LMFDB - Embedded newform 3.39.b.a.2.11

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			2.11
Root			$65373.8i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.39.b.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+784486. i q^{2} +(1.15997e9 - 7.30136e7i) q^{3} -3.40540e11 q^{4} +3.07374e13i q^{5} +(5.72781e13 + 9.09976e14i) q^{6} +1.07708e16 q^{7} -5.15107e16i q^{8} +(1.34019e18 - 1.69386e17i) q^{9} +O(q^{10})$	\(q+784486. i q^{2} +(1.15997e9 - 7.30136e7i) q^{3} -3.40540e11 q^{4} +3.07374e13i q^{5} +(5.72781e13 + 9.09976e14i) q^{6} +1.07708e16 q^{7} -5.15107e16i q^{8} +(1.34019e18 - 1.69386e17i) q^{9} -2.41131e19 q^{10} +2.63951e19i q^{11} +(-3.95014e20 + 2.48640e19i) q^{12} +2.34737e21 q^{13} +8.44954e21i q^{14} +(2.24425e21 + 3.56544e22i) q^{15} -5.31974e22 q^{16} +1.67135e23i q^{17} +(1.32881e23 + 1.05136e24i) q^{18} -9.52513e23 q^{19} -1.04673e25i q^{20} +(1.24938e25 - 7.86415e23i) q^{21} -2.07065e25 q^{22} -4.84019e25i q^{23} +(-3.76098e24 - 5.97506e25i) q^{24} -5.80992e26 q^{25} +1.84148e27i q^{26} +(1.54221e27 - 2.94335e26i) q^{27} -3.66789e27 q^{28} -8.06134e27i q^{29} +(-2.79703e28 + 1.76058e27i) q^{30} -1.15899e28 q^{31} -5.58918e28i q^{32} +(1.92720e27 + 3.06174e28i) q^{33} -1.31115e29 q^{34} +3.31067e29i q^{35} +(-4.56388e29 + 5.76828e28i) q^{36} -4.26694e29 q^{37} -7.47233e29i q^{38} +(2.72287e30 - 1.71390e29i) q^{39} +1.58331e30 q^{40} -7.27638e30i q^{41} +(6.16931e29 + 9.80118e30i) q^{42} +9.82872e30 q^{43} -8.98856e30i q^{44} +(5.20651e30 + 4.11940e31i) q^{45} +3.79706e31 q^{46} +8.44918e29i q^{47} +(-6.17072e31 + 3.88413e30i) q^{48} -1.39246e31 q^{49} -4.55780e32i q^{50} +(1.22031e31 + 1.93871e32i) q^{51} -7.99373e32 q^{52} -6.22306e31i q^{53} +(2.30901e32 + 1.20984e33i) q^{54} -8.11317e32 q^{55} -5.54811e32i q^{56} +(-1.10488e33 + 6.95464e31i) q^{57} +6.32401e33 q^{58} +5.85547e33i q^{59} +(-7.64256e32 - 1.21417e34i) q^{60} -2.26498e33 q^{61} -9.09213e33i q^{62} +(1.44349e34 - 1.82443e33i) q^{63} +2.92235e34 q^{64} +7.21522e34i q^{65} +(-2.40189e34 + 1.51186e33i) q^{66} -2.71859e34 q^{67} -5.69162e34i q^{68} +(-3.53399e33 - 5.61445e34i) q^{69} -2.59717e35 q^{70} +6.76007e34i q^{71} +(-8.72521e33 - 6.90341e34i) q^{72} +4.44073e35 q^{73} -3.34736e35i q^{74} +(-6.73931e35 + 4.24203e34i) q^{75} +3.24368e35 q^{76} +2.84296e35i q^{77} +(1.34453e35 + 2.13605e36i) q^{78} -1.68762e35 q^{79} -1.63515e36i q^{80} +(1.76742e36 - 4.54020e35i) q^{81} +5.70822e36 q^{82} -3.55603e36i q^{83} +(-4.25462e36 + 2.67805e35i) q^{84} -5.13731e36 q^{85} +7.71049e36i q^{86} +(-5.88587e35 - 9.35088e36i) q^{87} +1.35963e36 q^{88} +7.51232e36i q^{89} +(-3.23161e37 + 4.08443e36i) q^{90} +2.52831e37 q^{91} +1.64828e37i q^{92} +(-1.34439e37 + 8.46222e35i) q^{93} -6.62826e35 q^{94} -2.92778e37i q^{95} +(-4.08086e36 - 6.48325e37i) q^{96} +2.81399e37 q^{97} -1.09236e37i q^{98} +(4.47096e36 + 3.53744e37i) 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 $

$2$			784486.i			1.49629i	0.663537	+	0.748144i	$0.269055\pi$
$2$			784486.i			1.49629i	−0.663537	+	0.748144i	$0.730945\pi$
$3$	1.15997e9	−	7.30136e7i	0.998025	−	0.0628202i
$3$	1.15997e9	−	7.30136e7i	0.998025	−	0.0628202i
$4$	−3.40540e11			−1.23888
$5$			3.07374e13i			1.61153i	0.592237	+	0.805764i	$0.298245\pi$
$5$			3.07374e13i			1.61153i	−0.592237	+	0.805764i	$0.701755\pi$
$6$	5.72781e13	+	9.09976e14i	0.0939971	+	1.49333i
$7$	1.07708e16			0.944899			0.472449	−	0.881358i	$-0.343370\pi$
$7$	1.07708e16			0.944899			0.472449	+	0.881358i	$0.343370\pi$
$8$		−	5.15107e16i		−	0.357427i
$9$	1.34019e18	−	1.69386e17i	0.992107	−	0.125392i
$10$	−2.41131e19			−2.41131
$11$			2.63951e19i			0.431580i	0.976440	+	0.215790i	$0.0692327\pi$
$11$			2.63951e19i			0.431580i	−0.976440	+	0.215790i	$0.930767\pi$
$12$	−3.95014e20	+	2.48640e19i	−1.23643	+	0.0778265i
$13$	2.34737e21			1.60568			0.802839	−	0.596196i	$-0.203322\pi$
$13$	2.34737e21			1.60568			0.802839	+	0.596196i	$0.203322\pi$
$14$			8.44954e21i			1.41384i
$15$	2.24425e21	+	3.56544e22i	0.101237	+	1.60834i
$16$	−5.31974e22			−0.704062
$17$			1.67135e23i			0.699099i	0.936918	+	0.349550i	$0.113665\pi$
$17$			1.67135e23i			0.699099i	−0.936918	+	0.349550i	$0.886335\pi$
$18$	1.32881e23	+	1.05136e24i	0.187623	+	1.48448i
$19$	−9.52513e23			−0.481451			−0.240726	−	0.970593i	$-0.577385\pi$
$19$	−9.52513e23			−0.481451			−0.240726	+	0.970593i	$0.577385\pi$
$20$		−	1.04673e25i		−	1.99648i
$21$	1.24938e25	−	7.86415e23i	0.943033	−	0.0593588i
$22$	−2.07065e25			−0.645768
$23$		−	4.84019e25i		−	0.648684i	−0.945940	−	0.324342i	$-0.894857\pi$
$23$		−	4.84019e25i		−	0.648684i	0.945940	−	0.324342i	$-0.105143\pi$
$24$	−3.76098e24	−	5.97506e25i	−0.0224537	−	0.356721i
$25$	−5.80992e26			−1.59702
$26$			1.84148e27i			2.40255i
$27$	1.54221e27	−	2.94335e26i	0.982271	−	0.187469i
$28$	−3.66789e27			−1.17061
$29$		−	8.06134e27i		−	1.32083i	−0.750903	−	0.660413i	$-0.770381\pi$
$29$		−	8.06134e27i		−	1.32083i	0.750903	−	0.660413i	$-0.229619\pi$
$30$	−2.79703e28	+	1.76058e27i	−2.40655	+	0.151479i
$31$	−1.15899e28			−0.534821			−0.267411	−	0.963583i	$-0.586168\pi$
$31$	−1.15899e28			−0.534821			−0.267411	+	0.963583i	$0.586168\pi$
$32$		−	5.58918e28i		−	1.41091i
$33$	1.92720e27	+	3.06174e28i	0.0271120	+	0.430728i
$34$	−1.31115e29			−1.04605
$35$			3.31067e29i			1.52273i
$36$	−4.56388e29	+	5.76828e28i	−1.22910	+	0.155346i
$37$	−4.26694e29			−0.682785			−0.341393	−	0.939921i	$-0.610899\pi$
$37$	−4.26694e29			−0.682785			−0.341393	+	0.939921i	$0.610899\pi$
$38$		−	7.47233e29i		−	0.720390i
$39$	2.72287e30	−	1.71390e29i	1.60251	−	0.100869i
$40$	1.58331e30			0.576003
$41$		−	7.27638e30i		−	1.65585i	−0.560835	−	0.827927i	$-0.689520\pi$
$41$		−	7.27638e30i		−	1.65585i	0.560835	−	0.827927i	$-0.310480\pi$
$42$	6.16931e29	+	9.80118e30i	0.0888178	+	1.41105i
$43$	9.82872e30			0.904891			0.452446	−	0.891792i	$-0.350552\pi$
$43$	9.82872e30			0.904891			0.452446	+	0.891792i	$0.350552\pi$
$44$		−	8.98856e30i		−	0.534674i
$45$	5.20651e30	+	4.11940e31i	0.202073	+	1.59881i
$46$	3.79706e31			0.970618
$47$			8.44918e29i			0.0143534i	0.999974	+	0.00717671i	$0.00228444\pi$
$47$			8.44918e29i			0.0143534i	−0.999974	+	0.00717671i	$0.997716\pi$
$48$	−6.17072e31	+	3.88413e30i	−0.702672	+	0.0442294i
$49$	−1.39246e31			−0.107166
$50$		−	4.55780e32i		−	2.38960i
$51$	1.22031e31	+	1.93871e32i	0.0439176	+	0.697718i
$52$	−7.99373e32			−1.98923
$53$		−	6.22306e31i		−	0.107836i	−0.998545	−	0.0539178i	$-0.982829\pi$
$53$		−	6.22306e31i		−	0.107836i	0.998545	−	0.0539178i	$-0.0171709\pi$
$54$	2.30901e32	+	1.20984e33i	0.280508	+	1.46976i
$55$	−8.11317e32			−0.695503
$56$		−	5.54811e32i		−	0.337732i
$57$	−1.10488e33	+	6.95464e31i	−0.480501	+	0.0302449i
$58$	6.32401e33			1.97633
$59$			5.85547e33i			1.32243i	0.750195	+	0.661217i	$0.229960\pi$
$59$			5.85547e33i			1.32243i	−0.750195	+	0.661217i	$0.770040\pi$
$60$	−7.64256e32	−	1.21417e34i	−0.125420	−	1.99254i
$61$	−2.26498e33			−0.271518			−0.135759	−	0.990742i	$-0.543347\pi$
$61$	−2.26498e33			−0.271518			−0.135759	+	0.990742i	$0.543347\pi$
$62$		−	9.09213e33i		−	0.800246i
$63$	1.44349e34	−	1.82443e33i	0.937441	−	0.118483i
$64$	2.92235e34			1.40706
$65$			7.21522e34i			2.58759i
$66$	−2.40189e34	+	1.51186e33i	−0.644493	+	0.0405673i
$67$	−2.71859e34			−0.548180			−0.274090	−	0.961704i	$-0.588377\pi$
$67$	−2.71859e34			−0.548180			−0.274090	+	0.961704i	$0.588377\pi$
$68$		−	5.69162e34i		−	0.866097i
$69$	−3.53399e33	−	5.61445e34i	−0.0407505	−	0.647403i
$70$	−2.59717e35			−2.27844
$71$			6.76007e34i			0.452942i	0.974018	+	0.226471i	$0.0727189\pi$
$71$			6.76007e34i			0.452942i	−0.974018	+	0.226471i	$0.927281\pi$
$72$	−8.72521e33	−	6.90341e34i	−0.0448186	−	0.354606i
$73$	4.44073e35			1.75517			0.877587	−	0.479417i	$-0.159152\pi$
$73$	4.44073e35			1.75517			0.877587	+	0.479417i	$0.159152\pi$
