LMFDB - Embedded newform 3.39.b.a.2.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,39,Mod(2,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 39, names="a")

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

chi := DirichletCharacter("3.2");

S:= CuspForms(chi, 39);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 39 $
Character orbit:	$[\chi]$	$=$	3.b (of order $2$, degree $1$, 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:	$27.4390407101$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 17353504902 x^{10} + \cdots + 27\!\cdots\!00 $ x^12 + 17353504902x^10 + 111006258614054318328x^8 + 323765701965839203118204176384x^6 + 420150309279704216298413492838082805760x^4 + 190068212511425710374530430459662273636990976000*x^2 + 27342285412416035125187079526375866471795145886924800000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{75}\cdot 3^{91}\cdot 5^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2.9
Root			$53338.0i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.39.b.a.2.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+640056. i q^{2} +(2.88152e8 - 1.12598e9i) q^{3} -1.34793e11 q^{4} -3.15820e13i q^{5} +(7.20687e14 + 1.84433e14i) q^{6} +9.50531e15 q^{7} +8.96619e16i q^{8} +(-1.18479e18 - 6.48904e17i) q^{9} +O(q^{10})$	\(q+640056. i q^{2} +(2.88152e8 - 1.12598e9i) q^{3} -1.34793e11 q^{4} -3.15820e13i q^{5} +(7.20687e14 + 1.84433e14i) q^{6} +9.50531e15 q^{7} +8.96619e16i q^{8} +(-1.18479e18 - 6.48904e17i) q^{9} +2.02142e19 q^{10} -6.59450e19i q^{11} +(-3.88410e19 + 1.51774e20i) q^{12} -1.55676e21 q^{13} +6.08393e21i q^{14} +(-3.55605e22 - 9.10042e21i) q^{15} -9.44403e22 q^{16} +2.67217e23i q^{17} +(4.15335e23 - 7.58331e23i) q^{18} -1.27892e24 q^{19} +4.25704e24i q^{20} +(2.73898e24 - 1.07027e25i) q^{21} +4.22085e25 q^{22} -4.27683e25i q^{23} +(1.00957e26 + 2.58363e25i) q^{24} -6.33625e26 q^{25} -9.96411e26i q^{26} +(-1.07205e27 + 1.14706e27i) q^{27} -1.28125e27 q^{28} -6.33374e27i q^{29} +(5.82478e27 - 2.27607e28i) q^{30} +2.54059e28 q^{31} -3.58010e28i q^{32} +(-7.42524e28 - 1.90022e28i) q^{33} -1.71034e29 q^{34} -3.00197e29i q^{35} +(1.59702e29 + 8.74680e28i) q^{36} -9.87322e28 q^{37} -8.18580e29i q^{38} +(-4.48583e29 + 1.75287e30i) q^{39} +2.83170e30 q^{40} +3.57778e30i q^{41} +(6.85035e30 + 1.75310e30i) q^{42} -8.11666e30 q^{43} +8.88895e30i q^{44} +(-2.04937e31 + 3.74180e31i) q^{45} +2.73741e31 q^{46} -7.20582e31i q^{47} +(-2.72132e31 + 1.06337e32i) q^{48} -3.95839e31 q^{49} -4.05555e32i q^{50} +(3.00880e32 + 7.69993e31i) q^{51} +2.09841e32 q^{52} -4.09843e32i q^{53} +(-7.34182e32 - 6.86171e32i) q^{54} -2.08268e33 q^{55} +8.52264e32i q^{56} +(-3.68524e32 + 1.44003e33i) q^{57} +4.05394e33 q^{58} -1.03957e33i q^{59} +(4.79333e33 + 1.22668e33i) q^{60} +5.64098e33 q^{61} +1.62612e34i q^{62} +(-1.12618e34 - 6.16804e33i) q^{63} -3.04493e33 q^{64} +4.91655e34i q^{65} +(1.21625e34 - 4.75257e34i) q^{66} -6.14474e34 q^{67} -3.60191e34i q^{68} +(-4.81561e34 - 1.23238e34i) q^{69} +1.92143e35 q^{70} -1.97414e35i q^{71} +(5.81820e34 - 1.06230e35i) q^{72} -1.80385e35 q^{73} -6.31941e34i q^{74} +(-1.82580e35 + 7.13446e35i) q^{75} +1.72390e35 q^{76} -6.26828e35i q^{77} +(-1.12193e36 - 2.87118e35i) q^{78} +1.59780e36 q^{79} +2.98261e36i q^{80} +(9.82647e35 + 1.53763e36i) q^{81} -2.28998e36 q^{82} -2.62427e36i q^{83} +(-3.69196e35 + 1.44266e36i) q^{84} +8.43926e36 q^{85} -5.19512e36i q^{86} +(-7.13163e36 - 1.82508e36i) q^{87} +5.91276e36 q^{88} +3.89397e36i q^{89} +(-2.39496e37 - 1.31171e37i) q^{90} -1.47975e37 q^{91} +5.76489e36i q^{92} +(7.32076e36 - 2.86064e37i) q^{93} +4.61213e37 q^{94} +4.03909e37i q^{95} +(-4.03110e37 - 1.03161e37i) q^{96} +8.00800e37 q^{97} -2.53359e37i q^{98} +(-4.27920e37 + 7.81309e37i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 114742404 q^{3} - 1699274528448 q^{4} - 483611204680128 q^{6} + 81\!\cdots\!48 q^{7}+ \cdots - 42\!\cdots\!40 q^{9}+O(q^{10}) $ 12 * q - 114742404 * q^3 - 1699274528448 * q^4 - 483611204680128 * q^6 + 8107872236538648 * q^7 - 424319151461513940 * q^9	$ 12 q - 114742404 q^{3} - 1699274528448 q^{4} - 483611204680128 q^{6} + 81\!\cdots\!48 q^{7}+ \cdots - 34\!\cdots\!40 q^{99}+O(q^{100}) $ 12 * q - 114742404 * q^3 - 1699274528448 * q^4 - 483611204680128 * q^6 + 8107872236538648 * q^7 - 424319151461513940 * q^9 + 8521437485093339520 * q^10 - 2862564534392665536 * q^12 + 1069098773333431501752 * q^13 + 6325133233762551847680 * q^15 + 67078537203201948051456 * q^16 + 1420463738762719667349120 * q^18 - 4607058619794992781108360 * q^19 + 33320142533758881258920952 * q^21 - 136880063896016789094648960 * q^22 + 783927349783175843577206784 * q^24 - 1296747019384761463507120020 * q^25 + 3527882385497241000493515804 * q^27 - 772965222736808266417757568 * q^28 - 31212306699175351074822848640 * q^30 + 62426311865853800230409578584 * q^31 - 201583764927512776992433501440 * q^33 + 279954989831379847783072264704 * q^34 + 524806089486681368742761588544 * q^36 - 1044821541252033349072004239752 * q^37 + 3798009668755107990641466418968 * q^39 - 8640808308189045028871484272640 * q^40 + 3739179021877842175021096471680 * q^42 + 10033244180304067819165288107192 * q^43 - 61618154391458016749088317176320 * q^45 + 133876649746070235210936111300864 * q^46 - 169673882786170669254051959076864 * q^48 - 74274509875804693019854807543452 * q^49 + 717994133339248153525793387369472 * q^51 - 993185387699150183190245387663232 * q^52 + 1237237684228372752705008546718912 * q^54 - 147621918295658178296158670231040 * q^55 - 1942894316331924260346088046339112 * q^57 + 5456952458981587224214732301397120 * q^58 - 21422716753388621512702364409876480 * q^60 + 19261150877798591818539348576756024 * q^61 - 6850204156609697882698173452536488 * q^63 - 3354811274780051137580237339295744 * q^64 + 29491133770268183961996554653096320 * q^66 - 12293160890248249992597347473356552 * q^67 + 14368205812565646738112192879237632 * q^69 + 131887910392782907972479210848551680 * q^70 - 849782187269944662605305038851543040 * q^72 + 904634266610182985560078196407011672 * q^73 - 1950889856240531910659528579515703460 * q^75 + 3737782451304773339414088480976030848 * q^76 - 4783964522796872138966708226773738880 * q^78 + 3380994931932561121624661644777634520 * q^79 - 3842105375893366153709000791027089588 * q^81 + 9707181808332667829526886407699144960 * q^82 - 23112447300276128146951334880402529152 * q^84 + 16191233322474057038450787601892136960 * q^85 - 46435849480387750961684301913616613120 * q^87 + 111257699492994117641050357545187921920 * q^88 - 164148346324517317604081085509260974720 * q^90 + 128973762284915213743998856562037216624 * q^91 - 173596942201215499347713600620947459528 * q^93 + 323629532832623192615016136649966897664 * q^94 - 450074405332355244291177655815409434624 * q^96 + 248679388944018942060778750016570824728 * q^97 - 346605715634587898579110273074604669440 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$			640056.i			1.22081i	0.792090	+	0.610405i	$0.208993\pi$
$2$			640056.i			1.22081i	−0.792090	+	0.610405i	$0.791007\pi$
$3$	2.88152e8	−	1.12598e9i	0.247924	−	0.968780i
$3$	2.88152e8	−	1.12598e9i	0.247924	−	0.968780i
$4$	−1.34793e11			−0.490375
$5$		−	3.15820e13i		−	1.65581i	−0.560871	−	0.827903i	$-0.689534\pi$
$5$		−	3.15820e13i		−	1.65581i	0.560871	−	0.827903i	$-0.310466\pi$
$6$	7.20687e14	+	1.84433e14i	1.18270	+	0.302668i
$7$	9.50531e15			0.833880			0.416940	−	0.908934i	$-0.363103\pi$
$7$	9.50531e15			0.833880			0.416940	+	0.908934i	$0.363103\pi$
$8$			8.96619e16i			0.622154i
$9$	−1.18479e18	−	6.48904e17i	−0.877068	−	0.480367i
$10$	2.02142e19			2.02142
$11$		−	6.59450e19i		−	1.07825i	−0.842225	−	0.539127i	$-0.818754\pi$
$11$		−	6.59450e19i		−	1.07825i	0.842225	−	0.539127i	$-0.181246\pi$
$12$	−3.88410e19	+	1.51774e20i	−0.121576	+	0.475066i
$13$	−1.55676e21			−1.06487			−0.532436	−	0.846470i	$-0.678723\pi$
$13$	−1.55676e21			−1.06487			−0.532436	+	0.846470i	$0.678723\pi$
$14$			6.08393e21i			1.01801i
$15$	−3.55605e22	−	9.10042e21i	−1.60411	−	0.410514i
$16$	−9.44403e22			−1.24991
$17$			2.67217e23i			1.11773i	0.829260	+	0.558863i	$0.188762\pi$
$17$			2.67217e23i			1.11773i	−0.829260	+	0.558863i	$0.811238\pi$
$18$	4.15335e23	−	7.58331e23i	0.586436	−	1.07073i
$19$	−1.27892e24			−0.646436			−0.323218	−	0.946325i	$-0.604765\pi$
$19$	−1.27892e24			−0.646436			−0.323218	+	0.946325i	$0.604765\pi$
$20$			4.25704e24i			0.811967i
$21$	2.73898e24	−	1.07027e25i	0.206739	−	0.807846i
$22$	4.22085e25			1.31634
$23$		−	4.27683e25i		−	0.573183i	−0.958053	−	0.286592i	$-0.907478\pi$
$23$		−	4.27683e25i		−	0.573183i	0.958053	−	0.286592i	$-0.0925223\pi$
