LMFDB - Embedded newform 126.8.g.j.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,8,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, 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:	$39.3605132110$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
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} - x^{5} + 1111x^{4} + 2838x^{3} + 1231236x^{2} + 959040x + 746496 $ x^6 - x^5 + 1111x^4 + 2838x^3 + 1231236x^2 + 959040x + 746496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.3
Root			$-0.389676 - 0.674939i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.8.g.j.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(6.21726 - 10.7686i) q^{5} +(-879.593 + 223.290i) q^{7} -512.000 q^{8} +(-49.7381 - 86.1488i) q^{10} +(-3361.57 - 5822.41i) q^{11} +7231.99 q^{13} +(-1971.37 + 6987.16i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(7665.42 + 13276.9i) q^{17} +(-9457.32 + 16380.6i) q^{19} -795.809 q^{20} -53785.1 q^{22} +(-23860.2 + 41327.2i) q^{23} +(38985.2 + 67524.3i) q^{25} +(28928.0 - 50104.7i) q^{26} +(40523.0 + 41606.7i) q^{28} +67449.4 q^{29} +(-54888.1 - 95068.9i) q^{31} +(16384.0 + 28377.9i) q^{32} +122647. q^{34} +(-3064.13 + 10860.2i) q^{35} +(-304625. + 527626. i) q^{37} +(75658.5 + 131044. i) q^{38} +(-3183.24 + 5513.53i) q^{40} +808859. q^{41} -334949. q^{43} +(-215140. + 372634. i) q^{44} +(190882. + 330617. i) q^{46} +(-382587. + 662661. i) q^{47} +(723826. - 392809. i) q^{49} +623763. q^{50} +(-231424. - 400838. i) q^{52} +(622359. + 1.07796e6i) q^{53} -83598.9 q^{55} +(450352. - 114325. i) q^{56} +(269798. - 467303. i) q^{58} +(1.02330e6 + 1.77240e6i) q^{59} +(-70471.7 + 122061. i) q^{61} -878209. q^{62} +262144. q^{64} +(44963.1 - 77878.4i) q^{65} +(-1.46662e6 - 2.54027e6i) q^{67} +(490587. - 849721. i) q^{68} +(62985.4 + 64669.9i) q^{70} +615326. q^{71} +(711328. + 1.23206e6i) q^{73} +(2.43700e6 + 4.22101e6i) q^{74} +1.21054e6 q^{76} +(4.25690e6 + 4.37075e6i) q^{77} +(1.19370e6 - 2.06754e6i) q^{79} +(25465.9 + 44108.2i) q^{80} +(3.23544e6 - 5.60394e6i) q^{82} +7.53432e6 q^{83} +190631. q^{85} +(-1.33980e6 + 2.32060e6i) q^{86} +(1.72112e6 + 2.98107e6i) q^{88} +(-2.67757e6 + 4.63769e6i) q^{89} +(-6.36121e6 + 1.61483e6i) q^{91} +3.05411e6 q^{92} +(3.06070e6 + 5.30129e6i) q^{94} +(117597. + 203684. i) q^{95} -1.58174e7 q^{97} +(173842. - 6.58605e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 24 q^{2} - 192 q^{4} - 718 q^{5} - 1471 q^{7} - 3072 q^{8} + 5744 q^{10} + 208 q^{11} + 19394 q^{13} - 4504 q^{14} - 12288 q^{16} - 19244 q^{17} - 25419 q^{19} + 91904 q^{20} + 3328 q^{22} - 67400 q^{23}+ \cdots + 20461248 q^{98}+O(q^{100}) $ 6 * q + 24 * q^2 - 192 * q^4 - 718 * q^5 - 1471 * q^7 - 3072 * q^8 + 5744 * q^10 + 208 * q^11 + 19394 * q^13 - 4504 * q^14 - 12288 * q^16 - 19244 * q^17 - 25419 * q^19 + 91904 * q^20 + 3328 * q^22 - 67400 * q^23 - 93931 * q^25 + 77576 * q^26 + 58112 * q^28 + 33476 * q^29 + 78449 * q^31 + 98304 * q^32 - 307904 * q^34 - 602072 * q^35 - 496599 * q^37 + 203352 * q^38 + 367616 * q^40 + 1953168 * q^41 + 697470 * q^43 + 13312 * q^44 + 539200 * q^46 + 701328 * q^47 + 959673 * q^49 - 1502896 * q^50 - 620608 * q^52 + 2917374 * q^53 - 3275696 * q^55 + 753152 * q^56 + 133904 * q^58 - 492040 * q^59 + 3649370 * q^61 + 1255184 * q^62 + 1572864 * q^64 - 2707764 * q^65 - 3647153 * q^67 - 1231616 * q^68 - 503936 * q^70 + 3541216 * q^71 - 6183557 * q^73 + 3972792 * q^74 + 3253632 * q^76 + 13092290 * q^77 - 12453589 * q^79 - 2940928 * q^80 + 7812672 * q^82 + 11611120 * q^83 + 38154616 * q^85 + 2789880 * q^86 - 106496 * q^88 - 8292612 * q^89 + 366581 * q^91 + 8627200 * q^92 - 5610624 * q^94 - 8691056 * q^95 - 55949528 * q^97 + 20461248 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	6.21726	−	10.7686i	0.0222435	−	0.0385269i	−0.854689	−	0.519140i	$-0.826252\pi$
$5$	6.21726	−	10.7686i	0.0222435	−	0.0385269i	0.876933	+	0.480613i	$0.159586\pi$
$6$		0			0
$7$	−879.593	+	223.290i	−0.969257	+	0.246052i
$7$	−879.593	+	223.290i	−0.969257	+	0.246052i
$8$	−512.000			−0.353553
$9$		0			0
$10$	−49.7381	−	86.1488i	−0.0157286	−	0.0272427i
$11$	−3361.57	−	5822.41i	−0.761496	−	1.31895i	−0.942079	−	0.335390i	$-0.891132\pi$
$11$	−3361.57	−	5822.41i	−0.761496	−	1.31895i	0.180584	−	0.983560i	$-0.442201\pi$
$12$		0			0
$13$	7231.99			0.912969			0.456485	−	0.889731i	$-0.349108\pi$
$13$	7231.99			0.912969			0.456485	+	0.889731i	$0.349108\pi$
$14$	−1971.37	+	6987.16i	−0.192009	+	0.680539i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	7665.42	+	13276.9i	0.378412	+	0.655428i	0.990831	−	0.135105i	$-0.0431370\pi$
$17$	7665.42	+	13276.9i	0.378412	+	0.655428i	−0.612420	+	0.790533i	$0.709804\pi$
$18$		0			0
$19$	−9457.32	+	16380.6i	−0.316323	+	0.547887i	−0.979718	−	0.200382i	$-0.935782\pi$
$19$	−9457.32	+	16380.6i	−0.316323	+	0.547887i	0.663395	+	0.748269i	$0.269115\pi$
$20$	−795.809			−0.0222435
$21$		0			0
$22$	−53785.1			−1.07692
$23$	−23860.2	+	41327.2i	−0.408910	+	0.708253i	−0.994768	−	0.102161i	$-0.967424\pi$
$23$	−23860.2	+	41327.2i	−0.408910	+	0.708253i	0.585858	+	0.810414i	$0.300758\pi$
$24$		0			0
$25$	38985.2	+	67524.3i	0.499010	+	0.864311i
$26$	28928.0	−	50104.7i	0.322783	−	0.559077i
$27$		0			0
$28$	40523.0	+	41606.7i	0.348858	+	0.358188i
$29$	67449.4			0.513553			0.256776	−	0.966471i	$-0.417340\pi$
$29$	67449.4			0.513553			0.256776	+	0.966471i	$0.417340\pi$
$30$		0			0
$31$	−54888.1	−	95068.9i	−0.330912	−	0.573156i	0.651779	−	0.758409i	$-0.274023\pi$
$31$	−54888.1	−	95068.9i	−0.330912	−	0.573156i	−0.982691	+	0.185253i	$0.940690\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$		0			0
$34$	122647.			0.535155
$35$	−3064.13	+	10860.2i	−0.0120801	+	0.0428155i
$36$		0			0
$37$	−304625.	+	527626.i	−0.988688	+	1.71246i	−0.364454	+	0.931222i	$0.618744\pi$
$37$	−304625.	+	527626.i	−0.988688	+	1.71246i	−0.624235	+	0.781237i	$0.714589\pi$
$38$	75658.5	+	131044.i	0.223674	+	0.387415i
$39$		0			0
$40$	−3183.24	+	5513.53i	−0.00786428	+	0.0136213i
$41$	808859.			1.83286			0.916430	−	0.400195i	$-0.131057\pi$
$41$	808859.			1.83286			0.916430	+	0.400195i	$0.131057\pi$
$42$		0			0
$43$	−334949.			−0.642450			−0.321225	−	0.947003i	$-0.604095\pi$
$43$	−334949.			−0.642450			−0.321225	+	0.947003i	$0.604095\pi$
$44$	−215140.	+	372634.i	−0.380748	+	0.659475i
$45$		0			0
$46$	190882.	+	330617.i	0.289143	+	0.500810i
$47$	−382587.	+	662661.i	−0.537512	+	0.930998i	0.461525	+	0.887127i	$0.347302\pi$
$47$	−382587.	+	662661.i	−0.537512	+	0.930998i	−0.999037	+	0.0438710i	$0.986031\pi$
$48$		0			0
$49$	723826.	−	392809.i	0.878917	−	0.476975i
$50$	623763.			0.705707
$51$		0			0
$52$	−231424.	−	400838.i	−0.228242	−	0.395327i
$53$	622359.	+	1.07796e6i	0.574216	+	0.994572i	0.996126	+	0.0879342i	$0.0280265\pi$
$53$	622359.	+	1.07796e6i	0.574216	+	0.994572i	−0.421910	+	0.906638i	$0.638640\pi$
$54$		0			0
$55$	−83598.9			−0.0677534
$56$	450352.	−	114325.i	0.342684	−	0.0869924i
$57$		0			0
$58$	269798.	−	467303.i	0.181568	−	0.314486i
$59$	1.02330e6	+	1.77240e6i	0.648665	+	1.12352i	0.983442	+	0.181223i	$0.0580056\pi$
$59$	1.02330e6	+	1.77240e6i	0.648665	+	1.12352i	−0.334777	+	0.942297i	$0.608661\pi$
$60$		0			0
$61$	−70471.7	+	122061.i	−0.0397521	+	0.0688527i	−0.885217	−	0.465178i	$-0.845990\pi$
$61$	−70471.7	+	122061.i	−0.0397521	+	0.0688527i	0.845465	+	0.534031i	$0.179323\pi$
$62$	−878209.			−0.467980
$63$		0			0
$64$	262144.			0.125000
$65$	44963.1	−	77878.4i	0.0203077	−	0.0351739i
$66$		0			0
$67$	−1.46662e6	−	2.54027e6i	−0.595740	−	1.03185i	−0.993442	−	0.114338i	$-0.963525\pi$
$67$	−1.46662e6	−	2.54027e6i	−0.595740	−	1.03185i	0.397702	−	0.917515i	$-0.369808\pi$
