LMFDB - Embedded newform 6.17.b.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,17,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, 17, names="a")

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

chi := DirichletCharacter("6.5");

S:= CuspForms(chi, 17);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 17 $
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:	$9.73947263140$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 55116x^{4} + 758395257x^{2} + 123254139008 $ x^6 + 55116x^4 + 758395257x^2 + 123254139008
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{27}\cdot 3^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			5.5
Root			$172.725i$ of defining polynomial
Character	$\chi$	$=$	6.5
Dual form			6.17.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)

$f(q)$	$=$	$q+181.019i q^{2} +(1479.09 + 6392.11i) q^{3} -32768.0 q^{4} +441421. i q^{5} +(-1.15709e6 + 267744. i) q^{6} +2.81464e6 q^{7} -5.93164e6i q^{8} +(-3.86713e7 + 1.89090e7i) q^{9} +O(q^{10})$	\(q+181.019i q^{2} +(1479.09 + 6392.11i) q^{3} -32768.0 q^{4} +441421. i q^{5} +(-1.15709e6 + 267744. i) q^{6} +2.81464e6 q^{7} -5.93164e6i q^{8} +(-3.86713e7 + 1.89090e7i) q^{9} -7.99057e7 q^{10} -1.92938e8i q^{11} +(-4.84669e7 - 2.09456e8i) q^{12} -1.24215e9 q^{13} +5.09504e8i q^{14} +(-2.82161e9 + 6.52903e8i) q^{15} +1.07374e9 q^{16} +1.41634e9i q^{17} +(-3.42290e9 - 7.00025e9i) q^{18} +2.68017e10 q^{19} -1.44645e10i q^{20} +(4.16311e9 + 1.79915e10i) q^{21} +3.49256e10 q^{22} +1.20426e11i q^{23} +(3.79157e10 - 8.77345e9i) q^{24} -4.22647e10 q^{25} -2.24852e11i q^{26} +(-1.78067e11 - 2.19223e11i) q^{27} -9.22301e10 q^{28} +6.43715e11i q^{29} +(-1.18188e11 - 5.10766e11i) q^{30} -1.14352e12 q^{31} +1.94368e11i q^{32} +(1.23328e12 - 2.85374e11i) q^{33} -2.56386e11 q^{34} +1.24244e12i q^{35} +(1.26718e12 - 6.19611e11i) q^{36} +4.25212e12 q^{37} +4.85163e12i q^{38} +(-1.83725e12 - 7.93992e12i) q^{39} +2.61835e12 q^{40} +3.12148e12i q^{41} +(-3.25681e12 + 7.53604e11i) q^{42} +4.47086e12 q^{43} +6.32221e12i q^{44} +(-8.34684e12 - 1.70703e13i) q^{45} -2.17994e13 q^{46} +1.17679e13i q^{47} +(1.58816e12 + 6.86347e12i) q^{48} -2.53107e13 q^{49} -7.65072e12i q^{50} +(-9.05342e12 + 2.09490e12i) q^{51} +4.07026e13 q^{52} -4.41654e13i q^{53} +(3.96836e13 - 3.22336e13i) q^{54} +8.51671e13 q^{55} -1.66954e13i q^{56} +(3.96422e13 + 1.71319e14i) q^{57} -1.16525e14 q^{58} +1.42767e14i q^{59} +(9.24585e13 - 2.13943e13i) q^{60} +2.29855e13 q^{61} -2.06999e14i q^{62} +(-1.08846e14 + 5.32221e13i) q^{63} -3.51844e13 q^{64} -5.48309e14i q^{65} +(5.16582e13 + 2.23248e14i) q^{66} -1.94559e14 q^{67} -4.64107e13i q^{68} +(-7.69774e14 + 1.78121e14i) q^{69} -2.24906e14 q^{70} +3.85172e13i q^{71} +(1.12162e14 + 2.29384e14i) q^{72} +1.42218e15 q^{73} +7.69717e14i q^{74} +(-6.25133e13 - 2.70160e14i) q^{75} -8.78239e14 q^{76} -5.43052e14i q^{77} +(1.43728e15 - 3.32577e14i) q^{78} +1.03560e15 q^{79} +4.73972e14i q^{80} +(1.13792e15 - 1.46247e15i) q^{81} -5.65048e14 q^{82} +1.75783e15i q^{83} +(-1.36417e14 - 5.89545e14i) q^{84} -6.25204e14 q^{85} +8.09313e14i q^{86} +(-4.11469e15 + 9.52114e14i) q^{87} -1.14444e15 q^{88} +1.35243e15i q^{89} +(3.09006e15 - 1.51094e15i) q^{90} -3.49619e15 q^{91} -3.94611e15i q^{92} +(-1.69137e15 - 7.30951e15i) q^{93} -2.13022e15 q^{94} +1.18308e16i q^{95} +(-1.24242e15 + 2.87488e14i) q^{96} +5.20071e15 q^{97} -4.58173e15i q^{98} +(3.64828e15 + 7.46118e15i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6006 q^{3} - 196608 q^{4} + 159744 q^{6} - 167892 q^{7} - 10215738 q^{9}+O(q^{10}) $ 6 * q + 6006 * q^3 - 196608 * q^4 + 159744 * q^6 - 167892 * q^7 - 10215738 * q^9	$ 6 q + 6006 q^{3} - 196608 q^{4} + 159744 q^{6} - 167892 q^{7} - 10215738 q^{9} + 39297024 q^{10} - 196804608 q^{12} + 1763152140 q^{13} - 8080218432 q^{15} + 6442450944 q^{16} - 12549169152 q^{18} + 60306979692 q^{19} - 155770661748 q^{21} + 94233305088 q^{22} - 5234491392 q^{24} - 75722441466 q^{25} + 330190979958 q^{27} + 5501485056 q^{28} + 987679531008 q^{30} - 2846203650132 q^{31} + 3282289396416 q^{33} - 1812957659136 q^{34} + 334749302784 q^{36} + 2483836081932 q^{37} - 8759076866580 q^{39} - 1287684882432 q^{40} - 3652917731328 q^{42} + 46155081190764 q^{43} - 46496752783488 q^{45} - 17111605395456 q^{46} + 6448893394944 q^{48} + 42155513811090 q^{49} - 3055668993792 q^{51} - 57774969323520 q^{52} + 240022278328320 q^{54} - 155561818958208 q^{55} + 27052692784332 q^{57} - 366644114104320 q^{58} + 264772597579776 q^{60} + 306036501898764 q^{61} - 801652315914324 q^{63} - 211106232532992 q^{64} + 11\!\cdots\!72 q^{66}+ \cdots - 28\!\cdots\!72 q^{99}+O(q^{100}) $ 6 * q + 6006 * q^3 - 196608 * q^4 + 159744 * q^6 - 167892 * q^7 - 10215738 * q^9 + 39297024 * q^10 - 196804608 * q^12 + 1763152140 * q^13 - 8080218432 * q^15 + 6442450944 * q^16 - 12549169152 * q^18 + 60306979692 * q^19 - 155770661748 * q^21 + 94233305088 * q^22 - 5234491392 * q^24 - 75722441466 * q^25 + 330190979958 * q^27 + 5501485056 * q^28 + 987679531008 * q^30 - 2846203650132 * q^31 + 3282289396416 * q^33 - 1812957659136 * q^34 + 334749302784 * q^36 + 2483836081932 * q^37 - 8759076866580 * q^39 - 1287684882432 * q^40 - 3652917731328 * q^42 + 46155081190764 * q^43 - 46496752783488 * q^45 - 17111605395456 * q^46 + 6448893394944 * q^48 + 42155513811090 * q^49 - 3055668993792 * q^51 - 57774969323520 * q^52 + 240022278328320 * q^54 - 155561818958208 * q^55 + 27052692784332 * q^57 - 366644114104320 * q^58 + 264772597579776 * q^60 + 306036501898764 * q^61 - 801652315914324 * q^63 - 211106232532992 * q^64 + 1157574327017472 * q^66 + 1979846570008812 * q^67 - 2345782552693632 * q^69 - 2197723307360256 * q^70 + 411211174772736 * q^72 + 3864207384753420 * q^73 - 3376263465802122 * q^75 - 1976139110547456 * q^76 + 5837442492456960 * q^78 + 1835806484101548 * q^79 - 703356001465338 * q^81 - 9913023387353088 * q^82 + 5104293044158464 * q^84 + 2872972366990848 * q^85 - 3000080900606400 * q^87 - 3087836941123584 * q^88 + 12789804912058368 * q^90 - 1824281133603240 * q^91 - 11156835457641972 * q^93 - 4579876939530240 * q^94 + 171523813933056 * q^96 + 31097493125645196 * q^97 - 28794216850745472 * 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 $

$2$			181.019i			0.707107i
$2$			181.019i			0.707107i
$3$	1479.09	+	6392.11i	0.225437	+	0.974258i
$3$	1479.09	+	6392.11i	0.225437	+	0.974258i
$4$	−32768.0			−0.500000
$5$			441421.i			1.13004i	0.825078	+	0.565019i	$0.191131\pi$
$5$			441421.i			1.13004i	−0.825078	+	0.565019i	$0.808869\pi$
$6$	−1.15709e6	+	267744.i	−0.688904	+	0.159408i
$7$	2.81464e6			0.488246			0.244123	−	0.969744i	$-0.421500\pi$
$7$	2.81464e6			0.488246			0.244123	+	0.969744i	$0.421500\pi$
$8$		−	5.93164e6i		−	0.353553i
$9$	−3.86713e7	+	1.89090e7i	−0.898356	+	0.439268i
$10$	−7.99057e7			−0.799057
$11$		−	1.92938e8i		−	0.900072i	−0.893010	−	0.450036i	$-0.851411\pi$
$11$		−	1.92938e8i		−	0.900072i	0.893010	−	0.450036i	$-0.148589\pi$
$12$	−4.84669e7	−	2.09456e8i	−0.112719	−	0.487129i
$13$	−1.24215e9			−1.52274			−0.761370	−	0.648318i	$-0.775473\pi$
$13$	−1.24215e9			−1.52274			−0.761370	+	0.648318i	$0.775473\pi$
$14$			5.09504e8i			0.345242i
$15$	−2.82161e9	+	6.52903e8i	−1.10095	+	0.254752i
$16$	1.07374e9			0.250000
$17$			1.41634e9i			0.203038i	0.994834	+	0.101519i	$0.0323703\pi$
$17$			1.41634e9i			0.203038i	−0.994834	+	0.101519i	$0.967630\pi$
$18$	−3.42290e9	−	7.00025e9i	−0.310609	−	0.635234i
$19$	2.68017e10			1.57810			0.789049	−	0.614330i	$-0.210574\pi$
$19$	2.68017e10			1.57810			0.789049	+	0.614330i	$0.210574\pi$
$20$		−	1.44645e10i		−	0.565019i
$21$	4.16311e9	+	1.79915e10i	0.110069	+	0.475677i
$22$	3.49256e10			0.636447
$23$			1.20426e11i			1.53779i	0.639376	+	0.768895i	$0.279193\pi$
$23$			1.20426e11i			1.53779i	−0.639376	+	0.768895i	$0.720807\pi$
$24$	3.79157e10	−	8.77345e9i	0.344452	−	0.0797040i
$25$	−4.22647e10			−0.276986
$26$		−	2.24852e11i		−	1.07674i
$27$	−1.78067e11	−	2.19223e11i	−0.630483	−	0.776203i
$28$	−9.22301e10			−0.244123
$29$			6.43715e11i			1.28680i	0.765532	+	0.643398i	$0.222476\pi$
$29$			6.43715e11i			1.28680i	−0.765532	+	0.643398i	$0.777524\pi$
$30$	−1.18188e11	−	5.10766e11i	−0.180137	−	0.778488i
$31$	−1.14352e12			−1.34076			−0.670379	−	0.742019i	$-0.733869\pi$
$31$	−1.14352e12			−1.34076			−0.670379	+	0.742019i	$0.733869\pi$
$32$			1.94368e11i			0.176777i
$33$	1.23328e12	−	2.85374e11i	0.876902	−	0.202910i
$34$	−2.56386e11			−0.143570
$35$			1.24244e12i			0.551736i
$36$	1.26718e12	−	6.19611e11i	0.449178	−	0.219634i