$24$	1.00957e26	+	2.58363e25i	0.602731	+	0.154247i
$25$	−6.33625e26			−1.74170
$26$		−	9.96411e26i		−	1.30001i
$27$	−1.07205e27	+	1.14706e27i	−0.682815	+	0.730591i
$28$	−1.28125e27			−0.408914
$29$		−	6.33374e27i		−	1.03776i	−0.854846	−	0.518881i	$-0.826349\pi$
$29$		−	6.33374e27i		−	1.03776i	0.854846	−	0.518881i	$-0.173651\pi$
$30$	5.82478e27	−	2.27607e28i	0.501159	−	1.95831i
$31$	2.54059e28			1.17236			0.586182	−	0.810179i	$-0.300630\pi$
$31$	2.54059e28			1.17236			0.586182	+	0.810179i	$0.300630\pi$
$32$		−	3.58010e28i		−	0.903744i
$33$	−7.42524e28	−	1.90022e28i	−1.04459	−	0.267325i
$34$	−1.71034e29			−1.36453
$35$		−	3.00197e29i		−	1.38074i
$36$	1.59702e29	+	8.74680e28i	0.430092	+	0.235560i
$37$	−9.87322e28			−0.157989			−0.0789944	−	0.996875i	$-0.525171\pi$
$37$	−9.87322e28			−0.157989			−0.0789944	+	0.996875i	$0.525171\pi$
$38$		−	8.18580e29i		−	0.789175i
$39$	−4.48583e29	+	1.75287e30i	−0.264007	+	1.03163i
$40$	2.83170e30			1.03017
$41$			3.57778e30i			0.814180i	0.913388	+	0.407090i	$0.133457\pi$
$41$			3.57778e30i			0.814180i	−0.913388	+	0.407090i	$0.866543\pi$
$42$	6.85035e30	+	1.75310e30i	0.986226	+	0.252388i
$43$	−8.11666e30			−0.747269			−0.373634	−	0.927576i	$-0.621889\pi$
$43$	−8.11666e30			−0.747269			−0.373634	+	0.927576i	$0.621889\pi$
$44$			8.88895e30i			0.528749i
$45$	−2.04937e31	+	3.74180e31i	−0.795394	+	1.45225i
$46$	2.73741e31			0.699747
$47$		−	7.20582e31i		−	1.22412i	−0.790811	−	0.612060i	$-0.790341\pi$
$47$		−	7.20582e31i		−	1.22412i	0.790811	−	0.612060i	$-0.209659\pi$
$48$	−2.72132e31	+	1.06337e32i	−0.309882	+	1.21088i
$49$	−3.95839e31			−0.304644
$50$		−	4.05555e32i		−	2.12628i
$51$	3.00880e32	+	7.69993e31i	1.08283	+	0.277111i
$52$	2.09841e32			0.522187
$53$		−	4.09843e32i		−	0.710192i	−0.934830	−	0.355096i	$-0.884448\pi$
$53$		−	4.09843e32i		−	0.710192i	0.934830	−	0.355096i	$-0.115552\pi$
$54$	−7.34182e32	−	6.86171e32i	−0.891912	−	0.833587i
$55$	−2.08268e33			−1.78538
$56$			8.52264e32i			0.518802i
$57$	−3.68524e32	+	1.44003e33i	−0.160267	+	0.626254i
$58$	4.05394e33			1.26691
$59$		−	1.03957e33i		−	0.234783i	−0.993086	−	0.117392i	$-0.962547\pi$
$59$		−	1.03957e33i		−	0.234783i	0.993086	−	0.117392i	$-0.0374532\pi$
$60$	4.79333e33	+	1.22668e33i	0.786617	+	0.201306i
$61$	5.64098e33			0.676220			0.338110	−	0.941107i	$-0.390212\pi$
$61$	5.64098e33			0.676220			0.338110	+	0.941107i	$0.390212\pi$
$62$			1.62612e34i			1.43123i
$63$	−1.12618e34	−	6.16804e33i	−0.731369	−	0.400568i
$64$	−3.04493e33			−0.146608
$65$			4.91655e34i			1.76322i
$66$	1.21625e34	−	4.75257e34i	0.326352	−	1.27525i
$67$	−6.14474e34			−1.23903			−0.619515	−	0.784984i	$-0.712671\pi$
$67$	−6.14474e34			−1.23903			−0.619515	+	0.784984i	$0.712671\pi$
$68$		−	3.60191e34i		−	0.548105i
$69$	−4.81561e34	−	1.23238e34i	−0.555288	−	0.142106i
$70$	1.92143e35			1.68562
$71$		−	1.97414e35i		−	1.32272i	−0.750068	−	0.661361i	$-0.769979\pi$
$71$		−	1.97414e35i		−	1.32272i	0.750068	−	0.661361i	$-0.230021\pi$
$72$	5.81820e34	−	1.06230e35i	0.298862	−	0.545672i
$73$	−1.80385e35			−0.712962			−0.356481	−	0.934303i	$-0.616023\pi$
$73$	−1.80385e35			−0.712962			−0.356481	+	0.934303i	$0.616023\pi$
$74$		−	6.31941e34i		−	0.192874i
$75$	−1.82580e35	+	7.13446e35i	−0.431807	+	1.68732i
$76$	1.72390e35			0.316996
$77$		−	6.26828e35i		−	0.899134i
$78$	−1.12193e36	−	2.87118e35i	−1.25942	−	0.322302i
$79$	1.59780e36			1.40802			0.704009	−	0.710191i	$-0.251392\pi$
$79$	1.59780e36			1.40802			0.704009	+	0.710191i	$0.251392\pi$
$80$			2.98261e36i			2.06960i
$81$	9.82647e35	+	1.53763e36i	0.538495	+	0.842628i
$82$	−2.28998e36			−0.993959
$83$		−	2.62427e36i		−	0.904744i	−0.891829	−	0.452372i	$-0.850578\pi$
$83$		−	2.62427e36i		−	0.904744i	0.891829	−	0.452372i	$-0.149422\pi$
$84$	−3.69196e35	+	1.44266e36i	−0.101379	+	0.396148i
$85$	8.43926e36			1.85074
$86$		−	5.19512e36i		−	0.912273i
$87$	−7.13163e36	−	1.82508e36i	−1.00536	−	0.257286i
$88$	5.91276e36			0.670840
$89$			3.89397e36i			0.356437i	0.983991	+	0.178218i	$0.0570333\pi$
$89$			3.89397e36i			0.356437i	−0.983991	+	0.178218i	$0.942967\pi$
$90$	−2.39496e37	−	1.31171e37i	−1.77293	−	0.971025i
$91$	−1.47975e37			−0.887975
$92$			5.76489e36i			0.281075i
$93$	7.32076e36	−	2.86064e37i	0.290657	−	1.13576i
$94$	4.61213e37			1.49442
$95$			4.03909e37i			1.07037i
$96$	−4.03110e37	−	1.03161e37i	−0.875529	−	0.224060i
$97$	8.00800e37			1.42844			0.714219	−	0.699923i	$-0.246782\pi$
$97$	8.00800e37			1.42844			0.714219	+	0.699923i	$0.246782\pi$
$98$		−	2.53359e37i		−	0.371913i
$99$	−4.27920e37	+	7.81309e37i	−0.517957	+	0.945701i
$100$	8.54084e37			0.854084
$101$			5.86969e37i			0.485858i	0.970044	+	0.242929i	$0.0781082\pi$
$101$			5.86969e37i			0.485858i	−0.970044	+	0.242929i	$0.921892\pi$
$102$	−4.92838e37	+	1.92580e38i	−0.338299	+	1.32193i
$103$	−1.79233e38			−1.02214			−0.511071	−	0.859539i	$-0.670751\pi$
$103$	−1.79233e38			−1.02214			−0.511071	+	0.859539i	$0.670751\pi$
$104$		−	1.39582e38i		−	0.662515i
$105$	−3.38014e38	−	8.65023e37i	−1.33764	−	0.342319i
$106$	2.62322e38			0.867009
$107$			1.11640e38i			0.308694i	0.988017	+	0.154347i	$0.0493274\pi$
$107$			1.11640e38i			0.308694i	−0.988017	+	0.154347i	$0.950673\pi$
$108$	1.44505e38	−	1.54616e38i	0.334836	−	0.358264i
$109$	9.48509e38			1.84475			0.922376	−	0.386294i	$-0.126245\pi$
$109$	9.48509e38			1.84475			0.922376	+	0.386294i	$0.126245\pi$
$110$		−	1.33303e39i		−	2.17961i
$111$	−2.84499e37	+	1.11170e38i	−0.0391691	+	0.153056i
$112$	−8.97684e38			−1.04227
$113$			2.89986e38i			0.284372i	0.989840	+	0.142186i	$0.0454131\pi$
$113$			2.89986e38i			0.284372i	−0.989840	+	0.142186i	$0.954587\pi$
$114$	−9.21701e38	−	2.35876e38i	−0.764536	−	0.195655i
$115$	−1.35071e39			−0.949080
$116$			8.53746e38i			0.508893i
$117$	1.84443e39	+	1.01019e39i	0.933964	+	0.511529i
$118$	6.65385e38			0.286625
$119$			2.53998e39i			0.932049i
$120$	8.15961e38	−	3.18843e39i	0.255403	−	0.998005i
$121$	−6.08310e38			−0.162631
$122$			3.61054e39i			0.825536i
$123$	4.02849e39	+	1.03095e39i	0.788761	+	0.201855i
$124$	−3.42455e39			−0.574898
$125$			8.52168e39i			1.22810i
$126$	3.94789e39	−	7.20817e39i	0.489017	−	0.892862i
$127$	6.95430e39			0.741280			0.370640	−	0.928777i	$-0.379138\pi$
$127$	6.95430e39			0.741280			0.370640	+	0.928777i	$0.379138\pi$
$128$		−	1.17898e40i		−	1.08272i
$129$	−2.33883e39	+	9.13916e39i	−0.185266	+	0.723939i
$130$	−3.14687e40			−2.15256
$131$		−	2.23746e40i		−	1.32313i	−0.749889	−	0.661563i	$-0.769893\pi$
$131$		−	2.23746e40i		−	1.32313i	0.749889	−	0.661563i	$-0.230107\pi$
$132$	1.00087e40	+	2.56137e39i	0.512241	+	0.131089i
$133$	−1.21565e40			−0.539050
$134$		−	3.93297e40i		−	1.51262i
$135$	3.62264e40	+	3.38575e40i	1.20972	+	1.13061i
$136$	−2.39592e40			−0.695398
$137$			1.97371e40i			0.498416i	0.968450	+	0.249208i	$0.0801703\pi$
$137$			1.97371e40i			0.498416i	−0.968450	+	0.249208i	$0.919830\pi$
$138$	7.88791e39	−	3.08226e40i	0.173484	−	0.677901i
$139$	3.39057e40			0.650117			0.325059	−	0.945694i	$-0.394616\pi$
$139$	3.39057e40			0.650117			0.325059	+	0.945694i	$0.394616\pi$
$140$			4.04645e40i			0.677083i
$141$	−8.11358e40	−	2.07637e40i	−1.18590	−	0.303488i
$142$	1.26356e41			1.61479
$143$			1.02660e41i			1.14820i
$144$	1.11892e41	+	6.12827e40i	1.09625	+	0.600414i
$145$	−2.00032e41			−1.71833
$146$		−	1.15456e41i		−	0.870390i
$147$	−1.14062e40	+	4.45705e40i	−0.0755286	+	0.295133i
$148$	1.33084e40			0.0774738
$149$			3.13683e41i			1.60676i	0.595463	+	0.803382i	$0.296968\pi$
$149$			3.13683e41i			1.60676i	−0.595463	+	0.803382i	$0.703032\pi$
$150$	−4.56645e41	−	1.16862e41i	−2.05989	−	0.527155i
$151$	2.49290e41			0.991157			0.495578	−	0.868563i	$-0.334956\pi$
$151$	2.49290e41			0.991157			0.495578	+	0.868563i	$0.334956\pi$
$152$		−	1.14670e41i		−	0.402183i
$153$	1.73399e41	−	3.16596e41i	0.536918	−	0.980321i
$154$	4.01205e41			1.09767
$155$		−	8.02369e41i		−	1.94121i
$156$	6.04660e40	−	2.36275e41i	0.129462	−	0.505884i
$157$	3.35685e41			0.636559			0.318280	−	0.947997i	$-0.396895\pi$
$157$	3.35685e41			0.636559			0.318280	+	0.947997i	$0.396895\pi$
$158$			1.02268e42i			1.71892i
$159$	−4.61473e41	−	1.18097e41i	−0.688020	−	0.176073i
$160$	−1.13067e42			−1.49643
$161$		−	4.06526e41i		−	0.477966i
$162$	−9.84168e41	+	6.28949e41i	−1.02869	+	0.657400i
$163$	8.93945e41			0.831278			0.415639	−	0.909530i	$-0.363558\pi$
$163$	8.93945e41			0.831278			0.415639	+	0.909530i	$0.363558\pi$
$164$		−	4.82261e41i		−	0.399254i
$165$	−6.00127e41	+	2.34504e42i	−0.442638	+	1.72964i
$166$	1.67968e42			1.10452
$167$		−	1.94932e42i		−	1.14359i	−0.820396	−	0.571795i	$-0.806247\pi$
$167$		−	1.94932e42i		−	1.14359i	0.820396	−	0.571795i	$-0.193753\pi$
$168$	9.59628e41	+	2.45582e41i	0.502605	+	0.128623i
$169$	2.86282e41			0.133951
