LMFDB - Embedded newform 21.33.b.a.8.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,33,Mod(8,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 33, names="a")

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

chi := DirichletCharacter("21.8");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 33 $
Character orbit:	$[\chi]$	$=$	21.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:	$136.219975799$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			8.12
Character	$\chi$	$=$	21.8
Dual form			21.33.b.a.8.53

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-89686.4i q^{2} +(4.26712e7 + 5.67388e6i) q^{3} -3.74869e9 q^{4} -2.24090e11i q^{5} +(5.08870e11 - 3.82702e12i) q^{6} -1.25609e13 q^{7} -4.89938e13i q^{8} +(1.78863e15 + 4.84222e14i) q^{9} +O(q^{10})$	\(q-89686.4i q^{2} +(4.26712e7 + 5.67388e6i) q^{3} -3.74869e9 q^{4} -2.24090e11i q^{5} +(5.08870e11 - 3.82702e12i) q^{6} -1.25609e13 q^{7} -4.89938e13i q^{8} +(1.78863e15 + 4.84222e14i) q^{9} -2.00979e16 q^{10} +2.48023e16i q^{11} +(-1.59961e17 - 2.12696e16i) q^{12} -1.07393e18 q^{13} +1.12654e18i q^{14} +(1.27146e18 - 9.56220e18i) q^{15} -2.04946e19 q^{16} +7.51631e19i q^{17} +(4.34281e19 - 1.60416e20i) q^{18} +2.26669e20 q^{19} +8.40045e20i q^{20} +(-5.35987e20 - 7.12688e19i) q^{21} +2.22443e21 q^{22} +5.48033e21i q^{23} +(2.77985e20 - 2.09062e21i) q^{24} -2.69335e22 q^{25} +9.63172e22i q^{26} +(7.35757e22 + 3.08108e22i) q^{27} +4.70868e22 q^{28} +3.48830e23i q^{29} +(-8.57599e23 - 1.14033e23i) q^{30} +8.47678e23 q^{31} +1.62766e24i q^{32} +(-1.40725e23 + 1.05834e24i) q^{33} +6.74111e24 q^{34} +2.81477e24i q^{35} +(-6.70503e24 - 1.81520e24i) q^{36} -1.79369e25 q^{37} -2.03291e25i q^{38} +(-4.58260e25 - 6.09337e24i) q^{39} -1.09790e25 q^{40} +2.36246e25i q^{41} +(-6.39185e24 + 4.80707e25i) q^{42} +1.34327e26 q^{43} -9.29762e25i q^{44} +(1.08509e26 - 4.00816e26i) q^{45} +4.91511e26 q^{46} -2.75220e26i q^{47} +(-8.74527e26 - 1.16284e26i) q^{48} +1.57775e26 q^{49} +2.41557e27i q^{50} +(-4.26466e26 + 3.20730e27i) q^{51} +4.02584e27 q^{52} -5.55366e27i q^{53} +(2.76331e27 - 6.59874e27i) q^{54} +5.55797e27 q^{55} +6.15404e26i q^{56} +(9.67222e27 + 1.28609e27i) q^{57} +3.12853e28 q^{58} +2.33311e28i q^{59} +(-4.76632e27 + 3.58457e28i) q^{60} -2.61950e28 q^{61} -7.60252e28i q^{62} +(-2.24668e28 - 6.08225e27i) q^{63} +5.79554e28 q^{64} +2.40658e29i q^{65} +(9.49191e28 + 1.26212e28i) q^{66} -3.13190e29 q^{67} -2.81763e29i q^{68} +(-3.10947e28 + 2.33852e29i) q^{69} +2.52447e29 q^{70} +1.32003e29i q^{71} +(2.37239e28 - 8.76319e28i) q^{72} -5.41225e29 q^{73} +1.60870e30i q^{74} +(-1.14928e30 - 1.52817e29i) q^{75} -8.49711e29 q^{76} -3.11539e29i q^{77} +(-5.46492e29 + 4.10997e30i) q^{78} -1.76338e29 q^{79} +4.59264e30i q^{80} +(2.96474e30 + 1.73219e30i) q^{81} +2.11881e30 q^{82} +4.83920e30i q^{83} +(2.00925e30 + 2.67165e29i) q^{84} +1.68433e31 q^{85} -1.20473e31i q^{86} +(-1.97922e30 + 1.48850e31i) q^{87} +1.21516e30 q^{88} +1.94612e31i q^{89} +(-3.59477e31 - 9.73183e30i) q^{90} +1.34895e31 q^{91} -2.05441e31i q^{92} +(3.61714e31 + 4.80962e30i) q^{93} -2.46835e31 q^{94} -5.07943e31i q^{95} +(-9.23514e30 + 6.94541e31i) q^{96} -2.84242e29 q^{97} -1.41503e31i q^{98} +(-1.20098e31 + 4.43623e31i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 42774298 q^{3} - 128804556708 q^{4} + 933804622814 q^{6} - 26\!\cdots\!80 q^{9}+O(q^{10}) $ 64 * q + 42774298 * q^3 - 128804556708 * q^4 + 933804622814 * q^6 - 2661709321929080 * q^9	$ 64 q + 42774298 q^{3} - 128804556708 q^{4} + 933804622814 q^{6} - 26\!\cdots\!80 q^{9}+ \cdots + 43\!\cdots\!88 q^{99}+O(q^{100}) $ 64 * q + 42774298 * q^3 - 128804556708 * q^4 + 933804622814 * q^6 - 2661709321929080 * q^9 + 12700458777826876 * q^10 + 16560668213315618 * q^12 - 779662097386845540 * q^13 + 27876123863063359876 * q^15 + 228871642891389581316 * q^16 + 521413503785997440888 * q^18 - 681706881337157521692 * q^19 - 431503881158008113826 * q^21 + 19120468187392744108144 * q^22 - 45125095777673694858054 * q^24 - 237119983579497521268264 * q^25 + 74365326375203190687598 * q^27 - 260996322622686644022008 * q^28 + 852759618763392319765868 * q^30 - 1358180324906510744611784 * q^31 + 167404755195681713530156 * q^33 + 10642186773288746488261680 * q^34 - 11711812793758939011321604 * q^36 + 63659724279901954174127200 * q^37 + 20360640903448602426342556 * q^39 - 266207532467737680346702140 * q^40 + 96091334734695477693967150 * q^42 - 24813883332284263694074960 * q^43 - 295070024428567568989268180 * q^45 - 918028865892271951694570448 * q^46 - 6300988561174358262351979762 * q^48 + 10097624450230131623362735552 * q^49 - 4622010869824749895266142284 * q^51 + 17159412300004978195879866788 * q^52 - 6673593378082253401307883466 * q^54 + 2442354815144746218376572584 * q^55 + 2378509030520646137537303296 * q^57 + 190077506986526245795566340336 * q^58 - 374115780186052983158362561348 * q^60 + 99766669274989725702936459924 * q^61 - 30712401990673050365871429556 * q^63 + 400943516045473601608812787636 * q^64 - 720581678602395470219517737068 * q^66 + 73852404789389472034372092840 * q^67 - 1918774447093691762779494646608 * q^69 + 411148821544167628017331107740 * q^70 - 5739782432693959795949031524256 * q^72 + 3915537814122658222047778895512 * q^73 - 5610513809660665161777257057146 * q^75 + 15527044450561930247763678447284 * q^76 - 8815089651936141495775983174628 * q^78 - 1756119931827678230469250976128 * q^79 - 1723294285320428987738283283928 * q^81 - 26570441417976029198788879753576 * q^82 + 3988641463277435045591806322194 * q^84 - 13918207634511949564944022475904 * q^85 + 4214670677854102763671028064004 * q^87 - 41766265169004456915366483222312 * q^88 + 45890754779166227082585780071648 * q^90 - 28370228500765093177423738459588 * q^91 + 102872460014017329227733357232008 * q^93 - 344540199084263505892210158281184 * q^94 + 705553200246779133797316737679382 * q^96 - 501176499990824103029916368159648 * q^97 + 432901556854707300232201533648688 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$1$

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 $

$2$		−	89686.4i		−	1.36851i	−0.729245	−	0.684253i	$-0.760128\pi$
$2$		−	89686.4i		−	1.36851i	0.729245	−	0.684253i	$-0.239872\pi$
$3$	4.26712e7	+	5.67388e6i	0.991275	+	0.131807i
$3$	4.26712e7	+	5.67388e6i	0.991275	+	0.131807i
$4$	−3.74869e9			−0.872810
$5$		−	2.24090e11i		−	1.46860i	−0.678826	−	0.734300i	$-0.737511\pi$
$5$		−	2.24090e11i		−	1.46860i	0.678826	−	0.734300i	$-0.262489\pi$
$6$	5.08870e11	−	3.82702e12i	0.180379	−	1.35657i
$7$	−1.25609e13			−0.377964
$7$	−1.25609e13			−0.377964
$8$		−	4.89938e13i		−	0.174061i
$9$	1.78863e15	+	4.84222e14i	0.965254	+	0.261315i
$10$	−2.00979e16			−2.00979
$11$			2.48023e16i			0.539771i	0.962892	+	0.269886i	$0.0869859\pi$
$11$			2.48023e16i			0.539771i	−0.962892	+	0.269886i	$0.913014\pi$
$12$	−1.59961e17	−	2.12696e16i	−0.865195	−	0.115043i
$13$	−1.07393e18			−1.61393			−0.806963	−	0.590602i	$-0.798890\pi$
$13$	−1.07393e18			−1.61393			−0.806963	+	0.590602i	$0.798890\pi$
$14$			1.12654e18i			0.517247i
$15$	1.27146e18	−	9.56220e18i	0.193572	−	1.45579i
$16$	−2.04946e19			−1.11101
$17$			7.51631e19i			1.54462i	0.635245	+	0.772311i	$0.280899\pi$
$17$			7.51631e19i			1.54462i	−0.635245	+	0.772311i	$0.719101\pi$
$18$	4.34281e19	−	1.60416e20i	0.357611	−	1.32096i
$19$	2.26669e20			0.785840			0.392920	−	0.919573i	$-0.371465\pi$
$19$	2.26669e20			0.785840			0.392920	+	0.919573i	$0.371465\pi$
$20$			8.40045e20i			1.28181i
$21$	−5.35987e20	−	7.12688e19i	−0.374667	−	0.0498185i
$22$	2.22443e21			0.738680
$23$			5.48033e21i			0.893638i	0.894624	+	0.446819i	$0.147443\pi$
$23$			5.48033e21i			0.893638i	−0.894624	+	0.446819i	$0.852557\pi$
$24$	2.77985e20	−	2.09062e21i	0.0229425	−	0.172542i
$25$	−2.69335e22			−1.15678
$26$			9.63172e22i			2.20867i
$27$	7.35757e22	+	3.08108e22i	0.922389	+	0.386263i
$28$	4.70868e22			0.329891
$29$			3.48830e23i			1.39395i	0.717098	+	0.696973i	$0.245470\pi$
$29$			3.48830e23i			1.39395i	−0.717098	+	0.696973i	$0.754530\pi$
$30$	−8.57599e23	−	1.14033e23i	−1.99225	−	0.264905i
$31$	8.47678e23			1.16532			0.582658	−	0.812717i	$-0.302013\pi$
$31$	8.47678e23			1.16532			0.582658	+	0.812717i	$0.302013\pi$
$32$			1.62766e24i			1.34637i
$33$	−1.40725e23	+	1.05834e24i	−0.0711458	+	0.535062i
$34$	6.74111e24			2.11382
$35$			2.81477e24i			0.555078i
$36$	−6.70503e24	−	1.81520e24i	−0.842483	−	0.228078i
$37$	−1.79369e25			−1.45385			−0.726927	−	0.686715i	$-0.759052\pi$
