LMFDB - Embedded newform 10.16.b.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,16,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	10.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:	$14.2693505100$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4 x^{7} + 8 x^{6} + 6172534 x^{5} + 23752924445 x^{4} + 1095295465934 x^{3} + \cdots + 59\!\cdots\!64 $ x^8 - 4x^7 + 8x^6 + 6172534x^5 + 23752924445x^4 + 1095295465934x^3 + 14478882731282x^2 - 41384481648202964*x + 59143904715457383364
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{38}\cdot 3^{2}\cdot 5^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.1
Root			$-249.000 + 249.000i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.16.b.a.9.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-128.000i q^{2} -5042.00i q^{3} -16384.0 q^{4} +(79524.6 - 155542. i) q^{5} -645376. q^{6} -3.81841e6i q^{7} +2.09715e6i q^{8} -1.10729e7 q^{9} +O(q^{10})$	\(q-128.000i q^{2} -5042.00i q^{3} -16384.0 q^{4} +(79524.6 - 155542. i) q^{5} -645376. q^{6} -3.81841e6i q^{7} +2.09715e6i q^{8} -1.10729e7 q^{9} +(-1.99094e7 - 1.01791e7i) q^{10} +6.58816e7 q^{11} +8.26082e7i q^{12} +2.98243e7i q^{13} -4.88757e8 q^{14} +(-7.84245e8 - 4.00963e8i) q^{15} +2.68435e8 q^{16} +2.71990e9i q^{17} +1.41733e9i q^{18} -2.59055e8 q^{19} +(-1.30293e9 + 2.54841e9i) q^{20} -1.92524e10 q^{21} -8.43285e9i q^{22} +8.56893e9i q^{23} +1.05738e10 q^{24} +(-1.78693e10 - 2.47389e10i) q^{25} +3.81751e9 q^{26} -1.65177e10i q^{27} +6.25609e10i q^{28} +1.46270e11 q^{29} +(-5.13233e10 + 1.00383e11i) q^{30} +1.80940e11 q^{31} -3.43597e10i q^{32} -3.32175e11i q^{33} +3.48148e11 q^{34} +(-5.93925e11 - 3.03658e11i) q^{35} +1.81418e11 q^{36} -1.52555e11i q^{37} +3.31590e10i q^{38} +1.50374e11 q^{39} +(3.26196e11 + 1.66775e11i) q^{40} -1.17421e12 q^{41} +2.46431e12i q^{42} +8.75693e11i q^{43} -1.07940e12 q^{44} +(-8.80567e11 + 1.72230e12i) q^{45} +1.09682e12 q^{46} -5.72415e12i q^{47} -1.35345e12i q^{48} -9.83271e12 q^{49} +(-3.16658e12 + 2.28726e12i) q^{50} +1.37138e13 q^{51} -4.88641e11i q^{52} +8.50996e12i q^{53} -2.11426e12 q^{54} +(5.23921e12 - 1.02474e13i) q^{55} +8.00779e12 q^{56} +1.30616e12i q^{57} -1.87225e13i q^{58} +7.18836e12 q^{59} +(1.28491e13 + 6.56938e12i) q^{60} +5.57263e12 q^{61} -2.31603e13i q^{62} +4.22809e13i q^{63} -4.39805e12 q^{64} +(4.63894e12 + 2.37176e12i) q^{65} -4.25184e13 q^{66} -3.26451e12i q^{67} -4.45629e13i q^{68} +4.32046e13 q^{69} +(-3.88682e13 + 7.60224e13i) q^{70} -5.83158e13 q^{71} -2.32215e13i q^{72} +6.27971e13i q^{73} -1.95270e13 q^{74} +(-1.24734e14 + 9.00968e13i) q^{75} +4.24436e12 q^{76} -2.51563e14i q^{77} -1.92479e13i q^{78} +1.09818e14 q^{79} +(2.13472e13 - 4.17531e13i) q^{80} -2.42166e14 q^{81} +1.50298e14i q^{82} +2.82120e14i q^{83} +3.15432e14 q^{84} +(4.23060e14 + 2.16299e14i) q^{85} +1.12089e14 q^{86} -7.37491e14i q^{87} +1.38164e14i q^{88} -6.26105e13 q^{89} +(2.20455e14 + 1.12713e14i) q^{90} +1.13881e14 q^{91} -1.40393e14i q^{92} -9.12301e14i q^{93} -7.32691e14 q^{94} +(-2.06012e13 + 4.02940e13i) q^{95} -1.73242e14 q^{96} -6.53097e14i q^{97} +1.25859e15i q^{98} -7.29500e14 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 131072 q^{4} + 251400 q^{5} - 53248 q^{6} - 43491176 q^{9}+O(q^{10}) $ 8 * q - 131072 * q^4 + 251400 * q^5 - 53248 * q^6 - 43491176 * q^9	\( 8 q - 131072 q^{4} + 251400 q^{5} - 53248 q^{6} - 43491176 q^{9} + 4403200 q^{10} + 95435616 q^{11} - 499347456 q^{14} + 5448800 q^{15} + 2147483648 q^{16} + 6479216160 q^{19} - 4118937600 q^{20} - 14760325504 q^{21} + 872415232 q^{24} - 2241855000 q^{25} + 66288525312 q^{26} - 244549636560 q^{29} - 32701542400 q^{30} + 522311705216 q^{31} + 322563211264 q^{34} - 1829607146400 q^{35} + 712559427584 q^{36} - 2307595824192 q^{39} - 72142028800 q^{40} + 6699117519216 q^{41} - 1563617132544 q^{44} - 9090807477800 q^{45} + 12178733699072 q^{46} - 15809163185544 q^{49} - 13485542400000 q^{50} + 40555579650176 q^{51} - 7241111674880 q^{54} - 39746288199200 q^{55} + 8181308719104 q^{56} + 3791808509280 q^{59} - 89273139200 q^{60} + 57800629300816 q^{61} - 35184372088832 q^{64} + 58028394892800 q^{65} - 82398766186496 q^{66} + 59060996328448 q^{69} + 60817223987200 q^{70} - 245426235422784 q^{71} + 53331092987904 q^{74} + 226448486200000 q^{75} - 106155477565440 q^{76} + 624094605411840 q^{79} + 67484673638400 q^{80} - 13\!\cdots\!52 q^{81}+ \cdots + 16\!\cdots\!48 q^{99}+O(q^{100}) \) 8 * q - 131072 * q^4 + 251400 * q^5 - 53248 * q^6 - 43491176 * q^9 + 4403200 * q^10 + 95435616 * q^11 - 499347456 * q^14 + 5448800 * q^15 + 2147483648 * q^16 + 6479216160 * q^19 - 4118937600 * q^20 - 14760325504 * q^21 + 872415232 * q^24 - 2241855000 * q^25 + 66288525312 * q^26 - 244549636560 * q^29 - 32701542400 * q^30 + 522311705216 * q^31 + 322563211264 * q^34 - 1829607146400 * q^35 + 712559427584 * q^36 - 2307595824192 * q^39 - 72142028800 * q^40 + 6699117519216 * q^41 - 1563617132544 * q^44 - 9090807477800 * q^45 + 12178733699072 * q^46 - 15809163185544 * q^49 - 13485542400000 * q^50 + 40555579650176 * q^51 - 7241111674880 * q^54 - 39746288199200 * q^55 + 8181308719104 * q^56 + 3791808509280 * q^59 - 89273139200 * q^60 + 57800629300816 * q^61 - 35184372088832 * q^64 + 58028394892800 * q^65 - 82398766186496 * q^66 + 59060996328448 * q^69 + 60817223987200 * q^70 - 245426235422784 * q^71 + 53331092987904 * q^74 + 226448486200000 * q^75 - 106155477565440 * q^76 + 624094605411840 * q^79 + 67484673638400 * q^80 - 1376711600108152 * q^81 + 241833173057536 * q^84 + 1092463762441600 * q^85 - 8937574699008 * q^86 - 635249793637680 * q^89 + 851824438169600 * q^90 - 976491706492224 * q^91 - 537030386200576 * q^94 - 1859590136604000 * q^95 - 14293651161088 * q^96 + 1626246829353248 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$-1$

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 $

$2$		−	128.000i		−	0.707107i
$2$		−	128.000i		−	0.707107i
$3$		−	5042.00i		−	1.33105i	−0.746376	−	0.665524i	$-0.768208\pi$
$3$		−	5042.00i		−	1.33105i	0.746376	−	0.665524i	$-0.231792\pi$
$4$	−16384.0			−0.500000
$5$	79524.6	−	155542.i	0.455225	−	0.890376i
$5$	79524.6	−	155542.i	0.455225	−	0.890376i
$6$	−645376.			−0.941193
$7$		−	3.81841e6i		−	1.75246i	−0.481895	−	0.876229i	$-0.660052\pi$
$7$		−	3.81841e6i		−	1.75246i	0.481895	−	0.876229i	$-0.339948\pi$
$8$			2.09715e6i			0.353553i
$9$	−1.10729e7			−0.771689
$10$	−1.99094e7	−	1.01791e7i	−0.629591	−	0.321893i
$11$	6.58816e7			1.01934			0.509670	−	0.860370i	$-0.329767\pi$
$11$	6.58816e7			1.01934			0.509670	+	0.860370i	$0.329767\pi$
$12$			8.26082e7i			0.665524i
$13$			2.98243e7i			0.131824i	0.997825	+	0.0659120i	$0.0209957\pi$
$13$			2.98243e7i			0.131824i	−0.997825	+	0.0659120i	$0.979004\pi$
$14$	−4.88757e8			−1.23917
$15$	−7.84245e8	−	4.00963e8i	−1.18513	−	0.605927i
$16$	2.68435e8			0.250000
$17$			2.71990e9i			1.60763i	0.594878	+	0.803816i	$0.297200\pi$
$17$			2.71990e9i			1.60763i	−0.594878	+	0.803816i	$0.702800\pi$
$18$			1.41733e9i			0.545666i
$19$	−2.59055e8			−0.0664875			−0.0332437	−	0.999447i	$-0.510584\pi$
$19$	−2.59055e8			−0.0664875			−0.0332437	+	0.999447i	$0.510584\pi$
$20$	−1.30293e9	+	2.54841e9i	−0.227613	+	0.445188i
$21$	−1.92524e10			−2.33260
$22$		−	8.43285e9i		−	0.720782i
$23$			8.56893e9i			0.524769i	0.964963	+	0.262384i	$0.0845088\pi$
$23$			8.56893e9i			0.524769i	−0.964963	+	0.262384i	$0.915491\pi$
$24$	1.05738e10			0.470597
$25$	−1.78693e10	−	2.47389e10i	−0.585540	−	0.810644i
$26$	3.81751e9			0.0932137
$27$		−	1.65177e10i		−	0.303893i
$28$			6.25609e10i			0.876229i
$29$	1.46270e11			1.57459			0.787297	−	0.616573i	$-0.211480\pi$
$29$	1.46270e11			1.57459			0.787297	+	0.616573i	$0.211480\pi$
$30$	−5.13233e10	+	1.00383e11i	−0.428455	+	0.838016i
$31$	1.80940e11			1.18120			0.590598	−	0.806966i	$-0.298892\pi$
$31$	1.80940e11			1.18120			0.590598	+	0.806966i	$0.298892\pi$
$32$		−	3.43597e10i		−	0.176777i
$33$		−	3.32175e11i		−	1.35679i
$34$	3.48148e11			1.13677
$35$	−5.93925e11	−	3.03658e11i	−1.56035	−	0.797763i
$36$	1.81418e11			0.385844
$37$		−	1.52555e11i		−	0.264188i	−0.991237	−	0.132094i	$-0.957830\pi$