$68$	490587.	−	849721.i	0.189206	−	0.327714i
$69$		0			0
$70$	62985.4	+	64669.9i	0.0219481	+	0.0225351i
$71$	615326.			0.204033			0.102017	−	0.994783i	$-0.467470\pi$
$71$	615326.			0.204033			0.102017	+	0.994783i	$0.467470\pi$
$72$		0			0
$73$	711328.	+	1.23206e6i	0.214013	+	0.370681i	0.952967	−	0.303075i	$-0.0980132\pi$
$73$	711328.	+	1.23206e6i	0.214013	+	0.370681i	−0.738954	+	0.673756i	$0.764680\pi$
$74$	2.43700e6	+	4.22101e6i	0.699108	+	1.21089i
$75$		0			0
$76$	1.21054e6			0.316323
$77$	4.25690e6	+	4.37075e6i	1.06261	+	1.09103i
$78$		0			0
$79$	1.19370e6	−	2.06754e6i	0.272395	−	0.471802i	−0.697079	−	0.716994i	$-0.745518\pi$
$79$	1.19370e6	−	2.06754e6i	0.272395	−	0.471802i	0.969475	+	0.245192i	$0.0788509\pi$
$80$	25465.9	+	44108.2i	0.00556088	+	0.00963173i
$81$		0			0
$82$	3.23544e6	−	5.60394e6i	0.648014	−	1.12239i
$83$	7.53432e6			1.44634			0.723171	−	0.690669i	$-0.242684\pi$
$83$	7.53432e6			1.44634			0.723171	+	0.690669i	$0.242684\pi$
$84$		0			0
$85$	190631.			0.0336689
$86$	−1.33980e6	+	2.32060e6i	−0.227140	+	0.393419i
$87$		0			0
$88$	1.72112e6	+	2.98107e6i	0.269229	+	0.466319i
$89$	−2.67757e6	+	4.63769e6i	−0.402602	+	0.697327i	−0.994039	−	0.109024i	$-0.965227\pi$
$89$	−2.67757e6	+	4.63769e6i	−0.402602	+	0.697327i	0.591437	+	0.806351i	$0.298561\pi$
$90$		0			0
$91$	−6.36121e6	+	1.61483e6i	−0.884901	+	0.224638i
$92$	3.05411e6			0.408910
$93$		0			0
$94$	3.06070e6	+	5.30129e6i	0.380078	+	0.658315i
$95$	117597.	+	203684.i	0.0140723	+	0.0243739i
$96$		0			0
$97$	−1.58174e7			−1.75969			−0.879843	−	0.475265i	$-0.842352\pi$
$97$	−1.58174e7			−1.75969			−0.879843	+	0.475265i	$0.842352\pi$
$98$	173842.	−	6.58605e6i	0.0186580	−	0.706861i
$99$		0			0
$100$	2.49505e6	−	4.32156e6i	0.249505	−	0.432156i
$101$	−5.82603e6	−	1.00910e7i	−0.562662	−	0.974559i	−0.997263	−	0.0739362i	$-0.976444\pi$
$101$	−5.82603e6	−	1.00910e7i	−0.562662	−	0.974559i	0.434601	−	0.900623i	$-0.356889\pi$
$102$		0			0
$103$	−3.58003e6	+	6.20080e6i	−0.322817	+	0.559136i	−0.981068	−	0.193663i	$-0.937963\pi$
$103$	−3.58003e6	+	6.20080e6i	−0.322817	+	0.559136i	0.658251	+	0.752799i	$0.271297\pi$
$104$	−3.70278e6			−0.322783
$105$		0			0
$106$	9.95775e6			0.812065
$107$	−2.91738e6	+	5.05305e6i	−0.230224	+	0.398759i	−0.957874	−	0.287189i	$-0.907279\pi$
$107$	−2.91738e6	+	5.05305e6i	−0.230224	+	0.398759i	0.727650	+	0.685948i	$0.240612\pi$
$108$		0			0
$109$	4.66490e6	+	8.07985e6i	0.345024	+	0.597600i	0.985358	−	0.170497i	$-0.0545373\pi$
$109$	4.66490e6	+	8.07985e6i	0.345024	+	0.597600i	−0.640334	+	0.768097i	$0.721204\pi$
$110$	−334396.	+	579190.i	−0.0239545	+	0.0414903i
$111$		0			0
$112$	1.00934e6	−	3.57743e6i	0.0678853	−	0.240607i
$113$	−8.84372e6			−0.576581			−0.288290	−	0.957543i	$-0.593087\pi$
$113$	−8.84372e6			−0.576581			−0.288290	+	0.957543i	$0.593087\pi$
$114$		0			0
$115$	296691.	+	513883.i	0.0181912	+	0.0315081i
$116$	−2.15838e6	−	3.73842e6i	−0.128388	−	0.222375i
$117$		0			0
$118$	1.63728e7			0.917350
$119$	−9.70705e6	−	9.96665e6i	−0.528047	−	0.542169i
$120$		0			0
$121$	−1.28567e7	+	2.22684e7i	−0.659752	+	1.14272i
$122$	563773.	+	976484.i	0.0281090	+	0.0486862i
$123$		0			0
$124$	−3.51284e6	+	6.08441e6i	−0.165456	+	0.286578i
$125$	1.94097e6			0.0888861
$126$		0			0
$127$	−2.22621e7			−0.964393			−0.482196	−	0.876063i	$-0.660161\pi$
$127$	−2.22621e7			−0.964393			−0.482196	+	0.876063i	$0.660161\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−359705.	−	623027.i	−0.0143597	−	0.0248717i
$131$	5.45088e6	−	9.44120e6i	0.211844	−	0.366925i	−0.740447	−	0.672114i	$-0.765386\pi$
$131$	5.45088e6	−	9.44120e6i	0.211844	−	0.366925i	0.952292	+	0.305189i	$0.0987197\pi$
$132$		0			0
$133$	4.66098e6	−	1.65199e7i	0.171789	−	0.608875i
$134$	−2.34660e7			−0.842504
$135$		0			0
$136$	−3.92469e6	−	6.79777e6i	−0.133789	−	0.231729i
$137$	−1.60629e7	−	2.78218e7i	−0.533706	−	0.924406i	−0.999225	−	0.0393678i	$-0.987466\pi$
$137$	−1.60629e7	−	2.78218e7i	−0.533706	−	0.924406i	0.465519	−	0.885038i	$-0.345868\pi$
$138$		0			0
$139$	−1.89050e7			−0.597070			−0.298535	−	0.954399i	$-0.596498\pi$
$139$	−1.89050e7			−0.597070			−0.298535	+	0.954399i	$0.596498\pi$
$140$	699988.	−	177696.i	0.0215597	−	0.00547306i
$141$		0			0
$142$	2.46131e6	−	4.26311e6i	0.0721367	−	0.124944i
$143$	−2.43108e7	−	4.21076e7i	−0.695222	−	1.20416i
$144$		0			0
$145$	419350.	−	726336.i	0.0114232	−	0.0197856i
$146$	1.13813e7			0.302660
$147$		0			0
$148$	3.89920e7			0.988688
$149$	−2.77312e6	+	4.80319e6i	−0.0686779	+	0.118954i	−0.898320	−	0.439343i	$-0.855211\pi$
$149$	−2.77312e6	+	4.80319e6i	−0.0686779	+	0.118954i	0.829642	+	0.558296i	$0.188545\pi$
$150$		0			0
$151$	1.13319e7	+	1.96275e7i	0.267845	+	0.463922i	0.968305	−	0.249770i	$-0.0803550\pi$
$151$	1.13319e7	+	1.96275e7i	0.267845	+	0.463922i	−0.700460	+	0.713692i	$0.747022\pi$
$152$	4.84215e6	−	8.38684e6i	0.111837	−	0.193707i
$153$		0			0
$154$	4.73090e7	−	1.20097e7i	1.04381	−	0.264978i
$155$	−1.36501e6			−0.0294426
$156$		0			0
$157$	−3.25062e7	−	5.63025e7i	−0.670375	−	1.16112i	−0.977798	−	0.209551i	$-0.932800\pi$
$157$	−3.25062e7	−	5.63025e7i	−0.670375	−	1.16112i	0.307423	−	0.951573i	$-0.400533\pi$
$158$	−9.54958e6	−	1.65404e7i	−0.192612	−	0.333615i
$159$		0			0
$160$	407454.			0.00786428
$161$	1.17594e7	−	4.16789e7i	0.222072	−	0.787092i
$162$		0			0
$163$	−1.74670e7	+	3.02537e7i	−0.315908	+	0.547170i	−0.979630	−	0.200810i	$-0.935643\pi$
$163$	−1.74670e7	+	3.02537e7i	−0.315908	+	0.547170i	0.663722	+	0.747980i	$0.268976\pi$
$164$	−2.58835e7	−	4.48315e7i	−0.458215	−	0.793652i
$165$		0			0
$166$	3.01373e7	−	5.21993e7i	0.511359	−	0.885700i
$167$	−8.89524e7			−1.47792			−0.738959	−	0.673751i	$-0.764682\pi$
$167$	−8.89524e7			−1.47792			−0.738959	+	0.673751i	$0.764682\pi$
$168$		0			0
$169$	−1.04468e7			−0.166487
$170$	762526.	−	1.32073e6i	0.0119037	−	0.0206179i
$171$		0			0
$172$	1.07184e7	+	1.85648e7i	0.160612	+	0.278189i
$173$	−1.53819e7	+	2.66422e7i	−0.225865	+	0.391209i	−0.956578	−	0.291475i	$-0.905854\pi$
$173$	−1.53819e7	+	2.66422e7i	−0.225865	+	0.391209i	0.730714	+	0.682684i	$0.239187\pi$
$174$		0			0
$175$	−4.93686e7	−	5.06889e7i	−0.696335	−	0.714957i
$176$	2.75380e7			0.380748
$177$		0			0
$178$	2.14206e7	+	3.71015e7i	0.284683	+	0.493085i
$179$	5.15359e7	+	8.92628e7i	0.671621	+	1.16328i	0.977444	+	0.211194i	$0.0677351\pi$
$179$	5.15359e7	+	8.92628e7i	0.671621	+	1.16328i	−0.305823	+	0.952088i	$0.598932\pi$
$180$		0			0
$181$	−6.25682e7			−0.784294			−0.392147	−	0.919903i	$-0.628268\pi$
$181$	−6.25682e7			−0.784294			−0.392147	+	0.919903i	$0.628268\pi$
$182$	−1.42570e7	+	5.05311e7i	−0.175298	+	0.621311i
$183$		0			0
$184$	1.22164e7	−	2.11595e7i	0.144571	−	0.250405i
$185$	3.78786e6	+	6.56077e6i	0.0439838	+	0.0761822i
$186$		0			0
$187$	5.15356e7	−	8.92623e7i	0.576318	−	0.998212i
$188$	4.89712e7			0.537512
$189$		0			0
$190$	1.88155e6			0.0199012
$191$	3.95503e7	−	6.85031e7i	0.410707	−	0.711366i	−0.584260	−	0.811567i	$-0.698615\pi$
$191$	3.95503e7	−	6.85031e7i	0.410707	−	0.711366i	0.994967	+	0.100201i	$0.0319484\pi$
$192$		0			0
$193$	2.81447e7	+	4.87480e7i	0.281803	+	0.488097i	0.971829	−	0.235687i	$-0.0757342\pi$
$193$	2.81447e7	+	4.87480e7i	0.281803	+	0.488097i	−0.690026	+	0.723785i	$0.742401\pi$
$194$	−6.32697e7	+	1.09586e8i	−0.622143	+	1.07758i
$195$		0			0
$196$	−4.49341e7	−	2.75486e7i	−0.426265	−	0.261339i
$197$	4.91598e7			0.458119			0.229059	−	0.973412i	$-0.426435\pi$
$197$	4.91598e7			0.458119			0.229059	+	0.973412i	$0.426435\pi$
$198$		0			0
$199$	8.35475e7	+	1.44709e8i	0.751533	+	1.30169i	0.947080	+	0.320998i	$0.104018\pi$
$199$	8.35475e7	+	1.44709e8i	0.751533	+	1.30169i	−0.195547	+	0.980694i	$0.562648\pi$
