LMFDB - Embedded newform 81.12.c.b.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,12,Mod(28,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("81.28");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	81.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:	$62.2357976253$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			28.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	81.28
Dual form			81.12.c.b.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-12.0000 - 20.7846i) q^{2} +(736.000 - 1274.79i) q^{4} +(2415.00 - 4182.90i) q^{5} +(8372.00 + 14500.7i) q^{7} -84480.0 q^{8} +O(q^{10})$	\(q+(-12.0000 - 20.7846i) q^{2} +(736.000 - 1274.79i) q^{4} +(2415.00 - 4182.90i) q^{5} +(8372.00 + 14500.7i) q^{7} -84480.0 q^{8} -115920. q^{10} +(267306. + 462988. i) q^{11} +(288869. - 500336. i) q^{13} +(200928. - 348018. i) q^{14} +(-493568. - 854885. i) q^{16} +6.90593e6 q^{17} +1.06614e7 q^{19} +(-3.55488e6 - 6.15723e6i) q^{20} +(6.41534e6 - 1.11117e7i) q^{22} +(9.32164e6 - 1.61455e7i) q^{23} +(1.27496e7 + 2.20830e7i) q^{25} -1.38657e7 q^{26} +2.46472e7 q^{28} +(6.42033e7 + 1.11203e8i) q^{29} +(2.64216e7 - 4.57635e7i) q^{31} +(-9.83532e7 + 1.70353e8i) q^{32} +(-8.28712e7 - 1.43537e8i) q^{34} +8.08735e7 q^{35} -1.82213e8 q^{37} +(-1.27937e8 - 2.21593e8i) q^{38} +(-2.04019e8 + 3.53372e8i) q^{40} +(1.54060e8 - 2.66840e8i) q^{41} +(8.56285e6 + 1.48313e7i) q^{43} +7.86949e8 q^{44} -4.47439e8 q^{46} +(1.34367e9 + 2.32731e9i) q^{47} +(8.48483e8 - 1.46961e9i) q^{49} +(3.05991e8 - 5.29991e8i) q^{50} +(-4.25215e8 - 7.36494e8i) q^{52} +1.59606e9 q^{53} +2.58218e9 q^{55} +(-7.07267e8 - 1.22502e9i) q^{56} +(1.54088e9 - 2.66888e9i) q^{58} +(-2.59460e9 + 4.49398e9i) q^{59} +(-3.47824e9 - 6.02449e9i) q^{61} -1.26824e9 q^{62} +2.69930e9 q^{64} +(-1.39524e9 - 2.41662e9i) q^{65} +(7.74091e9 - 1.34077e10i) q^{67} +(5.08277e9 - 8.80361e9i) q^{68} +(-9.70482e8 - 1.68092e9i) q^{70} -9.79149e9 q^{71} +1.46379e9 q^{73} +(2.18656e9 + 3.78723e9i) q^{74} +(7.84681e9 - 1.35911e10i) q^{76} +(-4.47577e9 + 7.75226e9i) q^{77} +(-1.90584e10 - 3.30102e10i) q^{79} -4.76787e9 q^{80} -7.39489e9 q^{82} +(-1.46675e10 - 2.54049e10i) q^{83} +(1.66778e10 - 2.88868e10i) q^{85} +(2.05508e8 - 3.55951e8i) q^{86} +(-2.25820e10 - 3.91132e10i) q^{88} +2.49929e10 q^{89} +9.67365e9 q^{91} +(-1.37214e10 - 2.37662e10i) q^{92} +(3.22482e10 - 5.58555e10i) q^{94} +(2.57473e10 - 4.45957e10i) q^{95} +(-3.75068e10 - 6.49637e10i) q^{97} -4.07272e10 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 24 q^{2} + 1472 q^{4} + 4830 q^{5} + 16744 q^{7} - 168960 q^{8}+O(q^{10}) $ 2 * q - 24 * q^2 + 1472 * q^4 + 4830 * q^5 + 16744 * q^7 - 168960 * q^8	\( 2 q - 24 q^{2} + 1472 q^{4} + 4830 q^{5} + 16744 q^{7} - 168960 q^{8} - 231840 q^{10} + 534612 q^{11} + 577738 q^{13} + 401856 q^{14} - 987136 q^{16} + 13811868 q^{17} + 21322840 q^{19} - 7109760 q^{20} + 12830688 q^{22} + 18643272 q^{23} + 25499225 q^{25} - 27731424 q^{26} + 49294336 q^{28} + 128406630 q^{29} + 52843168 q^{31} - 196706304 q^{32} - 165742416 q^{34} + 161747040 q^{35} - 364426628 q^{37} - 255874080 q^{38} - 408038400 q^{40} + 308120442 q^{41} + 17125708 q^{43} + 1573897728 q^{44} - 894877056 q^{46} + 2687348496 q^{47} + 1696965207 q^{49} + 611981400 q^{50} - 850430336 q^{52} + 3192111396 q^{53} + 5164351920 q^{55} - 1414533120 q^{56} + 3081759120 q^{58} - 5189203740 q^{59} - 6956478662 q^{61} - 2536472064 q^{62} + 5398593536 q^{64} - 2790474540 q^{65} + 15481826884 q^{67} + 10165534848 q^{68} - 1940964480 q^{70} - 19582970544 q^{71} + 2927582644 q^{73} + 4373119536 q^{74} + 15693610240 q^{76} - 8951543328 q^{77} - 38116845680 q^{79} - 9535733760 q^{80} - 14789781216 q^{82} - 29335099668 q^{83} + 33355661220 q^{85} + 411016992 q^{86} - 45164021760 q^{88} + 49985834220 q^{89} + 19347290144 q^{91} - 27442896384 q^{92} + 64496363904 q^{94} + 51494658600 q^{95} - 75013568546 q^{97} - 81454329936 q^{98}+O(q^{100}) \) 2 * q - 24 * q^2 + 1472 * q^4 + 4830 * q^5 + 16744 * q^7 - 168960 * q^8 - 231840 * q^10 + 534612 * q^11 + 577738 * q^13 + 401856 * q^14 - 987136 * q^16 + 13811868 * q^17 + 21322840 * q^19 - 7109760 * q^20 + 12830688 * q^22 + 18643272 * q^23 + 25499225 * q^25 - 27731424 * q^26 + 49294336 * q^28 + 128406630 * q^29 + 52843168 * q^31 - 196706304 * q^32 - 165742416 * q^34 + 161747040 * q^35 - 364426628 * q^37 - 255874080 * q^38 - 408038400 * q^40 + 308120442 * q^41 + 17125708 * q^43 + 1573897728 * q^44 - 894877056 * q^46 + 2687348496 * q^47 + 1696965207 * q^49 + 611981400 * q^50 - 850430336 * q^52 + 3192111396 * q^53 + 5164351920 * q^55 - 1414533120 * q^56 + 3081759120 * q^58 - 5189203740 * q^59 - 6956478662 * q^61 - 2536472064 * q^62 + 5398593536 * q^64 - 2790474540 * q^65 + 15481826884 * q^67 + 10165534848 * q^68 - 1940964480 * q^70 - 19582970544 * q^71 + 2927582644 * q^73 + 4373119536 * q^74 + 15693610240 * q^76 - 8951543328 * q^77 - 38116845680 * q^79 - 9535733760 * q^80 - 14789781216 * q^82 - 29335099668 * q^83 + 33355661220 * q^85 + 411016992 * q^86 - 45164021760 * q^88 + 49985834220 * q^89 + 19347290144 * q^91 - 27442896384 * q^92 + 64496363904 * q^94 + 51494658600 * q^95 - 75013568546 * q^97 - 81454329936 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−12.0000	−	20.7846i	−0.265165	−	0.459279i	0.702442	−	0.711741i	$-0.252093\pi$
$2$	−12.0000	−	20.7846i	−0.265165	−	0.459279i	−0.967607	+	0.252462i	$0.918760\pi$
$3$		0			0
$3$		0			0
$4$	736.000	−	1274.79i	0.359375	−	0.622456i
$5$	2415.00	−	4182.90i	0.345607	−	0.598608i	−0.639857	−	0.768494i	$-0.721006\pi$
$5$	2415.00	−	4182.90i	0.345607	−	0.598608i	0.985464	+	0.169886i	$0.0543398\pi$
$6$		0			0
$7$	8372.00	+	14500.7i	0.188274	+	0.326100i	0.944675	−	0.328008i	$-0.106377\pi$
$7$	8372.00	+	14500.7i	0.188274	+	0.326100i	−0.756401	+	0.654108i	$0.773044\pi$
$8$	−84480.0			−0.911505
$9$		0			0
$10$	−115920.			−0.366571
$11$	267306.	+	462988.i	0.500436	+	0.866781i	1.00000		0.000504048i	$0.000160443\pi$
$11$	267306.	+	462988.i	0.500436	+	0.866781i	−0.499563	+	0.866277i	$0.666506\pi$
$12$		0			0
$13$	288869.	−	500336.i	0.215781	−	0.373743i	−0.737733	−	0.675092i	$-0.764104\pi$
$13$	288869.	−	500336.i	0.215781	−	0.373743i	0.953514	+	0.301349i	$0.0974371\pi$
$14$	200928.	−	348018.i	0.0998473	−	0.172941i
$15$		0			0
$16$	−493568.	−	854885.i	−0.117676	−	0.203820i
$17$	6.90593e6			1.17965			0.589825	−	0.807531i	$-0.299197\pi$
$17$	6.90593e6			1.17965			0.589825	+	0.807531i	$0.299197\pi$
$18$		0			0
$19$	1.06614e7			0.987803			0.493901	−	0.869518i	$-0.335570\pi$
$19$	1.06614e7			0.987803			0.493901	+	0.869518i	$0.335570\pi$
$20$	−3.55488e6	−	6.15723e6i	−0.248405	−	0.430250i
$21$		0			0
$22$	6.41534e6	−	1.11117e7i	0.265397	−	0.459680i
$23$	9.32164e6	−	1.61455e7i	0.301988	−	0.523058i	−0.674599	−	0.738185i	$-0.735683\pi$
$23$	9.32164e6	−	1.61455e7i	0.301988	−	0.523058i	0.976586	+	0.215127i	$0.0690166\pi$
$24$		0			0
$25$	1.27496e7	+	2.20830e7i	0.261112	+	0.452259i
$26$	−1.38657e7			−0.228870
$27$		0			0
$28$	2.46472e7			0.270644
$29$	6.42033e7	+	1.11203e8i	0.581257	+	1.00677i	0.995331	+	0.0965237i	$0.0307724\pi$
$29$	6.42033e7	+	1.11203e8i	0.581257	+	1.00677i	−0.414073	+	0.910244i	$0.635894\pi$
$30$		0			0
$31$	2.64216e7	−	4.57635e7i	0.165756	−	0.287098i	−0.771167	−	0.636632i	$-0.780327\pi$
$31$	2.64216e7	−	4.57635e7i	0.165756	−	0.287098i	0.936924	+	0.349534i	$0.113660\pi$
$32$	−9.83532e7	+	1.70353e8i	−0.518159	+	0.897478i
$33$		0			0
$34$	−8.28712e7	−	1.43537e8i	−0.312802	−	0.541789i
$35$	8.08735e7			0.260275
$36$		0			0
$37$	−1.82213e8			−0.431987			−0.215993	−	0.976395i	$-0.569299\pi$
$37$	−1.82213e8			−0.431987			−0.215993	+	0.976395i	$0.569299\pi$
$38$	−1.27937e8	−	2.21593e8i	−0.261931	−	0.453677i
$39$		0			0
$40$	−2.04019e8	+	3.53372e8i	−0.315022	+	0.545634i
$41$	1.54060e8	−	2.66840e8i	0.207673	−	0.359700i	−0.743308	−	0.668949i	$-0.766744\pi$
$41$	1.54060e8	−	2.66840e8i	0.207673	−	0.359700i	0.950981	+	0.309249i	$0.100078\pi$
$42$		0			0
$43$	8.56285e6	+	1.48313e7i	0.00888264	+	0.0153852i	0.870433	−	0.492288i	$-0.163839\pi$
$43$	8.56285e6	+	1.48313e7i	0.00888264	+	0.0153852i	−0.861550	+	0.507673i	$0.830506\pi$
$44$	7.86949e8			0.719377
$45$		0			0
$46$	−4.47439e8			−0.320306
$47$	1.34367e9	+	2.32731e9i	0.854586	+	1.48019i	0.877029	+	0.480438i	$0.159522\pi$
