LMFDB - Embedded newform 6.27.b.a.5.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,27,Mod(5,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 27, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 27);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 27 $
Character orbit:	$[\chi]$	$=$	6.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:	$25.6975752438$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 11609466 x^{6} - 3416571600 x^{5} + 38618090622117 x^{4} + \cdots + 60\!\cdots\!96 $ x^8 - 11609466x^6 - 3416571600x^5 + 38618090622117x^4 + 19832313245955600x^3 - 25659229618759655524x^2 - 8410094250198512820000x + 6059395276689883547331396
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{59}\cdot 3^{34}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.6
Root			$-891.970 - 1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.27.b.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5792.62i q^{2} +(-388622. + 1.54623e6i) q^{3} -3.35544e7 q^{4} +1.99247e8i q^{5} +(-8.95674e9 - 2.25114e9i) q^{6} -4.03334e9 q^{7} -1.94368e11i q^{8} +(-2.23981e12 - 1.20180e12i) q^{9} +O(q^{10})$	\(q+5792.62i q^{2} +(-388622. + 1.54623e6i) q^{3} -3.35544e7 q^{4} +1.99247e8i q^{5} +(-8.95674e9 - 2.25114e9i) q^{6} -4.03334e9 q^{7} -1.94368e11i q^{8} +(-2.23981e12 - 1.20180e12i) q^{9} -1.15416e12 q^{10} -4.12625e13i q^{11} +(1.30400e13 - 5.18830e13i) q^{12} -9.55028e13 q^{13} -2.33636e13i q^{14} +(-3.08082e14 - 7.74316e13i) q^{15} +1.12590e15 q^{16} -5.48391e15i q^{17} +(6.96157e15 - 1.29744e16i) q^{18} -2.57645e16 q^{19} -6.68561e15i q^{20} +(1.56744e15 - 6.23649e15i) q^{21} +2.39018e17 q^{22} +6.39440e17i q^{23} +(3.00538e17 + 7.55357e16i) q^{24} +1.45042e18 q^{25} -5.53212e17i q^{26} +(2.72870e18 - 2.99623e18i) q^{27} +1.35336e17 q^{28} -1.27163e19i q^{29} +(4.48532e17 - 1.78460e18i) q^{30} +4.74023e19 q^{31} +6.52191e18i q^{32} +(6.38015e19 + 1.60355e19i) q^{33} +3.17662e19 q^{34} -8.03630e17i q^{35} +(7.51556e19 + 4.03257e19i) q^{36} -6.19222e19 q^{37} -1.49244e20i q^{38} +(3.71145e19 - 1.47670e20i) q^{39} +3.87272e19 q^{40} +1.36040e20i q^{41} +(3.61256e19 + 9.07961e18i) q^{42} -2.89410e21 q^{43} +1.38454e21i q^{44} +(2.39455e20 - 4.46275e20i) q^{45} -3.70403e21 q^{46} -1.44479e21i q^{47} +(-4.37549e20 + 1.74090e21i) q^{48} -9.37121e21 q^{49} +8.40171e21i q^{50} +(8.47941e21 + 2.13117e21i) q^{51} +3.20454e21 q^{52} -1.68415e22i q^{53} +(1.73560e22 + 1.58063e22i) q^{54} +8.22141e21 q^{55} +7.83953e20i q^{56} +(1.00127e22 - 3.98380e22i) q^{57} +7.36604e22 q^{58} -1.69242e23i q^{59} +(1.03375e22 + 2.59817e21i) q^{60} +1.07249e23 q^{61} +2.74584e23i q^{62} +(9.03392e21 + 4.84727e21i) q^{63} -3.77789e22 q^{64} -1.90286e22i q^{65} +(-9.28876e22 + 3.69577e23i) q^{66} +7.95451e22 q^{67} +1.84010e23i q^{68} +(-9.88724e23 - 2.48501e23i) q^{69} +4.65512e21 q^{70} -1.77698e24i q^{71} +(-2.33592e23 + 4.35348e23i) q^{72} -2.59002e24 q^{73} -3.58692e23i q^{74} +(-5.63664e23 + 2.24268e24i) q^{75} +8.64514e23 q^{76} +1.66426e23i q^{77} +(8.55394e23 + 2.14990e23i) q^{78} +5.88312e24 q^{79} +2.24332e23i q^{80} +(3.57243e24 + 5.38362e24i) q^{81} -7.88030e23 q^{82} -7.37251e24i q^{83} +(-5.25947e22 + 2.09262e23i) q^{84} +1.09265e24 q^{85} -1.67644e25i q^{86} +(1.96623e25 + 4.94182e24i) q^{87} -8.02011e24 q^{88} -7.84189e24i q^{89} +(2.58510e24 + 1.38707e24i) q^{90} +3.85196e23 q^{91} -2.14561e25i q^{92} +(-1.84216e25 + 7.32951e25i) q^{93} +8.36910e24 q^{94} -5.13349e24i q^{95} +(-1.00844e25 - 2.53456e24i) q^{96} -7.65289e25 q^{97} -5.42839e25i q^{98} +(-4.95893e25 + 9.24202e25i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9}+O(q^{10}) $ 8 * q + 2194920 * q^3 - 268435456 * q^4 + 8978890752 * q^6 + 183211263760 * q^7 - 4853931303096 * q^9	$ 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9} + 18696278507520 q^{10} - 73649293885440 q^{12} + 512429022548560 q^{13} - 10\!\cdots\!40 q^{15}+ \cdots + 49\!\cdots\!36 q^{99}+O(q^{100}) $ 8 * q + 2194920 * q^3 - 268435456 * q^4 + 8978890752 * q^6 + 183211263760 * q^7 - 4853931303096 * q^9 + 18696278507520 * q^10 - 73649293885440 * q^12 + 512429022548560 * q^13 - 1064426665559040 * q^15 + 9007199254740992 * q^16 - 1881283573186560 * q^18 + 13250502825732304 * q^19 - 376087240418977584 * q^21 + 428662713355468800 * q^22 - 301281579173412864 * q^24 - 5623831579932691000 * q^25 + 11144542948278241320 * q^27 - 6147549891468984320 * q^28 - 12961438025281044480 * q^30 - 31284409294003569776 * q^31 - 27135100230528798720 * q^33 - 98764413849435635712 * q^34 + 162870907842406121472 * q^36 - 884494012218278308400 * q^37 + 1550610890749922311440 * q^39 - 627343005833641328640 * q^40 + 2912220856097001308160 * q^42 - 5161357724259210085040 * q^43 + 20490779480380306513920 * q^45 - 10789778429003593678848 * q^46 + 2471260223527012270080 * q^48 - 29984991896355791854440 * q^49 + 55593505357359326429184 * q^51 - 17194264791932123217920 * q^52 + 6309825934293776793600 * q^54 - 76225105088113564293120 * q^55 + 66535314651975639764880 * q^57 - 142582792844514288599040 * q^58 + 35716232168487549665280 * q^60 + 235221054408754640644432 * q^61 - 635461358798759743298160 * q^63 - 302231454903657293676544 * q^64 - 1507842687345202066489344 * q^66 + 4218736573110688595120080 * q^67 - 2608639506957020943089664 * q^69 + 1864568339879729269309440 * q^70 + 63125401729205450833920 * q^72 + 1648536069669962768198800 * q^73 + 2584159434345978668025000 * q^75 - 444613096031842444771328 * q^76 - 313072373593422745436160 * q^78 - 9378866636279258011040624 * q^79 - 746539638785265647226744 * q^81 - 6997685112389596533227520 * q^82 + 12619393734706234851852288 * q^84 - 41457721476781794937282560 * q^85 + 55271553720839002987729920 * q^87 - 14383533866221569677721600 * q^88 + 32441993904208401898536960 * q^90 - 71633324581325574226388320 * q^91 + 18549099857564620426167120 * q^93 + 67962530415252490428088320 * q^94 + 10109332261226898153013248 * q^96 - 92292347027073928712964080 * q^97 + 4908019641378975318951936 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/6\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$-1$

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 $

$2$			5792.62i			0.707107i
$2$			5792.62i			0.707107i
$3$	−388622.	+	1.54623e6i	−0.243754	+	0.969837i
$3$	−388622.	+	1.54623e6i	−0.243754	+	0.969837i
$4$	−3.35544e7			−0.500000
$5$			1.99247e8i			0.163223i	0.996664	+	0.0816114i	$0.0260066\pi$
$5$			1.99247e8i			0.163223i	−0.996664	+	0.0816114i	$0.973993\pi$
$6$	−8.95674e9	−	2.25114e9i	−0.685778	−	0.172360i
$7$	−4.03334e9			−0.0416285			−0.0208142	−	0.999783i	$-0.506626\pi$
$7$	−4.03334e9			−0.0416285			−0.0208142	+	0.999783i	$0.506626\pi$
$8$		−	1.94368e11i		−	0.353553i
$9$	−2.23981e12	−	1.20180e12i	−0.881168	−	0.472803i
$10$	−1.15416e12			−0.115416
$11$		−	4.12625e13i		−	1.19523i	−0.801784	−	0.597614i	$-0.796116\pi$
$11$		−	4.12625e13i		−	1.19523i	0.801784	−	0.597614i	$-0.203884\pi$
$12$	1.30400e13	−	5.18830e13i	0.121877	−	0.484919i
$13$	−9.55028e13			−0.315321			−0.157660	−	0.987493i	$-0.550395\pi$
$13$	−9.55028e13			−0.315321			−0.157660	+	0.987493i	$0.550395\pi$
$14$		−	2.33636e13i		−	0.0294358i
$15$	−3.08082e14	−	7.74316e13i	−0.158300	−	0.0397862i
$16$	1.12590e15			0.250000
$17$		−	5.48391e15i		−	0.553675i	−0.960917	−	0.276837i	$-0.910714\pi$
$17$		−	5.48391e15i		−	0.553675i	0.960917	−	0.276837i	$-0.0892863\pi$
$18$	6.96157e15	−	1.29744e16i	0.334322	−	0.623080i
$19$	−2.57645e16			−0.612668			−0.306334	−	0.951924i	$-0.599102\pi$
$19$	−2.57645e16			−0.612668			−0.306334	+	0.951924i	$0.599102\pi$
$20$		−	6.68561e15i		−	0.0816114i
$21$	1.56744e15	−	6.23649e15i	0.0101471	−	0.0403728i
$22$	2.39018e17			0.845153
$23$			6.39440e17i			1.26864i	0.773071	+	0.634320i	$0.218720\pi$
$23$			6.39440e17i			1.26864i	−0.773071	+	0.634320i	$0.781280\pi$
$24$	3.00538e17	+	7.55357e16i	0.342889	+	0.0861799i
$25$	1.45042e18			0.973358
$26$		−	5.53212e17i		−	0.222966i
$27$	2.72870e18	−	2.99623e18i	0.673330	−	0.739343i
$28$	1.35336e17			0.0208142
$29$		−	1.27163e19i		−	1.23933i	−0.784868	−	0.619663i	$-0.787269\pi$
$29$		−	1.27163e19i		−	1.23933i	0.784868	−	0.619663i	$-0.212731\pi$
$30$	4.48532e17	−	1.78460e18i	0.0281331	−	0.111935i
$31$	4.74023e19			1.94132			0.970662	−	0.240450i	$-0.0772950\pi$
$31$	4.74023e19			1.94132			0.970662	+	0.240450i	$0.0772950\pi$
$32$			6.52191e18i			0.176777i
$33$	6.38015e19	+	1.60355e19i	1.15918	+	0.291341i
$34$	3.17662e19			0.391507
$35$		−	8.03630e17i		−	0.00679472i
$36$	7.51556e19	+	4.03257e19i	0.440584	+	0.236401i
$37$	−6.19222e19			−0.254228			−0.127114	−	0.991888i	$-0.540571\pi$