$37$	−1.79369e25			−1.45385			−0.726927	+	0.686715i	$0.759052\pi$
$38$		−	2.03291e25i		−	1.07543i
$39$	−4.58260e25	−	6.09337e24i	−1.59984	−	0.212727i
$40$	−1.09790e25			−0.255626
$41$			2.36246e25i			0.370530i	0.982689	+	0.185265i	$0.0593143\pi$
$41$			2.36246e25i			0.370530i	−0.982689	+	0.185265i	$0.940686\pi$
$42$	−6.39185e24	+	4.80707e25i	−0.0681770	+	0.512734i
$43$	1.34327e26			0.983259			0.491630	−	0.870804i	$-0.336401\pi$
$43$	1.34327e26			0.983259			0.491630	+	0.870804i	$0.336401\pi$
$44$		−	9.29762e25i		−	0.471117i
$45$	1.08509e26	−	4.00816e26i	0.383767	−	1.41757i
$46$	4.91511e26			1.22295
$47$		−	2.75220e26i		−	0.485416i	−0.970099	−	0.242708i	$-0.921964\pi$
$47$		−	2.75220e26i		−	0.485416i	0.970099	−	0.242708i	$-0.0780357\pi$
$48$	−8.74527e26	−	1.16284e26i	−1.10132	−	0.146440i
$49$	1.57775e26			0.142857
$50$			2.41557e27i			1.58307i
$51$	−4.26466e26	+	3.20730e27i	−0.203593	+	1.53114i
$52$	4.02584e27			1.40865
$53$		−	5.55366e27i		−	1.43273i	−0.697724	−	0.716367i	$-0.745804\pi$
$53$		−	5.55366e27i		−	1.43273i	0.697724	−	0.716367i	$-0.254196\pi$
$54$	2.76331e27	−	6.59874e27i	0.528603	−	1.26229i
$55$	5.55797e27			0.792707
$56$			6.15404e26i			0.0657888i
$57$	9.67222e27	+	1.28609e27i	0.778984	+	0.103580i
$58$	3.12853e28			1.90762
$59$			2.33311e28i			1.08219i	0.840962	+	0.541093i	$0.181989\pi$
$59$			2.33311e28i			1.08219i	−0.840962	+	0.541093i	$0.818011\pi$
$60$	−4.76632e27	+	3.58457e28i	−0.168952	+	1.27062i
$61$	−2.61950e28			−0.712757			−0.356379	−	0.934342i	$-0.615989\pi$
$61$	−2.61950e28			−0.712757			−0.356379	+	0.934342i	$0.615989\pi$
$62$		−	7.60252e28i		−	1.59474i
$63$	−2.24668e28	−	6.08225e27i	−0.364832	−	0.0987678i
$64$	5.79554e28			0.731499
$65$			2.40658e29i			2.37021i
$66$	9.49191e28	+	1.26212e28i	0.732235	+	0.0973635i
$67$	−3.13190e29			−1.89938			−0.949689	−	0.313195i	$-0.898601\pi$
$67$	−3.13190e29			−1.89938			−0.949689	+	0.313195i	$0.898601\pi$
$68$		−	2.81763e29i		−	1.34816i
$69$	−3.10947e28	+	2.33852e29i	−0.117788	+	0.885841i
$70$	2.52447e29			0.759628
$71$			1.32003e29i			0.316555i	0.987395	+	0.158277i	$0.0505940\pi$
$71$			1.32003e29i			0.316555i	−0.987395	+	0.158277i	$0.949406\pi$
$72$	2.37239e28	−	8.76319e28i	0.0454847	−	0.168013i
$73$	−5.41225e29			−0.832170			−0.416085	−	0.909326i	$-0.636598\pi$
$73$	−5.41225e29			−0.832170			−0.416085	+	0.909326i	$0.636598\pi$
$74$			1.60870e30i			1.98961i
$75$	−1.14928e30	−	1.52817e29i	−1.14669	−	0.152473i
$76$	−8.49711e29			−0.685889
$77$		−	3.11539e29i		−	0.204014i
$78$	−5.46492e29	+	4.10997e30i	−0.291119	+	2.18940i
$79$	−1.76338e29			−0.0766149			−0.0383074	−	0.999266i	$-0.512197\pi$
$79$	−1.76338e29			−0.0766149			−0.0383074	+	0.999266i	$0.512197\pi$
$80$			4.59264e30i			1.63163i
$81$	2.96474e30	+	1.73219e30i	0.863429	+	0.504470i
$82$	2.11881e30			0.507072
$83$			4.83920e30i			0.953946i	0.878918	+	0.476973i	$0.158266\pi$
$83$			4.83920e30i			0.953946i	−0.878918	+	0.476973i	$0.841734\pi$
$84$	2.00925e30	+	2.67165e29i	0.327013	+	0.0434821i
$85$	1.68433e31			2.26843
$86$		−	1.20473e31i		−	1.34560i
$87$	−1.97922e30	+	1.48850e31i	−0.183732	+	1.38178i
$88$	1.21516e30			0.0939530
$89$			1.94612e31i			1.25582i	0.778285	+	0.627911i	$0.216090\pi$
$89$			1.94612e31i			1.25582i	−0.778285	+	0.627911i	$0.783910\pi$
$90$	−3.59477e31	−	9.73183e30i	−1.93995	−	0.525187i
$91$	1.34895e31			0.610007
$92$		−	2.05441e31i		−	0.779976i
$93$	3.61714e31	+	4.80962e30i	1.15515	+	0.153597i
$94$	−2.46835e31			−0.664295
$95$		−	5.07943e31i		−	1.15408i
$96$	−9.23514e30	+	6.94541e31i	−0.177461	+	1.33462i
$97$	−2.84242e29			−0.00462743			−0.00231371	−	0.999997i	$-0.500736\pi$
$97$	−2.84242e29			−0.00462743			−0.00231371	+	0.999997i	$0.500736\pi$
$98$		−	1.41503e31i		−	0.195501i
$99$	−1.20098e31	+	4.43623e31i	−0.141050	+	0.521016i
$100$	1.00965e32			1.00965
$101$		−	9.85274e31i		−	0.840262i	−0.907463	−	0.420131i	$-0.861984\pi$
$101$		−	9.85274e31i		−	0.840262i	0.907463	−	0.420131i	$-0.138016\pi$
$102$	2.87651e32	+	3.82482e31i	2.09538	+	0.278618i
$103$	−1.76993e32			−1.10296			−0.551480	−	0.834188i	$-0.685937\pi$
$103$	−1.76993e32			−1.10296			−0.551480	+	0.834188i	$0.685937\pi$
$104$			5.26160e31i			0.280921i
$105$	−1.59707e31	+	1.20109e32i	−0.0731635	+	0.550235i
$106$	−4.98088e32			−1.96071
$107$			2.15392e31i			0.0729607i	0.999334	+	0.0364803i	$0.0116146\pi$
$107$			2.15392e31i			0.0729607i	−0.999334	+	0.0364803i	$0.988385\pi$
$108$	−2.75812e32	−	1.15500e32i	−0.805070	−	0.337134i
$109$	5.60813e32			1.41252			0.706259	−	0.707954i	$-0.250381\pi$
$109$	5.60813e32			1.41252			0.706259	+	0.707954i	$0.250381\pi$
$110$		−	4.98474e32i		−	1.08482i
$111$	−7.65390e32	−	1.01772e32i	−1.44117	−	0.191629i
$112$	2.57430e32			0.419923
$113$		−	1.05550e33i		−	1.49350i	−0.665107	−	0.746748i	$-0.731614\pi$
$113$		−	1.05550e33i		−	1.49350i	0.665107	−	0.746748i	$-0.268386\pi$
$114$	1.15345e32	−	8.67467e32i	0.141749	−	1.06604i
$115$	1.22809e33			1.31240
$116$		−	1.30765e33i		−	1.21665i
$117$	−1.92087e33	−	5.20022e32i	−1.55785	−	0.421743i
$118$	2.09248e33			1.48098
$119$		−	9.44114e32i		−	0.583812i
$120$	−4.68488e32	−	6.22937e31i	−0.253395	−	0.0336934i
$121$	1.49622e33			0.708647
$122$			2.34934e33i			0.975413i
$123$	−1.34043e32	+	1.00809e33i	−0.0488386	+	0.367297i
$124$	−3.17768e33			−1.01710
$125$			8.18019e32i			0.230252i
$126$	−5.45495e32	+	2.01497e33i	−0.135164	+	0.499274i
$127$	−3.64144e33			−0.795085			−0.397543	−	0.917584i	$-0.630137\pi$
$127$	−3.64144e33			−0.795085			−0.397543	+	0.917584i	$0.630137\pi$
$128$			1.79293e33i			0.345306i
$129$	5.73189e33	+	7.62155e32i	0.974680	+	0.129601i
$130$	2.15838e34			3.24365
$131$			9.07204e32i			0.120605i	0.998180	+	0.0603023i	$0.0192065\pi$
$131$			9.07204e32i			0.120605i	−0.998180	+	0.0603023i	$0.980794\pi$
$132$	5.27536e32	−	3.96740e33i	0.0620968	−	0.467007i
$133$	−2.84716e33			−0.297020
$134$			2.80889e34i			2.59931i
$135$	6.90441e33	−	1.64876e34i	0.567265	−	1.35462i
$136$	3.68252e33			0.268858
$137$			4.62572e33i			0.300366i	0.988658	+	0.150183i	$0.0479863\pi$
$137$			4.62572e33i			0.300366i	−0.988658	+	0.150183i	$0.952014\pi$
$138$	2.09734e34	+	2.78878e33i	1.21228	+	0.161194i
$139$	−1.21131e34			−0.623763			−0.311882	−	0.950121i	$-0.600959\pi$
$139$	−1.21131e34			−0.623763			−0.311882	+	0.950121i	$0.600959\pi$
$140$		−	1.05517e34i		−	0.484478i
$141$	1.56156e33	−	1.17440e34i	0.0639815	−	0.481181i
$142$	1.18388e34			0.433207
$143$		−	2.66360e34i		−	0.871150i
$144$	−3.66573e34	−	9.92392e33i	−1.07241	−	0.290324i
$145$	7.81694e34			2.04715
$146$			4.85405e34i			1.13883i
$147$	6.73246e33	+	8.95198e32i	0.141611	+	0.0188296i
$148$	6.72400e34			1.26894
$149$			8.24194e34i			1.39653i	0.715841	+	0.698263i	$0.246044\pi$
$149$			8.24194e34i			1.39653i	−0.715841	+	0.698263i	$0.753956\pi$
$150$	−1.37056e34	+	1.03075e35i	−0.208660	+	1.56925i
$151$	5.26032e33			0.0720080			0.0360040	−	0.999352i	$-0.488537\pi$
$151$	5.26032e33			0.0720080			0.0360040	+	0.999352i	$0.488537\pi$
$152$		−	1.11054e34i		−	0.136784i
$153$	−3.63956e34	+	1.34439e35i	−0.403633	+	1.49095i
$154$	−2.79408e34			−0.279195
$155$		−	1.89956e35i		−	1.71138i
$156$	1.71787e35	+	2.28421e34i	1.39636	+	0.185671i
$157$	−8.79943e34			−0.645744			−0.322872	−	0.946443i	$-0.604648\pi$
$157$	−8.79943e34			−0.645744			−0.322872	+	0.946443i	$0.604648\pi$
$158$			1.58151e34i			0.104848i
$159$	3.15108e34	−	2.36981e35i	0.188845	−	1.42023i
$160$	3.64743e35			1.97727
$161$		−	6.88377e34i		−	0.337763i
$162$	1.55354e35	−	2.65897e35i	0.690371	−	1.18161i
$163$	−4.67157e35			−1.88131			−0.940657	−	0.339360i	$-0.889790\pi$
$163$	−4.67157e35			−1.88131			−0.940657	+	0.339360i	$0.889790\pi$
$164$		−	8.85614e34i		−	0.323402i
$165$	2.37165e35	+	3.15352e34i	0.785791	+	0.104485i
$166$	4.34010e35			1.30548
$167$		−	4.30325e35i		−	1.17580i	−0.808934	−	0.587899i	$-0.799955\pi$
$167$		−	4.30325e35i		−	1.17580i	0.808934	−	0.587899i	$-0.200045\pi$
$168$	−3.49173e33	+	2.62600e34i	−0.00867145	+	0.0652148i
$169$	7.10553e35			1.60476
$170$		−	1.51062e36i		−	3.10436i
$171$	4.05428e35	+	1.09758e35i	0.758535	+	0.205352i
$172$	−5.03550e35			−0.858198
$173$		−	3.84844e35i		−	0.597789i	−0.954286	−	0.298894i	$-0.903382\pi$
$173$		−	3.84844e35i		−	0.597789i	0.954286	−	0.298894i	$-0.0966178\pi$
$174$	1.33498e36	+	1.77509e35i	1.89098	+	0.251439i
$175$	3.38308e35			0.437223
$176$		−	5.08313e35i		−	0.599693i
$177$	−1.32378e35	+	9.95563e35i	−0.142640	+	1.07275i
$178$	1.74540e36			1.71860
$179$			1.91023e36i			1.71964i	0.510600	+	0.859818i	$0.329423\pi$
$179$			1.91023e36i			1.71964i	−0.510600	+	0.859818i	$0.670577\pi$
