LMFDB - Embedded newform 3.39.b.a.2.12

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			2.12
Root			$81459.4i$ of defining polynomial
Character	$\chi$	$=$	3.2
Dual form			3.39.b.a.2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+977513. i q^{2} +(-4.43499e8 + 1.07432e9i) q^{3} -6.80653e11 q^{4} -1.94075e13i q^{5} +(-1.05016e15 - 4.33526e14i) q^{6} -1.85443e15 q^{7} -3.96650e17i q^{8} +(-9.57469e17 - 9.52919e17i) q^{9} +O(q^{10})$	\(q+977513. i q^{2} +(-4.43499e8 + 1.07432e9i) q^{3} -6.80653e11 q^{4} -1.94075e13i q^{5} +(-1.05016e15 - 4.33526e14i) q^{6} -1.85443e15 q^{7} -3.96650e17i q^{8} +(-9.57469e17 - 9.52919e17i) q^{9} +1.89711e19 q^{10} +1.00331e20i q^{11} +(3.01869e20 - 7.31238e20i) q^{12} +5.34879e20 q^{13} -1.81273e21i q^{14} +(2.08499e22 + 8.60722e21i) q^{15} +2.00634e23 q^{16} -2.93124e23i q^{17} +(9.31490e23 - 9.35938e23i) q^{18} -2.13221e24 q^{19} +1.32098e25i q^{20} +(8.22439e23 - 1.99225e24i) q^{21} -9.80751e25 q^{22} -6.81549e25i q^{23} +(4.26128e26 + 1.75914e26i) q^{24} -1.28546e25 q^{25} +5.22851e26i q^{26} +(1.44837e27 - 6.06008e26i) q^{27} +1.26222e27 q^{28} +4.43183e27i q^{29} +(-8.41367e27 + 2.03810e28i) q^{30} +9.20206e27 q^{31} +8.70919e28i q^{32} +(-1.07788e29 - 4.44969e28i) q^{33} +2.86533e29 q^{34} +3.59900e28i q^{35} +(6.51704e29 + 6.48607e29i) q^{36} -1.71160e29 q^{37} -2.08426e30i q^{38} +(-2.37219e29 + 5.74631e29i) q^{39} -7.69800e30 q^{40} +3.25222e30i q^{41} +(1.94745e30 + 8.03944e29i) q^{42} +9.05664e30 q^{43} -6.82908e31i q^{44} +(-1.84938e31 + 1.85821e31i) q^{45} +6.66223e31 q^{46} -4.90800e31i q^{47} +(-8.89810e31 + 2.15545e32i) q^{48} -1.26496e32 q^{49} -1.25655e31i q^{50} +(3.14909e32 + 1.30000e32i) q^{51} -3.64067e32 q^{52} -3.19951e32i q^{53} +(5.92380e32 + 1.41580e33i) q^{54} +1.94718e33 q^{55} +7.35561e32i q^{56} +(9.45632e32 - 2.29067e33i) q^{57} -4.33217e33 q^{58} -2.55619e33i q^{59} +(-1.41915e34 - 5.85853e33i) q^{60} +1.24839e34 q^{61} +8.99513e33i q^{62} +(1.77556e33 + 1.76712e33i) q^{63} -2.99835e34 q^{64} -1.03807e34i q^{65} +(4.34962e34 - 1.05364e35i) q^{66} +4.69883e34 q^{67} +1.99516e35i q^{68} +(7.32201e34 + 3.02266e34i) q^{69} -3.51806e34 q^{70} -1.03720e35i q^{71} +(-3.77975e35 + 3.79780e35i) q^{72} -1.12163e35 q^{73} -1.67311e35i q^{74} +(5.70100e33 - 1.38099e34i) q^{75} +1.45129e36 q^{76} -1.86058e35i q^{77} +(-5.61709e35 - 2.31884e35i) q^{78} +5.18105e34 q^{79} -3.89381e36i q^{80} +(8.69280e33 + 1.82478e36i) q^{81} -3.17908e36 q^{82} -1.87566e35i q^{83} +(-5.59795e35 + 1.35603e36i) q^{84} -5.68882e36 q^{85} +8.85298e36i q^{86} +(-4.76120e36 - 1.96551e36i) q^{87} +3.97964e37 q^{88} -4.77590e36i q^{89} +(-1.81642e37 - 1.80779e37i) q^{90} -9.91898e35 q^{91} +4.63898e37i q^{92} +(-4.08111e36 + 9.88595e36i) q^{93} +4.79763e37 q^{94} +4.13809e37i q^{95} +(-9.35644e37 - 3.86252e37i) q^{96} -7.67399e37 q^{97} -1.23651e38i q^{98} +(9.56076e37 - 9.60641e37i) 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 $

$2$			977513.i			1.86446i	0.361870	+	0.932229i	$0.382138\pi$
$2$			977513.i			1.86446i	−0.361870	+	0.932229i	$0.617862\pi$
$3$	−4.43499e8	+	1.07432e9i	−0.381583	+	0.924335i
$3$	−4.43499e8	+	1.07432e9i	−0.381583	+	0.924335i
$4$	−6.80653e11			−2.47620
$5$		−	1.94075e13i		−	1.01751i	−0.860910	−	0.508757i	$-0.830105\pi$
$5$		−	1.94075e13i		−	1.01751i	0.860910	−	0.508757i	$-0.169895\pi$
$6$	−1.05016e15	−	4.33526e14i	−1.72338	−	0.711445i
$7$	−1.85443e15			−0.162685			−0.0813426	−	0.996686i	$-0.525921\pi$
$7$	−1.85443e15			−0.162685			−0.0813426	+	0.996686i	$0.525921\pi$
$8$		−	3.96650e17i		−	2.75231i
$9$	−9.57469e17	−	9.52919e17i	−0.708789	−	0.705421i
$10$	1.89711e19			1.89711
$11$			1.00331e20i			1.64050i	0.572007	+	0.820249i	$0.306165\pi$
$11$			1.00331e20i			1.64050i	−0.572007	+	0.820249i	$0.693835\pi$
$12$	3.01869e20	−	7.31238e20i	0.944876	−	2.28884i
$13$	5.34879e20			0.365875			0.182937	−	0.983125i	$-0.441439\pi$
$13$	5.34879e20			0.365875			0.182937	+	0.983125i	$0.441439\pi$
$14$		−	1.81273e21i		−	0.303320i
$15$	2.08499e22	+	8.60722e21i	0.940523	+	0.388266i
$16$	2.00634e23			2.65537
$17$		−	2.93124e23i		−	1.22609i	−0.790048	−	0.613045i	$-0.789944\pi$
$17$		−	2.93124e23i		−	1.22609i	0.790048	−	0.613045i	$-0.210056\pi$
$18$	9.31490e23	−	9.35938e23i	1.31523	−	1.32151i
$19$	−2.13221e24			−1.07773			−0.538866	−	0.842391i	$-0.681147\pi$
$19$	−2.13221e24			−1.07773			−0.538866	+	0.842391i	$0.681147\pi$
$20$			1.32098e25i			2.51957i
$21$	8.22439e23	−	1.99225e24i	0.0620779	−	0.150376i
$22$	−9.80751e25			−3.05864
$23$		−	6.81549e25i		−	0.913416i	−0.889617	−	0.456708i	$-0.849029\pi$
$23$		−	6.81549e25i		−	0.913416i	0.889617	−	0.456708i	$-0.150971\pi$
$24$	4.26128e26	+	1.75914e26i	2.54406	+	1.05024i
$25$	−1.28546e25			−0.0353344
$26$			5.22851e26i			0.682157i
$27$	1.44837e27	−	6.06008e26i	0.922506	−	0.385982i
$28$	1.26222e27			0.402841
$29$			4.43183e27i			0.726141i	0.931762	+	0.363071i	$0.118272\pi$
$29$			4.43183e27i			0.726141i	−0.931762	+	0.363071i	$0.881728\pi$
$30$	−8.41367e27	+	2.03810e28i	−0.723905	+	1.75357i
$31$	9.20206e27			0.424632			0.212316	−	0.977201i	$-0.431899\pi$
$31$	9.20206e27			0.424632			0.212316	+	0.977201i	$0.431899\pi$
$32$			8.70919e28i			2.19851i
$33$	−1.07788e29	−	4.44969e28i	−1.51637	−	0.625986i
$34$	2.86533e29			2.28599
$35$			3.59900e28i			0.165535i
$36$	6.51704e29	+	6.48607e29i	1.75510	+	1.74676i
$37$	−1.71160e29			−0.273886			−0.136943	−	0.990579i	$-0.543728\pi$
$37$	−1.71160e29			−0.273886			−0.136943	+	0.990579i	$0.543728\pi$
$38$		−	2.08426e30i		−	2.00939i
$39$	−2.37219e29	+	5.74631e29i	−0.139611	+	0.338190i
$40$	−7.69800e30			−2.80052
$41$			3.25222e30i			0.740093i	0.929013	+	0.370046i	$0.120658\pi$
$41$			3.25222e30i			0.740093i	−0.929013	+	0.370046i	$0.879342\pi$
$42$	1.94745e30	+	8.03944e29i	0.280369	+	0.115742i
$43$	9.05664e30			0.833809			0.416904	−	0.908950i	$-0.363115\pi$
$43$	9.05664e30			0.833809			0.416904	+	0.908950i	$0.363115\pi$
$44$		−	6.82908e31i		−	4.06220i
$45$	−1.84938e31	+	1.85821e31i	−0.717775	+	0.721203i
$46$	6.66223e31			1.70302
$47$		−	4.90800e31i		−	0.833769i	−0.908960	−	0.416884i	$-0.863122\pi$
$47$		−	4.90800e31i		−	0.833769i	0.908960	−	0.416884i	$-0.136878\pi$
$48$	−8.89810e31	+	2.15545e32i	−1.01324	+	2.45445i
$49$	−1.26496e32			−0.973534
$50$		−	1.25655e31i		−	0.0658795i
$51$	3.14909e32	+	1.30000e32i	1.13332	+	0.467855i
$52$	−3.64067e32			−0.905979
$53$		−	3.19951e32i		−	0.554425i	−0.960809	−	0.277212i	$-0.910589\pi$
$53$		−	3.19951e32i		−	0.554425i	0.960809	−	0.277212i	$-0.0894105\pi$
$54$	5.92380e32	+	1.41580e33i	0.719647	+	1.71997i
$55$	1.94718e33			1.66923
$56$			7.35561e32i			0.447761i
$57$	9.45632e32	−	2.29067e33i	0.411244	−	0.996186i
$58$	−4.33217e33			−1.35386
$59$		−	2.55619e33i		−	0.577304i	−0.957434	−	0.288652i	$-0.906793\pi$
$59$		−	2.55619e33i		−	0.577304i	0.957434	−	0.288652i	$-0.0932071\pi$
$60$	−1.41915e34	−	5.85853e33i	−2.32892	−	0.961424i
$61$	1.24839e34			1.49653			0.748263	−	0.663403i	$-0.230888\pi$
$61$	1.24839e34			1.49653			0.748263	+	0.663403i	$0.230888\pi$
$62$			8.99513e33i			0.791709i
$63$	1.77556e33	+	1.76712e33i	0.115310	+	0.114762i
$64$	−2.99835e34			−1.44366
$65$		−	1.03807e34i		−	0.372282i
$66$	4.34962e34	−	1.05364e35i	1.16712	−	2.82720i
$67$	4.69883e34			0.947476			0.473738	−	0.880666i	$-0.342904\pi$
$67$	4.69883e34			0.947476			0.473738	+	0.880666i	$0.342904\pi$
$68$			1.99516e35i			3.03605i
$69$	7.32201e34	+	3.02266e34i	0.844302	+	0.348544i
$70$	−3.51806e34			−0.308632
$71$		−	1.03720e35i		−	0.694949i	−0.937689	−	0.347475i	$-0.887039\pi$
$71$		−	1.03720e35i		−	0.694949i	0.937689	−	0.347475i	$-0.112961\pi$
$72$	−3.77975e35	+	3.79780e35i	−1.94154	+	1.95081i
$73$	−1.12163e35			−0.443317			−0.221659	−	0.975124i	$-0.571147\pi$
$73$	−1.12163e35			−0.443317			−0.221659	+	0.975124i	$0.571147\pi$
