LMFDB - Embedded newform 5.16.b.a.4.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,16,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, 16, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 16 $
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:	$7.13467525500$
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} + 29397x^{4} + 153469728x^{2} + 65015354624 $ x^6 + 29397x^4 + 153469728x^2 + 65015354624
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{4}\cdot 5^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.4
Root			$21.5470i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.16.b.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+43.0940i q^{2} +6725.99i q^{3} +30910.9 q^{4} +(-160365. - 69286.1i) q^{5} -289850. q^{6} +1.29717e6i q^{7} +2.74418e6i q^{8} -3.08900e7 q^{9} +O(q^{10})$	\(q+43.0940i q^{2} +6725.99i q^{3} +30910.9 q^{4} +(-160365. - 69286.1i) q^{5} -289850. q^{6} +1.29717e6i q^{7} +2.74418e6i q^{8} -3.08900e7 q^{9} +(2.98581e6 - 6.91078e6i) q^{10} -2.48560e7 q^{11} +2.07906e8i q^{12} -1.64842e8i q^{13} -5.59000e7 q^{14} +(4.66018e8 - 1.07862e9i) q^{15} +8.94631e8 q^{16} +2.49651e9i q^{17} -1.33117e9i q^{18} +3.47974e9 q^{19} +(-4.95704e9 - 2.14170e9i) q^{20} -8.72472e9 q^{21} -1.07114e9i q^{22} +1.39929e10i q^{23} -1.84573e10 q^{24} +(2.09165e10 + 2.22222e10i) q^{25} +7.10369e9 q^{26} -1.11256e11i q^{27} +4.00966e10i q^{28} +7.33587e10 q^{29} +(4.64818e10 + 2.00825e10i) q^{30} +6.63708e9 q^{31} +1.28474e11i q^{32} -1.67181e11i q^{33} -1.07584e11 q^{34} +(8.98755e10 - 2.08020e11i) q^{35} -9.54839e11 q^{36} +8.47925e11i q^{37} +1.49956e11i q^{38} +1.10873e12 q^{39} +(1.90133e11 - 4.40071e11i) q^{40} -7.77655e11 q^{41} -3.75983e11i q^{42} -2.03959e12i q^{43} -7.68321e11 q^{44} +(4.95369e12 + 2.14025e12i) q^{45} -6.03008e11 q^{46} -3.83108e12i q^{47} +6.01728e12i q^{48} +3.06492e12 q^{49} +(-9.57641e11 + 9.01373e11i) q^{50} -1.67915e13 q^{51} -5.09541e12i q^{52} -2.49472e12i q^{53} +4.79444e12 q^{54} +(3.98604e12 + 1.72217e12i) q^{55} -3.55965e12 q^{56} +2.34047e13i q^{57} +3.16132e12i q^{58} +1.33880e12 q^{59} +(1.44050e13 - 3.33410e13i) q^{60} +7.16455e12 q^{61} +2.86018e11i q^{62} -4.00695e13i q^{63} +2.37788e13 q^{64} +(-1.14213e13 + 2.64349e13i) q^{65} +7.20450e12 q^{66} +6.61388e12i q^{67} +7.71693e13i q^{68} -9.41158e13 q^{69} +(8.96442e12 + 3.87309e12i) q^{70} +1.42046e13 q^{71} -8.47677e13i q^{72} -5.85350e13i q^{73} -3.65405e13 q^{74} +(-1.49466e14 + 1.40684e14i) q^{75} +1.07562e14 q^{76} -3.22423e13i q^{77} +4.77794e13i q^{78} +2.48505e14 q^{79} +(-1.43468e14 - 6.19855e13i) q^{80} +3.05065e14 q^{81} -3.35122e13i q^{82} -6.66100e13i q^{83} -2.69689e14 q^{84} +(1.72973e14 - 4.00353e14i) q^{85} +8.78941e13 q^{86} +4.93410e14i q^{87} -6.82092e13i q^{88} -5.07426e14 q^{89} +(-9.22319e13 + 2.13474e14i) q^{90} +2.13827e14 q^{91} +4.32532e14i q^{92} +4.46409e13i q^{93} +1.65096e14 q^{94} +(-5.58029e14 - 2.41097e14i) q^{95} -8.64118e14 q^{96} -1.18734e15i q^{97} +1.32080e14i q^{98} +7.67802e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 38568 q^{4} - 238350 q^{5} - 515448 q^{6} - 11416662 q^{9}+O(q^{10}) $ 6 * q - 38568 * q^4 - 238350 * q^5 - 515448 * q^6 - 11416662 * q^9	\( 6 q - 38568 q^{4} - 238350 q^{5} - 515448 q^{6} - 11416662 q^{9} - 48274200 q^{10} - 108590088 q^{11} + 663751704 q^{14} + 297743400 q^{15} + 1155522336 q^{16} - 3630995640 q^{19} + 2533753800 q^{20} - 8917537608 q^{21} - 2959765920 q^{24} + 18250878750 q^{25} - 81970953168 q^{26} + 286168468740 q^{29} + 203897251800 q^{30} - 276236748288 q^{31} - 127784939136 q^{34} + 1171274911800 q^{35} - 3326879331864 q^{36} + 2186980965936 q^{39} + 4214283852000 q^{40} - 6153278882388 q^{41} + 8250173021664 q^{44} + 10442765857950 q^{45} - 23334602656488 q^{46} + 11613390856242 q^{49} + 23694218070000 q^{50} - 43487373385728 q^{51} + 10162879468560 q^{54} + 33977390365800 q^{55} - 59280484297440 q^{56} + 14903258326680 q^{59} + 39248254864800 q^{60} - 11352061428588 q^{61} + 73265851251072 q^{64} - 50675287275600 q^{65} + 76208211455904 q^{66} - 150489671962824 q^{69} - 156447825521400 q^{70} + 131693145807312 q^{71} - 353606797863216 q^{74} - 360965926890000 q^{75} + 959127540575520 q^{76} - 26081853939360 q^{79} - 552945514077600 q^{80} + 11\!\cdots\!46 q^{81}+ \cdots + 506999099666376 q^{99}+O(q^{100}) \) 6 * q - 38568 * q^4 - 238350 * q^5 - 515448 * q^6 - 11416662 * q^9 - 48274200 * q^10 - 108590088 * q^11 + 663751704 * q^14 + 297743400 * q^15 + 1155522336 * q^16 - 3630995640 * q^19 + 2533753800 * q^20 - 8917537608 * q^21 - 2959765920 * q^24 + 18250878750 * q^25 - 81970953168 * q^26 + 286168468740 * q^29 + 203897251800 * q^30 - 276236748288 * q^31 - 127784939136 * q^34 + 1171274911800 * q^35 - 3326879331864 * q^36 + 2186980965936 * q^39 + 4214283852000 * q^40 - 6153278882388 * q^41 + 8250173021664 * q^44 + 10442765857950 * q^45 - 23334602656488 * q^46 + 11613390856242 * q^49 + 23694218070000 * q^50 - 43487373385728 * q^51 + 10162879468560 * q^54 + 33977390365800 * q^55 - 59280484297440 * q^56 + 14903258326680 * q^59 + 39248254864800 * q^60 - 11352061428588 * q^61 + 73265851251072 * q^64 - 50675287275600 * q^65 + 76208211455904 * q^66 - 150489671962824 * q^69 - 156447825521400 * q^70 + 131693145807312 * q^71 - 353606797863216 * q^74 - 360965926890000 * q^75 + 959127540575520 * q^76 - 26081853939360 * q^79 - 552945514077600 * q^80 + 1148641568615646 * q^81 - 686155736066976 * q^84 - 548221025491200 * q^85 + 598387757484072 * q^86 + 59269690709820 * q^89 - 1014408610626600 * q^90 + 821206462566672 * q^91 - 308164835928456 * q^94 + 232287694599000 * q^95 - 1208921682814848 * q^96 + 506999099666376 * 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 $

$2$			43.0940i			0.238063i	0.992890	+	0.119031i	$0.0379789\pi$
$2$			43.0940i			0.238063i	−0.992890	+	0.119031i	$0.962021\pi$
$3$			6725.99i			1.77561i	0.460223	+	0.887803i	$0.347770\pi$
$3$			6725.99i			1.77561i	−0.460223	+	0.887803i	$0.652230\pi$
$4$	30910.9			0.943326
$5$	−160365.	−	69286.1i	−0.917984	−	0.396617i
$5$	−160365.	−	69286.1i	−0.917984	−	0.396617i
$6$	−289850.			−0.422706
$7$			1.29717e6i			0.595333i	0.954670	+	0.297667i	$0.0962084\pi$
$7$			1.29717e6i			0.595333i	−0.954670	+	0.297667i	$0.903792\pi$
$8$			2.74418e6i			0.462634i
$9$	−3.08900e7			−2.15278
$10$	2.98581e6	−	6.91078e6i	0.0944197	−	0.218538i
$11$	−2.48560e7			−0.384579			−0.192290	−	0.981338i	$-0.561591\pi$
$11$	−2.48560e7			−0.384579			−0.192290	+	0.981338i	$0.561591\pi$
$12$			2.07906e8i			1.67498i
$13$		−	1.64842e8i		−	0.728606i	−0.931281	−	0.364303i	$-0.881307\pi$
$13$		−	1.64842e8i		−	0.728606i	0.931281	−	0.364303i	$-0.118693\pi$
$14$	−5.59000e7			−0.141727
$15$	4.66018e8	−	1.07862e9i	0.704235	−	1.62998i
$16$	8.94631e8			0.833190
$17$			2.49651e9i			1.47559i	0.675024	+	0.737795i	$0.264133\pi$
$17$			2.49651e9i			1.47559i	−0.675024	+	0.737795i	$0.735867\pi$
$18$		−	1.33117e9i		−	0.512497i
$19$	3.47974e9			0.893088			0.446544	−	0.894762i	$-0.352655\pi$
$19$	3.47974e9			0.893088			0.446544	+	0.894762i	$0.352655\pi$
$20$	−4.95704e9	−	2.14170e9i	−0.865959	−	0.374139i
$21$	−8.72472e9			−1.05708
$22$		−	1.07114e9i		−	0.0915540i
$23$			1.39929e10i			0.856934i	0.903557	+	0.428467i	$0.140946\pi$
$23$			1.39929e10i			0.856934i	−0.903557	+	0.428467i	$0.859054\pi$
$24$	−1.84573e10			−0.821455
$25$	2.09165e10	+	2.22222e10i	0.685390	+	0.728176i
$26$	7.10369e9			0.173454
$27$		−	1.11256e11i		−	2.04688i
$28$			4.00966e10i			0.561593i
$29$	7.33587e10			0.789709			0.394854	−	0.918744i	$-0.370795\pi$
$29$	7.33587e10			0.789709			0.394854	+	0.918744i	$0.370795\pi$
$30$	4.64818e10	+	2.00825e10i	0.388037	+	0.167652i
$31$	6.63708e9			0.0433276			0.0216638	−	0.999765i	$-0.493104\pi$
$31$	6.63708e9			0.0433276			0.0216638	+	0.999765i	$0.493104\pi$
$32$			1.28474e11i			0.660985i
$33$		−	1.67181e11i		−	0.682862i
$34$	−1.07584e11			−0.351283
$35$	8.98755e10	−	2.08020e11i	0.236119	−	0.546506i
$36$	−9.54839e11			−2.03077
$37$			8.47925e11i			1.46840i	0.678933	+	0.734201i	$0.262443\pi$
$37$			8.47925e11i			1.46840i	−0.678933	+	0.734201i	$0.737557\pi$
