11i	0.111213	+	0.192627i
$609$		0			0
$610$	4.21702e10	−	7.30410e10i	0.0123317	−	0.0213591i
$611$	−1.43945e12			−0.417842
$612$		0			0
$613$	5.54993e12			1.58751			0.793753	−	0.608240i	$-0.208124\pi$
$613$	5.54993e12			1.58751			0.793753	+	0.608240i	$0.208124\pi$
$614$	6.47246e11	−	1.12106e12i	0.183786	−	0.318326i
$615$		0			0
$616$	−3.11440e12	−	5.39431e12i	−0.871489	−	1.50946i
$617$	−1.37092e12	−	2.37450e12i	−0.380828	−	0.659613i	0.610353	−	0.792129i	$-0.291028\pi$
$617$	−1.37092e12	−	2.37450e12i	−0.380828	−	0.659613i	−0.991181	+	0.132517i	$0.957694\pi$
$618$		0			0
$619$	−1.41847e12	+	2.45686e12i	−0.388339	+	0.672624i	−0.992226	−	0.124446i	$-0.960285\pi$
$619$	−1.41847e12	+	2.45686e12i	−0.388339	+	0.672624i	0.603887	+	0.797070i	$0.293618\pi$
$620$	7.56619e9			0.00205643
$621$		0			0
$622$	−6.05579e12			−1.62224
$623$	−1.26321e12	+	2.18795e12i	−0.335955	+	0.581891i
$624$		0			0
$625$	−1.90146e12	−	3.29343e12i	−0.498456	−	0.863352i
$626$	1.59620e12	+	2.76470e12i	0.415435	+	0.719555i
$627$		0			0
$628$	−1.34904e11	+	2.33660e11i	−0.0346103	+	0.0599468i
$629$	1.74831e11			0.0445338
$630$		0			0
$631$	4.50954e12			1.13240			0.566200	−	0.824268i	$-0.308413\pi$
$631$	4.50954e12			1.13240			0.566200	+	0.824268i	$0.308413\pi$
$632$	2.17452e12	−	3.76639e12i	0.542172	−	0.939070i
$633$		0			0
$634$	1.50725e12	+	2.61064e12i	0.370496	+	0.641719i
$635$	−2.59291e10	−	4.49106e10i	−0.00632858	−	0.0109614i
$636$		0			0
$637$	1.87870e12	−	3.25400e12i	0.452095	−	0.783051i
$638$	−6.25715e12			−1.49514
$639$		0			0
$640$	−1.12655e11			−0.0265424
$641$	2.81867e12	−	4.88208e12i	0.659453	−	1.14221i	−0.321305	−	0.946976i	$-0.604121\pi$
$641$	2.81867e12	−	4.88208e12i	0.659453	−	1.14221i	0.980758	−	0.195230i	$-0.0625452\pi$
$642$		0			0
$643$	−2.24664e12	−	3.89130e12i	−0.518304	−	0.897730i	−0.999774	−	0.0212667i	$-0.993230\pi$
$643$	−2.24664e12	−	3.89130e12i	−0.518304	−	0.897730i	0.481469	−	0.876463i	$-0.340103\pi$
$644$	−1.25813e11	−	2.17915e11i	−0.0288231	−	0.0499231i
$645$		0			0
$646$	−5.93682e10	+	1.02829e11i	−0.0134124	+	0.0232310i
$647$	−2.52863e12			−0.567304			−0.283652	−	0.958927i	$-0.591546\pi$
$647$	−2.52863e12			−0.567304			−0.283652	+	0.958927i	$0.591546\pi$
$648$		0			0
$649$	−3.57543e12			−0.791093
$650$	1.67599e12	−	2.90291e12i	0.368267	−	0.637857i
$651$		0			0
$652$	1.72227e11	+	2.98306e11i	0.0373239	+	0.0646469i
$653$	4.79425e11	+	8.30389e11i	0.103184	+	0.178720i	0.912995	−	0.407971i	$-0.133764\pi$
$653$	4.79425e11	+	8.30389e11i	0.103184	+	0.178720i	−0.809811	+	0.586691i	$0.800430\pi$
$654$		0			0
$655$	1.33364e11	−	2.30993e11i	0.0283109	−	0.0490358i
$656$	−7.43688e12			−1.56792
$657$		0			0
$658$	−3.61395e12			−0.751562
$659$	6.89533e11	−	1.19431e12i	0.142420	−	0.246679i	−0.785987	−	0.618242i	$-0.787845\pi$
$659$	6.89533e11	−	1.19431e12i	0.142420	−	0.246679i	0.928407	+	0.371564i	$0.121178\pi$
$660$		0			0