$74$		−	3.34736e35i		−	1.02164i
$75$	−6.73931e35	+	4.24203e34i	−1.59387	+	0.100325i
$76$	3.24368e35			0.596459
$77$			2.84296e35i			0.407800i
$78$	1.34453e35	+	2.13605e36i	0.150929	+	2.39781i
$79$	−1.68762e35			−0.148717			−0.0743584	−	0.997232i	$-0.523691\pi$
$79$	−1.68762e35			−0.148717			−0.0743584	+	0.997232i	$0.523691\pi$
$80$		−	1.63515e36i		−	1.13462i
$81$	1.76742e36	−	4.54020e35i	0.968554	−	0.248805i
$82$	5.70822e36			2.47763
$83$		−	3.55603e36i		−	1.22598i	−0.790092	−	0.612988i	$-0.789968\pi$
$83$		−	3.55603e36i		−	1.22598i	0.790092	−	0.612988i	$-0.210032\pi$
$84$	−4.25462e36	+	2.67805e35i	−1.16830	+	0.0735382i
$85$	−5.13731e36			−1.12662
$86$			7.71049e36i			1.35398i
$87$	−5.88587e35	−	9.35088e36i	−0.0829746	−	1.31822i
$88$	1.35963e36			0.154258
$89$			7.51232e36i			0.687644i	0.939035	+	0.343822i	$0.111722\pi$
$89$			7.51232e36i			0.687644i	−0.939035	+	0.343822i	$0.888278\pi$
$90$	−3.23161e37	+	4.08443e36i	−2.39228	+	0.302360i
$91$	2.52831e37			1.51720
$92$			1.64828e37i			0.803639i
$93$	−1.34439e37	+	8.46222e35i	−0.533765	+	0.0335976i
$94$	−6.62826e35			−0.0214768
$95$		−	2.92778e37i		−	0.775872i
$96$	−4.08086e36	−	6.48325e37i	−0.0886335	−	1.40812i
$97$	2.81399e37			0.501948			0.250974	−	0.967994i	$-0.419249\pi$
$97$	2.81399e37			0.501948			0.250974	+	0.967994i	$0.419249\pi$
$98$		−	1.09236e37i		−	0.160351i
$99$	4.47096e36	+	3.53744e37i	0.0541169	+	0.428174i
$100$	1.97851e38			1.97851
$101$			1.58783e38i			1.31431i	0.753757	+	0.657153i	$0.228240\pi$
$101$			1.58783e38i			1.31431i	−0.753757	+	0.657153i	$0.771760\pi$
$102$	−1.52089e38	+	9.57319e36i	−1.04399	+	0.0657133i
$103$	1.04178e38			0.594110			0.297055	−	0.954860i	$-0.403995\pi$
$103$	1.04178e38			0.594110			0.297055	+	0.954860i	$0.403995\pi$
$104$		−	1.20915e38i		−	0.573912i
$105$	2.41724e37	+	3.84026e38i	0.0956583	+	1.51972i
$106$	4.88190e37			0.161353
$107$		−	5.90450e38i		−	1.63264i	−0.577597	−	0.816322i	$-0.696009\pi$
$107$		−	5.90450e38i		−	1.63264i	0.577597	−	0.816322i	$-0.303991\pi$
$108$	−5.25183e38	+	1.00233e38i	−1.21691	+	0.232251i
$109$	−1.13397e38			−0.220546			−0.110273	−	0.993901i	$-0.535172\pi$
$109$	−1.13397e38			−0.220546			−0.110273	+	0.993901i	$0.535172\pi$
$110$		−	6.36466e38i		−	1.04067i
$111$	−4.94951e38	+	3.11545e37i	−0.681437	+	0.0428927i
$112$	−5.72979e38			−0.665268
$113$			6.92711e38i			0.679300i	0.940552	+	0.339650i	$0.110309\pi$
$113$			6.92711e38i			0.679300i	−0.940552	+	0.339650i	$0.889691\pi$
$114$	−5.45581e37	−	8.66764e38i	−0.0452551	−	0.718967i
$115$	1.48775e39			1.04537
$116$			2.74521e39i			1.63634i
$117$	3.14592e39	−	3.97613e38i	1.59300	−	0.201340i
$118$	−4.59353e39			−1.97874
$119$			1.80018e39i			0.660578i
$120$	1.83658e39	−	1.15603e38i	0.574866	−	0.0361847i
$121$	3.04374e39			0.813738
$122$		−	1.77685e39i		−	0.406269i
$123$	−5.31274e38	−	8.44035e39i	−0.104021	−	1.65258i
$124$	3.94683e39			0.662577
$125$		−	6.67601e39i		−	0.962114i
$126$	1.43124e39	+	1.13240e40i	0.177285	+	1.40268i
$127$	6.02500e39			0.642224			0.321112	−	0.947041i	$-0.395943\pi$
$127$	6.02500e39			0.642224			0.321112	+	0.947041i	$0.395943\pi$
$128$			7.56199e39i			0.694459i
$129$	1.14010e40	−	7.17630e38i	0.903104	−	0.0568455i
$130$	−5.66024e40			−3.87178
$131$			1.13980e40i			0.674021i	0.941501	+	0.337011i	$0.109416\pi$
$131$			1.13980e40i			0.674021i	−0.941501	+	0.337011i	$0.890584\pi$
$132$	−6.56287e38	−	1.04264e40i	−0.0335884	−	0.533618i
$133$	−1.02593e40			−0.454923
$134$		−	2.13270e40i		−	0.820235i
$135$	9.04709e39	+	4.74035e40i	0.302112	+	1.58296i
$136$	8.60925e39			0.249877
$137$		−	2.61641e40i		−	0.660715i	−0.943856	−	0.330358i	$-0.892831\pi$
$137$		−	2.61641e40i		−	0.660715i	0.943856	−	0.330358i	$-0.107169\pi$
$138$	4.40446e40	−	2.77237e39i	0.968701	−	0.0609745i
$139$	1.77183e40			0.339735			0.169867	−	0.985467i	$-0.445666\pi$
$139$	1.77183e40			0.339735			0.169867	+	0.985467i	$0.445666\pi$
$140$		−	1.12741e41i		−	1.88647i
$141$	6.16905e37	+	9.80076e38i	0.000901686	+	0.0143251i
$142$	−5.30318e40			−0.677732
$143$			6.19590e40i			0.692979i
$144$	−7.12947e40	+	9.01093e39i	−0.698505	+	0.0882840i
$145$	2.47785e41			2.12855
$146$			3.48369e41i			2.62625i
$147$	−1.61520e40	+	1.01668e39i	−0.106954	+	0.00673219i
$148$	1.45306e41			0.845886
$149$		−	1.85063e40i		−	0.0947938i	−0.998876	−	0.0473969i	$-0.984907\pi$
$149$		−	1.85063e40i		−	0.0947938i	0.998876	−	0.0473969i	$-0.0150926\pi$
$150$	−3.32781e40	−	5.28689e41i	−0.150115	−	2.38488i
$151$	−2.58190e41			−1.02654			−0.513272	−	0.858226i	$-0.671567\pi$
$151$	−2.58190e41			−1.02654			−0.513272	+	0.858226i	$0.671567\pi$
$152$			4.90646e40i			0.172084i
$153$	2.83105e40	+	2.23993e41i	0.0876617	+	0.693581i
$154$	−2.23026e41			−0.610186
$155$		−	3.56245e41i		−	0.861879i
$156$	−9.27246e41	+	5.83651e40i	−1.98531	+	0.124964i
$157$	−6.27539e40			−0.119000			−0.0595001	−	0.998228i	$-0.518951\pi$
$157$	−6.27539e40			−0.119000			−0.0595001	+	0.998228i	$0.518951\pi$
$158$		−	1.32391e41i		−	0.222523i
$159$	−4.54368e39	−	7.21854e40i	−0.00677426	−	0.107623i
$160$	1.71797e42			2.27371
$161$		−	5.21327e41i		−	0.612941i
$162$	3.56172e41	+	1.38651e42i	0.372284	+	1.44923i
$163$	−1.58317e42			−1.47219			−0.736094	−	0.676879i	$-0.763332\pi$
$163$	−1.58317e42			−1.47219			−0.736094	+	0.676879i	$0.763332\pi$
$164$			2.47790e42i			2.05140i
$165$	−9.41099e41	+	5.92371e40i	−0.694130	+	0.0436917i
$166$	2.78965e42			1.83441
$167$		−	2.76798e42i		−	1.62387i	−0.583749	−	0.811934i	$-0.698415\pi$
$167$		−	2.76798e42i		−	1.62387i	0.583749	−	0.811934i	$-0.301585\pi$
$168$	−4.05087e40	−	6.43562e41i	−0.0212164	−	0.337065i
$169$	3.37294e42			1.57820
$170$		−	4.03015e42i		−	1.68574i
$171$	−1.27655e42	+	1.61343e41i	−0.477651	+	0.0603703i
$172$	−3.34707e42			−1.12105
$173$			4.23364e42i			1.27010i	0.772471	+	0.635050i	$0.219021\pi$
$173$			4.23364e42i			1.27010i	−0.772471	+	0.635050i	$0.780979\pi$
$174$	7.33563e42	−	4.61738e41i	1.97243	−	0.124154i
$175$	−6.25776e42			−1.50902
$176$		−	1.40415e42i		−	0.303859i
$177$	4.27529e41	+	6.79215e42i	0.0830756	+	1.31982i
$178$	−5.89330e42			−1.02891
$179$			2.84670e42i			0.446821i	0.974724	+	0.223411i	$0.0717191\pi$
$179$			2.84670e42i			0.446821i	−0.974724	+	0.223411i	$0.928281\pi$
$180$	−1.77302e42	−	1.40282e43i	−0.250344	−	1.98072i
$181$	−2.20401e42			−0.280105			−0.140052	−	0.990144i	$-0.544727\pi$
$181$	−2.20401e42			−0.280105			−0.140052	+	0.990144i	$0.544727\pi$
$182$			1.98342e43i			2.27017i
$183$	−2.62730e42	+	1.65375e41i	−0.270981	+	0.0170568i
$184$	−2.49321e42			−0.231857
$185$		−	1.31155e43i		−	1.10033i
$186$	−6.63849e41	−	1.05466e43i	−0.0502717	−	0.798666i
$187$	−4.41155e42			−0.301717
$188$		−	2.87728e41i		−	0.0177821i
$189$	1.66108e43	−	3.17022e42i	0.928146	−	0.177139i
$190$	2.29680e43			1.16093
$191$		−	1.70688e43i		−	0.780852i	−0.920634	−	0.390426i	$-0.872328\pi$
$191$		−	1.70688e43i		−	0.780852i	0.920634	−	0.390426i	$-0.127672\pi$
$192$	3.38982e43	−	2.13371e42i	1.40428	−	0.0883918i
$193$	−2.36210e43			−0.886562			−0.443281	−	0.896383i	$-0.646186\pi$
$193$	−2.36210e43			−0.886562			−0.443281	+	0.896383i	$0.646186\pi$
$194$			2.20753e43i			0.751059i
$195$	5.26809e42	+	8.36941e43i	0.162553	+	2.58248i
$196$	4.74187e42			0.132765
$197$		−	5.31510e43i		−	1.35099i	−0.737363	−	0.675497i	$-0.763929\pi$
$197$		−	5.31510e43i		−	1.35099i	0.737363	−	0.675497i	$-0.236071\pi$
$198$	−2.77507e43	+	3.50741e42i	−0.640671	+	0.0809744i
$199$	2.82826e43			0.593350			0.296675	−	0.954978i	$-0.404122\pi$
$199$	2.82826e43			0.593350			0.296675	+	0.954978i	$0.404122\pi$
$200$			2.99273e43i			0.570818i
$201$	−3.15348e43	+	1.98494e42i	−0.547097	+	0.0344368i
$202$	−1.24563e44			−1.96658
$203$		−	8.68271e43i		−	1.24805i
$204$	−4.15565e42	−	6.60209e43i	−0.0544084	−	0.864386i
$205$	2.23657e44			2.66845
$206$			8.17258e43i			0.888960i