$200$	−1.99604e7	−	3.45725e7i	−0.176427	−	0.305580i
$201$		0			0
$202$	−9.32164e7			−0.795724
$203$	−5.93280e7	+	1.50608e7i	−0.497764	+	0.126361i
$204$		0			0
$205$	5.02888e6	−	8.71028e6i	0.0407693	−	0.0706145i
$206$	2.86403e7	+	4.96064e7i	0.228266	+	0.395369i
$207$		0			0
$208$	−1.48111e7	+	2.56536e7i	−0.114121	+	0.197664i
$209$	1.27166e8			0.963513
$210$		0			0
$211$	7.06109e7			0.517467			0.258734	−	0.965949i	$-0.416695\pi$
$211$	7.06109e7			0.517467			0.258734	+	0.965949i	$0.416695\pi$
$212$	3.98310e7	−	6.89893e7i	0.287108	−	0.497286i
$213$		0			0
$214$	2.33390e7	+	4.04244e7i	0.162793	+	0.281965i
$215$	−2.08246e6	+	3.60693e6i	−0.0142904	+	0.0247516i
$216$		0			0
$217$	6.95071e7	+	7.13660e7i	0.461764	+	0.474114i
$218$	7.46384e7			0.487938
$219$		0			0
$220$	2.67517e6	+	4.63352e6i	0.0169384	+	0.0293381i
$221$	5.54362e7	+	9.60183e7i	0.345478	+	0.598386i
$222$		0			0
$223$	−2.49891e8			−1.50898			−0.754489	−	0.656313i	$-0.772115\pi$
$223$	−2.49891e8			−1.50898			−0.754489	+	0.656313i	$0.772115\pi$
$224$	−2.07478e7	−	2.13026e7i	−0.123340	−	0.126638i
$225$		0			0
$226$	−3.53749e7	+	6.12711e7i	−0.203852	+	0.353082i
$227$	1.62335e8	+	2.81173e8i	0.921133	+	1.59545i	0.797665	+	0.603101i	$0.206068\pi$
$227$	1.62335e8	+	2.81173e8i	0.921133	+	1.59545i	0.123468	+	0.992349i	$0.460598\pi$
$228$		0			0
$229$	1.05242e7	−	1.82284e7i	0.0579115	−	0.100306i	−0.835616	−	0.549314i	$-0.814889\pi$
$229$	1.05242e7	−	1.82284e7i	0.0579115	−	0.100306i	0.893528	+	0.449008i	$0.148223\pi$
$230$	4.74705e6			0.0257262
$231$		0			0
$232$	−3.45341e7			−0.181568
$233$	−8.17424e7	+	1.41582e8i	−0.423352	+	0.733267i	−0.996265	−	0.0863491i	$-0.972480\pi$
$233$	−8.17424e7	+	1.41582e8i	−0.423352	+	0.733267i	0.572913	+	0.819616i	$0.305813\pi$
$234$		0			0
$235$	4.75729e6	+	8.23987e6i	0.0239123	+	0.0414174i
$236$	6.54911e7	−	1.13434e8i	0.324332	−	0.561760i
$237$		0			0
$238$	−1.07879e8	+	2.73858e7i	−0.518703	+	0.131676i
$239$	3.18177e8			1.50757			0.753784	−	0.657123i	$-0.228227\pi$
$239$	3.18177e8			1.50757			0.753784	+	0.657123i	$0.228227\pi$
$240$		0			0
$241$	6.47859e7	+	1.12213e8i	0.298141	+	0.516395i	0.975711	−	0.219064i	$-0.0703003\pi$
$241$	6.47859e7	+	1.12213e8i	0.298141	+	0.516395i	−0.677570	+	0.735458i	$0.736967\pi$
$242$	1.02854e8	+	1.78148e8i	0.466515	+	0.808027i
$243$		0			0
$244$	9.02038e6			0.0397521
$245$	270206.	−	1.02368e7i	0.00117385	−	0.0444716i
$246$		0			0
$247$	−6.83952e7	+	1.18464e8i	−0.288793	+	0.500204i
$248$	2.81027e7	+	4.86753e7i	0.116995	+	0.202641i
$249$		0			0
$250$	7.76388e6	−	1.34474e7i	0.0314260	−	0.0544314i
$251$	7.94873e7			0.317278			0.158639	−	0.987337i	$-0.449289\pi$
$251$	7.94873e7			0.317278			0.158639	+	0.987337i	$0.449289\pi$
$252$		0			0
$253$	3.20831e8			1.24553
$254$	−8.90486e7	+	1.54237e8i	−0.340964	+	0.590567i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−2.14513e8	+	3.71547e8i	−0.788293	+	1.36536i	0.138719	+	0.990332i	$0.455702\pi$
$257$	−2.14513e8	+	3.71547e8i	−0.788293	+	1.36536i	−0.927012	+	0.375032i	$0.877632\pi$
$258$		0			0
$259$	1.50132e8	−	5.32116e8i	0.536939	−	1.90308i
$260$	−5.75528e6			−0.0203077
$261$		0			0
$262$	−4.36070e7	−	7.55296e7i	−0.149797	−	0.259455i
$263$	−2.12061e7	−	3.67300e7i	−0.0718812	−	0.124502i	0.827845	−	0.560958i	$-0.189567\pi$
$263$	−2.12061e7	−	3.67300e7i	−0.0718812	−	0.124502i	−0.899726	+	0.436456i	$0.856234\pi$
$264$		0			0
$265$	1.54775e7			0.0510904
$266$	−9.58097e7	−	9.83720e7i	−0.312121	−	0.320469i
$267$		0			0
$268$	−9.38639e7	+	1.62577e8i	−0.297870	+	0.515926i
$269$	−2.60097e8	−	4.50501e8i	−0.814709	−	1.41112i	−0.909537	−	0.415624i	$-0.863563\pi$
$269$	−2.60097e8	−	4.50501e8i	−0.814709	−	1.41112i	0.0948278	−	0.995494i	$-0.469770\pi$
$270$		0			0
$271$	8.71406e7	−	1.50932e8i	0.265967	−	0.460668i	−0.701850	−	0.712325i	$-0.747642\pi$
$271$	8.71406e7	−	1.50932e8i	0.265967	−	0.460668i	0.967817	+	0.251657i	$0.0809754\pi$
$272$	−6.27951e7			−0.189206
$273$		0			0
$274$	−2.57006e8			−0.754774
$275$	2.62103e8	−	4.53975e8i	0.759989	−	1.31634i
$276$		0			0
$277$	3.38413e8	+	5.86149e8i	0.956683	+	1.65702i	0.730468	+	0.682947i	$0.239302\pi$
$277$	3.38413e8	+	5.86149e8i	0.956683	+	1.65702i	0.226216	+	0.974077i	$0.427365\pi$
$278$	−7.56200e7	+	1.30978e8i	−0.211096	+	0.365629i
$279$		0			0
$280$	1.56884e6	−	5.56045e6i	0.00427095	−	0.0151376i
$281$	3.51245e8			0.944360			0.472180	−	0.881502i	$-0.343467\pi$
$281$	3.51245e8			0.944360			0.472180	+	0.881502i	$0.343467\pi$
$282$		0			0
$283$	−3.24140e8	−	5.61428e8i	−0.850121	−	1.47245i	−0.881099	−	0.472932i	$-0.843196\pi$
$283$	−3.24140e8	−	5.61428e8i	−0.850121	−	1.47245i	0.0309780	−	0.999520i	$-0.490138\pi$
$284$	−1.96904e7	−	3.41048e7i	−0.0510083	−	0.0883490i
$285$		0			0
$286$	−3.88973e8			−0.983193
$287$	−7.11467e8	+	1.80610e8i	−1.77651	+	0.450979i
$288$		0			0
$289$	8.76521e7	−	1.51818e8i	0.213609	−	0.369982i
$290$	−3.35480e6	−	5.81069e6i	−0.00807744	−	0.0139905i
$291$		0			0
$292$	4.55250e7	−	7.88516e7i	0.107006	−	0.185341i
$293$	−6.35015e6			−0.0147485			−0.00737424	−	0.999973i	$-0.502347\pi$
$293$	−6.35015e6			−0.0147485			−0.00737424	+	0.999973i	$0.502347\pi$
$294$		0			0
$295$	2.54484e7			0.0577144
$296$	1.55968e8	−	2.70144e8i	0.349554	−	0.605445i
$297$		0			0
$298$	2.21850e7	+	3.84255e7i	0.0485626	+	0.0841129i
$299$	−1.72557e8	+	2.98878e8i	−0.373322	+	0.646613i
$300$		0			0
$301$	2.94619e8	−	7.47908e7i	0.622699	−	0.158076i
$302$	1.81311e8			0.378791
$303$		0			0
$304$	−3.87372e7	−	6.70947e7i	−0.0790807	−	0.136972i
$305$	876281.	+	1.51776e6i	0.00176845	+	0.00306305i
$306$		0			0
$307$	8.05452e8			1.58875			0.794375	−	0.607428i	$-0.207798\pi$
$307$	8.05452e8			1.58875			0.794375	+	0.607428i	$0.207798\pi$
$308$	1.06031e8	−	3.75805e8i	0.206778	−	0.732884i
$309$		0			0
$310$	−5.46005e6	+	9.45709e6i	−0.0104095	+	0.0180298i
$311$	−2.12401e8	−	3.67889e8i	−0.400401	−	0.693514i	0.593374	−	0.804927i	$-0.297796\pi$
$311$	−2.12401e8	−	3.67889e8i	−0.400401	−	0.693514i	−0.993774	+	0.111413i	$0.964462\pi$
$312$		0			0
$313$	2.08578e8	−	3.61268e8i	0.384472	−	0.665924i	−0.607224	−	0.794531i	$-0.707717\pi$
$313$	2.08578e8	−	3.61268e8i	0.384472	−	0.665924i	0.991696	+	0.128606i	$0.0410503\pi$
$314$	−5.20100e8			−0.948054
$315$		0			0
$316$	−1.52793e8			−0.272395
$317$	2.13997e8	−	3.70654e8i	0.377312	−	0.653523i	−0.613358	−	0.789805i	$-0.710182\pi$
$317$	2.13997e8	−	3.70654e8i	0.377312	−	0.653523i	0.990670	+	0.136282i	$0.0435152\pi$
$318$		0			0
$319$	−2.26736e8	−	3.92718e8i	−0.391068	−	0.677350i
$320$	1.62982e6	−	2.82292e6i	0.00278044	−	0.00481587i
$321$		0			0
$322$	−2.41722e8	−	2.48187e8i	−0.403479	−	0.414270i
$323$	−2.89977e8			−0.478801
$324$		0			0
$325$	2.81941e8	+	4.88335e8i	0.455581	+	0.789090i
$326$	1.39736e8	+	2.42030e8i	0.223381	+	0.386907i
$327$		0			0
$328$	−4.14136e8			−0.648014
$329$	1.88556e8	−	6.68300e8i	0.291913	−	1.03463i
$330$		0			0
$331$	−1.32553e8	+	2.29588e8i	−0.200905	+	0.347978i	−0.948820	−	0.315816i	$-0.897722\pi$
$331$	−1.32553e8	+	2.29588e8i	−0.200905	+	0.347978i	0.747915	+	0.663794i	$0.231055\pi$
$332$	−2.41098e8	−	4.17595e8i	−0.361586	−	0.626284i
$333$		0			0
$334$	−3.55810e8	+	6.16281e8i	−0.522523	+	0.905036i
$335$	−3.64735e7			−0.0530055
$336$		0			0
$337$	2.17646e8			0.309775			0.154887	−	0.987932i	$-0.450499\pi$
$337$	2.17646e8			0.309775			0.154887	+	0.987932i	$0.450499\pi$
$338$	−4.17874e7	+	7.23778e7i	−0.0588622	+	0.101952i
$339$		0			0
$340$	−6.10021e6	−	1.05659e7i	−0.00841721	−	0.0145790i
$341$	−3.69020e8	+	6.39161e8i	−0.503976	+	0.872911i
$342$		0			0
$343$	−5.48962e8	+	5.07136e8i	−0.734536	+	0.678570i
$344$	1.71494e8			0.227140
$345$		0			0
$346$	1.23055e8	+	2.13138e8i	0.159710	+	0.276626i
