LMFDB - Embedded newform 10.16.b.a.9.3

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			9.3
Root			$149.707 - 149.707i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.16.b.a.9.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-128.000i q^{2} +2932.14i q^{3} -16384.0 q^{4} +(-160703. + 68498.7i) q^{5} +375313. q^{6} -1.80018e6i q^{7} +2.09715e6i q^{8} +5.75148e6 q^{9} +O(q^{10})$	\(q-128.000i q^{2} +2932.14i q^{3} -16384.0 q^{4} +(-160703. + 68498.7i) q^{5} +375313. q^{6} -1.80018e6i q^{7} +2.09715e6i q^{8} +5.75148e6 q^{9} +(8.76783e6 + 2.05700e7i) q^{10} +8.15444e7 q^{11} -4.80401e7i q^{12} -1.37025e8i q^{13} -2.30423e8 q^{14} +(-2.00848e8 - 4.71204e8i) q^{15} +2.68435e8 q^{16} -2.67743e9i q^{17} -7.36190e8i q^{18} +2.47624e9 q^{19} +(2.63296e9 - 1.12228e9i) q^{20} +5.27837e9 q^{21} -1.04377e10i q^{22} -2.86848e9i q^{23} -6.14914e9 q^{24} +(2.11334e10 - 2.20159e10i) q^{25} -1.75391e10 q^{26} +5.89371e10i q^{27} +2.94941e10i q^{28} -1.20074e11 q^{29} +(-6.03141e10 + 2.57085e10i) q^{30} +1.95615e11 q^{31} -3.43597e10i q^{32} +2.39099e11i q^{33} -3.42712e11 q^{34} +(1.23310e11 + 2.89294e11i) q^{35} -9.42323e10 q^{36} +2.27246e11i q^{37} -3.16958e11i q^{38} +4.01775e11 q^{39} +(-1.43652e11 - 3.37019e11i) q^{40} +1.53448e12 q^{41} -6.75632e11i q^{42} -2.06170e12i q^{43} -1.33602e12 q^{44} +(-9.24281e11 + 3.93969e11i) q^{45} -3.67165e11 q^{46} -2.80483e12i q^{47} +7.87089e11i q^{48} +1.50692e12 q^{49} +(-2.81804e12 - 2.70508e12i) q^{50} +7.85061e12 q^{51} +2.24501e12i q^{52} +5.32023e12i q^{53} +7.54395e12 q^{54} +(-1.31044e13 + 5.58569e12i) q^{55} +3.77525e12 q^{56} +7.26066e12i q^{57} +1.53695e13i q^{58} -1.26129e13 q^{59} +(3.29069e12 + 7.72020e12i) q^{60} -3.42493e13 q^{61} -2.50388e13i q^{62} -1.03537e13i q^{63} -4.39805e12 q^{64} +(9.38601e12 + 2.20203e13i) q^{65} +3.06047e13 q^{66} -5.27028e13i q^{67} +4.38671e13i q^{68} +8.41077e12 q^{69} +(3.70297e13 - 1.57837e13i) q^{70} +2.86481e13 q^{71} +1.20617e13i q^{72} -1.30756e14i q^{73} +2.90875e13 q^{74} +(6.45537e13 + 6.19661e13i) q^{75} -4.05706e13 q^{76} -1.46795e14i q^{77} -5.14272e13i q^{78} -1.18489e14 q^{79} +(-4.31384e13 + 1.83875e13i) q^{80} -9.02841e13 q^{81} -1.96414e14i q^{82} +4.70309e14i q^{83} -8.64808e13 q^{84} +(1.83401e14 + 4.30272e14i) q^{85} -2.63898e14 q^{86} -3.52074e14i q^{87} +1.71011e14i q^{88} +5.97179e14 q^{89} +(5.04280e13 + 1.18308e14i) q^{90} -2.46669e14 q^{91} +4.69971e13i q^{92} +5.73571e14i q^{93} -3.59018e14 q^{94} +(-3.97939e14 + 1.69619e14i) q^{95} +1.00747e14 q^{96} -9.88593e14i q^{97} -1.92885e14i q^{98} +4.69001e14 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
$3$			2932.14i			0.774060i	0.922067	+	0.387030i	$0.126499\pi$
$3$			2932.14i			0.774060i	−0.922067	+	0.387030i	$0.873501\pi$
$4$	−16384.0			−0.500000
$5$	−160703.	+	68498.7i	−0.919919	+	0.392109i
$5$	−160703.	+	68498.7i	−0.919919	+	0.392109i
$6$	375313.			0.547343
$7$		−	1.80018e6i		−	0.826191i	−0.910688	−	0.413095i	$-0.864448\pi$
$7$		−	1.80018e6i		−	0.826191i	0.910688	−	0.413095i	$-0.135552\pi$
$8$			2.09715e6i			0.353553i
$9$	5.75148e6			0.400831
$10$	8.76783e6	+	2.05700e7i	0.277263	+	0.650481i
$11$	8.15444e7			1.26168			0.630840	−	0.775913i	$-0.282710\pi$
$11$	8.15444e7			1.26168			0.630840	+	0.775913i	$0.282710\pi$
$12$		−	4.80401e7i		−	0.387030i
$13$		−	1.37025e8i		−	0.605652i	−0.953046	−	0.302826i	$-0.902070\pi$
$13$		−	1.37025e8i		−	0.605652i	0.953046	−	0.302826i	$-0.0979301\pi$
$14$	−2.30423e8			−0.584205
$15$	−2.00848e8	−	4.71204e8i	−0.303516	−	0.712072i
$16$	2.68435e8			0.250000
$17$		−	2.67743e9i		−	1.58253i	−0.611473	−	0.791265i	$-0.709423\pi$
$17$		−	2.67743e9i		−	1.58253i	0.611473	−	0.791265i	$-0.290577\pi$
$18$		−	7.36190e8i		−	0.283430i
$19$	2.47624e9			0.635536			0.317768	−	0.948169i	$-0.397067\pi$
$19$	2.47624e9			0.635536			0.317768	+	0.948169i	$0.397067\pi$
$20$	2.63296e9	−	1.12228e9i	0.459959	−	0.196055i
$21$	5.27837e9			0.639522
$22$		−	1.04377e10i		−	0.892142i
$23$		−	2.86848e9i		−	0.175668i	−0.996135	−	0.0878340i	$-0.972005\pi$
$23$		−	2.86848e9i		−	0.175668i	0.996135	−	0.0878340i	$-0.0279945\pi$
$24$	−6.14914e9			−0.273672
$25$	2.11334e10	−	2.20159e10i	0.692500	−	0.721418i
$26$	−1.75391e10			−0.428261
$27$			5.89371e10i			1.08433i
$28$			2.94941e10i			0.413095i
$29$	−1.20074e11			−1.29260			−0.646300	−	0.763083i	$-0.723685\pi$
$29$	−1.20074e11			−1.29260			−0.646300	+	0.763083i	$0.723685\pi$
$30$	−6.03141e10	+	2.57085e10i	−0.503511	+	0.214618i
$31$	1.95615e11			1.27700			0.638499	−	0.769623i	$-0.279556\pi$
$31$	1.95615e11			1.27700			0.638499	+	0.769623i	$0.279556\pi$
$32$		−	3.43597e10i		−	0.176777i
$33$			2.39099e11i			0.976616i
$34$	−3.42712e11			−1.11902
$35$	1.23310e11	+	2.89294e11i	0.323957	+	0.760028i
$36$	−9.42323e10			−0.200415
$37$			2.27246e11i			0.393535i	0.980450	+	0.196767i	$0.0630443\pi$
$37$			2.27246e11i			0.393535i	−0.980450	+	0.196767i	$0.936956\pi$
$38$		−	3.16958e11i		−	0.449392i
$39$	4.01775e11			0.468811
$40$	−1.43652e11	−	3.37019e11i	−0.138632	−	0.325240i
$41$	1.53448e12			1.23051			0.615253	−	0.788330i	$-0.289054\pi$
$41$	1.53448e12			1.23051			0.615253	+	0.788330i	$0.289054\pi$
$42$		−	6.75632e11i		−	0.452210i
$43$		−	2.06170e12i		−	1.15668i	−0.815796	−	0.578340i	$-0.803701\pi$
$43$		−	2.06170e12i		−	1.15668i	0.815796	−	0.578340i	$-0.196299\pi$
$44$	−1.33602e12			−0.630840
$45$	−9.24281e11	+	3.93969e11i	−0.368732	+	0.157169i
$46$	−3.67165e11			−0.124216
$47$		−	2.80483e12i		−	0.807556i	−0.914857	−	0.403778i	$-0.867697\pi$
$47$		−	2.80483e12i		−	0.807556i	0.914857	−	0.403778i	$-0.132303\pi$
$48$			7.87089e11i			0.193515i
$49$	1.50692e12			0.317409
$50$	−2.81804e12	−	2.70508e12i	−0.510119	−	0.489672i
$51$	7.85061e12			1.22497
$52$			2.24501e12i			0.302826i
$53$			5.32023e12i			0.622101i	0.950393	+	0.311051i	$0.100681\pi$
$53$			5.32023e12i			0.622101i	−0.950393	+	0.311051i	$0.899319\pi$
$54$	7.54395e12			0.766735
$55$	−1.31044e13	+	5.58569e12i	−1.16064	+	0.494717i
$56$	3.77525e12			0.292103
$57$			7.26066e12i			0.491943i
$58$			1.53695e13i			0.914006i
$59$	−1.26129e13			−0.659817			−0.329909	−	0.944013i	$-0.607018\pi$
$59$	−1.26129e13			−0.659817			−0.329909	+	0.944013i	$0.607018\pi$
$60$	3.29069e12	+	7.72020e12i	0.151758	+	0.356036i
$61$	−3.42493e13			−1.39533			−0.697667	−	0.716422i	$-0.745778\pi$
$61$	−3.42493e13			−1.39533			−0.697667	+	0.716422i	$0.745778\pi$
$62$		−	2.50388e13i		−	0.902974i
$63$		−	1.03537e13i		−	0.331163i
$64$	−4.39805e12			−0.125000
$65$	9.38601e12	+	2.20203e13i	0.237482	+	0.557151i
$66$	3.06047e13			0.690572
$67$		−	5.27028e13i		−	1.06236i	−0.847258	−	0.531181i	$-0.821748\pi$
$67$		−	5.27028e13i		−	1.06236i	0.847258	−	0.531181i	$-0.178252\pi$
$68$			4.38671e13i			0.791265i
$69$	8.41077e12			0.135978
$70$	3.70297e13	−	1.57837e13i	0.537421	−	0.229072i
$71$	2.86481e13			0.373817			0.186908	−	0.982377i	$-0.440153\pi$
$71$	2.86481e13			0.373817			0.186908	+	0.982377i	$0.440153\pi$
$72$			1.20617e13i			0.141715i
$73$		−	1.30756e14i		−	1.38529i	−0.721280	−	0.692643i	$-0.756446\pi$
$73$		−	1.30756e14i		−	1.38529i	0.721280	−	0.692643i	$-0.243554\pi$
$74$	2.90875e13			0.278271
$75$	6.45537e13	+	6.19661e13i	0.558421	+	0.536037i
$76$	−4.05706e13			−0.317768
$77$		−	1.46795e14i		−	1.04239i
$78$		−	5.14272e13i		−	0.331500i
$79$	−1.18489e14			−0.694182			−0.347091	−	0.937831i	$-0.612831\pi$