$37$	4.25212e12			1.21058			0.605288	−	0.796007i	$-0.293058\pi$
$37$	4.25212e12			1.21058			0.605288	+	0.796007i	$0.293058\pi$
$38$			4.85163e12i			1.11588i
$39$	−1.83725e12	−	7.93992e12i	−0.343282	−	1.48354i
$40$	2.61835e12			0.399529
$41$			3.12148e12i			0.390921i	0.980712	+	0.195461i	$0.0626202\pi$
$41$			3.12148e12i			0.390921i	−0.980712	+	0.195461i	$0.937380\pi$
$42$	−3.25681e12	+	7.53604e11i	−0.336355	+	0.0778303i
$43$	4.47086e12			0.382511			0.191255	−	0.981540i	$-0.438744\pi$
$43$	4.47086e12			0.382511			0.191255	+	0.981540i	$0.438744\pi$
$44$			6.32221e12i			0.450036i
$45$	−8.34684e12	−	1.70703e13i	−0.496389	−	1.01518i
$46$	−2.17994e13			−1.08738
$47$			1.17679e13i			0.494217i	0.968988	+	0.247108i	$0.0794804\pi$
$47$			1.17679e13i			0.494217i	−0.968988	+	0.247108i	$0.920520\pi$
$48$	1.58816e12	+	6.86347e12i	0.0563593	+	0.243564i
$49$	−2.53107e13			−0.761616
$50$		−	7.65072e12i		−	0.195858i
$51$	−9.05342e12	+	2.09490e12i	−0.197811	+	0.0457723i
$52$	4.07026e13			0.761370
$53$		−	4.41654e13i		−	0.709374i	−0.934985	−	0.354687i	$-0.884587\pi$
$53$		−	4.41654e13i		−	0.709374i	0.934985	−	0.354687i	$-0.115413\pi$
$54$	3.96836e13	−	3.22336e13i	0.548859	−	0.445819i
$55$	8.51671e13			1.01712
$56$		−	1.66954e13i		−	0.172621i
$57$	3.96422e13	+	1.71319e14i	0.355762	+	1.53747i
$58$	−1.16525e14			−0.909902
$59$			1.42767e14i			0.972325i	0.873868	+	0.486163i	$0.161604\pi$
$59$			1.42767e14i			0.972325i	−0.873868	+	0.486163i	$0.838396\pi$
$60$	9.24585e13	−	2.13943e13i	0.550474	−	0.127376i
$61$	2.29855e13			0.119899			0.0599496	−	0.998201i	$-0.480906\pi$
$61$	2.29855e13			0.119899			0.0599496	+	0.998201i	$0.480906\pi$
$62$		−	2.06999e14i		−	0.948059i
$63$	−1.08846e14	+	5.32221e13i	−0.438619	+	0.214471i
$64$	−3.51844e13			−0.125000
$65$		−	5.48309e14i		−	1.72075i
$66$	5.16582e13	+	2.23248e14i	0.143479	+	0.620063i
$67$	−1.94559e14			−0.479129			−0.239565	−	0.970880i	$-0.577005\pi$
$67$	−1.94559e14			−0.479129			−0.239565	+	0.970880i	$0.577005\pi$
$68$		−	4.64107e13i		−	0.101519i
$69$	−7.69774e14	+	1.78121e14i	−1.49820	+	0.346675i
$70$	−2.24906e14			−0.390137
$71$			3.85172e13i			0.0596469i	0.999555	+	0.0298234i	$0.00949450\pi$
$71$			3.85172e13i			0.0596469i	−0.999555	+	0.0298234i	$0.990505\pi$
$72$	1.12162e14	+	2.29384e14i	0.155305	+	0.317617i
$73$	1.42218e15			1.76349			0.881743	−	0.471731i	$-0.156371\pi$
$73$	1.42218e15			1.76349			0.881743	+	0.471731i	$0.156371\pi$
$74$			7.69717e14i			0.856007i
$75$	−6.25133e13	−	2.70160e14i	−0.0624428	−	0.269855i
$76$	−8.78239e14			−0.789049
$77$		−	5.43052e14i		−	0.439456i
$78$	1.43728e15	−	3.32577e14i	1.04902	−	0.242737i
$79$	1.03560e15			0.682613			0.341307	−	0.939952i	$-0.389131\pi$
$79$	1.03560e15			0.682613			0.341307	+	0.939952i	$0.389131\pi$
$80$			4.73972e14i			0.282509i
$81$	1.13792e15	−	1.46247e15i	0.614088	−	0.789238i
$82$	−5.65048e14			−0.276423
$83$			1.75783e15i			0.780463i	0.920717	+	0.390232i	$0.127605\pi$
$83$			1.75783e15i			0.780463i	−0.920717	+	0.390232i	$0.872395\pi$
$84$	−1.36417e14	−	5.89545e14i	−0.0550344	−	0.237839i
$85$	−6.25204e14			−0.229441
$86$			8.09313e14i			0.270476i
$87$	−4.11469e15	+	9.52114e14i	−1.25367	+	0.290091i
$88$	−1.14444e15			−0.318223
$89$			1.35243e15i			0.343555i	0.985136	+	0.171777i	$0.0549510\pi$
$89$			1.35243e15i			0.343555i	−0.985136	+	0.171777i	$0.945049\pi$
$90$	3.09006e15	−	1.51094e15i	0.717838	−	0.351000i
$91$	−3.49619e15			−0.743472
$92$		−	3.94611e15i		−	0.768895i
$93$	−1.69137e15	−	7.30951e15i	−0.302257	−	1.30624i
$94$	−2.13022e15			−0.349464
$95$			1.18308e16i			1.78331i
$96$	−1.24242e15	+	2.87488e14i	−0.172226	+	0.0398520i
$97$	5.20071e15			0.663573			0.331786	−	0.943355i	$-0.392349\pi$
$97$	5.20071e15			0.663573			0.331786	+	0.943355i	$0.392349\pi$
$98$		−	4.58173e15i		−	0.538544i
$99$	3.64828e15	+	7.46118e15i	0.395372	+	0.808585i
$100$	1.38493e15			0.138493
$101$		−	1.01413e16i		−	0.936530i	−0.883588	−	0.468265i	$-0.844879\pi$
$101$		−	1.01413e16i		−	0.936530i	0.883588	−	0.468265i	$-0.155121\pi$
$102$	−3.79218e14	−	1.63884e15i	−0.0323659	−	0.139874i
$103$	1.78661e16			1.41037			0.705185	−	0.709024i	$-0.250864\pi$
$103$	1.78661e16			1.41037			0.705185	+	0.709024i	$0.250864\pi$
$104$			7.36796e15i			0.538370i
$105$	−7.94182e15	+	1.83769e15i	−0.537533	+	0.124382i
$106$	7.99479e15			0.501603
$107$		−	7.25364e15i		−	0.422169i	−0.977468	−	0.211084i	$-0.932301\pi$
$107$		−	7.25364e15i		−	0.422169i	0.977468	−	0.211084i	$-0.0676994\pi$
$108$	5.83490e15	+	7.18349e15i	0.315241	+	0.388102i
$109$	−1.26213e16			−0.633420			−0.316710	−	0.948522i	$-0.602578\pi$
$109$	−1.26213e16			−0.633420			−0.316710	+	0.948522i	$0.602578\pi$
$110$			1.54169e16i			0.719209i
$111$	6.28928e15	+	2.71800e16i	0.272909	+	1.17941i
$112$	3.02220e15			0.122061
$113$		−	5.30603e16i		−	1.99591i	−0.0638829	−	0.997957i	$-0.520348\pi$
$113$		−	5.30603e16i		−	1.99591i	0.0638829	−	0.997957i	$-0.479652\pi$
$114$	−3.10121e16	+	7.17601e15i	−1.08716	+	0.251562i
$115$	−5.31585e16			−1.73776
$116$		−	2.10933e16i		−	0.643398i
$117$	4.80354e16	−	2.34878e16i	1.36796	−	0.668890i
$118$	−2.58436e16			−0.687538
$119$			3.98650e15i			0.0991325i
$120$	3.87278e15	+	1.67368e16i	0.0900686	+	0.389244i
$121$	8.72451e15			0.189871
$122$			4.16083e15i			0.0847815i
$123$	−1.99528e16	+	4.61696e15i	−0.380858	+	0.0881282i
$124$	3.74709e16			0.670379
$125$			4.86990e16i			0.817034i
$126$	−9.63423e15	−	1.97032e16i	−0.151654	−	0.310150i
$127$	−1.76909e16			−0.261408			−0.130704	−	0.991421i	$-0.541724\pi$
$127$	−1.76909e16			−0.261408			−0.130704	+	0.991421i	$0.541724\pi$
$128$		−	6.36905e15i		−	0.0883883i
$129$	6.61282e15	+	2.85782e16i	0.0862321	+	0.372664i
$130$	9.92546e16			1.21676
$131$			6.29766e16i			0.726121i	0.931766	+	0.363060i	$0.118268\pi$
$131$			6.29766e16i			0.726121i	−0.931766	+	0.363060i	$0.881732\pi$
$132$	−4.04122e16	+	9.35113e15i	−0.438451	+	0.101455i
$133$	7.54373e16			0.770500
$134$		−	3.52189e16i		−	0.338795i
$135$	9.67695e16	−	7.86025e16i	0.877139	−	0.712469i
$136$	8.40124e15			0.0717848
$137$		−	1.05927e16i		−	0.0853579i	−0.999089	−	0.0426790i	$-0.986411\pi$
$137$		−	1.05927e16i		−	0.0853579i	0.999089	−	0.0426790i	$-0.0135893\pi$
$138$	−3.22433e16	−	1.39344e17i	−0.245136	−	1.05939i
$139$	−6.67031e16			−0.478660			−0.239330	−	0.970938i	$-0.576928\pi$
$139$	−6.67031e16			−0.478660			−0.239330	+	0.970938i	$0.576928\pi$
$140$		−	4.07123e16i		−	0.275868i
$141$	−7.52219e16	+	1.74059e16i	−0.481495	+	0.111415i
$142$	−6.97235e15			−0.0421767
$143$			2.39658e17i			1.37058i
$144$	−4.15230e16	+	2.03034e16i	−0.224589	+	0.109817i
$145$	−2.84149e17			−1.45413
$146$			2.57442e17i			1.24697i
$147$	−3.74369e16	−	1.61789e17i	−0.171696	−	0.742010i
$148$	−1.39334e17			−0.605288
$149$		−	6.45793e16i		−	0.265830i	−0.991127	−	0.132915i	$-0.957566\pi$
$149$		−	6.45793e16i		−	0.265830i	0.991127	−	0.132915i	$-0.0424337\pi$
$150$	4.89042e16	−	1.13161e16i	0.190817	−	0.0441538i
$151$	2.58366e17			0.955918			0.477959	−	0.878382i	$-0.341377\pi$
$151$	2.58366e17			0.955918			0.477959	+	0.878382i	$0.341377\pi$
$152$		−	1.58978e17i		−	0.557942i
$153$	−2.67817e16	−	5.47718e16i	−0.0891880	−	0.182400i
$154$	9.83030e16			0.310743
$155$		−	5.04774e17i		−	1.51511i
$156$	6.02029e16	+	2.60175e17i	0.171641	+	0.741770i
$157$	2.22147e16			0.0601788			0.0300894	−	0.999547i	$-0.490421\pi$
$157$	2.22147e16			0.0601788			0.0300894	+	0.999547i	$0.490421\pi$
$158$			1.87463e17i			0.482680i
$159$	2.82310e17	−	6.53247e16i	0.691113	−	0.159919i
$160$	−8.57981e16			−0.199764
$161$			3.38955e17i			0.750819i
$162$	2.64736e17	+	2.05985e17i	0.558075	+	0.434226i
$163$	1.19046e17			0.238898			0.119449	−	0.992840i	$-0.461887\pi$
$163$	1.19046e17			0.238898			0.119449	+	0.992840i	$0.461887\pi$
$164$		−	1.02285e17i		−	0.195461i
$165$	1.25970e17	+	5.44397e17i	0.229295	+	0.990932i
$166$	−3.18201e17			−0.551871
$167$		−	7.29738e17i		−	1.20624i	−0.797649	−	0.603122i	$-0.793923\pi$
$167$		−	7.29738e17i		−	1.20624i	0.797649	−	0.603122i	$-0.206077\pi$
$168$	1.06719e17	−	2.46941e16i	0.168177	−	0.0389152i
$169$	8.77509e17			1.31874
$170$		−	1.13174e17i		−	0.162239i
$171$	−1.03646e18	+	5.06795e17i	−1.41769	+	0.693207i
$172$	−1.46501e17			−0.191255
$173$			4.08345e17i			0.508930i	0.967082	+	0.254465i	$0.0818994\pi$
$173$			4.08345e17i			0.508930i	−0.967082	+	0.254465i	$0.918101\pi$
$174$	−1.72351e17	−	7.44839e17i	−0.205126	−	0.886479i
$175$	−1.18960e17			−0.135237
$176$		−	2.07166e17i		−	0.225018i
$177$	−9.12581e17	+	2.11165e17i	−0.947295	+	0.219198i
$178$	−2.44817e17			−0.242930
$179$		−	1.33787e18i		−	1.26937i	−0.772771	−	0.634685i	$-0.781130\pi$