$207$	−8.19862e42	−	6.48677e43i	−0.0813400	−	0.643564i
$208$	−1.24874e44			−1.13050
$209$		−	2.51416e43i		−	0.207785i
$210$	−3.01263e44	+	1.89629e43i	−2.27394	+	0.143132i
$211$	−7.14319e43			−0.492636			−0.246318	−	0.969189i	$-0.579221\pi$
$211$	−7.14319e43			−0.492636			−0.246318	+	0.969189i	$0.579221\pi$
$212$			2.11920e43i			0.133595i
$213$	4.93577e42	+	7.84145e43i	0.0284539	+	0.452047i
$214$	4.63200e44			2.44290
$215$			3.02110e44i			1.45826i
$216$	−1.51614e43	−	7.94401e43i	−0.0670065	−	0.351090i
$217$	−1.24833e44			−0.505352
$218$		−	8.89584e43i		−	0.330000i
$219$	5.15110e44	−	3.24234e43i	1.75171	−	0.110260i
$220$	2.76285e44			0.861642
$221$			3.92329e44i			1.12253i
$222$	−2.44402e43	−	3.88282e44i	−0.0641799	−	1.01962i
$223$	2.38406e44			0.574811			0.287405	−	0.957809i	$-0.407207\pi$
$223$	2.38406e44			0.574811			0.287405	+	0.957809i	$0.407207\pi$
$224$		−	6.01999e44i		−	1.33316i
$225$	−7.78640e44	+	9.84122e43i	−1.58441	+	0.200254i
$226$	−5.43421e44			−1.01643
$227$		−	7.53137e44i		−	1.29534i	−0.761922	−	0.647668i	$-0.775744\pi$
$227$		−	7.53137e44i		−	1.29534i	0.761922	−	0.647668i	$-0.224256\pi$
$228$	3.76256e44	−	2.36833e43i	0.595281	−	0.0374697i
$229$	−1.95667e44			−0.284867			−0.142434	−	0.989804i	$-0.545493\pi$
$229$	−1.95667e44			−0.284867			−0.142434	+	0.989804i	$0.545493\pi$
$230$			1.16712e45i			1.56418i
$231$	2.07575e43	+	3.29774e44i	0.0256181	+	0.406994i
$232$	−4.15245e44			−0.472099
$233$		−	8.52785e43i		−	0.0893464i	−0.999002	−	0.0446732i	$-0.985775\pi$
$233$		−	8.52785e43i		−	0.0893464i	0.999002	−	0.0446732i	$-0.0142246\pi$
$234$	3.11922e44	+	2.46793e45i	0.301262	+	2.38359i
$235$	−2.59706e43			−0.0231309
$236$		−	1.99402e45i		−	1.63833i
$237$	−1.95758e44	+	1.23219e43i	−0.148423	+	0.00934242i
$238$	−1.41222e45			−0.988415
$239$		−	1.01935e45i		−	0.658812i	−0.944188	−	0.329406i	$-0.893151\pi$
$239$		−	1.01935e45i		−	0.658812i	0.944188	−	0.329406i	$-0.106849\pi$
$240$	−1.19388e44	−	1.89672e45i	−0.0712768	−	1.13237i
$241$	−1.47874e45			−0.815769			−0.407884	−	0.913034i	$-0.633733\pi$
$241$	−1.47874e45			−0.815769			−0.407884	+	0.913034i	$0.633733\pi$
$242$			2.38777e45i			1.21759i
$243$	2.01699e45	−	6.55693e44i	0.951010	−	0.309159i
$244$	7.71317e44			0.336377
$245$		−	4.28006e44i		−	0.172701i
$246$	6.62134e45	−	4.16777e44i	2.47274	−	0.155646i
$247$	−2.23590e45			−0.773056
$248$			5.97005e44i			0.191160i
$249$	−2.59638e44	−	4.12487e45i	−0.0770161	−	1.22355i
$250$	5.23723e45			1.43960
$251$			5.02297e45i			1.27985i	0.768436	+	0.639926i	$0.221035\pi$
$251$			5.02297e45i			1.27985i	−0.768436	+	0.639926i	$0.778965\pi$
$252$	−4.91566e45	+	6.21290e44i	−1.16137	+	0.146786i
$253$	1.27757e45			0.279959
$254$			4.72653e45i			0.960952i
$255$	−5.95911e45	+	3.75093e44i	−1.12439	+	0.0707744i
$256$	2.10062e45			0.367950
$257$			4.58230e45i			0.745340i	0.927964	+	0.372670i	$0.121558\pi$
$257$			4.58230e45i			0.745340i	−0.927964	+	0.372670i	$0.878442\pi$
$258$	5.62970e44	+	8.94390e45i	0.0850572	+	1.35130i
$259$	−4.59584e45			−0.645163
$260$		−	2.45707e46i		−	3.20571i
$261$	−1.36548e45	−	1.08037e46i	−0.165621	−	1.31040i
$262$	−8.94155e45			−1.00853
$263$			3.11142e45i			0.326437i	0.986590	+	0.163219i	$0.0521876\pi$
$263$			3.11142e45i			0.326437i	−0.986590	+	0.163219i	$0.947812\pi$
$264$	1.57712e45	−	9.92712e43i	0.153954	−	0.00969056i
$265$	1.91281e45			0.173780
$266$		−	8.04830e45i		−	0.680696i
$267$	5.48501e44	+	8.71403e45i	0.0431980	+	0.686286i
$268$	9.25789e45			0.679127
$269$			2.16658e46i			1.48075i	0.672193	+	0.740376i	$0.265352\pi$
$269$			2.16658e46i			1.48075i	−0.672193	+	0.740376i	$0.734648\pi$
$270$	−3.71874e46	+	7.09731e45i	−2.36856	+	0.452046i
$271$	1.16365e46			0.690887			0.345444	−	0.938440i	$-0.387728\pi$
$271$	1.16365e46			0.690887			0.345444	+	0.938440i	$0.387728\pi$
$272$		−	8.89117e45i		−	0.492209i
$273$	2.93275e46	−	1.84601e45i	1.51421	−	0.0953110i
$274$	2.05253e46			0.988620
$275$		−	1.53353e46i		−	0.689242i
$276$	1.20346e45	+	1.91194e46i	0.0504848	+	0.802052i
$277$	−5.19583e45			−0.203488			−0.101744	−	0.994811i	$-0.532442\pi$
$277$	−5.19583e45			−0.203488			−0.101744	+	0.994811i	$0.532442\pi$
$278$			1.38997e46i			0.508341i
$279$	−1.55327e46	+	1.96318e45i	−0.530600	+	0.0670625i
$280$	1.70535e46			0.544265
$281$			3.03870e45i			0.0906292i	0.998973	+	0.0453146i	$0.0144290\pi$
$281$			3.03870e45i			0.0906292i	−0.998973	+	0.0453146i	$0.985571\pi$
$282$	−7.68856e44	+	4.83953e43i	−0.0214344	+	0.00134918i
$283$	4.82432e46			1.25746			0.628729	−	0.777624i	$-0.283575\pi$
$283$	4.82432e46			1.25746			0.628729	+	0.777624i	$0.283575\pi$
$284$		−	2.30207e46i		−	0.561139i
$285$	−2.13768e45	−	3.39613e46i	−0.0487405	−	0.774340i
$286$	−4.86060e46			−1.03690
$287$		−	7.83725e46i		−	1.56462i
$288$	−9.46731e45	−	7.49056e46i	−0.176917	−	1.39977i
$289$	2.92214e46			0.511260
$290$			1.94384e47i			3.18492i
$291$	3.26413e46	−	2.05459e45i	0.500957	−	0.0315325i
$292$	−1.51225e47			−2.17444
$293$			8.65440e46i			1.16614i	0.812421	+	0.583072i	$0.198149\pi$
$293$			8.65440e46i			1.16614i	−0.812421	+	0.583072i	$0.801851\pi$
$294$	−7.97573e44	−	1.26710e46i	−0.0100733	−	0.160034i
$295$	−1.79982e47			−2.13114
$296$			2.19793e46i			0.244046i
$297$	7.76898e45	+	4.07066e46i	0.0809080	+	0.423929i
$298$	1.45179e46			0.141839
$299$		−	1.13617e47i		−	1.04158i
$300$	2.29500e47	−	1.44458e46i	1.97460	−	0.124290i
$301$	1.05863e47			0.855031
$302$		−	2.02546e47i		−	1.53600i
$303$	1.15933e46	+	1.84182e47i	0.0825651	+	1.31171i
$304$	5.06713e46			0.338972
$305$		−	6.96198e46i		−	0.437558i
$306$	−1.75719e47	+	2.22091e46i	−1.03780	+	0.131167i
$307$	1.80284e46			0.100076			0.0500379	−	0.998747i	$-0.484066\pi$
$307$	1.80284e46			0.100076			0.0500379	+	0.998747i	$0.484066\pi$
$308$		−	9.68141e46i		−	0.505213i
$309$	1.20842e47	−	7.60638e45i	0.592937	−	0.0373222i
$310$	2.79469e47			1.28962
$311$			5.09327e46i			0.221080i	0.993872	+	0.110540i	$0.0352580\pi$
$311$			5.09327e46i			0.221080i	−0.993872	+	0.110540i	$0.964742\pi$
$312$	−8.82841e45	−	1.40257e47i	−0.0360533	−	0.572779i
$313$	−3.91522e47			−1.50458			−0.752288	−	0.658835i	$-0.771050\pi$
$313$	−3.91522e47			−1.50458			−0.752288	+	0.658835i	$0.771050\pi$
$314$		−	4.92295e46i		−	0.178058i
$315$	5.60783e46	+	4.43693e47i	0.190939	+	1.51071i
$316$	5.74701e46			0.184242
$317$			1.16993e47i			0.353212i	0.984282	+	0.176606i	$0.0565118\pi$
$317$			1.16993e47i			0.353212i	−0.984282	+	0.176606i	$0.943488\pi$
$318$	5.66284e46	−	3.56445e45i	0.161034	−	0.0101362i
$319$	2.12780e47			0.570042
$320$			8.98255e47i			2.26751i
$321$	−4.31109e46	−	6.84902e47i	−0.102563	−	1.62942i
$322$	4.08974e47			0.917136
$323$		−	1.59199e47i		−	0.336582i
$324$	−6.01875e47	+	1.54612e47i	−1.19992	+	0.308239i
$325$	−1.36381e48			−2.56430
$326$		−	1.24197e48i		−	2.20282i
$327$	−1.31537e47	+	8.27953e45i	−0.220110	+	0.0138547i
$328$	−3.74811e47			−0.591847
$329$			9.10045e45i			0.0135625i
$330$	−4.64706e46	−	7.38279e47i	−0.0653753	−	1.03862i
$331$	8.09163e47			1.07474			0.537371	−	0.843346i	$-0.319418\pi$
$331$	8.09163e47			1.07474			0.537371	+	0.843346i	$0.319418\pi$
$332$			1.21097e48i			1.51883i
$333$	−5.71851e47	+	7.22762e46i	−0.677396	+	0.0856160i
$334$	2.17144e48			2.42977
$335$		−	8.35626e47i		−	0.883407i
$336$	−6.64636e47	+	4.18353e46i	−0.663954	+	0.0417923i
$337$	7.40101e47			0.698751			0.349376	−	0.936983i	$-0.386394\pi$
$337$	7.40101e47			0.698751			0.349376	+	0.936983i	$0.386394\pi$
$338$			2.64603e48i			2.36144i
$339$	5.05773e46	+	8.03521e47i	0.0426738	+	0.677958i
$340$	1.74946e48			1.39574
$341$		−	3.05917e47i		−	0.230818i
$342$	−1.26571e47	−	1.00143e48i	−0.0903314	−	0.714704i
$343$	−1.54948e48			−1.04616
$344$		−	5.06284e47i		−	0.323433i
$345$	1.72574e48	−	1.08626e47i	1.04331	−	0.0656705i
$346$	−3.32123e48			−1.90044
$347$		−	1.40857e48i		−	0.762992i	−0.924371	−	0.381496i	$-0.875409\pi$