$170$			5.40160e42i			2.25940i
$171$	1.51525e42	+	8.29897e41i	0.566968	+	0.310526i
$172$	1.09407e42			0.366442
$173$		−	6.41502e42i		−	1.92452i	−0.272136	−	0.962259i	$-0.587730\pi$
$173$		−	6.41502e42i		−	1.92452i	0.272136	−	0.962259i	$-0.412270\pi$
$174$	1.16815e42	−	4.56464e42i	0.314097	−	1.22736i
$175$	−6.02280e42			−1.45236
$176$			6.22787e42i			1.34772i
$177$	−1.17053e42	−	2.99555e41i	−0.227453	−	0.0582083i
$178$	−2.49236e42			−0.435141
$179$			1.15790e42i			0.181745i	0.995863	+	0.0908726i	$0.0289656\pi$
$179$			1.15790e42i			0.181745i	−0.995863	+	0.0908726i	$0.971034\pi$
$180$	2.76241e42	−	5.04370e42i	0.390042	−	0.712150i
$181$	−1.08797e43			−1.38269			−0.691344	−	0.722526i	$-0.742981\pi$
$181$	−1.08797e43			−1.38269			−0.691344	+	0.722526i	$0.742981\pi$
$182$		−	9.47120e42i		−	1.08405i
$183$	1.62546e42	−	6.35161e42i	0.167651	−	0.655108i
$184$	3.83469e42			0.356609
$185$			3.11816e42i			0.261599i
$186$	1.83097e43	+	4.68570e42i	1.38655	+	0.354836i
$187$	1.76217e43			1.20519
$188$			9.71297e42i			0.600279i
$189$	−1.01902e43	+	1.09032e43i	−0.569386	+	0.609225i
$190$	−2.58524e43			−1.30672
$191$		−	1.16526e43i		−	0.533075i	−0.963825	−	0.266537i	$-0.914120\pi$
$191$		−	1.16526e43i		−	0.533075i	0.963825	−	0.266537i	$-0.0858796\pi$
$192$	−8.77404e41	+	3.42852e42i	−0.0363476	+	0.142031i
$193$	−1.38553e43			−0.520029			−0.260014	−	0.965605i	$-0.583727\pi$
$193$	−1.38553e43			−0.520029			−0.260014	+	0.965605i	$0.583727\pi$
$194$			5.12557e43i			1.74385i
$195$	5.53591e43	+	1.41671e43i	1.70817	+	0.437144i
$196$	5.33565e42			0.149390
$197$		−	1.34295e43i		−	0.341351i	−0.985327	−	0.170676i	$-0.945405\pi$
$197$		−	1.34295e43i		−	0.341351i	0.985327	−	0.170676i	$-0.0545950\pi$
$198$	−5.00081e43	−	2.73893e43i	−1.15452	−	0.632327i
$199$	8.89031e42			0.186513			0.0932563	−	0.995642i	$-0.470272\pi$
$199$	8.89031e42			0.186513			0.0932563	+	0.995642i	$0.470272\pi$
$200$		−	5.68120e43i		−	1.08360i
$201$	−1.77062e43	+	6.91882e43i	−0.307185	+	1.20035i
$202$	−3.75693e43			−0.593140
$203$		−	6.02041e43i		−	0.865369i
$204$	−4.05566e43	−	1.03790e43i	−0.530993	−	0.135888i
$205$	1.12994e44			1.34813
$206$		−	1.14719e44i		−	1.24784i
$207$	−2.77526e43	+	5.06714e43i	−0.275338	+	0.502720i
$208$	1.47021e44			1.33099
$209$			8.43384e43i			0.697021i
$210$	5.53663e43	−	2.16348e44i	0.417906	−	1.63300i
$211$	−1.25172e44			−0.863259			−0.431629	−	0.902051i	$-0.642061\pi$
$211$	−1.25172e44			−0.863259			−0.431629	+	0.902051i	$0.642061\pi$
$212$			5.52441e43i			0.348261i
$213$	−2.22283e44	−	5.68852e43i	−1.28143	−	0.327934i
$214$	−7.14559e43			−0.376857
$215$			2.56340e44i			1.23733i
$216$	−1.02848e44	−	9.61220e43i	−0.454540	−	0.424817i
$217$	2.41491e44			0.977611
$218$			6.07098e44i			2.25209i
$219$	−5.19783e43	+	2.03109e44i	−0.176760	+	0.690703i
$220$	2.80731e44			0.875506
$221$		−	4.15993e44i		−	1.19023i
$222$	−7.11550e43	−	1.82095e43i	−0.186852	−	0.0478181i
$223$	−6.66529e43			−0.160704			−0.0803520	−	0.996767i	$-0.525604\pi$
$223$	−6.66529e43			−0.160704			−0.0803520	+	0.996767i	$0.525604\pi$
$224$		−	3.40299e44i		−	0.753614i
$225$	7.50712e44	+	4.11162e44i	1.52758	+	0.836652i
$226$	−1.85607e44			−0.347164
$227$			7.05437e43i			0.121330i	0.998158	+	0.0606648i	$0.0193221\pi$
$227$			7.05437e43i			0.121330i	−0.998158	+	0.0606648i	$0.980678\pi$
$228$	4.96746e43	−	1.94107e44i	0.0785908	−	0.307099i
$229$	−9.62962e43			−0.140196			−0.0700979	−	0.997540i	$-0.522331\pi$
$229$	−9.62962e43			−0.140196			−0.0700979	+	0.997540i	$0.522331\pi$
$230$		−	8.64529e44i		−	1.15865i
$231$	−7.05792e44	−	1.80622e44i	−0.871063	−	0.222917i
$232$	5.67895e44			0.645649
$233$		−	4.41342e44i		−	0.462395i	−0.972907	−	0.231197i	$-0.925736\pi$
$233$		−	4.41342e44i		−	0.462395i	0.972907	−	0.231197i	$-0.0742643\pi$
$234$	−6.46576e44	+	1.18054e45i	−0.624479	+	1.14019i
$235$	−2.27574e45			−2.02691
$236$			1.40128e44i			0.115132i
$237$	4.60410e44	−	1.79908e45i	0.349081	−	1.36406i
$238$	−1.62573e45			−1.13785
$239$		−	1.33189e44i		−	0.0860813i	−0.999073	−	0.0430407i	$-0.986295\pi$
$239$		−	1.33189e44i		−	0.0860813i	0.999073	−	0.0430407i	$-0.0137045\pi$
$240$	3.35835e45	+	8.59447e44i	2.00499	+	0.513104i
$241$	2.28762e45			1.26200			0.631000	−	0.775783i	$-0.282645\pi$
$241$	2.28762e45			1.26200			0.631000	+	0.775783i	$0.282645\pi$
$242$		−	3.89352e44i		−	0.198541i
$243$	2.01448e45	−	6.63365e44i	0.949827	−	0.312776i
$244$	−7.60367e44			−0.331602
$245$			1.25014e45i			0.504432i
$246$	−6.59863e44	+	2.57846e45i	−0.246426	+	0.962927i
$247$	1.99097e45			0.688371
$248$			2.27794e45i			0.729391i
$249$	−2.95487e45	−	7.56190e44i	−0.876497	−	0.224307i
$250$	−5.45435e45			−1.49928
$251$			3.22130e45i			0.820787i	0.911908	+	0.410394i	$0.134609\pi$
$251$			3.22130e45i			0.820787i	−0.911908	+	0.410394i	$0.865391\pi$
$252$	1.51801e45	+	8.31410e44i	0.358645	+	0.196429i
$253$	−2.82036e45			−0.618037
$254$			4.45114e45i			0.904962i
$255$	2.43179e45	−	9.50240e45i	0.458842	−	1.79296i
$256$	6.70916e45			1.17519
$257$		−	3.34070e45i		−	0.543386i	−0.962384	−	0.271693i	$-0.912416\pi$
$257$		−	3.34070e45i		−	0.543386i	0.962384	−	0.271693i	$-0.0875835\pi$
$258$	−5.84957e45	−	1.49698e45i	−0.883791	−	0.226174i
$259$	−9.38480e44			−0.131744
$260$		−	6.62718e45i		−	0.864640i
$261$	−4.10999e45	+	7.50414e45i	−0.498507	+	0.910188i
$262$	1.43210e46			1.61529
$263$		−	4.17907e45i		−	0.438450i	−0.975674	−	0.219225i	$-0.929647\pi$
$263$		−	4.17907e45i		−	0.438450i	0.975674	−	0.219225i	$-0.0703529\pi$
$264$	1.70377e45	−	6.65762e45i	0.166317	−	0.649896i
$265$	−1.29437e46			−1.17594
$266$		−	7.78086e45i		−	0.658077i
$267$	4.38451e45	+	1.12206e45i	0.345309	+	0.0883691i
$268$	8.28270e45			0.607590
$269$		−	4.32268e45i		−	0.295433i	−0.989030	−	0.147717i	$-0.952808\pi$
$269$		−	4.32268e45i		−	0.295433i	0.989030	−	0.147717i	$-0.0471924\pi$
$270$	−2.16707e46	+	2.31869e46i	−1.38026	+	1.47683i
$271$	1.17659e46			0.698571			0.349285	−	0.937016i	$-0.386424\pi$
$271$	1.17659e46			0.698571			0.349285	+	0.937016i	$0.386424\pi$
$272$		−	2.52361e46i		−	1.39705i
$273$	−4.26392e45	+	1.66616e46i	−0.220150	+	0.860252i
$274$	−1.26328e46			−0.608471
$275$			4.17844e46i			1.87799i
$276$	6.49112e45	+	1.66116e45i	0.272300	+	0.0696851i
$277$	1.48250e46			0.580602			0.290301	−	0.956935i	$-0.406245\pi$
$277$	1.48250e46			0.580602			0.290301	+	0.956935i	$0.406245\pi$
$278$			2.17016e46i			0.793669i
$279$	−3.01006e46	−	1.64860e46i	−1.02824	−	0.563165i
$280$	2.69162e46			0.859036
$281$			1.30765e45i			0.0390005i	0.999810	+	0.0195003i	$0.00620752\pi$
$281$			1.30765e45i			0.0390005i	−0.999810	+	0.0195003i	$0.993792\pi$
$282$	1.32899e46	−	5.19314e46i	0.370502	−	1.44776i
$283$	2.61530e46			0.681679			0.340839	−	0.940122i	$-0.389289\pi$
$283$	2.61530e46			0.681679			0.340839	+	0.940122i	$0.389289\pi$
$284$			2.66100e46i			0.648630i
$285$	4.54791e46	+	1.16387e46i	1.03695	+	0.265371i
$286$	−6.57084e46			−1.40174
$287$			3.40079e46i			0.678929i
$288$	−2.32314e46	+	4.24166e46i	−0.434129	+	0.792645i
$289$	−1.42495e46			−0.249311
$290$		−	1.28032e47i		−	2.09776i
$291$	2.30752e46	−	9.01681e46i	0.354143	−	1.38384i
$292$	2.43147e46			0.349619
$293$		−	1.80643e46i		−	0.243408i	−0.992566	−	0.121704i	$-0.961164\pi$
$293$		−	1.80643e46i		−	0.243408i	0.992566	−	0.121704i	$-0.0388359\pi$
$294$	−2.85276e46	−	7.30060e45i	−0.360302	−	0.0922060i
$295$	−3.28318e46			−0.388755
$296$		−	8.85252e45i		−	0.0982934i
$297$	7.56428e46	+	7.06963e46i	0.787762	+	0.736248i
$298$	−2.00775e47			−1.96155
$299$			6.65799e46i			0.610366i
$300$	2.46106e46	−	9.61678e46i	0.211748	−	0.827419i
$301$	−7.71514e46			−0.623132
$302$			1.59559e47i			1.21001i
$303$	6.60913e46	+	1.69136e46i	0.470689	+	0.120456i
$304$	1.20782e47			0.807985
$305$		−	1.78154e47i		−	1.11969i
$306$	2.02639e47	+	1.10985e47i	1.19679	+	0.655475i
$307$	2.11365e46			0.117329			0.0586643	−	0.998278i	$-0.481316\pi$
$307$	2.11365e46			0.117329			0.0586643	+	0.998278i	$0.481316\pi$
$308$			8.44922e46i			0.440913i
$309$	−5.16464e46	+	2.01812e47i	−0.253413	+	0.990230i
$310$	5.13561e47			2.36984
$311$		−	1.90047e47i		−	0.824926i	−0.910974	−	0.412463i	$-0.864669\pi$
$311$		−	1.90047e47i		−	0.824926i	0.910974	−	0.412463i	$-0.135331\pi$
$312$	−1.57166e47	−	4.02208e46i	−0.641831	−	0.164253i
$313$	−4.36802e47			−1.67858			−0.839290	−	0.543684i	$-0.817029\pi$
$313$	−4.36802e47			−1.67858			−0.839290	+	0.543684i	$0.817029\pi$
$314$			2.14857e47i			0.777118i
$315$	−1.94799e47	+	3.55670e47i	−0.663263	+	1.21101i
$316$	−2.15373e47			−0.690457
$317$		−	2.82613e47i		−	0.853229i	−0.904434	−	0.426614i	$-0.859706\pi$
$317$		−	2.82613e47i		−	0.853229i	0.904434	−	0.426614i	$-0.140294\pi$
$318$	7.55887e46	−	2.95368e47i	0.214952	−	0.839941i