$79$	−1.18489e14			−0.694182			−0.347091	+	0.937831i	$0.612831\pi$
$80$	−4.31384e13	+	1.83875e13i	−0.229980	+	0.0980274i
$81$	−9.02841e13			−0.438504
$82$		−	1.96414e14i		−	0.870099i
$83$			4.70309e14i			1.90238i	0.308605	+	0.951190i	$0.400138\pi$
$83$			4.70309e14i			1.90238i	−0.308605	+	0.951190i	$0.599862\pi$
$84$	−8.64808e13			−0.319761
$85$	1.83401e14	+	4.30272e14i	0.620525	+	1.45580i
$86$	−2.63898e14			−0.817896
$87$		−	3.52074e14i		−	1.00055i
$88$			1.71011e14i			0.446071i
$89$	5.97179e14			1.43113			0.715565	−	0.698546i	$-0.246169\pi$
$89$	5.97179e14			1.43113			0.715565	+	0.698546i	$0.246169\pi$
$90$	5.04280e13	+	1.18308e14i	0.111136	+	0.260733i
$91$	−2.46669e14			−0.500384
$92$			4.69971e13i			0.0878340i
$93$			5.73571e14i			0.988474i
$94$	−3.59018e14			−0.571028
$95$	−3.97939e14	+	1.69619e14i	−0.584641	+	0.249200i
$96$	1.00747e14			0.136836
$97$		−	9.88593e14i		−	1.24231i	−0.783688	−	0.621154i	$-0.786664\pi$
$97$		−	9.88593e14i		−	1.24231i	0.783688	−	0.621154i	$-0.213336\pi$
$98$		−	1.92885e14i		−	0.224442i
$99$	4.69001e14			0.505720
$100$	−3.46250e14	+	3.60709e14i	−0.346250	+	0.360709i
$101$	1.00744e15			0.934995			0.467497	−	0.883994i	$-0.345156\pi$
$101$	1.00744e15			0.934995			0.467497	+	0.883994i	$0.345156\pi$
$102$		−	1.00488e15i		−	0.866187i
$103$		−	3.12884e14i		−	0.250671i	−0.992114	−	0.125336i	$-0.959999\pi$
$103$		−	3.12884e14i		−	0.250671i	0.992114	−	0.125336i	$-0.0400007\pi$
$104$	2.87361e14			0.214130
$105$	−8.48251e14	+	3.61562e14i	−0.588308	+	0.250762i
$106$	6.80989e14			0.439892
$107$		−	2.36883e15i		−	1.42612i	−0.701105	−	0.713058i	$-0.747310\pi$
$107$		−	2.36883e15i		−	1.42612i	0.701105	−	0.713058i	$-0.252690\pi$
$108$		−	9.65625e14i		−	0.542164i
$109$	−9.18620e14			−0.481324			−0.240662	−	0.970609i	$-0.577365\pi$
$109$	−9.18620e14			−0.481324			−0.240662	+	0.970609i	$0.577365\pi$
$110$	7.14968e14	+	1.67737e15i	0.349817	+	0.820698i
$111$	−6.66316e14			−0.304620
$112$		−	4.83232e14i		−	0.206548i
$113$			9.41502e14i			0.376472i	0.982124	+	0.188236i	$0.0602770\pi$
$113$			9.41502e14i			0.376472i	−0.982124	+	0.188236i	$0.939723\pi$
$114$	9.29364e14			0.347856
$115$	1.96487e14	+	4.60973e14i	0.0688811	+	0.161600i
$116$	1.96729e15			0.646300
$117$		−	7.88094e14i		−	0.242764i
$118$			1.61445e15i			0.466561i
$119$	−4.81986e15			−1.30747
$120$	9.88186e14	−	4.21208e14i	0.251756	−	0.107309i
$121$	2.47225e15			0.591836
$122$			4.38391e15i			0.986650i
$123$			4.49932e15i			0.952485i
$124$	−3.20496e15			−0.638499
$125$	−1.88815e15	+	4.98564e15i	−0.354169	+	0.935181i
$126$	−1.32527e15			−0.234167
$127$		−	4.76019e15i		−	0.792677i	−0.918105	−	0.396338i	$-0.870281\pi$
$127$		−	4.76019e15i		−	0.792677i	0.918105	−	0.396338i	$-0.129719\pi$
$128$			5.62950e14i			0.0883883i
$129$	6.04520e15			0.895339
$130$	2.81860e15	−	1.20141e15i	0.393965	−	0.167925i
$131$	−9.17516e15			−1.21082			−0.605409	−	0.795914i	$-0.706991\pi$
$131$	−9.17516e15			−1.21082			−0.605409	+	0.795914i	$0.706991\pi$
$132$		−	3.91740e15i		−	0.488308i
$133$		−	4.45767e15i		−	0.525074i
$134$	−6.74596e15			−0.751204
$135$	−4.03711e15	−	9.47138e15i	−0.425175	−	0.997493i
$136$	5.61499e15			0.559509
$137$			1.72888e16i			1.63065i	0.579005	+	0.815324i	$0.303441\pi$
$137$			1.72888e16i			1.63065i	−0.579005	+	0.815324i	$0.696559\pi$
$138$		−	1.07658e15i		−	0.0961507i
$139$	1.25044e16			1.05792			0.528959	−	0.848648i	$-0.322583\pi$
$139$	1.25044e16			1.05792			0.528959	+	0.848648i	$0.322583\pi$
$140$	−2.02031e15	−	4.73980e15i	−0.161979	−	0.380014i
$141$	8.22415e15			0.625097
$142$		−	3.66696e15i		−	0.264328i
$143$		−	1.11736e16i		−	0.764139i
$144$	1.54390e15			0.100208
$145$	1.92963e16	−	8.22492e15i	1.18909	−	0.506841i
$146$	−1.67368e16			−0.979546
$147$			4.41849e15i			0.245693i
$148$		−	3.72320e15i		−	0.196767i
$149$	3.48217e16			1.74966			0.874828	−	0.484434i	$-0.160974\pi$
$149$	3.48217e16			1.74966			0.874828	+	0.484434i	$0.160974\pi$
$150$	7.93166e15	−	8.26287e15i	0.379035	−	0.394863i
$151$	−2.46410e16			−1.12029			−0.560146	−	0.828394i	$-0.689255\pi$
$151$	−2.46410e16			−1.12029			−0.560146	+	0.828394i	$0.689255\pi$
$152$			5.19304e15i			0.224696i
$153$		−	1.53992e16i		−	0.634327i
$154$	−1.87897e16			−0.737080
$155$	−3.14360e16	+	1.33994e16i	−1.17473	+	0.500723i
$156$	−6.58268e15			−0.234406
$157$			3.72069e16i			1.26292i	0.775408	+	0.631461i	$0.217544\pi$
$157$			3.72069e16i			1.26292i	−0.775408	+	0.631461i	$0.782456\pi$
$158$			1.51666e16i			0.490861i
$159$	−1.55996e16			−0.481544
$160$	2.35360e15	+	5.52172e15i	0.0693158	+	0.162620i
$161$	−5.16377e15			−0.145135
$162$			1.15564e16i			0.310069i
$163$		−	2.70256e16i		−	0.692417i	−0.938158	−	0.346208i	$-0.887469\pi$
$163$		−	2.70256e16i		−	0.692417i	0.938158	−	0.346208i	$-0.112531\pi$
$164$	−2.51410e16			−0.615253
$165$	−1.63780e16	−	3.84240e16i	−0.382941	−	0.898407i
$166$	6.01995e16			1.34519
$167$			8.50773e16i			1.81736i	0.417498	+	0.908678i	$0.362907\pi$
$167$			8.50773e16i			1.81736i	−0.417498	+	0.908678i	$0.637093\pi$
$168$			1.10695e16i			0.226105i
$169$	3.24102e16			0.633185
$170$	5.50748e16	−	2.34753e16i	1.02941	−	0.438778i
$171$	1.42420e16			0.254742
$172$			3.37790e16i			0.578340i
$173$			7.01872e16i			1.15057i	0.817954	+	0.575284i	$0.195108\pi$
$173$			7.01872e16i			1.15057i	−0.817954	+	0.575284i	$0.804892\pi$
$174$	−4.50654e16			−0.707496
$175$	−3.96326e16	−	3.80440e16i	−0.596029	−	0.572137i
$176$	2.18894e16			0.315420
$177$		−	3.69827e16i		−	0.510738i
$178$		−	7.64389e16i		−	1.01196i
$179$	−6.77169e16			−0.859606			−0.429803	−	0.902923i	$-0.641417\pi$
$179$	−6.77169e16			−0.859606			−0.429803	+	0.902923i	$0.641417\pi$
$180$	1.51434e16	−	6.45479e15i	0.184366	−	0.0785847i
$181$	−3.46660e15			−0.0404869			−0.0202434	−	0.999795i	$-0.506444\pi$
$181$	−3.46660e15			−0.0404869			−0.0202434	+	0.999795i	$0.506444\pi$
$182$			3.15736e16i			0.353825i
$183$		−	1.00424e17i		−	1.08007i
$184$	6.01563e15			0.0621080
$185$	−1.55660e16	−	3.65191e16i	−0.154309	−	0.362020i
$186$	7.34171e16			0.698956
$187$		−	2.18330e17i		−	1.99665i
$188$			4.59543e16i			0.403778i
$189$	1.06097e17			0.895861
$190$	2.17112e16	+	5.09362e16i	0.176211	+	0.413404i
$191$	−5.41945e16			−0.422868			−0.211434	−	0.977392i	$-0.567813\pi$
$191$	−5.41945e16			−0.422868			−0.211434	+	0.977392i	$0.567813\pi$
$192$		−	1.28957e16i		−	0.0967575i
$193$			3.03943e16i			0.219338i	0.993968	+	0.109669i	$0.0349790\pi$
$193$			3.03943e16i			0.219338i	−0.993968	+	0.109669i	$0.965021\pi$
$194$	−1.26540e17			−0.878445
$195$	−6.45665e16	+	2.75211e16i	−0.431268	+	0.183825i
$196$	−2.46893e16			−0.158704
$197$			2.30365e17i			1.42534i	0.701499	+	0.712671i	$0.252515\pi$
$197$			2.30365e17i			1.42534i	−0.701499	+	0.712671i	$0.747485\pi$
$198$		−	6.00322e16i		−	0.357598i
$199$	2.41144e17			1.38318			0.691589	−	0.722292i	$-0.256911\pi$
$199$	2.41144e17			1.38318			0.691589	+	0.722292i	$0.256911\pi$
$200$	4.61707e16	+	4.43200e16i	0.255060	+	0.244836i
$201$	1.54532e17			0.822333
$202$		−	1.28952e17i		−	0.661141i
$203$			2.16155e17i			1.06793i
$204$	−1.28624e17			−0.612487
$205$	−2.46596e17	+	1.05110e17i	−1.13196	+	0.482493i
$206$	−4.00492e16			−0.177251
$207$		−	1.64980e16i		−	0.0704131i
$208$		−	3.67823e16i		−	0.151413i
$209$	2.01923e17			0.801842
$210$	4.62799e16	+	1.08576e17i	0.177316	+	0.415996i
$211$	−3.35425e17			−1.24016			−0.620079	−	0.784540i	$-0.712899\pi$