$38$			1.49956e11i			0.212611i
$39$	1.10873e12			1.29372
$40$	1.90133e11	−	4.40071e11i	0.183488	−	0.424690i
$41$	−7.77655e11			−0.623603			−0.311801	−	0.950147i	$-0.600932\pi$
$41$	−7.77655e11			−0.623603			−0.311801	+	0.950147i	$0.600932\pi$
$42$		−	3.75983e11i		−	0.251651i
$43$		−	2.03959e12i		−	1.14427i	−0.820158	−	0.572137i	$-0.806115\pi$
$43$		−	2.03959e12i		−	1.14427i	0.820158	−	0.572137i	$-0.193885\pi$
$44$	−7.68321e11			−0.362784
$45$	4.95369e12	+	2.14025e12i	1.97622	+	0.853828i
$46$	−6.03008e11			−0.204004
$47$		−	3.83108e12i		−	1.10303i	−0.834165	−	0.551514i	$-0.814050\pi$
$47$		−	3.83108e12i		−	1.10303i	0.834165	−	0.551514i	$-0.185950\pi$
$48$			6.01728e12i			1.47942i
$49$	3.06492e12			0.645578
$50$	−9.57641e11	+	9.01373e11i	−0.173352	+	0.163166i
$51$	−1.67915e13			−2.62007
$52$		−	5.09541e12i		−	0.687313i
$53$		−	2.49472e12i		−	0.291711i	−0.989306	−	0.145856i	$-0.953407\pi$
$53$		−	2.49472e12i		−	0.291711i	0.989306	−	0.145856i	$-0.0465935\pi$
$54$	4.79444e12			0.487287
$55$	3.98604e12	+	1.72217e12i	0.353038	+	0.152531i
$56$	−3.55965e12			−0.275421
$57$			2.34047e13i			1.58577i
$58$			3.16132e12i			0.188000i
$59$	1.33880e12			0.0700365			0.0350183	−	0.999387i	$-0.488851\pi$
$59$	1.33880e12			0.0700365			0.0350183	+	0.999387i	$0.488851\pi$
$60$	1.44050e13	−	3.33410e13i	0.664324	−	1.53760i
$61$	7.16455e12			0.291887			0.145944	−	0.989293i	$-0.453378\pi$
$61$	7.16455e12			0.291887			0.145944	+	0.989293i	$0.453378\pi$
$62$			2.86018e11i			0.0103147i
$63$		−	4.00695e13i		−	1.28162i
$64$	2.37788e13			0.675834
$65$	−1.14213e13	+	2.64349e13i	−0.288977	+	0.668849i
$66$	7.20450e12			0.162564
$67$			6.61388e12i			0.133320i	0.997776	+	0.0666600i	$0.0212343\pi$
$67$			6.61388e12i			0.133320i	−0.997776	+	0.0666600i	$0.978766\pi$
$68$			7.71693e13i			1.39196i
$69$	−9.41158e13			−1.52158
$70$	8.96442e12	+	3.87309e12i	0.130103	+	0.0562112i
$71$	1.42046e13			0.185349			0.0926746	−	0.995696i	$-0.470458\pi$
$71$	1.42046e13			0.185349			0.0926746	+	0.995696i	$0.470458\pi$
$72$		−	8.47677e13i		−	0.995948i
$73$		−	5.85350e13i		−	0.620147i	−0.950713	−	0.310073i	$-0.899646\pi$
$73$		−	5.85350e13i		−	0.620147i	0.950713	−	0.310073i	$-0.100354\pi$
$74$	−3.65405e13			−0.349572
$75$	−1.49466e14	+	1.40684e14i	−1.29295	+	1.21698i
$76$	1.07562e14			0.842473
$77$		−	3.22423e13i		−	0.228953i
$78$			4.77794e13i			0.307986i
$79$	2.48505e14			1.45590			0.727950	−	0.685630i	$-0.240473\pi$
$79$	2.48505e14			1.45590			0.727950	+	0.685630i	$0.240473\pi$
$80$	−1.43468e14	−	6.19855e13i	−0.764856	−	0.330457i
$81$	3.05065e14			1.48168
$82$		−	3.35122e13i		−	0.148457i
$83$		−	6.66100e13i		−	0.269435i	−0.990884	−	0.134717i	$-0.956987\pi$
$83$		−	6.66100e13i		−	0.269435i	0.990884	−	0.134717i	$-0.0430127\pi$
$84$	−2.69689e14			−0.997169
$85$	1.72973e14	−	4.00353e14i	0.585244	−	1.35457i
$86$	8.78941e13			0.272409
$87$			4.93410e14i			1.40221i
$88$		−	6.82092e13i		−	0.177919i
$89$	−5.07426e14			−1.21604			−0.608020	−	0.793922i	$-0.708036\pi$
$89$	−5.07426e14			−1.21604			−0.608020	+	0.793922i	$0.708036\pi$
$90$	−9.22319e13	+	2.13474e14i	−0.203265	+	0.470464i
$91$	2.13827e14			0.433763
$92$			4.32532e14i			0.808369i
$93$			4.46409e13i			0.0769327i
$94$	1.65096e14			0.262590
$95$	−5.58029e14	−	2.41097e14i	−0.819841	−	0.354214i
$96$	−8.64118e14			−1.17365
$97$		−	1.18734e15i		−	1.49206i	−0.665912	−	0.746030i	$-0.731957\pi$
$97$		−	1.18734e15i		−	1.49206i	0.665912	−	0.746030i	$-0.268043\pi$
$98$			1.32080e14i			0.153688i
$99$	7.67802e14			0.827915
$100$	6.46547e14	+	6.86907e14i	0.646547	+	0.686907i
$101$	1.97970e14			0.183734			0.0918671	−	0.995771i	$-0.470717\pi$
$101$	1.97970e14			0.183734			0.0918671	+	0.995771i	$0.470717\pi$
$102$		−	7.23612e14i		−	0.623741i
$103$			1.50015e15i			1.20186i	0.799301	+	0.600931i	$0.205203\pi$
$103$			1.50015e15i			1.20186i	−0.799301	+	0.600931i	$0.794797\pi$
$104$	4.52355e14			0.337077
$105$	1.39914e15	+	6.04502e14i	0.970381	+	0.419255i
$106$	1.07507e14			0.0694456
$107$		−	6.89575e14i		−	0.415148i	−0.978219	−	0.207574i	$-0.933443\pi$
$107$		−	6.89575e14i		−	0.415148i	0.978219	−	0.207574i	$-0.0665568\pi$
$108$		−	3.43901e15i		−	1.93088i
$109$	1.35369e15			0.709287			0.354644	−	0.935002i	$-0.384602\pi$
$109$	1.35369e15			0.709287			0.354644	+	0.935002i	$0.384602\pi$
$110$	−7.42153e13	+	1.71774e14i	−0.0363118	+	0.0840451i
$111$	−5.70314e15			−2.60730
$112$			1.16048e15i			0.496026i
$113$			2.28009e15i			0.911726i	0.890050	+	0.455863i	$0.150669\pi$
$113$			2.28009e15i			0.911726i	−0.890050	+	0.455863i	$0.849331\pi$
$114$	−1.00860e15			−0.377514
$115$	9.69510e14	−	2.24397e15i	0.339874	−	0.786652i
$116$	2.26759e15			0.744953
$117$			5.09197e15i			1.56853i
$118$			5.76941e13i			0.0166731i
$119$	−3.23838e15			−0.878468
$120$	2.95991e15	+	1.27883e15i	0.754083	+	0.325803i
$121$	−3.55943e15			−0.852099
$122$			3.08749e14i			0.0694875i
$123$		−	5.23050e15i		−	1.10727i
$124$	2.05158e14			0.0408720
$125$	−1.81459e15	−	5.01288e15i	−0.340371	−	0.940291i
$126$	1.72675e15			0.305106
$127$		−	2.82207e15i		−	0.469938i	−0.972003	−	0.234969i	$-0.924501\pi$
$127$		−	2.82207e15i		−	0.469938i	0.972003	−	0.234969i	$-0.0754988\pi$
$128$			5.23457e15i			0.821876i
$129$	1.37183e16			2.03178
$130$	−1.13919e15	−	4.92187e14i	−0.159228	−	0.0687947i
$131$	6.54539e15			0.863775			0.431888	−	0.901927i	$-0.357848\pi$
$131$	6.54539e15			0.863775			0.431888	+	0.901927i	$0.357848\pi$
$132$		−	5.16772e15i		−	0.644161i
$133$			4.51379e15i			0.531685i
$134$	−2.85019e14			−0.0317386
$135$	−7.70846e15	+	1.78415e16i	−0.811828	+	1.87901i
$136$	−6.85086e15			−0.682658
$137$		−	1.17625e16i		−	1.10941i	−0.832046	−	0.554707i	$-0.812830\pi$
$137$		−	1.17625e16i		−	1.10941i	0.832046	−	0.554707i	$-0.187170\pi$
$138$		−	4.05582e15i		−	0.362231i
$139$	−2.03768e16			−1.72395			−0.861976	−	0.506949i	$-0.830773\pi$
$139$	−2.03768e16			−1.72395			−0.861976	+	0.506949i	$0.830773\pi$
$140$	2.77813e15	−	6.43010e15i	0.222737	−	0.515534i
$141$	2.57678e16			1.95855
$142$			6.12132e14i			0.0441247i
$143$			4.09731e15i			0.280207i
$144$	−2.76352e16			−1.79368
$145$	−1.17642e16	−	5.08274e15i	−0.724940	−	0.313212i
$146$	2.52251e15			0.147634
$147$			2.06146e16i			1.14629i
$148$			2.62101e16i			1.38518i
$149$	2.89572e16			1.45499			0.727493	−	0.686115i	$-0.240685\pi$
$149$	2.89572e16			1.45499			0.727493	+	0.686115i	$0.240685\pi$
$150$	−6.06263e15	−	6.44108e15i	−0.289719	−	0.307804i
$151$	1.77226e13			0.000805748			0.000402874	−	1.00000i	$-0.499872\pi$
$151$	1.77226e13			0.000805748			0.000402874		1.00000i	$0.499872\pi$
$152$			9.54901e15i			0.413172i
$153$		−	7.71172e16i		−	3.17662i
$154$	1.38945e15			0.0545051
$155$	−1.06436e15	−	4.59857e14i	−0.0397740	−	0.0171844i
$156$	3.42717e16			1.22040
$157$			1.04137e16i			0.353475i	0.984258	+	0.176737i	$0.0565543\pi$
$157$			1.04137e16i			0.353475i	−0.984258	+	0.176737i	$0.943446\pi$
$158$			1.07091e16i			0.346596i
$159$	1.67795e16			0.517964
$160$	8.90149e15	−	2.06028e16i	0.262158	−	0.606774i
$161$	−1.81510e16			−0.510161
$162$			1.31465e16i			0.352733i
$163$			4.70622e16i			1.20577i	0.797827	+	0.602886i	$0.205983\pi$
$163$			4.70622e16i			1.20577i	−0.797827	+	0.602886i	$0.794017\pi$
$164$	−2.40380e16			−0.588261
$165$	−1.15833e16	+	2.68100e16i	−0.270834	+	0.626856i
$166$	2.87049e15			0.0641424
$167$		−	3.97751e16i		−	0.849646i	−0.905276	−	0.424823i	$-0.860336\pi$
$167$		−	3.97751e16i		−	0.849646i	0.905276	−	0.424823i	$-0.139664\pi$
$168$		−	2.39422e16i		−	0.489040i
$169$	2.40130e16			0.469134
$170$	1.72528e16	+	7.45410e15i	0.322472	+	0.139325i
$171$	−1.07489e17			−1.92262
$172$		−	6.30457e16i		−	1.07942i
$173$			6.30223e16i			1.03311i	0.856253	+	0.516557i	$0.172787\pi$
$173$			6.30223e16i			1.03311i	−0.856253	+	0.516557i	$0.827213\pi$
$174$	−2.12630e16			−0.333815
$175$	−2.88258e16	+	2.71321e16i	−0.433507	+	0.408036i
$176$	−2.22369e16			−0.320428
$177$			9.00474e15i			0.124357i
$178$		−	2.18670e16i		−	0.289494i
$179$	2.10684e16			0.267445			0.133722	−	0.991019i	$-0.457307\pi$
$179$	2.10684e16			0.267445			0.133722	+	0.991019i	$0.457307\pi$