$37$		−	1.52555e11i		−	0.264188i	0.991237	−	0.132094i	$-0.0421701\pi$
$38$			3.31590e10i			0.0470137i
$39$	1.50374e11			0.175464
$40$	3.26196e11	+	1.66775e11i	0.314796	+	0.160946i
$41$	−1.17421e12			−0.941598			−0.470799	−	0.882240i	$-0.656034\pi$
$41$	−1.17421e12			−0.941598			−0.470799	+	0.882240i	$0.656034\pi$
$42$			2.46431e12i			1.64940i
$43$			8.75693e11i			0.491290i	0.969360	+	0.245645i	$0.0789998\pi$
$43$			8.75693e11i			0.491290i	−0.969360	+	0.245645i	$0.921000\pi$
$44$	−1.07940e12			−0.509670
$45$	−8.80567e11	+	1.72230e12i	−0.351292	+	0.687093i
$46$	1.09682e12			0.371068
$47$		−	5.72415e12i		−	1.64807i	−0.566536	−	0.824037i	$-0.691717\pi$
$47$		−	5.72415e12i		−	1.64807i	0.566536	−	0.824037i	$-0.308283\pi$
$48$		−	1.35345e12i		−	0.332762i
$49$	−9.83271e12			−2.07111
$50$	−3.16658e12	+	2.28726e12i	−0.573212	+	0.414039i
$51$	1.37138e13			2.13983
$52$		−	4.88641e11i		−	0.0659120i
$53$			8.50996e12i			0.995081i	0.867441	+	0.497541i	$0.165763\pi$
$53$			8.50996e12i			0.995081i	−0.867441	+	0.497541i	$0.834237\pi$
$54$	−2.11426e12			−0.214885
$55$	5.23921e12	−	1.02474e13i	0.464030	−	0.907596i
$56$	8.00779e12			0.619587
$57$			1.30616e12i			0.0884980i
$58$		−	1.87225e13i		−	1.11341i
$59$	7.18836e12			0.376045			0.188023	−	0.982165i	$-0.439792\pi$
$59$	7.18836e12			0.376045			0.188023	+	0.982165i	$0.439792\pi$
$60$	1.28491e13	+	6.56938e12i	0.592567	+	0.302963i
$61$	5.57263e12			0.227032			0.113516	−	0.993536i	$-0.463789\pi$
$61$	5.57263e12			0.227032			0.113516	+	0.993536i	$0.463789\pi$
$62$		−	2.31603e13i		−	0.835232i
$63$			4.22809e13i			1.35235i
$64$	−4.39805e12			−0.125000
$65$	4.63894e12	+	2.37176e12i	0.117373	+	0.0600097i
$66$	−4.25184e13			−0.959396
$67$		−	3.26451e12i		−	0.0658046i	−0.999459	−	0.0329023i	$-0.989525\pi$
$67$		−	3.26451e12i		−	0.0658046i	0.999459	−	0.0329023i	$-0.0104750\pi$
$68$		−	4.45629e13i		−	0.803816i
$69$	4.32046e13			0.698493
$70$	−3.88682e13	+	7.60224e13i	−0.564104	+	1.10333i
$71$	−5.83158e13			−0.760937			−0.380469	−	0.924794i	$-0.624237\pi$
$71$	−5.83158e13			−0.760937			−0.380469	+	0.924794i	$0.624237\pi$
$72$		−	2.32215e13i		−	0.272833i
$73$			6.27971e13i			0.665301i	0.943050	+	0.332650i	$0.107943\pi$
$73$			6.27971e13i			0.665301i	−0.943050	+	0.332650i	$0.892057\pi$
$74$	−1.95270e13			−0.186809
$75$	−1.24734e14	+	9.00968e13i	−1.07901	+	0.779381i
$76$	4.24436e12			0.0332437
$77$		−	2.51563e14i		−	1.78635i
$78$		−	1.92479e13i		−	0.124072i
$79$	1.09818e14			0.643384			0.321692	−	0.946844i	$-0.395748\pi$
$79$	1.09818e14			0.643384			0.321692	+	0.946844i	$0.395748\pi$
$80$	2.13472e13	−	4.17531e13i	0.113806	−	0.222594i
$81$	−2.42166e14			−1.17619
$82$			1.50298e14i			0.665810i
$83$			2.82120e14i			1.14116i	0.821241	+	0.570582i	$0.193282\pi$
$83$			2.82120e14i			1.14116i	−0.821241	+	0.570582i	$0.806718\pi$
$84$	3.15432e14			1.16630
$85$	4.23060e14	+	2.16299e14i	1.43140	+	0.731835i
$86$	1.12089e14			0.347395
$87$		−	7.37491e14i		−	2.09586i
$88$			1.38164e14i			0.360391i
$89$	−6.26105e13			−0.150045			−0.0750226	−	0.997182i	$-0.523903\pi$
$89$	−6.26105e13			−0.150045			−0.0750226	+	0.997182i	$0.523903\pi$
$90$	2.20455e14	+	1.12713e14i	0.485848	+	0.248401i
$91$	1.13881e14			0.231016
$92$		−	1.40393e14i		−	0.262384i
$93$		−	9.12301e14i		−	1.57223i
$94$	−7.32691e14			−1.16536
$95$	−2.06012e13	+	4.02940e13i	−0.0302668	+	0.0591989i
$96$	−1.73242e14			−0.235298
$97$		−	6.53097e14i		−	0.820710i	−0.911926	−	0.410355i	$-0.865405\pi$
$97$		−	6.53097e14i		−	0.820710i	0.911926	−	0.410355i	$-0.134595\pi$
$98$			1.25859e15i			1.46449i
$99$	−7.29500e14			−0.786613
$100$	2.92770e14	+	4.05322e14i	0.292770	+	0.405322i
$101$	1.04808e15			0.972712			0.486356	−	0.873761i	$-0.338326\pi$
$101$	1.04808e15			0.972712			0.486356	+	0.873761i	$0.338326\pi$
$102$		−	1.75536e15i		−	1.51309i
$103$			2.11702e15i			1.69608i	0.529932	+	0.848040i	$0.322217\pi$
$103$			2.11702e15i			1.69608i	−0.529932	+	0.848040i	$0.677783\pi$
$104$	−6.25460e13			−0.0466068
$105$	−1.53104e15	+	2.99457e15i	−1.06186	+	2.07690i
$106$	1.08927e15			0.703629
$107$		−	4.25190e13i		−	0.0255980i	−0.999918	−	0.0127990i	$-0.995926\pi$
$107$		−	4.25190e13i		−	0.0255980i	0.999918	−	0.0127990i	$-0.00407415\pi$
$108$			2.70626e14i			0.151947i
$109$	−1.94135e15			−1.01720			−0.508598	−	0.861004i	$-0.669836\pi$
$109$	−1.94135e15			−1.01720			−0.508598	+	0.861004i	$0.669836\pi$
$110$	−1.31166e15	−	6.70619e14i	−0.641768	−	0.328118i
$111$	−7.69183e14			−0.351647
$112$		−	1.02500e15i		−	0.438114i
$113$		−	4.23147e15i		−	1.69201i	−0.533176	−	0.846004i	$-0.679002\pi$
$113$		−	4.23147e15i		−	1.69201i	0.533176	−	0.846004i	$-0.320998\pi$
$114$	1.67188e14			0.0625776
$115$	1.33283e15	+	6.81441e14i	0.467242	+	0.238888i
$116$	−2.39648e15			−0.787297
$117$		−	3.30241e14i		−	0.101727i
$118$		−	9.20110e14i		−	0.265904i
$119$	1.03857e16			2.81731
$120$	8.40881e14	−	1.64468e15i	0.214227	−	0.419008i
$121$	1.63141e14			0.0390546
$122$		−	7.13296e14i		−	0.160536i
$123$			5.92035e15i			1.25331i
$124$	−2.96452e15			−0.590598
$125$	−5.26899e15	+	8.12075e14i	−0.988330	+	0.152325i
$126$	5.41195e15			0.956257
$127$		−	3.51641e15i		−	0.585560i	−0.956180	−	0.292780i	$-0.905420\pi$
$127$		−	3.51641e15i		−	0.585560i	0.956180	−	0.292780i	$-0.0945803\pi$
$128$			5.62950e14i			0.0883883i
$129$	4.41525e15			0.653931
$130$	3.03586e14	−	5.93784e14i	0.0424332	−	0.0829953i
$131$	6.86455e15			0.905894			0.452947	−	0.891537i	$-0.350373\pi$
$131$	6.86455e15			0.905894			0.452947	+	0.891537i	$0.350373\pi$
$132$			5.44236e15i			0.678395i
$133$			9.89178e14i			0.116516i
$134$	−4.17857e14			−0.0465309
$135$	−2.56920e15	−	1.31356e15i	−0.270579	−	0.138340i
$136$	−5.70405e15			−0.568384
$137$		−	9.66931e15i		−	0.911993i	−0.889982	−	0.455996i	$-0.849283\pi$
$137$		−	9.66931e15i		−	0.911993i	0.889982	−	0.455996i	$-0.150717\pi$
$138$		−	5.53019e15i		−	0.493909i
$139$	−1.99151e16			−1.68489			−0.842444	−	0.538784i	$-0.818884\pi$
$139$	−1.99151e16			−1.68489			−0.842444	+	0.538784i	$0.818884\pi$
$140$	9.73086e15	+	4.97513e15i	0.780173	+	0.398882i
$141$	−2.88612e16			−2.19367
$142$			7.46442e15i			0.538064i
$143$			1.96487e15i			0.134374i
$144$	−2.97236e15			−0.192922
$145$	1.16320e16	−	2.27511e16i	0.716796	−	1.40198i
$146$	8.03803e15			0.470439
$147$			4.95765e16i			2.75674i
$148$			2.49946e15i			0.132094i
$149$	5.69937e15			0.286372			0.143186	−	0.989696i	$-0.454265\pi$
$149$	5.69937e15			0.286372			0.143186	+	0.989696i	$0.454265\pi$
$150$	1.15324e16	+	1.59659e16i	0.551106	+	0.762972i
$151$	−9.09809e15			−0.413640			−0.206820	−	0.978379i	$-0.566312\pi$
$151$	−9.09809e15			−0.413640			−0.206820	+	0.978379i	$0.566312\pi$
$152$		−	5.43278e14i		−	0.0235069i
$153$		−	3.01172e16i		−	1.24059i
$154$	−3.22001e16			−1.26314
$155$	1.43892e16	−	2.81438e16i	0.537711	−	1.05171i
$156$	−2.46373e15			−0.0877321
$157$		−	6.96026e15i		−	0.236254i	−0.992999	−	0.118127i	$-0.962311\pi$
$157$		−	6.96026e15i		−	0.236254i	0.992999	−	0.118127i	$-0.0376889\pi$
$158$		−	1.40567e16i		−	0.454941i
$159$	4.29072e16			1.32450
$160$	−5.34439e15	−	2.73244e15i	−0.157398	−	0.0804732i
$161$	3.27197e16			0.919635
$162$			3.09973e16i			0.831689i
$163$			1.50326e16i			0.385148i	0.981282	+	0.192574i	$0.0616836\pi$
$163$			1.50326e16i			0.385148i	−0.981282	+	0.192574i	$0.938316\pi$
$164$	1.92382e16			0.470799
$165$	−5.16673e16	−	2.64161e16i	−1.20805	−	0.617646i
$166$	3.61113e16			0.806925
$167$			5.36303e16i			1.14561i	0.819692	+	0.572805i	$0.194145\pi$
$167$			5.36303e16i			1.14561i	−0.819692	+	0.572805i	$0.805855\pi$
$168$		−	4.03753e16i		−	0.824700i
$169$	5.02964e16			0.982622
$170$	2.76863e16	−	5.41517e16i	0.517485	−	1.01215i
$171$	2.86849e15			0.0513076
$172$		−	1.43473e16i		−	0.245645i
$173$			1.73767e16i			0.284854i	0.989805	+	0.142427i	$0.0454906\pi$
$173$			1.73767e16i			0.284854i	−0.989805	+	0.142427i	$0.954509\pi$
$174$	−9.43989e16			−1.48200
$175$	−9.44632e16	+	6.82322e16i	−1.42062	+	1.02613i
$176$	1.76850e16			0.254835
$177$		−	3.62437e16i		−	0.500534i
$178$			8.01415e15i			0.106098i
$179$	1.03346e17			1.31189			0.655944	−	0.754809i	$-0.272271\pi$
