LMFDB - Embedded newform 3.39.b.a.2.7

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			2.7
Root			$18089.7i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.39.b.a.2.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+217076. i q^{2} +(7.82134e8 + 8.59720e8i) q^{3} +2.27756e11 q^{4} -1.16100e13i q^{5} +(-1.86625e14 + 1.69783e14i) q^{6} -8.59590e15 q^{7} +1.09110e17i q^{8} +(-1.27385e17 + 1.34483e18i) q^{9} +O(q^{10})$	\(q+217076. i q^{2} +(7.82134e8 + 8.59720e8i) q^{3} +2.27756e11 q^{4} -1.16100e13i q^{5} +(-1.86625e14 + 1.69783e14i) q^{6} -8.59590e15 q^{7} +1.09110e17i q^{8} +(-1.27385e17 + 1.34483e18i) q^{9} +2.52026e18 q^{10} +3.26530e19i q^{11} +(1.78136e20 + 1.95806e20i) q^{12} -6.39572e20 q^{13} -1.86596e21i q^{14} +(9.98136e21 - 9.08058e21i) q^{15} +3.89199e22 q^{16} +3.38515e23i q^{17} +(-2.91931e23 - 2.76523e22i) q^{18} +9.26108e23 q^{19} -2.64425e24i q^{20} +(-6.72314e24 - 7.39006e24i) q^{21} -7.08819e24 q^{22} +5.58717e25i q^{23} +(-9.38039e25 + 8.53384e25i) q^{24} +2.29005e26 q^{25} -1.38836e26i q^{26} +(-1.25581e27 + 9.42323e26i) q^{27} -1.95777e27 q^{28} +8.27744e27i q^{29} +(1.97118e27 + 2.16671e27i) q^{30} -3.97870e28 q^{31} +3.84405e28i q^{32} +(-2.80725e28 + 2.55390e28i) q^{33} -7.34836e28 q^{34} +9.97985e28i q^{35} +(-2.90127e28 + 3.06293e29i) q^{36} +2.19564e28 q^{37} +2.01036e29i q^{38} +(-5.00231e29 - 5.49853e29i) q^{39} +1.26677e30 q^{40} -8.17751e30i q^{41} +(1.60421e30 - 1.45943e30i) q^{42} +1.17242e31 q^{43} +7.43692e30i q^{44} +(1.56135e31 + 1.47894e30i) q^{45} -1.21284e31 q^{46} -8.05102e31i q^{47} +(3.04406e31 + 3.34603e31i) q^{48} -5.60454e31 q^{49} +4.97116e31i q^{50} +(-2.91028e32 + 2.64764e32i) q^{51} -1.45666e32 q^{52} +7.18608e32i q^{53} +(-2.04556e32 - 2.72607e32i) q^{54} +3.79102e32 q^{55} -9.37896e32i q^{56} +(7.24340e32 + 7.96194e32i) q^{57} -1.79683e33 q^{58} -4.73793e32i q^{59} +(2.27331e33 - 2.06816e33i) q^{60} +8.08012e33 q^{61} -8.63680e33i q^{62} +(1.09499e33 - 1.15600e34i) q^{63} +2.35373e33 q^{64} +7.42544e33i q^{65} +(-5.54391e33 - 6.09386e33i) q^{66} +1.06941e34 q^{67} +7.70989e34i q^{68} +(-4.80341e34 + 4.36992e34i) q^{69} -2.16639e34 q^{70} -1.81258e34i q^{71} +(-1.46734e35 - 1.38990e34i) q^{72} -1.52047e35 q^{73} +4.76621e33i q^{74} +(1.79113e35 + 1.96881e35i) q^{75} +2.10927e35 q^{76} -2.80682e35i q^{77} +(1.19360e35 - 1.08588e35i) q^{78} +1.40993e36 q^{79} -4.51861e35i q^{80} +(-1.79235e36 - 3.42624e35i) q^{81} +1.77514e36 q^{82} -2.75195e36i q^{83} +(-1.53123e36 - 1.68313e36i) q^{84} +3.93017e36 q^{85} +2.54504e36i q^{86} +(-7.11628e36 + 6.47406e36i) q^{87} -3.56276e36 q^{88} +1.01319e37i q^{89} +(-3.21043e35 + 3.38932e36i) q^{90} +5.49770e36 q^{91} +1.27251e37i q^{92} +(-3.11187e37 - 3.42056e37i) q^{93} +1.74768e37 q^{94} -1.07521e37i q^{95} +(-3.30480e37 + 3.00656e37i) q^{96} +8.94455e37 q^{97} -1.21661e37i q^{98} +(-4.39128e37 - 4.15951e36i) 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 $

$2$			217076.i			0.414040i	0.978337	+	0.207020i	$0.0663765\pi$
$2$			217076.i			0.414040i	−0.978337	+	0.207020i	$0.933624\pi$
$3$	7.82134e8	+	8.59720e8i	0.672941	+	0.739696i
$3$	7.82134e8	+	8.59720e8i	0.672941	+	0.739696i
$4$	2.27756e11			0.828571
$5$		−	1.16100e13i		−	0.608699i	−0.952560	−	0.304350i	$-0.901561\pi$
$5$		−	1.16100e13i		−	0.608699i	0.952560	−	0.304350i	$-0.0984391\pi$
$6$	−1.86625e14	+	1.69783e14i	−0.306263	+	0.278624i
$7$	−8.59590e15			−0.754099			−0.377050	−	0.926193i	$-0.623061\pi$
$7$	−8.59590e15			−0.754099			−0.377050	+	0.926193i	$0.623061\pi$
$8$			1.09110e17i			0.757101i
$9$	−1.27385e17	+	1.34483e18i	−0.0942999	+	0.995544i
$10$	2.52026e18			0.252026
$11$			3.26530e19i			0.533903i	0.963710	+	0.266952i	$0.0860164\pi$
$11$			3.26530e19i			0.533903i	−0.963710	+	0.266952i	$0.913984\pi$
$12$	1.78136e20	+	1.95806e20i	0.557580	+	0.612891i
$13$	−6.39572e20			−0.437488			−0.218744	−	0.975782i	$-0.570196\pi$
$13$	−6.39572e20			−0.437488			−0.218744	+	0.975782i	$0.570196\pi$
$14$		−	1.86596e21i		−	0.312227i
$15$	9.98136e21	−	9.08058e21i	0.450252	−	0.409619i
$16$	3.89199e22			0.515101
$17$			3.38515e23i			1.41595i	0.706236	+	0.707977i	$0.250392\pi$
$17$			3.38515e23i			1.41595i	−0.706236	+	0.707977i	$0.749608\pi$
$18$	−2.91931e23	−	2.76523e22i	−0.412195	−	0.0390439i
$19$	9.26108e23			0.468105			0.234053	−	0.972224i	$-0.424801\pi$
$19$	9.26108e23			0.468105			0.234053	+	0.972224i	$0.424801\pi$
$20$		−	2.64425e24i		−	0.504350i
$21$	−6.72314e24	−	7.39006e24i	−0.507464	−	0.557804i
$22$	−7.08819e24			−0.221057
$23$			5.58717e25i			0.748796i	0.927268	+	0.374398i	$0.122151\pi$
$23$			5.58717e25i			0.748796i	−0.927268	+	0.374398i	$0.877849\pi$
$24$	−9.38039e25	+	8.53384e25i	−0.560025	+	0.509485i
$25$	2.29005e26			0.629485
$26$		−	1.38836e26i		−	0.181137i
$27$	−1.25581e27	+	9.42323e26i	−0.799858	+	0.600189i
$28$	−1.95777e27			−0.624825
$29$			8.27744e27i			1.35623i	0.734955	+	0.678116i	$0.237203\pi$
$29$			8.27744e27i			1.35623i	−0.734955	+	0.678116i	$0.762797\pi$
$30$	1.97118e27	+	2.16671e27i	0.169598	+	0.186422i
$31$	−3.97870e28			−1.83598			−0.917991	−	0.396600i	$-0.870190\pi$
$31$	−3.97870e28			−1.83598			−0.917991	+	0.396600i	$0.870190\pi$
$32$			3.84405e28i			0.970373i
$33$	−2.80725e28	+	2.55390e28i	−0.394926	+	0.359285i
$34$	−7.34836e28			−0.586261
$35$			9.97985e28i			0.459019i
$36$	−2.90127e28	+	3.06293e29i	−0.0781342	+	0.824879i
$37$	2.19564e28			0.0351341			0.0175670	−	0.999846i	$-0.494408\pi$
$37$	2.19564e28			0.0351341			0.0175670	+	0.999846i	$0.494408\pi$
$38$			2.01036e29i			0.193814i
$39$	−5.00231e29	−	5.49853e29i	−0.294404	−	0.323608i
$40$	1.26677e30			0.460847
$41$		−	8.17751e30i		−	1.86092i	−0.366392	−	0.930461i	$-0.619407\pi$
$41$		−	8.17751e30i		−	1.86092i	0.366392	−	0.930461i	$-0.380593\pi$
$42$	1.60421e30	−	1.45943e30i	0.230953	−	0.210110i
$43$	1.17242e31			1.07940			0.539698	−	0.841858i	$-0.318538\pi$
$43$	1.17242e31			1.07940			0.539698	+	0.841858i	$0.318538\pi$
$44$			7.43692e30i			0.442377i
$45$	1.56135e31	+	1.47894e30i	0.605987	+	0.0574003i
$46$	−1.21284e31			−0.310031
$47$		−	8.05102e31i		−	1.36770i	−0.729622	−	0.683851i	$-0.760304\pi$
$47$		−	8.05102e31i		−	1.36770i	0.729622	−	0.683851i	$-0.239696\pi$
$48$	3.04406e31	+	3.34603e31i	0.346633	+	0.381018i
$49$	−5.60454e31			−0.431335
$50$			4.97116e31i			0.260632i
$51$	−2.91028e32	+	2.64764e32i	−1.04737	+	0.952853i
$52$	−1.45666e32			−0.362490
$53$			7.18608e32i			1.24523i	0.782527	+	0.622617i	$0.213930\pi$
$53$			7.18608e32i			1.24523i	−0.782527	+	0.622617i	$0.786070\pi$
$54$	−2.04556e32	−	2.72607e32i	−0.248502	−	0.331173i
$55$	3.79102e32			0.324986
$56$		−	9.37896e32i		−	0.570929i
$57$	7.24340e32	+	7.96194e32i	0.315007	+	0.346255i
$58$	−1.79683e33			−0.561534
$59$		−	4.73793e32i		−	0.107004i	−0.998568	−	0.0535020i	$-0.982962\pi$
$59$		−	4.73793e32i		−	0.107004i	0.998568	−	0.0535020i	$-0.0170384\pi$
$60$	2.27331e33	−	2.06816e33i	0.373066	−	0.339398i
$61$	8.08012e33			0.968615			0.484307	−	0.874898i	$-0.339072\pi$
$61$	8.08012e33			0.968615			0.484307	+	0.874898i	$0.339072\pi$
$62$		−	8.63680e33i		−	0.760170i
$63$	1.09499e33	−	1.15600e34i	0.0711115	−	0.750739i
$64$	2.35373e33			0.113328
$65$			7.42544e33i			0.266298i
$66$	−5.54391e33	−	6.09386e33i	−0.148758	−	0.163515i
$67$	1.06941e34			0.215636			0.107818	−	0.994171i	$-0.465614\pi$
$67$	1.06941e34			0.215636			0.107818	+	0.994171i	$0.465614\pi$
$68$			7.70989e34i			1.17322i
$69$	−4.80341e34	+	4.36992e34i	−0.553881	+	0.503896i
$70$	−2.16639e34			−0.190052
$71$		−	1.81258e34i		−	0.121448i	−0.998155	−	0.0607238i	$-0.980659\pi$
$71$		−	1.81258e34i		−	0.121448i	0.998155	−	0.0607238i	$-0.0193409\pi$
$72$	−1.46734e35	−	1.38990e34i	−0.753727	−	0.0713946i
$73$	−1.52047e35			−0.600959			−0.300479	−	0.953788i	$-0.597147\pi$
$73$	−1.52047e35			−0.600959			−0.300479	+	0.953788i	$0.597147\pi$