$180$	1.53123e17	+	6.61571e16i	1.86422	+	0.805439i
$181$	1.74536e16			0.203843			0.101922	−	0.994792i	$-0.467501\pi$
$181$	1.74536e16			0.203843			0.101922	+	0.994792i	$0.467501\pi$
$182$			9.21466e15i			0.103263i
$183$			4.81887e16i			0.518277i
$184$	−3.83989e16			−0.396447
$185$	5.87494e16	−	1.35978e17i	0.582392	−	1.34797i
$186$	−1.92375e15			−0.0183148
$187$		−	6.20531e16i		−	0.567482i
$188$		−	1.18422e17i		−	1.04052i
$189$	1.44317e17			1.21858
$190$	1.03898e16	−	2.40477e16i	0.0843251	−	0.195174i
$191$	−1.82919e17			−1.42728			−0.713639	−	0.700514i	$-0.752954\pi$
$191$	−1.82919e17			−1.42728			−0.713639	+	0.700514i	$0.752954\pi$
$192$			1.59936e17i			1.20002i
$193$		−	4.54299e16i		−	0.327840i	−0.986474	−	0.163920i	$-0.947586\pi$
$193$		−	4.54299e16i		−	0.327840i	0.986474	−	0.163920i	$-0.0524139\pi$
$194$	5.11671e16			0.355204
$195$	−1.77801e17	−	7.68192e16i	−1.18761	−	0.513110i
$196$	9.47396e16			0.608991
$197$			2.54430e17i			1.57425i	0.616797	+	0.787123i	$0.288430\pi$
$197$			2.54430e17i			1.57425i	−0.616797	+	0.787123i	$0.711570\pi$
$198$			3.30877e16i			0.197096i
$199$	1.75148e17			1.00463			0.502316	−	0.864684i	$-0.332482\pi$
$199$	1.75148e17			1.00463			0.502316	+	0.864684i	$0.332482\pi$
$200$	−6.09815e16	+	5.73985e16i	−0.336879	+	0.317085i
$201$	−4.44849e16			−0.236724
$202$			8.53133e15i			0.0437403i
$203$			9.51584e16i			0.470140i
$204$	−5.19040e17			−2.47158
$205$	1.24709e17	+	5.38807e16i	0.572457	+	0.247331i
$206$	−6.46473e16			−0.286119
$207$		−	4.32240e17i		−	1.84479i
$208$		−	1.47473e17i		−	0.607067i
$209$	−8.64923e16			−0.343463
$210$	−2.60504e16	+	6.02946e16i	−0.0998089	+	0.231012i
$211$	3.58937e17			1.32709			0.663545	−	0.748137i	$-0.269051\pi$
$211$	3.58937e17			1.32709			0.663545	+	0.748137i	$0.269051\pi$
$212$		−	7.71141e16i		−	0.275179i
$213$			9.55399e16i			0.329107i
$214$	2.97165e16			0.0988313
$215$	−1.41315e17	+	3.27080e17i	−0.453838	+	1.05043i
$216$	3.05305e17			0.946958
$217$			8.60939e15i			0.0257943i
$218$			5.83361e16i			0.168855i
$219$	3.93706e17			1.10114
$220$	1.23212e17	+	5.32340e16i	0.333030	+	0.143886i
$221$	4.11529e17			1.07512
$222$		−	2.45771e17i		−	0.620702i
$223$		−	8.51111e16i		−	0.207826i	−0.994586	−	0.103913i	$-0.966864\pi$
$223$		−	8.51111e16i		−	0.207826i	0.994586	−	0.103913i	$-0.0331364\pi$
$224$	−1.66653e17			−0.393506
$225$	−6.46110e17	−	6.86443e17i	−1.47549	−	1.56760i
$226$	−9.82583e16			−0.217048
$227$		−	8.22273e16i		−	0.175720i	−0.996133	−	0.0878602i	$-0.971997\pi$
$227$		−	8.22273e16i		−	0.175720i	0.996133	−	0.0878602i	$-0.0280029\pi$
$228$			7.23460e17i			1.49590i
$229$	−3.91258e17			−0.782884			−0.391442	−	0.920203i	$-0.628024\pi$
$229$	−3.91258e17			−0.782884			−0.391442	+	0.920203i	$0.628024\pi$
$230$	9.67015e16	+	4.17800e16i	0.187273	+	0.0809115i
$231$	2.16862e17			0.406530
$232$			2.01309e17i			0.365346i
$233$		−	9.50055e17i		−	1.66947i	−0.550650	−	0.834736i	$-0.685620\pi$
$233$		−	9.50055e17i		−	1.66947i	0.550650	−	0.834736i	$-0.314380\pi$
$234$	−2.19433e17			−0.373408
$235$	−2.65440e17	+	6.14371e17i	−0.437480	+	1.01256i
$236$	4.13834e16			0.0660673
$237$			1.67144e18i			2.58511i
$238$		−	1.39555e17i		−	0.209131i
$239$	3.05534e17			0.443685			0.221843	−	0.975082i	$-0.428793\pi$
$239$	3.05534e17			0.443685			0.221843	+	0.975082i	$0.428793\pi$
$240$	4.16914e17	−	9.64963e17i	0.586762	−	1.35808i
$241$	−1.24585e18			−1.69956			−0.849780	−	0.527137i	$-0.823266\pi$
$241$	−1.24585e18			−1.69956			−0.849780	+	0.527137i	$0.823266\pi$
$242$		−	1.53390e17i		−	0.202853i
$243$			4.55471e17i			0.584001i
$244$	2.21463e17			0.275345
$245$	−4.91507e17	−	2.12357e17i	−0.592631	−	0.256047i
$246$	2.25403e17			0.263601
$247$		−	5.73606e17i		−	0.650709i
$248$			1.82133e16i			0.0200448i
$249$	4.48018e17			0.478411
$250$	2.16025e17	−	7.81977e16i	0.223848	−	0.0810297i
$251$	3.78704e17			0.380844			0.190422	−	0.981702i	$-0.439014\pi$
$251$	3.78704e17			0.380844			0.190422	+	0.981702i	$0.439014\pi$
$252$		−	1.23858e18i		−	1.20899i
$253$		−	3.47806e17i		−	0.329559i
$254$	1.21614e17			0.111875
$255$	2.69277e18	+	1.16342e18i	2.40518	+	1.03916i
$256$	5.53605e17			0.480176
$257$			6.98680e16i			0.0588545i	0.999567	+	0.0294273i	$0.00936834\pi$
$257$			6.98680e16i			0.0588545i	−0.999567	+	0.0294273i	$0.990632\pi$
$258$			5.91175e17i			0.483691i
$259$	−1.09990e18			−0.874188
$260$	−3.53041e17	+	8.17127e17i	−0.272600	+	0.630942i
$261$	−2.26605e18			−1.70007
$262$			2.82067e17i			0.205633i
$263$		−	6.94838e17i		−	0.492284i	−0.969234	−	0.246142i	$-0.920837\pi$
$263$		−	6.94838e17i		−	0.492284i	0.969234	−	0.246142i	$-0.0791629\pi$
$264$	4.58775e17			0.315915
$265$	−1.72849e17	+	4.00067e17i	−0.115698	+	0.267786i
$266$	−1.94517e17			−0.126574
$267$		−	3.41294e18i		−	2.15921i
$268$			2.04441e17i			0.125764i
$269$	1.75703e18			1.05108			0.525542	−	0.850768i	$-0.323863\pi$
$269$	1.75703e18			1.05108			0.525542	+	0.850768i	$0.323863\pi$
$270$	−7.68862e17	−	3.32188e17i	−0.447322	−	0.193266i
$271$	−1.86384e18			−1.05472			−0.527362	−	0.849641i	$-0.676819\pi$
$271$	−1.86384e18			−1.05472			−0.527362	+	0.849641i	$0.676819\pi$
$272$			2.23345e18i			1.22945i
$273$			1.43820e18i			0.770193i
$274$	5.06891e17			0.264110
$275$	−5.19899e17	−	5.52354e17i	−0.263587	−	0.280041i
$276$	−2.90921e18			−1.43535
$277$			3.28806e18i			1.57885i	0.613846	+	0.789425i	$0.289621\pi$
$277$			3.28806e18i			1.57885i	−0.613846	+	0.789425i	$0.710379\pi$
$278$		−	8.78118e17i		−	0.410409i
$279$	−2.05020e17			−0.0932747
$280$	5.70844e17	+	2.46634e17i	0.252832	+	0.109237i
$281$	2.41481e18			1.04132			0.520662	−	0.853763i	$-0.325685\pi$
$281$	2.41481e18			1.04132			0.520662	+	0.853763i	$0.325685\pi$
$282$			1.11044e18i			0.466257i
$283$			1.11571e17i			0.0456199i	0.999740	+	0.0228099i	$0.00726126\pi$
$283$			1.11571e17i			0.0456199i	−0.999740	+	0.0228099i	$0.992739\pi$
$284$	4.39076e17			0.174845
$285$	1.62162e18	−	3.75330e18i	0.628944	−	1.45571i
$286$	−1.76569e17			−0.0667068
$287$		−	1.00875e18i		−	0.371251i
$288$		−	3.96858e18i		−	1.42296i
$289$	−3.37012e18			−1.17737
$290$	2.19035e17	−	5.06966e17i	0.0745640	−	0.172581i
$291$	7.98602e18			2.64931
$292$		−	1.80937e18i		−	0.585001i
$293$			2.59868e18i			0.818927i	0.912327	+	0.409463i	$0.134284\pi$
$293$			2.59868e18i			0.818927i	−0.912327	+	0.409463i	$0.865716\pi$
$294$	−8.88367e17			−0.272890
$295$	−2.14697e17	−	9.27600e16i	−0.0642924	−	0.0277777i
$296$	−2.32686e18			−0.679332
$297$			2.76537e18i			0.787189i
$298$			1.24788e18i			0.346378i
$299$	2.30661e18			0.624367
$300$	−4.62013e18	+	4.34867e18i	−1.21968	+	1.14801i
$301$	2.64569e18			0.681224
$302$			7.63735e14i			0.000191819i
$303$			1.33155e18i			0.326240i
$304$	3.11308e18			0.744112
$305$	−1.14895e18	−	4.96404e17i	−0.267948	−	0.115767i
$306$	3.32329e18			0.756236
$307$		−	7.96608e18i		−	1.76892i	−0.466621	−	0.884458i	$-0.654529\pi$
$307$		−	7.96608e18i		−	1.76892i	0.466621	−	0.884458i	$-0.345471\pi$
$308$		−	9.96640e17i		−	0.215977i
$309$	−1.00900e19			−2.13403
$310$	1.98171e16	−	4.58674e16i	0.00409097	−	0.00946871i
$311$	−8.72923e18			−1.75903			−0.879515	−	0.475872i	$-0.842133\pi$
$311$	−8.72923e18			−1.75903			−0.879515	+	0.475872i	$0.842133\pi$
$312$			3.04254e18i			0.598517i
$313$		−	3.04567e17i		−	0.0584926i	−0.999572	−	0.0292463i	$-0.990689\pi$
$313$		−	3.04567e17i		−	0.0584926i	0.999572	−	0.0292463i	$-0.00931071\pi$
$314$	−4.48768e17			−0.0841492
$315$	−2.77626e18	+	6.42575e18i	−0.508312	+	1.17651i
$316$	7.68151e18			1.37339
$317$		−	5.64109e18i		−	0.984961i	−0.870324	−	0.492480i	$-0.836090\pi$
$317$		−	5.64109e18i		−	0.984961i	0.870324	−	0.492480i	$-0.163910\pi$
$318$			7.23094e17i			0.123308i
$319$	−1.82340e18			−0.303706
$320$	−3.81329e18	−	1.64754e18i	−0.620405	−	0.268047i
$321$	4.63807e18			0.737140
$322$		−	7.82201e17i		−	0.121450i
$323$			8.68718e18i			1.31783i
$324$	9.42984e18			1.39771
$325$	3.66314e18	−	3.44791e18i	0.530553	−	0.499379i
$326$	−2.02810e18			−0.287050
$327$			9.10494e18i			1.25941i
$328$		−	2.13402e18i		−	0.288500i
$329$	4.96954e18			0.656670
$330$	−1.15535e18	−	4.99171e17i	−0.149231	−	0.0644756i
$331$	6.05049e18			0.763978			0.381989	−	0.924167i	$-0.375239\pi$