$179$	1.03346e17			1.31189			0.655944	+	0.754809i	$0.272271\pi$
$180$	1.44272e16	−	2.82182e16i	0.175646	−	0.343547i
$181$	−9.41305e16			−1.09936			−0.549681	−	0.835374i	$-0.685251\pi$
$181$	−9.41305e16			−1.09936			−0.549681	+	0.835374i	$0.685251\pi$
$182$		−	1.45768e16i		−	0.163353i
$183$		−	2.80972e16i		−	0.302190i
$184$	−1.79704e16			−0.185534
$185$	−2.37288e16	−	1.21319e16i	−0.235227	−	0.120265i
$186$	−1.16774e17			−1.11173
$187$			1.79192e17i			1.63872i
$188$			9.37844e16i			0.824037i
$189$	−6.30714e16			−0.532560
$190$	5.15763e15	+	2.63696e15i	0.0418599	+	0.0214019i
$191$	1.11137e17			0.867178			0.433589	−	0.901111i	$-0.357247\pi$
$191$	1.11137e17			0.867178			0.433589	+	0.901111i	$0.357247\pi$
$192$			2.21750e16i			0.166381i
$193$			7.35343e16i			0.530653i	0.964159	+	0.265326i	$0.0854797\pi$
$193$			7.35343e16i			0.530653i	−0.964159	+	0.265326i	$0.914520\pi$
$194$	−8.35965e16			−0.580330
$195$	1.19584e16	−	2.33895e16i	0.0798757	−	0.156229i
$196$	1.61099e17			1.03555
$197$		−	1.15175e17i		−	0.712629i	−0.934366	−	0.356314i	$-0.884033\pi$
$197$		−	1.15175e17i		−	0.712629i	0.934366	−	0.356314i	$-0.115967\pi$
$198$			9.33760e16i			0.556220i
$199$	7.91937e16			0.454248			0.227124	−	0.973866i	$-0.427068\pi$
$199$	7.91937e16			0.454248			0.227124	+	0.973866i	$0.427068\pi$
$200$	5.18812e16	−	3.74745e16i	0.286606	−	0.207020i
$201$	−1.64596e16			−0.0875891
$202$		−	1.34154e17i		−	0.687811i
$203$		−	5.58517e17i		−	2.75941i
$204$	−2.24686e17			−1.06992
$205$	−9.33783e16	+	1.82639e17i	−0.428639	+	0.838377i
$206$	2.70979e17			1.19931
$207$		−	9.48829e16i		−	0.404958i
$208$			8.00589e15i			0.0329560i
$209$	−1.70670e16			−0.0677734
$210$	3.83305e17	+	1.95974e17i	1.46859	+	0.750849i
$211$	−1.72304e17			−0.637056			−0.318528	−	0.947913i	$-0.603188\pi$
$211$	−1.72304e17			−0.637056			−0.318528	+	0.947913i	$0.603188\pi$
$212$		−	1.39427e17i		−	0.497541i
$213$			2.94029e17i			1.01284i
$214$	−5.44244e15			−0.0181005
$215$	1.36207e17	+	6.96391e16i	0.437433	+	0.223648i
$216$	3.46401e16			0.107443
$217$		−	6.90904e17i		−	2.07000i
$218$			2.48492e17i			0.719266i
$219$	3.16623e17			0.885547
$220$	−8.58392e16	+	1.67893e17i	−0.232015	+	0.453798i
$221$	−8.11191e16			−0.211925
$222$			9.84554e16i			0.248652i
$223$			6.00876e17i			1.46723i	0.679565	+	0.733615i	$0.262168\pi$
$223$			6.00876e17i			1.46723i	−0.679565	+	0.733615i	$0.737832\pi$
$224$	−1.31200e17			−0.309794
$225$	1.97864e17	+	2.73931e17i	0.451854	+	0.625565i
$226$	−5.41628e17			−1.19643
$227$		−	1.13161e17i		−	0.241826i	−0.992663	−	0.120913i	$-0.961418\pi$
$227$		−	1.13161e17i		−	0.241826i	0.992663	−	0.120913i	$-0.0385821\pi$
$228$		−	2.14001e16i		−	0.0442490i
$229$	5.81603e17			1.16375			0.581876	−	0.813277i	$-0.302319\pi$
$229$	5.81603e17			1.16375			0.581876	+	0.813277i	$0.302319\pi$
$230$	8.72245e16	−	1.70602e17i	0.168919	−	0.330390i
$231$	−1.26838e18			−2.37772
$232$			3.06749e17i			0.556703i
$233$			1.21206e17i			0.212988i	0.994313	+	0.106494i	$0.0339625\pi$
$233$			1.21206e17i			0.212988i	−0.994313	+	0.106494i	$0.966038\pi$
$234$	−4.22708e16			−0.0719320
$235$	−8.90347e17	−	4.55210e17i	−1.46741	−	0.750245i
$236$	−1.17774e17			−0.188023
$237$		−	5.53703e17i		−	0.856375i
$238$		−	1.32937e18i		−	1.99214i
$239$	−4.54537e17			−0.660063			−0.330031	−	0.943970i	$-0.607059\pi$
$239$	−4.54537e17			−0.660063			−0.330031	+	0.943970i	$0.607059\pi$
$240$	−2.10519e17	−	1.07633e17i	−0.296283	−	0.151482i
$241$	1.15683e18			1.57813			0.789065	−	0.614310i	$-0.210566\pi$
$241$	1.15683e18			1.57813			0.789065	+	0.614310i	$0.210566\pi$
$242$		−	2.08820e16i		−	0.0276157i
$243$			9.83991e17i			1.26167i
$244$	−9.13019e16			−0.113516
$245$	−7.81942e17	+	1.52940e18i	−0.942821	+	1.84406i
$246$	7.57805e17			0.886226
$247$		−	7.72613e15i		−	0.00876465i
$248$			3.79459e17i			0.417616i
$249$	1.42245e18			1.51894
$250$	1.03946e17	+	6.74431e17i	0.107710	+	0.698855i
$251$	1.19328e18			1.20003			0.600013	−	0.799990i	$-0.295162\pi$
$251$	1.19328e18			1.20003			0.600013	+	0.799990i	$0.295162\pi$
$252$		−	6.92729e17i		−	0.676176i
$253$			5.64535e17i			0.534918i
$254$	−4.50100e17			−0.414053
$255$	1.09058e18	−	2.13307e18i	0.974107	−	1.90526i
$256$	7.20576e16			0.0625000
$257$			1.14545e18i			0.964890i	0.875926	+	0.482445i	$0.160251\pi$
$257$			1.14545e18i			0.964890i	−0.875926	+	0.482445i	$0.839749\pi$
$258$		−	5.65151e17i		−	0.462399i
$259$	−5.82518e17			−0.462979
$260$	−7.60043e16	−	3.88590e16i	−0.0586865	−	0.0300048i
$261$	−1.61963e18			−1.21510
$262$		−	8.78663e17i		−	0.640564i
$263$		−	2.25180e18i		−	1.59537i	−0.603076	−	0.797684i	$-0.706058\pi$
$263$		−	2.25180e18i		−	1.59537i	0.603076	−	0.797684i	$-0.293942\pi$
$264$	6.96622e17			0.479698
$265$	1.32366e18	+	6.76751e17i	0.885997	+	0.452986i
$266$	1.26615e17			0.0823896
$267$			3.15683e17i			0.199717i
$268$			5.34857e16i			0.0329023i
$269$	−1.61251e18			−0.964632			−0.482316	−	0.875997i	$-0.660204\pi$
$269$	−1.61251e18			−0.964632			−0.482316	+	0.875997i	$0.660204\pi$
$270$	−1.68136e17	+	3.28858e17i	−0.0978211	+	0.191329i
$271$	2.98675e18			1.69016			0.845082	−	0.534637i	$-0.179552\pi$
$271$	2.98675e18			1.69016			0.845082	+	0.534637i	$0.179552\pi$
$272$			7.30118e17i			0.401908i
$273$		−	5.74190e17i		−	0.307493i
$274$	−1.23767e18			−0.644876
$275$	−1.17726e18	−	1.62984e18i	−0.596864	−	0.826322i
$276$	−7.07864e17			−0.349246
$277$			7.33903e17i			0.352404i	0.984354	+	0.176202i	$0.0563811\pi$
$277$			7.33903e17i			0.352404i	−0.984354	+	0.176202i	$0.943619\pi$
$278$			2.54913e18i			1.19140i
$279$	−2.00353e18			−0.911516
$280$	6.36816e17	−	1.24555e18i	0.282052	−	0.551666i
$281$	−1.80787e17			−0.0779598			−0.0389799	−	0.999240i	$-0.512411\pi$
$281$	−1.80787e17			−0.0779598			−0.0389799	+	0.999240i	$0.512411\pi$
$282$			3.69423e18i			1.55116i
$283$		−	1.81111e18i		−	0.740536i	−0.928925	−	0.370268i	$-0.879266\pi$
$283$		−	1.81111e18i		−	0.740536i	0.928925	−	0.370268i	$-0.120734\pi$
$284$	9.55446e17			0.380469
$285$	2.03163e17	+	1.03872e17i	0.0787965	+	0.0402865i
$286$	2.51504e17			0.0950165
$287$			4.48360e18i			1.65011i
$288$			3.80462e17i			0.136417i
$289$	−4.53545e18			−1.58448
$290$	−2.91214e18	−	1.48890e18i	−0.991351	−	0.506851i
$291$	−3.29292e18			−1.09240
$292$		−	1.02887e18i		−	0.332650i
$293$			9.38285e17i			0.295684i	0.989011	+	0.147842i	$0.0472327\pi$
$293$			9.38285e17i			0.295684i	−0.989011	+	0.147842i	$0.952767\pi$
$294$	6.34580e18			1.94931
$295$	5.71652e17	−	1.11809e18i	0.171185	−	0.334822i
$296$	3.19931e17			0.0934047
$297$		−	1.08821e18i		−	0.309771i
$298$		−	7.29520e17i		−	0.202495i
$299$	−2.55562e17			−0.0691772
$300$	2.04363e18	−	1.47615e18i	0.539503	−	0.389691i
$301$	3.34376e18			0.860966
$302$			1.16455e18i			0.292488i
$303$		−	5.28442e18i		−	1.29473i
$304$	−6.95395e16			−0.0166219
$305$	4.43161e17	−	8.66779e17i	0.103351	−	0.202143i
$306$	−3.85500e18			−0.877230
$307$			3.30085e18i			0.732973i	0.930423	+	0.366487i	$0.119439\pi$
$307$			3.30085e18i			0.732973i	−0.930423	+	0.366487i	$0.880561\pi$
$308$			4.12161e18i			0.893175i
$309$	1.06740e19			2.25756
$310$	−3.60241e18	−	1.84182e18i	−0.743671	−	0.380219i
$311$	−6.55235e18			−1.32037			−0.660183	−	0.751105i	$-0.729521\pi$
$311$	−6.55235e18			−1.32037			−0.660183	+	0.751105i	$0.729521\pi$
$312$			3.15357e17i			0.0620360i
$313$			1.25098e18i			0.240252i	0.992759	+	0.120126i	$0.0383298\pi$
$313$			1.25098e18i			0.240252i	−0.992759	+	0.120126i	$0.961670\pi$
$314$	−8.90914e17			−0.167056
$315$	6.57646e18	+	3.36237e18i	1.20410	+	0.615625i
$316$	−1.79926e18			−0.321692
$317$		−	8.16730e18i		−	1.42605i	−0.701140	−	0.713024i	$-0.747325\pi$
$317$		−	8.16730e18i		−	1.42605i	0.701140	−	0.713024i	$-0.252675\pi$
$318$		−	5.49213e18i		−	0.936563i
$319$	9.63647e18			1.60505
$320$	−3.49753e17	+	6.84082e17i	−0.0569032	+	0.111297i
$321$	−2.14381e17			−0.0340721
$322$		−	4.18812e18i		−	0.650280i
$323$		−	7.04604e17i		−	0.106887i
$324$	3.96765e18			0.588093
$325$	7.37819e17	−	5.32937e17i	0.106862	−	0.0771882i
$326$	1.92418e18			0.272341
$327$			9.78828e18i			1.35394i
$328$		−	2.46249e18i		−	0.332905i
$329$	−2.18571e19			−2.88818
