LMFDB - Embedded newform 5.20.b.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,20,Mod(4,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	5.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:	$11.4408348278$
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} + 726881x^{6} + 160513523376x^{4} + 10607307647230976x^{2} + 32429098232548950016 $ x^8 + 726881x^6 + 160513523376x^4 + 10607307647230976*x^2 + 32429098232548950016
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{8}\cdot 5^{13} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.3
Root			$-337.134i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.20.b.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-674.268i q^{2} +35433.1i q^{3} +69650.8 q^{4} +(-4.08230e6 + 1.55186e6i) q^{5} +2.38914e7 q^{6} -1.27830e8i q^{7} -4.00474e8i q^{8} -9.32466e7 q^{9} +O(q^{10})$	\(q-674.268i q^{2} +35433.1i q^{3} +69650.8 q^{4} +(-4.08230e6 + 1.55186e6i) q^{5} +2.38914e7 q^{6} -1.27830e8i q^{7} -4.00474e8i q^{8} -9.32466e7 q^{9} +(1.04637e9 + 2.75257e9i) q^{10} -1.50733e10 q^{11} +2.46795e9i q^{12} -2.83651e10i q^{13} -8.61916e10 q^{14} +(-5.49874e10 - 1.44649e11i) q^{15} -2.33510e11 q^{16} -2.72251e10i q^{17} +6.28732e10i q^{18} -5.36515e11 q^{19} +(-2.84336e11 + 1.08088e11i) q^{20} +4.52942e12 q^{21} +1.01634e13i q^{22} -1.00292e13i q^{23} +1.41901e13 q^{24} +(1.42569e13 - 1.26704e13i) q^{25} -1.91257e13 q^{26} +3.78786e13i q^{27} -8.90346e12i q^{28} -6.42276e13 q^{29} +(-9.75321e13 + 3.70762e13i) q^{30} -4.84548e12 q^{31} -5.25156e13i q^{32} -5.34095e14i q^{33} -1.83570e13 q^{34} +(1.98374e14 + 5.21841e14i) q^{35} -6.49470e12 q^{36} +3.59619e14i q^{37} +3.61755e14i q^{38} +1.00507e15 q^{39} +(6.21480e14 + 1.63486e15i) q^{40} +5.83658e14 q^{41} -3.05404e15i q^{42} -2.07276e15i q^{43} -1.04987e15 q^{44} +(3.80661e14 - 1.44706e14i) q^{45} -6.76236e15 q^{46} +1.09231e16i q^{47} -8.27398e15i q^{48} -4.94159e15 q^{49} +(-8.54321e15 - 9.61299e15i) q^{50} +9.64672e14 q^{51} -1.97565e15i q^{52} +3.14868e16i q^{53} +2.55403e16 q^{54} +(6.15338e16 - 2.33917e16i) q^{55} -5.11925e16 q^{56} -1.90104e16i q^{57} +4.33066e16i q^{58} +6.14646e16 q^{59} +(-3.82991e15 - 1.00749e16i) q^{60} +8.81781e15 q^{61} +3.26715e15i q^{62} +1.19197e16i q^{63} -1.57836e17 q^{64} +(4.40188e16 + 1.15795e17i) q^{65} -3.60123e17 q^{66} -2.91146e17i q^{67} -1.89625e15i q^{68} +3.55366e17 q^{69} +(3.51860e17 - 1.33758e17i) q^{70} -6.11399e17 q^{71} +3.73428e16i q^{72} -2.01992e17i q^{73} +2.42479e17 q^{74} +(4.48950e17 + 5.05168e17i) q^{75} -3.73687e16 q^{76} +1.92682e18i q^{77} -6.77684e17i q^{78} +7.58063e17 q^{79} +(9.53257e17 - 3.62375e17i) q^{80} -1.45053e18 q^{81} -3.93542e17i q^{82} -2.69045e18i q^{83} +3.15477e17 q^{84} +(4.22497e16 + 1.11141e17i) q^{85} -1.39760e18 q^{86} -2.27579e18i q^{87} +6.03646e18i q^{88} -3.94127e18 q^{89} +(-9.75705e16 - 2.56667e17i) q^{90} -3.62591e18 q^{91} -6.98541e17i q^{92} -1.71691e17i q^{93} +7.36509e18 q^{94} +(2.19022e18 - 8.32598e17i) q^{95} +1.86079e18 q^{96} -4.27223e18i q^{97} +3.33196e18i q^{98} +1.40553e18 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 1620744 q^{4} + 147000 q^{5} + 3365736 q^{6} + 345358584 q^{9}+O(q^{10}) $ 8 * q - 1620744 * q^4 + 147000 * q^5 + 3365736 * q^6 + 345358584 * q^9	$ 8 q - 1620744 q^{4} + 147000 q^{5} + 3365736 q^{6} + 345358584 q^{9} - 610691000 q^{10} - 3379575264 q^{11} + 177250591032 q^{14} - 242324628000 q^{15} - 312730276832 q^{16} + 4547188380640 q^{19} - 4180429431000 q^{20} - 2983154334624 q^{21} - 6176642779680 q^{24} + 17715709625000 q^{25} + 15909228128496 q^{26} - 188222300345040 q^{29} + 148501482939000 q^{30} + 72115006686976 q^{31} + 378440221985792 q^{34} - 299115755916000 q^{35} - 964020253238712 q^{36} + 30\!\cdots\!28 q^{39}+ \cdots - 16\!\cdots\!72 q^{99}+O(q^{100}) $ 8 * q - 1620744 * q^4 + 147000 * q^5 + 3365736 * q^6 + 345358584 * q^9 - 610691000 * q^10 - 3379575264 * q^11 + 177250591032 * q^14 - 242324628000 * q^15 - 312730276832 * q^16 + 4547188380640 * q^19 - 4180429431000 * q^20 - 2983154334624 * q^21 - 6176642779680 * q^24 + 17715709625000 * q^25 + 15909228128496 * q^26 - 188222300345040 * q^29 + 148501482939000 * q^30 + 72115006686976 * q^31 + 378440221985792 * q^34 - 299115755916000 * q^35 - 964020253238712 * q^36 + 3011653788049728 * q^39 - 213611427940000 * q^40 - 3314269428857904 * q^41 + 489119304867552 * q^44 + 10198157211261000 * q^45 - 13716870314831944 * q^46 - 11129258011816744 * q^49 + 50375043666750000 * q^50 - 46867071411404544 * q^51 + 86068650834185040 * q^54 + 69821226326124000 * q^55 - 303831778832907360 * q^56 + 259648032778012320 * q^59 + 318110620655844000 * q^60 - 582893562753226064 * q^61 + 525415747276109696 * q^64 + 747545324689032000 * q^65 - 1871067587999976288 * q^66 + 302144302523815008 * q^69 + 2638361065839633000 * q^70 - 2617007600602926144 * q^71 + 1847591013622215312 * q^74 + 2877932428209000000 * q^75 - 7494494299858276320 * q^76 + 3935092091109861760 * q^79 + 5465139505859292000 * q^80 - 8328177293660704152 * q^81 + 7683875738824129632 * q^84 + 3752387009219584000 * q^85 - 14358563079146095224 * q^86 + 2120141101636921680 * q^89 + 7589596726146267000 * q^90 - 3358638219973817664 * q^91 - 10251771654977709928 * q^94 + 6106065789884820000 * q^95 + 15670161523483353216 * q^96 - 16256944625235082272 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	674.268i		−	0.931210i	−0.884993	−	0.465605i	$-0.845837\pi$
$2$		−	674.268i		−	0.931210i	0.884993	−	0.465605i	$-0.154163\pi$
$3$			35433.1i			1.03934i	0.854367	+	0.519670i	$0.173945\pi$
$3$			35433.1i			1.03934i	−0.854367	+	0.519670i	$0.826055\pi$
$4$	69650.8			0.132848
$5$	−4.08230e6	+	1.55186e6i	−0.934739	+	0.355335i
$5$	−4.08230e6	+	1.55186e6i	−0.934739	+	0.355335i
$6$	2.38914e7			0.967844
$7$		−	1.27830e8i		−	1.19729i	−0.801013	−	0.598647i	$-0.795705\pi$
$7$		−	1.27830e8i		−	1.19729i	0.801013	−	0.598647i	$-0.204295\pi$
$8$		−	4.00474e8i		−	1.05492i
$9$	−9.32466e7			−0.0802286
$10$	1.04637e9	+	2.75257e9i	0.330892	+	0.870438i
$11$	−1.50733e10			−1.92743			−0.963713	−	0.266939i	$-0.913988\pi$
$11$	−1.50733e10			−1.92743			−0.963713	+	0.266939i	$0.913988\pi$
$12$			2.46795e9i			0.138075i
$13$		−	2.83651e10i		−	0.741862i	−0.928660	−	0.370931i	$-0.879039\pi$
$13$		−	2.83651e10i		−	0.741862i	0.928660	−	0.370931i	$-0.120961\pi$
$14$	−8.61916e10			−1.11493
$15$	−5.49874e10	−	1.44649e11i	−0.369314	−	0.971512i
$16$	−2.33510e11			−0.849503
$17$		−	2.72251e10i		−	0.0556808i	−0.999612	−	0.0278404i	$-0.991137\pi$
$17$		−	2.72251e10i		−	0.0556808i	0.999612	−	0.0278404i	$-0.00886302\pi$
$18$			6.28732e10i			0.0747096i
$19$	−5.36515e11			−0.381437			−0.190718	−	0.981645i	$-0.561082\pi$
$19$	−5.36515e11			−0.381437			−0.190718	+	0.981645i	$0.561082\pi$
$20$	−2.84336e11	+	1.08088e11i	−0.124179	+	0.0472057i
$21$	4.52942e12			1.24440
$22$			1.01634e13i			1.79484i
$23$		−	1.00292e13i		−	1.16105i	−0.814242	−	0.580525i	$-0.802847\pi$
$23$		−	1.00292e13i		−	1.16105i	0.814242	−	0.580525i	$-0.197153\pi$
$24$	1.41901e13			1.09642
$25$	1.42569e13	−	1.26704e13i	0.747474	−	0.664291i
$26$	−1.91257e13			−0.690829
$27$			3.78786e13i			0.955956i
$28$		−	8.90346e12i		−	0.159059i
$29$	−6.42276e13			−0.822130			−0.411065	−	0.911606i	$-0.634843\pi$
$29$	−6.42276e13			−0.822130			−0.411065	+	0.911606i	$0.634843\pi$
$30$	−9.75321e13	+	3.70762e13i	−0.904681	+	0.343909i
$31$	−4.84548e12			−0.0329155			−0.0164578	−	0.999865i	$-0.505239\pi$
$31$	−4.84548e12			−0.0329155			−0.0164578	+	0.999865i	$0.505239\pi$
$32$		−	5.25156e13i		−	0.263854i
$33$		−	5.34095e14i		−	2.00325i
$34$	−1.83570e13			−0.0518505
$35$	1.98374e14	+	5.21841e14i	0.425441	+	1.11916i
$36$	−6.49470e12			−0.0106582
$37$			3.59619e14i			0.454911i	0.973789	+	0.227455i	$0.0730406\pi$
$37$			3.59619e14i			0.454911i	−0.973789	+	0.227455i	$0.926959\pi$
$38$			3.61755e14i			0.355198i
$39$	1.00507e15			0.771047
$40$	6.21480e14	+	1.63486e15i	0.374850	+	0.986074i
$41$	5.83658e14			0.278427			0.139214	−	0.990262i	$-0.455543\pi$