$74$			4.76621e33i			0.0145469i
$75$	1.79113e35	+	1.96881e35i	0.423607	+	0.465628i
$76$	2.10927e35			0.387858
$77$		−	2.80682e35i		−	0.402616i
$78$	1.19360e35	−	1.08588e35i	0.133987	−	0.121895i
$79$	1.40993e36			1.24246			0.621232	−	0.783627i	$-0.286633\pi$
$79$	1.40993e36			1.24246			0.621232	+	0.783627i	$0.286633\pi$
$80$		−	4.51861e35i		−	0.313542i
$81$	−1.79235e36	−	3.42624e35i	−0.982215	−	0.187759i
$82$	1.77514e36			0.770495
$83$		−	2.75195e36i		−	0.948761i	−0.880320	−	0.474380i	$-0.842672\pi$
$83$		−	2.75195e36i		−	0.948761i	0.880320	−	0.474380i	$-0.157328\pi$
$84$	−1.53123e36	−	1.68313e36i	−0.420470	−	0.462180i
$85$	3.93017e36			0.861889
$86$			2.54504e36i			0.446913i
$87$	−7.11628e36	+	6.47406e36i	−1.00320	+	0.912665i
$88$	−3.56276e36			−0.404219
$89$			1.01319e37i			0.927432i	0.885984	+	0.463716i	$0.153484\pi$
$89$			1.01319e37i			0.927432i	−0.885984	+	0.463716i	$0.846516\pi$
$90$	−3.21043e35	+	3.38932e36i	−0.0237660	+	0.250903i
$91$	5.49770e36			0.329909
$92$			1.27251e37i			0.620430i
$93$	−3.11187e37	−	3.42056e37i	−1.23551	−	1.35807i
$94$	1.74768e37			0.566283
$95$		−	1.07521e37i		−	0.284935i
$96$	−3.30480e37	+	3.00656e37i	−0.717781	+	0.653004i
$97$	8.94455e37			1.59550			0.797748	−	0.602991i	$-0.206025\pi$
$97$	8.94455e37			1.59550			0.797748	+	0.602991i	$0.206025\pi$
$98$		−	1.21661e37i		−	0.178590i
$99$	−4.39128e37	−	4.15951e36i	−0.531524	−	0.0503470i
$100$	5.21573e37			0.521573
$101$		−	1.21156e38i		−	1.00286i	−0.865199	−	0.501429i	$-0.832808\pi$
$101$		−	1.21156e38i		−	1.00286i	0.865199	−	0.501429i	$-0.167192\pi$
$102$	−5.74740e37	−	6.31753e37i	−0.394519	−	0.433655i
$103$	2.96491e38			1.69084			0.845422	−	0.534099i	$-0.179349\pi$
$103$	2.96491e38			1.69084			0.845422	+	0.534099i	$0.179349\pi$
$104$		−	6.97836e37i		−	0.331222i
$105$	−8.57987e37	+	7.80558e37i	−0.339535	+	0.308893i
$106$	−1.55993e38			−0.515576
$107$			3.96227e38i			1.09560i	0.836609	+	0.547800i	$0.184535\pi$
$107$			3.96227e38i			1.09560i	−0.836609	+	0.547800i	$0.815465\pi$
$108$	−2.86018e38	+	2.14620e38i	−0.662739	+	0.497299i
$109$	−2.13957e38			−0.416124			−0.208062	−	0.978116i	$-0.566716\pi$
$109$	−2.13957e38			−0.416124			−0.208062	+	0.978116i	$0.566716\pi$
$110$			8.22940e37i			0.134557i
$111$	1.71729e37	+	1.88764e37i	0.0236432	+	0.0259885i
$112$	−3.34552e38			−0.388437
$113$		−	6.47368e38i		−	0.634835i	−0.948286	−	0.317417i	$-0.897184\pi$
$113$		−	6.47368e38i		−	0.634835i	0.948286	−	0.317417i	$-0.102816\pi$
$114$	−1.72835e38	+	1.57237e38i	−0.143363	+	0.130426i
$115$	6.48672e38			0.455791
$116$			1.88524e39i			1.12373i
$117$	8.14721e37	−	8.60117e38i	0.0412551	−	0.435538i
$118$	1.02849e38			0.0443039
$119$		−	2.90984e39i		−	1.06777i
$120$	9.90780e38	+	1.08906e39i	0.310123	+	0.340886i
$121$	2.67421e39			0.714947
$122$			1.75400e39i			0.401045i
$123$	7.03037e39	−	6.39591e39i	1.37652	−	1.25229i
$124$	−9.06171e39			−1.52124
$125$		−	6.88245e39i		−	0.991866i
$126$	2.50941e39	+	2.37696e38i	0.310836	+	0.0294430i
$127$	−1.00465e40			−1.07088			−0.535442	−	0.844572i	$-0.679855\pi$
$127$	−1.00465e40			−1.07088			−0.535442	+	0.844572i	$0.679855\pi$
$128$			1.10774e40i			1.01730i
$129$	9.16986e39	+	1.00795e40i	0.726371	+	0.798425i
$130$	−1.61189e39			−0.110258
$131$			6.17005e39i			0.364866i	0.983218	+	0.182433i	$0.0583973\pi$
$131$			6.17005e39i			0.364866i	−0.983218	+	0.182433i	$0.941603\pi$
$132$	−6.39367e39	+	5.81667e39i	−0.327224	+	0.297694i
$133$	−7.96073e39			−0.352998
$134$			2.32143e39i			0.0892819i
$135$	1.09404e40	+	1.45800e40i	0.365335	+	0.486873i
$136$	−3.69353e40			−1.07202
$137$		−	3.72731e40i		−	0.941249i	−0.882333	−	0.470625i	$-0.844029\pi$
$137$		−	3.72731e40i		−	0.941249i	0.882333	−	0.470625i	$-0.155971\pi$
$138$	−9.48605e39	−	1.04270e40i	−0.208633	−	0.229329i
$139$	2.18885e40			0.419696			0.209848	−	0.977734i	$-0.432703\pi$
$139$	2.18885e40			0.419696			0.209848	+	0.977734i	$0.432703\pi$
$140$			2.27297e40i			0.380330i
$141$	6.92162e40	−	6.29697e40i	1.01168	−	0.920383i
$142$	3.93468e39			0.0502841
$143$		−	2.08840e40i		−	0.233576i
$144$	−4.95783e39	+	5.23408e40i	−0.0485740	+	0.512806i
$145$	9.61012e40			0.825537
$146$		−	3.30059e40i		−	0.248821i
$147$	−4.38350e40	−	4.81833e40i	−0.290263	−	0.319056i
$148$	5.00070e39			0.0291111
$149$		−	4.85956e40i		−	0.248919i	−0.992225	−	0.124459i	$-0.960280\pi$
$149$		−	4.85956e40i		−	0.248919i	0.992225	−	0.124459i	$-0.0397197\pi$
$150$	−4.27381e40	+	3.88811e40i	−0.192788	+	0.175390i
$151$	1.04870e41			0.416956			0.208478	−	0.978027i	$-0.433149\pi$
$151$	1.04870e41			0.416956			0.208478	+	0.978027i	$0.433149\pi$
$152$			1.01047e41i			0.354403i
$153$	−4.55246e41	−	4.31219e40i	−1.40964	−	0.133524i
$154$	6.09294e40			0.166699
$155$			4.61927e41i			1.11756i
$156$	−1.13931e41	−	1.25232e41i	−0.243934	−	0.268132i
$157$	−4.20278e40			−0.0796972			−0.0398486	−	0.999206i	$-0.512688\pi$
$157$	−4.20278e40			−0.0796972			−0.0398486	+	0.999206i	$0.512688\pi$
$158$			3.06063e41i			0.514429i
$159$	−6.17802e41	+	5.62048e41i	−0.921094	+	0.837969i
$160$	4.46294e41			0.590665
$161$		−	4.80268e41i		−	0.564666i
$162$	7.43754e40	−	3.89076e41i	0.0777399	−	0.406676i
$163$	8.86187e41			0.824064			0.412032	−	0.911169i	$-0.364819\pi$
$163$	8.86187e41			0.824064			0.412032	+	0.911169i	$0.364819\pi$
$164$		−	1.86248e42i		−	1.54191i
$165$	2.96509e41	+	3.25922e41i	0.218697	+	0.240391i
$166$	5.97382e41			0.392825
$167$			6.53848e41i			0.383587i	0.981435	+	0.191793i	$0.0614304\pi$
$167$			6.53848e41i			0.383587i	−0.981435	+	0.191793i	$0.938570\pi$
$168$	8.06328e41	−	7.33560e41i	0.422314	−	0.384202i
$169$	−1.72816e42			−0.808604
$170$			8.53145e41i			0.356856i
$171$	−1.17973e41	+	1.24546e42i	−0.0441423	+	0.466019i
$172$	2.67025e42			0.894357
$173$		−	3.86083e42i		−	1.15826i	−0.815237	−	0.579128i	$-0.803393\pi$
$173$		−	3.86083e42i		−	1.15826i	0.815237	−	0.579128i	$-0.196607\pi$
$174$	−1.40536e42	−	1.54477e42i	−0.377879	−	0.415364i
$175$	−1.96851e42			−0.474694
$176$			1.27085e42i			0.275014i
$177$	4.07329e41	−	3.70569e41i	0.0791504	−	0.0720074i
$178$	−2.19940e42			−0.383994
$179$			1.20565e43i			1.89240i	0.323579	+	0.946201i	$0.395114\pi$
$179$			1.20565e43i			1.89240i	−0.323579	+	0.946201i	$0.604886\pi$
$180$	3.55607e42	+	3.36838e41i	0.502103	+	0.0475602i
$181$	−9.88749e42			−1.25659			−0.628294	−	0.777976i	$-0.716247\pi$
$181$	−9.88749e42			−1.25659			−0.628294	+	0.777976i	$0.716247\pi$
$182$			1.19342e42i			0.136595i
$183$	6.31974e42	+	6.94664e42i	0.651821	+	0.716480i
$184$	−6.09615e42			−0.566914
$185$		−	2.54914e41i		−	0.0213861i
$186$	7.42523e42	−	6.75513e42i	0.562295	−	0.511550i
$187$	−1.10536e43			−0.755982
$188$		−	1.83367e43i		−	1.13324i
$189$	1.07948e43	−	8.10011e42i	0.603172	−	0.452602i
$190$	2.33403e42			0.117974
$191$		−	1.45692e43i		−	0.666502i	−0.942838	−	0.333251i	$-0.891854\pi$
$191$		−	1.45692e43i		−	0.666502i	0.942838	−	0.333251i	$-0.108146\pi$
$192$	1.84093e42	+	2.02355e42i	0.0762630	+	0.0838282i
$193$	3.23505e43			1.21421			0.607103	−	0.794623i	$-0.292331\pi$
$193$	3.23505e43			1.21421			0.607103	+	0.794623i	$0.292331\pi$
$194$			1.94165e43i			0.660599i
$195$	−6.38380e42	+	5.80769e42i	−0.196980	+	0.179203i
$196$	−1.27647e43			−0.357391
$197$		−	9.62900e42i		−	0.244750i	−0.992484	−	0.122375i	$-0.960949\pi$
$197$		−	9.62900e42i		−	0.244750i	0.992484	−	0.122375i	$-0.0390511\pi$
$198$	9.02931e41	−	9.53243e42i	0.0208457	−	0.220072i
$199$	1.10540e43			0.231904			0.115952	−	0.993255i	$-0.463008\pi$
$199$	1.10540e43			0.231904			0.115952	+	0.993255i	$0.463008\pi$
$200$			2.49867e43i			0.476584i
$201$	8.36419e42	+	9.19390e42i	0.145110	+	0.159505i
$202$	2.63001e43			0.415223
$203$		−	7.11520e43i		−	1.02273i
$204$	−6.62834e43	+	6.03016e43i	−0.867824	+	0.789507i
$205$	−9.49410e43			−1.13274
$206$			6.43610e43i			0.700077i
$207$	−7.51381e43	−	7.11724e42i	−0.745459	−	0.0706114i
