LMFDB - Embedded newform 6.27.b.a.5.4

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			5.4
Root			$-2107.01 + 1.41421i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.27.b.a.5.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5792.62i q^{2} +(1.54011e6 - 412209. i) q^{3} -3.35544e7 q^{4} +1.23273e9i q^{5} +(-2.38777e9 - 8.92129e9i) q^{6} -6.52628e10 q^{7} +1.94368e11i q^{8} +(2.20203e12 - 1.26970e12i) q^{9} +O(q^{10})$	\(q-5792.62i q^{2} +(1.54011e6 - 412209. i) q^{3} -3.35544e7 q^{4} +1.23273e9i q^{5} +(-2.38777e9 - 8.92129e9i) q^{6} -6.52628e10 q^{7} +1.94368e11i q^{8} +(2.20203e12 - 1.26970e12i) q^{9} +7.14075e12 q^{10} -4.72129e13i q^{11} +(-5.16776e13 + 1.38314e13i) q^{12} +3.70280e14 q^{13} +3.78043e14i q^{14} +(5.08144e14 + 1.89855e15i) q^{15} +1.12590e15 q^{16} -2.98298e13i q^{17} +(-7.35488e15 - 1.27555e16i) q^{18} +7.01278e16 q^{19} -4.13636e16i q^{20} +(-1.00512e17 + 2.69019e16i) q^{21} -2.73486e17 q^{22} -4.09515e17i q^{23} +(8.01203e16 + 2.99349e17i) q^{24} -2.95138e16 q^{25} -2.14489e18i q^{26} +(2.86800e18 - 2.86318e18i) q^{27} +2.18986e18 q^{28} -1.48710e19i q^{29} +(1.09976e19 - 2.94348e18i) q^{30} +9.71798e18 q^{31} -6.52191e18i q^{32} +(-1.94616e19 - 7.27132e19i) q^{33} -1.72793e17 q^{34} -8.04516e19i q^{35} +(-7.38880e19 + 4.26040e19i) q^{36} -2.55385e19 q^{37} -4.06224e20i q^{38} +(5.70273e20 - 1.52633e20i) q^{39} -2.39604e20 q^{40} +1.47371e21i q^{41} +(1.55833e20 + 5.82229e20i) q^{42} -1.20352e21 q^{43} +1.58420e21i q^{44} +(1.56520e21 + 2.71452e21i) q^{45} -2.37217e21 q^{46} +2.01672e20i q^{47} +(1.73401e21 - 4.64106e20i) q^{48} -5.12824e21 q^{49} +1.70962e20i q^{50} +(-1.22961e19 - 4.59413e19i) q^{51} -1.24245e22 q^{52} +1.74636e22i q^{53} +(-1.65853e22 - 1.66132e22i) q^{54} +5.82009e22 q^{55} -1.26850e22i q^{56} +(1.08005e23 - 2.89073e22i) q^{57} -8.61421e22 q^{58} -1.75317e23i q^{59} +(-1.70505e22 - 6.37047e22i) q^{60} +8.70380e22 q^{61} -5.62926e22i q^{62} +(-1.43711e23 + 8.28641e22i) q^{63} -3.77789e22 q^{64} +4.56456e23i q^{65} +(-4.21200e23 + 1.12734e23i) q^{66} +4.13304e23 q^{67} +1.00092e21i q^{68} +(-1.68806e23 - 6.30700e23i) q^{69} -4.66026e23 q^{70} +1.95086e24i q^{71} +(2.46789e23 + 4.28005e23i) q^{72} +2.56630e24 q^{73} +1.47935e23i q^{74} +(-4.54547e22 + 1.21659e22i) q^{75} -2.35310e24 q^{76} +3.08125e24i q^{77} +(-8.84143e23 - 3.30337e24i) q^{78} -7.16146e24 q^{79} +1.38793e24i q^{80} +(3.23682e24 - 5.59183e24i) q^{81} +8.53666e24 q^{82} -1.27711e25i q^{83} +(3.37263e24 - 9.02679e23i) q^{84} +3.67722e22 q^{85} +6.97153e24i q^{86} +(-6.12996e24 - 2.29030e25i) q^{87} +9.17667e24 q^{88} +2.12054e25i q^{89} +(1.57242e25 - 9.06660e24i) q^{90} -2.41655e25 q^{91} +1.37411e25i q^{92} +(1.49668e25 - 4.00584e24i) q^{93} +1.16821e24 q^{94} +8.64489e25i q^{95} +(-2.68839e24 - 1.00445e25i) q^{96} -6.17710e25 q^{97} +2.97060e25i q^{98} +(-5.99461e25 - 1.03964e26i) 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
$3$	1.54011e6	−	412209.i	0.965998	−	0.258548i
$3$	1.54011e6	−	412209.i	0.965998	−	0.258548i
$4$	−3.35544e7			−0.500000
$5$			1.23273e9i			1.00985i	0.863162	+	0.504927i	$0.168481\pi$
$5$			1.23273e9i			1.00985i	−0.863162	+	0.504927i	$0.831519\pi$
$6$	−2.38777e9	−	8.92129e9i	−0.182821	−	0.683064i
$7$	−6.52628e10			−0.673583			−0.336792	−	0.941579i	$-0.609342\pi$
$7$	−6.52628e10			−0.673583			−0.336792	+	0.941579i	$0.609342\pi$
$8$			1.94368e11i			0.353553i
$9$	2.20203e12	−	1.26970e12i	0.866306	−	0.499514i
$10$	7.14075e12			0.714075
$11$		−	4.72129e13i		−	1.36759i	−0.729675	−	0.683794i	$-0.760329\pi$
$11$		−	4.72129e13i		−	1.36759i	0.729675	−	0.683794i	$-0.239671\pi$
$12$	−5.16776e13	+	1.38314e13i	−0.482999	+	0.129274i
$13$	3.70280e14			1.22255			0.611274	−	0.791419i	$-0.290657\pi$
$13$	3.70280e14			1.22255			0.611274	+	0.791419i	$0.290657\pi$
$14$			3.78043e14i			0.476295i
$15$	5.08144e14	+	1.89855e15i	0.261096	+	0.975518i
$16$	1.12590e15			0.250000
$17$		−	2.98298e13i		−	0.00301172i	−0.999999	−	0.00150586i	$-0.999521\pi$
$17$		−	2.98298e13i		−	0.00301172i	0.999999	−	0.00150586i	$-0.000479331\pi$
$18$	−7.35488e15	−	1.27555e16i	−0.353210	−	0.612571i
$19$	7.01278e16			1.66761			0.833803	−	0.552062i	$-0.186159\pi$
$19$	7.01278e16			1.66761			0.833803	+	0.552062i	$0.186159\pi$
$20$		−	4.13636e16i		−	0.504927i
$21$	−1.00512e17	+	2.69019e16i	−0.650681	+	0.174154i
$22$	−2.73486e17			−0.967031
$23$		−	4.09515e17i		−	0.812472i	−0.913768	−	0.406236i	$-0.866841\pi$
$23$		−	4.09515e17i		−	0.812472i	0.913768	−	0.406236i	$-0.133159\pi$
$24$	8.01203e16	+	2.99349e17i	0.0914106	+	0.341532i
$25$	−2.95138e16			−0.0198064
$26$		−	2.14489e18i		−	0.864473i
$27$	2.86800e18	−	2.86318e18i	0.707702	−	0.706512i
$28$	2.18986e18			0.336792
$29$		−	1.48710e19i		−	1.44933i	−0.689103	−	0.724663i	$-0.741995\pi$
$29$		−	1.48710e19i		−	1.44933i	0.689103	−	0.724663i	$-0.258005\pi$
$30$	1.09976e19	−	2.94348e18i	0.689795	−	0.184623i
$31$	9.71798e18			0.397992			0.198996	−	0.980000i	$-0.436232\pi$
$31$	9.71798e18			0.397992			0.198996	+	0.980000i	$0.436232\pi$
$32$		−	6.52191e18i		−	0.176777i
$33$	−1.94616e19	−	7.27132e19i	−0.353588	−	1.32109i
$34$	−1.72793e17			−0.00212961
$35$		−	8.04516e19i		−	0.680221i
$36$	−7.38880e19	+	4.26040e19i	−0.433153	+	0.249757i
$37$	−2.55385e19			−0.104851			−0.0524256	−	0.998625i	$-0.516695\pi$
$37$	−2.55385e19			−0.104851			−0.0524256	+	0.998625i	$0.516695\pi$
$38$		−	4.06224e20i		−	1.17918i
$39$	5.70273e20	−	1.52633e20i	1.18098	−	0.316088i
$40$	−2.39604e20			−0.357038
$41$			1.47371e21i			1.59303i	0.604621	+	0.796513i	$0.293325\pi$
$41$			1.47371e21i			1.59303i	−0.604621	+	0.796513i	$0.706675\pi$
$42$	1.55833e20	+	5.82229e20i	0.123145	+	0.460101i
$43$	−1.20352e21			−0.700428			−0.350214	−	0.936670i	$-0.613891\pi$
$43$	−1.20352e21			−0.700428			−0.350214	+	0.936670i	$0.613891\pi$
$44$			1.58420e21i			0.683794i
$45$	1.56520e21	+	2.71452e21i	0.504437	+	0.874843i
$46$	−2.37217e21			−0.574504
$47$			2.01672e20i			0.0369295i	0.999830	+	0.0184647i	$0.00587784\pi$
$47$			2.01672e20i			0.0369295i	−0.999830	+	0.0184647i	$0.994122\pi$
$48$	1.73401e21	−	4.64106e20i	0.241500	−	0.0646370i
$49$	−5.12824e21			−0.546285
$50$			1.70962e20i			0.0140052i
$51$	−1.22961e19	−	4.59413e19i	−0.000778675	−	0.00290932i
$52$	−1.24245e22			−0.611274
$53$			1.74636e22i			0.670731i	0.942088	+	0.335365i	$0.108860\pi$
$53$			1.74636e22i			0.670731i	−0.942088	+	0.335365i	$0.891140\pi$
$54$	−1.65853e22	−	1.66132e22i	−0.499579	−	0.500421i
$55$	5.82009e22			1.38107
$56$		−	1.26850e22i		−	0.238148i
$57$	1.08005e23	−	2.89073e22i	1.61091	−	0.431157i
$58$	−8.61421e22			−1.02483
$59$		−	1.75317e23i		−	1.67012i	−0.550159	−	0.835060i	$-0.685433\pi$
$59$		−	1.75317e23i		−	1.67012i	0.550159	−	0.835060i	$-0.314567\pi$
$60$	−1.70505e22	−	6.37047e22i	−0.130548	−	0.487759i
$61$	8.70380e22			0.537553			0.268776	−	0.963203i	$-0.413381\pi$
$61$	8.70380e22			0.537553			0.268776	+	0.963203i	$0.413381\pi$
$62$		−	5.62926e22i		−	0.281423i
$63$	−1.43711e23	+	8.28641e22i	−0.583529	+	0.336464i
$64$	−3.77789e22			−0.125000
$65$			4.56456e23i			1.23460i
$66$	−4.21200e23	+	1.12734e23i	−0.934151	+	0.250024i
$67$	4.13304e23			0.753870			0.376935	−	0.926240i	$-0.376978\pi$
$67$	4.13304e23			0.753870			0.376935	+	0.926240i	$0.376978\pi$
$68$			1.00092e21i			0.00150586i
$69$	−1.68806e23	−	6.30700e23i	−0.210063	−	0.784846i
$70$	−4.66026e23			−0.480989
$71$			1.95086e24i			1.67443i	0.546875	+	0.837214i	$0.315817\pi$
$71$			1.95086e24i			1.67443i	−0.546875	+	0.837214i	$0.684183\pi$
$72$	2.46789e23	+	4.28005e23i	0.176605	+	0.306285i
$73$	2.56630e24			1.53501			0.767503	−	0.641046i	$-0.221499\pi$
$73$	2.56630e24			1.53501			0.767503	+	0.641046i	$0.221499\pi$
$74$			1.47935e23i			0.0741410i
$75$	−4.54547e22	+	1.21659e22i	−0.0191330	+	0.00512091i
$76$	−2.35310e24			−0.833803
$77$			3.08125e24i			0.921185i