$47$	1.34367e9	+	2.32731e9i	0.854586	+	1.48019i	−0.0224426	+	0.999748i	$0.507144\pi$
$48$		0			0
$49$	8.48483e8	−	1.46961e9i	0.429106	−	0.743233i
$50$	3.05991e8	−	5.29991e8i	0.138476	−	0.239847i
$51$		0			0
$52$	−4.25215e8	−	7.36494e8i	−0.155092	−	0.268628i
$53$	1.59606e9			0.524241			0.262120	−	0.965035i	$-0.415578\pi$
$53$	1.59606e9			0.524241			0.262120	+	0.965035i	$0.415578\pi$
$54$		0			0
$55$	2.58218e9			0.691817
$56$	−7.07267e8	−	1.22502e9i	−0.171613	−	0.297242i
$57$		0			0
$58$	1.54088e9	−	2.66888e9i	0.308258	−	0.533919i
$59$	−2.59460e9	+	4.49398e9i	−0.472481	+	0.818362i	−0.999504	−	0.0314895i	$-0.989975\pi$
$59$	−2.59460e9	+	4.49398e9i	−0.472481	+	0.818362i	0.527023	+	0.849851i	$0.323308\pi$
$60$		0			0
$61$	−3.47824e9	−	6.02449e9i	−0.527285	−	0.913284i	−0.999494	−	0.0317979i	$-0.989877\pi$
$61$	−3.47824e9	−	6.02449e9i	−0.527285	−	0.913284i	0.472209	−	0.881486i	$-0.343457\pi$
$62$	−1.26824e9			−0.175811
$63$		0			0
$64$	2.69930e9			0.314240
$65$	−1.39524e9	−	2.41662e9i	−0.149150	−	0.258336i
$66$		0			0
$67$	7.74091e9	−	1.34077e10i	0.700456	−	1.21323i	−0.267851	−	0.963460i	$-0.586313\pi$
$67$	7.74091e9	−	1.34077e10i	0.700456	−	1.21323i	0.968307	−	0.249765i	$-0.0803533\pi$
$68$	5.08277e9	−	8.80361e9i	0.423937	−	0.734280i
$69$		0			0
$70$	−9.70482e8	−	1.68092e9i	−0.0690158	−	0.119539i
$71$	−9.79149e9			−0.644062			−0.322031	−	0.946729i	$-0.604366\pi$
$71$	−9.79149e9			−0.644062			−0.322031	+	0.946729i	$0.604366\pi$
$72$		0			0
$73$	1.46379e9			0.0826425			0.0413212	−	0.999146i	$-0.486843\pi$
$73$	1.46379e9			0.0826425			0.0413212	+	0.999146i	$0.486843\pi$
$74$	2.18656e9	+	3.78723e9i	0.114548	+	0.198403i
$75$		0			0
$76$	7.84681e9	−	1.35911e10i	0.354992	−	0.614864i
$77$	−4.47577e9	+	7.75226e9i	−0.188438	+	0.326385i
$78$		0			0
$79$	−1.90584e10	−	3.30102e10i	−0.696848	−	1.20698i	−0.969554	−	0.244878i	$-0.921252\pi$
$79$	−1.90584e10	−	3.30102e10i	−0.696848	−	1.20698i	0.272706	−	0.962097i	$-0.412081\pi$
$80$	−4.76787e9			−0.162678
$81$		0			0
$82$	−7.39489e9			−0.220270
$83$	−1.46675e10	−	2.54049e10i	−0.408722	−	0.707927i	0.586025	−	0.810293i	$-0.300692\pi$
$83$	−1.46675e10	−	2.54049e10i	−0.408722	−	0.707927i	−0.994747	+	0.102366i	$0.967359\pi$
$84$		0			0
$85$	1.66778e10	−	2.88868e10i	0.407695	−	0.706149i
$86$	2.05508e8	−	3.55951e8i	0.00471073	−	0.00815923i
$87$		0			0
$88$	−2.25820e10	−	3.91132e10i	−0.456150	−	0.790075i
$89$	2.49929e10			0.474430			0.237215	−	0.971457i	$-0.423765\pi$
$89$	2.49929e10			0.474430			0.237215	+	0.971457i	$0.423765\pi$
$90$		0			0
$91$	9.67365e9			0.162503
$92$	−1.37214e10	−	2.37662e10i	−0.217054	−	0.375948i
$93$		0			0
$94$	3.22482e10	−	5.58555e10i	0.453213	−	0.784987i
$95$	2.57473e10	−	4.45957e10i	0.341391	−	0.591307i
$96$		0			0
$97$	−3.75068e10	−	6.49637e10i	−0.443471	−	0.768114i	0.554473	−	0.832202i	$-0.312920\pi$
$97$	−3.75068e10	−	6.49637e10i	−0.443471	−	0.768114i	−0.997944	+	0.0640871i	$0.979586\pi$
$98$	−4.07272e10			−0.455136
$99$		0			0
$100$	3.75349e10			0.375349
$101$	4.08715e10	+	7.07915e10i	0.386948	+	0.670214i	0.992037	−	0.125944i	$-0.0401959\pi$
$101$	4.08715e10	+	7.07915e10i	0.386948	+	0.670214i	−0.605089	+	0.796158i	$0.706863\pi$
$102$		0			0
$103$	1.12878e11	−	1.95510e11i	0.959407	−	1.66174i	0.235463	−	0.971883i	$-0.424339\pi$
$103$	1.12878e11	−	1.95510e11i	0.959407	−	1.66174i	0.723944	−	0.689858i	$-0.242327\pi$
$104$	−2.44037e10	+	4.22684e10i	−0.196685	+	0.340669i
$105$		0			0
$106$	−1.91527e10	−	3.31734e10i	−0.139010	−	0.240773i
$107$	−9.02413e10			−0.622006			−0.311003	−	0.950409i	$-0.600665\pi$
$107$	−9.02413e10			−0.622006			−0.311003	+	0.950409i	$0.600665\pi$
$108$		0			0
$109$	7.34827e10			0.457445			0.228723	−	0.973492i	$-0.426545\pi$
$109$	7.34827e10			0.457445			0.228723	+	0.973492i	$0.426545\pi$
$110$	−3.09861e10	−	5.36695e10i	−0.183446	−	0.317737i
$111$		0			0
$112$	8.26430e9	−	1.43142e10i	0.0443105	−	0.0767481i
$113$	−4.25734e10	+	7.37393e10i	−0.217374	+	0.376502i	−0.954004	−	0.299793i	$-0.903082\pi$
$113$	−4.25734e10	+	7.37393e10i	−0.217374	+	0.376502i	0.736630	+	0.676295i	$0.236416\pi$
$114$		0			0
$115$	−4.50235e10	−	7.79830e10i	−0.208738	−	0.361545i
$116$	1.89015e11			0.835557
$117$		0			0
$118$	1.24541e11			0.501142
$119$	5.78165e10	+	1.00141e11i	0.222097	+	0.384684i
$120$		0			0
$121$	−2.49160e8	+	4.31558e8i	−0.000873290	+	0.00151258i
$122$	−8.34777e10	+	1.44588e11i	−0.279635	+	0.484342i
$123$		0			0
$124$	−3.88926e10	−	6.73639e10i	−0.119137	−	0.206352i
$125$	3.59001e11			1.05218
$126$		0			0
$127$	−2.62717e11			−0.705615			−0.352808	−	0.935696i	$-0.614773\pi$
$127$	−2.62717e11			−0.705615			−0.352808	+	0.935696i	$0.614773\pi$
$128$	1.69036e11	+	2.92778e11i	0.434834	+	0.753155i
$129$		0			0
$130$	−3.34857e10	+	5.79989e10i	−0.0790990	+	0.137003i
$131$	3.15764e11	−	5.46920e11i	0.715107	−	1.23860i	−0.247811	−	0.968808i	$-0.579711\pi$
$131$	3.15764e11	−	5.46920e11i	0.715107	−	1.23860i	0.962918	−	0.269793i	$-0.0869554\pi$
$132$		0			0
$133$	8.92574e10	+	1.54598e11i	0.185977	+	0.322122i
$134$	−3.71564e11			−0.742946
$135$		0			0
$136$	−5.83413e11			−1.07526
$137$	−1.48599e11	−	2.57382e11i	−0.263059	−	0.455632i	0.703994	−	0.710206i	$-0.251398\pi$
$137$	−1.48599e11	−	2.57382e11i	−0.263059	−	0.455632i	−0.967053	+	0.254574i	$0.918065\pi$
$138$		0			0
$139$	−2.98397e11	+	5.16838e11i	−0.487767	+	0.844838i	−0.999901	−	0.0140679i	$-0.995522\pi$
$139$	−2.98397e11	+	5.16838e11i	−0.487767	+	0.844838i	0.512134	+	0.858906i	$0.328855\pi$
$140$	5.95229e10	−	1.03097e11i	0.0935363	−	0.162010i
$141$		0			0
$142$	1.17498e11	+	2.03512e11i	0.170783	+	0.295804i
$143$	3.08866e11			0.431938
$144$		0			0
$145$	6.20204e11			0.803546
$146$	−1.75655e10	−	3.04243e10i	−0.0219139	−	0.0379560i
$147$		0			0
$148$	−1.34109e11	+	2.32284e11i	−0.155245	+	0.268893i
$149$	−5.57717e11	+	9.65994e11i	−0.622142	+	1.07758i	0.366945	+	0.930243i	$0.380404\pi$
$149$	−5.57717e11	+	9.65994e11i	−0.622142	+	1.07758i	−0.989086	+	0.147338i	$0.952929\pi$
$150$		0			0
$151$	4.12224e11	+	7.13992e11i	0.427326	+	0.740151i	0.996635	−	0.0819732i	$-0.0261222\pi$
$151$	4.12224e11	+	7.13992e11i	0.427326	+	0.740151i	−0.569308	+	0.822124i	$0.692789\pi$
$152$	−9.00677e11			−0.900387
$153$		0			0
$154$	2.14837e11			0.199869
$155$	−1.27616e11	−	2.21038e11i	−0.114573	−	0.198446i
$156$		0			0
$157$	−6.57558e11	+	1.13892e12i	−0.550156	+	0.952899i	0.448106	+	0.893980i	$0.352099\pi$
$157$	−6.57558e11	+	1.13892e12i	−0.550156	+	0.952899i	−0.998263	+	0.0589187i	$0.981235\pi$
$158$	−4.57402e11	+	7.92244e11i	−0.369559	+	0.640096i
$159$		0			0
$160$	4.75046e11	+	8.22803e11i	0.358159	+	0.620349i
$161$	3.12163e11			0.227425
$162$		0			0
$163$	−3.57833e11			−0.243584			−0.121792	−	0.992556i	$-0.538864\pi$
$163$	−3.57833e11			−0.243584			−0.121792	+	0.992556i	$0.538864\pi$
$164$	−2.26777e11	−	3.92789e11i	−0.149265	−	0.258534i
$165$		0			0
$166$	−3.52021e11	+	6.09719e11i	−0.216758	+	0.375435i
$167$	1.37742e12	−	2.38576e12i	0.820587	−	1.42130i	−0.0846581	−	0.996410i	$-0.526980\pi$
$167$	1.37742e12	−	2.38576e12i	0.820587	−	1.42130i	0.905245	−	0.424889i	$-0.139687\pi$
$168$		0			0
$169$	7.29190e11	+	1.26299e12i	0.406877	+	0.704732i
$170$	−8.00536e11			−0.432426
$171$		0			0
$172$	2.52090e10			0.0127688
$173$	−4.75194e11	−	8.23060e11i	−0.233140	−	0.403811i	0.725590	−	0.688127i	$-0.241567\pi$
$173$	−4.75194e11	−	8.23060e11i	−0.233140	−	0.403811i	−0.958731	+	0.284316i	$0.908233\pi$
$174$		0			0
$175$	−2.13480e11	+	3.69757e11i	−0.0983211	+	0.170297i
$176$	2.63867e11	−	4.57032e11i	0.117779	−	0.203998i
$177$		0			0
$178$	−2.99915e11	−	5.19468e11i	−0.125802	−	0.217896i
$179$	−1.68138e12			−0.683873			−0.341936	−	0.939723i	$-0.611083\pi$
$179$	−1.68138e12			−0.683873			−0.341936	+	0.939723i	$0.611083\pi$
$180$		0			0
$181$	−9.96774e11			−0.381386			−0.190693	−	0.981650i	$-0.561073\pi$
$181$	−9.96774e11			−0.381386			−0.190693	+	0.981650i	$0.561073\pi$
$182$	−1.16084e11	−	2.01063e11i	−0.0430902	−	0.0746345i
$183$		0			0
$184$	−7.87492e11	+	1.36398e12i	−0.275263	+	0.476770i
$185$	−4.40045e11	+	7.62181e11i	−0.149298	+	0.258591i
$186$		0			0
$187$	1.84600e12	+	3.19736e12i	0.590340	+	1.02250i
$188$	3.95578e12			1.22847
$189$		0			0
$190$	−1.23587e12			−0.362100
$191$	1.38120e12	+	2.39231e12i	0.393164	+	0.680980i	0.992865	−	0.119244i	$-0.0380472\pi$
$191$	1.38120e12	+	2.39231e12i	0.393164	+	0.680980i	−0.599701	+	0.800224i	$0.704714\pi$