$41$	5.83658e14			0.278427			0.139214	+	0.990262i	$0.455543\pi$
$42$		−	3.05404e15i		−	1.15879i
$43$		−	2.07276e15i		−	0.628926i	−0.949270	−	0.314463i	$-0.898176\pi$
$43$		−	2.07276e15i		−	0.628926i	0.949270	−	0.314463i	$-0.101824\pi$
$44$	−1.04987e15			−0.256055
$45$	3.80661e14	−	1.44706e14i	0.0749928	−	0.0285080i
$46$	−6.76236e15			−1.08118
$47$			1.09231e16i			1.42369i	0.702336	+	0.711845i	$0.252140\pi$
$47$			1.09231e16i			1.42369i	−0.702336	+	0.711845i	$0.747860\pi$
$48$		−	8.27398e15i		−	0.882923i
$49$	−4.94159e15			−0.433515
$50$	−8.54321e15	−	9.61299e15i	−0.618595	−	0.696055i
$51$	9.64672e14			0.0578713
$52$		−	1.97565e15i		−	0.0985551i
$53$			3.14868e16i			1.31071i	0.755320	+	0.655356i	$0.227482\pi$
$53$			3.14868e16i			1.31071i	−0.755320	+	0.655356i	$0.772518\pi$
$54$	2.55403e16			0.890195
$55$	6.15338e16	−	2.33917e16i	1.80164	−	0.684883i
$56$	−5.11925e16			−1.26305
$57$		−	1.90104e16i		−	0.396443i
$58$			4.33066e16i			0.765576i
$59$	6.14646e16			0.923700			0.461850	−	0.886958i	$-0.347186\pi$
$59$	6.14646e16			0.923700			0.461850	+	0.886958i	$0.347186\pi$
$60$	−3.82991e15	−	1.00749e16i	−0.0490628	−	0.129064i
$61$	8.81781e15			0.0965444			0.0482722	−	0.998834i	$-0.484629\pi$
$61$	8.81781e15			0.0965444			0.0482722	+	0.998834i	$0.484629\pi$
$62$			3.26715e15i			0.0306513i
$63$			1.19197e16i			0.0960573i
$64$	−1.57836e17			−1.09521
$65$	4.40188e16	+	1.15795e17i	0.263610	+	0.693447i
$66$	−3.60123e17			−1.86545
$67$		−	2.91146e17i		−	1.30738i	−0.756764	−	0.653688i	$-0.773221\pi$
$67$		−	2.91146e17i		−	1.30738i	0.756764	−	0.653688i	$-0.226779\pi$
$68$		−	1.89625e15i		−	0.00739710i
$69$	3.55366e17			1.20673
$70$	3.51860e17	−	1.33758e17i	1.04217	−	0.396175i
$71$	−6.11399e17			−1.58260			−0.791298	−	0.611430i	$-0.790594\pi$
$71$	−6.11399e17			−1.58260			−0.791298	+	0.611430i	$0.790594\pi$
$72$			3.73428e16i			0.0846347i
$73$		−	2.01992e17i		−	0.401574i	−0.979635	−	0.200787i	$-0.935650\pi$
$73$		−	2.01992e17i		−	0.401574i	0.979635	−	0.200787i	$-0.0643500\pi$
$74$	2.42479e17			0.423617
$75$	4.48950e17	+	5.05168e17i	0.690425	+	0.776880i
$76$	−3.73687e16			−0.0506733
$77$			1.92682e18i			2.30770i
$78$		−	6.77684e17i		−	0.718007i
$79$	7.58063e17			0.711620			0.355810	−	0.934558i	$-0.384205\pi$
$79$	7.58063e17			0.711620			0.355810	+	0.934558i	$0.384205\pi$
$80$	9.53257e17	−	3.62375e17i	0.794064	−	0.301858i
$81$	−1.45053e18			−1.07379
$82$		−	3.93542e17i		−	0.259274i
$83$		−	2.69045e18i		−	1.57973i	−0.613280	−	0.789866i	$-0.710150\pi$
$83$		−	2.69045e18i		−	1.57973i	0.613280	−	0.789866i	$-0.289850\pi$
$84$	3.15477e17			0.165316
$85$	4.22497e16	+	1.11141e17i	0.0197853	+	0.0520470i
$86$	−1.39760e18			−0.585662
$87$		−	2.27579e18i		−	0.854473i
$88$			6.03646e18i			2.03328i
$89$	−3.94127e18			−1.19242			−0.596212	−	0.802827i	$-0.703328\pi$
$89$	−3.94127e18			−1.19242			−0.596212	+	0.802827i	$0.703328\pi$
$90$	−9.75705e16	−	2.56667e17i	−0.0265470	−	0.0698340i
$91$	−3.62591e18			−0.888227
$92$		−	6.98541e17i		−	0.154244i
$93$		−	1.71691e17i		−	0.0342104i
$94$	7.36509e18			1.32575
$95$	2.19022e18	−	8.32598e17i	0.356544	−	0.135538i
$96$	1.86079e18			0.274234
$97$		−	4.27223e18i		−	0.570589i	−0.958440	−	0.285294i	$-0.907909\pi$
$97$		−	4.27223e18i		−	0.570589i	0.958440	−	0.285294i	$-0.0920913\pi$
$98$			3.33196e18i			0.403693i
$99$	1.40553e18			0.154635
$100$	9.93007e17	−	8.82500e17i	0.0993007	−	0.0882500i
$101$	1.40351e19			1.27692			0.638459	−	0.769656i	$-0.279572\pi$
$101$	1.40351e19			1.27692			0.638459	+	0.769656i	$0.279572\pi$
$102$		−	6.50448e17i		−	0.0538903i
$103$			7.95142e18i			0.600470i	0.953865	+	0.300235i	$0.0970651\pi$
$103$			7.95142e18i			0.600470i	−0.953865	+	0.300235i	$0.902935\pi$
$104$	−1.13595e19			−0.782605
$105$	−1.84905e19	+	7.02903e18i	−1.16319	+	0.442178i
$106$	2.12305e19			1.22055
$107$			3.61790e18i			0.190244i	0.995466	+	0.0951218i	$0.0303241\pi$
$107$			3.61790e18i			0.190244i	−0.995466	+	0.0951218i	$0.969676\pi$
$108$			2.63827e18i			0.126997i
$109$	−1.30814e19			−0.576902			−0.288451	−	0.957495i	$-0.593140\pi$
$109$	−1.30814e19			−0.576902			−0.288451	+	0.957495i	$0.593140\pi$
$110$	−1.57723e19	−	4.14903e19i	−0.637769	−	1.67771i
$111$	−1.27424e19			−0.472807
$112$			2.98495e19i			1.01711i
$113$		−	4.59431e19i		−	1.43872i	−0.694640	−	0.719358i	$-0.744436\pi$
$113$		−	4.59431e19i		−	1.43872i	0.694640	−	0.719358i	$-0.255564\pi$
$114$	−1.28181e19			−0.369171
$115$	1.55639e19	+	4.09422e19i	0.412562	+	1.08528i
$116$	−4.47350e18			−0.109219
$117$			2.64495e18i			0.0595185i
$118$		−	4.14436e19i		−	0.860159i
$119$	−3.48019e18			−0.0666663
$120$	−5.79281e19	+	2.20210e19i	−1.02487	+	0.389597i
$121$	1.66045e20			2.71497
$122$		−	5.94556e18i		−	0.0899031i
$123$			2.06808e19i			0.289381i
$124$	−3.37492e17			−0.00437277
$125$	−3.85385e19	+	7.38490e19i	−0.462647	+	0.886543i
$126$	8.03707e18			0.0894495
$127$		−	4.56134e19i		−	0.470930i	−0.971883	−	0.235465i	$-0.924339\pi$
$127$		−	4.56134e19i		−	0.470930i	0.971883	−	0.235465i	$-0.0756614\pi$
$128$			7.88904e19i			0.756013i
$129$	7.34446e19			0.653668
$130$	7.80769e19	−	2.96805e19i	0.645745	−	0.245476i
$131$	−6.43442e19			−0.494803			−0.247401	−	0.968913i	$-0.579577\pi$
$131$	−6.43442e19			−0.494803			−0.247401	+	0.968913i	$0.579577\pi$
$132$		−	3.72001e19i		−	0.266129i
$133$			6.85827e19i			0.456692i
$134$	−1.96311e20			−1.21744
$135$	−5.87823e19	−	1.54632e20i	−0.339685	−	0.893569i
$136$	−1.09030e19			−0.0587387
$137$		−	1.73092e20i		−	0.869823i	−0.900473	−	0.434912i	$-0.856780\pi$
$137$		−	1.73092e20i		−	0.869823i	0.900473	−	0.434912i	$-0.143220\pi$
$138$		−	2.39612e20i		−	1.12372i
$139$	1.19143e20			0.521709			0.260854	−	0.965378i	$-0.415996\pi$
$139$	1.19143e20			0.521709			0.260854	+	0.965378i	$0.415996\pi$
$140$	1.38169e19	+	3.63466e19i	0.0565191	+	0.148678i
$141$	−3.87039e20			−1.47970
$142$			4.12247e20i			1.47373i
$143$			4.27556e20i			1.42988i
$144$	2.17740e19			0.0681544
$145$	2.62197e20	−	9.96724e19i	0.768477	−	0.292132i
$146$	−1.36196e20			−0.373950
$147$		−	1.75096e20i		−	0.450570i
$148$			2.50477e19i			0.0604341i
$149$	1.97170e19			0.0446244			0.0223122	−	0.999751i	$-0.492897\pi$
$149$	1.97170e19			0.0446244			0.0223122	+	0.999751i	$0.492897\pi$
$150$	3.40619e20	−	3.02713e20i	0.723438	−	0.642930i
$151$	3.67901e19			0.0733585			0.0366792	−	0.999327i	$-0.488322\pi$
$151$	3.67901e19			0.0733585			0.0366792	+	0.999327i	$0.488322\pi$
$152$			2.14860e20i			0.402385i
$153$			2.53865e18i			0.00446719i
$154$	1.29919e21			2.14895
$155$	1.97807e19	−	7.51952e18i	0.0307674	−	0.0116960i
$156$	7.00037e19			0.102432
$157$		−	2.62677e20i		−	0.361722i	−0.983509	−	0.180861i	$-0.942112\pi$
$157$		−	2.62677e20i		−	0.361722i	0.983509	−	0.180861i	$-0.0578884\pi$
$158$		−	5.11138e20i		−	0.662667i
$159$	−1.11568e21			−1.36228
$160$	8.14970e19	+	2.14385e20i	0.0937566	+	0.246635i
$161$	−1.28203e21			−1.39012
$162$			9.78048e20i			0.999926i
$163$			3.18599e20i			0.307229i	0.988131	+	0.153615i	$0.0490914\pi$
$163$			3.18599e20i			0.307229i	−0.988131	+	0.153615i	$0.950909\pi$
$164$	4.06522e19			0.0369886
$165$	8.28841e20	+	2.18034e21i	0.711826	+	1.87252i
$166$	−1.81409e21			−1.47106
$167$		−	2.42404e21i		−	1.85666i	−0.371756	−	0.928330i	$-0.621244\pi$
$167$		−	2.42404e21i		−	1.85666i	0.371756	−	0.928330i	$-0.378756\pi$
$168$		−	1.81391e21i		−	1.31274i
$169$	6.57339e20			0.449641
$170$	7.49390e19	−	2.84876e19i	0.0484667	−	0.0184243i
$171$	5.00282e19			0.0306021
$172$		−	1.44370e20i		−	0.0835518i
$173$		−	5.57493e20i		−	0.305352i	−0.988276	−	0.152676i	$-0.951211\pi$
$173$		−	5.57493e20i		−	0.305352i	0.988276	−	0.152676i	$-0.0487891\pi$
$174$	−1.53449e21			−0.795694
$175$	−1.61965e21	−	1.82246e21i	−0.795353	−	0.894947i
$176$	3.51976e21			1.63735
$177$			2.17788e21i			0.960039i
$178$			2.65747e21i			1.11040i
$179$	2.36718e21			0.937836			0.468918	−	0.883242i	$-0.344644\pi$
$179$	2.36718e21			0.937836			0.468918	+	0.883242i	$0.344644\pi$
$180$	2.65133e19	−	1.00789e19i	0.00996267	−	0.00378725i
$181$	3.36524e21			1.19969			0.599845	−	0.800116i	$-0.295229\pi$