$74$		−	1.67311e35i		−	0.510649i
$75$	5.70100e33	−	1.38099e34i	0.0134830	−	0.0326608i
$76$	1.45129e36			2.66868
$77$		−	1.86058e35i		−	0.266885i
$78$	−5.61709e35	−	2.31884e35i	−0.630542	−	0.260300i
$79$	5.18105e34			0.0456565			0.0228283	−	0.999739i	$-0.492733\pi$
$79$	5.18105e34			0.0456565			0.0228283	+	0.999739i	$0.492733\pi$
$80$		−	3.89381e36i		−	2.70187i
$81$	8.69280e33	+	1.82478e36i	0.00476370	+	0.999989i
$82$	−3.17908e36			−1.37987
$83$		−	1.87566e35i		−	0.0646652i	−0.999477	−	0.0323326i	$-0.989706\pi$
$83$		−	1.87566e35i		−	0.0646652i	0.999477	−	0.0323326i	$-0.0102936\pi$
$84$	−5.59795e35	+	1.35603e36i	−0.153717	+	0.372360i
$85$	−5.68882e36			−1.24756
$86$			8.85298e36i			1.55460i
$87$	−4.76120e36	−	1.96551e36i	−0.671197	−	0.277083i
$88$	3.97964e37			4.51516
$89$		−	4.77590e36i		−	0.437164i	−0.975819	−	0.218582i	$-0.929857\pi$
$89$		−	4.77590e36i		−	0.437164i	0.975819	−	0.218582i	$-0.0701432\pi$
$90$	−1.81642e37	−	1.80779e37i	−1.34465	−	1.33826i
$91$	−9.91898e35			−0.0595224
$92$			4.63898e37i			2.26180i
$93$	−4.08111e36	+	9.88595e36i	−0.162032	+	0.392502i
$94$	4.79763e37			1.55453
$95$			4.13809e37i			1.09661i
$96$	−9.35644e37	−	3.86252e37i	−2.03216	−	0.838913i
$97$	−7.67399e37			−1.36886			−0.684428	−	0.729080i	$-0.739948\pi$
$97$	−7.67399e37			−1.36886			−0.684428	+	0.729080i	$0.739948\pi$
$98$		−	1.23651e38i		−	1.81511i
$99$	9.56076e37	−	9.60641e37i	1.15724	−	1.16277i
$100$	8.74951e36			0.0874951
$101$		−	4.54349e37i		−	0.376083i	−0.982161	−	0.188041i	$-0.939786\pi$
$101$		−	4.54349e37i		−	0.376083i	0.982161	−	0.188041i	$-0.0602139\pi$
$102$	−1.27077e38	+	3.07828e38i	−0.872296	+	2.11302i
$103$	2.67470e38			1.52535			0.762673	−	0.646785i	$-0.223887\pi$
$103$	2.67470e38			1.52535			0.762673	+	0.646785i	$0.223887\pi$
$104$		−	2.12160e38i		−	1.00700i
$105$	−3.86647e37	−	1.59615e37i	−0.153009	−	0.0631651i
$106$	3.12756e38			1.03370
$107$		−	5.88759e38i		−	1.62797i	−0.580887	−	0.813984i	$-0.697294\pi$
$107$		−	5.88759e38i		−	1.62797i	0.580887	−	0.813984i	$-0.302706\pi$
$108$	−9.85840e38	+	4.12481e38i	−2.28431	+	0.955768i
$109$	3.21551e38			0.625383			0.312691	−	0.949855i	$-0.398769\pi$
$109$	3.21551e38			0.625383			0.312691	+	0.949855i	$0.398769\pi$
$110$			1.90340e39i			3.11221i
$111$	7.59094e37	−	1.83881e38i	0.104510	−	0.253163i
$112$	−3.72062e38			−0.431989
$113$		−	8.86717e37i		−	0.0869550i	−0.999054	−	0.0434775i	$-0.986156\pi$
$113$		−	8.86717e37i		−	0.0869550i	0.999054	−	0.0434775i	$-0.0138437\pi$
$114$	2.23916e39	+	9.24367e38i	1.85735	+	0.766748i
$115$	−1.32272e39			−0.929413
$116$		−	3.01654e39i		−	1.79807i
$117$	−5.12130e38	−	5.09696e38i	−0.259328	−	0.258095i
$118$	2.49871e39			1.07636
$119$			5.43579e38i			0.199467i
$120$	3.41406e39	−	8.27010e39i	1.06863	−	2.58861i
$121$	−6.32594e39			−1.69123
$122$			1.22032e40i			2.79021i
$123$	−3.49392e39	−	1.44236e39i	−0.684094	−	0.282407i
$124$	−6.26341e39			−1.05147
$125$		−	6.81094e39i		−	0.981561i
$126$	−1.72738e39	+	1.73563e39i	−0.213968	+	0.214990i
$127$	3.29072e39			0.350768			0.175384	−	0.984500i	$-0.443883\pi$
$127$	3.29072e39			0.350768			0.175384	+	0.984500i	$0.443883\pi$
$128$		−	5.36966e39i		−	0.493125i
$129$	−4.01661e39	+	9.72972e39i	−0.318167	+	0.770718i
$130$	1.01473e40			0.694105
$131$		−	1.52248e40i		−	0.900322i	−0.892947	−	0.450161i	$-0.851367\pi$
$131$		−	1.52248e40i		−	0.900322i	0.892947	−	0.450161i	$-0.148633\pi$
$132$	7.33661e40	+	3.02869e40i	3.75483	+	1.55007i
$133$	3.95404e39			0.175331
$134$			4.59316e40i			1.76653i
$135$	−1.17611e40	−	2.81094e40i	−0.392742	−	0.938663i
$136$	−1.16268e41			−3.37458
$137$		−	7.34845e40i		−	1.85569i	−0.372969	−	0.927844i	$-0.621660\pi$
$137$		−	7.34845e40i		−	1.85569i	0.372969	−	0.927844i	$-0.378340\pi$
$138$	−2.95469e40	+	7.15736e40i	−0.649845	+	1.57416i
$139$	6.07971e38			0.0116574			0.00582870	−	0.999983i	$-0.498145\pi$
$139$	6.07971e38			0.0116574			0.00582870	+	0.999983i	$0.498145\pi$
$140$		−	2.44967e40i		−	0.409897i
$141$	5.27276e40	+	2.17669e40i	0.770681	+	0.318152i
$142$	1.01387e41			1.29570
$143$			5.36652e40i			0.600216i
$144$	−1.92101e41	−	1.91188e41i	−1.88210	−	1.87315i
$145$	8.60109e40			0.738859
$146$		−	1.09641e41i		−	0.826546i
$147$	5.61008e40	−	1.35897e41i	0.371484	−	0.899871i
$148$	1.16501e41			0.678197
$149$			1.48174e40i			0.0758983i	0.999280	+	0.0379491i	$0.0120825\pi$
$149$			1.48174e40i			0.0758983i	−0.999280	+	0.0379491i	$0.987918\pi$
$150$	1.34994e40	+	5.57280e39i	0.0608947	+	0.0251385i
$151$	−1.38443e41			−0.550438			−0.275219	−	0.961382i	$-0.588750\pi$
$151$	−1.38443e41			−0.550438			−0.275219	+	0.961382i	$0.588750\pi$
$152$			8.45740e41i			2.96626i
$153$	−2.79324e41	+	2.80658e41i	−0.864910	+	0.869040i
$154$	1.81874e41			0.497595
$155$		−	1.78589e41i		−	0.432069i
$156$	1.61463e41	−	3.91124e41i	0.345706	−	0.837427i
$157$	−7.44067e41			−1.41097			−0.705486	−	0.708723i	$-0.749271\pi$
$157$	−7.44067e41			−1.41097			−0.705486	+	0.708723i	$0.749271\pi$
$158$			5.06454e40i			0.0851247i
$159$	3.43730e41	+	1.41898e41i	0.512474	+	0.211559i
$160$	1.69024e42			2.23701
$161$			1.26389e41i			0.148599i
$162$	−1.78374e42	+	8.49732e39i	−1.86444	+	0.00888171i
$163$	1.76036e42			1.63695			0.818477	−	0.574539i	$-0.194819\pi$
$163$	1.76036e42			1.63695			0.818477	+	0.574539i	$0.194819\pi$
$164$		−	2.21363e42i		−	1.83262i
$165$	−8.63574e41	+	2.09190e42i	−0.636949	+	1.54293i
$166$	1.83348e41			0.120566
$167$		−	1.17329e42i		−	0.688321i	−0.938911	−	0.344161i	$-0.888164\pi$
$167$		−	1.17329e42i		−	0.688321i	0.938911	−	0.344161i	$-0.111836\pi$
$168$	−7.90226e41	−	3.26220e41i	−0.413881	−	0.170858i
$169$	−1.85111e42			−0.866136
$170$		−	5.56090e42i		−	2.32603i
$171$	2.04152e42	+	2.03182e42i	0.763885	+	0.760255i
$172$	−6.16443e42			−2.06468
$173$			3.20663e42i			0.961995i	0.876722	+	0.480998i	$0.159725\pi$
$173$			3.20663e42i			0.961995i	−0.876722	+	0.480998i	$0.840275\pi$
$174$	1.92131e42	−	4.65413e42i	0.516609	−	1.25142i
$175$	2.38380e40			0.00574839
$176$			2.01299e43i			4.35612i
$177$	2.74616e42	+	1.13367e42i	0.533622	+	0.220289i
$178$	4.66850e42			0.815074
$179$		−	1.08485e43i		−	1.70280i	−0.524520	−	0.851398i	$-0.675755\pi$
$179$		−	1.08485e43i		−	1.70280i	0.524520	−	0.851398i	$-0.324245\pi$
$180$	1.25879e43	−	1.26480e43i	1.77736	−	1.78584i
$181$	7.21699e42			0.917199			0.458599	−	0.888643i	$-0.348351\pi$
$181$	7.21699e42			0.917199			0.458599	+	0.888643i	$0.348351\pi$
$182$		−	9.69592e41i		−	0.110977i
$183$	−5.53661e42	+	1.34117e43i	−0.571048	+	1.38329i
$184$	−2.70337e43			−2.51400
$185$			3.32180e42i			0.278683i
$186$	−9.66364e42	−	3.98933e42i	−0.731804	−	0.302102i
$187$	2.94096e43			2.01140
$188$			3.34065e43i			2.06458i
$189$	−2.68591e42	+	1.12380e42i	−0.150078	+	0.0627936i
$190$	−4.04504e43			−2.04458
$191$		−	2.14694e43i		−	0.982168i	−0.871112	−	0.491084i	$-0.836601\pi$
$191$		−	2.14694e43i		−	0.982168i	0.871112	−	0.491084i	$-0.163399\pi$
$192$	1.32977e43	−	3.22119e43i	0.550874	−	1.33442i
$193$	−3.76780e43			−1.41416			−0.707081	−	0.707133i	$-0.749988\pi$
$193$	−3.76780e43			−1.41416			−0.707081	+	0.707133i	$0.749988\pi$
$194$		−	7.50142e43i		−	2.55218i
$195$	1.11522e43	+	4.60383e42i	0.344113	+	0.142057i
$196$	8.60998e43			2.41066
$197$		−	2.57608e43i		−	0.654789i	−0.944888	−	0.327395i	$-0.893829\pi$
$197$		−	2.57608e43i		−	0.654789i	0.944888	−	0.327395i	$-0.106171\pi$
$198$	9.39039e43	+	9.34576e43i	2.16793	+	2.15763i
$199$	−9.03602e43			−1.89570			−0.947848	−	0.318722i	$-0.896746\pi$
$199$	−9.03602e43			−1.89570			−0.947848	+	0.318722i	$0.896746\pi$
$200$			5.09877e42i			0.0972514i
$201$	−2.08393e43	+	5.04804e43i	−0.361541	+	0.875785i
$202$	4.44131e43			0.701190
$203$		−	8.21853e42i		−	0.118132i
$204$	−2.14344e44	−	8.84852e43i	−2.80632	−	1.15850i
$205$	6.31175e43			0.753055
$206$			2.61456e44i			2.84394i
