LMFDB - Embedded newform 5.12.b.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,12,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, 12, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 12 $
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:	$3.84171590280$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 142x^{2} - 2144x + 28656 $ x^4 - x^3 - 142x^2 - 2144x + 28656
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.3
Root			$-10.8434 + 10.0894i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.12.b.a.4.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+27.1071i q^{2} -524.040i q^{3} +1313.20 q^{4} +(6581.01 + 2349.13i) q^{5} +14205.2 q^{6} -66589.5i q^{7} +91112.6i q^{8} -97470.8 q^{9} +O(q^{10})$	\(q+27.1071i q^{2} -524.040i q^{3} +1313.20 q^{4} +(6581.01 + 2349.13i) q^{5} +14205.2 q^{6} -66589.5i q^{7} +91112.6i q^{8} -97470.8 q^{9} +(-63678.2 + 178392. i) q^{10} -374453. q^{11} -688170. i q^{12} +1.12751e6i q^{13} +1.80505e6 q^{14} +(1.23104e6 - 3.44871e6i) q^{15} +219635. q^{16} +5.82894e6i q^{17} -2.64216e6i q^{18} -6.03360e6 q^{19} +(8.64220e6 + 3.08488e6i) q^{20} -3.48955e7 q^{21} -1.01503e7i q^{22} +7.51593e6i q^{23} +4.77466e7 q^{24} +(3.77913e7 + 3.09193e7i) q^{25} -3.05636e7 q^{26} -4.17535e7i q^{27} -8.74454e7i q^{28} +4.87039e7 q^{29} +(9.34848e7 + 3.33699e7i) q^{30} -2.71596e8 q^{31} +1.92552e8i q^{32} +1.96228e8i q^{33} -1.58006e8 q^{34} +(1.56427e8 - 4.38226e8i) q^{35} -1.27999e8 q^{36} -542545. i q^{37} -1.63554e8i q^{38} +5.90860e8 q^{39} +(-2.14035e8 + 5.99613e8i) q^{40} +8.20963e8 q^{41} -9.45918e8i q^{42} +6.03499e8i q^{43} -4.91732e8 q^{44} +(-6.41456e8 - 2.28971e8i) q^{45} -2.03735e8 q^{46} +4.69204e8i q^{47} -1.15098e8i q^{48} -2.45683e9 q^{49} +(-8.38134e8 + 1.02441e9i) q^{50} +3.05460e9 q^{51} +1.48065e9i q^{52} -3.82491e9i q^{53} +1.13182e9 q^{54} +(-2.46428e9 - 8.79637e8i) q^{55} +6.06714e9 q^{56} +3.16185e9i q^{57} +1.32022e9i q^{58} +2.19696e9 q^{59} +(1.61660e9 - 4.52886e9i) q^{60} -7.28175e9 q^{61} -7.36220e9i q^{62} +6.49053e9i q^{63} -4.76973e9 q^{64} +(-2.64866e9 + 7.42015e9i) q^{65} -5.31918e9 q^{66} -2.11343e9i q^{67} +7.65458e9i q^{68} +3.93865e9 q^{69} +(1.18791e10 + 4.24029e9i) q^{70} -4.86982e9 q^{71} -8.88082e9i q^{72} -1.92542e10i q^{73} +1.47068e7 q^{74} +(1.62029e10 - 1.98042e10i) q^{75} -7.92334e9 q^{76} +2.49346e10i q^{77} +1.60165e10i q^{78} +4.54858e10 q^{79} +(1.44542e9 + 5.15952e8i) q^{80} -3.91472e10 q^{81} +2.22540e10i q^{82} -3.61471e10i q^{83} -4.58249e10 q^{84} +(-1.36929e10 + 3.83603e10i) q^{85} -1.63591e10 q^{86} -2.55228e10i q^{87} -3.41174e10i q^{88} -3.43834e9 q^{89} +(6.20676e9 - 1.73881e10i) q^{90} +7.50802e10 q^{91} +9.86994e9i q^{92} +1.42327e11i q^{93} -1.27188e10 q^{94} +(-3.97072e10 - 1.41737e10i) q^{95} +1.00905e11 q^{96} -1.57518e11i q^{97} -6.65976e10i q^{98} +3.64982e10 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 72 q^{4} - 300 q^{5} - 1752 q^{6} + 25452 q^{9}+O(q^{10}) $ 4 * q - 72 * q^4 - 300 * q^5 - 1752 * q^6 + 25452 * q^9	\( 4 q - 72 q^{4} - 300 q^{5} - 1752 q^{6} + 25452 q^{9} + 91400 q^{10} - 326352 q^{11} + 1080696 q^{14} + 3433200 q^{15} - 9834976 q^{16} + 15460880 q^{19} + 35447400 q^{20} - 81019872 q^{21} + 74415840 q^{24} + 159152500 q^{25} - 325970832 q^{26} + 216242520 q^{29} + 389993400 q^{30} - 684043072 q^{31} + 265782016 q^{34} + 394292400 q^{35} - 553353336 q^{36} + 5997024 q^{39} - 275204000 q^{40} + 1012873368 q^{41} - 1553573664 q^{44} - 2766384900 q^{45} + 5241789688 q^{46} - 1900646372 q^{49} - 4621170000 q^{50} + 8691953088 q^{51} - 6403356720 q^{54} - 7772763600 q^{55} + 10366738080 q^{56} + 3200971440 q^{59} + 1922954400 q^{60} - 2310471352 q^{61} - 5401150592 q^{64} + 3229723200 q^{65} - 17010985824 q^{66} + 32956101984 q^{69} + 40783573800 q^{70} - 60335466912 q^{71} - 5525992944 q^{74} + 19332540000 q^{75} - 52987638240 q^{76} + 74637768320 q^{79} + 72046927200 q^{80} - 77727716316 q^{81} - 76499865504 q^{84} - 46117585600 q^{85} + 39045421128 q^{86} + 118272499560 q^{89} + 36519766200 q^{90} + 51565095648 q^{91} - 266098749224 q^{94} - 264706278000 q^{95} + 313591828608 q^{96} + 119560366224 q^{99}+O(q^{100}) \) 4 * q - 72 * q^4 - 300 * q^5 - 1752 * q^6 + 25452 * q^9 + 91400 * q^10 - 326352 * q^11 + 1080696 * q^14 + 3433200 * q^15 - 9834976 * q^16 + 15460880 * q^19 + 35447400 * q^20 - 81019872 * q^21 + 74415840 * q^24 + 159152500 * q^25 - 325970832 * q^26 + 216242520 * q^29 + 389993400 * q^30 - 684043072 * q^31 + 265782016 * q^34 + 394292400 * q^35 - 553353336 * q^36 + 5997024 * q^39 - 275204000 * q^40 + 1012873368 * q^41 - 1553573664 * q^44 - 2766384900 * q^45 + 5241789688 * q^46 - 1900646372 * q^49 - 4621170000 * q^50 + 8691953088 * q^51 - 6403356720 * q^54 - 7772763600 * q^55 + 10366738080 * q^56 + 3200971440 * q^59 + 1922954400 * q^60 - 2310471352 * q^61 - 5401150592 * q^64 + 3229723200 * q^65 - 17010985824 * q^66 + 32956101984 * q^69 + 40783573800 * q^70 - 60335466912 * q^71 - 5525992944 * q^74 + 19332540000 * q^75 - 52987638240 * q^76 + 74637768320 * q^79 + 72046927200 * q^80 - 77727716316 * q^81 - 76499865504 * q^84 - 46117585600 * q^85 + 39045421128 * q^86 + 118272499560 * q^89 + 36519766200 * q^90 + 51565095648 * q^91 - 266098749224 * q^94 - 264706278000 * q^95 + 313591828608 * q^96 + 119560366224 * 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 $

$2$			27.1071i			0.598989i	0.954098	+	0.299495i	$0.0968180\pi$
$2$			27.1071i			0.598989i	−0.954098	+	0.299495i	$0.903182\pi$
$3$		−	524.040i		−	1.24508i	−0.782588	−	0.622540i	$-0.786101\pi$
$3$		−	524.040i		−	1.24508i	0.782588	−	0.622540i	$-0.213899\pi$
$4$	1313.20			0.641212
$5$	6581.01	+	2349.13i	0.941798	+	0.336180i
$5$	6581.01	+	2349.13i	0.941798	+	0.336180i
$6$	14205.2			0.745790
$7$		−	66589.5i		−	1.49750i	−0.662854	−	0.748749i	$-0.730655\pi$
$7$		−	66589.5i		−	1.49750i	0.662854	−	0.748749i	$-0.269345\pi$
$8$			91112.6i			0.983068i
$9$	−97470.8			−0.550225
$10$	−63678.2	+	178392.i	−0.201368	+	0.564127i
$11$	−374453.			−0.701031			−0.350515	−	0.936557i	$-0.613994\pi$
$11$	−374453.			−0.701031			−0.350515	+	0.936557i	$0.613994\pi$
$12$		−	688170.i		−	0.798361i
$13$			1.12751e6i			0.842232i	0.907007	+	0.421116i	$0.138361\pi$
$13$			1.12751e6i			0.842232i	−0.907007	+	0.421116i	$0.861639\pi$
$14$	1.80505e6			0.896985
$15$	1.23104e6	−	3.44871e6i	0.418571	−	1.17261i
$16$	219635.			0.0523651
$17$			5.82894e6i			0.995681i	0.867269	+	0.497841i	$0.165874\pi$
$17$			5.82894e6i			0.995681i	−0.867269	+	0.497841i	$0.834126\pi$
$18$		−	2.64216e6i		−	0.329579i
$19$	−6.03360e6			−0.559026			−0.279513	−	0.960142i	$-0.590173\pi$
$19$	−6.03360e6			−0.559026			−0.279513	+	0.960142i	$0.590173\pi$
$20$	8.64220e6	+	3.08488e6i	0.603892	+	0.215563i
$21$	−3.48955e7			−1.86451
$22$		−	1.01503e7i		−	0.419910i
$23$			7.51593e6i			0.243489i	0.992561	+	0.121745i	$0.0388489\pi$
$23$			7.51593e6i			0.243489i	−0.992561	+	0.121745i	$0.961151\pi$
$24$	4.77466e7			1.22400
$25$	3.77913e7	+	3.09193e7i	0.773966	+	0.633227i
$26$	−3.05636e7			−0.504488
$27$		−	4.17535e7i		−	0.560005i
$28$		−	8.74454e7i		−	0.960214i
$29$	4.87039e7			0.440935			0.220467	−	0.975394i	$-0.429242\pi$
$29$	4.87039e7			0.440935			0.220467	+	0.975394i	$0.429242\pi$
$30$	9.34848e7	+	3.33699e7i	0.702383	+	0.250719i
$31$	−2.71596e8			−1.70386			−0.851932	−	0.523653i	$-0.824569\pi$
$31$	−2.71596e8			−1.70386			−0.851932	+	0.523653i	$0.824569\pi$
$32$			1.92552e8i			1.01443i
$33$			1.96228e8i			0.872840i
$34$	−1.58006e8			−0.596402
$35$	1.56427e8	−	4.38226e8i	0.503429	−	1.41034i
$36$	−1.27999e8			−0.352811
$37$		−	542545.i		−	0.00128625i	−1.00000		0.000643126i	$-0.999795\pi$
$37$		−	542545.i		−	0.00128625i	1.00000		0.000643126i	$-0.000204713\pi$
$38$		−	1.63554e8i		−	0.334850i
$39$	5.90860e8			1.04865
$40$	−2.14035e8	+	5.99613e8i	−0.330488	+	0.925851i
$41$	8.20963e8			1.10666			0.553328	−	0.832964i	$-0.313358\pi$
$41$	8.20963e8			1.10666			0.553328	+	0.832964i	$0.313358\pi$
$42$		−	9.45918e8i		−	1.11682i
$43$			6.03499e8i			0.626037i	0.949747	+	0.313018i	$0.101340\pi$