$319$	−4.17678e47			−1.11897
$320$			9.61651e46i			0.242755i
$321$	1.25704e47	+	3.21694e46i	0.299057	+	0.0765327i
$322$	2.60199e47			0.583505
$323$		−	3.41750e47i		−	0.722538i
$324$	−1.32454e47	−	2.07262e47i	−0.264065	−	0.413204i
$325$	9.86400e47			1.85468
$326$			5.72175e47i			1.01483i
$327$	2.73315e47	−	1.06800e48i	0.457358	−	1.78716i
$328$	−3.20791e47			−0.506546
$329$		−	6.84936e47i		−	1.02077i
$330$	−1.50096e48	−	3.84115e47i	−2.11156	−	0.540376i
$331$	8.26572e47			1.09787			0.548933	−	0.835867i	$-0.315034\pi$
$331$	8.26572e47			1.09787			0.548933	+	0.835867i	$0.315034\pi$
$332$			3.53735e47i			0.443664i
$333$	1.16977e47	+	6.40678e46i	0.138567	+	0.0758925i
$334$	1.24767e48			1.39611
$335$			1.94063e48i			2.05160i
$336$	−2.58670e47	+	1.01077e48i	−0.258404	+	1.00973i
$337$	−1.06999e48			−1.01021			−0.505105	−	0.863058i	$-0.668546\pi$
$337$	−1.06999e48			−1.01021			−0.505105	+	0.863058i	$0.668546\pi$
$338$			1.83237e47i			0.163529i
$339$	3.26517e47	+	8.35601e46i	0.275494	+	0.0705025i
$340$	−1.13756e48			−0.907556
$341$		−	1.67539e48i		−	1.26411i
$342$	−5.31180e47	+	9.69845e47i	−0.379093	+	0.692159i
$343$	−1.61133e48			−1.08792
$344$		−	7.27756e47i		−	0.464917i
$345$	−3.89210e47	+	1.52087e48i	−0.235300	+	0.919450i
$346$	4.10597e48			2.34947
$347$			2.30805e48i			1.25022i	0.780539	+	0.625108i	$0.214945\pi$
$347$			2.30805e48i			1.25022i	−0.780539	+	0.625108i	$0.785055\pi$
$348$	9.61297e47	+	2.46009e47i	0.493005	+	0.126167i
$349$	2.58261e48			1.25423			0.627114	−	0.778928i	$-0.284236\pi$
$349$	2.58261e48			1.25423			0.627114	+	0.778928i	$0.284236\pi$
$350$		−	3.85493e48i		−	1.77306i
$351$	1.66892e48	−	1.78569e48i	0.727111	−	0.777985i
$352$	−2.36090e48			−0.974465
$353$			7.29378e47i			0.285255i	0.989776	+	0.142627i	$0.0455551\pi$
$353$			7.29378e47i			0.285255i	−0.989776	+	0.142627i	$0.954445\pi$
$354$	1.91732e47	−	7.49207e47i	0.0710612	−	0.277677i
$355$	−6.23472e48			−2.19017
$356$		−	5.24881e47i		−	0.174788i
$357$	2.85996e48	+	7.31902e47i	0.902950	+	0.231077i
$358$	−7.41120e47			−0.221876
$359$			2.35585e47i			0.0668888i	0.999441	+	0.0334444i	$0.0106477\pi$
$359$			2.35585e47i			0.0668888i	−0.999441	+	0.0334444i	$0.989352\pi$
$360$	−3.35497e48	−	1.83750e48i	−0.903527	−	0.494858i
$361$	−2.27851e48			−0.582121
$362$		−	6.96361e48i		−	1.68800i
$363$	−1.75286e47	+	6.84942e47i	−0.0403200	+	0.157553i
$364$	1.99460e48			0.435441
$365$			5.69692e48i			1.18053i
$366$	4.06538e48	+	1.04039e48i	0.799762	+	0.204670i
$367$	1.34691e48			0.251585			0.125793	−	0.992057i	$-0.459853\pi$
$367$	1.34691e48			0.251585			0.125793	+	0.992057i	$0.459853\pi$
$368$			4.03906e48i			0.716426i
$369$	2.32164e48	−	4.23891e48i	0.391105	−	0.714091i
$370$	−1.99580e48			−0.319362
$371$		−	3.89568e48i		−	0.592215i
$372$	−9.86790e47	+	3.85595e48i	−0.142531	+	0.556950i
$373$	−9.41851e48			−1.29275			−0.646375	−	0.763020i	$-0.723716\pi$
$373$	−9.41851e48			−1.29275			−0.646375	+	0.763020i	$0.723716\pi$
$374$			1.12788e49i			1.47131i
$375$	9.59520e48	+	2.45554e48i	1.18976	+	0.304476i
$376$	6.46088e48			0.761592
$377$			9.86009e48i			1.10508i
$378$	−6.97862e48	−	6.52227e48i	−0.743748	−	0.695112i
$379$	1.30347e49			1.32116			0.660580	−	0.750756i	$-0.270310\pi$
$379$	1.30347e49			1.32116			0.660580	+	0.750756i	$0.270310\pi$
$380$		−	5.44442e48i		−	0.524884i
$381$	2.00390e48	−	7.83037e48i	0.183781	−	0.718137i
$382$	7.45830e48			0.650782
$383$			1.34719e49i			1.11854i	0.828984	+	0.559272i	$0.188919\pi$
$383$			1.34719e49i			1.11854i	−0.828984	+	0.559272i	$0.811081\pi$
$384$	−1.32751e49	−	3.39726e48i	−1.04892	−	0.268433i
$385$	−1.97965e49			−1.48879
$386$		−	8.86817e48i		−	0.634856i
$387$	9.61653e48	+	5.26694e48i	0.655405	+	0.358963i
$388$	−1.07943e49			−0.700470
$389$		−	3.22298e49i		−	1.99166i	−0.0912415	−	0.995829i	$-0.529084\pi$
$389$		−	3.22298e49i		−	1.99166i	0.0912415	−	0.995829i	$-0.470916\pi$
$390$	−9.06776e48	+	3.54329e49i	−0.533670	+	2.08535i
$391$	1.14284e49			0.640662
$392$		−	3.54917e48i		−	0.189536i
$393$	−2.51933e49	−	6.44730e48i	−1.28182	−	0.328034i
$394$	8.59563e48			0.416725
$395$		−	5.04618e49i		−	2.33140i
$396$	5.76808e48	−	1.05315e49i	0.253993	−	0.463749i
$397$	1.66907e49			0.700574			0.350287	−	0.936642i	$-0.386084\pi$
$397$	1.66907e49			0.700574			0.350287	+	0.936642i	$0.386084\pi$
$398$			5.69029e48i			0.227696i
$399$	−3.50293e48	+	1.36880e49i	−0.133643	+	0.522220i
$400$	5.98398e49			2.17696
$401$			5.22212e49i			1.81177i	0.423522	+	0.905886i	$0.360794\pi$
$401$			5.22212e49i			1.81177i	−0.423522	+	0.905886i	$0.639206\pi$
$402$	−4.42843e49	−	1.13330e49i	−1.46540	−	0.375014i
$403$	−3.95508e49			−1.24842
$404$		−	7.91195e48i		−	0.238253i
$405$	4.85614e49	−	3.10340e49i	1.39523	−	0.891644i
$406$	3.85340e49			1.05645
$407$			6.51090e48i			0.170352i
$408$	−6.90390e48	+	2.69775e49i	−0.172406	+	0.673687i
$409$	−5.82974e49			−1.38965			−0.694826	−	0.719178i	$-0.744519\pi$
$409$	−5.82974e49			−1.38965			−0.694826	+	0.719178i	$0.744519\pi$
$410$			7.23221e49i			1.64580i
$411$	2.22234e49	+	5.68728e48i	0.482855	+	0.123569i
$412$	2.41594e49			0.501233
$413$		−	9.88146e48i		−	0.195781i
$414$	−3.24325e49	−	1.77632e49i	−0.613726	−	0.336135i
$415$	−8.28799e49			−1.49808
$416$			5.57335e49i			0.962371i
$417$	9.77001e48	−	3.81770e49i	0.161180	−	0.629820i
$418$	−5.39813e49			−0.850930
$419$			6.06466e49i			0.913567i	0.889578	+	0.456783i	$0.150999\pi$
$419$			6.06466e49i			0.913567i	−0.889578	+	0.456783i	$0.849001\pi$
$420$	4.55620e49	+	1.16599e49i	0.655944	+	0.167865i
$421$	1.33651e50			1.83913			0.919564	−	0.392941i	$-0.128542\pi$
$421$	1.33651e50			1.83913			0.919564	+	0.392941i	$0.128542\pi$
$422$		−	8.01172e49i		−	1.05387i
$423$	−4.67589e49	+	8.53737e49i	−0.588027	+	1.07364i
$424$	3.67473e49			0.441849
$425$		−	1.69316e50i		−	1.94674i
$426$	3.64097e49	−	1.42273e50i	0.400345	−	1.56438i
$427$	5.36193e49			0.563886
$428$		−	1.50484e49i		−	0.151376i
$429$	1.15593e50	+	2.95818e49i	1.11235	+	0.284666i
$430$	−1.64072e50			−1.51055
$431$		−	8.75519e49i		−	0.771254i	−0.922655	−	0.385627i	$-0.873985\pi$
$431$		−	8.75519e49i		−	0.771254i	0.922655	−	0.385627i	$-0.126015\pi$
$432$	1.01245e50	−	1.08329e50i	0.853456	−	0.913171i
$433$	−2.17140e50			−1.75174			−0.875871	−	0.482545i	$-0.839713\pi$
$433$	−2.17140e50			−1.75174			−0.875871	+	0.482545i	$0.839713\pi$
$434$			1.54568e50i			1.19348i
$435$	−5.76397e49	+	2.25231e50i	−0.426016	+	1.66469i
$436$	−1.27853e50			−0.904621
$437$			5.46973e49i			0.370526i
$438$	−1.30001e50	−	3.32690e49i	−0.843216	−	0.215790i
$439$	−6.53351e49			−0.405808			−0.202904	−	0.979199i	$-0.565038\pi$
$439$	−6.53351e49			−0.405808			−0.202904	+	0.979199i	$0.565038\pi$
$440$		−	1.86737e50i		−	1.11078i
$441$	4.68986e49	+	2.56862e49i	0.267194	+	0.146341i
$442$	2.66258e50			1.45305
$443$			1.65500e50i			0.865223i	0.901580	+	0.432612i	$0.142408\pi$
$443$			1.65500e50i			0.865223i	−0.901580	+	0.432612i	$0.857592\pi$
$444$	3.83486e48	−	1.49850e49i	0.0192076	−	0.0750550i
$445$	1.22979e50			0.590190
$446$		−	4.26616e49i		−	0.196189i
$447$	3.53200e50	+	9.03885e49i	1.55660	+	0.398355i
$448$	−2.89430e49			−0.122254
$449$		−	1.27526e50i		−	0.516321i	−0.966102	−	0.258160i	$-0.916884\pi$
$449$		−	1.27526e50i		−	0.516321i	0.966102	−	0.258160i	$-0.0831163\pi$
$450$	−2.63167e50	+	4.80497e50i	−1.02139	+	1.86489i
$451$	2.35937e50			0.877893
$452$		−	3.90882e49i		−	0.139449i
$453$	7.18334e49	−	2.80694e50i	0.245731	−	0.960213i
$454$	−4.51519e49			−0.148120
$455$			4.67333e50i			1.47031i
$456$	−1.29116e50	−	3.30425e49i	−0.389626	−	0.0997106i
$457$	−1.64482e50			−0.476112			−0.238056	−	0.971251i	$-0.576510\pi$
$457$	−1.64482e50			−0.476112			−0.238056	+	0.971251i	$0.576510\pi$
$458$		−	6.16349e49i		−	0.171152i
$459$	−3.06514e50	−	2.86470e50i	−0.816600	−	0.763200i
$460$	1.82067e50			0.465406
$461$		−	1.38516e50i		−	0.339767i	−0.985464	−	0.169884i	$-0.945661\pi$
$461$		−	1.38516e50i		−	0.339767i	0.985464	−	0.169884i	$-0.0543392\pi$
$462$	1.15608e50	−	4.51746e50i	0.272139	−	1.06340i
$463$	2.37863e50			0.537387			0.268694	−	0.963226i	$-0.413408\pi$
$463$	2.37863e50			0.537387			0.268694	+	0.963226i	$0.413408\pi$
$464$			5.98160e50i			1.29711i
$465$	−9.03448e50	−	2.31204e50i	−1.88060	−	0.481271i
$466$	2.82484e50			0.564496
$467$			2.32560e50i			0.446184i	0.974797	+	0.223092i	$0.0716151\pi$
$467$			2.32560e50i			0.446184i	−0.974797	+	0.223092i	$0.928385\pi$
$468$	−2.48617e50	−	1.36166e50i	−0.457993	−	0.250841i
$469$	−5.84076e50			−1.03320
$470$		−	1.45660e51i		−	2.47447i
$471$	9.67284e49	−	3.77973e50i	0.157818	−	0.616686i
$472$	9.32101e49			0.146071
$473$			5.35253e50i			0.805745i
$474$	1.15151e51	+	2.94688e50i	1.66526	+	0.426161i
$475$	8.10356e50			1.12589