$211$	−3.35425e17			−1.24016			−0.620079	+	0.784540i	$0.712899\pi$
$212$		−	8.71666e16i		−	0.311051i
$213$			8.40002e16i			0.289357i
$214$	−3.03210e17			−1.00842
$215$	1.41224e17	+	3.31322e17i	0.453545	+	1.06405i
$216$	−1.23600e17			−0.383368
$217$		−	3.52143e17i		−	1.05504i
$218$			1.17583e17i			0.340347i
$219$	3.83394e17			1.07230
$220$	2.14703e17	−	9.15159e16i	0.580321	−	0.247358i
$221$	−3.66874e17			−0.958463
$222$			8.52884e16i			0.215399i
$223$			2.67383e17i			0.652902i	0.945214	+	0.326451i	$0.105853\pi$
$223$			2.67383e17i			0.652902i	−0.945214	+	0.326451i	$0.894147\pi$
$224$	−6.18537e16			−0.146051
$225$	1.21549e17	−	1.26624e17i	0.277575	−	0.289166i
$226$	1.20512e17			0.266206
$227$		−	7.35095e17i		−	1.57090i	−0.618923	−	0.785452i	$-0.712431\pi$
$227$		−	7.35095e17i		−	1.57090i	0.618923	−	0.785452i	$-0.287569\pi$
$228$		−	1.18959e17i		−	0.245971i
$229$	−5.88905e16			−0.117836			−0.0589182	−	0.998263i	$-0.518765\pi$
$229$	−5.88905e16			−0.117836			−0.0589182	+	0.998263i	$0.518765\pi$
$230$	5.90046e16	−	2.51503e16i	0.114269	−	0.0487063i
$231$	4.30422e17			0.806872
$232$		−	2.51814e17i		−	0.457003i
$233$		−	7.66912e17i		−	1.34765i	−0.738893	−	0.673823i	$-0.764651\pi$
$233$		−	7.66912e17i		−	1.34765i	0.738893	−	0.673823i	$-0.235349\pi$
$234$	−1.00876e17			−0.171660
$235$	1.92127e17	+	4.50745e17i	0.316650	+	0.742886i
$236$	2.06649e17			0.329909
$237$		−	3.47425e17i		−	0.537339i
$238$			6.16942e17i			0.924522i
$239$	−4.82618e16			−0.0700840			−0.0350420	−	0.999386i	$-0.511156\pi$
$239$	−4.82618e16			−0.0700840			−0.0350420	+	0.999386i	$0.511156\pi$
$240$	−5.39146e16	−	1.26488e17i	−0.0758791	−	0.178018i
$241$	−4.73767e17			−0.646304			−0.323152	−	0.946347i	$-0.604743\pi$
$241$	−4.73767e17			−0.646304			−0.323152	+	0.946347i	$0.604743\pi$
$242$		−	3.16448e17i		−	0.418491i
$243$			5.80957e17i			0.744899i
$244$	5.61141e17			0.697667
$245$	−2.42166e17	+	1.03222e17i	−0.291990	+	0.124459i
$246$	5.75913e17			0.673509
$247$		−	3.39305e17i		−	0.384914i
$248$			4.10235e17i			0.451487i
$249$	−1.37901e18			−1.47256
$250$	6.38162e17	+	2.41683e17i	0.661273	+	0.250435i
$251$	5.82448e17			0.585739			0.292870	−	0.956152i	$-0.405390\pi$
$251$	5.82448e17			0.585739			0.292870	+	0.956152i	$0.405390\pi$
$252$			1.69635e17i			0.165581i
$253$		−	2.33908e17i		−	0.221637i
$254$	−6.09304e17			−0.560507
$255$	−1.26162e18	+	5.37756e17i	−1.12688	+	0.480324i
$256$	7.20576e16			0.0625000
$257$			1.58285e18i			1.33334i	0.745354	+	0.666669i	$0.232280\pi$
$257$			1.58285e18i			1.33334i	−0.745354	+	0.666669i	$0.767720\pi$
$258$		−	7.73785e17i		−	0.633101i
$259$	4.09083e17			0.325135
$260$	−1.53780e17	−	3.60780e17i	−0.118741	−	0.278575i
$261$	−6.90604e17			−0.518114
$262$			1.17442e18i			0.856178i
$263$		−	5.96866e17i		−	0.422872i	−0.977392	−	0.211436i	$-0.932186\pi$
$263$		−	5.96866e17i		−	0.422872i	0.977392	−	0.211436i	$-0.0678139\pi$
$264$	−5.01428e17			−0.345286
$265$	−3.64429e17	−	8.54977e17i	−0.243932	−	0.572282i
$266$	−5.70581e17			−0.371283
$267$			1.75101e18i			1.10778i
$268$			8.63483e17i			0.531181i
$269$	1.35961e18			0.813342			0.406671	−	0.913575i	$-0.366690\pi$
$269$	1.35961e18			0.813342			0.406671	+	0.913575i	$0.366690\pi$
$270$	−1.21234e18	+	5.16751e17i	−0.705334	+	0.300644i
$271$	1.11668e18			0.631915			0.315958	−	0.948773i	$-0.397674\pi$
$271$	1.11668e18			0.631915			0.315958	+	0.948773i	$0.397674\pi$
$272$		−	7.18718e17i		−	0.395633i
$273$		−	7.23267e17i		−	0.387328i
$274$	2.21296e18			1.15304
$275$	1.72331e18	−	1.79528e18i	0.873714	−	0.910198i
$276$	−1.37802e17			−0.0679888
$277$			7.79603e17i			0.374348i	0.982327	+	0.187174i	$0.0599328\pi$
$277$			7.79603e17i			0.374348i	−0.982327	+	0.187174i	$0.940067\pi$
$278$		−	1.60056e18i		−	0.748060i
$279$	1.12508e18			0.511860
$280$	−6.06694e17	+	2.58600e17i	−0.268711	+	0.114536i
$281$	1.22063e18			0.526364			0.263182	−	0.964746i	$-0.415228\pi$
$281$	1.22063e18			0.526364			0.263182	+	0.964746i	$0.415228\pi$
$282$		−	1.05269e18i		−	0.442010i
$283$			1.30936e18i			0.535376i	0.963506	+	0.267688i	$0.0862597\pi$
$283$			1.30936e18i			0.535376i	−0.963506	+	0.267688i	$0.913740\pi$
$284$	−4.69371e17			−0.186908
$285$	−4.97346e17	−	1.16681e18i	−0.192895	−	0.452547i
$286$	−1.43022e18			−0.540328
$287$		−	2.76235e18i		−	1.01663i
$288$		−	1.97619e17i		−	0.0708575i
$289$	−4.30624e18			−1.50440
$290$	−1.05279e18	−	2.46992e18i	−0.358391	−	0.840811i
$291$	2.89869e18			0.961622
$292$			2.14230e18i			0.692643i
$293$		−	1.68170e18i		−	0.529958i	−0.964254	−	0.264979i	$-0.914635\pi$
$293$		−	1.68170e18i		−	0.529958i	0.964254	−	0.264979i	$-0.0853650\pi$
$294$	5.65566e17			0.173731
$295$	2.02693e18	−	8.63965e17i	0.606978	−	0.258721i
$296$	−4.76569e17			−0.139135
$297$			4.80599e18i			1.36807i
$298$		−	4.45717e18i		−	1.23719i
$299$	−3.93052e17			−0.106394
$300$	−1.05765e18	−	1.01525e18i	−0.279210	−	0.268019i
$301$	−3.71144e18			−0.955638
$302$			3.15405e18i			0.792166i
$303$			2.95395e18i			0.723742i
$304$	6.64709e17			0.158884
$305$	5.50397e18	−	2.34603e18i	1.28359	−	0.547123i
$306$	−1.97110e18			−0.448537
$307$			4.15216e18i			0.922012i	0.887397	+	0.461006i	$0.152511\pi$
$307$			4.15216e18i			0.922012i	−0.887397	+	0.461006i	$0.847489\pi$
$308$			2.40508e18i			0.521194i
$309$	9.17419e17			0.194035
$310$	1.71512e18	+	4.02381e18i	0.354065	+	0.830663i
$311$	−4.91517e18			−0.990456			−0.495228	−	0.868763i	$-0.664915\pi$
$311$	−4.91517e18			−0.990456			−0.495228	+	0.868763i	$0.664915\pi$
$312$			8.42583e17i			0.165750i
$313$			1.20358e18i			0.231150i	0.993299	+	0.115575i	$0.0368710\pi$
$313$			1.20358e18i			0.231150i	−0.993299	+	0.115575i	$0.963129\pi$
$314$	4.76249e18			0.893021
$315$	7.09215e17	+	1.66387e18i	0.129852	+	0.304643i
$316$	1.94132e18			0.347091
$317$			5.86443e17i			0.102396i	0.998689	+	0.0511978i	$0.0163039\pi$
$317$			5.86443e17i			0.102396i	−0.998689	+	0.0511978i	$0.983696\pi$
$318$			1.99675e18i			0.340503i
$319$	−9.79137e18			−1.63085
$320$	7.06780e17	−	3.01260e17i	0.114990	−	0.0490137i
$321$	6.94572e18			1.10390
$322$			6.60963e17i			0.102626i
$323$		−	6.62996e18i		−	1.00575i
$324$	1.47922e18			0.219252
$325$	−3.01672e18	−	2.89580e18i	−0.436928	−	0.419414i
$326$	−3.45927e18			−0.489613
$327$		−	2.69352e18i		−	0.372574i
$328$			3.21805e18i			0.435049i
$329$	−5.04920e18			−0.667195
$330$	−4.91828e18	+	2.09638e18i	−0.635270	+	0.270780i
$331$	−1.10083e19			−1.38999			−0.694993	−	0.719016i	$-0.744593\pi$
$331$	−1.10083e19			−1.38999			−0.694993	+	0.719016i	$0.744593\pi$
$332$		−	7.70554e18i		−	0.951190i
$333$			1.30700e18i			0.157741i
$334$	1.08899e19			1.28506
$335$	3.61007e18	+	8.46951e18i	0.416562	+	0.977287i
$336$	1.41690e18			0.159880
$337$		−	5.71647e18i		−	0.630817i	−0.948956	−	0.315409i	$-0.897858\pi$
$337$		−	5.71647e18i		−	0.630817i	0.948956	−	0.315409i	$-0.102142\pi$
$338$		−	4.14850e18i		−	0.447730i
$339$	−2.76061e18			−0.291412
$340$	−3.00484e18	−	7.04958e18i	−0.310263	−	0.727899i
$341$	1.59513e19			1.61116
$342$		−	1.82298e18i		−	0.180130i
$343$		−	1.12592e19i		−	1.08843i
$344$	4.32371e18			0.408948
$345$	−1.35164e18	+	5.76127e17i	−0.125088	+	0.0533181i
$346$	8.98396e18			0.813574
$347$		−	9.54901e18i		−	0.846228i	−0.906077	−	0.423114i	$-0.860937\pi$
$347$		−	9.54901e18i		−	0.846228i	0.906077	−	0.423114i	$-0.139063\pi$
$348$			5.76837e18i			0.500275i
$349$	1.21412e19			1.03055			0.515277	−	0.857024i	$-0.327689\pi$