$192$		0			0
$193$	−2.72119e12	+	4.71325e12i	−0.731466	+	1.26694i	0.224790	+	0.974407i	$0.427830\pi$
$193$	−2.72119e12	+	4.71325e12i	−0.731466	+	1.26694i	−0.956256	+	0.292530i	$0.905503\pi$
$194$	−9.00163e11	+	1.55913e12i	−0.235186	+	0.407354i
$195$		0			0
$196$	−1.24897e12	−	2.16327e12i	−0.308420	−	0.534199i
$197$	2.87609e12			0.690619			0.345309	−	0.938489i	$-0.387774\pi$
$197$	2.87609e12			0.690619			0.345309	+	0.938489i	$0.387774\pi$
$198$		0			0
$199$	7.28391e11			0.165452			0.0827262	−	0.996572i	$-0.473637\pi$
$199$	7.28391e11			0.165452			0.0827262	+	0.996572i	$0.473637\pi$
$200$	−1.07709e12	−	1.86557e12i	−0.238005	−	0.412237i
$201$		0			0
$202$	9.80916e11	−	1.69900e12i	0.205210	−	0.355435i
$203$	−1.07502e12	+	1.86199e12i	−0.218871	+	0.379096i
$204$		0			0
$205$	−7.44111e11	−	1.28884e12i	−0.143546	−	0.248629i
$206$	−5.41812e12			−1.01760
$207$		0			0
$208$	−5.70306e11			−0.101569
$209$	2.84986e12	+	4.93610e12i	0.494333	+	0.856209i
$210$		0			0
$211$	3.39658e12	−	5.88306e12i	0.559099	−	0.968388i	−0.438473	−	0.898745i	$-0.644480\pi$
$211$	3.39658e12	−	5.88306e12i	0.559099	−	0.968388i	0.997572	−	0.0696437i	$-0.0221863\pi$
$212$	1.17470e12	−	2.03463e12i	0.188399	−	0.326317i
$213$		0			0
$214$	1.08290e12	+	1.87563e12i	0.164934	+	0.285674i
$215$	8.27172e10			0.0122796
$216$		0			0
$217$	8.84806e11			0.124830
$218$	−8.81792e11	−	1.52731e12i	−0.121299	−	0.210095i
$219$		0			0
$220$	1.90048e12	−	3.29173e12i	0.248622	−	0.430625i
$221$	1.99491e12	−	3.45529e12i	0.254546	−	0.440886i
$222$		0			0
$223$	−3.66743e12	−	6.35218e12i	−0.445333	−	0.771340i	0.552742	−	0.833352i	$-0.313582\pi$
$223$	−3.66743e12	−	6.35218e12i	−0.445333	−	0.771340i	−0.998075	+	0.0620124i	$0.980248\pi$
$224$	−3.29365e12			−0.390223
$225$		0			0
$226$	2.04352e12			0.230560
$227$	−6.79920e11	−	1.17766e12i	−0.0748713	−	0.129681i	0.826159	−	0.563437i	$-0.190521\pi$
$227$	−6.79920e11	−	1.17766e12i	−0.0748713	−	0.129681i	−0.901030	+	0.433756i	$0.857188\pi$
$228$		0			0
$229$	5.91221e12	−	1.02402e13i	0.620375	−	1.07452i	−0.369041	−	0.929413i	$-0.620314\pi$
$229$	5.91221e12	−	1.02402e13i	0.620375	−	1.07452i	0.989416	−	0.145108i	$-0.0463530\pi$
$230$	−1.08056e12	+	1.87159e12i	−0.110700	+	0.191738i
$231$		0			0
$232$	−5.42390e12	−	9.39446e12i	−0.529819	−	0.917673i
$233$	1.75634e13			1.67552			0.837761	−	0.546038i	$-0.183865\pi$
$233$	1.75634e13			1.67552			0.837761	+	0.546038i	$0.183865\pi$
$234$		0			0
$235$	1.29799e13			1.18140
$236$	3.81925e12	+	6.61514e12i	0.339596	+	0.588197i
$237$		0			0
$238$	1.38760e12	−	2.40339e12i	0.117785	−	0.204009i
$239$	−3.56979e12	+	6.18306e12i	−0.296111	+	0.512879i	−0.975243	−	0.221137i	$-0.929023\pi$
$239$	−3.56979e12	+	6.18306e12i	−0.296111	+	0.512879i	0.679132	+	0.734016i	$0.262356\pi$
$240$		0			0
$241$	1.15653e11	+	2.00318e11i	0.00916357	+	0.0158718i	0.870571	−	0.492043i	$-0.163750\pi$
$241$	1.15653e11	+	2.00318e11i	0.00916357	+	0.0158718i	−0.861407	+	0.507915i	$0.830416\pi$
$242$	1.19597e10			0.000926264
$243$		0			0
$244$	−1.02399e13			−0.757972
$245$	−4.09817e12	−	7.09824e12i	−0.296604	−	0.513733i
$246$		0			0
$247$	3.07975e12	−	5.33429e12i	0.213149	−	0.369184i
$248$	−2.23210e12	+	3.86610e12i	−0.151087	+	0.261691i
$249$		0			0
$250$	−4.30801e12	−	7.46170e12i	−0.279002	−	0.483245i
$251$	−1.29831e13			−0.822567			−0.411284	−	0.911507i	$-0.634919\pi$
$251$	−1.29831e13			−0.822567			−0.411284	+	0.911507i	$0.634919\pi$
$252$		0			0
$253$	9.96692e12			0.604502
$254$	3.15261e12	+	5.46047e12i	0.187105	+	0.324075i
$255$		0			0
$256$	6.82094e12	−	1.18142e13i	0.387725	−	0.671560i
$257$	1.19806e13	−	2.07510e13i	0.666571	−	1.15453i	−0.312286	−	0.949988i	$-0.601095\pi$
$257$	1.19806e13	−	2.07510e13i	0.666571	−	1.15453i	0.978857	−	0.204546i	$-0.0655719\pi$
$258$		0			0
$259$	−1.52549e12	−	2.64223e12i	−0.0813318	−	0.140871i
$260$	−4.10758e12			−0.214404
$261$		0			0
$262$	−1.51567e13			−0.758485
$263$	−1.21369e13	−	2.10217e13i	−0.594771	−	1.03017i	−0.993579	−	0.113139i	$-0.963909\pi$
$263$	−1.21369e13	−	2.10217e13i	−0.594771	−	1.03017i	0.398808	−	0.917034i	$-0.369424\pi$
$264$		0			0
$265$	3.85447e12	−	6.67615e12i	0.181181	−	0.313815i
$266$	2.14218e12	−	3.71036e12i	0.0986294	−	0.170831i
$267$		0			0
$268$	−1.13946e13	−	1.97361e13i	−0.503453	−	0.872006i
$269$	−2.58377e13			−1.11845			−0.559225	−	0.829016i	$-0.688901\pi$
$269$	−2.58377e13			−1.11845			−0.559225	+	0.829016i	$0.688901\pi$
$270$		0			0
$271$	−3.76793e12			−0.156593			−0.0782964	−	0.996930i	$-0.524948\pi$
$271$	−3.76793e12			−0.156593			−0.0782964	+	0.996930i	$0.524948\pi$
$272$	−3.40855e12	−	5.90378e12i	−0.138816	−	0.240437i
$273$		0			0
$274$	−3.56638e12	+	6.17716e12i	−0.139508	+	0.241636i
$275$	−6.81610e12	+	1.18058e13i	−0.261340	+	0.452654i
$276$		0			0
$277$	8.20947e12	+	1.42192e13i	0.302466	+	0.523886i	0.976694	−	0.214637i	$-0.0688569\pi$
$277$	8.20947e12	+	1.42192e13i	0.302466	+	0.523886i	−0.674228	+	0.738523i	$0.735524\pi$
$278$	1.43230e13			0.517355
$279$		0			0
$280$	−6.83219e12			−0.237242
$281$	1.05179e13	+	1.82175e13i	0.358132	+	0.620302i	0.987649	−	0.156684i	$-0.0500806\pi$
$281$	1.05179e13	+	1.82175e13i	0.358132	+	0.620302i	−0.629517	+	0.776987i	$0.716747\pi$
$282$		0			0
$283$	−8.35659e12	+	1.44740e13i	−0.273655	+	0.473985i	−0.969795	−	0.243922i	$-0.921566\pi$
$283$	−8.35659e12	+	1.44740e13i	−0.273655	+	0.473985i	0.696140	+	0.717906i	$0.254899\pi$
$284$	−7.20653e12	+	1.24821e13i	−0.231460	+	0.400900i
$285$		0			0
$286$	−3.70639e12	−	6.41965e12i	−0.114535	−	0.198380i
$287$	5.15917e12			0.156397
$288$		0			0
$289$	1.34200e13			0.391575
$290$	−7.44245e12	−	1.28907e13i	−0.213072	−	0.369052i
$291$		0			0
$292$	1.07735e12	−	1.86603e12i	0.0296996	−	0.0514413i
$293$	−1.19634e13	+	2.07213e13i	−0.323656	+	0.560589i	−0.981239	−	0.192793i	$-0.938245\pi$
$293$	−1.19634e13	+	2.07213e13i	−0.323656	+	0.560589i	0.657583	+	0.753382i	$0.271579\pi$
$294$		0			0
$295$	1.25319e13	+	2.17059e13i	0.326585	+	0.565663i
$296$	1.53934e13			0.393758
$297$		0			0
$298$	2.67704e13			0.659881
$299$	−5.38546e12	−	9.32790e12i	−0.130326	−	0.225731i
$300$		0			0
$301$	−1.43376e11	+	2.48335e11i	−0.00334474	+	0.00579326i
$302$	9.89337e12	−	1.71358e13i	0.226624	−	0.392524i
$303$		0			0
$304$	−5.26214e12	−	9.11429e12i	−0.116240	−	0.201334i
$305$	−3.35998e13			−0.728933
$306$		0			0
$307$	1.53111e13			0.320439			0.160219	−	0.987081i	$-0.448780\pi$
$307$	1.53111e13			0.320439			0.160219	+	0.987081i	$0.448780\pi$
$308$	6.58834e12	+	1.14113e13i	0.135440	+	0.234589i
$309$		0			0
$310$	−3.06279e12	+	5.30491e12i	−0.0607614	+	0.105242i
$311$	2.49376e13	−	4.31932e13i	0.486040	−	0.841846i	−0.513831	−	0.857891i	$-0.671774\pi$
$311$	2.49376e13	−	4.31932e13i	0.486040	−	0.841846i	0.999871	+	0.0160451i	$0.00510753\pi$
$312$		0			0
$313$	4.97404e13	+	8.61529e13i	0.935870	+	1.62097i	0.773075	+	0.634315i	$0.218718\pi$
$313$	4.97404e13	+	8.61529e13i	0.935870	+	1.62097i	0.162795	+	0.986660i	$0.447949\pi$
$314$	3.15628e13			0.583529
$315$		0			0
$316$	−5.61080e13			−1.00172
$317$	4.16846e13	+	7.21999e13i	0.731392	+	1.26681i	0.956289	+	0.292425i	$0.0944621\pi$
$317$	4.16846e13	+	7.21999e13i	0.731392	+	1.26681i	−0.224897	+	0.974383i	$0.572205\pi$
$318$		0			0
$319$	−3.43239e13	+	5.94507e13i	−0.581765	+	1.00765i
$320$	6.51880e12	−	1.12909e13i	0.108603	−	0.188106i
$321$		0			0
$322$	−3.74596e12	−	6.48819e12i	−0.0603053	−	0.104452i
$323$	7.36271e13			1.16526
$324$		0			0
$325$	1.47319e13			0.225372
$326$	4.29399e12	+	7.43741e12i	0.0645899	+	0.111873i
$327$		0			0
$328$	−1.30150e13	+	2.25427e13i	−0.189295	+	0.327868i
$329$	−2.24985e13	+	3.89685e13i	−0.321792	+	0.557361i
$330$		0			0
$331$	3.17920e13	+	5.50654e13i	0.439809	+	0.761771i	0.997674	−	0.0681600i	$-0.0217128\pi$
$331$	3.17920e13	+	5.50654e13i	0.439809	+	0.761771i	−0.557865	+	0.829931i	$0.688379\pi$
$332$	−4.31813e13			−0.587538
$333$		0			0
$334$	−6.61160e13			−0.870364
$335$	−3.73886e13	−	6.47590e13i	−0.484164	−	0.838597i
$336$		0			0
$337$	−6.05007e13	+	1.04790e14i	−0.758221	+	1.31328i	0.185535	+	0.982638i	$0.440598\pi$
$337$	−6.05007e13	+	1.04790e14i	−0.758221	+	1.31328i	−0.943757	+	0.330640i	$0.892735\pi$
$338$	1.75006e13	−	3.03118e13i	0.215779	−	0.373741i
$339$		0			0
$340$	−2.45498e13	−	4.25214e13i	−0.293031	−	0.507544i
$341$	2.82506e13			0.331802
$342$		0			0
$343$	6.15223e13			0.699705