$43$			6.03499e8i			0.626037i	−0.949747	+	0.313018i	$0.898660\pi$
$44$	−4.91732e8			−0.449509
$45$	−6.41456e8	−	2.28971e8i	−0.518201	−	0.184975i
$46$	−2.03735e8			−0.145847
$47$			4.69204e8i			0.298417i	0.988806	+	0.149208i	$0.0476725\pi$
$47$			4.69204e8i			0.298417i	−0.988806	+	0.149208i	$0.952327\pi$
$48$		−	1.15098e8i		−	0.0651988i
$49$	−2.45683e9			−1.24250
$50$	−8.38134e8	+	1.02441e9i	−0.379296	+	0.463597i
$51$	3.05460e9			1.23970
$52$			1.48065e9i			0.540049i
$53$		−	3.82491e9i		−	1.25633i	−0.778079	−	0.628166i	$-0.783806\pi$
$53$		−	3.82491e9i		−	1.25633i	0.778079	−	0.628166i	$-0.216194\pi$
$54$	1.13182e9			0.335437
$55$	−2.46428e9	−	8.79637e8i	−0.660229	−	0.235672i
$56$	6.06714e9			1.47214
$57$			3.16185e9i			0.696032i
$58$			1.32022e9i			0.264115i
$59$	2.19696e9			0.400069			0.200035	−	0.979789i	$-0.435895\pi$
$59$	2.19696e9			0.400069			0.200035	+	0.979789i	$0.435895\pi$
$60$	1.61660e9	−	4.52886e9i	0.268393	−	0.751894i
$61$	−7.28175e9			−1.10388			−0.551940	−	0.833884i	$-0.686112\pi$
$61$	−7.28175e9			−1.10388			−0.551940	+	0.833884i	$0.686112\pi$
$62$		−	7.36220e9i		−	1.02060i
$63$			6.49053e9i			0.823962i
$64$	−4.76973e9			−0.555270
$65$	−2.64866e9	+	7.42015e9i	−0.283141	+	0.793212i
$66$	−5.31918e9			−0.522821
$67$		−	2.11343e9i		−	0.191239i	−0.995418	−	0.0956197i	$-0.969517\pi$
$67$		−	2.11343e9i		−	0.191239i	0.995418	−	0.0956197i	$-0.0304833\pi$
$68$			7.65458e9i			0.638443i
$69$	3.93865e9			0.303164
$70$	1.18791e10	+	4.24029e9i	0.844778	+	0.301548i
$71$	−4.86982e9			−0.320326			−0.160163	−	0.987091i	$-0.551202\pi$
$71$	−4.86982e9			−0.320326			−0.160163	+	0.987091i	$0.551202\pi$
$72$		−	8.88082e9i		−	0.540909i
$73$		−	1.92542e10i		−	1.08705i	−0.839393	−	0.543524i	$-0.817090\pi$
$73$		−	1.92542e10i		−	1.08705i	0.839393	−	0.543524i	$-0.182910\pi$
$74$	1.47068e7			0.000770451
$75$	1.62029e10	−	1.98042e10i	0.788418	−	0.963650i
$76$	−7.92334e9			−0.358454
$77$			2.49346e10i			1.04979i
$78$			1.60165e10i			0.628128i
$79$	4.54858e10			1.66313			0.831566	−	0.555426i	$-0.187445\pi$
$79$	4.54858e10			1.66313			0.831566	+	0.555426i	$0.187445\pi$
$80$	1.44542e9	+	5.15952e8i	0.0493174	+	0.0176041i
$81$	−3.91472e10			−1.24748
$82$			2.22540e10i			0.662874i
$83$		−	3.61471e10i		−	1.00726i	−0.863918	−	0.503632i	$-0.831997\pi$
$83$		−	3.61471e10i		−	1.00726i	0.863918	−	0.503632i	$-0.168003\pi$
$84$	−4.58249e10			−1.19554
$85$	−1.36929e10	+	3.83603e10i	−0.334728	+	0.937730i
$86$	−1.63591e10			−0.374989
$87$		−	2.55228e10i		−	0.548999i
$88$		−	3.41174e10i		−	0.689161i
$89$	−3.43834e9			−0.0652685			−0.0326342	−	0.999467i	$-0.510390\pi$
$89$	−3.43834e9			−0.0652685			−0.0326342	+	0.999467i	$0.510390\pi$
$90$	6.20676e9	−	1.73881e10i	0.110798	−	0.310397i
$91$	7.50802e10			1.26124
$92$			9.86994e9i			0.156128i
$93$			1.42327e11i			2.12145i
$94$	−1.27188e10			−0.178748
$95$	−3.97072e10	−	1.41737e10i	−0.526489	−	0.187933i
$96$	1.00905e11			1.26305
$97$		−	1.57518e11i		−	1.86246i	−0.364436	−	0.931228i	$-0.618738\pi$
$97$		−	1.57518e11i		−	1.86246i	0.364436	−	0.931228i	$-0.381262\pi$
$98$		−	6.65976e10i		−	0.744244i
$99$	3.64982e10			0.385725
$100$	4.96277e10	+	4.06033e10i	0.496277	+	0.406033i
$101$	−3.14292e10			−0.297554			−0.148777	−	0.988871i	$-0.547534\pi$
$101$	−3.14292e10			−0.297554			−0.148777	+	0.988871i	$0.547534\pi$
$102$			8.28014e10i			0.742569i
$103$			3.42578e10i			0.291176i	0.989345	+	0.145588i	$0.0465074\pi$
$103$			3.42578e10i			0.291176i	−0.989345	+	0.145588i	$0.953493\pi$
$104$	−1.02730e11			−0.827971
$105$	−2.29648e11	−	8.19741e10i	−1.75599	−	0.626809i
$106$	1.03683e11			0.752529
$107$			2.10883e11i			1.45355i	0.686874	+	0.726776i	$0.258982\pi$
$107$			2.10883e11i			1.45355i	−0.686874	+	0.726776i	$0.741018\pi$
$108$		−	5.48308e10i		−	0.359082i
$109$	−1.44958e10			−0.0902394			−0.0451197	−	0.998982i	$-0.514367\pi$
$109$	−1.44958e10			−0.0902394			−0.0451197	+	0.998982i	$0.514367\pi$
$110$	2.38444e10	−	6.67995e10i	0.141165	−	0.395470i
$111$	−2.84315e8			−0.00160149
$112$		−	1.46254e10i		−	0.0784167i
$113$		−	2.14619e9i		−	0.0109581i	−0.999985	−	0.00547906i	$-0.998256\pi$
$113$		−	2.14619e9i		−	0.0109581i	0.999985	−	0.00547906i	$-0.00174405\pi$
$114$	−8.57087e10			−0.416916
$115$	−1.76559e10	+	4.94624e10i	−0.0818562	+	0.229318i
$116$	6.39580e10			0.282733
$117$		−	1.09899e11i		−	0.463417i
$118$			5.95532e10i			0.239637i
$119$	3.88146e11			1.49103
$120$	3.14221e11	+	1.12163e11i	1.15276	+	0.411484i
$121$	−1.45097e11			−0.508556
$122$		−	1.97388e11i		−	0.661212i
$123$		−	4.30217e11i		−	1.37787i
$124$	−3.56661e11			−1.09254
$125$	1.76072e11	+	2.92257e11i	0.516042	+	0.856563i
$126$	−1.75940e11			−0.493544
$127$			2.28294e8i			0.000613160i	1.00000		0.000306580i	$9.75875e-5\pi$
$127$			2.28294e8i			0.000613160i	−1.00000		0.000306580i	$0.999902\pi$
$128$			2.65053e11i			0.681834i
$129$	3.16257e11			0.779466
$130$	−2.01139e11	−	7.17977e10i	−0.475125	−	0.169599i
$131$	−5.23011e11			−1.18446			−0.592228	−	0.805771i	$-0.701751\pi$
$131$	−5.23011e11			−1.18446			−0.592228	+	0.805771i	$0.701751\pi$
$132$			2.57687e11i			0.559675i
$133$			4.01774e11i			0.837140i
$134$	5.72892e10			0.114550
$135$	9.80843e10	−	2.74780e11i	0.188263	−	0.527412i
$136$	−5.31090e11			−0.978822
$137$		−	2.04327e11i		−	0.361712i	−0.983510	−	0.180856i	$-0.942113\pi$
$137$		−	2.04327e11i		−	0.361712i	0.983510	−	0.180856i	$-0.0578868\pi$
$138$			1.06766e11i			0.181592i
$139$	1.10282e11			0.180270			0.0901348	−	0.995930i	$-0.471270\pi$
$139$	1.10282e11			0.180270			0.0901348	+	0.995930i	$0.471270\pi$
$140$	2.05421e11	−	5.75480e11i	0.322805	−	0.904327i
$141$	2.45881e11			0.371553
$142$		−	1.32007e11i		−	0.191872i
$143$		−	4.22199e11i		−	0.590430i
$144$	−2.14080e10			−0.0288126
$145$	3.20521e11	+	1.14412e11i	0.415272	+	0.148233i
$146$	5.21926e11			0.651130
$147$			1.28748e12i			1.54701i
$148$		−	7.12471e8i		−	0.000824761i
$149$	5.11067e11			0.570102			0.285051	−	0.958512i	$-0.407989\pi$
$149$	5.11067e11			0.570102			0.285051	+	0.958512i	$0.407989\pi$
$150$	5.36834e11	+	4.39215e11i	0.577216	+	0.472254i
$151$	−3.26638e10			−0.0338605			−0.0169303	−	0.999857i	$-0.505389\pi$
$151$	−3.26638e10			−0.0338605			−0.0169303	+	0.999857i	$0.505389\pi$
$152$		−	5.49737e11i		−	0.549560i
$153$		−	5.68151e11i		−	0.547849i
$154$	−6.75906e11			−0.628814
$155$	−1.78738e12	−	6.38015e11i	−1.60469	−	0.572804i
$156$	7.75919e11			0.672405
$157$		−	1.29615e12i		−	1.08444i	−0.840236	−	0.542221i	$-0.817584\pi$
$157$		−	1.29615e12i		−	1.08444i	0.840236	−	0.542221i	$-0.182416\pi$
$158$			1.23299e12i			0.996198i
$159$	−2.00441e12			−1.56423
$160$	−4.52330e11	+	1.26719e12i	−0.341032	+	0.955392i
$161$	5.00482e11			0.364625
$162$		−	1.06117e12i		−	0.747225i
$163$			9.53484e11i			0.649055i	0.945876	+	0.324527i	$0.105205\pi$
$163$			9.53484e11i			0.649055i	−0.945876	+	0.324527i	$0.894795\pi$
$164$	1.07809e12			0.709601
$165$	−4.60965e11	+	1.29138e12i	−0.293431	+	0.822038i
$166$	9.79844e11			0.603340
$167$			2.16450e12i			1.28949i	0.764398	+	0.644745i	$0.223036\pi$
$167$			2.16450e12i			1.28949i	−0.764398	+	0.644745i	$0.776964\pi$
$168$		−	3.17942e12i		−	1.83294i
$169$	5.20883e11			0.290645
$170$	−1.03984e12	−	3.71176e11i	−0.561690	−	0.200498i
$171$	5.88100e11			0.307590
$172$			7.92516e11i			0.401422i
$173$		−	3.76047e11i		−	0.184497i	−0.995736	−	0.0922483i	$-0.970595\pi$
$173$		−	3.76047e11i		−	0.184497i	0.995736	−	0.0922483i	$-0.0294054\pi$
$174$	6.91850e11			0.328845
$175$	2.05890e12	−	2.51650e12i	0.948256	−	1.15901i
$176$	−8.22430e10			−0.0367096
$177$		−	1.15129e12i		−	0.498119i
$178$		−	9.32035e10i		−	0.0390951i
$179$	−9.97885e11			−0.405872			−0.202936	−	0.979192i	$-0.565048\pi$
$179$	−9.97885e11			−0.405872			−0.202936	+	0.979192i	$0.565048\pi$
$180$	−8.42362e11	−	3.00686e11i	−0.332277	−	0.118608i
$181$	3.32751e12			1.27317			0.636587	−	0.771205i	$-0.280346\pi$
$181$	3.32751e12			1.27317			0.636587	+	0.771205i	$0.280346\pi$
$182$			2.03521e12i			0.755469i
$183$			3.81593e12i			1.37442i
$184$	−6.84796e11			−0.239366