$661$	5.80937e11	+	1.00621e12i	0.118365	+	0.205014i	0.919120	−	0.393978i	$-0.128901\pi$
$661$	5.80937e11	+	1.00621e12i	0.118365	+	0.205014i	−0.800755	+	0.598992i	$0.795568\pi$
$662$	−1.28051e12	−	2.21791e12i	−0.259132	−	0.448830i
$663$		0			0
$664$	2.80322e12	−	4.85532e12i	0.559630	−	0.969307i
$665$	2.69578e11			0.0534549
$666$		0			0
$667$	−2.81698e12			−0.551084
$668$	−1.46759e11	+	2.54195e11i	−0.0285175	+	0.0493938i
$669$		0			0
$670$	8.06315e10	+	1.39658e11i	0.0154585	+	0.0267750i
$671$	−2.41457e12	−	4.18216e12i	−0.459821	−	0.796433i
$672$		0			0
$673$	−1.13997e12	+	1.97449e12i	−0.214203	+	0.371010i	−0.953026	−	0.302889i	$-0.902049\pi$
$673$	−1.13997e12	+	1.97449e12i	−0.214203	+	0.371010i	0.738823	+	0.673900i	$0.235382\pi$
$674$	7.54578e12			1.40843
$675$		0			0
$676$	2.12459e11			0.0391304
$677$	1.06948e12	−	1.85240e12i	0.195670	−	0.338911i	−0.751450	−	0.659790i	$-0.770645\pi$
$677$	1.06948e12	−	1.85240e12i	0.195670	−	0.338911i	0.947120	+	0.320879i	$0.103978\pi$
$678$		0			0
$679$	7.05520e11	+	1.22200e12i	0.127378	+	0.220626i
$680$	2.32760e9	+	4.03152e9i	0.000417463	+	0.000723067i
$681$		0			0
$682$	−1.98078e12	+	3.43081e12i	−0.350595	+	0.607249i
$683$	−4.62393e11			−0.0813051			−0.0406526	−	0.999173i	$-0.512944\pi$
$683$	−4.62393e11			−0.0813051			−0.0406526	+	0.999173i	$0.512944\pi$
$684$		0			0
$685$	6.70226e10			0.0116309
$686$	6.65777e11	−	1.15316e12i	0.114781	−	0.198807i
$687$		0			0
$688$	−5.32407e11	−	9.22156e11i	−0.0905932	−	0.156912i
$689$	2.78105e12	+	4.81692e12i	0.470134	+	0.814297i
$690$		0			0
$691$	−4.60548e12	+	7.97693e12i	−0.768465	+	1.33102i	0.169930	+	0.985456i	$0.445646\pi$
$691$	−4.60548e12	+	7.97693e12i	−0.768465	+	1.33102i	−0.938395	+	0.345564i	$0.887688\pi$
$692$	−6.21676e11			−0.103059
$693$		0			0
$694$	7.67607e12			1.25609
$695$	−1.14987e11	+	1.99163e11i	−0.0186946	+	0.0323800i
$696$		0			0
$697$	1.36669e11	+	2.36718e11i	0.0219343	+	0.0379913i
$698$	4.62117e12	+	8.00410e12i	0.736890	+	1.27633i
$699$		0			0
$700$	−4.60153e11	+	7.97008e11i	−0.0724371	+	0.125465i
$701$	−1.30164e12			−0.203592			−0.101796	−	0.994805i	$-0.532459\pi$
$701$	−1.30164e12			−0.203592			−0.101796	+	0.994805i	$0.532459\pi$
$702$		0			0
$703$	−1.30906e13			−2.02143
$704$	−3.99092e12	+	6.91248e12i	−0.612345	+	1.06061i
$705$		0			0
$706$	5.57486e12	+	9.65594e12i	0.844525	+	1.46276i
$707$	1.45886e12	+	2.52682e12i	0.219597	+	0.380354i
$708$		0			0
$709$	6.16559e12	−	1.06791e13i	0.916361	−	1.58718i	0.111465	−	0.993768i	$-0.464446\pi$
$709$	6.16559e12	−	1.06791e13i	0.916361	−	1.58718i	0.804896	−	0.593416i	$-0.202221\pi$
$710$	−1.50273e11			−0.0221931
$711$		0			0
$712$	3.26664e12			0.476367
$713$	−8.91751e11	+	1.54456e12i	−0.129223	+	0.223821i
$714$		0			0
$715$	9.88911e10	+	1.71284e11i	0.0141508	+	0.0245099i
$716$	4.18316e11	+	7.24544e11i	0.0594833	+	0.103028i
$717$		0			0
$718$	4.53903e12	−	7.86184e12i	0.637387	−	1.10399i