$37$	−6.19222e19			−0.254228			−0.127114	+	0.991888i	$0.540571\pi$
$38$		−	1.49244e20i		−	0.433222i
$39$	3.71145e19	−	1.47670e20i	0.0768606	−	0.305810i
$40$	3.87272e19			0.0577080
$41$			1.36040e20i			0.147054i	0.997293	+	0.0735272i	$0.0234256\pi$
$41$			1.36040e20i			0.147054i	−0.997293	+	0.0735272i	$0.976574\pi$
$42$	3.61256e19	+	9.07961e18i	0.0285479	+	0.00717507i
$43$	−2.89410e21			−1.68432			−0.842158	−	0.539230i	$-0.818715\pi$
$43$	−2.89410e21			−1.68432			−0.842158	+	0.539230i	$0.818715\pi$
$44$			1.38454e21i			0.597614i
$45$	2.39455e20	−	4.46275e20i	0.0771722	−	0.143827i
$46$	−3.70403e21			−0.897063
$47$		−	1.44479e21i		−	0.264565i	−0.991212	−	0.132282i	$-0.957769\pi$
$47$		−	1.44479e21i		−	0.264565i	0.991212	−	0.132282i	$-0.0422305\pi$
$48$	−4.37549e20	+	1.74090e21i	−0.0609384	+	0.242459i
$49$	−9.37121e21			−0.998267
$50$			8.40171e21i			0.688268i
$51$	8.47941e21	+	2.13117e21i	0.536974	+	0.134960i
$52$	3.20454e21			0.157660
$53$		−	1.68415e22i		−	0.646835i	−0.946256	−	0.323418i	$-0.895168\pi$
$53$		−	1.68415e22i		−	0.646835i	0.946256	−	0.323418i	$-0.104832\pi$
$54$	1.73560e22	+	1.58063e22i	0.522794	+	0.476116i
$55$	8.22141e21			0.195088
$56$			7.83953e20i			0.0147179i
$57$	1.00127e22	−	3.98380e22i	0.149340	−	0.594188i
$58$	7.36604e22			0.876335
$59$		−	1.69242e23i		−	1.61225i	−0.591745	−	0.806125i	$-0.701561\pi$
$59$		−	1.69242e23i		−	1.61225i	0.591745	−	0.806125i	$-0.298439\pi$
$60$	1.03375e22	+	2.59817e21i	0.0791498	+	0.0198931i
$61$	1.07249e23			0.662375			0.331188	−	0.943565i	$-0.392551\pi$
$61$	1.07249e23			0.662375			0.331188	+	0.943565i	$0.392551\pi$
$62$			2.74584e23i			1.37272i
$63$	9.03392e21	+	4.84727e21i	0.0366817	+	0.0196820i
$64$	−3.77789e22			−0.125000
$65$		−	1.90286e22i		−	0.0514676i
$66$	−9.28876e22	+	3.69577e23i	−0.206009	+	0.819661i
$67$	7.95451e22			0.145091			0.0725456	−	0.997365i	$-0.476888\pi$
$67$	7.95451e22			0.145091			0.0725456	+	0.997365i	$0.476888\pi$
$68$			1.84010e23i			0.276837i
$69$	−9.88724e23	−	2.48501e23i	−1.23037	−	0.309235i
$70$	4.65512e21			0.00480459
$71$		−	1.77698e24i		−	1.52519i	−0.646875	−	0.762596i	$-0.723925\pi$
$71$		−	1.77698e24i		−	1.52519i	0.646875	−	0.762596i	$-0.276075\pi$
$72$	−2.33592e23	+	4.35348e23i	−0.167161	+	0.311540i
$73$	−2.59002e24			−1.54920			−0.774598	−	0.632454i	$-0.782048\pi$
$73$	−2.59002e24			−1.54920			−0.774598	+	0.632454i	$0.782048\pi$
$74$		−	3.58692e23i		−	0.179767i
$75$	−5.63664e23	+	2.24268e24i	−0.237260	+	0.943999i
$76$	8.64514e23			0.306334
$77$			1.66426e23i			0.0497555i
$78$	8.55394e23	+	2.14990e23i	0.216240	+	0.0543486i
$79$	5.88312e24			1.26025			0.630123	−	0.776495i	$-0.283004\pi$
$79$	5.88312e24			1.26025			0.630123	+	0.776495i	$0.283004\pi$
$80$			2.24332e23i			0.0408057i
$81$	3.57243e24	+	5.38362e24i	0.552915	+	0.833237i
$82$	−7.88030e23			−0.103983
$83$		−	7.37251e24i		−	0.830999i	−0.909594	−	0.415499i	$-0.863607\pi$
$83$		−	7.37251e24i		−	0.830999i	0.909594	−	0.415499i	$-0.136393\pi$
$84$	−5.25947e22	+	2.09262e23i	−0.00507354	+	0.0201864i
$85$	1.09265e24			0.0903724
$86$		−	1.67644e25i		−	1.19099i
$87$	1.96623e25	+	4.94182e24i	1.20194	+	0.302090i
$88$	−8.02011e24			−0.422577
$89$		−	7.84189e24i		−	0.356739i	−0.983964	−	0.178370i	$-0.942918\pi$
$89$		−	7.84189e24i		−	0.356739i	0.983964	−	0.178370i	$-0.0570823\pi$
$90$	2.58510e24	+	1.38707e24i	0.101701	+	0.0545690i
$91$	3.85196e23			0.0131263
$92$		−	2.14561e25i		−	0.634320i
$93$	−1.84216e25	+	7.32951e25i	−0.473204	+	1.88277i
$94$	8.36910e24			0.187075
$95$		−	5.13349e24i		−	0.100001i
$96$	−1.00844e25	−	2.53456e24i	−0.171445	−	0.0430900i
$97$	−7.65289e25			−1.13708			−0.568542	−	0.822654i	$-0.692492\pi$
$97$	−7.65289e25			−1.13708			−0.568542	+	0.822654i	$0.692492\pi$
$98$		−	5.42839e25i		−	0.705881i
$99$	−4.95893e25	+	9.24202e25i	−0.565107	+	1.05320i
$100$	−4.86679e25			−0.486679
$101$		−	5.94744e25i		−	0.522579i	−0.965260	−	0.261290i	$-0.915852\pi$
$101$		−	5.94744e25i		−	0.522579i	0.965260	−	0.261290i	$-0.0841478\pi$
$102$	−1.23451e25	+	4.91180e25i	−0.0954313	+	0.379698i
$103$	4.34463e25			0.295848			0.147924	−	0.988999i	$-0.452741\pi$
$103$	4.34463e25			0.295848			0.147924	+	0.988999i	$0.452741\pi$
$104$			1.85627e25i			0.111483i
$105$	1.24260e24	+	3.12308e23i	0.00658977	+	0.00165624i
$106$	9.75562e25			0.457382
$107$		−	1.98467e26i		−	0.823566i	−0.911282	−	0.411783i	$-0.864906\pi$
$107$		−	1.98467e26i		−	0.823566i	0.911282	−	0.411783i	$-0.135094\pi$
$108$	−9.15601e25	+	1.00537e26i	−0.336665	+	0.369671i
$109$	3.95889e26			1.29130			0.645652	−	0.763632i	$-0.276586\pi$
$109$	3.95889e26			1.29130			0.645652	+	0.763632i	$0.276586\pi$
$110$			4.76235e25i			0.137948i
$111$	2.40643e25	−	9.57463e25i	0.0619691	−	0.246560i
$112$	−4.54114e24			−0.0104071
$113$		−	5.13675e26i		−	1.04874i	−0.851490	−	0.524371i	$-0.824300\pi$
$113$		−	5.13675e26i		−	1.04874i	0.851490	−	0.524371i	$-0.175700\pi$
$114$	2.30766e26	+	5.79995e25i	0.420154	+	0.105599i
$115$	−1.27406e26			−0.207071
$116$			4.26687e26i			0.619663i
$117$	2.13908e26	+	1.14775e26i	0.277851	+	0.149085i
$118$	9.80355e26			1.14003
$119$			2.21185e25i			0.0230486i
$120$	−1.50502e25	+	5.98813e25i	−0.0140665	+	0.0559674i
$121$	−5.10775e26			−0.428568
$122$			6.21251e26i			0.468370i
$123$	−2.10350e26	−	5.28683e25i	−0.142619	−	0.0358450i
$124$	−1.59056e27			−0.970662
$125$			5.85891e26i			0.322097i
$126$	−2.80784e25	+	5.23301e25i	−0.0139173	+	0.0259379i
$127$	−3.52878e27			−1.57825			−0.789125	−	0.614232i	$-0.789466\pi$
$127$	−3.52878e27			−1.57825			−0.789125	+	0.614232i	$0.789466\pi$
$128$		−	2.18839e26i		−	0.0883883i
$129$	1.12471e27	−	4.47496e27i	0.410558	−	1.63351i
$130$	1.10226e26			0.0363931
$131$			2.15172e27i			0.643070i	0.946898	+	0.321535i	$0.104199\pi$
$131$			2.15172e27i			0.643070i	−0.946898	+	0.321535i	$0.895801\pi$
$132$	−2.14082e27	−	5.38062e26i	−0.579588	−	0.145670i
$133$	1.03917e26			0.0255044
$134$			4.60774e26i			0.102595i
$135$	5.96988e26	+	5.43685e26i	0.120678	+	0.109903i
$136$	−1.06590e27			−0.195754
$137$			1.10309e28i			1.84181i	0.389789	+	0.920904i	$0.372548\pi$
$137$			1.10309e28i			1.84181i	−0.389789	+	0.920904i	$0.627452\pi$
$138$	1.43947e27	−	5.72730e27i	0.218662	−	0.870005i
$139$	6.61489e27			0.914808			0.457404	−	0.889259i	$-0.348779\pi$
$139$	6.61489e27			0.914808			0.457404	+	0.889259i	$0.348779\pi$
$140$			2.69653e25i			0.00339736i
$141$	2.23398e27	+	5.61476e26i	0.256585	+	0.0644885i
$142$	1.02934e28			1.07847
$143$			3.94068e27i			0.376880i
$144$	−2.52180e27	−	1.35311e27i	−0.220292	−	0.118201i
$145$	2.53367e27			0.202286
$146$		−	1.50030e28i		−	1.09545i
$147$	3.64186e27	−	1.44901e28i	0.243331	−	0.968157i
$148$	2.07777e27			0.127114
$149$		−	3.21987e27i		−	0.180475i	−0.995920	−	0.0902373i	$-0.971237\pi$
$149$		−	3.21987e27i		−	0.180475i	0.995920	−	0.0902373i	$-0.0287626\pi$
$150$	−1.29910e28	−	3.26509e27i	−0.667508	−	0.167768i
$151$	7.32160e27			0.345069			0.172534	−	0.985003i	$-0.444804\pi$
$151$	7.32160e27			0.345069			0.172534	+	0.985003i	$0.444804\pi$
$152$			5.00780e27i			0.216611i
$153$	−6.59057e27	+	1.22829e28i	−0.261779	+	0.487881i
$154$	−9.64041e26			−0.0351824
$155$			9.44476e27i			0.316868i
$156$	−1.24536e27	+	4.95497e27i	−0.0384303	+	0.152905i
$157$	−3.69094e28			−1.04819			−0.524097	−	0.851659i	$-0.675597\pi$
$157$	−3.69094e28			−1.04819			−0.524097	+	0.851659i	$0.675597\pi$
$158$			3.40787e28i			0.891128i
$159$	2.60409e28	+	6.54497e27i	0.627325	+	0.157668i
$160$	−1.29947e27			−0.0288540
$161$		−	2.57908e27i		−	0.0528115i
$162$	−3.11852e28	+	2.06937e28i	−0.589188	+	0.390970i
$163$	−6.54606e28			−1.14167			−0.570836	−	0.821064i	$-0.693381\pi$
$163$	−6.54606e28			−1.14167			−0.570836	+	0.821064i	$0.693381\pi$
$164$		−	4.56476e27i		−	0.0735272i
$165$	−3.19502e27	+	1.27122e28i	−0.0475535	+	0.189204i
$166$	4.27061e28			0.587605
$167$		−	1.38931e29i		−	1.76802i	−0.467470	−	0.884009i	$-0.654835\pi$
$167$		−	1.38931e29i		−	1.76802i	0.467470	−	0.884009i	$-0.345165\pi$
$168$	−1.21217e27	−	3.04661e26i	−0.0142740	−	0.00358754i
$169$	−8.26125e28			−0.900573
$170$			6.32931e27i			0.0639029i
$171$	5.77077e28	+	3.09638e28i	0.539864	+	0.289671i
$172$	9.71099e28			0.842158
$173$		−	6.57510e28i		−	0.528814i	−0.964411	−	0.264407i	$-0.914824\pi$
$173$		−	6.57510e28i		−	0.528814i	0.964411	−	0.264407i	$-0.0851763\pi$
$174$	−2.86261e28	+	1.13896e29i	−0.213610	+	0.849902i
$175$	−5.85003e27			−0.0405194
$176$		−	4.64574e28i		−	0.298807i
$177$	2.61688e29	+	6.57712e28i	1.56362	+	0.392992i
$178$	4.54251e28			0.252253
$179$		−	1.58717e29i		−	0.819472i	−0.912204	−	0.409736i	$-0.865621\pi$