$179$		−	1.33787e18i		−	1.26937i	0.772771	−	0.634685i	$-0.218870\pi$
$180$	2.73509e17	+	5.59360e17i	0.248195	+	0.507588i
$181$	−1.05868e18			−0.919041			−0.459520	−	0.888167i	$-0.651979\pi$
$181$	−1.05868e18			−0.919041			−0.459520	+	0.888167i	$0.651979\pi$
$182$		−	6.32879e17i		−	0.525714i
$183$	3.39978e16	+	1.46926e17i	0.0270297	+	0.116813i
$184$	7.14323e17			0.543691
$185$			1.87698e18i			1.36800i
$186$	1.32316e18	−	3.06171e17i	0.923654	−	0.213728i
$187$	2.73267e17			0.182749
$188$		−	3.85612e17i		−	0.247108i
$189$	−5.01194e17	−	6.17033e17i	−0.307831	−	0.378978i
$190$	−2.14161e18			−1.26099
$191$			1.01818e18i			0.574855i	0.957802	+	0.287427i	$0.0928000\pi$
$191$			1.01818e18i			0.574855i	−0.957802	+	0.287427i	$0.907200\pi$
$192$	−5.20409e16	−	2.24902e17i	−0.0281796	−	0.121782i
$193$	2.82918e18			1.46961			0.734805	−	0.678278i	$-0.237274\pi$
$193$	2.82918e18			1.46961			0.734805	+	0.678278i	$0.237274\pi$
$194$			9.41429e17i			0.469217i
$195$	3.50485e18	−	8.11000e17i	1.67646	−	0.387922i
$196$	8.29382e17			0.380808
$197$			3.70725e17i			0.163426i	0.996656	+	0.0817132i	$0.0260391\pi$
$197$			3.70725e17i			0.163426i	−0.996656	+	0.0817132i	$0.973961\pi$
$198$	−1.35062e18	+	6.60409e17i	−0.571756	+	0.279570i
$199$	−1.24614e18			−0.506690			−0.253345	−	0.967376i	$-0.581531\pi$
$199$	−1.24614e18			−0.506690			−0.253345	+	0.967376i	$0.581531\pi$
$200$			2.50699e17i			0.0979292i
$201$	−2.87770e17	−	1.24364e18i	−0.108013	−	0.466795i
$202$	1.83577e18			0.662226
$203$			1.81183e18i			0.628273i
$204$	2.96662e17	−	6.86458e16i	0.0989057	−	0.0228861i
$205$	−1.37789e18			−0.441756
$206$			3.23412e18i			0.997282i
$207$	−2.27713e18	−	4.65702e18i	−0.675501	−	1.38148i
$208$	−1.33374e18			−0.380685
$209$		−	5.17108e18i		−	1.42040i
$210$	−3.32657e17	−	1.43762e18i	−0.0879512	−	0.380094i
$211$	−1.50137e18			−0.382145			−0.191073	−	0.981576i	$-0.561197\pi$
$211$	−1.50137e18			−0.382145			−0.191073	+	0.981576i	$0.561197\pi$
$212$			1.44721e18i			0.354687i
$213$	−2.46206e17	+	5.69705e16i	−0.0581114	+	0.0134466i
$214$	1.31305e18			0.298518
$215$			1.97353e18i			0.432252i
$216$	−1.30035e18	+	1.05623e18i	−0.274429	+	0.222909i
$217$	−3.21860e18			−0.654620
$218$		−	2.28470e18i		−	0.447895i
$219$	2.10354e18	+	9.09073e18i	0.397555	+	1.71809i
$220$	−2.79075e18			−0.508558
$221$		−	1.75930e18i		−	0.309174i
$222$	−4.92011e18	+	1.13848e18i	−0.833971	+	0.192976i
$223$	1.86081e17			0.0304273			0.0152137	−	0.999884i	$-0.495157\pi$
$223$	1.86081e17			0.0304273			0.0152137	+	0.999884i	$0.495157\pi$
$224$			5.47076e17i			0.0863105i
$225$	1.63443e18	−	7.99184e17i	0.248832	−	0.121671i
$226$	9.60494e18			1.41132
$227$			2.27536e18i			0.322733i	0.986895	+	0.161367i	$0.0515902\pi$
$227$			2.27536e18i			0.322733i	−0.986895	+	0.161367i	$0.948410\pi$
$228$	−1.29900e18	−	5.61380e18i	−0.177881	−	0.768737i
$229$	8.00708e18			1.05874			0.529371	−	0.848390i	$-0.322428\pi$
$229$	8.00708e18			1.05874			0.529371	+	0.848390i	$0.322428\pi$
$230$		−	9.62271e18i		−	1.22878i
$231$	3.47125e18	−	8.03224e17i	0.428144	−	0.0990698i
$232$	3.81829e18			0.454951
$233$		−	4.98299e18i		−	0.573645i	−0.957984	−	0.286822i	$-0.907401\pi$
$233$		−	4.98299e18i		−	0.573645i	0.957984	−	0.286822i	$-0.0925989\pi$
$234$	4.25174e18	+	8.69533e18i	0.472977	+	0.967296i
$235$	−5.19462e18			−0.558484
$236$		−	4.67819e18i		−	0.486163i
$237$	1.53175e18	+	6.61965e18i	0.153886	+	0.665041i
$238$	−7.21633e17			−0.0700972
$239$			1.29189e19i			1.21350i	0.794892	+	0.606751i	$0.207528\pi$
$239$			1.29189e19i			1.21350i	−0.794892	+	0.606751i	$0.792472\pi$
$240$	−3.02968e18	+	7.01049e17i	−0.275237	+	0.0636881i
$241$	−3.12668e18			−0.274756			−0.137378	−	0.990519i	$-0.543868\pi$
$241$	−3.12668e18			−0.274756			−0.137378	+	0.990519i	$0.543868\pi$
$242$			1.57930e18i			0.134259i
$243$	1.10314e19	+	5.11055e18i	0.907359	+	0.420357i
$244$	−7.53190e17			−0.0599496
$245$		−	1.11727e19i		−	0.860655i
$246$	−8.35758e17	−	3.61185e18i	−0.0623160	−	0.269307i
$247$	−3.32917e19			−2.40303
$248$			6.78296e18i			0.474030i
$249$	−1.12362e19	+	2.59999e18i	−0.760372	+	0.175945i
$250$	−8.81546e18			−0.577730
$251$		−	1.30882e19i		−	0.830791i	−0.909641	−	0.415395i	$-0.863643\pi$
$251$		−	1.30882e19i		−	0.830791i	0.909641	−	0.415395i	$-0.136357\pi$
$252$	3.56666e18	−	1.74398e18i	0.219309	−	0.107235i
$253$	2.32348e19			1.38412
$254$		−	3.20239e18i		−	0.184844i
$255$	−9.24734e17	−	3.99637e18i	−0.0517244	−	0.223534i
$256$	1.15292e18			0.0625000
$257$		−	7.73778e18i		−	0.406585i	−0.979118	−	0.203292i	$-0.934836\pi$
$257$		−	7.73778e18i		−	0.406585i	0.979118	−	0.203292i	$-0.0651642\pi$
$258$	−5.17321e18	+	1.19705e18i	−0.263513	+	0.0609753i
$259$	1.19682e19			0.591059
$260$			1.79670e19i			0.860377i
$261$	−1.21720e19	−	2.48933e19i	−0.565248	−	1.15600i
$262$	−1.14000e19			−0.513445
$263$		−	6.15684e17i		−	0.0268975i	−0.999910	−	0.0134487i	$-0.995719\pi$
$263$		−	6.15684e17i		−	0.0268975i	0.999910	−	0.0134487i	$-0.00428100\pi$
$264$	−1.69273e18	−	7.31539e18i	−0.0717394	−	0.310032i
$265$	1.94955e19			0.801620
$266$			1.36556e19i			0.544826i
$267$	−8.64490e18	+	2.00038e18i	−0.334711	+	0.0774500i
$268$	6.37530e18			0.239565
$269$			5.30026e19i			1.93321i	0.256272	+	0.966605i	$0.417506\pi$
$269$			5.30026e19i			1.93321i	−0.256272	+	0.966605i	$0.582494\pi$
$270$	1.42286e19	+	1.75172e19i	0.503792	+	0.620231i
$271$	3.19793e19			1.09930			0.549649	−	0.835396i	$-0.314762\pi$
$271$	3.19793e19			1.09930			0.549649	+	0.835396i	$0.314762\pi$
$272$			1.52079e18i			0.0507595i
$273$	−5.17119e18	−	2.23480e19i	−0.167606	−	0.724333i
$274$	1.91749e18			0.0603572
$275$			8.15448e18i			0.249307i
$276$	2.52240e19	−	5.83666e18i	0.749102	−	0.173337i
$277$	−2.34299e19			−0.675976			−0.337988	−	0.941150i	$-0.609746\pi$
$277$	−2.34299e19			−0.675976			−0.337988	+	0.941150i	$0.609746\pi$
$278$		−	1.20745e19i		−	0.338464i
$279$	4.42214e19	−	2.16229e19i	1.20448	−	0.588952i
$280$	7.36972e18			0.195068
$281$		−	2.11978e19i		−	0.545305i	−0.962113	−	0.272653i	$-0.912099\pi$
$281$		−	2.11978e19i		−	0.545305i	0.962113	−	0.272653i	$-0.0879010\pi$
$282$	−3.15080e18	−	1.36166e19i	−0.0787822	−	0.340468i
$283$	−1.42061e19			−0.345291			−0.172645	−	0.984984i	$-0.555231\pi$
$283$	−1.42061e19			−0.345291			−0.172645	+	0.984984i	$0.555231\pi$
$284$		−	1.26213e18i		−	0.0298234i
$285$	−7.56240e19	+	1.74989e19i	−1.73740	+	0.402024i
$286$	−4.33827e19			−0.969143
$287$			8.78584e18i			0.190866i
$288$	−3.67531e18	−	7.51646e18i	−0.0776523	−	0.158808i
$289$	4.66552e19			0.958776
$290$		−	5.14365e19i		−	1.02822i
$291$	7.69233e18	+	3.32435e19i	0.149594	+	0.646491i
$292$	−4.66020e19			−0.881743
$293$			8.88168e19i			1.63514i	0.575832	+	0.817568i	$0.304678\pi$
$293$			8.88168e19i			1.63514i	−0.575832	+	0.817568i	$0.695322\pi$
$294$	2.92869e19	−	6.77680e18i	0.524680	−	0.121408i
$295$	−6.30203e19			−1.09876
$296$		−	2.52221e19i		−	0.428003i
$297$	−4.22965e19	+	3.43559e19i	−0.698639	+	0.567480i
$298$	1.16901e19			0.187970
$299$		−	1.49586e20i		−	2.34165i
$300$	2.04844e18	+	8.85261e18i	0.0312214	+	0.134928i
$301$	1.25839e19			0.186759
$302$			4.67693e19i			0.675936i
$303$	6.48241e19	−	1.49999e19i	0.912421	−	0.211128i
$304$	2.87781e19			0.394525
$305$			1.01463e19i			0.135491i
$306$	9.91476e18	−	4.84800e18i	0.128977	−	0.0630654i
$307$	−9.48569e19			−1.20216			−0.601080	−	0.799189i	$-0.705263\pi$
$307$	−9.48569e19			−1.20216			−0.601080	+	0.799189i	$0.705263\pi$
$308$			1.77947e19i			0.219728i
$309$	2.64257e19	+	1.14202e20i	0.317949	+	1.37406i
$310$	9.13739e19			1.07134
$311$			1.90403e19i			0.217566i	0.994066	+	0.108783i	$0.0346953\pi$
$311$			1.90403e19i			0.217566i	−0.994066	+	0.108783i	$0.965305\pi$
$312$	−4.70968e19	+	1.08979e19i	−0.524511	+	0.121368i
$313$	1.33772e20			1.45215			0.726075	−	0.687616i	$-0.241343\pi$
$313$	1.33772e20			1.45215			0.726075	+	0.687616i	$0.241343\pi$
$314$			4.02129e18i			0.0425528i
$315$	−2.34934e19	−	4.80468e19i	−0.242360	−	0.495656i
$316$	−3.39345e19			−0.341307
$317$		−	1.62985e20i		−	1.59836i	−0.601094	−	0.799178i	$-0.705268\pi$
$317$		−	1.62985e20i		−	1.59836i	0.601094	−	0.799178i	$-0.294732\pi$
$318$	1.18250e19	+	5.11036e19i	0.113080	+	0.488691i
$319$	1.24197e20			1.15821
$320$		−	1.55311e19i		−	0.141255i
$321$	4.63660e19	−	1.07288e19i	0.411301	−	0.0951724i
$322$	−6.13575e19			−0.530909
$323$			3.79605e19i			0.320414i
$324$	−3.72873e19	+	4.79223e19i	−0.307044	+	0.394619i
$325$	5.24989e19			0.421777
$326$			2.15495e19i			0.168926i
$327$	−1.86680e19	−	8.06766e19i	−0.142796	−	0.617114i
$328$	1.85155e19			0.138212
$329$			3.31225e19i			0.241299i