$331$	6.05049e18			0.763978			0.381989	+	0.924167i	$0.375239\pi$
$332$		−	2.05898e18i		−	0.254165i
$333$		−	2.61925e19i		−	3.16114i
$334$	1.71407e18			0.202269
$335$	4.58250e17	−	1.06064e18i	0.0528770	−	0.122386i
$336$	−7.80541e18			−0.880747
$337$			1.58672e19i			1.75096i	0.483254	+	0.875480i	$0.339455\pi$
$337$			1.58672e19i			1.75096i	−0.483254	+	0.875480i	$0.660545\pi$
$338$			1.03482e18i			0.111683i
$339$	−1.53359e19			−1.61887
$340$	5.34676e18	−	1.23753e19i	0.552076	−	1.27780i
$341$	−1.64971e17			−0.0166629
$342$		−	4.63213e18i		−	0.457705i
$343$			1.01341e19i			0.979667i
$344$	5.59700e18			0.529380
$345$	1.50929e19	+	6.52092e18i	1.39679	+	0.603484i
$346$	−2.71588e18			−0.245946
$347$			5.47026e18i			0.484771i	0.970180	+	0.242386i	$0.0779299\pi$
$347$			5.47026e18i			0.484771i	−0.970180	+	0.242386i	$0.922070\pi$
$348$			1.52518e19i			1.32274i
$349$	−7.51980e18			−0.638287			−0.319143	−	0.947706i	$-0.603395\pi$
$349$	−7.51980e18			−0.638287			−0.319143	+	0.947706i	$0.603395\pi$
$350$	−1.16923e18	−	1.24222e18i	−0.0971381	−	0.103202i
$351$	−1.83396e19			−1.49137
$352$		−	3.19336e18i		−	0.254201i
$353$			3.96219e18i			0.308763i	0.988011	+	0.154382i	$0.0493385\pi$
$353$			3.96219e18i			0.308763i	−0.988011	+	0.154382i	$0.950662\pi$
$354$	−3.88050e17			−0.0296049
$355$	−2.27792e18	−	9.84179e17i	−0.170148	−	0.0735126i
$356$	−1.56850e19			−1.14712
$357$		−	2.17813e19i		−	1.55981i
$358$			9.07921e17i			0.0636686i
$359$	1.88540e19			1.29478			0.647390	−	0.762159i	$-0.275860\pi$
$359$	1.88540e19			1.29478			0.647390	+	0.762159i	$0.275860\pi$
$360$	−5.87322e18	+	1.35938e19i	−0.395010	+	0.914265i
$361$	−3.07257e18			−0.202394
$362$			7.52146e17i			0.0485275i
$363$		−	2.39407e19i		−	1.51299i
$364$	6.60959e18			0.409180
$365$	−4.05566e18	+	9.38699e18i	−0.245961	+	0.569285i
$366$	−2.07664e18			−0.123383
$367$		−	1.02228e19i		−	0.595077i	−0.954710	−	0.297538i	$-0.903834\pi$
$367$		−	1.02228e19i		−	0.595077i	0.954710	−	0.297538i	$-0.0961656\pi$
$368$			1.25184e19i			0.713989i
$369$	2.40218e19			1.34248
$370$	5.85982e18	+	2.53175e18i	0.320901	+	0.138646i
$371$	3.23607e18			0.173665
$372$			1.37989e18i			0.0725726i
$373$			1.86547e19i			0.961550i	0.876844	+	0.480775i	$0.159645\pi$
$373$			1.86547e19i			0.961550i	−0.876844	+	0.480775i	$0.840355\pi$
$374$	2.67412e18			0.135096
$375$	3.37166e19	−	1.22049e19i	1.66959	−	0.604365i
$376$	1.05131e19			0.510298
$377$		−	1.20926e19i		−	0.575386i
$378$			6.21918e18i			0.290098i
$379$	−3.62923e19			−1.65967			−0.829833	−	0.558012i	$-0.811564\pi$
$379$	−3.62923e19			−1.65967			−0.829833	+	0.558012i	$0.811564\pi$
$380$	−1.72492e19	−	7.45253e18i	−0.773377	−	0.334139i
$381$	1.89812e19			0.834425
$382$		−	7.88270e18i		−	0.339782i
$383$		−	3.39832e19i		−	1.43640i	−0.695839	−	0.718198i	$-0.744967\pi$
$383$		−	3.39832e19i		−	1.43640i	0.695839	−	0.718198i	$-0.255033\pi$
$384$	−3.52077e19			−1.45933
$385$	−2.23394e18	+	5.17055e18i	−0.0908065	+	0.210175i
$386$	1.95776e18			0.0780465
$387$			6.30031e19i			2.46337i
$388$		−	3.67017e19i		−	1.40750i
$389$	4.43693e19			1.66902			0.834508	−	0.550996i	$-0.185752\pi$
$389$	4.43693e19			1.66902			0.834508	+	0.550996i	$0.185752\pi$
$390$	3.31045e18	−	7.66215e18i	0.122152	−	0.282726i
$391$	−3.49333e19			−1.26448
$392$			8.41069e18i			0.298666i
$393$			4.40242e19i			1.53373i
$394$	−1.09644e19			−0.374769
$395$	−3.98516e19	−	1.72179e19i	−1.33649	−	0.577434i
$396$	2.37335e19			0.780993
$397$			1.44302e19i			0.465953i	0.972482	+	0.232977i	$0.0748466\pi$
$397$			1.44302e19i			0.465953i	−0.972482	+	0.232977i	$0.925153\pi$
$398$			7.54781e18i			0.239165i
$399$	−3.03597e19			−0.944063
$400$	1.87125e19	+	1.98806e19i	0.571061	+	0.606709i
$401$	2.34827e19			0.703339			0.351669	−	0.936124i	$-0.385614\pi$
$401$	2.34827e19			0.703339			0.351669	+	0.936124i	$0.385614\pi$
$402$		−	1.91703e18i		−	0.0563552i
$403$		−	1.09407e18i		−	0.0315687i
$404$	6.11945e18			0.173321
$405$	−4.89219e19	−	2.11368e19i	−1.36016	−	0.587660i
$406$	−4.10075e18			−0.111923
$407$		−	2.10760e19i		−	0.564717i
$408$		−	4.60788e19i		−	1.21213i
$409$	−3.99167e19			−1.03093			−0.515466	−	0.856910i	$-0.672381\pi$
$409$	−3.99167e19			−1.03093			−0.515466	+	0.856910i	$0.672381\pi$
$410$	−2.32193e18	+	5.37420e18i	−0.0588804	+	0.136281i
$411$	7.91142e19			1.96988
$412$			4.63709e19i			1.13375i
$413$			1.73664e18i			0.0416951i
$414$	1.86269e19			0.439176
$415$	−4.61515e18	+	1.06819e19i	−0.106862	+	0.247337i
$416$	2.11780e19			0.481598
$417$		−	1.37054e20i		−	3.06106i
$418$		−	3.72729e18i		−	0.0817658i
$419$	7.16449e19			1.54376			0.771881	−	0.635767i	$-0.219316\pi$
$419$	7.16449e19			1.54376			0.771881	+	0.635767i	$0.219316\pi$
$420$	4.32488e19	+	1.86857e19i	0.915385	+	0.395494i
$421$	−6.22202e18			−0.129365			−0.0646823	−	0.997906i	$-0.520603\pi$
$421$	−6.22202e18			−0.129365			−0.0646823	+	0.997906i	$0.520603\pi$
$422$			1.54680e19i			0.315931i
$423$			1.18342e20i			2.37458i
$424$	6.84596e18			0.134955
$425$	−5.54778e19	+	5.22181e19i	−1.07449	+	1.01136i
$426$	−4.11719e18			−0.0783482
$427$			9.29361e18i			0.173770i
$428$		−	2.13154e19i		−	0.391620i
$429$	−2.75585e19			−0.497537
$430$	−1.40952e19	−	6.08984e18i	−0.250067	−	0.108042i
$431$	−4.93032e19			−0.859598			−0.429799	−	0.902925i	$-0.641416\pi$
$431$	−4.93032e19			−0.859598			−0.429799	+	0.902925i	$0.641416\pi$
$432$		−	9.95327e19i		−	1.70544i
$433$		−	1.59414e19i		−	0.268453i	−0.990951	−	0.134226i	$-0.957145\pi$
$433$		−	1.59414e19i		−	0.268453i	0.990951	−	0.134226i	$-0.0428549\pi$
$434$	−3.71013e17			−0.00614067
$435$	3.41865e19	−	7.91259e19i	0.556141	−	1.28721i
$436$	4.18439e19			0.669089
$437$			4.86914e19i			0.765318i
$438$			1.69664e19i			0.262140i
$439$	−1.26174e19			−0.191640			−0.0958201	−	0.995399i	$-0.530547\pi$
$439$	−1.26174e19			−0.191640			−0.0958201	+	0.995399i	$0.530547\pi$
$440$	−4.72595e18	+	1.09384e19i	−0.0705658	+	0.163327i
$441$	−9.46756e19			−1.38979
$442$			1.77344e19i			0.255947i
$443$		−	7.89961e19i		−	1.12093i	−0.828179	−	0.560464i	$-0.810623\pi$
$443$		−	7.89961e19i		−	1.12093i	0.828179	−	0.560464i	$-0.189377\pi$
$444$	−1.76289e20			−2.45954
$445$	8.13735e19	+	3.51576e19i	1.11630	+	0.482301i
$446$	3.66778e18			0.0494756
$447$			1.94766e20i			2.58348i
$448$			3.08450e19i			0.402347i
$449$	4.36438e19			0.559854			0.279927	−	0.960021i	$-0.409690\pi$
$449$	4.36438e19			0.559854			0.279927	+	0.960021i	$0.409690\pi$
$450$	2.95816e19	−	2.78435e19i	0.373188	−	0.351260i
$451$	1.93294e19			0.239825
$452$			7.04798e19i			0.860055i
$453$			1.19202e17i			0.00143069i
$454$	3.54350e18			0.0418325
$455$	−3.42905e19	−	1.48153e19i	−0.398188	−	0.172038i
$456$	−6.42265e19			−0.733632
$457$		−	1.00520e20i		−	1.12949i	−0.825266	−	0.564744i	$-0.808975\pi$
$457$		−	1.00520e20i		−	1.12949i	0.825266	−	0.564744i	$-0.191025\pi$
$458$		−	1.68609e19i		−	0.186376i
$459$	2.77750e20			3.02036
$460$	2.99684e19	−	6.93631e19i	0.320612	−	0.742070i
$461$	−1.09258e20			−1.15000			−0.574999	−	0.818154i	$-0.694998\pi$
$461$	−1.09258e20			−1.15000			−0.574999	+	0.818154i	$0.694998\pi$
$462$			9.34543e18i			0.0967797i
$463$		−	1.81520e20i		−	1.84955i	−0.380510	−	0.924777i	$-0.624252\pi$
$463$		−	1.81520e20i		−	1.84955i	0.380510	−	0.924777i	$-0.375748\pi$
$464$	6.56290e19			0.657978
$465$	3.09299e18	−	7.15885e18i	0.0305128	−	0.0706230i
$466$	4.09416e19			0.397439
$467$		−	1.14048e20i		−	1.08946i	−0.838611	−	0.544731i	$-0.816632\pi$
$467$		−	1.14048e20i		−	1.08946i	0.838611	−	0.544731i	$-0.183368\pi$
$468$			1.57398e20i			1.47963i
$469$	−8.57930e18			−0.0793699
$470$	−2.64757e19	−	1.14389e19i	−0.241054	−	0.104148i
$471$	−7.00425e19			−0.627632
$472$			3.67390e18i			0.0324013i
$473$			5.06961e19i			0.440064i
$474$	−7.20290e19			−0.615418
$475$	7.27837e19	+	7.73272e19i	0.612114	+	0.650325i
$476$	−1.00101e20			−0.828682
$477$			7.70621e19i			0.627990i
$478$			1.31667e19i			0.105625i
$479$	1.21110e20			0.956451			0.478226	−	0.878237i	$-0.341280\pi$
$479$	1.21110e20			0.956451			0.478226	+	0.878237i	$0.341280\pi$
$480$	1.38574e20	+	5.98713e19i	1.07739	+	0.465489i
$481$	1.39774e20			1.06989