$179$		−	1.58717e29i		−	0.819472i	0.912204	−	0.409736i	$-0.134379\pi$
$180$	−8.03477e27	+	1.49745e28i	−0.0385861	+	0.0719134i
$181$	2.00621e29			0.896511			0.448256	−	0.893905i	$-0.352045\pi$
$181$	2.00621e29			0.896511			0.448256	+	0.893905i	$0.352045\pi$
$182$			2.23129e27i			0.00928171i
$183$	−4.16792e28	+	1.65832e29i	−0.161456	+	0.642396i
$184$	1.24287e29			0.448532
$185$		−	1.23378e28i		−	0.0414959i
$186$	−4.24571e29	−	1.06709e29i	−1.33132	−	0.334606i
$187$	−2.26280e29			−0.661767
$188$			4.84790e28i			0.132282i
$189$	−1.10058e28	+	1.20848e28i	−0.0280297	+	0.0307777i
$190$	2.97364e28			0.0707117
$191$			2.00475e29i			0.445273i	0.974902	+	0.222637i	$0.0714663\pi$
$191$			2.00475e29i			0.445273i	−0.974902	+	0.222637i	$0.928534\pi$
$192$	1.46817e28	−	5.84151e28i	0.0304692	−	0.121230i
$193$	−2.44005e29			−0.473319			−0.236659	−	0.971593i	$-0.576053\pi$
$193$	−2.44005e29			−0.473319			−0.236659	+	0.971593i	$0.576053\pi$
$194$		−	4.43303e29i		−	0.804040i
$195$	2.94227e28	+	7.39494e27i	0.0499152	+	0.0125454i
$196$	3.14446e29			0.499134
$197$			9.09004e29i			1.35053i	0.737575	+	0.675266i	$0.235971\pi$
$197$			9.09004e29i			1.35053i	−0.737575	+	0.675266i	$0.764029\pi$
$198$	−5.35355e29	−	2.87252e29i	−0.744722	−	0.399591i
$199$	−9.99042e29			−1.30165			−0.650824	−	0.759228i	$-0.725577\pi$
$199$	−9.99042e29			−1.30165			−0.650824	+	0.759228i	$0.725577\pi$
$200$		−	2.81915e29i		−	0.344134i
$201$	−3.09130e28	+	1.22995e29i	−0.0353665	+	0.140715i
$202$	3.44513e29			0.369519
$203$			5.12890e28i			0.0515912i
$204$	−2.84522e29	−	7.15102e28i	−0.268487	−	0.0674801i
$205$	−2.71056e28			−0.0240026
$206$			2.51668e29i			0.209196i
$207$	7.68480e29	−	1.43223e30i	0.599816	−	1.11788i
$208$	−1.07527e29			−0.0788302
$209$			1.06311e30i			0.732277i
$210$	−1.80908e27	+	7.19790e27i	−0.00117114	+	0.00465967i
$211$	1.04673e30			0.637037			0.318518	−	0.947917i	$-0.396815\pi$
$211$	1.04673e30			0.637037			0.318518	+	0.947917i	$0.396815\pi$
$212$			5.65106e29i			0.323418i
$213$	2.74763e30	+	6.90574e29i	1.47919	+	0.371771i
$214$	1.14964e30			0.582349
$215$		−	5.76640e29i		−	0.274919i
$216$	−5.82371e29	−	5.30373e29i	−0.261397	−	0.238058i
$217$	−1.91190e29			−0.0808143
$218$			2.29323e30i			0.913090i
$219$	1.00654e30	−	4.00478e30i	0.377622	−	1.50247i
$220$	−2.75865e29			−0.0975442
$221$			5.23729e29i			0.174585i
$222$	5.54622e29	+	1.39396e29i	0.174344	+	0.0438188i
$223$	−2.02884e30			−0.601567			−0.300784	−	0.953692i	$-0.597248\pi$
$223$	−2.02884e30			−0.601567			−0.300784	+	0.953692i	$0.597248\pi$
$224$		−	2.63051e28i		−	0.00735894i
$225$	−3.24866e30	−	1.74311e30i	−0.857693	−	0.460206i
$226$	2.97553e30			0.741573
$227$		−	3.80517e30i		−	0.895443i	−0.894173	−	0.447721i	$-0.852236\pi$
$227$		−	3.80517e30i		−	0.895443i	0.894173	−	0.447721i	$-0.147764\pi$
$228$	−3.35969e29	+	1.33674e30i	−0.0746700	+	0.297094i
$229$	−5.00927e30			−1.05175			−0.525875	−	0.850562i	$-0.676262\pi$
$229$	−5.00927e30			−1.05175			−0.525875	+	0.850562i	$0.676262\pi$
$230$		−	7.38016e29i		−	0.146421i
$231$	−2.57333e29	−	6.46767e28i	−0.0482547	−	0.0121281i
$232$	−2.47163e30			−0.438168
$233$			9.19718e30i			1.54180i	0.636957	+	0.770899i	$0.280193\pi$
$233$			9.19718e30i			1.54180i	−0.636957	+	0.770899i	$0.719807\pi$
$234$	−6.64850e29	+	1.23909e30i	−0.105419	+	0.196470i
$235$	2.87869e29			0.0431830
$236$			5.67883e30i			0.806125i
$237$	−2.28631e30	+	9.09667e30i	−0.307189	+	1.22223i
$238$	−1.28124e29			−0.0162978
$239$		−	1.25584e31i		−	1.51272i	−0.654153	−	0.756362i	$-0.726975\pi$
$239$		−	1.25584e31i		−	1.51272i	0.654153	−	0.756362i	$-0.273025\pi$
$240$	−3.46869e29	−	8.71803e28i	−0.0395749	−	0.00994654i
$241$	7.40927e30			0.800855			0.400427	−	0.916328i	$-0.368862\pi$
$241$	7.40927e30			0.800855			0.400427	+	0.916328i	$0.368862\pi$
$242$		−	2.95873e30i		−	0.303044i
$243$	−9.71265e30	+	3.43162e30i	−0.942880	+	0.333133i
$244$	−3.59867e30			−0.331188
$245$		−	1.86718e30i		−	0.162940i
$246$	3.06246e29	−	1.21848e30i	0.0253463	−	0.100847i
$247$	2.46058e30			0.193187
$248$		−	9.21350e30i		−	0.686361i
$249$	1.13996e31	+	2.86512e30i	0.805933	+	0.202559i
$250$	−3.39385e30			−0.227757
$251$		−	1.76290e31i		−	1.12323i	−0.827398	−	0.561616i	$-0.810180\pi$
$251$		−	1.76290e31i		−	1.12323i	0.827398	−	0.561616i	$-0.189820\pi$
$252$	−3.03128e29	−	1.62647e29i	−0.0183408	−	0.00984102i
$253$	2.63849e31			1.51631
$254$		−	2.04409e31i		−	1.11599i
$255$	−4.24628e29	+	1.68949e30i	−0.0220286	+	0.0876465i
$256$	1.26765e30			0.0625000
$257$			2.81444e31i			1.31905i	0.751683	+	0.659525i	$0.229243\pi$
$257$			2.81444e31i			1.31905i	−0.751683	+	0.659525i	$0.770757\pi$
$258$	2.59217e31	+	6.51502e30i	1.15507	+	0.290309i
$259$	2.49753e29			0.0105831
$260$			6.38495e29i			0.0257338i
$261$	−1.52824e31	+	2.84820e31i	−0.585956	+	1.09205i
$262$	−1.24641e31			−0.454719
$263$			6.44198e30i			0.223663i	0.993727	+	0.111832i	$0.0356717\pi$
$263$			6.44198e30i			0.223663i	−0.993727	+	0.111832i	$0.964328\pi$
$264$	3.11679e30	−	1.24010e31i	0.103005	−	0.409831i
$265$	3.35561e30			0.105578
$266$			6.01952e29i			0.0180344i
$267$	1.21254e31	+	3.04753e30i	0.345979	+	0.0869564i
$268$	−2.66909e30			−0.0725456
$269$		−	1.24739e31i		−	0.323016i	−0.986871	−	0.161508i	$-0.948364\pi$
$269$		−	1.24739e31i		−	0.323016i	0.986871	−	0.161508i	$-0.0516358\pi$
$270$	−3.14936e30	+	3.45812e30i	−0.0777130	+	0.0853319i
$271$	−4.79377e31			−1.12740			−0.563698	−	0.825981i	$-0.690622\pi$
$271$	−4.79377e31			−1.12740			−0.563698	+	0.825981i	$0.690622\pi$
$272$		−	6.17434e30i		−	0.138419i
$273$	−1.49695e29	+	5.95602e29i	−0.00319959	+	0.0127304i
$274$	−6.38979e31			−1.30236
$275$		−	5.98478e31i		−	1.16338i
$276$	3.31761e31	+	8.33829e30i	0.615187	+	0.154618i
$277$	−2.44766e30			−0.0433025			−0.0216513	−	0.999766i	$-0.506892\pi$
$277$	−2.44766e30			−0.0433025			−0.0216513	+	0.999766i	$0.506892\pi$
$278$			3.83175e31i			0.646867i
$279$	−1.06172e32	−	5.69682e31i	−1.71063	−	0.917863i
$280$	−1.56200e29			−0.00240230
$281$			5.30818e31i			0.779405i	0.920941	+	0.389703i	$0.127422\pi$
$281$			5.30818e31i			0.779405i	−0.920941	+	0.389703i	$0.872578\pi$
$282$	−3.25242e30	+	1.29406e31i	−0.0456003	+	0.181433i
$283$	7.03808e31			0.942390			0.471195	−	0.882029i	$-0.343823\pi$
$283$	7.03808e31			0.942390			0.471195	+	0.882029i	$0.343823\pi$
$284$			5.96256e31i			0.762596i
$285$	7.93758e30	+	1.99499e30i	0.0969851	+	0.0243757i
$286$	−2.28269e31			−0.266494
$287$		−	5.48697e29i		−	0.00612165i
$288$	7.83804e30	−	1.46078e31i	0.0835805	−	0.155770i
$289$	6.80274e31			0.693444
$290$			1.46766e31i			0.143038i
$291$	2.97408e31	−	1.18332e32i	0.277169	−	1.10279i
$292$	8.69067e31			0.774598
$293$			1.19580e32i			1.01948i	0.860328	+	0.509740i	$0.170259\pi$
$293$			1.19580e32i			1.01948i	−0.860328	+	0.509740i	$0.829741\pi$
$294$	8.39355e31	+	2.10959e31i	0.684590	+	0.172061i
$295$	3.37209e31			0.263156
$296$			1.20357e31i			0.0898833i
$297$	−1.23632e32	−	1.12593e32i	−0.883682	−	0.804782i
$298$	1.86515e31			0.127615
$299$		−	6.10684e31i		−	0.400028i
$300$	1.89134e31	−	7.52520e31i	0.118630	−	0.472000i
$301$	1.16729e31			0.0701155
$302$			4.24112e31i			0.244000i
$303$	9.19613e31	+	2.31131e31i	0.506817	+	0.127381i
$304$	−2.90083e31			−0.153167
$305$			2.13689e31i			0.108115i
$306$	−7.11504e31	−	3.81767e31i	−0.344984	−	0.185106i
$307$	2.46235e32			1.14433			0.572164	−	0.820139i	$-0.306104\pi$
$307$	2.46235e32			1.14433			0.572164	+	0.820139i	$0.306104\pi$
$308$		−	5.58432e30i		−	0.0248777i
$309$	−1.68842e31	+	6.71781e31i	−0.0721140	+	0.286925i
$310$	−5.47099e31			−0.224060
$311$			8.67204e31i			0.340593i	0.985393	+	0.170297i	$0.0544726\pi$
$311$			8.67204e31i			0.340593i	−0.985393	+	0.170297i	$0.945527\pi$
$312$	−2.87023e31	−	7.21387e30i	−0.108120	−	0.0271743i
$313$	−2.42548e32			−0.876438			−0.438219	−	0.898868i	$-0.644391\pi$
$313$	−2.42548e32			−0.876438			−0.438219	+	0.898868i	$0.644391\pi$
$314$		−	2.13802e32i		−	0.741184i
$315$	−9.65803e29	+	1.79998e30i	−0.00321256	+	0.00598729i
$316$	−1.97405e32			−0.630123
$317$			8.37317e31i			0.256519i	0.991741	+	0.128260i	$0.0409390\pi$
$317$			8.37317e31i			0.256519i	−0.991741	+	0.128260i	$0.959061\pi$
$318$	−3.79125e31	+	1.50845e32i	−0.111488	+	0.443586i
$319$	−5.24704e32			−1.48128
$320$		−	7.52733e30i		−	0.0204029i
$321$	3.06876e32	+	7.71285e31i	0.798725	+	0.200747i
$322$	1.49396e31			0.0373434
$323$			1.41290e32i			0.339219i
$324$	−1.19871e32	−	1.80644e32i	−0.276458	−	0.416619i
$325$	−1.38519e32			−0.306920
$326$		−	3.79188e32i		−	0.807284i
$327$	−1.53851e32	+	6.12136e32i	−0.314760	+	1.25235i
$328$	2.64419e31			0.0519916