$719$	1.63948e12			0.228784			0.114392	−	0.993436i	$-0.463508\pi$
$719$	1.63948e12			0.228784			0.114392	+	0.993436i	$0.463508\pi$
$720$		0			0
$721$	8.02443e12			1.10587
$722$	9.79055e11	−	1.69577e12i	0.134088	−	0.232247i
$723$		0			0
$724$	−2.68442e10	−	4.64955e10i	−0.00363100	−	0.00628908i
$725$	5.15145e12	+	8.92257e12i	0.692482	+	1.19941i
$726$		0			0
$727$	3.01670e12	−	5.22507e12i	0.400522	−	0.693725i	−0.593267	−	0.805006i	$-0.702162\pi$
$727$	3.01670e12	−	5.22507e12i	0.400522	−	0.693725i	0.993789	+	0.111281i	$0.0354953\pi$
$728$	−9.03078e12			−1.19161
$729$		0			0
$730$	−2.94173e11			−0.0383398
$731$	−1.95683e10	+	3.38934e10i	−0.00253470	+	0.00439022i
$732$		0			0
$733$	−4.71833e11	−	8.17239e11i	−0.0603699	−	0.104564i	0.834261	−	0.551370i	$-0.185895\pi$
$733$	−4.71833e11	−	8.17239e11i	−0.0603699	−	0.104564i	−0.894631	+	0.446806i	$0.852561\pi$
$734$	−2.01383e12	−	3.48806e12i	−0.256089	−	0.443559i
$735$		0			0
$736$	−3.10754e11	+	5.38241e11i	−0.0390361	+	0.0676124i
$737$	9.23356e12			1.15283
$738$		0			0
$739$	2.35026e12			0.289879			0.144939	−	0.989441i	$-0.453701\pi$
$739$	2.35026e12			0.289879			0.144939	+	0.989441i	$0.453701\pi$
$740$	−2.30264e10	+	3.98830e10i	−0.00282283	+	0.00488928i
$741$		0			0
$742$	6.98220e12	+	1.20935e13i	0.845619	+	1.46466i
$743$	−5.30074e12	−	9.18116e12i	−0.638098	−	1.10522i	−0.985850	−	0.167631i	$-0.946388\pi$
$743$	−5.30074e12	−	9.18116e12i	−0.638098	−	1.10522i	0.347752	−	0.937587i	$-0.386945\pi$
$744$		0			0
$745$	−2.33550e11	+	4.04521e11i	−0.0277765	+	0.0481102i
$746$	−7.61577e11			−0.0900304
$747$		0			0
$748$	2.39175e10			0.00279357
$749$	−1.11199e12	+	1.92602e12i	−0.129102	+	0.223611i
$750$		0			0
$751$	−7.14006e12	−	1.23669e13i	−0.819072	−	1.41867i	−0.906367	−	0.422492i	$-0.861156\pi$
$751$	−7.14006e12	−	1.23669e13i	−0.819072	−	1.41867i	0.0872949	−	0.996183i	$-0.472178\pi$
$752$	2.10382e12	+	3.64392e12i	0.239899	+	0.415517i
$753$		0			0
$754$	−4.53593e12	+	7.85646e12i	−0.511088	+	0.885230i
$755$	4.12493e10			0.00462014
$756$		0			0
$757$	2.98242e12			0.330094			0.165047	−	0.986286i	$-0.447222\pi$
$757$	2.98242e12			0.330094			0.165047	+	0.986286i	$0.447222\pi$
$758$	2.78123e12	−	4.81724e12i	0.306003	−	0.530013i
$759$		0			0
$760$	−1.74281e11	−	3.01863e11i	−0.0189491	−	0.0328208i
$761$	−5.75362e12	−	9.96555e12i	−0.621885	−	1.07714i	−0.989134	−	0.147014i	$-0.953034\pi$
$761$	−5.75362e12	−	9.96555e12i	−0.621885	−	1.07714i	0.367250	−	0.930122i	$-0.380299\pi$
$762$		0			0
$763$	−3.69072e12	+	6.39251e12i	−0.394230	+	0.682827i
$764$	−6.55709e11			−0.0696291
$765$		0			0
$766$	2.51377e12			0.263813
$767$	−2.59190e12	+	4.48931e12i	−0.270421	+	0.468382i
$768$		0			0
$769$	−7.67871e12	−	1.32999e13i	−0.791807	−	1.37145i	−0.924847	−	0.380340i	$-0.875807\pi$
$769$	−7.67871e12	−	1.32999e13i	−0.791807	−	1.37145i	0.133040	−	0.991111i	$-0.457526\pi$
$770$	2.48280e11	+	4.30033e11i	0.0254526	+	0.0440853i
