LMFDB - Embedded newform 5.12.b.a.4.4

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			4.4
Root			$11.3434 - 1.39818i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.12.b.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+58.2855i q^{2} +258.747i q^{3} -1349.20 q^{4} +(-6731.01 - 1876.59i) q^{5} -15081.2 q^{6} +21698.4i q^{7} +40729.8i q^{8} +110197. q^{9} +O(q^{10})$	\(q+58.2855i q^{2} +258.747i q^{3} -1349.20 q^{4} +(-6731.01 - 1876.59i) q^{5} -15081.2 q^{6} +21698.4i q^{7} +40729.8i q^{8} +110197. q^{9} +(109378. - 392321. i) q^{10} +211277. q^{11} -349103. i q^{12} +2.27195e6i q^{13} -1.26470e6 q^{14} +(485563. - 1.74163e6i) q^{15} -5.13712e6 q^{16} -4.99089e6i q^{17} +6.42288e6i q^{18} +1.37640e7 q^{19} +(9.08150e6 + 2.53190e6i) q^{20} -5.61440e6 q^{21} +1.23144e7i q^{22} -4.84620e7i q^{23} -1.05387e7 q^{24} +(4.17849e7 + 2.52627e7i) q^{25} -1.32422e8 q^{26} +7.43495e7i q^{27} -2.92755e7i q^{28} +5.94174e7 q^{29} +(1.01512e8 + 2.83013e7i) q^{30} -7.04251e7 q^{31} -2.16005e8i q^{32} +5.46673e7i q^{33} +2.90897e8 q^{34} +(4.07190e7 - 1.46052e8i) q^{35} -1.48678e8 q^{36} +4.76568e7i q^{37} +8.02244e8i q^{38} -5.87861e8 q^{39} +(7.64332e7 - 2.74153e8i) q^{40} -3.14526e8 q^{41} -3.27238e8i q^{42} -6.15622e8i q^{43} -2.85055e8 q^{44} +(-7.41736e8 - 2.06794e8i) q^{45} +2.82463e9 q^{46} +2.06450e9i q^{47} -1.32922e9i q^{48} +1.50651e9 q^{49} +(-1.47245e9 + 2.43546e9i) q^{50} +1.29138e9 q^{51} -3.06532e9i q^{52} -2.13487e9i q^{53} -4.33350e9 q^{54} +(-1.42211e9 - 3.96480e8i) q^{55} -8.83771e8 q^{56} +3.56141e9i q^{57} +3.46317e9i q^{58} -5.96471e8 q^{59} +(-6.55123e8 + 2.34981e9i) q^{60} +6.12652e9 q^{61} -4.10476e9i q^{62} +2.39109e9i q^{63} +2.06916e9 q^{64} +(4.26353e9 - 1.52925e10i) q^{65} -3.18631e9 q^{66} -1.60527e9i q^{67} +6.73373e9i q^{68} +1.25394e10 q^{69} +(8.51273e9 + 2.37333e9i) q^{70} -2.52979e10 q^{71} +4.48829e9i q^{72} +8.34067e9i q^{73} -2.77770e9 q^{74} +(-6.53667e9 + 1.08117e10i) q^{75} -1.85705e10 q^{76} +4.58436e9i q^{77} -3.42638e10i q^{78} -8.16692e9 q^{79} +(3.45780e10 + 9.64029e9i) q^{80} +2.83305e8 q^{81} -1.83323e10i q^{82} -1.64306e10i q^{83} +7.57497e9 q^{84} +(-9.36587e9 + 3.35938e10i) q^{85} +3.58818e10 q^{86} +1.53741e10i q^{87} +8.60525e9i q^{88} +6.25746e10 q^{89} +(1.20531e10 - 4.32325e10i) q^{90} -4.92977e10 q^{91} +6.53850e10i q^{92} -1.82223e10i q^{93} -1.20331e11 q^{94} +(-9.26459e10 - 2.58295e10i) q^{95} +5.58908e10 q^{96} -1.19293e11i q^{97} +8.78075e10i q^{98} +2.32820e10 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 $

$2$			58.2855i			1.28794i	0.765051	+	0.643970i	$0.222714\pi$
$2$			58.2855i			1.28794i	−0.765051	+	0.643970i	$0.777286\pi$
$3$			258.747i			0.614765i	0.951586	+	0.307382i	$0.0994531\pi$
$3$			258.747i			0.614765i	−0.951586	+	0.307382i	$0.900547\pi$
$4$	−1349.20			−0.658790
$5$	−6731.01	−	1876.59i	−0.963264	−	0.268556i
$5$	−6731.01	−	1876.59i	−0.963264	−	0.268556i
$6$	−15081.2			−0.791781
$7$			21698.4i			0.487965i	0.969780	+	0.243982i	$0.0784539\pi$
$7$			21698.4i			0.487965i	−0.969780	+	0.243982i	$0.921546\pi$
$8$			40729.8i			0.439458i
$9$	110197.			0.622064
$10$	109378.	−	392321.i	0.345884	−	1.24063i
$11$	211277.			0.395541			0.197771	−	0.980248i	$-0.436630\pi$
$11$	211277.			0.395541			0.197771	+	0.980248i	$0.436630\pi$
$12$		−	349103.i		−	0.405001i
$13$			2.27195e6i			1.69711i	0.529106	+	0.848556i	$0.322528\pi$
$13$			2.27195e6i			1.69711i	−0.529106	+	0.848556i	$0.677472\pi$
$14$	−1.26470e6			−0.628469
$15$	485563.	−	1.74163e6i	0.165099	−	0.592181i
$16$	−5.13712e6			−1.22479
$17$		−	4.99089e6i		−	0.852529i	−0.904599	−	0.426265i	$-0.859829\pi$
$17$		−	4.99089e6i		−	0.852529i	0.904599	−	0.426265i	$-0.140171\pi$
$18$			6.42288e6i			0.801181i
$19$	1.37640e7			1.27527			0.637634	−	0.770340i	$-0.279913\pi$
$19$	1.37640e7			1.27527			0.637634	+	0.770340i	$0.279913\pi$
$20$	9.08150e6	+	2.53190e6i	0.634589	+	0.176922i
$21$	−5.61440e6			−0.299984
$22$			1.23144e7i			0.509433i
$23$		−	4.84620e7i		−	1.56999i	−0.619500	−	0.784997i	$-0.712665\pi$
$23$		−	4.84620e7i		−	1.56999i	0.619500	−	0.784997i	$-0.287335\pi$
$24$	−1.05387e7			−0.270163
$25$	4.17849e7	+	2.52627e7i	0.855755	+	0.517381i
$26$	−1.32422e8			−2.18578
$27$			7.43495e7i			0.997188i
$28$		−	2.92755e7i		−	0.321466i
$29$	5.94174e7			0.537929			0.268964	−	0.963150i	$-0.413319\pi$
$29$	5.94174e7			0.537929			0.268964	+	0.963150i	$0.413319\pi$
$30$	1.01512e8	+	2.83013e7i	0.762694	+	0.212637i
$31$	−7.04251e7			−0.441813			−0.220906	−	0.975295i	$-0.570902\pi$
$31$	−7.04251e7			−0.441813			−0.220906	+	0.975295i	$0.570902\pi$
$32$		−	2.16005e8i		−	1.13799i
$33$			5.46673e7i			0.243165i
$34$	2.90897e8			1.09801
$35$	4.07190e7	−	1.46052e8i	0.131046	−	0.470039i
$36$	−1.48678e8			−0.409810
$37$			4.76568e7i			0.112984i	0.998403	+	0.0564918i	$0.0179915\pi$
$37$			4.76568e7i			0.112984i	−0.998403	+	0.0564918i	$0.982009\pi$
$38$			8.02244e8i			1.64247i
$39$	−5.87861e8			−1.04332
$40$	7.64332e7	−	2.74153e8i	0.118019	−	0.423314i
$41$	−3.14526e8			−0.423980			−0.211990	−	0.977272i	$-0.567994\pi$
$41$	−3.14526e8			−0.423980			−0.211990	+	0.977272i	$0.567994\pi$
$42$		−	3.27238e8i		−	0.386361i
$43$		−	6.15622e8i		−	0.638613i	−0.947652	−	0.319306i	$-0.896550\pi$
$43$		−	6.15622e8i		−	0.638613i	0.947652	−	0.319306i	$-0.103450\pi$
$44$	−2.85055e8			−0.260579
$45$	−7.41736e8	−	2.06794e8i	−0.599212	−	0.167059i
$46$	2.82463e9			2.02206
$47$			2.06450e9i			1.31304i	0.754310	+	0.656519i	$0.227972\pi$
$47$			2.06450e9i			1.31304i	−0.754310	+	0.656519i	$0.772028\pi$
$48$		−	1.32922e9i		−	0.752955i
$49$	1.50651e9			0.761890
$50$	−1.47245e9	+	2.43546e9i	−0.666355	+	1.10216i
$51$	1.29138e9			0.524105
$52$		−	3.06532e9i		−	1.11804i
$53$		−	2.13487e9i		−	0.701219i	−0.936522	−	0.350610i	$-0.885974\pi$
$53$		−	2.13487e9i		−	0.701219i	0.936522	−	0.350610i	$-0.114026\pi$
$54$	−4.33350e9			−1.28432
$55$	−1.42211e9	−	3.96480e8i	−0.381010	−	0.106225i
$56$	−8.83771e8			−0.214440
$57$			3.56141e9i			0.783989i
$58$			3.46317e9i			0.692820i
$59$	−5.96471e8			−0.108618			−0.0543092	−	0.998524i	$-0.517296\pi$
$59$	−5.96471e8			−0.108618			−0.0543092	+	0.998524i	$0.517296\pi$
$60$	−6.55123e8	+	2.34981e9i	−0.108765	+	0.390123i
$61$	6.12652e9			0.928752			0.464376	−	0.885638i	$-0.346279\pi$
$61$	6.12652e9			0.928752			0.464376	+	0.885638i	$0.346279\pi$
$62$		−	4.10476e9i		−	0.569028i
$63$			2.39109e9i			0.303545i
$64$	2.06916e9			0.240881
$65$	4.26353e9	−	1.52925e10i	0.455770	−	1.63477i
$66$	−3.18631e9			−0.313182
$67$		−	1.60527e9i		−	0.145257i	−0.997359	−	0.0726284i	$-0.976861\pi$
$67$		−	1.60527e9i		−	0.145257i	0.997359	−	0.0726284i	$-0.0231387\pi$
$68$			6.73373e9i			0.561638i
$69$	1.25394e10			0.965177
$70$	8.51273e9	+	2.37333e9i	0.605382	+	0.168779i
$71$	−2.52979e10			−1.66404			−0.832020	−	0.554745i	$-0.812816\pi$
$71$	−2.52979e10			−1.66404			−0.832020	+	0.554745i	$0.812816\pi$
$72$			4.48829e9i			0.273371i
$73$			8.34067e9i			0.470896i	0.971887	+	0.235448i	$0.0756558\pi$
$73$			8.34067e9i			0.470896i	−0.971887	+	0.235448i	$0.924344\pi$
$74$	−2.77770e9			−0.145516
$75$	−6.53667e9	+	1.08117e10i	−0.318068	+	0.526088i
$76$	−1.85705e10			−0.840134
$77$			4.58436e9i			0.193010i
$78$		−	3.42638e10i		−	1.34374i
$79$	−8.16692e9			−0.298613			−0.149307	−	0.988791i	$-0.547704\pi$
$79$	−8.16692e9			−0.298613			−0.149307	+	0.988791i	$0.547704\pi$