$185$	1.27451e9	−	3.57049e9i	0.000432412	−	0.00121139i
$186$	−3.85809e12			−1.27072
$187$		−	2.18266e12i		−	0.698003i
$188$			6.16160e11i			0.191348i
$189$	−2.78034e12			−0.838607
$190$	3.84209e11	−	1.07635e12i	0.112570	−	0.315361i
$191$	−4.02856e12			−1.14674			−0.573372	−	0.819295i	$-0.694365\pi$
$191$	−4.02856e12			−1.14674			−0.573372	+	0.819295i	$0.694365\pi$
$192$			2.49953e12i			0.691356i
$193$		−	1.01858e12i		−	0.273798i	−0.990585	−	0.136899i	$-0.956286\pi$
$193$		−	1.01858e12i		−	0.273798i	0.990585	−	0.136899i	$-0.0437135\pi$
$194$	4.26987e12			1.11559
$195$	3.88846e12	+	1.38801e12i	0.987613	+	0.352534i
$196$	−3.22631e12			−0.796706
$197$		−	4.56750e12i		−	1.09677i	−0.836227	−	0.548384i	$-0.815243\pi$
$197$		−	4.56750e12i		−	1.09677i	0.836227	−	0.548384i	$-0.184757\pi$
$198$			9.89362e11i			0.231045i
$199$	2.19872e12			0.499435			0.249717	−	0.968319i	$-0.419662\pi$
$199$	2.19872e12			0.499435			0.249717	+	0.968319i	$0.419662\pi$
$200$	−2.81714e12	+	3.44327e12i	−0.622505	+	0.760862i
$201$	−1.10752e12			−0.238108
$202$		−	8.51955e11i		−	0.178231i
$203$		−	3.24316e12i		−	0.660299i
$204$	4.01130e12			0.794913
$205$	5.40277e12	+	1.92855e12i	1.04225	+	0.372035i
$206$	−9.28632e11			−0.174411
$207$		−	7.32584e11i		−	0.133974i
$208$			2.47641e11i			0.0441036i
$209$	2.25930e12			0.391894
$210$	2.22208e12	−	6.22510e12i	0.375452	−	1.05182i
$211$	8.39469e11			0.138182			0.0690910	−	0.997610i	$-0.477990\pi$
$211$	8.39469e11			0.138182			0.0690910	+	0.997610i	$0.477990\pi$
$212$		−	5.02289e12i		−	0.805575i
$213$			2.55198e12i			0.398831i
$214$	−5.71644e12			−0.870662
$215$	−1.41770e12	+	3.97163e12i	−0.210461	+	0.589600i
$216$	3.80427e12			0.550524
$217$			1.80855e13i			2.55153i
$218$		−	3.92940e11i		−	0.0540524i
$219$	−1.00900e13			−1.35346
$220$	−3.23609e12	−	1.15514e12i	−0.423347	−	0.151116i
$221$	−6.57218e12			−0.838595
$222$		−	7.70697e9i		−	0.000959274i
$223$		−	1.61958e13i		−	1.96665i	−0.181867	−	0.983323i	$-0.558214\pi$
$223$		−	1.61958e13i		−	1.96665i	0.181867	−	0.983323i	$-0.441786\pi$
$224$	1.28220e13			1.51911
$225$	−3.68355e12	−	3.01373e12i	−0.425856	−	0.348418i
$226$	5.81770e10			0.00656379
$227$		−	6.08481e11i		−	0.0670046i	−0.999439	−	0.0335023i	$-0.989334\pi$
$227$		−	6.08481e11i		−	0.0670046i	0.999439	−	0.0335023i	$-0.0106661\pi$
$228$			4.15215e12i			0.446304i
$229$	−1.59740e13			−1.67617			−0.838083	−	0.545542i	$-0.816324\pi$
$229$	−1.59740e13			−1.67617			−0.838083	+	0.545542i	$0.816324\pi$
$230$	−1.34079e12	−	4.78601e11i	−0.137359	−	0.0490309i
$231$	1.30667e13			1.30708
$232$			4.43754e12i			0.433469i
$233$			1.09497e13i			1.04459i	0.852764	+	0.522296i	$0.174924\pi$
$233$			1.09497e13i			1.04459i	−0.852764	+	0.522296i	$0.825076\pi$
$234$	2.97905e12			0.277582
$235$	−1.10222e12	+	3.08784e12i	−0.100322	+	0.281048i
$236$	2.88505e12			0.256529
$237$		−	2.38364e13i		−	2.07073i
$238$			1.05215e13i			0.893111i
$239$	2.11532e13			1.75464			0.877321	−	0.479905i	$-0.159329\pi$
$239$	2.11532e13			1.75464			0.877321	+	0.479905i	$0.159329\pi$
$240$	2.70379e11	−	7.57459e11i	0.0219185	−	0.0614041i
$241$	1.41468e13			1.12089			0.560447	−	0.828190i	$-0.310629\pi$
$241$	1.41468e13			1.12089			0.560447	+	0.828190i	$0.310629\pi$
$242$		−	3.93317e12i		−	0.304619i
$243$			1.31182e13i			0.993204i
$244$	−9.56242e12			−0.707821
$245$	−1.61684e13	−	5.77141e12i	−1.17018	−	0.417704i
$246$	1.16620e13			0.825332
$247$		−	6.80294e12i		−	0.470829i
$248$		−	2.47459e13i		−	1.67501i
$249$	−1.89425e13			−1.25413
$250$	−7.92225e12	+	4.77280e12i	−0.513072	+	0.309103i
$251$	−1.64508e12			−0.104227			−0.0521136	−	0.998641i	$-0.516596\pi$
$251$	−1.64508e12			−0.104227			−0.0521136	+	0.998641i	$0.516596\pi$
$252$			8.52338e12i			0.528334i
$253$		−	2.81436e12i		−	0.170693i
$254$	−6.18840e9			−0.000367276
$255$	2.01023e13	+	7.17564e12i	1.16755	+	0.416763i
$256$	−1.69533e13			−0.963681
$257$			3.16010e13i			1.75820i	0.476635	+	0.879101i	$0.341856\pi$
$257$			3.16010e13i			1.75820i	−0.476635	+	0.879101i	$0.658144\pi$
$258$			8.57284e12i			0.466892i
$259$	−3.61278e10			−0.00192616
$260$	−3.47823e12	+	9.74416e12i	−0.181554	+	0.508617i
$261$	−4.74720e12			−0.242614
$262$		−	1.41773e13i		−	0.709476i
$263$			1.50443e12i			0.0737250i	0.999320	+	0.0368625i	$0.0117364\pi$
$263$			1.50443e12i			0.0737250i	−0.999320	+	0.0368625i	$0.988264\pi$
$264$	−1.78789e13			−0.858061
$265$	8.98521e12	−	2.51718e13i	0.422353	−	1.18321i
$266$	−1.08910e13			−0.501438
$267$			1.80183e12i			0.0812645i
$268$		−	2.77537e12i		−	0.122625i
$269$	3.90666e13			1.69110			0.845548	−	0.533900i	$-0.179274\pi$
$269$	3.90666e13			1.69110			0.845548	+	0.533900i	$0.179274\pi$
$270$	7.44851e12	+	2.65879e12i	0.315914	+	0.112767i
$271$	−4.54729e12			−0.188982			−0.0944912	−	0.995526i	$-0.530122\pi$
$271$	−4.54729e12			−0.188982			−0.0944912	+	0.995526i	$0.530122\pi$
$272$			1.28024e12i			0.0521390i
$273$		−	3.93450e13i		−	1.57035i
$274$	5.53873e12			0.216662
$275$	−1.41511e13	−	1.15778e13i	−0.542574	−	0.443911i
$276$	5.17224e12			0.194392
$277$			2.22049e13i			0.818105i	0.912511	+	0.409053i	$0.134141\pi$
$277$			2.22049e13i			0.818105i	−0.912511	+	0.409053i	$0.865859\pi$
$278$			2.98943e12i			0.107980i
$279$	2.64727e13			0.937509
$280$	3.99279e13	+	1.42525e13i	1.38646	+	0.494905i
$281$	−2.26709e13			−0.771941			−0.385970	−	0.922511i	$-0.626133\pi$
$281$	−2.26709e13			−0.771941			−0.385970	+	0.922511i	$0.626133\pi$
$282$			6.66515e12i			0.222556i
$283$			2.94259e13i			0.963617i	0.876276	+	0.481809i	$0.160020\pi$
$283$			2.94259e13i			0.963617i	−0.876276	+	0.481809i	$0.839980\pi$
$284$	−6.39505e12			−0.205397
$285$	−7.42758e12	+	2.08082e13i	−0.233992	+	0.655521i
$286$	1.14446e13			0.353661
$287$		−	5.46675e13i		−	1.65721i
$288$		−	1.87682e13i		−	0.558168i
$289$	2.95383e11			0.00861880
$290$	−3.10137e12	+	8.68840e12i	−0.0887902	+	0.248743i
$291$	−8.25458e13			−2.31891
$292$		−	2.52846e13i		−	0.697029i
$293$			4.02146e13i			1.08796i	0.839099	+	0.543979i	$0.183083\pi$
$293$			4.02146e13i			1.08796i	−0.839099	+	0.543979i	$0.816917\pi$
$294$	−3.48998e13			−0.926644
$295$	1.44582e13	+	5.16093e12i	0.376785	+	0.134495i
$296$	4.94327e10			0.00126447
$297$			1.56347e13i			0.392581i
$298$			1.38536e13i			0.341485i
$299$	−8.47428e12			−0.205074
$300$	2.12777e13	−	2.60069e13i	0.505543	−	0.617904i
$301$	4.01866e13			0.937489
$302$		−	8.85423e11i		−	0.0202821i
$303$			1.64701e13i			0.370478i
$304$	−1.32519e12			−0.0292735
$305$	−4.79213e13	−	1.71058e13i	−1.03963	−	0.371102i
$306$	1.54010e13			0.328156
$307$		−	1.17567e13i		−	0.246050i	−0.992404	−	0.123025i	$-0.960740\pi$
$307$		−	1.17567e13i		−	0.246050i	0.992404	−	0.123025i	$-0.0392595\pi$
$308$			3.27442e13i			0.673139i
$309$	1.79525e13			0.362537
$310$	1.72948e13	−	4.84508e13i	0.343104	−	0.961195i
$311$	9.66888e12			0.188449			0.0942245	−	0.995551i	$-0.469963\pi$
$311$	9.66888e12			0.188449			0.0942245	+	0.995551i	$0.469963\pi$
$312$			5.38348e13i			1.03089i
$313$		−	7.95938e13i		−	1.49756i	−0.662817	−	0.748782i	$-0.730639\pi$
$313$		−	7.95938e13i		−	1.49756i	0.662817	−	0.748782i	$-0.269361\pi$
$314$	3.51349e13			0.649569
$315$	−1.52471e13	+	4.27142e13i	−0.276999	+	0.776005i
$316$	5.97321e13			1.06642
$317$			3.01135e13i			0.528366i	0.964473	+	0.264183i	$0.0851023\pi$
$317$			3.01135e13i			0.528366i	−0.964473	+	0.264183i	$0.914898\pi$
$318$		−	5.43338e13i		−	0.936959i
$319$	−1.82373e13			−0.309109
$320$	−3.13897e13	−	1.12047e13i	−0.522952	−	0.186671i
$321$	1.10511e14			1.80979
$322$			1.35666e13i			0.218406i
$323$		−	3.51695e13i		−	0.556611i
$324$	−5.14082e13			−0.799898
$325$	−3.48618e13	+	4.26101e13i	−0.533324	+	0.651859i
$326$	−2.58462e13			−0.388777
$327$			7.59637e12i			0.112355i
$328$			7.48001e13i			1.08792i
$329$	3.12440e13			0.446879
$330$	−3.50056e13	−	1.24954e13i	−0.492392	−	0.175762i
$331$	−9.09460e13			−1.25814			−0.629071	−	0.777348i	$-0.716564\pi$
$331$	−9.09460e13			−1.25814			−0.629071	+	0.777348i	$0.716564\pi$
$332$		−	4.74684e13i		−	0.645870i
$333$			5.28823e10i			0.000707729i
$334$	−5.86735e13			−0.772390