$329$			5.82732e30i			0.0110134i
$330$	−7.36371e31	−	1.85075e31i	−0.133787	−	0.0336254i
$331$	−1.00165e32			−0.174965			−0.0874823	−	0.996166i	$-0.527882\pi$
$331$	−1.00165e32			−0.174965			−0.0874823	+	0.996166i	$0.527882\pi$
$332$			2.47380e32i			0.415499i
$333$	1.38694e32	+	7.44182e31i	0.224018	+	0.120200i
$334$	8.04777e32			1.25018
$335$			1.58491e31i			0.0236822i
$336$	1.76479e30	−	7.02166e30i	0.00253677	−	0.0100932i
$337$	3.56119e32			0.492500			0.246250	−	0.969206i	$-0.420802\pi$
$337$	3.56119e32			0.492500			0.246250	+	0.969206i	$0.420802\pi$
$338$		−	4.78543e32i		−	0.636801i
$339$	7.94262e32	+	1.99626e32i	1.01711	+	0.255635i
$340$	−3.66633e31			−0.0451862
$341$		−	1.95594e33i		−	2.32032i
$342$	−1.79362e32	+	3.34278e32i	−0.204828	+	0.381741i
$343$	7.56602e31			0.0831848
$344$			5.62521e32i			0.595496i
$345$	4.95129e31	−	1.97000e32i	0.0504743	−	0.200825i
$346$	3.80871e32			0.373928
$347$			7.10954e31i			0.0672293i	0.999435	+	0.0336146i	$0.0107019\pi$
$347$			7.10954e31i			0.0672293i	−0.999435	+	0.0336146i	$0.989298\pi$
$348$	−6.59757e32	−	1.65820e32i	−0.600972	−	0.151045i
$349$	2.85398e32			0.250450			0.125225	−	0.992128i	$-0.460035\pi$
$349$	2.85398e32			0.250450			0.125225	+	0.992128i	$0.460035\pi$
$350$		−	3.38870e31i		−	0.0286516i
$351$	−2.60599e32	+	2.86148e32i	−0.212315	+	0.233130i
$352$	2.69110e32			0.211288
$353$		−	1.60477e33i		−	1.21434i	−0.794571	−	0.607172i	$-0.792304\pi$
$353$		−	1.60477e33i		−	1.21434i	0.794571	−	0.607172i	$-0.207696\pi$
$354$	−3.80988e32	+	1.51586e33i	−0.277887	+	1.10565i
$355$	3.54058e32			0.248946
$356$			2.63130e32i			0.178370i
$357$	−3.42004e31	−	8.59573e30i	−0.0223534	−	0.00561819i
$358$	9.19387e32			0.579454
$359$			2.55043e33i			1.55019i	0.631843	+	0.775096i	$0.282299\pi$
$359$			2.55043e33i			1.55019i	−0.631843	+	0.775096i	$0.717701\pi$
$360$	−8.67416e31	−	4.65424e31i	−0.0508505	−	0.0272845i
$361$	−1.10464e33			−0.624638
$362$			1.16212e33i			0.633929i
$363$	1.98498e32	−	7.89778e32i	0.104465	−	0.415641i
$364$	−1.29250e31			−0.00656316
$365$		−	5.16053e32i		−	0.252864i
$366$	−9.60599e32	−	2.41432e32i	−0.454243	−	0.114167i
$367$	−3.19951e33			−1.46024			−0.730120	−	0.683319i	$-0.760536\pi$
$367$	−3.19951e33			−1.46024			−0.730120	+	0.683319i	$0.760536\pi$
$368$			7.19946e32i			0.317160i
$369$	1.63493e32	−	3.04705e32i	0.0695277	−	0.129580i
$370$	7.14682e31			0.0293420
$371$			6.79274e31i			0.0269268i
$372$	6.18126e32	−	2.45938e33i	0.236602	−	0.941384i
$373$	−4.56642e33			−1.68796			−0.843978	−	0.536378i	$-0.819792\pi$
$373$	−4.56642e33			−1.68796			−0.843978	+	0.536378i	$0.819792\pi$
$374$		−	1.31075e33i		−	0.467940i
$375$	−9.05925e32	−	2.27690e32i	−0.312382	−	0.0785123i
$376$	−2.80820e32			−0.0935377
$377$			1.21444e33i			0.390785i
$378$	−7.00027e31	−	6.37524e31i	−0.0217631	−	0.0198200i
$379$	5.63868e33			1.69382			0.846910	−	0.531736i	$-0.178460\pi$
$379$	5.63868e33			1.69382			0.846910	+	0.531736i	$0.178460\pi$
$380$			1.72251e32i			0.0500007i
$381$	1.37136e33	−	5.45631e33i	0.384704	−	1.53065i
$382$	−1.16128e33			−0.314856
$383$			2.74131e33i			0.718413i	0.933258	+	0.359206i	$0.116953\pi$
$383$			2.74131e33i			0.718413i	−0.933258	+	0.359206i	$0.883047\pi$
$384$	3.38376e32	+	8.50456e31i	0.0857223	+	0.0215450i
$385$	−3.31598e31			−0.00812123
$386$		−	1.41343e33i		−	0.334687i
$387$	6.48224e33	+	3.47813e33i	1.48417	+	0.796349i
$388$	2.56788e33			0.568542
$389$			7.42583e33i			1.59001i	0.606603	+	0.795005i	$0.292532\pi$
$389$			7.42583e33i			1.59001i	−0.606603	+	0.795005i	$0.707468\pi$
$390$	−4.28361e31	+	1.70434e32i	−0.00887094	+	0.0352953i
$391$	3.50663e33			0.702413
$392$			1.82146e33i			0.352941i
$393$	−3.32706e33	−	8.36204e32i	−0.623673	−	0.156751i
$394$	−5.26551e33			−0.954970
$395$			1.17219e33i			0.205701i
$396$	1.66394e33	−	3.10111e33i	0.282553	−	0.526598i
$397$	8.27071e33			1.35915			0.679573	−	0.733608i	$-0.262165\pi$
$397$	8.27071e33			1.35915			0.679573	+	0.733608i	$0.262165\pi$
$398$		−	5.78707e33i		−	0.920404i
$399$	−4.03845e31	+	1.60680e32i	−0.00621680	+	0.0247351i
$400$	1.63302e33			0.243340
$401$		−	9.03854e33i		−	1.30383i	−0.758291	−	0.651916i	$-0.773966\pi$
$401$		−	9.03854e33i		−	1.30383i	0.758291	−	0.651916i	$-0.226034\pi$
$402$	−7.12465e32	−	1.79067e32i	−0.0995004	−	0.0250079i
$403$	−4.52706e33			−0.612140
$404$			1.99563e33i			0.261290i
$405$	−1.07267e33	+	7.11795e32i	−0.136003	+	0.0902484i
$406$	−2.97098e32			−0.0364805
$407$			2.55507e33i			0.303861i
$408$	4.14231e32	−	1.64813e33i	0.0477156	−	0.189849i
$409$	−3.71355e33			−0.414368			−0.207184	−	0.978302i	$-0.566430\pi$
$409$	−3.71355e33			−0.414368			−0.207184	+	0.978302i	$0.566430\pi$
$410$		−	1.57012e32i		−	0.0169724i
$411$	−1.70564e34	−	4.28686e33i	−1.78625	−	0.448947i
$412$	−1.45782e33			−0.147924
$413$			6.82611e32i			0.0671155i
$414$	8.29634e33	+	4.45151e33i	0.790464	+	0.424134i
$415$	1.46895e33			0.135638
$416$		−	6.22861e32i		−	0.0557414i
$417$	−2.57069e33	+	1.02282e34i	−0.222988	+	0.887215i
$418$	−6.15818e33			−0.517798
$419$			1.56168e33i			0.127295i	0.997972	+	0.0636473i	$0.0202733\pi$
$419$			1.56168e33i			0.127295i	−0.997972	+	0.0636473i	$0.979727\pi$
$420$	−4.16947e31	−	1.04793e31i	−0.00329488	−	0.000828118i
$421$	1.38212e32			0.0105896			0.00529479	−	0.999986i	$-0.498315\pi$
$421$	1.38212e32			0.0105896			0.00529479	+	0.999986i	$0.498315\pi$
$422$			6.06333e33i			0.450453i
$423$	−1.73635e33	+	3.23605e33i	−0.125087	+	0.233126i
$424$	−3.27344e33			−0.228691
$425$		−	7.95396e33i		−	0.538924i
$426$	−4.00023e33	+	1.59160e34i	−0.262882	+	1.04594i
$427$	−4.32570e32			−0.0275737
$428$			6.65944e33i			0.411783i
$429$	−6.09322e33	−	1.53144e33i	−0.365512	−	0.0918659i
$430$	3.34026e33			0.194397
$431$		−	2.70071e34i		−	1.52501i	−0.646980	−	0.762507i	$-0.723968\pi$
$431$		−	2.70071e34i		−	1.52501i	0.646980	−	0.762507i	$-0.276032\pi$
$432$	3.07225e33	−	3.37345e33i	0.168332	−	0.184836i
$433$	2.22633e34			1.18371			0.591856	−	0.806043i	$-0.298395\pi$
$433$	2.22633e34			1.18371			0.591856	+	0.806043i	$0.298395\pi$
$434$		−	1.10749e33i		−	0.0571443i
$435$	−9.84640e32	+	3.91765e33i	−0.0493080	+	0.196185i
$436$	−1.32838e34			−0.645652
$437$		−	1.64749e34i		−	0.777254i
$438$	2.31982e34	+	5.83050e33i	1.06241	+	0.267019i
$439$	1.58623e33			0.0705226			0.0352613	−	0.999378i	$-0.488774\pi$
$439$	1.58623e33			0.0705226			0.0352613	+	0.999378i	$0.488774\pi$
$440$		−	1.59798e33i		−	0.0689742i
$441$	2.09898e34	+	1.12623e34i	0.879641	+	0.471983i
$442$	−3.03376e33			−0.123450
$443$		−	2.13843e34i		−	0.844982i	−0.906367	−	0.422491i	$-0.861156\pi$
$443$		−	2.13843e34i		−	0.844982i	0.906367	−	0.422491i	$-0.138844\pi$
$444$	−8.07465e32	+	3.21271e33i	−0.0309846	+	0.123280i
$445$	1.56247e33			0.0582280
$446$		−	1.17523e34i		−	0.425372i
$447$	4.97866e33	+	1.25131e33i	0.175031	+	0.0439913i
$448$	1.52375e32			0.00520356
$449$			2.33947e34i			0.776094i	0.921640	+	0.388047i	$0.126850\pi$
$449$			2.33947e34i			0.776094i	−0.921640	+	0.388047i	$0.873150\pi$
$450$	1.00972e34	−	1.88183e34i	0.325415	−	0.606480i
$451$	5.61337e33			0.175763
$452$			1.72361e34i			0.524371i
$453$	−2.84533e33	+	1.13209e34i	−0.0841118	+	0.334661i
$454$	2.20419e34			0.633174
$455$			7.67489e31i			0.00214252i
$456$	−7.74323e33	−	1.94614e33i	−0.210077	−	0.0527997i
$457$	−1.91059e34			−0.503797			−0.251899	−	0.967754i	$-0.581055\pi$
$457$	−1.91059e34			−0.503797			−0.251899	+	0.967754i	$0.581055\pi$
$458$		−	2.90168e34i		−	0.743700i
$459$	−1.64310e34	−	1.49640e34i	−0.409355	−	0.372805i
$460$	4.27505e33			0.103535
$461$			5.79099e34i			1.36346i	0.731606	+	0.681728i	$0.238771\pi$
$461$			5.79099e34i			1.36346i	−0.731606	+	0.681728i	$0.761229\pi$
$462$	3.74647e32	−	1.49063e33i	0.00857585	−	0.0341212i
$463$	−3.42700e33			−0.0762712			−0.0381356	−	0.999273i	$-0.512142\pi$
$463$	−3.42700e33			−0.0762712			−0.0381356	+	0.999273i	$0.512142\pi$
$464$		−	1.43172e34i		−	0.309831i
$465$	−1.46038e34	−	3.67044e33i	−0.307311	−	0.0772378i
$466$	−5.32757e34			−1.09022
$467$			2.12193e34i			0.422291i	0.977455	+	0.211145i	$0.0677193\pi$
$467$			2.12193e34i			0.422291i	−0.977455	+	0.211145i	$0.932281\pi$
$468$	−7.17757e33	−	3.85122e33i	−0.138925	−	0.0745423i
$469$	−3.20832e32			−0.00603992
$470$			1.66751e33i			0.0305350i
$471$	1.43438e34	−	5.70705e34i	0.255501	−	1.01658i
$472$	−3.28953e34			−0.570017
$473$			1.19418e35i			2.01314i
$474$	−5.26936e34	−	1.32437e34i	−0.864249	−	0.217216i
$475$	−3.73693e34			−0.596345
$476$		−	7.42174e32i		−	0.0115243i
$477$	−2.02401e34	+	3.77217e34i	−0.305825	+	0.569971i
$478$	7.27457e34			1.06966