$80$	3.45780e10	+	9.64029e9i	1.17979	+	0.328924i
$81$	2.83305e8			0.00902788
$82$		−	1.83323e10i		−	0.546061i
$83$		−	1.64306e10i		−	0.457852i	−0.973444	−	0.228926i	$-0.926479\pi$
$83$		−	1.64306e10i		−	0.457852i	0.973444	−	0.228926i	$-0.0735213\pi$
$84$	7.57497e9			0.197626
$85$	−9.36587e9	+	3.35938e10i	−0.228952	+	0.821211i
$86$	3.58818e10			0.822495
$87$			1.53741e10i			0.330700i
$88$			8.60525e9i			0.173824i
$89$	6.25746e10			1.18783			0.593913	−	0.804529i	$-0.297582\pi$
$89$	6.25746e10			1.18783			0.593913	+	0.804529i	$0.297582\pi$
$90$	1.20531e10	−	4.32325e10i	0.215162	−	0.771749i
$91$	−4.92977e10			−0.828131
$92$			6.53850e10i			1.03430i
$93$		−	1.82223e10i		−	0.271611i
$94$	−1.20331e11			−1.69111
$95$	−9.26459e10	−	2.58295e10i	−1.22842	−	0.342481i
$96$	5.58908e10			0.699598
$97$		−	1.19293e11i		−	1.41049i	−0.708962	−	0.705247i	$-0.750836\pi$
$97$		−	1.19293e11i		−	1.41049i	0.708962	−	0.705247i	$-0.249164\pi$
$98$			8.78075e10i			0.981269i
$99$	2.32820e10			0.246052
$100$	−5.63763e10	−	3.40845e10i	−0.563763	−	0.340845i
$101$	1.30104e11			1.23176			0.615878	−	0.787842i	$-0.288802\pi$
$101$	1.30104e11			1.23176			0.615878	+	0.787842i	$0.288802\pi$
$102$			7.52688e10i			0.675016i
$103$			1.50989e11i			1.28334i	0.766981	+	0.641670i	$0.221758\pi$
$103$			1.50989e11i			1.28334i	−0.766981	+	0.641670i	$0.778242\pi$
$104$	−9.25361e10			−0.745809
$105$	3.77906e10	+	1.05359e10i	0.288963	+	0.0805624i
$106$	1.24432e11			0.903128
$107$		−	1.02870e11i		−	0.709054i	−0.935046	−	0.354527i	$-0.884642\pi$
$107$		−	1.02870e11i		−	0.709054i	0.935046	−	0.354527i	$-0.115358\pi$
$108$		−	1.00312e11i		−	0.656938i
$109$	1.60543e11			0.999414			0.499707	−	0.866195i	$-0.333441\pi$
$109$	1.60543e11			0.999414			0.499707	+	0.866195i	$0.333441\pi$
$110$	2.31090e10	−	8.28881e10i	0.136811	−	0.490719i
$111$	−1.23311e10			−0.0694584
$112$		−	1.11467e11i		−	0.597652i
$113$		−	1.77558e11i		−	0.906587i	−0.891361	−	0.453293i	$-0.850249\pi$
$113$		−	1.77558e11i		−	0.906587i	0.891361	−	0.453293i	$-0.149751\pi$
$114$	−2.07579e11			−1.00973
$115$	−9.09433e10	+	3.26198e11i	−0.421631	+	1.51232i
$116$	−8.01661e10			−0.354382
$117$			2.50362e11i			1.05571i
$118$		−	3.47656e10i		−	0.139894i
$119$	1.08294e11			0.416004
$120$	7.09363e10	+	1.97769e10i	0.260239	+	0.0725540i
$121$	−2.40674e11			−0.843547
$122$			3.57087e11i			1.19618i
$123$		−	8.13828e10i		−	0.260648i
$124$	9.50177e10			0.291062
$125$	−2.33847e11	−	2.48457e11i	−0.685373	−	0.728192i
$126$	−1.39366e11			−0.390948
$127$		−	3.84449e11i		−	1.03257i	−0.856418	−	0.516283i	$-0.827315\pi$
$127$		−	3.84449e11i		−	1.03257i	0.856418	−	0.516283i	$-0.172685\pi$
$128$		−	3.21777e11i		−	0.827752i
$129$	1.59291e11			0.392597
$130$	8.91333e11	+	2.48502e11i	2.10548	+	0.587004i
$131$	−3.41125e11			−0.772540			−0.386270	−	0.922386i	$-0.626237\pi$
$131$	−3.41125e11			−0.772540			−0.386270	+	0.922386i	$0.626237\pi$
$132$		−	7.37572e10i		−	0.160195i
$133$			2.98658e11i			0.622285i
$134$	9.35639e10			0.187082
$135$	1.39524e11	−	5.00447e11i	0.267801	−	0.960555i
$136$	2.03278e11			0.374651
$137$			4.90035e11i			0.867489i	0.901036	+	0.433745i	$0.142808\pi$
$137$			4.90035e11i			0.867489i	−0.901036	+	0.433745i	$0.857192\pi$
$138$			7.30866e11i			1.24309i
$139$	2.14829e11			0.351166			0.175583	−	0.984465i	$-0.443819\pi$
$139$	2.14829e11			0.351166			0.175583	+	0.984465i	$0.443819\pi$
$140$	−5.49382e10	+	1.97054e11i	−0.0863317	+	0.309657i
$141$	−5.34185e11			−0.807209
$142$		−	1.47450e12i		−	2.14318i
$143$			4.80010e11i			0.671277i
$144$	−5.66095e11			−0.761895
$145$	−3.99939e11	−	1.11502e11i	−0.518167	−	0.144464i
$146$	−4.86141e11			−0.606487
$147$			3.89805e11i			0.468383i
$148$		−	6.42987e10i		−	0.0744325i
$149$	1.93535e11			0.215891			0.107945	−	0.994157i	$-0.465573\pi$
$149$	1.93535e11			0.215891			0.107945	+	0.994157i	$0.465573\pi$
$150$	−6.30168e11	−	3.80993e11i	−0.677570	−	0.409652i
$151$	8.89373e11			0.921957			0.460979	−	0.887411i	$-0.347499\pi$
$151$	8.89373e11			0.921957			0.460979	+	0.887411i	$0.347499\pi$
$152$			5.60606e11i			0.560426i
$153$		−	5.49981e11i		−	0.530328i
$154$	−2.67202e11			−0.248585
$155$	4.74032e11	+	1.32159e11i	0.425582	+	0.118651i
$156$	7.93144e11			0.687332
$157$			6.88503e11i			0.576047i	0.957623	+	0.288023i	$0.0929980\pi$
$157$			6.88503e11i			0.576047i	−0.957623	+	0.288023i	$0.907002\pi$
$158$		−	4.76013e11i		−	0.384596i
$159$	5.52392e11			0.431085
$160$	−4.05354e11	+	1.45393e12i	−0.305615	+	1.09619i
$161$	1.05155e12			0.766101
$162$			1.65126e10i			0.0116274i
$163$		−	1.98675e12i		−	1.35242i	−0.736709	−	0.676209i	$-0.763621\pi$
$163$		−	1.98675e12i		−	1.35242i	0.736709	−	0.676209i	$-0.236379\pi$
$164$	4.24360e11			0.279314
$165$	1.02588e11	−	3.67966e11i	0.0653033	−	0.234232i
$166$	9.57668e11			0.589686
$167$		−	1.91351e11i		−	0.113996i	−0.998374	−	0.0569982i	$-0.981847\pi$
$167$		−	1.91351e11i		−	0.113996i	0.998374	−	0.0569982i	$-0.0181529\pi$
$168$		−	2.28673e11i		−	0.131830i
$169$	−3.36960e12			−1.88019
$170$	−1.95803e12	−	5.45895e11i	−1.05767	−	0.294876i
$171$	1.51675e12			0.793298
$172$			8.30598e11i			0.420712i
$173$			4.07200e10i			0.0199781i	0.999950	+	0.00998906i	$0.00317967\pi$
$173$			4.07200e10i			0.0199781i	−0.999950	+	0.00998906i	$0.996820\pi$
$174$	−8.96087e11			−0.425921
$175$	−5.48161e11	+	9.06666e11i	−0.252464	+	0.417578i
$176$	−1.08535e12			−0.484453
$177$		−	1.54335e11i		−	0.0667747i
$178$			3.64719e12i			1.52985i
$179$	2.56842e12			1.04466			0.522330	−	0.852744i	$-0.325063\pi$
$179$	2.56842e12			1.04466			0.522330	+	0.852744i	$0.325063\pi$
$180$	1.00075e12	+	2.79008e11i	0.394755	+	0.110057i
$181$	−2.34419e12			−0.896935			−0.448467	−	0.893799i	$-0.648030\pi$
$181$	−2.34419e12			−0.896935			−0.448467	+	0.893799i	$0.648030\pi$
$182$		−	2.87334e12i		−	1.06658i
$183$			1.58522e12i			0.570964i
$184$	1.97384e12			0.689946
$185$	8.94324e10	−	3.20779e11i	0.0303424	−	0.108833i
$186$	1.06210e12			0.349819
$187$		−	1.05446e12i		−	0.337210i
$188$		−	2.78543e12i		−	0.865016i
$189$	−1.61326e12			−0.486593
$190$	1.50549e12	−	5.39992e12i	0.441095	−	1.58213i
$191$	−1.51930e12			−0.432475			−0.216237	−	0.976341i	$-0.569379\pi$
$191$	−1.51930e12			−0.432475			−0.216237	+	0.976341i	$0.569379\pi$
$192$			5.35389e11i			0.148085i
$193$			3.06580e12i			0.824097i	0.911162	+	0.412049i	$0.135187\pi$
$193$			3.06580e12i			0.824097i	−0.911162	+	0.412049i	$0.864813\pi$
$194$	6.95307e12			1.81663
$195$	3.95690e12	+	1.10318e12i	1.00500	+	0.280191i
$196$	−2.03258e12			−0.501926
$197$			1.85019e11i			0.0444276i	0.999753	+	0.0222138i	$0.00707145\pi$
$197$			1.85019e11i			0.0444276i	−0.999753	+	0.0222138i	$0.992929\pi$
$198$			1.35700e12i			0.316900i
$199$	−7.42934e12			−1.68756			−0.843778	−	0.536692i	$-0.819674\pi$
$199$	−7.42934e12			−1.68756			−0.843778	+	0.536692i	$0.819674\pi$
$200$	−1.02895e12	+	1.70189e12i	−0.227367	+	0.376068i
$201$	4.15359e11			0.0892988
$202$			7.58320e12i			1.58643i
$203$			1.28926e12i			0.262490i
$204$	−1.74233e12			−0.345275
$205$	2.11708e12	+	5.90237e11i	0.408405	+	0.113862i
$206$	−8.80050e12			−1.65287
$207$		−	5.34035e12i		−	0.976637i
$208$		−	1.16713e13i		−	2.07860i
$209$	2.90802e12			0.504420
$210$	−6.14093e11	+	2.20265e12i	−0.103760	+	0.372168i
$211$	−1.45982e12			−0.240296			−0.120148	−	0.992756i	$-0.538337\pi$
$211$	−1.45982e12			−0.240296			−0.120148	+	0.992756i	$0.538337\pi$
$212$			2.88037e12i			0.461956i