$335$	4.96473e12	−	1.39085e13i	0.0642908	−	0.180109i
$336$	−7.66429e12			−0.0976351
$337$		−	6.71550e13i		−	0.841616i	−0.907150	−	0.420808i	$-0.861747\pi$
$337$		−	6.71550e13i		−	0.841616i	0.907150	−	0.420808i	$-0.138253\pi$
$338$			1.41197e13i			0.174093i
$339$	−1.12469e12			−0.0136437
$340$	−1.79816e13	+	5.03749e13i	−0.214632	+	0.601284i
$341$	1.01700e14			1.19446
$342$			1.59417e13i			0.184243i
$343$			3.19298e13i			0.363144i
$344$	−5.49863e13			−0.615437
$345$	2.59203e13	+	9.25239e12i	0.285519	+	0.101918i
$346$	1.01936e13			0.110511
$347$			1.00178e14i			1.06895i	0.845183	+	0.534476i	$0.179491\pi$
$347$			1.00178e14i			1.06895i	−0.845183	+	0.534476i	$0.820509\pi$
$348$		−	3.35166e13i		−	0.352025i
$349$	−3.57336e12			−0.0369434			−0.0184717	−	0.999829i	$-0.505880\pi$
$349$	−3.57336e12			−0.0369434			−0.0184717	+	0.999829i	$0.505880\pi$
$350$	6.82152e13	+	5.58109e13i	0.694236	+	0.567995i
$351$	4.70775e13			0.471655
$352$		−	7.21017e13i		−	0.711149i
$353$		−	4.27043e13i		−	0.414677i	−0.978269	−	0.207339i	$-0.933520\pi$
$353$		−	4.27043e13i		−	0.414677i	0.978269	−	0.207339i	$-0.0664802\pi$
$354$	3.12083e13			0.298368
$355$	−3.20483e13	−	1.14398e13i	−0.301682	−	0.107687i
$356$	−4.51523e12			−0.0418509
$357$		−	2.03404e14i		−	1.85645i
$358$		−	2.70498e13i		−	0.243113i
$359$	1.34889e14			1.19387			0.596934	−	0.802290i	$-0.296385\pi$
$359$	1.34889e14			1.19387			0.596934	+	0.802290i	$0.296385\pi$
$360$	2.08622e13	−	5.84448e13i	0.181843	−	0.509427i
$361$	−8.00859e13			−0.687490
$362$			9.01994e13i			0.762617i
$363$			7.60366e13i			0.633193i
$364$	9.85956e13			0.808723
$365$	4.52305e13	−	1.26712e14i	0.365444	−	1.02378i
$366$	−1.03439e14			−0.823262
$367$			1.04526e14i			0.819519i	0.912193	+	0.409760i	$0.134387\pi$
$367$			1.04526e14i			0.819519i	−0.912193	+	0.409760i	$0.865613\pi$
$368$			1.65076e12i			0.0127503i
$369$	−8.00199e13			−0.608910
$370$	9.67859e10	+	3.45483e10i	0.000725609	+	0.000259010i
$371$	−2.54699e14			−1.88135
$372$			1.86905e14i			1.36030i
$373$			2.42814e14i			1.74131i	0.491896	+	0.870654i	$0.336304\pi$
$373$			2.42814e14i			1.74131i	−0.491896	+	0.870654i	$0.663696\pi$
$374$	5.91657e13			0.418096
$375$	1.53154e14	−	9.22686e13i	1.06649	−	0.642513i
$376$	−4.27504e13			−0.293364
$377$			5.49141e13i			0.371369i
$378$		−	7.53672e13i		−	0.502316i
$379$	−1.40487e14			−0.922827			−0.461413	−	0.887185i	$-0.652657\pi$
$379$	−1.40487e14			−0.922827			−0.461413	+	0.887185i	$0.652657\pi$
$380$	−5.21436e13	−	1.86129e13i	−0.337591	−	0.120505i
$381$	1.19635e11			0.000763434
$382$		−	1.09203e14i		−	0.686886i
$383$		−	2.17176e14i		−	1.34654i	−0.739398	−	0.673269i	$-0.764890\pi$
$383$		−	2.17176e14i		−	1.34654i	0.739398	−	0.673269i	$-0.235110\pi$
$384$	1.38899e14			0.848938
$385$	−5.85745e13	+	1.64095e14i	−0.352919	+	0.988692i
$386$	2.76108e13			0.164002
$387$		−	5.88235e13i		−	0.344461i
$388$		−	2.06853e14i		−	1.19423i
$389$	−2.28055e14			−1.29812			−0.649062	−	0.760735i	$-0.724839\pi$
$389$	−2.28055e14			−1.29812			−0.649062	+	0.760735i	$0.724839\pi$
$390$	−3.76249e13	+	1.05405e14i	−0.211164	+	0.591569i
$391$	−4.38099e13			−0.242438
$392$		−	2.23848e14i		−	1.22146i
$393$			2.74079e14i			1.47474i
$394$	1.23812e14			0.656951
$395$	2.99343e14	+	1.06852e14i	1.56633	+	0.559112i
$396$	4.79295e13			0.247332
$397$			7.68462e13i			0.391088i	0.980695	+	0.195544i	$0.0626473\pi$
$397$			7.68462e13i			0.391088i	−0.980695	+	0.195544i	$0.937353\pi$
$398$			5.96011e13i			0.299156i
$399$	2.10546e14			1.04231
$400$	8.30031e12	+	6.79097e12i	0.0405289	+	0.0331590i
$401$	2.93708e14			1.41456			0.707282	−	0.706932i	$-0.249921\pi$
$401$	2.93708e14			1.41456			0.707282	+	0.706932i	$0.249921\pi$
$402$		−	3.00218e13i		−	0.142624i
$403$		−	3.06228e14i		−	1.43505i
$404$	−4.12728e13			−0.190795
$405$	−2.57628e14	−	9.19617e13i	−1.17487	−	0.419377i
$406$	8.79129e13			0.395512
$407$			2.03157e11i			0.000901702i
$408$			2.78312e14i			1.21871i
$409$	−1.31901e14			−0.569861			−0.284930	−	0.958548i	$-0.591970\pi$
$409$	−1.31901e14			−0.569861			−0.284930	+	0.958548i	$0.591970\pi$
$410$	−5.22774e13	+	1.46454e14i	−0.222845	+	0.624294i
$411$	−1.07076e14			−0.450361
$412$			4.49875e13i			0.186705i
$413$		−	1.46294e14i		−	0.599103i
$414$	1.98583e13			0.0802489
$415$	8.49141e13	−	2.37884e14i	0.338622	−	0.948639i
$416$	−2.17105e14			−0.854389
$417$		−	5.77921e13i		−	0.224450i
$418$			6.12431e13i			0.234740i
$419$	−3.47913e14			−1.31612			−0.658058	−	0.752967i	$-0.728622\pi$
$419$	−3.47913e14			−1.31612			−0.658058	+	0.752967i	$0.728622\pi$
$420$	−3.01574e14	−	1.07649e14i	−1.12596	−	0.401918i
$421$	3.60019e14			1.32670			0.663351	−	0.748308i	$-0.269134\pi$
$421$	3.60019e14			1.32670			0.663351	+	0.748308i	$0.269134\pi$
$422$			2.27556e13i			0.0827695i
$423$		−	4.57337e13i		−	0.164197i
$424$	3.48498e14			1.23506
$425$	−1.80227e14	+	2.20283e14i	−0.630492	+	0.770624i
$426$	−6.91768e13			−0.238896
$427$			4.84888e14i			1.65306i
$428$			2.76932e14i			0.932035i
$429$	−2.21249e14			−0.735133
$430$	−1.07660e14	−	3.84297e13i	−0.353164	−	0.126064i
$431$	4.03045e14			1.30535			0.652677	−	0.757636i	$-0.273646\pi$
$431$	4.03045e14			1.30535			0.652677	+	0.757636i	$0.273646\pi$
$432$		−	9.17055e12i		−	0.0293248i
$433$		−	3.79440e14i		−	1.19801i	−0.800746	−	0.599004i	$-0.795563\pi$
$433$		−	3.79440e14i		−	1.19801i	0.800746	−	0.599004i	$-0.204437\pi$
$434$	−4.90245e14			−1.52834
$435$	5.99563e13	−	1.67966e14i	0.184563	−	0.517047i
$436$	−1.90359e13			−0.0578626
$437$		−	4.53481e13i		−	0.136117i
$438$		−	2.73510e14i		−	0.810710i
$439$	5.70014e14			1.66852			0.834259	−	0.551373i	$-0.185896\pi$
$439$	5.70014e14			1.66852			0.834259	+	0.551373i	$0.185896\pi$
$440$	8.01460e13	−	2.24527e14i	0.231682	−	0.649050i
$441$	2.39469e14			0.683655
$442$		−	1.78153e14i		−	0.502309i
$443$			6.54692e14i			1.82312i	0.411162	+	0.911562i	$0.365123\pi$
$443$			6.54692e14i			1.82312i	−0.411162	+	0.911562i	$0.634877\pi$
$444$	−3.73363e11			−0.00102689
$445$	−2.26277e13	−	8.07709e12i	−0.0614697	−	0.0219419i
$446$	4.39023e14			1.17800
$447$		−	2.67819e14i		−	0.709824i
$448$			3.17614e14i			0.831515i
$449$	−2.16742e14			−0.560515			−0.280258	−	0.959925i	$-0.590420\pi$
$449$	−2.16742e14			−0.560515			−0.280258	+	0.959925i	$0.590420\pi$
$450$	8.16935e13	−	9.98505e13i	0.208698	−	0.255083i
$451$	−3.07412e14			−0.775799
$452$		−	2.81838e12i		−	0.00702648i
$453$			1.71171e13i			0.0421591i
$454$	1.64942e13			0.0401350
$455$	4.94104e14	+	1.76373e14i	1.18783	+	0.424004i
$456$	−2.88084e14			−0.684247
$457$		−	4.04825e14i		−	0.950011i	−0.879983	−	0.475006i	$-0.842446\pi$
$457$		−	4.04825e14i		−	0.950011i	0.879983	−	0.475006i	$-0.157554\pi$
$458$		−	4.33008e14i		−	1.00401i
$459$	2.43379e14			0.557587
$460$	−2.31858e13	+	6.49542e13i	−0.0524872	+	0.147041i
$461$	−4.78062e14			−1.06937			−0.534686	−	0.845051i	$-0.679570\pi$
$461$	−4.78062e14			−1.06937			−0.534686	+	0.845051i	$0.679570\pi$
$462$			3.54202e14i			0.782924i
$463$		−	7.90859e13i		−	0.172744i	−0.996263	−	0.0863721i	$-0.972473\pi$
$463$		−	7.90859e13i		−	0.172744i	0.996263	−	0.0863721i	$-0.0275274\pi$
$464$	1.06971e13			0.0230896
$465$	−3.34345e14	+	9.36658e14i	−0.713188	+	1.99797i
$466$	−2.96816e14			−0.625699
$467$		−	3.83987e14i		−	0.799970i	−0.916522	−	0.399985i	$-0.869015\pi$
$467$		−	3.83987e14i		−	0.799970i	0.916522	−	0.399985i	$-0.130985\pi$
$468$		−	1.44320e14i		−	0.297149i
$469$	−1.40732e14			−0.286381
$470$	−8.37024e13	−	2.98780e13i	−0.168345	−	0.0600916i
$471$	−6.79233e14			−1.35022
$472$			2.00170e14i			0.393295i
$473$		−	2.25982e14i		−	0.438871i
$474$	6.46136e14			1.24035
$475$	−2.28018e14	−	1.86555e14i	−0.432667	−	0.353990i
$476$	5.09714e14			0.956067
$477$			3.72817e14i			0.691266i
$478$			5.73404e14i			1.05101i
$479$	−4.33999e14			−0.786400			−0.393200	−	0.919453i	$-0.628632\pi$
$479$	−4.33999e14			−0.786400			−0.393200	+	0.919453i	$0.628632\pi$
$480$	6.64058e14	+	2.37039e14i	1.18954	+	0.424613i
$481$	6.11724e11			0.00108332
$482$			3.83480e14i			0.671404i
$483$		−	2.62272e14i		−	0.453987i
$484$	−1.90542e14			−0.326092