$344$	−7.23390e11	−	1.25295e12i	−0.00809657	−	0.0140237i
$345$		0			0
$346$	−1.14046e13	+	1.97534e13i	−0.123641	+	0.214153i
$347$	−7.78308e13	+	1.34807e14i	−0.830499	+	1.43847i	0.0671435	+	0.997743i	$0.478611\pi$
$347$	−7.78308e13	+	1.34807e14i	−0.830499	+	1.43847i	−0.897643	+	0.440724i	$0.854722\pi$
$348$		0			0
$349$	1.28215e13	+	2.22075e13i	0.132556	+	0.229594i	0.924661	−	0.380791i	$-0.124348\pi$
$349$	1.28215e13	+	2.22075e13i	0.132556	+	0.229594i	−0.792105	+	0.610385i	$0.791015\pi$
$350$	1.02470e13			0.104285
$351$		0			0
$352$	−1.05162e14			−1.03722
$353$	1.24549e13	+	2.15725e13i	0.120943	+	0.209479i	0.920140	−	0.391590i	$-0.128075\pi$
$353$	1.24549e13	+	2.15725e13i	0.120943	+	0.209479i	−0.799197	+	0.601069i	$0.794742\pi$
$354$		0			0
$355$	−2.36464e13	+	4.09568e13i	−0.222592	+	0.385541i
$356$	1.83948e13	−	3.18607e13i	0.170498	−	0.295312i
$357$		0			0
$358$	2.01766e13	+	3.49469e13i	0.181339	+	0.314089i
$359$	−1.57584e14			−1.39474			−0.697370	−	0.716712i	$-0.745646\pi$
$359$	−1.57584e14			−1.39474			−0.697370	+	0.716712i	$0.745646\pi$
$360$		0			0
$361$	−2.82438e12			−0.0242457
$362$	1.19613e13	+	2.07176e13i	0.101130	+	0.175163i
$363$		0			0
$364$	7.11980e12	−	1.23319e13i	0.0583997	−	0.101151i
$365$	3.53506e12	−	6.12290e12i	0.0285618	−	0.0494705i
$366$		0			0
$367$	8.89506e13	+	1.54067e14i	0.697406	+	1.20794i	0.969363	+	0.245633i	$0.0789958\pi$
$367$	8.89506e13	+	1.54067e14i	0.697406	+	1.20794i	−0.271957	+	0.962309i	$0.587671\pi$
$368$	−1.84034e13			−0.142146
$369$		0			0
$370$	2.11222e13			0.158354
$371$	1.33622e13	+	2.31440e13i	0.0987008	+	0.170955i
$372$		0			0
$373$	2.75809e13	−	4.77715e13i	0.197792	−	0.342586i	−0.750020	−	0.661415i	$-0.769956\pi$
$373$	2.75809e13	−	4.77715e13i	0.197792	−	0.342586i	0.947812	+	0.318829i	$0.103290\pi$
$374$	4.43039e13	−	7.67367e13i	0.313075	−	0.542262i
$375$		0			0
$376$	−1.13514e14	−	1.96611e14i	−0.778959	−	1.34920i
$377$	7.41854e13			0.501696
$378$		0			0
$379$	1.46463e14			0.962083			0.481042	−	0.876698i	$-0.340259\pi$
$379$	1.46463e14			0.962083			0.481042	+	0.876698i	$0.340259\pi$
$380$	−3.79001e13	−	6.56448e13i	−0.245375	−	0.425002i
$381$		0			0
$382$	3.31488e13	−	5.74155e13i	0.208507	−	0.361144i
$383$	1.15725e14	−	2.00441e14i	0.717519	−	1.24278i	−0.244462	−	0.969659i	$-0.578611\pi$
$383$	1.15725e14	−	2.00441e14i	0.717519	−	1.24278i	0.961980	−	0.273120i	$-0.0880555\pi$
$384$		0			0
$385$	2.16180e13	+	3.74434e13i	0.130251	+	0.225601i
$386$	1.30617e14			0.775837
$387$		0			0
$388$	−1.10420e14			−0.637490
$389$	−7.49358e13	−	1.29793e14i	−0.426547	−	0.738800i	0.570017	−	0.821633i	$-0.306937\pi$
$389$	−7.49358e13	−	1.29793e14i	−0.426547	−	0.738800i	−0.996563	+	0.0828326i	$0.973603\pi$
$390$		0			0
$391$	6.43746e13	−	1.11500e14i	0.356240	−	0.617025i
$392$	−7.16798e13	+	1.24153e14i	−0.391132	+	0.677461i
$393$		0			0
$394$	−3.45131e13	−	5.97784e13i	−0.183128	−	0.317187i
$395$	−1.84104e14			−0.963341
$396$		0			0
$397$	2.08111e14			1.05912			0.529562	−	0.848271i	$-0.322356\pi$
$397$	2.08111e14			1.05912			0.529562	+	0.848271i	$0.322356\pi$
$398$	−8.74070e12	−	1.51393e13i	−0.0438722	−	0.0759888i
$399$		0			0
$400$	1.25856e13	−	2.17989e13i	0.0614531	−	0.106440i
$401$	−6.67040e13	+	1.15535e14i	−0.321261	+	0.556440i	−0.980748	−	0.195275i	$-0.937440\pi$
$401$	−6.67040e13	+	1.15535e14i	−0.321261	+	0.556440i	0.659488	+	0.751715i	$0.270773\pi$
$402$		0			0
$403$	−1.52648e13	−	2.64393e13i	−0.0715339	−	0.123900i
$404$	1.20326e14			0.556238
$405$		0			0
$406$	5.16010e13			0.232148
$407$	−4.87067e13	−	8.43625e13i	−0.216182	−	0.374438i
$408$		0			0
$409$	1.03084e14	−	1.78546e14i	0.445361	−	0.771388i	−0.552716	−	0.833369i	$-0.686409\pi$
$409$	1.03084e14	−	1.78546e14i	0.445361	−	0.771388i	0.998077	+	0.0619816i	$0.0197420\pi$
$410$	−1.78587e13	+	3.09321e13i	−0.0761268	+	0.131856i
$411$		0			0
$412$	−1.66156e14	−	2.87790e14i	−0.689574	−	1.19438i
$413$	−8.68880e13			−0.355824
$414$		0			0
$415$	−1.41689e14			−0.565028
$416$	5.68224e13	+	9.84192e13i	0.223618	+	0.387317i
$417$		0			0
$418$	6.83967e13	−	1.18467e14i	0.262159	−	0.454073i
$419$	3.67018e13	−	6.35693e13i	0.138838	−	0.240475i	−0.788219	−	0.615395i	$-0.788996\pi$
$419$	3.67018e13	−	6.35693e13i	0.138838	−	0.240475i	0.927057	+	0.374920i	$0.122330\pi$
$420$		0			0
$421$	−8.55560e13	−	1.48187e14i	−0.315282	−	0.546084i	0.664216	−	0.747541i	$-0.268766\pi$
$421$	−8.55560e13	−	1.48187e14i	−0.315282	−	0.546084i	−0.979497	+	0.201457i	$0.935432\pi$
$422$	−1.63036e14			−0.593014
$423$		0			0
$424$	−1.34835e14			−0.477848
$425$	8.80480e13	+	1.52504e14i	0.308021	+	0.533508i
$426$		0			0
$427$	5.82396e13	−	1.00874e14i	0.198548	−	0.343895i
$428$	−6.64176e13	+	1.15039e14i	−0.223533	+	0.387171i
$429$		0			0
$430$	−9.92606e11	−	1.71924e12i	−0.00325612	−	0.00563977i
$431$	7.17758e13			0.232463			0.116231	−	0.993222i	$-0.462919\pi$
$431$	7.17758e13			0.232463			0.116231	+	0.993222i	$0.462919\pi$
$432$		0			0
$433$	9.98812e13			0.315356			0.157678	−	0.987491i	$-0.449599\pi$
$433$	9.98812e13			0.315356			0.157678	+	0.987491i	$0.449599\pi$
$434$	−1.06177e13	−	1.83903e13i	−0.0331006	−	0.0573319i
$435$		0			0
$436$	5.40832e13	−	9.36749e13i	0.164394	−	0.284739i
$437$	9.93819e13	−	1.72134e14i	0.298304	−	0.516678i
$438$		0			0
$439$	1.45156e13	+	2.51418e13i	0.0424894	+	0.0735938i	0.886488	−	0.462752i	$-0.153138\pi$
$439$	1.45156e13	+	2.51418e13i	0.0424894	+	0.0735938i	−0.843999	+	0.536345i	$0.819804\pi$
$440$	−2.18142e14			−0.630594
$441$		0			0
$442$	−9.57557e13			−0.269987
$443$	1.64185e14	+	2.84377e14i	0.457207	+	0.791906i	0.998812	−	0.0487274i	$-0.0155166\pi$
$443$	1.64185e14	+	2.84377e14i	0.457207	+	0.791906i	−0.541605	+	0.840633i	$0.682183\pi$
$444$		0			0
$445$	6.03579e13	−	1.04543e14i	0.163966	−	0.283998i
$446$	−8.80184e13	+	1.52452e14i	−0.236174	+	0.409065i
$447$		0			0
$448$	2.25985e13	+	3.91418e13i	0.0591631	+	0.102473i
$449$	6.12368e14			1.58364			0.791822	−	0.610752i	$-0.209133\pi$
$449$	6.12368e14			1.58364			0.791822	+	0.610752i	$0.209133\pi$
$450$		0			0
$451$	1.64725e14			0.415708
$452$	6.26681e13	+	1.08544e14i	0.156237	+	0.270611i
$453$		0			0
$454$	−1.63181e13	+	2.82637e13i	−0.0397065	+	0.0687737i
$455$	2.33619e13	−	4.04639e13i	0.0561623	−	0.0972759i
$456$		0			0
$457$	−1.51742e14	−	2.62824e14i	−0.356095	−	0.616774i	0.631210	−	0.775612i	$-0.282559\pi$
$457$	−1.51742e14	−	2.62824e14i	−0.356095	−	0.616774i	−0.987305	+	0.158838i	$0.949225\pi$
$458$	−2.83786e14			−0.658007
$459$		0			0
$460$	−1.32549e14			−0.300061
$461$	−3.64654e14	−	6.31599e14i	−0.815691	−	1.41282i	−0.908830	−	0.417166i	$-0.863023\pi$
$461$	−3.64654e14	−	6.31599e14i	−0.815691	−	1.41282i	0.0931391	−	0.995653i	$-0.470310\pi$
$462$		0			0
$463$	−6.10941e13	+	1.05818e14i	−0.133445	+	0.231134i	−0.925003	−	0.379961i	$-0.875937\pi$
$463$	−6.10941e13	+	1.05818e14i	−0.133445	+	0.231134i	0.791557	+	0.611095i	$0.209271\pi$
$464$	6.33774e13	−	1.09773e14i	0.136800	−	0.236944i
$465$		0			0
$466$	−2.10760e14	−	3.65047e14i	−0.444290	−	0.769532i
$467$	6.17381e14			1.28621			0.643103	−	0.765780i	$-0.277647\pi$
$467$	6.17381e14			1.28621			0.643103	+	0.765780i	$0.277647\pi$
$468$		0			0
$469$	2.59228e14			0.527510
$470$	−1.55759e14	−	2.69782e14i	−0.313267	−	0.542594i
$471$		0			0
$472$	2.19192e14	−	3.79652e14i	0.430669	−	0.745941i
$473$	−4.57780e12	+	7.92899e12i	−0.00889039	+	0.0153986i
$474$		0			0
$475$	1.35929e14	+	2.35436e14i	0.257927	+	0.446743i
$476$	1.70212e14			0.319265
$477$		0			0
$478$	1.71350e14			0.314073
$479$	5.25419e14	+	9.10052e14i	0.952052	+	1.64900i	0.740976	+	0.671532i	$0.234363\pi$
$479$	5.25419e14	+	9.10052e14i	0.952052	+	1.64900i	0.211076	+	0.977470i	$0.432303\pi$
$480$		0			0
$481$	−5.26358e13	+	9.11678e13i	−0.0932144	+	0.161452i
$482$	2.77568e12	−	4.80762e12i	0.00485972	−	0.00841728i
$483$		0			0
$484$	3.66763e11	+	6.35253e11i	0.000627678	+	0.00108717i
$485$	−3.62316e14			−0.613066
$486$		0			0
$487$	−2.19910e14			−0.363777			−0.181889	−	0.983319i	$-0.558221\pi$
$487$	−2.19910e14			−0.363777			−0.181889	+	0.983319i	$0.558221\pi$
$488$	2.93842e14	+	5.08949e14i	0.480623	+	0.832463i
$489$		0			0
$490$	−9.83561e13	+	1.70358e14i	−0.157298	+	0.272448i
$491$	−2.41932e14	+	4.19038e14i	−0.382599	+	0.662682i	−0.991433	−	0.130616i	$-0.958304\pi$
$491$	−2.41932e14	+	4.19038e14i	−0.382599	+	0.662682i	0.608834	+	0.793298i	$0.291638\pi$