$207$	−6.49461e43	+	6.52562e43i	−0.644342	+	0.647419i
$208$	1.07315e44			0.971532
$209$		−	2.13927e44i		−	1.76802i
$210$	1.56026e43	−	3.77952e43i	0.117769	−	0.285279i
$211$	−7.21399e43			−0.497518			−0.248759	−	0.968565i	$-0.580023\pi$
$211$	−7.21399e43			−0.497518			−0.248759	+	0.968565i	$0.580023\pi$
$212$			2.17776e44i			1.37287i
$213$	1.11428e44	+	4.59996e43i	0.642366	+	0.265181i
$214$	5.75519e44			3.03528
$215$		−	1.75767e44i		−	0.848412i
$216$	−2.40373e44	−	5.74498e44i	−1.06234	−	2.53903i
$217$	−1.70646e43			−0.0690814
$218$			3.14320e44i			1.16600i
$219$	4.97441e43	−	1.20499e44i	0.169162	−	0.409773i
$220$	−1.32536e45			−4.13335
$221$		−	1.56786e44i		−	0.448595i
$222$	1.79746e44	+	7.42024e43i	0.472011	+	0.194855i
$223$	5.48150e44			1.32162			0.660811	−	0.750552i	$-0.270213\pi$
$223$	5.48150e44			1.32162			0.660811	+	0.750552i	$0.270213\pi$
$224$		−	1.61506e44i		−	0.357665i
$225$	1.23079e43	+	1.22494e43i	0.0250447	+	0.0249256i
$226$	8.66777e43			0.162124
$227$			2.52600e44i			0.434452i	0.976121	+	0.217226i	$0.0697008\pi$
$227$			2.52600e44i			0.434452i	−0.976121	+	0.217226i	$0.930299\pi$
$228$	−6.43647e44	+	1.55915e45i	−1.01832	+	2.46676i
$229$	6.92899e43			0.100878			0.0504389	−	0.998727i	$-0.483938\pi$
$229$	6.92899e43			0.100878			0.0504389	+	0.998727i	$0.483938\pi$
$230$		−	1.29297e45i		−	1.73285i
$231$	1.99885e44	+	8.25164e43i	0.246691	+	0.101839i
$232$	1.75789e45			1.99857
$233$		−	4.70136e44i		−	0.492563i	−0.969198	−	0.246281i	$-0.920791\pi$
$233$		−	4.70136e44i		−	0.492563i	0.969198	−	0.246281i	$-0.0792087\pi$
$234$	4.98235e44	−	5.00614e44i	0.481208	−	0.483506i
$235$	−9.52522e44			−0.848371
$236$			1.73988e45i			1.42952i
$237$	−2.29779e43	+	5.56610e43i	−0.0174218	+	0.0422019i
$238$	−5.31356e44			−0.371897
$239$			2.79152e45i			1.80418i	0.431545	+	0.902092i	$0.357969\pi$
$239$			2.79152e45i			1.80418i	−0.431545	+	0.902092i	$0.642031\pi$
$240$	4.18319e45	+	1.72690e45i	2.49744	+	1.03099i
$241$	−6.40166e44			−0.353158			−0.176579	−	0.984286i	$-0.556503\pi$
$241$	−6.40166e44			−0.353158			−0.176579	+	0.984286i	$0.556503\pi$
$242$		−	6.18369e45i		−	3.15323i
$243$	−1.96425e45	−	7.99949e44i	−0.926142	−	0.377175i
$244$	−8.49721e45			−3.70570
$245$			2.45497e45i			0.990584i
$246$	1.40992e45	−	3.41535e45i	0.526535	−	1.27546i
$247$	−1.14047e45			−0.394315
$248$		−	3.65000e45i		−	1.16872i
$249$	2.01506e44	+	8.31854e43i	0.0597723	+	0.0246751i
$250$	6.65778e45			1.83008
$251$			6.44255e45i			1.64156i	0.571243	+	0.820781i	$0.306461\pi$
$251$			6.44255e45i			1.64156i	−0.571243	+	0.820781i	$0.693539\pi$
$252$	−1.20854e45	−	1.20280e45i	−0.285529	−	0.284173i
$253$	6.83807e45			1.49846
$254$			3.21672e45i			0.653991i
$255$	2.52299e45	−	6.11161e45i	0.476049	−	1.15317i
$256$	−2.99290e45			−0.524244
$257$		−	3.63646e44i		−	0.0591492i	−0.999563	−	0.0295746i	$-0.990585\pi$
$257$		−	3.63646e44i		−	0.0591492i	0.999563	−	0.0295746i	$-0.00941527\pi$
$258$	−9.51092e45	−	3.92629e45i	−1.43697	−	0.593209i
$259$	3.17405e44			0.0445572
$260$			7.06565e45i			0.921846i
$261$	4.22317e45	−	4.24334e45i	0.512235	−	0.514681i
$262$	1.48825e46			1.67861
$263$		−	9.58317e45i		−	1.00543i	−0.864454	−	0.502713i	$-0.832335\pi$
$263$		−	9.58317e45i		−	1.00543i	0.864454	−	0.502713i	$-0.167665\pi$
$264$	−1.76497e46	+	4.27540e46i	−1.72291	+	4.17352i
$265$	−6.20947e45			−0.564135
$266$			3.86512e45i			0.326898i
$267$	5.13083e45	+	2.11811e45i	0.404086	+	0.166814i
$268$	−3.19827e46			−2.34614
$269$			9.07840e45i			0.620463i	0.950661	+	0.310231i	$0.100407\pi$
$269$			9.07840e45i			0.620463i	−0.950661	+	0.310231i	$0.899593\pi$
$270$	2.74773e46	−	1.14966e46i	1.75010	−	0.732250i
$271$	1.17965e46			0.700383			0.350192	−	0.936678i	$-0.386116\pi$
$271$	1.17965e46			0.700383			0.350192	+	0.936678i	$0.386116\pi$
$272$		−	5.88107e46i		−	3.25572i
$273$	4.39906e44	−	1.06561e45i	0.0227127	−	0.0550186i
$274$	7.18320e46			3.45985
$275$		−	1.28972e45i		−	0.0579660i
$276$	−4.98375e46	−	2.05739e46i	−2.09066	−	0.863064i
$277$	−3.13591e46			−1.22814			−0.614071	−	0.789251i	$-0.710469\pi$
$277$	−3.13591e46			−1.22814			−0.614071	+	0.789251i	$0.710469\pi$
$278$			5.94299e44i			0.0217347i
$279$	−8.81069e45	−	8.76882e45i	−0.300975	−	0.299544i
$280$	1.42754e46			0.455603
$281$			2.23453e45i			0.0666447i	0.999445	+	0.0333224i	$0.0106088\pi$
$281$			2.23453e45i			0.0666447i	−0.999445	+	0.0333224i	$0.989391\pi$
$282$	−2.12775e46	+	5.15419e46i	−0.593180	+	1.43690i
$283$	−1.42833e45			−0.0372295			−0.0186147	−	0.999827i	$-0.505926\pi$
$283$	−1.42833e45			−0.0372295			−0.0186147	+	0.999827i	$0.505926\pi$
$284$			7.05972e46i			1.72083i
$285$	−4.44563e46	−	1.83524e46i	−1.01363	−	0.418447i
$286$	−5.24584e46			−1.11908
$287$		−	6.03102e45i		−	0.120402i
$288$	8.29915e46	−	8.33877e46i	1.55087	−	1.55828i
$289$	−2.87663e46			−0.503298
$290$			8.40767e46i			1.37757i
$291$	3.40341e46	−	8.24431e46i	0.522332	−	1.26528i
$292$	7.63439e46			1.09774
$293$		−	8.13702e45i		−	0.109643i	−0.998496	−	0.0548214i	$-0.982541\pi$
$293$		−	8.13702e45i		−	0.109643i	0.998496	−	0.0548214i	$-0.0174590\pi$
$294$	1.32841e47	+	5.48392e46i	1.67777	+	0.692615i
$295$	−4.96093e46			−0.587415
$296$			6.78907e46i			0.753820i
$297$	6.08016e46	+	1.45317e47i	0.633202	+	1.51337i
$298$	−1.44842e46			−0.141509
$299$		−	3.64547e46i		−	0.334195i
$300$	−3.88040e45	+	9.39976e45i	−0.0333866	+	0.0808748i
$301$	−1.67949e46			−0.135648
$302$		−	1.35330e47i		−	1.02627i
$303$	4.88115e46	+	2.01503e46i	0.347626	+	0.143507i
$304$	−4.27793e47			−2.86178
$305$		−	2.42282e47i		−	1.52274i
$306$	−2.74346e47	−	2.73042e47i	−1.62029	−	1.61259i
$307$	1.21487e47			0.674375			0.337188	−	0.941437i	$-0.390524\pi$
$307$	1.21487e47			0.674375			0.337188	+	0.941437i	$0.390524\pi$
$308$			1.26641e47i			0.660860i
$309$	−1.18623e47	+	2.87348e47i	−0.582046	+	1.40993i
$310$	1.74573e47			0.805575
$311$			2.51496e47i			1.09165i	0.837899	+	0.545825i	$0.183784\pi$
$311$			2.51496e47i			1.09165i	−0.837899	+	0.545825i	$0.816216\pi$
$312$	2.27927e47	+	9.40927e46i	0.930806	+	0.384254i
$313$	3.84707e47			1.47838			0.739192	−	0.673495i	$-0.235208\pi$
$313$	3.84707e47			1.47838			0.739192	+	0.673495i	$0.235208\pi$
$314$		−	7.27335e47i		−	2.63070i
$315$	3.42955e46	−	3.44593e46i	0.116771	−	0.117329i
$316$	−3.52650e46			−0.113055
$317$		−	5.94628e47i		−	1.79523i	−0.440784	−	0.897613i	$-0.645299\pi$
$317$		−	5.94628e47i		−	1.79523i	0.440784	−	0.897613i	$-0.354701\pi$
$318$	−1.38707e47	+	3.36000e47i	−0.394443	+	0.955485i
$319$	−4.44651e47			−1.19123
$320$			5.81907e47i			1.46894i
$321$	6.32515e47	+	2.61114e47i	1.50479	+	0.621205i
$322$	−1.23547e47			−0.277057
$323$			6.25002e47i			1.32140i
$324$	−5.91678e45	−	1.24204e48i	−0.0117959	−	2.47617i
$325$	−6.87565e45			−0.0129280
$326$			1.72077e48i			3.05203i
$327$	−1.42607e47	+	3.45448e47i	−0.238635	+	0.578063i
$328$	1.28999e48			2.03697
$329$			9.10156e46i			0.135642i
$330$	−2.04485e48	−	8.44155e47i	−2.87672	−	1.18756i
$331$	−5.89042e47			−0.782374			−0.391187	−	0.920311i	$-0.627935\pi$
$331$	−5.89042e47			−0.782374			−0.391187	+	0.920311i	$0.627935\pi$
$332$			1.27667e47i			0.160124i
$333$	1.63881e47	+	1.63102e47i	0.194128	+	0.193205i
$334$	1.14690e48			1.28335
$335$		−	9.11927e47i		−	0.964070i
$336$	1.65009e47	−	3.99713e47i	0.164840	−	0.399303i
$337$	−1.54032e48			−1.45426			−0.727132	−	0.686498i	$-0.759147\pi$
$337$	−1.54032e48			−1.45426			−0.727132	+	0.686498i	$0.759147\pi$
$338$		−	1.80949e48i		−	1.61487i
$339$	9.52617e46	+	3.93258e46i	0.0803755	+	0.0331806i
$340$	3.87211e48			3.08922
$341$			9.23255e47i			0.696608i
$342$	−1.98613e48	+	1.99561e48i	−1.41746	+	1.42423i
$343$	4.75533e47			0.321065
$344$		−	3.59232e48i		−	2.29490i
$345$	5.86625e47	−	1.42102e48i	0.354648	−	0.859089i
$346$	−3.13452e48			−1.79360