$476$		−	3.42373e50i		−	0.457054i
$477$	−2.65949e50	+	4.85577e50i	−0.341153	+	0.622887i
$478$	8.52485e49			0.105089
$479$		−	2.65576e50i		−	0.314640i	−0.987548	−	0.157320i	$-0.949715\pi$
$479$		−	2.65576e50i		−	0.314640i	0.987548	−	0.157320i	$-0.0502854\pi$
$480$	−3.25804e50	+	1.27310e51i	−0.370999	+	1.44971i
$481$	1.53702e50			0.168238
$482$			1.46420e51i			1.54066i
$483$	−4.57738e50	−	1.17141e50i	−0.463044	−	0.118499i
$484$	8.19961e49			0.0797501
$485$		−	2.52909e51i		−	2.36522i
$486$	4.24590e50	+	1.28938e51i	0.381840	+	1.15956i
$487$	−1.00479e51			−0.869014			−0.434507	−	0.900669i	$-0.643077\pi$
$487$	−1.00479e51			−0.869014			−0.434507	+	0.900669i	$0.643077\pi$
$488$			5.05781e50i			0.420713i
$489$	2.57592e50	−	1.00656e51i	0.206094	−	0.805325i
$490$	−8.00159e50			−0.615816
$491$			2.22260e51i			1.64556i	0.568362	+	0.822779i	$0.307577\pi$
$491$			2.22260e51i			1.64556i	−0.568362	+	0.822779i	$0.692423\pi$
$492$	−5.43014e50	−	1.38965e50i	−0.386789	−	0.0989845i
$493$	1.69248e51			1.15993
$494$			1.27433e51i			0.840369i
$495$	2.46753e51	+	1.35146e51i	1.56590	+	0.857637i
$496$	−2.39934e51			−1.46535
$497$		−	1.87648e51i		−	1.10299i
$498$	4.84004e50	−	1.89128e51i	0.273837	−	1.07004i
$499$	2.09860e50			0.114293			0.0571465	−	0.998366i	$-0.481800\pi$
$499$	2.09860e50			0.114293			0.0571465	+	0.998366i	$0.481800\pi$
$500$		−	1.14867e51i		−	0.602232i
$501$	−2.19489e51	−	5.61701e50i	−1.10789	−	0.283523i
$502$	−2.06181e51			−1.00202
$503$			1.59022e51i			0.744157i	0.928201	+	0.372078i	$0.121355\pi$
$503$			1.59022e51i			0.744157i	−0.928201	+	0.372078i	$0.878645\pi$
$504$	5.53038e50	−	1.00975e51i	0.249215	−	0.455025i
$505$	1.85377e51			0.804486
$506$		−	1.80519e51i		−	0.754505i
$507$	8.24928e49	−	3.22347e50i	0.0332097	−	0.129769i
$508$	−9.37393e50			−0.363506
$509$		−	4.63601e51i		−	1.73183i	−0.500188	−	0.865917i	$-0.666736\pi$
$509$		−	4.63601e51i		−	1.73183i	0.500188	−	0.865917i	$-0.333264\pi$
$510$	6.08206e51	+	1.55648e51i	2.18886	+	0.560158i
$511$	−1.71462e51			−0.594524
$512$			1.05347e51i			0.351961i
$513$	1.37107e51	−	1.46700e51i	0.441396	−	0.472280i
$514$	2.13824e51			0.663371
$515$			5.66054e51i			1.69247i
$516$	3.15259e50	−	1.23190e51i	0.0908497	−	0.355002i
$517$	−4.75188e51			−1.31991
$518$		−	6.00680e50i		−	0.160834i
$519$	−7.22315e51	−	1.84850e51i	−1.86443	−	0.477133i
$520$	−4.40827e51			−1.09700
$521$			3.58692e51i			0.860606i	0.902684	+	0.430303i	$0.141593\pi$
$521$			3.58692e51i			0.860606i	−0.902684	+	0.430303i	$0.858407\pi$
$522$	−4.80307e51	−	2.63062e51i	−1.11117	−	0.608582i
$523$	8.65118e51			1.92994			0.964969	−	0.262365i	$-0.0845024\pi$
$523$	8.65118e51			1.92994			0.964969	+	0.262365i	$0.0845024\pi$
$524$			3.01595e51i			0.648829i
$525$	−1.73548e51	+	6.78152e51i	−0.360076	+	1.40702i
$526$	2.67484e51			0.535264
$527$			6.78890e51i			1.31038i
$528$	7.01243e51	+	1.79457e51i	1.30564	+	0.334131i
$529$	3.73834e51			0.671461
$530$		−	8.28466e51i		−	1.43560i
$531$	−6.74583e50	+	1.23167e51i	−0.112782	+	0.205921i
$532$	1.63862e51			0.264337
$533$		−	5.56974e51i		−	0.866997i
$534$	−7.18178e50	+	2.80633e51i	−0.107882	+	0.421556i
$535$	3.52582e51			0.511138
$536$		−	5.50949e51i		−	0.770869i
$537$	1.30377e51	+	3.33651e50i	0.176071	+	0.0450589i
$538$	2.76675e51			0.360668
$539$			2.61036e51i			0.328484i
$540$	−4.88308e51	−	4.56376e51i	−0.593216	−	0.554423i
$541$	−8.93589e51			−1.04807			−0.524034	−	0.851697i	$-0.675574\pi$
$541$	−8.93589e51			−1.04807			−0.524034	+	0.851697i	$0.675574\pi$
$542$			7.53086e51i			0.852821i
$543$	−3.13501e51	+	1.22503e52i	−0.342801	+	1.33952i
$544$	9.56665e51			1.01014
$545$		−	2.99558e52i		−	3.05455i
$546$	−1.06643e52	−	2.72915e51i	−1.05020	−	0.268761i
$547$	4.41976e51			0.420378			0.210189	−	0.977661i	$-0.432592\pi$
$547$	4.41976e51			0.420378			0.210189	+	0.977661i	$0.432592\pi$
$548$		−	2.66043e51i		−	0.244411i
$549$	−6.68337e51	−	3.66046e51i	−0.593091	−	0.324834i
$550$	−2.67443e52			−2.29267
$551$			8.10035e51i			0.670847i
$552$	1.10497e51	−	4.31777e51i	0.0884117	−	0.345475i
$553$	1.51876e52			1.17412
$554$			9.48882e51i			0.708805i
$555$	3.51097e51	+	8.98505e50i	0.253432	+	0.0648565i
$556$	−4.57027e51			−0.318802
$557$			1.02056e52i			0.688005i	0.938969	+	0.344003i	$0.111783\pi$
$557$			1.02056e52i			0.688005i	−0.938969	+	0.344003i	$0.888217\pi$
$558$	1.05520e52	−	1.92661e52i	0.687517	−	1.25529i
$559$	1.26357e52			0.795745
$560$			2.83507e52i			1.72580i
$561$	5.07772e51	−	1.98415e52i	0.298796	−	1.16757i
$562$	−8.36967e50			−0.0476122
$563$		−	2.11318e52i		−	1.16219i	−0.813837	−	0.581094i	$-0.802625\pi$
$563$		−	2.11318e52i		−	1.16219i	0.813837	−	0.581094i	$-0.197375\pi$
$564$	1.09366e52	+	2.79881e51i	0.581538	+	0.148823i
$565$	9.15834e51			0.470865
$566$			1.67394e52i			0.832200i
$567$	9.34036e51	+	1.46156e52i	0.449040	+	0.702651i
$568$	1.77005e52			0.822937
$569$			9.67361e51i			0.434966i	0.976064	+	0.217483i	$0.0697847\pi$
$569$			9.67361e51i			0.434966i	−0.976064	+	0.217483i	$0.930215\pi$
$570$	−7.44943e51	+	2.91092e52i	−0.323967	+	1.26592i
$571$	−3.71935e52			−1.56452			−0.782260	−	0.622952i	$-0.785933\pi$
$571$	−3.71935e52			−1.56452			−0.782260	+	0.622952i	$0.785933\pi$
$572$		−	1.38379e52i		−	0.563050i
$573$	−1.31205e52	−	3.35772e51i	−0.516432	−	0.132162i
$574$	−2.17670e52			−0.828842
$575$			2.70991e52i			0.998310i
$576$	3.60760e51	+	1.97587e51i	0.128585	+	0.0704257i
$577$	−4.10688e52			−1.41635			−0.708177	−	0.706035i	$-0.750482\pi$
$577$	−4.10688e52			−1.41635			−0.708177	+	0.706035i	$0.750482\pi$
$578$		−	9.12048e51i		−	0.304361i
$579$	−3.99244e51	+	1.56007e52i	−0.128927	+	0.503793i
$580$	2.69630e52			0.842629
$581$		−	2.49445e52i		−	0.754448i
$582$	5.77126e52	+	1.47694e52i	1.68941	+	0.432342i
$583$	−2.70271e52			−0.765767
$584$		−	1.61737e52i		−	0.443572i
$585$	3.19037e52	−	5.82507e52i	0.846993	−	1.54646i
$586$	1.15621e52			0.297155
$587$		−	6.81962e52i		−	1.69682i	−0.529338	−	0.848411i	$-0.677560\pi$
$587$		−	6.81962e52i		−	1.69682i	0.529338	−	0.848411i	$-0.322440\pi$
$588$	1.53748e51	−	6.00781e51i	0.0370374	−	0.144726i
$589$	−3.24921e52			−0.757858
$590$		−	2.10142e52i		−	0.474596i
$591$	−1.51213e52	−	3.86974e51i	−0.330694	−	0.0846291i
$592$	9.32430e51			0.197471
$593$			8.57574e52i			1.75886i	0.476025	+	0.879432i	$0.342077\pi$
$593$			8.57574e52i			1.75886i	−0.476025	+	0.879432i	$0.657923\pi$
$594$	−4.52496e52	+	4.84156e52i	−0.898819	+	0.961708i
$595$	8.02178e52			1.54329
$596$		−	4.22824e52i		−	0.787918i
$597$	2.56176e51	−	1.00103e52i	0.0462409	−	0.180690i
$598$	−4.26149e52			−0.745141
$599$		−	8.74442e51i		−	0.148123i	−0.997254	−	0.0740613i	$-0.976404\pi$
$599$		−	8.74442e51i		−	0.148123i	0.997254	−	0.0740613i	$-0.0235960\pi$
$600$	−6.39689e52	−	1.63705e52i	−1.04977	−	0.268651i
$601$	4.20628e52			0.668780			0.334390	−	0.942435i	$-0.391470\pi$
$601$	4.20628e52			0.668780			0.334390	+	0.942435i	$0.391470\pi$
$602$		−	4.93812e52i		−	0.760726i
$603$	7.28022e52	+	3.98735e52i	1.08671	+	0.595189i
$604$	−3.36026e52			−0.486039
$605$			1.92116e52i			0.269285i
$606$	−1.08257e52	+	4.23021e52i	−0.147053	+	0.574622i
$607$	−1.96991e52			−0.259335			−0.129667	−	0.991558i	$-0.541391\pi$
$607$	−1.96991e52			−0.259335			−0.129667	+	0.991558i	$0.541391\pi$
$608$			4.57866e52i			0.584212i
$609$	−6.77884e52	−	1.73479e52i	−0.838352	−	0.214546i
$610$	1.14028e53			1.36693
$611$			1.12177e53i			1.30353i
$612$	−2.33730e52	+	4.26750e52i	−0.263292	+	0.480725i
$613$	−8.00587e52			−0.874298			−0.437149	−	0.899389i	$-0.644012\pi$
$613$	−8.00587e52			−0.874298			−0.437149	+	0.899389i	$0.644012\pi$
$614$			1.35285e52i			0.143236i
$615$	3.25593e52	−	1.27228e53i	0.334232	−	1.30604i
$616$	5.62026e52			0.559400
$617$			9.48033e52i			0.914966i	0.889218	+	0.457483i	$0.151249\pi$
$617$			9.48033e52i			0.914966i	−0.889218	+	0.457483i	$0.848751\pi$
$618$	−1.29171e53	−	3.30566e52i	−1.20888	−	0.309369i
$619$	6.24570e52			0.566838			0.283419	−	0.958996i	$-0.408531\pi$
$619$	6.24570e52			0.566838			0.283419	+	0.958996i	$0.408531\pi$
$620$			1.08154e53i			0.951920i
$621$	4.90578e52	+	4.58498e52i	0.418762	+	0.391378i
$622$	1.21641e53			1.00708
$623$			3.70134e52i			0.297225i
$624$	4.23643e52	−	1.65542e53i	0.329984	−	1.28944i
$625$	3.86203e52			0.291807
$626$		−	2.79577e53i		−	2.04923i
$627$	9.49630e52	+	2.43023e52i	0.675260	+	0.172808i
$628$	−4.52481e52			−0.312153
$629$		−	2.63830e52i		−	0.176588i
$630$	−2.27648e53	−	1.24682e53i	−1.47841	−	0.809718i
$631$	−1.78963e53			−1.12773			−0.563866	−	0.825867i	$-0.690686\pi$
$631$	−1.78963e53			−1.12773			−0.563866	+	0.825867i	$0.690686\pi$
$632$			1.43262e53i			0.876005i
$633$	−3.60686e52	+	1.40941e53i	−0.214022	+	0.836308i
$634$	1.80888e53			1.04163