$492$		0			0
$493$	4.43384e14	+	7.67963e14i	0.685681	+	1.18763i
$494$	−1.47828e14			−0.226078
$495$		0			0
$496$	−5.21634e13			−0.0780219
$497$	−8.19743e13	−	1.41984e14i	−0.121260	−	0.210029i
$498$		0			0
$499$	5.44389e13	−	9.42909e13i	0.0787691	−	0.136432i	−0.823950	−	0.566663i	$-0.808234\pi$
$499$	5.44389e13	−	9.42909e13i	0.0787691	−	0.136432i	0.902719	+	0.430230i	$0.141568\pi$
$500$	2.64225e14	−	4.57651e14i	0.378128	−	0.654937i
$501$		0			0
$502$	1.55797e14	+	2.69848e14i	0.218116	+	0.377788i
$503$	−5.06588e14			−0.701506			−0.350753	−	0.936468i	$-0.614074\pi$
$503$	−5.06588e14			−0.701506			−0.350753	+	0.936468i	$0.614074\pi$
$504$		0			0
$505$	3.94818e14			0.534927
$506$	−1.19603e14	−	2.07158e14i	−0.160293	−	0.277635i
$507$		0			0
$508$	−1.93360e14	+	3.34909e14i	−0.253581	+	0.439214i
$509$	4.28767e13	−	7.42646e13i	0.0556254	−	0.0963461i	−0.836872	−	0.547399i	$-0.815618\pi$
$509$	4.28767e13	−	7.42646e13i	0.0556254	−	0.0963461i	0.892497	+	0.451053i	$0.148951\pi$
$510$		0			0
$511$	1.22549e13	+	2.12260e13i	0.0155594	+	0.0269497i
$512$	3.64965e14			0.458423
$513$		0			0
$514$	−5.75069e14			−0.707005
$515$	−5.45199e14	−	9.44312e14i	−0.663155	−	1.14862i
$516$		0			0
$517$	−7.18344e14	+	1.24421e15i	−0.855332	+	1.48148i
$518$	−3.66118e13	+	6.34134e13i	−0.0431327	+	0.0747081i
$519$		0			0
$520$	1.17870e14	+	2.04156e14i	0.135951	+	0.235475i
$521$	−9.27575e14			−1.05862			−0.529312	−	0.848428i	$-0.677550\pi$
$521$	−9.27575e14			−1.05862			−0.529312	+	0.848428i	$0.677550\pi$
$522$		0			0
$523$	−2.18187e13			−0.0243820			−0.0121910	−	0.999926i	$-0.503881\pi$
$523$	−2.18187e13			−0.0243820			−0.0121910	+	0.999926i	$0.503881\pi$
$524$	−4.64805e14	−	8.05066e14i	−0.513983	−	0.890245i
$525$		0			0
$526$	−2.91285e14	+	5.04520e14i	−0.315425	+	0.546332i
$527$	1.82466e14	−	3.16040e14i	0.195534	−	0.338675i
$528$		0			0
$529$	3.02619e14	+	5.24152e14i	0.317607	+	0.550112i
$530$	−1.85015e14			−0.192172
$531$		0			0
$532$	2.62774e14			0.267343
$533$	−8.90064e13	−	1.54164e14i	−0.0896235	−	0.155232i
$534$		0			0
$535$	−2.17933e14	+	3.77470e14i	−0.214969	+	0.372338i
$536$	−6.53952e14	+	1.13268e15i	−0.638469	+	1.10586i
$537$		0			0
$538$	3.10052e14	+	5.37027e14i	0.296574	+	0.513681i
$539$	9.07218e14			0.858961
$540$		0			0
$541$	−1.69527e15			−1.57273			−0.786363	−	0.617765i	$-0.788038\pi$
$541$	−1.69527e15			−1.57273			−0.786363	+	0.617765i	$0.788038\pi$
$542$	4.52152e13	+	7.83150e13i	0.0415230	+	0.0719199i
$543$		0			0
$544$	−6.79220e14	+	1.17644e15i	−0.611247	+	1.05871i
$545$	1.77461e14	−	3.07371e14i	0.158096	−	0.273831i
$546$		0			0
$547$	−3.76072e14	−	6.51376e14i	−0.328353	−	0.568724i	0.653832	−	0.756640i	$-0.273160\pi$
$547$	−3.76072e14	−	6.51376e14i	−0.328353	−	0.568724i	−0.982185	+	0.187915i	$0.939827\pi$
$548$	−4.37477e14			−0.378148
$549$		0			0
$550$	3.27173e14			0.277193
$551$	6.84499e14	+	1.18559e15i	0.574168	+	0.994488i
$552$		0			0
$553$	3.19114e14	−	5.52722e14i	0.262396	−	0.454484i
$554$	1.97027e14	−	3.41261e14i	0.160407	−	0.277833i
$555$		0			0
$556$	4.39240e14	+	7.60786e14i	0.350583	+	0.607227i
$557$	−1.87489e14			−0.148174			−0.0740870	−	0.997252i	$-0.523604\pi$
$557$	−1.87489e14			−0.148174			−0.0740870	+	0.997252i	$0.523604\pi$
$558$		0			0
$559$	9.89417e12			0.00766681
$560$	−3.99166e13	−	6.91375e13i	−0.0306280	−	0.0530493i
$561$		0			0
$562$	2.52429e14	−	4.37219e14i	0.189928	−	0.328965i
$563$	1.22486e14	−	2.12151e14i	0.0912618	−	0.158070i	−0.816781	−	0.576949i	$-0.804243\pi$
$563$	1.22486e14	−	2.12151e14i	0.0912618	−	0.158070i	0.908042	+	0.418878i	$0.137577\pi$
$564$		0			0
$565$	2.05630e14	+	3.56161e14i	0.150252	+	0.260244i
$566$	4.01116e14			0.290255
$567$		0			0
$568$	8.27185e14			0.587066
$569$	6.76213e14	+	1.17124e15i	0.475298	+	0.823240i	0.999600	−	0.0282923i	$-0.00900691\pi$
$569$	6.76213e14	+	1.17124e15i	0.475298	+	0.823240i	−0.524302	+	0.851533i	$0.675674\pi$
$570$		0			0
$571$	−7.16114e14	+	1.24035e15i	−0.493723	+	0.855154i	−0.999974	−	0.00723249i	$-0.997698\pi$
$571$	−7.16114e14	+	1.24035e15i	−0.493723	+	0.855154i	0.506250	+	0.862387i	$0.331031\pi$
$572$	2.27325e14	−	3.93739e14i	0.155228	−	0.268862i
$573$		0			0
$574$	−6.19100e13	−	1.07231e14i	−0.0414711	−	0.0718301i
$575$	4.75389e14			0.315410
$576$		0			0
$577$	−8.77659e14			−0.571293			−0.285647	−	0.958335i	$-0.592208\pi$
$577$	−8.77659e14			−0.571293			−0.285647	+	0.958335i	$0.592208\pi$
$578$	−1.61040e14	−	2.78930e14i	−0.103832	−	0.179842i
$579$		0			0
$580$	4.56470e14	−	7.90630e14i	0.288774	−	0.500172i
$581$	2.45593e14	−	4.25380e14i	0.153903	−	0.266568i
$582$		0			0
$583$	4.26635e14	+	7.38954e14i	0.262349	+	0.454402i
$584$	−1.23661e14			−0.0753290
$585$		0			0
$586$	5.74245e14			0.343289
$587$	−1.21713e15	−	2.10812e15i	−0.720818	−	1.24849i	−0.960672	−	0.277685i	$-0.910433\pi$
$587$	−1.21713e15	−	2.10812e15i	−0.720818	−	1.24849i	0.239854	−	0.970809i	$-0.422900\pi$
$588$		0			0
$589$	2.81692e14	−	4.87904e14i	0.163734	−	0.283596i
$590$	3.00766e14	−	5.20942e14i	0.173198	−	0.299988i
$591$		0			0
$592$	8.99347e13	+	1.55771e14i	0.0508344	+	0.0880478i
$593$	3.03318e14			0.169863			0.0849313	−	0.996387i	$-0.472933\pi$
$593$	3.03318e14			0.169863			0.0849313	+	0.996387i	$0.472933\pi$
$594$		0			0
$595$	5.58507e14			0.307033
$596$	8.20959e14	+	1.42194e15i	0.447164	+	0.774511i
$597$		0			0
$598$	−1.29251e14	+	2.23870e14i	−0.0691159	+	0.119712i
$599$	−8.50992e14	+	1.47396e15i	−0.450898	+	0.780978i	−0.998442	−	0.0557990i	$-0.982229\pi$
$599$	−8.50992e14	+	1.47396e15i	−0.450898	+	0.780978i	0.547544	+	0.836777i	$0.315563\pi$
$600$		0			0
$601$	−1.16961e15	−	2.02582e15i	−0.608458	−	1.05388i	−0.991495	−	0.130147i	$-0.958455\pi$
$601$	−1.16961e15	−	2.02582e15i	−0.608458	−	1.05388i	0.383036	−	0.923733i	$-0.374878\pi$
$602$	6.88207e12			0.00354763
$603$		0			0
$604$	1.21359e15			0.614282
$605$	1.20344e12	+	2.08442e12i	0.000603630	+	0.00104552i
$606$		0			0
$607$	1.24804e15	−	2.16166e15i	0.614737	−	1.06476i	−0.375694	−	0.926744i	$-0.622595\pi$
$607$	1.24804e15	−	2.16166e15i	0.614737	−	1.06476i	0.990431	−	0.138012i	$-0.0440712\pi$
$608$	−1.04858e15	+	1.81620e15i	−0.511839	+	0.886532i
$609$		0			0
$610$	4.03198e14	+	6.98359e14i	0.193287	+	0.334784i
$611$	1.55258e15			0.737612
$612$		0			0
$613$	2.47301e15			1.15397			0.576983	−	0.816756i	$-0.304230\pi$
$613$	2.47301e15			1.15397			0.576983	+	0.816756i	$0.304230\pi$
$614$	−1.83733e14	−	3.18235e14i	−0.0849692	−	0.147171i
$615$		0			0
$616$	3.78113e14	−	6.54911e14i	0.171762	−	0.297501i
$617$	1.21684e13	−	2.10763e13i	0.00547854	−	0.00948911i	−0.863273	−	0.504737i	$-0.831589\pi$
$617$	1.21684e13	−	2.10763e13i	0.00547854	−	0.00948911i	0.868752	+	0.495248i	$0.164923\pi$
$618$		0			0
$619$	−2.11273e15	−	3.65935e15i	−0.934425	−	1.61847i	−0.775656	−	0.631156i	$-0.782581\pi$
$619$	−2.11273e15	−	3.65935e15i	−0.934425	−	1.61847i	−0.158769	−	0.987316i	$-0.550753\pi$
$620$	−3.75702e14			−0.164698
$621$		0			0
$622$	−1.19700e15			−0.515523
$623$	2.09241e14	+	3.62416e14i	0.0893227	+	0.154711i
$624$		0			0
$625$	2.44448e14	−	4.23396e14i	0.102529	−	0.177585i
$626$	1.19377e15	−	2.06767e15i	0.496320	−	0.859652i
$627$		0			0
$628$	9.67926e14	+	1.67650e15i	0.395425	+	0.684896i
$629$	−1.25835e15			−0.509594
$630$		0			0
$631$	−4.26326e15			−1.69660			−0.848302	−	0.529513i	$-0.822375\pi$
$631$	−4.26326e15			−1.69660			−0.848302	+	0.529513i	$0.822375\pi$
$632$	1.61006e15	+	2.78870e15i	0.635180	+	1.10016i
$633$		0			0
$634$	1.00043e15	−	1.73280e15i	0.387879	−	0.671826i
$635$	−6.34462e14	+	1.09892e15i	−0.243865	+	0.422387i
$636$		0			0
$637$	−4.90201e14	−	8.49052e14i	−0.185186	−	0.320751i
$638$	1.64755e15			0.617055
$639$		0			0
$640$	1.63288e15			0.601126
$641$	5.04148e14	+	8.73210e14i	0.184009	+	0.318713i	0.943242	−	0.332106i	$-0.107759\pi$
$641$	5.04148e14	+	8.73210e14i	0.184009	+	0.318713i	−0.759233	+	0.650819i	$0.774426\pi$
$642$		0			0
$643$	−1.51991e14	+	2.63256e14i	−0.0545328	+	0.0944536i	−0.892003	−	0.452029i	$-0.850700\pi$
$643$	−1.51991e14	+	2.63256e14i	−0.0545328	+	0.0944536i	0.837470	+	0.546483i	$0.184034\pi$
$644$	2.29752e14	−	3.97942e14i	0.0817310	−	0.141562i
$645$		0			0
$646$	−8.83525e14	−	1.53031e15i	−0.308987	−	0.535181i
$647$	−3.43583e15			−1.19140			−0.595700	−	0.803207i	$-0.703125\pi$
$647$	−3.43583e15			−1.19140			−0.595700	+	0.803207i	$0.703125\pi$