$771$		0			0
$772$	−2.82427e11	+	4.89177e11i	−0.0286172	+	0.0495665i
$773$	1.55153e13			1.56298			0.781491	−	0.623917i	$-0.214460\pi$
$773$	1.55153e13			1.56298			0.781491	+	0.623917i	$0.214460\pi$
$774$		0			0
$775$	6.52302e12			0.649518
$776$	9.12229e11	−	1.58003e12i	0.0903080	−	0.156418i
$777$		0			0
$778$	−4.47246e12	−	7.74652e12i	−0.437661	−	0.758051i
$779$	−1.02332e13	−	1.77244e13i	−0.995620	−	1.72446i
$780$		0			0
$781$	−4.30214e12	+	7.45152e12i	−0.413766	+	0.716664i
$782$	−9.84642e10			−0.00941560
$783$		0			0
$784$	−1.09832e13			−1.03826
$785$	1.19852e11	−	2.07590e11i	0.0112650	−	0.0195116i
$786$		0			0
$787$	7.46149e12	+	1.29237e13i	0.693329	+	1.20088i	0.970741	+	0.240130i	$0.0771901\pi$
$787$	7.46149e12	+	1.29237e13i	0.693329	+	1.20088i	−0.277412	+	0.960751i	$0.589477\pi$
$788$	8.15911e11	+	1.41320e12i	0.0753832	+	0.130568i
$789$		0			0
$790$	−1.73353e11	+	3.00256e11i	−0.0158347	+	0.0274264i
$791$	4.91843e11			0.0446717
$792$		0			0
$793$	−7.00149e12			−0.628725
$794$	−4.97383e12	+	8.61493e12i	−0.444118	+	0.769236i
$795$		0			0
$796$	1.88272e11	+	3.26096e11i	0.0166217	+	0.0287897i
$797$	−4.03047e11	−	6.98098e11i	−0.0353829	−	0.0612849i	0.847792	−	0.530329i	$-0.177932\pi$
$797$	−4.03047e11	−	6.98098e11i	−0.0353829	−	0.0612849i	−0.883175	+	0.469044i	$0.844598\pi$
$798$		0			0
$799$	7.73248e10	−	1.33931e11i	0.00671210	−	0.0116257i
$800$	2.27312e12			0.196208
$801$		0			0
$802$	−1.36627e13			−1.16614
$803$	−8.42183e12	+	1.45870e13i	−0.714803	+	1.23808i
$804$		0			0
$805$	1.11776e11	+	1.93602e11i	0.00938140	+	0.0162491i
$806$	2.87181e12	+	4.97412e12i	0.239689	+	0.415154i
$807$		0			0
$808$	1.88629e12	−	3.26715e12i	0.155689	−	0.269661i
$809$	−1.37229e13			−1.12636			−0.563179	−	0.826335i	$-0.690422\pi$
$809$	−1.37229e13			−1.12636			−0.563179	+	0.826335i	$0.690422\pi$
$810$		0			0
$811$	6.34290e12			0.514866			0.257433	−	0.966296i	$-0.417123\pi$
$811$	6.34290e12			0.514866			0.257433	+	0.966296i	$0.417123\pi$
$812$	1.24536e12	−	2.15703e12i	0.100530	−	0.174122i
$813$		0			0
$814$	−1.20563e13	−	2.08822e13i	−0.962511	−	1.66712i
$815$	−1.53011e11	−	2.65023e11i	−0.0121483	−	0.0210414i
$816$		0			0
$817$	1.46519e12	−	2.53779e12i	0.115052	−	0.199277i
$818$	2.64112e12			0.206252
$819$		0			0
$820$	−7.20013e10			−0.00556132
$821$	6.19717e12	−	1.07338e13i	0.476046	−	0.824536i	−0.523577	−	0.851978i	$-0.675403\pi$
$821$	6.19717e12	−	1.07338e13i	0.476046	−	0.824536i	0.999623	+	0.0274419i	$0.00873614\pi$
$822$		0			0
$823$	5.70558e12	+	9.88236e12i	0.433511	+	0.750864i	0.997173	−	0.0751421i	$-0.0239410\pi$
$823$	5.70558e12	+	9.88236e12i	0.433511	+	0.750864i	−0.563661	+	0.826006i	$0.690608\pi$
$824$	−5.18775e12	−	8.98545e12i	−0.392019	−	0.678996i
$825$		0			0
$826$	−6.50733e12	+	1.12710e13i	−0.486399	+	0.842468i
$827$	1.74662e13			1.29844			0.649222	−	0.760599i	$-0.275095\pi$
$827$	1.74662e13			1.29844			0.649222	+	0.760599i	$0.275095\pi$