$330$	−9.85464e19	+	2.28030e19i	−0.700695	+	0.162136i
$331$	−1.82914e20			−1.26947			−0.634736	−	0.772729i	$-0.718891\pi$
$331$	−1.82914e20			−1.26947			−0.634736	+	0.772729i	$0.718891\pi$
$332$		−	5.76006e19i		−	0.390232i
$333$	−1.64435e20	+	8.04035e19i	−1.08753	+	0.531767i
$334$	1.32097e20			0.852944
$335$		−	8.58824e19i		−	0.541434i
$336$	4.47011e18	+	1.93182e19i	0.0275172	+	0.118919i
$337$	−3.00874e20			−1.80861			−0.904306	−	0.426884i	$-0.859611\pi$
$337$	−3.00874e20			−1.80861			−0.904306	+	0.426884i	$0.859611\pi$
$338$			1.58846e20i			0.932487i
$339$	3.39167e20	−	7.84811e19i	1.94454	−	0.449953i
$340$	2.04867e19			0.114720
$341$			2.20629e20i			1.20678i
$342$	−9.17396e19	−	1.87619e20i	−0.490172	−	1.00246i
$343$	−1.64779e20			−0.860102
$344$		−	2.65196e19i		−	0.135238i
$345$	−7.86263e19	−	3.39795e20i	−0.391756	−	1.69303i
$346$	−7.39183e19			−0.359868
$347$			2.75354e20i			1.30995i	0.755650	+	0.654976i	$0.227321\pi$
$347$			2.75354e20i			1.30995i	−0.755650	+	0.654976i	$0.772679\pi$
$348$	1.34830e20	−	3.11989e19i	0.626835	−	0.145046i
$349$	1.22450e20			0.556358			0.278179	−	0.960529i	$-0.410269\pi$
$349$	1.22450e20			0.556358			0.278179	+	0.960529i	$0.410269\pi$
$350$		−	2.15340e19i		−	0.0956271i
$351$	2.21185e20	+	2.72307e20i	0.960061	+	1.18196i
$352$	3.75011e19			0.159112
$353$		−	4.25336e20i		−	1.76415i	−0.471113	−	0.882073i	$-0.656148\pi$
$353$		−	4.25336e20i		−	1.76415i	0.471113	−	0.882073i	$-0.343852\pi$
$354$	−3.82250e19	−	1.65195e20i	−0.154996	−	0.669839i
$355$	−1.70023e19			−0.0674032
$356$		−	4.43166e19i		−	0.171777i
$357$	−2.54821e19	+	5.89640e18i	−0.0965806	+	0.0223481i
$358$	2.42180e20			0.897581
$359$			3.68750e20i			1.33652i	0.743927	+	0.668261i	$0.232961\pi$
$359$			3.68750e20i			1.33652i	−0.743927	+	0.668261i	$0.767039\pi$
$360$	−1.01255e20	+	4.95105e19i	−0.358919	+	0.175500i
$361$	4.29892e20			1.49039
$362$		−	1.91641e20i		−	0.649860i
$363$	1.29044e19	+	5.57680e19i	0.0428039	+	0.184983i
$364$	1.14563e20			0.371736
$365$			6.27780e20i			1.99281i
$366$	−2.65965e19	+	6.15425e18i	−0.0825991	+	0.0191129i
$367$	−1.52019e20			−0.461922			−0.230961	−	0.972963i	$-0.574187\pi$
$367$	−1.52019e20			−0.461922			−0.230961	+	0.972963i	$0.574187\pi$
$368$			1.29306e20i			0.384447i
$369$	−5.90241e19	−	1.20712e20i	−0.171719	−	0.351187i
$370$	−3.39769e20			−0.967320
$371$		−	1.24310e20i		−	0.346349i
$372$	5.54229e19	+	2.39518e20i	0.151128	+	0.653122i
$373$	1.18257e20			0.315614			0.157807	−	0.987470i	$-0.449558\pi$
$373$	1.18257e20			0.315614			0.157807	+	0.987470i	$0.449558\pi$
$374$			4.94666e19i			0.129223i
$375$	−3.11289e20	+	7.20303e19i	−0.796001	+	0.184190i
$376$	6.98032e19			0.174732
$377$		−	7.99588e20i		−	1.95946i
$378$	1.11695e20	−	9.07259e19i	0.267978	−	0.217669i
$379$	−3.06672e20			−0.720378			−0.360189	−	0.932879i	$-0.617288\pi$
$379$	−3.06672e20			−0.720378			−0.360189	+	0.932879i	$0.617288\pi$
$380$		−	3.87673e20i		−	0.891656i
$381$	−2.61664e19	−	1.13082e20i	−0.0589311	−	0.254679i
$382$	−1.84310e20			−0.406484
$383$		−	5.53470e20i		−	1.19537i	−0.801730	−	0.597687i	$-0.796087\pi$
$383$		−	5.53470e20i		−	1.19537i	0.801730	−	0.597687i	$-0.203913\pi$
$384$	4.07116e19	−	9.42042e18i	0.0861130	−	0.0199260i
$385$	2.39715e20			0.496602
$386$			5.12136e20i			1.03917i
$387$	−1.72894e20	+	8.45397e19i	−0.343631	+	0.168025i
$388$	−1.70417e20			−0.331786
$389$		−	1.22013e20i		−	0.232707i	−0.993208	−	0.116353i	$-0.962879\pi$
$389$		−	1.22013e20i		−	0.232707i	0.993208	−	0.116353i	$-0.0371205\pi$
$390$	1.46807e20	+	6.34446e20i	0.274302	+	1.18543i
$391$	−1.70564e20			−0.312230
$392$			1.50134e20i			0.269272i
$393$	−4.02553e20	+	9.31482e19i	−0.707429	+	0.163695i
$394$	−6.71084e19			−0.115560
$395$			4.57135e20i			0.771379i
$396$	−1.19547e20	−	2.44488e20i	−0.197686	−	0.404293i
$397$	−2.64665e20			−0.428916			−0.214458	−	0.976733i	$-0.568798\pi$
$397$	−2.64665e20			−0.428916			−0.214458	+	0.976733i	$0.568798\pi$
$398$		−	2.25575e20i		−	0.358284i
$399$	1.11579e20	+	4.82203e20i	0.173699	+	0.750666i
$400$	−4.53813e19			−0.0692464
$401$		−	4.93340e20i		−	0.737889i	−0.929451	−	0.368945i	$-0.879719\pi$
$401$		−	4.93340e20i		−	0.737889i	0.929451	−	0.368945i	$-0.120281\pi$
$402$	2.25123e20	−	5.20920e19i	0.330074	−	0.0763770i
$403$	1.42042e21			2.04163
$404$			3.32309e20i			0.468265i
$405$	6.45566e20	+	5.02301e20i	0.891868	+	0.693943i
$406$	−3.27976e20			−0.444256
$407$		−	8.20398e20i		−	1.08961i
$408$	1.24262e19	+	5.37016e19i	0.0161829	+	0.0699369i
$409$	8.22840e20			1.05082			0.525411	−	0.850849i	$-0.323912\pi$
$409$	8.22840e20			1.05082			0.525411	+	0.850849i	$0.323912\pi$
$410$		−	2.49424e20i		−	0.312369i
$411$	6.77099e19	−	1.56676e19i	0.0831606	−	0.0192428i
$412$	−5.85438e20			−0.705185
$413$			4.01838e20i			0.474734i
$414$	8.43011e20	−	4.12205e20i	0.976856	−	0.477651i
$415$	−7.75944e20			−0.881953
$416$		−	2.41433e20i		−	0.269185i
$417$	−9.86600e19	−	4.26373e20i	−0.107908	−	0.466339i
$418$	9.36066e20			1.00438
$419$			1.34475e21i			1.41556i	0.706430	+	0.707782i	$0.250304\pi$
$419$			1.34475e21i			1.41556i	−0.706430	+	0.707782i	$0.749696\pi$
$420$	2.60237e20	−	6.02173e19i	0.268767	−	0.0621909i
$421$	−1.13149e21			−1.14655			−0.573277	−	0.819362i	$-0.694328\pi$
$421$	−1.13149e21			−1.14655			−0.573277	+	0.819362i	$0.694328\pi$
$422$		−	2.71777e20i		−	0.270217i
$423$	−2.22520e20	−	4.55081e20i	−0.217093	−	0.443983i
$424$	−2.61973e20			−0.250802
$425$		−	5.98613e19i		−	0.0562386i
$426$	−1.03128e19	−	4.45680e19i	−0.00950819	−	0.0410910i
$427$	6.46961e19			0.0585403
$428$			2.37687e20i			0.211084i
$429$	−1.53192e21	+	3.54476e20i	−1.33529	+	0.308978i
$430$	−3.57248e20			−0.305648
$431$			4.50754e20i			0.378548i	0.981924	+	0.189274i	$0.0606135\pi$
$431$			4.50754e20i			0.378548i	−0.981924	+	0.189274i	$0.939386\pi$
$432$	−1.91198e20	−	2.35389e20i	−0.157621	−	0.194051i
$433$	9.42632e18			0.00762849			0.00381425	−	0.999993i	$-0.498786\pi$
$433$	9.42632e18			0.00762849			0.00381425	+	0.999993i	$0.498786\pi$
$434$		−	5.82629e20i		−	0.462886i
$435$	−4.20283e20	−	1.81631e21i	−0.327814	−	1.41670i
$436$	4.13574e20			0.316710
$437$			3.22762e21i			2.42678i
$438$	−1.64560e21	+	3.80781e20i	−1.21487	+	0.281114i
$439$	6.88142e20			0.498841			0.249420	−	0.968395i	$-0.419760\pi$
$439$	6.88142e20			0.498841			0.249420	+	0.968395i	$0.419760\pi$
$440$		−	5.05181e20i		−	0.359605i
$441$	9.78799e20	−	4.78601e20i	0.684202	−	0.334553i
$442$	3.18468e20			0.218619
$443$		−	7.22543e20i		−	0.487118i	−0.969886	−	0.243559i	$-0.921685\pi$
$443$		−	7.22543e20i		−	0.487118i	0.969886	−	0.243559i	$-0.0783149\pi$
$444$	−2.06087e20	−	8.90635e20i	−0.136454	−	0.589707i
$445$	−5.96993e20			−0.388230
$446$			3.36843e19i			0.0215154i
$447$	4.12798e20	−	9.55188e19i	0.258987	−	0.0599278i
$448$	−9.90314e19			−0.0610307
$449$		−	1.67231e21i		−	1.01239i	−0.862420	−	0.506193i	$-0.831052\pi$
$449$		−	1.67231e21i		−	1.01239i	0.862420	−	0.506193i	$-0.168948\pi$
$450$	1.44668e20	+	2.95863e20i	0.0860343	+	0.175951i
$451$	6.02253e20			0.351857
$452$			1.73868e21i			0.997957i
$453$	3.82148e20	+	1.65151e21i	0.215499	+	0.931310i
$454$	−4.11885e20			−0.228207
$455$		−	1.54329e21i		−	0.840151i
$456$	1.01621e21	−	2.35144e20i	0.543579	−	0.125781i
$457$	−3.48956e20			−0.183417			−0.0917087	−	0.995786i	$-0.529233\pi$
$457$	−3.48956e20			−0.183417			−0.0917087	+	0.995786i	$0.529233\pi$
$458$			1.44944e21i			0.748644i
$459$	3.10495e20	−	2.52204e20i	0.157599	−	0.128012i
$460$	1.74190e21			0.868880
$461$			2.25305e20i			0.110449i	0.998474	+	0.0552246i	$0.0175875\pi$
$461$			2.25305e20i			0.110449i	−0.998474	+	0.0552246i	$0.982413\pi$
$462$	1.45399e20	+	6.28363e20i	0.0700529	+	0.302743i
$463$	1.94832e20			0.0922599			0.0461300	−	0.998935i	$-0.485311\pi$
$463$	1.94832e20			0.0922599			0.0461300	+	0.998935i	$0.485311\pi$
$464$			6.91184e20i			0.321699i
$465$	3.22657e21	−	7.46608e20i	1.47611	−	0.341561i
$466$	9.02018e20			0.405628
$467$		−	1.22910e21i		−	0.543317i	−0.962394	−	0.271658i	$-0.912428\pi$
$467$		−	1.22910e21i		−	0.543317i	0.962394	−	0.271658i	$-0.0875720\pi$
$468$	−1.57402e21	+	7.69647e20i	−0.683981	+	0.334445i
$469$	−5.47613e20			−0.233933
$470$		−	9.40326e20i		−	0.394908i
$471$	3.28576e19	+	1.41999e20i	0.0135665	+	0.0586296i
$472$	8.46842e20			0.343769
$473$		−	8.62601e20i		−	0.344287i
$474$	−1.19829e21	+	2.77276e20i	−0.470255	+	0.108814i
$475$	−1.13277e21			−0.437111
$476$		−	1.30630e20i		−	0.0495662i
$477$	8.35125e20	+	1.70793e21i	0.311605	+	0.637271i
$478$	−2.33856e21			−0.858076
$479$			9.86668e19i			0.0356030i	0.999842	+	0.0178015i	$0.00566669\pi$
$479$			9.86668e19i			0.0356030i	−0.999842	+	0.0178015i	$0.994333\pi$