$208$	−2.48921e43			−0.225350
$209$			3.02402e43i			0.249923i
$210$	−1.69440e43	−	1.86249e43i	−0.127894	−	0.140581i
$211$	2.65656e44			1.83212			0.916058	−	0.401045i	$-0.131353\pi$
$211$	2.65656e44			1.83212			0.916058	+	0.401045i	$0.131353\pi$
$212$			1.63667e44i			1.03176i
$213$	1.55831e43	−	1.41768e43i	0.0898342	−	0.0817271i
$214$	−8.60114e43			−0.453622
$215$		−	1.36118e44i		−	0.657028i
$216$	−1.02817e44	−	1.37021e44i	−0.454404	−	0.605573i
$217$	3.42005e44			1.38451
$218$		−	4.64449e43i		−	0.172292i
$219$	−1.18921e44	−	1.30718e44i	−0.404410	−	0.444527i
$220$	8.63427e43			0.269274
$221$		−	2.16505e44i		−	0.619462i
$222$	−4.09761e42	+	3.72782e42i	−0.0107603	+	0.00978922i
$223$	9.47786e43			0.228517			0.114258	−	0.993451i	$-0.463551\pi$
$223$	9.47786e43			0.228517			0.114258	+	0.993451i	$0.463551\pi$
$224$		−	3.30430e44i		−	0.731758i
$225$	−2.91719e43	+	3.07974e44i	−0.0593605	+	0.626680i
$226$	1.40528e44			0.262847
$227$			5.00665e44i			0.861105i	0.902566	+	0.430553i	$0.141681\pi$
$227$			5.00665e44i			0.861105i	−0.902566	+	0.430553i	$0.858319\pi$
$228$	1.64973e44	+	1.81338e44i	0.261006	+	0.286897i
$229$	−7.07940e44			−1.03068			−0.515338	−	0.856987i	$-0.672334\pi$
$229$	−7.07940e44			−1.03068			−0.515338	+	0.856987i	$0.672334\pi$
$230$			1.40811e44i			0.188716i
$231$	2.41308e44	−	2.19531e44i	0.297813	−	0.270937i
$232$	−9.03149e44			−1.02680
$233$			5.35452e44i			0.560994i	0.959855	+	0.280497i	$0.0904993\pi$
$233$			5.35452e44i			0.560994i	−0.959855	+	0.280497i	$0.909501\pi$
$234$	1.86711e44	+	1.76856e43i	0.180330	+	0.0170812i
$235$	−9.34724e44			−0.832519
$236$		−	1.07909e44i		−	0.0886604i
$237$	1.10276e45	+	1.21215e45i	0.836105	+	0.919045i
$238$	6.31657e44			0.442099
$239$		−	8.20152e44i		−	0.530071i	−0.964239	−	0.265036i	$-0.914616\pi$
$239$		−	8.20152e44i		−	0.530071i	0.964239	−	0.265036i	$-0.0853837\pi$
$240$	3.88474e44	−	3.53416e44i	0.231925	−	0.210995i
$241$	−1.70773e45			−0.942094			−0.471047	−	0.882108i	$-0.656124\pi$
$241$	−1.70773e45			−0.942094			−0.471047	+	0.882108i	$0.656124\pi$
$242$			5.80508e44i			0.296017i
$243$	−1.10729e45	−	1.80889e45i	−0.522088	−	0.852892i
$244$	1.84030e45			0.802566
$245$			6.50687e44i			0.262553i
$246$	1.38840e45	+	1.52613e45i	0.518498	+	0.569932i
$247$	−5.92313e44			−0.204790
$248$		−	4.34115e45i		−	1.39002i
$249$	2.36591e45	−	2.15239e45i	0.701794	−	0.638460i
$250$	1.49402e45			0.410672
$251$			1.10103e45i			0.280544i	0.990113	+	0.140272i	$0.0447976\pi$
$251$			1.10103e45i			0.280544i	−0.990113	+	0.140272i	$0.955202\pi$
$252$	2.49391e44	−	2.63287e45i	0.0589209	−	0.622040i
$253$	−1.82438e45			−0.399784
$254$		−	2.18084e45i		−	0.443388i
$255$	3.07392e45	+	3.37884e45i	0.580001	+	0.637536i
$256$	−1.75764e45			−0.307873
$257$			1.01754e46i			1.65509i	0.561400	+	0.827544i	$0.310263\pi$
$257$			1.01754e46i			1.65509i	−0.561400	+	0.827544i	$0.689737\pi$
$258$	−2.18802e45	+	1.99056e45i	−0.330580	+	0.300746i
$259$	−1.88735e44			−0.0264946
$260$			1.69119e45i			0.220647i
$261$	−1.11318e46	−	1.05442e45i	−1.35019	−	0.127893i
$262$	−1.33937e45			−0.151069
$263$			1.50075e45i			0.157452i	0.996896	+	0.0787262i	$0.0250853\pi$
$263$			1.50075e45i			0.157452i	−0.996896	+	0.0787262i	$0.974915\pi$
$264$	−2.78656e45	−	3.06298e45i	−0.272015	−	0.298999i
$265$	8.34305e45			0.757972
$266$		−	1.72808e45i		−	0.146155i
$267$	−8.71063e45	+	7.92453e45i	−0.686018	+	0.624108i
$268$	2.43564e45			0.178670
$269$		−	2.53416e46i		−	1.73197i	−0.500067	−	0.865987i	$-0.666691\pi$
$269$		−	2.53416e46i		−	1.73197i	0.500067	−	0.865987i	$-0.333309\pi$
$270$	−3.16497e45	+	2.37490e45i	−0.201585	+	0.151263i
$271$	1.10594e46			0.656621			0.328311	−	0.944570i	$-0.393521\pi$
$271$	1.10594e46			0.656621			0.328311	+	0.944570i	$0.393521\pi$
$272$			1.31750e46i			0.729359i
$273$	4.29993e45	+	4.72648e45i	0.222009	+	0.244032i
$274$	8.09110e45			0.389715
$275$			7.47772e45i			0.336084i
$276$	−1.09400e46	+	9.95274e45i	−0.458930	+	0.417513i
$277$	3.23361e46			1.26640			0.633201	−	0.773987i	$-0.281741\pi$
$277$	3.23361e46			1.26640			0.633201	+	0.773987i	$0.281741\pi$
$278$			4.75147e45i			0.173771i
$279$	5.06827e45	−	5.35068e46i	0.173133	−	1.82780i
$280$	−1.08890e46			−0.347524
$281$		−	5.22440e46i		−	1.55818i	−0.626914	−	0.779088i	$-0.715682\pi$
$281$		−	5.22440e46i		−	1.55818i	0.626914	−	0.779088i	$-0.284318\pi$
$282$	1.36692e46	+	1.50252e46i	0.381075	+	0.418877i
$283$	−1.78433e46			−0.465087			−0.232543	−	0.972586i	$-0.574705\pi$
$283$	−1.78433e46			−0.465087			−0.232543	+	0.972586i	$0.574705\pi$
$284$		−	4.12826e45i		−	0.100628i
$285$	9.24382e45	−	8.40960e45i	0.210765	−	0.191745i
$286$	4.53341e45			0.0967098
$287$			7.02931e46i			1.40332i
$288$	−5.16960e46	−	4.89675e45i	−0.966049	−	0.0915062i
$289$	−5.74370e46			−1.00492
$290$			2.08613e46i			0.341805i
$291$	6.99584e46	+	7.68981e46i	1.07367	+	1.18018i
$292$	−3.46297e46			−0.497937
$293$			2.83698e46i			0.382271i	0.981564	+	0.191135i	$0.0612170\pi$
$293$			2.83698e46i			0.382271i	−0.981564	+	0.191135i	$0.938783\pi$
$294$	1.04594e46	−	9.51552e45i	0.132102	−	0.120180i
$295$	−5.50074e45			−0.0651332
$296$			2.39566e45i			0.0266001i
$297$	−3.07697e46	−	4.10060e46i	−0.320443	−	0.427047i
$298$	1.05489e46			0.103062
$299$		−	3.57340e46i		−	0.327589i
$300$	4.07940e46	+	4.48407e46i	0.350988	+	0.385806i
$301$	−1.00780e47			−0.813972
$302$			2.27648e46i			0.172636i
$303$	1.04160e47	−	9.47604e46i	0.741811	−	0.674865i
$304$	3.60441e46			0.241121
$305$		−	9.38103e46i		−	0.589595i
$306$	9.36073e45	−	9.88231e46i	0.0552844	−	0.583648i
$307$	−7.42296e46			−0.412048			−0.206024	−	0.978547i	$-0.566052\pi$
$307$	−7.42296e46			−0.412048			−0.206024	+	0.978547i	$0.566052\pi$
$308$		−	6.39270e46i		−	0.333596i
$309$	2.31895e47	+	2.54899e47i	1.13784	+	1.25071i
$310$	−1.00273e47			−0.462715
$311$		−	1.65900e47i		−	0.720111i	−0.932931	−	0.360056i	$-0.882758\pi$
$311$		−	1.65900e47i		−	0.720111i	0.932931	−	0.360056i	$-0.117242\pi$
$312$	5.99943e46	−	5.45801e46i	0.245004	−	0.222893i
$313$	1.39272e47			0.535208			0.267604	−	0.963529i	$-0.413768\pi$
$313$	1.39272e47			0.535208			0.267604	+	0.963529i	$0.413768\pi$
$314$		−	9.12323e45i		−	0.0329978i
$315$	−1.34212e47	−	1.27129e46i	−0.456974	−	0.0432855i
$316$	3.21120e47			1.02947
$317$			1.64475e47i			0.496562i	0.968688	+	0.248281i	$0.0798656\pi$
$317$			1.64475e47i			0.496562i	−0.968688	+	0.248281i	$0.920134\pi$
$318$	−1.22007e47	−	1.34110e47i	−0.346952	−	0.381369i
$319$	−2.70283e47			−0.724097
$320$		−	2.73268e46i		−	0.0689826i
$321$	−3.40644e47	+	3.09902e47i	−0.810411	+	0.737275i
$322$	1.04255e47			0.233794
$323$			3.13502e47i			0.662815i
$324$	−4.08217e47	−	7.80345e46i	−0.813835	−	0.155572i
$325$	−1.46466e47			−0.275392
$326$			1.92370e47i			0.341195i
$327$	−1.67343e47	−	1.83943e47i	−0.280027	−	0.307805i
$328$	8.92247e47			1.40891
$329$			6.92057e47i			1.03138i
$330$	−7.07498e46	+	6.43649e46i	−0.0995315	+	0.0905491i
$331$	−5.39840e47			−0.717023			−0.358511	−	0.933525i	$-0.616716\pi$
$331$	−5.39840e47			−0.717023			−0.358511	+	0.933525i	$0.616716\pi$
$332$		−	6.26773e47i		−	0.786116i
$333$	−2.79692e45	+	2.95277e46i	−0.00331314	+	0.0349775i
$334$	−1.41935e47			−0.158820
$335$		−	1.24158e47i		−	0.131257i
$336$	−2.61664e47	−	2.87621e47i	−0.261396	−	0.287325i
$337$	5.79296e47			0.546931			0.273465	−	0.961882i	$-0.411830\pi$
$337$	5.79296e47			0.546931			0.273465	+	0.961882i	$0.411830\pi$
$338$		−	3.75142e47i		−	0.334794i
$339$	5.56555e47	−	5.06328e47i	0.469585	−	0.427206i
$340$	8.95119e47			0.714137
$341$		−	1.29916e48i		−	0.980237i
$342$	−2.70360e47	−	2.56090e46i	−0.192950	−	0.0182767i
$343$	1.59867e48			1.07937
$344$			1.27922e48i			0.817213i
$345$	5.07348e47	+	5.57676e47i	0.306721	+	0.337147i
$346$	8.38093e47			0.479564
$347$		−	1.23811e48i		−	0.670654i	−0.942102	−	0.335327i	$-0.891153\pi$