$479$		−	7.13681e34i		−	1.02127i	−0.859796	−	0.510637i	$-0.829409\pi$
$479$		−	7.13681e34i		−	1.02127i	0.859796	−	0.510637i	$-0.170591\pi$
$480$	5.05002e32	−	2.00928e33i	0.00703327	−	0.0279837i
$481$	5.91375e33			0.0801635
$482$			4.29191e34i			0.566290i
$483$	3.98786e33	+	1.00229e33i	0.0512186	+	0.0128730i
$484$	1.71388e34			0.214284
$485$		−	1.52481e34i		−	0.185598i
$486$	−1.98781e34	−	5.62617e34i	−0.235561	−	0.666717i
$487$	1.14744e35			1.32390			0.661949	−	0.749548i	$-0.269729\pi$
$487$	1.14744e35			1.32390			0.661949	+	0.749548i	$0.269729\pi$
$488$		−	2.08457e34i		−	0.234185i
$489$	2.54394e34	−	1.01217e35i	0.278287	−	1.10724i
$490$	1.08159e34			0.115216
$491$			2.87007e33i			0.0297738i	0.999889	+	0.0148869i	$0.00473881\pi$
$491$			2.87007e33i			0.0297738i	−0.999889	+	0.0148869i	$0.995261\pi$
$492$	7.05818e33	+	1.77397e33i	0.0713094	+	0.0179225i
$493$	−6.97348e34			−0.686183
$494$			1.42532e34i			0.136604i
$495$	−1.84144e34	−	9.88050e33i	−0.171906	−	0.0922383i
$496$	5.33703e34			0.485331
$497$			7.16717e33i			0.0634914i
$498$	−1.65965e34	+	6.60337e34i	−0.143231	+	0.569881i
$499$	−9.84238e34			−0.827548			−0.413774	−	0.910380i	$-0.635790\pi$
$499$	−9.84238e34			−0.827548			−0.413774	+	0.910380i	$0.635790\pi$
$500$		−	1.96593e34i		−	0.161049i
$501$	2.14821e35	+	5.39918e34i	1.71469	+	0.430961i
$502$	1.02118e35			0.794246
$503$			3.39681e34i			0.257447i	0.991681	+	0.128723i	$0.0410879\pi$
$503$			3.39681e34i			0.257447i	−0.991681	+	0.128723i	$0.958912\pi$
$504$	9.42155e32	−	1.75591e33i	0.00695865	−	0.0129689i
$505$	1.18501e34			0.0852969
$506$			1.52838e35i			1.07219i
$507$	3.21050e34	−	1.27738e35i	0.219518	−	0.873409i
$508$	1.18406e35			0.789125
$509$		−	8.05402e34i		−	0.523217i	−0.965174	−	0.261608i	$-0.915747\pi$
$509$		−	8.05402e34i		−	0.523217i	0.965174	−	0.261608i	$-0.0842529\pi$
$510$	−9.78660e33	−	2.45971e33i	−0.0619754	−	0.0155766i
$511$	1.04464e34			0.0644906
$512$			7.34302e33i			0.0441942i
$513$	−7.03038e34	+	7.71963e34i	−0.412527	+	0.452971i
$514$	−1.63030e35			−0.932709
$515$			8.65653e33i			0.0482892i
$516$	−3.77391e34	+	1.50155e35i	−0.205279	+	0.816757i
$517$	−5.96155e34			−0.316215
$518$			1.44673e33i			0.00748341i
$519$	1.01666e35	+	2.55523e34i	0.512864	+	0.128900i
$520$	−3.69856e33			−0.0181965
$521$		−	2.73419e35i		−	1.31201i	−0.754755	−	0.656007i	$-0.772244\pi$
$521$		−	2.73419e35i		−	1.31201i	0.754755	−	0.656007i	$-0.227756\pi$
$522$	−1.64985e35	−	8.85251e34i	−0.772199	−	0.414334i
$523$	−3.50620e35			−1.60072			−0.800358	−	0.599522i	$-0.795357\pi$
$523$	−3.50620e35			−1.60072			−0.800358	+	0.599522i	$0.795357\pi$
$524$		−	7.21996e34i		−	0.321535i
$525$	2.27345e33	−	9.04551e33i	0.00987675	−	0.0392972i
$526$	−3.73159e34			−0.158154
$527$		−	2.59950e35i		−	1.07486i
$528$	7.18340e34	+	1.80544e34i	0.289794	+	0.0728352i
$529$	−1.54831e35			−0.609445
$530$			1.94378e34i			0.0746551i
$531$	−2.03395e35	+	3.79071e35i	−0.762276	+	1.42066i
$532$	−3.48688e33			−0.0127522
$533$		−	1.29922e34i		−	0.0463693i
$534$	−1.76532e34	+	7.02378e34i	−0.0614875	+	0.244644i
$535$	3.95438e34			0.134425
$536$		−	1.54610e34i		−	0.0512975i
$537$	2.45414e35	+	6.16809e34i	0.794754	+	0.199749i
$538$	7.22568e34			0.228407
$539$			3.86680e35i			1.19316i
$540$	−2.00316e34	−	1.82431e34i	−0.0603388	−	0.0549514i
$541$	1.45441e35			0.427684			0.213842	−	0.976868i	$-0.431402\pi$
$541$	1.45441e35			0.427684			0.213842	+	0.976868i	$0.431402\pi$
$542$		−	2.77685e35i		−	0.797189i
$543$	−7.79659e34	+	3.10208e35i	−0.218528	+	0.869470i
$544$	3.57656e34			0.0978768
$545$			7.88795e34i			0.210770i
$546$	−3.45010e33	−	8.67129e32i	−0.00900175	−	0.00226245i
$547$	6.55744e35			1.67070			0.835351	−	0.549716i	$-0.185264\pi$
$547$	6.55744e35			1.67070			0.835351	+	0.549716i	$0.185264\pi$
$548$		−	3.70136e35i		−	0.920904i
$549$	−2.40217e35	−	1.28892e35i	−0.583664	−	0.313173i
$550$	3.46676e35			0.822637
$551$			3.27628e35i			0.759295i
$552$	−4.83006e34	+	1.92176e35i	−0.109331	+	0.435003i
$553$	−2.37286e34			−0.0524621
$554$		−	1.41783e34i		−	0.0306195i
$555$	1.90771e34	+	4.79474e33i	0.0402443	+	0.0101148i
$556$	−2.21959e35			−0.457404
$557$		−	4.83657e35i		−	0.973688i	−0.873489	−	0.486844i	$-0.838148\pi$
$557$		−	4.83657e35i		−	0.973688i	0.873489	−	0.486844i	$-0.161852\pi$
$558$	3.29995e35	−	6.15016e35i	0.649027	−	1.20960i
$559$	2.76395e35			0.531100
$560$		−	9.04807e32i		−	0.00169868i
$561$	8.79373e34	−	3.49882e35i	0.161308	−	0.641806i
$562$	−3.07482e35			−0.551123
$563$		−	4.39043e35i		−	0.768949i	−0.923136	−	0.384475i	$-0.874383\pi$
$563$		−	4.39043e35i		−	0.768949i	0.923136	−	0.384475i	$-0.125617\pi$
$564$	−7.49599e34	−	1.88400e34i	−0.128292	−	0.0322443i
$565$	1.02348e35			0.171179
$566$			4.07689e35i			0.666370i
$567$	−1.44088e34	−	2.17140e34i	−0.0230170	−	0.0346864i
$568$	−3.45388e35			−0.539237
$569$			4.01860e35i			0.613218i	0.951836	+	0.306609i	$0.0991944\pi$
$569$			4.01860e35i			0.613218i	−0.951836	+	0.306609i	$0.900806\pi$
$570$	−1.15562e34	+	4.59794e34i	−0.0172362	+	0.0685788i
$571$	8.98546e35			1.31000			0.655000	−	0.755629i	$-0.272669\pi$
$571$	8.98546e35			1.31000			0.655000	+	0.755629i	$0.272669\pi$
$572$		−	1.32227e35i		−	0.188440i
$573$	−3.09981e35	−	7.79090e34i	−0.431842	−	0.108537i
$574$	3.17839e33			0.00432866
$575$			9.27455e35i			1.23484i
$576$	8.46177e34	+	4.54027e34i	0.110146	+	0.0591003i
$577$	−8.51916e35			−1.08420			−0.542102	−	0.840313i	$-0.682371\pi$
$577$	−8.51916e35			−1.08420			−0.542102	+	0.840313i	$0.682371\pi$
$578$			3.94057e35i			0.490339i
$579$	9.48257e34	−	3.77289e35i	0.115373	−	0.459042i
$580$	−8.50159e34			−0.101143
$581$			2.97359e34i			0.0345932i
$582$	6.85450e35	+	1.72277e35i	0.779788	+	0.195988i
$583$	−6.94921e35			−0.773115
$584$			5.03418e35i			0.547723i
$585$	−2.28686e34	+	4.26205e34i	−0.0243340	+	0.0453516i
$586$	−6.92681e35			−0.720882
$587$			6.08763e35i			0.619659i	0.950792	+	0.309830i	$0.100272\pi$
$587$			6.08763e35i			0.619659i	−0.950792	+	0.309830i	$0.899728\pi$
$588$	−1.22201e35	+	4.86207e35i	−0.121666	+	0.484078i
$589$	−1.22130e36			−1.18939
$590$			1.95333e35i			0.186079i
$591$	−1.40553e36	−	3.53259e35i	−1.30980	−	0.329197i
$592$	−6.97182e34			−0.0635571
$593$		−	9.84305e35i		−	0.877847i	−0.898524	−	0.438923i	$-0.855360\pi$
$593$		−	9.84305e35i		−	0.877847i	0.898524	−	0.438923i	$-0.144640\pi$
$594$	6.52209e35	−	7.16152e35i	0.569067	−	0.624858i
$595$	−4.40704e33			−0.00376206
$596$			1.08041e35i			0.0902373i
$597$	3.88250e35	−	1.54475e36i	0.317282	−	1.26239i
$598$	3.53746e35			0.282863
$599$			3.01279e35i			0.235733i	0.993029	+	0.117867i	$0.0376055\pi$
$599$			3.01279e35i			0.235733i	−0.993029	+	0.117867i	$0.962394\pi$
$600$	4.35906e35	+	1.09558e35i	0.333754	+	0.0838839i
$601$	9.39897e35			0.704226			0.352113	−	0.935957i	$-0.385463\pi$
$601$	9.39897e35			0.704226			0.352113	+	0.935957i	$0.385463\pi$
$602$			6.76166e34i			0.0495792i
$603$	−1.78166e35	−	9.55973e34i	−0.127850	−	0.0685995i
$604$	−2.45672e35			−0.172534
$605$		−	1.01770e35i		−	0.0699521i
$606$	−1.33885e35	+	5.32697e35i	−0.0900717	+	0.358374i
$607$	1.91036e36			1.25795			0.628975	−	0.777426i	$-0.283475\pi$
$607$	1.91036e36			1.25795			0.628975	+	0.777426i	$0.283475\pi$
$608$		−	1.68034e35i		−	0.108305i
$609$	−7.93048e34	−	1.99320e34i	−0.0500351	−	0.0125755i
$610$	−1.23782e35			−0.0764487
$611$			1.37981e35i			0.0834227i
$612$	2.21143e35	−	4.12147e35i	0.130889	−	0.243940i
$613$	−5.74819e34			−0.0333077			−0.0166539	−	0.999861i	$-0.505301\pi$
$613$	−5.74819e34			−0.0333077			−0.0166539	+	0.999861i	$0.505301\pi$
$614$			1.42634e36i			0.809162i
$615$	1.05338e34	−	4.19116e34i	0.00585073	−	0.0232786i
$616$	3.23478e34			0.0175912
$617$		−	1.15761e36i		−	0.616387i	−0.951324	−	0.308194i	$-0.900276\pi$
$617$		−	1.15761e36i		−	0.616387i	0.951324	−	0.308194i	$-0.0997245\pi$
$618$	−3.89137e35	−	9.78036e34i	−0.202886	−	0.0509923i
$619$	2.06441e36			1.05395			0.526973	−	0.849882i	$-0.323327\pi$
$619$	2.06441e36			1.05395			0.526973	+	0.849882i	$0.323327\pi$
$620$		−	3.16913e35i		−	0.158434i
$621$	1.91591e36	+	1.74484e36i	0.937959	+	0.854212i
$622$	−5.02338e35			−0.240836
$623$			3.16290e34i			0.0148505i
$624$	4.17872e34	−	1.66261e35i	0.0192151	−	0.0764525i
$625$	2.04455e36			0.920785
$626$		−	1.40499e36i		−	0.619735i
$627$	−1.64381e36	−	4.13147e35i	−0.710190	−	0.178495i
$628$	1.23847e36			0.524097
$629$			3.39576e35i			0.140760i
$630$	−1.04266e34	−	5.59453e33i	−0.00423365	−	0.00227162i
$631$	−2.52526e36			−1.00444			−0.502221	−	0.864739i	$-0.667484\pi$
$631$	−2.52526e36			−1.00444			−0.502221	+	0.864739i	$0.667484\pi$
$632$		−	1.14349e36i		−	0.445564i