$180$	−4.06768e35	+	1.50253e36i	−0.334955	+	1.23727i
$181$	6.04622e35			0.455645			0.227823	−	0.973703i	$-0.426839\pi$
$181$	6.04622e35			0.455645			0.227823	+	0.973703i	$0.426839\pi$
$182$		−	1.20983e36i		−	0.834798i
$183$	−1.11777e36	−	1.48627e35i	−0.706539	−	0.0939467i
$184$	2.68502e35			0.155547
$185$			4.01950e36i			2.13513i
$186$	4.31358e35	−	3.24408e36i	0.210199	−	1.58083i
$187$	−1.86422e36			−0.833742
$188$			1.03171e36i			0.423676i
$189$	−9.24174e35	−	3.87010e35i	−0.348630	−	0.145994i
$190$	−4.55556e36			−1.57937
$191$		−	1.64239e36i		−	0.523532i	−0.965131	−	0.261766i	$-0.915695\pi$
$191$		−	1.64239e36i		−	0.523532i	0.965131	−	0.261766i	$-0.0843048\pi$
$192$	2.47302e36	+	3.28832e35i	0.725117	+	0.0964171i
$193$	5.34728e36			1.44283			0.721416	−	0.692501i	$-0.243491\pi$
$193$	5.34728e36			1.44283			0.721416	+	0.692501i	$0.243491\pi$
$194$			2.54926e34i			0.00633267i
$195$	−1.36547e36	+	1.02692e37i	−0.312411	+	2.34953i
$196$	−5.91451e35			−0.124687
$197$		−	3.54215e36i		−	0.688347i	−0.938906	−	0.344174i	$-0.888159\pi$
$197$		−	3.54215e36i		−	0.688347i	0.938906	−	0.344174i	$-0.111841\pi$
$198$	3.97870e36	+	1.07712e36i	0.713014	+	0.193028i
$199$	−3.09822e35			−0.0512228			−0.0256114	−	0.999672i	$-0.508153\pi$
$199$	−3.09822e35			−0.0512228			−0.0256114	+	0.999672i	$0.508153\pi$
$200$			1.31957e36i			0.201351i
$201$	−1.33642e37	−	1.77700e36i	−1.88281	−	0.250352i
$202$	−8.83657e36			−1.14990
$203$		−	4.38161e36i		−	0.526862i
$204$	1.59869e36	−	1.20232e37i	0.177698	−	1.33640i
$205$	5.29405e36			0.544160
$206$			1.58739e37i			1.50941i
$207$	−2.65370e36	+	9.80231e36i	−0.233521	+	0.862587i
$208$	2.20098e37			1.79309
$209$			5.62192e36i			0.424174i
$210$	1.07722e37	+	1.43235e36i	0.753001	+	0.100125i
$211$	−2.99623e36			−0.194113			−0.0970567	−	0.995279i	$-0.530943\pi$
$211$	−2.99623e36			−0.194113			−0.0970567	+	0.995279i	$0.530943\pi$
$212$			2.08190e37i			1.25050i
$213$	−7.48966e35	+	5.63270e36i	−0.0417243	+	0.313793i
$214$	1.93177e36			0.0998471
$215$		−	3.01014e37i		−	1.44401i
$216$	1.50954e36	−	3.60475e36i	0.0672332	−	0.160552i
$217$	−1.06476e37			−0.440448
$218$		−	5.02973e37i		−	1.93304i
$219$	−2.30947e37	−	3.07084e36i	−0.824909	−	0.109686i
$220$	−2.08351e37			−0.691883
$221$		−	8.07202e37i		−	2.49290i
$222$	−9.12757e36	+	6.86451e37i	−0.262245	+	1.97225i
$223$	−4.30595e37			−1.15131			−0.575653	−	0.817694i	$-0.695252\pi$
$223$	−4.30595e37			−1.15131			−0.575653	+	0.817694i	$0.695252\pi$
$224$		−	2.04448e37i		−	0.508879i
$225$	−4.81741e37	−	1.30418e37i	−1.11659	−	0.302285i
$226$	−9.46642e37			−2.04386
$227$			5.09302e37i			1.02462i	0.858801	+	0.512309i	$0.171210\pi$
$227$			5.09302e37i			1.02462i	−0.858801	+	0.512309i	$0.828790\pi$
$228$	−3.62582e37	−	4.82116e36i	−0.679905	−	0.0904053i
$229$	3.54101e37			0.619097			0.309549	−	0.950884i	$-0.399822\pi$
$229$	3.54101e37			0.619097			0.309549	+	0.950884i	$0.399822\pi$
$230$		−	1.10143e38i		−	1.79602i
$231$	1.76763e36	−	1.32937e37i	0.0268906	−	0.202234i
$232$	1.70905e37			0.242631
$233$		−	6.48079e37i		−	0.858882i	−0.903095	−	0.429441i	$-0.858711\pi$
$233$		−	6.48079e37i		−	0.858882i	0.903095	−	0.429441i	$-0.141289\pi$
$234$	−4.66389e37	+	1.72276e38i	−0.577158	+	2.13192i
$235$	−6.16742e37			−0.712882
$236$		−	8.74609e37i		−	0.944543i
$237$	−7.52456e36	−	1.00052e36i	−0.0759464	−	0.0100984i
$238$	−8.46742e37			−0.798950
$239$			1.36760e38i			1.20668i	0.797484	+	0.603340i	$0.206164\pi$
$239$			1.36760e38i			1.20668i	−0.797484	+	0.603340i	$0.793836\pi$
$240$	−2.60581e37	+	1.95973e38i	−0.215061	+	1.61740i
$241$	−1.78184e37			−0.137593			−0.0687964	−	0.997631i	$-0.521916\pi$
$241$	−1.78184e37			−0.137593			−0.0687964	+	0.997631i	$0.521916\pi$
$242$		−	1.34191e38i		−	0.969788i
$243$	1.16681e38	+	9.07362e37i	0.789403	+	0.613875i
$244$	9.81971e37			0.622102
$245$		−	3.53560e37i		−	0.209800i
$246$	9.04120e37	+	1.20219e37i	0.502648	+	0.0668359i
$247$	−2.43427e38			−1.26829
$248$		−	4.15309e37i		−	0.202836i
$249$	−2.74570e37	+	2.06494e38i	−0.125737	+	0.945623i
$250$	7.33652e37			0.315101
$251$			1.82073e37i			0.0733611i	0.999327	+	0.0366805i	$0.0116784\pi$
$251$			1.82073e37i			0.0733611i	−0.999327	+	0.0366805i	$0.988322\pi$
$252$	8.42210e37	+	2.28005e37i	0.318429	+	0.0862055i
$253$	−1.35925e38			−0.482360
$254$			3.26588e38i			1.08808i
$255$	7.18725e38	+	9.55670e37i	2.24864	+	0.298996i
$256$	4.09718e38			1.20405
$257$			3.82075e38i			1.05492i	0.849580	+	0.527459i	$0.176855\pi$
$257$			3.82075e38i			1.05492i	−0.849580	+	0.527459i	$0.823145\pi$
$258$	6.83550e37	−	5.14072e38i	0.177360	−	1.33386i
$259$	2.25303e38			0.549505
$260$		−	9.02152e38i		−	2.06874i
$261$	−1.68911e38	+	6.23929e38i	−0.364259	+	1.34551i
$262$	8.13639e37			0.165048
$263$		−	2.81845e38i		−	0.537922i	−0.963151	−	0.268961i	$-0.913320\pi$
$263$		−	2.81845e38i		−	0.537922i	0.963151	−	0.268961i	$-0.0866802\pi$
$264$	5.18523e37	+	6.89467e36i	0.0931333	+	0.0123837i
$265$	−1.24452e39			−2.10411
$266$			2.55351e38i			0.406473i
$267$	−1.10420e38	+	8.30430e38i	−0.165527	+	1.24487i
$268$	1.17405e39			1.65780
$269$			6.49651e38i			0.864258i	0.901812	+	0.432129i	$0.142237\pi$
$269$			6.49651e38i			0.864258i	−0.901812	+	0.432129i	$0.857763\pi$
$270$	−1.47871e39	−	6.19232e38i	−1.85381	−	0.776306i
$271$	3.68249e38			0.435144			0.217572	−	0.976044i	$-0.430186\pi$
$271$	3.68249e38			0.435144			0.217572	+	0.976044i	$0.430186\pi$
$272$		−	1.54044e39i		−	1.71609i
$273$	5.75614e38	+	7.65380e37i	0.604685	+	0.0804034i
$274$	4.14865e38			0.411052
$275$		−	6.68013e38i		−	0.624398i
$276$	1.16565e38	−	8.76639e38i	0.102807	−	0.773171i
$277$	1.59498e39			1.32763			0.663816	−	0.747896i	$-0.268936\pi$
$277$	1.59498e39			1.32763			0.663816	+	0.747896i	$0.268936\pi$
$278$			1.08638e39i			0.853624i
$279$	1.51619e39	+	4.10464e38i	1.12483	+	0.304514i
$280$	1.37906e38			0.0966174
$281$		−	3.27170e38i		−	0.216507i	−0.994123	−	0.108254i	$-0.965474\pi$
$281$		−	3.27170e38i		−	0.216507i	0.994123	−	0.108254i	$-0.0345258\pi$
$282$	−1.05327e39	−	1.40051e38i	−0.658499	−	0.0875590i
$283$	2.45165e39			1.44835			0.724177	−	0.689614i	$-0.242220\pi$
$283$	2.45165e39			1.44835			0.724177	+	0.689614i	$0.242220\pi$
$284$		−	4.94837e38i		−	0.276292i
$285$	2.88201e38	−	2.16745e39i	0.152117	−	1.14402i
$286$	−2.38889e39			−1.19217
$287$		−	2.96746e38i		−	0.140047i
$288$	−7.88148e38	+	2.91129e39i	−0.351826	+	1.29959i
$289$	−3.28158e39			−1.38585
$290$		−	7.01074e39i		−	2.80153i
$291$	−1.21289e37	−	1.61275e36i	−0.00458706	−	0.000609930i
$292$	2.02888e39			0.726326
$293$			3.33376e39i			1.12993i	0.825114	+	0.564966i	$0.191111\pi$
$293$			3.33376e39i			1.12993i	−0.825114	+	0.564966i	$0.808889\pi$
$294$	8.02871e37	−	6.03810e38i	0.0257685	−	0.193795i
$295$	5.22827e39			1.58930
$296$			8.78798e38i			0.253059i
$297$	−7.64180e38	+	1.82485e39i	−0.208493	+	0.497879i
$298$	7.39190e39			1.91116
$299$		−	5.88551e39i		−	1.44227i
$300$	4.30830e39	+	5.72864e38i	1.00084	+	0.133080i
$301$	−1.68726e39			−0.371637
$302$		−	4.71779e38i		−	0.0985434i
$303$	5.59032e38	−	4.20428e39i	0.110753	−	0.832931i
$304$	−4.64548e39			−0.873079
$305$			5.87006e39i			1.04675i
$306$	1.20574e40	+	3.26419e39i	2.04038	+	0.552374i
$307$	−6.55166e38			−0.105229			−0.0526147	−	0.998615i	$-0.516756\pi$
$307$	−6.55166e38			−0.105229			−0.0526147	+	0.998615i	$0.516756\pi$
$308$			1.16786e39i			0.178066i
$309$	−7.55249e39	−	1.00424e39i	−1.09334	−	0.145378i
$310$	−1.70365e40			−2.34204
$311$			5.24685e39i			0.685066i	0.939506	+	0.342533i	$0.111285\pi$
$311$			5.24685e39i			0.685066i	−0.939506	+	0.342533i	$0.888715\pi$
$312$	−2.98537e38	+	2.24519e39i	−0.0370275	+	0.278470i
$313$	8.17188e39			0.962969			0.481485	−	0.876455i	$-0.340098\pi$
$313$	8.17188e39			0.962969			0.481485	+	0.876455i	$0.340098\pi$
$314$			7.89190e39i			0.883705i
$315$	−1.36297e39	+	5.03459e39i	−0.145050	+	0.535791i
$316$	6.61037e38			0.0668702
$317$			4.94650e39i			0.475719i	0.971300	+	0.237859i	$0.0764457\pi$
$317$			4.94650e39i			0.475719i	−0.971300	+	0.237859i	$0.923554\pi$
$318$	−2.12540e40	−	2.82609e39i	−1.94360	−	0.258436i
$319$	−8.65179e39			−0.752411
$320$		−	1.29872e40i		−	1.07428i
$321$	−1.22211e38	+	9.19102e38i	−0.00961676	+	0.0723241i
$322$	−6.17381e39			−0.462231
$323$			1.70371e40i			1.21383i
$324$	−1.11139e40	−	6.49345e39i	−0.753609	−	0.440307i
$325$	2.89247e40			1.86696
$326$			4.18976e40i			2.57459i
$327$	2.39305e40	+	3.18198e39i	1.40019	+	0.186180i
$328$	1.15746e39			0.0644947
$329$			3.45700e39i			0.183470i
$330$	2.82828e39	−	2.12705e40i	0.142988	−	1.07536i