$347$		−	1.23811e48i		−	0.670654i	0.942102	−	0.335327i	$-0.108847\pi$
$348$	−1.62077e48	+	1.47451e48i	−0.831222	+	0.756207i
$349$	−3.02513e48			−1.46913			−0.734566	−	0.678537i	$-0.762614\pi$
$349$	−3.02513e48			−1.46913			−0.734566	+	0.678537i	$0.762614\pi$
$350$		−	4.27316e47i		−	0.196542i
$351$	8.03182e47	−	6.02684e47i	0.349928	−	0.262575i
$352$	−1.25520e48			−0.518085
$353$			1.78026e47i			0.0696249i	0.999394	+	0.0348125i	$0.0110834\pi$
$353$			1.78026e47i			0.0696249i	−0.999394	+	0.0348125i	$0.988917\pi$
$354$	8.04417e46	+	8.84214e46i	0.0298139	+	0.0327714i
$355$	−2.10441e47			−0.0739250
$356$			2.30761e48i			0.768444i
$357$	2.50165e48	−	2.27589e48i	0.789824	−	0.718546i
$358$	−2.61718e48			−0.783530
$359$			2.59770e48i			0.737555i	0.929518	+	0.368777i	$0.120224\pi$
$359$			2.59770e48i			0.737555i	−0.929518	+	0.368777i	$0.879776\pi$
$360$	−1.61367e47	+	1.70359e48i	−0.0434578	+	0.458793i
$361$	−3.05647e48			−0.780878
$362$		−	2.14634e48i		−	0.520278i
$363$	2.09159e48	+	2.29908e48i	0.481118	+	0.528844i
$364$	1.25213e48			0.273353
$365$			1.76527e48i			0.365803i
$366$	−1.50795e48	+	1.37186e48i	−0.296651	+	0.269880i
$367$	−3.22556e48			−0.602491			−0.301245	−	0.953547i	$-0.597402\pi$
$367$	−3.22556e48			−0.602491			−0.301245	+	0.953547i	$0.597402\pi$
$368$			2.17452e48i			0.385705i
$369$	1.09974e49	+	1.04169e48i	1.85263	+	0.175485i
$370$	5.53358e46			0.00885469
$371$		−	6.17708e48i		−	0.939029i
$372$	−7.08747e48	−	7.79054e48i	−1.02371	−	1.12526i
$373$	−3.04854e48			−0.418431			−0.209216	−	0.977870i	$-0.567091\pi$
$373$	−3.04854e48			−0.418431			−0.209216	+	0.977870i	$0.567091\pi$
$374$		−	2.39946e48i		−	0.313007i
$375$	5.91698e48	−	5.38300e48i	0.733679	−	0.667468i
$376$	8.78444e48			1.03549
$377$		−	5.29402e48i		−	0.593335i
$378$	1.75834e48	+	2.34330e48i	0.187395	+	0.249737i
$379$	2.53209e48			0.256646			0.128323	−	0.991732i	$-0.459041\pi$
$379$	2.53209e48			0.256646			0.128323	+	0.991732i	$0.459041\pi$
$380$		−	2.44886e48i		−	0.236089i
$381$	−7.85767e48	−	8.63714e48i	−0.720642	−	0.792128i
$382$	3.16262e48			0.275958
$383$			1.59490e49i			1.32421i	0.749413	+	0.662103i	$0.230336\pi$
$383$			1.59490e49i			1.32421i	−0.749413	+	0.662103i	$0.769664\pi$
$384$	−9.52344e48	+	8.66398e48i	−0.752489	+	0.684580i
$385$	−3.25872e48			−0.245072
$386$			7.02253e48i			0.502730i
$387$	−1.49349e48	+	1.57670e49i	−0.101787	+	1.07459i
$388$	2.03717e49			1.32198
$389$		−	3.60823e48i		−	0.222973i	−0.993766	−	0.111487i	$-0.964439\pi$
$389$		−	3.60823e48i		−	0.222973i	0.993766	−	0.111487i	$-0.0355612\pi$
$390$	−1.26071e48	−	1.38577e48i	−0.0741972	−	0.0815575i
$391$	−1.89134e49			−1.06026
$392$		−	6.11510e48i		−	0.326564i
$393$	−5.30451e48	+	4.82580e48i	−0.269890	+	0.245534i
$394$	2.09023e48			0.101336
$395$		−	1.63693e49i		−	0.756286i
$396$	−1.00014e49	−	9.47354e47i	−0.440405	−	0.0417161i
$397$	−1.50901e49			−0.633391			−0.316695	−	0.948527i	$-0.602573\pi$
$397$	−1.50901e49			−0.633391			−0.316695	+	0.948527i	$0.602573\pi$
$398$			2.39955e48i			0.0960177i
$399$	−6.22636e48	−	6.84400e48i	−0.237547	−	0.261111i
$400$	8.91288e48			0.324249
$401$			4.28089e49i			1.48522i	0.669724	+	0.742610i	$0.266413\pi$
$401$			4.28089e49i			1.48522i	−0.669724	+	0.742610i	$0.733587\pi$
$402$	−1.99578e48	+	1.81567e48i	−0.0660415	+	0.0600815i
$403$	2.54466e49			0.803220
$404$		−	2.75941e49i		−	0.830940i
$405$	−3.97786e48	+	2.08092e49i	−0.114289	+	0.597873i
$406$	1.54454e49			0.423452
$407$			7.16944e47i			0.0187582i
$408$	−2.88884e49	−	3.17540e49i	−0.721406	−	0.792969i
$409$	1.75084e49			0.417353			0.208676	−	0.977985i	$-0.433084\pi$
$409$	1.75084e49			0.417353			0.208676	+	0.977985i	$0.433084\pi$
$410$		−	2.06094e49i		−	0.469000i
$411$	3.20444e49	−	2.91525e49i	0.696238	−	0.633406i
$412$	6.75275e49			1.40098
$413$			4.07267e48i			0.0806916i
$414$	1.54498e48	−	1.63107e49i	0.0292359	−	0.308650i
$415$	−3.19502e49			−0.577510
$416$		−	2.45854e49i		−	0.424526i
$417$	1.71197e49	+	1.88180e49i	0.282431	+	0.310447i
$418$	−6.56443e48			−0.103478
$419$		−	2.94106e49i		−	0.443034i	−0.975156	−	0.221517i	$-0.928899\pi$
$419$		−	2.94106e49i		−	0.443034i	0.975156	−	0.221517i	$-0.0711009\pi$
$420$	−1.95412e49	+	1.77777e49i	−0.281329	+	0.255940i
$421$	−9.87880e49			−1.35939			−0.679695	−	0.733495i	$-0.737888\pi$
$421$	−9.87880e49			−1.35939			−0.679695	+	0.733495i	$0.737888\pi$
$422$			5.76676e49i			0.758569i
$423$	1.08273e50	+	1.02558e49i	1.36161	+	0.128974i
$424$	−7.84072e49			−0.942767
$425$			7.75219e49i			0.891322i
$426$	3.07745e48	+	3.38272e48i	0.0338383	+	0.0371950i
$427$	−6.94559e49			−0.730432
$428$			9.02430e49i			0.907783i
$429$	1.79544e49	−	1.63341e49i	0.172775	−	0.157183i
$430$	2.95479e49			0.272036
$431$		−	1.98622e50i		−	1.74968i	−0.484413	−	0.874840i	$-0.660967\pi$
$431$		−	1.98622e50i		−	1.74968i	0.484413	−	0.874840i	$-0.339033\pi$
$432$	−4.88761e49	+	3.66752e49i	−0.412008	+	0.309158i
$433$	−8.49777e49			−0.685544			−0.342772	−	0.939419i	$-0.611366\pi$
$433$	−8.49777e49			−0.685544			−0.342772	+	0.939419i	$0.611366\pi$
$434$			7.42410e49i			0.573243i
$435$	7.51640e49	+	8.26201e49i	0.555538	+	0.610646i
$436$	−4.87299e49			−0.344788
$437$			5.17433e49i			0.350515i
$438$	2.83758e49	−	2.58150e49i	0.184052	−	0.167442i
$439$	5.61434e49			0.348717			0.174358	−	0.984682i	$-0.444215\pi$
$439$	5.61434e49			0.348717			0.174358	+	0.984682i	$0.444215\pi$
$440$			4.13637e49i			0.246048i
$441$	7.13935e48	−	7.53716e49i	0.0406748	−	0.429412i
$442$	4.69981e49			0.256482
$443$		−	2.44317e50i		−	1.27727i	−0.769511	−	0.638634i	$-0.779500\pi$
$443$		−	2.44317e50i		−	1.27727i	0.769511	−	0.638634i	$-0.220500\pi$
$444$	3.91122e48	+	4.29921e48i	0.0195901	+	0.0215334i
$445$	1.17632e50			0.564527
$446$			2.05742e49i			0.0946150i
$447$	4.17786e49	−	3.80082e49i	0.184124	−	0.167508i
$448$	−2.02324e49			−0.0854605
$449$		−	1.96170e49i		−	0.0794242i	−0.999211	−	0.0397121i	$-0.987356\pi$
$449$		−	1.96170e49i		−	0.0794242i	0.999211	−	0.0397121i	$-0.0126441\pi$
$450$	−6.68538e49	−	6.33253e48i	−0.259471	−	0.0245776i
$451$	2.67021e50			0.993552
$452$		−	1.47442e50i		−	0.526006i
$453$	8.20226e49	+	9.01591e49i	0.280587	+	0.308421i
$454$	−1.08682e50			−0.356532
$455$		−	6.38283e49i		−	0.200815i
$456$	−8.68725e49	+	7.90326e49i	−0.262150	+	0.238492i
$457$	−1.68065e50			−0.486486			−0.243243	−	0.969965i	$-0.578211\pi$
$457$	−1.68065e50			−0.486486			−0.243243	+	0.969965i	$0.578211\pi$
$458$		−	1.53677e50i		−	0.426741i
$459$	−3.18991e50	−	4.25111e50i	−0.849840	−	1.13256i
$460$	1.47739e50			0.377655
$461$			4.39671e50i			1.07848i	0.842154	+	0.539238i	$0.181288\pi$
$461$			4.39671e50i			1.07848i	−0.842154	+	0.539238i	$0.818712\pi$
$462$	4.76549e49	+	5.23822e49i	0.112179	+	0.123307i
$463$	3.58690e50			0.810365			0.405183	−	0.914236i	$-0.367208\pi$
$463$	3.58690e50			0.810365			0.405183	+	0.914236i	$0.367208\pi$
$464$			3.22157e50i			0.698597i
$465$	−3.97128e50	+	3.61289e50i	−0.826655	+	0.752053i
$466$	−1.16234e50			−0.232274
$467$			7.02904e50i			1.34858i	0.738468	+	0.674288i	$0.235549\pi$
$467$			7.02904e50i			1.34858i	−0.738468	+	0.674288i	$0.764451\pi$
$468$	1.85557e49	−	1.95897e50i	0.0341828	−	0.360874i
$469$	−9.19251e49			−0.162611
$470$		−	2.02906e50i		−	0.344696i
$471$	−3.28714e49	−	3.61321e49i	−0.0536316	−	0.0589517i
$472$	5.16954e49			0.0810129
$473$			3.82829e50i			0.576293i
$474$	−2.63128e50	+	2.39382e50i	−0.380521	+	0.346181i
$475$	2.12084e50			0.294665
$476$		−	6.62734e50i		−	0.884723i
$477$	−9.66407e50	−	9.15401e49i	−1.23968	−	0.117425i
$478$	1.78035e50			0.219471
$479$		−	1.03282e51i		−	1.22363i	−0.790999	−	0.611817i	$-0.790439\pi$
$479$		−	1.03282e51i		−	1.22363i	0.790999	−	0.611817i	$-0.209561\pi$
$480$	3.49062e50	+	3.83688e50i	0.397483	+	0.436913i
$481$	−1.40427e49			−0.0153707
$482$		−	3.70707e50i		−	0.390065i