$635$		−	2.19631e53i		−	1.22742i
$636$	6.22035e52	+	1.59187e52i	0.337388	+	0.0863421i
$637$	6.16226e52			0.324407
$638$		−	2.67337e53i		−	1.36605i
$639$	−1.28103e53	+	2.33893e53i	−0.635392	+	1.16012i
$640$	−3.72346e53			−1.79278
$641$		−	2.19558e53i		−	1.02624i	−0.858318	−	0.513118i	$-0.828490\pi$
$641$		−	2.19558e53i		−	1.02624i	0.858318	−	0.513118i	$-0.171510\pi$
$642$	−2.05902e52	+	8.04576e52i	−0.0934318	+	0.365091i
$643$	−3.76988e52			−0.166081			−0.0830403	−	0.996546i	$-0.526463\pi$
$643$	−3.76988e52			−0.166081			−0.0830403	+	0.996546i	$0.526463\pi$
$644$			5.47970e52i			0.234383i
$645$	2.88633e53	+	7.38651e52i	1.19870	+	0.306764i
$646$	2.18739e53			0.882081
$647$			2.71575e52i			0.106343i	0.998585	+	0.0531715i	$0.0169330\pi$
$647$			2.71575e52i			0.106343i	−0.998585	+	0.0531715i	$0.983067\pi$
$648$	−1.37867e53	+	8.81060e52i	−0.524245	+	0.335027i
$649$	−6.85547e52			−0.253156
$650$			6.31351e53i			2.26421i
$651$	6.95861e52	−	2.71913e53i	0.242373	−	0.947089i
$652$	−1.20498e53			−0.407638
$653$		−	1.97468e52i		−	0.0648852i	−0.999474	−	0.0324426i	$-0.989671\pi$
$653$		−	1.97468e52i		−	0.0648852i	0.999474	−	0.0324426i	$-0.0103286\pi$
$654$	6.83578e53	+	1.74937e53i	2.18178	+	0.558346i
$655$	−7.06636e53			−2.19084
$656$		−	3.37887e53i		−	1.01765i
$657$	2.13718e53	+	1.17053e53i	0.625316	+	0.342483i
$658$	4.38397e53			1.24616
$659$		−	6.36429e51i		−	0.0175763i	−0.999961	−	0.00878814i	$-0.997203\pi$
$659$		−	6.36429e51i		−	0.0175763i	0.999961	−	0.00878814i	$-0.00279739\pi$
$660$	8.08932e52	−	3.16096e53i	0.217059	−	0.848172i
$661$	6.25141e53			1.62986			0.814930	−	0.579560i	$-0.196775\pi$
$661$	6.25141e53			1.62986			0.814930	+	0.579560i	$0.196775\pi$
$662$			5.29052e53i			1.34028i
$663$	−4.68397e53	−	1.19869e53i	−1.15307	−	0.295087i
$664$	2.35297e53			0.562890
$665$			3.83928e53i			0.892562i
$666$	−4.10069e52	+	7.48717e52i	−0.0926503	+	0.169164i
$667$	−2.70883e53			−0.594828
$668$			2.62756e53i			0.560789i
$669$	−1.92062e52	+	7.50495e52i	−0.0398423	+	0.155687i
$670$	−1.24211e54			−2.50461
$671$		−	3.71995e53i		−	0.729137i
$672$	−3.83169e53	−	9.80580e52i	−0.730086	−	0.186839i
$673$	−8.96991e53			−1.66151			−0.830753	−	0.556641i	$-0.812090\pi$
$673$	−8.96991e53			−1.66151			−0.830753	+	0.556641i	$0.812090\pi$
$674$		−	6.84854e53i		−	1.23327i
$675$	6.79277e53	−	7.26805e53i	1.18926	−	1.27247i
$676$	−3.85889e52			−0.0656864
$677$		−	2.57942e53i		−	0.426911i	−0.976953	−	0.213455i	$-0.931528\pi$
$677$		−	2.57942e53i		−	0.426911i	0.976953	−	0.213455i	$-0.0684718\pi$
$678$	−5.34831e52	+	2.08989e53i	−0.0860701	+	0.336325i
$679$	7.61185e53			1.19114
$680$			7.56680e53i			1.15144i
$681$	7.94305e52	+	2.03273e52i	0.117542	+	0.0300805i
$682$	1.07234e54			1.54323
$683$		−	7.21883e53i		−	1.01035i	−0.863016	−	0.505177i	$-0.831427\pi$
$683$		−	7.21883e53i		−	1.01035i	0.863016	−	0.505177i	$-0.168573\pi$
$684$	−2.04246e53	−	1.11865e53i	−0.278027	−	0.152274i
$685$	6.23336e53			0.825280
$686$		−	1.03134e54i		−	1.32814i
$687$	−2.77480e52	+	1.08427e53i	−0.0347579	+	0.135819i
$688$	7.66540e53			0.934017
$689$			6.38026e53i			0.756263i
$690$	−9.73439e53	−	2.49116e53i	−1.12247	−	0.287256i
$691$	6.84772e53			0.768181			0.384090	−	0.923296i	$-0.374515\pi$
$691$	6.84772e53			0.768181			0.384090	+	0.923296i	$0.374515\pi$
$692$			8.64702e53i			0.943736i
$693$	−4.06751e53	+	7.42658e53i	−0.431914	+	0.788601i
$694$	−1.47728e54			−1.52627
$695$		−	1.07081e54i		−	1.07647i
$696$	1.63640e53	−	6.39436e53i	0.160072	−	0.625491i
$697$	−9.56046e53			−0.910030
$698$			1.65302e54i			1.53117i
$699$	−4.96940e53	−	1.27174e53i	−0.447959	−	0.114639i
$700$	8.11834e53			0.712204
$701$			6.20423e53i			0.529719i	0.964287	+	0.264860i	$0.0853256\pi$
$701$			6.20423e53i			0.529719i	−0.964287	+	0.264860i	$0.914674\pi$
$702$	1.14294e54	+	1.06820e54i	0.949772	+	0.887663i
$703$	1.26271e53			0.102130
$704$			2.00798e53i			0.158081i
$705$	−6.55760e53	+	2.56243e54i	−0.502518	+	1.96363i
$706$	−4.66842e53			−0.348242
$707$			5.57932e53i			0.405147i
$708$	1.57780e53	+	4.03781e52i	0.111537	+	0.0285439i
$709$	1.50676e54			1.03697			0.518485	−	0.855087i	$-0.326496\pi$
$709$	1.50676e54			1.03697			0.518485	+	0.855087i	$0.326496\pi$
$710$		−	3.99057e54i		−	2.67378i
$711$	−1.89306e54	−	1.03682e54i	−1.23493	−	0.676365i
$712$	−3.49141e53			−0.221759
$713$		−	1.08657e54i		−	0.671979i
$714$	−4.68458e53	+	1.83053e54i	−0.282101	+	1.10233i
$715$	3.24222e54			1.90120
$716$		−	1.56077e53i		−	0.0891234i
$717$	−1.49968e53	−	3.83788e52i	−0.0833939	−	0.0213416i
$718$	−1.50788e53			−0.0816584
$719$			2.78504e54i			1.46887i	0.678681	+	0.734434i	$0.262552\pi$
$719$			2.78504e54i			1.46887i	−0.678681	+	0.734434i	$0.737448\pi$
$720$	1.93543e54	−	3.53377e54i	0.994169	−	1.81518i
$721$	−1.70367e54			−0.852343
$722$		−	1.45837e54i		−	0.710659i
$723$	6.59181e53	−	2.57580e54i	0.312880	−	1.22260i
$724$	1.46651e54			0.678036
$725$			4.01321e54i			1.80747i
$726$	−4.38401e53	−	1.12193e53i	−0.192343	−	0.0492231i
$727$	−1.29791e54			−0.554743			−0.277371	−	0.960763i	$-0.589463\pi$
$727$	−1.29791e54			−0.554743			−0.277371	+	0.960763i	$0.589463\pi$
$728$		−	1.32677e54i		−	0.552458i
$729$	−1.66455e53	−	2.45941e54i	−0.0675263	−	0.997717i
$730$	−3.64635e54			−1.44120
$731$		−	2.16891e54i		−	0.835242i
$732$	−2.19101e53	+	8.56155e53i	−0.0822119	+	0.321249i
$733$	−3.00923e54			−1.10022			−0.550111	−	0.835092i	$-0.685415\pi$
$733$	−3.00923e54			−1.10022			−0.550111	+	0.835092i	$0.685415\pi$
$734$			8.62100e53i			0.307137i
$735$	1.40763e54	+	3.60230e53i	0.488684	+	0.125061i
$736$	−1.53115e54			−0.518011
$737$			4.05215e54i			1.33599i
$738$	2.71314e54	+	1.48598e54i	0.871769	+	0.477465i
$739$	−3.54901e54			−1.11138			−0.555690	−	0.831389i	$-0.687546\pi$
$739$	−3.54901e54			−1.11138			−0.555690	+	0.831389i	$0.687546\pi$
$740$		−	4.20307e53i		−	0.128282i
$741$	5.73702e53	−	2.24178e54i	0.170663	−	0.666880i
$742$	2.49345e54			0.722982
$743$			7.43135e53i			0.210030i	0.994471	+	0.105015i	$0.0334890\pi$
$743$			7.43135e53i			0.210030i	−0.994471	+	0.105015i	$0.966511\pi$
$744$	2.56491e54	+	6.56394e53i	0.706620	+	0.180833i
$745$	9.90675e54			2.66049
$746$		−	6.02837e54i		−	1.57820i
$747$	−1.70290e54	+	3.10921e54i	−0.434609	+	0.793521i
$748$	−2.37528e54			−0.590996
$749$			1.06117e54i			0.257414i
$750$	−1.57168e54	+	6.14146e54i	−0.371707	+	1.45247i
$751$	−5.13765e54			−1.18469			−0.592346	−	0.805684i	$-0.701798\pi$
$751$	−5.13765e54			−1.18469			−0.592346	+	0.805684i	$0.701798\pi$
$752$			6.80520e54i			1.53004i
$753$	3.62711e54	+	9.28225e53i	0.795162	+	0.203493i
$754$	−6.31101e54			−1.34910
$755$		−	7.87307e54i		−	1.64116i
$756$	1.37357e54	−	1.46967e54i	0.279213	−	0.298749i
$757$	8.88483e54			1.76128			0.880638	−	0.473789i	$-0.157114\pi$
$757$	8.88483e54			1.76128			0.880638	+	0.473789i	$0.157114\pi$
$758$			8.34292e54i			1.61288i
$759$	−8.12692e53	+	3.17565e54i	−0.153226	+	0.598741i
$760$	−3.62152e54			−0.665937
$761$		−	8.14284e54i		−	1.46039i	−0.683241	−	0.730193i	$-0.739430\pi$
$761$		−	8.14284e54i		−	1.46039i	0.683241	−	0.730193i	$-0.260570\pi$
$762$	5.01187e54	+	1.28260e54i	0.876709	+	0.224362i
$763$	9.01587e54			1.53830
$764$			1.57069e54i			0.261407i
$765$	−9.99874e54	−	5.47627e54i	−1.62322	−	0.889033i
$766$	−8.62278e54			−1.36553
$767$			1.61836e54i			0.250014i
$768$	1.93326e54	−	7.55435e54i	0.291358	−	1.13850i
$769$	2.06056e54			0.302959			0.151480	−	0.988460i	$-0.451596\pi$
$769$	2.06056e54			0.302959			0.151480	+	0.988460i	$0.451596\pi$
$770$		−	1.26708e55i		−	1.81753i
$771$	−3.76155e54	−	9.62630e53i	−0.526421	−	0.134718i
$772$	1.86760e54			0.255009
$773$			4.04901e52i			0.00539434i	0.999996	+	0.00269717i	$0.000858537\pi$
$773$			4.04901e52i			0.00539434i	−0.999996	+	0.00269717i	$0.999141\pi$
$774$	−3.37113e54	+	6.15511e54i	−0.438226	+	0.800125i
$775$	−1.60978e55			−2.04190
$776$			7.18013e54i			0.888709i
$777$	−2.70425e53	+	1.05671e54i	−0.0326624	+	0.127631i
$778$	2.06288e55			2.43143
$779$		−	4.57570e54i		−	0.526315i
$780$	−7.46204e54	−	1.90964e54i	−0.837646	−	0.214365i
$781$	−1.30184e55			−1.42623
$782$			7.31484e54i			0.782126i
$783$	7.26517e54	+	6.79008e54i	0.758180	+	0.708600i
$784$	3.73832e54			0.380777
$785$		−	1.06016e55i		−	1.05402i
$786$	4.12663e54	−	1.61251e55i	0.400467	−	1.56486i
$787$	9.33817e54			0.884589			0.442295	−	0.896870i	$-0.354165\pi$
$787$	9.33817e54			0.884589			0.442295	+	0.896870i	$0.354165\pi$
$788$			1.81021e54i			0.167390i
$789$	−4.70553e54	−	1.20421e54i	−0.424762	−	0.108702i
$790$	3.22983e55			2.84620
$791$			2.75641e54i			0.237132i
$792$	−7.00536e54	−	3.83681e54i	−0.588372	−	0.322249i
$793$	−8.78164e54			−0.720087
$794$			1.06830e55i			0.855267i
$795$	−3.72974e54	+	1.45742e55i	−0.291544	+	1.13923i