$347$			1.35408e48i			0.733473i	0.930325	+	0.366736i	$0.119525\pi$
$347$			1.35408e48i			0.733473i	−0.930325	+	0.366736i	$0.880475\pi$
$348$	3.24072e48	+	1.33783e48i	1.66202	+	0.686113i
$349$	2.81170e47			0.136548			0.0682740	−	0.997667i	$-0.478251\pi$
$349$	2.81170e47			0.136548			0.0682740	+	0.997667i	$0.478251\pi$
$350$			2.33019e46i			0.0107176i
$351$	7.74706e47	−	3.24141e47i	0.337522	−	0.141221i
$352$	−8.73804e48			−3.60665
$353$		−	1.03153e47i		−	0.0403425i	−0.999797	−	0.0201712i	$-0.993579\pi$
$353$		−	1.03153e47i		−	0.0403425i	0.999797	−	0.0201712i	$-0.00642114\pi$
$354$	−1.10817e48	+	2.68441e48i	−0.410720	+	0.994916i
$355$	−2.01295e48			−0.707121
$356$			3.25073e48i			1.08251i
$357$	−5.83978e47	−	2.41077e47i	−0.184374	−	0.0761131i
$358$	1.06046e49			3.17479
$359$		−	4.39348e48i		−	1.24742i	−0.781654	−	0.623712i	$-0.785624\pi$
$359$		−	4.39348e48i		−	1.24742i	0.781654	−	0.623712i	$-0.214376\pi$
$360$	7.37059e48	+	7.33557e48i	1.98497	+	1.97554i
$361$	6.32167e47			0.161508
$362$			7.05470e48i			1.71008i
$363$	2.80555e48	−	6.79608e48i	0.645345	−	1.56326i
$364$	6.75138e47			0.147389
$365$			2.17680e48i			0.451081i
$366$	−1.31101e49	−	5.41210e48i	−2.57909	−	1.06470i
$367$	2.89773e48			0.541257			0.270628	−	0.962684i	$-0.412769\pi$
$367$	2.89773e48			0.541257			0.270628	+	0.962684i	$0.412769\pi$
$368$		−	1.36742e49i		−	2.42545i
$369$	3.09910e48	−	3.11390e48i	0.522077	−	0.524570i
$370$	−3.24710e48			−0.519593
$371$			5.93328e47i			0.0901967i
$372$	2.77782e48	−	6.72890e48i	0.401225	−	0.971914i
$373$	−9.95641e48			−1.36658			−0.683290	−	0.730147i	$-0.739452\pi$
$373$	−9.95641e48			−1.36658			−0.683290	+	0.730147i	$0.739452\pi$
$374$			2.87482e49i			3.75017i
$375$	7.31712e48	+	3.02065e48i	0.907290	+	0.374547i
$376$	−1.94676e49			−2.29479
$377$			2.37049e48i			0.265677i
$378$	−1.09853e48	−	2.62551e48i	−0.117076	−	0.279814i
$379$	−6.31988e48			−0.640566			−0.320283	−	0.947322i	$-0.603778\pi$
$379$	−6.31988e48			−0.640566			−0.320283	+	0.947322i	$0.603778\pi$
$380$		−	2.81660e49i		−	2.71542i
$381$	−1.45943e48	+	3.53528e48i	−0.133847	+	0.324227i
$382$	2.09866e49			1.83121
$383$			4.72786e48i			0.392544i	0.980549	+	0.196272i	$0.0628835\pi$
$383$			4.72786e48i			0.392544i	−0.980549	+	0.196272i	$0.937116\pi$
$384$	5.76873e48	+	2.38144e48i	0.455813	+	0.188168i
$385$	−3.61092e48			−0.271559
$386$		−	3.68307e49i		−	2.63664i
$387$	−8.67145e48	−	8.63024e48i	−0.590994	−	0.588186i
$388$	5.22332e49			3.38956
$389$			2.31399e49i			1.42994i	0.699153	+	0.714972i	$0.253561\pi$
$389$			2.31399e49i			1.42994i	−0.699153	+	0.714972i	$0.746439\pi$
$390$	−4.50030e48	+	1.09014e49i	−0.264858	+	0.641585i
$391$	−1.99779e49			−1.11993
$392$			5.01746e49i			2.67947i
$393$	1.63563e49	+	6.75220e48i	0.832199	+	0.343547i
$394$	2.51815e49			1.22083
$395$		−	1.00551e48i		−	0.0464562i
$396$	−6.50756e49	+	6.53863e49i	−2.86556	+	2.87924i
$397$	−9.52386e48			−0.399755			−0.199877	−	0.979821i	$-0.564054\pi$
$397$	−9.52386e48			−0.399755			−0.199877	+	0.979821i	$0.564054\pi$
$398$		−	8.83282e49i		−	3.53444i
$399$	−1.75361e48	+	4.24789e48i	−0.0669034	+	0.162065i
$400$	−2.57907e48			−0.0938259
$401$			1.71356e48i			0.0594506i	0.999558	+	0.0297253i	$0.00946325\pi$
$401$			1.71356e48i			0.0594506i	−0.999558	+	0.0297253i	$0.990537\pi$
$402$	−4.93452e49	−	2.03706e49i	−1.63286	−	0.674077i
$403$	4.92199e48			0.155362
$404$			3.09254e49i			0.931256i
$405$	3.54145e49	−	1.68706e47i	1.01750	−	0.00484713i
$406$	8.03371e48			0.220253
$407$		−	1.71727e49i		−	0.449310i
$408$	5.15647e49	−	1.24909e50i	1.28768	−	3.11925i
$409$	5.80638e49			1.38408			0.692042	−	0.721857i	$-0.256711\pi$
$409$	5.80638e49			1.38408			0.692042	+	0.721857i	$0.256711\pi$
$410$			6.16982e49i			1.40404i
$411$	7.89457e49	+	3.25903e49i	1.71528	+	0.708099i
$412$	−1.82054e50			−3.77706
$413$			4.74028e48i			0.0939189i
$414$	−6.37888e49	−	6.34856e49i	−1.20708	−	1.20135i
$415$	−3.64020e48			−0.0657978
$416$			4.65836e49i			0.804378i
$417$	−2.69635e47	+	6.53155e47i	−0.00444826	+	0.0107753i
$418$	2.09117e50			3.29639
$419$		−	8.20553e49i		−	1.23606i	−0.786154	−	0.618031i	$-0.787931\pi$
$419$		−	8.20553e49i		−	1.23606i	0.786154	−	0.618031i	$-0.212069\pi$
$420$	2.63172e49	+	1.08642e49i	0.378882	+	0.156410i
$421$	−1.10651e50			−1.52263			−0.761315	−	0.648382i	$-0.775446\pi$
$421$	−1.10651e50			−1.52263			−0.761315	+	0.648382i	$0.775446\pi$
$422$		−	7.05176e49i		−	0.927601i
$423$	−4.67693e49	+	4.69926e49i	−0.588157	+	0.590966i
$424$	−1.26909e50			−1.52595
$425$			3.76799e48i			0.0433232i
$426$	−4.49652e49	+	1.08922e50i	−0.494418	+	1.19766i
$427$	−2.31506e49			−0.243463
$428$			4.00741e50i			4.03118i
$429$	−5.76535e49	−	2.38004e49i	−0.554801	−	0.229032i
$430$	1.71815e50			1.58183
$431$		−	1.46867e50i		−	1.29377i	−0.762587	−	0.646885i	$-0.776071\pi$
$431$		−	1.46867e50i		−	1.29377i	0.762587	−	0.646885i	$-0.223929\pi$
$432$	2.90593e50	−	1.21586e50i	2.44959	−	1.02492i
$433$	1.20647e50			0.973296			0.486648	−	0.873598i	$-0.338219\pi$
$433$	1.20647e50			0.973296			0.486648	+	0.873598i	$0.338219\pi$
$434$		−	1.66809e49i		−	0.128799i
$435$	−3.81458e49	+	9.24031e49i	−0.281936	+	0.682953i
$436$	−2.18864e50			−1.54857
$437$			1.45320e50i			0.984418i
$438$	1.17789e50	+	4.86255e49i	0.764005	+	0.315396i
$439$	−2.49606e50			−1.55035			−0.775175	−	0.631746i	$-0.782338\pi$
$439$	−2.49606e50			−1.55035			−0.775175	+	0.631746i	$0.782338\pi$
$440$		−	7.72351e50i		−	4.59424i
$441$	1.21116e50	+	1.20540e50i	0.690030	+	0.686751i
$442$	1.53261e50			0.836387
$443$		−	1.99617e50i		−	1.04358i	−0.853074	−	0.521790i	$-0.825264\pi$
$443$		−	1.99617e50i		−	1.04358i	0.853074	−	0.521790i	$-0.174736\pi$
$444$	−5.16680e49	+	1.25159e50i	−0.258788	+	0.626881i
$445$	−9.26884e49			−0.444821
$446$			5.35824e50i			2.46411i
$447$	−1.59186e49	−	6.57149e48i	−0.0701554	−	0.0289615i
$448$	5.56025e49			0.234861
$449$		−	2.63311e50i		−	1.06608i	−0.846090	−	0.533039i	$-0.821050\pi$
$449$		−	2.63311e50i		−	1.06608i	0.846090	−	0.533039i	$-0.178950\pi$
$450$	−1.19739e49	+	1.20311e49i	−0.0464728	+	0.0466947i
$451$	−3.26299e50			−1.21412
$452$			6.03547e49i			0.215318i
$453$	6.13993e49	−	1.48732e50i	0.210038	−	0.508789i
$454$	−2.46919e50			−0.810016
$455$			1.92503e49i			0.0605649i
$456$	−9.08595e50	−	3.75085e50i	−2.74181	−	1.13187i
$457$	3.95099e50			1.14366			0.571832	−	0.820371i	$-0.306233\pi$
$457$	3.95099e50			1.14366			0.571832	+	0.820371i	$0.306233\pi$
$458$			6.77317e49i			0.188082i
$459$	−1.77636e50	−	4.24554e50i	−0.473249	−	1.13108i
$460$	9.00313e50			2.30141
$461$			5.51810e50i			1.35354i	0.736193	+	0.676771i	$0.236621\pi$
$461$			5.51810e50i			1.35354i	−0.736193	+	0.676771i	$0.763379\pi$
$462$	−8.06608e49	+	1.95390e50i	−0.189874	+	0.459944i
$463$	7.87996e50			1.78027			0.890133	−	0.455700i	$-0.150611\pi$
$463$	7.87996e50			1.78027			0.890133	+	0.455700i	$0.150611\pi$
$464$			8.89175e50i			1.92817i
$465$	1.91862e50	+	7.92042e49i	0.399377	+	0.164870i
$466$	4.59564e50			0.918362
$467$			2.60117e49i			0.0499054i	0.999689	+	0.0249527i	$0.00794351\pi$
$467$			2.60117e49i			0.0499054i	−0.999689	+	0.0249527i	$0.992056\pi$
$468$	3.48583e50	+	3.46926e50i	0.642148	+	0.639096i
$469$	−8.71366e49			−0.154140
$470$		−	9.31103e50i		−	1.58175i
$471$	3.29993e50	−	7.99365e50i	0.538403	−	1.30421i
$472$	−1.01391e51			−1.58892
$473$			9.08665e50i			1.36786i
$474$	−5.44093e49	−	2.24612e49i	−0.0786837	−	0.0324821i
$475$	2.74087e49			0.0380811
$476$		−	3.69989e50i		−	0.493920i
$477$	−3.04888e50	+	3.06343e50i	−0.391102	+	0.392970i
$478$	−2.72875e51			−3.36382
$479$		−	3.83296e50i		−	0.454108i	−0.973882	−	0.227054i	$-0.927091\pi$
$479$		−	3.83296e50i		−	0.454108i	0.973882	−	0.227054i	$-0.0729095\pi$
$480$	−7.49619e50	+	1.81585e51i	−0.853605	+	2.06775i
$481$	−9.15501e49			−0.100208
$482$		−	6.25770e50i		−	0.658448i