$213$		−	6.54577e12i		−	1.02299i
$214$	5.99585e12			0.913219
$215$	−1.15527e12	+	4.14376e12i	−0.171503	+	0.615153i
$216$	−3.02824e12			−0.438222
$217$		−	1.52811e12i		−	0.215589i
$218$			9.35732e12i			1.28718i
$219$	−2.15813e12			−0.289491
$220$	1.91871e12	+	5.34932e11i	0.251006	+	0.0699799i
$221$	1.13391e13			1.44684
$222$		−	7.18723e11i		−	0.0894583i
$223$		−	1.19451e11i		−	0.0145049i	−0.999974	−	0.00725245i	$-0.997691\pi$
$223$		−	1.19451e11i		−	0.0145049i	0.999974	−	0.00725245i	$-0.00230855\pi$
$224$	4.68697e12			0.555300
$225$	4.60457e12	+	2.78387e12i	0.532335	+	0.321844i
$226$	1.03491e13			1.16763
$227$		−	3.14220e12i		−	0.346013i	−0.984921	−	0.173006i	$-0.944652\pi$
$227$		−	3.14220e12i		−	0.346013i	0.984921	−	0.173006i	$-0.0553481\pi$
$228$		−	4.80506e12i		−	0.516485i
$229$	−2.40096e12			−0.251936			−0.125968	−	0.992034i	$-0.540204\pi$
$229$	−2.40096e12			−0.251936			−0.125968	+	0.992034i	$0.540204\pi$
$230$	−1.90126e13	−	5.30068e12i	−1.94778	−	0.543036i
$231$	−1.18619e12			−0.118656
$232$			2.42006e12i			0.236397i
$233$			7.86743e12i			0.750542i	0.926915	+	0.375271i	$0.122450\pi$
$233$			7.86743e12i			0.750542i	−0.926915	+	0.375271i	$0.877550\pi$
$234$	−1.45925e13			−1.35969
$235$	3.87423e12	−	1.38962e13i	0.352624	−	1.26480i
$236$	8.04760e11			0.0715567
$237$		−	2.11317e12i		−	0.183577i
$238$			6.31200e12i			0.535789i
$239$	−3.91932e12			−0.325104			−0.162552	−	0.986700i	$-0.551973\pi$
$239$	−3.91932e12			−0.325104			−0.162552	+	0.986700i	$0.551973\pi$
$240$	−2.49440e12	+	8.94698e12i	−0.202211	+	0.725295i
$241$	9.03207e12			0.715638			0.357819	−	0.933791i	$-0.383520\pi$
$241$	9.03207e12			0.715638			0.357819	+	0.933791i	$0.383520\pi$
$242$		−	1.40278e13i		−	1.08644i
$243$			1.32441e13i			1.00274i
$244$	−8.26591e12			−0.611853
$245$	−1.01403e13	−	2.82710e12i	−0.733902	−	0.204610i
$246$	4.74344e12			0.335699
$247$			3.12712e13i			2.16427i
$248$		−	2.86840e12i		−	0.194158i
$249$	4.25138e12			0.281471
$250$	1.44814e13	−	1.36299e13i	0.937868	−	0.882719i
$251$	−1.22505e13			−0.776157			−0.388078	−	0.921626i	$-0.626861\pi$
$251$	−1.22505e13			−0.776157			−0.388078	+	0.921626i	$0.626861\pi$
$252$		−	3.22607e12i		−	0.199973i
$253$		−	1.02389e13i		−	0.620997i
$254$	2.24078e13			1.32988
$255$	−8.69230e12	−	2.42340e12i	−0.504852	−	0.140752i
$256$	2.29926e13			1.30698
$257$		−	1.76783e13i		−	0.983576i	−0.870715	−	0.491788i	$-0.836343\pi$
$257$		−	1.76783e13i		−	0.983576i	0.870715	−	0.491788i	$-0.163657\pi$
$258$			9.28433e12i			0.505641i
$259$	−1.03408e12			−0.0551320
$260$	−5.75236e12	+	2.06327e13i	−0.300257	+	1.07697i
$261$	6.54761e12			0.334626
$262$		−	1.98826e13i		−	0.994986i
$263$		−	3.37515e13i		−	1.65401i	−0.562198	−	0.827003i	$-0.690044\pi$
$263$		−	3.37515e13i		−	1.65401i	0.562198	−	0.827003i	$-0.309956\pi$
$264$	−2.22659e12			−0.106861
$265$	−4.00628e12	+	1.43698e13i	−0.188317	+	0.675459i
$266$	−1.74074e13			−0.801466
$267$			1.61910e13i			0.730234i
$268$			2.16583e12i			0.0956937i
$269$	1.12892e13			0.488681			0.244340	−	0.969690i	$-0.421429\pi$
$269$	1.12892e13			0.488681			0.244340	+	0.969690i	$0.421429\pi$
$270$	2.91688e13	+	8.13221e12i	1.23714	+	0.344912i
$271$	−3.39607e13			−1.41138			−0.705692	−	0.708519i	$-0.749364\pi$
$271$	−3.39607e13			−1.41138			−0.705692	+	0.708519i	$0.749364\pi$
$272$			2.56388e13i			1.04417i
$273$		−	1.27556e13i		−	0.509106i
$274$	−2.85620e13			−1.11727
$275$	8.82818e12	+	5.33742e12i	0.338486	+	0.204645i
$276$	−1.69182e13			−0.635849
$277$			1.76433e13i			0.650042i	0.945707	+	0.325021i	$0.105371\pi$
$277$			1.76433e13i			0.650042i	−0.945707	+	0.325021i	$0.894629\pi$
$278$			1.25214e13i			0.452281i
$279$	−7.76062e12			−0.274836
$280$	5.94867e12	+	1.65848e12i	0.206562	+	0.0575891i
$281$	−1.29321e13			−0.440336			−0.220168	−	0.975462i	$-0.570661\pi$
$281$	−1.29321e13			−0.440336			−0.220168	+	0.975462i	$0.570661\pi$
$282$		−	3.11352e13i		−	1.03964i
$283$			1.86657e12i			0.0611248i	0.999533	+	0.0305624i	$0.00972984\pi$
$283$			1.86657e12i			0.0611248i	−0.999533	+	0.0305624i	$0.990270\pi$
$284$	3.41320e13			1.09625
$285$	6.68331e12	−	2.39719e13i	0.210545	−	0.755189i
$286$	−2.79776e13			−0.864565
$287$		−	6.82471e12i		−	0.206887i
$288$		−	2.38031e13i		−	0.707905i
$289$	9.36287e12			0.273194
$290$	6.49896e12	−	2.33107e13i	0.186061	−	0.667368i
$291$	3.08668e13			0.867122
$292$		−	1.12533e13i		−	0.310222i
$293$			4.98589e13i			1.34887i	0.738334	+	0.674435i	$0.235613\pi$
$293$			4.98589e13i			1.34887i	−0.738334	+	0.674435i	$0.764387\pi$
$294$	−2.27200e13			−0.603250
$295$	4.01485e12	+	1.11933e12i	0.104628	+	0.0291701i
$296$	−1.94105e12			−0.0496516
$297$			1.57083e13i			0.394429i
$298$			1.12803e13i			0.278055i
$299$	1.10103e14			2.66445
$300$	8.81928e12	−	1.45872e13i	0.209540	−	0.346582i
$301$	1.33580e13			0.311620
$302$			5.18376e13i			1.18743i
$303$			3.36642e13i			0.757240i
$304$	−7.07076e13			−1.56193
$305$	−4.12377e13	−	1.14970e13i	−0.894633	−	0.249422i
$306$	3.20559e13			0.683031
$307$		−	7.80715e13i		−	1.63392i	−0.576692	−	0.816962i	$-0.695657\pi$
$307$		−	7.80715e13i		−	1.63392i	0.576692	−	0.816962i	$-0.304343\pi$
$308$		−	6.18523e12i		−	0.127153i
$309$	−3.90681e13			−0.788953
$310$	−7.70297e12	+	2.76292e13i	−0.152816	+	0.548125i
$311$	−5.98338e13			−1.16618			−0.583088	−	0.812409i	$-0.698156\pi$
$311$	−5.98338e13			−1.16618			−0.583088	+	0.812409i	$0.698156\pi$
$312$		−	2.39435e13i		−	0.458497i
$313$		−	1.62840e13i		−	0.306385i	−0.988196	−	0.153192i	$-0.951045\pi$
$313$		−	1.62840e13i		−	0.306385i	0.988196	−	0.153192i	$-0.0489554\pi$
$314$	−4.01297e13			−0.741914
$315$	4.48711e12	−	1.60945e13i	0.0815189	−	0.292394i
$316$	1.10188e13			0.196724
$317$		−	1.89712e13i		−	0.332866i	−0.986053	−	0.166433i	$-0.946775\pi$
$317$		−	1.89712e13i		−	0.332866i	0.986053	−	0.166433i	$-0.0532250\pi$
$318$			3.21964e13i			0.555212i
$319$	1.25535e13			0.212773
$320$	−1.39275e13	−	3.88296e12i	−0.232032	−	0.0646902i
$321$	2.66174e13			0.435901
$322$			6.12899e13i			0.986693i
$323$		−	6.86949e13i		−	1.08720i
$324$	−3.82235e11			−0.00594748
$325$	−5.73957e13	+	9.49333e13i	−0.878053	+	1.45231i
$326$	1.15799e14			1.74183
$327$			4.15400e13i			0.614404i
$328$		−	1.28106e13i		−	0.186321i
$329$	−4.47964e13			−0.640716
$330$	2.14471e13	+	5.97940e12i	0.301677	+	0.0841068i
$331$	7.06499e13			0.977366			0.488683	−	0.872461i	$-0.337477\pi$
$331$	7.06499e13			0.977366			0.488683	+	0.872461i	$0.337477\pi$
$332$			2.21683e13i			0.301628i
$333$			5.25163e12i			0.0702831i
$334$	1.11530e13			0.146820
$335$	−3.01243e12	+	1.08051e13i	−0.0390096	+	0.139921i
$336$	2.88419e13			0.367416
$337$		−	1.09252e14i		−	1.36920i	−0.728920	−	0.684599i	$-0.759977\pi$
$337$		−	1.09252e14i		−	1.36920i	0.728920	−	0.684599i	$-0.240023\pi$
$338$		−	1.96399e14i		−	2.42157i
$339$	4.59427e13			0.557338
$340$	1.26365e13	−	4.53248e13i	0.150831	−	0.541006i
$341$	−1.48792e13			−0.174755
$342$			8.84048e13i			1.02172i
$343$			7.55936e13i			0.859740i
$344$	2.50741e13			0.280643
$345$	−8.44029e13	−	2.35313e13i	−0.929720	−	0.259204i
$346$	−2.37339e12			−0.0257306
$347$			7.74366e13i			0.826293i	0.910664	+	0.413147i	$0.135570\pi$
$347$			7.74366e13i			0.826293i	−0.910664	+	0.413147i	$0.864430\pi$
$348$		−	2.07428e13i		−	0.217862i
$349$	2.96909e12			0.0306961			0.0153481	−	0.999882i	$-0.495114\pi$
$349$	2.96909e12			0.0306961			0.0153481	+	0.999882i	$0.495114\pi$