$347$	−3.24979e8	−	5.62880e8i	−0.417544	−	0.723207i	0.578148	−	0.815932i	$-0.303776\pi$
$347$	−3.24979e8	−	5.62880e8i	−0.417544	−	0.723207i	−0.995692	+	0.0927250i	$0.970442\pi$
$348$		0			0
$349$	−7.11539e8			−0.896003			−0.448002	−	0.894033i	$-0.647864\pi$
$349$	−7.11539e8			−0.896003			−0.448002	+	0.894033i	$0.647864\pi$
$350$	−5.48658e8	+	1.39280e8i	−0.684012	+	0.173641i
$351$		0			0
$352$	1.10152e8	−	1.90789e8i	0.134615	−	0.233160i
$353$	−7.74200e8	−	1.34095e9i	−0.936788	−	1.62257i	−0.771413	−	0.636335i	$-0.780450\pi$
$353$	−7.74200e8	−	1.34095e9i	−0.936788	−	1.62257i	−0.165375	−	0.986231i	$-0.552884\pi$
$354$		0			0
$355$	3.82564e6	−	6.62621e6i	0.00453842	−	0.00786078i
$356$	3.42729e8			0.402602
$357$		0			0
$358$	8.24575e8			0.949816
$359$	8.43823e7	−	1.46154e8i	0.0962544	−	0.166718i	−0.813877	−	0.581037i	$-0.802647\pi$
$359$	8.43823e7	−	1.46154e8i	0.0962544	−	0.166718i	0.910131	+	0.414320i	$0.135980\pi$
$360$		0			0
$361$	2.68054e8	+	4.64284e8i	0.299880	+	0.519407i
$362$	−2.50273e8	+	4.33486e8i	−0.277290	+	0.480280i
$363$		0			0
$364$	2.93062e8	+	3.00899e8i	0.318496	+	0.327014i
$365$	1.76900e7			0.0190416
$366$		0			0
$367$	1.71858e8	+	2.97666e8i	0.181484	+	0.314339i	0.942386	−	0.334527i	$-0.108577\pi$
$367$	1.71858e8	+	2.97666e8i	0.181484	+	0.314339i	−0.760902	+	0.648867i	$0.775243\pi$
$368$	−9.77316e7	−	1.69276e8i	−0.102227	−	0.177063i
$369$		0			0
$370$	6.06058e7			0.0622025
$371$	−7.88120e8	−	8.09198e8i	−0.801279	−	0.822709i
$372$		0			0
$373$	6.96771e7	−	1.20684e8i	0.0695199	−	0.120412i	−0.829170	−	0.558996i	$-0.811187\pi$
$373$	6.96771e7	−	1.20684e8i	0.0695199	−	0.120412i	0.898690	+	0.438584i	$0.144520\pi$
$374$	−4.12285e8	−	7.14099e8i	−0.407518	−	0.705842i
$375$		0			0
$376$	1.95885e8	−	3.39282e8i	0.190039	−	0.329158i
$377$	4.87793e8			0.468858
$378$		0			0
$379$	−7.74462e8			−0.730740			−0.365370	−	0.930862i	$-0.619057\pi$
$379$	−7.74462e8			−0.730740			−0.365370	+	0.930862i	$0.619057\pi$
$380$	7.52621e6	−	1.30358e7i	0.00703613	−	0.0121869i
$381$		0			0
$382$	−3.16402e8	−	5.48024e8i	−0.290414	−	0.503012i
$383$	−6.53115e8	+	1.13123e9i	−0.594011	+	1.02886i	0.399675	+	0.916657i	$0.369123\pi$
$383$	−6.53115e8	+	1.13123e9i	−0.594011	+	1.02886i	−0.993686	+	0.112200i	$0.964210\pi$
$384$		0			0
$385$	7.35331e7	−	1.86668e7i	0.0656705	−	0.0166709i
$386$	4.50315e8			0.398530
$387$		0			0
$388$	5.06158e8	+	8.76691e8i	0.439921	+	0.761966i
$389$	1.10694e9	+	1.91728e9i	0.953455	+	1.65143i	0.737864	+	0.674949i	$0.235834\pi$
$389$	1.10694e9	+	1.91728e9i	0.953455	+	1.65143i	0.215591	+	0.976484i	$0.430832\pi$
$390$		0			0
$391$	−7.31595e8			−0.618945
$392$	−3.70599e8	+	2.01118e8i	−0.310744	+	0.168636i
$393$		0			0
$394$	1.96639e8	−	3.40589e8i	0.161969	−	0.280539i
$395$	−1.48430e7	−	2.57089e7i	−0.0121181	−	0.0209891i
$396$		0			0
$397$	−5.85561e8	+	1.01422e9i	−0.469684	+	0.813516i	−0.999399	−	0.0346591i	$-0.988965\pi$
$397$	−5.85561e8	+	1.01422e9i	−0.469684	+	0.813516i	0.529715	+	0.848176i	$0.322299\pi$
$398$	1.33676e9			1.06283
$399$		0			0
$400$	−3.19367e8			−0.249505
$401$	−7.49819e8	+	1.29872e9i	−0.580699	+	1.00580i	0.414698	+	0.909959i	$0.363887\pi$
$401$	−7.49819e8	+	1.29872e9i	−0.580699	+	1.00580i	−0.995397	+	0.0958406i	$0.969446\pi$
$402$		0			0
$403$	−3.96950e8	−	6.87538e8i	−0.302112	−	0.523274i
$404$	−3.72866e8	+	6.45822e8i	−0.281331	+	0.487280i
$405$		0			0
$406$	−1.32968e8	+	4.71280e8i	−0.0986066	+	0.349492i
$407$	4.09607e9			3.01153
$408$		0			0
$409$	3.74802e7	+	6.49176e7i	0.0270876	+	0.0469171i	0.879251	−	0.476358i	$-0.158043\pi$
$409$	3.74802e7	+	6.49176e7i	0.0270876	+	0.0469171i	−0.852164	+	0.523275i	$0.824710\pi$
$410$	−4.02311e7	−	6.96823e7i	−0.0288282	−	0.0499320i
$411$		0			0
$412$	4.58244e8			0.322817
$413$	−1.29585e9	−	1.33050e9i	−0.905167	−	0.929374i
$414$		0			0
$415$	4.68428e7	−	8.11342e7i	0.0321718	−	0.0557231i
$416$	1.18489e8	+	2.05229e8i	0.0806958	+	0.139769i
$417$		0			0
$418$	5.08663e8	−	8.81029e8i	0.340653	−	0.590029i
$419$	8.47037e7			0.0562540			0.0281270	−	0.999604i	$-0.491046\pi$
$419$	8.47037e7			0.0562540			0.0281270	+	0.999604i	$0.491046\pi$
$420$		0			0
$421$	−6.03152e8			−0.393949			−0.196974	−	0.980409i	$-0.563112\pi$
$421$	−6.03152e8			−0.393949			−0.196974	+	0.980409i	$0.563112\pi$
$422$	2.82443e8	−	4.89206e8i	0.182952	−	0.316883i
$423$		0			0
$424$	−3.18648e8	−	5.51914e8i	−0.203016	−	0.351634i
$425$	−5.97675e8	+	1.03520e9i	−0.377663	+	0.654131i
$426$		0			0
$427$	3.47315e7	−	1.23099e8i	0.0215887	−	0.0765170i
$428$	3.73425e8			0.230224
$429$		0			0
$430$	1.66597e7	+	2.88555e7i	0.0101048	+	0.0175020i
$431$	1.30326e9	+	2.25732e9i	0.784081	+	1.35807i	0.929546	+	0.368705i	$0.120199\pi$
$431$	1.30326e9	+	2.25732e9i	0.784081	+	1.35807i	−0.145465	+	0.989363i	$0.546468\pi$
$432$		0			0
$433$	3.09676e9			1.83316			0.916579	−	0.399854i	$-0.130939\pi$
$433$	3.09676e9			1.83316			0.916579	+	0.399854i	$0.130939\pi$
$434$	7.72467e8	−	1.96095e8i	0.453592	−	0.115147i
$435$		0			0
$436$	2.98554e8	−	5.17110e8i	0.172512	−	0.298800i
$437$	−4.51308e8	−	7.81688e8i	−0.258695	−	0.448073i
$438$		0			0
$439$	3.02299e8	−	5.23597e8i	0.170534	−	0.295374i	−0.768073	−	0.640363i	$-0.778784\pi$
$439$	3.02299e8	−	5.23597e8i	0.170534	−	0.295374i	0.938607	+	0.344989i	$0.112117\pi$
$440$	4.28026e7			0.0239545
$441$		0			0
$442$	8.86979e8			0.488580
$443$	1.08327e9	−	1.87628e9i	0.592003	−	1.02538i	−0.401959	−	0.915658i	$-0.631671\pi$
$443$	1.08327e9	−	1.87628e9i	0.592003	−	1.02538i	0.993962	−	0.109722i	$-0.0349960\pi$
$444$		0			0
$445$	3.32943e7	+	5.76674e7i	0.0179106	+	0.0310220i
$446$	−9.99562e8	+	1.73129e9i	−0.533504	+	0.924056i
$447$		0			0
$448$	−2.30580e8	+	5.85342e7i	−0.121157	+	0.0307565i
$449$	1.01304e9			0.528161			0.264080	−	0.964501i	$-0.414932\pi$
$449$	1.01304e9			0.528161			0.264080	+	0.964501i	$0.414932\pi$
$450$		0			0
$451$	−2.71903e9	−	4.70951e9i	−1.39572	−	2.41745i
$452$	2.82999e8	+	4.90169e8i	0.144145	+	0.249667i
$453$		0			0
$454$	2.59736e9			1.30268
$455$	−2.21598e7	+	7.85412e7i	−0.0110287	+	0.0390893i
$456$		0			0
$457$	−8.04203e8	+	1.39292e9i	−0.394148	+	0.682684i	−0.992992	−	0.118182i	$-0.962293\pi$
$457$	−8.04203e8	+	1.39292e9i	−0.394148	+	0.682684i	0.598844	+	0.800865i	$0.295627\pi$
$458$	−8.41936e7	−	1.45828e8i	−0.0409496	−	0.0709268i
$459$		0			0
$460$	1.89882e7	−	3.28885e7i	0.00909560	−	0.0157540i
$461$	2.98355e9			1.41834			0.709169	−	0.705039i	$-0.249070\pi$
$461$	2.98355e9			1.41834			0.709169	+	0.705039i	$0.249070\pi$
$462$		0			0
$463$	−2.83402e9			−1.32700			−0.663499	−	0.748178i	$-0.730929\pi$
$463$	−2.83402e9			−1.32700			−0.663499	+	0.748178i	$0.730929\pi$
$464$	−1.38136e8	+	2.39259e8i	−0.0641941	+	0.111187i
$465$		0			0
$466$	6.53939e8	+	1.13266e9i	0.299355	+	0.518498i
$467$	−2.15916e9	+	3.73977e9i	−0.981014	+	1.69917i	−0.322555	+	0.946551i	$0.604542\pi$
$467$	−2.15916e9	+	3.73977e9i	−0.981014	+	1.69917i	−0.658460	+	0.752616i	$0.728792\pi$
$468$		0			0
$469$	1.85725e9	+	1.90692e9i	0.831314	+	0.853547i
$470$	7.61166e7			0.0338171
$471$		0			0
$472$	−5.23929e8	−	9.07471e8i	−0.229338	−	0.397224i
$473$	1.12595e9	+	1.95021e9i	0.489223	+	0.847359i
$474$		0			0
$475$	−1.47478e9			−0.631393
$476$	−2.41782e8	+	8.56952e8i	−0.102754	+	0.364194i
$477$		0			0
$478$	1.27271e9	−	2.20440e9i	0.533006	−	0.923193i
$479$	−4.10161e8	−	7.10420e8i	−0.170522	−	0.295353i	0.768081	−	0.640353i	$-0.221212\pi$
$479$	−4.10161e8	−	7.10420e8i	−0.170522	−	0.295353i	−0.938602	+	0.345001i	$0.887879\pi$
$480$		0			0
$481$	−2.20304e9	+	3.81578e9i	−0.902642	+	1.56342i
$482$	1.03657e9			0.421634
$483$		0			0
$484$	1.64566e9			0.659752
$485$	−9.83410e7	+	1.70332e8i	−0.0391416	+	0.0677953i