$349$	1.21412e19			1.03055			0.515277	+	0.857024i	$0.327689\pi$
$350$	−4.86963e18	+	5.07297e18i	−0.404562	+	0.421456i
$351$	8.07583e18			0.656725
$352$		−	2.80185e18i		−	0.223036i
$353$			1.54261e19i			1.20212i	0.799205	+	0.601059i	$0.205254\pi$
$353$			1.54261e19i			1.20212i	−0.799205	+	0.601059i	$0.794746\pi$
$354$	−4.73378e18			−0.361147
$355$	−4.60384e18	+	1.96236e18i	−0.343881	+	0.146577i
$356$	−9.78418e18			−0.715565
$357$		−	1.41325e19i		−	1.01206i
$358$			8.66776e18i			0.607833i
$359$	−1.09726e19			−0.753534			−0.376767	−	0.926308i	$-0.622964\pi$
$359$	−1.09726e19			−0.753534			−0.376767	+	0.926308i	$0.622964\pi$
$360$	−8.26213e17	−	1.93836e18i	−0.0555678	−	0.130366i
$361$	−9.04939e18			−0.596095
$362$			4.43725e17i			0.0286286i
$363$			7.24896e18i			0.458117i
$364$	4.04142e18			0.250192
$365$	8.95661e18	+	2.10129e19i	0.543184	+	1.27435i
$366$	−1.28542e19			−0.763726
$367$		−	2.66762e18i		−	0.155285i	−0.996981	−	0.0776424i	$-0.975261\pi$
$367$		−	2.66762e18i		−	0.155285i	0.996981	−	0.0776424i	$-0.0247392\pi$
$368$		−	7.70001e17i		−	0.0439170i
$369$	8.82556e18			0.493224
$370$	−4.67445e18	+	1.99245e18i	−0.255987	+	0.109113i
$371$	9.57736e18			0.513974
$372$		−	9.39739e18i		−	0.494237i
$373$			4.43961e18i			0.228838i	0.993433	+	0.114419i	$0.0365007\pi$
$373$			4.43961e18i			0.228838i	−0.993433	+	0.114419i	$0.963499\pi$
$374$	−2.79462e19			−1.41184
$375$	−1.46186e19	−	5.53631e18i	−0.723887	−	0.274148i
$376$	5.88216e18			0.285514
$377$			1.64531e19i			0.782866i
$378$		−	1.35805e19i		−	0.633470i
$379$	1.62503e18			0.0743136			0.0371568	−	0.999309i	$-0.488170\pi$
$379$	1.62503e18			0.0743136			0.0371568	+	0.999309i	$0.488170\pi$
$380$	6.51983e18	−	2.77904e18i	0.292320	−	0.124600i
$381$	1.39575e19			0.613580
$382$			6.93689e18i			0.299013i
$383$			2.37535e19i			1.00401i	0.864866	+	0.502003i	$0.167403\pi$
$383$			2.37535e19i			1.00401i	−0.864866	+	0.502003i	$0.832597\pi$
$384$	−1.65065e18			−0.0684179
$385$	1.00552e19	+	2.35904e19i	0.408730	+	0.958912i
$386$	3.89048e18			0.155095
$387$		−	1.18579e19i		−	0.463632i
$388$			1.61971e19i			0.621154i
$389$	−3.45721e19			−1.30048			−0.650240	−	0.759729i	$-0.725332\pi$
$389$	−3.45721e19			−1.30048			−0.650240	+	0.759729i	$0.725332\pi$
$390$	3.52269e18	+	8.26451e18i	0.129984	+	0.304953i
$391$	−7.68016e18			−0.278000
$392$			3.16023e18i			0.112221i
$393$		−	2.69028e19i		−	0.937247i
$394$	2.94867e19			1.00787
$395$	1.90415e19	−	8.11632e18i	0.638591	−	0.272196i
$396$	−7.68412e18			−0.252860
$397$		−	4.33383e19i		−	1.39940i	−0.714435	−	0.699701i	$-0.753316\pi$
$397$		−	4.33383e19i		−	1.39940i	0.714435	−	0.699701i	$-0.246684\pi$
$398$		−	3.08664e19i		−	0.978054i
$399$	1.30705e19			0.406439
$400$	5.67296e18	−	5.90985e18i	0.173125	−	0.180354i
$401$	−6.36106e18			−0.190523			−0.0952613	−	0.995452i	$-0.530369\pi$
$401$	−6.36106e18			−0.190523			−0.0952613	+	0.995452i	$0.530369\pi$
$402$		−	1.97801e19i		−	0.581477i
$403$		−	2.68041e19i		−	0.773417i
$404$	−1.65059e19			−0.467497
$405$	1.45089e19	−	6.18435e18i	0.403388	−	0.171942i
$406$	2.76678e19			0.755144
$407$			1.85306e19i			0.496515i
$408$			1.64639e19i			0.433094i
$409$	4.06251e19			1.04923			0.524614	−	0.851340i	$-0.324210\pi$
$409$	4.06251e19			1.04923			0.524614	+	0.851340i	$0.324210\pi$
$410$	1.34541e19	+	3.15643e19i	0.341174	+	0.800420i
$411$	−5.06931e19			−1.26222
$412$			5.12629e18i			0.125336i
$413$			2.27054e19i			0.545135i
$414$	−2.11174e18			−0.0497896
$415$	−3.22155e19	−	7.55801e19i	−0.745942	−	1.75004i
$416$	−4.70813e18			−0.107065
$417$			3.66646e19i			0.818892i
$418$		−	2.58462e19i		−	0.566988i
$419$	2.97156e19			0.640294			0.320147	−	0.947368i	$-0.396268\pi$
$419$	2.97156e19			0.640294			0.320147	+	0.947368i	$0.396268\pi$
$420$	1.38977e19	−	5.92382e18i	0.294154	−	0.125381i
$421$	−4.47909e19			−0.931266			−0.465633	−	0.884978i	$-0.654173\pi$
$421$	−4.47909e19			−0.931266			−0.465633	+	0.884978i	$0.654173\pi$
$422$			4.29344e19i			0.876924i
$423$		−	1.61319e19i		−	0.323693i
$424$	−1.11573e19			−0.219946
$425$	−5.89462e19	−	5.65834e19i	−1.14167	−	1.09590i
$426$	1.07520e19			0.204606
$427$			6.16549e19i			1.15281i
$428$			3.88108e19i			0.713058i
$429$	3.27625e19			0.591490
$430$	4.24093e19	−	1.80767e19i	0.752397	−	0.320705i
$431$	−3.23124e19			−0.563366			−0.281683	−	0.959508i	$-0.590893\pi$
$431$	−3.23124e19			−0.563366			−0.281683	+	0.959508i	$0.590893\pi$
$432$			1.58208e19i			0.271082i
$433$			1.18270e19i			0.199167i	0.995029	+	0.0995834i	$0.0317510\pi$
$433$			1.18270e19i			0.199167i	−0.995029	+	0.0995834i	$0.968249\pi$
$434$	−4.50743e19			−0.746029
$435$	2.41166e19	+	5.65793e19i	0.392325	+	0.920425i
$436$	1.50507e19			0.240662
$437$		−	7.10302e18i		−	0.111643i
$438$		−	4.90744e19i		−	0.758228i
$439$	1.16358e19			0.176731			0.0883656	−	0.996088i	$-0.471836\pi$
$439$	1.16358e19			0.176731			0.0883656	+	0.996088i	$0.471836\pi$
$440$	−1.17140e19	−	2.74820e19i	−0.174909	−	0.410349i
$441$	8.66700e18			0.127227
$442$			4.69599e19i			0.677736i
$443$			6.84430e19i			0.971184i	0.874186	+	0.485592i	$0.161396\pi$
$443$			6.84430e19i			0.971184i	−0.874186	+	0.485592i	$0.838604\pi$
$444$	1.09169e19			0.152310
$445$	−9.59685e19	+	4.09060e19i	−1.31652	+	0.561160i
$446$	3.42251e19			0.461671
$447$			1.02102e20i			1.35434i
$448$			7.91727e18i			0.103274i
$449$	−3.80933e19			−0.488653			−0.244326	−	0.969693i	$-0.578567\pi$
$449$	−3.80933e19			−0.488653			−0.244326	+	0.969693i	$0.578567\pi$
$450$	−1.62079e19	−	1.55582e19i	−0.204471	−	0.196275i
$451$	1.25129e20			1.55250
$452$		−	1.54256e19i		−	0.188236i
$453$		−	7.22508e19i		−	0.867174i
$454$	−9.40921e19			−1.11080
$455$	3.96405e19	−	1.68965e19i	0.460313	−	0.196205i
$456$	−1.52267e19			−0.173928
$457$		−	2.72368e19i		−	0.306044i	−0.988223	−	0.153022i	$-0.951099\pi$
$457$		−	2.72368e19i		−	0.306044i	0.988223	−	0.153022i	$-0.0489006\pi$
$458$			7.53799e18i			0.0833229i
$459$	1.57800e20			1.71598
$460$	−3.21924e18	−	7.55259e18i	−0.0344405	−	0.0808001i
$461$	8.49835e19			0.894494			0.447247	−	0.894410i	$-0.352404\pi$
$461$	8.49835e19			0.894494			0.447247	+	0.894410i	$0.352404\pi$
$462$		−	5.50940e19i		−	0.570544i
$463$		−	6.86537e19i		−	0.699530i	−0.936837	−	0.349765i	$-0.886261\pi$
$463$		−	6.86537e19i		−	0.699530i	0.936837	−	0.349765i	$-0.113739\pi$
$464$	−3.22321e19			−0.323150
$465$	−3.92889e19	−	9.21747e19i	−0.387590	−	0.909315i
$466$	−9.81647e19			−0.952930
$467$			4.35028e19i			0.415567i	0.978175	+	0.207783i	$0.0666249\pi$
$467$			4.35028e19i			0.415567i	−0.978175	+	0.207783i	$0.933375\pi$
$468$			1.29121e19i			0.121382i
$469$	−9.48745e19			−0.877714
$470$	5.76954e19	−	2.45923e19i	0.525300	−	0.223906i
$471$	−1.09096e20			−0.977578
$472$		−	2.64511e19i		−	0.233281i
$473$		−	1.68120e20i		−	1.45936i
$474$	−4.44704e19			−0.379956
$475$	5.23313e19	−	5.45166e19i	0.440109	−	0.458487i
$476$	7.89686e19			0.653736
$477$			3.05992e19i			0.249357i
$478$			6.17751e18i			0.0495569i
$479$	−2.27604e18			−0.0179748			−0.00898738	−	0.999960i	$-0.502861\pi$
$479$	−2.27604e18			−0.0179748			−0.00898738	+	0.999960i	$0.502861\pi$
$480$	−1.61904e19	+	6.90107e18i	−0.125878	+	0.0536546i
$481$	3.11383e19			0.238345
$482$			6.06422e19i			0.457006i
$483$		−	1.51409e19i		−	0.112343i
$484$	−4.05053e19			−0.295918
$485$	6.77173e19	+	1.58870e20i	0.487121	+	1.14282i
$486$	7.43625e19			0.526723
$487$		−	7.99044e19i		−	0.557319i	−0.960390	−	0.278659i	$-0.910110\pi$
