LMFDB - Embedded newform 81.12.c.d.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.d.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	0.967607	−	0.252462i	$-0.0812402\pi$
$2$	12.0000	+	20.7846i	0.265165	+	0.459279i	−0.702442	+	0.711741i	$0.747907\pi$
$3$		0			0
$3$		0			0
$4$	736.000	−	1274.79i	0.359375	−	0.622456i
$5$	−2415.00	+	4182.90i	−0.345607	+	0.598608i	−0.985464	−	0.169886i	$-0.945660\pi$
$5$	−2415.00	+	4182.90i	−0.345607	+	0.598608i	0.639857	+	0.768494i	$0.278994\pi$
$6$		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	$-0.999840\pi$
$11$	−267306.	−	462988.i	−0.500436	−	0.866781i	0.499563	−	0.866277i	$-0.333494\pi$
$12$		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	$-0.700803\pi$
$17$	−6.90593e6			−1.17965			−0.589825	+	0.807531i	$0.700803\pi$
$18$		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	−0.976586	−	0.215127i	$-0.930983\pi$
$23$	−9.32164e6	+	1.61455e7i	−0.301988	+	0.523058i	0.674599	+	0.738185i	$0.264317\pi$
$24$		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	$-0.969228\pi$
$29$	−6.42033e7	−	1.11203e8i	−0.581257	−	1.00677i	0.414073	−	0.910244i	$-0.364106\pi$
$30$		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	−0.950981	−	0.309249i	$-0.899922\pi$
$41$	−1.54060e8	+	2.66840e8i	−0.207673	+	0.359700i	0.743308	+	0.668949i	$0.233256\pi$
$42$		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	$-0.840478\pi$
$47$	−1.34367e9	−	2.32731e9i	−0.854586	−	1.48019i	0.0224426	−	0.999748i	$-0.492856\pi$
$48$		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	$-0.584422\pi$
$53$	−1.59606e9			−0.524241			−0.262120	+	0.965035i	$0.584422\pi$
$54$		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	−0.527023	−	0.849851i	$-0.676692\pi$
$59$	2.59460e9	−	4.49398e9i	0.472481	−	0.818362i	0.999504	+	0.0314895i	$0.0100251\pi$
$60$		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	$-0.395634\pi$
$71$	9.79149e9			0.644062			0.322031	+	0.946729i	$0.395634\pi$
$72$		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	0.994747	−	0.102366i	$-0.0326412\pi$
$83$	1.46675e10	+	2.54049e10i	0.408722	+	0.707927i	−0.586025	+	0.810293i	$0.699308\pi$
$84$		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	$-0.576235\pi$
$89$	−2.49929e10			−0.474430			−0.237215	+	0.971457i	$0.576235\pi$
$90$		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	0.605089	−	0.796158i	$-0.293137\pi$
$101$	−4.08715e10	−	7.07915e10i	−0.386948	−	0.670214i	−0.992037	+	0.125944i	$0.959804\pi$
$102$		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	$-0.399335\pi$
$107$	9.02413e10			0.622006			0.311003	+	0.950409i	$0.399335\pi$
$108$		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	−0.736630	−	0.676295i	$-0.763584\pi$
$113$	4.25734e10	−	7.37393e10i	0.217374	−	0.376502i	0.954004	+	0.299793i	$0.0969176\pi$
$114$		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	$0.420289\pi$
$131$	−3.15764e11	+	5.46920e11i	−0.715107	+	1.23860i	−0.962918	+	0.269793i	$0.913045\pi$
$132$		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	0.967053	−	0.254574i	$-0.0819351\pi$
$137$	1.48599e11	+	2.57382e11i	0.263059	+	0.455632i	−0.703994	+	0.710206i	$0.748602\pi$
$138$		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	$-0.619596\pi$
$149$	5.57717e11	−	9.65994e11i	0.622142	−	1.07758i	0.989086	−	0.147338i	$-0.0470705\pi$