$350$	−5.28455e13	−	3.19498e13i	−0.537816	−	0.325158i
$351$	−1.68918e14			−1.69234
$352$		−	4.56369e13i		−	0.450123i
$353$			1.36521e14i			1.32568i	0.748763	+	0.662838i	$0.230648\pi$
$353$			1.36521e14i			1.32568i	−0.748763	+	0.662838i	$0.769352\pi$
$354$	8.99551e12			0.0860019
$355$	1.70281e14	+	4.74739e13i	1.60291	+	0.446888i
$356$	−8.44258e13			−0.782528
$357$			2.80209e13i			0.255745i
$358$			1.49702e14i			1.34546i
$359$	−1.23288e14			−1.09119			−0.545595	−	0.838049i	$-0.683696\pi$
$359$	−1.23288e14			−1.09119			−0.545595	+	0.838049i	$0.683696\pi$
$360$	8.42269e12	−	3.02107e13i	0.0734154	−	0.263328i
$361$	7.29586e13			0.626306
$362$		−	1.36632e14i		−	1.15520i
$363$		−	6.22737e13i		−	0.518583i
$364$	6.65126e13			0.545564
$365$	1.56520e13	−	5.61412e13i	0.126462	−	0.453598i
$366$	−9.23954e13			−0.735367
$367$		−	1.27435e14i		−	0.999141i	−0.866273	−	0.499570i	$-0.833491\pi$
$367$		−	1.27435e14i		−	0.999141i	0.866273	−	0.499570i	$-0.166509\pi$
$368$			2.48955e14i			1.92291i
$369$	−3.46598e13			−0.263743
$370$	1.86968e13	+	5.21262e12i	0.140171	+	0.0390793i
$371$	4.63232e13			0.342170
$372$			2.45856e13i			0.178935i
$373$		−	2.55959e14i		−	1.83558i	−0.397071	−	0.917788i	$-0.629973\pi$
$373$		−	2.55959e14i		−	1.83558i	0.397071	−	0.917788i	$-0.370027\pi$
$374$	6.14597e13			0.434307
$375$	6.42876e13	−	6.05073e13i	0.447667	−	0.421343i
$376$	−8.40867e13			−0.577025
$377$			1.34993e14i			0.912925i
$378$		−	9.40299e13i		−	0.626702i
$379$	1.63930e14			1.07682			0.538410	−	0.842683i	$-0.319025\pi$
$379$	1.63930e14			1.07682			0.538410	+	0.842683i	$0.319025\pi$
$380$	1.24998e14	+	3.48492e13i	0.809270	+	0.225623i
$381$	9.94752e13			0.634786
$382$		−	8.85533e13i		−	0.557002i
$383$			1.25194e14i			0.776231i	0.921611	+	0.388116i	$0.126874\pi$
$383$			1.25194e14i			0.776231i	−0.921611	+	0.388116i	$0.873126\pi$
$384$	8.32590e13			0.508873
$385$	8.60298e12	−	3.08574e13i	0.0518340	−	0.185920i
$386$	−1.78692e14			−1.06139
$387$		−	6.78395e13i		−	0.397258i
$388$			1.60951e14i			0.929220i
$389$	−4.63473e13			−0.263817			−0.131908	−	0.991262i	$-0.542110\pi$
$389$	−4.63473e13			−0.263817			−0.131908	+	0.991262i	$0.542110\pi$
$390$	−6.42992e13	+	2.30630e14i	−0.360870	+	1.29438i
$391$	−2.41868e14			−1.33847
$392$			6.13597e13i			0.334819i
$393$		−	8.82651e13i		−	0.474931i
$394$	−1.07839e13			−0.0572201
$395$	5.49716e13	+	1.53260e13i	0.287643	+	0.0801944i
$396$	−3.14121e13			−0.162097
$397$			3.40799e14i			1.73441i	0.497956	+	0.867203i	$0.334084\pi$
$397$			3.40799e14i			1.73441i	−0.497956	+	0.867203i	$0.665916\pi$
$398$		−	4.33023e14i		−	2.17347i
$399$	−7.72769e13			−0.382559
$400$	−2.14654e14	−	1.29778e14i	−1.04812	−	0.633680i
$401$	3.20861e14			1.54534			0.772669	−	0.634809i	$-0.218921\pi$
$401$	3.20861e14			1.54534			0.772669	+	0.634809i	$0.218921\pi$
$402$			2.42094e13i			0.115011i
$403$		−	1.60002e14i		−	0.749806i
$404$	−1.75537e14			−0.811468
$405$	−1.90693e12	−	5.31647e11i	−0.00869624	−	0.00242449i
$406$	−7.51453e13			−0.338072
$407$			1.00688e13i			0.0446897i
$408$			5.25977e13i			0.230322i
$409$	−1.06163e14			−0.458666			−0.229333	−	0.973348i	$-0.573654\pi$
$409$	−1.06163e14			−0.458666			−0.229333	+	0.973348i	$0.573654\pi$
$410$	−3.44023e13	+	1.23395e14i	−0.146648	+	0.526001i
$411$	−1.26795e14			−0.533302
$412$		−	2.03715e14i		−	0.845452i
$413$		−	1.29425e13i		−	0.0530019i
$414$	3.11265e14			1.25785
$415$	−3.08336e13	+	1.10595e14i	−0.122959	+	0.441032i
$416$	4.90754e14			1.93130
$417$			5.55865e13i			0.215884i
$418$			1.69495e14i			0.649663i
$419$	−2.61611e14			−0.989644			−0.494822	−	0.868994i	$-0.664767\pi$
$419$	−2.61611e14			−0.989644			−0.494822	+	0.868994i	$0.664767\pi$
$420$	−5.09872e13	−	1.42151e13i	−0.190366	−	0.0530737i
$421$	4.43437e14			1.63411			0.817053	−	0.576563i	$-0.195606\pi$
$421$	4.43437e14			1.63411			0.817053	+	0.576563i	$0.195606\pi$
$422$		−	8.50865e13i		−	0.309487i
$423$			2.27502e14i			0.816794i
$424$	8.69527e13			0.308156
$425$	1.26084e14	−	2.08544e14i	0.441082	−	0.729556i
$426$	3.81524e14			1.31755
$427$			1.32936e14i			0.453198i
$428$			1.38793e14i			0.467118i
$429$	−1.24201e14			−0.412678
$430$	−2.41521e14	−	6.73356e13i	−0.792280	−	0.220886i
$431$	−4.84691e14			−1.56979			−0.784893	−	0.619631i	$-0.787282\pi$
$431$	−4.84691e14			−1.56979			−0.784893	+	0.619631i	$0.787282\pi$
$432$		−	3.81942e14i		−	1.22134i
$433$			1.36604e14i			0.431301i	0.976471	+	0.215651i	$0.0691872\pi$
$433$			1.36604e14i			0.431301i	−0.976471	+	0.215651i	$0.930813\pi$
$434$	8.90668e13			0.277666
$435$	2.88509e13	−	1.03483e14i	0.0888114	−	0.318551i
$436$	−2.16605e14			−0.658404
$437$		−	6.67032e14i		−	2.00216i
$438$		−	1.25788e14i		−	0.372847i
$439$	−1.70412e14			−0.498823			−0.249412	−	0.968398i	$-0.580237\pi$
$439$	−1.70412e14			−0.498823			−0.249412	+	0.968398i	$0.580237\pi$
$440$	1.61485e13	−	5.79220e13i	0.0466814	−	0.167438i
$441$	1.66012e14			0.473945
$442$			6.60903e14i			1.86344i
$443$			2.82230e14i			0.785927i	0.919554	+	0.392964i	$0.128550\pi$
$443$			2.82230e14i			0.785927i	−0.919554	+	0.392964i	$0.871450\pi$
$444$	1.66371e13			0.0457585
$445$	−4.21190e14	−	1.17427e14i	−1.14419	−	0.318998i
$446$	6.96229e12			0.0186814
$447$			5.00766e13i			0.132722i
$448$			4.48974e13i			0.117542i
$449$	−1.62691e14			−0.420735			−0.210367	−	0.977622i	$-0.567466\pi$
$449$	−1.62691e14			−0.420735			−0.210367	+	0.977622i	$0.567466\pi$
$450$	−1.62259e14	+	2.68379e14i	−0.414516	+	0.685615i
$451$	−6.64520e13			−0.167702
$452$			2.39562e14i			0.597250i
$453$			2.30123e14i			0.566787i
$454$	1.83145e14			0.445644
$455$	3.31823e14	+	9.25117e13i	0.797709	+	0.222399i
$456$	−1.45055e14			−0.344530
$457$			2.83347e14i			0.664936i	0.943114	+	0.332468i	$0.107881\pi$
$457$			2.83347e14i			0.664936i	−0.943114	+	0.332468i	$0.892119\pi$
$458$		−	1.39941e14i		−	0.324478i
$459$	3.71070e14			0.850132
$460$	1.22701e14	−	4.40107e14i	0.277766	−	0.996300i
$461$	3.77595e14			0.844639			0.422319	−	0.906447i	$-0.361216\pi$
$461$	3.77595e14			0.844639			0.422319	+	0.906447i	$0.361216\pi$
$462$		−	6.91378e13i		−	0.152822i
$463$		−	7.54964e14i		−	1.64904i	−0.565833	−	0.824520i	$-0.691445\pi$
$463$		−	7.54964e14i		−	1.64904i	0.565833	−	0.824520i	$-0.308555\pi$
$464$	−3.05234e14			−0.658847
$465$	−3.41958e13	+	1.22655e14i	−0.0729428	+	0.261633i
$466$	−4.58557e14			−0.966653
$467$		−	2.79315e14i		−	0.581903i	−0.956738	−	0.290952i	$-0.906028\pi$
$467$		−	2.79315e14i		−	0.581903i	0.956738	−	0.290952i	$-0.0939719\pi$
$468$		−	3.37789e14i		−	0.695493i
$469$	3.48318e13			0.0708802
$470$	8.09947e14	+	2.25811e14i	1.62899	+	0.454159i
$471$	−1.78148e14			−0.354133
$472$		−	2.42941e13i		−	0.0477332i
$473$		−	1.30066e14i		−	0.252597i
$474$	1.23167e14			0.236436
$475$	5.75129e14	+	3.47717e14i	1.09132	+	0.659799i
$476$	−1.46111e14			−0.274060
$477$		−	2.35256e14i		−	0.436203i
$478$		−	2.28440e14i		−	0.418715i
$479$	3.14043e14			0.569041			0.284521	−	0.958670i	$-0.408166\pi$
$479$	3.14043e14			0.569041			0.284521	+	0.958670i	$0.408166\pi$
$480$	−3.76202e14	−	1.04884e14i	−0.673898	−	0.187881i
$481$	−1.08274e14			−0.191746
$482$			5.26439e14i			0.921700i
$483$			2.72085e14i			0.470972i
$484$	3.24718e14			0.555721
$485$	−2.23865e14	+	8.02964e14i	−0.378797	+	1.35868i
$486$	−7.71939e14			−1.29147
$487$			4.06650e14i			0.672685i	0.941740	+	0.336343i	$0.109190\pi$
$487$			4.06650e14i			0.672685i	−0.941740	+	0.336343i	$0.890810\pi$