$78$	−8.84143e23	−	3.30337e24i	−0.223508	−	0.835079i
$79$	−7.16146e24			−1.53408			−0.767042	−	0.641597i	$-0.778272\pi$
$79$	−7.16146e24			−1.53408			−0.767042	+	0.641597i	$0.778272\pi$
$80$			1.38793e24i			0.252464i
$81$	3.23682e24	−	5.59183e24i	0.500971	−	0.865464i
$82$	8.53666e24			1.12644
$83$		−	1.27711e25i		−	1.43951i	−0.694229	−	0.719755i	$-0.744254\pi$
$83$		−	1.27711e25i		−	1.43951i	0.694229	−	0.719755i	$-0.255746\pi$
$84$	3.37263e24	−	9.02679e23i	0.325340	−	0.0870769i
$85$	3.67722e22			0.00304140
$86$			6.97153e24i			0.495277i
$87$	−6.12996e24	−	2.29030e25i	−0.374721	−	1.40005i
$88$	9.17667e24			0.483516
$89$			2.12054e25i			0.964666i	0.875988	+	0.482333i	$0.160210\pi$
$89$			2.12054e25i			0.964666i	−0.875988	+	0.482333i	$0.839790\pi$
$90$	1.57242e25	−	9.06660e24i	0.618607	−	0.356691i
$91$	−2.41655e25			−0.823489
$92$			1.37411e25i			0.406236i
$93$	1.49668e25	−	4.00584e24i	0.384460	−	0.102900i
$94$	1.16821e24			0.0261131
$95$			8.64489e25i			1.68404i
$96$	−2.68839e24	−	1.00445e25i	−0.0457053	−	0.170766i
$97$	−6.17710e25			−0.917809			−0.458904	−	0.888486i	$-0.651758\pi$
$97$	−6.17710e25			−0.917809			−0.458904	+	0.888486i	$0.651758\pi$
$98$			2.97060e25i			0.386282i
$99$	−5.99461e25	−	1.03964e26i	−0.683130	−	1.18475i
$100$	9.90320e23			0.00990320
$101$			1.41146e26i			1.24020i	0.784524	+	0.620099i	$0.212908\pi$
$101$			1.41146e26i			1.24020i	−0.784524	+	0.620099i	$0.787092\pi$
$102$	−2.66121e23	+	7.12268e22i	−0.00205720	+	0.000550606i
$103$	1.15485e26			0.786399			0.393199	−	0.919453i	$-0.371368\pi$
$103$	1.15485e26			0.786399			0.393199	+	0.919453i	$0.371368\pi$
$104$			7.19705e25i			0.432236i
$105$	−3.31629e25	−	1.23905e26i	−0.175870	−	0.657093i
$106$	1.01160e26			0.474278
$107$			7.52135e25i			0.312109i	0.987748	+	0.156055i	$0.0498776\pi$
$107$			7.52135e25i			0.312109i	−0.987748	+	0.156055i	$0.950122\pi$
$108$	−9.62341e25	+	9.60723e25i	−0.353851	+	0.353256i
$109$	1.76550e26			0.575868			0.287934	−	0.957650i	$-0.407032\pi$
$109$	1.76550e26			0.575868			0.287934	+	0.957650i	$0.407032\pi$
$110$		−	3.37135e26i		−	0.976561i
$111$	−3.93322e25	+	1.05272e25i	−0.101286	+	0.0271091i
$112$	−7.34794e25			−0.168396
$113$		−	5.42487e26i		−	1.10757i	−0.832661	−	0.553783i	$-0.813184\pi$
$113$		−	5.42487e26i		−	1.10757i	0.832661	−	0.553783i	$-0.186816\pi$
$114$	−1.67449e26	−	6.25631e26i	−0.304874	−	1.13908i
$115$	5.04823e26			0.820478
$116$			4.98988e26i			0.724663i
$117$	8.15368e26	−	4.70143e26i	1.05910	−	0.610680i
$118$	−1.01554e27			−1.18095
$119$			1.94678e24i			0.00202865i
$120$	−3.69017e26	+	9.87669e25i	−0.344898	+	0.0923114i
$121$	−1.03724e27			−0.870299
$122$		−	5.04178e26i		−	0.380107i
$123$	6.07478e26	+	2.26969e27i	0.411874	+	1.53886i
$124$	−3.26081e26			−0.198996
$125$			1.80053e27i			0.989853i
$126$	4.80000e26	+	8.32463e26i	0.237916	+	0.412617i
$127$	1.64192e27			0.734352			0.367176	−	0.930152i	$-0.380325\pi$
$127$	1.64192e27			0.734352			0.367176	+	0.930152i	$0.380325\pi$
$128$			2.18839e26i			0.0883883i
$129$	−1.85356e27	+	4.96102e26i	−0.676612	+	0.181094i
$130$	2.64407e27			0.872992
$131$		−	3.57069e27i		−	1.06715i	−0.845753	−	0.533575i	$-0.820848\pi$
$131$		−	3.57069e27i		−	1.06715i	0.845753	−	0.533575i	$-0.179152\pi$
$132$	6.53022e26	+	2.43985e27i	0.176794	+	0.660544i
$133$	−4.57674e27			−1.12327
$134$		−	2.39411e27i		−	0.533067i
$135$	3.52953e27	+	3.53548e27i	0.713474	+	0.714676i
$136$	5.79797e24			0.00106480
$137$		−	2.69983e27i		−	0.450785i	−0.974268	−	0.225393i	$-0.927634\pi$
$137$		−	2.69983e27i		−	0.450785i	0.974268	−	0.225393i	$-0.0723665\pi$
$138$	−3.65340e27	+	9.77829e26i	−0.554970	+	0.148537i
$139$	−1.15296e28			−1.59449			−0.797244	−	0.603658i	$-0.793709\pi$
$139$	−1.15296e28			−1.59449			−0.797244	+	0.603658i	$0.793709\pi$
$140$			2.69951e27i			0.340111i
$141$	8.31310e25	+	3.10598e26i	0.00954805	+	0.0356738i
$142$	1.13006e28			1.18400
$143$		−	1.74820e28i		−	1.67194i
$144$	2.47927e27	−	1.42955e27i	0.216576	−	0.124879i
$145$	1.83320e28			1.46361
$146$		−	1.48656e28i		−	1.08541i
$147$	−7.89808e27	+	2.11391e27i	−0.527711	+	0.141241i
$148$	8.56931e26			0.0524256
$149$		−	1.77789e27i		−	0.0996516i	−0.998758	−	0.0498258i	$-0.984133\pi$
$149$		−	1.77789e27i		−	0.0996516i	0.998758	−	0.0498258i	$-0.0158666\pi$
$150$	7.04723e25	+	2.63301e26i	0.00362103	+	0.0135290i
$151$	−2.36660e26			−0.0111539			−0.00557693	−	0.999984i	$-0.501775\pi$
$151$	−2.36660e26			−0.0111539			−0.00557693	+	0.999984i	$0.501775\pi$
$152$			1.36306e28i			0.589588i
$153$	−3.78749e25	−	6.56863e25i	−0.00150440	−	0.00260907i
$154$	1.78485e28			0.651376
$155$			1.19797e28i			0.401914i
$156$	−1.91352e28	+	5.12150e27i	−0.590490	+	0.158044i
$157$	−4.48717e28			−1.27431			−0.637157	−	0.770734i	$-0.719890\pi$
$157$	−4.48717e28			−1.27431			−0.637157	+	0.770734i	$0.719890\pi$
$158$			4.14836e28i			1.08476i
$159$	7.19867e27	+	2.68960e28i	0.173416	+	0.647925i
$160$	8.03977e27			0.178519
$161$			2.67261e28i			0.547267i
$162$	−3.23914e28	−	1.87496e28i	−0.611975	−	0.354240i
$163$	−2.42227e28			−0.422458			−0.211229	−	0.977437i	$-0.567747\pi$
$163$	−2.42227e28			−0.422458			−0.211229	+	0.977437i	$0.567747\pi$
$164$		−	4.94496e28i		−	0.796513i
$165$	8.96359e28	−	2.39909e28i	1.33411	−	0.357072i
$166$	−7.39783e28			−1.01789
$167$			6.59270e28i			0.838975i	0.907761	+	0.419488i	$0.137790\pi$
$167$			6.59270e28i			0.838975i	−0.907761	+	0.419488i	$0.862210\pi$
$168$	−5.22888e27	−	1.95364e28i	−0.0615726	−	0.230050i
$169$	4.53737e28			0.494626
$170$		−	2.13007e26i		−	0.00215060i
$171$	1.54424e29	−	8.90412e28i	1.44466	−	0.832993i
$172$	4.03834e28			0.350214
$173$			1.62424e29i			1.30633i	0.757218	+	0.653163i	$0.226558\pi$
$173$			1.62424e29i			1.30633i	−0.757218	+	0.653163i	$0.773442\pi$
$174$	−1.32669e29	+	3.55085e28i	−0.989983	+	0.264968i
$175$	1.92616e27			0.0133413
$176$		−	5.31570e28i		−	0.341897i
$177$	−7.22672e28	−	2.70008e29i	−0.431806	−	1.61333i
$178$	1.22835e29			0.682122
$179$		−	1.69124e29i		−	0.873206i	−0.899654	−	0.436603i	$-0.856181\pi$
$179$		−	1.69124e29i		−	0.873206i	0.899654	−	0.436603i	$-0.143819\pi$
$180$	−5.25193e28	−	9.10841e28i	−0.252218	−	0.437421i
$181$	−1.87674e29			−0.838653			−0.419327	−	0.907835i	$-0.637734\pi$
$181$	−1.87674e29			−0.838653			−0.419327	+	0.907835i	$0.637734\pi$
$182$			1.39982e29i			0.582294i
$183$	1.34048e29	−	3.58779e28i	0.519275	−	0.138983i
$184$	7.95967e28			0.287252
$185$		−	3.14822e28i		−	0.105884i
$186$	−2.32043e28	−	8.66970e28i	−0.0727613	−	0.271854i
$187$	−1.40835e27			−0.00411880
$188$		−	6.76699e27i		−	0.0184647i
$189$	−1.87174e29	+	1.86859e29i	−0.476696	+	0.475894i
$190$	5.00765e29			1.19080
$191$			2.40262e29i			0.533644i	0.963746	+	0.266822i	$0.0859737\pi$
$191$			2.40262e29i			0.533644i	−0.963746	+	0.266822i	$0.914026\pi$
$192$	−5.81838e28	+	1.55728e28i	−0.120750	+	0.0323185i
$193$	−8.59177e29			−1.66662			−0.833312	−	0.552803i	$-0.813558\pi$
$193$	−8.59177e29			−1.66662			−0.833312	+	0.552803i	$0.813558\pi$
$194$			3.57816e29i			0.648989i
$195$	1.88155e29	+	7.02994e29i	0.319203	+	1.19262i
$196$	1.72075e29			0.273143
$197$		−	1.82524e29i		−	0.271181i	−0.990765	−	0.135591i	$-0.956707\pi$
$197$		−	1.82524e29i		−	0.271181i	0.990765	−	0.135591i	$-0.0432932\pi$
$198$	−6.02226e29	+	3.47245e29i	−0.837745	+	0.483046i
$199$	6.18385e29			0.805692			0.402846	−	0.915268i	$-0.368021\pi$
$199$	6.18385e29			0.805692			0.402846	+	0.915268i	$0.368021\pi$
$200$		−	5.73655e27i		−	0.00700262i
$201$	6.36534e29	−	1.70368e29i	0.728238	−	0.194912i
$202$	8.17605e29			0.876952
$203$			9.70524e29i			0.976243i
$204$	4.12590e26	+	1.54154e27i	0.000389337	+	0.00145466i
$205$	−1.81670e30			−1.60873
$206$		−	6.68962e29i		−	0.556068i
$207$	−5.19961e29	−	9.01766e29i	−0.405841	−	0.703849i
$208$	4.16898e29			0.305637
$209$		−	3.31094e30i		−	2.28060i
$210$	−7.17732e29	+	1.92100e29i	−0.464635	+	0.124359i