$330$	−3.38126e18	+	6.61342e18i	−0.436741	+	0.854223i
$331$	8.19945e18			1.03532			0.517660	−	0.855586i	$-0.326803\pi$
$331$	8.19945e18			1.03532			0.517660	+	0.855586i	$0.326803\pi$
$332$		−	4.62225e18i		−	0.570582i
$333$			1.68923e18i			0.203871i
$334$	6.86468e18			0.810068
$335$	−5.07769e17	−	2.59609e17i	−0.0585909	−	0.0299559i
$336$	−5.16804e18			−0.583151
$337$			1.33250e19i			1.47042i	0.677838	+	0.735212i	$0.262917\pi$
$337$			1.33250e19i			1.47042i	−0.677838	+	0.735212i	$0.737083\pi$
$338$		−	6.43794e18i		−	0.694819i
$339$	−2.13351e19			−2.25214
$340$	−6.93142e18	−	3.54385e18i	−0.715699	−	0.365917i
$341$	1.19206e19			1.20404
$342$		−	3.67166e17i		−	0.0362800i
$343$			1.94172e19i			1.87707i
$344$	−1.83646e18			−0.173697
$345$	3.43583e18	−	6.72014e18i	0.317972	−	0.621921i
$346$	2.22422e18			0.201422
$347$		−	1.08670e19i		−	0.963027i	−0.876439	−	0.481513i	$-0.840087\pi$
$347$		−	1.08670e19i		−	0.963027i	0.876439	−	0.481513i	$-0.159913\pi$
$348$			1.20831e19i			1.04793i
$349$	−4.69536e18			−0.398546			−0.199273	−	0.979944i	$-0.563858\pi$
$349$	−4.69536e18			−0.398546			−0.199273	+	0.979944i	$0.563858\pi$
$350$	8.73372e18	+	1.20913e19i	0.725586	+	1.00453i
$351$	4.92628e17			0.0400605
$352$		−	2.26368e18i		−	0.180196i
$353$			3.69821e18i			0.288191i	0.989564	+	0.144096i	$0.0460273\pi$
$353$			3.69821e18i			0.288191i	−0.989564	+	0.144096i	$0.953973\pi$
$354$	−4.63920e18			−0.353931
$355$	−4.63754e18	+	9.07058e18i	−0.346398	+	0.677520i
$356$	1.02581e18			0.0750226
$357$		−	5.23648e19i		−	3.74997i
$358$		−	1.32283e19i		−	0.927645i
$359$	2.86790e18			0.196950			0.0984749	−	0.995140i	$-0.468604\pi$
$359$	2.86790e18			0.196950			0.0984749	+	0.995140i	$0.468604\pi$
$360$	−3.61193e18	−	1.84668e18i	−0.242924	−	0.124201i
$361$	−1.51140e19			−0.995579
$362$			1.20487e19i			0.777367i
$363$		−	8.22555e17i		−	0.0519835i
$364$	−1.86583e18			−0.115508
$365$	9.76760e18	+	4.99391e18i	0.592368	+	0.302862i
$366$	−3.59644e18			−0.213680
$367$		−	1.62272e19i		−	0.944600i	−0.881438	−	0.472300i	$-0.843424\pi$
$367$		−	1.62272e19i		−	0.944600i	0.881438	−	0.472300i	$-0.156576\pi$
$368$			2.30021e18i			0.131192i
$369$	1.30019e19			0.726621
$370$	−1.55288e18	+	3.03728e18i	−0.0850404	+	0.166331i
$371$	3.24945e19			1.74384
$372$			1.49471e19i			0.786115i
$373$			1.81528e18i			0.0935681i	0.998905	+	0.0467841i	$0.0148973\pi$
$373$			1.81528e18i			0.0935681i	−0.998905	+	0.0467841i	$0.985103\pi$
$374$	2.29365e19			1.15875
$375$	4.09449e18	+	2.65663e19i	0.202752	+	1.31552i
$376$	1.20044e19			0.582682
$377$			4.36238e18i			0.207570i
$378$			8.07313e18i			0.376577i
$379$	2.29492e19			1.04948			0.524739	−	0.851263i	$-0.324163\pi$
$379$	2.29492e19			1.04948			0.524739	+	0.851263i	$0.324163\pi$
$380$	3.37531e17	−	6.60177e17i	0.0151334	−	0.0295994i
$381$	−1.77297e19			−0.779408
$382$		−	1.42255e19i		−	0.613188i
$383$			3.26097e18i			0.137834i	0.997622	+	0.0689170i	$0.0219544\pi$
$383$			3.26097e18i			0.137834i	−0.997622	+	0.0689170i	$0.978046\pi$
$384$	2.83840e18			0.117649
$385$	−3.91287e19	−	2.00055e19i	−1.59052	−	0.813192i
$386$	9.41239e18			0.375228
$387$		−	9.69645e18i		−	0.379123i
$388$			1.07003e19i			0.410355i
$389$	−1.59231e19			−0.598971			−0.299485	−	0.954101i	$-0.596815\pi$
$389$	−1.59231e19			−0.598971			−0.299485	+	0.954101i	$0.596815\pi$
$390$	−2.99386e18	−	1.53068e18i	−0.110471	−	0.0564807i
$391$	−2.33067e19			−0.843635
$392$		−	2.06207e19i		−	0.732247i
$393$		−	3.46111e19i		−	1.20579i
$394$	−1.47425e19			−0.503905
$395$	8.73323e18	−	1.70813e19i	0.292885	−	0.572854i
$396$	1.19521e19			0.393307
$397$			5.88909e19i			1.90160i	0.309806	+	0.950800i	$0.399736\pi$
$397$			5.88909e19i			1.90160i	−0.309806	+	0.950800i	$0.600264\pi$
$398$		−	1.01368e19i		−	0.321201i
$399$	4.98744e18			0.155089
$400$	−4.79674e18	−	6.64079e18i	−0.146385	−	0.202661i
$401$	−5.88679e18			−0.176318			−0.0881588	−	0.996106i	$-0.528098\pi$
$401$	−5.88679e18			−0.176318			−0.0881588	+	0.996106i	$0.528098\pi$
$402$			2.10683e18i			0.0619349i
$403$			5.39641e18i			0.155710i
$404$	−1.71717e19			−0.486356
$405$	−1.92582e19	+	3.76671e19i	−0.535429	+	1.04725i
$406$	−7.14902e19			−1.95120
$407$		−	1.00506e19i		−	0.269298i
$408$			2.87598e19i			0.756546i
$409$	4.43754e19			1.14609			0.573044	−	0.819525i	$-0.305762\pi$
$409$	4.43754e19			1.14609			0.573044	+	0.819525i	$0.305762\pi$
$410$	2.33778e19	+	1.19524e19i	0.592822	+	0.303094i
$411$	−4.87527e19			−1.21391
$412$		−	3.46853e19i		−	0.848040i
$413$		−	2.74481e19i		−	0.659003i
$414$	−1.21450e19			−0.286349
$415$	4.38816e19	+	2.24355e19i	1.01607	+	0.519487i
$416$	1.02475e18			0.0233034
$417$			1.00412e20i			2.24267i
$418$			2.18457e18i			0.0479230i
$419$	−5.09132e17			−0.0109705			−0.00548524	−	0.999985i	$-0.501746\pi$
$419$	−5.09132e17			−0.0109705			−0.00548524	+	0.999985i	$0.501746\pi$
$420$	2.50846e19	−	4.90630e19i	0.530930	−	1.03845i
$421$	1.71471e19			0.356513			0.178256	−	0.983984i	$-0.442954\pi$
$421$	1.71471e19			0.356513			0.178256	+	0.983984i	$0.442954\pi$
$422$			2.20549e19i			0.450467i
$423$			6.33828e19i			1.27180i
$424$	−1.78467e19			−0.351814
$425$	6.72874e19	−	4.86026e19i	1.30322	−	0.941332i
$426$	3.76357e19			0.716189
$427$		−	2.12786e19i		−	0.397863i
$428$			6.96632e17i			0.0127990i
$429$	9.90689e18			0.178858
$430$	8.91381e18	−	1.74345e19i	0.158143	−	0.309312i
$431$	1.91150e19			0.333269			0.166635	−	0.986019i	$-0.446710\pi$
$431$	1.91150e19			0.333269			0.166635	+	0.986019i	$0.446710\pi$
$432$		−	4.43393e18i		−	0.0759733i
$433$		−	8.78686e19i		−	1.47970i	−0.672770	−	0.739852i	$-0.734896\pi$
$433$		−	8.78686e19i		−	1.47970i	0.672770	−	0.739852i	$-0.265104\pi$
$434$	−8.84357e19			−1.46371
$435$	−1.14711e20	−	5.86487e19i	−1.86611	−	0.954089i
$436$	3.18070e19			0.508598
$437$		−	2.21982e18i		−	0.0348906i
$438$		−	4.05278e19i		−	0.626176i
$439$	−1.77525e19			−0.269634			−0.134817	−	0.990870i	$-0.543045\pi$
$439$	−1.77525e19			−0.269634			−0.134817	+	0.990870i	$0.543045\pi$
$440$	2.14903e19	+	1.09874e19i	0.320884	+	0.164059i
$441$	1.08876e20			1.59825
$442$			1.03833e19i			0.149853i
$443$		−	1.61332e19i		−	0.228924i	−0.993428	−	0.114462i	$-0.963486\pi$
$443$		−	1.61332e19i		−	0.228924i	0.993428	−	0.114462i	$-0.0365145\pi$
$444$	1.26023e19			0.175824
$445$	−4.97908e18	+	9.73859e18i	−0.0683044	+	0.133597i
$446$	7.69121e19			1.03749
$447$		−	2.87363e19i		−	0.381174i
$448$			1.67936e19i			0.219057i
$449$	3.38252e19			0.433904			0.216952	−	0.976182i	$-0.430389\pi$
$449$	3.38252e19			0.433904			0.216952	+	0.976182i	$0.430389\pi$
$450$	3.50632e19	−	2.53266e19i	0.442341	−	0.319509i
$451$	−7.73586e19			−0.959809
$452$			6.93283e19i			0.846004i
$453$			4.58726e19i			0.550575i
$454$	−1.44846e19			−0.170997
$455$	9.05637e18	−	1.77134e19i	0.105164	−	0.205691i
$456$	−2.73921e18			−0.0312888
$457$			1.55141e20i			1.74323i	0.490195	+	0.871613i	$0.336926\pi$
$457$			1.55141e20i			1.74323i	−0.490195	+	0.871613i	$0.663074\pi$
$458$		−	7.44452e19i		−	0.822898i
$459$	4.49265e19			0.488549
$460$	−2.18371e19	−	1.11647e19i	−0.233621	−	0.119444i
$461$	−4.95610e19			−0.521654			−0.260827	−	0.965386i	$-0.583995\pi$
$461$	−4.95610e19			−0.521654			−0.260827	+	0.965386i	$0.583995\pi$
$462$			1.62353e20i			1.68130i
$463$		−	5.11362e19i		−	0.521040i	−0.965468	−	0.260520i	$-0.916106\pi$
$463$		−	5.11362e19i		−	0.521040i	0.965468	−	0.260520i	$-0.0838940\pi$
$464$	3.92639e19			0.393649
$465$	−1.41901e20	−	7.25503e19i	−1.39988	−	0.715719i
$466$	1.55144e19			0.150605
$467$		−	3.72339e19i		−	0.355682i	−0.984059	−	0.177841i	$-0.943089\pi$
$467$		−	3.72339e19i		−	0.355682i	0.984059	−	0.177841i	$-0.0569113\pi$
$468$			5.41067e18i			0.0508636i
$469$	−1.24652e19			−0.115320
$470$	−5.82669e19	+	1.13964e20i	−0.530504	+	1.03761i
$471$	−3.50937e19			−0.314465
$472$			1.50751e19i			0.132952i
$473$			5.76921e19i			0.500792i
$474$	−7.08739e19			−0.605549
$475$	4.62912e18	+	6.40873e18i	0.0389311	+	0.0538977i
$476$	−1.70159e20			−1.40865
$477$		−	9.42298e19i		−	0.767893i
$478$			5.81808e19i			0.466735i
$479$	1.09530e20			0.865001			0.432500	−	0.901634i	$-0.357631\pi$
$479$	1.09530e20			0.865001			0.432500	+	0.901634i	$0.357631\pi$