$480$	−1.26903e20	−	5.48431e20i	−0.0450343	−	0.194622i
$481$	−5.28176e21			−1.84339
$482$		−	5.65990e20i		−	0.194282i
$483$	−2.16664e21	+	5.01346e20i	−0.731492	+	0.169263i
$484$	−2.85885e20			−0.0949354
$485$			2.29570e21i			0.749863i
$486$	−9.25109e20	+	1.99689e21i	−0.297237	+	0.641600i
$487$	4.91198e21			1.55248			0.776238	−	0.630439i	$-0.217125\pi$
$487$	4.91198e21			1.55248			0.776238	+	0.630439i	$0.217125\pi$
$488$		−	1.36342e20i		−	0.0423908i
$489$	1.76079e20	+	7.60952e20i	0.0538564	+	0.232748i
$490$	2.02247e21			0.608575
$491$		−	6.30381e21i		−	1.86617i	−0.359657	−	0.933085i	$-0.617106\pi$
$491$		−	6.30381e21i		−	1.86617i	0.359657	−	0.933085i	$-0.382894\pi$
$492$	6.53814e20	−	1.51288e20i	0.190429	−	0.0440641i
$493$	−9.11722e20			−0.261268
$494$		−	6.02643e21i		−	1.69920i
$495$	−3.29352e21	+	1.61043e21i	−0.913732	+	0.446786i
$496$	−1.22785e21			−0.335190
$497$			1.08412e20i			0.0291223i
$498$	−4.70649e20	−	2.03398e21i	−0.124412	−	0.537664i
$499$	−6.31209e21			−1.64198			−0.820991	−	0.570941i	$-0.806579\pi$
$499$	−6.31209e21			−1.64198			−0.820991	+	0.570941i	$0.806579\pi$
$500$		−	1.59577e21i		−	0.408517i
$501$	4.66456e21	−	1.07935e21i	1.17519	−	0.271932i
$502$	2.36922e21			0.587458
$503$			4.03528e21i			0.984758i	0.870381	+	0.492379i	$0.163873\pi$
$503$			4.03528e21i			0.984758i	−0.870381	+	0.492379i	$0.836127\pi$
$504$	3.15695e20	+	6.45634e20i	0.0758268	+	0.155075i
$505$	4.47657e21			1.05831
$506$			4.20594e21i			0.978721i
$507$	1.29792e21	+	5.60913e21i	0.297292	+	1.28479i
$508$	5.79694e20			0.130704
$509$			1.68915e21i			0.374908i	0.982273	+	0.187454i	$0.0600236\pi$
$509$			1.68915e21i			0.374908i	−0.982273	+	0.187454i	$0.939976\pi$
$510$	7.23420e20	−	1.67395e20i	0.158063	−	0.0365747i
$511$	4.00293e21			0.861015
$512$			2.08701e20i			0.0441942i
$513$	−4.77250e21	−	5.87555e21i	−0.994964	−	1.22493i
$514$	1.40069e21			0.287499
$515$			7.88649e21i			1.59377i
$516$	−2.16689e20	−	9.36452e20i	−0.0431161	−	0.186332i
$517$	2.27049e21			0.444831
$518$			2.16648e21i			0.417942i
$519$	−2.61018e21	+	6.03980e20i	−0.495829	+	0.114732i
$520$	−3.25237e21			−0.608378
$521$		−	3.87836e21i		−	0.714409i	−0.934026	−	0.357204i	$-0.883730\pi$
$521$		−	3.87836e21i		−	0.714409i	0.934026	−	0.357204i	$-0.116270\pi$
$522$	4.50617e21	−	2.20337e21i	0.817416	−	0.399690i
$523$	1.01818e22			1.81891			0.909455	−	0.415803i	$-0.136499\pi$
$523$	1.01818e22			1.81891			0.909455	+	0.415803i	$0.136499\pi$
$524$		−	2.06362e21i		−	0.363060i
$525$	−1.75953e20	−	7.60404e20i	−0.0304875	−	0.131756i
$526$	1.11451e20			0.0190194
$527$		−	1.61962e21i		−	0.272225i
$528$	1.32423e21	−	3.06418e20i	0.219225	−	0.0507274i
$529$	−8.36976e21			−1.36480
$530$			3.52907e21i			0.566831i
$531$	−2.69958e21	−	5.52098e21i	−0.427111	−	0.873494i
$532$	−2.47193e21			−0.385250
$533$		−	3.87733e21i		−	0.595272i
$534$	−3.62107e20	−	1.56489e21i	−0.0547654	−	0.236676i
$535$	3.20191e21			0.477066
$536$			1.15405e21i			0.169398i
$537$	8.55178e21	−	1.97883e21i	1.23669	−	0.286163i
$538$	−9.59449e21			−1.36699
$539$			4.88341e21i			0.685509i
$540$	−3.17094e21	+	2.57565e21i	−0.438570	+	0.356235i
$541$	−1.11108e22			−1.51414			−0.757070	−	0.653333i	$-0.773370\pi$
$541$	−1.11108e22			−1.51414			−0.757070	+	0.653333i	$0.773370\pi$
$542$			5.78888e21i			0.777320i
$543$	−1.56588e21	−	6.76717e21i	−0.207186	−	0.895383i
$544$	−2.75292e20			−0.0358924
$545$		−	5.57130e21i		−	0.715788i
$546$	4.04543e21	−	9.36086e20i	0.512181	−	0.118515i
$547$	−1.91151e21			−0.238494			−0.119247	−	0.992865i	$-0.538048\pi$
$547$	−1.91151e21			−0.238494			−0.119247	+	0.992865i	$0.538048\pi$
$548$			3.47103e20i			0.0426790i
$549$	−8.88881e20	+	4.34634e20i	−0.107712	+	0.0526678i
$550$	−1.47612e21			−0.176287
$551$			1.72527e22i			2.03069i
$552$	1.05655e21	+	4.56603e21i	0.122568	+	0.529695i
$553$	2.91484e21			0.333283
$554$		−	4.24126e21i		−	0.477987i
$555$	−1.19978e22	+	2.77622e21i	−1.33278	+	0.308397i
$556$	2.18573e21			0.239330
$557$		−	1.06013e22i		−	1.14424i	−0.820170	−	0.572120i	$-0.806121\pi$
$557$		−	1.06013e22i		−	1.14424i	0.820170	−	0.572120i	$-0.193879\pi$
$558$	3.91416e21	+	8.00493e21i	0.416452	+	0.851695i
$559$	−5.55346e21			−0.582465
$560$			1.33406e21i			0.137934i
$561$	4.04187e20	+	1.74675e21i	0.0411983	+	0.178044i
$562$	3.83721e21			0.385589
$563$		−	1.37945e22i		−	1.36659i	−0.730141	−	0.683297i	$-0.760545\pi$
$563$		−	1.37945e22i		−	1.36659i	0.730141	−	0.683297i	$-0.239455\pi$
$564$	2.46487e21	−	5.70356e20i	0.240747	−	0.0557074i
$565$	2.34219e22			2.25546
$566$		−	2.57159e21i		−	0.244157i
$567$	3.20283e21	−	4.11634e21i	0.299826	−	0.385342i
$568$	2.28470e20			0.0210884
$569$			1.17330e22i			1.06785i	0.845531	+	0.533926i	$0.179284\pi$
$569$			1.17330e22i			1.06785i	−0.845531	+	0.533926i	$0.820716\pi$
$570$	−3.16764e21	−	1.36894e22i	−0.284274	−	1.22853i
$571$	6.61823e21			0.585670			0.292835	−	0.956163i	$-0.405401\pi$
$571$	6.61823e21			0.585670			0.292835	+	0.956163i	$0.405401\pi$
$572$		−	7.85310e21i		−	0.685288i
$573$	−6.50832e21	+	1.50598e21i	−0.560057	+	0.129594i
$574$	−1.59041e21			−0.134963
$575$		−	5.08976e21i		−	0.425946i
$576$	1.36063e21	−	6.65302e20i	0.112295	−	0.0549084i
$577$	1.60264e22			1.30446			0.652228	−	0.758023i	$-0.273835\pi$
$577$	1.60264e22			1.30446			0.652228	+	0.758023i	$0.273835\pi$
$578$			8.44549e21i			0.677957i
$579$	4.18462e21	+	1.80844e22i	0.331305	+	1.43178i
$580$	9.31101e21			0.727064
$581$			4.94766e21i			0.381058i
$582$	−6.01771e21	+	1.39246e21i	−0.457138	+	0.105779i
$583$	−8.52120e21			−0.638488
$584$		−	8.43587e21i		−	0.623486i
$585$	1.03680e22	+	2.12038e22i	0.755871	+	1.54585i
$586$	−1.60776e22			−1.15622
$587$			3.97771e21i			0.282181i	0.989997	+	0.141091i	$0.0450609\pi$
$587$			3.97771e21i			0.282181i	−0.989997	+	0.141091i	$0.954939\pi$
$588$	1.22673e21	+	5.30150e21i	0.0858482	+	0.371005i
$589$	−3.06483e22			−2.11585
$590$		−	1.14079e22i		−	0.776944i
$591$	−2.36971e21	+	5.48337e20i	−0.159219	+	0.0368424i
$592$	4.56568e21			0.302644
$593$		−	1.12212e22i		−	0.733839i	−0.930253	−	0.366919i	$-0.880412\pi$
$593$		−	1.12212e22i		−	0.733839i	0.930253	−	0.366919i	$-0.119588\pi$
$594$	−6.21909e21	−	7.65648e21i	−0.401269	−	0.494012i
$595$	−1.75972e21			−0.112023
$596$			2.11614e21i			0.132915i
$597$	−1.84316e21	−	7.96545e21i	−0.114227	−	0.493646i
$598$	2.70780e22			1.65580
$599$		−	1.31221e22i		−	0.791749i	−0.918305	−	0.395874i	$-0.870442\pi$
$599$		−	1.31221e22i		−	0.791749i	0.918305	−	0.395874i	$-0.129558\pi$
$600$	−1.60249e21	+	3.70807e20i	−0.0954083	+	0.0220769i
$601$	−1.55544e22			−0.913816			−0.456908	−	0.889514i	$-0.651043\pi$
$601$	−1.55544e22			−0.913816			−0.456908	+	0.889514i	$0.651043\pi$
$602$			2.27792e21i			0.132059i
$603$	7.52384e21	−	3.67892e21i	0.430429	−	0.210466i
$604$	−8.46615e21			−0.477959
$605$			3.85118e21i			0.214561i
$606$	2.71527e21	+	1.17344e22i	0.149290	+	0.645179i
$607$	−1.22510e22			−0.664756			−0.332378	−	0.943146i	$-0.607851\pi$
$607$	−1.22510e22			−0.664756			−0.332378	+	0.943146i	$0.607851\pi$
$608$			5.20940e21i			0.278971i
$609$	−1.15814e22	+	2.67986e21i	−0.612100	+	0.141636i
$610$	−1.83668e21			−0.0958063
$611$		−	1.46175e22i		−	0.752564i
$612$	8.77582e20	+	1.79476e21i	0.0445940	+	0.0912002i
$613$	−6.85336e21			−0.343732			−0.171866	−	0.985120i	$-0.554980\pi$
$613$	−6.85336e21			−0.343732			−0.171866	+	0.985120i	$0.554980\pi$
$614$		−	1.71709e22i		−	0.850055i
$615$	−2.03802e21	−	8.80759e21i	−0.0995882	−	0.430384i
$616$	−3.22119e21			−0.155371
$617$			2.44104e22i			1.16223i	0.813820	+	0.581117i	$0.197384\pi$
$617$			2.44104e22i			1.16223i	−0.813820	+	0.581117i	$0.802616\pi$
$618$	−2.06728e22	+	4.78356e21i	−0.971609	+	0.224824i
$619$	3.66015e22			1.69814			0.849070	−	0.528281i	$-0.177163\pi$
$619$	3.66015e22			1.69814			0.849070	+	0.528281i	$0.177163\pi$
$620$			1.65404e22i			0.757554i
$621$	2.64001e22	−	2.14438e22i	1.19364	−	0.969549i
$622$	−3.44666e21			−0.153842
$623$			3.80662e21i			0.167739i
$624$	−1.97273e21	−	8.52543e21i	−0.0858205	−	0.370885i
$625$	−2.79458e22			−1.20026
$626$			2.42154e22i			1.02682i
$627$	3.30541e22	−	7.64851e21i	1.38384	−	0.320211i
$628$	−7.27931e20			−0.0300894
$629$			6.02247e21i			0.245793i
$630$	8.69740e21	−	4.25275e21i	0.350482	−	0.171374i
$631$	1.59443e22			0.634413			0.317206	−	0.948357i	$-0.397255\pi$
$631$	1.59443e22			0.634413			0.317206	+	0.948357i	$0.397255\pi$
$632$		−	6.14280e21i		−	0.241340i
$633$	−2.22067e21	−	9.59692e21i	−0.0861497	−	0.372308i
$634$	2.95034e22			1.13021
$635$		−	7.80912e21i		−	0.295401i
$636$	−9.25073e21	+	2.14056e21i	−0.345557	+	0.0799596i