$633$	−4.06784e35	+	1.61850e36i	−0.155280	+	0.617822i
$634$	−4.85026e35			−0.181386
$635$		−	7.03097e35i		−	0.257607i
$636$	−8.73786e35	−	2.19613e35i	−0.313662	−	0.0788342i
$637$	8.94977e35			0.314774
$638$		−	3.03941e36i		−	1.04742i
$639$	−2.13558e36	+	3.98010e36i	−0.721114	+	1.34395i
$640$	4.36029e34			0.0144270
$641$			2.46243e36i			0.798380i	0.916868	+	0.399190i	$0.130709\pi$
$641$			2.46243e36i			0.798380i	−0.916868	+	0.399190i	$0.869291\pi$
$642$	−4.46776e35	+	1.77762e36i	−0.141950	+	0.564784i
$643$	−1.48487e36			−0.462324			−0.231162	−	0.972915i	$-0.574253\pi$
$643$	−1.48487e36			−0.462324			−0.231162	+	0.972915i	$0.574253\pi$
$644$			8.65396e34i			0.0264057i
$645$	8.91620e35	+	2.24095e35i	0.266627	+	0.0670125i
$646$	−8.18441e35			−0.239864
$647$		−	3.16799e36i		−	0.909974i	−0.890498	−	0.454987i	$-0.849644\pi$
$647$		−	3.16799e36i		−	0.909974i	0.890498	−	0.454987i	$-0.150356\pi$
$648$	1.04640e36	−	6.94367e35i	0.294594	−	0.195485i
$649$	−6.98335e36			−1.92701
$650$		−	8.02387e35i		−	0.217025i
$651$	7.43006e34	−	2.95624e35i	0.0196988	−	0.0783767i
$652$	2.19649e36			0.570836
$653$			1.31750e36i			0.335645i	0.985817	+	0.167822i	$0.0536735\pi$
$653$			1.31750e36i			0.335645i	−0.985817	+	0.167822i	$0.946327\pi$
$654$	−3.54587e36	−	8.91200e35i	−0.885548	−	0.222569i
$655$	−4.28722e35			−0.104964
$656$			1.53168e35i			0.0367636i
$657$	5.80116e36	+	3.11269e36i	1.36510	+	0.732464i
$658$	−3.37554e34			−0.00778766
$659$		−	2.84913e36i		−	0.644470i	−0.946660	−	0.322235i	$-0.895566\pi$
$659$		−	2.84913e36i		−	0.644470i	0.946660	−	0.322235i	$-0.104434\pi$
$660$	1.07207e35	−	4.26551e35i	0.0237767	−	0.0946020i
$661$	−3.98627e36			−0.866857			−0.433428	−	0.901188i	$-0.642696\pi$
$661$	−3.98627e36			−0.866857			−0.433428	+	0.901188i	$0.642696\pi$
$662$		−	5.80215e35i		−	0.123719i
$663$	−8.09808e35	−	2.03533e35i	−0.169319	−	0.0425558i
$664$	−1.43298e36			−0.293802
$665$			2.07051e34i			0.00416290i
$666$	−4.31076e35	+	8.03402e35i	−0.0849942	+	0.158405i
$667$	8.13128e36			1.57226
$668$			4.66177e36i			0.884009i
$669$	7.88451e35	−	3.13706e36i	0.146634	−	0.583423i
$670$	−9.18077e34			−0.0167458
$671$		−	4.42535e36i		−	0.791689i
$672$	4.06738e34	+	1.02227e34i	0.00713698	+	0.00179377i
$673$	−2.05191e36			−0.353153			−0.176576	−	0.984287i	$-0.556502\pi$
$673$	−2.05191e36			−0.353153			−0.176576	+	0.984287i	$0.556502\pi$
$674$			2.06286e36i			0.348250i
$675$	3.95776e36	−	4.34578e36i	0.655391	−	0.719645i
$676$	2.77202e36			0.450286
$677$			8.21218e36i			1.30860i	0.756237	+	0.654298i	$0.227036\pi$
$677$			8.21218e36i			1.30860i	−0.756237	+	0.654298i	$0.772964\pi$
$678$	−1.15635e36	+	4.60086e36i	−0.180761	+	0.719205i
$679$	3.08667e35			0.0473351
$680$		−	2.12377e35i		−	0.0319515i
$681$	5.88368e36	+	1.47877e36i	0.868434	+	0.218267i
$682$	1.13300e37			1.64072
$683$		−	4.42105e36i		−	0.628140i	−0.949400	−	0.314070i	$-0.898307\pi$
$683$		−	4.42105e36i		−	0.628140i	0.949400	−	0.314070i	$-0.101693\pi$
$684$	−1.93635e36	−	1.03897e36i	−0.269932	−	0.144835i
$685$	−2.19787e36			−0.300625
$686$			4.38271e35i			0.0588205i
$687$	1.94671e36	−	7.74550e36i	0.256368	−	1.02003i
$688$	−3.25847e36			−0.421079
$689$			1.60841e36i			0.203961i
$690$	1.14115e36	+	2.86809e35i	0.142005	+	0.0356907i
$691$	−1.13020e36			−0.138020			−0.0690098	−	0.997616i	$-0.521984\pi$
$691$	−1.13020e36			−0.138020			−0.0690098	+	0.997616i	$0.521984\pi$
$692$			2.20624e36i			0.264407i
$693$	2.00011e35	−	3.72762e35i	0.0235245	−	0.0438430i
$694$	−4.11829e35			−0.0475383
$695$			1.31799e36i			0.149318i
$696$	9.60531e35	−	3.82172e36i	0.106805	−	0.424951i
$697$	7.46034e35			0.0814203
$698$			1.65320e36i			0.177095i
$699$	−1.42210e37	−	3.57423e36i	−1.49529	−	0.375819i
$700$	1.96294e35			0.0202597
$701$		−	1.06882e37i		−	1.08285i	−0.840749	−	0.541425i	$-0.817885\pi$
$701$		−	1.06882e37i		−	1.08285i	0.840749	−	0.541425i	$-0.182115\pi$
$702$	−1.65755e36	−	1.50955e36i	−0.164848	−	0.150129i
$703$	1.59540e36			0.155758
$704$			1.55885e36i			0.149403i
$705$	−1.11872e35	+	4.45113e35i	−0.0105260	+	0.0418805i
$706$	9.29582e36			0.858670
$707$			2.39881e35i			0.0217542i
$708$	−8.78079e36	−	2.20692e36i	−0.781810	−	0.196496i
$709$	−1.42893e37			−1.24913			−0.624567	−	0.780971i	$-0.714725\pi$
$709$	−1.42893e37			−1.24913			−0.624567	+	0.780971i	$0.714725\pi$
$710$			2.05092e36i			0.176031i
$711$	−1.31771e37	−	7.07033e36i	−1.11049	−	0.595848i
$712$	−1.52421e36			−0.126126
$713$			3.03110e37i			2.46284i
$714$	4.97918e34	−	1.98110e35i	0.00397266	−	0.0158063i
$715$	−7.85168e35			−0.0615154
$716$			5.32566e36i			0.409736i
$717$	1.94181e37	+	4.88045e36i	1.46710	+	0.368732i
$718$	−1.47737e37			−1.09615
$719$			1.63810e37i			1.19362i	0.802383	+	0.596810i	$0.203565\pi$
$719$			1.63810e37i			1.19362i	−0.802383	+	0.596810i	$0.796435\pi$
$720$	2.69602e35	−	5.02461e35i	0.0192930	−	0.0359567i
$721$	−1.75234e35			−0.0123157
$722$		−	6.39878e36i		−	0.441686i
$723$	−2.87940e36	+	1.14565e37i	−0.195211	+	0.776699i
$724$	−6.73174e36			−0.448256
$725$		−	1.84439e37i		−	1.20631i
$726$	4.57488e36	+	1.14983e36i	0.293903	+	0.0738679i
$727$	2.51319e37			1.58591			0.792955	−	0.609280i	$-0.208542\pi$
$727$	2.51319e37			1.58591			0.792955	+	0.609280i	$0.208542\pi$
$728$		−	7.48697e34i		−	0.00464086i
$729$	−1.53154e36	−	1.63516e37i	−0.0932548	−	0.995642i
$730$	2.98930e36			0.178802
$731$			1.58710e37i			0.932564i
$732$	1.39852e36	−	5.56438e36i	0.0807282	−	0.321198i
$733$	−4.05807e35			−0.0230127			−0.0115064	−	0.999934i	$-0.503663\pi$
$733$	−4.05807e35			−0.0230127			−0.0115064	+	0.999934i	$0.503663\pi$
$734$		−	1.85335e37i		−	1.03255i
$735$	2.88710e36	+	7.25628e35i	0.158025	+	0.0397172i
$736$	−4.17037e36			−0.224266
$737$		−	3.28223e36i		−	0.173417i
$738$	1.76504e36	+	9.47055e35i	0.0916266	+	0.0491635i
$739$	−1.08881e37			−0.555362			−0.277681	−	0.960673i	$-0.589566\pi$
$739$	−1.08881e37			−0.555362			−0.277681	+	0.960673i	$0.589566\pi$
$740$			4.13988e35i			0.0207479i
$741$	−9.56237e35	+	3.80464e36i	−0.0470900	+	0.187360i
$742$	−3.93478e35			−0.0190401
$743$		−	3.21362e37i		−	1.52806i	−0.645181	−	0.764030i	$-0.723218\pi$
$743$		−	3.21362e37i		−	1.52806i	0.645181	−	0.764030i	$-0.276782\pi$
$744$	1.42462e37	+	3.58057e36i	0.665659	+	0.167303i
$745$	6.41547e35			0.0294576
$746$		−	2.64515e37i		−	1.19356i
$747$	−8.86029e36	+	1.65130e37i	−0.392898	+	0.732250i
$748$	7.59269e36			0.330884
$749$			8.00484e35i			0.0342838i
$750$	1.31892e36	−	5.24768e36i	0.0555166	−	0.220887i
$751$	1.92251e37			0.795332			0.397666	−	0.917530i	$-0.369820\pi$
$751$	1.92251e37			0.795332			0.397666	+	0.917530i	$0.369820\pi$
$752$		−	1.62669e36i		−	0.0661411i
$753$	2.72586e37	+	6.85102e36i	1.08935	+	0.273792i
$754$	−7.03478e36			−0.276327
$755$			1.45880e36i			0.0563231i
$756$	3.69293e35	−	4.05499e35i	0.0140148	−	0.0153888i
$757$	2.54837e37			0.950639			0.475319	−	0.879813i	$-0.342332\pi$
$757$	2.54837e37			0.950639			0.475319	+	0.879813i	$0.342332\pi$
$758$			3.26627e37i			1.19771i
$759$	−1.02537e37	+	4.07972e37i	−0.369606	+	1.47058i
$760$	−9.97787e35			−0.0353558
$761$		−	1.84678e37i		−	0.643300i	−0.946859	−	0.321650i	$-0.895763\pi$
$761$		−	1.84678e37i		−	0.643300i	0.946859	−	0.321650i	$-0.104237\pi$
$762$	3.16064e37	+	7.94377e36i	1.08233	+	0.272027i
$763$	−1.59675e36			−0.0537550
$764$		−	6.72682e36i		−	0.222637i
$765$	−2.44733e36	−	1.31315e36i	−0.0796333	−	0.0427283i
$766$	−1.58794e37			−0.507994
$767$			1.61631e37i			0.508376i
$768$	−4.92637e35	+	1.96008e36i	−0.0152346	+	0.0606148i
$769$	−5.19677e37			−1.58012			−0.790062	−	0.613027i	$-0.789952\pi$
$769$	−5.19677e37			−1.58012			−0.790062	+	0.613027i	$0.789952\pi$
$770$		−	1.92082e35i		−	0.00574258i
$771$	−4.35178e37	−	1.09375e37i	−1.27926	−	0.321523i
$772$	8.18745e36			0.236659
$773$		−	5.04089e37i		−	1.43276i	−0.697709	−	0.716381i	$-0.745797\pi$
$773$		−	5.04089e37i		−	1.43276i	0.697709	−	0.716381i	$-0.254203\pi$
$774$	−2.01475e37	+	3.75492e37i	−0.563104	+	1.04946i
$775$	6.87532e37			1.88960
$776$			1.48748e37i			0.402020i
$777$	−9.70597e34	+	3.86177e35i	−0.00257968	+	0.0102639i
$778$	−4.30150e37			−1.12431
$779$		−	3.50502e36i		−	0.0900955i
$780$	−9.87262e35	−	2.48133e35i	−0.0249576	−	0.00627270i
$781$	−7.33227e37			−1.82295
$782$			2.03126e37i			0.496681i
$783$	−3.81008e37	−	3.46989e37i	−0.916286	−	0.834474i
$784$	−1.05510e37			−0.249567
$785$		−	7.35407e36i		−	0.171089i
$786$	4.84381e36	−	1.92724e37i	0.110839	−	0.441004i
$787$	5.33111e37			1.19990			0.599951	−	0.800037i	$-0.295187\pi$
$787$	5.33111e37			1.19990			0.599951	+	0.800037i	$0.295187\pi$
$788$		−	3.05011e37i		−	0.675266i