$331$	−2.65308e40			−1.27791			−0.638957	−	0.769242i	$-0.720634\pi$
$331$	−2.65308e40			−1.27791			−0.638957	+	0.769242i	$0.720634\pi$
$332$		−	1.81406e40i		−	0.832613i
$333$	−3.20826e40	−	8.68546e39i	−1.40334	−	0.379914i
$334$	−3.85943e40			−1.60909
$335$			7.01829e40i			2.78942i
$336$	1.09848e40	+	1.46062e39i	0.416260	+	0.0553490i
$337$	1.27031e40			0.459020			0.229510	−	0.973306i	$-0.426288\pi$
$337$	1.27031e40			0.459020			0.229510	+	0.973306i	$0.426288\pi$
$338$		−	6.37270e40i		−	2.19612i
$339$	5.98879e39	−	4.50395e40i	0.196854	−	1.48047i
$340$	−6.31404e40			−1.97991
$341$			2.10244e40i			0.629004i
$342$	9.84381e39	−	3.63614e40i	0.281025	−	1.03806i
$343$	−1.98180e39			−0.0539949
$344$		−	6.58118e39i		−	0.171147i
$345$	5.24040e40	+	6.96803e39i	1.30095	+	0.172984i
$346$	−3.45153e40			−0.818077
$347$			4.36893e39i			0.0988789i	0.998777	+	0.0494395i	$0.0157435\pi$
$347$			4.36893e39i			0.0988789i	−0.998777	+	0.0494395i	$0.984257\pi$
$348$	7.41947e39	−	5.57991e40i	0.160363	−	1.20603i
$349$	−9.18119e40			−1.89536			−0.947681	−	0.319218i	$-0.896580\pi$
$349$	−9.18119e40			−1.89536			−0.947681	+	0.319218i	$0.896580\pi$
$350$		−	3.03416e40i		−	0.598343i
$351$	−7.90154e40	−	3.30887e40i	−1.48867	−	0.623399i
$352$	−4.03697e40			−0.726730
$353$			6.77162e40i			1.16492i	0.812858	+	0.582462i	$0.197910\pi$
$353$			6.77162e40i			1.16492i	−0.812858	+	0.582462i	$0.802090\pi$
$354$	8.92885e40	+	1.18725e40i	1.46806	+	0.195204i
$355$	2.95805e40			0.464892
$356$		−	7.29538e40i		−	1.09609i
$357$	5.35679e39	−	4.02864e40i	0.0769508	−	0.578718i
$358$	1.71322e41			2.35333
$359$			7.34034e40i			0.964285i	0.876093	+	0.482142i	$0.160141\pi$
$359$			7.34034e40i			0.964285i	−0.876093	+	0.482142i	$0.839859\pi$
$360$	−1.96375e40	−	5.31629e39i	−0.246744	−	0.0667988i
$361$	−3.18197e40			−0.382455
$362$		−	5.42264e40i		−	0.623553i
$363$	6.38455e40	+	8.48938e39i	0.702465	+	0.0934050i
$364$	−5.05681e40			−0.532420
$365$			1.21283e41i			1.22212i
$366$	−1.33299e40	+	1.00249e41i	−0.128567	+	0.966903i
$367$	−6.00040e40			−0.554017			−0.277008	−	0.960868i	$-0.589343\pi$
$367$	−6.00040e40			−0.554017			−0.277008	+	0.960868i	$0.589343\pi$
$368$		−	1.12317e41i		−	0.992843i
$369$	−1.14396e40	+	4.22558e40i	−0.0968250	+	0.357655i
$370$	3.60494e41			2.92194
$371$			6.97588e40i			0.541523i
$372$	−1.35595e41	−	1.80298e40i	−1.00823	−	0.134061i
$373$	4.94188e40			0.352007			0.176003	−	0.984390i	$-0.443683\pi$
$373$	4.94188e40			0.352007			0.176003	+	0.984390i	$0.443683\pi$
$374$			1.67195e41i			1.14098i
$375$	−4.64134e39	+	3.49058e40i	−0.0303489	+	0.228243i
$376$	−1.34841e40			−0.0844919
$377$		−	3.74620e41i		−	2.24972i
$378$	−3.47096e40	+	8.28859e40i	−0.199793	+	0.477103i
$379$	2.79047e41			1.53975			0.769876	−	0.638194i	$-0.220318\pi$
$379$	2.79047e41			1.53975			0.769876	+	0.638194i	$0.220318\pi$
$380$			1.90412e41i			1.00730i
$381$	−1.55384e41	−	2.06611e40i	−0.788148	−	0.104798i
$382$	−1.47300e41			−0.716457
$383$			1.56476e41i			0.729907i	0.931026	+	0.364954i	$0.118915\pi$
$383$			1.56476e41i			0.729907i	−0.931026	+	0.364954i	$0.881085\pi$
$384$	−1.01729e40	+	7.65064e40i	−0.0455139	+	0.342293i
$385$	−6.98129e40			−0.299615
$386$		−	4.79579e41i		−	1.97453i
$387$	2.40262e41	+	6.50441e40i	0.949094	+	0.256940i
$388$	1.06553e39			0.00403886
$389$			1.41036e41i			0.513023i	0.966541	+	0.256511i	$0.0825731\pi$
$389$			1.41036e41i			0.513023i	−0.966541	+	0.256511i	$0.917427\pi$
$390$	9.21004e41	+	1.22464e41i	3.21535	+	0.427537i
$391$	−4.11919e41			−1.38033
$392$		−	7.73001e39i		−	0.0248658i
$393$	−5.14736e39	+	3.87114e40i	−0.0158966	+	0.119552i
$394$	−3.17683e41			−0.942008
$395$			3.95157e40i			0.112517i
$396$	4.50211e40	−	1.66300e41i	0.123110	−	0.454748i
$397$	5.71068e41			1.49982			0.749911	−	0.661538i	$-0.230096\pi$
$397$	5.71068e41			1.49982			0.749911	+	0.661538i	$0.230096\pi$
$398$			2.77869e40i			0.0700988i
$399$	−1.21492e41	−	1.61544e40i	−0.294428	−	0.0391494i
$400$	5.51990e41			1.28520
$401$			2.71037e41i			0.606343i	0.952936	+	0.303172i	$0.0980455\pi$
$401$			2.71037e41i			0.606343i	−0.952936	+	0.303172i	$0.901954\pi$
$402$	−1.59373e41	+	1.19859e42i	−0.342608	+	2.57663i
$403$	−9.10349e41			−1.88073
$404$			3.69348e41i			0.733389i
$405$	3.88168e41	−	6.64370e41i	0.740865	−	1.26803i
$406$	−3.92971e41			−0.721014
$407$		−	4.44878e41i		−	0.784748i
$408$	1.57138e41	+	2.08942e40i	0.266512	+	0.0354375i
$409$	−7.02816e40			−0.114622			−0.0573111	−	0.998356i	$-0.518253\pi$
$409$	−7.02816e40			−0.114622			−0.0573111	+	0.998356i	$0.518253\pi$
$410$		−	4.74805e41i		−	0.744686i
$411$	−2.62458e40	+	1.97385e41i	−0.0395904	+	0.297745i
$412$	6.63491e41			0.962675
$413$		−	2.93058e41i		−	0.409028i
$414$	8.79134e41	+	2.38001e41i	1.18046	+	0.319575i
$415$	1.08442e42			1.40096
$416$		−	1.74800e42i		−	2.17294i
$417$	−5.16882e41	−	6.87285e40i	−0.618321	−	0.0822167i
$418$	5.04210e41			0.580485
$419$		−	9.45347e41i		−	1.04753i	−0.851862	−	0.523766i	$-0.824527\pi$
$419$		−	9.45347e41i		−	1.04753i	0.851862	−	0.523766i	$-0.175473\pi$
$420$	5.98691e40	−	4.50253e41i	0.0638578	−	0.480251i
$421$	−8.47532e41			−0.870247			−0.435123	−	0.900371i	$-0.643295\pi$
$421$	−8.47532e41			−0.870247			−0.435123	+	0.900371i	$0.643295\pi$
$422$			2.68721e41i			0.265645i
$423$	1.33268e41	−	4.92268e41i	0.126846	−	0.468550i
$424$	−2.72095e41			−0.249383
$425$		−	2.02440e42i		−	1.78679i
$426$	5.05177e41	+	6.71721e40i	0.429428	+	0.0570999i
$427$	3.29032e41			0.269397
$428$		−	8.07437e40i		−	0.0636808i
$429$	1.51130e41	−	1.13659e42i	0.114824	−	0.863550i
$430$	−2.69969e42			−1.97614
$431$			1.89669e42i			1.33771i	0.743394	+	0.668854i	$0.233215\pi$
$431$			1.89669e42i			1.33771i	−0.743394	+	0.668854i	$0.766785\pi$
$432$	−1.50790e42	−	6.31454e41i	−1.02479	−	0.429143i
$433$	−3.01728e42			−1.97610			−0.988050	−	0.154133i	$-0.950742\pi$
$433$	−3.01728e42			−1.97610			−0.988050	+	0.154133i	$0.950742\pi$
$434$			9.54942e41i			0.602756i
$435$	3.33558e42	+	4.43524e41i	2.02929	+	0.269829i
$436$	−2.10231e42			−1.23286
$437$			1.24222e42i			0.702257i
$438$	−2.75413e41	+	2.07128e42i	−0.150106	+	1.12889i
$439$	−1.91788e42			−1.00783			−0.503916	−	0.863753i	$-0.668108\pi$
$439$	−1.91788e42			−1.00783			−0.503916	+	0.863753i	$0.668108\pi$
$440$		−	2.72306e41i		−	0.137979i
$441$	2.82202e41	+	7.63983e40i	0.137893	+	0.0373307i
$442$	−7.23950e42			−3.41156
$443$		−	8.90586e41i		−	0.404778i	−0.979305	−	0.202389i	$-0.935130\pi$
$443$		−	8.90586e41i		−	0.404778i	0.979305	−	0.202389i	$-0.0648705\pi$
$444$	2.86921e42	+	3.81512e41i	1.25787	+	0.167255i
$445$	4.36106e42			1.84430
$446$			3.86185e42i			1.57557i
$447$	−4.67638e41	+	3.51693e42i	−0.184073	+	1.38434i
$448$	−7.27970e41			−0.276481
$449$		−	2.09536e42i		−	0.767922i	−0.923349	−	0.383961i	$-0.874560\pi$
$449$		−	2.09536e42i		−	0.767922i	0.923349	−	0.383961i	$-0.125440\pi$
$450$	−1.16967e42	+	4.32056e42i	−0.413679	+	1.52806i
$451$	−5.85946e41			−0.200001
$452$			3.95675e42i			1.30354i
$453$	2.24464e41	+	2.98464e40i	0.0713797	+	0.00949119i
$454$	4.56775e42			1.40220
$455$		−	3.02287e42i		−	0.895855i
$456$	6.30105e40	−	4.73879e41i	0.0180292	−	0.135591i
$457$	−5.15505e42			−1.42421			−0.712105	−	0.702073i	$-0.752258\pi$
$457$	−5.15505e42			−1.42421			−0.712105	+	0.702073i	$0.752258\pi$
$458$		−	3.17580e42i		−	0.847238i
$459$	−2.31584e42	+	5.53018e42i	−0.596630	+	1.42474i
$460$	−4.60373e42			−1.14547
$461$			1.31423e42i			0.315832i	0.987453	+	0.157916i	$0.0504776\pi$
$461$			1.31423e42i			0.315832i	−0.987453	+	0.157916i	$0.949522\pi$
$462$	−1.19227e42	−	1.58533e41i	−0.276759	−	0.0368000i
$463$	1.01590e42			0.227800			0.113900	−	0.993492i	$-0.463666\pi$
$463$	1.01590e42			0.227800			0.113900	+	0.993492i	$0.463666\pi$
$464$		−	7.14912e42i		−	1.54869i
$465$	1.07779e42	−	8.10566e42i	0.225573	−	1.69645i
$466$	−5.81239e42			−1.17539
$467$			1.89098e41i			0.0369502i	0.999829	+	0.0184751i	$0.00588115\pi$
$467$			1.89098e41i			0.0369502i	−0.999829	+	0.0184751i	$0.994119\pi$
$468$	7.20076e42	+	1.94940e42i	1.35970	+	0.368101i
$469$	3.93394e42			0.717897
$470$			5.53134e42i			0.975583i
$471$	−3.75482e42	−	4.99269e41i	−0.640110	−	0.0851138i
$472$	1.14308e42			0.188366
$473$			3.33162e42i			0.530735i
$474$	−8.97332e40	+	6.74851e41i	−0.0138197	+	0.103933i
$475$	−6.10498e42			−0.909047
$476$			3.53919e42i			0.509557i
$477$	2.68921e42	−	9.93347e42i	0.374395	−	1.38295i
$478$	1.22655e43			1.65135
$479$		−	8.22179e42i		−	1.07053i	−0.844685	−	0.535264i	$-0.820212\pi$
$479$		−	8.22179e42i		−	1.07053i	0.844685	−	0.535264i	$-0.179788\pi$