$483$	−1.35782e50	−	5.60533e49i	−0.137355	−	0.0567029i
$484$	4.30577e51			4.18783
$485$			1.48933e51i			1.39283i
$486$	7.81960e50	−	1.92008e51i	0.703227	−	1.72675i
$487$	−5.23031e50			−0.452353			−0.226176	−	0.974086i	$-0.572623\pi$
$487$	−5.23031e50			−0.452353			−0.226176	+	0.974086i	$0.572623\pi$
$488$		−	4.95175e51i		−	4.11891i
$489$	−7.80717e50	+	1.89119e51i	−0.624634	+	1.51309i
$490$	−2.39977e51			−1.84690
$491$		−	2.96080e50i		−	0.219210i	−0.993975	−	0.109605i	$-0.965041\pi$
$491$		−	2.96080e50i		−	0.219210i	0.993975	−	0.109605i	$-0.0349586\pi$
$492$	2.37814e51	+	9.81743e50i	1.69395	+	0.699296i
$493$	1.29908e51			0.890315
$494$		−	1.11483e51i		−	0.735183i
$495$	−1.86437e51	−	1.85551e51i	−1.18313	−	1.17751i
$496$	1.84625e51			1.12755
$497$			1.92341e50i			0.113058i
$498$	−8.13148e49	+	1.96974e50i	−0.0460057	+	0.111443i
$499$	5.15637e50			0.280823			0.140412	−	0.990093i	$-0.455157\pi$
$499$	5.15637e50			0.280823			0.140412	+	0.990093i	$0.455157\pi$
$500$			4.63589e51i			2.43054i
$501$	1.26048e51	+	5.20352e50i	0.636239	+	0.262652i
$502$	−6.29767e51			−3.06062
$503$			1.33918e51i			0.626682i	0.949641	+	0.313341i	$0.101448\pi$
$503$			1.33918e51i			0.626682i	−0.949641	+	0.313341i	$0.898552\pi$
$504$	7.00929e50	−	7.04276e50i	0.315860	−	0.317368i
$505$	−8.81779e50			−0.382669
$506$			6.68430e51i			2.79381i
$507$	8.20968e50	−	1.98869e51i	0.330503	−	0.800599i
$508$	−2.23983e51			−0.868571
$509$			7.06657e50i			0.263980i	0.991251	+	0.131990i	$0.0421367\pi$
$509$			7.06657e50i			0.263980i	−0.991251	+	0.131990i	$0.957863\pi$
$510$	5.97417e51	+	2.46625e51i	2.15003	+	0.887573i
$511$	2.07998e50			0.0721212
$512$		−	4.40160e51i		−	1.47056i
$513$	−3.08824e51	+	1.29214e51i	−0.994216	+	0.415985i
$514$	3.55468e50			0.110281
$515$		−	5.19094e51i		−	1.55206i
$516$	2.73392e51	−	6.62256e51i	0.787846	−	1.90845i
$517$	4.92426e51			1.36780
$518$			3.10267e50i			0.0830751i
$519$	−3.44494e51	−	1.42214e51i	−0.889206	−	0.367081i
$520$	−4.11750e51			−1.02464
$521$		−	3.23363e50i		−	0.0775843i	−0.999247	−	0.0387922i	$-0.987649\pi$
$521$		−	3.23363e50i		−	0.0775843i	0.999247	−	0.0387922i	$-0.0123510\pi$
$522$	4.14792e51	+	4.12820e51i	0.959600	+	0.955040i
$523$	3.56990e51			0.796386			0.398193	−	0.917302i	$-0.369637\pi$
$523$	3.56990e51			0.796386			0.398193	+	0.917302i	$0.369637\pi$
$524$			1.03628e52i			2.22938i
$525$	−1.05721e49	+	2.56096e49i	−0.00219349	+	0.00531344i
$526$	9.36767e51			1.87457
$527$		−	2.69735e51i		−	0.520638i
$528$	−2.16259e52	−	8.92758e51i	−4.02652	−	1.66222i
$529$	9.22374e50			0.165672
$530$		−	6.06983e51i		−	1.05180i
$531$	−2.43584e51	+	2.44747e51i	−0.407242	+	0.409187i
$532$	−2.69133e51			−0.434155
$533$			1.73954e51i			0.270781i
$534$	−2.07047e51	+	5.01545e51i	−0.311018	+	0.753401i
$535$	−1.14264e52			−1.65648
$536$		−	1.86379e52i		−	2.60775i
$537$	1.16548e52	+	4.81131e51i	1.57395	+	0.649758i
$538$	−8.87425e51			−1.15683
$539$		−	1.26915e52i		−	1.59708i
$540$	8.00524e51	+	1.91327e52i	0.972507	+	2.32432i
$541$	1.47773e52			1.73319			0.866594	−	0.499014i	$-0.166304\pi$
$541$	1.47773e52			1.73319			0.866594	+	0.499014i	$0.166304\pi$
$542$			1.15312e52i			1.30583i
$543$	−3.20073e51	+	7.75335e51i	−0.349987	+	0.847799i
$544$	2.55288e52			2.69557
$545$		−	6.24051e51i		−	0.636336i
$546$	1.04165e51	+	4.30013e50i	0.102580	+	0.0423469i
$547$	−1.26863e52			−1.20663			−0.603317	−	0.797501i	$-0.706155\pi$
$547$	−1.26863e52			−1.20663			−0.603317	+	0.797501i	$0.706155\pi$
$548$			5.00174e52i			4.59505i
$549$	−1.19530e52	−	1.18962e52i	−1.06072	−	1.05568i
$550$	1.26072e51			0.108075
$551$		−	9.44958e51i		−	0.782586i
$552$	1.19894e52	−	2.90428e52i	0.959301	−	2.32378i
$553$	−9.60791e49			−0.00742765
$554$		−	3.06539e52i		−	2.28982i
$555$	−3.56867e51	−	1.47321e51i	−0.257596	−	0.106341i
$556$	−4.13817e50			−0.0288661
$557$			2.59652e52i			1.75042i	0.483740	+	0.875212i	$0.339278\pi$
$557$			2.59652e52i			1.75042i	−0.483740	+	0.875212i	$0.660722\pi$
$558$	8.57163e51	−	8.61256e51i	0.558488	−	0.561154i
$559$	4.84421e51			0.305069
$560$			7.22081e51i			0.439555i
$561$	−1.30431e52	+	3.15952e52i	−0.767515	+	1.85921i
$562$	−2.18428e51			−0.124256
$563$			3.13079e51i			0.172184i	0.996287	+	0.0860922i	$0.0274380\pi$
$563$			3.13079e51i			0.172184i	−0.996287	+	0.0860922i	$0.972562\pi$
$564$	−3.58892e52	−	1.48157e52i	−1.90836	−	0.787808i
$565$	−1.72090e51			−0.0884779
$566$		−	1.39621e51i		−	0.0694127i
$567$	−1.61202e49	−	3.38393e51i	−0.000774984	−	0.162683i
$568$	−4.11405e52			−1.91272
$569$			1.09157e52i			0.490816i	0.969420	+	0.245408i	$0.0789218\pi$
$569$			1.09157e52i			0.490816i	−0.969420	+	0.245408i	$0.921078\pi$
$570$	1.79397e52	−	4.34566e52i	0.780176	−	1.88988i
$571$	2.15960e52			0.908422			0.454211	−	0.890894i	$-0.349921\pi$
$571$	2.15960e52			0.908422			0.454211	+	0.890894i	$0.349921\pi$
$572$		−	3.65273e52i		−	1.48626i
$573$	2.30650e52	+	9.52165e51i	0.907852	+	0.374778i
$574$	5.89539e51			0.224485
$575$			8.76104e50i			0.0322750i
$576$	2.87083e52	+	2.85719e52i	1.02325	+	1.01838i
$577$	−2.05789e52			−0.709713			−0.354856	−	0.934921i	$-0.615470\pi$
$577$	−2.05789e52			−0.709713			−0.354856	+	0.934921i	$0.615470\pi$
$578$		−	2.81195e52i		−	0.938378i
$579$	1.67102e52	−	4.04782e52i	0.539620	−	1.30716i
$580$	−5.85436e52			−1.82956
$581$			3.47829e50i			0.0105201i
$582$	8.05891e52	+	3.32687e52i	2.35906	+	0.973866i
$583$	3.21011e52			0.909532
$584$			4.44894e52i			1.22015i
$585$	−9.89195e51	+	9.93919e51i	−0.262616	+	0.263870i
$586$	7.95404e51			0.204424
$587$		−	4.30984e51i		−	0.107235i	−0.998562	−	0.0536176i	$-0.982925\pi$
$587$		−	4.30984e51i		−	0.107235i	0.998562	−	0.0536176i	$-0.0170752\pi$
$588$	−3.81852e52	+	9.24986e52i	−0.919868	+	2.22826i
$589$	−1.96207e52			−0.457640
$590$		−	4.84937e52i		−	1.09521i
$591$	2.76753e52	+	1.14249e52i	0.605244	+	0.249856i
$592$	−3.43406e52			−0.727269
$593$			4.71208e52i			0.966437i	0.875500	+	0.483218i	$0.160532\pi$
$593$			4.71208e52i			0.966437i	−0.875500	+	0.483218i	$0.839468\pi$
$594$	−1.42050e53	+	5.94343e52i	−2.82161	+	1.18058i
$595$	1.05495e52			0.202960
$596$		−	1.00855e52i		−	0.187939i
$597$	4.00747e52	−	9.70756e52i	0.723365	−	1.75226i
$598$	3.56349e52			0.623093
$599$		−	2.00006e52i		−	0.338793i	−0.985548	−	0.169396i	$-0.945818\pi$
$599$		−	2.00006e52i		−	0.338793i	0.985548	−	0.169396i	$-0.0541818\pi$
$600$	−5.47771e51	−	2.26130e51i	−0.0898928	−	0.0371095i
$601$	5.78120e52			0.919185			0.459592	−	0.888130i	$-0.347996\pi$
$601$	5.78120e52			0.919185			0.459592	+	0.888130i	$0.347996\pi$
$602$		−	1.64172e52i		−	0.252911i
$603$	−4.49898e52	−	4.47760e52i	−0.671561	−	0.668369i
$604$	9.42315e52			1.36300
$605$			1.22771e53i			1.72085i
$606$	−1.96972e52	+	4.77139e52i	−0.267562	+	0.648134i
$607$	−1.31976e53			−1.73744			−0.868721	−	0.495301i	$-0.835058\pi$
$607$	−1.31976e53			−1.73744			−0.868721	+	0.495301i	$0.835058\pi$
$608$		−	1.85698e53i		−	2.36940i
$609$	8.82932e51	+	3.64491e51i	0.109194	+	0.0450773i
$610$	2.36834e53			2.83907
$611$		−	2.62519e52i		−	0.305055i
$612$	1.90122e53	−	1.91030e53i	2.14169	−	2.15192i
$613$	−5.15273e52			−0.562715			−0.281357	−	0.959603i	$-0.590785\pi$
$613$	−5.15273e52			−0.562715			−0.281357	+	0.959603i	$0.590785\pi$
$614$			1.18755e53i			1.25734i
$615$	−2.79926e52	+	6.78083e52i	−0.287353	+	0.696075i
$616$	−7.37998e52			−0.734550
$617$		−	1.13864e53i		−	1.09893i	−0.835517	−	0.549465i	$-0.814832\pi$
$617$		−	1.13864e53i		−	1.09893i	0.835517	−	0.549465i	$-0.185168\pi$
$618$	−2.80887e53	−	1.15955e53i	−2.62875	−	1.08520i
$619$	−6.36249e52			−0.577437			−0.288718	−	0.957414i	$-0.593229\pi$
$619$	−6.36249e52			−0.577437			−0.288718	+	0.957414i	$0.593229\pi$
$620$			1.21557e53i			1.06989i
$621$	−4.13024e52	−	9.87139e52i	−0.352562	−	0.842632i
$622$	−2.45840e53			−2.03534
$623$			8.85658e51i			0.0711202i