$828$		0			0
$829$	−4.32053e12			−0.317718			−0.158859	−	0.987301i	$-0.550781\pi$
$829$	−4.32053e12			−0.317718			−0.158859	+	0.987301i	$0.550781\pi$
$830$	−2.23472e11	+	3.87065e11i	−0.0163445	+	0.0283095i
$831$		0			0
$832$	5.78620e12	+	1.00220e13i	0.418638	+	0.725102i
$833$	2.01840e11	+	3.49598e11i	0.0145246	+	0.0251574i
$834$		0			0
$835$	1.30385e11	−	2.25834e11i	0.00928194	−	0.0160768i
$836$	−1.79084e12			−0.126803
$837$		0			0
$838$	1.84344e13			1.29131
$839$	1.97625e12	−	3.42296e12i	0.137693	−	0.238491i	−0.788930	−	0.614483i	$-0.789365\pi$
$839$	1.97625e12	−	3.42296e12i	0.137693	−	0.238491i	0.926623	+	0.375992i	$0.122698\pi$
$840$		0			0
$841$	−6.68837e12	−	1.15846e13i	−0.461040	−	0.798545i
$842$	2.84751e12	+	4.93204e12i	0.195237	+	0.338160i
$843$		0			0
$844$	9.32798e11	−	1.61565e12i	0.0632771	−	0.109599i
$845$	−1.88754e11			−0.0127362
$846$		0			0
$847$	6.39554e12			0.426975
$848$	8.12924e12	−	1.40802e13i	0.539844	−	0.935037i
$849$		0			0
$850$	1.80063e11	+	3.11878e11i	0.0118315	+	0.0204927i
$851$	−5.42779e12	−	9.40121e12i	−0.354765	−	0.614470i
$852$		0			0
$853$	7.49575e12	−	1.29830e13i	0.484780	−	0.839663i	−0.515067	−	0.857150i	$-0.672233\pi$
$853$	7.49575e12	−	1.29830e13i	0.484780	−	0.839663i	0.999847	+	0.0174864i	$0.00556639\pi$
$854$	−1.75782e13			−1.13087
$855$		0			0
$856$	2.87557e12			0.183060
$857$	−7.05290e12	+	1.22160e13i	−0.446636	+	0.773597i	−0.998165	−	0.0605596i	$-0.980711\pi$
$857$	−7.05290e12	+	1.22160e13i	−0.446636	+	0.773597i	0.551528	+	0.834156i	$0.314045\pi$
$858$		0			0
$859$	1.12478e13	+	1.94818e13i	0.704853	+	1.22084i	0.966744	+	0.255744i	$0.0823205\pi$
$859$	1.12478e13	+	1.94818e13i	0.704853	+	1.22084i	−0.261891	+	0.965097i	$0.584346\pi$
$860$	−5.15458e9	−	8.92800e9i	−0.000321329	−	0.000556559i
$861$		0			0
$862$	2.89074e12	−	5.00691e12i	0.178331	−	0.308878i
$863$	1.15572e13			0.709259			0.354629	−	0.935007i	$-0.384607\pi$
$863$	1.15572e13			0.709259			0.354629	+	0.935007i	$0.384607\pi$
$864$		0			0
$865$	5.52315e11			0.0335439
$866$	−1.15030e13	+	1.99237e13i	−0.694991	+	1.20376i
$867$		0			0
$868$	−7.88471e11	−	1.36567e12i	−0.0471462	−	0.0816596i
$869$	9.92578e12	+	1.71920e13i	0.590440	+	1.02267i
$870$		0			0
$871$	6.69359e12	−	1.15936e13i	0.394074	−	0.682556i
$872$	9.54411e12			0.558999
$873$		0			0
$874$	7.37258e12			0.427384
$875$	8.18047e11	−	1.41690e12i	0.0471783	−	0.0817151i
$876$		0			0
$877$	9.73218e12	+	1.68566e13i	0.555536	+	0.962216i	0.997862	+	0.0653615i	$0.0208201\pi$
$877$	9.73218e12	+	1.68566e13i	0.555536	+	0.962216i	−0.442326	+	0.896854i	$0.645847\pi$
$878$	−5.50868e12	−	9.54131e12i	−0.312840	−	0.541855i
$879$		0			0
$880$	2.89067e11	−	5.00679e11i	0.0162490	−	0.0281441i
$881$	8.46829e12			0.473592			0.236796	−	0.971559i	$-0.423903\pi$
$881$	8.46829e12			0.473592			0.236796	+	0.971559i	$0.423903\pi$
$882$		0			0