$485$	3.70030e14	−	1.03663e15i	0.626120	−	1.75406i
$486$	−3.55596e14			−0.594918
$487$			3.35969e14i			0.555763i	0.960615	+	0.277881i	$0.0896322\pi$
$487$			3.35969e14i			0.555763i	−0.960615	+	0.277881i	$0.910368\pi$
$488$		−	6.63460e14i		−	1.08519i
$489$	4.99663e14			0.808126
$490$	1.56446e14	−	4.38280e14i	0.250200	−	0.700928i
$491$	−6.44062e14			−1.01854			−0.509272	−	0.860606i	$-0.670085\pi$
$491$	−6.44062e14			−1.01854			−0.509272	+	0.860606i	$0.670085\pi$
$492$		−	5.64962e14i		−	0.883510i
$493$			2.83892e14i			0.439031i
$494$	1.84408e14			0.282022
$495$	2.40195e14	+	8.57389e13i	0.363275	+	0.129673i
$496$	−5.96522e13			−0.0892231
$497$			3.24278e14i			0.479687i
$498$		−	5.13477e14i		−	0.751207i
$499$	6.77869e14			0.980828			0.490414	−	0.871490i	$-0.336846\pi$
$499$	6.77869e14			0.980828			0.490414	+	0.871490i	$0.336846\pi$
$500$	2.31218e14	+	3.83792e14i	0.330892	+	0.549239i
$501$	1.13429e15			1.60552
$502$		−	4.45934e13i		−	0.0624310i
$503$			9.66327e14i			1.33814i	0.743202	+	0.669068i	$0.233306\pi$
$503$			9.66327e14i			1.33814i	−0.743202	+	0.669068i	$0.766694\pi$
$504$	−5.91369e14			−0.810010
$505$	−2.06836e14	−	7.38311e13i	−0.280235	−	0.100032i
$506$	7.62893e13			0.102243
$507$		−	2.72963e14i		−	0.361877i
$508$			2.99796e11i			0.000393166i
$509$	−1.19572e13			−0.0155125			−0.00775626	−	0.999970i	$-0.502469\pi$
$509$	−1.19572e13			−0.0155125			−0.00775626	+	0.999970i	$0.502469\pi$
$510$	−1.94511e14	+	5.44917e14i	−0.249637	+	0.699350i
$511$	−1.28212e15			−1.62785
$512$			8.32750e13i			0.104600i
$513$			2.51924e14i			0.313057i
$514$	−8.56614e14			−1.05314
$515$	−8.04760e13	+	2.25451e14i	−0.0978874	+	0.274229i
$516$	4.15310e14			0.499803
$517$		−	1.75695e14i		−	0.209199i
$518$		−	9.79321e11i		−	0.00115375i
$519$	−1.97064e14			−0.229713
$520$	−6.76070e14	−	2.41327e14i	−0.779782	−	0.278347i
$521$	1.26458e15			1.44324			0.721618	−	0.692292i	$-0.243399\pi$
$521$	1.26458e15			1.44324			0.721618	+	0.692292i	$0.243399\pi$
$522$		−	1.28683e14i		−	0.145323i
$523$			7.08792e13i			0.0792062i	0.999215	+	0.0396031i	$0.0126094\pi$
$523$			7.08792e13i			0.0792062i	−0.999215	+	0.0396031i	$0.987391\pi$
$524$	−6.86820e14			−0.759487
$525$	−1.31875e15	−	1.07894e15i	−1.44306	−	1.18066i
$526$	−4.07807e13			−0.0441605
$527$		−	1.58312e15i		−	1.69650i
$528$			4.30986e13i			0.0457064i
$529$	8.96321e14			0.940713
$530$	6.82336e14	+	2.43563e14i	0.708730	+	0.252985i
$531$	−2.14139e14			−0.220128
$532$			5.27611e14i			0.536784i
$533$			9.25643e14i			0.932060i
$534$	−4.88424e13			−0.0486765
$535$	−4.95391e14	+	1.38782e15i	−0.488655	+	1.36895i
$536$	1.92560e14			0.188001
$537$			5.22932e14i			0.505343i
$538$			1.05898e15i			1.01295i
$539$	9.19966e14			0.871031
$540$	1.28805e14	−	3.60842e14i	0.120716	−	0.338183i
$541$	1.90242e15			1.76491			0.882453	−	0.470400i	$-0.155890\pi$
$541$	1.90242e15			1.76491			0.882453	+	0.470400i	$0.155890\pi$
$542$		−	1.23264e14i		−	0.113198i
$543$		−	1.74375e15i		−	1.58520i
$544$	−1.12238e15			−1.01005
$545$	−9.53970e13	−	3.40525e13i	−0.0849873	−	0.0303367i
$546$	1.06653e15			0.940620
$547$		−	1.94867e13i		−	0.0170141i	−0.999964	−	0.00850704i	$-0.997292\pi$
$547$		−	1.94867e13i		−	0.0170141i	0.999964	−	0.00850704i	$-0.00270791\pi$
$548$		−	2.68323e14i		−	0.231934i
$549$	7.09758e14			0.607383
$550$	3.13841e14	−	3.83595e14i	0.265898	−	0.324996i
$551$	−2.93860e14			−0.246494
$552$			3.58861e14i			0.298031i
$553$		−	3.02888e15i		−	2.49054i
$554$	−6.01910e14			−0.490036
$555$	−1.87108e12	−	6.67893e11i	−0.00150828	−	0.000538388i
$556$	1.44822e14			0.115591
$557$			1.67247e15i			1.32177i	0.750489	+	0.660883i	$0.229818\pi$
$557$			1.67247e15i			1.32177i	−0.750489	+	0.660883i	$0.770182\pi$
$558$			7.17600e14i			0.561558i
$559$	−6.80450e14			−0.527268
$560$	3.43569e13	−	9.62499e13i	0.0263621	−	0.0738527i
$561$	−1.14380e15			−0.869070
$562$		−	6.14544e14i		−	0.462384i
$563$			7.96866e13i			0.0593730i	0.999559	+	0.0296865i	$0.00945090\pi$
$563$			7.96866e13i			0.0593730i	−0.999559	+	0.0296865i	$0.990549\pi$
$564$	3.22892e14			0.238244
$565$	5.04166e12	−	1.41241e13i	0.00368390	−	0.0103203i
$566$	−7.97653e14			−0.577196
$567$			2.60679e15i			1.86810i
$568$		−	4.43702e14i		−	0.314902i
$569$	−2.11263e15			−1.48493			−0.742467	−	0.669883i	$-0.766344\pi$
$569$	−2.11263e15			−1.48493			−0.742467	+	0.669883i	$0.766344\pi$
$570$	−5.64050e14	−	2.01341e14i	−0.392650	−	0.140159i
$571$	1.05231e15			0.725513			0.362756	−	0.931884i	$-0.381836\pi$
$571$	1.05231e15			0.725513			0.362756	+	0.931884i	$0.381836\pi$
$572$		−	5.54432e14i		−	0.378591i
$573$			2.11113e15i			1.42779i
$574$	1.48188e15			0.992653
$575$	−2.32387e14	+	2.84037e14i	−0.154184	+	0.188452i
$576$	4.64910e14			0.305524
$577$		−	1.13168e15i		−	0.736642i	−0.929699	−	0.368321i	$-0.879933\pi$
$577$		−	1.13168e15i		−	0.736642i	0.929699	−	0.368321i	$-0.120067\pi$
$578$			8.00698e12i			0.00516257i
$579$	−5.33776e14			−0.340900
$580$	4.20909e14	+	1.50246e14i	0.266277	+	0.0950491i
$581$	−2.40701e15			−1.50838
$582$		−	2.23758e15i		−	1.38900i
$583$			1.43225e15i			0.880727i
$584$	1.75430e15			1.06864
$585$	2.58167e14	−	7.23248e14i	0.155792	−	0.436446i
$586$	−1.09010e15			−0.651675
$587$		−	8.84276e14i		−	0.523695i	−0.965109	−	0.261847i	$-0.915668\pi$
$587$		−	8.84276e14i		−	0.523695i	0.965109	−	0.261847i	$-0.0843317\pi$
$588$			1.69072e15i			0.991964i
$589$	1.63870e15			0.952503
$590$	−1.39898e14	+	3.91921e14i	−0.0805612	+	0.225690i
$591$	−2.39355e15			−1.36556
$592$		−	1.19162e11i		−	6.73548e-5i
$593$		−	2.89873e15i		−	1.62333i	−0.584123	−	0.811665i	$-0.698562\pi$
$593$		−	2.89873e15i		−	1.62333i	0.584123	−	0.811665i	$-0.301438\pi$
$594$	−4.23812e14			−0.235152
$595$	2.55439e15	+	9.11804e14i	1.40425	+	0.501254i
$596$	6.71134e14			0.365557
$597$		−	1.15222e15i		−	0.621836i
$598$		−	2.29714e14i		−	0.122837i
$599$	2.28284e15			1.20956			0.604781	−	0.796392i	$-0.293261\pi$
$599$	2.28284e15			1.20956			0.604781	+	0.796392i	$0.293261\pi$
$600$	1.80441e15	+	1.47629e15i	0.947334	+	0.775069i
$601$	1.28437e15			0.668159			0.334080	−	0.942545i	$-0.391575\pi$
$601$	1.28437e15			0.668159			0.334080	+	0.942545i	$0.391575\pi$
$602$			1.08935e15i			0.561545i
$603$			2.05998e14i			0.105225i
$604$	−4.28942e13			−0.0217118
$605$	−9.54885e14	−	3.40851e14i	−0.478957	−	0.170966i
$606$	−4.46458e14			−0.221912
$607$		−	5.70541e14i		−	0.281027i	−0.990079	−	0.140514i	$-0.955125\pi$
$607$		−	5.70541e14i		−	0.281027i	0.990079	−	0.140514i	$-0.0448754\pi$
$608$		−	1.16178e15i		−	0.567095i
$609$	−1.69955e15			−0.822126
$610$	4.63689e14	−	1.29901e15i	0.222286	−	0.622728i
$611$	−5.29032e14			−0.251336
$612$		−	7.46098e14i		−	0.351288i
$613$			3.14628e15i			1.46813i	0.679080	+	0.734065i	$0.262379\pi$
$613$			3.14628e15i			1.46813i	−0.679080	+	0.734065i	$0.737621\pi$
$614$	3.18690e14			0.147381
$615$	1.01064e15	−	2.83127e15i	0.463214	−	1.29768i
$616$	−2.27186e15			−1.03202
$617$			3.60874e15i			1.62475i	0.583135	+	0.812375i	$0.301826\pi$
$617$			3.60874e15i			1.62475i	−0.583135	+	0.812375i	$0.698174\pi$
$618$			4.86640e14i			0.217156i
$619$	−2.19239e15			−0.969660			−0.484830	−	0.874608i	$-0.661118\pi$
$619$	−2.19239e15			−0.969660			−0.484830	+	0.874608i	$0.661118\pi$
$620$	−2.34719e15	−	8.37843e14i	−1.02895	−	0.367289i
$621$	3.13817e14			0.136355
$622$			2.62096e14i			0.112879i
$623$			2.28957e14i			0.0977394i
$624$	1.29774e14			0.0549125
$625$	4.72182e14	+	2.33696e15i	0.198048	+	0.980192i
$626$	2.15756e15			0.897024
$627$		−	1.18396e15i		−	0.487940i
$628$		−	1.70210e15i		−	0.695357i
$629$	3.16246e12			0.00128070
$630$	−1.15786e15	−	4.13305e14i	−0.464819	−	0.165920i
$631$	3.99257e14			0.158888			0.0794441	−	0.996839i	$-0.474685\pi$
$631$	3.99257e14			0.158888			0.0794441	+	0.996839i	$0.474685\pi$
$632$			4.14433e15i			1.63497i
$633$		−	4.39915e14i		−	0.172048i
$634$	−8.16291e14			−0.316486
$635$	−5.36292e11	+	1.50241e12i	−0.000206132	+	0.000577473i
$636$	−2.63219e15			−1.00301
$637$		−	2.77010e15i		−	1.04647i
$638$		−	4.94361e14i		−	0.185153i
$639$	4.74665e14			0.176251
$640$	−6.22644e14	+	1.74432e15i	−0.229219	+	0.642149i