$624$	−4.75941e52	+	1.15290e53i	−0.370720	+	0.898020i
$625$	−1.36860e53			−1.03409
$626$			3.76056e53i			2.75638i
$627$	2.29826e53	+	9.48765e52i	1.63424	+	0.674645i
$628$	5.06451e53			3.49385
$629$			5.01713e52i			0.335809i
$630$	3.36844e52	+	3.35243e52i	0.218755	+	0.217715i
$631$	−1.55428e53			−0.979427			−0.489713	−	0.871883i	$-0.662899\pi$
$631$	−1.55428e53			−0.979427			−0.489713	+	0.871883i	$0.662899\pi$
$632$		−	2.05506e52i		−	0.125661i
$633$	3.19940e52	−	7.75012e52i	0.189844	−	0.459873i
$634$	5.81256e53			3.34712
$635$		−	6.38647e52i		−	0.356911i
$636$	−2.33961e53	−	9.65834e52i	−1.26899	−	0.523862i
$637$	−6.76600e52			−0.356191
$638$		−	4.34652e53i		−	2.22100i
$639$	−9.88365e52	+	9.93085e52i	−0.490232	+	0.492572i
$640$	−1.04212e53			−0.501762
$641$		−	3.62328e53i		−	1.69356i	−0.531947	−	0.846778i	$-0.678539\pi$
$641$		−	3.62328e53i		−	1.69356i	0.531947	−	0.846778i	$-0.321461\pi$
$642$	−2.55242e53	+	6.18291e53i	−1.15821	+	2.80561i
$643$	4.40218e53			1.93937			0.969683	−	0.244367i	$-0.0785801\pi$
$643$	4.40218e53			1.93937			0.969683	+	0.244367i	$0.0785801\pi$
$644$		−	8.60268e52i		−	0.367962i
$645$	1.88830e53	+	7.79525e52i	0.784217	+	0.323739i
$646$	−6.10948e53			−2.46369
$647$			3.53960e53i			1.38603i	0.720923	+	0.693015i	$0.243718\pi$
$647$			3.53960e53i			1.38603i	−0.720923	+	0.693015i	$0.756282\pi$
$648$	7.23799e53	−	3.44800e51i	2.75228	−	0.0131112i
$649$	2.56466e53			0.947066
$650$		−	6.72104e51i		−	0.0241036i
$651$	7.56814e51	−	1.83328e52i	0.0263603	−	0.0638543i
$652$	−1.19819e54			−4.05343
$653$		−	4.16045e53i		−	1.36707i	−0.729919	−	0.683534i	$-0.760442\pi$
$653$		−	4.16045e53i		−	1.36707i	0.729919	−	0.683534i	$-0.239558\pi$
$654$	−3.37680e53	−	1.39401e53i	−1.07777	−	0.444926i
$655$	−2.95476e53			−0.916090
$656$			6.52505e53i			1.96522i
$657$	1.07392e53	+	1.06882e53i	0.314218	+	0.312725i
$658$	−8.89689e52			−0.252898
$659$		−	1.42734e53i		−	0.394189i	−0.980384	−	0.197095i	$-0.936849\pi$
$659$		−	1.42734e53i		−	0.394189i	0.980384	−	0.197095i	$-0.0631506\pi$
$660$	5.87794e53	−	1.42385e54i	1.57721	−	3.82059i
$661$	7.90981e51			0.0206224			0.0103112	−	0.999947i	$-0.496718\pi$
$661$	7.90981e51			0.0206224			0.0103112	+	0.999947i	$0.496718\pi$
$662$		−	5.75796e53i		−	1.45870i
$663$	1.68438e53	+	6.95346e52i	0.414652	+	0.171176i
$664$	−7.43981e52			−0.177979
$665$		−	7.67381e52i		−	0.178402i
$666$	−1.59434e53	+	1.60195e53i	−0.360222	+	0.361942i
$667$	3.02051e53			0.663269
$668$			7.98601e53i			1.70442i
$669$	−2.43104e53	+	5.88888e53i	−0.504308	+	1.22162i
$670$	8.91420e53			1.79747
$671$			1.25253e54i			2.45505i
$672$	1.73509e53	+	7.16277e52i	0.330602	+	0.136479i
$673$	−3.96213e53			−0.733910			−0.366955	−	0.930239i	$-0.619600\pi$
$673$	−3.96213e53			−0.733910			−0.366955	+	0.930239i	$0.619600\pi$
$674$		−	1.50568e54i		−	2.71141i
$675$	−1.86183e52	+	7.78998e51i	−0.0325962	+	0.0136384i
$676$	1.25997e54			2.14473
$677$		−	4.33082e53i		−	0.716779i	−0.933572	−	0.358390i	$-0.883326\pi$
$677$		−	4.33082e53i		−	0.716779i	0.933572	−	0.358390i	$-0.116674\pi$
$678$	−3.84415e52	+	9.31195e52i	−0.0618637	+	0.149857i
$679$	1.42309e53			0.222693
$680$			2.25647e54i			3.43369i
$681$	−2.71372e53	−	1.12028e53i	−0.401579	−	0.165779i
$682$	−9.02493e53			−1.29880
$683$			2.18362e53i			0.305621i	0.988255	+	0.152811i	$0.0488325\pi$
$683$			2.18362e53i			0.305621i	−0.988255	+	0.152811i	$0.951168\pi$
$684$	−1.38957e54	−	1.38296e54i	−1.89153	−	1.88254i
$685$	−1.42615e54			−1.88819
$686$			4.64840e53i			0.598612i
$687$	−3.07300e52	+	7.44394e52i	−0.0384932	+	0.0932448i
$688$	1.81707e54			2.21407
$689$		−	1.71135e53i		−	0.202850i
$690$	1.38907e54	+	5.73433e53i	1.60173	+	0.661226i
$691$	−8.19021e52			−0.0918782			−0.0459391	−	0.998944i	$-0.514628\pi$
$691$	−8.19021e52			−0.0918782			−0.0459391	+	0.998944i	$0.514628\pi$
$692$		−	2.18260e54i		−	2.38209i
$693$	−1.77298e53	+	1.78144e53i	−0.188266	+	0.189165i
$694$	−1.32363e54			−1.36753
$695$		−	1.17992e52i		−	0.0118616i
$696$	−7.79620e53	+	1.88853e54i	−0.762619	+	1.84735i
$697$	9.53304e53			0.907421
$698$			2.74847e53i			0.254588i
$699$	5.05076e53	+	2.08505e53i	0.455293	+	0.187953i
$700$	−1.62254e52			−0.0142342
$701$		−	1.27469e54i		−	1.08834i	−0.838976	−	0.544169i	$-0.816845\pi$
$701$		−	1.27469e54i		−	1.08834i	0.838976	−	0.544169i	$-0.183155\pi$
$702$	3.16852e53	+	7.57285e53i	0.263300	+	0.629295i
$703$	3.64949e53			0.295176
$704$		−	3.00829e54i		−	2.36831i
$705$	4.22443e53	−	1.02331e54i	0.323724	−	0.784179i
$706$	1.00833e53			0.0752168
$707$			8.42559e52i			0.0611831i
$708$	−1.86918e54	−	7.71634e53i	−1.32136	−	0.545481i
$709$	2.05256e54			1.41260			0.706298	−	0.707914i	$-0.250364\pi$
$709$	2.05256e54			1.41260			0.706298	+	0.707914i	$0.250364\pi$
$710$		−	1.96768e54i		−	1.31840i
$711$	−4.96069e52	−	4.93712e52i	−0.0323609	−	0.0322071i
$712$	−1.89436e54			−1.20321
$713$		−	6.27166e53i		−	0.387866i
$714$	2.35656e53	−	5.70845e53i	0.141910	−	0.343758i
$715$	1.04151e54			0.610728
$716$			7.38407e54i			4.21647i
$717$	−2.99898e54	−	1.23804e54i	−1.66767	−	0.688445i
$718$	4.29468e54			2.32577
$719$			1.72629e54i			0.910469i	0.890371	+	0.455235i	$0.150445\pi$
$719$			1.72629e54i			0.910469i	−0.890371	+	0.455235i	$0.849555\pi$
$720$	−3.71048e54	+	3.72820e54i	−1.90596	+	1.91506i
$721$	−4.96005e53			−0.248151
$722$			6.17951e53i			0.301125i
$723$	2.83913e53	−	6.87742e53i	0.134759	−	0.326436i
$724$	−4.91227e54			−2.27117
$725$		−	5.69693e52i		−	0.0256578i
$726$	6.64325e54	+	2.74246e54i	2.91464	+	1.20322i
$727$	−1.24366e53			−0.0531555			−0.0265778	−	0.999647i	$-0.508461\pi$
$727$	−1.24366e53			−0.0531555			−0.0265778	+	0.999647i	$0.508461\pi$
$728$			3.93436e53i			0.163824i
$729$	1.73054e54	−	1.75545e54i	0.702036	−	0.712141i
$730$	−2.12785e54			−0.841022
$731$		−	2.65472e54i		−	1.02233i
$732$	3.76851e54	−	9.12871e54i	1.41403	−	3.42530i
$733$	−4.38973e54			−1.60495			−0.802476	−	0.596685i	$-0.796484\pi$
$733$	−4.38973e54			−1.60495			−0.802476	+	0.596685i	$0.796484\pi$
$734$			2.83257e54i			1.00915i
$735$	−2.63742e54	−	1.08878e54i	−0.915631	−	0.377990i
$736$	5.93574e54			2.00815
$737$			4.71440e54i			1.55433i
$738$	3.04387e54	+	3.02941e54i	0.978038	+	0.973390i
$739$	4.48590e54			1.40477			0.702384	−	0.711798i	$-0.252119\pi$
$739$	4.48590e54			1.40477			0.702384	+	0.711798i	$0.252119\pi$
$740$		−	2.26099e54i		−	0.690075i
$741$	5.05799e53	−	1.22523e54i	0.150464	−	0.364479i
$742$	−5.79986e53			−0.168168
$743$			3.32855e54i			0.940736i	0.882470	+	0.470368i	$0.155879\pi$
$743$			3.32855e54i			0.940736i	−0.882470	+	0.470368i	$0.844121\pi$
$744$	3.92126e54	+	1.61877e54i	1.08029	+	0.445964i
$745$	2.87569e53			0.0772275
$746$		−	9.73252e54i		−	2.54793i
$747$	−1.78735e53	+	1.79589e53i	−0.0456162	+	0.0458340i
$748$	−2.00177e55			−4.98063
$749$			1.09181e54i			0.264846i
$750$	−2.95272e54	+	7.15258e54i	−0.698326	+	1.69160i
$751$	−1.83280e54			−0.422627			−0.211313	−	0.977418i	$-0.567774\pi$
$751$	−1.83280e54			−0.422627			−0.211313	+	0.977418i	$0.567774\pi$
$752$		−	9.84712e54i		−	2.21396i
$753$	−6.92135e54	−	2.85727e54i	−1.51735	−	0.626392i
$754$	−2.31719e54			−0.495343
$755$			2.68683e54i			0.560078i
$756$	1.82817e54	−	7.64918e53i	0.371624	−	0.155489i
$757$	7.97431e54			1.58078			0.790390	−	0.612604i	$-0.209878\pi$
$757$	7.97431e54			1.58078			0.790390	+	0.612604i	$0.209878\pi$
$758$		−	6.17776e54i		−	1.19431i
$759$	−3.03268e54	+	7.34627e54i	−0.571785	+	1.38507i
$760$	1.64137e55			3.01821
$761$		−	4.06921e54i		−	0.729796i	−0.931048	−	0.364898i	$-0.881104\pi$
$761$		−	4.06921e54i		−	0.729796i	0.931048	−	0.364898i	$-0.118896\pi$
$762$	−3.45578e54	−	1.42661e54i	−0.604507	−	0.249552i
$763$	−5.96294e53			−0.101741
$764$			1.46132e55i			2.43204i
$765$	5.44687e54	+	5.42099e54i	0.884260	+	0.880057i
$766$	−4.62155e54			−0.731881
$767$		−	1.36725e54i		−	0.211221i