$648$		0			0
$649$	−2.77421e15			−0.945788
$650$	−1.76782e14	−	3.06196e14i	−0.0597607	−	0.103509i
$651$		0			0
$652$	−2.63365e14	+	4.56161e14i	−0.0875379	+	0.151620i
$653$	−5.92694e14	+	1.02658e15i	−0.195347	+	0.338352i	−0.947014	−	0.321191i	$-0.895917\pi$
$653$	−5.92694e14	+	1.02658e15i	−0.195347	+	0.338352i	0.751667	+	0.659543i	$0.229250\pi$
$654$		0			0
$655$	−1.52514e15	−	2.64162e15i	−0.494291	−	0.856138i
$656$	−3.04157e14			−0.0977522
$657$		0			0
$658$	1.07993e15			0.341312
$659$	−1.13255e15	−	1.96164e15i	−0.354967	−	0.614821i	0.632145	−	0.774850i	$-0.282175\pi$
$659$	−1.13255e15	−	1.96164e15i	−0.354967	−	0.614821i	−0.987112	+	0.160029i	$0.948841\pi$
$660$		0			0
$661$	2.66506e15	−	4.61602e15i	0.821484	−	1.42285i	−0.0830931	−	0.996542i	$-0.526480\pi$
$661$	2.66506e15	−	4.61602e15i	0.821484	−	1.42285i	0.904577	−	0.426310i	$-0.140187\pi$
$662$	7.63008e14	−	1.32157e15i	0.233244	−	0.403990i
$663$		0			0
$664$	1.23911e15	+	2.14621e15i	0.372552	+	0.645279i
$665$	8.62227e14			0.257100
$666$		0			0
$667$	2.39392e15			0.702130
$668$	−2.02756e15	−	3.51183e15i	−0.589797	−	1.02156i
$669$		0			0
$670$	−8.97327e14	+	1.55422e15i	−0.256767	+	0.444733i
$671$	1.85951e15	−	3.22076e15i	0.527745	−	0.914082i
$672$		0			0
$673$	−2.37060e15	−	4.10600e15i	−0.661874	−	1.14640i	−0.980123	−	0.198392i	$-0.936428\pi$
$673$	−2.37060e15	−	4.10600e15i	−0.661874	−	1.14640i	0.318249	−	0.948007i	$-0.396905\pi$
$674$	2.90403e15			0.804215
$675$		0			0
$676$	2.14673e15			0.584886
$677$	−7.06536e14	−	1.22376e15i	−0.190940	−	0.330717i	0.754622	−	0.656160i	$-0.227820\pi$
$677$	−7.06536e14	−	1.22376e15i	−0.190940	−	0.330717i	−0.945562	+	0.325442i	$0.894487\pi$
$678$		0			0
$679$	6.28014e14	−	1.08775e15i	0.166988	−	0.289232i
$680$	−1.40894e15	+	2.44036e15i	−0.371616	+	0.643658i
$681$		0			0
$682$	−3.39007e14	−	5.87178e14i	−0.0879822	−	0.152390i
$683$	3.03116e15			0.780359			0.390180	−	0.920739i	$-0.372413\pi$
$683$	3.03116e15			0.780359			0.390180	+	0.920739i	$0.372413\pi$
$684$		0			0
$685$	−1.43547e15			−0.363660
$686$	−7.38268e14	−	1.27872e15i	−0.185537	−	0.321360i
$687$		0			0
$688$	8.45270e12	−	1.46405e13i	0.00209054	−	0.00362093i
$689$	4.61051e14	−	7.98564e14i	0.113121	−	0.195931i
$690$		0			0
$691$	1.37366e15	+	2.37924e15i	0.331703	+	0.574526i	0.982846	−	0.184429i	$-0.0590436\pi$
$691$	1.37366e15	+	2.37924e15i	0.331703	+	0.574526i	−0.651143	+	0.758955i	$0.725710\pi$
$692$	−1.39897e15			−0.335139
$693$		0			0
$694$	3.73588e15			0.880878
$695$	1.44126e15	+	2.49633e15i	0.337151	+	0.583963i
$696$		0			0
$697$	1.06393e15	−	1.84278e15i	0.244981	−	0.424320i
$698$	3.07716e14	−	5.32980e14i	0.0702984	−	0.121760i
$699$		0			0
$700$	3.14242e14	+	5.44283e14i	0.0706683	+	0.122401i
$701$	−5.72747e15			−1.27795			−0.638974	−	0.769228i	$-0.720641\pi$
$701$	−5.72747e15			−1.27795			−0.638974	+	0.769228i	$0.720641\pi$
$702$		0			0
$703$	−1.94265e15			−0.426718
$704$	7.21538e14	+	1.24974e15i	0.157257	+	0.272377i
$705$		0			0
$706$	2.98918e14	−	5.17741e14i	0.0641395	−	0.111093i
$707$	−6.84352e14	+	1.18533e15i	−0.145704	+	0.252368i
$708$		0			0
$709$	−3.49163e14	−	6.04768e14i	−0.0731938	−	0.126775i	0.827106	−	0.562047i	$-0.189986\pi$
$709$	−3.49163e14	−	6.04768e14i	−0.0731938	−	0.126775i	−0.900299	+	0.435271i	$0.856652\pi$
$710$	1.13503e15			0.236095
$711$		0			0
$712$	−2.11140e15			−0.432445
$713$	−4.92585e14	−	8.53182e14i	−0.100113	−	0.173400i
$714$		0			0
$715$	7.45911e14	−	1.29196e15i	0.149281	−	0.258562i
$716$	−1.23750e15	+	2.14341e15i	−0.245767	+	0.425681i
$717$		0			0
$718$	1.89101e15	+	3.27533e15i	0.369836	+	0.640575i
$719$	−9.70979e15			−1.88452			−0.942260	−	0.334882i	$-0.891304\pi$
$719$	−9.70979e15			−1.88452			−0.942260	+	0.334882i	$0.891304\pi$
$720$		0			0
$721$	3.78004e15			0.722525
$722$	3.38926e13	+	5.87037e13i	0.00642910	+	0.0111355i
$723$		0			0
$724$	−7.33626e14	+	1.27068e15i	−0.137061	+	0.237396i
$725$	−1.63713e15	+	2.83560e15i	−0.303547	+	0.525758i
$726$		0			0
$727$	−1.23234e15	−	2.13448e15i	−0.225057	−	0.389810i	0.731280	−	0.682078i	$-0.238923\pi$
$727$	−1.23234e15	−	2.13448e15i	−0.225057	−	0.389810i	−0.956337	+	0.292268i	$0.905590\pi$
$728$	−8.17230e14			−0.148123
$729$		0			0
$730$	−1.69683e14			−0.0302944
$731$	5.91345e13	+	1.02424e14i	0.0104784	+	0.0181491i
$732$		0			0
$733$	−3.95643e15	+	6.85273e15i	−0.690607	+	1.19617i	0.281032	+	0.959698i	$0.409323\pi$
$733$	−3.95643e15	+	6.85273e15i	−0.690607	+	1.19617i	−0.971639	+	0.236469i	$0.924010\pi$
$734$	2.13481e15	−	3.69761e15i	0.369855	−	0.640608i
$735$		0			0
$736$	1.83362e15	+	3.17593e15i	0.312955	+	0.542055i
$737$	8.27677e15			1.40213
$738$		0			0
$739$	−8.40694e15			−1.40312			−0.701558	−	0.712613i	$-0.747512\pi$
$739$	−8.40694e15			−1.40312			−0.701558	+	0.712613i	$0.747512\pi$
$740$	6.47746e14	+	1.12193e15i	0.107308	+	0.185862i
$741$		0			0
$742$	3.20692e14	−	5.55455e14i	0.0523440	−	0.0906625i
$743$	6.81435e14	−	1.18028e15i	0.110404	−	0.191226i	−0.805529	−	0.592556i	$-0.798119\pi$
$743$	6.81435e14	−	1.18028e15i	0.110404	−	0.191226i	0.915933	+	0.401330i	$0.131452\pi$
$744$		0			0
$745$	2.69377e15	+	4.66575e15i	0.430033	+	0.744838i
$746$	−1.32388e15			−0.209790
$747$		0			0
$748$	5.43462e15			0.848614
$749$	−7.55500e14	−	1.30856e15i	−0.117107	−	0.202836i
$750$		0			0
$751$	−3.40861e15	+	5.90389e15i	−0.520664	+	0.901817i	0.479047	+	0.877789i	$0.340982\pi$
$751$	−3.40861e15	+	5.90389e15i	−0.520664	+	0.901817i	−0.999711	+	0.0240276i	$0.992351\pi$
$752$	1.32639e15	−	2.29737e15i	0.201128	−	0.348364i
$753$		0			0
$754$	−8.90225e14	−	1.54191e15i	−0.133032	−	0.230419i
$755$	3.98208e15			0.590747
$756$		0			0
$757$	−6.67049e14			−0.0975282			−0.0487641	−	0.998810i	$-0.515528\pi$
$757$	−6.67049e14			−0.0975282			−0.0487641	+	0.998810i	$0.515528\pi$
$758$	−1.75756e15	−	3.04418e15i	−0.255111	−	0.441865i
$759$		0			0
$760$	−2.17513e15	+	3.76744e15i	−0.311180	+	0.538979i
$761$	−3.87204e15	+	6.70657e15i	−0.549951	+	0.952544i	0.448326	+	0.893870i	$0.352020\pi$
$761$	−3.87204e15	+	6.70657e15i	−0.549951	+	0.952544i	−0.998277	+	0.0586734i	$0.981313\pi$
$762$		0			0
$763$	6.15197e14	+	1.06555e15i	0.0861250	+	0.149173i
$764$	4.06626e15			0.565173
$765$		0			0
$766$	−5.55479e15			−0.761043
$767$	1.49900e15	+	2.59634e15i	0.203905	+	0.353173i
$768$		0			0
$769$	−1.26206e15	+	2.18594e15i	−0.169232	+	0.293119i	−0.938150	−	0.346228i	$-0.887462\pi$
$769$	−1.26206e15	+	2.18594e15i	−0.169232	+	0.293119i	0.768918	+	0.639348i	$0.220796\pi$
$770$	5.18831e14	−	8.98642e14i	0.0690760	−	0.119643i
$771$		0			0
$772$	4.00560e15	+	6.93790e15i	0.525741	+	0.910611i
$773$	1.11453e16			1.45246			0.726229	−	0.687453i	$-0.241271\pi$
$773$	1.11453e16			1.45246			0.726229	+	0.687453i	$0.241271\pi$
$774$		0			0
$775$	1.34746e15			0.173124
$776$	3.16857e15	+	5.48813e15i	0.404226	+	0.700140i
$777$		0			0
$778$	−1.79846e15	+	3.11502e15i	−0.226210	+	0.391808i
$779$	1.64250e15	−	2.84489e15i	0.205140	−	0.355312i
$780$		0			0
$781$	−2.61732e15	−	4.53334e15i	−0.322312	−	0.558261i
$782$	−3.08998e15			−0.377849
$783$		0			0
$784$	−1.67514e15			−0.201981
$785$	3.17601e15	+	5.50101e15i	0.380275	+	0.658656i
$786$		0			0
$787$	−6.61355e15	+	1.14550e16i	−0.780861	+	1.35249i	0.150580	+	0.988598i	$0.451886\pi$
$787$	−6.61355e15	+	1.14550e16i	−0.780861	+	1.35249i	−0.931441	+	0.363893i	$0.881447\pi$
$788$	2.11680e15	−	3.66641e15i	0.248191	−	0.429880i
$789$		0			0
$790$	2.20925e15	+	3.82654e15i	0.255444	+	0.442443i
$791$	−1.42570e15			−0.163703
$792$		0			0
$793$	−4.01902e15			−0.455112
$794$	−2.49733e15	−	4.32550e15i	−0.280843	−	0.486434i
$795$		0			0
$796$	5.36096e14	−	9.28546e14i	0.0594594	−	0.102987i
$797$	1.15124e15	−	1.99400e15i	0.126807	−	0.219637i	−0.795631	−	0.605782i	$-0.792860\pi$
$797$	1.15124e15	−	1.99400e15i	0.126807	−	0.219637i	0.922438	+	0.386145i	$0.126194\pi$
$798$		0			0
$799$	9.27933e15	+	1.60723e16i	1.00811	+	1.74610i
$800$	−5.01586e15			−0.541191
$801$		0			0
$802$	3.20179e15			0.340748
$803$	3.91280e14	+	6.77717e14i	0.0413573	+	0.0716330i
$804$		0			0
$805$	7.53874e14	−	1.30575e15i	0.0785997	−	0.136139i
$806$	−3.66354e14	+	6.34544e14i	−0.0379366	+	0.0657081i
$807$		0			0
$808$	−3.45282e15	−	5.98046e15i	−0.352705	−	0.610903i
$809$	−5.60472e15			−0.568639			−0.284320	−	0.958730i	$-0.591768\pi$
$809$	−5.60472e15			−0.568639			−0.284320	+	0.958730i	$0.591768\pi$