$487$		−	7.99044e19i		−	0.557319i	0.960390	−	0.278659i	$-0.0898900\pi$
$488$		−	7.18260e19i		−	0.493325i
$489$	7.92426e19			0.535973
$490$	1.32124e19	+	3.09973e19i	0.0880057	+	0.206468i
$491$	1.67214e20			1.09688			0.548442	−	0.836189i	$-0.315221\pi$
$491$	1.67214e20			1.09688			0.548442	+	0.836189i	$0.315221\pi$
$492$		−	7.37168e19i		−	0.476243i
$493$			3.21490e20i			2.04558i
$494$	−4.34310e19			−0.272175
$495$	−7.53700e19	+	3.21260e19i	−0.465221	+	0.198298i
$496$	5.25101e19			0.319250
$497$		−	5.15717e19i		−	0.308844i
$498$			1.76513e20i			1.04126i
$499$	8.92922e19			0.518871			0.259436	−	0.965760i	$-0.416463\pi$
$499$	8.92922e19			0.518871			0.259436	+	0.965760i	$0.416463\pi$
$500$	3.09354e19	−	8.16847e19i	0.177085	−	0.467591i
$501$	−2.49458e20			−1.40674
$502$		−	7.45534e19i		−	0.414180i
$503$		−	1.15120e20i		−	0.630074i	−0.949079	−	0.315037i	$-0.897983\pi$
$503$		−	1.15120e20i		−	0.630074i	0.949079	−	0.315037i	$-0.102017\pi$
$504$	2.17133e19			0.117084
$505$	−1.61899e20	+	6.90084e19i	−0.860119	+	0.366620i
$506$	−2.99403e19			−0.156721
$507$			9.50310e19i			0.490124i
$508$			7.79909e19i			0.396338i
$509$	−1.53223e20			−0.767258			−0.383629	−	0.923487i	$-0.625326\pi$
$509$	−1.53223e20			−0.767258			−0.383629	+	0.923487i	$0.625326\pi$
$510$	6.88328e19	+	1.61487e20i	0.339640	+	0.796822i
$511$	−2.35384e20			−1.14451
$512$		−	9.22337e18i		−	0.0441942i
$513$			1.45942e20i			0.689129i
$514$	2.02604e20			0.942812
$515$	2.14321e19	+	5.02814e19i	0.0982905	+	0.230597i
$516$	−9.90445e19			−0.447670
$517$		−	2.28718e20i		−	1.01888i
$518$		−	5.23626e19i		−	0.229905i
$519$	−2.05799e20			−0.890609
$520$	−4.61799e19	+	1.96839e19i	−0.196983	+	0.0839626i
$521$	−1.17337e20			−0.493348			−0.246674	−	0.969099i	$-0.579338\pi$
$521$	−1.17337e20			−0.493348			−0.246674	+	0.969099i	$0.579338\pi$
$522$			8.83973e19i			0.366362i
$523$			2.07030e20i			0.845805i	0.906175	+	0.422902i	$0.138989\pi$
$523$			2.07030e20i			0.845805i	−0.906175	+	0.422902i	$0.861011\pi$
$524$	1.50326e20			0.605409
$525$	1.11550e20	−	1.16208e20i	0.442869	−	0.461362i
$526$	−7.63988e19			−0.299015
$527$		−	5.23747e20i		−	2.02089i
$528$			6.41828e19i			0.244154i
$529$	2.58407e20			0.969141
$530$	−1.09437e20	+	4.66469e19i	−0.404665	+	0.172486i
$531$	−7.25427e19			−0.264475
$532$			7.30344e19i			0.262537i
$533$		−	2.10262e20i		−	0.745258i
$534$	2.24129e20			0.783320
$535$	1.62262e20	+	3.80678e20i	0.559194	+	1.31191i
$536$	1.10526e20			0.375602
$537$		−	1.98555e20i		−	0.665387i
$538$		−	1.74030e20i		−	0.575120i
$539$	1.22881e20			0.400468
$540$	6.61441e19	+	1.55179e20i	0.212588	+	0.498746i
$541$	4.75197e20			1.50624			0.753120	−	0.657883i	$-0.228548\pi$
$541$	4.75197e20			1.50624			0.753120	+	0.657883i	$0.228548\pi$
$542$		−	1.42935e20i		−	0.446832i
$543$		−	1.01645e19i		−	0.0313393i
$544$	−9.19960e19			−0.279754
$545$	1.47625e20	−	6.29243e19i	0.442779	−	0.188732i
$546$	−9.25781e19			−0.273882
$547$		−	7.58426e19i		−	0.221314i	−0.993859	−	0.110657i	$-0.964705\pi$
$547$		−	7.58426e19i		−	0.221314i	0.993859	−	0.110657i	$-0.0352955\pi$
$548$		−	2.83259e20i		−	0.815324i
$549$	−1.96984e20			−0.559292
$550$	−2.29795e20	−	2.20584e20i	−0.643607	−	0.617809i
$551$	−2.97332e20			−0.821493
$552$			1.76387e19i			0.0480754i
$553$			2.13301e20i			0.573527i
$554$	9.97892e19			0.264704
$555$	1.07079e20	−	4.56418e19i	0.280225	−	0.119444i
$556$	−2.04872e20			−0.528959
$557$			8.93309e19i			0.227556i	0.993506	+	0.113778i	$0.0362952\pi$
$557$			8.93309e19i			0.227556i	−0.993506	+	0.113778i	$0.963705\pi$
$558$		−	1.44010e20i		−	0.361940i
$559$	−2.82504e20			−0.700545
$560$	3.31008e19	+	7.76569e19i	0.0809893	+	0.190007i
$561$	6.40173e20			1.54552
$562$		−	1.56241e20i		−	0.372196i
$563$			2.15653e19i			0.0506923i	0.999679	+	0.0253461i	$0.00806879\pi$
$563$			2.15653e19i			0.0506923i	−0.999679	+	0.0253461i	$0.991931\pi$
$564$	−1.34744e20			−0.312549
$565$	−6.44917e19	−	1.51302e20i	−0.147618	−	0.346324i
$566$	1.67597e20			0.378568
$567$			1.62528e20i			0.362288i
$568$			6.00795e19i			0.132164i
$569$	−5.96755e20			−1.29555			−0.647775	−	0.761832i	$-0.724300\pi$
$569$	−5.96755e20			−1.29555			−0.647775	+	0.761832i	$0.724300\pi$
$570$	−1.49352e20	+	6.36603e19i	−0.319999	+	0.136398i
$571$	2.54392e19			0.0537939			0.0268969	−	0.999638i	$-0.491437\pi$
$571$	2.54392e19			0.0537939			0.0268969	+	0.999638i	$0.491437\pi$
$572$			1.83068e20i			0.382070i
$573$		−	1.58906e20i		−	0.327325i
$574$	−3.53580e20			−0.718868
$575$	−6.31522e19	−	6.06208e19i	−0.126730	−	0.121650i
$576$	−2.52953e19			−0.0501038
$577$			8.43979e20i			1.65011i	0.565052	+	0.825055i	$0.308856\pi$
$577$			8.43979e20i			1.65011i	−0.565052	+	0.825055i	$0.691144\pi$
$578$			5.51198e20i			1.06377i
$579$	−8.91204e19			−0.169781
$580$	−3.16150e20	+	1.34757e20i	−0.594543	+	0.253420i
$581$	8.46640e20			1.57173
$582$		−	3.71032e20i		−	0.679969i
$583$			4.33835e20i			0.784892i
$584$	2.74215e20			0.489773
$585$	5.39834e19	+	1.26649e20i	0.0951900	+	0.223323i
$586$	−2.15258e20			−0.374737
$587$		−	8.66726e19i		−	0.148969i	−0.997222	−	0.0744845i	$-0.976269\pi$
$587$		−	8.66726e19i		−	0.148969i	0.997222	−	0.0744845i	$-0.0237311\pi$
$588$		−	7.23925e19i		−	0.122847i
$589$	4.84390e20			0.811578
$590$	−1.10588e20	−	2.59447e20i	−0.182943	−	0.429198i
$591$	−6.75460e20			−1.10330
$592$			6.10008e19i			0.0983836i
$593$			5.56467e19i			0.0886195i	0.999018	+	0.0443097i	$0.0141088\pi$
$593$			5.56467e19i			0.0886195i	−0.999018	+	0.0443097i	$0.985891\pi$
$594$	6.15167e20			0.967374
$595$	7.74567e20	−	3.30154e20i	1.20277	−	0.512672i
$596$	−5.70518e20			−0.874828
$597$			7.07066e20i			1.07066i
$598$			5.03106e19i			0.0752317i
$599$	−9.17498e20			−1.35489			−0.677445	−	0.735573i	$-0.736913\pi$
$599$	−9.17498e20			−1.35489			−0.677445	+	0.735573i	$0.736913\pi$
$600$	−1.29952e20	+	1.35379e20i	−0.189518	+	0.197432i
$601$	5.94279e20			0.855917			0.427959	−	0.903798i	$-0.359233\pi$
$601$	5.94279e20			0.855917			0.427959	+	0.903798i	$0.359233\pi$
$602$			4.75064e20i			0.675738i
$603$		−	3.03119e20i		−	0.425827i
$604$	4.03718e20			0.560146
$605$	−3.97298e20	+	1.69346e20i	−0.544441	+	0.232065i
$606$	3.78106e20			0.511763
$607$		−	8.74378e20i		−	1.16892i	−0.811423	−	0.584459i	$-0.801307\pi$
$607$		−	8.74378e20i		−	1.16892i	0.811423	−	0.584459i	$-0.198693\pi$
$608$		−	8.50828e19i		−	0.112348i
$609$	−6.33795e20			−0.826646
$610$	−3.00292e20	−	7.04508e20i	−0.386875	−	0.907637i
$611$	−3.84331e20			−0.489098
$612$			2.52301e20i			0.317163i
$613$		−	9.64419e20i		−	1.19760i	−0.800898	−	0.598800i	$-0.795644\pi$
$613$		−	9.64419e20i		−	1.19760i	0.800898	−	0.598800i	$-0.204356\pi$
$614$	5.31477e20			0.651961
$615$	−3.08197e20	−	7.23055e20i	−0.373479	−	0.876209i
$616$	3.07851e20			0.368540
$617$			1.07113e21i			1.26679i	0.773828	+	0.633396i	$0.218340\pi$
$617$			1.07113e21i			1.26679i	−0.773828	+	0.633396i	$0.781660\pi$
$618$		−	1.17430e20i		−	0.137203i
$619$	6.20752e20			0.716536			0.358268	−	0.933619i	$-0.383367\pi$
$619$	6.20752e20			0.716536			0.358268	+	0.933619i	$0.383367\pi$
$620$	5.15048e20	−	2.19536e20i	0.587367	−	0.250362i
$621$	1.69060e20			0.190482
$622$			6.29141e20i			0.700358i
$623$		−	1.07503e21i		−	1.18239i
$624$	1.07851e20			0.117203
$625$	−3.80786e19	−	9.30544e20i	−0.0408866	−	0.999164i
$626$	1.54058e20			0.163447
$627$			5.92066e20i			0.620674i
$628$		−	6.09598e20i		−	0.631461i