$347$		−	1.40857e48i		−	0.762992i	0.924371	−	0.381496i	$-0.124591\pi$
$348$	2.00437e47	+	3.18435e48i	0.102795	+	1.63311i
$349$	1.01432e48			0.492597			0.246299	−	0.969194i	$-0.420786\pi$
$349$	1.01432e48			0.492597			0.246299	+	0.969194i	$0.420786\pi$
$350$		−	4.90912e48i		−	2.25793i
$351$	3.62013e48	−	6.90913e47i	1.57721	−	0.301015i
$352$	1.47527e48			0.608919
$353$			1.52516e48i			0.596479i	0.954491	+	0.298240i	$0.0963995\pi$
$353$			1.52516e48i			0.596479i	−0.954491	+	0.298240i	$0.903601\pi$
$354$	−5.32834e48	+	3.35390e47i	−1.97483	+	0.124305i
$355$	−2.07787e48			−0.729929
$356$		−	2.55824e48i		−	0.851906i
$357$	1.31438e47	+	2.08815e48i	0.0414977	+	0.659273i
$358$	−2.23319e48			−0.668573
$359$			2.00126e48i			0.568209i	0.958793	+	0.284105i	$0.0916963\pi$
$359$			2.00126e48i			0.568209i	−0.958793	+	0.284105i	$0.908304\pi$
$360$	2.12193e48	−	2.68191e47i	0.571457	−	0.0722264i
$361$	−3.00686e48			−0.768204
$362$		−	1.72901e48i		−	0.419117i
$363$	3.53063e48	−	2.22234e47i	0.812131	−	0.0511193i
$364$	−8.60989e48			−1.87963
$365$			1.36497e49i			2.82851i
$366$	−1.29734e47	−	2.06108e48i	−0.0255219	−	0.405466i
$367$	1.39146e48			0.259905			0.129953	−	0.991520i	$-0.458517\pi$
$367$	1.39146e48			0.259905			0.129953	+	0.991520i	$0.458517\pi$
$368$			2.57486e48i			0.456714i
$369$	−1.23252e48	−	9.75173e48i	−0.207631	−	1.64279i
$370$	1.02889e49			1.64641
$371$		−	6.70274e47i		−	0.101894i
$372$	4.57819e48	−	2.88172e47i	0.661268	−	0.0416233i
$373$	9.04311e48			1.24122			0.620612	−	0.784118i	$-0.286884\pi$
$373$	9.04311e48			1.24122			0.620612	+	0.784118i	$0.286884\pi$
$374$		−	3.46079e48i		−	0.451456i
$375$	−4.87439e47	−	7.74394e48i	−0.0604402	−	0.960213i
$376$	4.35223e46			0.00513030
$377$		−	1.89230e49i		−	2.12082i
$378$	2.48699e48	+	1.30309e49i	0.265051	+	1.38877i
$379$	−1.74074e49			−1.76437			−0.882184	−	0.470904i	$-0.843928\pi$
$379$	−1.74074e49			−1.76437			−0.882184	+	0.470904i	$0.843928\pi$
$380$			9.97026e48i			0.961209i
$381$	6.98880e48	−	4.39907e47i	0.640956	−	0.0403447i
$382$	1.33902e49			1.16838
$383$			2.24202e49i			1.86150i	0.365662	+	0.930748i	$0.380843\pi$
$383$			2.24202e49i			1.86150i	−0.365662	+	0.930748i	$0.619157\pi$
$384$	5.52127e47	+	8.77165e48i	0.0436261	+	0.693087i
$385$	−8.73853e48			−0.657180
$386$		−	1.85303e49i		−	1.32655i
$387$	1.31724e49	−	1.66485e48i	0.897749	−	0.113466i
$388$	−9.58274e48			−0.621852
$389$		−	6.09185e48i		−	0.376449i	−0.982126	−	0.188225i	$-0.939727\pi$
$389$		−	6.09185e48i		−	0.376449i	0.982126	−	0.188225i	$-0.0602733\pi$
$390$	−6.56568e49	+	4.13274e48i	−3.86413	+	0.243226i
$391$	8.08966e48			0.453495
$392$			7.17265e47i			0.0383040i
$393$	8.32207e47	+	1.32213e49i	0.0423422	+	0.672690i
$394$	4.16962e49			2.02147
$395$		−	5.18731e48i		−	0.239661i
$396$	−1.52254e48	−	1.20464e49i	−0.0670441	−	0.530454i
$397$	−2.98327e49			−1.25220			−0.626098	−	0.779744i	$-0.715349\pi$
$397$	−2.98327e49			−1.25220			−0.626098	+	0.779744i	$0.715349\pi$
$398$			2.21873e49i			0.887823i
$399$	−1.19005e49	+	7.49070e47i	−0.454024	+	0.0285784i
$400$	3.09073e49			1.12440
$401$		−	5.09325e49i		−	1.76706i	−0.468371	−	0.883532i	$-0.655159\pi$
$401$		−	5.09325e49i		−	1.76706i	0.468371	−	0.883532i	$-0.344841\pi$
$402$	−1.55716e48	−	2.47386e49i	−0.0515274	−	0.818615i
$403$	−2.72059e49			−0.858750
$404$		−	5.40717e49i		−	1.62826i
$405$	1.39554e49	+	5.43259e49i	0.400956	+	1.56085i
$406$	6.81146e49			1.86744
$407$		−	1.12626e49i		−	0.294677i
$408$	9.98644e48	−	6.28592e47i	0.249383	−	0.0156973i
$409$	−4.95505e49			−1.18115			−0.590575	−	0.806983i	$-0.701099\pi$
$409$	−4.95505e49			−1.18115			−0.590575	+	0.806983i	$0.701099\pi$
$410$			1.75456e50i			3.99277i
$411$	−1.91033e48	−	3.03494e49i	−0.0415063	−	0.659410i
$412$	−3.54766e49			−0.736029
$413$			6.30682e49i			1.24957i
$414$	5.08878e49	−	6.43170e48i	0.962957	−	0.121708i
$415$	1.09303e50			1.97569
$416$		−	1.31199e50i		−	2.26546i
$417$	2.05526e49	−	1.29367e48i	0.339064	−	0.0213422i
$418$	1.97232e49			0.310906
$419$			1.15930e50i			1.74634i	0.487415	+	0.873170i	$0.337940\pi$
$419$			1.15930e50i			1.74634i	−0.487415	+	0.873170i	$0.662060\pi$
$420$	−8.23165e48	−	1.30776e50i	−0.118509	−	1.88275i
$421$	−1.23857e50			−1.70436			−0.852179	−	0.523251i	$-0.824719\pi$
$421$	−1.23857e50			−1.70436			−0.852179	+	0.523251i	$0.824719\pi$
$422$		−	5.60373e49i		−	0.737125i
$423$	1.43118e47	+	1.13235e48i	0.00179981	+	0.0142401i
$424$	−3.20554e48			−0.0385434
$425$		−	9.71044e49i		−	1.11648i
$426$	−6.15151e49	+	3.87204e48i	−0.676393	+	0.0425753i
$427$	−2.43957e49			−0.256557
$428$			2.01072e50i			2.02264i
$429$	4.52385e48	+	7.18703e49i	0.0435331	+	0.691610i
$430$	−2.37001e50			−2.18197
$431$		−	2.16186e50i		−	1.90441i	−0.305463	−	0.952204i	$-0.598811\pi$
$431$		−	2.16186e50i		−	1.90441i	0.305463	−	0.952204i	$-0.401189\pi$
$432$	−8.20415e49	+	1.56578e49i	−0.691580	+	0.131990i
$433$	2.59340e48			0.0209218			0.0104609	−	0.999945i	$-0.496670\pi$
$433$	2.59340e48			0.0209218			0.0104609	+	0.999945i	$0.496670\pi$
$434$		−	9.79296e49i		−	0.756152i
$435$	2.87422e50	−	1.80917e49i	2.12434	−	0.133716i
$436$	3.86162e49			0.273229
$437$			4.61034e49i			0.312310i
$438$	2.54357e49	+	4.04096e50i	0.164981	+	2.62106i
$439$	2.42061e50			1.50348			0.751742	−	0.659457i	$-0.229214\pi$
$439$	2.42061e50			1.50348			0.751742	+	0.659457i	$0.229214\pi$
$440$			4.17915e49i			0.248592i
$441$	−1.86616e49	+	2.35864e48i	−0.106320	+	0.0134378i
$442$	−3.07776e50			−1.67962
$443$		−	8.62313e49i		−	0.450811i	−0.974265	−	0.225405i	$-0.927629\pi$
$443$		−	8.62313e49i		−	0.450811i	0.974265	−	0.225405i	$-0.0723707\pi$
$444$	1.68550e50	−	1.06093e49i	0.844215	−	0.0531388i
$445$	−2.30909e50			−1.10816
$446$			1.87026e50i			0.860082i
$447$	−1.35121e48	−	2.14667e49i	−0.00595497	−	0.0946066i
$448$	3.14760e50			1.32953
$449$		−	3.61936e50i		−	1.46538i	−0.680560	−	0.732692i	$-0.738264\pi$
$449$		−	3.61936e50i		−	1.46538i	0.680560	−	0.732692i	$-0.261736\pi$
$450$	−7.72030e49	−	6.10832e50i	−0.299638	−	2.37074i
$451$	1.92060e50			0.714634
$452$		−	2.35895e50i		−	0.841568i
$453$	−2.99492e50	+	1.88514e49i	−1.02452	+	0.0644877i
$454$	5.90825e50			1.93820
$455$			7.77137e50i			2.44501i
$456$	3.58238e48	+	5.69132e49i	0.0108103	+	0.171744i
$457$	2.96698e50			0.858830			0.429415	−	0.903107i	$-0.358720\pi$
$457$	2.96698e50			0.858830			0.429415	+	0.903107i	$0.358720\pi$
$458$		−	1.53498e50i		−	0.426243i
$459$	4.91937e49	+	2.57757e50i	0.131059	+	0.686704i
$460$	−5.06638e50			−1.29509
$461$			2.23978e50i			0.549399i	0.961530	+	0.274700i	$0.0885784\pi$
$461$			2.23978e50i			0.549399i	−0.961530	+	0.274700i	$0.911422\pi$
$462$	−2.58703e50	+	1.62839e49i	−0.608980	+	0.0383320i
$463$	−3.71785e50			−0.839948			−0.419974	−	0.907536i	$-0.637961\pi$
$463$	−3.71785e50			−0.839948			−0.419974	+	0.907536i	$0.637961\pi$
$464$			4.28843e50i			0.929943i
$465$	−2.60107e49	−	4.13232e50i	−0.0541434	−	0.860177i
$466$	6.68997e49			0.133688
$467$		−	3.00718e50i		−	0.576950i	−0.957487	−	0.288475i	$-0.906852\pi$
$467$		−	3.00718e50i		−	0.576950i	0.957487	−	0.288475i	$-0.0931482\pi$
$468$	−1.07131e51	+	1.35403e50i	−1.97353	+	0.249435i
$469$	−2.92815e50			−0.517975
$470$		−	2.03736e49i		−	0.0346105i
$471$	−7.27924e49	+	4.58189e48i	−0.118765	+	0.00747562i
$472$	3.01619e50			0.472673
$473$			2.59430e50i			0.390533i
$474$	−9.66636e48	−	1.53569e50i	−0.0139789	−	0.222083i
$475$	5.53403e50			0.768888
$476$		−	6.13033e50i		−	0.818374i
$477$	−1.05410e49	−	8.34008e49i	−0.0135218	−	0.106985i
$478$	7.99662e50			0.985772
$479$			1.86336e49i			0.0220760i	0.999939	+	0.0110380i	$0.00351358\pi$
$479$			1.86336e49i			0.0220760i	−0.999939	+	0.0110380i	$0.996486\pi$
$480$	1.99279e51	−	1.25435e50i	2.26922	−	0.142835i
$481$	−1.00161e51			−1.09633
$482$		−	1.16005e51i		−	1.22062i