$150$		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	$0.473020\pi$
$167$	−1.37742e12	+	2.38576e12i	−0.820587	+	1.42130i	−0.905245	+	0.424889i	$0.860313\pi$
$168$		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	0.958731	−	0.284316i	$-0.0917666\pi$
$173$	4.75194e11	+	8.23060e11i	0.233140	+	0.403811i	−0.725590	+	0.688127i	$0.758433\pi$
$174$		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	$-0.388917\pi$
$179$	1.68138e12			0.683873			0.341936	+	0.939723i	$0.388917\pi$
$180$		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	0.599701	−	0.800224i	$-0.295286\pi$
$191$	−1.38120e12	−	2.39231e12i	−0.393164	−	0.680980i	−0.992865	+	0.119244i	$0.961953\pi$
$192$		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	$-0.612226\pi$
$197$	−2.87609e12			−0.690619			−0.345309	+	0.938489i	$0.612226\pi$
$198$		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	0.901030	−	0.433756i	$-0.142812\pi$
$227$	6.79920e11	+	1.17766e12i	0.0748713	+	0.129681i	−0.826159	+	0.563437i	$0.809479\pi$
$228$		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	$-0.816135\pi$
$233$	−1.75634e13			−1.67552			−0.837761	+	0.546038i	$0.816135\pi$
$234$		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	−0.679132	−	0.734016i	$-0.737644\pi$
$239$	3.56979e12	−	6.18306e12i	0.296111	−	0.512879i	0.975243	+	0.221137i	$0.0709769\pi$
$240$		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	$-0.365081\pi$
$251$	1.29831e13			0.822567			0.411284	+	0.911507i	$0.365081\pi$
$252$		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	$0.398905\pi$
$257$	−1.19806e13	+	2.07510e13i	−0.666571	+	1.15453i	−0.978857	+	0.204546i	$0.934428\pi$
$258$		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	$0.0360907\pi$
$263$	1.21369e13	+	2.10217e13i	0.594771	+	1.03017i	−0.398808	+	0.917034i	$0.630576\pi$
$264$		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	$-0.311099\pi$
$269$	2.58377e13			1.11845			0.559225	+	0.829016i	$0.311099\pi$
$270$		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	0.629517	−	0.776987i	$-0.283253\pi$
$281$	−1.05179e13	−	1.82175e13i	−0.358132	−	0.620302i	−0.987649	+	0.156684i	$0.949919\pi$
$282$		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	−0.657583	−	0.753382i	$-0.728421\pi$
$293$	1.19634e13	−	2.07213e13i	0.323656	−	0.560589i	0.981239	+	0.192793i	$0.0617546\pi$
$294$		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	−0.999871	−	0.0160451i	$-0.994892\pi$
$311$	−2.49376e13	+	4.31932e13i	−0.486040	+	0.841846i	0.513831	+	0.857891i	$0.328226\pi$
$312$		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	$-0.905538\pi$
$317$	−4.16846e13	−	7.21999e13i	−0.731392	−	1.26681i	0.224897	−	0.974383i	$-0.427795\pi$
$318$		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	$-0.521389\pi$
$347$	7.78308e13	−	1.34807e14i	0.830499	−	1.43847i	0.897643	−	0.440724i	$-0.145278\pi$
$348$		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	0.799197	−	0.601069i	$-0.205258\pi$
$353$	−1.24549e13	−	2.15725e13i	−0.120943	−	0.209479i	−0.920140	+	0.391590i	$0.871925\pi$
$354$		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	$-0.254354\pi$
$359$	1.57584e14			1.39474			0.697370	+	0.716712i	$0.254354\pi$
$360$		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	$0.421389\pi$
$383$	−1.15725e14	+	2.00441e14i	−0.717519	+	1.24278i	−0.961980	+	0.273120i	$0.911945\pi$