$482$		−	5.36885e19i		−	0.404602i
$483$		−	1.22084e20i		−	0.905846i
$484$	−1.10025e20			−0.803807
$485$	−8.22660e19	+	1.90408e20i	−0.591776	+	1.36969i
$486$	−1.96280e19			−0.139029
$487$		−	1.00069e20i		−	0.697963i	−0.937130	−	0.348982i	$-0.886528\pi$
$487$		−	1.00069e20i		−	0.697963i	0.937130	−	0.348982i	$-0.113472\pi$
$488$			1.96608e19i			0.135037i
$489$	−3.16540e20			−2.14098
$490$	9.15129e18	−	2.11810e19i	0.0609553	−	0.141083i
$491$	−1.32724e20			−0.870641			−0.435321	−	0.900276i	$-0.643365\pi$
$491$	−1.32724e20			−0.870641			−0.435321	+	0.900276i	$0.643365\pi$
$492$		−	1.61679e20i		−	1.04452i
$493$			1.83141e20i			1.16529i
$494$	2.47190e19			0.154910
$495$	−1.23129e20	−	5.31980e19i	−0.760013	−	0.328365i
$496$	5.93774e18			0.0361001
$497$			1.84257e19i			0.110345i
$498$			1.93069e19i			0.113892i
$499$	−9.34938e18			−0.0543286			−0.0271643	−	0.999631i	$-0.508648\pi$
$499$	−9.34938e18			−0.0543286			−0.0271643	+	0.999631i	$0.508648\pi$
$500$	−5.60905e19	−	1.54953e20i	−0.321081	−	0.887001i
$501$	2.67527e20			1.50864
$502$			1.63198e19i			0.0906647i
$503$			1.56622e20i			0.857223i	0.903489	+	0.428612i	$0.140997\pi$
$503$			1.56622e20i			0.857223i	−0.903489	+	0.428612i	$0.859003\pi$
$504$	1.09958e20			0.592921
$505$	−3.17476e19	−	1.37166e19i	−0.168665	−	0.0728720i
$506$	1.49884e19			0.0784558
$507$			1.61511e20i			0.832997i
$508$		−	8.72329e19i		−	0.443305i
$509$	1.94050e20			0.971698			0.485849	−	0.874043i	$-0.338511\pi$
$509$	1.94050e20			0.971698			0.485849	+	0.874043i	$0.338511\pi$
$510$	−5.01362e19	+	1.16042e20i	−0.247386	+	0.572584i
$511$	7.59296e19			0.369194
$512$			1.95384e20i			0.936188i
$513$		−	3.87140e20i		−	1.82805i
$514$	−3.01089e18			−0.0140111
$515$	1.03939e20	−	2.40571e20i	0.476678	−	1.10329i
$516$	4.24045e20			1.91663
$517$			9.52252e19i			0.424202i
$518$		−	4.73990e19i		−	0.208112i
$519$	−4.23887e20			−1.83441
$520$	−7.25421e19	−	3.13419e19i	−0.309432	−	0.133691i
$521$	−6.43719e19			−0.270653			−0.135327	−	0.990801i	$-0.543208\pi$
$521$	−6.43719e19			−0.270653			−0.135327	+	0.990801i	$0.543208\pi$
$522$		−	9.76533e19i		−	0.404723i
$523$			1.94571e20i			0.794904i	0.917623	+	0.397452i	$0.130105\pi$
$523$			1.94571e20i			0.794904i	−0.917623	+	0.397452i	$0.869895\pi$
$524$	2.02324e20			0.814822
$525$	−1.82490e20	−	1.93882e20i	−0.724511	−	0.769738i
$526$	2.99433e19			0.117194
$527$			1.65695e19i			0.0639337i
$528$		−	1.49565e20i		−	0.568954i
$529$	7.08352e19			0.265663
$530$	−1.72405e19	−	7.44877e18i	−0.0637500	−	0.0275433i
$531$	−4.13555e19			−0.150773
$532$			1.39525e20i			0.501552i
$533$			1.28190e20i			0.454360i
$534$	1.47077e20			0.514027
$535$	−4.77779e19	+	1.10584e20i	−0.164655	+	0.381099i
$536$	−1.81497e19			−0.0616784
$537$			1.41706e20i			0.474877i
$538$			7.57175e19i			0.250224i
$539$	−7.61817e19			−0.248276
$540$	−2.38275e20	+	5.51498e20i	−0.765819	+	1.77252i
$541$	1.81403e19			0.0574996			0.0287498	−	0.999587i	$-0.490847\pi$
$541$	1.81403e19			0.0574996			0.0287498	+	0.999587i	$0.490847\pi$
$542$		−	8.03202e19i		−	0.251090i
$543$			1.17393e20i			0.361945i
$544$	−3.20737e20			−0.975344
$545$	−2.17086e20	−	9.37922e19i	−0.651114	−	0.281315i
$546$	−6.19777e19			−0.183354
$547$		−	6.00592e20i		−	1.75257i	−0.481796	−	0.876283i	$-0.660015\pi$
$547$		−	6.00592e20i		−	1.75257i	0.481796	−	0.876283i	$-0.339985\pi$
$548$		−	3.63588e20i		−	1.04654i
$549$	−2.21313e20			−0.628369
$550$	2.38031e19	−	2.24045e19i	0.0666674	−	0.0627502i
$551$	2.55269e20			0.705279
$552$		−	2.58270e20i		−	0.703934i
$553$			3.22352e20i			0.866746i
$554$	−1.41695e20			−0.375866
$555$	9.14585e20	+	3.95148e20i	2.39346	+	1.03410i
$556$	−6.29866e20			−1.62625
$557$		−	2.29611e20i		−	0.584895i	−0.956282	−	0.292447i	$-0.905530\pi$
$557$		−	2.29611e20i		−	0.584895i	0.956282	−	0.292447i	$-0.0944697\pi$
$558$		−	8.83511e18i		−	0.0222052i
$559$	−3.36210e20			−0.833725
$560$	8.04054e19	−	1.86101e20i	0.196732	−	0.455344i
$561$	4.17369e20			1.00762
$562$			1.04064e20i			0.247901i
$563$			5.26651e20i			1.23797i	0.785403	+	0.618985i	$0.212456\pi$
$563$			5.26651e20i			1.23797i	−0.785403	+	0.618985i	$0.787544\pi$
$564$	7.96506e20			1.84755
$565$	1.57979e20	−	3.65648e20i	0.361606	−	0.836950i
$566$	−4.80805e18			−0.0108604
$567$			3.95720e20i			0.882095i
$568$			3.89799e19i			0.0857488i
$569$	5.86825e20			1.27399			0.636996	−	0.770868i	$-0.280177\pi$
$569$	5.86825e20			1.27399			0.636996	+	0.770868i	$0.280177\pi$
$570$	1.61744e20	+	6.98819e19i	0.346552	+	0.149728i
$571$	−2.76080e20			−0.583800			−0.291900	−	0.956449i	$-0.594287\pi$
$571$	−2.76080e20			−0.583800			−0.291900	+	0.956449i	$0.594287\pi$
$572$			1.26652e20i			0.264326i
$573$		−	1.23031e21i		−	2.53428i
$574$	4.34709e19			0.0883811
$575$	−3.10952e20	+	2.92681e20i	−0.623999	+	0.587335i
$576$	−7.34528e20			−1.45492
$577$			1.42599e20i			0.278804i	0.990236	+	0.139402i	$0.0445180\pi$
$577$			1.42599e20i			0.278804i	−0.990236	+	0.139402i	$0.955482\pi$
$578$		−	1.45232e20i		−	0.280287i
$579$	3.05561e20			0.582115
$580$	−3.63642e20	−	1.57112e20i	−0.683855	−	0.295461i
$581$	8.64042e19			0.160404
$582$			3.44149e20i			0.630703i
$583$			6.20088e19i			0.112186i
$584$	1.60630e20			0.286901
$585$	3.52803e20	−	8.16576e20i	0.622104	−	1.43988i
$586$	−1.11987e20			−0.194956
$587$		−	7.48323e20i		−	1.28618i	−0.765789	−	0.643092i	$-0.777651\pi$
$587$		−	7.48323e20i		−	1.28618i	0.765789	−	0.643092i	$-0.222349\pi$
$588$			6.37217e20i			1.08133i
$589$	2.30953e19			0.0386953
$590$	3.99740e18	−	9.25212e18i	0.00661283	−	0.0153056i
$591$	−1.71130e21			−2.79524
$592$			7.58581e20i			1.22346i
$593$			3.21784e20i			0.512454i	0.966617	+	0.256227i	$0.0824794\pi$
$593$			3.21784e20i			0.512454i	−0.966617	+	0.256227i	$0.917521\pi$
$594$	−1.19171e20			−0.187400
$595$	5.19324e20	+	2.24375e20i	0.806420	+	0.348415i
$596$	8.95092e20			1.37253
$597$			1.17804e21i			1.78383i
$598$			9.94010e19i			0.148639i
$599$	−1.08146e21			−1.59702			−0.798509	−	0.601983i	$-0.794377\pi$
$599$	−1.08146e21			−1.59702			−0.798509	+	0.601983i	$0.794377\pi$
$600$	−3.86061e20	−	4.10161e20i	−0.563018	−	0.598164i
$601$	5.36803e20			0.773136			0.386568	−	0.922261i	$-0.373660\pi$
$601$	5.36803e20			0.773136			0.386568	+	0.922261i	$0.373660\pi$
$602$			1.14013e20i			0.162174i
$603$		−	2.04303e20i		−	0.287009i
$604$	5.47820e17			0.000760083
$605$	5.70809e20	+	2.46619e20i	0.782213	+	0.337957i
$606$	−5.73816e19			−0.0776655
$607$		−	4.11434e20i		−	0.550029i	−0.961440	−	0.275014i	$-0.911317\pi$
$607$		−	4.11434e20i		−	0.550029i	0.961440	−	0.275014i	$-0.0886826\pi$
$608$			4.47057e20i			0.590318i
$609$	−6.40035e20			−0.834783
$610$	2.13920e19	−	4.95126e19i	0.0275599	−	0.0637885i
$611$	−6.31522e20			−0.803673
$612$		−	2.38376e21i		−	2.99659i
$613$		−	5.44101e20i		−	0.675656i	−0.941208	−	0.337828i	$-0.890308\pi$
$613$		−	5.44101e20i		−	0.675656i	0.941208	−	0.337828i	$-0.109692\pi$
$614$	3.43290e20			0.421113
$615$	−3.62401e20	+	8.38790e20i	−0.439163	+	1.01646i
$616$	8.84786e19			0.105921
$617$			4.65828e20i			0.550918i	0.961313	+	0.275459i	$0.0888298\pi$
$617$			4.65828e20i			0.550918i	−0.961313	+	0.275459i	$0.911170\pi$
$618$		−	4.34817e20i		−	0.508034i
$619$	1.51736e21			1.75150			0.875749	−	0.482767i	$-0.160368\pi$
$619$	1.51736e21			1.75150			0.875749	+	0.482767i	$0.160368\pi$
$620$	−3.29002e19	−	1.42146e19i	−0.0375199	−	0.0162105i
$621$	1.55678e21			1.75405
$622$		−	3.76177e20i		−	0.418759i
$623$		−	6.58215e20i		−	0.723948i
$624$	9.91900e20			1.07791
$625$	−5.63262e19	+	9.29618e20i	−0.0604798	+	0.998169i
$626$	1.31250e19			0.0139249
$627$		−	5.81746e20i		−	0.609855i
$628$			3.21897e20i			0.333442i
$629$	−2.11685e21			−2.16676
$630$	−2.76911e20	−	1.19640e20i	−0.280083	−	0.121010i
$631$	5.94310e20			0.594009			0.297004	−	0.954876i	$-0.404012\pi$
$631$	5.94310e20			0.594009			0.297004	+	0.954876i	$0.404012\pi$
$632$			6.81941e20i			0.673549i
$633$			2.41421e21i			2.35639i
$634$	2.43097e20			0.234482
$635$	−1.95530e20	+	4.52563e20i	−0.186385	+	0.431396i
$636$	5.18669e20			0.488609
$637$		−	5.05228e20i		−	0.470372i
$638$		−	7.85777e19i		−	0.0723010i
$639$	−4.38780e20			−0.399016