$483$	−3.80639e49	−	6.04722e50i	−0.0385051	−	0.611730i
$484$	−1.03651e51			−1.00812
$485$			8.64947e50i			0.808903i
$486$	5.14382e50	+	1.58230e51i	0.462590	+	1.42298i
$487$	1.36286e51			1.17869			0.589347	−	0.807880i	$-0.299385\pi$
$487$	1.36286e51			1.17869			0.589347	+	0.807880i	$0.299385\pi$
$488$			1.16671e50i			0.0970478i
$489$	−1.83642e51	+	1.15593e50i	−1.46928	+	0.0924832i
$490$	3.35765e50			0.258410
$491$		−	2.61038e50i		−	0.193266i	−0.995320	−	0.0966330i	$-0.969193\pi$
$491$		−	2.61038e50i		−	0.193266i	0.995320	−	0.0966330i	$-0.0308073\pi$
$492$	1.80920e50	+	2.87428e51i	0.128869	+	2.04735i
$493$	1.34733e51			0.923388
$494$		−	1.75403e51i		−	1.15671i
$495$	−1.08732e51	+	1.37426e50i	−0.690014	+	0.0872108i
$496$	6.16555e50			0.376547
$497$			7.28114e50i			0.427985i
$498$	3.23590e51	−	2.03683e50i	1.83079	−	0.115238i
$499$	−1.22608e51			−0.667740			−0.333870	−	0.942619i	$-0.608355\pi$
$499$	−1.22608e51			−0.667740			−0.333870	+	0.942619i	$0.608355\pi$
$500$			2.27344e51i			1.19194i
$501$	−2.02100e50	−	3.21077e51i	−0.102012	−	1.62066i
$502$	−3.94045e51			−1.91503
$503$		−	4.03344e51i		−	1.88749i	−0.330680	−	0.943743i	$-0.607278\pi$
$503$		−	4.03344e51i		−	1.88749i	0.330680	−	0.943743i	$-0.392722\pi$
$504$	−9.39775e49	−	7.43553e50i	−0.0423491	−	0.335067i
$505$	−4.88057e51			−2.11804
$506$			1.00224e51i			0.418900i
$507$	3.91250e51	−	2.46271e50i	1.57508	−	0.0991429i
$508$	−2.05175e51			−0.795636
$509$			2.06249e51i			0.770467i	0.922819	+	0.385234i	$0.125879\pi$
$509$			2.06249e51i			0.770467i	−0.922819	+	0.385234i	$0.874121\pi$
$510$	−2.94255e50	−	4.67483e51i	−0.105899	−	1.68241i
$511$	4.78303e51			1.65846
$512$			3.72653e51i			1.24502i
$513$	−1.46897e51	+	2.80357e50i	−0.472916	+	0.0902573i
$514$	−3.59475e51			−1.11524
$515$			3.20215e51i			0.957425i
$516$	−3.88249e51	+	2.44381e50i	−1.11883	+	0.0704245i
$517$	−2.23017e49			−0.00619465
$518$		−	3.60537e51i		−	0.965349i
$519$	3.09113e50	+	4.91088e51i	0.0797881	+	1.26759i
$520$	3.71661e51			0.924876
$521$			4.54680e51i			1.09091i	0.838140	+	0.545455i	$0.183643\pi$
$521$			4.54680e51i			1.09091i	−0.838140	+	0.545455i	$0.816357\pi$
$522$	8.47537e51	−	1.07120e51i	1.96074	−	0.247817i
$523$	7.86068e51			1.75359			0.876795	−	0.480865i	$-0.159677\pi$
$523$	7.86068e51			1.75359			0.876795	+	0.480865i	$0.159677\pi$
$524$		−	3.88147e51i		−	0.835028i
$525$	−7.25878e51	+	4.56901e50i	−1.50604	+	0.0947972i
$526$	−2.44087e51			−0.488444
$527$		−	1.93709e51i		−	0.373893i
$528$	−1.02522e50	−	1.62877e51i	−0.0190885	−	0.303259i
$529$	3.22473e51			0.579209
$530$			1.50057e51i			0.260025i
$531$	9.91838e50	+	7.84744e51i	0.165823	+	1.31200i
$532$	3.49371e51			0.563593
$533$		−	1.70804e52i		−	2.65877i
$534$	−6.83603e51	+	4.30291e50i	−1.02688	+	0.0646366i
$535$	1.81489e52			2.63105
$536$			1.40037e51i			0.195934i
$537$	2.07848e50	+	3.30207e51i	0.0280694	+	0.445939i
$538$	−1.69965e52			−2.21563
$539$		−	3.67540e50i		−	0.0462507i
$540$	−3.08089e51	−	1.61428e52i	−0.374279	−	1.96109i
$541$	−1.20983e52			−1.41898			−0.709488	−	0.704717i	$-0.751074\pi$
$541$	−1.20983e52			−1.41898			−0.709488	+	0.704717i	$0.751074\pi$
$542$			9.12869e51i			1.03377i
$543$	−2.55657e51	+	1.60922e50i	−0.279551	+	0.0175962i
$544$	9.34149e51			0.986364
$545$		−	3.48554e51i		−	0.355415i
$546$	1.44817e51	+	2.30070e52i	0.142613	+	2.26569i
$547$	−1.38323e52			−1.31563			−0.657817	−	0.753178i	$-0.728520\pi$
$547$	−1.38323e52			−1.31563			−0.657817	+	0.753178i	$0.728520\pi$
$548$			8.90990e51i			0.818545i
$549$	−3.03551e51	+	3.83658e50i	−0.269375	+	0.0340462i
$550$	1.20303e52			1.03130
$551$			7.67853e51i			0.635913i
$552$	−2.89204e51	+	1.82038e50i	−0.231399	+	0.0145653i
$553$	−1.81770e51			−0.140522
$554$		−	4.07606e51i		−	0.304477i
$555$	−9.57609e50	−	1.52135e52i	−0.0691228	−	1.09815i
$556$	−6.03377e51			−0.420889
$557$			5.55345e50i			0.0374382i	0.999825	+	0.0187191i	$0.00595882\pi$
$557$			5.55345e50i			0.0374382i	−0.999825	+	0.0187191i	$0.994041\pi$
$558$	−1.54008e51	−	1.21852e52i	−0.100345	−	0.793930i
$559$	2.30717e52			1.45296
$560$		−	1.76119e52i		−	1.07210i
$561$	−5.11724e51	+	3.22103e50i	−0.301121	+	0.0189540i
$562$	−2.38382e51			−0.135607
$563$		−	2.22042e52i		−	1.22117i	−0.791950	−	0.610585i	$-0.790934\pi$
$563$		−	2.22042e52i		−	1.22117i	0.791950	−	0.610585i	$-0.209066\pi$
$564$	−2.10081e49	−	3.33755e50i	−0.00111708	−	0.0177470i
$565$	−2.12922e52			−1.09471
$566$			3.78461e52i			1.88152i
$567$	1.90365e52	−	4.89016e51i	0.915185	−	0.235096i
$568$	3.48216e51			0.161894
$569$			3.40546e52i			1.53124i	0.643295	+	0.765618i	$0.277567\pi$
$569$			3.40546e52i			1.53124i	−0.643295	+	0.765618i	$0.722433\pi$
$570$	2.66421e52	−	1.67698e51i	1.15863	−	0.0729298i
$571$	1.11181e52			0.467676			0.233838	−	0.972276i	$-0.424871\pi$
$571$	1.11181e52			0.467676			0.233838	+	0.972276i	$0.424871\pi$
$572$		−	2.10995e52i		−	0.858514i
$573$	−1.24625e51	−	1.97992e52i	−0.0490533	−	0.779310i
$574$	6.14821e52			2.34111
$575$			2.81211e52i			1.03596i
$576$	3.91650e52	−	4.95006e51i	1.39595	−	0.176434i
$577$	−4.20380e52			−1.44978			−0.724889	−	0.688866i	$-0.758109\pi$
$577$	−4.20380e52			−1.44978			−0.724889	+	0.688866i	$0.758109\pi$
$578$			2.29238e52i			0.764992i
$579$	−2.73995e52	+	1.72465e51i	−0.884811	+	0.0556941i
$580$	−8.43806e52			−2.63700
$581$		−	3.83013e52i		−	1.15842i
$582$	1.61180e51	+	2.56066e52i	0.0471817	+	0.749575i
$583$	1.64258e51			0.0465398
$584$		−	2.28745e52i		−	0.627347i
$585$	1.22216e52	+	9.66977e52i	0.324464	+	2.56717i
$586$	−6.78925e52			−1.74489
$587$			2.39246e52i			0.595280i	0.954678	+	0.297640i	$0.0961996\pi$
$587$			2.39246e52i			0.595280i	−0.954678	+	0.297640i	$0.903800\pi$
$588$	5.50041e51	−	3.46221e50i	0.132503	−	0.00834035i
$589$	1.10396e52			0.257490
$590$		−	1.41193e53i		−	3.18879i
$591$	−3.88074e51	−	6.16534e52i	−0.0848697	−	1.34832i
$592$	2.26990e52			0.480723
$593$		−	3.91007e52i		−	0.801946i	−0.916090	−	0.400973i	$-0.868672\pi$
$593$		−	3.91007e52i		−	0.801946i	0.916090	−	0.400973i	$-0.131328\pi$
$594$	−3.19338e52	+	6.09465e51i	−0.634319	+	0.121062i
$595$	−5.53330e52			−1.06454
$596$			6.30212e51i			0.117438i
$597$	3.28069e52	−	2.06502e51i	0.592179	−	0.0372744i
$598$	8.91311e52			1.55850
$599$			2.82304e52i			0.478197i	0.970995	+	0.239099i	$0.0768519\pi$
$599$			2.82304e52i			0.478197i	−0.970995	+	0.239099i	$0.923148\pi$
$600$	2.18510e51	+	3.47147e52i	0.0358589	+	0.569691i
$601$	5.62593e52			0.894497			0.447249	−	0.894410i	$-0.352404\pi$
$601$	5.62593e52			0.894497			0.447249	+	0.894410i	$0.352404\pi$
$602$			8.30482e52i			1.27937i
$603$	−3.64343e52	+	4.60493e51i	−0.543853	+	0.0687376i
$604$	8.79240e52			1.27176
$605$			9.35566e52i			1.31136i
$606$	−1.44488e53	+	9.09476e51i	−1.96270	+	0.123541i
$607$	−1.00427e53			−1.32210			−0.661051	−	0.750341i	$-0.729889\pi$
$607$	−1.00427e53			−1.32210			−0.661051	+	0.750341i	$0.729889\pi$
$608$			5.32376e52i			0.679283i
$609$	−6.33956e51	−	1.00716e53i	−0.0784026	−	1.24558i
$610$	5.46157e52			0.654713
$611$			1.98334e51i			0.0230470i
$612$	−9.64083e51	−	7.62785e52i	−0.108602	−	0.859261i
$613$	9.17938e52			1.00245			0.501227	−	0.865316i	$-0.332882\pi$
$613$	9.17938e52			1.00245			0.501227	+	0.865316i	$0.332882\pi$
$614$			1.41430e52i			0.149742i
$615$	2.59435e53	−	1.63300e52i	2.66318	−	0.167633i
$616$	1.46443e52			0.145759
$617$		−	1.23754e53i		−	1.19438i	−0.802101	−	0.597189i	$-0.796284\pi$
$617$		−	1.23754e53i		−	1.19438i	0.802101	−	0.597189i	$-0.203716\pi$
$618$	5.96709e51	+	9.47992e52i	0.0558447	+	0.887204i
$619$	1.86035e52			0.168839			0.0844195	−	0.996430i	$-0.473096\pi$
$619$	1.86035e52			0.168839			0.0844195	+	0.996430i	$0.473096\pi$
$620$			1.21315e53i			1.06776i
$621$	−1.42463e52	−	7.46457e52i	−0.121608	−	0.637183i
$622$	−3.99560e52			−0.330799
$623$			8.09137e52i			0.649754i