$789$	−9.96080e36	−	2.50349e36i	−0.216917	−	0.0545187i
$790$	−6.79006e36			−0.145453
$791$			2.07183e36i			0.0436576i
$792$	1.79635e37	+	9.63857e36i	0.372361	+	0.199795i
$793$	−1.02426e37			−0.208861
$794$			4.79090e37i			0.961061i
$795$	−1.30406e36	+	5.18855e36i	−0.0257351	+	0.102394i
$796$	3.35223e37			0.650824
$797$		−	6.88122e37i		−	1.31434i	−0.753743	−	0.657170i	$-0.771754\pi$
$797$		−	6.88122e37i		−	1.31434i	0.753743	−	0.657170i	$-0.228246\pi$
$798$	−9.30758e35	−	2.33932e35i	−0.0174904	−	0.00439594i
$799$	−7.92309e36			−0.146483
$800$			9.45949e36i			0.172067i
$801$	−9.42439e36	+	1.75644e37i	−0.168667	+	0.314347i
$802$	5.23568e37			0.921948
$803$			1.06871e38i			1.85164i
$804$	1.03727e36	−	4.12704e36i	0.0176832	−	0.0703574i
$805$	5.13873e35			0.00862004
$806$		−	2.62235e37i		−	0.432848i
$807$	1.92876e37	+	4.84765e36i	0.313273	+	0.0787363i
$808$	−1.15599e37			−0.184760
$809$			3.44148e37i			0.541271i	0.962682	+	0.270636i	$0.0872338\pi$
$809$			3.44148e37i			0.541271i	−0.962682	+	0.270636i	$0.912766\pi$
$810$	−4.12316e36	−	6.21355e36i	−0.0638153	−	0.0961689i
$811$	5.43479e37			0.827773			0.413887	−	0.910328i	$-0.364171\pi$
$811$	5.43479e37			0.827773			0.413887	+	0.910328i	$0.364171\pi$
$812$		−	1.72097e36i		−	0.0257956i
$813$	1.86296e37	−	7.41229e37i	0.274807	−	1.09339i
$814$	−1.48005e37			−0.214862
$815$		−	1.30428e37i		−	0.186347i
$816$	9.54697e36	+	2.39948e36i	0.134244	+	0.0337400i
$817$	7.45651e37			1.03193
$818$		−	2.15112e37i		−	0.293002i
$819$	−8.62765e35	−	4.62928e35i	−0.0115665	−	0.00620616i
$820$	9.09513e35			0.0120013
$821$			7.96369e37i			1.03432i	0.855890	+	0.517158i	$0.173010\pi$
$821$			7.96369e37i			1.03432i	−0.855890	+	0.517158i	$0.826990\pi$
$822$	2.48321e37	−	9.88011e37i	0.317454	−	1.26307i
$823$	−3.85518e37			−0.485118			−0.242559	−	0.970137i	$-0.577987\pi$
$823$	−3.85518e37			−0.485118			−0.242559	+	0.970137i	$0.577987\pi$
$824$		−	8.44457e36i		−	0.104598i
$825$	9.25387e37	+	2.32582e37i	1.12829	+	0.283579i
$826$	−3.95411e36			−0.0474578
$827$		−	6.89741e37i		−	0.814919i	−0.913223	−	0.407460i	$-0.866415\pi$
$827$		−	6.89741e37i		−	0.814919i	0.913223	−	0.407460i	$-0.133585\pi$
$828$	−2.57859e37	+	4.80575e37i	−0.299908	+	0.558942i
$829$	−8.96887e37			−1.02690			−0.513451	−	0.858119i	$-0.671633\pi$
$829$	−8.96887e37			−1.02690			−0.513451	+	0.858119i	$0.671633\pi$
$830$			8.50906e36i			0.0959105i
$831$	9.51213e35	−	3.78465e36i	0.0105551	−	0.0419964i
$832$	3.60800e36			0.0394151
$833$			5.13909e37i			0.552715i
$834$	−5.92479e37	−	1.48910e37i	−0.627356	−	0.157676i
$835$	2.76816e37			0.288581
$836$		−	3.56720e37i		−	0.366139i
$837$	1.29347e38	−	1.42028e38i	1.30715	−	1.43530i
$838$	−9.04623e36			−0.0900109
$839$			1.99204e38i			1.95161i	0.218638	+	0.975806i	$0.429839\pi$
$839$			1.99204e38i			1.95161i	−0.218638	+	0.975806i	$0.570161\pi$
$840$	6.07027e34	−	2.41522e35i	0.000585568	−	0.00232984i
$841$	−5.64226e37			−0.535927
$842$			8.00610e35i			0.00748796i
$843$	−8.20768e37	−	2.06287e37i	−0.755896	−	0.189983i
$844$	−3.51226e37			−0.318518
$845$		−	1.64603e37i		−	0.146994i
$846$	−1.87452e37	−	1.00580e37i	−0.164845	−	0.0884497i
$847$	2.06013e36			0.0178406
$848$		−	1.89618e37i		−	0.161709i
$849$	−2.73515e37	+	1.08825e38i	−0.229711	+	0.913965i
$850$	4.60743e37			0.381077
$851$		−	3.95956e37i		−	0.322524i
$852$	−9.21951e37	−	2.31718e37i	−0.739594	−	0.185885i
$853$	−1.93327e38			−1.52741			−0.763704	−	0.645566i	$-0.776621\pi$
$853$	−1.93327e38			−1.52741			−0.763704	+	0.645566i	$0.776621\pi$
$854$		−	2.50572e36i		−	0.0194975i
$855$	−6.16944e36	+	1.14981e37i	−0.0472809	+	0.0881181i
$856$	−3.85756e37			−0.291175
$857$			1.25009e38i			0.929373i	0.885475	+	0.464686i	$0.153833\pi$
$857$			1.25009e38i			0.929373i	−0.885475	+	0.464686i	$0.846167\pi$
$858$	8.87103e36	−	3.52957e37i	0.0649590	−	0.258456i
$859$	−1.07653e38			−0.776454			−0.388227	−	0.921564i	$-0.626912\pi$
$859$	−1.07653e38			−0.776454			−0.388227	+	0.921564i	$0.626912\pi$
$860$			1.93488e37i			0.137460i
$861$	8.48414e35	+	2.13236e35i	0.00593700	+	0.00149217i
$862$	1.56442e38			1.07835
$863$		−	1.43668e38i		−	0.975482i	−0.872988	−	0.487741i	$-0.837821\pi$
$863$		−	1.43668e38i		−	0.975482i	0.872988	−	0.487741i	$-0.162179\pi$
$864$	1.95411e37	+	1.77964e37i	0.130699	+	0.119029i
$865$	1.31007e37			0.0863146
$866$			1.28963e38i			0.837011i
$867$	−2.64369e37	+	1.05186e38i	−0.169030	+	0.672528i
$868$	6.41527e36			0.0404072
$869$		−	2.42752e38i		−	1.50628i
$870$	−2.26934e37	−	5.70365e36i	−0.138723	−	0.0348660i
$871$	−7.59678e36			−0.0457503
$872$		−	7.69481e37i		−	0.456545i
$873$	1.71410e38	+	9.19725e37i	1.00196	+	0.537617i
$874$	9.54326e37			0.549602
$875$		−	2.36310e36i		−	0.0134084i
$876$	−3.37739e37	+	1.34378e38i	−0.188811	+	0.751234i
$877$	2.28109e38			1.25646			0.628228	−	0.778029i	$-0.283781\pi$
$877$	2.28109e38			1.25646			0.628228	+	0.778029i	$0.283781\pi$
$878$			9.18844e36i			0.0498670i
$879$	−1.84898e38	−	4.64714e37i	−0.988731	−	0.248502i
$880$	9.25649e36			0.0487721
$881$			1.10315e38i			0.572727i	0.958121	+	0.286364i	$0.0924465\pi$
$881$			1.10315e38i			0.572727i	−0.958121	+	0.286364i	$0.907553\pi$
$882$	−6.52384e37	+	1.21586e38i	−0.333743	+	0.622000i
$883$	8.65378e37			0.436231			0.218116	−	0.975923i	$-0.430009\pi$
$883$	8.65378e37			0.436231			0.218116	+	0.975923i	$0.430009\pi$
$884$		−	1.75734e37i		−	0.0872926i
$885$	−1.31047e37	+	5.21404e37i	−0.0641452	+	0.255219i
$886$	1.23871e38			0.597493
$887$		−	3.64360e38i		−	1.73190i	−0.500130	−	0.865951i	$-0.666714\pi$
$887$		−	3.64360e38i		−	1.73190i	0.500130	−	0.865951i	$-0.333286\pi$
$888$	−1.86100e37	−	4.67734e36i	−0.0871722	−	0.0219094i
$889$	1.42328e37			0.0657001
$890$			9.05080e36i			0.0411734i
$891$	2.22141e38	−	1.47407e38i	0.995908	−	0.660860i
$892$	6.80765e37			0.300784
$893$			3.72242e37i			0.162090i
$894$	−7.24836e36	+	2.88395e37i	−0.0311066	+	0.123766i
$895$	3.16238e37			0.133757
$896$			8.82652e35i			0.00367947i
$897$	9.44259e37	+	2.37325e37i	0.387962	+	0.0975083i
$898$	−1.35516e38			−0.548782
$899$		−	6.02780e38i		−	2.40593i
$900$	1.09007e38	+	5.84891e37i	0.428846	+	0.230103i
$901$	−9.23572e37			−0.358136
$902$			3.25161e37i			0.124283i
$903$	−4.53634e36	+	1.80490e37i	−0.0170909	+	0.0680007i
$904$	−9.98421e37			−0.370787
$905$			3.99731e37i			0.146331i
$906$	−6.55777e37	−	1.64819e37i	−0.236641	−	0.0594760i
$907$	2.31669e38			0.824088			0.412044	−	0.911164i	$-0.364815\pi$
$907$	2.31669e38			0.824088			0.412044	+	0.911164i	$0.364815\pi$
$908$			1.27680e38i			0.447721i
$909$	−7.14764e37	+	1.33211e38i	−0.247077	+	0.460480i
$910$	−4.44577e35			−0.00151499
$911$			4.57368e38i			1.53648i	0.640161	+	0.768241i	$0.278868\pi$
$911$			4.57368e38i			1.53648i	−0.640161	+	0.768241i	$0.721132\pi$
$912$	1.12732e37	−	4.48536e37i	0.0373350	−	0.148547i
$913$	−3.04208e38			−0.993232
$914$		−	1.10673e38i		−	0.356239i
$915$	−3.30414e37	−	8.30444e36i	−0.104854	−	0.0263534i
$916$	1.68083e38			0.525875
$917$		−	8.67861e36i		−	0.0267700i
$918$	8.66806e37	−	9.51788e37i	0.263613	−	0.289458i
$919$	−3.89512e38			−1.16794			−0.583968	−	0.811777i	$-0.698501\pi$
$919$	−3.89512e38			−1.16794			−0.583968	+	0.811777i	$0.698501\pi$
$920$			2.47637e37i			0.0732106i
$921$	−9.56923e37	+	3.80737e38i	−0.278934	+	1.10981i
$922$	−3.35450e38			−0.964108
$923$			1.69707e38i			0.480925i
$924$	8.63466e36	+	2.17019e36i	0.0241274	+	0.00606404i
$925$	−8.98131e37			−0.247455
$926$		−	1.98513e37i		−	0.0539319i
$927$	−9.73115e37	−	5.22138e37i	−0.260692	−	0.139878i
$928$	8.29343e37			0.219084
$929$			6.90197e38i			1.79791i	0.438037	+	0.898957i	$0.355674\pi$
$929$			6.90197e38i			1.79791i	−0.438037	+	0.898957i	$0.644326\pi$
$930$	2.12615e37	−	8.45943e37i	0.0546154	−	0.217301i
$931$	2.41445e38			0.611606
$932$		−	3.08606e38i		−	0.770899i
$933$	−1.34090e38	−	3.37014e37i	−0.330320	−	0.0830208i
$934$	−1.22915e38			−0.298605
$935$		−	4.50855e37i		−	0.108016i
$936$	2.23087e37	−	4.15770e37i	0.0527093	−	0.0982351i
$937$	−1.16765e38			−0.272080			−0.136040	−	0.990703i	$-0.543438\pi$
$937$	−1.16765e38			−0.272080			−0.136040	+	0.990703i	$0.543438\pi$
$938$		−	1.85846e36i		−	0.00427087i
$939$	9.42595e37	−	3.75036e38i	0.213635	−	0.850002i
$940$	−9.65928e36			−0.0215915
$941$		−	6.26879e38i		−	1.38203i	−0.722838	−	0.691017i	$-0.757163\pi$
$941$		−	6.26879e38i		−	1.38203i	0.722838	−	0.691017i	$-0.242837\pi$
$942$	3.30588e38	+	8.30881e37i	0.718828	+	0.180666i
$943$	−8.69897e37			−0.186559
$944$		−	1.90550e38i		−	0.403063i
$945$	−2.40786e36	−	2.19287e36i	−0.00502362	−	0.00457508i
$946$	−6.91742e38			−1.42351
$947$			1.38297e38i			0.280714i	0.990101	+	0.140357i	$0.0448250\pi$