$181$	3.36524e21			1.19969			0.599845	+	0.800116i	$0.295229\pi$
$182$			2.44484e21i			0.827126i
$183$			3.12443e20i			0.100343i
$184$	−4.01643e21			−1.22481
$185$	−5.58079e20	−	1.46807e21i	−0.161646	−	0.425223i
$186$	−1.15765e20			−0.0318571
$187$			4.10373e20i			0.107321i
$188$			7.60802e20i			0.189135i
$189$	4.84201e21			1.14456
$190$	−5.61394e20	−	1.47679e21i	−0.126214	−	0.332017i
$191$	2.48413e20			0.0531322			0.0265661	−	0.999647i	$-0.491543\pi$
$191$	2.48413e20			0.0531322			0.0265661	+	0.999647i	$0.491543\pi$
$192$		−	5.59262e21i		−	1.13829i
$193$		−	4.27907e20i		−	0.0829002i	−0.999141	−	0.0414501i	$-0.986802\pi$
$193$		−	4.27907e20i		−	0.0829002i	0.999141	−	0.0414501i	$-0.0131978\pi$
$194$	−2.88063e21			−0.531338
$195$	−4.10299e21	+	1.55972e21i	−0.720728	+	0.273980i
$196$	−3.44186e20			−0.0575917
$197$			4.26831e21i			0.680498i	0.940335	+	0.340249i	$0.110511\pi$
$197$			4.26831e21i			0.680498i	−0.940335	+	0.340249i	$0.889489\pi$
$198$		−	9.47706e20i		−	0.143997i
$199$	−1.12036e22			−1.62276			−0.811381	−	0.584517i	$-0.801284\pi$
$199$	−1.12036e22			−1.62276			−0.811381	+	0.584517i	$0.801284\pi$
$200$	−5.07414e21	−	5.70953e21i	−0.700774	−	0.788525i
$201$	1.03162e22			1.35881
$202$		−	9.46343e21i		−	1.18908i
$203$			8.21021e21i			0.984332i
$204$	6.71902e19			0.00768810
$205$	−2.38267e21	+	9.05756e20i	−0.260257	+	0.0989349i
$206$	5.36139e21			0.559164
$207$			9.35187e20i			0.0931494i
$208$			6.62353e21i			0.630214i
$209$	8.08705e21			0.735192
$210$	4.73945e21	+	1.24675e22i	0.411761	+	1.08317i
$211$	−9.61089e21			−0.798142			−0.399071	−	0.916920i	$-0.630667\pi$
$211$	−9.61089e21			−0.798142			−0.399071	+	0.916920i	$0.630667\pi$
$212$			2.19308e21i			0.174126i
$213$		−	2.16638e22i		−	1.64486i
$214$	2.43943e21			0.177157
$215$	3.21665e21	+	8.46165e21i	0.223480	+	0.587882i
$216$	1.51694e22			1.00846
$217$			6.19397e20i			0.0394096i
$218$			8.82035e21i			0.537216i
$219$	7.15720e21			0.417373
$220$	4.28588e21	−	1.62925e21i	0.239345	−	0.0909855i
$221$	−7.72245e20			−0.0413074
$222$			8.59181e21i			0.440283i
$223$		−	3.73694e22i		−	1.83493i	−0.397813	−	0.917467i	$-0.630231\pi$
$223$		−	3.73694e22i		−	1.83493i	0.397813	−	0.917467i	$-0.369769\pi$
$224$	−6.71307e21			−0.315911
$225$	−1.32941e21	+	1.18147e21i	−0.0599688	+	0.0532951i
$226$	−3.09779e22			−1.33975
$227$			4.61966e21i			0.191586i	0.995401	+	0.0957931i	$0.0305387\pi$
$227$			4.61966e21i			0.191586i	−0.995401	+	0.0957931i	$0.969461\pi$
$228$		−	1.32409e21i		−	0.0526668i
$229$	6.78401e21			0.258851			0.129425	−	0.991589i	$-0.458687\pi$
$229$	6.78401e21			0.258851			0.129425	+	0.991589i	$0.458687\pi$
$230$	2.76060e22	−	1.04942e22i	1.01062	−	0.384182i
$231$	−6.82733e22			−2.39848
$232$			2.57215e22i			0.867281i
$233$			3.45140e22i			1.11716i	0.829452	+	0.558578i	$0.188653\pi$
$233$			3.45140e22i			1.11716i	−0.829452	+	0.558578i	$0.811347\pi$
$234$	1.78341e21			0.0554242
$235$	−1.69511e22	−	4.45914e22i	−0.505887	−	1.33078i
$236$	4.28106e21			0.122712
$237$			2.68606e22i			0.739615i
$238$			2.34658e21i			0.0620803i
$239$	−8.55663e21			−0.217532			−0.108766	−	0.994067i	$-0.534690\pi$
$239$	−8.55663e21			−0.217532			−0.108766	+	0.994067i	$0.534690\pi$
$240$	1.28401e22	+	3.37769e22i	0.313734	+	0.825302i
$241$	3.62819e22			0.852173			0.426087	−	0.904682i	$-0.359892\pi$
$241$	3.62819e22			0.852173			0.426087	+	0.904682i	$0.359892\pi$
$242$		−	1.11959e23i		−	2.52821i
$243$		−	7.37218e21i		−	0.160080i
$244$	6.14167e20			0.0128258
$245$	2.01731e22	−	7.66867e21i	0.405223	−	0.154043i
$246$	1.39444e22			0.269474
$247$			1.52183e22i			0.282973i
$248$			1.94049e21i			0.0347232i
$249$	9.53312e22			1.64188
$250$	4.97940e22	+	2.59853e22i	0.825557	+	0.430821i
$251$	−7.85908e22			−1.25450			−0.627251	−	0.778817i	$-0.715820\pi$
$251$	−7.85908e22			−1.25450			−0.627251	+	0.778817i	$0.715820\pi$
$252$			8.30217e20i			0.0127610i
$253$			1.51173e23i			2.23784i
$254$	−3.07556e22			−0.438535
$255$	−3.93809e21	+	1.49704e21i	−0.0540945	+	0.0205637i
$256$	−2.95582e22			−0.391200
$257$		−	5.05378e21i		−	0.0644543i	−0.999481	−	0.0322271i	$-0.989740\pi$
$257$		−	5.05378e21i		−	0.0644543i	0.999481	−	0.0322271i	$-0.0102600\pi$
$258$		−	4.95213e22i		−	0.608702i
$259$	4.59701e22			0.544662
$260$	3.06594e21	+	8.06522e21i	0.0350201	+	0.0921233i
$261$	5.98900e21			0.0659583
$262$			4.33852e22i			0.460765i
$263$		−	3.61033e22i		−	0.369800i	−0.982757	−	0.184900i	$-0.940804\pi$
$263$		−	3.61033e22i		−	0.369800i	0.982757	−	0.184900i	$-0.0591962\pi$
$264$	−2.13891e23			−2.11327
$265$	−4.88632e22	−	1.28539e23i	−0.465742	−	1.22517i
$266$	4.62431e22			0.425276
$267$		−	1.39651e23i		−	1.23933i
$268$		−	2.02786e22i		−	0.173683i
$269$	1.18177e23			0.976982			0.488491	−	0.872569i	$-0.337548\pi$
$269$	1.18177e23			0.976982			0.488491	+	0.872569i	$0.337548\pi$
$270$	−1.04263e23	+	3.96350e22i	−0.832100	+	0.316318i
$271$	1.74152e23			1.34190			0.670951	−	0.741502i	$-0.265886\pi$
$271$	1.74152e23			1.34190			0.670951	+	0.741502i	$0.265886\pi$
$272$			6.35733e21i			0.0473010i
$273$		−	1.28478e23i		−	0.923171i
$274$	−1.16710e23			−0.809988
$275$	−2.14899e23	+	1.90984e23i	−1.44070	+	1.28037i
$276$	2.47515e22			0.160312
$277$			2.52452e23i			1.57987i	0.613191	+	0.789935i	$0.289886\pi$
$277$			2.52452e23i			1.57987i	−0.613191	+	0.789935i	$0.710114\pi$
$278$		−	8.03344e22i		−	0.485821i
$279$	4.51825e20			0.00264077
$280$	2.08984e23	−	7.94438e22i	1.18062	−	0.448806i
$281$	−1.42048e22			−0.0775758			−0.0387879	−	0.999247i	$-0.512350\pi$
$281$	−1.42048e22			−0.0775758			−0.0387879	+	0.999247i	$0.512350\pi$
$282$			2.60968e23i			1.37791i
$283$		−	1.12989e23i		−	0.576855i	−0.957502	−	0.288428i	$-0.906868\pi$
$283$		−	1.12989e23i		−	0.576855i	0.957502	−	0.288428i	$-0.0931324\pi$
$284$	−4.25844e22			−0.210245
$285$	2.95016e22	+	7.76063e22i	0.140870	+	0.370570i
$286$	2.88287e23			1.33152
$287$		−	7.46089e22i		−	0.333359i
$288$			4.89690e21i			0.0211686i
$289$	2.38331e23			0.996900
$290$	−6.72059e22	−	1.76791e23i	−0.272036	−	0.715614i
$291$	1.51379e23			0.593036
$292$		−	1.40689e22i		−	0.0533485i
$293$			1.87783e23i			0.689310i	0.938729	+	0.344655i	$0.112004\pi$
$293$			1.87783e23i			0.689310i	−0.938729	+	0.344655i	$0.887996\pi$
$294$	−1.18062e23			−0.419575
$295$	−2.50917e23	+	9.53846e22i	−0.863419	+	0.328223i
$296$	1.44018e23			0.479894
$297$		−	5.70955e23i		−	1.84253i
$298$		−	1.32946e22i		−	0.0415547i
$299$	−2.84479e23			−0.861339
$300$	3.12698e22	+	3.51854e22i	0.0917218	+	0.103207i
$301$	−2.64961e23			−0.753010
$302$		−	2.48064e22i		−	0.0683121i
$303$			4.97308e23i			1.32715i
$304$	1.25281e23			0.324032
$305$	−3.59970e22	+	1.36840e22i	−0.0902438	+	0.0343056i
$306$	1.71173e21			0.00415989
$307$		−	6.11797e22i		−	0.144143i	−0.997399	−	0.0720713i	$-0.977039\pi$
$307$		−	6.11797e22i		−	0.144143i	0.997399	−	0.0720713i	$-0.0229609\pi$
$308$			1.34204e23i			0.306574i
$309$	−2.81744e23			−0.624093
$310$	−5.07017e21	−	1.33375e22i	−0.0108915	−	0.0286509i
$311$	−4.82214e23			−1.00465			−0.502326	−	0.864678i	$-0.667522\pi$
$311$	−4.82214e23			−1.00465			−0.502326	+	0.864678i	$0.667522\pi$
$312$		−	4.02503e23i		−	0.813393i
$313$		−	6.94366e23i		−	1.36119i	−0.732662	−	0.680593i	$-0.761722\pi$
$313$		−	6.94366e23i		−	1.36119i	0.732662	−	0.680593i	$-0.238278\pi$
$314$	−1.77115e23			−0.336839
$315$	−1.84977e22	−	4.86599e22i	−0.0341325	−	0.0897885i
$316$	5.27997e22			0.0945375
$317$			4.13628e23i			0.718700i	0.933203	+	0.359350i	$0.117001\pi$
$317$			4.13628e23i			0.718700i	−0.933203	+	0.359350i	$0.882999\pi$
$318$			7.52264e23i			1.26857i
$319$	9.68122e23			1.58460
$320$	6.44334e23	−	2.44940e23i	1.02373	−	0.389165i
$321$	−1.28193e23			−0.197728
$322$			8.64431e23i			1.29449i
$323$			1.46067e22i			0.0212387i
$324$	−1.01031e23			−0.142651
$325$	−3.59396e23	−	4.04400e23i	−0.492812	−	0.554522i
$326$	2.14821e23			0.286095
$327$		−	4.63514e23i		−	0.599597i
$328$		−	2.33740e23i		−	0.293718i
$329$	1.39630e24			1.70458
$330$	1.47013e24	−	5.58861e23i	1.74371	−	0.662859i
$331$	−1.18945e24			−1.37082			−0.685408	−	0.728160i	$-0.740376\pi$