$480$	−1.37770e19	+	2.69464e19i	−0.107114	+	0.209504i
$481$	4.54984e18			0.0348264
$482$		−	1.48075e20i		−	1.11591i
$483$		−	1.64973e20i		−	1.22408i
$484$	−2.67290e18			−0.0195273
$485$	−1.01584e20	−	5.19373e19i	−0.730741	−	0.373608i
$486$	1.25951e20			0.892132
$487$		−	8.59385e19i		−	0.599405i	−0.954033	−	0.299703i	$-0.903113\pi$
$487$		−	8.59385e19i		−	0.599405i	0.954033	−	0.299703i	$-0.0968874\pi$
$488$			1.16866e19i			0.0802678i
$489$	7.57946e19			0.512651
$490$	1.95763e20	+	1.00089e20i	1.30395	+	0.666675i
$491$	−1.91469e20			−1.25599			−0.627997	−	0.778215i	$-0.716125\pi$
$491$	−1.91469e20			−1.25599			−0.627997	+	0.778215i	$0.716125\pi$
$492$		−	9.69991e19i		−	0.626656i
$493$			3.97839e20i			2.53137i
$494$	−9.88944e17			−0.00619754
$495$	−5.80132e19	+	1.13468e20i	−0.358086	+	0.700382i
$496$	4.85707e19			0.295299
$497$			2.22674e20i			1.33351i
$498$		−	1.82074e20i		−	1.07406i
$499$	6.42565e19			0.373390			0.186695	−	0.982418i	$-0.440222\pi$
$499$	6.42565e19			0.373390			0.186695	+	0.982418i	$0.440222\pi$
$500$	8.63271e19	−	1.33050e19i	0.494165	−	0.0761625i
$501$	2.70404e20			1.52486
$502$		−	1.52740e20i		−	0.848547i
$503$		−	1.44519e19i		−	0.0790977i	−0.999218	−	0.0395488i	$-0.987408\pi$
$503$		−	1.44519e19i		−	0.0790977i	0.999218	−	0.0395488i	$-0.0125921\pi$
$504$	−8.86694e19			−0.478128
$505$	8.33481e19	−	1.63021e20i	0.442803	−	0.866079i
$506$	7.22605e19			0.378244
$507$		−	2.53595e20i		−	1.30792i
$508$			5.76128e19i			0.292780i
$509$	−2.88288e20			−1.44359			−0.721793	−	0.692109i	$-0.756682\pi$
$509$	−2.88288e20			−1.44359			−0.721793	+	0.692109i	$0.756682\pi$
$510$	−2.73033e20	−	1.39594e20i	−1.34722	−	0.688798i
$511$	2.39785e20			1.16591
$512$		−	9.22337e18i		−	0.0441942i
$513$			4.27899e18i			0.0202051i
$514$	1.46618e20			0.682280
$515$	3.29287e20	+	1.68355e20i	1.51015	+	0.772099i
$516$	−7.23394e19			−0.326966
$517$		−	3.77116e20i		−	1.67995i
$518$			7.45623e19i			0.327375i
$519$	8.76134e19			0.379154
$520$	−4.97395e18	+	9.72856e18i	−0.0212166	+	0.0414976i
$521$	−2.05016e20			−0.861997			−0.430999	−	0.902353i	$-0.641839\pi$
$521$	−2.05016e20			−0.861997			−0.430999	+	0.902353i	$0.641839\pi$
$522$			2.07312e20i			0.859203i
$523$		−	1.23440e20i		−	0.504307i	−0.967687	−	0.252153i	$-0.918861\pi$
$523$		−	1.23440e20i		−	0.504307i	0.967687	−	0.252153i	$-0.0811388\pi$
$524$	−1.12469e20			−0.452947
$525$	3.44027e20	+	4.76284e20i	1.36583	+	1.89091i
$526$	−2.88230e20			−1.12810
$527$			4.92140e20i			1.89893i
$528$		−	8.91676e19i		−	0.339198i
$529$	1.93209e20			0.724618
$530$	8.66241e19	−	1.69428e20i	0.320310	−	0.626494i
$531$	−7.95959e19			−0.290190
$532$		−	1.62067e19i		−	0.0582582i
$533$		−	3.50199e19i		−	0.124125i
$534$	4.04074e19			0.141222
$535$	−6.61351e18	−	3.38131e18i	−0.0227918	−	0.0116528i
$536$	6.84616e18			0.0232654
$537$		−	5.21072e20i		−	1.74619i
$538$			2.06402e20i			0.682098i
$539$	−6.47795e20			−2.11116
$540$	4.20938e19	+	2.15214e19i	0.135290	+	0.0691700i
$541$	−4.82550e20			−1.52955			−0.764774	−	0.644299i	$-0.777149\pi$
$541$	−4.82550e20			−1.52955			−0.764774	+	0.644299i	$0.777149\pi$
$542$		−	3.82304e20i		−	1.19513i
$543$			4.74606e20i			1.46330i
$544$	9.34552e19			0.284192
$545$	−1.54385e20	+	3.01962e20i	−0.463053	+	0.905687i
$546$	−7.34963e19			−0.217431
$547$		−	3.26428e20i		−	0.952539i	−0.879299	−	0.476269i	$-0.841989\pi$
$547$		−	3.26428e20i		−	0.952539i	0.879299	−	0.476269i	$-0.158011\pi$
$548$			1.58422e20i			0.455996i
$549$	−6.17051e19			−0.175198
$550$	−2.08619e20	+	1.50689e20i	−0.584298	+	0.422047i
$551$	−3.78918e19			−0.104691
$552$			9.06066e19i			0.246954i
$553$		−	4.19330e20i		−	1.12750i
$554$	9.39396e19			0.249187
$555$	−6.11690e19	+	1.19641e20i	−0.160079	+	0.313098i
$556$	3.26289e20			0.842444
$557$		−	1.21694e20i		−	0.309995i	−0.987915	−	0.154997i	$-0.950463\pi$
$557$		−	1.21694e20i		−	0.309995i	0.987915	−	0.154997i	$-0.0495369\pi$
$558$			2.56452e20i			0.644539i
$559$	−2.61169e19			−0.0647639
$560$	−1.59430e20	−	8.15125e19i	−0.390087	−	0.199441i
$561$	9.03485e20			2.18122
$562$			2.31408e19i			0.0551259i
$563$		−	3.47821e20i		−	0.817603i	−0.912623	−	0.408801i	$-0.865947\pi$
$563$		−	3.47821e20i		−	0.817603i	0.912623	−	0.408801i	$-0.134053\pi$
$564$	4.72861e20			1.09683
$565$	−6.58172e20	−	3.36506e20i	−1.50652	−	0.770245i
$566$	−2.31822e20			−0.523638
$567$			9.24690e20i			2.06121i
$568$		−	1.22297e20i		−	0.269032i
$569$	−1.09895e20			−0.238580			−0.119290	−	0.992859i	$-0.538062\pi$
$569$	−1.09895e20			−0.238580			−0.119290	+	0.992859i	$0.538062\pi$
$570$	1.32956e19	−	2.60048e19i	0.0284869	−	0.0557176i
$571$	−2.43662e20			−0.515249			−0.257624	−	0.966245i	$-0.582940\pi$
$571$	−2.43662e20			−0.515249			−0.257624	+	0.966245i	$0.582940\pi$
$572$		−	3.21925e19i		−	0.0671868i
$573$		−	5.60353e20i		−	1.15426i
$574$	5.73901e20			1.16680
$575$	2.11986e20	−	1.53120e20i	0.425401	−	0.307273i
$576$	4.86991e19			0.0964611
$577$		−	1.44534e20i		−	0.282587i	−0.989968	−	0.141293i	$-0.954874\pi$
$577$		−	1.44534e20i		−	0.282587i	0.989968	−	0.141293i	$-0.0451261\pi$
$578$			5.80538e20i			1.12040i
$579$	3.70760e20			0.706324
$580$	−1.90579e20	+	3.72754e20i	−0.358398	+	0.700991i
$581$	1.07725e21			1.99984
$582$			4.21494e20i			0.772447i
$583$			5.60650e20i			1.01433i
$584$	−1.31695e20			−0.235219
$585$	−5.13664e19	−	2.62623e19i	−0.0905754	−	0.0463088i
$586$	1.20100e20			0.209080
$587$		−	1.40670e19i		−	0.0241778i	−0.999927	−	0.0120889i	$-0.996152\pi$
$587$		−	1.40670e19i		−	0.0241778i	0.999927	−	0.0120889i	$-0.00384811\pi$
$588$		−	8.12262e20i		−	1.37837i
$589$	−4.68734e19			−0.0785348
$590$	−1.43116e20	−	7.31714e19i	−0.236755	−	0.121046i
$591$	−5.80715e20			−0.948543
$592$		−	4.09512e19i		−	0.0660471i
$593$		−	2.23822e20i		−	0.356445i	−0.983990	−	0.178223i	$-0.942965\pi$
$593$		−	2.23822e20i		−	0.356445i	0.983990	−	0.178223i	$-0.0570347\pi$
$594$	−1.39291e20			−0.219041
$595$	8.25920e20	−	1.61542e21i	1.28251	−	2.50846i
$596$	−9.33785e19			−0.143186
$597$		−	3.99295e20i		−	0.604625i
$598$			3.27120e19i			0.0489156i
$599$	8.06304e20			1.19069			0.595343	−	0.803471i	$-0.297016\pi$
$599$	8.06304e20			1.19069			0.595343	+	0.803471i	$0.297016\pi$
$600$	−1.88947e20	−	2.61585e20i	−0.275553	−	0.381486i
$601$	−4.18833e20			−0.603229			−0.301615	−	0.953430i	$-0.597526\pi$
$601$	−4.18833e20			−0.603229			−0.301615	+	0.953430i	$0.597526\pi$
$602$		−	4.28001e20i		−	0.608795i
$603$			3.61475e19i			0.0507807i
$604$	1.49063e20			0.206820
$605$	1.29737e19	−	2.53753e19i	0.0177786	−	0.0347733i
$606$	−6.76406e20			−0.915509
$607$			1.32503e21i			1.77138i	0.464277	+	0.885690i	$0.346314\pi$
$607$			1.32503e21i			1.77138i	−0.464277	+	0.885690i	$0.653686\pi$
$608$			8.90106e18i			0.0117534i
$609$	−2.81605e21			−3.67291
$610$	−1.10948e20	−	5.67246e19i	−0.142937	−	0.0730799i
$611$	1.70719e20			0.217256
$612$			4.93440e20i			0.620296i
$613$			8.57196e20i			1.06445i	0.846602	+	0.532227i	$0.178645\pi$
$613$			8.57196e20i			1.06445i	−0.846602	+	0.532227i	$0.821355\pi$
$614$	4.22509e20			0.518290
$615$	9.20866e20	+	4.70814e20i	1.11592	+	0.570540i
$616$	5.27566e20			0.631570
$617$			8.40232e20i			0.993712i	0.867833	+	0.496856i	$0.165512\pi$
$617$			8.40232e20i			0.993712i	−0.867833	+	0.496856i	$0.834488\pi$
$618$		−	1.36628e21i		−	1.59634i
$619$	−8.53361e20			−0.985038			−0.492519	−	0.870302i	$-0.663924\pi$
$619$	−8.53361e20			−0.985038			−0.492519	+	0.870302i	$0.663924\pi$
$620$	−2.35753e20	+	4.61109e20i	−0.268855	+	0.525855i
$621$	1.41539e20			0.159474
$622$			8.38701e20i			0.933639i
$623$			2.39073e20i			0.262948i
$624$	4.03657e19			0.0438660
$625$	−2.92702e20	+	8.84131e20i	−0.314287	+	0.949328i
$626$	1.60125e20			0.169884
$627$			8.60517e19i			0.0902096i
$628$			1.14037e20i			0.118127i
$629$	4.14935e20			0.424718
$630$	4.30383e20	−	8.41787e20i	0.435312	−	0.851428i
$631$	9.99690e20			0.999184			0.499592	−	0.866261i	$-0.333483\pi$
$631$	9.99690e20			0.999184			0.499592	+	0.866261i	$0.333483\pi$
$632$			2.30305e20i			0.227471i
$633$			8.68759e20i			0.847952i
$634$	−1.04541e21			−1.00837
$635$	−5.46950e20	−	2.79641e20i	−0.521369	−	0.266562i
$636$	−7.02992e20			−0.662250