$624$	−1.44850e53	+	9.11751e51i	−1.12826	+	0.0710181i
$625$	−6.16050e51			−0.0465474
$626$		−	3.07143e53i		−	2.25128i
$627$	−1.83568e51	−	2.91634e52i	−0.0130531	−	0.207375i
$628$	2.13702e52			0.147426
$629$		−	7.13157e52i		−	0.477335i
$630$	−3.48070e53	+	4.39926e52i	−2.26046	+	0.285699i
$631$	7.67791e52			0.483822			0.241911	−	0.970298i	$-0.422226\pi$
$631$	7.67791e52			0.483822			0.241911	+	0.970298i	$0.422226\pi$
$632$			8.69304e51i			0.0531554i
$633$	−8.28586e52	+	5.21550e51i	−0.491663	+	0.0309475i
$634$	−9.17796e52			−0.528507
$635$			1.85193e53i			1.03496i
$636$	1.54730e51	+	2.45820e52i	0.00839247	+	0.133331i
$637$	−3.26862e52			−0.172074
$638$			1.66922e53i			0.852947i
$639$	1.14506e52	+	9.05978e52i	0.0567955	+	0.449367i
$640$	−2.32436e53			−1.11914
$641$			8.05357e52i			0.376431i	0.982128	+	0.188216i	$0.0602704\pi$
$641$			8.05357e52i			0.376431i	−0.982128	+	0.188216i	$0.939730\pi$
$642$	5.37296e53	−	3.38199e52i	2.43808	−	0.153464i
$643$	−4.12888e52			−0.181896			−0.0909481	−	0.995856i	$-0.528990\pi$
$643$	−4.12888e52			−0.181896			−0.0909481	+	0.995856i	$0.528990\pi$
$644$			1.77533e53i			0.759358i
$645$	2.20581e52	+	3.50437e53i	0.0916080	+	1.45538i
$646$	1.24889e53			0.503624
$647$		−	4.04774e53i		−	1.58501i	−0.609867	−	0.792504i	$-0.708777\pi$
$647$		−	4.04774e53i		−	1.58501i	0.609867	−	0.792504i	$-0.291223\pi$
$648$	−2.33869e52	−	9.10408e52i	−0.0889297	−	0.346187i
$649$	−1.54556e53			−0.570736
$650$		−	1.06989e54i		−	3.83693i
$651$	−1.44802e53	+	9.11449e51i	−0.504354	+	0.0317463i
$652$	5.39133e53			1.82386
$653$			4.23994e53i			1.39319i	0.717466	+	0.696593i	$0.245302\pi$
$653$			4.23994e53i			1.39319i	−0.717466	+	0.696593i	$0.754698\pi$
$654$	−6.49517e51	−	1.03189e53i	−0.0207307	−	0.329348i
$655$	−3.50345e53			−1.08620
$656$			3.87085e53i			1.16582i
$657$	5.95142e53	−	7.52200e52i	1.74132	−	0.220085i
$658$	−7.13917e51			−0.0202934
$659$		−	5.50402e53i		−	1.52005i	−0.649895	−	0.760024i	$-0.725187\pi$
$659$		−	5.50402e53i		−	1.52005i	0.649895	−	0.760024i	$-0.274813\pi$
$660$	3.20482e53	−	2.01726e52i	0.859940	−	0.0541286i
$661$	−2.36596e53			−0.616850			−0.308425	−	0.951249i	$-0.599802\pi$
$661$	−2.36596e53			−0.616850			−0.308425	+	0.951249i	$0.599802\pi$
$662$			6.34776e53i			1.60812i
$663$	2.86453e52	+	4.55088e53i	0.0705175	+	1.12031i
$664$	−1.83174e53			−0.438197
$665$		−	3.15346e53i		−	0.733121i
$666$	−5.66997e52	−	4.48609e53i	−0.128106	−	1.01358i
$667$	−3.90184e53			−0.856798
$668$			9.42608e53i			2.01177i
$669$	2.76543e53	−	1.74069e52i	0.573675	−	0.0361098i
$670$	6.55537e53			1.32183
$671$		−	5.97844e52i		−	0.117182i
$672$	−4.39541e52	−	6.98299e53i	−0.0837497	−	1.33053i
$673$	1.52102e53			0.281740			0.140870	−	0.990028i	$-0.455010\pi$
$673$	1.52102e53			0.281740			0.140870	+	0.990028i	$0.455010\pi$
$674$			5.80598e53i			1.04553i
$675$	−8.96011e53	+	1.71006e53i	−1.56871	+	0.299392i
$676$	−1.14862e54			−1.95519
$677$			4.27880e53i			0.708169i	0.935213	+	0.354084i	$0.115207\pi$
$677$			4.27880e53i			0.708169i	−0.935213	+	0.354084i	$0.884793\pi$
$678$	−6.30350e53	+	3.96771e52i	−1.01442	+	0.0638522i
$679$	3.03089e53			0.474290
$680$			2.64626e53i			0.402684i
$681$	−5.49892e52	−	8.73613e53i	−0.0813734	−	1.29278i
$682$	2.39987e53			0.345370
$683$		−	6.97682e53i		−	0.976482i	−0.872709	−	0.488241i	$-0.837639\pi$
$683$		−	6.97682e53i		−	0.976482i	0.872709	−	0.488241i	$-0.162361\pi$
$684$	4.34715e53	−	5.49436e52i	0.591751	−	0.0747913i
$685$	8.04217e53			1.06476
$686$		−	1.21555e54i		−	1.56536i
$687$	−2.26966e53	+	1.42863e52i	−0.284305	+	0.0178954i
$688$	−5.22863e53			−0.637100
$689$		−	1.46078e53i		−	0.173149i
$690$	8.52154e52	+	1.35382e54i	0.0982620	+	1.56109i
$691$	−1.52764e54			−1.71372			−0.856859	−	0.515552i	$-0.827587\pi$
$691$	−1.52764e54			−1.71372			−0.856859	+	0.515552i	$0.827587\pi$
$692$		−	1.44172e54i		−	1.57350i
$693$	4.81559e52	+	3.81011e53i	0.0511350	+	0.404581i
$694$	1.10501e54			1.14165
$695$			5.44614e53i			0.547492i
$696$	−4.81670e53	+	3.03185e52i	−0.471166	+	0.0296574i
$697$	1.21614e54			1.15761
$698$			7.95719e53i			0.737067i
$699$	−6.22648e51	−	9.89201e52i	−0.00561276	−	0.0891699i
$700$	2.13101e54			1.86949
$701$		−	8.65568e53i		−	0.739024i	−0.929226	−	0.369512i	$-0.879525\pi$
$701$		−	8.65568e53i		−	0.739024i	0.929226	−	0.369512i	$-0.120475\pi$
$702$	5.42011e53	+	2.83994e54i	0.450405	+	2.35996i
$703$	4.06432e53			0.328728
$704$			7.71355e53i			0.607259i
$705$	−3.01250e52	+	1.89621e51i	−0.0230852	+	0.00145309i
$706$	−1.19646e54			−0.892504
$707$			1.71022e54i			1.24189i
$708$	−1.45591e53	−	2.31300e54i	−0.102920	−	1.63509i
$709$	1.69444e54			1.16613			0.583066	−	0.812425i	$-0.301853\pi$
$709$	1.69444e54			1.16613			0.583066	+	0.812425i	$0.301853\pi$
$710$		−	1.63006e54i		−	1.09218i
$711$	−2.26173e53	+	2.85860e52i	−0.147543	+	0.0186479i
$712$	3.86964e53			0.245783
$713$			5.60974e53i			0.346930i
$714$	−1.63812e54	+	1.03111e53i	−0.986462	+	0.0620925i
$715$	−1.90446e54			−1.11675
$716$		−	9.69414e53i		−	0.553556i
$717$	−7.44261e52	−	1.18241e54i	−0.0413867	−	0.657511i
$718$	−1.56996e54			−0.850205
$719$		−	4.81902e53i		−	0.254162i	−0.991892	−	0.127081i	$-0.959439\pi$
$719$		−	4.81902e53i		−	0.254162i	0.991892	−	0.127081i	$-0.0405608\pi$
$720$	−2.76973e53	−	2.19142e54i	−0.142272	−	1.12566i
$721$	1.12208e54			0.561374
$722$		−	2.35884e54i		−	1.14945i
$723$	−1.71528e54	+	1.07968e53i	−0.814157	+	0.0512468i
$724$	7.50552e53			0.347015
$725$			4.68358e54i			2.10938i
$726$	1.74339e53	+	2.76973e54i	0.0764891	+	1.21518i
$727$	3.91570e54			1.67361			0.836807	−	0.547498i	$-0.184420\pi$
$727$	3.91570e54			1.67361			0.836807	+	0.547498i	$0.184420\pi$
$728$		−	1.30235e54i		−	0.542289i
$729$	2.29177e54	−	9.07849e53i	0.929711	−	0.368291i
$730$	−1.07080e55			−4.23227
$731$			1.64273e54i			0.632609i
$732$	8.94701e53	−	5.63166e52i	0.335712	−	0.0211313i
$733$	3.14878e54			1.15124			0.575621	−	0.817716i	$-0.304760\pi$
$733$	3.14878e54			1.15124			0.575621	+	0.817716i	$0.304760\pi$
$734$			1.09158e54i			0.388893i
$735$	−3.12502e52	−	4.96472e53i	−0.0108491	−	0.172360i
$736$	−2.70527e54			−0.915233
$737$		−	7.17575e53i		−	0.236584i
$738$	7.65009e54	−	9.66894e53i	2.45808	−	0.310676i
$739$	−5.09600e54			−1.59582			−0.797912	−	0.602774i	$-0.794062\pi$
$739$	−5.09600e54			−1.59582			−0.797912	+	0.602774i	$0.794062\pi$
$740$			4.46634e54i			1.36317i
$741$	−2.59357e54	+	1.63251e53i	−0.771529	+	0.0485635i
$742$	5.25820e53			0.152462
$743$		−	3.04691e54i		−	0.861137i	−0.902558	−	0.430569i	$-0.858313\pi$
$743$		−	3.04691e54i		−	0.861137i	0.902558	−	0.430569i	$-0.141687\pi$
$744$	4.35895e52	+	6.92505e53i	0.0120087	+	0.190782i
$745$	5.68836e53			0.152763
$746$			7.09419e54i			1.85723i
$747$	−6.02343e53	−	4.76576e54i	−0.153728	−	1.21630i
$748$	1.50231e54			0.373790
$749$		−	6.35962e54i		−	1.54268i
$750$	6.07501e54	−	3.82389e53i	1.43676	−	0.0904359i
$751$	2.68533e54			0.619211			0.309606	−	0.950865i	$-0.399803\pi$
$751$	2.68533e54			0.619211			0.309606	+	0.950865i	$0.399803\pi$
$752$		−	4.49475e52i		−	0.0101057i
$753$	3.66745e53	+	5.82647e54i	0.0804006	+	1.27732i
$754$	1.48448e55			3.17335
$755$		−	7.93610e54i		−	1.65430i
$756$	−5.65664e54	+	1.07959e54i	−1.14986	+	0.219454i
$757$	−2.41058e54			−0.477858			−0.238929	−	0.971037i	$-0.576796\pi$
$757$	−2.41058e54			−0.477858			−0.238929	+	0.971037i	$0.576796\pi$
$758$		−	1.36559e55i		−	2.64000i
$759$	1.48194e54	−	9.32799e52i	0.279406	−	0.0175871i
$760$	−1.50812e54			−0.277318
$761$			5.21893e54i			0.935994i	0.883730	+	0.467997i	$0.155024\pi$
$761$			5.21893e54i			0.935994i	−0.883730	+	0.467997i	$0.844976\pi$
$762$	3.45101e53	+	5.48261e54i	0.0603672	+	0.959054i
$763$	−1.22138e54			−0.208393
$764$			5.81260e54i			0.967379i
$765$	−6.88497e54	+	8.70191e53i	−1.11773	+	0.141269i
$766$	−1.75883e55			−2.78533
$767$			1.37450e55i			2.12340i