$331$	−1.18945e24			−1.37082			−0.685408	+	0.728160i	$0.740376\pi$
$332$		−	1.87392e23i		−	0.209865i
$333$		−	3.35332e22i		−	0.0364968i
$334$	−1.63445e24			−1.72894
$335$	4.51819e23	+	1.18855e24i	0.464557	+	1.22206i
$336$	−1.05766e24			−1.05712
$337$			1.48032e24i			1.43838i	0.694815	+	0.719189i	$0.255486\pi$
$337$			1.48032e24i			1.43838i	−0.694815	+	0.719189i	$0.744514\pi$
$338$		−	4.43223e23i		−	0.418710i
$339$	1.62791e24			1.49531
$340$	2.94272e21	+	7.74108e21i	0.00262845	+	0.00691436i
$341$	7.30374e22			0.0634423
$342$		−	3.37324e22i		−	0.0284970i
$343$		−	8.25437e23i		−	0.678250i
$344$	−8.30088e23			−0.663466
$345$	−1.45071e24	+	5.51479e23i	−1.12797	+	0.428793i
$346$	−3.75899e23			−0.284347
$347$		−	1.67749e24i		−	1.23461i	−0.786725	−	0.617304i	$-0.788225\pi$
$347$		−	1.67749e24i		−	1.23461i	0.786725	−	0.617304i	$-0.211775\pi$
$348$		−	1.58510e23i		−	0.113515i
$349$	−2.36999e24			−1.65160			−0.825799	−	0.563965i	$-0.809275\pi$
$349$	−2.36999e24			−1.65160			−0.825799	+	0.563965i	$0.809275\pi$
$350$	−1.22883e24	+	1.09208e24i	−0.833383	+	0.740640i
$351$	1.07443e24			0.709187
$352$			7.91584e23i			0.508559i
$353$		−	1.84396e24i		−	1.15317i	−0.817038	−	0.576583i	$-0.804386\pi$
$353$		−	1.84396e24i		−	1.15317i	0.817038	−	0.576583i	$-0.195614\pi$
$354$	1.46848e24			0.893998
$355$	2.49592e24	−	9.48807e23i	1.47931	−	0.562352i
$356$	−2.74512e23			−0.158412
$357$		−	1.23314e23i		−	0.0692890i
$358$		−	1.59611e24i		−	0.873322i
$359$	1.62533e24			0.866050			0.433025	−	0.901382i	$-0.357446\pi$
$359$	1.62533e24			0.866050			0.433025	+	0.901382i	$0.357446\pi$
$360$	−5.79509e22	−	1.52445e23i	−0.0300737	−	0.0791113i
$361$	−1.69057e24			−0.854506
$362$		−	2.26907e24i		−	1.11716i
$363$			5.88351e24i			2.82178i
$364$	−2.52548e23			−0.118000
$365$	3.13463e23	+	8.24591e23i	0.142694	+	0.375367i
$366$	2.10670e23			0.0934399
$367$			4.40988e23i			0.190590i	0.995449	+	0.0952948i	$0.0303794\pi$
$367$			4.40988e23i			0.190590i	−0.995449	+	0.0952948i	$0.969621\pi$
$368$			2.34191e24i			0.986316i
$369$	−5.44241e22			−0.0223378
$370$	−9.89875e23	+	3.76295e23i	−0.395972	+	0.150526i
$371$	4.02495e24			1.56931
$372$		−	1.19584e22i		−	0.00454480i
$373$			8.16387e23i			0.302456i	0.988499	+	0.151228i	$0.0483228\pi$
$373$			8.16387e23i			0.302456i	−0.988499	+	0.151228i	$0.951677\pi$
$374$	2.76701e23			0.0999380
$375$	−2.61670e24	−	1.36554e24i	−0.921420	−	0.480848i
$376$	4.37441e24			1.50188
$377$			1.82182e24i			0.609907i
$378$		−	3.26481e24i		−	1.06583i
$379$	−1.58257e24			−0.503837			−0.251919	−	0.967748i	$-0.581062\pi$
$379$	−1.58257e24			−0.503837			−0.251919	+	0.967748i	$0.581062\pi$
$380$	1.52550e23	−	5.79911e22i	0.0473663	−	0.0180060i
$381$	1.61622e24			0.489457
$382$		−	1.67497e23i		−	0.0494772i
$383$		−	1.29938e24i		−	0.374411i	−0.982321	−	0.187206i	$-0.940057\pi$
$383$		−	1.29938e24i		−	0.374411i	0.982321	−	0.187206i	$-0.0599431\pi$
$384$	−2.79533e24			−0.785755
$385$	−2.99016e24	−	7.86586e24i	−0.820006	−	2.15710i
$386$	−2.88524e23			−0.0771974
$387$			1.93278e23i			0.0504578i
$388$		−	2.97564e23i		−	0.0758018i
$389$	−3.59072e24			−0.892608			−0.446304	−	0.894882i	$-0.647260\pi$
$389$	−3.59072e24			−0.892608			−0.446304	+	0.894882i	$0.647260\pi$
$390$	1.05167e24	+	2.76651e24i	0.255133	+	0.671149i
$391$	−2.73046e23			−0.0646482
$392$			1.97898e24i			0.457323i
$393$		−	2.27992e24i		−	0.514269i
$394$	2.87798e24			0.633686
$395$	−3.09464e24	+	1.17641e24i	−0.665179	+	0.252864i
$396$	9.78966e22			0.0205430
$397$			4.10642e24i			0.841305i	0.907222	+	0.420652i	$0.138199\pi$
$397$			4.10642e24i			0.841305i	−0.907222	+	0.420652i	$0.861801\pi$
$398$			7.55426e24i			1.51113i
$399$	−2.43010e24			−0.474659
$400$	−3.32913e24	+	2.95865e24i	−0.634981	+	0.564317i
$401$	−5.10194e24			−0.950307			−0.475153	−	0.879903i	$-0.657607\pi$
$401$	−5.10194e24			−0.950307			−0.475153	+	0.879903i	$0.657607\pi$
$402$		−	6.95590e24i		−	1.26534i
$403$			1.37443e23i			0.0244188i
$404$	9.77557e23			0.169636
$405$	5.92152e24	−	2.25103e24i	1.00372	−	0.381556i
$406$	5.53588e24			0.916620
$407$		−	5.42064e24i		−	0.876807i
$408$		−	3.86326e23i		−	0.0610495i
$409$	4.30020e24			0.663922			0.331961	−	0.943293i	$-0.392290\pi$
$409$	4.30020e24			0.663922			0.331961	+	0.943293i	$0.392290\pi$
$410$	6.10722e23	+	1.60656e24i	0.0921292	+	0.242354i
$411$	6.13319e24			0.904043
$412$			5.53823e23i			0.0797714i
$413$		−	7.85702e24i		−	1.10594i
$414$	6.30567e23			0.0867417
$415$	4.17521e24	+	1.09832e25i	0.561334	+	1.47664i
$416$	−1.48961e24			−0.195743
$417$			4.22162e24i			0.542233i
$418$		−	5.45284e24i		−	0.684618i
$419$	1.78598e24			0.219202			0.109601	−	0.993976i	$-0.465043\pi$
$419$	1.78598e24			0.219202			0.109601	+	0.993976i	$0.465043\pi$
$420$	−1.28787e24	+	4.89578e23i	−0.154527	+	0.0587426i
$421$	−3.16819e24			−0.371647			−0.185824	−	0.982583i	$-0.559495\pi$
$421$	−3.16819e24			−0.371647			−0.185824	+	0.982583i	$0.559495\pi$
$422$			6.48031e24i			0.743237i
$423$		−	1.01854e24i		−	0.114221i
$424$	1.26096e25			1.38270
$425$	−3.44952e23	−	3.88147e23i	−0.0369883	−	0.0416199i
$426$	−1.46072e25			−1.53171
$427$		−	1.12718e24i		−	0.115592i
$428$			2.51989e23i			0.0252736i
$429$	−1.51497e25			−1.48614
$430$	5.70542e24	−	2.16888e24i	0.547441	−	0.208106i
$431$	−4.64035e24			−0.435529			−0.217764	−	0.976001i	$-0.569876\pi$
$431$	−4.64035e24			−0.435529			−0.217764	+	0.976001i	$0.569876\pi$
$432$		−	8.84501e24i		−	0.812087i
$433$			7.27039e24i			0.653015i	0.945195	+	0.326507i	$0.105872\pi$
$433$			7.27039e24i			0.653015i	−0.945195	+	0.326507i	$0.894128\pi$
$434$	4.17640e23			0.0366986
$435$	3.53171e24	+	9.29045e24i	0.303624	+	0.798709i
$436$	−9.11128e23			−0.0766404
$437$			5.38081e24i			0.442867i
$438$		−	4.82587e24i		−	0.388661i
$439$	−8.02562e24			−0.632507			−0.316254	−	0.948675i	$-0.602425\pi$
$439$	−8.02562e24			−0.632507			−0.316254	+	0.948675i	$0.602425\pi$
$440$	−9.36776e24	−	2.46427e25i	−0.722496	−	1.90059i
$441$	4.60787e23			0.0347803
$442$			5.20700e23i			0.0384659i
$443$		−	2.01059e24i		−	0.145375i	−0.997355	−	0.0726873i	$-0.976842\pi$
$443$		−	2.01059e24i		−	0.145375i	0.997355	−	0.0726873i	$-0.0231575\pi$
$444$	−8.87520e23			−0.0628116
$445$	1.60894e25	−	6.11630e24i	1.11460	−	0.423710i
$446$	−2.51970e25			−1.70871
$447$			6.98637e23i			0.0463799i
$448$			2.01761e25i			1.31128i
$449$	2.71710e25			1.72888			0.864441	−	0.502734i	$-0.167673\pi$
$449$	2.71710e25			1.72888			0.864441	+	0.502734i	$0.167673\pi$
$450$	7.96625e23	+	8.96379e23i	0.0496290	+	0.0558435i
$451$	−8.79765e24			−0.536648
$452$		−	3.19997e24i		−	0.191131i
$453$			1.30359e24i			0.0762444i
$454$	3.11489e24			0.178407
$455$	1.48021e25	−	5.62692e24i	0.830261	−	0.315618i
$456$	−7.61317e24			−0.418215
$457$		−	6.05088e24i		−	0.325548i	−0.986663	−	0.162774i	$-0.947956\pi$
$457$		−	6.05088e24i		−	0.325548i	0.986663	−	0.162774i	$-0.0520441\pi$
$458$		−	4.57424e24i		−	0.241044i
$459$	1.03125e24			0.0532284
$460$	1.08404e24	+	2.85166e24i	0.0548082	+	0.144178i
$461$	2.52577e25			1.25094			0.625469	−	0.780249i	$-0.284908\pi$
$461$	2.52577e25			1.25094			0.625469	+	0.780249i	$0.284908\pi$
$462$			4.60345e25i			2.23349i
$463$		−	1.70798e24i		−	0.0811827i	−0.999176	−	0.0405913i	$-0.987076\pi$
$463$		−	1.70798e24i		−	0.0811827i	0.999176	−	0.0405913i	$-0.0129242\pi$
$464$	1.49978e25			0.698402
$465$	2.66440e23	+	7.00893e23i	0.0121562	+	0.0319778i
$466$	2.32717e25			1.04031
$467$		−	2.49486e25i		−	1.09279i	−0.837528	−	0.546395i	$-0.816000\pi$
$467$		−	2.49486e25i		−	1.09279i	0.837528	−	0.546395i	$-0.184000\pi$
$468$			1.84223e23i			0.00790694i
$469$	−3.72172e25			−1.56531
$470$	−3.00665e25	+	1.14296e25i	−1.23923	+	0.471087i
$471$	9.30747e24			0.375952
$472$		−	2.46150e25i		−	0.974429i
$473$			3.12434e25i			1.21221i
$474$	1.81112e25			0.688737
$475$	−7.64906e24	+	6.79783e24i	−0.285114	+	0.253385i
$476$	−2.42398e23			−0.00885651
$477$		−	2.93604e24i		−	0.105157i
$478$			5.76946e24i			0.202568i
$479$	−3.57303e25			−1.22984			−0.614922	−	0.788588i	$-0.710812\pi$
$479$	−3.57303e25			−1.22984			−0.614922	+	0.788588i	$0.710812\pi$