$810$		0			0
$811$	−5.08516e15			−0.508968			−0.254484	−	0.967077i	$-0.581906\pi$
$811$	−5.08516e15			−0.508968			−0.254484	+	0.967077i	$0.581906\pi$
$812$	1.58243e15	+	2.74085e15i	0.157314	+	0.272475i
$813$		0			0
$814$	−1.16896e15	+	2.02470e15i	−0.114648	+	0.198576i
$815$	−8.64166e14	+	1.49678e15i	−0.0841842	+	0.145811i
$816$		0			0
$817$	9.12922e13	+	1.58123e14i	0.00877430	+	0.0151975i
$818$	−4.94802e15			−0.472377
$819$		0			0
$820$	−2.19066e15			−0.206348
$821$	1.39555e14	+	2.41717e14i	0.0130575	+	0.0226162i	0.872480	−	0.488649i	$-0.162510\pi$
$821$	1.39555e14	+	2.41717e14i	0.0130575	+	0.0226162i	−0.859423	+	0.511265i	$0.829177\pi$
$822$		0			0
$823$	6.76326e15	−	1.17143e16i	0.624391	−	1.08148i	−0.364267	−	0.931295i	$-0.618680\pi$
$823$	6.76326e15	−	1.17143e16i	0.624391	−	1.08148i	0.988658	−	0.150183i	$-0.0479863\pi$
$824$	−9.53590e15	+	1.65167e16i	−0.874504	+	1.51469i
$825$		0			0
$826$	1.04266e15	+	1.80593e15i	0.0943520	+	0.163422i
$827$	−2.72544e14			−0.0244994			−0.0122497	−	0.999925i	$-0.503899\pi$
$827$	−2.72544e14			−0.0244994			−0.0122497	+	0.999925i	$0.503899\pi$
$828$		0			0
$829$	1.80459e16			1.60077			0.800385	−	0.599486i	$-0.204628\pi$
$829$	1.80459e16			1.60077			0.800385	+	0.599486i	$0.204628\pi$
$830$	1.70026e15	+	2.94494e15i	0.149826	+	0.259506i
$831$		0			0
$832$	7.79743e14	−	1.35055e15i	0.0678068	−	0.117445i
$833$	5.85956e15	−	1.01491e16i	0.506195	−	0.876755i
$834$		0			0
$835$	−6.65292e15	−	1.15232e16i	−0.567201	−	0.982421i
$836$	8.38999e15			0.710603
$837$		0			0
$838$	−1.76168e15			−0.147260
$839$	−3.98092e15	−	6.89515e15i	−0.330592	−	0.572602i	0.652036	−	0.758188i	$-0.273915\pi$
$839$	−3.98092e15	−	6.89515e15i	−0.330592	−	0.572602i	−0.982628	+	0.185586i	$0.940582\pi$
$840$		0			0
$841$	−2.14388e15	+	3.71330e15i	−0.175720	+	0.304356i
$842$	−2.05334e15	+	3.55649e15i	−0.167203	+	0.289605i
$843$		0			0
$844$	−4.99977e15	−	8.65986e15i	−0.401853	−	0.696029i
$845$	7.04397e15			0.562478
$846$		0			0
$847$	−8.34387e12			−0.000657671
$848$	−7.87762e14	−	1.36444e15i	−0.0616904	−	0.106851i
$849$		0			0
$850$	2.11315e15	−	3.66009e15i	0.163353	−	0.282935i
$851$	−1.69853e15	+	2.94193e15i	−0.130455	+	0.225954i
$852$		0			0
$853$	7.49132e15	+	1.29754e16i	0.567988	+	0.983783i	0.996765	+	0.0803730i	$0.0256112\pi$
$853$	7.49132e15	+	1.29754e16i	0.567988	+	0.983783i	−0.428777	+	0.903410i	$0.641056\pi$
$854$	−2.79550e15			−0.210592
$855$		0			0
$856$	7.62358e15			0.566961
$857$	−1.11281e16	−	1.92744e16i	−0.822290	−	1.42425i	−0.903973	−	0.427590i	$-0.859363\pi$
$857$	−1.11281e16	−	1.92744e16i	−0.822290	−	1.42425i	0.0816825	−	0.996658i	$-0.473971\pi$
$858$		0			0
$859$	−2.72118e15	+	4.71323e15i	−0.198516	+	0.343840i	−0.948047	−	0.318129i	$-0.896945\pi$
$859$	−2.72118e15	+	4.71323e15i	−0.198516	+	0.343840i	0.749532	+	0.661969i	$0.230279\pi$
$860$	6.08798e13	−	1.05447e14i	0.00441298	−	0.00764351i
$861$		0			0
$862$	−8.61310e14	−	1.49183e15i	−0.0616410	−	0.106765i
$863$	−1.08110e16			−0.768787			−0.384393	−	0.923169i	$-0.625589\pi$
$863$	−1.08110e16			−0.768787			−0.384393	+	0.923169i	$0.625589\pi$
$864$		0			0
$865$	−4.59037e15			−0.322299
$866$	−1.19857e15	−	2.07599e15i	−0.0836213	−	0.144836i
$867$		0			0
$868$	6.51217e14	−	1.12794e15i	0.0448608	−	0.0777013i
$869$	1.01889e16	−	1.76476e16i	0.697456	−	1.20803i
$870$		0			0
$871$	−4.47222e15	−	7.74611e15i	−0.302290	−	0.523581i
$872$	−6.20782e15			−0.416964
$873$		0			0
$874$	−4.77033e15			−0.316399
$875$	3.00556e15	+	5.20578e15i	0.198098	+	0.343116i
$876$		0			0
$877$	1.40512e16	−	2.43374e16i	0.914568	−	1.58408i	0.107037	−	0.994255i	$-0.465864\pi$
$877$	1.40512e16	−	2.43374e16i	0.914568	−	1.58408i	0.807532	−	0.589824i	$-0.200803\pi$
$878$	3.48375e14	−	6.03403e14i	0.0225334	−	0.0390290i
$879$		0			0
$880$	−1.27448e15	−	2.20746e15i	−0.0814101	−	0.141006i
$881$	−4.22209e15			−0.268016			−0.134008	−	0.990980i	$-0.542785\pi$
$881$	−4.22209e15			−0.268016			−0.134008	+	0.990980i	$0.542785\pi$
$882$		0			0
$883$	5.16092e14			0.0323551			0.0161776	−	0.999869i	$-0.494850\pi$
$883$	5.16092e14			0.0323551			0.0161776	+	0.999869i	$0.494850\pi$
$884$	−2.93651e15	−	5.08618e15i	−0.182955	−	0.316887i
$885$		0			0
$886$	3.94044e15	−	6.82504e15i	0.242471	−	0.419971i
$887$	2.85953e15	−	4.95285e15i	0.174870	−	0.302883i	−0.765246	−	0.643737i	$-0.777383\pi$
$887$	2.85953e15	−	4.95285e15i	0.174870	−	0.302883i	0.940116	+	0.340854i	$0.110716\pi$
$888$		0			0
$889$	−2.19947e15	−	3.80959e15i	−0.132849	−	0.230101i
$890$	−2.89718e15			−0.173912
$891$		0			0
$892$	−1.07969e16			−0.640167
$893$	1.43255e16	+	2.48125e16i	0.844162	+	1.46213i
$894$		0			0
$895$	−4.06054e15	+	7.03307e15i	−0.236351	+	0.409372i
$896$	−2.83033e15	+	4.90228e15i	−0.163736	+	0.283599i
$897$		0			0
$898$	−7.34842e15	−	1.27278e16i	−0.419927	−	0.727335i
$899$	6.78541e15			0.385388
$900$		0			0
$901$	1.10223e16			0.618421
$902$	−1.97670e15	−	3.42374e15i	−0.110231	−	0.190926i
$903$		0			0
$904$	3.59660e15	−	6.22950e15i	0.198137	−	0.343184i
$905$	−2.40721e15	+	4.16941e15i	−0.131810	+	0.228301i
$906$		0			0
$907$	4.21889e13	+	7.30733e13i	0.00228222	+	0.00395293i	0.867164	−	0.498022i	$-0.165940\pi$
$907$	4.21889e13	+	7.30733e13i	0.00228222	+	0.00395293i	−0.864882	+	0.501975i	$0.832607\pi$
$908$	−2.00168e15			−0.107628
$909$		0			0
$910$	−1.12137e15			−0.0595691
$911$	−5.50453e15	−	9.53412e15i	−0.290649	−	0.503419i	0.683314	−	0.730124i	$-0.260538\pi$
$911$	−5.50453e15	−	9.53412e15i	−0.290649	−	0.503419i	−0.973963	+	0.226705i	$0.927205\pi$
$912$		0			0
$913$	7.84145e15	−	1.35818e16i	0.409079	−	0.708545i
$914$	−3.64180e15	+	6.30778e15i	−0.188848	+	0.327094i
$915$		0			0
$916$	−8.70277e15	−	1.50736e16i	−0.445895	−	0.772312i
$917$	1.05743e16			0.538544
$918$		0			0
$919$	−4.86351e15			−0.244746			−0.122373	−	0.992484i	$-0.539050\pi$
$919$	−4.86351e15			−0.244746			−0.122373	+	0.992484i	$0.539050\pi$
$920$	3.80359e15	+	6.58800e15i	0.190266	+	0.329550i
$921$		0			0
$922$	−8.75170e15	+	1.51584e16i	−0.432586	+	0.749260i
$923$	−2.82846e15	+	4.89903e15i	−0.138976	+	0.240714i
$924$		0			0
$925$	−2.32315e15	−	4.02381e15i	−0.112797	−	0.195370i
$926$	2.93252e15			0.141540
$927$		0			0
$928$	−2.52584e16			−1.20474
$929$	1.78767e15	+	3.09634e15i	0.0847620	+	0.146812i	0.905290	−	0.424795i	$-0.139654\pi$
$929$	1.78767e15	+	3.09634e15i	0.0847620	+	0.146812i	−0.820528	+	0.571607i	$0.806320\pi$
$930$		0			0
$931$	9.04603e15	−	1.56682e16i	0.423872	−	0.734168i
$932$	1.29266e16	−	2.23896e16i	0.602140	−	1.04294i
$933$		0			0
$934$	−7.40857e15	−	1.28320e16i	−0.341057	−	0.590727i
$935$	1.78323e16			0.816102
$936$		0			0
$937$	3.86373e16			1.74759			0.873795	−	0.486295i	$-0.161652\pi$
$937$	3.86373e16			1.74759			0.873795	+	0.486295i	$0.161652\pi$
$938$	−3.11073e15	−	5.38795e15i	−0.139877	−	0.242274i
$939$		0			0
$940$	9.55320e15	−	1.65466e16i	0.424567	−	0.735371i
$941$	−1.74499e16	+	3.02241e16i	−0.770991	+	1.33539i	0.166030	+	0.986121i	$0.446905\pi$
$941$	−1.74499e16	+	3.02241e16i	−0.770991	+	1.33539i	−0.937021	+	0.349274i	$0.886428\pi$
$942$		0			0
$943$	−2.87219e15	−	4.97477e15i	−0.125429	−	0.217250i
$944$	5.12245e15			0.222398
$945$		0			0
$946$	2.19735e14			0.00942969
$947$	−1.42561e16	−	2.46924e16i	−0.608243	−	1.05351i	−0.991530	−	0.129879i	$-0.958541\pi$
$947$	−1.42561e16	−	2.46924e16i	−0.608243	−	1.05351i	0.383287	−	0.923629i	$-0.374792\pi$
$948$		0			0
$949$	4.22844e14	−	7.32387e14i	0.0178327	−	0.0308871i
$950$	3.26230e15	−	5.65046e15i	0.136787	−	0.236921i
$951$		0			0
$952$	−4.88434e15	−	8.45992e15i	−0.202443	−	0.350641i
$953$	−4.00334e16			−1.64973			−0.824863	−	0.565332i	$-0.808748\pi$
$953$	−4.00334e16			−1.64973			−0.824863	+	0.565332i	$0.808748\pi$
$954$		0			0
$955$	1.33424e16			0.543520
$956$	5.25473e15	+	9.10146e15i	0.212830	+	0.368632i
$957$		0			0
$958$	1.26101e16	−	2.18413e16i	0.504902	−	0.874515i
$959$	2.48815e15	−	4.30960e15i	0.0990544	−	0.171567i
$960$		0			0
$961$	1.13080e16	+	1.95861e16i	0.445050	+	0.770849i
$962$	2.52652e15			0.0988688
$963$		0			0
$964$	3.40484e14			0.0131726
$965$	1.31434e16	+	2.27650e16i	0.505599	+	0.875724i
$966$		0			0
$967$	−9.24765e15	+	1.60174e16i	−0.351711	+	0.609181i	−0.986549	−	0.163464i	$-0.947733\pi$
$967$	−9.24765e15	+	1.60174e16i	−0.351711	+	0.609181i	0.634838	+	0.772645i	$0.281067\pi$
$968$	2.10490e13	−	3.64580e13i	0.000796008	−	0.00137873i