$629$	6.08436e20			0.622780
$630$	2.12976e20	−	9.07795e19i	0.215415	−	0.0918192i
$631$	−1.48924e21			−1.48848			−0.744240	−	0.667912i	$-0.767188\pi$
$631$	−1.48924e21			−1.48848			−0.744240	+	0.667912i	$0.767188\pi$
$632$		−	2.48489e20i		−	0.245431i
$633$		−	9.83511e20i		−	0.959957i
$634$	7.50647e19			0.0724047
$635$	3.26067e20	+	7.64977e20i	0.310816	+	0.729198i
$636$	2.55584e20			0.240772
$637$		−	2.06485e20i		−	0.192239i
$638$			1.25330e21i			1.15318i
$639$	1.64769e20			0.149837
$640$	−3.85613e19	−	9.04678e19i	−0.0346579	−	0.0813101i
$641$	−4.55470e20			−0.404598			−0.202299	−	0.979324i	$-0.564841\pi$
$641$	−4.55470e20			−0.404598			−0.202299	+	0.979324i	$0.564841\pi$
$642$		−	8.89052e20i		−	0.780575i
$643$			1.33479e21i			1.15833i	0.815212	+	0.579163i	$0.196621\pi$
$643$			1.33479e21i			1.15833i	−0.815212	+	0.579163i	$0.803379\pi$
$644$	8.46033e19			0.0725677
$645$	−9.71482e20	+	4.14088e20i	−0.823639	+	0.351071i
$646$	−8.48635e20			−0.711176
$647$			8.29661e20i			0.687256i	0.939106	+	0.343628i	$0.111656\pi$
$647$			8.29661e20i			0.687256i	−0.939106	+	0.343628i	$0.888344\pi$
$648$		−	1.89340e20i		−	0.155035i
$649$	−1.02851e21			−0.832478
$650$	−3.70662e20	+	3.86140e20i	−0.296571	+	0.308955i
$651$	1.03253e21			0.816668
$652$			4.42787e20i			0.346208i
$653$			3.86005e20i			0.298362i	0.988810	+	0.149181i	$0.0476638\pi$
$653$			3.86005e20i			0.298362i	−0.988810	+	0.149181i	$0.952336\pi$
$654$	−3.44771e20			−0.263449
$655$	1.47448e21	−	6.28487e20i	1.11385	−	0.474773i
$656$	4.11910e20			0.307626
$657$		−	7.52040e20i		−	0.555265i
$658$			6.46297e20i			0.471778i
$659$	2.01339e21			1.45307			0.726535	−	0.687129i	$-0.241129\pi$
$659$	2.01339e21			1.45307			0.726535	+	0.687129i	$0.241129\pi$
$660$	2.68337e20	+	6.29539e20i	0.191470	+	0.449204i
$661$	−4.28641e20			−0.302401			−0.151200	−	0.988503i	$-0.548314\pi$
$661$	−4.28641e20			−0.302401			−0.151200	+	0.988503i	$0.548314\pi$
$662$			1.40906e21i			0.982869i
$663$		−	1.07573e21i		−	0.741908i
$664$	−9.86309e20			−0.672593
$665$	3.05344e20	+	7.16361e20i	0.205886	+	0.483025i
$666$	1.67296e20			0.111540
$667$			3.44430e20i			0.227068i
$668$		−	1.39391e21i		−	0.908678i
$669$	−7.84004e20			−0.505385
$670$	1.08410e21	−	4.62089e20i	0.691046	−	0.294554i
$671$	−2.79284e21			−1.76046
$672$		−	1.81363e20i		−	0.113053i
$673$			3.08459e21i			1.90145i	0.310040	+	0.950723i	$0.399658\pi$
$673$			3.08459e21i			1.90145i	−0.310040	+	0.950723i	$0.600342\pi$
$674$	−7.31708e20			−0.446055
$675$	1.29755e21	+	1.24554e21i	0.782253	+	0.750897i
$676$	−5.31008e20			−0.316593
$677$			2.46065e20i			0.145089i	0.997365	+	0.0725446i	$0.0231120\pi$
$677$			2.46065e20i			0.145089i	−0.997365	+	0.0725446i	$0.976888\pi$
$678$			3.53358e20i			0.206059i
$679$	−1.77964e21			−1.02638
$680$	−9.02346e20	+	3.84619e20i	−0.514703	+	0.219389i
$681$	2.15540e21			1.21597
$682$		−	2.04177e21i		−	1.13926i
$683$			1.37009e21i			0.756123i	0.925780	+	0.378062i	$0.123409\pi$
$683$			1.37009e21i			0.756123i	−0.925780	+	0.378062i	$0.876591\pi$
$684$	−2.33341e20			−0.127371
$685$	−1.18426e21	−	2.77836e21i	−0.639392	−	1.50006i
$686$	−1.44118e21			−0.769637
$687$		−	1.72675e20i		−	0.0912125i
$688$		−	5.53434e20i		−	0.289170i
$689$	7.29002e20			0.376777
$690$	7.37442e19	+	1.73010e20i	0.0377016	+	0.0884508i
$691$	3.69456e21			1.86843			0.934216	−	0.356708i	$-0.116101\pi$
$691$	3.69456e21			1.86843			0.934216	+	0.356708i	$0.116101\pi$
$692$		−	1.14995e21i		−	0.575284i
$693$		−	8.44286e20i		−	0.417821i
$694$	−1.22227e21			−0.598373
$695$	−2.00950e21	+	8.56535e20i	−0.973198	+	0.414819i
$696$	7.38352e20			0.353748
$697$		−	4.10848e21i		−	1.94731i
$698$		−	1.55407e21i		−	0.728712i
$699$	2.24869e21			1.04316
$700$	6.49340e20	+	6.23312e20i	0.298014	+	0.286069i
$701$	9.34623e20			0.424376			0.212188	−	0.977229i	$-0.431941\pi$
$701$	9.34623e20			0.424376			0.212188	+	0.977229i	$0.431941\pi$
$702$		−	1.03371e21i		−	0.464375i
$703$			5.62714e20i			0.250105i
$704$	−3.58636e20			−0.157710
$705$	−1.32165e21	+	5.63343e20i	−0.575038	+	0.245106i
$706$	1.97455e21			0.850025
$707$		−	1.81357e21i		−	0.772484i
$708$			6.05924e20i			0.255369i
$709$	1.12785e21			0.470333			0.235167	−	0.971955i	$-0.424436\pi$
$709$	1.12785e21			0.470333			0.235167	+	0.971955i	$0.424436\pi$
$710$	2.51182e20	+	5.89292e20i	0.103646	+	0.243160i
$711$	−6.81485e20			−0.278250
$712$			1.25237e21i			0.505981i
$713$		−	5.61118e20i		−	0.224328i
$714$	−1.80896e21			−0.715636
$715$	7.65377e20	+	1.79563e21i	0.299626	+	0.702946i
$716$	1.10947e21			0.429803
$717$		−	1.41510e20i		−	0.0542492i
$718$			1.40450e21i			0.532829i
$719$	5.09306e21			1.91211			0.956053	−	0.293195i	$-0.0947185\pi$
$719$	5.09306e21			1.91211			0.956053	+	0.293195i	$0.0947185\pi$
$720$	−2.48110e20	+	1.05755e20i	−0.0921829	+	0.0392924i
$721$	−5.63247e20			−0.207102
$722$			1.15832e21i			0.421502i
$723$		−	1.38915e21i		−	0.500279i
$724$	5.67968e19			0.0202434
$725$	−2.53758e21	+	2.64354e21i	−0.895126	+	0.932504i
$726$	9.27867e20			0.323938
$727$		−	1.49658e21i		−	0.517121i	−0.965995	−	0.258560i	$-0.916752\pi$
$727$		−	1.49658e21i		−	0.517121i	0.965995	−	0.258560i	$-0.0832481\pi$
$728$		−	5.17302e20i		−	0.176913i
$729$	−2.99892e21			−1.01510
$730$	2.68965e21	−	1.14645e21i	0.901102	−	0.384089i
$731$	−5.52008e21			−1.83048
$732$			1.64534e21i			0.540036i
$733$			6.17207e20i			0.200517i	0.994961	+	0.100258i	$0.0319670\pi$
$733$			6.17207e20i			0.200517i	−0.994961	+	0.100258i	$0.968033\pi$
$734$	−3.41456e20			−0.109803
$735$	−3.02661e20	−	7.10065e20i	−0.0963387	−	0.226018i
$736$	−9.85601e19			−0.0310540
$737$		−	4.29762e21i		−	1.34036i
$738$		−	1.12967e21i		−	0.348762i
$739$	2.47963e21			0.757799			0.378899	−	0.925438i	$-0.376303\pi$
$739$	2.47963e21			0.757799			0.378899	+	0.925438i	$0.376303\pi$
$740$	2.55034e20	+	5.98329e20i	0.0771543	+	0.181010i
$741$	9.94889e20			0.297946
$742$		−	1.22590e21i		−	0.363435i
$743$			2.36607e21i			0.694403i	0.937791	+	0.347201i	$0.112868\pi$
$743$			2.36607e21i			0.694403i	−0.937791	+	0.347201i	$0.887132\pi$
$744$	−1.20287e21			−0.349478
$745$	−5.59595e21	+	2.38524e21i	−1.60954	+	0.686057i
$746$	5.68270e20			0.161813
$747$			2.70497e21i			0.762533i
$748$			3.57712e21i			0.998323i
$749$	−4.26431e21			−1.17824
$750$	−7.08647e20	+	1.87118e21i	−0.193852	+	0.511865i
$751$	−4.52714e21			−1.22610			−0.613048	−	0.790046i	$-0.710057\pi$
$751$	−4.52714e21			−1.22610			−0.613048	+	0.790046i	$0.710057\pi$
$752$		−	7.52916e20i		−	0.201889i
$753$			1.70782e21i			0.453398i
$754$	2.10600e21			0.553570
$755$	3.95989e21	−	1.68788e21i	1.03058	−	0.439277i
$756$	−1.73830e21			−0.447931
$757$			3.44941e21i			0.880087i	0.897976	+	0.440044i	$0.145037\pi$
$757$			3.44941e21i			0.880087i	−0.897976	+	0.440044i	$0.854963\pi$
$758$		−	2.08004e20i		−	0.0525476i
$759$	6.85851e20			0.171560
$760$	−3.55717e20	−	8.34538e20i	−0.0881053	−	0.206702i
$761$	4.82361e21			1.18301			0.591504	−	0.806302i	$-0.298534\pi$
$761$	4.82361e21			1.18301			0.591504	+	0.806302i	$0.298534\pi$
$762$		−	1.78656e21i		−	0.433866i
$763$			1.65368e21i			0.397665i
$764$	8.87922e20			0.211434
$765$	1.05483e21	+	2.47470e21i	0.248725	+	0.583529i
$766$	3.04044e21			0.709939
$767$			1.72827e21i			0.399620i
$768$			2.11283e20i			0.0483788i
$769$	−3.79053e20			−0.0859513			−0.0429757	−	0.999076i	$-0.513684\pi$
$769$	−3.79053e20			−0.0859513			−0.0429757	+	0.999076i	$0.513684\pi$