$211$	−3.84159e25			−2.33797e−5			−1.16899e−5	−	1.00000i	$-0.500004\pi$
$211$	−3.84159e25			−2.33797e−5			−1.16899e−5		1.00000i	$0.500004\pi$
$212$		−	5.85982e29i		−	0.335365i
$213$	8.04161e29	+	3.00454e30i	0.432920	+	1.61750i
$214$	4.35683e29			0.220695
$215$		−	1.48362e30i		−	0.707330i
$216$	5.56510e29	+	5.57447e29i	0.249790	+	0.250210i
$217$	−6.34223e29			−0.268081
$218$		−	1.02269e30i		−	0.407200i
$219$	3.95239e30	−	1.05785e30i	1.48281	−	0.396873i
$220$	−1.95290e30			−0.690533
$221$		−	1.10454e28i		−	0.00368198i
$222$	6.09802e28	+	2.27837e29i	0.0191690	+	0.0716201i
$223$	1.71022e30			0.507096			0.253548	−	0.967323i	$-0.418402\pi$
$223$	1.71022e30			0.507096			0.253548	+	0.967323i	$0.418402\pi$
$224$			4.25638e29i			0.119074i
$225$	−6.49904e28	+	3.74737e28i	−0.0171584	+	0.00989358i
$226$	−3.14242e30			−0.783168
$227$			6.90133e29i			0.162404i	0.996698	+	0.0812020i	$0.0258759\pi$
$227$			6.90133e29i			0.162404i	−0.996698	+	0.0812020i	$0.974124\pi$
$228$	−3.62404e30	+	9.69969e29i	−0.805453	+	0.215578i
$229$	3.56889e30			0.749328			0.374664	−	0.927161i	$-0.377758\pi$
$229$	3.56889e30			0.749328			0.374664	+	0.927161i	$0.377758\pi$
$230$		−	2.92425e30i		−	0.580166i
$231$	1.27012e30	+	4.74547e30i	0.238171	+	0.889863i
$232$	2.89045e30			0.512414
$233$			4.74026e30i			0.794649i	0.917678	+	0.397325i	$0.130061\pi$
$233$			4.74026e30i			0.794649i	−0.917678	+	0.397325i	$0.869939\pi$
$234$	−2.72336e30	−	4.72312e30i	−0.431816	−	0.748898i
$235$	−2.48608e29			−0.0372934
$236$			5.88266e30i			0.835060i
$237$	−1.10295e31	+	2.95202e30i	−1.48192	+	0.396635i
$238$	1.12770e28			0.00143447
$239$			7.68710e30i			0.925955i	0.886370	+	0.462978i	$0.153219\pi$
$239$			7.68710e30i			0.925955i	−0.886370	+	0.462978i	$0.846781\pi$
$240$	5.72119e29	+	2.13758e30i	0.0652740	+	0.243879i
$241$	−1.02374e31			−1.10654			−0.553270	−	0.833002i	$-0.686620\pi$
$241$	−1.02374e31			−1.10654			−0.553270	+	0.833002i	$0.686620\pi$
$242$			6.00832e30i			0.615395i
$243$	2.68006e30	−	9.94630e30i	0.260173	−	0.965562i
$244$	−2.92051e30			−0.268776
$245$		−	6.32175e30i		−	0.551669i
$246$	1.31474e31	−	3.51889e30i	1.08814	−	0.291239i
$247$	2.59669e31			2.03873
$248$			1.88887e30i			0.140711i
$249$	−5.26438e30	−	1.96690e31i	−0.372182	−	1.39056i
$250$	1.04298e31			0.699932
$251$		−	3.66724e30i		−	0.233658i	−0.993152	−	0.116829i	$-0.962727\pi$
$251$		−	3.66724e30i		−	0.233658i	0.993152	−	0.116829i	$-0.0372729\pi$
$252$	4.82214e30	−	2.78046e30i	0.291765	−	0.168232i
$253$	−1.93344e31			−1.11113
$254$		−	9.51103e30i		−	0.519265i
$255$	5.66334e28	−	1.51578e28i	0.00293799	−	0.000786348i
$256$	1.26765e30			0.0625000
$257$			6.75971e30i			0.316809i	0.987374	+	0.158405i	$0.0506350\pi$
$257$			6.75971e30i			0.316809i	−0.987374	+	0.158405i	$0.949365\pi$
$258$	2.87373e30	+	1.07369e31i	0.128053	+	0.478437i
$259$	1.66672e30			0.0706260
$260$		−	1.53161e31i		−	0.617298i
$261$	−1.88817e31	−	3.27464e31i	−0.723959	−	1.25556i
$262$	−2.06836e31			−0.754588
$263$			3.46577e31i			1.20330i	0.798758	+	0.601652i	$0.205491\pi$
$263$			3.46577e31i			1.20330i	−0.798758	+	0.601652i	$0.794509\pi$
$264$	1.41331e31	−	3.78271e30i	0.467075	−	0.125012i
$265$	−2.15280e31			−0.677341
$266$			2.65113e31i			0.794273i
$267$	8.74107e30	+	3.26588e31i	0.249413	+	0.931866i
$268$	−1.38682e31			−0.376935
$269$		−	3.16346e31i		−	0.819187i	−0.912268	−	0.409593i	$-0.865671\pi$
$269$		−	3.16346e31i		−	0.819187i	0.912268	−	0.409593i	$-0.134329\pi$
$270$	2.04797e31	−	2.04452e31i	0.505352	−	0.504502i
$271$	7.38389e31			1.73654			0.868269	−	0.496093i	$-0.165233\pi$
$271$	7.38389e31			1.73654			0.868269	+	0.496093i	$0.165233\pi$
$272$		−	3.35854e28i		−	0.000752930i
$273$	−3.72176e31	+	9.96124e30i	−0.795489	+	0.212911i
$274$	−1.56391e31			−0.318753
$275$			1.39343e30i			0.0270870i
$276$	5.66419e30	+	2.11628e31i	0.105032	+	0.392423i
$277$	−5.06025e31			−0.895230			−0.447615	−	0.894226i	$-0.647727\pi$
$277$	−5.06025e31			−0.895230			−0.447615	+	0.894226i	$0.647727\pi$
$278$			6.67865e31i			1.12747i
$279$	2.13993e31	−	1.23389e31i	0.344783	−	0.198803i
$280$	1.56372e31			0.240495
$281$			9.60687e31i			1.41059i	0.708916	+	0.705293i	$0.249185\pi$
$281$			9.60687e31i			1.41059i	−0.708916	+	0.705293i	$0.750815\pi$
$282$	1.79917e30	−	4.81546e29i	0.0252252	−	0.00675149i
$283$	2.44285e31			0.327095			0.163548	−	0.986535i	$-0.447706\pi$
$283$	2.44285e31			0.327095			0.163548	+	0.986535i	$0.447706\pi$
$284$		−	6.54599e31i		−	0.837214i
$285$	3.56350e31	+	1.33141e32i	0.435405	+	1.62678i
$286$	−1.01266e32			−1.18224
$287$		−	9.61787e31i		−	1.07304i
$288$	−8.28085e30	−	1.43615e31i	−0.0883025	−	0.153143i
$289$	9.80998e31			0.999991
$290$		−	1.06190e32i		−	1.03493i
$291$	−9.51344e31	+	2.54626e31i	−0.886602	+	0.237298i
$292$	−8.61107e31			−0.767503
$293$		−	2.03701e32i		−	1.73666i	−0.495989	−	0.868329i	$-0.665195\pi$
$293$		−	2.03701e32i		−	1.73666i	0.495989	−	0.868329i	$-0.334805\pi$
$294$	1.22451e31	+	4.57505e31i	0.0998725	+	0.373148i
$295$	2.16119e32			1.68658
$296$		−	4.96387e30i		−	0.0370705i
$297$	−1.35179e32	−	1.35407e32i	−0.966217	−	0.967845i
$298$	−1.02987e31			−0.0704643
$299$		−	1.51635e32i		−	0.993286i
$300$	1.52521e30	−	4.08219e29i	0.00956648	−	0.00256045i
$301$	7.85451e31			0.471797
$302$			1.37088e30i			0.00788697i
$303$	5.81817e31	+	2.17381e32i	0.320651	+	1.19803i
$304$	7.89569e31			0.416902
$305$			1.07295e32i			0.542850i
$306$	−3.80496e29	+	2.19395e29i	−0.00184489	+	0.00106377i
$307$	−1.82282e32			−0.847118			−0.423559	−	0.905869i	$-0.639219\pi$
$307$	−1.82282e32			−0.847118			−0.423559	+	0.905869i	$0.639219\pi$
$308$		−	1.03389e32i		−	0.460593i
$309$	1.77860e32	−	4.76041e31i	0.759660	−	0.203322i
$310$	6.93937e31			0.284196
$311$			1.88339e32i			0.739701i	0.929091	+	0.369851i	$0.120591\pi$
$311$			1.88339e32i			0.739701i	−0.929091	+	0.369851i	$0.879409\pi$
$312$	2.96669e31	+	1.10843e32i	0.111754	+	0.417540i
$313$	−2.20811e32			−0.797892			−0.398946	−	0.916974i	$-0.630624\pi$
$313$	−2.20811e32			−0.797892			−0.398946	+	0.916974i	$0.630624\pi$
$314$			2.59924e32i			0.901076i
$315$	−1.02149e32	−	1.77157e32i	−0.339780	−	0.589280i
$316$	2.40299e32			0.767042
$317$			1.52978e32i			0.468660i	0.972157	+	0.234330i	$0.0752897\pi$
$317$			1.52978e32i			0.468660i	−0.972157	+	0.234330i	$0.924710\pi$
$318$	1.55798e32	−	4.16991e31i	0.458152	−	0.122624i
$319$	−7.02103e32			−1.98208
$320$		−	4.65713e31i		−	0.126232i
$321$	3.10037e31	+	1.15837e32i	0.0806953	+	0.301497i
$322$	1.54814e32			0.386977
$323$		−	2.09190e30i		−	0.00502237i
$324$	−1.08610e32	+	1.87631e32i	−0.250486	+	0.432732i
$325$	−1.09284e31			−0.0242143
$326$			1.40313e32i			0.298723i
$327$	2.71907e32	−	7.27755e31i	0.556287	−	0.148890i
$328$	−2.86443e32			−0.563220
$329$		−	1.31617e31i		−	0.0248751i
$330$	−1.38970e32	−	5.19227e32i	−0.252488	−	0.943356i
$331$	7.16363e31			0.125132			0.0625661	−	0.998041i	$-0.480072\pi$
$331$	7.16363e31			0.125132			0.0625661	+	0.998041i	$0.480072\pi$
$332$			4.28528e32i			0.719755i
$333$	−5.62367e31	+	3.24262e31i	−0.0908332	+	0.0523747i
$334$	3.81890e32			0.593245
$335$			5.09493e32i			0.761299i
$336$	−1.13167e32	+	3.02889e31i	−0.162670	+	0.0435384i
$337$	1.68287e32			0.232736			0.116368	−	0.993206i	$-0.462875\pi$
$337$	1.68287e32			0.232736			0.116368	+	0.993206i	$0.462875\pi$
$338$		−	2.62832e32i		−	0.349753i
$339$	−2.23618e32	−	8.35492e32i	−0.286359	−	1.06991i
$340$	−1.23387e30			−0.00152070
$341$		−	4.58814e32i		−	0.544289i
$342$	−5.15781e32	−	8.94518e32i	−0.589015	−	1.02153i
$343$	9.47337e32			1.04155
$344$		−	2.33926e32i		−	0.247639i
$345$	7.77484e32	−	2.08093e32i	0.792581	−	0.212133i
$346$	9.40861e32			0.923712
$347$			1.44656e32i			0.136790i	0.997658	+	0.0683948i	$0.0217878\pi$
$347$			1.44656e32i			0.136790i	−0.997658	+	0.0683948i	$0.978212\pi$
$348$	2.05687e32	+	7.68498e32i	0.187360	+	0.700024i