$637$		−	2.93253e20i		−	0.273022i
$638$		−	1.23347e21i		−	1.13494i
$639$	6.45725e20			0.587207
$640$	8.75625e19	+	4.47684e19i	0.0786989	+	0.0402366i
$641$	1.69488e20			0.150558			0.0752788	−	0.997163i	$-0.476015\pi$
$641$	1.69488e20			0.150558			0.0752788	+	0.997163i	$0.476015\pi$
$642$			2.74408e19i			0.0240926i
$643$		−	4.61444e20i		−	0.400439i	−0.979751	−	0.200220i	$-0.935834\pi$
$643$		−	4.61444e20i		−	0.400439i	0.979751	−	0.200220i	$-0.0641656\pi$
$644$	−5.36080e20			−0.459818
$645$	3.51121e20	−	6.86758e20i	0.297686	−	0.582245i
$646$	−9.01894e19			−0.0755808
$647$			4.81849e18i			0.00399144i	0.999998	+	0.00199572i	$0.000635257\pi$
$647$			4.81849e18i			0.00399144i	−0.999998	+	0.00199572i	$0.999365\pi$
$648$		−	5.07859e20i		−	0.415844i
$649$	4.73581e20			0.383318
$650$	−6.82160e19	−	9.44409e19i	−0.0545803	−	0.0755631i
$651$	−3.48354e21			−2.75526
$652$		−	2.46295e20i		−	0.192574i
$653$		−	2.12619e21i		−	1.64344i	−0.569894	−	0.821718i	$-0.693016\pi$
$653$		−	2.12619e21i		−	1.64344i	0.569894	−	0.821718i	$-0.306984\pi$
$654$	1.25290e21			0.957377
$655$	5.45901e20	−	1.06773e21i	0.412386	−	0.806587i
$656$	−3.15199e20			−0.235400
$657$		−	6.95345e20i		−	0.513405i
$658$			2.79772e21i			2.04225i
$659$	1.96153e21			1.41565			0.707823	−	0.706390i	$-0.249678\pi$
$659$	1.96153e21			1.41565			0.707823	+	0.706390i	$0.249678\pi$
$660$	8.46518e20	+	4.32802e20i	0.604027	+	0.308823i
$661$	1.73858e21			1.22654			0.613271	−	0.789872i	$-0.289853\pi$
$661$	1.73858e21			1.22654			0.613271	+	0.789872i	$0.289853\pi$
$662$		−	1.04953e21i		−	0.732082i
$663$			4.09003e20i			0.282082i
$664$	−5.91648e20			−0.403462
$665$	1.53859e20	+	7.86640e19i	0.103744	+	0.0530413i
$666$	2.16221e20			0.144159
$667$			1.25337e21i			0.826298i
$668$		−	8.78678e20i		−	0.572805i
$669$	3.02962e21			1.95295
$670$	−3.32299e19	+	6.49944e19i	−0.0211820	+	0.0414300i
$671$	3.67134e20			0.231422
$672$			6.61509e20i			0.412350i
$673$		−	3.18606e19i		−	0.0196400i	−0.999952	−	0.00981998i	$-0.996874\pi$
$673$		−	3.18606e19i		−	0.0196400i	0.999952	−	0.00981998i	$-0.00312585\pi$
$674$	1.70560e21			1.03975
$675$	−4.08629e20	+	2.95159e20i	−0.246349	+	0.177942i
$676$	−8.24056e20			−0.491311
$677$			1.90729e21i			1.12461i	0.826930	+	0.562304i	$0.190085\pi$
$677$			1.90729e21i			1.12461i	−0.826930	+	0.562304i	$0.809915\pi$
$678$			2.73089e21i			1.59251i
$679$	−2.49379e21			−1.43826
$680$	−4.53612e20	+	8.87221e20i	−0.258743	+	0.506075i
$681$	−5.70557e20			−0.321882
$682$		−	1.52584e21i		−	0.851386i
$683$		−	2.46776e21i		−	1.36191i	−0.732326	−	0.680955i	$-0.761565\pi$
$683$		−	2.46776e21i		−	1.36191i	0.732326	−	0.680955i	$-0.238435\pi$
$684$	−4.69973e19			−0.0256538
$685$	−1.50399e21	−	7.68948e20i	−0.812017	−	0.415162i
$686$	2.48540e21			1.32729
$687$		−	2.93245e21i		−	1.54901i
$688$			2.35067e20i			0.122823i
$689$	−2.53803e20			−0.131176
$690$	−8.60178e20	−	4.39786e20i	−0.439765	−	0.224840i
$691$	−2.73418e21			−1.38274			−0.691372	−	0.722499i	$-0.742993\pi$
$691$	−2.73418e21			−1.38274			−0.691372	+	0.722499i	$0.742993\pi$
$692$		−	2.84700e20i		−	0.142427i
$693$			2.78553e21i			1.37851i
$694$	−1.39098e21			−0.680963
$695$	−1.58374e21	+	3.09764e21i	−0.767004	+	1.50018i
$696$	1.54663e21			0.740999
$697$		−	3.19373e21i		−	1.51374i
$698$			6.01007e20i			0.281815i
$699$	6.11121e20			0.283497
$700$	1.54769e21	−	1.11792e21i	0.710309	−	0.513067i
$701$	9.00624e20			0.408939			0.204469	−	0.978873i	$-0.434453\pi$
$701$	9.00624e20			0.408939			0.204469	+	0.978873i	$0.434453\pi$
$702$		−	6.30564e19i		−	0.0283270i
$703$			3.95201e19i			0.0175652i
$704$	−2.89750e20			−0.127418
$705$	−2.29517e21	+	4.48913e21i	−0.998613	+	1.95319i
$706$	4.73371e20			0.203782
$707$		−	4.00200e21i		−	1.70464i
$708$			5.93818e20i			0.250267i
$709$	−2.98281e21			−1.24388			−0.621941	−	0.783064i	$-0.713656\pi$
$709$	−2.98281e21			−1.24388			−0.621941	+	0.783064i	$0.713656\pi$
$710$	1.16103e21	+	5.93605e20i	0.479079	+	0.244940i
$711$	−1.21600e21			−0.496492
$712$		−	1.31304e20i		−	0.0530490i
$713$			1.55046e21i			0.619855i
$714$	−6.70269e21			−2.65163
$715$	3.05621e20	+	1.56256e20i	0.119643	+	0.0611703i
$716$	−1.69322e21			−0.655944
$717$			2.29178e21i			0.878575i
$718$		−	3.67091e20i		−	0.139265i
$719$	3.34379e21			1.25537			0.627686	−	0.778467i	$-0.284002\pi$
$719$	3.34379e21			1.25537			0.627686	+	0.778467i	$0.284002\pi$
$720$	−2.36375e20	+	4.62327e20i	−0.0878231	+	0.171773i
$721$	8.08367e21			2.97231
$722$			1.93459e21i			0.703981i
$723$		−	5.83275e21i		−	2.10057i
$724$	1.54223e21			0.549681
$725$	−2.61373e21	−	3.61854e21i	−0.921988	−	1.27644i
$726$	−1.05287e20			−0.0367579
$727$			5.56511e20i			0.192294i	0.995367	+	0.0961469i	$0.0306519\pi$
$727$			5.56511e20i			0.192294i	−0.995367	+	0.0961469i	$0.969348\pi$
$728$			2.38827e20i			0.0816765i
$729$	1.48647e21			0.503152
$730$	6.39221e20	−	1.25025e21i	0.214156	−	0.418867i
$731$	−2.38180e21			−0.789814
$732$			4.60345e20i			0.151095i
$733$			5.77641e21i			1.87663i	0.345782	+	0.938315i	$0.387614\pi$
$733$			5.77641e21i			1.87663i	−0.345782	+	0.938315i	$0.612386\pi$
$734$	−2.07708e21			−0.667933
$735$	7.71125e21	+	3.94256e21i	2.45454	+	1.25494i
$736$	2.94426e20			0.0927669
$737$		−	2.15071e20i		−	0.0670773i
$738$		−	1.66424e21i		−	0.513798i
$739$	−1.90658e21			−0.582670			−0.291335	−	0.956621i	$-0.594099\pi$
$739$	−1.90658e21			−0.582670			−0.291335	+	0.956621i	$0.594099\pi$
$740$	3.88772e20	+	1.98769e20i	0.117614	+	0.0601326i
$741$	−3.89551e19			−0.0116662
$742$		−	4.15930e21i		−	1.23308i
$743$			3.50311e21i			1.02811i	0.857758	+	0.514053i	$0.171857\pi$
$743$			3.50311e21i			1.02811i	−0.857758	+	0.514053i	$0.828143\pi$
$744$	1.91323e21			0.555867
$745$	4.53240e20	−	8.86494e20i	0.130364	−	0.254979i
$746$	2.32356e20			0.0661627
$747$		−	3.12388e21i		−	0.880623i
$748$		−	2.93588e21i		−	0.819362i
$749$	−1.62355e20			−0.0448593
$750$	3.40048e21	−	5.24094e20i	0.930210	−	0.143367i
$751$	−3.96156e21			−1.07292			−0.536460	−	0.843926i	$-0.680239\pi$
$751$	−3.96156e21			−1.07292			−0.536460	+	0.843926i	$0.680239\pi$
$752$		−	1.53656e21i		−	0.412019i
$753$		−	6.01654e21i		−	1.59729i
$754$	5.58385e20			0.146774
$755$	−7.23522e20	+	1.41514e21i	−0.188300	+	0.368296i
$756$	1.03336e21			0.266280
$757$			2.36000e21i			0.602133i	0.953603	+	0.301067i	$0.0973427\pi$
$757$			2.36000e21i			0.602133i	−0.953603	+	0.301067i	$0.902657\pi$
$758$		−	2.93750e21i		−	0.742093i
$759$	2.84639e21			0.712002
$760$	−8.45027e19	−	4.32039e19i	−0.0209300	−	0.0107009i
$761$	3.45546e20			0.0847463			0.0423731	−	0.999102i	$-0.486508\pi$
$761$	3.45546e20			0.0847463			0.0423731	+	0.999102i	$0.486508\pi$
$762$			2.26941e21i			0.551125i
$763$			7.41286e21i			1.78259i
$764$	−1.82087e21			−0.433589
$765$	−4.68450e21	−	2.39506e21i	−1.10459	−	0.564749i
$766$	4.17405e20			0.0974634
$767$			2.14388e20i			0.0495718i
$768$		−	3.63315e20i		−	0.0831905i
$769$	8.12285e21			1.84188			0.920939	−	0.389707i	$-0.127424\pi$
$769$	8.12285e21			1.84188			0.920939	+	0.389707i	$0.127424\pi$
$770$	−2.56070e21	+	5.00848e21i	−0.575014	+	1.12467i
$771$	5.77536e21			1.28431
$772$		−	1.20479e21i		−	0.265326i
$773$			1.01919e21i			0.222284i	0.993805	+	0.111142i	$0.0354508\pi$
$773$			1.01919e21i			0.222284i	−0.993805	+	0.111142i	$0.964549\pi$
$774$	−1.24115e21			−0.268081
$775$	−3.23326e21	−	4.47626e21i	−0.691637	−	0.957530i
$776$	1.36964e21			0.290165
$777$			2.93706e21i			0.616247i
$778$			2.03816e21i			0.423536i
$779$	3.04184e20			0.0626045
$780$	−1.95927e20	+	3.83214e20i	−0.0399379	+	0.0781146i
$781$	−3.84194e21			−0.775654
$782$			2.98325e21i			0.596540i
$783$		−	2.41604e21i		−	0.478509i
$784$	−2.63945e21			−0.517777
$785$	−1.08262e21	−	5.53512e20i	−0.210355	−	0.107549i
$786$	−4.43022e21			−0.852621
$787$		−	5.71362e21i		−	1.08918i	−0.838702	−	0.544591i	$-0.816685\pi$
$787$		−	5.71362e21i		−	1.08918i	0.838702	−	0.544591i	$-0.183315\pi$
$788$			1.88704e21i			0.356314i
$789$	−1.13536e22			−2.12351
$790$	−2.18641e21	−	1.11785e21i	−0.405069	−	0.207101i
$791$	−1.61575e22			−2.96517
$792$		−	1.52987e21i		−	0.278110i
$793$			1.66200e20i			0.0299282i
$794$	7.53803e21			1.34463