$637$	3.14396e22			1.15974
$638$			2.24821e22i			0.818977i
$639$	−7.28322e20	−	1.48951e21i	−0.0262009	−	0.0535841i
$640$	2.81143e21			0.0998822
$641$			4.87647e22i			1.71097i	0.517831	+	0.855483i	$0.326740\pi$
$641$			4.87647e22i			1.71097i	−0.517831	+	0.855483i	$0.673260\pi$
$642$	1.94212e21	+	8.39315e21i	0.0672971	+	0.290834i
$643$	−3.78640e22			−1.29580			−0.647900	−	0.761725i	$-0.724353\pi$
$643$	−3.78640e22			−1.29580			−0.647900	+	0.761725i	$0.724353\pi$
$644$		−	1.11069e22i		−	0.375410i
$645$	−1.26150e22	+	2.91904e21i	−0.421125	+	0.0974456i
$646$	−6.87158e21			−0.226567
$647$		−	2.51160e22i		−	0.817932i	−0.912550	−	0.408966i	$-0.865890\pi$
$647$		−	2.51160e22i		−	0.817932i	0.912550	−	0.408966i	$-0.134110\pi$
$648$	−8.67487e21	−	6.74972e21i	−0.279038	−	0.217113i
$649$	2.75452e22			0.875162
$650$			9.50331e21i			0.298241i
$651$	−4.76061e21	−	2.05736e22i	−0.147576	−	0.637769i
$652$	−3.90088e21			−0.119449
$653$		−	4.06843e22i		−	1.23061i	−0.788289	−	0.615306i	$-0.789033\pi$
$653$		−	4.06843e22i		−	1.23061i	0.788289	−	0.615306i	$-0.210967\pi$
$654$	1.46040e22	−	3.37928e21i	0.436365	−	0.100972i
$655$	−2.77992e22			−0.820544
$656$			3.35166e21i			0.0977304i
$657$	−5.49976e22	+	2.68921e22i	−1.58424	+	0.774642i
$658$	−5.99582e21			−0.170624
$659$			2.10016e22i			0.590432i	0.955431	+	0.295216i	$0.0953916\pi$
$659$			2.10016e22i			0.590432i	−0.955431	+	0.295216i	$0.904608\pi$
$660$	−4.12778e21	−	1.78388e22i	−0.114648	−	0.495466i
$661$	3.87747e22			1.06399			0.531994	−	0.846748i	$-0.321443\pi$
$661$	3.87747e22			1.06399			0.531994	+	0.846748i	$0.321443\pi$
$662$		−	3.31110e22i		−	0.897652i
$663$	1.12457e22	−	2.60217e21i	0.301215	−	0.0696993i
$664$	1.04268e22			0.275935
$665$			3.32996e22i			0.870694i
$666$	−1.45546e22	−	2.97659e22i	−0.376016	−	0.768999i
$667$	−7.75199e22			−1.97882
$668$			2.39121e22i			0.603122i
$669$	2.75231e20	+	1.18945e21i	0.00685944	+	0.0296440i
$670$	1.55464e22			0.382852
$671$		−	4.43479e21i		−	0.107918i
$672$	−3.49697e21	+	8.09176e20i	−0.0840887	+	0.0194576i
$673$	1.98456e22			0.471568			0.235784	−	0.971805i	$-0.424234\pi$
$673$	1.98456e22			0.471568			0.235784	+	0.971805i	$0.424234\pi$
$674$		−	5.44640e22i		−	1.27888i
$675$	7.52594e21	+	9.26538e21i	0.174635	+	0.214997i
$676$	−2.87542e22			−0.659368
$677$		−	3.60090e22i		−	0.816022i	−0.912977	−	0.408011i	$-0.866223\pi$
$677$		−	3.60090e22i		−	0.816022i	0.912977	−	0.408011i	$-0.133777\pi$
$678$	1.42066e22	+	6.13958e22i	0.318165	+	1.37499i
$679$	1.46381e22			0.323987
$680$			3.70849e21i			0.0811195i
$681$	−1.45444e22	+	3.36547e21i	−0.314425	+	0.0727560i
$682$	−3.99381e22			−0.853322
$683$			4.37055e22i			0.922935i	0.887157	+	0.461467i	$0.152677\pi$
$683$			4.37055e22i			0.922935i	−0.887157	+	0.461467i	$0.847323\pi$
$684$	3.39626e22	−	1.66067e22i	0.708847	−	0.346604i
$685$	4.67586e21			0.0964577
$686$		−	2.98283e22i		−	0.608184i
$687$	1.18432e22	+	5.11821e22i	0.238680	+	1.03149i
$688$	4.80055e21			0.0956277
$689$			5.48599e22i			1.08019i
$690$	6.15094e22	−	1.42329e22i	1.19715	−	0.277013i
$691$	2.56278e22			0.493046			0.246523	−	0.969137i	$-0.420712\pi$
$691$	2.56278e22			0.493046			0.246523	+	0.969137i	$0.420712\pi$
$692$		−	1.33806e22i		−	0.254465i
$693$	1.02686e22	+	2.10005e22i	0.193039	+	0.394788i
$694$	−4.98444e22			−0.926276
$695$		−	2.94441e22i		−	0.540904i
$696$	5.64760e21	+	2.44069e22i	0.102563	+	0.443240i
$697$	−4.42109e21			−0.0793719
$698$			2.21658e22i			0.393404i
$699$	3.18518e22	−	7.37031e21i	0.558878	−	0.129321i
$700$	3.89808e21			0.0676186
$701$		−	1.07149e23i		−	1.83756i	−0.394765	−	0.918782i	$-0.629174\pi$
$701$		−	1.07149e23i		−	1.83756i	0.394765	−	0.918782i	$-0.370826\pi$
$702$	−4.92928e22	+	4.00388e22i	−0.835769	+	0.678866i
$703$	1.13964e23			1.91041
$704$			6.78842e21i			0.112509i
$705$	−7.68332e21	−	3.32045e22i	−0.125903	−	0.544107i
$706$	7.69940e22			1.24744
$707$		−	2.85440e22i		−	0.457257i
$708$	2.99035e22	−	6.91947e21i	0.473648	−	0.109599i
$709$	1.93543e22			0.303115			0.151557	−	0.988448i	$-0.451571\pi$
$709$	1.93543e22			0.303115			0.151557	+	0.988448i	$0.451571\pi$
$710$		−	3.07774e21i		−	0.0476613i
$711$	−4.00479e22	+	1.95822e22i	−0.613230	+	0.299850i
$712$	8.02215e21			0.121465
$713$		−	1.37709e23i		−	2.06180i
$714$	−1.06736e21	−	4.61276e21i	−0.0158025	−	0.0682928i
$715$	−1.05790e23			−1.54880
$716$			4.38392e22i			0.634685i
$717$	−8.25787e22	+	1.91082e22i	−1.18226	+	0.273568i
$718$	−6.67508e22			−0.945064
$719$			1.30967e23i			1.83370i	0.399227	+	0.916852i	$0.369279\pi$
$719$			1.30967e23i			1.83370i	−0.399227	+	0.916852i	$0.630721\pi$
$720$	−8.96235e21	−	1.83291e22i	−0.124097	−	0.253794i
$721$	5.02868e22			0.688607
$722$			7.78187e22i			1.05387i
$723$	−4.62465e21	−	1.99861e22i	−0.0619402	−	0.267683i
$724$	3.46907e22			0.459520
$725$		−	2.72064e22i		−	0.356424i
$726$	−1.00951e22	+	2.33594e21i	−0.130803	+	0.0302669i
$727$	−8.27839e22			−1.06089			−0.530445	−	0.847719i	$-0.677975\pi$
$727$	−8.27839e22			−1.06089			−0.530445	+	0.847719i	$0.677975\pi$
$728$			2.07382e22i			0.262857i
$729$	−1.63508e22	+	7.80726e22i	−0.204983	+	0.978765i
$730$	−1.13640e23			−1.40913
$731$			6.33228e21i			0.0776642i
$732$	−1.11404e21	−	4.81447e21i	−0.0135149	−	0.0584063i
$733$	1.45000e22			0.173994			0.0869972	−	0.996209i	$-0.472273\pi$
$733$	1.45000e22			0.173994			0.0869972	+	0.996209i	$0.472273\pi$
$734$		−	2.75183e22i		−	0.326628i
$735$	7.14170e22	−	1.65254e22i	0.838500	−	0.194023i
$736$	−2.34069e22			−0.271845
$737$			3.75379e22i			0.431251i
$738$	2.18511e22	−	1.06845e22i	0.248327	−	0.121424i
$739$	7.61614e22			0.856208			0.428104	−	0.903729i	$-0.359182\pi$
$739$	7.61614e22			0.856208			0.428104	+	0.903729i	$0.359182\pi$
$740$		−	6.15048e22i		−	0.683998i
$741$	−4.92414e22	−	2.12804e23i	−0.541733	−	2.34117i
$742$	2.25025e22			0.244906
$743$			4.12674e22i			0.444321i	0.975010	+	0.222160i	$0.0713109\pi$
$743$			4.12674e22i			0.444321i	−0.975010	+	0.222160i	$0.928689\pi$
$744$	−4.33574e22	+	1.00326e22i	−0.461827	+	0.106864i
$745$	2.85067e22			0.300398
$746$			2.14068e22i			0.223173i
$747$	−3.32389e22	−	6.79776e22i	−0.342832	−	0.701134i
$748$	−8.95441e21			−0.0913744
$749$		−	2.04164e22i		−	0.206122i
$750$	−1.30389e22	−	5.63493e22i	−0.130242	−	0.562858i
$751$	−9.47521e22			−0.936417			−0.468209	−	0.883618i	$-0.655100\pi$
$751$	−9.47521e22			−0.936417			−0.468209	+	0.883618i	$0.655100\pi$
$752$			1.26357e22i			0.123554i
$753$	8.36614e22	−	1.93587e22i	0.809404	−	0.187291i
$754$	1.44741e23			1.38554
$755$			1.14048e23i			1.08022i
$756$	1.64231e22	+	2.02189e22i	0.153915	+	0.189489i
$757$	6.67430e22			0.618926			0.309463	−	0.950911i	$-0.399851\pi$
$757$	6.67430e22			0.618926			0.309463	+	0.950911i	$0.399851\pi$
$758$		−	5.55136e22i		−	0.509384i
$759$	3.43664e22	+	1.48519e23i	0.312032	+	1.34849i
$760$	7.01764e22			0.630496
$761$			2.20313e23i			1.95867i	0.202234	+	0.979337i	$0.435180\pi$
$761$			2.20313e23i			1.95867i	−0.202234	+	0.979337i	$0.564820\pi$
$762$	2.04700e22	−	4.73663e21i	0.180085	−	0.0416706i
$763$	−3.55244e22			−0.309265
$764$		−	3.33638e22i		−	0.287427i
$765$	2.41774e22	−	1.18220e22i	0.206119	−	0.100786i
$766$	1.00189e23			0.845257
$767$		−	1.77337e23i		−	1.48060i
$768$	1.70528e21	+	7.36960e21i	0.0140898	+	0.0608911i
$769$	−1.14604e23			−0.937108			−0.468554	−	0.883435i	$-0.655225\pi$
$769$	−1.14604e23			−0.937108			−0.468554	+	0.883435i	$0.655225\pi$
$770$			4.33930e22i			0.351151i
$771$	4.94607e22	−	1.14449e22i	0.396118	−	0.0916593i
$772$	−9.27066e22			−0.734805
$773$			1.02991e23i			0.807913i	0.914778	+	0.403956i	$0.132365\pi$
$773$			1.02991e23i			0.807913i	−0.914778	+	0.403956i	$0.867635\pi$
$774$	−1.53033e22	−	3.12972e22i	−0.118811	−	0.242984i
$775$	4.83305e22			0.371371
$776$		−	3.08487e22i		−	0.234608i
$777$	1.77021e22	+	7.65020e22i	0.133247	+	0.575844i
$778$	2.20867e22			0.164549
$779$			8.36610e22i			0.616913i
$780$	−1.14847e23	+	2.65748e22i	−0.838229	+	0.193961i
$781$	7.43144e21			0.0536865
$782$		−	3.08754e22i		−	0.220780i
$783$	1.41117e23	−	1.14624e23i	0.998815	−	0.811302i
$784$	−2.71772e22			−0.190404
$785$			9.80604e21i			0.0680043i
$786$	−1.68616e22	−	7.28699e22i	−0.115750	−	0.500228i
$787$	−1.93687e23			−1.31614			−0.658071	−	0.752956i	$-0.728627\pi$
$787$	−1.93687e23			−1.31614			−0.658071	+	0.752956i	$0.728627\pi$
$788$		−	1.21479e22i		−	0.0817132i
$789$	3.93551e21	−	9.10653e20i	0.0262051	−	0.00606369i
$790$	−8.27502e22			−0.545447
$791$		−	1.49346e23i		−	0.974497i
$792$	4.42570e22	−	2.16403e22i	0.285878	−	0.139785i
$793$	−2.85514e22			−0.182575
$794$		−	4.79094e22i		−	0.303289i