$796$	−1.19835e54			−0.0914612
$797$			9.06547e54i			0.675589i	0.941220	+	0.337794i	$0.109681\pi$
$797$			9.06547e54i			0.675589i	−0.941220	+	0.337794i	$0.890319\pi$
$798$	−8.76106e54	−	2.24207e54i	−0.637531	−	0.163153i
$799$	1.92552e55			1.36823
$800$			2.26844e55i			1.57405i
$801$	2.52681e54	−	4.61353e54i	0.171220	−	0.312619i
$802$	−3.34245e55			−2.21183
$803$			1.18955e55i			0.768753i
$804$	2.38668e54	−	9.32611e54i	0.150636	−	0.588621i
$805$	−1.28389e55			−0.791419
$806$		−	2.53147e55i		−	1.52408i
$807$	−4.86723e54	−	1.24559e54i	−0.286210	−	0.0732449i
$808$	−5.26288e54			−0.302279
$809$			1.36999e55i			0.768591i	0.923210	+	0.384296i	$0.125556\pi$
$809$			1.36999e55i			0.768591i	−0.923210	+	0.384296i	$0.874444\pi$
$810$	1.98635e55	+	3.10820e55i	1.08853	+	1.70331i
$811$	1.50149e55			0.803761			0.401880	−	0.915692i	$-0.368357\pi$
$811$	1.50149e55			0.803761			0.401880	+	0.915692i	$0.368357\pi$
$812$			8.11512e54i			0.424356i
$813$	3.39038e54	−	1.32482e55i	0.173192	−	0.676761i
$814$	−4.16734e54			−0.207967
$815$		−	2.82326e55i		−	1.37644i
$816$	−2.84152e55	−	7.27184e54i	−1.35344	−	0.346363i
$817$	1.03806e55			0.483061
$818$		−	3.73136e55i		−	1.69650i
$819$	1.75319e55	+	9.60213e54i	0.778814	+	0.426554i
$820$	−1.52308e55			−0.661087
$821$		−	3.10003e55i		−	1.31476i	−0.753560	−	0.657380i	$-0.771665\pi$
$821$		−	3.10003e55i		−	1.31476i	0.753560	−	0.657380i	$-0.228335\pi$
$822$	−3.64017e54	+	1.42242e55i	−0.150854	+	0.589474i
$823$	1.06953e55			0.433107			0.216554	−	0.976271i	$-0.430518\pi$
$823$	1.06953e55			0.433107			0.216554	+	0.976271i	$0.430518\pi$
$824$		−	1.60704e55i		−	0.635930i
$825$	4.70482e55	+	1.20403e55i	1.81936	+	0.465598i
$826$	6.32469e54			0.239011
$827$			4.53445e55i			1.67464i	0.546716	+	0.837318i	$0.315878\pi$
$827$			4.53445e55i			1.67464i	−0.546716	+	0.837318i	$0.684122\pi$
$828$	3.74086e54	−	6.83017e54i	0.135019	−	0.246522i
$829$	−2.66453e55			−0.939906			−0.469953	−	0.882691i	$-0.655729\pi$
$829$	−2.66453e55			−0.939906			−0.469953	+	0.882691i	$0.655729\pi$
$830$		−	5.30477e55i		−	1.82887i
$831$	4.27185e54	−	1.66926e55i	0.143945	−	0.562475i
$832$	4.74022e54			0.156119
$833$		−	1.05775e55i		−	0.340509i
$834$	2.44354e55	+	6.25335e54i	0.768891	+	0.196769i
$835$	−6.15635e55			−1.89357
$836$		−	1.13683e55i		−	0.341802i
$837$	−2.72364e55	+	2.91421e55i	−0.800508	+	0.856518i
$838$	−3.88172e55			−1.11529
$839$			6.89502e55i			1.93668i	0.249630	+	0.968341i	$0.419691\pi$
$839$			6.89502e55i			1.93668i	−0.249630	+	0.968341i	$0.580309\pi$
$840$	7.75596e54	−	3.03070e55i	0.212975	−	0.832216i
$841$	−2.86644e54			−0.0769517
$842$			8.55440e55i			2.24522i
$843$	1.47238e54	+	3.76802e53i	0.0377829	+	0.00966916i
$844$	1.68724e55			0.423321
$845$		−	9.04137e54i		−	0.221797i
$846$	−5.46439e55	−	2.99283e55i	−1.31071	−	0.717869i
$847$	−5.78217e54			−0.135615
$848$			3.87057e55i			0.887675i
$849$	7.53605e54	−	2.94477e55i	0.169004	−	0.660397i
$850$	1.08371e56			2.37660
$851$			4.22261e54i			0.0905565i
$852$	2.99622e55	+	7.66774e54i	0.628380	+	0.160811i
$853$	4.16393e55			0.854026			0.427013	−	0.904245i	$-0.359566\pi$
$853$	4.16393e55			0.854026			0.427013	+	0.904245i	$0.359566\pi$
$854$			3.43193e55i			0.688398i
$855$	2.62098e55	−	4.78546e55i	0.514171	−	0.938789i
$856$	−1.00099e55			−0.192056
$857$		−	4.14276e55i		−	0.777416i	−0.921361	−	0.388708i	$-0.872921\pi$
$857$		−	4.14276e55i		−	0.777416i	0.921361	−	0.388708i	$-0.127079\pi$
$858$	−1.89340e55	+	7.39860e55i	−0.347523	+	1.35797i
$859$	2.72913e54			0.0489952			0.0244976	−	0.999700i	$-0.492201\pi$
$859$	2.72913e54			0.0489952			0.0244976	+	0.999700i	$0.492201\pi$
$860$		−	3.45530e55i		−	0.606757i
$861$	3.82921e55	+	9.79946e54i	0.657732	+	0.168322i
$862$	5.60381e55			0.941554
$863$			7.71673e55i			1.26832i	0.773203	+	0.634159i	$0.218654\pi$
$863$			7.71673e55i			1.26832i	−0.773203	+	0.634159i	$0.781346\pi$
$864$	4.10659e55	+	3.83804e55i	0.660267	+	0.617090i
$865$	−2.02599e56			−3.18663
$866$		−	1.38982e56i		−	2.13854i
$867$	−4.10603e54	+	1.60446e55i	−0.0618100	+	0.241527i
$868$	−3.25514e55			−0.479396
$869$		−	1.05367e56i		−	1.51820i
$870$	−1.44161e56	−	3.68926e55i	−2.03227	−	0.520084i
$871$	9.56587e55			1.31941
$872$			8.50451e55i			1.14772i
$873$	−9.48779e55	−	5.19643e55i	−1.25284	−	0.686174i
$874$	−3.50093e55			−0.452342
$875$			8.10012e55i			1.02409i
$876$	7.00633e54	−	2.73778e55i	0.0866788	−	0.338704i
$877$	1.33125e56			1.61164			0.805820	−	0.592160i	$-0.201725\pi$
$877$	1.33125e56			1.61164			0.805820	+	0.592160i	$0.201725\pi$
$878$		−	4.18181e55i		−	0.495414i
$879$	−2.03399e55	−	5.20526e54i	−0.235809	−	0.0603467i
$880$	1.96689e56			2.23156
$881$		−	1.40199e56i		−	1.55669i	−0.627834	−	0.778347i	$-0.716058\pi$
$881$		−	1.40199e56i		−	1.55669i	0.627834	−	0.778347i	$-0.283942\pi$
$882$	−1.64406e55	+	3.00177e55i	−0.178655	+	0.326193i
$883$	−1.26801e56			−1.34855			−0.674277	−	0.738479i	$-0.735545\pi$
$883$	−1.26801e56			−1.34855			−0.674277	+	0.738479i	$0.735545\pi$
$884$			5.60730e55i			0.583662i
$885$	−9.46055e54	+	3.69678e55i	−0.0963817	+	0.376618i
$886$	−1.05929e56			−1.05627
$887$		−	9.99145e55i		−	0.975169i	−0.873076	−	0.487585i	$-0.837878\pi$
$887$		−	9.99145e55i		−	0.975169i	0.873076	−	0.487585i	$-0.162122\pi$
$888$	−9.96772e54	−	2.55087e54i	−0.0952246	−	0.0243693i
$889$	6.61027e55			0.618139
$890$			7.87136e55i			0.720509i
$891$	1.01399e56	−	6.48006e55i	0.908567	−	0.580635i
$892$	8.98437e54			0.0788053
$893$			9.21567e55i			0.791315i
$894$	−5.78537e55	+	2.26067e56i	−0.486316	+	1.90031i
$895$	3.65688e55			0.300935
$896$		−	1.12066e56i		−	0.902862i
$897$	7.49673e55	+	1.91851e55i	0.591311	+	0.151324i
$898$	8.16240e55			0.630329
$899$		−	1.60914e56i		−	1.21664i
$900$	−1.01191e56	−	5.54219e55i	−0.749090	−	0.410274i
$901$	1.09517e56			0.793800
$902$			1.51013e56i			1.07174i
$903$	−2.22313e55	+	8.68706e55i	−0.154489	+	0.603678i
$904$	−2.60007e55			−0.176923
$905$			3.43603e56i			2.28946i
$906$	1.79660e56	+	4.59774e55i	1.17224	+	0.299991i
$907$	−4.50442e55			−0.287806			−0.143903	−	0.989592i	$-0.545965\pi$
$907$	−4.50442e55			−0.287806			−0.143903	+	0.989592i	$0.545965\pi$
$908$		−	9.50882e54i		−	0.0594971i
$909$	3.80887e55	−	6.95434e55i	0.233390	−	0.426130i
$910$	−2.99119e56			−1.79497
$911$			1.25668e56i			0.738541i	0.929322	+	0.369271i	$0.120392\pi$
$911$			1.25668e56i			0.738541i	−0.929322	+	0.369271i	$0.879608\pi$
$912$	3.48035e55	−	1.35997e56i	0.200319	−	0.782759i
$913$	−1.73058e56			−0.975543
$914$		−	1.05277e56i		−	0.581242i
$915$	−2.00597e56	−	5.13353e55i	−1.08473	−	0.277598i
$916$	1.29801e55			0.0687486
$917$		−	2.12678e56i		−	1.10333i
$918$	1.83357e56	−	1.96186e56i	0.931722	−	0.996913i
$919$	−5.34481e55			−0.266034			−0.133017	−	0.991114i	$-0.542467\pi$
$919$	−5.34481e55			−0.266034			−0.133017	+	0.991114i	$0.542467\pi$
$920$		−	1.21107e56i		−	0.590475i
$921$	6.09052e54	−	2.37992e55i	0.0290885	−	0.113665i
$922$	8.86578e55			0.414791
$923$			3.07325e56i			1.40853i
$924$	9.51361e55	+	2.43466e55i	0.427148	+	0.109313i
$925$	6.25592e55			0.275168
$926$			1.52245e56i			0.656047i
$927$	2.12353e56	+	1.16305e56i	0.896487	+	0.491003i
$928$	−2.26754e56			−0.937872
$929$			1.02772e55i			0.0416463i	0.999783	+	0.0208231i	$0.00662869\pi$
$929$			1.02772e55i			0.0416463i	−0.999783	+	0.0208231i	$0.993371\pi$
$930$	1.47984e56	−	5.78257e56i	0.587541	−	2.29586i
$931$	5.06247e55			0.196933
$932$			5.94900e55i			0.226747i
$933$	−2.13989e56	−	5.47626e55i	−0.799171	−	0.204519i
$934$	−1.48851e56			−0.544706
$935$		−	5.56527e56i		−	1.99556i
$936$	−9.05753e55	+	1.65375e56i	−0.318250	+	0.581070i
$937$	−5.35132e55			−0.184251			−0.0921253	−	0.995747i	$-0.529366\pi$
$937$	−5.35132e55			−0.184251			−0.0921253	+	0.995747i	$0.529366\pi$
$938$		−	3.73841e56i		−	1.26134i
$939$	−1.25865e56	+	4.91828e56i	−0.416160	+	1.62617i
$940$	3.06755e56			0.993945
$941$			7.35304e55i			0.233488i	0.993162	+	0.116744i	$0.0372457\pi$
$941$			7.35304e55i			0.233488i	−0.993162	+	0.116744i	$0.962754\pi$
$942$	2.41924e56	+	6.19116e55i	0.752856	+	0.192666i
$943$	1.53016e56			0.466675
$944$			9.81776e55i			0.293457i
$945$	3.44343e56	+	3.21826e56i	1.00876	+	0.942793i
$946$	−3.42592e56			−0.983661
$947$		−	4.43729e56i		−	1.24873i	−0.781133	−	0.624365i	$-0.785358\pi$
$947$		−	4.43729e56i		−	1.24873i	0.781133	−	0.624365i	$-0.214642\pi$
$948$	−6.20602e55	+	2.42505e56i	−0.171181	+	0.668901i
$949$	2.80816e56			0.759213
$950$			5.18673e56i			1.37450i
$951$	−3.18215e56	−	8.14354e55i	−0.826590	−	0.211536i
$952$	−2.27740e56			−0.579878
$953$			2.15698e56i			0.538371i	0.963088	+	0.269185i	$0.0867545\pi$
$953$			2.15698e56i			0.538371i	−0.963088	+	0.269185i	$0.913246\pi$