$641$	−1.23875e15			−0.452132			−0.226066	−	0.974112i	$-0.572586\pi$
$641$	−1.23875e15			−0.452132			−0.226066	+	0.974112i	$0.572586\pi$
$642$			2.99564e15i			1.08404i
$643$		−	2.78159e15i		−	0.998005i	−0.866601	−	0.499003i	$-0.833700\pi$
$643$		−	2.78159e15i		−	0.998005i	0.866601	−	0.499003i	$-0.166300\pi$
$644$	6.57234e14			0.233802
$645$	2.08129e15	+	7.42929e14i	0.734099	+	0.262041i
$646$	9.53345e14			0.333404
$647$		−	3.99567e15i		−	1.38553i	−0.721163	−	0.692766i	$-0.756392\pi$
$647$		−	3.99567e15i		−	1.38553i	0.721163	−	0.692766i	$-0.243608\pi$
$648$		−	3.56680e15i		−	1.22636i
$649$	−8.22656e14			−0.280461
$650$	−1.15504e15	−	9.45003e14i	−0.390456	−	0.319455i
$651$	9.47750e15			3.17686
$652$			1.25212e15i			0.416182i
$653$			1.37144e15i			0.452016i	0.974125	+	0.226008i	$0.0725675\pi$
$653$			1.37144e15i			0.452016i	−0.974125	+	0.226008i	$0.927432\pi$
$654$	−2.05916e14			−0.0672996
$655$	−3.44194e15	−	1.22862e15i	−1.11552	−	0.398190i
$656$	1.80312e14			0.0579502
$657$			1.87672e15i			0.598122i
$658$			8.46936e14i			0.267675i
$659$	4.53043e15			1.41994			0.709969	−	0.704233i	$-0.248709\pi$
$659$	4.53043e15			1.41994			0.709969	+	0.704233i	$0.248709\pi$
$660$	−6.05340e14	+	1.69584e15i	−0.188152	+	0.527101i
$661$	−8.53788e13			−0.0263174			−0.0131587	−	0.999913i	$-0.504189\pi$
$661$	−8.53788e13			−0.0263174			−0.0131587	+	0.999913i	$0.504189\pi$
$662$		−	2.46529e15i		−	0.753613i
$663$			3.44409e15i			1.04412i
$664$	3.29345e15			0.990209
$665$	−9.43819e14	+	2.64408e15i	−0.281430	+	0.788417i
$666$	−1.43349e12			−0.000423922
$667$			3.66055e14i			0.107363i
$668$			2.84243e15i			0.826836i
$669$	−8.48726e15			−2.44863
$670$	3.77021e14	+	1.34580e14i	0.107883	+	0.0385095i
$671$	2.72667e15			0.773854
$672$		−	6.71922e15i		−	1.89142i
$673$		−	2.76196e13i		−	0.00771143i	−0.999993	−	0.00385571i	$-0.998773\pi$
$673$		−	2.76196e13i		−	0.00771143i	0.999993	−	0.00385571i	$-0.00122732\pi$
$674$	1.82038e15			0.504119
$675$	1.29099e15	−	1.57792e15i	0.354611	−	0.433425i
$676$	6.84025e14			0.186365
$677$		−	5.40053e15i		−	1.45948i	−0.683724	−	0.729741i	$-0.739641\pi$
$677$		−	5.40053e15i		−	1.45948i	0.683724	−	0.729741i	$-0.260359\pi$
$678$		−	3.04871e13i		−	0.00817245i
$679$	−1.04891e16			−2.78903
$680$	−3.49511e15	−	1.24760e15i	−0.921853	−	0.329060i
$681$	−3.18868e14			−0.0834261
$682$			2.75680e15i			0.715469i
$683$			1.45094e15i			0.373539i	0.982404	+	0.186769i	$0.0598017\pi$
$683$			1.45094e15i			0.373539i	−0.982404	+	0.186769i	$0.940198\pi$
$684$	7.72294e14			0.197231
$685$	4.79991e14	−	1.34468e15i	0.121600	−	0.340660i
$686$	−8.65527e14			−0.217519
$687$			8.37099e15i			2.08696i
$688$			1.32550e14i			0.0327825i
$689$	4.31263e15			1.05812
$690$	−2.50806e14	+	7.02625e14i	−0.0610475	+	0.171023i
$691$	−3.79473e15			−0.916330			−0.458165	−	0.888867i	$-0.651493\pi$
$691$	−3.79473e15			−0.916330			−0.458165	+	0.888867i	$0.651493\pi$
$692$		−	4.93826e14i		−	0.118302i
$693$		−	2.43039e15i		−	0.577622i
$694$	−2.71553e15			−0.640291
$695$	7.25766e14	+	2.59066e14i	0.169778	+	0.0606030i
$696$	2.32545e15			0.539704
$697$			4.78534e15i			1.10188i
$698$		−	9.68636e13i		−	0.0221287i
$699$	5.73810e15			1.30060
$700$	2.70375e15	−	3.30468e15i	0.608033	−	0.743173i
$701$	−3.00014e15			−0.669410			−0.334705	−	0.942323i	$-0.608637\pi$
$701$	−3.00014e15			−0.669410			−0.334705	+	0.942323i	$0.608637\pi$
$702$			1.27614e15i			0.282516i
$703$			3.27350e12i			0.000719048i
$704$	1.78604e15			0.389261
$705$	1.61815e15	+	5.77607e14i	0.349928	+	0.124909i
$706$	1.15759e15			0.248387
$707$			2.09285e15i			0.445586i
$708$		−	1.51188e15i		−	0.319400i
$709$	3.33135e14			0.0698338			0.0349169	−	0.999390i	$-0.488883\pi$
$709$	3.33135e14			0.0698338			0.0349169	+	0.999390i	$0.488883\pi$
$710$	3.10101e14	−	8.68739e14i	0.0645033	−	0.180704i
$711$	−4.43354e15			−0.915098
$712$		−	3.13276e14i		−	0.0641634i
$713$		−	2.04130e15i		−	0.414872i
$714$	5.51370e15			1.11200
$715$	9.91799e14	−	2.77850e15i	0.198491	−	0.556066i
$716$	−1.31043e15			−0.260250
$717$		−	1.10851e16i		−	2.18467i
$718$			3.65645e15i			0.715114i
$719$	−1.88706e15			−0.366249			−0.183124	−	0.983090i	$-0.558621\pi$
$719$	−1.88706e15			−0.366249			−0.183124	+	0.983090i	$0.558621\pi$
$720$	−1.40887e14	−	5.02902e13i	−0.0271357	−	0.00968623i
$721$	2.28121e15			0.436035
$722$		−	2.17090e15i		−	0.411799i
$723$		−	7.41349e15i		−	1.39560i
$724$	4.36970e15			0.816374
$725$	1.84058e15	+	1.50589e15i	0.341269	+	0.279212i
$726$	−2.06114e15			−0.379276
$727$			3.20690e15i			0.585660i	0.956164	+	0.292830i	$0.0945970\pi$
$727$			3.20690e15i			0.585660i	−0.956164	+	0.292830i	$0.905403\pi$
$728$			6.84076e15i			1.23989i
$729$	−6.03607e13			−0.0108581
$730$	3.43480e15	+	1.22607e15i	0.613233	+	0.218897i
$731$	−3.51776e15			−0.623333
$732$			5.01109e15i			0.881294i
$733$			4.94602e15i			0.863344i	0.902031	+	0.431672i	$0.142076\pi$
$733$			4.94602e15i			0.863344i	−0.902031	+	0.431672i	$0.857924\pi$
$734$	−2.83339e15			−0.490883
$735$	−3.02445e15	+	8.47290e15i	−0.520075	+	1.45697i
$736$	−1.44721e15			−0.247004
$737$			7.91381e14i			0.134065i
$738$		−	2.16911e15i		−	0.364730i
$739$	−2.24992e15			−0.375511			−0.187756	−	0.982216i	$-0.560121\pi$
$739$	−2.24992e15			−0.375511			−0.187756	+	0.982216i	$0.560121\pi$
$740$	1.67369e12	−	4.68878e12i	0.000277268	−	0.000776758i
$741$	−3.56501e15			−0.586220
$742$		−	6.90416e15i		−	1.12691i
$743$		−	6.59378e15i		−	1.06831i	−0.845387	−	0.534154i	$-0.820630\pi$
$743$		−	6.59378e15i		−	1.06831i	0.845387	−	0.534154i	$-0.179370\pi$
$744$	−1.29678e16			−2.08553
$745$	3.36333e15	+	1.20056e15i	0.536921	+	0.191657i
$746$	−6.58200e15			−1.04302
$747$			3.52328e15i			0.554222i
$748$		−	2.86628e15i		−	0.447568i
$749$	1.40426e16			2.17669
$750$	2.50114e15	+	4.15157e15i	0.384858	+	0.638816i
$751$	4.76790e15			0.728295			0.364147	−	0.931341i	$-0.381360\pi$
$751$	4.76790e15			0.728295			0.364147	+	0.931341i	$0.381360\pi$
$752$			1.03054e14i			0.0156266i
$753$			8.62087e14i			0.129771i
$754$	−1.48856e15			−0.222446
$755$	−2.14961e14	−	7.67315e13i	−0.0318898	−	0.0113832i
$756$	−3.65115e15			−0.537725
$757$		−	3.60332e15i		−	0.526836i	−0.964682	−	0.263418i	$-0.915150\pi$
$757$		−	3.60332e15i		−	0.526836i	0.964682	−	0.263418i	$-0.0848499\pi$
$758$		−	3.80820e15i		−	0.552763i
$759$	−1.47484e15			−0.212527
$760$	1.29140e15	−	3.61783e15i	0.184751	−	0.517575i
$761$	−1.00138e16			−1.42227			−0.711136	−	0.703054i	$-0.751819\pi$
$761$	−1.00138e16			−1.42227			−0.711136	+	0.703054i	$0.751819\pi$
$762$			3.24297e12i			0.000457289i
$763$			9.65267e14i			0.135133i
$764$	−5.29031e15			−0.735306
$765$	1.33466e15	−	3.73901e15i	0.184176	−	0.515963i
$766$	5.88702e15			0.806561
$767$			2.47709e15i			0.336951i
$768$			8.88418e15i			1.19986i
$769$	1.14898e16			1.54070			0.770351	−	0.637620i	$-0.220081\pi$
$769$	1.14898e16			1.54070			0.770351	+	0.637620i	$0.220081\pi$
$770$	−4.44814e15	−	1.58779e15i	−0.592216	−	0.211395i
$771$	1.65602e16			2.18910
$772$		−	1.33760e15i		−	0.175562i
$773$			1.24078e16i			1.61699i	0.588501	+	0.808497i	$0.299718\pi$
$773$			1.24078e16i			1.61699i	−0.588501	+	0.808497i	$0.700282\pi$
$774$	1.59454e15			0.206329
$775$	−1.02640e16	−	8.39757e15i	−1.31873	−	1.07893i
$776$	1.43519e16			1.83092
$777$			1.89324e13i			0.00239822i
$778$		−	6.18192e15i		−	0.777562i
$779$	−4.95336e15			−0.618649
$780$	5.10633e15	+	1.82273e15i	0.633269	+	0.226049i
$781$	1.82352e15			0.224558
$782$		−	1.18756e15i		−	0.145217i
$783$		−	2.03356e15i		−	0.246926i
$784$	−5.39607e14			−0.0650637
$785$	3.04482e15	−	8.52996e15i	0.364568	−	1.02133i
$786$	−7.42949e15			−0.883355
$787$			3.57890e15i			0.422560i	0.977426	+	0.211280i	$0.0677631\pi$
$787$			3.57890e15i			0.422560i	−0.977426	+	0.211280i	$0.932237\pi$
$788$		−	5.99805e15i		−	0.703260i
$789$	7.88380e14			0.0917935
$790$	−2.89645e15	+	8.11433e15i	−0.334902	+	0.938217i
$791$	−1.42913e14			−0.0164098
$792$			3.32545e15i			0.379194i
$793$		−	8.21024e15i		−	0.929723i
$794$	−2.08308e15			−0.234258
$795$	−1.31910e16	−	4.70861e15i	−1.47319	−	0.525864i