$640$	3.62683e20	−	8.39444e20i	0.325970	−	0.754469i
$641$	9.48383e20			0.842458			0.421229	−	0.906954i	$-0.361599\pi$
$641$	9.48383e20			0.842458			0.421229	+	0.906954i	$0.361599\pi$
$642$			1.99873e20i			0.175486i
$643$		−	2.15909e21i		−	1.87365i	−0.349800	−	0.936824i	$-0.613750\pi$
$643$		−	2.15909e21i		−	1.87365i	0.349800	−	0.936824i	$-0.386250\pi$
$644$	−5.61065e20			−0.481249
$645$	−2.19994e21	−	9.50486e20i	−1.86514	−	0.805838i
$646$	−3.74365e20			−0.313727
$647$			2.26989e20i			0.188028i	0.995571	+	0.0940139i	$0.0299698\pi$
$647$			2.26989e20i			0.188028i	−0.995571	+	0.0940139i	$0.970030\pi$
$648$			8.37153e20i			0.685476i
$649$	−3.32771e19			−0.0269346
$650$	1.48584e20	+	1.57859e20i	0.118884	+	0.126305i
$651$	−5.79067e19			−0.0458006
$652$			1.45474e21i			1.13744i
$653$		−	2.12810e21i		−	1.64491i	−0.568830	−	0.822455i	$-0.692604\pi$
$653$		−	2.12810e21i		−	1.64491i	0.568830	−	0.822455i	$-0.307396\pi$
$654$	−3.92368e20			−0.299820
$655$	−1.04965e21	−	4.53504e20i	−0.792932	−	0.342588i
$656$	−6.95714e20			−0.519580
$657$			1.80815e21i			1.33504i
$658$			2.14157e20i			0.156329i
$659$	3.97715e20			0.287032			0.143516	−	0.989648i	$-0.454159\pi$
$659$	3.97715e20			0.287032			0.143516	+	0.989648i	$0.454159\pi$
$660$	−3.58051e20	+	8.28723e20i	−0.255485	+	0.591330i
$661$	1.97089e20			0.139044			0.0695218	−	0.997580i	$-0.477853\pi$
$661$	1.97089e20			0.139044			0.0695218	+	0.997580i	$0.477853\pi$
$662$			2.60740e20i			0.181875i
$663$			2.76794e21i			1.90900i
$664$	1.82790e20			0.124650
$665$	3.12743e20	−	7.23855e20i	0.210875	−	0.488078i
$666$	1.12874e21			0.752551
$667$			1.02650e21i			0.676729i
$668$		−	1.22949e21i		−	0.801493i
$669$	5.72457e20			0.369017
$670$	4.57071e19	+	1.97478e19i	0.0291355	+	0.0125880i
$671$	−1.78082e20			−0.112254
$672$		−	1.12090e21i		−	0.698713i
$673$		−	1.12563e21i		−	0.693876i	−0.937888	−	0.346938i	$-0.887221\pi$
$673$		−	1.12563e21i		−	0.693876i	0.937888	−	0.346938i	$-0.112779\pi$
$674$	−6.83781e20			−0.416839
$675$	2.47234e21	−	2.32707e21i	1.49049	−	1.40292i
$676$	7.42265e20			0.442546
$677$		−	2.01414e21i		−	1.18761i	−0.804608	−	0.593806i	$-0.797625\pi$
$677$		−	2.01414e21i		−	1.18761i	0.804608	−	0.593806i	$-0.202375\pi$
$678$		−	6.60884e20i		−	0.385392i
$679$	1.54017e21			0.888273
$680$	1.09864e21	+	4.74669e20i	0.626669	+	0.270753i
$681$	5.53060e20			0.312010
$682$		−	7.10926e18i		−	0.00396681i
$683$			2.93860e21i			1.62176i	0.585215	+	0.810878i	$0.301010\pi$
$683$			2.93860e21i			1.62176i	−0.585215	+	0.810878i	$0.698990\pi$
$684$	−3.32259e21			−1.81366
$685$	−8.14974e20	+	1.88629e21i	−0.440012	+	1.01842i
$686$	−4.36718e20			−0.233222
$687$		−	2.63160e21i		−	1.39009i
$688$		−	1.82468e21i		−	0.953398i
$689$	−4.11235e20			−0.212542
$690$	−2.81012e20	+	6.50413e20i	−0.143667	+	0.332523i
$691$	−1.85211e20			−0.0936661			−0.0468330	−	0.998903i	$-0.514913\pi$
$691$	−1.85211e20			−0.0936661			−0.0468330	+	0.998903i	$0.514913\pi$
$692$			1.94808e21i			0.974564i
$693$			9.95967e20i			0.492885i
$694$	−2.35735e20			−0.115406
$695$	3.26773e21	+	1.41183e21i	1.58256	+	0.683748i
$696$	−1.35400e21			−0.648711
$697$		−	1.94142e21i		−	0.920182i
$698$		−	3.24058e20i		−	0.151952i
$699$	6.39006e21			2.96433
$700$	−8.91032e20	+	8.38678e20i	−0.408939	+	0.384911i
$701$	−1.53115e21			−0.695236			−0.347618	−	0.937636i	$-0.613009\pi$
$701$	−1.53115e21			−0.695236			−0.347618	+	0.937636i	$0.613009\pi$
$702$		−	7.90325e20i		−	0.355040i
$703$			2.95056e21i			1.31141i
$704$	−5.91046e20			−0.259912
$705$	−4.13226e21	−	1.78535e21i	−1.79791	−	0.776792i
$706$	−1.70747e20			−0.0735050
$707$			2.56800e20i			0.109383i
$708$			2.78345e20i			0.117310i
$709$	−1.28361e19			−0.00535287			−0.00267643	−	0.999996i	$-0.500852\pi$
$709$	−1.28361e19			−0.00535287			−0.00267643	+	0.999996i	$0.500852\pi$
$710$	4.24122e19	−	9.81646e19i	0.0175006	−	0.0405058i
$711$	−7.67633e21			−3.13423
$712$		−	1.39247e21i		−	0.562581i
$713$			9.28717e19i			0.0371289i
$714$	9.38644e20			0.371334
$715$	2.83886e20	−	6.57066e20i	0.111135	−	0.257225i
$716$	6.51244e20			0.252288
$717$			2.05502e21i			0.787811i
$718$			8.12495e20i			0.308239i
$719$	−3.14657e21			−1.18133			−0.590665	−	0.806917i	$-0.701134\pi$
$719$	−3.14657e21			−1.18133			−0.590665	+	0.806917i	$0.701134\pi$
$720$	4.43173e21	+	1.91473e21i	1.64657	+	0.711402i
$721$	−1.94594e21			−0.715508
$722$		−	1.32409e20i		−	0.0481825i
$723$		−	8.37955e21i		−	3.01775i
$724$	5.39507e20			0.192291
$725$	1.53440e21	+	1.63019e21i	0.541259	+	0.575047i
$726$	1.03170e21			0.360187
$727$			4.52609e21i			1.56392i	0.623327	+	0.781962i	$0.285781\pi$
$727$			4.52609e21i			1.56392i	−0.623327	+	0.781962i	$0.714219\pi$
$728$			5.86780e20i			0.200673i
$729$	1.31386e21			0.444726
$730$	−4.04522e20	−	1.74775e20i	−0.135526	−	0.0585540i
$731$	5.09186e21			1.68848
$732$			1.48956e21i			0.488904i
$733$			2.68116e21i			0.871048i	0.900177	+	0.435524i	$0.143437\pi$
$733$			2.68116e21i			0.871048i	−0.900177	+	0.435524i	$0.856563\pi$
$734$	4.40539e20			0.141666
$735$	1.42831e21	−	3.30587e21i	0.454639	−	1.05228i
$736$	−1.79772e21			−0.566421
$737$		−	1.64395e20i		−	0.0512721i
$738$			1.03519e21i			0.319594i
$739$	−1.15277e21			−0.352298			−0.176149	−	0.984364i	$-0.556364\pi$
$739$	−1.15277e21			−0.352298			−0.176149	+	0.984364i	$0.556364\pi$
$740$	1.81600e21	−	4.20320e21i	0.549386	−	1.27157i
$741$	3.85807e21			1.15540
$742$			1.39455e20i			0.0413433i
$743$		−	2.64683e21i		−	0.776801i	−0.921491	−	0.388400i	$-0.873028\pi$
$743$		−	2.64683e21i		−	0.776801i	0.921491	−	0.388400i	$-0.126972\pi$
$744$	−1.22503e20			−0.0355917
$745$	−4.64372e21	−	2.00633e21i	−1.33565	−	0.577072i
$746$	−8.03905e20			−0.228909
$747$			2.05759e21i			0.580034i
$748$		−	1.91812e21i		−	0.535320i
$749$	8.94493e20			0.247151
$750$	5.25957e20	+	1.45298e21i	0.143877	+	0.397467i
$751$	−4.36972e21			−1.18346			−0.591730	−	0.806136i	$-0.701555\pi$
$751$	−4.36972e21			−1.18346			−0.591730	+	0.806136i	$0.701555\pi$
$752$		−	3.42740e21i		−	0.919033i
$753$			2.54716e21i			0.676229i
$754$	5.21118e20			0.136978
$755$	−2.84208e18	−	1.22793e18i	−0.000739664	−	0.000319573i
$756$	4.46096e21			1.14952
$757$		−	7.25274e20i		−	0.185047i	−0.995710	−	0.0925237i	$-0.970507\pi$
$757$		−	7.25274e20i		−	0.185047i	0.995710	−	0.0925237i	$-0.0294934\pi$
$758$		−	1.56398e21i		−	0.395105i
$759$	2.33934e21			0.585168
$760$	6.61613e20	−	1.53133e21i	0.163871	−	0.379286i
$761$	2.04957e21			0.502665			0.251333	−	0.967901i	$-0.419131\pi$
$761$	2.04957e21			0.502665			0.251333	+	0.967901i	$0.419131\pi$
$762$			8.17977e20i			0.198646i
$763$			1.75597e21i			0.422262i
$764$	−5.65419e21			−1.34639
$765$	−5.34315e21	+	1.23669e22i	−1.25990	+	2.91609i
$766$	1.46447e21			0.341952
$767$		−	2.20690e20i		−	0.0510290i
$768$			3.72354e21i			0.852604i
$769$	−2.52209e21			−0.571891			−0.285945	−	0.958246i	$-0.592308\pi$
$769$	−2.52209e21			−0.571891			−0.285945	+	0.958246i	$0.592308\pi$
$770$	−2.22819e20	−	9.62695e19i	−0.0500349	−	0.0216176i
$771$	−4.69931e20			−0.104503
$772$		−	1.40428e21i		−	0.309260i
$773$			2.53203e21i			0.552233i	0.961124	+	0.276117i	$0.0890476\pi$
$773$			2.53203e21i			0.552233i	−0.961124	+	0.276117i	$0.910952\pi$
$774$	−2.71505e21			−0.586437
$775$	1.38824e20	+	1.47490e20i	0.0296963	+	0.0315501i
$776$	3.25827e21			0.690277
$777$		−	7.39791e21i		−	1.55221i
$778$			1.91205e21i			0.397330i
$779$	−2.70603e21			−0.556932
$780$	−5.49599e21	−	2.37455e21i	−1.12031	−	0.484030i
$781$	−3.53069e20			−0.0712815
$782$		−	1.50541e21i		−	0.301027i
$783$		−	8.16157e21i		−	1.61644i
$784$	2.74198e21			0.537890
$785$	7.21525e20	−	1.67000e21i	0.140194	−	0.324484i
$786$	−1.89718e21			−0.365123
$787$		−	1.39343e21i		−	0.265629i	−0.991141	−	0.132814i	$-0.957599\pi$
$787$		−	1.39343e21i		−	0.265629i	0.991141	−	0.132814i	$-0.0424014\pi$
$788$			7.86468e21i			1.48503i
$789$	4.67347e21			0.874102
$790$	7.41989e20	−	1.71736e21i	0.137466	−	0.318169i
$791$	−2.95766e21			−0.542781
$792$			2.10699e21i			0.383021i
$793$		−	1.18102e21i		−	0.212671i
$794$	−6.21853e20			−0.110926
$795$	−2.69085e21	−	1.16258e21i	−0.475483	−	0.205433i