$770$	3.01957e21	−	1.28707e21i	0.678053	−	0.289016i
$771$	−4.64112e21			−1.03208
$772$		−	4.97981e20i		−	0.109669i
$773$		−	6.32549e21i		−	1.37958i	−0.724008	−	0.689792i	$-0.757702\pi$
$773$		−	6.32549e21i		−	1.37958i	0.724008	−	0.689792i	$-0.242298\pi$
$774$	−1.51780e21			−0.327838
$775$	4.13402e21	−	4.30665e21i	0.884322	−	0.921249i
$776$	2.07323e21			0.439222
$777$			1.19949e21i			0.251674i
$778$			4.42523e21i			0.919578i
$779$	3.79974e21			0.782030
$780$	1.05786e21	−	4.50905e20i	0.215634	−	0.0919127i
$781$	2.33609e21			0.471637
$782$			9.83061e20i			0.196576i
$783$		−	7.07681e21i		−	1.40160i
$784$	4.04510e20			0.0793522
$785$	−2.54863e21	−	5.97927e21i	−0.495204	−	1.16179i
$786$	−3.44356e21			−0.662733
$787$			2.05488e21i			0.391719i	0.980632	+	0.195860i	$0.0627497\pi$
$787$			2.05488e21i			0.391719i	−0.980632	+	0.195860i	$0.937250\pi$
$788$		−	3.77429e21i		−	0.712671i
$789$	1.75009e21			0.327328
$790$	−1.03889e21	−	2.43731e21i	−0.192471	−	0.451552i
$791$	1.69487e21			0.311038
$792$			9.83567e20i			0.178799i
$793$			4.69300e21i			0.845087i
$794$	−5.54730e21			−0.989527
$795$	2.50691e21	−	1.06855e21i	0.442981	−	0.188818i
$796$	−3.95090e21			−0.691589
$797$			1.53752e21i			0.266614i	0.991075	+	0.133307i	$0.0425597\pi$
$797$			1.53752e21i			0.266614i	−0.991075	+	0.133307i	$0.957440\pi$
$798$		−	1.67302e21i		−	0.287396i
$799$	−7.50975e21			−1.27798
$800$	−7.56461e20	−	7.26139e20i	−0.127530	−	0.122418i
$801$	3.43466e21			0.573641
$802$			8.14216e20i			0.134720i
$803$		−	1.06624e22i		−	1.74779i
$804$	−2.53185e21			−0.411166
$805$	8.29835e20	−	3.53712e20i	0.133513	−	0.0569089i
$806$	−3.43093e21			−0.546888
$807$			3.98657e21i			0.629576i
$808$			2.11276e21i			0.330571i
$809$	1.22702e22			1.90212			0.951059	−	0.309008i	$-0.0999970\pi$
$809$	1.22702e22			1.90212			0.951059	+	0.309008i	$0.0999970\pi$
$810$	−7.91596e20	−	1.85714e21i	−0.121581	−	0.285238i
$811$	−9.42677e21			−1.43452			−0.717260	−	0.696806i	$-0.754604\pi$
$811$	−9.42677e21			−1.43452			−0.717260	+	0.696806i	$0.754604\pi$
$812$		−	3.54148e21i		−	0.533967i
$813$			3.27426e21i			0.489141i
$814$	2.37192e21			0.351089
$815$	1.85122e21	+	4.34309e21i	0.271503	+	0.636967i
$816$	2.10738e21			0.306243
$817$		−	5.10526e21i		−	0.735111i
$818$		−	5.20001e21i		−	0.741916i
$819$	−1.41871e21			−0.200569
$820$	4.04024e21	−	1.72213e21i	0.565982	−	0.241246i
$821$	8.15704e21			1.13229			0.566147	−	0.824304i	$-0.308434\pi$
$821$	8.15704e21			1.13229			0.566147	+	0.824304i	$0.308434\pi$
$822$			6.48871e21i			0.892524i
$823$			1.16074e22i			1.58211i	0.611747	+	0.791054i	$0.290467\pi$
$823$			1.16074e22i			1.58211i	−0.611747	+	0.791054i	$0.709533\pi$
$824$	6.56165e20			0.0886256
$825$	5.26399e21	+	5.05299e21i	0.704548	+	0.676307i
$826$	2.90629e21			0.385469
$827$			1.14386e22i			1.50342i	0.659493	+	0.751711i	$0.270771\pi$
$827$			1.14386e22i			1.50342i	−0.659493	+	0.751711i	$0.729229\pi$
$828$			2.70303e20i			0.0352066i
$829$	−6.40925e21			−0.827272			−0.413636	−	0.910442i	$-0.635741\pi$
$829$	−6.40925e21			−0.827272			−0.413636	+	0.910442i	$0.635741\pi$
$830$	−9.67426e21	+	4.12359e21i	−1.23746	+	0.527460i
$831$	−2.28590e21			−0.289768
$832$			6.02640e20i			0.0757065i
$833$		−	4.03467e21i		−	0.502309i
$834$	4.69307e21			0.579044
$835$	−5.82768e21	−	1.36722e22i	−0.712602	−	1.67182i
$836$	−3.30831e21			−0.400921
$837$			1.15290e22i			1.38468i
$838$		−	3.80360e21i		−	0.452756i
$839$	−4.19440e21			−0.494829			−0.247414	−	0.968910i	$-0.579581\pi$
$839$	−4.19440e21			−0.494829			−0.247414	+	0.968910i	$0.579581\pi$
$840$	−7.58250e20	−	1.77891e21i	−0.0886579	−	0.207998i
$841$	5.78859e21			0.670815
$842$			5.73323e21i			0.658504i
$843$			3.57905e21i			0.407438i
$844$	5.49560e21			0.620079
$845$	−5.20841e21	+	2.22005e21i	−0.582479	+	0.248278i
$846$	−2.06489e21			−0.228886
$847$		−	4.45049e21i		−	0.488970i
$848$			1.42814e21i			0.155525i
$849$	−3.83921e21			−0.414414
$850$	−7.24267e21	+	7.54511e21i	−0.774920	+	0.807279i
$851$	6.51849e20			0.0691314
$852$		−	1.37626e21i		−	0.144678i
$853$		−	8.64192e20i		−	0.0900518i	−0.998986	−	0.0450259i	$-0.985663\pi$
$853$		−	8.64192e20i		−	0.0900518i	0.998986	−	0.0450259i	$-0.0143370\pi$
$854$	7.89182e21			0.815161
$855$	−2.28874e21	+	9.75560e20i	−0.234342	+	0.0998868i
$856$	4.96779e21			0.504208
$857$			8.85666e21i			0.891074i	0.895263	+	0.445537i	$0.146987\pi$
$857$			8.85666e21i			0.891074i	−0.895263	+	0.445537i	$0.853013\pi$
$858$		−	4.19360e21i		−	0.418246i
$859$	−1.91941e21			−0.189766			−0.0948829	−	0.995488i	$-0.530248\pi$
$859$	−1.91941e21			−0.189766			−0.0948829	+	0.995488i	$0.530248\pi$
$860$	−2.31381e21	−	5.42838e21i	−0.226772	−	0.532025i
$861$	8.09958e21			0.786935
$862$			4.13599e21i			0.398360i
$863$		−	4.83006e21i		−	0.461181i	−0.973051	−	0.230591i	$-0.925934\pi$
$863$		−	4.83006e21i		−	0.461181i	0.973051	−	0.230591i	$-0.0740658\pi$
$864$	2.02506e21			0.191684
$865$	−4.80773e21	−	1.12793e22i	−0.451149	−	1.05843i
$866$	1.51386e21			0.140832
$867$		−	1.26265e22i		−	1.16450i
$868$			5.76951e21i			0.527522i
$869$	−9.66209e21			−0.875836
$870$	7.24215e21	−	3.08692e21i	0.650839	−	0.277416i
$871$	−7.22158e21			−0.643422
$872$		−	1.92649e21i		−	0.170174i
$873$		−	5.68587e21i		−	0.497955i
$874$	−9.09187e20			−0.0789437
$875$	8.97504e21	+	3.39900e21i	0.772638	+	0.292611i
$876$	−6.28153e21			−0.536148
$877$		−	1.87647e22i		−	1.58798i	−0.607934	−	0.793988i	$-0.708001\pi$
$877$		−	1.87647e22i		−	1.58798i	0.607934	−	0.793988i	$-0.291999\pi$
$878$		−	1.48939e21i		−	0.124968i
$879$	4.93097e21			0.410219
$880$	−3.51770e21	+	1.49940e21i	−0.290161	+	0.123679i
$881$	6.69553e21			0.547603			0.273801	−	0.961786i	$-0.411719\pi$
$881$	6.69553e21			0.547603			0.273801	+	0.961786i	$0.411719\pi$
$882$		−	1.10938e21i		−	0.0899631i
$883$			1.41366e22i			1.13669i	0.822791	+	0.568344i	$0.192416\pi$
$883$			1.41366e22i			1.13669i	−0.822791	+	0.568344i	$0.807584\pi$
$884$	6.01087e21			0.479232
$885$	2.53326e21	+	5.94323e21i	0.200265	+	0.469838i
$886$	8.76071e21			0.686731
$887$		−	1.23996e22i		−	0.963785i	−0.876230	−	0.481892i	$-0.839950\pi$
$887$		−	1.23996e22i		−	0.963785i	0.876230	−	0.481892i	$-0.160050\pi$
$888$		−	1.39737e21i		−	0.107699i
$889$	−8.56919e21			−0.654902
$890$	5.23596e21	+	1.22840e22i	0.396800	+	0.930923i
$891$	−7.36217e21			−0.553252
$892$		−	4.38081e21i		−	0.326451i
$893$		−	6.94542e21i		−	0.513231i
$894$	1.30690e22			0.957662
$895$	1.08823e22	−	4.63852e21i	0.790767	−	0.337060i
$896$	1.01341e21			0.0730256
$897$		−	1.15248e21i		−	0.0823552i
$898$			4.87594e21i			0.345530i
$899$	−2.34883e22			−1.65065
$900$	−1.99145e21	+	2.07461e21i	−0.138788	+	0.144583i
$901$	1.42446e22			0.984494
$902$		−	1.60165e22i		−	1.09779i
$903$		−	1.08824e22i		−	0.739721i
$904$	−1.97447e21			−0.133103
$905$	5.57094e20	−	2.37458e20i	0.0372446	−	0.0158753i
$906$	−9.24810e21			−0.613184
$907$		−	3.22552e21i		−	0.212102i	−0.994361	−	0.106051i	$-0.966179\pi$
$907$		−	3.22552e21i		−	0.212102i	0.994361	−	0.106051i	$-0.0338207\pi$
$908$			1.20438e22i			0.785452i
$909$	5.79428e21			0.374775
$910$	−2.16275e21	−	5.07398e21i	−0.138738	−	0.325490i
$911$	−1.00022e22			−0.636366			−0.318183	−	0.948029i	$-0.603073\pi$
$911$	−1.00022e22			−0.636366			−0.318183	+	0.948029i	$0.603073\pi$
$912$			1.94902e21i			0.122986i
$913$			3.83511e22i			2.40020i
$914$	−3.48631e21			−0.216406
$915$	6.87889e21	+	1.61384e22i	0.423507	+	0.993578i