$883$	−1.77577e13			−0.983025			−0.491513	−	0.870870i	$-0.663556\pi$
$883$	−1.77577e13			−0.983025			−0.491513	+	0.870870i	$0.663556\pi$
$884$	1.73383e10	−	3.00308e10i	0.000954930	−	0.00165399i
$885$		0			0
$886$	−2.47298e12	−	4.28334e12i	−0.134825	−	0.233523i
$887$	1.23119e13	+	2.13248e13i	0.667833	+	1.15672i	0.978509	+	0.206205i	$0.0661112\pi$
$887$	1.23119e13	+	2.13248e13i	0.667833	+	1.15672i	−0.310676	+	0.950516i	$0.600555\pi$
$888$		0			0
$889$	−5.40414e12	+	9.36024e12i	−0.290181	+	0.502608i
$890$	−2.60416e11			−0.0139127
$891$		0			0
$892$	−8.85903e11			−0.0468538
$893$	−5.78975e12	+	1.00281e13i	−0.304669	+	0.527703i
$894$		0			0
$895$	−3.71643e11	−	6.43705e11i	−0.0193608	−	0.0335338i
$896$	1.17397e13	+	2.03338e13i	0.608517	+	1.05398i
$897$		0			0
$898$	1.17223e13	−	2.03037e13i	0.601548	−	1.04191i
$899$	−1.76540e13			−0.901414
$900$		0			0
$901$	−5.97571e11			−0.0302084
$902$	1.88494e13	−	3.26482e13i	0.948133	−	1.64221i
$903$		0			0
$904$	−3.17974e11	−	5.50747e11i	−0.0158356	−	0.0274280i
$905$	2.38491e10	+	4.13079e10i	0.00118183	+	0.00204698i
$906$		0			0
$907$	1.13193e12	−	1.96056e12i	0.0555376	−	0.0961939i	−0.836920	−	0.547325i	$-0.815646\pi$
$907$	1.13193e12	−	1.96056e12i	0.0555376	−	0.0961939i	0.892458	+	0.451131i	$0.148979\pi$
$908$	1.77770e12			0.0867904
$909$		0			0
$910$	7.19932e11			0.0348021
$911$	−1.22110e13	+	2.11500e13i	−0.587377	+	1.01737i	0.407197	+	0.913340i	$0.366506\pi$
$911$	−1.22110e13	+	2.11500e13i	−0.587377	+	1.01737i	−0.994574	+	0.104027i	$0.966827\pi$
$912$		0			0
$913$	1.27955e13	+	2.21625e13i	0.609451	+	1.05560i
$914$	−9.83785e11	−	1.70397e12i	−0.0466275	−	0.0807613i
$915$		0			0
$916$	9.08457e11	−	1.57349e12i	0.0426358	−	0.0738474i
$917$	−5.55914e13			−2.59624
$918$		0			0
$919$	−9.43274e12			−0.436233			−0.218116	−	0.975923i	$-0.569991\pi$
$919$	−9.43274e12			−0.436233			−0.218116	+	0.975923i	$0.569991\pi$
$920$	1.44525e11	−	2.50325e11i	0.00665118	−	0.0115202i
$921$		0			0
$922$	−5.00363e12	−	8.66655e12i	−0.228032	−	0.394964i
$923$	6.23741e12	+	1.08035e13i	0.282877	+	0.489957i
$924$		0			0
$925$	−1.98517e13	+	3.43842e13i	−0.891581	+	1.54426i
$926$	2.29812e13			1.02713
$927$		0			0
$928$	−6.15199e12			−0.272301
$929$	1.38200e13	−	2.39370e13i	0.608749	−	1.05438i	−0.382698	−	0.923874i	$-0.625005\pi$
$929$	1.38200e13	−	2.39370e13i	0.608749	−	1.05438i	0.991447	−	0.130511i	$-0.0416618\pi$
$930$		0			0
$931$	−1.51129e13	−	2.61764e13i	−0.659289	−	1.14192i
$932$	−3.09223e11	−	5.35589e11i	−0.0134246	−	0.0232520i
$933$		0			0
$934$	−1.40306e13	+	2.43017e13i	−0.603276	+	1.04490i
$935$	−2.12490e10			−0.000909256
$936$		0			0
$937$	−2.24945e13			−0.953341			−0.476671	−	0.879082i	$-0.658157\pi$
$937$	−2.24945e13			−0.953341			−0.476671	+	0.879082i	$0.658157\pi$
$938$	1.68052e13	−	2.91074e13i	0.708811	−	1.22770i
$939$		0			0
$940$	2.03685e10	+	3.52792e10i	0.000850909	+	0.00147382i