$488$			2.49532e14i			0.408147i
$489$	5.14066e14			0.831420
$490$	1.64779e14	−	5.91033e14i	0.263526	−	0.945222i
$491$	−7.04594e14			−1.11427			−0.557135	−	0.830422i	$-0.688099\pi$
$491$	−7.04594e14			−1.11427			−0.557135	+	0.830422i	$0.688099\pi$
$492$			1.09802e14i			0.171712i
$493$		−	2.96546e14i		−	0.458600i
$494$	−1.82266e15			−2.78745
$495$	−1.56711e14	−	4.36908e13i	−0.237013	−	0.0660787i
$496$	3.61782e14			0.541126
$497$		−	5.48924e14i		−	0.811993i
$498$			2.47794e14i			0.362518i
$499$	9.69339e14			1.40256			0.701282	−	0.712884i	$-0.252611\pi$
$499$	9.69339e14			1.40256			0.701282	+	0.712884i	$0.252611\pi$
$500$	3.15507e14	+	3.35219e14i	0.451517	+	0.479726i
$501$	4.95117e13			0.0700810
$502$		−	7.14029e14i		−	0.999644i
$503$			1.46009e14i			0.202188i	0.994877	+	0.101094i	$0.0322342\pi$
$503$			1.46009e14i			0.202188i	−0.994877	+	0.101094i	$0.967766\pi$
$504$	−9.73887e13			−0.133395
$505$	−8.75734e14	−	2.44153e14i	−1.18651	−	0.330795i
$506$	5.96778e14			0.799807
$507$		−	8.71875e14i		−	1.15587i
$508$			5.18699e14i			0.680245i
$509$	−4.15139e14			−0.538574			−0.269287	−	0.963060i	$-0.586788\pi$
$509$	−4.15139e14			−0.538574			−0.269287	+	0.963060i	$0.586788\pi$
$510$	1.41249e14	−	5.06635e14i	0.181280	−	0.650219i
$511$	−1.80979e14			−0.229781
$512$			6.81135e14i			0.855556i
$513$			1.02335e15i			1.27168i
$514$	1.03039e15			1.26679
$515$	2.83346e14	−	1.01631e15i	0.344649	−	1.23620i
$516$	−2.14915e14			−0.258639
$517$			4.36181e14i			0.519360i
$518$		−	6.02717e13i		−	0.0710068i
$519$	−1.05362e13			−0.0122818
$520$	6.22861e14	+	1.73652e14i	0.718411	+	0.200292i
$521$	6.87600e14			0.784745			0.392373	−	0.919806i	$-0.371654\pi$
$521$	6.87600e14			0.784745			0.392373	+	0.919806i	$0.371654\pi$
$522$			3.81631e14i			0.430978i
$523$		−	9.86334e13i		−	0.110221i	−0.998480	−	0.0551105i	$-0.982449\pi$
$523$		−	9.86334e13i		−	0.110221i	0.998480	−	0.0551105i	$-0.0175511\pi$
$524$	4.60246e14			0.508942
$525$	−2.34597e14	−	1.41835e14i	−0.256713	−	0.155206i
$526$	1.96723e15			2.13026
$527$			3.51484e14i			0.376658i
$528$		−	2.80832e14i		−	0.297825i
$529$	−1.39575e15			−1.46488
$530$	−8.37553e14	−	2.33508e14i	−0.869951	−	0.242541i
$531$	−6.57292e13			−0.0675676
$532$		−	4.02950e14i		−	0.409956i
$533$		−	7.14588e14i		−	0.719542i
$534$	−9.43702e14			−0.940498
$535$	−1.93046e14	+	6.92421e14i	−0.190421	+	0.683006i
$536$	6.53822e13			0.0638342
$537$			6.64572e14i			0.642220i
$538$			6.57996e14i			0.629391i
$539$	3.18289e14			0.301359
$540$	−1.88246e14	+	6.75204e14i	−0.176425	+	0.632805i
$541$	−8.79405e14			−0.815838			−0.407919	−	0.913018i	$-0.633745\pi$
$541$	−8.79405e14			−0.815838			−0.407919	+	0.913018i	$0.633745\pi$
$542$		−	1.97942e15i		−	1.81778i
$543$		−	6.06553e14i		−	0.551404i
$544$	−1.07806e15			−0.970172
$545$	−1.08062e15	−	3.01273e14i	−0.962699	−	0.268399i
$546$	7.43470e14			0.655698
$547$			5.92404e14i			0.517234i	0.965980	+	0.258617i	$0.0832668\pi$
$547$			5.92404e14i			0.517234i	−0.965980	+	0.258617i	$0.916733\pi$
$548$		−	6.61157e14i		−	0.571493i
$549$	6.75123e14			0.577743
$550$	−3.11094e14	+	5.14555e14i	−0.263571	+	0.435950i
$551$	8.17823e14			0.686003
$552$			5.10727e14i			0.424154i
$553$		−	1.77209e14i		−	0.145713i
$554$	−1.02835e15			−0.837215
$555$	8.30006e13	+	2.31404e13i	0.0669068	+	0.0186535i
$556$	−2.89848e14			−0.231345
$557$			1.68479e15i			1.33150i	0.746173	+	0.665752i	$0.231889\pi$
$557$			1.68479e15i			1.33150i	−0.746173	+	0.665752i	$0.768111\pi$
$558$		−	4.52332e14i		−	0.353972i
$559$	1.39866e15			1.08380
$560$	−2.09179e14	+	7.50288e14i	−0.160503	+	0.575697i
$561$	2.72838e14			0.207305
$562$		−	7.53754e14i		−	0.567126i
$563$			5.71345e14i			0.425698i	0.977085	+	0.212849i	$0.0682743\pi$
$563$			5.71345e14i			0.425698i	−0.977085	+	0.212849i	$0.931726\pi$
$564$	7.20723e14			0.531782
$565$	−3.33204e14	+	1.19515e15i	−0.243469	+	0.873282i
$566$	−1.08794e14			−0.0787251
$567$			6.14725e12i			0.00440529i
$568$		−	1.03038e15i		−	0.731275i
$569$	9.59711e14			0.674564			0.337282	−	0.941404i	$-0.390492\pi$
$569$	9.59711e14			0.674564			0.337282	+	0.941404i	$0.390492\pi$
$570$	1.39721e15	+	3.89540e14i	0.972638	+	0.271170i
$571$	−7.89612e14			−0.544397			−0.272198	−	0.962241i	$-0.587751\pi$
$571$	−7.89612e14			−0.544397			−0.272198	+	0.962241i	$0.587751\pi$
$572$		−	6.47631e14i		−	0.442231i
$573$		−	3.93116e14i		−	0.265870i
$574$	3.97782e14			0.266459
$575$	1.22428e15	−	2.02498e15i	0.812284	−	1.34353i
$576$	2.28014e14			0.149844
$577$		−	2.81088e15i		−	1.82968i	−0.403814	−	0.914841i	$-0.632316\pi$
$577$		−	2.81088e15i		−	1.82968i	0.403814	−	0.914841i	$-0.367684\pi$
$578$			5.45720e14i			0.351857i
$579$	−7.93267e14			−0.506626
$580$	5.39599e14	+	1.50439e14i	0.341364	+	0.0951714i
$581$	3.56518e14			0.223415
$582$			1.79909e15i			1.11680i
$583$		−	4.51048e14i		−	0.277361i
$584$	−3.39714e14			−0.206939
$585$	4.69827e14	−	1.68519e15i	0.283518	−	1.01693i
$586$	−2.90605e15			−1.73727
$587$			2.56195e15i			1.51727i	0.651518	+	0.758633i	$0.274132\pi$
$587$			2.56195e15i			1.51727i	−0.651518	+	0.758633i	$0.725868\pi$
$588$		−	5.25925e14i		−	0.308566i
$589$	−9.69334e14			−0.563429
$590$	−6.52409e13	+	2.34008e14i	−0.0375694	+	0.134755i
$591$	−4.78732e13			−0.0273125
$592$		−	2.44819e14i		−	0.138381i
$593$			1.54154e15i			0.863282i	0.902046	+	0.431641i	$0.142065\pi$
$593$			1.54154e15i			0.863282i	−0.902046	+	0.431641i	$0.857935\pi$
$594$	−9.15566e14			−0.508001
$595$	−7.28931e14	−	2.03224e14i	−0.400722	−	0.111720i
$596$	−2.61118e14			−0.142227
$597$		−	1.92232e15i		−	1.03745i
$598$			6.41742e15i			3.43166i
$599$	2.51856e15			1.33446			0.667228	−	0.744853i	$-0.267480\pi$
$599$	2.51856e15			1.33446			0.667228	+	0.744853i	$0.267480\pi$
$600$	−4.40360e14	−	2.66237e14i	−0.231194	−	0.139777i
$601$	6.35251e14			0.330473			0.165237	−	0.986254i	$-0.447161\pi$
$601$	6.35251e14			0.330473			0.165237	+	0.986254i	$0.447161\pi$
$602$			7.78578e14i			0.401348i
$603$		−	1.76895e14i		−	0.0903590i
$604$	−1.19994e15			−0.607376
$605$	1.61998e15	+	4.51647e14i	0.812559	+	0.226540i
$606$	−1.96213e15			−0.975280
$607$		−	6.13569e14i		−	0.302222i	−0.988517	−	0.151111i	$-0.951715\pi$
$607$		−	6.13569e14i		−	0.302222i	0.988517	−	0.151111i	$-0.0482850\pi$
$608$		−	2.97311e15i		−	1.45125i
$609$	−3.33593e14			−0.161370
$610$	6.70107e14	−	2.40356e15i	0.321240	−	1.15223i
$611$	−4.69045e15			−2.22837
$612$			7.42035e14i			0.349375i
$613$		−	1.97983e14i		−	0.0923837i	−0.998933	−	0.0461918i	$-0.985291\pi$
$613$		−	1.97983e14i		−	0.0923837i	0.998933	−	0.0461918i	$-0.0147086\pi$
$614$	4.55044e15			2.10440
$615$	−1.52722e14	+	5.47789e14i	−0.0699986	+	0.251073i
$616$	−1.86720e14			−0.0848198
$617$		−	3.12681e13i		−	0.0140778i	−0.999975	−	0.00703888i	$-0.997759\pi$
$617$		−	3.12681e13i		−	0.0140778i	0.999975	−	0.00703888i	$-0.00224056\pi$
$618$		−	2.27711e15i		−	1.01612i
$619$	−3.56400e15			−1.57630			−0.788150	−	0.615483i	$-0.788961\pi$
$619$	−3.56400e15			−1.57630			−0.788150	+	0.615483i	$0.788961\pi$
$620$	−6.39566e14	−	1.78310e14i	−0.280369	−	0.0781664i
$621$	3.60312e15			1.56558
$622$		−	3.48744e15i		−	1.50197i
$623$			1.35777e15i			0.579617i
$624$	3.01992e15			1.27785
$625$	1.10777e15	+	2.11120e15i	0.464634	+	0.885503i
$626$	9.49121e14			0.394605
$627$			7.52442e14i			0.310100i
$628$		−	9.28930e14i		−	0.379494i
$629$	2.37850e14			0.0963219