$796$	2.88737e15			0.320244
$797$			1.25596e16i			1.38343i	0.722172	+	0.691714i	$0.243144\pi$
$797$			1.25596e16i			1.38343i	−0.722172	+	0.691714i	$0.756856\pi$
$798$			5.70729e15i			0.624330i
$799$	−2.73496e15			−0.297128
$800$	−5.95358e15	+	7.27681e15i	−0.642367	+	0.785138i
$801$	3.35137e14			0.0359124
$802$			7.96160e15i			0.847308i
$803$			7.20977e15i			0.762055i
$804$	−1.45440e15			−0.152678
$805$	3.29368e15	+	1.17570e15i	0.343403	+	0.122579i
$806$	8.30095e15			0.859578
$807$		−	2.04725e16i		−	2.10555i
$808$		−	2.86359e15i		−	0.292515i
$809$	−8.95686e15			−0.908738			−0.454369	−	0.890813i	$-0.650135\pi$
$809$	−8.95686e15			−0.908738			−0.454369	+	0.890813i	$0.650135\pi$
$810$	2.49282e15	−	6.98356e15i	0.251202	−	0.703735i
$811$	−8.33940e15			−0.834680			−0.417340	−	0.908750i	$-0.637038\pi$
$811$	−8.33940e15			−0.834680			−0.417340	+	0.908750i	$0.637038\pi$
$812$		−	4.25893e15i		−	0.423392i
$813$			2.38296e15i			0.235298i
$814$	−5.50702e12			−0.000540110
$815$	−2.23985e15	+	6.27489e15i	−0.218199	+	0.611278i
$816$	6.70897e14			0.0649173
$817$		−	3.64127e15i		−	0.349971i
$818$		−	3.57545e15i		−	0.341340i
$819$	−7.31813e15			−0.693967
$820$	7.09493e15	+	2.53257e15i	0.668300	+	0.238553i
$821$	3.07549e15			0.287757			0.143879	−	0.989595i	$-0.454042\pi$
$821$	3.07549e15			0.287757			0.143879	+	0.989595i	$0.454042\pi$
$822$		−	2.90251e15i		−	0.269761i
$823$			1.67606e16i			1.54736i	0.633579	+	0.773678i	$0.281585\pi$
$823$			1.67606e16i			1.54736i	−0.633579	+	0.773678i	$0.718415\pi$
$824$	−3.12132e15			−0.286246
$825$	−6.06723e15	+	7.41572e15i	−0.552705	+	0.675548i
$826$	3.96562e15			0.358856
$827$		−	1.18413e16i		−	1.06443i	−0.846608	−	0.532217i	$-0.821359\pi$
$827$		−	1.18413e16i		−	1.06443i	0.846608	−	0.532217i	$-0.178641\pi$
$828$		−	9.62031e14i		−	0.0859057i
$829$	3.10234e15			0.275195			0.137597	−	0.990488i	$-0.456062\pi$
$829$	3.10234e15			0.275195			0.137597	+	0.990488i	$0.456062\pi$
$830$	6.44836e15	+	2.30178e15i	0.568225	+	0.202831i
$831$	1.16362e16			1.01861
$832$		−	5.37792e15i		−	0.467666i
$833$		−	1.43207e16i		−	1.23713i
$834$	1.56658e15			0.134443
$835$	−5.08470e15	+	1.42446e16i	−0.433500	+	1.21444i
$836$	2.96691e15			0.251287
$837$			1.13401e16i			0.954173i
$838$		−	9.43094e15i		−	0.788339i
$839$	2.08909e16			1.73487			0.867436	−	0.497549i	$-0.165767\pi$
$839$	2.08909e16			1.73487			0.867436	+	0.497549i	$0.165767\pi$
$840$	7.46887e15	−	2.09238e16i	0.616196	−	1.72626i
$841$	−9.82844e15			−0.805576
$842$			9.75908e15i			0.794680i
$843$			1.18805e16i			0.961129i
$844$	1.10239e15			0.0886039
$845$	3.42794e15	+	1.22362e15i	0.273729	+	0.0977091i
$846$	1.23971e15			0.0983519
$847$			9.66193e15i			0.761562i
$848$		−	8.40086e14i		−	0.0657880i
$849$	1.54204e16			1.19978
$850$	−5.97125e15	−	4.88543e15i	−0.461595	−	0.377658i
$851$	4.07773e12			0.000313189
$852$			3.35126e15i			0.255735i
$853$		−	2.42451e16i		−	1.83825i	−0.393968	−	0.919124i	$-0.628898\pi$
$853$		−	2.42451e16i		−	1.83825i	0.393968	−	0.919124i	$-0.371102\pi$
$854$	−1.31439e16			−0.990164
$855$	3.87029e15	+	1.38152e15i	0.289688	+	0.103406i
$856$	−1.92141e16			−1.42894
$857$		−	9.53835e15i		−	0.704821i	−0.935846	−	0.352410i	$-0.885362\pi$
$857$		−	9.53835e15i		−	0.704821i	0.935846	−	0.352410i	$-0.114638\pi$
$858$		−	5.99743e15i		−	0.440337i
$859$	−4.70173e15			−0.343001			−0.171500	−	0.985184i	$-0.554861\pi$
$859$	−4.70173e15			−0.343001			−0.171500	+	0.985184i	$0.554861\pi$
$860$	−1.86172e15	+	5.21556e15i	−0.134950	+	0.378059i
$861$	−2.86479e16			−2.06336
$862$			1.09254e16i			0.781893i
$863$		−	1.12556e16i		−	0.800401i	−0.916428	−	0.400201i	$-0.868940\pi$
$863$		−	1.12556e16i		−	0.800401i	0.916428	−	0.400201i	$-0.131060\pi$
$864$	8.03974e15			0.568089
$865$	8.83383e14	−	2.47477e15i	0.0620241	−	0.173759i
$866$	1.02855e16			0.717593
$867$		−	1.54792e14i		−	0.0107311i
$868$			2.37499e16i			1.63607i
$869$	−1.70323e16			−1.16591
$870$	4.55307e15	+	1.62524e15i	0.309705	+	0.110551i
$871$	2.38292e15			0.161068
$872$		−	1.32075e15i		−	0.0887115i
$873$			1.53534e16i			1.02477i
$874$	1.22926e15			0.0815324
$875$	1.94612e16	−	1.17245e16i	1.28270	−	0.772771i
$876$	−1.32501e16			−0.867857
$877$			9.19338e15i			0.598381i	0.954193	+	0.299190i	$0.0967165\pi$
$877$			9.19338e15i			0.598381i	−0.954193	+	0.299190i	$0.903283\pi$
$878$			1.54515e16i			0.999424i
$879$	2.10741e16			1.35460
$880$	−5.41242e14	−	1.93199e14i	−0.0345730	−	0.0123410i
$881$	−1.98624e16			−1.26085			−0.630425	−	0.776250i	$-0.717120\pi$
$881$	−1.98624e16			−1.26085			−0.630425	+	0.776250i	$0.717120\pi$
$882$			6.49133e15i			0.409502i
$883$			5.79702e15i			0.363430i	0.983351	+	0.181715i	$0.0581648\pi$
$883$			5.79702e15i			0.363430i	−0.983351	+	0.181715i	$0.941835\pi$
$884$	−8.63061e15			−0.537717
$885$	2.70453e15	−	7.57667e15i	0.167457	−	0.469127i
$886$	−1.77468e16			−1.09203
$887$		−	8.29351e15i		−	0.507176i	−0.967312	−	0.253588i	$-0.918389\pi$
$887$		−	8.29351e15i		−	0.507176i	0.967312	−	0.253588i	$-0.0816107\pi$
$888$		−	2.59047e13i		−	0.00157437i
$889$	1.52020e13			0.000918206
$890$	2.18947e14	−	6.13374e14i	0.0131430	−	0.0368197i
$891$	1.46588e16			0.874520
$892$		−	2.12684e16i		−	1.26104i
$893$		−	2.83099e15i		−	0.166823i
$894$	7.25982e15			0.425176
$895$	−6.56710e15	−	2.34416e15i	−0.382249	−	0.136446i
$896$	1.76498e16			1.02104
$897$			4.44086e15i			0.255334i
$898$		−	5.87525e15i		−	0.335742i
$899$	−1.32278e16			−0.751293
$900$	−4.83725e15	−	3.95763e15i	−0.273064	−	0.223410i
$901$	2.22952e16			1.25091
$902$		−	8.33305e15i		−	0.464695i
$903$		−	2.10594e16i		−	1.16725i
$904$	1.95545e14			0.0107726
$905$	2.18984e16	+	7.81675e15i	1.19907	+	0.428015i
$906$	−4.63997e14			−0.0252528
$907$		−	2.89763e16i		−	1.56748i	−0.621088	−	0.783741i	$-0.713309\pi$
$907$		−	2.89763e16i		−	1.56748i	0.621088	−	0.783741i	$-0.286691\pi$
$908$		−	7.99059e14i		−	0.0429642i
$909$	3.06342e15			0.163722
$910$	−4.78097e15	+	1.33938e16i	−0.253974	+	0.711499i
$911$	1.91910e16			1.01332			0.506659	−	0.862147i	$-0.330880\pi$
$911$	1.91910e16			1.01332			0.506659	+	0.862147i	$0.330880\pi$
$912$			6.94454e14i			0.0364478i
$913$			1.35354e16i			0.706123i
$914$	1.09737e16			0.569046
$915$	−8.96411e15	+	2.51127e16i	−0.462052	+	1.29443i
$916$	−2.09770e16			−1.07478
$917$			3.48270e16i			1.77372i
$918$			6.59730e15i			0.333988i
$919$	5.30946e15			0.267187			0.133593	−	0.991036i	$-0.457348\pi$
$919$	5.30946e15			0.267187			0.133593	+	0.991036i	$0.457348\pi$
$920$	−4.50665e15	−	1.60867e15i	−0.225435	−	0.0804702i
$921$	−6.16096e15			−0.306352
$922$		−	1.29589e16i		−	0.640542i
$923$		−	5.49076e15i		−	0.269788i
$924$	1.71593e16			0.838113
$925$	1.67751e13	−	2.05035e13i	0.000814489	−	0.000995516i
$926$	2.14379e15			0.103472
$927$		−	3.33914e15i		−	0.160212i
$928$			9.37804e15i			0.447299i
$929$	−3.41655e16			−1.61995			−0.809974	−	0.586466i	$-0.800519\pi$
$929$	−3.41655e16			−1.61995			−0.809974	+	0.586466i	$0.800519\pi$
$930$	−2.53901e16	−	9.06314e15i	−1.19676	−	0.427192i
$931$	1.48235e16			0.694590
$932$			1.43792e16i			0.669805i
$933$		−	5.06688e15i		−	0.234634i
$934$	1.04088e16			0.479174
$935$	5.12735e15	−	1.43641e16i	0.234655	−	0.657378i
$936$	1.00132e16			0.455571
$937$		−	1.15303e16i		−	0.521524i	−0.965403	−	0.260762i	$-0.916026\pi$
$937$		−	1.15303e16i		−	0.521524i	0.965403	−	0.260762i	$-0.0839738\pi$
$938$		−	3.81485e15i		−	0.171539i
$939$	−4.17103e16			−1.86459
$940$	−1.44744e15	+	4.05495e15i	−0.0643275	+	0.180212i
$941$	−3.10666e16			−1.37262			−0.686310	−	0.727309i	$-0.740771\pi$
$941$	−3.10666e16			−1.37262			−0.686310	+	0.727309i	$0.740771\pi$
$942$		−	1.84121e16i		−	0.808766i
$943$			6.17030e15i			0.269459i
$944$	4.82529e14			0.0209497
$945$	−1.82975e16	−	6.53138e15i	−0.789798	−	0.281923i
$946$	6.12572e15			0.262879
$947$			3.79319e16i			1.61838i	0.587550	+	0.809188i	$0.300092\pi$
$947$			3.79319e16i			1.61838i	−0.587550	+	0.809188i	$0.699908\pi$
$948$		−	3.13020e16i		−	1.32778i
$949$	2.17093e16			0.915547
$950$	5.05696e15	−	6.18091e15i	0.212036	−	0.259163i
$951$	1.57807e16			0.657858