$480$	1.55640e43	+	2.06951e42i	1.96002	+	0.260619i
$481$	1.92631e43			2.34641
$482$			1.59807e42i			0.188297i
$483$	3.90577e41	−	2.93739e42i	0.0445197	−	0.334816i
$484$	−5.60887e42			−0.618514
$485$			6.36958e40i			0.00679584i
$486$	8.13781e42	−	1.04647e43i	0.840092	−	1.08030i
$487$	1.23799e42			0.123667			0.0618336	−	0.998086i	$-0.480305\pi$
$487$	1.23799e42			0.123667			0.0618336	+	0.998086i	$0.480305\pi$
$488$			1.28339e42i			0.124063i
$489$	−1.99341e43	−	2.65059e42i	−1.86490	−	0.247971i
$490$	−3.17095e42			−0.287112
$491$			1.46245e43i			1.28168i	0.767676	+	0.640838i	$0.221413\pi$
$491$			1.46245e43i			1.28168i	−0.767676	+	0.640838i	$0.778587\pi$
$492$	5.02486e41	−	3.77902e42i	0.0426268	−	0.320580i
$493$	−2.62191e43			−2.15312
$494$			2.18321e43i			1.73566i
$495$	9.94117e42	+	2.69129e42i	0.765163	+	0.207146i
$496$	−1.73728e43			−1.29468
$497$		−	1.65807e42i		−	0.119646i
$498$	1.85197e43	+	2.46252e42i	1.29409	+	0.172072i
$499$	−1.92798e43			−1.30465			−0.652326	−	0.757939i	$-0.726207\pi$
$499$	−1.92798e43			−1.30465			−0.652326	+	0.757939i	$0.726207\pi$
$500$		−	3.06650e42i		−	0.200966i
$501$	2.44161e42	−	1.83624e43i	0.154979	−	1.16554i
$502$	1.63295e42			0.100395
$503$		−	2.63351e43i		−	1.56836i	−0.620531	−	0.784182i	$-0.713083\pi$
$503$		−	2.63351e43i		−	1.56836i	0.620531	−	0.784182i	$-0.286917\pi$
$504$	−2.97992e41	+	1.10073e42i	−0.0171916	+	0.0635029i
$505$	−2.20790e43			−1.23401
$506$			1.21906e43i			0.660112i
$507$	3.03201e43	+	4.03159e42i	1.59076	+	0.211519i
$508$	1.36506e43			0.693958
$509$			2.75980e42i			0.135954i	0.997687	+	0.0679772i	$0.0216545\pi$
$509$			2.75980e42i			0.135954i	−0.997687	+	0.0679772i	$0.978345\pi$
$510$	8.57107e42	−	6.44598e43i	0.409178	−	3.07728i
$511$	6.79825e42			0.314531
$512$		−	2.90456e43i		−	1.30245i
$513$	1.66773e43	+	6.98385e42i	0.724850	+	0.303541i
$514$	3.42670e43			1.44366
$515$			3.96624e43i			1.61981i
$516$	−2.14871e43	−	2.85708e42i	−0.850710	−	0.113117i
$517$	6.82610e42			0.262014
$518$		−	2.02067e43i		−	0.752001i
$519$	2.18356e42	−	1.64218e43i	0.0787930	−	0.592573i
$520$	1.17907e43			0.412561
$521$		−	2.56707e42i		−	0.0871033i	−0.999051	−	0.0435516i	$-0.986133\pi$
$521$		−	2.56707e42i		−	0.0871033i	0.999051	−	0.0435516i	$-0.0138673\pi$
$522$	5.59580e43	+	1.51490e43i	1.84134	+	0.498490i
$523$	−3.73148e43			−1.19084			−0.595421	−	0.803414i	$-0.703015\pi$
$523$	−3.73148e43			−1.19084			−0.595421	+	0.803414i	$0.703015\pi$
$524$		−	3.40082e42i		−	0.105265i
$525$	1.44360e43	+	1.91952e42i	0.433408	+	0.0576293i
$526$	−2.52777e43			−0.736149
$527$			6.37141e43i			1.79997i
$528$	2.88411e42	−	2.16903e43i	0.0790440	−	0.594460i
$529$	7.57487e42			0.201412
$530$			1.11617e44i			2.87949i
$531$	−1.12974e43	+	4.17307e43i	−0.282792	+	1.04458i
$532$	1.06731e43			0.259242
$533$		−	2.53713e43i		−	0.598008i
$534$	7.44783e43	+	9.90319e42i	1.70361	+	0.226524i
$535$	4.82672e42			0.107150
$536$			1.53444e43i			0.330607i
$537$	−1.08384e43	+	8.15116e43i	−0.226661	+	1.70463i
$538$	5.82649e43			1.18274
$539$			3.91320e42i			0.0771101i
$540$	−2.58825e43	+	6.18069e43i	−0.495114	+	1.18232i
$541$	−3.88571e42			−0.0721629			−0.0360814	−	0.999349i	$-0.511488\pi$
$541$	−3.88571e42			−0.0721629			−0.0360814	+	0.999349i	$0.511488\pi$
$542$		−	3.30270e43i		−	0.595498i
$543$	2.57999e43	+	3.43055e42i	0.451670	+	0.0600574i
$544$	−1.22340e44			−2.07963
$545$		−	1.25673e44i		−	2.07442i
$546$	6.86442e42	−	5.16248e43i	0.110033	−	0.827515i
$547$	4.12360e42			0.0641917			0.0320959	−	0.999485i	$-0.489782\pi$
$547$	4.12360e42			0.0641917			0.0320959	+	0.999485i	$0.489782\pi$
$548$		−	1.73404e43i		−	0.262162i
$549$	−4.68534e43	−	1.26842e43i	−0.687992	−	0.186254i
$550$	−5.99117e43			−0.854493
$551$			7.90689e43i			1.09542i
$552$	1.14573e43	+	1.52345e42i	0.154190	+	0.0205023i
$553$	2.21496e42			0.0289577
$554$		−	1.43048e44i		−	1.81687i
$555$	−2.28061e43	+	1.71517e44i	−0.281426	+	2.11650i
$556$	4.54084e43			0.544427
$557$			6.81942e43i			0.794446i	0.917722	+	0.397223i	$0.130026\pi$
$557$			6.81942e43i			0.794446i	−0.917722	+	0.397223i	$0.869974\pi$
$558$	3.68131e43	−	1.35981e44i	0.416730	−	1.53933i
$559$	−1.44258e44			−1.58691
$560$		−	5.76875e43i		−	0.616699i
$561$	−7.95484e43	−	1.05774e43i	−0.826468	−	0.109893i
$562$	−2.93427e43			−0.296291
$563$			5.60542e43i			0.550141i	0.961424	+	0.275070i	$0.0887011\pi$
$563$			5.60542e43i			0.550141i	−0.961424	+	0.275070i	$0.911299\pi$
$564$	−5.85382e42	+	4.40244e43i	−0.0558436	+	0.419979i
$565$	−2.36528e44			−2.19335
$566$		−	2.19879e44i		−	1.98208i
$567$	−3.72397e43	−	2.17578e43i	−0.326345	−	0.190672i
$568$	6.46730e42			0.0550998
$569$		−	1.35859e44i		−	1.12536i	−0.826674	−	0.562680i	$-0.809770\pi$
$569$		−	1.35859e44i		−	1.12536i	0.826674	−	0.562680i	$-0.190230\pi$
$570$	−1.94391e44	−	2.58477e43i	−1.56559	−	0.208173i
$571$	−9.60263e43			−0.751991			−0.375995	−	0.926622i	$-0.622699\pi$
$571$	−9.60263e43			−0.751991			−0.375995	+	0.926622i	$0.622699\pi$
$572$			9.98502e43i			0.760348i
$573$	9.31873e42	−	7.00828e43i	0.0690054	−	0.518964i
$574$	−2.66141e43			−0.191655
$575$		−	1.47604e44i		−	1.03375i
$576$	1.03661e44	+	2.80633e43i	0.706083	+	0.191152i
$577$	9.00632e43			0.596670			0.298335	−	0.954461i	$-0.403569\pi$
$577$	9.00632e43			0.596670			0.298335	+	0.954461i	$0.403569\pi$
$578$			2.94313e44i			1.89655i
$579$	2.28175e44	+	3.03398e43i	1.43024	+	0.190176i
$580$	−2.93033e44			−1.78677
$581$		−	6.07845e43i		−	0.360558i
$582$	−1.44642e41	+	1.08780e42i	−0.000834693	+	0.00627742i
$583$	1.37744e44			0.773348
$584$			2.65166e43i			0.144848i
$585$	−1.16532e44	+	4.30449e44i	−0.619371	+	2.28785i
$586$	2.98993e44			1.54632
$587$			8.41297e43i			0.423389i	0.977336	+	0.211694i	$0.0678982\pi$
$587$			8.41297e43i			0.423389i	−0.977336	+	0.211694i	$0.932102\pi$
$588$	−2.52379e43	−	3.35582e42i	−0.123599	−	0.0164347i
$589$	1.92142e44			0.915752
$590$		−	4.68905e44i		−	2.17497i
$591$	2.00977e43	−	1.51148e44i	0.0907293	−	0.682342i
$592$	3.67610e44			1.61525
$593$		−	6.97182e43i		−	0.298175i	−0.988824	−	0.149087i	$-0.952366\pi$
$593$		−	6.97182e43i		−	0.298175i	0.988824	−	0.149087i	$-0.0476336\pi$
$594$	1.63664e44	+	6.85366e43i	0.681350	+	0.285325i
$595$	−2.11567e44			−0.857386
$596$		−	3.08965e44i		−	1.21890i
$597$	−1.32205e43	−	1.75790e42i	−0.0507759	−	0.00675155i
$598$	−5.27850e44			−1.97375
$599$			3.29310e44i			1.19888i	0.800420	+	0.599440i	$0.204610\pi$
$599$			3.29310e44i			1.19888i	−0.800420	+	0.599440i	$0.795390\pi$
$600$	−7.48709e42	+	5.63076e43i	−0.0265395	+	0.199594i
$601$	4.25782e44			1.46959			0.734794	−	0.678290i	$-0.237279\pi$
$601$	4.25782e44			1.46959			0.734794	+	0.678290i	$0.237279\pi$
$602$			1.51325e44i			0.508588i
$603$	−5.60183e44	−	1.51654e44i	−1.83338	−	0.496336i
$604$	−1.97193e43			−0.0628493
$605$		−	3.35289e44i		−	1.04072i
$606$	−3.77067e44	−	5.01376e43i	−1.13987	−	0.151566i
$607$	−2.19522e43			−0.0646338			−0.0323169	−	0.999478i	$-0.510289\pi$
$607$	−2.19522e43			−0.0646338			−0.0323169	+	0.999478i	$0.510289\pi$
$608$			3.68940e44i			1.05803i
$609$	2.48607e43	−	1.86968e44i	0.0694443	−	0.522265i
$610$	5.26465e44			1.43249
$611$			2.95568e44i			0.783426i
$612$	1.36436e44	−	5.03971e44i	0.352294	−	1.30132i
$613$	3.53614e44			0.889531			0.444766	−	0.895647i	$-0.353287\pi$
$613$	3.53614e44			0.889531			0.444766	+	0.895647i	$0.353287\pi$
$614$			5.87595e43i			0.144007i
$615$	2.25903e44	+	3.00378e43i	0.539412	+	0.0717243i
$616$	−1.52635e43			−0.0355109
$617$			4.32509e44i			0.980467i	0.871591	+	0.490233i	$0.163088\pi$
$617$			4.32509e44i			0.980467i	−0.871591	+	0.490233i	$0.836912\pi$
$618$	−9.00663e43	+	6.77356e44i	−0.198951	+	1.49624i
$619$	−1.21922e43			−0.0262440			−0.0131220	−	0.999914i	$-0.504177\pi$
$619$	−1.21922e43			−0.0262440			−0.0131220	+	0.999914i	$0.504177\pi$
$620$			7.12088e44i			1.49371i
$621$	−1.68853e44	+	4.03219e44i	−0.345179	+	0.824282i
$622$	4.70571e44			0.937517
$623$		−	2.44449e44i		−	0.474656i
$624$	9.39184e44	+	1.24881e44i	1.77745	+	0.236343i
$625$	−4.43783e44			−0.818636
$626$		−	7.32907e44i		−	1.31783i
$627$	−3.18981e43	+	2.39894e44i	−0.0559093	+	0.420473i
$628$	3.29863e44			0.563611
$629$		−	1.34820e45i		−	2.24565i
$630$	4.51535e44	+	1.22240e44i	0.733234	+	0.198502i
$631$	−9.43577e44			−1.49385			−0.746926	−	0.664907i	$-0.768471\pi$
$631$	−9.43577e44			−1.49385			−0.746926	+	0.664907i	$0.768471\pi$
$632$			8.63947e42i			0.0133356i
$633$	−1.27853e44	−	1.70002e43i	−0.192420	−	0.0255856i
$634$	4.43634e44			0.651024
$635$			8.16012e44i			1.16766i