$480$	−7.59633e24	+	2.88770e24i	−0.256337	+	0.0974450i
$481$	1.02006e25			0.337481
$482$		−	2.44637e25i		−	0.793552i
$483$		−	4.54263e25i		−	1.44481i
$484$	1.15652e25			0.360680
$485$	6.62991e24	+	1.74405e25i	0.202750	+	0.533351i
$486$	−4.97083e24			−0.149068
$487$		−	2.88849e25i		−	0.849466i	−0.905319	−	0.424733i	$-0.860368\pi$
$487$		−	2.88849e25i		−	0.849466i	0.905319	−	0.424733i	$-0.139632\pi$
$488$		−	3.53130e24i		−	0.101847i
$489$	−1.12890e25			−0.319316
$490$	−5.17074e24	−	1.36021e25i	−0.143446	−	0.377348i
$491$	−3.62846e25			−0.987299			−0.493650	−	0.869661i	$-0.664337\pi$
$491$	−3.62846e25			−0.987299			−0.493650	+	0.869661i	$0.664337\pi$
$492$			1.44044e24i			0.0384437i
$493$			1.74860e24i			0.0457769i
$494$	1.02612e25			0.263508
$495$	−5.73782e24	+	2.18120e24i	−0.144543	+	0.0549472i
$496$	1.13147e24			0.0279618
$497$			7.81550e25i			1.89483i
$498$		−	6.42787e25i		−	1.52893i
$499$	−6.25615e25			−1.46000			−0.729999	−	0.683448i	$-0.760479\pi$
$499$	−6.25615e25			−1.46000			−0.729999	+	0.683448i	$0.760479\pi$
$500$	−2.68424e24	+	5.14364e24i	−0.0614619	+	0.117776i
$501$	8.58912e25			1.92970
$502$			5.29913e25i			1.16820i
$503$			2.34853e25i			0.508043i	0.967199	+	0.254022i	$0.0817534\pi$
$503$			2.34853e25i			0.508043i	−0.967199	+	0.254022i	$0.918247\pi$
$504$	4.77353e24			0.101333
$505$	−5.72956e25	+	2.17806e25i	−1.19359	+	0.453734i
$506$	1.01931e26			2.08390
$507$			2.32916e25i			0.467330i
$508$		−	3.17701e24i		−	0.0625623i
$509$	6.15824e25			1.19025			0.595124	−	0.803634i	$-0.297103\pi$
$509$	6.15824e25			1.19025			0.595124	+	0.803634i	$0.297103\pi$
$510$	1.00941e24	+	2.65532e24i	0.0191491	+	0.0503734i
$511$	−2.58206e25			−0.480803
$512$			6.12914e25i			1.12030i
$513$		−	2.03224e25i		−	0.364637i
$514$	−3.40760e24			−0.0600205
$515$	−1.23395e25	−	3.24601e25i	−0.213368	−	0.561283i
$516$	5.11547e24			0.0868387
$517$		−	1.64647e26i		−	2.74406i
$518$		−	3.09961e25i		−	0.507195i
$519$	1.97537e25			0.317365
$520$	4.63729e25	−	1.76284e25i	0.731531	−	0.278087i
$521$	−6.52311e24			−0.101041			−0.0505203	−	0.998723i	$-0.516088\pi$
$521$	−6.52311e24			−0.101041			−0.0505203	+	0.998723i	$0.516088\pi$
$522$		−	4.03819e24i		−	0.0614211i
$523$			8.50107e25i			1.26972i	0.772628	+	0.634859i	$0.218942\pi$
$523$			8.50107e25i			1.26972i	−0.772628	+	0.634859i	$0.781058\pi$
$524$	−4.48163e24			−0.0657338
$525$	6.45756e25	−	5.73893e25i	0.930154	−	0.826642i
$526$	−2.43433e25			−0.344362
$527$			1.31919e23i			0.00183276i
$528$			1.24716e26i			1.70177i
$529$	−2.59691e25			−0.348039
$530$	−8.66695e25	+	3.29469e25i	−1.14089	+	0.433704i
$531$	−5.73137e24			−0.0741072
$532$			4.77684e24i			0.0606708i
$533$		−	1.65555e25i		−	0.206554i
$534$	−9.41625e25			−1.15408
$535$	−5.61448e24	−	1.47694e25i	−0.0676003	−	0.177828i
$536$	−1.16596e26			−1.37918
$537$			8.38765e25i			0.974731i
$538$		−	7.96830e25i		−	0.909775i
$539$	7.44861e25			0.835568
$540$	−4.09424e24	−	1.07702e25i	−0.0451265	−	0.118709i
$541$	−7.41271e25			−0.802792			−0.401396	−	0.915905i	$-0.631475\pi$
$541$	−7.41271e25			−0.802792			−0.401396	+	0.915905i	$0.631475\pi$
$542$		−	1.17425e26i		−	1.24959i
$543$			1.19241e26i			1.24689i
$544$	−1.42974e24			−0.0146916
$545$	5.34022e25	−	2.03005e25i	0.539252	−	0.204993i
$546$	−8.66283e25			−0.859666
$547$		−	4.10864e25i		−	0.400699i	−0.979725	−	0.200349i	$-0.935792\pi$
$547$		−	4.10864e25i		−	0.400699i	0.979725	−	0.200349i	$-0.0642077\pi$
$548$		−	1.20560e25i		−	0.115555i
$549$	−8.22230e23			−0.00774562
$550$	1.28774e26	+	1.44900e26i	1.19230	+	1.34159i
$551$	3.44591e25			0.313591
$552$		−	1.42315e26i		−	1.27300i
$553$		−	9.69031e25i		−	0.852019i
$554$	1.70220e26			1.47119
$555$	5.20185e25	−	1.97745e25i	0.441951	−	0.168005i
$556$	8.29841e24			0.0693082
$557$			7.43502e25i			0.610461i	0.952279	+	0.305230i	$0.0987335\pi$
$557$			7.43502e25i			0.610461i	−0.952279	+	0.305230i	$0.901266\pi$
$558$		−	3.04651e23i		−	0.00245911i
$559$	−5.87942e25			−0.466576
$560$	−4.63223e25	−	1.21855e26i	−0.361413	−	0.950728i
$561$	−1.45408e25			−0.111543
$562$			9.57787e24i			0.0722394i
$563$		−	7.54386e25i		−	0.559453i	−0.960080	−	0.279727i	$-0.909756\pi$
$563$		−	7.54386e25i		−	0.559453i	0.960080	−	0.279727i	$-0.0902439\pi$
$564$	−2.69576e25			−0.196576
$565$	7.12973e25	+	1.87554e26i	0.511226	+	1.34482i
$566$	−7.61852e25			−0.537173
$567$			1.85422e26i			1.28565i
$568$			2.44849e26i			1.66951i
$569$	1.89497e26			1.27068			0.635340	−	0.772233i	$-0.280860\pi$
$569$	1.89497e26			1.27068			0.635340	+	0.772233i	$0.280860\pi$
$570$	5.23274e25	−	1.98919e25i	0.345079	−	0.131180i
$571$	1.30455e26			0.846095			0.423047	−	0.906108i	$-0.360960\pi$
$571$	1.30455e26			0.846095			0.423047	+	0.906108i	$0.360960\pi$
$572$			2.97796e25i			0.189958i
$573$			8.80206e24i			0.0552224i
$574$	−5.03064e25			−0.310427
$575$	−1.27073e26	−	1.42985e26i	−0.771276	−	0.867855i
$576$	1.47177e25			0.0878669
$577$			1.53787e26i			0.903126i	0.892239	+	0.451563i	$0.149133\pi$
$577$			1.53787e26i			0.903126i	−0.892239	+	0.451563i	$0.850867\pi$
$578$		−	1.60699e26i		−	0.928323i
$579$	1.51621e25			0.0861615
$580$	1.82622e25	−	6.94226e24i	0.102091	−	0.0388092i
$581$	−3.43920e26			−1.89140
$582$		−	1.02070e26i		−	0.552241i
$583$		−	4.74610e26i		−	2.52630i
$584$	−8.08923e25			−0.423629
$585$	−4.10460e24	−	1.07975e25i	−0.0211490	−	0.0556343i
$586$	1.26616e26			0.641893
$587$			2.87389e26i			1.43353i	0.697313	+	0.716767i	$0.254379\pi$
$587$			2.87389e26i			1.43353i	−0.697313	+	0.716767i	$0.745621\pi$
$588$		−	1.21956e25i		−	0.0598574i
$589$	2.59967e24			0.0125552
$590$	6.43148e25	+	1.69185e26i	0.305645	+	0.804024i
$591$	−1.51240e26			−0.707269
$592$		−	8.39745e25i		−	0.386448i
$593$		−	1.93537e25i		−	0.0876487i	−0.999039	−	0.0438244i	$-0.986046\pi$
$593$		−	1.93537e25i		−	0.0876487i	0.999039	−	0.0438244i	$-0.0139542\pi$
$594$	−3.84977e26			−1.71579
$595$	1.42072e25	−	5.40077e24i	0.0623156	−	0.0236889i
$596$	1.37331e24			0.00592827
$597$		−	3.96980e26i		−	1.68660i
$598$			1.91815e26i			0.802088i
$599$	3.65000e26			1.50223			0.751117	−	0.660169i	$-0.229515\pi$
$599$	3.65000e26			1.50223			0.751117	+	0.660169i	$0.229515\pi$
$600$	2.02307e26	−	1.79793e26i	0.819546	−	0.728343i
$601$	−4.33211e25			−0.172740			−0.0863699	−	0.996263i	$-0.527527\pi$
$601$	−4.33211e25			−0.172740			−0.0863699	+	0.996263i	$0.527527\pi$
$602$			1.78655e26i			0.701210i
$603$			2.71484e25i			0.104889i
$604$	2.56246e24			0.00974555
$605$	−6.77848e26	+	2.57680e26i	−2.53779	+	0.964726i
$606$	3.35319e26			1.23586
$607$		−	1.19334e26i		−	0.432983i	−0.976285	−	0.216491i	$-0.930539\pi$
$607$		−	1.19334e26i		−	0.432983i	0.976285	−	0.216491i	$-0.0694613\pi$
$608$			2.81754e25i			0.100644i
$609$	−2.90914e26			−1.02306
$610$	9.22670e24	+	2.42716e25i	0.0319457	+	0.0840359i
$611$	3.09835e26			1.05618
$612$			1.76819e23i			0.000593459i
$613$			4.30993e26i			1.42428i	0.702036	+	0.712141i	$0.252274\pi$
$613$			4.30993e26i			1.42428i	−0.702036	+	0.712141i	$0.747726\pi$
$614$	−4.12515e25			−0.134227
$615$	−3.20938e25	−	8.44254e25i	−0.102827	−	0.270495i
$616$	7.71641e26			2.43444
$617$		−	6.35860e26i		−	1.97539i	−0.156398	−	0.987694i	$-0.549988\pi$
$617$		−	6.35860e26i		−	1.97539i	0.156398	−	0.987694i	$-0.450012\pi$
$618$			1.89971e26i			0.581161i
$619$	2.23476e26			0.673239			0.336619	−	0.941641i	$-0.390716\pi$
$619$	2.23476e26			0.673239			0.336619	+	0.941641i	$0.390716\pi$
$620$	1.37774e24	−	5.23741e23i	0.00408740	−	0.00155380i
$621$	3.79891e26			1.10991
$622$			3.25141e26i			0.935542i
$623$			5.03812e26i			1.42768i
$624$	−2.34693e26			−0.655007
$625$	4.27223e25	−	3.61281e26i	0.117434	−	0.993081i
$626$	−4.68189e26			−1.26755
$627$			2.86550e26i			0.764114i
$628$		−	1.82957e25i		−	0.0480542i
$629$	9.79067e24			0.0253298
$630$	−3.28098e25	+	1.24724e25i	−0.0836119	+	0.0317845i
$631$	−3.45823e26			−0.868111			−0.434055	−	0.900886i	$-0.642918\pi$
$631$	−3.45823e26			−0.868111			−0.434055	+	0.900886i	$0.642918\pi$
$632$		−	3.03584e26i		−	0.750702i
$633$		−	3.40544e26i		−	0.829541i
$634$	2.78896e26			0.669260