$384$		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	0.996563	−	0.0828326i	$-0.0263967\pi$
$389$	7.49358e13	+	1.29793e14i	0.426547	+	0.738800i	−0.570017	+	0.821633i	$0.693063\pi$
$390$		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	−0.659488	−	0.751715i	$-0.729227\pi$
$401$	6.67040e13	−	1.15535e14i	0.321261	−	0.556440i	0.980748	+	0.195275i	$0.0625601\pi$
$402$		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	−0.927057	−	0.374920i	$-0.877670\pi$
$419$	−3.67018e13	+	6.35693e13i	−0.138838	+	0.240475i	0.788219	+	0.615395i	$0.211004\pi$
$420$		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	$-0.537081\pi$
$431$	−7.17758e13			−0.232463			−0.116231	+	0.993222i	$0.537081\pi$
$432$		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	0.541605	−	0.840633i	$-0.317817\pi$
$443$	−1.64185e14	−	2.84377e14i	−0.457207	−	0.791906i	−0.998812	+	0.0487274i	$0.984483\pi$
$444$		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	$-0.790867\pi$
$449$	−6.12368e14			−1.58364			−0.791822	+	0.610752i	$0.790867\pi$
$450$		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	$0.136977\pi$
$461$	3.64654e14	+	6.31599e14i	0.815691	+	1.41282i	−0.0931391	+	0.995653i	$0.529690\pi$
$462$		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	$-0.722353\pi$
$467$	−6.17381e14			−1.28621			−0.643103	+	0.765780i	$0.722353\pi$
$468$		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	$-0.765637\pi$
$479$	−5.25419e14	−	9.10052e14i	−0.952052	−	1.64900i	−0.211076	−	0.977470i	$-0.567697\pi$
$480$		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	−0.608834	−	0.793298i	$-0.708362\pi$
$491$	2.41932e14	−	4.19038e14i	0.382599	−	0.662682i	0.991433	+	0.130616i	$0.0416956\pi$
$492$		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	$-0.385926\pi$
$503$	5.06588e14			0.701506			0.350753	+	0.936468i	$0.385926\pi$
$504$		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	−0.892497	−	0.451053i	$-0.851049\pi$
$509$	−4.28767e13	+	7.42646e13i	−0.0556254	+	0.0963461i	0.836872	+	0.547399i	$0.184382\pi$
$510$		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	$-0.322450\pi$
$521$	9.27575e14			1.05862			0.529312	+	0.848428i	$0.322450\pi$
$522$		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	$-0.476396\pi$
$557$	1.87489e14			0.148174			0.0740870	+	0.997252i	$0.476396\pi$
$558$		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	−0.908042	−	0.418878i	$-0.862423\pi$
$563$	−1.22486e14	+	2.12151e14i	−0.0912618	+	0.158070i	0.816781	+	0.576949i	$0.195757\pi$
$564$		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	0.524302	−	0.851533i	$-0.324326\pi$
$569$	−6.76213e14	−	1.17124e15i	−0.475298	−	0.823240i	−0.999600	+	0.0282923i	$0.990993\pi$
$570$		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	$0.0895671\pi$
$587$	1.21713e15	+	2.10812e15i	0.720818	+	1.24849i	−0.239854	+	0.970809i	$0.577100\pi$
$588$		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	$-0.527067\pi$
$593$	−3.03318e14			−0.169863			−0.0849313	+	0.996387i	$0.527067\pi$
$594$		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	−0.547544	−	0.836777i	$-0.684437\pi$
$599$	8.50992e14	−	1.47396e15i	0.450898	−	0.780978i	0.998442	+	0.0557990i	$0.0177706\pi$
$600$		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	−0.868752	−	0.495248i	$-0.835077\pi$