$483$	4.12896e50	−	3.75634e50i	0.417681	−	0.379987i
$484$	6.09068e50			0.592385
$485$		−	1.03846e51i		−	0.971177i
$486$	3.92667e50	−	2.40367e50i	0.353131	−	0.216165i
$487$	9.70405e50			0.839272			0.419636	−	0.907692i	$-0.362158\pi$
$487$	9.70405e50			0.839272			0.419636	+	0.907692i	$0.362158\pi$
$488$			8.81620e50i			0.733339i
$489$	6.93117e50	+	7.61873e50i	0.554547	+	0.609557i
$490$	−1.41249e50			−0.108707
$491$			1.32882e51i			0.983823i	0.870645	+	0.491911i	$0.163702\pi$
$491$			1.32882e51i			0.983823i	−0.870645	+	0.491911i	$0.836298\pi$
$492$	1.60121e51	−	1.45671e51i	1.14054	−	1.03761i
$493$	−2.80204e51			−1.92036
$494$		−	1.28577e50i		−	0.0847913i
$495$	−4.82920e49	+	5.09829e50i	−0.0306462	+	0.323538i
$496$	−1.54851e51			−0.945717
$497$			1.55808e50i			0.0915835i
$498$	4.67233e50	+	5.13582e50i	0.264348	+	0.290571i
$499$	1.14247e51			0.622205			0.311102	−	0.950376i	$-0.399302\pi$
$499$	1.14247e51			0.622205			0.311102	+	0.950376i	$0.399302\pi$
$500$		−	1.56752e51i		−	0.821832i
$501$	−5.62126e50	+	5.11397e50i	−0.283738	+	0.258131i
$502$	−2.39008e50			−0.116156
$503$		−	6.96254e49i		−	0.0325819i	−0.999867	−	0.0162909i	$-0.994814\pi$
$503$		−	6.96254e49i		−	0.0325819i	0.999867	−	0.0162909i	$-0.00518579\pi$
$504$	1.26131e51	+	1.19474e50i	0.568385	+	0.0538386i
$505$	−1.40663e51			−0.610439
$506$		−	3.96030e50i		−	0.165527i
$507$	−1.35165e51	−	1.48573e51i	−0.544143	−	0.598121i
$508$	−2.28814e51			−0.887303
$509$			4.65910e51i			1.74046i	0.492644	+	0.870231i	$0.336030\pi$
$509$			4.65910e51i			1.74046i	−0.492644	+	0.870231i	$0.663970\pi$
$510$	−7.33466e50	+	6.67274e50i	−0.263965	+	0.240143i
$511$	1.30698e51			0.453183
$512$			2.66338e51i			0.889824i
$513$	−1.16302e51	+	8.72693e50i	−0.374418	+	0.280952i
$514$	−2.20883e51			−0.685272
$515$		−	3.44226e51i		−	1.02922i
$516$	2.08849e51	+	2.29566e51i	0.601850	+	0.661552i
$517$	2.62890e51			0.730220
$518$		−	4.09699e49i		−	0.0109698i
$519$	3.31923e51	−	3.01968e51i	0.856757	−	0.779438i
$520$	−8.10188e50			−0.201615
$521$			4.37767e50i			0.105033i	0.998620	+	0.0525166i	$0.0167242\pi$
$521$			4.37767e50i			0.105033i	−0.998620	+	0.0525166i	$0.983276\pi$
$522$	2.28890e50	−	2.41644e51i	0.0529526	−	0.559032i
$523$	4.43924e51			0.990322			0.495161	−	0.868801i	$-0.335109\pi$
$523$	4.43924e51			0.990322			0.495161	+	0.868801i	$0.335109\pi$
$524$			1.40526e51i			0.302318i
$525$	−1.53964e51	−	1.69237e51i	−0.319442	−	0.351130i
$526$	−3.25777e50			−0.0651916
$527$		−	1.34685e52i		−	2.59967i
$528$	−1.09258e51	+	9.93978e50i	−0.203427	+	0.185068i
$529$	2.44582e51			0.439305
$530$			1.81108e51i			0.313831i
$531$	6.37172e50	+	6.03542e49i	0.106527	+	0.0100905i
$532$	−1.81310e51			−0.292484
$533$			5.23011e51i			0.814130i
$534$	−1.72023e51	−	1.89087e51i	−0.258405	−	0.284039i
$535$	4.60020e51			0.666891
$536$			1.16683e51i			0.163258i
$537$	−1.03652e52	+	9.42979e51i	−1.39980	+	1.27348i
$538$	5.50106e51			0.717106
$539$		−	1.83005e51i		−	0.230291i
$540$	2.49174e51	+	3.32068e51i	0.302706	+	0.403409i
$541$	4.03992e51			0.473832			0.236916	−	0.971530i	$-0.423863\pi$
$541$	4.03992e51			0.473832			0.236916	+	0.971530i	$0.423863\pi$
$542$			2.40073e51i			0.271867i
$543$	−7.73334e51	−	8.50047e51i	−0.845610	−	0.929493i
$544$	−1.30127e52			−1.37400
$545$			2.48404e51i			0.253294i
$546$	−1.02601e51	+	9.33413e50i	−0.101039	+	0.0919208i
$547$	1.41630e52			1.34709			0.673544	−	0.739147i	$-0.264771\pi$
$547$	1.41630e52			1.34709			0.673544	+	0.739147i	$0.264771\pi$
$548$		−	8.48917e51i		−	0.779892i
$549$	−1.02929e51	+	1.08664e52i	−0.0913403	+	0.964299i
$550$	−1.62323e51			−0.139152
$551$			7.66580e51i			0.634859i
$552$	−4.76801e51	−	5.24098e51i	−0.381500	−	0.419344i
$553$	−1.21196e52			−0.936940
$554$			7.01939e51i			0.524341i
$555$	2.19155e50	−	1.99377e50i	0.0158192	−	0.0143916i
$556$	4.98523e51			0.347748
$557$			1.20730e52i			0.813892i	0.913452	+	0.406946i	$0.133406\pi$
$557$			1.20730e52i			0.813892i	−0.913452	+	0.406946i	$0.866594\pi$
$558$	1.16150e52	+	1.10020e51i	0.756782	+	0.0716840i
$559$	−7.49845e51			−0.472223
$560$			3.88415e51i			0.236441i
$561$	−8.64536e51	−	9.50296e51i	−0.508731	−	0.559197i
$562$	1.13409e52			0.645147
$563$		−	2.27823e52i		−	1.25296i	−0.779436	−	0.626482i	$-0.784494\pi$
$563$		−	2.27823e52i		−	1.25296i	0.779436	−	0.626482i	$-0.215506\pi$
$564$	1.57644e52	−	1.43417e52i	0.838251	−	0.762603i
$565$	−7.51595e51			−0.386423
$566$		−	3.87336e51i		−	0.192564i
$567$	1.54068e52	+	2.94516e51i	0.740687	+	0.141589i
$568$	1.97770e51			0.0919481
$569$		−	1.55143e52i		−	0.697587i	−0.937200	−	0.348793i	$-0.886591\pi$
$569$		−	1.55143e52i		−	0.697587i	0.937200	−	0.348793i	$-0.113409\pi$
$570$	1.82552e51	+	2.00661e51i	0.0793899	+	0.0872652i
$571$	−2.97040e51			−0.124948			−0.0624740	−	0.998047i	$-0.519899\pi$
$571$	−2.97040e51			−0.124948			−0.0624740	+	0.998047i	$0.519899\pi$
$572$		−	4.75645e51i		−	0.193534i
$573$	1.25254e52	−	1.13951e52i	0.493009	−	0.448517i
$574$	−1.52589e52			−0.581030
$575$			1.27949e52i			0.471356i
$576$	−2.99830e50	+	3.16537e51i	−0.0106868	+	0.112823i
$577$	−8.21294e51			−0.283242			−0.141621	−	0.989921i	$-0.545231\pi$
$577$	−8.21294e51			−0.283242			−0.141621	+	0.989921i	$0.545231\pi$
$578$		−	1.24682e52i		−	0.416078i
$579$	2.53024e52	+	2.78124e52i	0.817090	+	0.898144i
$580$	2.18876e52			0.684016
$581$			2.36555e52i			0.715460i
$582$	−1.66927e52	+	1.51863e52i	−0.488642	+	0.444544i
$583$	−2.34647e52			−0.664834
$584$		−	1.65899e52i		−	0.454987i
$585$	−9.98597e51	−	9.45892e50i	−0.265112	−	0.0251119i
$586$	−6.15840e51			−0.158275
$587$			3.58770e52i			0.892673i	0.894865	+	0.446337i	$0.147272\pi$
$587$			3.58770e52i			0.892673i	−0.894865	+	0.446337i	$0.852728\pi$
$588$	−9.98367e51	−	1.09740e52i	−0.240503	−	0.264361i
$589$	−3.68470e52			−0.859433
$590$		−	1.19408e51i		−	0.0269677i
$591$	8.27825e51	−	7.53117e51i	0.181041	−	0.164703i
$592$	8.54543e50			0.0180976
$593$			4.28826e52i			0.879513i	0.898117	+	0.439756i	$0.144935\pi$
$593$			4.28826e52i			0.879513i	−0.898117	+	0.439756i	$0.855065\pi$
$594$	8.90143e51	−	6.67937e51i	0.176814	−	0.132676i
$595$	−3.37833e52			−0.649950
$596$		−	1.10679e52i		−	0.206247i
$597$	8.64567e51	+	9.50330e51i	0.156058	+	0.171539i
$598$	7.75700e51			0.135635
$599$		−	6.18793e52i		−	1.04818i	−0.851663	−	0.524090i	$-0.824405\pi$
$599$		−	6.18793e52i		−	1.04818i	0.851663	−	0.524090i	$-0.175595\pi$
$600$	−2.14816e52	+	1.95430e52i	−0.352527	+	0.320713i
$601$	−2.85517e52			−0.453960			−0.226980	−	0.973899i	$-0.572885\pi$
$601$	−2.85517e52			−0.453960			−0.226980	+	0.973899i	$0.572885\pi$
$602$		−	2.18769e52i		−	0.337017i
$603$	−1.36227e51	+	1.43817e52i	−0.0203345	+	0.214675i
$604$	2.38848e52			0.345478
$605$		−	3.10477e52i		−	0.435188i
$606$	2.05702e52	+	2.26107e52i	0.279421	+	0.307139i
$607$	1.49174e53			1.96385			0.981927	−	0.189262i	$-0.0606094\pi$
$607$	1.49174e53			1.96385			0.981927	+	0.189262i	$0.0606094\pi$
$608$			3.56000e52i			0.454237i
$609$	6.11708e52	−	5.56504e52i	0.756512	−	0.688240i
$610$	2.03640e52			0.244116
$611$			5.14921e52i			0.598353i
$612$	−1.03685e53	−	9.82126e51i	−1.16799	−	0.110634i
$613$	5.96551e52			0.651476			0.325738	−	0.945460i	$-0.394387\pi$
$613$	5.96551e52			0.651476			0.325738	+	0.945460i	$0.394387\pi$
$614$		−	1.61135e52i		−	0.170604i
$615$	−7.42566e52	−	8.16227e52i	−0.762268	−	0.837884i
$616$	3.06252e52			0.304821
$617$		−	9.54719e52i		−	0.921420i	−0.887551	−	0.460710i	$-0.847595\pi$
$617$		−	9.54719e52i		−	0.921420i	0.887551	−	0.460710i	$-0.152405\pi$
$618$	−5.53325e52	+	5.03389e52i	−0.517844	+	0.471111i
$619$	4.48839e52			0.407350			0.203675	−	0.979039i	$-0.434711\pi$
$619$	4.48839e52			0.407350			0.203675	+	0.979039i	$0.434711\pi$
$620$			1.05207e53i			0.925979i
$621$	−5.26492e52	−	7.01644e52i	−0.449419	−	0.598930i
$622$	3.60130e52			0.298155
$623$		−	8.70931e52i		−	0.699376i