$795$	2.88357e22	+	1.24618e23i	0.180715	+	0.780984i
$796$	4.08335e22			0.253345
$797$		−	6.17499e22i		−	0.379289i	−0.981853	−	0.189644i	$-0.939266\pi$
$797$		−	6.17499e22i		−	0.379289i	0.981853	−	0.189644i	$-0.0607335\pi$
$798$	−8.72880e22	+	2.01979e22i	−0.530801	+	0.122824i
$799$	−1.66674e22			−0.100345
$800$		−	8.21490e21i		−	0.0489646i
$801$	−2.55732e22	−	5.23004e22i	−0.150913	−	0.308635i
$802$	8.93041e22			0.521767
$803$		−	2.74393e23i		−	1.58726i
$804$	9.42966e21	+	4.07516e22i	0.0540067	+	0.233398i
$805$	−1.49622e23			−0.848454
$806$			2.57123e23i			1.44365i
$807$	−3.38798e23	+	7.83957e22i	−1.88344	+	0.435817i
$808$	−6.01544e22			−0.331113
$809$		−	1.89858e23i		−	1.03476i	−0.855754	−	0.517382i	$-0.826907\pi$
$809$		−	1.89858e23i		−	1.03476i	0.855754	−	0.517382i	$-0.173093\pi$
$810$	−9.09261e22	+	1.16860e23i	−0.490692	+	0.630646i
$811$	1.21902e23			0.651393			0.325697	−	0.945474i	$-0.394401\pi$
$811$	1.21902e23			0.651393			0.325697	+	0.945474i	$0.394401\pi$
$812$		−	5.93699e22i		−	0.314136i
$813$	4.73004e22	+	2.04415e23i	0.247822	+	1.07100i
$814$	1.48508e23			0.770467
$815$			5.25492e22i			0.269964i
$816$	−9.72103e21	+	2.24939e21i	−0.0494528	+	0.0114431i
$817$	1.19827e23			0.603640
$818$			1.48950e23i			0.743043i
$819$	1.35202e23	−	6.61096e22i	0.667902	−	0.326583i
$820$	4.51506e22			0.220878
$821$			1.39374e23i			0.675205i	0.941289	+	0.337602i	$0.109616\pi$
$821$			1.39374e23i			0.675205i	−0.941289	+	0.337602i	$0.890384\pi$
$822$	2.83615e21	+	1.22568e22i	0.0136067	+	0.0588035i
$823$	1.07352e23			0.510047			0.255024	−	0.966935i	$-0.417917\pi$
$823$	1.07352e23			0.510047			0.255024	+	0.966935i	$0.417917\pi$
$824$		−	1.05976e23i		−	0.498641i
$825$	−5.21243e22	+	1.20612e22i	−0.242889	+	0.0562030i
$826$	−7.27404e22			−0.335687
$827$		−	2.73634e23i		−	1.25062i	−0.780375	−	0.625312i	$-0.784972\pi$
$827$		−	2.73634e23i		−	1.25062i	0.780375	−	0.625312i	$-0.215028\pi$
$828$	7.46172e22	+	1.52601e23i	0.337750	+	0.690741i
$829$	1.13470e23			0.508680			0.254340	−	0.967115i	$-0.418142\pi$
$829$	1.13470e23			0.508680			0.254340	+	0.967115i	$0.418142\pi$
$830$		−	1.40461e23i		−	0.623635i
$831$	−3.46549e22	−	1.49766e23i	−0.152390	−	0.658575i
$832$	4.37041e22			0.190342
$833$		−	3.58487e22i		−	0.154637i
$834$	7.71818e22	−	1.78594e22i	0.329751	−	0.0763023i
$835$	3.22122e23			1.36310
$836$			1.69446e23i			0.710201i
$837$	2.03623e23	+	2.50686e23i	0.845325	+	1.04070i
$838$	−2.43426e23			−1.00096
$839$		−	6.08836e22i		−	0.247973i	−0.992284	−	0.123987i	$-0.960432\pi$
$839$		−	6.08836e22i		−	0.247973i	0.992284	−	0.123987i	$-0.0395680\pi$
$840$	1.09005e22	+	4.71080e22i	0.0439756	+	0.190047i
$841$	−1.64123e23			−0.655844
$842$		−	2.04822e23i		−	0.810736i
$843$	1.35498e23	−	3.13535e22i	0.531268	−	0.122932i
$844$	4.91969e22			0.191073
$845$			3.87351e23i			1.49022i
$846$	8.23785e22	−	4.02805e22i	0.313943	−	0.153508i
$847$	2.45564e22			0.0927036
$848$		−	4.74223e22i		−	0.177344i
$849$	−2.10122e22	−	9.08072e22i	−0.0778413	−	0.336402i
$850$	1.08360e22			0.0397667
$851$			5.12065e23i			1.86161i
$852$	8.06767e21	−	1.86681e21i	0.0290557	−	0.00672331i
$853$	−4.28891e23			−1.53022			−0.765111	−	0.643898i	$-0.777316\pi$
$853$	−4.28891e23			−1.53022			−0.765111	+	0.643898i	$0.777316\pi$
$854$			1.17112e22i			0.0413942i
$855$	−2.23710e23	−	4.57514e23i	−0.783351	−	1.60205i
$856$	−4.30260e22			−0.149259
$857$		−	3.38676e23i		−	1.16396i	−0.813203	−	0.581980i	$-0.802278\pi$
$857$		−	3.38676e23i		−	1.16396i	0.813203	−	0.581980i	$-0.197722\pi$
$858$	−6.41670e22	−	2.77306e23i	−0.218481	−	0.944195i
$859$	1.64009e22			0.0553252			0.0276626	−	0.999617i	$-0.491194\pi$
$859$	1.64009e22			0.0553252			0.0276626	+	0.999617i	$0.491194\pi$
$860$		−	6.46687e22i		−	0.216126i
$861$	−5.61600e22	+	1.29951e22i	−0.185953	+	0.0430282i
$862$	−8.15952e22			−0.267674
$863$			1.53690e23i			0.499527i	0.968307	+	0.249764i	$0.0803529\pi$
$863$			1.53690e23i			0.499527i	−0.968307	+	0.249764i	$0.919647\pi$
$864$	4.26099e22	−	3.46105e22i	0.137215	−	0.111455i
$865$	−1.80252e23			−0.575111
$866$			1.70635e21i			0.00539416i
$867$	6.90073e22	+	2.98225e23i	0.216144	+	0.934095i
$868$	1.05467e23			0.327310
$869$		−	1.99807e23i		−	0.614401i
$870$	3.28788e23	−	7.60794e22i	1.00176	−	0.231800i
$871$	2.41670e23			0.729589
$872$			7.48649e22i			0.223948i
$873$	−2.01118e23	+	9.83404e22i	−0.596125	+	0.291486i
$874$	−5.84262e23			−1.71599
$875$			1.37070e23i			0.398913i
$876$	−6.89287e22	−	2.97885e23i	−0.198777	−	0.859045i
$877$	3.47450e23			0.992877			0.496439	−	0.868072i	$-0.334641\pi$
$877$	3.47450e23			0.992877			0.496439	+	0.868072i	$0.334641\pi$
$878$			1.24567e23i			0.352734i
$879$	−5.67726e23	+	1.31368e23i	−1.59304	+	0.368620i
$880$	9.14474e22			0.254279
$881$			4.75184e23i			1.30935i	0.755912	+	0.654673i	$0.227194\pi$
$881$			4.75184e23i			1.30935i	−0.755912	+	0.654673i	$0.772806\pi$
$882$	8.66361e22	+	1.77181e23i	0.236565	+	0.483804i
$883$	−4.38612e23			−1.18685			−0.593424	−	0.804890i	$-0.702224\pi$
$883$	−4.38612e23			−1.18685			−0.593424	+	0.804890i	$0.702224\pi$
$884$			5.76489e22i			0.154587i
$885$	−9.32129e22	−	4.02833e23i	−0.247702	−	1.07048i
$886$	1.30794e23			0.344444
$887$			1.34369e23i			0.350680i	0.984508	+	0.175340i	$0.0561024\pi$
$887$			1.34369e23i			0.350680i	−0.984508	+	0.175340i	$0.943898\pi$
$888$	1.61222e23	−	3.73058e22i	0.416985	−	0.0964878i
$889$	−4.97934e22			−0.127632
$890$		−	1.08067e23i		−	0.274520i
$891$	−2.82167e23	−	2.19548e23i	−0.710370	−	0.552723i
$892$	−6.09751e21			−0.0152137
$893$			3.15401e23i			0.779923i
$894$	1.72907e22	+	7.47244e22i	0.0423754	+	0.183131i
$895$	5.90562e23			1.43444
$896$		−	1.79266e22i		−	0.0431553i
$897$	9.56172e23	−	2.21252e23i	2.28137	−	0.527895i
$898$	3.02721e23			0.715865
$899$		−	7.36102e23i		−	1.72528i
$900$	−5.35570e22	+	2.61877e22i	−0.124416	+	0.0608354i
$901$	6.25534e22			0.144030
$902$			1.09019e23i			0.248801i
$903$	1.86127e22	+	8.04375e22i	0.0421025	+	0.181952i
$904$	−3.14735e23			−0.705662
$905$		−	4.67322e23i		−	1.03855i
$906$	−2.98954e23	+	6.91761e22i	−0.658536	+	0.152381i
$907$	3.84085e23			0.838628			0.419314	−	0.907841i	$-0.362271\pi$
$907$	3.84085e23			0.838628			0.419314	+	0.907841i	$0.362271\pi$
$908$		−	7.45591e22i		−	0.161367i
$909$	1.91762e23	+	3.92176e23i	0.411387	+	0.841337i
$910$	2.79366e23			0.594076
$911$			4.59314e23i			0.968194i	0.875014	+	0.484097i	$0.160852\pi$
$911$			4.59314e23i			0.968194i	−0.875014	+	0.484097i	$0.839148\pi$
$912$	4.25655e22	+	1.83953e23i	0.0889405	+	0.384369i
$913$	3.39153e23			0.702473
$914$		−	6.31677e22i		−	0.129696i
$915$	−6.48562e22	+	1.50073e22i	−0.132003	+	0.0305446i
$916$	−2.62376e23			−0.529371
$917$			1.77257e23i			0.354526i
$918$	4.56538e22	+	5.62056e22i	0.0905181	+	0.111439i
$919$	1.72165e23			0.338392			0.169196	−	0.985582i	$-0.445883\pi$
$919$	1.72165e23			0.338392			0.169196	+	0.985582i	$0.445883\pi$
$920$			3.15317e23i			0.614391i
$921$	−1.40302e23	−	6.06335e23i	−0.271011	−	1.17121i
$922$	−4.07845e22			−0.0780994
$923$		−	4.78439e22i		−	0.0908267i
$924$	−1.13746e23	+	2.63201e22i	−0.214072	+	0.0495349i
$925$	−1.79715e23			−0.335312
$926$			3.52684e22i			0.0652376i
$927$	−6.90907e23	+	3.37831e23i	−1.26701	+	0.619529i
$928$	−1.25118e23			−0.227476
$929$		−	6.33946e23i		−	1.14269i	−0.820712	−	0.571343i	$-0.806423\pi$
$929$		−	6.33946e23i		−	1.14269i	0.820712	−	0.571343i	$-0.193577\pi$
$930$	1.35150e23	+	5.84072e23i	0.241520	+	1.04376i
$931$	−6.78371e23			−1.20190
$932$			1.63283e23i			0.286822i
$933$	−1.21708e23	+	2.81624e22i	−0.211965	+	0.0490474i
$934$	2.22491e23			0.384183
$935$			1.20626e23i			0.206513i
$936$	−1.39321e23	−	2.84929e23i	−0.236488	−	0.483648i
$937$	5.47951e22			0.0922200			0.0461100	−	0.998936i	$-0.485318\pi$
$937$	5.47951e22			0.0922200			0.0461100	+	0.998936i	$0.485318\pi$
$938$		−	9.91286e22i		−	0.165415i
$939$	1.97861e23	+	8.55086e23i	0.327368	+	1.41477i
$940$	1.70217e23			0.279242
$941$		−	7.34763e23i		−	1.19517i	−0.801805	−	0.597586i	$-0.796127\pi$
$941$		−	7.34763e23i		−	1.19517i	0.801805	−	0.597586i	$-0.203873\pi$
$942$	−2.57045e22	+	5.94786e21i	−0.0414574	+	0.00959298i
$943$	−3.75907e23			−0.601155
$944$			1.53295e23i			0.243081i
$945$	2.72371e23	−	2.21238e23i	0.428260	−	0.347860i
$946$	1.56148e23			0.243448
$947$		−	2.01422e23i		−	0.311392i	−0.987805	−	0.155696i	$-0.950238\pi$
$947$		−	2.01422e23i		−	0.311392i	0.987805	−	0.155696i	$-0.0497620\pi$
$948$	−5.01922e22	−	2.16913e23i	−0.0769431	−	0.332521i
$949$	−1.76656e24			−2.68533
$950$		−	2.05053e23i		−	0.309084i
$951$	1.04182e24	−	2.41070e23i	1.55721	−	0.360329i