$768$	2.43665e54	−	1.53374e53i	0.367223	−	0.0231147i
$769$	−9.27367e54			−1.36349			−0.681744	−	0.731591i	$-0.738778\pi$
$769$	−9.27367e54			−1.36349			−0.681744	+	0.731591i	$0.738778\pi$
$770$		−	6.85525e54i		−	0.983331i
$771$	3.34570e53	+	5.31531e54i	0.0468224	+	0.743868i
$772$	8.04388e54			1.09834
$773$		−	1.03769e55i		−	1.38248i	−0.722626	−	0.691239i	$-0.757065\pi$
$773$		−	1.03769e55i		−	1.38248i	0.722626	−	0.691239i	$-0.242935\pi$
$774$	1.30605e54	+	1.03335e55i	0.169778	+	1.34329i
$775$	6.73366e54			0.854120
$776$		−	1.44950e54i		−	0.179410i
$777$	−5.33102e54	+	3.35559e53i	−0.643889	+	0.0405293i
$778$	4.77896e54			0.563276
$779$			6.93085e54i			0.797214i
$780$	−1.79399e54	−	2.85012e55i	−0.201383	−	3.19937i
$781$	−1.78432e54			−0.195481
$782$			6.34622e54i			0.678558i
$783$	−2.37273e54	−	1.24323e55i	−0.247614	−	1.29741i
$784$	7.40752e53			0.0754515
$785$		−	1.92890e54i		−	0.191772i
$786$	−1.03719e55	+	6.52855e53i	−1.00654	+	0.0633561i
$787$	1.45876e55			1.38186			0.690929	−	0.722922i	$-0.257202\pi$
$787$	1.45876e55			1.38186			0.690929	+	0.722922i	$0.257202\pi$
$788$			1.81000e55i			1.67371i
$789$	2.27176e53	+	3.60915e54i	0.0205069	+	0.325793i
$790$	4.06937e54			0.358602
$791$			7.46105e54i			0.641870i
$792$	1.82216e54	−	2.30302e53i	0.153041	−	0.0193428i
$793$	−5.31676e54			−0.435970
$794$		−	2.34033e55i		−	1.87365i
$795$	2.21879e54	−	1.39661e53i	0.173437	−	0.0109169i
$796$	−9.63136e54			−0.735088
$797$		−	1.87556e55i		−	1.39773i	−0.715253	−	0.698866i	$-0.753689\pi$
$797$		−	1.87556e55i		−	1.39773i	0.715253	−	0.698866i	$-0.246311\pi$
$798$	−5.87635e53	−	9.33575e54i	−0.0427615	−	0.679351i
$799$	−1.41216e53			−0.0100345
$800$			3.24727e55i			2.25325i
$801$	1.27248e54	+	1.00679e55i	0.0862253	+	0.682217i
$802$	3.99558e55			2.64403
$803$			1.17213e55i			0.757499i
$804$	1.07388e55	−	6.75952e53i	0.677786	−	0.0426629i
$805$	1.60243e55			0.987771
$806$		−	2.13426e55i		−	1.28494i
$807$	1.58190e54	+	2.51316e55i	0.0930212	+	1.47783i
$808$	8.17899e54			0.469769
$809$			1.55621e55i			0.873066i	0.899688	+	0.436533i	$0.143794\pi$
$809$			1.55621e55i			0.873066i	−0.899688	+	0.436533i	$0.856206\pi$
$810$	−4.26179e55	+	1.09478e55i	−2.33548	+	0.599946i
$811$	−3.06479e55			−1.64061			−0.820304	−	0.571928i	$-0.806196\pi$
$811$	−3.06479e55			−1.64061			−0.820304	+	0.571928i	$0.806196\pi$
$812$			2.95681e55i			1.54617i
$813$	1.34980e55	−	8.49625e53i	0.689522	−	0.0434017i
$814$	8.83536e54			0.440921
$815$		−	4.86626e55i		−	2.37247i
$816$	−6.49176e53	−	1.03135e55i	−0.0309207	−	0.491237i
$817$	−9.36198e54			−0.435661
$818$		−	3.88716e55i		−	1.76734i
$819$	3.38841e55	−	4.28261e54i	1.50523	−	0.190246i
$820$	−7.61642e55			−3.30588
$821$		−	1.63860e55i		−	0.694951i	−0.937689	−	0.347475i	$-0.887039\pi$
$821$		−	1.63860e55i		−	0.694951i	0.937689	−	0.347475i	$-0.112961\pi$
$822$	2.38087e55	−	1.49863e54i	0.986668	−	0.0621054i
$823$	−5.01161e54			−0.202946			−0.101473	−	0.994838i	$-0.532356\pi$
$823$	−5.01161e54			−0.202946			−0.101473	+	0.994838i	$0.532356\pi$
$824$		−	5.36626e54i		−	0.212351i
$825$	−1.11969e54	−	1.77885e55i	−0.0432984	−	0.687881i
$826$	−4.94761e55			−1.86971
$827$		−	1.88297e55i		−	0.695407i	−0.937605	−	0.347704i	$-0.886962\pi$
$827$		−	1.88297e55i		−	0.695407i	0.937605	−	0.347704i	$-0.113038\pi$
$828$	2.79196e54	+	2.20900e55i	0.100770	+	0.797296i
$829$	−2.14483e55			−0.756585			−0.378292	−	0.925686i	$-0.623489\pi$
$829$	−2.14483e55			−0.756585			−0.378292	+	0.925686i	$0.623489\pi$
$830$			8.57468e55i			2.95620i
$831$	−6.02699e54	+	3.79366e53i	−0.203086	+	0.0127832i
$832$	6.85984e55			2.25928
$833$		−	2.32729e54i		−	0.0749196i
$834$	1.01487e54	+	1.61232e55i	0.0319341	+	0.507337i
$835$	8.50808e55			2.61691
$836$			8.56172e54i			0.257420i
$837$	−1.78741e55	+	3.41132e54i	−0.525339	+	0.100262i
$838$	−9.09453e55			−2.61303
$839$		−	2.48552e54i		−	0.0698136i	−0.999391	−	0.0349068i	$-0.988887\pi$
$839$		−	2.48552e54i		−	0.0698136i	0.999391	−	0.0349068i	$-0.0111134\pi$
$840$	1.97815e55	−	1.24514e54i	0.543190	−	0.0341909i
$841$	−2.77354e55			−0.744579
$842$		−	9.71640e55i		−	2.55021i
$843$	2.21867e53	+	3.52479e54i	0.00569335	+	0.0904502i
$844$	2.43254e55			0.610314
$845$			1.03676e56i			2.54331i
$846$	−8.88313e53	+	1.12274e53i	−0.0213073	+	0.00269303i
$847$	3.27835e55			0.768901
$848$			3.31051e54i			0.0759230i
$849$	5.59604e55	−	3.52240e54i	1.25497	−	0.0789938i
$850$	7.61770e55			1.67057
$851$			2.06528e55i			0.442912i
$852$	−1.68082e54	−	2.67033e55i	−0.0352509	−	0.560031i
$853$	−1.68012e55			−0.344594			−0.172297	−	0.985045i	$-0.555119\pi$
$853$	−1.68012e55			−0.344594			−0.172297	+	0.985045i	$0.555119\pi$
$854$		−	1.91381e55i		−	0.383883i
$855$	−4.95927e54	−	3.92378e55i	−0.0972884	−	0.769748i
$856$	−3.04145e55			−0.583551
$857$			5.32727e55i			0.999699i	0.866112	+	0.499850i	$0.166611\pi$
$857$			5.32727e55i			0.999699i	−0.866112	+	0.499850i	$0.833389\pi$
$858$	−5.63812e55	+	3.54889e54i	−1.03485	+	0.0651380i
$859$	−5.11449e55			−0.918190			−0.459095	−	0.888387i	$-0.651826\pi$
$859$	−5.11449e55			−0.918190			−0.459095	+	0.888387i	$0.651826\pi$
$860$		−	1.02880e56i		−	1.80660i
$861$	−5.72225e54	−	9.09094e55i	−0.0982895	−	1.56152i
$862$	1.69595e56			2.84954
$863$			8.75182e55i			1.43845i	0.694780	+	0.719223i	$0.255502\pi$
$863$			8.75182e55i			1.43845i	−0.694780	+	0.719223i	$0.744498\pi$
$864$	−1.64509e55	−	8.61967e55i	−0.264501	−	1.38589i
$865$	−1.30131e56			−2.04680
$866$			2.03448e54i			0.0313050i
$867$	3.38958e55	−	2.13356e54i	0.510251	−	0.0321175i
$868$	4.25105e55			0.626068
$869$		−	4.45448e54i		−	0.0641832i
$870$	1.41926e55	+	2.25478e56i	0.200077	+	3.17863i
$871$	−6.38155e55			−0.880200
$872$			5.84116e54i			0.0788290i
$873$	3.77128e55	−	4.76651e54i	0.497987	−	0.0629405i
$874$	−3.61675e55			−0.467305
$875$		−	7.19059e55i		−	0.909100i
$876$	−1.75415e56	+	1.10414e55i	−2.17015	+	0.136599i
$877$	−6.75242e55			−0.817461			−0.408731	−	0.912655i	$-0.634028\pi$
$877$	−6.75242e55			−0.817461			−0.408731	+	0.912655i	$0.634028\pi$
$878$			1.89893e56i			2.24964i
$879$	6.31888e54	+	1.00388e56i	0.0732574	+	1.16384i
$880$	4.31600e55			0.489678
$881$		−	1.35710e56i		−	1.50685i	−0.657533	−	0.753426i	$-0.728400\pi$
$881$		−	1.35710e56i		−	1.50685i	0.657533	−	0.753426i	$-0.271600\pi$
$882$	−1.85032e54	−	1.46397e55i	−0.0201068	−	0.159085i
$883$	1.63496e56			1.73881			0.869407	−	0.494096i	$-0.164501\pi$
$883$	1.63496e56			1.73881			0.869407	+	0.494096i	$0.164501\pi$
$884$		−	1.33604e56i		−	1.39067i
$885$	−2.08773e56	+	1.31411e55i	−2.12693	+	0.133879i
$886$	6.76472e55			0.674543
$887$		−	5.14800e55i		−	0.502446i	−0.967929	−	0.251223i	$-0.919167\pi$
$887$		−	5.14800e55i		−	0.502446i	0.967929	−	0.251223i	$-0.0808328\pi$
$888$	1.60479e54	+	2.54952e55i	0.0153310	+	0.243564i
$889$	6.48941e55			0.606837
$890$		−	1.81145e56i		−	1.65812i
$891$	1.19839e55	+	4.66511e55i	0.107379	+	0.418009i
$892$	−8.11867e55			−0.712119
$893$		−	8.04796e53i		−	0.00691048i
$894$	1.68403e55	−	1.06000e54i	0.141559	−	0.00891035i
$895$	−8.75002e55			−0.720065
$896$			8.14487e55i			0.656193i
$897$	−8.29560e54	−	1.31792e56i	−0.0654321	−	1.03952i
$898$	2.83934e56			2.19264
$899$			9.34304e55i			0.706405i
$900$	2.65158e56	−	3.35133e55i	1.96289	−	0.248090i
$901$	1.04009e55			0.0753878
$902$			1.50669e56i			1.06930i
$903$	1.22798e56	−	7.72945e54i	0.853342	−	0.0537132i
$904$	3.56820e55			0.242800
$905$		−	6.77456e55i		−	0.451396i
$906$	−1.47886e55	−	2.34947e56i	−0.0964922	−	1.53297i
$907$	7.75407e55			0.495440			0.247720	−	0.968832i	$-0.420319\pi$
$907$	7.75407e55			0.495440			0.247720	+	0.968832i	$0.420319\pi$
$908$			2.56473e56i			1.60476i
$909$	2.68956e55	+	2.12799e56i	0.164804	+	1.30393i
$910$	−6.09653e56			−3.65844
$911$		−	1.76900e56i		−	1.03963i	−0.854279	−	0.519815i	$-0.826001\pi$