$947$			1.38297e38i			0.280714i	−0.990101	+	0.140357i	$0.955175\pi$
$948$	7.67158e37	−	3.05234e38i	0.153595	−	0.611117i
$949$	2.47354e38			0.488494
$950$		−	2.16466e38i		−	0.421680i
$951$	−1.29469e38	−	3.25400e37i	−0.248782	−	0.0625274i
$952$	4.29913e36			0.00814892
$953$			8.95177e38i			1.67379i	0.547363	+	0.836895i	$0.315632\pi$
$953$			8.95177e38i			1.67379i	−0.547363	+	0.836895i	$0.684368\pi$
$954$	−2.18508e38	−	1.17243e38i	−0.403030	−	0.216251i
$955$	−3.99440e37			−0.0726787
$956$			4.21388e38i			0.756362i
$957$	2.03912e38	−	8.11315e38i	0.361066	−	1.43660i
$958$	4.13408e38			0.722150
$959$		−	4.44915e37i		−	0.0766717i
$960$	1.16390e37	+	2.92528e36i	0.0197874	+	0.00497327i
$961$	1.65077e39			2.76874
$962$			3.42561e37i			0.0566842i
$963$	−2.38517e38	+	4.44528e38i	−0.389384	+	0.725701i
$964$	−2.48614e38			−0.400427
$965$		−	4.86172e37i		−	0.0772564i
$966$	−5.80587e36	+	2.31002e37i	−0.00910258	+	0.0362170i
$967$	8.55983e38			1.32410			0.662050	−	0.749460i	$-0.269687\pi$
$967$	8.55983e38			1.32410			0.662050	+	0.749460i	$0.269687\pi$
$968$			9.92784e37i			0.151522i
$969$	−2.18468e38	−	5.49085e37i	−0.328987	−	0.0826858i
$970$	8.83266e37			0.131238
$971$			3.58716e38i			0.525897i	0.964810	+	0.262948i	$0.0846949\pi$
$971$			3.58716e38i			0.525897i	−0.964810	+	0.262948i	$0.915305\pi$
$972$	3.25903e38	−	1.15146e38i	0.471440	−	0.166567i
$973$	−2.66801e37			−0.0380821
$974$			6.64670e38i			0.936138i
$975$	5.38315e37	−	2.14183e38i	0.0748129	−	0.297663i
$976$	1.20751e38			0.165594
$977$			3.80695e38i			0.515167i	0.966256	+	0.257584i	$0.0829263\pi$
$977$			3.80695e38i			0.515167i	−0.966256	+	0.257584i	$0.917074\pi$
$978$	5.86314e38	+	1.47361e38i	0.782934	+	0.196778i
$979$	−3.23576e38			−0.426384
$980$			6.26523e37i			0.0814700i
$981$	−8.86716e38	−	4.75779e38i	−1.13786	−	0.610532i
$982$	−1.66252e37			−0.0210532
$983$			2.95744e38i			0.369591i	0.982777	+	0.184795i	$0.0591622\pi$
$983$			2.95744e38i			0.369591i	−0.982777	+	0.184795i	$0.940838\pi$
$984$	−1.02759e37	+	4.08854e37i	−0.0126731	+	0.0504233i
$985$	−1.81116e38			−0.220438
$986$		−	4.03947e38i		−	0.485205i
$987$	−9.01039e36	−	2.26462e36i	−0.0106812	−	0.00268456i
$988$	−8.25635e37			−0.0965935
$989$		−	1.85060e39i		−	2.13679i
$990$	5.72340e37	−	1.06668e38i	0.0652223	−	0.121556i
$991$	−7.67955e38			−0.863730			−0.431865	−	0.901938i	$-0.642144\pi$
$991$	−7.67955e38			−0.863730			−0.431865	+	0.901938i	$0.642144\pi$
$992$			3.09154e38i			0.343181i
$993$	3.89261e37	−	1.54878e38i	0.0426482	−	0.169687i
$994$	−4.15167e37			−0.0448952
$995$		−	1.99056e38i		−	0.212459i
$996$	−3.82508e38	−	9.61375e37i	−0.402967	−	0.101279i
$997$	−9.62075e38			−1.00040			−0.500198	−	0.865911i	$-0.666739\pi$
$997$	−9.62075e38			−1.00040			−0.500198	+	0.865911i	$0.666739\pi$
$998$		−	5.70132e38i		−	0.585165i
$999$	−1.68968e38	+	1.85533e38i	−0.171180	+	0.187962i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.27.b.a.5.6	yes	8
3.2	odd	2	inner	6.27.b.a.5.2	✓	8
4.3	odd	2		48.27.e.b.17.5		8
12.11	even	2		48.27.e.b.17.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.27.b.a.5.2	✓	8	3.2	odd	2	inner
6.27.b.a.5.6	yes	8	1.1	even	1	trivial
48.27.e.b.17.5		8	4.3	odd	2
48.27.e.b.17.6		8	12.11	even	2

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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 27 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5792.62i q^{2} +(-388622. + 1.54623e6i) q^{3} -3.35544e7 q^{4} +1.99247e8i q^{5} +(-8.95674e9 - 2.25114e9i) q^{6} -4.03334e9 q^{7} -1.94368e11i q^{8} +(-2.23981e12 - 1.20180e12i) q^{9} +O(q^{10})\)	\(q+5792.62i q^{2} +(-388622. + 1.54623e6i) q^{3} -3.35544e7 q^{4} +1.99247e8i q^{5} +(-8.95674e9 - 2.25114e9i) q^{6} -4.03334e9 q^{7} -1.94368e11i q^{8} +(-2.23981e12 - 1.20180e12i) q^{9} -1.15416e12 q^{10} -4.12625e13i q^{11} +(1.30400e13 - 5.18830e13i) q^{12} -9.55028e13 q^{13} -2.33636e13i q^{14} +(-3.08082e14 - 7.74316e13i) q^{15} +1.12590e15 q^{16} -5.48391e15i q^{17} +(6.96157e15 - 1.29744e16i) q^{18} -2.57645e16 q^{19} -6.68561e15i q^{20} +(1.56744e15 - 6.23649e15i) q^{21} +2.39018e17 q^{22} +6.39440e17i q^{23} +(3.00538e17 + 7.55357e16i) q^{24} +1.45042e18 q^{25} -5.53212e17i q^{26} +(2.72870e18 - 2.99623e18i) q^{27} +1.35336e17 q^{28} -1.27163e19i q^{29} +(4.48532e17 - 1.78460e18i) q^{30} +4.74023e19 q^{31} +6.52191e18i q^{32} +(6.38015e19 + 1.60355e19i) q^{33} +3.17662e19 q^{34} -8.03630e17i q^{35} +(7.51556e19 + 4.03257e19i) q^{36} -6.19222e19 q^{37} -1.49244e20i q^{38} +(3.71145e19 - 1.47670e20i) q^{39} +3.87272e19 q^{40} +1.36040e20i q^{41} +(3.61256e19 + 9.07961e18i) q^{42} -2.89410e21 q^{43} +1.38454e21i q^{44} +(2.39455e20 - 4.46275e20i) q^{45} -3.70403e21 q^{46} -1.44479e21i q^{47} +(-4.37549e20 + 1.74090e21i) q^{48} -9.37121e21 q^{49} +8.40171e21i q^{50} +(8.47941e21 + 2.13117e21i) q^{51} +3.20454e21 q^{52} -1.68415e22i q^{53} +(1.73560e22 + 1.58063e22i) q^{54} +8.22141e21 q^{55} +7.83953e20i q^{56} +(1.00127e22 - 3.98380e22i) q^{57} +7.36604e22 q^{58} -1.69242e23i q^{59} +(1.03375e22 + 2.59817e21i) q^{60} +1.07249e23 q^{61} +2.74584e23i q^{62} +(9.03392e21 + 4.84727e21i) q^{63} -3.77789e22 q^{64} -1.90286e22i q^{65} +(-9.28876e22 + 3.69577e23i) q^{66} +7.95451e22 q^{67} +1.84010e23i q^{68} +(-9.88724e23 - 2.48501e23i) q^{69} +4.65512e21 q^{70} -1.77698e24i q^{71} +(-2.33592e23 + 4.35348e23i) q^{72} -2.59002e24 q^{73} -3.58692e23i q^{74} +(-5.63664e23 + 2.24268e24i) q^{75} +8.64514e23 q^{76} +1.66426e23i q^{77} +(8.55394e23 + 2.14990e23i) q^{78} +5.88312e24 q^{79} +2.24332e23i q^{80} +(3.57243e24 + 5.38362e24i) q^{81} -7.88030e23 q^{82} -7.37251e24i q^{83} +(-5.25947e22 + 2.09262e23i) q^{84} +1.09265e24 q^{85} -1.67644e25i q^{86} +(1.96623e25 + 4.94182e24i) q^{87} -8.02011e24 q^{88} -7.84189e24i q^{89} +(2.58510e24 + 1.38707e24i) q^{90} +3.85196e23 q^{91} -2.14561e25i q^{92} +(-1.84216e25 + 7.32951e25i) q^{93} +8.36910e24 q^{94} -5.13349e24i q^{95} +(-1.00844e25 - 2.53456e24i) q^{96} -7.65289e25 q^{97} -5.42839e25i q^{98} +(-4.95893e25 + 9.24202e25i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9}+O(q^{10}) \) 8 * q + 2194920 * q^3 - 268435456 * q^4 + 8978890752 * q^6 + 183211263760 * q^7 - 4853931303096 * q^9	\( 8 q + 2194920 q^{3} - 268435456 q^{4} + 8978890752 q^{6} + 183211263760 q^{7} - 4853931303096 q^{9} + 18696278507520 q^{10} - 73649293885440 q^{12} + 512429022548560 q^{13} - 10\!\cdots\!40 q^{15}+ \cdots + 49\!\cdots\!36 q^{99}+O(q^{100}) \) 8 * q + 2194920 * q^3 - 268435456 * q^4 + 8978890752 * q^6 + 183211263760 * q^7 - 4853931303096 * q^9 + 18696278507520 * q^10 - 73649293885440 * q^12 + 512429022548560 * q^13 - 1064426665559040 * q^15 + 9007199254740992 * q^16 - 1881283573186560 * q^18 + 13250502825732304 * q^19 - 376087240418977584 * q^21 + 428662713355468800 * q^22 - 301281579173412864 * q^24 - 5623831579932691000 * q^25 + 11144542948278241320 * q^27 - 6147549891468984320 * q^28 - 12961438025281044480 * q^30 - 31284409294003569776 * q^31 - 27135100230528798720 * q^33 - 98764413849435635712 * q^34 + 162870907842406121472 * q^36 - 884494012218278308400 * q^37 + 1550610890749922311440 * q^39 - 627343005833641328640 * q^40 + 2912220856097001308160 * q^42 - 5161357724259210085040 * q^43 + 20490779480380306513920 * q^45 - 10789778429003593678848 * q^46 + 2471260223527012270080 * q^48 - 29984991896355791854440 * q^49 + 55593505357359326429184 * q^51 - 17194264791932123217920 * q^52 + 6309825934293776793600 * q^54 - 76225105088113564293120 * q^55 + 66535314651975639764880 * q^57 - 142582792844514288599040 * q^58 + 35716232168487549665280 * q^60 + 235221054408754640644432 * q^61 - 635461358798759743298160 * q^63 - 302231454903657293676544 * q^64 - 1507842687345202066489344 * q^66 + 4218736573110688595120080 * q^67 - 2608639506957020943089664 * q^69 + 1864568339879729269309440 * q^70 + 63125401729205450833920 * q^72 + 1648536069669962768198800 * q^73 + 2584159434345978668025000 * q^75 - 444613096031842444771328 * q^76 - 313072373593422745436160 * q^78 - 9378866636279258011040624 * q^79 - 746539638785265647226744 * q^81 - 6997685112389596533227520 * q^82 + 12619393734706234851852288 * q^84 - 41457721476781794937282560 * q^85 + 55271553720839002987729920 * q^87 - 14383533866221569677721600 * q^88 + 32441993904208401898536960 * q^90 - 71633324581325574226388320 * q^91 + 18549099857564620426167120 * q^93 + 67962530415252490428088320 * q^94 + 10109332261226898153013248 * q^96 - 92292347027073928712964080 * q^97 + 4908019641378975318951936 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more