$969$		0			0
$970$	4.34779e15	+	7.53059e15i	0.162564	+	0.281569i
$971$	2.14877e16			0.798884			0.399442	−	0.916759i	$-0.369204\pi$
$971$	2.14877e16			0.798884			0.399442	+	0.916759i	$0.369204\pi$
$972$		0			0
$973$	−9.99271e15			−0.367335
$974$	2.63892e15	+	4.57074e15i	0.0964610	+	0.167075i
$975$		0			0
$976$	−3.43350e15	+	5.94699e15i	−0.124097	+	0.214943i
$977$	−4.36940e15	+	7.56802e15i	−0.157037	+	0.271996i	−0.933799	−	0.357798i	$-0.883527\pi$
$977$	−4.36940e15	+	7.56802e15i	−0.157037	+	0.271996i	0.776762	+	0.629794i	$0.216861\pi$
$978$		0			0
$979$	6.68076e15	+	1.15714e16i	0.237422	+	0.411227i
$980$	−1.20650e16			−0.426368
$981$		0			0
$982$	1.16127e16			0.405808
$983$	5.94621e15	+	1.02991e16i	0.206631	+	0.357896i	0.950651	−	0.310261i	$-0.100417\pi$
$983$	5.94621e15	+	1.02991e16i	0.206631	+	0.357896i	−0.744020	+	0.668157i	$0.767083\pi$
$984$		0			0
$985$	6.94576e15	−	1.20304e16i	0.238682	−	0.413410i
$986$	1.06412e16	−	1.84311e16i	0.363637	−	0.629838i
$987$		0			0
$988$	−4.53340e15	−	7.85207e15i	−0.153201	−	0.265351i
$989$	3.19279e14			0.0107298
$990$		0			0
$991$	2.34409e16			0.779056			0.389528	−	0.921015i	$-0.372638\pi$
$991$	2.34409e16			0.779056			0.389528	+	0.921015i	$0.372638\pi$
$992$	5.19729e15	+	9.00197e15i	0.171776	+	0.297525i
$993$		0			0
$994$	−1.96738e15	+	3.40761e15i	−0.0643078	+	0.111384i
$995$	1.75907e15	−	3.04679e15i	0.0571814	−	0.0990411i
$996$		0			0
$997$	1.07002e16	+	1.85333e16i	0.344008	+	0.595840i	0.985173	−	0.171563i	$-0.0548819\pi$
$997$	1.07002e16	+	1.85333e16i	0.344008	+	0.595840i	−0.641165	+	0.767403i	$0.721549\pi$
$998$	−2.61307e15			−0.0835473
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.12.c.b.28.1		2
3.2	odd	2		81.12.c.d.28.1		2
9.2	odd	6		81.12.c.d.55.1		2
9.4	even	3		9.12.a.b.1.1		1
9.5	odd	6		1.12.a.a.1.1	✓	1
9.7	even	3	inner	81.12.c.b.55.1		2
36.23	even	6		16.12.a.a.1.1		1
36.31	odd	6		144.12.a.d.1.1		1
45.4	even	6		225.12.a.b.1.1		1
45.13	odd	12		225.12.b.d.199.1		2
45.14	odd	6		25.12.a.b.1.1		1
45.22	odd	12		225.12.b.d.199.2		2
45.23	even	12		25.12.b.b.24.2		2
45.32	even	12		25.12.b.b.24.1		2
63.5	even	6		49.12.c.c.18.1		2
63.23	odd	6		49.12.c.b.18.1		2
63.32	odd	6		49.12.c.b.30.1		2
63.41	even	6		49.12.a.a.1.1		1
63.59	even	6		49.12.c.c.30.1		2
72.5	odd	6		64.12.a.b.1.1		1
72.59	even	6		64.12.a.f.1.1		1
99.32	even	6		121.12.a.b.1.1		1
117.77	odd	6		169.12.a.a.1.1		1
144.5	odd	12		256.12.b.e.129.1		2
144.59	even	12		256.12.b.c.129.2		2
144.77	odd	12		256.12.b.e.129.2		2
144.131	even	12		256.12.b.c.129.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.12.a.a.1.1	✓	1	9.5	odd	6
9.12.a.b.1.1		1	9.4	even	3
16.12.a.a.1.1		1	36.23	even	6
25.12.a.b.1.1		1	45.14	odd	6
25.12.b.b.24.1		2	45.32	even	12
25.12.b.b.24.2		2	45.23	even	12
49.12.a.a.1.1		1	63.41	even	6
49.12.c.b.18.1		2	63.23	odd	6
49.12.c.b.30.1		2	63.32	odd	6
49.12.c.c.18.1		2	63.5	even	6
49.12.c.c.30.1		2	63.59	even	6
64.12.a.b.1.1		1	72.5	odd	6
64.12.a.f.1.1		1	72.59	even	6
81.12.c.b.28.1		2	1.1	even	1	trivial
81.12.c.b.55.1		2	9.7	even	3	inner
81.12.c.d.28.1		2	3.2	odd	2
81.12.c.d.55.1		2	9.2	odd	6
121.12.a.b.1.1		1	99.32	even	6
144.12.a.d.1.1		1	36.31	odd	6
169.12.a.a.1.1		1	117.77	odd	6
225.12.a.b.1.1		1	45.4	even	6
225.12.b.d.199.1		2	45.13	odd	12
225.12.b.d.199.2		2	45.22	odd	12
256.12.b.c.129.1		2	144.131	even	12
256.12.b.c.129.2		2	144.59	even	12
256.12.b.e.129.1		2	144.5	odd	12
256.12.b.e.129.2		2	144.77	odd	12

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	81.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-12.0000 - 20.7846i) q^{2} +(736.000 - 1274.79i) q^{4} +(2415.00 - 4182.90i) q^{5} +(8372.00 + 14500.7i) q^{7} -84480.0 q^{8} +O(q^{10})\)	\(q+(-12.0000 - 20.7846i) q^{2} +(736.000 - 1274.79i) q^{4} +(2415.00 - 4182.90i) q^{5} +(8372.00 + 14500.7i) q^{7} -84480.0 q^{8} -115920. q^{10} +(267306. + 462988. i) q^{11} +(288869. - 500336. i) q^{13} +(200928. - 348018. i) q^{14} +(-493568. - 854885. i) q^{16} +6.90593e6 q^{17} +1.06614e7 q^{19} +(-3.55488e6 - 6.15723e6i) q^{20} +(6.41534e6 - 1.11117e7i) q^{22} +(9.32164e6 - 1.61455e7i) q^{23} +(1.27496e7 + 2.20830e7i) q^{25} -1.38657e7 q^{26} +2.46472e7 q^{28} +(6.42033e7 + 1.11203e8i) q^{29} +(2.64216e7 - 4.57635e7i) q^{31} +(-9.83532e7 + 1.70353e8i) q^{32} +(-8.28712e7 - 1.43537e8i) q^{34} +8.08735e7 q^{35} -1.82213e8 q^{37} +(-1.27937e8 - 2.21593e8i) q^{38} +(-2.04019e8 + 3.53372e8i) q^{40} +(1.54060e8 - 2.66840e8i) q^{41} +(8.56285e6 + 1.48313e7i) q^{43} +7.86949e8 q^{44} -4.47439e8 q^{46} +(1.34367e9 + 2.32731e9i) q^{47} +(8.48483e8 - 1.46961e9i) q^{49} +(3.05991e8 - 5.29991e8i) q^{50} +(-4.25215e8 - 7.36494e8i) q^{52} +1.59606e9 q^{53} +2.58218e9 q^{55} +(-7.07267e8 - 1.22502e9i) q^{56} +(1.54088e9 - 2.66888e9i) q^{58} +(-2.59460e9 + 4.49398e9i) q^{59} +(-3.47824e9 - 6.02449e9i) q^{61} -1.26824e9 q^{62} +2.69930e9 q^{64} +(-1.39524e9 - 2.41662e9i) q^{65} +(7.74091e9 - 1.34077e10i) q^{67} +(5.08277e9 - 8.80361e9i) q^{68} +(-9.70482e8 - 1.68092e9i) q^{70} -9.79149e9 q^{71} +1.46379e9 q^{73} +(2.18656e9 + 3.78723e9i) q^{74} +(7.84681e9 - 1.35911e10i) q^{76} +(-4.47577e9 + 7.75226e9i) q^{77} +(-1.90584e10 - 3.30102e10i) q^{79} -4.76787e9 q^{80} -7.39489e9 q^{82} +(-1.46675e10 - 2.54049e10i) q^{83} +(1.66778e10 - 2.88868e10i) q^{85} +(2.05508e8 - 3.55951e8i) q^{86} +(-2.25820e10 - 3.91132e10i) q^{88} +2.49929e10 q^{89} +9.67365e9 q^{91} +(-1.37214e10 - 2.37662e10i) q^{92} +(3.22482e10 - 5.58555e10i) q^{94} +(2.57473e10 - 4.45957e10i) q^{95} +(-3.75068e10 - 6.49637e10i) q^{97} -4.07272e10 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 24 q^{2} + 1472 q^{4} + 4830 q^{5} + 16744 q^{7} - 168960 q^{8}+O(q^{10}) \) 2 * q - 24 * q^2 + 1472 * q^4 + 4830 * q^5 + 16744 * q^7 - 168960 * q^8	\( 2 q - 24 q^{2} + 1472 q^{4} + 4830 q^{5} + 16744 q^{7} - 168960 q^{8} - 231840 q^{10} + 534612 q^{11} + 577738 q^{13} + 401856 q^{14} - 987136 q^{16} + 13811868 q^{17} + 21322840 q^{19} - 7109760 q^{20} + 12830688 q^{22} + 18643272 q^{23} + 25499225 q^{25} - 27731424 q^{26} + 49294336 q^{28} + 128406630 q^{29} + 52843168 q^{31} - 196706304 q^{32} - 165742416 q^{34} + 161747040 q^{35} - 364426628 q^{37} - 255874080 q^{38} - 408038400 q^{40} + 308120442 q^{41} + 17125708 q^{43} + 1573897728 q^{44} - 894877056 q^{46} + 2687348496 q^{47} + 1696965207 q^{49} + 611981400 q^{50} - 850430336 q^{52} + 3192111396 q^{53} + 5164351920 q^{55} - 1414533120 q^{56} + 3081759120 q^{58} - 5189203740 q^{59} - 6956478662 q^{61} - 2536472064 q^{62} + 5398593536 q^{64} - 2790474540 q^{65} + 15481826884 q^{67} + 10165534848 q^{68} - 1940964480 q^{70} - 19582970544 q^{71} + 2927582644 q^{73} + 4373119536 q^{74} + 15693610240 q^{76} - 8951543328 q^{77} - 38116845680 q^{79} - 9535733760 q^{80} - 14789781216 q^{82} - 29335099668 q^{83} + 33355661220 q^{85} + 411016992 q^{86} - 45164021760 q^{88} + 49985834220 q^{89} + 19347290144 q^{91} - 27442896384 q^{92} + 64496363904 q^{94} + 51494658600 q^{95} - 75013568546 q^{97} - 81454329936 q^{98}+O(q^{100}) \) 2 * q - 24 * q^2 + 1472 * q^4 + 4830 * q^5 + 16744 * q^7 - 168960 * q^8 - 231840 * q^10 + 534612 * q^11 + 577738 * q^13 + 401856 * q^14 - 987136 * q^16 + 13811868 * q^17 + 21322840 * q^19 - 7109760 * q^20 + 12830688 * q^22 + 18643272 * q^23 + 25499225 * q^25 - 27731424 * q^26 + 49294336 * q^28 + 128406630 * q^29 + 52843168 * q^31 - 196706304 * q^32 - 165742416 * q^34 + 161747040 * q^35 - 364426628 * q^37 - 255874080 * q^38 - 408038400 * q^40 + 308120442 * q^41 + 17125708 * q^43 + 1573897728 * q^44 - 894877056 * q^46 + 2687348496 * q^47 + 1696965207 * q^49 + 611981400 * q^50 - 850430336 * q^52 + 3192111396 * q^53 + 5164351920 * q^55 - 1414533120 * q^56 + 3081759120 * q^58 - 5189203740 * q^59 - 6956478662 * q^61 - 2536472064 * q^62 + 5398593536 * q^64 - 2790474540 * q^65 + 15481826884 * q^67 + 10165534848 * q^68 - 1940964480 * q^70 - 19582970544 * q^71 + 2927582644 * q^73 + 4373119536 * q^74 + 15693610240 * q^76 - 8951543328 * q^77 - 38116845680 * q^79 - 9535733760 * q^80 - 14789781216 * q^82 - 29335099668 * q^83 + 33355661220 * q^85 + 411016992 * q^86 - 45164021760 * q^88 + 49985834220 * q^89 + 19347290144 * q^91 - 27442896384 * q^92 + 64496363904 * q^94 + 51494658600 * q^95 - 75013568546 * q^97 - 81454329936 * q^98

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