$630$	9.38075e14	+	2.61533e14i	0.376586	+	0.104992i
$631$	2.31127e15			0.919792			0.459896	−	0.887973i	$-0.347887\pi$
$631$	2.31127e15			0.919792			0.459896	+	0.887973i	$0.347887\pi$
$632$		−	3.32637e14i		−	0.131228i
$633$		−	3.77725e14i		−	0.147726i
$634$	1.10575e15			0.428712
$635$	−7.21454e14	+	2.58773e15i	−0.277302	+	0.994635i
$636$	−7.45288e14			−0.283995
$637$			3.42271e15i			1.29301i
$638$			7.31687e14i			0.274039i
$639$	−2.78775e15			−1.03514
$640$	−6.03844e14	+	2.16589e15i	−0.222298	+	0.797344i
$641$	−1.11524e15			−0.407051			−0.203526	−	0.979070i	$-0.565240\pi$
$641$	−1.11524e15			−0.407051			−0.203526	+	0.979070i	$0.565240\pi$
$642$			1.55141e15i			0.561415i
$643$		−	2.77877e15i		−	0.996992i	−0.866892	−	0.498496i	$-0.833886\pi$
$643$		−	2.77877e15i		−	0.996992i	0.866892	−	0.498496i	$-0.166114\pi$
$644$	−1.41875e15			−0.504700
$645$	−1.07219e15	−	2.98923e14i	−0.378174	−	0.105434i
$646$	4.00392e15			1.40025
$647$		−	4.60671e15i		−	1.59741i	−0.601720	−	0.798707i	$-0.705518\pi$
$647$		−	4.60671e15i		−	1.59741i	0.601720	−	0.798707i	$-0.294482\pi$
$648$			1.15389e13i			0.00396737i
$649$	−1.26020e14			−0.0429630
$650$	−5.53324e15	−	3.34534e15i	−1.87049	−	1.13088i
$651$	3.95395e14			0.132537
$652$			2.68053e15i			0.890960i
$653$		−	2.14847e15i		−	0.708119i	−0.935223	−	0.354060i	$-0.884801\pi$
$653$		−	2.14847e15i		−	0.708119i	0.935223	−	0.354060i	$-0.115199\pi$
$654$	−2.42118e15			−0.791316
$655$	2.29611e15	+	6.40152e14i	0.744160	+	0.207470i
$656$	1.61576e15			0.519285
$657$			9.19116e14i			0.292928i
$658$		−	2.61098e15i		−	0.825204i
$659$	−5.35253e15			−1.67760			−0.838802	−	0.544437i	$-0.816743\pi$
$659$	−5.35253e15			−1.67760			−0.838802	+	0.544437i	$0.816743\pi$
$660$	−1.38412e14	+	4.96461e14i	−0.0430212	+	0.154310i
$661$	−1.21133e15			−0.373383			−0.186691	−	0.982419i	$-0.559776\pi$
$661$	−1.21133e15			−0.373383			−0.186691	+	0.982419i	$0.559776\pi$
$662$			4.11786e15i			1.25879i
$663$			2.93395e15i			0.889465i
$664$	6.69216e14			0.201206
$665$	5.60459e14	−	2.01027e15i	0.167118	−	0.599425i
$666$	−3.06094e14			−0.0905204
$667$		−	2.87948e15i		−	0.844544i
$668$			2.58172e14i			0.0750997i
$669$	3.09077e13			0.00891710
$670$	−6.29780e14	−	1.75581e14i	−0.180209	−	0.0502420i
$671$	1.29439e15			0.367359
$672$			1.21274e15i			0.341379i
$673$			1.29501e15i			0.361569i	0.983523	+	0.180784i	$0.0578636\pi$
$673$			1.29501e15i			0.361569i	−0.983523	+	0.180784i	$0.942136\pi$
$674$	6.36783e15			1.76344
$675$	−1.87827e15	+	3.10669e15i	−0.515926	+	0.853349i
$676$	4.54627e15			1.23865
$677$		−	3.19069e15i		−	0.862276i	−0.902286	−	0.431138i	$-0.858112\pi$
$677$		−	3.19069e15i		−	0.862276i	0.902286	−	0.431138i	$-0.141888\pi$
$678$			2.67780e15i			0.717818i
$679$	2.58847e15			0.688271
$680$	−1.36827e15	−	3.81470e14i	−0.360887	−	0.100615i
$681$	8.13037e14			0.212716
$682$		−	8.67240e14i		−	0.225074i
$683$			8.62453e14i			0.222035i	0.993818	+	0.111017i	$0.0354110\pi$
$683$			8.62453e14i			0.222035i	−0.993818	+	0.111017i	$0.964589\pi$
$684$	−2.04641e15			−0.522617
$685$	9.19596e14	−	3.29843e15i	0.232969	−	0.835621i
$686$	−4.40601e15			−1.10729
$687$		−	6.21242e14i		−	0.154881i
$688$			3.16253e15i			0.782164i
$689$	4.85032e15			1.19005
$690$	1.37154e15	−	4.91947e15i	0.333839	−	1.19742i
$691$	6.24276e15			1.50747			0.753733	−	0.657181i	$-0.228251\pi$
$691$	6.24276e15			1.50747			0.753733	+	0.657181i	$0.228251\pi$
$692$		−	5.49396e13i		−	0.0131614i
$693$			5.05182e14i			0.120065i
$694$	−4.51343e15			−1.06422
$695$	−1.44602e15	−	4.03147e14i	−0.338265	−	0.0943077i
$696$	−6.26183e14			−0.145328
$697$			1.56977e15i			0.361456i
$698$			1.73055e14i			0.0395348i
$699$	−2.03568e15			−0.461407
$700$	7.39580e14	−	1.22328e15i	0.166321	−	0.275097i
$701$	−7.04856e14			−0.157272			−0.0786360	−	0.996903i	$-0.525056\pi$
$701$	−7.04856e14			−0.157272			−0.0786360	+	0.996903i	$0.525056\pi$
$702$		−	9.84549e15i		−	2.17963i
$703$			6.55951e14i			0.144084i
$704$	4.37164e14			0.0952785
$705$	3.59560e15	+	1.00245e15i	0.777556	+	0.216781i
$706$	−7.95718e15			−1.70739
$707$			2.82306e15i			0.601053i
$708$			2.08229e14i			0.0439905i
$709$	−2.29698e15			−0.481508			−0.240754	−	0.970586i	$-0.577395\pi$
$709$	−2.29698e15			−0.481508			−0.240754	+	0.970586i	$0.577395\pi$
$710$	−2.76704e15	+	9.92489e15i	−0.575565	+	2.06445i
$711$	−8.99968e14			−0.185757
$712$			2.54865e15i			0.522000i
$713$			3.41294e15i			0.693643i
$714$	−1.63321e15			−0.329384
$715$	9.00783e14	−	3.23095e15i	0.180276	−	0.646617i
$716$	−3.46532e15			−0.688211
$717$		−	1.01411e15i		−	0.199863i
$718$		−	7.18588e15i		−	1.40539i
$719$	6.04235e14			0.117273			0.0586364	−	0.998279i	$-0.481325\pi$
$719$	6.04235e14			0.117273			0.0586364	+	0.998279i	$0.481325\pi$
$720$	3.81039e15	+	1.06233e15i	0.733906	+	0.204612i
$721$	−3.27623e15			−0.626225
$722$			4.25243e15i			0.806645i
$723$			2.33703e15i			0.439949i
$724$	3.16279e15			0.590892
$725$	2.48275e15	+	1.50105e15i	0.460335	+	0.278314i
$726$	3.62966e15			0.667904
$727$			5.97716e15i			1.09158i	0.837922	+	0.545790i	$0.183770\pi$
$727$			5.97716e15i			1.09158i	−0.837922	+	0.545790i	$0.816230\pi$
$728$		−	2.00788e15i		−	0.363929i
$729$	−3.37669e15			−0.607420
$730$	3.27222e15	+	9.12288e14i	0.584207	+	0.162876i
$731$	−3.07250e15			−0.544436
$732$		−	2.13878e15i		−	0.376145i
$733$		−	6.83099e15i		−	1.19237i	−0.802846	−	0.596186i	$-0.796682\pi$
$733$		−	6.83099e15i		−	1.19237i	0.802846	−	0.596186i	$-0.203318\pi$
$734$	7.42764e15			1.28683
$735$	7.31504e14	−	2.62378e15i	0.125787	−	0.451177i
$736$	−1.04680e16			−1.78664
$737$		−	3.39156e14i		−	0.0574550i
$738$		−	2.02016e15i		−	0.339685i
$739$	7.02991e15			1.17329			0.586645	−	0.809844i	$-0.300449\pi$
$739$	7.02991e15			1.17329			0.586645	+	0.809844i	$0.300449\pi$
$740$	−1.20662e14	+	4.32795e14i	−0.0199893	+	0.0716982i
$741$	−8.09135e15			−1.33052
$742$			2.69997e15i			0.440695i
$743$		−	8.68230e15i		−	1.40668i	−0.710852	−	0.703342i	$-0.751690\pi$
$743$		−	8.68230e15i		−	1.40668i	0.710852	−	0.703342i	$-0.248310\pi$
$744$	7.42191e14			0.119362
$745$	−1.30268e15	−	3.63186e14i	−0.207960	−	0.0579788i
$746$	1.49187e16			2.36411
$747$		−	1.81060e15i		−	0.284813i
$748$			1.42268e15i			0.222151i
$749$	2.23212e15			0.345993
$750$	3.52670e15	+	3.74704e15i	0.542665	+	0.576569i
$751$	9.54817e15			1.45848			0.729240	−	0.684258i	$-0.239874\pi$
$751$	9.54817e15			1.45848			0.729240	+	0.684258i	$0.239874\pi$
$752$		−	1.06056e16i		−	1.60819i
$753$		−	3.16979e15i		−	0.477154i
$754$	−7.86816e15			−1.17579
$755$	−5.98638e15	−	1.66899e15i	−0.888088	−	0.247597i
$756$	2.17662e15			0.320562
$757$			1.23655e16i			1.80794i	0.427592	+	0.903972i	$0.359362\pi$
$757$			1.23655e16i			1.80794i	−0.427592	+	0.903972i	$0.640638\pi$
$758$			9.55476e15i			1.38688i
$759$	2.64928e15			0.381767
$760$	1.05203e15	−	3.77345e15i	0.150506	−	0.539838i
$761$	−9.99982e15			−1.42029			−0.710144	−	0.704056i	$-0.751370\pi$
$761$	−9.99982e15			−1.42029			−0.710144	+	0.704056i	$0.751370\pi$
$762$			5.79796e15i			0.817566i
$763$			3.48352e15i			0.487679i
$764$	2.04985e15			0.284910
$765$	−1.03209e15	+	3.70193e15i	−0.142423	+	0.510846i
$766$	−7.29701e15			−0.999739
$767$		−	1.35515e15i		−	0.184337i
$768$			5.94927e15i			0.803483i
$769$	−1.04255e16			−1.39799			−0.698993	−	0.715129i	$-0.746368\pi$
$769$	−1.04255e16			−1.39799			−0.698993	+	0.715129i	$0.746368\pi$
$770$	1.79854e15	+	5.01429e14i	0.239453	+	0.0667591i