$486$		0			0
$487$	−2.16713e9	−	3.75359e9i	−0.850226	−	1.47263i	−0.881004	−	0.473108i	$-0.843132\pi$
$487$	−2.16713e9	−	3.75359e9i	−0.850226	−	1.47263i	0.0307785	−	0.999526i	$-0.490201\pi$
$488$	3.60815e7	−	6.24950e7i	0.0140545	−	0.0243431i
$489$		0			0
$490$	−6.98417e7	−	4.28192e7i	−0.0268181	−	0.0164419i
$491$	1.79725e9			0.685208			0.342604	−	0.939480i	$-0.388691\pi$
$491$	1.79725e9			0.685208			0.342604	+	0.939480i	$0.388691\pi$
$492$		0			0
$493$	5.17028e8	+	8.95518e8i	0.194334	+	0.336597i
$494$	5.47162e8	+	9.47712e8i	0.204207	+	0.353697i
$495$		0			0
$496$	4.49643e8			0.165456
$497$	−5.41237e8	+	1.37396e8i	−0.197761	+	0.0502028i
$498$		0			0
$499$	−4.07065e8	+	7.05058e8i	−0.146660	+	0.254023i	−0.929991	−	0.367582i	$-0.880186\pi$
$499$	−4.07065e8	+	7.05058e8i	−0.146660	+	0.254023i	0.783331	+	0.621605i	$0.213519\pi$
$500$	−6.21110e7	−	1.07579e8i	−0.0222215	−	0.0384888i
$501$		0			0
$502$	3.17949e8	−	5.50704e8i	0.112175	−	0.194292i
$503$	−3.03176e9			−1.06220			−0.531101	−	0.847309i	$-0.678221\pi$
$503$	−3.03176e9			−1.06220			−0.531101	+	0.847309i	$0.678221\pi$
$504$		0			0
$505$	−1.44888e8			−0.0500624
$506$	1.28333e9	−	2.22279e9i	0.440362	−	0.762730i
$507$		0			0
$508$	7.12388e8	+	1.23389e9i	0.241098	+	0.417594i
$509$	−1.34515e9	+	2.32986e9i	−0.452124	+	0.783101i	−0.998518	−	0.0544271i	$-0.982667\pi$
$509$	−1.34515e9	+	2.32986e9i	−0.452124	+	0.783101i	0.546394	+	0.837528i	$0.316000\pi$
$510$		0			0
$511$	−9.00786e8	−	9.24876e8i	−0.298640	−	0.306627i
$512$	−1.34218e8			−0.0441942
$513$		0			0
$514$	1.71610e9	+	2.97238e9i	0.557407	+	0.965458i
$515$	4.45160e7	+	7.71039e7i	0.0143612	+	0.0248743i
$516$		0			0
$517$	5.14437e9			1.63725
$518$	−3.08608e9	−	3.16861e9i	−0.975557	−	1.00165i
$519$		0			0
$520$	−2.30211e7	+	3.98738e7i	−0.00717984	+	0.0124359i
$521$	−1.84690e9	−	3.19892e9i	−0.572152	−	0.990996i	−0.996345	−	0.0854238i	$-0.972776\pi$
$521$	−1.84690e9	−	3.19892e9i	−0.572152	−	0.990996i	0.424193	−	0.905572i	$-0.360558\pi$
$522$		0			0
$523$	−1.36893e9	+	2.37105e9i	−0.418432	+	0.724745i	−0.995782	−	0.0917518i	$-0.970753\pi$
$523$	−1.36893e9	+	2.37105e9i	−0.418432	+	0.724745i	0.577350	+	0.816497i	$0.304087\pi$
$524$	−6.97712e8			−0.211844
$525$		0			0
$526$	−3.39297e8			−0.101655
$527$	8.41480e8	−	1.45749e9i	0.250442	−	0.433778i
$528$		0			0
$529$	5.63790e8	+	9.76512e8i	0.165585	+	0.286802i
$530$	6.19099e7	−	1.07231e8i	0.0180632	−	0.0312864i
$531$		0			0
$532$	−1.06478e9	+	2.70301e8i	−0.306598	+	0.0778317i
$533$	5.84966e9			1.67334
$534$		0			0
$535$	3.62762e7	+	6.28322e7i	0.0102420	+	0.0177396i
$536$	7.50912e8	+	1.30062e9i	0.210626	+	0.364815i
$537$		0			0
$538$	−4.16155e9			−1.15217
$539$	−4.72028e9	−	2.89395e9i	−1.29840	−	0.796033i
$540$		0			0
$541$	−1.26385e9	+	2.18905e9i	−0.343167	+	0.594382i	−0.985019	−	0.172446i	$-0.944833\pi$
$541$	−1.26385e9	+	2.18905e9i	−0.343167	+	0.594382i	0.641852	+	0.766828i	$0.278166\pi$
$542$	−6.97124e8	−	1.20745e9i	−0.188067	−	0.325742i
$543$		0			0
$544$	−2.51180e8	+	4.35057e8i	−0.0668944	+	0.115864i
$545$	1.16012e8			0.0306982
$546$		0			0
$547$	1.49324e8			0.0390098			0.0195049	−	0.999810i	$-0.493791\pi$
$547$	1.49324e8			0.0390098			0.0195049	+	0.999810i	$0.493791\pi$
$548$	−1.02803e9	+	1.78059e9i	−0.266853	+	0.462203i
$549$		0			0
$550$	−2.09682e9	−	3.63180e9i	−0.537393	−	0.930792i
$551$	−6.37890e8	+	1.10486e9i	−0.162448	+	0.281369i
$552$		0			0
$553$	−5.88306e8	+	2.08514e9i	−0.147933	+	0.524321i
$554$	5.41461e9			1.35295
$555$		0			0
$556$	6.04960e8	+	1.04782e9i	0.149267	+	0.258539i
$557$	−2.77646e9	−	4.80896e9i	−0.680766	−	1.17912i	−0.974748	−	0.223310i	$-0.928314\pi$
$557$	−2.77646e9	−	4.80896e9i	−0.680766	−	1.17912i	0.293982	−	0.955811i	$-0.405019\pi$
$558$		0			0
$559$	−2.42235e9			−0.586537
$560$	−3.22486e7	−	3.31110e7i	−0.00775983	−	0.00796736i
$561$		0			0
$562$	1.40498e9	−	2.43350e9i	0.333882	−	0.578300i
$563$	−1.41867e9	−	2.45721e9i	−0.335045	−	0.580315i	0.648449	−	0.761258i	$-0.275418\pi$
$563$	−1.41867e9	−	2.45721e9i	−0.335045	−	0.580315i	−0.983493	+	0.180944i	$0.942085\pi$
$564$		0			0
$565$	−5.49837e7	+	9.52345e7i	−0.0128252	+	0.0222139i
$566$	−5.18625e9			−1.20225
$567$		0			0
$568$	−3.15047e8			−0.0721367
$569$	4.10087e9	−	7.10291e9i	0.933217	−	1.61638i	0.155435	−	0.987846i	$-0.450322\pi$
$569$	4.10087e9	−	7.10291e9i	0.933217	−	1.61638i	0.777782	−	0.628534i	$-0.216345\pi$
$570$		0			0
$571$	−2.70322e7	−	4.68211e7i	−0.00607651	−	0.0105248i	0.862971	−	0.505253i	$-0.168601\pi$
$571$	−2.70322e7	−	4.68211e7i	−0.00607651	−	0.0105248i	−0.869048	+	0.494728i	$0.835268\pi$
$572$	−1.55589e9	+	2.69489e9i	−0.347611	+	0.602080i
$573$		0			0
$574$	−1.59456e9	+	5.65163e9i	−0.351925	+	1.24733i
$575$	−3.72079e9			−0.816201
$576$		0			0
$577$	7.27103e8	+	1.25938e9i	0.157573	+	0.272924i	0.933993	−	0.357292i	$-0.116300\pi$
$577$	7.27103e8	+	1.25938e9i	0.157573	+	0.272924i	−0.776420	+	0.630216i	$0.782967\pi$
$578$	−7.01217e8	−	1.21454e9i	−0.151044	−	0.261617i
$579$		0			0
$580$	−5.36768e7			−0.0114232
$581$	−6.62714e9	+	1.68234e9i	−1.40188	+	0.355875i
$582$		0			0
$583$	4.18421e9	−	7.24726e9i	0.874527	−	1.51472i
$584$	−3.64200e8	−	6.30813e8i	−0.0756650	−	0.131056i
$585$		0			0
$586$	−2.54006e7	+	4.39951e7i	−0.00521437	+	0.00903156i
$587$	7.30976e9			1.49166			0.745830	−	0.666137i	$-0.232053\pi$
$587$	7.30976e9			1.49166			0.745830	+	0.666137i	$0.232053\pi$
$588$		0			0
$589$	2.07638e9			0.418699
$590$	1.01794e8	−	1.76312e8i	0.0204051	−	0.0353427i
$591$		0			0
$592$	−1.24774e9	−	2.16116e9i	−0.247172	−	0.428115i
$593$	−2.16461e9	+	3.74922e9i	−0.426274	+	0.738329i	−0.996538	−	0.0831327i	$-0.973507\pi$
$593$	−2.16461e9	+	3.74922e9i	−0.426274	+	0.738329i	0.570264	+	0.821461i	$0.306841\pi$
$594$		0			0
$595$	−1.67678e8	+	4.25661e7i	−0.0326338	+	0.00828428i
$596$	3.54959e8			0.0686779
$597$		0			0
$598$	1.38046e9	+	2.39102e9i	0.263979	+	0.457224i
$599$	−1.44898e9	−	2.50970e9i	−0.275466	−	0.477121i	0.694787	−	0.719216i	$-0.255499\pi$
$599$	−1.44898e9	−	2.50970e9i	−0.275466	−	0.477121i	−0.970253	+	0.242095i	$0.922165\pi$
$600$		0			0
$601$	7.87385e9			1.47954			0.739770	−	0.672860i	$-0.234935\pi$
$601$	7.87385e9			1.47954			0.739770	+	0.672860i	$0.234935\pi$
$602$	6.60310e8	−	2.34034e9i	0.123356	−	0.437212i
$603$		0			0
$604$	7.25243e8	−	1.25616e9i	0.133923	−	0.231961i
$605$	1.59867e8	+	2.76897e8i	0.0293504	+	0.0508364i
$606$		0			0
$607$	1.80092e9	−	3.11928e9i	0.326838	−	0.566101i	−0.655044	−	0.755591i	$-0.727350\pi$
$607$	1.80092e9	−	3.11928e9i	0.326838	−	0.566101i	0.981883	+	0.189490i	$0.0606834\pi$
$608$	−6.19795e8			−0.111837
$609$		0			0
$610$	1.40205e7			0.00250097
$611$	−2.76687e9	+	4.79236e9i	−0.490732	+	0.849973i
$612$		0			0
$613$	1.97224e9	+	3.41602e9i	0.345819	+	0.598976i	0.985502	−	0.169663i	$-0.0542678\pi$
$613$	1.97224e9	+	3.41602e9i	0.345819	+	0.598976i	−0.639683	+	0.768639i	$0.720934\pi$
$614$	3.22181e9	−	5.58034e9i	0.561708	−	0.972907i
$615$		0			0
$616$	−2.17953e9	−	2.23782e9i	−0.375691	−	0.385738i
$617$	−4.54305e9			−0.778663			−0.389331	−	0.921098i	$-0.627294\pi$
$617$	−4.54305e9			−0.778663			−0.389331	+	0.921098i	$0.627294\pi$
$618$		0			0
$619$	−3.82703e9	−	6.62860e9i	−0.648551	−	1.12332i	−0.983469	−	0.181076i	$-0.942042\pi$
$619$	−3.82703e9	−	6.62860e9i	−0.648551	−	1.12332i	0.334918	−	0.942247i	$-0.391291\pi$
$620$	4.36804e7	+	7.56567e7i	0.00736064	+	0.0127490i
$621$		0			0
$622$	−3.39841e9			−0.566252
$623$	1.31962e9	−	4.67716e9i	0.218646	−	0.774950i
$624$		0			0
$625$	−3.03365e9	+	5.25444e9i	−0.497033	+	0.860887i
$626$	−1.66863e9	−	2.89015e9i	−0.271862	−	0.470880i
$627$		0			0
$628$	−2.08040e9	+	3.60336e9i	−0.335188	+	0.580562i