$617$	−1.21684e13	+	2.10763e13i	−0.00547854	+	0.00948911i	0.863273	+	0.504737i	$0.168411\pi$
$618$		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	0.759233	−	0.650819i	$-0.225574\pi$
$641$	−5.04148e14	−	8.73210e14i	−0.184009	−	0.318713i	−0.943242	+	0.332106i	$0.892241\pi$
$642$		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	$-0.296875\pi$
$647$	3.43583e15			1.19140			0.595700	+	0.803207i	$0.296875\pi$
$648$		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	−0.751667	−	0.659543i	$-0.770750\pi$
$653$	5.92694e14	−	1.02658e15i	0.195347	−	0.338352i	0.947014	+	0.321191i	$0.104083\pi$
$654$		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	0.987112	−	0.160029i	$-0.0511587\pi$
$659$	1.13255e15	+	1.96164e15i	0.354967	+	0.614821i	−0.632145	+	0.774850i	$0.717825\pi$
$660$		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	0.945562	−	0.325442i	$-0.105513\pi$
$677$	7.06536e14	+	1.22376e15i	0.190940	+	0.330717i	−0.754622	+	0.656160i	$0.772180\pi$
$678$		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	$-0.627587\pi$
$683$	−3.03116e15			−0.780359			−0.390180	+	0.920739i	$0.627587\pi$
$684$		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	$-0.279359\pi$
$701$	5.72747e15			1.27795			0.638974	+	0.769228i	$0.279359\pi$
$702$		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	$-0.108696\pi$
$719$	9.70979e15			1.88452			0.942260	+	0.334882i	$0.108696\pi$
$720$		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	−0.915933	−	0.401330i	$-0.868548\pi$
$743$	−6.81435e14	+	1.18028e15i	−0.110404	+	0.191226i	0.805529	+	0.592556i	$0.201881\pi$
$744$		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	$-0.647980\pi$
$761$	3.87204e15	−	6.70657e15i	0.549951	−	0.952544i	0.998277	−	0.0586734i	$-0.0186871\pi$
$762$		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	$-0.758729\pi$
$773$	−1.11453e16			−1.45246			−0.726229	+	0.687453i	$0.758729\pi$
$774$		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	−0.922438	−	0.386145i	$-0.873806\pi$
$797$	−1.15124e15	+	1.99400e15i	−0.126807	+	0.219637i	0.795631	+	0.605782i	$0.207140\pi$
$798$		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	$-0.408232\pi$
$809$	5.60472e15			0.568639			0.284320	+	0.958730i	$0.408232\pi$
$810$		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	0.859423	−	0.511265i	$-0.170823\pi$
$821$	−1.39555e14	−	2.41717e14i	−0.0130575	−	0.0226162i	−0.872480	+	0.488649i	$0.837490\pi$
$822$		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	$-0.496101\pi$
$827$	2.72544e14			0.0244994			0.0122497	+	0.999925i	$0.496101\pi$
$828$		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	0.982628	−	0.185586i	$-0.0594183\pi$
$839$	3.98092e15	+	6.89515e15i	0.330592	+	0.572602i	−0.652036	+	0.758188i	$0.726085\pi$
$840$		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	$0.140637\pi$
$857$	1.11281e16	+	1.92744e16i	0.822290	+	1.42425i	−0.0816825	+	0.996658i	$0.526029\pi$
$858$		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	$-0.374411\pi$
$863$	1.08110e16			0.768787			0.384393	+	0.923169i	$0.374411\pi$
$864$		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	$-0.457215\pi$
$881$	4.22209e15			0.268016			0.134008	+	0.990980i	$0.457215\pi$
$882$		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	−0.940116	−	0.340854i	$-0.889284\pi$