$349$	−5.46703e32			−0.479757			−0.239878	−	0.970803i	$-0.577108\pi$
$349$	−5.46703e32			−0.479757			−0.239878	+	0.970803i	$0.577108\pi$
$350$		−	1.11575e31i		−	0.00943370i
$351$	1.06196e33	−	1.06018e33i	0.865200	−	0.863745i
$352$	−3.07918e32			−0.241758
$353$		−	1.31891e31i		−	0.00998029i	−0.999988	−	0.00499015i	$-0.998412\pi$
$353$		−	1.31891e31i		−	0.00998029i	0.999988	−	0.00499015i	$-0.00158842\pi$
$354$	−1.56405e33	+	4.18617e32i	−1.14080	+	0.305333i
$355$	−2.40488e33			−1.69093
$356$		−	7.11536e32i		−	0.482333i
$357$	8.02480e29	+	2.99826e30i	0.000524503	+	0.00195967i
$358$	−9.79673e32			−0.617450
$359$			1.00670e33i			0.611888i	0.952049	+	0.305944i	$0.0989721\pi$
$359$			1.00670e33i			0.611888i	−0.952049	+	0.305944i	$0.901028\pi$
$360$	−5.27616e32	+	3.04224e32i	−0.309304	+	0.178345i
$361$	3.14946e33			1.78091
$362$			1.08712e33i			0.593017i
$363$	−1.59746e33	+	4.27559e32i	−0.840708	+	0.225014i
$364$	8.10860e32			0.411744
$365$			3.16356e33i			1.55013i
$366$	−2.07827e32	−	7.76491e32i	−0.0982760	−	0.367183i
$367$	−1.54039e33			−0.703029			−0.351514	−	0.936182i	$-0.614333\pi$
$367$	−1.54039e33			−0.703029			−0.351514	+	0.936182i	$0.614333\pi$
$368$		−	4.61073e32i		−	0.203118i
$369$	1.87117e33	+	3.24517e33i	0.795739	+	1.38005i
$370$	−1.82364e32			−0.0748716
$371$		−	1.13973e33i		−	0.451793i
$372$	−5.02202e32	+	1.34414e32i	−0.192230	+	0.0514500i
$373$	2.89395e33			1.06973			0.534867	−	0.844936i	$-0.320362\pi$
$373$	2.89395e33			1.06973			0.534867	+	0.844936i	$0.320362\pi$
$374$			8.15805e30i			0.00291243i
$375$	7.42196e32	+	2.77302e33i	0.255925	+	0.956196i
$376$	−3.91986e31			−0.0130565
$377$		−	5.50643e33i		−	1.77187i
$378$	1.08240e33	+	1.08423e33i	0.336508	+	0.337075i
$379$	−4.99203e33			−1.49957			−0.749786	−	0.661680i	$-0.769844\pi$
$379$	−4.99203e33			−1.49957			−0.749786	+	0.661680i	$0.769844\pi$
$380$		−	2.90074e33i		−	0.842020i
$381$	2.52875e33	−	6.76815e32i	0.709383	−	0.189865i
$382$	1.39175e33			0.377344
$383$		−	4.67193e33i		−	1.22437i	−0.790715	−	0.612184i	$-0.790291\pi$
$383$		−	4.67193e33i		−	1.22437i	0.790715	−	0.612184i	$-0.209709\pi$
$384$	9.02074e31	+	3.37037e32i	0.0228526	+	0.0853830i
$385$	−3.79835e33			−0.930263
$386$			4.97689e33i			1.17848i
$387$	−2.65019e33	+	1.52811e33i	−0.606785	+	0.349874i
$388$	2.07269e33			0.458904
$389$			1.99238e33i			0.426605i	0.976986	+	0.213303i	$0.0684220\pi$
$389$			1.99238e33i			0.426605i	−0.976986	+	0.213303i	$0.931578\pi$
$390$	4.07217e33	−	1.08991e33i	0.843309	−	0.225710i
$391$	−1.22158e31			−0.00244694
$392$		−	9.96766e32i		−	0.193141i
$393$	−1.47187e33	−	5.49927e33i	−0.275909	−	1.03086i
$394$	−1.05729e33			−0.191754
$395$		−	8.82816e33i		−	1.54920i
$396$	2.01146e33	+	3.48846e33i	0.341565	+	0.592375i
$397$	−1.32621e33			−0.217939			−0.108969	−	0.994045i	$-0.534755\pi$
$397$	−1.32621e33			−0.217939			−0.108969	+	0.994045i	$0.534755\pi$
$398$		−	3.58207e33i		−	0.569711i
$399$	−7.04870e33	+	1.88657e33i	−1.08508	+	0.290420i
$400$	−3.32296e31			−0.00495160
$401$			3.44450e33i			0.496878i	0.968648	+	0.248439i	$0.0799175\pi$
$401$			3.44450e33i			0.496878i	−0.968648	+	0.248439i	$0.920083\pi$
$402$	−9.86874e32	−	3.68720e33i	−0.137823	−	0.514942i
$403$	3.59837e33			0.486564
$404$		−	4.73608e33i		−	0.620099i
$405$	6.89324e33	+	3.99013e33i	0.873993	+	0.505908i
$406$	5.62187e33			0.690308
$407$			1.20575e33i			0.143393i
$408$	8.92952e30	−	2.38997e30i	0.00102860	−	0.000275303i
$409$	8.30731e33			0.926952			0.463476	−	0.886109i	$-0.346602\pi$
$409$	8.30731e33			0.926952			0.463476	+	0.886109i	$0.346602\pi$
$410$			1.05234e34i			1.13754i
$411$	−1.11290e33	−	4.15805e33i	−0.116550	−	0.435458i
$412$	−3.87504e33			−0.393199
$413$			1.14417e34i			1.12497i
$414$	−5.22359e33	+	3.01193e33i	−0.497696	+	0.286973i
$415$	1.57434e34			1.45370
$416$		−	2.41493e33i		−	0.216118i
$417$	−1.77569e34	+	4.75260e33i	−1.54027	+	0.412252i
$418$	−1.91790e34			−1.61263
$419$			1.64797e34i			1.34328i	0.740879	+	0.671639i	$0.234409\pi$
$419$			1.64797e34i			1.34328i	−0.740879	+	0.671639i	$0.765591\pi$
$420$	1.11276e33	+	4.15755e33i	0.0879350	+	0.328546i
$421$	−7.23393e33			−0.554252			−0.277126	−	0.960834i	$-0.589382\pi$
$421$	−7.23393e33			−0.554252			−0.277126	+	0.960834i	$0.589382\pi$
$422$			2.22529e29i			1.65320e-5i
$423$	2.56062e32	+	4.44088e32i	0.0184468	+	0.0319922i
$424$	−3.39437e33			−0.237139
$425$			8.80393e29i			5.96514e-5i
$426$	1.74042e34	−	4.65820e33i	1.14374	−	0.306121i
$427$	−5.68034e33			−0.362086
$428$		−	2.52375e33i		−	0.156055i
$429$	−7.20623e33	−	2.69242e34i	−0.432278	−	1.61510i
$430$	−8.59403e33			−0.500158
$431$			1.32435e34i			0.747821i	0.927465	+	0.373911i	$0.121983\pi$
$431$			1.32435e34i			0.747821i	−0.927465	+	0.373911i	$0.878017\pi$
$432$	3.22908e33	−	3.22365e33i	0.176925	−	0.176628i
$433$	2.51472e34			1.33705			0.668524	−	0.743691i	$-0.266926\pi$
$433$	2.51472e34			1.33705			0.668524	+	0.743691i	$0.266926\pi$
$434$			3.67381e33i			0.189562i
$435$	2.82333e34	−	7.55661e33i	1.41384	−	0.378413i
$436$	−5.92403e33			−0.287934
$437$		−	2.87184e34i		−	1.35488i
$438$	−6.12773e33	−	2.28947e34i	−0.280631	−	1.04851i
$439$	3.90176e33			0.173469			0.0867344	−	0.996231i	$-0.472357\pi$
$439$	3.90176e33			0.173469			0.0867344	+	0.996231i	$0.472357\pi$
$440$			1.13124e34i			0.488281i
$441$	−1.12926e34	+	6.51132e33i	−0.473250	+	0.272877i
$442$	−6.39817e31			−0.00260355
$443$			1.27696e34i			0.504579i	0.967652	+	0.252290i	$0.0811836\pi$
$443$			1.27696e34i			0.504579i	−0.967652	+	0.252290i	$0.918816\pi$
$444$	1.31977e33	−	3.53235e32i	0.0506431	−	0.0135545i
$445$	−2.61406e34			−0.974172
$446$		−	9.90668e33i		−	0.358571i
$447$	−7.32864e32	−	2.73816e33i	−0.0257647	−	0.0962633i
$448$	2.46556e33			0.0841979
$449$			8.73088e32i			0.0289638i	0.999895	+	0.0144819i	$0.00460990\pi$
$449$			8.73088e32i			0.0289638i	−0.999895	+	0.0144819i	$0.995390\pi$
$450$	2.17071e32	+	3.76465e32i	0.00699581	+	0.0121328i
$451$	6.95783e34			2.17861
$452$			1.82028e34i			0.553783i
$453$	−3.64484e32	+	9.75536e31i	−0.0107746	+	0.00288381i
$454$	3.99768e33			0.114837
$455$		−	2.97896e34i		−	0.831604i
$456$	5.61866e33	+	2.09927e34i	0.152437	+	0.569541i
$457$	−5.37341e34			−1.41690			−0.708450	−	0.705761i	$-0.750605\pi$
$457$	−5.37341e34			−1.41690			−0.708450	+	0.705761i	$0.750605\pi$
$458$		−	2.06732e34i		−	0.529855i
$459$	−8.54081e31	−	8.55519e31i	−0.00212782	−	0.00213140i
$460$	−1.69390e34			−0.410239
$461$		−	9.06898e33i		−	0.213524i	−0.994285	−	0.106762i	$-0.965952\pi$
$461$		−	9.06898e33i		−	0.213524i	0.994285	−	0.106762i	$-0.0340483\pi$
$462$	2.74887e34	−	7.35731e33i	0.629228	−	0.168412i
$463$	−4.75355e34			−1.05795			−0.528976	−	0.848637i	$-0.677424\pi$
$463$	−4.75355e34			−1.05795			−0.528976	+	0.848637i	$0.677424\pi$
$464$		−	1.67433e34i		−	0.362332i
$465$	4.93813e33	+	1.84501e34i	0.103914	+	0.388248i
$466$	2.74585e34			0.561902
$467$			4.90538e34i			0.976232i	0.872779	+	0.488116i	$0.162316\pi$
$467$			4.90538e34i			0.976232i	−0.872779	+	0.488116i	$0.837684\pi$
$468$	−2.73592e34	+	1.57754e34i	−0.529551	+	0.305340i
$469$	−2.69734e34			−0.507795
$470$			1.44009e33i			0.0263704i
$471$	−6.91074e34	+	1.84965e34i	−1.23099	+	0.329472i
$472$	3.40760e34			0.590477
$473$			5.68216e34i			0.957897i
$474$	1.70999e34	+	6.38894e34i	0.280463	+	1.04788i
$475$	−2.06974e33			−0.0330293
$476$		−	6.53231e31i		−	0.00101432i
$477$	2.21735e34	+	3.84555e34i	0.335039	+	0.581058i
$478$	4.45285e34			0.654749
$479$		−	1.03793e35i		−	1.48527i	−0.669698	−	0.742633i	$-0.733577\pi$
$479$		−	1.03793e35i		−	1.48527i	0.669698	−	0.742633i	$-0.266423\pi$
$480$	1.23822e34	−	3.31407e33i	0.172449	−	0.0461557i
$481$	−9.45640e33			−0.128186
$482$			5.93012e34i			0.782442i
$483$	1.10168e34	+	4.11613e34i	0.141495	+	0.528659i
$484$	3.48039e34			0.435150
$485$		−	7.61471e34i		−	0.926853i
$486$	−5.76151e34	−	1.55246e34i	−0.682755	−	0.183970i