$635$	7.07857e25	+	1.86208e26i	0.167338	+	0.440197i
$636$	−7.77077e25			−0.180976
$637$			1.40169e26i			0.321608i
$638$		−	6.52774e26i		−	1.47559i
$639$	5.70108e25			0.126969
$640$	−1.22427e26	−	3.22054e26i	−0.268638	−	0.706675i
$641$	2.52301e26			0.545465			0.272733	−	0.962090i	$-0.412073\pi$
$641$	2.52301e26			0.545465			0.272733	+	0.962090i	$0.412073\pi$
$642$			8.64367e25i			0.184126i
$643$		−	3.17517e26i		−	0.666443i	−0.942849	−	0.333222i	$-0.891864\pi$
$643$		−	3.17517e26i		−	0.666443i	0.942849	−	0.333222i	$-0.108136\pi$
$644$	−8.92944e25			−0.184675
$645$	−2.99823e26	+	1.13976e26i	−0.611009	+	0.232271i
$646$	9.84882e24			0.0197777
$647$		−	1.00120e25i		−	0.0198121i	−0.999951	−	0.00990603i	$-0.996847\pi$
$647$		−	1.00120e25i		−	0.0198121i	0.999951	−	0.00990603i	$-0.00315324\pi$
$648$			5.80901e26i			1.13276i
$649$	−9.26475e26			−1.78036
$650$	−2.72674e26	+	2.42329e26i	−0.516377	+	0.458912i
$651$	−2.19472e25			−0.0409600
$652$			2.21907e25i			0.0408149i
$653$			4.02906e26i			0.730345i	0.930940	+	0.365173i	$0.118990\pi$
$653$			4.02906e26i			0.730345i	−0.930940	+	0.365173i	$0.881010\pi$
$654$	−3.12533e26			−0.558351
$655$	2.62673e26	−	9.98534e25i	0.462512	−	0.175821i
$656$	−1.36290e26			−0.236525
$657$			1.88350e25i			0.0322177i
$658$		−	9.41478e26i		−	1.58732i
$659$	1.10397e27			1.83462			0.917311	−	0.398172i	$-0.130355\pi$
$659$	1.10397e27			1.83462			0.917311	+	0.398172i	$0.130355\pi$
$660$	5.77295e25	+	1.51862e26i	0.0945649	+	0.248761i
$661$	−2.08247e26			−0.336252			−0.168126	−	0.985766i	$-0.553772\pi$
$661$	−2.08247e26			−0.336252			−0.168126	+	0.985766i	$0.553772\pi$
$662$			8.02005e26i			1.27652i
$663$		−	2.73631e25i		−	0.0429325i
$664$	−1.07746e27			−1.66649
$665$	−1.06431e26	−	2.79975e26i	−0.162279	−	0.426888i
$666$	−2.26104e25			−0.0339862
$667$			6.44150e26i			0.954535i
$668$		−	1.68836e26i		−	0.246654i
$669$	1.32412e27			1.90712
$670$	8.01399e26	−	3.04647e26i	1.13799	−	0.432600i
$671$	−1.32913e26			−0.186082
$672$		−	2.37865e26i		−	0.328339i
$673$			5.36141e26i			0.729686i	0.931069	+	0.364843i	$0.118877\pi$
$673$			5.36141e26i			0.729686i	−0.931069	+	0.364843i	$0.881123\pi$
$674$	9.98135e26			1.33943
$675$	4.79935e26	+	5.40032e26i	0.635033	+	0.714552i
$676$	4.57842e25			0.0597341
$677$		−	1.21119e27i		−	1.55819i	−0.626908	−	0.779093i	$-0.715680\pi$
$677$		−	1.21119e27i		−	1.55819i	0.626908	−	0.779093i	$-0.284320\pi$
$678$		−	1.09765e27i		−	1.39245i
$679$	−5.46119e26			−0.683163
$680$	4.45092e25	−	1.69199e25i	0.0549054	−	0.0208719i
$681$	−1.63689e26			−0.199123
$682$		−	4.92468e25i		−	0.0590781i
$683$		−	8.03801e25i		−	0.0950937i	−0.998869	−	0.0475469i	$-0.984860\pi$
$683$		−	8.03801e25i		−	0.0950937i	0.998869	−	0.0475469i	$-0.0151403\pi$
$684$	3.48450e24			0.00406544
$685$	2.68615e26	+	7.06613e26i	0.309079	+	0.813058i
$686$	−5.56565e26			−0.631593
$687$			2.40379e26i			0.269034i
$688$			4.84010e26i			0.534275i
$689$	8.93127e26			0.972368
$690$	3.71844e26	+	9.78167e26i	0.399296	+	1.05038i
$691$	−2.01363e26			−0.213274			−0.106637	−	0.994298i	$-0.534008\pi$
$691$	−2.01363e26			−0.213274			−0.106637	+	0.994298i	$0.534008\pi$
$692$		−	3.88298e25i		−	0.0405656i
$693$		−	1.79669e26i		−	0.185143i
$694$	−1.13108e27			−1.14968
$695$	−4.86378e26	+	1.84894e26i	−0.487662	+	0.185382i
$696$	−9.11393e26			−0.901400
$697$		−	1.58902e25i		−	0.0155030i
$698$			1.59801e27i			1.53798i
$699$	−1.22294e27			−1.16111
$700$	−1.12810e26	−	1.26936e26i	−0.105661	−	0.118892i
$701$	−1.12215e27			−1.03688			−0.518440	−	0.855114i	$-0.673487\pi$
$701$	−1.12215e27			−1.03688			−0.518440	+	0.855114i	$0.673487\pi$
$702$		−	7.24454e26i		−	0.660402i
$703$		−	1.92941e26i		−	0.173520i
$704$	2.37911e27			2.11093
$705$	1.58001e27	−	6.00632e26i	1.38313	−	0.525789i
$706$	−1.24332e27			−1.07384
$707$		−	1.79411e27i		−	1.52885i
$708$			1.51691e26i			0.127540i
$709$	−4.93589e26			−0.409474			−0.204737	−	0.978817i	$-0.565634\pi$
$709$	−4.93589e26			−0.409474			−0.204737	+	0.978817i	$0.565634\pi$
$710$	−6.39750e26	−	1.68292e27i	−0.523668	−	1.37755i
$711$	−7.06868e25			−0.0570922
$712$			1.57837e27i			1.25791i
$713$			4.85962e25i			0.0382166i
$714$	−8.31467e25			−0.0645226
$715$	−6.63509e26	−	1.74542e27i	−0.508088	−	1.33657i
$716$	1.64876e26			0.124590
$717$		−	3.03188e26i		−	0.226089i
$718$		−	1.09590e27i		−	0.806474i
$719$	−5.64392e26			−0.409880			−0.204940	−	0.978775i	$-0.565700\pi$
$719$	−5.64392e26			−0.409880			−0.204940	+	0.978775i	$0.565700\pi$
$720$	−8.88880e25	+	3.37902e25i	−0.0637066	+	0.0242177i
$721$	1.01643e27			0.718940
$722$			1.13990e27i			0.795724i
$723$			1.28558e27i			0.885698i
$724$	2.34392e26			0.159377
$725$	−9.15688e26	+	8.13786e26i	−0.614521	+	0.546134i
$726$	3.96706e27			2.62767
$727$		−	1.71223e26i		−	0.111940i	−0.998432	−	0.0559700i	$-0.982175\pi$
$727$		−	1.71223e26i		−	0.111940i	0.998432	−	0.0559700i	$-0.0178251\pi$
$728$			1.45208e27i			0.937008i
$729$	−1.42468e27			−0.907415
$730$	5.55995e26	−	2.11358e26i	0.349546	−	0.132878i
$731$	−5.64313e25			−0.0350191
$732$			2.17619e25i			0.0133303i
$733$			1.17936e26i			0.0713114i	0.999364	+	0.0356557i	$0.0113520\pi$
$733$			1.17936e26i			0.0713114i	−0.999364	+	0.0356557i	$0.988648\pi$
$734$	2.97344e26			0.177479
$735$	2.71725e26	+	7.14796e26i	0.160103	+	0.421165i
$736$	−5.26689e26			−0.306348
$737$			4.38853e27i			2.51987i
$738$			3.66964e25i			0.0208012i
$739$	1.72358e27			0.964513			0.482256	−	0.876030i	$-0.339817\pi$
$739$	1.72358e27			0.964513			0.482256	+	0.876030i	$0.339817\pi$
$740$	−3.88707e25	−	1.02253e26i	−0.0214744	−	0.0564901i
$741$	−5.39233e26			−0.294106
$742$		−	2.71390e27i		−	1.46136i
$743$		−	2.40878e27i		−	1.28057i	−0.768138	−	0.640284i	$-0.778817\pi$
$743$		−	2.40878e27i		−	1.28057i	0.768138	−	0.640284i	$-0.221183\pi$
$744$	−6.87576e25			−0.0360893
$745$	−8.04909e25	+	3.05981e25i	−0.0417121	+	0.0158566i
$746$	5.50464e26			0.281650
$747$			2.50875e26i			0.126740i
$748$			2.85828e25i			0.0142574i
$749$	4.62475e26			0.227778
$750$	−9.20740e26	+	1.76436e27i	−0.447770	+	0.858035i
$751$	6.12281e26			0.294016			0.147008	−	0.989135i	$-0.453036\pi$
$751$	6.12281e26			0.294016			0.147008	+	0.989135i	$0.453036\pi$
$752$		−	2.55065e27i		−	1.20943i
$753$		−	2.78472e27i		−	1.30385i
$754$	1.22840e27			0.567952
$755$	−1.50188e26	+	5.70932e25i	−0.0685710	+	0.0260668i
$756$	3.37250e26			0.152053
$757$			1.57835e27i			0.702737i	0.936237	+	0.351369i	$0.114284\pi$
$757$			1.57835e27i			0.702737i	−0.936237	+	0.351369i	$0.885716\pi$
$758$			1.06708e27i			0.469178i
$759$	−5.35653e27			−2.32588
$760$	−3.33434e26	−	8.77125e26i	−0.142982	−	0.376125i
$761$	2.78294e27			1.17855			0.589276	−	0.807931i	$-0.299413\pi$
$761$	2.78294e27			1.17855			0.589276	+	0.807931i	$0.299413\pi$
$762$		−	1.08977e27i		−	0.455787i
$763$			1.67219e27i			0.690721i
$764$	1.73022e25			0.00705852
$765$	−3.93964e24	−	1.03635e25i	−0.00158735	−	0.00417566i
$766$	−8.76133e26			−0.348655
$767$		−	1.74345e27i		−	0.685258i
$768$		−	1.04734e27i		−	0.406590i
$769$	−2.07413e27			−0.795307			−0.397653	−	0.917536i	$-0.630175\pi$
$769$	−2.07413e27			−0.795307			−0.397653	+	0.917536i	$0.630175\pi$
$770$	−5.30370e27	+	2.01617e27i	−2.00871	+	0.763598i
$771$	1.79071e26			0.0669899
$772$		−	2.98041e25i		−	0.0110131i
$773$		−	1.84235e27i		−	0.672462i	−0.941780	−	0.336231i	$-0.890848\pi$
$773$		−	1.84235e27i		−	0.672462i	0.941780	−	0.336231i	$-0.109152\pi$
$774$	1.30321e26			0.0469868
$775$	−6.90817e25	+	6.13939e25i	−0.0246035	+	0.0218655i
$776$	−1.71092e27			−0.601925
$777$			1.62886e27i			0.566089i
$778$			2.42111e27i			0.831205i
$779$	−3.13141e26			−0.106202
$780$	−2.85776e26	+	1.08636e26i	−0.0957475	+	0.0363978i
$781$	9.21580e27			3.05034
$782$			1.84106e26i			0.0602010i
$783$		−	2.43285e27i		−	0.785920i
$784$	1.15391e27			0.368272
$785$	4.07638e26	+	1.07233e27i	0.128533	+	0.338116i
$786$	−1.53728e27			−0.478892
$787$			2.38921e26i			0.0735351i	0.999324	+	0.0367676i	$0.0117061\pi$
$787$			2.38921e26i			0.0735351i	−0.999324	+	0.0367676i	$0.988294\pi$
$788$			2.97291e26i			0.0904030i