$954$	−3.10796e56	−	1.70222e56i	−0.760426	−	0.416482i
$955$	−3.68012e56			−0.882668
$956$			1.79530e55i			0.0422122i
$957$	−1.20355e56	+	4.70295e56i	−0.277420	+	1.08404i
$958$	1.69983e56			0.384115
$959$			1.87607e56i			0.415619i
$960$	1.08279e56	+	2.77102e55i	0.235176	+	0.0601847i
$961$	1.75842e56			0.374437
$962$			9.83779e55i			0.205386i
$963$	7.24438e55	−	1.32270e56i	0.148287	−	0.270746i
$964$	−3.08355e56			−0.618854
$965$			4.37578e56i			0.861067i
$966$	7.49770e55	−	2.92978e56i	0.144665	−	0.565288i
$967$	6.13156e56			1.16003			0.580014	−	0.814607i	$-0.303047\pi$
$967$	6.13156e56			1.16003			0.580014	+	0.814607i	$0.303047\pi$
$968$		−	5.45422e55i		−	0.101181i
$969$	−3.84802e56	−	9.84760e55i	−0.699980	−	0.179134i
$970$	1.61876e57			2.88748
$971$		−	6.07445e56i		−	1.06253i	−0.847205	−	0.531266i	$-0.821717\pi$
$971$		−	6.07445e56i		−	1.06253i	0.847205	−	0.531266i	$-0.178283\pi$
$972$	−2.71539e56	+	8.94172e55i	−0.465772	+	0.153378i
$973$	3.22284e56			0.542120
$974$		−	6.43124e56i		−	1.06090i
$975$	2.84233e56	−	1.11066e57i	0.459819	−	1.79678i
$976$	−5.32736e56			−0.845212
$977$			7.49738e56i			1.16658i	0.812266	+	0.583288i	$0.198234\pi$
$977$			7.49738e56i			1.16658i	−0.812266	+	0.583288i	$0.801766\pi$
$978$	6.44254e56	+	1.64873e56i	0.983149	+	0.251601i
$979$	2.56788e56			0.384329
$980$		−	1.68510e56i		−	0.247361i
$981$	−1.12378e57	−	6.15491e56i	−1.61797	−	0.886157i
$982$	−1.42259e57			−2.00891
$983$		−	8.64716e56i		−	1.19772i	−0.800852	−	0.598862i	$-0.795620\pi$
$983$		−	8.64716e56i		−	1.19772i	0.800852	−	0.598862i	$-0.204380\pi$
$984$	−9.24366e55	+	3.61202e56i	−0.125585	+	0.490731i
$985$	−4.24131e56			−0.565212
$986$			1.08328e57i			1.41606i
$987$	−7.71220e56	−	1.97366e56i	−0.988901	−	0.253073i
$988$	−2.68369e56			−0.337560
$989$			3.47136e56i			0.428322i
$990$	−8.65008e56	+	1.57936e57i	−1.04701	+	1.91166i
$991$	1.11029e57			1.31836			0.659182	−	0.751983i	$-0.270903\pi$
$991$	1.11029e57			1.31836			0.659182	+	0.751983i	$0.270903\pi$
$992$		−	9.09556e56i		−	1.05952i
$993$	2.38179e56	−	9.30700e56i	0.272187	−	1.06359i
$994$	1.20105e57			1.34654
$995$		−	2.80774e56i		−	0.308829i
$996$	3.98297e56	+	1.01929e56i	0.429813	+	0.109995i
$997$	−6.64488e56			−0.703524			−0.351762	−	0.936089i	$-0.614417\pi$
$997$	−6.64488e56			−0.703524			−0.351762	+	0.936089i	$0.614417\pi$
$998$			1.34322e56i			0.139530i
$999$	1.05846e56	−	1.13252e56i	0.107877	−	0.115425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.39.b.a.2.9	yes	12
3.2	odd	2	inner	3.39.b.a.2.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.39.b.a.2.4	✓	12	3.2	odd	2	inner
3.39.b.a.2.9	yes	12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 39 \)
Character orbit:	\([\chi]\)	\(=\)	3.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+640056. i q^{2} +(2.88152e8 - 1.12598e9i) q^{3} -1.34793e11 q^{4} -3.15820e13i q^{5} +(7.20687e14 + 1.84433e14i) q^{6} +9.50531e15 q^{7} +8.96619e16i q^{8} +(-1.18479e18 - 6.48904e17i) q^{9} +O(q^{10})\)	\(q+640056. i q^{2} +(2.88152e8 - 1.12598e9i) q^{3} -1.34793e11 q^{4} -3.15820e13i q^{5} +(7.20687e14 + 1.84433e14i) q^{6} +9.50531e15 q^{7} +8.96619e16i q^{8} +(-1.18479e18 - 6.48904e17i) q^{9} +2.02142e19 q^{10} -6.59450e19i q^{11} +(-3.88410e19 + 1.51774e20i) q^{12} -1.55676e21 q^{13} +6.08393e21i q^{14} +(-3.55605e22 - 9.10042e21i) q^{15} -9.44403e22 q^{16} +2.67217e23i q^{17} +(4.15335e23 - 7.58331e23i) q^{18} -1.27892e24 q^{19} +4.25704e24i q^{20} +(2.73898e24 - 1.07027e25i) q^{21} +4.22085e25 q^{22} -4.27683e25i q^{23} +(1.00957e26 + 2.58363e25i) q^{24} -6.33625e26 q^{25} -9.96411e26i q^{26} +(-1.07205e27 + 1.14706e27i) q^{27} -1.28125e27 q^{28} -6.33374e27i q^{29} +(5.82478e27 - 2.27607e28i) q^{30} +2.54059e28 q^{31} -3.58010e28i q^{32} +(-7.42524e28 - 1.90022e28i) q^{33} -1.71034e29 q^{34} -3.00197e29i q^{35} +(1.59702e29 + 8.74680e28i) q^{36} -9.87322e28 q^{37} -8.18580e29i q^{38} +(-4.48583e29 + 1.75287e30i) q^{39} +2.83170e30 q^{40} +3.57778e30i q^{41} +(6.85035e30 + 1.75310e30i) q^{42} -8.11666e30 q^{43} +8.88895e30i q^{44} +(-2.04937e31 + 3.74180e31i) q^{45} +2.73741e31 q^{46} -7.20582e31i q^{47} +(-2.72132e31 + 1.06337e32i) q^{48} -3.95839e31 q^{49} -4.05555e32i q^{50} +(3.00880e32 + 7.69993e31i) q^{51} +2.09841e32 q^{52} -4.09843e32i q^{53} +(-7.34182e32 - 6.86171e32i) q^{54} -2.08268e33 q^{55} +8.52264e32i q^{56} +(-3.68524e32 + 1.44003e33i) q^{57} +4.05394e33 q^{58} -1.03957e33i q^{59} +(4.79333e33 + 1.22668e33i) q^{60} +5.64098e33 q^{61} +1.62612e34i q^{62} +(-1.12618e34 - 6.16804e33i) q^{63} -3.04493e33 q^{64} +4.91655e34i q^{65} +(1.21625e34 - 4.75257e34i) q^{66} -6.14474e34 q^{67} -3.60191e34i q^{68} +(-4.81561e34 - 1.23238e34i) q^{69} +1.92143e35 q^{70} -1.97414e35i q^{71} +(5.81820e34 - 1.06230e35i) q^{72} -1.80385e35 q^{73} -6.31941e34i q^{74} +(-1.82580e35 + 7.13446e35i) q^{75} +1.72390e35 q^{76} -6.26828e35i q^{77} +(-1.12193e36 - 2.87118e35i) q^{78} +1.59780e36 q^{79} +2.98261e36i q^{80} +(9.82647e35 + 1.53763e36i) q^{81} -2.28998e36 q^{82} -2.62427e36i q^{83} +(-3.69196e35 + 1.44266e36i) q^{84} +8.43926e36 q^{85} -5.19512e36i q^{86} +(-7.13163e36 - 1.82508e36i) q^{87} +5.91276e36 q^{88} +3.89397e36i q^{89} +(-2.39496e37 - 1.31171e37i) q^{90} -1.47975e37 q^{91} +5.76489e36i q^{92} +(7.32076e36 - 2.86064e37i) q^{93} +4.61213e37 q^{94} +4.03909e37i q^{95} +(-4.03110e37 - 1.03161e37i) q^{96} +8.00800e37 q^{97} -2.53359e37i q^{98} +(-4.27920e37 + 7.81309e37i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 114742404 q^{3} - 1699274528448 q^{4} - 483611204680128 q^{6} + 81\!\cdots\!48 q^{7}+ \cdots - 42\!\cdots\!40 q^{9}+O(q^{10}) \) 12 * q - 114742404 * q^3 - 1699274528448 * q^4 - 483611204680128 * q^6 + 8107872236538648 * q^7 - 424319151461513940 * q^9	\( 12 q - 114742404 q^{3} - 1699274528448 q^{4} - 483611204680128 q^{6} + 81\!\cdots\!48 q^{7}+ \cdots - 34\!\cdots\!40 q^{99}+O(q^{100}) \) 12 * q - 114742404 * q^3 - 1699274528448 * q^4 - 483611204680128 * q^6 + 8107872236538648 * q^7 - 424319151461513940 * q^9 + 8521437485093339520 * q^10 - 2862564534392665536 * q^12 + 1069098773333431501752 * q^13 + 6325133233762551847680 * q^15 + 67078537203201948051456 * q^16 + 1420463738762719667349120 * q^18 - 4607058619794992781108360 * q^19 + 33320142533758881258920952 * q^21 - 136880063896016789094648960 * q^22 + 783927349783175843577206784 * q^24 - 1296747019384761463507120020 * q^25 + 3527882385497241000493515804 * q^27 - 772965222736808266417757568 * q^28 - 31212306699175351074822848640 * q^30 + 62426311865853800230409578584 * q^31 - 201583764927512776992433501440 * q^33 + 279954989831379847783072264704 * q^34 + 524806089486681368742761588544 * q^36 - 1044821541252033349072004239752 * q^37 + 3798009668755107990641466418968 * q^39 - 8640808308189045028871484272640 * q^40 + 3739179021877842175021096471680 * q^42 + 10033244180304067819165288107192 * q^43 - 61618154391458016749088317176320 * q^45 + 133876649746070235210936111300864 * q^46 - 169673882786170669254051959076864 * q^48 - 74274509875804693019854807543452 * q^49 + 717994133339248153525793387369472 * q^51 - 993185387699150183190245387663232 * q^52 + 1237237684228372752705008546718912 * q^54 - 147621918295658178296158670231040 * q^55 - 1942894316331924260346088046339112 * q^57 + 5456952458981587224214732301397120 * q^58 - 21422716753388621512702364409876480 * q^60 + 19261150877798591818539348576756024 * q^61 - 6850204156609697882698173452536488 * q^63 - 3354811274780051137580237339295744 * q^64 + 29491133770268183961996554653096320 * q^66 - 12293160890248249992597347473356552 * q^67 + 14368205812565646738112192879237632 * q^69 + 131887910392782907972479210848551680 * q^70 - 849782187269944662605305038851543040 * q^72 + 904634266610182985560078196407011672 * q^73 - 1950889856240531910659528579515703460 * q^75 + 3737782451304773339414088480976030848 * q^76 - 4783964522796872138966708226773738880 * q^78 + 3380994931932561121624661644777634520 * q^79 - 3842105375893366153709000791027089588 * q^81 + 9707181808332667829526886407699144960 * q^82 - 23112447300276128146951334880402529152 * q^84 + 16191233322474057038450787601892136960 * q^85 - 46435849480387750961684301913616613120 * q^87 + 111257699492994117641050357545187921920 * q^88 - 164148346324517317604081085509260974720 * q^90 + 128973762284915213743998856562037216624 * q^91 - 173596942201215499347713600620947459528 * q^93 + 323629532832623192615016136649966897664 * q^94 - 450074405332355244291177655815409434624 * q^96 + 248679388944018942060778750016570824728 * q^97 - 346605715634587898579110273074604669440 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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