$487$	7.44999e34			0.859565			0.429783	−	0.902932i	$-0.358590\pi$
$487$	7.44999e34			0.859565			0.429783	+	0.902932i	$0.358590\pi$
$488$			1.69174e34i			0.190054i
$489$	−3.73057e34	+	9.98481e33i	−0.408093	+	0.109226i
$490$	−3.66195e34			−0.390089
$491$		−	2.15002e34i		−	0.223040i	−0.993762	−	0.111520i	$-0.964428\pi$
$491$		−	2.15002e34i		−	0.223040i	0.993762	−	0.111520i	$-0.0355719\pi$
$492$	−2.03836e34	−	7.61580e34i	−0.205937	−	0.769430i
$493$	−4.43600e32			−0.00436497
$494$		−	1.50416e35i		−	1.44160i
$495$	1.28160e35	−	7.38975e34i	1.19643	−	0.689862i
$496$	1.09415e34			0.0994980
$497$		−	1.27318e35i		−	1.12787i
$498$	−1.13935e35	+	3.04946e34i	−0.983277	+	0.263173i
$499$	1.00391e35			0.844089			0.422045	−	0.906575i	$-0.361313\pi$
$499$	1.00391e35			0.844089			0.422045	+	0.906575i	$0.361313\pi$
$500$		−	6.04158e34i		−	0.494927i
$501$	2.71757e34	+	1.01535e35i	0.216915	+	0.810449i
$502$	−2.12429e34			−0.165221
$503$			1.24283e35i			0.941948i	0.882147	+	0.470974i	$0.156097\pi$
$503$			1.24283e35i			0.941948i	−0.882147	+	0.470974i	$0.843903\pi$
$504$	−1.61061e34	−	2.79328e34i	−0.118958	−	0.206309i
$505$	−1.73995e35			−1.25242
$506$			1.11997e35i			0.785686i
$507$	6.98806e34	−	1.87034e34i	0.477808	−	0.127885i
$508$	−5.50938e34			−0.367176
$509$		−	6.87195e34i		−	0.446425i	−0.974770	−	0.223213i	$-0.928346\pi$
$509$		−	6.87195e34i		−	0.446425i	0.974770	−	0.223213i	$-0.0716544\pi$
$510$	−8.78036e31	−	3.28056e32i	−0.000556032	−	0.00207747i
$511$	−1.67484e35			−1.03395
$512$		−	7.34302e33i		−	0.0441942i
$513$	2.01127e35	−	2.00788e35i	1.18017	−	1.17818i
$514$	3.91564e34			0.224018
$515$			1.42363e35i			0.794148i
$516$	6.21951e34	−	1.66464e34i	0.338306	−	0.0905471i
$517$	9.52151e33			0.0505043
$518$		−	9.65466e33i		−	0.0499402i
$519$	6.69528e34	+	2.50152e35i	0.337748	+	1.26191i
$520$	−8.87204e34			−0.436496
$521$			1.10872e35i			0.532024i	0.963970	+	0.266012i	$0.0857061\pi$
$521$			1.10872e35i			0.532024i	−0.963970	+	0.266012i	$0.914294\pi$
$522$	−1.89688e35	+	1.09374e35i	−0.887815	+	0.511916i
$523$	8.28471e34			0.378229			0.189115	−	0.981955i	$-0.439438\pi$
$523$	8.28471e34			0.378229			0.189115	+	0.981955i	$0.439438\pi$
$524$			1.19812e35i			0.533575i
$525$	2.96650e33	−	7.93979e32i	0.0128876	−	0.00344936i
$526$	2.00759e35			0.850865
$527$		−	2.89886e32i		−	0.00119864i
$528$	−2.19118e34	−	8.18678e34i	−0.0883969	−	0.330272i
$529$	8.63499e34			0.339890
$530$			1.24703e35i			0.478952i
$531$	−2.22599e35	−	3.86054e35i	−0.834248	−	1.44683i
$532$	1.53570e35			0.561636
$533$			5.45686e35i			1.94755i
$534$	1.89180e35	−	5.06337e34i	0.658929	−	0.176361i
$535$	−9.27182e34			−0.315185
$536$			8.03330e34i			0.266533i
$537$	−6.97146e34	−	2.60471e35i	−0.225766	−	0.843516i
$538$	−1.83247e35			−0.579252
$539$			2.42119e35i			0.747094i
$540$	−1.18431e35	−	1.18631e35i	−0.356737	−	0.357338i
$541$	−3.35003e35			−0.985108			−0.492554	−	0.870282i	$-0.663937\pi$
$541$	−3.35003e35			−0.985108			−0.492554	+	0.870282i	$0.663937\pi$
$542$		−	4.27721e35i		−	1.22792i
$543$	−2.89039e35	+	7.73609e34i	−0.810138	+	0.216832i
$544$	−1.94547e32			−0.000532402
$545$			2.17639e35i			0.581543i
$546$	5.77017e34	+	2.15587e35i	0.150551	+	0.562495i
$547$	1.04505e35			0.266257			0.133129	−	0.991099i	$-0.457498\pi$
$547$	1.04505e35			0.266257			0.133129	+	0.991099i	$0.457498\pi$
$548$			9.05914e34i			0.225393i
$549$	1.91660e35	−	1.10512e35i	0.465685	−	0.268515i
$550$	8.07163e33			0.0191534
$551$		−	1.04287e36i		−	2.41691i
$552$	1.22588e35	−	3.28105e34i	0.277485	−	0.0742685i
$553$	4.67377e35			1.03333
$554$			2.93121e35i			0.633023i
$555$	−1.29772e34	−	4.84861e34i	−0.0273762	−	0.102284i
$556$	3.86869e35			0.797244
$557$		−	4.53529e35i		−	0.913035i	−0.889714	−	0.456518i	$-0.849097\pi$
$557$		−	4.53529e35i		−	0.913035i	0.889714	−	0.456518i	$-0.150903\pi$
$558$	−7.14746e34	−	1.23958e35i	−0.140575	−	0.243798i
$559$	−4.45639e35			−0.856307
$560$		−	9.05805e34i		−	0.170055i
$561$	−2.16902e33	+	5.80536e32i	−0.00397875	+	0.00106491i
$562$	5.56489e35			0.997435
$563$		−	2.28384e35i		−	0.399997i	−0.979796	−	0.199998i	$-0.935906\pi$
$563$		−	2.28384e35i		−	0.399997i	0.979796	−	0.199998i	$-0.0640937\pi$
$564$	−2.78941e33	−	1.04219e34i	−0.00477402	−	0.0178369i
$565$	6.68742e35			1.11848
$566$		−	1.41505e35i		−	0.231291i
$567$	−2.11244e35	+	3.64939e35i	−0.337446	+	0.582962i
$568$	−3.79184e35			−0.592000
$569$		−	8.90482e33i		−	0.0135883i	−0.999977	−	0.00679416i	$-0.997837\pi$
$569$		−	8.90482e33i		−	0.0135883i	0.999977	−	0.00679416i	$-0.00216266\pi$
$570$	7.71235e35	−	2.06420e35i	1.15031	−	0.307878i
$571$	−8.88319e35			−1.29509			−0.647545	−	0.762028i	$-0.724204\pi$
$571$	−8.88319e35			−1.29509			−0.647545	+	0.762028i	$0.724204\pi$
$572$			5.86597e35i			0.835972i
$573$	9.90384e34	+	3.70031e35i	0.137973	+	0.515500i
$574$	−5.57127e35			−0.758751
$575$			1.20864e34i			0.0160921i
$576$	−8.31905e34	+	4.79678e34i	−0.108288	+	0.0624393i
$577$	3.80265e35			0.483950			0.241975	−	0.970282i	$-0.422205\pi$
$577$	3.80265e35			0.483950			0.241975	+	0.970282i	$0.422205\pi$
$578$		−	5.68255e35i		−	0.707100i
$579$	−1.32323e36	+	3.54161e35i	−1.60996	+	0.430903i
$580$	−6.15119e35			−0.731805
$581$			8.33481e35i			0.969630i
$582$	1.47495e35	+	5.51077e35i	0.167795	+	0.626922i
$583$	8.24508e35			0.917284
$584$			4.98806e35i			0.542706i
$585$	5.79561e35	+	1.00513e36i	0.616698	+	1.06954i
$586$	−1.17996e36			−1.22800
$587$			2.03170e35i			0.206806i	0.994640	+	0.103403i	$0.0329732\pi$
$587$			2.03170e35i			0.206806i	−0.994640	+	0.103403i	$0.967027\pi$
$588$	2.65015e35	−	7.09310e34i	0.263855	−	0.0706205i
$589$	6.81501e35			0.663694
$590$		−	1.25189e36i		−	1.19259i
$591$	−7.52382e34	−	2.81108e35i	−0.0701134	−	0.261961i
$592$	−2.87538e34			−0.0262128
$593$		−	8.83883e35i		−	0.788286i	−0.919049	−	0.394143i	$-0.871042\pi$
$593$		−	8.83883e35i		−	0.788286i	0.919049	−	0.394143i	$-0.128958\pi$
$594$	−7.84358e35	+	7.83039e35i	−0.684370	+	0.683219i
$595$	−2.39986e33			−0.00204864
$596$			5.96562e34i			0.0498258i
$597$	9.52384e35	−	2.54904e35i	0.778297	−	0.208310i
$598$	−8.78365e35			−0.702359
$599$			1.00161e36i			0.783700i	0.920029	+	0.391850i	$0.128165\pi$
$599$			1.00161e36i			0.783700i	−0.920029	+	0.391850i	$0.871835\pi$
$600$	−2.36466e33	−	8.83493e33i	−0.00181051	−	0.00676452i
$601$	−6.62507e35			−0.496389			−0.248195	−	0.968710i	$-0.579837\pi$
$601$	−6.62507e35			−0.496389			−0.248195	+	0.968710i	$0.579837\pi$
$602$		−	4.54982e35i		−	0.333611i
$603$	9.10108e35	−	5.24771e35i	0.653082	−	0.376569i
$604$	7.94101e33			0.00557693
$605$		−	1.27864e36i		−	0.878876i
$606$	1.25921e36	−	3.37024e35i	0.847134	−	0.226734i
$607$	1.65391e36			1.08908			0.544539	−	0.838736i	$-0.316705\pi$
$607$	1.65391e36			1.08908			0.544539	+	0.838736i	$0.316705\pi$
$608$		−	4.57367e35i		−	0.294794i
$609$	4.00059e35	+	1.49472e36i	0.252406	+	0.943049i
$610$	6.21516e35			0.383853
$611$			7.46750e34i			0.0451481i
$612$	1.27087e33	+	2.20407e33i	0.000752199	+	0.00130454i
$613$	−1.51404e35			−0.0877305			−0.0438653	−	0.999037i	$-0.513967\pi$
$613$	−1.51404e35			−0.0877305			−0.0438653	+	0.999037i	$0.513967\pi$
$614$			1.05589e36i			0.599003i
$615$	−2.79792e36	+	7.48858e35i	−1.55403	+	0.415933i
$616$	−5.98896e35			−0.325688
$617$		−	1.42196e36i		−	0.757145i	−0.925572	−	0.378573i	$-0.876415\pi$
$617$		−	1.42196e36i		−	0.757145i	0.925572	−	0.378573i	$-0.123585\pi$
$618$	−2.75752e35	−	1.03028e36i	−0.143770	−	0.537161i
$619$	1.10493e36			0.564102			0.282051	−	0.959399i	$-0.408985\pi$
$619$	1.10493e36			0.564102			0.282051	+	0.959399i	$0.408985\pi$
$620$		−	4.01971e35i		−	0.200957i
$621$	−1.17251e36	−	1.17449e36i	−0.574021	−	0.574987i
$622$	1.09098e36			0.523048
$623$		−	1.38393e36i		−	0.649783i
$624$	6.42070e35	−	1.71849e35i	0.295245	−	0.0790219i
$625$	−2.26355e36			−1.01941
$626$			1.27907e36i			0.564195i