$771$	4.57421e15			0.604668
$772$		−	4.13638e15i		−	0.542907i
$773$			9.17342e14i			0.119549i	0.998212	+	0.0597743i	$0.0190381\pi$
$773$			9.17342e14i			0.119549i	−0.998212	+	0.0597743i	$0.980962\pi$
$774$	3.95406e15			0.511645
$775$	−2.94271e15	−	1.77913e15i	−0.378084	−	0.228585i
$776$	4.85879e15			0.619853
$777$		−	2.67565e14i		−	0.0338932i
$778$		−	2.70138e15i		−	0.339780i
$779$	−4.32915e15			−0.540688
$780$	−5.33866e15	−	1.48841e15i	−0.662082	−	0.184587i
$781$	−5.34486e15			−0.658196
$782$		−	1.40974e16i		−	1.72386i
$783$			4.41765e15i			0.536416i
$784$	−7.73911e15			−0.933152
$785$	1.29204e15	−	4.63432e15i	0.154701	−	0.554885i
$786$	5.14458e15			0.611682
$787$		−	1.13643e16i		−	1.34178i	−0.741558	−	0.670889i	$-0.765913\pi$
$787$		−	1.13643e16i		−	1.34178i	0.741558	−	0.670889i	$-0.234087\pi$
$788$		−	2.49628e14i		−	0.0292685i
$789$	8.73312e15			1.01682
$790$	−8.93282e14	+	3.20405e15i	−0.103286	+	0.370468i
$791$	3.85273e15			0.442382
$792$			9.48271e14i			0.108129i
$793$			1.39191e16i			1.57620i
$794$	−1.98636e16			−2.23381
$795$	−3.71815e15	−	1.03661e15i	−0.415249	−	0.115770i
$796$	1.00237e16			1.11175
$797$			3.42959e15i			0.377765i	0.982000	+	0.188883i	$0.0604866\pi$
$797$			3.42959e15i			0.377765i	−0.982000	+	0.188883i	$0.939513\pi$
$798$		−	4.50412e15i		−	0.492713i
$799$	1.03037e16			1.11940
$800$	5.45688e15	−	9.02577e15i	0.588776	−	0.973844i
$801$	6.89552e15			0.738904
$802$			1.87016e16i			1.99030i
$803$			1.76219e15i			0.186259i
$804$	−5.60404e14			−0.0588292
$805$	−7.07797e15	−	1.97332e15i	−0.737958	−	0.205741i
$806$	9.32582e15			0.965705
$807$			2.92105e15i			0.300424i
$808$			5.29912e15i			0.541304i
$809$	1.70981e16			1.73472			0.867361	−	0.497679i	$-0.165814\pi$
$809$	1.70981e16			1.73472			0.867361	+	0.497679i	$0.165814\pi$
$810$	3.09873e13	−	1.11146e14i	0.00312260	−	0.0112002i
$811$	1.35100e16			1.35220			0.676102	−	0.736808i	$-0.263668\pi$
$811$	1.35100e16			1.35220			0.676102	+	0.736808i	$0.263668\pi$
$812$		−	1.73948e15i		−	0.172926i
$813$		−	8.78723e15i		−	0.867669i
$814$	−5.86864e14			−0.0575576
$815$	−3.72832e15	+	1.33728e16i	−0.363200	+	1.30274i
$816$	−6.63398e15			−0.641916
$817$		−	8.47344e15i		−	0.814402i
$818$		−	6.18779e15i		−	0.590734i
$819$	−5.43245e15			−0.515150
$820$	−2.85637e15	−	7.96350e14i	−0.269053	−	0.0750115i
$821$	−1.00494e16			−0.940270			−0.470135	−	0.882595i	$-0.655795\pi$
$821$	−1.00494e16			−0.940270			−0.470135	+	0.882595i	$0.655795\pi$
$822$		−	7.39033e15i		−	0.686861i
$823$		−	1.68296e16i		−	1.55373i	−0.629667	−	0.776865i	$-0.716809\pi$
$823$		−	1.68296e16i		−	1.55373i	0.629667	−	0.776865i	$-0.283191\pi$
$824$	−6.14977e15			−0.563974
$825$	−1.38104e15	+	2.28427e15i	−0.125809	+	0.208090i
$826$	7.54358e14			0.0682633
$827$			1.10226e16i			0.990837i	0.868654	+	0.495419i	$0.164985\pi$
$827$			1.10226e16i			0.990837i	−0.868654	+	0.495419i	$0.835015\pi$
$828$			7.20522e15i			0.643399i
$829$	3.70605e15			0.328747			0.164373	−	0.986398i	$-0.447440\pi$
$829$	3.70605e15			0.328747			0.164373	+	0.986398i	$0.447440\pi$
$830$	−6.44608e15	−	1.79715e15i	−0.568023	−	0.158364i
$831$	−4.56516e15			−0.399623
$832$			4.70102e15i			0.408803i
$833$		−	7.51881e15i		−	0.649534i
$834$	−3.23989e15			−0.278046
$835$	−3.59088e14	+	1.28799e15i	−0.0306144	+	0.109809i
$836$	−3.92351e15			−0.332307
$837$		−	5.23607e15i		−	0.440570i
$838$		−	1.52481e16i		−	1.27460i
$839$	−4.81130e15			−0.399550			−0.199775	−	0.979842i	$-0.564021\pi$
$839$	−4.81130e15			−0.399550			−0.199775	+	0.979842i	$0.564021\pi$
$840$	−4.29127e14	+	1.53920e15i	−0.0354038	+	0.126987i
$841$	−8.67008e15			−0.710633
$842$			2.58459e16i			2.10463i
$843$		−	3.34614e15i		−	0.270703i
$844$	1.96960e15			0.158305
$845$	2.26808e16	+	6.32337e15i	1.81112	+	0.504936i
$846$	−1.32600e16			−1.05198
$847$		−	5.22224e15i		−	0.411621i
$848$			1.09671e16i			0.858843i
$849$	−4.82969e14			−0.0375774
$850$	1.21551e16	+	7.34885e15i	0.939625	+	0.568088i
$851$	2.30954e15			0.177384
$852$			8.83157e15i			0.673938i
$853$			1.61259e16i			1.22266i	0.791377	+	0.611328i	$0.209365\pi$
$853$			1.61259e16i			1.22266i	−0.791377	+	0.611328i	$0.790635\pi$
$854$	−7.74822e15			−0.583692
$855$	−1.02093e16	−	2.84633e15i	−0.764155	−	0.213045i
$856$	4.18989e15			0.311599
$857$		−	1.14447e16i		−	0.845687i	−0.906203	−	0.422843i	$-0.861032\pi$
$857$		−	1.14447e16i		−	0.845687i	0.906203	−	0.422843i	$-0.138968\pi$
$858$		−	7.23914e15i		−	0.531504i
$859$	−3.58303e14			−0.0261390			−0.0130695	−	0.999915i	$-0.504160\pi$
$859$	−3.58303e14			−0.0261390			−0.0130695	+	0.999915i	$0.504160\pi$
$860$	1.55869e15	−	5.59077e15i	0.112985	−	0.405257i
$861$	1.76588e15			0.127187
$862$		−	2.82505e16i		−	2.02179i
$863$			8.67793e15i			0.617102i	0.951208	+	0.308551i	$0.0998440\pi$
$863$			8.67793e15i			0.617102i	−0.951208	+	0.308551i	$0.900156\pi$
$864$	1.60599e16			1.13479
$865$	7.64149e13	−	2.74087e14i	0.00536524	−	0.0192442i
$866$	−7.96205e15			−0.555490
$867$			2.42262e15i			0.167950i
$868$			2.06173e15i			0.142028i
$869$	−1.72548e15			−0.118114
$870$	6.03157e15	+	1.68159e15i	0.410275	+	0.114384i
$871$	3.64709e15			0.246517
$872$			6.53887e15i			0.439200i
$873$		−	1.31457e16i		−	0.877418i
$874$	3.88783e16			2.57866
$875$	5.39112e15	−	5.07411e15i	0.355332	−	0.334438i
$876$	2.91175e15			0.190714
$877$		−	2.73873e16i		−	1.78259i	−0.453421	−	0.891296i	$-0.649797\pi$
$877$		−	2.73873e16i		−	1.78259i	0.453421	−	0.891296i	$-0.350203\pi$
$878$		−	9.93258e15i		−	0.642454i
$879$	−1.29008e16			−0.829238
$880$	7.30553e15	+	2.03677e15i	0.466656	+	0.130103i
$881$	−1.35191e16			−0.858184			−0.429092	−	0.903261i	$-0.641166\pi$
$881$	−1.35191e16			−0.858184			−0.429092	+	0.903261i	$0.641166\pi$
$882$			9.67611e15i			0.610412i
$883$			2.98350e16i			1.87043i	0.354076	+	0.935217i	$0.384795\pi$
$883$			2.98350e16i			1.87043i	−0.354076	+	0.935217i	$0.615205\pi$
$884$	−1.52987e16			−0.953163
$885$	−2.89624e14	+	1.03883e15i	−0.0179328	+	0.0643217i
$886$	−1.64499e16			−1.01223
$887$			4.26536e15i			0.260841i	0.991459	+	0.130421i	$0.0416327\pi$
$887$			4.26536e15i			0.260841i	−0.991459	+	0.130421i	$0.958367\pi$
$888$		−	5.02242e14i		−	0.0305240i
$889$	8.34193e15			0.503856
$890$	6.84429e15	−	2.45493e16i	0.410850	−	1.47365i
$891$	5.98556e13			0.00357090
$892$			1.61164e14i			0.00955568i
$893$			2.84159e16i			1.67447i
$894$	−2.91874e15			−0.170938
$895$	−1.72881e16	−	4.81988e15i	−1.00628	−	0.280550i
$896$	6.98205e15			0.403914
$897$			2.84889e16i			1.63801i
$898$		−	9.48253e15i		−	0.541881i
$899$	−4.18448e15			−0.237664
$900$	−6.21249e15	−	3.75601e15i	−0.350697	−	0.212028i
$901$	−1.06549e16			−0.597810
$902$		−	3.87319e15i		−	0.215990i
$903$			3.45635e15i			0.191573i
$904$	7.23191e15			0.398406
$905$	1.57788e16	+	4.39909e15i	0.863985	+	0.240877i
$906$	−1.34128e16			−0.729988
$907$		−	8.90270e14i		−	0.0481595i	−0.999710	−	0.0240797i	$-0.992334\pi$
$907$		−	8.90270e14i		−	0.0481595i	0.999710	−	0.0240797i	$-0.00766556\pi$
$908$			4.23947e15i			0.227950i
$909$	1.43371e16			0.766231
$910$	−5.39209e15	+	1.93405e16i	−0.286437	+	1.02740i
$911$	−1.49747e16			−0.790690			−0.395345	−	0.918533i	$-0.629375\pi$
$911$	−1.49747e16			−0.790690			−0.395345	+	0.918533i	$0.629375\pi$
$912$		−	1.82954e16i		−	0.960219i
$913$		−	3.47141e15i		−	0.181099i
$914$	−1.65150e16			−0.856398
$915$	2.97481e15	−	1.06701e16i	0.153336	−	0.549989i
$916$	3.23938e15			0.165973