$629$	−9.34031e9			−1.49652
$630$		0			0
$631$	−7.11407e9			−1.12724			−0.563619	−	0.826035i	$-0.690591\pi$
$631$	−7.11407e9			−1.12724			−0.563619	+	0.826035i	$0.690591\pi$
$632$	−6.11173e8	+	1.05858e9i	−0.0963062	+	0.166807i
$633$		0			0
$634$	−1.71198e9	−	2.96523e9i	−0.266800	−	0.462111i
$635$	−1.38409e8	+	2.39732e8i	−0.0214515	+	0.0371551i
$636$		0			0
$637$	5.23470e9	−	2.84079e9i	0.802424	−	0.435463i
$638$	−3.62777e9			−0.553054
$639$		0			0
$640$	−1.30385e7	−	2.25834e7i	−0.00196607	−	0.00340533i
$641$	1.99141e9	+	3.44923e9i	0.298647	+	0.517271i	0.975827	−	0.218546i	$-0.0701314\pi$
$641$	1.99141e9	+	3.44923e9i	0.298647	+	0.517271i	−0.677180	+	0.735818i	$0.736798\pi$
$642$		0			0
$643$	3.89465e9			0.577737			0.288869	−	0.957369i	$-0.406721\pi$
$643$	3.89465e9			0.577737			0.288869	+	0.957369i	$0.406721\pi$
$644$	−2.68638e9	+	6.81953e8i	−0.396339	+	0.100613i
$645$		0			0
$646$	−1.15991e9	+	2.00902e9i	−0.169282	+	0.293204i
$647$	−2.55065e9	−	4.41786e9i	−0.370243	−	0.641279i	0.619360	−	0.785107i	$-0.287392\pi$
$647$	−2.55065e9	−	4.41786e9i	−0.370243	−	0.641279i	−0.989603	+	0.143828i	$0.954059\pi$
$648$		0			0
$649$	6.87977e9	−	1.19161e10i	0.987911	−	1.71111i
$650$	4.51105e9			0.644289
$651$		0			0
$652$	2.23577e9			0.315908
$653$	4.67227e9	−	8.09262e9i	0.656647	−	1.13735i	−0.324831	−	0.945772i	$-0.605307\pi$
$653$	4.67227e9	−	8.09262e9i	0.656647	−	1.13735i	0.981478	−	0.191574i	$-0.0613593\pi$
$654$		0			0
$655$	−6.77790e7	−	1.17397e8i	−0.00942433	−	0.0163234i
$656$	−1.65654e9	+	2.86922e9i	−0.229108	+	0.396826i
$657$		0			0
$658$	−3.87590e9	−	3.97955e9i	−0.530373	−	0.544557i
$659$	1.00669e10			1.37024			0.685120	−	0.728430i	$-0.259750\pi$
$659$	1.00669e10			1.37024			0.685120	+	0.728430i	$0.259750\pi$
$660$		0			0
$661$	−7.51511e8	−	1.30166e9i	−0.101212	−	0.175304i	0.810973	−	0.585084i	$-0.198939\pi$
$661$	−7.51511e8	−	1.30166e9i	−0.101212	−	0.175304i	−0.912184	+	0.409781i	$0.865605\pi$
$662$	1.06042e9	+	1.83671e9i	0.142062	+	0.246058i
$663$		0			0
$664$	−3.85757e9			−0.511359
$665$	−1.48918e8	−	1.52901e8i	−0.0196369	−	0.0201620i
$666$		0			0
$667$	−1.60936e9	+	2.78749e9i	−0.209997	+	0.363725i
$668$	2.84648e9	+	4.93024e9i	0.369479	+	0.639957i
$669$		0			0
$670$	−1.45894e8	+	2.52696e8i	−0.0187403	+	0.0324591i
$671$	9.47581e8			0.121084
$672$		0			0
$673$	3.90495e9			0.493814			0.246907	−	0.969039i	$-0.420586\pi$
$673$	3.90495e9			0.493814			0.246907	+	0.969039i	$0.420586\pi$
$674$	8.70584e8	−	1.50790e9i	0.109522	−	0.189697i
$675$		0			0
$676$	3.34299e8	+	5.79023e8i	0.0416219	+	0.0720912i
$677$	−3.20795e9	+	5.55633e9i	−0.397344	+	0.688220i	−0.993397	−	0.114725i	$-0.963401\pi$
$677$	−3.20795e9	+	5.55633e9i	−0.397344	+	0.688220i	0.596053	+	0.802945i	$0.296735\pi$
$678$		0			0
$679$	1.39129e10	−	3.53188e9i	1.70559	−	0.432974i
$680$	−9.76033e7			−0.0119037
$681$		0			0
$682$	2.95216e9	+	5.11329e9i	0.356365	+	0.617242i
$683$	4.58428e9	+	7.94021e9i	0.550553	+	0.953585i	0.998235	+	0.0593923i	$0.0189163\pi$
$683$	4.58428e9	+	7.94021e9i	0.550553	+	0.953585i	−0.447682	+	0.894193i	$0.647750\pi$
$684$		0			0
$685$	−3.99469e8			−0.0474860
$686$	1.31769e9	+	5.83186e9i	0.155840	+	0.689720i
$687$		0			0
$688$	6.85976e8	−	1.18814e9i	0.0803062	−	0.139094i
$689$	4.50090e9	+	7.79578e9i	0.524242	+	0.908013i
$690$		0			0
$691$	−4.12922e9	+	7.15202e9i	−0.476096	+	0.824623i	−0.999625	−	0.0273851i	$-0.991282\pi$
$691$	−4.12922e9	+	7.15202e9i	−0.476096	+	0.824623i	0.523529	+	0.852008i	$0.324615\pi$
$692$	1.96888e9			0.225865
$693$		0			0
$694$	−5.19966e9			−0.590496
$695$	−1.17537e8	+	2.03581e8i	−0.0132809	+	0.0230033i
$696$		0			0
$697$	6.20024e9	+	1.07391e10i	0.693576	+	1.20131i
$698$	−2.84615e9	+	4.92969e9i	−0.316785	+	0.548688i
$699$		0			0
$700$	−1.22967e9	+	4.35833e9i	−0.135502	+	0.480261i
$701$	1.35693e10			1.48779			0.743897	−	0.668294i	$-0.232975\pi$
$701$	1.35693e10			1.48779			0.743897	+	0.668294i	$0.232975\pi$
$702$		0			0
$703$	−5.76187e9	−	9.97985e9i	−0.625489	−	1.08338i
$704$	−8.81215e8	−	1.52631e9i	−0.0951870	−	0.164869i
$705$		0			0
$706$	−1.23872e10			−1.32482
$707$	7.37775e9	+	7.57506e9i	0.785156	+	0.806154i
$708$		0			0
$709$	−3.01524e9	+	5.22255e9i	−0.317731	+	0.550327i	−0.980014	−	0.198927i	$-0.936254\pi$
$709$	−3.01524e9	+	5.22255e9i	−0.317731	+	0.550327i	0.662283	+	0.749254i	$0.269588\pi$
$710$	−3.06051e7	−	5.30096e7i	−0.00320915	−	0.00555841i
$711$		0			0
$712$	1.37092e9	−	2.37450e9i	0.142341	−	0.246542i
$713$	5.23857e9			0.541252
$714$		0			0
$715$	−6.04587e8			−0.0618568
$716$	3.29830e9	−	5.71282e9i	0.335811	−	0.581641i
$717$		0			0
$718$	−6.75058e8	−	1.16923e9i	−0.0680621	−	0.117887i
$719$	−4.88166e8	+	8.45527e8i	−0.0489797	+	0.0848353i	−0.889476	−	0.456982i	$-0.848930\pi$
$719$	−4.88166e8	+	8.45527e8i	−0.0489797	+	0.0848353i	0.840496	+	0.541818i	$0.182264\pi$
$720$		0			0
$721$	1.76440e9	−	6.25357e9i	0.175316	−	0.621376i
$722$	4.28887e9			0.424094
$723$		0			0
$724$	2.00218e9	+	3.46788e9i	0.196074	+	0.339609i
$725$	2.62953e9	+	4.55447e9i	0.256268	+	0.443869i
$726$		0			0
$727$	1.25379e10			1.21019			0.605095	−	0.796153i	$-0.293135\pi$
$727$	1.25379e10			1.21019			0.605095	+	0.796153i	$0.293135\pi$
$728$	3.25694e9	−	8.26794e8i	0.312860	−	0.0794214i
$729$		0			0
$730$	7.07602e7	−	1.22560e8i	0.00673223	−	0.0116606i
$731$	−2.56752e9	−	4.44708e9i	−0.243111	−	0.421080i
$732$		0			0
$733$	−6.39843e9	+	1.10824e10i	−0.600080	+	1.03937i	0.392728	+	0.919655i	$0.371531\pi$
$733$	−6.39843e9	+	1.10824e10i	−0.600080	+	1.03937i	−0.992808	+	0.119715i	$0.961802\pi$
$734$	2.74972e9			0.256657
$735$		0			0
$736$	−1.56371e9			−0.144571
$737$	−9.86031e9	+	1.70786e10i	−0.907307	+	1.57150i
$738$		0			0
$739$	2.26030e9	+	3.91495e9i	0.206020	+	0.356838i	0.950457	−	0.310855i	$-0.100615\pi$
$739$	2.26030e9	+	3.91495e9i	0.206020	+	0.356838i	−0.744437	+	0.667693i	$0.767282\pi$
$740$	2.42423e8	−	4.19889e8i	0.0219919	−	0.0380911i
$741$		0			0
$742$	−8.75877e9	+	2.22347e9i	−0.787099	+	0.199810i
$743$	−1.42321e10			−1.27294			−0.636469	−	0.771303i	$-0.719606\pi$
$743$	−1.42321e10			−1.27294			−0.636469	+	0.771303i	$0.719606\pi$
$744$		0			0
$745$	3.44824e7	+	5.97253e7i	0.00305528	+	0.00529190i
$746$	−5.57417e8	−	9.65474e8i	−0.0491580	−	0.0851442i
$747$		0			0
$748$	−6.59656e9			−0.576318
$749$	1.43781e9	−	5.09605e9i	0.125030	−	0.443147i
$750$		0			0
$751$	−7.44123e9	+	1.28886e10i	−0.641069	+	1.11036i	0.344125	+	0.938924i	$0.388175\pi$
$751$	−7.44123e9	+	1.28886e10i	−0.641069	+	1.11036i	−0.985194	+	0.171441i	$0.945158\pi$
$752$	−1.56708e9	−	2.71426e9i	−0.134378	−	0.232750i
$753$		0			0
$754$	1.95117e9	−	3.37953e9i	0.165766	−	0.287116i
$755$	2.81814e8			0.0238313
$756$		0			0
$757$	1.24473e10			1.04289			0.521445	−	0.853285i	$-0.325393\pi$
$757$	1.24473e10			1.04289			0.521445	+	0.853285i	$0.325393\pi$
$758$	−3.09785e9	+	5.36563e9i	−0.258356	+	0.447485i
$759$		0			0
$760$	−6.02097e7	−	1.04286e8i	−0.00497530	−	0.00861747i
$761$	1.15160e10	−	1.99463e10i	0.947230	−	1.64065i	0.196007	−	0.980602i	$-0.437202\pi$
$761$	1.15160e10	−	1.99463e10i	0.947230	−	1.64065i	0.751223	−	0.660049i	$-0.229464\pi$
$762$		0			0
$763$	−5.90737e9	−	6.06535e9i	−0.481458	−	0.494334i
$764$	−5.06243e9			−0.410707
$765$		0			0
$766$	5.22492e9	+	9.04983e9i	0.420029	+	0.727511i
$767$	7.40048e9	+	1.28180e10i	0.592211	+	1.02574i
$768$		0			0
$769$	−1.08864e10			−0.863265			−0.431632	−	0.902050i	$-0.642062\pi$
$769$	−1.08864e10			−0.863265			−0.431632	+	0.902050i	$0.642062\pi$
$770$	1.64805e8	−	5.84119e8i	0.0130092	−	0.0461088i
$771$		0			0
$772$	1.80126e9	−	3.11987e9i	0.140902	−	0.244049i
$773$	7.34907e9	+	1.27290e10i	0.572275	+	0.991209i	0.996332	+	0.0855732i	$0.0272722\pi$