$636$	−1.18124e44	+	8.88369e44i	−0.164826	+	1.23959i
$637$	−1.69440e44			−0.230561
$638$			7.75949e44i			1.02968i
$639$	−6.39185e43	+	2.36104e44i	−0.0827205	+	0.305556i
$640$	4.01779e44			0.507116
$641$			7.71362e44i			0.949577i	0.880100	+	0.474788i	$0.157475\pi$
$641$			7.71362e44i			0.949577i	−0.880100	+	0.474788i	$0.842525\pi$
$642$	8.24309e43	+	1.09606e43i	0.0989760	+	0.0131606i
$643$	−3.25286e44			−0.380970			−0.190485	−	0.981690i	$-0.561006\pi$
$643$	−3.25286e44			−0.380970			−0.190485	+	0.981690i	$0.561006\pi$
$644$			2.58051e44i			0.294803i
$645$	1.70792e44	−	1.28446e45i	0.190332	−	1.43141i
$646$	1.52800e45			1.66113
$647$		−	1.28822e44i		−	0.136622i	−0.997664	−	0.0683110i	$-0.978239\pi$
$647$		−	1.28822e44i		−	0.136622i	0.997664	−	0.0683110i	$-0.0217610\pi$
$648$	8.48666e43	−	1.45254e44i	0.0878085	−	0.150289i
$649$	−5.78665e44			−0.584133
$650$		−	2.59416e45i		−	2.55495i
$651$	−4.54344e44	−	6.04130e43i	−0.436605	−	0.0580543i
$652$	1.75123e45			1.64203
$653$		−	6.72906e44i		−	0.615663i	−0.951441	−	0.307832i	$-0.900397\pi$
$653$		−	6.72906e44i		−	0.615663i	0.951441	−	0.307832i	$-0.0996034\pi$
$654$	2.85381e44	−	2.14624e45i	0.254789	−	1.91617i
$655$	2.03296e44			0.177120
$656$		−	4.84177e44i		−	0.411663i
$657$	−9.68053e44	−	2.62073e44i	−0.803255	−	0.217458i
$658$	3.10046e44			0.251080
$659$		−	1.33609e45i		−	1.05601i	−0.849240	−	0.528006i	$-0.822940\pi$
$659$		−	1.33609e45i		−	1.05601i	0.849240	−	0.528006i	$-0.177060\pi$
$660$	−8.89057e44	−	1.18216e44i	−0.685846	−	0.0911953i
$661$	6.68187e44			0.503123			0.251562	−	0.967841i	$-0.419056\pi$
$661$	6.68187e44			0.503123			0.251562	+	0.967841i	$0.419056\pi$
$662$			2.37945e45i			1.74883i
$663$	4.57996e44	−	3.44442e45i	0.328583	−	2.47115i
$664$	2.37090e44			0.166045
$665$			6.38021e44i			0.436203i
$666$	−7.78968e44	+	2.87738e45i	−0.519914	+	1.92048i
$667$	−1.91170e45			−1.24568
$668$			1.61315e45i			1.02625i
$669$	−1.83740e45	−	2.44314e44i	−1.14126	−	0.151751i
$670$	6.29446e45			3.81734
$671$		−	6.49698e44i		−	0.384726i
$672$	1.16001e44	−	8.72403e44i	0.0670741	−	0.504439i
$673$	−7.15281e44			−0.403865			−0.201932	−	0.979399i	$-0.564722\pi$
$673$	−7.15281e44			−0.403865			−0.201932	+	0.979399i	$0.564722\pi$
$674$		−	1.13930e45i		−	0.628172i
$675$	−1.98165e45	−	8.29842e44i	−1.06700	−	0.446822i
$676$	−2.66364e45			−1.40065
$677$			2.48095e45i			1.27409i	0.770828	+	0.637044i	$0.219843\pi$
$677$			2.48095e45i			1.27409i	−0.770828	+	0.637044i	$0.780157\pi$
$678$	−4.03943e45	−	5.37113e44i	−2.02603	−	0.269396i
$679$	3.57032e42			0.00174900
$680$		−	8.25218e44i		−	0.394845i
$681$	−2.88972e44	+	2.17325e45i	−0.135052	+	1.01568i
$682$	1.88560e45			0.860796
$683$		−	1.89582e45i		−	0.845409i	−0.906268	−	0.422704i	$-0.861081\pi$
$683$		−	1.89582e45i		−	0.845409i	0.906268	−	0.422704i	$-0.138919\pi$
$684$	−1.51982e45	−	4.11449e44i	−0.662057	−	0.179233i
$685$	1.03658e45			0.441117
$686$			1.77740e44i			0.0738924i
$687$	1.51099e45	+	2.00912e44i	0.613696	+	0.0816016i
$688$	−2.75297e45			−1.09241
$689$			5.96426e45i			2.31233i
$690$	6.24938e44	−	4.69993e45i	0.236729	−	1.78035i
$691$	1.30703e45			0.483767			0.241884	−	0.970305i	$-0.422235\pi$
$691$	1.30703e45			0.483767			0.241884	+	0.970305i	$0.422235\pi$
$692$			1.44266e45i			0.521756i
$693$	1.50854e44	−	5.57229e44i	0.0533120	−	0.196925i
$694$	3.91834e44			0.135316
$695$			2.71444e45i			0.916058i
$696$	7.29271e44	+	9.69694e43i	0.240514	+	0.0319806i
$697$	−1.77570e45			−0.572328
$698$			8.23429e45i			2.59382i
$699$	3.67712e44	−	2.76543e45i	0.113207	−	0.851388i
$700$	−1.26821e45			−0.381612
$701$		−	2.52051e45i		−	0.741309i	−0.928771	−	0.370655i	$-0.879133\pi$
$701$		−	2.52051e45i		−	0.741309i	0.928771	−	0.370655i	$-0.120867\pi$
$702$	−2.96761e45	+	7.08661e45i	−0.853126	+	2.03725i
$703$	−4.06575e45			−1.14250
$704$			1.43743e45i			0.394842i
$705$	−2.63171e45	−	3.49932e44i	−0.706662	−	0.0939631i
$706$	6.07323e45			1.59421
$707$			1.23759e45i			0.317589i
$708$	4.96242e44	−	3.73206e45i	0.124498	−	0.936302i
$709$	−5.75107e45			−1.41062			−0.705308	−	0.708901i	$-0.749191\pi$
$709$	−5.75107e45			−1.41062			−0.705308	+	0.708901i	$0.749191\pi$
$710$		−	2.65297e45i		−	0.636208i
$711$	−3.15405e44	−	8.53868e43i	−0.0739528	−	0.0200206i
$712$	9.53475e44			0.218590
$713$			4.64556e45i			1.04137i
$714$	−3.61315e45	−	4.80431e44i	−0.791980	−	0.105308i
$715$	−5.96888e45			−1.27937
$716$		−	7.16085e45i		−	1.50092i
$717$	−7.75958e44	+	5.83570e45i	−0.159049	+	1.19615i
$718$	6.58329e45			1.31963
$719$		−	5.68200e45i		−	1.11388i	−0.830552	−	0.556941i	$-0.811975\pi$
$719$		−	5.68200e45i		−	1.11388i	0.830552	−	0.556941i	$-0.188025\pi$
$720$	−2.22386e45	+	8.21455e45i	−0.426370	+	1.57494i
$721$	2.22318e45			0.416880
$722$			2.85379e45i			0.523392i
$723$	−7.60332e44	−	1.01099e44i	−0.136392	−	0.0181358i
$724$	−2.26654e45			−0.397691
$725$		−	9.39520e45i		−	1.61249i
$726$	7.61382e44	−	5.72608e45i	0.127825	−	0.961327i
$727$	−2.50811e45			−0.411904			−0.205952	−	0.978562i	$-0.566029\pi$
$727$	−2.50811e45			−0.411904			−0.205952	+	0.978562i	$0.566029\pi$
$728$		−	6.60903e44i		−	0.106178i
$729$	4.46407e45	+	4.53385e45i	0.701602	+	0.712569i
$730$	1.08775e46			1.67248
$731$			1.00964e46i			1.51876i
$732$	4.19018e45	+	5.57158e44i	0.616674	+	0.0819976i
$733$	−5.38506e45			−0.775402			−0.387701	−	0.921785i	$-0.626731\pi$
$733$	−5.38506e45			−0.775402			−0.387701	+	0.921785i	$0.626731\pi$
$734$			5.38154e45i			0.758175i
$735$	2.00605e44	−	1.50868e45i	0.0276532	−	0.207969i
$736$	−8.92011e45			−1.20316
$737$		−	7.76785e45i		−	1.02523i
$738$	3.78977e45	+	1.02597e45i	0.489454	+	0.132506i
$739$	3.71630e45			0.469678			0.234839	−	0.972034i	$-0.424544\pi$
$739$	3.71630e45			0.469678			0.234839	+	0.972034i	$0.424544\pi$
$740$		−	1.50678e46i		−	1.86356i
$741$	−1.03873e46	−	1.38118e45i	−1.25722	−	0.167170i
$742$	6.25642e45			0.741077
$743$		−	1.17145e46i		−	1.35801i	−0.734133	−	0.679006i	$-0.762411\pi$
$743$		−	1.17145e46i		−	1.35801i	0.734133	−	0.679006i	$-0.237589\pi$
$744$	2.35641e44	−	1.77217e45i	0.0267353	−	0.201066i
$745$	1.84694e46			2.05094
$746$		−	4.43220e45i		−	0.481723i
$747$	−2.34324e45	+	8.65555e45i	−0.249280	+	0.920800i
$748$	6.98838e45			0.727698
$749$		−	2.70551e44i		−	0.0275765i
$750$	3.13058e45	+	4.16265e44i	0.312352	+	0.0415327i
$751$	1.39199e46			1.35956			0.679779	−	0.733417i	$-0.262076\pi$
$751$	1.39199e46			1.35956			0.679779	+	0.733417i	$0.262076\pi$
$752$			5.64051e45i			0.539304i
$753$	−1.03306e44	+	7.76926e44i	−0.00966954	+	0.0727210i
$754$	−3.35983e46			−3.07876
$755$		−	1.17879e45i		−	0.105751i
$756$	3.46444e45	+	1.45078e45i	0.304288	+	0.127425i
$757$	9.30514e45			0.800182			0.400091	−	0.916475i	$-0.368979\pi$
$757$	9.30514e45			0.800182			0.400091	+	0.916475i	$0.368979\pi$
$758$		−	2.50268e46i		−	2.10716i
$759$	−5.80008e45	−	7.71222e44i	−0.478151	−	0.0635786i
$760$	−2.48861e45			−0.200881
$761$		−	1.53994e46i		−	1.21716i	−0.793492	−	0.608580i	$-0.791739\pi$
$761$		−	1.53994e46i		−	1.21716i	0.793492	−	0.608580i	$-0.208261\pi$
$762$	−1.85302e45	+	1.39359e46i	−0.143417	+	1.07859i
$763$	−7.04429e45			−0.533882
$764$			6.15682e45i			0.456944i
$765$	3.01266e46	+	8.15591e45i	2.18961	+	0.592775i
$766$	1.40338e46			0.998883
$767$		−	2.50560e46i		−	1.74657i
$768$	1.74831e46	+	2.32469e45i	1.19355	+	0.158703i
$769$	1.81330e46			1.21241			0.606204	−	0.795309i	$-0.292691\pi$
$769$	1.81330e46			1.21241			0.606204	+	0.795309i	$0.292691\pi$
$770$			6.26127e45i			0.410025i
$771$	−2.16785e45	+	1.63036e46i	−0.139046	+	1.04572i
$772$	−2.00453e46			−1.25932
$773$			1.03192e46i			0.635002i	0.948258	+	0.317501i	$0.102844\pi$
$773$			1.03192e46i			0.635002i	−0.948258	+	0.317501i	$0.897156\pi$
$774$	5.83357e45	−	2.15482e46i	0.351624	−	1.29884i
$775$	−2.28309e46			−1.34802
$776$			1.39261e43i			0.000805454i
$777$	9.61396e45	+	1.27834e45i	0.544711	+	0.0724289i
$778$	1.26490e46			0.702075
$779$			5.35497e45i			0.291177i
$780$	5.11870e45	−	3.84959e46i	0.272676	−	2.05069i
$781$	−3.27397e45			−0.170867
$782$			3.69435e46i			1.88899i
$783$	−1.07477e46	+	2.56654e46i	−0.538429	+	1.28576i
$784$	−3.23354e45			−0.158716
$785$			1.97187e46i			0.948339i
$786$	3.47189e45	+	4.61649e44i	0.163608	+	0.0217546i
$787$	−1.93225e46			−0.892211			−0.446105	−	0.894980i	$-0.647189\pi$
$787$	−1.93225e46			−0.892211			−0.446105	+	0.894980i	$0.647189\pi$
$788$			1.32784e46i			0.600796i
$789$	1.59916e45	−	1.20267e46i	0.0709021	−	0.533229i
$790$	3.54402e45			0.153980
$791$			1.32580e46i			0.564489i
$792$	2.17348e45	+	5.88407e44i	0.0906885	+	0.0245513i