$624$	−1.94690e52	−	2.14002e52i	−0.151648	−	0.166691i
$625$	3.40633e51			0.0257375
$626$			3.02327e52i			0.221598i
$627$	−2.59981e52	+	2.36519e52i	−0.184867	+	0.168183i
$628$	−9.57208e51			−0.0660348
$629$			7.43259e51i			0.0497482i
$630$	2.75966e51	−	2.91343e52i	0.0179219	−	0.189205i
$631$	−2.42722e53			−1.52951			−0.764755	−	0.644321i	$-0.777140\pi$
$631$	−2.42722e53			−1.52951			−0.764755	+	0.644321i	$0.777140\pi$
$632$			1.53837e53i			0.940670i
$633$	2.07779e53	+	2.28390e53i	1.23291	+	1.35521i
$634$	−3.57035e52			−0.205596
$635$			1.16639e53i			0.651846i
$636$	−1.40708e53	+	1.28010e53i	−0.763192	+	0.694317i
$637$	3.58451e52			0.188704
$638$		−	5.86721e52i		−	0.299805i
$639$	2.43762e52	+	2.30896e51i	0.120906	+	0.0114525i
$640$	1.28608e53			0.619227
$641$			6.15370e52i			0.287630i	0.989605	+	0.143815i	$0.0459370\pi$
$641$			6.15370e52i			0.287630i	−0.989605	+	0.143815i	$0.954063\pi$
$642$	−6.72724e52	−	7.39457e52i	−0.305261	−	0.335542i
$643$	−2.28770e53			−1.00784			−0.503919	−	0.863751i	$-0.668109\pi$
$643$	−2.28770e53			−1.00784			−0.503919	+	0.863751i	$0.668109\pi$
$644$		−	1.09384e53i		−	0.467866i
$645$	1.17023e53	−	1.06462e53i	0.486001	−	0.442141i
$646$	−6.80538e52			−0.274432
$647$		−	3.20559e53i		−	1.25524i	−0.778520	−	0.627620i	$-0.784029\pi$
$647$		−	3.20559e53i		−	1.25524i	0.778520	−	0.627620i	$-0.215971\pi$
$648$	3.73836e52	−	1.95563e53i	0.142153	−	0.743636i
$649$	1.54708e52			0.0571298
$650$		−	3.17942e52i		−	0.114023i
$651$	2.67493e53	+	2.94028e53i	0.931696	+	1.02412i
$652$	2.01834e53			0.682796
$653$			1.70418e52i			0.0559969i	0.999608	+	0.0279984i	$0.00891335\pi$
$653$			1.70418e52i			0.0559969i	−0.999608	+	0.0279984i	$0.991087\pi$
$654$	3.99296e52	−	3.63261e52i	0.127443	−	0.115942i
$655$	7.16343e52			0.222094
$656$		−	3.18268e53i		−	0.958563i
$657$	1.93686e52	−	2.04478e53i	0.0566704	−	0.598281i
$658$	−1.50229e53			−0.427033
$659$			4.17454e53i			1.15288i	0.817138	+	0.576442i	$0.195559\pi$
$659$			4.17454e53i			1.15288i	−0.817138	+	0.576442i	$0.804441\pi$
$660$	6.75316e52	+	7.42306e52i	0.181206	+	0.199181i
$661$	−3.32313e53			−0.866401			−0.433201	−	0.901298i	$-0.642616\pi$
$661$	−3.32313e53			−0.866401			−0.433201	+	0.901298i	$0.642616\pi$
$662$		−	1.17186e53i		−	0.296876i
$663$	1.86134e53	−	1.69336e53i	0.458214	−	0.416862i
$664$	3.00265e53			0.718308
$665$			9.24242e52i			0.214869i
$666$	−6.40976e51	−	6.07145e50i	−0.0144821	−	0.00137177i
$667$	−4.62475e53			−1.01554
$668$			1.48918e53i			0.317829i
$669$	7.41295e52	+	8.14830e52i	0.153778	+	0.169033i
$670$	2.69518e52			0.0543458
$671$			2.63841e53i			0.517147i
$672$	2.84077e53	−	2.58441e53i	0.541278	−	0.492430i
$673$	4.02945e53			0.746380			0.373190	−	0.927755i	$-0.378264\pi$
$673$	4.02945e53			0.746380			0.373190	+	0.927755i	$0.378264\pi$
$674$			1.25751e53i			0.226451i
$675$	−2.87588e53	+	2.15797e53i	−0.503499	+	0.377810i
$676$	−3.93598e53			−0.669986
$677$		−	1.02881e54i		−	1.70275i	−0.524560	−	0.851374i	$-0.675770\pi$
$677$		−	1.02881e54i		−	1.70275i	0.524560	−	0.851374i	$-0.324230\pi$
$678$	1.09912e53	+	1.20815e53i	0.176880	+	0.194427i
$679$	−7.68864e53			−1.20316
$680$			4.28820e53i			0.652537i
$681$	−4.30432e53	+	3.91587e53i	−0.636956	+	0.579473i
$682$	2.82018e53			0.405857
$683$			1.37499e54i			1.92445i	0.272261	+	0.962223i	$0.412229\pi$
$683$			1.37499e54i			1.92445i	−0.272261	+	0.962223i	$0.587771\pi$
$684$	−2.68689e52	+	2.83661e53i	−0.0365750	+	0.386130i
$685$	−4.32741e53			−0.572938
$686$			3.47032e53i			0.446901i
$687$	−5.53703e53	−	6.08630e53i	−0.693584	−	0.762386i
$688$	4.56304e53			0.555999
$689$		−	4.59602e53i		−	0.544774i
$690$	−1.21058e53	+	1.10133e53i	−0.139592	+	0.126995i
$691$	4.56403e53			0.511995			0.255998	−	0.966677i	$-0.417596\pi$
$691$	4.56403e53			0.511995			0.255998	+	0.966677i	$0.417596\pi$
$692$		−	8.79326e53i		−	0.959697i
$693$	3.77470e53	+	3.57548e52i	0.400822	+	0.0379667i
$694$	2.68764e53			0.277677
$695$		−	2.54126e53i		−	0.255468i
$696$	−7.06384e53	−	7.76456e53i	−0.690979	−	0.759523i
$697$	2.76821e54			2.63498
$698$		−	6.56684e53i		−	0.608279i
$699$	−4.60339e53	+	4.18795e53i	−0.414965	+	0.377516i
$700$	−4.48339e53			−0.393318
$701$		−	7.40728e53i		−	0.632435i	−0.948687	−	0.316218i	$-0.897587\pi$
$701$		−	7.40728e53i		−	0.632435i	0.948687	−	0.316218i	$-0.102413\pi$
$702$	1.30828e53	+	1.74352e53i	0.108717	+	0.144884i
$703$	2.03340e52			0.0164464
$704$			7.68564e52i			0.0605061i
$705$	−7.31079e53	−	8.03601e53i	−0.560236	−	0.615811i
$706$	−3.86453e52			−0.0288275
$707$			1.04145e54i			0.756255i
$708$	9.27716e52	−	8.43993e52i	0.0655818	−	0.0596633i
$709$	2.08847e54			1.43731			0.718653	−	0.695369i	$-0.244759\pi$
$709$	2.08847e54			1.43731			0.718653	+	0.695369i	$0.244759\pi$
$710$		−	4.56817e52i		−	0.0306079i
$711$	−1.79605e53	+	1.89612e54i	−0.117164	+	1.23693i
$712$	−1.10549e54			−0.702160
$713$		−	2.22297e54i		−	1.37478i
$714$	4.94041e53	+	5.43048e53i	0.297507	+	0.327019i
$715$	−2.42463e53			−0.142178
$716$			2.74594e54i			1.56799i
$717$	7.05101e53	−	6.41468e53i	0.392091	−	0.356707i
$718$	−5.63898e53			−0.305377
$719$		−	1.00454e54i		−	0.529809i	−0.964275	−	0.264904i	$-0.914660\pi$
$719$		−	1.00454e54i		−	0.529809i	0.964275	−	0.264904i	$-0.0853404\pi$
$720$	6.07677e53	+	5.75604e52i	0.312144	+	0.0295670i
$721$	−2.54860e54			−1.27506
$722$		−	6.63486e53i		−	0.323314i
$723$	−1.33567e54	−	1.46817e54i	−0.633974	−	0.696863i
$724$	−2.25193e54			−1.04117
$725$			1.89558e54i			0.853728i
$726$	−4.99074e53	+	4.54035e53i	−0.218962	+	0.199202i
$727$	9.26127e53			0.395837			0.197919	−	0.980218i	$-0.436582\pi$
$727$	9.26127e53			0.395837			0.197919	+	0.980218i	$0.436582\pi$
$728$			5.99852e53i			0.249775i
$729$	6.89090e53	−	2.36676e54i	0.279546	−	0.960132i
$730$	−3.83198e53			−0.151457
$731$			3.96881e54i			1.52838i
$732$	1.43936e54	+	1.58214e54i	0.540080	+	0.593655i
$733$	1.72136e54			0.629355			0.314678	−	0.949199i	$-0.398104\pi$
$733$	1.72136e54			0.629355			0.314678	+	0.949199i	$0.398104\pi$
$734$		−	7.00193e53i		−	0.249455i
$735$	−5.59409e53	+	5.08925e53i	−0.194209	+	0.176683i
$736$	−2.14774e54			−0.726611
$737$			3.49194e53i			0.115129i
$738$	−2.26127e53	+	2.38727e54i	−0.0726577	+	0.767062i
$739$	1.06435e54			0.333303			0.166652	−	0.986016i	$-0.446704\pi$
$739$	1.06435e54			0.333303			0.166652	+	0.986016i	$0.446704\pi$
$740$		−	5.80582e52i		−	0.0177199i
$741$	−4.63268e53	−	5.09223e53i	−0.137812	−	0.151482i
$742$	1.34090e54			0.388795
$743$		−	4.26412e54i		−	1.20515i	−0.798061	−	0.602577i	$-0.794141\pi$
$743$		−	4.26412e54i		−	1.20515i	0.798061	−	0.602577i	$-0.205859\pi$
$744$	3.73217e54	−	3.39536e54i	1.02820	−	0.935405i
$745$	−5.64195e53			−0.151517
$746$		−	6.61765e53i		−	0.173247i
$747$	3.70091e54	+	3.50558e53i	0.944533	+	0.0894681i
$748$	−2.51751e54			−0.626385
$749$		−	3.40593e54i		−	0.826191i
$750$	1.16852e54	+	1.28444e54i	0.276358	+	0.303772i
$751$	−1.53622e54			−0.354237			−0.177119	−	0.984190i	$-0.556678\pi$
$751$	−1.53622e54			−0.354237			−0.177119	+	0.984190i	$0.556678\pi$
$752$		−	3.13345e54i		−	0.704505i
$753$	−9.46582e53	+	8.61156e53i	−0.207517	+	0.188789i
$754$	1.14920e54			0.245664
$755$		−	1.21755e54i		−	0.253801i
$756$	2.45858e54	−	1.84485e54i	0.499771	−	0.375013i
$757$	−3.98519e54			−0.790000			−0.395000	−	0.918681i	$-0.629255\pi$
$757$	−3.98519e54			−0.790000			−0.395000	+	0.918681i	$0.629255\pi$
$758$			5.49657e53i			0.106262i
$759$	−1.42691e54	−	1.56846e54i	−0.269031	−	0.295719i
$760$	1.17316e54			0.215725
$761$			9.31200e54i			1.67007i	0.550197	+	0.835035i	$0.314552\pi$
$761$			9.31200e54i			1.67007i	−0.550197	+	0.835035i	$0.685448\pi$
$762$	1.87492e54	−	1.70571e54i	0.327972	−	0.298374i
$763$	1.83915e54			0.313798
$764$		−	3.31822e54i		−	0.552244i
$765$	−5.00645e53	+	5.28542e54i	−0.0812761	+	0.858049i
$766$	−3.46214e54			−0.548274
$767$			3.03025e53i			0.0468129i