$916$	9.64863e20			0.0589182
$917$			1.65169e22i			1.00037i
$918$		−	2.01984e22i		−	1.21338i
$919$	1.94031e22			1.15612			0.578062	−	0.815992i	$-0.303809\pi$
$919$	1.94031e22			1.15612			0.578062	+	0.815992i	$0.303809\pi$
$920$	−9.66731e20	+	4.12063e20i	−0.0571343	+	0.0243531i
$921$	−1.21747e22			−0.713693
$922$		−	1.08779e22i		−	0.632503i
$923$		−	3.92550e21i		−	0.226403i
$924$	−7.05203e21			−0.403436
$925$	5.00302e21	+	4.80248e21i	0.283903	+	0.272523i
$926$	−8.78767e21			−0.494642
$927$		−	1.79955e21i		−	0.100477i
$928$			4.12571e21i			0.228502i
$929$	−1.34815e22			−0.740662			−0.370331	−	0.928900i	$-0.620756\pi$
$929$	−1.34815e22			−0.740662			−0.370331	+	0.928900i	$0.620756\pi$
$930$	−1.17984e22	+	5.02898e21i	−0.642983	+	0.274067i
$931$	3.73148e21			0.201724
$932$			1.25651e22i			0.673823i
$933$		−	1.44119e22i		−	0.766673i
$934$	5.56836e21			0.293850
$935$	1.49553e22	+	3.50863e22i	0.782904	+	1.83675i
$936$	1.65275e21			0.0858300
$937$		−	1.11157e22i		−	0.572649i	−0.958133	−	0.286325i	$-0.907566\pi$
$937$		−	1.11157e22i		−	0.572649i	0.958133	−	0.286325i	$-0.0924336\pi$
$938$			1.21439e22i			0.620638i
$939$	−3.52907e21			−0.178924
$940$	−3.14781e21	−	7.38501e21i	−0.158325	−	0.371443i
$941$	8.75133e21			0.436669			0.218334	−	0.975874i	$-0.429938\pi$
$941$	8.75133e21			0.436669			0.218334	+	0.975874i	$0.429938\pi$
$942$			1.39643e22i			0.691252i
$943$		−	4.40163e21i		−	0.216160i
$944$	−3.38574e21			−0.164954
$945$	−1.70502e22	+	7.26753e21i	−0.824120	+	0.351276i
$946$	−2.15194e22			−1.03192
$947$		−	2.22968e22i		−	1.06076i	−0.847759	−	0.530382i	$-0.822049\pi$
$947$		−	2.22968e22i		−	1.06076i	0.847759	−	0.530382i	$-0.177951\pi$
$948$			5.69221e21i			0.268670i
$949$	−1.79168e22			−0.839002
$950$	−6.97812e21	−	6.69841e21i	−0.324199	−	0.311204i
$951$	−1.71953e21			−0.0792604
$952$		−	1.01080e22i		−	0.462261i
$953$			2.46708e22i			1.11940i	0.828695	+	0.559701i	$0.189084\pi$
$953$			2.46708e22i			1.11940i	−0.828695	+	0.559701i	$0.810916\pi$
$954$	3.91669e21			0.176322
$955$	8.70922e21	−	3.71225e21i	0.389004	−	0.165811i
$956$	7.90721e20			0.0350420
$957$		−	2.87096e22i		−	1.26237i
$958$			2.91333e20i			0.0127101i
$959$	3.11229e22			1.34723
$960$	8.83337e20	+	2.07238e21i	0.0379395	+	0.0890091i
$961$	1.48001e22			0.630724
$962$		−	3.98570e21i		−	0.168535i
$963$		−	1.36243e22i		−	0.571631i
$964$	7.76220e21			0.323152
$965$	−2.08197e21	−	4.88447e21i	−0.0860043	−	0.201773i
$966$	−1.93803e21			−0.0794388
$967$			3.27485e22i			1.33197i	0.745967	+	0.665983i	$0.231987\pi$
$967$			3.27485e22i			1.33197i	−0.745967	+	0.665983i	$0.768013\pi$
$968$			5.18468e21i			0.209246i
$969$	1.94399e22			0.778514
$970$	2.03354e22	−	8.66782e21i	0.808098	−	0.344447i
$971$	−3.73062e22			−1.47108			−0.735541	−	0.677480i	$-0.763072\pi$
$971$	−3.73062e22			−1.47108			−0.735541	+	0.677480i	$0.763072\pi$
$972$		−	9.51841e21i		−	0.372449i
$973$		−	2.25101e22i		−	0.874041i
$974$	−1.02278e22			−0.394084
$975$	8.49088e21	−	8.84544e21i	0.324652	−	0.338209i
$976$	−9.19373e21			−0.348833
$977$			2.37366e22i			0.893737i	0.894600	+	0.446869i	$0.147461\pi$
$977$			2.37366e22i			0.893737i	−0.894600	+	0.446869i	$0.852539\pi$
$978$		−	1.01431e22i		−	0.378990i
$979$	4.86966e22			1.80563
$980$	3.96765e21	−	1.69119e21i	0.145995	−	0.0622295i
$981$	−5.28343e21			−0.192929
$982$		−	2.14033e22i		−	0.775613i
$983$			1.87132e22i			0.672970i	0.941689	+	0.336485i	$0.109238\pi$
$983$			1.87132e22i			0.672970i	−0.941689	+	0.336485i	$0.890762\pi$
$984$	−9.43575e21			−0.336754
$985$	−1.57797e22	−	3.70203e22i	−0.558890	−	1.31120i
$986$	4.11508e22			1.44644
$987$		−	1.48049e22i		−	0.516449i
$988$			5.55917e21i			0.192457i
$989$	−5.91395e21			−0.203191
$990$	4.11213e21	+	9.64736e21i	0.140218	+	0.328961i
$991$	4.86572e22			1.64662			0.823312	−	0.567588i	$-0.192124\pi$
$991$	4.86572e22			1.64662			0.823312	+	0.567588i	$0.192124\pi$
$992$		−	6.72129e21i		−	0.225744i
$993$		−	3.22779e22i		−	1.07593i
$994$	−6.60118e21			−0.218386
$995$	−3.87526e22	+	1.65180e22i	−1.27241	+	0.542357i
$996$	2.25937e22			0.736279
$997$		−	1.33512e22i		−	0.431824i	−0.976413	−	0.215912i	$-0.930728\pi$
$997$		−	1.33512e22i		−	0.431824i	0.976413	−	0.215912i	$-0.0692724\pi$
$998$		−	1.14294e22i		−	0.366897i
$999$	−1.33932e22			−0.426720

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.16.b.a.9.3	✓	8
3.2	odd	2		90.16.c.c.19.8		8
4.3	odd	2		80.16.c.c.49.4		8
5.2	odd	4		50.16.a.k.1.3		4
5.3	odd	4		50.16.a.j.1.2		4
5.4	even	2	inner	10.16.b.a.9.6	yes	8
15.14	odd	2		90.16.c.c.19.4		8
20.19	odd	2		80.16.c.c.49.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.16.b.a.9.3	✓	8	1.1	even	1	trivial
10.16.b.a.9.6	yes	8	5.4	even	2	inner
50.16.a.j.1.2		4	5.3	odd	4
50.16.a.k.1.3		4	5.2	odd	4
80.16.c.c.49.4		8	4.3	odd	2
80.16.c.c.49.5		8	20.19	odd	2
90.16.c.c.19.4		8	15.14	odd	2
90.16.c.c.19.8		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)

\(f(q)\)	\(=\)	\(q-128.000i q^{2} +2932.14i q^{3} -16384.0 q^{4} +(-160703. + 68498.7i) q^{5} +375313. q^{6} -1.80018e6i q^{7} +2.09715e6i q^{8} +5.75148e6 q^{9} +O(q^{10})\)	\(q-128.000i q^{2} +2932.14i q^{3} -16384.0 q^{4} +(-160703. + 68498.7i) q^{5} +375313. q^{6} -1.80018e6i q^{7} +2.09715e6i q^{8} +5.75148e6 q^{9} +(8.76783e6 + 2.05700e7i) q^{10} +8.15444e7 q^{11} -4.80401e7i q^{12} -1.37025e8i q^{13} -2.30423e8 q^{14} +(-2.00848e8 - 4.71204e8i) q^{15} +2.68435e8 q^{16} -2.67743e9i q^{17} -7.36190e8i q^{18} +2.47624e9 q^{19} +(2.63296e9 - 1.12228e9i) q^{20} +5.27837e9 q^{21} -1.04377e10i q^{22} -2.86848e9i q^{23} -6.14914e9 q^{24} +(2.11334e10 - 2.20159e10i) q^{25} -1.75391e10 q^{26} +5.89371e10i q^{27} +2.94941e10i q^{28} -1.20074e11 q^{29} +(-6.03141e10 + 2.57085e10i) q^{30} +1.95615e11 q^{31} -3.43597e10i q^{32} +2.39099e11i q^{33} -3.42712e11 q^{34} +(1.23310e11 + 2.89294e11i) q^{35} -9.42323e10 q^{36} +2.27246e11i q^{37} -3.16958e11i q^{38} +4.01775e11 q^{39} +(-1.43652e11 - 3.37019e11i) q^{40} +1.53448e12 q^{41} -6.75632e11i q^{42} -2.06170e12i q^{43} -1.33602e12 q^{44} +(-9.24281e11 + 3.93969e11i) q^{45} -3.67165e11 q^{46} -2.80483e12i q^{47} +7.87089e11i q^{48} +1.50692e12 q^{49} +(-2.81804e12 - 2.70508e12i) q^{50} +7.85061e12 q^{51} +2.24501e12i q^{52} +5.32023e12i q^{53} +7.54395e12 q^{54} +(-1.31044e13 + 5.58569e12i) q^{55} +3.77525e12 q^{56} +7.26066e12i q^{57} +1.53695e13i q^{58} -1.26129e13 q^{59} +(3.29069e12 + 7.72020e12i) q^{60} -3.42493e13 q^{61} -2.50388e13i q^{62} -1.03537e13i q^{63} -4.39805e12 q^{64} +(9.38601e12 + 2.20203e13i) q^{65} +3.06047e13 q^{66} -5.27028e13i q^{67} +4.38671e13i q^{68} +8.41077e12 q^{69} +(3.70297e13 - 1.57837e13i) q^{70} +2.86481e13 q^{71} +1.20617e13i q^{72} -1.30756e14i q^{73} +2.90875e13 q^{74} +(6.45537e13 + 6.19661e13i) q^{75} -4.05706e13 q^{76} -1.46795e14i q^{77} -5.14272e13i q^{78} -1.18489e14 q^{79} +(-4.31384e13 + 1.83875e13i) q^{80} -9.02841e13 q^{81} -1.96414e14i q^{82} +4.70309e14i q^{83} -8.64808e13 q^{84} +(1.83401e14 + 4.30272e14i) q^{85} -2.63898e14 q^{86} -3.52074e14i q^{87} +1.71011e14i q^{88} +5.97179e14 q^{89} +(5.04280e13 + 1.18308e14i) q^{90} -2.46669e14 q^{91} +4.69971e13i q^{92} +5.73571e14i q^{93} -3.59018e14 q^{94} +(-3.97939e14 + 1.69619e14i) q^{95} +1.00747e14 q^{96} -9.88593e14i q^{97} -1.92885e14i q^{98} +4.69001e14 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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