$941$	−1.64166e12	−	2.84344e12i	−0.0682542	−	0.118220i	0.829879	−	0.557944i	$-0.188410\pi$
$941$	−1.64166e12	−	2.84344e12i	−0.0682542	−	0.118220i	−0.898133	+	0.439724i	$0.855076\pi$
$942$		0			0
$943$	8.48607e12	−	1.46983e13i	0.349465	−	0.605291i
$944$	1.51527e13			0.621035
$945$		0			0
$946$	5.39774e12			0.219130
$947$	2.32562e13	−	4.02809e13i	0.939645	−	1.62751i	0.173511	−	0.984832i	$-0.444489\pi$
$947$	2.32562e13	−	4.02809e13i	0.939645	−	1.62751i	0.766134	−	0.642681i	$-0.222178\pi$
$948$		0			0
$949$	1.22103e13	+	2.11489e13i	0.488685	+	0.846427i
$950$	−1.34823e13	−	2.33521e13i	−0.537043	−	0.930185i
$951$		0			0
$952$	4.85117e11	−	8.40247e11i	0.0191417	−	0.0331544i
$953$	−3.34707e13			−1.31446			−0.657229	−	0.753691i	$-0.728271\pi$
$953$	−3.34707e13			−1.31446			−0.657229	+	0.753691i	$0.728271\pi$
$954$		0			0
$955$	5.82550e11			0.0226630
$956$	−3.17115e11	+	5.49258e11i	−0.0122788	+	0.0212675i
$957$		0			0
$958$	−2.29485e13	−	3.97480e13i	−0.880257	−	1.52465i
$959$	−6.98441e12	−	1.20974e13i	−0.266653	−	0.461856i
$960$		0			0
$961$	7.63122e12	−	1.32177e13i	0.288628	−	0.499919i
$962$	−3.49595e13			−1.31607
$963$		0			0
$964$	−5.79941e11			−0.0216290
$965$	2.50916e11	−	4.34599e11i	0.00931440	−	0.0161330i
$966$		0			0
$967$	−2.49162e13	−	4.31562e13i	−0.916354	−	1.58717i	−0.804907	−	0.593401i	$-0.797785\pi$
$967$	−2.49162e13	−	4.31562e13i	−0.916354	−	1.58717i	−0.111447	−	0.993770i	$-0.535548\pi$
$968$	−4.13468e12	−	7.16148e12i	−0.151357	−	0.262158i
$969$		0			0
$970$	−7.27227e10	+	1.25959e11i	−0.00263753	+	0.00456834i
$971$	2.07241e13			0.748149			0.374075	−	0.927399i	$-0.377960\pi$
$971$	2.07241e13			0.748149			0.374075	+	0.927399i	$0.377960\pi$
$972$		0			0
$973$	4.79309e13			1.71438
$974$	−1.55016e13	+	2.68496e13i	−0.551902	+	0.955923i
$975$		0			0
$976$	1.02330e13	+	1.77240e13i	0.360975	+	0.625227i
$977$	−3.97242e11	−	6.88044e11i	−0.0139486	−	0.0241596i	0.858967	−	0.512031i	$-0.171107\pi$
$977$	−3.97242e11	−	6.88044e11i	−0.0139486	−	0.0241596i	−0.872915	+	0.487872i	$0.837773\pi$
$978$		0			0
$979$	−7.45542e12	+	1.29132e13i	−0.259388	+	0.449273i
$980$	−1.06335e11			−0.00368265
$981$		0			0
$982$	−1.66179e13			−0.570263
$983$	−2.66645e13	+	4.61842e13i	−0.910840	+	1.57762i	−0.0979604	+	0.995190i	$0.531232\pi$
$983$	−2.66645e13	+	4.61842e13i	−0.910840	+	1.57762i	−0.812880	+	0.582431i	$0.802101\pi$
$984$		0			0
$985$	−7.24878e11	−	1.25553e12i	−0.0245359	−	0.0424974i
$986$	−4.87324e11	−	8.44070e11i	−0.0164199	−	0.0284402i
$987$		0			0
$988$	−1.29822e12	+	2.24858e12i	−0.0433453	+	0.0750762i
$989$	2.43007e12			0.0807674
$990$		0			0
$991$	3.10566e13			1.02288			0.511438	−	0.859320i	$-0.329113\pi$
$991$	3.10566e13			1.02288			0.511438	+	0.859320i	$0.329113\pi$
$992$	−1.94749e12	+	3.37315e12i	−0.0638517	+	0.110594i
$993$		0			0
$994$	1.56599e13	+	2.71237e13i	0.508803	+	0.881273i
$995$	−1.67266e11	−	2.89713e11i	−0.00541008	−	0.00937053i
$996$		0			0