$627$	−1.36480e36	−	5.09922e36i	−0.589645	−	2.20306i
$628$	1.50564e36			0.637157
$629$			7.61810e32i			0.000315783i
$630$	−1.02620e36	+	5.91712e35i	−0.416684	+	0.240261i
$631$	2.72500e36			1.08389			0.541945	−	0.840414i	$-0.317688\pi$
$631$	2.72500e36			1.08389			0.541945	+	0.840414i	$0.317688\pi$
$632$		−	1.39196e36i		−	0.542381i
$633$	−5.91649e31	+	1.58354e31i	−2.25848e−5	+	6.04478e-6i
$634$	8.86143e35			0.331393
$635$			2.02405e36i			0.741589i
$636$	−2.41547e35	−	9.02479e35i	−0.0867081	−	0.323962i
$637$	−1.89888e36			−0.667860
$638$			4.06701e36i			1.40154i
$639$	2.47700e36	+	4.29585e36i	0.836401	+	1.45057i
$640$	−2.69770e35			−0.0892594
$641$			4.23037e36i			1.37159i	0.727795	+	0.685794i	$0.240545\pi$
$641$			4.23037e36i			1.37159i	−0.727795	+	0.685794i	$0.759455\pi$
$642$	6.71002e35	−	1.79593e35i	0.213191	−	0.0570602i
$643$	−4.42616e35			−0.137811			−0.0689055	−	0.997623i	$-0.521951\pi$
$643$	−4.42616e35			−0.137811			−0.0689055	+	0.997623i	$0.521951\pi$
$644$		−	8.96780e35i		−	0.273634i
$645$	−6.11561e35	−	2.28494e36i	−0.182879	−	0.683280i
$646$	−1.21176e34			−0.00355135
$647$			3.01210e36i			0.865196i	0.901587	+	0.432598i	$0.142403\pi$
$647$			3.01210e36i			0.865196i	−0.901587	+	0.432598i	$0.857597\pi$
$648$	1.08687e36	+	6.29134e35i	0.305988	+	0.177120i
$649$	−8.27721e36			−2.28404
$650$			6.33039e34i			0.0171221i
$651$	−9.76776e35	+	2.61433e35i	−0.258966	+	0.0693118i
$652$	8.12778e35			0.211229
$653$			5.44100e36i			1.38614i	0.720870	+	0.693070i	$0.243742\pi$
$653$			5.44100e36i			1.38614i	−0.720870	+	0.693070i	$0.756258\pi$
$654$	−4.21560e35	−	1.57505e36i	−0.105281	−	0.393355i
$655$	4.40170e36			1.07767
$656$			1.65925e36i			0.398257i
$657$	5.65107e36	−	3.25842e36i	1.32978	−	0.766757i
$658$	−7.62406e34			−0.0175893
$659$		−	7.89289e35i		−	0.178536i	−0.996008	−	0.0892679i	$-0.971547\pi$
$659$		−	7.89289e35i		−	0.178536i	0.996008	−	0.0892679i	$-0.0284527\pi$
$660$	−3.00768e36	+	8.05002e35i	−0.667054	+	0.178536i
$661$	1.16185e36			0.252658			0.126329	−	0.991988i	$-0.459681\pi$
$661$	1.16185e36			0.252658			0.126329	+	0.991988i	$0.459681\pi$
$662$		−	4.14962e35i		−	0.0884818i
$663$	−4.55301e33	−	1.70111e34i	−0.000951968	−	0.00355678i
$664$	2.48230e36			0.508943
$665$		−	5.64190e36i		−	1.13434i
$666$	1.87833e35	+	3.25758e35i	0.0370345	+	0.0642288i
$667$	−6.08990e36			−1.17754
$668$		−	2.21214e36i		−	0.419488i
$669$	2.63394e36	−	7.04970e35i	0.489854	−	0.131109i
$670$	2.95130e36			0.538320
$671$		−	4.10931e36i		−	0.735151i
$672$	1.75452e35	+	6.55531e35i	0.0307863	+	0.115025i
$673$	−5.33483e36			−0.918174			−0.459087	−	0.888391i	$-0.651823\pi$
$673$	−5.33483e36			−0.918174			−0.459087	+	0.888391i	$0.651823\pi$
$674$		−	9.74825e35i		−	0.164569i
$675$	−8.46457e34	+	8.45033e34i	−0.0140170	+	0.0139934i
$676$	−1.52249e36			−0.247313
$677$		−	9.77752e36i		−	1.55803i	−0.627005	−	0.779015i	$-0.715720\pi$
$677$		−	9.77752e36i		−	1.55803i	0.627005	−	0.779015i	$-0.284280\pi$
$678$	−4.83969e36	+	1.29533e36i	−0.756539	+	0.202486i
$679$	4.03135e36			0.618221
$680$			7.14734e33i			0.00107530i
$681$	2.84479e35	+	1.06288e36i	0.0419892	+	0.156882i
$682$	−2.65773e36			−0.384871
$683$			8.66850e36i			1.23162i	0.787897	+	0.615808i	$0.211170\pi$
$683$			8.66850e36i			1.23162i	−0.787897	+	0.615808i	$0.788830\pi$
$684$	−5.18160e36	+	2.98773e36i	−0.722329	+	0.416497i
$685$	3.32817e36			0.455228
$686$		−	5.48756e36i		−	0.736489i
$687$	5.49650e36	−	1.47113e36i	0.723850	−	0.193737i
$688$	−1.35504e36			−0.175107
$689$			6.46643e36i			0.820001i
$690$	−1.20540e36	−	4.50367e36i	−0.150001	−	0.560439i
$691$	1.30702e37			1.59613			0.798064	−	0.602573i	$-0.205858\pi$
$691$	1.30702e37			1.59613			0.798064	+	0.602573i	$0.205858\pi$
$692$		−	5.45005e36i		−	0.653163i
$693$	3.91225e36	+	6.78501e36i	0.460145	+	0.798028i
$694$	8.37937e35			0.0967249
$695$		−	1.42129e37i		−	1.61020i
$696$	4.45162e36	−	1.19147e36i	0.494991	−	0.132484i
$697$	4.39606e34			0.00479775
$698$			3.16684e36i			0.339239i
$699$	1.95398e36	+	7.30054e36i	0.205455	+	0.767630i
$700$	−6.46311e34			−0.00667063
$701$			5.40690e36i			0.547790i	0.961760	+	0.273895i	$0.0883121\pi$
$701$			5.40690e36i			0.547790i	−0.961760	+	0.273895i	$0.911688\pi$
$702$	−6.14120e36	−	6.15154e36i	−0.610760	−	0.611789i
$703$	−1.79096e36			−0.174851
$704$			1.78365e36i			0.170949i
$705$	−3.82884e35	+	1.02478e35i	−0.0360254	+	0.00964214i
$706$	−7.63993e34			−0.00705713
$707$		−	9.21159e36i		−	0.835377i
$708$	2.42489e36	+	9.05996e36i	0.215903	+	0.806666i
$709$	−2.22348e37			−1.94371			−0.971856	−	0.235576i	$-0.924302\pi$
$709$	−2.22348e37			−1.94371			−0.971856	+	0.235576i	$0.924302\pi$
$710$			1.39306e37i			1.19567i
$711$	−1.57698e37	+	9.09289e36i	−1.32899	+	0.766297i
$712$	−4.12166e36			−0.341061
$713$		−	3.97966e36i		−	0.323357i
$714$	1.73678e34	−	4.64846e33i	0.00138569	−	0.000370879i
$715$	2.15506e37			1.68842
$716$			5.67487e36i			0.436603i
$717$	3.16869e36	+	1.18390e37i	0.239404	+	0.894471i
$718$	5.83143e36			0.432670
$719$			9.65459e36i			0.703490i	0.936096	+	0.351745i	$0.114412\pi$
$719$			9.65459e36i			0.703490i	−0.936096	+	0.351745i	$0.885588\pi$
$720$	1.76226e36	+	3.05628e36i	0.126109	+	0.218711i
$721$	−7.53690e36			−0.529705
$722$		−	1.82436e37i		−	1.25929i
$723$	−1.57667e37	+	4.21994e36i	−1.06892	+	0.286094i
$724$	6.29729e36			0.419327
$725$			4.38900e35i			0.0287059i
$726$	2.47669e36	+	9.25350e36i	0.159109	+	0.594470i
$727$	−7.33417e36			−0.462811			−0.231406	−	0.972857i	$-0.574332\pi$
$727$	−7.33417e36			−0.462811			−0.231406	+	0.972857i	$0.574332\pi$
$728$		−	4.69700e36i		−	0.291147i
$729$	2.76386e34	−	1.64232e37i	0.00168290	−	0.999999i
$730$	1.83253e37			1.09611
$731$			3.59008e34i			0.00210949i
$732$	−4.49792e36	+	1.20386e36i	−0.259637	+	0.0694916i
$733$	−3.17191e37			−1.79874			−0.899372	−	0.437184i	$-0.855976\pi$
$733$	−3.17191e37			−1.79874			−0.899372	+	0.437184i	$0.855976\pi$
$734$			8.92292e36i			0.497116i
$735$	−2.60588e36	−	9.73622e36i	−0.142633	−	0.532911i
$736$	−2.67082e36			−0.143626
$737$		−	1.95132e37i		−	1.03098i
$738$	1.87980e37	−	1.08390e37i	0.975841	−	0.562673i
$739$	2.99143e37			1.52581			0.762906	−	0.646509i	$-0.223772\pi$
$739$	2.99143e37			1.52581			0.762906	+	0.646509i	$0.223772\pi$
$740$			1.05637e36i			0.0529422i
$741$	3.99920e37	−	1.07038e37i	1.96941	−	0.527110i
$742$	−6.60200e36			−0.319466
$743$			2.54738e37i			1.21126i	0.795745	+	0.605632i	$0.207080\pi$
$743$			2.54738e37i			1.21126i	−0.795745	+	0.605632i	$0.792920\pi$
$744$	7.78608e35	+	2.90907e36i	0.0363807	+	0.135927i
$745$	2.19167e36			0.100634
$746$		−	1.67635e37i		−	0.756417i
$747$	−1.62155e37	−	2.81225e37i	−0.719055	−	1.24706i
$748$	4.72565e34			0.00205940
$749$		−	4.90865e36i		−	0.210232i
$750$	1.60631e37	−	4.29926e36i	0.676133	−	0.180966i
$751$	−6.06599e36			−0.250947			−0.125474	−	0.992097i	$-0.540045\pi$
$751$	−6.06599e36			−0.250947			−0.125474	+	0.992097i	$0.540045\pi$
$752$			2.27062e35i			0.00923237i
$753$	−1.51167e36	−	5.64796e36i	−0.0604118	−	0.225713i
$754$	−3.18966e37			−1.25290
$755$		−	2.91739e35i		−	0.0112638i
$756$	6.28051e36	−	6.26995e36i	0.238348	−	0.237947i
$757$	4.44956e37			1.65986			0.829928	−	0.557870i	$-0.188381\pi$
$757$	4.44956e37			1.65986			0.829928	+	0.557870i	$0.188381\pi$
$758$			2.89169e37i			1.06036i
$759$	−2.97772e37	+	7.96981e36i	−1.07335	+	0.287280i
$760$	−1.68029e37			−0.595398
$761$			3.56186e37i			1.24073i	0.784314	+	0.620364i	$0.213015\pi$
$761$			3.56186e37i			1.24073i	−0.784314	+	0.620364i	$0.786985\pi$
$762$	−3.92053e36	−	1.46481e37i	−0.134255	−	0.501609i
$763$	−1.15221e37			−0.387895
$764$		−	8.06187e36i		−	0.266822i
$765$	8.09736e34	−	4.66896e34i	0.00263478	−	0.00151922i
$766$	−2.70627e37			−0.865759
$767$		−	6.49163e37i		−	2.04180i
$768$	1.95233e36	−	5.22537e35i	0.0603749	−	0.0161593i
$769$	−3.93126e37			−1.19533			−0.597667	−	0.801744i	$-0.703906\pi$