$773$	7.34907e9	+	1.27290e10i	0.572275	+	0.991209i	−0.424057	+	0.905635i	$0.639395\pi$
$774$		0			0
$775$	4.27964e9	−	7.41256e9i	0.330257	−	0.572021i
$776$	8.09853e9			0.622143
$777$		0			0
$778$	1.77110e10			1.34839
$779$	−7.64964e9	+	1.32496e10i	−0.579775	+	1.00420i
$780$		0			0
$781$	−2.06846e9	−	3.58268e9i	−0.155371	−	0.269110i
$782$	−2.92638e9	+	5.06864e9i	−0.218830	+	0.379025i
$783$		0			0
$784$	−8.90073e7	+	3.37206e9i	−0.00659659	+	0.249913i
$785$	−8.08398e8			−0.0596460
$786$		0			0
$787$	4.29872e8	+	7.44560e8i	0.0314360	+	0.0544488i	0.881315	−	0.472528i	$-0.156659\pi$
$787$	4.29872e8	+	7.44560e8i	0.0314360	+	0.0544488i	−0.849879	+	0.526977i	$0.823325\pi$
$788$	−1.57311e9	−	2.72471e9i	−0.114530	−	0.198371i
$789$		0			0
$790$	−2.37489e8			−0.0171375
$791$	7.77888e9	−	1.97472e9i	0.558855	−	0.141869i
$792$		0			0
$793$	−5.09651e8	+	8.82741e8i	−0.0362925	+	0.0628604i
$794$	4.68449e9	+	8.11378e9i	0.332117	+	0.575243i
$795$		0			0
$796$	5.34704e9	−	9.26135e9i	0.375766	−	0.650846i
$797$	−4.31200e9			−0.301699			−0.150850	−	0.988557i	$-0.548201\pi$
$797$	−4.31200e9			−0.301699			−0.150850	+	0.988557i	$0.548201\pi$
$798$		0			0
$799$	−1.17308e10			−0.813603
$800$	−1.27747e9	+	2.21264e9i	−0.0882134	+	0.152790i
$801$		0			0
$802$	5.99855e9	+	1.03898e10i	0.410616	+	0.711208i
$803$	4.78236e9	−	8.28329e9i	0.325940	−	0.564545i
$804$		0			0
$805$	−3.75712e8	−	3.85760e8i	−0.0253846	−	0.0260634i
$806$	−6.35120e9			−0.427251
$807$		0			0
$808$	2.98293e9	+	5.16658e9i	0.198931	+	0.344559i
$809$	−9.94355e9	−	1.72227e10i	−0.660270	−	1.14362i	−0.980545	−	0.196296i	$-0.937108\pi$
$809$	−9.94355e9	−	1.72227e10i	−0.660270	−	1.14362i	0.320275	−	0.947325i	$-0.396225\pi$
$810$		0			0
$811$	−2.58957e10			−1.70473			−0.852363	−	0.522950i	$-0.824831\pi$
$811$	−2.58957e10			−1.70473			−0.852363	+	0.522950i	$0.824831\pi$
$812$	2.73325e9	+	2.80635e9i	0.179157	+	0.183948i
$813$		0			0
$814$	1.63843e10	−	2.83784e10i	1.06474	−	1.84418i
$815$	2.17193e8	+	3.76190e8i	0.0140538	+	0.0243420i
$816$		0			0
$817$	3.16772e9	−	5.48665e9i	0.203221	−	0.351990i
$818$	5.99683e8			0.0383076
$819$		0			0
$820$	−6.43697e8			−0.0407693
$821$	1.06287e9	−	1.84094e9i	0.0670314	−	0.116102i	−0.830562	−	0.556926i	$-0.811981\pi$
$821$	1.06287e9	−	1.84094e9i	0.0670314	−	0.116102i	0.897593	+	0.440825i	$0.145314\pi$
$822$		0			0
$823$	7.58631e9	+	1.31399e10i	0.474385	+	0.821660i	0.999570	−	0.0293289i	$-0.00933701\pi$
$823$	7.58631e9	+	1.31399e10i	0.474385	+	0.821660i	−0.525184	+	0.850988i	$0.676004\pi$
$824$	1.83298e9	−	3.17481e9i	0.114133	−	0.197684i
$825$		0			0
$826$	−1.44014e10	+	3.65588e9i	−0.889148	+	0.225716i
$827$	−1.94463e10			−1.19555			−0.597776	−	0.801663i	$-0.703949\pi$
$827$	−1.94463e10			−1.19555			−0.597776	+	0.801663i	$0.703949\pi$
$828$		0			0
$829$	1.84579e9	+	3.19701e9i	0.112523	+	0.194896i	0.916787	−	0.399376i	$-0.130773\pi$
$829$	1.84579e9	+	3.19701e9i	0.112523	+	0.194896i	−0.804264	+	0.594273i	$0.797440\pi$
$830$	−3.74743e8	−	6.49073e8i	−0.0227489	−	0.0394022i
$831$		0			0
$832$	1.89582e9			0.114121
$833$	1.07637e10	+	6.59911e9i	0.645215	+	0.395574i
$834$		0			0
$835$	−5.53040e8	+	9.57894e8i	−0.0328741	+	0.0569396i
$836$	−4.06930e9	−	7.04823e9i	−0.240878	−	0.417214i
$837$		0			0
$838$	3.38815e8	−	5.86844e8i	0.0198888	−	0.0344484i
$839$	9.94899e9			0.581584			0.290792	−	0.956786i	$-0.406081\pi$
$839$	9.94899e9			0.581584			0.290792	+	0.956786i	$0.406081\pi$
$840$		0			0
$841$	−1.27005e10			−0.736264
$842$	−2.41261e9	+	4.17876e9i	−0.139282	+	0.241243i
$843$		0			0
$844$	−2.25955e9	−	3.91365e9i	−0.129367	−	0.224070i
$845$	−6.49507e7	+	1.12498e8i	−0.00370327	+	0.00641425i
$846$		0			0
$847$	6.33634e9	−	2.24580e10i	0.358300	−	1.26993i
$848$	−5.09837e9			−0.287108
$849$		0			0
$850$	4.78140e9	+	8.28163e9i	0.267048	+	0.462541i
$851$	−1.45369e10	−	2.51786e10i	−0.808569	−	1.40048i
$852$		0			0
$853$	3.15287e9			0.173934			0.0869669	−	0.996211i	$-0.472283\pi$
$853$	3.15287e9			0.173934			0.0869669	+	0.996211i	$0.472283\pi$
$854$	−7.13931e8	−	7.33024e8i	−0.0392242	−	0.0402732i
$855$		0			0
$856$	1.49370e9	−	2.58716e9i	0.0813963	−	0.140983i
$857$	8.54798e7	+	1.48055e8i	0.00463907	+	0.00803510i	0.868336	−	0.495977i	$-0.165190\pi$
$857$	8.54798e7	+	1.48055e8i	0.00463907	+	0.00803510i	−0.863697	+	0.504012i	$0.831857\pi$
$858$		0			0
$859$	9.17292e9	−	1.58880e10i	0.493778	−	0.855248i	−0.506197	−	0.862418i	$-0.668949\pi$
$859$	9.17292e9	−	1.58880e10i	0.493778	−	0.855248i	0.999974	+	0.00717006i	$0.00228232\pi$
$860$	2.66555e8			0.0142904
$861$		0			0
$862$	2.08522e10			1.10886
$863$	1.05965e10	−	1.83536e10i	0.561208	−	0.972040i	−0.436184	−	0.899858i	$-0.643670\pi$
$863$	1.05965e10	−	1.83536e10i	0.561208	−	0.972040i	0.997391	−	0.0721827i	$-0.0229965\pi$
$864$		0			0
$865$	1.91266e8	+	3.31283e8i	0.0100481	+	0.0174037i
$866$	1.23870e10	−	2.14550e10i	0.648119	−	1.12258i
$867$		0			0
$868$	1.73128e9	−	6.13619e9i	0.0898562	−	0.318478i
$869$	−1.60508e10			−0.829711
$870$		0			0
$871$	−1.06066e10	−	1.83712e10i	−0.543893	−	0.942049i
$872$	−2.38843e9	−	4.13688e9i	−0.121985	−	0.211283i
$873$		0			0
$874$	−7.22092e9			−0.365850
$875$	−1.70726e9	+	4.33400e8i	−0.0861534	+	0.0218706i
$876$		0			0
$877$	−1.29471e10	+	2.24251e10i	−0.648148	+	1.12263i	0.335417	+	0.942070i	$0.391123\pi$
$877$	−1.29471e10	+	2.24251e10i	−0.648148	+	1.12263i	−0.983565	+	0.180556i	$0.942210\pi$
$878$	−2.41839e9	−	4.18878e9i	−0.120586	−	0.208861i
$879$		0			0
$880$	1.71211e8	−	2.96545e8i	0.00846918	−	0.0146690i
$881$	−2.45497e10			−1.20957			−0.604785	−	0.796389i	$-0.706741\pi$
$881$	−2.45497e10			−1.20957			−0.604785	+	0.796389i	$0.706741\pi$
$882$		0			0
$883$	2.01403e10			0.984473			0.492237	−	0.870461i	$-0.336179\pi$
$883$	2.01403e10			0.984473			0.492237	+	0.870461i	$0.336179\pi$
$884$	3.54792e9	−	6.14517e9i	0.172739	−	0.299193i
$885$		0			0
$886$	−8.66617e9	−	1.50102e10i	−0.418609	−	0.725053i
$887$	7.24531e8	−	1.25492e9i	0.0348597	−	0.0603788i	−0.848069	−	0.529886i	$-0.822235\pi$
$887$	7.24531e8	−	1.25492e9i	0.0348597	−	0.0603788i	0.882929	+	0.469507i	$0.155568\pi$
$888$		0			0
$889$	1.95816e10	−	4.97092e9i	0.934744	−	0.237291i
$890$	5.32709e8			0.0253294
$891$		0			0
$892$	7.99650e9	+	1.38503e10i	0.377244	+	0.653407i
$893$	−7.23650e9	−	1.25340e10i	−0.340054	−	0.588992i
$894$		0			0
$895$	1.28165e9			0.0597569
$896$	−5.16784e8	+	1.83164e9i	−0.0240011	+	0.0850673i
$897$		0			0
$898$	4.05218e9	−	7.01858e9i	0.186733	−	0.323431i
$899$	−3.70217e9	−	6.41234e9i	−0.169941	−	0.294346i
$900$		0			0
$901$	−9.54129e9	+	1.65260e10i	−0.434580	+	0.752715i
$902$	−4.35046e10			−1.97384
$903$		0			0
$904$	4.52798e9			0.203852
$905$	−3.89003e8	+	6.73773e8i	−0.0174455	+	0.0302164i
$906$		0			0
$907$	1.54863e9	+	2.68231e9i	0.0689165	+	0.119367i	0.898425	−	0.439128i	$-0.144712\pi$
$907$	1.54863e9	+	2.68231e9i	0.0689165	+	0.119367i	−0.829508	+	0.558495i	$0.811379\pi$
$908$	1.03895e10	−	1.79951e10i	0.460567	−	0.797725i
$909$		0			0
$910$	4.55510e8	+	4.67692e8i	0.0200379	+	0.0205738i
$911$	−2.29298e10			−1.00481			−0.502406	−	0.864632i	$-0.667552\pi$
$911$	−2.29298e10			−1.00481			−0.502406	+	0.864632i	$0.667552\pi$
$912$		0			0
$913$	−2.53271e10	−	4.38679e10i	−1.10138	−	1.90765i
$914$	6.43362e9	+	1.11434e10i	0.278705	+	0.482730i
$915$		0			0
$916$	−1.34710e9			−0.0579115
$917$	−2.68643e9	+	9.52154e9i	−0.115049	+	0.407769i
$918$		0			0
$919$	−2.23880e10	+	3.87772e10i	−0.951506	+	1.64806i	−0.209338	+	0.977843i	$0.567131\pi$
$919$	−2.23880e10	+	3.87772e10i	−0.951506	+	1.64806i	−0.742168	+	0.670213i	$0.766203\pi$
$920$	−1.51906e8	−	2.63108e8i	−0.00643156	−	0.0111398i
$921$		0			0