$795$	3.41218e21	−	6.67389e21i	0.602946	−	1.17930i
$796$	−1.29751e21			−0.227124
$797$			1.04166e22i			1.80630i	0.429328	+	0.903149i	$0.358750\pi$
$797$			1.04166e22i			1.80630i	−0.429328	+	0.903149i	$0.641250\pi$
$798$		−	6.38392e20i		−	0.109664i
$799$	1.55691e22			2.64950
$800$	−8.50022e20	+	6.13983e20i	−0.143303	+	0.103510i
$801$	6.93279e20			0.115788
$802$			7.53509e20i			0.124675i
$803$			4.13717e21i			0.678168i
$804$	2.69675e20			0.0437946
$805$	2.60202e21	−	5.08930e21i	0.418641	−	0.818821i
$806$	6.90740e20			0.110104
$807$			8.13030e21i			1.28397i
$808$			2.19798e21i			0.343906i
$809$	−5.31828e21			−0.824437			−0.412218	−	0.911085i	$-0.635246\pi$
$809$	−5.31828e21			−0.824437			−0.412218	+	0.911085i	$0.635246\pi$
$810$	4.82139e21	+	2.46505e21i	0.740516	+	0.378606i
$811$	−2.55694e21			−0.389102			−0.194551	−	0.980892i	$-0.562325\pi$
$811$	−2.55694e21			−0.389102			−0.194551	+	0.980892i	$0.562325\pi$
$812$			9.15075e21i			1.37971i
$813$		−	1.50592e22i		−	2.24969i
$814$	−1.28647e21			−0.190422
$815$	2.33821e21	+	1.19546e21i	0.342927	+	0.175329i
$816$	3.68126e21			0.534959
$817$		−	2.26853e20i		−	0.0326647i
$818$		−	5.68006e21i		−	0.810406i
$819$	−1.26100e21			−0.178272
$820$	1.52991e21	−	2.99235e21i	0.214320	−	0.419188i
$821$	9.61860e21			1.33517			0.667587	−	0.744531i	$-0.267327\pi$
$821$	9.61860e21			1.33517			0.667587	+	0.744531i	$0.267327\pi$
$822$			6.24035e21i			0.858361i
$823$			1.02614e22i			1.39865i	0.714805	+	0.699324i	$0.246515\pi$
$823$			1.02614e22i			1.39865i	−0.714805	+	0.699324i	$0.753485\pi$
$824$	−4.43972e21			−0.599655
$825$	−8.21765e21	+	5.93573e21i	−1.09987	+	0.794455i
$826$	−3.51336e21			−0.465985
$827$		−	3.28610e21i		−	0.431906i	−0.976404	−	0.215953i	$-0.930714\pi$
$827$		−	3.28610e21i		−	0.431906i	0.976404	−	0.215953i	$-0.0692857\pi$
$828$			1.55456e21i			0.202479i
$829$	−2.32835e21			−0.300531			−0.150266	−	0.988646i	$-0.548013\pi$
$829$	−2.32835e21			−0.300531			−0.150266	+	0.988646i	$0.548013\pi$
$830$	2.87174e21	−	5.61684e21i	0.367333	−	0.718467i
$831$	3.70034e21			0.469066
$832$		−	1.31169e20i		−	0.0164780i
$833$		−	2.67440e22i		−	3.32958i
$834$	1.28527e22			1.58580
$835$	8.34178e21	+	4.26493e21i	1.02002	+	0.521510i
$836$	2.79625e20			0.0338867
$837$		−	2.98871e21i		−	0.358958i
$838$			6.51689e19i			0.00775729i
$839$	−1.52420e22			−1.79816			−0.899079	−	0.437786i	$-0.855763\pi$
$839$	−1.52420e22			−1.79816			−0.899079	+	0.437786i	$0.855763\pi$
$840$	−6.28007e21	−	3.21083e21i	−0.734294	−	0.375425i
$841$	1.27656e22			1.47935
$842$		−	2.19483e21i		−	0.252092i
$843$			9.11531e20i			0.103768i
$844$	2.82303e21			0.318528
$845$	3.99980e21	−	7.82322e21i	0.447315	−	0.874904i
$846$	8.11300e21			0.899299
$847$		−	6.22938e20i		−	0.0684415i
$848$			2.28437e21i			0.248770i
$849$	−9.13162e21			−0.985689
$850$	−6.22114e21	−	8.61278e21i	−0.665622	−	0.921513i
$851$	1.30723e21			0.138638
$852$		−	4.81736e21i		−	0.506422i
$853$			1.69959e22i			1.77104i	0.464605	+	0.885518i	$0.346196\pi$
$853$			1.69959e22i			1.77104i	−0.464605	+	0.885518i	$0.653804\pi$
$854$	−2.72366e21			−0.281332
$855$	2.28115e20	−	4.46171e20i	0.0233565	−	0.0456831i
$856$	8.91689e19			0.00905024
$857$			1.53882e21i			0.154821i	0.996999	+	0.0774107i	$0.0246653\pi$
$857$			1.53882e21i			0.154821i	−0.996999	+	0.0774107i	$0.975335\pi$
$858$		−	1.26808e21i		−	0.126471i
$859$	−9.05890e21			−0.895626			−0.447813	−	0.894127i	$-0.647797\pi$
$859$	−9.05890e21			−0.895626			−0.447813	+	0.894127i	$0.647797\pi$
$860$	−2.23162e21	−	1.14097e21i	−0.218717	−	0.111824i
$861$	2.26063e22			2.19638
$862$		−	2.44672e21i		−	0.235657i
$863$		−	5.29023e21i		−	0.505119i	−0.967581	−	0.252559i	$-0.918728\pi$
$863$		−	5.29023e21i		−	0.505119i	0.967581	−	0.252559i	$-0.0812723\pi$
$864$	−5.67544e20			−0.0537213
$865$	2.70281e21	+	1.38188e21i	0.253627	+	0.129673i
$866$	−1.12472e22			−1.04631
$867$			2.28678e22i			2.10902i
$868$			1.13198e22i			1.03500i
$869$	7.23499e21			0.655827
$870$	−7.50703e21	+	1.46830e22i	−0.674643	+	1.31954i
$871$	9.73615e19			0.00867463
$872$		−	4.07130e21i		−	0.359633i
$873$			7.23167e21i			0.633333i
$874$	−2.84138e20			−0.0246714
$875$	3.10084e21	+	2.01192e22i	0.266943	+	1.73201i
$876$	−5.18755e21			−0.442774
$877$		−	1.19812e22i		−	1.01392i	−0.861970	−	0.506960i	$-0.830769\pi$
$877$		−	1.19812e22i		−	1.01392i	0.861970	−	0.506960i	$-0.169231\pi$
$878$			2.27232e21i			0.190660i
$879$	4.73083e21			0.393569
$880$	1.40639e21	−	2.75076e21i	0.116007	−	0.226899i
$881$	−1.94299e22			−1.58910			−0.794549	−	0.607200i	$-0.792293\pi$
$881$	−1.94299e22			−1.58910			−0.794549	+	0.607200i	$0.792293\pi$
$882$		−	1.39362e22i		−	1.13013i
$883$			1.29139e21i			0.103837i	0.998651	+	0.0519184i	$0.0165336\pi$
$883$			1.29139e21i			0.103837i	−0.998651	+	0.0519184i	$0.983466\pi$
$884$	1.32906e21			0.105962
$885$	−5.63744e21	−	2.88227e21i	−0.445664	−	0.227856i
$886$	−2.06505e21			−0.161874
$887$			3.30690e21i			0.257036i	0.991707	+	0.128518i	$0.0410220\pi$
$887$			3.30690e21i			0.257036i	−0.991707	+	0.128518i	$0.958978\pi$
$888$		−	1.61309e21i		−	0.124326i
$889$	−1.34271e22			−1.02617
$890$	1.24654e21	+	6.37322e20i	0.0944672	+	0.0482985i
$891$	−1.59543e22			−1.19893
$892$		−	9.84475e21i		−	0.733615i
$893$			1.48287e21i			0.109576i
$894$	−3.67824e21			−0.269531
$895$	8.21857e21	−	1.60747e22i	0.597205	−	1.16807i
$896$	2.14957e21			0.154897
$897$			1.28855e21i			0.0920781i
$898$		−	4.32963e21i		−	0.306816i
$899$	2.64660e22			1.85991
$900$	−3.24181e21	−	4.48808e21i	−0.225927	−	0.312782i
$901$	−2.31463e22			−1.59972
$902$			9.90191e21i			0.678687i
$903$		−	1.68592e22i		−	1.14599i
$904$	8.87403e21			0.598215
$905$	−7.48569e21	+	1.46413e22i	−0.500458	+	0.978847i
$906$	5.87169e21			0.389315
$907$		−	2.53575e21i		−	0.166745i	−0.996518	−	0.0833723i	$-0.973431\pi$
$907$		−	2.53575e21i		−	0.166745i	0.996518	−	0.0833723i	$-0.0265691\pi$
$908$			1.85403e21i			0.120913i
$909$	−1.16053e22			−0.750631
$910$	−2.26731e21	−	1.15922e21i	−0.145446	−	0.0743625i
$911$	1.82827e22			1.16319			0.581597	−	0.813477i	$-0.302428\pi$
$911$	1.82827e22			1.16319			0.581597	+	0.813477i	$0.302428\pi$
$912$			3.50619e20i			0.0221245i
$913$			1.85865e22i			1.16323i
$914$	1.98580e22			1.23265
$915$	−4.37030e21	−	2.23442e21i	−0.269063	−	0.137564i
$916$	−9.52899e21			−0.581876
$917$		−	2.62117e22i		−	1.58754i
$918$		−	5.75060e21i		−	0.345456i
$919$	−8.20865e21			−0.489109			−0.244554	−	0.969636i	$-0.578642\pi$
$919$	−8.20865e21			−0.489109			−0.244554	+	0.969636i	$0.578642\pi$
$920$	−1.42909e21	+	2.79515e21i	−0.0844597	+	0.165195i
$921$	1.66429e22			0.975622
$922$			6.34380e21i			0.368865i
$923$		−	1.73923e21i		−	0.100310i
$924$	2.07812e22			1.18886
$925$	−3.77404e21	+	2.72604e21i	−0.214163	+	0.154693i
$926$	−6.54544e21			−0.368431
$927$		−	2.34416e22i		−	1.30885i
$928$		−	5.02578e21i		−	0.278352i
$929$	1.31215e22			0.720887			0.360443	−	0.932781i	$-0.382625\pi$
$929$	1.31215e22			0.720887			0.360443	+	0.932781i	$0.382625\pi$
$930$	−9.28644e21	+	1.81634e22i	−0.506090	+	0.989861i
$931$	2.54721e21			0.137703
$932$		−	1.98584e21i		−	0.106494i
$933$			3.30370e22i			1.75747i
$934$	−4.76594e21			−0.251505
$935$	2.78719e22	+	1.42501e22i	1.45908	+	0.745989i
$936$	6.92565e20			0.0359660
$937$		−	3.86691e21i		−	0.199213i	−0.995027	−	0.0996065i	$-0.968242\pi$
$937$		−	3.86691e21i		−	0.199213i	0.995027	−	0.0996065i	$-0.0317584\pi$
$938$			1.59555e21i			0.0815434i
$939$	6.30743e21			0.319787
$940$	1.45874e22	+	7.45817e21i	0.733703	+	0.375123i
$941$	2.91264e22			1.45333			0.726665	−	0.686992i	$-0.241069\pi$
$941$	2.91264e22			1.45333			0.726665	+	0.686992i	$0.241069\pi$
$942$			4.49199e21i			0.222360i
$943$		−	1.00617e22i		−	0.494121i
$944$	1.92961e21			0.0940113
$945$	−5.01572e21	+	9.81027e21i	−0.242435	+	0.474179i
$946$	7.38458e21			0.354113
$947$		−	1.76075e22i		−	0.837671i	−0.908062	−	0.418835i	$-0.862438\pi$
$947$		−	1.76075e22i		−	0.837671i	0.908062	−	0.418835i	$-0.137562\pi$
$948$			9.07186e21i			0.428187i
$949$	−1.87288e21			−0.0877026
$950$	8.20317e20	−	5.92527e20i	0.0381114	−	0.0275284i
$951$	−4.11795e22			−1.89814
$952$			2.17804e22i			0.996068i