$911$		−	1.76900e56i		−	1.03963i	0.854279	−	0.519815i	$-0.173999\pi$
$912$	5.87769e55	−	3.69969e54i	0.338302	−	0.0212943i
$913$	9.38616e55			0.529107
$914$			2.32756e56i			1.28506i
$915$	−5.08319e54	−	8.07566e55i	−0.0274875	−	0.436694i
$916$	6.66322e55			0.352915
$917$			1.22765e56i			0.636882i
$918$	−2.02207e56	+	3.85917e55i	−1.02751	+	0.196103i
$919$	−1.34682e56			−0.670370			−0.335185	−	0.942152i	$-0.608799\pi$
$919$	−1.34682e56			−0.670370			−0.335185	+	0.942152i	$0.608799\pi$
$920$		−	7.66350e55i		−	0.373644i
$921$	2.09124e55	−	1.31632e54i	0.0998781	−	0.00628678i
$922$	−1.75708e56			−0.822059
$923$			1.58684e56i			0.727279i
$924$	−7.06874e54	−	1.12301e56i	−0.0317376	−	0.504215i
$925$	2.47906e56			1.09042
$926$		−	2.91660e56i		−	1.25680i
$927$	1.39618e56	−	1.76463e55i	0.589421	−	0.0744969i
$928$	−4.50563e56			−1.86356
$929$		−	2.18020e56i		−	0.883484i	−0.897142	−	0.441742i	$-0.854361\pi$
$929$		−	2.18020e56i		−	0.883484i	0.897142	−	0.441742i	$-0.145639\pi$
$930$	3.24174e56	−	2.04050e55i	1.28707	−	0.0810141i
$931$	1.32633e55			0.0515952
$932$			2.90407e55i			0.110689i
$933$	3.71878e54	+	5.90802e55i	0.0138883	+	0.220643i
$934$	2.35909e56			0.863283
$935$		−	1.35600e56i		−	0.486226i
$936$	−2.04813e55	−	1.62049e56i	−0.0719642	−	0.569383i
$937$	−2.73306e56			−0.941017			−0.470509	−	0.882395i	$-0.655929\pi$
$937$	−2.73306e56			−0.941017			−0.470509	+	0.882395i	$0.655929\pi$
$938$		−	2.29709e56i		−	0.775039i
$939$	−4.54152e56	+	2.85864e55i	−1.50160	+	0.0945178i
$940$	8.84403e54			0.0286564
$941$			4.80036e56i			1.52430i	0.647400	+	0.762151i	$0.275856\pi$
$941$			4.80036e56i			1.52430i	−0.647400	+	0.762151i	$0.724144\pi$
$942$	−3.59442e54	−	5.71046e55i	−0.0111857	−	0.177707i
$943$	−3.52191e56			−1.07413
$944$		−	3.11496e56i		−	0.931075i
$945$	9.74444e55	+	5.10574e56i	0.285465	+	1.49573i
$946$	−2.03519e56			−0.584350
$947$			1.20587e56i			0.339353i	0.985500	+	0.169676i	$0.0542723\pi$
$947$			1.20587e56i			0.339353i	−0.985500	+	0.169676i	$0.945728\pi$
$948$	6.66634e55	−	4.19610e54i	0.183878	−	0.0115741i
$949$	1.04241e57			2.81824
$950$			4.34137e56i			1.15048i
$951$	8.54211e54	+	1.35708e56i	0.0221889	+	0.352514i
$952$	9.27286e55			0.236108
$953$		−	1.71835e56i		−	0.428891i	−0.976736	−	0.214446i	$-0.931206\pi$
$953$		−	1.71835e56i		−	0.428891i	0.976736	−	0.214446i	$-0.0687945\pi$
$954$	6.54267e55	−	8.26928e54i	0.160080	−	0.0202325i
$955$	5.24651e56			1.25836
$956$			3.47128e56i			0.816187i
$957$	2.46817e56	−	1.55358e55i	0.568916	−	0.0358102i
$958$	−1.46178e55			−0.0330321
$959$		−	2.81808e56i		−	0.624309i
$960$	6.55848e55	+	1.04195e57i	0.142446	+	2.26304i
$961$	−3.35291e56			−0.713966
$962$		−	7.85749e56i		−	1.64043i
$963$	−1.00014e56	−	7.91315e56i	−0.204721	−	1.61976i
$964$	5.03568e56			1.01064
$965$		−	7.26049e56i		−	1.42872i
$966$	4.74395e56	−	2.98606e55i	0.915325	−	0.0576147i
$967$	−1.46743e56			−0.277623			−0.138812	−	0.990319i	$-0.544328\pi$
$967$	−1.46743e56			−0.277623			−0.138812	+	0.990319i	$0.544328\pi$
$968$		−	1.56785e56i		−	0.290852i
$969$	−1.16237e55	−	1.84665e56i	−0.0211442	−	0.335918i
$970$	−6.78539e56			−1.21035
$971$			1.46891e56i			0.256939i	0.991713	+	0.128470i	$0.0410064\pi$
$971$			1.46891e56i			0.256939i	−0.991713	+	0.128470i	$0.958994\pi$
$972$	−6.86866e56	+	2.23289e56i	−1.17818	+	0.383009i
$973$	1.90840e56			0.321015
$974$			1.06914e57i			1.76367i
$975$	−1.58197e57	+	9.95763e55i	−2.55923	+	0.161090i
$976$	1.20491e56			0.191165
$977$		−	1.36285e56i		−	0.212057i	−0.994363	−	0.106028i	$-0.966187\pi$
$977$		−	1.36285e56i		−	0.212057i	0.994363	−	0.106028i	$-0.0338134\pi$
$978$	−9.06810e55	−	1.44065e57i	−0.138381	−	2.19847i
$979$	−1.98288e56			−0.296774
$980$			1.45753e56i			0.213955i
$981$	−1.51974e56	+	1.92079e55i	−0.218805	+	0.0276547i
$982$	2.04781e56			0.289181
$983$			7.83108e56i			1.08469i	0.840157	+	0.542344i	$0.182463\pi$
$983$			7.83108e56i			1.08469i	−0.840157	+	0.542344i	$0.817537\pi$
$984$	−4.34768e56	+	2.73663e55i	−0.590678	+	0.0371800i
$985$	1.63373e57			2.17716
$986$			1.05696e57i			1.38165i
$987$	6.64456e53	+	1.05562e55i	0.000852002	+	0.0135357i
$988$	7.61413e56			0.957720
$989$		−	4.75729e56i		−	0.586989i
$990$	−1.07809e56	−	8.52985e56i	−0.130492	−	1.03246i
$991$	−1.27416e57			−1.51295			−0.756477	−	0.654021i	$-0.773081\pi$
$991$	−1.27416e57			−1.51295			−0.756477	+	0.654021i	$0.773081\pi$
$992$			6.47782e56i			0.754583i
$993$	9.38601e56	−	5.90798e55i	1.07262	−	0.0675155i
$994$	−5.71195e56			−0.640388
$995$			8.69336e56i			0.956200i
$996$	8.84172e55	+	1.40468e57i	0.0954134	+	1.51583i
$997$	−1.45879e57			−1.54449			−0.772246	−	0.635324i	$-0.780867\pi$
$997$	−1.45879e57			−1.54449			−0.772246	+	0.635324i	$0.780867\pi$
$998$		−	9.61840e56i		−	0.999131i
$999$	−6.58051e56	+	1.25591e56i	−0.670680	+	0.128001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.39.b.a.2.11	yes	12
3.2	odd	2	inner	3.39.b.a.2.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.39.b.a.2.2	✓	12	3.2	odd	2	inner
3.39.b.a.2.11	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)

\(f(q)\)	\(=\)	\(q+784486. i q^{2} +(1.15997e9 - 7.30136e7i) q^{3} -3.40540e11 q^{4} +3.07374e13i q^{5} +(5.72781e13 + 9.09976e14i) q^{6} +1.07708e16 q^{7} -5.15107e16i q^{8} +(1.34019e18 - 1.69386e17i) q^{9} +O(q^{10})\)	\(q+784486. i q^{2} +(1.15997e9 - 7.30136e7i) q^{3} -3.40540e11 q^{4} +3.07374e13i q^{5} +(5.72781e13 + 9.09976e14i) q^{6} +1.07708e16 q^{7} -5.15107e16i q^{8} +(1.34019e18 - 1.69386e17i) q^{9} -2.41131e19 q^{10} +2.63951e19i q^{11} +(-3.95014e20 + 2.48640e19i) q^{12} +2.34737e21 q^{13} +8.44954e21i q^{14} +(2.24425e21 + 3.56544e22i) q^{15} -5.31974e22 q^{16} +1.67135e23i q^{17} +(1.32881e23 + 1.05136e24i) q^{18} -9.52513e23 q^{19} -1.04673e25i q^{20} +(1.24938e25 - 7.86415e23i) q^{21} -2.07065e25 q^{22} -4.84019e25i q^{23} +(-3.76098e24 - 5.97506e25i) q^{24} -5.80992e26 q^{25} +1.84148e27i q^{26} +(1.54221e27 - 2.94335e26i) q^{27} -3.66789e27 q^{28} -8.06134e27i q^{29} +(-2.79703e28 + 1.76058e27i) q^{30} -1.15899e28 q^{31} -5.58918e28i q^{32} +(1.92720e27 + 3.06174e28i) q^{33} -1.31115e29 q^{34} +3.31067e29i q^{35} +(-4.56388e29 + 5.76828e28i) q^{36} -4.26694e29 q^{37} -7.47233e29i q^{38} +(2.72287e30 - 1.71390e29i) q^{39} +1.58331e30 q^{40} -7.27638e30i q^{41} +(6.16931e29 + 9.80118e30i) q^{42} +9.82872e30 q^{43} -8.98856e30i q^{44} +(5.20651e30 + 4.11940e31i) q^{45} +3.79706e31 q^{46} +8.44918e29i q^{47} +(-6.17072e31 + 3.88413e30i) q^{48} -1.39246e31 q^{49} -4.55780e32i q^{50} +(1.22031e31 + 1.93871e32i) q^{51} -7.99373e32 q^{52} -6.22306e31i q^{53} +(2.30901e32 + 1.20984e33i) q^{54} -8.11317e32 q^{55} -5.54811e32i q^{56} +(-1.10488e33 + 6.95464e31i) q^{57} +6.32401e33 q^{58} +5.85547e33i q^{59} +(-7.64256e32 - 1.21417e34i) q^{60} -2.26498e33 q^{61} -9.09213e33i q^{62} +(1.44349e34 - 1.82443e33i) q^{63} +2.92235e34 q^{64} +7.21522e34i q^{65} +(-2.40189e34 + 1.51186e33i) q^{66} -2.71859e34 q^{67} -5.69162e34i q^{68} +(-3.53399e33 - 5.61445e34i) q^{69} -2.59717e35 q^{70} +6.76007e34i q^{71} +(-8.72521e33 - 6.90341e34i) q^{72} +4.44073e35 q^{73} -3.34736e35i q^{74} +(-6.73931e35 + 4.24203e34i) q^{75} +3.24368e35 q^{76} +2.84296e35i q^{77} +(1.34453e35 + 2.13605e36i) q^{78} -1.68762e35 q^{79} -1.63515e36i q^{80} +(1.76742e36 - 4.54020e35i) q^{81} +5.70822e36 q^{82} -3.55603e36i q^{83} +(-4.25462e36 + 2.67805e35i) q^{84} -5.13731e36 q^{85} +7.71049e36i q^{86} +(-5.88587e35 - 9.35088e36i) q^{87} +1.35963e36 q^{88} +7.51232e36i q^{89} +(-3.23161e37 + 4.08443e36i) q^{90} +2.52831e37 q^{91} +1.64828e37i q^{92} +(-1.34439e37 + 8.46222e35i) q^{93} -6.62826e35 q^{94} -2.92778e37i q^{95} +(-4.08086e36 - 6.48325e37i) q^{96} +2.81399e37 q^{97} -1.09236e37i q^{98} +(4.47096e36 + 3.53744e37i) 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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