$768$	1.32735e54	−	3.21533e54i	0.200042	−	0.484577i
$769$	−4.87719e54			−0.717082			−0.358541	−	0.933514i	$-0.616726\pi$
$769$	−4.87719e54			−0.717082			−0.358541	+	0.933514i	$0.616726\pi$
$770$		−	3.52972e54i		−	0.506310i
$771$	3.90671e53	+	1.61277e53i	0.0546737	+	0.0225703i
$772$	2.56456e55			3.50175
$773$		−	7.25727e54i		−	0.966858i	−0.875384	−	0.483429i	$-0.839391\pi$
$773$		−	7.25727e54i		−	0.966858i	0.875384	−	0.483429i	$-0.160609\pi$
$774$	8.43617e54	−	8.47645e54i	1.09665	−	1.10188i
$775$	−1.18289e53			−0.0150041
$776$			3.04389e55i			3.76752i
$777$	−1.40769e53	+	3.40994e53i	−0.0170023	+	0.0411858i
$778$	−2.26195e55			−2.66607
$779$		−	6.93440e54i		−	0.797623i
$780$	−7.59075e54	−	3.13361e54i	−0.852094	−	0.351761i
$781$	1.04063e55			1.14006
$782$		−	1.95286e55i		−	2.08806i
$783$	2.68572e54	+	6.41895e54i	0.280277	+	0.669870i
$784$	−2.53794e55			−2.58509
$785$			1.44405e55i			1.43568i
$786$	−6.60036e54	+	1.59885e55i	−0.640529	+	1.55160i
$787$	1.12718e54			0.106776			0.0533880	−	0.998574i	$-0.482998\pi$
$787$	1.12718e54			0.106776			0.0533880	+	0.998574i	$0.482998\pi$
$788$			1.75342e55i			1.62139i
$789$	1.02954e55	+	4.25013e54i	0.929350	+	0.383653i
$790$	9.82903e53			0.0866155
$791$			1.64436e53i			0.0141463i
$792$	−3.81038e55	−	3.79228e55i	−3.20030	−	3.18509i
$793$	6.67739e54			0.547540
$794$		−	9.30969e54i		−	0.745325i
$795$	2.75389e54	−	6.67095e54i	0.215264	−	0.521449i
$796$	6.15039e55			4.69412
$797$		−	4.35977e54i		−	0.324904i	−0.986716	−	0.162452i	$-0.948060\pi$
$797$		−	4.35977e54i		−	0.324904i	0.986716	−	0.162452i	$-0.0519403\pi$
$798$	−4.15237e54	−	1.71418e54i	−0.302163	−	0.124739i
$799$	−1.43866e55			−1.02228
$800$		−	1.11953e54i		−	0.0776830i
$801$	−4.55104e54	+	4.57277e54i	−0.308385	+	0.309857i
$802$	−1.67503e54			−0.110843
$803$		−	1.12534e55i		−	0.727261i
$804$	1.41843e55	−	3.43596e55i	0.895247	−	2.16862i
$805$	2.45289e54			0.151202
$806$			4.81131e54i			0.289666i
$807$	−9.75309e54	−	4.02626e54i	−0.573515	−	0.236758i
$808$	−1.80217e55			−1.03510
$809$		−	4.16420e54i		−	0.233620i	−0.993154	−	0.116810i	$-0.962733\pi$
$809$		−	4.16420e54i		−	0.233620i	0.993154	−	0.116810i	$-0.0372668\pi$
$810$	1.64912e53	+	3.46181e55i	0.00903726	+	1.89709i
$811$	−8.66827e54			−0.464019			−0.232010	−	0.972713i	$-0.574530\pi$
$811$	−8.66827e54			−0.464019			−0.232010	+	0.972713i	$0.574530\pi$
$812$			5.59396e54i			0.292520i
$813$	−5.23173e54	+	1.26732e55i	−0.267254	+	0.647389i
$814$	1.67866e55			0.837719
$815$		−	3.41642e55i		−	1.66562i
$816$	6.31814e55	+	2.60825e55i	3.00938	+	1.24233i
$817$	−1.93106e55			−0.898623
$818$			5.67581e55i			2.58057i
$819$	9.49711e53	+	9.45198e53i	0.0421888	+	0.0419883i
$820$	−4.29611e55			−1.86471
$821$			1.22436e55i			0.519267i	0.965707	+	0.259634i	$0.0836018\pi$
$821$			1.22436e55i			0.519267i	−0.965707	+	0.259634i	$0.916398\pi$
$822$	−3.18574e55	+	7.71705e55i	−1.32022	+	3.19806i
$823$	1.60452e55			0.649755			0.324877	−	0.945756i	$-0.394677\pi$
$823$	1.60452e55			0.649755			0.324877	+	0.945756i	$0.394677\pi$
$824$		−	1.06092e56i		−	4.19823i
$825$	1.38557e54	+	5.71989e53i	0.0535800	+	0.0221188i
$826$	−4.63368e54			−0.175108
$827$			3.02976e54i			0.111893i	0.998434	+	0.0559465i	$0.0178176\pi$
$827$			3.02976e54i			0.111893i	−0.998434	+	0.0559465i	$0.982182\pi$
$828$	4.42057e55	−	4.44168e55i	1.59552	−	1.60314i
$829$	−3.83145e55			−1.35153			−0.675767	−	0.737116i	$-0.736187\pi$
$829$	−3.83145e55			−1.35153			−0.675767	+	0.737116i	$0.736187\pi$
$830$		−	3.55834e54i		−	0.122677i
$831$	1.39077e55	−	3.36897e55i	0.468638	−	1.13521i
$832$	−1.60376e55			−0.528197
$833$			3.70790e55i			1.19364i
$834$	−6.38467e53	−	2.63571e53i	−0.0200902	−	0.00829360i
$835$	−2.27706e55			−0.700376
$836$			1.45610e56i			4.37797i
$837$	1.33280e55	−	5.57652e54i	0.391726	−	0.163900i
$838$	8.02101e55			2.30459
$839$		−	3.56264e55i		−	1.00068i	−0.865829	−	0.500339i	$-0.833209\pi$
$839$		−	3.56264e55i		−	1.00068i	0.865829	−	0.500339i	$-0.166791\pi$
$840$	−6.33114e54	+	1.53363e55i	−0.173850	+	0.421129i
$841$	1.76087e55			0.472719
$842$		−	1.08163e56i		−	2.83888i
$843$	−2.40059e54	−	9.91011e53i	−0.0616020	−	0.0254305i
$844$	4.91022e55			1.23195
$845$			3.59256e55i			0.881305i
$846$	−4.59359e55	−	4.57175e55i	−1.10183	−	1.09659i
$847$	1.17310e55			0.275138
$848$		−	6.41931e55i		−	1.47220i
$849$	6.33464e53	−	1.53448e54i	0.0142061	−	0.0344125i
$850$	−3.68326e54			−0.0807743
$851$			1.16654e55i			0.250172i
$852$	−7.58439e55	−	3.13098e55i	−1.59063	−	0.656641i
$853$	−1.55865e55			−0.319681			−0.159841	−	0.987143i	$-0.551098\pi$
$853$	−1.55865e55			−0.319681			−0.159841	+	0.987143i	$0.551098\pi$
$854$		−	2.26300e55i		−	0.453926i
$855$	3.94326e55	−	3.96209e55i	0.773570	−	0.777264i
$856$	−2.33531e56			−4.48068
$857$			3.51881e55i			0.660329i	0.943923	+	0.330165i	$0.107104\pi$
$857$			3.51881e55i			0.660329i	−0.943923	+	0.330165i	$0.892896\pi$
$858$	2.32652e55	−	5.63570e55i	0.427021	−	1.03440i
$859$	−3.48134e55			−0.624995			−0.312498	−	0.949919i	$-0.601166\pi$
$859$	−3.48134e55			−0.624995			−0.312498	+	0.949919i	$0.601166\pi$
$860$			1.19636e56i			2.10084i
$861$	6.47923e54	+	2.67475e54i	0.111292	+	0.0459434i
$862$	1.43565e56			2.41218
$863$		−	6.24240e54i		−	0.102600i	−0.998683	−	0.0512999i	$-0.983664\pi$
$863$		−	6.24240e54i		−	0.102600i	0.998683	−	0.0512999i	$-0.0163364\pi$
$864$	5.27784e55	+	1.26142e56i	0.848584	+	2.02814i
$865$	6.22328e55			0.978844
$866$			1.17934e56i			1.81467i
$867$	1.27578e55	−	3.09042e55i	0.192050	−	0.465216i
$868$	1.16151e55			0.171059
$869$			5.19822e54i			0.0748994i
$870$	−9.03252e55	−	3.72879e55i	−1.27334	−	0.525657i
$871$	2.51331e55			0.346657
$872$		−	1.27543e56i		−	1.72125i
$873$	7.34760e55	+	7.31268e55i	0.970231	+	0.965620i
$874$	−1.42053e56			−1.83541
$875$			1.26304e55i			0.159685i
$876$	−3.38585e55	+	8.20177e55i	−0.418880	+	1.01468i
$877$	5.20887e55			0.630597			0.315298	−	0.948993i	$-0.397895\pi$
$877$	5.20887e55			0.630597			0.315298	+	0.948993i	$0.397895\pi$
$878$		−	2.43993e56i		−	2.89056i
$879$	8.74175e54	+	3.60876e54i	0.101347	+	0.0418378i
$880$	3.90671e56			4.43242
$881$		−	7.60630e55i		−	0.844562i	−0.906465	−	0.422281i	$-0.861230\pi$
$881$		−	7.60630e55i		−	0.844562i	0.906465	−	0.422281i	$-0.138770\pi$
$882$	−1.17830e56	+	1.18392e56i	−1.28042	+	1.28653i
$883$	−4.82205e55			−0.512836			−0.256418	−	0.966566i	$-0.582542\pi$
$883$	−4.82205e55			−0.512836			−0.256418	+	0.966566i	$0.582542\pi$
$884$			1.06717e56i			1.11081i
$885$	2.20017e55	−	5.32962e55i	0.224148	−	0.542968i
$886$	1.95128e56			1.94571
$887$			1.72116e56i			1.67986i	0.542693	+	0.839931i	$0.317405\pi$
$887$			1.72116e56i			1.67986i	−0.542693	+	0.839931i	$0.682595\pi$
$888$	−7.29363e55	−	3.01095e55i	−0.696782	−	0.287645i
$889$	−6.10241e54			−0.0570647
$890$		−	9.06041e55i		−	0.829349i
$891$	−1.83083e56	+	8.72160e53i	−1.64048	+	0.00781483i
$892$	−3.73100e56			−3.27260
$893$			1.04649e56i			0.898580i
$894$	6.42371e54	−	1.55606e55i	0.0539974	−	0.130802i
$895$	−2.10543e56			−1.73262
$896$			9.95767e54i			0.0802242i
$897$	3.91639e55	+	1.61676e55i	0.308908	+	0.127523i
$898$	2.57390e56			1.98766
$899$			4.07820e55i			0.308343i
$900$	−8.37739e54	−	8.33757e54i	−0.0620156	−	0.0617209i
$901$	−9.37856e55			−0.679775
$902$		−	3.18962e56i		−	2.26368i
$903$	7.44853e54	−	1.80431e55i	0.0517611	−	0.125385i
$904$	−3.51716e55			−0.239327
$905$		−	1.40064e56i		−	0.933262i
$906$	1.45387e56	+	6.00186e55i	0.948615	+	0.391606i
$907$	−3.53652e55			−0.225963			−0.112982	−	0.993597i	$-0.536040\pi$
$907$	−3.53652e55			−0.225963			−0.112982	+	0.993597i	$0.536040\pi$
$908$		−	1.71933e56i		−	1.07579i
$909$	−4.32957e55	+	4.35025e55i	−0.265296	+	0.266563i
$910$	−1.88174e55			−0.112921
$911$		−	1.65257e55i		−	0.0971205i	−0.998820	−	0.0485603i	$-0.984537\pi$