$953$		−	3.28538e22i		−	1.49069i	−0.666677	−	0.745347i	$-0.732284\pi$
$953$		−	3.28538e22i		−	1.49069i	0.666677	−	0.745347i	$-0.267716\pi$
$954$	−1.20614e22			−0.542982
$955$	8.83813e21	−	1.72865e22i	0.394762	−	0.772115i
$956$	7.44714e21			0.330031
$957$		−	4.85871e22i		−	2.13640i
$958$		−	1.40198e22i		−	0.611648i
$959$	−3.69214e22			−1.59823
$960$	3.44915e21	+	1.76346e21i	0.148142	+	0.0757409i
$961$	9.27406e21			0.395225
$962$		−	5.82380e20i		−	0.0246260i
$963$			4.70809e20i			0.0197536i
$964$	−1.89535e22			−0.789065
$965$	1.14377e22	+	5.84779e21i	0.472481	+	0.241567i
$966$	−2.11165e22			−0.865554
$967$		−	2.77962e22i		−	1.13054i	−0.824905	−	0.565272i	$-0.808771\pi$
$967$		−	2.77962e22i		−	1.13054i	0.824905	−	0.565272i	$-0.191229\pi$
$968$			3.42131e20i			0.0138079i
$969$	−3.55262e21			−0.142272
$970$	−6.64798e21	+	1.30028e22i	−0.264181	+	0.516712i
$971$	−4.39922e22			−1.73473			−0.867365	−	0.497673i	$-0.834188\pi$
$971$	−4.39922e22			−1.73473			−0.867365	+	0.497673i	$0.834188\pi$
$972$		−	1.61217e22i		−	0.630833i
$973$			7.60440e22i			2.95269i
$974$	−1.10001e22			−0.423843
$975$	−2.68707e21	−	3.72009e21i	−0.102741	−	0.142239i
$976$	1.49589e21			0.0567579
$977$			5.03867e22i			1.89717i	0.316520	+	0.948586i	$0.397486\pi$
$977$			5.03867e22i			1.89717i	−0.316520	+	0.948586i	$0.602514\pi$
$978$		−	9.70171e21i		−	0.362499i
$979$	−4.12488e21			−0.152947
$980$	1.28113e22	−	2.50577e22i	0.471410	−	0.922032i
$981$	2.14963e22			0.784958
$982$			2.45081e22i			0.888123i
$983$		−	7.99986e21i		−	0.287694i	−0.989600	−	0.143847i	$-0.954053\pi$
$983$		−	7.99986e21i		−	0.287694i	0.989600	−	0.143847i	$-0.0459474\pi$
$984$	−1.24159e22			−0.443113
$985$	−1.79147e22	−	9.15929e21i	−0.634508	−	0.324407i
$986$	5.09234e22			1.78995
$987$			1.10204e23i			3.84431i
$988$			1.26585e20i			0.00438233i
$989$	−7.50375e21			−0.257814
$990$	1.45239e22	+	7.42569e21i	0.495245	+	0.253205i
$991$	−2.28991e22			−0.774937			−0.387469	−	0.921883i	$-0.626650\pi$
$991$	−2.28991e22			−0.774937			−0.387469	+	0.921883i	$0.626650\pi$
$992$		−	6.21705e21i		−	0.208808i
$993$		−	4.13416e22i		−	1.37806i
$994$	2.85022e22			0.942934
$995$	6.29785e21	−	1.23180e22i	0.206785	−	0.404451i
$996$	−2.33054e22			−0.759472
$997$		−	2.70362e22i		−	0.874443i	−0.899354	−	0.437222i	$-0.855963\pi$
$997$		−	2.70362e22i		−	0.874443i	0.899354	−	0.437222i	$-0.144037\pi$
$998$		−	8.22483e21i		−	0.264027i
$999$	−2.51986e21			−0.0802851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.16.b.a.9.1	✓	8
3.2	odd	2		90.16.c.c.19.6		8
4.3	odd	2		80.16.c.c.49.7		8
5.2	odd	4		50.16.a.k.1.1		4
5.3	odd	4		50.16.a.j.1.4		4
5.4	even	2	inner	10.16.b.a.9.8	yes	8
15.14	odd	2		90.16.c.c.19.2		8
20.19	odd	2		80.16.c.c.49.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.16.b.a.9.1	✓	8	1.1	even	1	trivial
10.16.b.a.9.8	yes	8	5.4	even	2	inner
50.16.a.j.1.4		4	5.3	odd	4
50.16.a.k.1.1		4	5.2	odd	4
80.16.c.c.49.2		8	20.19	odd	2
80.16.c.c.49.7		8	4.3	odd	2
90.16.c.c.19.2		8	15.14	odd	2
90.16.c.c.19.6		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-128.000i q^{2} -5042.00i q^{3} -16384.0 q^{4} +(79524.6 - 155542. i) q^{5} -645376. q^{6} -3.81841e6i q^{7} +2.09715e6i q^{8} -1.10729e7 q^{9} +O(q^{10})\)	\(q-128.000i q^{2} -5042.00i q^{3} -16384.0 q^{4} +(79524.6 - 155542. i) q^{5} -645376. q^{6} -3.81841e6i q^{7} +2.09715e6i q^{8} -1.10729e7 q^{9} +(-1.99094e7 - 1.01791e7i) q^{10} +6.58816e7 q^{11} +8.26082e7i q^{12} +2.98243e7i q^{13} -4.88757e8 q^{14} +(-7.84245e8 - 4.00963e8i) q^{15} +2.68435e8 q^{16} +2.71990e9i q^{17} +1.41733e9i q^{18} -2.59055e8 q^{19} +(-1.30293e9 + 2.54841e9i) q^{20} -1.92524e10 q^{21} -8.43285e9i q^{22} +8.56893e9i q^{23} +1.05738e10 q^{24} +(-1.78693e10 - 2.47389e10i) q^{25} +3.81751e9 q^{26} -1.65177e10i q^{27} +6.25609e10i q^{28} +1.46270e11 q^{29} +(-5.13233e10 + 1.00383e11i) q^{30} +1.80940e11 q^{31} -3.43597e10i q^{32} -3.32175e11i q^{33} +3.48148e11 q^{34} +(-5.93925e11 - 3.03658e11i) q^{35} +1.81418e11 q^{36} -1.52555e11i q^{37} +3.31590e10i q^{38} +1.50374e11 q^{39} +(3.26196e11 + 1.66775e11i) q^{40} -1.17421e12 q^{41} +2.46431e12i q^{42} +8.75693e11i q^{43} -1.07940e12 q^{44} +(-8.80567e11 + 1.72230e12i) q^{45} +1.09682e12 q^{46} -5.72415e12i q^{47} -1.35345e12i q^{48} -9.83271e12 q^{49} +(-3.16658e12 + 2.28726e12i) q^{50} +1.37138e13 q^{51} -4.88641e11i q^{52} +8.50996e12i q^{53} -2.11426e12 q^{54} +(5.23921e12 - 1.02474e13i) q^{55} +8.00779e12 q^{56} +1.30616e12i q^{57} -1.87225e13i q^{58} +7.18836e12 q^{59} +(1.28491e13 + 6.56938e12i) q^{60} +5.57263e12 q^{61} -2.31603e13i q^{62} +4.22809e13i q^{63} -4.39805e12 q^{64} +(4.63894e12 + 2.37176e12i) q^{65} -4.25184e13 q^{66} -3.26451e12i q^{67} -4.45629e13i q^{68} +4.32046e13 q^{69} +(-3.88682e13 + 7.60224e13i) q^{70} -5.83158e13 q^{71} -2.32215e13i q^{72} +6.27971e13i q^{73} -1.95270e13 q^{74} +(-1.24734e14 + 9.00968e13i) q^{75} +4.24436e12 q^{76} -2.51563e14i q^{77} -1.92479e13i q^{78} +1.09818e14 q^{79} +(2.13472e13 - 4.17531e13i) q^{80} -2.42166e14 q^{81} +1.50298e14i q^{82} +2.82120e14i q^{83} +3.15432e14 q^{84} +(4.23060e14 + 2.16299e14i) q^{85} +1.12089e14 q^{86} -7.37491e14i q^{87} +1.38164e14i q^{88} -6.26105e13 q^{89} +(2.20455e14 + 1.12713e14i) q^{90} +1.13881e14 q^{91} -1.40393e14i q^{92} -9.12301e14i q^{93} -7.32691e14 q^{94} +(-2.06012e13 + 4.02940e13i) q^{95} -1.73242e14 q^{96} -6.53097e14i q^{97} +1.25859e15i q^{98} -7.29500e14 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 131072 q^{4} + 251400 q^{5} - 53248 q^{6} - 43491176 q^{9}+O(q^{10}) \) 8 * q - 131072 * q^4 + 251400 * q^5 - 53248 * q^6 - 43491176 * q^9	\( 8 q - 131072 q^{4} + 251400 q^{5} - 53248 q^{6} - 43491176 q^{9} + 4403200 q^{10} + 95435616 q^{11} - 499347456 q^{14} + 5448800 q^{15} + 2147483648 q^{16} + 6479216160 q^{19} - 4118937600 q^{20} - 14760325504 q^{21} + 872415232 q^{24} - 2241855000 q^{25} + 66288525312 q^{26} - 244549636560 q^{29} - 32701542400 q^{30} + 522311705216 q^{31} + 322563211264 q^{34} - 1829607146400 q^{35} + 712559427584 q^{36} - 2307595824192 q^{39} - 72142028800 q^{40} + 6699117519216 q^{41} - 1563617132544 q^{44} - 9090807477800 q^{45} + 12178733699072 q^{46} - 15809163185544 q^{49} - 13485542400000 q^{50} + 40555579650176 q^{51} - 7241111674880 q^{54} - 39746288199200 q^{55} + 8181308719104 q^{56} + 3791808509280 q^{59} - 89273139200 q^{60} + 57800629300816 q^{61} - 35184372088832 q^{64} + 58028394892800 q^{65} - 82398766186496 q^{66} + 59060996328448 q^{69} + 60817223987200 q^{70} - 245426235422784 q^{71} + 53331092987904 q^{74} + 226448486200000 q^{75} - 106155477565440 q^{76} + 624094605411840 q^{79} + 67484673638400 q^{80} - 13\!\cdots\!52 q^{81}+ \cdots + 16\!\cdots\!48 q^{99}+O(q^{100}) \) 8 * q - 131072 * q^4 + 251400 * q^5 - 53248 * q^6 - 43491176 * q^9 + 4403200 * q^10 + 95435616 * q^11 - 499347456 * q^14 + 5448800 * q^15 + 2147483648 * q^16 + 6479216160 * q^19 - 4118937600 * q^20 - 14760325504 * q^21 + 872415232 * q^24 - 2241855000 * q^25 + 66288525312 * q^26 - 244549636560 * q^29 - 32701542400 * q^30 + 522311705216 * q^31 + 322563211264 * q^34 - 1829607146400 * q^35 + 712559427584 * q^36 - 2307595824192 * q^39 - 72142028800 * q^40 + 6699117519216 * q^41 - 1563617132544 * q^44 - 9090807477800 * q^45 + 12178733699072 * q^46 - 15809163185544 * q^49 - 13485542400000 * q^50 + 40555579650176 * q^51 - 7241111674880 * q^54 - 39746288199200 * q^55 + 8181308719104 * q^56 + 3791808509280 * q^59 - 89273139200 * q^60 + 57800629300816 * q^61 - 35184372088832 * q^64 + 58028394892800 * q^65 - 82398766186496 * q^66 + 59060996328448 * q^69 + 60817223987200 * q^70 - 245426235422784 * q^71 + 53331092987904 * q^74 + 226448486200000 * q^75 - 106155477565440 * q^76 + 624094605411840 * q^79 + 67484673638400 * q^80 - 1376711600108152 * q^81 + 241833173057536 * q^84 + 1092463762441600 * q^85 - 8937574699008 * q^86 - 635249793637680 * q^89 + 851824438169600 * q^90 - 976491706492224 * q^91 - 537030386200576 * q^94 - 1859590136604000 * q^95 - 14293651161088 * q^96 + 1626246829353248 * q^99

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