$917$		−	7.40186e15i		−	0.376972i
$918$			2.16280e16i			1.09492i
$919$	−3.01647e16			−1.51797			−0.758987	−	0.651106i	$-0.774305\pi$
$919$	−3.01647e16			−1.51797			−0.758987	+	0.651106i	$0.774305\pi$
$920$	−1.32860e16	−	3.70410e15i	−0.664600	−	0.185289i
$921$	2.02008e16			1.00448
$922$			2.20083e16i			1.08784i
$923$		−	5.74756e16i		−	2.82406i
$924$	1.60041e15			0.0781693
$925$	−1.20394e15	+	1.99134e15i	−0.0584556	+	0.0966864i
$926$	4.40035e16			2.12386
$927$			1.66386e16i			0.798320i
$928$		−	1.28345e16i		−	0.612159i
$929$	−5.56333e15			−0.263784			−0.131892	−	0.991264i	$-0.542105\pi$
$929$	−5.56333e15			−0.263784			−0.131892	+	0.991264i	$0.542105\pi$
$930$	−7.14899e15	−	1.99312e15i	−0.336968	−	0.0939459i
$931$	2.07356e16			0.971614
$932$		−	1.06147e16i		−	0.494450i
$933$		−	1.54818e16i		−	0.716924i
$934$	1.62800e16			0.749456
$935$	−1.97879e15	+	7.09758e15i	−0.0905598	+	0.324823i
$936$	−1.01972e16			−0.463941
$937$		−	8.56747e15i		−	0.387512i	−0.981050	−	0.193756i	$-0.937933\pi$
$937$		−	8.56747e15i		−	0.387512i	0.981050	−	0.193756i	$-0.0620670\pi$
$938$			2.03019e15i			0.0912894i
$939$	4.21344e15			0.188354
$940$	−5.22712e15	+	1.87488e16i	−0.232305	+	0.833239i
$941$	3.30328e16			1.45950			0.729748	−	0.683717i	$-0.239638\pi$
$941$	3.30328e16			1.45950			0.729748	+	0.683717i	$0.239638\pi$
$942$		−	1.03835e16i		−	0.456102i
$943$			1.52426e16i			0.665646i
$944$	3.06414e15			0.133034
$945$	1.08589e16	+	3.02744e15i	0.468717	+	0.130677i
$946$	7.58099e15			0.325330
$947$			1.46596e16i			0.625455i	0.949843	+	0.312728i	$0.101243\pi$
$947$			1.46596e16i			0.625455i	−0.949843	+	0.312728i	$0.898757\pi$
$948$			2.85109e15i			0.120939i
$949$	−1.89496e16			−0.799164
$950$	−2.02669e16	+	3.35217e16i	−0.849781	+	1.40555i
$951$	4.90876e15			0.204635
$952$			4.41081e15i			0.182816i
$953$		−	2.55668e16i		−	1.05357i	−0.849997	−	0.526787i	$-0.823397\pi$
$953$		−	2.55668e16i		−	1.05357i	0.849997	−	0.526787i	$-0.176603\pi$
$954$	1.37120e16			0.561804
$955$	1.02264e16	+	2.85111e15i	0.416587	+	0.116144i
$956$	5.28796e15			0.214176
$957$			3.24819e15i			0.130805i
$958$			1.83042e16i			0.732891i
$959$	−1.06330e16			−0.423304
$960$	1.00471e15	−	3.60371e15i	0.0397692	−	0.142645i
$961$	−2.04488e16			−0.804802
$962$		−	6.31081e15i		−	0.246957i
$963$		−	1.13360e16i		−	0.441077i
$964$	−1.21861e16			−0.471456
$965$	5.75325e15	−	2.06359e16i	0.221316	−	0.793823i
$966$	−1.58586e16			−0.606584
$967$		−	1.34808e15i		−	0.0512710i	−0.999671	−	0.0256355i	$-0.991839\pi$
$967$		−	1.34808e15i		−	0.0512710i	0.999671	−	0.0256355i	$-0.00816092\pi$
$968$		−	9.80260e15i		−	0.370703i
$969$	1.77746e16			0.668374
$970$	−4.68012e16	−	1.30481e16i	−1.74990	−	0.487868i
$971$	7.16461e15			0.266371			0.133185	−	0.991091i	$-0.457479\pi$
$971$	7.16461e15			0.266371			0.133185	+	0.991091i	$0.457479\pi$
$972$		−	1.78690e16i		−	0.660594i
$973$			4.66145e15i			0.171357i
$974$	−2.37018e16			−0.866378
$975$	−2.45637e16	−	1.48510e16i	−0.892831	−	0.539796i
$976$	−3.14727e16			−1.13752
$977$			2.98604e16i			1.07319i	0.843841	+	0.536594i	$0.180289\pi$
$977$			2.98604e16i			1.07319i	−0.843841	+	0.536594i	$0.819711\pi$
$978$			2.99626e16i			1.07082i
$979$	1.32205e16			0.469834
$980$	1.36813e16	+	3.81433e15i	0.483487	+	0.134795i
$981$	1.76913e16			0.621699
$982$		−	4.10676e16i		−	1.43511i
$983$			3.75516e16i			1.30492i	0.757823	+	0.652460i	$0.226263\pi$
$983$			3.75516e16i			1.30492i	−0.757823	+	0.652460i	$0.773737\pi$
$984$	3.31470e15			0.114544
$985$	3.47206e14	−	1.24537e15i	0.0119313	−	0.0427955i
$986$	1.72843e16			0.590649
$987$		−	1.15909e16i		−	0.393890i
$988$		−	4.21912e16i		−	1.42580i
$989$	−2.98342e16			−1.00262
$990$	2.54654e15	−	9.13401e15i	0.0851054	−	0.305258i
$991$	2.73463e15			0.0908851			0.0454426	−	0.998967i	$-0.485530\pi$
$991$	2.73463e15			0.0908851			0.0454426	+	0.998967i	$0.485530\pi$
$992$			1.52122e16i			0.502780i
$993$			1.82805e16i			0.600850i
$994$	3.19943e16			1.04580
$995$	5.00070e16	+	1.39418e16i	1.62556	+	0.453204i
$996$	−5.73598e15			−0.185430
$997$			4.78031e16i			1.53686i	0.639937	+	0.768428i	$0.278961\pi$
$997$			4.78031e16i			1.53686i	−0.639937	+	0.768428i	$0.721039\pi$
$998$			5.64984e16i			1.80642i
$999$	−3.54326e15			−0.112666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.12.b.a.4.4	yes	4
3.2	odd	2		45.12.b.b.19.1		4
4.3	odd	2		80.12.c.a.49.2		4
5.2	odd	4		25.12.a.e.1.1		4
5.3	odd	4		25.12.a.e.1.4		4
5.4	even	2	inner	5.12.b.a.4.1	✓	4
15.2	even	4		225.12.a.r.1.4		4
15.8	even	4		225.12.a.r.1.1		4
15.14	odd	2		45.12.b.b.19.4		4
20.19	odd	2		80.12.c.a.49.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.12.b.a.4.1	✓	4	5.4	even	2	inner
5.12.b.a.4.4	yes	4	1.1	even	1	trivial
25.12.a.e.1.1		4	5.2	odd	4
25.12.a.e.1.4		4	5.3	odd	4
45.12.b.b.19.1		4	3.2	odd	2
45.12.b.b.19.4		4	15.14	odd	2
80.12.c.a.49.2		4	4.3	odd	2
80.12.c.a.49.3		4	20.19	odd	2
225.12.a.r.1.1		4	15.8	even	4
225.12.a.r.1.4		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)

\(f(q)\)	\(=\)	\(q+58.2855i q^{2} +258.747i q^{3} -1349.20 q^{4} +(-6731.01 - 1876.59i) q^{5} -15081.2 q^{6} +21698.4i q^{7} +40729.8i q^{8} +110197. q^{9} +O(q^{10})\)	\(q+58.2855i q^{2} +258.747i q^{3} -1349.20 q^{4} +(-6731.01 - 1876.59i) q^{5} -15081.2 q^{6} +21698.4i q^{7} +40729.8i q^{8} +110197. q^{9} +(109378. - 392321. i) q^{10} +211277. q^{11} -349103. i q^{12} +2.27195e6i q^{13} -1.26470e6 q^{14} +(485563. - 1.74163e6i) q^{15} -5.13712e6 q^{16} -4.99089e6i q^{17} +6.42288e6i q^{18} +1.37640e7 q^{19} +(9.08150e6 + 2.53190e6i) q^{20} -5.61440e6 q^{21} +1.23144e7i q^{22} -4.84620e7i q^{23} -1.05387e7 q^{24} +(4.17849e7 + 2.52627e7i) q^{25} -1.32422e8 q^{26} +7.43495e7i q^{27} -2.92755e7i q^{28} +5.94174e7 q^{29} +(1.01512e8 + 2.83013e7i) q^{30} -7.04251e7 q^{31} -2.16005e8i q^{32} +5.46673e7i q^{33} +2.90897e8 q^{34} +(4.07190e7 - 1.46052e8i) q^{35} -1.48678e8 q^{36} +4.76568e7i q^{37} +8.02244e8i q^{38} -5.87861e8 q^{39} +(7.64332e7 - 2.74153e8i) q^{40} -3.14526e8 q^{41} -3.27238e8i q^{42} -6.15622e8i q^{43} -2.85055e8 q^{44} +(-7.41736e8 - 2.06794e8i) q^{45} +2.82463e9 q^{46} +2.06450e9i q^{47} -1.32922e9i q^{48} +1.50651e9 q^{49} +(-1.47245e9 + 2.43546e9i) q^{50} +1.29138e9 q^{51} -3.06532e9i q^{52} -2.13487e9i q^{53} -4.33350e9 q^{54} +(-1.42211e9 - 3.96480e8i) q^{55} -8.83771e8 q^{56} +3.56141e9i q^{57} +3.46317e9i q^{58} -5.96471e8 q^{59} +(-6.55123e8 + 2.34981e9i) q^{60} +6.12652e9 q^{61} -4.10476e9i q^{62} +2.39109e9i q^{63} +2.06916e9 q^{64} +(4.26353e9 - 1.52925e10i) q^{65} -3.18631e9 q^{66} -1.60527e9i q^{67} +6.73373e9i q^{68} +1.25394e10 q^{69} +(8.51273e9 + 2.37333e9i) q^{70} -2.52979e10 q^{71} +4.48829e9i q^{72} +8.34067e9i q^{73} -2.77770e9 q^{74} +(-6.53667e9 + 1.08117e10i) q^{75} -1.85705e10 q^{76} +4.58436e9i q^{77} -3.42638e10i q^{78} -8.16692e9 q^{79} +(3.45780e10 + 9.64029e9i) q^{80} +2.83305e8 q^{81} -1.83323e10i q^{82} -1.64306e10i q^{83} +7.57497e9 q^{84} +(-9.36587e9 + 3.35938e10i) q^{85} +3.58818e10 q^{86} +1.53741e10i q^{87} +8.60525e9i q^{88} +6.25746e10 q^{89} +(1.20531e10 - 4.32325e10i) q^{90} -4.92977e10 q^{91} +6.53850e10i q^{92} -1.82223e10i q^{93} -1.20331e11 q^{94} +(-9.26459e10 - 2.58295e10i) q^{95} +5.58908e10 q^{96} -1.19293e11i q^{97} +8.78075e10i q^{98} +2.32820e10 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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