$952$	2.36465e22			0.0350486
$953$		−	1.12815e24i		−	1.65815i	−0.559135	−	0.829076i	$-0.688867\pi$
$953$		−	1.12815e24i		−	1.65815i	0.559135	−	0.829076i	$-0.311133\pi$
$954$	−3.09169e23	+	1.51174e23i	−0.450618	+	0.220338i
$955$	−4.49446e23			−0.649607
$956$		−	4.23325e23i		−	0.606751i
$957$	1.83699e23	+	7.93882e23i	0.261103	+	1.12839i
$958$	−1.78606e22			−0.0251751
$959$		−	2.98148e22i		−	0.0416757i
$960$	9.92766e22	−	2.29720e22i	0.137619	−	0.0318441i
$961$	5.80217e23			0.797633
$962$		−	9.56100e23i		−	1.30348i
$963$	1.37159e23	+	2.80508e23i	0.185445	+	0.379258i
$964$	1.02455e23			0.137378
$965$			1.24886e24i			1.66072i
$966$	−9.07534e22	−	3.92203e23i	−0.119687	−	0.517243i
$967$	1.30398e24			1.70552			0.852762	−	0.522300i	$-0.174926\pi$
$967$	1.30398e24			1.70552			0.852762	+	0.522300i	$0.174926\pi$
$968$		−	5.17507e22i		−	0.0671294i
$969$	−2.42647e23	+	5.61470e22i	−0.312166	+	0.0722332i
$970$	−4.15567e23			−0.530233
$971$			8.54524e23i			1.08136i	0.841228	+	0.540680i	$0.181833\pi$
$971$			8.54524e23i			1.08136i	−0.841228	+	0.540680i	$0.818167\pi$
$972$	−3.61476e23	−	1.67463e23i	−0.453679	−	0.210178i
$973$	−1.87745e23			−0.233704
$974$			8.89164e23i			1.09777i
$975$	7.76507e22	+	3.35578e23i	0.0950842	+	0.410920i
$976$	2.46805e22			0.0299748
$977$			1.37465e23i			0.165590i	0.996567	+	0.0827952i	$0.0263847\pi$
$977$			1.37465e23i			0.165590i	−0.996567	+	0.0827952i	$0.973615\pi$
$978$	−1.37747e23	+	3.18738e22i	−0.164578	+	0.0380823i
$979$	2.60936e23			0.309224
$980$			3.66107e23i			0.430327i
$981$	4.88081e23	−	2.38656e23i	0.569036	−	0.278241i
$982$	1.14111e24			1.31958
$983$			8.07871e23i			0.926646i	0.886189	+	0.463323i	$0.153343\pi$
$983$			8.07871e23i			0.926646i	−0.886189	+	0.463323i	$0.846657\pi$
$984$	2.73861e22	+	1.18353e23i	0.0311580	+	0.134654i
$985$	−1.63646e23			−0.184678
$986$		−	1.65039e23i		−	0.184745i
$987$	−2.11723e23	+	4.89913e22i	−0.235088	+	0.0543978i
$988$	1.09090e24			1.20152
$989$			5.38407e23i			0.588221i
$990$	−2.91518e23	−	5.96191e23i	−0.315925	−	0.646106i
$991$	2.15967e23			0.232165			0.116083	−	0.993240i	$-0.462966\pi$
$991$	2.15967e23			0.232165			0.116083	+	0.993240i	$0.462966\pi$
$992$		−	2.22264e23i		−	0.237015i
$993$	−2.70547e23	−	1.16921e24i	−0.286186	−	1.23679i
$994$	−1.96247e22			−0.0205926
$995$		−	5.50072e23i		−	0.572578i
$996$	3.68189e23	−	8.51966e22i	0.380186	−	0.0879726i
$997$	1.80908e23			0.185309			0.0926545	−	0.995698i	$-0.470465\pi$
$997$	1.80908e23			0.185309			0.0926545	+	0.995698i	$0.470465\pi$
$998$		−	1.14261e24i		−	1.16106i
$999$	−7.57162e23	−	9.32162e23i	−0.763247	−	0.939653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.17.b.a.5.5	yes	6
3.2	odd	2	inner	6.17.b.a.5.2	✓	6
4.3	odd	2		48.17.e.d.17.3		6
12.11	even	2		48.17.e.d.17.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.17.b.a.5.2	✓	6	3.2	odd	2	inner
6.17.b.a.5.5	yes	6	1.1	even	1	trivial
48.17.e.d.17.3		6	4.3	odd	2
48.17.e.d.17.4		6	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:	\( k \)	\(=\)	\( 17 \)
Character orbit:	\([\chi]\)	\(=\)	6.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+181.019i q^{2} +(1479.09 + 6392.11i) q^{3} -32768.0 q^{4} +441421. i q^{5} +(-1.15709e6 + 267744. i) q^{6} +2.81464e6 q^{7} -5.93164e6i q^{8} +(-3.86713e7 + 1.89090e7i) q^{9} +O(q^{10})\)	\(q+181.019i q^{2} +(1479.09 + 6392.11i) q^{3} -32768.0 q^{4} +441421. i q^{5} +(-1.15709e6 + 267744. i) q^{6} +2.81464e6 q^{7} -5.93164e6i q^{8} +(-3.86713e7 + 1.89090e7i) q^{9} -7.99057e7 q^{10} -1.92938e8i q^{11} +(-4.84669e7 - 2.09456e8i) q^{12} -1.24215e9 q^{13} +5.09504e8i q^{14} +(-2.82161e9 + 6.52903e8i) q^{15} +1.07374e9 q^{16} +1.41634e9i q^{17} +(-3.42290e9 - 7.00025e9i) q^{18} +2.68017e10 q^{19} -1.44645e10i q^{20} +(4.16311e9 + 1.79915e10i) q^{21} +3.49256e10 q^{22} +1.20426e11i q^{23} +(3.79157e10 - 8.77345e9i) q^{24} -4.22647e10 q^{25} -2.24852e11i q^{26} +(-1.78067e11 - 2.19223e11i) q^{27} -9.22301e10 q^{28} +6.43715e11i q^{29} +(-1.18188e11 - 5.10766e11i) q^{30} -1.14352e12 q^{31} +1.94368e11i q^{32} +(1.23328e12 - 2.85374e11i) q^{33} -2.56386e11 q^{34} +1.24244e12i q^{35} +(1.26718e12 - 6.19611e11i) q^{36} +4.25212e12 q^{37} +4.85163e12i q^{38} +(-1.83725e12 - 7.93992e12i) q^{39} +2.61835e12 q^{40} +3.12148e12i q^{41} +(-3.25681e12 + 7.53604e11i) q^{42} +4.47086e12 q^{43} +6.32221e12i q^{44} +(-8.34684e12 - 1.70703e13i) q^{45} -2.17994e13 q^{46} +1.17679e13i q^{47} +(1.58816e12 + 6.86347e12i) q^{48} -2.53107e13 q^{49} -7.65072e12i q^{50} +(-9.05342e12 + 2.09490e12i) q^{51} +4.07026e13 q^{52} -4.41654e13i q^{53} +(3.96836e13 - 3.22336e13i) q^{54} +8.51671e13 q^{55} -1.66954e13i q^{56} +(3.96422e13 + 1.71319e14i) q^{57} -1.16525e14 q^{58} +1.42767e14i q^{59} +(9.24585e13 - 2.13943e13i) q^{60} +2.29855e13 q^{61} -2.06999e14i q^{62} +(-1.08846e14 + 5.32221e13i) q^{63} -3.51844e13 q^{64} -5.48309e14i q^{65} +(5.16582e13 + 2.23248e14i) q^{66} -1.94559e14 q^{67} -4.64107e13i q^{68} +(-7.69774e14 + 1.78121e14i) q^{69} -2.24906e14 q^{70} +3.85172e13i q^{71} +(1.12162e14 + 2.29384e14i) q^{72} +1.42218e15 q^{73} +7.69717e14i q^{74} +(-6.25133e13 - 2.70160e14i) q^{75} -8.78239e14 q^{76} -5.43052e14i q^{77} +(1.43728e15 - 3.32577e14i) q^{78} +1.03560e15 q^{79} +4.73972e14i q^{80} +(1.13792e15 - 1.46247e15i) q^{81} -5.65048e14 q^{82} +1.75783e15i q^{83} +(-1.36417e14 - 5.89545e14i) q^{84} -6.25204e14 q^{85} +8.09313e14i q^{86} +(-4.11469e15 + 9.52114e14i) q^{87} -1.14444e15 q^{88} +1.35243e15i q^{89} +(3.09006e15 - 1.51094e15i) q^{90} -3.49619e15 q^{91} -3.94611e15i q^{92} +(-1.69137e15 - 7.30951e15i) q^{93} -2.13022e15 q^{94} +1.18308e16i q^{95} +(-1.24242e15 + 2.87488e14i) q^{96} +5.20071e15 q^{97} -4.58173e15i q^{98} +(3.64828e15 + 7.46118e15i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6006 q^{3} - 196608 q^{4} + 159744 q^{6} - 167892 q^{7} - 10215738 q^{9}+O(q^{10}) \) 6 * q + 6006 * q^3 - 196608 * q^4 + 159744 * q^6 - 167892 * q^7 - 10215738 * q^9	\( 6 q + 6006 q^{3} - 196608 q^{4} + 159744 q^{6} - 167892 q^{7} - 10215738 q^{9} + 39297024 q^{10} - 196804608 q^{12} + 1763152140 q^{13} - 8080218432 q^{15} + 6442450944 q^{16} - 12549169152 q^{18} + 60306979692 q^{19} - 155770661748 q^{21} + 94233305088 q^{22} - 5234491392 q^{24} - 75722441466 q^{25} + 330190979958 q^{27} + 5501485056 q^{28} + 987679531008 q^{30} - 2846203650132 q^{31} + 3282289396416 q^{33} - 1812957659136 q^{34} + 334749302784 q^{36} + 2483836081932 q^{37} - 8759076866580 q^{39} - 1287684882432 q^{40} - 3652917731328 q^{42} + 46155081190764 q^{43} - 46496752783488 q^{45} - 17111605395456 q^{46} + 6448893394944 q^{48} + 42155513811090 q^{49} - 3055668993792 q^{51} - 57774969323520 q^{52} + 240022278328320 q^{54} - 155561818958208 q^{55} + 27052692784332 q^{57} - 366644114104320 q^{58} + 264772597579776 q^{60} + 306036501898764 q^{61} - 801652315914324 q^{63} - 211106232532992 q^{64} + 11\!\cdots\!72 q^{66}+ \cdots - 28\!\cdots\!72 q^{99}+O(q^{100}) \) 6 * q + 6006 * q^3 - 196608 * q^4 + 159744 * q^6 - 167892 * q^7 - 10215738 * q^9 + 39297024 * q^10 - 196804608 * q^12 + 1763152140 * q^13 - 8080218432 * q^15 + 6442450944 * q^16 - 12549169152 * q^18 + 60306979692 * q^19 - 155770661748 * q^21 + 94233305088 * q^22 - 5234491392 * q^24 - 75722441466 * q^25 + 330190979958 * q^27 + 5501485056 * q^28 + 987679531008 * q^30 - 2846203650132 * q^31 + 3282289396416 * q^33 - 1812957659136 * q^34 + 334749302784 * q^36 + 2483836081932 * q^37 - 8759076866580 * q^39 - 1287684882432 * q^40 - 3652917731328 * q^42 + 46155081190764 * q^43 - 46496752783488 * q^45 - 17111605395456 * q^46 + 6448893394944 * q^48 + 42155513811090 * q^49 - 3055668993792 * q^51 - 57774969323520 * q^52 + 240022278328320 * q^54 - 155561818958208 * q^55 + 27052692784332 * q^57 - 366644114104320 * q^58 + 264772597579776 * q^60 + 306036501898764 * q^61 - 801652315914324 * q^63 - 211106232532992 * q^64 + 1157574327017472 * q^66 + 1979846570008812 * q^67 - 2345782552693632 * q^69 - 2197723307360256 * q^70 + 411211174772736 * q^72 + 3864207384753420 * q^73 - 3376263465802122 * q^75 - 1976139110547456 * q^76 + 5837442492456960 * q^78 + 1835806484101548 * q^79 - 703356001465338 * q^81 - 9913023387353088 * q^82 + 5104293044158464 * q^84 + 2872972366990848 * q^85 - 3000080900606400 * q^87 - 3087836941123584 * q^88 + 12789804912058368 * q^90 - 1824281133603240 * q^91 - 11156835457641972 * q^93 - 4579876939530240 * q^94 + 171523813933056 * q^96 + 31097493125645196 * q^97 - 28794216850745472 * q^99

Introduction

L-functions

Modular forms

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