$769$	−3.93126e37			−1.19533			−0.597667	+	0.801744i	$0.703906\pi$
$770$			2.20024e37i			0.657795i
$771$	2.78642e36	+	1.04107e37i	0.0819104	+	0.306037i
$772$	2.88292e37			0.833312
$773$			5.09642e37i			1.44855i	0.689514	+	0.724273i	$0.257824\pi$
$773$			5.09642e37i			1.44855i	−0.689514	+	0.724273i	$0.742176\pi$
$774$	8.85174e36	+	1.53515e37i	0.247398	+	0.429061i
$775$	−2.86815e35			−0.00788279
$776$		−	1.20063e37i		−	0.324494i
$777$	2.56693e36	−	6.87036e35i	0.0682246	−	0.0182602i
$778$	1.15411e37			0.301656
$779$			1.03348e38i			2.65654i
$780$	−6.31344e36	−	2.35886e37i	−0.159601	−	0.596309i
$781$	9.21055e37			2.28993
$782$			7.07613e34i			0.00173025i
$783$	−4.25783e37	−	4.26500e37i	−1.02397	−	1.02569i
$784$	−5.77389e36			−0.136571
$785$		−	5.53148e37i		−	1.28687i
$786$	−3.18551e37	+	8.52599e36i	−0.728931	+	0.195097i
$787$	2.84046e37			0.639319			0.319660	−	0.947532i	$-0.396431\pi$
$787$	2.84046e37			0.639319			0.319660	+	0.947532i	$0.396431\pi$
$788$			6.12450e36i			0.135591i
$789$	1.42862e37	+	5.33768e37i	0.311112	+	1.16239i
$790$	−5.11382e37			−1.09545
$791$			3.54043e37i			0.746038i
$792$	2.02073e37	−	1.16516e37i	0.418872	−	0.241523i
$793$	3.22284e37			0.657184
$794$			7.68221e36i			0.154106i
$795$	−3.31555e37	+	8.87404e36i	−0.654310	+	0.175125i
$796$	−2.07496e37			−0.402846
$797$		−	2.82373e37i		−	0.539343i	−0.962952	−	0.269671i	$-0.913085\pi$
$797$		−	2.82373e37i		−	0.539343i	0.962952	−	0.269671i	$-0.0869151\pi$
$798$	1.09282e37	+	4.08304e37i	0.205358	+	0.767267i
$799$	6.01584e33			0.000111221
$800$			1.92487e35i			0.00350131i
$801$	2.69245e37	+	4.66950e37i	0.481864	+	0.835696i
$802$	1.99527e37			0.351346
$803$		−	1.21162e38i		−	2.09926i
$804$	−2.13585e37	+	5.71658e36i	−0.364119	+	0.0974559i
$805$	−3.29462e37			−0.552661
$806$		−	2.08440e37i		−	0.344053i
$807$	−1.30401e37	−	4.87209e37i	−0.211799	−	0.791333i
$808$	−2.74343e37			−0.438476
$809$			1.01040e38i			1.58914i	0.607170	+	0.794572i	$0.292305\pi$
$809$			1.01040e38i			1.58914i	−0.607170	+	0.794572i	$0.707695\pi$
$810$	2.31133e37	−	3.99299e37i	0.357731	−	0.618006i
$811$	−3.30637e37			−0.503594			−0.251797	−	0.967780i	$-0.581022\pi$
$811$	−3.30637e37			−0.503594			−0.251797	+	0.967780i	$0.581022\pi$
$812$		−	3.25654e37i		−	0.488121i
$813$	1.13720e38	−	3.04371e37i	1.67749	−	0.448979i
$814$	6.98444e36			0.101394
$815$		−	2.98601e37i		−	0.426621i
$816$	−1.38442e34	−	5.17253e34i	−0.000194669	−	0.000727330i
$817$	−8.44002e37			−1.16804
$818$		−	4.81211e37i		−	0.655454i
$819$	−5.32132e37	+	3.06829e37i	−0.713393	+	0.411344i
$820$	6.09582e37			0.804363
$821$		−	1.25524e38i		−	1.63029i	−0.579255	−	0.815146i	$-0.696656\pi$
$821$		−	1.25524e38i		−	1.63029i	0.579255	−	0.815146i	$-0.303344\pi$
$822$	−2.40860e37	+	6.44658e36i	−0.307915	+	0.0824131i
$823$	5.67168e37			0.713697			0.356849	−	0.934162i	$-0.383851\pi$
$823$	5.67168e37			0.713697			0.356849	+	0.934162i	$0.383851\pi$
$824$			2.24467e37i			0.278034i
$825$	5.74386e35	+	2.14605e36i	0.00700330	+	0.0261660i
$826$	6.62773e37			0.795470
$827$		−	9.79011e37i		−	1.15669i	−0.815793	−	0.578343i	$-0.803699\pi$
$827$		−	9.79011e37i		−	1.15669i	0.815793	−	0.578343i	$-0.196301\pi$
$828$	1.74470e37	+	3.02582e37i	0.202921	+	0.351924i
$829$	1.00335e37			0.114880			0.0574400	−	0.998349i	$-0.481706\pi$
$829$	1.00335e37			0.114880			0.0574400	+	0.998349i	$0.481706\pi$
$830$		−	9.11955e37i		−	1.02792i
$831$	−7.79336e37	+	2.08588e37i	−0.864791	+	0.231460i
$832$	−1.39888e37			−0.152819
$833$			1.52975e35i			0.00164526i
$834$	2.75300e37	+	1.02859e38i	0.291506	+	1.08914i
$835$	−8.12704e37			−0.847243
$836$			1.11097e38i			1.14030i
$837$	2.78712e37	−	2.78243e37i	0.281659	−	0.281186i
$838$	9.54603e37			0.949841
$839$			1.06504e38i			1.04342i	0.853123	+	0.521710i	$0.174706\pi$
$839$			1.06504e38i			1.04342i	−0.853123	+	0.521710i	$0.825294\pi$
$840$	2.40831e37	−	6.44581e36i	0.232317	−	0.0621794i
$841$	−1.15866e38			−1.10055
$842$			4.19034e37i			0.391915i
$843$	3.96004e37	+	1.47957e38i	0.364705	+	1.36262i
$844$	1.28902e33			1.16899e−5
$845$			5.59336e37i			0.499500i
$846$	2.57243e36	−	1.48327e36i	0.0226219	−	0.0130439i
$847$	6.76931e37			0.586219
$848$			1.96623e37i			0.167683i
$849$	3.76227e37	−	1.00697e37i	0.315973	−	0.0845698i
$850$	5.09978e33			4.21799e−5
$851$			1.04584e37i			0.0851886i
$852$	−2.69832e37	−	1.00816e38i	−0.216460	−	0.808748i
$853$	−2.09525e38			−1.65538			−0.827690	−	0.561186i	$-0.810345\pi$
$853$	−2.09525e38			−1.65538			−0.827690	+	0.561186i	$0.810345\pi$
$854$			3.29041e37i			0.256034i
$855$	1.09764e38	+	1.90363e38i	0.841202	+	1.45889i
$856$	−1.46191e37			−0.110347
$857$		−	2.08673e38i		−	1.55137i	−0.631121	−	0.775684i	$-0.717405\pi$
$857$		−	2.08673e38i		−	1.55137i	0.631121	−	0.775684i	$-0.282595\pi$
$858$	−1.55962e38	+	4.17429e37i	−1.14204	+	0.305667i
$859$	8.21778e37			0.592711			0.296356	−	0.955078i	$-0.404229\pi$
$859$	8.21778e37			0.592711			0.296356	+	0.955078i	$0.404229\pi$
$860$			4.97820e37i			0.353665i
$861$	−3.96458e37	−	1.48126e38i	−0.277432	−	1.03655i
$862$	7.67145e37			0.528789
$863$			5.83092e37i			0.395910i	0.980211	+	0.197955i	$0.0634300\pi$
$863$			5.83092e37i			0.395910i	−0.980211	+	0.197955i	$0.936570\pi$
$864$	−1.86734e37	−	1.87048e37i	−0.124895	−	0.125105i
$865$	−2.00226e38			−1.31920
$866$		−	1.45668e38i		−	0.945436i
$867$	1.51085e38	−	4.04376e37i	0.965990	−	0.258546i
$868$	2.12810e37			0.134040
$869$			3.38113e38i			2.09800i
$870$	−4.37725e37	−	1.63545e38i	−0.267579	−	0.999739i
$871$	1.53038e38			0.921643
$872$			3.43156e37i			0.203600i
$873$	−1.36022e38	+	7.84305e37i	−0.795103	+	0.458458i
$874$	−1.66355e38			−0.958047
$875$		−	1.17508e38i		−	0.666749i
$876$	−1.32620e38	+	3.54956e37i	−0.741406	+	0.198436i
$877$	2.86982e38			1.58074			0.790369	−	0.612632i	$-0.209889\pi$
$877$	2.86982e38			1.58074			0.790369	+	0.612632i	$0.209889\pi$
$878$		−	2.26014e37i		−	0.122661i
$879$	−8.39674e37	−	3.13723e38i	−0.449009	−	1.67761i
$880$	6.55283e37			0.345266
$881$			6.75270e37i			0.350583i	0.984517	+	0.175291i	$0.0560868\pi$
$881$			6.75270e37i			0.350583i	−0.984517	+	0.175291i	$0.943913\pi$
$882$	3.77176e37	+	6.54135e37i	0.192953	+	0.334638i
$883$	7.62414e37			0.384328			0.192164	−	0.981363i	$-0.438450\pi$
$883$	7.62414e37			0.384328			0.192164	+	0.981363i	$0.438450\pi$
$884$			3.70621e35i			0.00184099i
$885$	3.32848e38	−	8.90862e37i	1.62923	−	0.436062i
$886$	7.39696e37			0.356792
$887$			1.38408e38i			0.657889i	0.944349	+	0.328944i	$0.106693\pi$
$887$			1.38408e38i			0.657889i	−0.944349	+	0.328944i	$0.893307\pi$
$888$	−2.04615e36	−	7.64493e36i	−0.00958451	−	0.0358100i
$889$	−1.07156e38			−0.494647
$890$			1.51423e38i			0.688844i
$891$	−2.64007e38	−	1.52819e38i	−1.18360	−	0.685123i
$892$	−5.73856e37			−0.253548
$893$			1.41428e37i			0.0615838i
$894$	−1.58611e37	+	4.24520e36i	−0.0680684	+	0.0182184i
$895$	2.08485e38			0.881812
$896$		−	1.42821e37i		−	0.0595369i
$897$	−6.25054e37	−	2.33535e38i	−0.256812	−	0.959513i
$898$	5.05747e36			0.0204805
$899$		−	1.44516e38i		−	0.576820i
$900$	2.18072e36	−	1.25741e36i	0.00857920	−	0.00494679i
$901$	5.20937e35			0.00202005
$902$		−	4.03040e38i		−	1.54051i
$903$	1.20968e38	−	3.23770e37i	0.455755	−	0.121982i
$904$	1.05442e38			0.391584
$905$		−	2.31352e38i		−	0.846918i
$906$	5.65091e35	+	2.11132e36i	0.00203916	+	0.00761880i
$907$	2.62402e38			0.933411			0.466706	−	0.884413i	$-0.345441\pi$
$907$	2.62402e38			0.933411			0.466706	+	0.884413i	$0.345441\pi$
$908$		−	2.31570e37i		−	0.0812020i
$909$	1.79213e38	+	3.10808e38i	0.619496	+	1.07439i
$910$	−1.72560e38			−0.588033
$911$			1.63746e38i			0.550089i	0.961432	+	0.275044i	$0.0886925\pi$
$911$			1.63746e38i			0.550089i	−0.961432	+	0.275044i	$0.911307\pi$
$912$	1.21603e38	−	3.25468e37i	0.402726	−	0.107789i
$913$	−6.02962e38			−1.96866
$914$			3.11261e38i			1.00190i