$796$	5.41398e21			0.947695
$797$		−	9.55241e20i		−	0.165644i	−0.996564	−	0.0828220i	$-0.973607\pi$
$797$		−	9.55241e20i		−	0.165644i	0.996564	−	0.0828220i	$-0.0263933\pi$
$798$		−	1.30832e21i		−	0.224746i
$799$	9.56431e21			1.62762
$800$	−2.85498e21	+	2.68723e21i	−0.481313	+	0.453033i
$801$	1.56744e22			2.61787
$802$			1.01196e21i			0.167439i
$803$			1.45495e21i			0.238496i
$804$	−1.37507e21			−0.223308
$805$	2.91080e21	+	1.25762e21i	0.468320	+	0.202339i
$806$	4.71478e19			0.00751533
$807$			1.18178e22i			1.86631i
$808$			5.43266e20i			0.0850016i
$809$	−9.73892e21			−1.50972			−0.754861	−	0.655885i	$-0.772296\pi$
$809$	−9.73892e21			−1.50972			−0.754861	+	0.655885i	$0.772296\pi$
$810$	9.10867e20	−	2.10824e21i	0.139900	−	0.323804i
$811$	4.03949e20			0.0614711			0.0307355	−	0.999528i	$-0.490215\pi$
$811$	4.03949e20			0.0614711			0.0307355	+	0.999528i	$0.490215\pi$
$812$			2.94143e21i			0.443495i
$813$		−	1.25362e22i		−	1.87277i
$814$	9.08249e20			0.134438
$815$	3.26076e21	−	7.54715e21i	0.478230	−	1.10688i
$816$	−1.50222e22			−2.18302
$817$		−	7.09724e21i		−	1.02194i
$818$		−	1.72017e21i		−	0.245427i
$819$	−6.60513e21			−0.933797
$820$	3.85486e21	+	1.66550e21i	0.540014	+	0.233314i
$821$	1.42068e22			1.97207			0.986034	−	0.166541i	$-0.0532599\pi$
$821$	1.42068e22			1.97207			0.986034	+	0.166541i	$0.0532599\pi$
$822$			3.40934e21i			0.468956i
$823$			6.03911e21i			0.823141i	0.911378	+	0.411570i	$0.135020\pi$
$823$			6.03911e21i			0.823141i	−0.911378	+	0.411570i	$0.864980\pi$
$824$	−4.11667e21			−0.556022
$825$	3.71513e21	−	3.49684e21i	0.497243	−	0.468027i
$826$	−7.48387e19			−0.00992604
$827$			1.20995e22i			1.59029i	0.606421	+	0.795144i	$0.292605\pi$
$827$			1.20995e22i			1.59029i	−0.606421	+	0.795144i	$0.707395\pi$
$828$		−	1.33609e22i		−	1.74024i
$829$	−5.90195e21			−0.761792			−0.380896	−	0.924618i	$-0.624384\pi$
$829$	−5.90195e21			−0.761792			−0.380896	+	0.924618i	$0.624384\pi$
$830$	−4.60327e20	−	1.98885e20i	−0.0588818	−	0.0254400i
$831$	−2.21154e22			−2.80342
$832$		−	3.91974e21i		−	0.492417i
$833$			7.65160e21i			0.952610i
$834$	5.90621e21			0.728725
$835$	−2.75586e21	+	6.37855e21i	−0.336984	+	0.779962i
$836$	−2.67355e21			−0.323998
$837$		−	7.38412e20i		−	0.0886865i
$838$			3.08746e21i			0.367512i
$839$	1.29661e22			1.52966			0.764831	−	0.644231i	$-0.222822\pi$
$839$	1.29661e22			1.52966			0.764831	+	0.644231i	$0.222822\pi$
$840$	−1.65886e21	+	3.83949e21i	−0.193961	+	0.448931i
$841$	−3.24768e21			−0.376360
$842$		−	2.68131e20i		−	0.0307969i
$843$			1.62420e22i			1.84898i
$844$	1.10951e22			1.25188
$845$	−3.85086e21	−	1.66377e21i	−0.430657	−	0.186066i
$846$	−5.09983e21			−0.565299
$847$		−	4.61717e21i		−	0.507283i
$848$		−	2.23186e21i		−	0.243051i
$849$	−7.50427e20			−0.0810029
$850$	−2.25028e21	−	2.39076e21i	−0.240766	−	0.255796i
$851$	−1.18649e22			−1.25832
$852$			2.95322e21i			0.310456i
$853$		−	9.05799e21i		−	0.943874i	−0.881632	−	0.471937i	$-0.843555\pi$
$853$		−	9.05799e21i		−	0.943874i	0.881632	−	0.471937i	$-0.156445\pi$
$854$	−4.00499e20			−0.0413682
$855$	1.72375e22	+	7.44750e21i	1.76494	+	0.762544i
$856$	1.89232e21			0.192061
$857$		−	1.80435e22i		−	1.81536i	−0.419660	−	0.907682i	$-0.637851\pi$
$857$		−	1.80435e22i		−	1.81536i	0.419660	−	0.907682i	$-0.362149\pi$
$858$		−	1.18760e21i		−	0.118445i
$859$	−2.44689e21			−0.241916			−0.120958	−	0.992658i	$-0.538597\pi$
$859$	−2.44689e21			−0.241916			−0.120958	+	0.992658i	$0.538597\pi$
$860$	−4.36819e21	+	1.01103e22i	−0.428117	+	0.990894i
$861$	6.78482e21			0.659196
$862$		−	2.12467e21i		−	0.204638i
$863$		−	9.95152e21i		−	0.950185i	−0.879936	−	0.475093i	$-0.842415\pi$
$863$		−	9.95152e21i		−	0.950185i	0.879936	−	0.475093i	$-0.157585\pi$
$864$	1.42935e22			1.35296
$865$	4.36657e21	−	1.01066e22i	0.409750	−	0.948383i
$866$	6.86979e20			0.0639086
$867$		−	2.26674e22i		−	2.09054i
$868$			2.66124e20i			0.0243325i
$869$	−6.17683e21			−0.559909
$870$	3.40985e21	+	1.47323e21i	0.306437	+	0.132396i
$871$	1.09025e21			0.0971378
$872$			3.71478e21i			0.328140i
$873$			3.66769e22i			3.21208i
$874$	−2.09831e21			−0.182194
$875$	6.50254e21	−	2.35382e21i	0.559786	−	0.202634i
$876$	1.21698e22			1.03873
$877$			1.75476e22i			1.48498i	0.669855	+	0.742492i	$0.266356\pi$
$877$			1.75476e22i			1.48498i	−0.669855	+	0.742492i	$0.733644\pi$
$878$		−	5.43734e20i		−	0.0456224i
$879$	−1.74787e22			−1.45409
$880$	3.56603e21	+	1.54071e21i	0.294148	+	0.127087i
$881$	−1.45628e22			−1.19104			−0.595520	−	0.803341i	$-0.703054\pi$
$881$	−1.45628e22			−1.19104			−0.595520	+	0.803341i	$0.703054\pi$
$882$		−	4.07995e21i		−	0.330857i
$883$		−	1.28619e22i		−	1.03419i	−0.855928	−	0.517095i	$-0.827013\pi$
$883$		−	1.28619e22i		−	1.03419i	0.855928	−	0.517095i	$-0.172987\pi$
$884$	1.27207e22			1.01419
$885$	6.23903e20	−	1.44405e21i	0.0493222	−	0.114158i
$886$	3.40425e21			0.266851
$887$			1.46337e22i			1.13743i	0.822534	+	0.568716i	$0.192560\pi$
$887$			1.46337e22i			1.13743i	−0.822534	+	0.568716i	$0.807440\pi$
$888$		−	1.56504e22i		−	1.20623i
$889$	3.66070e21			0.279770
$890$	−1.51508e21	+	3.50671e21i	−0.114818	+	0.265751i
$891$	−7.58270e21			−0.569824
$892$		−	2.63086e21i		−	0.196048i
$893$		−	1.33311e22i		−	0.985102i
$894$	−8.39322e21			−0.615031
$895$	−3.37864e21	−	1.45975e21i	−0.245510	−	0.106073i
$896$	−6.79011e21			−0.489290
$897$			1.55142e22i			1.10863i
$898$			1.88078e21i			0.133280i
$899$	4.86888e20			0.0342162
$900$	−1.99719e22	−	2.12186e22i	−1.39187	−	1.47876i
$901$	6.22809e21			0.430446
$902$			8.32980e20i			0.0570933i
$903$			1.77949e22i			1.20959i
$904$	−6.25698e21			−0.421795
$905$	−2.79895e21	−	1.20929e21i	−0.187125	−	0.0808476i
$906$	−5.13688e18			−0.000340595
$907$			4.06427e21i			0.267256i	0.991032	+	0.133628i	$0.0426627\pi$
$907$			4.06427e21i			0.267256i	−0.991032	+	0.133628i	$0.957337\pi$
$908$		−	2.54172e21i		−	0.165762i
$909$	−6.11531e21			−0.395539
$910$	6.38448e20	−	1.47771e21i	0.0409558	−	0.0947937i
$911$	6.36749e21			0.405117			0.202558	−	0.979270i	$-0.435074\pi$
$911$	6.36749e21			0.405117			0.202558	+	0.979270i	$0.435074\pi$
$912$			2.09385e22i			1.32125i
$913$			1.65566e21i			0.103619i
$914$	4.33181e21			0.268889
$915$	3.33881e21	−	7.72780e21i	0.205557	−	0.475770i
$916$	−1.20942e22			−0.738515
$917$			8.49045e21i			0.514234i
$918$			1.19694e22i			0.719036i
$919$	−2.93596e22			−1.74938			−0.874690	−	0.484682i	$-0.838935\pi$
$919$	−2.93596e22			−1.74938			−0.874690	+	0.484682i	$0.838935\pi$
$920$	6.15785e21	+	2.66051e21i	0.363932	+	0.157237i
$921$	5.35798e22			3.14090
$922$		−	4.70837e21i		−	0.273772i
$923$		−	2.34151e21i		−	0.135046i
$924$	6.70339e21			0.383491
$925$	−1.88427e22	+	1.77356e22i	−1.06925	+	1.00643i
$926$	7.82241e21			0.440310
$927$		−	4.63396e22i		−	2.58734i
$928$			9.42472e21i			0.521986i
$929$	3.30652e22			1.81658			0.908288	−	0.418347i	$-0.137390\pi$
$929$	3.30652e22			1.81658			0.908288	+	0.418347i	$0.137390\pi$
$930$	3.08503e20	+	1.33289e20i	0.0168127	+	0.00726396i
$931$	1.06651e22			0.576558
$932$		−	2.93671e22i		−	1.57486i
$933$		−	5.87127e22i		−	3.12334i
$934$	4.91479e21			0.259360
$935$	−4.29942e21	+	9.95117e21i	−0.225073	+	0.520939i
$936$	−1.39733e22			−0.725654
$937$			3.47429e22i			1.78986i	0.446205	+	0.894931i	$0.352775\pi$
$937$			3.47429e22i			1.78986i	−0.446205	+	0.894931i	$0.647225\pi$
$938$		−	3.69716e20i		−	0.0188950i
$939$	2.04852e21			0.103860
$940$	−8.20500e21	+	1.89908e22i	−0.412686	+	0.955177i
$941$	−2.80935e21			−0.140179			−0.0700897	−	0.997541i	$-0.522329\pi$
$941$	−2.80935e21			−0.140179			−0.0700897	+	0.997541i	$0.522329\pi$
$942$		−	3.01841e21i		−	0.149416i
$943$		−	1.08816e22i		−	0.534387i
$944$	1.19773e21			0.0583538
$945$	−2.31434e22	−	9.99915e21i	−1.11864	−	0.483308i
$946$	−2.18470e21			−0.104763
$947$		−	9.11666e21i		−	0.433722i	−0.976203	−	0.216861i	$-0.930418\pi$
$947$		−	9.11666e21i		−	0.433722i	0.976203	−	0.216861i	$-0.0695818\pi$
$948$			5.16658e22i			2.43860i
$949$	−9.64903e21			−0.451842
$950$	−3.33234e21	+	3.13654e21i	−0.154818	+	0.145722i
$951$	3.79419e22			1.74890
$952$		−	8.88669e21i		−	0.406409i
$953$			1.41863e22i			0.643682i	0.946794	+	0.321841i	$0.104302\pi$