$768$	−1.37471e54	−	1.51108e54i	−0.207180	−	0.227732i
$769$	5.92466e54			0.871090			0.435545	−	0.900167i	$-0.356556\pi$
$769$	5.92466e54			0.871090			0.435545	+	0.900167i	$0.356556\pi$
$770$		−	7.07391e53i		−	0.101470i
$771$	−8.74798e54	+	7.95851e54i	−1.22426	+	1.11378i
$772$	7.36802e54			1.00606
$773$			5.59994e54i			0.746059i	0.927820	+	0.373029i	$0.121681\pi$
$773$			5.59994e54i			0.746059i	−0.927820	+	0.373029i	$0.878319\pi$
$774$	−3.42264e54	−	3.24200e53i	−0.444922	−	0.0421439i
$775$	−9.11143e54			−1.15572
$776$			9.75938e54i			1.20795i
$777$	−1.47616e53	−	1.62259e53i	−0.0178293	−	0.0195979i
$778$	7.83261e53			0.0923197
$779$		−	7.57326e54i		−	0.871106i
$780$	−1.45395e54	+	1.32274e54i	−0.163212	+	0.148483i
$781$	5.91863e53			0.0648412
$782$		−	4.10566e54i		−	0.438990i
$783$	−7.80002e54	−	1.03949e55i	−0.813996	−	1.08479i
$784$	−2.18128e54			−0.222181
$785$			4.87943e53i			0.0485116i
$786$	−1.04757e54	−	1.15148e54i	−0.101661	−	0.111745i
$787$	1.54068e55			1.45946			0.729728	−	0.683737i	$-0.239647\pi$
$787$	1.54068e55			1.45946			0.729728	+	0.683737i	$0.239647\pi$
$788$		−	2.19306e54i		−	0.202793i
$789$	−1.29023e54	+	1.17379e54i	−0.116467	+	0.105956i
$790$	3.55339e54			0.313132
$791$			5.56471e54i			0.478728i
$792$	4.53844e53	−	4.79132e54i	0.0381178	−	0.402417i
$793$	−5.16782e54			−0.423757
$794$		−	3.27569e54i		−	0.262249i
$795$	6.52538e54	+	7.17269e54i	0.510071	+	0.560669i
$796$	2.51760e54			0.192149
$797$		−	1.08247e55i		−	0.806696i	−0.915047	−	0.403348i	$-0.867846\pi$
$797$		−	1.08247e55i		−	0.806696i	0.915047	−	0.403348i	$-0.132154\pi$
$798$	1.48567e54	−	1.35159e54i	0.108110	−	0.0983538i
$799$	2.72539e55			1.93660
$800$			8.80307e54i			0.610836i
$801$	−1.36258e55	−	1.29066e54i	−0.923300	−	0.0874568i
$802$	−9.29279e54			−0.614940
$803$		−	4.96481e54i		−	0.320854i
$804$	1.90499e54	+	2.09396e54i	0.120234	+	0.132161i
$805$	−5.57591e54			−0.343712
$806$			5.52386e54i			0.332565i
$807$	2.17867e55	−	1.98206e55i	1.28113	−	1.16552i
$808$	1.32193e55			0.759266
$809$			2.04769e54i			0.114880i	0.998349	+	0.0574398i	$0.0182937\pi$
$809$			2.04769e54i			0.114880i	−0.998349	+	0.0574398i	$0.981706\pi$
$810$	−4.51717e54	−	8.63499e53i	−0.247543	−	0.0473202i
$811$	−3.39927e55			−1.81966			−0.909829	−	0.414984i	$-0.863787\pi$
$811$	−3.39927e55			−1.81966			−0.909829	+	0.414984i	$0.863787\pi$
$812$		−	1.62053e55i		−	0.847407i
$813$	8.64993e54	+	9.50798e54i	0.441868	+	0.485700i
$814$	−1.55631e53			−0.00776664
$815$		−	1.02886e55i		−	0.501607i
$816$	−1.13268e55	+	1.03046e55i	−0.539504	+	0.490816i
$817$	1.08578e55			0.505271
$818$			3.80065e54i			0.172801i
$819$	−7.00325e53	+	7.39348e54i	−0.0311104	+	0.328439i
$820$	−2.16234e55			−0.938556
$821$			2.66656e55i			1.13092i	0.824777	+	0.565459i	$0.191301\pi$
$821$			2.66656e55i			1.13092i	−0.824777	+	0.565459i	$0.808699\pi$
$822$	6.32832e54	+	6.95608e54i	0.262255	+	0.288270i
$823$	2.50675e54			0.101511			0.0507555	−	0.998711i	$-0.483837\pi$
$823$	2.50675e54			0.101511			0.0507555	+	0.998711i	$0.483837\pi$
$824$			3.23500e55i			1.28014i
$825$	−6.42875e54	+	5.84858e54i	−0.248600	+	0.226165i
$826$	−8.84080e53			−0.0334095
$827$		−	2.07247e55i		−	0.765391i	−0.923875	−	0.382696i	$-0.874996\pi$
$827$		−	2.07247e55i		−	0.765391i	0.923875	−	0.382696i	$-0.125004\pi$
$828$	−1.71131e55	−	1.62099e54i	−0.617666	−	0.0585066i
$829$	−4.84744e55			−1.70992			−0.854962	−	0.518691i	$-0.826419\pi$
$829$	−4.84744e55			−1.70992			−0.854962	+	0.518691i	$0.826419\pi$
$830$		−	6.93562e54i		−	0.239112i
$831$	2.52911e55	+	2.78000e55i	0.852215	+	0.936753i
$832$	−1.50538e54			−0.0495796
$833$		−	1.89722e55i		−	0.610749i
$834$	−4.08493e54	+	3.71628e54i	−0.128538	+	0.116938i
$835$	7.59118e54			0.233489
$836$			6.88739e54i			0.207079i
$837$	4.99649e55	−	3.74922e55i	1.46853	−	1.10194i
$838$	6.38434e54			0.183434
$839$		−	2.09325e54i		−	0.0587954i	−0.999568	−	0.0293977i	$-0.990641\pi$
$839$		−	2.09325e54i		−	0.0587954i	0.999568	−	0.0293977i	$-0.00935893\pi$
$840$	−8.51665e54	−	9.36148e54i	−0.233863	−	0.257062i
$841$	−3.12662e55			−0.839365
$842$		−	2.14445e55i		−	0.562842i
$843$	4.49153e55	−	4.08618e55i	1.15258	−	1.04856i
$844$	6.05047e55			1.51804
$845$			2.00639e55i			0.492197i
$846$	−2.22629e54	+	2.35034e55i	−0.0534004	+	0.563759i
$847$	−2.29873e55			−0.539141
$848$			2.79682e55i			0.641421i
$849$	−1.39559e55	−	1.53403e55i	−0.312976	−	0.344023i
$850$	−1.68281e55			−0.369043
$851$			1.22674e54i			0.0263083i
$852$	3.54915e54	−	3.22885e54i	0.0744341	−	0.0677167i
$853$	1.63064e55			0.334446			0.167223	−	0.985919i	$-0.446520\pi$
$853$	1.63064e55			0.334446			0.167223	+	0.985919i	$0.446520\pi$
$854$		−	1.50772e55i		−	0.302428i
$855$	1.44598e55	+	1.36966e54i	0.283665	+	0.0268694i
$856$	−4.32322e55			−0.829480
$857$		−	3.59043e55i		−	0.673768i	−0.941546	−	0.336884i	$-0.890627\pi$
$857$		−	3.59043e55i		−	0.673768i	0.941546	−	0.336884i	$-0.109373\pi$
$858$	3.54573e54	+	3.89746e54i	0.0650800	+	0.0715358i
$859$	7.81174e55			1.40242			0.701209	−	0.712955i	$-0.252644\pi$
$859$	7.81174e55			1.40242			0.701209	+	0.712955i	$0.252644\pi$
$860$		−	3.10016e55i		−	0.544394i
$861$	−6.04323e55	+	5.49786e55i	−1.03803	+	0.944351i
$862$	4.31160e55			0.724437
$863$			2.49548e55i			0.410156i	0.978746	+	0.205078i	$0.0657448\pi$
$863$			2.49548e55i			0.410156i	−0.978746	+	0.205078i	$0.934255\pi$
$864$	−3.62233e55	−	4.82740e55i	−0.582408	−	0.776161i
$865$	−4.48242e55			−0.705029
$866$		−	1.84466e55i		−	0.283842i
$867$	−4.49234e55	−	4.93798e55i	−0.676255	−	0.743338i
$868$	7.78936e55			1.14717
$869$			4.60386e55i			0.663355i
$870$	−1.79348e55	+	1.63163e55i	−0.252832	+	0.230015i
$871$	−6.83963e54			−0.0943382
$872$		−	2.33448e55i		−	0.315048i
$873$	−1.13940e55	+	1.20289e56i	−0.150455	+	1.58839i
$874$	−1.12322e55			−0.145127
$875$			5.91609e55i			0.747965i
$876$	−2.70851e55	−	2.97718e55i	−0.335082	−	0.368322i
$877$	7.79885e54			0.0944145			0.0472072	−	0.998885i	$-0.484968\pi$
$877$	7.79885e54			0.0944145			0.0472072	+	0.998885i	$0.484968\pi$
$878$			1.21874e55i			0.144383i
$879$	−2.43901e55	+	2.21890e55i	−0.282764	+	0.257246i
$880$	1.47546e55			0.167401
$881$			1.37266e56i			1.52413i	0.647501	+	0.762065i	$0.275814\pi$
$881$			1.37266e56i			1.52413i	−0.647501	+	0.762065i	$0.724186\pi$
$882$	1.63614e55	+	1.54978e54i	0.177794	+	0.0168410i
$883$	−1.49520e56			−1.59018			−0.795089	−	0.606493i	$-0.792576\pi$
$883$	−1.49520e56			−1.59018			−0.795089	+	0.606493i	$0.792576\pi$
$884$		−	4.93103e55i		−	0.513268i
$885$	−4.30231e54	−	4.72909e54i	−0.0438308	−	0.0481788i
$886$	5.30353e55			0.528840
$887$		−	4.52939e55i		−	0.442070i	−0.975266	−	0.221035i	$-0.929057\pi$
$887$		−	4.52939e55i		−	0.442070i	0.975266	−	0.221035i	$-0.0709434\pi$
$888$	−2.05960e54	+	1.87373e54i	−0.0196760	+	0.0179003i
$889$	8.63583e55			0.807552
$890$			2.55351e55i			0.233737i
$891$	1.11877e55	−	5.85255e55i	0.100245	−	0.524408i
$892$	2.15864e55			0.189342
$893$		−	7.45611e55i		−	0.640228i
$894$	8.25068e54	+	9.06913e54i	0.0693549	+	0.0762347i
$895$	1.39976e56			1.15190
$896$		−	9.52199e55i		−	0.767142i
$897$	3.07212e55	−	2.79488e55i	0.242316	−	0.220448i
$898$	4.25839e54			0.0328848
$899$		−	3.29334e56i		−	2.49002i
$900$	−6.64408e54	+	7.01429e55i	−0.0491844	+	0.519249i
$901$	−2.43260e56			−1.76319
$902$			5.79638e55i			0.411370i
$903$	−7.88232e55	−	8.66423e55i	−0.547756	−	0.602092i
$904$	7.06341e55			0.480634
$905$			1.14794e56i			0.764884i
$906$	−1.95714e55	+	1.78051e55i	−0.127698	+	0.116174i
$907$	1.77666e56			1.13518			0.567591	−	0.823311i	$-0.307876\pi$
$907$	1.77666e56			1.13518			0.567591	+	0.823311i	$0.307876\pi$
$908$			1.14029e56i			0.713487i
$909$	1.62935e56	+	1.54335e55i	0.998390	+	0.0945695i
$910$	1.38556e55			0.0831455
$911$			2.11287e56i			1.24172i	0.783922	+	0.620860i	$0.213216\pi$
$911$			2.11287e56i			1.24172i	−0.783922	+	0.620860i	$0.786784\pi$