$997$	1.24632e13	−	2.15868e13i	0.399484	−	0.691927i	−0.594178	−	0.804334i	$-0.702523\pi$
$997$	1.24632e13	−	2.15868e13i	0.399484	−	0.691927i	0.993662	+	0.112406i	$0.0358558\pi$
$998$	1.11688e13			0.356384
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.10.c.a.19.6		16
3.2	odd	2		9.10.c.a.7.3	yes	16
9.2	odd	6		81.10.a.c.1.6		8
9.4	even	3	inner	27.10.c.a.10.6		16
9.5	odd	6		9.10.c.a.4.3	✓	16
9.7	even	3		81.10.a.d.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.10.c.a.4.3	✓	16	9.5	odd	6
9.10.c.a.7.3	yes	16	3.2	odd	2
27.10.c.a.10.6		16	9.4	even	3	inner
27.10.c.a.19.6		16	1.1	even	1	trivial
81.10.a.c.1.6		8	9.2	odd	6
81.10.a.d.1.3		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)

\(f(q)\)	\(=\)	\(q+(10.7416 - 18.6050i) q^{2} +(25.2357 + 43.7094i) q^{4} +(-22.4201 - 38.8327i) q^{5} +(-4672.78 + 8093.49i) q^{7} +12083.7 q^{8} +O(q^{10})\)	\(q+(10.7416 - 18.6050i) q^{2} +(25.2357 + 43.7094i) q^{4} +(-22.4201 - 38.8327i) q^{5} +(-4672.78 + 8093.49i) q^{7} +12083.7 q^{8} -963.310 q^{10} +(-27578.5 + 47767.3i) q^{11} +(39984.4 + 69255.0i) q^{13} +(100386. + 173874. i) q^{14} +(116878. - 202438. i) q^{16} -8591.55 q^{17} +643299. q^{19} +(1131.57 - 1959.94i) q^{20} +(592474. + 1.02620e6i) q^{22} +(266733. + 461996. i) q^{23} +(975557. - 1.68971e6i) q^{25} +1.71799e6 q^{26} -471682. q^{28} +(-2.64026e6 + 4.57306e6i) q^{29} +(1.67161e6 + 2.89532e6i) q^{31} +(582517. + 1.00895e6i) q^{32} +(-92287.1 + 159846. i) q^{34} +419056. q^{35} -2.03491e7 q^{37} +(6.91007e6 - 1.19686e7i) q^{38} +(-270917. - 469242. i) q^{40} +(-1.59074e7 - 2.75524e7i) q^{41} +(2.27763e6 - 3.94496e6i) q^{43} -2.78384e6 q^{44} +1.14606e7 q^{46} +(-9.00010e6 + 1.55886e7i) q^{47} +(-2.34929e7 - 4.06909e7i) q^{49} +(-2.09581e7 - 3.63005e7i) q^{50} +(-2.01806e6 + 3.49539e6i) q^{52} +6.95534e7 q^{53} +2.47324e6 q^{55} +(-5.64644e7 + 9.77992e7i) q^{56} +(5.67213e7 + 9.82441e7i) q^{58} +(3.24115e7 + 5.61383e7i) q^{59} +(-4.37764e7 + 7.58229e7i) q^{61} +7.18233e7 q^{62} +1.44711e8 q^{64} +(1.79290e6 - 3.10540e6i) q^{65} +(-8.37026e7 - 1.44977e8i) q^{67} +(-216813. - 375532. i) q^{68} +(4.50133e6 - 7.79654e6i) q^{70} +1.55996e8 q^{71} +3.05377e8 q^{73} +(-2.18582e8 + 3.78596e8i) q^{74} +(1.62341e7 + 2.81182e7i) q^{76} +(-2.57736e8 - 4.46412e8i) q^{77} +(1.79955e8 - 3.11692e8i) q^{79} -1.04816e7 q^{80} -6.83484e8 q^{82} +(2.31984e8 - 4.01807e8i) q^{83} +(192623. + 333633. i) q^{85} +(-4.89307e7 - 8.47505e7i) q^{86} +(-3.33250e8 + 5.77206e8i) q^{88} +2.70335e8 q^{89} -7.47352e8 q^{91} +(-1.34624e7 + 2.33175e7i) q^{92} +(1.93351e8 + 3.34894e8i) q^{94} +(-1.44228e7 - 2.49810e7i) q^{95} +(7.54926e7 - 1.30757e8i) q^{97} -1.00941e9 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 15 q^{2} - 1793 q^{4} - 453 q^{5} - 343 q^{7} + 14478 q^{8}+O(q^{10}) \) 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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