$922$	1.19342e10	−	2.06706e10i	0.501458	−	0.868551i
$923$	4.45003e9			0.186276
$924$		0			0
$925$	−4.75034e10			−1.97346
$926$	−1.13361e10	+	1.96347e10i	−0.469164	+	0.812616i
$927$		0			0
$928$	1.10509e9	+	1.91407e9i	0.0453921	+	0.0786214i
$929$	1.49225e10	−	2.58466e10i	0.610644	−	1.05767i	−0.380488	−	0.924786i	$-0.624244\pi$
$929$	1.49225e10	−	2.58466e10i	0.610644	−	1.05767i	0.991132	−	0.132880i	$-0.0424226\pi$
$930$		0			0
$931$	−4.11020e8	+	1.55716e10i	−0.0166932	+	0.632425i
$932$	1.04630e10			0.423352
$933$		0			0
$934$	1.72733e10	+	2.99182e10i	0.693682	+	1.20149i
$935$	−6.40821e8	−	1.10993e9i	−0.0256387	−	0.0444075i
$936$		0			0
$937$	1.43090e10			0.568227			0.284113	−	0.958791i	$-0.408301\pi$
$937$	1.43090e10			0.568227			0.284113	+	0.958791i	$0.408301\pi$
$938$	2.06405e10	−	5.23972e9i	0.816603	−	0.207300i
$939$		0			0
$940$	3.04466e8	−	5.27351e8i	0.0119562	−	0.0207087i
$941$	−3.30316e9	−	5.72124e9i	−0.129231	−	0.223834i	0.794148	−	0.607724i	$-0.207917\pi$
$941$	−3.30316e9	−	5.72124e9i	−0.129231	−	0.223834i	−0.923379	+	0.383890i	$0.874584\pi$
$942$		0			0
$943$	−1.92996e10	+	3.34279e10i	−0.749475	+	1.29813i
$944$	−8.38286e9			−0.324332
$945$		0			0
$946$	1.80153e10			0.691866
$947$	−9.94687e9	+	1.72285e10i	−0.380594	+	0.659208i	−0.991147	−	0.132767i	$-0.957614\pi$
$947$	−9.94687e9	+	1.72285e10i	−0.380594	+	0.659208i	0.610553	+	0.791975i	$0.290947\pi$
$948$		0			0
$949$	5.14432e9	+	8.91022e9i	0.195387	+	0.338421i
$950$	−5.89912e9	+	1.02176e10i	−0.223231	+	0.386648i
$951$		0			0
$952$	4.97001e9	+	5.10293e9i	0.186693	+	0.191686i
$953$	−4.15702e10			−1.55581			−0.777905	−	0.628382i	$-0.783717\pi$
$953$	−4.15702e10			−1.55581			−0.777905	+	0.628382i	$0.783717\pi$
$954$		0			0
$955$	−4.91788e8	−	8.51802e8i	−0.0182712	−	0.0316466i
$956$	−1.01817e10	−	1.76352e10i	−0.376892	−	0.652796i
$957$		0			0
$958$	−6.56258e9			−0.241154
$959$	2.03411e10	+	2.08851e10i	0.744750	+	0.764667i
$960$		0			0
$961$	7.73091e9	−	1.33903e10i	0.280995	−	0.486698i
$962$	1.76244e10	+	3.05263e10i	0.638264	+	1.10551i
$963$		0			0
$964$	4.14630e9	−	7.18160e9i	0.149070	−	0.258197i
$965$	6.99931e8			0.0250732
$966$		0			0
$967$	−2.38376e10			−0.847755			−0.423877	−	0.905720i	$-0.639331\pi$
$967$	−2.38376e10			−0.847755			−0.423877	+	0.905720i	$0.639331\pi$
$968$	6.58263e9	−	1.14014e10i	0.233257	−	0.404014i
$969$		0			0
$970$	7.86728e8	+	1.36265e9i	0.0276773	+	0.0479385i
$971$	2.49541e10	−	4.32218e10i	0.874732	−	1.51508i	0.0176850	−	0.999844i	$-0.494370\pi$
$971$	2.49541e10	−	4.32218e10i	0.874732	−	1.51508i	0.857047	−	0.515237i	$-0.172296\pi$
$972$		0			0
$973$	1.66287e10	−	4.22130e9i	0.578714	−	0.146910i
$974$	−3.46741e10			−1.20240
$975$		0			0
$976$	−2.88652e8	−	4.99960e8i	−0.00993803	−	0.0172132i
$977$	−1.06421e10	−	1.84327e10i	−0.365087	−	0.632350i	0.623703	−	0.781662i	$-0.285628\pi$
$977$	−1.06421e10	−	1.84327e10i	−0.365087	−	0.632350i	−0.988790	+	0.149312i	$0.952294\pi$
$978$		0			0
$979$	3.60034e10			1.22632
$980$	−5.76027e8	+	3.12601e8i	−0.0195502	+	0.0106096i
$981$		0			0
$982$	7.18899e9	−	1.24517e10i	0.242258	−	0.419603i
$983$	2.02849e10	+	3.51344e10i	0.681138	+	1.17977i	0.974634	+	0.223805i	$0.0718479\pi$
$983$	2.02849e10	+	3.51344e10i	0.681138	+	1.17977i	−0.293496	+	0.955960i	$0.594819\pi$
$984$		0			0
$985$	3.05639e8	−	5.29382e8i	0.0101902	−	0.0176499i
$986$	8.27244e9			0.274830
$987$		0			0
$988$	8.75459e9			0.288793
$989$	7.99197e9	−	1.38425e10i	0.262704	−	0.455017i
$990$		0			0
$991$	1.53510e10	+	2.65888e10i	0.501048	+	0.867841i	0.999999	+	0.00121109i	$0.000385502\pi$
$991$	1.53510e10	+	2.65888e10i	0.501048	+	0.867841i	−0.498951	+	0.866630i	$0.666281\pi$
$992$	1.79857e9	−	3.11522e9i	0.0584975	−	0.101321i
$993$		0			0
$994$	−1.21304e9	+	4.29938e9i	−0.0391762	+	0.138853i
$995$	2.07775e9			0.0668670
$996$		0			0
$997$	−1.94876e10	−	3.37534e10i	−0.622765	−	1.07866i	−0.988968	−	0.148126i	$-0.952676\pi$
$997$	−1.94876e10	−	3.37534e10i	−0.622765	−	1.07866i	0.366203	−	0.930535i	$-0.380657\pi$
$998$	3.25652e9	+	5.64046e9i	0.103704	+	0.179621i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.j.37.3	yes	6
3.2	odd	2		126.8.g.i.37.1	✓	6
7.4	even	3	inner	126.8.g.j.109.3	yes	6
21.11	odd	6		126.8.g.i.109.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.8.g.i.37.1	✓	6	3.2	odd	2
126.8.g.i.109.1	yes	6	21.11	odd	6
126.8.g.j.37.3	yes	6	1.1	even	1	trivial
126.8.g.j.109.3	yes	6	7.4	even	3	inner

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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(6.21726 - 10.7686i) q^{5} +(-879.593 + 223.290i) q^{7} -512.000 q^{8} +(-49.7381 - 86.1488i) q^{10} +(-3361.57 - 5822.41i) q^{11} +7231.99 q^{13} +(-1971.37 + 6987.16i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(7665.42 + 13276.9i) q^{17} +(-9457.32 + 16380.6i) q^{19} -795.809 q^{20} -53785.1 q^{22} +(-23860.2 + 41327.2i) q^{23} +(38985.2 + 67524.3i) q^{25} +(28928.0 - 50104.7i) q^{26} +(40523.0 + 41606.7i) q^{28} +67449.4 q^{29} +(-54888.1 - 95068.9i) q^{31} +(16384.0 + 28377.9i) q^{32} +122647. q^{34} +(-3064.13 + 10860.2i) q^{35} +(-304625. + 527626. i) q^{37} +(75658.5 + 131044. i) q^{38} +(-3183.24 + 5513.53i) q^{40} +808859. q^{41} -334949. q^{43} +(-215140. + 372634. i) q^{44} +(190882. + 330617. i) q^{46} +(-382587. + 662661. i) q^{47} +(723826. - 392809. i) q^{49} +623763. q^{50} +(-231424. - 400838. i) q^{52} +(622359. + 1.07796e6i) q^{53} -83598.9 q^{55} +(450352. - 114325. i) q^{56} +(269798. - 467303. i) q^{58} +(1.02330e6 + 1.77240e6i) q^{59} +(-70471.7 + 122061. i) q^{61} -878209. q^{62} +262144. q^{64} +(44963.1 - 77878.4i) q^{65} +(-1.46662e6 - 2.54027e6i) q^{67} +(490587. - 849721. i) q^{68} +(62985.4 + 64669.9i) q^{70} +615326. q^{71} +(711328. + 1.23206e6i) q^{73} +(2.43700e6 + 4.22101e6i) q^{74} +1.21054e6 q^{76} +(4.25690e6 + 4.37075e6i) q^{77} +(1.19370e6 - 2.06754e6i) q^{79} +(25465.9 + 44108.2i) q^{80} +(3.23544e6 - 5.60394e6i) q^{82} +7.53432e6 q^{83} +190631. q^{85} +(-1.33980e6 + 2.32060e6i) q^{86} +(1.72112e6 + 2.98107e6i) q^{88} +(-2.67757e6 + 4.63769e6i) q^{89} +(-6.36121e6 + 1.61483e6i) q^{91} +3.05411e6 q^{92} +(3.06070e6 + 5.30129e6i) q^{94} +(117597. + 203684. i) q^{95} -1.58174e7 q^{97} +(173842. - 6.58605e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24 q^{2} - 192 q^{4} - 718 q^{5} - 1471 q^{7} - 3072 q^{8} + 5744 q^{10} + 208 q^{11} + 19394 q^{13} - 4504 q^{14} - 12288 q^{16} - 19244 q^{17} - 25419 q^{19} + 91904 q^{20} + 3328 q^{22} - 67400 q^{23}+ \cdots + 20461248 q^{98}+O(q^{100}) \) 6 * q + 24 * q^2 - 192 * q^4 - 718 * q^5 - 1471 * q^7 - 3072 * q^8 + 5744 * q^10 + 208 * q^11 + 19394 * q^13 - 4504 * q^14 - 12288 * q^16 - 19244 * q^17 - 25419 * q^19 + 91904 * q^20 + 3328 * q^22 - 67400 * q^23 - 93931 * q^25 + 77576 * q^26 + 58112 * q^28 + 33476 * q^29 + 78449 * q^31 + 98304 * q^32 - 307904 * q^34 - 602072 * q^35 - 496599 * q^37 + 203352 * q^38 + 367616 * q^40 + 1953168 * q^41 + 697470 * q^43 + 13312 * q^44 + 539200 * q^46 + 701328 * q^47 + 959673 * q^49 - 1502896 * q^50 - 620608 * q^52 + 2917374 * q^53 - 3275696 * q^55 + 753152 * q^56 + 133904 * q^58 - 492040 * q^59 + 3649370 * q^61 + 1255184 * q^62 + 1572864 * q^64 - 2707764 * q^65 - 3647153 * q^67 - 1231616 * q^68 - 503936 * q^70 + 3541216 * q^71 - 6183557 * q^73 + 3972792 * q^74 + 3253632 * q^76 + 13092290 * q^77 - 12453589 * q^79 - 2940928 * q^80 + 7812672 * q^82 + 11611120 * q^83 + 38154616 * q^85 + 2789880 * q^86 - 106496 * q^88 - 8292612 * q^89 + 366581 * q^91 + 8627200 * q^92 - 5610624 * q^94 - 8691056 * q^95 - 55949528 * q^97 + 20461248 * q^98

Introduction

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