$912$	2.81913e55	+	3.09878e55i	0.162261	+	0.178357i
$913$	8.98595e55			0.506546
$914$		−	3.64830e55i		−	0.201425i
$915$	8.06506e55	−	7.33722e55i	0.436121	−	0.396763i
$916$	−1.61237e56			−0.853988
$917$		−	5.30371e55i		−	0.275145i
$918$	9.22815e55	−	6.92453e55i	0.468925	−	0.351868i
$919$	−2.67937e56			−1.33364			−0.666820	−	0.745219i	$-0.732345\pi$
$919$	−2.67937e56			−1.33364			−0.666820	+	0.745219i	$0.732345\pi$
$920$			7.07764e55i			0.345080i
$921$	−5.80574e55	−	6.38166e55i	−0.277284	−	0.304790i
$922$	−9.54421e55			−0.446532
$923$			1.15928e55i			0.0531318i
$924$	5.49593e55	−	4.99995e55i	0.246760	−	0.224490i
$925$	5.02814e54			0.0221164
$926$			7.78631e55i			0.335523i
$927$	−3.77685e55	+	3.98730e56i	−0.159447	+	1.68331i
$928$	−3.18188e56			−1.31605
$929$		−	1.54432e56i		−	0.625806i	−0.949785	−	0.312903i	$-0.898699\pi$
$929$		−	1.54432e56i		−	0.625806i	0.949785	−	0.312903i	$-0.101301\pi$
$930$	−7.84272e55	−	8.62070e55i	−0.311380	−	0.342268i
$931$	−5.19041e55			−0.201910
$932$			1.21952e56i			0.464823i
$933$	1.42628e56	−	1.29756e56i	0.532663	−	0.484593i
$934$	−1.52584e56			−0.558364
$935$			1.28332e56i			0.460165i
$936$	9.38472e55	+	8.88940e54i	0.329746	+	0.0312343i
$937$	5.97214e55			0.205626			0.102813	−	0.994701i	$-0.467216\pi$
$937$	5.97214e55			0.205626			0.102813	+	0.994701i	$0.467216\pi$
$938$		−	1.99547e55i		−	0.0673274i
$939$	1.08930e56	+	1.19735e56i	0.360164	+	0.395891i
$940$	−2.12889e56			−0.689801
$941$		−	3.95301e55i		−	0.125523i	−0.998029	−	0.0627617i	$-0.980009\pi$
$941$		−	3.95301e55i		−	0.125523i	0.998029	−	0.0627617i	$-0.0199908\pi$
$942$	7.84342e54	−	7.13559e54i	0.0244084	−	0.0222056i
$943$	4.56892e56			1.39345
$944$		−	1.84400e55i		−	0.0551179i
$945$	−9.40424e55	−	1.25328e56i	−0.275499	−	0.367150i
$946$	−8.31031e55			−0.238608
$947$		−	7.30872e55i		−	0.205680i	−0.994698	−	0.102840i	$-0.967207\pi$
$947$		−	7.30872e55i		−	0.205680i	0.994698	−	0.102840i	$-0.0327929\pi$
$948$	2.51159e56	+	2.76074e56i	0.692772	+	0.761494i
$949$	9.72453e55			0.262912
$950$			4.60383e55i			0.122003i
$951$	−1.41402e56	+	1.28641e56i	−0.367305	+	0.334157i
$952$	3.17492e56			0.808409
$953$		−	7.24647e56i		−	1.80868i	−0.426815	−	0.904339i	$-0.640365\pi$
$953$		−	7.24647e56i		−	1.80868i	0.426815	−	0.904339i	$-0.359635\pi$
$954$	1.98712e55	−	2.09784e56i	0.0486188	−	0.513279i
$955$	−1.69149e56			−0.405699
$956$		−	1.86794e56i		−	0.439202i
$957$	−2.11398e56	−	2.32368e56i	−0.487274	−	0.535611i
$958$	2.24202e56			0.506633
$959$			3.20396e56i			0.709795i
$960$	2.34934e55	−	2.13732e55i	0.0510261	−	0.0464212i
$961$	1.11338e57			2.37083
$962$		−	3.04834e54i		−	0.00636410i
$963$	−5.32859e56	−	5.04735e55i	−1.09072	−	0.103315i
$964$	−3.88945e56			−0.780592
$965$		−	3.75590e56i		−	0.739086i
$966$	8.15411e55	+	8.96298e55i	0.157330	+	0.172937i
$967$	−1.74722e56			−0.330555			−0.165278	−	0.986247i	$-0.552852\pi$
$967$	−1.74722e56			−0.330555			−0.165278	+	0.986247i	$0.552852\pi$
$968$			2.91783e56i			0.541287i
$969$	−2.69524e56	+	2.45200e56i	−0.490281	+	0.446035i
$970$	2.25426e56			0.402106
$971$			1.30628e56i			0.228492i	0.993452	+	0.114246i	$0.0364453\pi$
$971$			1.30628e56i			0.228492i	−0.993452	+	0.114246i	$0.963555\pi$
$972$	−2.52193e56	−	4.11986e56i	−0.432587	−	0.706681i
$973$	−1.88151e56			−0.316492
$974$			2.10652e56i			0.347492i
$975$	−1.14556e56	−	1.25919e56i	−0.185323	−	0.203706i
$976$	3.14478e56			0.498935
$977$			6.53462e56i			1.01677i	0.861129	+	0.508386i	$0.169758\pi$
$977$			6.53462e56i			1.01677i	−0.861129	+	0.508386i	$0.830242\pi$
$978$	−1.65384e56	+	1.50459e56i	−0.252381	+	0.229604i
$979$	−3.30838e56			−0.495159
$980$			1.48198e56i			0.217544i
$981$	2.72549e55	−	2.87736e56i	0.0392404	−	0.414269i
$982$	−2.88454e56			−0.407342
$983$			7.04214e56i			0.975411i	0.873008	+	0.487706i	$0.162166\pi$
$983$			7.04214e56i			0.975411i	−0.873008	+	0.487706i	$0.837834\pi$
$984$	6.97856e56	+	7.67082e56i	0.948111	+	1.04216i
$985$	−1.11793e56			−0.148979
$986$		−	6.08256e56i		−	0.795106i
$987$	−5.94975e56	+	5.41281e56i	−0.762909	+	0.694060i
$988$	−1.34903e56			−0.169683
$989$			6.55049e56i			0.808248i
$990$	−1.10672e56	−	1.04830e55i	−0.133958	−	0.0126887i
$991$	−3.10495e56			−0.368684			−0.184342	−	0.982862i	$-0.559015\pi$
$991$	−3.10495e56			−0.368684			−0.184342	+	0.982862i	$0.559015\pi$
$992$		−	1.52943e57i		−	1.78159i
$993$	−4.22227e56	−	4.64111e56i	−0.482514	−	0.530379i
$994$	−3.38221e55			−0.0379192
$995$		−	1.28337e56i		−	0.141160i
$996$	5.38849e56	−	4.90220e56i	0.581486	−	0.529010i
$997$	9.36970e56			0.992013			0.496007	−	0.868319i	$-0.334799\pi$
$997$	9.36970e56			0.992013			0.496007	+	0.868319i	$0.334799\pi$
$998$			2.48002e56i			0.257618i
$999$	−2.75731e55	+	2.06900e55i	−0.0281023	+	0.0210871i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.39.b.a.2.7	yes	12
3.2	odd	2	inner	3.39.b.a.2.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.39.b.a.2.6	✓	12	3.2	odd	2	inner
3.39.b.a.2.7	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)

\(f(q)\)	\(=\)	\(q+217076. i q^{2} +(7.82134e8 + 8.59720e8i) q^{3} +2.27756e11 q^{4} -1.16100e13i q^{5} +(-1.86625e14 + 1.69783e14i) q^{6} -8.59590e15 q^{7} +1.09110e17i q^{8} +(-1.27385e17 + 1.34483e18i) q^{9} +O(q^{10})\)	\(q+217076. i q^{2} +(7.82134e8 + 8.59720e8i) q^{3} +2.27756e11 q^{4} -1.16100e13i q^{5} +(-1.86625e14 + 1.69783e14i) q^{6} -8.59590e15 q^{7} +1.09110e17i q^{8} +(-1.27385e17 + 1.34483e18i) q^{9} +2.52026e18 q^{10} +3.26530e19i q^{11} +(1.78136e20 + 1.95806e20i) q^{12} -6.39572e20 q^{13} -1.86596e21i q^{14} +(9.98136e21 - 9.08058e21i) q^{15} +3.89199e22 q^{16} +3.38515e23i q^{17} +(-2.91931e23 - 2.76523e22i) q^{18} +9.26108e23 q^{19} -2.64425e24i q^{20} +(-6.72314e24 - 7.39006e24i) q^{21} -7.08819e24 q^{22} +5.58717e25i q^{23} +(-9.38039e25 + 8.53384e25i) q^{24} +2.29005e26 q^{25} -1.38836e26i q^{26} +(-1.25581e27 + 9.42323e26i) q^{27} -1.95777e27 q^{28} +8.27744e27i q^{29} +(1.97118e27 + 2.16671e27i) q^{30} -3.97870e28 q^{31} +3.84405e28i q^{32} +(-2.80725e28 + 2.55390e28i) q^{33} -7.34836e28 q^{34} +9.97985e28i q^{35} +(-2.90127e28 + 3.06293e29i) q^{36} +2.19564e28 q^{37} +2.01036e29i q^{38} +(-5.00231e29 - 5.49853e29i) q^{39} +1.26677e30 q^{40} -8.17751e30i q^{41} +(1.60421e30 - 1.45943e30i) q^{42} +1.17242e31 q^{43} +7.43692e30i q^{44} +(1.56135e31 + 1.47894e30i) q^{45} -1.21284e31 q^{46} -8.05102e31i q^{47} +(3.04406e31 + 3.34603e31i) q^{48} -5.60454e31 q^{49} +4.97116e31i q^{50} +(-2.91028e32 + 2.64764e32i) q^{51} -1.45666e32 q^{52} +7.18608e32i q^{53} +(-2.04556e32 - 2.72607e32i) q^{54} +3.79102e32 q^{55} -9.37896e32i q^{56} +(7.24340e32 + 7.96194e32i) q^{57} -1.79683e33 q^{58} -4.73793e32i q^{59} +(2.27331e33 - 2.06816e33i) q^{60} +8.08012e33 q^{61} -8.63680e33i q^{62} +(1.09499e33 - 1.15600e34i) q^{63} +2.35373e33 q^{64} +7.42544e33i q^{65} +(-5.54391e33 - 6.09386e33i) q^{66} +1.06941e34 q^{67} +7.70989e34i q^{68} +(-4.80341e34 + 4.36992e34i) q^{69} -2.16639e34 q^{70} -1.81258e34i q^{71} +(-1.46734e35 - 1.38990e34i) q^{72} -1.52047e35 q^{73} +4.76621e33i q^{74} +(1.79113e35 + 1.96881e35i) q^{75} +2.10927e35 q^{76} -2.80682e35i q^{77} +(1.19360e35 - 1.08588e35i) q^{78} +1.40993e36 q^{79} -4.51861e35i q^{80} +(-1.79235e36 - 3.42624e35i) q^{81} +1.77514e36 q^{82} -2.75195e36i q^{83} +(-1.53123e36 - 1.68313e36i) q^{84} +3.93017e36 q^{85} +2.54504e36i q^{86} +(-7.11628e36 + 6.47406e36i) q^{87} -3.56276e36 q^{88} +1.01319e37i q^{89} +(-3.21043e35 + 3.38932e36i) q^{90} +5.49770e36 q^{91} +1.27251e37i q^{92} +(-3.11187e37 - 3.42056e37i) q^{93} +1.74768e37 q^{94} -1.07521e37i q^{95} +(-3.30480e37 + 3.00656e37i) q^{96} +8.94455e37 q^{97} -1.21661e37i q^{98} +(-4.39128e37 - 4.15951e36i) 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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