$953$			1.41863e22i			0.643682i	−0.946794	+	0.321841i	$0.895698\pi$
$954$	−3.32091e21			−0.149501
$955$	2.93338e22	+	1.26737e22i	1.31022	+	0.566082i
$956$	9.44433e21			0.418540
$957$		−	1.22642e22i		−	0.539262i
$958$			5.21910e21i			0.227695i
$959$	1.52578e22			0.660471
$960$	1.10813e22	−	2.56482e22i	0.475946	−	1.10160i
$961$	−2.34212e22			−0.998123
$962$			6.02340e21i			0.254700i
$963$			2.13010e22i			0.893723i
$964$	−3.85102e22			−1.60324
$965$	−3.14766e21	+	7.28538e21i	−0.130027	+	0.300952i
$966$	5.26107e21			0.215648
$967$		−	1.40091e22i		−	0.569785i	−0.958560	−	0.284892i	$-0.908042\pi$
$967$		−	1.40091e22i		−	0.569785i	0.958560	−	0.284892i	$-0.0919578\pi$
$968$		−	9.76770e21i		−	0.394210i
$969$	−5.84299e22			−2.33995
$970$	−8.20543e21	−	3.54517e21i	−0.326072	−	0.140880i
$971$	−3.55233e22			−1.40078			−0.700388	−	0.713762i	$-0.746990\pi$
$971$	−3.55233e22			−1.40078			−0.700388	+	0.713762i	$0.746990\pi$
$972$			1.40790e22i			0.550903i
$973$		−	2.64321e22i		−	1.02633i
$974$	4.31237e21			0.166159
$975$	2.31906e22	+	2.46383e22i	0.886702	+	0.942054i
$976$	6.40963e21			0.243198
$977$			2.18841e22i			0.823985i	0.911187	+	0.411993i	$0.135167\pi$
$977$			2.18841e22i			0.823985i	−0.911187	+	0.411993i	$0.864833\pi$
$978$		−	1.36410e22i		−	0.509687i
$979$	1.26126e22			0.467663
$980$	−1.51929e22	−	6.56413e21i	−0.559044	−	0.241536i
$981$	−4.18157e22			−1.52694
$982$		−	5.71962e21i		−	0.207267i
$983$		−	6.12627e21i		−	0.220315i	−0.993914	−	0.110158i	$-0.964864\pi$
$983$		−	6.12627e21i		−	0.220315i	0.993914	−	0.110158i	$-0.0351356\pi$
$984$	1.43534e22			0.512262
$985$	1.76285e22	−	4.08018e22i	0.624372	−	1.44513i
$986$	−7.89226e21			−0.277411
$987$			3.34251e22i			1.16599i
$988$		−	1.77307e22i		−	0.613831i
$989$	2.85397e22			0.980568
$990$	2.29251e21	−	5.30611e21i	0.0781714	−	0.180931i
$991$	3.50331e22			1.18557			0.592784	−	0.805361i	$-0.298029\pi$
$991$	3.50331e22			1.18557			0.592784	+	0.805361i	$0.298029\pi$
$992$			8.52695e20i			0.0286389i
$993$			4.06956e22i			1.35652i
$994$	−7.94036e20			−0.0262689
$995$	−2.80876e22	−	1.21353e22i	−0.922236	−	0.398453i
$996$	1.38487e22			0.451297
$997$			3.84796e22i			1.24456i	0.782793	+	0.622282i	$0.213794\pi$
$997$			3.84796e22i			1.24456i	−0.782793	+	0.622282i	$0.786206\pi$
$998$		−	4.02902e20i		−	0.0129336i
$999$	9.43364e22			3.00565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.16.b.a.4.4	yes	6
3.2	odd	2		45.16.b.b.19.3		6
4.3	odd	2		80.16.c.a.49.1		6
5.2	odd	4		25.16.a.f.1.3		6
5.3	odd	4		25.16.a.f.1.4		6
5.4	even	2	inner	5.16.b.a.4.3	✓	6
15.14	odd	2		45.16.b.b.19.4		6
20.19	odd	2		80.16.c.a.49.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.16.b.a.4.3	✓	6	5.4	even	2	inner
5.16.b.a.4.4	yes	6	1.1	even	1	trivial
25.16.a.f.1.3		6	5.2	odd	4
25.16.a.f.1.4		6	5.3	odd	4
45.16.b.b.19.3		6	3.2	odd	2
45.16.b.b.19.4		6	15.14	odd	2
80.16.c.a.49.1		6	4.3	odd	2
80.16.c.a.49.6		6	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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+43.0940i q^{2} +6725.99i q^{3} +30910.9 q^{4} +(-160365. - 69286.1i) q^{5} -289850. q^{6} +1.29717e6i q^{7} +2.74418e6i q^{8} -3.08900e7 q^{9} +O(q^{10})\)	\(q+43.0940i q^{2} +6725.99i q^{3} +30910.9 q^{4} +(-160365. - 69286.1i) q^{5} -289850. q^{6} +1.29717e6i q^{7} +2.74418e6i q^{8} -3.08900e7 q^{9} +(2.98581e6 - 6.91078e6i) q^{10} -2.48560e7 q^{11} +2.07906e8i q^{12} -1.64842e8i q^{13} -5.59000e7 q^{14} +(4.66018e8 - 1.07862e9i) q^{15} +8.94631e8 q^{16} +2.49651e9i q^{17} -1.33117e9i q^{18} +3.47974e9 q^{19} +(-4.95704e9 - 2.14170e9i) q^{20} -8.72472e9 q^{21} -1.07114e9i q^{22} +1.39929e10i q^{23} -1.84573e10 q^{24} +(2.09165e10 + 2.22222e10i) q^{25} +7.10369e9 q^{26} -1.11256e11i q^{27} +4.00966e10i q^{28} +7.33587e10 q^{29} +(4.64818e10 + 2.00825e10i) q^{30} +6.63708e9 q^{31} +1.28474e11i q^{32} -1.67181e11i q^{33} -1.07584e11 q^{34} +(8.98755e10 - 2.08020e11i) q^{35} -9.54839e11 q^{36} +8.47925e11i q^{37} +1.49956e11i q^{38} +1.10873e12 q^{39} +(1.90133e11 - 4.40071e11i) q^{40} -7.77655e11 q^{41} -3.75983e11i q^{42} -2.03959e12i q^{43} -7.68321e11 q^{44} +(4.95369e12 + 2.14025e12i) q^{45} -6.03008e11 q^{46} -3.83108e12i q^{47} +6.01728e12i q^{48} +3.06492e12 q^{49} +(-9.57641e11 + 9.01373e11i) q^{50} -1.67915e13 q^{51} -5.09541e12i q^{52} -2.49472e12i q^{53} +4.79444e12 q^{54} +(3.98604e12 + 1.72217e12i) q^{55} -3.55965e12 q^{56} +2.34047e13i q^{57} +3.16132e12i q^{58} +1.33880e12 q^{59} +(1.44050e13 - 3.33410e13i) q^{60} +7.16455e12 q^{61} +2.86018e11i q^{62} -4.00695e13i q^{63} +2.37788e13 q^{64} +(-1.14213e13 + 2.64349e13i) q^{65} +7.20450e12 q^{66} +6.61388e12i q^{67} +7.71693e13i q^{68} -9.41158e13 q^{69} +(8.96442e12 + 3.87309e12i) q^{70} +1.42046e13 q^{71} -8.47677e13i q^{72} -5.85350e13i q^{73} -3.65405e13 q^{74} +(-1.49466e14 + 1.40684e14i) q^{75} +1.07562e14 q^{76} -3.22423e13i q^{77} +4.77794e13i q^{78} +2.48505e14 q^{79} +(-1.43468e14 - 6.19855e13i) q^{80} +3.05065e14 q^{81} -3.35122e13i q^{82} -6.66100e13i q^{83} -2.69689e14 q^{84} +(1.72973e14 - 4.00353e14i) q^{85} +8.78941e13 q^{86} +4.93410e14i q^{87} -6.82092e13i q^{88} -5.07426e14 q^{89} +(-9.22319e13 + 2.13474e14i) q^{90} +2.13827e14 q^{91} +4.32532e14i q^{92} +4.46409e13i q^{93} +1.65096e14 q^{94} +(-5.58029e14 - 2.41097e14i) q^{95} -8.64118e14 q^{96} -1.18734e15i q^{97} +1.32080e14i q^{98} +7.67802e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 38568 q^{4} - 238350 q^{5} - 515448 q^{6} - 11416662 q^{9}+O(q^{10}) \) 6 * q - 38568 * q^4 - 238350 * q^5 - 515448 * q^6 - 11416662 * q^9	\( 6 q - 38568 q^{4} - 238350 q^{5} - 515448 q^{6} - 11416662 q^{9} - 48274200 q^{10} - 108590088 q^{11} + 663751704 q^{14} + 297743400 q^{15} + 1155522336 q^{16} - 3630995640 q^{19} + 2533753800 q^{20} - 8917537608 q^{21} - 2959765920 q^{24} + 18250878750 q^{25} - 81970953168 q^{26} + 286168468740 q^{29} + 203897251800 q^{30} - 276236748288 q^{31} - 127784939136 q^{34} + 1171274911800 q^{35} - 3326879331864 q^{36} + 2186980965936 q^{39} + 4214283852000 q^{40} - 6153278882388 q^{41} + 8250173021664 q^{44} + 10442765857950 q^{45} - 23334602656488 q^{46} + 11613390856242 q^{49} + 23694218070000 q^{50} - 43487373385728 q^{51} + 10162879468560 q^{54} + 33977390365800 q^{55} - 59280484297440 q^{56} + 14903258326680 q^{59} + 39248254864800 q^{60} - 11352061428588 q^{61} + 73265851251072 q^{64} - 50675287275600 q^{65} + 76208211455904 q^{66} - 150489671962824 q^{69} - 156447825521400 q^{70} + 131693145807312 q^{71} - 353606797863216 q^{74} - 360965926890000 q^{75} + 959127540575520 q^{76} - 26081853939360 q^{79} - 552945514077600 q^{80} + 11\!\cdots\!46 q^{81}+ \cdots + 506999099666376 q^{99}+O(q^{100}) \) 6 * q - 38568 * q^4 - 238350 * q^5 - 515448 * q^6 - 11416662 * q^9 - 48274200 * q^10 - 108590088 * q^11 + 663751704 * q^14 + 297743400 * q^15 + 1155522336 * q^16 - 3630995640 * q^19 + 2533753800 * q^20 - 8917537608 * q^21 - 2959765920 * q^24 + 18250878750 * q^25 - 81970953168 * q^26 + 286168468740 * q^29 + 203897251800 * q^30 - 276236748288 * q^31 - 127784939136 * q^34 + 1171274911800 * q^35 - 3326879331864 * q^36 + 2186980965936 * q^39 + 4214283852000 * q^40 - 6153278882388 * q^41 + 8250173021664 * q^44 + 10442765857950 * q^45 - 23334602656488 * q^46 + 11613390856242 * q^49 + 23694218070000 * q^50 - 43487373385728 * q^51 + 10162879468560 * q^54 + 33977390365800 * q^55 - 59280484297440 * q^56 + 14903258326680 * q^59 + 39248254864800 * q^60 - 11352061428588 * q^61 + 73265851251072 * q^64 - 50675287275600 * q^65 + 76208211455904 * q^66 - 150489671962824 * q^69 - 156447825521400 * q^70 + 131693145807312 * q^71 - 353606797863216 * q^74 - 360965926890000 * q^75 + 959127540575520 * q^76 - 26081853939360 * q^79 - 552945514077600 * q^80 + 1148641568615646 * q^81 - 686155736066976 * q^84 - 548221025491200 * q^85 + 598387757484072 * q^86 + 59269690709820 * q^89 - 1014408610626600 * q^90 + 821206462566672 * q^91 - 308164835928456 * q^94 + 232287694599000 * q^95 - 1208921682814848 * q^96 + 506999099666376 * q^99

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