$793$	2.81317e46			1.15034
$794$		−	5.12171e46i		−	2.05252i
$795$	−5.31052e46	−	7.06127e45i	−2.08575	−	0.277338i
$796$	1.16143e45			0.0447078
$797$			1.44224e46i			0.544132i	0.962279	+	0.272066i	$0.0877069\pi$
$797$			1.44224e46i			0.544132i	−0.962279	+	0.272066i	$0.912293\pi$
$798$	−1.44883e45	+	1.08961e46i	−0.0535762	+	0.402927i
$799$	2.06864e46			0.749784
$800$		−	4.38385e46i		−	1.55746i
$801$	−9.42351e45	+	3.48089e46i	−0.328165	+	1.21219i
$802$	2.43083e46			0.829784
$803$		−	1.34236e46i		−	0.449181i
$804$	5.00982e46	+	6.66143e45i	1.64333	+	0.218510i
$805$	−1.54259e46			−0.496039
$806$			8.16460e46i			2.57380i
$807$	−3.68604e45	+	2.77213e46i	−0.113916	+	0.856718i
$808$	−4.82723e45			−0.146257
$809$			1.55359e46i			0.461486i	0.973015	+	0.230743i	$0.0741157\pi$
$809$			1.55359e46i			0.461486i	−0.973015	+	0.230743i	$0.925884\pi$
$810$	−5.95850e46	−	3.48134e46i	−1.73531	−	1.01388i
$811$	−2.35488e46			−0.672412			−0.336206	−	0.941788i	$-0.609144\pi$
$811$	−2.35488e46			−0.672412			−0.336206	+	0.941788i	$0.609144\pi$
$812$			1.64253e46i			0.459850i
$813$	1.57136e46	+	2.08940e45i	0.431348	+	0.0573553i
$814$	−3.98995e46			−1.07393
$815$			1.04685e47i			2.76289i
$816$	8.74025e45	−	6.57322e46i	0.226194	−	1.70112i
$817$	3.04477e46			0.772685
$818$			6.30331e45i			0.156861i
$819$	2.41278e46	+	6.53193e45i	0.588811	+	0.159404i
$820$	−1.98458e46			−0.474948
$821$		−	4.16668e45i		−	0.0977911i	−0.998804	−	0.0488955i	$-0.984430\pi$
$821$		−	4.16668e45i		−	0.0977911i	0.998804	−	0.0488955i	$-0.0155701\pi$
$822$	1.77027e46	+	2.35389e45i	0.407466	+	0.0541798i
$823$	3.85309e46			0.869784			0.434892	−	0.900483i	$-0.356786\pi$
$823$	3.85309e46			0.869784			0.434892	+	0.900483i	$0.356786\pi$
$824$			8.67154e45i			0.191982i
$825$	3.79022e45	−	2.85049e46i	0.0823003	−	0.618950i
$826$	−2.62834e46			−0.559758
$827$		−	8.39173e46i		−	1.75293i	−0.481469	−	0.876463i	$-0.659897\pi$
$827$		−	8.39173e46i		−	1.75293i	0.481469	−	0.876463i	$-0.340103\pi$
$828$	9.94788e45	−	3.67458e46i	0.203819	−	0.752874i
$829$	2.64452e46			0.531464			0.265732	−	0.964047i	$-0.414386\pi$
$829$	2.64452e46			0.531464			0.265732	+	0.964047i	$0.414386\pi$
$830$		−	9.72575e46i		−	1.91723i
$831$	6.80595e46	+	9.04970e45i	1.31605	+	0.174992i
$832$	−6.22402e46			−1.18059
$833$			1.18589e46i			0.220660i
$834$	−6.16401e45	+	4.63573e46i	−0.112514	+	0.846177i
$835$	−9.64316e46			−1.72678
$836$		−	2.10748e46i		−	0.370223i
$837$	6.23685e46	+	2.61176e46i	1.07487	+	0.450118i
$838$	−8.47848e46			−1.43355
$839$		−	1.82421e46i		−	0.302610i	−0.988487	−	0.151305i	$-0.951652\pi$
$839$		−	1.82421e46i		−	0.302610i	0.988487	−	0.151305i	$-0.0483476\pi$
$840$	5.88462e45	+	7.82463e44i	0.0957744	+	0.0127349i
$841$	−5.90590e46			−0.943084
$842$			7.60121e46i			1.19094i
$843$	1.85632e45	−	1.39607e46i	0.0285372	−	0.214618i
$844$	1.12319e46			0.169424
$845$		−	1.59228e47i		−	2.35674i
$846$	−4.41497e46	−	1.19523e46i	−0.641213	−	0.173590i
$847$	−1.87938e46			−0.267843
$848$			1.13820e47i			1.59179i
$849$	1.04615e47	+	1.39103e46i	1.43572	+	0.190904i
$850$	−1.81561e47			−2.44524
$851$		−	9.83004e46i		−	1.29922i
$852$	2.80764e45	−	2.11152e46i	0.0364173	−	0.273881i
$853$	−1.25447e47			−1.59689			−0.798444	−	0.602069i	$-0.794343\pi$
$853$	−1.25447e47			−1.59689			−0.798444	+	0.602069i	$0.794343\pi$
$854$		−	2.95097e46i		−	0.368671i
$855$	2.45957e46	−	9.08525e46i	0.301580	−	1.11398i
$856$	1.05529e45			0.0126996
$857$		−	1.48833e47i		−	1.75795i	−0.476871	−	0.878973i	$-0.658229\pi$
$857$		−	1.48833e47i		−	1.75795i	0.476871	−	0.878973i	$-0.341771\pi$
$858$	−1.01937e47	−	1.35543e46i	−1.18177	−	0.157138i
$859$	−1.19219e47			−1.35661			−0.678305	−	0.734781i	$-0.737285\pi$
$859$	−1.19219e47			−1.35661			−0.678305	+	0.734781i	$0.737285\pi$
$860$			1.12841e47i			1.26035i
$861$	1.68370e45	−	1.26625e46i	0.0184593	−	0.138825i
$862$	1.70108e47			1.83066
$863$			8.67599e46i			0.916529i	0.888816	+	0.458264i	$0.151529\pi$
$863$			8.67599e46i			0.916529i	−0.888816	+	0.458264i	$0.848471\pi$
$864$	−5.01495e46	+	1.19756e47i	−0.520052	+	1.24187i
$865$	−8.62400e46			−0.877912
$866$			2.70609e47i			2.70431i
$867$	−1.40029e47	−	1.86193e46i	−1.37376	−	0.182666i
$868$	3.99144e46			0.384427
$869$		−	4.37360e45i		−	0.0413545i
$870$	3.97781e46	−	2.99156e47i	0.369263	−	2.77709i
$871$	3.36345e47			3.06545
$872$		−	2.74763e46i		−	0.245864i
$873$	−5.08404e44	−	1.37636e44i	−0.00446664	−	0.00120922i
$874$	1.11410e47			0.961043
$875$		−	1.02750e46i		−	0.0870271i
$876$	8.65748e46	+	1.15116e46i	0.719989	+	0.0957351i
$877$	−2.14662e47			−1.75292			−0.876459	−	0.481476i	$-0.840101\pi$
$877$	−2.14662e47			−1.75292			−0.876459	+	0.481476i	$0.840101\pi$
$878$			1.72007e47i			1.37922i
$879$	−1.89153e46	+	1.42255e47i	−0.148933	+	1.12007i
$880$	−1.13908e47			−0.880708
$881$			1.00074e47i			0.759811i	0.925025	+	0.379906i	$0.124044\pi$
$881$			1.00074e47i			0.759811i	−0.925025	+	0.379906i	$0.875956\pi$
$882$	6.85189e45	−	2.53097e46i	0.0510873	−	0.188708i
$883$	−1.48510e47			−1.08739			−0.543694	−	0.839284i	$-0.682975\pi$
$883$	−1.48510e47			−1.08739			−0.543694	+	0.839284i	$0.682975\pi$
$884$			3.02595e47i			2.17583i
$885$	2.23096e47	+	2.96646e46i	1.57543	+	0.209481i
$886$	−7.98735e46			−0.553941
$887$		−	6.20957e46i		−	0.422945i	−0.977384	−	0.211472i	$-0.932174\pi$
$887$		−	6.20957e46i		−	0.422945i	0.977384	−	0.211472i	$-0.0678258\pi$
$888$	−4.98619e45	+	3.74993e46i	−0.0333551	+	0.250851i
$889$	4.57396e46			0.300514
$890$		−	3.91128e47i		−	2.52394i
$891$	−4.29624e46	+	7.35325e46i	−0.272298	+	0.466054i
$892$	1.61416e47			1.00487
$893$		−	6.23838e46i		−	0.381460i
$894$	3.15421e47	+	4.19408e46i	1.89448	+	0.251905i
$895$	4.28064e47			2.52546
$896$		−	2.25208e46i		−	0.130513i
$897$	3.33937e46	−	2.51142e47i	0.190101	−	1.42968i
$898$	−1.87925e47			−1.05091
$899$			2.95695e47i			1.62439i
$900$	1.80590e47	+	4.88895e46i	0.974570	+	0.263837i
$901$	4.17431e47			2.21303
$902$			5.25514e46i			0.273703i
$903$	−7.19975e46	−	9.57333e45i	−0.368395	−	0.0489845i
$904$	−5.17130e46			−0.259959
$905$		−	1.35490e47i		−	0.669160i
$906$	2.67682e45	−	2.01314e46i	0.0129888	−	0.0976836i
$907$	3.61263e47			1.72229			0.861146	−	0.508358i	$-0.169747\pi$
$907$	3.61263e47			1.72229			0.861146	+	0.508358i	$0.169747\pi$
$908$		−	1.90922e47i		−	0.894296i
$909$	4.77091e46	−	1.76229e47i	0.219573	−	0.811066i
$910$	−2.71111e47			−1.22598
$911$		−	1.42792e47i		−	0.634470i	−0.948347	−	0.317235i	$-0.897246\pi$
$911$		−	1.42792e47i		−	0.634470i	0.948347	−	0.317235i	$-0.102754\pi$
$912$	−1.98228e47	−	2.63579e46i	−0.865462	−	0.115078i
$913$	−1.20023e47			−0.514912
$914$			4.62338e47i			1.94904i
$915$	−3.33060e46	+	2.50482e47i	−0.137970	+	1.03762i
$916$	−1.32741e47			−0.540354
$917$		−	1.13953e46i		−	0.0455843i
$918$	4.95982e47	+	2.07699e47i	1.94977	+	0.816491i
$919$	−1.94898e47			−0.752938			−0.376469	−	0.926429i	$-0.622862\pi$
$919$	−1.94898e47			−0.752938			−0.376469	+	0.926429i	$0.622862\pi$
$920$		−	6.01688e46i		−	0.228437i
$921$	−2.79567e46	−	3.71733e45i	−0.104311	−	0.0138700i
$922$	1.17869e47			0.432219
$923$		−	1.41762e47i		−	0.510896i
$924$	−6.62631e45	+	4.98340e46i	−0.0234704	+	0.176512i
$925$	4.83104e47			1.68179
$926$		−	9.11122e46i		−	0.311746i
$927$	−3.16575e47	−	8.57038e46i	−1.06464	−	0.288220i
$928$	−5.67776e47			−1.87676
$929$		−	4.77350e47i		−	1.55091i	−0.631405	−	0.775453i	$-0.717521\pi$
$929$		−	4.77350e47i		−	1.55091i	0.631405	−	0.775453i	$-0.282479\pi$
$930$	−7.26968e47	−	9.66631e46i	−2.32160	−	0.308698i
$931$	3.57628e46			0.112263
$932$			2.42945e47i			0.749640i
$933$	−2.97700e46	+	2.23889e47i	−0.0902968	+	0.679089i
$934$	1.69595e46			0.0505666
$935$			4.17754e47i			1.22443i
$936$	−2.54778e46	+	9.41108e46i	−0.0734089	+	0.271160i
$937$	6.39416e47			1.81113			0.905565	−	0.424207i	$-0.139447\pi$
$937$	6.39416e47			1.81113			0.905565	+	0.424207i	$0.139447\pi$
$938$		−	3.52821e47i		−	0.982447i
$939$	3.48703e47	+	4.63662e46i	0.954568	+	0.126927i
$940$	2.31197e47			0.622210
$941$		−	6.91194e47i		−	1.82880i	−0.404814	−	0.914399i	$-0.632664\pi$
$941$		−	6.91194e47i		−	1.82880i	0.404814	−	0.914399i	$-0.367336\pi$
$942$	−4.47777e46	+	3.36756e47i	−0.116479	+	0.875994i
$943$	−1.29471e47			−0.331119
$944$		−	4.78160e47i		−	1.20232i
$945$	−8.67253e46	+	2.07099e47i	−0.214406	+	0.511998i
$946$	2.98801e47			0.726314
$947$			4.17508e47i			0.997850i	0.866645	+	0.498925i	$0.166272\pi$
$947$			4.17508e47i			0.997850i	−0.866645	+	0.498925i	$0.833728\pi$
$948$	2.82072e46	+	3.75064e45i	0.0662868	+	0.00881399i
$949$	5.81239e47			1.34306