$952$			3.53650e16i			1.46578i
$953$			1.52578e16i			0.628756i	0.949298	+	0.314378i	$0.101796\pi$
$953$			1.52578e16i			0.628756i	−0.949298	+	0.314378i	$0.898204\pi$
$954$	−1.01060e16			−0.414061
$955$	−2.65120e16	−	9.46360e15i	−1.08000	−	0.385512i
$956$	2.77785e16			1.12510
$957$			9.55707e15i			0.384865i
$958$		−	1.17645e16i		−	0.471045i
$959$	−1.36060e16			−0.541663
$960$	−5.87171e15	+	1.64494e16i	−0.232420	+	0.651117i
$961$	4.83561e16			1.90315
$962$			1.65821e13i			0.000648898i
$963$		−	2.05549e16i		−	0.799782i
$964$	1.85776e16			0.718731
$965$	2.39277e15	−	6.70328e15i	0.0920452	−	0.257862i
$966$	7.10946e15			0.271933
$967$		−	8.70387e15i		−	0.331029i	−0.986207	−	0.165515i	$-0.947071\pi$
$967$		−	8.70387e15i		−	0.331029i	0.986207	−	0.165515i	$-0.0529285\pi$
$968$		−	1.32202e16i		−	0.499945i
$969$	−1.84302e16			−0.693026
$970$	2.81001e16	+	1.00305e16i	1.05066	+	0.375039i
$971$	−6.67861e15			−0.248302			−0.124151	−	0.992263i	$-0.539621\pi$
$971$	−6.67861e15			−0.248302			−0.124151	+	0.992263i	$0.539621\pi$
$972$			1.72268e16i			0.636855i
$973$		−	7.34361e15i		−	0.269953i
$974$	−9.10715e15			−0.332896
$975$	2.23294e16	+	1.82690e16i	0.811617	+	0.664031i
$976$	−1.59933e15			−0.0578048
$977$		−	3.64352e16i		−	1.30949i	−0.755851	−	0.654744i	$-0.772777\pi$
$977$		−	3.64352e16i		−	1.30949i	0.755851	−	0.654744i	$-0.227223\pi$
$978$			1.35445e16i			0.484058i
$979$	1.28749e15			0.0457552
$980$	−2.12324e16	−	7.57903e15i	−0.750336	−	0.267837i
$981$	1.41292e15			0.0496520
$982$		−	1.74587e16i		−	0.610097i
$983$			3.91117e16i			1.35913i	0.733613	+	0.679567i	$0.237832\pi$
$983$			3.91117e16i			1.35913i	−0.733613	+	0.679567i	$0.762168\pi$
$984$	3.91982e16			1.35454
$985$	1.07296e16	−	3.00588e16i	0.368711	−	1.03293i
$986$	−7.69550e15			−0.262975
$987$		−	1.63731e16i		−	0.556400i
$988$		−	8.93364e15i		−	0.301901i
$989$	−4.53585e15			−0.152433
$990$	−2.32414e15	+	6.51100e15i	−0.0776727	+	0.217598i
$991$	−3.51778e15			−0.116913			−0.0584566	−	0.998290i	$-0.518618\pi$
$991$	−3.51778e15			−0.116913			−0.0584566	+	0.998290i	$0.518618\pi$
$992$		−	5.22965e16i		−	1.72846i
$993$			4.76593e16i			1.56649i
$994$	−8.79026e15			−0.287327
$995$	1.44698e16	+	5.16508e15i	0.470366	+	0.167900i
$996$	−2.48753e16			−0.804160
$997$		−	2.71445e15i		−	0.0872687i	−0.999048	−	0.0436343i	$-0.986106\pi$
$997$		−	2.71445e15i		−	0.0872687i	0.999048	−	0.0436343i	$-0.0138937\pi$
$998$			1.83751e16i			0.587505i
$999$	−2.26532e13			−0.000720308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.12.b.a.4.3	yes	4
3.2	odd	2		45.12.b.b.19.2		4
4.3	odd	2		80.12.c.a.49.4		4
5.2	odd	4		25.12.a.e.1.2		4
5.3	odd	4		25.12.a.e.1.3		4
5.4	even	2	inner	5.12.b.a.4.2	✓	4
15.2	even	4		225.12.a.r.1.3		4
15.8	even	4		225.12.a.r.1.2		4
15.14	odd	2		45.12.b.b.19.3		4
20.19	odd	2		80.12.c.a.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.12.b.a.4.2	✓	4	5.4	even	2	inner
5.12.b.a.4.3	yes	4	1.1	even	1	trivial
25.12.a.e.1.2		4	5.2	odd	4
25.12.a.e.1.3		4	5.3	odd	4
45.12.b.b.19.2		4	3.2	odd	2
45.12.b.b.19.3		4	15.14	odd	2
80.12.c.a.49.1		4	20.19	odd	2
80.12.c.a.49.4		4	4.3	odd	2
225.12.a.r.1.2		4	15.8	even	4
225.12.a.r.1.3		4	15.2	even	4

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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+27.1071i q^{2} -524.040i q^{3} +1313.20 q^{4} +(6581.01 + 2349.13i) q^{5} +14205.2 q^{6} -66589.5i q^{7} +91112.6i q^{8} -97470.8 q^{9} +O(q^{10})\)	\(q+27.1071i q^{2} -524.040i q^{3} +1313.20 q^{4} +(6581.01 + 2349.13i) q^{5} +14205.2 q^{6} -66589.5i q^{7} +91112.6i q^{8} -97470.8 q^{9} +(-63678.2 + 178392. i) q^{10} -374453. q^{11} -688170. i q^{12} +1.12751e6i q^{13} +1.80505e6 q^{14} +(1.23104e6 - 3.44871e6i) q^{15} +219635. q^{16} +5.82894e6i q^{17} -2.64216e6i q^{18} -6.03360e6 q^{19} +(8.64220e6 + 3.08488e6i) q^{20} -3.48955e7 q^{21} -1.01503e7i q^{22} +7.51593e6i q^{23} +4.77466e7 q^{24} +(3.77913e7 + 3.09193e7i) q^{25} -3.05636e7 q^{26} -4.17535e7i q^{27} -8.74454e7i q^{28} +4.87039e7 q^{29} +(9.34848e7 + 3.33699e7i) q^{30} -2.71596e8 q^{31} +1.92552e8i q^{32} +1.96228e8i q^{33} -1.58006e8 q^{34} +(1.56427e8 - 4.38226e8i) q^{35} -1.27999e8 q^{36} -542545. i q^{37} -1.63554e8i q^{38} +5.90860e8 q^{39} +(-2.14035e8 + 5.99613e8i) q^{40} +8.20963e8 q^{41} -9.45918e8i q^{42} +6.03499e8i q^{43} -4.91732e8 q^{44} +(-6.41456e8 - 2.28971e8i) q^{45} -2.03735e8 q^{46} +4.69204e8i q^{47} -1.15098e8i q^{48} -2.45683e9 q^{49} +(-8.38134e8 + 1.02441e9i) q^{50} +3.05460e9 q^{51} +1.48065e9i q^{52} -3.82491e9i q^{53} +1.13182e9 q^{54} +(-2.46428e9 - 8.79637e8i) q^{55} +6.06714e9 q^{56} +3.16185e9i q^{57} +1.32022e9i q^{58} +2.19696e9 q^{59} +(1.61660e9 - 4.52886e9i) q^{60} -7.28175e9 q^{61} -7.36220e9i q^{62} +6.49053e9i q^{63} -4.76973e9 q^{64} +(-2.64866e9 + 7.42015e9i) q^{65} -5.31918e9 q^{66} -2.11343e9i q^{67} +7.65458e9i q^{68} +3.93865e9 q^{69} +(1.18791e10 + 4.24029e9i) q^{70} -4.86982e9 q^{71} -8.88082e9i q^{72} -1.92542e10i q^{73} +1.47068e7 q^{74} +(1.62029e10 - 1.98042e10i) q^{75} -7.92334e9 q^{76} +2.49346e10i q^{77} +1.60165e10i q^{78} +4.54858e10 q^{79} +(1.44542e9 + 5.15952e8i) q^{80} -3.91472e10 q^{81} +2.22540e10i q^{82} -3.61471e10i q^{83} -4.58249e10 q^{84} +(-1.36929e10 + 3.83603e10i) q^{85} -1.63591e10 q^{86} -2.55228e10i q^{87} -3.41174e10i q^{88} -3.43834e9 q^{89} +(6.20676e9 - 1.73881e10i) q^{90} +7.50802e10 q^{91} +9.86994e9i q^{92} +1.42327e11i q^{93} -1.27188e10 q^{94} +(-3.97072e10 - 1.41737e10i) q^{95} +1.00905e11 q^{96} -1.57518e11i q^{97} -6.65976e10i q^{98} +3.64982e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 72 q^{4} - 300 q^{5} - 1752 q^{6} + 25452 q^{9}+O(q^{10}) \) 4 * q - 72 * q^4 - 300 * q^5 - 1752 * q^6 + 25452 * q^9	\( 4 q - 72 q^{4} - 300 q^{5} - 1752 q^{6} + 25452 q^{9} + 91400 q^{10} - 326352 q^{11} + 1080696 q^{14} + 3433200 q^{15} - 9834976 q^{16} + 15460880 q^{19} + 35447400 q^{20} - 81019872 q^{21} + 74415840 q^{24} + 159152500 q^{25} - 325970832 q^{26} + 216242520 q^{29} + 389993400 q^{30} - 684043072 q^{31} + 265782016 q^{34} + 394292400 q^{35} - 553353336 q^{36} + 5997024 q^{39} - 275204000 q^{40} + 1012873368 q^{41} - 1553573664 q^{44} - 2766384900 q^{45} + 5241789688 q^{46} - 1900646372 q^{49} - 4621170000 q^{50} + 8691953088 q^{51} - 6403356720 q^{54} - 7772763600 q^{55} + 10366738080 q^{56} + 3200971440 q^{59} + 1922954400 q^{60} - 2310471352 q^{61} - 5401150592 q^{64} + 3229723200 q^{65} - 17010985824 q^{66} + 32956101984 q^{69} + 40783573800 q^{70} - 60335466912 q^{71} - 5525992944 q^{74} + 19332540000 q^{75} - 52987638240 q^{76} + 74637768320 q^{79} + 72046927200 q^{80} - 77727716316 q^{81} - 76499865504 q^{84} - 46117585600 q^{85} + 39045421128 q^{86} + 118272499560 q^{89} + 36519766200 q^{90} + 51565095648 q^{91} - 266098749224 q^{94} - 264706278000 q^{95} + 313591828608 q^{96} + 119560366224 q^{99}+O(q^{100}) \) 4 * q - 72 * q^4 - 300 * q^5 - 1752 * q^6 + 25452 * q^9 + 91400 * q^10 - 326352 * q^11 + 1080696 * q^14 + 3433200 * q^15 - 9834976 * q^16 + 15460880 * q^19 + 35447400 * q^20 - 81019872 * q^21 + 74415840 * q^24 + 159152500 * q^25 - 325970832 * q^26 + 216242520 * q^29 + 389993400 * q^30 - 684043072 * q^31 + 265782016 * q^34 + 394292400 * q^35 - 553353336 * q^36 + 5997024 * q^39 - 275204000 * q^40 + 1012873368 * q^41 - 1553573664 * q^44 - 2766384900 * q^45 + 5241789688 * q^46 - 1900646372 * q^49 - 4621170000 * q^50 + 8691953088 * q^51 - 6403356720 * q^54 - 7772763600 * q^55 + 10366738080 * q^56 + 3200971440 * q^59 + 1922954400 * q^60 - 2310471352 * q^61 - 5401150592 * q^64 + 3229723200 * q^65 - 17010985824 * q^66 + 32956101984 * q^69 + 40783573800 * q^70 - 60335466912 * q^71 - 5525992944 * q^74 + 19332540000 * q^75 - 52987638240 * q^76 + 74637768320 * q^79 + 72046927200 * q^80 - 77727716316 * q^81 - 76499865504 * q^84 - 46117585600 * q^85 + 39045421128 * q^86 + 118272499560 * q^89 + 36519766200 * q^90 + 51565095648 * q^91 - 266098749224 * q^94 - 264706278000 * q^95 + 313591828608 * q^96 + 119560366224 * q^99

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