$789$	1.27925e27			0.384348
$790$	7.93215e26	+	2.08662e27i	0.235469	+	0.619421i
$791$	−5.87290e27			−1.72257
$792$		−	5.62880e26i		−	0.163127i
$793$		−	2.50118e26i		−	0.0716226i
$794$	2.76883e27			0.783431
$795$	4.55453e27	−	1.73138e27i	1.27337	−	0.484065i
$796$	−7.80343e26			−0.215581
$797$		−	2.97143e27i		−	0.811171i	−0.914057	−	0.405585i	$-0.867068\pi$
$797$		−	2.97143e27i		−	0.811171i	0.914057	−	0.405585i	$-0.132932\pi$
$798$			1.63854e27i			0.442007i
$799$	2.97382e26			0.0792722
$800$	−6.65391e26	−	7.48712e26i	−0.175276	−	0.197224i
$801$	3.67510e26			0.0956665
$802$			3.44007e27i			0.884935i
$803$			3.04468e27i			0.774005i
$804$	7.18533e26			0.180515
$805$	5.23364e27	−	1.98953e27i	1.29940	−	0.493959i
$806$	9.26732e25			0.0227390
$807$			4.18739e27i			1.01542i
$808$		−	5.62070e27i		−	1.34705i
$809$	2.32459e27			0.550599			0.275299	−	0.961359i	$-0.411223\pi$
$809$	2.32459e27			0.550599			0.275299	+	0.961359i	$0.411223\pi$
$810$	−1.51780e27	−	3.99269e27i	−0.355309	−	0.934669i
$811$	5.80764e26			0.134370			0.0671848	−	0.997741i	$-0.478598\pi$
$811$	5.80764e26			0.134370			0.0671848	+	0.997741i	$0.478598\pi$
$812$			5.71847e26i			0.130767i
$813$			6.17076e27i			1.39469i
$814$	−3.65497e27			−0.816491
$815$	−4.94422e26	−	1.30062e27i	−0.109169	−	0.287179i
$816$	−2.25260e26			−0.0491618
$817$			1.11207e27i			0.239896i
$818$		−	2.89949e27i		−	0.618251i
$819$	3.38104e26			0.0712612
$820$	−1.65955e26	+	6.30867e25i	−0.0345747	+	0.0131433i
$821$	−3.65637e27			−0.752993			−0.376496	−	0.926418i	$-0.622871\pi$
$821$	−3.65637e27			−0.752993			−0.376496	+	0.926418i	$0.622871\pi$
$822$		−	4.13541e27i		−	0.841853i
$823$			7.95910e27i			1.60164i	0.598904	+	0.800821i	$0.295603\pi$
$823$			7.95910e27i			1.60164i	−0.598904	+	0.800821i	$0.704397\pi$
$824$	3.18434e27			0.633447
$825$	−6.76717e27	−	7.61455e27i	−1.33074	−	1.49738i
$826$	−5.29773e27			−1.02986
$827$		−	3.53767e27i		−	0.679852i	−0.940452	−	0.339926i	$-0.889598\pi$
$827$		−	3.53767e27i		−	0.679852i	0.940452	−	0.339926i	$-0.110402\pi$
$828$			6.51365e25i			0.0123747i
$829$	−6.08626e27			−1.14310			−0.571548	−	0.820569i	$-0.693657\pi$
$829$	−6.08626e27			−1.14310			−0.571548	+	0.820569i	$0.693657\pi$
$830$	7.40565e27	−	2.81521e27i	1.37506	−	0.522720i
$831$	−8.94517e27			−1.64202
$832$			4.47704e27i			0.812492i
$833$			1.34535e26i			0.0241384i
$834$	2.84650e27			0.504933
$835$	3.76177e27	+	9.89565e27i	0.659737	+	1.73549i
$836$	5.63270e26			0.0976690
$837$		−	1.83540e26i		−	0.0314658i
$838$		−	1.20423e27i		−	0.204123i
$839$	−1.11094e27			−0.186187			−0.0930937	−	0.995657i	$-0.529676\pi$
$839$	−1.11094e27			−0.186187			−0.0930937	+	0.995657i	$0.529676\pi$
$840$	2.81494e27	+	7.40494e27i	0.466462	+	1.22707i
$841$	−1.97808e27			−0.324102
$842$			2.13621e27i			0.346082i
$843$		−	5.03322e26i		−	0.0806277i
$844$	−6.69406e26			−0.106032
$845$	−2.68346e27	+	1.02010e27i	−0.420297	+	0.159773i
$846$	−6.86769e26			−0.106363
$847$		−	2.12256e28i		−	3.25062i
$848$		−	7.35247e27i		−	1.11345i
$849$	4.00357e27			0.599549
$850$	−2.61715e26	+	2.32590e26i	−0.0387569	+	0.0344438i
$851$	3.60668e27			0.528174
$852$		−	1.50890e27i		−	0.218516i
$853$		−	7.37660e27i		−	1.05643i	−0.849111	−	0.528215i	$-0.822862\pi$
$853$		−	7.37660e27i		−	1.05643i	0.849111	−	0.528215i	$-0.177138\pi$
$854$	−7.60021e26			−0.107641
$855$	−2.04230e26	+	7.76369e25i	−0.0286050	+	0.0108740i
$856$	1.44887e27			0.200692
$857$			1.22495e28i			1.67803i	0.544110	+	0.839014i	$0.316868\pi$
$857$			1.22495e28i			1.67803i	−0.544110	+	0.839014i	$0.683132\pi$
$858$			1.02149e28i			1.38391i
$859$	1.38657e28			1.85784			0.928919	−	0.370283i	$-0.120739\pi$
$859$	1.38657e28			1.85784			0.928919	+	0.370283i	$0.120739\pi$
$860$	2.24042e26	+	5.89361e26i	0.0296889	+	0.0780991i
$861$	2.64363e27			0.346474
$862$			3.12884e27i			0.405569i
$863$		−	4.68266e27i		−	0.600330i	−0.953887	−	0.300165i	$-0.902958\pi$
$863$		−	4.68266e27i		−	0.600330i	0.953887	−	0.300165i	$-0.0970417\pi$
$864$	1.98922e27			0.252233
$865$	8.65152e26	+	2.27586e27i	0.108502	+	0.285425i
$866$	4.90219e27			0.608094
$867$			8.44483e27i			1.03612i
$868$			4.31415e25i			0.00523550i
$869$	−1.14265e28			−1.37159
$870$	6.26425e27	−	2.38132e27i	0.743766	−	0.282738i
$871$	−8.25840e27			−0.969892
$872$			5.23875e27i			0.608585i
$873$			3.98371e26i			0.0457775i
$874$	3.62811e27			0.412403
$875$	9.44011e27	+	4.92637e27i	1.06145	+	0.553925i
$876$	4.98504e26			0.0554473
$877$		−	7.75996e27i		−	0.853814i	−0.904296	−	0.426907i	$-0.859603\pi$
$877$		−	7.75996e27i		−	0.853814i	0.904296	−	0.426907i	$-0.140397\pi$
$878$			5.41142e27i			0.588997i
$879$	−6.65376e27			−0.716428
$880$	−1.43687e28	+	5.46219e27i	−1.53050	+	0.581810i
$881$	−3.50823e27			−0.369672			−0.184836	−	0.982769i	$-0.559175\pi$
$881$	−3.50823e27			−0.369672			−0.184836	+	0.982769i	$0.559175\pi$
$882$		−	3.10694e26i		−	0.0323877i
$883$		−	6.98993e27i		−	0.720852i	−0.932788	−	0.360426i	$-0.882631\pi$
$883$		−	6.98993e27i		−	0.720852i	0.932788	−	0.360426i	$-0.117369\pi$
$884$	−5.37875e25			−0.00548763
$885$	−3.37978e27	−	8.89079e27i	−0.341136	−	0.897386i
$886$	−1.35568e27			−0.135374
$887$			3.86742e27i			0.382073i	0.981583	+	0.191037i	$0.0611849\pi$
$887$			3.86742e27i			0.382073i	−0.981583	+	0.191037i	$0.938815\pi$
$888$			5.10301e27i			0.498773i
$889$	−5.83075e27			−0.563842
$890$	−4.12403e27	−	1.08486e28i	−0.394563	−	1.03793i
$891$	2.18643e28			2.06966
$892$		−	2.60281e27i		−	0.243768i
$893$		−	5.86040e27i		−	0.543048i
$894$	4.71068e26			0.0431894
$895$	−9.66354e27	+	3.67353e27i	−0.876632	+	0.333246i
$896$	1.00845e28			0.905170
$897$		−	1.00800e28i		−	0.895225i
$898$		−	1.83205e28i		−	1.60995i
$899$	3.11214e26			0.0270609
$900$	−9.25945e25	+	8.22901e25i	−0.00796675	+	0.00708017i
$901$	8.57232e26			0.0729815
$902$			5.93197e27i			0.499732i
$903$		−	9.38841e27i		−	0.782634i
$904$	−1.83990e28			−1.51773
$905$	−1.37379e28	+	5.22239e27i	−1.12140	+	0.426292i
$906$	8.78969e26			0.0709995
$907$			9.46283e27i			0.756400i	0.925724	+	0.378200i	$0.123457\pi$
$907$			9.46283e27i			0.756400i	−0.925724	+	0.378200i	$0.876543\pi$
$908$			3.21763e26i			0.0254519i
$909$	−1.30873e27			−0.102445
$910$	−3.79405e27	−	9.98057e27i	−0.293907	−	0.773147i
$911$	2.24083e27			0.171784			0.0858921	−	0.996304i	$-0.472626\pi$
$911$	2.24083e27			0.171784			0.0858921	+	0.996304i	$0.472626\pi$
$912$			4.43911e27i			0.336779i
$913$			4.05540e28i			3.04482i
$914$	−4.07991e27			−0.303153
$915$	−4.84868e26	−	1.27549e27i	−0.0356552	−	0.0937941i
$916$	4.72512e26			0.0343879
$917$			8.22512e27i			0.592425i
$918$		−	6.95338e26i		−	0.0495668i
$919$	1.75583e28			1.23876			0.619378	−	0.785093i	$-0.287385\pi$
$919$	1.75583e28			1.23876			0.619378	+	0.785093i	$0.287385\pi$
$920$	1.63963e28	−	6.23294e27i	1.14488	−	0.435220i
$921$	2.16779e27			0.149813
$922$		−	1.70305e28i		−	1.16488i
$923$			1.73424e28i			1.17407i
$924$	−4.75529e27			−0.318635
$925$	4.55650e27	+	5.12706e27i	0.302193	+	0.340034i
$926$	−1.15164e27			−0.0755981
$927$		−	7.41443e26i		−	0.0481749i
$928$			3.37295e27i			0.216922i
$929$	2.24692e28			1.43034			0.715169	−	0.698952i	$-0.246350\pi$
$929$	2.24692e28			1.43034			0.715169	+	0.698952i	$0.246350\pi$
$930$	4.72590e26	−	1.79652e26i	0.0297781	−	0.0113199i
$931$	2.65124e27			0.165359
$932$			2.40393e27i			0.148412i
$933$		−	1.70864e28i		−	1.04418i
$934$	−1.68221e28			−1.01762
$935$	−6.36842e26	−	1.67527e27i	−0.0381348	−	0.100317i
$936$	1.05923e27			0.0627873
$937$		−	2.63567e28i		−	1.54655i	−0.634068	−	0.773277i	$-0.718616\pi$
$937$		−	2.63567e28i		−	1.54655i	0.634068	−	0.773277i	$-0.281384\pi$
$938$			2.50944e28i			1.45764i
$939$	2.46036e28			1.41474
$940$	−1.18066e27	−	3.10582e27i	−0.0672063	−	0.176792i
$941$	1.42871e28			0.805086			0.402543	−	0.915401i	$-0.368126\pi$
$941$	1.42871e28			0.805086			0.402543	+	0.915401i	$0.368126\pi$
$942$		−	6.27573e27i		−	0.350091i
$943$		−	5.85361e27i		−	0.323268i
$944$	−1.43526e28			−0.784686
$945$	−1.97666e28	+	7.51414e27i	−1.06987	+	0.406703i
$946$	2.10664e28			1.12882