$915$	4.42278e37	+	1.65246e38i	0.140353	+	0.524392i
$916$	−1.19752e38			−0.374664
$917$			2.33033e38i			0.718814i
$918$	−4.95570e35	+	4.94736e35i	−0.00150713	+	0.00150459i
$919$	−2.98598e38			−0.895334			−0.447667	−	0.894200i	$-0.647745\pi$
$919$	−2.98598e38			−0.895334			−0.447667	+	0.894200i	$0.647745\pi$
$920$			9.81214e37i			0.290083i
$921$	−2.80734e38	+	7.51381e37i	−0.818315	+	0.219021i
$922$	−5.25331e37			−0.150984
$923$			7.22362e38i			2.04707i
$924$	−4.26181e37	−	1.59232e38i	−0.119085	−	0.444932i
$925$	7.53740e35			0.00207673
$926$			2.75355e38i			0.748084i
$927$	2.54302e38	−	1.46631e38i	0.681262	−	0.392817i
$928$	−9.69873e37			−0.256207
$929$		−	4.73188e38i		−	1.23262i	−0.787503	−	0.616310i	$-0.788627\pi$
$929$		−	4.73188e38i		−	1.23262i	0.787503	−	0.616310i	$-0.211373\pi$
$930$	1.06874e38	−	2.86047e37i	0.274533	−	0.0734784i
$931$	−3.59633e38			−0.910989
$932$		−	1.59057e38i		−	0.397325i
$933$	7.76352e37	+	2.90064e38i	0.191248	+	0.714550i
$934$	2.84150e38			0.690301
$935$		−	1.73612e36i		−	0.00415939i
$936$	9.13808e37	+	1.58481e38i	0.215908	+	0.374449i
$937$	−3.11039e37			−0.0724770			−0.0362385	−	0.999343i	$-0.511538\pi$
$937$	−3.11039e37			−0.0724770			−0.0362385	+	0.999343i	$0.511538\pi$
$938$			1.56246e38i			0.359065i
$939$	−3.40074e38	+	9.10203e37i	−0.770763	+	0.206294i
$940$	8.34188e36			0.0186467
$941$		−	1.36991e37i		−	0.0302013i	−0.999886	−	0.0151007i	$-0.995193\pi$
$941$		−	1.36991e37i		−	0.0302013i	0.999886	−	0.0151007i	$-0.00480687\pi$
$942$	1.07143e38	+	4.00313e38i	0.232972	+	0.870438i
$943$	6.03508e38			1.29429
$944$		−	1.97389e38i		−	0.417530i
$945$	−2.30347e38	−	2.30735e38i	−0.480584	−	0.481394i
$946$	3.29146e38			0.677336
$947$		−	9.70144e38i		−	1.96919i	−0.174864	−	0.984593i	$-0.555948\pi$
$947$		−	9.70144e38i		−	1.96919i	0.174864	−	0.984593i	$-0.444052\pi$
$948$	3.70087e38	−	9.90533e37i	0.740962	−	0.198317i
$949$	9.50248e38			1.87662
$950$			1.19892e37i			0.0233552i
$951$	6.30589e37	+	2.35603e38i	0.121171	+	0.452725i
$952$	−3.78392e35			−0.000717235
$953$		−	1.80732e38i		−	0.337931i	−0.985622	−	0.168966i	$-0.945957\pi$
$953$		−	1.80732e38i		−	0.337931i	0.985622	−	0.168966i	$-0.0540427\pi$
$954$	2.22758e38	−	1.28443e38i	0.410870	−	0.236909i
$955$	−2.96179e38			−0.538903
$956$		−	2.57936e38i		−	0.462978i
$957$	−1.08132e39	+	2.89413e38i	−1.91469	+	0.512464i
$958$	−6.01230e38			−1.05024
$959$			1.76199e38i			0.303641i
$960$	−1.91971e37	−	7.17251e37i	−0.0326370	−	0.121940i
$961$	−5.01777e38			−0.841602
$962$			5.47773e37i			0.0906410i
$963$	9.54984e37	+	1.65623e38i	0.155903	+	0.270382i
$964$	3.43509e38			0.553270
$965$		−	1.05914e39i		−	1.68305i
$966$	2.38432e38	−	6.38159e37i	0.373819	−	0.100052i
$967$	−5.18014e38			−0.801304			−0.400652	−	0.916230i	$-0.631216\pi$
$967$	−5.18014e38			−0.801304			−0.400652	+	0.916230i	$0.631216\pi$
$968$		−	2.01606e38i		−	0.307697i
$969$	−8.62301e35	−	3.22177e36i	−0.00129852	−	0.00485160i
$970$	−4.41091e38			−0.655384
$971$		−	4.02923e38i		−	0.590706i	−0.955388	−	0.295353i	$-0.904563\pi$
$971$		−	4.02923e38i		−	0.590706i	0.955388	−	0.295353i	$-0.0954373\pi$
$972$	−8.99279e37	+	3.33743e38i	−0.130087	+	0.482781i
$973$	7.52453e38			1.07402
$974$		−	4.31549e38i		−	0.607805i
$975$	−1.68309e37	+	4.50478e36i	−0.0233910	+	0.00626056i
$976$	9.79960e37			0.134388
$977$			7.78610e38i			1.05364i	0.849978	+	0.526818i	$0.176615\pi$
$977$			7.78610e38i			1.05364i	−0.849978	+	0.526818i	$0.823385\pi$
$978$	5.78382e37	+	2.16097e38i	0.0772342	+	0.288566i
$979$	1.00117e39			1.31927
$980$			2.12123e38i			0.275834i
$981$	3.88769e38	−	2.24165e38i	0.498878	−	0.287654i
$982$	−1.24542e38			−0.157713
$983$		−	5.24245e38i		−	0.655147i	−0.944826	−	0.327574i	$-0.893769\pi$
$983$		−	5.24245e38i		−	0.655147i	0.944826	−	0.327574i	$-0.106231\pi$
$984$	−4.41154e38	+	1.18074e38i	−0.544070	+	0.145619i
$985$	2.25004e38			0.273854
$986$			2.56960e36i			0.00308650i
$987$	−5.42537e36	−	2.02705e37i	−0.00643141	−	0.0240293i
$988$	−8.71305e38			−1.01937
$989$			4.92860e38i			0.569078i
$990$	−4.28060e38	−	7.42383e38i	−0.487806	−	0.846001i
$991$	−2.10773e37			−0.0237059			−0.0118530	−	0.999930i	$-0.503773\pi$
$991$	−2.10773e37			−0.0237059			−0.0118530	+	0.999930i	$0.503773\pi$
$992$		−	6.33798e37i		−	0.0703557i
$993$	1.10328e38	−	2.95291e37i	0.120877	−	0.0323527i
$994$	−7.37507e38			−0.797523
$995$			7.62304e38i			0.813632i
$996$	1.76643e38	+	6.59982e38i	0.186091	+	0.695282i
$997$	1.52641e39			1.58721			0.793604	−	0.608434i	$-0.208202\pi$
$997$	1.52641e39			1.58721			0.793604	+	0.608434i	$0.208202\pi$
$998$		−	5.81528e38i		−	0.596861i
$999$	−7.32445e37	+	7.31213e37i	−0.0742034	+	0.0740786i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.27.b.a.5.4	✓	8
3.2	odd	2	inner	6.27.b.a.5.8	yes	8
4.3	odd	2		48.27.e.b.17.2		8
12.11	even	2		48.27.e.b.17.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.27.b.a.5.4	✓	8	1.1	even	1	trivial
6.27.b.a.5.8	yes	8	3.2	odd	2	inner
48.27.e.b.17.1		8	12.11	even	2
48.27.e.b.17.2		8	4.3	odd	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)

\(f(q)\)	\(=\)	\(q-5792.62i q^{2} +(1.54011e6 - 412209. i) q^{3} -3.35544e7 q^{4} +1.23273e9i q^{5} +(-2.38777e9 - 8.92129e9i) q^{6} -6.52628e10 q^{7} +1.94368e11i q^{8} +(2.20203e12 - 1.26970e12i) q^{9} +O(q^{10})\)	\(q-5792.62i q^{2} +(1.54011e6 - 412209. i) q^{3} -3.35544e7 q^{4} +1.23273e9i q^{5} +(-2.38777e9 - 8.92129e9i) q^{6} -6.52628e10 q^{7} +1.94368e11i q^{8} +(2.20203e12 - 1.26970e12i) q^{9} +7.14075e12 q^{10} -4.72129e13i q^{11} +(-5.16776e13 + 1.38314e13i) q^{12} +3.70280e14 q^{13} +3.78043e14i q^{14} +(5.08144e14 + 1.89855e15i) q^{15} +1.12590e15 q^{16} -2.98298e13i q^{17} +(-7.35488e15 - 1.27555e16i) q^{18} +7.01278e16 q^{19} -4.13636e16i q^{20} +(-1.00512e17 + 2.69019e16i) q^{21} -2.73486e17 q^{22} -4.09515e17i q^{23} +(8.01203e16 + 2.99349e17i) q^{24} -2.95138e16 q^{25} -2.14489e18i q^{26} +(2.86800e18 - 2.86318e18i) q^{27} +2.18986e18 q^{28} -1.48710e19i q^{29} +(1.09976e19 - 2.94348e18i) q^{30} +9.71798e18 q^{31} -6.52191e18i q^{32} +(-1.94616e19 - 7.27132e19i) q^{33} -1.72793e17 q^{34} -8.04516e19i q^{35} +(-7.38880e19 + 4.26040e19i) q^{36} -2.55385e19 q^{37} -4.06224e20i q^{38} +(5.70273e20 - 1.52633e20i) q^{39} -2.39604e20 q^{40} +1.47371e21i q^{41} +(1.55833e20 + 5.82229e20i) q^{42} -1.20352e21 q^{43} +1.58420e21i q^{44} +(1.56520e21 + 2.71452e21i) q^{45} -2.37217e21 q^{46} +2.01672e20i q^{47} +(1.73401e21 - 4.64106e20i) q^{48} -5.12824e21 q^{49} +1.70962e20i q^{50} +(-1.22961e19 - 4.59413e19i) q^{51} -1.24245e22 q^{52} +1.74636e22i q^{53} +(-1.65853e22 - 1.66132e22i) q^{54} +5.82009e22 q^{55} -1.26850e22i q^{56} +(1.08005e23 - 2.89073e22i) q^{57} -8.61421e22 q^{58} -1.75317e23i q^{59} +(-1.70505e22 - 6.37047e22i) q^{60} +8.70380e22 q^{61} -5.62926e22i q^{62} +(-1.43711e23 + 8.28641e22i) q^{63} -3.77789e22 q^{64} +4.56456e23i q^{65} +(-4.21200e23 + 1.12734e23i) q^{66} +4.13304e23 q^{67} +1.00092e21i q^{68} +(-1.68806e23 - 6.30700e23i) q^{69} -4.66026e23 q^{70} +1.95086e24i q^{71} +(2.46789e23 + 4.28005e23i) q^{72} +2.56630e24 q^{73} +1.47935e23i q^{74} +(-4.54547e22 + 1.21659e22i) q^{75} -2.35310e24 q^{76} +3.08125e24i q^{77} +(-8.84143e23 - 3.30337e24i) q^{78} -7.16146e24 q^{79} +1.38793e24i q^{80} +(3.23682e24 - 5.59183e24i) q^{81} +8.53666e24 q^{82} -1.27711e25i q^{83} +(3.37263e24 - 9.02679e23i) q^{84} +3.67722e22 q^{85} +6.97153e24i q^{86} +(-6.12996e24 - 2.29030e25i) q^{87} +9.17667e24 q^{88} +2.12054e25i q^{89} +(1.57242e25 - 9.06660e24i) q^{90} -2.41655e25 q^{91} +1.37411e25i q^{92} +(1.49668e25 - 4.00584e24i) q^{93} +1.16821e24 q^{94} +8.64489e25i q^{95} +(-2.68839e24 - 1.00445e25i) q^{96} -6.17710e25 q^{97} +2.97060e25i q^{98} +(-5.99461e25 - 1.03964e26i) 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

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