$911$		−	1.65257e55i		−	0.0971205i	0.998820	−	0.0485603i	$-0.0154633\pi$
$912$	1.89726e56	−	4.59586e56i	1.09201	−	2.64524i
$913$	1.88188e55			0.106083
$914$			3.86214e56i			2.13231i
$915$	2.60288e56	+	1.07452e56i	1.40752	+	0.581050i
$916$	−4.71623e55			−0.249794
$917$			2.82334e55i			0.146469i
$918$	4.15007e56	−	1.73641e56i	2.10884	−	0.882352i
$919$	3.29364e56			1.63939			0.819694	−	0.572802i	$-0.194143\pi$
$919$	3.29364e56			1.63939			0.819694	+	0.572802i	$0.194143\pi$
$920$			5.24657e56i			2.55803i
$921$	−5.38795e55	+	1.30516e56i	−0.257330	+	0.623348i
$922$	−5.39401e56			−2.52362
$923$		−	5.54776e55i		−	0.254264i
$924$	−1.36052e56	−	5.61650e55i	−0.610856	−	0.252173i
$925$	2.20019e54			0.00967761
$926$			7.70276e56i			3.31923i
$927$	−2.56094e56	−	2.54877e56i	−1.08115	−	1.07601i
$928$	−3.85976e56			−1.59643
$929$		−	4.60431e56i		−	1.86580i	−0.360130	−	0.932902i	$-0.617268\pi$
$929$		−	4.60431e56i		−	1.86580i	0.360130	−	0.932902i	$-0.382732\pi$
$930$	−7.74231e55	+	1.87547e56i	−0.307393	+	0.744620i
$931$	2.69716e56			1.04921
$932$			3.20000e56i			1.21968i
$933$	−2.70187e56	−	1.11538e56i	−1.00905	−	0.416555i
$934$	−2.54267e55			−0.0930464
$935$		−	5.70767e56i		−	2.04663i
$936$	−2.02171e56	+	2.03137e56i	−0.710359	+	0.713751i
$937$	1.45541e56			0.501109			0.250555	−	0.968102i	$-0.419387\pi$
$937$	1.45541e56			0.501109			0.250555	+	0.968102i	$0.419387\pi$
$938$		−	8.51771e55i		−	0.287388i
$939$	−1.70617e56	+	4.13297e56i	−0.564126	+	1.36652i
$940$	6.48337e56			2.10074
$941$		−	1.33855e56i		−	0.425042i	−0.977157	−	0.212521i	$-0.931833\pi$
$941$		−	1.33855e56i		−	0.425042i	0.977157	−	0.212521i	$-0.0681673\pi$
$942$	7.81389e56	+	3.22572e56i	2.43165	+	1.00383i
$943$	2.21655e56			0.676012
$944$		−	5.12858e56i		−	1.53296i
$945$	2.18102e55	+	5.21269e55i	0.0638933	+	0.152707i
$946$	−8.88231e56			−2.55032
$947$			1.51962e55i			0.0427647i	0.999771	+	0.0213823i	$0.00680673\pi$
$947$			1.51962e55i			0.0427647i	−0.999771	+	0.0213823i	$0.993193\pi$
$948$	1.56400e55	−	3.78858e55i	0.0431398	−	0.104500i
$949$	−5.99936e55			−0.162198
$950$			2.67923e55i			0.0710005i
$951$	6.38820e56	+	2.63717e56i	1.65939	+	0.685028i
$952$	2.15611e56			0.548995
$953$			1.88445e56i			0.470349i	0.971953	+	0.235175i	$0.0755662\pi$
$953$			1.88445e56i			0.470349i	−0.971953	+	0.235175i	$0.924434\pi$
$954$	−2.99455e56	−	2.98031e56i	−0.732676	−	0.729194i
$955$	−4.16668e56			−0.999369
$956$		−	1.90006e57i		−	4.46752i
$957$	1.97202e56	−	4.77697e56i	0.454554	−	1.10110i
$958$	3.74677e56			0.846666
$959$			1.36272e56i			0.301893i
$960$	−6.25153e56	−	2.58075e56i	−1.35779	−	0.560522i
$961$	−3.84940e56			−0.819687
$962$		−	8.94914e55i		−	0.186833i
$963$	−5.61040e56	+	5.63719e56i	−1.14840	+	1.15389i
$964$	4.35731e56			0.874489
$965$			7.31237e56i			1.43893i
$966$	5.47928e55	−	1.32728e56i	0.105720	−	0.256093i
$967$	1.89028e56			0.357621			0.178810	−	0.983884i	$-0.442775\pi$
$967$	1.89028e56			0.357621			0.178810	+	0.983884i	$0.442775\pi$
$968$			2.50918e57i			4.65480i
$969$	−6.71452e56	−	2.77188e56i	−1.22141	−	0.504223i
$970$	−1.45584e57			−2.59687
$971$		−	3.38305e56i		−	0.591757i	−0.955226	−	0.295878i	$-0.904388\pi$
$971$		−	3.38305e56i		−	0.591757i	0.955226	−	0.295878i	$-0.0956123\pi$
$972$	1.33697e57	+	5.44488e56i	2.29331	+	0.933962i
$973$	−1.12744e54			−0.00189649
$974$		−	5.11270e56i		−	0.843393i
$975$	3.04935e54	−	7.38664e54i	0.00493309	−	0.0119498i
$976$	2.50470e57			3.97383
$977$			2.50646e56i			0.389999i	0.980803	+	0.194999i	$0.0624705\pi$
$977$			2.50646e56i			0.389999i	−0.980803	+	0.194999i	$0.937529\pi$
$978$	−1.84866e57	−	7.63161e56i	−2.82110	−	1.16460i
$979$	4.79172e56			0.717167
$980$		−	1.67098e57i		−	2.45288i
$981$	−3.07875e56	−	3.06412e56i	−0.443265	−	0.441158i
$982$	2.89422e56			0.408708
$983$			9.01690e56i			1.24894i	0.781050	+	0.624468i	$0.214684\pi$
$983$			9.01690e56i			1.24894i	−0.781050	+	0.624468i	$0.785316\pi$
$984$	−5.72110e56	+	1.38586e57i	−0.777272	+	1.88284i
$985$	−4.99954e56			−0.666257
$986$			1.26986e57i			1.65995i
$987$	−9.77797e55	−	4.03653e55i	−0.125378	−	0.0517586i
$988$	7.76267e56			0.976403
$989$		−	6.17255e56i		−	0.761614i
$990$	1.81378e57	−	1.82244e57i	2.19541	−	2.20590i
$991$	1.10910e57			1.31696			0.658480	−	0.752598i	$-0.271200\pi$
$991$	1.10910e57			1.31696			0.658480	+	0.752598i	$0.271200\pi$
$992$			8.01425e56i			0.933557i
$993$	2.61240e56	−	6.32819e56i	0.298541	−	0.723175i
$994$	−1.88016e56			−0.210792
$995$			1.75367e57i			1.92890i
$996$	−1.37155e56	−	5.66204e55i	−0.148008	−	0.0611006i
$997$	2.04331e56			0.216335			0.108168	−	0.994133i	$-0.465502\pi$
$997$	2.04331e56			0.216335			0.108168	+	0.994133i	$0.465502\pi$
$998$			5.04041e56i			0.523583i
$999$	−2.47904e56	+	1.03724e56i	−0.252662	+	0.105715i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.39.b.a.2.12	yes	12
3.2	odd	2	inner	3.39.b.a.2.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.39.b.a.2.1	✓	12	3.2	odd	2	inner
3.39.b.a.2.12	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)

\(f(q)\)	\(=\)	\(q+977513. i q^{2} +(-4.43499e8 + 1.07432e9i) q^{3} -6.80653e11 q^{4} -1.94075e13i q^{5} +(-1.05016e15 - 4.33526e14i) q^{6} -1.85443e15 q^{7} -3.96650e17i q^{8} +(-9.57469e17 - 9.52919e17i) q^{9} +O(q^{10})\)	\(q+977513. i q^{2} +(-4.43499e8 + 1.07432e9i) q^{3} -6.80653e11 q^{4} -1.94075e13i q^{5} +(-1.05016e15 - 4.33526e14i) q^{6} -1.85443e15 q^{7} -3.96650e17i q^{8} +(-9.57469e17 - 9.52919e17i) q^{9} +1.89711e19 q^{10} +1.00331e20i q^{11} +(3.01869e20 - 7.31238e20i) q^{12} +5.34879e20 q^{13} -1.81273e21i q^{14} +(2.08499e22 + 8.60722e21i) q^{15} +2.00634e23 q^{16} -2.93124e23i q^{17} +(9.31490e23 - 9.35938e23i) q^{18} -2.13221e24 q^{19} +1.32098e25i q^{20} +(8.22439e23 - 1.99225e24i) q^{21} -9.80751e25 q^{22} -6.81549e25i q^{23} +(4.26128e26 + 1.75914e26i) q^{24} -1.28546e25 q^{25} +5.22851e26i q^{26} +(1.44837e27 - 6.06008e26i) q^{27} +1.26222e27 q^{28} +4.43183e27i q^{29} +(-8.41367e27 + 2.03810e28i) q^{30} +9.20206e27 q^{31} +8.70919e28i q^{32} +(-1.07788e29 - 4.44969e28i) q^{33} +2.86533e29 q^{34} +3.59900e28i q^{35} +(6.51704e29 + 6.48607e29i) q^{36} -1.71160e29 q^{37} -2.08426e30i q^{38} +(-2.37219e29 + 5.74631e29i) q^{39} -7.69800e30 q^{40} +3.25222e30i q^{41} +(1.94745e30 + 8.03944e29i) q^{42} +9.05664e30 q^{43} -6.82908e31i q^{44} +(-1.84938e31 + 1.85821e31i) q^{45} +6.66223e31 q^{46} -4.90800e31i q^{47} +(-8.89810e31 + 2.15545e32i) q^{48} -1.26496e32 q^{49} -1.25655e31i q^{50} +(3.14909e32 + 1.30000e32i) q^{51} -3.64067e32 q^{52} -3.19951e32i q^{53} +(5.92380e32 + 1.41580e33i) q^{54} +1.94718e33 q^{55} +7.35561e32i q^{56} +(9.45632e32 - 2.29067e33i) q^{57} -4.33217e33 q^{58} -2.55619e33i q^{59} +(-1.41915e34 - 5.85853e33i) q^{60} +1.24839e34 q^{61} +8.99513e33i q^{62} +(1.77556e33 + 1.76712e33i) q^{63} -2.99835e34 q^{64} -1.03807e34i q^{65} +(4.34962e34 - 1.05364e35i) q^{66} +4.69883e34 q^{67} +1.99516e35i q^{68} +(7.32201e34 + 3.02266e34i) q^{69} -3.51806e34 q^{70} -1.03720e35i q^{71} +(-3.77975e35 + 3.79780e35i) q^{72} -1.12163e35 q^{73} -1.67311e35i q^{74} +(5.70100e33 - 1.38099e34i) q^{75} +1.45129e36 q^{76} -1.86058e35i q^{77} +(-5.61709e35 - 2.31884e35i) q^{78} +5.18105e34 q^{79} -3.89381e36i q^{80} +(8.69280e33 + 1.82478e36i) q^{81} -3.17908e36 q^{82} -1.87566e35i q^{83} +(-5.59795e35 + 1.35603e36i) q^{84} -5.68882e36 q^{85} +8.85298e36i q^{86} +(-4.76120e36 - 1.96551e36i) q^{87} +3.97964e37 q^{88} -4.77590e36i q^{89} +(-1.81642e37 - 1.80779e37i) q^{90} -9.91898e35 q^{91} +4.63898e37i q^{92} +(-4.08111e36 + 9.88595e36i) q^{93} +4.79763e37 q^{94} +4.13809e37i q^{95} +(-9.35644e37 - 3.86252e37i) q^{96} -7.67399e37 q^{97} -1.23651e38i q^{98} +(9.56076e37 - 9.60641e37i) 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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