$947$		−	2.09836e28i		−	1.11316i	−0.830795	−	0.556578i	$-0.812114\pi$
$947$		−	2.09836e28i		−	1.11316i	0.830795	−	0.556578i	$-0.187886\pi$
$948$			1.87086e27i			0.0982567i
$949$	−5.72952e27			−0.297913
$950$	4.58356e27	+	5.15751e27i	0.235955	+	0.265501i
$951$	−1.46562e28			−0.746974
$952$			1.39372e27i			0.0703276i
$953$		−	2.59095e28i		−	1.29443i	−0.762309	−	0.647213i	$-0.775935\pi$
$953$		−	2.59095e28i		−	1.29443i	0.762309	−	0.647213i	$-0.224065\pi$
$954$	−1.97967e27			−0.0979229
$955$	−1.01410e27	+	3.85503e26i	−0.0496647	+	0.0188797i
$956$	−5.95976e26			−0.0288987
$957$			3.43036e28i			1.64693i
$958$			2.40918e28i			1.14524i
$959$	−2.21263e28			−1.04144
$960$	8.67898e27	+	2.28308e28i	0.404475	+	1.06401i
$961$	−2.16472e28			−0.998917
$962$		−	6.87796e27i		−	0.314266i
$963$		−	3.37356e26i		−	0.0152630i
$964$	2.52706e27			0.113210
$965$	6.64053e26	+	1.74685e27i	0.0294573	+	0.0774900i
$966$	−3.06295e28			−1.34542
$967$			3.76693e28i			1.63846i	0.573466	+	0.819229i	$0.305598\pi$
$967$			3.76693e28i			1.63846i	−0.573466	+	0.819229i	$0.694402\pi$
$968$		−	6.64968e28i		−	2.86408i
$969$	−5.17561e26			−0.0220742
$970$	1.17596e28	−	4.47034e27i	0.496662	−	0.188803i
$971$	−2.78506e28			−1.16480			−0.582400	−	0.812902i	$-0.697886\pi$
$971$	−2.78506e28			−1.16480			−0.582400	+	0.812902i	$0.697886\pi$
$972$		−	5.13478e26i		−	0.0212663i
$973$		−	1.52301e28i		−	0.624639i
$974$	−1.94762e28			−0.791031
$975$	1.43292e28	−	1.27345e28i	0.576337	−	0.512200i
$976$	−2.05904e27			−0.0820148
$977$		−	3.62210e28i		−	1.42877i	−0.699753	−	0.714385i	$-0.746707\pi$
$977$		−	3.62210e28i		−	1.42877i	0.699753	−	0.714385i	$-0.253293\pi$
$978$			7.61179e27i			0.297350i
$979$	5.94079e28			2.29831
$980$	1.40507e27	−	5.34129e26i	0.0538332	−	0.0204644i
$981$	1.21979e27			0.0462840
$982$			2.44656e28i			0.919382i
$983$			2.07343e28i			0.771668i	0.922568	+	0.385834i	$0.126086\pi$
$983$			2.07343e28i			0.771668i	−0.922568	+	0.385834i	$0.873914\pi$
$984$	8.28213e27			0.305273
$985$	−6.62383e27	−	1.74245e28i	−0.241805	−	0.636088i
$986$	1.17903e27			0.0426279
$987$			4.94752e28i			1.77164i
$988$			1.05997e27i			0.0375926i
$989$	−2.07881e28			−0.730215
$990$	1.47071e27	+	3.86883e27i	0.0511673	+	0.134600i
$991$	−5.13372e28			−1.76902			−0.884509	−	0.466524i	$-0.845506\pi$
$991$	−5.13372e28			−1.76902			−0.884509	+	0.466524i	$0.845506\pi$
$992$			2.54463e26i			0.00868489i
$993$		−	4.21458e28i		−	1.42474i
$994$	5.26974e28			1.76449
$995$	4.57367e28	−	1.73865e28i	1.51686	−	0.576625i
$996$	6.63989e27			0.218121
$997$			1.12061e28i			0.364628i	0.983240	+	0.182314i	$0.0583588\pi$
$997$			1.12061e28i			0.364628i	−0.983240	+	0.182314i	$0.941641\pi$
$998$			4.21832e28i			1.35956i
$999$	−1.36218e28			−0.434874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.20.b.a.4.3	✓	8
3.2	odd	2		45.20.b.b.19.6		8
4.3	odd	2		80.20.c.a.49.2		8
5.2	odd	4		25.20.a.f.1.6		8
5.3	odd	4		25.20.a.f.1.3		8
5.4	even	2	inner	5.20.b.a.4.6	yes	8
15.14	odd	2		45.20.b.b.19.3		8
20.19	odd	2		80.20.c.a.49.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.20.b.a.4.3	✓	8	1.1	even	1	trivial
5.20.b.a.4.6	yes	8	5.4	even	2	inner
25.20.a.f.1.3		8	5.3	odd	4
25.20.a.f.1.6		8	5.2	odd	4
45.20.b.b.19.3		8	15.14	odd	2
45.20.b.b.19.6		8	3.2	odd	2
80.20.c.a.49.2		8	4.3	odd	2
80.20.c.a.49.7		8	20.19	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-674.268i q^{2} +35433.1i q^{3} +69650.8 q^{4} +(-4.08230e6 + 1.55186e6i) q^{5} +2.38914e7 q^{6} -1.27830e8i q^{7} -4.00474e8i q^{8} -9.32466e7 q^{9} +O(q^{10})\)	\(q-674.268i q^{2} +35433.1i q^{3} +69650.8 q^{4} +(-4.08230e6 + 1.55186e6i) q^{5} +2.38914e7 q^{6} -1.27830e8i q^{7} -4.00474e8i q^{8} -9.32466e7 q^{9} +(1.04637e9 + 2.75257e9i) q^{10} -1.50733e10 q^{11} +2.46795e9i q^{12} -2.83651e10i q^{13} -8.61916e10 q^{14} +(-5.49874e10 - 1.44649e11i) q^{15} -2.33510e11 q^{16} -2.72251e10i q^{17} +6.28732e10i q^{18} -5.36515e11 q^{19} +(-2.84336e11 + 1.08088e11i) q^{20} +4.52942e12 q^{21} +1.01634e13i q^{22} -1.00292e13i q^{23} +1.41901e13 q^{24} +(1.42569e13 - 1.26704e13i) q^{25} -1.91257e13 q^{26} +3.78786e13i q^{27} -8.90346e12i q^{28} -6.42276e13 q^{29} +(-9.75321e13 + 3.70762e13i) q^{30} -4.84548e12 q^{31} -5.25156e13i q^{32} -5.34095e14i q^{33} -1.83570e13 q^{34} +(1.98374e14 + 5.21841e14i) q^{35} -6.49470e12 q^{36} +3.59619e14i q^{37} +3.61755e14i q^{38} +1.00507e15 q^{39} +(6.21480e14 + 1.63486e15i) q^{40} +5.83658e14 q^{41} -3.05404e15i q^{42} -2.07276e15i q^{43} -1.04987e15 q^{44} +(3.80661e14 - 1.44706e14i) q^{45} -6.76236e15 q^{46} +1.09231e16i q^{47} -8.27398e15i q^{48} -4.94159e15 q^{49} +(-8.54321e15 - 9.61299e15i) q^{50} +9.64672e14 q^{51} -1.97565e15i q^{52} +3.14868e16i q^{53} +2.55403e16 q^{54} +(6.15338e16 - 2.33917e16i) q^{55} -5.11925e16 q^{56} -1.90104e16i q^{57} +4.33066e16i q^{58} +6.14646e16 q^{59} +(-3.82991e15 - 1.00749e16i) q^{60} +8.81781e15 q^{61} +3.26715e15i q^{62} +1.19197e16i q^{63} -1.57836e17 q^{64} +(4.40188e16 + 1.15795e17i) q^{65} -3.60123e17 q^{66} -2.91146e17i q^{67} -1.89625e15i q^{68} +3.55366e17 q^{69} +(3.51860e17 - 1.33758e17i) q^{70} -6.11399e17 q^{71} +3.73428e16i q^{72} -2.01992e17i q^{73} +2.42479e17 q^{74} +(4.48950e17 + 5.05168e17i) q^{75} -3.73687e16 q^{76} +1.92682e18i q^{77} -6.77684e17i q^{78} +7.58063e17 q^{79} +(9.53257e17 - 3.62375e17i) q^{80} -1.45053e18 q^{81} -3.93542e17i q^{82} -2.69045e18i q^{83} +3.15477e17 q^{84} +(4.22497e16 + 1.11141e17i) q^{85} -1.39760e18 q^{86} -2.27579e18i q^{87} +6.03646e18i q^{88} -3.94127e18 q^{89} +(-9.75705e16 - 2.56667e17i) q^{90} -3.62591e18 q^{91} -6.98541e17i q^{92} -1.71691e17i q^{93} +7.36509e18 q^{94} +(2.19022e18 - 8.32598e17i) q^{95} +1.86079e18 q^{96} -4.27223e18i q^{97} +3.33196e18i q^{98} +1.40553e18 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 1620744 q^{4} + 147000 q^{5} + 3365736 q^{6} + 345358584 q^{9}+O(q^{10}) \) 8 * q - 1620744 * q^4 + 147000 * q^5 + 3365736 * q^6 + 345358584 * q^9	\( 8 q - 1620744 q^{4} + 147000 q^{5} + 3365736 q^{6} + 345358584 q^{9} - 610691000 q^{10} - 3379575264 q^{11} + 177250591032 q^{14} - 242324628000 q^{15} - 312730276832 q^{16} + 4547188380640 q^{19} - 4180429431000 q^{20} - 2983154334624 q^{21} - 6176642779680 q^{24} + 17715709625000 q^{25} + 15909228128496 q^{26} - 188222300345040 q^{29} + 148501482939000 q^{30} + 72115006686976 q^{31} + 378440221985792 q^{34} - 299115755916000 q^{35} - 964020253238712 q^{36} + 30\!\cdots\!28 q^{39}+ \cdots - 16\!\cdots\!72 q^{99}+O(q^{100}) \) 8 * q - 1620744 * q^4 + 147000 * q^5 + 3365736 * q^6 + 345358584 * q^9 - 610691000 * q^10 - 3379575264 * q^11 + 177250591032 * q^14 - 242324628000 * q^15 - 312730276832 * q^16 + 4547188380640 * q^19 - 4180429431000 * q^20 - 2983154334624 * q^21 - 6176642779680 * q^24 + 17715709625000 * q^25 + 15909228128496 * q^26 - 188222300345040 * q^29 + 148501482939000 * q^30 + 72115006686976 * q^31 + 378440221985792 * q^34 - 299115755916000 * q^35 - 964020253238712 * q^36 + 3011653788049728 * q^39 - 213611427940000 * q^40 - 3314269428857904 * q^41 + 489119304867552 * q^44 + 10198157211261000 * q^45 - 13716870314831944 * q^46 - 11129258011816744 * q^49 + 50375043666750000 * q^50 - 46867071411404544 * q^51 + 86068650834185040 * q^54 + 69821226326124000 * q^55 - 303831778832907360 * q^56 + 259648032778012320 * q^59 + 318110620655844000 * q^60 - 582893562753226064 * q^61 + 525415747276109696 * q^64 + 747545324689032000 * q^65 - 1871067587999976288 * q^66 + 302144302523815008 * q^69 + 2638361065839633000 * q^70 - 2617007600602926144 * q^71 + 1847591013622215312 * q^74 + 2877932428209000000 * q^75 - 7494494299858276320 * q^76 + 3935092091109861760 * q^79 + 5465139505859292000 * q^80 - 8328177293660704152 * q^81 + 7683875738824129632 * q^84 + 3752387009219584000 * q^85 - 14358563079146095224 * q^86 + 2120141101636921680 * q^89 + 7589596726146267000 * q^90 - 3358638219973817664 * q^91 - 10251771654977709928 * q^94 + 6106065789884820000 * q^95 + 15670161523483353216 * q^96 - 16256944625235082272 * q^99

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