$887$	−2.85953e15	+	4.95285e15i	−0.174870	+	0.302883i	0.765246	+	0.643737i	$0.222617\pi$
$888$		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	0.973963	−	0.226705i	$-0.0727954\pi$
$911$	5.50453e15	+	9.53412e15i	0.290649	+	0.503419i	−0.683314	+	0.730124i	$0.739462\pi$
$912$		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	0.820528	−	0.571607i	$-0.193680\pi$
$929$	−1.78767e15	−	3.09634e15i	−0.0847620	−	0.146812i	−0.905290	+	0.424795i	$0.860346\pi$
$930$		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	$-0.553095\pi$
$941$	1.74499e16	−	3.02241e16i	0.770991	−	1.33539i	0.937021	−	0.349274i	$-0.113572\pi$
$942$		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	$0.0414588\pi$
$947$	1.42561e16	+	2.46924e16i	0.608243	+	1.05351i	−0.383287	+	0.923629i	$0.625208\pi$
$948$		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	$-0.191252\pi$
$953$	4.00334e16			1.64973			0.824863	+	0.565332i	$0.191252\pi$
$954$		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	$-0.630796\pi$
$971$	−2.14877e16			−0.798884			−0.399442	+	0.916759i	$0.630796\pi$
$972$		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	−0.776762	−	0.629794i	$-0.783139\pi$
$977$	4.36940e15	−	7.56802e15i	0.157037	−	0.271996i	0.933799	+	0.357798i	$0.116473\pi$
$978$		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	0.744020	−	0.668157i	$-0.232917\pi$
$983$	−5.94621e15	−	1.02991e16i	−0.206631	−	0.357896i	−0.950651	+	0.310261i	$0.899583\pi$
$984$		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.d.28.1		2
3.2	odd	2		81.12.c.b.28.1		2
9.2	odd	6		81.12.c.b.55.1		2
9.4	even	3		1.12.a.a.1.1	✓	1
9.5	odd	6		9.12.a.b.1.1		1
9.7	even	3	inner	81.12.c.d.55.1		2
36.23	even	6		144.12.a.d.1.1		1
36.31	odd	6		16.12.a.a.1.1		1
45.4	even	6		25.12.a.b.1.1		1
45.13	odd	12		25.12.b.b.24.2		2
45.14	odd	6		225.12.a.b.1.1		1
45.22	odd	12		25.12.b.b.24.1		2
45.23	even	12		225.12.b.d.199.1		2
45.32	even	12		225.12.b.d.199.2		2
63.4	even	3		49.12.c.b.30.1		2
63.13	odd	6		49.12.a.a.1.1		1
63.31	odd	6		49.12.c.c.30.1		2
63.40	odd	6		49.12.c.c.18.1		2
63.58	even	3		49.12.c.b.18.1		2
72.13	even	6		64.12.a.b.1.1		1
72.67	odd	6		64.12.a.f.1.1		1
99.76	odd	6		121.12.a.b.1.1		1
117.103	even	6		169.12.a.a.1.1		1
144.13	even	12		256.12.b.e.129.2		2
144.67	odd	12		256.12.b.c.129.1		2
144.85	even	12		256.12.b.e.129.1		2
144.139	odd	12		256.12.b.c.129.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.12.a.a.1.1	✓	1	9.4	even	3
9.12.a.b.1.1		1	9.5	odd	6
16.12.a.a.1.1		1	36.31	odd	6
25.12.a.b.1.1		1	45.4	even	6
25.12.b.b.24.1		2	45.22	odd	12
25.12.b.b.24.2		2	45.13	odd	12
49.12.a.a.1.1		1	63.13	odd	6
49.12.c.b.18.1		2	63.58	even	3
49.12.c.b.30.1		2	63.4	even	3
49.12.c.c.18.1		2	63.40	odd	6
49.12.c.c.30.1		2	63.31	odd	6
64.12.a.b.1.1		1	72.13	even	6
64.12.a.f.1.1		1	72.67	odd	6
81.12.c.b.28.1		2	3.2	odd	2
81.12.c.b.55.1		2	9.2	odd	6
81.12.c.d.28.1		2	1.1	even	1	trivial
81.12.c.d.55.1		2	9.7	even	3	inner
121.12.a.b.1.1		1	99.76	odd	6
144.12.a.d.1.1		1	36.23	even	6
169.12.a.a.1.1		1	117.103	even	6
225.12.a.b.1.1		1	45.14	odd	6
225.12.b.d.199.1		2	45.23	even	12
225.12.b.d.199.2		2	45.32	even	12
256.12.b.c.129.1		2	144.67	odd	12
256.12.b.c.129.2		2	144.139	odd	12
256.12.b.e.129.1		2	144.85	even	12
256.12.b.e.129.2		2	144.13	even	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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more