$950$			5.47534e47i			1.24404i
$951$	−2.80659e46	+	2.11073e47i	−0.0627032	+	0.471568i
$952$	−4.62557e46			−0.101619
$953$			2.42876e47i			0.524685i	0.964975	+	0.262342i	$0.0844950\pi$
$953$			2.42876e47i			0.524685i	−0.964975	+	0.262342i	$0.915505\pi$
$954$	−8.90898e47	−	2.41185e47i	−1.89258	−	0.512362i
$955$	−3.68044e47			−0.768858
$956$		−	5.12670e47i		−	1.05320i
$957$	−3.69182e47	−	4.90892e46i	−0.745847	−	0.0991734i
$958$	−7.37383e47			−1.46502
$959$		−	5.81031e46i		−	0.113528i
$960$	7.36880e46	−	5.54181e47i	0.141598	−	1.06491i
$961$	1.89413e47			0.357961
$962$		−	1.72764e48i		−	3.21108i
$963$	−1.04297e46	+	3.85257e46i	−0.0190657	+	0.0704255i
$964$	6.67956e46			0.120092
$965$		−	1.19827e48i		−	2.11894i
$966$	−2.63444e47	−	3.50294e46i	−0.458198	−	0.0609255i
$967$	−7.34412e47			−1.25637			−0.628183	−	0.778066i	$-0.716201\pi$
$967$	−7.34412e47			−1.25637			−0.628183	+	0.778066i	$0.716201\pi$
$968$		−	7.33056e46i		−	0.123348i
$969$	−9.66667e46	+	7.26994e47i	−0.159991	+	1.20324i
$970$	5.71265e45			0.00930015
$971$		−	7.84234e47i		−	1.25585i	−0.778274	−	0.627925i	$-0.783904\pi$
$971$		−	7.84234e47i		−	1.25585i	0.778274	−	0.627925i	$-0.216096\pi$
$972$	−4.37400e47	−	3.40142e47i	−0.688998	−	0.535796i
$973$	1.52152e47			0.235760
$974$		−	1.11031e47i		−	0.169239i
$975$	1.23425e48	+	1.64115e47i	1.85067	+	0.246080i
$976$	5.36856e47			0.791883
$977$			5.48021e47i			0.795215i	0.917556	+	0.397607i	$0.130159\pi$
$977$			5.48021e47i			0.795215i	−0.917556	+	0.397607i	$0.869841\pi$
$978$	−2.37722e47	+	1.78782e48i	−0.339350	+	2.55213i
$979$	−4.82682e47			−0.677857
$980$			1.32538e47i			0.183115i
$981$	1.00309e48	+	2.71558e47i	1.36344	+	0.369112i
$982$	1.31162e48			1.75398
$983$		−	8.57325e47i		−	1.12795i	−0.825792	−	0.563974i	$-0.809272\pi$
$983$		−	8.57325e47i		−	1.12795i	0.825792	−	0.563974i	$-0.190728\pi$
$984$	4.93901e46	+	6.56728e45i	0.0639320	+	0.00850089i
$985$	−7.93762e47			−1.01091
$986$			2.35150e48i			2.94656i
$987$	−1.96146e46	+	1.47514e47i	−0.0241827	+	0.181869i
$988$	9.12533e47			1.10697
$989$			7.36156e47i			0.878677i
$990$	2.41372e47	−	8.91588e47i	0.283481	−	1.04713i
$991$	3.48734e47			0.403010			0.201505	−	0.979487i	$-0.435417\pi$
$991$	3.48734e47			0.403010			0.201505	+	0.979487i	$0.435417\pi$
$992$			1.37973e48i			1.56894i
$993$	−1.13210e48	−	1.50532e47i	−1.26677	−	0.168439i
$994$	−1.48706e47			−0.163737
$995$			6.94283e46i			0.0752258i
$996$	1.02928e47	−	7.74082e47i	0.109745	−	0.825349i
$997$	2.05167e47			0.215271			0.107635	−	0.994190i	$-0.465672\pi$
$997$	2.05167e47			0.215271			0.107635	+	0.994190i	$0.465672\pi$
$998$			1.72914e48i			1.78542i
$999$	−1.31972e48	−	5.52651e47i	−1.34102	−	0.561569i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.33.b.a.8.12	✓	64
3.2	odd	2	inner	21.33.b.a.8.53	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.33.b.a.8.12	✓	64	1.1	even	1	trivial
21.33.b.a.8.53	yes	64	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	21.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-89686.4i q^{2} +(4.26712e7 + 5.67388e6i) q^{3} -3.74869e9 q^{4} -2.24090e11i q^{5} +(5.08870e11 - 3.82702e12i) q^{6} -1.25609e13 q^{7} -4.89938e13i q^{8} +(1.78863e15 + 4.84222e14i) q^{9} +O(q^{10})\)	\(q-89686.4i q^{2} +(4.26712e7 + 5.67388e6i) q^{3} -3.74869e9 q^{4} -2.24090e11i q^{5} +(5.08870e11 - 3.82702e12i) q^{6} -1.25609e13 q^{7} -4.89938e13i q^{8} +(1.78863e15 + 4.84222e14i) q^{9} -2.00979e16 q^{10} +2.48023e16i q^{11} +(-1.59961e17 - 2.12696e16i) q^{12} -1.07393e18 q^{13} +1.12654e18i q^{14} +(1.27146e18 - 9.56220e18i) q^{15} -2.04946e19 q^{16} +7.51631e19i q^{17} +(4.34281e19 - 1.60416e20i) q^{18} +2.26669e20 q^{19} +8.40045e20i q^{20} +(-5.35987e20 - 7.12688e19i) q^{21} +2.22443e21 q^{22} +5.48033e21i q^{23} +(2.77985e20 - 2.09062e21i) q^{24} -2.69335e22 q^{25} +9.63172e22i q^{26} +(7.35757e22 + 3.08108e22i) q^{27} +4.70868e22 q^{28} +3.48830e23i q^{29} +(-8.57599e23 - 1.14033e23i) q^{30} +8.47678e23 q^{31} +1.62766e24i q^{32} +(-1.40725e23 + 1.05834e24i) q^{33} +6.74111e24 q^{34} +2.81477e24i q^{35} +(-6.70503e24 - 1.81520e24i) q^{36} -1.79369e25 q^{37} -2.03291e25i q^{38} +(-4.58260e25 - 6.09337e24i) q^{39} -1.09790e25 q^{40} +2.36246e25i q^{41} +(-6.39185e24 + 4.80707e25i) q^{42} +1.34327e26 q^{43} -9.29762e25i q^{44} +(1.08509e26 - 4.00816e26i) q^{45} +4.91511e26 q^{46} -2.75220e26i q^{47} +(-8.74527e26 - 1.16284e26i) q^{48} +1.57775e26 q^{49} +2.41557e27i q^{50} +(-4.26466e26 + 3.20730e27i) q^{51} +4.02584e27 q^{52} -5.55366e27i q^{53} +(2.76331e27 - 6.59874e27i) q^{54} +5.55797e27 q^{55} +6.15404e26i q^{56} +(9.67222e27 + 1.28609e27i) q^{57} +3.12853e28 q^{58} +2.33311e28i q^{59} +(-4.76632e27 + 3.58457e28i) q^{60} -2.61950e28 q^{61} -7.60252e28i q^{62} +(-2.24668e28 - 6.08225e27i) q^{63} +5.79554e28 q^{64} +2.40658e29i q^{65} +(9.49191e28 + 1.26212e28i) q^{66} -3.13190e29 q^{67} -2.81763e29i q^{68} +(-3.10947e28 + 2.33852e29i) q^{69} +2.52447e29 q^{70} +1.32003e29i q^{71} +(2.37239e28 - 8.76319e28i) q^{72} -5.41225e29 q^{73} +1.60870e30i q^{74} +(-1.14928e30 - 1.52817e29i) q^{75} -8.49711e29 q^{76} -3.11539e29i q^{77} +(-5.46492e29 + 4.10997e30i) q^{78} -1.76338e29 q^{79} +4.59264e30i q^{80} +(2.96474e30 + 1.73219e30i) q^{81} +2.11881e30 q^{82} +4.83920e30i q^{83} +(2.00925e30 + 2.67165e29i) q^{84} +1.68433e31 q^{85} -1.20473e31i q^{86} +(-1.97922e30 + 1.48850e31i) q^{87} +1.21516e30 q^{88} +1.94612e31i q^{89} +(-3.59477e31 - 9.73183e30i) q^{90} +1.34895e31 q^{91} -2.05441e31i q^{92} +(3.61714e31 + 4.80962e30i) q^{93} -2.46835e31 q^{94} -5.07943e31i q^{95} +(-9.23514e30 + 6.94541e31i) q^{96} -2.84242e29 q^{97} -1.41503e31i q^{98} +(-1.20098e31 + 4.43623e31i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 42774298 q^{3} - 128804556708 q^{4} + 933804622814 q^{6} - 26\!\cdots\!80 q^{9}+O(q^{10}) \) 64 * q + 42774298 * q^3 - 128804556708 * q^4 + 933804622814 * q^6 - 2661709321929080 * q^9	\( 64 q + 42774298 q^{3} - 128804556708 q^{4} + 933804622814 q^{6} - 26\!\cdots\!80 q^{9}+ \cdots + 43\!\cdots\!88 q^{99}+O(q^{100}) \) 64 * q + 42774298 * q^3 - 128804556708 * q^4 + 933804622814 * q^6 - 2661709321929080 * q^9 + 12700458777826876 * q^10 + 16560668213315618 * q^12 - 779662097386845540 * q^13 + 27876123863063359876 * q^15 + 228871642891389581316 * q^16 + 521413503785997440888 * q^18 - 681706881337157521692 * q^19 - 431503881158008113826 * q^21 + 19120468187392744108144 * q^22 - 45125095777673694858054 * q^24 - 237119983579497521268264 * q^25 + 74365326375203190687598 * q^27 - 260996322622686644022008 * q^28 + 852759618763392319765868 * q^30 - 1358180324906510744611784 * q^31 + 167404755195681713530156 * q^33 + 10642186773288746488261680 * q^34 - 11711812793758939011321604 * q^36 + 63659724279901954174127200 * q^37 + 20360640903448602426342556 * q^39 - 266207532467737680346702140 * q^40 + 96091334734695477693967150 * q^42 - 24813883332284263694074960 * q^43 - 295070024428567568989268180 * q^45 - 918028865892271951694570448 * q^46 - 6300988561174358262351979762 * q^48 + 10097624450230131623362735552 * q^49 - 4622010869824749895266142284 * q^51 + 17159412300004978195879866788 * q^52 - 6673593378082253401307883466 * q^54 + 2442354815144746218376572584 * q^55 + 2378509030520646137537303296 * q^57 + 190077506986526245795566340336 * q^58 - 374115780186052983158362561348 * q^60 + 99766669274989725702936459924 * q^61 - 30712401990673050365871429556 * q^63 + 400943516045473601608812787636 * q^64 - 720581678602395470219517737068 * q^66 + 73852404789389472034372092840 * q^67 - 1918774447093691762779494646608 * q^69 + 411148821544167628017331107740 * q^70 - 5739782432693959795949031524256 * q^72 + 3915537814122658222047778895512 * q^73 - 5610513809660665161777257057146 * q^75 + 15527044450561930247763678447284 * q^76 - 8815089651936141495775983174628 * q^78 - 1756119931827678230469250976128 * q^79 - 1723294285320428987738283283928 * q^81 - 26570441417976029198788879753576 * q^82 + 3988641463277435045591806322194 * q^84 - 13918207634511949564944022475904 * q^85 + 4214670677854102763671028064004 * q^87 - 41766265169004456915366483222312 * q^88 + 45890754779166227082585780071648 * q^90 - 28370228500765093177423738459588 * q^91 + 102872460014017329227733357232008 * q^93 - 344540199084263505892210158281184 * q^94 + 705553200246779133797316737679382 * q^96 - 501176499990824103029916368159648 * q^97 + 432901556854707300232201533648688 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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